TSTP Solution File: NUM457+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM457+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 6.14s 2.12s
% Output : Proof 13.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM457+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n028.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 : Wed Jul 6 05:34:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.65/0.63 ____ _
% 0.65/0.63 ___ / __ \_____(_)___ ________ __________
% 0.65/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.65/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.65/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.65/0.63
% 0.65/0.63 A Theorem Prover for First-Order Logic
% 0.65/0.64 (ePrincess v.1.0)
% 0.65/0.64
% 0.65/0.64 (c) Philipp Rümmer, 2009-2015
% 0.65/0.64 (c) Peter Backeman, 2014-2015
% 0.65/0.64 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.65/0.64 Free software under GNU Lesser General Public License (LGPL).
% 0.65/0.64 Bug reports to peter@backeman.se
% 0.65/0.64
% 0.65/0.64 For more information, visit http://user.uu.se/~petba168/breu/
% 0.65/0.64
% 0.65/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.53/1.02 Prover 0: Preprocessing ...
% 2.67/1.36 Prover 0: Constructing countermodel ...
% 4.18/1.69 Prover 0: gave up
% 4.18/1.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.18/1.72 Prover 1: Preprocessing ...
% 4.61/1.78 Prover 1: Constructing countermodel ...
% 4.79/1.82 Prover 1: gave up
% 4.79/1.82 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.79/1.84 Prover 2: Preprocessing ...
% 5.21/1.95 Prover 2: Warning: ignoring some quantifiers
% 5.21/1.96 Prover 2: Constructing countermodel ...
% 6.14/2.12 Prover 2: proved (297ms)
% 6.14/2.12
% 6.14/2.12 No countermodel exists, formula is valid
% 6.14/2.12 % SZS status Theorem for theBenchmark
% 6.14/2.12
% 6.14/2.12 Generating proof ... Warning: ignoring some quantifiers
% 13.01/3.75 found it (size 190)
% 13.01/3.75
% 13.01/3.75 % SZS output start Proof for theBenchmark
% 13.01/3.75 Assumed formulas after preprocessing and simplification:
% 13.01/3.75 | (0) ~ (xn = sz00) & ~ (xm = sz00) & ~ (sz10 = sz00) & sdtasdt0(xm, xn) = sz00 & aNaturalNumber0(xn) = 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] : (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] : (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] : (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 | ~ (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] : ( ~ (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] : sdtasdt0(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : sdtpldt0(v1, v0) = v2 & ? [v0] : ? [v1] : aNaturalNumber0(v0) = v1
% 13.18/3.82 | Applying alpha-rule on (0) yields:
% 13.18/3.82 | (1) ! [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)))
% 13.18/3.82 | (2) ! [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)))
% 13.18/3.82 | (3) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ? [v2] : ((v2 = sz00 & v1 = sz00 & sdtasdt0(sz00, v0) = sz00) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 13.18/3.82 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 13.18/3.82 | (5) aNaturalNumber0(xn) = 0
% 13.18/3.82 | (6) aNaturalNumber0(sz00) = 0
% 13.18/3.82 | (7) ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | (sdtasdt0(v0, sz10) = v0 & sdtasdt0(sz10, v0) = v0))
% 13.18/3.82 | (8) ? [v0] : ? [v1] : aNaturalNumber0(v0) = v1
% 13.18/3.82 | (9) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 13.18/3.82 | (10) ! [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)))
% 13.18/3.82 | (11) aNaturalNumber0(sz10) = 0
% 13.18/3.82 | (12) ~ (xn = sz00)
% 13.18/3.82 | (13) ! [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)))
% 13.18/3.82 | (14) ! [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)))
% 13.18/3.82 | (15) ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | (sdtpldt0(v0, sz00) = v0 & sdtpldt0(sz00, v0) = v0))
% 13.18/3.82 | (16) ! [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)))
% 13.18/3.82 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ((v3 = v2 & sdtasdt0(v1, v0) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 13.18/3.83 | (18) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ((v2 = sz00 & v1 = sz00 & sdtasdt0(v0, sz00) = sz00) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 13.18/3.83 | (19) ~ (sz10 = sz00)
% 13.18/3.83 | (20) ! [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)))
% 13.18/3.83 | (21) ! [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)))
% 13.18/3.83 | (22) ? [v0] : ? [v1] : ? [v2] : sdtpldt0(v1, v0) = v2
% 13.18/3.83 | (23) ! [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)))
% 13.18/3.83 | (24) ! [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)))
% 13.18/3.83 | (25) ! [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)))
% 13.18/3.83 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 13.18/3.83 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ((v3 = v2 & sdtpldt0(v1, v0) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 13.18/3.83 | (28) ! [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)))
% 13.18/3.83 | (29) ! [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)))
% 13.18/3.83 | (30) aNaturalNumber0(xm) = 0
% 13.18/3.83 | (31) ! [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))
% 13.18/3.83 | (32) ! [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)))
% 13.18/3.83 | (33) ! [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)))
% 13.18/3.83 | (34) ! [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)))
% 13.18/3.83 | (35) ! [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)))
% 13.18/3.83 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0))
% 13.18/3.83 | (37) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtasdt0(sz10, v0) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 13.18/3.83 | (38) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtpldt0(v0, sz00) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 13.18/3.84 | (39) sdtasdt0(xm, xn) = sz00
% 13.18/3.84 | (40) ~ (xm = sz00)
% 13.18/3.84 | (41) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtpldt0(sz00, v0) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 13.18/3.84 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ((v3 = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 13.18/3.84 | (43) ! [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)))
% 13.18/3.84 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ((v3 = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 13.18/3.84 | (45) ! [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)))
% 13.18/3.84 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ? [v3] : ((v3 = v2 & sdtpldt0(v0, v1) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 13.18/3.84 | (47) ! [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)))
% 13.61/3.84 | (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)))
% 13.61/3.84 | (49) ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | (sdtasdt0(v0, sz00) = sz00 & sdtasdt0(sz00, v0) = sz00))
% 13.61/3.84 | (50) ! [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)))
% 13.61/3.84 | (51) ! [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))
