TSTP Solution File: NUM483+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM483+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.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 08:44:58 EDT 2022
% Result : Theorem 43.18s 16.84s
% Output : Proof 210.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM483+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 5 08:22:37 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.57/0.59 ____ _
% 0.57/0.59 ___ / __ \_____(_)___ ________ __________
% 0.57/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.59
% 0.57/0.59 A Theorem Prover for First-Order Logic
% 0.57/0.59 (ePrincess v.1.0)
% 0.57/0.59
% 0.57/0.59 (c) Philipp Rümmer, 2009-2015
% 0.57/0.59 (c) Peter Backeman, 2014-2015
% 0.57/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.59 Bug reports to peter@backeman.se
% 0.57/0.59
% 0.57/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.59
% 0.57/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.87/0.97 Prover 0: Preprocessing ...
% 3.41/1.42 Prover 0: Constructing countermodel ...
% 18.49/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 18.97/6.02 Prover 1: Preprocessing ...
% 19.37/6.17 Prover 1: Constructing countermodel ...
% 28.71/8.53 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 28.71/8.57 Prover 2: Preprocessing ...
% 29.61/8.74 Prover 2: Warning: ignoring some quantifiers
% 29.61/8.75 Prover 2: Constructing countermodel ...
% 35.27/11.54 Prover 0: stopped
% 35.57/11.74 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 35.60/11.77 Prover 3: Preprocessing ...
% 35.93/11.82 Prover 3: Constructing countermodel ...
% 43.18/16.84 Prover 3: proved (5099ms)
% 43.18/16.84 Prover 1: stopped
% 43.18/16.84 Prover 2: stopped
% 43.18/16.84
% 43.18/16.84 No countermodel exists, formula is valid
% 43.18/16.84 % SZS status Theorem for theBenchmark
% 43.18/16.84
% 43.18/16.84 Generating proof ... found it (size 339)
% 209.28/158.63
% 209.28/158.63 % SZS output start Proof for theBenchmark
% 209.28/158.63 Assumed formulas after preprocessing and simplification:
% 209.28/158.63 | (0) ~ (xk = sz10) & ~ (xk = sz00) & ~ (sz10 = sz00) & aNaturalNumber0(xk) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ isPrime0(xk) & ~ isPrime0(sz10) & ~ isPrime0(sz00) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v3, v2) = v5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1)) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0) & ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2))) & ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2))) & ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ iLess0(v0, xk) | ~ aNaturalNumber0(v0) | ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1))) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1] : ( ~ (v1 = v0) & ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1))) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) & ! [v0] : ( ~ isPrime0(v0) | ~ doDivides0(v0, xk) | ~ aNaturalNumber0(v0)) & ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 209.54/158.70 | Applying alpha-rule on (0) yields:
% 209.54/158.70 | (1) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 209.54/158.70 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 209.54/158.70 | (3) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 209.54/158.70 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5))
% 209.54/158.70 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6)))
% 209.54/158.70 | (6) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 209.54/158.70 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6)))
% 209.54/158.70 | (8) ~ isPrime0(xk)
% 209.54/158.70 | (9) aNaturalNumber0(sz10)
% 209.54/158.70 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4))
% 209.54/158.70 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4))
% 209.54/158.70 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 209.54/158.70 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 209.54/158.70 | (14) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1] : ( ~ (v1 = v0) & ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 209.54/158.70 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 209.54/158.70 | (16) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 209.54/158.70 | (17) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 209.54/158.70 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 209.54/158.70 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 209.54/158.70 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 209.54/158.70 | (21) aNaturalNumber0(xk)
% 209.54/158.70 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6))
% 209.54/158.71 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 209.54/158.71 | (24) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 209.54/158.71 | (25) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 209.54/158.71 | (26) ~ isPrime0(sz00)
% 209.54/158.71 | (27) ~ (sz10 = sz00)
% 209.54/158.71 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4))
% 209.54/158.71 | (29) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 209.54/158.71 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 209.54/158.71 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 209.54/158.71 | (32) ~ (xk = sz10)
% 209.54/158.71 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 209.54/158.71 | (34) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 209.54/158.71 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 209.54/158.71 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 209.54/158.71 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 209.54/158.71 | (38) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 209.54/158.71 | (39) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 209.54/158.71 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 209.54/158.71 | (41) ! [v0] : ( ~ isPrime0(v0) | ~ doDivides0(v0, xk) | ~ aNaturalNumber0(v0))
% 209.54/158.71 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 209.54/158.71 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 209.54/158.71 | (44) ~ (xk = sz00)
% 209.54/158.71 | (45) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ iLess0(v0, xk) | ~ aNaturalNumber0(v0) | ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 209.54/158.71 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v3, v2) = v5)
% 209.54/158.71 | (47) ~ isPrime0(sz10)
% 209.54/158.71 | (48) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 209.54/158.71 | (49) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 209.54/158.71 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5))
% 209.54/158.72 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 209.54/158.72 | (52) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 209.54/158.72 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 209.54/158.72 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3))
% 209.54/158.72 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 209.54/158.72 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 209.54/158.72 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 209.54/158.72 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 209.54/158.72 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 209.54/158.72 | (60) ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 209.54/158.72 | (61) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 209.54/158.72 | (62) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 209.54/158.72 | (63) aNaturalNumber0(sz00)
% 209.54/158.72 |
% 209.54/158.72 | Instantiating formula (61) with xk, xk and discharging atoms aNaturalNumber0(xk), yields:
% 209.54/158.72 | (64) sdtlseqdt0(xk, xk)
% 209.54/158.72 |
% 209.54/158.72 | Instantiating formula (14) with xk and discharging atoms aNaturalNumber0(xk), ~ isPrime0(xk), yields:
% 209.54/158.72 | (65) xk = sz10 | xk = sz00 | ? [v0] : ( ~ (v0 = xk) & ~ (v0 = sz10) & doDivides0(v0, xk) & aNaturalNumber0(v0))
% 209.54/158.72 |
% 209.54/158.72 | Instantiating formula (29) with xk and discharging atoms aNaturalNumber0(xk), yields:
% 209.54/158.72 | (66) xk = sz10 | xk = sz00 | sdtlseqdt0(sz10, xk)
% 209.54/158.72 |
% 209.54/158.72 | Instantiating formula (61) with sz10, sz10 and discharging atoms aNaturalNumber0(sz10), yields:
% 209.54/158.72 | (67) sdtlseqdt0(sz10, sz10)
% 209.54/158.72 |
% 209.54/158.72 | Instantiating formula (61) with sz00, sz00 and discharging atoms aNaturalNumber0(sz00), yields:
% 209.54/158.72 | (68) sdtlseqdt0(sz00, sz00)
% 209.54/158.72 |
% 209.54/158.72 +-Applying beta-rule and splitting (66), into two cases.
% 209.54/158.72 |-Branch one:
% 209.54/158.72 | (69) sdtlseqdt0(sz10, xk)
% 209.54/158.72 |
% 209.54/158.72 +-Applying beta-rule and splitting (65), into two cases.
% 209.54/158.72 |-Branch one:
% 209.54/158.72 | (70) xk = sz00
% 209.54/158.72 |
% 209.54/158.72 | Equations (70) can reduce 44 to:
% 209.54/158.72 | (71) $false
% 209.54/158.72 |
% 209.54/158.72 |-The branch is then unsatisfiable
% 209.54/158.72 |-Branch two:
% 209.54/158.72 | (44) ~ (xk = sz00)
% 209.54/158.72 | (73) xk = sz10 | ? [v0] : ( ~ (v0 = xk) & ~ (v0 = sz10) & doDivides0(v0, xk) & aNaturalNumber0(v0))
% 209.54/158.72 |
% 209.54/158.72 +-Applying beta-rule and splitting (73), into two cases.
% 209.54/158.72 |-Branch one:
% 209.54/158.72 | (74) xk = sz10
% 209.54/158.72 |
% 209.54/158.72 | Equations (74) can reduce 32 to:
% 209.54/158.72 | (71) $false
% 209.54/158.72 |
% 209.54/158.72 |-The branch is then unsatisfiable
% 209.54/158.72 |-Branch two:
% 209.54/158.72 | (32) ~ (xk = sz10)
% 209.54/158.72 | (77) ? [v0] : ( ~ (v0 = xk) & ~ (v0 = sz10) & doDivides0(v0, xk) & aNaturalNumber0(v0))
% 209.54/158.72 |
% 209.54/158.72 | Instantiating (77) with all_19_0_0 yields:
% 209.54/158.72 | (78) ~ (all_19_0_0 = xk) & ~ (all_19_0_0 = sz10) & doDivides0(all_19_0_0, xk) & aNaturalNumber0(all_19_0_0)
% 209.54/158.73 |
% 209.54/158.73 | Applying alpha-rule on (78) yields:
% 209.54/158.73 | (79) ~ (all_19_0_0 = xk)
% 209.54/158.73 | (80) ~ (all_19_0_0 = sz10)
% 209.54/158.73 | (81) doDivides0(all_19_0_0, xk)
% 209.54/158.73 | (82) aNaturalNumber0(all_19_0_0)
% 209.54/158.73 |
% 209.54/158.73 | Instantiating formula (38) with xk, xk and discharging atoms sdtlseqdt0(xk, xk), aNaturalNumber0(xk), yields:
% 209.54/158.73 | (83) ? [v0] : (sdtpldt0(xk, v0) = xk & aNaturalNumber0(v0))
% 209.54/158.73 |
% 209.54/158.73 | Instantiating formula (38) with xk, sz10 and discharging atoms sdtlseqdt0(sz10, xk), aNaturalNumber0(xk), aNaturalNumber0(sz10), yields:
% 209.54/158.73 | (84) ? [v0] : (sdtpldt0(sz10, v0) = xk & aNaturalNumber0(v0))
% 209.54/158.73 |
% 209.54/158.73 | Instantiating formula (38) with sz10, sz10 and discharging atoms sdtlseqdt0(sz10, sz10), aNaturalNumber0(sz10), yields:
% 209.54/158.73 | (85) ? [v0] : (sdtpldt0(sz10, v0) = sz10 & aNaturalNumber0(v0))
% 209.54/158.73 |
% 209.54/158.73 | Instantiating formula (38) with sz00, sz00 and discharging atoms sdtlseqdt0(sz00, sz00), aNaturalNumber0(sz00), yields:
% 209.54/158.73 | (86) ? [v0] : (sdtpldt0(sz00, v0) = sz00 & aNaturalNumber0(v0))
% 209.54/158.73 |
% 209.54/158.73 | Instantiating formula (60) with xk, all_19_0_0 and discharging atoms doDivides0(all_19_0_0, xk), aNaturalNumber0(all_19_0_0), aNaturalNumber0(xk), yields:
% 209.54/158.73 | (87) xk = sz00 | sdtlseqdt0(all_19_0_0, xk)
% 209.54/158.73 |
% 209.54/158.73 | Instantiating formula (62) with xk, all_19_0_0 and discharging atoms doDivides0(all_19_0_0, xk), aNaturalNumber0(all_19_0_0), aNaturalNumber0(xk), yields:
% 209.54/158.73 | (88) ? [v0] : (sdtasdt0(all_19_0_0, v0) = xk & aNaturalNumber0(v0))
% 209.54/158.73 |
% 209.54/158.73 | Instantiating formula (61) with all_19_0_0, all_19_0_0 and discharging atoms aNaturalNumber0(all_19_0_0), yields:
% 209.54/158.73 | (89) sdtlseqdt0(all_19_0_0, all_19_0_0)
% 209.54/158.73 |
% 209.54/158.73 | Instantiating formula (29) with all_19_0_0 and discharging atoms aNaturalNumber0(all_19_0_0), yields:
% 209.54/158.73 | (90) all_19_0_0 = sz10 | all_19_0_0 = sz00 | sdtlseqdt0(sz10, all_19_0_0)
% 209.54/158.73 |
% 209.54/158.73 | Instantiating (88) with all_27_0_1 yields:
% 209.54/158.73 | (91) sdtasdt0(all_19_0_0, all_27_0_1) = xk & aNaturalNumber0(all_27_0_1)
% 209.54/158.73 |
% 209.54/158.73 | Applying alpha-rule on (91) yields:
% 209.54/158.73 | (92) sdtasdt0(all_19_0_0, all_27_0_1) = xk
% 209.54/158.73 | (93) aNaturalNumber0(all_27_0_1)
% 209.54/158.73 |
% 209.54/158.73 | Instantiating (85) with all_29_0_2 yields:
% 209.54/158.73 | (94) sdtpldt0(sz10, all_29_0_2) = sz10 & aNaturalNumber0(all_29_0_2)
% 209.54/158.73 |
% 209.54/158.73 | Applying alpha-rule on (94) yields:
% 209.54/158.73 | (95) sdtpldt0(sz10, all_29_0_2) = sz10
% 209.54/158.73 | (96) aNaturalNumber0(all_29_0_2)
% 209.54/158.73 |
% 209.54/158.73 | Instantiating (83) with all_31_0_3 yields:
% 209.54/158.73 | (97) sdtpldt0(xk, all_31_0_3) = xk & aNaturalNumber0(all_31_0_3)
% 209.54/158.73 |
% 209.54/158.73 | Applying alpha-rule on (97) yields:
% 209.54/158.73 | (98) sdtpldt0(xk, all_31_0_3) = xk
% 209.54/158.73 | (99) aNaturalNumber0(all_31_0_3)
% 209.54/158.73 |
% 209.54/158.73 | Instantiating (84) with all_33_0_4 yields:
% 209.54/158.73 | (100) sdtpldt0(sz10, all_33_0_4) = xk & aNaturalNumber0(all_33_0_4)
% 209.54/158.73 |
% 209.54/158.73 | Applying alpha-rule on (100) yields:
% 209.54/158.73 | (101) sdtpldt0(sz10, all_33_0_4) = xk
% 209.54/158.73 | (102) aNaturalNumber0(all_33_0_4)
% 209.54/158.73 |
% 209.54/158.73 | Instantiating (86) with all_35_0_5 yields:
% 209.54/158.73 | (103) sdtpldt0(sz00, all_35_0_5) = sz00 & aNaturalNumber0(all_35_0_5)
% 209.54/158.73 |
% 209.54/158.73 | Applying alpha-rule on (103) yields:
% 209.54/158.73 | (104) sdtpldt0(sz00, all_35_0_5) = sz00
% 209.54/158.73 | (105) aNaturalNumber0(all_35_0_5)
% 209.54/158.73 |
% 209.54/158.73 +-Applying beta-rule and splitting (87), into two cases.
