TSTP Solution File: NUM375+1.020 by ePrincess---1.0
View Problem
- Process Solution
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% File : ePrincess---1.0
% Problem : NUM375+1.020 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n006.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 08:43:44 EDT 2022
% Result : Unsatisfiable 12.68s 4.37s
% Output : Proof 32.63s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM375+1.020 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n006.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 05:56:22 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.20/0.60 ____ _
% 0.20/0.60 ___ / __ \_____(_)___ ________ __________
% 0.20/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.20/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic
% 0.20/0.60 (ePrincess v.1.0)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2015
% 0.20/0.60 (c) Peter Backeman, 2014-2015
% 0.20/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.60 Bug reports to peter@backeman.se
% 0.20/0.60
% 0.20/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.91/1.22 Prover 0: Preprocessing ...
% 4.55/1.68 Prover 0: Constructing countermodel ...
% 12.68/4.37 Prover 0: proved (3720ms)
% 12.68/4.37
% 12.68/4.37 No countermodel exists, formula is valid
% 12.68/4.37 % SZS status Unsatisfiable for theBenchmark
% 12.68/4.37
% 12.68/4.37 Generating proof ... found it (size 7623)
% 27.94/9.55
% 27.94/9.55 % SZS output start Proof for theBenchmark
% 27.94/9.56 Assumed formulas after preprocessing and simplification:
% 27.94/9.56 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v2 = n20) & ~ (v2 = n19) & ~ (v2 = n18) & ~ (v2 = n17) & ~ (v2 = n16) & ~ (v2 = n15) & ~ (v2 = n14) & ~ (v2 = n13) & ~ (v2 = n12) & ~ (v2 = n11) & ~ (v2 = n10) & ~ (v2 = n9) & ~ (v2 = n8) & ~ (v2 = n7) & ~ (v2 = n6) & ~ (v2 = n5) & ~ (v2 = n4) & ~ (v2 = n3) & ~ (v2 = n2) & ~ (v2 = n1) & ~ (v2 = n0) & ~ (n20 = n19) & ~ (n20 = n18) & ~ (n20 = n17) & ~ (n20 = n16) & ~ (n20 = n15) & ~ (n20 = n14) & ~ (n20 = n13) & ~ (n20 = n12) & ~ (n20 = n11) & ~ (n20 = n10) & ~ (n20 = n9) & ~ (n20 = n8) & ~ (n20 = n7) & ~ (n20 = n6) & ~ (n20 = n5) & ~ (n20 = n4) & ~ (n20 = n3) & ~ (n20 = n2) & ~ (n20 = n1) & ~ (n20 = n0) & ~ (n19 = n18) & ~ (n19 = n17) & ~ (n19 = n16) & ~ (n19 = n15) & ~ (n19 = n14) & ~ (n19 = n13) & ~ (n19 = n12) & ~ (n19 = n11) & ~ (n19 = n10) & ~ (n19 = n9) & ~ (n19 = n8) & ~ (n19 = n7) & ~ (n19 = n6) & ~ (n19 = n5) & ~ (n19 = n4) & ~ (n19 = n3) & ~ (n19 = n2) & ~ (n19 = n1) & ~ (n19 = n0) & ~ (n18 = n17) & ~ (n18 = n16) & ~ (n18 = n15) & ~ (n18 = n14) & ~ (n18 = n13) & ~ (n18 = n12) & ~ (n18 = n11) & ~ (n18 = n10) & ~ (n18 = n9) & ~ (n18 = n8) & ~ (n18 = n7) & ~ (n18 = n6) & ~ (n18 = n5) & ~ (n18 = n4) & ~ (n18 = n3) & ~ (n18 = n2) & ~ (n18 = n1) & ~ (n18 = n0) & ~ (n17 = n16) & ~ (n17 = n15) & ~ (n17 = n14) & ~ (n17 = n13) & ~ (n17 = n12) & ~ (n17 = n11) & ~ (n17 = n10) & ~ (n17 = n9) & ~ (n17 = n8) & ~ (n17 = n7) & ~ (n17 = n6) & ~ (n17 = n5) & ~ (n17 = n4) & ~ (n17 = n3) & ~ (n17 = n2) & ~ (n17 = n1) & ~ (n17 = n0) & ~ (n16 = n15) & ~ (n16 = n14) & ~ (n16 = n13) & ~ (n16 = n12) & ~ (n16 = n11) & ~ (n16 = n10) & ~ (n16 = n9) & ~ (n16 = n8) & ~ (n16 = n7) & ~ (n16 = n6) & ~ (n16 = n5) & ~ (n16 = n4) & ~ (n16 = n3) & ~ (n16 = n2) & ~ (n16 = n1) & ~ (n16 = n0) & ~ (n15 = n14) & ~ (n15 = n13) & ~ (n15 = n12) & ~ (n15 = n11) & ~ (n15 = n10) & ~ (n15 = n9) & ~ (n15 = n8) & ~ (n15 = n7) & ~ (n15 = n6) & ~ (n15 = n5) & ~ (n15 = n4) & ~ (n15 = n3) & ~ (n15 = n2) & ~ (n15 = n1) & ~ (n15 = n0) & ~ (n14 = n13) & ~ (n14 = n12) & ~ (n14 = n11) & ~ (n14 = n10) & ~ (n14 = n9) & ~ (n14 = n8) & ~ (n14 = n7) & ~ (n14 = n6) & ~ (n14 = n5) & ~ (n14 = n4) & ~ (n14 = n3) & ~ (n14 = n2) & ~ (n14 = n1) & ~ (n14 = n0) & ~ (n13 = n12) & ~ (n13 = n11) & ~ (n13 = n10) & ~ (n13 = n9) & ~ (n13 = n8) & ~ (n13 = n7) & ~ (n13 = n6) & ~ (n13 = n5) & ~ (n13 = n4) & ~ (n13 = n3) & ~ (n13 = n2) & ~ (n13 = n1) & ~ (n13 = n0) & ~ (n12 = n11) & ~ (n12 = n10) & ~ (n12 = n9) & ~ (n12 = n8) & ~ (n12 = n7) & ~ (n12 = n6) & ~ (n12 = n5) & ~ (n12 = n4) & ~ (n12 = n3) & ~ (n12 = n2) & ~ (n12 = n1) & ~ (n12 = n0) & ~ (n11 = n10) & ~ (n11 = n9) & ~ (n11 = n8) & ~ (n11 = n7) & ~ (n11 = n6) & ~ (n11 = n5) & ~ (n11 = n4) & ~ (n11 = n3) & ~ (n11 = n2) & ~ (n11 = n1) & ~ (n11 = n0) & ~ (n10 = n9) & ~ (n10 = n8) & ~ (n10 = n7) & ~ (n10 = n6) & ~ (n10 = n5) & ~ (n10 = n4) & ~ (n10 = n3) & ~ (n10 = n2) & ~ (n10 = n1) & ~ (n10 = n0) & ~ (n9 = n8) & ~ (n9 = n7) & ~ (n9 = n6) & ~ (n9 = n5) & ~ (n9 = n4) & ~ (n9 = n3) & ~ (n9 = n2) & ~ (n9 = n1) & ~ (n9 = n0) & ~ (n8 = n7) & ~ (n8 = n6) & ~ (n8 = n5) & ~ (n8 = n4) & ~ (n8 = n3) & ~ (n8 = n2) & ~ (n8 = n1) & ~ (n8 = n0) & ~ (n7 = n6) & ~ (n7 = n5) & ~ (n7 = n4) & ~ (n7 = n3) & ~ (n7 = n2) & ~ (n7 = n1) & ~ (n7 = n0) & ~ (n6 = n5) & ~ (n6 = n4) & ~ (n6 = n3) & ~ (n6 = n2) & ~ (n6 = n1) & ~ (n6 = n0) & ~ (n5 = n4) & ~ (n5 = n3) & ~ (n5 = n2) & ~ (n5 = n1) & ~ (n5 = n0) & ~ (n4 = n3) & ~ (n4 = n2) & ~ (n4 = n1) & ~ (n4 = n0) & ~ (n3 = n2) & ~ (n3 = n1) & ~ (n3 = n0) & ~ (n2 = n1) & ~ (n2 = n0) & ~ (n1 = n0) & succ(v1) = v3 & succ(n20) = n0 & succ(n19) = n20 & succ(n18) = n19 & succ(n17) = n18 & succ(n16) = n17 & succ(n15) = n16 & succ(n14) = n15 & succ(n13) = n14 & succ(n12) = n13 & succ(n11) = n12 & succ(n10) = n11 & succ(n9) = n10 & succ(n8) = n9 & succ(n7) = n8 & succ(n6) = n7 & succ(n5) = n6 & succ(n4) = n5 & succ(n3) = n4 & succ(n2) = n3 & succ(n1) = n2 & succ(n0) = n1 & pred(v6) = v7 & pred(v4) = v5 & pred(n20) = n19 & pred(n19) = n18 & pred(n18) = n17 & pred(n17) = n16 & pred(n16) = n15 & pred(n15) = n14 & pred(n14) = n13 & pred(n13) = n12 & pred(n12) = n11 & pred(n11) = n10 & pred(n10) = n9 & pred(n9) = n8 & pred(n8) = n7 & pred(n7) = n6 & pred(n6) = n5 & pred(n5) = n4 & pred(n4) = n3 & pred(n3) = n2 & pred(n2) = n1 & pred(n1) = n0 & pred(n0) = n20 & sum(v5, v8) = v2 & sum(v1, v7) = v8 & sum(v0, v3) = v4 & sum(v0, v1) = v6 & sum(n20, n20) = n19 & sum(n20, n19) = n18 & sum(n20, n18) = n17 & sum(n20, n17) = n16 & sum(n20, n16) = n15 & sum(n20, n15) = n14 & sum(n20, n14) = n13 & sum(n20, n13) = n12 & sum(n20, n12) = n11 & sum(n20, n11) = n10 & sum(n20, n10) = n9 & sum(n20, n9) = n8 & sum(n20, n8) = n7 & sum(n20, n7) = n6 & sum(n20, n6) = n5 & sum(n20, n5) = n4 & sum(n20, n4) = n3 & sum(n20, n3) = n2 & sum(n20, n2) = n1 & sum(n20, n1) = n0 & sum(n20, n0) = n20 & sum(n19, n20) = n18 & sum(n19, n19) = n17 & sum(n19, n18) = n16 & sum(n19, n17) = n15 & sum(n19, n16) = n14 & sum(n19, n15) = n13 & sum(n19, n14) = n12 & sum(n19, n13) = n11 & sum(n19, n12) = n10 & sum(n19, n11) = n9 & sum(n19, n10) = n8 & sum(n19, n9) = n7 & sum(n19, n8) = n6 & sum(n19, n7) = n5 & sum(n19, n6) = n4 & sum(n19, n5) = n3 & sum(n19, n4) = n2 & sum(n19, n3) = n1 & sum(n19, n2) = n0 & sum(n19, n1) = n20 & sum(n19, n0) = n19 & sum(n18, n20) = n17 & sum(n18, n19) = n16 & sum(n18, n18) = n15 & sum(n18, n17) = n14 & sum(n18, n16) = n13 & sum(n18, n15) = n12 & sum(n18, n14) = n11 & sum(n18, n13) = n10 & sum(n18, n12) = n9 & sum(n18, n11) = n8 & sum(n18, n10) = n7 & sum(n18, n9) = n6 & sum(n18, n8) = n5 & sum(n18, n7) = n4 & sum(n18, n6) = n3 & sum(n18, n5) = n2 & sum(n18, n4) = n1 & sum(n18, n3) = n0 & sum(n18, n2) = n20 & sum(n18, n1) = n19 & sum(n18, n0) = n18 & sum(n17, n20) = n16 & sum(n17, n19) = n15 & sum(n17, n18) = n14 & sum(n17, n17) = n13 & sum(n17, n16) = n12 & sum(n17, n15) = n11 & sum(n17, n14) = n10 & sum(n17, n13) = n9 & sum(n17, n12) = n8 & sum(n17, n11) = n7 & sum(n17, n10) = n6 & sum(n17, n9) = n5 & sum(n17, n8) = n4 & sum(n17, n7) = n3 & sum(n17, n6) = n2 & sum(n17, n5) = n1 & sum(n17, n4) = n0 & sum(n17, n3) = n20 & sum(n17, n2) = n19 & sum(n17, n1) = n18 & sum(n17, n0) = n17 & sum(n16, n20) = n15 & sum(n16, n19) = n14 & sum(n16, n18) = n13 & sum(n16, n17) = n12 & sum(n16, n16) = n11 & sum(n16, n15) = n10 & sum(n16, n14) = n9 & sum(n16, n13) = n8 & sum(n16, n12) = n7 & sum(n16, n11) = n6 & sum(n16, n10) = n5 & sum(n16, n9) = n4 & sum(n16, n8) = n3 & sum(n16, n7) = n2 & sum(n16, n6) = n1 & sum(n16, n5) = n0 & sum(n16, n4) = n20 & sum(n16, n3) = n19 & sum(n16, n2) = n18 & sum(n16, n1) = n17 & sum(n16, n0) = n16 & sum(n15, n20) = n14 & sum(n15, n19) = n13 & sum(n15, n18) = n12 & sum(n15, n17) = n11 & sum(n15, n16) = n10 & sum(n15, n15) = n9 & sum(n15, n14) = n8 & sum(n15, n13) = n7 & sum(n15, n12) = n6 & sum(n15, n11) = n5 & sum(n15, n10) = n4 & sum(n15, n9) = n3 & sum(n15, n8) = n2 & sum(n15, n7) = n1 & sum(n15, n6) = n0 & sum(n15, n5) = n20 & sum(n15, n4) = n19 & sum(n15, n3) = n18 & sum(n15, n2) = n17 & sum(n15, n1) = n16 & sum(n15, n0) = n15 & sum(n14, n20) = n13 & sum(n14, n19) = n12 & sum(n14, n18) = n11 & sum(n14, n17) = n10 & sum(n14, n16) = n9 & sum(n14, n15) = n8 & sum(n14, n14) = n7 & sum(n14, n13) = n6 & sum(n14, n12) = n5 & sum(n14, n11) = n4 & sum(n14, n10) = n3 & sum(n14, n9) = n2 & sum(n14, n8) = n1 & sum(n14, n7) = n0 & sum(n14, n6) = n20 & sum(n14, n5) = n19 & sum(n14, n4) = n18 & sum(n14, n3) = n17 & sum(n14, n2) = n16 & sum(n14, n1) = n15 & sum(n14, n0) = n14 & sum(n13, n20) = n12 & sum(n13, n19) = n11 & sum(n13, n18) = n10 & sum(n13, n17) = n9 & sum(n13, n16) = n8 & sum(n13, n15) = n7 & sum(n13, n14) = n6 & sum(n13, n13) = n5 & sum(n13, n12) = n4 & sum(n13, n11) = n3 & sum(n13, n10) = n2 & sum(n13, n9) = n1 & sum(n13, n8) = n0 & sum(n13, n7) = n20 & sum(n13, n6) = n19 & sum(n13, n5) = n18 & sum(n13, n4) = n17 & sum(n13, n3) = n16 & sum(n13, n2) = n15 & sum(n13, n1) = n14 & sum(n13, n0) = n13 & sum(n12, n20) = n11 & sum(n12, n19) = n10 & sum(n12, n18) = n9 & sum(n12, n17) = n8 & sum(n12, n16) = n7 & sum(n12, n15) = n6 & sum(n12, n14) = n5 & sum(n12, n13) = n4 & sum(n12, n12) = n3 & sum(n12, n11) = n2 & sum(n12, n10) = n1 & sum(n12, n9) = n0 & sum(n12, n8) = n20 & sum(n12, n7) = n19 & sum(n12, n6) = n18 & sum(n12, n5) = n17 & sum(n12, n4) = n16 & sum(n12, n3) = n15 & sum(n12, n2) = n14 & sum(n12, n1) = n13 & sum(n12, n0) = n12 & sum(n11, n20) = n10 & sum(n11, n19) = n9 & sum(n11, n18) = n8 & sum(n11, n17) = n7 & sum(n11, n16) = n6 & sum(n11, n15) = n5 & sum(n11, n14) = n4 & sum(n11, n13) = n3 & sum(n11, n12) = n2 & sum(n11, n11) = n1 & sum(n11, n10) = n0 & sum(n11, n9) = n20 & sum(n11, n8) = n19 & sum(n11, n7) = n18 & sum(n11, n6) = n17 & sum(n11, n5) = n16 & sum(n11, n4) = n15 & sum(n11, n3) = n14 & sum(n11, n2) = n13 & sum(n11, n1) = n12 & sum(n11, n0) = n11 & sum(n10, n20) = n9 & sum(n10, n19) = n8 & sum(n10, n18) = n7 & sum(n10, n17) = n6 & sum(n10, n16) = n5 & sum(n10, n15) = n4 & sum(n10, n14) = n3 & sum(n10, n13) = n2 & sum(n10, n12) = n1 & sum(n10, n11) = n0 & sum(n10, n10) = n20 & sum(n10, n9) = n19 & sum(n10, n8) = n18 & sum(n10, n7) = n17 & sum(n10, n6) = n16 & sum(n10, n5) = n15 & sum(n10, n4) = n14 & sum(n10, n3) = n13 & sum(n10, n2) = n12 & sum(n10, n1) = n11 & sum(n10, n0) = n10 & sum(n9, n20) = n8 & sum(n9, n19) = n7 & sum(n9, n18) = n6 & sum(n9, n17) = n5 & sum(n9, n16) = n4 & sum(n9, n15) = n3 & sum(n9, n14) = n2 & sum(n9, n13) = n1 & sum(n9, n12) = n0 & sum(n9, n11) = n20 & sum(n9, n10) = n19 & sum(n9, n9) = n18 & sum(n9, n8) = n17 & sum(n9, n7) = n16 & sum(n9, n6) = n15 & sum(n9, n5) = n14 & sum(n9, n4) = n13 & sum(n9, n3) = n12 & sum(n9, n2) = n11 & sum(n9, n1) = n10 & sum(n9, n0) = n9 & sum(n8, n20) = n7 & sum(n8, n19) = n6 & sum(n8, n18) = n5 & sum(n8, n17) = n4 & sum(n8, n16) = n3 & sum(n8, n15) = n2 & sum(n8, n14) = n1 & sum(n8, n13) = n0 & sum(n8, n12) = n20 & sum(n8, n11) = n19 & sum(n8, n10) = n18 & sum(n8, n9) = n17 & sum(n8, n8) = n16 & sum(n8, n7) = n15 & sum(n8, n6) = n14 & sum(n8, n5) = n13 & sum(n8, n4) = n12 & sum(n8, n3) = n11 & sum(n8, n2) = n10 & sum(n8, n1) = n9 & sum(n8, n0) = n8 & sum(n7, n20) = n6 & sum(n7, n19) = n5 & sum(n7, n18) = n4 & sum(n7, n17) = n3 & sum(n7, n16) = n2 & sum(n7, n15) = n1 & sum(n7, n14) = n0 & sum(n7, n13) = n20 & sum(n7, n12) = n19 & sum(n7, n11) = n18 & sum(n7, n10) = n17 & sum(n7, n9) = n16 & sum(n7, n8) = n15 & sum(n7, n7) = n14 & sum(n7, n6) = n13 & sum(n7, n5) = n12 & sum(n7, n4) = n11 & sum(n7, n3) = n10 & sum(n7, n2) = n9 & sum(n7, n1) = n8 & sum(n7, n0) = n7 & sum(n6, n20) = n5 & sum(n6, n19) = n4 & sum(n6, n18) = n3 & sum(n6, n17) = n2 & sum(n6, n16) = n1 & sum(n6, n15) = n0 & sum(n6, n14) = n20 & sum(n6, n13) = n19 & sum(n6, n12) = n18 & sum(n6, n11) = n17 & sum(n6, n10) = n16 & sum(n6, n9) = n15 & sum(n6, n8) = n14 & sum(n6, n7) = n13 & sum(n6, n6) = n12 & sum(n6, n5) = n11 & sum(n6, n4) = n10 & sum(n6, n3) = n9 & sum(n6, n2) = n8 & sum(n6, n1) = n7 & sum(n6, n0) = n6 & sum(n5, n20) = n4 & sum(n5, n19) = n3 & sum(n5, n18) = n2 & sum(n5, n17) = n1 & sum(n5, n16) = n0 & sum(n5, n15) = n20 & sum(n5, n14) = n19 & sum(n5, n13) = n18 & sum(n5, n12) = n17 & sum(n5, n11) = n16 & sum(n5, n10) = n15 & sum(n5, n9) = n14 & sum(n5, n8) = n13 & sum(n5, n7) = n12 & sum(n5, n6) = n11 & sum(n5, n5) = n10 & sum(n5, n4) = n9 & sum(n5, n3) = n8 & sum(n5, n2) = n7 & sum(n5, n1) = n6 & sum(n5, n0) = n5 & sum(n4, n20) = n3 & sum(n4, n19) = n2 & sum(n4, n18) = n1 & sum(n4, n17) = n0 & sum(n4, n16) = n20 & sum(n4, n15) = n19 & sum(n4, n14) = n18 & sum(n4, n13) = n17 & sum(n4, n12) = n16 & sum(n4, n11) = n15 & sum(n4, n10) = n14 & sum(n4, n9) = n13 & sum(n4, n8) = n12 & sum(n4, n7) = n11 & sum(n4, n6) = n10 & sum(n4, n5) = n9 & sum(n4, n4) = n8 & sum(n4, n3) = n7 & sum(n4, n2) = n6 & sum(n4, n1) = n5 & sum(n4, n0) = n4 & sum(n3, n20) = n2 & sum(n3, n19) = n1 & sum(n3, n18) = n0 & sum(n3, n17) = n20 & sum(n3, n16) = n19 & sum(n3, n15) = n18 & sum(n3, n14) = n17 & sum(n3, n13) = n16 & sum(n3, n12) = n15 & sum(n3, n11) = n14 & sum(n3, n10) = n13 & sum(n3, n9) = n12 & sum(n3, n8) = n11 & sum(n3, n7) = n10 & sum(n3, n6) = n9 & sum(n3, n5) = n8 & sum(n3, n4) = n7 & sum(n3, n3) = n6 & sum(n3, n2) = n5 & sum(n3, n1) = n4 & sum(n3, n0) = n3 & sum(n2, n20) = n1 & sum(n2, n19) = n0 & sum(n2, n18) = n20 & sum(n2, n17) = n19 & sum(n2, n16) = n18 & sum(n2, n15) = n17 & sum(n2, n14) = n16 & sum(n2, n13) = n15 & sum(n2, n12) = n14 & sum(n2, n11) = n13 & sum(n2, n10) = n12 & sum(n2, n9) = n11 & sum(n2, n8) = n10 & sum(n2, n7) = n9 & sum(n2, n6) = n8 & sum(n2, n5) = n7 & sum(n2, n4) = n6 & sum(n2, n3) = n5 & sum(n2, n2) = n4 & sum(n2, n1) = n3 & sum(n2, n0) = n2 & sum(n1, n20) = n0 & sum(n1, n19) = n20 & sum(n1, n18) = n19 & sum(n1, n17) = n18 & sum(n1, n16) = n17 & sum(n1, n15) = n16 & sum(n1, n14) = n15 & sum(n1, n13) = n14 & sum(n1, n12) = n13 & sum(n1, n11) = n12 & sum(n1, n10) = n11 & sum(n1, n9) = n10 & sum(n1, n8) = n9 & sum(n1, n7) = n8 & sum(n1, n6) = n7 & sum(n1, n5) = n6 & sum(n1, n4) = n5 & sum(n1, n3) = n4 & sum(n1, n2) = n3 & sum(n1, n1) = n2 & sum(n1, n0) = n1 & sum(n0, n20) = n20 & sum(n0, n19) = n19 & sum(n0, n18) = n18 & sum(n0, n17) = n17 & sum(n0, n16) = n16 & sum(n0, n15) = n15 & sum(n0, n14) = n14 & sum(n0, n13) = n13 & sum(n0, n12) = n12 & sum(n0, n11) = n11 & sum(n0, n10) = n10 & sum(n0, n9) = n9 & sum(n0, n8) = n8 & sum(n0, n7) = n7 & sum(n0, n6) = n6 & sum(n0, n5) = n5 & sum(n0, n4) = n4 & sum(n0, n3) = n3 & sum(n0, n2) = n2 & sum(n0, n1) = n1 & sum(n0, n0) = n0 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sum(v12, v11) = v10) | ~ (sum(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (succ(v11) = v10) | ~ (succ(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (pred(v11) = v10) | ~ (pred(v11) = v9)) & (v1 = n20 | v1 = n19 | v1 = n18 | v1 = n17 | v1 = n16 | v1 = n15 | v1 = n14 | v1 = n13 | v1 = n12 | v1 = n11 | v1 = n10 | v1 = n9 | v1 = n8 | v1 = n7 | v1 = n6 | v1 = n5 | v1 = n4 | v1 = n3 | v1 = n2 | v1 = n1 | v1 = n0) & (v0 = n20 | v0 = n19 | v0 = n18 | v0 = n17 | v0 = n16 | v0 = n15 | v0 = n14 | v0 = n13 | v0 = n12 | v0 = n11 | v0 = n10 | v0 = n9 | v0 = n8 | v0 = n7 | v0 = n6 | v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0))
% 28.37/9.67 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 yields:
% 28.37/9.67 | (1) ~ (all_0_6_6 = n20) & ~ (all_0_6_6 = n19) & ~ (all_0_6_6 = n18) & ~ (all_0_6_6 = n17) & ~ (all_0_6_6 = n16) & ~ (all_0_6_6 = n15) & ~ (all_0_6_6 = n14) & ~ (all_0_6_6 = n13) & ~ (all_0_6_6 = n12) & ~ (all_0_6_6 = n11) & ~ (all_0_6_6 = n10) & ~ (all_0_6_6 = n9) & ~ (all_0_6_6 = n8) & ~ (all_0_6_6 = n7) & ~ (all_0_6_6 = n6) & ~ (all_0_6_6 = n5) & ~ (all_0_6_6 = n4) & ~ (all_0_6_6 = n3) & ~ (all_0_6_6 = n2) & ~ (all_0_6_6 = n1) & ~ (all_0_6_6 = n0) & ~ (n20 = n19) & ~ (n20 = n18) & ~ (n20 = n17) & ~ (n20 = n16) & ~ (n20 = n15) & ~ (n20 = n14) & ~ (n20 = n13) & ~ (n20 = n12) & ~ (n20 = n11) & ~ (n20 = n10) & ~ (n20 = n9) & ~ (n20 = n8) & ~ (n20 = n7) & ~ (n20 = n6) & ~ (n20 = n5) & ~ (n20 = n4) & ~ (n20 = n3) & ~ (n20 = n2) & ~ (n20 = n1) & ~ (n20 = n0) & ~ (n19 = n18) & ~ (n19 = n17) & ~ (n19 = n16) & ~ (n19 = n15) & ~ (n19 = n14) & ~ (n19 = n13) & ~ (n19 = n12) & ~ (n19 = n11) & ~ (n19 = n10) & ~ (n19 = n9) & ~ (n19 = n8) & ~ (n19 = n7) & ~ (n19 = n6) & ~ (n19 = n5) & ~ (n19 = n4) & ~ (n19 = n3) & ~ (n19 = n2) & ~ (n19 = n1) & ~ (n19 = n0) & ~ (n18 = n17) & ~ (n18 = n16) & ~ (n18 = n15) & ~ (n18 = n14) & ~ (n18 = n13) & ~ (n18 = n12) & ~ (n18 = n11) & ~ (n18 = n10) & ~ (n18 = n9) & ~ (n18 = n8) & ~ (n18 = n7) & ~ (n18 = n6) & ~ (n18 = n5) & ~ (n18 = n4) & ~ (n18 = n3) & ~ (n18 = n2) & ~ (n18 = n1) & ~ (n18 = n0) & ~ (n17 = n16) & ~ (n17 = n15) & ~ (n17 = n14) & ~ (n17 = n13) & ~ (n17 = n12) & ~ (n17 = n11) & ~ (n17 = n10) & ~ (n17 = n9) & ~ (n17 = n8) & ~ (n17 = n7) & ~ (n17 = n6) & ~ (n17 = n5) & ~ (n17 = n4) & ~ (n17 = n3) & ~ (n17 = n2) & ~ (n17 = n1) & ~ (n17 = n0) & ~ (n16 = n15) & ~ (n16 = n14) & ~ (n16 = n13) & ~ (n16 = n12) & ~ (n16 = n11) & ~ (n16 = n10) & ~ (n16 = n9) & ~ (n16 = n8) & ~ (n16 = n7) & ~ (n16 = n6) & ~ (n16 = n5) & ~ (n16 = n4) & ~ (n16 = n3) & ~ (n16 = n2) & ~ (n16 = n1) & ~ (n16 = n0) & ~ (n15 = n14) & ~ (n15 = n13) & ~ (n15 = n12) & ~ (n15 = n11) & ~ (n15 = n10) & ~ (n15 = n9) & ~ (n15 = n8) & ~ (n15 = n7) & ~ (n15 = n6) & ~ (n15 = n5) & ~ (n15 = n4) & ~ (n15 = n3) & ~ (n15 = n2) & ~ (n15 = n1) & ~ (n15 = n0) & ~ (n14 = n13) & ~ (n14 = n12) & ~ (n14 = n11) & ~ (n14 = n10) & ~ (n14 = n9) & ~ (n14 = n8) & ~ (n14 = n7) & ~ (n14 = n6) & ~ (n14 = n5) & ~ (n14 = n4) & ~ (n14 = n3) & ~ (n14 = n2) & ~ (n14 = n1) & ~ (n14 = n0) & ~ (n13 = n12) & ~ (n13 = n11) & ~ (n13 = n10) & ~ (n13 = n9) & ~ (n13 = n8) & ~ (n13 = n7) & ~ (n13 = n6) & ~ (n13 = n5) & ~ (n13 = n4) & ~ (n13 = n3) & ~ (n13 = n2) & ~ (n13 = n1) & ~ (n13 = n0) & ~ (n12 = n11) & ~ (n12 = n10) & ~ (n12 = n9) & ~ (n12 = n8) & ~ (n12 = n7) & ~ (n12 = n6) & ~ (n12 = n5) & ~ (n12 = n4) & ~ (n12 = n3) & ~ (n12 = n2) & ~ (n12 = n1) & ~ (n12 = n0) & ~ (n11 = n10) & ~ (n11 = n9) & ~ (n11 = n8) & ~ (n11 = n7) & ~ (n11 = n6) & ~ (n11 = n5) & ~ (n11 = n4) & ~ (n11 = n3) & ~ (n11 = n2) & ~ (n11 = n1) & ~ (n11 = n0) & ~ (n10 = n9) & ~ (n10 = n8) & ~ (n10 = n7) & ~ (n10 = n6) & ~ (n10 = n5) & ~ (n10 = n4) & ~ (n10 = n3) & ~ (n10 = n2) & ~ (n10 = n1) & ~ (n10 = n0) & ~ (n9 = n8) & ~ (n9 = n7) & ~ (n9 = n6) & ~ (n9 = n5) & ~ (n9 = n4) & ~ (n9 = n3) & ~ (n9 = n2) & ~ (n9 = n1) & ~ (n9 = n0) & ~ (n8 = n7) & ~ (n8 = n6) & ~ (n8 = n5) & ~ (n8 = n4) & ~ (n8 = n3) & ~ (n8 = n2) & ~ (n8 = n1) & ~ (n8 = n0) & ~ (n7 = n6) & ~ (n7 = n5) & ~ (n7 = n4) & ~ (n7 = n3) & ~ (n7 = n2) & ~ (n7 = n1) & ~ (n7 = n0) & ~ (n6 = n5) & ~ (n6 = n4) & ~ (n6 = n3) & ~ (n6 = n2) & ~ (n6 = n1) & ~ (n6 = n0) & ~ (n5 = n4) & ~ (n5 = n3) & ~ (n5 = n2) & ~ (n5 = n1) & ~ (n5 = n0) & ~ (n4 = n3) & ~ (n4 = n2) & ~ (n4 = n1) & ~ (n4 = n0) & ~ (n3 = n2) & ~ (n3 = n1) & ~ (n3 = n0) & ~ (n2 = n1) & ~ (n2 = n0) & ~ (n1 = n0) & succ(all_0_7_7) = all_0_5_5 & succ(n20) = n0 & succ(n19) = n20 & succ(n18) = n19 & succ(n17) = n18 & succ(n16) = n17 & succ(n15) = n16 & succ(n14) = n15 & succ(n13) = n14 & succ(n12) = n13 & succ(n11) = n12 & succ(n10) = n11 & succ(n9) = n10 & succ(n8) = n9 & succ(n7) = n8 & succ(n6) = n7 & succ(n5) = n6 & succ(n4) = n5 & succ(n3) = n4 & succ(n2) = n3 & succ(n1) = n2 & succ(n0) = n1 & pred(all_0_2_2) = all_0_1_1 & pred(all_0_4_4) = all_0_3_3 & pred(n20) = n19 & pred(n19) = n18 & pred(n18) = n17 & pred(n17) = n16 & pred(n16) = n15 & pred(n15) = n14 & pred(n14) = n13 & pred(n13) = n12 & pred(n12) = n11 & pred(n11) = n10 & pred(n10) = n9 & pred(n9) = n8 & pred(n8) = n7 & pred(n7) = n6 & pred(n6) = n5 & pred(n5) = n4 & pred(n4) = n3 & pred(n3) = n2 & pred(n2) = n1 & pred(n1) = n0 & pred(n0) = n20 & sum(all_0_3_3, all_0_0_0) = all_0_6_6 & sum(all_0_7_7, all_0_1_1) = all_0_0_0 & sum(all_0_8_8, all_0_5_5) = all_0_4_4 & sum(all_0_8_8, all_0_7_7) = all_0_2_2 & sum(n20, n20) = n19 & sum(n20, n19) = n18 & sum(n20, n18) = n17 & sum(n20, n17) = n16 & sum(n20, n16) = n15 & sum(n20, n15) = n14 & sum(n20, n14) = n13 & sum(n20, n13) = n12 & sum(n20, n12) = n11 & sum(n20, n11) = n10 & sum(n20, n10) = n9 & sum(n20, n9) = n8 & sum(n20, n8) = n7 & sum(n20, n7) = n6 & sum(n20, n6) = n5 & sum(n20, n5) = n4 & sum(n20, n4) = n3 & sum(n20, n3) = n2 & sum(n20, n2) = n1 & sum(n20, n1) = n0 & sum(n20, n0) = n20 & sum(n19, n20) = n18 & sum(n19, n19) = n17 & sum(n19, n18) = n16 & sum(n19, n17) = n15 & sum(n19, n16) = n14 & sum(n19, n15) = n13 & sum(n19, n14) = n12 & sum(n19, n13) = n11 & sum(n19, n12) = n10 & sum(n19, n11) = n9 & sum(n19, n10) = n8 & sum(n19, n9) = n7 & sum(n19, n8) = n6 & sum(n19, n7) = n5 & sum(n19, n6) = n4 & sum(n19, n5) = n3 & sum(n19, n4) = n2 & sum(n19, n3) = n1 & sum(n19, n2) = n0 & sum(n19, n1) = n20 & sum(n19, n0) = n19 & sum(n18, n20) = n17 & sum(n18, n19) = n16 & sum(n18, n18) = n15 & sum(n18, n17) = n14 & sum(n18, n16) = n13 & sum(n18, n15) = n12 & sum(n18, n14) = n11 & sum(n18, n13) = n10 & sum(n18, n12) = n9 & sum(n18, n11) = n8 & sum(n18, n10) = n7 & sum(n18, n9) = n6 & sum(n18, n8) = n5 & sum(n18, n7) = n4 & sum(n18, n6) = n3 & sum(n18, n5) = n2 & sum(n18, n4) = n1 & sum(n18, n3) = n0 & sum(n18, n2) = n20 & sum(n18, n1) = n19 & sum(n18, n0) = n18 & sum(n17, n20) = n16 & sum(n17, n19) = n15 & sum(n17, n18) = n14 & sum(n17, n17) = n13 & sum(n17, n16) = n12 & sum(n17, n15) = n11 & sum(n17, n14) = n10 & sum(n17, n13) = n9 & sum(n17, n12) = n8 & sum(n17, n11) = n7 & sum(n17, n10) = n6 & sum(n17, n9) = n5 & sum(n17, n8) = n4 & sum(n17, n7) = n3 & sum(n17, n6) = n2 & sum(n17, n5) = n1 & sum(n17, n4) = n0 & sum(n17, n3) = n20 & sum(n17, n2) = n19 & sum(n17, n1) = n18 & sum(n17, n0) = n17 & sum(n16, n20) = n15 & sum(n16, n19) = n14 & sum(n16, n18) = n13 & sum(n16, n17) = n12 & sum(n16, n16) = n11 & sum(n16, n15) = n10 & sum(n16, n14) = n9 & sum(n16, n13) = n8 & sum(n16, n12) = n7 & sum(n16, n11) = n6 & sum(n16, n10) = n5 & sum(n16, n9) = n4 & sum(n16, n8) = n3 & sum(n16, n7) = n2 & sum(n16, n6) = n1 & sum(n16, n5) = n0 & sum(n16, n4) = n20 & sum(n16, n3) = n19 & sum(n16, n2) = n18 & sum(n16, n1) = n17 & sum(n16, n0) = n16 & sum(n15, n20) = n14 & sum(n15, n19) = n13 & sum(n15, n18) = n12 & sum(n15, n17) = n11 & sum(n15, n16) = n10 & sum(n15, n15) = n9 & sum(n15, n14) = n8 & sum(n15, n13) = n7 & sum(n15, n12) = n6 & sum(n15, n11) = n5 & sum(n15, n10) = n4 & sum(n15, n9) = n3 & sum(n15, n8) = n2 & sum(n15, n7) = n1 & sum(n15, n6) = n0 & sum(n15, n5) = n20 & sum(n15, n4) = n19 & sum(n15, n3) = n18 & sum(n15, n2) = n17 & sum(n15, n1) = n16 & sum(n15, n0) = n15 & sum(n14, n20) = n13 & sum(n14, n19) = n12 & sum(n14, n18) = n11 & sum(n14, n17) = n10 & sum(n14, n16) = n9 & sum(n14, n15) = n8 & sum(n14, n14) = n7 & sum(n14, n13) = n6 & sum(n14, n12) = n5 & sum(n14, n11) = n4 & sum(n14, n10) = n3 & sum(n14, n9) = n2 & sum(n14, n8) = n1 & sum(n14, n7) = n0 & sum(n14, n6) = n20 & sum(n14, n5) = n19 & sum(n14, n4) = n18 & sum(n14, n3) = n17 & sum(n14, n2) = n16 & sum(n14, n1) = n15 & sum(n14, n0) = n14 & sum(n13, n20) = n12 & sum(n13, n19) = n11 & sum(n13, n18) = n10 & sum(n13, n17) = n9 & sum(n13, n16) = n8 & sum(n13, n15) = n7 & sum(n13, n14) = n6 & sum(n13, n13) = n5 & sum(n13, n12) = n4 & sum(n13, n11) = n3 & sum(n13, n10) = n2 & sum(n13, n9) = n1 & sum(n13, n8) = n0 & sum(n13, n7) = n20 & sum(n13, n6) = n19 & sum(n13, n5) = n18 & sum(n13, n4) = n17 & sum(n13, n3) = n16 & sum(n13, n2) = n15 & sum(n13, n1) = n14 & sum(n13, n0) = n13 & sum(n12, n20) = n11 & sum(n12, n19) = n10 & sum(n12, n18) = n9 & sum(n12, n17) = n8 & sum(n12, n16) = n7 & sum(n12, n15) = n6 & sum(n12, n14) = n5 & sum(n12, n13) = n4 & sum(n12, n12) = n3 & sum(n12, n11) = n2 & sum(n12, n10) = n1 & sum(n12, n9) = n0 & sum(n12, n8) = n20 & sum(n12, n7) = n19 & sum(n12, n6) = n18 & sum(n12, n5) = n17 & sum(n12, n4) = n16 & sum(n12, n3) = n15 & sum(n12, n2) = n14 & sum(n12, n1) = n13 & sum(n12, n0) = n12 & sum(n11, n20) = n10 & sum(n11, n19) = n9 & sum(n11, n18) = n8 & sum(n11, n17) = n7 & sum(n11, n16) = n6 & sum(n11, n15) = n5 & sum(n11, n14) = n4 & sum(n11, n13) = n3 & sum(n11, n12) = n2 & sum(n11, n11) = n1 & sum(n11, n10) = n0 & sum(n11, n9) = n20 & sum(n11, n8) = n19 & sum(n11, n7) = n18 & sum(n11, n6) = n17 & sum(n11, n5) = n16 & sum(n11, n4) = n15 & sum(n11, n3) = n14 & sum(n11, n2) = n13 & sum(n11, n1) = n12 & sum(n11, n0) = n11 & sum(n10, n20) = n9 & sum(n10, n19) = n8 & sum(n10, n18) = n7 & sum(n10, n17) = n6 & sum(n10, n16) = n5 & sum(n10, n15) = n4 & sum(n10, n14) = n3 & sum(n10, n13) = n2 & sum(n10, n12) = n1 & sum(n10, n11) = n0 & sum(n10, n10) = n20 & sum(n10, n9) = n19 & sum(n10, n8) = n18 & sum(n10, n7) = n17 & sum(n10, n6) = n16 & sum(n10, n5) = n15 & sum(n10, n4) = n14 & sum(n10, n3) = n13 & sum(n10, n2) = n12 & sum(n10, n1) = n11 & sum(n10, n0) = n10 & sum(n9, n20) = n8 & sum(n9, n19) = n7 & sum(n9, n18) = n6 & sum(n9, n17) = n5 & sum(n9, n16) = n4 & sum(n9, n15) = n3 & sum(n9, n14) = n2 & sum(n9, n13) = n1 & sum(n9, n12) = n0 & sum(n9, n11) = n20 & sum(n9, n10) = n19 & sum(n9, n9) = n18 & sum(n9, n8) = n17 & sum(n9, n7) = n16 & sum(n9, n6) = n15 & sum(n9, n5) = n14 & sum(n9, n4) = n13 & sum(n9, n3) = n12 & sum(n9, n2) = n11 & sum(n9, n1) = n10 & sum(n9, n0) = n9 & sum(n8, n20) = n7 & sum(n8, n19) = n6 & sum(n8, n18) = n5 & sum(n8, n17) = n4 & sum(n8, n16) = n3 & sum(n8, n15) = n2 & sum(n8, n14) = n1 & sum(n8, n13) = n0 & sum(n8, n12) = n20 & sum(n8, n11) = n19 & sum(n8, n10) = n18 & sum(n8, n9) = n17 & sum(n8, n8) = n16 & sum(n8, n7) = n15 & sum(n8, n6) = n14 & sum(n8, n5) = n13 & sum(n8, n4) = n12 & sum(n8, n3) = n11 & sum(n8, n2) = n10 & sum(n8, n1) = n9 & sum(n8, n0) = n8 & sum(n7, n20) = n6 & sum(n7, n19) = n5 & sum(n7, n18) = n4 & sum(n7, n17) = n3 & sum(n7, n16) = n2 & sum(n7, n15) = n1 & sum(n7, n14) = n0 & sum(n7, n13) = n20 & sum(n7, n12) = n19 & sum(n7, n11) = n18 & sum(n7, n10) = n17 & sum(n7, n9) = n16 & sum(n7, n8) = n15 & sum(n7, n7) = n14 & sum(n7, n6) = n13 & sum(n7, n5) = n12 & sum(n7, n4) = n11 & sum(n7, n3) = n10 & sum(n7, n2) = n9 & sum(n7, n1) = n8 & sum(n7, n0) = n7 & sum(n6, n20) = n5 & sum(n6, n19) = n4 & sum(n6, n18) = n3 & sum(n6, n17) = n2 & sum(n6, n16) = n1 & sum(n6, n15) = n0 & sum(n6, n14) = n20 & sum(n6, n13) = n19 & sum(n6, n12) = n18 & sum(n6, n11) = n17 & sum(n6, n10) = n16 & sum(n6, n9) = n15 & sum(n6, n8) = n14 & sum(n6, n7) = n13 & sum(n6, n6) = n12 & sum(n6, n5) = n11 & sum(n6, n4) = n10 & sum(n6, n3) = n9 & sum(n6, n2) = n8 & sum(n6, n1) = n7 & sum(n6, n0) = n6 & sum(n5, n20) = n4 & sum(n5, n19) = n3 & sum(n5, n18) = n2 & sum(n5, n17) = n1 & sum(n5, n16) = n0 & sum(n5, n15) = n20 & sum(n5, n14) = n19 & sum(n5, n13) = n18 & sum(n5, n12) = n17 & sum(n5, n11) = n16 & sum(n5, n10) = n15 & sum(n5, n9) = n14 & sum(n5, n8) = n13 & sum(n5, n7) = n12 & sum(n5, n6) = n11 & sum(n5, n5) = n10 & sum(n5, n4) = n9 & sum(n5, n3) = n8 & sum(n5, n2) = n7 & sum(n5, n1) = n6 & sum(n5, n0) = n5 & sum(n4, n20) = n3 & sum(n4, n19) = n2 & sum(n4, n18) = n1 & sum(n4, n17) = n0 & sum(n4, n16) = n20 & sum(n4, n15) = n19 & sum(n4, n14) = n18 & sum(n4, n13) = n17 & sum(n4, n12) = n16 & sum(n4, n11) = n15 & sum(n4, n10) = n14 & sum(n4, n9) = n13 & sum(n4, n8) = n12 & sum(n4, n7) = n11 & sum(n4, n6) = n10 & sum(n4, n5) = n9 & sum(n4, n4) = n8 & sum(n4, n3) = n7 & sum(n4, n2) = n6 & sum(n4, n1) = n5 & sum(n4, n0) = n4 & sum(n3, n20) = n2 & sum(n3, n19) = n1 & sum(n3, n18) = n0 & sum(n3, n17) = n20 & sum(n3, n16) = n19 & sum(n3, n15) = n18 & sum(n3, n14) = n17 & sum(n3, n13) = n16 & sum(n3, n12) = n15 & sum(n3, n11) = n14 & sum(n3, n10) = n13 & sum(n3, n9) = n12 & sum(n3, n8) = n11 & sum(n3, n7) = n10 & sum(n3, n6) = n9 & sum(n3, n5) = n8 & sum(n3, n4) = n7 & sum(n3, n3) = n6 & sum(n3, n2) = n5 & sum(n3, n1) = n4 & sum(n3, n0) = n3 & sum(n2, n20) = n1 & sum(n2, n19) = n0 & sum(n2, n18) = n20 & sum(n2, n17) = n19 & sum(n2, n16) = n18 & sum(n2, n15) = n17 & sum(n2, n14) = n16 & sum(n2, n13) = n15 & sum(n2, n12) = n14 & sum(n2, n11) = n13 & sum(n2, n10) = n12 & sum(n2, n9) = n11 & sum(n2, n8) = n10 & sum(n2, n7) = n9 & sum(n2, n6) = n8 & sum(n2, n5) = n7 & sum(n2, n4) = n6 & sum(n2, n3) = n5 & sum(n2, n2) = n4 & sum(n2, n1) = n3 & sum(n2, n0) = n2 & sum(n1, n20) = n0 & sum(n1, n19) = n20 & sum(n1, n18) = n19 & sum(n1, n17) = n18 & sum(n1, n16) = n17 & sum(n1, n15) = n16 & sum(n1, n14) = n15 & sum(n1, n13) = n14 & sum(n1, n12) = n13 & sum(n1, n11) = n12 & sum(n1, n10) = n11 & sum(n1, n9) = n10 & sum(n1, n8) = n9 & sum(n1, n7) = n8 & sum(n1, n6) = n7 & sum(n1, n5) = n6 & sum(n1, n4) = n5 & sum(n1, n3) = n4 & sum(n1, n2) = n3 & sum(n1, n1) = n2 & sum(n1, n0) = n1 & sum(n0, n20) = n20 & sum(n0, n19) = n19 & sum(n0, n18) = n18 & sum(n0, n17) = n17 & sum(n0, n16) = n16 & sum(n0, n15) = n15 & sum(n0, n14) = n14 & sum(n0, n13) = n13 & sum(n0, n12) = n12 & sum(n0, n11) = n11 & sum(n0, n10) = n10 & sum(n0, n9) = n9 & sum(n0, n8) = n8 & sum(n0, n7) = n7 & sum(n0, n6) = n6 & sum(n0, n5) = n5 & sum(n0, n4) = n4 & sum(n0, n3) = n3 & sum(n0, n2) = n2 & sum(n0, n1) = n1 & sum(n0, n0) = n0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) & (all_0_7_7 = n20 | all_0_7_7 = n19 | all_0_7_7 = n18 | all_0_7_7 = n17 | all_0_7_7 = n16 | all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0) & (all_0_8_8 = n20 | all_0_8_8 = n19 | all_0_8_8 = n18 | all_0_8_8 = n17 | all_0_8_8 = n16 | all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0)
% 28.37/9.71 |
% 28.37/9.71 | Applying alpha-rule on (1) yields:
% 28.37/9.71 | (2) ~ (all_0_6_6 = n11)
% 28.37/9.71 | (3) ~ (n14 = n6)
% 28.37/9.71 | (4) sum(n13, n18) = n10
% 28.37/9.71 | (5) sum(n10, n0) = n10
% 28.64/9.71 | (6) sum(n7, n19) = n5
% 28.64/9.71 | (7) sum(n1, n11) = n12
% 28.64/9.71 | (8) sum(all_0_7_7, all_0_1_1) = all_0_0_0
% 28.64/9.71 | (9) sum(n13, n1) = n14
% 28.64/9.71 | (10) sum(n16, n10) = n5
% 28.64/9.71 | (11) sum(n1, n9) = n10
% 28.64/9.71 | (12) sum(n6, n5) = n11
% 28.64/9.71 | (13) sum(n19, n18) = n16
% 28.64/9.71 | (14) pred(n18) = n17
% 28.64/9.71 | (15) ~ (n13 = n11)
% 28.64/9.71 | (16) ~ (n12 = n8)
% 28.64/9.71 | (17) all_0_7_7 = n20 | all_0_7_7 = n19 | all_0_7_7 = n18 | all_0_7_7 = n17 | all_0_7_7 = n16 | all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 28.64/9.71 | (18) ~ (n5 = n4)
% 28.64/9.71 | (19) ~ (n12 = n1)
% 28.64/9.71 | (20) ~ (n14 = n2)
% 28.64/9.71 | (21) sum(n6, n11) = n17
% 28.64/9.71 | (22) sum(n12, n9) = n0
% 28.64/9.71 | (23) ~ (n6 = n1)
% 28.64/9.71 | (24) ~ (n20 = n17)
% 28.64/9.71 | (25) sum(n7, n3) = n10
% 28.64/9.71 | (26) sum(n7, n4) = n11
% 28.64/9.71 | (27) sum(n7, n10) = n17
% 28.64/9.71 | (28) ~ (all_0_6_6 = n1)
% 28.64/9.71 | (29) sum(n12, n7) = n19
% 28.64/9.71 | (30) sum(n7, n2) = n9
% 28.64/9.71 | (31) ~ (all_0_6_6 = n19)
% 28.64/9.71 | (32) sum(n2, n11) = n13
% 28.64/9.71 | (33) sum(n10, n19) = n8
% 28.64/9.71 | (34) ~ (n15 = n10)
% 28.64/9.71 | (35) sum(n13, n5) = n18
% 28.64/9.71 | (36) succ(n6) = n7
% 28.64/9.71 | (37) ~ (n11 = n9)
% 28.64/9.71 | (38) sum(n3, n2) = n5
% 28.64/9.71 | (39) ~ (n11 = n4)
% 28.64/9.71 | (40) sum(n7, n17) = n3
% 28.64/9.72 | (41) ~ (n18 = n2)
% 28.64/9.72 | (42) sum(n15, n2) = n17
% 28.64/9.72 | (43) ~ (n13 = n4)
% 28.64/9.72 | (44) ~ (n19 = n2)
% 28.64/9.72 | (45) ~ (n9 = n4)
% 28.64/9.72 | (46) ~ (n16 = n0)
% 28.64/9.72 | (47) sum(n13, n12) = n4
% 28.64/9.72 | (48) ~ (all_0_6_6 = n4)
% 28.64/9.72 | (49) sum(n9, n15) = n3
% 28.64/9.72 | (50) ~ (n16 = n3)
% 28.64/9.72 | (51) sum(n8, n0) = n8
% 28.64/9.72 | (52) ~ (n20 = n14)
% 28.64/9.72 | (53) ~ (n11 = n3)
% 28.64/9.72 | (54) sum(n4, n6) = n10
% 28.64/9.72 | (55) sum(n16, n7) = n2
% 28.64/9.72 | (56) ~ (all_0_6_6 = n2)
% 28.64/9.72 | (57) ~ (n12 = n3)
% 28.64/9.72 | (58) sum(n16, n11) = n6
% 28.64/9.72 | (59) sum(n0, n7) = n7
% 28.64/9.72 | (60) sum(n20, n13) = n12
% 28.64/9.72 | (61) sum(n16, n17) = n12
% 28.64/9.72 | (62) sum(n9, n4) = n13
% 28.64/9.72 | (63) sum(n19, n10) = n8
% 28.64/9.72 | (64) sum(n1, n12) = n13
% 28.64/9.72 | (65) pred(n20) = n19
% 28.64/9.72 | (66) sum(n0, n5) = n5
% 28.64/9.72 | (67) sum(n17, n15) = n11
% 28.64/9.72 | (68) sum(n5, n18) = n2
% 28.64/9.72 | (69) sum(n19, n1) = n20
% 28.64/9.72 | (70) sum(n15, n3) = n18
% 28.64/9.72 | (71) sum(n6, n13) = n19
% 28.64/9.72 | (72) ~ (n19 = n10)
% 28.64/9.72 | (73) sum(n2, n15) = n17
% 28.64/9.72 | (74) ~ (n20 = n1)
% 28.64/9.72 | (75) ~ (n16 = n11)
% 28.64/9.72 | (76) ~ (all_0_6_6 = n12)
% 28.64/9.72 | (77) sum(n20, n18) = n17
% 28.64/9.72 | (78) sum(n13, n8) = n0
% 28.64/9.72 | (79) sum(n12, n4) = n16
% 28.64/9.72 | (80) ~ (n18 = n11)
% 28.64/9.72 | (81) ~ (n20 = n10)
% 28.64/9.72 | (82) sum(n6, n7) = n13
% 28.64/9.72 | (83) sum(n11, n17) = n7
% 28.64/9.72 | (84) sum(n3, n20) = n2
% 28.64/9.72 | (85) sum(n8, n14) = n1
% 28.64/9.72 | (86) sum(n6, n17) = n2
% 28.64/9.72 | (87) ~ (n15 = n9)
% 28.64/9.72 | (88) sum(n0, n2) = n2
% 28.64/9.72 | (89) sum(n20, n5) = n4
% 28.64/9.72 | (90) ~ (n9 = n0)
% 28.64/9.72 | (91) ~ (n15 = n12)
% 28.64/9.72 | (92) succ(n18) = n19
% 28.64/9.72 | (93) ~ (n6 = n3)
% 28.64/9.72 | (94) sum(n11, n2) = n13
% 28.64/9.72 | (95) ~ (n14 = n12)
% 28.64/9.72 | (96) sum(n3, n10) = n13
% 28.64/9.72 | (97) sum(n16, n9) = n4
% 28.64/9.72 | (98) ~ (n18 = n16)
% 28.64/9.72 | (99) sum(n9, n0) = n9
% 28.64/9.72 | (100) sum(n3, n4) = n7
% 28.64/9.72 | (101) ~ (n7 = n5)
% 28.64/9.72 | (102) sum(n19, n15) = n13
% 28.64/9.72 | (103) pred(n6) = n5
% 28.64/9.72 | (104) ~ (n11 = n7)
% 28.64/9.72 | (105) sum(n12, n0) = n12
% 28.64/9.72 | (106) sum(n2, n6) = n8
% 28.64/9.72 | (107) sum(n18, n2) = n20
% 28.64/9.72 | (108) sum(n18, n6) = n3
% 28.64/9.72 | (109) sum(n0, n18) = n18
% 28.64/9.72 | (110) sum(n19, n19) = n17
% 28.64/9.72 | (111) sum(n1, n15) = n16
% 28.64/9.72 | (112) ~ (n13 = n12)
% 28.64/9.72 | (113) sum(n14, n5) = n19
% 28.64/9.72 | (114) sum(n8, n18) = n5
% 28.64/9.72 | (115) sum(n10, n8) = n18
% 28.64/9.72 | (116) sum(n3, n13) = n16
% 28.64/9.72 | (117) succ(n8) = n9
% 28.64/9.72 | (118) ~ (n14 = n4)
% 28.64/9.72 | (119) sum(n5, n13) = n18
% 28.64/9.72 | (120) sum(n4, n15) = n19
% 28.64/9.72 | (121) sum(n11, n12) = n2
% 28.64/9.72 | (122) sum(n5, n11) = n16
% 28.64/9.72 | (123) sum(n5, n2) = n7
% 28.64/9.72 | (124) sum(n16, n13) = n8
% 28.64/9.72 | (125) ~ (n19 = n18)
% 28.64/9.72 | (126) sum(n10, n5) = n15
% 28.64/9.72 | (127) sum(n3, n0) = n3
% 28.64/9.72 | (128) pred(n9) = n8
% 28.64/9.72 | (129) sum(n4, n12) = n16
% 28.64/9.72 | (130) sum(n14, n2) = n16
% 28.64/9.72 | (131) sum(n8, n11) = n19
% 28.64/9.72 | (132) sum(n4, n11) = n15
% 28.64/9.72 | (133) ~ (n19 = n14)
% 28.64/9.72 | (134) sum(n13, n3) = n16
% 28.64/9.72 | (135) ~ (n20 = n19)
% 28.64/9.73 | (136) sum(n4, n19) = n2
% 28.64/9.73 | (137) ~ (n10 = n3)
% 28.64/9.73 | (138) sum(n13, n7) = n20
% 28.64/9.73 | (139) sum(n15, n15) = n9
% 28.64/9.73 | (140) sum(n1, n1) = n2
% 28.64/9.73 | (141) sum(n12, n16) = n7
% 28.64/9.73 | (142) sum(n1, n20) = n0
% 28.64/9.73 | (143) ~ (n14 = n3)
% 28.64/9.73 | (144) sum(n19, n12) = n10
% 28.64/9.73 | (145) ~ (n17 = n10)
% 28.64/9.73 | (146) sum(n5, n1) = n6
% 28.64/9.73 | (147) sum(n6, n16) = n1
% 28.64/9.73 | (148) ~ (n19 = n0)
% 28.64/9.73 | (149) sum(n5, n7) = n12
% 28.64/9.73 | (150) sum(n6, n0) = n6
% 28.64/9.73 | (151) sum(n18, n16) = n13
% 28.64/9.73 | (152) succ(n7) = n8
% 28.64/9.73 | (153) sum(n10, n6) = n16
% 28.64/9.73 | (154) sum(n9, n7) = n16
% 28.64/9.73 | (155) ~ (n4 = n2)
% 28.64/9.73 | (156) sum(n0, n17) = n17
% 28.64/9.73 | (157) ~ (n4 = n0)
% 28.64/9.73 | (158) sum(n14, n0) = n14
% 28.64/9.73 | (159) ~ (n9 = n1)
% 28.64/9.73 | (160) sum(n4, n17) = n0
% 28.64/9.73 | (161) succ(n20) = n0
% 28.64/9.73 | (162) sum(n20, n12) = n11
% 28.64/9.73 | (163) ~ (all_0_6_6 = n16)
% 28.64/9.73 | (164) ~ (n20 = n5)
% 28.64/9.73 | (165) sum(n13, n11) = n3
% 28.64/9.73 | (166) sum(n16, n3) = n19
% 28.64/9.73 | (167) sum(n18, n9) = n6
% 28.64/9.73 | (168) sum(n15, n17) = n11
% 28.64/9.73 | (169) sum(n0, n3) = n3
% 28.64/9.73 | (170) sum(n19, n14) = n12
% 28.64/9.73 | (171) sum(n12, n15) = n6
% 28.64/9.73 | (172) ~ (n14 = n5)
% 28.64/9.73 | (173) ~ (n6 = n0)
% 28.64/9.73 | (174) sum(n1, n7) = n8
% 28.64/9.73 | (175) sum(n15, n1) = n16
% 28.64/9.73 | (176) ~ (all_0_6_6 = n10)
% 28.64/9.73 | (177) sum(n15, n16) = n10
% 28.64/9.73 | (178) sum(n5, n10) = n15
% 28.64/9.73 | (179) sum(n9, n14) = n2
% 28.64/9.73 | (180) sum(n10, n7) = n17
% 28.64/9.73 | (181) sum(n1, n6) = n7
% 28.64/9.73 | (182) ~ (n17 = n14)
% 28.64/9.73 | (183) pred(n14) = n13
% 28.64/9.73 | (184) sum(n17, n20) = n16
% 28.64/9.73 | (185) ~ (n9 = n3)
% 28.64/9.73 | (186) sum(n14, n3) = n17
% 28.64/9.73 | (187) ~ (n8 = n6)
% 28.64/9.73 | (188) sum(n20, n9) = n8
% 28.64/9.73 | (189) ~ (n10 = n0)
% 28.64/9.73 | (190) ~ (n13 = n8)
% 28.64/9.73 | (191) ~ (n15 = n0)
% 28.64/9.73 | (192) sum(n15, n19) = n13
% 28.64/9.73 | (193) sum(n14, n6) = n20
% 28.64/9.73 | (194) ~ (n14 = n11)
% 28.64/9.73 | (195) sum(n7, n5) = n12
% 28.64/9.73 | (196) sum(n6, n18) = n3
% 28.64/9.73 | (197) ~ (n12 = n10)
% 28.64/9.73 | (198) pred(n13) = n12
% 28.64/9.73 | (199) sum(n17, n13) = n9
% 28.64/9.73 | (200) sum(n0, n10) = n10
% 28.64/9.73 | (201) sum(n18, n1) = n19
% 28.64/9.73 | (202) ~ (n10 = n4)
% 28.64/9.73 | (203) sum(n18, n20) = n17
% 28.64/9.73 | (204) sum(n0, n4) = n4
% 28.64/9.73 | (205) all_0_8_8 = n20 | all_0_8_8 = n19 | all_0_8_8 = n18 | all_0_8_8 = n17 | all_0_8_8 = n16 | all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.64/9.73 | (206) ~ (n5 = n1)
% 28.64/9.73 | (207) succ(n15) = n16
% 28.64/9.73 | (208) sum(n20, n1) = n0
% 28.64/9.73 | (209) sum(n6, n1) = n7
% 28.64/9.73 | (210) sum(n11, n19) = n9
% 28.64/9.73 | (211) ~ (n18 = n7)
% 28.64/9.73 | (212) ~ (n19 = n11)
% 28.64/9.73 | (213) sum(n4, n20) = n3
% 28.64/9.73 | (214) sum(n1, n8) = n9
% 28.64/9.73 | (215) sum(n9, n9) = n18
% 28.64/9.73 | (216) sum(n5, n19) = n3
% 28.64/9.73 | (217) sum(n17, n4) = n0
% 28.64/9.73 | (218) sum(n14, n14) = n7
% 28.64/9.73 | (219) succ(n19) = n20
% 28.64/9.73 | (220) sum(n4, n14) = n18
% 28.64/9.73 | (221) ~ (n5 = n2)
% 28.64/9.73 | (222) ~ (n8 = n0)
% 28.64/9.73 | (223) ~ (n20 = n7)
% 28.64/9.73 | (224) sum(n15, n14) = n8
% 28.64/9.73 | (225) sum(n2, n20) = n1
% 28.64/9.73 | (226) sum(n8, n9) = n17
% 28.64/9.73 | (227) sum(n6, n8) = n14
% 28.64/9.73 | (228) ~ (n15 = n6)
% 28.64/9.73 | (229) ~ (n15 = n7)
% 28.64/9.73 | (230) succ(n13) = n14
% 28.64/9.73 | (231) sum(n8, n20) = n7
% 28.64/9.73 | (232) sum(all_0_3_3, all_0_0_0) = all_0_6_6
% 28.64/9.73 | (233) sum(n4, n2) = n6
% 28.64/9.73 | (234) ~ (n13 = n0)
% 28.64/9.73 | (235) sum(n18, n13) = n10
% 28.64/9.73 | (236) sum(n4, n10) = n14
% 28.64/9.73 | (237) ~ (n10 = n7)
% 28.64/9.73 | (238) ~ (n20 = n2)
% 28.64/9.74 | (239) sum(n10, n2) = n12
% 28.64/9.74 | (240) ~ (n12 = n2)
% 28.64/9.74 | (241) succ(n9) = n10
% 28.64/9.74 | (242) pred(n10) = n9
% 28.64/9.74 | (243) sum(n4, n9) = n13
% 28.64/9.74 | (244) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 28.64/9.74 | (245) sum(n18, n8) = n5
% 28.64/9.74 | (246) sum(n19, n20) = n18
% 28.64/9.74 | (247) sum(n7, n16) = n2
% 28.64/9.74 | (248) ~ (n15 = n3)
% 28.64/9.74 | (249) sum(n8, n12) = n20
% 28.64/9.74 | (250) sum(n18, n10) = n7
% 28.64/9.74 | (251) sum(n7, n18) = n4
% 28.64/9.74 | (252) sum(n6, n14) = n20
% 28.64/9.74 | (253) sum(n17, n8) = n4
% 28.64/9.74 | (254) sum(n0, n13) = n13
% 28.64/9.74 | (255) sum(n3, n9) = n12
% 28.64/9.74 | (256) ~ (n18 = n13)
% 28.64/9.74 | (257) sum(n18, n15) = n12
% 28.64/9.74 | (258) ~ (n7 = n6)
% 28.64/9.74 | (259) ~ (n3 = n0)
% 28.64/9.74 | (260) ~ (n5 = n0)
% 28.64/9.74 | (261) sum(n17, n2) = n19
% 28.64/9.74 | (262) ~ (n19 = n1)
% 28.64/9.74 | (263) sum(n7, n13) = n20
% 28.64/9.74 | (264) sum(n8, n2) = n10
% 28.64/9.74 | (265) sum(n8, n17) = n4
% 28.64/9.74 | (266) sum(n12, n12) = n3
% 28.64/9.74 | (267) ~ (n13 = n2)
% 28.64/9.74 | (268) sum(n11, n10) = n0
% 28.64/9.74 | (269) sum(n20, n4) = n3
% 28.64/9.74 | (270) sum(n10, n3) = n13
% 28.64/9.74 | (271) sum(n13, n10) = n2
% 28.64/9.74 | (272) ~ (n10 = n2)
% 28.64/9.74 | (273) sum(n20, n7) = n6
% 28.64/9.74 | (274) ~ (n18 = n14)
% 28.64/9.74 | (275) sum(n9, n10) = n19
% 28.64/9.74 | (276) sum(n1, n14) = n15
% 28.64/9.74 | (277) sum(n12, n6) = n18
% 28.64/9.74 | (278) ~ (n19 = n16)
% 28.64/9.74 | (279) sum(n4, n3) = n7
% 28.64/9.74 | (280) sum(n5, n4) = n9
% 28.64/9.74 | (281) sum(n9, n3) = n12
% 28.64/9.74 | (282) sum(n12, n1) = n13
% 28.64/9.74 | (283) sum(n11, n0) = n11
% 28.64/9.74 | (284) sum(n13, n13) = n5
% 28.64/9.74 | (285) sum(n20, n14) = n13
% 28.64/9.74 | (286) ~ (n8 = n7)
% 28.64/9.74 | (287) sum(n13, n16) = n8
% 28.64/9.74 | (288) ~ (n17 = n13)
% 28.64/9.74 | (289) ~ (n20 = n15)
% 28.64/9.74 | (290) sum(n5, n14) = n19
% 28.64/9.74 | (291) sum(n16, n20) = n15
% 28.64/9.74 | (292) sum(n5, n12) = n17
% 28.64/9.74 | (293) ~ (all_0_6_6 = n13)
% 28.64/9.74 | (294) ~ (n18 = n10)
% 28.64/9.74 | (295) sum(n2, n5) = n7
% 28.64/9.74 | (296) ~ (n8 = n1)
% 28.64/9.74 | (297) ~ (n10 = n5)
% 28.64/9.74 | (298) sum(n10, n11) = n0
% 28.64/9.74 | (299) sum(n17, n11) = n7
% 28.64/9.74 | (300) sum(n16, n6) = n1
% 28.64/9.74 | (301) sum(n11, n15) = n5
% 28.64/9.74 | (302) sum(n17, n1) = n18
% 28.64/9.74 | (303) ~ (n16 = n5)
% 28.64/9.74 | (304) sum(n11, n20) = n10
% 28.64/9.74 | (305) sum(n15, n20) = n14
% 28.64/9.74 | (306) ~ (n15 = n2)
% 28.64/9.74 | (307) sum(n8, n6) = n14
% 28.64/9.74 | (308) sum(n13, n4) = n17
% 28.64/9.74 | (309) sum(n1, n2) = n3
% 28.64/9.74 | (310) ~ (n11 = n1)
% 28.64/9.74 | (311) sum(n4, n1) = n5
% 28.64/9.74 | (312) ~ (n18 = n17)
% 28.64/9.74 | (313) ~ (n17 = n5)
% 28.64/9.74 | (314) pred(n0) = n20
% 28.64/9.74 | (315) ~ (n20 = n16)
% 28.64/9.74 | (316) ~ (n18 = n4)
% 28.64/9.74 | (317) sum(n7, n9) = n16
% 28.64/9.74 | (318) sum(n11, n9) = n20
% 28.64/9.74 | (319) sum(n14, n9) = n2
% 28.64/9.74 | (320) sum(n7, n0) = n7
% 28.64/9.74 | (321) sum(n15, n9) = n3
% 28.64/9.74 | (322) sum(n0, n16) = n16
% 28.64/9.74 | (323) sum(n0, n19) = n19
% 28.64/9.74 | (324) ~ (n18 = n15)
% 28.64/9.74 | (325) sum(n17, n12) = n8
% 28.64/9.74 | (326) sum(n12, n18) = n9
% 28.64/9.74 | (327) ~ (n8 = n2)
% 28.64/9.74 | (328) pred(n12) = n11
% 28.64/9.74 | (329) sum(n8, n5) = n13
% 28.64/9.74 | (330) sum(n1, n16) = n17
% 28.64/9.74 | (331) pred(n15) = n14
% 28.64/9.74 | (332) sum(n20, n8) = n7
% 28.64/9.74 | (333) ~ (n17 = n8)
% 28.64/9.74 | (334) sum(n4, n8) = n12
% 28.64/9.74 | (335) sum(n18, n7) = n4
% 28.64/9.74 | (336) sum(n2, n13) = n15
% 28.64/9.74 | (337) sum(n17, n0) = n17
% 28.64/9.74 | (338) ~ (n12 = n0)
% 28.64/9.74 | (339) ~ (n20 = n6)
% 28.64/9.74 | (340) ~ (n7 = n4)
% 28.64/9.74 | (341) sum(n10, n14) = n3
% 28.64/9.74 | (342) sum(n17, n19) = n15
% 28.64/9.74 | (343) ~ (n10 = n8)
% 28.64/9.74 | (344) sum(n2, n7) = n9
% 28.64/9.74 | (345) sum(n8, n15) = n2
% 28.64/9.74 | (346) sum(n9, n13) = n1
% 28.64/9.74 | (347) sum(n17, n17) = n13
% 28.64/9.74 | (348) ~ (n14 = n7)
% 28.64/9.74 | (349) sum(n18, n19) = n16
% 28.64/9.74 | (350) ~ (n12 = n9)
% 28.64/9.74 | (351) ~ (n15 = n14)
% 28.64/9.74 | (352) sum(n16, n2) = n18
% 28.64/9.74 | (353) ~ (all_0_6_6 = n14)
% 28.64/9.74 | (354) ~ (n8 = n3)
% 28.64/9.75 | (355) sum(n13, n6) = n19
% 28.64/9.75 | (356) sum(n14, n18) = n11
% 28.64/9.75 | (357) ~ (all_0_6_6 = n8)
% 28.64/9.75 | (358) sum(n15, n5) = n20
% 28.64/9.75 | (359) ~ (n11 = n2)
% 28.64/9.75 | (360) sum(n15, n11) = n5
% 28.64/9.75 | (361) ~ (n4 = n1)
% 28.64/9.75 | (362) ~ (n19 = n13)
% 28.64/9.75 | (363) sum(n8, n4) = n12
% 28.64/9.75 | (364) sum(n7, n7) = n14
% 28.64/9.75 | (365) sum(n10, n18) = n7
% 28.64/9.75 | (366) sum(n0, n15) = n15
% 28.64/9.75 | (367) ~ (n12 = n11)
% 28.64/9.75 | (368) ~ (n7 = n0)
% 28.64/9.75 | (369) sum(n2, n14) = n16
% 28.64/9.75 | (370) sum(n18, n3) = n0
% 28.64/9.75 | (371) sum(n1, n3) = n4
% 28.64/9.75 | (372) sum(n9, n19) = n7
% 28.64/9.75 | (373) sum(n3, n17) = n20
% 28.64/9.75 | (374) sum(n2, n16) = n18
% 28.64/9.75 | (375) sum(n19, n7) = n5
% 28.64/9.75 | (376) sum(n6, n9) = n15
% 28.64/9.75 | (377) ~ (n15 = n13)
% 28.64/9.75 | (378) sum(all_0_8_8, all_0_7_7) = all_0_2_2
% 28.64/9.75 | (379) sum(n12, n19) = n10
% 28.64/9.75 | (380) ~ (n10 = n9)
% 28.64/9.75 | (381) ~ (all_0_6_6 = n20)
% 28.64/9.75 | (382) sum(n15, n10) = n4
% 28.64/9.75 | (383) pred(n2) = n1
% 28.64/9.75 | (384) ~ (n20 = n0)
% 28.64/9.75 | (385) sum(n10, n1) = n11
% 28.64/9.75 | (386) sum(n12, n3) = n15
% 28.64/9.75 | (387) ~ (n2 = n1)
% 28.64/9.75 | (388) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0))
% 28.64/9.75 | (389) ~ (n19 = n12)
% 28.64/9.75 | (390) ~ (n19 = n3)
% 28.64/9.75 | (391) sum(n18, n14) = n11
% 28.64/9.75 | (392) sum(n4, n4) = n8
% 28.64/9.75 | (393) sum(n20, n3) = n2
% 28.64/9.75 | (394) sum(n19, n0) = n19
% 28.64/9.75 | (395) sum(n19, n13) = n11
% 28.64/9.75 | (396) ~ (n11 = n6)
% 28.64/9.75 | (397) sum(n2, n2) = n4
% 28.64/9.75 | (398) sum(n13, n19) = n11
% 28.64/9.75 | (399) sum(n0, n11) = n11
% 28.64/9.75 | (400) sum(n4, n5) = n9
% 28.64/9.75 | (401) sum(n17, n3) = n20
% 28.64/9.75 | (402) sum(n16, n8) = n3
% 28.64/9.75 | (403) ~ (n2 = n0)
% 28.64/9.75 | (404) ~ (n19 = n8)
% 28.64/9.75 | (405) succ(n1) = n2
% 28.64/9.75 | (406) sum(n5, n6) = n11
% 28.64/9.75 | (407) sum(n9, n8) = n17
% 28.64/9.75 | (408) sum(n19, n9) = n7
% 28.64/9.75 | (409) sum(n9, n17) = n5
% 28.64/9.75 | (410) sum(n9, n6) = n15
% 28.64/9.75 | (411) sum(n3, n5) = n8
% 28.64/9.75 | (412) sum(n5, n8) = n13
% 28.64/9.75 | (413) sum(n15, n4) = n19
% 28.64/9.75 | (414) sum(n15, n0) = n15
% 28.64/9.75 | (415) sum(n4, n18) = n1
% 28.64/9.75 | (416) ~ (all_0_6_6 = n3)
% 28.64/9.75 | (417) sum(n4, n0) = n4
% 28.64/9.75 | (418) ~ (n12 = n4)
% 28.64/9.75 | (419) sum(n16, n19) = n14
% 28.64/9.75 | (420) sum(n2, n19) = n0
% 28.64/9.75 | (421) sum(n13, n0) = n13
% 28.64/9.75 | (422) sum(n4, n13) = n17
% 28.64/9.75 | (423) ~ (n20 = n12)
% 28.64/9.75 | (424) sum(n9, n16) = n4
% 28.64/9.75 | (425) sum(n13, n17) = n9
% 28.64/9.75 | (426) ~ (n13 = n6)
% 28.64/9.75 | (427) sum(n3, n6) = n9
% 28.64/9.75 | (428) sum(n17, n14) = n10
% 28.64/9.75 | (429) sum(n3, n16) = n19
% 28.64/9.75 | (430) sum(n11, n8) = n19
% 28.64/9.75 | (431) sum(n3, n19) = n1
% 28.64/9.75 | (432) sum(n4, n16) = n20
% 28.64/9.75 | (433) sum(n2, n9) = n11
% 28.64/9.75 | (434) sum(n4, n7) = n11
% 28.64/9.75 | (435) ~ (n16 = n2)
% 28.64/9.75 | (436) sum(n20, n15) = n14
% 28.64/9.75 | (437) sum(n12, n10) = n1
% 28.64/9.75 | (438) sum(n20, n0) = n20
% 28.64/9.75 | (439) sum(n14, n16) = n9
% 28.64/9.75 | (440) sum(n8, n19) = n6
% 28.64/9.75 | (441) ~ (n15 = n4)
% 28.64/9.75 | (442) sum(n3, n14) = n17
% 28.64/9.75 | (443) sum(n6, n2) = n8
% 28.64/9.75 | (444) sum(n1, n5) = n6
% 28.64/9.75 | (445) ~ (n12 = n5)
% 28.64/9.75 | (446) sum(n8, n3) = n11
% 28.64/9.75 | (447) sum(n20, n17) = n16
% 28.64/9.75 | (448) sum(n20, n19) = n18
% 28.64/9.75 | (449) sum(n9, n11) = n20
% 28.64/9.75 | (450) ~ (n18 = n0)
% 28.64/9.75 | (451) ~ (n15 = n1)
% 28.64/9.75 | (452) sum(n11, n6) = n17
% 28.64/9.75 | (453) sum(n0, n0) = n0
% 28.64/9.75 | (454) succ(n3) = n4
% 28.64/9.75 | (455) sum(n15, n13) = n7
% 28.64/9.75 | (456) ~ (all_0_6_6 = n15)
% 28.64/9.75 | (457) sum(n17, n18) = n14
% 28.64/9.75 | (458) sum(n7, n6) = n13
% 28.64/9.75 | (459) sum(n5, n0) = n5
% 28.64/9.75 | (460) sum(n17, n9) = n5
% 28.64/9.75 | (461) sum(n1, n4) = n5
% 28.64/9.75 | (462) ~ (all_0_6_6 = n5)
% 28.64/9.75 | (463) sum(n9, n5) = n14
% 28.64/9.75 | (464) ~ (n13 = n7)
% 28.64/9.75 | (465) sum(n11, n5) = n16
% 28.64/9.75 | (466) sum(n16, n12) = n7
% 28.64/9.75 | (467) ~ (n17 = n4)
% 28.64/9.75 | (468) pred(n5) = n4
% 28.64/9.76 | (469) ~ (n18 = n5)
% 28.64/9.76 | (470) sum(n16, n16) = n11
% 28.64/9.76 | (471) ~ (n5 = n3)
% 28.64/9.76 | (472) ~ (n9 = n2)
% 28.64/9.76 | (473) pred(all_0_2_2) = all_0_1_1
% 28.64/9.76 | (474) sum(n5, n3) = n8
% 28.64/9.76 | (475) sum(n18, n0) = n18
% 28.64/9.76 | (476) ~ (n16 = n8)
% 28.64/9.76 | (477) sum(n18, n11) = n8
% 28.64/9.76 | (478) ~ (n9 = n6)
% 28.64/9.76 | (479) ~ (n13 = n5)
% 28.64/9.76 | (480) sum(n8, n1) = n9
% 28.64/9.76 | (481) ~ (n14 = n1)
% 28.64/9.76 | (482) succ(n5) = n6
% 28.64/9.76 | (483) ~ (n17 = n12)
% 28.64/9.76 | (484) ~ (n16 = n9)
% 28.64/9.76 | (485) sum(n0, n14) = n14
% 28.64/9.76 | (486) sum(n7, n20) = n6
% 28.64/9.76 | (487) succ(n17) = n18
% 28.64/9.76 | (488) ~ (n16 = n12)
% 28.64/9.76 | (489) ~ (n9 = n8)
% 28.64/9.76 | (490) ~ (n20 = n9)
% 28.64/9.76 | (491) ~ (n14 = n10)
% 28.64/9.76 | (492) ~ (n8 = n5)
% 28.64/9.76 | (493) sum(n1, n17) = n18
% 28.64/9.76 | (494) ~ (n19 = n4)
% 28.64/9.76 | (495) succ(n0) = n1
% 28.64/9.76 | (496) sum(n5, n20) = n4
% 28.64/9.76 | (497) ~ (n7 = n1)
% 28.64/9.76 | (498) ~ (all_0_6_6 = n6)
% 28.64/9.76 | (499) sum(n15, n6) = n0
% 28.64/9.76 | (500) pred(n1) = n0
% 28.64/9.76 | (501) sum(n3, n18) = n0
% 28.64/9.76 | (502) sum(n6, n12) = n18
% 28.64/9.76 | (503) sum(n11, n13) = n3
% 28.64/9.76 | (504) sum(n10, n13) = n2
% 28.64/9.76 | (505) succ(n14) = n15
% 28.64/9.76 | (506) sum(n14, n4) = n18
% 28.64/9.76 | (507) sum(n5, n9) = n14
% 28.64/9.76 | (508) ~ (n15 = n11)
% 28.64/9.76 | (509) ~ (n12 = n7)
% 28.64/9.76 | (510) ~ (n16 = n7)
% 28.64/9.76 | (511) ~ (n13 = n1)
% 28.64/9.76 | (512) sum(n18, n18) = n15
% 28.64/9.76 | (513) sum(n20, n6) = n5
% 28.64/9.76 | (514) sum(n20, n2) = n1
% 28.64/9.76 | (515) ~ (n13 = n3)
% 28.64/9.76 | (516) sum(n5, n5) = n10
% 28.64/9.76 | (517) ~ (n20 = n11)
% 28.64/9.76 | (518) sum(n0, n6) = n6
% 28.64/9.76 | (519) sum(n1, n19) = n20
% 28.64/9.76 | (520) ~ (n18 = n8)
% 28.64/9.76 | (521) sum(n10, n12) = n1
% 28.64/9.76 | (522) sum(n19, n8) = n6
% 28.64/9.76 | (523) ~ (n6 = n5)
% 28.64/9.76 | (524) sum(n16, n1) = n17
% 28.64/9.76 | (525) sum(n9, n1) = n10
% 28.64/9.76 | (526) ~ (n8 = n4)
% 28.64/9.76 | (527) pred(n3) = n2
% 28.64/9.76 | (528) ~ (n16 = n6)
% 28.64/9.76 | (529) ~ (n19 = n17)
% 28.64/9.76 | (530) sum(n12, n17) = n8
% 28.64/9.76 | (531) sum(n19, n11) = n9
% 28.64/9.76 | (532) sum(n14, n20) = n13
% 28.64/9.76 | (533) sum(n16, n0) = n16
% 28.64/9.76 | (534) sum(n14, n7) = n0
% 28.64/9.76 | (535) sum(n3, n1) = n4
% 28.64/9.76 | (536) ~ (n10 = n1)
% 28.64/9.76 | (537) succ(n10) = n11
% 28.64/9.76 | (538) sum(n10, n16) = n5
% 28.64/9.76 | (539) sum(n11, n1) = n12
% 28.64/9.76 | (540) sum(n16, n4) = n20
% 28.64/9.76 | (541) sum(n9, n20) = n8
% 28.64/9.76 | (542) sum(n3, n11) = n14
% 28.64/9.76 | (543) pred(n16) = n15
% 28.64/9.76 | (544) ~ (n20 = n3)
% 28.64/9.76 | (545) sum(n10, n15) = n4
% 28.64/9.76 | (546) sum(n18, n4) = n1
% 28.64/9.76 | (547) sum(n6, n20) = n5
% 28.64/9.76 | (548) sum(n14, n19) = n12
% 28.64/9.76 | (549) ~ (n17 = n2)
% 28.64/9.76 | (550) sum(n5, n17) = n1
% 28.64/9.76 | (551) sum(n17, n7) = n3
% 28.64/9.76 | (552) sum(n13, n14) = n6
% 28.64/9.76 | (553) ~ (n6 = n2)
% 28.64/9.76 | (554) sum(n15, n12) = n6
% 28.64/9.76 | (555) ~ (n14 = n13)
% 28.64/9.76 | (556) sum(n14, n15) = n8
% 28.64/9.76 | (557) ~ (all_0_6_6 = n7)
% 28.64/9.76 | (558) sum(n7, n15) = n1
% 28.64/9.76 | (559) sum(n11, n4) = n15
% 28.64/9.76 | (560) sum(n13, n15) = n7
% 28.64/9.76 | (561) sum(n19, n2) = n0
% 28.64/9.76 | (562) ~ (n11 = n10)
% 28.64/9.76 | (563) sum(n20, n10) = n9
% 28.64/9.76 | (564) ~ (n17 = n1)
% 28.64/9.76 | (565) sum(n12, n5) = n17
% 28.64/9.76 | (566) ~ (n17 = n6)
% 28.64/9.76 | (567) sum(n19, n3) = n1
% 28.64/9.76 | (568) ~ (n11 = n8)
% 28.64/9.76 | (569) sum(n10, n20) = n9
% 28.64/9.76 | (570) sum(n7, n11) = n18
% 28.64/9.76 | (571) sum(n2, n10) = n12
% 28.64/9.77 | (572) ~ (n4 = n3)
% 28.64/9.77 | (573) ~ (n18 = n12)
% 28.64/9.77 | (574) pred(n7) = n6
% 28.64/9.77 | (575) sum(n0, n20) = n20
% 28.64/9.77 | (576) sum(n0, n12) = n12
% 28.64/9.77 | (577) sum(n6, n19) = n4
% 28.64/9.77 | (578) sum(n13, n20) = n12
% 28.64/9.77 | (579) sum(n12, n11) = n2
% 28.64/9.77 | (580) sum(n16, n5) = n0
% 28.64/9.77 | (581) sum(n1, n13) = n14
% 28.64/9.77 | (582) sum(n2, n1) = n3
% 28.64/9.77 | (583) ~ (n16 = n14)
% 28.64/9.77 | (584) ~ (n16 = n4)
% 28.64/9.77 | (585) sum(n20, n16) = n15
% 28.64/9.77 | (586) pred(n4) = n3
% 28.64/9.77 | (587) ~ (n18 = n1)
% 28.64/9.77 | (588) sum(n2, n0) = n2
% 28.64/9.77 | (589) sum(n3, n7) = n10
% 28.64/9.77 | (590) sum(n2, n17) = n19
% 28.64/9.77 | (591) sum(n13, n2) = n15
% 28.64/9.77 | (592) sum(n19, n17) = n15
% 28.64/9.77 | (593) ~ (all_0_6_6 = n9)
% 28.64/9.77 | (594) sum(n3, n15) = n18
% 28.64/9.77 | (595) sum(n14, n8) = n1
% 28.64/9.77 | (596) sum(n11, n14) = n4
% 28.64/9.77 | (597) ~ (n15 = n5)
% 28.64/9.77 | (598) ~ (n16 = n10)
% 28.64/9.77 | (599) ~ (n7 = n2)
% 28.64/9.77 | (600) sum(n1, n18) = n19
% 28.64/9.77 | (601) ~ (n13 = n10)
% 28.64/9.77 | (602) ~ (n19 = n9)
% 28.64/9.77 | (603) sum(n8, n16) = n3
% 28.64/9.77 | (604) ~ (n13 = n9)
% 28.64/9.77 | (605) sum(n5, n16) = n0
% 28.64/9.77 | (606) sum(n17, n16) = n12
% 28.64/9.77 | (607) sum(n14, n13) = n6
% 28.64/9.77 | (608) ~ (n20 = n13)
% 28.64/9.77 | (609) sum(n15, n8) = n2
% 28.64/9.77 | (610) sum(n0, n9) = n9
% 28.64/9.77 | (611) sum(n8, n10) = n18
% 28.64/9.77 | (612) ~ (n11 = n5)
% 28.64/9.77 | (613) succ(n12) = n13
% 28.64/9.77 | (614) sum(n6, n4) = n10
% 28.64/9.77 | (615) sum(n17, n6) = n2
% 28.64/9.77 | (616) ~ (n20 = n8)
% 28.64/9.77 | (617) sum(n10, n17) = n6
% 28.64/9.77 | (618) ~ (n20 = n18)
% 28.64/9.77 | (619) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0))
% 28.64/9.77 | (620) sum(n17, n10) = n6
% 28.64/9.77 | (621) ~ (n9 = n5)
% 28.64/9.77 | (622) ~ (all_0_6_6 = n18)
% 28.64/9.77 | (623) ~ (n17 = n11)
% 28.64/9.77 | (624) sum(n11, n3) = n14
% 28.64/9.77 | (625) sum(n7, n14) = n0
% 28.64/9.77 | (626) ~ (n15 = n8)
% 28.64/9.77 | (627) ~ (n17 = n7)
% 28.64/9.77 | (628) pred(n11) = n10
% 28.64/9.77 | (629) pred(n17) = n16
% 28.64/9.77 | (630) succ(n4) = n5
% 28.64/9.77 | (631) ~ (n3 = n2)
% 28.64/9.77 | (632) ~ (n17 = n16)
% 28.64/9.77 | (633) sum(n8, n8) = n16
% 28.64/9.77 | (634) sum(n14, n12) = n5
% 28.64/9.77 | (635) ~ (n3 = n1)
% 28.64/9.77 | (636) ~ (n16 = n13)
% 28.64/9.77 | (637) sum(n19, n16) = n14
% 28.64/9.77 | (638) sum(n12, n20) = n11
% 28.64/9.77 | (639) sum(n11, n7) = n18
% 28.64/9.77 | (640) succ(n11) = n12
% 28.64/9.77 | (641) sum(n19, n5) = n3
% 28.64/9.77 | (642) ~ (n9 = n7)
% 28.64/9.77 | (643) ~ (n10 = n6)
% 28.64/9.77 | (644) succ(n2) = n3
% 28.64/9.77 | (645) sum(n16, n15) = n10
% 28.64/9.77 | (646) ~ (n12 = n6)
% 28.64/9.77 | (647) sum(n3, n8) = n11
% 28.64/9.77 | (648) sum(n11, n11) = n1
% 28.64/9.77 | (649) sum(n18, n12) = n9
% 28.64/9.77 | (650) sum(n16, n18) = n13
% 28.64/9.77 | (651) ~ (n18 = n3)
% 28.64/9.77 | (652) ~ (n14 = n8)
% 28.64/9.77 | (653) sum(n2, n18) = n20
% 28.64/9.77 | (654) sum(n1, n10) = n11
% 28.64/9.77 | (655) ~ (n16 = n15)
% 28.64/9.77 | (656) ~ (n19 = n7)
% 28.64/9.77 | (657) ~ (n17 = n3)
% 28.64/9.77 | (658) sum(n1, n0) = n1
% 28.64/9.77 | (659) sum(n3, n3) = n6
% 28.64/9.77 | (660) ~ (n17 = n9)
% 28.64/9.77 | (661) pred(n8) = n7
% 28.64/9.77 | (662) sum(n12, n14) = n5
% 28.64/9.77 | (663) sum(n11, n18) = n8
% 28.64/9.77 | (664) ~ (n14 = n9)
% 28.64/9.77 | (665) ~ (n14 = n0)
% 28.64/9.77 | (666) sum(n6, n6) = n12
% 28.64/9.77 | (667) succ(n16) = n17
% 28.64/9.77 | (668) sum(n3, n12) = n15
% 28.64/9.77 | (669) ~ (all_0_6_6 = n17)
% 28.64/9.77 | (670) sum(n11, n16) = n6
% 28.64/9.77 | (671) sum(n19, n4) = n2
% 28.64/9.77 | (672) sum(n15, n18) = n12
% 28.64/9.77 | (673) sum(n19, n6) = n4
% 28.64/9.77 | (674) sum(n14, n17) = n10
% 28.64/9.77 | (675) sum(n5, n15) = n20
% 28.64/9.77 | (676) ~ (all_0_6_6 = n0)
% 28.64/9.77 | (677) sum(n6, n15) = n0
% 28.64/9.77 | (678) ~ (n1 = n0)
% 28.64/9.77 | (679) sum(n18, n17) = n14
% 28.64/9.77 | (680) ~ (n19 = n15)
% 28.64/9.77 | (681) sum(n12, n2) = n14
% 28.64/9.77 | (682) sum(n2, n4) = n6
% 28.64/9.77 | (683) succ(all_0_7_7) = all_0_5_5
% 28.64/9.77 | (684) sum(n20, n11) = n10
% 28.64/9.77 | (685) ~ (n18 = n9)
% 28.64/9.77 | (686) ~ (n19 = n6)
% 28.64/9.77 | (687) ~ (n17 = n0)
% 28.64/9.78 | (688) sum(n9, n2) = n11
% 28.64/9.78 | (689) sum(n6, n10) = n16
% 28.64/9.78 | (690) sum(n14, n1) = n15
% 28.64/9.78 | (691) sum(n6, n3) = n9
% 28.64/9.78 | (692) ~ (n17 = n15)
% 28.64/9.78 | (693) sum(n12, n8) = n20
% 28.64/9.78 | (694) sum(n2, n12) = n14
% 28.64/9.78 | (695) sum(n10, n10) = n20
% 28.64/9.78 | (696) sum(n9, n12) = n0
% 28.64/9.78 | (697) ~ (n19 = n5)
% 28.64/9.78 | (698) sum(n13, n9) = n1
% 28.64/9.78 | (699) sum(n10, n4) = n14
% 28.64/9.78 | (700) sum(n0, n1) = n1
% 28.64/9.78 | (701) sum(n17, n5) = n1
% 28.64/9.78 | (702) sum(n14, n11) = n4
% 28.64/9.78 | (703) sum(n14, n10) = n3
% 28.64/9.78 | (704) sum(n7, n8) = n15
% 28.64/9.78 | (705) sum(n2, n3) = n5
% 28.64/9.78 | (706) sum(n7, n1) = n8
% 28.64/9.78 | (707) ~ (n16 = n1)
% 28.64/9.78 | (708) sum(all_0_8_8, all_0_5_5) = all_0_4_4
% 28.64/9.78 | (709) sum(n8, n7) = n15
% 28.64/9.78 | (710) ~ (n18 = n6)
% 28.64/9.78 | (711) sum(n18, n5) = n2
% 28.64/9.78 | (712) sum(n12, n13) = n4
% 28.64/9.78 | (713) sum(n10, n9) = n19
% 28.64/9.78 | (714) sum(n16, n14) = n9
% 28.64/9.78 | (715) ~ (n6 = n4)
% 28.64/9.78 | (716) pred(all_0_4_4) = all_0_3_3
% 28.64/9.78 | (717) sum(n15, n7) = n1
% 28.64/9.78 | (718) pred(n19) = n18
% 28.64/9.78 | (719) sum(n0, n8) = n8
% 28.64/9.78 | (720) sum(n9, n18) = n6
% 28.64/9.78 | (721) sum(n2, n8) = n10
% 28.64/9.78 | (722) ~ (n20 = n4)
% 28.64/9.78 | (723) sum(n8, n13) = n0
% 28.64/9.78 | (724) ~ (n11 = n0)
% 28.64/9.78 | (725) sum(n20, n20) = n19
% 28.64/9.78 | (726) sum(n7, n12) = n19
% 28.64/9.78 | (727) ~ (n7 = n3)
% 28.64/9.78 |
% 28.64/9.78 +-Applying beta-rule and splitting (17), into two cases.
% 28.64/9.78 |-Branch one:
% 28.64/9.78 | (728) all_0_7_7 = n20
% 28.64/9.78 |
% 28.64/9.78 | From (728) and (683) follows:
% 28.64/9.78 | (729) succ(n20) = all_0_5_5
% 28.64/9.78 |
% 28.64/9.78 | From (728) and (8) follows:
% 28.64/9.78 | (730) sum(n20, all_0_1_1) = all_0_0_0
% 28.64/9.78 |
% 28.64/9.78 | From (728) and (378) follows:
% 28.64/9.78 | (731) sum(all_0_8_8, n20) = all_0_2_2
% 28.64/9.78 |
% 28.64/9.78 | Instantiating formula (388) with n20, all_0_5_5, n0 and discharging atoms succ(n20) = all_0_5_5, succ(n20) = n0, yields:
% 28.64/9.78 | (732) all_0_5_5 = n0
% 28.64/9.78 |
% 28.64/9.78 | From (732) and (708) follows:
% 28.64/9.78 | (733) sum(all_0_8_8, n0) = all_0_4_4
% 28.64/9.78 |
% 28.64/9.78 +-Applying beta-rule and splitting (205), into two cases.
% 28.64/9.78 |-Branch one:
% 28.64/9.78 | (734) all_0_8_8 = n20
% 28.64/9.78 |
% 28.64/9.78 | From (734) and (731) follows:
% 28.64/9.78 | (735) sum(n20, n20) = all_0_2_2
% 28.64/9.78 |
% 28.64/9.78 | From (734) and (733) follows:
% 28.64/9.78 | (736) sum(n20, n0) = all_0_4_4
% 28.64/9.78 |
% 28.64/9.78 | Instantiating formula (619) with n20, n20, all_0_2_2, n19 and discharging atoms sum(n20, n20) = all_0_2_2, sum(n20, n20) = n19, yields:
% 28.64/9.78 | (737) all_0_2_2 = n19
% 28.64/9.78 |
% 28.64/9.78 | Instantiating formula (619) with n20, n0, all_0_4_4, n20 and discharging atoms sum(n20, n0) = all_0_4_4, sum(n20, n0) = n20, yields:
% 28.64/9.78 | (738) all_0_4_4 = n20
% 28.64/9.78 |
% 28.64/9.78 | From (737) and (473) follows:
% 28.64/9.78 | (739) pred(n19) = all_0_1_1
% 28.64/9.78 |
% 28.64/9.78 | From (738) and (716) follows:
% 28.64/9.78 | (740) pred(n20) = all_0_3_3
% 28.64/9.78 |
% 28.64/9.78 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 28.64/9.78 | (741) all_0_3_3 = n19
% 28.64/9.78 |
% 28.64/9.78 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 28.64/9.78 | (742) all_0_1_1 = n18
% 28.64/9.78 |
% 28.64/9.78 | From (741) and (232) follows:
% 28.64/9.78 | (743) sum(n19, all_0_0_0) = all_0_6_6
% 28.64/9.78 |
% 28.64/9.78 | From (742) and (730) follows:
% 28.64/9.78 | (744) sum(n20, n18) = all_0_0_0
% 28.64/9.78 |
% 28.64/9.78 | Instantiating formula (619) with n20, n18, all_0_0_0, n17 and discharging atoms sum(n20, n18) = all_0_0_0, sum(n20, n18) = n17, yields:
% 28.64/9.78 | (745) all_0_0_0 = n17
% 28.64/9.78 |
% 28.64/9.78 | From (745) and (743) follows:
% 28.64/9.78 | (746) sum(n19, n17) = all_0_6_6
% 28.64/9.78 |
% 28.64/9.78 | Instantiating formula (619) with n19, n17, all_0_6_6, n15 and discharging atoms sum(n19, n17) = all_0_6_6, sum(n19, n17) = n15, yields:
% 28.64/9.78 | (747) all_0_6_6 = n15
% 28.64/9.78 |
% 28.64/9.78 | Equations (747) can reduce 456 to:
% 28.64/9.78 | (748) $false
% 28.64/9.78 |
% 28.98/9.78 |-The branch is then unsatisfiable
% 28.98/9.78 |-Branch two:
% 28.98/9.78 | (749) ~ (all_0_8_8 = n20)
% 28.98/9.78 | (750) all_0_8_8 = n19 | all_0_8_8 = n18 | all_0_8_8 = n17 | all_0_8_8 = n16 | all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.78 |
% 28.98/9.78 +-Applying beta-rule and splitting (750), into two cases.
% 28.98/9.78 |-Branch one:
% 28.98/9.78 | (751) all_0_8_8 = n19
% 28.98/9.78 |
% 28.98/9.78 | From (751) and (731) follows:
% 28.98/9.78 | (752) sum(n19, n20) = all_0_2_2
% 28.98/9.78 |
% 28.98/9.78 | From (751) and (733) follows:
% 28.98/9.78 | (753) sum(n19, n0) = all_0_4_4
% 28.98/9.78 |
% 28.98/9.78 | Instantiating formula (619) with n19, n20, all_0_2_2, n18 and discharging atoms sum(n19, n20) = all_0_2_2, sum(n19, n20) = n18, yields:
% 28.98/9.78 | (754) all_0_2_2 = n18
% 28.98/9.78 |
% 28.98/9.78 | Instantiating formula (619) with n19, n0, all_0_4_4, n19 and discharging atoms sum(n19, n0) = all_0_4_4, sum(n19, n0) = n19, yields:
% 28.98/9.79 | (755) all_0_4_4 = n19
% 28.98/9.79 |
% 28.98/9.79 | From (754) and (473) follows:
% 28.98/9.79 | (756) pred(n18) = all_0_1_1
% 28.98/9.79 |
% 28.98/9.79 | From (755) and (716) follows:
% 28.98/9.79 | (757) pred(n19) = all_0_3_3
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 28.98/9.79 | (758) all_0_3_3 = n18
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 28.98/9.79 | (759) all_0_1_1 = n17
% 28.98/9.79 |
% 28.98/9.79 | From (758) and (232) follows:
% 28.98/9.79 | (760) sum(n18, all_0_0_0) = all_0_6_6
% 28.98/9.79 |
% 28.98/9.79 | From (759) and (730) follows:
% 28.98/9.79 | (761) sum(n20, n17) = all_0_0_0
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (619) with n20, n17, all_0_0_0, n16 and discharging atoms sum(n20, n17) = all_0_0_0, sum(n20, n17) = n16, yields:
% 28.98/9.79 | (762) all_0_0_0 = n16
% 28.98/9.79 |
% 28.98/9.79 | From (762) and (760) follows:
% 28.98/9.79 | (763) sum(n18, n16) = all_0_6_6
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (619) with n18, n16, all_0_6_6, n13 and discharging atoms sum(n18, n16) = all_0_6_6, sum(n18, n16) = n13, yields:
% 28.98/9.79 | (764) all_0_6_6 = n13
% 28.98/9.79 |
% 28.98/9.79 | Equations (764) can reduce 293 to:
% 28.98/9.79 | (748) $false
% 28.98/9.79 |
% 28.98/9.79 |-The branch is then unsatisfiable
% 28.98/9.79 |-Branch two:
% 28.98/9.79 | (766) ~ (all_0_8_8 = n19)
% 28.98/9.79 | (767) all_0_8_8 = n18 | all_0_8_8 = n17 | all_0_8_8 = n16 | all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.79 |
% 28.98/9.79 +-Applying beta-rule and splitting (767), into two cases.
% 28.98/9.79 |-Branch one:
% 28.98/9.79 | (768) all_0_8_8 = n18
% 28.98/9.79 |
% 28.98/9.79 | From (768) and (731) follows:
% 28.98/9.79 | (769) sum(n18, n20) = all_0_2_2
% 28.98/9.79 |
% 28.98/9.79 | From (768) and (733) follows:
% 28.98/9.79 | (770) sum(n18, n0) = all_0_4_4
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (619) with n18, n20, all_0_2_2, n17 and discharging atoms sum(n18, n20) = all_0_2_2, sum(n18, n20) = n17, yields:
% 28.98/9.79 | (771) all_0_2_2 = n17
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (619) with n18, n0, all_0_4_4, n18 and discharging atoms sum(n18, n0) = all_0_4_4, sum(n18, n0) = n18, yields:
% 28.98/9.79 | (772) all_0_4_4 = n18
% 28.98/9.79 |
% 28.98/9.79 | From (771) and (473) follows:
% 28.98/9.79 | (773) pred(n17) = all_0_1_1
% 28.98/9.79 |
% 28.98/9.79 | From (772) and (716) follows:
% 28.98/9.79 | (774) pred(n18) = all_0_3_3
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 28.98/9.79 | (775) all_0_3_3 = n17
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 28.98/9.79 | (776) all_0_1_1 = n16
% 28.98/9.79 |
% 28.98/9.79 | From (775) and (232) follows:
% 28.98/9.79 | (777) sum(n17, all_0_0_0) = all_0_6_6
% 28.98/9.79 |
% 28.98/9.79 | From (776) and (730) follows:
% 28.98/9.79 | (778) sum(n20, n16) = all_0_0_0
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (619) with n20, n16, all_0_0_0, n15 and discharging atoms sum(n20, n16) = all_0_0_0, sum(n20, n16) = n15, yields:
% 28.98/9.79 | (779) all_0_0_0 = n15
% 28.98/9.79 |
% 28.98/9.79 | From (779) and (777) follows:
% 28.98/9.79 | (780) sum(n17, n15) = all_0_6_6
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (619) with n17, n15, all_0_6_6, n11 and discharging atoms sum(n17, n15) = all_0_6_6, sum(n17, n15) = n11, yields:
% 28.98/9.79 | (781) all_0_6_6 = n11
% 28.98/9.79 |
% 28.98/9.79 | Equations (781) can reduce 2 to:
% 28.98/9.79 | (748) $false
% 28.98/9.79 |
% 28.98/9.79 |-The branch is then unsatisfiable
% 28.98/9.79 |-Branch two:
% 28.98/9.79 | (783) ~ (all_0_8_8 = n18)
% 28.98/9.79 | (784) all_0_8_8 = n17 | all_0_8_8 = n16 | all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.79 |
% 28.98/9.79 +-Applying beta-rule and splitting (784), into two cases.
% 28.98/9.79 |-Branch one:
% 28.98/9.79 | (785) all_0_8_8 = n17
% 28.98/9.79 |
% 28.98/9.79 | From (785) and (731) follows:
% 28.98/9.79 | (786) sum(n17, n20) = all_0_2_2
% 28.98/9.79 |
% 28.98/9.79 | From (785) and (733) follows:
% 28.98/9.79 | (787) sum(n17, n0) = all_0_4_4
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (619) with n17, n20, all_0_2_2, n16 and discharging atoms sum(n17, n20) = all_0_2_2, sum(n17, n20) = n16, yields:
% 28.98/9.79 | (788) all_0_2_2 = n16
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (619) with n17, n0, all_0_4_4, n17 and discharging atoms sum(n17, n0) = all_0_4_4, sum(n17, n0) = n17, yields:
% 28.98/9.79 | (789) all_0_4_4 = n17
% 28.98/9.79 |
% 28.98/9.79 | From (788) and (473) follows:
% 28.98/9.79 | (790) pred(n16) = all_0_1_1
% 28.98/9.79 |
% 28.98/9.79 | From (789) and (716) follows:
% 28.98/9.79 | (791) pred(n17) = all_0_3_3
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 28.98/9.79 | (792) all_0_3_3 = n16
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 28.98/9.79 | (793) all_0_1_1 = n15
% 28.98/9.79 |
% 28.98/9.79 | From (792) and (232) follows:
% 28.98/9.79 | (794) sum(n16, all_0_0_0) = all_0_6_6
% 28.98/9.79 |
% 28.98/9.79 | From (793) and (730) follows:
% 28.98/9.79 | (795) sum(n20, n15) = all_0_0_0
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (619) with n20, n15, all_0_0_0, n14 and discharging atoms sum(n20, n15) = all_0_0_0, sum(n20, n15) = n14, yields:
% 28.98/9.79 | (796) all_0_0_0 = n14
% 28.98/9.79 |
% 28.98/9.79 | From (796) and (794) follows:
% 28.98/9.79 | (797) sum(n16, n14) = all_0_6_6
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (619) with n16, n14, all_0_6_6, n9 and discharging atoms sum(n16, n14) = all_0_6_6, sum(n16, n14) = n9, yields:
% 28.98/9.79 | (798) all_0_6_6 = n9
% 28.98/9.79 |
% 28.98/9.79 | Equations (798) can reduce 593 to:
% 28.98/9.79 | (748) $false
% 28.98/9.79 |
% 28.98/9.79 |-The branch is then unsatisfiable
% 28.98/9.79 |-Branch two:
% 28.98/9.79 | (800) ~ (all_0_8_8 = n17)
% 28.98/9.79 | (801) all_0_8_8 = n16 | all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.79 |
% 28.98/9.79 +-Applying beta-rule and splitting (801), into two cases.
% 28.98/9.79 |-Branch one:
% 28.98/9.79 | (802) all_0_8_8 = n16
% 28.98/9.79 |
% 28.98/9.79 | From (802) and (731) follows:
% 28.98/9.79 | (803) sum(n16, n20) = all_0_2_2
% 28.98/9.79 |
% 28.98/9.79 | From (802) and (733) follows:
% 28.98/9.79 | (804) sum(n16, n0) = all_0_4_4
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (619) with n16, n20, all_0_2_2, n15 and discharging atoms sum(n16, n20) = all_0_2_2, sum(n16, n20) = n15, yields:
% 28.98/9.79 | (805) all_0_2_2 = n15
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (619) with n16, n0, all_0_4_4, n16 and discharging atoms sum(n16, n0) = all_0_4_4, sum(n16, n0) = n16, yields:
% 28.98/9.79 | (806) all_0_4_4 = n16
% 28.98/9.79 |
% 28.98/9.79 | From (805) and (473) follows:
% 28.98/9.79 | (807) pred(n15) = all_0_1_1
% 28.98/9.79 |
% 28.98/9.79 | From (806) and (716) follows:
% 28.98/9.79 | (808) pred(n16) = all_0_3_3
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 28.98/9.79 | (809) all_0_3_3 = n15
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 28.98/9.79 | (810) all_0_1_1 = n14
% 28.98/9.79 |
% 28.98/9.79 | From (809) and (232) follows:
% 28.98/9.79 | (811) sum(n15, all_0_0_0) = all_0_6_6
% 28.98/9.79 |
% 28.98/9.79 | From (810) and (730) follows:
% 28.98/9.79 | (812) sum(n20, n14) = all_0_0_0
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (619) with n20, n14, all_0_0_0, n13 and discharging atoms sum(n20, n14) = all_0_0_0, sum(n20, n14) = n13, yields:
% 28.98/9.79 | (813) all_0_0_0 = n13
% 28.98/9.79 |
% 28.98/9.79 | From (813) and (811) follows:
% 28.98/9.79 | (814) sum(n15, n13) = all_0_6_6
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (619) with n15, n13, all_0_6_6, n7 and discharging atoms sum(n15, n13) = all_0_6_6, sum(n15, n13) = n7, yields:
% 28.98/9.79 | (815) all_0_6_6 = n7
% 28.98/9.79 |
% 28.98/9.79 | Equations (815) can reduce 557 to:
% 28.98/9.79 | (748) $false
% 28.98/9.79 |
% 28.98/9.79 |-The branch is then unsatisfiable
% 28.98/9.79 |-Branch two:
% 28.98/9.79 | (817) ~ (all_0_8_8 = n16)
% 28.98/9.79 | (818) all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.79 |
% 28.98/9.79 +-Applying beta-rule and splitting (818), into two cases.
% 28.98/9.79 |-Branch one:
% 28.98/9.79 | (819) all_0_8_8 = n15
% 28.98/9.79 |
% 28.98/9.79 | From (819) and (731) follows:
% 28.98/9.79 | (820) sum(n15, n20) = all_0_2_2
% 28.98/9.79 |
% 28.98/9.79 | From (819) and (733) follows:
% 28.98/9.79 | (821) sum(n15, n0) = all_0_4_4
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (619) with n15, n20, all_0_2_2, n14 and discharging atoms sum(n15, n20) = all_0_2_2, sum(n15, n20) = n14, yields:
% 28.98/9.79 | (822) all_0_2_2 = n14
% 28.98/9.79 |
% 28.98/9.79 | Instantiating formula (619) with n15, n0, all_0_4_4, n15 and discharging atoms sum(n15, n0) = all_0_4_4, sum(n15, n0) = n15, yields:
% 28.98/9.79 | (823) all_0_4_4 = n15
% 28.98/9.79 |
% 28.98/9.80 | From (822) and (473) follows:
% 28.98/9.80 | (824) pred(n14) = all_0_1_1
% 28.98/9.80 |
% 28.98/9.80 | From (823) and (716) follows:
% 28.98/9.80 | (825) pred(n15) = all_0_3_3
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 28.98/9.80 | (826) all_0_3_3 = n14
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 28.98/9.80 | (827) all_0_1_1 = n13
% 28.98/9.80 |
% 28.98/9.80 | From (826) and (232) follows:
% 28.98/9.80 | (828) sum(n14, all_0_0_0) = all_0_6_6
% 28.98/9.80 |
% 28.98/9.80 | From (827) and (730) follows:
% 28.98/9.80 | (829) sum(n20, n13) = all_0_0_0
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n20, n13, all_0_0_0, n12 and discharging atoms sum(n20, n13) = all_0_0_0, sum(n20, n13) = n12, yields:
% 28.98/9.80 | (830) all_0_0_0 = n12
% 28.98/9.80 |
% 28.98/9.80 | From (830) and (828) follows:
% 28.98/9.80 | (831) sum(n14, n12) = all_0_6_6
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n14, n12, all_0_6_6, n5 and discharging atoms sum(n14, n12) = all_0_6_6, sum(n14, n12) = n5, yields:
% 28.98/9.80 | (832) all_0_6_6 = n5
% 28.98/9.80 |
% 28.98/9.80 | Equations (832) can reduce 462 to:
% 28.98/9.80 | (748) $false
% 28.98/9.80 |
% 28.98/9.80 |-The branch is then unsatisfiable
% 28.98/9.80 |-Branch two:
% 28.98/9.80 | (834) ~ (all_0_8_8 = n15)
% 28.98/9.80 | (835) all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.80 |
% 28.98/9.80 +-Applying beta-rule and splitting (835), into two cases.
% 28.98/9.80 |-Branch one:
% 28.98/9.80 | (836) all_0_8_8 = n14
% 28.98/9.80 |
% 28.98/9.80 | From (836) and (731) follows:
% 28.98/9.80 | (837) sum(n14, n20) = all_0_2_2
% 28.98/9.80 |
% 28.98/9.80 | From (836) and (733) follows:
% 28.98/9.80 | (838) sum(n14, n0) = all_0_4_4
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n14, n20, all_0_2_2, n13 and discharging atoms sum(n14, n20) = all_0_2_2, sum(n14, n20) = n13, yields:
% 28.98/9.80 | (839) all_0_2_2 = n13
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n14, n0, all_0_4_4, n14 and discharging atoms sum(n14, n0) = all_0_4_4, sum(n14, n0) = n14, yields:
% 28.98/9.80 | (840) all_0_4_4 = n14
% 28.98/9.80 |
% 28.98/9.80 | From (839) and (473) follows:
% 28.98/9.80 | (841) pred(n13) = all_0_1_1
% 28.98/9.80 |
% 28.98/9.80 | From (840) and (716) follows:
% 28.98/9.80 | (842) pred(n14) = all_0_3_3
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 28.98/9.80 | (843) all_0_3_3 = n13
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 28.98/9.80 | (844) all_0_1_1 = n12
% 28.98/9.80 |
% 28.98/9.80 | From (843) and (232) follows:
% 28.98/9.80 | (845) sum(n13, all_0_0_0) = all_0_6_6
% 28.98/9.80 |
% 28.98/9.80 | From (844) and (730) follows:
% 28.98/9.80 | (846) sum(n20, n12) = all_0_0_0
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n20, n12, all_0_0_0, n11 and discharging atoms sum(n20, n12) = all_0_0_0, sum(n20, n12) = n11, yields:
% 28.98/9.80 | (847) all_0_0_0 = n11
% 28.98/9.80 |
% 28.98/9.80 | From (847) and (845) follows:
% 28.98/9.80 | (848) sum(n13, n11) = all_0_6_6
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n13, n11, all_0_6_6, n3 and discharging atoms sum(n13, n11) = all_0_6_6, sum(n13, n11) = n3, yields:
% 28.98/9.80 | (849) all_0_6_6 = n3
% 28.98/9.80 |
% 28.98/9.80 | Equations (849) can reduce 416 to:
% 28.98/9.80 | (748) $false
% 28.98/9.80 |
% 28.98/9.80 |-The branch is then unsatisfiable
% 28.98/9.80 |-Branch two:
% 28.98/9.80 | (851) ~ (all_0_8_8 = n14)
% 28.98/9.80 | (852) all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.80 |
% 28.98/9.80 +-Applying beta-rule and splitting (852), into two cases.
% 28.98/9.80 |-Branch one:
% 28.98/9.80 | (853) all_0_8_8 = n13
% 28.98/9.80 |
% 28.98/9.80 | From (853) and (731) follows:
% 28.98/9.80 | (854) sum(n13, n20) = all_0_2_2
% 28.98/9.80 |
% 28.98/9.80 | From (853) and (733) follows:
% 28.98/9.80 | (855) sum(n13, n0) = all_0_4_4
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n13, n20, all_0_2_2, n12 and discharging atoms sum(n13, n20) = all_0_2_2, sum(n13, n20) = n12, yields:
% 28.98/9.80 | (856) all_0_2_2 = n12
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n13, n0, all_0_4_4, n13 and discharging atoms sum(n13, n0) = all_0_4_4, sum(n13, n0) = n13, yields:
% 28.98/9.80 | (857) all_0_4_4 = n13
% 28.98/9.80 |
% 28.98/9.80 | From (856) and (473) follows:
% 28.98/9.80 | (858) pred(n12) = all_0_1_1
% 28.98/9.80 |
% 28.98/9.80 | From (857) and (716) follows:
% 28.98/9.80 | (859) pred(n13) = all_0_3_3
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 28.98/9.80 | (860) all_0_3_3 = n12
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 28.98/9.80 | (861) all_0_1_1 = n11
% 28.98/9.80 |
% 28.98/9.80 | From (860) and (232) follows:
% 28.98/9.80 | (862) sum(n12, all_0_0_0) = all_0_6_6
% 28.98/9.80 |
% 28.98/9.80 | From (861) and (730) follows:
% 28.98/9.80 | (863) sum(n20, n11) = all_0_0_0
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n20, n11, all_0_0_0, n10 and discharging atoms sum(n20, n11) = all_0_0_0, sum(n20, n11) = n10, yields:
% 28.98/9.80 | (864) all_0_0_0 = n10
% 28.98/9.80 |
% 28.98/9.80 | From (864) and (862) follows:
% 28.98/9.80 | (865) sum(n12, n10) = all_0_6_6
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n12, n10, all_0_6_6, n1 and discharging atoms sum(n12, n10) = all_0_6_6, sum(n12, n10) = n1, yields:
% 28.98/9.80 | (866) all_0_6_6 = n1
% 28.98/9.80 |
% 28.98/9.80 | Equations (866) can reduce 28 to:
% 28.98/9.80 | (748) $false
% 28.98/9.80 |
% 28.98/9.80 |-The branch is then unsatisfiable
% 28.98/9.80 |-Branch two:
% 28.98/9.80 | (868) ~ (all_0_8_8 = n13)
% 28.98/9.80 | (869) all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.80 |
% 28.98/9.80 +-Applying beta-rule and splitting (869), into two cases.
% 28.98/9.80 |-Branch one:
% 28.98/9.80 | (870) all_0_8_8 = n12
% 28.98/9.80 |
% 28.98/9.80 | From (870) and (731) follows:
% 28.98/9.80 | (871) sum(n12, n20) = all_0_2_2
% 28.98/9.80 |
% 28.98/9.80 | From (870) and (733) follows:
% 28.98/9.80 | (872) sum(n12, n0) = all_0_4_4
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n12, n20, all_0_2_2, n11 and discharging atoms sum(n12, n20) = all_0_2_2, sum(n12, n20) = n11, yields:
% 28.98/9.80 | (873) all_0_2_2 = n11
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n12, n0, all_0_4_4, n12 and discharging atoms sum(n12, n0) = all_0_4_4, sum(n12, n0) = n12, yields:
% 28.98/9.80 | (874) all_0_4_4 = n12
% 28.98/9.80 |
% 28.98/9.80 | From (873) and (473) follows:
% 28.98/9.80 | (875) pred(n11) = all_0_1_1
% 28.98/9.80 |
% 28.98/9.80 | From (874) and (716) follows:
% 28.98/9.80 | (876) pred(n12) = all_0_3_3
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 28.98/9.80 | (877) all_0_3_3 = n11
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 28.98/9.80 | (878) all_0_1_1 = n10
% 28.98/9.80 |
% 28.98/9.80 | From (877) and (232) follows:
% 28.98/9.80 | (879) sum(n11, all_0_0_0) = all_0_6_6
% 28.98/9.80 |
% 28.98/9.80 | From (878) and (730) follows:
% 28.98/9.80 | (880) sum(n20, n10) = all_0_0_0
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n20, n10, all_0_0_0, n9 and discharging atoms sum(n20, n10) = all_0_0_0, sum(n20, n10) = n9, yields:
% 28.98/9.80 | (881) all_0_0_0 = n9
% 28.98/9.80 |
% 28.98/9.80 | From (881) and (879) follows:
% 28.98/9.80 | (882) sum(n11, n9) = all_0_6_6
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n11, n9, all_0_6_6, n20 and discharging atoms sum(n11, n9) = all_0_6_6, sum(n11, n9) = n20, yields:
% 28.98/9.80 | (883) all_0_6_6 = n20
% 28.98/9.80 |
% 28.98/9.80 | Equations (883) can reduce 381 to:
% 28.98/9.80 | (748) $false
% 28.98/9.80 |
% 28.98/9.80 |-The branch is then unsatisfiable
% 28.98/9.80 |-Branch two:
% 28.98/9.80 | (885) ~ (all_0_8_8 = n12)
% 28.98/9.80 | (886) all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.80 |
% 28.98/9.80 +-Applying beta-rule and splitting (886), into two cases.
% 28.98/9.80 |-Branch one:
% 28.98/9.80 | (887) all_0_8_8 = n11
% 28.98/9.80 |
% 28.98/9.80 | From (887) and (731) follows:
% 28.98/9.80 | (888) sum(n11, n20) = all_0_2_2
% 28.98/9.80 |
% 28.98/9.80 | From (887) and (733) follows:
% 28.98/9.80 | (889) sum(n11, n0) = all_0_4_4
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n11, n20, all_0_2_2, n10 and discharging atoms sum(n11, n20) = all_0_2_2, sum(n11, n20) = n10, yields:
% 28.98/9.80 | (890) all_0_2_2 = n10
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n11, n0, all_0_4_4, n11 and discharging atoms sum(n11, n0) = all_0_4_4, sum(n11, n0) = n11, yields:
% 28.98/9.80 | (891) all_0_4_4 = n11
% 28.98/9.80 |
% 28.98/9.80 | From (890) and (473) follows:
% 28.98/9.80 | (892) pred(n10) = all_0_1_1
% 28.98/9.80 |
% 28.98/9.80 | From (891) and (716) follows:
% 28.98/9.80 | (893) pred(n11) = all_0_3_3
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 28.98/9.80 | (894) all_0_3_3 = n10
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 28.98/9.80 | (895) all_0_1_1 = n9
% 28.98/9.80 |
% 28.98/9.80 | From (894) and (232) follows:
% 28.98/9.80 | (896) sum(n10, all_0_0_0) = all_0_6_6
% 28.98/9.80 |
% 28.98/9.80 | From (895) and (730) follows:
% 28.98/9.80 | (897) sum(n20, n9) = all_0_0_0
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n20, n9, all_0_0_0, n8 and discharging atoms sum(n20, n9) = all_0_0_0, sum(n20, n9) = n8, yields:
% 28.98/9.80 | (898) all_0_0_0 = n8
% 28.98/9.80 |
% 28.98/9.80 | From (898) and (896) follows:
% 28.98/9.80 | (899) sum(n10, n8) = all_0_6_6
% 28.98/9.80 |
% 28.98/9.80 | Instantiating formula (619) with n10, n8, all_0_6_6, n18 and discharging atoms sum(n10, n8) = all_0_6_6, sum(n10, n8) = n18, yields:
% 28.98/9.80 | (900) all_0_6_6 = n18
% 28.98/9.80 |
% 28.98/9.81 | Equations (900) can reduce 622 to:
% 28.98/9.81 | (748) $false
% 28.98/9.81 |
% 28.98/9.81 |-The branch is then unsatisfiable
% 28.98/9.81 |-Branch two:
% 28.98/9.81 | (902) ~ (all_0_8_8 = n11)
% 28.98/9.81 | (903) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.81 |
% 28.98/9.81 +-Applying beta-rule and splitting (903), into two cases.
% 28.98/9.81 |-Branch one:
% 28.98/9.81 | (904) all_0_8_8 = n10
% 28.98/9.81 |
% 28.98/9.81 | From (904) and (731) follows:
% 28.98/9.81 | (905) sum(n10, n20) = all_0_2_2
% 28.98/9.81 |
% 28.98/9.81 | From (904) and (733) follows:
% 28.98/9.81 | (906) sum(n10, n0) = all_0_4_4
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n10, n20, all_0_2_2, n9 and discharging atoms sum(n10, n20) = all_0_2_2, sum(n10, n20) = n9, yields:
% 28.98/9.81 | (907) all_0_2_2 = n9
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n10, n0, all_0_4_4, n10 and discharging atoms sum(n10, n0) = all_0_4_4, sum(n10, n0) = n10, yields:
% 28.98/9.81 | (908) all_0_4_4 = n10
% 28.98/9.81 |
% 28.98/9.81 | From (907) and (473) follows:
% 28.98/9.81 | (909) pred(n9) = all_0_1_1
% 28.98/9.81 |
% 28.98/9.81 | From (908) and (716) follows:
% 28.98/9.81 | (910) pred(n10) = all_0_3_3
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 28.98/9.81 | (911) all_0_3_3 = n9
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 28.98/9.81 | (912) all_0_1_1 = n8
% 28.98/9.81 |
% 28.98/9.81 | From (911) and (232) follows:
% 28.98/9.81 | (913) sum(n9, all_0_0_0) = all_0_6_6
% 28.98/9.81 |
% 28.98/9.81 | From (912) and (730) follows:
% 28.98/9.81 | (914) sum(n20, n8) = all_0_0_0
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n20, n8, all_0_0_0, n7 and discharging atoms sum(n20, n8) = all_0_0_0, sum(n20, n8) = n7, yields:
% 28.98/9.81 | (915) all_0_0_0 = n7
% 28.98/9.81 |
% 28.98/9.81 | From (915) and (913) follows:
% 28.98/9.81 | (916) sum(n9, n7) = all_0_6_6
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n9, n7, all_0_6_6, n16 and discharging atoms sum(n9, n7) = all_0_6_6, sum(n9, n7) = n16, yields:
% 28.98/9.81 | (917) all_0_6_6 = n16
% 28.98/9.81 |
% 28.98/9.81 | Equations (917) can reduce 163 to:
% 28.98/9.81 | (748) $false
% 28.98/9.81 |
% 28.98/9.81 |-The branch is then unsatisfiable
% 28.98/9.81 |-Branch two:
% 28.98/9.81 | (919) ~ (all_0_8_8 = n10)
% 28.98/9.81 | (920) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.81 |
% 28.98/9.81 +-Applying beta-rule and splitting (920), into two cases.
% 28.98/9.81 |-Branch one:
% 28.98/9.81 | (921) all_0_8_8 = n9
% 28.98/9.81 |
% 28.98/9.81 | From (921) and (731) follows:
% 28.98/9.81 | (922) sum(n9, n20) = all_0_2_2
% 28.98/9.81 |
% 28.98/9.81 | From (921) and (733) follows:
% 28.98/9.81 | (923) sum(n9, n0) = all_0_4_4
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n9, n20, all_0_2_2, n8 and discharging atoms sum(n9, n20) = all_0_2_2, sum(n9, n20) = n8, yields:
% 28.98/9.81 | (924) all_0_2_2 = n8
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n9, n0, all_0_4_4, n9 and discharging atoms sum(n9, n0) = all_0_4_4, sum(n9, n0) = n9, yields:
% 28.98/9.81 | (925) all_0_4_4 = n9
% 28.98/9.81 |
% 28.98/9.81 | From (924) and (473) follows:
% 28.98/9.81 | (926) pred(n8) = all_0_1_1
% 28.98/9.81 |
% 28.98/9.81 | From (925) and (716) follows:
% 28.98/9.81 | (927) pred(n9) = all_0_3_3
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 28.98/9.81 | (928) all_0_3_3 = n8
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 28.98/9.81 | (929) all_0_1_1 = n7
% 28.98/9.81 |
% 28.98/9.81 | From (928) and (232) follows:
% 28.98/9.81 | (930) sum(n8, all_0_0_0) = all_0_6_6
% 28.98/9.81 |
% 28.98/9.81 | From (929) and (730) follows:
% 28.98/9.81 | (931) sum(n20, n7) = all_0_0_0
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n20, n7, all_0_0_0, n6 and discharging atoms sum(n20, n7) = all_0_0_0, sum(n20, n7) = n6, yields:
% 28.98/9.81 | (932) all_0_0_0 = n6
% 28.98/9.81 |
% 28.98/9.81 | From (932) and (930) follows:
% 28.98/9.81 | (933) sum(n8, n6) = all_0_6_6
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n8, n6, all_0_6_6, n14 and discharging atoms sum(n8, n6) = all_0_6_6, sum(n8, n6) = n14, yields:
% 28.98/9.81 | (934) all_0_6_6 = n14
% 28.98/9.81 |
% 28.98/9.81 | Equations (934) can reduce 353 to:
% 28.98/9.81 | (748) $false
% 28.98/9.81 |
% 28.98/9.81 |-The branch is then unsatisfiable
% 28.98/9.81 |-Branch two:
% 28.98/9.81 | (936) ~ (all_0_8_8 = n9)
% 28.98/9.81 | (937) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.81 |
% 28.98/9.81 +-Applying beta-rule and splitting (937), into two cases.