% 13.61/3.84 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ? [v3] : ((v3 = v2 & sdtasdt0(v0, v1) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 13.61/3.84 | (53) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 13.61/3.84 | (54) ? [v0] : ? [v1] : ? [v2] : sdtasdt0(v1, v0) = v2
% 13.61/3.84 | (55) ! [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)))
% 13.61/3.84 | (56) ! [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)))
% 13.61/3.84 | (57) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtasdt0(v0, sz10) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 13.61/3.84 |
% 13.61/3.84 | Instantiating formula (49) with xm and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 13.61/3.85 | (58) sdtasdt0(xm, sz00) = sz00 & sdtasdt0(sz00, xm) = sz00
% 13.61/3.85 |
% 13.61/3.85 | Applying alpha-rule on (58) yields:
% 13.61/3.85 | (59) sdtasdt0(xm, sz00) = sz00
% 13.61/3.85 | (60) sdtasdt0(sz00, xm) = sz00
% 13.61/3.85 |
% 13.61/3.85 | Instantiating formula (56) with sz00, xm, sz00, xn and discharging atoms sdtasdt0(xm, xn) = sz00, aNaturalNumber0(xn) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.85 | (61) xn = sz00 | xm = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v2 = sz00) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v1 & sdtasdt0(xn, sz00) = v0 & sdtasdt0(sz00, xn) = v2) | ( ~ (v0 = 0) & aNaturalNumber0(xm) = v0))
% 13.61/3.85 |
% 13.61/3.85 | Instantiating formula (23) with sz00, sz00, xm, xn and discharging atoms sdtasdt0(xm, xn) = sz00, aNaturalNumber0(xn) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.85 | (62) xn = sz00 | xm = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v2 = sz00) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v0 & sdtasdt0(xn, sz00) = v1 & sdtasdt0(sz00, xn) = v2) | ( ~ (v0 = 0) & aNaturalNumber0(xm) = v0))
% 13.61/3.85 |
% 13.61/3.85 | Instantiating formula (25) with sz00, xn, sz00, xm and discharging atoms sdtasdt0(xm, xn) = sz00, aNaturalNumber0(xm) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.85 | (63) xn = sz00 | xm = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v2 = v1) & ~ (v0 = sz00) & sdtasdt0(xn, xm) = v2 & sdtasdt0(xm, sz00) = v0 & sdtasdt0(sz00, xm) = v1) | ( ~ (v0 = 0) & aNaturalNumber0(xn) = v0))
% 13.61/3.85 |
% 13.61/3.85 | Instantiating formula (33) with sz00, sz00, xn, xm and discharging atoms sdtasdt0(xm, xn) = sz00, aNaturalNumber0(xm) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.85 | (64) xn = sz00 | xm = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v2 = v1) & ~ (v0 = sz00) & sdtasdt0(xn, xm) = v1 & sdtasdt0(xm, sz00) = v0 & sdtasdt0(sz00, xm) = v2) | ( ~ (v0 = 0) & aNaturalNumber0(xn) = v0))
% 13.61/3.85 |
% 13.61/3.85 | Instantiating formula (51) with sz00, xn, xn and discharging atoms aNaturalNumber0(xn) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.85 | (65) xn = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xn) = v2 & sdtasdt0(xn, xn) = v0 & sdtasdt0(xn, sz00) = v1 & sdtasdt0(sz00, xn) = v3)
% 13.61/3.85 |
% 13.61/3.85 | Instantiating formula (51) with xn, sz00, xn and discharging atoms aNaturalNumber0(xn) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.85 | (66) xn = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xn) = v3 & sdtasdt0(xn, xn) = v1 & sdtasdt0(xn, sz00) = v0 & sdtasdt0(sz00, xn) = v2)
% 13.61/3.85 |
% 13.61/3.85 | Instantiating formula (31) with sz00, xn, xn and discharging atoms aNaturalNumber0(xn) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.85 | (67) xn = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, xn) = v2 & sdtpldt0(xn, xn) = v0 & sdtpldt0(xn, sz00) = v1 & sdtpldt0(sz00, xn) = v3)
% 13.61/3.85 |
% 13.61/3.85 | Instantiating formula (31) with xn, sz00, xn and discharging atoms aNaturalNumber0(xn) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.85 | (68) xn = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, xn) = v3 & sdtpldt0(xn, xn) = v1 & sdtpldt0(xn, sz00) = v0 & sdtpldt0(sz00, xn) = v2)
% 13.61/3.85 |
% 13.61/3.85 | Instantiating formula (51) with sz00, xn, xm and discharging atoms aNaturalNumber0(xn) = 0, aNaturalNumber0(xm) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.85 | (69) xn = sz00 | xm = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v2 & sdtasdt0(xm, xn) = v0 & sdtasdt0(xm, sz00) = v1 & sdtasdt0(sz00, xm) = v3)
% 13.61/3.85 |
% 13.61/3.85 | Instantiating formula (31) with sz00, xn, xm and discharging atoms aNaturalNumber0(xn) = 0, aNaturalNumber0(xm) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.85 | (70) xn = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, xm) = v2 & sdtpldt0(xm, xn) = v0 & sdtpldt0(xm, sz00) = v1 & sdtpldt0(sz00, xm) = v3)
% 13.61/3.85 |
% 13.61/3.85 | Instantiating formula (31) with xn, sz00, xm and discharging atoms aNaturalNumber0(xn) = 0, aNaturalNumber0(xm) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.85 | (71) xn = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, xm) = v3 & sdtpldt0(xm, xn) = v1 & sdtpldt0(xm, sz00) = v0 & sdtpldt0(sz00, xm) = v2)
% 13.61/3.85 |
% 13.61/3.85 | Instantiating formula (31) with sz00, xn, sz10 and discharging atoms aNaturalNumber0(xn) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.85 | (72) xn = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, sz10) = v2 & sdtpldt0(sz10, xn) = v0 & sdtpldt0(sz10, sz00) = v1 & sdtpldt0(sz00, sz10) = v3)
% 13.61/3.85 |
% 13.61/3.85 | Instantiating formula (31) with xn, sz00, sz10 and discharging atoms aNaturalNumber0(xn) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.85 | (73) xn = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, sz10) = v3 & sdtpldt0(sz10, xn) = v1 & sdtpldt0(sz10, sz00) = v0 & sdtpldt0(sz00, sz10) = v2)
% 13.61/3.85 |
% 13.61/3.85 | Instantiating formula (31) with xn, sz00, sz00 and discharging atoms aNaturalNumber0(xn) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.85 | (74) xn = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, sz00) = v3 & sdtpldt0(sz00, xn) = v1 & sdtpldt0(sz00, sz00) = v2 & sdtpldt0(sz00, sz00) = v0)
% 13.61/3.85 |
% 13.61/3.85 | Instantiating formula (51) with sz00, xm, xn and discharging atoms aNaturalNumber0(xn) = 0, aNaturalNumber0(xm) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.85 | (75) xn = sz00 | xm = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v0 & sdtasdt0(xn, sz00) = v1 & sdtasdt0(xm, xn) = v2 & sdtasdt0(sz00, xn) = v3)
% 13.61/3.86 |
% 13.61/3.86 | Instantiating formula (51) with xm, sz00, xn and discharging atoms aNaturalNumber0(xn) = 0, aNaturalNumber0(xm) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.86 | (76) xn = sz00 | xm = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v1 & sdtasdt0(xn, sz00) = v0 & sdtasdt0(xm, xn) = v3 & sdtasdt0(sz00, xn) = v2)
% 13.61/3.86 |
% 13.61/3.86 | Instantiating formula (31) with sz00, xm, xn and discharging atoms aNaturalNumber0(xn) = 0, aNaturalNumber0(xm) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.86 | (77) xm = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, xm) = v0 & sdtpldt0(xn, sz00) = v1 & sdtpldt0(xm, xn) = v2 & sdtpldt0(sz00, xn) = v3)
% 13.61/3.86 |
% 13.61/3.86 | Instantiating formula (31) with xm, sz00, xn and discharging atoms aNaturalNumber0(xn) = 0, aNaturalNumber0(xm) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.86 | (78) xm = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, xm) = v1 & sdtpldt0(xn, sz00) = v0 & sdtpldt0(xm, xn) = v3 & sdtpldt0(sz00, xn) = v2)