% 209.54/158.73 |-Branch one:
% 209.54/158.73 | (106) sdtlseqdt0(all_19_0_0, xk)
% 209.54/158.73 |
% 209.54/158.73 | Instantiating formula (25) with sz00, all_35_0_5 and discharging atoms sdtpldt0(sz00, all_35_0_5) = sz00, aNaturalNumber0(all_35_0_5), yields:
% 209.54/158.73 | (107) all_35_0_5 = sz00
% 209.54/158.73 |
% 209.54/158.73 | Instantiating formula (48) with xk, all_27_0_1 and discharging atoms aNaturalNumber0(all_27_0_1), yields:
% 209.54/158.73 | (108) xk = sz00 | ~ (sdtasdt0(sz00, all_27_0_1) = xk)
% 209.54/158.73 |
% 209.54/158.73 | From (107) and (105) follows:
% 209.54/158.73 | (63) aNaturalNumber0(sz00)
% 209.54/158.73 |
% 209.54/158.73 +-Applying beta-rule and splitting (108), into two cases.
% 209.54/158.73 |-Branch one:
% 209.54/158.73 | (110) ~ (sdtasdt0(sz00, all_27_0_1) = xk)
% 209.54/158.73 |
% 209.54/158.73 | Using (92) and (110) yields:
% 209.54/158.73 | (111) ~ (all_19_0_0 = sz00)
% 209.54/158.73 |
% 209.54/158.73 +-Applying beta-rule and splitting (90), into two cases.
% 209.54/158.73 |-Branch one:
% 209.54/158.73 | (112) sdtlseqdt0(sz10, all_19_0_0)
% 209.54/158.73 |
% 209.54/158.73 | Instantiating formula (18) with xk, sz10, all_19_0_0 and discharging atoms aNaturalNumber0(all_19_0_0), aNaturalNumber0(sz10), yields:
% 209.54/158.73 | (113) ~ (sdtasdt0(all_19_0_0, sz10) = xk) | sdtasdt0(sz10, all_19_0_0) = xk
% 209.54/158.73 |
% 209.54/158.73 | Instantiating formula (18) with xk, sz00, all_19_0_0 and discharging atoms aNaturalNumber0(all_19_0_0), aNaturalNumber0(sz00), yields:
% 209.54/158.73 | (114) ~ (sdtasdt0(all_19_0_0, sz00) = xk) | sdtasdt0(sz00, all_19_0_0) = xk
% 209.54/158.73 |
% 209.54/158.73 | Instantiating formula (38) with all_19_0_0, all_19_0_0 and discharging atoms sdtlseqdt0(all_19_0_0, all_19_0_0), aNaturalNumber0(all_19_0_0), yields:
% 209.54/158.73 | (115) ? [v0] : (sdtpldt0(all_19_0_0, v0) = all_19_0_0 & aNaturalNumber0(v0))
% 209.54/158.73 |
% 209.54/158.73 | Instantiating formula (35) with xk, all_19_0_0 and discharging atoms sdtlseqdt0(all_19_0_0, xk), aNaturalNumber0(all_19_0_0), aNaturalNumber0(xk), yields:
% 209.54/158.73 | (116) all_19_0_0 = xk | iLess0(all_19_0_0, xk)
% 209.54/158.73 |
% 209.54/158.73 | Instantiating formula (38) with xk, all_19_0_0 and discharging atoms sdtlseqdt0(all_19_0_0, xk), aNaturalNumber0(all_19_0_0), aNaturalNumber0(xk), yields:
% 209.54/158.73 | (117) ? [v0] : (sdtpldt0(all_19_0_0, v0) = xk & aNaturalNumber0(v0))
% 209.54/158.74 |
% 209.54/158.74 | Instantiating formula (38) with all_19_0_0, sz10 and discharging atoms sdtlseqdt0(sz10, all_19_0_0), aNaturalNumber0(all_19_0_0), aNaturalNumber0(sz10), yields:
% 209.54/158.74 | (118) ? [v0] : (sdtpldt0(sz10, v0) = all_19_0_0 & aNaturalNumber0(v0))
% 209.54/158.74 |
% 209.54/158.74 | Instantiating formula (57) with xk, all_31_0_3, xk and discharging atoms sdtpldt0(xk, all_31_0_3) = xk, aNaturalNumber0(all_31_0_3), aNaturalNumber0(xk), yields:
% 209.54/158.74 | (119) sdtpldt0(all_31_0_3, xk) = xk
% 209.54/158.74 |
% 209.54/158.74 | Instantiating formula (7) with xk, all_33_0_4, xk, sz10 and discharging atoms sdtpldt0(sz10, all_33_0_4) = xk, sdtlseqdt0(sz10, xk), aNaturalNumber0(all_33_0_4), aNaturalNumber0(xk), aNaturalNumber0(sz10), yields:
% 209.54/158.74 | (120) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xk) & ~ (v1 = v0) & sdtpldt0(all_33_0_4, xk) = v1 & sdtpldt0(all_33_0_4, sz10) = v0 & sdtpldt0(xk, all_33_0_4) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xk, v2))
% 209.54/158.74 |
% 209.54/158.74 | Instantiating formula (7) with xk, all_33_0_4, all_19_0_0, sz10 and discharging atoms sdtpldt0(sz10, all_33_0_4) = xk, sdtlseqdt0(sz10, all_19_0_0), aNaturalNumber0(all_33_0_4), aNaturalNumber0(all_19_0_0), aNaturalNumber0(sz10), yields:
% 209.54/158.74 | (121) all_19_0_0 = sz10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xk) & ~ (v1 = v0) & sdtpldt0(all_33_0_4, all_19_0_0) = v1 & sdtpldt0(all_33_0_4, sz10) = v0 & sdtpldt0(all_19_0_0, all_33_0_4) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xk, v2))
% 209.54/158.74 |
% 209.54/158.74 | Instantiating formula (57) with xk, all_33_0_4, sz10 and discharging atoms sdtpldt0(sz10, all_33_0_4) = xk, aNaturalNumber0(all_33_0_4), aNaturalNumber0(sz10), yields:
% 209.54/158.74 | (122) sdtpldt0(all_33_0_4, sz10) = xk
% 209.54/158.74 |
% 209.54/158.74 | Instantiating formula (7) with sz10, all_29_0_2, xk, sz10 and discharging atoms sdtpldt0(sz10, all_29_0_2) = sz10, sdtlseqdt0(sz10, xk), aNaturalNumber0(all_29_0_2), aNaturalNumber0(xk), aNaturalNumber0(sz10), yields:
% 209.54/158.74 | (123) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = sz10) & ~ (v1 = v0) & sdtpldt0(all_29_0_2, xk) = v1 & sdtpldt0(all_29_0_2, sz10) = v0 & sdtpldt0(xk, all_29_0_2) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(sz10, v2))
% 209.54/158.74 |
% 209.54/158.74 | Instantiating formula (7) with sz10, all_29_0_2, all_19_0_0, sz10 and discharging atoms sdtpldt0(sz10, all_29_0_2) = sz10, sdtlseqdt0(sz10, all_19_0_0), aNaturalNumber0(all_29_0_2), aNaturalNumber0(all_19_0_0), aNaturalNumber0(sz10), yields:
% 209.54/158.74 | (124) all_19_0_0 = sz10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = sz10) & ~ (v1 = v0) & sdtpldt0(all_29_0_2, all_19_0_0) = v1 & sdtpldt0(all_29_0_2, sz10) = v0 & sdtpldt0(all_19_0_0, all_29_0_2) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(sz10, v2))
% 209.54/158.74 |
% 209.54/158.74 | Instantiating formula (57) with sz10, all_29_0_2, sz10 and discharging atoms sdtpldt0(sz10, all_29_0_2) = sz10, aNaturalNumber0(all_29_0_2), aNaturalNumber0(sz10), yields:
% 209.54/158.74 | (125) sdtpldt0(all_29_0_2, sz10) = sz10
% 209.54/158.74 |
% 209.54/158.74 | Instantiating formula (10) with xk, sz10, all_33_0_4, all_29_0_2, sz10 and discharging atoms sdtpldt0(sz10, all_33_0_4) = xk, sdtpldt0(sz10, all_29_0_2) = sz10, aNaturalNumber0(all_33_0_4), aNaturalNumber0(all_29_0_2), aNaturalNumber0(sz10), yields:
% 209.54/158.74 | (126) ? [v0] : (sdtpldt0(all_29_0_2, all_33_0_4) = v0 & sdtpldt0(sz10, v0) = xk)
% 209.54/158.74 |
% 209.54/158.74 | Instantiating formula (10) with sz10, sz10, all_29_0_2, all_29_0_2, sz10 and discharging atoms sdtpldt0(sz10, all_29_0_2) = sz10, aNaturalNumber0(all_29_0_2), aNaturalNumber0(sz10), yields:
% 209.54/158.74 | (127) ? [v0] : (sdtpldt0(all_29_0_2, all_29_0_2) = v0 & sdtpldt0(sz10, v0) = sz10)
% 209.54/158.74 |
% 209.54/158.74 | Instantiating formula (29) with all_27_0_1 and discharging atoms aNaturalNumber0(all_27_0_1), yields:
% 209.54/158.74 | (128) all_27_0_1 = sz10 | all_27_0_1 = sz00 | sdtlseqdt0(sz10, all_27_0_1)
% 209.54/158.74 |
% 209.54/158.74 | Instantiating (118) with all_79_0_6 yields:
% 209.54/158.74 | (129) sdtpldt0(sz10, all_79_0_6) = all_19_0_0 & aNaturalNumber0(all_79_0_6)
% 209.54/158.74 |
% 209.54/158.74 | Applying alpha-rule on (129) yields:
% 209.54/158.74 | (130) sdtpldt0(sz10, all_79_0_6) = all_19_0_0
% 209.54/158.74 | (131) aNaturalNumber0(all_79_0_6)
% 209.54/158.74 |
% 209.54/158.74 | Instantiating (126) with all_81_0_7 yields:
% 209.54/158.74 | (132) sdtpldt0(all_29_0_2, all_33_0_4) = all_81_0_7 & sdtpldt0(sz10, all_81_0_7) = xk
% 209.54/158.74 |
% 209.54/158.74 | Applying alpha-rule on (132) yields:
% 209.54/158.74 | (133) sdtpldt0(all_29_0_2, all_33_0_4) = all_81_0_7
% 209.54/158.74 | (134) sdtpldt0(sz10, all_81_0_7) = xk
% 209.54/158.74 |
% 209.54/158.74 | Instantiating (127) with all_83_0_8 yields:
% 209.54/158.74 | (135) sdtpldt0(all_29_0_2, all_29_0_2) = all_83_0_8 & sdtpldt0(sz10, all_83_0_8) = sz10
% 209.54/158.74 |
% 209.54/158.74 | Applying alpha-rule on (135) yields:
% 209.54/158.74 | (136) sdtpldt0(all_29_0_2, all_29_0_2) = all_83_0_8
% 209.54/158.74 | (137) sdtpldt0(sz10, all_83_0_8) = sz10
% 209.54/158.74 |
% 209.54/158.74 | Instantiating (117) with all_85_0_9 yields:
% 209.54/158.74 | (138) sdtpldt0(all_19_0_0, all_85_0_9) = xk & aNaturalNumber0(all_85_0_9)
% 209.54/158.74 |
% 209.54/158.74 | Applying alpha-rule on (138) yields:
% 209.54/158.74 | (139) sdtpldt0(all_19_0_0, all_85_0_9) = xk
% 209.54/158.74 | (140) aNaturalNumber0(all_85_0_9)
% 209.54/158.74 |
% 209.54/158.74 | Instantiating (115) with all_87_0_10 yields:
% 209.54/158.74 | (141) sdtpldt0(all_19_0_0, all_87_0_10) = all_19_0_0 & aNaturalNumber0(all_87_0_10)
% 209.54/158.74 |
% 209.54/158.74 | Applying alpha-rule on (141) yields:
% 209.54/158.74 | (142) sdtpldt0(all_19_0_0, all_87_0_10) = all_19_0_0
% 209.54/158.74 | (143) aNaturalNumber0(all_87_0_10)
% 209.54/158.74 |
% 209.54/158.74 +-Applying beta-rule and splitting (116), into two cases.
% 209.54/158.74 |-Branch one:
% 209.54/158.74 | (144) iLess0(all_19_0_0, xk)
% 209.54/158.74 |
% 209.54/158.75 +-Applying beta-rule and splitting (121), into two cases.