% 28.98/9.81 |-Branch one:
% 28.98/9.81 | (938) all_0_8_8 = n8
% 28.98/9.81 |
% 28.98/9.81 | From (938) and (731) follows:
% 28.98/9.81 | (939) sum(n8, n20) = all_0_2_2
% 28.98/9.81 |
% 28.98/9.81 | From (938) and (733) follows:
% 28.98/9.81 | (940) sum(n8, n0) = all_0_4_4
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n8, n20, all_0_2_2, n7 and discharging atoms sum(n8, n20) = all_0_2_2, sum(n8, n20) = n7, yields:
% 28.98/9.81 | (941) all_0_2_2 = n7
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n8, n0, all_0_4_4, n8 and discharging atoms sum(n8, n0) = all_0_4_4, sum(n8, n0) = n8, yields:
% 28.98/9.81 | (942) all_0_4_4 = n8
% 28.98/9.81 |
% 28.98/9.81 | From (941) and (473) follows:
% 28.98/9.81 | (943) pred(n7) = all_0_1_1
% 28.98/9.81 |
% 28.98/9.81 | From (942) and (716) follows:
% 28.98/9.81 | (944) pred(n8) = all_0_3_3
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 28.98/9.81 | (945) all_0_3_3 = n7
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 28.98/9.81 | (946) all_0_1_1 = n6
% 28.98/9.81 |
% 28.98/9.81 | From (945) and (232) follows:
% 28.98/9.81 | (947) sum(n7, all_0_0_0) = all_0_6_6
% 28.98/9.81 |
% 28.98/9.81 | From (946) and (730) follows:
% 28.98/9.81 | (948) sum(n20, n6) = all_0_0_0
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n20, n6, all_0_0_0, n5 and discharging atoms sum(n20, n6) = all_0_0_0, sum(n20, n6) = n5, yields:
% 28.98/9.81 | (949) all_0_0_0 = n5
% 28.98/9.81 |
% 28.98/9.81 | From (949) and (947) follows:
% 28.98/9.81 | (950) sum(n7, n5) = all_0_6_6
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n7, n5, all_0_6_6, n12 and discharging atoms sum(n7, n5) = all_0_6_6, sum(n7, n5) = n12, yields:
% 28.98/9.81 | (951) all_0_6_6 = n12
% 28.98/9.81 |
% 28.98/9.81 | Equations (951) can reduce 76 to:
% 28.98/9.81 | (748) $false
% 28.98/9.81 |
% 28.98/9.81 |-The branch is then unsatisfiable
% 28.98/9.81 |-Branch two:
% 28.98/9.81 | (953) ~ (all_0_8_8 = n8)
% 28.98/9.81 | (954) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.81 |
% 28.98/9.81 +-Applying beta-rule and splitting (954), into two cases.
% 28.98/9.81 |-Branch one:
% 28.98/9.81 | (955) all_0_8_8 = n7
% 28.98/9.81 |
% 28.98/9.81 | From (955) and (731) follows:
% 28.98/9.81 | (956) sum(n7, n20) = all_0_2_2
% 28.98/9.81 |
% 28.98/9.81 | From (955) and (733) follows:
% 28.98/9.81 | (957) sum(n7, n0) = all_0_4_4
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n7, n20, all_0_2_2, n6 and discharging atoms sum(n7, n20) = all_0_2_2, sum(n7, n20) = n6, yields:
% 28.98/9.81 | (958) all_0_2_2 = n6
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n7, n0, all_0_4_4, n7 and discharging atoms sum(n7, n0) = all_0_4_4, sum(n7, n0) = n7, yields:
% 28.98/9.81 | (959) all_0_4_4 = n7
% 28.98/9.81 |
% 28.98/9.81 | From (958) and (473) follows:
% 28.98/9.81 | (960) pred(n6) = all_0_1_1
% 28.98/9.81 |
% 28.98/9.81 | From (959) and (716) follows:
% 28.98/9.81 | (961) pred(n7) = all_0_3_3
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 28.98/9.81 | (962) all_0_3_3 = n6
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 28.98/9.81 | (963) all_0_1_1 = n5
% 28.98/9.81 |
% 28.98/9.81 | From (962) and (232) follows:
% 28.98/9.81 | (964) sum(n6, all_0_0_0) = all_0_6_6
% 28.98/9.81 |
% 28.98/9.81 | From (963) and (730) follows:
% 28.98/9.81 | (965) sum(n20, n5) = all_0_0_0
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n20, n5, all_0_0_0, n4 and discharging atoms sum(n20, n5) = all_0_0_0, sum(n20, n5) = n4, yields:
% 28.98/9.81 | (966) all_0_0_0 = n4
% 28.98/9.81 |
% 28.98/9.81 | From (966) and (964) follows:
% 28.98/9.81 | (967) sum(n6, n4) = all_0_6_6
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n6, n4, all_0_6_6, n10 and discharging atoms sum(n6, n4) = all_0_6_6, sum(n6, n4) = n10, yields:
% 28.98/9.81 | (968) all_0_6_6 = n10
% 28.98/9.81 |
% 28.98/9.81 | Equations (968) can reduce 176 to:
% 28.98/9.81 | (748) $false
% 28.98/9.81 |
% 28.98/9.81 |-The branch is then unsatisfiable
% 28.98/9.81 |-Branch two:
% 28.98/9.81 | (970) ~ (all_0_8_8 = n7)
% 28.98/9.81 | (971) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.81 |
% 28.98/9.81 +-Applying beta-rule and splitting (971), into two cases.
% 28.98/9.81 |-Branch one:
% 28.98/9.81 | (972) all_0_8_8 = n6
% 28.98/9.81 |
% 28.98/9.81 | From (972) and (731) follows:
% 28.98/9.81 | (973) sum(n6, n20) = all_0_2_2
% 28.98/9.81 |
% 28.98/9.81 | From (972) and (733) follows:
% 28.98/9.81 | (974) sum(n6, n0) = all_0_4_4
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n6, n20, all_0_2_2, n5 and discharging atoms sum(n6, n20) = all_0_2_2, sum(n6, n20) = n5, yields:
% 28.98/9.81 | (975) all_0_2_2 = n5
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (619) with n6, n0, all_0_4_4, n6 and discharging atoms sum(n6, n0) = all_0_4_4, sum(n6, n0) = n6, yields:
% 28.98/9.81 | (976) all_0_4_4 = n6
% 28.98/9.81 |
% 28.98/9.81 | From (975) and (473) follows:
% 28.98/9.81 | (977) pred(n5) = all_0_1_1
% 28.98/9.81 |
% 28.98/9.81 | From (976) and (716) follows:
% 28.98/9.81 | (978) pred(n6) = all_0_3_3
% 28.98/9.81 |
% 28.98/9.81 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 28.98/9.81 | (979) all_0_3_3 = n5
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 28.98/9.82 | (980) all_0_1_1 = n4
% 28.98/9.82 |
% 28.98/9.82 | From (979) and (232) follows:
% 28.98/9.82 | (981) sum(n5, all_0_0_0) = all_0_6_6
% 28.98/9.82 |
% 28.98/9.82 | From (980) and (730) follows:
% 28.98/9.82 | (982) sum(n20, n4) = all_0_0_0
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n20, n4, all_0_0_0, n3 and discharging atoms sum(n20, n4) = all_0_0_0, sum(n20, n4) = n3, yields:
% 28.98/9.82 | (983) all_0_0_0 = n3
% 28.98/9.82 |
% 28.98/9.82 | From (983) and (981) follows:
% 28.98/9.82 | (984) sum(n5, n3) = all_0_6_6
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n5, n3, all_0_6_6, n8 and discharging atoms sum(n5, n3) = all_0_6_6, sum(n5, n3) = n8, yields:
% 28.98/9.82 | (985) all_0_6_6 = n8
% 28.98/9.82 |
% 28.98/9.82 | Equations (985) can reduce 357 to:
% 28.98/9.82 | (748) $false
% 28.98/9.82 |
% 28.98/9.82 |-The branch is then unsatisfiable
% 28.98/9.82 |-Branch two:
% 28.98/9.82 | (987) ~ (all_0_8_8 = n6)
% 28.98/9.82 | (988) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.82 |
% 28.98/9.82 +-Applying beta-rule and splitting (988), into two cases.
% 28.98/9.82 |-Branch one:
% 28.98/9.82 | (989) all_0_8_8 = n5
% 28.98/9.82 |
% 28.98/9.82 | From (989) and (731) follows:
% 28.98/9.82 | (990) sum(n5, n20) = all_0_2_2
% 28.98/9.82 |
% 28.98/9.82 | From (989) and (733) follows:
% 28.98/9.82 | (991) sum(n5, n0) = all_0_4_4
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n5, n20, all_0_2_2, n4 and discharging atoms sum(n5, n20) = all_0_2_2, sum(n5, n20) = n4, yields:
% 28.98/9.82 | (992) all_0_2_2 = n4
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n5, n0, all_0_4_4, n5 and discharging atoms sum(n5, n0) = all_0_4_4, sum(n5, n0) = n5, yields:
% 28.98/9.82 | (993) all_0_4_4 = n5
% 28.98/9.82 |
% 28.98/9.82 | From (992) and (473) follows:
% 28.98/9.82 | (994) pred(n4) = all_0_1_1
% 28.98/9.82 |
% 28.98/9.82 | From (993) and (716) follows:
% 28.98/9.82 | (995) pred(n5) = all_0_3_3
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 28.98/9.82 | (996) all_0_3_3 = n4
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 28.98/9.82 | (997) all_0_1_1 = n3
% 28.98/9.82 |
% 28.98/9.82 | From (996) and (232) follows:
% 28.98/9.82 | (998) sum(n4, all_0_0_0) = all_0_6_6
% 28.98/9.82 |
% 28.98/9.82 | From (997) and (730) follows:
% 28.98/9.82 | (999) sum(n20, n3) = all_0_0_0
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n20, n3, all_0_0_0, n2 and discharging atoms sum(n20, n3) = all_0_0_0, sum(n20, n3) = n2, yields:
% 28.98/9.82 | (1000) all_0_0_0 = n2
% 28.98/9.82 |
% 28.98/9.82 | From (1000) and (998) follows:
% 28.98/9.82 | (1001) sum(n4, n2) = all_0_6_6
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n4, n2, all_0_6_6, n6 and discharging atoms sum(n4, n2) = all_0_6_6, sum(n4, n2) = n6, yields:
% 28.98/9.82 | (1002) all_0_6_6 = n6
% 28.98/9.82 |
% 28.98/9.82 | Equations (1002) can reduce 498 to:
% 28.98/9.82 | (748) $false
% 28.98/9.82 |
% 28.98/9.82 |-The branch is then unsatisfiable
% 28.98/9.82 |-Branch two:
% 28.98/9.82 | (1004) ~ (all_0_8_8 = n5)
% 28.98/9.82 | (1005) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.82 |
% 28.98/9.82 +-Applying beta-rule and splitting (1005), into two cases.
% 28.98/9.82 |-Branch one:
% 28.98/9.82 | (1006) all_0_8_8 = n4
% 28.98/9.82 |
% 28.98/9.82 | From (1006) and (731) follows:
% 28.98/9.82 | (1007) sum(n4, n20) = all_0_2_2
% 28.98/9.82 |
% 28.98/9.82 | From (1006) and (733) follows:
% 28.98/9.82 | (1008) sum(n4, n0) = all_0_4_4
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n4, n20, all_0_2_2, n3 and discharging atoms sum(n4, n20) = all_0_2_2, sum(n4, n20) = n3, yields:
% 28.98/9.82 | (1009) all_0_2_2 = n3
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n4, n0, all_0_4_4, n4 and discharging atoms sum(n4, n0) = all_0_4_4, sum(n4, n0) = n4, yields:
% 28.98/9.82 | (1010) all_0_4_4 = n4
% 28.98/9.82 |
% 28.98/9.82 | From (1009) and (473) follows:
% 28.98/9.82 | (1011) pred(n3) = all_0_1_1
% 28.98/9.82 |
% 28.98/9.82 | From (1010) and (716) follows:
% 28.98/9.82 | (1012) pred(n4) = all_0_3_3
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 28.98/9.82 | (1013) all_0_3_3 = n3
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 28.98/9.82 | (1014) all_0_1_1 = n2
% 28.98/9.82 |
% 28.98/9.82 | From (1013) and (232) follows:
% 28.98/9.82 | (1015) sum(n3, all_0_0_0) = all_0_6_6
% 28.98/9.82 |
% 28.98/9.82 | From (1014) and (730) follows:
% 28.98/9.82 | (1016) sum(n20, n2) = all_0_0_0
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n20, n2, all_0_0_0, n1 and discharging atoms sum(n20, n2) = all_0_0_0, sum(n20, n2) = n1, yields:
% 28.98/9.82 | (1017) all_0_0_0 = n1
% 28.98/9.82 |
% 28.98/9.82 | From (1017) and (1015) follows:
% 28.98/9.82 | (1018) sum(n3, n1) = all_0_6_6
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n3, n1, all_0_6_6, n4 and discharging atoms sum(n3, n1) = all_0_6_6, sum(n3, n1) = n4, yields:
% 28.98/9.82 | (1019) all_0_6_6 = n4
% 28.98/9.82 |
% 28.98/9.82 | Equations (1019) can reduce 48 to:
% 28.98/9.82 | (748) $false
% 28.98/9.82 |
% 28.98/9.82 |-The branch is then unsatisfiable
% 28.98/9.82 |-Branch two:
% 28.98/9.82 | (1021) ~ (all_0_8_8 = n4)
% 28.98/9.82 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.82 |
% 28.98/9.82 +-Applying beta-rule and splitting (1022), into two cases.
% 28.98/9.82 |-Branch one:
% 28.98/9.82 | (1023) all_0_8_8 = n3
% 28.98/9.82 |
% 28.98/9.82 | From (1023) and (731) follows:
% 28.98/9.82 | (1024) sum(n3, n20) = all_0_2_2
% 28.98/9.82 |
% 28.98/9.82 | From (1023) and (733) follows:
% 28.98/9.82 | (1025) sum(n3, n0) = all_0_4_4
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n3, n20, all_0_2_2, n2 and discharging atoms sum(n3, n20) = all_0_2_2, sum(n3, n20) = n2, yields:
% 28.98/9.82 | (1026) all_0_2_2 = n2
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n3, n0, all_0_4_4, n3 and discharging atoms sum(n3, n0) = all_0_4_4, sum(n3, n0) = n3, yields:
% 28.98/9.82 | (1027) all_0_4_4 = n3
% 28.98/9.82 |
% 28.98/9.82 | From (1026) and (473) follows:
% 28.98/9.82 | (1028) pred(n2) = all_0_1_1
% 28.98/9.82 |
% 28.98/9.82 | From (1027) and (716) follows:
% 28.98/9.82 | (1029) pred(n3) = all_0_3_3
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 28.98/9.82 | (1030) all_0_3_3 = n2
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 28.98/9.82 | (1031) all_0_1_1 = n1
% 28.98/9.82 |
% 28.98/9.82 | From (1030) and (232) follows:
% 28.98/9.82 | (1032) sum(n2, all_0_0_0) = all_0_6_6
% 28.98/9.82 |
% 28.98/9.82 | From (1031) and (730) follows:
% 28.98/9.82 | (1033) sum(n20, n1) = all_0_0_0
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n20, n1, all_0_0_0, n0 and discharging atoms sum(n20, n1) = all_0_0_0, sum(n20, n1) = n0, yields:
% 28.98/9.82 | (1034) all_0_0_0 = n0
% 28.98/9.82 |
% 28.98/9.82 | From (1034) and (1032) follows:
% 28.98/9.82 | (1035) sum(n2, n0) = all_0_6_6
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n2, n0, all_0_6_6, n2 and discharging atoms sum(n2, n0) = all_0_6_6, sum(n2, n0) = n2, yields:
% 28.98/9.82 | (1036) all_0_6_6 = n2
% 28.98/9.82 |
% 28.98/9.82 | Equations (1036) can reduce 56 to:
% 28.98/9.82 | (748) $false
% 28.98/9.82 |
% 28.98/9.82 |-The branch is then unsatisfiable
% 28.98/9.82 |-Branch two:
% 28.98/9.82 | (1038) ~ (all_0_8_8 = n3)
% 28.98/9.82 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.82 |
% 28.98/9.82 +-Applying beta-rule and splitting (1039), into two cases.
% 28.98/9.82 |-Branch one:
% 28.98/9.82 | (1040) all_0_8_8 = n2
% 28.98/9.82 |
% 28.98/9.82 | From (1040) and (731) follows:
% 28.98/9.82 | (1041) sum(n2, n20) = all_0_2_2
% 28.98/9.82 |
% 28.98/9.82 | From (1040) and (733) follows:
% 28.98/9.82 | (1042) sum(n2, n0) = all_0_4_4
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n2, n20, all_0_2_2, n1 and discharging atoms sum(n2, n20) = all_0_2_2, sum(n2, n20) = n1, yields:
% 28.98/9.82 | (1043) all_0_2_2 = n1
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n2, n0, all_0_4_4, n2 and discharging atoms sum(n2, n0) = all_0_4_4, sum(n2, n0) = n2, yields:
% 28.98/9.82 | (1044) all_0_4_4 = n2
% 28.98/9.82 |
% 28.98/9.82 | From (1043) and (473) follows:
% 28.98/9.82 | (1045) pred(n1) = all_0_1_1
% 28.98/9.82 |
% 28.98/9.82 | From (1044) and (716) follows:
% 28.98/9.82 | (1046) pred(n2) = all_0_3_3
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 28.98/9.82 | (1047) all_0_3_3 = n1
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 28.98/9.82 | (1048) all_0_1_1 = n0
% 28.98/9.82 |
% 28.98/9.82 | From (1047) and (232) follows:
% 28.98/9.82 | (1049) sum(n1, all_0_0_0) = all_0_6_6
% 28.98/9.82 |
% 28.98/9.82 | From (1048) and (730) follows:
% 28.98/9.82 | (1050) sum(n20, n0) = all_0_0_0
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n20, n0, all_0_0_0, n20 and discharging atoms sum(n20, n0) = all_0_0_0, sum(n20, n0) = n20, yields:
% 28.98/9.82 | (1051) all_0_0_0 = n20
% 28.98/9.82 |
% 28.98/9.82 | From (1051) and (1049) follows:
% 28.98/9.82 | (1052) sum(n1, n20) = all_0_6_6
% 28.98/9.82 |
% 28.98/9.82 | Instantiating formula (619) with n1, n20, all_0_6_6, n0 and discharging atoms sum(n1, n20) = all_0_6_6, sum(n1, n20) = n0, yields:
% 28.98/9.82 | (1053) all_0_6_6 = n0
% 28.98/9.82 |
% 28.98/9.82 | Equations (1053) can reduce 676 to:
% 28.98/9.82 | (748) $false
% 28.98/9.82 |
% 28.98/9.82 |-The branch is then unsatisfiable
% 28.98/9.82 |-Branch two:
% 28.98/9.82 | (1055) ~ (all_0_8_8 = n2)
% 28.98/9.82 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 28.98/9.82 |
% 28.98/9.82 +-Applying beta-rule and splitting (1056), into two cases.
% 28.98/9.82 |-Branch one:
% 28.98/9.82 | (1057) all_0_8_8 = n1
% 28.98/9.82 |
% 28.98/9.82 | From (1057) and (731) follows:
% 28.98/9.82 | (1058) sum(n1, n20) = all_0_2_2
% 28.98/9.83 |
% 28.98/9.83 | From (1057) and (733) follows:
% 28.98/9.83 | (1059) sum(n1, n0) = all_0_4_4
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (619) with n1, n20, all_0_2_2, n0 and discharging atoms sum(n1, n20) = all_0_2_2, sum(n1, n20) = n0, yields:
% 28.98/9.83 | (1060) all_0_2_2 = n0
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (619) with n1, n0, all_0_4_4, n1 and discharging atoms sum(n1, n0) = all_0_4_4, sum(n1, n0) = n1, yields:
% 28.98/9.83 | (1061) all_0_4_4 = n1
% 28.98/9.83 |
% 28.98/9.83 | From (1060) and (473) follows:
% 28.98/9.83 | (1062) pred(n0) = all_0_1_1
% 28.98/9.83 |
% 28.98/9.83 | From (1061) and (716) follows:
% 28.98/9.83 | (1063) pred(n1) = all_0_3_3
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 28.98/9.83 | (1064) all_0_3_3 = n0
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 28.98/9.83 | (1065) all_0_1_1 = n20
% 28.98/9.83 |
% 28.98/9.83 | From (1064) and (232) follows:
% 28.98/9.83 | (1066) sum(n0, all_0_0_0) = all_0_6_6
% 28.98/9.83 |
% 28.98/9.83 | From (1065) and (730) follows:
% 28.98/9.83 | (1067) sum(n20, n20) = all_0_0_0
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (619) with n20, n20, all_0_0_0, n19 and discharging atoms sum(n20, n20) = all_0_0_0, sum(n20, n20) = n19, yields:
% 28.98/9.83 | (1068) all_0_0_0 = n19
% 28.98/9.83 |
% 28.98/9.83 | From (1068) and (1066) follows:
% 28.98/9.83 | (1069) sum(n0, n19) = all_0_6_6
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (619) with n0, n19, all_0_6_6, n19 and discharging atoms sum(n0, n19) = all_0_6_6, sum(n0, n19) = n19, yields:
% 28.98/9.83 | (1070) all_0_6_6 = n19
% 28.98/9.83 |
% 28.98/9.83 | Equations (1070) can reduce 31 to:
% 28.98/9.83 | (748) $false
% 28.98/9.83 |
% 28.98/9.83 |-The branch is then unsatisfiable
% 28.98/9.83 |-Branch two:
% 28.98/9.83 | (1072) ~ (all_0_8_8 = n1)
% 28.98/9.83 | (1073) all_0_8_8 = n0
% 28.98/9.83 |
% 28.98/9.83 | From (1073) and (731) follows:
% 28.98/9.83 | (1074) sum(n0, n20) = all_0_2_2
% 28.98/9.83 |
% 28.98/9.83 | From (1073) and (733) follows:
% 28.98/9.83 | (1075) sum(n0, n0) = all_0_4_4
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (619) with n0, n20, all_0_2_2, n20 and discharging atoms sum(n0, n20) = all_0_2_2, sum(n0, n20) = n20, yields:
% 28.98/9.83 | (1076) all_0_2_2 = n20
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (619) with n0, n0, all_0_4_4, n0 and discharging atoms sum(n0, n0) = all_0_4_4, sum(n0, n0) = n0, yields:
% 28.98/9.83 | (1077) all_0_4_4 = n0
% 28.98/9.83 |
% 28.98/9.83 | From (1076) and (473) follows:
% 28.98/9.83 | (1078) pred(n20) = all_0_1_1
% 28.98/9.83 |
% 28.98/9.83 | From (1077) and (716) follows:
% 28.98/9.83 | (1079) pred(n0) = all_0_3_3
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 28.98/9.83 | (1080) all_0_1_1 = n19
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 28.98/9.83 | (1081) all_0_3_3 = n20
% 28.98/9.83 |
% 28.98/9.83 | From (1081) and (232) follows:
% 28.98/9.83 | (1082) sum(n20, all_0_0_0) = all_0_6_6
% 28.98/9.83 |
% 28.98/9.83 | From (1080) and (730) follows:
% 28.98/9.83 | (1083) sum(n20, n19) = all_0_0_0
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (619) with n20, n19, all_0_0_0, n18 and discharging atoms sum(n20, n19) = all_0_0_0, sum(n20, n19) = n18, yields:
% 28.98/9.83 | (1084) all_0_0_0 = n18
% 28.98/9.83 |
% 28.98/9.83 | From (1084) and (1082) follows:
% 28.98/9.83 | (1085) sum(n20, n18) = all_0_6_6
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (619) with n20, n18, all_0_6_6, n17 and discharging atoms sum(n20, n18) = all_0_6_6, sum(n20, n18) = n17, yields:
% 28.98/9.83 | (1086) all_0_6_6 = n17
% 28.98/9.83 |
% 28.98/9.83 | Equations (1086) can reduce 669 to:
% 28.98/9.83 | (748) $false
% 28.98/9.83 |
% 28.98/9.83 |-The branch is then unsatisfiable
% 28.98/9.83 |-Branch two:
% 28.98/9.83 | (1088) ~ (all_0_7_7 = n20)
% 28.98/9.83 | (1089) all_0_7_7 = n19 | all_0_7_7 = n18 | all_0_7_7 = n17 | all_0_7_7 = n16 | all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 28.98/9.83 |
% 28.98/9.83 +-Applying beta-rule and splitting (205), into two cases.
% 28.98/9.83 |-Branch one:
% 28.98/9.83 | (734) all_0_8_8 = n20
% 28.98/9.83 |
% 28.98/9.83 | From (734) and (708) follows:
% 28.98/9.83 | (1091) sum(n20, all_0_5_5) = all_0_4_4
% 28.98/9.83 |
% 28.98/9.83 | From (734) and (378) follows:
% 28.98/9.83 | (1092) sum(n20, all_0_7_7) = all_0_2_2
% 28.98/9.83 |
% 28.98/9.83 +-Applying beta-rule and splitting (1089), into two cases.
% 28.98/9.83 |-Branch one:
% 28.98/9.83 | (1093) all_0_7_7 = n19
% 28.98/9.83 |
% 28.98/9.83 | From (1093) and (683) follows:
% 28.98/9.83 | (1094) succ(n19) = all_0_5_5
% 28.98/9.83 |
% 28.98/9.83 | From (1093) and (8) follows:
% 28.98/9.83 | (1095) sum(n19, all_0_1_1) = all_0_0_0
% 28.98/9.83 |
% 28.98/9.83 | From (1093) and (1092) follows:
% 28.98/9.83 | (1096) sum(n20, n19) = all_0_2_2
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (388) with n19, all_0_5_5, n20 and discharging atoms succ(n19) = all_0_5_5, succ(n19) = n20, yields:
% 28.98/9.83 | (1097) all_0_5_5 = n20
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (619) with n20, n19, all_0_2_2, n18 and discharging atoms sum(n20, n19) = all_0_2_2, sum(n20, n19) = n18, yields:
% 28.98/9.83 | (754) all_0_2_2 = n18
% 28.98/9.83 |
% 28.98/9.83 | From (754) and (473) follows:
% 28.98/9.83 | (756) pred(n18) = all_0_1_1
% 28.98/9.83 |
% 28.98/9.83 | From (1097) and (1091) follows:
% 28.98/9.83 | (1100) sum(n20, n20) = all_0_4_4
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 28.98/9.83 | (759) all_0_1_1 = n17
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (619) with n20, n20, all_0_4_4, n19 and discharging atoms sum(n20, n20) = all_0_4_4, sum(n20, n20) = n19, yields:
% 28.98/9.83 | (755) all_0_4_4 = n19
% 28.98/9.83 |
% 28.98/9.83 | From (755) and (716) follows:
% 28.98/9.83 | (757) pred(n19) = all_0_3_3
% 28.98/9.83 |
% 28.98/9.83 | From (759) and (1095) follows:
% 28.98/9.83 | (1104) sum(n19, n17) = all_0_0_0
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 28.98/9.83 | (758) all_0_3_3 = n18
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (619) with n19, n17, all_0_0_0, n15 and discharging atoms sum(n19, n17) = all_0_0_0, sum(n19, n17) = n15, yields:
% 28.98/9.83 | (779) all_0_0_0 = n15
% 28.98/9.83 |
% 28.98/9.83 | From (758)(779) and (232) follows:
% 28.98/9.83 | (1107) sum(n18, n15) = all_0_6_6
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (619) with n18, n15, all_0_6_6, n12 and discharging atoms sum(n18, n15) = all_0_6_6, sum(n18, n15) = n12, yields:
% 28.98/9.83 | (951) all_0_6_6 = n12
% 28.98/9.83 |
% 28.98/9.83 | Equations (951) can reduce 76 to:
% 28.98/9.83 | (748) $false
% 28.98/9.83 |
% 28.98/9.83 |-The branch is then unsatisfiable
% 28.98/9.83 |-Branch two:
% 28.98/9.83 | (1110) ~ (all_0_7_7 = n19)
% 28.98/9.83 | (1111) all_0_7_7 = n18 | all_0_7_7 = n17 | all_0_7_7 = n16 | all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 28.98/9.83 |
% 28.98/9.83 +-Applying beta-rule and splitting (1111), into two cases.
% 28.98/9.83 |-Branch one:
% 28.98/9.83 | (1112) all_0_7_7 = n18
% 28.98/9.83 |
% 28.98/9.83 | From (1112) and (683) follows:
% 28.98/9.83 | (1113) succ(n18) = all_0_5_5
% 28.98/9.83 |
% 28.98/9.83 | From (1112) and (8) follows:
% 28.98/9.83 | (1114) sum(n18, all_0_1_1) = all_0_0_0
% 28.98/9.83 |
% 28.98/9.83 | From (1112) and (1092) follows:
% 28.98/9.83 | (1115) sum(n20, n18) = all_0_2_2
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (388) with n18, all_0_5_5, n19 and discharging atoms succ(n18) = all_0_5_5, succ(n18) = n19, yields:
% 28.98/9.83 | (1116) all_0_5_5 = n19
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (619) with n20, n18, all_0_2_2, n17 and discharging atoms sum(n20, n18) = all_0_2_2, sum(n20, n18) = n17, yields:
% 28.98/9.83 | (771) all_0_2_2 = n17
% 28.98/9.83 |
% 28.98/9.83 | From (771) and (473) follows:
% 28.98/9.83 | (773) pred(n17) = all_0_1_1
% 28.98/9.83 |
% 28.98/9.83 | From (1116) and (1091) follows:
% 28.98/9.83 | (1119) sum(n20, n19) = all_0_4_4
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 28.98/9.83 | (776) all_0_1_1 = n16
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (619) with n20, n19, all_0_4_4, n18 and discharging atoms sum(n20, n19) = all_0_4_4, sum(n20, n19) = n18, yields:
% 28.98/9.83 | (772) all_0_4_4 = n18
% 28.98/9.83 |
% 28.98/9.83 | From (772) and (716) follows:
% 28.98/9.83 | (774) pred(n18) = all_0_3_3
% 28.98/9.83 |
% 28.98/9.83 | From (776) and (1114) follows:
% 28.98/9.83 | (1123) sum(n18, n16) = all_0_0_0
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 28.98/9.83 | (775) all_0_3_3 = n17
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (619) with n18, n16, all_0_0_0, n13 and discharging atoms sum(n18, n16) = all_0_0_0, sum(n18, n16) = n13, yields:
% 28.98/9.83 | (813) all_0_0_0 = n13
% 28.98/9.83 |
% 28.98/9.83 | From (775)(813) and (232) follows:
% 28.98/9.83 | (1126) sum(n17, n13) = all_0_6_6
% 28.98/9.83 |
% 28.98/9.83 | Instantiating formula (619) with n17, n13, all_0_6_6, n9 and discharging atoms sum(n17, n13) = all_0_6_6, sum(n17, n13) = n9, yields:
% 28.98/9.83 | (798) all_0_6_6 = n9
% 28.98/9.83 |
% 28.98/9.83 | Equations (798) can reduce 593 to:
% 28.98/9.83 | (748) $false
% 28.98/9.83 |
% 28.98/9.83 |-The branch is then unsatisfiable
% 28.98/9.83 |-Branch two:
% 28.98/9.83 | (1129) ~ (all_0_7_7 = n18)
% 28.98/9.83 | (1130) all_0_7_7 = n17 | all_0_7_7 = n16 | all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 28.98/9.83 |
% 28.98/9.83 +-Applying beta-rule and splitting (1130), into two cases.
% 28.98/9.83 |-Branch one:
% 28.98/9.83 | (1131) all_0_7_7 = n17
% 28.98/9.83 |
% 28.98/9.83 | From (1131) and (683) follows:
% 28.98/9.83 | (1132) succ(n17) = all_0_5_5
% 28.98/9.83 |
% 28.98/9.83 | From (1131) and (8) follows:
% 28.98/9.83 | (1133) sum(n17, all_0_1_1) = all_0_0_0
% 28.98/9.83 |
% 28.98/9.83 | From (1131) and (1092) follows:
% 28.98/9.84 | (1134) sum(n20, n17) = all_0_2_2
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (388) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 28.98/9.84 | (1135) all_0_5_5 = n18
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (619) with n20, n17, all_0_2_2, n16 and discharging atoms sum(n20, n17) = all_0_2_2, sum(n20, n17) = n16, yields:
% 28.98/9.84 | (788) all_0_2_2 = n16
% 28.98/9.84 |
% 28.98/9.84 | From (788) and (473) follows:
% 28.98/9.84 | (790) pred(n16) = all_0_1_1
% 28.98/9.84 |
% 28.98/9.84 | From (1135) and (1091) follows:
% 28.98/9.84 | (1138) sum(n20, n18) = all_0_4_4
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 28.98/9.84 | (793) all_0_1_1 = n15
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (619) with n20, n18, all_0_4_4, n17 and discharging atoms sum(n20, n18) = all_0_4_4, sum(n20, n18) = n17, yields:
% 28.98/9.84 | (789) all_0_4_4 = n17
% 28.98/9.84 |
% 28.98/9.84 | From (789) and (716) follows:
% 28.98/9.84 | (791) pred(n17) = all_0_3_3
% 28.98/9.84 |
% 28.98/9.84 | From (793) and (1133) follows:
% 28.98/9.84 | (1142) sum(n17, n15) = all_0_0_0
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 28.98/9.84 | (792) all_0_3_3 = n16
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (619) with n17, n15, all_0_0_0, n11 and discharging atoms sum(n17, n15) = all_0_0_0, sum(n17, n15) = n11, yields:
% 28.98/9.84 | (847) all_0_0_0 = n11
% 28.98/9.84 |
% 28.98/9.84 | From (792)(847) and (232) follows:
% 28.98/9.84 | (1145) sum(n16, n11) = all_0_6_6
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (619) with n16, n11, all_0_6_6, n6 and discharging atoms sum(n16, n11) = all_0_6_6, sum(n16, n11) = n6, yields:
% 28.98/9.84 | (1002) all_0_6_6 = n6
% 28.98/9.84 |
% 28.98/9.84 | Equations (1002) can reduce 498 to:
% 28.98/9.84 | (748) $false
% 28.98/9.84 |
% 28.98/9.84 |-The branch is then unsatisfiable
% 28.98/9.84 |-Branch two:
% 28.98/9.84 | (1148) ~ (all_0_7_7 = n17)
% 28.98/9.84 | (1149) all_0_7_7 = n16 | all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 28.98/9.84 |
% 28.98/9.84 +-Applying beta-rule and splitting (1149), into two cases.
% 28.98/9.84 |-Branch one:
% 28.98/9.84 | (1150) all_0_7_7 = n16
% 28.98/9.84 |
% 28.98/9.84 | From (1150) and (683) follows:
% 28.98/9.84 | (1151) succ(n16) = all_0_5_5
% 28.98/9.84 |
% 28.98/9.84 | From (1150) and (8) follows:
% 28.98/9.84 | (1152) sum(n16, all_0_1_1) = all_0_0_0
% 28.98/9.84 |
% 28.98/9.84 | From (1150) and (1092) follows:
% 28.98/9.84 | (1153) sum(n20, n16) = all_0_2_2
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (388) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 28.98/9.84 | (1154) all_0_5_5 = n17
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (619) with n20, n16, all_0_2_2, n15 and discharging atoms sum(n20, n16) = all_0_2_2, sum(n20, n16) = n15, yields:
% 28.98/9.84 | (805) all_0_2_2 = n15
% 28.98/9.84 |
% 28.98/9.84 | From (805) and (473) follows:
% 28.98/9.84 | (807) pred(n15) = all_0_1_1
% 28.98/9.84 |
% 28.98/9.84 | From (1154) and (1091) follows:
% 28.98/9.84 | (1157) sum(n20, n17) = all_0_4_4
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 28.98/9.84 | (810) all_0_1_1 = n14
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (619) with n20, n17, all_0_4_4, n16 and discharging atoms sum(n20, n17) = all_0_4_4, sum(n20, n17) = n16, yields:
% 28.98/9.84 | (806) all_0_4_4 = n16
% 28.98/9.84 |
% 28.98/9.84 | From (806) and (716) follows:
% 28.98/9.84 | (808) pred(n16) = all_0_3_3
% 28.98/9.84 |
% 28.98/9.84 | From (810) and (1152) follows:
% 28.98/9.84 | (1161) sum(n16, n14) = all_0_0_0
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 28.98/9.84 | (809) all_0_3_3 = n15
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (619) with n16, n14, all_0_0_0, n9 and discharging atoms sum(n16, n14) = all_0_0_0, sum(n16, n14) = n9, yields:
% 28.98/9.84 | (881) all_0_0_0 = n9
% 28.98/9.84 |
% 28.98/9.84 | From (809)(881) and (232) follows:
% 28.98/9.84 | (1164) sum(n15, n9) = all_0_6_6
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (619) with n15, n9, all_0_6_6, n3 and discharging atoms sum(n15, n9) = all_0_6_6, sum(n15, n9) = n3, yields:
% 28.98/9.84 | (849) all_0_6_6 = n3
% 28.98/9.84 |
% 28.98/9.84 | Equations (849) can reduce 416 to:
% 28.98/9.84 | (748) $false
% 28.98/9.84 |
% 28.98/9.84 |-The branch is then unsatisfiable
% 28.98/9.84 |-Branch two:
% 28.98/9.84 | (1167) ~ (all_0_7_7 = n16)
% 28.98/9.84 | (1168) all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 28.98/9.84 |
% 28.98/9.84 +-Applying beta-rule and splitting (1168), into two cases.
% 28.98/9.84 |-Branch one:
% 28.98/9.84 | (1169) all_0_7_7 = n15
% 28.98/9.84 |
% 28.98/9.84 | From (1169) and (683) follows:
% 28.98/9.84 | (1170) succ(n15) = all_0_5_5
% 28.98/9.84 |
% 28.98/9.84 | From (1169) and (8) follows:
% 28.98/9.84 | (1171) sum(n15, all_0_1_1) = all_0_0_0
% 28.98/9.84 |
% 28.98/9.84 | From (1169) and (1092) follows:
% 28.98/9.84 | (1172) sum(n20, n15) = all_0_2_2
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (388) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 28.98/9.84 | (1173) all_0_5_5 = n16
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (619) with n20, n15, all_0_2_2, n14 and discharging atoms sum(n20, n15) = all_0_2_2, sum(n20, n15) = n14, yields:
% 28.98/9.84 | (822) all_0_2_2 = n14
% 28.98/9.84 |
% 28.98/9.84 | From (822) and (473) follows:
% 28.98/9.84 | (824) pred(n14) = all_0_1_1
% 28.98/9.84 |
% 28.98/9.84 | From (1173) and (1091) follows:
% 28.98/9.84 | (1176) sum(n20, n16) = all_0_4_4
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 28.98/9.84 | (827) all_0_1_1 = n13
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (619) with n20, n16, all_0_4_4, n15 and discharging atoms sum(n20, n16) = all_0_4_4, sum(n20, n16) = n15, yields:
% 28.98/9.84 | (823) all_0_4_4 = n15
% 28.98/9.84 |
% 28.98/9.84 | From (823) and (716) follows:
% 28.98/9.84 | (825) pred(n15) = all_0_3_3
% 28.98/9.84 |
% 28.98/9.84 | From (827) and (1171) follows:
% 28.98/9.84 | (1180) sum(n15, n13) = all_0_0_0
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 28.98/9.84 | (826) all_0_3_3 = n14
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (619) with n15, n13, all_0_0_0, n7 and discharging atoms sum(n15, n13) = all_0_0_0, sum(n15, n13) = n7, yields:
% 28.98/9.84 | (915) all_0_0_0 = n7
% 28.98/9.84 |
% 28.98/9.84 | From (826)(915) and (232) follows:
% 28.98/9.84 | (1183) sum(n14, n7) = all_0_6_6
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (619) with n14, n7, all_0_6_6, n0 and discharging atoms sum(n14, n7) = all_0_6_6, sum(n14, n7) = n0, yields:
% 28.98/9.84 | (1053) all_0_6_6 = n0
% 28.98/9.84 |
% 28.98/9.84 | Equations (1053) can reduce 676 to:
% 28.98/9.84 | (748) $false
% 28.98/9.84 |
% 28.98/9.84 |-The branch is then unsatisfiable
% 28.98/9.84 |-Branch two:
% 28.98/9.84 | (1186) ~ (all_0_7_7 = n15)
% 28.98/9.84 | (1187) all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 28.98/9.84 |
% 28.98/9.84 +-Applying beta-rule and splitting (1187), into two cases.
% 28.98/9.84 |-Branch one:
% 28.98/9.84 | (1188) all_0_7_7 = n14
% 28.98/9.84 |
% 28.98/9.84 | From (1188) and (683) follows:
% 28.98/9.84 | (1189) succ(n14) = all_0_5_5
% 28.98/9.84 |
% 28.98/9.84 | From (1188) and (8) follows:
% 28.98/9.84 | (1190) sum(n14, all_0_1_1) = all_0_0_0
% 28.98/9.84 |
% 28.98/9.84 | From (1188) and (1092) follows:
% 28.98/9.84 | (1191) sum(n20, n14) = all_0_2_2
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (388) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 28.98/9.84 | (1192) all_0_5_5 = n15
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (619) with n20, n14, all_0_2_2, n13 and discharging atoms sum(n20, n14) = all_0_2_2, sum(n20, n14) = n13, yields:
% 28.98/9.84 | (839) all_0_2_2 = n13
% 28.98/9.84 |
% 28.98/9.84 | From (839) and (473) follows:
% 28.98/9.84 | (841) pred(n13) = all_0_1_1
% 28.98/9.84 |
% 28.98/9.84 | From (1192) and (1091) follows:
% 28.98/9.84 | (1195) sum(n20, n15) = all_0_4_4
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 28.98/9.84 | (844) all_0_1_1 = n12
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (619) with n20, n15, all_0_4_4, n14 and discharging atoms sum(n20, n15) = all_0_4_4, sum(n20, n15) = n14, yields:
% 28.98/9.84 | (840) all_0_4_4 = n14
% 28.98/9.84 |
% 28.98/9.84 | From (840) and (716) follows:
% 28.98/9.84 | (842) pred(n14) = all_0_3_3
% 28.98/9.84 |
% 28.98/9.84 | From (844) and (1190) follows:
% 28.98/9.84 | (1199) sum(n14, n12) = all_0_0_0
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 28.98/9.84 | (843) all_0_3_3 = n13
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (619) with n14, n12, all_0_0_0, n5 and discharging atoms sum(n14, n12) = all_0_0_0, sum(n14, n12) = n5, yields:
% 28.98/9.84 | (949) all_0_0_0 = n5
% 28.98/9.84 |
% 28.98/9.84 | From (843)(949) and (232) follows:
% 28.98/9.84 | (1202) sum(n13, n5) = all_0_6_6
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (619) with n13, n5, all_0_6_6, n18 and discharging atoms sum(n13, n5) = all_0_6_6, sum(n13, n5) = n18, yields:
% 28.98/9.84 | (900) all_0_6_6 = n18
% 28.98/9.84 |
% 28.98/9.84 | Equations (900) can reduce 622 to:
% 28.98/9.84 | (748) $false
% 28.98/9.84 |
% 28.98/9.84 |-The branch is then unsatisfiable
% 28.98/9.84 |-Branch two:
% 28.98/9.84 | (1205) ~ (all_0_7_7 = n14)
% 28.98/9.84 | (1206) all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 28.98/9.84 |
% 28.98/9.84 +-Applying beta-rule and splitting (1206), into two cases.
% 28.98/9.84 |-Branch one:
% 28.98/9.84 | (1207) all_0_7_7 = n13
% 28.98/9.84 |
% 28.98/9.84 | From (1207) and (683) follows:
% 28.98/9.84 | (1208) succ(n13) = all_0_5_5
% 28.98/9.84 |
% 28.98/9.84 | From (1207) and (8) follows:
% 28.98/9.84 | (1209) sum(n13, all_0_1_1) = all_0_0_0
% 28.98/9.84 |
% 28.98/9.84 | From (1207) and (1092) follows:
% 28.98/9.84 | (1210) sum(n20, n13) = all_0_2_2
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (388) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 28.98/9.84 | (1211) all_0_5_5 = n14
% 28.98/9.84 |
% 28.98/9.84 | Instantiating formula (619) with n20, n13, all_0_2_2, n12 and discharging atoms sum(n20, n13) = all_0_2_2, sum(n20, n13) = n12, yields:
% 28.98/9.84 | (856) all_0_2_2 = n12
% 28.98/9.84 |
% 28.98/9.84 | From (856) and (473) follows:
% 28.98/9.84 | (858) pred(n12) = all_0_1_1
% 28.98/9.84 |
% 28.98/9.84 | From (1211) and (1091) follows:
% 28.98/9.84 | (1214) sum(n20, n14) = all_0_4_4
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 28.98/9.85 | (861) all_0_1_1 = n11
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (619) with n20, n14, all_0_4_4, n13 and discharging atoms sum(n20, n14) = all_0_4_4, sum(n20, n14) = n13, yields:
% 28.98/9.85 | (857) all_0_4_4 = n13
% 28.98/9.85 |
% 28.98/9.85 | From (857) and (716) follows:
% 28.98/9.85 | (859) pred(n13) = all_0_3_3
% 28.98/9.85 |
% 28.98/9.85 | From (861) and (1209) follows:
% 28.98/9.85 | (1218) sum(n13, n11) = all_0_0_0
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 28.98/9.85 | (860) all_0_3_3 = n12
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (619) with n13, n11, all_0_0_0, n3 and discharging atoms sum(n13, n11) = all_0_0_0, sum(n13, n11) = n3, yields:
% 28.98/9.85 | (983) all_0_0_0 = n3
% 28.98/9.85 |
% 28.98/9.85 | From (860)(983) and (232) follows:
% 28.98/9.85 | (1221) sum(n12, n3) = all_0_6_6
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (619) with n12, n3, all_0_6_6, n15 and discharging atoms sum(n12, n3) = all_0_6_6, sum(n12, n3) = n15, yields:
% 28.98/9.85 | (747) all_0_6_6 = n15
% 28.98/9.85 |
% 28.98/9.85 | Equations (747) can reduce 456 to:
% 28.98/9.85 | (748) $false
% 28.98/9.85 |
% 28.98/9.85 |-The branch is then unsatisfiable
% 28.98/9.85 |-Branch two:
% 28.98/9.85 | (1224) ~ (all_0_7_7 = n13)
% 28.98/9.85 | (1225) all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 28.98/9.85 |
% 28.98/9.85 +-Applying beta-rule and splitting (1225), into two cases.
% 28.98/9.85 |-Branch one:
% 28.98/9.85 | (1226) all_0_7_7 = n12
% 28.98/9.85 |
% 28.98/9.85 | From (1226) and (683) follows:
% 28.98/9.85 | (1227) succ(n12) = all_0_5_5
% 28.98/9.85 |
% 28.98/9.85 | From (1226) and (8) follows:
% 28.98/9.85 | (1228) sum(n12, all_0_1_1) = all_0_0_0
% 28.98/9.85 |
% 28.98/9.85 | From (1226) and (1092) follows:
% 28.98/9.85 | (1229) sum(n20, n12) = all_0_2_2
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (388) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 28.98/9.85 | (1230) all_0_5_5 = n13
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (619) with n20, n12, all_0_2_2, n11 and discharging atoms sum(n20, n12) = all_0_2_2, sum(n20, n12) = n11, yields:
% 28.98/9.85 | (873) all_0_2_2 = n11
% 28.98/9.85 |
% 28.98/9.85 | From (873) and (473) follows:
% 28.98/9.85 | (875) pred(n11) = all_0_1_1
% 28.98/9.85 |
% 28.98/9.85 | From (1230) and (1091) follows:
% 28.98/9.85 | (1233) sum(n20, n13) = all_0_4_4
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 28.98/9.85 | (878) all_0_1_1 = n10
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (619) with n20, n13, all_0_4_4, n12 and discharging atoms sum(n20, n13) = all_0_4_4, sum(n20, n13) = n12, yields:
% 28.98/9.85 | (874) all_0_4_4 = n12
% 28.98/9.85 |
% 28.98/9.85 | From (874) and (716) follows:
% 28.98/9.85 | (876) pred(n12) = all_0_3_3
% 28.98/9.85 |
% 28.98/9.85 | From (878) and (1228) follows:
% 28.98/9.85 | (1237) sum(n12, n10) = all_0_0_0
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 28.98/9.85 | (877) all_0_3_3 = n11
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (619) with n12, n10, all_0_0_0, n1 and discharging atoms sum(n12, n10) = all_0_0_0, sum(n12, n10) = n1, yields:
% 28.98/9.85 | (1017) all_0_0_0 = n1
% 28.98/9.85 |
% 28.98/9.85 | From (877)(1017) and (232) follows:
% 28.98/9.85 | (1240) sum(n11, n1) = all_0_6_6
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (619) with n11, n1, all_0_6_6, n12 and discharging atoms sum(n11, n1) = all_0_6_6, sum(n11, n1) = n12, yields:
% 28.98/9.85 | (951) all_0_6_6 = n12
% 28.98/9.85 |
% 28.98/9.85 | Equations (951) can reduce 76 to:
% 28.98/9.85 | (748) $false
% 28.98/9.85 |
% 28.98/9.85 |-The branch is then unsatisfiable
% 28.98/9.85 |-Branch two:
% 28.98/9.85 | (1243) ~ (all_0_7_7 = n12)
% 28.98/9.85 | (1244) all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 28.98/9.85 |
% 28.98/9.85 +-Applying beta-rule and splitting (1244), into two cases.
% 28.98/9.85 |-Branch one:
% 28.98/9.85 | (1245) all_0_7_7 = n11
% 28.98/9.85 |
% 28.98/9.85 | From (1245) and (683) follows:
% 28.98/9.85 | (1246) succ(n11) = all_0_5_5
% 28.98/9.85 |
% 28.98/9.85 | From (1245) and (8) follows:
% 28.98/9.85 | (1247) sum(n11, all_0_1_1) = all_0_0_0
% 28.98/9.85 |
% 28.98/9.85 | From (1245) and (1092) follows:
% 28.98/9.85 | (1248) sum(n20, n11) = all_0_2_2
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (388) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 28.98/9.85 | (1249) all_0_5_5 = n12
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (619) with n20, n11, all_0_2_2, n10 and discharging atoms sum(n20, n11) = all_0_2_2, sum(n20, n11) = n10, yields:
% 28.98/9.85 | (890) all_0_2_2 = n10
% 28.98/9.85 |
% 28.98/9.85 | From (890) and (473) follows:
% 28.98/9.85 | (892) pred(n10) = all_0_1_1
% 28.98/9.85 |
% 28.98/9.85 | From (1249) and (1091) follows:
% 28.98/9.85 | (1252) sum(n20, n12) = all_0_4_4
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 28.98/9.85 | (895) all_0_1_1 = n9
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (619) with n20, n12, all_0_4_4, n11 and discharging atoms sum(n20, n12) = all_0_4_4, sum(n20, n12) = n11, yields:
% 28.98/9.85 | (891) all_0_4_4 = n11
% 28.98/9.85 |
% 28.98/9.85 | From (891) and (716) follows:
% 28.98/9.85 | (893) pred(n11) = all_0_3_3
% 28.98/9.85 |
% 28.98/9.85 | From (895) and (1247) follows:
% 28.98/9.85 | (1256) sum(n11, n9) = all_0_0_0
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 28.98/9.85 | (894) all_0_3_3 = n10
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (619) with n11, n9, all_0_0_0, n20 and discharging atoms sum(n11, n9) = all_0_0_0, sum(n11, n9) = n20, yields:
% 28.98/9.85 | (1051) all_0_0_0 = n20
% 28.98/9.85 |
% 28.98/9.85 | From (894)(1051) and (232) follows:
% 28.98/9.85 | (1259) sum(n10, n20) = all_0_6_6
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (619) with n10, n20, all_0_6_6, n9 and discharging atoms sum(n10, n20) = all_0_6_6, sum(n10, n20) = n9, yields:
% 28.98/9.85 | (798) all_0_6_6 = n9
% 28.98/9.85 |
% 28.98/9.85 | Equations (798) can reduce 593 to:
% 28.98/9.85 | (748) $false
% 28.98/9.85 |
% 28.98/9.85 |-The branch is then unsatisfiable
% 28.98/9.85 |-Branch two:
% 28.98/9.85 | (1262) ~ (all_0_7_7 = n11)
% 28.98/9.85 | (1263) all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 28.98/9.85 |
% 28.98/9.85 +-Applying beta-rule and splitting (1263), into two cases.
% 28.98/9.85 |-Branch one:
% 28.98/9.85 | (1264) all_0_7_7 = n10
% 28.98/9.85 |
% 28.98/9.85 | From (1264) and (683) follows:
% 28.98/9.85 | (1265) succ(n10) = all_0_5_5
% 28.98/9.85 |
% 28.98/9.85 | From (1264) and (8) follows:
% 28.98/9.85 | (1266) sum(n10, all_0_1_1) = all_0_0_0
% 28.98/9.85 |
% 28.98/9.85 | From (1264) and (1092) follows:
% 28.98/9.85 | (1267) sum(n20, n10) = all_0_2_2
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (388) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 28.98/9.85 | (1268) all_0_5_5 = n11
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (619) with n20, n10, all_0_2_2, n9 and discharging atoms sum(n20, n10) = all_0_2_2, sum(n20, n10) = n9, yields:
% 28.98/9.85 | (907) all_0_2_2 = n9
% 28.98/9.85 |
% 28.98/9.85 | From (907) and (473) follows:
% 28.98/9.85 | (909) pred(n9) = all_0_1_1
% 28.98/9.85 |
% 28.98/9.85 | From (1268) and (1091) follows:
% 28.98/9.85 | (1271) sum(n20, n11) = all_0_4_4
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 28.98/9.85 | (912) all_0_1_1 = n8
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (619) with n20, n11, all_0_4_4, n10 and discharging atoms sum(n20, n11) = all_0_4_4, sum(n20, n11) = n10, yields:
% 28.98/9.85 | (908) all_0_4_4 = n10
% 28.98/9.85 |
% 28.98/9.85 | From (908) and (716) follows:
% 28.98/9.85 | (910) pred(n10) = all_0_3_3
% 28.98/9.85 |
% 28.98/9.85 | From (912) and (1266) follows:
% 28.98/9.85 | (1275) sum(n10, n8) = all_0_0_0
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 28.98/9.85 | (911) all_0_3_3 = n9
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (619) with n10, n8, all_0_0_0, n18 and discharging atoms sum(n10, n8) = all_0_0_0, sum(n10, n8) = n18, yields:
% 28.98/9.85 | (1084) all_0_0_0 = n18
% 28.98/9.85 |
% 28.98/9.85 | From (911)(1084) and (232) follows:
% 28.98/9.85 | (1278) sum(n9, n18) = all_0_6_6
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (619) with n9, n18, all_0_6_6, n6 and discharging atoms sum(n9, n18) = all_0_6_6, sum(n9, n18) = n6, yields:
% 28.98/9.85 | (1002) all_0_6_6 = n6
% 28.98/9.85 |
% 28.98/9.85 | Equations (1002) can reduce 498 to:
% 28.98/9.85 | (748) $false
% 28.98/9.85 |
% 28.98/9.85 |-The branch is then unsatisfiable
% 28.98/9.85 |-Branch two:
% 28.98/9.85 | (1281) ~ (all_0_7_7 = n10)
% 28.98/9.85 | (1282) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 28.98/9.85 |
% 28.98/9.85 +-Applying beta-rule and splitting (1282), into two cases.
% 28.98/9.85 |-Branch one:
% 28.98/9.85 | (1283) all_0_7_7 = n9
% 28.98/9.85 |
% 28.98/9.85 | From (1283) and (683) follows:
% 28.98/9.85 | (1284) succ(n9) = all_0_5_5
% 28.98/9.85 |
% 28.98/9.85 | From (1283) and (8) follows:
% 28.98/9.85 | (1285) sum(n9, all_0_1_1) = all_0_0_0
% 28.98/9.85 |
% 28.98/9.85 | From (1283) and (1092) follows:
% 28.98/9.85 | (1286) sum(n20, n9) = all_0_2_2
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (388) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 28.98/9.85 | (1287) all_0_5_5 = n10
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (619) with n20, n9, all_0_2_2, n8 and discharging atoms sum(n20, n9) = all_0_2_2, sum(n20, n9) = n8, yields:
% 28.98/9.85 | (924) all_0_2_2 = n8
% 28.98/9.85 |
% 28.98/9.85 | From (924) and (473) follows:
% 28.98/9.85 | (926) pred(n8) = all_0_1_1
% 28.98/9.85 |
% 28.98/9.85 | From (1287) and (1091) follows:
% 28.98/9.85 | (1290) sum(n20, n10) = all_0_4_4
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 28.98/9.85 | (929) all_0_1_1 = n7
% 28.98/9.85 |
% 28.98/9.85 | Instantiating formula (619) with n20, n10, all_0_4_4, n9 and discharging atoms sum(n20, n10) = all_0_4_4, sum(n20, n10) = n9, yields:
% 28.98/9.85 | (925) all_0_4_4 = n9
% 28.98/9.85 |
% 28.98/9.85 | From (925) and (716) follows:
% 28.98/9.85 | (927) pred(n9) = all_0_3_3
% 28.98/9.85 |
% 28.98/9.85 | From (929) and (1285) follows:
% 28.98/9.86 | (1294) sum(n9, n7) = all_0_0_0
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 28.98/9.86 | (928) all_0_3_3 = n8
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (619) with n9, n7, all_0_0_0, n16 and discharging atoms sum(n9, n7) = all_0_0_0, sum(n9, n7) = n16, yields:
% 28.98/9.86 | (762) all_0_0_0 = n16
% 28.98/9.86 |
% 28.98/9.86 | From (928)(762) and (232) follows:
% 28.98/9.86 | (1297) sum(n8, n16) = all_0_6_6
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (619) with n8, n16, all_0_6_6, n3 and discharging atoms sum(n8, n16) = all_0_6_6, sum(n8, n16) = n3, yields:
% 28.98/9.86 | (849) all_0_6_6 = n3
% 28.98/9.86 |
% 28.98/9.86 | Equations (849) can reduce 416 to:
% 28.98/9.86 | (748) $false
% 28.98/9.86 |
% 28.98/9.86 |-The branch is then unsatisfiable
% 28.98/9.86 |-Branch two:
% 28.98/9.86 | (1300) ~ (all_0_7_7 = n9)
% 28.98/9.86 | (1301) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 28.98/9.86 |
% 28.98/9.86 +-Applying beta-rule and splitting (1301), into two cases.
% 28.98/9.86 |-Branch one:
% 28.98/9.86 | (1302) all_0_7_7 = n8
% 28.98/9.86 |
% 28.98/9.86 | From (1302) and (683) follows:
% 28.98/9.86 | (1303) succ(n8) = all_0_5_5
% 28.98/9.86 |
% 28.98/9.86 | From (1302) and (8) follows:
% 28.98/9.86 | (1304) sum(n8, all_0_1_1) = all_0_0_0
% 28.98/9.86 |
% 28.98/9.86 | From (1302) and (1092) follows:
% 28.98/9.86 | (1305) sum(n20, n8) = all_0_2_2
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (388) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 28.98/9.86 | (1306) all_0_5_5 = n9
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (619) with n20, n8, all_0_2_2, n7 and discharging atoms sum(n20, n8) = all_0_2_2, sum(n20, n8) = n7, yields:
% 28.98/9.86 | (941) all_0_2_2 = n7
% 28.98/9.86 |
% 28.98/9.86 | From (941) and (473) follows:
% 28.98/9.86 | (943) pred(n7) = all_0_1_1
% 28.98/9.86 |
% 28.98/9.86 | From (1306) and (1091) follows:
% 28.98/9.86 | (1309) sum(n20, n9) = all_0_4_4
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 28.98/9.86 | (946) all_0_1_1 = n6
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (619) with n20, n9, all_0_4_4, n8 and discharging atoms sum(n20, n9) = all_0_4_4, sum(n20, n9) = n8, yields:
% 28.98/9.86 | (942) all_0_4_4 = n8
% 28.98/9.86 |
% 28.98/9.86 | From (942) and (716) follows:
% 28.98/9.86 | (944) pred(n8) = all_0_3_3
% 28.98/9.86 |
% 28.98/9.86 | From (946) and (1304) follows:
% 28.98/9.86 | (1313) sum(n8, n6) = all_0_0_0
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 28.98/9.86 | (945) all_0_3_3 = n7
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (619) with n8, n6, all_0_0_0, n14 and discharging atoms sum(n8, n6) = all_0_0_0, sum(n8, n6) = n14, yields:
% 28.98/9.86 | (796) all_0_0_0 = n14
% 28.98/9.86 |
% 28.98/9.86 | From (945)(796) and (232) follows:
% 28.98/9.86 | (1316) sum(n7, n14) = all_0_6_6
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (619) with n7, n14, all_0_6_6, n0 and discharging atoms sum(n7, n14) = all_0_6_6, sum(n7, n14) = n0, yields:
% 28.98/9.86 | (1053) all_0_6_6 = n0
% 28.98/9.86 |
% 28.98/9.86 | Equations (1053) can reduce 676 to:
% 28.98/9.86 | (748) $false
% 28.98/9.86 |
% 28.98/9.86 |-The branch is then unsatisfiable
% 28.98/9.86 |-Branch two:
% 28.98/9.86 | (1319) ~ (all_0_7_7 = n8)
% 28.98/9.86 | (1320) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 28.98/9.86 |
% 28.98/9.86 +-Applying beta-rule and splitting (1320), into two cases.
% 28.98/9.86 |-Branch one:
% 28.98/9.86 | (1321) all_0_7_7 = n7
% 28.98/9.86 |
% 28.98/9.86 | From (1321) and (683) follows:
% 28.98/9.86 | (1322) succ(n7) = all_0_5_5
% 28.98/9.86 |
% 28.98/9.86 | From (1321) and (8) follows:
% 28.98/9.86 | (1323) sum(n7, all_0_1_1) = all_0_0_0
% 28.98/9.86 |
% 28.98/9.86 | From (1321) and (1092) follows:
% 28.98/9.86 | (1324) sum(n20, n7) = all_0_2_2
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (388) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 28.98/9.86 | (1325) all_0_5_5 = n8
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (619) with n20, n7, all_0_2_2, n6 and discharging atoms sum(n20, n7) = all_0_2_2, sum(n20, n7) = n6, yields:
% 28.98/9.86 | (958) all_0_2_2 = n6
% 28.98/9.86 |
% 28.98/9.86 | From (958) and (473) follows:
% 28.98/9.86 | (960) pred(n6) = all_0_1_1
% 28.98/9.86 |
% 28.98/9.86 | From (1325) and (1091) follows:
% 28.98/9.86 | (1328) sum(n20, n8) = all_0_4_4
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 28.98/9.86 | (963) all_0_1_1 = n5
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (619) with n20, n8, all_0_4_4, n7 and discharging atoms sum(n20, n8) = all_0_4_4, sum(n20, n8) = n7, yields:
% 28.98/9.86 | (959) all_0_4_4 = n7
% 28.98/9.86 |
% 28.98/9.86 | From (959) and (716) follows:
% 28.98/9.86 | (961) pred(n7) = all_0_3_3
% 28.98/9.86 |
% 28.98/9.86 | From (963) and (1323) follows:
% 28.98/9.86 | (1332) sum(n7, n5) = all_0_0_0
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 28.98/9.86 | (962) all_0_3_3 = n6
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (619) with n7, n5, all_0_0_0, n12 and discharging atoms sum(n7, n5) = all_0_0_0, sum(n7, n5) = n12, yields:
% 28.98/9.86 | (830) all_0_0_0 = n12
% 28.98/9.86 |
% 28.98/9.86 | From (962)(830) and (232) follows:
% 28.98/9.86 | (1335) sum(n6, n12) = all_0_6_6
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (619) with n6, n12, all_0_6_6, n18 and discharging atoms sum(n6, n12) = all_0_6_6, sum(n6, n12) = n18, yields:
% 28.98/9.86 | (900) all_0_6_6 = n18
% 28.98/9.86 |
% 28.98/9.86 | Equations (900) can reduce 622 to:
% 28.98/9.86 | (748) $false
% 28.98/9.86 |
% 28.98/9.86 |-The branch is then unsatisfiable
% 28.98/9.86 |-Branch two:
% 28.98/9.86 | (1338) ~ (all_0_7_7 = n7)
% 28.98/9.86 | (1339) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 28.98/9.86 |
% 28.98/9.86 +-Applying beta-rule and splitting (1339), into two cases.
% 28.98/9.86 |-Branch one:
% 28.98/9.86 | (1340) all_0_7_7 = n6
% 28.98/9.86 |
% 28.98/9.86 | From (1340) and (683) follows:
% 28.98/9.86 | (1341) succ(n6) = all_0_5_5
% 28.98/9.86 |
% 28.98/9.86 | From (1340) and (8) follows:
% 28.98/9.86 | (1342) sum(n6, all_0_1_1) = all_0_0_0
% 28.98/9.86 |
% 28.98/9.86 | From (1340) and (1092) follows:
% 28.98/9.86 | (1343) sum(n20, n6) = all_0_2_2
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (388) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 28.98/9.86 | (1344) all_0_5_5 = n7
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (619) with n20, n6, all_0_2_2, n5 and discharging atoms sum(n20, n6) = all_0_2_2, sum(n20, n6) = n5, yields:
% 28.98/9.86 | (975) all_0_2_2 = n5
% 28.98/9.86 |
% 28.98/9.86 | From (975) and (473) follows:
% 28.98/9.86 | (977) pred(n5) = all_0_1_1
% 28.98/9.86 |
% 28.98/9.86 | From (1344) and (1091) follows:
% 28.98/9.86 | (1347) sum(n20, n7) = all_0_4_4
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 28.98/9.86 | (980) all_0_1_1 = n4
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (619) with n20, n7, all_0_4_4, n6 and discharging atoms sum(n20, n7) = all_0_4_4, sum(n20, n7) = n6, yields:
% 28.98/9.86 | (976) all_0_4_4 = n6
% 28.98/9.86 |
% 28.98/9.86 | From (976) and (716) follows:
% 28.98/9.86 | (978) pred(n6) = all_0_3_3
% 28.98/9.86 |
% 28.98/9.86 | From (980) and (1342) follows:
% 28.98/9.86 | (1351) sum(n6, n4) = all_0_0_0
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 28.98/9.86 | (979) all_0_3_3 = n5
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (619) with n6, n4, all_0_0_0, n10 and discharging atoms sum(n6, n4) = all_0_0_0, sum(n6, n4) = n10, yields:
% 28.98/9.86 | (864) all_0_0_0 = n10
% 28.98/9.86 |
% 28.98/9.86 | From (979)(864) and (232) follows:
% 28.98/9.86 | (1354) sum(n5, n10) = all_0_6_6
% 28.98/9.86 |
% 28.98/9.86 | Instantiating formula (619) with n5, n10, all_0_6_6, n15 and discharging atoms sum(n5, n10) = all_0_6_6, sum(n5, n10) = n15, yields:
% 28.98/9.86 | (747) all_0_6_6 = n15
% 28.98/9.86 |
% 28.98/9.86 | Equations (747) can reduce 456 to:
% 28.98/9.86 | (748) $false
% 28.98/9.86 |
% 28.98/9.86 |-The branch is then unsatisfiable
% 28.98/9.86 |-Branch two:
% 28.98/9.86 | (1357) ~ (all_0_7_7 = n6)
% 28.98/9.86 | (1358) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 28.98/9.86 |
% 28.98/9.86 +-Applying beta-rule and splitting (1358), into two cases.
% 28.98/9.86 |-Branch one:
% 28.98/9.86 | (1359) all_0_7_7 = n5
% 28.98/9.86 |
% 28.98/9.86 | From (1359) and (683) follows:
% 28.98/9.86 | (1360) succ(n5) = all_0_5_5
% 28.98/9.86 |
% 28.98/9.86 | From (1359) and (8) follows:
% 28.98/9.87 | (1361) sum(n5, all_0_1_1) = all_0_0_0
% 28.98/9.87 |
% 28.98/9.87 | From (1359) and (1092) follows:
% 28.98/9.87 | (1362) sum(n20, n5) = all_0_2_2
% 28.98/9.87 |
% 28.98/9.87 | Instantiating formula (388) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 28.98/9.87 | (1363) all_0_5_5 = n6
% 28.98/9.87 |
% 28.98/9.87 | Instantiating formula (619) with n20, n5, all_0_2_2, n4 and discharging atoms sum(n20, n5) = all_0_2_2, sum(n20, n5) = n4, yields:
% 28.98/9.87 | (992) all_0_2_2 = n4
% 28.98/9.87 |
% 28.98/9.87 | From (992) and (473) follows:
% 28.98/9.87 | (994) pred(n4) = all_0_1_1
% 28.98/9.87 |
% 28.98/9.87 | From (1363) and (1091) follows:
% 28.98/9.87 | (1366) sum(n20, n6) = all_0_4_4
% 28.98/9.87 |
% 28.98/9.87 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 28.98/9.87 | (997) all_0_1_1 = n3
% 28.98/9.87 |
% 28.98/9.87 | Instantiating formula (619) with n20, n6, all_0_4_4, n5 and discharging atoms sum(n20, n6) = all_0_4_4, sum(n20, n6) = n5, yields:
% 28.98/9.87 | (993) all_0_4_4 = n5
% 28.98/9.87 |
% 28.98/9.87 | From (993) and (716) follows:
% 28.98/9.87 | (995) pred(n5) = all_0_3_3
% 28.98/9.87 |
% 28.98/9.87 | From (997) and (1361) follows:
% 28.98/9.87 | (1370) sum(n5, n3) = all_0_0_0
% 28.98/9.87 |
% 28.98/9.87 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 28.98/9.87 | (996) all_0_3_3 = n4
% 28.98/9.87 |
% 28.98/9.87 | Instantiating formula (619) with n5, n3, all_0_0_0, n8 and discharging atoms sum(n5, n3) = all_0_0_0, sum(n5, n3) = n8, yields:
% 28.98/9.87 | (898) all_0_0_0 = n8
% 28.98/9.87 |
% 28.98/9.87 | From (996)(898) and (232) follows:
% 28.98/9.87 | (1373) sum(n4, n8) = all_0_6_6
% 28.98/9.87 |
% 28.98/9.87 | Instantiating formula (619) with n4, n8, all_0_6_6, n12 and discharging atoms sum(n4, n8) = all_0_6_6, sum(n4, n8) = n12, yields:
% 28.98/9.87 | (951) all_0_6_6 = n12
% 28.98/9.87 |
% 28.98/9.87 | Equations (951) can reduce 76 to:
% 28.98/9.87 | (748) $false
% 28.98/9.87 |
% 28.98/9.87 |-The branch is then unsatisfiable
% 28.98/9.87 |-Branch two:
% 28.98/9.87 | (1376) ~ (all_0_7_7 = n5)
% 28.98/9.87 | (1377) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 28.98/9.87 |
% 28.98/9.87 +-Applying beta-rule and splitting (1377), into two cases.
% 28.98/9.87 |-Branch one:
% 28.98/9.87 | (1378) all_0_7_7 = n4
% 28.98/9.87 |
% 28.98/9.87 | From (1378) and (683) follows:
% 28.98/9.87 | (1379) succ(n4) = all_0_5_5
% 28.98/9.87 |
% 28.98/9.87 | From (1378) and (8) follows:
% 28.98/9.87 | (1380) sum(n4, all_0_1_1) = all_0_0_0
% 28.98/9.87 |
% 28.98/9.87 | From (1378) and (1092) follows:
% 28.98/9.87 | (1381) sum(n20, n4) = all_0_2_2
% 28.98/9.87 |
% 28.98/9.87 | Instantiating formula (388) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 28.98/9.87 | (1382) all_0_5_5 = n5
% 28.98/9.87 |
% 28.98/9.87 | Instantiating formula (619) with n20, n4, all_0_2_2, n3 and discharging atoms sum(n20, n4) = all_0_2_2, sum(n20, n4) = n3, yields:
% 28.98/9.87 | (1009) all_0_2_2 = n3
% 28.98/9.87 |
% 28.98/9.87 | From (1009) and (473) follows:
% 28.98/9.87 | (1011) pred(n3) = all_0_1_1
% 28.98/9.87 |
% 28.98/9.87 | From (1382) and (1091) follows:
% 28.98/9.87 | (1385) sum(n20, n5) = all_0_4_4
% 28.98/9.87 |
% 28.98/9.87 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 28.98/9.87 | (1014) all_0_1_1 = n2
% 28.98/9.87 |
% 28.98/9.87 | Instantiating formula (619) with n20, n5, all_0_4_4, n4 and discharging atoms sum(n20, n5) = all_0_4_4, sum(n20, n5) = n4, yields:
% 28.98/9.87 | (1010) all_0_4_4 = n4
% 28.98/9.87 |
% 28.98/9.87 | From (1010) and (716) follows:
% 28.98/9.87 | (1012) pred(n4) = all_0_3_3
% 28.98/9.87 |
% 28.98/9.87 | From (1014) and (1380) follows:
% 28.98/9.87 | (1389) sum(n4, n2) = all_0_0_0
% 28.98/9.87 |
% 28.98/9.87 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 28.98/9.87 | (1013) all_0_3_3 = n3
% 28.98/9.87 |
% 28.98/9.87 | Instantiating formula (619) with n4, n2, all_0_0_0, n6 and discharging atoms sum(n4, n2) = all_0_0_0, sum(n4, n2) = n6, yields:
% 28.98/9.87 | (932) all_0_0_0 = n6
% 28.98/9.87 |
% 28.98/9.87 | From (1013)(932) and (232) follows:
% 28.98/9.87 | (1392) sum(n3, n6) = all_0_6_6
% 28.98/9.87 |
% 28.98/9.87 | Instantiating formula (619) with n3, n6, all_0_6_6, n9 and discharging atoms sum(n3, n6) = all_0_6_6, sum(n3, n6) = n9, yields:
% 29.33/9.87 | (798) all_0_6_6 = n9
% 29.33/9.87 |
% 29.33/9.87 | Equations (798) can reduce 593 to:
% 29.33/9.87 | (748) $false
% 29.33/9.87 |
% 29.33/9.87 |-The branch is then unsatisfiable
% 29.33/9.87 |-Branch two:
% 29.33/9.87 | (1395) ~ (all_0_7_7 = n4)
% 29.33/9.87 | (1396) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.33/9.87 |
% 29.33/9.87 +-Applying beta-rule and splitting (1396), into two cases.
% 29.33/9.87 |-Branch one:
% 29.33/9.87 | (1397) all_0_7_7 = n3
% 29.33/9.87 |
% 29.33/9.87 | From (1397) and (683) follows:
% 29.33/9.87 | (1398) succ(n3) = all_0_5_5
% 29.33/9.87 |
% 29.33/9.87 | From (1397) and (8) follows:
% 29.33/9.87 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 29.33/9.87 |
% 29.33/9.87 | From (1397) and (1092) follows:
% 29.33/9.87 | (1400) sum(n20, n3) = all_0_2_2
% 29.33/9.87 |
% 29.33/9.87 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 29.33/9.87 | (1401) all_0_5_5 = n4
% 29.33/9.87 |
% 29.33/9.87 | Instantiating formula (619) with n20, n3, all_0_2_2, n2 and discharging atoms sum(n20, n3) = all_0_2_2, sum(n20, n3) = n2, yields:
% 29.33/9.87 | (1026) all_0_2_2 = n2
% 29.33/9.87 |
% 29.33/9.87 | From (1026) and (473) follows:
% 29.33/9.87 | (1028) pred(n2) = all_0_1_1
% 29.33/9.87 |
% 29.33/9.87 | From (1401) and (1091) follows:
% 29.33/9.87 | (1404) sum(n20, n4) = all_0_4_4
% 29.33/9.87 |
% 29.33/9.87 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 29.33/9.87 | (1031) all_0_1_1 = n1
% 29.33/9.87 |
% 29.33/9.87 | Instantiating formula (619) with n20, n4, all_0_4_4, n3 and discharging atoms sum(n20, n4) = all_0_4_4, sum(n20, n4) = n3, yields:
% 29.33/9.87 | (1027) all_0_4_4 = n3
% 29.33/9.87 |
% 29.33/9.87 | From (1027) and (716) follows:
% 29.33/9.87 | (1029) pred(n3) = all_0_3_3
% 29.33/9.87 |
% 29.33/9.87 | From (1031) and (1399) follows:
% 29.33/9.87 | (1408) sum(n3, n1) = all_0_0_0
% 29.33/9.87 |
% 29.33/9.87 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 29.33/9.87 | (1030) all_0_3_3 = n2
% 29.33/9.87 |
% 29.33/9.87 | Instantiating formula (619) with n3, n1, all_0_0_0, n4 and discharging atoms sum(n3, n1) = all_0_0_0, sum(n3, n1) = n4, yields:
% 29.33/9.87 | (966) all_0_0_0 = n4
% 29.33/9.87 |
% 29.33/9.87 | From (1030)(966) and (232) follows:
% 29.33/9.87 | (1411) sum(n2, n4) = all_0_6_6
% 29.33/9.87 |
% 29.33/9.87 | Instantiating formula (619) with n2, n4, all_0_6_6, n6 and discharging atoms sum(n2, n4) = all_0_6_6, sum(n2, n4) = n6, yields:
% 29.33/9.87 | (1002) all_0_6_6 = n6
% 29.33/9.87 |
% 29.33/9.87 | Equations (1002) can reduce 498 to:
% 29.33/9.87 | (748) $false
% 29.33/9.87 |
% 29.33/9.87 |-The branch is then unsatisfiable
% 29.33/9.87 |-Branch two:
% 29.33/9.87 | (1414) ~ (all_0_7_7 = n3)
% 29.33/9.87 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.33/9.87 |
% 29.33/9.87 +-Applying beta-rule and splitting (1415), into two cases.
% 29.33/9.87 |-Branch one:
% 29.33/9.87 | (1416) all_0_7_7 = n2
% 29.33/9.87 |
% 29.33/9.87 | From (1416) and (683) follows:
% 29.33/9.87 | (1417) succ(n2) = all_0_5_5
% 29.33/9.87 |
% 29.33/9.87 | From (1416) and (8) follows:
% 29.33/9.87 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 29.33/9.87 |
% 29.33/9.87 | From (1416) and (1092) follows:
% 29.33/9.87 | (1419) sum(n20, n2) = all_0_2_2
% 29.33/9.87 |
% 29.33/9.87 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 29.33/9.87 | (1420) all_0_5_5 = n3
% 29.33/9.87 |
% 29.33/9.87 | Instantiating formula (619) with n20, n2, all_0_2_2, n1 and discharging atoms sum(n20, n2) = all_0_2_2, sum(n20, n2) = n1, yields:
% 29.33/9.87 | (1043) all_0_2_2 = n1
% 29.33/9.87 |
% 29.33/9.87 | From (1043) and (473) follows:
% 29.33/9.87 | (1045) pred(n1) = all_0_1_1
% 29.33/9.87 |
% 29.33/9.87 | From (1420) and (1091) follows:
% 29.33/9.87 | (1423) sum(n20, n3) = all_0_4_4
% 29.33/9.87 |
% 29.33/9.87 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 29.33/9.87 | (1048) all_0_1_1 = n0
% 29.33/9.87 |
% 29.33/9.87 | Instantiating formula (619) with n20, n3, all_0_4_4, n2 and discharging atoms sum(n20, n3) = all_0_4_4, sum(n20, n3) = n2, yields:
% 29.33/9.87 | (1044) all_0_4_4 = n2
% 29.33/9.87 |
% 29.33/9.87 | From (1044) and (716) follows:
% 29.33/9.87 | (1046) pred(n2) = all_0_3_3
% 29.33/9.87 |
% 29.33/9.87 | From (1048) and (1418) follows:
% 29.33/9.87 | (1427) sum(n2, n0) = all_0_0_0
% 29.33/9.87 |
% 29.33/9.87 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 29.33/9.87 | (1047) all_0_3_3 = n1
% 29.33/9.87 |
% 29.33/9.87 | Instantiating formula (619) with n2, n0, all_0_0_0, n2 and discharging atoms sum(n2, n0) = all_0_0_0, sum(n2, n0) = n2, yields:
% 29.33/9.87 | (1000) all_0_0_0 = n2
% 29.33/9.87 |
% 29.33/9.87 | From (1047)(1000) and (232) follows:
% 29.33/9.87 | (1430) sum(n1, n2) = all_0_6_6
% 29.33/9.87 |
% 29.33/9.87 | Instantiating formula (619) with n1, n2, all_0_6_6, n3 and discharging atoms sum(n1, n2) = all_0_6_6, sum(n1, n2) = n3, yields:
% 29.33/9.87 | (849) all_0_6_6 = n3
% 29.33/9.87 |
% 29.33/9.87 | Equations (849) can reduce 416 to:
% 29.33/9.87 | (748) $false
% 29.33/9.87 |
% 29.33/9.87 |-The branch is then unsatisfiable
% 29.33/9.87 |-Branch two:
% 29.33/9.87 | (1433) ~ (all_0_7_7 = n2)
% 29.33/9.87 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 29.33/9.87 |
% 29.33/9.87 +-Applying beta-rule and splitting (1434), into two cases.
% 29.33/9.87 |-Branch one:
% 29.33/9.87 | (1435) all_0_7_7 = n1
% 29.33/9.87 |
% 29.33/9.87 | From (1435) and (683) follows:
% 29.33/9.87 | (1436) succ(n1) = all_0_5_5
% 29.33/9.87 |
% 29.33/9.87 | From (1435) and (8) follows:
% 29.33/9.87 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 29.33/9.87 |
% 29.33/9.87 | From (1435) and (1092) follows:
% 29.33/9.88 | (1438) sum(n20, n1) = all_0_2_2
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 29.33/9.88 | (1439) all_0_5_5 = n2
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (619) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 29.33/9.88 | (1060) all_0_2_2 = n0
% 29.33/9.88 |
% 29.33/9.88 | From (1060) and (473) follows:
% 29.33/9.88 | (1062) pred(n0) = all_0_1_1
% 29.33/9.88 |
% 29.33/9.88 | From (1439) and (1091) follows:
% 29.33/9.88 | (1442) sum(n20, n2) = all_0_4_4
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 29.33/9.88 | (1065) all_0_1_1 = n20
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (619) with n20, n2, all_0_4_4, n1 and discharging atoms sum(n20, n2) = all_0_4_4, sum(n20, n2) = n1, yields:
% 29.33/9.88 | (1061) all_0_4_4 = n1
% 29.33/9.88 |
% 29.33/9.88 | From (1061) and (716) follows:
% 29.33/9.88 | (1063) pred(n1) = all_0_3_3
% 29.33/9.88 |
% 29.33/9.88 | From (1065) and (1437) follows:
% 29.33/9.88 | (1446) sum(n1, n20) = all_0_0_0
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 29.33/9.88 | (1064) all_0_3_3 = n0
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (619) with n1, n20, all_0_0_0, n0 and discharging atoms sum(n1, n20) = all_0_0_0, sum(n1, n20) = n0, yields:
% 29.33/9.88 | (1034) all_0_0_0 = n0
% 29.33/9.88 |
% 29.33/9.88 | From (1064)(1034) and (232) follows:
% 29.33/9.88 | (1449) sum(n0, n0) = all_0_6_6
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (619) with n0, n0, all_0_6_6, n0 and discharging atoms sum(n0, n0) = all_0_6_6, sum(n0, n0) = n0, yields:
% 29.33/9.88 | (1053) all_0_6_6 = n0
% 29.33/9.88 |
% 29.33/9.88 | Equations (1053) can reduce 676 to:
% 29.33/9.88 | (748) $false
% 29.33/9.88 |
% 29.33/9.88 |-The branch is then unsatisfiable
% 29.33/9.88 |-Branch two:
% 29.33/9.88 | (1452) ~ (all_0_7_7 = n1)
% 29.33/9.88 | (1453) all_0_7_7 = n0
% 29.33/9.88 |
% 29.33/9.88 | From (1453) and (683) follows:
% 29.33/9.88 | (1454) succ(n0) = all_0_5_5
% 29.33/9.88 |
% 29.33/9.88 | From (1453) and (8) follows:
% 29.33/9.88 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 29.33/9.88 |
% 29.33/9.88 | From (1453) and (1092) follows:
% 29.33/9.88 | (1456) sum(n20, n0) = all_0_2_2
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 29.33/9.88 | (1457) all_0_5_5 = n1
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (619) with n20, n0, all_0_2_2, n20 and discharging atoms sum(n20, n0) = all_0_2_2, sum(n20, n0) = n20, yields:
% 29.33/9.88 | (1076) all_0_2_2 = n20
% 29.33/9.88 |
% 29.33/9.88 | From (1076) and (473) follows:
% 29.33/9.88 | (1078) pred(n20) = all_0_1_1
% 29.33/9.88 |
% 29.33/9.88 | From (1457) and (1091) follows:
% 29.33/9.88 | (1460) sum(n20, n1) = all_0_4_4
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 29.33/9.88 | (1080) all_0_1_1 = n19
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (619) with n20, n1, all_0_4_4, n0 and discharging atoms sum(n20, n1) = all_0_4_4, sum(n20, n1) = n0, yields:
% 29.33/9.88 | (1077) all_0_4_4 = n0
% 29.33/9.88 |
% 29.33/9.88 | From (1077) and (716) follows:
% 29.33/9.88 | (1079) pred(n0) = all_0_3_3
% 29.33/9.88 |
% 29.33/9.88 | From (1080) and (1455) follows:
% 29.33/9.88 | (1464) sum(n0, n19) = all_0_0_0
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 29.33/9.88 | (1081) all_0_3_3 = n20
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (619) with n0, n19, all_0_0_0, n19 and discharging atoms sum(n0, n19) = all_0_0_0, sum(n0, n19) = n19, yields:
% 29.33/9.88 | (1068) all_0_0_0 = n19
% 29.33/9.88 |
% 29.33/9.88 | From (1081)(1068) and (232) follows:
% 29.33/9.88 | (1467) sum(n20, n19) = all_0_6_6
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (619) with n20, n19, all_0_6_6, n18 and discharging atoms sum(n20, n19) = all_0_6_6, sum(n20, n19) = n18, yields:
% 29.33/9.88 | (900) all_0_6_6 = n18
% 29.33/9.88 |
% 29.33/9.88 | Equations (900) can reduce 622 to:
% 29.33/9.88 | (748) $false
% 29.33/9.88 |
% 29.33/9.88 |-The branch is then unsatisfiable
% 29.33/9.88 |-Branch two:
% 29.33/9.88 | (749) ~ (all_0_8_8 = n20)
% 29.33/9.88 | (750) all_0_8_8 = n19 | all_0_8_8 = n18 | all_0_8_8 = n17 | all_0_8_8 = n16 | all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.33/9.88 |
% 29.33/9.88 +-Applying beta-rule and splitting (1089), into two cases.
% 29.33/9.88 |-Branch one:
% 29.33/9.88 | (1093) all_0_7_7 = n19
% 29.33/9.88 |
% 29.33/9.88 | From (1093) and (683) follows:
% 29.33/9.88 | (1094) succ(n19) = all_0_5_5
% 29.33/9.88 |
% 29.33/9.88 | From (1093) and (8) follows:
% 29.33/9.88 | (1095) sum(n19, all_0_1_1) = all_0_0_0
% 29.33/9.88 |
% 29.33/9.88 | From (1093) and (378) follows:
% 29.33/9.88 | (1475) sum(all_0_8_8, n19) = all_0_2_2
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (388) with n19, all_0_5_5, n20 and discharging atoms succ(n19) = all_0_5_5, succ(n19) = n20, yields:
% 29.33/9.88 | (1097) all_0_5_5 = n20
% 29.33/9.88 |
% 29.33/9.88 | From (1097) and (708) follows:
% 29.33/9.88 | (1477) sum(all_0_8_8, n20) = all_0_4_4
% 29.33/9.88 |
% 29.33/9.88 +-Applying beta-rule and splitting (750), into two cases.
% 29.33/9.88 |-Branch one:
% 29.33/9.88 | (751) all_0_8_8 = n19
% 29.33/9.88 |
% 29.33/9.88 | From (751) and (1477) follows:
% 29.33/9.88 | (1479) sum(n19, n20) = all_0_4_4
% 29.33/9.88 |
% 29.33/9.88 | From (751) and (1475) follows:
% 29.33/9.88 | (1480) sum(n19, n19) = all_0_2_2
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (619) with n19, n20, all_0_4_4, n18 and discharging atoms sum(n19, n20) = all_0_4_4, sum(n19, n20) = n18, yields:
% 29.33/9.88 | (772) all_0_4_4 = n18
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (619) with n19, n19, all_0_2_2, n17 and discharging atoms sum(n19, n19) = all_0_2_2, sum(n19, n19) = n17, yields:
% 29.33/9.88 | (771) all_0_2_2 = n17
% 29.33/9.88 |
% 29.33/9.88 | From (771) and (473) follows:
% 29.33/9.88 | (773) pred(n17) = all_0_1_1
% 29.33/9.88 |
% 29.33/9.88 | From (772) and (716) follows:
% 29.33/9.88 | (774) pred(n18) = all_0_3_3
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 29.33/9.88 | (775) all_0_3_3 = n17
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 29.33/9.88 | (776) all_0_1_1 = n16
% 29.33/9.88 |
% 29.33/9.88 | From (775) and (232) follows:
% 29.33/9.88 | (777) sum(n17, all_0_0_0) = all_0_6_6
% 29.33/9.88 |
% 29.33/9.88 | From (776) and (1095) follows:
% 29.33/9.88 | (1488) sum(n19, n16) = all_0_0_0
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (619) with n19, n16, all_0_0_0, n14 and discharging atoms sum(n19, n16) = all_0_0_0, sum(n19, n16) = n14, yields:
% 29.33/9.88 | (796) all_0_0_0 = n14
% 29.33/9.88 |
% 29.33/9.88 | From (796) and (777) follows:
% 29.33/9.88 | (1490) sum(n17, n14) = all_0_6_6
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (619) with n17, n14, all_0_6_6, n10 and discharging atoms sum(n17, n14) = all_0_6_6, sum(n17, n14) = n10, yields:
% 29.33/9.88 | (968) all_0_6_6 = n10
% 29.33/9.88 |
% 29.33/9.88 | Equations (968) can reduce 176 to:
% 29.33/9.88 | (748) $false
% 29.33/9.88 |
% 29.33/9.88 |-The branch is then unsatisfiable
% 29.33/9.88 |-Branch two:
% 29.33/9.88 | (766) ~ (all_0_8_8 = n19)
% 29.33/9.88 | (767) all_0_8_8 = n18 | all_0_8_8 = n17 | all_0_8_8 = n16 | all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.33/9.88 |
% 29.33/9.88 +-Applying beta-rule and splitting (767), into two cases.
% 29.33/9.88 |-Branch one:
% 29.33/9.88 | (768) all_0_8_8 = n18
% 29.33/9.88 |
% 29.33/9.88 | From (768) and (1477) follows:
% 29.33/9.88 | (1496) sum(n18, n20) = all_0_4_4
% 29.33/9.88 |
% 29.33/9.88 | From (768) and (1475) follows:
% 29.33/9.88 | (1497) sum(n18, n19) = all_0_2_2
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (619) with n18, n20, all_0_4_4, n17 and discharging atoms sum(n18, n20) = all_0_4_4, sum(n18, n20) = n17, yields:
% 29.33/9.88 | (789) all_0_4_4 = n17
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (619) with n18, n19, all_0_2_2, n16 and discharging atoms sum(n18, n19) = all_0_2_2, sum(n18, n19) = n16, yields:
% 29.33/9.88 | (788) all_0_2_2 = n16
% 29.33/9.88 |
% 29.33/9.88 | From (788) and (473) follows:
% 29.33/9.88 | (790) pred(n16) = all_0_1_1
% 29.33/9.88 |
% 29.33/9.88 | From (789) and (716) follows:
% 29.33/9.88 | (791) pred(n17) = all_0_3_3
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 29.33/9.88 | (792) all_0_3_3 = n16
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 29.33/9.88 | (793) all_0_1_1 = n15
% 29.33/9.88 |
% 29.33/9.88 | From (792) and (232) follows:
% 29.33/9.88 | (794) sum(n16, all_0_0_0) = all_0_6_6
% 29.33/9.88 |
% 29.33/9.88 | From (793) and (1095) follows:
% 29.33/9.88 | (1505) sum(n19, n15) = all_0_0_0
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (619) with n19, n15, all_0_0_0, n13 and discharging atoms sum(n19, n15) = all_0_0_0, sum(n19, n15) = n13, yields:
% 29.33/9.88 | (813) all_0_0_0 = n13
% 29.33/9.88 |
% 29.33/9.88 | From (813) and (794) follows:
% 29.33/9.88 | (1507) sum(n16, n13) = all_0_6_6
% 29.33/9.88 |
% 29.33/9.88 | Instantiating formula (619) with n16, n13, all_0_6_6, n8 and discharging atoms sum(n16, n13) = all_0_6_6, sum(n16, n13) = n8, yields:
% 29.33/9.88 | (985) all_0_6_6 = n8
% 29.33/9.88 |
% 29.33/9.88 | Equations (985) can reduce 357 to:
% 29.33/9.88 | (748) $false
% 29.33/9.88 |
% 29.33/9.88 |-The branch is then unsatisfiable
% 29.33/9.88 |-Branch two:
% 29.33/9.88 | (783) ~ (all_0_8_8 = n18)
% 29.33/9.88 | (784) all_0_8_8 = n17 | all_0_8_8 = n16 | all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.33/9.88 |
% 29.33/9.88 +-Applying beta-rule and splitting (784), into two cases.
% 29.33/9.88 |-Branch one:
% 29.33/9.88 | (785) all_0_8_8 = n17
% 29.33/9.88 |
% 29.33/9.88 | From (785) and (1477) follows:
% 29.33/9.89 | (1513) sum(n17, n20) = all_0_4_4
% 29.33/9.89 |
% 29.33/9.89 | From (785) and (1475) follows:
% 29.33/9.89 | (1514) sum(n17, n19) = all_0_2_2
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n17, n20, all_0_4_4, n16 and discharging atoms sum(n17, n20) = all_0_4_4, sum(n17, n20) = n16, yields:
% 29.33/9.89 | (806) all_0_4_4 = n16
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n17, n19, all_0_2_2, n15 and discharging atoms sum(n17, n19) = all_0_2_2, sum(n17, n19) = n15, yields:
% 29.33/9.89 | (805) all_0_2_2 = n15
% 29.33/9.89 |
% 29.33/9.89 | From (805) and (473) follows:
% 29.33/9.89 | (807) pred(n15) = all_0_1_1
% 29.33/9.89 |
% 29.33/9.89 | From (806) and (716) follows:
% 29.33/9.89 | (808) pred(n16) = all_0_3_3
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 29.33/9.89 | (809) all_0_3_3 = n15
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 29.33/9.89 | (810) all_0_1_1 = n14
% 29.33/9.89 |
% 29.33/9.89 | From (809) and (232) follows:
% 29.33/9.89 | (811) sum(n15, all_0_0_0) = all_0_6_6
% 29.33/9.89 |
% 29.33/9.89 | From (810) and (1095) follows:
% 29.33/9.89 | (1522) sum(n19, n14) = all_0_0_0
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n19, n14, all_0_0_0, n12 and discharging atoms sum(n19, n14) = all_0_0_0, sum(n19, n14) = n12, yields:
% 29.33/9.89 | (830) all_0_0_0 = n12
% 29.33/9.89 |
% 29.33/9.89 | From (830) and (811) follows:
% 29.33/9.89 | (1524) sum(n15, n12) = all_0_6_6
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n15, n12, all_0_6_6, n6 and discharging atoms sum(n15, n12) = all_0_6_6, sum(n15, n12) = n6, yields:
% 29.33/9.89 | (1002) all_0_6_6 = n6
% 29.33/9.89 |
% 29.33/9.89 | Equations (1002) can reduce 498 to:
% 29.33/9.89 | (748) $false
% 29.33/9.89 |
% 29.33/9.89 |-The branch is then unsatisfiable
% 29.33/9.89 |-Branch two:
% 29.33/9.89 | (800) ~ (all_0_8_8 = n17)
% 29.33/9.89 | (801) all_0_8_8 = n16 | all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.33/9.89 |
% 29.33/9.89 +-Applying beta-rule and splitting (801), into two cases.
% 29.33/9.89 |-Branch one:
% 29.33/9.89 | (802) all_0_8_8 = n16
% 29.33/9.89 |
% 29.33/9.89 | From (802) and (1477) follows:
% 29.33/9.89 | (1530) sum(n16, n20) = all_0_4_4
% 29.33/9.89 |
% 29.33/9.89 | From (802) and (1475) follows:
% 29.33/9.89 | (1531) sum(n16, n19) = all_0_2_2
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n16, n20, all_0_4_4, n15 and discharging atoms sum(n16, n20) = all_0_4_4, sum(n16, n20) = n15, yields:
% 29.33/9.89 | (823) all_0_4_4 = n15
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n16, n19, all_0_2_2, n14 and discharging atoms sum(n16, n19) = all_0_2_2, sum(n16, n19) = n14, yields:
% 29.33/9.89 | (822) all_0_2_2 = n14
% 29.33/9.89 |
% 29.33/9.89 | From (822) and (473) follows:
% 29.33/9.89 | (824) pred(n14) = all_0_1_1
% 29.33/9.89 |
% 29.33/9.89 | From (823) and (716) follows:
% 29.33/9.89 | (825) pred(n15) = all_0_3_3
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 29.33/9.89 | (826) all_0_3_3 = n14
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 29.33/9.89 | (827) all_0_1_1 = n13
% 29.33/9.89 |
% 29.33/9.89 | From (826) and (232) follows:
% 29.33/9.89 | (828) sum(n14, all_0_0_0) = all_0_6_6
% 29.33/9.89 |
% 29.33/9.89 | From (827) and (1095) follows:
% 29.33/9.89 | (1539) sum(n19, n13) = all_0_0_0
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n19, n13, all_0_0_0, n11 and discharging atoms sum(n19, n13) = all_0_0_0, sum(n19, n13) = n11, yields:
% 29.33/9.89 | (847) all_0_0_0 = n11
% 29.33/9.89 |
% 29.33/9.89 | From (847) and (828) follows:
% 29.33/9.89 | (1541) sum(n14, n11) = all_0_6_6
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n14, n11, all_0_6_6, n4 and discharging atoms sum(n14, n11) = all_0_6_6, sum(n14, n11) = n4, yields:
% 29.33/9.89 | (1019) all_0_6_6 = n4
% 29.33/9.89 |
% 29.33/9.89 | Equations (1019) can reduce 48 to:
% 29.33/9.89 | (748) $false
% 29.33/9.89 |
% 29.33/9.89 |-The branch is then unsatisfiable
% 29.33/9.89 |-Branch two:
% 29.33/9.89 | (817) ~ (all_0_8_8 = n16)
% 29.33/9.89 | (818) all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.33/9.89 |
% 29.33/9.89 +-Applying beta-rule and splitting (818), into two cases.
% 29.33/9.89 |-Branch one:
% 29.33/9.89 | (819) all_0_8_8 = n15
% 29.33/9.89 |
% 29.33/9.89 | From (819) and (1477) follows:
% 29.33/9.89 | (1547) sum(n15, n20) = all_0_4_4
% 29.33/9.89 |
% 29.33/9.89 | From (819) and (1475) follows:
% 29.33/9.89 | (1548) sum(n15, n19) = all_0_2_2
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n15, n20, all_0_4_4, n14 and discharging atoms sum(n15, n20) = all_0_4_4, sum(n15, n20) = n14, yields:
% 29.33/9.89 | (840) all_0_4_4 = n14
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n15, n19, all_0_2_2, n13 and discharging atoms sum(n15, n19) = all_0_2_2, sum(n15, n19) = n13, yields:
% 29.33/9.89 | (839) all_0_2_2 = n13
% 29.33/9.89 |
% 29.33/9.89 | From (839) and (473) follows:
% 29.33/9.89 | (841) pred(n13) = all_0_1_1
% 29.33/9.89 |
% 29.33/9.89 | From (840) and (716) follows:
% 29.33/9.89 | (842) pred(n14) = all_0_3_3
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 29.33/9.89 | (843) all_0_3_3 = n13
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 29.33/9.89 | (844) all_0_1_1 = n12
% 29.33/9.89 |
% 29.33/9.89 | From (843) and (232) follows:
% 29.33/9.89 | (845) sum(n13, all_0_0_0) = all_0_6_6
% 29.33/9.89 |
% 29.33/9.89 | From (844) and (1095) follows:
% 29.33/9.89 | (1556) sum(n19, n12) = all_0_0_0
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n19, n12, all_0_0_0, n10 and discharging atoms sum(n19, n12) = all_0_0_0, sum(n19, n12) = n10, yields:
% 29.33/9.89 | (864) all_0_0_0 = n10
% 29.33/9.89 |
% 29.33/9.89 | From (864) and (845) follows:
% 29.33/9.89 | (1558) sum(n13, n10) = all_0_6_6
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n13, n10, all_0_6_6, n2 and discharging atoms sum(n13, n10) = all_0_6_6, sum(n13, n10) = n2, yields:
% 29.33/9.89 | (1036) all_0_6_6 = n2
% 29.33/9.89 |
% 29.33/9.89 | Equations (1036) can reduce 56 to:
% 29.33/9.89 | (748) $false
% 29.33/9.89 |
% 29.33/9.89 |-The branch is then unsatisfiable
% 29.33/9.89 |-Branch two:
% 29.33/9.89 | (834) ~ (all_0_8_8 = n15)
% 29.33/9.89 | (835) all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.33/9.89 |
% 29.33/9.89 +-Applying beta-rule and splitting (835), into two cases.
% 29.33/9.89 |-Branch one:
% 29.33/9.89 | (836) all_0_8_8 = n14
% 29.33/9.89 |
% 29.33/9.89 | From (836) and (1477) follows:
% 29.33/9.89 | (1564) sum(n14, n20) = all_0_4_4
% 29.33/9.89 |
% 29.33/9.89 | From (836) and (1475) follows:
% 29.33/9.89 | (1565) sum(n14, n19) = all_0_2_2
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n14, n20, all_0_4_4, n13 and discharging atoms sum(n14, n20) = all_0_4_4, sum(n14, n20) = n13, yields:
% 29.33/9.89 | (857) all_0_4_4 = n13
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n14, n19, all_0_2_2, n12 and discharging atoms sum(n14, n19) = all_0_2_2, sum(n14, n19) = n12, yields:
% 29.33/9.89 | (856) all_0_2_2 = n12
% 29.33/9.89 |
% 29.33/9.89 | From (856) and (473) follows:
% 29.33/9.89 | (858) pred(n12) = all_0_1_1
% 29.33/9.89 |
% 29.33/9.89 | From (857) and (716) follows:
% 29.33/9.89 | (859) pred(n13) = all_0_3_3
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 29.33/9.89 | (860) all_0_3_3 = n12
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 29.33/9.89 | (861) all_0_1_1 = n11
% 29.33/9.89 |
% 29.33/9.89 | From (860) and (232) follows:
% 29.33/9.89 | (862) sum(n12, all_0_0_0) = all_0_6_6
% 29.33/9.89 |
% 29.33/9.89 | From (861) and (1095) follows:
% 29.33/9.89 | (1573) sum(n19, n11) = all_0_0_0
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n19, n11, all_0_0_0, n9 and discharging atoms sum(n19, n11) = all_0_0_0, sum(n19, n11) = n9, yields:
% 29.33/9.89 | (881) all_0_0_0 = n9
% 29.33/9.89 |
% 29.33/9.89 | From (881) and (862) follows:
% 29.33/9.89 | (1575) sum(n12, n9) = all_0_6_6
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n12, n9, all_0_6_6, n0 and discharging atoms sum(n12, n9) = all_0_6_6, sum(n12, n9) = n0, yields:
% 29.33/9.89 | (1053) all_0_6_6 = n0
% 29.33/9.89 |
% 29.33/9.89 | Equations (1053) can reduce 676 to:
% 29.33/9.89 | (748) $false
% 29.33/9.89 |
% 29.33/9.89 |-The branch is then unsatisfiable
% 29.33/9.89 |-Branch two:
% 29.33/9.89 | (851) ~ (all_0_8_8 = n14)
% 29.33/9.89 | (852) all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.33/9.89 |
% 29.33/9.89 +-Applying beta-rule and splitting (852), into two cases.
% 29.33/9.89 |-Branch one:
% 29.33/9.89 | (853) all_0_8_8 = n13
% 29.33/9.89 |
% 29.33/9.89 | From (853) and (1477) follows:
% 29.33/9.89 | (1581) sum(n13, n20) = all_0_4_4
% 29.33/9.89 |
% 29.33/9.89 | From (853) and (1475) follows:
% 29.33/9.89 | (1582) sum(n13, n19) = all_0_2_2
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n13, n20, all_0_4_4, n12 and discharging atoms sum(n13, n20) = all_0_4_4, sum(n13, n20) = n12, yields:
% 29.33/9.89 | (874) all_0_4_4 = n12
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n13, n19, all_0_2_2, n11 and discharging atoms sum(n13, n19) = all_0_2_2, sum(n13, n19) = n11, yields:
% 29.33/9.89 | (873) all_0_2_2 = n11
% 29.33/9.89 |
% 29.33/9.89 | From (873) and (473) follows:
% 29.33/9.89 | (875) pred(n11) = all_0_1_1
% 29.33/9.89 |
% 29.33/9.89 | From (874) and (716) follows:
% 29.33/9.89 | (876) pred(n12) = all_0_3_3
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 29.33/9.89 | (877) all_0_3_3 = n11
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 29.33/9.89 | (878) all_0_1_1 = n10
% 29.33/9.89 |
% 29.33/9.89 | From (877) and (232) follows:
% 29.33/9.89 | (879) sum(n11, all_0_0_0) = all_0_6_6
% 29.33/9.89 |
% 29.33/9.89 | From (878) and (1095) follows:
% 29.33/9.89 | (1590) sum(n19, n10) = all_0_0_0
% 29.33/9.89 |
% 29.33/9.89 | Instantiating formula (619) with n19, n10, all_0_0_0, n8 and discharging atoms sum(n19, n10) = all_0_0_0, sum(n19, n10) = n8, yields:
% 29.33/9.89 | (898) all_0_0_0 = n8
% 29.33/9.89 |
% 29.33/9.89 | From (898) and (879) follows:
% 29.33/9.90 | (1592) sum(n11, n8) = all_0_6_6
% 29.33/9.90 |
% 29.33/9.90 | Instantiating formula (619) with n11, n8, all_0_6_6, n19 and discharging atoms sum(n11, n8) = all_0_6_6, sum(n11, n8) = n19, yields:
% 29.33/9.90 | (1070) all_0_6_6 = n19
% 29.33/9.90 |
% 29.33/9.90 | Equations (1070) can reduce 31 to:
% 29.33/9.90 | (748) $false
% 29.33/9.90 |
% 29.33/9.90 |-The branch is then unsatisfiable
% 29.33/9.90 |-Branch two:
% 29.33/9.90 | (868) ~ (all_0_8_8 = n13)
% 29.33/9.90 | (869) all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.33/9.90 |
% 29.33/9.90 +-Applying beta-rule and splitting (869), into two cases.
% 29.33/9.90 |-Branch one:
% 29.33/9.90 | (870) all_0_8_8 = n12
% 29.33/9.90 |
% 29.33/9.90 | From (870) and (1477) follows:
% 29.33/9.90 | (1598) sum(n12, n20) = all_0_4_4
% 29.33/9.90 |
% 29.33/9.90 | From (870) and (1475) follows:
% 29.33/9.90 | (1599) sum(n12, n19) = all_0_2_2
% 29.33/9.90 |
% 29.33/9.90 | Instantiating formula (619) with n12, n20, all_0_4_4, n11 and discharging atoms sum(n12, n20) = all_0_4_4, sum(n12, n20) = n11, yields:
% 29.33/9.90 | (891) all_0_4_4 = n11
% 29.33/9.90 |
% 29.33/9.90 | Instantiating formula (619) with n12, n19, all_0_2_2, n10 and discharging atoms sum(n12, n19) = all_0_2_2, sum(n12, n19) = n10, yields:
% 29.33/9.90 | (890) all_0_2_2 = n10
% 29.33/9.90 |
% 29.33/9.90 | From (890) and (473) follows:
% 29.33/9.90 | (892) pred(n10) = all_0_1_1
% 29.33/9.90 |
% 29.33/9.90 | From (891) and (716) follows:
% 29.33/9.90 | (893) pred(n11) = all_0_3_3
% 29.33/9.90 |
% 29.33/9.90 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 29.33/9.90 | (894) all_0_3_3 = n10
% 29.33/9.90 |
% 29.33/9.90 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 29.33/9.90 | (895) all_0_1_1 = n9
% 29.33/9.90 |
% 29.33/9.90 | From (894) and (232) follows:
% 29.33/9.90 | (896) sum(n10, all_0_0_0) = all_0_6_6
% 29.33/9.90 |
% 29.33/9.90 | From (895) and (1095) follows:
% 29.33/9.90 | (1607) sum(n19, n9) = all_0_0_0
% 29.33/9.90 |
% 29.33/9.90 | Instantiating formula (619) with n19, n9, all_0_0_0, n7 and discharging atoms sum(n19, n9) = all_0_0_0, sum(n19, n9) = n7, yields:
% 29.33/9.90 | (915) all_0_0_0 = n7
% 29.33/9.90 |
% 29.33/9.90 | From (915) and (896) follows:
% 29.33/9.90 | (1609) sum(n10, n7) = all_0_6_6
% 29.33/9.90 |
% 29.33/9.90 | Instantiating formula (619) with n10, n7, all_0_6_6, n17 and discharging atoms sum(n10, n7) = all_0_6_6, sum(n10, n7) = n17, yields:
% 29.33/9.90 | (1086) all_0_6_6 = n17
% 29.33/9.90 |
% 29.33/9.90 | Equations (1086) can reduce 669 to:
% 29.33/9.90 | (748) $false
% 29.33/9.90 |
% 29.33/9.90 |-The branch is then unsatisfiable
% 29.33/9.90 |-Branch two:
% 29.33/9.90 | (885) ~ (all_0_8_8 = n12)
% 29.33/9.90 | (886) all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.33/9.90 |
% 29.33/9.90 +-Applying beta-rule and splitting (886), into two cases.
% 29.33/9.90 |-Branch one:
% 29.33/9.90 | (887) all_0_8_8 = n11
% 29.33/9.90 |
% 29.33/9.90 | From (887) and (1477) follows:
% 29.33/9.90 | (1615) sum(n11, n20) = all_0_4_4
% 29.33/9.90 |
% 29.33/9.90 | From (887) and (1475) follows:
% 29.33/9.90 | (1616) sum(n11, n19) = all_0_2_2
% 29.33/9.90 |
% 29.33/9.90 | Instantiating formula (619) with n11, n20, all_0_4_4, n10 and discharging atoms sum(n11, n20) = all_0_4_4, sum(n11, n20) = n10, yields:
% 29.33/9.90 | (908) all_0_4_4 = n10
% 29.33/9.90 |
% 29.33/9.90 | Instantiating formula (619) with n11, n19, all_0_2_2, n9 and discharging atoms sum(n11, n19) = all_0_2_2, sum(n11, n19) = n9, yields:
% 29.33/9.90 | (907) all_0_2_2 = n9
% 29.33/9.90 |
% 29.33/9.90 | From (907) and (473) follows:
% 29.33/9.90 | (909) pred(n9) = all_0_1_1
% 29.33/9.90 |
% 29.33/9.90 | From (908) and (716) follows:
% 29.33/9.90 | (910) pred(n10) = all_0_3_3
% 29.33/9.90 |
% 29.33/9.90 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 29.33/9.90 | (911) all_0_3_3 = n9
% 29.33/9.90 |
% 29.33/9.90 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 29.33/9.90 | (912) all_0_1_1 = n8
% 29.33/9.90 |
% 29.33/9.90 | From (911) and (232) follows:
% 29.33/9.90 | (913) sum(n9, all_0_0_0) = all_0_6_6
% 29.33/9.90 |
% 29.33/9.90 | From (912) and (1095) follows:
% 29.33/9.90 | (1624) sum(n19, n8) = all_0_0_0
% 29.33/9.90 |
% 29.33/9.90 | Instantiating formula (619) with n19, n8, all_0_0_0, n6 and discharging atoms sum(n19, n8) = all_0_0_0, sum(n19, n8) = n6, yields:
% 29.33/9.90 | (932) all_0_0_0 = n6
% 29.33/9.90 |
% 29.33/9.90 | From (932) and (913) follows:
% 29.33/9.90 | (1626) sum(n9, n6) = all_0_6_6
% 29.33/9.90 |
% 29.33/9.90 | Instantiating formula (619) with n9, n6, all_0_6_6, n15 and discharging atoms sum(n9, n6) = all_0_6_6, sum(n9, n6) = n15, yields:
% 29.33/9.90 | (747) all_0_6_6 = n15
% 29.33/9.90 |
% 29.33/9.90 | Equations (747) can reduce 456 to:
% 29.33/9.90 | (748) $false
% 29.33/9.90 |
% 29.33/9.90 |-The branch is then unsatisfiable
% 29.33/9.90 |-Branch two:
% 29.33/9.90 | (902) ~ (all_0_8_8 = n11)
% 29.33/9.90 | (903) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.33/9.90 |
% 29.45/9.90 +-Applying beta-rule and splitting (903), into two cases.
% 29.45/9.90 |-Branch one:
% 29.45/9.90 | (904) all_0_8_8 = n10
% 29.45/9.90 |
% 29.45/9.90 | From (904) and (1477) follows:
% 29.45/9.90 | (1632) sum(n10, n20) = all_0_4_4
% 29.45/9.90 |
% 29.45/9.90 | From (904) and (1475) follows:
% 29.45/9.90 | (1633) sum(n10, n19) = all_0_2_2
% 29.45/9.90 |
% 29.45/9.90 | Instantiating formula (619) with n10, n20, all_0_4_4, n9 and discharging atoms sum(n10, n20) = all_0_4_4, sum(n10, n20) = n9, yields:
% 29.45/9.90 | (925) all_0_4_4 = n9
% 29.45/9.90 |
% 29.45/9.90 | Instantiating formula (619) with n10, n19, all_0_2_2, n8 and discharging atoms sum(n10, n19) = all_0_2_2, sum(n10, n19) = n8, yields:
% 29.45/9.90 | (924) all_0_2_2 = n8
% 29.45/9.90 |
% 29.45/9.90 | From (924) and (473) follows:
% 29.45/9.90 | (926) pred(n8) = all_0_1_1
% 29.45/9.90 |
% 29.45/9.90 | From (925) and (716) follows:
% 29.45/9.90 | (927) pred(n9) = all_0_3_3
% 29.45/9.90 |
% 29.45/9.90 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 29.45/9.90 | (928) all_0_3_3 = n8
% 29.45/9.90 |
% 29.45/9.90 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 29.45/9.90 | (929) all_0_1_1 = n7
% 29.45/9.90 |
% 29.45/9.90 | From (928) and (232) follows:
% 29.45/9.90 | (930) sum(n8, all_0_0_0) = all_0_6_6
% 29.45/9.90 |
% 29.45/9.90 | From (929) and (1095) follows:
% 29.45/9.90 | (1641) sum(n19, n7) = all_0_0_0
% 29.45/9.90 |
% 29.45/9.90 | Instantiating formula (619) with n19, n7, all_0_0_0, n5 and discharging atoms sum(n19, n7) = all_0_0_0, sum(n19, n7) = n5, yields:
% 29.45/9.90 | (949) all_0_0_0 = n5
% 29.45/9.90 |
% 29.45/9.90 | From (949) and (930) follows:
% 29.45/9.90 | (1643) sum(n8, n5) = all_0_6_6
% 29.45/9.90 |
% 29.45/9.90 | Instantiating formula (619) with n8, n5, all_0_6_6, n13 and discharging atoms sum(n8, n5) = all_0_6_6, sum(n8, n5) = n13, yields:
% 29.45/9.90 | (764) all_0_6_6 = n13
% 29.45/9.90 |
% 29.45/9.90 | Equations (764) can reduce 293 to:
% 29.45/9.90 | (748) $false
% 29.45/9.90 |
% 29.45/9.90 |-The branch is then unsatisfiable
% 29.45/9.90 |-Branch two:
% 29.45/9.90 | (919) ~ (all_0_8_8 = n10)
% 29.45/9.90 | (920) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.45/9.90 |
% 29.45/9.90 +-Applying beta-rule and splitting (920), into two cases.
% 29.45/9.90 |-Branch one:
% 29.45/9.90 | (921) all_0_8_8 = n9
% 29.45/9.90 |
% 29.45/9.90 | From (921) and (1477) follows:
% 29.45/9.90 | (1649) sum(n9, n20) = all_0_4_4
% 29.45/9.90 |
% 29.45/9.90 | From (921) and (1475) follows:
% 29.45/9.90 | (1650) sum(n9, n19) = all_0_2_2
% 29.45/9.90 |
% 29.45/9.90 | Instantiating formula (619) with n9, n20, all_0_4_4, n8 and discharging atoms sum(n9, n20) = all_0_4_4, sum(n9, n20) = n8, yields:
% 29.45/9.90 | (942) all_0_4_4 = n8
% 29.45/9.90 |
% 29.45/9.90 | Instantiating formula (619) with n9, n19, all_0_2_2, n7 and discharging atoms sum(n9, n19) = all_0_2_2, sum(n9, n19) = n7, yields:
% 29.45/9.90 | (941) all_0_2_2 = n7
% 29.45/9.90 |
% 29.45/9.90 | From (941) and (473) follows:
% 29.45/9.90 | (943) pred(n7) = all_0_1_1
% 29.45/9.90 |
% 29.45/9.90 | From (942) and (716) follows:
% 29.45/9.90 | (944) pred(n8) = all_0_3_3
% 29.45/9.90 |
% 29.45/9.90 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 29.45/9.90 | (945) all_0_3_3 = n7
% 29.45/9.90 |
% 29.45/9.90 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 29.45/9.90 | (946) all_0_1_1 = n6
% 29.45/9.90 |
% 29.45/9.90 | From (945) and (232) follows:
% 29.45/9.90 | (947) sum(n7, all_0_0_0) = all_0_6_6
% 29.45/9.90 |
% 29.45/9.90 | From (946) and (1095) follows:
% 29.45/9.90 | (1658) sum(n19, n6) = all_0_0_0
% 29.45/9.90 |
% 29.45/9.90 | Instantiating formula (619) with n19, n6, all_0_0_0, n4 and discharging atoms sum(n19, n6) = all_0_0_0, sum(n19, n6) = n4, yields:
% 29.45/9.90 | (966) all_0_0_0 = n4
% 29.45/9.90 |
% 29.45/9.90 | From (966) and (947) follows:
% 29.45/9.90 | (1660) sum(n7, n4) = all_0_6_6
% 29.45/9.90 |
% 29.45/9.90 | Instantiating formula (619) with n7, n4, all_0_6_6, n11 and discharging atoms sum(n7, n4) = all_0_6_6, sum(n7, n4) = n11, yields:
% 29.45/9.90 | (781) all_0_6_6 = n11
% 29.45/9.90 |
% 29.45/9.90 | Equations (781) can reduce 2 to:
% 29.45/9.90 | (748) $false
% 29.45/9.90 |
% 29.45/9.90 |-The branch is then unsatisfiable
% 29.45/9.90 |-Branch two:
% 29.45/9.90 | (936) ~ (all_0_8_8 = n9)
% 29.45/9.90 | (937) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.45/9.90 |
% 29.45/9.90 +-Applying beta-rule and splitting (937), into two cases.
% 29.45/9.90 |-Branch one:
% 29.45/9.90 | (938) all_0_8_8 = n8
% 29.45/9.90 |
% 29.45/9.90 | From (938) and (1477) follows:
% 29.45/9.90 | (1666) sum(n8, n20) = all_0_4_4
% 29.45/9.90 |
% 29.45/9.90 | From (938) and (1475) follows:
% 29.45/9.90 | (1667) sum(n8, n19) = all_0_2_2
% 29.45/9.90 |
% 29.45/9.90 | Instantiating formula (619) with n8, n20, all_0_4_4, n7 and discharging atoms sum(n8, n20) = all_0_4_4, sum(n8, n20) = n7, yields:
% 29.45/9.90 | (959) all_0_4_4 = n7
% 29.45/9.90 |
% 29.45/9.90 | Instantiating formula (619) with n8, n19, all_0_2_2, n6 and discharging atoms sum(n8, n19) = all_0_2_2, sum(n8, n19) = n6, yields:
% 29.45/9.90 | (958) all_0_2_2 = n6
% 29.45/9.90 |
% 29.45/9.90 | From (958) and (473) follows:
% 29.45/9.91 | (960) pred(n6) = all_0_1_1
% 29.45/9.91 |
% 29.45/9.91 | From (959) and (716) follows:
% 29.45/9.91 | (961) pred(n7) = all_0_3_3
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 29.45/9.91 | (962) all_0_3_3 = n6
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 29.45/9.91 | (963) all_0_1_1 = n5
% 29.45/9.91 |
% 29.45/9.91 | From (962) and (232) follows:
% 29.45/9.91 | (964) sum(n6, all_0_0_0) = all_0_6_6
% 29.45/9.91 |
% 29.45/9.91 | From (963) and (1095) follows:
% 29.45/9.91 | (1675) sum(n19, n5) = all_0_0_0
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (619) with n19, n5, all_0_0_0, n3 and discharging atoms sum(n19, n5) = all_0_0_0, sum(n19, n5) = n3, yields:
% 29.45/9.91 | (983) all_0_0_0 = n3
% 29.45/9.91 |
% 29.45/9.91 | From (983) and (964) follows:
% 29.45/9.91 | (1677) sum(n6, n3) = all_0_6_6
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (619) with n6, n3, all_0_6_6, n9 and discharging atoms sum(n6, n3) = all_0_6_6, sum(n6, n3) = n9, yields:
% 29.45/9.91 | (798) all_0_6_6 = n9
% 29.45/9.91 |
% 29.45/9.91 | Equations (798) can reduce 593 to:
% 29.45/9.91 | (748) $false
% 29.45/9.91 |
% 29.45/9.91 |-The branch is then unsatisfiable
% 29.45/9.91 |-Branch two:
% 29.45/9.91 | (953) ~ (all_0_8_8 = n8)
% 29.45/9.91 | (954) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.45/9.91 |
% 29.45/9.91 +-Applying beta-rule and splitting (954), into two cases.
% 29.45/9.91 |-Branch one:
% 29.45/9.91 | (955) all_0_8_8 = n7
% 29.45/9.91 |
% 29.45/9.91 | From (955) and (1477) follows:
% 29.45/9.91 | (1683) sum(n7, n20) = all_0_4_4
% 29.45/9.91 |
% 29.45/9.91 | From (955) and (1475) follows:
% 29.45/9.91 | (1684) sum(n7, n19) = all_0_2_2
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (619) with n7, n20, all_0_4_4, n6 and discharging atoms sum(n7, n20) = all_0_4_4, sum(n7, n20) = n6, yields:
% 29.45/9.91 | (976) all_0_4_4 = n6
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (619) with n7, n19, all_0_2_2, n5 and discharging atoms sum(n7, n19) = all_0_2_2, sum(n7, n19) = n5, yields:
% 29.45/9.91 | (975) all_0_2_2 = n5
% 29.45/9.91 |
% 29.45/9.91 | From (975) and (473) follows:
% 29.45/9.91 | (977) pred(n5) = all_0_1_1
% 29.45/9.91 |
% 29.45/9.91 | From (976) and (716) follows:
% 29.45/9.91 | (978) pred(n6) = all_0_3_3
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 29.45/9.91 | (979) all_0_3_3 = n5
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 29.45/9.91 | (980) all_0_1_1 = n4
% 29.45/9.91 |
% 29.45/9.91 | From (979) and (232) follows:
% 29.45/9.91 | (981) sum(n5, all_0_0_0) = all_0_6_6
% 29.45/9.91 |
% 29.45/9.91 | From (980) and (1095) follows:
% 29.45/9.91 | (1692) sum(n19, n4) = all_0_0_0
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (619) with n19, n4, all_0_0_0, n2 and discharging atoms sum(n19, n4) = all_0_0_0, sum(n19, n4) = n2, yields:
% 29.45/9.91 | (1000) all_0_0_0 = n2
% 29.45/9.91 |
% 29.45/9.91 | From (1000) and (981) follows:
% 29.45/9.91 | (1694) sum(n5, n2) = all_0_6_6
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (619) with n5, n2, all_0_6_6, n7 and discharging atoms sum(n5, n2) = all_0_6_6, sum(n5, n2) = n7, yields:
% 29.45/9.91 | (815) all_0_6_6 = n7
% 29.45/9.91 |
% 29.45/9.91 | Equations (815) can reduce 557 to:
% 29.45/9.91 | (748) $false
% 29.45/9.91 |
% 29.45/9.91 |-The branch is then unsatisfiable
% 29.45/9.91 |-Branch two:
% 29.45/9.91 | (970) ~ (all_0_8_8 = n7)
% 29.45/9.91 | (971) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.45/9.91 |
% 29.45/9.91 +-Applying beta-rule and splitting (971), into two cases.
% 29.45/9.91 |-Branch one:
% 29.45/9.91 | (972) all_0_8_8 = n6
% 29.45/9.91 |
% 29.45/9.91 | From (972) and (1477) follows:
% 29.45/9.91 | (1700) sum(n6, n20) = all_0_4_4
% 29.45/9.91 |
% 29.45/9.91 | From (972) and (1475) follows:
% 29.45/9.91 | (1701) sum(n6, n19) = all_0_2_2
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (619) with n6, n20, all_0_4_4, n5 and discharging atoms sum(n6, n20) = all_0_4_4, sum(n6, n20) = n5, yields:
% 29.45/9.91 | (993) all_0_4_4 = n5
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (619) with n6, n19, all_0_2_2, n4 and discharging atoms sum(n6, n19) = all_0_2_2, sum(n6, n19) = n4, yields:
% 29.45/9.91 | (992) all_0_2_2 = n4
% 29.45/9.91 |
% 29.45/9.91 | From (992) and (473) follows:
% 29.45/9.91 | (994) pred(n4) = all_0_1_1
% 29.45/9.91 |
% 29.45/9.91 | From (993) and (716) follows:
% 29.45/9.91 | (995) pred(n5) = all_0_3_3
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 29.45/9.91 | (996) all_0_3_3 = n4
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 29.45/9.91 | (997) all_0_1_1 = n3
% 29.45/9.91 |
% 29.45/9.91 | From (996) and (232) follows:
% 29.45/9.91 | (998) sum(n4, all_0_0_0) = all_0_6_6
% 29.45/9.91 |
% 29.45/9.91 | From (997) and (1095) follows:
% 29.45/9.91 | (1709) sum(n19, n3) = all_0_0_0
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (619) with n19, n3, all_0_0_0, n1 and discharging atoms sum(n19, n3) = all_0_0_0, sum(n19, n3) = n1, yields:
% 29.45/9.91 | (1017) all_0_0_0 = n1
% 29.45/9.91 |
% 29.45/9.91 | From (1017) and (998) follows:
% 29.45/9.91 | (1711) sum(n4, n1) = all_0_6_6
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (619) with n4, n1, all_0_6_6, n5 and discharging atoms sum(n4, n1) = all_0_6_6, sum(n4, n1) = n5, yields:
% 29.45/9.91 | (832) all_0_6_6 = n5
% 29.45/9.91 |
% 29.45/9.91 | Equations (832) can reduce 462 to:
% 29.45/9.91 | (748) $false
% 29.45/9.91 |
% 29.45/9.91 |-The branch is then unsatisfiable
% 29.45/9.91 |-Branch two:
% 29.45/9.91 | (987) ~ (all_0_8_8 = n6)
% 29.45/9.91 | (988) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.45/9.91 |
% 29.45/9.91 +-Applying beta-rule and splitting (988), into two cases.
% 29.45/9.91 |-Branch one:
% 29.45/9.91 | (989) all_0_8_8 = n5
% 29.45/9.91 |
% 29.45/9.91 | From (989) and (1477) follows:
% 29.45/9.91 | (1717) sum(n5, n20) = all_0_4_4
% 29.45/9.91 |
% 29.45/9.91 | From (989) and (1475) follows:
% 29.45/9.91 | (1718) sum(n5, n19) = all_0_2_2
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (619) with n5, n20, all_0_4_4, n4 and discharging atoms sum(n5, n20) = all_0_4_4, sum(n5, n20) = n4, yields:
% 29.45/9.91 | (1010) all_0_4_4 = n4
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (619) with n5, n19, all_0_2_2, n3 and discharging atoms sum(n5, n19) = all_0_2_2, sum(n5, n19) = n3, yields:
% 29.45/9.91 | (1009) all_0_2_2 = n3
% 29.45/9.91 |
% 29.45/9.91 | From (1009) and (473) follows:
% 29.45/9.91 | (1011) pred(n3) = all_0_1_1
% 29.45/9.91 |
% 29.45/9.91 | From (1010) and (716) follows:
% 29.45/9.91 | (1012) pred(n4) = all_0_3_3
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 29.45/9.91 | (1013) all_0_3_3 = n3
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 29.45/9.91 | (1014) all_0_1_1 = n2
% 29.45/9.91 |
% 29.45/9.91 | From (1013) and (232) follows:
% 29.45/9.91 | (1015) sum(n3, all_0_0_0) = all_0_6_6
% 29.45/9.91 |
% 29.45/9.91 | From (1014) and (1095) follows:
% 29.45/9.91 | (1726) sum(n19, n2) = all_0_0_0
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (619) with n19, n2, all_0_0_0, n0 and discharging atoms sum(n19, n2) = all_0_0_0, sum(n19, n2) = n0, yields:
% 29.45/9.91 | (1034) all_0_0_0 = n0
% 29.45/9.91 |
% 29.45/9.91 | From (1034) and (1015) follows:
% 29.45/9.91 | (1728) sum(n3, n0) = all_0_6_6
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (619) with n3, n0, all_0_6_6, n3 and discharging atoms sum(n3, n0) = all_0_6_6, sum(n3, n0) = n3, yields:
% 29.45/9.91 | (849) all_0_6_6 = n3
% 29.45/9.91 |
% 29.45/9.91 | Equations (849) can reduce 416 to:
% 29.45/9.91 | (748) $false
% 29.45/9.91 |
% 29.45/9.91 |-The branch is then unsatisfiable
% 29.45/9.91 |-Branch two:
% 29.45/9.91 | (1004) ~ (all_0_8_8 = n5)
% 29.45/9.91 | (1005) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.45/9.91 |
% 29.45/9.91 +-Applying beta-rule and splitting (1005), into two cases.