% 13.61/3.86 |
% 13.61/3.86 | Instantiating formula (51) with sz00, xm, xm and discharging atoms aNaturalNumber0(xm) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.86 | (79) xm = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xm, xm) = v2 & sdtasdt0(xm, xm) = v0 & sdtasdt0(xm, sz00) = v1 & sdtasdt0(sz00, xm) = v3)
% 13.61/3.86 |
% 13.61/3.86 | Instantiating formula (51) with xm, sz00, xm and discharging atoms aNaturalNumber0(xm) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.86 | (80) xm = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xm, xm) = v3 & sdtasdt0(xm, xm) = v1 & sdtasdt0(xm, sz00) = v0 & sdtasdt0(sz00, xm) = v2)
% 13.61/3.86 |
% 13.61/3.86 | Instantiating formula (31) with sz00, xm, sz10 and discharging atoms aNaturalNumber0(xm) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.86 | (81) xm = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xm, sz10) = v2 & sdtpldt0(sz10, xm) = v0 & sdtpldt0(sz10, sz00) = v1 & sdtpldt0(sz00, sz10) = v3)
% 13.61/3.86 |
% 13.61/3.86 | Instantiating formula (31) with sz00, xm, sz00 and discharging atoms aNaturalNumber0(xm) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.86 | (82) xm = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xm, sz00) = v2 & sdtpldt0(sz00, xm) = v0 & sdtpldt0(sz00, sz00) = v3 & sdtpldt0(sz00, sz00) = v1)
% 13.61/3.86 |
% 13.61/3.86 | Instantiating formula (31) with xm, sz00, sz00 and discharging atoms aNaturalNumber0(xm) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.86 | (83) xm = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xm, sz00) = v3 & sdtpldt0(sz00, xm) = v1 & sdtpldt0(sz00, sz00) = v2 & sdtpldt0(sz00, sz00) = v0)
% 13.61/3.86 |
% 13.61/3.86 | Instantiating formula (51) with sz10, sz00, xn and discharging atoms aNaturalNumber0(xn) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.86 | (84) xn = sz00 | sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, sz10) = v1 & sdtasdt0(xn, sz00) = v0 & sdtasdt0(sz10, xn) = v3 & sdtasdt0(sz00, xn) = v2)
% 13.61/3.86 |
% 13.61/3.86 | Instantiating formula (31) with sz10, sz00, xn and discharging atoms aNaturalNumber0(xn) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.86 | (85) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, sz10) = v1 & sdtpldt0(xn, sz00) = v0 & sdtpldt0(sz10, xn) = v3 & sdtpldt0(sz00, xn) = v2)
% 13.61/3.86 |
% 13.61/3.86 | Instantiating formula (51) with sz00, sz10, xm and discharging atoms aNaturalNumber0(xm) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.86 | (86) xm = sz00 | sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xm, sz10) = v0 & sdtasdt0(xm, sz00) = v1 & sdtasdt0(sz10, xm) = v2 & sdtasdt0(sz00, xm) = v3)
% 13.61/3.86 |
% 13.61/3.86 | Instantiating formula (51) with sz10, sz00, xm and discharging atoms aNaturalNumber0(xm) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.86 | (87) xm = sz00 | sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xm, sz10) = v1 & sdtasdt0(xm, sz00) = v0 & sdtasdt0(sz10, xm) = v3 & sdtasdt0(sz00, xm) = v2)
% 13.61/3.86 |
% 13.61/3.86 | Instantiating formula (31) with sz10, sz00, xm and discharging atoms aNaturalNumber0(xm) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.86 | (88) 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)
% 13.61/3.86 |
% 13.61/3.86 | Instantiating formula (31) with sz00, sz10, sz10 and discharging atoms aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.86 | (89) 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)
% 13.61/3.86 |
% 13.61/3.86 | Instantiating formula (31) with sz10, sz00, sz10 and discharging atoms aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.86 | (90) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz10) = v3 & sdtpldt0(sz10, sz10) = v1 & sdtpldt0(sz10, sz00) = v0 & sdtpldt0(sz00, sz10) = v2)
% 13.61/3.86 |
% 13.61/3.86 | Instantiating formula (31) with sz00, sz10, sz00 and discharging atoms aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.86 | (91) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz00) = v2 & sdtpldt0(sz00, sz10) = v0 & sdtpldt0(sz00, sz00) = v3 & sdtpldt0(sz00, sz00) = v1)
% 13.61/3.86 |
% 13.61/3.86 | Instantiating formula (31) with sz10, sz00, sz00 and discharging atoms aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 13.61/3.87 | (92) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz00) = v3 & sdtpldt0(sz00, sz10) = v1 & sdtpldt0(sz00, sz00) = v2 & sdtpldt0(sz00, sz00) = v0)
% 13.61/3.87 |
% 13.61/3.87 +-Applying beta-rule and splitting (68), into two cases.
% 13.61/3.87 |-Branch one:
% 13.61/3.87 | (93) xn = sz00
% 13.61/3.87 |
% 13.61/3.87 | Equations (93) can reduce 12 to:
% 13.61/3.87 | (94) $false
% 13.61/3.87 |
% 13.61/3.87 |-The branch is then unsatisfiable
% 13.61/3.87 |-Branch two:
% 13.61/3.87 | (12) ~ (xn = sz00)
% 13.61/3.87 | (96) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, xn) = v3 & sdtpldt0(xn, xn) = v1 & sdtpldt0(xn, sz00) = v0 & sdtpldt0(sz00, xn) = v2)
% 13.61/3.87 |
% 13.61/3.87 +-Applying beta-rule and splitting (67), into two cases.
% 13.61/3.87 |-Branch one:
% 13.61/3.87 | (93) xn = sz00
% 13.61/3.87 |
% 13.61/3.87 | Equations (93) can reduce 12 to:
% 13.61/3.87 | (94) $false
% 13.61/3.87 |
% 13.61/3.87 |-The branch is then unsatisfiable
% 13.61/3.87 |-Branch two:
% 13.61/3.87 | (12) ~ (xn = sz00)
% 13.61/3.87 | (100) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, xn) = v2 & sdtpldt0(xn, xn) = v0 & sdtpldt0(xn, sz00) = v1 & sdtpldt0(sz00, xn) = v3)
% 13.61/3.87 |
% 13.61/3.87 +-Applying beta-rule and splitting (64), into two cases.
% 13.61/3.87 |-Branch one:
% 13.61/3.87 | (93) xn = sz00
% 13.61/3.87 |
% 13.61/3.87 | Equations (93) can reduce 12 to:
% 13.61/3.87 | (94) $false
% 13.61/3.87 |
% 13.61/3.87 |-The branch is then unsatisfiable
% 13.61/3.87 |-Branch two:
% 13.61/3.87 | (12) ~ (xn = sz00)
% 13.61/3.87 | (104) xm = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v2 = v1) & ~ (v0 = sz00) & sdtasdt0(xn, xm) = v1 & sdtasdt0(xm, sz00) = v0 & sdtasdt0(sz00, xm) = v2) | ( ~ (v0 = 0) & aNaturalNumber0(xn) = v0))
% 13.61/3.87 |
% 13.61/3.87 +-Applying beta-rule and splitting (66), into two cases.
% 13.61/3.87 |-Branch one:
% 13.61/3.87 | (93) xn = sz00
% 13.61/3.87 |
% 13.61/3.87 | Equations (93) can reduce 12 to:
% 13.61/3.87 | (94) $false
% 13.61/3.87 |
% 13.61/3.87 |-The branch is then unsatisfiable
% 13.61/3.87 |-Branch two:
% 13.61/3.87 | (12) ~ (xn = sz00)
% 13.61/3.87 | (108) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xn) = v3 & sdtasdt0(xn, xn) = v1 & sdtasdt0(xn, sz00) = v0 & sdtasdt0(sz00, xn) = v2)
% 13.61/3.87 |
% 13.61/3.87 +-Applying beta-rule and splitting (65), into two cases.
% 13.61/3.87 |-Branch one:
% 13.61/3.87 | (93) xn = sz00
% 13.61/3.87 |
% 13.61/3.87 | Equations (93) can reduce 12 to:
% 13.61/3.87 | (94) $false
% 13.61/3.87 |
% 13.61/3.87 |-The branch is then unsatisfiable
% 13.61/3.87 |-Branch two:
% 13.61/3.87 | (12) ~ (xn = sz00)
% 13.61/3.87 | (112) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xn) = v2 & sdtasdt0(xn, xn) = v0 & sdtasdt0(xn, sz00) = v1 & sdtasdt0(sz00, xn) = v3)
% 13.61/3.87 |
% 13.61/3.87 +-Applying beta-rule and splitting (104), into two cases.