% 209.54/158.75 |-Branch one:
% 209.54/158.75 | (145) all_19_0_0 = sz10
% 209.54/158.75 |
% 209.54/158.75 | Equations (145) can reduce 80 to:
% 209.54/158.75 | (71) $false
% 209.54/158.75 |
% 209.54/158.75 |-The branch is then unsatisfiable
% 209.54/158.75 |-Branch two:
% 209.54/158.75 | (80) ~ (all_19_0_0 = sz10)
% 209.54/158.75 | (148) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xk) & ~ (v1 = v0) & sdtpldt0(all_33_0_4, all_19_0_0) = v1 & sdtpldt0(all_33_0_4, sz10) = v0 & sdtpldt0(all_19_0_0, all_33_0_4) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xk, v2))
% 209.54/158.75 |
% 209.54/158.75 | Instantiating (148) with all_100_0_13, all_100_1_14, all_100_2_15 yields:
% 209.54/158.75 | (149) ~ (all_100_0_13 = xk) & ~ (all_100_1_14 = all_100_2_15) & sdtpldt0(all_33_0_4, all_19_0_0) = all_100_1_14 & sdtpldt0(all_33_0_4, sz10) = all_100_2_15 & sdtpldt0(all_19_0_0, all_33_0_4) = all_100_0_13 & sdtlseqdt0(all_100_2_15, all_100_1_14) & sdtlseqdt0(xk, all_100_0_13)
% 209.54/158.75 |
% 209.54/158.75 | Applying alpha-rule on (149) yields:
% 209.54/158.75 | (150) sdtlseqdt0(xk, all_100_0_13)
% 209.54/158.75 | (151) sdtpldt0(all_33_0_4, all_19_0_0) = all_100_1_14
% 209.54/158.75 | (152) ~ (all_100_0_13 = xk)
% 209.54/158.75 | (153) ~ (all_100_1_14 = all_100_2_15)
% 209.54/158.75 | (154) sdtpldt0(all_33_0_4, sz10) = all_100_2_15
% 209.54/158.75 | (155) sdtlseqdt0(all_100_2_15, all_100_1_14)
% 209.54/158.75 | (156) sdtpldt0(all_19_0_0, all_33_0_4) = all_100_0_13
% 209.54/158.75 |
% 209.54/158.75 +-Applying beta-rule and splitting (120), into two cases.
% 209.54/158.75 |-Branch one:
% 209.54/158.75 | (74) xk = sz10
% 209.54/158.75 |
% 209.54/158.75 | Equations (74) can reduce 32 to:
% 209.54/158.75 | (71) $false
% 209.54/158.75 |
% 209.54/158.75 |-The branch is then unsatisfiable
% 209.54/158.75 |-Branch two:
% 209.54/158.75 | (32) ~ (xk = sz10)
% 209.54/158.75 | (160) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xk) & ~ (v1 = v0) & sdtpldt0(all_33_0_4, xk) = v1 & sdtpldt0(all_33_0_4, sz10) = v0 & sdtpldt0(xk, all_33_0_4) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xk, v2))
% 209.54/158.75 |
% 209.54/158.75 | Instantiating (160) with all_113_0_16, all_113_1_17, all_113_2_18 yields:
% 209.54/158.75 | (161) ~ (all_113_0_16 = xk) & ~ (all_113_1_17 = all_113_2_18) & sdtpldt0(all_33_0_4, xk) = all_113_1_17 & sdtpldt0(all_33_0_4, sz10) = all_113_2_18 & sdtpldt0(xk, all_33_0_4) = all_113_0_16 & sdtlseqdt0(all_113_2_18, all_113_1_17) & sdtlseqdt0(xk, all_113_0_16)
% 209.54/158.75 |
% 209.54/158.75 | Applying alpha-rule on (161) yields:
% 209.54/158.75 | (162) sdtpldt0(all_33_0_4, sz10) = all_113_2_18
% 209.54/158.75 | (163) sdtpldt0(xk, all_33_0_4) = all_113_0_16
% 209.54/158.75 | (164) ~ (all_113_1_17 = all_113_2_18)
% 209.54/158.75 | (165) sdtpldt0(all_33_0_4, xk) = all_113_1_17
% 209.54/158.75 | (166) sdtlseqdt0(all_113_2_18, all_113_1_17)
% 209.54/158.75 | (167) ~ (all_113_0_16 = xk)
% 209.54/158.75 | (168) sdtlseqdt0(xk, all_113_0_16)
% 209.54/158.75 |
% 209.54/158.75 +-Applying beta-rule and splitting (123), into two cases.
% 209.54/158.75 |-Branch one:
% 209.54/158.75 | (74) xk = sz10
% 209.54/158.75 |
% 209.54/158.75 | Equations (74) can reduce 32 to:
% 209.54/158.75 | (71) $false
% 209.54/158.75 |
% 209.54/158.75 |-The branch is then unsatisfiable
% 209.54/158.75 |-Branch two:
% 209.54/158.75 | (32) ~ (xk = sz10)
% 209.54/158.75 | (172) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = sz10) & ~ (v1 = v0) & sdtpldt0(all_29_0_2, xk) = v1 & sdtpldt0(all_29_0_2, sz10) = v0 & sdtpldt0(xk, all_29_0_2) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(sz10, v2))
% 209.54/158.75 |
% 209.54/158.75 | Instantiating (172) with all_119_0_19, all_119_1_20, all_119_2_21 yields:
% 209.54/158.75 | (173) ~ (all_119_0_19 = sz10) & ~ (all_119_1_20 = all_119_2_21) & sdtpldt0(all_29_0_2, xk) = all_119_1_20 & sdtpldt0(all_29_0_2, sz10) = all_119_2_21 & sdtpldt0(xk, all_29_0_2) = all_119_0_19 & sdtlseqdt0(all_119_2_21, all_119_1_20) & sdtlseqdt0(sz10, all_119_0_19)
% 209.54/158.75 |
% 209.54/158.75 | Applying alpha-rule on (173) yields:
% 209.54/158.75 | (174) sdtlseqdt0(all_119_2_21, all_119_1_20)
% 209.54/158.75 | (175) ~ (all_119_0_19 = sz10)
% 209.54/158.75 | (176) sdtpldt0(all_29_0_2, xk) = all_119_1_20
% 209.54/158.75 | (177) sdtlseqdt0(sz10, all_119_0_19)
% 209.54/158.75 | (178) sdtpldt0(all_29_0_2, sz10) = all_119_2_21
% 209.54/158.75 | (179) sdtpldt0(xk, all_29_0_2) = all_119_0_19
% 209.54/158.75 | (180) ~ (all_119_1_20 = all_119_2_21)
% 209.54/158.75 |
% 209.54/158.75 +-Applying beta-rule and splitting (124), into two cases.
% 209.54/158.75 |-Branch one:
% 209.54/158.75 | (145) all_19_0_0 = sz10
% 209.54/158.75 |
% 209.54/158.75 | Equations (145) can reduce 80 to:
% 209.54/158.75 | (71) $false
% 209.54/158.75 |
% 209.54/158.75 |-The branch is then unsatisfiable
% 209.54/158.75 |-Branch two:
% 209.54/158.75 | (80) ~ (all_19_0_0 = sz10)
% 209.54/158.75 | (184) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = sz10) & ~ (v1 = v0) & sdtpldt0(all_29_0_2, all_19_0_0) = v1 & sdtpldt0(all_29_0_2, sz10) = v0 & sdtpldt0(all_19_0_0, all_29_0_2) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(sz10, v2))
% 209.54/158.75 |
% 209.54/158.75 | Instantiating (184) with all_124_0_22, all_124_1_23, all_124_2_24 yields:
% 209.54/158.75 | (185) ~ (all_124_0_22 = sz10) & ~ (all_124_1_23 = all_124_2_24) & sdtpldt0(all_29_0_2, all_19_0_0) = all_124_1_23 & sdtpldt0(all_29_0_2, sz10) = all_124_2_24 & sdtpldt0(all_19_0_0, all_29_0_2) = all_124_0_22 & sdtlseqdt0(all_124_2_24, all_124_1_23) & sdtlseqdt0(sz10, all_124_0_22)
% 209.54/158.75 |
% 209.54/158.75 | Applying alpha-rule on (185) yields:
% 209.54/158.75 | (186) sdtpldt0(all_29_0_2, sz10) = all_124_2_24
% 209.54/158.75 | (187) sdtpldt0(all_19_0_0, all_29_0_2) = all_124_0_22
% 209.54/158.75 | (188) ~ (all_124_0_22 = sz10)
% 209.54/158.75 | (189) sdtpldt0(all_29_0_2, all_19_0_0) = all_124_1_23
% 209.54/158.75 | (190) ~ (all_124_1_23 = all_124_2_24)
% 209.54/158.76 | (191) sdtlseqdt0(all_124_2_24, all_124_1_23)
% 209.54/158.76 | (192) sdtlseqdt0(sz10, all_124_0_22)
% 209.54/158.76 |
% 209.54/158.76 | Instantiating formula (49) with xk, all_19_0_0 and discharging atoms aNaturalNumber0(all_19_0_0), yields:
% 209.54/158.76 | (193) all_19_0_0 = xk | ~ (sdtasdt0(sz10, all_19_0_0) = xk)
% 209.54/158.76 |
% 209.54/158.76 | Instantiating formula (48) with xk, all_19_0_0 and discharging atoms aNaturalNumber0(all_19_0_0), yields:
% 209.54/158.76 | (194) xk = sz00 | ~ (sdtasdt0(sz00, all_19_0_0) = xk)
% 209.54/158.76 |
% 209.54/158.76 | Instantiating formula (53) with all_33_0_4, sz10, all_100_2_15, all_113_2_18 and discharging atoms sdtpldt0(all_33_0_4, sz10) = all_113_2_18, sdtpldt0(all_33_0_4, sz10) = all_100_2_15, yields:
% 209.54/158.76 | (195) all_113_2_18 = all_100_2_15
% 209.54/158.76 |
% 209.54/158.76 | Instantiating formula (53) with all_33_0_4, sz10, xk, all_113_2_18 and discharging atoms sdtpldt0(all_33_0_4, sz10) = all_113_2_18, sdtpldt0(all_33_0_4, sz10) = xk, yields:
% 209.54/158.76 | (196) all_113_2_18 = xk
% 209.54/158.76 |
% 209.54/158.76 | Instantiating formula (53) with all_29_0_2, xk, all_119_1_20, xk and discharging atoms sdtpldt0(all_29_0_2, xk) = all_119_1_20, yields:
% 209.54/158.76 | (197) all_119_1_20 = xk | ~ (sdtpldt0(all_29_0_2, xk) = xk)
% 209.54/158.76 |
% 209.54/158.76 | Instantiating formula (53) with all_29_0_2, sz10, all_119_2_21, all_124_2_24 and discharging atoms sdtpldt0(all_29_0_2, sz10) = all_124_2_24, sdtpldt0(all_29_0_2, sz10) = all_119_2_21, yields:
% 209.54/158.76 | (198) all_124_2_24 = all_119_2_21
% 209.54/158.76 |
% 209.54/158.76 | Instantiating formula (53) with all_29_0_2, sz10, sz10, all_124_2_24 and discharging atoms sdtpldt0(all_29_0_2, sz10) = all_124_2_24, sdtpldt0(all_29_0_2, sz10) = sz10, yields:
% 209.54/158.76 | (199) all_124_2_24 = sz10
% 209.54/158.76 |
% 209.54/158.76 | Instantiating formula (20) with xk, all_33_0_4, all_81_0_7, sz10 and discharging atoms sdtpldt0(sz10, all_81_0_7) = xk, sdtpldt0(sz10, all_33_0_4) = xk, aNaturalNumber0(all_33_0_4), aNaturalNumber0(sz10), yields:
% 209.54/158.76 | (200) all_81_0_7 = all_33_0_4 | ~ aNaturalNumber0(all_81_0_7)
% 209.54/158.76 |
% 209.54/158.76 | Instantiating formula (20) with sz10, all_29_0_2, all_83_0_8, sz10 and discharging atoms sdtpldt0(sz10, all_83_0_8) = sz10, sdtpldt0(sz10, all_29_0_2) = sz10, aNaturalNumber0(all_29_0_2), aNaturalNumber0(sz10), yields:
% 209.54/158.76 | (201) all_83_0_8 = all_29_0_2 | ~ aNaturalNumber0(all_83_0_8)
% 209.54/158.76 |
% 209.54/158.76 | Combining equations (198,199) yields a new equation:
% 209.54/158.76 | (202) all_119_2_21 = sz10
% 209.54/158.76 |
% 209.54/158.76 | Simplifying 202 yields:
% 209.54/158.76 | (203) all_119_2_21 = sz10
% 209.54/158.76 |
% 209.54/158.76 | Combining equations (195,196) yields a new equation:
% 209.54/158.76 | (204) all_100_2_15 = xk
% 209.54/158.76 |
% 209.54/158.76 | Simplifying 204 yields:
% 209.54/158.76 | (205) all_100_2_15 = xk
% 209.54/158.76 |
% 209.54/158.76 | From (205) and (154) follows:
% 209.54/158.76 | (122) sdtpldt0(all_33_0_4, sz10) = xk
% 209.54/158.76 |
% 209.54/158.76 | From (203) and (178) follows:
% 209.54/158.76 | (125) sdtpldt0(all_29_0_2, sz10) = sz10
% 209.54/158.76 |
% 209.54/158.76 +-Applying beta-rule and splitting (194), into two cases.
% 209.54/158.76 |-Branch one:
% 209.54/158.76 | (208) ~ (sdtasdt0(sz00, all_19_0_0) = xk)
% 209.54/158.76 |
% 209.54/158.76 +-Applying beta-rule and splitting (114), into two cases.
% 209.54/158.76 |-Branch one:
% 209.54/158.76 | (209) ~ (sdtasdt0(all_19_0_0, sz00) = xk)
% 209.54/158.76 |
% 209.54/158.76 +-Applying beta-rule and splitting (193), into two cases.
% 209.54/158.76 |-Branch one:
% 209.54/158.76 | (210) ~ (sdtasdt0(sz10, all_19_0_0) = xk)
% 209.54/158.76 |
% 209.54/158.76 +-Applying beta-rule and splitting (113), into two cases.
% 209.54/158.76 |-Branch one:
% 209.54/158.76 | (211) ~ (sdtasdt0(all_19_0_0, sz10) = xk)
% 209.54/158.76 |
% 209.54/158.76 | Using (92) and (211) yields:
% 209.54/158.76 | (212) ~ (all_27_0_1 = sz10)
% 209.54/158.76 |
% 209.54/158.76 | Using (92) and (209) yields:
% 209.54/158.76 | (213) ~ (all_27_0_1 = sz00)
% 209.54/158.76 |
% 209.54/158.76 +-Applying beta-rule and splitting (128), into two cases.