% 29.45/9.91 |-Branch one:
% 29.45/9.91 | (1006) all_0_8_8 = n4
% 29.45/9.91 |
% 29.45/9.91 | From (1006) and (1477) follows:
% 29.45/9.91 | (1734) sum(n4, n20) = all_0_4_4
% 29.45/9.91 |
% 29.45/9.91 | From (1006) and (1475) follows:
% 29.45/9.91 | (1735) sum(n4, n19) = all_0_2_2
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (619) with n4, n20, all_0_4_4, n3 and discharging atoms sum(n4, n20) = all_0_4_4, sum(n4, n20) = n3, yields:
% 29.45/9.91 | (1027) all_0_4_4 = n3
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (619) with n4, n19, all_0_2_2, n2 and discharging atoms sum(n4, n19) = all_0_2_2, sum(n4, n19) = n2, yields:
% 29.45/9.91 | (1026) all_0_2_2 = n2
% 29.45/9.91 |
% 29.45/9.91 | From (1026) and (473) follows:
% 29.45/9.91 | (1028) pred(n2) = all_0_1_1
% 29.45/9.91 |
% 29.45/9.91 | From (1027) and (716) follows:
% 29.45/9.91 | (1029) pred(n3) = all_0_3_3
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 29.45/9.91 | (1030) all_0_3_3 = n2
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 29.45/9.91 | (1031) all_0_1_1 = n1
% 29.45/9.91 |
% 29.45/9.91 | From (1030) and (232) follows:
% 29.45/9.91 | (1032) sum(n2, all_0_0_0) = all_0_6_6
% 29.45/9.91 |
% 29.45/9.91 | From (1031) and (1095) follows:
% 29.45/9.91 | (1743) sum(n19, n1) = all_0_0_0
% 29.45/9.91 |
% 29.45/9.91 | Instantiating formula (619) with n19, n1, all_0_0_0, n20 and discharging atoms sum(n19, n1) = all_0_0_0, sum(n19, n1) = n20, yields:
% 29.45/9.91 | (1051) all_0_0_0 = n20
% 29.45/9.92 |
% 29.45/9.92 | From (1051) and (1032) follows:
% 29.45/9.92 | (1745) sum(n2, n20) = all_0_6_6
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (619) with n2, n20, all_0_6_6, n1 and discharging atoms sum(n2, n20) = all_0_6_6, sum(n2, n20) = n1, yields:
% 29.45/9.92 | (866) all_0_6_6 = n1
% 29.45/9.92 |
% 29.45/9.92 | Equations (866) can reduce 28 to:
% 29.45/9.92 | (748) $false
% 29.45/9.92 |
% 29.45/9.92 |-The branch is then unsatisfiable
% 29.45/9.92 |-Branch two:
% 29.45/9.92 | (1021) ~ (all_0_8_8 = n4)
% 29.45/9.92 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.45/9.92 |
% 29.45/9.92 +-Applying beta-rule and splitting (1022), into two cases.
% 29.45/9.92 |-Branch one:
% 29.45/9.92 | (1023) all_0_8_8 = n3
% 29.45/9.92 |
% 29.45/9.92 | From (1023) and (1477) follows:
% 29.45/9.92 | (1751) sum(n3, n20) = all_0_4_4
% 29.45/9.92 |
% 29.45/9.92 | From (1023) and (1475) follows:
% 29.45/9.92 | (1752) sum(n3, n19) = all_0_2_2
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (619) with n3, n20, all_0_4_4, n2 and discharging atoms sum(n3, n20) = all_0_4_4, sum(n3, n20) = n2, yields:
% 29.45/9.92 | (1044) all_0_4_4 = n2
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (619) with n3, n19, all_0_2_2, n1 and discharging atoms sum(n3, n19) = all_0_2_2, sum(n3, n19) = n1, yields:
% 29.45/9.92 | (1043) all_0_2_2 = n1
% 29.45/9.92 |
% 29.45/9.92 | From (1043) and (473) follows:
% 29.45/9.92 | (1045) pred(n1) = all_0_1_1
% 29.45/9.92 |
% 29.45/9.92 | From (1044) and (716) follows:
% 29.45/9.92 | (1046) pred(n2) = all_0_3_3
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 29.45/9.92 | (1047) all_0_3_3 = n1
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 29.45/9.92 | (1048) all_0_1_1 = n0
% 29.45/9.92 |
% 29.45/9.92 | From (1047) and (232) follows:
% 29.45/9.92 | (1049) sum(n1, all_0_0_0) = all_0_6_6
% 29.45/9.92 |
% 29.45/9.92 | From (1048) and (1095) follows:
% 29.45/9.92 | (1760) sum(n19, n0) = all_0_0_0
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (619) with n19, n0, all_0_0_0, n19 and discharging atoms sum(n19, n0) = all_0_0_0, sum(n19, n0) = n19, yields:
% 29.45/9.92 | (1068) all_0_0_0 = n19
% 29.45/9.92 |
% 29.45/9.92 | From (1068) and (1049) follows:
% 29.45/9.92 | (1762) sum(n1, n19) = all_0_6_6
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (619) with n1, n19, all_0_6_6, n20 and discharging atoms sum(n1, n19) = all_0_6_6, sum(n1, n19) = n20, yields:
% 29.45/9.92 | (883) all_0_6_6 = n20
% 29.45/9.92 |
% 29.45/9.92 | Equations (883) can reduce 381 to:
% 29.45/9.92 | (748) $false
% 29.45/9.92 |
% 29.45/9.92 |-The branch is then unsatisfiable
% 29.45/9.92 |-Branch two:
% 29.45/9.92 | (1038) ~ (all_0_8_8 = n3)
% 29.45/9.92 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.45/9.92 |
% 29.45/9.92 +-Applying beta-rule and splitting (1039), into two cases.
% 29.45/9.92 |-Branch one:
% 29.45/9.92 | (1040) all_0_8_8 = n2
% 29.45/9.92 |
% 29.45/9.92 | From (1040) and (1477) follows:
% 29.45/9.92 | (1768) sum(n2, n20) = all_0_4_4
% 29.45/9.92 |
% 29.45/9.92 | From (1040) and (1475) follows:
% 29.45/9.92 | (1769) sum(n2, n19) = all_0_2_2
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (619) with n2, n20, all_0_4_4, n1 and discharging atoms sum(n2, n20) = all_0_4_4, sum(n2, n20) = n1, yields:
% 29.45/9.92 | (1061) all_0_4_4 = n1
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (619) with n2, n19, all_0_2_2, n0 and discharging atoms sum(n2, n19) = all_0_2_2, sum(n2, n19) = n0, yields:
% 29.45/9.92 | (1060) all_0_2_2 = n0
% 29.45/9.92 |
% 29.45/9.92 | From (1060) and (473) follows:
% 29.45/9.92 | (1062) pred(n0) = all_0_1_1
% 29.45/9.92 |
% 29.45/9.92 | From (1061) and (716) follows:
% 29.45/9.92 | (1063) pred(n1) = all_0_3_3
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 29.45/9.92 | (1064) all_0_3_3 = n0
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 29.45/9.92 | (1065) all_0_1_1 = n20
% 29.45/9.92 |
% 29.45/9.92 | From (1064) and (232) follows:
% 29.45/9.92 | (1066) sum(n0, all_0_0_0) = all_0_6_6
% 29.45/9.92 |
% 29.45/9.92 | From (1065) and (1095) follows:
% 29.45/9.92 | (1777) sum(n19, n20) = all_0_0_0
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (619) with n19, n20, all_0_0_0, n18 and discharging atoms sum(n19, n20) = all_0_0_0, sum(n19, n20) = n18, yields:
% 29.45/9.92 | (1084) all_0_0_0 = n18
% 29.45/9.92 |
% 29.45/9.92 | From (1084) and (1066) follows:
% 29.45/9.92 | (1779) sum(n0, n18) = all_0_6_6
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (619) with n0, n18, all_0_6_6, n18 and discharging atoms sum(n0, n18) = all_0_6_6, sum(n0, n18) = n18, yields:
% 29.45/9.92 | (900) all_0_6_6 = n18
% 29.45/9.92 |
% 29.45/9.92 | Equations (900) can reduce 622 to:
% 29.45/9.92 | (748) $false
% 29.45/9.92 |
% 29.45/9.92 |-The branch is then unsatisfiable
% 29.45/9.92 |-Branch two:
% 29.45/9.92 | (1055) ~ (all_0_8_8 = n2)
% 29.45/9.92 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 29.45/9.92 |
% 29.45/9.92 +-Applying beta-rule and splitting (1056), into two cases.
% 29.45/9.92 |-Branch one:
% 29.45/9.92 | (1057) all_0_8_8 = n1
% 29.45/9.92 |
% 29.45/9.92 | From (1057) and (1477) follows:
% 29.45/9.92 | (1785) sum(n1, n20) = all_0_4_4
% 29.45/9.92 |
% 29.45/9.92 | From (1057) and (1475) follows:
% 29.45/9.92 | (1786) sum(n1, n19) = all_0_2_2
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (619) with n1, n20, all_0_4_4, n0 and discharging atoms sum(n1, n20) = all_0_4_4, sum(n1, n20) = n0, yields:
% 29.45/9.92 | (1077) all_0_4_4 = n0
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (619) with n1, n19, all_0_2_2, n20 and discharging atoms sum(n1, n19) = all_0_2_2, sum(n1, n19) = n20, yields:
% 29.45/9.92 | (1076) all_0_2_2 = n20
% 29.45/9.92 |
% 29.45/9.92 | From (1076) and (473) follows:
% 29.45/9.92 | (1078) pred(n20) = all_0_1_1
% 29.45/9.92 |
% 29.45/9.92 | From (1077) and (716) follows:
% 29.45/9.92 | (1079) pred(n0) = all_0_3_3
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 29.45/9.92 | (1080) all_0_1_1 = n19
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 29.45/9.92 | (1081) all_0_3_3 = n20
% 29.45/9.92 |
% 29.45/9.92 | From (1081) and (232) follows:
% 29.45/9.92 | (1082) sum(n20, all_0_0_0) = all_0_6_6
% 29.45/9.92 |
% 29.45/9.92 | From (1080) and (1095) follows:
% 29.45/9.92 | (1794) sum(n19, n19) = all_0_0_0
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (619) with n19, n19, all_0_0_0, n17 and discharging atoms sum(n19, n19) = all_0_0_0, sum(n19, n19) = n17, yields:
% 29.45/9.92 | (745) all_0_0_0 = n17
% 29.45/9.92 |
% 29.45/9.92 | From (745) and (1082) follows:
% 29.45/9.92 | (1796) sum(n20, n17) = all_0_6_6
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (619) with n20, n17, all_0_6_6, n16 and discharging atoms sum(n20, n17) = all_0_6_6, sum(n20, n17) = n16, yields:
% 29.45/9.92 | (917) all_0_6_6 = n16
% 29.45/9.92 |
% 29.45/9.92 | Equations (917) can reduce 163 to:
% 29.45/9.92 | (748) $false
% 29.45/9.92 |
% 29.45/9.92 |-The branch is then unsatisfiable
% 29.45/9.92 |-Branch two:
% 29.45/9.92 | (1072) ~ (all_0_8_8 = n1)
% 29.45/9.92 | (1073) all_0_8_8 = n0
% 29.45/9.92 |
% 29.45/9.92 | From (1073) and (1477) follows:
% 29.45/9.92 | (1801) sum(n0, n20) = all_0_4_4
% 29.45/9.92 |
% 29.45/9.92 | From (1073) and (1475) follows:
% 29.45/9.92 | (1802) sum(n0, n19) = all_0_2_2
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (619) with n0, n20, all_0_4_4, n20 and discharging atoms sum(n0, n20) = all_0_4_4, sum(n0, n20) = n20, yields:
% 29.45/9.92 | (738) all_0_4_4 = n20
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (619) with n0, n19, all_0_2_2, n19 and discharging atoms sum(n0, n19) = all_0_2_2, sum(n0, n19) = n19, yields:
% 29.45/9.92 | (737) all_0_2_2 = n19
% 29.45/9.92 |
% 29.45/9.92 | From (737) and (473) follows:
% 29.45/9.92 | (739) pred(n19) = all_0_1_1
% 29.45/9.92 |
% 29.45/9.92 | From (738) and (716) follows:
% 29.45/9.92 | (740) pred(n20) = all_0_3_3
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 29.45/9.92 | (741) all_0_3_3 = n19
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 29.45/9.92 | (742) all_0_1_1 = n18
% 29.45/9.92 |
% 29.45/9.92 | From (741) and (232) follows:
% 29.45/9.92 | (743) sum(n19, all_0_0_0) = all_0_6_6
% 29.45/9.92 |
% 29.45/9.92 | From (742) and (1095) follows:
% 29.45/9.92 | (1810) sum(n19, n18) = all_0_0_0
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (619) with n19, n18, all_0_0_0, n16 and discharging atoms sum(n19, n18) = all_0_0_0, sum(n19, n18) = n16, yields:
% 29.45/9.92 | (762) all_0_0_0 = n16
% 29.45/9.92 |
% 29.45/9.92 | From (762) and (743) follows:
% 29.45/9.92 | (1812) sum(n19, n16) = all_0_6_6
% 29.45/9.92 |
% 29.45/9.92 | Instantiating formula (619) with n19, n16, all_0_6_6, n14 and discharging atoms sum(n19, n16) = all_0_6_6, sum(n19, n16) = n14, yields:
% 29.45/9.92 | (934) all_0_6_6 = n14
% 29.45/9.92 |
% 29.45/9.92 | Equations (934) can reduce 353 to:
% 29.45/9.92 | (748) $false
% 29.45/9.92 |
% 29.45/9.92 |-The branch is then unsatisfiable
% 29.45/9.92 |-Branch two:
% 29.45/9.92 | (1110) ~ (all_0_7_7 = n19)
% 29.45/9.92 | (1111) all_0_7_7 = n18 | all_0_7_7 = n17 | all_0_7_7 = n16 | all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.45/9.93 |
% 29.45/9.93 +-Applying beta-rule and splitting (750), into two cases.
% 29.45/9.93 |-Branch one:
% 29.45/9.93 | (751) all_0_8_8 = n19
% 29.45/9.93 |
% 29.45/9.93 | From (751) and (708) follows:
% 29.45/9.93 | (1818) sum(n19, all_0_5_5) = all_0_4_4
% 29.45/9.93 |
% 29.45/9.93 | From (751) and (378) follows:
% 29.45/9.93 | (1819) sum(n19, all_0_7_7) = all_0_2_2
% 29.45/9.93 |
% 29.45/9.93 +-Applying beta-rule and splitting (1111), into two cases.
% 29.45/9.93 |-Branch one:
% 29.45/9.93 | (1112) all_0_7_7 = n18
% 29.45/9.93 |
% 29.45/9.93 | From (1112) and (683) follows:
% 29.45/9.93 | (1113) succ(n18) = all_0_5_5
% 29.45/9.93 |
% 29.45/9.93 | From (1112) and (8) follows:
% 29.45/9.93 | (1114) sum(n18, all_0_1_1) = all_0_0_0
% 29.45/9.93 |
% 29.45/9.93 | From (1112) and (1819) follows:
% 29.45/9.93 | (1823) sum(n19, n18) = all_0_2_2
% 29.45/9.93 |
% 29.45/9.93 | Instantiating formula (388) with n18, all_0_5_5, n19 and discharging atoms succ(n18) = all_0_5_5, succ(n18) = n19, yields:
% 29.45/9.93 | (1116) all_0_5_5 = n19
% 29.45/9.93 |
% 29.45/9.93 | Instantiating formula (619) with n19, n18, all_0_2_2, n16 and discharging atoms sum(n19, n18) = all_0_2_2, sum(n19, n18) = n16, yields:
% 29.45/9.93 | (788) all_0_2_2 = n16
% 29.45/9.93 |
% 29.45/9.93 | From (788) and (473) follows:
% 29.45/9.93 | (790) pred(n16) = all_0_1_1
% 29.45/9.93 |
% 29.45/9.93 | From (1116) and (1818) follows:
% 29.45/9.93 | (1827) sum(n19, n19) = all_0_4_4
% 29.45/9.93 |
% 29.45/9.93 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 29.45/9.93 | (793) all_0_1_1 = n15
% 29.45/9.93 |
% 29.45/9.93 | Instantiating formula (619) with n19, n19, all_0_4_4, n17 and discharging atoms sum(n19, n19) = all_0_4_4, sum(n19, n19) = n17, yields:
% 29.45/9.93 | (789) all_0_4_4 = n17
% 29.45/9.93 |
% 29.45/9.93 | From (789) and (716) follows:
% 29.45/9.93 | (791) pred(n17) = all_0_3_3
% 29.45/9.93 |
% 29.45/9.93 | From (793) and (1114) follows:
% 29.45/9.93 | (1831) sum(n18, n15) = all_0_0_0
% 29.45/9.93 |
% 29.45/9.93 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 29.56/9.93 | (792) all_0_3_3 = n16
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (619) with n18, n15, all_0_0_0, n12 and discharging atoms sum(n18, n15) = all_0_0_0, sum(n18, n15) = n12, yields:
% 29.56/9.93 | (830) all_0_0_0 = n12
% 29.56/9.93 |
% 29.56/9.93 | From (792)(830) and (232) follows:
% 29.56/9.93 | (1834) sum(n16, n12) = all_0_6_6
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (619) with n16, n12, all_0_6_6, n7 and discharging atoms sum(n16, n12) = all_0_6_6, sum(n16, n12) = n7, yields:
% 29.56/9.93 | (815) all_0_6_6 = n7
% 29.56/9.93 |
% 29.56/9.93 | Equations (815) can reduce 557 to:
% 29.56/9.93 | (748) $false
% 29.56/9.93 |
% 29.56/9.93 |-The branch is then unsatisfiable
% 29.56/9.93 |-Branch two:
% 29.56/9.93 | (1129) ~ (all_0_7_7 = n18)
% 29.56/9.93 | (1130) all_0_7_7 = n17 | all_0_7_7 = n16 | all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/9.93 |
% 29.56/9.93 +-Applying beta-rule and splitting (1130), into two cases.
% 29.56/9.93 |-Branch one:
% 29.56/9.93 | (1131) all_0_7_7 = n17
% 29.56/9.93 |
% 29.56/9.93 | From (1131) and (683) follows:
% 29.56/9.93 | (1132) succ(n17) = all_0_5_5
% 29.56/9.93 |
% 29.56/9.93 | From (1131) and (8) follows:
% 29.56/9.93 | (1133) sum(n17, all_0_1_1) = all_0_0_0
% 29.56/9.93 |
% 29.56/9.93 | From (1131) and (1819) follows:
% 29.56/9.93 | (1842) sum(n19, n17) = all_0_2_2
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (388) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 29.56/9.93 | (1135) all_0_5_5 = n18
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (619) with n19, n17, all_0_2_2, n15 and discharging atoms sum(n19, n17) = all_0_2_2, sum(n19, n17) = n15, yields:
% 29.56/9.93 | (805) all_0_2_2 = n15
% 29.56/9.93 |
% 29.56/9.93 | From (805) and (473) follows:
% 29.56/9.93 | (807) pred(n15) = all_0_1_1
% 29.56/9.93 |
% 29.56/9.93 | From (1135) and (1818) follows:
% 29.56/9.93 | (1846) sum(n19, n18) = all_0_4_4
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 29.56/9.93 | (810) all_0_1_1 = n14
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (619) with n19, n18, all_0_4_4, n16 and discharging atoms sum(n19, n18) = all_0_4_4, sum(n19, n18) = n16, yields:
% 29.56/9.93 | (806) all_0_4_4 = n16
% 29.56/9.93 |
% 29.56/9.93 | From (806) and (716) follows:
% 29.56/9.93 | (808) pred(n16) = all_0_3_3
% 29.56/9.93 |
% 29.56/9.93 | From (810) and (1133) follows:
% 29.56/9.93 | (1850) sum(n17, n14) = all_0_0_0
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 29.56/9.93 | (809) all_0_3_3 = n15
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (619) with n17, n14, all_0_0_0, n10 and discharging atoms sum(n17, n14) = all_0_0_0, sum(n17, n14) = n10, yields:
% 29.56/9.93 | (864) all_0_0_0 = n10
% 29.56/9.93 |
% 29.56/9.93 | From (809)(864) and (232) follows:
% 29.56/9.93 | (1853) sum(n15, n10) = all_0_6_6
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (619) with n15, n10, all_0_6_6, n4 and discharging atoms sum(n15, n10) = all_0_6_6, sum(n15, n10) = n4, yields:
% 29.56/9.93 | (1019) all_0_6_6 = n4
% 29.56/9.93 |
% 29.56/9.93 | Equations (1019) can reduce 48 to:
% 29.56/9.93 | (748) $false
% 29.56/9.93 |
% 29.56/9.93 |-The branch is then unsatisfiable
% 29.56/9.93 |-Branch two:
% 29.56/9.93 | (1148) ~ (all_0_7_7 = n17)
% 29.56/9.93 | (1149) all_0_7_7 = n16 | all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/9.93 |
% 29.56/9.93 +-Applying beta-rule and splitting (1149), into two cases.
% 29.56/9.93 |-Branch one:
% 29.56/9.93 | (1150) all_0_7_7 = n16
% 29.56/9.93 |
% 29.56/9.93 | From (1150) and (683) follows:
% 29.56/9.93 | (1151) succ(n16) = all_0_5_5
% 29.56/9.93 |
% 29.56/9.93 | From (1150) and (8) follows:
% 29.56/9.93 | (1152) sum(n16, all_0_1_1) = all_0_0_0
% 29.56/9.93 |
% 29.56/9.93 | From (1150) and (1819) follows:
% 29.56/9.93 | (1861) sum(n19, n16) = all_0_2_2
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (388) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 29.56/9.93 | (1154) all_0_5_5 = n17
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (619) with n19, n16, all_0_2_2, n14 and discharging atoms sum(n19, n16) = all_0_2_2, sum(n19, n16) = n14, yields:
% 29.56/9.93 | (822) all_0_2_2 = n14
% 29.56/9.93 |
% 29.56/9.93 | From (822) and (473) follows:
% 29.56/9.93 | (824) pred(n14) = all_0_1_1
% 29.56/9.93 |
% 29.56/9.93 | From (1154) and (1818) follows:
% 29.56/9.93 | (1865) sum(n19, n17) = all_0_4_4
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 29.56/9.93 | (827) all_0_1_1 = n13
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (619) with n19, n17, all_0_4_4, n15 and discharging atoms sum(n19, n17) = all_0_4_4, sum(n19, n17) = n15, yields:
% 29.56/9.93 | (823) all_0_4_4 = n15
% 29.56/9.93 |
% 29.56/9.93 | From (823) and (716) follows:
% 29.56/9.93 | (825) pred(n15) = all_0_3_3
% 29.56/9.93 |
% 29.56/9.93 | From (827) and (1152) follows:
% 29.56/9.93 | (1869) sum(n16, n13) = all_0_0_0
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 29.56/9.93 | (826) all_0_3_3 = n14
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (619) with n16, n13, all_0_0_0, n8 and discharging atoms sum(n16, n13) = all_0_0_0, sum(n16, n13) = n8, yields:
% 29.56/9.93 | (898) all_0_0_0 = n8
% 29.56/9.93 |
% 29.56/9.93 | From (826)(898) and (232) follows:
% 29.56/9.93 | (1872) sum(n14, n8) = all_0_6_6
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (619) with n14, n8, all_0_6_6, n1 and discharging atoms sum(n14, n8) = all_0_6_6, sum(n14, n8) = n1, yields:
% 29.56/9.93 | (866) all_0_6_6 = n1
% 29.56/9.93 |
% 29.56/9.93 | Equations (866) can reduce 28 to:
% 29.56/9.93 | (748) $false
% 29.56/9.93 |
% 29.56/9.93 |-The branch is then unsatisfiable
% 29.56/9.93 |-Branch two:
% 29.56/9.93 | (1167) ~ (all_0_7_7 = n16)
% 29.56/9.93 | (1168) all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/9.93 |
% 29.56/9.93 +-Applying beta-rule and splitting (1168), into two cases.
% 29.56/9.93 |-Branch one:
% 29.56/9.93 | (1169) all_0_7_7 = n15
% 29.56/9.93 |
% 29.56/9.93 | From (1169) and (683) follows:
% 29.56/9.93 | (1170) succ(n15) = all_0_5_5
% 29.56/9.93 |
% 29.56/9.93 | From (1169) and (8) follows:
% 29.56/9.93 | (1171) sum(n15, all_0_1_1) = all_0_0_0
% 29.56/9.93 |
% 29.56/9.93 | From (1169) and (1819) follows:
% 29.56/9.93 | (1880) sum(n19, n15) = all_0_2_2
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (388) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 29.56/9.93 | (1173) all_0_5_5 = n16
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (619) with n19, n15, all_0_2_2, n13 and discharging atoms sum(n19, n15) = all_0_2_2, sum(n19, n15) = n13, yields:
% 29.56/9.93 | (839) all_0_2_2 = n13
% 29.56/9.93 |
% 29.56/9.93 | From (839) and (473) follows:
% 29.56/9.93 | (841) pred(n13) = all_0_1_1
% 29.56/9.93 |
% 29.56/9.93 | From (1173) and (1818) follows:
% 29.56/9.93 | (1884) sum(n19, n16) = all_0_4_4
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 29.56/9.93 | (844) all_0_1_1 = n12
% 29.56/9.93 |
% 29.56/9.93 | Instantiating formula (619) with n19, n16, all_0_4_4, n14 and discharging atoms sum(n19, n16) = all_0_4_4, sum(n19, n16) = n14, yields:
% 29.56/9.93 | (840) all_0_4_4 = n14
% 29.56/9.93 |
% 29.56/9.93 | From (840) and (716) follows:
% 29.56/9.93 | (842) pred(n14) = all_0_3_3
% 29.56/9.93 |
% 29.56/9.93 | From (844) and (1171) follows:
% 29.56/9.94 | (1888) sum(n15, n12) = all_0_0_0
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 29.56/9.94 | (843) all_0_3_3 = n13
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (619) with n15, n12, all_0_0_0, n6 and discharging atoms sum(n15, n12) = all_0_0_0, sum(n15, n12) = n6, yields:
% 29.56/9.94 | (932) all_0_0_0 = n6
% 29.56/9.94 |
% 29.56/9.94 | From (843)(932) and (232) follows:
% 29.56/9.94 | (1891) sum(n13, n6) = all_0_6_6
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (619) with n13, n6, all_0_6_6, n19 and discharging atoms sum(n13, n6) = all_0_6_6, sum(n13, n6) = n19, yields:
% 29.56/9.94 | (1070) all_0_6_6 = n19
% 29.56/9.94 |
% 29.56/9.94 | Equations (1070) can reduce 31 to:
% 29.56/9.94 | (748) $false
% 29.56/9.94 |
% 29.56/9.94 |-The branch is then unsatisfiable
% 29.56/9.94 |-Branch two:
% 29.56/9.94 | (1186) ~ (all_0_7_7 = n15)
% 29.56/9.94 | (1187) all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/9.94 |
% 29.56/9.94 +-Applying beta-rule and splitting (1187), into two cases.
% 29.56/9.94 |-Branch one:
% 29.56/9.94 | (1188) all_0_7_7 = n14
% 29.56/9.94 |
% 29.56/9.94 | From (1188) and (683) follows:
% 29.56/9.94 | (1189) succ(n14) = all_0_5_5
% 29.56/9.94 |
% 29.56/9.94 | From (1188) and (8) follows:
% 29.56/9.94 | (1190) sum(n14, all_0_1_1) = all_0_0_0
% 29.56/9.94 |
% 29.56/9.94 | From (1188) and (1819) follows:
% 29.56/9.94 | (1899) sum(n19, n14) = all_0_2_2
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (388) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 29.56/9.94 | (1192) all_0_5_5 = n15
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (619) with n19, n14, all_0_2_2, n12 and discharging atoms sum(n19, n14) = all_0_2_2, sum(n19, n14) = n12, yields:
% 29.56/9.94 | (856) all_0_2_2 = n12
% 29.56/9.94 |
% 29.56/9.94 | From (856) and (473) follows:
% 29.56/9.94 | (858) pred(n12) = all_0_1_1
% 29.56/9.94 |
% 29.56/9.94 | From (1192) and (1818) follows:
% 29.56/9.94 | (1903) sum(n19, n15) = all_0_4_4
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 29.56/9.94 | (861) all_0_1_1 = n11
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (619) with n19, n15, all_0_4_4, n13 and discharging atoms sum(n19, n15) = all_0_4_4, sum(n19, n15) = n13, yields:
% 29.56/9.94 | (857) all_0_4_4 = n13
% 29.56/9.94 |
% 29.56/9.94 | From (857) and (716) follows:
% 29.56/9.94 | (859) pred(n13) = all_0_3_3
% 29.56/9.94 |
% 29.56/9.94 | From (861) and (1190) follows:
% 29.56/9.94 | (1907) sum(n14, n11) = all_0_0_0
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 29.56/9.94 | (860) all_0_3_3 = n12
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (619) with n14, n11, all_0_0_0, n4 and discharging atoms sum(n14, n11) = all_0_0_0, sum(n14, n11) = n4, yields:
% 29.56/9.94 | (966) all_0_0_0 = n4
% 29.56/9.94 |
% 29.56/9.94 | From (860)(966) and (232) follows:
% 29.56/9.94 | (1910) sum(n12, n4) = all_0_6_6
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (619) with n12, n4, all_0_6_6, n16 and discharging atoms sum(n12, n4) = all_0_6_6, sum(n12, n4) = n16, yields:
% 29.56/9.94 | (917) all_0_6_6 = n16
% 29.56/9.94 |
% 29.56/9.94 | Equations (917) can reduce 163 to:
% 29.56/9.94 | (748) $false
% 29.56/9.94 |
% 29.56/9.94 |-The branch is then unsatisfiable
% 29.56/9.94 |-Branch two:
% 29.56/9.94 | (1205) ~ (all_0_7_7 = n14)
% 29.56/9.94 | (1206) all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/9.94 |
% 29.56/9.94 +-Applying beta-rule and splitting (1206), into two cases.
% 29.56/9.94 |-Branch one:
% 29.56/9.94 | (1207) all_0_7_7 = n13
% 29.56/9.94 |
% 29.56/9.94 | From (1207) and (683) follows:
% 29.56/9.94 | (1208) succ(n13) = all_0_5_5
% 29.56/9.94 |
% 29.56/9.94 | From (1207) and (8) follows:
% 29.56/9.94 | (1209) sum(n13, all_0_1_1) = all_0_0_0
% 29.56/9.94 |
% 29.56/9.94 | From (1207) and (1819) follows:
% 29.56/9.94 | (1918) sum(n19, n13) = all_0_2_2
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (388) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 29.56/9.94 | (1211) all_0_5_5 = n14
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (619) with n19, n13, all_0_2_2, n11 and discharging atoms sum(n19, n13) = all_0_2_2, sum(n19, n13) = n11, yields:
% 29.56/9.94 | (873) all_0_2_2 = n11
% 29.56/9.94 |
% 29.56/9.94 | From (873) and (473) follows:
% 29.56/9.94 | (875) pred(n11) = all_0_1_1
% 29.56/9.94 |
% 29.56/9.94 | From (1211) and (1818) follows:
% 29.56/9.94 | (1922) sum(n19, n14) = all_0_4_4
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 29.56/9.94 | (878) all_0_1_1 = n10
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (619) with n19, n14, all_0_4_4, n12 and discharging atoms sum(n19, n14) = all_0_4_4, sum(n19, n14) = n12, yields:
% 29.56/9.94 | (874) all_0_4_4 = n12
% 29.56/9.94 |
% 29.56/9.94 | From (874) and (716) follows:
% 29.56/9.94 | (876) pred(n12) = all_0_3_3
% 29.56/9.94 |
% 29.56/9.94 | From (878) and (1209) follows:
% 29.56/9.94 | (1926) sum(n13, n10) = all_0_0_0
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 29.56/9.94 | (877) all_0_3_3 = n11
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (619) with n13, n10, all_0_0_0, n2 and discharging atoms sum(n13, n10) = all_0_0_0, sum(n13, n10) = n2, yields:
% 29.56/9.94 | (1000) all_0_0_0 = n2
% 29.56/9.94 |
% 29.56/9.94 | From (877)(1000) and (232) follows:
% 29.56/9.94 | (1929) sum(n11, n2) = all_0_6_6
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (619) with n11, n2, all_0_6_6, n13 and discharging atoms sum(n11, n2) = all_0_6_6, sum(n11, n2) = n13, yields:
% 29.56/9.94 | (764) all_0_6_6 = n13
% 29.56/9.94 |
% 29.56/9.94 | Equations (764) can reduce 293 to:
% 29.56/9.94 | (748) $false
% 29.56/9.94 |
% 29.56/9.94 |-The branch is then unsatisfiable
% 29.56/9.94 |-Branch two:
% 29.56/9.94 | (1224) ~ (all_0_7_7 = n13)
% 29.56/9.94 | (1225) all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/9.94 |
% 29.56/9.94 +-Applying beta-rule and splitting (1225), into two cases.
% 29.56/9.94 |-Branch one:
% 29.56/9.94 | (1226) all_0_7_7 = n12
% 29.56/9.94 |
% 29.56/9.94 | From (1226) and (683) follows:
% 29.56/9.94 | (1227) succ(n12) = all_0_5_5
% 29.56/9.94 |
% 29.56/9.94 | From (1226) and (8) follows:
% 29.56/9.94 | (1228) sum(n12, all_0_1_1) = all_0_0_0
% 29.56/9.94 |
% 29.56/9.94 | From (1226) and (1819) follows:
% 29.56/9.94 | (1937) sum(n19, n12) = all_0_2_2
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (388) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 29.56/9.94 | (1230) all_0_5_5 = n13
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (619) with n19, n12, all_0_2_2, n10 and discharging atoms sum(n19, n12) = all_0_2_2, sum(n19, n12) = n10, yields:
% 29.56/9.94 | (890) all_0_2_2 = n10
% 29.56/9.94 |
% 29.56/9.94 | From (890) and (473) follows:
% 29.56/9.94 | (892) pred(n10) = all_0_1_1
% 29.56/9.94 |
% 29.56/9.94 | From (1230) and (1818) follows:
% 29.56/9.94 | (1941) sum(n19, n13) = all_0_4_4
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 29.56/9.94 | (895) all_0_1_1 = n9
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (619) with n19, n13, all_0_4_4, n11 and discharging atoms sum(n19, n13) = all_0_4_4, sum(n19, n13) = n11, yields:
% 29.56/9.94 | (891) all_0_4_4 = n11
% 29.56/9.94 |
% 29.56/9.94 | From (891) and (716) follows:
% 29.56/9.94 | (893) pred(n11) = all_0_3_3
% 29.56/9.94 |
% 29.56/9.94 | From (895) and (1228) follows:
% 29.56/9.94 | (1945) sum(n12, n9) = all_0_0_0
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 29.56/9.94 | (894) all_0_3_3 = n10
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (619) with n12, n9, all_0_0_0, n0 and discharging atoms sum(n12, n9) = all_0_0_0, sum(n12, n9) = n0, yields:
% 29.56/9.94 | (1034) all_0_0_0 = n0
% 29.56/9.94 |
% 29.56/9.94 | From (894)(1034) and (232) follows:
% 29.56/9.94 | (1948) sum(n10, n0) = all_0_6_6
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (619) with n10, n0, all_0_6_6, n10 and discharging atoms sum(n10, n0) = all_0_6_6, sum(n10, n0) = n10, yields:
% 29.56/9.94 | (968) all_0_6_6 = n10
% 29.56/9.94 |
% 29.56/9.94 | Equations (968) can reduce 176 to:
% 29.56/9.94 | (748) $false
% 29.56/9.94 |
% 29.56/9.94 |-The branch is then unsatisfiable
% 29.56/9.94 |-Branch two:
% 29.56/9.94 | (1243) ~ (all_0_7_7 = n12)
% 29.56/9.94 | (1244) all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/9.94 |
% 29.56/9.94 +-Applying beta-rule and splitting (1244), into two cases.
% 29.56/9.94 |-Branch one:
% 29.56/9.94 | (1245) all_0_7_7 = n11
% 29.56/9.94 |
% 29.56/9.94 | From (1245) and (683) follows:
% 29.56/9.94 | (1246) succ(n11) = all_0_5_5
% 29.56/9.94 |
% 29.56/9.94 | From (1245) and (8) follows:
% 29.56/9.94 | (1247) sum(n11, all_0_1_1) = all_0_0_0
% 29.56/9.94 |
% 29.56/9.94 | From (1245) and (1819) follows:
% 29.56/9.94 | (1956) sum(n19, n11) = all_0_2_2
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (388) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 29.56/9.94 | (1249) all_0_5_5 = n12
% 29.56/9.94 |
% 29.56/9.94 | Instantiating formula (619) with n19, n11, all_0_2_2, n9 and discharging atoms sum(n19, n11) = all_0_2_2, sum(n19, n11) = n9, yields:
% 29.56/9.94 | (907) all_0_2_2 = n9
% 29.56/9.94 |
% 29.56/9.94 | From (907) and (473) follows:
% 29.56/9.94 | (909) pred(n9) = all_0_1_1
% 29.56/9.94 |
% 29.56/9.94 | From (1249) and (1818) follows:
% 29.56/9.94 | (1960) sum(n19, n12) = all_0_4_4
% 29.56/9.94 |
% 29.56/9.95 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 29.56/9.95 | (912) all_0_1_1 = n8
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (619) with n19, n12, all_0_4_4, n10 and discharging atoms sum(n19, n12) = all_0_4_4, sum(n19, n12) = n10, yields:
% 29.56/9.95 | (908) all_0_4_4 = n10
% 29.56/9.95 |
% 29.56/9.95 | From (908) and (716) follows:
% 29.56/9.95 | (910) pred(n10) = all_0_3_3
% 29.56/9.95 |
% 29.56/9.95 | From (912) and (1247) follows:
% 29.56/9.95 | (1964) sum(n11, n8) = all_0_0_0
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 29.56/9.95 | (911) all_0_3_3 = n9
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (619) with n11, n8, all_0_0_0, n19 and discharging atoms sum(n11, n8) = all_0_0_0, sum(n11, n8) = n19, yields:
% 29.56/9.95 | (1068) all_0_0_0 = n19
% 29.56/9.95 |
% 29.56/9.95 | From (911)(1068) and (232) follows:
% 29.56/9.95 | (1967) sum(n9, n19) = all_0_6_6
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (619) with n9, n19, all_0_6_6, n7 and discharging atoms sum(n9, n19) = all_0_6_6, sum(n9, n19) = n7, yields:
% 29.56/9.95 | (815) all_0_6_6 = n7
% 29.56/9.95 |
% 29.56/9.95 | Equations (815) can reduce 557 to:
% 29.56/9.95 | (748) $false
% 29.56/9.95 |
% 29.56/9.95 |-The branch is then unsatisfiable
% 29.56/9.95 |-Branch two:
% 29.56/9.95 | (1262) ~ (all_0_7_7 = n11)
% 29.56/9.95 | (1263) all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/9.95 |
% 29.56/9.95 +-Applying beta-rule and splitting (1263), into two cases.
% 29.56/9.95 |-Branch one:
% 29.56/9.95 | (1264) all_0_7_7 = n10
% 29.56/9.95 |
% 29.56/9.95 | From (1264) and (683) follows:
% 29.56/9.95 | (1265) succ(n10) = all_0_5_5
% 29.56/9.95 |
% 29.56/9.95 | From (1264) and (8) follows:
% 29.56/9.95 | (1266) sum(n10, all_0_1_1) = all_0_0_0
% 29.56/9.95 |
% 29.56/9.95 | From (1264) and (1819) follows:
% 29.56/9.95 | (1975) sum(n19, n10) = all_0_2_2
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (388) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 29.56/9.95 | (1268) all_0_5_5 = n11
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (619) with n19, n10, all_0_2_2, n8 and discharging atoms sum(n19, n10) = all_0_2_2, sum(n19, n10) = n8, yields:
% 29.56/9.95 | (924) all_0_2_2 = n8
% 29.56/9.95 |
% 29.56/9.95 | From (924) and (473) follows:
% 29.56/9.95 | (926) pred(n8) = all_0_1_1
% 29.56/9.95 |
% 29.56/9.95 | From (1268) and (1818) follows:
% 29.56/9.95 | (1979) sum(n19, n11) = all_0_4_4
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 29.56/9.95 | (929) all_0_1_1 = n7
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (619) with n19, n11, all_0_4_4, n9 and discharging atoms sum(n19, n11) = all_0_4_4, sum(n19, n11) = n9, yields:
% 29.56/9.95 | (925) all_0_4_4 = n9
% 29.56/9.95 |
% 29.56/9.95 | From (925) and (716) follows:
% 29.56/9.95 | (927) pred(n9) = all_0_3_3
% 29.56/9.95 |
% 29.56/9.95 | From (929) and (1266) follows:
% 29.56/9.95 | (1983) sum(n10, n7) = all_0_0_0
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 29.56/9.95 | (928) all_0_3_3 = n8
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (619) with n10, n7, all_0_0_0, n17 and discharging atoms sum(n10, n7) = all_0_0_0, sum(n10, n7) = n17, yields:
% 29.56/9.95 | (745) all_0_0_0 = n17
% 29.56/9.95 |
% 29.56/9.95 | From (928)(745) and (232) follows:
% 29.56/9.95 | (1986) sum(n8, n17) = all_0_6_6
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (619) with n8, n17, all_0_6_6, n4 and discharging atoms sum(n8, n17) = all_0_6_6, sum(n8, n17) = n4, yields:
% 29.56/9.95 | (1019) all_0_6_6 = n4
% 29.56/9.95 |
% 29.56/9.95 | Equations (1019) can reduce 48 to:
% 29.56/9.95 | (748) $false
% 29.56/9.95 |
% 29.56/9.95 |-The branch is then unsatisfiable
% 29.56/9.95 |-Branch two:
% 29.56/9.95 | (1281) ~ (all_0_7_7 = n10)
% 29.56/9.95 | (1282) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/9.95 |
% 29.56/9.95 +-Applying beta-rule and splitting (1282), into two cases.
% 29.56/9.95 |-Branch one:
% 29.56/9.95 | (1283) all_0_7_7 = n9
% 29.56/9.95 |
% 29.56/9.95 | From (1283) and (683) follows:
% 29.56/9.95 | (1284) succ(n9) = all_0_5_5
% 29.56/9.95 |
% 29.56/9.95 | From (1283) and (8) follows:
% 29.56/9.95 | (1285) sum(n9, all_0_1_1) = all_0_0_0
% 29.56/9.95 |
% 29.56/9.95 | From (1283) and (1819) follows:
% 29.56/9.95 | (1994) sum(n19, n9) = all_0_2_2
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (388) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 29.56/9.95 | (1287) all_0_5_5 = n10
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (619) with n19, n9, all_0_2_2, n7 and discharging atoms sum(n19, n9) = all_0_2_2, sum(n19, n9) = n7, yields:
% 29.56/9.95 | (941) all_0_2_2 = n7
% 29.56/9.95 |
% 29.56/9.95 | From (941) and (473) follows:
% 29.56/9.95 | (943) pred(n7) = all_0_1_1
% 29.56/9.95 |
% 29.56/9.95 | From (1287) and (1818) follows:
% 29.56/9.95 | (1998) sum(n19, n10) = all_0_4_4
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 29.56/9.95 | (946) all_0_1_1 = n6
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (619) with n19, n10, all_0_4_4, n8 and discharging atoms sum(n19, n10) = all_0_4_4, sum(n19, n10) = n8, yields:
% 29.56/9.95 | (942) all_0_4_4 = n8
% 29.56/9.95 |
% 29.56/9.95 | From (942) and (716) follows:
% 29.56/9.95 | (944) pred(n8) = all_0_3_3
% 29.56/9.95 |
% 29.56/9.95 | From (946) and (1285) follows:
% 29.56/9.95 | (2002) sum(n9, n6) = all_0_0_0
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 29.56/9.95 | (945) all_0_3_3 = n7
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (619) with n9, n6, all_0_0_0, n15 and discharging atoms sum(n9, n6) = all_0_0_0, sum(n9, n6) = n15, yields:
% 29.56/9.95 | (779) all_0_0_0 = n15
% 29.56/9.95 |
% 29.56/9.95 | From (945)(779) and (232) follows:
% 29.56/9.95 | (2005) sum(n7, n15) = all_0_6_6
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (619) with n7, n15, all_0_6_6, n1 and discharging atoms sum(n7, n15) = all_0_6_6, sum(n7, n15) = n1, yields:
% 29.56/9.95 | (866) all_0_6_6 = n1
% 29.56/9.95 |
% 29.56/9.95 | Equations (866) can reduce 28 to:
% 29.56/9.95 | (748) $false
% 29.56/9.95 |
% 29.56/9.95 |-The branch is then unsatisfiable
% 29.56/9.95 |-Branch two:
% 29.56/9.95 | (1300) ~ (all_0_7_7 = n9)
% 29.56/9.95 | (1301) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/9.95 |
% 29.56/9.95 +-Applying beta-rule and splitting (1301), into two cases.
% 29.56/9.95 |-Branch one:
% 29.56/9.95 | (1302) all_0_7_7 = n8
% 29.56/9.95 |
% 29.56/9.95 | From (1302) and (683) follows:
% 29.56/9.95 | (1303) succ(n8) = all_0_5_5
% 29.56/9.95 |
% 29.56/9.95 | From (1302) and (8) follows:
% 29.56/9.95 | (1304) sum(n8, all_0_1_1) = all_0_0_0
% 29.56/9.95 |
% 29.56/9.95 | From (1302) and (1819) follows:
% 29.56/9.95 | (2013) sum(n19, n8) = all_0_2_2
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (388) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 29.56/9.95 | (1306) all_0_5_5 = n9
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (619) with n19, n8, all_0_2_2, n6 and discharging atoms sum(n19, n8) = all_0_2_2, sum(n19, n8) = n6, yields:
% 29.56/9.95 | (958) all_0_2_2 = n6
% 29.56/9.95 |
% 29.56/9.95 | From (958) and (473) follows:
% 29.56/9.95 | (960) pred(n6) = all_0_1_1
% 29.56/9.95 |
% 29.56/9.95 | From (1306) and (1818) follows:
% 29.56/9.95 | (2017) sum(n19, n9) = all_0_4_4
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 29.56/9.95 | (963) all_0_1_1 = n5
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (619) with n19, n9, all_0_4_4, n7 and discharging atoms sum(n19, n9) = all_0_4_4, sum(n19, n9) = n7, yields:
% 29.56/9.95 | (959) all_0_4_4 = n7
% 29.56/9.95 |
% 29.56/9.95 | From (959) and (716) follows:
% 29.56/9.95 | (961) pred(n7) = all_0_3_3
% 29.56/9.95 |
% 29.56/9.95 | From (963) and (1304) follows:
% 29.56/9.95 | (2021) sum(n8, n5) = all_0_0_0
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 29.56/9.95 | (962) all_0_3_3 = n6
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (619) with n8, n5, all_0_0_0, n13 and discharging atoms sum(n8, n5) = all_0_0_0, sum(n8, n5) = n13, yields:
% 29.56/9.95 | (813) all_0_0_0 = n13
% 29.56/9.95 |
% 29.56/9.95 | From (962)(813) and (232) follows:
% 29.56/9.95 | (2024) sum(n6, n13) = all_0_6_6
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (619) with n6, n13, all_0_6_6, n19 and discharging atoms sum(n6, n13) = all_0_6_6, sum(n6, n13) = n19, yields:
% 29.56/9.95 | (1070) all_0_6_6 = n19
% 29.56/9.95 |
% 29.56/9.95 | Equations (1070) can reduce 31 to:
% 29.56/9.95 | (748) $false
% 29.56/9.95 |
% 29.56/9.95 |-The branch is then unsatisfiable
% 29.56/9.95 |-Branch two:
% 29.56/9.95 | (1319) ~ (all_0_7_7 = n8)
% 29.56/9.95 | (1320) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/9.95 |
% 29.56/9.95 +-Applying beta-rule and splitting (1320), into two cases.
% 29.56/9.95 |-Branch one:
% 29.56/9.95 | (1321) all_0_7_7 = n7
% 29.56/9.95 |
% 29.56/9.95 | From (1321) and (683) follows:
% 29.56/9.95 | (1322) succ(n7) = all_0_5_5
% 29.56/9.95 |
% 29.56/9.95 | From (1321) and (8) follows:
% 29.56/9.95 | (1323) sum(n7, all_0_1_1) = all_0_0_0
% 29.56/9.95 |
% 29.56/9.95 | From (1321) and (1819) follows:
% 29.56/9.95 | (2032) sum(n19, n7) = all_0_2_2
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (388) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 29.56/9.95 | (1325) all_0_5_5 = n8
% 29.56/9.95 |
% 29.56/9.95 | Instantiating formula (619) with n19, n7, all_0_2_2, n5 and discharging atoms sum(n19, n7) = all_0_2_2, sum(n19, n7) = n5, yields:
% 29.56/9.96 | (975) all_0_2_2 = n5
% 29.56/9.96 |
% 29.56/9.96 | From (975) and (473) follows:
% 29.56/9.96 | (977) pred(n5) = all_0_1_1
% 29.56/9.96 |
% 29.56/9.96 | From (1325) and (1818) follows:
% 29.56/9.96 | (2036) sum(n19, n8) = all_0_4_4
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 29.56/9.96 | (980) all_0_1_1 = n4
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (619) with n19, n8, all_0_4_4, n6 and discharging atoms sum(n19, n8) = all_0_4_4, sum(n19, n8) = n6, yields:
% 29.56/9.96 | (976) all_0_4_4 = n6
% 29.56/9.96 |
% 29.56/9.96 | From (976) and (716) follows:
% 29.56/9.96 | (978) pred(n6) = all_0_3_3
% 29.56/9.96 |
% 29.56/9.96 | From (980) and (1323) follows:
% 29.56/9.96 | (2040) sum(n7, n4) = all_0_0_0
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 29.56/9.96 | (979) all_0_3_3 = n5
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (619) with n7, n4, all_0_0_0, n11 and discharging atoms sum(n7, n4) = all_0_0_0, sum(n7, n4) = n11, yields:
% 29.56/9.96 | (847) all_0_0_0 = n11
% 29.56/9.96 |
% 29.56/9.96 | From (979)(847) and (232) follows:
% 29.56/9.96 | (2043) sum(n5, n11) = all_0_6_6
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (619) with n5, n11, all_0_6_6, n16 and discharging atoms sum(n5, n11) = all_0_6_6, sum(n5, n11) = n16, yields:
% 29.56/9.96 | (917) all_0_6_6 = n16
% 29.56/9.96 |
% 29.56/9.96 | Equations (917) can reduce 163 to:
% 29.56/9.96 | (748) $false
% 29.56/9.96 |
% 29.56/9.96 |-The branch is then unsatisfiable
% 29.56/9.96 |-Branch two:
% 29.56/9.96 | (1338) ~ (all_0_7_7 = n7)
% 29.56/9.96 | (1339) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/9.96 |
% 29.56/9.96 +-Applying beta-rule and splitting (1339), into two cases.
% 29.56/9.96 |-Branch one:
% 29.56/9.96 | (1340) all_0_7_7 = n6
% 29.56/9.96 |
% 29.56/9.96 | From (1340) and (683) follows:
% 29.56/9.96 | (1341) succ(n6) = all_0_5_5
% 29.56/9.96 |
% 29.56/9.96 | From (1340) and (8) follows:
% 29.56/9.96 | (1342) sum(n6, all_0_1_1) = all_0_0_0
% 29.56/9.96 |
% 29.56/9.96 | From (1340) and (1819) follows:
% 29.56/9.96 | (2051) sum(n19, n6) = all_0_2_2
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (388) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 29.56/9.96 | (1344) all_0_5_5 = n7
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (619) with n19, n6, all_0_2_2, n4 and discharging atoms sum(n19, n6) = all_0_2_2, sum(n19, n6) = n4, yields:
% 29.56/9.96 | (992) all_0_2_2 = n4
% 29.56/9.96 |
% 29.56/9.96 | From (992) and (473) follows:
% 29.56/9.96 | (994) pred(n4) = all_0_1_1
% 29.56/9.96 |
% 29.56/9.96 | From (1344) and (1818) follows:
% 29.56/9.96 | (2055) sum(n19, n7) = all_0_4_4
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 29.56/9.96 | (997) all_0_1_1 = n3
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (619) with n19, n7, all_0_4_4, n5 and discharging atoms sum(n19, n7) = all_0_4_4, sum(n19, n7) = n5, yields:
% 29.56/9.96 | (993) all_0_4_4 = n5
% 29.56/9.96 |
% 29.56/9.96 | From (993) and (716) follows:
% 29.56/9.96 | (995) pred(n5) = all_0_3_3
% 29.56/9.96 |
% 29.56/9.96 | From (997) and (1342) follows:
% 29.56/9.96 | (2059) sum(n6, n3) = all_0_0_0
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 29.56/9.96 | (996) all_0_3_3 = n4
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (619) with n6, n3, all_0_0_0, n9 and discharging atoms sum(n6, n3) = all_0_0_0, sum(n6, n3) = n9, yields:
% 29.56/9.96 | (881) all_0_0_0 = n9
% 29.56/9.96 |
% 29.56/9.96 | From (996)(881) and (232) follows:
% 29.56/9.96 | (2062) sum(n4, n9) = all_0_6_6
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (619) with n4, n9, all_0_6_6, n13 and discharging atoms sum(n4, n9) = all_0_6_6, sum(n4, n9) = n13, yields:
% 29.56/9.96 | (764) all_0_6_6 = n13
% 29.56/9.96 |
% 29.56/9.96 | Equations (764) can reduce 293 to:
% 29.56/9.96 | (748) $false
% 29.56/9.96 |
% 29.56/9.96 |-The branch is then unsatisfiable
% 29.56/9.96 |-Branch two:
% 29.56/9.96 | (1357) ~ (all_0_7_7 = n6)
% 29.56/9.96 | (1358) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/9.96 |
% 29.56/9.96 +-Applying beta-rule and splitting (1358), into two cases.
% 29.56/9.96 |-Branch one:
% 29.56/9.96 | (1359) all_0_7_7 = n5
% 29.56/9.96 |
% 29.56/9.96 | From (1359) and (683) follows:
% 29.56/9.96 | (1360) succ(n5) = all_0_5_5
% 29.56/9.96 |
% 29.56/9.96 | From (1359) and (8) follows:
% 29.56/9.96 | (1361) sum(n5, all_0_1_1) = all_0_0_0
% 29.56/9.96 |
% 29.56/9.96 | From (1359) and (1819) follows:
% 29.56/9.96 | (2070) sum(n19, n5) = all_0_2_2
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (388) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 29.56/9.96 | (1363) all_0_5_5 = n6
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (619) with n19, n5, all_0_2_2, n3 and discharging atoms sum(n19, n5) = all_0_2_2, sum(n19, n5) = n3, yields:
% 29.56/9.96 | (1009) all_0_2_2 = n3
% 29.56/9.96 |
% 29.56/9.96 | From (1009) and (473) follows:
% 29.56/9.96 | (1011) pred(n3) = all_0_1_1
% 29.56/9.96 |
% 29.56/9.96 | From (1363) and (1818) follows:
% 29.56/9.96 | (2074) sum(n19, n6) = all_0_4_4
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 29.56/9.96 | (1014) all_0_1_1 = n2
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (619) with n19, n6, all_0_4_4, n4 and discharging atoms sum(n19, n6) = all_0_4_4, sum(n19, n6) = n4, yields:
% 29.56/9.96 | (1010) all_0_4_4 = n4
% 29.56/9.96 |
% 29.56/9.96 | From (1010) and (716) follows:
% 29.56/9.96 | (1012) pred(n4) = all_0_3_3
% 29.56/9.96 |
% 29.56/9.96 | From (1014) and (1361) follows:
% 29.56/9.96 | (2078) sum(n5, n2) = all_0_0_0
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 29.56/9.96 | (1013) all_0_3_3 = n3
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (619) with n5, n2, all_0_0_0, n7 and discharging atoms sum(n5, n2) = all_0_0_0, sum(n5, n2) = n7, yields:
% 29.56/9.96 | (915) all_0_0_0 = n7
% 29.56/9.96 |
% 29.56/9.96 | From (1013)(915) and (232) follows:
% 29.56/9.96 | (2081) sum(n3, n7) = all_0_6_6
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (619) with n3, n7, all_0_6_6, n10 and discharging atoms sum(n3, n7) = all_0_6_6, sum(n3, n7) = n10, yields:
% 29.56/9.96 | (968) all_0_6_6 = n10
% 29.56/9.96 |
% 29.56/9.96 | Equations (968) can reduce 176 to:
% 29.56/9.96 | (748) $false
% 29.56/9.96 |
% 29.56/9.96 |-The branch is then unsatisfiable
% 29.56/9.96 |-Branch two:
% 29.56/9.96 | (1376) ~ (all_0_7_7 = n5)
% 29.56/9.96 | (1377) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/9.96 |
% 29.56/9.96 +-Applying beta-rule and splitting (1377), into two cases.
% 29.56/9.96 |-Branch one:
% 29.56/9.96 | (1378) all_0_7_7 = n4
% 29.56/9.96 |
% 29.56/9.96 | From (1378) and (683) follows:
% 29.56/9.96 | (1379) succ(n4) = all_0_5_5
% 29.56/9.96 |
% 29.56/9.96 | From (1378) and (8) follows:
% 29.56/9.96 | (1380) sum(n4, all_0_1_1) = all_0_0_0
% 29.56/9.96 |
% 29.56/9.96 | From (1378) and (1819) follows:
% 29.56/9.96 | (2089) sum(n19, n4) = all_0_2_2
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (388) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 29.56/9.96 | (1382) all_0_5_5 = n5
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (619) with n19, n4, all_0_2_2, n2 and discharging atoms sum(n19, n4) = all_0_2_2, sum(n19, n4) = n2, yields:
% 29.56/9.96 | (1026) all_0_2_2 = n2
% 29.56/9.96 |
% 29.56/9.96 | From (1026) and (473) follows:
% 29.56/9.96 | (1028) pred(n2) = all_0_1_1
% 29.56/9.96 |
% 29.56/9.96 | From (1382) and (1818) follows:
% 29.56/9.96 | (2093) sum(n19, n5) = all_0_4_4
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 29.56/9.96 | (1031) all_0_1_1 = n1
% 29.56/9.96 |
% 29.56/9.96 | Instantiating formula (619) with n19, n5, all_0_4_4, n3 and discharging atoms sum(n19, n5) = all_0_4_4, sum(n19, n5) = n3, yields:
% 29.56/9.96 | (1027) all_0_4_4 = n3
% 29.56/9.96 |
% 29.56/9.96 | From (1027) and (716) follows:
% 29.56/9.96 | (1029) pred(n3) = all_0_3_3
% 29.56/9.96 |
% 29.56/9.96 | From (1031) and (1380) follows:
% 29.56/9.96 | (2097) sum(n4, n1) = all_0_0_0
% 29.56/9.96 |
% 29.56/9.97 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 29.56/9.97 | (1030) all_0_3_3 = n2
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (619) with n4, n1, all_0_0_0, n5 and discharging atoms sum(n4, n1) = all_0_0_0, sum(n4, n1) = n5, yields:
% 29.56/9.97 | (949) all_0_0_0 = n5
% 29.56/9.97 |
% 29.56/9.97 | From (1030)(949) and (232) follows:
% 29.56/9.97 | (2100) sum(n2, n5) = all_0_6_6
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (619) with n2, n5, all_0_6_6, n7 and discharging atoms sum(n2, n5) = all_0_6_6, sum(n2, n5) = n7, yields:
% 29.56/9.97 | (815) all_0_6_6 = n7
% 29.56/9.97 |
% 29.56/9.97 | Equations (815) can reduce 557 to:
% 29.56/9.97 | (748) $false
% 29.56/9.97 |
% 29.56/9.97 |-The branch is then unsatisfiable
% 29.56/9.97 |-Branch two:
% 29.56/9.97 | (1395) ~ (all_0_7_7 = n4)
% 29.56/9.97 | (1396) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/9.97 |
% 29.56/9.97 +-Applying beta-rule and splitting (1396), into two cases.
% 29.56/9.97 |-Branch one:
% 29.56/9.97 | (1397) all_0_7_7 = n3
% 29.56/9.97 |
% 29.56/9.97 | From (1397) and (683) follows:
% 29.56/9.97 | (1398) succ(n3) = all_0_5_5
% 29.56/9.97 |
% 29.56/9.97 | From (1397) and (8) follows:
% 29.56/9.97 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 29.56/9.97 |
% 29.56/9.97 | From (1397) and (1819) follows:
% 29.56/9.97 | (2108) sum(n19, n3) = all_0_2_2
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 29.56/9.97 | (1401) all_0_5_5 = n4
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (619) with n19, n3, all_0_2_2, n1 and discharging atoms sum(n19, n3) = all_0_2_2, sum(n19, n3) = n1, yields:
% 29.56/9.97 | (1043) all_0_2_2 = n1
% 29.56/9.97 |
% 29.56/9.97 | From (1043) and (473) follows:
% 29.56/9.97 | (1045) pred(n1) = all_0_1_1
% 29.56/9.97 |
% 29.56/9.97 | From (1401) and (1818) follows:
% 29.56/9.97 | (2112) sum(n19, n4) = all_0_4_4
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 29.56/9.97 | (1048) all_0_1_1 = n0
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (619) with n19, n4, all_0_4_4, n2 and discharging atoms sum(n19, n4) = all_0_4_4, sum(n19, n4) = n2, yields:
% 29.56/9.97 | (1044) all_0_4_4 = n2
% 29.56/9.97 |
% 29.56/9.97 | From (1044) and (716) follows:
% 29.56/9.97 | (1046) pred(n2) = all_0_3_3
% 29.56/9.97 |
% 29.56/9.97 | From (1048) and (1399) follows:
% 29.56/9.97 | (2116) sum(n3, n0) = all_0_0_0
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 29.56/9.97 | (1047) all_0_3_3 = n1
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (619) with n3, n0, all_0_0_0, n3 and discharging atoms sum(n3, n0) = all_0_0_0, sum(n3, n0) = n3, yields:
% 29.56/9.97 | (983) all_0_0_0 = n3
% 29.56/9.97 |
% 29.56/9.97 | From (1047)(983) and (232) follows:
% 29.56/9.97 | (2119) sum(n1, n3) = all_0_6_6
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (619) with n1, n3, all_0_6_6, n4 and discharging atoms sum(n1, n3) = all_0_6_6, sum(n1, n3) = n4, yields:
% 29.56/9.97 | (1019) all_0_6_6 = n4
% 29.56/9.97 |
% 29.56/9.97 | Equations (1019) can reduce 48 to:
% 29.56/9.97 | (748) $false
% 29.56/9.97 |
% 29.56/9.97 |-The branch is then unsatisfiable
% 29.56/9.97 |-Branch two:
% 29.56/9.97 | (1414) ~ (all_0_7_7 = n3)
% 29.56/9.97 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/9.97 |
% 29.56/9.97 +-Applying beta-rule and splitting (1415), into two cases.
% 29.56/9.97 |-Branch one:
% 29.56/9.97 | (1416) all_0_7_7 = n2
% 29.56/9.97 |
% 29.56/9.97 | From (1416) and (683) follows:
% 29.56/9.97 | (1417) succ(n2) = all_0_5_5
% 29.56/9.97 |
% 29.56/9.97 | From (1416) and (8) follows:
% 29.56/9.97 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 29.56/9.97 |
% 29.56/9.97 | From (1416) and (1819) follows:
% 29.56/9.97 | (2127) sum(n19, n2) = all_0_2_2
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 29.56/9.97 | (1420) all_0_5_5 = n3
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (619) with n19, n2, all_0_2_2, n0 and discharging atoms sum(n19, n2) = all_0_2_2, sum(n19, n2) = n0, yields:
% 29.56/9.97 | (1060) all_0_2_2 = n0
% 29.56/9.97 |
% 29.56/9.97 | From (1060) and (473) follows:
% 29.56/9.97 | (1062) pred(n0) = all_0_1_1
% 29.56/9.97 |
% 29.56/9.97 | From (1420) and (1818) follows:
% 29.56/9.97 | (2131) sum(n19, n3) = all_0_4_4
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 29.56/9.97 | (1065) all_0_1_1 = n20
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (619) with n19, n3, all_0_4_4, n1 and discharging atoms sum(n19, n3) = all_0_4_4, sum(n19, n3) = n1, yields:
% 29.56/9.97 | (1061) all_0_4_4 = n1
% 29.56/9.97 |
% 29.56/9.97 | From (1061) and (716) follows:
% 29.56/9.97 | (1063) pred(n1) = all_0_3_3
% 29.56/9.97 |
% 29.56/9.97 | From (1065) and (1418) follows:
% 29.56/9.97 | (2135) sum(n2, n20) = all_0_0_0
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 29.56/9.97 | (1064) all_0_3_3 = n0
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (619) with n2, n20, all_0_0_0, n1 and discharging atoms sum(n2, n20) = all_0_0_0, sum(n2, n20) = n1, yields:
% 29.56/9.97 | (1017) all_0_0_0 = n1
% 29.56/9.97 |
% 29.56/9.97 | From (1064)(1017) and (232) follows:
% 29.56/9.97 | (2138) sum(n0, n1) = all_0_6_6
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (619) with n0, n1, all_0_6_6, n1 and discharging atoms sum(n0, n1) = all_0_6_6, sum(n0, n1) = n1, yields:
% 29.56/9.97 | (866) all_0_6_6 = n1
% 29.56/9.97 |
% 29.56/9.97 | Equations (866) can reduce 28 to:
% 29.56/9.97 | (748) $false
% 29.56/9.97 |
% 29.56/9.97 |-The branch is then unsatisfiable
% 29.56/9.97 |-Branch two:
% 29.56/9.97 | (1433) ~ (all_0_7_7 = n2)
% 29.56/9.97 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/9.97 |
% 29.56/9.97 +-Applying beta-rule and splitting (1434), into two cases.
% 29.56/9.97 |-Branch one:
% 29.56/9.97 | (1435) all_0_7_7 = n1
% 29.56/9.97 |
% 29.56/9.97 | From (1435) and (683) follows:
% 29.56/9.97 | (1436) succ(n1) = all_0_5_5
% 29.56/9.97 |
% 29.56/9.97 | From (1435) and (8) follows:
% 29.56/9.97 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 29.56/9.97 |
% 29.56/9.97 | From (1435) and (1819) follows:
% 29.56/9.97 | (2146) sum(n19, n1) = all_0_2_2
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 29.56/9.97 | (1439) all_0_5_5 = n2
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (619) with n19, n1, all_0_2_2, n20 and discharging atoms sum(n19, n1) = all_0_2_2, sum(n19, n1) = n20, yields:
% 29.56/9.97 | (1076) all_0_2_2 = n20
% 29.56/9.97 |
% 29.56/9.97 | From (1076) and (473) follows:
% 29.56/9.97 | (1078) pred(n20) = all_0_1_1
% 29.56/9.97 |
% 29.56/9.97 | From (1439) and (1818) follows:
% 29.56/9.97 | (2150) sum(n19, n2) = all_0_4_4
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 29.56/9.97 | (1080) all_0_1_1 = n19
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (619) with n19, n2, all_0_4_4, n0 and discharging atoms sum(n19, n2) = all_0_4_4, sum(n19, n2) = n0, yields:
% 29.56/9.97 | (1077) all_0_4_4 = n0
% 29.56/9.97 |
% 29.56/9.97 | From (1077) and (716) follows:
% 29.56/9.97 | (1079) pred(n0) = all_0_3_3
% 29.56/9.97 |
% 29.56/9.97 | From (1080) and (1437) follows:
% 29.56/9.97 | (2154) sum(n1, n19) = all_0_0_0
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 29.56/9.97 | (1081) all_0_3_3 = n20
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (619) with n1, n19, all_0_0_0, n20 and discharging atoms sum(n1, n19) = all_0_0_0, sum(n1, n19) = n20, yields:
% 29.56/9.97 | (1051) all_0_0_0 = n20
% 29.56/9.97 |
% 29.56/9.97 | From (1081)(1051) and (232) follows:
% 29.56/9.97 | (2157) sum(n20, n20) = all_0_6_6
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (619) with n20, n20, all_0_6_6, n19 and discharging atoms sum(n20, n20) = all_0_6_6, sum(n20, n20) = n19, yields:
% 29.56/9.97 | (1070) all_0_6_6 = n19
% 29.56/9.97 |
% 29.56/9.97 | Equations (1070) can reduce 31 to:
% 29.56/9.97 | (748) $false
% 29.56/9.97 |
% 29.56/9.97 |-The branch is then unsatisfiable
% 29.56/9.97 |-Branch two:
% 29.56/9.97 | (1452) ~ (all_0_7_7 = n1)
% 29.56/9.97 | (1453) all_0_7_7 = n0
% 29.56/9.97 |
% 29.56/9.97 | From (1453) and (683) follows:
% 29.56/9.97 | (1454) succ(n0) = all_0_5_5
% 29.56/9.97 |
% 29.56/9.97 | From (1453) and (8) follows:
% 29.56/9.97 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 29.56/9.97 |
% 29.56/9.97 | From (1453) and (1819) follows:
% 29.56/9.97 | (2164) sum(n19, n0) = all_0_2_2
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 29.56/9.97 | (1457) all_0_5_5 = n1
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (619) with n19, n0, all_0_2_2, n19 and discharging atoms sum(n19, n0) = all_0_2_2, sum(n19, n0) = n19, yields:
% 29.56/9.97 | (737) all_0_2_2 = n19
% 29.56/9.97 |
% 29.56/9.97 | From (737) and (473) follows:
% 29.56/9.97 | (739) pred(n19) = all_0_1_1
% 29.56/9.97 |
% 29.56/9.97 | From (1457) and (1818) follows:
% 29.56/9.97 | (2168) sum(n19, n1) = all_0_4_4
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 29.56/9.97 | (742) all_0_1_1 = n18
% 29.56/9.97 |
% 29.56/9.97 | Instantiating formula (619) with n19, n1, all_0_4_4, n20 and discharging atoms sum(n19, n1) = all_0_4_4, sum(n19, n1) = n20, yields:
% 29.56/9.97 | (738) all_0_4_4 = n20
% 29.56/9.97 |
% 29.56/9.97 | From (738) and (716) follows:
% 29.56/9.97 | (740) pred(n20) = all_0_3_3
% 29.56/9.97 |
% 29.56/9.97 | From (742) and (1455) follows:
% 29.56/9.98 | (2172) sum(n0, n18) = all_0_0_0
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 29.56/9.98 | (741) all_0_3_3 = n19
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (619) with n0, n18, all_0_0_0, n18 and discharging atoms sum(n0, n18) = all_0_0_0, sum(n0, n18) = n18, yields:
% 29.56/9.98 | (1084) all_0_0_0 = n18
% 29.56/9.98 |
% 29.56/9.98 | From (741)(1084) and (232) follows:
% 29.56/9.98 | (2175) sum(n19, n18) = all_0_6_6
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (619) with n19, n18, all_0_6_6, n16 and discharging atoms sum(n19, n18) = all_0_6_6, sum(n19, n18) = n16, yields:
% 29.56/9.98 | (917) all_0_6_6 = n16
% 29.56/9.98 |
% 29.56/9.98 | Equations (917) can reduce 163 to:
% 29.56/9.98 | (748) $false
% 29.56/9.98 |
% 29.56/9.98 |-The branch is then unsatisfiable
% 29.56/9.98 |-Branch two:
% 29.56/9.98 | (766) ~ (all_0_8_8 = n19)
% 29.56/9.98 | (767) all_0_8_8 = n18 | all_0_8_8 = n17 | all_0_8_8 = n16 | all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/9.98 |
% 29.56/9.98 +-Applying beta-rule and splitting (1111), into two cases.
% 29.56/9.98 |-Branch one:
% 29.56/9.98 | (1112) all_0_7_7 = n18
% 29.56/9.98 |
% 29.56/9.98 | From (1112) and (683) follows:
% 29.56/9.98 | (1113) succ(n18) = all_0_5_5
% 29.56/9.98 |
% 29.56/9.98 | From (1112) and (8) follows:
% 29.56/9.98 | (1114) sum(n18, all_0_1_1) = all_0_0_0
% 29.56/9.98 |
% 29.56/9.98 | From (1112) and (378) follows:
% 29.56/9.98 | (2183) sum(all_0_8_8, n18) = all_0_2_2
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (388) with n18, all_0_5_5, n19 and discharging atoms succ(n18) = all_0_5_5, succ(n18) = n19, yields:
% 29.56/9.98 | (1116) all_0_5_5 = n19
% 29.56/9.98 |
% 29.56/9.98 | From (1116) and (708) follows:
% 29.56/9.98 | (2185) sum(all_0_8_8, n19) = all_0_4_4
% 29.56/9.98 |
% 29.56/9.98 +-Applying beta-rule and splitting (767), into two cases.
% 29.56/9.98 |-Branch one:
% 29.56/9.98 | (768) all_0_8_8 = n18
% 29.56/9.98 |
% 29.56/9.98 | From (768) and (2185) follows:
% 29.56/9.98 | (2187) sum(n18, n19) = all_0_4_4
% 29.56/9.98 |
% 29.56/9.98 | From (768) and (2183) follows:
% 29.56/9.98 | (2188) sum(n18, n18) = all_0_2_2
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (619) with n18, n19, all_0_4_4, n16 and discharging atoms sum(n18, n19) = all_0_4_4, sum(n18, n19) = n16, yields:
% 29.56/9.98 | (806) all_0_4_4 = n16
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (619) with n18, n18, all_0_2_2, n15 and discharging atoms sum(n18, n18) = all_0_2_2, sum(n18, n18) = n15, yields:
% 29.56/9.98 | (805) all_0_2_2 = n15
% 29.56/9.98 |
% 29.56/9.98 | From (805) and (473) follows:
% 29.56/9.98 | (807) pred(n15) = all_0_1_1
% 29.56/9.98 |
% 29.56/9.98 | From (806) and (716) follows:
% 29.56/9.98 | (808) pred(n16) = all_0_3_3
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 29.56/9.98 | (809) all_0_3_3 = n15
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 29.56/9.98 | (810) all_0_1_1 = n14
% 29.56/9.98 |
% 29.56/9.98 | From (809) and (232) follows:
% 29.56/9.98 | (811) sum(n15, all_0_0_0) = all_0_6_6
% 29.56/9.98 |
% 29.56/9.98 | From (810) and (1114) follows:
% 29.56/9.98 | (2196) sum(n18, n14) = all_0_0_0
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (619) with n18, n14, all_0_0_0, n11 and discharging atoms sum(n18, n14) = all_0_0_0, sum(n18, n14) = n11, yields:
% 29.56/9.98 | (847) all_0_0_0 = n11
% 29.56/9.98 |
% 29.56/9.98 | From (847) and (811) follows:
% 29.56/9.98 | (2198) sum(n15, n11) = all_0_6_6
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (619) with n15, n11, all_0_6_6, n5 and discharging atoms sum(n15, n11) = all_0_6_6, sum(n15, n11) = n5, yields:
% 29.56/9.98 | (832) all_0_6_6 = n5
% 29.56/9.98 |
% 29.56/9.98 | Equations (832) can reduce 462 to:
% 29.56/9.98 | (748) $false
% 29.56/9.98 |
% 29.56/9.98 |-The branch is then unsatisfiable
% 29.56/9.98 |-Branch two:
% 29.56/9.98 | (783) ~ (all_0_8_8 = n18)
% 29.56/9.98 | (784) all_0_8_8 = n17 | all_0_8_8 = n16 | all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/9.98 |
% 29.56/9.98 +-Applying beta-rule and splitting (784), into two cases.
% 29.56/9.98 |-Branch one:
% 29.56/9.98 | (785) all_0_8_8 = n17
% 29.56/9.98 |
% 29.56/9.98 | From (785) and (2185) follows:
% 29.56/9.98 | (2204) sum(n17, n19) = all_0_4_4
% 29.56/9.98 |
% 29.56/9.98 | From (785) and (2183) follows:
% 29.56/9.98 | (2205) sum(n17, n18) = all_0_2_2
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (619) with n17, n19, all_0_4_4, n15 and discharging atoms sum(n17, n19) = all_0_4_4, sum(n17, n19) = n15, yields:
% 29.56/9.98 | (823) all_0_4_4 = n15
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (619) with n17, n18, all_0_2_2, n14 and discharging atoms sum(n17, n18) = all_0_2_2, sum(n17, n18) = n14, yields:
% 29.56/9.98 | (822) all_0_2_2 = n14
% 29.56/9.98 |
% 29.56/9.98 | From (822) and (473) follows:
% 29.56/9.98 | (824) pred(n14) = all_0_1_1
% 29.56/9.98 |
% 29.56/9.98 | From (823) and (716) follows:
% 29.56/9.98 | (825) pred(n15) = all_0_3_3
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 29.56/9.98 | (826) all_0_3_3 = n14
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 29.56/9.98 | (827) all_0_1_1 = n13
% 29.56/9.98 |
% 29.56/9.98 | From (826) and (232) follows:
% 29.56/9.98 | (828) sum(n14, all_0_0_0) = all_0_6_6
% 29.56/9.98 |
% 29.56/9.98 | From (827) and (1114) follows:
% 29.56/9.98 | (2213) sum(n18, n13) = all_0_0_0
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (619) with n18, n13, all_0_0_0, n10 and discharging atoms sum(n18, n13) = all_0_0_0, sum(n18, n13) = n10, yields:
% 29.56/9.98 | (864) all_0_0_0 = n10
% 29.56/9.98 |
% 29.56/9.98 | From (864) and (828) follows:
% 29.56/9.98 | (2215) sum(n14, n10) = all_0_6_6
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (619) with n14, n10, all_0_6_6, n3 and discharging atoms sum(n14, n10) = all_0_6_6, sum(n14, n10) = n3, yields:
% 29.56/9.98 | (849) all_0_6_6 = n3
% 29.56/9.98 |
% 29.56/9.98 | Equations (849) can reduce 416 to:
% 29.56/9.98 | (748) $false
% 29.56/9.98 |
% 29.56/9.98 |-The branch is then unsatisfiable
% 29.56/9.98 |-Branch two:
% 29.56/9.98 | (800) ~ (all_0_8_8 = n17)
% 29.56/9.98 | (801) all_0_8_8 = n16 | all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/9.98 |
% 29.56/9.98 +-Applying beta-rule and splitting (801), into two cases.
% 29.56/9.98 |-Branch one:
% 29.56/9.98 | (802) all_0_8_8 = n16
% 29.56/9.98 |
% 29.56/9.98 | From (802) and (2185) follows:
% 29.56/9.98 | (2221) sum(n16, n19) = all_0_4_4
% 29.56/9.98 |
% 29.56/9.98 | From (802) and (2183) follows:
% 29.56/9.98 | (2222) sum(n16, n18) = all_0_2_2
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (619) with n16, n19, all_0_4_4, n14 and discharging atoms sum(n16, n19) = all_0_4_4, sum(n16, n19) = n14, yields:
% 29.56/9.98 | (840) all_0_4_4 = n14
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (619) with n16, n18, all_0_2_2, n13 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = n13, yields:
% 29.56/9.98 | (839) all_0_2_2 = n13
% 29.56/9.98 |
% 29.56/9.98 | From (839) and (473) follows:
% 29.56/9.98 | (841) pred(n13) = all_0_1_1
% 29.56/9.98 |
% 29.56/9.98 | From (840) and (716) follows:
% 29.56/9.98 | (842) pred(n14) = all_0_3_3
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 29.56/9.98 | (843) all_0_3_3 = n13
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 29.56/9.98 | (844) all_0_1_1 = n12
% 29.56/9.98 |
% 29.56/9.98 | From (843) and (232) follows:
% 29.56/9.98 | (845) sum(n13, all_0_0_0) = all_0_6_6
% 29.56/9.98 |
% 29.56/9.98 | From (844) and (1114) follows:
% 29.56/9.98 | (2230) sum(n18, n12) = all_0_0_0
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (619) with n18, n12, all_0_0_0, n9 and discharging atoms sum(n18, n12) = all_0_0_0, sum(n18, n12) = n9, yields:
% 29.56/9.98 | (881) all_0_0_0 = n9
% 29.56/9.98 |
% 29.56/9.98 | From (881) and (845) follows:
% 29.56/9.98 | (2232) sum(n13, n9) = all_0_6_6
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (619) with n13, n9, all_0_6_6, n1 and discharging atoms sum(n13, n9) = all_0_6_6, sum(n13, n9) = n1, yields:
% 29.56/9.98 | (866) all_0_6_6 = n1
% 29.56/9.98 |
% 29.56/9.98 | Equations (866) can reduce 28 to:
% 29.56/9.98 | (748) $false
% 29.56/9.98 |
% 29.56/9.98 |-The branch is then unsatisfiable
% 29.56/9.98 |-Branch two:
% 29.56/9.98 | (817) ~ (all_0_8_8 = n16)
% 29.56/9.98 | (818) all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/9.98 |
% 29.56/9.98 +-Applying beta-rule and splitting (818), into two cases.
% 29.56/9.98 |-Branch one:
% 29.56/9.98 | (819) all_0_8_8 = n15
% 29.56/9.98 |
% 29.56/9.98 | From (819) and (2185) follows:
% 29.56/9.98 | (2238) sum(n15, n19) = all_0_4_4
% 29.56/9.98 |
% 29.56/9.98 | From (819) and (2183) follows:
% 29.56/9.98 | (2239) sum(n15, n18) = all_0_2_2
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (619) with n15, n19, all_0_4_4, n13 and discharging atoms sum(n15, n19) = all_0_4_4, sum(n15, n19) = n13, yields:
% 29.56/9.98 | (857) all_0_4_4 = n13
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (619) with n15, n18, all_0_2_2, n12 and discharging atoms sum(n15, n18) = all_0_2_2, sum(n15, n18) = n12, yields:
% 29.56/9.98 | (856) all_0_2_2 = n12
% 29.56/9.98 |
% 29.56/9.98 | From (856) and (473) follows:
% 29.56/9.98 | (858) pred(n12) = all_0_1_1
% 29.56/9.98 |
% 29.56/9.98 | From (857) and (716) follows:
% 29.56/9.98 | (859) pred(n13) = all_0_3_3
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 29.56/9.98 | (860) all_0_3_3 = n12
% 29.56/9.98 |
% 29.56/9.98 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 29.56/9.99 | (861) all_0_1_1 = n11
% 29.56/9.99 |
% 29.56/9.99 | From (860) and (232) follows:
% 29.56/9.99 | (862) sum(n12, all_0_0_0) = all_0_6_6
% 29.56/9.99 |
% 29.56/9.99 | From (861) and (1114) follows:
% 29.56/9.99 | (2247) sum(n18, n11) = all_0_0_0
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n18, n11, all_0_0_0, n8 and discharging atoms sum(n18, n11) = all_0_0_0, sum(n18, n11) = n8, yields:
% 29.56/9.99 | (898) all_0_0_0 = n8
% 29.56/9.99 |
% 29.56/9.99 | From (898) and (862) follows:
% 29.56/9.99 | (2249) sum(n12, n8) = all_0_6_6
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n12, n8, all_0_6_6, n20 and discharging atoms sum(n12, n8) = all_0_6_6, sum(n12, n8) = n20, yields:
% 29.56/9.99 | (883) all_0_6_6 = n20
% 29.56/9.99 |
% 29.56/9.99 | Equations (883) can reduce 381 to:
% 29.56/9.99 | (748) $false
% 29.56/9.99 |
% 29.56/9.99 |-The branch is then unsatisfiable
% 29.56/9.99 |-Branch two:
% 29.56/9.99 | (834) ~ (all_0_8_8 = n15)
% 29.56/9.99 | (835) all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/9.99 |
% 29.56/9.99 +-Applying beta-rule and splitting (835), into two cases.
% 29.56/9.99 |-Branch one:
% 29.56/9.99 | (836) all_0_8_8 = n14
% 29.56/9.99 |
% 29.56/9.99 | From (836) and (2185) follows:
% 29.56/9.99 | (2255) sum(n14, n19) = all_0_4_4
% 29.56/9.99 |
% 29.56/9.99 | From (836) and (2183) follows:
% 29.56/9.99 | (2256) sum(n14, n18) = all_0_2_2
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n14, n19, all_0_4_4, n12 and discharging atoms sum(n14, n19) = all_0_4_4, sum(n14, n19) = n12, yields:
% 29.56/9.99 | (874) all_0_4_4 = n12
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n14, n18, all_0_2_2, n11 and discharging atoms sum(n14, n18) = all_0_2_2, sum(n14, n18) = n11, yields:
% 29.56/9.99 | (873) all_0_2_2 = n11
% 29.56/9.99 |
% 29.56/9.99 | From (873) and (473) follows:
% 29.56/9.99 | (875) pred(n11) = all_0_1_1
% 29.56/9.99 |
% 29.56/9.99 | From (874) and (716) follows:
% 29.56/9.99 | (876) pred(n12) = all_0_3_3
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 29.56/9.99 | (877) all_0_3_3 = n11
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 29.56/9.99 | (878) all_0_1_1 = n10
% 29.56/9.99 |
% 29.56/9.99 | From (877) and (232) follows:
% 29.56/9.99 | (879) sum(n11, all_0_0_0) = all_0_6_6
% 29.56/9.99 |
% 29.56/9.99 | From (878) and (1114) follows:
% 29.56/9.99 | (2264) sum(n18, n10) = all_0_0_0
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n18, n10, all_0_0_0, n7 and discharging atoms sum(n18, n10) = all_0_0_0, sum(n18, n10) = n7, yields:
% 29.56/9.99 | (915) all_0_0_0 = n7
% 29.56/9.99 |
% 29.56/9.99 | From (915) and (879) follows:
% 29.56/9.99 | (2266) sum(n11, n7) = all_0_6_6
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n11, n7, all_0_6_6, n18 and discharging atoms sum(n11, n7) = all_0_6_6, sum(n11, n7) = n18, yields:
% 29.56/9.99 | (900) all_0_6_6 = n18
% 29.56/9.99 |
% 29.56/9.99 | Equations (900) can reduce 622 to:
% 29.56/9.99 | (748) $false
% 29.56/9.99 |
% 29.56/9.99 |-The branch is then unsatisfiable
% 29.56/9.99 |-Branch two:
% 29.56/9.99 | (851) ~ (all_0_8_8 = n14)
% 29.56/9.99 | (852) all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/9.99 |
% 29.56/9.99 +-Applying beta-rule and splitting (852), into two cases.
% 29.56/9.99 |-Branch one:
% 29.56/9.99 | (853) all_0_8_8 = n13
% 29.56/9.99 |
% 29.56/9.99 | From (853) and (2185) follows:
% 29.56/9.99 | (2272) sum(n13, n19) = all_0_4_4
% 29.56/9.99 |
% 29.56/9.99 | From (853) and (2183) follows:
% 29.56/9.99 | (2273) sum(n13, n18) = all_0_2_2
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n13, n19, all_0_4_4, n11 and discharging atoms sum(n13, n19) = all_0_4_4, sum(n13, n19) = n11, yields:
% 29.56/9.99 | (891) all_0_4_4 = n11
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n13, n18, all_0_2_2, n10 and discharging atoms sum(n13, n18) = all_0_2_2, sum(n13, n18) = n10, yields:
% 29.56/9.99 | (890) all_0_2_2 = n10
% 29.56/9.99 |
% 29.56/9.99 | From (890) and (473) follows:
% 29.56/9.99 | (892) pred(n10) = all_0_1_1
% 29.56/9.99 |
% 29.56/9.99 | From (891) and (716) follows:
% 29.56/9.99 | (893) pred(n11) = all_0_3_3
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 29.56/9.99 | (894) all_0_3_3 = n10
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 29.56/9.99 | (895) all_0_1_1 = n9
% 29.56/9.99 |
% 29.56/9.99 | From (894) and (232) follows:
% 29.56/9.99 | (896) sum(n10, all_0_0_0) = all_0_6_6
% 29.56/9.99 |
% 29.56/9.99 | From (895) and (1114) follows:
% 29.56/9.99 | (2281) sum(n18, n9) = all_0_0_0
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n18, n9, all_0_0_0, n6 and discharging atoms sum(n18, n9) = all_0_0_0, sum(n18, n9) = n6, yields:
% 29.56/9.99 | (932) all_0_0_0 = n6
% 29.56/9.99 |
% 29.56/9.99 | From (932) and (896) follows:
% 29.56/9.99 | (2283) sum(n10, n6) = all_0_6_6
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n10, n6, all_0_6_6, n16 and discharging atoms sum(n10, n6) = all_0_6_6, sum(n10, n6) = n16, yields:
% 29.56/9.99 | (917) all_0_6_6 = n16
% 29.56/9.99 |
% 29.56/9.99 | Equations (917) can reduce 163 to:
% 29.56/9.99 | (748) $false
% 29.56/9.99 |
% 29.56/9.99 |-The branch is then unsatisfiable
% 29.56/9.99 |-Branch two:
% 29.56/9.99 | (868) ~ (all_0_8_8 = n13)
% 29.56/9.99 | (869) all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/9.99 |
% 29.56/9.99 +-Applying beta-rule and splitting (869), into two cases.
% 29.56/9.99 |-Branch one:
% 29.56/9.99 | (870) all_0_8_8 = n12
% 29.56/9.99 |
% 29.56/9.99 | From (870) and (2185) follows:
% 29.56/9.99 | (2289) sum(n12, n19) = all_0_4_4
% 29.56/9.99 |
% 29.56/9.99 | From (870) and (2183) follows:
% 29.56/9.99 | (2290) sum(n12, n18) = all_0_2_2
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n12, n19, all_0_4_4, n10 and discharging atoms sum(n12, n19) = all_0_4_4, sum(n12, n19) = n10, yields:
% 29.56/9.99 | (908) all_0_4_4 = n10
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n12, n18, all_0_2_2, n9 and discharging atoms sum(n12, n18) = all_0_2_2, sum(n12, n18) = n9, yields:
% 29.56/9.99 | (907) all_0_2_2 = n9
% 29.56/9.99 |
% 29.56/9.99 | From (907) and (473) follows:
% 29.56/9.99 | (909) pred(n9) = all_0_1_1
% 29.56/9.99 |
% 29.56/9.99 | From (908) and (716) follows:
% 29.56/9.99 | (910) pred(n10) = all_0_3_3
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 29.56/9.99 | (911) all_0_3_3 = n9
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 29.56/9.99 | (912) all_0_1_1 = n8
% 29.56/9.99 |
% 29.56/9.99 | From (911) and (232) follows:
% 29.56/9.99 | (913) sum(n9, all_0_0_0) = all_0_6_6
% 29.56/9.99 |
% 29.56/9.99 | From (912) and (1114) follows:
% 29.56/9.99 | (2298) sum(n18, n8) = all_0_0_0
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n18, n8, all_0_0_0, n5 and discharging atoms sum(n18, n8) = all_0_0_0, sum(n18, n8) = n5, yields:
% 29.56/9.99 | (949) all_0_0_0 = n5
% 29.56/9.99 |
% 29.56/9.99 | From (949) and (913) follows:
% 29.56/9.99 | (2300) sum(n9, n5) = all_0_6_6
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n9, n5, all_0_6_6, n14 and discharging atoms sum(n9, n5) = all_0_6_6, sum(n9, n5) = n14, yields:
% 29.56/9.99 | (934) all_0_6_6 = n14
% 29.56/9.99 |
% 29.56/9.99 | Equations (934) can reduce 353 to:
% 29.56/9.99 | (748) $false
% 29.56/9.99 |
% 29.56/9.99 |-The branch is then unsatisfiable
% 29.56/9.99 |-Branch two:
% 29.56/9.99 | (885) ~ (all_0_8_8 = n12)
% 29.56/9.99 | (886) all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/9.99 |
% 29.56/9.99 +-Applying beta-rule and splitting (886), into two cases.
% 29.56/9.99 |-Branch one:
% 29.56/9.99 | (887) all_0_8_8 = n11
% 29.56/9.99 |
% 29.56/9.99 | From (887) and (2185) follows:
% 29.56/9.99 | (2306) sum(n11, n19) = all_0_4_4
% 29.56/9.99 |
% 29.56/9.99 | From (887) and (2183) follows:
% 29.56/9.99 | (2307) sum(n11, n18) = all_0_2_2
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n11, n19, all_0_4_4, n9 and discharging atoms sum(n11, n19) = all_0_4_4, sum(n11, n19) = n9, yields:
% 29.56/9.99 | (925) all_0_4_4 = n9
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n11, n18, all_0_2_2, n8 and discharging atoms sum(n11, n18) = all_0_2_2, sum(n11, n18) = n8, yields:
% 29.56/9.99 | (924) all_0_2_2 = n8
% 29.56/9.99 |
% 29.56/9.99 | From (924) and (473) follows:
% 29.56/9.99 | (926) pred(n8) = all_0_1_1
% 29.56/9.99 |
% 29.56/9.99 | From (925) and (716) follows:
% 29.56/9.99 | (927) pred(n9) = all_0_3_3
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 29.56/9.99 | (928) all_0_3_3 = n8
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 29.56/9.99 | (929) all_0_1_1 = n7
% 29.56/9.99 |
% 29.56/9.99 | From (928) and (232) follows:
% 29.56/9.99 | (930) sum(n8, all_0_0_0) = all_0_6_6
% 29.56/9.99 |
% 29.56/9.99 | From (929) and (1114) follows:
% 29.56/9.99 | (2315) sum(n18, n7) = all_0_0_0
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n18, n7, all_0_0_0, n4 and discharging atoms sum(n18, n7) = all_0_0_0, sum(n18, n7) = n4, yields:
% 29.56/9.99 | (966) all_0_0_0 = n4
% 29.56/9.99 |
% 29.56/9.99 | From (966) and (930) follows:
% 29.56/9.99 | (2317) sum(n8, n4) = all_0_6_6
% 29.56/9.99 |
% 29.56/9.99 | Instantiating formula (619) with n8, n4, all_0_6_6, n12 and discharging atoms sum(n8, n4) = all_0_6_6, sum(n8, n4) = n12, yields:
% 29.56/9.99 | (951) all_0_6_6 = n12
% 29.56/9.99 |
% 29.56/9.99 | Equations (951) can reduce 76 to:
% 29.56/9.99 | (748) $false
% 29.56/9.99 |
% 29.56/9.99 |-The branch is then unsatisfiable
% 29.56/9.99 |-Branch two:
% 29.56/9.99 | (902) ~ (all_0_8_8 = n11)
% 29.56/9.99 | (903) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/9.99 |
% 29.56/9.99 +-Applying beta-rule and splitting (903), into two cases.
% 29.56/9.99 |-Branch one:
% 29.56/9.99 | (904) all_0_8_8 = n10
% 29.56/9.99 |
% 29.56/9.99 | From (904) and (2185) follows:
% 29.56/9.99 | (2323) sum(n10, n19) = all_0_4_4
% 29.56/10.00 |
% 29.56/10.00 | From (904) and (2183) follows:
% 29.56/10.00 | (2324) sum(n10, n18) = all_0_2_2
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n10, n19, all_0_4_4, n8 and discharging atoms sum(n10, n19) = all_0_4_4, sum(n10, n19) = n8, yields:
% 29.56/10.00 | (942) all_0_4_4 = n8
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n10, n18, all_0_2_2, n7 and discharging atoms sum(n10, n18) = all_0_2_2, sum(n10, n18) = n7, yields:
% 29.56/10.00 | (941) all_0_2_2 = n7
% 29.56/10.00 |
% 29.56/10.00 | From (941) and (473) follows:
% 29.56/10.00 | (943) pred(n7) = all_0_1_1
% 29.56/10.00 |
% 29.56/10.00 | From (942) and (716) follows:
% 29.56/10.00 | (944) pred(n8) = all_0_3_3
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 29.56/10.00 | (945) all_0_3_3 = n7
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 29.56/10.00 | (946) all_0_1_1 = n6
% 29.56/10.00 |
% 29.56/10.00 | From (945) and (232) follows:
% 29.56/10.00 | (947) sum(n7, all_0_0_0) = all_0_6_6
% 29.56/10.00 |
% 29.56/10.00 | From (946) and (1114) follows:
% 29.56/10.00 | (2332) sum(n18, n6) = all_0_0_0
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n18, n6, all_0_0_0, n3 and discharging atoms sum(n18, n6) = all_0_0_0, sum(n18, n6) = n3, yields:
% 29.56/10.00 | (983) all_0_0_0 = n3
% 29.56/10.00 |
% 29.56/10.00 | From (983) and (947) follows:
% 29.56/10.00 | (2334) sum(n7, n3) = all_0_6_6
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n7, n3, all_0_6_6, n10 and discharging atoms sum(n7, n3) = all_0_6_6, sum(n7, n3) = n10, yields:
% 29.56/10.00 | (968) all_0_6_6 = n10
% 29.56/10.00 |
% 29.56/10.00 | Equations (968) can reduce 176 to:
% 29.56/10.00 | (748) $false
% 29.56/10.00 |
% 29.56/10.00 |-The branch is then unsatisfiable
% 29.56/10.00 |-Branch two:
% 29.56/10.00 | (919) ~ (all_0_8_8 = n10)
% 29.56/10.00 | (920) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/10.00 |
% 29.56/10.00 +-Applying beta-rule and splitting (920), into two cases.
% 29.56/10.00 |-Branch one:
% 29.56/10.00 | (921) all_0_8_8 = n9
% 29.56/10.00 |
% 29.56/10.00 | From (921) and (2185) follows:
% 29.56/10.00 | (2340) sum(n9, n19) = all_0_4_4
% 29.56/10.00 |
% 29.56/10.00 | From (921) and (2183) follows:
% 29.56/10.00 | (2341) sum(n9, n18) = all_0_2_2
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n9, n19, all_0_4_4, n7 and discharging atoms sum(n9, n19) = all_0_4_4, sum(n9, n19) = n7, yields:
% 29.56/10.00 | (959) all_0_4_4 = n7
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n9, n18, all_0_2_2, n6 and discharging atoms sum(n9, n18) = all_0_2_2, sum(n9, n18) = n6, yields:
% 29.56/10.00 | (958) all_0_2_2 = n6
% 29.56/10.00 |
% 29.56/10.00 | From (958) and (473) follows:
% 29.56/10.00 | (960) pred(n6) = all_0_1_1
% 29.56/10.00 |
% 29.56/10.00 | From (959) and (716) follows:
% 29.56/10.00 | (961) pred(n7) = all_0_3_3
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 29.56/10.00 | (962) all_0_3_3 = n6
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 29.56/10.00 | (963) all_0_1_1 = n5
% 29.56/10.00 |
% 29.56/10.00 | From (962) and (232) follows:
% 29.56/10.00 | (964) sum(n6, all_0_0_0) = all_0_6_6
% 29.56/10.00 |
% 29.56/10.00 | From (963) and (1114) follows:
% 29.56/10.00 | (2349) sum(n18, n5) = all_0_0_0
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n18, n5, all_0_0_0, n2 and discharging atoms sum(n18, n5) = all_0_0_0, sum(n18, n5) = n2, yields:
% 29.56/10.00 | (1000) all_0_0_0 = n2
% 29.56/10.00 |
% 29.56/10.00 | From (1000) and (964) follows:
% 29.56/10.00 | (2351) sum(n6, n2) = all_0_6_6
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n6, n2, all_0_6_6, n8 and discharging atoms sum(n6, n2) = all_0_6_6, sum(n6, n2) = n8, yields:
% 29.56/10.00 | (985) all_0_6_6 = n8
% 29.56/10.00 |
% 29.56/10.00 | Equations (985) can reduce 357 to:
% 29.56/10.00 | (748) $false
% 29.56/10.00 |
% 29.56/10.00 |-The branch is then unsatisfiable
% 29.56/10.00 |-Branch two:
% 29.56/10.00 | (936) ~ (all_0_8_8 = n9)
% 29.56/10.00 | (937) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/10.00 |
% 29.56/10.00 +-Applying beta-rule and splitting (937), into two cases.
% 29.56/10.00 |-Branch one:
% 29.56/10.00 | (938) all_0_8_8 = n8
% 29.56/10.00 |
% 29.56/10.00 | From (938) and (2185) follows:
% 29.56/10.00 | (2357) sum(n8, n19) = all_0_4_4
% 29.56/10.00 |
% 29.56/10.00 | From (938) and (2183) follows:
% 29.56/10.00 | (2358) sum(n8, n18) = all_0_2_2
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n8, n19, all_0_4_4, n6 and discharging atoms sum(n8, n19) = all_0_4_4, sum(n8, n19) = n6, yields:
% 29.56/10.00 | (976) all_0_4_4 = n6
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n8, n18, all_0_2_2, n5 and discharging atoms sum(n8, n18) = all_0_2_2, sum(n8, n18) = n5, yields:
% 29.56/10.00 | (975) all_0_2_2 = n5
% 29.56/10.00 |
% 29.56/10.00 | From (975) and (473) follows:
% 29.56/10.00 | (977) pred(n5) = all_0_1_1
% 29.56/10.00 |
% 29.56/10.00 | From (976) and (716) follows:
% 29.56/10.00 | (978) pred(n6) = all_0_3_3
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 29.56/10.00 | (979) all_0_3_3 = n5
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 29.56/10.00 | (980) all_0_1_1 = n4
% 29.56/10.00 |
% 29.56/10.00 | From (979) and (232) follows:
% 29.56/10.00 | (981) sum(n5, all_0_0_0) = all_0_6_6
% 29.56/10.00 |
% 29.56/10.00 | From (980) and (1114) follows:
% 29.56/10.00 | (2366) sum(n18, n4) = all_0_0_0
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n18, n4, all_0_0_0, n1 and discharging atoms sum(n18, n4) = all_0_0_0, sum(n18, n4) = n1, yields:
% 29.56/10.00 | (1017) all_0_0_0 = n1
% 29.56/10.00 |
% 29.56/10.00 | From (1017) and (981) follows:
% 29.56/10.00 | (2368) sum(n5, n1) = all_0_6_6
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n5, n1, all_0_6_6, n6 and discharging atoms sum(n5, n1) = all_0_6_6, sum(n5, n1) = n6, yields:
% 29.56/10.00 | (1002) all_0_6_6 = n6
% 29.56/10.00 |
% 29.56/10.00 | Equations (1002) can reduce 498 to:
% 29.56/10.00 | (748) $false
% 29.56/10.00 |
% 29.56/10.00 |-The branch is then unsatisfiable
% 29.56/10.00 |-Branch two:
% 29.56/10.00 | (953) ~ (all_0_8_8 = n8)
% 29.56/10.00 | (954) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/10.00 |
% 29.56/10.00 +-Applying beta-rule and splitting (954), into two cases.
% 29.56/10.00 |-Branch one:
% 29.56/10.00 | (955) all_0_8_8 = n7
% 29.56/10.00 |
% 29.56/10.00 | From (955) and (2185) follows:
% 29.56/10.00 | (2374) sum(n7, n19) = all_0_4_4
% 29.56/10.00 |
% 29.56/10.00 | From (955) and (2183) follows:
% 29.56/10.00 | (2375) sum(n7, n18) = all_0_2_2
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n7, n19, all_0_4_4, n5 and discharging atoms sum(n7, n19) = all_0_4_4, sum(n7, n19) = n5, yields:
% 29.56/10.00 | (993) all_0_4_4 = n5
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n7, n18, all_0_2_2, n4 and discharging atoms sum(n7, n18) = all_0_2_2, sum(n7, n18) = n4, yields:
% 29.56/10.00 | (992) all_0_2_2 = n4
% 29.56/10.00 |
% 29.56/10.00 | From (992) and (473) follows:
% 29.56/10.00 | (994) pred(n4) = all_0_1_1
% 29.56/10.00 |
% 29.56/10.00 | From (993) and (716) follows:
% 29.56/10.00 | (995) pred(n5) = all_0_3_3
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 29.56/10.00 | (996) all_0_3_3 = n4
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 29.56/10.00 | (997) all_0_1_1 = n3
% 29.56/10.00 |
% 29.56/10.00 | From (996) and (232) follows:
% 29.56/10.00 | (998) sum(n4, all_0_0_0) = all_0_6_6
% 29.56/10.00 |
% 29.56/10.00 | From (997) and (1114) follows:
% 29.56/10.00 | (2383) sum(n18, n3) = all_0_0_0
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n18, n3, all_0_0_0, n0 and discharging atoms sum(n18, n3) = all_0_0_0, sum(n18, n3) = n0, yields:
% 29.56/10.00 | (1034) all_0_0_0 = n0
% 29.56/10.00 |
% 29.56/10.00 | From (1034) and (998) follows:
% 29.56/10.00 | (2385) sum(n4, n0) = all_0_6_6
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n4, n0, all_0_6_6, n4 and discharging atoms sum(n4, n0) = all_0_6_6, sum(n4, n0) = n4, yields:
% 29.56/10.00 | (1019) all_0_6_6 = n4
% 29.56/10.00 |
% 29.56/10.00 | Equations (1019) can reduce 48 to:
% 29.56/10.00 | (748) $false
% 29.56/10.00 |
% 29.56/10.00 |-The branch is then unsatisfiable
% 29.56/10.00 |-Branch two:
% 29.56/10.00 | (970) ~ (all_0_8_8 = n7)
% 29.56/10.00 | (971) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/10.00 |
% 29.56/10.00 +-Applying beta-rule and splitting (971), into two cases.
% 29.56/10.00 |-Branch one:
% 29.56/10.00 | (972) all_0_8_8 = n6
% 29.56/10.00 |
% 29.56/10.00 | From (972) and (2185) follows:
% 29.56/10.00 | (2391) sum(n6, n19) = all_0_4_4
% 29.56/10.00 |
% 29.56/10.00 | From (972) and (2183) follows:
% 29.56/10.00 | (2392) sum(n6, n18) = all_0_2_2
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n6, n19, all_0_4_4, n4 and discharging atoms sum(n6, n19) = all_0_4_4, sum(n6, n19) = n4, yields:
% 29.56/10.00 | (1010) all_0_4_4 = n4
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n6, n18, all_0_2_2, n3 and discharging atoms sum(n6, n18) = all_0_2_2, sum(n6, n18) = n3, yields:
% 29.56/10.00 | (1009) all_0_2_2 = n3
% 29.56/10.00 |
% 29.56/10.00 | From (1009) and (473) follows:
% 29.56/10.00 | (1011) pred(n3) = all_0_1_1
% 29.56/10.00 |
% 29.56/10.00 | From (1010) and (716) follows:
% 29.56/10.00 | (1012) pred(n4) = all_0_3_3
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 29.56/10.00 | (1013) all_0_3_3 = n3
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 29.56/10.00 | (1014) all_0_1_1 = n2
% 29.56/10.00 |
% 29.56/10.00 | From (1013) and (232) follows:
% 29.56/10.00 | (1015) sum(n3, all_0_0_0) = all_0_6_6
% 29.56/10.00 |
% 29.56/10.00 | From (1014) and (1114) follows:
% 29.56/10.00 | (2400) sum(n18, n2) = all_0_0_0
% 29.56/10.00 |
% 29.56/10.00 | Instantiating formula (619) with n18, n2, all_0_0_0, n20 and discharging atoms sum(n18, n2) = all_0_0_0, sum(n18, n2) = n20, yields:
% 29.56/10.00 | (1051) all_0_0_0 = n20
% 29.56/10.00 |
% 29.56/10.00 | From (1051) and (1015) follows:
% 29.56/10.01 | (2402) sum(n3, n20) = all_0_6_6
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n3, n20, all_0_6_6, n2 and discharging atoms sum(n3, n20) = all_0_6_6, sum(n3, n20) = n2, yields:
% 29.56/10.01 | (1036) all_0_6_6 = n2
% 29.56/10.01 |
% 29.56/10.01 | Equations (1036) can reduce 56 to:
% 29.56/10.01 | (748) $false
% 29.56/10.01 |
% 29.56/10.01 |-The branch is then unsatisfiable
% 29.56/10.01 |-Branch two:
% 29.56/10.01 | (987) ~ (all_0_8_8 = n6)
% 29.56/10.01 | (988) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/10.01 |
% 29.56/10.01 +-Applying beta-rule and splitting (988), into two cases.
% 29.56/10.01 |-Branch one:
% 29.56/10.01 | (989) all_0_8_8 = n5
% 29.56/10.01 |
% 29.56/10.01 | From (989) and (2185) follows:
% 29.56/10.01 | (2408) sum(n5, n19) = all_0_4_4
% 29.56/10.01 |
% 29.56/10.01 | From (989) and (2183) follows:
% 29.56/10.01 | (2409) sum(n5, n18) = all_0_2_2
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n5, n19, all_0_4_4, n3 and discharging atoms sum(n5, n19) = all_0_4_4, sum(n5, n19) = n3, yields:
% 29.56/10.01 | (1027) all_0_4_4 = n3
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n5, n18, all_0_2_2, n2 and discharging atoms sum(n5, n18) = all_0_2_2, sum(n5, n18) = n2, yields:
% 29.56/10.01 | (1026) all_0_2_2 = n2
% 29.56/10.01 |
% 29.56/10.01 | From (1026) and (473) follows:
% 29.56/10.01 | (1028) pred(n2) = all_0_1_1
% 29.56/10.01 |
% 29.56/10.01 | From (1027) and (716) follows:
% 29.56/10.01 | (1029) pred(n3) = all_0_3_3
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 29.56/10.01 | (1030) all_0_3_3 = n2
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 29.56/10.01 | (1031) all_0_1_1 = n1
% 29.56/10.01 |
% 29.56/10.01 | From (1030) and (232) follows:
% 29.56/10.01 | (1032) sum(n2, all_0_0_0) = all_0_6_6
% 29.56/10.01 |
% 29.56/10.01 | From (1031) and (1114) follows:
% 29.56/10.01 | (2417) sum(n18, n1) = all_0_0_0
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n18, n1, all_0_0_0, n19 and discharging atoms sum(n18, n1) = all_0_0_0, sum(n18, n1) = n19, yields:
% 29.56/10.01 | (1068) all_0_0_0 = n19
% 29.56/10.01 |
% 29.56/10.01 | From (1068) and (1032) follows:
% 29.56/10.01 | (2419) sum(n2, n19) = all_0_6_6
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n2, n19, all_0_6_6, n0 and discharging atoms sum(n2, n19) = all_0_6_6, sum(n2, n19) = n0, yields:
% 29.56/10.01 | (1053) all_0_6_6 = n0
% 29.56/10.01 |
% 29.56/10.01 | Equations (1053) can reduce 676 to:
% 29.56/10.01 | (748) $false
% 29.56/10.01 |
% 29.56/10.01 |-The branch is then unsatisfiable
% 29.56/10.01 |-Branch two:
% 29.56/10.01 | (1004) ~ (all_0_8_8 = n5)
% 29.56/10.01 | (1005) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/10.01 |
% 29.56/10.01 +-Applying beta-rule and splitting (1005), into two cases.
% 29.56/10.01 |-Branch one:
% 29.56/10.01 | (1006) all_0_8_8 = n4
% 29.56/10.01 |
% 29.56/10.01 | From (1006) and (2185) follows:
% 29.56/10.01 | (2425) sum(n4, n19) = all_0_4_4
% 29.56/10.01 |
% 29.56/10.01 | From (1006) and (2183) follows:
% 29.56/10.01 | (2426) sum(n4, n18) = all_0_2_2
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n4, n19, all_0_4_4, n2 and discharging atoms sum(n4, n19) = all_0_4_4, sum(n4, n19) = n2, yields:
% 29.56/10.01 | (1044) all_0_4_4 = n2
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n4, n18, all_0_2_2, n1 and discharging atoms sum(n4, n18) = all_0_2_2, sum(n4, n18) = n1, yields:
% 29.56/10.01 | (1043) all_0_2_2 = n1
% 29.56/10.01 |
% 29.56/10.01 | From (1043) and (473) follows:
% 29.56/10.01 | (1045) pred(n1) = all_0_1_1
% 29.56/10.01 |
% 29.56/10.01 | From (1044) and (716) follows:
% 29.56/10.01 | (1046) pred(n2) = all_0_3_3
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 29.56/10.01 | (1047) all_0_3_3 = n1
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 29.56/10.01 | (1048) all_0_1_1 = n0
% 29.56/10.01 |
% 29.56/10.01 | From (1047) and (232) follows:
% 29.56/10.01 | (1049) sum(n1, all_0_0_0) = all_0_6_6
% 29.56/10.01 |
% 29.56/10.01 | From (1048) and (1114) follows:
% 29.56/10.01 | (2434) sum(n18, n0) = all_0_0_0
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n18, n0, all_0_0_0, n18 and discharging atoms sum(n18, n0) = all_0_0_0, sum(n18, n0) = n18, yields:
% 29.56/10.01 | (1084) all_0_0_0 = n18
% 29.56/10.01 |
% 29.56/10.01 | From (1084) and (1049) follows:
% 29.56/10.01 | (2436) sum(n1, n18) = all_0_6_6
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n1, n18, all_0_6_6, n19 and discharging atoms sum(n1, n18) = all_0_6_6, sum(n1, n18) = n19, yields:
% 29.56/10.01 | (1070) all_0_6_6 = n19
% 29.56/10.01 |
% 29.56/10.01 | Equations (1070) can reduce 31 to:
% 29.56/10.01 | (748) $false
% 29.56/10.01 |
% 29.56/10.01 |-The branch is then unsatisfiable
% 29.56/10.01 |-Branch two:
% 29.56/10.01 | (1021) ~ (all_0_8_8 = n4)
% 29.56/10.01 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/10.01 |
% 29.56/10.01 +-Applying beta-rule and splitting (1022), into two cases.
% 29.56/10.01 |-Branch one:
% 29.56/10.01 | (1023) all_0_8_8 = n3
% 29.56/10.01 |
% 29.56/10.01 | From (1023) and (2185) follows:
% 29.56/10.01 | (2442) sum(n3, n19) = all_0_4_4
% 29.56/10.01 |
% 29.56/10.01 | From (1023) and (2183) follows:
% 29.56/10.01 | (2443) sum(n3, n18) = all_0_2_2
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n3, n19, all_0_4_4, n1 and discharging atoms sum(n3, n19) = all_0_4_4, sum(n3, n19) = n1, yields:
% 29.56/10.01 | (1061) all_0_4_4 = n1
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n3, n18, all_0_2_2, n0 and discharging atoms sum(n3, n18) = all_0_2_2, sum(n3, n18) = n0, yields:
% 29.56/10.01 | (1060) all_0_2_2 = n0
% 29.56/10.01 |
% 29.56/10.01 | From (1060) and (473) follows:
% 29.56/10.01 | (1062) pred(n0) = all_0_1_1
% 29.56/10.01 |
% 29.56/10.01 | From (1061) and (716) follows:
% 29.56/10.01 | (1063) pred(n1) = all_0_3_3
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 29.56/10.01 | (1064) all_0_3_3 = n0
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 29.56/10.01 | (1065) all_0_1_1 = n20
% 29.56/10.01 |
% 29.56/10.01 | From (1064) and (232) follows:
% 29.56/10.01 | (1066) sum(n0, all_0_0_0) = all_0_6_6
% 29.56/10.01 |
% 29.56/10.01 | From (1065) and (1114) follows:
% 29.56/10.01 | (2451) sum(n18, n20) = all_0_0_0
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n18, n20, all_0_0_0, n17 and discharging atoms sum(n18, n20) = all_0_0_0, sum(n18, n20) = n17, yields:
% 29.56/10.01 | (745) all_0_0_0 = n17
% 29.56/10.01 |
% 29.56/10.01 | From (745) and (1066) follows:
% 29.56/10.01 | (2453) sum(n0, n17) = all_0_6_6
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n0, n17, all_0_6_6, n17 and discharging atoms sum(n0, n17) = all_0_6_6, sum(n0, n17) = n17, yields:
% 29.56/10.01 | (1086) all_0_6_6 = n17
% 29.56/10.01 |
% 29.56/10.01 | Equations (1086) can reduce 669 to:
% 29.56/10.01 | (748) $false
% 29.56/10.01 |
% 29.56/10.01 |-The branch is then unsatisfiable
% 29.56/10.01 |-Branch two:
% 29.56/10.01 | (1038) ~ (all_0_8_8 = n3)
% 29.56/10.01 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/10.01 |
% 29.56/10.01 +-Applying beta-rule and splitting (1039), into two cases.
% 29.56/10.01 |-Branch one:
% 29.56/10.01 | (1040) all_0_8_8 = n2
% 29.56/10.01 |
% 29.56/10.01 | From (1040) and (2185) follows:
% 29.56/10.01 | (2459) sum(n2, n19) = all_0_4_4
% 29.56/10.01 |
% 29.56/10.01 | From (1040) and (2183) follows:
% 29.56/10.01 | (2460) sum(n2, n18) = all_0_2_2
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n2, n19, all_0_4_4, n0 and discharging atoms sum(n2, n19) = all_0_4_4, sum(n2, n19) = n0, yields:
% 29.56/10.01 | (1077) all_0_4_4 = n0
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n2, n18, all_0_2_2, n20 and discharging atoms sum(n2, n18) = all_0_2_2, sum(n2, n18) = n20, yields:
% 29.56/10.01 | (1076) all_0_2_2 = n20
% 29.56/10.01 |
% 29.56/10.01 | From (1076) and (473) follows:
% 29.56/10.01 | (1078) pred(n20) = all_0_1_1
% 29.56/10.01 |
% 29.56/10.01 | From (1077) and (716) follows:
% 29.56/10.01 | (1079) pred(n0) = all_0_3_3
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 29.56/10.01 | (1080) all_0_1_1 = n19
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 29.56/10.01 | (1081) all_0_3_3 = n20
% 29.56/10.01 |
% 29.56/10.01 | From (1081) and (232) follows:
% 29.56/10.01 | (1082) sum(n20, all_0_0_0) = all_0_6_6
% 29.56/10.01 |
% 29.56/10.01 | From (1080) and (1114) follows:
% 29.56/10.01 | (2468) sum(n18, n19) = all_0_0_0
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n18, n19, all_0_0_0, n16 and discharging atoms sum(n18, n19) = all_0_0_0, sum(n18, n19) = n16, yields:
% 29.56/10.01 | (762) all_0_0_0 = n16
% 29.56/10.01 |
% 29.56/10.01 | From (762) and (1082) follows:
% 29.56/10.01 | (2470) sum(n20, n16) = all_0_6_6
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n20, n16, all_0_6_6, n15 and discharging atoms sum(n20, n16) = all_0_6_6, sum(n20, n16) = n15, yields:
% 29.56/10.01 | (747) all_0_6_6 = n15
% 29.56/10.01 |
% 29.56/10.01 | Equations (747) can reduce 456 to:
% 29.56/10.01 | (748) $false
% 29.56/10.01 |
% 29.56/10.01 |-The branch is then unsatisfiable
% 29.56/10.01 |-Branch two:
% 29.56/10.01 | (1055) ~ (all_0_8_8 = n2)
% 29.56/10.01 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 29.56/10.01 |
% 29.56/10.01 +-Applying beta-rule and splitting (1056), into two cases.
% 29.56/10.01 |-Branch one:
% 29.56/10.01 | (1057) all_0_8_8 = n1
% 29.56/10.01 |
% 29.56/10.01 | From (1057) and (2185) follows:
% 29.56/10.01 | (2476) sum(n1, n19) = all_0_4_4
% 29.56/10.01 |
% 29.56/10.01 | From (1057) and (2183) follows:
% 29.56/10.01 | (2477) sum(n1, n18) = all_0_2_2
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n1, n19, all_0_4_4, n20 and discharging atoms sum(n1, n19) = all_0_4_4, sum(n1, n19) = n20, yields:
% 29.56/10.01 | (738) all_0_4_4 = n20
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n1, n18, all_0_2_2, n19 and discharging atoms sum(n1, n18) = all_0_2_2, sum(n1, n18) = n19, yields:
% 29.56/10.01 | (737) all_0_2_2 = n19
% 29.56/10.01 |
% 29.56/10.01 | From (737) and (473) follows:
% 29.56/10.01 | (739) pred(n19) = all_0_1_1
% 29.56/10.01 |
% 29.56/10.01 | From (738) and (716) follows:
% 29.56/10.01 | (740) pred(n20) = all_0_3_3
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 29.56/10.01 | (741) all_0_3_3 = n19
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 29.56/10.01 | (742) all_0_1_1 = n18
% 29.56/10.01 |
% 29.56/10.01 | From (741) and (232) follows:
% 29.56/10.01 | (743) sum(n19, all_0_0_0) = all_0_6_6
% 29.56/10.01 |
% 29.56/10.01 | From (742) and (1114) follows:
% 29.56/10.01 | (2485) sum(n18, n18) = all_0_0_0
% 29.56/10.01 |
% 29.56/10.01 | Instantiating formula (619) with n18, n18, all_0_0_0, n15 and discharging atoms sum(n18, n18) = all_0_0_0, sum(n18, n18) = n15, yields:
% 29.56/10.02 | (779) all_0_0_0 = n15
% 29.56/10.02 |
% 29.56/10.02 | From (779) and (743) follows:
% 29.56/10.02 | (2487) sum(n19, n15) = all_0_6_6
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (619) with n19, n15, all_0_6_6, n13 and discharging atoms sum(n19, n15) = all_0_6_6, sum(n19, n15) = n13, yields:
% 29.56/10.02 | (764) all_0_6_6 = n13
% 29.56/10.02 |
% 29.56/10.02 | Equations (764) can reduce 293 to:
% 29.56/10.02 | (748) $false
% 29.56/10.02 |
% 29.56/10.02 |-The branch is then unsatisfiable
% 29.56/10.02 |-Branch two:
% 29.56/10.02 | (1072) ~ (all_0_8_8 = n1)
% 29.56/10.02 | (1073) all_0_8_8 = n0
% 29.56/10.02 |
% 29.56/10.02 | From (1073) and (2185) follows:
% 29.56/10.02 | (2492) sum(n0, n19) = all_0_4_4
% 29.56/10.02 |
% 29.56/10.02 | From (1073) and (2183) follows:
% 29.56/10.02 | (2493) sum(n0, n18) = all_0_2_2
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (619) with n0, n19, all_0_4_4, n19 and discharging atoms sum(n0, n19) = all_0_4_4, sum(n0, n19) = n19, yields:
% 29.56/10.02 | (755) all_0_4_4 = n19
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (619) with n0, n18, all_0_2_2, n18 and discharging atoms sum(n0, n18) = all_0_2_2, sum(n0, n18) = n18, yields:
% 29.56/10.02 | (754) all_0_2_2 = n18
% 29.56/10.02 |
% 29.56/10.02 | From (754) and (473) follows:
% 29.56/10.02 | (756) pred(n18) = all_0_1_1
% 29.56/10.02 |
% 29.56/10.02 | From (755) and (716) follows:
% 29.56/10.02 | (757) pred(n19) = all_0_3_3
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 29.56/10.02 | (758) all_0_3_3 = n18
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 29.56/10.02 | (759) all_0_1_1 = n17
% 29.56/10.02 |
% 29.56/10.02 | From (758) and (232) follows:
% 29.56/10.02 | (760) sum(n18, all_0_0_0) = all_0_6_6
% 29.56/10.02 |
% 29.56/10.02 | From (759) and (1114) follows:
% 29.56/10.02 | (2501) sum(n18, n17) = all_0_0_0
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (619) with n18, n17, all_0_0_0, n14 and discharging atoms sum(n18, n17) = all_0_0_0, sum(n18, n17) = n14, yields:
% 29.56/10.02 | (796) all_0_0_0 = n14
% 29.56/10.02 |
% 29.56/10.02 | From (796) and (760) follows:
% 29.56/10.02 | (2503) sum(n18, n14) = all_0_6_6
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (619) with n18, n14, all_0_6_6, n11 and discharging atoms sum(n18, n14) = all_0_6_6, sum(n18, n14) = n11, yields:
% 29.56/10.02 | (781) all_0_6_6 = n11
% 29.56/10.02 |
% 29.56/10.02 | Equations (781) can reduce 2 to:
% 29.56/10.02 | (748) $false
% 29.56/10.02 |
% 29.56/10.02 |-The branch is then unsatisfiable
% 29.56/10.02 |-Branch two:
% 29.56/10.02 | (1129) ~ (all_0_7_7 = n18)
% 29.56/10.02 | (1130) all_0_7_7 = n17 | all_0_7_7 = n16 | all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/10.02 |
% 29.56/10.02 +-Applying beta-rule and splitting (767), into two cases.
% 29.56/10.02 |-Branch one:
% 29.56/10.02 | (768) all_0_8_8 = n18
% 29.56/10.02 |
% 29.56/10.02 | From (768) and (708) follows:
% 29.56/10.02 | (2509) sum(n18, all_0_5_5) = all_0_4_4
% 29.56/10.02 |
% 29.56/10.02 | From (768) and (378) follows:
% 29.56/10.02 | (2510) sum(n18, all_0_7_7) = all_0_2_2
% 29.56/10.02 |
% 29.56/10.02 +-Applying beta-rule and splitting (1130), into two cases.
% 29.56/10.02 |-Branch one:
% 29.56/10.02 | (1131) all_0_7_7 = n17
% 29.56/10.02 |
% 29.56/10.02 | From (1131) and (683) follows:
% 29.56/10.02 | (1132) succ(n17) = all_0_5_5
% 29.56/10.02 |
% 29.56/10.02 | From (1131) and (8) follows:
% 29.56/10.02 | (1133) sum(n17, all_0_1_1) = all_0_0_0
% 29.56/10.02 |
% 29.56/10.02 | From (1131) and (2510) follows:
% 29.56/10.02 | (2514) sum(n18, n17) = all_0_2_2
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (388) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 29.56/10.02 | (1135) all_0_5_5 = n18
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (619) with n18, n17, all_0_2_2, n14 and discharging atoms sum(n18, n17) = all_0_2_2, sum(n18, n17) = n14, yields:
% 29.56/10.02 | (822) all_0_2_2 = n14
% 29.56/10.02 |
% 29.56/10.02 | From (822) and (473) follows:
% 29.56/10.02 | (824) pred(n14) = all_0_1_1
% 29.56/10.02 |
% 29.56/10.02 | From (1135) and (2509) follows:
% 29.56/10.02 | (2518) sum(n18, n18) = all_0_4_4
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 29.56/10.02 | (827) all_0_1_1 = n13
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (619) with n18, n18, all_0_4_4, n15 and discharging atoms sum(n18, n18) = all_0_4_4, sum(n18, n18) = n15, yields:
% 29.56/10.02 | (823) all_0_4_4 = n15
% 29.56/10.02 |
% 29.56/10.02 | From (823) and (716) follows:
% 29.56/10.02 | (825) pred(n15) = all_0_3_3
% 29.56/10.02 |
% 29.56/10.02 | From (827) and (1133) follows:
% 29.56/10.02 | (2522) sum(n17, n13) = all_0_0_0
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 29.56/10.02 | (826) all_0_3_3 = n14
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (619) with n17, n13, all_0_0_0, n9 and discharging atoms sum(n17, n13) = all_0_0_0, sum(n17, n13) = n9, yields:
% 29.56/10.02 | (881) all_0_0_0 = n9
% 29.56/10.02 |
% 29.56/10.02 | From (826)(881) and (232) follows:
% 29.56/10.02 | (2525) sum(n14, n9) = all_0_6_6
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (619) with n14, n9, all_0_6_6, n2 and discharging atoms sum(n14, n9) = all_0_6_6, sum(n14, n9) = n2, yields:
% 29.56/10.02 | (1036) all_0_6_6 = n2
% 29.56/10.02 |
% 29.56/10.02 | Equations (1036) can reduce 56 to:
% 29.56/10.02 | (748) $false
% 29.56/10.02 |
% 29.56/10.02 |-The branch is then unsatisfiable
% 29.56/10.02 |-Branch two:
% 29.56/10.02 | (1148) ~ (all_0_7_7 = n17)
% 29.56/10.02 | (1149) all_0_7_7 = n16 | all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/10.02 |
% 29.56/10.02 +-Applying beta-rule and splitting (1149), into two cases.
% 29.56/10.02 |-Branch one:
% 29.56/10.02 | (1150) all_0_7_7 = n16
% 29.56/10.02 |
% 29.56/10.02 | From (1150) and (683) follows:
% 29.56/10.02 | (1151) succ(n16) = all_0_5_5
% 29.56/10.02 |
% 29.56/10.02 | From (1150) and (8) follows:
% 29.56/10.02 | (1152) sum(n16, all_0_1_1) = all_0_0_0
% 29.56/10.02 |
% 29.56/10.02 | From (1150) and (2510) follows:
% 29.56/10.02 | (2533) sum(n18, n16) = all_0_2_2
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (388) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 29.56/10.02 | (1154) all_0_5_5 = n17
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (619) with n18, n16, all_0_2_2, n13 and discharging atoms sum(n18, n16) = all_0_2_2, sum(n18, n16) = n13, yields:
% 29.56/10.02 | (839) all_0_2_2 = n13
% 29.56/10.02 |
% 29.56/10.02 | From (839) and (473) follows:
% 29.56/10.02 | (841) pred(n13) = all_0_1_1
% 29.56/10.02 |
% 29.56/10.02 | From (1154) and (2509) follows:
% 29.56/10.02 | (2537) sum(n18, n17) = all_0_4_4
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 29.56/10.02 | (844) all_0_1_1 = n12
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (619) with n18, n17, all_0_4_4, n14 and discharging atoms sum(n18, n17) = all_0_4_4, sum(n18, n17) = n14, yields:
% 29.56/10.02 | (840) all_0_4_4 = n14
% 29.56/10.02 |
% 29.56/10.02 | From (840) and (716) follows:
% 29.56/10.02 | (842) pred(n14) = all_0_3_3
% 29.56/10.02 |
% 29.56/10.02 | From (844) and (1152) follows:
% 29.56/10.02 | (2541) sum(n16, n12) = all_0_0_0
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 29.56/10.02 | (843) all_0_3_3 = n13
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (619) with n16, n12, all_0_0_0, n7 and discharging atoms sum(n16, n12) = all_0_0_0, sum(n16, n12) = n7, yields:
% 29.56/10.02 | (915) all_0_0_0 = n7
% 29.56/10.02 |
% 29.56/10.02 | From (843)(915) and (232) follows:
% 29.56/10.02 | (2544) sum(n13, n7) = all_0_6_6
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (619) with n13, n7, all_0_6_6, n20 and discharging atoms sum(n13, n7) = all_0_6_6, sum(n13, n7) = n20, yields:
% 29.56/10.02 | (883) all_0_6_6 = n20
% 29.56/10.02 |
% 29.56/10.02 | Equations (883) can reduce 381 to:
% 29.56/10.02 | (748) $false
% 29.56/10.02 |
% 29.56/10.02 |-The branch is then unsatisfiable
% 29.56/10.02 |-Branch two:
% 29.56/10.02 | (1167) ~ (all_0_7_7 = n16)
% 29.56/10.02 | (1168) all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.56/10.02 |
% 29.56/10.02 +-Applying beta-rule and splitting (1168), into two cases.