% 13.61/3.87 |-Branch one:
% 13.61/3.87 | (113) xm = sz00
% 13.61/3.87 |
% 13.61/3.87 | Equations (113) can reduce 40 to:
% 13.61/3.87 | (94) $false
% 13.61/3.87 |
% 13.61/3.87 |-The branch is then unsatisfiable
% 13.61/3.87 |-Branch two:
% 13.61/3.87 | (40) ~ (xm = sz00)
% 13.61/3.87 | (116) ? [v0] : ? [v1] : ? [v2] : (( ~ (v2 = v1) & ~ (v0 = sz00) & sdtasdt0(xn, xm) = v1 & sdtasdt0(xm, sz00) = v0 & sdtasdt0(sz00, xm) = v2) | ( ~ (v0 = 0) & aNaturalNumber0(xn) = v0))
% 13.61/3.87 |
% 13.61/3.87 | Instantiating (116) with all_49_0_25, all_49_1_26, all_49_2_27 yields:
% 13.61/3.87 | (117) ( ~ (all_49_0_25 = all_49_1_26) & ~ (all_49_2_27 = sz00) & sdtasdt0(xn, xm) = all_49_1_26 & sdtasdt0(xm, sz00) = all_49_2_27 & sdtasdt0(sz00, xm) = all_49_0_25) | ( ~ (all_49_2_27 = 0) & aNaturalNumber0(xn) = all_49_2_27)
% 13.61/3.87 |
% 13.61/3.87 +-Applying beta-rule and splitting (117), into two cases.
% 13.61/3.87 |-Branch one:
% 13.61/3.87 | (118) ~ (all_49_0_25 = all_49_1_26) & ~ (all_49_2_27 = sz00) & sdtasdt0(xn, xm) = all_49_1_26 & sdtasdt0(xm, sz00) = all_49_2_27 & sdtasdt0(sz00, xm) = all_49_0_25
% 13.61/3.87 |
% 13.61/3.87 | Applying alpha-rule on (118) yields:
% 13.61/3.87 | (119) ~ (all_49_2_27 = sz00)
% 13.61/3.87 | (120) sdtasdt0(sz00, xm) = all_49_0_25
% 13.61/3.87 | (121) ~ (all_49_0_25 = all_49_1_26)
% 13.61/3.87 | (122) sdtasdt0(xm, sz00) = all_49_2_27
% 13.61/3.87 | (123) sdtasdt0(xn, xm) = all_49_1_26
% 13.61/3.87 |
% 13.61/3.87 +-Applying beta-rule and splitting (62), into two cases.
% 13.61/3.87 |-Branch one:
% 13.61/3.87 | (93) xn = sz00
% 13.61/3.87 |
% 13.61/3.87 | Equations (93) can reduce 12 to:
% 13.61/3.87 | (94) $false
% 13.61/3.87 |
% 13.61/3.87 |-The branch is then unsatisfiable
% 13.61/3.87 |-Branch two:
% 13.61/3.87 | (12) ~ (xn = sz00)
% 13.61/3.87 | (127) xm = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v2 = sz00) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v0 & sdtasdt0(xn, sz00) = v1 & sdtasdt0(sz00, xn) = v2) | ( ~ (v0 = 0) & aNaturalNumber0(xm) = v0))
% 13.61/3.87 |
% 13.61/3.87 +-Applying beta-rule and splitting (88), into two cases.
% 13.61/3.87 |-Branch one:
% 13.61/3.87 | (128) sz10 = sz00
% 13.61/3.87 |
% 13.61/3.87 | Equations (128) can reduce 19 to:
% 13.61/3.87 | (94) $false
% 13.61/3.87 |
% 13.61/3.87 |-The branch is then unsatisfiable
% 13.61/3.87 |-Branch two:
% 13.61/3.87 | (19) ~ (sz10 = sz00)
% 13.61/3.87 | (131) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xm, sz10) = v1 & sdtpldt0(xm, sz00) = v0 & sdtpldt0(sz10, xm) = v3 & sdtpldt0(sz00, xm) = v2)
% 13.61/3.87 |
% 13.61/3.88 +-Applying beta-rule and splitting (89), into two cases.
% 13.61/3.88 |-Branch one:
% 13.61/3.88 | (128) sz10 = sz00
% 13.61/3.88 |
% 13.61/3.88 | Equations (128) can reduce 19 to:
% 13.61/3.88 | (94) $false
% 13.61/3.88 |
% 13.61/3.88 |-The branch is then unsatisfiable
% 13.61/3.88 |-Branch two:
% 13.61/3.88 | (19) ~ (sz10 = sz00)
% 13.61/3.88 | (135) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz10) = v2 & sdtpldt0(sz10, sz10) = v0 & sdtpldt0(sz10, sz00) = v1 & sdtpldt0(sz00, sz10) = v3)
% 13.61/3.88 |
% 13.61/3.88 +-Applying beta-rule and splitting (90), into two cases.
% 13.61/3.88 |-Branch one:
% 13.61/3.88 | (128) sz10 = sz00
% 13.61/3.88 |
% 13.61/3.88 | Equations (128) can reduce 19 to:
% 13.61/3.88 | (94) $false
% 13.61/3.88 |
% 13.61/3.88 |-The branch is then unsatisfiable
% 13.61/3.88 |-Branch two:
% 13.61/3.88 | (19) ~ (sz10 = sz00)
% 13.61/3.88 | (139) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz10) = v3 & sdtpldt0(sz10, sz10) = v1 & sdtpldt0(sz10, sz00) = v0 & sdtpldt0(sz00, sz10) = v2)
% 13.61/3.88 |
% 13.61/3.88 +-Applying beta-rule and splitting (61), into two cases.
% 13.61/3.88 |-Branch one:
% 13.61/3.88 | (93) xn = sz00
% 13.61/3.88 |
% 13.61/3.88 | Equations (93) can reduce 12 to:
% 13.61/3.88 | (94) $false
% 13.61/3.88 |
% 13.61/3.88 |-The branch is then unsatisfiable
% 13.61/3.88 |-Branch two:
% 13.61/3.88 | (12) ~ (xn = sz00)
% 13.61/3.88 | (143) xm = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v2 = sz00) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v1 & sdtasdt0(xn, sz00) = v0 & sdtasdt0(sz00, xn) = v2) | ( ~ (v0 = 0) & aNaturalNumber0(xm) = v0))
% 13.61/3.88 |
% 13.61/3.88 +-Applying beta-rule and splitting (127), into two cases.
% 13.61/3.88 |-Branch one:
% 13.61/3.88 | (113) xm = sz00
% 13.61/3.88 |
% 13.61/3.88 | Equations (113) can reduce 40 to:
% 13.61/3.88 | (94) $false
% 13.61/3.88 |
% 13.61/3.88 |-The branch is then unsatisfiable
% 13.61/3.88 |-Branch two:
% 13.61/3.88 | (40) ~ (xm = sz00)
% 13.61/3.88 | (147) ? [v0] : ? [v1] : ? [v2] : (( ~ (v2 = sz00) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v0 & sdtasdt0(xn, sz00) = v1 & sdtasdt0(sz00, xn) = v2) | ( ~ (v0 = 0) & aNaturalNumber0(xm) = v0))
% 13.61/3.88 |
% 13.61/3.88 +-Applying beta-rule and splitting (143), into two cases.
% 13.61/3.88 |-Branch one:
% 13.61/3.88 | (113) xm = sz00
% 13.61/3.88 |
% 13.61/3.88 | Equations (113) can reduce 40 to:
% 13.61/3.88 | (94) $false
% 13.61/3.88 |
% 13.61/3.88 |-The branch is then unsatisfiable
% 13.61/3.88 |-Branch two:
% 13.61/3.88 | (40) ~ (xm = sz00)
% 13.61/3.88 | (151) ? [v0] : ? [v1] : ? [v2] : (( ~ (v2 = sz00) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v1 & sdtasdt0(xn, sz00) = v0 & sdtasdt0(sz00, xn) = v2) | ( ~ (v0 = 0) & aNaturalNumber0(xm) = v0))
% 13.61/3.88 |
% 13.61/3.88 +-Applying beta-rule and splitting (92), into two cases.