% 209.54/158.76 |-Branch one:
% 209.54/158.76 | (214) sdtlseqdt0(sz10, all_27_0_1)
% 209.54/158.76 |
% 209.54/158.76 | Instantiating formula (4) with all_113_1_17, all_100_1_14, xk, all_19_0_0, all_33_0_4 and discharging atoms sdtpldt0(all_33_0_4, all_19_0_0) = all_100_1_14, sdtpldt0(all_33_0_4, xk) = all_113_1_17, aNaturalNumber0(all_33_0_4), aNaturalNumber0(all_19_0_0), aNaturalNumber0(xk), yields:
% 209.54/158.76 | (215) all_19_0_0 = xk | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_19_0_0, all_33_0_4) = v0 & sdtpldt0(xk, all_33_0_4) = v1)
% 209.54/158.76 |
% 209.54/158.76 | Instantiating formula (4) with all_100_1_14, all_113_1_17, all_19_0_0, xk, all_33_0_4 and discharging atoms sdtpldt0(all_33_0_4, all_19_0_0) = all_100_1_14, sdtpldt0(all_33_0_4, xk) = all_113_1_17, aNaturalNumber0(all_33_0_4), aNaturalNumber0(all_19_0_0), aNaturalNumber0(xk), yields:
% 209.54/158.76 | (216) all_19_0_0 = xk | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_19_0_0, all_33_0_4) = v1 & sdtpldt0(xk, all_33_0_4) = v0)
% 209.54/158.76 |
% 209.54/158.76 | Instantiating formula (37) with xk, xk, all_29_0_2 and discharging atoms aNaturalNumber0(all_29_0_2), aNaturalNumber0(xk), yields:
% 209.54/158.76 | (217) ~ (sdtpldt0(all_29_0_2, xk) = xk) | sdtlseqdt0(all_29_0_2, xk)
% 209.54/158.76 |
% 209.54/158.76 | Instantiating formula (51) with all_81_0_7, all_33_0_4, all_29_0_2 and discharging atoms sdtpldt0(all_29_0_2, all_33_0_4) = all_81_0_7, aNaturalNumber0(all_33_0_4), aNaturalNumber0(all_29_0_2), yields:
% 209.54/158.76 | (218) aNaturalNumber0(all_81_0_7)
% 209.54/158.76 |
% 209.54/158.76 | Instantiating formula (51) with all_83_0_8, all_29_0_2, all_29_0_2 and discharging atoms sdtpldt0(all_29_0_2, all_29_0_2) = all_83_0_8, aNaturalNumber0(all_29_0_2), yields:
% 209.54/158.77 | (219) aNaturalNumber0(all_83_0_8)
% 209.54/158.77 |
% 209.54/158.77 | Instantiating formula (10) with all_124_1_23, all_29_0_2, all_19_0_0, all_29_0_2, all_29_0_2 and discharging atoms sdtpldt0(all_29_0_2, all_19_0_0) = all_124_1_23, aNaturalNumber0(all_29_0_2), aNaturalNumber0(all_19_0_0), yields:
% 209.54/158.77 | (220) ~ (sdtpldt0(all_29_0_2, all_29_0_2) = all_29_0_2) | ? [v0] : (sdtpldt0(all_29_0_2, v0) = all_124_1_23 & sdtpldt0(all_29_0_2, all_19_0_0) = v0)
% 209.54/158.77 |
% 209.54/158.77 | Instantiating formula (4) with all_119_1_20, all_124_1_23, xk, all_19_0_0, all_29_0_2 and discharging atoms sdtpldt0(all_29_0_2, all_19_0_0) = all_124_1_23, sdtpldt0(all_29_0_2, xk) = all_119_1_20, aNaturalNumber0(all_29_0_2), aNaturalNumber0(all_19_0_0), aNaturalNumber0(xk), yields:
% 209.54/158.77 | (221) all_19_0_0 = xk | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_19_0_0, all_29_0_2) = v0 & sdtpldt0(xk, all_29_0_2) = v1)
% 209.54/158.77 |
% 209.54/158.77 | Instantiating formula (57) with all_119_1_20, xk, all_29_0_2 and discharging atoms sdtpldt0(all_29_0_2, xk) = all_119_1_20, aNaturalNumber0(all_29_0_2), aNaturalNumber0(xk), yields:
% 209.54/158.77 | (222) sdtpldt0(xk, all_29_0_2) = all_119_1_20
% 209.54/158.77 |
% 209.54/158.77 | Instantiating formula (10) with xk, sz10, all_33_0_4, sz10, all_29_0_2 and discharging atoms sdtpldt0(all_29_0_2, sz10) = sz10, sdtpldt0(sz10, all_33_0_4) = xk, aNaturalNumber0(all_33_0_4), aNaturalNumber0(all_29_0_2), aNaturalNumber0(sz10), yields:
% 209.54/158.77 | (223) ? [v0] : (sdtpldt0(all_29_0_2, v0) = xk & sdtpldt0(sz10, all_33_0_4) = v0)
% 209.54/158.77 |
% 209.54/158.77 | Instantiating formula (7) with all_100_0_13, all_33_0_4, xk, all_19_0_0 and discharging atoms sdtpldt0(all_19_0_0, all_33_0_4) = all_100_0_13, sdtlseqdt0(all_19_0_0, xk), aNaturalNumber0(all_33_0_4), aNaturalNumber0(all_19_0_0), aNaturalNumber0(xk), yields:
% 209.54/158.77 | (224) all_19_0_0 = xk | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_100_0_13) & ~ (v1 = v0) & sdtpldt0(all_33_0_4, all_19_0_0) = v0 & sdtpldt0(all_33_0_4, xk) = v1 & sdtpldt0(xk, all_33_0_4) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_100_0_13, v2))
% 209.54/158.77 |
% 209.54/158.77 | Instantiating formula (7) with all_124_0_22, all_29_0_2, xk, all_19_0_0 and discharging atoms sdtpldt0(all_19_0_0, all_29_0_2) = all_124_0_22, sdtlseqdt0(all_19_0_0, xk), aNaturalNumber0(all_29_0_2), aNaturalNumber0(all_19_0_0), aNaturalNumber0(xk), yields:
% 209.54/158.77 | (225) all_19_0_0 = xk | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_124_0_22) & ~ (v1 = v0) & sdtpldt0(all_29_0_2, all_19_0_0) = v0 & sdtpldt0(all_29_0_2, xk) = v1 & sdtpldt0(xk, all_29_0_2) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_124_0_22, v2))
% 209.54/158.77 |
% 209.54/158.77 | Instantiating formula (57) with all_124_0_22, all_29_0_2, all_19_0_0 and discharging atoms sdtpldt0(all_19_0_0, all_29_0_2) = all_124_0_22, aNaturalNumber0(all_29_0_2), aNaturalNumber0(all_19_0_0), yields:
% 209.54/158.77 | (226) sdtpldt0(all_29_0_2, all_19_0_0) = all_124_0_22
% 209.54/158.77 |
% 209.54/158.77 | Instantiating formula (51) with all_124_0_22, all_29_0_2, all_19_0_0 and discharging atoms sdtpldt0(all_19_0_0, all_29_0_2) = all_124_0_22, aNaturalNumber0(all_29_0_2), aNaturalNumber0(all_19_0_0), yields:
% 209.54/158.77 | (227) aNaturalNumber0(all_124_0_22)
% 209.54/158.77 |
% 209.54/158.77 | Instantiating formula (10) with all_113_0_16, xk, all_33_0_4, sz10, all_33_0_4 and discharging atoms sdtpldt0(all_33_0_4, sz10) = xk, sdtpldt0(xk, all_33_0_4) = all_113_0_16, aNaturalNumber0(all_33_0_4), aNaturalNumber0(sz10), yields:
% 209.54/158.77 | (228) ? [v0] : (sdtpldt0(all_33_0_4, v0) = all_113_0_16 & sdtpldt0(sz10, all_33_0_4) = v0)
% 209.54/158.77 |
% 209.54/158.77 | Instantiating formula (10) with all_119_0_19, xk, all_29_0_2, xk, all_31_0_3 and discharging atoms sdtpldt0(all_31_0_3, xk) = xk, sdtpldt0(xk, all_29_0_2) = all_119_0_19, aNaturalNumber0(all_31_0_3), aNaturalNumber0(all_29_0_2), aNaturalNumber0(xk), yields:
% 209.54/158.77 | (229) ? [v0] : (sdtpldt0(all_31_0_3, v0) = all_119_0_19 & sdtpldt0(xk, all_29_0_2) = v0)
% 209.93/158.77 |
% 209.93/158.77 | Instantiating formula (10) with all_119_0_19, xk, all_29_0_2, xk, all_29_0_2 and discharging atoms sdtpldt0(xk, all_29_0_2) = all_119_0_19, aNaturalNumber0(all_29_0_2), aNaturalNumber0(xk), yields:
% 209.93/158.77 | (230) ~ (sdtpldt0(all_29_0_2, xk) = xk) | ? [v0] : (sdtpldt0(all_29_0_2, v0) = all_119_0_19 & sdtpldt0(xk, all_29_0_2) = v0)
% 209.93/158.77 |
% 209.93/158.77 | Instantiating formula (51) with all_119_0_19, all_29_0_2, xk and discharging atoms sdtpldt0(xk, all_29_0_2) = all_119_0_19, aNaturalNumber0(all_29_0_2), aNaturalNumber0(xk), yields:
% 209.93/158.77 | (231) aNaturalNumber0(all_119_0_19)
% 209.93/158.77 |
% 209.93/158.77 | Instantiating formula (45) with all_19_0_0 and discharging atoms iLess0(all_19_0_0, xk), aNaturalNumber0(all_19_0_0), yields:
% 209.93/158.77 | (232) all_19_0_0 = sz10 | all_19_0_0 = sz00 | ? [v0] : (isPrime0(v0) & doDivides0(v0, all_19_0_0) & aNaturalNumber0(v0))
% 209.93/158.77 |
% 209.93/158.77 | Instantiating formula (7) with all_19_0_0, all_87_0_10, xk, all_19_0_0 and discharging atoms sdtpldt0(all_19_0_0, all_87_0_10) = all_19_0_0, sdtlseqdt0(all_19_0_0, xk), aNaturalNumber0(all_87_0_10), aNaturalNumber0(all_19_0_0), aNaturalNumber0(xk), yields:
% 209.93/158.77 | (233) all_19_0_0 = xk | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_19_0_0) & ~ (v1 = v0) & sdtpldt0(all_87_0_10, all_19_0_0) = v0 & sdtpldt0(all_87_0_10, xk) = v1 & sdtpldt0(xk, all_87_0_10) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_19_0_0, v2))
% 209.93/158.77 |
% 209.93/158.77 | Instantiating formula (7) with xk, all_85_0_9, xk, all_19_0_0 and discharging atoms sdtpldt0(all_19_0_0, all_85_0_9) = xk, sdtlseqdt0(all_19_0_0, xk), aNaturalNumber0(all_85_0_9), aNaturalNumber0(all_19_0_0), aNaturalNumber0(xk), yields:
% 209.93/158.77 | (234) all_19_0_0 = xk | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xk) & ~ (v1 = v0) & sdtpldt0(all_85_0_9, all_19_0_0) = v0 & sdtpldt0(all_85_0_9, xk) = v1 & sdtpldt0(xk, all_85_0_9) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xk, v2))
% 209.93/158.77 |
% 209.93/158.77 | Instantiating formula (7) with sz10, all_83_0_8, all_19_0_0, sz10 and discharging atoms sdtpldt0(sz10, all_83_0_8) = sz10, sdtlseqdt0(sz10, all_19_0_0), aNaturalNumber0(all_19_0_0), aNaturalNumber0(sz10), yields:
% 209.93/158.78 | (235) all_19_0_0 = sz10 | ~ aNaturalNumber0(all_83_0_8) | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = sz10) & ~ (v1 = v0) & sdtpldt0(all_83_0_8, all_19_0_0) = v1 & sdtpldt0(all_83_0_8, sz10) = v0 & sdtpldt0(all_19_0_0, all_83_0_8) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(sz10, v2))
% 209.93/158.78 |
% 209.93/158.78 | Instantiating formula (7) with sz10, all_83_0_8, xk, sz10 and discharging atoms sdtpldt0(sz10, all_83_0_8) = sz10, sdtlseqdt0(sz10, xk), aNaturalNumber0(xk), aNaturalNumber0(sz10), yields:
% 209.93/158.78 | (236) xk = sz10 | ~ aNaturalNumber0(all_83_0_8) | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = sz10) & ~ (v1 = v0) & sdtpldt0(all_83_0_8, xk) = v1 & sdtpldt0(all_83_0_8, sz10) = v0 & sdtpldt0(xk, all_83_0_8) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(sz10, v2))
% 209.93/158.78 |
% 209.93/158.78 | Instantiating formula (7) with sz10, all_83_0_8, all_27_0_1, sz10 and discharging atoms sdtpldt0(sz10, all_83_0_8) = sz10, sdtlseqdt0(sz10, all_27_0_1), aNaturalNumber0(all_27_0_1), aNaturalNumber0(sz10), yields:
% 209.93/158.78 | (237) all_27_0_1 = sz10 | ~ aNaturalNumber0(all_83_0_8) | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = sz10) & ~ (v1 = v0) & sdtpldt0(all_83_0_8, all_27_0_1) = v1 & sdtpldt0(all_83_0_8, sz10) = v0 & sdtpldt0(all_27_0_1, all_83_0_8) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(sz10, v2))
% 209.93/158.78 |
% 209.93/158.78 | Instantiating formula (57) with sz10, all_83_0_8, sz10 and discharging atoms sdtpldt0(sz10, all_83_0_8) = sz10, aNaturalNumber0(sz10), yields:
% 209.93/158.78 | (238) ~ aNaturalNumber0(all_83_0_8) | sdtpldt0(all_83_0_8, sz10) = sz10
% 209.93/158.78 |
% 209.93/158.78 | Instantiating formula (10) with xk, sz10, all_81_0_7, sz10, all_29_0_2 and discharging atoms sdtpldt0(all_29_0_2, sz10) = sz10, sdtpldt0(sz10, all_81_0_7) = xk, aNaturalNumber0(all_29_0_2), aNaturalNumber0(sz10), yields:
% 209.93/158.78 | (239) ~ aNaturalNumber0(all_81_0_7) | ? [v0] : (sdtpldt0(all_29_0_2, v0) = xk & sdtpldt0(sz10, all_81_0_7) = v0)
% 209.97/158.78 |
% 209.97/158.78 | Instantiating formula (7) with xk, all_81_0_7, all_19_0_0, sz10 and discharging atoms sdtpldt0(sz10, all_81_0_7) = xk, sdtlseqdt0(sz10, all_19_0_0), aNaturalNumber0(all_19_0_0), aNaturalNumber0(sz10), yields:
% 209.97/158.78 | (240) all_19_0_0 = sz10 | ~ aNaturalNumber0(all_81_0_7) | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xk) & ~ (v1 = v0) & sdtpldt0(all_81_0_7, all_19_0_0) = v1 & sdtpldt0(all_81_0_7, sz10) = v0 & sdtpldt0(all_19_0_0, all_81_0_7) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xk, v2))
% 209.97/158.78 |
% 209.97/158.78 | Instantiating formula (7) with xk, all_81_0_7, xk, sz10 and discharging atoms sdtpldt0(sz10, all_81_0_7) = xk, sdtlseqdt0(sz10, xk), aNaturalNumber0(xk), aNaturalNumber0(sz10), yields:
% 209.97/158.78 | (241) xk = sz10 | ~ aNaturalNumber0(all_81_0_7) | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xk) & ~ (v1 = v0) & sdtpldt0(all_81_0_7, xk) = v1 & sdtpldt0(all_81_0_7, sz10) = v0 & sdtpldt0(xk, all_81_0_7) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xk, v2))
% 209.97/158.78 |
% 209.97/158.78 | Instantiating formula (7) with xk, all_81_0_7, all_27_0_1, sz10 and discharging atoms sdtpldt0(sz10, all_81_0_7) = xk, sdtlseqdt0(sz10, all_27_0_1), aNaturalNumber0(all_27_0_1), aNaturalNumber0(sz10), yields:
% 209.97/158.78 | (242) all_27_0_1 = sz10 | ~ aNaturalNumber0(all_81_0_7) | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xk) & ~ (v1 = v0) & sdtpldt0(all_81_0_7, all_27_0_1) = v1 & sdtpldt0(all_81_0_7, sz10) = v0 & sdtpldt0(all_27_0_1, all_81_0_7) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xk, v2))
% 209.97/158.78 |
% 209.97/158.78 | Instantiating formula (7) with all_19_0_0, all_79_0_6, all_19_0_0, sz10 and discharging atoms sdtpldt0(sz10, all_79_0_6) = all_19_0_0, sdtlseqdt0(sz10, all_19_0_0), aNaturalNumber0(all_79_0_6), aNaturalNumber0(all_19_0_0), aNaturalNumber0(sz10), yields:
% 209.97/158.78 | (243) all_19_0_0 = sz10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_19_0_0) & ~ (v1 = v0) & sdtpldt0(all_79_0_6, all_19_0_0) = v1 & sdtpldt0(all_79_0_6, sz10) = v0 & sdtpldt0(all_19_0_0, all_79_0_6) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_19_0_0, v2))
% 209.97/158.78 |
% 209.97/158.78 | Instantiating (223) with all_236_0_31 yields:
% 209.97/158.78 | (244) sdtpldt0(all_29_0_2, all_236_0_31) = xk & sdtpldt0(sz10, all_33_0_4) = all_236_0_31
% 209.97/158.78 |
% 209.97/158.78 | Applying alpha-rule on (244) yields:
% 209.97/158.78 | (245) sdtpldt0(all_29_0_2, all_236_0_31) = xk
% 209.97/158.78 | (246) sdtpldt0(sz10, all_33_0_4) = all_236_0_31
% 209.97/158.78 |
% 209.97/158.78 | Instantiating (228) with all_242_0_34 yields:
% 209.97/158.78 | (247) sdtpldt0(all_33_0_4, all_242_0_34) = all_113_0_16 & sdtpldt0(sz10, all_33_0_4) = all_242_0_34
% 209.97/158.78 |
% 209.97/158.78 | Applying alpha-rule on (247) yields:
% 209.97/158.78 | (248) sdtpldt0(all_33_0_4, all_242_0_34) = all_113_0_16
% 209.97/158.78 | (249) sdtpldt0(sz10, all_33_0_4) = all_242_0_34
% 209.97/158.78 |
% 209.97/158.78 | Instantiating (229) with all_256_0_41 yields:
% 209.97/158.78 | (250) sdtpldt0(all_31_0_3, all_256_0_41) = all_119_0_19 & sdtpldt0(xk, all_29_0_2) = all_256_0_41
% 209.97/158.78 |
% 209.97/158.78 | Applying alpha-rule on (250) yields:
% 209.97/158.78 | (251) sdtpldt0(all_31_0_3, all_256_0_41) = all_119_0_19
% 209.97/158.78 | (252) sdtpldt0(xk, all_29_0_2) = all_256_0_41
% 209.97/158.78 |
% 209.97/158.78 +-Applying beta-rule and splitting (200), into two cases.
% 209.97/158.78 |-Branch one:
% 209.97/158.78 | (253) ~ aNaturalNumber0(all_81_0_7)
% 209.97/158.78 |
% 209.97/158.78 | Using (218) and (253) yields:
% 209.97/158.78 | (254) $false
% 209.97/158.78 |
% 209.97/158.78 |-The branch is then unsatisfiable
% 209.97/158.78 |-Branch two:
% 209.97/158.79 | (218) aNaturalNumber0(all_81_0_7)
% 209.97/158.79 | (256) all_81_0_7 = all_33_0_4
% 209.97/158.79 |
% 209.97/158.79 | From (256) and (134) follows:
% 209.97/158.79 | (101) sdtpldt0(sz10, all_33_0_4) = xk
% 209.97/158.79 |
% 209.97/158.79 | From (256) and (218) follows:
% 209.97/158.79 | (102) aNaturalNumber0(all_33_0_4)
% 209.97/158.79 |
% 209.97/158.79 +-Applying beta-rule and splitting (238), into two cases.
% 209.97/158.79 |-Branch one:
% 209.97/158.79 | (259) ~ aNaturalNumber0(all_83_0_8)
% 209.97/158.79 |
% 209.97/158.79 | Using (219) and (259) yields:
% 209.97/158.79 | (254) $false
% 209.97/158.79 |
% 209.97/158.79 |-The branch is then unsatisfiable
% 209.97/158.79 |-Branch two:
% 209.97/158.79 | (219) aNaturalNumber0(all_83_0_8)
% 209.97/158.79 | (262) sdtpldt0(all_83_0_8, sz10) = sz10
% 209.97/158.79 |
% 209.97/158.79 +-Applying beta-rule and splitting (201), into two cases.
% 209.97/158.79 |-Branch one:
% 209.97/158.79 | (259) ~ aNaturalNumber0(all_83_0_8)
% 209.97/158.79 |
% 209.97/158.79 | Using (219) and (259) yields:
% 209.97/158.79 | (254) $false
% 209.97/158.79 |
% 209.97/158.79 |-The branch is then unsatisfiable
% 209.97/158.79 |-Branch two:
% 209.97/158.79 | (219) aNaturalNumber0(all_83_0_8)
% 209.97/158.79 | (266) all_83_0_8 = all_29_0_2
% 209.97/158.79 |
% 209.97/158.79 | From (266) and (136) follows:
% 209.97/158.79 | (267) sdtpldt0(all_29_0_2, all_29_0_2) = all_29_0_2
% 209.97/158.79 |
% 209.97/158.79 | From (266) and (219) follows:
% 209.97/158.79 | (96) aNaturalNumber0(all_29_0_2)
% 209.97/158.79 |
% 209.97/158.79 +-Applying beta-rule and splitting (239), into two cases.
% 209.97/158.79 |-Branch one:
% 209.97/158.79 | (253) ~ aNaturalNumber0(all_81_0_7)
% 209.97/158.79 |
% 209.97/158.79 | From (256) and (253) follows:
% 209.97/158.79 | (270) ~ aNaturalNumber0(all_33_0_4)
% 209.97/158.79 |
% 209.97/158.79 | Using (102) and (270) yields:
% 209.97/158.79 | (254) $false
% 209.97/158.79 |
% 209.97/158.79 |-The branch is then unsatisfiable
% 209.97/158.79 |-Branch two:
% 209.97/158.79 | (218) aNaturalNumber0(all_81_0_7)
% 209.97/158.79 | (273) ? [v0] : (sdtpldt0(all_29_0_2, v0) = xk & sdtpldt0(sz10, all_81_0_7) = v0)
% 209.97/158.79 |
% 209.97/158.79 | Instantiating (273) with all_306_0_54 yields:
% 209.97/158.79 | (274) sdtpldt0(all_29_0_2, all_306_0_54) = xk & sdtpldt0(sz10, all_81_0_7) = all_306_0_54
% 209.97/158.79 |
% 209.97/158.79 | Applying alpha-rule on (274) yields:
% 209.97/158.79 | (275) sdtpldt0(all_29_0_2, all_306_0_54) = xk
% 209.97/158.79 | (276) sdtpldt0(sz10, all_81_0_7) = all_306_0_54
% 209.97/158.79 |
% 209.97/158.79 | From (256) and (276) follows:
% 209.97/158.79 | (277) sdtpldt0(sz10, all_33_0_4) = all_306_0_54
% 209.97/158.79 |
% 209.97/158.79 | From (256) and (218) follows:
% 209.97/158.79 | (102) aNaturalNumber0(all_33_0_4)
% 209.97/158.79 |
% 209.97/158.79 +-Applying beta-rule and splitting (242), into two cases.
% 209.97/158.79 |-Branch one:
% 209.97/158.79 | (253) ~ aNaturalNumber0(all_81_0_7)
% 209.97/158.79 |
% 209.97/158.79 | From (256) and (253) follows:
% 209.97/158.79 | (270) ~ aNaturalNumber0(all_33_0_4)
% 209.97/158.79 |
% 209.97/158.79 | Using (102) and (270) yields:
% 209.97/158.79 | (254) $false
% 209.97/158.79 |
% 209.97/158.79 |-The branch is then unsatisfiable
% 209.97/158.79 |-Branch two:
% 209.97/158.79 | (218) aNaturalNumber0(all_81_0_7)
% 209.97/158.79 | (283) all_27_0_1 = sz10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xk) & ~ (v1 = v0) & sdtpldt0(all_81_0_7, all_27_0_1) = v1 & sdtpldt0(all_81_0_7, sz10) = v0 & sdtpldt0(all_27_0_1, all_81_0_7) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xk, v2))
% 209.97/158.79 |
% 209.97/158.79 | From (256) and (218) follows:
% 209.97/158.79 | (102) aNaturalNumber0(all_33_0_4)
% 209.97/158.79 |
% 209.97/158.79 +-Applying beta-rule and splitting (234), into two cases.
% 209.97/158.79 |-Branch one:
% 209.97/158.79 | (285) all_19_0_0 = xk
% 209.97/158.79 |
% 209.97/158.79 | Equations (285) can reduce 79 to:
% 209.97/158.79 | (71) $false
% 209.97/158.79 |
% 209.97/158.79 |-The branch is then unsatisfiable
% 209.97/158.79 |-Branch two:
% 209.97/158.79 | (79) ~ (all_19_0_0 = xk)
% 209.97/158.79 | (288) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xk) & ~ (v1 = v0) & sdtpldt0(all_85_0_9, all_19_0_0) = v0 & sdtpldt0(all_85_0_9, xk) = v1 & sdtpldt0(xk, all_85_0_9) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xk, v2))
% 209.97/158.80 |
% 209.97/158.80 +-Applying beta-rule and splitting (225), into two cases.
% 209.97/158.80 |-Branch one:
% 209.97/158.80 | (285) all_19_0_0 = xk
% 209.97/158.80 |
% 209.97/158.80 | Equations (285) can reduce 79 to:
% 209.97/158.80 | (71) $false
% 209.97/158.80 |
% 209.97/158.80 |-The branch is then unsatisfiable
% 209.97/158.80 |-Branch two:
% 209.97/158.80 | (79) ~ (all_19_0_0 = xk)
% 209.97/158.80 | (292) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_124_0_22) & ~ (v1 = v0) & sdtpldt0(all_29_0_2, all_19_0_0) = v0 & sdtpldt0(all_29_0_2, xk) = v1 & sdtpldt0(xk, all_29_0_2) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_124_0_22, v2))
% 209.97/158.80 |
% 209.97/158.80 | Instantiating (292) with all_336_0_58, all_336_1_59, all_336_2_60 yields:
% 209.97/158.80 | (293) ~ (all_336_0_58 = all_124_0_22) & ~ (all_336_1_59 = all_336_2_60) & sdtpldt0(all_29_0_2, all_19_0_0) = all_336_2_60 & sdtpldt0(all_29_0_2, xk) = all_336_1_59 & sdtpldt0(xk, all_29_0_2) = all_336_0_58 & sdtlseqdt0(all_336_2_60, all_336_1_59) & sdtlseqdt0(all_124_0_22, all_336_0_58)
% 209.97/158.80 |
% 209.97/158.80 | Applying alpha-rule on (293) yields:
% 209.97/158.80 | (294) ~ (all_336_1_59 = all_336_2_60)
% 209.97/158.80 | (295) sdtlseqdt0(all_124_0_22, all_336_0_58)
% 209.97/158.80 | (296) sdtpldt0(all_29_0_2, xk) = all_336_1_59
% 209.97/158.80 | (297) sdtlseqdt0(all_336_2_60, all_336_1_59)
% 209.97/158.80 | (298) ~ (all_336_0_58 = all_124_0_22)
% 209.97/158.80 | (299) sdtpldt0(xk, all_29_0_2) = all_336_0_58
% 209.97/158.80 | (300) sdtpldt0(all_29_0_2, all_19_0_0) = all_336_2_60
% 209.97/158.80 |
% 209.97/158.80 +-Applying beta-rule and splitting (233), into two cases.