% 29.56/10.02 |-Branch one:
% 29.56/10.02 | (1169) all_0_7_7 = n15
% 29.56/10.02 |
% 29.56/10.02 | From (1169) and (683) follows:
% 29.56/10.02 | (1170) succ(n15) = all_0_5_5
% 29.56/10.02 |
% 29.56/10.02 | From (1169) and (8) follows:
% 29.56/10.02 | (1171) sum(n15, all_0_1_1) = all_0_0_0
% 29.56/10.02 |
% 29.56/10.02 | From (1169) and (2510) follows:
% 29.56/10.02 | (2552) sum(n18, n15) = all_0_2_2
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (388) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 29.56/10.02 | (1173) all_0_5_5 = n16
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (619) with n18, n15, all_0_2_2, n12 and discharging atoms sum(n18, n15) = all_0_2_2, sum(n18, n15) = n12, yields:
% 29.56/10.02 | (856) all_0_2_2 = n12
% 29.56/10.02 |
% 29.56/10.02 | From (856) and (473) follows:
% 29.56/10.02 | (858) pred(n12) = all_0_1_1
% 29.56/10.02 |
% 29.56/10.02 | From (1173) and (2509) follows:
% 29.56/10.02 | (2556) sum(n18, n16) = all_0_4_4
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 29.56/10.02 | (861) all_0_1_1 = n11
% 29.56/10.02 |
% 29.56/10.02 | Instantiating formula (619) with n18, n16, all_0_4_4, n13 and discharging atoms sum(n18, n16) = all_0_4_4, sum(n18, n16) = n13, yields:
% 29.94/10.02 | (857) all_0_4_4 = n13
% 29.94/10.02 |
% 29.94/10.02 | From (857) and (716) follows:
% 29.94/10.02 | (859) pred(n13) = all_0_3_3
% 29.94/10.02 |
% 29.94/10.02 | From (861) and (1171) follows:
% 29.94/10.02 | (2560) sum(n15, n11) = all_0_0_0
% 29.94/10.02 |
% 29.94/10.02 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 29.94/10.02 | (860) all_0_3_3 = n12
% 29.94/10.02 |
% 29.94/10.02 | Instantiating formula (619) with n15, n11, all_0_0_0, n5 and discharging atoms sum(n15, n11) = all_0_0_0, sum(n15, n11) = n5, yields:
% 29.94/10.02 | (949) all_0_0_0 = n5
% 29.94/10.02 |
% 29.94/10.02 | From (860)(949) and (232) follows:
% 29.94/10.03 | (2563) sum(n12, n5) = all_0_6_6
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (619) with n12, n5, all_0_6_6, n17 and discharging atoms sum(n12, n5) = all_0_6_6, sum(n12, n5) = n17, yields:
% 29.94/10.03 | (1086) all_0_6_6 = n17
% 29.94/10.03 |
% 29.94/10.03 | Equations (1086) can reduce 669 to:
% 29.94/10.03 | (748) $false
% 29.94/10.03 |
% 29.94/10.03 |-The branch is then unsatisfiable
% 29.94/10.03 |-Branch two:
% 29.94/10.03 | (1186) ~ (all_0_7_7 = n15)
% 29.94/10.03 | (1187) all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.94/10.03 |
% 29.94/10.03 +-Applying beta-rule and splitting (1187), into two cases.
% 29.94/10.03 |-Branch one:
% 29.94/10.03 | (1188) all_0_7_7 = n14
% 29.94/10.03 |
% 29.94/10.03 | From (1188) and (683) follows:
% 29.94/10.03 | (1189) succ(n14) = all_0_5_5
% 29.94/10.03 |
% 29.94/10.03 | From (1188) and (8) follows:
% 29.94/10.03 | (1190) sum(n14, all_0_1_1) = all_0_0_0
% 29.94/10.03 |
% 29.94/10.03 | From (1188) and (2510) follows:
% 29.94/10.03 | (2571) sum(n18, n14) = all_0_2_2
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (388) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 29.94/10.03 | (1192) all_0_5_5 = n15
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (619) with n18, n14, all_0_2_2, n11 and discharging atoms sum(n18, n14) = all_0_2_2, sum(n18, n14) = n11, yields:
% 29.94/10.03 | (873) all_0_2_2 = n11
% 29.94/10.03 |
% 29.94/10.03 | From (873) and (473) follows:
% 29.94/10.03 | (875) pred(n11) = all_0_1_1
% 29.94/10.03 |
% 29.94/10.03 | From (1192) and (2509) follows:
% 29.94/10.03 | (2575) sum(n18, n15) = all_0_4_4
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 29.94/10.03 | (878) all_0_1_1 = n10
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (619) with n18, n15, all_0_4_4, n12 and discharging atoms sum(n18, n15) = all_0_4_4, sum(n18, n15) = n12, yields:
% 29.94/10.03 | (874) all_0_4_4 = n12
% 29.94/10.03 |
% 29.94/10.03 | From (874) and (716) follows:
% 29.94/10.03 | (876) pred(n12) = all_0_3_3
% 29.94/10.03 |
% 29.94/10.03 | From (878) and (1190) follows:
% 29.94/10.03 | (2579) sum(n14, n10) = all_0_0_0
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 29.94/10.03 | (877) all_0_3_3 = n11
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (619) with n14, n10, all_0_0_0, n3 and discharging atoms sum(n14, n10) = all_0_0_0, sum(n14, n10) = n3, yields:
% 29.94/10.03 | (983) all_0_0_0 = n3
% 29.94/10.03 |
% 29.94/10.03 | From (877)(983) and (232) follows:
% 29.94/10.03 | (2582) sum(n11, n3) = all_0_6_6
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (619) with n11, n3, all_0_6_6, n14 and discharging atoms sum(n11, n3) = all_0_6_6, sum(n11, n3) = n14, yields:
% 29.94/10.03 | (934) all_0_6_6 = n14
% 29.94/10.03 |
% 29.94/10.03 | Equations (934) can reduce 353 to:
% 29.94/10.03 | (748) $false
% 29.94/10.03 |
% 29.94/10.03 |-The branch is then unsatisfiable
% 29.94/10.03 |-Branch two:
% 29.94/10.03 | (1205) ~ (all_0_7_7 = n14)
% 29.94/10.03 | (1206) all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.94/10.03 |
% 29.94/10.03 +-Applying beta-rule and splitting (1206), into two cases.
% 29.94/10.03 |-Branch one:
% 29.94/10.03 | (1207) all_0_7_7 = n13
% 29.94/10.03 |
% 29.94/10.03 | From (1207) and (683) follows:
% 29.94/10.03 | (1208) succ(n13) = all_0_5_5
% 29.94/10.03 |
% 29.94/10.03 | From (1207) and (8) follows:
% 29.94/10.03 | (1209) sum(n13, all_0_1_1) = all_0_0_0
% 29.94/10.03 |
% 29.94/10.03 | From (1207) and (2510) follows:
% 29.94/10.03 | (2590) sum(n18, n13) = all_0_2_2
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (388) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 29.94/10.03 | (1211) all_0_5_5 = n14
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (619) with n18, n13, all_0_2_2, n10 and discharging atoms sum(n18, n13) = all_0_2_2, sum(n18, n13) = n10, yields:
% 29.94/10.03 | (890) all_0_2_2 = n10
% 29.94/10.03 |
% 29.94/10.03 | From (890) and (473) follows:
% 29.94/10.03 | (892) pred(n10) = all_0_1_1
% 29.94/10.03 |
% 29.94/10.03 | From (1211) and (2509) follows:
% 29.94/10.03 | (2594) sum(n18, n14) = all_0_4_4
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 29.94/10.03 | (895) all_0_1_1 = n9
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (619) with n18, n14, all_0_4_4, n11 and discharging atoms sum(n18, n14) = all_0_4_4, sum(n18, n14) = n11, yields:
% 29.94/10.03 | (891) all_0_4_4 = n11
% 29.94/10.03 |
% 29.94/10.03 | From (891) and (716) follows:
% 29.94/10.03 | (893) pred(n11) = all_0_3_3
% 29.94/10.03 |
% 29.94/10.03 | From (895) and (1209) follows:
% 29.94/10.03 | (2598) sum(n13, n9) = all_0_0_0
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 29.94/10.03 | (894) all_0_3_3 = n10
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (619) with n13, n9, all_0_0_0, n1 and discharging atoms sum(n13, n9) = all_0_0_0, sum(n13, n9) = n1, yields:
% 29.94/10.03 | (1017) all_0_0_0 = n1
% 29.94/10.03 |
% 29.94/10.03 | From (894)(1017) and (232) follows:
% 29.94/10.03 | (2601) sum(n10, n1) = all_0_6_6
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (619) with n10, n1, all_0_6_6, n11 and discharging atoms sum(n10, n1) = all_0_6_6, sum(n10, n1) = n11, yields:
% 29.94/10.03 | (781) all_0_6_6 = n11
% 29.94/10.03 |
% 29.94/10.03 | Equations (781) can reduce 2 to:
% 29.94/10.03 | (748) $false
% 29.94/10.03 |
% 29.94/10.03 |-The branch is then unsatisfiable
% 29.94/10.03 |-Branch two:
% 29.94/10.03 | (1224) ~ (all_0_7_7 = n13)
% 29.94/10.03 | (1225) all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.94/10.03 |
% 29.94/10.03 +-Applying beta-rule and splitting (1225), into two cases.
% 29.94/10.03 |-Branch one:
% 29.94/10.03 | (1226) all_0_7_7 = n12
% 29.94/10.03 |
% 29.94/10.03 | From (1226) and (683) follows:
% 29.94/10.03 | (1227) succ(n12) = all_0_5_5
% 29.94/10.03 |
% 29.94/10.03 | From (1226) and (8) follows:
% 29.94/10.03 | (1228) sum(n12, all_0_1_1) = all_0_0_0
% 29.94/10.03 |
% 29.94/10.03 | From (1226) and (2510) follows:
% 29.94/10.03 | (2609) sum(n18, n12) = all_0_2_2
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (388) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 29.94/10.03 | (1230) all_0_5_5 = n13
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (619) with n18, n12, all_0_2_2, n9 and discharging atoms sum(n18, n12) = all_0_2_2, sum(n18, n12) = n9, yields:
% 29.94/10.03 | (907) all_0_2_2 = n9
% 29.94/10.03 |
% 29.94/10.03 | From (907) and (473) follows:
% 29.94/10.03 | (909) pred(n9) = all_0_1_1
% 29.94/10.03 |
% 29.94/10.03 | From (1230) and (2509) follows:
% 29.94/10.03 | (2613) sum(n18, n13) = all_0_4_4
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 29.94/10.03 | (912) all_0_1_1 = n8
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (619) with n18, n13, all_0_4_4, n10 and discharging atoms sum(n18, n13) = all_0_4_4, sum(n18, n13) = n10, yields:
% 29.94/10.03 | (908) all_0_4_4 = n10
% 29.94/10.03 |
% 29.94/10.03 | From (908) and (716) follows:
% 29.94/10.03 | (910) pred(n10) = all_0_3_3
% 29.94/10.03 |
% 29.94/10.03 | From (912) and (1228) follows:
% 29.94/10.03 | (2617) sum(n12, n8) = all_0_0_0
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 29.94/10.03 | (911) all_0_3_3 = n9
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (619) with n12, n8, all_0_0_0, n20 and discharging atoms sum(n12, n8) = all_0_0_0, sum(n12, n8) = n20, yields:
% 29.94/10.03 | (1051) all_0_0_0 = n20
% 29.94/10.03 |
% 29.94/10.03 | From (911)(1051) and (232) follows:
% 29.94/10.03 | (2620) sum(n9, n20) = all_0_6_6
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (619) with n9, n20, all_0_6_6, n8 and discharging atoms sum(n9, n20) = all_0_6_6, sum(n9, n20) = n8, yields:
% 29.94/10.03 | (985) all_0_6_6 = n8
% 29.94/10.03 |
% 29.94/10.03 | Equations (985) can reduce 357 to:
% 29.94/10.03 | (748) $false
% 29.94/10.03 |
% 29.94/10.03 |-The branch is then unsatisfiable
% 29.94/10.03 |-Branch two:
% 29.94/10.03 | (1243) ~ (all_0_7_7 = n12)
% 29.94/10.03 | (1244) all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.94/10.03 |
% 29.94/10.03 +-Applying beta-rule and splitting (1244), into two cases.
% 29.94/10.03 |-Branch one:
% 29.94/10.03 | (1245) all_0_7_7 = n11
% 29.94/10.03 |
% 29.94/10.03 | From (1245) and (683) follows:
% 29.94/10.03 | (1246) succ(n11) = all_0_5_5
% 29.94/10.03 |
% 29.94/10.03 | From (1245) and (8) follows:
% 29.94/10.03 | (1247) sum(n11, all_0_1_1) = all_0_0_0
% 29.94/10.03 |
% 29.94/10.03 | From (1245) and (2510) follows:
% 29.94/10.03 | (2628) sum(n18, n11) = all_0_2_2
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (388) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 29.94/10.03 | (1249) all_0_5_5 = n12
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (619) with n18, n11, all_0_2_2, n8 and discharging atoms sum(n18, n11) = all_0_2_2, sum(n18, n11) = n8, yields:
% 29.94/10.03 | (924) all_0_2_2 = n8
% 29.94/10.03 |
% 29.94/10.03 | From (924) and (473) follows:
% 29.94/10.03 | (926) pred(n8) = all_0_1_1
% 29.94/10.03 |
% 29.94/10.03 | From (1249) and (2509) follows:
% 29.94/10.03 | (2632) sum(n18, n12) = all_0_4_4
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 29.94/10.03 | (929) all_0_1_1 = n7
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (619) with n18, n12, all_0_4_4, n9 and discharging atoms sum(n18, n12) = all_0_4_4, sum(n18, n12) = n9, yields:
% 29.94/10.03 | (925) all_0_4_4 = n9
% 29.94/10.03 |
% 29.94/10.03 | From (925) and (716) follows:
% 29.94/10.03 | (927) pred(n9) = all_0_3_3
% 29.94/10.03 |
% 29.94/10.03 | From (929) and (1247) follows:
% 29.94/10.03 | (2636) sum(n11, n7) = all_0_0_0
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 29.94/10.03 | (928) all_0_3_3 = n8
% 29.94/10.03 |
% 29.94/10.03 | Instantiating formula (619) with n11, n7, all_0_0_0, n18 and discharging atoms sum(n11, n7) = all_0_0_0, sum(n11, n7) = n18, yields:
% 29.94/10.03 | (1084) all_0_0_0 = n18
% 29.94/10.03 |
% 29.94/10.03 | From (928)(1084) and (232) follows:
% 29.94/10.04 | (2639) sum(n8, n18) = all_0_6_6
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (619) with n8, n18, all_0_6_6, n5 and discharging atoms sum(n8, n18) = all_0_6_6, sum(n8, n18) = n5, yields:
% 29.94/10.04 | (832) all_0_6_6 = n5
% 29.94/10.04 |
% 29.94/10.04 | Equations (832) can reduce 462 to:
% 29.94/10.04 | (748) $false
% 29.94/10.04 |
% 29.94/10.04 |-The branch is then unsatisfiable
% 29.94/10.04 |-Branch two:
% 29.94/10.04 | (1262) ~ (all_0_7_7 = n11)
% 29.94/10.04 | (1263) all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.94/10.04 |
% 29.94/10.04 +-Applying beta-rule and splitting (1263), into two cases.
% 29.94/10.04 |-Branch one:
% 29.94/10.04 | (1264) all_0_7_7 = n10
% 29.94/10.04 |
% 29.94/10.04 | From (1264) and (683) follows:
% 29.94/10.04 | (1265) succ(n10) = all_0_5_5
% 29.94/10.04 |
% 29.94/10.04 | From (1264) and (8) follows:
% 29.94/10.04 | (1266) sum(n10, all_0_1_1) = all_0_0_0
% 29.94/10.04 |
% 29.94/10.04 | From (1264) and (2510) follows:
% 29.94/10.04 | (2647) sum(n18, n10) = all_0_2_2
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (388) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 29.94/10.04 | (1268) all_0_5_5 = n11
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (619) with n18, n10, all_0_2_2, n7 and discharging atoms sum(n18, n10) = all_0_2_2, sum(n18, n10) = n7, yields:
% 29.94/10.04 | (941) all_0_2_2 = n7
% 29.94/10.04 |
% 29.94/10.04 | From (941) and (473) follows:
% 29.94/10.04 | (943) pred(n7) = all_0_1_1
% 29.94/10.04 |
% 29.94/10.04 | From (1268) and (2509) follows:
% 29.94/10.04 | (2651) sum(n18, n11) = all_0_4_4
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 29.94/10.04 | (946) all_0_1_1 = n6
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (619) with n18, n11, all_0_4_4, n8 and discharging atoms sum(n18, n11) = all_0_4_4, sum(n18, n11) = n8, yields:
% 29.94/10.04 | (942) all_0_4_4 = n8
% 29.94/10.04 |
% 29.94/10.04 | From (942) and (716) follows:
% 29.94/10.04 | (944) pred(n8) = all_0_3_3
% 29.94/10.04 |
% 29.94/10.04 | From (946) and (1266) follows:
% 29.94/10.04 | (2655) sum(n10, n6) = all_0_0_0
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 29.94/10.04 | (945) all_0_3_3 = n7
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (619) with n10, n6, all_0_0_0, n16 and discharging atoms sum(n10, n6) = all_0_0_0, sum(n10, n6) = n16, yields:
% 29.94/10.04 | (762) all_0_0_0 = n16
% 29.94/10.04 |
% 29.94/10.04 | From (945)(762) and (232) follows:
% 29.94/10.04 | (2658) sum(n7, n16) = all_0_6_6
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (619) with n7, n16, all_0_6_6, n2 and discharging atoms sum(n7, n16) = all_0_6_6, sum(n7, n16) = n2, yields:
% 29.94/10.04 | (1036) all_0_6_6 = n2
% 29.94/10.04 |
% 29.94/10.04 | Equations (1036) can reduce 56 to:
% 29.94/10.04 | (748) $false
% 29.94/10.04 |
% 29.94/10.04 |-The branch is then unsatisfiable
% 29.94/10.04 |-Branch two:
% 29.94/10.04 | (1281) ~ (all_0_7_7 = n10)
% 29.94/10.04 | (1282) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.94/10.04 |
% 29.94/10.04 +-Applying beta-rule and splitting (1282), into two cases.
% 29.94/10.04 |-Branch one:
% 29.94/10.04 | (1283) all_0_7_7 = n9
% 29.94/10.04 |
% 29.94/10.04 | From (1283) and (683) follows:
% 29.94/10.04 | (1284) succ(n9) = all_0_5_5
% 29.94/10.04 |
% 29.94/10.04 | From (1283) and (8) follows:
% 29.94/10.04 | (1285) sum(n9, all_0_1_1) = all_0_0_0
% 29.94/10.04 |
% 29.94/10.04 | From (1283) and (2510) follows:
% 29.94/10.04 | (2666) sum(n18, n9) = all_0_2_2
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (388) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 29.94/10.04 | (1287) all_0_5_5 = n10
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (619) with n18, n9, all_0_2_2, n6 and discharging atoms sum(n18, n9) = all_0_2_2, sum(n18, n9) = n6, yields:
% 29.94/10.04 | (958) all_0_2_2 = n6
% 29.94/10.04 |
% 29.94/10.04 | From (958) and (473) follows:
% 29.94/10.04 | (960) pred(n6) = all_0_1_1
% 29.94/10.04 |
% 29.94/10.04 | From (1287) and (2509) follows:
% 29.94/10.04 | (2670) sum(n18, n10) = all_0_4_4
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 29.94/10.04 | (963) all_0_1_1 = n5
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (619) with n18, n10, all_0_4_4, n7 and discharging atoms sum(n18, n10) = all_0_4_4, sum(n18, n10) = n7, yields:
% 29.94/10.04 | (959) all_0_4_4 = n7
% 29.94/10.04 |
% 29.94/10.04 | From (959) and (716) follows:
% 29.94/10.04 | (961) pred(n7) = all_0_3_3
% 29.94/10.04 |
% 29.94/10.04 | From (963) and (1285) follows:
% 29.94/10.04 | (2674) sum(n9, n5) = all_0_0_0
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 29.94/10.04 | (962) all_0_3_3 = n6
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (619) with n9, n5, all_0_0_0, n14 and discharging atoms sum(n9, n5) = all_0_0_0, sum(n9, n5) = n14, yields:
% 29.94/10.04 | (796) all_0_0_0 = n14
% 29.94/10.04 |
% 29.94/10.04 | From (962)(796) and (232) follows:
% 29.94/10.04 | (2677) sum(n6, n14) = all_0_6_6
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (619) with n6, n14, all_0_6_6, n20 and discharging atoms sum(n6, n14) = all_0_6_6, sum(n6, n14) = n20, yields:
% 29.94/10.04 | (883) all_0_6_6 = n20
% 29.94/10.04 |
% 29.94/10.04 | Equations (883) can reduce 381 to:
% 29.94/10.04 | (748) $false
% 29.94/10.04 |
% 29.94/10.04 |-The branch is then unsatisfiable
% 29.94/10.04 |-Branch two:
% 29.94/10.04 | (1300) ~ (all_0_7_7 = n9)
% 29.94/10.04 | (1301) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.94/10.04 |
% 29.94/10.04 +-Applying beta-rule and splitting (1301), into two cases.
% 29.94/10.04 |-Branch one:
% 29.94/10.04 | (1302) all_0_7_7 = n8
% 29.94/10.04 |
% 29.94/10.04 | From (1302) and (683) follows:
% 29.94/10.04 | (1303) succ(n8) = all_0_5_5
% 29.94/10.04 |
% 29.94/10.04 | From (1302) and (8) follows:
% 29.94/10.04 | (1304) sum(n8, all_0_1_1) = all_0_0_0
% 29.94/10.04 |
% 29.94/10.04 | From (1302) and (2510) follows:
% 29.94/10.04 | (2685) sum(n18, n8) = all_0_2_2
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (388) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 29.94/10.04 | (1306) all_0_5_5 = n9
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (619) with n18, n8, all_0_2_2, n5 and discharging atoms sum(n18, n8) = all_0_2_2, sum(n18, n8) = n5, yields:
% 29.94/10.04 | (975) all_0_2_2 = n5
% 29.94/10.04 |
% 29.94/10.04 | From (975) and (473) follows:
% 29.94/10.04 | (977) pred(n5) = all_0_1_1
% 29.94/10.04 |
% 29.94/10.04 | From (1306) and (2509) follows:
% 29.94/10.04 | (2689) sum(n18, n9) = all_0_4_4
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 29.94/10.04 | (980) all_0_1_1 = n4
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (619) with n18, n9, all_0_4_4, n6 and discharging atoms sum(n18, n9) = all_0_4_4, sum(n18, n9) = n6, yields:
% 29.94/10.04 | (976) all_0_4_4 = n6
% 29.94/10.04 |
% 29.94/10.04 | From (976) and (716) follows:
% 29.94/10.04 | (978) pred(n6) = all_0_3_3
% 29.94/10.04 |
% 29.94/10.04 | From (980) and (1304) follows:
% 29.94/10.04 | (2693) sum(n8, n4) = all_0_0_0
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 29.94/10.04 | (979) all_0_3_3 = n5
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (619) with n8, n4, all_0_0_0, n12 and discharging atoms sum(n8, n4) = all_0_0_0, sum(n8, n4) = n12, yields:
% 29.94/10.04 | (830) all_0_0_0 = n12
% 29.94/10.04 |
% 29.94/10.04 | From (979)(830) and (232) follows:
% 29.94/10.04 | (2696) sum(n5, n12) = all_0_6_6
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (619) with n5, n12, all_0_6_6, n17 and discharging atoms sum(n5, n12) = all_0_6_6, sum(n5, n12) = n17, yields:
% 29.94/10.04 | (1086) all_0_6_6 = n17
% 29.94/10.04 |
% 29.94/10.04 | Equations (1086) can reduce 669 to:
% 29.94/10.04 | (748) $false
% 29.94/10.04 |
% 29.94/10.04 |-The branch is then unsatisfiable
% 29.94/10.04 |-Branch two:
% 29.94/10.04 | (1319) ~ (all_0_7_7 = n8)
% 29.94/10.04 | (1320) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.94/10.04 |
% 29.94/10.04 +-Applying beta-rule and splitting (1320), into two cases.
% 29.94/10.04 |-Branch one:
% 29.94/10.04 | (1321) all_0_7_7 = n7
% 29.94/10.04 |
% 29.94/10.04 | From (1321) and (683) follows:
% 29.94/10.04 | (1322) succ(n7) = all_0_5_5
% 29.94/10.04 |
% 29.94/10.04 | From (1321) and (8) follows:
% 29.94/10.04 | (1323) sum(n7, all_0_1_1) = all_0_0_0
% 29.94/10.04 |
% 29.94/10.04 | From (1321) and (2510) follows:
% 29.94/10.04 | (2704) sum(n18, n7) = all_0_2_2
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (388) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 29.94/10.04 | (1325) all_0_5_5 = n8
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (619) with n18, n7, all_0_2_2, n4 and discharging atoms sum(n18, n7) = all_0_2_2, sum(n18, n7) = n4, yields:
% 29.94/10.04 | (992) all_0_2_2 = n4
% 29.94/10.04 |
% 29.94/10.04 | From (992) and (473) follows:
% 29.94/10.04 | (994) pred(n4) = all_0_1_1
% 29.94/10.04 |
% 29.94/10.04 | From (1325) and (2509) follows:
% 29.94/10.04 | (2708) sum(n18, n8) = all_0_4_4
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 29.94/10.04 | (997) all_0_1_1 = n3
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (619) with n18, n8, all_0_4_4, n5 and discharging atoms sum(n18, n8) = all_0_4_4, sum(n18, n8) = n5, yields:
% 29.94/10.04 | (993) all_0_4_4 = n5
% 29.94/10.04 |
% 29.94/10.04 | From (993) and (716) follows:
% 29.94/10.04 | (995) pred(n5) = all_0_3_3
% 29.94/10.04 |
% 29.94/10.04 | From (997) and (1323) follows:
% 29.94/10.04 | (2712) sum(n7, n3) = all_0_0_0
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 29.94/10.04 | (996) all_0_3_3 = n4
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (619) with n7, n3, all_0_0_0, n10 and discharging atoms sum(n7, n3) = all_0_0_0, sum(n7, n3) = n10, yields:
% 29.94/10.04 | (864) all_0_0_0 = n10
% 29.94/10.04 |
% 29.94/10.04 | From (996)(864) and (232) follows:
% 29.94/10.04 | (2715) sum(n4, n10) = all_0_6_6
% 29.94/10.04 |
% 29.94/10.04 | Instantiating formula (619) with n4, n10, all_0_6_6, n14 and discharging atoms sum(n4, n10) = all_0_6_6, sum(n4, n10) = n14, yields:
% 29.94/10.04 | (934) all_0_6_6 = n14
% 29.94/10.04 |
% 29.94/10.04 | Equations (934) can reduce 353 to:
% 29.94/10.04 | (748) $false
% 29.94/10.04 |
% 29.94/10.04 |-The branch is then unsatisfiable
% 29.94/10.04 |-Branch two:
% 29.94/10.04 | (1338) ~ (all_0_7_7 = n7)
% 29.94/10.04 | (1339) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.94/10.05 |
% 29.94/10.05 +-Applying beta-rule and splitting (1339), into two cases.
% 29.94/10.05 |-Branch one:
% 29.94/10.05 | (1340) all_0_7_7 = n6
% 29.94/10.05 |
% 29.94/10.05 | From (1340) and (683) follows:
% 29.94/10.05 | (1341) succ(n6) = all_0_5_5
% 29.94/10.05 |
% 29.94/10.05 | From (1340) and (8) follows:
% 29.94/10.05 | (1342) sum(n6, all_0_1_1) = all_0_0_0
% 29.94/10.05 |
% 29.94/10.05 | From (1340) and (2510) follows:
% 29.94/10.05 | (2723) sum(n18, n6) = all_0_2_2
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (388) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 29.94/10.05 | (1344) all_0_5_5 = n7
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (619) with n18, n6, all_0_2_2, n3 and discharging atoms sum(n18, n6) = all_0_2_2, sum(n18, n6) = n3, yields:
% 29.94/10.05 | (1009) all_0_2_2 = n3
% 29.94/10.05 |
% 29.94/10.05 | From (1009) and (473) follows:
% 29.94/10.05 | (1011) pred(n3) = all_0_1_1
% 29.94/10.05 |
% 29.94/10.05 | From (1344) and (2509) follows:
% 29.94/10.05 | (2727) sum(n18, n7) = all_0_4_4
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 29.94/10.05 | (1014) all_0_1_1 = n2
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (619) with n18, n7, all_0_4_4, n4 and discharging atoms sum(n18, n7) = all_0_4_4, sum(n18, n7) = n4, yields:
% 29.94/10.05 | (1010) all_0_4_4 = n4
% 29.94/10.05 |
% 29.94/10.05 | From (1010) and (716) follows:
% 29.94/10.05 | (1012) pred(n4) = all_0_3_3
% 29.94/10.05 |
% 29.94/10.05 | From (1014) and (1342) follows:
% 29.94/10.05 | (2731) sum(n6, n2) = all_0_0_0
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 29.94/10.05 | (1013) all_0_3_3 = n3
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (619) with n6, n2, all_0_0_0, n8 and discharging atoms sum(n6, n2) = all_0_0_0, sum(n6, n2) = n8, yields:
% 29.94/10.05 | (898) all_0_0_0 = n8
% 29.94/10.05 |
% 29.94/10.05 | From (1013)(898) and (232) follows:
% 29.94/10.05 | (2734) sum(n3, n8) = all_0_6_6
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (619) with n3, n8, all_0_6_6, n11 and discharging atoms sum(n3, n8) = all_0_6_6, sum(n3, n8) = n11, yields:
% 29.94/10.05 | (781) all_0_6_6 = n11
% 29.94/10.05 |
% 29.94/10.05 | Equations (781) can reduce 2 to:
% 29.94/10.05 | (748) $false
% 29.94/10.05 |
% 29.94/10.05 |-The branch is then unsatisfiable
% 29.94/10.05 |-Branch two:
% 29.94/10.05 | (1357) ~ (all_0_7_7 = n6)
% 29.94/10.05 | (1358) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.94/10.05 |
% 29.94/10.05 +-Applying beta-rule and splitting (1358), into two cases.
% 29.94/10.05 |-Branch one:
% 29.94/10.05 | (1359) all_0_7_7 = n5
% 29.94/10.05 |
% 29.94/10.05 | From (1359) and (683) follows:
% 29.94/10.05 | (1360) succ(n5) = all_0_5_5
% 29.94/10.05 |
% 29.94/10.05 | From (1359) and (8) follows:
% 29.94/10.05 | (1361) sum(n5, all_0_1_1) = all_0_0_0
% 29.94/10.05 |
% 29.94/10.05 | From (1359) and (2510) follows:
% 29.94/10.05 | (2742) sum(n18, n5) = all_0_2_2
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (388) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 29.94/10.05 | (1363) all_0_5_5 = n6
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (619) with n18, n5, all_0_2_2, n2 and discharging atoms sum(n18, n5) = all_0_2_2, sum(n18, n5) = n2, yields:
% 29.94/10.05 | (1026) all_0_2_2 = n2
% 29.94/10.05 |
% 29.94/10.05 | From (1026) and (473) follows:
% 29.94/10.05 | (1028) pred(n2) = all_0_1_1
% 29.94/10.05 |
% 29.94/10.05 | From (1363) and (2509) follows:
% 29.94/10.05 | (2746) sum(n18, n6) = all_0_4_4
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 29.94/10.05 | (1031) all_0_1_1 = n1
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (619) with n18, n6, all_0_4_4, n3 and discharging atoms sum(n18, n6) = all_0_4_4, sum(n18, n6) = n3, yields:
% 29.94/10.05 | (1027) all_0_4_4 = n3
% 29.94/10.05 |
% 29.94/10.05 | From (1027) and (716) follows:
% 29.94/10.05 | (1029) pred(n3) = all_0_3_3
% 29.94/10.05 |
% 29.94/10.05 | From (1031) and (1361) follows:
% 29.94/10.05 | (2750) sum(n5, n1) = all_0_0_0
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 29.94/10.05 | (1030) all_0_3_3 = n2
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (619) with n5, n1, all_0_0_0, n6 and discharging atoms sum(n5, n1) = all_0_0_0, sum(n5, n1) = n6, yields:
% 29.94/10.05 | (932) all_0_0_0 = n6
% 29.94/10.05 |
% 29.94/10.05 | From (1030)(932) and (232) follows:
% 29.94/10.05 | (2753) sum(n2, n6) = all_0_6_6
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (619) with n2, n6, all_0_6_6, n8 and discharging atoms sum(n2, n6) = all_0_6_6, sum(n2, n6) = n8, yields:
% 29.94/10.05 | (985) all_0_6_6 = n8
% 29.94/10.05 |
% 29.94/10.05 | Equations (985) can reduce 357 to:
% 29.94/10.05 | (748) $false
% 29.94/10.05 |
% 29.94/10.05 |-The branch is then unsatisfiable
% 29.94/10.05 |-Branch two:
% 29.94/10.05 | (1376) ~ (all_0_7_7 = n5)
% 29.94/10.05 | (1377) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.94/10.05 |
% 29.94/10.05 +-Applying beta-rule and splitting (1377), into two cases.
% 29.94/10.05 |-Branch one:
% 29.94/10.05 | (1378) all_0_7_7 = n4
% 29.94/10.05 |
% 29.94/10.05 | From (1378) and (683) follows:
% 29.94/10.05 | (1379) succ(n4) = all_0_5_5
% 29.94/10.05 |
% 29.94/10.05 | From (1378) and (8) follows:
% 29.94/10.05 | (1380) sum(n4, all_0_1_1) = all_0_0_0
% 29.94/10.05 |
% 29.94/10.05 | From (1378) and (2510) follows:
% 29.94/10.05 | (2761) sum(n18, n4) = all_0_2_2
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (388) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 29.94/10.05 | (1382) all_0_5_5 = n5
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (619) with n18, n4, all_0_2_2, n1 and discharging atoms sum(n18, n4) = all_0_2_2, sum(n18, n4) = n1, yields:
% 29.94/10.05 | (1043) all_0_2_2 = n1
% 29.94/10.05 |
% 29.94/10.05 | From (1043) and (473) follows:
% 29.94/10.05 | (1045) pred(n1) = all_0_1_1
% 29.94/10.05 |
% 29.94/10.05 | From (1382) and (2509) follows:
% 29.94/10.05 | (2765) sum(n18, n5) = all_0_4_4
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 29.94/10.05 | (1048) all_0_1_1 = n0
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (619) with n18, n5, all_0_4_4, n2 and discharging atoms sum(n18, n5) = all_0_4_4, sum(n18, n5) = n2, yields:
% 29.94/10.05 | (1044) all_0_4_4 = n2
% 29.94/10.05 |
% 29.94/10.05 | From (1044) and (716) follows:
% 29.94/10.05 | (1046) pred(n2) = all_0_3_3
% 29.94/10.05 |
% 29.94/10.05 | From (1048) and (1380) follows:
% 29.94/10.05 | (2769) sum(n4, n0) = all_0_0_0
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 29.94/10.05 | (1047) all_0_3_3 = n1
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (619) with n4, n0, all_0_0_0, n4 and discharging atoms sum(n4, n0) = all_0_0_0, sum(n4, n0) = n4, yields:
% 29.94/10.05 | (966) all_0_0_0 = n4
% 29.94/10.05 |
% 29.94/10.05 | From (1047)(966) and (232) follows:
% 29.94/10.05 | (2772) sum(n1, n4) = all_0_6_6
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (619) with n1, n4, all_0_6_6, n5 and discharging atoms sum(n1, n4) = all_0_6_6, sum(n1, n4) = n5, yields:
% 29.94/10.05 | (832) all_0_6_6 = n5
% 29.94/10.05 |
% 29.94/10.05 | Equations (832) can reduce 462 to:
% 29.94/10.05 | (748) $false
% 29.94/10.05 |
% 29.94/10.05 |-The branch is then unsatisfiable
% 29.94/10.05 |-Branch two:
% 29.94/10.05 | (1395) ~ (all_0_7_7 = n4)
% 29.94/10.05 | (1396) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.94/10.05 |
% 29.94/10.05 +-Applying beta-rule and splitting (1396), into two cases.
% 29.94/10.05 |-Branch one:
% 29.94/10.05 | (1397) all_0_7_7 = n3
% 29.94/10.05 |
% 29.94/10.05 | From (1397) and (683) follows:
% 29.94/10.05 | (1398) succ(n3) = all_0_5_5
% 29.94/10.05 |
% 29.94/10.05 | From (1397) and (8) follows:
% 29.94/10.05 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 29.94/10.05 |
% 29.94/10.05 | From (1397) and (2510) follows:
% 29.94/10.05 | (2780) sum(n18, n3) = all_0_2_2
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 29.94/10.05 | (1401) all_0_5_5 = n4
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (619) with n18, n3, all_0_2_2, n0 and discharging atoms sum(n18, n3) = all_0_2_2, sum(n18, n3) = n0, yields:
% 29.94/10.05 | (1060) all_0_2_2 = n0
% 29.94/10.05 |
% 29.94/10.05 | From (1060) and (473) follows:
% 29.94/10.05 | (1062) pred(n0) = all_0_1_1
% 29.94/10.05 |
% 29.94/10.05 | From (1401) and (2509) follows:
% 29.94/10.05 | (2784) sum(n18, n4) = all_0_4_4
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 29.94/10.05 | (1065) all_0_1_1 = n20
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (619) with n18, n4, all_0_4_4, n1 and discharging atoms sum(n18, n4) = all_0_4_4, sum(n18, n4) = n1, yields:
% 29.94/10.05 | (1061) all_0_4_4 = n1
% 29.94/10.05 |
% 29.94/10.05 | From (1061) and (716) follows:
% 29.94/10.05 | (1063) pred(n1) = all_0_3_3
% 29.94/10.05 |
% 29.94/10.05 | From (1065) and (1399) follows:
% 29.94/10.05 | (2788) sum(n3, n20) = all_0_0_0
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 29.94/10.05 | (1064) all_0_3_3 = n0
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (619) with n3, n20, all_0_0_0, n2 and discharging atoms sum(n3, n20) = all_0_0_0, sum(n3, n20) = n2, yields:
% 29.94/10.05 | (1000) all_0_0_0 = n2
% 29.94/10.05 |
% 29.94/10.05 | From (1064)(1000) and (232) follows:
% 29.94/10.05 | (2791) sum(n0, n2) = all_0_6_6
% 29.94/10.05 |
% 29.94/10.05 | Instantiating formula (619) with n0, n2, all_0_6_6, n2 and discharging atoms sum(n0, n2) = all_0_6_6, sum(n0, n2) = n2, yields:
% 29.94/10.05 | (1036) all_0_6_6 = n2
% 29.94/10.05 |
% 29.94/10.05 | Equations (1036) can reduce 56 to:
% 29.94/10.05 | (748) $false
% 29.94/10.05 |
% 29.94/10.05 |-The branch is then unsatisfiable
% 29.94/10.05 |-Branch two:
% 29.94/10.05 | (1414) ~ (all_0_7_7 = n3)
% 29.94/10.05 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 29.94/10.05 |
% 29.94/10.05 +-Applying beta-rule and splitting (1415), into two cases.
% 29.94/10.05 |-Branch one:
% 29.94/10.05 | (1416) all_0_7_7 = n2
% 29.94/10.05 |
% 29.94/10.05 | From (1416) and (683) follows:
% 29.94/10.05 | (1417) succ(n2) = all_0_5_5
% 29.94/10.05 |
% 29.94/10.05 | From (1416) and (8) follows:
% 29.94/10.06 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 29.94/10.06 |
% 29.94/10.06 | From (1416) and (2510) follows:
% 29.94/10.06 | (2799) sum(n18, n2) = all_0_2_2
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 29.94/10.06 | (1420) all_0_5_5 = n3
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (619) with n18, n2, all_0_2_2, n20 and discharging atoms sum(n18, n2) = all_0_2_2, sum(n18, n2) = n20, yields:
% 29.94/10.06 | (1076) all_0_2_2 = n20
% 29.94/10.06 |
% 29.94/10.06 | From (1076) and (473) follows:
% 29.94/10.06 | (1078) pred(n20) = all_0_1_1
% 29.94/10.06 |
% 29.94/10.06 | From (1420) and (2509) follows:
% 29.94/10.06 | (2803) sum(n18, n3) = all_0_4_4
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 29.94/10.06 | (1080) all_0_1_1 = n19
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (619) with n18, n3, all_0_4_4, n0 and discharging atoms sum(n18, n3) = all_0_4_4, sum(n18, n3) = n0, yields:
% 29.94/10.06 | (1077) all_0_4_4 = n0
% 29.94/10.06 |
% 29.94/10.06 | From (1077) and (716) follows:
% 29.94/10.06 | (1079) pred(n0) = all_0_3_3
% 29.94/10.06 |
% 29.94/10.06 | From (1080) and (1418) follows:
% 29.94/10.06 | (2807) sum(n2, n19) = all_0_0_0
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 29.94/10.06 | (1081) all_0_3_3 = n20
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (619) with n2, n19, all_0_0_0, n0 and discharging atoms sum(n2, n19) = all_0_0_0, sum(n2, n19) = n0, yields:
% 29.94/10.06 | (1034) all_0_0_0 = n0
% 29.94/10.06 |
% 29.94/10.06 | From (1081)(1034) and (232) follows:
% 29.94/10.06 | (2810) sum(n20, n0) = all_0_6_6
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (619) with n20, n0, all_0_6_6, n20 and discharging atoms sum(n20, n0) = all_0_6_6, sum(n20, n0) = n20, yields:
% 29.94/10.06 | (883) all_0_6_6 = n20
% 29.94/10.06 |
% 29.94/10.06 | Equations (883) can reduce 381 to:
% 29.94/10.06 | (748) $false
% 29.94/10.06 |
% 29.94/10.06 |-The branch is then unsatisfiable
% 29.94/10.06 |-Branch two:
% 29.94/10.06 | (1433) ~ (all_0_7_7 = n2)
% 29.94/10.06 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 29.94/10.06 |
% 29.94/10.06 +-Applying beta-rule and splitting (1434), into two cases.
% 29.94/10.06 |-Branch one:
% 29.94/10.06 | (1435) all_0_7_7 = n1
% 29.94/10.06 |
% 29.94/10.06 | From (1435) and (683) follows:
% 29.94/10.06 | (1436) succ(n1) = all_0_5_5
% 29.94/10.06 |
% 29.94/10.06 | From (1435) and (8) follows:
% 29.94/10.06 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 29.94/10.06 |
% 29.94/10.06 | From (1435) and (2510) follows:
% 29.94/10.06 | (2818) sum(n18, n1) = all_0_2_2
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 29.94/10.06 | (1439) all_0_5_5 = n2
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (619) with n18, n1, all_0_2_2, n19 and discharging atoms sum(n18, n1) = all_0_2_2, sum(n18, n1) = n19, yields:
% 29.94/10.06 | (737) all_0_2_2 = n19
% 29.94/10.06 |
% 29.94/10.06 | From (737) and (473) follows:
% 29.94/10.06 | (739) pred(n19) = all_0_1_1
% 29.94/10.06 |
% 29.94/10.06 | From (1439) and (2509) follows:
% 29.94/10.06 | (2822) sum(n18, n2) = all_0_4_4
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 29.94/10.06 | (742) all_0_1_1 = n18
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (619) with n18, n2, all_0_4_4, n20 and discharging atoms sum(n18, n2) = all_0_4_4, sum(n18, n2) = n20, yields:
% 29.94/10.06 | (738) all_0_4_4 = n20
% 29.94/10.06 |
% 29.94/10.06 | From (738) and (716) follows:
% 29.94/10.06 | (740) pred(n20) = all_0_3_3
% 29.94/10.06 |
% 29.94/10.06 | From (742) and (1437) follows:
% 29.94/10.06 | (2826) sum(n1, n18) = all_0_0_0
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 29.94/10.06 | (741) all_0_3_3 = n19
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (619) with n1, n18, all_0_0_0, n19 and discharging atoms sum(n1, n18) = all_0_0_0, sum(n1, n18) = n19, yields:
% 29.94/10.06 | (1068) all_0_0_0 = n19
% 29.94/10.06 |
% 29.94/10.06 | From (741)(1068) and (232) follows:
% 29.94/10.06 | (2829) sum(n19, n19) = all_0_6_6
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (619) with n19, n19, all_0_6_6, n17 and discharging atoms sum(n19, n19) = all_0_6_6, sum(n19, n19) = n17, yields:
% 29.94/10.06 | (1086) all_0_6_6 = n17
% 29.94/10.06 |
% 29.94/10.06 | Equations (1086) can reduce 669 to:
% 29.94/10.06 | (748) $false
% 29.94/10.06 |
% 29.94/10.06 |-The branch is then unsatisfiable
% 29.94/10.06 |-Branch two:
% 29.94/10.06 | (1452) ~ (all_0_7_7 = n1)
% 29.94/10.06 | (1453) all_0_7_7 = n0
% 29.94/10.06 |
% 29.94/10.06 | From (1453) and (683) follows:
% 29.94/10.06 | (1454) succ(n0) = all_0_5_5
% 29.94/10.06 |
% 29.94/10.06 | From (1453) and (8) follows:
% 29.94/10.06 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 29.94/10.06 |
% 29.94/10.06 | From (1453) and (2510) follows:
% 29.94/10.06 | (2836) sum(n18, n0) = all_0_2_2
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 29.94/10.06 | (1457) all_0_5_5 = n1
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (619) with n18, n0, all_0_2_2, n18 and discharging atoms sum(n18, n0) = all_0_2_2, sum(n18, n0) = n18, yields:
% 29.94/10.06 | (754) all_0_2_2 = n18
% 29.94/10.06 |
% 29.94/10.06 | From (754) and (473) follows:
% 29.94/10.06 | (756) pred(n18) = all_0_1_1
% 29.94/10.06 |
% 29.94/10.06 | From (1457) and (2509) follows:
% 29.94/10.06 | (2840) sum(n18, n1) = all_0_4_4
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 29.94/10.06 | (759) all_0_1_1 = n17
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (619) with n18, n1, all_0_4_4, n19 and discharging atoms sum(n18, n1) = all_0_4_4, sum(n18, n1) = n19, yields:
% 29.94/10.06 | (755) all_0_4_4 = n19
% 29.94/10.06 |
% 29.94/10.06 | From (755) and (716) follows:
% 29.94/10.06 | (757) pred(n19) = all_0_3_3
% 29.94/10.06 |
% 29.94/10.06 | From (759) and (1455) follows:
% 29.94/10.06 | (2844) sum(n0, n17) = all_0_0_0
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 29.94/10.06 | (758) all_0_3_3 = n18
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (619) with n0, n17, all_0_0_0, n17 and discharging atoms sum(n0, n17) = all_0_0_0, sum(n0, n17) = n17, yields:
% 29.94/10.06 | (745) all_0_0_0 = n17
% 29.94/10.06 |
% 29.94/10.06 | From (758)(745) and (232) follows:
% 29.94/10.06 | (2847) sum(n18, n17) = all_0_6_6
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (619) with n18, n17, all_0_6_6, n14 and discharging atoms sum(n18, n17) = all_0_6_6, sum(n18, n17) = n14, yields:
% 29.94/10.06 | (934) all_0_6_6 = n14
% 29.94/10.06 |
% 29.94/10.06 | Equations (934) can reduce 353 to:
% 29.94/10.06 | (748) $false
% 29.94/10.06 |
% 29.94/10.06 |-The branch is then unsatisfiable
% 29.94/10.06 |-Branch two:
% 29.94/10.06 | (783) ~ (all_0_8_8 = n18)
% 29.94/10.06 | (784) all_0_8_8 = n17 | all_0_8_8 = n16 | all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.94/10.06 |
% 29.94/10.06 +-Applying beta-rule and splitting (1130), into two cases.
% 29.94/10.06 |-Branch one:
% 29.94/10.06 | (1131) all_0_7_7 = n17
% 29.94/10.06 |
% 29.94/10.06 | From (1131) and (683) follows:
% 29.94/10.06 | (1132) succ(n17) = all_0_5_5
% 29.94/10.06 |
% 29.94/10.06 | From (1131) and (8) follows:
% 29.94/10.06 | (1133) sum(n17, all_0_1_1) = all_0_0_0
% 29.94/10.06 |
% 29.94/10.06 | From (1131) and (378) follows:
% 29.94/10.06 | (2855) sum(all_0_8_8, n17) = all_0_2_2
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (388) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 29.94/10.06 | (1135) all_0_5_5 = n18
% 29.94/10.06 |
% 29.94/10.06 | From (1135) and (708) follows:
% 29.94/10.06 | (2857) sum(all_0_8_8, n18) = all_0_4_4
% 29.94/10.06 |
% 29.94/10.06 +-Applying beta-rule and splitting (784), into two cases.
% 29.94/10.06 |-Branch one:
% 29.94/10.06 | (785) all_0_8_8 = n17
% 29.94/10.06 |
% 29.94/10.06 | From (785) and (2857) follows:
% 29.94/10.06 | (2859) sum(n17, n18) = all_0_4_4
% 29.94/10.06 |
% 29.94/10.06 | From (785) and (2855) follows:
% 29.94/10.06 | (2860) sum(n17, n17) = all_0_2_2
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (619) with n17, n18, all_0_4_4, n14 and discharging atoms sum(n17, n18) = all_0_4_4, sum(n17, n18) = n14, yields:
% 29.94/10.06 | (840) all_0_4_4 = n14
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (619) with n17, n17, all_0_2_2, n13 and discharging atoms sum(n17, n17) = all_0_2_2, sum(n17, n17) = n13, yields:
% 29.94/10.06 | (839) all_0_2_2 = n13
% 29.94/10.06 |
% 29.94/10.06 | From (839) and (473) follows:
% 29.94/10.06 | (841) pred(n13) = all_0_1_1
% 29.94/10.06 |
% 29.94/10.06 | From (840) and (716) follows:
% 29.94/10.06 | (842) pred(n14) = all_0_3_3
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 29.94/10.06 | (843) all_0_3_3 = n13
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 29.94/10.06 | (844) all_0_1_1 = n12
% 29.94/10.06 |
% 29.94/10.06 | From (843) and (232) follows:
% 29.94/10.06 | (845) sum(n13, all_0_0_0) = all_0_6_6
% 29.94/10.06 |
% 29.94/10.06 | From (844) and (1133) follows:
% 29.94/10.06 | (2868) sum(n17, n12) = all_0_0_0
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (619) with n17, n12, all_0_0_0, n8 and discharging atoms sum(n17, n12) = all_0_0_0, sum(n17, n12) = n8, yields:
% 29.94/10.06 | (898) all_0_0_0 = n8
% 29.94/10.06 |
% 29.94/10.06 | From (898) and (845) follows:
% 29.94/10.06 | (2870) sum(n13, n8) = all_0_6_6
% 29.94/10.06 |
% 29.94/10.06 | Instantiating formula (619) with n13, n8, all_0_6_6, n0 and discharging atoms sum(n13, n8) = all_0_6_6, sum(n13, n8) = n0, yields:
% 29.94/10.06 | (1053) all_0_6_6 = n0
% 29.94/10.06 |
% 29.94/10.07 | Equations (1053) can reduce 676 to:
% 29.94/10.07 | (748) $false
% 29.94/10.07 |
% 29.94/10.07 |-The branch is then unsatisfiable
% 29.94/10.07 |-Branch two:
% 29.94/10.07 | (800) ~ (all_0_8_8 = n17)
% 29.94/10.07 | (801) all_0_8_8 = n16 | all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.94/10.07 |
% 29.94/10.07 +-Applying beta-rule and splitting (801), into two cases.
% 29.94/10.07 |-Branch one:
% 29.94/10.07 | (802) all_0_8_8 = n16
% 29.94/10.07 |
% 29.94/10.07 | From (802) and (2857) follows:
% 29.94/10.07 | (2876) sum(n16, n18) = all_0_4_4
% 29.94/10.07 |
% 29.94/10.07 | From (802) and (2855) follows:
% 29.94/10.07 | (2877) sum(n16, n17) = all_0_2_2
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n16, n18, all_0_4_4, n13 and discharging atoms sum(n16, n18) = all_0_4_4, sum(n16, n18) = n13, yields:
% 29.94/10.07 | (857) all_0_4_4 = n13
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n16, n17, all_0_2_2, n12 and discharging atoms sum(n16, n17) = all_0_2_2, sum(n16, n17) = n12, yields:
% 29.94/10.07 | (856) all_0_2_2 = n12
% 29.94/10.07 |
% 29.94/10.07 | From (856) and (473) follows:
% 29.94/10.07 | (858) pred(n12) = all_0_1_1
% 29.94/10.07 |
% 29.94/10.07 | From (857) and (716) follows:
% 29.94/10.07 | (859) pred(n13) = all_0_3_3
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 29.94/10.07 | (860) all_0_3_3 = n12
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 29.94/10.07 | (861) all_0_1_1 = n11
% 29.94/10.07 |
% 29.94/10.07 | From (860) and (232) follows:
% 29.94/10.07 | (862) sum(n12, all_0_0_0) = all_0_6_6
% 29.94/10.07 |
% 29.94/10.07 | From (861) and (1133) follows:
% 29.94/10.07 | (2885) sum(n17, n11) = all_0_0_0
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n17, n11, all_0_0_0, n7 and discharging atoms sum(n17, n11) = all_0_0_0, sum(n17, n11) = n7, yields:
% 29.94/10.07 | (915) all_0_0_0 = n7
% 29.94/10.07 |
% 29.94/10.07 | From (915) and (862) follows:
% 29.94/10.07 | (2887) sum(n12, n7) = all_0_6_6
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n12, n7, all_0_6_6, n19 and discharging atoms sum(n12, n7) = all_0_6_6, sum(n12, n7) = n19, yields:
% 29.94/10.07 | (1070) all_0_6_6 = n19
% 29.94/10.07 |
% 29.94/10.07 | Equations (1070) can reduce 31 to:
% 29.94/10.07 | (748) $false
% 29.94/10.07 |
% 29.94/10.07 |-The branch is then unsatisfiable
% 29.94/10.07 |-Branch two:
% 29.94/10.07 | (817) ~ (all_0_8_8 = n16)
% 29.94/10.07 | (818) all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.94/10.07 |
% 29.94/10.07 +-Applying beta-rule and splitting (818), into two cases.
% 29.94/10.07 |-Branch one:
% 29.94/10.07 | (819) all_0_8_8 = n15
% 29.94/10.07 |
% 29.94/10.07 | From (819) and (2857) follows:
% 29.94/10.07 | (2893) sum(n15, n18) = all_0_4_4
% 29.94/10.07 |
% 29.94/10.07 | From (819) and (2855) follows:
% 29.94/10.07 | (2894) sum(n15, n17) = all_0_2_2
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n15, n18, all_0_4_4, n12 and discharging atoms sum(n15, n18) = all_0_4_4, sum(n15, n18) = n12, yields:
% 29.94/10.07 | (874) all_0_4_4 = n12
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n15, n17, all_0_2_2, n11 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n11, yields:
% 29.94/10.07 | (873) all_0_2_2 = n11
% 29.94/10.07 |
% 29.94/10.07 | From (873) and (473) follows:
% 29.94/10.07 | (875) pred(n11) = all_0_1_1
% 29.94/10.07 |
% 29.94/10.07 | From (874) and (716) follows:
% 29.94/10.07 | (876) pred(n12) = all_0_3_3
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 29.94/10.07 | (877) all_0_3_3 = n11
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 29.94/10.07 | (878) all_0_1_1 = n10
% 29.94/10.07 |
% 29.94/10.07 | From (877) and (232) follows:
% 29.94/10.07 | (879) sum(n11, all_0_0_0) = all_0_6_6
% 29.94/10.07 |
% 29.94/10.07 | From (878) and (1133) follows:
% 29.94/10.07 | (2902) sum(n17, n10) = all_0_0_0
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n17, n10, all_0_0_0, n6 and discharging atoms sum(n17, n10) = all_0_0_0, sum(n17, n10) = n6, yields:
% 29.94/10.07 | (932) all_0_0_0 = n6
% 29.94/10.07 |
% 29.94/10.07 | From (932) and (879) follows:
% 29.94/10.07 | (2904) sum(n11, n6) = all_0_6_6
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n11, n6, all_0_6_6, n17 and discharging atoms sum(n11, n6) = all_0_6_6, sum(n11, n6) = n17, yields:
% 29.94/10.07 | (1086) all_0_6_6 = n17
% 29.94/10.07 |
% 29.94/10.07 | Equations (1086) can reduce 669 to:
% 29.94/10.07 | (748) $false
% 29.94/10.07 |
% 29.94/10.07 |-The branch is then unsatisfiable
% 29.94/10.07 |-Branch two:
% 29.94/10.07 | (834) ~ (all_0_8_8 = n15)
% 29.94/10.07 | (835) all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.94/10.07 |
% 29.94/10.07 +-Applying beta-rule and splitting (835), into two cases.
% 29.94/10.07 |-Branch one:
% 29.94/10.07 | (836) all_0_8_8 = n14
% 29.94/10.07 |
% 29.94/10.07 | From (836) and (2857) follows:
% 29.94/10.07 | (2910) sum(n14, n18) = all_0_4_4
% 29.94/10.07 |
% 29.94/10.07 | From (836) and (2855) follows:
% 29.94/10.07 | (2911) sum(n14, n17) = all_0_2_2
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n14, n18, all_0_4_4, n11 and discharging atoms sum(n14, n18) = all_0_4_4, sum(n14, n18) = n11, yields:
% 29.94/10.07 | (891) all_0_4_4 = n11
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n14, n17, all_0_2_2, n10 and discharging atoms sum(n14, n17) = all_0_2_2, sum(n14, n17) = n10, yields:
% 29.94/10.07 | (890) all_0_2_2 = n10
% 29.94/10.07 |
% 29.94/10.07 | From (890) and (473) follows:
% 29.94/10.07 | (892) pred(n10) = all_0_1_1
% 29.94/10.07 |
% 29.94/10.07 | From (891) and (716) follows:
% 29.94/10.07 | (893) pred(n11) = all_0_3_3
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 29.94/10.07 | (894) all_0_3_3 = n10
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 29.94/10.07 | (895) all_0_1_1 = n9
% 29.94/10.07 |
% 29.94/10.07 | From (894) and (232) follows:
% 29.94/10.07 | (896) sum(n10, all_0_0_0) = all_0_6_6
% 29.94/10.07 |
% 29.94/10.07 | From (895) and (1133) follows:
% 29.94/10.07 | (2919) sum(n17, n9) = all_0_0_0
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n17, n9, all_0_0_0, n5 and discharging atoms sum(n17, n9) = all_0_0_0, sum(n17, n9) = n5, yields:
% 29.94/10.07 | (949) all_0_0_0 = n5
% 29.94/10.07 |
% 29.94/10.07 | From (949) and (896) follows:
% 29.94/10.07 | (2921) sum(n10, n5) = all_0_6_6
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n10, n5, all_0_6_6, n15 and discharging atoms sum(n10, n5) = all_0_6_6, sum(n10, n5) = n15, yields:
% 29.94/10.07 | (747) all_0_6_6 = n15
% 29.94/10.07 |
% 29.94/10.07 | Equations (747) can reduce 456 to:
% 29.94/10.07 | (748) $false
% 29.94/10.07 |
% 29.94/10.07 |-The branch is then unsatisfiable
% 29.94/10.07 |-Branch two:
% 29.94/10.07 | (851) ~ (all_0_8_8 = n14)
% 29.94/10.07 | (852) all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.94/10.07 |
% 29.94/10.07 +-Applying beta-rule and splitting (852), into two cases.
% 29.94/10.07 |-Branch one:
% 29.94/10.07 | (853) all_0_8_8 = n13
% 29.94/10.07 |
% 29.94/10.07 | From (853) and (2857) follows:
% 29.94/10.07 | (2927) sum(n13, n18) = all_0_4_4
% 29.94/10.07 |
% 29.94/10.07 | From (853) and (2855) follows:
% 29.94/10.07 | (2928) sum(n13, n17) = all_0_2_2
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n13, n18, all_0_4_4, n10 and discharging atoms sum(n13, n18) = all_0_4_4, sum(n13, n18) = n10, yields:
% 29.94/10.07 | (908) all_0_4_4 = n10
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n13, n17, all_0_2_2, n9 and discharging atoms sum(n13, n17) = all_0_2_2, sum(n13, n17) = n9, yields:
% 29.94/10.07 | (907) all_0_2_2 = n9
% 29.94/10.07 |
% 29.94/10.07 | From (907) and (473) follows:
% 29.94/10.07 | (909) pred(n9) = all_0_1_1
% 29.94/10.07 |
% 29.94/10.07 | From (908) and (716) follows:
% 29.94/10.07 | (910) pred(n10) = all_0_3_3
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 29.94/10.07 | (911) all_0_3_3 = n9
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 29.94/10.07 | (912) all_0_1_1 = n8
% 29.94/10.07 |
% 29.94/10.07 | From (911) and (232) follows:
% 29.94/10.07 | (913) sum(n9, all_0_0_0) = all_0_6_6
% 29.94/10.07 |
% 29.94/10.07 | From (912) and (1133) follows:
% 29.94/10.07 | (2936) sum(n17, n8) = all_0_0_0
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n17, n8, all_0_0_0, n4 and discharging atoms sum(n17, n8) = all_0_0_0, sum(n17, n8) = n4, yields:
% 29.94/10.07 | (966) all_0_0_0 = n4
% 29.94/10.07 |
% 29.94/10.07 | From (966) and (913) follows:
% 29.94/10.07 | (2938) sum(n9, n4) = all_0_6_6
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n9, n4, all_0_6_6, n13 and discharging atoms sum(n9, n4) = all_0_6_6, sum(n9, n4) = n13, yields:
% 29.94/10.07 | (764) all_0_6_6 = n13
% 29.94/10.07 |
% 29.94/10.07 | Equations (764) can reduce 293 to:
% 29.94/10.07 | (748) $false
% 29.94/10.07 |
% 29.94/10.07 |-The branch is then unsatisfiable
% 29.94/10.07 |-Branch two:
% 29.94/10.07 | (868) ~ (all_0_8_8 = n13)
% 29.94/10.07 | (869) all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.94/10.07 |
% 29.94/10.07 +-Applying beta-rule and splitting (869), into two cases.
% 29.94/10.07 |-Branch one:
% 29.94/10.07 | (870) all_0_8_8 = n12
% 29.94/10.07 |
% 29.94/10.07 | From (870) and (2857) follows:
% 29.94/10.07 | (2944) sum(n12, n18) = all_0_4_4
% 29.94/10.07 |
% 29.94/10.07 | From (870) and (2855) follows:
% 29.94/10.07 | (2945) sum(n12, n17) = all_0_2_2
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n12, n18, all_0_4_4, n9 and discharging atoms sum(n12, n18) = all_0_4_4, sum(n12, n18) = n9, yields:
% 29.94/10.07 | (925) all_0_4_4 = n9
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (619) with n12, n17, all_0_2_2, n8 and discharging atoms sum(n12, n17) = all_0_2_2, sum(n12, n17) = n8, yields:
% 29.94/10.07 | (924) all_0_2_2 = n8
% 29.94/10.07 |
% 29.94/10.07 | From (924) and (473) follows:
% 29.94/10.07 | (926) pred(n8) = all_0_1_1
% 29.94/10.07 |
% 29.94/10.07 | From (925) and (716) follows:
% 29.94/10.07 | (927) pred(n9) = all_0_3_3
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 29.94/10.07 | (928) all_0_3_3 = n8
% 29.94/10.07 |
% 29.94/10.07 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 29.94/10.07 | (929) all_0_1_1 = n7
% 29.94/10.07 |
% 29.94/10.07 | From (928) and (232) follows:
% 29.94/10.08 | (930) sum(n8, all_0_0_0) = all_0_6_6
% 29.94/10.08 |
% 29.94/10.08 | From (929) and (1133) follows:
% 29.94/10.08 | (2953) sum(n17, n7) = all_0_0_0
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n17, n7, all_0_0_0, n3 and discharging atoms sum(n17, n7) = all_0_0_0, sum(n17, n7) = n3, yields:
% 29.94/10.08 | (983) all_0_0_0 = n3
% 29.94/10.08 |
% 29.94/10.08 | From (983) and (930) follows:
% 29.94/10.08 | (2955) sum(n8, n3) = all_0_6_6
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n8, n3, all_0_6_6, n11 and discharging atoms sum(n8, n3) = all_0_6_6, sum(n8, n3) = n11, yields:
% 29.94/10.08 | (781) all_0_6_6 = n11
% 29.94/10.08 |
% 29.94/10.08 | Equations (781) can reduce 2 to:
% 29.94/10.08 | (748) $false
% 29.94/10.08 |
% 29.94/10.08 |-The branch is then unsatisfiable
% 29.94/10.08 |-Branch two:
% 29.94/10.08 | (885) ~ (all_0_8_8 = n12)
% 29.94/10.08 | (886) all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.94/10.08 |
% 29.94/10.08 +-Applying beta-rule and splitting (886), into two cases.
% 29.94/10.08 |-Branch one:
% 29.94/10.08 | (887) all_0_8_8 = n11
% 29.94/10.08 |
% 29.94/10.08 | From (887) and (2857) follows:
% 29.94/10.08 | (2961) sum(n11, n18) = all_0_4_4
% 29.94/10.08 |
% 29.94/10.08 | From (887) and (2855) follows:
% 29.94/10.08 | (2962) sum(n11, n17) = all_0_2_2
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n11, n18, all_0_4_4, n8 and discharging atoms sum(n11, n18) = all_0_4_4, sum(n11, n18) = n8, yields:
% 29.94/10.08 | (942) all_0_4_4 = n8
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n11, n17, all_0_2_2, n7 and discharging atoms sum(n11, n17) = all_0_2_2, sum(n11, n17) = n7, yields:
% 29.94/10.08 | (941) all_0_2_2 = n7
% 29.94/10.08 |
% 29.94/10.08 | From (941) and (473) follows:
% 29.94/10.08 | (943) pred(n7) = all_0_1_1
% 29.94/10.08 |
% 29.94/10.08 | From (942) and (716) follows:
% 29.94/10.08 | (944) pred(n8) = all_0_3_3
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 29.94/10.08 | (945) all_0_3_3 = n7
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 29.94/10.08 | (946) all_0_1_1 = n6
% 29.94/10.08 |
% 29.94/10.08 | From (945) and (232) follows:
% 29.94/10.08 | (947) sum(n7, all_0_0_0) = all_0_6_6
% 29.94/10.08 |
% 29.94/10.08 | From (946) and (1133) follows:
% 29.94/10.08 | (2970) sum(n17, n6) = all_0_0_0
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n17, n6, all_0_0_0, n2 and discharging atoms sum(n17, n6) = all_0_0_0, sum(n17, n6) = n2, yields:
% 29.94/10.08 | (1000) all_0_0_0 = n2
% 29.94/10.08 |
% 29.94/10.08 | From (1000) and (947) follows:
% 29.94/10.08 | (2972) sum(n7, n2) = all_0_6_6
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n7, n2, all_0_6_6, n9 and discharging atoms sum(n7, n2) = all_0_6_6, sum(n7, n2) = n9, yields:
% 29.94/10.08 | (798) all_0_6_6 = n9
% 29.94/10.08 |
% 29.94/10.08 | Equations (798) can reduce 593 to:
% 29.94/10.08 | (748) $false
% 29.94/10.08 |
% 29.94/10.08 |-The branch is then unsatisfiable
% 29.94/10.08 |-Branch two:
% 29.94/10.08 | (902) ~ (all_0_8_8 = n11)
% 29.94/10.08 | (903) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.94/10.08 |
% 29.94/10.08 +-Applying beta-rule and splitting (903), into two cases.
% 29.94/10.08 |-Branch one:
% 29.94/10.08 | (904) all_0_8_8 = n10
% 29.94/10.08 |
% 29.94/10.08 | From (904) and (2857) follows:
% 29.94/10.08 | (2978) sum(n10, n18) = all_0_4_4
% 29.94/10.08 |
% 29.94/10.08 | From (904) and (2855) follows:
% 29.94/10.08 | (2979) sum(n10, n17) = all_0_2_2
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n10, n18, all_0_4_4, n7 and discharging atoms sum(n10, n18) = all_0_4_4, sum(n10, n18) = n7, yields:
% 29.94/10.08 | (959) all_0_4_4 = n7
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n10, n17, all_0_2_2, n6 and discharging atoms sum(n10, n17) = all_0_2_2, sum(n10, n17) = n6, yields:
% 29.94/10.08 | (958) all_0_2_2 = n6
% 29.94/10.08 |
% 29.94/10.08 | From (958) and (473) follows:
% 29.94/10.08 | (960) pred(n6) = all_0_1_1
% 29.94/10.08 |
% 29.94/10.08 | From (959) and (716) follows:
% 29.94/10.08 | (961) pred(n7) = all_0_3_3
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 29.94/10.08 | (962) all_0_3_3 = n6
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 29.94/10.08 | (963) all_0_1_1 = n5
% 29.94/10.08 |
% 29.94/10.08 | From (962) and (232) follows:
% 29.94/10.08 | (964) sum(n6, all_0_0_0) = all_0_6_6
% 29.94/10.08 |
% 29.94/10.08 | From (963) and (1133) follows:
% 29.94/10.08 | (2987) sum(n17, n5) = all_0_0_0
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n17, n5, all_0_0_0, n1 and discharging atoms sum(n17, n5) = all_0_0_0, sum(n17, n5) = n1, yields:
% 29.94/10.08 | (1017) all_0_0_0 = n1
% 29.94/10.08 |
% 29.94/10.08 | From (1017) and (964) follows:
% 29.94/10.08 | (2989) sum(n6, n1) = all_0_6_6
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n6, n1, all_0_6_6, n7 and discharging atoms sum(n6, n1) = all_0_6_6, sum(n6, n1) = n7, yields:
% 29.94/10.08 | (815) all_0_6_6 = n7
% 29.94/10.08 |
% 29.94/10.08 | Equations (815) can reduce 557 to:
% 29.94/10.08 | (748) $false
% 29.94/10.08 |
% 29.94/10.08 |-The branch is then unsatisfiable
% 29.94/10.08 |-Branch two:
% 29.94/10.08 | (919) ~ (all_0_8_8 = n10)
% 29.94/10.08 | (920) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.94/10.08 |
% 29.94/10.08 +-Applying beta-rule and splitting (920), into two cases.
% 29.94/10.08 |-Branch one:
% 29.94/10.08 | (921) all_0_8_8 = n9
% 29.94/10.08 |
% 29.94/10.08 | From (921) and (2857) follows:
% 29.94/10.08 | (2995) sum(n9, n18) = all_0_4_4
% 29.94/10.08 |
% 29.94/10.08 | From (921) and (2855) follows:
% 29.94/10.08 | (2996) sum(n9, n17) = all_0_2_2
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n9, n18, all_0_4_4, n6 and discharging atoms sum(n9, n18) = all_0_4_4, sum(n9, n18) = n6, yields:
% 29.94/10.08 | (976) all_0_4_4 = n6
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n9, n17, all_0_2_2, n5 and discharging atoms sum(n9, n17) = all_0_2_2, sum(n9, n17) = n5, yields:
% 29.94/10.08 | (975) all_0_2_2 = n5
% 29.94/10.08 |
% 29.94/10.08 | From (975) and (473) follows:
% 29.94/10.08 | (977) pred(n5) = all_0_1_1
% 29.94/10.08 |
% 29.94/10.08 | From (976) and (716) follows:
% 29.94/10.08 | (978) pred(n6) = all_0_3_3
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 29.94/10.08 | (979) all_0_3_3 = n5
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 29.94/10.08 | (980) all_0_1_1 = n4
% 29.94/10.08 |
% 29.94/10.08 | From (979) and (232) follows:
% 29.94/10.08 | (981) sum(n5, all_0_0_0) = all_0_6_6
% 29.94/10.08 |
% 29.94/10.08 | From (980) and (1133) follows:
% 29.94/10.08 | (3004) sum(n17, n4) = all_0_0_0
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n17, n4, all_0_0_0, n0 and discharging atoms sum(n17, n4) = all_0_0_0, sum(n17, n4) = n0, yields:
% 29.94/10.08 | (1034) all_0_0_0 = n0
% 29.94/10.08 |
% 29.94/10.08 | From (1034) and (981) follows:
% 29.94/10.08 | (3006) sum(n5, n0) = all_0_6_6
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n5, n0, all_0_6_6, n5 and discharging atoms sum(n5, n0) = all_0_6_6, sum(n5, n0) = n5, yields:
% 29.94/10.08 | (832) all_0_6_6 = n5
% 29.94/10.08 |
% 29.94/10.08 | Equations (832) can reduce 462 to:
% 29.94/10.08 | (748) $false
% 29.94/10.08 |
% 29.94/10.08 |-The branch is then unsatisfiable
% 29.94/10.08 |-Branch two:
% 29.94/10.08 | (936) ~ (all_0_8_8 = n9)
% 29.94/10.08 | (937) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.94/10.08 |
% 29.94/10.08 +-Applying beta-rule and splitting (937), into two cases.
% 29.94/10.08 |-Branch one:
% 29.94/10.08 | (938) all_0_8_8 = n8
% 29.94/10.08 |
% 29.94/10.08 | From (938) and (2857) follows:
% 29.94/10.08 | (3012) sum(n8, n18) = all_0_4_4
% 29.94/10.08 |
% 29.94/10.08 | From (938) and (2855) follows:
% 29.94/10.08 | (3013) sum(n8, n17) = all_0_2_2
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n8, n18, all_0_4_4, n5 and discharging atoms sum(n8, n18) = all_0_4_4, sum(n8, n18) = n5, yields:
% 29.94/10.08 | (993) all_0_4_4 = n5
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n8, n17, all_0_2_2, n4 and discharging atoms sum(n8, n17) = all_0_2_2, sum(n8, n17) = n4, yields:
% 29.94/10.08 | (992) all_0_2_2 = n4
% 29.94/10.08 |
% 29.94/10.08 | From (992) and (473) follows:
% 29.94/10.08 | (994) pred(n4) = all_0_1_1
% 29.94/10.08 |
% 29.94/10.08 | From (993) and (716) follows:
% 29.94/10.08 | (995) pred(n5) = all_0_3_3
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 29.94/10.08 | (996) all_0_3_3 = n4
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 29.94/10.08 | (997) all_0_1_1 = n3
% 29.94/10.08 |
% 29.94/10.08 | From (996) and (232) follows:
% 29.94/10.08 | (998) sum(n4, all_0_0_0) = all_0_6_6
% 29.94/10.08 |
% 29.94/10.08 | From (997) and (1133) follows:
% 29.94/10.08 | (3021) sum(n17, n3) = all_0_0_0
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n17, n3, all_0_0_0, n20 and discharging atoms sum(n17, n3) = all_0_0_0, sum(n17, n3) = n20, yields:
% 29.94/10.08 | (1051) all_0_0_0 = n20
% 29.94/10.08 |
% 29.94/10.08 | From (1051) and (998) follows:
% 29.94/10.08 | (3023) sum(n4, n20) = all_0_6_6
% 29.94/10.08 |
% 29.94/10.08 | Instantiating formula (619) with n4, n20, all_0_6_6, n3 and discharging atoms sum(n4, n20) = all_0_6_6, sum(n4, n20) = n3, yields:
% 29.94/10.08 | (849) all_0_6_6 = n3
% 29.94/10.08 |
% 29.94/10.08 | Equations (849) can reduce 416 to:
% 29.94/10.08 | (748) $false
% 29.94/10.08 |
% 29.94/10.08 |-The branch is then unsatisfiable
% 29.94/10.08 |-Branch two:
% 29.94/10.08 | (953) ~ (all_0_8_8 = n8)
% 29.94/10.08 | (954) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.94/10.08 |
% 29.94/10.08 +-Applying beta-rule and splitting (954), into two cases.
% 29.94/10.08 |-Branch one:
% 29.94/10.08 | (955) all_0_8_8 = n7
% 29.94/10.08 |
% 29.94/10.08 | From (955) and (2857) follows:
% 29.94/10.08 | (3029) sum(n7, n18) = all_0_4_4
% 29.94/10.08 |
% 29.94/10.08 | From (955) and (2855) follows:
% 29.94/10.09 | (3030) sum(n7, n17) = all_0_2_2
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (619) with n7, n18, all_0_4_4, n4 and discharging atoms sum(n7, n18) = all_0_4_4, sum(n7, n18) = n4, yields:
% 29.94/10.09 | (1010) all_0_4_4 = n4
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (619) with n7, n17, all_0_2_2, n3 and discharging atoms sum(n7, n17) = all_0_2_2, sum(n7, n17) = n3, yields:
% 29.94/10.09 | (1009) all_0_2_2 = n3
% 29.94/10.09 |
% 29.94/10.09 | From (1009) and (473) follows:
% 29.94/10.09 | (1011) pred(n3) = all_0_1_1
% 29.94/10.09 |
% 29.94/10.09 | From (1010) and (716) follows:
% 29.94/10.09 | (1012) pred(n4) = all_0_3_3
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 29.94/10.09 | (1013) all_0_3_3 = n3
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 29.94/10.09 | (1014) all_0_1_1 = n2
% 29.94/10.09 |
% 29.94/10.09 | From (1013) and (232) follows:
% 29.94/10.09 | (1015) sum(n3, all_0_0_0) = all_0_6_6
% 29.94/10.09 |
% 29.94/10.09 | From (1014) and (1133) follows:
% 29.94/10.09 | (3038) sum(n17, n2) = all_0_0_0
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (619) with n17, n2, all_0_0_0, n19 and discharging atoms sum(n17, n2) = all_0_0_0, sum(n17, n2) = n19, yields:
% 29.94/10.09 | (1068) all_0_0_0 = n19
% 29.94/10.09 |
% 29.94/10.09 | From (1068) and (1015) follows:
% 29.94/10.09 | (3040) sum(n3, n19) = all_0_6_6
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (619) with n3, n19, all_0_6_6, n1 and discharging atoms sum(n3, n19) = all_0_6_6, sum(n3, n19) = n1, yields:
% 29.94/10.09 | (866) all_0_6_6 = n1
% 29.94/10.09 |
% 29.94/10.09 | Equations (866) can reduce 28 to:
% 29.94/10.09 | (748) $false
% 29.94/10.09 |
% 29.94/10.09 |-The branch is then unsatisfiable
% 29.94/10.09 |-Branch two:
% 29.94/10.09 | (970) ~ (all_0_8_8 = n7)
% 29.94/10.09 | (971) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.94/10.09 |
% 29.94/10.09 +-Applying beta-rule and splitting (971), into two cases.
% 29.94/10.09 |-Branch one:
% 29.94/10.09 | (972) all_0_8_8 = n6
% 29.94/10.09 |
% 29.94/10.09 | From (972) and (2857) follows:
% 29.94/10.09 | (3046) sum(n6, n18) = all_0_4_4
% 29.94/10.09 |
% 29.94/10.09 | From (972) and (2855) follows:
% 29.94/10.09 | (3047) sum(n6, n17) = all_0_2_2
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (619) with n6, n18, all_0_4_4, n3 and discharging atoms sum(n6, n18) = all_0_4_4, sum(n6, n18) = n3, yields:
% 29.94/10.09 | (1027) all_0_4_4 = n3
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (619) with n6, n17, all_0_2_2, n2 and discharging atoms sum(n6, n17) = all_0_2_2, sum(n6, n17) = n2, yields:
% 29.94/10.09 | (1026) all_0_2_2 = n2
% 29.94/10.09 |
% 29.94/10.09 | From (1026) and (473) follows:
% 29.94/10.09 | (1028) pred(n2) = all_0_1_1
% 29.94/10.09 |
% 29.94/10.09 | From (1027) and (716) follows:
% 29.94/10.09 | (1029) pred(n3) = all_0_3_3
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 29.94/10.09 | (1030) all_0_3_3 = n2
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 29.94/10.09 | (1031) all_0_1_1 = n1
% 29.94/10.09 |
% 29.94/10.09 | From (1030) and (232) follows:
% 29.94/10.09 | (1032) sum(n2, all_0_0_0) = all_0_6_6
% 29.94/10.09 |
% 29.94/10.09 | From (1031) and (1133) follows:
% 29.94/10.09 | (3055) sum(n17, n1) = all_0_0_0
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (619) with n17, n1, all_0_0_0, n18 and discharging atoms sum(n17, n1) = all_0_0_0, sum(n17, n1) = n18, yields:
% 29.94/10.09 | (1084) all_0_0_0 = n18
% 29.94/10.09 |
% 29.94/10.09 | From (1084) and (1032) follows:
% 29.94/10.09 | (3057) sum(n2, n18) = all_0_6_6
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (619) with n2, n18, all_0_6_6, n20 and discharging atoms sum(n2, n18) = all_0_6_6, sum(n2, n18) = n20, yields:
% 29.94/10.09 | (883) all_0_6_6 = n20
% 29.94/10.09 |
% 29.94/10.09 | Equations (883) can reduce 381 to:
% 29.94/10.09 | (748) $false
% 29.94/10.09 |
% 29.94/10.09 |-The branch is then unsatisfiable
% 29.94/10.09 |-Branch two:
% 29.94/10.09 | (987) ~ (all_0_8_8 = n6)
% 29.94/10.09 | (988) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.94/10.09 |
% 29.94/10.09 +-Applying beta-rule and splitting (988), into two cases.
% 29.94/10.09 |-Branch one:
% 29.94/10.09 | (989) all_0_8_8 = n5
% 29.94/10.09 |
% 29.94/10.09 | From (989) and (2857) follows:
% 29.94/10.09 | (3063) sum(n5, n18) = all_0_4_4
% 29.94/10.09 |
% 29.94/10.09 | From (989) and (2855) follows:
% 29.94/10.09 | (3064) sum(n5, n17) = all_0_2_2
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (619) with n5, n18, all_0_4_4, n2 and discharging atoms sum(n5, n18) = all_0_4_4, sum(n5, n18) = n2, yields:
% 29.94/10.09 | (1044) all_0_4_4 = n2
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (619) with n5, n17, all_0_2_2, n1 and discharging atoms sum(n5, n17) = all_0_2_2, sum(n5, n17) = n1, yields:
% 29.94/10.09 | (1043) all_0_2_2 = n1
% 29.94/10.09 |
% 29.94/10.09 | From (1043) and (473) follows:
% 29.94/10.09 | (1045) pred(n1) = all_0_1_1
% 29.94/10.09 |
% 29.94/10.09 | From (1044) and (716) follows:
% 29.94/10.09 | (1046) pred(n2) = all_0_3_3
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 29.94/10.09 | (1047) all_0_3_3 = n1
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 29.94/10.09 | (1048) all_0_1_1 = n0
% 29.94/10.09 |
% 29.94/10.09 | From (1047) and (232) follows:
% 29.94/10.09 | (1049) sum(n1, all_0_0_0) = all_0_6_6
% 29.94/10.09 |
% 29.94/10.09 | From (1048) and (1133) follows:
% 29.94/10.09 | (3072) sum(n17, n0) = all_0_0_0
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (619) with n17, n0, all_0_0_0, n17 and discharging atoms sum(n17, n0) = all_0_0_0, sum(n17, n0) = n17, yields:
% 29.94/10.09 | (745) all_0_0_0 = n17
% 29.94/10.09 |
% 29.94/10.09 | From (745) and (1049) follows:
% 29.94/10.09 | (3074) sum(n1, n17) = all_0_6_6
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (619) with n1, n17, all_0_6_6, n18 and discharging atoms sum(n1, n17) = all_0_6_6, sum(n1, n17) = n18, yields:
% 29.94/10.09 | (900) all_0_6_6 = n18
% 29.94/10.09 |
% 29.94/10.09 | Equations (900) can reduce 622 to:
% 29.94/10.09 | (748) $false
% 29.94/10.09 |
% 29.94/10.09 |-The branch is then unsatisfiable
% 29.94/10.09 |-Branch two:
% 29.94/10.09 | (1004) ~ (all_0_8_8 = n5)
% 29.94/10.09 | (1005) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.94/10.09 |
% 29.94/10.09 +-Applying beta-rule and splitting (1005), into two cases.
% 29.94/10.09 |-Branch one:
% 29.94/10.09 | (1006) all_0_8_8 = n4
% 29.94/10.09 |
% 29.94/10.09 | From (1006) and (2857) follows:
% 29.94/10.09 | (3080) sum(n4, n18) = all_0_4_4
% 29.94/10.09 |
% 29.94/10.09 | From (1006) and (2855) follows:
% 29.94/10.09 | (3081) sum(n4, n17) = all_0_2_2
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (619) with n4, n18, all_0_4_4, n1 and discharging atoms sum(n4, n18) = all_0_4_4, sum(n4, n18) = n1, yields:
% 29.94/10.09 | (1061) all_0_4_4 = n1
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (619) with n4, n17, all_0_2_2, n0 and discharging atoms sum(n4, n17) = all_0_2_2, sum(n4, n17) = n0, yields:
% 29.94/10.09 | (1060) all_0_2_2 = n0
% 29.94/10.09 |
% 29.94/10.09 | From (1060) and (473) follows:
% 29.94/10.09 | (1062) pred(n0) = all_0_1_1
% 29.94/10.09 |
% 29.94/10.09 | From (1061) and (716) follows:
% 29.94/10.09 | (1063) pred(n1) = all_0_3_3
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 29.94/10.09 | (1064) all_0_3_3 = n0
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 29.94/10.09 | (1065) all_0_1_1 = n20
% 29.94/10.09 |
% 29.94/10.09 | From (1064) and (232) follows:
% 29.94/10.09 | (1066) sum(n0, all_0_0_0) = all_0_6_6
% 29.94/10.09 |
% 29.94/10.09 | From (1065) and (1133) follows:
% 29.94/10.09 | (3089) sum(n17, n20) = all_0_0_0
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (619) with n17, n20, all_0_0_0, n16 and discharging atoms sum(n17, n20) = all_0_0_0, sum(n17, n20) = n16, yields:
% 29.94/10.09 | (762) all_0_0_0 = n16
% 29.94/10.09 |
% 29.94/10.09 | From (762) and (1066) follows:
% 29.94/10.09 | (3091) sum(n0, n16) = all_0_6_6
% 29.94/10.09 |
% 29.94/10.09 | Instantiating formula (619) with n0, n16, all_0_6_6, n16 and discharging atoms sum(n0, n16) = all_0_6_6, sum(n0, n16) = n16, yields:
% 29.94/10.09 | (917) all_0_6_6 = n16
% 29.94/10.09 |
% 29.94/10.09 | Equations (917) can reduce 163 to:
% 29.94/10.09 | (748) $false
% 29.94/10.09 |
% 29.94/10.09 |-The branch is then unsatisfiable
% 29.94/10.09 |-Branch two:
% 29.94/10.09 | (1021) ~ (all_0_8_8 = n4)
% 29.94/10.09 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 29.94/10.09 |
% 29.94/10.09 +-Applying beta-rule and splitting (1022), into two cases.
% 29.94/10.09 |-Branch one:
% 29.94/10.09 | (1023) all_0_8_8 = n3
% 29.94/10.09 |
% 29.94/10.09 | From (1023) and (2857) follows:
% 29.94/10.09 | (3097) sum(n3, n18) = all_0_4_4
% 29.94/10.09 |
% 29.94/10.09 | From (1023) and (2855) follows:
% 30.15/10.09 | (3098) sum(n3, n17) = all_0_2_2
% 30.15/10.09 |
% 30.15/10.09 | Instantiating formula (619) with n3, n18, all_0_4_4, n0 and discharging atoms sum(n3, n18) = all_0_4_4, sum(n3, n18) = n0, yields:
% 30.15/10.09 | (1077) all_0_4_4 = n0
% 30.15/10.09 |
% 30.15/10.09 | Instantiating formula (619) with n3, n17, all_0_2_2, n20 and discharging atoms sum(n3, n17) = all_0_2_2, sum(n3, n17) = n20, yields:
% 30.15/10.09 | (1076) all_0_2_2 = n20
% 30.15/10.09 |
% 30.15/10.09 | From (1076) and (473) follows:
% 30.15/10.09 | (1078) pred(n20) = all_0_1_1
% 30.15/10.09 |
% 30.15/10.09 | From (1077) and (716) follows:
% 30.15/10.09 | (1079) pred(n0) = all_0_3_3
% 30.15/10.09 |
% 30.15/10.09 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 30.15/10.09 | (1080) all_0_1_1 = n19
% 30.15/10.09 |
% 30.15/10.09 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 30.15/10.09 | (1081) all_0_3_3 = n20
% 30.15/10.09 |
% 30.15/10.09 | From (1081) and (232) follows:
% 30.15/10.09 | (1082) sum(n20, all_0_0_0) = all_0_6_6
% 30.15/10.09 |
% 30.15/10.09 | From (1080) and (1133) follows:
% 30.15/10.10 | (3106) sum(n17, n19) = all_0_0_0
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (619) with n17, n19, all_0_0_0, n15 and discharging atoms sum(n17, n19) = all_0_0_0, sum(n17, n19) = n15, yields:
% 30.15/10.10 | (779) all_0_0_0 = n15
% 30.15/10.10 |
% 30.15/10.10 | From (779) and (1082) follows:
% 30.15/10.10 | (3108) sum(n20, n15) = all_0_6_6
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (619) with n20, n15, all_0_6_6, n14 and discharging atoms sum(n20, n15) = all_0_6_6, sum(n20, n15) = n14, yields:
% 30.15/10.10 | (934) all_0_6_6 = n14
% 30.15/10.10 |
% 30.15/10.10 | Equations (934) can reduce 353 to:
% 30.15/10.10 | (748) $false
% 30.15/10.10 |
% 30.15/10.10 |-The branch is then unsatisfiable
% 30.15/10.10 |-Branch two:
% 30.15/10.10 | (1038) ~ (all_0_8_8 = n3)
% 30.15/10.10 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.15/10.10 |
% 30.15/10.10 +-Applying beta-rule and splitting (1039), into two cases.
% 30.15/10.10 |-Branch one:
% 30.15/10.10 | (1040) all_0_8_8 = n2
% 30.15/10.10 |
% 30.15/10.10 | From (1040) and (2857) follows:
% 30.15/10.10 | (3114) sum(n2, n18) = all_0_4_4
% 30.15/10.10 |
% 30.15/10.10 | From (1040) and (2855) follows:
% 30.15/10.10 | (3115) sum(n2, n17) = all_0_2_2
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (619) with n2, n18, all_0_4_4, n20 and discharging atoms sum(n2, n18) = all_0_4_4, sum(n2, n18) = n20, yields:
% 30.15/10.10 | (738) all_0_4_4 = n20
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (619) with n2, n17, all_0_2_2, n19 and discharging atoms sum(n2, n17) = all_0_2_2, sum(n2, n17) = n19, yields:
% 30.15/10.10 | (737) all_0_2_2 = n19
% 30.15/10.10 |
% 30.15/10.10 | From (737) and (473) follows:
% 30.15/10.10 | (739) pred(n19) = all_0_1_1
% 30.15/10.10 |
% 30.15/10.10 | From (738) and (716) follows:
% 30.15/10.10 | (740) pred(n20) = all_0_3_3
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 30.15/10.10 | (741) all_0_3_3 = n19
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 30.15/10.10 | (742) all_0_1_1 = n18
% 30.15/10.10 |
% 30.15/10.10 | From (741) and (232) follows:
% 30.15/10.10 | (743) sum(n19, all_0_0_0) = all_0_6_6
% 30.15/10.10 |
% 30.15/10.10 | From (742) and (1133) follows:
% 30.15/10.10 | (3123) sum(n17, n18) = all_0_0_0
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (619) with n17, n18, all_0_0_0, n14 and discharging atoms sum(n17, n18) = all_0_0_0, sum(n17, n18) = n14, yields:
% 30.15/10.10 | (796) all_0_0_0 = n14
% 30.15/10.10 |
% 30.15/10.10 | From (796) and (743) follows:
% 30.15/10.10 | (3125) sum(n19, n14) = all_0_6_6
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (619) with n19, n14, all_0_6_6, n12 and discharging atoms sum(n19, n14) = all_0_6_6, sum(n19, n14) = n12, yields:
% 30.15/10.10 | (951) all_0_6_6 = n12
% 30.15/10.10 |
% 30.15/10.10 | Equations (951) can reduce 76 to:
% 30.15/10.10 | (748) $false
% 30.15/10.10 |
% 30.15/10.10 |-The branch is then unsatisfiable
% 30.15/10.10 |-Branch two:
% 30.15/10.10 | (1055) ~ (all_0_8_8 = n2)
% 30.15/10.10 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 30.15/10.10 |
% 30.15/10.10 +-Applying beta-rule and splitting (1056), into two cases.
% 30.15/10.10 |-Branch one:
% 30.15/10.10 | (1057) all_0_8_8 = n1
% 30.15/10.10 |
% 30.15/10.10 | From (1057) and (2857) follows:
% 30.15/10.10 | (3131) sum(n1, n18) = all_0_4_4
% 30.15/10.10 |
% 30.15/10.10 | From (1057) and (2855) follows:
% 30.15/10.10 | (3132) sum(n1, n17) = all_0_2_2
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (619) with n1, n18, all_0_4_4, n19 and discharging atoms sum(n1, n18) = all_0_4_4, sum(n1, n18) = n19, yields:
% 30.15/10.10 | (755) all_0_4_4 = n19
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (619) with n1, n17, all_0_2_2, n18 and discharging atoms sum(n1, n17) = all_0_2_2, sum(n1, n17) = n18, yields:
% 30.15/10.10 | (754) all_0_2_2 = n18
% 30.15/10.10 |
% 30.15/10.10 | From (754) and (473) follows:
% 30.15/10.10 | (756) pred(n18) = all_0_1_1
% 30.15/10.10 |
% 30.15/10.10 | From (755) and (716) follows:
% 30.15/10.10 | (757) pred(n19) = all_0_3_3
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 30.15/10.10 | (758) all_0_3_3 = n18
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 30.15/10.10 | (759) all_0_1_1 = n17
% 30.15/10.10 |
% 30.15/10.10 | From (758) and (232) follows:
% 30.15/10.10 | (760) sum(n18, all_0_0_0) = all_0_6_6
% 30.15/10.10 |
% 30.15/10.10 | From (759) and (1133) follows:
% 30.15/10.10 | (3140) sum(n17, n17) = all_0_0_0
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (619) with n17, n17, all_0_0_0, n13 and discharging atoms sum(n17, n17) = all_0_0_0, sum(n17, n17) = n13, yields:
% 30.15/10.10 | (813) all_0_0_0 = n13
% 30.15/10.10 |
% 30.15/10.10 | From (813) and (760) follows:
% 30.15/10.10 | (3142) sum(n18, n13) = all_0_6_6
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (619) with n18, n13, all_0_6_6, n10 and discharging atoms sum(n18, n13) = all_0_6_6, sum(n18, n13) = n10, yields:
% 30.15/10.10 | (968) all_0_6_6 = n10
% 30.15/10.10 |
% 30.15/10.10 | Equations (968) can reduce 176 to:
% 30.15/10.10 | (748) $false
% 30.15/10.10 |
% 30.15/10.10 |-The branch is then unsatisfiable
% 30.15/10.10 |-Branch two:
% 30.15/10.10 | (1072) ~ (all_0_8_8 = n1)
% 30.15/10.10 | (1073) all_0_8_8 = n0
% 30.15/10.10 |
% 30.15/10.10 | From (1073) and (2857) follows:
% 30.15/10.10 | (3147) sum(n0, n18) = all_0_4_4
% 30.15/10.10 |
% 30.15/10.10 | From (1073) and (2855) follows:
% 30.15/10.10 | (3148) sum(n0, n17) = all_0_2_2
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (619) with n0, n18, all_0_4_4, n18 and discharging atoms sum(n0, n18) = all_0_4_4, sum(n0, n18) = n18, yields:
% 30.15/10.10 | (772) all_0_4_4 = n18
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (619) with n0, n17, all_0_2_2, n17 and discharging atoms sum(n0, n17) = all_0_2_2, sum(n0, n17) = n17, yields:
% 30.15/10.10 | (771) all_0_2_2 = n17
% 30.15/10.10 |
% 30.15/10.10 | From (771) and (473) follows:
% 30.15/10.10 | (773) pred(n17) = all_0_1_1
% 30.15/10.10 |
% 30.15/10.10 | From (772) and (716) follows:
% 30.15/10.10 | (774) pred(n18) = all_0_3_3
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 30.15/10.10 | (775) all_0_3_3 = n17
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 30.15/10.10 | (776) all_0_1_1 = n16
% 30.15/10.10 |
% 30.15/10.10 | From (775) and (232) follows:
% 30.15/10.10 | (777) sum(n17, all_0_0_0) = all_0_6_6
% 30.15/10.10 |
% 30.15/10.10 | From (776) and (1133) follows:
% 30.15/10.10 | (3156) sum(n17, n16) = all_0_0_0
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (619) with n17, n16, all_0_0_0, n12 and discharging atoms sum(n17, n16) = all_0_0_0, sum(n17, n16) = n12, yields:
% 30.15/10.10 | (830) all_0_0_0 = n12
% 30.15/10.10 |
% 30.15/10.10 | From (830) and (777) follows:
% 30.15/10.10 | (3158) sum(n17, n12) = all_0_6_6
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (619) with n17, n12, all_0_6_6, n8 and discharging atoms sum(n17, n12) = all_0_6_6, sum(n17, n12) = n8, yields:
% 30.15/10.10 | (985) all_0_6_6 = n8
% 30.15/10.10 |
% 30.15/10.10 | Equations (985) can reduce 357 to:
% 30.15/10.10 | (748) $false
% 30.15/10.10 |
% 30.15/10.10 |-The branch is then unsatisfiable
% 30.15/10.10 |-Branch two:
% 30.15/10.10 | (1148) ~ (all_0_7_7 = n17)
% 30.15/10.10 | (1149) all_0_7_7 = n16 | all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.15/10.10 |
% 30.15/10.10 +-Applying beta-rule and splitting (784), into two cases.
% 30.15/10.10 |-Branch one:
% 30.15/10.10 | (785) all_0_8_8 = n17
% 30.15/10.10 |
% 30.15/10.10 | From (785) and (708) follows:
% 30.15/10.10 | (3164) sum(n17, all_0_5_5) = all_0_4_4
% 30.15/10.10 |
% 30.15/10.10 | From (785) and (378) follows:
% 30.15/10.10 | (3165) sum(n17, all_0_7_7) = all_0_2_2
% 30.15/10.10 |
% 30.15/10.10 +-Applying beta-rule and splitting (1149), into two cases.
% 30.15/10.10 |-Branch one:
% 30.15/10.10 | (1150) all_0_7_7 = n16
% 30.15/10.10 |
% 30.15/10.10 | From (1150) and (683) follows:
% 30.15/10.10 | (1151) succ(n16) = all_0_5_5
% 30.15/10.10 |
% 30.15/10.10 | From (1150) and (8) follows:
% 30.15/10.10 | (1152) sum(n16, all_0_1_1) = all_0_0_0
% 30.15/10.10 |
% 30.15/10.10 | From (1150) and (3165) follows:
% 30.15/10.10 | (3169) sum(n17, n16) = all_0_2_2
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (388) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 30.15/10.10 | (1154) all_0_5_5 = n17
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (619) with n17, n16, all_0_2_2, n12 and discharging atoms sum(n17, n16) = all_0_2_2, sum(n17, n16) = n12, yields:
% 30.15/10.10 | (856) all_0_2_2 = n12
% 30.15/10.10 |
% 30.15/10.10 | From (856) and (473) follows:
% 30.15/10.10 | (858) pred(n12) = all_0_1_1
% 30.15/10.10 |
% 30.15/10.10 | From (1154) and (3164) follows:
% 30.15/10.10 | (3173) sum(n17, n17) = all_0_4_4
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 30.15/10.10 | (861) all_0_1_1 = n11
% 30.15/10.10 |
% 30.15/10.10 | Instantiating formula (619) with n17, n17, all_0_4_4, n13 and discharging atoms sum(n17, n17) = all_0_4_4, sum(n17, n17) = n13, yields:
% 30.15/10.10 | (857) all_0_4_4 = n13
% 30.15/10.10 |
% 30.15/10.10 | From (857) and (716) follows:
% 30.15/10.10 | (859) pred(n13) = all_0_3_3
% 30.15/10.10 |
% 30.15/10.10 | From (861) and (1152) follows:
% 30.15/10.11 | (3177) sum(n16, n11) = all_0_0_0
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 30.15/10.11 | (860) all_0_3_3 = n12
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (619) with n16, n11, all_0_0_0, n6 and discharging atoms sum(n16, n11) = all_0_0_0, sum(n16, n11) = n6, yields:
% 30.15/10.11 | (932) all_0_0_0 = n6
% 30.15/10.11 |
% 30.15/10.11 | From (860)(932) and (232) follows:
% 30.15/10.11 | (3180) sum(n12, n6) = all_0_6_6
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (619) with n12, n6, all_0_6_6, n18 and discharging atoms sum(n12, n6) = all_0_6_6, sum(n12, n6) = n18, yields:
% 30.15/10.11 | (900) all_0_6_6 = n18
% 30.15/10.11 |
% 30.15/10.11 | Equations (900) can reduce 622 to:
% 30.15/10.11 | (748) $false
% 30.15/10.11 |
% 30.15/10.11 |-The branch is then unsatisfiable
% 30.15/10.11 |-Branch two:
% 30.15/10.11 | (1167) ~ (all_0_7_7 = n16)
% 30.15/10.11 | (1168) all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.15/10.11 |
% 30.15/10.11 +-Applying beta-rule and splitting (1168), into two cases.
% 30.15/10.11 |-Branch one:
% 30.15/10.11 | (1169) all_0_7_7 = n15
% 30.15/10.11 |
% 30.15/10.11 | From (1169) and (683) follows:
% 30.15/10.11 | (1170) succ(n15) = all_0_5_5
% 30.15/10.11 |
% 30.15/10.11 | From (1169) and (8) follows:
% 30.15/10.11 | (1171) sum(n15, all_0_1_1) = all_0_0_0
% 30.15/10.11 |
% 30.15/10.11 | From (1169) and (3165) follows:
% 30.15/10.11 | (3188) sum(n17, n15) = all_0_2_2
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (388) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 30.15/10.11 | (1173) all_0_5_5 = n16
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (619) with n17, n15, all_0_2_2, n11 and discharging atoms sum(n17, n15) = all_0_2_2, sum(n17, n15) = n11, yields:
% 30.15/10.11 | (873) all_0_2_2 = n11
% 30.15/10.11 |
% 30.15/10.11 | From (873) and (473) follows:
% 30.15/10.11 | (875) pred(n11) = all_0_1_1
% 30.15/10.11 |
% 30.15/10.11 | From (1173) and (3164) follows:
% 30.15/10.11 | (3192) sum(n17, n16) = all_0_4_4
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 30.15/10.11 | (878) all_0_1_1 = n10
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (619) with n17, n16, all_0_4_4, n12 and discharging atoms sum(n17, n16) = all_0_4_4, sum(n17, n16) = n12, yields:
% 30.15/10.11 | (874) all_0_4_4 = n12
% 30.15/10.11 |
% 30.15/10.11 | From (874) and (716) follows:
% 30.15/10.11 | (876) pred(n12) = all_0_3_3
% 30.15/10.11 |
% 30.15/10.11 | From (878) and (1171) follows:
% 30.15/10.11 | (3196) sum(n15, n10) = all_0_0_0
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 30.15/10.11 | (877) all_0_3_3 = n11
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (619) with n15, n10, all_0_0_0, n4 and discharging atoms sum(n15, n10) = all_0_0_0, sum(n15, n10) = n4, yields:
% 30.15/10.11 | (966) all_0_0_0 = n4
% 30.15/10.11 |
% 30.15/10.11 | From (877)(966) and (232) follows:
% 30.15/10.11 | (3199) sum(n11, n4) = all_0_6_6
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (619) with n11, n4, all_0_6_6, n15 and discharging atoms sum(n11, n4) = all_0_6_6, sum(n11, n4) = n15, yields:
% 30.15/10.11 | (747) all_0_6_6 = n15
% 30.15/10.11 |
% 30.15/10.11 | Equations (747) can reduce 456 to:
% 30.15/10.11 | (748) $false
% 30.15/10.11 |
% 30.15/10.11 |-The branch is then unsatisfiable
% 30.15/10.11 |-Branch two:
% 30.15/10.11 | (1186) ~ (all_0_7_7 = n15)
% 30.15/10.11 | (1187) all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.15/10.11 |
% 30.15/10.11 +-Applying beta-rule and splitting (1187), into two cases.
% 30.15/10.11 |-Branch one:
% 30.15/10.11 | (1188) all_0_7_7 = n14
% 30.15/10.11 |
% 30.15/10.11 | From (1188) and (683) follows:
% 30.15/10.11 | (1189) succ(n14) = all_0_5_5
% 30.15/10.11 |
% 30.15/10.11 | From (1188) and (8) follows:
% 30.15/10.11 | (1190) sum(n14, all_0_1_1) = all_0_0_0
% 30.15/10.11 |
% 30.15/10.11 | From (1188) and (3165) follows:
% 30.15/10.11 | (3207) sum(n17, n14) = all_0_2_2
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (388) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 30.15/10.11 | (1192) all_0_5_5 = n15
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (619) with n17, n14, all_0_2_2, n10 and discharging atoms sum(n17, n14) = all_0_2_2, sum(n17, n14) = n10, yields:
% 30.15/10.11 | (890) all_0_2_2 = n10
% 30.15/10.11 |
% 30.15/10.11 | From (890) and (473) follows:
% 30.15/10.11 | (892) pred(n10) = all_0_1_1
% 30.15/10.11 |
% 30.15/10.11 | From (1192) and (3164) follows:
% 30.15/10.11 | (3211) sum(n17, n15) = all_0_4_4
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 30.15/10.11 | (895) all_0_1_1 = n9
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (619) with n17, n15, all_0_4_4, n11 and discharging atoms sum(n17, n15) = all_0_4_4, sum(n17, n15) = n11, yields:
% 30.15/10.11 | (891) all_0_4_4 = n11
% 30.15/10.11 |
% 30.15/10.11 | From (891) and (716) follows:
% 30.15/10.11 | (893) pred(n11) = all_0_3_3
% 30.15/10.11 |
% 30.15/10.11 | From (895) and (1190) follows:
% 30.15/10.11 | (3215) sum(n14, n9) = all_0_0_0
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 30.15/10.11 | (894) all_0_3_3 = n10
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (619) with n14, n9, all_0_0_0, n2 and discharging atoms sum(n14, n9) = all_0_0_0, sum(n14, n9) = n2, yields:
% 30.15/10.11 | (1000) all_0_0_0 = n2
% 30.15/10.11 |
% 30.15/10.11 | From (894)(1000) and (232) follows:
% 30.15/10.11 | (3218) sum(n10, n2) = all_0_6_6
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (619) with n10, n2, all_0_6_6, n12 and discharging atoms sum(n10, n2) = all_0_6_6, sum(n10, n2) = n12, yields:
% 30.15/10.11 | (951) all_0_6_6 = n12
% 30.15/10.11 |
% 30.15/10.11 | Equations (951) can reduce 76 to:
% 30.15/10.11 | (748) $false
% 30.15/10.11 |
% 30.15/10.11 |-The branch is then unsatisfiable
% 30.15/10.11 |-Branch two:
% 30.15/10.11 | (1205) ~ (all_0_7_7 = n14)
% 30.15/10.11 | (1206) all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.15/10.11 |
% 30.15/10.11 +-Applying beta-rule and splitting (1206), into two cases.
% 30.15/10.11 |-Branch one:
% 30.15/10.11 | (1207) all_0_7_7 = n13
% 30.15/10.11 |
% 30.15/10.11 | From (1207) and (683) follows:
% 30.15/10.11 | (1208) succ(n13) = all_0_5_5
% 30.15/10.11 |
% 30.15/10.11 | From (1207) and (8) follows:
% 30.15/10.11 | (1209) sum(n13, all_0_1_1) = all_0_0_0
% 30.15/10.11 |
% 30.15/10.11 | From (1207) and (3165) follows:
% 30.15/10.11 | (3226) sum(n17, n13) = all_0_2_2
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (388) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 30.15/10.11 | (1211) all_0_5_5 = n14
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (619) with n17, n13, all_0_2_2, n9 and discharging atoms sum(n17, n13) = all_0_2_2, sum(n17, n13) = n9, yields:
% 30.15/10.11 | (907) all_0_2_2 = n9
% 30.15/10.11 |
% 30.15/10.11 | From (907) and (473) follows:
% 30.15/10.11 | (909) pred(n9) = all_0_1_1
% 30.15/10.11 |
% 30.15/10.11 | From (1211) and (3164) follows:
% 30.15/10.11 | (3230) sum(n17, n14) = all_0_4_4
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 30.15/10.11 | (912) all_0_1_1 = n8
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (619) with n17, n14, all_0_4_4, n10 and discharging atoms sum(n17, n14) = all_0_4_4, sum(n17, n14) = n10, yields:
% 30.15/10.11 | (908) all_0_4_4 = n10
% 30.15/10.11 |
% 30.15/10.11 | From (908) and (716) follows:
% 30.15/10.11 | (910) pred(n10) = all_0_3_3
% 30.15/10.11 |
% 30.15/10.11 | From (912) and (1209) follows:
% 30.15/10.11 | (3234) sum(n13, n8) = all_0_0_0
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 30.15/10.11 | (911) all_0_3_3 = n9
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (619) with n13, n8, all_0_0_0, n0 and discharging atoms sum(n13, n8) = all_0_0_0, sum(n13, n8) = n0, yields:
% 30.15/10.11 | (1034) all_0_0_0 = n0
% 30.15/10.11 |
% 30.15/10.11 | From (911)(1034) and (232) follows:
% 30.15/10.11 | (3237) sum(n9, n0) = all_0_6_6
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (619) with n9, n0, all_0_6_6, n9 and discharging atoms sum(n9, n0) = all_0_6_6, sum(n9, n0) = n9, yields:
% 30.15/10.11 | (798) all_0_6_6 = n9
% 30.15/10.11 |
% 30.15/10.11 | Equations (798) can reduce 593 to:
% 30.15/10.11 | (748) $false
% 30.15/10.11 |
% 30.15/10.11 |-The branch is then unsatisfiable
% 30.15/10.11 |-Branch two:
% 30.15/10.11 | (1224) ~ (all_0_7_7 = n13)
% 30.15/10.11 | (1225) all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.15/10.11 |
% 30.15/10.11 +-Applying beta-rule and splitting (1225), into two cases.
% 30.15/10.11 |-Branch one:
% 30.15/10.11 | (1226) all_0_7_7 = n12
% 30.15/10.11 |
% 30.15/10.11 | From (1226) and (683) follows:
% 30.15/10.11 | (1227) succ(n12) = all_0_5_5
% 30.15/10.11 |
% 30.15/10.11 | From (1226) and (8) follows:
% 30.15/10.11 | (1228) sum(n12, all_0_1_1) = all_0_0_0
% 30.15/10.11 |
% 30.15/10.11 | From (1226) and (3165) follows:
% 30.15/10.11 | (3245) sum(n17, n12) = all_0_2_2
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (388) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 30.15/10.11 | (1230) all_0_5_5 = n13
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (619) with n17, n12, all_0_2_2, n8 and discharging atoms sum(n17, n12) = all_0_2_2, sum(n17, n12) = n8, yields:
% 30.15/10.11 | (924) all_0_2_2 = n8
% 30.15/10.11 |
% 30.15/10.11 | From (924) and (473) follows:
% 30.15/10.11 | (926) pred(n8) = all_0_1_1
% 30.15/10.11 |
% 30.15/10.11 | From (1230) and (3164) follows:
% 30.15/10.11 | (3249) sum(n17, n13) = all_0_4_4
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 30.15/10.11 | (929) all_0_1_1 = n7
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (619) with n17, n13, all_0_4_4, n9 and discharging atoms sum(n17, n13) = all_0_4_4, sum(n17, n13) = n9, yields:
% 30.15/10.11 | (925) all_0_4_4 = n9
% 30.15/10.11 |
% 30.15/10.11 | From (925) and (716) follows:
% 30.15/10.11 | (927) pred(n9) = all_0_3_3
% 30.15/10.11 |
% 30.15/10.11 | From (929) and (1228) follows:
% 30.15/10.11 | (3253) sum(n12, n7) = all_0_0_0
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 30.15/10.11 | (928) all_0_3_3 = n8
% 30.15/10.11 |
% 30.15/10.11 | Instantiating formula (619) with n12, n7, all_0_0_0, n19 and discharging atoms sum(n12, n7) = all_0_0_0, sum(n12, n7) = n19, yields:
% 30.15/10.11 | (1068) all_0_0_0 = n19
% 30.15/10.11 |
% 30.15/10.11 | From (928)(1068) and (232) follows:
% 30.15/10.11 | (3256) sum(n8, n19) = all_0_6_6
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (619) with n8, n19, all_0_6_6, n6 and discharging atoms sum(n8, n19) = all_0_6_6, sum(n8, n19) = n6, yields:
% 30.15/10.12 | (1002) all_0_6_6 = n6
% 30.15/10.12 |
% 30.15/10.12 | Equations (1002) can reduce 498 to:
% 30.15/10.12 | (748) $false
% 30.15/10.12 |
% 30.15/10.12 |-The branch is then unsatisfiable
% 30.15/10.12 |-Branch two:
% 30.15/10.12 | (1243) ~ (all_0_7_7 = n12)
% 30.15/10.12 | (1244) all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.15/10.12 |
% 30.15/10.12 +-Applying beta-rule and splitting (1244), into two cases.
% 30.15/10.12 |-Branch one:
% 30.15/10.12 | (1245) all_0_7_7 = n11
% 30.15/10.12 |
% 30.15/10.12 | From (1245) and (683) follows:
% 30.15/10.12 | (1246) succ(n11) = all_0_5_5
% 30.15/10.12 |
% 30.15/10.12 | From (1245) and (8) follows:
% 30.15/10.12 | (1247) sum(n11, all_0_1_1) = all_0_0_0
% 30.15/10.12 |
% 30.15/10.12 | From (1245) and (3165) follows:
% 30.15/10.12 | (3264) sum(n17, n11) = all_0_2_2
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (388) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 30.15/10.12 | (1249) all_0_5_5 = n12
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (619) with n17, n11, all_0_2_2, n7 and discharging atoms sum(n17, n11) = all_0_2_2, sum(n17, n11) = n7, yields:
% 30.15/10.12 | (941) all_0_2_2 = n7
% 30.15/10.12 |
% 30.15/10.12 | From (941) and (473) follows:
% 30.15/10.12 | (943) pred(n7) = all_0_1_1
% 30.15/10.12 |
% 30.15/10.12 | From (1249) and (3164) follows:
% 30.15/10.12 | (3268) sum(n17, n12) = all_0_4_4
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 30.15/10.12 | (946) all_0_1_1 = n6
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (619) with n17, n12, all_0_4_4, n8 and discharging atoms sum(n17, n12) = all_0_4_4, sum(n17, n12) = n8, yields:
% 30.15/10.12 | (942) all_0_4_4 = n8
% 30.15/10.12 |
% 30.15/10.12 | From (942) and (716) follows:
% 30.15/10.12 | (944) pred(n8) = all_0_3_3
% 30.15/10.12 |
% 30.15/10.12 | From (946) and (1247) follows:
% 30.15/10.12 | (3272) sum(n11, n6) = all_0_0_0
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 30.15/10.12 | (945) all_0_3_3 = n7
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (619) with n11, n6, all_0_0_0, n17 and discharging atoms sum(n11, n6) = all_0_0_0, sum(n11, n6) = n17, yields:
% 30.15/10.12 | (745) all_0_0_0 = n17
% 30.15/10.12 |
% 30.15/10.12 | From (945)(745) and (232) follows:
% 30.15/10.12 | (3275) sum(n7, n17) = all_0_6_6
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (619) with n7, n17, all_0_6_6, n3 and discharging atoms sum(n7, n17) = all_0_6_6, sum(n7, n17) = n3, yields:
% 30.15/10.12 | (849) all_0_6_6 = n3
% 30.15/10.12 |
% 30.15/10.12 | Equations (849) can reduce 416 to:
% 30.15/10.12 | (748) $false
% 30.15/10.12 |
% 30.15/10.12 |-The branch is then unsatisfiable
% 30.15/10.12 |-Branch two:
% 30.15/10.12 | (1262) ~ (all_0_7_7 = n11)
% 30.15/10.12 | (1263) all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.15/10.12 |
% 30.15/10.12 +-Applying beta-rule and splitting (1263), into two cases.
% 30.15/10.12 |-Branch one:
% 30.15/10.12 | (1264) all_0_7_7 = n10
% 30.15/10.12 |
% 30.15/10.12 | From (1264) and (683) follows:
% 30.15/10.12 | (1265) succ(n10) = all_0_5_5
% 30.15/10.12 |
% 30.15/10.12 | From (1264) and (8) follows:
% 30.15/10.12 | (1266) sum(n10, all_0_1_1) = all_0_0_0
% 30.15/10.12 |
% 30.15/10.12 | From (1264) and (3165) follows:
% 30.15/10.12 | (3283) sum(n17, n10) = all_0_2_2
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (388) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 30.15/10.12 | (1268) all_0_5_5 = n11
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (619) with n17, n10, all_0_2_2, n6 and discharging atoms sum(n17, n10) = all_0_2_2, sum(n17, n10) = n6, yields:
% 30.15/10.12 | (958) all_0_2_2 = n6
% 30.15/10.12 |
% 30.15/10.12 | From (958) and (473) follows:
% 30.15/10.12 | (960) pred(n6) = all_0_1_1
% 30.15/10.12 |
% 30.15/10.12 | From (1268) and (3164) follows:
% 30.15/10.12 | (3287) sum(n17, n11) = all_0_4_4
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 30.15/10.12 | (963) all_0_1_1 = n5
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (619) with n17, n11, all_0_4_4, n7 and discharging atoms sum(n17, n11) = all_0_4_4, sum(n17, n11) = n7, yields:
% 30.15/10.12 | (959) all_0_4_4 = n7
% 30.15/10.12 |
% 30.15/10.12 | From (959) and (716) follows:
% 30.15/10.12 | (961) pred(n7) = all_0_3_3
% 30.15/10.12 |
% 30.15/10.12 | From (963) and (1266) follows:
% 30.15/10.12 | (3291) sum(n10, n5) = all_0_0_0
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 30.15/10.12 | (962) all_0_3_3 = n6
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (619) with n10, n5, all_0_0_0, n15 and discharging atoms sum(n10, n5) = all_0_0_0, sum(n10, n5) = n15, yields:
% 30.15/10.12 | (779) all_0_0_0 = n15
% 30.15/10.12 |
% 30.15/10.12 | From (962)(779) and (232) follows:
% 30.15/10.12 | (3294) sum(n6, n15) = all_0_6_6
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (619) with n6, n15, all_0_6_6, n0 and discharging atoms sum(n6, n15) = all_0_6_6, sum(n6, n15) = n0, yields:
% 30.15/10.12 | (1053) all_0_6_6 = n0
% 30.15/10.12 |
% 30.15/10.12 | Equations (1053) can reduce 676 to:
% 30.15/10.12 | (748) $false
% 30.15/10.12 |
% 30.15/10.12 |-The branch is then unsatisfiable
% 30.15/10.12 |-Branch two:
% 30.15/10.12 | (1281) ~ (all_0_7_7 = n10)
% 30.15/10.12 | (1282) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.15/10.12 |
% 30.15/10.12 +-Applying beta-rule and splitting (1282), into two cases.
% 30.15/10.12 |-Branch one:
% 30.15/10.12 | (1283) all_0_7_7 = n9
% 30.15/10.12 |
% 30.15/10.12 | From (1283) and (683) follows:
% 30.15/10.12 | (1284) succ(n9) = all_0_5_5
% 30.15/10.12 |
% 30.15/10.12 | From (1283) and (8) follows:
% 30.15/10.12 | (1285) sum(n9, all_0_1_1) = all_0_0_0
% 30.15/10.12 |
% 30.15/10.12 | From (1283) and (3165) follows:
% 30.15/10.12 | (3302) sum(n17, n9) = all_0_2_2
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (388) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 30.15/10.12 | (1287) all_0_5_5 = n10
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (619) with n17, n9, all_0_2_2, n5 and discharging atoms sum(n17, n9) = all_0_2_2, sum(n17, n9) = n5, yields:
% 30.15/10.12 | (975) all_0_2_2 = n5
% 30.15/10.12 |
% 30.15/10.12 | From (975) and (473) follows:
% 30.15/10.12 | (977) pred(n5) = all_0_1_1
% 30.15/10.12 |
% 30.15/10.12 | From (1287) and (3164) follows:
% 30.15/10.12 | (3306) sum(n17, n10) = all_0_4_4
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 30.15/10.12 | (980) all_0_1_1 = n4
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (619) with n17, n10, all_0_4_4, n6 and discharging atoms sum(n17, n10) = all_0_4_4, sum(n17, n10) = n6, yields:
% 30.15/10.12 | (976) all_0_4_4 = n6
% 30.15/10.12 |
% 30.15/10.12 | From (976) and (716) follows:
% 30.15/10.12 | (978) pred(n6) = all_0_3_3
% 30.15/10.12 |
% 30.15/10.12 | From (980) and (1285) follows:
% 30.15/10.12 | (3310) sum(n9, n4) = all_0_0_0
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 30.15/10.12 | (979) all_0_3_3 = n5
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (619) with n9, n4, all_0_0_0, n13 and discharging atoms sum(n9, n4) = all_0_0_0, sum(n9, n4) = n13, yields:
% 30.15/10.12 | (813) all_0_0_0 = n13
% 30.15/10.12 |
% 30.15/10.12 | From (979)(813) and (232) follows:
% 30.15/10.12 | (3313) sum(n5, n13) = all_0_6_6
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (619) with n5, n13, all_0_6_6, n18 and discharging atoms sum(n5, n13) = all_0_6_6, sum(n5, n13) = n18, yields:
% 30.15/10.12 | (900) all_0_6_6 = n18
% 30.15/10.12 |
% 30.15/10.12 | Equations (900) can reduce 622 to:
% 30.15/10.12 | (748) $false
% 30.15/10.12 |
% 30.15/10.12 |-The branch is then unsatisfiable
% 30.15/10.12 |-Branch two:
% 30.15/10.12 | (1300) ~ (all_0_7_7 = n9)
% 30.15/10.12 | (1301) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.15/10.12 |
% 30.15/10.12 +-Applying beta-rule and splitting (1301), into two cases.
% 30.15/10.12 |-Branch one:
% 30.15/10.12 | (1302) all_0_7_7 = n8
% 30.15/10.12 |
% 30.15/10.12 | From (1302) and (683) follows:
% 30.15/10.12 | (1303) succ(n8) = all_0_5_5
% 30.15/10.12 |
% 30.15/10.12 | From (1302) and (8) follows:
% 30.15/10.12 | (1304) sum(n8, all_0_1_1) = all_0_0_0
% 30.15/10.12 |
% 30.15/10.12 | From (1302) and (3165) follows:
% 30.15/10.12 | (3321) sum(n17, n8) = all_0_2_2
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (388) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 30.15/10.12 | (1306) all_0_5_5 = n9
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (619) with n17, n8, all_0_2_2, n4 and discharging atoms sum(n17, n8) = all_0_2_2, sum(n17, n8) = n4, yields:
% 30.15/10.12 | (992) all_0_2_2 = n4
% 30.15/10.12 |
% 30.15/10.12 | From (992) and (473) follows:
% 30.15/10.12 | (994) pred(n4) = all_0_1_1
% 30.15/10.12 |
% 30.15/10.12 | From (1306) and (3164) follows:
% 30.15/10.12 | (3325) sum(n17, n9) = all_0_4_4
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 30.15/10.12 | (997) all_0_1_1 = n3
% 30.15/10.12 |
% 30.15/10.12 | Instantiating formula (619) with n17, n9, all_0_4_4, n5 and discharging atoms sum(n17, n9) = all_0_4_4, sum(n17, n9) = n5, yields:
% 30.15/10.12 | (993) all_0_4_4 = n5
% 30.15/10.12 |
% 30.15/10.12 | From (993) and (716) follows:
% 30.15/10.12 | (995) pred(n5) = all_0_3_3
% 30.15/10.12 |
% 30.15/10.12 | From (997) and (1304) follows:
% 30.15/10.14 | (3329) sum(n8, n3) = all_0_0_0
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 30.15/10.14 | (996) all_0_3_3 = n4
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (619) with n8, n3, all_0_0_0, n11 and discharging atoms sum(n8, n3) = all_0_0_0, sum(n8, n3) = n11, yields:
% 30.15/10.14 | (847) all_0_0_0 = n11
% 30.15/10.14 |
% 30.15/10.14 | From (996)(847) and (232) follows:
% 30.15/10.14 | (3332) sum(n4, n11) = all_0_6_6
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (619) with n4, n11, all_0_6_6, n15 and discharging atoms sum(n4, n11) = all_0_6_6, sum(n4, n11) = n15, yields:
% 30.15/10.14 | (747) all_0_6_6 = n15
% 30.15/10.14 |
% 30.15/10.14 | Equations (747) can reduce 456 to:
% 30.15/10.14 | (748) $false
% 30.15/10.14 |
% 30.15/10.14 |-The branch is then unsatisfiable
% 30.15/10.14 |-Branch two:
% 30.15/10.14 | (1319) ~ (all_0_7_7 = n8)
% 30.15/10.14 | (1320) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.15/10.14 |
% 30.15/10.14 +-Applying beta-rule and splitting (1320), into two cases.
% 30.15/10.14 |-Branch one:
% 30.15/10.14 | (1321) all_0_7_7 = n7
% 30.15/10.14 |
% 30.15/10.14 | From (1321) and (683) follows:
% 30.15/10.14 | (1322) succ(n7) = all_0_5_5
% 30.15/10.14 |
% 30.15/10.14 | From (1321) and (8) follows:
% 30.15/10.14 | (1323) sum(n7, all_0_1_1) = all_0_0_0
% 30.15/10.14 |
% 30.15/10.14 | From (1321) and (3165) follows:
% 30.15/10.14 | (3340) sum(n17, n7) = all_0_2_2
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (388) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 30.15/10.14 | (1325) all_0_5_5 = n8
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (619) with n17, n7, all_0_2_2, n3 and discharging atoms sum(n17, n7) = all_0_2_2, sum(n17, n7) = n3, yields:
% 30.15/10.14 | (1009) all_0_2_2 = n3
% 30.15/10.14 |
% 30.15/10.14 | From (1009) and (473) follows:
% 30.15/10.14 | (1011) pred(n3) = all_0_1_1
% 30.15/10.14 |
% 30.15/10.14 | From (1325) and (3164) follows:
% 30.15/10.14 | (3344) sum(n17, n8) = all_0_4_4
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 30.15/10.14 | (1014) all_0_1_1 = n2
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (619) with n17, n8, all_0_4_4, n4 and discharging atoms sum(n17, n8) = all_0_4_4, sum(n17, n8) = n4, yields:
% 30.15/10.14 | (1010) all_0_4_4 = n4
% 30.15/10.14 |
% 30.15/10.14 | From (1010) and (716) follows:
% 30.15/10.14 | (1012) pred(n4) = all_0_3_3
% 30.15/10.14 |
% 30.15/10.14 | From (1014) and (1323) follows:
% 30.15/10.14 | (3348) sum(n7, n2) = all_0_0_0
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 30.15/10.14 | (1013) all_0_3_3 = n3
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (619) with n7, n2, all_0_0_0, n9 and discharging atoms sum(n7, n2) = all_0_0_0, sum(n7, n2) = n9, yields:
% 30.15/10.14 | (881) all_0_0_0 = n9
% 30.15/10.14 |
% 30.15/10.14 | From (1013)(881) and (232) follows:
% 30.15/10.14 | (3351) sum(n3, n9) = all_0_6_6
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (619) with n3, n9, all_0_6_6, n12 and discharging atoms sum(n3, n9) = all_0_6_6, sum(n3, n9) = n12, yields:
% 30.15/10.14 | (951) all_0_6_6 = n12
% 30.15/10.14 |
% 30.15/10.14 | Equations (951) can reduce 76 to:
% 30.15/10.14 | (748) $false
% 30.15/10.14 |
% 30.15/10.14 |-The branch is then unsatisfiable
% 30.15/10.14 |-Branch two:
% 30.15/10.14 | (1338) ~ (all_0_7_7 = n7)
% 30.15/10.14 | (1339) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.15/10.14 |
% 30.15/10.14 +-Applying beta-rule and splitting (1339), into two cases.
% 30.15/10.14 |-Branch one:
% 30.15/10.14 | (1340) all_0_7_7 = n6
% 30.15/10.14 |
% 30.15/10.14 | From (1340) and (683) follows:
% 30.15/10.14 | (1341) succ(n6) = all_0_5_5
% 30.15/10.14 |
% 30.15/10.14 | From (1340) and (8) follows:
% 30.15/10.14 | (1342) sum(n6, all_0_1_1) = all_0_0_0
% 30.15/10.14 |
% 30.15/10.14 | From (1340) and (3165) follows:
% 30.15/10.14 | (3359) sum(n17, n6) = all_0_2_2
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (388) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 30.15/10.14 | (1344) all_0_5_5 = n7
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (619) with n17, n6, all_0_2_2, n2 and discharging atoms sum(n17, n6) = all_0_2_2, sum(n17, n6) = n2, yields:
% 30.15/10.14 | (1026) all_0_2_2 = n2
% 30.15/10.14 |
% 30.15/10.14 | From (1026) and (473) follows:
% 30.15/10.14 | (1028) pred(n2) = all_0_1_1
% 30.15/10.14 |
% 30.15/10.14 | From (1344) and (3164) follows:
% 30.15/10.14 | (3363) sum(n17, n7) = all_0_4_4
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 30.15/10.14 | (1031) all_0_1_1 = n1
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (619) with n17, n7, all_0_4_4, n3 and discharging atoms sum(n17, n7) = all_0_4_4, sum(n17, n7) = n3, yields:
% 30.15/10.14 | (1027) all_0_4_4 = n3
% 30.15/10.14 |
% 30.15/10.14 | From (1027) and (716) follows:
% 30.15/10.14 | (1029) pred(n3) = all_0_3_3
% 30.15/10.14 |
% 30.15/10.14 | From (1031) and (1342) follows:
% 30.15/10.14 | (3367) sum(n6, n1) = all_0_0_0
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 30.15/10.14 | (1030) all_0_3_3 = n2
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (619) with n6, n1, all_0_0_0, n7 and discharging atoms sum(n6, n1) = all_0_0_0, sum(n6, n1) = n7, yields:
% 30.15/10.14 | (915) all_0_0_0 = n7
% 30.15/10.14 |
% 30.15/10.14 | From (1030)(915) and (232) follows:
% 30.15/10.14 | (3370) sum(n2, n7) = all_0_6_6
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (619) with n2, n7, all_0_6_6, n9 and discharging atoms sum(n2, n7) = all_0_6_6, sum(n2, n7) = n9, yields:
% 30.15/10.14 | (798) all_0_6_6 = n9
% 30.15/10.14 |
% 30.15/10.14 | Equations (798) can reduce 593 to:
% 30.15/10.14 | (748) $false
% 30.15/10.14 |
% 30.15/10.14 |-The branch is then unsatisfiable
% 30.15/10.14 |-Branch two:
% 30.15/10.14 | (1357) ~ (all_0_7_7 = n6)
% 30.15/10.14 | (1358) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.15/10.14 |
% 30.15/10.14 +-Applying beta-rule and splitting (1358), into two cases.