% 13.61/3.88 |-Branch one:
% 13.61/3.88 | (128) sz10 = sz00
% 13.61/3.88 |
% 13.61/3.88 | Equations (128) can reduce 19 to:
% 13.61/3.88 | (94) $false
% 13.61/3.88 |
% 13.61/3.88 |-The branch is then unsatisfiable
% 13.61/3.88 |-Branch two:
% 13.61/3.88 | (19) ~ (sz10 = sz00)
% 13.61/3.88 | (155) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz00) = v3 & sdtpldt0(sz00, sz10) = v1 & sdtpldt0(sz00, sz00) = v2 & sdtpldt0(sz00, sz00) = v0)
% 13.61/3.88 |
% 13.61/3.88 +-Applying beta-rule and splitting (87), into two cases.
% 13.61/3.88 |-Branch one:
% 13.61/3.88 | (113) xm = sz00
% 13.61/3.88 |
% 13.61/3.88 | Equations (113) can reduce 40 to:
% 13.61/3.88 | (94) $false
% 13.61/3.88 |
% 13.61/3.88 |-The branch is then unsatisfiable
% 13.61/3.88 |-Branch two:
% 13.61/3.88 | (40) ~ (xm = sz00)
% 13.61/3.88 | (159) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xm, sz10) = v1 & sdtasdt0(xm, sz00) = v0 & sdtasdt0(sz10, xm) = v3 & sdtasdt0(sz00, xm) = v2)
% 13.61/3.88 |
% 13.61/3.88 +-Applying beta-rule and splitting (63), into two cases.
% 13.61/3.88 |-Branch one:
% 13.61/3.88 | (93) xn = sz00
% 13.61/3.88 |
% 13.61/3.88 | Equations (93) can reduce 12 to:
% 13.61/3.88 | (94) $false
% 13.61/3.88 |
% 13.61/3.88 |-The branch is then unsatisfiable
% 13.61/3.88 |-Branch two:
% 13.61/3.88 | (12) ~ (xn = sz00)
% 13.61/3.88 | (163) xm = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v2 = v1) & ~ (v0 = sz00) & sdtasdt0(xn, xm) = v2 & sdtasdt0(xm, sz00) = v0 & sdtasdt0(sz00, xm) = v1) | ( ~ (v0 = 0) & aNaturalNumber0(xn) = v0))
% 13.61/3.88 |
% 13.61/3.88 +-Applying beta-rule and splitting (159), into two cases.
% 13.61/3.88 |-Branch one:
% 13.61/3.88 | (128) sz10 = sz00
% 13.61/3.88 |
% 13.61/3.88 | Equations (128) can reduce 19 to:
% 13.61/3.88 | (94) $false
% 13.61/3.88 |
% 13.61/3.88 |-The branch is then unsatisfiable
% 13.61/3.88 |-Branch two:
% 13.61/3.88 | (19) ~ (sz10 = sz00)
% 13.61/3.88 | (167) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xm, sz10) = v1 & sdtasdt0(xm, sz00) = v0 & sdtasdt0(sz10, xm) = v3 & sdtasdt0(sz00, xm) = v2)
% 13.61/3.88 |
% 13.61/3.88 | Instantiating (167) with all_113_0_50, all_113_1_51, all_113_2_52, all_113_3_53 yields:
% 13.61/3.88 | (168) ~ (all_113_0_50 = all_113_1_51) & ~ (all_113_2_52 = all_113_3_53) & sdtasdt0(xm, sz10) = all_113_2_52 & sdtasdt0(xm, sz00) = all_113_3_53 & sdtasdt0(sz10, xm) = all_113_0_50 & sdtasdt0(sz00, xm) = all_113_1_51
% 13.61/3.88 |
% 13.61/3.88 | Applying alpha-rule on (168) yields:
% 13.61/3.88 | (169) ~ (all_113_2_52 = all_113_3_53)
% 13.61/3.88 | (170) sdtasdt0(sz10, xm) = all_113_0_50
% 13.61/3.88 | (171) sdtasdt0(xm, sz10) = all_113_2_52
% 13.61/3.88 | (172) sdtasdt0(sz00, xm) = all_113_1_51
% 13.61/3.88 | (173) ~ (all_113_0_50 = all_113_1_51)
% 13.61/3.88 | (174) sdtasdt0(xm, sz00) = all_113_3_53
% 13.61/3.88 |
% 13.61/3.88 +-Applying beta-rule and splitting (69), into two cases.
% 13.61/3.88 |-Branch one:
% 13.61/3.88 | (93) xn = sz00
% 13.61/3.88 |
% 13.61/3.88 | Equations (93) can reduce 12 to:
% 13.61/3.88 | (94) $false
% 13.61/3.88 |
% 13.61/3.88 |-The branch is then unsatisfiable
% 13.61/3.88 |-Branch two:
% 13.61/3.88 | (12) ~ (xn = sz00)
% 13.61/3.88 | (178) xm = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v2 & sdtasdt0(xm, xn) = v0 & sdtasdt0(xm, sz00) = v1 & sdtasdt0(sz00, xm) = v3)
% 13.61/3.88 |
% 13.61/3.88 +-Applying beta-rule and splitting (178), into two cases.
% 13.61/3.88 |-Branch one:
% 13.61/3.88 | (113) xm = sz00
% 13.61/3.88 |
% 13.61/3.88 | Equations (113) can reduce 40 to:
% 13.61/3.88 | (94) $false
% 13.61/3.88 |
% 13.61/3.88 |-The branch is then unsatisfiable
% 13.61/3.88 |-Branch two:
% 13.61/3.88 | (40) ~ (xm = sz00)
% 13.61/3.88 | (182) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v2 & sdtasdt0(xm, xn) = v0 & sdtasdt0(xm, sz00) = v1 & sdtasdt0(sz00, xm) = v3)
% 13.61/3.88 |
% 13.61/3.88 | Instantiating (182) with all_123_0_54, all_123_1_55, all_123_2_56, all_123_3_57 yields:
% 13.61/3.88 | (183) ~ (all_123_0_54 = all_123_1_55) & ~ (all_123_2_56 = all_123_3_57) & sdtasdt0(xn, xm) = all_123_1_55 & sdtasdt0(xm, xn) = all_123_3_57 & sdtasdt0(xm, sz00) = all_123_2_56 & sdtasdt0(sz00, xm) = all_123_0_54
% 13.61/3.88 |
% 13.61/3.88 | Applying alpha-rule on (183) yields:
% 13.61/3.88 | (184) sdtasdt0(xn, xm) = all_123_1_55
% 13.61/3.88 | (185) ~ (all_123_0_54 = all_123_1_55)
% 13.61/3.88 | (186) sdtasdt0(sz00, xm) = all_123_0_54
% 13.61/3.88 | (187) ~ (all_123_2_56 = all_123_3_57)
% 13.84/3.88 | (188) sdtasdt0(xm, xn) = all_123_3_57
% 13.84/3.88 | (189) sdtasdt0(xm, sz00) = all_123_2_56
% 13.84/3.88 |
% 13.84/3.88 +-Applying beta-rule and splitting (163), into two cases.
% 13.84/3.88 |-Branch one:
% 13.84/3.88 | (113) xm = sz00
% 13.84/3.88 |
% 13.84/3.88 | Equations (113) can reduce 40 to:
% 13.84/3.88 | (94) $false
% 13.84/3.88 |
% 13.84/3.88 |-The branch is then unsatisfiable
% 13.84/3.88 |-Branch two:
% 13.84/3.88 | (40) ~ (xm = sz00)
% 13.84/3.88 | (193) ? [v0] : ? [v1] : ? [v2] : (( ~ (v2 = v1) & ~ (v0 = sz00) & sdtasdt0(xn, xm) = v2 & sdtasdt0(xm, sz00) = v0 & sdtasdt0(sz00, xm) = v1) | ( ~ (v0 = 0) & aNaturalNumber0(xn) = v0))
% 13.84/3.89 |
% 13.84/3.89 +-Applying beta-rule and splitting (91), into two cases.