% 209.97/158.80 |-Branch one:
% 209.97/158.80 | (285) all_19_0_0 = xk
% 209.97/158.80 |
% 209.97/158.80 | Equations (285) can reduce 79 to:
% 209.97/158.80 | (71) $false
% 209.97/158.80 |
% 209.97/158.80 |-The branch is then unsatisfiable
% 209.97/158.80 |-Branch two:
% 209.97/158.80 | (79) ~ (all_19_0_0 = xk)
% 209.97/158.80 | (304) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_19_0_0) & ~ (v1 = v0) & sdtpldt0(all_87_0_10, all_19_0_0) = v0 & sdtpldt0(all_87_0_10, xk) = v1 & sdtpldt0(xk, all_87_0_10) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_19_0_0, v2))
% 209.97/158.80 |
% 209.97/158.80 +-Applying beta-rule and splitting (224), into two cases.
% 209.97/158.80 |-Branch one:
% 209.97/158.80 | (285) all_19_0_0 = xk
% 209.97/158.80 |
% 209.97/158.80 | Equations (285) can reduce 79 to:
% 209.97/158.80 | (71) $false
% 209.97/158.80 |
% 209.97/158.80 |-The branch is then unsatisfiable
% 209.97/158.80 |-Branch two:
% 209.97/158.80 | (79) ~ (all_19_0_0 = xk)
% 209.97/158.80 | (308) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_100_0_13) & ~ (v1 = v0) & sdtpldt0(all_33_0_4, all_19_0_0) = v0 & sdtpldt0(all_33_0_4, xk) = v1 & sdtpldt0(xk, all_33_0_4) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_100_0_13, v2))
% 209.97/158.80 |
% 209.97/158.80 +-Applying beta-rule and splitting (236), into two cases.
% 209.97/158.80 |-Branch one:
% 209.97/158.80 | (259) ~ aNaturalNumber0(all_83_0_8)
% 209.97/158.80 |
% 209.97/158.80 | From (266) and (259) follows:
% 209.97/158.80 | (310) ~ aNaturalNumber0(all_29_0_2)
% 209.97/158.80 |
% 209.97/158.80 | Using (96) and (310) yields:
% 209.97/158.80 | (254) $false
% 209.97/158.80 |
% 209.97/158.80 |-The branch is then unsatisfiable
% 209.97/158.80 |-Branch two:
% 209.97/158.80 | (219) aNaturalNumber0(all_83_0_8)
% 209.97/158.80 | (313) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = sz10) & ~ (v1 = v0) & sdtpldt0(all_83_0_8, xk) = v1 & sdtpldt0(all_83_0_8, sz10) = v0 & sdtpldt0(xk, all_83_0_8) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(sz10, v2))
% 209.97/158.80 |
% 209.97/158.80 | From (266) and (219) follows:
% 209.97/158.80 | (96) aNaturalNumber0(all_29_0_2)
% 209.97/158.80 |
% 209.97/158.80 +-Applying beta-rule and splitting (237), into two cases.
% 209.97/158.80 |-Branch one:
% 209.97/158.80 | (259) ~ aNaturalNumber0(all_83_0_8)
% 209.97/158.80 |
% 209.97/158.80 | From (266) and (259) follows:
% 209.97/158.80 | (310) ~ aNaturalNumber0(all_29_0_2)
% 209.97/158.80 |
% 209.97/158.80 | Using (96) and (310) yields:
% 209.97/158.80 | (254) $false
% 209.97/158.80 |
% 209.97/158.80 |-The branch is then unsatisfiable
% 209.97/158.80 |-Branch two:
% 209.97/158.80 | (219) aNaturalNumber0(all_83_0_8)
% 209.97/158.80 | (319) all_27_0_1 = sz10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = sz10) & ~ (v1 = v0) & sdtpldt0(all_83_0_8, all_27_0_1) = v1 & sdtpldt0(all_83_0_8, sz10) = v0 & sdtpldt0(all_27_0_1, all_83_0_8) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(sz10, v2))
% 209.97/158.80 |
% 209.97/158.80 | From (266) and (219) follows:
% 209.97/158.80 | (96) aNaturalNumber0(all_29_0_2)
% 209.97/158.80 |
% 209.97/158.80 +-Applying beta-rule and splitting (241), into two cases.
% 209.97/158.80 |-Branch one:
% 209.97/158.80 | (253) ~ aNaturalNumber0(all_81_0_7)
% 209.97/158.80 |
% 209.97/158.80 | From (256) and (253) follows:
% 209.97/158.80 | (270) ~ aNaturalNumber0(all_33_0_4)
% 209.97/158.80 |
% 209.97/158.80 | Using (102) and (270) yields:
% 209.97/158.80 | (254) $false
% 209.97/158.80 |
% 209.97/158.80 |-The branch is then unsatisfiable
% 209.97/158.80 |-Branch two:
% 209.97/158.80 | (218) aNaturalNumber0(all_81_0_7)
% 209.97/158.80 | (325) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xk) & ~ (v1 = v0) & sdtpldt0(all_81_0_7, xk) = v1 & sdtpldt0(all_81_0_7, sz10) = v0 & sdtpldt0(xk, all_81_0_7) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xk, v2))
% 209.97/158.80 |
% 209.97/158.80 | From (256) and (218) follows:
% 209.97/158.81 | (102) aNaturalNumber0(all_33_0_4)
% 209.97/158.81 |
% 209.97/158.81 +-Applying beta-rule and splitting (235), into two cases.
% 209.97/158.81 |-Branch one:
% 209.97/158.81 | (259) ~ aNaturalNumber0(all_83_0_8)
% 209.97/158.81 |
% 209.97/158.81 | From (266) and (259) follows:
% 209.97/158.81 | (310) ~ aNaturalNumber0(all_29_0_2)
% 209.97/158.81 |
% 209.97/158.81 | Using (96) and (310) yields:
% 209.97/158.81 | (254) $false
% 209.97/158.81 |
% 209.97/158.81 |-The branch is then unsatisfiable
% 209.97/158.81 |-Branch two:
% 209.97/158.81 | (219) aNaturalNumber0(all_83_0_8)
% 209.97/158.81 | (331) all_19_0_0 = sz10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = sz10) & ~ (v1 = v0) & sdtpldt0(all_83_0_8, all_19_0_0) = v1 & sdtpldt0(all_83_0_8, sz10) = v0 & sdtpldt0(all_19_0_0, all_83_0_8) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(sz10, v2))
% 209.97/158.81 |
% 209.97/158.81 | From (266) and (219) follows:
% 209.97/158.81 | (96) aNaturalNumber0(all_29_0_2)
% 209.97/158.81 |
% 209.97/158.81 +-Applying beta-rule and splitting (325), into two cases.
% 209.97/158.81 |-Branch one:
% 209.97/158.81 | (74) xk = sz10
% 209.97/158.81 |
% 209.97/158.81 | Equations (74) can reduce 32 to:
% 209.97/158.81 | (71) $false
% 209.97/158.81 |
% 209.97/158.81 |-The branch is then unsatisfiable
% 209.97/158.81 |-Branch two:
% 209.97/158.81 | (32) ~ (xk = sz10)
% 209.97/158.81 | (336) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xk) & ~ (v1 = v0) & sdtpldt0(all_81_0_7, xk) = v1 & sdtpldt0(all_81_0_7, sz10) = v0 & sdtpldt0(xk, all_81_0_7) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xk, v2))
% 209.97/158.81 |
% 209.97/158.81 +-Applying beta-rule and splitting (331), into two cases.
% 209.97/158.81 |-Branch one:
% 209.97/158.81 | (145) all_19_0_0 = sz10
% 209.97/158.81 |
% 209.97/158.81 | Equations (145) can reduce 80 to:
% 209.97/158.81 | (71) $false
% 209.97/158.81 |
% 209.97/158.81 |-The branch is then unsatisfiable
% 209.97/158.81 |-Branch two:
% 209.97/158.81 | (80) ~ (all_19_0_0 = sz10)
% 209.97/158.81 | (340) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = sz10) & ~ (v1 = v0) & sdtpldt0(all_83_0_8, all_19_0_0) = v1 & sdtpldt0(all_83_0_8, sz10) = v0 & sdtpldt0(all_19_0_0, all_83_0_8) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(sz10, v2))
% 209.97/158.81 |
% 209.97/158.81 | Instantiating (340) with all_396_0_76, all_396_1_77, all_396_2_78 yields:
% 209.97/158.81 | (341) ~ (all_396_0_76 = sz10) & ~ (all_396_1_77 = all_396_2_78) & sdtpldt0(all_83_0_8, all_19_0_0) = all_396_1_77 & sdtpldt0(all_83_0_8, sz10) = all_396_2_78 & sdtpldt0(all_19_0_0, all_83_0_8) = all_396_0_76 & sdtlseqdt0(all_396_2_78, all_396_1_77) & sdtlseqdt0(sz10, all_396_0_76)
% 209.97/158.81 |
% 209.97/158.81 | Applying alpha-rule on (341) yields:
% 209.97/158.81 | (342) sdtpldt0(all_83_0_8, all_19_0_0) = all_396_1_77
% 209.97/158.81 | (343) sdtlseqdt0(all_396_2_78, all_396_1_77)
% 209.97/158.81 | (344) ~ (all_396_1_77 = all_396_2_78)
% 209.97/158.81 | (345) sdtpldt0(all_19_0_0, all_83_0_8) = all_396_0_76
% 209.97/158.81 | (346) ~ (all_396_0_76 = sz10)
% 209.97/158.81 | (347) sdtpldt0(all_83_0_8, sz10) = all_396_2_78
% 209.97/158.81 | (348) sdtlseqdt0(sz10, all_396_0_76)
% 209.97/158.81 |
% 209.97/158.81 | From (266) and (342) follows:
% 209.97/158.81 | (349) sdtpldt0(all_29_0_2, all_19_0_0) = all_396_1_77
% 209.97/158.81 |
% 209.97/158.81 +-Applying beta-rule and splitting (313), into two cases.
% 209.97/158.81 |-Branch one:
% 209.97/158.81 | (74) xk = sz10
% 209.97/158.81 |
% 209.97/158.81 | Equations (74) can reduce 32 to:
% 209.97/158.81 | (71) $false
% 209.97/158.81 |
% 209.97/158.81 |-The branch is then unsatisfiable
% 209.97/158.81 |-Branch two:
% 209.97/158.81 | (32) ~ (xk = sz10)
% 209.97/158.81 | (353) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = sz10) & ~ (v1 = v0) & sdtpldt0(all_83_0_8, xk) = v1 & sdtpldt0(all_83_0_8, sz10) = v0 & sdtpldt0(xk, all_83_0_8) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(sz10, v2))
% 209.97/158.81 |
% 209.97/158.81 | Instantiating (353) with all_411_0_82, all_411_1_83, all_411_2_84 yields:
% 209.97/158.81 | (354) ~ (all_411_0_82 = sz10) & ~ (all_411_1_83 = all_411_2_84) & sdtpldt0(all_83_0_8, xk) = all_411_1_83 & sdtpldt0(all_83_0_8, sz10) = all_411_2_84 & sdtpldt0(xk, all_83_0_8) = all_411_0_82 & sdtlseqdt0(all_411_2_84, all_411_1_83) & sdtlseqdt0(sz10, all_411_0_82)
% 209.97/158.81 |
% 209.97/158.81 | Applying alpha-rule on (354) yields:
% 209.97/158.81 | (355) ~ (all_411_0_82 = sz10)
% 209.97/158.81 | (356) sdtpldt0(all_83_0_8, sz10) = all_411_2_84
% 209.97/158.81 | (357) sdtlseqdt0(all_411_2_84, all_411_1_83)
% 209.97/158.81 | (358) sdtpldt0(all_83_0_8, xk) = all_411_1_83
% 209.97/158.81 | (359) sdtlseqdt0(sz10, all_411_0_82)
% 209.97/158.81 | (360) sdtpldt0(xk, all_83_0_8) = all_411_0_82
% 209.97/158.81 | (361) ~ (all_411_1_83 = all_411_2_84)
% 209.97/158.81 |
% 209.97/158.81 | From (266) and (360) follows:
% 209.97/158.81 | (362) sdtpldt0(xk, all_29_0_2) = all_411_0_82
% 209.97/158.81 |
% 209.97/158.81 +-Applying beta-rule and splitting (240), into two cases.
% 209.97/158.81 |-Branch one:
% 209.97/158.81 | (253) ~ aNaturalNumber0(all_81_0_7)
% 209.97/158.81 |
% 209.97/158.81 | From (256) and (253) follows:
% 210.15/158.81 | (270) ~ aNaturalNumber0(all_33_0_4)
% 210.15/158.81 |
% 210.15/158.81 | Using (102) and (270) yields:
% 210.15/158.81 | (254) $false
% 210.15/158.81 |
% 210.15/158.81 |-The branch is then unsatisfiable
% 210.15/158.81 |-Branch two:
% 210.15/158.81 | (218) aNaturalNumber0(all_81_0_7)
% 210.15/158.81 | (367) all_19_0_0 = sz10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xk) & ~ (v1 = v0) & sdtpldt0(all_81_0_7, all_19_0_0) = v1 & sdtpldt0(all_81_0_7, sz10) = v0 & sdtpldt0(all_19_0_0, all_81_0_7) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xk, v2))
% 210.15/158.81 |
% 210.15/158.81 +-Applying beta-rule and splitting (216), into two cases.
% 210.15/158.81 |-Branch one:
% 210.15/158.81 | (285) all_19_0_0 = xk
% 210.15/158.81 |
% 210.15/158.81 | Equations (285) can reduce 79 to:
% 210.15/158.81 | (71) $false
% 210.15/158.81 |
% 210.15/158.81 |-The branch is then unsatisfiable
% 210.15/158.81 |-Branch two:
% 210.15/158.81 | (79) ~ (all_19_0_0 = xk)
% 210.15/158.82 | (371) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_19_0_0, all_33_0_4) = v1 & sdtpldt0(xk, all_33_0_4) = v0)
% 210.15/158.82 |
% 210.15/158.82 +-Applying beta-rule and splitting (232), into two cases.