% 30.15/10.14 |-Branch one:
% 30.15/10.14 | (1359) all_0_7_7 = n5
% 30.15/10.14 |
% 30.15/10.14 | From (1359) and (683) follows:
% 30.15/10.14 | (1360) succ(n5) = all_0_5_5
% 30.15/10.14 |
% 30.15/10.14 | From (1359) and (8) follows:
% 30.15/10.14 | (1361) sum(n5, all_0_1_1) = all_0_0_0
% 30.15/10.14 |
% 30.15/10.14 | From (1359) and (3165) follows:
% 30.15/10.14 | (3378) sum(n17, n5) = all_0_2_2
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (388) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 30.15/10.14 | (1363) all_0_5_5 = n6
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (619) with n17, n5, all_0_2_2, n1 and discharging atoms sum(n17, n5) = all_0_2_2, sum(n17, n5) = n1, yields:
% 30.15/10.14 | (1043) all_0_2_2 = n1
% 30.15/10.14 |
% 30.15/10.14 | From (1043) and (473) follows:
% 30.15/10.14 | (1045) pred(n1) = all_0_1_1
% 30.15/10.14 |
% 30.15/10.14 | From (1363) and (3164) follows:
% 30.15/10.14 | (3382) sum(n17, n6) = all_0_4_4
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 30.15/10.14 | (1048) all_0_1_1 = n0
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (619) with n17, n6, all_0_4_4, n2 and discharging atoms sum(n17, n6) = all_0_4_4, sum(n17, n6) = n2, yields:
% 30.15/10.14 | (1044) all_0_4_4 = n2
% 30.15/10.14 |
% 30.15/10.14 | From (1044) and (716) follows:
% 30.15/10.14 | (1046) pred(n2) = all_0_3_3
% 30.15/10.14 |
% 30.15/10.14 | From (1048) and (1361) follows:
% 30.15/10.14 | (3386) sum(n5, n0) = all_0_0_0
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 30.15/10.14 | (1047) all_0_3_3 = n1
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (619) with n5, n0, all_0_0_0, n5 and discharging atoms sum(n5, n0) = all_0_0_0, sum(n5, n0) = n5, yields:
% 30.15/10.14 | (949) all_0_0_0 = n5
% 30.15/10.14 |
% 30.15/10.14 | From (1047)(949) and (232) follows:
% 30.15/10.14 | (3389) sum(n1, n5) = all_0_6_6
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (619) with n1, n5, all_0_6_6, n6 and discharging atoms sum(n1, n5) = all_0_6_6, sum(n1, n5) = n6, yields:
% 30.15/10.14 | (1002) all_0_6_6 = n6
% 30.15/10.14 |
% 30.15/10.14 | Equations (1002) can reduce 498 to:
% 30.15/10.14 | (748) $false
% 30.15/10.14 |
% 30.15/10.14 |-The branch is then unsatisfiable
% 30.15/10.14 |-Branch two:
% 30.15/10.14 | (1376) ~ (all_0_7_7 = n5)
% 30.15/10.14 | (1377) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.15/10.14 |
% 30.15/10.14 +-Applying beta-rule and splitting (1377), into two cases.
% 30.15/10.14 |-Branch one:
% 30.15/10.14 | (1378) all_0_7_7 = n4
% 30.15/10.14 |
% 30.15/10.14 | From (1378) and (683) follows:
% 30.15/10.14 | (1379) succ(n4) = all_0_5_5
% 30.15/10.14 |
% 30.15/10.14 | From (1378) and (8) follows:
% 30.15/10.14 | (1380) sum(n4, all_0_1_1) = all_0_0_0
% 30.15/10.14 |
% 30.15/10.14 | From (1378) and (3165) follows:
% 30.15/10.14 | (3397) sum(n17, n4) = all_0_2_2
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (388) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 30.15/10.14 | (1382) all_0_5_5 = n5
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (619) with n17, n4, all_0_2_2, n0 and discharging atoms sum(n17, n4) = all_0_2_2, sum(n17, n4) = n0, yields:
% 30.15/10.14 | (1060) all_0_2_2 = n0
% 30.15/10.14 |
% 30.15/10.14 | From (1060) and (473) follows:
% 30.15/10.14 | (1062) pred(n0) = all_0_1_1
% 30.15/10.14 |
% 30.15/10.14 | From (1382) and (3164) follows:
% 30.15/10.14 | (3401) sum(n17, n5) = all_0_4_4
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 30.15/10.14 | (1065) all_0_1_1 = n20
% 30.15/10.14 |
% 30.15/10.14 | Instantiating formula (619) with n17, n5, all_0_4_4, n1 and discharging atoms sum(n17, n5) = all_0_4_4, sum(n17, n5) = n1, yields:
% 30.15/10.14 | (1061) all_0_4_4 = n1
% 30.15/10.14 |
% 30.15/10.14 | From (1061) and (716) follows:
% 30.15/10.14 | (1063) pred(n1) = all_0_3_3
% 30.15/10.14 |
% 30.15/10.14 | From (1065) and (1380) follows:
% 30.15/10.15 | (3405) sum(n4, n20) = all_0_0_0
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 30.15/10.15 | (1064) all_0_3_3 = n0
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n4, n20, all_0_0_0, n3 and discharging atoms sum(n4, n20) = all_0_0_0, sum(n4, n20) = n3, yields:
% 30.15/10.15 | (983) all_0_0_0 = n3
% 30.15/10.15 |
% 30.15/10.15 | From (1064)(983) and (232) follows:
% 30.15/10.15 | (3408) sum(n0, n3) = all_0_6_6
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n0, n3, all_0_6_6, n3 and discharging atoms sum(n0, n3) = all_0_6_6, sum(n0, n3) = n3, yields:
% 30.15/10.15 | (849) all_0_6_6 = n3
% 30.15/10.15 |
% 30.15/10.15 | Equations (849) can reduce 416 to:
% 30.15/10.15 | (748) $false
% 30.15/10.15 |
% 30.15/10.15 |-The branch is then unsatisfiable
% 30.15/10.15 |-Branch two:
% 30.15/10.15 | (1395) ~ (all_0_7_7 = n4)
% 30.15/10.15 | (1396) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.15/10.15 |
% 30.15/10.15 +-Applying beta-rule and splitting (1396), into two cases.
% 30.15/10.15 |-Branch one:
% 30.15/10.15 | (1397) all_0_7_7 = n3
% 30.15/10.15 |
% 30.15/10.15 | From (1397) and (683) follows:
% 30.15/10.15 | (1398) succ(n3) = all_0_5_5
% 30.15/10.15 |
% 30.15/10.15 | From (1397) and (8) follows:
% 30.15/10.15 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 30.15/10.15 |
% 30.15/10.15 | From (1397) and (3165) follows:
% 30.15/10.15 | (3416) sum(n17, n3) = all_0_2_2
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 30.15/10.15 | (1401) all_0_5_5 = n4
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n17, n3, all_0_2_2, n20 and discharging atoms sum(n17, n3) = all_0_2_2, sum(n17, n3) = n20, yields:
% 30.15/10.15 | (1076) all_0_2_2 = n20
% 30.15/10.15 |
% 30.15/10.15 | From (1076) and (473) follows:
% 30.15/10.15 | (1078) pred(n20) = all_0_1_1
% 30.15/10.15 |
% 30.15/10.15 | From (1401) and (3164) follows:
% 30.15/10.15 | (3420) sum(n17, n4) = all_0_4_4
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 30.15/10.15 | (1080) all_0_1_1 = n19
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n17, n4, all_0_4_4, n0 and discharging atoms sum(n17, n4) = all_0_4_4, sum(n17, n4) = n0, yields:
% 30.15/10.15 | (1077) all_0_4_4 = n0
% 30.15/10.15 |
% 30.15/10.15 | From (1077) and (716) follows:
% 30.15/10.15 | (1079) pred(n0) = all_0_3_3
% 30.15/10.15 |
% 30.15/10.15 | From (1080) and (1399) follows:
% 30.15/10.15 | (3424) sum(n3, n19) = all_0_0_0
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 30.15/10.15 | (1081) all_0_3_3 = n20
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n3, n19, all_0_0_0, n1 and discharging atoms sum(n3, n19) = all_0_0_0, sum(n3, n19) = n1, yields:
% 30.15/10.15 | (1017) all_0_0_0 = n1
% 30.15/10.15 |
% 30.15/10.15 | From (1081)(1017) and (232) follows:
% 30.15/10.15 | (3427) sum(n20, n1) = all_0_6_6
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n20, n1, all_0_6_6, n0 and discharging atoms sum(n20, n1) = all_0_6_6, sum(n20, n1) = n0, yields:
% 30.15/10.15 | (1053) all_0_6_6 = n0
% 30.15/10.15 |
% 30.15/10.15 | Equations (1053) can reduce 676 to:
% 30.15/10.15 | (748) $false
% 30.15/10.15 |
% 30.15/10.15 |-The branch is then unsatisfiable
% 30.15/10.15 |-Branch two:
% 30.15/10.15 | (1414) ~ (all_0_7_7 = n3)
% 30.15/10.15 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.15/10.15 |
% 30.15/10.15 +-Applying beta-rule and splitting (1415), into two cases.
% 30.15/10.15 |-Branch one:
% 30.15/10.15 | (1416) all_0_7_7 = n2
% 30.15/10.15 |
% 30.15/10.15 | From (1416) and (683) follows:
% 30.15/10.15 | (1417) succ(n2) = all_0_5_5
% 30.15/10.15 |
% 30.15/10.15 | From (1416) and (8) follows:
% 30.15/10.15 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 30.15/10.15 |
% 30.15/10.15 | From (1416) and (3165) follows:
% 30.15/10.15 | (3435) sum(n17, n2) = all_0_2_2
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 30.15/10.15 | (1420) all_0_5_5 = n3
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n17, n2, all_0_2_2, n19 and discharging atoms sum(n17, n2) = all_0_2_2, sum(n17, n2) = n19, yields:
% 30.15/10.15 | (737) all_0_2_2 = n19
% 30.15/10.15 |
% 30.15/10.15 | From (737) and (473) follows:
% 30.15/10.15 | (739) pred(n19) = all_0_1_1
% 30.15/10.15 |
% 30.15/10.15 | From (1420) and (3164) follows:
% 30.15/10.15 | (3439) sum(n17, n3) = all_0_4_4
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 30.15/10.15 | (742) all_0_1_1 = n18
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n17, n3, all_0_4_4, n20 and discharging atoms sum(n17, n3) = all_0_4_4, sum(n17, n3) = n20, yields:
% 30.15/10.15 | (738) all_0_4_4 = n20
% 30.15/10.15 |
% 30.15/10.15 | From (738) and (716) follows:
% 30.15/10.15 | (740) pred(n20) = all_0_3_3
% 30.15/10.15 |
% 30.15/10.15 | From (742) and (1418) follows:
% 30.15/10.15 | (3443) sum(n2, n18) = all_0_0_0
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 30.15/10.15 | (741) all_0_3_3 = n19
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n2, n18, all_0_0_0, n20 and discharging atoms sum(n2, n18) = all_0_0_0, sum(n2, n18) = n20, yields:
% 30.15/10.15 | (1051) all_0_0_0 = n20
% 30.15/10.15 |
% 30.15/10.15 | From (741)(1051) and (232) follows:
% 30.15/10.15 | (3446) sum(n19, n20) = all_0_6_6
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n19, n20, all_0_6_6, n18 and discharging atoms sum(n19, n20) = all_0_6_6, sum(n19, n20) = n18, yields:
% 30.15/10.15 | (900) all_0_6_6 = n18
% 30.15/10.15 |
% 30.15/10.15 | Equations (900) can reduce 622 to:
% 30.15/10.15 | (748) $false
% 30.15/10.15 |
% 30.15/10.15 |-The branch is then unsatisfiable
% 30.15/10.15 |-Branch two:
% 30.15/10.15 | (1433) ~ (all_0_7_7 = n2)
% 30.15/10.15 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 30.15/10.15 |
% 30.15/10.15 +-Applying beta-rule and splitting (1434), into two cases.
% 30.15/10.15 |-Branch one:
% 30.15/10.15 | (1435) all_0_7_7 = n1
% 30.15/10.15 |
% 30.15/10.15 | From (1435) and (683) follows:
% 30.15/10.15 | (1436) succ(n1) = all_0_5_5
% 30.15/10.15 |
% 30.15/10.15 | From (1435) and (8) follows:
% 30.15/10.15 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 30.15/10.15 |
% 30.15/10.15 | From (1435) and (3165) follows:
% 30.15/10.15 | (3454) sum(n17, n1) = all_0_2_2
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 30.15/10.15 | (1439) all_0_5_5 = n2
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n17, n1, all_0_2_2, n18 and discharging atoms sum(n17, n1) = all_0_2_2, sum(n17, n1) = n18, yields:
% 30.15/10.15 | (754) all_0_2_2 = n18
% 30.15/10.15 |
% 30.15/10.15 | From (754) and (473) follows:
% 30.15/10.15 | (756) pred(n18) = all_0_1_1
% 30.15/10.15 |
% 30.15/10.15 | From (1439) and (3164) follows:
% 30.15/10.15 | (3458) sum(n17, n2) = all_0_4_4
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 30.15/10.15 | (759) all_0_1_1 = n17
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n17, n2, all_0_4_4, n19 and discharging atoms sum(n17, n2) = all_0_4_4, sum(n17, n2) = n19, yields:
% 30.15/10.15 | (755) all_0_4_4 = n19
% 30.15/10.15 |
% 30.15/10.15 | From (755) and (716) follows:
% 30.15/10.15 | (757) pred(n19) = all_0_3_3
% 30.15/10.15 |
% 30.15/10.15 | From (759) and (1437) follows:
% 30.15/10.15 | (3462) sum(n1, n17) = all_0_0_0
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 30.15/10.15 | (758) all_0_3_3 = n18
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n1, n17, all_0_0_0, n18 and discharging atoms sum(n1, n17) = all_0_0_0, sum(n1, n17) = n18, yields:
% 30.15/10.15 | (1084) all_0_0_0 = n18
% 30.15/10.15 |
% 30.15/10.15 | From (758)(1084) and (232) follows:
% 30.15/10.15 | (3465) sum(n18, n18) = all_0_6_6
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n18, n18, all_0_6_6, n15 and discharging atoms sum(n18, n18) = all_0_6_6, sum(n18, n18) = n15, yields:
% 30.15/10.15 | (747) all_0_6_6 = n15
% 30.15/10.15 |
% 30.15/10.15 | Equations (747) can reduce 456 to:
% 30.15/10.15 | (748) $false
% 30.15/10.15 |
% 30.15/10.15 |-The branch is then unsatisfiable
% 30.15/10.15 |-Branch two:
% 30.15/10.15 | (1452) ~ (all_0_7_7 = n1)
% 30.15/10.15 | (1453) all_0_7_7 = n0
% 30.15/10.15 |
% 30.15/10.15 | From (1453) and (683) follows:
% 30.15/10.15 | (1454) succ(n0) = all_0_5_5
% 30.15/10.15 |
% 30.15/10.15 | From (1453) and (8) follows:
% 30.15/10.15 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 30.15/10.15 |
% 30.15/10.15 | From (1453) and (3165) follows:
% 30.15/10.15 | (3472) sum(n17, n0) = all_0_2_2
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 30.15/10.15 | (1457) all_0_5_5 = n1
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n17, n0, all_0_2_2, n17 and discharging atoms sum(n17, n0) = all_0_2_2, sum(n17, n0) = n17, yields:
% 30.15/10.15 | (771) all_0_2_2 = n17
% 30.15/10.15 |
% 30.15/10.15 | From (771) and (473) follows:
% 30.15/10.15 | (773) pred(n17) = all_0_1_1
% 30.15/10.15 |
% 30.15/10.15 | From (1457) and (3164) follows:
% 30.15/10.15 | (3476) sum(n17, n1) = all_0_4_4
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 30.15/10.15 | (776) all_0_1_1 = n16
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n17, n1, all_0_4_4, n18 and discharging atoms sum(n17, n1) = all_0_4_4, sum(n17, n1) = n18, yields:
% 30.15/10.15 | (772) all_0_4_4 = n18
% 30.15/10.15 |
% 30.15/10.15 | From (772) and (716) follows:
% 30.15/10.15 | (774) pred(n18) = all_0_3_3
% 30.15/10.15 |
% 30.15/10.15 | From (776) and (1455) follows:
% 30.15/10.15 | (3480) sum(n0, n16) = all_0_0_0
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 30.15/10.15 | (775) all_0_3_3 = n17
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n0, n16, all_0_0_0, n16 and discharging atoms sum(n0, n16) = all_0_0_0, sum(n0, n16) = n16, yields:
% 30.15/10.15 | (762) all_0_0_0 = n16
% 30.15/10.15 |
% 30.15/10.15 | From (775)(762) and (232) follows:
% 30.15/10.15 | (3483) sum(n17, n16) = all_0_6_6
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n17, n16, all_0_6_6, n12 and discharging atoms sum(n17, n16) = all_0_6_6, sum(n17, n16) = n12, yields:
% 30.15/10.15 | (951) all_0_6_6 = n12
% 30.15/10.15 |
% 30.15/10.15 | Equations (951) can reduce 76 to:
% 30.15/10.15 | (748) $false
% 30.15/10.15 |
% 30.15/10.15 |-The branch is then unsatisfiable
% 30.15/10.15 |-Branch two:
% 30.15/10.15 | (800) ~ (all_0_8_8 = n17)
% 30.15/10.15 | (801) all_0_8_8 = n16 | all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.15/10.15 |
% 30.15/10.15 +-Applying beta-rule and splitting (1149), into two cases.
% 30.15/10.15 |-Branch one:
% 30.15/10.15 | (1150) all_0_7_7 = n16
% 30.15/10.15 |
% 30.15/10.15 | From (1150) and (683) follows:
% 30.15/10.15 | (1151) succ(n16) = all_0_5_5
% 30.15/10.15 |
% 30.15/10.15 | From (1150) and (8) follows:
% 30.15/10.15 | (1152) sum(n16, all_0_1_1) = all_0_0_0
% 30.15/10.15 |
% 30.15/10.15 | From (1150) and (378) follows:
% 30.15/10.15 | (3491) sum(all_0_8_8, n16) = all_0_2_2
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (388) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 30.15/10.15 | (1154) all_0_5_5 = n17
% 30.15/10.15 |
% 30.15/10.15 | From (1154) and (708) follows:
% 30.15/10.15 | (3493) sum(all_0_8_8, n17) = all_0_4_4
% 30.15/10.15 |
% 30.15/10.15 +-Applying beta-rule and splitting (801), into two cases.
% 30.15/10.15 |-Branch one:
% 30.15/10.15 | (802) all_0_8_8 = n16
% 30.15/10.15 |
% 30.15/10.15 | From (802) and (3493) follows:
% 30.15/10.15 | (3495) sum(n16, n17) = all_0_4_4
% 30.15/10.15 |
% 30.15/10.15 | From (802) and (3491) follows:
% 30.15/10.15 | (3496) sum(n16, n16) = all_0_2_2
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n16, n17, all_0_4_4, n12 and discharging atoms sum(n16, n17) = all_0_4_4, sum(n16, n17) = n12, yields:
% 30.15/10.15 | (874) all_0_4_4 = n12
% 30.15/10.15 |
% 30.15/10.15 | Instantiating formula (619) with n16, n16, all_0_2_2, n11 and discharging atoms sum(n16, n16) = all_0_2_2, sum(n16, n16) = n11, yields:
% 30.15/10.15 | (873) all_0_2_2 = n11
% 30.15/10.15 |
% 30.15/10.15 | From (873) and (473) follows:
% 30.15/10.15 | (875) pred(n11) = all_0_1_1
% 30.15/10.15 |
% 30.15/10.15 | From (874) and (716) follows:
% 30.15/10.16 | (876) pred(n12) = all_0_3_3
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 30.15/10.16 | (877) all_0_3_3 = n11
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 30.15/10.16 | (878) all_0_1_1 = n10
% 30.15/10.16 |
% 30.15/10.16 | From (877) and (232) follows:
% 30.15/10.16 | (879) sum(n11, all_0_0_0) = all_0_6_6
% 30.15/10.16 |
% 30.15/10.16 | From (878) and (1152) follows:
% 30.15/10.16 | (3504) sum(n16, n10) = all_0_0_0
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n16, n10, all_0_0_0, n5 and discharging atoms sum(n16, n10) = all_0_0_0, sum(n16, n10) = n5, yields:
% 30.15/10.16 | (949) all_0_0_0 = n5
% 30.15/10.16 |
% 30.15/10.16 | From (949) and (879) follows:
% 30.15/10.16 | (3506) sum(n11, n5) = all_0_6_6
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n11, n5, all_0_6_6, n16 and discharging atoms sum(n11, n5) = all_0_6_6, sum(n11, n5) = n16, yields:
% 30.15/10.16 | (917) all_0_6_6 = n16
% 30.15/10.16 |
% 30.15/10.16 | Equations (917) can reduce 163 to:
% 30.15/10.16 | (748) $false
% 30.15/10.16 |
% 30.15/10.16 |-The branch is then unsatisfiable
% 30.15/10.16 |-Branch two:
% 30.15/10.16 | (817) ~ (all_0_8_8 = n16)
% 30.15/10.16 | (818) all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.15/10.16 |
% 30.15/10.16 +-Applying beta-rule and splitting (818), into two cases.
% 30.15/10.16 |-Branch one:
% 30.15/10.16 | (819) all_0_8_8 = n15
% 30.15/10.16 |
% 30.15/10.16 | From (819) and (3493) follows:
% 30.15/10.16 | (3512) sum(n15, n17) = all_0_4_4
% 30.15/10.16 |
% 30.15/10.16 | From (819) and (3491) follows:
% 30.15/10.16 | (3513) sum(n15, n16) = all_0_2_2
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n15, n17, all_0_4_4, n11 and discharging atoms sum(n15, n17) = all_0_4_4, sum(n15, n17) = n11, yields:
% 30.15/10.16 | (891) all_0_4_4 = n11
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n15, n16, all_0_2_2, n10 and discharging atoms sum(n15, n16) = all_0_2_2, sum(n15, n16) = n10, yields:
% 30.15/10.16 | (890) all_0_2_2 = n10
% 30.15/10.16 |
% 30.15/10.16 | From (890) and (473) follows:
% 30.15/10.16 | (892) pred(n10) = all_0_1_1
% 30.15/10.16 |
% 30.15/10.16 | From (891) and (716) follows:
% 30.15/10.16 | (893) pred(n11) = all_0_3_3
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 30.15/10.16 | (894) all_0_3_3 = n10
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 30.15/10.16 | (895) all_0_1_1 = n9
% 30.15/10.16 |
% 30.15/10.16 | From (894) and (232) follows:
% 30.15/10.16 | (896) sum(n10, all_0_0_0) = all_0_6_6
% 30.15/10.16 |
% 30.15/10.16 | From (895) and (1152) follows:
% 30.15/10.16 | (3521) sum(n16, n9) = all_0_0_0
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n16, n9, all_0_0_0, n4 and discharging atoms sum(n16, n9) = all_0_0_0, sum(n16, n9) = n4, yields:
% 30.15/10.16 | (966) all_0_0_0 = n4
% 30.15/10.16 |
% 30.15/10.16 | From (966) and (896) follows:
% 30.15/10.16 | (3523) sum(n10, n4) = all_0_6_6
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n10, n4, all_0_6_6, n14 and discharging atoms sum(n10, n4) = all_0_6_6, sum(n10, n4) = n14, yields:
% 30.15/10.16 | (934) all_0_6_6 = n14
% 30.15/10.16 |
% 30.15/10.16 | Equations (934) can reduce 353 to:
% 30.15/10.16 | (748) $false
% 30.15/10.16 |
% 30.15/10.16 |-The branch is then unsatisfiable
% 30.15/10.16 |-Branch two:
% 30.15/10.16 | (834) ~ (all_0_8_8 = n15)
% 30.15/10.16 | (835) all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.15/10.16 |
% 30.15/10.16 +-Applying beta-rule and splitting (835), into two cases.
% 30.15/10.16 |-Branch one:
% 30.15/10.16 | (836) all_0_8_8 = n14
% 30.15/10.16 |
% 30.15/10.16 | From (836) and (3493) follows:
% 30.15/10.16 | (3529) sum(n14, n17) = all_0_4_4
% 30.15/10.16 |
% 30.15/10.16 | From (836) and (3491) follows:
% 30.15/10.16 | (3530) sum(n14, n16) = all_0_2_2
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n14, n17, all_0_4_4, n10 and discharging atoms sum(n14, n17) = all_0_4_4, sum(n14, n17) = n10, yields:
% 30.15/10.16 | (908) all_0_4_4 = n10
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n14, n16, all_0_2_2, n9 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n9, yields:
% 30.15/10.16 | (907) all_0_2_2 = n9
% 30.15/10.16 |
% 30.15/10.16 | From (907) and (473) follows:
% 30.15/10.16 | (909) pred(n9) = all_0_1_1
% 30.15/10.16 |
% 30.15/10.16 | From (908) and (716) follows:
% 30.15/10.16 | (910) pred(n10) = all_0_3_3
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 30.15/10.16 | (911) all_0_3_3 = n9
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 30.15/10.16 | (912) all_0_1_1 = n8
% 30.15/10.16 |
% 30.15/10.16 | From (911) and (232) follows:
% 30.15/10.16 | (913) sum(n9, all_0_0_0) = all_0_6_6
% 30.15/10.16 |
% 30.15/10.16 | From (912) and (1152) follows:
% 30.15/10.16 | (3538) sum(n16, n8) = all_0_0_0
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n16, n8, all_0_0_0, n3 and discharging atoms sum(n16, n8) = all_0_0_0, sum(n16, n8) = n3, yields:
% 30.15/10.16 | (983) all_0_0_0 = n3
% 30.15/10.16 |
% 30.15/10.16 | From (983) and (913) follows:
% 30.15/10.16 | (3540) sum(n9, n3) = all_0_6_6
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n9, n3, all_0_6_6, n12 and discharging atoms sum(n9, n3) = all_0_6_6, sum(n9, n3) = n12, yields:
% 30.15/10.16 | (951) all_0_6_6 = n12
% 30.15/10.16 |
% 30.15/10.16 | Equations (951) can reduce 76 to:
% 30.15/10.16 | (748) $false
% 30.15/10.16 |
% 30.15/10.16 |-The branch is then unsatisfiable
% 30.15/10.16 |-Branch two:
% 30.15/10.16 | (851) ~ (all_0_8_8 = n14)
% 30.15/10.16 | (852) all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.15/10.16 |
% 30.15/10.16 +-Applying beta-rule and splitting (852), into two cases.
% 30.15/10.16 |-Branch one:
% 30.15/10.16 | (853) all_0_8_8 = n13
% 30.15/10.16 |
% 30.15/10.16 | From (853) and (3493) follows:
% 30.15/10.16 | (3546) sum(n13, n17) = all_0_4_4
% 30.15/10.16 |
% 30.15/10.16 | From (853) and (3491) follows:
% 30.15/10.16 | (3547) sum(n13, n16) = all_0_2_2
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n13, n17, all_0_4_4, n9 and discharging atoms sum(n13, n17) = all_0_4_4, sum(n13, n17) = n9, yields:
% 30.15/10.16 | (925) all_0_4_4 = n9
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n13, n16, all_0_2_2, n8 and discharging atoms sum(n13, n16) = all_0_2_2, sum(n13, n16) = n8, yields:
% 30.15/10.16 | (924) all_0_2_2 = n8
% 30.15/10.16 |
% 30.15/10.16 | From (924) and (473) follows:
% 30.15/10.16 | (926) pred(n8) = all_0_1_1
% 30.15/10.16 |
% 30.15/10.16 | From (925) and (716) follows:
% 30.15/10.16 | (927) pred(n9) = all_0_3_3
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 30.15/10.16 | (928) all_0_3_3 = n8
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 30.15/10.16 | (929) all_0_1_1 = n7
% 30.15/10.16 |
% 30.15/10.16 | From (928) and (232) follows:
% 30.15/10.16 | (930) sum(n8, all_0_0_0) = all_0_6_6
% 30.15/10.16 |
% 30.15/10.16 | From (929) and (1152) follows:
% 30.15/10.16 | (3555) sum(n16, n7) = all_0_0_0
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n16, n7, all_0_0_0, n2 and discharging atoms sum(n16, n7) = all_0_0_0, sum(n16, n7) = n2, yields:
% 30.15/10.16 | (1000) all_0_0_0 = n2
% 30.15/10.16 |
% 30.15/10.16 | From (1000) and (930) follows:
% 30.15/10.16 | (3557) sum(n8, n2) = all_0_6_6
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n8, n2, all_0_6_6, n10 and discharging atoms sum(n8, n2) = all_0_6_6, sum(n8, n2) = n10, yields:
% 30.15/10.16 | (968) all_0_6_6 = n10
% 30.15/10.16 |
% 30.15/10.16 | Equations (968) can reduce 176 to:
% 30.15/10.16 | (748) $false
% 30.15/10.16 |
% 30.15/10.16 |-The branch is then unsatisfiable
% 30.15/10.16 |-Branch two:
% 30.15/10.16 | (868) ~ (all_0_8_8 = n13)
% 30.15/10.16 | (869) all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.15/10.16 |
% 30.15/10.16 +-Applying beta-rule and splitting (869), into two cases.
% 30.15/10.16 |-Branch one:
% 30.15/10.16 | (870) all_0_8_8 = n12
% 30.15/10.16 |
% 30.15/10.16 | From (870) and (3493) follows:
% 30.15/10.16 | (3563) sum(n12, n17) = all_0_4_4
% 30.15/10.16 |
% 30.15/10.16 | From (870) and (3491) follows:
% 30.15/10.16 | (3564) sum(n12, n16) = all_0_2_2
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n12, n17, all_0_4_4, n8 and discharging atoms sum(n12, n17) = all_0_4_4, sum(n12, n17) = n8, yields:
% 30.15/10.16 | (942) all_0_4_4 = n8
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n12, n16, all_0_2_2, n7 and discharging atoms sum(n12, n16) = all_0_2_2, sum(n12, n16) = n7, yields:
% 30.15/10.16 | (941) all_0_2_2 = n7
% 30.15/10.16 |
% 30.15/10.16 | From (941) and (473) follows:
% 30.15/10.16 | (943) pred(n7) = all_0_1_1
% 30.15/10.16 |
% 30.15/10.16 | From (942) and (716) follows:
% 30.15/10.16 | (944) pred(n8) = all_0_3_3
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 30.15/10.16 | (945) all_0_3_3 = n7
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 30.15/10.16 | (946) all_0_1_1 = n6
% 30.15/10.16 |
% 30.15/10.16 | From (945) and (232) follows:
% 30.15/10.16 | (947) sum(n7, all_0_0_0) = all_0_6_6
% 30.15/10.16 |
% 30.15/10.16 | From (946) and (1152) follows:
% 30.15/10.16 | (3572) sum(n16, n6) = all_0_0_0
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n16, n6, all_0_0_0, n1 and discharging atoms sum(n16, n6) = all_0_0_0, sum(n16, n6) = n1, yields:
% 30.15/10.16 | (1017) all_0_0_0 = n1
% 30.15/10.16 |
% 30.15/10.16 | From (1017) and (947) follows:
% 30.15/10.16 | (3574) sum(n7, n1) = all_0_6_6
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n7, n1, all_0_6_6, n8 and discharging atoms sum(n7, n1) = all_0_6_6, sum(n7, n1) = n8, yields:
% 30.15/10.16 | (985) all_0_6_6 = n8
% 30.15/10.16 |
% 30.15/10.16 | Equations (985) can reduce 357 to:
% 30.15/10.16 | (748) $false
% 30.15/10.16 |
% 30.15/10.16 |-The branch is then unsatisfiable
% 30.15/10.16 |-Branch two:
% 30.15/10.16 | (885) ~ (all_0_8_8 = n12)
% 30.15/10.16 | (886) all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.15/10.16 |
% 30.15/10.16 +-Applying beta-rule and splitting (886), into two cases.
% 30.15/10.16 |-Branch one:
% 30.15/10.16 | (887) all_0_8_8 = n11
% 30.15/10.16 |
% 30.15/10.16 | From (887) and (3493) follows:
% 30.15/10.16 | (3580) sum(n11, n17) = all_0_4_4
% 30.15/10.16 |
% 30.15/10.16 | From (887) and (3491) follows:
% 30.15/10.16 | (3581) sum(n11, n16) = all_0_2_2
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n11, n17, all_0_4_4, n7 and discharging atoms sum(n11, n17) = all_0_4_4, sum(n11, n17) = n7, yields:
% 30.15/10.16 | (959) all_0_4_4 = n7
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n11, n16, all_0_2_2, n6 and discharging atoms sum(n11, n16) = all_0_2_2, sum(n11, n16) = n6, yields:
% 30.15/10.16 | (958) all_0_2_2 = n6
% 30.15/10.16 |
% 30.15/10.16 | From (958) and (473) follows:
% 30.15/10.16 | (960) pred(n6) = all_0_1_1
% 30.15/10.16 |
% 30.15/10.16 | From (959) and (716) follows:
% 30.15/10.16 | (961) pred(n7) = all_0_3_3
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 30.15/10.16 | (962) all_0_3_3 = n6
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 30.15/10.16 | (963) all_0_1_1 = n5
% 30.15/10.16 |
% 30.15/10.16 | From (962) and (232) follows:
% 30.15/10.16 | (964) sum(n6, all_0_0_0) = all_0_6_6
% 30.15/10.16 |
% 30.15/10.16 | From (963) and (1152) follows:
% 30.15/10.16 | (3589) sum(n16, n5) = all_0_0_0
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n16, n5, all_0_0_0, n0 and discharging atoms sum(n16, n5) = all_0_0_0, sum(n16, n5) = n0, yields:
% 30.15/10.16 | (1034) all_0_0_0 = n0
% 30.15/10.16 |
% 30.15/10.16 | From (1034) and (964) follows:
% 30.15/10.16 | (3591) sum(n6, n0) = all_0_6_6
% 30.15/10.16 |
% 30.15/10.16 | Instantiating formula (619) with n6, n0, all_0_6_6, n6 and discharging atoms sum(n6, n0) = all_0_6_6, sum(n6, n0) = n6, yields:
% 30.15/10.16 | (1002) all_0_6_6 = n6
% 30.15/10.16 |
% 30.15/10.16 | Equations (1002) can reduce 498 to:
% 30.15/10.16 | (748) $false
% 30.15/10.16 |
% 30.15/10.16 |-The branch is then unsatisfiable
% 30.15/10.16 |-Branch two:
% 30.15/10.16 | (902) ~ (all_0_8_8 = n11)
% 30.15/10.16 | (903) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.15/10.16 |
% 30.15/10.16 +-Applying beta-rule and splitting (903), into two cases.
% 30.15/10.16 |-Branch one:
% 30.15/10.16 | (904) all_0_8_8 = n10
% 30.15/10.16 |
% 30.15/10.16 | From (904) and (3493) follows:
% 30.15/10.16 | (3597) sum(n10, n17) = all_0_4_4
% 30.15/10.16 |
% 30.15/10.16 | From (904) and (3491) follows:
% 30.15/10.17 | (3598) sum(n10, n16) = all_0_2_2
% 30.15/10.17 |
% 30.15/10.17 | Instantiating formula (619) with n10, n17, all_0_4_4, n6 and discharging atoms sum(n10, n17) = all_0_4_4, sum(n10, n17) = n6, yields:
% 30.15/10.17 | (976) all_0_4_4 = n6
% 30.15/10.17 |
% 30.15/10.17 | Instantiating formula (619) with n10, n16, all_0_2_2, n5 and discharging atoms sum(n10, n16) = all_0_2_2, sum(n10, n16) = n5, yields:
% 30.15/10.17 | (975) all_0_2_2 = n5
% 30.15/10.17 |
% 30.15/10.17 | From (975) and (473) follows:
% 30.15/10.17 | (977) pred(n5) = all_0_1_1
% 30.15/10.17 |
% 30.15/10.17 | From (976) and (716) follows:
% 30.15/10.17 | (978) pred(n6) = all_0_3_3
% 30.15/10.17 |
% 30.15/10.17 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 30.15/10.17 | (979) all_0_3_3 = n5
% 30.15/10.17 |
% 30.15/10.17 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 30.15/10.17 | (980) all_0_1_1 = n4
% 30.15/10.17 |
% 30.15/10.17 | From (979) and (232) follows:
% 30.15/10.17 | (981) sum(n5, all_0_0_0) = all_0_6_6
% 30.15/10.17 |
% 30.15/10.17 | From (980) and (1152) follows:
% 30.15/10.17 | (3606) sum(n16, n4) = all_0_0_0
% 30.15/10.17 |
% 30.15/10.17 | Instantiating formula (619) with n16, n4, all_0_0_0, n20 and discharging atoms sum(n16, n4) = all_0_0_0, sum(n16, n4) = n20, yields:
% 30.15/10.17 | (1051) all_0_0_0 = n20
% 30.15/10.17 |
% 30.15/10.17 | From (1051) and (981) follows:
% 30.15/10.17 | (3608) sum(n5, n20) = all_0_6_6
% 30.15/10.17 |
% 30.15/10.17 | Instantiating formula (619) with n5, n20, all_0_6_6, n4 and discharging atoms sum(n5, n20) = all_0_6_6, sum(n5, n20) = n4, yields:
% 30.15/10.17 | (1019) all_0_6_6 = n4
% 30.15/10.17 |
% 30.15/10.17 | Equations (1019) can reduce 48 to:
% 30.15/10.17 | (748) $false
% 30.15/10.17 |
% 30.15/10.17 |-The branch is then unsatisfiable
% 30.15/10.17 |-Branch two:
% 30.15/10.17 | (919) ~ (all_0_8_8 = n10)
% 30.15/10.17 | (920) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.15/10.17 |
% 30.43/10.17 +-Applying beta-rule and splitting (920), into two cases.
% 30.43/10.17 |-Branch one:
% 30.43/10.17 | (921) all_0_8_8 = n9
% 30.43/10.17 |
% 30.43/10.17 | From (921) and (3493) follows:
% 30.43/10.17 | (3614) sum(n9, n17) = all_0_4_4
% 30.43/10.17 |
% 30.43/10.17 | From (921) and (3491) follows:
% 30.43/10.17 | (3615) sum(n9, n16) = all_0_2_2
% 30.43/10.17 |
% 30.43/10.17 | Instantiating formula (619) with n9, n17, all_0_4_4, n5 and discharging atoms sum(n9, n17) = all_0_4_4, sum(n9, n17) = n5, yields:
% 30.43/10.17 | (993) all_0_4_4 = n5
% 30.43/10.17 |
% 30.43/10.17 | Instantiating formula (619) with n9, n16, all_0_2_2, n4 and discharging atoms sum(n9, n16) = all_0_2_2, sum(n9, n16) = n4, yields:
% 30.43/10.17 | (992) all_0_2_2 = n4
% 30.43/10.17 |
% 30.43/10.17 | From (992) and (473) follows:
% 30.43/10.17 | (994) pred(n4) = all_0_1_1
% 30.43/10.17 |
% 30.43/10.17 | From (993) and (716) follows:
% 30.43/10.17 | (995) pred(n5) = all_0_3_3
% 30.43/10.17 |
% 30.43/10.17 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 30.43/10.17 | (996) all_0_3_3 = n4
% 30.43/10.17 |
% 30.43/10.17 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 30.43/10.17 | (997) all_0_1_1 = n3
% 30.43/10.17 |
% 30.43/10.17 | From (996) and (232) follows:
% 30.43/10.17 | (998) sum(n4, all_0_0_0) = all_0_6_6
% 30.43/10.17 |
% 30.43/10.17 | From (997) and (1152) follows:
% 30.43/10.17 | (3623) sum(n16, n3) = all_0_0_0
% 30.43/10.17 |
% 30.43/10.17 | Instantiating formula (619) with n16, n3, all_0_0_0, n19 and discharging atoms sum(n16, n3) = all_0_0_0, sum(n16, n3) = n19, yields:
% 30.43/10.17 | (1068) all_0_0_0 = n19
% 30.43/10.17 |
% 30.43/10.17 | From (1068) and (998) follows:
% 30.43/10.17 | (3625) sum(n4, n19) = all_0_6_6
% 30.43/10.17 |
% 30.43/10.17 | Instantiating formula (619) with n4, n19, all_0_6_6, n2 and discharging atoms sum(n4, n19) = all_0_6_6, sum(n4, n19) = n2, yields:
% 30.43/10.17 | (1036) all_0_6_6 = n2
% 30.43/10.17 |
% 30.43/10.17 | Equations (1036) can reduce 56 to:
% 30.43/10.17 | (748) $false
% 30.43/10.17 |
% 30.43/10.17 |-The branch is then unsatisfiable
% 30.43/10.17 |-Branch two:
% 30.43/10.17 | (936) ~ (all_0_8_8 = n9)
% 30.43/10.17 | (937) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.43/10.17 |
% 30.43/10.17 +-Applying beta-rule and splitting (937), into two cases.
% 30.43/10.17 |-Branch one:
% 30.43/10.17 | (938) all_0_8_8 = n8
% 30.43/10.17 |
% 30.43/10.17 | From (938) and (3493) follows:
% 30.43/10.17 | (3631) sum(n8, n17) = all_0_4_4
% 30.43/10.17 |
% 30.43/10.17 | From (938) and (3491) follows:
% 30.43/10.17 | (3632) sum(n8, n16) = all_0_2_2
% 30.43/10.17 |
% 30.43/10.17 | Instantiating formula (619) with n8, n17, all_0_4_4, n4 and discharging atoms sum(n8, n17) = all_0_4_4, sum(n8, n17) = n4, yields:
% 30.43/10.17 | (1010) all_0_4_4 = n4
% 30.43/10.17 |
% 30.43/10.17 | Instantiating formula (619) with n8, n16, all_0_2_2, n3 and discharging atoms sum(n8, n16) = all_0_2_2, sum(n8, n16) = n3, yields:
% 30.44/10.17 | (1009) all_0_2_2 = n3
% 30.44/10.17 |
% 30.44/10.17 | From (1009) and (473) follows:
% 30.44/10.17 | (1011) pred(n3) = all_0_1_1
% 30.44/10.17 |
% 30.44/10.17 | From (1010) and (716) follows:
% 30.44/10.17 | (1012) pred(n4) = all_0_3_3
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 30.44/10.17 | (1013) all_0_3_3 = n3
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 30.44/10.17 | (1014) all_0_1_1 = n2
% 30.44/10.17 |
% 30.44/10.17 | From (1013) and (232) follows:
% 30.44/10.17 | (1015) sum(n3, all_0_0_0) = all_0_6_6
% 30.44/10.17 |
% 30.44/10.17 | From (1014) and (1152) follows:
% 30.44/10.17 | (3640) sum(n16, n2) = all_0_0_0
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (619) with n16, n2, all_0_0_0, n18 and discharging atoms sum(n16, n2) = all_0_0_0, sum(n16, n2) = n18, yields:
% 30.44/10.17 | (1084) all_0_0_0 = n18
% 30.44/10.17 |
% 30.44/10.17 | From (1084) and (1015) follows:
% 30.44/10.17 | (3642) sum(n3, n18) = all_0_6_6
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (619) with n3, n18, all_0_6_6, n0 and discharging atoms sum(n3, n18) = all_0_6_6, sum(n3, n18) = n0, yields:
% 30.44/10.17 | (1053) all_0_6_6 = n0
% 30.44/10.17 |
% 30.44/10.17 | Equations (1053) can reduce 676 to:
% 30.44/10.17 | (748) $false
% 30.44/10.17 |
% 30.44/10.17 |-The branch is then unsatisfiable
% 30.44/10.17 |-Branch two:
% 30.44/10.17 | (953) ~ (all_0_8_8 = n8)
% 30.44/10.17 | (954) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.44/10.17 |
% 30.44/10.17 +-Applying beta-rule and splitting (954), into two cases.
% 30.44/10.17 |-Branch one:
% 30.44/10.17 | (955) all_0_8_8 = n7
% 30.44/10.17 |
% 30.44/10.17 | From (955) and (3493) follows:
% 30.44/10.17 | (3648) sum(n7, n17) = all_0_4_4
% 30.44/10.17 |
% 30.44/10.17 | From (955) and (3491) follows:
% 30.44/10.17 | (3649) sum(n7, n16) = all_0_2_2
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (619) with n7, n17, all_0_4_4, n3 and discharging atoms sum(n7, n17) = all_0_4_4, sum(n7, n17) = n3, yields:
% 30.44/10.17 | (1027) all_0_4_4 = n3
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (619) with n7, n16, all_0_2_2, n2 and discharging atoms sum(n7, n16) = all_0_2_2, sum(n7, n16) = n2, yields:
% 30.44/10.17 | (1026) all_0_2_2 = n2
% 30.44/10.17 |
% 30.44/10.17 | From (1026) and (473) follows:
% 30.44/10.17 | (1028) pred(n2) = all_0_1_1
% 30.44/10.17 |
% 30.44/10.17 | From (1027) and (716) follows:
% 30.44/10.17 | (1029) pred(n3) = all_0_3_3
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 30.44/10.17 | (1030) all_0_3_3 = n2
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 30.44/10.17 | (1031) all_0_1_1 = n1
% 30.44/10.17 |
% 30.44/10.17 | From (1030) and (232) follows:
% 30.44/10.17 | (1032) sum(n2, all_0_0_0) = all_0_6_6
% 30.44/10.17 |
% 30.44/10.17 | From (1031) and (1152) follows:
% 30.44/10.17 | (3657) sum(n16, n1) = all_0_0_0
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (619) with n16, n1, all_0_0_0, n17 and discharging atoms sum(n16, n1) = all_0_0_0, sum(n16, n1) = n17, yields:
% 30.44/10.17 | (745) all_0_0_0 = n17
% 30.44/10.17 |
% 30.44/10.17 | From (745) and (1032) follows:
% 30.44/10.17 | (3659) sum(n2, n17) = all_0_6_6
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (619) with n2, n17, all_0_6_6, n19 and discharging atoms sum(n2, n17) = all_0_6_6, sum(n2, n17) = n19, yields:
% 30.44/10.17 | (1070) all_0_6_6 = n19
% 30.44/10.17 |
% 30.44/10.17 | Equations (1070) can reduce 31 to:
% 30.44/10.17 | (748) $false
% 30.44/10.17 |
% 30.44/10.17 |-The branch is then unsatisfiable
% 30.44/10.17 |-Branch two:
% 30.44/10.17 | (970) ~ (all_0_8_8 = n7)
% 30.44/10.17 | (971) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.44/10.17 |
% 30.44/10.17 +-Applying beta-rule and splitting (971), into two cases.
% 30.44/10.17 |-Branch one:
% 30.44/10.17 | (972) all_0_8_8 = n6
% 30.44/10.17 |
% 30.44/10.17 | From (972) and (3493) follows:
% 30.44/10.17 | (3665) sum(n6, n17) = all_0_4_4
% 30.44/10.17 |
% 30.44/10.17 | From (972) and (3491) follows:
% 30.44/10.17 | (3666) sum(n6, n16) = all_0_2_2
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (619) with n6, n17, all_0_4_4, n2 and discharging atoms sum(n6, n17) = all_0_4_4, sum(n6, n17) = n2, yields:
% 30.44/10.17 | (1044) all_0_4_4 = n2
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (619) with n6, n16, all_0_2_2, n1 and discharging atoms sum(n6, n16) = all_0_2_2, sum(n6, n16) = n1, yields:
% 30.44/10.17 | (1043) all_0_2_2 = n1
% 30.44/10.17 |
% 30.44/10.17 | From (1043) and (473) follows:
% 30.44/10.17 | (1045) pred(n1) = all_0_1_1
% 30.44/10.17 |
% 30.44/10.17 | From (1044) and (716) follows:
% 30.44/10.17 | (1046) pred(n2) = all_0_3_3
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 30.44/10.17 | (1047) all_0_3_3 = n1
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 30.44/10.17 | (1048) all_0_1_1 = n0
% 30.44/10.17 |
% 30.44/10.17 | From (1047) and (232) follows:
% 30.44/10.17 | (1049) sum(n1, all_0_0_0) = all_0_6_6
% 30.44/10.17 |
% 30.44/10.17 | From (1048) and (1152) follows:
% 30.44/10.17 | (3674) sum(n16, n0) = all_0_0_0
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (619) with n16, n0, all_0_0_0, n16 and discharging atoms sum(n16, n0) = all_0_0_0, sum(n16, n0) = n16, yields:
% 30.44/10.17 | (762) all_0_0_0 = n16
% 30.44/10.17 |
% 30.44/10.17 | From (762) and (1049) follows:
% 30.44/10.17 | (3676) sum(n1, n16) = all_0_6_6
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (619) with n1, n16, all_0_6_6, n17 and discharging atoms sum(n1, n16) = all_0_6_6, sum(n1, n16) = n17, yields:
% 30.44/10.17 | (1086) all_0_6_6 = n17
% 30.44/10.17 |
% 30.44/10.17 | Equations (1086) can reduce 669 to:
% 30.44/10.17 | (748) $false
% 30.44/10.17 |
% 30.44/10.17 |-The branch is then unsatisfiable
% 30.44/10.17 |-Branch two:
% 30.44/10.17 | (987) ~ (all_0_8_8 = n6)
% 30.44/10.17 | (988) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.44/10.17 |
% 30.44/10.17 +-Applying beta-rule and splitting (988), into two cases.
% 30.44/10.17 |-Branch one:
% 30.44/10.17 | (989) all_0_8_8 = n5
% 30.44/10.17 |
% 30.44/10.17 | From (989) and (3493) follows:
% 30.44/10.17 | (3682) sum(n5, n17) = all_0_4_4
% 30.44/10.17 |
% 30.44/10.17 | From (989) and (3491) follows:
% 30.44/10.17 | (3683) sum(n5, n16) = all_0_2_2
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (619) with n5, n17, all_0_4_4, n1 and discharging atoms sum(n5, n17) = all_0_4_4, sum(n5, n17) = n1, yields:
% 30.44/10.17 | (1061) all_0_4_4 = n1
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (619) with n5, n16, all_0_2_2, n0 and discharging atoms sum(n5, n16) = all_0_2_2, sum(n5, n16) = n0, yields:
% 30.44/10.17 | (1060) all_0_2_2 = n0
% 30.44/10.17 |
% 30.44/10.17 | From (1060) and (473) follows:
% 30.44/10.17 | (1062) pred(n0) = all_0_1_1
% 30.44/10.17 |
% 30.44/10.17 | From (1061) and (716) follows:
% 30.44/10.17 | (1063) pred(n1) = all_0_3_3
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 30.44/10.17 | (1064) all_0_3_3 = n0
% 30.44/10.17 |
% 30.44/10.17 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 30.44/10.17 | (1065) all_0_1_1 = n20
% 30.44/10.17 |
% 30.44/10.17 | From (1064) and (232) follows:
% 30.44/10.18 | (1066) sum(n0, all_0_0_0) = all_0_6_6
% 30.44/10.18 |
% 30.44/10.18 | From (1065) and (1152) follows:
% 30.44/10.18 | (3691) sum(n16, n20) = all_0_0_0
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n16, n20, all_0_0_0, n15 and discharging atoms sum(n16, n20) = all_0_0_0, sum(n16, n20) = n15, yields:
% 30.44/10.18 | (779) all_0_0_0 = n15
% 30.44/10.18 |
% 30.44/10.18 | From (779) and (1066) follows:
% 30.44/10.18 | (3693) sum(n0, n15) = all_0_6_6
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n0, n15, all_0_6_6, n15 and discharging atoms sum(n0, n15) = all_0_6_6, sum(n0, n15) = n15, yields:
% 30.44/10.18 | (747) all_0_6_6 = n15
% 30.44/10.18 |
% 30.44/10.18 | Equations (747) can reduce 456 to:
% 30.44/10.18 | (748) $false
% 30.44/10.18 |
% 30.44/10.18 |-The branch is then unsatisfiable
% 30.44/10.18 |-Branch two:
% 30.44/10.18 | (1004) ~ (all_0_8_8 = n5)
% 30.44/10.18 | (1005) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.44/10.18 |
% 30.44/10.18 +-Applying beta-rule and splitting (1005), into two cases.
% 30.44/10.18 |-Branch one:
% 30.44/10.18 | (1006) all_0_8_8 = n4
% 30.44/10.18 |
% 30.44/10.18 | From (1006) and (3493) follows:
% 30.44/10.18 | (3699) sum(n4, n17) = all_0_4_4
% 30.44/10.18 |
% 30.44/10.18 | From (1006) and (3491) follows:
% 30.44/10.18 | (3700) sum(n4, n16) = all_0_2_2
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n4, n17, all_0_4_4, n0 and discharging atoms sum(n4, n17) = all_0_4_4, sum(n4, n17) = n0, yields:
% 30.44/10.18 | (1077) all_0_4_4 = n0
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n4, n16, all_0_2_2, n20 and discharging atoms sum(n4, n16) = all_0_2_2, sum(n4, n16) = n20, yields:
% 30.44/10.18 | (1076) all_0_2_2 = n20
% 30.44/10.18 |
% 30.44/10.18 | From (1076) and (473) follows:
% 30.44/10.18 | (1078) pred(n20) = all_0_1_1
% 30.44/10.18 |
% 30.44/10.18 | From (1077) and (716) follows:
% 30.44/10.18 | (1079) pred(n0) = all_0_3_3
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 30.44/10.18 | (1080) all_0_1_1 = n19
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 30.44/10.18 | (1081) all_0_3_3 = n20
% 30.44/10.18 |
% 30.44/10.18 | From (1081) and (232) follows:
% 30.44/10.18 | (1082) sum(n20, all_0_0_0) = all_0_6_6
% 30.44/10.18 |
% 30.44/10.18 | From (1080) and (1152) follows:
% 30.44/10.18 | (3708) sum(n16, n19) = all_0_0_0
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n16, n19, all_0_0_0, n14 and discharging atoms sum(n16, n19) = all_0_0_0, sum(n16, n19) = n14, yields:
% 30.44/10.18 | (796) all_0_0_0 = n14
% 30.44/10.18 |
% 30.44/10.18 | From (796) and (1082) follows:
% 30.44/10.18 | (3710) sum(n20, n14) = all_0_6_6
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n20, n14, all_0_6_6, n13 and discharging atoms sum(n20, n14) = all_0_6_6, sum(n20, n14) = n13, yields:
% 30.44/10.18 | (764) all_0_6_6 = n13
% 30.44/10.18 |
% 30.44/10.18 | Equations (764) can reduce 293 to:
% 30.44/10.18 | (748) $false
% 30.44/10.18 |
% 30.44/10.18 |-The branch is then unsatisfiable
% 30.44/10.18 |-Branch two:
% 30.44/10.18 | (1021) ~ (all_0_8_8 = n4)
% 30.44/10.18 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.44/10.18 |
% 30.44/10.18 +-Applying beta-rule and splitting (1022), into two cases.
% 30.44/10.18 |-Branch one:
% 30.44/10.18 | (1023) all_0_8_8 = n3
% 30.44/10.18 |
% 30.44/10.18 | From (1023) and (3493) follows:
% 30.44/10.18 | (3716) sum(n3, n17) = all_0_4_4
% 30.44/10.18 |
% 30.44/10.18 | From (1023) and (3491) follows:
% 30.44/10.18 | (3717) sum(n3, n16) = all_0_2_2
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n3, n17, all_0_4_4, n20 and discharging atoms sum(n3, n17) = all_0_4_4, sum(n3, n17) = n20, yields:
% 30.44/10.18 | (738) all_0_4_4 = n20
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n3, n16, all_0_2_2, n19 and discharging atoms sum(n3, n16) = all_0_2_2, sum(n3, n16) = n19, yields:
% 30.44/10.18 | (737) all_0_2_2 = n19
% 30.44/10.18 |
% 30.44/10.18 | From (737) and (473) follows:
% 30.44/10.18 | (739) pred(n19) = all_0_1_1
% 30.44/10.18 |
% 30.44/10.18 | From (738) and (716) follows:
% 30.44/10.18 | (740) pred(n20) = all_0_3_3
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 30.44/10.18 | (741) all_0_3_3 = n19
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 30.44/10.18 | (742) all_0_1_1 = n18
% 30.44/10.18 |
% 30.44/10.18 | From (741) and (232) follows:
% 30.44/10.18 | (743) sum(n19, all_0_0_0) = all_0_6_6
% 30.44/10.18 |
% 30.44/10.18 | From (742) and (1152) follows:
% 30.44/10.18 | (3725) sum(n16, n18) = all_0_0_0
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n16, n18, all_0_0_0, n13 and discharging atoms sum(n16, n18) = all_0_0_0, sum(n16, n18) = n13, yields:
% 30.44/10.18 | (813) all_0_0_0 = n13
% 30.44/10.18 |
% 30.44/10.18 | From (813) and (743) follows:
% 30.44/10.18 | (3727) sum(n19, n13) = all_0_6_6
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n19, n13, all_0_6_6, n11 and discharging atoms sum(n19, n13) = all_0_6_6, sum(n19, n13) = n11, yields:
% 30.44/10.18 | (781) all_0_6_6 = n11
% 30.44/10.18 |
% 30.44/10.18 | Equations (781) can reduce 2 to:
% 30.44/10.18 | (748) $false
% 30.44/10.18 |
% 30.44/10.18 |-The branch is then unsatisfiable
% 30.44/10.18 |-Branch two:
% 30.44/10.18 | (1038) ~ (all_0_8_8 = n3)
% 30.44/10.18 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.44/10.18 |
% 30.44/10.18 +-Applying beta-rule and splitting (1039), into two cases.
% 30.44/10.18 |-Branch one:
% 30.44/10.18 | (1040) all_0_8_8 = n2
% 30.44/10.18 |
% 30.44/10.18 | From (1040) and (3493) follows:
% 30.44/10.18 | (3733) sum(n2, n17) = all_0_4_4
% 30.44/10.18 |
% 30.44/10.18 | From (1040) and (3491) follows:
% 30.44/10.18 | (3734) sum(n2, n16) = all_0_2_2
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n2, n17, all_0_4_4, n19 and discharging atoms sum(n2, n17) = all_0_4_4, sum(n2, n17) = n19, yields:
% 30.44/10.18 | (755) all_0_4_4 = n19
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n2, n16, all_0_2_2, n18 and discharging atoms sum(n2, n16) = all_0_2_2, sum(n2, n16) = n18, yields:
% 30.44/10.18 | (754) all_0_2_2 = n18
% 30.44/10.18 |
% 30.44/10.18 | From (754) and (473) follows:
% 30.44/10.18 | (756) pred(n18) = all_0_1_1
% 30.44/10.18 |
% 30.44/10.18 | From (755) and (716) follows:
% 30.44/10.18 | (757) pred(n19) = all_0_3_3
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 30.44/10.18 | (758) all_0_3_3 = n18
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 30.44/10.18 | (759) all_0_1_1 = n17
% 30.44/10.18 |
% 30.44/10.18 | From (758) and (232) follows:
% 30.44/10.18 | (760) sum(n18, all_0_0_0) = all_0_6_6
% 30.44/10.18 |
% 30.44/10.18 | From (759) and (1152) follows:
% 30.44/10.18 | (3742) sum(n16, n17) = all_0_0_0
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n16, n17, all_0_0_0, n12 and discharging atoms sum(n16, n17) = all_0_0_0, sum(n16, n17) = n12, yields:
% 30.44/10.18 | (830) all_0_0_0 = n12
% 30.44/10.18 |
% 30.44/10.18 | From (830) and (760) follows:
% 30.44/10.18 | (3744) sum(n18, n12) = all_0_6_6
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n18, n12, all_0_6_6, n9 and discharging atoms sum(n18, n12) = all_0_6_6, sum(n18, n12) = n9, yields:
% 30.44/10.18 | (798) all_0_6_6 = n9
% 30.44/10.18 |
% 30.44/10.18 | Equations (798) can reduce 593 to:
% 30.44/10.18 | (748) $false
% 30.44/10.18 |
% 30.44/10.18 |-The branch is then unsatisfiable
% 30.44/10.18 |-Branch two:
% 30.44/10.18 | (1055) ~ (all_0_8_8 = n2)
% 30.44/10.18 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 30.44/10.18 |
% 30.44/10.18 +-Applying beta-rule and splitting (1056), into two cases.
% 30.44/10.18 |-Branch one:
% 30.44/10.18 | (1057) all_0_8_8 = n1
% 30.44/10.18 |
% 30.44/10.18 | From (1057) and (3493) follows:
% 30.44/10.18 | (3750) sum(n1, n17) = all_0_4_4
% 30.44/10.18 |
% 30.44/10.18 | From (1057) and (3491) follows:
% 30.44/10.18 | (3751) sum(n1, n16) = all_0_2_2
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n1, n17, all_0_4_4, n18 and discharging atoms sum(n1, n17) = all_0_4_4, sum(n1, n17) = n18, yields:
% 30.44/10.18 | (772) all_0_4_4 = n18
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n1, n16, all_0_2_2, n17 and discharging atoms sum(n1, n16) = all_0_2_2, sum(n1, n16) = n17, yields:
% 30.44/10.18 | (771) all_0_2_2 = n17
% 30.44/10.18 |
% 30.44/10.18 | From (771) and (473) follows:
% 30.44/10.18 | (773) pred(n17) = all_0_1_1
% 30.44/10.18 |
% 30.44/10.18 | From (772) and (716) follows:
% 30.44/10.18 | (774) pred(n18) = all_0_3_3
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 30.44/10.18 | (775) all_0_3_3 = n17
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 30.44/10.18 | (776) all_0_1_1 = n16
% 30.44/10.18 |
% 30.44/10.18 | From (775) and (232) follows:
% 30.44/10.18 | (777) sum(n17, all_0_0_0) = all_0_6_6
% 30.44/10.18 |
% 30.44/10.18 | From (776) and (1152) follows:
% 30.44/10.18 | (3759) sum(n16, n16) = all_0_0_0
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n16, n16, all_0_0_0, n11 and discharging atoms sum(n16, n16) = all_0_0_0, sum(n16, n16) = n11, yields:
% 30.44/10.18 | (847) all_0_0_0 = n11
% 30.44/10.18 |
% 30.44/10.18 | From (847) and (777) follows:
% 30.44/10.18 | (3761) sum(n17, n11) = all_0_6_6
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n17, n11, all_0_6_6, n7 and discharging atoms sum(n17, n11) = all_0_6_6, sum(n17, n11) = n7, yields:
% 30.44/10.18 | (815) all_0_6_6 = n7
% 30.44/10.18 |
% 30.44/10.18 | Equations (815) can reduce 557 to:
% 30.44/10.18 | (748) $false
% 30.44/10.18 |
% 30.44/10.18 |-The branch is then unsatisfiable
% 30.44/10.18 |-Branch two:
% 30.44/10.18 | (1072) ~ (all_0_8_8 = n1)
% 30.44/10.18 | (1073) all_0_8_8 = n0
% 30.44/10.18 |
% 30.44/10.18 | From (1073) and (3493) follows:
% 30.44/10.18 | (3766) sum(n0, n17) = all_0_4_4
% 30.44/10.18 |
% 30.44/10.18 | From (1073) and (3491) follows:
% 30.44/10.18 | (3767) sum(n0, n16) = all_0_2_2
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n0, n17, all_0_4_4, n17 and discharging atoms sum(n0, n17) = all_0_4_4, sum(n0, n17) = n17, yields:
% 30.44/10.18 | (789) all_0_4_4 = n17
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n0, n16, all_0_2_2, n16 and discharging atoms sum(n0, n16) = all_0_2_2, sum(n0, n16) = n16, yields:
% 30.44/10.18 | (788) all_0_2_2 = n16
% 30.44/10.18 |
% 30.44/10.18 | From (788) and (473) follows:
% 30.44/10.18 | (790) pred(n16) = all_0_1_1
% 30.44/10.18 |
% 30.44/10.18 | From (789) and (716) follows:
% 30.44/10.18 | (791) pred(n17) = all_0_3_3
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 30.44/10.18 | (792) all_0_3_3 = n16
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 30.44/10.18 | (793) all_0_1_1 = n15
% 30.44/10.18 |
% 30.44/10.18 | From (792) and (232) follows:
% 30.44/10.18 | (794) sum(n16, all_0_0_0) = all_0_6_6
% 30.44/10.18 |
% 30.44/10.18 | From (793) and (1152) follows:
% 30.44/10.18 | (3775) sum(n16, n15) = all_0_0_0
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n16, n15, all_0_0_0, n10 and discharging atoms sum(n16, n15) = all_0_0_0, sum(n16, n15) = n10, yields:
% 30.44/10.18 | (864) all_0_0_0 = n10
% 30.44/10.18 |
% 30.44/10.18 | From (864) and (794) follows:
% 30.44/10.18 | (3777) sum(n16, n10) = all_0_6_6
% 30.44/10.18 |
% 30.44/10.18 | Instantiating formula (619) with n16, n10, all_0_6_6, n5 and discharging atoms sum(n16, n10) = all_0_6_6, sum(n16, n10) = n5, yields:
% 30.44/10.18 | (832) all_0_6_6 = n5
% 30.44/10.18 |
% 30.44/10.18 | Equations (832) can reduce 462 to:
% 30.44/10.18 | (748) $false
% 30.44/10.18 |
% 30.44/10.18 |-The branch is then unsatisfiable
% 30.44/10.18 |-Branch two:
% 30.44/10.18 | (1167) ~ (all_0_7_7 = n16)
% 30.44/10.18 | (1168) all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.44/10.18 |
% 30.44/10.18 +-Applying beta-rule and splitting (801), into two cases.
% 30.44/10.18 |-Branch one:
% 30.44/10.18 | (802) all_0_8_8 = n16
% 30.44/10.18 |
% 30.44/10.18 | From (802) and (708) follows:
% 30.44/10.18 | (3783) sum(n16, all_0_5_5) = all_0_4_4
% 30.44/10.18 |
% 30.44/10.18 | From (802) and (378) follows:
% 30.44/10.18 | (3784) sum(n16, all_0_7_7) = all_0_2_2
% 30.44/10.18 |
% 30.44/10.18 +-Applying beta-rule and splitting (1168), into two cases.
% 30.44/10.18 |-Branch one:
% 30.44/10.18 | (1169) all_0_7_7 = n15
% 30.44/10.18 |
% 30.44/10.18 | From (1169) and (683) follows:
% 30.44/10.18 | (1170) succ(n15) = all_0_5_5
% 30.44/10.18 |
% 30.44/10.18 | From (1169) and (8) follows:
% 30.44/10.18 | (1171) sum(n15, all_0_1_1) = all_0_0_0
% 30.44/10.18 |
% 30.44/10.18 | From (1169) and (3784) follows:
% 30.44/10.19 | (3788) sum(n16, n15) = all_0_2_2
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (388) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 30.44/10.19 | (1173) all_0_5_5 = n16
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n16, n15, all_0_2_2, n10 and discharging atoms sum(n16, n15) = all_0_2_2, sum(n16, n15) = n10, yields:
% 30.44/10.19 | (890) all_0_2_2 = n10
% 30.44/10.19 |
% 30.44/10.19 | From (890) and (473) follows:
% 30.44/10.19 | (892) pred(n10) = all_0_1_1
% 30.44/10.19 |
% 30.44/10.19 | From (1173) and (3783) follows:
% 30.44/10.19 | (3792) sum(n16, n16) = all_0_4_4
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 30.44/10.19 | (895) all_0_1_1 = n9
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n16, n16, all_0_4_4, n11 and discharging atoms sum(n16, n16) = all_0_4_4, sum(n16, n16) = n11, yields:
% 30.44/10.19 | (891) all_0_4_4 = n11
% 30.44/10.19 |
% 30.44/10.19 | From (891) and (716) follows:
% 30.44/10.19 | (893) pred(n11) = all_0_3_3
% 30.44/10.19 |
% 30.44/10.19 | From (895) and (1171) follows:
% 30.44/10.19 | (3796) sum(n15, n9) = all_0_0_0
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 30.44/10.19 | (894) all_0_3_3 = n10
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n15, n9, all_0_0_0, n3 and discharging atoms sum(n15, n9) = all_0_0_0, sum(n15, n9) = n3, yields:
% 30.44/10.19 | (983) all_0_0_0 = n3
% 30.44/10.19 |
% 30.44/10.19 | From (894)(983) and (232) follows:
% 30.44/10.19 | (3799) sum(n10, n3) = all_0_6_6
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n10, n3, all_0_6_6, n13 and discharging atoms sum(n10, n3) = all_0_6_6, sum(n10, n3) = n13, yields:
% 30.44/10.19 | (764) all_0_6_6 = n13
% 30.44/10.19 |
% 30.44/10.19 | Equations (764) can reduce 293 to:
% 30.44/10.19 | (748) $false
% 30.44/10.19 |
% 30.44/10.19 |-The branch is then unsatisfiable
% 30.44/10.19 |-Branch two:
% 30.44/10.19 | (1186) ~ (all_0_7_7 = n15)
% 30.44/10.19 | (1187) all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.44/10.19 |
% 30.44/10.19 +-Applying beta-rule and splitting (1187), into two cases.
% 30.44/10.19 |-Branch one:
% 30.44/10.19 | (1188) all_0_7_7 = n14
% 30.44/10.19 |
% 30.44/10.19 | From (1188) and (683) follows:
% 30.44/10.19 | (1189) succ(n14) = all_0_5_5
% 30.44/10.19 |
% 30.44/10.19 | From (1188) and (8) follows:
% 30.44/10.19 | (1190) sum(n14, all_0_1_1) = all_0_0_0
% 30.44/10.19 |
% 30.44/10.19 | From (1188) and (3784) follows:
% 30.44/10.19 | (3807) sum(n16, n14) = all_0_2_2
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (388) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 30.44/10.19 | (1192) all_0_5_5 = n15
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n16, n14, all_0_2_2, n9 and discharging atoms sum(n16, n14) = all_0_2_2, sum(n16, n14) = n9, yields:
% 30.44/10.19 | (907) all_0_2_2 = n9
% 30.44/10.19 |
% 30.44/10.19 | From (907) and (473) follows:
% 30.44/10.19 | (909) pred(n9) = all_0_1_1
% 30.44/10.19 |
% 30.44/10.19 | From (1192) and (3783) follows:
% 30.44/10.19 | (3811) sum(n16, n15) = all_0_4_4
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 30.44/10.19 | (912) all_0_1_1 = n8
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n16, n15, all_0_4_4, n10 and discharging atoms sum(n16, n15) = all_0_4_4, sum(n16, n15) = n10, yields:
% 30.44/10.19 | (908) all_0_4_4 = n10
% 30.44/10.19 |
% 30.44/10.19 | From (908) and (716) follows:
% 30.44/10.19 | (910) pred(n10) = all_0_3_3
% 30.44/10.19 |
% 30.44/10.19 | From (912) and (1190) follows:
% 30.44/10.19 | (3815) sum(n14, n8) = all_0_0_0
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 30.44/10.19 | (911) all_0_3_3 = n9
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n14, n8, all_0_0_0, n1 and discharging atoms sum(n14, n8) = all_0_0_0, sum(n14, n8) = n1, yields:
% 30.44/10.19 | (1017) all_0_0_0 = n1
% 30.44/10.19 |
% 30.44/10.19 | From (911)(1017) and (232) follows:
% 30.44/10.19 | (3818) sum(n9, n1) = all_0_6_6
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n9, n1, all_0_6_6, n10 and discharging atoms sum(n9, n1) = all_0_6_6, sum(n9, n1) = n10, yields:
% 30.44/10.19 | (968) all_0_6_6 = n10
% 30.44/10.19 |
% 30.44/10.19 | Equations (968) can reduce 176 to:
% 30.44/10.19 | (748) $false
% 30.44/10.19 |
% 30.44/10.19 |-The branch is then unsatisfiable
% 30.44/10.19 |-Branch two:
% 30.44/10.19 | (1205) ~ (all_0_7_7 = n14)
% 30.44/10.19 | (1206) all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.44/10.19 |
% 30.44/10.19 +-Applying beta-rule and splitting (1206), into two cases.
% 30.44/10.19 |-Branch one:
% 30.44/10.19 | (1207) all_0_7_7 = n13
% 30.44/10.19 |
% 30.44/10.19 | From (1207) and (683) follows:
% 30.44/10.19 | (1208) succ(n13) = all_0_5_5
% 30.44/10.19 |
% 30.44/10.19 | From (1207) and (8) follows:
% 30.44/10.19 | (1209) sum(n13, all_0_1_1) = all_0_0_0
% 30.44/10.19 |
% 30.44/10.19 | From (1207) and (3784) follows:
% 30.44/10.19 | (3826) sum(n16, n13) = all_0_2_2
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (388) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 30.44/10.19 | (1211) all_0_5_5 = n14
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n16, n13, all_0_2_2, n8 and discharging atoms sum(n16, n13) = all_0_2_2, sum(n16, n13) = n8, yields:
% 30.44/10.19 | (924) all_0_2_2 = n8
% 30.44/10.19 |
% 30.44/10.19 | From (924) and (473) follows:
% 30.44/10.19 | (926) pred(n8) = all_0_1_1
% 30.44/10.19 |
% 30.44/10.19 | From (1211) and (3783) follows:
% 30.44/10.19 | (3830) sum(n16, n14) = all_0_4_4
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 30.44/10.19 | (929) all_0_1_1 = n7
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n16, n14, all_0_4_4, n9 and discharging atoms sum(n16, n14) = all_0_4_4, sum(n16, n14) = n9, yields:
% 30.44/10.19 | (925) all_0_4_4 = n9
% 30.44/10.19 |
% 30.44/10.19 | From (925) and (716) follows:
% 30.44/10.19 | (927) pred(n9) = all_0_3_3
% 30.44/10.19 |
% 30.44/10.19 | From (929) and (1209) follows:
% 30.44/10.19 | (3834) sum(n13, n7) = all_0_0_0
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 30.44/10.19 | (928) all_0_3_3 = n8
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n13, n7, all_0_0_0, n20 and discharging atoms sum(n13, n7) = all_0_0_0, sum(n13, n7) = n20, yields:
% 30.44/10.19 | (1051) all_0_0_0 = n20
% 30.44/10.19 |
% 30.44/10.19 | From (928)(1051) and (232) follows:
% 30.44/10.19 | (3837) sum(n8, n20) = all_0_6_6
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n8, n20, all_0_6_6, n7 and discharging atoms sum(n8, n20) = all_0_6_6, sum(n8, n20) = n7, yields:
% 30.44/10.19 | (815) all_0_6_6 = n7
% 30.44/10.19 |
% 30.44/10.19 | Equations (815) can reduce 557 to:
% 30.44/10.19 | (748) $false
% 30.44/10.19 |
% 30.44/10.19 |-The branch is then unsatisfiable
% 30.44/10.19 |-Branch two:
% 30.44/10.19 | (1224) ~ (all_0_7_7 = n13)
% 30.44/10.19 | (1225) all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.44/10.19 |
% 30.44/10.19 +-Applying beta-rule and splitting (1225), into two cases.
% 30.44/10.19 |-Branch one:
% 30.44/10.19 | (1226) all_0_7_7 = n12
% 30.44/10.19 |
% 30.44/10.19 | From (1226) and (683) follows:
% 30.44/10.19 | (1227) succ(n12) = all_0_5_5
% 30.44/10.19 |
% 30.44/10.19 | From (1226) and (8) follows:
% 30.44/10.19 | (1228) sum(n12, all_0_1_1) = all_0_0_0
% 30.44/10.19 |
% 30.44/10.19 | From (1226) and (3784) follows:
% 30.44/10.19 | (3845) sum(n16, n12) = all_0_2_2
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (388) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 30.44/10.19 | (1230) all_0_5_5 = n13
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n16, n12, all_0_2_2, n7 and discharging atoms sum(n16, n12) = all_0_2_2, sum(n16, n12) = n7, yields:
% 30.44/10.19 | (941) all_0_2_2 = n7
% 30.44/10.19 |
% 30.44/10.19 | From (941) and (473) follows:
% 30.44/10.19 | (943) pred(n7) = all_0_1_1
% 30.44/10.19 |
% 30.44/10.19 | From (1230) and (3783) follows:
% 30.44/10.19 | (3849) sum(n16, n13) = all_0_4_4
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 30.44/10.19 | (946) all_0_1_1 = n6
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n16, n13, all_0_4_4, n8 and discharging atoms sum(n16, n13) = all_0_4_4, sum(n16, n13) = n8, yields:
% 30.44/10.19 | (942) all_0_4_4 = n8
% 30.44/10.19 |
% 30.44/10.19 | From (942) and (716) follows:
% 30.44/10.19 | (944) pred(n8) = all_0_3_3
% 30.44/10.19 |
% 30.44/10.19 | From (946) and (1228) follows:
% 30.44/10.19 | (3853) sum(n12, n6) = all_0_0_0
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 30.44/10.19 | (945) all_0_3_3 = n7
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n12, n6, all_0_0_0, n18 and discharging atoms sum(n12, n6) = all_0_0_0, sum(n12, n6) = n18, yields:
% 30.44/10.19 | (1084) all_0_0_0 = n18
% 30.44/10.19 |
% 30.44/10.19 | From (945)(1084) and (232) follows:
% 30.44/10.19 | (3856) sum(n7, n18) = all_0_6_6
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n7, n18, all_0_6_6, n4 and discharging atoms sum(n7, n18) = all_0_6_6, sum(n7, n18) = n4, yields:
% 30.44/10.19 | (1019) all_0_6_6 = n4
% 30.44/10.19 |
% 30.44/10.19 | Equations (1019) can reduce 48 to:
% 30.44/10.19 | (748) $false
% 30.44/10.19 |
% 30.44/10.19 |-The branch is then unsatisfiable
% 30.44/10.19 |-Branch two:
% 30.44/10.19 | (1243) ~ (all_0_7_7 = n12)
% 30.44/10.19 | (1244) all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.44/10.19 |
% 30.44/10.19 +-Applying beta-rule and splitting (1244), into two cases.
% 30.44/10.19 |-Branch one:
% 30.44/10.19 | (1245) all_0_7_7 = n11
% 30.44/10.19 |
% 30.44/10.19 | From (1245) and (683) follows:
% 30.44/10.19 | (1246) succ(n11) = all_0_5_5
% 30.44/10.19 |
% 30.44/10.19 | From (1245) and (8) follows:
% 30.44/10.19 | (1247) sum(n11, all_0_1_1) = all_0_0_0
% 30.44/10.19 |
% 30.44/10.19 | From (1245) and (3784) follows:
% 30.44/10.19 | (3864) sum(n16, n11) = all_0_2_2
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (388) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 30.44/10.19 | (1249) all_0_5_5 = n12
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n16, n11, all_0_2_2, n6 and discharging atoms sum(n16, n11) = all_0_2_2, sum(n16, n11) = n6, yields:
% 30.44/10.19 | (958) all_0_2_2 = n6
% 30.44/10.19 |
% 30.44/10.19 | From (958) and (473) follows:
% 30.44/10.19 | (960) pred(n6) = all_0_1_1
% 30.44/10.19 |
% 30.44/10.19 | From (1249) and (3783) follows:
% 30.44/10.19 | (3868) sum(n16, n12) = all_0_4_4
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 30.44/10.19 | (963) all_0_1_1 = n5
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n16, n12, all_0_4_4, n7 and discharging atoms sum(n16, n12) = all_0_4_4, sum(n16, n12) = n7, yields:
% 30.44/10.19 | (959) all_0_4_4 = n7
% 30.44/10.19 |
% 30.44/10.19 | From (959) and (716) follows:
% 30.44/10.19 | (961) pred(n7) = all_0_3_3
% 30.44/10.19 |
% 30.44/10.19 | From (963) and (1247) follows:
% 30.44/10.19 | (3872) sum(n11, n5) = all_0_0_0
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 30.44/10.19 | (962) all_0_3_3 = n6
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n11, n5, all_0_0_0, n16 and discharging atoms sum(n11, n5) = all_0_0_0, sum(n11, n5) = n16, yields:
% 30.44/10.19 | (762) all_0_0_0 = n16
% 30.44/10.19 |
% 30.44/10.19 | From (962)(762) and (232) follows:
% 30.44/10.19 | (3875) sum(n6, n16) = all_0_6_6
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n6, n16, all_0_6_6, n1 and discharging atoms sum(n6, n16) = all_0_6_6, sum(n6, n16) = n1, yields:
% 30.44/10.19 | (866) all_0_6_6 = n1
% 30.44/10.19 |
% 30.44/10.19 | Equations (866) can reduce 28 to:
% 30.44/10.19 | (748) $false
% 30.44/10.19 |
% 30.44/10.19 |-The branch is then unsatisfiable
% 30.44/10.19 |-Branch two:
% 30.44/10.19 | (1262) ~ (all_0_7_7 = n11)
% 30.44/10.19 | (1263) all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.44/10.19 |
% 30.44/10.19 +-Applying beta-rule and splitting (1263), into two cases.
% 30.44/10.19 |-Branch one:
% 30.44/10.19 | (1264) all_0_7_7 = n10
% 30.44/10.19 |
% 30.44/10.19 | From (1264) and (683) follows:
% 30.44/10.19 | (1265) succ(n10) = all_0_5_5
% 30.44/10.19 |
% 30.44/10.19 | From (1264) and (8) follows:
% 30.44/10.19 | (1266) sum(n10, all_0_1_1) = all_0_0_0
% 30.44/10.19 |
% 30.44/10.19 | From (1264) and (3784) follows:
% 30.44/10.19 | (3883) sum(n16, n10) = all_0_2_2
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (388) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 30.44/10.19 | (1268) all_0_5_5 = n11
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n16, n10, all_0_2_2, n5 and discharging atoms sum(n16, n10) = all_0_2_2, sum(n16, n10) = n5, yields:
% 30.44/10.19 | (975) all_0_2_2 = n5
% 30.44/10.19 |
% 30.44/10.19 | From (975) and (473) follows:
% 30.44/10.19 | (977) pred(n5) = all_0_1_1
% 30.44/10.19 |
% 30.44/10.19 | From (1268) and (3783) follows:
% 30.44/10.19 | (3887) sum(n16, n11) = all_0_4_4
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 30.44/10.19 | (980) all_0_1_1 = n4
% 30.44/10.19 |
% 30.44/10.19 | Instantiating formula (619) with n16, n11, all_0_4_4, n6 and discharging atoms sum(n16, n11) = all_0_4_4, sum(n16, n11) = n6, yields:
% 30.44/10.19 | (976) all_0_4_4 = n6
% 30.44/10.19 |
% 30.44/10.19 | From (976) and (716) follows:
% 30.44/10.19 | (978) pred(n6) = all_0_3_3
% 30.44/10.19 |
% 30.44/10.19 | From (980) and (1266) follows:
% 30.44/10.20 | (3891) sum(n10, n4) = all_0_0_0
% 30.44/10.20 |
% 30.44/10.20 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 30.44/10.20 | (979) all_0_3_3 = n5
% 30.44/10.20 |
% 30.44/10.20 | Instantiating formula (619) with n10, n4, all_0_0_0, n14 and discharging atoms sum(n10, n4) = all_0_0_0, sum(n10, n4) = n14, yields:
% 30.44/10.20 | (796) all_0_0_0 = n14
% 30.44/10.20 |
% 30.44/10.20 | From (979)(796) and (232) follows:
% 30.44/10.20 | (3894) sum(n5, n14) = all_0_6_6
% 30.44/10.20 |
% 30.44/10.20 | Instantiating formula (619) with n5, n14, all_0_6_6, n19 and discharging atoms sum(n5, n14) = all_0_6_6, sum(n5, n14) = n19, yields:
% 30.44/10.20 | (1070) all_0_6_6 = n19
% 30.44/10.20 |
% 30.44/10.20 | Equations (1070) can reduce 31 to:
% 30.44/10.20 | (748) $false
% 30.44/10.20 |
% 30.44/10.20 |-The branch is then unsatisfiable
% 30.44/10.20 |-Branch two:
% 30.44/10.20 | (1281) ~ (all_0_7_7 = n10)
% 30.44/10.20 | (1282) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.44/10.20 |
% 30.44/10.20 +-Applying beta-rule and splitting (1282), into two cases.
% 30.44/10.20 |-Branch one:
% 30.44/10.20 | (1283) all_0_7_7 = n9
% 30.44/10.20 |
% 30.44/10.20 | From (1283) and (683) follows:
% 30.44/10.20 | (1284) succ(n9) = all_0_5_5
% 30.44/10.20 |
% 30.44/10.20 | From (1283) and (8) follows:
% 30.44/10.20 | (1285) sum(n9, all_0_1_1) = all_0_0_0
% 30.44/10.20 |
% 30.44/10.20 | From (1283) and (3784) follows:
% 30.44/10.20 | (3902) sum(n16, n9) = all_0_2_2
% 30.44/10.20 |
% 30.44/10.20 | Instantiating formula (388) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 30.44/10.20 | (1287) all_0_5_5 = n10
% 30.44/10.20 |
% 30.44/10.20 | Instantiating formula (619) with n16, n9, all_0_2_2, n4 and discharging atoms sum(n16, n9) = all_0_2_2, sum(n16, n9) = n4, yields:
% 30.44/10.20 | (992) all_0_2_2 = n4
% 30.44/10.20 |
% 30.44/10.20 | From (992) and (473) follows:
% 30.44/10.20 | (994) pred(n4) = all_0_1_1
% 30.44/10.20 |
% 30.44/10.20 | From (1287) and (3783) follows:
% 30.44/10.20 | (3906) sum(n16, n10) = all_0_4_4
% 30.44/10.20 |
% 30.44/10.20 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 30.44/10.20 | (997) all_0_1_1 = n3
% 30.44/10.20 |
% 30.44/10.20 | Instantiating formula (619) with n16, n10, all_0_4_4, n5 and discharging atoms sum(n16, n10) = all_0_4_4, sum(n16, n10) = n5, yields:
% 30.44/10.20 | (993) all_0_4_4 = n5
% 30.44/10.20 |
% 30.44/10.20 | From (993) and (716) follows:
% 30.44/10.20 | (995) pred(n5) = all_0_3_3
% 30.44/10.20 |
% 30.44/10.20 | From (997) and (1285) follows:
% 30.44/10.20 | (3910) sum(n9, n3) = all_0_0_0
% 30.44/10.20 |
% 30.44/10.20 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 30.44/10.20 | (996) all_0_3_3 = n4
% 30.44/10.20 |
% 30.44/10.20 | Instantiating formula (619) with n9, n3, all_0_0_0, n12 and discharging atoms sum(n9, n3) = all_0_0_0, sum(n9, n3) = n12, yields:
% 30.44/10.20 | (830) all_0_0_0 = n12
% 30.44/10.20 |
% 30.44/10.20 | From (996)(830) and (232) follows:
% 30.44/10.20 | (3913) sum(n4, n12) = all_0_6_6
% 30.44/10.20 |
% 30.44/10.20 | Instantiating formula (619) with n4, n12, all_0_6_6, n16 and discharging atoms sum(n4, n12) = all_0_6_6, sum(n4, n12) = n16, yields:
% 30.44/10.20 | (917) all_0_6_6 = n16
% 30.44/10.20 |
% 30.44/10.20 | Equations (917) can reduce 163 to:
% 30.44/10.20 | (748) $false
% 30.44/10.20 |
% 30.44/10.20 |-The branch is then unsatisfiable
% 30.44/10.20 |-Branch two:
% 30.44/10.20 | (1300) ~ (all_0_7_7 = n9)
% 30.44/10.20 | (1301) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.44/10.20 |
% 30.44/10.20 +-Applying beta-rule and splitting (1301), into two cases.
% 30.44/10.20 |-Branch one:
% 30.44/10.20 | (1302) all_0_7_7 = n8
% 30.44/10.20 |
% 30.44/10.20 | From (1302) and (683) follows:
% 30.44/10.20 | (1303) succ(n8) = all_0_5_5
% 30.44/10.20 |
% 30.44/10.20 | From (1302) and (8) follows:
% 30.44/10.20 | (1304) sum(n8, all_0_1_1) = all_0_0_0
% 30.44/10.20 |
% 30.44/10.20 | From (1302) and (3784) follows:
% 30.44/10.20 | (3921) sum(n16, n8) = all_0_2_2
% 30.44/10.20 |
% 30.44/10.20 | Instantiating formula (388) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 30.44/10.20 | (1306) all_0_5_5 = n9
% 30.44/10.20 |
% 30.44/10.20 | Instantiating formula (619) with n16, n8, all_0_2_2, n3 and discharging atoms sum(n16, n8) = all_0_2_2, sum(n16, n8) = n3, yields:
% 30.44/10.20 | (1009) all_0_2_2 = n3
% 30.44/10.20 |
% 30.44/10.20 | From (1009) and (473) follows:
% 30.44/10.20 | (1011) pred(n3) = all_0_1_1
% 30.44/10.20 |
% 30.44/10.20 | From (1306) and (3783) follows:
% 30.44/10.20 | (3925) sum(n16, n9) = all_0_4_4
% 30.44/10.20 |
% 30.44/10.20 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 30.44/10.20 | (1014) all_0_1_1 = n2
% 30.44/10.20 |
% 30.44/10.20 | Instantiating formula (619) with n16, n9, all_0_4_4, n4 and discharging atoms sum(n16, n9) = all_0_4_4, sum(n16, n9) = n4, yields:
% 30.44/10.20 | (1010) all_0_4_4 = n4
% 30.44/10.20 |
% 30.44/10.20 | From (1010) and (716) follows:
% 30.44/10.20 | (1012) pred(n4) = all_0_3_3
% 30.44/10.20 |
% 30.44/10.20 | From (1014) and (1304) follows:
% 30.44/10.20 | (3929) sum(n8, n2) = all_0_0_0
% 30.44/10.20 |
% 30.44/10.20 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 30.44/10.20 | (1013) all_0_3_3 = n3
% 30.44/10.20 |
% 30.44/10.20 | Instantiating formula (619) with n8, n2, all_0_0_0, n10 and discharging atoms sum(n8, n2) = all_0_0_0, sum(n8, n2) = n10, yields:
% 30.44/10.20 | (864) all_0_0_0 = n10
% 30.44/10.20 |
% 30.44/10.20 | From (1013)(864) and (232) follows:
% 30.44/10.20 | (3932) sum(n3, n10) = all_0_6_6
% 30.44/10.20 |
% 30.44/10.20 | Instantiating formula (619) with n3, n10, all_0_6_6, n13 and discharging atoms sum(n3, n10) = all_0_6_6, sum(n3, n10) = n13, yields:
% 30.44/10.20 | (764) all_0_6_6 = n13
% 30.44/10.20 |
% 30.44/10.20 | Equations (764) can reduce 293 to:
% 30.44/10.20 | (748) $false
% 30.44/10.20 |
% 30.44/10.20 |-The branch is then unsatisfiable
% 30.44/10.20 |-Branch two:
% 30.44/10.20 | (1319) ~ (all_0_7_7 = n8)
% 30.44/10.20 | (1320) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.44/10.20 |
% 30.44/10.20 +-Applying beta-rule and splitting (1320), into two cases.
% 30.54/10.20 |-Branch one:
% 30.54/10.20 | (1321) all_0_7_7 = n7
% 30.54/10.20 |
% 30.54/10.20 | From (1321) and (683) follows:
% 30.54/10.20 | (1322) succ(n7) = all_0_5_5
% 30.54/10.20 |
% 30.54/10.20 | From (1321) and (8) follows:
% 30.54/10.20 | (1323) sum(n7, all_0_1_1) = all_0_0_0
% 30.54/10.20 |
% 30.54/10.20 | From (1321) and (3784) follows:
% 30.54/10.20 | (3940) sum(n16, n7) = all_0_2_2
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (388) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 30.54/10.20 | (1325) all_0_5_5 = n8
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (619) with n16, n7, all_0_2_2, n2 and discharging atoms sum(n16, n7) = all_0_2_2, sum(n16, n7) = n2, yields:
% 30.54/10.20 | (1026) all_0_2_2 = n2
% 30.54/10.20 |
% 30.54/10.20 | From (1026) and (473) follows:
% 30.54/10.20 | (1028) pred(n2) = all_0_1_1
% 30.54/10.20 |
% 30.54/10.20 | From (1325) and (3783) follows:
% 30.54/10.20 | (3944) sum(n16, n8) = all_0_4_4
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 30.54/10.20 | (1031) all_0_1_1 = n1
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (619) with n16, n8, all_0_4_4, n3 and discharging atoms sum(n16, n8) = all_0_4_4, sum(n16, n8) = n3, yields:
% 30.54/10.20 | (1027) all_0_4_4 = n3
% 30.54/10.20 |
% 30.54/10.20 | From (1027) and (716) follows:
% 30.54/10.20 | (1029) pred(n3) = all_0_3_3
% 30.54/10.20 |
% 30.54/10.20 | From (1031) and (1323) follows:
% 30.54/10.20 | (3948) sum(n7, n1) = all_0_0_0
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 30.54/10.20 | (1030) all_0_3_3 = n2
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (619) with n7, n1, all_0_0_0, n8 and discharging atoms sum(n7, n1) = all_0_0_0, sum(n7, n1) = n8, yields:
% 30.54/10.20 | (898) all_0_0_0 = n8
% 30.54/10.20 |
% 30.54/10.20 | From (1030)(898) and (232) follows:
% 30.54/10.20 | (3951) sum(n2, n8) = all_0_6_6
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (619) with n2, n8, all_0_6_6, n10 and discharging atoms sum(n2, n8) = all_0_6_6, sum(n2, n8) = n10, yields:
% 30.54/10.20 | (968) all_0_6_6 = n10
% 30.54/10.20 |
% 30.54/10.20 | Equations (968) can reduce 176 to:
% 30.54/10.20 | (748) $false
% 30.54/10.20 |
% 30.54/10.20 |-The branch is then unsatisfiable
% 30.54/10.20 |-Branch two:
% 30.54/10.20 | (1338) ~ (all_0_7_7 = n7)
% 30.54/10.20 | (1339) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.54/10.20 |
% 30.54/10.20 +-Applying beta-rule and splitting (1339), into two cases.
% 30.54/10.20 |-Branch one:
% 30.54/10.20 | (1340) all_0_7_7 = n6
% 30.54/10.20 |
% 30.54/10.20 | From (1340) and (683) follows:
% 30.54/10.20 | (1341) succ(n6) = all_0_5_5
% 30.54/10.20 |
% 30.54/10.20 | From (1340) and (8) follows:
% 30.54/10.20 | (1342) sum(n6, all_0_1_1) = all_0_0_0
% 30.54/10.20 |
% 30.54/10.20 | From (1340) and (3784) follows:
% 30.54/10.20 | (3959) sum(n16, n6) = all_0_2_2
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (388) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 30.54/10.20 | (1344) all_0_5_5 = n7
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (619) with n16, n6, all_0_2_2, n1 and discharging atoms sum(n16, n6) = all_0_2_2, sum(n16, n6) = n1, yields:
% 30.54/10.20 | (1043) all_0_2_2 = n1
% 30.54/10.20 |
% 30.54/10.20 | From (1043) and (473) follows:
% 30.54/10.20 | (1045) pred(n1) = all_0_1_1
% 30.54/10.20 |
% 30.54/10.20 | From (1344) and (3783) follows:
% 30.54/10.20 | (3963) sum(n16, n7) = all_0_4_4
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 30.54/10.20 | (1048) all_0_1_1 = n0
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (619) with n16, n7, all_0_4_4, n2 and discharging atoms sum(n16, n7) = all_0_4_4, sum(n16, n7) = n2, yields:
% 30.54/10.20 | (1044) all_0_4_4 = n2
% 30.54/10.20 |
% 30.54/10.20 | From (1044) and (716) follows:
% 30.54/10.20 | (1046) pred(n2) = all_0_3_3
% 30.54/10.20 |
% 30.54/10.20 | From (1048) and (1342) follows:
% 30.54/10.20 | (3967) sum(n6, n0) = all_0_0_0
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 30.54/10.20 | (1047) all_0_3_3 = n1
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (619) with n6, n0, all_0_0_0, n6 and discharging atoms sum(n6, n0) = all_0_0_0, sum(n6, n0) = n6, yields:
% 30.54/10.20 | (932) all_0_0_0 = n6
% 30.54/10.20 |
% 30.54/10.20 | From (1047)(932) and (232) follows:
% 30.54/10.20 | (3970) sum(n1, n6) = all_0_6_6
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (619) with n1, n6, all_0_6_6, n7 and discharging atoms sum(n1, n6) = all_0_6_6, sum(n1, n6) = n7, yields:
% 30.54/10.20 | (815) all_0_6_6 = n7
% 30.54/10.20 |
% 30.54/10.20 | Equations (815) can reduce 557 to:
% 30.54/10.20 | (748) $false
% 30.54/10.20 |
% 30.54/10.20 |-The branch is then unsatisfiable
% 30.54/10.20 |-Branch two:
% 30.54/10.20 | (1357) ~ (all_0_7_7 = n6)
% 30.54/10.20 | (1358) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.54/10.20 |
% 30.54/10.20 +-Applying beta-rule and splitting (1358), into two cases.
% 30.54/10.20 |-Branch one:
% 30.54/10.20 | (1359) all_0_7_7 = n5
% 30.54/10.20 |
% 30.54/10.20 | From (1359) and (683) follows:
% 30.54/10.20 | (1360) succ(n5) = all_0_5_5
% 30.54/10.20 |
% 30.54/10.20 | From (1359) and (8) follows:
% 30.54/10.20 | (1361) sum(n5, all_0_1_1) = all_0_0_0
% 30.54/10.20 |
% 30.54/10.20 | From (1359) and (3784) follows:
% 30.54/10.20 | (3978) sum(n16, n5) = all_0_2_2
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (388) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 30.54/10.20 | (1363) all_0_5_5 = n6
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (619) with n16, n5, all_0_2_2, n0 and discharging atoms sum(n16, n5) = all_0_2_2, sum(n16, n5) = n0, yields:
% 30.54/10.20 | (1060) all_0_2_2 = n0
% 30.54/10.20 |
% 30.54/10.20 | From (1060) and (473) follows:
% 30.54/10.20 | (1062) pred(n0) = all_0_1_1
% 30.54/10.20 |
% 30.54/10.20 | From (1363) and (3783) follows:
% 30.54/10.20 | (3982) sum(n16, n6) = all_0_4_4
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 30.54/10.20 | (1065) all_0_1_1 = n20
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (619) with n16, n6, all_0_4_4, n1 and discharging atoms sum(n16, n6) = all_0_4_4, sum(n16, n6) = n1, yields:
% 30.54/10.20 | (1061) all_0_4_4 = n1
% 30.54/10.20 |
% 30.54/10.20 | From (1061) and (716) follows:
% 30.54/10.20 | (1063) pred(n1) = all_0_3_3
% 30.54/10.20 |
% 30.54/10.20 | From (1065) and (1361) follows:
% 30.54/10.20 | (3986) sum(n5, n20) = all_0_0_0
% 30.54/10.20 |
% 30.54/10.20 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 30.54/10.21 | (1064) all_0_3_3 = n0
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n5, n20, all_0_0_0, n4 and discharging atoms sum(n5, n20) = all_0_0_0, sum(n5, n20) = n4, yields:
% 30.54/10.21 | (966) all_0_0_0 = n4
% 30.54/10.21 |
% 30.54/10.21 | From (1064)(966) and (232) follows:
% 30.54/10.21 | (3989) sum(n0, n4) = all_0_6_6
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n0, n4, all_0_6_6, n4 and discharging atoms sum(n0, n4) = all_0_6_6, sum(n0, n4) = n4, yields:
% 30.54/10.21 | (1019) all_0_6_6 = n4
% 30.54/10.21 |
% 30.54/10.21 | Equations (1019) can reduce 48 to:
% 30.54/10.21 | (748) $false
% 30.54/10.21 |
% 30.54/10.21 |-The branch is then unsatisfiable
% 30.54/10.21 |-Branch two:
% 30.54/10.21 | (1376) ~ (all_0_7_7 = n5)
% 30.54/10.21 | (1377) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.54/10.21 |
% 30.54/10.21 +-Applying beta-rule and splitting (1377), into two cases.
% 30.54/10.21 |-Branch one:
% 30.54/10.21 | (1378) all_0_7_7 = n4
% 30.54/10.21 |
% 30.54/10.21 | From (1378) and (683) follows:
% 30.54/10.21 | (1379) succ(n4) = all_0_5_5
% 30.54/10.21 |
% 30.54/10.21 | From (1378) and (8) follows:
% 30.54/10.21 | (1380) sum(n4, all_0_1_1) = all_0_0_0
% 30.54/10.21 |
% 30.54/10.21 | From (1378) and (3784) follows:
% 30.54/10.21 | (3997) sum(n16, n4) = all_0_2_2
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (388) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 30.54/10.21 | (1382) all_0_5_5 = n5
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n16, n4, all_0_2_2, n20 and discharging atoms sum(n16, n4) = all_0_2_2, sum(n16, n4) = n20, yields:
% 30.54/10.21 | (1076) all_0_2_2 = n20
% 30.54/10.21 |
% 30.54/10.21 | From (1076) and (473) follows:
% 30.54/10.21 | (1078) pred(n20) = all_0_1_1
% 30.54/10.21 |
% 30.54/10.21 | From (1382) and (3783) follows:
% 30.54/10.21 | (4001) sum(n16, n5) = all_0_4_4
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 30.54/10.21 | (1080) all_0_1_1 = n19
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n16, n5, all_0_4_4, n0 and discharging atoms sum(n16, n5) = all_0_4_4, sum(n16, n5) = n0, yields:
% 30.54/10.21 | (1077) all_0_4_4 = n0
% 30.54/10.21 |
% 30.54/10.21 | From (1077) and (716) follows:
% 30.54/10.21 | (1079) pred(n0) = all_0_3_3
% 30.54/10.21 |
% 30.54/10.21 | From (1080) and (1380) follows:
% 30.54/10.21 | (4005) sum(n4, n19) = all_0_0_0
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 30.54/10.21 | (1081) all_0_3_3 = n20
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n4, n19, all_0_0_0, n2 and discharging atoms sum(n4, n19) = all_0_0_0, sum(n4, n19) = n2, yields:
% 30.54/10.21 | (1000) all_0_0_0 = n2
% 30.54/10.21 |
% 30.54/10.21 | From (1081)(1000) and (232) follows:
% 30.54/10.21 | (4008) sum(n20, n2) = all_0_6_6
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n20, n2, all_0_6_6, n1 and discharging atoms sum(n20, n2) = all_0_6_6, sum(n20, n2) = n1, yields:
% 30.54/10.21 | (866) all_0_6_6 = n1
% 30.54/10.21 |
% 30.54/10.21 | Equations (866) can reduce 28 to:
% 30.54/10.21 | (748) $false
% 30.54/10.21 |
% 30.54/10.21 |-The branch is then unsatisfiable
% 30.54/10.21 |-Branch two:
% 30.54/10.21 | (1395) ~ (all_0_7_7 = n4)
% 30.54/10.21 | (1396) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.54/10.21 |
% 30.54/10.21 +-Applying beta-rule and splitting (1396), into two cases.
% 30.54/10.21 |-Branch one:
% 30.54/10.21 | (1397) all_0_7_7 = n3
% 30.54/10.21 |
% 30.54/10.21 | From (1397) and (683) follows:
% 30.54/10.21 | (1398) succ(n3) = all_0_5_5
% 30.54/10.21 |
% 30.54/10.21 | From (1397) and (8) follows:
% 30.54/10.21 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 30.54/10.21 |
% 30.54/10.21 | From (1397) and (3784) follows:
% 30.54/10.21 | (4016) sum(n16, n3) = all_0_2_2
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 30.54/10.21 | (1401) all_0_5_5 = n4
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n16, n3, all_0_2_2, n19 and discharging atoms sum(n16, n3) = all_0_2_2, sum(n16, n3) = n19, yields:
% 30.54/10.21 | (737) all_0_2_2 = n19
% 30.54/10.21 |
% 30.54/10.21 | From (737) and (473) follows:
% 30.54/10.21 | (739) pred(n19) = all_0_1_1
% 30.54/10.21 |
% 30.54/10.21 | From (1401) and (3783) follows:
% 30.54/10.21 | (4020) sum(n16, n4) = all_0_4_4
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 30.54/10.21 | (742) all_0_1_1 = n18
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n16, n4, all_0_4_4, n20 and discharging atoms sum(n16, n4) = all_0_4_4, sum(n16, n4) = n20, yields:
% 30.54/10.21 | (738) all_0_4_4 = n20
% 30.54/10.21 |
% 30.54/10.21 | From (738) and (716) follows:
% 30.54/10.21 | (740) pred(n20) = all_0_3_3
% 30.54/10.21 |
% 30.54/10.21 | From (742) and (1399) follows:
% 30.54/10.21 | (4024) sum(n3, n18) = all_0_0_0
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 30.54/10.21 | (741) all_0_3_3 = n19
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n3, n18, all_0_0_0, n0 and discharging atoms sum(n3, n18) = all_0_0_0, sum(n3, n18) = n0, yields:
% 30.54/10.21 | (1034) all_0_0_0 = n0
% 30.54/10.21 |
% 30.54/10.21 | From (741)(1034) and (232) follows:
% 30.54/10.21 | (4027) sum(n19, n0) = all_0_6_6
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n19, n0, all_0_6_6, n19 and discharging atoms sum(n19, n0) = all_0_6_6, sum(n19, n0) = n19, yields:
% 30.54/10.21 | (1070) all_0_6_6 = n19
% 30.54/10.21 |
% 30.54/10.21 | Equations (1070) can reduce 31 to:
% 30.54/10.21 | (748) $false
% 30.54/10.21 |
% 30.54/10.21 |-The branch is then unsatisfiable
% 30.54/10.21 |-Branch two:
% 30.54/10.21 | (1414) ~ (all_0_7_7 = n3)
% 30.54/10.21 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.54/10.21 |
% 30.54/10.21 +-Applying beta-rule and splitting (1415), into two cases.
% 30.54/10.21 |-Branch one:
% 30.54/10.21 | (1416) all_0_7_7 = n2
% 30.54/10.21 |
% 30.54/10.21 | From (1416) and (683) follows:
% 30.54/10.21 | (1417) succ(n2) = all_0_5_5
% 30.54/10.21 |
% 30.54/10.21 | From (1416) and (8) follows:
% 30.54/10.21 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 30.54/10.21 |
% 30.54/10.21 | From (1416) and (3784) follows:
% 30.54/10.21 | (4035) sum(n16, n2) = all_0_2_2
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 30.54/10.21 | (1420) all_0_5_5 = n3
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n16, n2, all_0_2_2, n18 and discharging atoms sum(n16, n2) = all_0_2_2, sum(n16, n2) = n18, yields:
% 30.54/10.21 | (754) all_0_2_2 = n18
% 30.54/10.21 |
% 30.54/10.21 | From (754) and (473) follows:
% 30.54/10.21 | (756) pred(n18) = all_0_1_1
% 30.54/10.21 |
% 30.54/10.21 | From (1420) and (3783) follows:
% 30.54/10.21 | (4039) sum(n16, n3) = all_0_4_4
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 30.54/10.21 | (759) all_0_1_1 = n17
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n16, n3, all_0_4_4, n19 and discharging atoms sum(n16, n3) = all_0_4_4, sum(n16, n3) = n19, yields:
% 30.54/10.21 | (755) all_0_4_4 = n19
% 30.54/10.21 |
% 30.54/10.21 | From (755) and (716) follows:
% 30.54/10.21 | (757) pred(n19) = all_0_3_3
% 30.54/10.21 |
% 30.54/10.21 | From (759) and (1418) follows:
% 30.54/10.21 | (4043) sum(n2, n17) = all_0_0_0
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 30.54/10.21 | (758) all_0_3_3 = n18
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n2, n17, all_0_0_0, n19 and discharging atoms sum(n2, n17) = all_0_0_0, sum(n2, n17) = n19, yields:
% 30.54/10.21 | (1068) all_0_0_0 = n19
% 30.54/10.21 |
% 30.54/10.21 | From (758)(1068) and (232) follows:
% 30.54/10.21 | (4046) sum(n18, n19) = all_0_6_6
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n18, n19, all_0_6_6, n16 and discharging atoms sum(n18, n19) = all_0_6_6, sum(n18, n19) = n16, yields:
% 30.54/10.21 | (917) all_0_6_6 = n16
% 30.54/10.21 |
% 30.54/10.21 | Equations (917) can reduce 163 to:
% 30.54/10.21 | (748) $false
% 30.54/10.21 |
% 30.54/10.21 |-The branch is then unsatisfiable
% 30.54/10.21 |-Branch two:
% 30.54/10.21 | (1433) ~ (all_0_7_7 = n2)
% 30.54/10.21 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 30.54/10.21 |
% 30.54/10.21 +-Applying beta-rule and splitting (1434), into two cases.
% 30.54/10.21 |-Branch one:
% 30.54/10.21 | (1435) all_0_7_7 = n1
% 30.54/10.21 |
% 30.54/10.21 | From (1435) and (683) follows:
% 30.54/10.21 | (1436) succ(n1) = all_0_5_5
% 30.54/10.21 |
% 30.54/10.21 | From (1435) and (8) follows:
% 30.54/10.21 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 30.54/10.21 |
% 30.54/10.21 | From (1435) and (3784) follows:
% 30.54/10.21 | (4054) sum(n16, n1) = all_0_2_2
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 30.54/10.21 | (1439) all_0_5_5 = n2
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n16, n1, all_0_2_2, n17 and discharging atoms sum(n16, n1) = all_0_2_2, sum(n16, n1) = n17, yields:
% 30.54/10.21 | (771) all_0_2_2 = n17
% 30.54/10.21 |
% 30.54/10.21 | From (771) and (473) follows:
% 30.54/10.21 | (773) pred(n17) = all_0_1_1
% 30.54/10.21 |
% 30.54/10.21 | From (1439) and (3783) follows:
% 30.54/10.21 | (4058) sum(n16, n2) = all_0_4_4
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 30.54/10.21 | (776) all_0_1_1 = n16
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n16, n2, all_0_4_4, n18 and discharging atoms sum(n16, n2) = all_0_4_4, sum(n16, n2) = n18, yields:
% 30.54/10.21 | (772) all_0_4_4 = n18
% 30.54/10.21 |
% 30.54/10.21 | From (772) and (716) follows:
% 30.54/10.21 | (774) pred(n18) = all_0_3_3
% 30.54/10.21 |
% 30.54/10.21 | From (776) and (1437) follows:
% 30.54/10.21 | (4062) sum(n1, n16) = all_0_0_0
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 30.54/10.21 | (775) all_0_3_3 = n17
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n1, n16, all_0_0_0, n17 and discharging atoms sum(n1, n16) = all_0_0_0, sum(n1, n16) = n17, yields:
% 30.54/10.21 | (745) all_0_0_0 = n17
% 30.54/10.21 |
% 30.54/10.21 | From (775)(745) and (232) follows:
% 30.54/10.21 | (4065) sum(n17, n17) = all_0_6_6
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n17, n17, all_0_6_6, n13 and discharging atoms sum(n17, n17) = all_0_6_6, sum(n17, n17) = n13, yields:
% 30.54/10.21 | (764) all_0_6_6 = n13
% 30.54/10.21 |
% 30.54/10.21 | Equations (764) can reduce 293 to:
% 30.54/10.21 | (748) $false
% 30.54/10.21 |
% 30.54/10.21 |-The branch is then unsatisfiable
% 30.54/10.21 |-Branch two:
% 30.54/10.21 | (1452) ~ (all_0_7_7 = n1)
% 30.54/10.21 | (1453) all_0_7_7 = n0
% 30.54/10.21 |
% 30.54/10.21 | From (1453) and (683) follows:
% 30.54/10.21 | (1454) succ(n0) = all_0_5_5
% 30.54/10.21 |
% 30.54/10.21 | From (1453) and (8) follows:
% 30.54/10.21 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 30.54/10.21 |
% 30.54/10.21 | From (1453) and (3784) follows:
% 30.54/10.21 | (4072) sum(n16, n0) = all_0_2_2
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 30.54/10.21 | (1457) all_0_5_5 = n1
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n16, n0, all_0_2_2, n16 and discharging atoms sum(n16, n0) = all_0_2_2, sum(n16, n0) = n16, yields:
% 30.54/10.21 | (788) all_0_2_2 = n16
% 30.54/10.21 |
% 30.54/10.21 | From (788) and (473) follows:
% 30.54/10.21 | (790) pred(n16) = all_0_1_1
% 30.54/10.21 |
% 30.54/10.21 | From (1457) and (3783) follows:
% 30.54/10.21 | (4076) sum(n16, n1) = all_0_4_4
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 30.54/10.21 | (793) all_0_1_1 = n15
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n16, n1, all_0_4_4, n17 and discharging atoms sum(n16, n1) = all_0_4_4, sum(n16, n1) = n17, yields:
% 30.54/10.21 | (789) all_0_4_4 = n17
% 30.54/10.21 |
% 30.54/10.21 | From (789) and (716) follows:
% 30.54/10.21 | (791) pred(n17) = all_0_3_3
% 30.54/10.21 |
% 30.54/10.21 | From (793) and (1455) follows:
% 30.54/10.21 | (4080) sum(n0, n15) = all_0_0_0
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 30.54/10.21 | (792) all_0_3_3 = n16
% 30.54/10.21 |
% 30.54/10.21 | Instantiating formula (619) with n0, n15, all_0_0_0, n15 and discharging atoms sum(n0, n15) = all_0_0_0, sum(n0, n15) = n15, yields:
% 30.54/10.21 | (779) all_0_0_0 = n15
% 30.54/10.21 |
% 30.54/10.21 | From (792)(779) and (232) follows:
% 30.54/10.22 | (4083) sum(n16, n15) = all_0_6_6
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n16, n15, all_0_6_6, n10 and discharging atoms sum(n16, n15) = all_0_6_6, sum(n16, n15) = n10, yields:
% 30.54/10.22 | (968) all_0_6_6 = n10
% 30.54/10.22 |
% 30.54/10.22 | Equations (968) can reduce 176 to:
% 30.54/10.22 | (748) $false
% 30.54/10.22 |
% 30.54/10.22 |-The branch is then unsatisfiable
% 30.54/10.22 |-Branch two:
% 30.54/10.22 | (817) ~ (all_0_8_8 = n16)
% 30.54/10.22 | (818) all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.54/10.22 |
% 30.54/10.22 +-Applying beta-rule and splitting (1168), into two cases.
% 30.54/10.22 |-Branch one:
% 30.54/10.22 | (1169) all_0_7_7 = n15
% 30.54/10.22 |
% 30.54/10.22 | From (1169) and (683) follows:
% 30.54/10.22 | (1170) succ(n15) = all_0_5_5
% 30.54/10.22 |
% 30.54/10.22 | From (1169) and (8) follows:
% 30.54/10.22 | (1171) sum(n15, all_0_1_1) = all_0_0_0
% 30.54/10.22 |
% 30.54/10.22 | From (1169) and (378) follows:
% 30.54/10.22 | (4091) sum(all_0_8_8, n15) = all_0_2_2
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (388) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 30.54/10.22 | (1173) all_0_5_5 = n16
% 30.54/10.22 |
% 30.54/10.22 | From (1173) and (708) follows:
% 30.54/10.22 | (4093) sum(all_0_8_8, n16) = all_0_4_4
% 30.54/10.22 |
% 30.54/10.22 +-Applying beta-rule and splitting (818), into two cases.
% 30.54/10.22 |-Branch one:
% 30.54/10.22 | (819) all_0_8_8 = n15
% 30.54/10.22 |
% 30.54/10.22 | From (819) and (4093) follows:
% 30.54/10.22 | (4095) sum(n15, n16) = all_0_4_4
% 30.54/10.22 |
% 30.54/10.22 | From (819) and (4091) follows:
% 30.54/10.22 | (4096) sum(n15, n15) = all_0_2_2
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n15, n16, all_0_4_4, n10 and discharging atoms sum(n15, n16) = all_0_4_4, sum(n15, n16) = n10, yields:
% 30.54/10.22 | (908) all_0_4_4 = n10
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n15, n15, all_0_2_2, n9 and discharging atoms sum(n15, n15) = all_0_2_2, sum(n15, n15) = n9, yields:
% 30.54/10.22 | (907) all_0_2_2 = n9
% 30.54/10.22 |
% 30.54/10.22 | From (907) and (473) follows:
% 30.54/10.22 | (909) pred(n9) = all_0_1_1
% 30.54/10.22 |
% 30.54/10.22 | From (908) and (716) follows:
% 30.54/10.22 | (910) pred(n10) = all_0_3_3
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 30.54/10.22 | (911) all_0_3_3 = n9
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 30.54/10.22 | (912) all_0_1_1 = n8
% 30.54/10.22 |
% 30.54/10.22 | From (911) and (232) follows:
% 30.54/10.22 | (913) sum(n9, all_0_0_0) = all_0_6_6
% 30.54/10.22 |
% 30.54/10.22 | From (912) and (1171) follows:
% 30.54/10.22 | (4104) sum(n15, n8) = all_0_0_0
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n15, n8, all_0_0_0, n2 and discharging atoms sum(n15, n8) = all_0_0_0, sum(n15, n8) = n2, yields:
% 30.54/10.22 | (1000) all_0_0_0 = n2
% 30.54/10.22 |
% 30.54/10.22 | From (1000) and (913) follows:
% 30.54/10.22 | (4106) sum(n9, n2) = all_0_6_6
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n9, n2, all_0_6_6, n11 and discharging atoms sum(n9, n2) = all_0_6_6, sum(n9, n2) = n11, yields:
% 30.54/10.22 | (781) all_0_6_6 = n11
% 30.54/10.22 |
% 30.54/10.22 | Equations (781) can reduce 2 to:
% 30.54/10.22 | (748) $false
% 30.54/10.22 |
% 30.54/10.22 |-The branch is then unsatisfiable
% 30.54/10.22 |-Branch two:
% 30.54/10.22 | (834) ~ (all_0_8_8 = n15)
% 30.54/10.22 | (835) all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.54/10.22 |
% 30.54/10.22 +-Applying beta-rule and splitting (835), into two cases.
% 30.54/10.22 |-Branch one:
% 30.54/10.22 | (836) all_0_8_8 = n14
% 30.54/10.22 |
% 30.54/10.22 | From (836) and (4093) follows:
% 30.54/10.22 | (4112) sum(n14, n16) = all_0_4_4
% 30.54/10.22 |
% 30.54/10.22 | From (836) and (4091) follows:
% 30.54/10.22 | (4113) sum(n14, n15) = all_0_2_2
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n14, n16, all_0_4_4, n9 and discharging atoms sum(n14, n16) = all_0_4_4, sum(n14, n16) = n9, yields:
% 30.54/10.22 | (925) all_0_4_4 = n9
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n14, n15, all_0_2_2, n8 and discharging atoms sum(n14, n15) = all_0_2_2, sum(n14, n15) = n8, yields:
% 30.54/10.22 | (924) all_0_2_2 = n8
% 30.54/10.22 |
% 30.54/10.22 | From (924) and (473) follows:
% 30.54/10.22 | (926) pred(n8) = all_0_1_1
% 30.54/10.22 |
% 30.54/10.22 | From (925) and (716) follows:
% 30.54/10.22 | (927) pred(n9) = all_0_3_3
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 30.54/10.22 | (928) all_0_3_3 = n8
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 30.54/10.22 | (929) all_0_1_1 = n7
% 30.54/10.22 |
% 30.54/10.22 | From (928) and (232) follows:
% 30.54/10.22 | (930) sum(n8, all_0_0_0) = all_0_6_6
% 30.54/10.22 |
% 30.54/10.22 | From (929) and (1171) follows:
% 30.54/10.22 | (4121) sum(n15, n7) = all_0_0_0
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n15, n7, all_0_0_0, n1 and discharging atoms sum(n15, n7) = all_0_0_0, sum(n15, n7) = n1, yields:
% 30.54/10.22 | (1017) all_0_0_0 = n1
% 30.54/10.22 |
% 30.54/10.22 | From (1017) and (930) follows:
% 30.54/10.22 | (4123) sum(n8, n1) = all_0_6_6
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n8, n1, all_0_6_6, n9 and discharging atoms sum(n8, n1) = all_0_6_6, sum(n8, n1) = n9, yields:
% 30.54/10.22 | (798) all_0_6_6 = n9
% 30.54/10.22 |
% 30.54/10.22 | Equations (798) can reduce 593 to:
% 30.54/10.22 | (748) $false
% 30.54/10.22 |
% 30.54/10.22 |-The branch is then unsatisfiable
% 30.54/10.22 |-Branch two:
% 30.54/10.22 | (851) ~ (all_0_8_8 = n14)
% 30.54/10.22 | (852) all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.54/10.22 |
% 30.54/10.22 +-Applying beta-rule and splitting (852), into two cases.
% 30.54/10.22 |-Branch one:
% 30.54/10.22 | (853) all_0_8_8 = n13
% 30.54/10.22 |
% 30.54/10.22 | From (853) and (4093) follows:
% 30.54/10.22 | (4129) sum(n13, n16) = all_0_4_4
% 30.54/10.22 |
% 30.54/10.22 | From (853) and (4091) follows:
% 30.54/10.22 | (4130) sum(n13, n15) = all_0_2_2
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n13, n16, all_0_4_4, n8 and discharging atoms sum(n13, n16) = all_0_4_4, sum(n13, n16) = n8, yields:
% 30.54/10.22 | (942) all_0_4_4 = n8
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n13, n15, all_0_2_2, n7 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n7, yields:
% 30.54/10.22 | (941) all_0_2_2 = n7
% 30.54/10.22 |
% 30.54/10.22 | From (941) and (473) follows:
% 30.54/10.22 | (943) pred(n7) = all_0_1_1
% 30.54/10.22 |
% 30.54/10.22 | From (942) and (716) follows:
% 30.54/10.22 | (944) pred(n8) = all_0_3_3
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 30.54/10.22 | (945) all_0_3_3 = n7
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 30.54/10.22 | (946) all_0_1_1 = n6
% 30.54/10.22 |
% 30.54/10.22 | From (945) and (232) follows:
% 30.54/10.22 | (947) sum(n7, all_0_0_0) = all_0_6_6
% 30.54/10.22 |
% 30.54/10.22 | From (946) and (1171) follows:
% 30.54/10.22 | (4138) sum(n15, n6) = all_0_0_0
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n15, n6, all_0_0_0, n0 and discharging atoms sum(n15, n6) = all_0_0_0, sum(n15, n6) = n0, yields:
% 30.54/10.22 | (1034) all_0_0_0 = n0
% 30.54/10.22 |
% 30.54/10.22 | From (1034) and (947) follows:
% 30.54/10.22 | (4140) sum(n7, n0) = all_0_6_6
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n7, n0, all_0_6_6, n7 and discharging atoms sum(n7, n0) = all_0_6_6, sum(n7, n0) = n7, yields:
% 30.54/10.22 | (815) all_0_6_6 = n7
% 30.54/10.22 |
% 30.54/10.22 | Equations (815) can reduce 557 to:
% 30.54/10.22 | (748) $false
% 30.54/10.22 |
% 30.54/10.22 |-The branch is then unsatisfiable
% 30.54/10.22 |-Branch two:
% 30.54/10.22 | (868) ~ (all_0_8_8 = n13)
% 30.54/10.22 | (869) all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.54/10.22 |
% 30.54/10.22 +-Applying beta-rule and splitting (869), into two cases.
% 30.54/10.22 |-Branch one:
% 30.54/10.22 | (870) all_0_8_8 = n12
% 30.54/10.22 |
% 30.54/10.22 | From (870) and (4093) follows:
% 30.54/10.22 | (4146) sum(n12, n16) = all_0_4_4
% 30.54/10.22 |
% 30.54/10.22 | From (870) and (4091) follows:
% 30.54/10.22 | (4147) sum(n12, n15) = all_0_2_2
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n12, n16, all_0_4_4, n7 and discharging atoms sum(n12, n16) = all_0_4_4, sum(n12, n16) = n7, yields:
% 30.54/10.22 | (959) all_0_4_4 = n7
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n12, n15, all_0_2_2, n6 and discharging atoms sum(n12, n15) = all_0_2_2, sum(n12, n15) = n6, yields:
% 30.54/10.22 | (958) all_0_2_2 = n6
% 30.54/10.22 |
% 30.54/10.22 | From (958) and (473) follows:
% 30.54/10.22 | (960) pred(n6) = all_0_1_1
% 30.54/10.22 |
% 30.54/10.22 | From (959) and (716) follows:
% 30.54/10.22 | (961) pred(n7) = all_0_3_3
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 30.54/10.22 | (962) all_0_3_3 = n6
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 30.54/10.22 | (963) all_0_1_1 = n5
% 30.54/10.22 |
% 30.54/10.22 | From (962) and (232) follows:
% 30.54/10.22 | (964) sum(n6, all_0_0_0) = all_0_6_6
% 30.54/10.22 |
% 30.54/10.22 | From (963) and (1171) follows:
% 30.54/10.22 | (4155) sum(n15, n5) = all_0_0_0
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n15, n5, all_0_0_0, n20 and discharging atoms sum(n15, n5) = all_0_0_0, sum(n15, n5) = n20, yields:
% 30.54/10.22 | (1051) all_0_0_0 = n20
% 30.54/10.22 |
% 30.54/10.22 | From (1051) and (964) follows:
% 30.54/10.22 | (4157) sum(n6, n20) = all_0_6_6
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n6, n20, all_0_6_6, n5 and discharging atoms sum(n6, n20) = all_0_6_6, sum(n6, n20) = n5, yields:
% 30.54/10.22 | (832) all_0_6_6 = n5
% 30.54/10.22 |
% 30.54/10.22 | Equations (832) can reduce 462 to:
% 30.54/10.22 | (748) $false
% 30.54/10.22 |
% 30.54/10.22 |-The branch is then unsatisfiable
% 30.54/10.22 |-Branch two:
% 30.54/10.22 | (885) ~ (all_0_8_8 = n12)
% 30.54/10.22 | (886) all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.54/10.22 |
% 30.54/10.22 +-Applying beta-rule and splitting (886), into two cases.
% 30.54/10.22 |-Branch one:
% 30.54/10.22 | (887) all_0_8_8 = n11
% 30.54/10.22 |
% 30.54/10.22 | From (887) and (4093) follows:
% 30.54/10.22 | (4163) sum(n11, n16) = all_0_4_4
% 30.54/10.22 |
% 30.54/10.22 | From (887) and (4091) follows:
% 30.54/10.22 | (4164) sum(n11, n15) = all_0_2_2
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n11, n16, all_0_4_4, n6 and discharging atoms sum(n11, n16) = all_0_4_4, sum(n11, n16) = n6, yields:
% 30.54/10.22 | (976) all_0_4_4 = n6
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n11, n15, all_0_2_2, n5 and discharging atoms sum(n11, n15) = all_0_2_2, sum(n11, n15) = n5, yields:
% 30.54/10.22 | (975) all_0_2_2 = n5
% 30.54/10.22 |
% 30.54/10.22 | From (975) and (473) follows:
% 30.54/10.22 | (977) pred(n5) = all_0_1_1
% 30.54/10.22 |
% 30.54/10.22 | From (976) and (716) follows:
% 30.54/10.22 | (978) pred(n6) = all_0_3_3
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 30.54/10.22 | (979) all_0_3_3 = n5
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 30.54/10.22 | (980) all_0_1_1 = n4
% 30.54/10.22 |
% 30.54/10.22 | From (979) and (232) follows:
% 30.54/10.22 | (981) sum(n5, all_0_0_0) = all_0_6_6
% 30.54/10.22 |
% 30.54/10.22 | From (980) and (1171) follows:
% 30.54/10.22 | (4172) sum(n15, n4) = all_0_0_0
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n15, n4, all_0_0_0, n19 and discharging atoms sum(n15, n4) = all_0_0_0, sum(n15, n4) = n19, yields:
% 30.54/10.22 | (1068) all_0_0_0 = n19
% 30.54/10.22 |
% 30.54/10.22 | From (1068) and (981) follows:
% 30.54/10.22 | (4174) sum(n5, n19) = all_0_6_6
% 30.54/10.22 |
% 30.54/10.22 | Instantiating formula (619) with n5, n19, all_0_6_6, n3 and discharging atoms sum(n5, n19) = all_0_6_6, sum(n5, n19) = n3, yields:
% 30.54/10.22 | (849) all_0_6_6 = n3
% 30.54/10.22 |
% 30.54/10.22 | Equations (849) can reduce 416 to:
% 30.54/10.23 | (748) $false
% 30.54/10.23 |
% 30.54/10.23 |-The branch is then unsatisfiable
% 30.54/10.23 |-Branch two:
% 30.54/10.23 | (902) ~ (all_0_8_8 = n11)
% 30.54/10.23 | (903) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.54/10.23 |
% 30.54/10.23 +-Applying beta-rule and splitting (903), into two cases.
% 30.54/10.23 |-Branch one:
% 30.54/10.23 | (904) all_0_8_8 = n10
% 30.54/10.23 |
% 30.54/10.23 | From (904) and (4093) follows:
% 30.54/10.23 | (4180) sum(n10, n16) = all_0_4_4
% 30.54/10.23 |
% 30.54/10.23 | From (904) and (4091) follows:
% 30.54/10.23 | (4181) sum(n10, n15) = all_0_2_2
% 30.54/10.23 |
% 30.54/10.23 | Instantiating formula (619) with n10, n16, all_0_4_4, n5 and discharging atoms sum(n10, n16) = all_0_4_4, sum(n10, n16) = n5, yields:
% 30.54/10.23 | (993) all_0_4_4 = n5
% 30.54/10.23 |
% 30.54/10.23 | Instantiating formula (619) with n10, n15, all_0_2_2, n4 and discharging atoms sum(n10, n15) = all_0_2_2, sum(n10, n15) = n4, yields:
% 30.54/10.23 | (992) all_0_2_2 = n4
% 30.54/10.23 |
% 30.54/10.23 | From (992) and (473) follows:
% 30.54/10.23 | (994) pred(n4) = all_0_1_1
% 30.54/10.23 |
% 30.54/10.23 | From (993) and (716) follows:
% 30.54/10.23 | (995) pred(n5) = all_0_3_3
% 30.54/10.23 |
% 30.54/10.23 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 30.54/10.23 | (996) all_0_3_3 = n4
% 30.54/10.23 |
% 30.54/10.23 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 30.54/10.23 | (997) all_0_1_1 = n3
% 30.54/10.23 |
% 30.54/10.23 | From (996) and (232) follows:
% 30.54/10.23 | (998) sum(n4, all_0_0_0) = all_0_6_6
% 30.54/10.23 |
% 30.54/10.23 | From (997) and (1171) follows:
% 30.54/10.23 | (4189) sum(n15, n3) = all_0_0_0
% 30.54/10.23 |
% 30.54/10.23 | Instantiating formula (619) with n15, n3, all_0_0_0, n18 and discharging atoms sum(n15, n3) = all_0_0_0, sum(n15, n3) = n18, yields:
% 30.54/10.23 | (1084) all_0_0_0 = n18
% 30.54/10.23 |
% 30.54/10.23 | From (1084) and (998) follows:
% 30.54/10.23 | (4191) sum(n4, n18) = all_0_6_6
% 30.54/10.23 |
% 30.54/10.23 | Instantiating formula (619) with n4, n18, all_0_6_6, n1 and discharging atoms sum(n4, n18) = all_0_6_6, sum(n4, n18) = n1, yields:
% 30.54/10.23 | (866) all_0_6_6 = n1
% 30.54/10.23 |
% 30.54/10.23 | Equations (866) can reduce 28 to:
% 30.54/10.23 | (748) $false
% 30.54/10.23 |
% 30.54/10.23 |-The branch is then unsatisfiable
% 30.54/10.23 |-Branch two:
% 30.54/10.23 | (919) ~ (all_0_8_8 = n10)
% 30.54/10.23 | (920) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.54/10.23 |
% 30.54/10.23 +-Applying beta-rule and splitting (920), into two cases.