% 13.84/3.89 |-Branch one:
% 13.84/3.89 | (128) sz10 = sz00
% 13.84/3.89 |
% 13.84/3.89 | Equations (128) can reduce 19 to:
% 13.84/3.89 | (94) $false
% 13.84/3.89 |
% 13.84/3.89 |-The branch is then unsatisfiable
% 13.84/3.89 |-Branch two:
% 13.84/3.89 | (19) ~ (sz10 = sz00)
% 13.84/3.89 | (197) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz00) = v2 & sdtpldt0(sz00, sz10) = v0 & sdtpldt0(sz00, sz00) = v3 & sdtpldt0(sz00, sz00) = v1)
% 13.84/3.89 |
% 13.84/3.89 +-Applying beta-rule and splitting (83), into two cases.
% 13.84/3.89 |-Branch one:
% 13.84/3.89 | (113) xm = sz00
% 13.84/3.89 |
% 13.84/3.89 | Equations (113) can reduce 40 to:
% 13.84/3.89 | (94) $false
% 13.84/3.89 |
% 13.84/3.89 |-The branch is then unsatisfiable
% 13.84/3.89 |-Branch two:
% 13.84/3.89 | (40) ~ (xm = sz00)
% 13.84/3.89 | (201) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xm, sz00) = v3 & sdtpldt0(sz00, xm) = v1 & sdtpldt0(sz00, sz00) = v2 & sdtpldt0(sz00, sz00) = v0)
% 13.84/3.89 |
% 13.84/3.89 +-Applying beta-rule and splitting (84), into two cases.
% 13.84/3.89 |-Branch one:
% 13.84/3.89 | (93) xn = sz00
% 13.84/3.89 |
% 13.84/3.89 | Equations (93) can reduce 12 to:
% 13.84/3.89 | (94) $false
% 13.84/3.89 |
% 13.84/3.89 |-The branch is then unsatisfiable
% 13.84/3.89 |-Branch two:
% 13.84/3.89 | (12) ~ (xn = sz00)
% 13.84/3.89 | (205) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, sz10) = v1 & sdtasdt0(xn, sz00) = v0 & sdtasdt0(sz10, xn) = v3 & sdtasdt0(sz00, xn) = v2)
% 13.84/3.89 |
% 13.84/3.89 +-Applying beta-rule and splitting (79), into two cases.
% 13.84/3.89 |-Branch one:
% 13.84/3.89 | (113) xm = sz00
% 13.84/3.89 |
% 13.84/3.89 | Equations (113) can reduce 40 to:
% 13.84/3.89 | (94) $false
% 13.84/3.89 |
% 13.84/3.89 |-The branch is then unsatisfiable
% 13.84/3.89 |-Branch two:
% 13.84/3.89 | (40) ~ (xm = sz00)
% 13.84/3.89 | (209) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xm, xm) = v2 & sdtasdt0(xm, xm) = v0 & sdtasdt0(xm, sz00) = v1 & sdtasdt0(sz00, xm) = v3)
% 13.84/3.89 |
% 13.84/3.89 | Instantiating (209) with all_153_0_157, all_153_1_158, all_153_2_159, all_153_3_160 yields:
% 13.84/3.89 | (210) ~ (all_153_0_157 = all_153_1_158) & ~ (all_153_2_159 = all_153_3_160) & sdtasdt0(xm, xm) = all_153_1_158 & sdtasdt0(xm, xm) = all_153_3_160 & sdtasdt0(xm, sz00) = all_153_2_159 & sdtasdt0(sz00, xm) = all_153_0_157
% 13.84/3.89 |
% 13.84/3.89 | Applying alpha-rule on (210) yields:
% 13.84/3.89 | (211) sdtasdt0(xm, sz00) = all_153_2_159
% 13.84/3.89 | (212) ~ (all_153_2_159 = all_153_3_160)
% 13.84/3.89 | (213) sdtasdt0(xm, xm) = all_153_1_158
% 13.84/3.89 | (214) sdtasdt0(xm, xm) = all_153_3_160
% 13.84/3.89 | (215) sdtasdt0(sz00, xm) = all_153_0_157
% 13.84/3.89 | (216) ~ (all_153_0_157 = all_153_1_158)
% 13.84/3.89 |
% 13.84/3.89 +-Applying beta-rule and splitting (74), into two cases.
% 13.84/3.89 |-Branch one:
% 13.84/3.89 | (93) xn = sz00
% 13.84/3.89 |
% 13.84/3.89 | Equations (93) can reduce 12 to:
% 13.84/3.89 | (94) $false
% 13.84/3.89 |
% 13.84/3.89 |-The branch is then unsatisfiable
% 13.84/3.89 |-Branch two:
% 13.84/3.89 | (12) ~ (xn = sz00)
% 13.84/3.89 | (220) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, sz00) = v3 & sdtpldt0(sz00, xn) = v1 & sdtpldt0(sz00, sz00) = v2 & sdtpldt0(sz00, sz00) = v0)
% 13.84/3.89 |
% 13.84/3.89 +-Applying beta-rule and splitting (70), into two cases.
% 13.84/3.89 |-Branch one:
% 13.84/3.89 | (93) xn = sz00
% 13.84/3.89 |
% 13.84/3.89 | Equations (93) can reduce 12 to:
% 13.84/3.89 | (94) $false
% 13.84/3.89 |
% 13.84/3.89 |-The branch is then unsatisfiable
% 13.84/3.89 |-Branch two:
% 13.84/3.89 | (12) ~ (xn = sz00)
% 13.84/3.89 | (224) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, xm) = v2 & sdtpldt0(xm, xn) = v0 & sdtpldt0(xm, sz00) = v1 & sdtpldt0(sz00, xm) = v3)
% 13.84/3.89 |
% 13.84/3.89 +-Applying beta-rule and splitting (71), into two cases.
% 13.84/3.89 |-Branch one:
% 13.84/3.89 | (93) xn = sz00
% 13.84/3.89 |
% 13.84/3.89 | Equations (93) can reduce 12 to:
% 13.84/3.89 | (94) $false
% 13.84/3.89 |
% 13.84/3.89 |-The branch is then unsatisfiable
% 13.84/3.89 |-Branch two:
% 13.84/3.89 | (12) ~ (xn = sz00)
% 13.84/3.89 | (228) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, xm) = v3 & sdtpldt0(xm, xn) = v1 & sdtpldt0(xm, sz00) = v0 & sdtpldt0(sz00, xm) = v2)
% 13.84/3.89 |
% 13.84/3.89 +-Applying beta-rule and splitting (73), into two cases.
% 13.84/3.89 |-Branch one:
% 13.84/3.89 | (93) xn = sz00
% 13.84/3.89 |
% 13.84/3.89 | Equations (93) can reduce 12 to:
% 13.84/3.89 | (94) $false
% 13.84/3.89 |
% 13.84/3.89 |-The branch is then unsatisfiable
% 13.84/3.89 |-Branch two:
% 13.84/3.89 | (12) ~ (xn = sz00)
% 13.84/3.89 | (232) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, sz10) = v3 & sdtpldt0(sz10, xn) = v1 & sdtpldt0(sz10, sz00) = v0 & sdtpldt0(sz00, sz10) = v2)
% 13.84/3.89 |
% 13.84/3.89 +-Applying beta-rule and splitting (72), into two cases.
% 13.84/3.89 |-Branch one:
% 13.84/3.89 | (93) xn = sz00
% 13.84/3.89 |
% 13.84/3.89 | Equations (93) can reduce 12 to:
% 13.84/3.89 | (94) $false
% 13.84/3.89 |
% 13.84/3.89 |-The branch is then unsatisfiable
% 13.84/3.89 |-Branch two:
% 13.84/3.89 | (12) ~ (xn = sz00)
% 13.84/3.89 | (236) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, sz10) = v2 & sdtpldt0(sz10, xn) = v0 & sdtpldt0(sz10, sz00) = v1 & sdtpldt0(sz00, sz10) = v3)
% 13.84/3.89 |
% 13.84/3.89 +-Applying beta-rule and splitting (77), into two cases.