% 210.15/158.82 |-Branch one:
% 210.15/158.82 | (372) all_19_0_0 = sz00
% 210.15/158.82 |
% 210.15/158.82 | Equations (372) can reduce 111 to:
% 210.15/158.82 | (71) $false
% 210.15/158.82 |
% 210.15/158.82 |-The branch is then unsatisfiable
% 210.15/158.82 |-Branch two:
% 210.15/158.82 | (111) ~ (all_19_0_0 = sz00)
% 210.15/158.82 | (375) all_19_0_0 = sz10 | ? [v0] : (isPrime0(v0) & doDivides0(v0, all_19_0_0) & aNaturalNumber0(v0))
% 210.15/158.82 |
% 210.15/158.82 +-Applying beta-rule and splitting (367), into two cases.
% 210.15/158.82 |-Branch one:
% 210.15/158.82 | (145) all_19_0_0 = sz10
% 210.15/158.82 |
% 210.15/158.82 | Equations (145) can reduce 80 to:
% 210.15/158.82 | (71) $false
% 210.15/158.82 |
% 210.15/158.82 |-The branch is then unsatisfiable
% 210.15/158.82 |-Branch two:
% 210.15/158.82 | (80) ~ (all_19_0_0 = sz10)
% 210.15/158.82 | (379) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xk) & ~ (v1 = v0) & sdtpldt0(all_81_0_7, all_19_0_0) = v1 & sdtpldt0(all_81_0_7, sz10) = v0 & sdtpldt0(all_19_0_0, all_81_0_7) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xk, v2))
% 210.15/158.82 |
% 210.15/158.82 +-Applying beta-rule and splitting (215), into two cases.
% 210.15/158.82 |-Branch one:
% 210.15/158.82 | (285) all_19_0_0 = xk
% 210.15/158.82 |
% 210.15/158.82 | Equations (285) can reduce 79 to:
% 210.15/158.82 | (71) $false
% 210.15/158.82 |
% 210.15/158.82 |-The branch is then unsatisfiable
% 210.15/158.82 |-Branch two:
% 210.15/158.82 | (79) ~ (all_19_0_0 = xk)
% 210.15/158.82 | (383) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_19_0_0, all_33_0_4) = v0 & sdtpldt0(xk, all_33_0_4) = v1)
% 210.15/158.82 |
% 210.15/158.82 +-Applying beta-rule and splitting (220), into two cases.
% 210.15/158.82 |-Branch one:
% 210.15/158.82 | (384) ~ (sdtpldt0(all_29_0_2, all_29_0_2) = all_29_0_2)
% 210.15/158.82 |
% 210.15/158.82 | Using (267) and (384) yields:
% 210.15/158.82 | (254) $false
% 210.15/158.82 |
% 210.15/158.82 |-The branch is then unsatisfiable
% 210.15/158.82 |-Branch two:
% 210.15/158.82 | (267) sdtpldt0(all_29_0_2, all_29_0_2) = all_29_0_2
% 210.15/158.82 | (387) ? [v0] : (sdtpldt0(all_29_0_2, v0) = all_124_1_23 & sdtpldt0(all_29_0_2, all_19_0_0) = v0)
% 210.15/158.82 |
% 210.15/158.82 | Instantiating (387) with all_450_0_92 yields:
% 210.15/158.82 | (388) sdtpldt0(all_29_0_2, all_450_0_92) = all_124_1_23 & sdtpldt0(all_29_0_2, all_19_0_0) = all_450_0_92
% 210.15/158.82 |
% 210.15/158.82 | Applying alpha-rule on (388) yields:
% 210.15/158.82 | (389) sdtpldt0(all_29_0_2, all_450_0_92) = all_124_1_23
% 210.15/158.82 | (390) sdtpldt0(all_29_0_2, all_19_0_0) = all_450_0_92
% 210.15/158.82 |
% 210.15/158.82 +-Applying beta-rule and splitting (243), into two cases.
% 210.15/158.82 |-Branch one:
% 210.15/158.82 | (145) all_19_0_0 = sz10
% 210.15/158.82 |
% 210.15/158.82 | Equations (145) can reduce 80 to:
% 210.15/158.82 | (71) $false
% 210.15/158.82 |
% 210.15/158.82 |-The branch is then unsatisfiable
% 210.15/158.82 |-Branch two:
% 210.15/158.82 | (80) ~ (all_19_0_0 = sz10)
% 210.15/158.82 | (394) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_19_0_0) & ~ (v1 = v0) & sdtpldt0(all_79_0_6, all_19_0_0) = v1 & sdtpldt0(all_79_0_6, sz10) = v0 & sdtpldt0(all_19_0_0, all_79_0_6) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_19_0_0, v2))
% 210.15/158.82 |
% 210.15/158.82 +-Applying beta-rule and splitting (375), into two cases.
% 210.15/158.82 |-Branch one:
% 210.15/158.82 | (145) all_19_0_0 = sz10
% 210.15/158.82 |
% 210.15/158.82 | Equations (145) can reduce 80 to:
% 210.15/158.82 | (71) $false
% 210.15/158.82 |
% 210.15/158.82 |-The branch is then unsatisfiable
% 210.15/158.82 |-Branch two:
% 210.15/158.82 | (80) ~ (all_19_0_0 = sz10)
% 210.15/158.82 | (398) ? [v0] : (isPrime0(v0) & doDivides0(v0, all_19_0_0) & aNaturalNumber0(v0))
% 210.15/158.82 |
% 210.15/158.82 | Instantiating (398) with all_487_0_100 yields:
% 210.15/158.82 | (399) isPrime0(all_487_0_100) & doDivides0(all_487_0_100, all_19_0_0) & aNaturalNumber0(all_487_0_100)
% 210.15/158.82 |
% 210.15/158.82 | Applying alpha-rule on (399) yields:
% 210.15/158.82 | (400) isPrime0(all_487_0_100)
% 210.15/158.82 | (401) doDivides0(all_487_0_100, all_19_0_0)
% 210.15/158.82 | (402) aNaturalNumber0(all_487_0_100)
% 210.15/158.82 |
% 210.15/158.82 +-Applying beta-rule and splitting (221), into two cases.
% 210.15/158.82 |-Branch one:
% 210.15/158.82 | (285) all_19_0_0 = xk
% 210.15/158.82 |
% 210.15/158.82 | Equations (285) can reduce 79 to:
% 210.15/158.82 | (71) $false
% 210.15/158.82 |
% 210.15/158.82 |-The branch is then unsatisfiable
% 210.15/158.82 |-Branch two:
% 210.15/158.82 | (79) ~ (all_19_0_0 = xk)
% 210.15/158.82 | (406) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_19_0_0, all_29_0_2) = v0 & sdtpldt0(xk, all_29_0_2) = v1)
% 210.15/158.82 |
% 210.15/158.82 | Instantiating (406) with all_493_0_101, all_493_1_102 yields:
% 210.15/158.82 | (407) ~ (all_493_0_101 = all_493_1_102) & sdtpldt0(all_19_0_0, all_29_0_2) = all_493_1_102 & sdtpldt0(xk, all_29_0_2) = all_493_0_101
% 210.15/158.82 |
% 210.15/158.82 | Applying alpha-rule on (407) yields:
% 210.15/158.82 | (408) ~ (all_493_0_101 = all_493_1_102)
% 210.15/158.82 | (409) sdtpldt0(all_19_0_0, all_29_0_2) = all_493_1_102
% 210.15/158.82 | (410) sdtpldt0(xk, all_29_0_2) = all_493_0_101
% 210.15/158.82 |
% 210.15/158.82 | Instantiating formula (53) with all_29_0_2, all_19_0_0, all_450_0_92, all_124_1_23 and discharging atoms sdtpldt0(all_29_0_2, all_19_0_0) = all_450_0_92, sdtpldt0(all_29_0_2, all_19_0_0) = all_124_1_23, yields:
% 210.15/158.82 | (411) all_450_0_92 = all_124_1_23
% 210.15/158.82 |
% 210.15/158.82 | Instantiating formula (53) with all_29_0_2, all_19_0_0, all_396_1_77, all_450_0_92 and discharging atoms sdtpldt0(all_29_0_2, all_19_0_0) = all_450_0_92, sdtpldt0(all_29_0_2, all_19_0_0) = all_396_1_77, yields:
% 210.15/158.82 | (412) all_450_0_92 = all_396_1_77
% 210.15/158.82 |
% 210.15/158.82 | Instantiating formula (53) with all_29_0_2, all_19_0_0, all_336_2_60, all_450_0_92 and discharging atoms sdtpldt0(all_29_0_2, all_19_0_0) = all_450_0_92, sdtpldt0(all_29_0_2, all_19_0_0) = all_336_2_60, yields:
% 210.15/158.82 | (413) all_450_0_92 = all_336_2_60
% 210.15/158.82 |
% 210.15/158.82 | Instantiating formula (53) with all_29_0_2, all_19_0_0, all_124_0_22, all_336_2_60 and discharging atoms sdtpldt0(all_29_0_2, all_19_0_0) = all_336_2_60, sdtpldt0(all_29_0_2, all_19_0_0) = all_124_0_22, yields:
% 210.15/158.82 | (414) all_336_2_60 = all_124_0_22
% 210.15/158.82 |
% 210.15/158.82 | Instantiating formula (53) with xk, all_29_0_2, all_411_0_82, all_493_0_101 and discharging atoms sdtpldt0(xk, all_29_0_2) = all_493_0_101, sdtpldt0(xk, all_29_0_2) = all_411_0_82, yields:
% 210.15/158.82 | (415) all_493_0_101 = all_411_0_82
% 210.15/158.82 |
% 210.15/158.82 | Instantiating formula (53) with xk, all_29_0_2, all_336_0_58, all_119_0_19 and discharging atoms sdtpldt0(xk, all_29_0_2) = all_336_0_58, sdtpldt0(xk, all_29_0_2) = all_119_0_19, yields:
% 210.15/158.82 | (416) all_336_0_58 = all_119_0_19
% 210.15/158.82 |
% 210.15/158.82 | Instantiating formula (53) with xk, all_29_0_2, all_336_0_58, all_411_0_82 and discharging atoms sdtpldt0(xk, all_29_0_2) = all_411_0_82, sdtpldt0(xk, all_29_0_2) = all_336_0_58, yields:
% 210.15/158.82 | (417) all_411_0_82 = all_336_0_58
% 210.15/158.82 |
% 210.15/158.82 | Instantiating formula (53) with xk, all_29_0_2, all_256_0_41, all_493_0_101 and discharging atoms sdtpldt0(xk, all_29_0_2) = all_493_0_101, sdtpldt0(xk, all_29_0_2) = all_256_0_41, yields:
% 210.15/158.82 | (418) all_493_0_101 = all_256_0_41
% 210.15/158.82 |
% 210.15/158.82 | Instantiating formula (53) with xk, all_29_0_2, all_119_1_20, all_336_0_58 and discharging atoms sdtpldt0(xk, all_29_0_2) = all_336_0_58, sdtpldt0(xk, all_29_0_2) = all_119_1_20, yields:
% 210.15/158.82 | (419) all_336_0_58 = all_119_1_20
% 210.15/158.82 |
% 210.15/158.82 | Instantiating formula (53) with sz10, all_33_0_4, all_306_0_54, xk and discharging atoms sdtpldt0(sz10, all_33_0_4) = all_306_0_54, sdtpldt0(sz10, all_33_0_4) = xk, yields:
% 210.15/158.82 | (420) all_306_0_54 = xk
% 210.15/158.82 |
% 210.15/158.82 | Instantiating formula (53) with sz10, all_33_0_4, all_242_0_34, all_306_0_54 and discharging atoms sdtpldt0(sz10, all_33_0_4) = all_306_0_54, sdtpldt0(sz10, all_33_0_4) = all_242_0_34, yields:
% 210.15/158.82 | (421) all_306_0_54 = all_242_0_34
% 210.15/158.82 |
% 210.15/158.82 | Instantiating formula (53) with sz10, all_33_0_4, all_236_0_31, all_242_0_34 and discharging atoms sdtpldt0(sz10, all_33_0_4) = all_242_0_34, sdtpldt0(sz10, all_33_0_4) = all_236_0_31, yields:
% 210.15/158.82 | (422) all_242_0_34 = all_236_0_31
% 210.15/158.82 |
% 210.15/158.82 | Instantiating formula (20) with all_124_1_23, all_19_0_0, all_124_0_22, all_29_0_2 and discharging atoms sdtpldt0(all_29_0_2, all_19_0_0) = all_124_1_23, aNaturalNumber0(all_124_0_22), aNaturalNumber0(all_29_0_2), aNaturalNumber0(all_19_0_0), yields:
% 210.15/158.82 | (423) all_124_0_22 = all_19_0_0 | ~ (sdtpldt0(all_29_0_2, all_124_0_22) = all_124_1_23)
% 210.15/158.82 |
% 210.15/158.82 | Combining equations (415,418) yields a new equation:
% 210.15/158.82 | (424) all_411_0_82 = all_256_0_41
% 210.15/158.82 |
% 210.15/158.82 | Simplifying 424 yields:
% 210.15/158.82 | (425) all_411_0_82 = all_256_0_41
% 210.15/158.82 |
% 210.15/158.82 | Combining equations (411,412) yields a new equation:
% 210.15/158.82 | (426) all_396_1_77 = all_124_1_23
% 210.15/158.82 |
% 210.15/158.82 | Combining equations (413,412) yields a new equation:
% 210.15/158.82 | (427) all_396_1_77 = all_336_2_60
% 210.15/158.82 |
% 210.15/158.82 | Combining equations (417,425) yields a new equation:
% 210.15/158.82 | (428) all_336_0_58 = all_256_0_41
% 210.15/158.82 |
% 210.15/158.82 | Simplifying 428 yields:
% 210.15/158.82 | (429) all_336_0_58 = all_256_0_41
% 210.15/158.82 |
% 210.15/158.82 | Combining equations (427,426) yields a new equation:
% 210.15/158.82 | (430) all_336_2_60 = all_124_1_23
% 210.15/158.83 |
% 210.15/158.83 | Simplifying 430 yields:
% 210.15/158.83 | (431) all_336_2_60 = all_124_1_23
% 210.15/158.83 |
% 210.15/158.83 | Combining equations (416,429) yields a new equation:
% 210.15/158.83 | (432) all_256_0_41 = all_119_0_19
% 210.15/158.83 |
% 210.15/158.83 | Combining equations (419,429) yields a new equation:
% 210.15/158.83 | (433) all_256_0_41 = all_119_1_20
% 210.15/158.83 |
% 210.15/158.83 | Combining equations (414,431) yields a new equation:
% 210.15/158.83 | (434) all_124_0_22 = all_124_1_23
% 210.15/158.83 |
% 210.15/158.83 | Simplifying 434 yields:
% 210.15/158.83 | (435) all_124_0_22 = all_124_1_23
% 210.15/158.83 |
% 210.15/158.83 | Combining equations (421,420) yields a new equation:
% 210.15/158.83 | (436) all_242_0_34 = xk
% 210.15/158.83 |
% 210.15/158.83 | Simplifying 436 yields:
% 210.15/158.83 | (437) all_242_0_34 = xk
% 210.15/158.83 |
% 210.15/158.83 | Combining equations (433,432) yields a new equation:
% 210.15/158.83 | (438) all_119_0_19 = all_119_1_20
% 210.15/158.83 |
% 210.15/158.83 | Combining equations (437,422) yields a new equation:
% 210.15/158.83 | (439) all_236_0_31 = xk
% 210.15/158.83 |
% 210.15/158.83 | Combining equations (426,412) yields a new equation:
% 210.15/158.83 | (411) all_450_0_92 = all_124_1_23
% 210.15/158.83 |
% 210.15/158.83 | From (411) and (389) follows:
% 210.15/158.83 | (441) sdtpldt0(all_29_0_2, all_124_1_23) = all_124_1_23
% 210.15/158.83 |
% 210.15/158.83 | From (439) and (245) follows:
% 210.15/158.83 | (442) sdtpldt0(all_29_0_2, xk) = xk
% 210.15/158.83 |
% 210.15/158.83 | From (435) and (227) follows:
% 210.15/158.83 | (443) aNaturalNumber0(all_124_1_23)
% 210.15/158.83 |
% 210.15/158.83 | From (438) and (231) follows:
% 210.15/158.83 | (444) aNaturalNumber0(all_119_1_20)
% 210.15/158.83 |
% 210.15/158.83 +-Applying beta-rule and splitting (217), into two cases.