% 30.54/10.23 |-Branch one:
% 30.54/10.23 | (921) all_0_8_8 = n9
% 30.54/10.23 |
% 30.54/10.23 | From (921) and (4093) follows:
% 30.54/10.23 | (4197) sum(n9, n16) = all_0_4_4
% 30.65/10.23 |
% 30.65/10.23 | From (921) and (4091) follows:
% 30.65/10.23 | (4198) sum(n9, n15) = all_0_2_2
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n9, n16, all_0_4_4, n4 and discharging atoms sum(n9, n16) = all_0_4_4, sum(n9, n16) = n4, yields:
% 30.65/10.23 | (1010) all_0_4_4 = n4
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n9, n15, all_0_2_2, n3 and discharging atoms sum(n9, n15) = all_0_2_2, sum(n9, n15) = n3, yields:
% 30.65/10.23 | (1009) all_0_2_2 = n3
% 30.65/10.23 |
% 30.65/10.23 | From (1009) and (473) follows:
% 30.65/10.23 | (1011) pred(n3) = all_0_1_1
% 30.65/10.23 |
% 30.65/10.23 | From (1010) and (716) follows:
% 30.65/10.23 | (1012) pred(n4) = all_0_3_3
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 30.65/10.23 | (1013) all_0_3_3 = n3
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 30.65/10.23 | (1014) all_0_1_1 = n2
% 30.65/10.23 |
% 30.65/10.23 | From (1013) and (232) follows:
% 30.65/10.23 | (1015) sum(n3, all_0_0_0) = all_0_6_6
% 30.65/10.23 |
% 30.65/10.23 | From (1014) and (1171) follows:
% 30.65/10.23 | (4206) sum(n15, n2) = all_0_0_0
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n15, n2, all_0_0_0, n17 and discharging atoms sum(n15, n2) = all_0_0_0, sum(n15, n2) = n17, yields:
% 30.65/10.23 | (745) all_0_0_0 = n17
% 30.65/10.23 |
% 30.65/10.23 | From (745) and (1015) follows:
% 30.65/10.23 | (4208) sum(n3, n17) = all_0_6_6
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n3, n17, all_0_6_6, n20 and discharging atoms sum(n3, n17) = all_0_6_6, sum(n3, n17) = n20, yields:
% 30.65/10.23 | (883) all_0_6_6 = n20
% 30.65/10.23 |
% 30.65/10.23 | Equations (883) can reduce 381 to:
% 30.65/10.23 | (748) $false
% 30.65/10.23 |
% 30.65/10.23 |-The branch is then unsatisfiable
% 30.65/10.23 |-Branch two:
% 30.65/10.23 | (936) ~ (all_0_8_8 = n9)
% 30.65/10.23 | (937) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.23 |
% 30.65/10.23 +-Applying beta-rule and splitting (937), into two cases.
% 30.65/10.23 |-Branch one:
% 30.65/10.23 | (938) all_0_8_8 = n8
% 30.65/10.23 |
% 30.65/10.23 | From (938) and (4093) follows:
% 30.65/10.23 | (4214) sum(n8, n16) = all_0_4_4
% 30.65/10.23 |
% 30.65/10.23 | From (938) and (4091) follows:
% 30.65/10.23 | (4215) sum(n8, n15) = all_0_2_2
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n8, n16, all_0_4_4, n3 and discharging atoms sum(n8, n16) = all_0_4_4, sum(n8, n16) = n3, yields:
% 30.65/10.23 | (1027) all_0_4_4 = n3
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n8, n15, all_0_2_2, n2 and discharging atoms sum(n8, n15) = all_0_2_2, sum(n8, n15) = n2, yields:
% 30.65/10.23 | (1026) all_0_2_2 = n2
% 30.65/10.23 |
% 30.65/10.23 | From (1026) and (473) follows:
% 30.65/10.23 | (1028) pred(n2) = all_0_1_1
% 30.65/10.23 |
% 30.65/10.23 | From (1027) and (716) follows:
% 30.65/10.23 | (1029) pred(n3) = all_0_3_3
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 30.65/10.23 | (1030) all_0_3_3 = n2
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 30.65/10.23 | (1031) all_0_1_1 = n1
% 30.65/10.23 |
% 30.65/10.23 | From (1030) and (232) follows:
% 30.65/10.23 | (1032) sum(n2, all_0_0_0) = all_0_6_6
% 30.65/10.23 |
% 30.65/10.23 | From (1031) and (1171) follows:
% 30.65/10.23 | (4223) sum(n15, n1) = all_0_0_0
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n15, n1, all_0_0_0, n16 and discharging atoms sum(n15, n1) = all_0_0_0, sum(n15, n1) = n16, yields:
% 30.65/10.23 | (762) all_0_0_0 = n16
% 30.65/10.23 |
% 30.65/10.23 | From (762) and (1032) follows:
% 30.65/10.23 | (4225) sum(n2, n16) = all_0_6_6
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n2, n16, all_0_6_6, n18 and discharging atoms sum(n2, n16) = all_0_6_6, sum(n2, n16) = n18, yields:
% 30.65/10.23 | (900) all_0_6_6 = n18
% 30.65/10.23 |
% 30.65/10.23 | Equations (900) can reduce 622 to:
% 30.65/10.23 | (748) $false
% 30.65/10.23 |
% 30.65/10.23 |-The branch is then unsatisfiable
% 30.65/10.23 |-Branch two:
% 30.65/10.23 | (953) ~ (all_0_8_8 = n8)
% 30.65/10.23 | (954) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.23 |
% 30.65/10.23 +-Applying beta-rule and splitting (954), into two cases.
% 30.65/10.23 |-Branch one:
% 30.65/10.23 | (955) all_0_8_8 = n7
% 30.65/10.23 |
% 30.65/10.23 | From (955) and (4093) follows:
% 30.65/10.23 | (4231) sum(n7, n16) = all_0_4_4
% 30.65/10.23 |
% 30.65/10.23 | From (955) and (4091) follows:
% 30.65/10.23 | (4232) sum(n7, n15) = all_0_2_2
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n7, n16, all_0_4_4, n2 and discharging atoms sum(n7, n16) = all_0_4_4, sum(n7, n16) = n2, yields:
% 30.65/10.23 | (1044) all_0_4_4 = n2
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n7, n15, all_0_2_2, n1 and discharging atoms sum(n7, n15) = all_0_2_2, sum(n7, n15) = n1, yields:
% 30.65/10.23 | (1043) all_0_2_2 = n1
% 30.65/10.23 |
% 30.65/10.23 | From (1043) and (473) follows:
% 30.65/10.23 | (1045) pred(n1) = all_0_1_1
% 30.65/10.23 |
% 30.65/10.23 | From (1044) and (716) follows:
% 30.65/10.23 | (1046) pred(n2) = all_0_3_3
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 30.65/10.23 | (1047) all_0_3_3 = n1
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 30.65/10.23 | (1048) all_0_1_1 = n0
% 30.65/10.23 |
% 30.65/10.23 | From (1047) and (232) follows:
% 30.65/10.23 | (1049) sum(n1, all_0_0_0) = all_0_6_6
% 30.65/10.23 |
% 30.65/10.23 | From (1048) and (1171) follows:
% 30.65/10.23 | (4240) sum(n15, n0) = all_0_0_0
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n15, n0, all_0_0_0, n15 and discharging atoms sum(n15, n0) = all_0_0_0, sum(n15, n0) = n15, yields:
% 30.65/10.23 | (779) all_0_0_0 = n15
% 30.65/10.23 |
% 30.65/10.23 | From (779) and (1049) follows:
% 30.65/10.23 | (4242) sum(n1, n15) = all_0_6_6
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n1, n15, all_0_6_6, n16 and discharging atoms sum(n1, n15) = all_0_6_6, sum(n1, n15) = n16, yields:
% 30.65/10.23 | (917) all_0_6_6 = n16
% 30.65/10.23 |
% 30.65/10.23 | Equations (917) can reduce 163 to:
% 30.65/10.23 | (748) $false
% 30.65/10.23 |
% 30.65/10.23 |-The branch is then unsatisfiable
% 30.65/10.23 |-Branch two:
% 30.65/10.23 | (970) ~ (all_0_8_8 = n7)
% 30.65/10.23 | (971) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.23 |
% 30.65/10.23 +-Applying beta-rule and splitting (971), into two cases.
% 30.65/10.23 |-Branch one:
% 30.65/10.23 | (972) all_0_8_8 = n6
% 30.65/10.23 |
% 30.65/10.23 | From (972) and (4093) follows:
% 30.65/10.23 | (4248) sum(n6, n16) = all_0_4_4
% 30.65/10.23 |
% 30.65/10.23 | From (972) and (4091) follows:
% 30.65/10.23 | (4249) sum(n6, n15) = all_0_2_2
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n6, n16, all_0_4_4, n1 and discharging atoms sum(n6, n16) = all_0_4_4, sum(n6, n16) = n1, yields:
% 30.65/10.23 | (1061) all_0_4_4 = n1
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n6, n15, all_0_2_2, n0 and discharging atoms sum(n6, n15) = all_0_2_2, sum(n6, n15) = n0, yields:
% 30.65/10.23 | (1060) all_0_2_2 = n0
% 30.65/10.23 |
% 30.65/10.23 | From (1060) and (473) follows:
% 30.65/10.23 | (1062) pred(n0) = all_0_1_1
% 30.65/10.23 |
% 30.65/10.23 | From (1061) and (716) follows:
% 30.65/10.23 | (1063) pred(n1) = all_0_3_3
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 30.65/10.23 | (1064) all_0_3_3 = n0
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 30.65/10.23 | (1065) all_0_1_1 = n20
% 30.65/10.23 |
% 30.65/10.23 | From (1064) and (232) follows:
% 30.65/10.23 | (1066) sum(n0, all_0_0_0) = all_0_6_6
% 30.65/10.23 |
% 30.65/10.23 | From (1065) and (1171) follows:
% 30.65/10.23 | (4257) sum(n15, n20) = all_0_0_0
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n15, n20, all_0_0_0, n14 and discharging atoms sum(n15, n20) = all_0_0_0, sum(n15, n20) = n14, yields:
% 30.65/10.23 | (796) all_0_0_0 = n14
% 30.65/10.23 |
% 30.65/10.23 | From (796) and (1066) follows:
% 30.65/10.23 | (4259) sum(n0, n14) = all_0_6_6
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n0, n14, all_0_6_6, n14 and discharging atoms sum(n0, n14) = all_0_6_6, sum(n0, n14) = n14, yields:
% 30.65/10.23 | (934) all_0_6_6 = n14
% 30.65/10.23 |
% 30.65/10.23 | Equations (934) can reduce 353 to:
% 30.65/10.23 | (748) $false
% 30.65/10.23 |
% 30.65/10.23 |-The branch is then unsatisfiable
% 30.65/10.23 |-Branch two:
% 30.65/10.23 | (987) ~ (all_0_8_8 = n6)
% 30.65/10.23 | (988) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.23 |
% 30.65/10.23 +-Applying beta-rule and splitting (988), into two cases.
% 30.65/10.23 |-Branch one:
% 30.65/10.23 | (989) all_0_8_8 = n5
% 30.65/10.23 |
% 30.65/10.23 | From (989) and (4093) follows:
% 30.65/10.23 | (4265) sum(n5, n16) = all_0_4_4
% 30.65/10.23 |
% 30.65/10.23 | From (989) and (4091) follows:
% 30.65/10.23 | (4266) sum(n5, n15) = all_0_2_2
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n5, n16, all_0_4_4, n0 and discharging atoms sum(n5, n16) = all_0_4_4, sum(n5, n16) = n0, yields:
% 30.65/10.23 | (1077) all_0_4_4 = n0
% 30.65/10.23 |
% 30.65/10.23 | Instantiating formula (619) with n5, n15, all_0_2_2, n20 and discharging atoms sum(n5, n15) = all_0_2_2, sum(n5, n15) = n20, yields:
% 30.65/10.23 | (1076) all_0_2_2 = n20
% 30.65/10.23 |
% 30.65/10.23 | From (1076) and (473) follows:
% 30.65/10.23 | (1078) pred(n20) = all_0_1_1
% 30.65/10.23 |
% 30.65/10.23 | From (1077) and (716) follows:
% 30.65/10.23 | (1079) pred(n0) = all_0_3_3
% 30.65/10.23 |
% 30.65/10.24 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 30.65/10.24 | (1080) all_0_1_1 = n19
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 30.65/10.24 | (1081) all_0_3_3 = n20
% 30.65/10.24 |
% 30.65/10.24 | From (1081) and (232) follows:
% 30.65/10.24 | (1082) sum(n20, all_0_0_0) = all_0_6_6
% 30.65/10.24 |
% 30.65/10.24 | From (1080) and (1171) follows:
% 30.65/10.24 | (4274) sum(n15, n19) = all_0_0_0
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n15, n19, all_0_0_0, n13 and discharging atoms sum(n15, n19) = all_0_0_0, sum(n15, n19) = n13, yields:
% 30.65/10.24 | (813) all_0_0_0 = n13
% 30.65/10.24 |
% 30.65/10.24 | From (813) and (1082) follows:
% 30.65/10.24 | (4276) sum(n20, n13) = all_0_6_6
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n20, n13, all_0_6_6, n12 and discharging atoms sum(n20, n13) = all_0_6_6, sum(n20, n13) = n12, yields:
% 30.65/10.24 | (951) all_0_6_6 = n12
% 30.65/10.24 |
% 30.65/10.24 | Equations (951) can reduce 76 to:
% 30.65/10.24 | (748) $false
% 30.65/10.24 |
% 30.65/10.24 |-The branch is then unsatisfiable
% 30.65/10.24 |-Branch two:
% 30.65/10.24 | (1004) ~ (all_0_8_8 = n5)
% 30.65/10.24 | (1005) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.24 |
% 30.65/10.24 +-Applying beta-rule and splitting (1005), into two cases.
% 30.65/10.24 |-Branch one:
% 30.65/10.24 | (1006) all_0_8_8 = n4
% 30.65/10.24 |
% 30.65/10.24 | From (1006) and (4093) follows:
% 30.65/10.24 | (4282) sum(n4, n16) = all_0_4_4
% 30.65/10.24 |
% 30.65/10.24 | From (1006) and (4091) follows:
% 30.65/10.24 | (4283) sum(n4, n15) = all_0_2_2
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n4, n16, all_0_4_4, n20 and discharging atoms sum(n4, n16) = all_0_4_4, sum(n4, n16) = n20, yields:
% 30.65/10.24 | (738) all_0_4_4 = n20
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n4, n15, all_0_2_2, n19 and discharging atoms sum(n4, n15) = all_0_2_2, sum(n4, n15) = n19, yields:
% 30.65/10.24 | (737) all_0_2_2 = n19
% 30.65/10.24 |
% 30.65/10.24 | From (737) and (473) follows:
% 30.65/10.24 | (739) pred(n19) = all_0_1_1
% 30.65/10.24 |
% 30.65/10.24 | From (738) and (716) follows:
% 30.65/10.24 | (740) pred(n20) = all_0_3_3
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 30.65/10.24 | (741) all_0_3_3 = n19
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 30.65/10.24 | (742) all_0_1_1 = n18
% 30.65/10.24 |
% 30.65/10.24 | From (741) and (232) follows:
% 30.65/10.24 | (743) sum(n19, all_0_0_0) = all_0_6_6
% 30.65/10.24 |
% 30.65/10.24 | From (742) and (1171) follows:
% 30.65/10.24 | (4291) sum(n15, n18) = all_0_0_0
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n15, n18, all_0_0_0, n12 and discharging atoms sum(n15, n18) = all_0_0_0, sum(n15, n18) = n12, yields:
% 30.65/10.24 | (830) all_0_0_0 = n12
% 30.65/10.24 |
% 30.65/10.24 | From (830) and (743) follows:
% 30.65/10.24 | (4293) sum(n19, n12) = all_0_6_6
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n19, n12, all_0_6_6, n10 and discharging atoms sum(n19, n12) = all_0_6_6, sum(n19, n12) = n10, yields:
% 30.65/10.24 | (968) all_0_6_6 = n10
% 30.65/10.24 |
% 30.65/10.24 | Equations (968) can reduce 176 to:
% 30.65/10.24 | (748) $false
% 30.65/10.24 |
% 30.65/10.24 |-The branch is then unsatisfiable
% 30.65/10.24 |-Branch two:
% 30.65/10.24 | (1021) ~ (all_0_8_8 = n4)
% 30.65/10.24 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.24 |
% 30.65/10.24 +-Applying beta-rule and splitting (1022), into two cases.
% 30.65/10.24 |-Branch one:
% 30.65/10.24 | (1023) all_0_8_8 = n3
% 30.65/10.24 |
% 30.65/10.24 | From (1023) and (4093) follows:
% 30.65/10.24 | (4299) sum(n3, n16) = all_0_4_4
% 30.65/10.24 |
% 30.65/10.24 | From (1023) and (4091) follows:
% 30.65/10.24 | (4300) sum(n3, n15) = all_0_2_2
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n3, n16, all_0_4_4, n19 and discharging atoms sum(n3, n16) = all_0_4_4, sum(n3, n16) = n19, yields:
% 30.65/10.24 | (755) all_0_4_4 = n19
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n3, n15, all_0_2_2, n18 and discharging atoms sum(n3, n15) = all_0_2_2, sum(n3, n15) = n18, yields:
% 30.65/10.24 | (754) all_0_2_2 = n18
% 30.65/10.24 |
% 30.65/10.24 | From (754) and (473) follows:
% 30.65/10.24 | (756) pred(n18) = all_0_1_1
% 30.65/10.24 |
% 30.65/10.24 | From (755) and (716) follows:
% 30.65/10.24 | (757) pred(n19) = all_0_3_3
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 30.65/10.24 | (758) all_0_3_3 = n18
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 30.65/10.24 | (759) all_0_1_1 = n17
% 30.65/10.24 |
% 30.65/10.24 | From (758) and (232) follows:
% 30.65/10.24 | (760) sum(n18, all_0_0_0) = all_0_6_6
% 30.65/10.24 |
% 30.65/10.24 | From (759) and (1171) follows:
% 30.65/10.24 | (4308) sum(n15, n17) = all_0_0_0
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n15, n17, all_0_0_0, n11 and discharging atoms sum(n15, n17) = all_0_0_0, sum(n15, n17) = n11, yields:
% 30.65/10.24 | (847) all_0_0_0 = n11
% 30.65/10.24 |
% 30.65/10.24 | From (847) and (760) follows:
% 30.65/10.24 | (4310) sum(n18, n11) = all_0_6_6
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n18, n11, all_0_6_6, n8 and discharging atoms sum(n18, n11) = all_0_6_6, sum(n18, n11) = n8, yields:
% 30.65/10.24 | (985) all_0_6_6 = n8
% 30.65/10.24 |
% 30.65/10.24 | Equations (985) can reduce 357 to:
% 30.65/10.24 | (748) $false
% 30.65/10.24 |
% 30.65/10.24 |-The branch is then unsatisfiable
% 30.65/10.24 |-Branch two:
% 30.65/10.24 | (1038) ~ (all_0_8_8 = n3)
% 30.65/10.24 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.24 |
% 30.65/10.24 +-Applying beta-rule and splitting (1039), into two cases.
% 30.65/10.24 |-Branch one:
% 30.65/10.24 | (1040) all_0_8_8 = n2
% 30.65/10.24 |
% 30.65/10.24 | From (1040) and (4093) follows:
% 30.65/10.24 | (4316) sum(n2, n16) = all_0_4_4
% 30.65/10.24 |
% 30.65/10.24 | From (1040) and (4091) follows:
% 30.65/10.24 | (4317) sum(n2, n15) = all_0_2_2
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n2, n16, all_0_4_4, n18 and discharging atoms sum(n2, n16) = all_0_4_4, sum(n2, n16) = n18, yields:
% 30.65/10.24 | (772) all_0_4_4 = n18
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n2, n15, all_0_2_2, n17 and discharging atoms sum(n2, n15) = all_0_2_2, sum(n2, n15) = n17, yields:
% 30.65/10.24 | (771) all_0_2_2 = n17
% 30.65/10.24 |
% 30.65/10.24 | From (771) and (473) follows:
% 30.65/10.24 | (773) pred(n17) = all_0_1_1
% 30.65/10.24 |
% 30.65/10.24 | From (772) and (716) follows:
% 30.65/10.24 | (774) pred(n18) = all_0_3_3
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 30.65/10.24 | (775) all_0_3_3 = n17
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 30.65/10.24 | (776) all_0_1_1 = n16
% 30.65/10.24 |
% 30.65/10.24 | From (775) and (232) follows:
% 30.65/10.24 | (777) sum(n17, all_0_0_0) = all_0_6_6
% 30.65/10.24 |
% 30.65/10.24 | From (776) and (1171) follows:
% 30.65/10.24 | (4325) sum(n15, n16) = all_0_0_0
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n15, n16, all_0_0_0, n10 and discharging atoms sum(n15, n16) = all_0_0_0, sum(n15, n16) = n10, yields:
% 30.65/10.24 | (864) all_0_0_0 = n10
% 30.65/10.24 |
% 30.65/10.24 | From (864) and (777) follows:
% 30.65/10.24 | (4327) sum(n17, n10) = all_0_6_6
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n17, n10, all_0_6_6, n6 and discharging atoms sum(n17, n10) = all_0_6_6, sum(n17, n10) = n6, yields:
% 30.65/10.24 | (1002) all_0_6_6 = n6
% 30.65/10.24 |
% 30.65/10.24 | Equations (1002) can reduce 498 to:
% 30.65/10.24 | (748) $false
% 30.65/10.24 |
% 30.65/10.24 |-The branch is then unsatisfiable
% 30.65/10.24 |-Branch two:
% 30.65/10.24 | (1055) ~ (all_0_8_8 = n2)
% 30.65/10.24 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.24 |
% 30.65/10.24 +-Applying beta-rule and splitting (1056), into two cases.
% 30.65/10.24 |-Branch one:
% 30.65/10.24 | (1057) all_0_8_8 = n1
% 30.65/10.24 |
% 30.65/10.24 | From (1057) and (4093) follows:
% 30.65/10.24 | (4333) sum(n1, n16) = all_0_4_4
% 30.65/10.24 |
% 30.65/10.24 | From (1057) and (4091) follows:
% 30.65/10.24 | (4334) sum(n1, n15) = all_0_2_2
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n1, n16, all_0_4_4, n17 and discharging atoms sum(n1, n16) = all_0_4_4, sum(n1, n16) = n17, yields:
% 30.65/10.24 | (789) all_0_4_4 = n17
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n1, n15, all_0_2_2, n16 and discharging atoms sum(n1, n15) = all_0_2_2, sum(n1, n15) = n16, yields:
% 30.65/10.24 | (788) all_0_2_2 = n16
% 30.65/10.24 |
% 30.65/10.24 | From (788) and (473) follows:
% 30.65/10.24 | (790) pred(n16) = all_0_1_1
% 30.65/10.24 |
% 30.65/10.24 | From (789) and (716) follows:
% 30.65/10.24 | (791) pred(n17) = all_0_3_3
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 30.65/10.24 | (792) all_0_3_3 = n16
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 30.65/10.24 | (793) all_0_1_1 = n15
% 30.65/10.24 |
% 30.65/10.24 | From (792) and (232) follows:
% 30.65/10.24 | (794) sum(n16, all_0_0_0) = all_0_6_6
% 30.65/10.24 |
% 30.65/10.24 | From (793) and (1171) follows:
% 30.65/10.24 | (4342) sum(n15, n15) = all_0_0_0
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n15, n15, all_0_0_0, n9 and discharging atoms sum(n15, n15) = all_0_0_0, sum(n15, n15) = n9, yields:
% 30.65/10.24 | (881) all_0_0_0 = n9
% 30.65/10.24 |
% 30.65/10.24 | From (881) and (794) follows:
% 30.65/10.24 | (4344) sum(n16, n9) = all_0_6_6
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n16, n9, all_0_6_6, n4 and discharging atoms sum(n16, n9) = all_0_6_6, sum(n16, n9) = n4, yields:
% 30.65/10.24 | (1019) all_0_6_6 = n4
% 30.65/10.24 |
% 30.65/10.24 | Equations (1019) can reduce 48 to:
% 30.65/10.24 | (748) $false
% 30.65/10.24 |
% 30.65/10.24 |-The branch is then unsatisfiable
% 30.65/10.24 |-Branch two:
% 30.65/10.24 | (1072) ~ (all_0_8_8 = n1)
% 30.65/10.24 | (1073) all_0_8_8 = n0
% 30.65/10.24 |
% 30.65/10.24 | From (1073) and (4093) follows:
% 30.65/10.24 | (4349) sum(n0, n16) = all_0_4_4
% 30.65/10.24 |
% 30.65/10.24 | From (1073) and (4091) follows:
% 30.65/10.24 | (4350) sum(n0, n15) = all_0_2_2
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n0, n16, all_0_4_4, n16 and discharging atoms sum(n0, n16) = all_0_4_4, sum(n0, n16) = n16, yields:
% 30.65/10.24 | (806) all_0_4_4 = n16
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n0, n15, all_0_2_2, n15 and discharging atoms sum(n0, n15) = all_0_2_2, sum(n0, n15) = n15, yields:
% 30.65/10.24 | (805) all_0_2_2 = n15
% 30.65/10.24 |
% 30.65/10.24 | From (805) and (473) follows:
% 30.65/10.24 | (807) pred(n15) = all_0_1_1
% 30.65/10.24 |
% 30.65/10.24 | From (806) and (716) follows:
% 30.65/10.24 | (808) pred(n16) = all_0_3_3
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 30.65/10.24 | (809) all_0_3_3 = n15
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 30.65/10.24 | (810) all_0_1_1 = n14
% 30.65/10.24 |
% 30.65/10.24 | From (809) and (232) follows:
% 30.65/10.24 | (811) sum(n15, all_0_0_0) = all_0_6_6
% 30.65/10.24 |
% 30.65/10.24 | From (810) and (1171) follows:
% 30.65/10.24 | (4358) sum(n15, n14) = all_0_0_0
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n15, n14, all_0_0_0, n8 and discharging atoms sum(n15, n14) = all_0_0_0, sum(n15, n14) = n8, yields:
% 30.65/10.24 | (898) all_0_0_0 = n8
% 30.65/10.24 |
% 30.65/10.24 | From (898) and (811) follows:
% 30.65/10.24 | (4360) sum(n15, n8) = all_0_6_6
% 30.65/10.24 |
% 30.65/10.24 | Instantiating formula (619) with n15, n8, all_0_6_6, n2 and discharging atoms sum(n15, n8) = all_0_6_6, sum(n15, n8) = n2, yields:
% 30.65/10.24 | (1036) all_0_6_6 = n2
% 30.65/10.24 |
% 30.65/10.24 | Equations (1036) can reduce 56 to:
% 30.65/10.24 | (748) $false
% 30.65/10.24 |
% 30.65/10.24 |-The branch is then unsatisfiable
% 30.65/10.24 |-Branch two:
% 30.65/10.24 | (1186) ~ (all_0_7_7 = n15)
% 30.65/10.24 | (1187) all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.24 |
% 30.65/10.24 +-Applying beta-rule and splitting (818), into two cases.
% 30.65/10.24 |-Branch one:
% 30.65/10.24 | (819) all_0_8_8 = n15
% 30.65/10.24 |
% 30.65/10.24 | From (819) and (708) follows:
% 30.65/10.24 | (4366) sum(n15, all_0_5_5) = all_0_4_4
% 30.65/10.25 |
% 30.65/10.25 | From (819) and (378) follows:
% 30.65/10.25 | (4367) sum(n15, all_0_7_7) = all_0_2_2
% 30.65/10.25 |
% 30.65/10.25 +-Applying beta-rule and splitting (1187), into two cases.
% 30.65/10.25 |-Branch one:
% 30.65/10.25 | (1188) all_0_7_7 = n14
% 30.65/10.25 |
% 30.65/10.25 | From (1188) and (683) follows:
% 30.65/10.25 | (1189) succ(n14) = all_0_5_5
% 30.65/10.25 |
% 30.65/10.25 | From (1188) and (8) follows:
% 30.65/10.25 | (1190) sum(n14, all_0_1_1) = all_0_0_0
% 30.65/10.25 |
% 30.65/10.25 | From (1188) and (4367) follows:
% 30.65/10.25 | (4371) sum(n15, n14) = all_0_2_2
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (388) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 30.65/10.25 | (1192) all_0_5_5 = n15
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n15, n14, all_0_2_2, n8 and discharging atoms sum(n15, n14) = all_0_2_2, sum(n15, n14) = n8, yields:
% 30.65/10.25 | (924) all_0_2_2 = n8
% 30.65/10.25 |
% 30.65/10.25 | From (924) and (473) follows:
% 30.65/10.25 | (926) pred(n8) = all_0_1_1
% 30.65/10.25 |
% 30.65/10.25 | From (1192) and (4366) follows:
% 30.65/10.25 | (4375) sum(n15, n15) = all_0_4_4
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 30.65/10.25 | (929) all_0_1_1 = n7
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n15, n15, all_0_4_4, n9 and discharging atoms sum(n15, n15) = all_0_4_4, sum(n15, n15) = n9, yields:
% 30.65/10.25 | (925) all_0_4_4 = n9
% 30.65/10.25 |
% 30.65/10.25 | From (925) and (716) follows:
% 30.65/10.25 | (927) pred(n9) = all_0_3_3
% 30.65/10.25 |
% 30.65/10.25 | From (929) and (1190) follows:
% 30.65/10.25 | (4379) sum(n14, n7) = all_0_0_0
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 30.65/10.25 | (928) all_0_3_3 = n8
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n14, n7, all_0_0_0, n0 and discharging atoms sum(n14, n7) = all_0_0_0, sum(n14, n7) = n0, yields:
% 30.65/10.25 | (1034) all_0_0_0 = n0
% 30.65/10.25 |
% 30.65/10.25 | From (928)(1034) and (232) follows:
% 30.65/10.25 | (4382) sum(n8, n0) = all_0_6_6
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n8, n0, all_0_6_6, n8 and discharging atoms sum(n8, n0) = all_0_6_6, sum(n8, n0) = n8, yields:
% 30.65/10.25 | (985) all_0_6_6 = n8
% 30.65/10.25 |
% 30.65/10.25 | Equations (985) can reduce 357 to:
% 30.65/10.25 | (748) $false
% 30.65/10.25 |
% 30.65/10.25 |-The branch is then unsatisfiable
% 30.65/10.25 |-Branch two:
% 30.65/10.25 | (1205) ~ (all_0_7_7 = n14)
% 30.65/10.25 | (1206) all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.25 |
% 30.65/10.25 +-Applying beta-rule and splitting (1206), into two cases.
% 30.65/10.25 |-Branch one:
% 30.65/10.25 | (1207) all_0_7_7 = n13
% 30.65/10.25 |
% 30.65/10.25 | From (1207) and (683) follows:
% 30.65/10.25 | (1208) succ(n13) = all_0_5_5
% 30.65/10.25 |
% 30.65/10.25 | From (1207) and (8) follows:
% 30.65/10.25 | (1209) sum(n13, all_0_1_1) = all_0_0_0
% 30.65/10.25 |
% 30.65/10.25 | From (1207) and (4367) follows:
% 30.65/10.25 | (4390) sum(n15, n13) = all_0_2_2
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (388) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 30.65/10.25 | (1211) all_0_5_5 = n14
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n15, n13, all_0_2_2, n7 and discharging atoms sum(n15, n13) = all_0_2_2, sum(n15, n13) = n7, yields:
% 30.65/10.25 | (941) all_0_2_2 = n7
% 30.65/10.25 |
% 30.65/10.25 | From (941) and (473) follows:
% 30.65/10.25 | (943) pred(n7) = all_0_1_1
% 30.65/10.25 |
% 30.65/10.25 | From (1211) and (4366) follows:
% 30.65/10.25 | (4394) sum(n15, n14) = all_0_4_4
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 30.65/10.25 | (946) all_0_1_1 = n6
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n15, n14, all_0_4_4, n8 and discharging atoms sum(n15, n14) = all_0_4_4, sum(n15, n14) = n8, yields:
% 30.65/10.25 | (942) all_0_4_4 = n8
% 30.65/10.25 |
% 30.65/10.25 | From (942) and (716) follows:
% 30.65/10.25 | (944) pred(n8) = all_0_3_3
% 30.65/10.25 |
% 30.65/10.25 | From (946) and (1209) follows:
% 30.65/10.25 | (4398) sum(n13, n6) = all_0_0_0
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 30.65/10.25 | (945) all_0_3_3 = n7
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n13, n6, all_0_0_0, n19 and discharging atoms sum(n13, n6) = all_0_0_0, sum(n13, n6) = n19, yields:
% 30.65/10.25 | (1068) all_0_0_0 = n19
% 30.65/10.25 |
% 30.65/10.25 | From (945)(1068) and (232) follows:
% 30.65/10.25 | (4401) sum(n7, n19) = all_0_6_6
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n7, n19, all_0_6_6, n5 and discharging atoms sum(n7, n19) = all_0_6_6, sum(n7, n19) = n5, yields:
% 30.65/10.25 | (832) all_0_6_6 = n5
% 30.65/10.25 |
% 30.65/10.25 | Equations (832) can reduce 462 to:
% 30.65/10.25 | (748) $false
% 30.65/10.25 |
% 30.65/10.25 |-The branch is then unsatisfiable
% 30.65/10.25 |-Branch two:
% 30.65/10.25 | (1224) ~ (all_0_7_7 = n13)
% 30.65/10.25 | (1225) all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.25 |
% 30.65/10.25 +-Applying beta-rule and splitting (1225), into two cases.
% 30.65/10.25 |-Branch one:
% 30.65/10.25 | (1226) all_0_7_7 = n12
% 30.65/10.25 |
% 30.65/10.25 | From (1226) and (683) follows:
% 30.65/10.25 | (1227) succ(n12) = all_0_5_5
% 30.65/10.25 |
% 30.65/10.25 | From (1226) and (8) follows:
% 30.65/10.25 | (1228) sum(n12, all_0_1_1) = all_0_0_0
% 30.65/10.25 |
% 30.65/10.25 | From (1226) and (4367) follows:
% 30.65/10.25 | (4409) sum(n15, n12) = all_0_2_2
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (388) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 30.65/10.25 | (1230) all_0_5_5 = n13
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n15, n12, all_0_2_2, n6 and discharging atoms sum(n15, n12) = all_0_2_2, sum(n15, n12) = n6, yields:
% 30.65/10.25 | (958) all_0_2_2 = n6
% 30.65/10.25 |
% 30.65/10.25 | From (958) and (473) follows:
% 30.65/10.25 | (960) pred(n6) = all_0_1_1
% 30.65/10.25 |
% 30.65/10.25 | From (1230) and (4366) follows:
% 30.65/10.25 | (4413) sum(n15, n13) = all_0_4_4
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 30.65/10.25 | (963) all_0_1_1 = n5
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n15, n13, all_0_4_4, n7 and discharging atoms sum(n15, n13) = all_0_4_4, sum(n15, n13) = n7, yields:
% 30.65/10.25 | (959) all_0_4_4 = n7
% 30.65/10.25 |
% 30.65/10.25 | From (959) and (716) follows:
% 30.65/10.25 | (961) pred(n7) = all_0_3_3
% 30.65/10.25 |
% 30.65/10.25 | From (963) and (1228) follows:
% 30.65/10.25 | (4417) sum(n12, n5) = all_0_0_0
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 30.65/10.25 | (962) all_0_3_3 = n6
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n12, n5, all_0_0_0, n17 and discharging atoms sum(n12, n5) = all_0_0_0, sum(n12, n5) = n17, yields:
% 30.65/10.25 | (745) all_0_0_0 = n17
% 30.65/10.25 |
% 30.65/10.25 | From (962)(745) and (232) follows:
% 30.65/10.25 | (4420) sum(n6, n17) = all_0_6_6
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n6, n17, all_0_6_6, n2 and discharging atoms sum(n6, n17) = all_0_6_6, sum(n6, n17) = n2, yields:
% 30.65/10.25 | (1036) all_0_6_6 = n2
% 30.65/10.25 |
% 30.65/10.25 | Equations (1036) can reduce 56 to:
% 30.65/10.25 | (748) $false
% 30.65/10.25 |
% 30.65/10.25 |-The branch is then unsatisfiable
% 30.65/10.25 |-Branch two:
% 30.65/10.25 | (1243) ~ (all_0_7_7 = n12)
% 30.65/10.25 | (1244) all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.25 |
% 30.65/10.25 +-Applying beta-rule and splitting (1244), into two cases.
% 30.65/10.25 |-Branch one:
% 30.65/10.25 | (1245) all_0_7_7 = n11
% 30.65/10.25 |
% 30.65/10.25 | From (1245) and (683) follows:
% 30.65/10.25 | (1246) succ(n11) = all_0_5_5
% 30.65/10.25 |
% 30.65/10.25 | From (1245) and (8) follows:
% 30.65/10.25 | (1247) sum(n11, all_0_1_1) = all_0_0_0
% 30.65/10.25 |
% 30.65/10.25 | From (1245) and (4367) follows:
% 30.65/10.25 | (4428) sum(n15, n11) = all_0_2_2
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (388) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 30.65/10.25 | (1249) all_0_5_5 = n12
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n15, n11, all_0_2_2, n5 and discharging atoms sum(n15, n11) = all_0_2_2, sum(n15, n11) = n5, yields:
% 30.65/10.25 | (975) all_0_2_2 = n5
% 30.65/10.25 |
% 30.65/10.25 | From (975) and (473) follows:
% 30.65/10.25 | (977) pred(n5) = all_0_1_1
% 30.65/10.25 |
% 30.65/10.25 | From (1249) and (4366) follows:
% 30.65/10.25 | (4432) sum(n15, n12) = all_0_4_4
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 30.65/10.25 | (980) all_0_1_1 = n4
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n15, n12, all_0_4_4, n6 and discharging atoms sum(n15, n12) = all_0_4_4, sum(n15, n12) = n6, yields:
% 30.65/10.25 | (976) all_0_4_4 = n6
% 30.65/10.25 |
% 30.65/10.25 | From (976) and (716) follows:
% 30.65/10.25 | (978) pred(n6) = all_0_3_3
% 30.65/10.25 |
% 30.65/10.25 | From (980) and (1247) follows:
% 30.65/10.25 | (4436) sum(n11, n4) = all_0_0_0
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 30.65/10.25 | (979) all_0_3_3 = n5
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n11, n4, all_0_0_0, n15 and discharging atoms sum(n11, n4) = all_0_0_0, sum(n11, n4) = n15, yields:
% 30.65/10.25 | (779) all_0_0_0 = n15
% 30.65/10.25 |
% 30.65/10.25 | From (979)(779) and (232) follows:
% 30.65/10.25 | (4439) sum(n5, n15) = all_0_6_6
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n5, n15, all_0_6_6, n20 and discharging atoms sum(n5, n15) = all_0_6_6, sum(n5, n15) = n20, yields:
% 30.65/10.25 | (883) all_0_6_6 = n20
% 30.65/10.25 |
% 30.65/10.25 | Equations (883) can reduce 381 to:
% 30.65/10.25 | (748) $false
% 30.65/10.25 |
% 30.65/10.25 |-The branch is then unsatisfiable
% 30.65/10.25 |-Branch two:
% 30.65/10.25 | (1262) ~ (all_0_7_7 = n11)
% 30.65/10.25 | (1263) all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.25 |
% 30.65/10.25 +-Applying beta-rule and splitting (1263), into two cases.
% 30.65/10.25 |-Branch one:
% 30.65/10.25 | (1264) all_0_7_7 = n10
% 30.65/10.25 |
% 30.65/10.25 | From (1264) and (683) follows:
% 30.65/10.25 | (1265) succ(n10) = all_0_5_5
% 30.65/10.25 |
% 30.65/10.25 | From (1264) and (8) follows:
% 30.65/10.25 | (1266) sum(n10, all_0_1_1) = all_0_0_0
% 30.65/10.25 |
% 30.65/10.25 | From (1264) and (4367) follows:
% 30.65/10.25 | (4447) sum(n15, n10) = all_0_2_2
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (388) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 30.65/10.25 | (1268) all_0_5_5 = n11
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n15, n10, all_0_2_2, n4 and discharging atoms sum(n15, n10) = all_0_2_2, sum(n15, n10) = n4, yields:
% 30.65/10.25 | (992) all_0_2_2 = n4
% 30.65/10.25 |
% 30.65/10.25 | From (992) and (473) follows:
% 30.65/10.25 | (994) pred(n4) = all_0_1_1
% 30.65/10.25 |
% 30.65/10.25 | From (1268) and (4366) follows:
% 30.65/10.25 | (4451) sum(n15, n11) = all_0_4_4
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 30.65/10.25 | (997) all_0_1_1 = n3
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n15, n11, all_0_4_4, n5 and discharging atoms sum(n15, n11) = all_0_4_4, sum(n15, n11) = n5, yields:
% 30.65/10.25 | (993) all_0_4_4 = n5
% 30.65/10.25 |
% 30.65/10.25 | From (993) and (716) follows:
% 30.65/10.25 | (995) pred(n5) = all_0_3_3
% 30.65/10.25 |
% 30.65/10.25 | From (997) and (1266) follows:
% 30.65/10.25 | (4455) sum(n10, n3) = all_0_0_0
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 30.65/10.25 | (996) all_0_3_3 = n4
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n10, n3, all_0_0_0, n13 and discharging atoms sum(n10, n3) = all_0_0_0, sum(n10, n3) = n13, yields:
% 30.65/10.25 | (813) all_0_0_0 = n13
% 30.65/10.25 |
% 30.65/10.25 | From (996)(813) and (232) follows:
% 30.65/10.25 | (4458) sum(n4, n13) = all_0_6_6
% 30.65/10.25 |
% 30.65/10.25 | Instantiating formula (619) with n4, n13, all_0_6_6, n17 and discharging atoms sum(n4, n13) = all_0_6_6, sum(n4, n13) = n17, yields:
% 30.65/10.25 | (1086) all_0_6_6 = n17
% 30.65/10.25 |
% 30.65/10.25 | Equations (1086) can reduce 669 to:
% 30.65/10.25 | (748) $false
% 30.65/10.25 |
% 30.65/10.25 |-The branch is then unsatisfiable
% 30.65/10.25 |-Branch two:
% 30.65/10.25 | (1281) ~ (all_0_7_7 = n10)
% 30.65/10.25 | (1282) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.26 |
% 30.65/10.26 +-Applying beta-rule and splitting (1282), into two cases.
% 30.65/10.26 |-Branch one:
% 30.65/10.26 | (1283) all_0_7_7 = n9
% 30.65/10.26 |
% 30.65/10.26 | From (1283) and (683) follows:
% 30.65/10.26 | (1284) succ(n9) = all_0_5_5
% 30.65/10.26 |
% 30.65/10.26 | From (1283) and (8) follows:
% 30.65/10.26 | (1285) sum(n9, all_0_1_1) = all_0_0_0
% 30.65/10.26 |
% 30.65/10.26 | From (1283) and (4367) follows:
% 30.65/10.26 | (4466) sum(n15, n9) = all_0_2_2
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (388) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 30.65/10.26 | (1287) all_0_5_5 = n10
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n15, n9, all_0_2_2, n3 and discharging atoms sum(n15, n9) = all_0_2_2, sum(n15, n9) = n3, yields:
% 30.65/10.26 | (1009) all_0_2_2 = n3
% 30.65/10.26 |
% 30.65/10.26 | From (1009) and (473) follows:
% 30.65/10.26 | (1011) pred(n3) = all_0_1_1
% 30.65/10.26 |
% 30.65/10.26 | From (1287) and (4366) follows:
% 30.65/10.26 | (4470) sum(n15, n10) = all_0_4_4
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 30.65/10.26 | (1014) all_0_1_1 = n2
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n15, n10, all_0_4_4, n4 and discharging atoms sum(n15, n10) = all_0_4_4, sum(n15, n10) = n4, yields:
% 30.65/10.26 | (1010) all_0_4_4 = n4
% 30.65/10.26 |
% 30.65/10.26 | From (1010) and (716) follows:
% 30.65/10.26 | (1012) pred(n4) = all_0_3_3
% 30.65/10.26 |
% 30.65/10.26 | From (1014) and (1285) follows:
% 30.65/10.26 | (4474) sum(n9, n2) = all_0_0_0
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 30.65/10.26 | (1013) all_0_3_3 = n3
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n9, n2, all_0_0_0, n11 and discharging atoms sum(n9, n2) = all_0_0_0, sum(n9, n2) = n11, yields:
% 30.65/10.26 | (847) all_0_0_0 = n11
% 30.65/10.26 |
% 30.65/10.26 | From (1013)(847) and (232) follows:
% 30.65/10.26 | (4477) sum(n3, n11) = all_0_6_6
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n3, n11, all_0_6_6, n14 and discharging atoms sum(n3, n11) = all_0_6_6, sum(n3, n11) = n14, yields:
% 30.65/10.26 | (934) all_0_6_6 = n14
% 30.65/10.26 |
% 30.65/10.26 | Equations (934) can reduce 353 to:
% 30.65/10.26 | (748) $false
% 30.65/10.26 |
% 30.65/10.26 |-The branch is then unsatisfiable
% 30.65/10.26 |-Branch two:
% 30.65/10.26 | (1300) ~ (all_0_7_7 = n9)
% 30.65/10.26 | (1301) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.26 |
% 30.65/10.26 +-Applying beta-rule and splitting (1301), into two cases.
% 30.65/10.26 |-Branch one:
% 30.65/10.26 | (1302) all_0_7_7 = n8
% 30.65/10.26 |
% 30.65/10.26 | From (1302) and (683) follows:
% 30.65/10.26 | (1303) succ(n8) = all_0_5_5
% 30.65/10.26 |
% 30.65/10.26 | From (1302) and (8) follows:
% 30.65/10.26 | (1304) sum(n8, all_0_1_1) = all_0_0_0
% 30.65/10.26 |
% 30.65/10.26 | From (1302) and (4367) follows:
% 30.65/10.26 | (4485) sum(n15, n8) = all_0_2_2
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (388) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 30.65/10.26 | (1306) all_0_5_5 = n9
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n15, n8, all_0_2_2, n2 and discharging atoms sum(n15, n8) = all_0_2_2, sum(n15, n8) = n2, yields:
% 30.65/10.26 | (1026) all_0_2_2 = n2
% 30.65/10.26 |
% 30.65/10.26 | From (1026) and (473) follows:
% 30.65/10.26 | (1028) pred(n2) = all_0_1_1
% 30.65/10.26 |
% 30.65/10.26 | From (1306) and (4366) follows:
% 30.65/10.26 | (4489) sum(n15, n9) = all_0_4_4
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 30.65/10.26 | (1031) all_0_1_1 = n1
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n15, n9, all_0_4_4, n3 and discharging atoms sum(n15, n9) = all_0_4_4, sum(n15, n9) = n3, yields:
% 30.65/10.26 | (1027) all_0_4_4 = n3
% 30.65/10.26 |
% 30.65/10.26 | From (1027) and (716) follows:
% 30.65/10.26 | (1029) pred(n3) = all_0_3_3
% 30.65/10.26 |
% 30.65/10.26 | From (1031) and (1304) follows:
% 30.65/10.26 | (4493) sum(n8, n1) = all_0_0_0
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 30.65/10.26 | (1030) all_0_3_3 = n2
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n8, n1, all_0_0_0, n9 and discharging atoms sum(n8, n1) = all_0_0_0, sum(n8, n1) = n9, yields:
% 30.65/10.26 | (881) all_0_0_0 = n9
% 30.65/10.26 |
% 30.65/10.26 | From (1030)(881) and (232) follows:
% 30.65/10.26 | (4496) sum(n2, n9) = all_0_6_6
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n2, n9, all_0_6_6, n11 and discharging atoms sum(n2, n9) = all_0_6_6, sum(n2, n9) = n11, yields:
% 30.65/10.26 | (781) all_0_6_6 = n11
% 30.65/10.26 |
% 30.65/10.26 | Equations (781) can reduce 2 to:
% 30.65/10.26 | (748) $false
% 30.65/10.26 |
% 30.65/10.26 |-The branch is then unsatisfiable
% 30.65/10.26 |-Branch two:
% 30.65/10.26 | (1319) ~ (all_0_7_7 = n8)
% 30.65/10.26 | (1320) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.26 |
% 30.65/10.26 +-Applying beta-rule and splitting (1320), into two cases.
% 30.65/10.26 |-Branch one:
% 30.65/10.26 | (1321) all_0_7_7 = n7
% 30.65/10.26 |
% 30.65/10.26 | From (1321) and (683) follows:
% 30.65/10.26 | (1322) succ(n7) = all_0_5_5
% 30.65/10.26 |
% 30.65/10.26 | From (1321) and (8) follows:
% 30.65/10.26 | (1323) sum(n7, all_0_1_1) = all_0_0_0
% 30.65/10.26 |
% 30.65/10.26 | From (1321) and (4367) follows:
% 30.65/10.26 | (4504) sum(n15, n7) = all_0_2_2
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (388) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 30.65/10.26 | (1325) all_0_5_5 = n8
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n15, n7, all_0_2_2, n1 and discharging atoms sum(n15, n7) = all_0_2_2, sum(n15, n7) = n1, yields:
% 30.65/10.26 | (1043) all_0_2_2 = n1
% 30.65/10.26 |
% 30.65/10.26 | From (1043) and (473) follows:
% 30.65/10.26 | (1045) pred(n1) = all_0_1_1
% 30.65/10.26 |
% 30.65/10.26 | From (1325) and (4366) follows:
% 30.65/10.26 | (4508) sum(n15, n8) = all_0_4_4
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 30.65/10.26 | (1048) all_0_1_1 = n0
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n15, n8, all_0_4_4, n2 and discharging atoms sum(n15, n8) = all_0_4_4, sum(n15, n8) = n2, yields:
% 30.65/10.26 | (1044) all_0_4_4 = n2
% 30.65/10.26 |
% 30.65/10.26 | From (1044) and (716) follows:
% 30.65/10.26 | (1046) pred(n2) = all_0_3_3
% 30.65/10.26 |
% 30.65/10.26 | From (1048) and (1323) follows:
% 30.65/10.26 | (4512) sum(n7, n0) = all_0_0_0
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 30.65/10.26 | (1047) all_0_3_3 = n1
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n7, n0, all_0_0_0, n7 and discharging atoms sum(n7, n0) = all_0_0_0, sum(n7, n0) = n7, yields:
% 30.65/10.26 | (915) all_0_0_0 = n7
% 30.65/10.26 |
% 30.65/10.26 | From (1047)(915) and (232) follows:
% 30.65/10.26 | (4515) sum(n1, n7) = all_0_6_6
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n1, n7, all_0_6_6, n8 and discharging atoms sum(n1, n7) = all_0_6_6, sum(n1, n7) = n8, yields:
% 30.65/10.26 | (985) all_0_6_6 = n8
% 30.65/10.26 |
% 30.65/10.26 | Equations (985) can reduce 357 to:
% 30.65/10.26 | (748) $false
% 30.65/10.26 |
% 30.65/10.26 |-The branch is then unsatisfiable
% 30.65/10.26 |-Branch two:
% 30.65/10.26 | (1338) ~ (all_0_7_7 = n7)
% 30.65/10.26 | (1339) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.26 |
% 30.65/10.26 +-Applying beta-rule and splitting (1339), into two cases.
% 30.65/10.26 |-Branch one:
% 30.65/10.26 | (1340) all_0_7_7 = n6
% 30.65/10.26 |
% 30.65/10.26 | From (1340) and (683) follows:
% 30.65/10.26 | (1341) succ(n6) = all_0_5_5
% 30.65/10.26 |
% 30.65/10.26 | From (1340) and (8) follows:
% 30.65/10.26 | (1342) sum(n6, all_0_1_1) = all_0_0_0
% 30.65/10.26 |
% 30.65/10.26 | From (1340) and (4367) follows:
% 30.65/10.26 | (4523) sum(n15, n6) = all_0_2_2
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (388) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 30.65/10.26 | (1344) all_0_5_5 = n7
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n15, n6, all_0_2_2, n0 and discharging atoms sum(n15, n6) = all_0_2_2, sum(n15, n6) = n0, yields:
% 30.65/10.26 | (1060) all_0_2_2 = n0
% 30.65/10.26 |
% 30.65/10.26 | From (1060) and (473) follows:
% 30.65/10.26 | (1062) pred(n0) = all_0_1_1
% 30.65/10.26 |
% 30.65/10.26 | From (1344) and (4366) follows:
% 30.65/10.26 | (4527) sum(n15, n7) = all_0_4_4
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 30.65/10.26 | (1065) all_0_1_1 = n20
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n15, n7, all_0_4_4, n1 and discharging atoms sum(n15, n7) = all_0_4_4, sum(n15, n7) = n1, yields:
% 30.65/10.26 | (1061) all_0_4_4 = n1
% 30.65/10.26 |
% 30.65/10.26 | From (1061) and (716) follows:
% 30.65/10.26 | (1063) pred(n1) = all_0_3_3
% 30.65/10.26 |
% 30.65/10.26 | From (1065) and (1342) follows:
% 30.65/10.26 | (4531) sum(n6, n20) = all_0_0_0
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 30.65/10.26 | (1064) all_0_3_3 = n0
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n6, n20, all_0_0_0, n5 and discharging atoms sum(n6, n20) = all_0_0_0, sum(n6, n20) = n5, yields:
% 30.65/10.26 | (949) all_0_0_0 = n5
% 30.65/10.26 |
% 30.65/10.26 | From (1064)(949) and (232) follows:
% 30.65/10.26 | (4534) sum(n0, n5) = all_0_6_6
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n0, n5, all_0_6_6, n5 and discharging atoms sum(n0, n5) = all_0_6_6, sum(n0, n5) = n5, yields:
% 30.65/10.26 | (832) all_0_6_6 = n5
% 30.65/10.26 |
% 30.65/10.26 | Equations (832) can reduce 462 to:
% 30.65/10.26 | (748) $false
% 30.65/10.26 |
% 30.65/10.26 |-The branch is then unsatisfiable
% 30.65/10.26 |-Branch two:
% 30.65/10.26 | (1357) ~ (all_0_7_7 = n6)
% 30.65/10.26 | (1358) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.26 |
% 30.65/10.26 +-Applying beta-rule and splitting (1358), into two cases.
% 30.65/10.26 |-Branch one:
% 30.65/10.26 | (1359) all_0_7_7 = n5
% 30.65/10.26 |
% 30.65/10.26 | From (1359) and (683) follows:
% 30.65/10.26 | (1360) succ(n5) = all_0_5_5
% 30.65/10.26 |
% 30.65/10.26 | From (1359) and (8) follows:
% 30.65/10.26 | (1361) sum(n5, all_0_1_1) = all_0_0_0
% 30.65/10.26 |
% 30.65/10.26 | From (1359) and (4367) follows:
% 30.65/10.26 | (4542) sum(n15, n5) = all_0_2_2
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (388) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 30.65/10.26 | (1363) all_0_5_5 = n6
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n15, n5, all_0_2_2, n20 and discharging atoms sum(n15, n5) = all_0_2_2, sum(n15, n5) = n20, yields:
% 30.65/10.26 | (1076) all_0_2_2 = n20
% 30.65/10.26 |
% 30.65/10.26 | From (1076) and (473) follows:
% 30.65/10.26 | (1078) pred(n20) = all_0_1_1
% 30.65/10.26 |
% 30.65/10.26 | From (1363) and (4366) follows:
% 30.65/10.26 | (4546) sum(n15, n6) = all_0_4_4
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 30.65/10.26 | (1080) all_0_1_1 = n19
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n15, n6, all_0_4_4, n0 and discharging atoms sum(n15, n6) = all_0_4_4, sum(n15, n6) = n0, yields:
% 30.65/10.26 | (1077) all_0_4_4 = n0
% 30.65/10.26 |
% 30.65/10.26 | From (1077) and (716) follows:
% 30.65/10.26 | (1079) pred(n0) = all_0_3_3
% 30.65/10.26 |
% 30.65/10.26 | From (1080) and (1361) follows:
% 30.65/10.26 | (4550) sum(n5, n19) = all_0_0_0
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 30.65/10.26 | (1081) all_0_3_3 = n20
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n5, n19, all_0_0_0, n3 and discharging atoms sum(n5, n19) = all_0_0_0, sum(n5, n19) = n3, yields:
% 30.65/10.26 | (983) all_0_0_0 = n3
% 30.65/10.26 |
% 30.65/10.26 | From (1081)(983) and (232) follows:
% 30.65/10.26 | (4553) sum(n20, n3) = all_0_6_6
% 30.65/10.26 |
% 30.65/10.26 | Instantiating formula (619) with n20, n3, all_0_6_6, n2 and discharging atoms sum(n20, n3) = all_0_6_6, sum(n20, n3) = n2, yields:
% 30.65/10.26 | (1036) all_0_6_6 = n2
% 30.65/10.26 |
% 30.65/10.26 | Equations (1036) can reduce 56 to:
% 30.65/10.26 | (748) $false
% 30.65/10.27 |
% 30.65/10.27 |-The branch is then unsatisfiable
% 30.65/10.27 |-Branch two:
% 30.65/10.27 | (1376) ~ (all_0_7_7 = n5)
% 30.65/10.27 | (1377) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.27 |
% 30.65/10.27 +-Applying beta-rule and splitting (1377), into two cases.
% 30.65/10.27 |-Branch one:
% 30.65/10.27 | (1378) all_0_7_7 = n4
% 30.65/10.27 |
% 30.65/10.27 | From (1378) and (683) follows:
% 30.65/10.27 | (1379) succ(n4) = all_0_5_5
% 30.65/10.27 |
% 30.65/10.27 | From (1378) and (8) follows:
% 30.65/10.27 | (1380) sum(n4, all_0_1_1) = all_0_0_0
% 30.65/10.27 |
% 30.65/10.27 | From (1378) and (4367) follows:
% 30.65/10.27 | (4561) sum(n15, n4) = all_0_2_2
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (388) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 30.65/10.27 | (1382) all_0_5_5 = n5
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n15, n4, all_0_2_2, n19 and discharging atoms sum(n15, n4) = all_0_2_2, sum(n15, n4) = n19, yields:
% 30.65/10.27 | (737) all_0_2_2 = n19
% 30.65/10.27 |
% 30.65/10.27 | From (737) and (473) follows:
% 30.65/10.27 | (739) pred(n19) = all_0_1_1
% 30.65/10.27 |
% 30.65/10.27 | From (1382) and (4366) follows:
% 30.65/10.27 | (4565) sum(n15, n5) = all_0_4_4
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 30.65/10.27 | (742) all_0_1_1 = n18
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n15, n5, all_0_4_4, n20 and discharging atoms sum(n15, n5) = all_0_4_4, sum(n15, n5) = n20, yields:
% 30.65/10.27 | (738) all_0_4_4 = n20
% 30.65/10.27 |
% 30.65/10.27 | From (738) and (716) follows:
% 30.65/10.27 | (740) pred(n20) = all_0_3_3
% 30.65/10.27 |
% 30.65/10.27 | From (742) and (1380) follows:
% 30.65/10.27 | (4569) sum(n4, n18) = all_0_0_0
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 30.65/10.27 | (741) all_0_3_3 = n19
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n4, n18, all_0_0_0, n1 and discharging atoms sum(n4, n18) = all_0_0_0, sum(n4, n18) = n1, yields:
% 30.65/10.27 | (1017) all_0_0_0 = n1
% 30.65/10.27 |
% 30.65/10.27 | From (741)(1017) and (232) follows:
% 30.65/10.27 | (4572) sum(n19, n1) = all_0_6_6
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n19, n1, all_0_6_6, n20 and discharging atoms sum(n19, n1) = all_0_6_6, sum(n19, n1) = n20, yields:
% 30.65/10.27 | (883) all_0_6_6 = n20
% 30.65/10.27 |
% 30.65/10.27 | Equations (883) can reduce 381 to:
% 30.65/10.27 | (748) $false
% 30.65/10.27 |
% 30.65/10.27 |-The branch is then unsatisfiable
% 30.65/10.27 |-Branch two:
% 30.65/10.27 | (1395) ~ (all_0_7_7 = n4)
% 30.65/10.27 | (1396) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.27 |
% 30.65/10.27 +-Applying beta-rule and splitting (1396), into two cases.
% 30.65/10.27 |-Branch one:
% 30.65/10.27 | (1397) all_0_7_7 = n3
% 30.65/10.27 |
% 30.65/10.27 | From (1397) and (683) follows:
% 30.65/10.27 | (1398) succ(n3) = all_0_5_5
% 30.65/10.27 |
% 30.65/10.27 | From (1397) and (8) follows:
% 30.65/10.27 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 30.65/10.27 |
% 30.65/10.27 | From (1397) and (4367) follows:
% 30.65/10.27 | (4580) sum(n15, n3) = all_0_2_2
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 30.65/10.27 | (1401) all_0_5_5 = n4
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n15, n3, all_0_2_2, n18 and discharging atoms sum(n15, n3) = all_0_2_2, sum(n15, n3) = n18, yields:
% 30.65/10.27 | (754) all_0_2_2 = n18
% 30.65/10.27 |
% 30.65/10.27 | From (754) and (473) follows:
% 30.65/10.27 | (756) pred(n18) = all_0_1_1
% 30.65/10.27 |
% 30.65/10.27 | From (1401) and (4366) follows:
% 30.65/10.27 | (4584) sum(n15, n4) = all_0_4_4
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 30.65/10.27 | (759) all_0_1_1 = n17
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n15, n4, all_0_4_4, n19 and discharging atoms sum(n15, n4) = all_0_4_4, sum(n15, n4) = n19, yields:
% 30.65/10.27 | (755) all_0_4_4 = n19
% 30.65/10.27 |
% 30.65/10.27 | From (755) and (716) follows:
% 30.65/10.27 | (757) pred(n19) = all_0_3_3
% 30.65/10.27 |
% 30.65/10.27 | From (759) and (1399) follows:
% 30.65/10.27 | (4588) sum(n3, n17) = all_0_0_0
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 30.65/10.27 | (758) all_0_3_3 = n18
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n3, n17, all_0_0_0, n20 and discharging atoms sum(n3, n17) = all_0_0_0, sum(n3, n17) = n20, yields:
% 30.65/10.27 | (1051) all_0_0_0 = n20
% 30.65/10.27 |
% 30.65/10.27 | From (758)(1051) and (232) follows:
% 30.65/10.27 | (4591) sum(n18, n20) = all_0_6_6
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n18, n20, all_0_6_6, n17 and discharging atoms sum(n18, n20) = all_0_6_6, sum(n18, n20) = n17, yields:
% 30.65/10.27 | (1086) all_0_6_6 = n17
% 30.65/10.27 |
% 30.65/10.27 | Equations (1086) can reduce 669 to:
% 30.65/10.27 | (748) $false
% 30.65/10.27 |
% 30.65/10.27 |-The branch is then unsatisfiable
% 30.65/10.27 |-Branch two:
% 30.65/10.27 | (1414) ~ (all_0_7_7 = n3)
% 30.65/10.27 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.27 |
% 30.65/10.27 +-Applying beta-rule and splitting (1415), into two cases.
% 30.65/10.27 |-Branch one:
% 30.65/10.27 | (1416) all_0_7_7 = n2
% 30.65/10.27 |
% 30.65/10.27 | From (1416) and (683) follows:
% 30.65/10.27 | (1417) succ(n2) = all_0_5_5
% 30.65/10.27 |
% 30.65/10.27 | From (1416) and (8) follows:
% 30.65/10.27 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 30.65/10.27 |
% 30.65/10.27 | From (1416) and (4367) follows:
% 30.65/10.27 | (4599) sum(n15, n2) = all_0_2_2
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 30.65/10.27 | (1420) all_0_5_5 = n3
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n15, n2, all_0_2_2, n17 and discharging atoms sum(n15, n2) = all_0_2_2, sum(n15, n2) = n17, yields:
% 30.65/10.27 | (771) all_0_2_2 = n17
% 30.65/10.27 |
% 30.65/10.27 | From (771) and (473) follows:
% 30.65/10.27 | (773) pred(n17) = all_0_1_1
% 30.65/10.27 |
% 30.65/10.27 | From (1420) and (4366) follows:
% 30.65/10.27 | (4603) sum(n15, n3) = all_0_4_4
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 30.65/10.27 | (776) all_0_1_1 = n16
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n15, n3, all_0_4_4, n18 and discharging atoms sum(n15, n3) = all_0_4_4, sum(n15, n3) = n18, yields:
% 30.65/10.27 | (772) all_0_4_4 = n18
% 30.65/10.27 |
% 30.65/10.27 | From (772) and (716) follows:
% 30.65/10.27 | (774) pred(n18) = all_0_3_3
% 30.65/10.27 |
% 30.65/10.27 | From (776) and (1418) follows:
% 30.65/10.27 | (4607) sum(n2, n16) = all_0_0_0
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 30.65/10.27 | (775) all_0_3_3 = n17
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n2, n16, all_0_0_0, n18 and discharging atoms sum(n2, n16) = all_0_0_0, sum(n2, n16) = n18, yields:
% 30.65/10.27 | (1084) all_0_0_0 = n18
% 30.65/10.27 |
% 30.65/10.27 | From (775)(1084) and (232) follows:
% 30.65/10.27 | (4610) sum(n17, n18) = all_0_6_6
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n17, n18, all_0_6_6, n14 and discharging atoms sum(n17, n18) = all_0_6_6, sum(n17, n18) = n14, yields:
% 30.65/10.27 | (934) all_0_6_6 = n14
% 30.65/10.27 |
% 30.65/10.27 | Equations (934) can reduce 353 to:
% 30.65/10.27 | (748) $false
% 30.65/10.27 |
% 30.65/10.27 |-The branch is then unsatisfiable
% 30.65/10.27 |-Branch two:
% 30.65/10.27 | (1433) ~ (all_0_7_7 = n2)
% 30.65/10.27 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.27 |
% 30.65/10.27 +-Applying beta-rule and splitting (1434), into two cases.
% 30.65/10.27 |-Branch one:
% 30.65/10.27 | (1435) all_0_7_7 = n1
% 30.65/10.27 |
% 30.65/10.27 | From (1435) and (683) follows:
% 30.65/10.27 | (1436) succ(n1) = all_0_5_5
% 30.65/10.27 |
% 30.65/10.27 | From (1435) and (8) follows:
% 30.65/10.27 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 30.65/10.27 |
% 30.65/10.27 | From (1435) and (4367) follows:
% 30.65/10.27 | (4618) sum(n15, n1) = all_0_2_2
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 30.65/10.27 | (1439) all_0_5_5 = n2
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n15, n1, all_0_2_2, n16 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n16, yields:
% 30.65/10.27 | (788) all_0_2_2 = n16
% 30.65/10.27 |
% 30.65/10.27 | From (788) and (473) follows:
% 30.65/10.27 | (790) pred(n16) = all_0_1_1
% 30.65/10.27 |
% 30.65/10.27 | From (1439) and (4366) follows:
% 30.65/10.27 | (4622) sum(n15, n2) = all_0_4_4
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 30.65/10.27 | (793) all_0_1_1 = n15
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n15, n2, all_0_4_4, n17 and discharging atoms sum(n15, n2) = all_0_4_4, sum(n15, n2) = n17, yields:
% 30.65/10.27 | (789) all_0_4_4 = n17
% 30.65/10.27 |
% 30.65/10.27 | From (789) and (716) follows:
% 30.65/10.27 | (791) pred(n17) = all_0_3_3
% 30.65/10.27 |
% 30.65/10.27 | From (793) and (1437) follows:
% 30.65/10.27 | (4626) sum(n1, n15) = all_0_0_0
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 30.65/10.27 | (792) all_0_3_3 = n16
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n1, n15, all_0_0_0, n16 and discharging atoms sum(n1, n15) = all_0_0_0, sum(n1, n15) = n16, yields:
% 30.65/10.27 | (762) all_0_0_0 = n16
% 30.65/10.27 |
% 30.65/10.27 | From (792)(762) and (232) follows:
% 30.65/10.27 | (4629) sum(n16, n16) = all_0_6_6
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n16, n16, all_0_6_6, n11 and discharging atoms sum(n16, n16) = all_0_6_6, sum(n16, n16) = n11, yields:
% 30.65/10.27 | (781) all_0_6_6 = n11
% 30.65/10.27 |
% 30.65/10.27 | Equations (781) can reduce 2 to:
% 30.65/10.27 | (748) $false
% 30.65/10.27 |
% 30.65/10.27 |-The branch is then unsatisfiable
% 30.65/10.27 |-Branch two:
% 30.65/10.27 | (1452) ~ (all_0_7_7 = n1)
% 30.65/10.27 | (1453) all_0_7_7 = n0
% 30.65/10.27 |
% 30.65/10.27 | From (1453) and (683) follows:
% 30.65/10.27 | (1454) succ(n0) = all_0_5_5
% 30.65/10.27 |
% 30.65/10.27 | From (1453) and (8) follows:
% 30.65/10.27 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 30.65/10.27 |
% 30.65/10.27 | From (1453) and (4367) follows:
% 30.65/10.27 | (4636) sum(n15, n0) = all_0_2_2
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 30.65/10.27 | (1457) all_0_5_5 = n1
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n15, n0, all_0_2_2, n15 and discharging atoms sum(n15, n0) = all_0_2_2, sum(n15, n0) = n15, yields:
% 30.65/10.27 | (805) all_0_2_2 = n15
% 30.65/10.27 |
% 30.65/10.27 | From (805) and (473) follows:
% 30.65/10.27 | (807) pred(n15) = all_0_1_1
% 30.65/10.27 |
% 30.65/10.27 | From (1457) and (4366) follows:
% 30.65/10.27 | (4640) sum(n15, n1) = all_0_4_4
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 30.65/10.27 | (810) all_0_1_1 = n14
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n15, n1, all_0_4_4, n16 and discharging atoms sum(n15, n1) = all_0_4_4, sum(n15, n1) = n16, yields:
% 30.65/10.27 | (806) all_0_4_4 = n16
% 30.65/10.27 |
% 30.65/10.27 | From (806) and (716) follows:
% 30.65/10.27 | (808) pred(n16) = all_0_3_3
% 30.65/10.27 |
% 30.65/10.27 | From (810) and (1455) follows:
% 30.65/10.27 | (4644) sum(n0, n14) = all_0_0_0
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 30.65/10.27 | (809) all_0_3_3 = n15
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n0, n14, all_0_0_0, n14 and discharging atoms sum(n0, n14) = all_0_0_0, sum(n0, n14) = n14, yields:
% 30.65/10.27 | (796) all_0_0_0 = n14
% 30.65/10.27 |
% 30.65/10.27 | From (809)(796) and (232) follows:
% 30.65/10.27 | (4647) sum(n15, n14) = all_0_6_6
% 30.65/10.27 |
% 30.65/10.27 | Instantiating formula (619) with n15, n14, all_0_6_6, n8 and discharging atoms sum(n15, n14) = all_0_6_6, sum(n15, n14) = n8, yields:
% 30.65/10.27 | (985) all_0_6_6 = n8
% 30.65/10.27 |
% 30.65/10.27 | Equations (985) can reduce 357 to:
% 30.65/10.27 | (748) $false
% 30.65/10.28 |
% 30.65/10.28 |-The branch is then unsatisfiable
% 30.65/10.28 |-Branch two:
% 30.65/10.28 | (834) ~ (all_0_8_8 = n15)
% 30.65/10.28 | (835) all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.28 |
% 30.65/10.28 +-Applying beta-rule and splitting (1187), into two cases.
% 30.65/10.28 |-Branch one:
% 30.65/10.28 | (1188) all_0_7_7 = n14
% 30.65/10.28 |
% 30.65/10.28 | From (1188) and (683) follows:
% 30.65/10.28 | (1189) succ(n14) = all_0_5_5
% 30.65/10.28 |
% 30.65/10.28 | From (1188) and (8) follows:
% 30.65/10.28 | (1190) sum(n14, all_0_1_1) = all_0_0_0
% 30.65/10.28 |
% 30.65/10.28 | From (1188) and (378) follows:
% 30.65/10.28 | (4655) sum(all_0_8_8, n14) = all_0_2_2
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (388) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 30.65/10.28 | (1192) all_0_5_5 = n15
% 30.65/10.28 |
% 30.65/10.28 | From (1192) and (708) follows:
% 30.65/10.28 | (4657) sum(all_0_8_8, n15) = all_0_4_4
% 30.65/10.28 |
% 30.65/10.28 +-Applying beta-rule and splitting (835), into two cases.
% 30.65/10.28 |-Branch one:
% 30.65/10.28 | (836) all_0_8_8 = n14
% 30.65/10.28 |
% 30.65/10.28 | From (836) and (4657) follows:
% 30.65/10.28 | (4659) sum(n14, n15) = all_0_4_4
% 30.65/10.28 |
% 30.65/10.28 | From (836) and (4655) follows:
% 30.65/10.28 | (4660) sum(n14, n14) = all_0_2_2
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n14, n15, all_0_4_4, n8 and discharging atoms sum(n14, n15) = all_0_4_4, sum(n14, n15) = n8, yields:
% 30.65/10.28 | (942) all_0_4_4 = n8
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n14, n14, all_0_2_2, n7 and discharging atoms sum(n14, n14) = all_0_2_2, sum(n14, n14) = n7, yields:
% 30.65/10.28 | (941) all_0_2_2 = n7
% 30.65/10.28 |
% 30.65/10.28 | From (941) and (473) follows:
% 30.65/10.28 | (943) pred(n7) = all_0_1_1
% 30.65/10.28 |
% 30.65/10.28 | From (942) and (716) follows:
% 30.65/10.28 | (944) pred(n8) = all_0_3_3
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 30.65/10.28 | (945) all_0_3_3 = n7
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 30.65/10.28 | (946) all_0_1_1 = n6
% 30.65/10.28 |
% 30.65/10.28 | From (945) and (232) follows:
% 30.65/10.28 | (947) sum(n7, all_0_0_0) = all_0_6_6
% 30.65/10.28 |
% 30.65/10.28 | From (946) and (1190) follows:
% 30.65/10.28 | (4668) sum(n14, n6) = all_0_0_0
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n14, n6, all_0_0_0, n20 and discharging atoms sum(n14, n6) = all_0_0_0, sum(n14, n6) = n20, yields:
% 30.65/10.28 | (1051) all_0_0_0 = n20
% 30.65/10.28 |
% 30.65/10.28 | From (1051) and (947) follows:
% 30.65/10.28 | (4670) sum(n7, n20) = all_0_6_6
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n7, n20, all_0_6_6, n6 and discharging atoms sum(n7, n20) = all_0_6_6, sum(n7, n20) = n6, yields:
% 30.65/10.28 | (1002) all_0_6_6 = n6
% 30.65/10.28 |
% 30.65/10.28 | Equations (1002) can reduce 498 to:
% 30.65/10.28 | (748) $false
% 30.65/10.28 |
% 30.65/10.28 |-The branch is then unsatisfiable
% 30.65/10.28 |-Branch two:
% 30.65/10.28 | (851) ~ (all_0_8_8 = n14)
% 30.65/10.28 | (852) all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.28 |
% 30.65/10.28 +-Applying beta-rule and splitting (852), into two cases.
% 30.65/10.28 |-Branch one:
% 30.65/10.28 | (853) all_0_8_8 = n13
% 30.65/10.28 |
% 30.65/10.28 | From (853) and (4657) follows:
% 30.65/10.28 | (4676) sum(n13, n15) = all_0_4_4
% 30.65/10.28 |
% 30.65/10.28 | From (853) and (4655) follows:
% 30.65/10.28 | (4677) sum(n13, n14) = all_0_2_2
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n13, n15, all_0_4_4, n7 and discharging atoms sum(n13, n15) = all_0_4_4, sum(n13, n15) = n7, yields:
% 30.65/10.28 | (959) all_0_4_4 = n7
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n13, n14, all_0_2_2, n6 and discharging atoms sum(n13, n14) = all_0_2_2, sum(n13, n14) = n6, yields:
% 30.65/10.28 | (958) all_0_2_2 = n6
% 30.65/10.28 |
% 30.65/10.28 | From (958) and (473) follows:
% 30.65/10.28 | (960) pred(n6) = all_0_1_1
% 30.65/10.28 |
% 30.65/10.28 | From (959) and (716) follows:
% 30.65/10.28 | (961) pred(n7) = all_0_3_3
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 30.65/10.28 | (962) all_0_3_3 = n6
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 30.65/10.28 | (963) all_0_1_1 = n5
% 30.65/10.28 |
% 30.65/10.28 | From (962) and (232) follows:
% 30.65/10.28 | (964) sum(n6, all_0_0_0) = all_0_6_6
% 30.65/10.28 |
% 30.65/10.28 | From (963) and (1190) follows:
% 30.65/10.28 | (4685) sum(n14, n5) = all_0_0_0
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n14, n5, all_0_0_0, n19 and discharging atoms sum(n14, n5) = all_0_0_0, sum(n14, n5) = n19, yields:
% 30.65/10.28 | (1068) all_0_0_0 = n19
% 30.65/10.28 |
% 30.65/10.28 | From (1068) and (964) follows:
% 30.65/10.28 | (4687) sum(n6, n19) = all_0_6_6
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n6, n19, all_0_6_6, n4 and discharging atoms sum(n6, n19) = all_0_6_6, sum(n6, n19) = n4, yields:
% 30.65/10.28 | (1019) all_0_6_6 = n4
% 30.65/10.28 |
% 30.65/10.28 | Equations (1019) can reduce 48 to:
% 30.65/10.28 | (748) $false
% 30.65/10.28 |
% 30.65/10.28 |-The branch is then unsatisfiable
% 30.65/10.28 |-Branch two:
% 30.65/10.28 | (868) ~ (all_0_8_8 = n13)
% 30.65/10.28 | (869) all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.28 |
% 30.65/10.28 +-Applying beta-rule and splitting (869), into two cases.
% 30.65/10.28 |-Branch one:
% 30.65/10.28 | (870) all_0_8_8 = n12
% 30.65/10.28 |
% 30.65/10.28 | From (870) and (4657) follows:
% 30.65/10.28 | (4693) sum(n12, n15) = all_0_4_4
% 30.65/10.28 |
% 30.65/10.28 | From (870) and (4655) follows:
% 30.65/10.28 | (4694) sum(n12, n14) = all_0_2_2
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n12, n15, all_0_4_4, n6 and discharging atoms sum(n12, n15) = all_0_4_4, sum(n12, n15) = n6, yields:
% 30.65/10.28 | (976) all_0_4_4 = n6
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n12, n14, all_0_2_2, n5 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n5, yields:
% 30.65/10.28 | (975) all_0_2_2 = n5
% 30.65/10.28 |
% 30.65/10.28 | From (975) and (473) follows:
% 30.65/10.28 | (977) pred(n5) = all_0_1_1
% 30.65/10.28 |
% 30.65/10.28 | From (976) and (716) follows:
% 30.65/10.28 | (978) pred(n6) = all_0_3_3
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 30.65/10.28 | (979) all_0_3_3 = n5
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 30.65/10.28 | (980) all_0_1_1 = n4
% 30.65/10.28 |
% 30.65/10.28 | From (979) and (232) follows:
% 30.65/10.28 | (981) sum(n5, all_0_0_0) = all_0_6_6
% 30.65/10.28 |
% 30.65/10.28 | From (980) and (1190) follows:
% 30.65/10.28 | (4702) sum(n14, n4) = all_0_0_0
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n14, n4, all_0_0_0, n18 and discharging atoms sum(n14, n4) = all_0_0_0, sum(n14, n4) = n18, yields:
% 30.65/10.28 | (1084) all_0_0_0 = n18
% 30.65/10.28 |
% 30.65/10.28 | From (1084) and (981) follows:
% 30.65/10.28 | (4704) sum(n5, n18) = all_0_6_6
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n5, n18, all_0_6_6, n2 and discharging atoms sum(n5, n18) = all_0_6_6, sum(n5, n18) = n2, yields:
% 30.65/10.28 | (1036) all_0_6_6 = n2
% 30.65/10.28 |
% 30.65/10.28 | Equations (1036) can reduce 56 to:
% 30.65/10.28 | (748) $false
% 30.65/10.28 |
% 30.65/10.28 |-The branch is then unsatisfiable
% 30.65/10.28 |-Branch two:
% 30.65/10.28 | (885) ~ (all_0_8_8 = n12)
% 30.65/10.28 | (886) all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.28 |
% 30.65/10.28 +-Applying beta-rule and splitting (886), into two cases.
% 30.65/10.28 |-Branch one:
% 30.65/10.28 | (887) all_0_8_8 = n11
% 30.65/10.28 |
% 30.65/10.28 | From (887) and (4657) follows:
% 30.65/10.28 | (4710) sum(n11, n15) = all_0_4_4
% 30.65/10.28 |
% 30.65/10.28 | From (887) and (4655) follows:
% 30.65/10.28 | (4711) sum(n11, n14) = all_0_2_2
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n11, n15, all_0_4_4, n5 and discharging atoms sum(n11, n15) = all_0_4_4, sum(n11, n15) = n5, yields:
% 30.65/10.28 | (993) all_0_4_4 = n5
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n11, n14, all_0_2_2, n4 and discharging atoms sum(n11, n14) = all_0_2_2, sum(n11, n14) = n4, yields:
% 30.65/10.28 | (992) all_0_2_2 = n4
% 30.65/10.28 |
% 30.65/10.28 | From (992) and (473) follows:
% 30.65/10.28 | (994) pred(n4) = all_0_1_1
% 30.65/10.28 |
% 30.65/10.28 | From (993) and (716) follows:
% 30.65/10.28 | (995) pred(n5) = all_0_3_3
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 30.65/10.28 | (996) all_0_3_3 = n4
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 30.65/10.28 | (997) all_0_1_1 = n3
% 30.65/10.28 |
% 30.65/10.28 | From (996) and (232) follows:
% 30.65/10.28 | (998) sum(n4, all_0_0_0) = all_0_6_6
% 30.65/10.28 |
% 30.65/10.28 | From (997) and (1190) follows:
% 30.65/10.28 | (4719) sum(n14, n3) = all_0_0_0
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n14, n3, all_0_0_0, n17 and discharging atoms sum(n14, n3) = all_0_0_0, sum(n14, n3) = n17, yields:
% 30.65/10.28 | (745) all_0_0_0 = n17
% 30.65/10.28 |
% 30.65/10.28 | From (745) and (998) follows:
% 30.65/10.28 | (4721) sum(n4, n17) = all_0_6_6
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n4, n17, all_0_6_6, n0 and discharging atoms sum(n4, n17) = all_0_6_6, sum(n4, n17) = n0, yields:
% 30.65/10.28 | (1053) all_0_6_6 = n0
% 30.65/10.28 |
% 30.65/10.28 | Equations (1053) can reduce 676 to:
% 30.65/10.28 | (748) $false
% 30.65/10.28 |
% 30.65/10.28 |-The branch is then unsatisfiable
% 30.65/10.28 |-Branch two:
% 30.65/10.28 | (902) ~ (all_0_8_8 = n11)
% 30.65/10.28 | (903) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.28 |
% 30.65/10.28 +-Applying beta-rule and splitting (903), into two cases.
% 30.65/10.28 |-Branch one:
% 30.65/10.28 | (904) all_0_8_8 = n10
% 30.65/10.28 |
% 30.65/10.28 | From (904) and (4657) follows:
% 30.65/10.28 | (4727) sum(n10, n15) = all_0_4_4
% 30.65/10.28 |
% 30.65/10.28 | From (904) and (4655) follows:
% 30.65/10.28 | (4728) sum(n10, n14) = all_0_2_2
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n10, n15, all_0_4_4, n4 and discharging atoms sum(n10, n15) = all_0_4_4, sum(n10, n15) = n4, yields:
% 30.65/10.28 | (1010) all_0_4_4 = n4
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n10, n14, all_0_2_2, n3 and discharging atoms sum(n10, n14) = all_0_2_2, sum(n10, n14) = n3, yields:
% 30.65/10.28 | (1009) all_0_2_2 = n3
% 30.65/10.28 |
% 30.65/10.28 | From (1009) and (473) follows:
% 30.65/10.28 | (1011) pred(n3) = all_0_1_1
% 30.65/10.28 |
% 30.65/10.28 | From (1010) and (716) follows:
% 30.65/10.28 | (1012) pred(n4) = all_0_3_3
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 30.65/10.28 | (1013) all_0_3_3 = n3
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 30.65/10.28 | (1014) all_0_1_1 = n2
% 30.65/10.28 |
% 30.65/10.28 | From (1013) and (232) follows:
% 30.65/10.28 | (1015) sum(n3, all_0_0_0) = all_0_6_6
% 30.65/10.28 |
% 30.65/10.28 | From (1014) and (1190) follows:
% 30.65/10.28 | (4736) sum(n14, n2) = all_0_0_0
% 30.65/10.28 |
% 30.65/10.28 | Instantiating formula (619) with n14, n2, all_0_0_0, n16 and discharging atoms sum(n14, n2) = all_0_0_0, sum(n14, n2) = n16, yields:
% 30.65/10.29 | (762) all_0_0_0 = n16
% 30.65/10.29 |
% 30.65/10.29 | From (762) and (1015) follows:
% 30.65/10.29 | (4738) sum(n3, n16) = all_0_6_6
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n3, n16, all_0_6_6, n19 and discharging atoms sum(n3, n16) = all_0_6_6, sum(n3, n16) = n19, yields:
% 30.65/10.29 | (1070) all_0_6_6 = n19
% 30.65/10.29 |
% 30.65/10.29 | Equations (1070) can reduce 31 to:
% 30.65/10.29 | (748) $false
% 30.65/10.29 |
% 30.65/10.29 |-The branch is then unsatisfiable
% 30.65/10.29 |-Branch two:
% 30.65/10.29 | (919) ~ (all_0_8_8 = n10)
% 30.65/10.29 | (920) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.29 |
% 30.65/10.29 +-Applying beta-rule and splitting (920), into two cases.
% 30.65/10.29 |-Branch one:
% 30.65/10.29 | (921) all_0_8_8 = n9
% 30.65/10.29 |
% 30.65/10.29 | From (921) and (4657) follows:
% 30.65/10.29 | (4744) sum(n9, n15) = all_0_4_4
% 30.65/10.29 |
% 30.65/10.29 | From (921) and (4655) follows:
% 30.65/10.29 | (4745) sum(n9, n14) = all_0_2_2
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n9, n15, all_0_4_4, n3 and discharging atoms sum(n9, n15) = all_0_4_4, sum(n9, n15) = n3, yields:
% 30.65/10.29 | (1027) all_0_4_4 = n3
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n9, n14, all_0_2_2, n2 and discharging atoms sum(n9, n14) = all_0_2_2, sum(n9, n14) = n2, yields:
% 30.65/10.29 | (1026) all_0_2_2 = n2
% 30.65/10.29 |
% 30.65/10.29 | From (1026) and (473) follows:
% 30.65/10.29 | (1028) pred(n2) = all_0_1_1
% 30.65/10.29 |
% 30.65/10.29 | From (1027) and (716) follows:
% 30.65/10.29 | (1029) pred(n3) = all_0_3_3
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 30.65/10.29 | (1030) all_0_3_3 = n2
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 30.65/10.29 | (1031) all_0_1_1 = n1
% 30.65/10.29 |
% 30.65/10.29 | From (1030) and (232) follows:
% 30.65/10.29 | (1032) sum(n2, all_0_0_0) = all_0_6_6
% 30.65/10.29 |
% 30.65/10.29 | From (1031) and (1190) follows:
% 30.65/10.29 | (4753) sum(n14, n1) = all_0_0_0
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n14, n1, all_0_0_0, n15 and discharging atoms sum(n14, n1) = all_0_0_0, sum(n14, n1) = n15, yields:
% 30.65/10.29 | (779) all_0_0_0 = n15
% 30.65/10.29 |
% 30.65/10.29 | From (779) and (1032) follows:
% 30.65/10.29 | (4755) sum(n2, n15) = all_0_6_6
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n2, n15, all_0_6_6, n17 and discharging atoms sum(n2, n15) = all_0_6_6, sum(n2, n15) = n17, yields:
% 30.65/10.29 | (1086) all_0_6_6 = n17
% 30.65/10.29 |
% 30.65/10.29 | Equations (1086) can reduce 669 to:
% 30.65/10.29 | (748) $false
% 30.65/10.29 |
% 30.65/10.29 |-The branch is then unsatisfiable
% 30.65/10.29 |-Branch two:
% 30.65/10.29 | (936) ~ (all_0_8_8 = n9)
% 30.65/10.29 | (937) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.29 |
% 30.65/10.29 +-Applying beta-rule and splitting (937), into two cases.
% 30.65/10.29 |-Branch one:
% 30.65/10.29 | (938) all_0_8_8 = n8
% 30.65/10.29 |
% 30.65/10.29 | From (938) and (4657) follows:
% 30.65/10.29 | (4761) sum(n8, n15) = all_0_4_4
% 30.65/10.29 |
% 30.65/10.29 | From (938) and (4655) follows:
% 30.65/10.29 | (4762) sum(n8, n14) = all_0_2_2
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n8, n15, all_0_4_4, n2 and discharging atoms sum(n8, n15) = all_0_4_4, sum(n8, n15) = n2, yields:
% 30.65/10.29 | (1044) all_0_4_4 = n2
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n8, n14, all_0_2_2, n1 and discharging atoms sum(n8, n14) = all_0_2_2, sum(n8, n14) = n1, yields:
% 30.65/10.29 | (1043) all_0_2_2 = n1
% 30.65/10.29 |
% 30.65/10.29 | From (1043) and (473) follows:
% 30.65/10.29 | (1045) pred(n1) = all_0_1_1
% 30.65/10.29 |
% 30.65/10.29 | From (1044) and (716) follows:
% 30.65/10.29 | (1046) pred(n2) = all_0_3_3
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 30.65/10.29 | (1047) all_0_3_3 = n1
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 30.65/10.29 | (1048) all_0_1_1 = n0
% 30.65/10.29 |
% 30.65/10.29 | From (1047) and (232) follows:
% 30.65/10.29 | (1049) sum(n1, all_0_0_0) = all_0_6_6
% 30.65/10.29 |
% 30.65/10.29 | From (1048) and (1190) follows:
% 30.65/10.29 | (4770) sum(n14, n0) = all_0_0_0
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n14, n0, all_0_0_0, n14 and discharging atoms sum(n14, n0) = all_0_0_0, sum(n14, n0) = n14, yields:
% 30.65/10.29 | (796) all_0_0_0 = n14
% 30.65/10.29 |
% 30.65/10.29 | From (796) and (1049) follows:
% 30.65/10.29 | (4772) sum(n1, n14) = all_0_6_6
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n1, n14, all_0_6_6, n15 and discharging atoms sum(n1, n14) = all_0_6_6, sum(n1, n14) = n15, yields:
% 30.65/10.29 | (747) all_0_6_6 = n15
% 30.65/10.29 |
% 30.65/10.29 | Equations (747) can reduce 456 to:
% 30.65/10.29 | (748) $false
% 30.65/10.29 |
% 30.65/10.29 |-The branch is then unsatisfiable
% 30.65/10.29 |-Branch two:
% 30.65/10.29 | (953) ~ (all_0_8_8 = n8)
% 30.65/10.29 | (954) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.29 |
% 30.65/10.29 +-Applying beta-rule and splitting (954), into two cases.
% 30.65/10.29 |-Branch one:
% 30.65/10.29 | (955) all_0_8_8 = n7
% 30.65/10.29 |
% 30.65/10.29 | From (955) and (4657) follows:
% 30.65/10.29 | (4778) sum(n7, n15) = all_0_4_4
% 30.65/10.29 |
% 30.65/10.29 | From (955) and (4655) follows:
% 30.65/10.29 | (4779) sum(n7, n14) = all_0_2_2
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n7, n15, all_0_4_4, n1 and discharging atoms sum(n7, n15) = all_0_4_4, sum(n7, n15) = n1, yields:
% 30.65/10.29 | (1061) all_0_4_4 = n1
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n7, n14, all_0_2_2, n0 and discharging atoms sum(n7, n14) = all_0_2_2, sum(n7, n14) = n0, yields:
% 30.65/10.29 | (1060) all_0_2_2 = n0
% 30.65/10.29 |
% 30.65/10.29 | From (1060) and (473) follows:
% 30.65/10.29 | (1062) pred(n0) = all_0_1_1
% 30.65/10.29 |
% 30.65/10.29 | From (1061) and (716) follows:
% 30.65/10.29 | (1063) pred(n1) = all_0_3_3
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 30.65/10.29 | (1064) all_0_3_3 = n0
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 30.65/10.29 | (1065) all_0_1_1 = n20
% 30.65/10.29 |
% 30.65/10.29 | From (1064) and (232) follows:
% 30.65/10.29 | (1066) sum(n0, all_0_0_0) = all_0_6_6
% 30.65/10.29 |
% 30.65/10.29 | From (1065) and (1190) follows:
% 30.65/10.29 | (4787) sum(n14, n20) = all_0_0_0
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n14, n20, all_0_0_0, n13 and discharging atoms sum(n14, n20) = all_0_0_0, sum(n14, n20) = n13, yields:
% 30.65/10.29 | (813) all_0_0_0 = n13
% 30.65/10.29 |
% 30.65/10.29 | From (813) and (1066) follows:
% 30.65/10.29 | (4789) sum(n0, n13) = all_0_6_6
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n0, n13, all_0_6_6, n13 and discharging atoms sum(n0, n13) = all_0_6_6, sum(n0, n13) = n13, yields:
% 30.65/10.29 | (764) all_0_6_6 = n13
% 30.65/10.29 |
% 30.65/10.29 | Equations (764) can reduce 293 to:
% 30.65/10.29 | (748) $false
% 30.65/10.29 |
% 30.65/10.29 |-The branch is then unsatisfiable
% 30.65/10.29 |-Branch two:
% 30.65/10.29 | (970) ~ (all_0_8_8 = n7)
% 30.65/10.29 | (971) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.29 |
% 30.65/10.29 +-Applying beta-rule and splitting (971), into two cases.
% 30.65/10.29 |-Branch one:
% 30.65/10.29 | (972) all_0_8_8 = n6
% 30.65/10.29 |
% 30.65/10.29 | From (972) and (4657) follows:
% 30.65/10.29 | (4795) sum(n6, n15) = all_0_4_4
% 30.65/10.29 |
% 30.65/10.29 | From (972) and (4655) follows:
% 30.65/10.29 | (4796) sum(n6, n14) = all_0_2_2
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n6, n15, all_0_4_4, n0 and discharging atoms sum(n6, n15) = all_0_4_4, sum(n6, n15) = n0, yields:
% 30.65/10.29 | (1077) all_0_4_4 = n0
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n6, n14, all_0_2_2, n20 and discharging atoms sum(n6, n14) = all_0_2_2, sum(n6, n14) = n20, yields:
% 30.65/10.29 | (1076) all_0_2_2 = n20
% 30.65/10.29 |
% 30.65/10.29 | From (1076) and (473) follows:
% 30.65/10.29 | (1078) pred(n20) = all_0_1_1
% 30.65/10.29 |
% 30.65/10.29 | From (1077) and (716) follows:
% 30.65/10.29 | (1079) pred(n0) = all_0_3_3
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 30.65/10.29 | (1080) all_0_1_1 = n19
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 30.65/10.29 | (1081) all_0_3_3 = n20
% 30.65/10.29 |
% 30.65/10.29 | From (1081) and (232) follows:
% 30.65/10.29 | (1082) sum(n20, all_0_0_0) = all_0_6_6
% 30.65/10.29 |
% 30.65/10.29 | From (1080) and (1190) follows:
% 30.65/10.29 | (4804) sum(n14, n19) = all_0_0_0
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n14, n19, all_0_0_0, n12 and discharging atoms sum(n14, n19) = all_0_0_0, sum(n14, n19) = n12, yields:
% 30.65/10.29 | (830) all_0_0_0 = n12
% 30.65/10.29 |
% 30.65/10.29 | From (830) and (1082) follows:
% 30.65/10.29 | (4806) sum(n20, n12) = all_0_6_6
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n20, n12, all_0_6_6, n11 and discharging atoms sum(n20, n12) = all_0_6_6, sum(n20, n12) = n11, yields:
% 30.65/10.29 | (781) all_0_6_6 = n11
% 30.65/10.29 |
% 30.65/10.29 | Equations (781) can reduce 2 to:
% 30.65/10.29 | (748) $false
% 30.65/10.29 |
% 30.65/10.29 |-The branch is then unsatisfiable
% 30.65/10.29 |-Branch two:
% 30.65/10.29 | (987) ~ (all_0_8_8 = n6)
% 30.65/10.29 | (988) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.29 |
% 30.65/10.29 +-Applying beta-rule and splitting (988), into two cases.
% 30.65/10.29 |-Branch one:
% 30.65/10.29 | (989) all_0_8_8 = n5
% 30.65/10.29 |
% 30.65/10.29 | From (989) and (4657) follows:
% 30.65/10.29 | (4812) sum(n5, n15) = all_0_4_4
% 30.65/10.29 |
% 30.65/10.29 | From (989) and (4655) follows:
% 30.65/10.29 | (4813) sum(n5, n14) = all_0_2_2
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n5, n15, all_0_4_4, n20 and discharging atoms sum(n5, n15) = all_0_4_4, sum(n5, n15) = n20, yields:
% 30.65/10.29 | (738) all_0_4_4 = n20
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n5, n14, all_0_2_2, n19 and discharging atoms sum(n5, n14) = all_0_2_2, sum(n5, n14) = n19, yields:
% 30.65/10.29 | (737) all_0_2_2 = n19
% 30.65/10.29 |
% 30.65/10.29 | From (737) and (473) follows:
% 30.65/10.29 | (739) pred(n19) = all_0_1_1
% 30.65/10.29 |
% 30.65/10.29 | From (738) and (716) follows:
% 30.65/10.29 | (740) pred(n20) = all_0_3_3
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 30.65/10.29 | (741) all_0_3_3 = n19
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 30.65/10.29 | (742) all_0_1_1 = n18
% 30.65/10.29 |
% 30.65/10.29 | From (741) and (232) follows:
% 30.65/10.29 | (743) sum(n19, all_0_0_0) = all_0_6_6
% 30.65/10.29 |
% 30.65/10.29 | From (742) and (1190) follows:
% 30.65/10.29 | (4821) sum(n14, n18) = all_0_0_0
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n14, n18, all_0_0_0, n11 and discharging atoms sum(n14, n18) = all_0_0_0, sum(n14, n18) = n11, yields:
% 30.65/10.29 | (847) all_0_0_0 = n11
% 30.65/10.29 |
% 30.65/10.29 | From (847) and (743) follows:
% 30.65/10.29 | (4823) sum(n19, n11) = all_0_6_6
% 30.65/10.29 |
% 30.65/10.29 | Instantiating formula (619) with n19, n11, all_0_6_6, n9 and discharging atoms sum(n19, n11) = all_0_6_6, sum(n19, n11) = n9, yields:
% 30.65/10.29 | (798) all_0_6_6 = n9
% 30.65/10.29 |
% 30.65/10.29 | Equations (798) can reduce 593 to:
% 30.65/10.29 | (748) $false
% 30.65/10.29 |
% 30.65/10.29 |-The branch is then unsatisfiable
% 30.65/10.29 |-Branch two:
% 30.65/10.29 | (1004) ~ (all_0_8_8 = n5)
% 30.65/10.29 | (1005) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.29 |
% 30.65/10.29 +-Applying beta-rule and splitting (1005), into two cases.
% 30.65/10.29 |-Branch one:
% 30.65/10.29 | (1006) all_0_8_8 = n4
% 30.65/10.29 |
% 30.65/10.29 | From (1006) and (4657) follows:
% 30.65/10.30 | (4829) sum(n4, n15) = all_0_4_4
% 30.65/10.30 |
% 30.65/10.30 | From (1006) and (4655) follows:
% 30.65/10.30 | (4830) sum(n4, n14) = all_0_2_2
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n4, n15, all_0_4_4, n19 and discharging atoms sum(n4, n15) = all_0_4_4, sum(n4, n15) = n19, yields:
% 30.65/10.30 | (755) all_0_4_4 = n19
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n4, n14, all_0_2_2, n18 and discharging atoms sum(n4, n14) = all_0_2_2, sum(n4, n14) = n18, yields:
% 30.65/10.30 | (754) all_0_2_2 = n18
% 30.65/10.30 |
% 30.65/10.30 | From (754) and (473) follows:
% 30.65/10.30 | (756) pred(n18) = all_0_1_1
% 30.65/10.30 |
% 30.65/10.30 | From (755) and (716) follows:
% 30.65/10.30 | (757) pred(n19) = all_0_3_3
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 30.65/10.30 | (758) all_0_3_3 = n18
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 30.65/10.30 | (759) all_0_1_1 = n17
% 30.65/10.30 |
% 30.65/10.30 | From (758) and (232) follows:
% 30.65/10.30 | (760) sum(n18, all_0_0_0) = all_0_6_6
% 30.65/10.30 |
% 30.65/10.30 | From (759) and (1190) follows:
% 30.65/10.30 | (4838) sum(n14, n17) = all_0_0_0
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n14, n17, all_0_0_0, n10 and discharging atoms sum(n14, n17) = all_0_0_0, sum(n14, n17) = n10, yields:
% 30.65/10.30 | (864) all_0_0_0 = n10
% 30.65/10.30 |
% 30.65/10.30 | From (864) and (760) follows:
% 30.65/10.30 | (4840) sum(n18, n10) = all_0_6_6
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n18, n10, all_0_6_6, n7 and discharging atoms sum(n18, n10) = all_0_6_6, sum(n18, n10) = n7, yields:
% 30.65/10.30 | (815) all_0_6_6 = n7
% 30.65/10.30 |
% 30.65/10.30 | Equations (815) can reduce 557 to:
% 30.65/10.30 | (748) $false
% 30.65/10.30 |
% 30.65/10.30 |-The branch is then unsatisfiable
% 30.65/10.30 |-Branch two:
% 30.65/10.30 | (1021) ~ (all_0_8_8 = n4)
% 30.65/10.30 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.30 |
% 30.65/10.30 +-Applying beta-rule and splitting (1022), into two cases.
% 30.65/10.30 |-Branch one:
% 30.65/10.30 | (1023) all_0_8_8 = n3
% 30.65/10.30 |
% 30.65/10.30 | From (1023) and (4657) follows:
% 30.65/10.30 | (4846) sum(n3, n15) = all_0_4_4
% 30.65/10.30 |
% 30.65/10.30 | From (1023) and (4655) follows:
% 30.65/10.30 | (4847) sum(n3, n14) = all_0_2_2
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n3, n15, all_0_4_4, n18 and discharging atoms sum(n3, n15) = all_0_4_4, sum(n3, n15) = n18, yields:
% 30.65/10.30 | (772) all_0_4_4 = n18
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n3, n14, all_0_2_2, n17 and discharging atoms sum(n3, n14) = all_0_2_2, sum(n3, n14) = n17, yields:
% 30.65/10.30 | (771) all_0_2_2 = n17
% 30.65/10.30 |
% 30.65/10.30 | From (771) and (473) follows:
% 30.65/10.30 | (773) pred(n17) = all_0_1_1
% 30.65/10.30 |
% 30.65/10.30 | From (772) and (716) follows:
% 30.65/10.30 | (774) pred(n18) = all_0_3_3
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 30.65/10.30 | (775) all_0_3_3 = n17
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 30.65/10.30 | (776) all_0_1_1 = n16
% 30.65/10.30 |
% 30.65/10.30 | From (775) and (232) follows:
% 30.65/10.30 | (777) sum(n17, all_0_0_0) = all_0_6_6
% 30.65/10.30 |
% 30.65/10.30 | From (776) and (1190) follows:
% 30.65/10.30 | (4855) sum(n14, n16) = all_0_0_0
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n14, n16, all_0_0_0, n9 and discharging atoms sum(n14, n16) = all_0_0_0, sum(n14, n16) = n9, yields:
% 30.65/10.30 | (881) all_0_0_0 = n9
% 30.65/10.30 |
% 30.65/10.30 | From (881) and (777) follows:
% 30.65/10.30 | (4857) sum(n17, n9) = all_0_6_6
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n17, n9, all_0_6_6, n5 and discharging atoms sum(n17, n9) = all_0_6_6, sum(n17, n9) = n5, yields:
% 30.65/10.30 | (832) all_0_6_6 = n5
% 30.65/10.30 |
% 30.65/10.30 | Equations (832) can reduce 462 to:
% 30.65/10.30 | (748) $false
% 30.65/10.30 |
% 30.65/10.30 |-The branch is then unsatisfiable
% 30.65/10.30 |-Branch two:
% 30.65/10.30 | (1038) ~ (all_0_8_8 = n3)
% 30.65/10.30 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.30 |
% 30.65/10.30 +-Applying beta-rule and splitting (1039), into two cases.
% 30.65/10.30 |-Branch one:
% 30.65/10.30 | (1040) all_0_8_8 = n2
% 30.65/10.30 |
% 30.65/10.30 | From (1040) and (4657) follows:
% 30.65/10.30 | (4863) sum(n2, n15) = all_0_4_4
% 30.65/10.30 |
% 30.65/10.30 | From (1040) and (4655) follows:
% 30.65/10.30 | (4864) sum(n2, n14) = all_0_2_2
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n2, n15, all_0_4_4, n17 and discharging atoms sum(n2, n15) = all_0_4_4, sum(n2, n15) = n17, yields:
% 30.65/10.30 | (789) all_0_4_4 = n17
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n2, n14, all_0_2_2, n16 and discharging atoms sum(n2, n14) = all_0_2_2, sum(n2, n14) = n16, yields:
% 30.65/10.30 | (788) all_0_2_2 = n16
% 30.65/10.30 |
% 30.65/10.30 | From (788) and (473) follows:
% 30.65/10.30 | (790) pred(n16) = all_0_1_1
% 30.65/10.30 |
% 30.65/10.30 | From (789) and (716) follows:
% 30.65/10.30 | (791) pred(n17) = all_0_3_3
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 30.65/10.30 | (792) all_0_3_3 = n16
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 30.65/10.30 | (793) all_0_1_1 = n15
% 30.65/10.30 |
% 30.65/10.30 | From (792) and (232) follows:
% 30.65/10.30 | (794) sum(n16, all_0_0_0) = all_0_6_6
% 30.65/10.30 |
% 30.65/10.30 | From (793) and (1190) follows:
% 30.65/10.30 | (4872) sum(n14, n15) = all_0_0_0
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n14, n15, all_0_0_0, n8 and discharging atoms sum(n14, n15) = all_0_0_0, sum(n14, n15) = n8, yields:
% 30.65/10.30 | (898) all_0_0_0 = n8
% 30.65/10.30 |
% 30.65/10.30 | From (898) and (794) follows:
% 30.65/10.30 | (4874) sum(n16, n8) = all_0_6_6
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n16, n8, all_0_6_6, n3 and discharging atoms sum(n16, n8) = all_0_6_6, sum(n16, n8) = n3, yields:
% 30.65/10.30 | (849) all_0_6_6 = n3
% 30.65/10.30 |
% 30.65/10.30 | Equations (849) can reduce 416 to:
% 30.65/10.30 | (748) $false
% 30.65/10.30 |
% 30.65/10.30 |-The branch is then unsatisfiable
% 30.65/10.30 |-Branch two:
% 30.65/10.30 | (1055) ~ (all_0_8_8 = n2)
% 30.65/10.30 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 30.65/10.30 |
% 30.65/10.30 +-Applying beta-rule and splitting (1056), into two cases.
% 30.65/10.30 |-Branch one:
% 30.65/10.30 | (1057) all_0_8_8 = n1
% 30.65/10.30 |
% 30.65/10.30 | From (1057) and (4657) follows:
% 30.65/10.30 | (4880) sum(n1, n15) = all_0_4_4
% 30.65/10.30 |
% 30.65/10.30 | From (1057) and (4655) follows:
% 30.65/10.30 | (4881) sum(n1, n14) = all_0_2_2
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n1, n15, all_0_4_4, n16 and discharging atoms sum(n1, n15) = all_0_4_4, sum(n1, n15) = n16, yields:
% 30.65/10.30 | (806) all_0_4_4 = n16
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n1, n14, all_0_2_2, n15 and discharging atoms sum(n1, n14) = all_0_2_2, sum(n1, n14) = n15, yields:
% 30.65/10.30 | (805) all_0_2_2 = n15
% 30.65/10.30 |
% 30.65/10.30 | From (805) and (473) follows:
% 30.65/10.30 | (807) pred(n15) = all_0_1_1
% 30.65/10.30 |
% 30.65/10.30 | From (806) and (716) follows:
% 30.65/10.30 | (808) pred(n16) = all_0_3_3
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 30.65/10.30 | (809) all_0_3_3 = n15
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 30.65/10.30 | (810) all_0_1_1 = n14
% 30.65/10.30 |
% 30.65/10.30 | From (809) and (232) follows:
% 30.65/10.30 | (811) sum(n15, all_0_0_0) = all_0_6_6
% 30.65/10.30 |
% 30.65/10.30 | From (810) and (1190) follows:
% 30.65/10.30 | (4889) sum(n14, n14) = all_0_0_0
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n14, n14, all_0_0_0, n7 and discharging atoms sum(n14, n14) = all_0_0_0, sum(n14, n14) = n7, yields:
% 30.65/10.30 | (915) all_0_0_0 = n7
% 30.65/10.30 |
% 30.65/10.30 | From (915) and (811) follows:
% 30.65/10.30 | (4891) sum(n15, n7) = all_0_6_6
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n15, n7, all_0_6_6, n1 and discharging atoms sum(n15, n7) = all_0_6_6, sum(n15, n7) = n1, yields:
% 30.65/10.30 | (866) all_0_6_6 = n1
% 30.65/10.30 |
% 30.65/10.30 | Equations (866) can reduce 28 to:
% 30.65/10.30 | (748) $false
% 30.65/10.30 |
% 30.65/10.30 |-The branch is then unsatisfiable
% 30.65/10.30 |-Branch two:
% 30.65/10.30 | (1072) ~ (all_0_8_8 = n1)
% 30.65/10.30 | (1073) all_0_8_8 = n0
% 30.65/10.30 |
% 30.65/10.30 | From (1073) and (4657) follows:
% 30.65/10.30 | (4896) sum(n0, n15) = all_0_4_4
% 30.65/10.30 |
% 30.65/10.30 | From (1073) and (4655) follows:
% 30.65/10.30 | (4897) sum(n0, n14) = all_0_2_2
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n0, n15, all_0_4_4, n15 and discharging atoms sum(n0, n15) = all_0_4_4, sum(n0, n15) = n15, yields:
% 30.65/10.30 | (823) all_0_4_4 = n15
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n0, n14, all_0_2_2, n14 and discharging atoms sum(n0, n14) = all_0_2_2, sum(n0, n14) = n14, yields:
% 30.65/10.30 | (822) all_0_2_2 = n14
% 30.65/10.30 |
% 30.65/10.30 | From (822) and (473) follows:
% 30.65/10.30 | (824) pred(n14) = all_0_1_1
% 30.65/10.30 |
% 30.65/10.30 | From (823) and (716) follows:
% 30.65/10.30 | (825) pred(n15) = all_0_3_3
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 30.65/10.30 | (826) all_0_3_3 = n14
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 30.65/10.30 | (827) all_0_1_1 = n13
% 30.65/10.30 |
% 30.65/10.30 | From (826) and (232) follows:
% 30.65/10.30 | (828) sum(n14, all_0_0_0) = all_0_6_6
% 30.65/10.30 |
% 30.65/10.30 | From (827) and (1190) follows:
% 30.65/10.30 | (4905) sum(n14, n13) = all_0_0_0
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n14, n13, all_0_0_0, n6 and discharging atoms sum(n14, n13) = all_0_0_0, sum(n14, n13) = n6, yields:
% 30.65/10.30 | (932) all_0_0_0 = n6
% 30.65/10.30 |
% 30.65/10.30 | From (932) and (828) follows:
% 30.65/10.30 | (4907) sum(n14, n6) = all_0_6_6
% 30.65/10.30 |
% 30.65/10.30 | Instantiating formula (619) with n14, n6, all_0_6_6, n20 and discharging atoms sum(n14, n6) = all_0_6_6, sum(n14, n6) = n20, yields:
% 30.65/10.30 | (883) all_0_6_6 = n20
% 30.65/10.30 |
% 30.65/10.30 | Equations (883) can reduce 381 to:
% 30.65/10.30 | (748) $false
% 30.65/10.30 |
% 30.65/10.30 |-The branch is then unsatisfiable
% 30.65/10.30 |-Branch two:
% 30.65/10.30 | (1205) ~ (all_0_7_7 = n14)
% 30.65/10.30 | (1206) all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.30 |
% 30.65/10.30 +-Applying beta-rule and splitting (835), into two cases.
% 30.65/10.30 |-Branch one:
% 30.65/10.30 | (836) all_0_8_8 = n14
% 30.65/10.30 |
% 30.65/10.30 | From (836) and (708) follows:
% 30.65/10.30 | (4913) sum(n14, all_0_5_5) = all_0_4_4
% 30.65/10.30 |
% 30.65/10.30 | From (836) and (378) follows:
% 30.65/10.30 | (4914) sum(n14, all_0_7_7) = all_0_2_2
% 30.65/10.30 |
% 30.65/10.30 +-Applying beta-rule and splitting (1206), into two cases.
% 30.65/10.30 |-Branch one:
% 30.65/10.30 | (1207) all_0_7_7 = n13
% 30.65/10.30 |
% 30.65/10.30 | From (1207) and (683) follows:
% 30.65/10.30 | (1208) succ(n13) = all_0_5_5
% 30.65/10.30 |
% 30.65/10.30 | From (1207) and (8) follows:
% 30.65/10.30 | (1209) sum(n13, all_0_1_1) = all_0_0_0
% 30.65/10.30 |
% 30.65/10.30 | From (1207) and (4914) follows:
% 30.65/10.31 | (4918) sum(n14, n13) = all_0_2_2
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (388) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 30.65/10.31 | (1211) all_0_5_5 = n14
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n14, n13, all_0_2_2, n6 and discharging atoms sum(n14, n13) = all_0_2_2, sum(n14, n13) = n6, yields:
% 30.65/10.31 | (958) all_0_2_2 = n6
% 30.65/10.31 |
% 30.65/10.31 | From (958) and (473) follows:
% 30.65/10.31 | (960) pred(n6) = all_0_1_1
% 30.65/10.31 |
% 30.65/10.31 | From (1211) and (4913) follows:
% 30.65/10.31 | (4922) sum(n14, n14) = all_0_4_4
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 30.65/10.31 | (963) all_0_1_1 = n5
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n14, n14, all_0_4_4, n7 and discharging atoms sum(n14, n14) = all_0_4_4, sum(n14, n14) = n7, yields:
% 30.65/10.31 | (959) all_0_4_4 = n7
% 30.65/10.31 |
% 30.65/10.31 | From (959) and (716) follows:
% 30.65/10.31 | (961) pred(n7) = all_0_3_3
% 30.65/10.31 |
% 30.65/10.31 | From (963) and (1209) follows:
% 30.65/10.31 | (4926) sum(n13, n5) = all_0_0_0
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 30.65/10.31 | (962) all_0_3_3 = n6
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n13, n5, all_0_0_0, n18 and discharging atoms sum(n13, n5) = all_0_0_0, sum(n13, n5) = n18, yields:
% 30.65/10.31 | (1084) all_0_0_0 = n18
% 30.65/10.31 |
% 30.65/10.31 | From (962)(1084) and (232) follows:
% 30.65/10.31 | (4929) sum(n6, n18) = all_0_6_6
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n6, n18, all_0_6_6, n3 and discharging atoms sum(n6, n18) = all_0_6_6, sum(n6, n18) = n3, yields:
% 30.65/10.31 | (849) all_0_6_6 = n3
% 30.65/10.31 |
% 30.65/10.31 | Equations (849) can reduce 416 to:
% 30.65/10.31 | (748) $false
% 30.65/10.31 |
% 30.65/10.31 |-The branch is then unsatisfiable
% 30.65/10.31 |-Branch two:
% 30.65/10.31 | (1224) ~ (all_0_7_7 = n13)
% 30.65/10.31 | (1225) all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.31 |
% 30.65/10.31 +-Applying beta-rule and splitting (1225), into two cases.
% 30.65/10.31 |-Branch one:
% 30.65/10.31 | (1226) all_0_7_7 = n12
% 30.65/10.31 |
% 30.65/10.31 | From (1226) and (683) follows:
% 30.65/10.31 | (1227) succ(n12) = all_0_5_5
% 30.65/10.31 |
% 30.65/10.31 | From (1226) and (8) follows:
% 30.65/10.31 | (1228) sum(n12, all_0_1_1) = all_0_0_0
% 30.65/10.31 |
% 30.65/10.31 | From (1226) and (4914) follows:
% 30.65/10.31 | (4937) sum(n14, n12) = all_0_2_2
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (388) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 30.65/10.31 | (1230) all_0_5_5 = n13
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n14, n12, all_0_2_2, n5 and discharging atoms sum(n14, n12) = all_0_2_2, sum(n14, n12) = n5, yields:
% 30.65/10.31 | (975) all_0_2_2 = n5
% 30.65/10.31 |
% 30.65/10.31 | From (975) and (473) follows:
% 30.65/10.31 | (977) pred(n5) = all_0_1_1
% 30.65/10.31 |
% 30.65/10.31 | From (1230) and (4913) follows:
% 30.65/10.31 | (4941) sum(n14, n13) = all_0_4_4
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 30.65/10.31 | (980) all_0_1_1 = n4
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n14, n13, all_0_4_4, n6 and discharging atoms sum(n14, n13) = all_0_4_4, sum(n14, n13) = n6, yields:
% 30.65/10.31 | (976) all_0_4_4 = n6
% 30.65/10.31 |
% 30.65/10.31 | From (976) and (716) follows:
% 30.65/10.31 | (978) pred(n6) = all_0_3_3
% 30.65/10.31 |
% 30.65/10.31 | From (980) and (1228) follows:
% 30.65/10.31 | (4945) sum(n12, n4) = all_0_0_0
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 30.65/10.31 | (979) all_0_3_3 = n5
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n12, n4, all_0_0_0, n16 and discharging atoms sum(n12, n4) = all_0_0_0, sum(n12, n4) = n16, yields:
% 30.65/10.31 | (762) all_0_0_0 = n16
% 30.65/10.31 |
% 30.65/10.31 | From (979)(762) and (232) follows:
% 30.65/10.31 | (4948) sum(n5, n16) = all_0_6_6
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n5, n16, all_0_6_6, n0 and discharging atoms sum(n5, n16) = all_0_6_6, sum(n5, n16) = n0, yields:
% 30.65/10.31 | (1053) all_0_6_6 = n0
% 30.65/10.31 |
% 30.65/10.31 | Equations (1053) can reduce 676 to:
% 30.65/10.31 | (748) $false
% 30.65/10.31 |
% 30.65/10.31 |-The branch is then unsatisfiable
% 30.65/10.31 |-Branch two:
% 30.65/10.31 | (1243) ~ (all_0_7_7 = n12)
% 30.65/10.31 | (1244) all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.31 |
% 30.65/10.31 +-Applying beta-rule and splitting (1244), into two cases.
% 30.65/10.31 |-Branch one:
% 30.65/10.31 | (1245) all_0_7_7 = n11
% 30.65/10.31 |
% 30.65/10.31 | From (1245) and (683) follows:
% 30.65/10.31 | (1246) succ(n11) = all_0_5_5
% 30.65/10.31 |
% 30.65/10.31 | From (1245) and (8) follows:
% 30.65/10.31 | (1247) sum(n11, all_0_1_1) = all_0_0_0
% 30.65/10.31 |
% 30.65/10.31 | From (1245) and (4914) follows:
% 30.65/10.31 | (4956) sum(n14, n11) = all_0_2_2
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (388) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 30.65/10.31 | (1249) all_0_5_5 = n12
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n14, n11, all_0_2_2, n4 and discharging atoms sum(n14, n11) = all_0_2_2, sum(n14, n11) = n4, yields:
% 30.65/10.31 | (992) all_0_2_2 = n4
% 30.65/10.31 |
% 30.65/10.31 | From (992) and (473) follows:
% 30.65/10.31 | (994) pred(n4) = all_0_1_1
% 30.65/10.31 |
% 30.65/10.31 | From (1249) and (4913) follows:
% 30.65/10.31 | (4960) sum(n14, n12) = all_0_4_4
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 30.65/10.31 | (997) all_0_1_1 = n3
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n14, n12, all_0_4_4, n5 and discharging atoms sum(n14, n12) = all_0_4_4, sum(n14, n12) = n5, yields:
% 30.65/10.31 | (993) all_0_4_4 = n5
% 30.65/10.31 |
% 30.65/10.31 | From (993) and (716) follows:
% 30.65/10.31 | (995) pred(n5) = all_0_3_3
% 30.65/10.31 |
% 30.65/10.31 | From (997) and (1247) follows:
% 30.65/10.31 | (4964) sum(n11, n3) = all_0_0_0
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 30.65/10.31 | (996) all_0_3_3 = n4
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n11, n3, all_0_0_0, n14 and discharging atoms sum(n11, n3) = all_0_0_0, sum(n11, n3) = n14, yields:
% 30.65/10.31 | (796) all_0_0_0 = n14
% 30.65/10.31 |
% 30.65/10.31 | From (996)(796) and (232) follows:
% 30.65/10.31 | (4967) sum(n4, n14) = all_0_6_6
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n4, n14, all_0_6_6, n18 and discharging atoms sum(n4, n14) = all_0_6_6, sum(n4, n14) = n18, yields:
% 30.65/10.31 | (900) all_0_6_6 = n18
% 30.65/10.31 |
% 30.65/10.31 | Equations (900) can reduce 622 to:
% 30.65/10.31 | (748) $false
% 30.65/10.31 |
% 30.65/10.31 |-The branch is then unsatisfiable
% 30.65/10.31 |-Branch two:
% 30.65/10.31 | (1262) ~ (all_0_7_7 = n11)
% 30.65/10.31 | (1263) all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.31 |
% 30.65/10.31 +-Applying beta-rule and splitting (1263), into two cases.
% 30.65/10.31 |-Branch one:
% 30.65/10.31 | (1264) all_0_7_7 = n10
% 30.65/10.31 |
% 30.65/10.31 | From (1264) and (683) follows:
% 30.65/10.31 | (1265) succ(n10) = all_0_5_5
% 30.65/10.31 |
% 30.65/10.31 | From (1264) and (8) follows:
% 30.65/10.31 | (1266) sum(n10, all_0_1_1) = all_0_0_0
% 30.65/10.31 |
% 30.65/10.31 | From (1264) and (4914) follows:
% 30.65/10.31 | (4975) sum(n14, n10) = all_0_2_2
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (388) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 30.65/10.31 | (1268) all_0_5_5 = n11
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n14, n10, all_0_2_2, n3 and discharging atoms sum(n14, n10) = all_0_2_2, sum(n14, n10) = n3, yields:
% 30.65/10.31 | (1009) all_0_2_2 = n3
% 30.65/10.31 |
% 30.65/10.31 | From (1009) and (473) follows:
% 30.65/10.31 | (1011) pred(n3) = all_0_1_1
% 30.65/10.31 |
% 30.65/10.31 | From (1268) and (4913) follows:
% 30.65/10.31 | (4979) sum(n14, n11) = all_0_4_4
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 30.65/10.31 | (1014) all_0_1_1 = n2
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n14, n11, all_0_4_4, n4 and discharging atoms sum(n14, n11) = all_0_4_4, sum(n14, n11) = n4, yields:
% 30.65/10.31 | (1010) all_0_4_4 = n4
% 30.65/10.31 |
% 30.65/10.31 | From (1010) and (716) follows:
% 30.65/10.31 | (1012) pred(n4) = all_0_3_3
% 30.65/10.31 |
% 30.65/10.31 | From (1014) and (1266) follows:
% 30.65/10.31 | (4983) sum(n10, n2) = all_0_0_0
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 30.65/10.31 | (1013) all_0_3_3 = n3
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n10, n2, all_0_0_0, n12 and discharging atoms sum(n10, n2) = all_0_0_0, sum(n10, n2) = n12, yields:
% 30.65/10.31 | (830) all_0_0_0 = n12
% 30.65/10.31 |
% 30.65/10.31 | From (1013)(830) and (232) follows:
% 30.65/10.31 | (4986) sum(n3, n12) = all_0_6_6
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n3, n12, all_0_6_6, n15 and discharging atoms sum(n3, n12) = all_0_6_6, sum(n3, n12) = n15, yields:
% 30.65/10.31 | (747) all_0_6_6 = n15
% 30.65/10.31 |
% 30.65/10.31 | Equations (747) can reduce 456 to:
% 30.65/10.31 | (748) $false
% 30.65/10.31 |
% 30.65/10.31 |-The branch is then unsatisfiable
% 30.65/10.31 |-Branch two:
% 30.65/10.31 | (1281) ~ (all_0_7_7 = n10)
% 30.65/10.31 | (1282) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.31 |
% 30.65/10.31 +-Applying beta-rule and splitting (1282), into two cases.
% 30.65/10.31 |-Branch one:
% 30.65/10.31 | (1283) all_0_7_7 = n9
% 30.65/10.31 |
% 30.65/10.31 | From (1283) and (683) follows:
% 30.65/10.31 | (1284) succ(n9) = all_0_5_5
% 30.65/10.31 |
% 30.65/10.31 | From (1283) and (8) follows:
% 30.65/10.31 | (1285) sum(n9, all_0_1_1) = all_0_0_0
% 30.65/10.31 |
% 30.65/10.31 | From (1283) and (4914) follows:
% 30.65/10.31 | (4994) sum(n14, n9) = all_0_2_2
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (388) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 30.65/10.31 | (1287) all_0_5_5 = n10
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n14, n9, all_0_2_2, n2 and discharging atoms sum(n14, n9) = all_0_2_2, sum(n14, n9) = n2, yields:
% 30.65/10.31 | (1026) all_0_2_2 = n2
% 30.65/10.31 |
% 30.65/10.31 | From (1026) and (473) follows:
% 30.65/10.31 | (1028) pred(n2) = all_0_1_1
% 30.65/10.31 |
% 30.65/10.31 | From (1287) and (4913) follows:
% 30.65/10.31 | (4998) sum(n14, n10) = all_0_4_4
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 30.65/10.31 | (1031) all_0_1_1 = n1
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n14, n10, all_0_4_4, n3 and discharging atoms sum(n14, n10) = all_0_4_4, sum(n14, n10) = n3, yields:
% 30.65/10.31 | (1027) all_0_4_4 = n3
% 30.65/10.31 |
% 30.65/10.31 | From (1027) and (716) follows:
% 30.65/10.31 | (1029) pred(n3) = all_0_3_3
% 30.65/10.31 |
% 30.65/10.31 | From (1031) and (1285) follows:
% 30.65/10.31 | (5002) sum(n9, n1) = all_0_0_0
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 30.65/10.31 | (1030) all_0_3_3 = n2
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n9, n1, all_0_0_0, n10 and discharging atoms sum(n9, n1) = all_0_0_0, sum(n9, n1) = n10, yields:
% 30.65/10.31 | (864) all_0_0_0 = n10
% 30.65/10.31 |
% 30.65/10.31 | From (1030)(864) and (232) follows:
% 30.65/10.31 | (5005) sum(n2, n10) = all_0_6_6
% 30.65/10.31 |
% 30.65/10.31 | Instantiating formula (619) with n2, n10, all_0_6_6, n12 and discharging atoms sum(n2, n10) = all_0_6_6, sum(n2, n10) = n12, yields:
% 30.65/10.31 | (951) all_0_6_6 = n12
% 30.65/10.31 |
% 30.65/10.31 | Equations (951) can reduce 76 to:
% 30.65/10.32 | (748) $false
% 30.65/10.32 |
% 30.65/10.32 |-The branch is then unsatisfiable
% 30.65/10.32 |-Branch two:
% 30.65/10.32 | (1300) ~ (all_0_7_7 = n9)
% 30.65/10.32 | (1301) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.32 |
% 30.65/10.32 +-Applying beta-rule and splitting (1301), into two cases.
% 30.65/10.32 |-Branch one:
% 30.65/10.32 | (1302) all_0_7_7 = n8
% 30.65/10.32 |
% 30.65/10.32 | From (1302) and (683) follows:
% 30.65/10.32 | (1303) succ(n8) = all_0_5_5
% 30.65/10.32 |
% 30.65/10.32 | From (1302) and (8) follows:
% 30.65/10.32 | (1304) sum(n8, all_0_1_1) = all_0_0_0
% 30.65/10.32 |
% 30.65/10.32 | From (1302) and (4914) follows:
% 30.65/10.32 | (5013) sum(n14, n8) = all_0_2_2
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (388) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 30.65/10.32 | (1306) all_0_5_5 = n9
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (619) with n14, n8, all_0_2_2, n1 and discharging atoms sum(n14, n8) = all_0_2_2, sum(n14, n8) = n1, yields:
% 30.65/10.32 | (1043) all_0_2_2 = n1
% 30.65/10.32 |
% 30.65/10.32 | From (1043) and (473) follows:
% 30.65/10.32 | (1045) pred(n1) = all_0_1_1
% 30.65/10.32 |
% 30.65/10.32 | From (1306) and (4913) follows:
% 30.65/10.32 | (5017) sum(n14, n9) = all_0_4_4
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 30.65/10.32 | (1048) all_0_1_1 = n0
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (619) with n14, n9, all_0_4_4, n2 and discharging atoms sum(n14, n9) = all_0_4_4, sum(n14, n9) = n2, yields:
% 30.65/10.32 | (1044) all_0_4_4 = n2
% 30.65/10.32 |
% 30.65/10.32 | From (1044) and (716) follows:
% 30.65/10.32 | (1046) pred(n2) = all_0_3_3
% 30.65/10.32 |
% 30.65/10.32 | From (1048) and (1304) follows:
% 30.65/10.32 | (5021) sum(n8, n0) = all_0_0_0
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 30.65/10.32 | (1047) all_0_3_3 = n1
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (619) with n8, n0, all_0_0_0, n8 and discharging atoms sum(n8, n0) = all_0_0_0, sum(n8, n0) = n8, yields:
% 30.65/10.32 | (898) all_0_0_0 = n8
% 30.65/10.32 |
% 30.65/10.32 | From (1047)(898) and (232) follows:
% 30.65/10.32 | (5024) sum(n1, n8) = all_0_6_6
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (619) with n1, n8, all_0_6_6, n9 and discharging atoms sum(n1, n8) = all_0_6_6, sum(n1, n8) = n9, yields:
% 30.65/10.32 | (798) all_0_6_6 = n9
% 30.65/10.32 |
% 30.65/10.32 | Equations (798) can reduce 593 to:
% 30.65/10.32 | (748) $false
% 30.65/10.32 |
% 30.65/10.32 |-The branch is then unsatisfiable
% 30.65/10.32 |-Branch two:
% 30.65/10.32 | (1319) ~ (all_0_7_7 = n8)
% 30.65/10.32 | (1320) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.32 |
% 30.65/10.32 +-Applying beta-rule and splitting (1320), into two cases.