% 13.84/3.89 |-Branch one:
% 13.84/3.89 | (113) xm = sz00
% 13.84/3.89 |
% 13.84/3.89 | Equations (113) can reduce 40 to:
% 13.84/3.89 | (94) $false
% 13.84/3.89 |
% 13.84/3.89 |-The branch is then unsatisfiable
% 13.84/3.89 |-Branch two:
% 13.84/3.89 | (40) ~ (xm = sz00)
% 13.84/3.89 | (240) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, xm) = v0 & sdtpldt0(xn, sz00) = v1 & sdtpldt0(xm, xn) = v2 & sdtpldt0(sz00, xn) = v3)
% 13.84/3.89 |
% 13.84/3.89 +-Applying beta-rule and splitting (78), into two cases.
% 13.84/3.89 |-Branch one:
% 13.84/3.89 | (113) xm = sz00
% 13.84/3.89 |
% 13.84/3.89 | Equations (113) can reduce 40 to:
% 13.84/3.89 | (94) $false
% 13.84/3.89 |
% 13.84/3.89 |-The branch is then unsatisfiable
% 13.84/3.89 |-Branch two:
% 13.84/3.89 | (40) ~ (xm = sz00)
% 13.84/3.89 | (244) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, xm) = v1 & sdtpldt0(xn, sz00) = v0 & sdtpldt0(xm, xn) = v3 & sdtpldt0(sz00, xn) = v2)
% 13.84/3.89 |
% 13.84/3.89 +-Applying beta-rule and splitting (82), into two cases.
% 13.84/3.89 |-Branch one:
% 13.84/3.89 | (113) xm = sz00
% 13.84/3.89 |
% 13.84/3.89 | Equations (113) can reduce 40 to:
% 13.84/3.89 | (94) $false
% 13.84/3.89 |
% 13.84/3.89 |-The branch is then unsatisfiable
% 13.84/3.89 |-Branch two:
% 13.84/3.89 | (40) ~ (xm = sz00)
% 13.84/3.89 | (248) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xm, sz00) = v2 & sdtpldt0(sz00, xm) = v0 & sdtpldt0(sz00, sz00) = v3 & sdtpldt0(sz00, sz00) = v1)
% 13.84/3.90 |
% 13.84/3.90 +-Applying beta-rule and splitting (85), into two cases.
% 13.84/3.90 |-Branch one:
% 13.84/3.90 | (128) sz10 = sz00
% 13.84/3.90 |
% 13.84/3.90 | Equations (128) can reduce 19 to:
% 13.84/3.90 | (94) $false
% 13.84/3.90 |
% 13.84/3.90 |-The branch is then unsatisfiable
% 13.84/3.90 |-Branch two:
% 13.84/3.90 | (19) ~ (sz10 = sz00)
% 13.84/3.90 | (252) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xn, sz10) = v1 & sdtpldt0(xn, sz00) = v0 & sdtpldt0(sz10, xn) = v3 & sdtpldt0(sz00, xn) = v2)
% 13.84/3.90 |
% 13.84/3.90 +-Applying beta-rule and splitting (81), into two cases.
% 13.84/3.90 |-Branch one:
% 13.84/3.90 | (113) xm = sz00
% 13.84/3.90 |
% 13.84/3.90 | Equations (113) can reduce 40 to:
% 13.84/3.90 | (94) $false
% 13.84/3.90 |
% 13.84/3.90 |-The branch is then unsatisfiable
% 13.84/3.90 |-Branch two:
% 13.84/3.90 | (40) ~ (xm = sz00)
% 13.84/3.90 | (256) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xm, sz10) = v2 & sdtpldt0(sz10, xm) = v0 & sdtpldt0(sz10, sz00) = v1 & sdtpldt0(sz00, sz10) = v3)
% 13.84/3.90 |
% 13.84/3.90 +-Applying beta-rule and splitting (86), into two cases.
% 13.84/3.90 |-Branch one:
% 13.84/3.90 | (113) xm = sz00
% 13.84/3.90 |
% 13.84/3.90 | Equations (113) can reduce 40 to:
% 13.84/3.90 | (94) $false
% 13.84/3.90 |
% 13.84/3.90 |-The branch is then unsatisfiable
% 13.84/3.90 |-Branch two:
% 13.84/3.90 | (40) ~ (xm = sz00)
% 13.84/3.90 | (260) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xm, sz10) = v0 & sdtasdt0(xm, sz00) = v1 & sdtasdt0(sz10, xm) = v2 & sdtasdt0(sz00, xm) = v3)
% 13.84/3.90 |
% 13.84/3.90 +-Applying beta-rule and splitting (260), into two cases.
% 13.84/3.90 |-Branch one:
% 13.84/3.90 | (128) sz10 = sz00
% 13.84/3.90 |
% 13.84/3.90 | Equations (128) can reduce 19 to:
% 13.84/3.90 | (94) $false
% 13.84/3.90 |
% 13.84/3.90 |-The branch is then unsatisfiable
% 13.84/3.90 |-Branch two:
% 13.84/3.90 | (19) ~ (sz10 = sz00)
% 13.84/3.90 | (264) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xm, sz10) = v0 & sdtasdt0(xm, sz00) = v1 & sdtasdt0(sz10, xm) = v2 & sdtasdt0(sz00, xm) = v3)
% 13.84/3.90 |
% 13.84/3.90 | Instantiating (264) with all_217_0_201, all_217_1_202, all_217_2_203, all_217_3_204 yields:
% 13.84/3.90 | (265) ~ (all_217_0_201 = all_217_1_202) & ~ (all_217_2_203 = all_217_3_204) & sdtasdt0(xm, sz10) = all_217_3_204 & sdtasdt0(xm, sz00) = all_217_2_203 & sdtasdt0(sz10, xm) = all_217_1_202 & sdtasdt0(sz00, xm) = all_217_0_201
% 13.84/3.90 |
% 13.84/3.90 | Applying alpha-rule on (265) yields:
% 13.84/3.90 | (266) sdtasdt0(xm, sz10) = all_217_3_204
% 13.84/3.90 | (267) sdtasdt0(sz00, xm) = all_217_0_201
% 13.84/3.90 | (268) ~ (all_217_0_201 = all_217_1_202)
% 13.84/3.90 | (269) ~ (all_217_2_203 = all_217_3_204)
% 13.84/3.90 | (270) sdtasdt0(xm, sz00) = all_217_2_203
% 13.84/3.90 | (271) sdtasdt0(sz10, xm) = all_217_1_202
% 13.84/3.90 |
% 13.84/3.90 +-Applying beta-rule and splitting (76), into two cases.
% 13.84/3.90 |-Branch one:
% 13.84/3.90 | (93) xn = sz00
% 13.84/3.90 |
% 13.84/3.90 | Equations (93) can reduce 12 to:
% 13.84/3.90 | (94) $false
% 13.84/3.90 |
% 13.84/3.90 |-The branch is then unsatisfiable
% 13.84/3.90 |-Branch two:
% 13.84/3.90 | (12) ~ (xn = sz00)
% 13.84/3.90 | (275) xm = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v1 & sdtasdt0(xn, sz00) = v0 & sdtasdt0(xm, xn) = v3 & sdtasdt0(sz00, xn) = v2)
% 13.84/3.90 |
% 13.84/3.90 +-Applying beta-rule and splitting (75), into two cases.
% 13.84/3.90 |-Branch one:
% 13.84/3.90 | (93) xn = sz00
% 13.84/3.90 |
% 13.84/3.90 | Equations (93) can reduce 12 to:
% 13.84/3.90 | (94) $false
% 13.84/3.90 |
% 13.84/3.90 |-The branch is then unsatisfiable
% 13.84/3.90 |-Branch two:
% 13.84/3.90 | (12) ~ (xn = sz00)
% 13.84/3.90 | (279) xm = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v0 & sdtasdt0(xn, sz00) = v1 & sdtasdt0(xm, xn) = v2 & sdtasdt0(sz00, xn) = v3)
% 13.84/3.90 |
% 13.84/3.90 +-Applying beta-rule and splitting (279), into two cases.