% 210.15/158.83 |-Branch one:
% 210.15/158.83 | (445) ~ (sdtpldt0(all_29_0_2, xk) = xk)
% 210.15/158.83 |
% 210.15/158.83 | Using (442) and (445) yields:
% 210.15/158.83 | (254) $false
% 210.15/158.83 |
% 210.15/158.83 |-The branch is then unsatisfiable
% 210.15/158.83 |-Branch two:
% 210.15/158.83 | (442) sdtpldt0(all_29_0_2, xk) = xk
% 210.15/158.83 | (448) sdtlseqdt0(all_29_0_2, xk)
% 210.15/158.83 |
% 210.15/158.83 +-Applying beta-rule and splitting (423), into two cases.
% 210.15/158.83 |-Branch one:
% 210.15/158.83 | (449) ~ (sdtpldt0(all_29_0_2, all_124_0_22) = all_124_1_23)
% 210.15/158.83 |
% 210.15/158.83 | From (435) and (449) follows:
% 210.15/158.83 | (450) ~ (sdtpldt0(all_29_0_2, all_124_1_23) = all_124_1_23)
% 210.15/158.83 |
% 210.15/158.83 | Using (441) and (450) yields:
% 210.15/158.83 | (254) $false
% 210.15/158.83 |
% 210.15/158.83 |-The branch is then unsatisfiable
% 210.15/158.83 |-Branch two:
% 210.15/158.83 | (452) sdtpldt0(all_29_0_2, all_124_0_22) = all_124_1_23
% 210.15/158.83 | (453) all_124_0_22 = all_19_0_0
% 210.15/158.83 |
% 210.15/158.83 | Combining equations (435,453) yields a new equation:
% 210.15/158.83 | (454) all_124_1_23 = all_19_0_0
% 210.15/158.83 |
% 210.15/158.83 | Simplifying 454 yields:
% 210.15/158.83 | (455) all_124_1_23 = all_19_0_0
% 210.15/158.83 |
% 210.15/158.83 | From (455) and (443) follows:
% 210.15/158.83 | (82) aNaturalNumber0(all_19_0_0)
% 210.15/158.83 |
% 210.15/158.83 +-Applying beta-rule and splitting (230), into two cases.
% 210.15/158.83 |-Branch one:
% 210.15/158.83 | (445) ~ (sdtpldt0(all_29_0_2, xk) = xk)
% 210.15/158.83 |
% 210.15/158.83 | Using (442) and (445) yields:
% 210.15/158.83 | (254) $false
% 210.15/158.83 |
% 210.15/158.83 |-The branch is then unsatisfiable
% 210.15/158.83 |-Branch two:
% 210.15/158.83 | (442) sdtpldt0(all_29_0_2, xk) = xk
% 210.15/158.83 | (460) ? [v0] : (sdtpldt0(all_29_0_2, v0) = all_119_0_19 & sdtpldt0(xk, all_29_0_2) = v0)
% 210.15/158.83 |
% 210.15/158.83 +-Applying beta-rule and splitting (197), into two cases.
% 210.15/158.83 |-Branch one:
% 210.15/158.83 | (445) ~ (sdtpldt0(all_29_0_2, xk) = xk)
% 210.15/158.83 |
% 210.15/158.83 | Using (442) and (445) yields:
% 210.15/158.83 | (254) $false
% 210.15/158.83 |
% 210.15/158.83 |-The branch is then unsatisfiable
% 210.15/158.83 |-Branch two:
% 210.15/158.83 | (442) sdtpldt0(all_29_0_2, xk) = xk
% 210.15/158.83 | (464) all_119_1_20 = xk
% 210.15/158.83 |
% 210.15/158.83 | From (464) and (444) follows:
% 210.15/158.83 | (21) aNaturalNumber0(xk)
% 210.15/158.83 |
% 210.15/158.83 | Instantiating formula (33) with xk, all_19_0_0, all_487_0_100 and discharging atoms doDivides0(all_487_0_100, all_19_0_0), doDivides0(all_19_0_0, xk), aNaturalNumber0(all_487_0_100), aNaturalNumber0(all_19_0_0), aNaturalNumber0(xk), yields:
% 210.15/158.83 | (466) doDivides0(all_487_0_100, xk)
% 210.15/158.83 |
% 210.15/158.83 | Instantiating formula (41) with all_487_0_100 and discharging atoms isPrime0(all_487_0_100), doDivides0(all_487_0_100, xk), aNaturalNumber0(all_487_0_100), yields:
% 210.15/158.83 | (254) $false
% 210.15/158.83 |
% 210.15/158.83 |-The branch is then unsatisfiable
% 210.15/158.83 |-Branch two:
% 210.15/158.83 | (468) ~ sdtlseqdt0(sz10, all_27_0_1)
% 210.15/158.83 | (469) all_27_0_1 = sz10 | all_27_0_1 = sz00
% 210.15/158.83 |
% 210.15/158.83 +-Applying beta-rule and splitting (469), into two cases.
% 210.15/158.83 |-Branch one:
% 210.15/158.83 | (470) all_27_0_1 = sz00
% 210.15/158.83 |
% 210.15/158.83 | Equations (470) can reduce 213 to:
% 210.15/158.83 | (71) $false
% 210.15/158.83 |
% 210.15/158.83 |-The branch is then unsatisfiable
% 210.15/158.83 |-Branch two:
% 210.15/158.83 | (213) ~ (all_27_0_1 = sz00)
% 210.15/158.83 | (473) all_27_0_1 = sz10
% 210.15/158.83 |
% 210.15/158.83 | Equations (473) can reduce 212 to:
% 210.15/158.83 | (71) $false
% 210.15/158.83 |
% 210.15/158.83 |-The branch is then unsatisfiable
% 210.15/158.83 |-Branch two:
% 210.15/158.83 | (475) sdtasdt0(all_19_0_0, sz10) = xk
% 210.15/158.83 | (476) sdtasdt0(sz10, all_19_0_0) = xk
% 210.15/158.83 |
% 210.15/158.83 | Using (476) and (210) yields:
% 210.15/158.83 | (254) $false
% 210.15/158.83 |
% 210.15/158.83 |-The branch is then unsatisfiable
% 210.15/158.83 |-Branch two:
% 210.15/158.83 | (476) sdtasdt0(sz10, all_19_0_0) = xk
% 210.15/158.83 | (285) all_19_0_0 = xk
% 210.15/158.83 |
% 210.15/158.83 | Equations (285) can reduce 79 to:
% 210.15/158.83 | (71) $false
% 210.15/158.83 |
% 210.15/158.83 |-The branch is then unsatisfiable
% 210.15/158.83 |-Branch two:
% 210.15/158.83 | (481) sdtasdt0(all_19_0_0, sz00) = xk
% 210.15/158.83 | (482) sdtasdt0(sz00, all_19_0_0) = xk
% 210.15/158.83 |
% 210.15/158.83 | Using (482) and (208) yields:
% 210.15/158.83 | (254) $false
% 210.15/158.83 |
% 210.15/158.83 |-The branch is then unsatisfiable
% 210.15/158.83 |-Branch two:
% 210.15/158.83 | (482) sdtasdt0(sz00, all_19_0_0) = xk
% 210.15/158.83 | (70) xk = sz00
% 210.15/158.83 |
% 210.15/158.83 | Equations (70) can reduce 44 to:
% 210.15/158.83 | (71) $false
% 210.15/158.83 |
% 210.15/158.83 |-The branch is then unsatisfiable
% 210.15/158.83 |-Branch two:
% 210.15/158.83 | (487) ~ iLess0(all_19_0_0, xk)
% 210.15/158.83 | (285) all_19_0_0 = xk
% 210.15/158.83 |
% 210.15/158.83 | Equations (285) can reduce 79 to:
% 210.15/158.83 | (71) $false
% 210.15/158.83 |
% 210.15/158.83 |-The branch is then unsatisfiable
% 210.15/158.83 |-Branch two:
% 210.15/158.83 | (490) ~ sdtlseqdt0(sz10, all_19_0_0)
% 210.15/158.83 | (491) all_19_0_0 = sz10 | all_19_0_0 = sz00
% 210.15/158.83 |
% 210.15/158.83 +-Applying beta-rule and splitting (491), into two cases.
% 210.15/158.83 |-Branch one:
% 210.15/158.83 | (372) all_19_0_0 = sz00
% 210.15/158.83 |
% 210.15/158.83 | Equations (372) can reduce 111 to:
% 210.15/158.83 | (71) $false
% 210.15/158.83 |
% 210.15/158.83 |-The branch is then unsatisfiable
% 210.15/158.83 |-Branch two:
% 210.15/158.83 | (111) ~ (all_19_0_0 = sz00)
% 210.15/158.83 | (145) all_19_0_0 = sz10
% 210.23/158.83 |
% 210.23/158.83 | Equations (145) can reduce 80 to:
% 210.23/158.83 | (71) $false
% 210.23/158.83 |
% 210.23/158.83 |-The branch is then unsatisfiable
% 210.23/158.83 |-Branch two:
% 210.23/158.83 | (497) sdtasdt0(sz00, all_27_0_1) = xk
% 210.23/158.83 | (70) xk = sz00
% 210.23/158.83 |
% 210.23/158.83 | Equations (70) can reduce 44 to:
% 210.23/158.83 | (71) $false
% 210.23/158.83 |
% 210.23/158.83 |-The branch is then unsatisfiable
% 210.23/158.83 |-Branch two:
% 210.23/158.83 | (500) ~ sdtlseqdt0(all_19_0_0, xk)
% 210.23/158.83 | (70) xk = sz00
% 210.23/158.83 |
% 210.23/158.83 | Equations (70) can reduce 44 to:
% 210.23/158.83 | (71) $false
% 210.23/158.83 |
% 210.23/158.83 |-The branch is then unsatisfiable
% 210.23/158.83 |-Branch two:
% 210.23/158.83 | (503) ~ sdtlseqdt0(sz10, xk)
% 210.23/158.83 | (504) xk = sz10 | xk = sz00
% 210.23/158.83 |
% 210.23/158.83 +-Applying beta-rule and splitting (65), into two cases.
% 210.23/158.83 |-Branch one:
% 210.23/158.83 | (70) xk = sz00
% 210.23/158.83 |
% 210.23/158.83 | Equations (70) can reduce 44 to:
% 210.23/158.83 | (71) $false
% 210.23/158.83 |
% 210.23/158.83 |-The branch is then unsatisfiable
% 210.23/158.83 |-Branch two:
% 210.23/158.83 | (44) ~ (xk = sz00)
% 210.23/158.83 | (73) xk = sz10 | ? [v0] : ( ~ (v0 = xk) & ~ (v0 = sz10) & doDivides0(v0, xk) & aNaturalNumber0(v0))
% 210.23/158.83 |
% 210.23/158.83 +-Applying beta-rule and splitting (504), into two cases.
% 210.23/158.83 |-Branch one:
% 210.23/158.83 | (70) xk = sz00
% 210.23/158.83 |
% 210.23/158.83 | Equations (70) can reduce 44 to:
% 210.23/158.83 | (71) $false
% 210.23/158.83 |
% 210.23/158.83 |-The branch is then unsatisfiable
% 210.23/158.83 |-Branch two:
% 210.23/158.83 | (44) ~ (xk = sz00)
% 210.23/158.83 | (74) xk = sz10
% 210.23/158.83 |
% 210.23/158.83 | Equations (74) can reduce 32 to:
% 210.23/158.83 | (71) $false
% 210.23/158.83 |
% 210.23/158.83 |-The branch is then unsatisfiable
% 210.23/158.83 % SZS output end Proof for theBenchmark
% 210.23/158.83
% 210.23/158.83 158233ms
%------------------------------------------------------------------------------