% 30.65/10.32 |-Branch one:
% 30.65/10.32 | (1321) all_0_7_7 = n7
% 30.65/10.32 |
% 30.65/10.32 | From (1321) and (683) follows:
% 30.65/10.32 | (1322) succ(n7) = all_0_5_5
% 30.65/10.32 |
% 30.65/10.32 | From (1321) and (8) follows:
% 30.65/10.32 | (1323) sum(n7, all_0_1_1) = all_0_0_0
% 30.65/10.32 |
% 30.65/10.32 | From (1321) and (4914) follows:
% 30.65/10.32 | (5032) sum(n14, n7) = all_0_2_2
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (388) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 30.65/10.32 | (1325) all_0_5_5 = n8
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (619) with n14, n7, all_0_2_2, n0 and discharging atoms sum(n14, n7) = all_0_2_2, sum(n14, n7) = n0, yields:
% 30.65/10.32 | (1060) all_0_2_2 = n0
% 30.65/10.32 |
% 30.65/10.32 | From (1060) and (473) follows:
% 30.65/10.32 | (1062) pred(n0) = all_0_1_1
% 30.65/10.32 |
% 30.65/10.32 | From (1325) and (4913) follows:
% 30.65/10.32 | (5036) sum(n14, n8) = all_0_4_4
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 30.65/10.32 | (1065) all_0_1_1 = n20
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (619) with n14, n8, all_0_4_4, n1 and discharging atoms sum(n14, n8) = all_0_4_4, sum(n14, n8) = n1, yields:
% 30.65/10.32 | (1061) all_0_4_4 = n1
% 30.65/10.32 |
% 30.65/10.32 | From (1061) and (716) follows:
% 30.65/10.32 | (1063) pred(n1) = all_0_3_3
% 30.65/10.32 |
% 30.65/10.32 | From (1065) and (1323) follows:
% 30.65/10.32 | (5040) sum(n7, n20) = all_0_0_0
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 30.65/10.32 | (1064) all_0_3_3 = n0
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (619) with n7, n20, all_0_0_0, n6 and discharging atoms sum(n7, n20) = all_0_0_0, sum(n7, n20) = n6, yields:
% 30.65/10.32 | (932) all_0_0_0 = n6
% 30.65/10.32 |
% 30.65/10.32 | From (1064)(932) and (232) follows:
% 30.65/10.32 | (5043) sum(n0, n6) = all_0_6_6
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (619) with n0, n6, all_0_6_6, n6 and discharging atoms sum(n0, n6) = all_0_6_6, sum(n0, n6) = n6, yields:
% 30.65/10.32 | (1002) all_0_6_6 = n6
% 30.65/10.32 |
% 30.65/10.32 | Equations (1002) can reduce 498 to:
% 30.65/10.32 | (748) $false
% 30.65/10.32 |
% 30.65/10.32 |-The branch is then unsatisfiable
% 30.65/10.32 |-Branch two:
% 30.65/10.32 | (1338) ~ (all_0_7_7 = n7)
% 30.65/10.32 | (1339) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.32 |
% 30.65/10.32 +-Applying beta-rule and splitting (1339), into two cases.
% 30.65/10.32 |-Branch one:
% 30.65/10.32 | (1340) all_0_7_7 = n6
% 30.65/10.32 |
% 30.65/10.32 | From (1340) and (683) follows:
% 30.65/10.32 | (1341) succ(n6) = all_0_5_5
% 30.65/10.32 |
% 30.65/10.32 | From (1340) and (8) follows:
% 30.65/10.32 | (1342) sum(n6, all_0_1_1) = all_0_0_0
% 30.65/10.32 |
% 30.65/10.32 | From (1340) and (4914) follows:
% 30.65/10.32 | (5051) sum(n14, n6) = all_0_2_2
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (388) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 30.65/10.32 | (1344) all_0_5_5 = n7
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (619) with n14, n6, all_0_2_2, n20 and discharging atoms sum(n14, n6) = all_0_2_2, sum(n14, n6) = n20, yields:
% 30.65/10.32 | (1076) all_0_2_2 = n20
% 30.65/10.32 |
% 30.65/10.32 | From (1076) and (473) follows:
% 30.65/10.32 | (1078) pred(n20) = all_0_1_1
% 30.65/10.32 |
% 30.65/10.32 | From (1344) and (4913) follows:
% 30.65/10.32 | (5055) sum(n14, n7) = all_0_4_4
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 30.65/10.32 | (1080) all_0_1_1 = n19
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (619) with n14, n7, all_0_4_4, n0 and discharging atoms sum(n14, n7) = all_0_4_4, sum(n14, n7) = n0, yields:
% 30.65/10.32 | (1077) all_0_4_4 = n0
% 30.65/10.32 |
% 30.65/10.32 | From (1077) and (716) follows:
% 30.65/10.32 | (1079) pred(n0) = all_0_3_3
% 30.65/10.32 |
% 30.65/10.32 | From (1080) and (1342) follows:
% 30.65/10.32 | (5059) sum(n6, n19) = all_0_0_0
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 30.65/10.32 | (1081) all_0_3_3 = n20
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (619) with n6, n19, all_0_0_0, n4 and discharging atoms sum(n6, n19) = all_0_0_0, sum(n6, n19) = n4, yields:
% 30.65/10.32 | (966) all_0_0_0 = n4
% 30.65/10.32 |
% 30.65/10.32 | From (1081)(966) and (232) follows:
% 30.65/10.32 | (5062) sum(n20, n4) = all_0_6_6
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (619) with n20, n4, all_0_6_6, n3 and discharging atoms sum(n20, n4) = all_0_6_6, sum(n20, n4) = n3, yields:
% 30.65/10.32 | (849) all_0_6_6 = n3
% 30.65/10.32 |
% 30.65/10.32 | Equations (849) can reduce 416 to:
% 30.65/10.32 | (748) $false
% 30.65/10.32 |
% 30.65/10.32 |-The branch is then unsatisfiable
% 30.65/10.32 |-Branch two:
% 30.65/10.32 | (1357) ~ (all_0_7_7 = n6)
% 30.65/10.32 | (1358) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.32 |
% 30.65/10.32 +-Applying beta-rule and splitting (1358), into two cases.
% 30.65/10.32 |-Branch one:
% 30.65/10.32 | (1359) all_0_7_7 = n5
% 30.65/10.32 |
% 30.65/10.32 | From (1359) and (683) follows:
% 30.65/10.32 | (1360) succ(n5) = all_0_5_5
% 30.65/10.32 |
% 30.65/10.32 | From (1359) and (8) follows:
% 30.65/10.32 | (1361) sum(n5, all_0_1_1) = all_0_0_0
% 30.65/10.32 |
% 30.65/10.32 | From (1359) and (4914) follows:
% 30.65/10.32 | (5070) sum(n14, n5) = all_0_2_2
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (388) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 30.65/10.32 | (1363) all_0_5_5 = n6
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (619) with n14, n5, all_0_2_2, n19 and discharging atoms sum(n14, n5) = all_0_2_2, sum(n14, n5) = n19, yields:
% 30.65/10.32 | (737) all_0_2_2 = n19
% 30.65/10.32 |
% 30.65/10.32 | From (737) and (473) follows:
% 30.65/10.32 | (739) pred(n19) = all_0_1_1
% 30.65/10.32 |
% 30.65/10.32 | From (1363) and (4913) follows:
% 30.65/10.32 | (5074) sum(n14, n6) = all_0_4_4
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 30.65/10.32 | (742) all_0_1_1 = n18
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (619) with n14, n6, all_0_4_4, n20 and discharging atoms sum(n14, n6) = all_0_4_4, sum(n14, n6) = n20, yields:
% 30.65/10.32 | (738) all_0_4_4 = n20
% 30.65/10.32 |
% 30.65/10.32 | From (738) and (716) follows:
% 30.65/10.32 | (740) pred(n20) = all_0_3_3
% 30.65/10.32 |
% 30.65/10.32 | From (742) and (1361) follows:
% 30.65/10.32 | (5078) sum(n5, n18) = all_0_0_0
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 30.65/10.32 | (741) all_0_3_3 = n19
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (619) with n5, n18, all_0_0_0, n2 and discharging atoms sum(n5, n18) = all_0_0_0, sum(n5, n18) = n2, yields:
% 30.65/10.32 | (1000) all_0_0_0 = n2
% 30.65/10.32 |
% 30.65/10.32 | From (741)(1000) and (232) follows:
% 30.65/10.32 | (5081) sum(n19, n2) = all_0_6_6
% 30.65/10.32 |
% 30.65/10.32 | Instantiating formula (619) with n19, n2, all_0_6_6, n0 and discharging atoms sum(n19, n2) = all_0_6_6, sum(n19, n2) = n0, yields:
% 30.65/10.32 | (1053) all_0_6_6 = n0
% 30.65/10.32 |
% 30.65/10.32 | Equations (1053) can reduce 676 to:
% 30.65/10.32 | (748) $false
% 30.65/10.32 |
% 30.65/10.32 |-The branch is then unsatisfiable
% 30.65/10.32 |-Branch two:
% 30.65/10.32 | (1376) ~ (all_0_7_7 = n5)
% 30.65/10.32 | (1377) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 30.65/10.32 |
% 30.65/10.32 +-Applying beta-rule and splitting (1377), into two cases.
% 30.65/10.32 |-Branch one:
% 30.65/10.32 | (1378) all_0_7_7 = n4
% 30.65/10.32 |
% 30.65/10.32 | From (1378) and (683) follows:
% 30.65/10.32 | (1379) succ(n4) = all_0_5_5
% 30.65/10.32 |
% 30.65/10.32 | From (1378) and (8) follows:
% 30.65/10.32 | (1380) sum(n4, all_0_1_1) = all_0_0_0
% 30.65/10.32 |
% 30.65/10.32 | From (1378) and (4914) follows:
% 31.04/10.32 | (5089) sum(n14, n4) = all_0_2_2
% 31.04/10.32 |
% 31.04/10.32 | Instantiating formula (388) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 31.04/10.32 | (1382) all_0_5_5 = n5
% 31.04/10.32 |
% 31.04/10.32 | Instantiating formula (619) with n14, n4, all_0_2_2, n18 and discharging atoms sum(n14, n4) = all_0_2_2, sum(n14, n4) = n18, yields:
% 31.04/10.32 | (754) all_0_2_2 = n18
% 31.04/10.32 |
% 31.04/10.32 | From (754) and (473) follows:
% 31.04/10.32 | (756) pred(n18) = all_0_1_1
% 31.04/10.32 |
% 31.04/10.32 | From (1382) and (4913) follows:
% 31.04/10.32 | (5093) sum(n14, n5) = all_0_4_4
% 31.04/10.32 |
% 31.04/10.32 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 31.04/10.32 | (759) all_0_1_1 = n17
% 31.04/10.32 |
% 31.04/10.32 | Instantiating formula (619) with n14, n5, all_0_4_4, n19 and discharging atoms sum(n14, n5) = all_0_4_4, sum(n14, n5) = n19, yields:
% 31.04/10.32 | (755) all_0_4_4 = n19
% 31.04/10.32 |
% 31.04/10.32 | From (755) and (716) follows:
% 31.04/10.32 | (757) pred(n19) = all_0_3_3
% 31.04/10.32 |
% 31.04/10.32 | From (759) and (1380) follows:
% 31.04/10.33 | (5097) sum(n4, n17) = all_0_0_0
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 31.04/10.33 | (758) all_0_3_3 = n18
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n4, n17, all_0_0_0, n0 and discharging atoms sum(n4, n17) = all_0_0_0, sum(n4, n17) = n0, yields:
% 31.04/10.33 | (1034) all_0_0_0 = n0
% 31.04/10.33 |
% 31.04/10.33 | From (758)(1034) and (232) follows:
% 31.04/10.33 | (5100) sum(n18, n0) = all_0_6_6
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n18, n0, all_0_6_6, n18 and discharging atoms sum(n18, n0) = all_0_6_6, sum(n18, n0) = n18, yields:
% 31.04/10.33 | (900) all_0_6_6 = n18
% 31.04/10.33 |
% 31.04/10.33 | Equations (900) can reduce 622 to:
% 31.04/10.33 | (748) $false
% 31.04/10.33 |
% 31.04/10.33 |-The branch is then unsatisfiable
% 31.04/10.33 |-Branch two:
% 31.04/10.33 | (1395) ~ (all_0_7_7 = n4)
% 31.04/10.33 | (1396) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.04/10.33 |
% 31.04/10.33 +-Applying beta-rule and splitting (1396), into two cases.
% 31.04/10.33 |-Branch one:
% 31.04/10.33 | (1397) all_0_7_7 = n3
% 31.04/10.33 |
% 31.04/10.33 | From (1397) and (683) follows:
% 31.04/10.33 | (1398) succ(n3) = all_0_5_5
% 31.04/10.33 |
% 31.04/10.33 | From (1397) and (8) follows:
% 31.04/10.33 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 31.04/10.33 |
% 31.04/10.33 | From (1397) and (4914) follows:
% 31.04/10.33 | (5108) sum(n14, n3) = all_0_2_2
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 31.04/10.33 | (1401) all_0_5_5 = n4
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n14, n3, all_0_2_2, n17 and discharging atoms sum(n14, n3) = all_0_2_2, sum(n14, n3) = n17, yields:
% 31.04/10.33 | (771) all_0_2_2 = n17
% 31.04/10.33 |
% 31.04/10.33 | From (771) and (473) follows:
% 31.04/10.33 | (773) pred(n17) = all_0_1_1
% 31.04/10.33 |
% 31.04/10.33 | From (1401) and (4913) follows:
% 31.04/10.33 | (5112) sum(n14, n4) = all_0_4_4
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 31.04/10.33 | (776) all_0_1_1 = n16
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n14, n4, all_0_4_4, n18 and discharging atoms sum(n14, n4) = all_0_4_4, sum(n14, n4) = n18, yields:
% 31.04/10.33 | (772) all_0_4_4 = n18
% 31.04/10.33 |
% 31.04/10.33 | From (772) and (716) follows:
% 31.04/10.33 | (774) pred(n18) = all_0_3_3
% 31.04/10.33 |
% 31.04/10.33 | From (776) and (1399) follows:
% 31.04/10.33 | (5116) sum(n3, n16) = all_0_0_0
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 31.04/10.33 | (775) all_0_3_3 = n17
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n3, n16, all_0_0_0, n19 and discharging atoms sum(n3, n16) = all_0_0_0, sum(n3, n16) = n19, yields:
% 31.04/10.33 | (1068) all_0_0_0 = n19
% 31.04/10.33 |
% 31.04/10.33 | From (775)(1068) and (232) follows:
% 31.04/10.33 | (5119) sum(n17, n19) = all_0_6_6
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n17, n19, all_0_6_6, n15 and discharging atoms sum(n17, n19) = all_0_6_6, sum(n17, n19) = n15, yields:
% 31.04/10.33 | (747) all_0_6_6 = n15
% 31.04/10.33 |
% 31.04/10.33 | Equations (747) can reduce 456 to:
% 31.04/10.33 | (748) $false
% 31.04/10.33 |
% 31.04/10.33 |-The branch is then unsatisfiable
% 31.04/10.33 |-Branch two:
% 31.04/10.33 | (1414) ~ (all_0_7_7 = n3)
% 31.04/10.33 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.04/10.33 |
% 31.04/10.33 +-Applying beta-rule and splitting (1415), into two cases.
% 31.04/10.33 |-Branch one:
% 31.04/10.33 | (1416) all_0_7_7 = n2
% 31.04/10.33 |
% 31.04/10.33 | From (1416) and (683) follows:
% 31.04/10.33 | (1417) succ(n2) = all_0_5_5
% 31.04/10.33 |
% 31.04/10.33 | From (1416) and (8) follows:
% 31.04/10.33 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 31.04/10.33 |
% 31.04/10.33 | From (1416) and (4914) follows:
% 31.04/10.33 | (5127) sum(n14, n2) = all_0_2_2
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.04/10.33 | (1420) all_0_5_5 = n3
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n14, n2, all_0_2_2, n16 and discharging atoms sum(n14, n2) = all_0_2_2, sum(n14, n2) = n16, yields:
% 31.04/10.33 | (788) all_0_2_2 = n16
% 31.04/10.33 |
% 31.04/10.33 | From (788) and (473) follows:
% 31.04/10.33 | (790) pred(n16) = all_0_1_1
% 31.04/10.33 |
% 31.04/10.33 | From (1420) and (4913) follows:
% 31.04/10.33 | (5131) sum(n14, n3) = all_0_4_4
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 31.04/10.33 | (793) all_0_1_1 = n15
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n14, n3, all_0_4_4, n17 and discharging atoms sum(n14, n3) = all_0_4_4, sum(n14, n3) = n17, yields:
% 31.04/10.33 | (789) all_0_4_4 = n17
% 31.04/10.33 |
% 31.04/10.33 | From (789) and (716) follows:
% 31.04/10.33 | (791) pred(n17) = all_0_3_3
% 31.04/10.33 |
% 31.04/10.33 | From (793) and (1418) follows:
% 31.04/10.33 | (5135) sum(n2, n15) = all_0_0_0
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 31.04/10.33 | (792) all_0_3_3 = n16
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n2, n15, all_0_0_0, n17 and discharging atoms sum(n2, n15) = all_0_0_0, sum(n2, n15) = n17, yields:
% 31.04/10.33 | (745) all_0_0_0 = n17
% 31.04/10.33 |
% 31.04/10.33 | From (792)(745) and (232) follows:
% 31.04/10.33 | (5138) sum(n16, n17) = all_0_6_6
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n16, n17, all_0_6_6, n12 and discharging atoms sum(n16, n17) = all_0_6_6, sum(n16, n17) = n12, yields:
% 31.04/10.33 | (951) all_0_6_6 = n12
% 31.04/10.33 |
% 31.04/10.33 | Equations (951) can reduce 76 to:
% 31.04/10.33 | (748) $false
% 31.04/10.33 |
% 31.04/10.33 |-The branch is then unsatisfiable
% 31.04/10.33 |-Branch two:
% 31.04/10.33 | (1433) ~ (all_0_7_7 = n2)
% 31.04/10.33 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 31.04/10.33 |
% 31.04/10.33 +-Applying beta-rule and splitting (1434), into two cases.
% 31.04/10.33 |-Branch one:
% 31.04/10.33 | (1435) all_0_7_7 = n1
% 31.04/10.33 |
% 31.04/10.33 | From (1435) and (683) follows:
% 31.04/10.33 | (1436) succ(n1) = all_0_5_5
% 31.04/10.33 |
% 31.04/10.33 | From (1435) and (8) follows:
% 31.04/10.33 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 31.04/10.33 |
% 31.04/10.33 | From (1435) and (4914) follows:
% 31.04/10.33 | (5146) sum(n14, n1) = all_0_2_2
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.04/10.33 | (1439) all_0_5_5 = n2
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n14, n1, all_0_2_2, n15 and discharging atoms sum(n14, n1) = all_0_2_2, sum(n14, n1) = n15, yields:
% 31.04/10.33 | (805) all_0_2_2 = n15
% 31.04/10.33 |
% 31.04/10.33 | From (805) and (473) follows:
% 31.04/10.33 | (807) pred(n15) = all_0_1_1
% 31.04/10.33 |
% 31.04/10.33 | From (1439) and (4913) follows:
% 31.04/10.33 | (5150) sum(n14, n2) = all_0_4_4
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 31.04/10.33 | (810) all_0_1_1 = n14
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n14, n2, all_0_4_4, n16 and discharging atoms sum(n14, n2) = all_0_4_4, sum(n14, n2) = n16, yields:
% 31.04/10.33 | (806) all_0_4_4 = n16
% 31.04/10.33 |
% 31.04/10.33 | From (806) and (716) follows:
% 31.04/10.33 | (808) pred(n16) = all_0_3_3
% 31.04/10.33 |
% 31.04/10.33 | From (810) and (1437) follows:
% 31.04/10.33 | (5154) sum(n1, n14) = all_0_0_0
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 31.04/10.33 | (809) all_0_3_3 = n15
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n1, n14, all_0_0_0, n15 and discharging atoms sum(n1, n14) = all_0_0_0, sum(n1, n14) = n15, yields:
% 31.04/10.33 | (779) all_0_0_0 = n15
% 31.04/10.33 |
% 31.04/10.33 | From (809)(779) and (232) follows:
% 31.04/10.33 | (5157) sum(n15, n15) = all_0_6_6
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n15, n15, all_0_6_6, n9 and discharging atoms sum(n15, n15) = all_0_6_6, sum(n15, n15) = n9, yields:
% 31.04/10.33 | (798) all_0_6_6 = n9
% 31.04/10.33 |
% 31.04/10.33 | Equations (798) can reduce 593 to:
% 31.04/10.33 | (748) $false
% 31.04/10.33 |
% 31.04/10.33 |-The branch is then unsatisfiable
% 31.04/10.33 |-Branch two:
% 31.04/10.33 | (1452) ~ (all_0_7_7 = n1)
% 31.04/10.33 | (1453) all_0_7_7 = n0
% 31.04/10.33 |
% 31.04/10.33 | From (1453) and (683) follows:
% 31.04/10.33 | (1454) succ(n0) = all_0_5_5
% 31.04/10.33 |
% 31.04/10.33 | From (1453) and (8) follows:
% 31.04/10.33 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 31.04/10.33 |
% 31.04/10.33 | From (1453) and (4914) follows:
% 31.04/10.33 | (5164) sum(n14, n0) = all_0_2_2
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.04/10.33 | (1457) all_0_5_5 = n1
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n14, n0, all_0_2_2, n14 and discharging atoms sum(n14, n0) = all_0_2_2, sum(n14, n0) = n14, yields:
% 31.04/10.33 | (822) all_0_2_2 = n14
% 31.04/10.33 |
% 31.04/10.33 | From (822) and (473) follows:
% 31.04/10.33 | (824) pred(n14) = all_0_1_1
% 31.04/10.33 |
% 31.04/10.33 | From (1457) and (4913) follows:
% 31.04/10.33 | (5168) sum(n14, n1) = all_0_4_4
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 31.04/10.33 | (827) all_0_1_1 = n13
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n14, n1, all_0_4_4, n15 and discharging atoms sum(n14, n1) = all_0_4_4, sum(n14, n1) = n15, yields:
% 31.04/10.33 | (823) all_0_4_4 = n15
% 31.04/10.33 |
% 31.04/10.33 | From (823) and (716) follows:
% 31.04/10.33 | (825) pred(n15) = all_0_3_3
% 31.04/10.33 |
% 31.04/10.33 | From (827) and (1455) follows:
% 31.04/10.33 | (5172) sum(n0, n13) = all_0_0_0
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 31.04/10.33 | (826) all_0_3_3 = n14
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n0, n13, all_0_0_0, n13 and discharging atoms sum(n0, n13) = all_0_0_0, sum(n0, n13) = n13, yields:
% 31.04/10.33 | (813) all_0_0_0 = n13
% 31.04/10.33 |
% 31.04/10.33 | From (826)(813) and (232) follows:
% 31.04/10.33 | (5175) sum(n14, n13) = all_0_6_6
% 31.04/10.33 |
% 31.04/10.33 | Instantiating formula (619) with n14, n13, all_0_6_6, n6 and discharging atoms sum(n14, n13) = all_0_6_6, sum(n14, n13) = n6, yields:
% 31.04/10.33 | (1002) all_0_6_6 = n6
% 31.04/10.33 |
% 31.04/10.33 | Equations (1002) can reduce 498 to:
% 31.04/10.33 | (748) $false
% 31.04/10.33 |
% 31.04/10.33 |-The branch is then unsatisfiable
% 31.04/10.33 |-Branch two:
% 31.04/10.33 | (851) ~ (all_0_8_8 = n14)
% 31.04/10.33 | (852) all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.33 |
% 31.04/10.33 +-Applying beta-rule and splitting (1206), into two cases.
% 31.04/10.33 |-Branch one:
% 31.04/10.33 | (1207) all_0_7_7 = n13
% 31.04/10.33 |
% 31.04/10.33 | From (1207) and (683) follows:
% 31.04/10.33 | (1208) succ(n13) = all_0_5_5
% 31.04/10.33 |
% 31.04/10.33 | From (1207) and (8) follows:
% 31.04/10.33 | (1209) sum(n13, all_0_1_1) = all_0_0_0
% 31.04/10.33 |
% 31.04/10.33 | From (1207) and (378) follows:
% 31.04/10.34 | (5183) sum(all_0_8_8, n13) = all_0_2_2
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (388) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 31.04/10.34 | (1211) all_0_5_5 = n14
% 31.04/10.34 |
% 31.04/10.34 | From (1211) and (708) follows:
% 31.04/10.34 | (5185) sum(all_0_8_8, n14) = all_0_4_4
% 31.04/10.34 |
% 31.04/10.34 +-Applying beta-rule and splitting (852), into two cases.
% 31.04/10.34 |-Branch one:
% 31.04/10.34 | (853) all_0_8_8 = n13
% 31.04/10.34 |
% 31.04/10.34 | From (853) and (5185) follows:
% 31.04/10.34 | (5187) sum(n13, n14) = all_0_4_4
% 31.04/10.34 |
% 31.04/10.34 | From (853) and (5183) follows:
% 31.04/10.34 | (5188) sum(n13, n13) = all_0_2_2
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n13, n14, all_0_4_4, n6 and discharging atoms sum(n13, n14) = all_0_4_4, sum(n13, n14) = n6, yields:
% 31.04/10.34 | (976) all_0_4_4 = n6
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n13, n13, all_0_2_2, n5 and discharging atoms sum(n13, n13) = all_0_2_2, sum(n13, n13) = n5, yields:
% 31.04/10.34 | (975) all_0_2_2 = n5
% 31.04/10.34 |
% 31.04/10.34 | From (975) and (473) follows:
% 31.04/10.34 | (977) pred(n5) = all_0_1_1
% 31.04/10.34 |
% 31.04/10.34 | From (976) and (716) follows:
% 31.04/10.34 | (978) pred(n6) = all_0_3_3
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 31.04/10.34 | (979) all_0_3_3 = n5
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 31.04/10.34 | (980) all_0_1_1 = n4
% 31.04/10.34 |
% 31.04/10.34 | From (979) and (232) follows:
% 31.04/10.34 | (981) sum(n5, all_0_0_0) = all_0_6_6
% 31.04/10.34 |
% 31.04/10.34 | From (980) and (1209) follows:
% 31.04/10.34 | (5196) sum(n13, n4) = all_0_0_0
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n13, n4, all_0_0_0, n17 and discharging atoms sum(n13, n4) = all_0_0_0, sum(n13, n4) = n17, yields:
% 31.04/10.34 | (745) all_0_0_0 = n17
% 31.04/10.34 |
% 31.04/10.34 | From (745) and (981) follows:
% 31.04/10.34 | (5198) sum(n5, n17) = all_0_6_6
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n5, n17, all_0_6_6, n1 and discharging atoms sum(n5, n17) = all_0_6_6, sum(n5, n17) = n1, yields:
% 31.04/10.34 | (866) all_0_6_6 = n1
% 31.04/10.34 |
% 31.04/10.34 | Equations (866) can reduce 28 to:
% 31.04/10.34 | (748) $false
% 31.04/10.34 |
% 31.04/10.34 |-The branch is then unsatisfiable
% 31.04/10.34 |-Branch two:
% 31.04/10.34 | (868) ~ (all_0_8_8 = n13)
% 31.04/10.34 | (869) all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.34 |
% 31.04/10.34 +-Applying beta-rule and splitting (869), into two cases.
% 31.04/10.34 |-Branch one:
% 31.04/10.34 | (870) all_0_8_8 = n12
% 31.04/10.34 |
% 31.04/10.34 | From (870) and (5185) follows:
% 31.04/10.34 | (5204) sum(n12, n14) = all_0_4_4
% 31.04/10.34 |
% 31.04/10.34 | From (870) and (5183) follows:
% 31.04/10.34 | (5205) sum(n12, n13) = all_0_2_2
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n12, n14, all_0_4_4, n5 and discharging atoms sum(n12, n14) = all_0_4_4, sum(n12, n14) = n5, yields:
% 31.04/10.34 | (993) all_0_4_4 = n5
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n12, n13, all_0_2_2, n4 and discharging atoms sum(n12, n13) = all_0_2_2, sum(n12, n13) = n4, yields:
% 31.04/10.34 | (992) all_0_2_2 = n4
% 31.04/10.34 |
% 31.04/10.34 | From (992) and (473) follows:
% 31.04/10.34 | (994) pred(n4) = all_0_1_1
% 31.04/10.34 |
% 31.04/10.34 | From (993) and (716) follows:
% 31.04/10.34 | (995) pred(n5) = all_0_3_3
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 31.04/10.34 | (996) all_0_3_3 = n4
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 31.04/10.34 | (997) all_0_1_1 = n3
% 31.04/10.34 |
% 31.04/10.34 | From (996) and (232) follows:
% 31.04/10.34 | (998) sum(n4, all_0_0_0) = all_0_6_6
% 31.04/10.34 |
% 31.04/10.34 | From (997) and (1209) follows:
% 31.04/10.34 | (5213) sum(n13, n3) = all_0_0_0
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n13, n3, all_0_0_0, n16 and discharging atoms sum(n13, n3) = all_0_0_0, sum(n13, n3) = n16, yields:
% 31.04/10.34 | (762) all_0_0_0 = n16
% 31.04/10.34 |
% 31.04/10.34 | From (762) and (998) follows:
% 31.04/10.34 | (5215) sum(n4, n16) = all_0_6_6
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n4, n16, all_0_6_6, n20 and discharging atoms sum(n4, n16) = all_0_6_6, sum(n4, n16) = n20, yields:
% 31.04/10.34 | (883) all_0_6_6 = n20
% 31.04/10.34 |
% 31.04/10.34 | Equations (883) can reduce 381 to:
% 31.04/10.34 | (748) $false
% 31.04/10.34 |
% 31.04/10.34 |-The branch is then unsatisfiable
% 31.04/10.34 |-Branch two:
% 31.04/10.34 | (885) ~ (all_0_8_8 = n12)
% 31.04/10.34 | (886) all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.34 |
% 31.04/10.34 +-Applying beta-rule and splitting (886), into two cases.
% 31.04/10.34 |-Branch one:
% 31.04/10.34 | (887) all_0_8_8 = n11
% 31.04/10.34 |
% 31.04/10.34 | From (887) and (5185) follows:
% 31.04/10.34 | (5221) sum(n11, n14) = all_0_4_4
% 31.04/10.34 |
% 31.04/10.34 | From (887) and (5183) follows:
% 31.04/10.34 | (5222) sum(n11, n13) = all_0_2_2
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n11, n14, all_0_4_4, n4 and discharging atoms sum(n11, n14) = all_0_4_4, sum(n11, n14) = n4, yields:
% 31.04/10.34 | (1010) all_0_4_4 = n4
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n11, n13, all_0_2_2, n3 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n3, yields:
% 31.04/10.34 | (1009) all_0_2_2 = n3
% 31.04/10.34 |
% 31.04/10.34 | From (1009) and (473) follows:
% 31.04/10.34 | (1011) pred(n3) = all_0_1_1
% 31.04/10.34 |
% 31.04/10.34 | From (1010) and (716) follows:
% 31.04/10.34 | (1012) pred(n4) = all_0_3_3
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 31.04/10.34 | (1013) all_0_3_3 = n3
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 31.04/10.34 | (1014) all_0_1_1 = n2
% 31.04/10.34 |
% 31.04/10.34 | From (1013) and (232) follows:
% 31.04/10.34 | (1015) sum(n3, all_0_0_0) = all_0_6_6
% 31.04/10.34 |
% 31.04/10.34 | From (1014) and (1209) follows:
% 31.04/10.34 | (5230) sum(n13, n2) = all_0_0_0
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n13, n2, all_0_0_0, n15 and discharging atoms sum(n13, n2) = all_0_0_0, sum(n13, n2) = n15, yields:
% 31.04/10.34 | (779) all_0_0_0 = n15
% 31.04/10.34 |
% 31.04/10.34 | From (779) and (1015) follows:
% 31.04/10.34 | (5232) sum(n3, n15) = all_0_6_6
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n3, n15, all_0_6_6, n18 and discharging atoms sum(n3, n15) = all_0_6_6, sum(n3, n15) = n18, yields:
% 31.04/10.34 | (900) all_0_6_6 = n18
% 31.04/10.34 |
% 31.04/10.34 | Equations (900) can reduce 622 to:
% 31.04/10.34 | (748) $false
% 31.04/10.34 |
% 31.04/10.34 |-The branch is then unsatisfiable
% 31.04/10.34 |-Branch two:
% 31.04/10.34 | (902) ~ (all_0_8_8 = n11)
% 31.04/10.34 | (903) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.34 |
% 31.04/10.34 +-Applying beta-rule and splitting (903), into two cases.
% 31.04/10.34 |-Branch one:
% 31.04/10.34 | (904) all_0_8_8 = n10
% 31.04/10.34 |
% 31.04/10.34 | From (904) and (5185) follows:
% 31.04/10.34 | (5238) sum(n10, n14) = all_0_4_4
% 31.04/10.34 |
% 31.04/10.34 | From (904) and (5183) follows:
% 31.04/10.34 | (5239) sum(n10, n13) = all_0_2_2
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n10, n14, all_0_4_4, n3 and discharging atoms sum(n10, n14) = all_0_4_4, sum(n10, n14) = n3, yields:
% 31.04/10.34 | (1027) all_0_4_4 = n3
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n10, n13, all_0_2_2, n2 and discharging atoms sum(n10, n13) = all_0_2_2, sum(n10, n13) = n2, yields:
% 31.04/10.34 | (1026) all_0_2_2 = n2
% 31.04/10.34 |
% 31.04/10.34 | From (1026) and (473) follows:
% 31.04/10.34 | (1028) pred(n2) = all_0_1_1
% 31.04/10.34 |
% 31.04/10.34 | From (1027) and (716) follows:
% 31.04/10.34 | (1029) pred(n3) = all_0_3_3
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 31.04/10.34 | (1030) all_0_3_3 = n2
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 31.04/10.34 | (1031) all_0_1_1 = n1
% 31.04/10.34 |
% 31.04/10.34 | From (1030) and (232) follows:
% 31.04/10.34 | (1032) sum(n2, all_0_0_0) = all_0_6_6
% 31.04/10.34 |
% 31.04/10.34 | From (1031) and (1209) follows:
% 31.04/10.34 | (5247) sum(n13, n1) = all_0_0_0
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n13, n1, all_0_0_0, n14 and discharging atoms sum(n13, n1) = all_0_0_0, sum(n13, n1) = n14, yields:
% 31.04/10.34 | (796) all_0_0_0 = n14
% 31.04/10.34 |
% 31.04/10.34 | From (796) and (1032) follows:
% 31.04/10.34 | (5249) sum(n2, n14) = all_0_6_6
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n2, n14, all_0_6_6, n16 and discharging atoms sum(n2, n14) = all_0_6_6, sum(n2, n14) = n16, yields:
% 31.04/10.34 | (917) all_0_6_6 = n16
% 31.04/10.34 |
% 31.04/10.34 | Equations (917) can reduce 163 to:
% 31.04/10.34 | (748) $false
% 31.04/10.34 |
% 31.04/10.34 |-The branch is then unsatisfiable
% 31.04/10.34 |-Branch two:
% 31.04/10.34 | (919) ~ (all_0_8_8 = n10)
% 31.04/10.34 | (920) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.34 |
% 31.04/10.34 +-Applying beta-rule and splitting (920), into two cases.
% 31.04/10.34 |-Branch one:
% 31.04/10.34 | (921) all_0_8_8 = n9
% 31.04/10.34 |
% 31.04/10.34 | From (921) and (5185) follows:
% 31.04/10.34 | (5255) sum(n9, n14) = all_0_4_4
% 31.04/10.34 |
% 31.04/10.34 | From (921) and (5183) follows:
% 31.04/10.34 | (5256) sum(n9, n13) = all_0_2_2
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n9, n14, all_0_4_4, n2 and discharging atoms sum(n9, n14) = all_0_4_4, sum(n9, n14) = n2, yields:
% 31.04/10.34 | (1044) all_0_4_4 = n2
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (619) with n9, n13, all_0_2_2, n1 and discharging atoms sum(n9, n13) = all_0_2_2, sum(n9, n13) = n1, yields:
% 31.04/10.34 | (1043) all_0_2_2 = n1
% 31.04/10.34 |
% 31.04/10.34 | From (1043) and (473) follows:
% 31.04/10.34 | (1045) pred(n1) = all_0_1_1
% 31.04/10.34 |
% 31.04/10.34 | From (1044) and (716) follows:
% 31.04/10.34 | (1046) pred(n2) = all_0_3_3
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 31.04/10.34 | (1047) all_0_3_3 = n1
% 31.04/10.34 |
% 31.04/10.34 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 31.04/10.34 | (1048) all_0_1_1 = n0
% 31.04/10.34 |
% 31.04/10.34 | From (1047) and (232) follows:
% 31.04/10.34 | (1049) sum(n1, all_0_0_0) = all_0_6_6
% 31.04/10.34 |
% 31.04/10.34 | From (1048) and (1209) follows:
% 31.04/10.34 | (5264) sum(n13, n0) = all_0_0_0
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n13, n0, all_0_0_0, n13 and discharging atoms sum(n13, n0) = all_0_0_0, sum(n13, n0) = n13, yields:
% 31.04/10.35 | (813) all_0_0_0 = n13
% 31.04/10.35 |
% 31.04/10.35 | From (813) and (1049) follows:
% 31.04/10.35 | (5266) sum(n1, n13) = all_0_6_6
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n1, n13, all_0_6_6, n14 and discharging atoms sum(n1, n13) = all_0_6_6, sum(n1, n13) = n14, yields:
% 31.04/10.35 | (934) all_0_6_6 = n14
% 31.04/10.35 |
% 31.04/10.35 | Equations (934) can reduce 353 to:
% 31.04/10.35 | (748) $false
% 31.04/10.35 |
% 31.04/10.35 |-The branch is then unsatisfiable
% 31.04/10.35 |-Branch two:
% 31.04/10.35 | (936) ~ (all_0_8_8 = n9)
% 31.04/10.35 | (937) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.35 |
% 31.04/10.35 +-Applying beta-rule and splitting (937), into two cases.
% 31.04/10.35 |-Branch one:
% 31.04/10.35 | (938) all_0_8_8 = n8
% 31.04/10.35 |
% 31.04/10.35 | From (938) and (5185) follows:
% 31.04/10.35 | (5272) sum(n8, n14) = all_0_4_4
% 31.04/10.35 |
% 31.04/10.35 | From (938) and (5183) follows:
% 31.04/10.35 | (5273) sum(n8, n13) = all_0_2_2
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n8, n14, all_0_4_4, n1 and discharging atoms sum(n8, n14) = all_0_4_4, sum(n8, n14) = n1, yields:
% 31.04/10.35 | (1061) all_0_4_4 = n1
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n8, n13, all_0_2_2, n0 and discharging atoms sum(n8, n13) = all_0_2_2, sum(n8, n13) = n0, yields:
% 31.04/10.35 | (1060) all_0_2_2 = n0
% 31.04/10.35 |
% 31.04/10.35 | From (1060) and (473) follows:
% 31.04/10.35 | (1062) pred(n0) = all_0_1_1
% 31.04/10.35 |
% 31.04/10.35 | From (1061) and (716) follows:
% 31.04/10.35 | (1063) pred(n1) = all_0_3_3
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 31.04/10.35 | (1064) all_0_3_3 = n0
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 31.04/10.35 | (1065) all_0_1_1 = n20
% 31.04/10.35 |
% 31.04/10.35 | From (1064) and (232) follows:
% 31.04/10.35 | (1066) sum(n0, all_0_0_0) = all_0_6_6
% 31.04/10.35 |
% 31.04/10.35 | From (1065) and (1209) follows:
% 31.04/10.35 | (5281) sum(n13, n20) = all_0_0_0
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n13, n20, all_0_0_0, n12 and discharging atoms sum(n13, n20) = all_0_0_0, sum(n13, n20) = n12, yields:
% 31.04/10.35 | (830) all_0_0_0 = n12
% 31.04/10.35 |
% 31.04/10.35 | From (830) and (1066) follows:
% 31.04/10.35 | (5283) sum(n0, n12) = all_0_6_6
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n0, n12, all_0_6_6, n12 and discharging atoms sum(n0, n12) = all_0_6_6, sum(n0, n12) = n12, yields:
% 31.04/10.35 | (951) all_0_6_6 = n12
% 31.04/10.35 |
% 31.04/10.35 | Equations (951) can reduce 76 to:
% 31.04/10.35 | (748) $false
% 31.04/10.35 |
% 31.04/10.35 |-The branch is then unsatisfiable
% 31.04/10.35 |-Branch two:
% 31.04/10.35 | (953) ~ (all_0_8_8 = n8)
% 31.04/10.35 | (954) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.35 |
% 31.04/10.35 +-Applying beta-rule and splitting (954), into two cases.
% 31.04/10.35 |-Branch one:
% 31.04/10.35 | (955) all_0_8_8 = n7
% 31.04/10.35 |
% 31.04/10.35 | From (955) and (5185) follows:
% 31.04/10.35 | (5289) sum(n7, n14) = all_0_4_4
% 31.04/10.35 |
% 31.04/10.35 | From (955) and (5183) follows:
% 31.04/10.35 | (5290) sum(n7, n13) = all_0_2_2
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n7, n14, all_0_4_4, n0 and discharging atoms sum(n7, n14) = all_0_4_4, sum(n7, n14) = n0, yields:
% 31.04/10.35 | (1077) all_0_4_4 = n0
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n7, n13, all_0_2_2, n20 and discharging atoms sum(n7, n13) = all_0_2_2, sum(n7, n13) = n20, yields:
% 31.04/10.35 | (1076) all_0_2_2 = n20
% 31.04/10.35 |
% 31.04/10.35 | From (1076) and (473) follows:
% 31.04/10.35 | (1078) pred(n20) = all_0_1_1
% 31.04/10.35 |
% 31.04/10.35 | From (1077) and (716) follows:
% 31.04/10.35 | (1079) pred(n0) = all_0_3_3
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 31.04/10.35 | (1080) all_0_1_1 = n19
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 31.04/10.35 | (1081) all_0_3_3 = n20
% 31.04/10.35 |
% 31.04/10.35 | From (1081) and (232) follows:
% 31.04/10.35 | (1082) sum(n20, all_0_0_0) = all_0_6_6
% 31.04/10.35 |
% 31.04/10.35 | From (1080) and (1209) follows:
% 31.04/10.35 | (5298) sum(n13, n19) = all_0_0_0
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n13, n19, all_0_0_0, n11 and discharging atoms sum(n13, n19) = all_0_0_0, sum(n13, n19) = n11, yields:
% 31.04/10.35 | (847) all_0_0_0 = n11
% 31.04/10.35 |
% 31.04/10.35 | From (847) and (1082) follows:
% 31.04/10.35 | (5300) sum(n20, n11) = all_0_6_6
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n20, n11, all_0_6_6, n10 and discharging atoms sum(n20, n11) = all_0_6_6, sum(n20, n11) = n10, yields:
% 31.04/10.35 | (968) all_0_6_6 = n10
% 31.04/10.35 |
% 31.04/10.35 | Equations (968) can reduce 176 to:
% 31.04/10.35 | (748) $false
% 31.04/10.35 |
% 31.04/10.35 |-The branch is then unsatisfiable
% 31.04/10.35 |-Branch two:
% 31.04/10.35 | (970) ~ (all_0_8_8 = n7)
% 31.04/10.35 | (971) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.35 |
% 31.04/10.35 +-Applying beta-rule and splitting (971), into two cases.
% 31.04/10.35 |-Branch one:
% 31.04/10.35 | (972) all_0_8_8 = n6
% 31.04/10.35 |
% 31.04/10.35 | From (972) and (5185) follows:
% 31.04/10.35 | (5306) sum(n6, n14) = all_0_4_4
% 31.04/10.35 |
% 31.04/10.35 | From (972) and (5183) follows:
% 31.04/10.35 | (5307) sum(n6, n13) = all_0_2_2
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n6, n14, all_0_4_4, n20 and discharging atoms sum(n6, n14) = all_0_4_4, sum(n6, n14) = n20, yields:
% 31.04/10.35 | (738) all_0_4_4 = n20
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n6, n13, all_0_2_2, n19 and discharging atoms sum(n6, n13) = all_0_2_2, sum(n6, n13) = n19, yields:
% 31.04/10.35 | (737) all_0_2_2 = n19
% 31.04/10.35 |
% 31.04/10.35 | From (737) and (473) follows:
% 31.04/10.35 | (739) pred(n19) = all_0_1_1
% 31.04/10.35 |
% 31.04/10.35 | From (738) and (716) follows:
% 31.04/10.35 | (740) pred(n20) = all_0_3_3
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 31.04/10.35 | (741) all_0_3_3 = n19
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 31.04/10.35 | (742) all_0_1_1 = n18
% 31.04/10.35 |
% 31.04/10.35 | From (741) and (232) follows:
% 31.04/10.35 | (743) sum(n19, all_0_0_0) = all_0_6_6
% 31.04/10.35 |
% 31.04/10.35 | From (742) and (1209) follows:
% 31.04/10.35 | (5315) sum(n13, n18) = all_0_0_0
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n13, n18, all_0_0_0, n10 and discharging atoms sum(n13, n18) = all_0_0_0, sum(n13, n18) = n10, yields:
% 31.04/10.35 | (864) all_0_0_0 = n10
% 31.04/10.35 |
% 31.04/10.35 | From (864) and (743) follows:
% 31.04/10.35 | (5317) sum(n19, n10) = all_0_6_6
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n19, n10, all_0_6_6, n8 and discharging atoms sum(n19, n10) = all_0_6_6, sum(n19, n10) = n8, yields:
% 31.04/10.35 | (985) all_0_6_6 = n8
% 31.04/10.35 |
% 31.04/10.35 | Equations (985) can reduce 357 to:
% 31.04/10.35 | (748) $false
% 31.04/10.35 |
% 31.04/10.35 |-The branch is then unsatisfiable
% 31.04/10.35 |-Branch two:
% 31.04/10.35 | (987) ~ (all_0_8_8 = n6)
% 31.04/10.35 | (988) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.35 |
% 31.04/10.35 +-Applying beta-rule and splitting (988), into two cases.
% 31.04/10.35 |-Branch one:
% 31.04/10.35 | (989) all_0_8_8 = n5
% 31.04/10.35 |
% 31.04/10.35 | From (989) and (5185) follows:
% 31.04/10.35 | (5323) sum(n5, n14) = all_0_4_4
% 31.04/10.35 |
% 31.04/10.35 | From (989) and (5183) follows:
% 31.04/10.35 | (5324) sum(n5, n13) = all_0_2_2
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n5, n14, all_0_4_4, n19 and discharging atoms sum(n5, n14) = all_0_4_4, sum(n5, n14) = n19, yields:
% 31.04/10.35 | (755) all_0_4_4 = n19
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n5, n13, all_0_2_2, n18 and discharging atoms sum(n5, n13) = all_0_2_2, sum(n5, n13) = n18, yields:
% 31.04/10.35 | (754) all_0_2_2 = n18
% 31.04/10.35 |
% 31.04/10.35 | From (754) and (473) follows:
% 31.04/10.35 | (756) pred(n18) = all_0_1_1
% 31.04/10.35 |
% 31.04/10.35 | From (755) and (716) follows:
% 31.04/10.35 | (757) pred(n19) = all_0_3_3
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 31.04/10.35 | (758) all_0_3_3 = n18
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 31.04/10.35 | (759) all_0_1_1 = n17
% 31.04/10.35 |
% 31.04/10.35 | From (758) and (232) follows:
% 31.04/10.35 | (760) sum(n18, all_0_0_0) = all_0_6_6
% 31.04/10.35 |
% 31.04/10.35 | From (759) and (1209) follows:
% 31.04/10.35 | (5332) sum(n13, n17) = all_0_0_0
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n13, n17, all_0_0_0, n9 and discharging atoms sum(n13, n17) = all_0_0_0, sum(n13, n17) = n9, yields:
% 31.04/10.35 | (881) all_0_0_0 = n9
% 31.04/10.35 |
% 31.04/10.35 | From (881) and (760) follows:
% 31.04/10.35 | (5334) sum(n18, n9) = all_0_6_6
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n18, n9, all_0_6_6, n6 and discharging atoms sum(n18, n9) = all_0_6_6, sum(n18, n9) = n6, yields:
% 31.04/10.35 | (1002) all_0_6_6 = n6
% 31.04/10.35 |
% 31.04/10.35 | Equations (1002) can reduce 498 to:
% 31.04/10.35 | (748) $false
% 31.04/10.35 |
% 31.04/10.35 |-The branch is then unsatisfiable
% 31.04/10.35 |-Branch two:
% 31.04/10.35 | (1004) ~ (all_0_8_8 = n5)
% 31.04/10.35 | (1005) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.35 |
% 31.04/10.35 +-Applying beta-rule and splitting (1005), into two cases.
% 31.04/10.35 |-Branch one:
% 31.04/10.35 | (1006) all_0_8_8 = n4
% 31.04/10.35 |
% 31.04/10.35 | From (1006) and (5185) follows:
% 31.04/10.35 | (5340) sum(n4, n14) = all_0_4_4
% 31.04/10.35 |
% 31.04/10.35 | From (1006) and (5183) follows:
% 31.04/10.35 | (5341) sum(n4, n13) = all_0_2_2
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n4, n14, all_0_4_4, n18 and discharging atoms sum(n4, n14) = all_0_4_4, sum(n4, n14) = n18, yields:
% 31.04/10.35 | (772) all_0_4_4 = n18
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n4, n13, all_0_2_2, n17 and discharging atoms sum(n4, n13) = all_0_2_2, sum(n4, n13) = n17, yields:
% 31.04/10.35 | (771) all_0_2_2 = n17
% 31.04/10.35 |
% 31.04/10.35 | From (771) and (473) follows:
% 31.04/10.35 | (773) pred(n17) = all_0_1_1
% 31.04/10.35 |
% 31.04/10.35 | From (772) and (716) follows:
% 31.04/10.35 | (774) pred(n18) = all_0_3_3
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 31.04/10.35 | (775) all_0_3_3 = n17
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 31.04/10.35 | (776) all_0_1_1 = n16
% 31.04/10.35 |
% 31.04/10.35 | From (775) and (232) follows:
% 31.04/10.35 | (777) sum(n17, all_0_0_0) = all_0_6_6
% 31.04/10.35 |
% 31.04/10.35 | From (776) and (1209) follows:
% 31.04/10.35 | (5349) sum(n13, n16) = all_0_0_0
% 31.04/10.35 |
% 31.04/10.35 | Instantiating formula (619) with n13, n16, all_0_0_0, n8 and discharging atoms sum(n13, n16) = all_0_0_0, sum(n13, n16) = n8, yields:
% 31.04/10.35 | (898) all_0_0_0 = n8
% 31.04/10.35 |
% 31.04/10.35 | From (898) and (777) follows:
% 31.04/10.36 | (5351) sum(n17, n8) = all_0_6_6
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n17, n8, all_0_6_6, n4 and discharging atoms sum(n17, n8) = all_0_6_6, sum(n17, n8) = n4, yields:
% 31.04/10.36 | (1019) all_0_6_6 = n4
% 31.04/10.36 |
% 31.04/10.36 | Equations (1019) can reduce 48 to:
% 31.04/10.36 | (748) $false
% 31.04/10.36 |
% 31.04/10.36 |-The branch is then unsatisfiable
% 31.04/10.36 |-Branch two:
% 31.04/10.36 | (1021) ~ (all_0_8_8 = n4)
% 31.04/10.36 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.36 |
% 31.04/10.36 +-Applying beta-rule and splitting (1022), into two cases.
% 31.04/10.36 |-Branch one:
% 31.04/10.36 | (1023) all_0_8_8 = n3
% 31.04/10.36 |
% 31.04/10.36 | From (1023) and (5185) follows:
% 31.04/10.36 | (5357) sum(n3, n14) = all_0_4_4
% 31.04/10.36 |
% 31.04/10.36 | From (1023) and (5183) follows:
% 31.04/10.36 | (5358) sum(n3, n13) = all_0_2_2
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n3, n14, all_0_4_4, n17 and discharging atoms sum(n3, n14) = all_0_4_4, sum(n3, n14) = n17, yields:
% 31.04/10.36 | (789) all_0_4_4 = n17
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n3, n13, all_0_2_2, n16 and discharging atoms sum(n3, n13) = all_0_2_2, sum(n3, n13) = n16, yields:
% 31.04/10.36 | (788) all_0_2_2 = n16
% 31.04/10.36 |
% 31.04/10.36 | From (788) and (473) follows:
% 31.04/10.36 | (790) pred(n16) = all_0_1_1
% 31.04/10.36 |
% 31.04/10.36 | From (789) and (716) follows:
% 31.04/10.36 | (791) pred(n17) = all_0_3_3
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 31.04/10.36 | (792) all_0_3_3 = n16
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 31.04/10.36 | (793) all_0_1_1 = n15
% 31.04/10.36 |
% 31.04/10.36 | From (792) and (232) follows:
% 31.04/10.36 | (794) sum(n16, all_0_0_0) = all_0_6_6
% 31.04/10.36 |
% 31.04/10.36 | From (793) and (1209) follows:
% 31.04/10.36 | (5366) sum(n13, n15) = all_0_0_0
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n13, n15, all_0_0_0, n7 and discharging atoms sum(n13, n15) = all_0_0_0, sum(n13, n15) = n7, yields:
% 31.04/10.36 | (915) all_0_0_0 = n7
% 31.04/10.36 |
% 31.04/10.36 | From (915) and (794) follows:
% 31.04/10.36 | (5368) sum(n16, n7) = all_0_6_6
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n16, n7, all_0_6_6, n2 and discharging atoms sum(n16, n7) = all_0_6_6, sum(n16, n7) = n2, yields:
% 31.04/10.36 | (1036) all_0_6_6 = n2
% 31.04/10.36 |
% 31.04/10.36 | Equations (1036) can reduce 56 to:
% 31.04/10.36 | (748) $false
% 31.04/10.36 |
% 31.04/10.36 |-The branch is then unsatisfiable
% 31.04/10.36 |-Branch two:
% 31.04/10.36 | (1038) ~ (all_0_8_8 = n3)
% 31.04/10.36 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.36 |
% 31.04/10.36 +-Applying beta-rule and splitting (1039), into two cases.
% 31.04/10.36 |-Branch one:
% 31.04/10.36 | (1040) all_0_8_8 = n2
% 31.04/10.36 |
% 31.04/10.36 | From (1040) and (5185) follows:
% 31.04/10.36 | (5374) sum(n2, n14) = all_0_4_4
% 31.04/10.36 |
% 31.04/10.36 | From (1040) and (5183) follows:
% 31.04/10.36 | (5375) sum(n2, n13) = all_0_2_2
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n2, n14, all_0_4_4, n16 and discharging atoms sum(n2, n14) = all_0_4_4, sum(n2, n14) = n16, yields:
% 31.04/10.36 | (806) all_0_4_4 = n16
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n2, n13, all_0_2_2, n15 and discharging atoms sum(n2, n13) = all_0_2_2, sum(n2, n13) = n15, yields:
% 31.04/10.36 | (805) all_0_2_2 = n15
% 31.04/10.36 |
% 31.04/10.36 | From (805) and (473) follows:
% 31.04/10.36 | (807) pred(n15) = all_0_1_1
% 31.04/10.36 |
% 31.04/10.36 | From (806) and (716) follows:
% 31.04/10.36 | (808) pred(n16) = all_0_3_3
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 31.04/10.36 | (809) all_0_3_3 = n15
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 31.04/10.36 | (810) all_0_1_1 = n14
% 31.04/10.36 |
% 31.04/10.36 | From (809) and (232) follows:
% 31.04/10.36 | (811) sum(n15, all_0_0_0) = all_0_6_6
% 31.04/10.36 |
% 31.04/10.36 | From (810) and (1209) follows:
% 31.04/10.36 | (5383) sum(n13, n14) = all_0_0_0
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n13, n14, all_0_0_0, n6 and discharging atoms sum(n13, n14) = all_0_0_0, sum(n13, n14) = n6, yields:
% 31.04/10.36 | (932) all_0_0_0 = n6
% 31.04/10.36 |
% 31.04/10.36 | From (932) and (811) follows:
% 31.04/10.36 | (5385) sum(n15, n6) = all_0_6_6
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n15, n6, all_0_6_6, n0 and discharging atoms sum(n15, n6) = all_0_6_6, sum(n15, n6) = n0, yields:
% 31.04/10.36 | (1053) all_0_6_6 = n0
% 31.04/10.36 |
% 31.04/10.36 | Equations (1053) can reduce 676 to:
% 31.04/10.36 | (748) $false
% 31.04/10.36 |
% 31.04/10.36 |-The branch is then unsatisfiable
% 31.04/10.36 |-Branch two:
% 31.04/10.36 | (1055) ~ (all_0_8_8 = n2)
% 31.04/10.36 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.36 |
% 31.04/10.36 +-Applying beta-rule and splitting (1056), into two cases.
% 31.04/10.36 |-Branch one:
% 31.04/10.36 | (1057) all_0_8_8 = n1
% 31.04/10.36 |
% 31.04/10.36 | From (1057) and (5185) follows:
% 31.04/10.36 | (5391) sum(n1, n14) = all_0_4_4
% 31.04/10.36 |
% 31.04/10.36 | From (1057) and (5183) follows:
% 31.04/10.36 | (5392) sum(n1, n13) = all_0_2_2
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n1, n14, all_0_4_4, n15 and discharging atoms sum(n1, n14) = all_0_4_4, sum(n1, n14) = n15, yields:
% 31.04/10.36 | (823) all_0_4_4 = n15
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n1, n13, all_0_2_2, n14 and discharging atoms sum(n1, n13) = all_0_2_2, sum(n1, n13) = n14, yields:
% 31.04/10.36 | (822) all_0_2_2 = n14
% 31.04/10.36 |
% 31.04/10.36 | From (822) and (473) follows:
% 31.04/10.36 | (824) pred(n14) = all_0_1_1
% 31.04/10.36 |
% 31.04/10.36 | From (823) and (716) follows:
% 31.04/10.36 | (825) pred(n15) = all_0_3_3
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 31.04/10.36 | (826) all_0_3_3 = n14
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 31.04/10.36 | (827) all_0_1_1 = n13
% 31.04/10.36 |
% 31.04/10.36 | From (826) and (232) follows:
% 31.04/10.36 | (828) sum(n14, all_0_0_0) = all_0_6_6
% 31.04/10.36 |
% 31.04/10.36 | From (827) and (1209) follows:
% 31.04/10.36 | (5400) sum(n13, n13) = all_0_0_0
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n13, n13, all_0_0_0, n5 and discharging atoms sum(n13, n13) = all_0_0_0, sum(n13, n13) = n5, yields:
% 31.04/10.36 | (949) all_0_0_0 = n5
% 31.04/10.36 |
% 31.04/10.36 | From (949) and (828) follows:
% 31.04/10.36 | (5402) sum(n14, n5) = all_0_6_6
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n14, n5, all_0_6_6, n19 and discharging atoms sum(n14, n5) = all_0_6_6, sum(n14, n5) = n19, yields:
% 31.04/10.36 | (1070) all_0_6_6 = n19
% 31.04/10.36 |
% 31.04/10.36 | Equations (1070) can reduce 31 to:
% 31.04/10.36 | (748) $false
% 31.04/10.36 |
% 31.04/10.36 |-The branch is then unsatisfiable
% 31.04/10.36 |-Branch two:
% 31.04/10.36 | (1072) ~ (all_0_8_8 = n1)
% 31.04/10.36 | (1073) all_0_8_8 = n0
% 31.04/10.36 |
% 31.04/10.36 | From (1073) and (5185) follows:
% 31.04/10.36 | (5407) sum(n0, n14) = all_0_4_4
% 31.04/10.36 |
% 31.04/10.36 | From (1073) and (5183) follows:
% 31.04/10.36 | (5408) sum(n0, n13) = all_0_2_2
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n0, n14, all_0_4_4, n14 and discharging atoms sum(n0, n14) = all_0_4_4, sum(n0, n14) = n14, yields:
% 31.04/10.36 | (840) all_0_4_4 = n14
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n0, n13, all_0_2_2, n13 and discharging atoms sum(n0, n13) = all_0_2_2, sum(n0, n13) = n13, yields:
% 31.04/10.36 | (839) all_0_2_2 = n13
% 31.04/10.36 |
% 31.04/10.36 | From (839) and (473) follows:
% 31.04/10.36 | (841) pred(n13) = all_0_1_1
% 31.04/10.36 |
% 31.04/10.36 | From (840) and (716) follows:
% 31.04/10.36 | (842) pred(n14) = all_0_3_3
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 31.04/10.36 | (843) all_0_3_3 = n13
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 31.04/10.36 | (844) all_0_1_1 = n12
% 31.04/10.36 |
% 31.04/10.36 | From (843) and (232) follows:
% 31.04/10.36 | (845) sum(n13, all_0_0_0) = all_0_6_6
% 31.04/10.36 |
% 31.04/10.36 | From (844) and (1209) follows:
% 31.04/10.36 | (5416) sum(n13, n12) = all_0_0_0
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n13, n12, all_0_0_0, n4 and discharging atoms sum(n13, n12) = all_0_0_0, sum(n13, n12) = n4, yields:
% 31.04/10.36 | (966) all_0_0_0 = n4
% 31.04/10.36 |
% 31.04/10.36 | From (966) and (845) follows:
% 31.04/10.36 | (5418) sum(n13, n4) = all_0_6_6
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n13, n4, all_0_6_6, n17 and discharging atoms sum(n13, n4) = all_0_6_6, sum(n13, n4) = n17, yields:
% 31.04/10.36 | (1086) all_0_6_6 = n17
% 31.04/10.36 |
% 31.04/10.36 | Equations (1086) can reduce 669 to:
% 31.04/10.36 | (748) $false
% 31.04/10.36 |
% 31.04/10.36 |-The branch is then unsatisfiable
% 31.04/10.36 |-Branch two:
% 31.04/10.36 | (1224) ~ (all_0_7_7 = n13)
% 31.04/10.36 | (1225) all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.04/10.36 |
% 31.04/10.36 +-Applying beta-rule and splitting (852), into two cases.
% 31.04/10.36 |-Branch one:
% 31.04/10.36 | (853) all_0_8_8 = n13
% 31.04/10.36 |
% 31.04/10.36 | From (853) and (708) follows:
% 31.04/10.36 | (5424) sum(n13, all_0_5_5) = all_0_4_4
% 31.04/10.36 |
% 31.04/10.36 | From (853) and (378) follows:
% 31.04/10.36 | (5425) sum(n13, all_0_7_7) = all_0_2_2
% 31.04/10.36 |
% 31.04/10.36 +-Applying beta-rule and splitting (1225), into two cases.
% 31.04/10.36 |-Branch one:
% 31.04/10.36 | (1226) all_0_7_7 = n12
% 31.04/10.36 |
% 31.04/10.36 | From (1226) and (683) follows:
% 31.04/10.36 | (1227) succ(n12) = all_0_5_5
% 31.04/10.36 |
% 31.04/10.36 | From (1226) and (8) follows:
% 31.04/10.36 | (1228) sum(n12, all_0_1_1) = all_0_0_0
% 31.04/10.36 |
% 31.04/10.36 | From (1226) and (5425) follows:
% 31.04/10.36 | (5429) sum(n13, n12) = all_0_2_2
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (388) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 31.04/10.36 | (1230) all_0_5_5 = n13
% 31.04/10.36 |
% 31.04/10.36 | Instantiating formula (619) with n13, n12, all_0_2_2, n4 and discharging atoms sum(n13, n12) = all_0_2_2, sum(n13, n12) = n4, yields:
% 31.04/10.36 | (992) all_0_2_2 = n4
% 31.04/10.36 |
% 31.04/10.36 | From (992) and (473) follows:
% 31.04/10.36 | (994) pred(n4) = all_0_1_1
% 31.04/10.36 |
% 31.04/10.36 | From (1230) and (5424) follows:
% 31.04/10.37 | (5433) sum(n13, n13) = all_0_4_4
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 31.04/10.37 | (997) all_0_1_1 = n3
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n13, n13, all_0_4_4, n5 and discharging atoms sum(n13, n13) = all_0_4_4, sum(n13, n13) = n5, yields:
% 31.04/10.37 | (993) all_0_4_4 = n5
% 31.04/10.37 |
% 31.04/10.37 | From (993) and (716) follows:
% 31.04/10.37 | (995) pred(n5) = all_0_3_3
% 31.04/10.37 |
% 31.04/10.37 | From (997) and (1228) follows:
% 31.04/10.37 | (5437) sum(n12, n3) = all_0_0_0
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 31.04/10.37 | (996) all_0_3_3 = n4
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n12, n3, all_0_0_0, n15 and discharging atoms sum(n12, n3) = all_0_0_0, sum(n12, n3) = n15, yields:
% 31.04/10.37 | (779) all_0_0_0 = n15
% 31.04/10.37 |
% 31.04/10.37 | From (996)(779) and (232) follows:
% 31.04/10.37 | (5440) sum(n4, n15) = all_0_6_6
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n4, n15, all_0_6_6, n19 and discharging atoms sum(n4, n15) = all_0_6_6, sum(n4, n15) = n19, yields:
% 31.04/10.37 | (1070) all_0_6_6 = n19
% 31.04/10.37 |
% 31.04/10.37 | Equations (1070) can reduce 31 to:
% 31.04/10.37 | (748) $false
% 31.04/10.37 |
% 31.04/10.37 |-The branch is then unsatisfiable
% 31.04/10.37 |-Branch two:
% 31.04/10.37 | (1243) ~ (all_0_7_7 = n12)
% 31.04/10.37 | (1244) all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.04/10.37 |
% 31.04/10.37 +-Applying beta-rule and splitting (1244), into two cases.
% 31.04/10.37 |-Branch one:
% 31.04/10.37 | (1245) all_0_7_7 = n11
% 31.04/10.37 |
% 31.04/10.37 | From (1245) and (683) follows:
% 31.04/10.37 | (1246) succ(n11) = all_0_5_5
% 31.04/10.37 |
% 31.04/10.37 | From (1245) and (8) follows:
% 31.04/10.37 | (1247) sum(n11, all_0_1_1) = all_0_0_0
% 31.04/10.37 |
% 31.04/10.37 | From (1245) and (5425) follows:
% 31.04/10.37 | (5448) sum(n13, n11) = all_0_2_2
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (388) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 31.04/10.37 | (1249) all_0_5_5 = n12
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n13, n11, all_0_2_2, n3 and discharging atoms sum(n13, n11) = all_0_2_2, sum(n13, n11) = n3, yields:
% 31.04/10.37 | (1009) all_0_2_2 = n3
% 31.04/10.37 |
% 31.04/10.37 | From (1009) and (473) follows:
% 31.04/10.37 | (1011) pred(n3) = all_0_1_1
% 31.04/10.37 |
% 31.04/10.37 | From (1249) and (5424) follows:
% 31.04/10.37 | (5452) sum(n13, n12) = all_0_4_4
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 31.04/10.37 | (1014) all_0_1_1 = n2
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n13, n12, all_0_4_4, n4 and discharging atoms sum(n13, n12) = all_0_4_4, sum(n13, n12) = n4, yields:
% 31.04/10.37 | (1010) all_0_4_4 = n4
% 31.04/10.37 |
% 31.04/10.37 | From (1010) and (716) follows:
% 31.04/10.37 | (1012) pred(n4) = all_0_3_3
% 31.04/10.37 |
% 31.04/10.37 | From (1014) and (1247) follows:
% 31.04/10.37 | (5456) sum(n11, n2) = all_0_0_0
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 31.04/10.37 | (1013) all_0_3_3 = n3
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n11, n2, all_0_0_0, n13 and discharging atoms sum(n11, n2) = all_0_0_0, sum(n11, n2) = n13, yields:
% 31.04/10.37 | (813) all_0_0_0 = n13
% 31.04/10.37 |
% 31.04/10.37 | From (1013)(813) and (232) follows:
% 31.04/10.37 | (5459) sum(n3, n13) = all_0_6_6
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n3, n13, all_0_6_6, n16 and discharging atoms sum(n3, n13) = all_0_6_6, sum(n3, n13) = n16, yields:
% 31.04/10.37 | (917) all_0_6_6 = n16
% 31.04/10.37 |
% 31.04/10.37 | Equations (917) can reduce 163 to:
% 31.04/10.37 | (748) $false
% 31.04/10.37 |
% 31.04/10.37 |-The branch is then unsatisfiable
% 31.04/10.37 |-Branch two:
% 31.04/10.37 | (1262) ~ (all_0_7_7 = n11)
% 31.04/10.37 | (1263) all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.04/10.37 |
% 31.04/10.37 +-Applying beta-rule and splitting (1263), into two cases.
% 31.04/10.37 |-Branch one:
% 31.04/10.37 | (1264) all_0_7_7 = n10
% 31.04/10.37 |
% 31.04/10.37 | From (1264) and (683) follows:
% 31.04/10.37 | (1265) succ(n10) = all_0_5_5
% 31.04/10.37 |
% 31.04/10.37 | From (1264) and (8) follows:
% 31.04/10.37 | (1266) sum(n10, all_0_1_1) = all_0_0_0
% 31.04/10.37 |
% 31.04/10.37 | From (1264) and (5425) follows:
% 31.04/10.37 | (5467) sum(n13, n10) = all_0_2_2
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (388) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 31.04/10.37 | (1268) all_0_5_5 = n11
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n13, n10, all_0_2_2, n2 and discharging atoms sum(n13, n10) = all_0_2_2, sum(n13, n10) = n2, yields:
% 31.04/10.37 | (1026) all_0_2_2 = n2
% 31.04/10.37 |
% 31.04/10.37 | From (1026) and (473) follows:
% 31.04/10.37 | (1028) pred(n2) = all_0_1_1
% 31.04/10.37 |
% 31.04/10.37 | From (1268) and (5424) follows:
% 31.04/10.37 | (5471) sum(n13, n11) = all_0_4_4
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 31.04/10.37 | (1031) all_0_1_1 = n1
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n13, n11, all_0_4_4, n3 and discharging atoms sum(n13, n11) = all_0_4_4, sum(n13, n11) = n3, yields:
% 31.04/10.37 | (1027) all_0_4_4 = n3
% 31.04/10.37 |
% 31.04/10.37 | From (1027) and (716) follows:
% 31.04/10.37 | (1029) pred(n3) = all_0_3_3
% 31.04/10.37 |
% 31.04/10.37 | From (1031) and (1266) follows:
% 31.04/10.37 | (5475) sum(n10, n1) = all_0_0_0
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 31.04/10.37 | (1030) all_0_3_3 = n2
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n10, n1, all_0_0_0, n11 and discharging atoms sum(n10, n1) = all_0_0_0, sum(n10, n1) = n11, yields:
% 31.04/10.37 | (847) all_0_0_0 = n11
% 31.04/10.37 |
% 31.04/10.37 | From (1030)(847) and (232) follows:
% 31.04/10.37 | (5478) sum(n2, n11) = all_0_6_6
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n2, n11, all_0_6_6, n13 and discharging atoms sum(n2, n11) = all_0_6_6, sum(n2, n11) = n13, yields:
% 31.04/10.37 | (764) all_0_6_6 = n13
% 31.04/10.37 |
% 31.04/10.37 | Equations (764) can reduce 293 to:
% 31.04/10.37 | (748) $false
% 31.04/10.37 |
% 31.04/10.37 |-The branch is then unsatisfiable
% 31.04/10.37 |-Branch two:
% 31.04/10.37 | (1281) ~ (all_0_7_7 = n10)
% 31.04/10.37 | (1282) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.04/10.37 |
% 31.04/10.37 +-Applying beta-rule and splitting (1282), into two cases.
% 31.04/10.37 |-Branch one:
% 31.04/10.37 | (1283) all_0_7_7 = n9
% 31.04/10.37 |
% 31.04/10.37 | From (1283) and (683) follows:
% 31.04/10.37 | (1284) succ(n9) = all_0_5_5
% 31.04/10.37 |
% 31.04/10.37 | From (1283) and (8) follows:
% 31.04/10.37 | (1285) sum(n9, all_0_1_1) = all_0_0_0
% 31.04/10.37 |
% 31.04/10.37 | From (1283) and (5425) follows:
% 31.04/10.37 | (5486) sum(n13, n9) = all_0_2_2
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (388) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 31.04/10.37 | (1287) all_0_5_5 = n10
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n13, n9, all_0_2_2, n1 and discharging atoms sum(n13, n9) = all_0_2_2, sum(n13, n9) = n1, yields:
% 31.04/10.37 | (1043) all_0_2_2 = n1
% 31.04/10.37 |
% 31.04/10.37 | From (1043) and (473) follows:
% 31.04/10.37 | (1045) pred(n1) = all_0_1_1
% 31.04/10.37 |
% 31.04/10.37 | From (1287) and (5424) follows:
% 31.04/10.37 | (5490) sum(n13, n10) = all_0_4_4
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 31.04/10.37 | (1048) all_0_1_1 = n0
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n13, n10, all_0_4_4, n2 and discharging atoms sum(n13, n10) = all_0_4_4, sum(n13, n10) = n2, yields:
% 31.04/10.37 | (1044) all_0_4_4 = n2
% 31.04/10.37 |
% 31.04/10.37 | From (1044) and (716) follows:
% 31.04/10.37 | (1046) pred(n2) = all_0_3_3
% 31.04/10.37 |
% 31.04/10.37 | From (1048) and (1285) follows:
% 31.04/10.37 | (5494) sum(n9, n0) = all_0_0_0
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 31.04/10.37 | (1047) all_0_3_3 = n1
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n9, n0, all_0_0_0, n9 and discharging atoms sum(n9, n0) = all_0_0_0, sum(n9, n0) = n9, yields:
% 31.04/10.37 | (881) all_0_0_0 = n9
% 31.04/10.37 |
% 31.04/10.37 | From (1047)(881) and (232) follows:
% 31.04/10.37 | (5497) sum(n1, n9) = all_0_6_6
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n1, n9, all_0_6_6, n10 and discharging atoms sum(n1, n9) = all_0_6_6, sum(n1, n9) = n10, yields:
% 31.04/10.37 | (968) all_0_6_6 = n10
% 31.04/10.37 |
% 31.04/10.37 | Equations (968) can reduce 176 to:
% 31.04/10.37 | (748) $false
% 31.04/10.37 |
% 31.04/10.37 |-The branch is then unsatisfiable
% 31.04/10.37 |-Branch two:
% 31.04/10.37 | (1300) ~ (all_0_7_7 = n9)
% 31.04/10.37 | (1301) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.04/10.37 |
% 31.04/10.37 +-Applying beta-rule and splitting (1301), into two cases.
% 31.04/10.37 |-Branch one:
% 31.04/10.37 | (1302) all_0_7_7 = n8
% 31.04/10.37 |
% 31.04/10.37 | From (1302) and (683) follows:
% 31.04/10.37 | (1303) succ(n8) = all_0_5_5
% 31.04/10.37 |
% 31.04/10.37 | From (1302) and (8) follows:
% 31.04/10.37 | (1304) sum(n8, all_0_1_1) = all_0_0_0
% 31.04/10.37 |
% 31.04/10.37 | From (1302) and (5425) follows:
% 31.04/10.37 | (5505) sum(n13, n8) = all_0_2_2
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (388) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 31.04/10.37 | (1306) all_0_5_5 = n9
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n13, n8, all_0_2_2, n0 and discharging atoms sum(n13, n8) = all_0_2_2, sum(n13, n8) = n0, yields:
% 31.04/10.37 | (1060) all_0_2_2 = n0
% 31.04/10.37 |
% 31.04/10.37 | From (1060) and (473) follows:
% 31.04/10.37 | (1062) pred(n0) = all_0_1_1
% 31.04/10.37 |
% 31.04/10.37 | From (1306) and (5424) follows:
% 31.04/10.37 | (5509) sum(n13, n9) = all_0_4_4
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 31.04/10.37 | (1065) all_0_1_1 = n20
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n13, n9, all_0_4_4, n1 and discharging atoms sum(n13, n9) = all_0_4_4, sum(n13, n9) = n1, yields:
% 31.04/10.37 | (1061) all_0_4_4 = n1
% 31.04/10.37 |
% 31.04/10.37 | From (1061) and (716) follows:
% 31.04/10.37 | (1063) pred(n1) = all_0_3_3
% 31.04/10.37 |
% 31.04/10.37 | From (1065) and (1304) follows:
% 31.04/10.37 | (5513) sum(n8, n20) = all_0_0_0
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 31.04/10.37 | (1064) all_0_3_3 = n0
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n8, n20, all_0_0_0, n7 and discharging atoms sum(n8, n20) = all_0_0_0, sum(n8, n20) = n7, yields:
% 31.04/10.37 | (915) all_0_0_0 = n7
% 31.04/10.37 |
% 31.04/10.37 | From (1064)(915) and (232) follows:
% 31.04/10.37 | (5516) sum(n0, n7) = all_0_6_6
% 31.04/10.37 |
% 31.04/10.37 | Instantiating formula (619) with n0, n7, all_0_6_6, n7 and discharging atoms sum(n0, n7) = all_0_6_6, sum(n0, n7) = n7, yields:
% 31.04/10.37 | (815) all_0_6_6 = n7
% 31.04/10.37 |
% 31.04/10.37 | Equations (815) can reduce 557 to:
% 31.04/10.37 | (748) $false
% 31.04/10.37 |
% 31.04/10.37 |-The branch is then unsatisfiable
% 31.04/10.37 |-Branch two:
% 31.04/10.37 | (1319) ~ (all_0_7_7 = n8)
% 31.04/10.37 | (1320) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.04/10.37 |
% 31.04/10.37 +-Applying beta-rule and splitting (1320), into two cases.
% 31.04/10.37 |-Branch one:
% 31.04/10.37 | (1321) all_0_7_7 = n7
% 31.04/10.37 |
% 31.04/10.37 | From (1321) and (683) follows:
% 31.04/10.38 | (1322) succ(n7) = all_0_5_5
% 31.04/10.38 |
% 31.04/10.38 | From (1321) and (8) follows:
% 31.04/10.38 | (1323) sum(n7, all_0_1_1) = all_0_0_0
% 31.04/10.38 |
% 31.04/10.38 | From (1321) and (5425) follows:
% 31.04/10.38 | (5524) sum(n13, n7) = all_0_2_2
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (388) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 31.04/10.38 | (1325) all_0_5_5 = n8
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n13, n7, all_0_2_2, n20 and discharging atoms sum(n13, n7) = all_0_2_2, sum(n13, n7) = n20, yields:
% 31.04/10.38 | (1076) all_0_2_2 = n20
% 31.04/10.38 |
% 31.04/10.38 | From (1076) and (473) follows:
% 31.04/10.38 | (1078) pred(n20) = all_0_1_1
% 31.04/10.38 |
% 31.04/10.38 | From (1325) and (5424) follows:
% 31.04/10.38 | (5528) sum(n13, n8) = all_0_4_4
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 31.04/10.38 | (1080) all_0_1_1 = n19
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n13, n8, all_0_4_4, n0 and discharging atoms sum(n13, n8) = all_0_4_4, sum(n13, n8) = n0, yields:
% 31.04/10.38 | (1077) all_0_4_4 = n0
% 31.04/10.38 |
% 31.04/10.38 | From (1077) and (716) follows:
% 31.04/10.38 | (1079) pred(n0) = all_0_3_3
% 31.04/10.38 |
% 31.04/10.38 | From (1080) and (1323) follows:
% 31.04/10.38 | (5532) sum(n7, n19) = all_0_0_0
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 31.04/10.38 | (1081) all_0_3_3 = n20
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n7, n19, all_0_0_0, n5 and discharging atoms sum(n7, n19) = all_0_0_0, sum(n7, n19) = n5, yields:
% 31.04/10.38 | (949) all_0_0_0 = n5
% 31.04/10.38 |
% 31.04/10.38 | From (1081)(949) and (232) follows:
% 31.04/10.38 | (5535) sum(n20, n5) = all_0_6_6
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n20, n5, all_0_6_6, n4 and discharging atoms sum(n20, n5) = all_0_6_6, sum(n20, n5) = n4, yields:
% 31.04/10.38 | (1019) all_0_6_6 = n4
% 31.04/10.38 |
% 31.04/10.38 | Equations (1019) can reduce 48 to:
% 31.04/10.38 | (748) $false
% 31.04/10.38 |
% 31.04/10.38 |-The branch is then unsatisfiable
% 31.04/10.38 |-Branch two:
% 31.04/10.38 | (1338) ~ (all_0_7_7 = n7)
% 31.04/10.38 | (1339) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.04/10.38 |
% 31.04/10.38 +-Applying beta-rule and splitting (1339), into two cases.
% 31.04/10.38 |-Branch one:
% 31.04/10.38 | (1340) all_0_7_7 = n6
% 31.04/10.38 |
% 31.04/10.38 | From (1340) and (683) follows:
% 31.04/10.38 | (1341) succ(n6) = all_0_5_5
% 31.04/10.38 |
% 31.04/10.38 | From (1340) and (8) follows:
% 31.04/10.38 | (1342) sum(n6, all_0_1_1) = all_0_0_0
% 31.04/10.38 |
% 31.04/10.38 | From (1340) and (5425) follows:
% 31.04/10.38 | (5543) sum(n13, n6) = all_0_2_2
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (388) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 31.04/10.38 | (1344) all_0_5_5 = n7
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n13, n6, all_0_2_2, n19 and discharging atoms sum(n13, n6) = all_0_2_2, sum(n13, n6) = n19, yields:
% 31.04/10.38 | (737) all_0_2_2 = n19
% 31.04/10.38 |
% 31.04/10.38 | From (737) and (473) follows:
% 31.04/10.38 | (739) pred(n19) = all_0_1_1
% 31.04/10.38 |
% 31.04/10.38 | From (1344) and (5424) follows:
% 31.04/10.38 | (5547) sum(n13, n7) = all_0_4_4
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 31.04/10.38 | (742) all_0_1_1 = n18
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n13, n7, all_0_4_4, n20 and discharging atoms sum(n13, n7) = all_0_4_4, sum(n13, n7) = n20, yields:
% 31.04/10.38 | (738) all_0_4_4 = n20
% 31.04/10.38 |
% 31.04/10.38 | From (738) and (716) follows:
% 31.04/10.38 | (740) pred(n20) = all_0_3_3
% 31.04/10.38 |
% 31.04/10.38 | From (742) and (1342) follows:
% 31.04/10.38 | (5551) sum(n6, n18) = all_0_0_0
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 31.04/10.38 | (741) all_0_3_3 = n19
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n6, n18, all_0_0_0, n3 and discharging atoms sum(n6, n18) = all_0_0_0, sum(n6, n18) = n3, yields:
% 31.04/10.38 | (983) all_0_0_0 = n3
% 31.04/10.38 |
% 31.04/10.38 | From (741)(983) and (232) follows:
% 31.04/10.38 | (5554) sum(n19, n3) = all_0_6_6
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n19, n3, all_0_6_6, n1 and discharging atoms sum(n19, n3) = all_0_6_6, sum(n19, n3) = n1, yields:
% 31.04/10.38 | (866) all_0_6_6 = n1
% 31.04/10.38 |
% 31.04/10.38 | Equations (866) can reduce 28 to:
% 31.04/10.38 | (748) $false
% 31.04/10.38 |
% 31.04/10.38 |-The branch is then unsatisfiable
% 31.04/10.38 |-Branch two:
% 31.04/10.38 | (1357) ~ (all_0_7_7 = n6)
% 31.04/10.38 | (1358) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.04/10.38 |
% 31.04/10.38 +-Applying beta-rule and splitting (1358), into two cases.
% 31.04/10.38 |-Branch one:
% 31.04/10.38 | (1359) all_0_7_7 = n5
% 31.04/10.38 |
% 31.04/10.38 | From (1359) and (683) follows:
% 31.04/10.38 | (1360) succ(n5) = all_0_5_5
% 31.04/10.38 |
% 31.04/10.38 | From (1359) and (8) follows:
% 31.04/10.38 | (1361) sum(n5, all_0_1_1) = all_0_0_0
% 31.04/10.38 |
% 31.04/10.38 | From (1359) and (5425) follows:
% 31.04/10.38 | (5562) sum(n13, n5) = all_0_2_2
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (388) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 31.04/10.38 | (1363) all_0_5_5 = n6
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n13, n5, all_0_2_2, n18 and discharging atoms sum(n13, n5) = all_0_2_2, sum(n13, n5) = n18, yields:
% 31.04/10.38 | (754) all_0_2_2 = n18
% 31.04/10.38 |
% 31.04/10.38 | From (754) and (473) follows:
% 31.04/10.38 | (756) pred(n18) = all_0_1_1
% 31.04/10.38 |
% 31.04/10.38 | From (1363) and (5424) follows:
% 31.04/10.38 | (5566) sum(n13, n6) = all_0_4_4
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 31.04/10.38 | (759) all_0_1_1 = n17
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n13, n6, all_0_4_4, n19 and discharging atoms sum(n13, n6) = all_0_4_4, sum(n13, n6) = n19, yields:
% 31.04/10.38 | (755) all_0_4_4 = n19
% 31.04/10.38 |
% 31.04/10.38 | From (755) and (716) follows:
% 31.04/10.38 | (757) pred(n19) = all_0_3_3
% 31.04/10.38 |
% 31.04/10.38 | From (759) and (1361) follows:
% 31.04/10.38 | (5570) sum(n5, n17) = all_0_0_0
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 31.04/10.38 | (758) all_0_3_3 = n18
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n5, n17, all_0_0_0, n1 and discharging atoms sum(n5, n17) = all_0_0_0, sum(n5, n17) = n1, yields:
% 31.04/10.38 | (1017) all_0_0_0 = n1
% 31.04/10.38 |
% 31.04/10.38 | From (758)(1017) and (232) follows:
% 31.04/10.38 | (5573) sum(n18, n1) = all_0_6_6
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n18, n1, all_0_6_6, n19 and discharging atoms sum(n18, n1) = all_0_6_6, sum(n18, n1) = n19, yields:
% 31.04/10.38 | (1070) all_0_6_6 = n19
% 31.04/10.38 |
% 31.04/10.38 | Equations (1070) can reduce 31 to:
% 31.04/10.38 | (748) $false
% 31.04/10.38 |
% 31.04/10.38 |-The branch is then unsatisfiable
% 31.04/10.38 |-Branch two:
% 31.04/10.38 | (1376) ~ (all_0_7_7 = n5)
% 31.04/10.38 | (1377) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.04/10.38 |
% 31.04/10.38 +-Applying beta-rule and splitting (1377), into two cases.
% 31.04/10.38 |-Branch one:
% 31.04/10.38 | (1378) all_0_7_7 = n4
% 31.04/10.38 |
% 31.04/10.38 | From (1378) and (683) follows:
% 31.04/10.38 | (1379) succ(n4) = all_0_5_5
% 31.04/10.38 |
% 31.04/10.38 | From (1378) and (8) follows:
% 31.04/10.38 | (1380) sum(n4, all_0_1_1) = all_0_0_0
% 31.04/10.38 |
% 31.04/10.38 | From (1378) and (5425) follows:
% 31.04/10.38 | (5581) sum(n13, n4) = all_0_2_2
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (388) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 31.04/10.38 | (1382) all_0_5_5 = n5
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n13, n4, all_0_2_2, n17 and discharging atoms sum(n13, n4) = all_0_2_2, sum(n13, n4) = n17, yields:
% 31.04/10.38 | (771) all_0_2_2 = n17
% 31.04/10.38 |
% 31.04/10.38 | From (771) and (473) follows:
% 31.04/10.38 | (773) pred(n17) = all_0_1_1
% 31.04/10.38 |
% 31.04/10.38 | From (1382) and (5424) follows:
% 31.04/10.38 | (5585) sum(n13, n5) = all_0_4_4
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 31.04/10.38 | (776) all_0_1_1 = n16
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n13, n5, all_0_4_4, n18 and discharging atoms sum(n13, n5) = all_0_4_4, sum(n13, n5) = n18, yields:
% 31.04/10.38 | (772) all_0_4_4 = n18
% 31.04/10.38 |
% 31.04/10.38 | From (772) and (716) follows:
% 31.04/10.38 | (774) pred(n18) = all_0_3_3
% 31.04/10.38 |
% 31.04/10.38 | From (776) and (1380) follows:
% 31.04/10.38 | (5589) sum(n4, n16) = all_0_0_0
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 31.04/10.38 | (775) all_0_3_3 = n17
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n4, n16, all_0_0_0, n20 and discharging atoms sum(n4, n16) = all_0_0_0, sum(n4, n16) = n20, yields:
% 31.04/10.38 | (1051) all_0_0_0 = n20
% 31.04/10.38 |
% 31.04/10.38 | From (775)(1051) and (232) follows:
% 31.04/10.38 | (5592) sum(n17, n20) = all_0_6_6
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n17, n20, all_0_6_6, n16 and discharging atoms sum(n17, n20) = all_0_6_6, sum(n17, n20) = n16, yields:
% 31.04/10.38 | (917) all_0_6_6 = n16
% 31.04/10.38 |
% 31.04/10.38 | Equations (917) can reduce 163 to:
% 31.04/10.38 | (748) $false
% 31.04/10.38 |
% 31.04/10.38 |-The branch is then unsatisfiable
% 31.04/10.38 |-Branch two:
% 31.04/10.38 | (1395) ~ (all_0_7_7 = n4)
% 31.04/10.38 | (1396) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.04/10.38 |
% 31.04/10.38 +-Applying beta-rule and splitting (1396), into two cases.
% 31.04/10.38 |-Branch one:
% 31.04/10.38 | (1397) all_0_7_7 = n3
% 31.04/10.38 |
% 31.04/10.38 | From (1397) and (683) follows:
% 31.04/10.38 | (1398) succ(n3) = all_0_5_5
% 31.04/10.38 |
% 31.04/10.38 | From (1397) and (8) follows:
% 31.04/10.38 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 31.04/10.38 |
% 31.04/10.38 | From (1397) and (5425) follows:
% 31.04/10.38 | (5600) sum(n13, n3) = all_0_2_2
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 31.04/10.38 | (1401) all_0_5_5 = n4
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n13, n3, all_0_2_2, n16 and discharging atoms sum(n13, n3) = all_0_2_2, sum(n13, n3) = n16, yields:
% 31.04/10.38 | (788) all_0_2_2 = n16
% 31.04/10.38 |
% 31.04/10.38 | From (788) and (473) follows:
% 31.04/10.38 | (790) pred(n16) = all_0_1_1
% 31.04/10.38 |
% 31.04/10.38 | From (1401) and (5424) follows:
% 31.04/10.38 | (5604) sum(n13, n4) = all_0_4_4
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 31.04/10.38 | (793) all_0_1_1 = n15
% 31.04/10.38 |
% 31.04/10.38 | Instantiating formula (619) with n13, n4, all_0_4_4, n17 and discharging atoms sum(n13, n4) = all_0_4_4, sum(n13, n4) = n17, yields:
% 31.04/10.38 | (789) all_0_4_4 = n17
% 31.04/10.38 |
% 31.04/10.38 | From (789) and (716) follows:
% 31.04/10.38 | (791) pred(n17) = all_0_3_3
% 31.04/10.38 |
% 31.04/10.38 | From (793) and (1399) follows:
% 31.04/10.39 | (5608) sum(n3, n15) = all_0_0_0
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 31.04/10.39 | (792) all_0_3_3 = n16
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (619) with n3, n15, all_0_0_0, n18 and discharging atoms sum(n3, n15) = all_0_0_0, sum(n3, n15) = n18, yields:
% 31.04/10.39 | (1084) all_0_0_0 = n18
% 31.04/10.39 |
% 31.04/10.39 | From (792)(1084) and (232) follows:
% 31.04/10.39 | (5611) sum(n16, n18) = all_0_6_6
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (619) with n16, n18, all_0_6_6, n13 and discharging atoms sum(n16, n18) = all_0_6_6, sum(n16, n18) = n13, yields:
% 31.04/10.39 | (764) all_0_6_6 = n13
% 31.04/10.39 |
% 31.04/10.39 | Equations (764) can reduce 293 to:
% 31.04/10.39 | (748) $false
% 31.04/10.39 |
% 31.04/10.39 |-The branch is then unsatisfiable
% 31.04/10.39 |-Branch two:
% 31.04/10.39 | (1414) ~ (all_0_7_7 = n3)
% 31.04/10.39 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.04/10.39 |
% 31.04/10.39 +-Applying beta-rule and splitting (1415), into two cases.
% 31.04/10.39 |-Branch one:
% 31.04/10.39 | (1416) all_0_7_7 = n2
% 31.04/10.39 |
% 31.04/10.39 | From (1416) and (683) follows:
% 31.04/10.39 | (1417) succ(n2) = all_0_5_5
% 31.04/10.39 |
% 31.04/10.39 | From (1416) and (8) follows:
% 31.04/10.39 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 31.04/10.39 |
% 31.04/10.39 | From (1416) and (5425) follows:
% 31.04/10.39 | (5619) sum(n13, n2) = all_0_2_2
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.04/10.39 | (1420) all_0_5_5 = n3
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (619) with n13, n2, all_0_2_2, n15 and discharging atoms sum(n13, n2) = all_0_2_2, sum(n13, n2) = n15, yields:
% 31.04/10.39 | (805) all_0_2_2 = n15
% 31.04/10.39 |
% 31.04/10.39 | From (805) and (473) follows:
% 31.04/10.39 | (807) pred(n15) = all_0_1_1
% 31.04/10.39 |
% 31.04/10.39 | From (1420) and (5424) follows:
% 31.04/10.39 | (5623) sum(n13, n3) = all_0_4_4
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 31.04/10.39 | (810) all_0_1_1 = n14
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (619) with n13, n3, all_0_4_4, n16 and discharging atoms sum(n13, n3) = all_0_4_4, sum(n13, n3) = n16, yields:
% 31.04/10.39 | (806) all_0_4_4 = n16
% 31.04/10.39 |
% 31.04/10.39 | From (806) and (716) follows:
% 31.04/10.39 | (808) pred(n16) = all_0_3_3
% 31.04/10.39 |
% 31.04/10.39 | From (810) and (1418) follows:
% 31.04/10.39 | (5627) sum(n2, n14) = all_0_0_0
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 31.04/10.39 | (809) all_0_3_3 = n15
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (619) with n2, n14, all_0_0_0, n16 and discharging atoms sum(n2, n14) = all_0_0_0, sum(n2, n14) = n16, yields:
% 31.04/10.39 | (762) all_0_0_0 = n16
% 31.04/10.39 |
% 31.04/10.39 | From (809)(762) and (232) follows:
% 31.04/10.39 | (5630) sum(n15, n16) = all_0_6_6
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (619) with n15, n16, all_0_6_6, n10 and discharging atoms sum(n15, n16) = all_0_6_6, sum(n15, n16) = n10, yields:
% 31.04/10.39 | (968) all_0_6_6 = n10
% 31.04/10.39 |
% 31.04/10.39 | Equations (968) can reduce 176 to:
% 31.04/10.39 | (748) $false
% 31.04/10.39 |
% 31.04/10.39 |-The branch is then unsatisfiable
% 31.04/10.39 |-Branch two:
% 31.04/10.39 | (1433) ~ (all_0_7_7 = n2)
% 31.04/10.39 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 31.04/10.39 |
% 31.04/10.39 +-Applying beta-rule and splitting (1434), into two cases.
% 31.04/10.39 |-Branch one:
% 31.04/10.39 | (1435) all_0_7_7 = n1
% 31.04/10.39 |
% 31.04/10.39 | From (1435) and (683) follows:
% 31.04/10.39 | (1436) succ(n1) = all_0_5_5
% 31.04/10.39 |
% 31.04/10.39 | From (1435) and (8) follows:
% 31.04/10.39 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 31.04/10.39 |
% 31.04/10.39 | From (1435) and (5425) follows:
% 31.04/10.39 | (5638) sum(n13, n1) = all_0_2_2
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.04/10.39 | (1439) all_0_5_5 = n2
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (619) with n13, n1, all_0_2_2, n14 and discharging atoms sum(n13, n1) = all_0_2_2, sum(n13, n1) = n14, yields:
% 31.04/10.39 | (822) all_0_2_2 = n14
% 31.04/10.39 |
% 31.04/10.39 | From (822) and (473) follows:
% 31.04/10.39 | (824) pred(n14) = all_0_1_1
% 31.04/10.39 |
% 31.04/10.39 | From (1439) and (5424) follows:
% 31.04/10.39 | (5642) sum(n13, n2) = all_0_4_4
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 31.04/10.39 | (827) all_0_1_1 = n13
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (619) with n13, n2, all_0_4_4, n15 and discharging atoms sum(n13, n2) = all_0_4_4, sum(n13, n2) = n15, yields:
% 31.04/10.39 | (823) all_0_4_4 = n15
% 31.04/10.39 |
% 31.04/10.39 | From (823) and (716) follows:
% 31.04/10.39 | (825) pred(n15) = all_0_3_3
% 31.04/10.39 |
% 31.04/10.39 | From (827) and (1437) follows:
% 31.04/10.39 | (5646) sum(n1, n13) = all_0_0_0
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 31.04/10.39 | (826) all_0_3_3 = n14
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (619) with n1, n13, all_0_0_0, n14 and discharging atoms sum(n1, n13) = all_0_0_0, sum(n1, n13) = n14, yields:
% 31.04/10.39 | (796) all_0_0_0 = n14
% 31.04/10.39 |
% 31.04/10.39 | From (826)(796) and (232) follows:
% 31.04/10.39 | (5649) sum(n14, n14) = all_0_6_6
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (619) with n14, n14, all_0_6_6, n7 and discharging atoms sum(n14, n14) = all_0_6_6, sum(n14, n14) = n7, yields:
% 31.04/10.39 | (815) all_0_6_6 = n7
% 31.04/10.39 |
% 31.04/10.39 | Equations (815) can reduce 557 to:
% 31.04/10.39 | (748) $false
% 31.04/10.39 |
% 31.04/10.39 |-The branch is then unsatisfiable
% 31.04/10.39 |-Branch two:
% 31.04/10.39 | (1452) ~ (all_0_7_7 = n1)
% 31.04/10.39 | (1453) all_0_7_7 = n0
% 31.04/10.39 |
% 31.04/10.39 | From (1453) and (683) follows:
% 31.04/10.39 | (1454) succ(n0) = all_0_5_5
% 31.04/10.39 |
% 31.04/10.39 | From (1453) and (8) follows:
% 31.04/10.39 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 31.04/10.39 |
% 31.04/10.39 | From (1453) and (5425) follows:
% 31.04/10.39 | (5656) sum(n13, n0) = all_0_2_2
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.04/10.39 | (1457) all_0_5_5 = n1
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (619) with n13, n0, all_0_2_2, n13 and discharging atoms sum(n13, n0) = all_0_2_2, sum(n13, n0) = n13, yields:
% 31.04/10.39 | (839) all_0_2_2 = n13
% 31.04/10.39 |
% 31.04/10.39 | From (839) and (473) follows:
% 31.04/10.39 | (841) pred(n13) = all_0_1_1
% 31.04/10.39 |
% 31.04/10.39 | From (1457) and (5424) follows:
% 31.04/10.39 | (5660) sum(n13, n1) = all_0_4_4
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 31.04/10.39 | (844) all_0_1_1 = n12
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (619) with n13, n1, all_0_4_4, n14 and discharging atoms sum(n13, n1) = all_0_4_4, sum(n13, n1) = n14, yields:
% 31.04/10.39 | (840) all_0_4_4 = n14
% 31.04/10.39 |
% 31.04/10.39 | From (840) and (716) follows:
% 31.04/10.39 | (842) pred(n14) = all_0_3_3
% 31.04/10.39 |
% 31.04/10.39 | From (844) and (1455) follows:
% 31.04/10.39 | (5664) sum(n0, n12) = all_0_0_0
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 31.04/10.39 | (843) all_0_3_3 = n13
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (619) with n0, n12, all_0_0_0, n12 and discharging atoms sum(n0, n12) = all_0_0_0, sum(n0, n12) = n12, yields:
% 31.04/10.39 | (830) all_0_0_0 = n12
% 31.04/10.39 |
% 31.04/10.39 | From (843)(830) and (232) follows:
% 31.04/10.39 | (5667) sum(n13, n12) = all_0_6_6
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (619) with n13, n12, all_0_6_6, n4 and discharging atoms sum(n13, n12) = all_0_6_6, sum(n13, n12) = n4, yields:
% 31.04/10.39 | (1019) all_0_6_6 = n4
% 31.04/10.39 |
% 31.04/10.39 | Equations (1019) can reduce 48 to:
% 31.04/10.39 | (748) $false
% 31.04/10.39 |
% 31.04/10.39 |-The branch is then unsatisfiable
% 31.04/10.39 |-Branch two:
% 31.04/10.39 | (868) ~ (all_0_8_8 = n13)
% 31.04/10.39 | (869) all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.39 |
% 31.04/10.39 +-Applying beta-rule and splitting (1225), into two cases.
% 31.04/10.39 |-Branch one:
% 31.04/10.39 | (1226) all_0_7_7 = n12
% 31.04/10.39 |
% 31.04/10.39 | From (1226) and (683) follows:
% 31.04/10.39 | (1227) succ(n12) = all_0_5_5
% 31.04/10.39 |
% 31.04/10.39 | From (1226) and (8) follows:
% 31.04/10.39 | (1228) sum(n12, all_0_1_1) = all_0_0_0
% 31.04/10.39 |
% 31.04/10.39 | From (1226) and (378) follows:
% 31.04/10.39 | (5675) sum(all_0_8_8, n12) = all_0_2_2
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (388) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 31.04/10.39 | (1230) all_0_5_5 = n13
% 31.04/10.39 |
% 31.04/10.39 | From (1230) and (708) follows:
% 31.04/10.39 | (5677) sum(all_0_8_8, n13) = all_0_4_4
% 31.04/10.39 |
% 31.04/10.39 +-Applying beta-rule and splitting (869), into two cases.
% 31.04/10.39 |-Branch one:
% 31.04/10.39 | (870) all_0_8_8 = n12
% 31.04/10.39 |
% 31.04/10.39 | From (870) and (5677) follows:
% 31.04/10.39 | (5679) sum(n12, n13) = all_0_4_4
% 31.04/10.39 |
% 31.04/10.39 | From (870) and (5675) follows:
% 31.04/10.39 | (5680) sum(n12, n12) = all_0_2_2
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (619) with n12, n13, all_0_4_4, n4 and discharging atoms sum(n12, n13) = all_0_4_4, sum(n12, n13) = n4, yields:
% 31.04/10.39 | (1010) all_0_4_4 = n4
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (619) with n12, n12, all_0_2_2, n3 and discharging atoms sum(n12, n12) = all_0_2_2, sum(n12, n12) = n3, yields:
% 31.04/10.39 | (1009) all_0_2_2 = n3
% 31.04/10.39 |
% 31.04/10.39 | From (1009) and (473) follows:
% 31.04/10.39 | (1011) pred(n3) = all_0_1_1
% 31.04/10.39 |
% 31.04/10.39 | From (1010) and (716) follows:
% 31.04/10.39 | (1012) pred(n4) = all_0_3_3
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 31.04/10.39 | (1013) all_0_3_3 = n3
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 31.04/10.39 | (1014) all_0_1_1 = n2
% 31.04/10.39 |
% 31.04/10.39 | From (1013) and (232) follows:
% 31.04/10.39 | (1015) sum(n3, all_0_0_0) = all_0_6_6
% 31.04/10.39 |
% 31.04/10.39 | From (1014) and (1228) follows:
% 31.04/10.39 | (5688) sum(n12, n2) = all_0_0_0
% 31.04/10.39 |
% 31.04/10.39 | Instantiating formula (619) with n12, n2, all_0_0_0, n14 and discharging atoms sum(n12, n2) = all_0_0_0, sum(n12, n2) = n14, yields:
% 31.04/10.39 | (796) all_0_0_0 = n14
% 31.04/10.39 |
% 31.04/10.39 | From (796) and (1015) follows:
% 31.04/10.40 | (5690) sum(n3, n14) = all_0_6_6
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (619) with n3, n14, all_0_6_6, n17 and discharging atoms sum(n3, n14) = all_0_6_6, sum(n3, n14) = n17, yields:
% 31.04/10.40 | (1086) all_0_6_6 = n17
% 31.04/10.40 |
% 31.04/10.40 | Equations (1086) can reduce 669 to:
% 31.04/10.40 | (748) $false
% 31.04/10.40 |
% 31.04/10.40 |-The branch is then unsatisfiable
% 31.04/10.40 |-Branch two:
% 31.04/10.40 | (885) ~ (all_0_8_8 = n12)
% 31.04/10.40 | (886) all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.40 |
% 31.04/10.40 +-Applying beta-rule and splitting (886), into two cases.
% 31.04/10.40 |-Branch one:
% 31.04/10.40 | (887) all_0_8_8 = n11
% 31.04/10.40 |
% 31.04/10.40 | From (887) and (5677) follows:
% 31.04/10.40 | (5696) sum(n11, n13) = all_0_4_4
% 31.04/10.40 |
% 31.04/10.40 | From (887) and (5675) follows:
% 31.04/10.40 | (5697) sum(n11, n12) = all_0_2_2
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (619) with n11, n13, all_0_4_4, n3 and discharging atoms sum(n11, n13) = all_0_4_4, sum(n11, n13) = n3, yields:
% 31.04/10.40 | (1027) all_0_4_4 = n3
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (619) with n11, n12, all_0_2_2, n2 and discharging atoms sum(n11, n12) = all_0_2_2, sum(n11, n12) = n2, yields:
% 31.04/10.40 | (1026) all_0_2_2 = n2
% 31.04/10.40 |
% 31.04/10.40 | From (1026) and (473) follows:
% 31.04/10.40 | (1028) pred(n2) = all_0_1_1
% 31.04/10.40 |
% 31.04/10.40 | From (1027) and (716) follows:
% 31.04/10.40 | (1029) pred(n3) = all_0_3_3
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 31.04/10.40 | (1030) all_0_3_3 = n2
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 31.04/10.40 | (1031) all_0_1_1 = n1
% 31.04/10.40 |
% 31.04/10.40 | From (1030) and (232) follows:
% 31.04/10.40 | (1032) sum(n2, all_0_0_0) = all_0_6_6
% 31.04/10.40 |
% 31.04/10.40 | From (1031) and (1228) follows:
% 31.04/10.40 | (5705) sum(n12, n1) = all_0_0_0
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (619) with n12, n1, all_0_0_0, n13 and discharging atoms sum(n12, n1) = all_0_0_0, sum(n12, n1) = n13, yields:
% 31.04/10.40 | (813) all_0_0_0 = n13
% 31.04/10.40 |
% 31.04/10.40 | From (813) and (1032) follows:
% 31.04/10.40 | (5707) sum(n2, n13) = all_0_6_6
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (619) with n2, n13, all_0_6_6, n15 and discharging atoms sum(n2, n13) = all_0_6_6, sum(n2, n13) = n15, yields:
% 31.04/10.40 | (747) all_0_6_6 = n15
% 31.04/10.40 |
% 31.04/10.40 | Equations (747) can reduce 456 to:
% 31.04/10.40 | (748) $false
% 31.04/10.40 |
% 31.04/10.40 |-The branch is then unsatisfiable
% 31.04/10.40 |-Branch two:
% 31.04/10.40 | (902) ~ (all_0_8_8 = n11)
% 31.04/10.40 | (903) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.40 |
% 31.04/10.40 +-Applying beta-rule and splitting (903), into two cases.
% 31.04/10.40 |-Branch one:
% 31.04/10.40 | (904) all_0_8_8 = n10
% 31.04/10.40 |
% 31.04/10.40 | From (904) and (5677) follows:
% 31.04/10.40 | (5713) sum(n10, n13) = all_0_4_4
% 31.04/10.40 |
% 31.04/10.40 | From (904) and (5675) follows:
% 31.04/10.40 | (5714) sum(n10, n12) = all_0_2_2
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (619) with n10, n13, all_0_4_4, n2 and discharging atoms sum(n10, n13) = all_0_4_4, sum(n10, n13) = n2, yields:
% 31.04/10.40 | (1044) all_0_4_4 = n2
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (619) with n10, n12, all_0_2_2, n1 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n1, yields:
% 31.04/10.40 | (1043) all_0_2_2 = n1
% 31.04/10.40 |
% 31.04/10.40 | From (1043) and (473) follows:
% 31.04/10.40 | (1045) pred(n1) = all_0_1_1
% 31.04/10.40 |
% 31.04/10.40 | From (1044) and (716) follows:
% 31.04/10.40 | (1046) pred(n2) = all_0_3_3
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 31.04/10.40 | (1047) all_0_3_3 = n1
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 31.04/10.40 | (1048) all_0_1_1 = n0
% 31.04/10.40 |
% 31.04/10.40 | From (1047) and (232) follows:
% 31.04/10.40 | (1049) sum(n1, all_0_0_0) = all_0_6_6
% 31.04/10.40 |
% 31.04/10.40 | From (1048) and (1228) follows:
% 31.04/10.40 | (5722) sum(n12, n0) = all_0_0_0
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (619) with n12, n0, all_0_0_0, n12 and discharging atoms sum(n12, n0) = all_0_0_0, sum(n12, n0) = n12, yields:
% 31.04/10.40 | (830) all_0_0_0 = n12
% 31.04/10.40 |
% 31.04/10.40 | From (830) and (1049) follows:
% 31.04/10.40 | (5724) sum(n1, n12) = all_0_6_6
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (619) with n1, n12, all_0_6_6, n13 and discharging atoms sum(n1, n12) = all_0_6_6, sum(n1, n12) = n13, yields:
% 31.04/10.40 | (764) all_0_6_6 = n13
% 31.04/10.40 |
% 31.04/10.40 | Equations (764) can reduce 293 to:
% 31.04/10.40 | (748) $false
% 31.04/10.40 |
% 31.04/10.40 |-The branch is then unsatisfiable
% 31.04/10.40 |-Branch two:
% 31.04/10.40 | (919) ~ (all_0_8_8 = n10)
% 31.04/10.40 | (920) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.40 |
% 31.04/10.40 +-Applying beta-rule and splitting (920), into two cases.
% 31.04/10.40 |-Branch one:
% 31.04/10.40 | (921) all_0_8_8 = n9
% 31.04/10.40 |
% 31.04/10.40 | From (921) and (5677) follows:
% 31.04/10.40 | (5730) sum(n9, n13) = all_0_4_4
% 31.04/10.40 |
% 31.04/10.40 | From (921) and (5675) follows:
% 31.04/10.40 | (5731) sum(n9, n12) = all_0_2_2
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (619) with n9, n13, all_0_4_4, n1 and discharging atoms sum(n9, n13) = all_0_4_4, sum(n9, n13) = n1, yields:
% 31.04/10.40 | (1061) all_0_4_4 = n1
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (619) with n9, n12, all_0_2_2, n0 and discharging atoms sum(n9, n12) = all_0_2_2, sum(n9, n12) = n0, yields:
% 31.04/10.40 | (1060) all_0_2_2 = n0
% 31.04/10.40 |
% 31.04/10.40 | From (1060) and (473) follows:
% 31.04/10.40 | (1062) pred(n0) = all_0_1_1
% 31.04/10.40 |
% 31.04/10.40 | From (1061) and (716) follows:
% 31.04/10.40 | (1063) pred(n1) = all_0_3_3
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 31.04/10.40 | (1064) all_0_3_3 = n0
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 31.04/10.40 | (1065) all_0_1_1 = n20
% 31.04/10.40 |
% 31.04/10.40 | From (1064) and (232) follows:
% 31.04/10.40 | (1066) sum(n0, all_0_0_0) = all_0_6_6
% 31.04/10.40 |
% 31.04/10.40 | From (1065) and (1228) follows:
% 31.04/10.40 | (5739) sum(n12, n20) = all_0_0_0
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (619) with n12, n20, all_0_0_0, n11 and discharging atoms sum(n12, n20) = all_0_0_0, sum(n12, n20) = n11, yields:
% 31.04/10.40 | (847) all_0_0_0 = n11
% 31.04/10.40 |
% 31.04/10.40 | From (847) and (1066) follows:
% 31.04/10.40 | (5741) sum(n0, n11) = all_0_6_6
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (619) with n0, n11, all_0_6_6, n11 and discharging atoms sum(n0, n11) = all_0_6_6, sum(n0, n11) = n11, yields:
% 31.04/10.40 | (781) all_0_6_6 = n11
% 31.04/10.40 |
% 31.04/10.40 | Equations (781) can reduce 2 to:
% 31.04/10.40 | (748) $false
% 31.04/10.40 |
% 31.04/10.40 |-The branch is then unsatisfiable
% 31.04/10.40 |-Branch two:
% 31.04/10.40 | (936) ~ (all_0_8_8 = n9)
% 31.04/10.40 | (937) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.40 |
% 31.04/10.40 +-Applying beta-rule and splitting (937), into two cases.
% 31.04/10.40 |-Branch one:
% 31.04/10.40 | (938) all_0_8_8 = n8
% 31.04/10.40 |
% 31.04/10.40 | From (938) and (5677) follows:
% 31.04/10.40 | (5747) sum(n8, n13) = all_0_4_4
% 31.04/10.40 |
% 31.04/10.40 | From (938) and (5675) follows:
% 31.04/10.40 | (5748) sum(n8, n12) = all_0_2_2
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (619) with n8, n13, all_0_4_4, n0 and discharging atoms sum(n8, n13) = all_0_4_4, sum(n8, n13) = n0, yields:
% 31.04/10.40 | (1077) all_0_4_4 = n0
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (619) with n8, n12, all_0_2_2, n20 and discharging atoms sum(n8, n12) = all_0_2_2, sum(n8, n12) = n20, yields:
% 31.04/10.40 | (1076) all_0_2_2 = n20
% 31.04/10.40 |
% 31.04/10.40 | From (1076) and (473) follows:
% 31.04/10.40 | (1078) pred(n20) = all_0_1_1
% 31.04/10.40 |
% 31.04/10.40 | From (1077) and (716) follows:
% 31.04/10.40 | (1079) pred(n0) = all_0_3_3
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 31.04/10.40 | (1080) all_0_1_1 = n19
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 31.04/10.40 | (1081) all_0_3_3 = n20
% 31.04/10.40 |
% 31.04/10.40 | From (1081) and (232) follows:
% 31.04/10.40 | (1082) sum(n20, all_0_0_0) = all_0_6_6
% 31.04/10.40 |
% 31.04/10.40 | From (1080) and (1228) follows:
% 31.04/10.40 | (5756) sum(n12, n19) = all_0_0_0
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (619) with n12, n19, all_0_0_0, n10 and discharging atoms sum(n12, n19) = all_0_0_0, sum(n12, n19) = n10, yields:
% 31.04/10.40 | (864) all_0_0_0 = n10
% 31.04/10.40 |
% 31.04/10.40 | From (864) and (1082) follows:
% 31.04/10.40 | (5758) sum(n20, n10) = all_0_6_6
% 31.04/10.40 |
% 31.04/10.40 | Instantiating formula (619) with n20, n10, all_0_6_6, n9 and discharging atoms sum(n20, n10) = all_0_6_6, sum(n20, n10) = n9, yields:
% 31.04/10.40 | (798) all_0_6_6 = n9
% 31.04/10.40 |
% 31.04/10.40 | Equations (798) can reduce 593 to:
% 31.04/10.40 | (748) $false
% 31.04/10.40 |
% 31.04/10.40 |-The branch is then unsatisfiable
% 31.04/10.40 |-Branch two:
% 31.04/10.40 | (953) ~ (all_0_8_8 = n8)
% 31.04/10.40 | (954) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.04/10.40 |
% 31.04/10.40 +-Applying beta-rule and splitting (954), into two cases.
% 31.04/10.40 |-Branch one:
% 31.04/10.40 | (955) all_0_8_8 = n7
% 31.04/10.40 |
% 31.04/10.40 | From (955) and (5677) follows:
% 31.36/10.40 | (5764) sum(n7, n13) = all_0_4_4
% 31.36/10.40 |
% 31.36/10.40 | From (955) and (5675) follows:
% 31.36/10.40 | (5765) sum(n7, n12) = all_0_2_2
% 31.36/10.40 |
% 31.36/10.40 | Instantiating formula (619) with n7, n13, all_0_4_4, n20 and discharging atoms sum(n7, n13) = all_0_4_4, sum(n7, n13) = n20, yields:
% 31.36/10.40 | (738) all_0_4_4 = n20
% 31.36/10.40 |
% 31.36/10.40 | Instantiating formula (619) with n7, n12, all_0_2_2, n19 and discharging atoms sum(n7, n12) = all_0_2_2, sum(n7, n12) = n19, yields:
% 31.36/10.40 | (737) all_0_2_2 = n19
% 31.36/10.40 |
% 31.36/10.40 | From (737) and (473) follows:
% 31.36/10.40 | (739) pred(n19) = all_0_1_1
% 31.36/10.40 |
% 31.36/10.41 | From (738) and (716) follows:
% 31.36/10.41 | (740) pred(n20) = all_0_3_3
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 31.36/10.41 | (741) all_0_3_3 = n19
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 31.36/10.41 | (742) all_0_1_1 = n18
% 31.36/10.41 |
% 31.36/10.41 | From (741) and (232) follows:
% 31.36/10.41 | (743) sum(n19, all_0_0_0) = all_0_6_6
% 31.36/10.41 |
% 31.36/10.41 | From (742) and (1228) follows:
% 31.36/10.41 | (5773) sum(n12, n18) = all_0_0_0
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n12, n18, all_0_0_0, n9 and discharging atoms sum(n12, n18) = all_0_0_0, sum(n12, n18) = n9, yields:
% 31.36/10.41 | (881) all_0_0_0 = n9
% 31.36/10.41 |
% 31.36/10.41 | From (881) and (743) follows:
% 31.36/10.41 | (5775) sum(n19, n9) = all_0_6_6
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n19, n9, all_0_6_6, n7 and discharging atoms sum(n19, n9) = all_0_6_6, sum(n19, n9) = n7, yields:
% 31.36/10.41 | (815) all_0_6_6 = n7
% 31.36/10.41 |
% 31.36/10.41 | Equations (815) can reduce 557 to:
% 31.36/10.41 | (748) $false
% 31.36/10.41 |
% 31.36/10.41 |-The branch is then unsatisfiable
% 31.36/10.41 |-Branch two:
% 31.36/10.41 | (970) ~ (all_0_8_8 = n7)
% 31.36/10.41 | (971) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.36/10.41 |
% 31.36/10.41 +-Applying beta-rule and splitting (971), into two cases.
% 31.36/10.41 |-Branch one:
% 31.36/10.41 | (972) all_0_8_8 = n6
% 31.36/10.41 |
% 31.36/10.41 | From (972) and (5677) follows:
% 31.36/10.41 | (5781) sum(n6, n13) = all_0_4_4
% 31.36/10.41 |
% 31.36/10.41 | From (972) and (5675) follows:
% 31.36/10.41 | (5782) sum(n6, n12) = all_0_2_2
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n6, n13, all_0_4_4, n19 and discharging atoms sum(n6, n13) = all_0_4_4, sum(n6, n13) = n19, yields:
% 31.36/10.41 | (755) all_0_4_4 = n19
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n6, n12, all_0_2_2, n18 and discharging atoms sum(n6, n12) = all_0_2_2, sum(n6, n12) = n18, yields:
% 31.36/10.41 | (754) all_0_2_2 = n18
% 31.36/10.41 |
% 31.36/10.41 | From (754) and (473) follows:
% 31.36/10.41 | (756) pred(n18) = all_0_1_1
% 31.36/10.41 |
% 31.36/10.41 | From (755) and (716) follows:
% 31.36/10.41 | (757) pred(n19) = all_0_3_3
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 31.36/10.41 | (758) all_0_3_3 = n18
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 31.36/10.41 | (759) all_0_1_1 = n17
% 31.36/10.41 |
% 31.36/10.41 | From (758) and (232) follows:
% 31.36/10.41 | (760) sum(n18, all_0_0_0) = all_0_6_6
% 31.36/10.41 |
% 31.36/10.41 | From (759) and (1228) follows:
% 31.36/10.41 | (5790) sum(n12, n17) = all_0_0_0
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n12, n17, all_0_0_0, n8 and discharging atoms sum(n12, n17) = all_0_0_0, sum(n12, n17) = n8, yields:
% 31.36/10.41 | (898) all_0_0_0 = n8
% 31.36/10.41 |
% 31.36/10.41 | From (898) and (760) follows:
% 31.36/10.41 | (5792) sum(n18, n8) = all_0_6_6
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n18, n8, all_0_6_6, n5 and discharging atoms sum(n18, n8) = all_0_6_6, sum(n18, n8) = n5, yields:
% 31.36/10.41 | (832) all_0_6_6 = n5
% 31.36/10.41 |
% 31.36/10.41 | Equations (832) can reduce 462 to:
% 31.36/10.41 | (748) $false
% 31.36/10.41 |
% 31.36/10.41 |-The branch is then unsatisfiable
% 31.36/10.41 |-Branch two:
% 31.36/10.41 | (987) ~ (all_0_8_8 = n6)
% 31.36/10.41 | (988) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.36/10.41 |
% 31.36/10.41 +-Applying beta-rule and splitting (988), into two cases.
% 31.36/10.41 |-Branch one:
% 31.36/10.41 | (989) all_0_8_8 = n5
% 31.36/10.41 |
% 31.36/10.41 | From (989) and (5677) follows:
% 31.36/10.41 | (5798) sum(n5, n13) = all_0_4_4
% 31.36/10.41 |
% 31.36/10.41 | From (989) and (5675) follows:
% 31.36/10.41 | (5799) sum(n5, n12) = all_0_2_2
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n5, n13, all_0_4_4, n18 and discharging atoms sum(n5, n13) = all_0_4_4, sum(n5, n13) = n18, yields:
% 31.36/10.41 | (772) all_0_4_4 = n18
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n5, n12, all_0_2_2, n17 and discharging atoms sum(n5, n12) = all_0_2_2, sum(n5, n12) = n17, yields:
% 31.36/10.41 | (771) all_0_2_2 = n17
% 31.36/10.41 |
% 31.36/10.41 | From (771) and (473) follows:
% 31.36/10.41 | (773) pred(n17) = all_0_1_1
% 31.36/10.41 |
% 31.36/10.41 | From (772) and (716) follows:
% 31.36/10.41 | (774) pred(n18) = all_0_3_3
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 31.36/10.41 | (775) all_0_3_3 = n17
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 31.36/10.41 | (776) all_0_1_1 = n16
% 31.36/10.41 |
% 31.36/10.41 | From (775) and (232) follows:
% 31.36/10.41 | (777) sum(n17, all_0_0_0) = all_0_6_6
% 31.36/10.41 |
% 31.36/10.41 | From (776) and (1228) follows:
% 31.36/10.41 | (5807) sum(n12, n16) = all_0_0_0
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n12, n16, all_0_0_0, n7 and discharging atoms sum(n12, n16) = all_0_0_0, sum(n12, n16) = n7, yields:
% 31.36/10.41 | (915) all_0_0_0 = n7
% 31.36/10.41 |
% 31.36/10.41 | From (915) and (777) follows:
% 31.36/10.41 | (5809) sum(n17, n7) = all_0_6_6
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n17, n7, all_0_6_6, n3 and discharging atoms sum(n17, n7) = all_0_6_6, sum(n17, n7) = n3, yields:
% 31.36/10.41 | (849) all_0_6_6 = n3
% 31.36/10.41 |
% 31.36/10.41 | Equations (849) can reduce 416 to:
% 31.36/10.41 | (748) $false
% 31.36/10.41 |
% 31.36/10.41 |-The branch is then unsatisfiable
% 31.36/10.41 |-Branch two:
% 31.36/10.41 | (1004) ~ (all_0_8_8 = n5)
% 31.36/10.41 | (1005) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.36/10.41 |
% 31.36/10.41 +-Applying beta-rule and splitting (1005), into two cases.
% 31.36/10.41 |-Branch one:
% 31.36/10.41 | (1006) all_0_8_8 = n4
% 31.36/10.41 |
% 31.36/10.41 | From (1006) and (5677) follows:
% 31.36/10.41 | (5815) sum(n4, n13) = all_0_4_4
% 31.36/10.41 |
% 31.36/10.41 | From (1006) and (5675) follows:
% 31.36/10.41 | (5816) sum(n4, n12) = all_0_2_2
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n4, n13, all_0_4_4, n17 and discharging atoms sum(n4, n13) = all_0_4_4, sum(n4, n13) = n17, yields:
% 31.36/10.41 | (789) all_0_4_4 = n17
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n4, n12, all_0_2_2, n16 and discharging atoms sum(n4, n12) = all_0_2_2, sum(n4, n12) = n16, yields:
% 31.36/10.41 | (788) all_0_2_2 = n16
% 31.36/10.41 |
% 31.36/10.41 | From (788) and (473) follows:
% 31.36/10.41 | (790) pred(n16) = all_0_1_1
% 31.36/10.41 |
% 31.36/10.41 | From (789) and (716) follows:
% 31.36/10.41 | (791) pred(n17) = all_0_3_3
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 31.36/10.41 | (792) all_0_3_3 = n16
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 31.36/10.41 | (793) all_0_1_1 = n15
% 31.36/10.41 |
% 31.36/10.41 | From (792) and (232) follows:
% 31.36/10.41 | (794) sum(n16, all_0_0_0) = all_0_6_6
% 31.36/10.41 |
% 31.36/10.41 | From (793) and (1228) follows:
% 31.36/10.41 | (5824) sum(n12, n15) = all_0_0_0
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n12, n15, all_0_0_0, n6 and discharging atoms sum(n12, n15) = all_0_0_0, sum(n12, n15) = n6, yields:
% 31.36/10.41 | (932) all_0_0_0 = n6
% 31.36/10.41 |
% 31.36/10.41 | From (932) and (794) follows:
% 31.36/10.41 | (5826) sum(n16, n6) = all_0_6_6
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n16, n6, all_0_6_6, n1 and discharging atoms sum(n16, n6) = all_0_6_6, sum(n16, n6) = n1, yields:
% 31.36/10.41 | (866) all_0_6_6 = n1
% 31.36/10.41 |
% 31.36/10.41 | Equations (866) can reduce 28 to:
% 31.36/10.41 | (748) $false
% 31.36/10.41 |
% 31.36/10.41 |-The branch is then unsatisfiable
% 31.36/10.41 |-Branch two:
% 31.36/10.41 | (1021) ~ (all_0_8_8 = n4)
% 31.36/10.41 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.36/10.41 |
% 31.36/10.41 +-Applying beta-rule and splitting (1022), into two cases.
% 31.36/10.41 |-Branch one:
% 31.36/10.41 | (1023) all_0_8_8 = n3
% 31.36/10.41 |
% 31.36/10.41 | From (1023) and (5677) follows:
% 31.36/10.41 | (5832) sum(n3, n13) = all_0_4_4
% 31.36/10.41 |
% 31.36/10.41 | From (1023) and (5675) follows:
% 31.36/10.41 | (5833) sum(n3, n12) = all_0_2_2
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n3, n13, all_0_4_4, n16 and discharging atoms sum(n3, n13) = all_0_4_4, sum(n3, n13) = n16, yields:
% 31.36/10.41 | (806) all_0_4_4 = n16
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n3, n12, all_0_2_2, n15 and discharging atoms sum(n3, n12) = all_0_2_2, sum(n3, n12) = n15, yields:
% 31.36/10.41 | (805) all_0_2_2 = n15
% 31.36/10.41 |
% 31.36/10.41 | From (805) and (473) follows:
% 31.36/10.41 | (807) pred(n15) = all_0_1_1
% 31.36/10.41 |
% 31.36/10.41 | From (806) and (716) follows:
% 31.36/10.41 | (808) pred(n16) = all_0_3_3
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 31.36/10.41 | (809) all_0_3_3 = n15
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 31.36/10.41 | (810) all_0_1_1 = n14
% 31.36/10.41 |
% 31.36/10.41 | From (809) and (232) follows:
% 31.36/10.41 | (811) sum(n15, all_0_0_0) = all_0_6_6
% 31.36/10.41 |
% 31.36/10.41 | From (810) and (1228) follows:
% 31.36/10.41 | (5841) sum(n12, n14) = all_0_0_0
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n12, n14, all_0_0_0, n5 and discharging atoms sum(n12, n14) = all_0_0_0, sum(n12, n14) = n5, yields:
% 31.36/10.41 | (949) all_0_0_0 = n5
% 31.36/10.41 |
% 31.36/10.41 | From (949) and (811) follows:
% 31.36/10.41 | (5843) sum(n15, n5) = all_0_6_6
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n15, n5, all_0_6_6, n20 and discharging atoms sum(n15, n5) = all_0_6_6, sum(n15, n5) = n20, yields:
% 31.36/10.41 | (883) all_0_6_6 = n20
% 31.36/10.41 |
% 31.36/10.41 | Equations (883) can reduce 381 to:
% 31.36/10.41 | (748) $false
% 31.36/10.41 |
% 31.36/10.41 |-The branch is then unsatisfiable
% 31.36/10.41 |-Branch two:
% 31.36/10.41 | (1038) ~ (all_0_8_8 = n3)
% 31.36/10.41 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.36/10.41 |
% 31.36/10.41 +-Applying beta-rule and splitting (1039), into two cases.