% 13.84/3.90 |-Branch one:
% 13.84/3.90 | (113) xm = sz00
% 13.84/3.90 |
% 13.84/3.90 | Equations (113) can reduce 40 to:
% 13.84/3.90 | (94) $false
% 13.84/3.90 |
% 13.84/3.90 |-The branch is then unsatisfiable
% 13.84/3.90 |-Branch two:
% 13.84/3.90 | (40) ~ (xm = sz00)
% 13.84/3.90 | (283) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v0 & sdtasdt0(xn, sz00) = v1 & sdtasdt0(xm, xn) = v2 & sdtasdt0(sz00, xn) = v3)
% 13.84/3.90 |
% 13.84/3.90 +-Applying beta-rule and splitting (80), into two cases.
% 13.84/3.90 |-Branch one:
% 13.84/3.90 | (113) xm = sz00
% 13.84/3.90 |
% 13.84/3.90 | Equations (113) can reduce 40 to:
% 13.84/3.90 | (94) $false
% 13.84/3.90 |
% 13.84/3.90 |-The branch is then unsatisfiable
% 13.84/3.90 |-Branch two:
% 13.84/3.90 | (40) ~ (xm = sz00)
% 13.84/3.90 | (287) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xm, xm) = v3 & sdtasdt0(xm, xm) = v1 & sdtasdt0(xm, sz00) = v0 & sdtasdt0(sz00, xm) = v2)
% 13.84/3.90 |
% 13.84/3.90 | Instantiating (287) with all_253_0_217, all_253_1_218, all_253_2_219, all_253_3_220 yields:
% 13.84/3.90 | (288) ~ (all_253_0_217 = all_253_1_218) & ~ (all_253_2_219 = all_253_3_220) & sdtasdt0(xm, xm) = all_253_0_217 & sdtasdt0(xm, xm) = all_253_2_219 & sdtasdt0(xm, sz00) = all_253_3_220 & sdtasdt0(sz00, xm) = all_253_1_218
% 13.84/3.90 |
% 13.84/3.90 | Applying alpha-rule on (288) yields:
% 13.84/3.90 | (289) sdtasdt0(xm, xm) = all_253_2_219
% 13.84/3.90 | (290) sdtasdt0(xm, xm) = all_253_0_217
% 13.84/3.90 | (291) sdtasdt0(xm, sz00) = all_253_3_220
% 13.84/3.90 | (292) ~ (all_253_2_219 = all_253_3_220)
% 13.84/3.90 | (293) sdtasdt0(sz00, xm) = all_253_1_218
% 13.84/3.90 | (294) ~ (all_253_0_217 = all_253_1_218)
% 13.84/3.90 |
% 13.84/3.90 | Instantiating formula (26) with xm, sz00, all_153_2_159, all_217_2_203 and discharging atoms sdtasdt0(xm, sz00) = all_217_2_203, sdtasdt0(xm, sz00) = all_153_2_159, yields:
% 13.84/3.90 | (295) all_217_2_203 = all_153_2_159
% 13.84/3.90 |
% 13.84/3.90 | Instantiating formula (26) with xm, sz00, all_123_2_56, all_253_3_220 and discharging atoms sdtasdt0(xm, sz00) = all_253_3_220, sdtasdt0(xm, sz00) = all_123_2_56, yields:
% 13.84/3.90 | (296) all_253_3_220 = all_123_2_56
% 13.84/3.90 |
% 13.84/3.90 | Instantiating formula (26) with xm, sz00, all_113_3_53, all_153_2_159 and discharging atoms sdtasdt0(xm, sz00) = all_153_2_159, sdtasdt0(xm, sz00) = all_113_3_53, yields:
% 13.84/3.90 | (297) all_153_2_159 = all_113_3_53
% 13.84/3.90 |
% 13.84/3.91 | Instantiating formula (26) with xm, sz00, all_113_3_53, all_123_2_56 and discharging atoms sdtasdt0(xm, sz00) = all_123_2_56, sdtasdt0(xm, sz00) = all_113_3_53, yields:
% 13.84/3.91 | (298) all_123_2_56 = all_113_3_53
% 13.84/3.91 |
% 13.84/3.91 | Instantiating formula (26) with xm, sz00, all_49_2_27, all_217_2_203 and discharging atoms sdtasdt0(xm, sz00) = all_217_2_203, sdtasdt0(xm, sz00) = all_49_2_27, yields:
% 13.84/3.91 | (299) all_217_2_203 = all_49_2_27
% 13.84/3.91 |
% 13.84/3.91 | Instantiating formula (26) with xm, sz00, sz00, all_253_3_220 and discharging atoms sdtasdt0(xm, sz00) = all_253_3_220, sdtasdt0(xm, sz00) = sz00, yields:
% 13.84/3.91 | (300) all_253_3_220 = sz00
% 13.84/3.91 |
% 13.84/3.91 | Combining equations (296,300) yields a new equation:
% 13.84/3.91 | (301) all_123_2_56 = sz00
% 13.84/3.91 |
% 13.84/3.91 | Simplifying 301 yields:
% 13.84/3.91 | (302) all_123_2_56 = sz00
% 13.84/3.91 |
% 13.84/3.91 | Combining equations (295,299) yields a new equation:
% 13.84/3.91 | (303) all_153_2_159 = all_49_2_27
% 13.84/3.91 |
% 13.84/3.91 | Simplifying 303 yields:
% 13.84/3.91 | (304) all_153_2_159 = all_49_2_27
% 13.84/3.91 |
% 13.84/3.91 | Combining equations (297,304) yields a new equation:
% 13.84/3.91 | (305) all_113_3_53 = all_49_2_27
% 13.84/3.91 |
% 13.84/3.91 | Simplifying 305 yields:
% 13.84/3.91 | (306) all_113_3_53 = all_49_2_27
% 13.84/3.91 |
% 13.84/3.91 | Combining equations (298,302) yields a new equation:
% 13.84/3.91 | (307) all_113_3_53 = sz00
% 13.84/3.91 |
% 13.84/3.91 | Simplifying 307 yields:
% 13.84/3.91 | (308) all_113_3_53 = sz00
% 13.84/3.91 |
% 13.84/3.91 | Combining equations (306,308) yields a new equation:
% 13.84/3.91 | (309) all_49_2_27 = sz00
% 13.84/3.91 |
% 13.84/3.91 | Simplifying 309 yields:
% 13.84/3.91 | (310) all_49_2_27 = sz00
% 13.84/3.91 |
% 13.84/3.91 | Equations (310) can reduce 119 to:
% 13.84/3.91 | (94) $false
% 13.84/3.91 |
% 13.84/3.91 |-The branch is then unsatisfiable
% 13.84/3.91 |-Branch two:
% 13.84/3.91 | (312) ~ (all_49_2_27 = 0) & aNaturalNumber0(xn) = all_49_2_27
% 13.84/3.91 |
% 13.84/3.91 | Applying alpha-rule on (312) yields:
% 13.84/3.91 | (313) ~ (all_49_2_27 = 0)
% 13.84/3.91 | (314) aNaturalNumber0(xn) = all_49_2_27
% 13.84/3.91 |
% 13.84/3.91 | Instantiating formula (36) with xn, all_49_2_27, 0 and discharging atoms aNaturalNumber0(xn) = all_49_2_27, aNaturalNumber0(xn) = 0, yields:
% 13.84/3.91 | (315) all_49_2_27 = 0
% 13.84/3.91 |
% 13.84/3.91 | Equations (315) can reduce 313 to:
% 13.84/3.91 | (94) $false
% 13.84/3.91 |
% 13.84/3.91 |-The branch is then unsatisfiable
% 13.84/3.91 % SZS output end Proof for theBenchmark
% 13.84/3.91
% 13.84/3.91 3260ms
%------------------------------------------------------------------------------