% 31.36/10.41 |-Branch one:
% 31.36/10.41 | (1040) all_0_8_8 = n2
% 31.36/10.41 |
% 31.36/10.41 | From (1040) and (5677) follows:
% 31.36/10.41 | (5849) sum(n2, n13) = all_0_4_4
% 31.36/10.41 |
% 31.36/10.41 | From (1040) and (5675) follows:
% 31.36/10.41 | (5850) sum(n2, n12) = all_0_2_2
% 31.36/10.41 |
% 31.36/10.41 | Instantiating formula (619) with n2, n13, all_0_4_4, n15 and discharging atoms sum(n2, n13) = all_0_4_4, sum(n2, n13) = n15, yields:
% 31.36/10.42 | (823) all_0_4_4 = n15
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n2, n12, all_0_2_2, n14 and discharging atoms sum(n2, n12) = all_0_2_2, sum(n2, n12) = n14, yields:
% 31.36/10.42 | (822) all_0_2_2 = n14
% 31.36/10.42 |
% 31.36/10.42 | From (822) and (473) follows:
% 31.36/10.42 | (824) pred(n14) = all_0_1_1
% 31.36/10.42 |
% 31.36/10.42 | From (823) and (716) follows:
% 31.36/10.42 | (825) pred(n15) = all_0_3_3
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 31.36/10.42 | (826) all_0_3_3 = n14
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 31.36/10.42 | (827) all_0_1_1 = n13
% 31.36/10.42 |
% 31.36/10.42 | From (826) and (232) follows:
% 31.36/10.42 | (828) sum(n14, all_0_0_0) = all_0_6_6
% 31.36/10.42 |
% 31.36/10.42 | From (827) and (1228) follows:
% 31.36/10.42 | (5858) sum(n12, n13) = all_0_0_0
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n12, n13, all_0_0_0, n4 and discharging atoms sum(n12, n13) = all_0_0_0, sum(n12, n13) = n4, yields:
% 31.36/10.42 | (966) all_0_0_0 = n4
% 31.36/10.42 |
% 31.36/10.42 | From (966) and (828) follows:
% 31.36/10.42 | (5860) sum(n14, n4) = all_0_6_6
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n14, n4, all_0_6_6, n18 and discharging atoms sum(n14, n4) = all_0_6_6, sum(n14, n4) = n18, yields:
% 31.36/10.42 | (900) all_0_6_6 = n18
% 31.36/10.42 |
% 31.36/10.42 | Equations (900) can reduce 622 to:
% 31.36/10.42 | (748) $false
% 31.36/10.42 |
% 31.36/10.42 |-The branch is then unsatisfiable
% 31.36/10.42 |-Branch two:
% 31.36/10.42 | (1055) ~ (all_0_8_8 = n2)
% 31.36/10.42 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 31.36/10.42 |
% 31.36/10.42 +-Applying beta-rule and splitting (1056), into two cases.
% 31.36/10.42 |-Branch one:
% 31.36/10.42 | (1057) all_0_8_8 = n1
% 31.36/10.42 |
% 31.36/10.42 | From (1057) and (5677) follows:
% 31.36/10.42 | (5866) sum(n1, n13) = all_0_4_4
% 31.36/10.42 |
% 31.36/10.42 | From (1057) and (5675) follows:
% 31.36/10.42 | (5867) sum(n1, n12) = all_0_2_2
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n1, n13, all_0_4_4, n14 and discharging atoms sum(n1, n13) = all_0_4_4, sum(n1, n13) = n14, yields:
% 31.36/10.42 | (840) all_0_4_4 = n14
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n1, n12, all_0_2_2, n13 and discharging atoms sum(n1, n12) = all_0_2_2, sum(n1, n12) = n13, yields:
% 31.36/10.42 | (839) all_0_2_2 = n13
% 31.36/10.42 |
% 31.36/10.42 | From (839) and (473) follows:
% 31.36/10.42 | (841) pred(n13) = all_0_1_1
% 31.36/10.42 |
% 31.36/10.42 | From (840) and (716) follows:
% 31.36/10.42 | (842) pred(n14) = all_0_3_3
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 31.36/10.42 | (843) all_0_3_3 = n13
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 31.36/10.42 | (844) all_0_1_1 = n12
% 31.36/10.42 |
% 31.36/10.42 | From (843) and (232) follows:
% 31.36/10.42 | (845) sum(n13, all_0_0_0) = all_0_6_6
% 31.36/10.42 |
% 31.36/10.42 | From (844) and (1228) follows:
% 31.36/10.42 | (5875) sum(n12, n12) = all_0_0_0
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n12, n12, all_0_0_0, n3 and discharging atoms sum(n12, n12) = all_0_0_0, sum(n12, n12) = n3, yields:
% 31.36/10.42 | (983) all_0_0_0 = n3
% 31.36/10.42 |
% 31.36/10.42 | From (983) and (845) follows:
% 31.36/10.42 | (5877) sum(n13, n3) = all_0_6_6
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n13, n3, all_0_6_6, n16 and discharging atoms sum(n13, n3) = all_0_6_6, sum(n13, n3) = n16, yields:
% 31.36/10.42 | (917) all_0_6_6 = n16
% 31.36/10.42 |
% 31.36/10.42 | Equations (917) can reduce 163 to:
% 31.36/10.42 | (748) $false
% 31.36/10.42 |
% 31.36/10.42 |-The branch is then unsatisfiable
% 31.36/10.42 |-Branch two:
% 31.36/10.42 | (1072) ~ (all_0_8_8 = n1)
% 31.36/10.42 | (1073) all_0_8_8 = n0
% 31.36/10.42 |
% 31.36/10.42 | From (1073) and (5677) follows:
% 31.36/10.42 | (5882) sum(n0, n13) = all_0_4_4
% 31.36/10.42 |
% 31.36/10.42 | From (1073) and (5675) follows:
% 31.36/10.42 | (5883) sum(n0, n12) = all_0_2_2
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n0, n13, all_0_4_4, n13 and discharging atoms sum(n0, n13) = all_0_4_4, sum(n0, n13) = n13, yields:
% 31.36/10.42 | (857) all_0_4_4 = n13
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n0, n12, all_0_2_2, n12 and discharging atoms sum(n0, n12) = all_0_2_2, sum(n0, n12) = n12, yields:
% 31.36/10.42 | (856) all_0_2_2 = n12
% 31.36/10.42 |
% 31.36/10.42 | From (856) and (473) follows:
% 31.36/10.42 | (858) pred(n12) = all_0_1_1
% 31.36/10.42 |
% 31.36/10.42 | From (857) and (716) follows:
% 31.36/10.42 | (859) pred(n13) = all_0_3_3
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 31.36/10.42 | (860) all_0_3_3 = n12
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 31.36/10.42 | (861) all_0_1_1 = n11
% 31.36/10.42 |
% 31.36/10.42 | From (860) and (232) follows:
% 31.36/10.42 | (862) sum(n12, all_0_0_0) = all_0_6_6
% 31.36/10.42 |
% 31.36/10.42 | From (861) and (1228) follows:
% 31.36/10.42 | (5891) sum(n12, n11) = all_0_0_0
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n12, n11, all_0_0_0, n2 and discharging atoms sum(n12, n11) = all_0_0_0, sum(n12, n11) = n2, yields:
% 31.36/10.42 | (1000) all_0_0_0 = n2
% 31.36/10.42 |
% 31.36/10.42 | From (1000) and (862) follows:
% 31.36/10.42 | (5893) sum(n12, n2) = all_0_6_6
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n12, n2, all_0_6_6, n14 and discharging atoms sum(n12, n2) = all_0_6_6, sum(n12, n2) = n14, yields:
% 31.36/10.42 | (934) all_0_6_6 = n14
% 31.36/10.42 |
% 31.36/10.42 | Equations (934) can reduce 353 to:
% 31.36/10.42 | (748) $false
% 31.36/10.42 |
% 31.36/10.42 |-The branch is then unsatisfiable
% 31.36/10.42 |-Branch two:
% 31.36/10.42 | (1243) ~ (all_0_7_7 = n12)
% 31.36/10.42 | (1244) all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.36/10.42 |
% 31.36/10.42 +-Applying beta-rule and splitting (869), into two cases.
% 31.36/10.42 |-Branch one:
% 31.36/10.42 | (870) all_0_8_8 = n12
% 31.36/10.42 |
% 31.36/10.42 | From (870) and (708) follows:
% 31.36/10.42 | (5899) sum(n12, all_0_5_5) = all_0_4_4
% 31.36/10.42 |
% 31.36/10.42 | From (870) and (378) follows:
% 31.36/10.42 | (5900) sum(n12, all_0_7_7) = all_0_2_2
% 31.36/10.42 |
% 31.36/10.42 +-Applying beta-rule and splitting (1244), into two cases.
% 31.36/10.42 |-Branch one:
% 31.36/10.42 | (1245) all_0_7_7 = n11
% 31.36/10.42 |
% 31.36/10.42 | From (1245) and (683) follows:
% 31.36/10.42 | (1246) succ(n11) = all_0_5_5
% 31.36/10.42 |
% 31.36/10.42 | From (1245) and (8) follows:
% 31.36/10.42 | (1247) sum(n11, all_0_1_1) = all_0_0_0
% 31.36/10.42 |
% 31.36/10.42 | From (1245) and (5900) follows:
% 31.36/10.42 | (5904) sum(n12, n11) = all_0_2_2
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (388) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 31.36/10.42 | (1249) all_0_5_5 = n12
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n12, n11, all_0_2_2, n2 and discharging atoms sum(n12, n11) = all_0_2_2, sum(n12, n11) = n2, yields:
% 31.36/10.42 | (1026) all_0_2_2 = n2
% 31.36/10.42 |
% 31.36/10.42 | From (1026) and (473) follows:
% 31.36/10.42 | (1028) pred(n2) = all_0_1_1
% 31.36/10.42 |
% 31.36/10.42 | From (1249) and (5899) follows:
% 31.36/10.42 | (5908) sum(n12, n12) = all_0_4_4
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 31.36/10.42 | (1031) all_0_1_1 = n1
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n12, n12, all_0_4_4, n3 and discharging atoms sum(n12, n12) = all_0_4_4, sum(n12, n12) = n3, yields:
% 31.36/10.42 | (1027) all_0_4_4 = n3
% 31.36/10.42 |
% 31.36/10.42 | From (1027) and (716) follows:
% 31.36/10.42 | (1029) pred(n3) = all_0_3_3
% 31.36/10.42 |
% 31.36/10.42 | From (1031) and (1247) follows:
% 31.36/10.42 | (5912) sum(n11, n1) = all_0_0_0
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 31.36/10.42 | (1030) all_0_3_3 = n2
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n11, n1, all_0_0_0, n12 and discharging atoms sum(n11, n1) = all_0_0_0, sum(n11, n1) = n12, yields:
% 31.36/10.42 | (830) all_0_0_0 = n12
% 31.36/10.42 |
% 31.36/10.42 | From (1030)(830) and (232) follows:
% 31.36/10.42 | (5915) sum(n2, n12) = all_0_6_6
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n2, n12, all_0_6_6, n14 and discharging atoms sum(n2, n12) = all_0_6_6, sum(n2, n12) = n14, yields:
% 31.36/10.42 | (934) all_0_6_6 = n14
% 31.36/10.42 |
% 31.36/10.42 | Equations (934) can reduce 353 to:
% 31.36/10.42 | (748) $false
% 31.36/10.42 |
% 31.36/10.42 |-The branch is then unsatisfiable
% 31.36/10.42 |-Branch two:
% 31.36/10.42 | (1262) ~ (all_0_7_7 = n11)
% 31.36/10.42 | (1263) all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.36/10.42 |
% 31.36/10.42 +-Applying beta-rule and splitting (1263), into two cases.
% 31.36/10.42 |-Branch one:
% 31.36/10.42 | (1264) all_0_7_7 = n10
% 31.36/10.42 |
% 31.36/10.42 | From (1264) and (683) follows:
% 31.36/10.42 | (1265) succ(n10) = all_0_5_5
% 31.36/10.42 |
% 31.36/10.42 | From (1264) and (8) follows:
% 31.36/10.42 | (1266) sum(n10, all_0_1_1) = all_0_0_0
% 31.36/10.42 |
% 31.36/10.42 | From (1264) and (5900) follows:
% 31.36/10.42 | (5923) sum(n12, n10) = all_0_2_2
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (388) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 31.36/10.42 | (1268) all_0_5_5 = n11
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n12, n10, all_0_2_2, n1 and discharging atoms sum(n12, n10) = all_0_2_2, sum(n12, n10) = n1, yields:
% 31.36/10.42 | (1043) all_0_2_2 = n1
% 31.36/10.42 |
% 31.36/10.42 | From (1043) and (473) follows:
% 31.36/10.42 | (1045) pred(n1) = all_0_1_1
% 31.36/10.42 |
% 31.36/10.42 | From (1268) and (5899) follows:
% 31.36/10.42 | (5927) sum(n12, n11) = all_0_4_4
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 31.36/10.42 | (1048) all_0_1_1 = n0
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n12, n11, all_0_4_4, n2 and discharging atoms sum(n12, n11) = all_0_4_4, sum(n12, n11) = n2, yields:
% 31.36/10.42 | (1044) all_0_4_4 = n2
% 31.36/10.42 |
% 31.36/10.42 | From (1044) and (716) follows:
% 31.36/10.42 | (1046) pred(n2) = all_0_3_3
% 31.36/10.42 |
% 31.36/10.42 | From (1048) and (1266) follows:
% 31.36/10.42 | (5931) sum(n10, n0) = all_0_0_0
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 31.36/10.42 | (1047) all_0_3_3 = n1
% 31.36/10.42 |
% 31.36/10.42 | Instantiating formula (619) with n10, n0, all_0_0_0, n10 and discharging atoms sum(n10, n0) = all_0_0_0, sum(n10, n0) = n10, yields:
% 31.36/10.42 | (864) all_0_0_0 = n10
% 31.36/10.42 |
% 31.36/10.42 | From (1047)(864) and (232) follows:
% 31.36/10.43 | (5934) sum(n1, n10) = all_0_6_6
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n1, n10, all_0_6_6, n11 and discharging atoms sum(n1, n10) = all_0_6_6, sum(n1, n10) = n11, yields:
% 31.36/10.43 | (781) all_0_6_6 = n11
% 31.36/10.43 |
% 31.36/10.43 | Equations (781) can reduce 2 to:
% 31.36/10.43 | (748) $false
% 31.36/10.43 |
% 31.36/10.43 |-The branch is then unsatisfiable
% 31.36/10.43 |-Branch two:
% 31.36/10.43 | (1281) ~ (all_0_7_7 = n10)
% 31.36/10.43 | (1282) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.36/10.43 |
% 31.36/10.43 +-Applying beta-rule and splitting (1282), into two cases.
% 31.36/10.43 |-Branch one:
% 31.36/10.43 | (1283) all_0_7_7 = n9
% 31.36/10.43 |
% 31.36/10.43 | From (1283) and (683) follows:
% 31.36/10.43 | (1284) succ(n9) = all_0_5_5
% 31.36/10.43 |
% 31.36/10.43 | From (1283) and (8) follows:
% 31.36/10.43 | (1285) sum(n9, all_0_1_1) = all_0_0_0
% 31.36/10.43 |
% 31.36/10.43 | From (1283) and (5900) follows:
% 31.36/10.43 | (5942) sum(n12, n9) = all_0_2_2
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (388) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 31.36/10.43 | (1287) all_0_5_5 = n10
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n12, n9, all_0_2_2, n0 and discharging atoms sum(n12, n9) = all_0_2_2, sum(n12, n9) = n0, yields:
% 31.36/10.43 | (1060) all_0_2_2 = n0
% 31.36/10.43 |
% 31.36/10.43 | From (1060) and (473) follows:
% 31.36/10.43 | (1062) pred(n0) = all_0_1_1
% 31.36/10.43 |
% 31.36/10.43 | From (1287) and (5899) follows:
% 31.36/10.43 | (5946) sum(n12, n10) = all_0_4_4
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 31.36/10.43 | (1065) all_0_1_1 = n20
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n12, n10, all_0_4_4, n1 and discharging atoms sum(n12, n10) = all_0_4_4, sum(n12, n10) = n1, yields:
% 31.36/10.43 | (1061) all_0_4_4 = n1
% 31.36/10.43 |
% 31.36/10.43 | From (1061) and (716) follows:
% 31.36/10.43 | (1063) pred(n1) = all_0_3_3
% 31.36/10.43 |
% 31.36/10.43 | From (1065) and (1285) follows:
% 31.36/10.43 | (5950) sum(n9, n20) = all_0_0_0
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 31.36/10.43 | (1064) all_0_3_3 = n0
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n9, n20, all_0_0_0, n8 and discharging atoms sum(n9, n20) = all_0_0_0, sum(n9, n20) = n8, yields:
% 31.36/10.43 | (898) all_0_0_0 = n8
% 31.36/10.43 |
% 31.36/10.43 | From (1064)(898) and (232) follows:
% 31.36/10.43 | (5953) sum(n0, n8) = all_0_6_6
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n0, n8, all_0_6_6, n8 and discharging atoms sum(n0, n8) = all_0_6_6, sum(n0, n8) = n8, yields:
% 31.36/10.43 | (985) all_0_6_6 = n8
% 31.36/10.43 |
% 31.36/10.43 | Equations (985) can reduce 357 to:
% 31.36/10.43 | (748) $false
% 31.36/10.43 |
% 31.36/10.43 |-The branch is then unsatisfiable
% 31.36/10.43 |-Branch two:
% 31.36/10.43 | (1300) ~ (all_0_7_7 = n9)
% 31.36/10.43 | (1301) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.36/10.43 |
% 31.36/10.43 +-Applying beta-rule and splitting (1301), into two cases.
% 31.36/10.43 |-Branch one:
% 31.36/10.43 | (1302) all_0_7_7 = n8
% 31.36/10.43 |
% 31.36/10.43 | From (1302) and (683) follows:
% 31.36/10.43 | (1303) succ(n8) = all_0_5_5
% 31.36/10.43 |
% 31.36/10.43 | From (1302) and (8) follows:
% 31.36/10.43 | (1304) sum(n8, all_0_1_1) = all_0_0_0
% 31.36/10.43 |
% 31.36/10.43 | From (1302) and (5900) follows:
% 31.36/10.43 | (5961) sum(n12, n8) = all_0_2_2
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (388) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 31.36/10.43 | (1306) all_0_5_5 = n9
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n12, n8, all_0_2_2, n20 and discharging atoms sum(n12, n8) = all_0_2_2, sum(n12, n8) = n20, yields:
% 31.36/10.43 | (1076) all_0_2_2 = n20
% 31.36/10.43 |
% 31.36/10.43 | From (1076) and (473) follows:
% 31.36/10.43 | (1078) pred(n20) = all_0_1_1
% 31.36/10.43 |
% 31.36/10.43 | From (1306) and (5899) follows:
% 31.36/10.43 | (5965) sum(n12, n9) = all_0_4_4
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 31.36/10.43 | (1080) all_0_1_1 = n19
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n12, n9, all_0_4_4, n0 and discharging atoms sum(n12, n9) = all_0_4_4, sum(n12, n9) = n0, yields:
% 31.36/10.43 | (1077) all_0_4_4 = n0
% 31.36/10.43 |
% 31.36/10.43 | From (1077) and (716) follows:
% 31.36/10.43 | (1079) pred(n0) = all_0_3_3
% 31.36/10.43 |
% 31.36/10.43 | From (1080) and (1304) follows:
% 31.36/10.43 | (5969) sum(n8, n19) = all_0_0_0
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 31.36/10.43 | (1081) all_0_3_3 = n20
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n8, n19, all_0_0_0, n6 and discharging atoms sum(n8, n19) = all_0_0_0, sum(n8, n19) = n6, yields:
% 31.36/10.43 | (932) all_0_0_0 = n6
% 31.36/10.43 |
% 31.36/10.43 | From (1081)(932) and (232) follows:
% 31.36/10.43 | (5972) sum(n20, n6) = all_0_6_6
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n20, n6, all_0_6_6, n5 and discharging atoms sum(n20, n6) = all_0_6_6, sum(n20, n6) = n5, yields:
% 31.36/10.43 | (832) all_0_6_6 = n5
% 31.36/10.43 |
% 31.36/10.43 | Equations (832) can reduce 462 to:
% 31.36/10.43 | (748) $false
% 31.36/10.43 |
% 31.36/10.43 |-The branch is then unsatisfiable
% 31.36/10.43 |-Branch two:
% 31.36/10.43 | (1319) ~ (all_0_7_7 = n8)
% 31.36/10.43 | (1320) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.36/10.43 |
% 31.36/10.43 +-Applying beta-rule and splitting (1320), into two cases.
% 31.36/10.43 |-Branch one:
% 31.36/10.43 | (1321) all_0_7_7 = n7
% 31.36/10.43 |
% 31.36/10.43 | From (1321) and (683) follows:
% 31.36/10.43 | (1322) succ(n7) = all_0_5_5
% 31.36/10.43 |
% 31.36/10.43 | From (1321) and (8) follows:
% 31.36/10.43 | (1323) sum(n7, all_0_1_1) = all_0_0_0
% 31.36/10.43 |
% 31.36/10.43 | From (1321) and (5900) follows:
% 31.36/10.43 | (5980) sum(n12, n7) = all_0_2_2
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (388) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 31.36/10.43 | (1325) all_0_5_5 = n8
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n12, n7, all_0_2_2, n19 and discharging atoms sum(n12, n7) = all_0_2_2, sum(n12, n7) = n19, yields:
% 31.36/10.43 | (737) all_0_2_2 = n19
% 31.36/10.43 |
% 31.36/10.43 | From (737) and (473) follows:
% 31.36/10.43 | (739) pred(n19) = all_0_1_1
% 31.36/10.43 |
% 31.36/10.43 | From (1325) and (5899) follows:
% 31.36/10.43 | (5984) sum(n12, n8) = all_0_4_4
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 31.36/10.43 | (742) all_0_1_1 = n18
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n12, n8, all_0_4_4, n20 and discharging atoms sum(n12, n8) = all_0_4_4, sum(n12, n8) = n20, yields:
% 31.36/10.43 | (738) all_0_4_4 = n20
% 31.36/10.43 |
% 31.36/10.43 | From (738) and (716) follows:
% 31.36/10.43 | (740) pred(n20) = all_0_3_3
% 31.36/10.43 |
% 31.36/10.43 | From (742) and (1323) follows:
% 31.36/10.43 | (5988) sum(n7, n18) = all_0_0_0
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 31.36/10.43 | (741) all_0_3_3 = n19
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n7, n18, all_0_0_0, n4 and discharging atoms sum(n7, n18) = all_0_0_0, sum(n7, n18) = n4, yields:
% 31.36/10.43 | (966) all_0_0_0 = n4
% 31.36/10.43 |
% 31.36/10.43 | From (741)(966) and (232) follows:
% 31.36/10.43 | (5991) sum(n19, n4) = all_0_6_6
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n19, n4, all_0_6_6, n2 and discharging atoms sum(n19, n4) = all_0_6_6, sum(n19, n4) = n2, yields:
% 31.36/10.43 | (1036) all_0_6_6 = n2
% 31.36/10.43 |
% 31.36/10.43 | Equations (1036) can reduce 56 to:
% 31.36/10.43 | (748) $false
% 31.36/10.43 |
% 31.36/10.43 |-The branch is then unsatisfiable
% 31.36/10.43 |-Branch two:
% 31.36/10.43 | (1338) ~ (all_0_7_7 = n7)
% 31.36/10.43 | (1339) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.36/10.43 |
% 31.36/10.43 +-Applying beta-rule and splitting (1339), into two cases.
% 31.36/10.43 |-Branch one:
% 31.36/10.43 | (1340) all_0_7_7 = n6
% 31.36/10.43 |
% 31.36/10.43 | From (1340) and (683) follows:
% 31.36/10.43 | (1341) succ(n6) = all_0_5_5
% 31.36/10.43 |
% 31.36/10.43 | From (1340) and (8) follows:
% 31.36/10.43 | (1342) sum(n6, all_0_1_1) = all_0_0_0
% 31.36/10.43 |
% 31.36/10.43 | From (1340) and (5900) follows:
% 31.36/10.43 | (5999) sum(n12, n6) = all_0_2_2
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (388) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 31.36/10.43 | (1344) all_0_5_5 = n7
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n12, n6, all_0_2_2, n18 and discharging atoms sum(n12, n6) = all_0_2_2, sum(n12, n6) = n18, yields:
% 31.36/10.43 | (754) all_0_2_2 = n18
% 31.36/10.43 |
% 31.36/10.43 | From (754) and (473) follows:
% 31.36/10.43 | (756) pred(n18) = all_0_1_1
% 31.36/10.43 |
% 31.36/10.43 | From (1344) and (5899) follows:
% 31.36/10.43 | (6003) sum(n12, n7) = all_0_4_4
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 31.36/10.43 | (759) all_0_1_1 = n17
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n12, n7, all_0_4_4, n19 and discharging atoms sum(n12, n7) = all_0_4_4, sum(n12, n7) = n19, yields:
% 31.36/10.43 | (755) all_0_4_4 = n19
% 31.36/10.43 |
% 31.36/10.43 | From (755) and (716) follows:
% 31.36/10.43 | (757) pred(n19) = all_0_3_3
% 31.36/10.43 |
% 31.36/10.43 | From (759) and (1342) follows:
% 31.36/10.43 | (6007) sum(n6, n17) = all_0_0_0
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 31.36/10.43 | (758) all_0_3_3 = n18
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n6, n17, all_0_0_0, n2 and discharging atoms sum(n6, n17) = all_0_0_0, sum(n6, n17) = n2, yields:
% 31.36/10.43 | (1000) all_0_0_0 = n2
% 31.36/10.43 |
% 31.36/10.43 | From (758)(1000) and (232) follows:
% 31.36/10.43 | (6010) sum(n18, n2) = all_0_6_6
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n18, n2, all_0_6_6, n20 and discharging atoms sum(n18, n2) = all_0_6_6, sum(n18, n2) = n20, yields:
% 31.36/10.43 | (883) all_0_6_6 = n20
% 31.36/10.43 |
% 31.36/10.43 | Equations (883) can reduce 381 to:
% 31.36/10.43 | (748) $false
% 31.36/10.43 |
% 31.36/10.43 |-The branch is then unsatisfiable
% 31.36/10.43 |-Branch two:
% 31.36/10.43 | (1357) ~ (all_0_7_7 = n6)
% 31.36/10.43 | (1358) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.36/10.43 |
% 31.36/10.43 +-Applying beta-rule and splitting (1358), into two cases.
% 31.36/10.43 |-Branch one:
% 31.36/10.43 | (1359) all_0_7_7 = n5
% 31.36/10.43 |
% 31.36/10.43 | From (1359) and (683) follows:
% 31.36/10.43 | (1360) succ(n5) = all_0_5_5
% 31.36/10.43 |
% 31.36/10.43 | From (1359) and (8) follows:
% 31.36/10.43 | (1361) sum(n5, all_0_1_1) = all_0_0_0
% 31.36/10.43 |
% 31.36/10.43 | From (1359) and (5900) follows:
% 31.36/10.43 | (6018) sum(n12, n5) = all_0_2_2
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (388) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 31.36/10.43 | (1363) all_0_5_5 = n6
% 31.36/10.43 |
% 31.36/10.43 | Instantiating formula (619) with n12, n5, all_0_2_2, n17 and discharging atoms sum(n12, n5) = all_0_2_2, sum(n12, n5) = n17, yields:
% 31.36/10.44 | (771) all_0_2_2 = n17
% 31.36/10.44 |
% 31.36/10.44 | From (771) and (473) follows:
% 31.36/10.44 | (773) pred(n17) = all_0_1_1
% 31.36/10.44 |
% 31.36/10.44 | From (1363) and (5899) follows:
% 31.36/10.44 | (6022) sum(n12, n6) = all_0_4_4
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 31.36/10.44 | (776) all_0_1_1 = n16
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n12, n6, all_0_4_4, n18 and discharging atoms sum(n12, n6) = all_0_4_4, sum(n12, n6) = n18, yields:
% 31.36/10.44 | (772) all_0_4_4 = n18
% 31.36/10.44 |
% 31.36/10.44 | From (772) and (716) follows:
% 31.36/10.44 | (774) pred(n18) = all_0_3_3
% 31.36/10.44 |
% 31.36/10.44 | From (776) and (1361) follows:
% 31.36/10.44 | (6026) sum(n5, n16) = all_0_0_0
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 31.36/10.44 | (775) all_0_3_3 = n17
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n5, n16, all_0_0_0, n0 and discharging atoms sum(n5, n16) = all_0_0_0, sum(n5, n16) = n0, yields:
% 31.36/10.44 | (1034) all_0_0_0 = n0
% 31.36/10.44 |
% 31.36/10.44 | From (775)(1034) and (232) follows:
% 31.36/10.44 | (6029) sum(n17, n0) = all_0_6_6
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n17, n0, all_0_6_6, n17 and discharging atoms sum(n17, n0) = all_0_6_6, sum(n17, n0) = n17, yields:
% 31.36/10.44 | (1086) all_0_6_6 = n17
% 31.36/10.44 |
% 31.36/10.44 | Equations (1086) can reduce 669 to:
% 31.36/10.44 | (748) $false
% 31.36/10.44 |
% 31.36/10.44 |-The branch is then unsatisfiable
% 31.36/10.44 |-Branch two:
% 31.36/10.44 | (1376) ~ (all_0_7_7 = n5)
% 31.36/10.44 | (1377) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.36/10.44 |
% 31.36/10.44 +-Applying beta-rule and splitting (1377), into two cases.
% 31.36/10.44 |-Branch one:
% 31.36/10.44 | (1378) all_0_7_7 = n4
% 31.36/10.44 |
% 31.36/10.44 | From (1378) and (683) follows:
% 31.36/10.44 | (1379) succ(n4) = all_0_5_5
% 31.36/10.44 |
% 31.36/10.44 | From (1378) and (8) follows:
% 31.36/10.44 | (1380) sum(n4, all_0_1_1) = all_0_0_0
% 31.36/10.44 |
% 31.36/10.44 | From (1378) and (5900) follows:
% 31.36/10.44 | (6037) sum(n12, n4) = all_0_2_2
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (388) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 31.36/10.44 | (1382) all_0_5_5 = n5
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n12, n4, all_0_2_2, n16 and discharging atoms sum(n12, n4) = all_0_2_2, sum(n12, n4) = n16, yields:
% 31.36/10.44 | (788) all_0_2_2 = n16
% 31.36/10.44 |
% 31.36/10.44 | From (788) and (473) follows:
% 31.36/10.44 | (790) pred(n16) = all_0_1_1
% 31.36/10.44 |
% 31.36/10.44 | From (1382) and (5899) follows:
% 31.36/10.44 | (6041) sum(n12, n5) = all_0_4_4
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 31.36/10.44 | (793) all_0_1_1 = n15
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n12, n5, all_0_4_4, n17 and discharging atoms sum(n12, n5) = all_0_4_4, sum(n12, n5) = n17, yields:
% 31.36/10.44 | (789) all_0_4_4 = n17
% 31.36/10.44 |
% 31.36/10.44 | From (789) and (716) follows:
% 31.36/10.44 | (791) pred(n17) = all_0_3_3
% 31.36/10.44 |
% 31.36/10.44 | From (793) and (1380) follows:
% 31.36/10.44 | (6045) sum(n4, n15) = all_0_0_0
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 31.36/10.44 | (792) all_0_3_3 = n16
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n4, n15, all_0_0_0, n19 and discharging atoms sum(n4, n15) = all_0_0_0, sum(n4, n15) = n19, yields:
% 31.36/10.44 | (1068) all_0_0_0 = n19
% 31.36/10.44 |
% 31.36/10.44 | From (792)(1068) and (232) follows:
% 31.36/10.44 | (6048) sum(n16, n19) = all_0_6_6
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n16, n19, all_0_6_6, n14 and discharging atoms sum(n16, n19) = all_0_6_6, sum(n16, n19) = n14, yields:
% 31.36/10.44 | (934) all_0_6_6 = n14
% 31.36/10.44 |
% 31.36/10.44 | Equations (934) can reduce 353 to:
% 31.36/10.44 | (748) $false
% 31.36/10.44 |
% 31.36/10.44 |-The branch is then unsatisfiable
% 31.36/10.44 |-Branch two:
% 31.36/10.44 | (1395) ~ (all_0_7_7 = n4)
% 31.36/10.44 | (1396) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.36/10.44 |
% 31.36/10.44 +-Applying beta-rule and splitting (1396), into two cases.
% 31.36/10.44 |-Branch one:
% 31.36/10.44 | (1397) all_0_7_7 = n3
% 31.36/10.44 |
% 31.36/10.44 | From (1397) and (683) follows:
% 31.36/10.44 | (1398) succ(n3) = all_0_5_5
% 31.36/10.44 |
% 31.36/10.44 | From (1397) and (8) follows:
% 31.36/10.44 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 31.36/10.44 |
% 31.36/10.44 | From (1397) and (5900) follows:
% 31.36/10.44 | (6056) sum(n12, n3) = all_0_2_2
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 31.36/10.44 | (1401) all_0_5_5 = n4
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n12, n3, all_0_2_2, n15 and discharging atoms sum(n12, n3) = all_0_2_2, sum(n12, n3) = n15, yields:
% 31.36/10.44 | (805) all_0_2_2 = n15
% 31.36/10.44 |
% 31.36/10.44 | From (805) and (473) follows:
% 31.36/10.44 | (807) pred(n15) = all_0_1_1
% 31.36/10.44 |
% 31.36/10.44 | From (1401) and (5899) follows:
% 31.36/10.44 | (6060) sum(n12, n4) = all_0_4_4
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 31.36/10.44 | (810) all_0_1_1 = n14
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n12, n4, all_0_4_4, n16 and discharging atoms sum(n12, n4) = all_0_4_4, sum(n12, n4) = n16, yields:
% 31.36/10.44 | (806) all_0_4_4 = n16
% 31.36/10.44 |
% 31.36/10.44 | From (806) and (716) follows:
% 31.36/10.44 | (808) pred(n16) = all_0_3_3
% 31.36/10.44 |
% 31.36/10.44 | From (810) and (1399) follows:
% 31.36/10.44 | (6064) sum(n3, n14) = all_0_0_0
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 31.36/10.44 | (809) all_0_3_3 = n15
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n3, n14, all_0_0_0, n17 and discharging atoms sum(n3, n14) = all_0_0_0, sum(n3, n14) = n17, yields:
% 31.36/10.44 | (745) all_0_0_0 = n17
% 31.36/10.44 |
% 31.36/10.44 | From (809)(745) and (232) follows:
% 31.36/10.44 | (6067) sum(n15, n17) = all_0_6_6
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n15, n17, all_0_6_6, n11 and discharging atoms sum(n15, n17) = all_0_6_6, sum(n15, n17) = n11, yields:
% 31.36/10.44 | (781) all_0_6_6 = n11
% 31.36/10.44 |
% 31.36/10.44 | Equations (781) can reduce 2 to:
% 31.36/10.44 | (748) $false
% 31.36/10.44 |
% 31.36/10.44 |-The branch is then unsatisfiable
% 31.36/10.44 |-Branch two:
% 31.36/10.44 | (1414) ~ (all_0_7_7 = n3)
% 31.36/10.44 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.36/10.44 |
% 31.36/10.44 +-Applying beta-rule and splitting (1415), into two cases.
% 31.36/10.44 |-Branch one:
% 31.36/10.44 | (1416) all_0_7_7 = n2
% 31.36/10.44 |
% 31.36/10.44 | From (1416) and (683) follows:
% 31.36/10.44 | (1417) succ(n2) = all_0_5_5
% 31.36/10.44 |
% 31.36/10.44 | From (1416) and (8) follows:
% 31.36/10.44 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 31.36/10.44 |
% 31.36/10.44 | From (1416) and (5900) follows:
% 31.36/10.44 | (6075) sum(n12, n2) = all_0_2_2
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.36/10.44 | (1420) all_0_5_5 = n3
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n12, n2, all_0_2_2, n14 and discharging atoms sum(n12, n2) = all_0_2_2, sum(n12, n2) = n14, yields:
% 31.36/10.44 | (822) all_0_2_2 = n14
% 31.36/10.44 |
% 31.36/10.44 | From (822) and (473) follows:
% 31.36/10.44 | (824) pred(n14) = all_0_1_1
% 31.36/10.44 |
% 31.36/10.44 | From (1420) and (5899) follows:
% 31.36/10.44 | (6079) sum(n12, n3) = all_0_4_4
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 31.36/10.44 | (827) all_0_1_1 = n13
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n12, n3, all_0_4_4, n15 and discharging atoms sum(n12, n3) = all_0_4_4, sum(n12, n3) = n15, yields:
% 31.36/10.44 | (823) all_0_4_4 = n15
% 31.36/10.44 |
% 31.36/10.44 | From (823) and (716) follows:
% 31.36/10.44 | (825) pred(n15) = all_0_3_3
% 31.36/10.44 |
% 31.36/10.44 | From (827) and (1418) follows:
% 31.36/10.44 | (6083) sum(n2, n13) = all_0_0_0
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 31.36/10.44 | (826) all_0_3_3 = n14
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n2, n13, all_0_0_0, n15 and discharging atoms sum(n2, n13) = all_0_0_0, sum(n2, n13) = n15, yields:
% 31.36/10.44 | (779) all_0_0_0 = n15
% 31.36/10.44 |
% 31.36/10.44 | From (826)(779) and (232) follows:
% 31.36/10.44 | (6086) sum(n14, n15) = all_0_6_6
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n14, n15, all_0_6_6, n8 and discharging atoms sum(n14, n15) = all_0_6_6, sum(n14, n15) = n8, yields:
% 31.36/10.44 | (985) all_0_6_6 = n8
% 31.36/10.44 |
% 31.36/10.44 | Equations (985) can reduce 357 to:
% 31.36/10.44 | (748) $false
% 31.36/10.44 |
% 31.36/10.44 |-The branch is then unsatisfiable
% 31.36/10.44 |-Branch two:
% 31.36/10.44 | (1433) ~ (all_0_7_7 = n2)
% 31.36/10.44 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 31.36/10.44 |
% 31.36/10.44 +-Applying beta-rule and splitting (1434), into two cases.
% 31.36/10.44 |-Branch one:
% 31.36/10.44 | (1435) all_0_7_7 = n1
% 31.36/10.44 |
% 31.36/10.44 | From (1435) and (683) follows:
% 31.36/10.44 | (1436) succ(n1) = all_0_5_5
% 31.36/10.44 |
% 31.36/10.44 | From (1435) and (8) follows:
% 31.36/10.44 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 31.36/10.44 |
% 31.36/10.44 | From (1435) and (5900) follows:
% 31.36/10.44 | (6094) sum(n12, n1) = all_0_2_2
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.36/10.44 | (1439) all_0_5_5 = n2
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n12, n1, all_0_2_2, n13 and discharging atoms sum(n12, n1) = all_0_2_2, sum(n12, n1) = n13, yields:
% 31.36/10.44 | (839) all_0_2_2 = n13
% 31.36/10.44 |
% 31.36/10.44 | From (839) and (473) follows:
% 31.36/10.44 | (841) pred(n13) = all_0_1_1
% 31.36/10.44 |
% 31.36/10.44 | From (1439) and (5899) follows:
% 31.36/10.44 | (6098) sum(n12, n2) = all_0_4_4
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 31.36/10.44 | (844) all_0_1_1 = n12
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n12, n2, all_0_4_4, n14 and discharging atoms sum(n12, n2) = all_0_4_4, sum(n12, n2) = n14, yields:
% 31.36/10.44 | (840) all_0_4_4 = n14
% 31.36/10.44 |
% 31.36/10.44 | From (840) and (716) follows:
% 31.36/10.44 | (842) pred(n14) = all_0_3_3
% 31.36/10.44 |
% 31.36/10.44 | From (844) and (1437) follows:
% 31.36/10.44 | (6102) sum(n1, n12) = all_0_0_0
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 31.36/10.44 | (843) all_0_3_3 = n13
% 31.36/10.44 |
% 31.36/10.44 | Instantiating formula (619) with n1, n12, all_0_0_0, n13 and discharging atoms sum(n1, n12) = all_0_0_0, sum(n1, n12) = n13, yields:
% 31.36/10.44 | (813) all_0_0_0 = n13
% 31.36/10.44 |
% 31.36/10.44 | From (843)(813) and (232) follows:
% 31.36/10.45 | (6105) sum(n13, n13) = all_0_6_6
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (619) with n13, n13, all_0_6_6, n5 and discharging atoms sum(n13, n13) = all_0_6_6, sum(n13, n13) = n5, yields:
% 31.36/10.45 | (832) all_0_6_6 = n5
% 31.36/10.45 |
% 31.36/10.45 | Equations (832) can reduce 462 to:
% 31.36/10.45 | (748) $false
% 31.36/10.45 |
% 31.36/10.45 |-The branch is then unsatisfiable
% 31.36/10.45 |-Branch two:
% 31.36/10.45 | (1452) ~ (all_0_7_7 = n1)
% 31.36/10.45 | (1453) all_0_7_7 = n0
% 31.36/10.45 |
% 31.36/10.45 | From (1453) and (683) follows:
% 31.36/10.45 | (1454) succ(n0) = all_0_5_5
% 31.36/10.45 |
% 31.36/10.45 | From (1453) and (8) follows:
% 31.36/10.45 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 31.36/10.45 |
% 31.36/10.45 | From (1453) and (5900) follows:
% 31.36/10.45 | (6112) sum(n12, n0) = all_0_2_2
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.36/10.45 | (1457) all_0_5_5 = n1
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (619) with n12, n0, all_0_2_2, n12 and discharging atoms sum(n12, n0) = all_0_2_2, sum(n12, n0) = n12, yields:
% 31.36/10.45 | (856) all_0_2_2 = n12
% 31.36/10.45 |
% 31.36/10.45 | From (856) and (473) follows:
% 31.36/10.45 | (858) pred(n12) = all_0_1_1
% 31.36/10.45 |
% 31.36/10.45 | From (1457) and (5899) follows:
% 31.36/10.45 | (6116) sum(n12, n1) = all_0_4_4
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 31.36/10.45 | (861) all_0_1_1 = n11
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (619) with n12, n1, all_0_4_4, n13 and discharging atoms sum(n12, n1) = all_0_4_4, sum(n12, n1) = n13, yields:
% 31.36/10.45 | (857) all_0_4_4 = n13
% 31.36/10.45 |
% 31.36/10.45 | From (857) and (716) follows:
% 31.36/10.45 | (859) pred(n13) = all_0_3_3
% 31.36/10.45 |
% 31.36/10.45 | From (861) and (1455) follows:
% 31.36/10.45 | (6120) sum(n0, n11) = all_0_0_0
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 31.36/10.45 | (860) all_0_3_3 = n12
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (619) with n0, n11, all_0_0_0, n11 and discharging atoms sum(n0, n11) = all_0_0_0, sum(n0, n11) = n11, yields:
% 31.36/10.45 | (847) all_0_0_0 = n11
% 31.36/10.45 |
% 31.36/10.45 | From (860)(847) and (232) follows:
% 31.36/10.45 | (6123) sum(n12, n11) = all_0_6_6
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (619) with n12, n11, all_0_6_6, n2 and discharging atoms sum(n12, n11) = all_0_6_6, sum(n12, n11) = n2, yields:
% 31.36/10.45 | (1036) all_0_6_6 = n2
% 31.36/10.45 |
% 31.36/10.45 | Equations (1036) can reduce 56 to:
% 31.36/10.45 | (748) $false
% 31.36/10.45 |
% 31.36/10.45 |-The branch is then unsatisfiable
% 31.36/10.45 |-Branch two:
% 31.36/10.45 | (885) ~ (all_0_8_8 = n12)
% 31.36/10.45 | (886) all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.36/10.45 |
% 31.36/10.45 +-Applying beta-rule and splitting (1244), into two cases.
% 31.36/10.45 |-Branch one:
% 31.36/10.45 | (1245) all_0_7_7 = n11
% 31.36/10.45 |
% 31.36/10.45 | From (1245) and (683) follows:
% 31.36/10.45 | (1246) succ(n11) = all_0_5_5
% 31.36/10.45 |
% 31.36/10.45 | From (1245) and (8) follows:
% 31.36/10.45 | (1247) sum(n11, all_0_1_1) = all_0_0_0
% 31.36/10.45 |
% 31.36/10.45 | From (1245) and (378) follows:
% 31.36/10.45 | (6131) sum(all_0_8_8, n11) = all_0_2_2
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (388) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 31.36/10.45 | (1249) all_0_5_5 = n12
% 31.36/10.45 |
% 31.36/10.45 | From (1249) and (708) follows:
% 31.36/10.45 | (6133) sum(all_0_8_8, n12) = all_0_4_4
% 31.36/10.45 |
% 31.36/10.45 +-Applying beta-rule and splitting (886), into two cases.
% 31.36/10.45 |-Branch one:
% 31.36/10.45 | (887) all_0_8_8 = n11
% 31.36/10.45 |
% 31.36/10.45 | From (887) and (6133) follows:
% 31.36/10.45 | (6135) sum(n11, n12) = all_0_4_4
% 31.36/10.45 |
% 31.36/10.45 | From (887) and (6131) follows:
% 31.36/10.45 | (6136) sum(n11, n11) = all_0_2_2
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (619) with n11, n12, all_0_4_4, n2 and discharging atoms sum(n11, n12) = all_0_4_4, sum(n11, n12) = n2, yields:
% 31.36/10.45 | (1044) all_0_4_4 = n2
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (619) with n11, n11, all_0_2_2, n1 and discharging atoms sum(n11, n11) = all_0_2_2, sum(n11, n11) = n1, yields:
% 31.36/10.45 | (1043) all_0_2_2 = n1
% 31.36/10.45 |
% 31.36/10.45 | From (1043) and (473) follows:
% 31.36/10.45 | (1045) pred(n1) = all_0_1_1
% 31.36/10.45 |
% 31.36/10.45 | From (1044) and (716) follows:
% 31.36/10.45 | (1046) pred(n2) = all_0_3_3
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 31.36/10.45 | (1047) all_0_3_3 = n1
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 31.36/10.45 | (1048) all_0_1_1 = n0
% 31.36/10.45 |
% 31.36/10.45 | From (1047) and (232) follows:
% 31.36/10.45 | (1049) sum(n1, all_0_0_0) = all_0_6_6
% 31.36/10.45 |
% 31.36/10.45 | From (1048) and (1247) follows:
% 31.36/10.45 | (6144) sum(n11, n0) = all_0_0_0
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (619) with n11, n0, all_0_0_0, n11 and discharging atoms sum(n11, n0) = all_0_0_0, sum(n11, n0) = n11, yields:
% 31.36/10.45 | (847) all_0_0_0 = n11
% 31.36/10.45 |
% 31.36/10.45 | From (847) and (1049) follows:
% 31.36/10.45 | (6146) sum(n1, n11) = all_0_6_6
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (619) with n1, n11, all_0_6_6, n12 and discharging atoms sum(n1, n11) = all_0_6_6, sum(n1, n11) = n12, yields:
% 31.36/10.45 | (951) all_0_6_6 = n12
% 31.36/10.45 |
% 31.36/10.45 | Equations (951) can reduce 76 to:
% 31.36/10.45 | (748) $false
% 31.36/10.45 |
% 31.36/10.45 |-The branch is then unsatisfiable
% 31.36/10.45 |-Branch two:
% 31.36/10.45 | (902) ~ (all_0_8_8 = n11)
% 31.36/10.45 | (903) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.36/10.45 |
% 31.36/10.45 +-Applying beta-rule and splitting (903), into two cases.
% 31.36/10.45 |-Branch one:
% 31.36/10.45 | (904) all_0_8_8 = n10
% 31.36/10.45 |
% 31.36/10.45 | From (904) and (6133) follows:
% 31.36/10.45 | (6152) sum(n10, n12) = all_0_4_4
% 31.36/10.45 |
% 31.36/10.45 | From (904) and (6131) follows:
% 31.36/10.45 | (6153) sum(n10, n11) = all_0_2_2
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (619) with n10, n12, all_0_4_4, n1 and discharging atoms sum(n10, n12) = all_0_4_4, sum(n10, n12) = n1, yields:
% 31.36/10.45 | (1061) all_0_4_4 = n1
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (619) with n10, n11, all_0_2_2, n0 and discharging atoms sum(n10, n11) = all_0_2_2, sum(n10, n11) = n0, yields:
% 31.36/10.45 | (1060) all_0_2_2 = n0
% 31.36/10.45 |
% 31.36/10.45 | From (1060) and (473) follows:
% 31.36/10.45 | (1062) pred(n0) = all_0_1_1
% 31.36/10.45 |
% 31.36/10.45 | From (1061) and (716) follows:
% 31.36/10.45 | (1063) pred(n1) = all_0_3_3
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 31.36/10.45 | (1064) all_0_3_3 = n0
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 31.36/10.45 | (1065) all_0_1_1 = n20
% 31.36/10.45 |
% 31.36/10.45 | From (1064) and (232) follows:
% 31.36/10.45 | (1066) sum(n0, all_0_0_0) = all_0_6_6
% 31.36/10.45 |
% 31.36/10.45 | From (1065) and (1247) follows:
% 31.36/10.45 | (6161) sum(n11, n20) = all_0_0_0
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (619) with n11, n20, all_0_0_0, n10 and discharging atoms sum(n11, n20) = all_0_0_0, sum(n11, n20) = n10, yields:
% 31.36/10.45 | (864) all_0_0_0 = n10
% 31.36/10.45 |
% 31.36/10.45 | From (864) and (1066) follows:
% 31.36/10.45 | (6163) sum(n0, n10) = all_0_6_6
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (619) with n0, n10, all_0_6_6, n10 and discharging atoms sum(n0, n10) = all_0_6_6, sum(n0, n10) = n10, yields:
% 31.36/10.45 | (968) all_0_6_6 = n10
% 31.36/10.45 |
% 31.36/10.45 | Equations (968) can reduce 176 to:
% 31.36/10.45 | (748) $false
% 31.36/10.45 |
% 31.36/10.45 |-The branch is then unsatisfiable
% 31.36/10.45 |-Branch two:
% 31.36/10.45 | (919) ~ (all_0_8_8 = n10)
% 31.36/10.45 | (920) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.36/10.45 |
% 31.36/10.45 +-Applying beta-rule and splitting (920), into two cases.
% 31.36/10.45 |-Branch one:
% 31.36/10.45 | (921) all_0_8_8 = n9
% 31.36/10.45 |
% 31.36/10.45 | From (921) and (6133) follows:
% 31.36/10.45 | (6169) sum(n9, n12) = all_0_4_4
% 31.36/10.45 |
% 31.36/10.45 | From (921) and (6131) follows:
% 31.36/10.45 | (6170) sum(n9, n11) = all_0_2_2
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (619) with n9, n12, all_0_4_4, n0 and discharging atoms sum(n9, n12) = all_0_4_4, sum(n9, n12) = n0, yields:
% 31.36/10.45 | (1077) all_0_4_4 = n0
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (619) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 31.36/10.45 | (1076) all_0_2_2 = n20
% 31.36/10.45 |
% 31.36/10.45 | From (1076) and (473) follows:
% 31.36/10.45 | (1078) pred(n20) = all_0_1_1
% 31.36/10.45 |
% 31.36/10.45 | From (1077) and (716) follows:
% 31.36/10.45 | (1079) pred(n0) = all_0_3_3
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 31.36/10.45 | (1080) all_0_1_1 = n19
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 31.36/10.45 | (1081) all_0_3_3 = n20
% 31.36/10.45 |
% 31.36/10.45 | From (1081) and (232) follows:
% 31.36/10.45 | (1082) sum(n20, all_0_0_0) = all_0_6_6
% 31.36/10.45 |
% 31.36/10.45 | From (1080) and (1247) follows:
% 31.36/10.45 | (6178) sum(n11, n19) = all_0_0_0
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (619) with n11, n19, all_0_0_0, n9 and discharging atoms sum(n11, n19) = all_0_0_0, sum(n11, n19) = n9, yields:
% 31.36/10.45 | (881) all_0_0_0 = n9
% 31.36/10.45 |
% 31.36/10.45 | From (881) and (1082) follows:
% 31.36/10.45 | (6180) sum(n20, n9) = all_0_6_6
% 31.36/10.45 |
% 31.36/10.45 | Instantiating formula (619) with n20, n9, all_0_6_6, n8 and discharging atoms sum(n20, n9) = all_0_6_6, sum(n20, n9) = n8, yields:
% 31.36/10.46 | (985) all_0_6_6 = n8
% 31.36/10.46 |
% 31.36/10.46 | Equations (985) can reduce 357 to:
% 31.36/10.46 | (748) $false
% 31.36/10.46 |
% 31.36/10.46 |-The branch is then unsatisfiable
% 31.36/10.46 |-Branch two:
% 31.36/10.46 | (936) ~ (all_0_8_8 = n9)
% 31.36/10.46 | (937) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.36/10.46 |
% 31.36/10.46 +-Applying beta-rule and splitting (937), into two cases.
% 31.36/10.46 |-Branch one:
% 31.36/10.46 | (938) all_0_8_8 = n8
% 31.36/10.46 |
% 31.36/10.46 | From (938) and (6133) follows:
% 31.36/10.46 | (6186) sum(n8, n12) = all_0_4_4
% 31.36/10.46 |
% 31.36/10.46 | From (938) and (6131) follows:
% 31.36/10.46 | (6187) sum(n8, n11) = all_0_2_2
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n8, n12, all_0_4_4, n20 and discharging atoms sum(n8, n12) = all_0_4_4, sum(n8, n12) = n20, yields:
% 31.36/10.46 | (738) all_0_4_4 = n20
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n8, n11, all_0_2_2, n19 and discharging atoms sum(n8, n11) = all_0_2_2, sum(n8, n11) = n19, yields:
% 31.36/10.46 | (737) all_0_2_2 = n19
% 31.36/10.46 |
% 31.36/10.46 | From (737) and (473) follows:
% 31.36/10.46 | (739) pred(n19) = all_0_1_1
% 31.36/10.46 |
% 31.36/10.46 | From (738) and (716) follows:
% 31.36/10.46 | (740) pred(n20) = all_0_3_3
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 31.36/10.46 | (741) all_0_3_3 = n19
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 31.36/10.46 | (742) all_0_1_1 = n18
% 31.36/10.46 |
% 31.36/10.46 | From (741) and (232) follows:
% 31.36/10.46 | (743) sum(n19, all_0_0_0) = all_0_6_6
% 31.36/10.46 |
% 31.36/10.46 | From (742) and (1247) follows:
% 31.36/10.46 | (6195) sum(n11, n18) = all_0_0_0
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n11, n18, all_0_0_0, n8 and discharging atoms sum(n11, n18) = all_0_0_0, sum(n11, n18) = n8, yields:
% 31.36/10.46 | (898) all_0_0_0 = n8
% 31.36/10.46 |
% 31.36/10.46 | From (898) and (743) follows:
% 31.36/10.46 | (6197) sum(n19, n8) = all_0_6_6
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n19, n8, all_0_6_6, n6 and discharging atoms sum(n19, n8) = all_0_6_6, sum(n19, n8) = n6, yields:
% 31.36/10.46 | (1002) all_0_6_6 = n6
% 31.36/10.46 |
% 31.36/10.46 | Equations (1002) can reduce 498 to:
% 31.36/10.46 | (748) $false
% 31.36/10.46 |
% 31.36/10.46 |-The branch is then unsatisfiable
% 31.36/10.46 |-Branch two:
% 31.36/10.46 | (953) ~ (all_0_8_8 = n8)
% 31.36/10.46 | (954) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.36/10.46 |
% 31.36/10.46 +-Applying beta-rule and splitting (954), into two cases.
% 31.36/10.46 |-Branch one:
% 31.36/10.46 | (955) all_0_8_8 = n7
% 31.36/10.46 |
% 31.36/10.46 | From (955) and (6133) follows:
% 31.36/10.46 | (6203) sum(n7, n12) = all_0_4_4
% 31.36/10.46 |
% 31.36/10.46 | From (955) and (6131) follows:
% 31.36/10.46 | (6204) sum(n7, n11) = all_0_2_2
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n7, n12, all_0_4_4, n19 and discharging atoms sum(n7, n12) = all_0_4_4, sum(n7, n12) = n19, yields:
% 31.36/10.46 | (755) all_0_4_4 = n19
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n7, n11, all_0_2_2, n18 and discharging atoms sum(n7, n11) = all_0_2_2, sum(n7, n11) = n18, yields:
% 31.36/10.46 | (754) all_0_2_2 = n18
% 31.36/10.46 |
% 31.36/10.46 | From (754) and (473) follows:
% 31.36/10.46 | (756) pred(n18) = all_0_1_1
% 31.36/10.46 |
% 31.36/10.46 | From (755) and (716) follows:
% 31.36/10.46 | (757) pred(n19) = all_0_3_3
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 31.36/10.46 | (758) all_0_3_3 = n18
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 31.36/10.46 | (759) all_0_1_1 = n17
% 31.36/10.46 |
% 31.36/10.46 | From (758) and (232) follows:
% 31.36/10.46 | (760) sum(n18, all_0_0_0) = all_0_6_6
% 31.36/10.46 |
% 31.36/10.46 | From (759) and (1247) follows:
% 31.36/10.46 | (6212) sum(n11, n17) = all_0_0_0
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n11, n17, all_0_0_0, n7 and discharging atoms sum(n11, n17) = all_0_0_0, sum(n11, n17) = n7, yields:
% 31.36/10.46 | (915) all_0_0_0 = n7
% 31.36/10.46 |
% 31.36/10.46 | From (915) and (760) follows:
% 31.36/10.46 | (6214) sum(n18, n7) = all_0_6_6
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n18, n7, all_0_6_6, n4 and discharging atoms sum(n18, n7) = all_0_6_6, sum(n18, n7) = n4, yields:
% 31.36/10.46 | (1019) all_0_6_6 = n4
% 31.36/10.46 |
% 31.36/10.46 | Equations (1019) can reduce 48 to:
% 31.36/10.46 | (748) $false
% 31.36/10.46 |
% 31.36/10.46 |-The branch is then unsatisfiable
% 31.36/10.46 |-Branch two:
% 31.36/10.46 | (970) ~ (all_0_8_8 = n7)
% 31.36/10.46 | (971) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.36/10.46 |
% 31.36/10.46 +-Applying beta-rule and splitting (971), into two cases.
% 31.36/10.46 |-Branch one:
% 31.36/10.46 | (972) all_0_8_8 = n6
% 31.36/10.46 |
% 31.36/10.46 | From (972) and (6133) follows:
% 31.36/10.46 | (6220) sum(n6, n12) = all_0_4_4
% 31.36/10.46 |
% 31.36/10.46 | From (972) and (6131) follows:
% 31.36/10.46 | (6221) sum(n6, n11) = all_0_2_2
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n6, n12, all_0_4_4, n18 and discharging atoms sum(n6, n12) = all_0_4_4, sum(n6, n12) = n18, yields:
% 31.36/10.46 | (772) all_0_4_4 = n18
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n6, n11, all_0_2_2, n17 and discharging atoms sum(n6, n11) = all_0_2_2, sum(n6, n11) = n17, yields:
% 31.36/10.46 | (771) all_0_2_2 = n17
% 31.36/10.46 |
% 31.36/10.46 | From (771) and (473) follows:
% 31.36/10.46 | (773) pred(n17) = all_0_1_1
% 31.36/10.46 |
% 31.36/10.46 | From (772) and (716) follows:
% 31.36/10.46 | (774) pred(n18) = all_0_3_3
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 31.36/10.46 | (775) all_0_3_3 = n17
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 31.36/10.46 | (776) all_0_1_1 = n16
% 31.36/10.46 |
% 31.36/10.46 | From (775) and (232) follows:
% 31.36/10.46 | (777) sum(n17, all_0_0_0) = all_0_6_6
% 31.36/10.46 |
% 31.36/10.46 | From (776) and (1247) follows:
% 31.36/10.46 | (6229) sum(n11, n16) = all_0_0_0
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n11, n16, all_0_0_0, n6 and discharging atoms sum(n11, n16) = all_0_0_0, sum(n11, n16) = n6, yields:
% 31.36/10.46 | (932) all_0_0_0 = n6
% 31.36/10.46 |
% 31.36/10.46 | From (932) and (777) follows:
% 31.36/10.46 | (6231) sum(n17, n6) = all_0_6_6
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n17, n6, all_0_6_6, n2 and discharging atoms sum(n17, n6) = all_0_6_6, sum(n17, n6) = n2, yields:
% 31.36/10.46 | (1036) all_0_6_6 = n2
% 31.36/10.46 |
% 31.36/10.46 | Equations (1036) can reduce 56 to:
% 31.36/10.46 | (748) $false
% 31.36/10.46 |
% 31.36/10.46 |-The branch is then unsatisfiable
% 31.36/10.46 |-Branch two:
% 31.36/10.46 | (987) ~ (all_0_8_8 = n6)
% 31.36/10.46 | (988) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.36/10.46 |
% 31.36/10.46 +-Applying beta-rule and splitting (988), into two cases.
% 31.36/10.46 |-Branch one:
% 31.36/10.46 | (989) all_0_8_8 = n5
% 31.36/10.46 |
% 31.36/10.46 | From (989) and (6133) follows:
% 31.36/10.46 | (6237) sum(n5, n12) = all_0_4_4
% 31.36/10.46 |
% 31.36/10.46 | From (989) and (6131) follows:
% 31.36/10.46 | (6238) sum(n5, n11) = all_0_2_2
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n5, n12, all_0_4_4, n17 and discharging atoms sum(n5, n12) = all_0_4_4, sum(n5, n12) = n17, yields:
% 31.36/10.46 | (789) all_0_4_4 = n17
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n5, n11, all_0_2_2, n16 and discharging atoms sum(n5, n11) = all_0_2_2, sum(n5, n11) = n16, yields:
% 31.36/10.46 | (788) all_0_2_2 = n16
% 31.36/10.46 |
% 31.36/10.46 | From (788) and (473) follows:
% 31.36/10.46 | (790) pred(n16) = all_0_1_1
% 31.36/10.46 |
% 31.36/10.46 | From (789) and (716) follows:
% 31.36/10.46 | (791) pred(n17) = all_0_3_3
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 31.36/10.46 | (792) all_0_3_3 = n16
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 31.36/10.46 | (793) all_0_1_1 = n15
% 31.36/10.46 |
% 31.36/10.46 | From (792) and (232) follows:
% 31.36/10.46 | (794) sum(n16, all_0_0_0) = all_0_6_6
% 31.36/10.46 |
% 31.36/10.46 | From (793) and (1247) follows:
% 31.36/10.46 | (6246) sum(n11, n15) = all_0_0_0
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n11, n15, all_0_0_0, n5 and discharging atoms sum(n11, n15) = all_0_0_0, sum(n11, n15) = n5, yields:
% 31.36/10.46 | (949) all_0_0_0 = n5
% 31.36/10.46 |
% 31.36/10.46 | From (949) and (794) follows:
% 31.36/10.46 | (6248) sum(n16, n5) = all_0_6_6
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n16, n5, all_0_6_6, n0 and discharging atoms sum(n16, n5) = all_0_6_6, sum(n16, n5) = n0, yields:
% 31.36/10.46 | (1053) all_0_6_6 = n0
% 31.36/10.46 |
% 31.36/10.46 | Equations (1053) can reduce 676 to:
% 31.36/10.46 | (748) $false
% 31.36/10.46 |
% 31.36/10.46 |-The branch is then unsatisfiable
% 31.36/10.46 |-Branch two:
% 31.36/10.46 | (1004) ~ (all_0_8_8 = n5)
% 31.36/10.46 | (1005) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.36/10.46 |
% 31.36/10.46 +-Applying beta-rule and splitting (1005), into two cases.
% 31.36/10.46 |-Branch one:
% 31.36/10.46 | (1006) all_0_8_8 = n4
% 31.36/10.46 |
% 31.36/10.46 | From (1006) and (6133) follows:
% 31.36/10.46 | (6254) sum(n4, n12) = all_0_4_4
% 31.36/10.46 |
% 31.36/10.46 | From (1006) and (6131) follows:
% 31.36/10.46 | (6255) sum(n4, n11) = all_0_2_2
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n4, n12, all_0_4_4, n16 and discharging atoms sum(n4, n12) = all_0_4_4, sum(n4, n12) = n16, yields:
% 31.36/10.46 | (806) all_0_4_4 = n16
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (619) with n4, n11, all_0_2_2, n15 and discharging atoms sum(n4, n11) = all_0_2_2, sum(n4, n11) = n15, yields:
% 31.36/10.46 | (805) all_0_2_2 = n15
% 31.36/10.46 |
% 31.36/10.46 | From (805) and (473) follows:
% 31.36/10.46 | (807) pred(n15) = all_0_1_1
% 31.36/10.46 |
% 31.36/10.46 | From (806) and (716) follows:
% 31.36/10.46 | (808) pred(n16) = all_0_3_3
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 31.36/10.46 | (809) all_0_3_3 = n15
% 31.36/10.46 |
% 31.36/10.46 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 31.36/10.46 | (810) all_0_1_1 = n14
% 31.36/10.46 |
% 31.36/10.46 | From (809) and (232) follows:
% 31.36/10.46 | (811) sum(n15, all_0_0_0) = all_0_6_6
% 31.36/10.46 |
% 31.36/10.46 | From (810) and (1247) follows:
% 31.36/10.47 | (6263) sum(n11, n14) = all_0_0_0
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n11, n14, all_0_0_0, n4 and discharging atoms sum(n11, n14) = all_0_0_0, sum(n11, n14) = n4, yields:
% 31.36/10.47 | (966) all_0_0_0 = n4
% 31.36/10.47 |
% 31.36/10.47 | From (966) and (811) follows:
% 31.36/10.47 | (6265) sum(n15, n4) = all_0_6_6
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n15, n4, all_0_6_6, n19 and discharging atoms sum(n15, n4) = all_0_6_6, sum(n15, n4) = n19, yields:
% 31.36/10.47 | (1070) all_0_6_6 = n19
% 31.36/10.47 |
% 31.36/10.47 | Equations (1070) can reduce 31 to:
% 31.36/10.47 | (748) $false
% 31.36/10.47 |
% 31.36/10.47 |-The branch is then unsatisfiable
% 31.36/10.47 |-Branch two:
% 31.36/10.47 | (1021) ~ (all_0_8_8 = n4)
% 31.36/10.47 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.36/10.47 |
% 31.36/10.47 +-Applying beta-rule and splitting (1022), into two cases.
% 31.36/10.47 |-Branch one:
% 31.36/10.47 | (1023) all_0_8_8 = n3
% 31.36/10.47 |
% 31.36/10.47 | From (1023) and (6133) follows:
% 31.36/10.47 | (6271) sum(n3, n12) = all_0_4_4
% 31.36/10.47 |
% 31.36/10.47 | From (1023) and (6131) follows:
% 31.36/10.47 | (6272) sum(n3, n11) = all_0_2_2
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n3, n12, all_0_4_4, n15 and discharging atoms sum(n3, n12) = all_0_4_4, sum(n3, n12) = n15, yields:
% 31.36/10.47 | (823) all_0_4_4 = n15
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n3, n11, all_0_2_2, n14 and discharging atoms sum(n3, n11) = all_0_2_2, sum(n3, n11) = n14, yields:
% 31.36/10.47 | (822) all_0_2_2 = n14
% 31.36/10.47 |
% 31.36/10.47 | From (822) and (473) follows:
% 31.36/10.47 | (824) pred(n14) = all_0_1_1
% 31.36/10.47 |
% 31.36/10.47 | From (823) and (716) follows:
% 31.36/10.47 | (825) pred(n15) = all_0_3_3
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 31.36/10.47 | (826) all_0_3_3 = n14
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 31.36/10.47 | (827) all_0_1_1 = n13
% 31.36/10.47 |
% 31.36/10.47 | From (826) and (232) follows:
% 31.36/10.47 | (828) sum(n14, all_0_0_0) = all_0_6_6
% 31.36/10.47 |
% 31.36/10.47 | From (827) and (1247) follows:
% 31.36/10.47 | (6280) sum(n11, n13) = all_0_0_0
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n11, n13, all_0_0_0, n3 and discharging atoms sum(n11, n13) = all_0_0_0, sum(n11, n13) = n3, yields:
% 31.36/10.47 | (983) all_0_0_0 = n3
% 31.36/10.47 |
% 31.36/10.47 | From (983) and (828) follows:
% 31.36/10.47 | (6282) sum(n14, n3) = all_0_6_6
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n14, n3, all_0_6_6, n17 and discharging atoms sum(n14, n3) = all_0_6_6, sum(n14, n3) = n17, yields:
% 31.36/10.47 | (1086) all_0_6_6 = n17
% 31.36/10.47 |
% 31.36/10.47 | Equations (1086) can reduce 669 to:
% 31.36/10.47 | (748) $false
% 31.36/10.47 |
% 31.36/10.47 |-The branch is then unsatisfiable
% 31.36/10.47 |-Branch two:
% 31.36/10.47 | (1038) ~ (all_0_8_8 = n3)
% 31.36/10.47 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.36/10.47 |
% 31.36/10.47 +-Applying beta-rule and splitting (1039), into two cases.
% 31.36/10.47 |-Branch one:
% 31.36/10.47 | (1040) all_0_8_8 = n2
% 31.36/10.47 |
% 31.36/10.47 | From (1040) and (6133) follows:
% 31.36/10.47 | (6288) sum(n2, n12) = all_0_4_4
% 31.36/10.47 |
% 31.36/10.47 | From (1040) and (6131) follows:
% 31.36/10.47 | (6289) sum(n2, n11) = all_0_2_2
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n2, n12, all_0_4_4, n14 and discharging atoms sum(n2, n12) = all_0_4_4, sum(n2, n12) = n14, yields:
% 31.36/10.47 | (840) all_0_4_4 = n14
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n2, n11, all_0_2_2, n13 and discharging atoms sum(n2, n11) = all_0_2_2, sum(n2, n11) = n13, yields:
% 31.36/10.47 | (839) all_0_2_2 = n13
% 31.36/10.47 |
% 31.36/10.47 | From (839) and (473) follows:
% 31.36/10.47 | (841) pred(n13) = all_0_1_1
% 31.36/10.47 |
% 31.36/10.47 | From (840) and (716) follows:
% 31.36/10.47 | (842) pred(n14) = all_0_3_3
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 31.36/10.47 | (843) all_0_3_3 = n13
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 31.36/10.47 | (844) all_0_1_1 = n12
% 31.36/10.47 |
% 31.36/10.47 | From (843) and (232) follows:
% 31.36/10.47 | (845) sum(n13, all_0_0_0) = all_0_6_6
% 31.36/10.47 |
% 31.36/10.47 | From (844) and (1247) follows:
% 31.36/10.47 | (6297) sum(n11, n12) = all_0_0_0
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n11, n12, all_0_0_0, n2 and discharging atoms sum(n11, n12) = all_0_0_0, sum(n11, n12) = n2, yields:
% 31.36/10.47 | (1000) all_0_0_0 = n2
% 31.36/10.47 |
% 31.36/10.47 | From (1000) and (845) follows:
% 31.36/10.47 | (6299) sum(n13, n2) = all_0_6_6
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n13, n2, all_0_6_6, n15 and discharging atoms sum(n13, n2) = all_0_6_6, sum(n13, n2) = n15, yields:
% 31.36/10.47 | (747) all_0_6_6 = n15
% 31.36/10.47 |
% 31.36/10.47 | Equations (747) can reduce 456 to:
% 31.36/10.47 | (748) $false
% 31.36/10.47 |
% 31.36/10.47 |-The branch is then unsatisfiable
% 31.36/10.47 |-Branch two:
% 31.36/10.47 | (1055) ~ (all_0_8_8 = n2)
% 31.36/10.47 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 31.36/10.47 |
% 31.36/10.47 +-Applying beta-rule and splitting (1056), into two cases.
% 31.36/10.47 |-Branch one:
% 31.36/10.47 | (1057) all_0_8_8 = n1
% 31.36/10.47 |
% 31.36/10.47 | From (1057) and (6133) follows:
% 31.36/10.47 | (6305) sum(n1, n12) = all_0_4_4
% 31.36/10.47 |
% 31.36/10.47 | From (1057) and (6131) follows:
% 31.36/10.47 | (6306) sum(n1, n11) = all_0_2_2
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n1, n12, all_0_4_4, n13 and discharging atoms sum(n1, n12) = all_0_4_4, sum(n1, n12) = n13, yields:
% 31.36/10.47 | (857) all_0_4_4 = n13
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n1, n11, all_0_2_2, n12 and discharging atoms sum(n1, n11) = all_0_2_2, sum(n1, n11) = n12, yields:
% 31.36/10.47 | (856) all_0_2_2 = n12
% 31.36/10.47 |
% 31.36/10.47 | From (856) and (473) follows:
% 31.36/10.47 | (858) pred(n12) = all_0_1_1
% 31.36/10.47 |
% 31.36/10.47 | From (857) and (716) follows:
% 31.36/10.47 | (859) pred(n13) = all_0_3_3
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 31.36/10.47 | (860) all_0_3_3 = n12
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 31.36/10.47 | (861) all_0_1_1 = n11
% 31.36/10.47 |
% 31.36/10.47 | From (860) and (232) follows:
% 31.36/10.47 | (862) sum(n12, all_0_0_0) = all_0_6_6
% 31.36/10.47 |
% 31.36/10.47 | From (861) and (1247) follows:
% 31.36/10.47 | (6314) sum(n11, n11) = all_0_0_0
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n11, n11, all_0_0_0, n1 and discharging atoms sum(n11, n11) = all_0_0_0, sum(n11, n11) = n1, yields:
% 31.36/10.47 | (1017) all_0_0_0 = n1
% 31.36/10.47 |
% 31.36/10.47 | From (1017) and (862) follows:
% 31.36/10.47 | (6316) sum(n12, n1) = all_0_6_6
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n12, n1, all_0_6_6, n13 and discharging atoms sum(n12, n1) = all_0_6_6, sum(n12, n1) = n13, yields:
% 31.36/10.47 | (764) all_0_6_6 = n13
% 31.36/10.47 |
% 31.36/10.47 | Equations (764) can reduce 293 to:
% 31.36/10.47 | (748) $false
% 31.36/10.47 |
% 31.36/10.47 |-The branch is then unsatisfiable
% 31.36/10.47 |-Branch two:
% 31.36/10.47 | (1072) ~ (all_0_8_8 = n1)
% 31.36/10.47 | (1073) all_0_8_8 = n0
% 31.36/10.47 |
% 31.36/10.47 | From (1073) and (6133) follows:
% 31.36/10.47 | (6321) sum(n0, n12) = all_0_4_4
% 31.36/10.47 |
% 31.36/10.47 | From (1073) and (6131) follows:
% 31.36/10.47 | (6322) sum(n0, n11) = all_0_2_2
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n0, n12, all_0_4_4, n12 and discharging atoms sum(n0, n12) = all_0_4_4, sum(n0, n12) = n12, yields:
% 31.36/10.47 | (874) all_0_4_4 = n12
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n0, n11, all_0_2_2, n11 and discharging atoms sum(n0, n11) = all_0_2_2, sum(n0, n11) = n11, yields:
% 31.36/10.47 | (873) all_0_2_2 = n11
% 31.36/10.47 |
% 31.36/10.47 | From (873) and (473) follows:
% 31.36/10.47 | (875) pred(n11) = all_0_1_1
% 31.36/10.47 |
% 31.36/10.47 | From (874) and (716) follows:
% 31.36/10.47 | (876) pred(n12) = all_0_3_3
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 31.36/10.47 | (877) all_0_3_3 = n11
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 31.36/10.47 | (878) all_0_1_1 = n10
% 31.36/10.47 |
% 31.36/10.47 | From (877) and (232) follows:
% 31.36/10.47 | (879) sum(n11, all_0_0_0) = all_0_6_6
% 31.36/10.47 |
% 31.36/10.47 | From (878) and (1247) follows:
% 31.36/10.47 | (6330) sum(n11, n10) = all_0_0_0
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n11, n10, all_0_0_0, n0 and discharging atoms sum(n11, n10) = all_0_0_0, sum(n11, n10) = n0, yields:
% 31.36/10.47 | (1034) all_0_0_0 = n0
% 31.36/10.47 |
% 31.36/10.47 | From (1034) and (879) follows:
% 31.36/10.47 | (6332) sum(n11, n0) = all_0_6_6
% 31.36/10.47 |
% 31.36/10.47 | Instantiating formula (619) with n11, n0, all_0_6_6, n11 and discharging atoms sum(n11, n0) = all_0_6_6, sum(n11, n0) = n11, yields:
% 31.36/10.47 | (781) all_0_6_6 = n11
% 31.36/10.47 |
% 31.36/10.47 | Equations (781) can reduce 2 to:
% 31.36/10.47 | (748) $false
% 31.36/10.47 |
% 31.36/10.47 |-The branch is then unsatisfiable
% 31.36/10.47 |-Branch two:
% 31.36/10.47 | (1262) ~ (all_0_7_7 = n11)
% 31.36/10.47 | (1263) all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.36/10.47 |
% 31.36/10.47 +-Applying beta-rule and splitting (886), into two cases.
% 31.36/10.47 |-Branch one:
% 31.36/10.47 | (887) all_0_8_8 = n11
% 31.36/10.47 |
% 31.36/10.47 | From (887) and (708) follows:
% 31.36/10.48 | (6338) sum(n11, all_0_5_5) = all_0_4_4
% 31.36/10.48 |
% 31.36/10.48 | From (887) and (378) follows:
% 31.36/10.48 | (6339) sum(n11, all_0_7_7) = all_0_2_2
% 31.36/10.48 |
% 31.36/10.48 +-Applying beta-rule and splitting (1263), into two cases.
% 31.36/10.48 |-Branch one:
% 31.36/10.48 | (1264) all_0_7_7 = n10
% 31.36/10.48 |
% 31.36/10.48 | From (1264) and (683) follows:
% 31.36/10.48 | (1265) succ(n10) = all_0_5_5
% 31.36/10.48 |
% 31.36/10.48 | From (1264) and (8) follows:
% 31.36/10.48 | (1266) sum(n10, all_0_1_1) = all_0_0_0
% 31.36/10.48 |
% 31.36/10.48 | From (1264) and (6339) follows:
% 31.36/10.48 | (6343) sum(n11, n10) = all_0_2_2
% 31.36/10.48 |
% 31.36/10.48 | Instantiating formula (388) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 31.36/10.48 | (1268) all_0_5_5 = n11
% 31.36/10.48 |
% 31.36/10.48 | Instantiating formula (619) with n11, n10, all_0_2_2, n0 and discharging atoms sum(n11, n10) = all_0_2_2, sum(n11, n10) = n0, yields:
% 31.36/10.48 | (1060) all_0_2_2 = n0
% 31.36/10.48 |
% 31.36/10.48 | From (1060) and (473) follows:
% 31.36/10.48 | (1062) pred(n0) = all_0_1_1
% 31.36/10.48 |
% 31.36/10.48 | From (1268) and (6338) follows:
% 31.65/10.48 | (6347) sum(n11, n11) = all_0_4_4
% 31.65/10.48 |
% 31.65/10.48 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 31.65/10.48 | (1065) all_0_1_1 = n20
% 31.65/10.48 |
% 31.65/10.48 | Instantiating formula (619) with n11, n11, all_0_4_4, n1 and discharging atoms sum(n11, n11) = all_0_4_4, sum(n11, n11) = n1, yields:
% 31.65/10.48 | (1061) all_0_4_4 = n1
% 31.65/10.48 |
% 31.65/10.48 | From (1061) and (716) follows:
% 31.65/10.48 | (1063) pred(n1) = all_0_3_3
% 31.65/10.48 |
% 31.65/10.48 | From (1065) and (1266) follows:
% 31.65/10.48 | (6351) sum(n10, n20) = all_0_0_0
% 31.65/10.48 |
% 31.65/10.48 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 31.65/10.48 | (1064) all_0_3_3 = n0
% 31.65/10.48 |
% 31.65/10.48 | Instantiating formula (619) with n10, n20, all_0_0_0, n9 and discharging atoms sum(n10, n20) = all_0_0_0, sum(n10, n20) = n9, yields:
% 31.65/10.48 | (881) all_0_0_0 = n9
% 31.65/10.48 |
% 31.65/10.48 | From (1064)(881) and (232) follows:
% 31.65/10.48 | (6354) sum(n0, n9) = all_0_6_6
% 31.65/10.48 |
% 31.65/10.48 | Instantiating formula (619) with n0, n9, all_0_6_6, n9 and discharging atoms sum(n0, n9) = all_0_6_6, sum(n0, n9) = n9, yields:
% 31.65/10.48 | (798) all_0_6_6 = n9
% 31.65/10.48 |
% 31.65/10.48 | Equations (798) can reduce 593 to:
% 31.65/10.48 | (748) $false
% 31.65/10.48 |
% 31.65/10.48 |-The branch is then unsatisfiable
% 31.65/10.48 |-Branch two:
% 31.65/10.48 | (1281) ~ (all_0_7_7 = n10)
% 31.65/10.48 | (1282) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.65/10.48 |
% 31.65/10.48 +-Applying beta-rule and splitting (1282), into two cases.
% 31.65/10.48 |-Branch one:
% 31.65/10.48 | (1283) all_0_7_7 = n9
% 31.65/10.48 |
% 31.65/10.48 | From (1283) and (683) follows:
% 31.65/10.48 | (1284) succ(n9) = all_0_5_5
% 31.65/10.48 |
% 31.65/10.48 | From (1283) and (8) follows:
% 31.65/10.48 | (1285) sum(n9, all_0_1_1) = all_0_0_0
% 31.65/10.48 |
% 31.65/10.48 | From (1283) and (6339) follows:
% 31.65/10.48 | (6362) sum(n11, n9) = all_0_2_2
% 31.65/10.48 |
% 31.65/10.48 | Instantiating formula (388) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 31.65/10.48 | (1287) all_0_5_5 = n10
% 31.65/10.48 |
% 31.65/10.48 | Instantiating formula (619) with n11, n9, all_0_2_2, n20 and discharging atoms sum(n11, n9) = all_0_2_2, sum(n11, n9) = n20, yields:
% 31.65/10.48 | (1076) all_0_2_2 = n20
% 31.65/10.48 |
% 31.65/10.48 | From (1076) and (473) follows:
% 31.65/10.48 | (1078) pred(n20) = all_0_1_1
% 31.65/10.48 |
% 31.65/10.48 | From (1287) and (6338) follows:
% 31.65/10.48 | (6366) sum(n11, n10) = all_0_4_4
% 31.65/10.48 |
% 31.65/10.48 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 31.65/10.48 | (1080) all_0_1_1 = n19
% 31.65/10.48 |
% 31.65/10.48 | Instantiating formula (619) with n11, n10, all_0_4_4, n0 and discharging atoms sum(n11, n10) = all_0_4_4, sum(n11, n10) = n0, yields:
% 31.66/10.48 | (1077) all_0_4_4 = n0
% 31.66/10.48 |
% 31.66/10.48 | From (1077) and (716) follows:
% 31.66/10.48 | (1079) pred(n0) = all_0_3_3
% 31.66/10.48 |
% 31.66/10.48 | From (1080) and (1285) follows:
% 31.66/10.48 | (6370) sum(n9, n19) = all_0_0_0
% 31.66/10.48 |
% 31.66/10.48 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 31.66/10.48 | (1081) all_0_3_3 = n20
% 31.66/10.48 |
% 31.66/10.48 | Instantiating formula (619) with n9, n19, all_0_0_0, n7 and discharging atoms sum(n9, n19) = all_0_0_0, sum(n9, n19) = n7, yields:
% 31.66/10.48 | (915) all_0_0_0 = n7
% 31.66/10.48 |
% 31.66/10.48 | From (1081)(915) and (232) follows:
% 31.66/10.48 | (6373) sum(n20, n7) = all_0_6_6
% 31.66/10.48 |
% 31.66/10.48 | Instantiating formula (619) with n20, n7, all_0_6_6, n6 and discharging atoms sum(n20, n7) = all_0_6_6, sum(n20, n7) = n6, yields:
% 31.66/10.48 | (1002) all_0_6_6 = n6
% 31.66/10.48 |
% 31.66/10.48 | Equations (1002) can reduce 498 to:
% 31.66/10.48 | (748) $false
% 31.66/10.48 |
% 31.66/10.48 |-The branch is then unsatisfiable
% 31.66/10.48 |-Branch two:
% 31.66/10.48 | (1300) ~ (all_0_7_7 = n9)
% 31.66/10.48 | (1301) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.66/10.48 |
% 31.66/10.48 +-Applying beta-rule and splitting (1301), into two cases.
% 31.66/10.48 |-Branch one:
% 31.66/10.48 | (1302) all_0_7_7 = n8
% 31.66/10.48 |
% 31.66/10.48 | From (1302) and (683) follows:
% 31.66/10.48 | (1303) succ(n8) = all_0_5_5
% 31.66/10.48 |
% 31.66/10.48 | From (1302) and (8) follows:
% 31.66/10.48 | (1304) sum(n8, all_0_1_1) = all_0_0_0
% 31.66/10.48 |
% 31.66/10.48 | From (1302) and (6339) follows:
% 31.66/10.48 | (6381) sum(n11, n8) = all_0_2_2
% 31.66/10.48 |
% 31.66/10.48 | Instantiating formula (388) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 31.66/10.48 | (1306) all_0_5_5 = n9
% 31.66/10.48 |
% 31.66/10.48 | Instantiating formula (619) with n11, n8, all_0_2_2, n19 and discharging atoms sum(n11, n8) = all_0_2_2, sum(n11, n8) = n19, yields:
% 31.66/10.48 | (737) all_0_2_2 = n19
% 31.66/10.48 |
% 31.66/10.48 | From (737) and (473) follows:
% 31.66/10.48 | (739) pred(n19) = all_0_1_1
% 31.66/10.48 |
% 31.66/10.48 | From (1306) and (6338) follows:
% 31.66/10.48 | (6385) sum(n11, n9) = all_0_4_4
% 31.66/10.48 |
% 31.66/10.48 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 31.66/10.48 | (742) all_0_1_1 = n18
% 31.66/10.48 |
% 31.66/10.48 | Instantiating formula (619) with n11, n9, all_0_4_4, n20 and discharging atoms sum(n11, n9) = all_0_4_4, sum(n11, n9) = n20, yields:
% 31.66/10.48 | (738) all_0_4_4 = n20
% 31.66/10.48 |
% 31.66/10.48 | From (738) and (716) follows:
% 31.66/10.48 | (740) pred(n20) = all_0_3_3
% 31.66/10.48 |
% 31.66/10.48 | From (742) and (1304) follows:
% 31.66/10.48 | (6389) sum(n8, n18) = all_0_0_0
% 31.66/10.48 |
% 31.66/10.48 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 31.66/10.48 | (741) all_0_3_3 = n19
% 31.66/10.48 |
% 31.66/10.48 | Instantiating formula (619) with n8, n18, all_0_0_0, n5 and discharging atoms sum(n8, n18) = all_0_0_0, sum(n8, n18) = n5, yields:
% 31.66/10.48 | (949) all_0_0_0 = n5
% 31.66/10.48 |
% 31.66/10.48 | From (741)(949) and (232) follows:
% 31.66/10.48 | (6392) sum(n19, n5) = all_0_6_6
% 31.66/10.48 |
% 31.66/10.48 | Instantiating formula (619) with n19, n5, all_0_6_6, n3 and discharging atoms sum(n19, n5) = all_0_6_6, sum(n19, n5) = n3, yields:
% 31.66/10.48 | (849) all_0_6_6 = n3
% 31.66/10.48 |
% 31.66/10.48 | Equations (849) can reduce 416 to:
% 31.66/10.48 | (748) $false
% 31.66/10.48 |
% 31.66/10.48 |-The branch is then unsatisfiable
% 31.66/10.48 |-Branch two:
% 31.66/10.48 | (1319) ~ (all_0_7_7 = n8)
% 31.66/10.48 | (1320) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.66/10.48 |
% 31.66/10.48 +-Applying beta-rule and splitting (1320), into two cases.
% 31.66/10.48 |-Branch one:
% 31.66/10.48 | (1321) all_0_7_7 = n7
% 31.66/10.48 |
% 31.66/10.48 | From (1321) and (683) follows:
% 31.66/10.48 | (1322) succ(n7) = all_0_5_5
% 31.66/10.48 |
% 31.66/10.48 | From (1321) and (8) follows:
% 31.66/10.48 | (1323) sum(n7, all_0_1_1) = all_0_0_0
% 31.66/10.48 |
% 31.66/10.48 | From (1321) and (6339) follows:
% 31.66/10.48 | (6400) sum(n11, n7) = all_0_2_2
% 31.66/10.48 |
% 31.66/10.48 | Instantiating formula (388) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 31.66/10.48 | (1325) all_0_5_5 = n8
% 31.66/10.48 |
% 31.66/10.48 | Instantiating formula (619) with n11, n7, all_0_2_2, n18 and discharging atoms sum(n11, n7) = all_0_2_2, sum(n11, n7) = n18, yields:
% 31.66/10.48 | (754) all_0_2_2 = n18
% 31.66/10.48 |
% 31.66/10.48 | From (754) and (473) follows:
% 31.66/10.48 | (756) pred(n18) = all_0_1_1
% 31.66/10.48 |
% 31.66/10.48 | From (1325) and (6338) follows:
% 31.66/10.48 | (6404) sum(n11, n8) = all_0_4_4
% 31.66/10.48 |
% 31.66/10.48 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 31.66/10.48 | (759) all_0_1_1 = n17
% 31.66/10.48 |
% 31.66/10.48 | Instantiating formula (619) with n11, n8, all_0_4_4, n19 and discharging atoms sum(n11, n8) = all_0_4_4, sum(n11, n8) = n19, yields:
% 31.66/10.48 | (755) all_0_4_4 = n19
% 31.66/10.48 |
% 31.66/10.48 | From (755) and (716) follows:
% 31.66/10.48 | (757) pred(n19) = all_0_3_3
% 31.66/10.48 |
% 31.66/10.48 | From (759) and (1323) follows:
% 31.66/10.48 | (6408) sum(n7, n17) = all_0_0_0
% 31.66/10.48 |
% 31.66/10.48 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 31.66/10.48 | (758) all_0_3_3 = n18
% 31.66/10.48 |
% 31.66/10.48 | Instantiating formula (619) with n7, n17, all_0_0_0, n3 and discharging atoms sum(n7, n17) = all_0_0_0, sum(n7, n17) = n3, yields:
% 31.66/10.48 | (983) all_0_0_0 = n3
% 31.66/10.48 |
% 31.66/10.48 | From (758)(983) and (232) follows:
% 31.66/10.49 | (6411) sum(n18, n3) = all_0_6_6
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (619) with n18, n3, all_0_6_6, n0 and discharging atoms sum(n18, n3) = all_0_6_6, sum(n18, n3) = n0, yields:
% 31.66/10.49 | (1053) all_0_6_6 = n0
% 31.66/10.49 |
% 31.66/10.49 | Equations (1053) can reduce 676 to:
% 31.66/10.49 | (748) $false
% 31.66/10.49 |
% 31.66/10.49 |-The branch is then unsatisfiable
% 31.66/10.49 |-Branch two:
% 31.66/10.49 | (1338) ~ (all_0_7_7 = n7)
% 31.66/10.49 | (1339) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.66/10.49 |
% 31.66/10.49 +-Applying beta-rule and splitting (1339), into two cases.
% 31.66/10.49 |-Branch one:
% 31.66/10.49 | (1340) all_0_7_7 = n6
% 31.66/10.49 |
% 31.66/10.49 | From (1340) and (683) follows:
% 31.66/10.49 | (1341) succ(n6) = all_0_5_5
% 31.66/10.49 |
% 31.66/10.49 | From (1340) and (8) follows:
% 31.66/10.49 | (1342) sum(n6, all_0_1_1) = all_0_0_0
% 31.66/10.49 |
% 31.66/10.49 | From (1340) and (6339) follows:
% 31.66/10.49 | (6419) sum(n11, n6) = all_0_2_2
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (388) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 31.66/10.49 | (1344) all_0_5_5 = n7
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (619) with n11, n6, all_0_2_2, n17 and discharging atoms sum(n11, n6) = all_0_2_2, sum(n11, n6) = n17, yields:
% 31.66/10.49 | (771) all_0_2_2 = n17
% 31.66/10.49 |
% 31.66/10.49 | From (771) and (473) follows:
% 31.66/10.49 | (773) pred(n17) = all_0_1_1
% 31.66/10.49 |
% 31.66/10.49 | From (1344) and (6338) follows:
% 31.66/10.49 | (6423) sum(n11, n7) = all_0_4_4
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 31.66/10.49 | (776) all_0_1_1 = n16
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (619) with n11, n7, all_0_4_4, n18 and discharging atoms sum(n11, n7) = all_0_4_4, sum(n11, n7) = n18, yields:
% 31.66/10.49 | (772) all_0_4_4 = n18
% 31.66/10.49 |
% 31.66/10.49 | From (772) and (716) follows:
% 31.66/10.49 | (774) pred(n18) = all_0_3_3
% 31.66/10.49 |
% 31.66/10.49 | From (776) and (1342) follows:
% 31.66/10.49 | (6427) sum(n6, n16) = all_0_0_0
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 31.66/10.49 | (775) all_0_3_3 = n17
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (619) with n6, n16, all_0_0_0, n1 and discharging atoms sum(n6, n16) = all_0_0_0, sum(n6, n16) = n1, yields:
% 31.66/10.49 | (1017) all_0_0_0 = n1
% 31.66/10.49 |
% 31.66/10.49 | From (775)(1017) and (232) follows:
% 31.66/10.49 | (6430) sum(n17, n1) = all_0_6_6
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (619) with n17, n1, all_0_6_6, n18 and discharging atoms sum(n17, n1) = all_0_6_6, sum(n17, n1) = n18, yields:
% 31.66/10.49 | (900) all_0_6_6 = n18
% 31.66/10.49 |
% 31.66/10.49 | Equations (900) can reduce 622 to:
% 31.66/10.49 | (748) $false
% 31.66/10.49 |
% 31.66/10.49 |-The branch is then unsatisfiable
% 31.66/10.49 |-Branch two:
% 31.66/10.49 | (1357) ~ (all_0_7_7 = n6)
% 31.66/10.49 | (1358) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.66/10.49 |
% 31.66/10.49 +-Applying beta-rule and splitting (1358), into two cases.
% 31.66/10.49 |-Branch one:
% 31.66/10.49 | (1359) all_0_7_7 = n5
% 31.66/10.49 |
% 31.66/10.49 | From (1359) and (683) follows:
% 31.66/10.49 | (1360) succ(n5) = all_0_5_5
% 31.66/10.49 |
% 31.66/10.49 | From (1359) and (8) follows:
% 31.66/10.49 | (1361) sum(n5, all_0_1_1) = all_0_0_0
% 31.66/10.49 |
% 31.66/10.49 | From (1359) and (6339) follows:
% 31.66/10.49 | (6438) sum(n11, n5) = all_0_2_2
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (388) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 31.66/10.49 | (1363) all_0_5_5 = n6
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (619) with n11, n5, all_0_2_2, n16 and discharging atoms sum(n11, n5) = all_0_2_2, sum(n11, n5) = n16, yields:
% 31.66/10.49 | (788) all_0_2_2 = n16
% 31.66/10.49 |
% 31.66/10.49 | From (788) and (473) follows:
% 31.66/10.49 | (790) pred(n16) = all_0_1_1
% 31.66/10.49 |
% 31.66/10.49 | From (1363) and (6338) follows:
% 31.66/10.49 | (6442) sum(n11, n6) = all_0_4_4
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 31.66/10.49 | (793) all_0_1_1 = n15
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (619) with n11, n6, all_0_4_4, n17 and discharging atoms sum(n11, n6) = all_0_4_4, sum(n11, n6) = n17, yields:
% 31.66/10.49 | (789) all_0_4_4 = n17
% 31.66/10.49 |
% 31.66/10.49 | From (789) and (716) follows:
% 31.66/10.49 | (791) pred(n17) = all_0_3_3
% 31.66/10.49 |
% 31.66/10.49 | From (793) and (1361) follows:
% 31.66/10.49 | (6446) sum(n5, n15) = all_0_0_0
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 31.66/10.49 | (792) all_0_3_3 = n16
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (619) with n5, n15, all_0_0_0, n20 and discharging atoms sum(n5, n15) = all_0_0_0, sum(n5, n15) = n20, yields:
% 31.66/10.49 | (1051) all_0_0_0 = n20
% 31.66/10.49 |
% 31.66/10.49 | From (792)(1051) and (232) follows:
% 31.66/10.49 | (6449) sum(n16, n20) = all_0_6_6
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (619) with n16, n20, all_0_6_6, n15 and discharging atoms sum(n16, n20) = all_0_6_6, sum(n16, n20) = n15, yields:
% 31.66/10.49 | (747) all_0_6_6 = n15
% 31.66/10.49 |
% 31.66/10.49 | Equations (747) can reduce 456 to:
% 31.66/10.49 | (748) $false
% 31.66/10.49 |
% 31.66/10.49 |-The branch is then unsatisfiable
% 31.66/10.49 |-Branch two:
% 31.66/10.49 | (1376) ~ (all_0_7_7 = n5)
% 31.66/10.49 | (1377) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.66/10.49 |
% 31.66/10.49 +-Applying beta-rule and splitting (1377), into two cases.
% 31.66/10.49 |-Branch one:
% 31.66/10.49 | (1378) all_0_7_7 = n4
% 31.66/10.49 |
% 31.66/10.49 | From (1378) and (683) follows:
% 31.66/10.49 | (1379) succ(n4) = all_0_5_5
% 31.66/10.49 |
% 31.66/10.49 | From (1378) and (8) follows:
% 31.66/10.49 | (1380) sum(n4, all_0_1_1) = all_0_0_0
% 31.66/10.49 |
% 31.66/10.49 | From (1378) and (6339) follows:
% 31.66/10.49 | (6457) sum(n11, n4) = all_0_2_2
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (388) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 31.66/10.49 | (1382) all_0_5_5 = n5
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (619) with n11, n4, all_0_2_2, n15 and discharging atoms sum(n11, n4) = all_0_2_2, sum(n11, n4) = n15, yields:
% 31.66/10.49 | (805) all_0_2_2 = n15
% 31.66/10.49 |
% 31.66/10.49 | From (805) and (473) follows:
% 31.66/10.49 | (807) pred(n15) = all_0_1_1
% 31.66/10.49 |
% 31.66/10.49 | From (1382) and (6338) follows:
% 31.66/10.49 | (6461) sum(n11, n5) = all_0_4_4
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 31.66/10.49 | (810) all_0_1_1 = n14
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (619) with n11, n5, all_0_4_4, n16 and discharging atoms sum(n11, n5) = all_0_4_4, sum(n11, n5) = n16, yields:
% 31.66/10.49 | (806) all_0_4_4 = n16
% 31.66/10.49 |
% 31.66/10.49 | From (806) and (716) follows:
% 31.66/10.49 | (808) pred(n16) = all_0_3_3
% 31.66/10.49 |
% 31.66/10.49 | From (810) and (1380) follows:
% 31.66/10.49 | (6465) sum(n4, n14) = all_0_0_0
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 31.66/10.49 | (809) all_0_3_3 = n15
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (619) with n4, n14, all_0_0_0, n18 and discharging atoms sum(n4, n14) = all_0_0_0, sum(n4, n14) = n18, yields:
% 31.66/10.49 | (1084) all_0_0_0 = n18
% 31.66/10.49 |
% 31.66/10.49 | From (809)(1084) and (232) follows:
% 31.66/10.49 | (6468) sum(n15, n18) = all_0_6_6
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (619) with n15, n18, all_0_6_6, n12 and discharging atoms sum(n15, n18) = all_0_6_6, sum(n15, n18) = n12, yields:
% 31.66/10.49 | (951) all_0_6_6 = n12
% 31.66/10.49 |
% 31.66/10.49 | Equations (951) can reduce 76 to:
% 31.66/10.49 | (748) $false
% 31.66/10.49 |
% 31.66/10.49 |-The branch is then unsatisfiable
% 31.66/10.49 |-Branch two:
% 31.66/10.49 | (1395) ~ (all_0_7_7 = n4)
% 31.66/10.49 | (1396) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.66/10.49 |
% 31.66/10.49 +-Applying beta-rule and splitting (1396), into two cases.
% 31.66/10.49 |-Branch one:
% 31.66/10.49 | (1397) all_0_7_7 = n3
% 31.66/10.49 |
% 31.66/10.49 | From (1397) and (683) follows:
% 31.66/10.49 | (1398) succ(n3) = all_0_5_5
% 31.66/10.49 |
% 31.66/10.49 | From (1397) and (8) follows:
% 31.66/10.49 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 31.66/10.49 |
% 31.66/10.49 | From (1397) and (6339) follows:
% 31.66/10.49 | (6476) sum(n11, n3) = all_0_2_2
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 31.66/10.49 | (1401) all_0_5_5 = n4
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (619) with n11, n3, all_0_2_2, n14 and discharging atoms sum(n11, n3) = all_0_2_2, sum(n11, n3) = n14, yields:
% 31.66/10.49 | (822) all_0_2_2 = n14
% 31.66/10.49 |
% 31.66/10.49 | From (822) and (473) follows:
% 31.66/10.49 | (824) pred(n14) = all_0_1_1
% 31.66/10.49 |
% 31.66/10.49 | From (1401) and (6338) follows:
% 31.66/10.49 | (6480) sum(n11, n4) = all_0_4_4
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 31.66/10.49 | (827) all_0_1_1 = n13
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (619) with n11, n4, all_0_4_4, n15 and discharging atoms sum(n11, n4) = all_0_4_4, sum(n11, n4) = n15, yields:
% 31.66/10.49 | (823) all_0_4_4 = n15
% 31.66/10.49 |
% 31.66/10.49 | From (823) and (716) follows:
% 31.66/10.49 | (825) pred(n15) = all_0_3_3
% 31.66/10.49 |
% 31.66/10.49 | From (827) and (1399) follows:
% 31.66/10.49 | (6484) sum(n3, n13) = all_0_0_0
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 31.66/10.49 | (826) all_0_3_3 = n14
% 31.66/10.49 |
% 31.66/10.49 | Instantiating formula (619) with n3, n13, all_0_0_0, n16 and discharging atoms sum(n3, n13) = all_0_0_0, sum(n3, n13) = n16, yields:
% 31.66/10.49 | (762) all_0_0_0 = n16
% 31.66/10.49 |
% 31.66/10.49 | From (826)(762) and (232) follows:
% 31.66/10.50 | (6487) sum(n14, n16) = all_0_6_6
% 31.66/10.50 |
% 31.66/10.50 | Instantiating formula (619) with n14, n16, all_0_6_6, n9 and discharging atoms sum(n14, n16) = all_0_6_6, sum(n14, n16) = n9, yields:
% 31.66/10.50 | (798) all_0_6_6 = n9
% 31.66/10.50 |
% 31.66/10.50 | Equations (798) can reduce 593 to:
% 31.66/10.50 | (748) $false
% 31.66/10.50 |
% 31.66/10.50 |-The branch is then unsatisfiable
% 31.66/10.50 |-Branch two:
% 31.66/10.50 | (1414) ~ (all_0_7_7 = n3)
% 31.66/10.50 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.66/10.50 |
% 31.66/10.50 +-Applying beta-rule and splitting (1415), into two cases.
% 31.66/10.50 |-Branch one:
% 31.66/10.50 | (1416) all_0_7_7 = n2
% 31.66/10.50 |
% 31.66/10.50 | From (1416) and (683) follows:
% 31.66/10.50 | (1417) succ(n2) = all_0_5_5
% 31.66/10.50 |
% 31.66/10.50 | From (1416) and (8) follows:
% 31.66/10.50 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 31.66/10.50 |
% 31.66/10.50 | From (1416) and (6339) follows:
% 31.66/10.50 | (6495) sum(n11, n2) = all_0_2_2
% 31.66/10.50 |
% 31.66/10.50 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.66/10.50 | (1420) all_0_5_5 = n3
% 31.66/10.50 |
% 31.66/10.50 | Instantiating formula (619) with n11, n2, all_0_2_2, n13 and discharging atoms sum(n11, n2) = all_0_2_2, sum(n11, n2) = n13, yields:
% 31.66/10.50 | (839) all_0_2_2 = n13
% 31.66/10.50 |
% 31.66/10.50 | From (839) and (473) follows:
% 31.66/10.50 | (841) pred(n13) = all_0_1_1
% 31.66/10.50 |
% 31.66/10.50 | From (1420) and (6338) follows:
% 31.66/10.50 | (6499) sum(n11, n3) = all_0_4_4
% 31.66/10.50 |
% 31.66/10.50 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 31.66/10.50 | (844) all_0_1_1 = n12
% 31.66/10.50 |
% 31.66/10.50 | Instantiating formula (619) with n11, n3, all_0_4_4, n14 and discharging atoms sum(n11, n3) = all_0_4_4, sum(n11, n3) = n14, yields:
% 31.66/10.50 | (840) all_0_4_4 = n14
% 31.66/10.50 |
% 31.66/10.50 | From (840) and (716) follows:
% 31.66/10.50 | (842) pred(n14) = all_0_3_3
% 31.66/10.50 |
% 31.66/10.50 | From (844) and (1418) follows:
% 31.66/10.50 | (6503) sum(n2, n12) = all_0_0_0
% 31.66/10.50 |
% 31.66/10.50 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 31.66/10.50 | (843) all_0_3_3 = n13
% 31.66/10.50 |
% 31.66/10.50 | Instantiating formula (619) with n2, n12, all_0_0_0, n14 and discharging atoms sum(n2, n12) = all_0_0_0, sum(n2, n12) = n14, yields:
% 31.66/10.50 | (796) all_0_0_0 = n14
% 31.66/10.50 |
% 31.66/10.50 | From (843)(796) and (232) follows:
% 31.66/10.50 | (6506) sum(n13, n14) = all_0_6_6
% 31.66/10.50 |
% 31.66/10.50 | Instantiating formula (619) with n13, n14, all_0_6_6, n6 and discharging atoms sum(n13, n14) = all_0_6_6, sum(n13, n14) = n6, yields:
% 31.66/10.50 | (1002) all_0_6_6 = n6
% 31.66/10.50 |
% 31.66/10.50 | Equations (1002) can reduce 498 to:
% 31.66/10.50 | (748) $false
% 31.66/10.50 |
% 31.66/10.50 |-The branch is then unsatisfiable
% 31.66/10.50 |-Branch two:
% 31.66/10.50 | (1433) ~ (all_0_7_7 = n2)
% 31.66/10.50 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 31.66/10.50 |
% 31.66/10.50 +-Applying beta-rule and splitting (1434), into two cases.
% 31.66/10.50 |-Branch one:
% 31.66/10.50 | (1435) all_0_7_7 = n1
% 31.66/10.50 |
% 31.66/10.50 | From (1435) and (683) follows:
% 31.66/10.50 | (1436) succ(n1) = all_0_5_5
% 31.66/10.50 |
% 31.66/10.50 | From (1435) and (8) follows:
% 31.66/10.50 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 31.66/10.50 |
% 31.66/10.50 | From (1435) and (6339) follows:
% 31.66/10.50 | (6514) sum(n11, n1) = all_0_2_2
% 31.66/10.50 |
% 31.74/10.50 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.74/10.50 | (1439) all_0_5_5 = n2
% 31.74/10.50 |
% 31.74/10.50 | Instantiating formula (619) with n11, n1, all_0_2_2, n12 and discharging atoms sum(n11, n1) = all_0_2_2, sum(n11, n1) = n12, yields:
% 31.74/10.50 | (856) all_0_2_2 = n12
% 31.74/10.50 |
% 31.74/10.50 | From (856) and (473) follows:
% 31.74/10.50 | (858) pred(n12) = all_0_1_1
% 31.74/10.50 |
% 31.74/10.50 | From (1439) and (6338) follows:
% 31.74/10.50 | (6518) sum(n11, n2) = all_0_4_4
% 31.74/10.50 |
% 31.74/10.50 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 31.74/10.50 | (861) all_0_1_1 = n11
% 31.74/10.50 |
% 31.74/10.50 | Instantiating formula (619) with n11, n2, all_0_4_4, n13 and discharging atoms sum(n11, n2) = all_0_4_4, sum(n11, n2) = n13, yields:
% 31.74/10.50 | (857) all_0_4_4 = n13
% 31.74/10.50 |
% 31.74/10.50 | From (857) and (716) follows:
% 31.74/10.50 | (859) pred(n13) = all_0_3_3
% 31.74/10.50 |
% 31.74/10.50 | From (861) and (1437) follows:
% 31.74/10.50 | (6522) sum(n1, n11) = all_0_0_0
% 31.74/10.50 |
% 31.74/10.50 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 31.74/10.50 | (860) all_0_3_3 = n12
% 31.74/10.50 |
% 31.74/10.50 | Instantiating formula (619) with n1, n11, all_0_0_0, n12 and discharging atoms sum(n1, n11) = all_0_0_0, sum(n1, n11) = n12, yields:
% 31.74/10.50 | (830) all_0_0_0 = n12
% 31.74/10.50 |
% 31.74/10.50 | From (860)(830) and (232) follows:
% 31.74/10.50 | (6525) sum(n12, n12) = all_0_6_6
% 31.74/10.50 |
% 31.74/10.50 | Instantiating formula (619) with n12, n12, all_0_6_6, n3 and discharging atoms sum(n12, n12) = all_0_6_6, sum(n12, n12) = n3, yields:
% 31.74/10.50 | (849) all_0_6_6 = n3
% 31.74/10.50 |
% 31.74/10.50 | Equations (849) can reduce 416 to:
% 31.74/10.50 | (748) $false
% 31.74/10.50 |
% 31.74/10.50 |-The branch is then unsatisfiable
% 31.74/10.50 |-Branch two:
% 31.74/10.50 | (1452) ~ (all_0_7_7 = n1)
% 31.74/10.50 | (1453) all_0_7_7 = n0
% 31.74/10.50 |
% 31.74/10.50 | From (1453) and (683) follows:
% 31.74/10.50 | (1454) succ(n0) = all_0_5_5
% 31.74/10.50 |
% 31.74/10.50 | From (1453) and (8) follows:
% 31.74/10.50 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 31.74/10.50 |
% 31.74/10.50 | From (1453) and (6339) follows:
% 31.74/10.50 | (6532) sum(n11, n0) = all_0_2_2
% 31.74/10.50 |
% 31.74/10.50 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.74/10.50 | (1457) all_0_5_5 = n1
% 31.74/10.50 |
% 31.74/10.50 | Instantiating formula (619) with n11, n0, all_0_2_2, n11 and discharging atoms sum(n11, n0) = all_0_2_2, sum(n11, n0) = n11, yields:
% 31.74/10.50 | (873) all_0_2_2 = n11
% 31.74/10.50 |
% 31.74/10.50 | From (873) and (473) follows:
% 31.74/10.50 | (875) pred(n11) = all_0_1_1
% 31.74/10.50 |
% 31.74/10.50 | From (1457) and (6338) follows:
% 31.74/10.50 | (6536) sum(n11, n1) = all_0_4_4
% 31.74/10.50 |
% 31.74/10.50 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 31.74/10.50 | (878) all_0_1_1 = n10
% 31.74/10.50 |
% 31.74/10.50 | Instantiating formula (619) with n11, n1, all_0_4_4, n12 and discharging atoms sum(n11, n1) = all_0_4_4, sum(n11, n1) = n12, yields:
% 31.74/10.50 | (874) all_0_4_4 = n12
% 31.74/10.50 |
% 31.74/10.50 | From (874) and (716) follows:
% 31.74/10.50 | (876) pred(n12) = all_0_3_3
% 31.74/10.50 |
% 31.74/10.50 | From (878) and (1455) follows:
% 31.74/10.50 | (6540) sum(n0, n10) = all_0_0_0
% 31.74/10.50 |
% 31.74/10.50 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 31.74/10.50 | (877) all_0_3_3 = n11
% 31.74/10.50 |
% 31.74/10.50 | Instantiating formula (619) with n0, n10, all_0_0_0, n10 and discharging atoms sum(n0, n10) = all_0_0_0, sum(n0, n10) = n10, yields:
% 31.74/10.50 | (864) all_0_0_0 = n10
% 31.74/10.50 |
% 31.74/10.50 | From (877)(864) and (232) follows:
% 31.74/10.50 | (6543) sum(n11, n10) = all_0_6_6
% 31.74/10.50 |
% 31.74/10.50 | Instantiating formula (619) with n11, n10, all_0_6_6, n0 and discharging atoms sum(n11, n10) = all_0_6_6, sum(n11, n10) = n0, yields:
% 31.74/10.50 | (1053) all_0_6_6 = n0
% 31.74/10.50 |
% 31.74/10.50 | Equations (1053) can reduce 676 to:
% 31.74/10.50 | (748) $false
% 31.74/10.50 |
% 31.74/10.50 |-The branch is then unsatisfiable
% 31.74/10.50 |-Branch two:
% 31.74/10.50 | (902) ~ (all_0_8_8 = n11)
% 31.74/10.50 | (903) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.74/10.50 |
% 31.74/10.50 +-Applying beta-rule and splitting (1263), into two cases.
% 31.74/10.50 |-Branch one:
% 31.74/10.50 | (1264) all_0_7_7 = n10
% 31.74/10.50 |
% 31.74/10.50 | From (1264) and (683) follows:
% 31.74/10.50 | (1265) succ(n10) = all_0_5_5
% 31.74/10.50 |
% 31.74/10.50 | From (1264) and (8) follows:
% 31.74/10.50 | (1266) sum(n10, all_0_1_1) = all_0_0_0
% 31.74/10.50 |
% 31.74/10.50 | From (1264) and (378) follows:
% 31.74/10.50 | (6551) sum(all_0_8_8, n10) = all_0_2_2
% 31.74/10.50 |
% 31.74/10.50 | Instantiating formula (388) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 31.74/10.50 | (1268) all_0_5_5 = n11
% 31.74/10.50 |
% 31.74/10.50 | From (1268) and (708) follows:
% 31.74/10.50 | (6553) sum(all_0_8_8, n11) = all_0_4_4
% 31.74/10.50 |
% 31.74/10.50 +-Applying beta-rule and splitting (903), into two cases.
% 31.74/10.50 |-Branch one:
% 31.74/10.50 | (904) all_0_8_8 = n10
% 31.74/10.50 |
% 31.74/10.50 | From (904) and (6553) follows:
% 31.74/10.50 | (6555) sum(n10, n11) = all_0_4_4
% 31.74/10.50 |
% 31.74/10.50 | From (904) and (6551) follows:
% 31.74/10.50 | (6556) sum(n10, n10) = all_0_2_2
% 31.74/10.50 |
% 31.74/10.50 | Instantiating formula (619) with n10, n11, all_0_4_4, n0 and discharging atoms sum(n10, n11) = all_0_4_4, sum(n10, n11) = n0, yields:
% 31.74/10.50 | (1077) all_0_4_4 = n0
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n10, n10, all_0_2_2, n20 and discharging atoms sum(n10, n10) = all_0_2_2, sum(n10, n10) = n20, yields:
% 31.74/10.51 | (1076) all_0_2_2 = n20
% 31.74/10.51 |
% 31.74/10.51 | From (1076) and (473) follows:
% 31.74/10.51 | (1078) pred(n20) = all_0_1_1
% 31.74/10.51 |
% 31.74/10.51 | From (1077) and (716) follows:
% 31.74/10.51 | (1079) pred(n0) = all_0_3_3
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (244) with n20, all_0_1_1, n19 and discharging atoms pred(n20) = all_0_1_1, pred(n20) = n19, yields:
% 31.74/10.51 | (1080) all_0_1_1 = n19
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (244) with n0, all_0_3_3, n20 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n20, yields:
% 31.74/10.51 | (1081) all_0_3_3 = n20
% 31.74/10.51 |
% 31.74/10.51 | From (1081) and (232) follows:
% 31.74/10.51 | (1082) sum(n20, all_0_0_0) = all_0_6_6
% 31.74/10.51 |
% 31.74/10.51 | From (1080) and (1266) follows:
% 31.74/10.51 | (6564) sum(n10, n19) = all_0_0_0
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n10, n19, all_0_0_0, n8 and discharging atoms sum(n10, n19) = all_0_0_0, sum(n10, n19) = n8, yields:
% 31.74/10.51 | (898) all_0_0_0 = n8
% 31.74/10.51 |
% 31.74/10.51 | From (898) and (1082) follows:
% 31.74/10.51 | (6566) sum(n20, n8) = all_0_6_6
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n20, n8, all_0_6_6, n7 and discharging atoms sum(n20, n8) = all_0_6_6, sum(n20, n8) = n7, yields:
% 31.74/10.51 | (815) all_0_6_6 = n7
% 31.74/10.51 |
% 31.74/10.51 | Equations (815) can reduce 557 to:
% 31.74/10.51 | (748) $false
% 31.74/10.51 |
% 31.74/10.51 |-The branch is then unsatisfiable
% 31.74/10.51 |-Branch two:
% 31.74/10.51 | (919) ~ (all_0_8_8 = n10)
% 31.74/10.51 | (920) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.74/10.51 |
% 31.74/10.51 +-Applying beta-rule and splitting (920), into two cases.
% 31.74/10.51 |-Branch one:
% 31.74/10.51 | (921) all_0_8_8 = n9
% 31.74/10.51 |
% 31.74/10.51 | From (921) and (6553) follows:
% 31.74/10.51 | (6572) sum(n9, n11) = all_0_4_4
% 31.74/10.51 |
% 31.74/10.51 | From (921) and (6551) follows:
% 31.74/10.51 | (6573) sum(n9, n10) = all_0_2_2
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n9, n11, all_0_4_4, n20 and discharging atoms sum(n9, n11) = all_0_4_4, sum(n9, n11) = n20, yields:
% 31.74/10.51 | (738) all_0_4_4 = n20
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n9, n10, all_0_2_2, n19 and discharging atoms sum(n9, n10) = all_0_2_2, sum(n9, n10) = n19, yields:
% 31.74/10.51 | (737) all_0_2_2 = n19
% 31.74/10.51 |
% 31.74/10.51 | From (737) and (473) follows:
% 31.74/10.51 | (739) pred(n19) = all_0_1_1
% 31.74/10.51 |
% 31.74/10.51 | From (738) and (716) follows:
% 31.74/10.51 | (740) pred(n20) = all_0_3_3
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 31.74/10.51 | (741) all_0_3_3 = n19
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 31.74/10.51 | (742) all_0_1_1 = n18
% 31.74/10.51 |
% 31.74/10.51 | From (741) and (232) follows:
% 31.74/10.51 | (743) sum(n19, all_0_0_0) = all_0_6_6
% 31.74/10.51 |
% 31.74/10.51 | From (742) and (1266) follows:
% 31.74/10.51 | (6581) sum(n10, n18) = all_0_0_0
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n10, n18, all_0_0_0, n7 and discharging atoms sum(n10, n18) = all_0_0_0, sum(n10, n18) = n7, yields:
% 31.74/10.51 | (915) all_0_0_0 = n7
% 31.74/10.51 |
% 31.74/10.51 | From (915) and (743) follows:
% 31.74/10.51 | (6583) sum(n19, n7) = all_0_6_6
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n19, n7, all_0_6_6, n5 and discharging atoms sum(n19, n7) = all_0_6_6, sum(n19, n7) = n5, yields:
% 31.74/10.51 | (832) all_0_6_6 = n5
% 31.74/10.51 |
% 31.74/10.51 | Equations (832) can reduce 462 to:
% 31.74/10.51 | (748) $false
% 31.74/10.51 |
% 31.74/10.51 |-The branch is then unsatisfiable
% 31.74/10.51 |-Branch two:
% 31.74/10.51 | (936) ~ (all_0_8_8 = n9)
% 31.74/10.51 | (937) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.74/10.51 |
% 31.74/10.51 +-Applying beta-rule and splitting (937), into two cases.
% 31.74/10.51 |-Branch one:
% 31.74/10.51 | (938) all_0_8_8 = n8
% 31.74/10.51 |
% 31.74/10.51 | From (938) and (6553) follows:
% 31.74/10.51 | (6589) sum(n8, n11) = all_0_4_4
% 31.74/10.51 |
% 31.74/10.51 | From (938) and (6551) follows:
% 31.74/10.51 | (6590) sum(n8, n10) = all_0_2_2
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n8, n11, all_0_4_4, n19 and discharging atoms sum(n8, n11) = all_0_4_4, sum(n8, n11) = n19, yields:
% 31.74/10.51 | (755) all_0_4_4 = n19
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 31.74/10.51 | (754) all_0_2_2 = n18
% 31.74/10.51 |
% 31.74/10.51 | From (754) and (473) follows:
% 31.74/10.51 | (756) pred(n18) = all_0_1_1
% 31.74/10.51 |
% 31.74/10.51 | From (755) and (716) follows:
% 31.74/10.51 | (757) pred(n19) = all_0_3_3
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 31.74/10.51 | (758) all_0_3_3 = n18
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 31.74/10.51 | (759) all_0_1_1 = n17
% 31.74/10.51 |
% 31.74/10.51 | From (758) and (232) follows:
% 31.74/10.51 | (760) sum(n18, all_0_0_0) = all_0_6_6
% 31.74/10.51 |
% 31.74/10.51 | From (759) and (1266) follows:
% 31.74/10.51 | (6598) sum(n10, n17) = all_0_0_0
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n10, n17, all_0_0_0, n6 and discharging atoms sum(n10, n17) = all_0_0_0, sum(n10, n17) = n6, yields:
% 31.74/10.51 | (932) all_0_0_0 = n6
% 31.74/10.51 |
% 31.74/10.51 | From (932) and (760) follows:
% 31.74/10.51 | (6600) sum(n18, n6) = all_0_6_6
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n18, n6, all_0_6_6, n3 and discharging atoms sum(n18, n6) = all_0_6_6, sum(n18, n6) = n3, yields:
% 31.74/10.51 | (849) all_0_6_6 = n3
% 31.74/10.51 |
% 31.74/10.51 | Equations (849) can reduce 416 to:
% 31.74/10.51 | (748) $false
% 31.74/10.51 |
% 31.74/10.51 |-The branch is then unsatisfiable
% 31.74/10.51 |-Branch two:
% 31.74/10.51 | (953) ~ (all_0_8_8 = n8)
% 31.74/10.51 | (954) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.74/10.51 |
% 31.74/10.51 +-Applying beta-rule and splitting (954), into two cases.
% 31.74/10.51 |-Branch one:
% 31.74/10.51 | (955) all_0_8_8 = n7
% 31.74/10.51 |
% 31.74/10.51 | From (955) and (6553) follows:
% 31.74/10.51 | (6606) sum(n7, n11) = all_0_4_4
% 31.74/10.51 |
% 31.74/10.51 | From (955) and (6551) follows:
% 31.74/10.51 | (6607) sum(n7, n10) = all_0_2_2
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n7, n11, all_0_4_4, n18 and discharging atoms sum(n7, n11) = all_0_4_4, sum(n7, n11) = n18, yields:
% 31.74/10.51 | (772) all_0_4_4 = n18
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n7, n10, all_0_2_2, n17 and discharging atoms sum(n7, n10) = all_0_2_2, sum(n7, n10) = n17, yields:
% 31.74/10.51 | (771) all_0_2_2 = n17
% 31.74/10.51 |
% 31.74/10.51 | From (771) and (473) follows:
% 31.74/10.51 | (773) pred(n17) = all_0_1_1
% 31.74/10.51 |
% 31.74/10.51 | From (772) and (716) follows:
% 31.74/10.51 | (774) pred(n18) = all_0_3_3
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 31.74/10.51 | (775) all_0_3_3 = n17
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 31.74/10.51 | (776) all_0_1_1 = n16
% 31.74/10.51 |
% 31.74/10.51 | From (775) and (232) follows:
% 31.74/10.51 | (777) sum(n17, all_0_0_0) = all_0_6_6
% 31.74/10.51 |
% 31.74/10.51 | From (776) and (1266) follows:
% 31.74/10.51 | (6615) sum(n10, n16) = all_0_0_0
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n10, n16, all_0_0_0, n5 and discharging atoms sum(n10, n16) = all_0_0_0, sum(n10, n16) = n5, yields:
% 31.74/10.51 | (949) all_0_0_0 = n5
% 31.74/10.51 |
% 31.74/10.51 | From (949) and (777) follows:
% 31.74/10.51 | (6617) sum(n17, n5) = all_0_6_6
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n17, n5, all_0_6_6, n1 and discharging atoms sum(n17, n5) = all_0_6_6, sum(n17, n5) = n1, yields:
% 31.74/10.51 | (866) all_0_6_6 = n1
% 31.74/10.51 |
% 31.74/10.51 | Equations (866) can reduce 28 to:
% 31.74/10.51 | (748) $false
% 31.74/10.51 |
% 31.74/10.51 |-The branch is then unsatisfiable
% 31.74/10.51 |-Branch two:
% 31.74/10.51 | (970) ~ (all_0_8_8 = n7)
% 31.74/10.51 | (971) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.74/10.51 |
% 31.74/10.51 +-Applying beta-rule and splitting (971), into two cases.
% 31.74/10.51 |-Branch one:
% 31.74/10.51 | (972) all_0_8_8 = n6
% 31.74/10.51 |
% 31.74/10.51 | From (972) and (6553) follows:
% 31.74/10.51 | (6623) sum(n6, n11) = all_0_4_4
% 31.74/10.51 |
% 31.74/10.51 | From (972) and (6551) follows:
% 31.74/10.51 | (6624) sum(n6, n10) = all_0_2_2
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n6, n11, all_0_4_4, n17 and discharging atoms sum(n6, n11) = all_0_4_4, sum(n6, n11) = n17, yields:
% 31.74/10.51 | (789) all_0_4_4 = n17
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n6, n10, all_0_2_2, n16 and discharging atoms sum(n6, n10) = all_0_2_2, sum(n6, n10) = n16, yields:
% 31.74/10.51 | (788) all_0_2_2 = n16
% 31.74/10.51 |
% 31.74/10.51 | From (788) and (473) follows:
% 31.74/10.51 | (790) pred(n16) = all_0_1_1
% 31.74/10.51 |
% 31.74/10.51 | From (789) and (716) follows:
% 31.74/10.51 | (791) pred(n17) = all_0_3_3
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 31.74/10.51 | (792) all_0_3_3 = n16
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 31.74/10.51 | (793) all_0_1_1 = n15
% 31.74/10.51 |
% 31.74/10.51 | From (792) and (232) follows:
% 31.74/10.51 | (794) sum(n16, all_0_0_0) = all_0_6_6
% 31.74/10.51 |
% 31.74/10.51 | From (793) and (1266) follows:
% 31.74/10.51 | (6632) sum(n10, n15) = all_0_0_0
% 31.74/10.51 |
% 31.74/10.51 | Instantiating formula (619) with n10, n15, all_0_0_0, n4 and discharging atoms sum(n10, n15) = all_0_0_0, sum(n10, n15) = n4, yields:
% 31.74/10.51 | (966) all_0_0_0 = n4
% 31.74/10.51 |
% 31.74/10.51 | From (966) and (794) follows:
% 31.74/10.52 | (6634) sum(n16, n4) = all_0_6_6
% 31.74/10.52 |
% 31.74/10.52 | Instantiating formula (619) with n16, n4, all_0_6_6, n20 and discharging atoms sum(n16, n4) = all_0_6_6, sum(n16, n4) = n20, yields:
% 31.74/10.52 | (883) all_0_6_6 = n20
% 31.74/10.52 |
% 31.74/10.52 | Equations (883) can reduce 381 to:
% 31.74/10.52 | (748) $false
% 31.74/10.52 |
% 31.74/10.52 |-The branch is then unsatisfiable
% 31.74/10.52 |-Branch two:
% 31.74/10.52 | (987) ~ (all_0_8_8 = n6)
% 31.74/10.52 | (988) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.74/10.52 |
% 31.74/10.52 +-Applying beta-rule and splitting (988), into two cases.
% 31.74/10.52 |-Branch one:
% 31.74/10.52 | (989) all_0_8_8 = n5
% 31.74/10.52 |
% 31.74/10.52 | From (989) and (6553) follows:
% 31.74/10.52 | (6640) sum(n5, n11) = all_0_4_4
% 31.74/10.52 |
% 31.74/10.52 | From (989) and (6551) follows:
% 31.80/10.52 | (6641) sum(n5, n10) = all_0_2_2
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (619) with n5, n11, all_0_4_4, n16 and discharging atoms sum(n5, n11) = all_0_4_4, sum(n5, n11) = n16, yields:
% 31.80/10.52 | (806) all_0_4_4 = n16
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (619) with n5, n10, all_0_2_2, n15 and discharging atoms sum(n5, n10) = all_0_2_2, sum(n5, n10) = n15, yields:
% 31.80/10.52 | (805) all_0_2_2 = n15
% 31.80/10.52 |
% 31.80/10.52 | From (805) and (473) follows:
% 31.80/10.52 | (807) pred(n15) = all_0_1_1
% 31.80/10.52 |
% 31.80/10.52 | From (806) and (716) follows:
% 31.80/10.52 | (808) pred(n16) = all_0_3_3
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 31.80/10.52 | (809) all_0_3_3 = n15
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 31.80/10.52 | (810) all_0_1_1 = n14
% 31.80/10.52 |
% 31.80/10.52 | From (809) and (232) follows:
% 31.80/10.52 | (811) sum(n15, all_0_0_0) = all_0_6_6
% 31.80/10.52 |
% 31.80/10.52 | From (810) and (1266) follows:
% 31.80/10.52 | (6649) sum(n10, n14) = all_0_0_0
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (619) with n10, n14, all_0_0_0, n3 and discharging atoms sum(n10, n14) = all_0_0_0, sum(n10, n14) = n3, yields:
% 31.80/10.52 | (983) all_0_0_0 = n3
% 31.80/10.52 |
% 31.80/10.52 | From (983) and (811) follows:
% 31.80/10.52 | (6651) sum(n15, n3) = all_0_6_6
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (619) with n15, n3, all_0_6_6, n18 and discharging atoms sum(n15, n3) = all_0_6_6, sum(n15, n3) = n18, yields:
% 31.80/10.52 | (900) all_0_6_6 = n18
% 31.80/10.52 |
% 31.80/10.52 | Equations (900) can reduce 622 to:
% 31.80/10.52 | (748) $false
% 31.80/10.52 |
% 31.80/10.52 |-The branch is then unsatisfiable
% 31.80/10.52 |-Branch two:
% 31.80/10.52 | (1004) ~ (all_0_8_8 = n5)
% 31.80/10.52 | (1005) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.52 |
% 31.80/10.52 +-Applying beta-rule and splitting (1005), into two cases.
% 31.80/10.52 |-Branch one:
% 31.80/10.52 | (1006) all_0_8_8 = n4
% 31.80/10.52 |
% 31.80/10.52 | From (1006) and (6553) follows:
% 31.80/10.52 | (6657) sum(n4, n11) = all_0_4_4
% 31.80/10.52 |
% 31.80/10.52 | From (1006) and (6551) follows:
% 31.80/10.52 | (6658) sum(n4, n10) = all_0_2_2
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (619) with n4, n11, all_0_4_4, n15 and discharging atoms sum(n4, n11) = all_0_4_4, sum(n4, n11) = n15, yields:
% 31.80/10.52 | (823) all_0_4_4 = n15
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (619) with n4, n10, all_0_2_2, n14 and discharging atoms sum(n4, n10) = all_0_2_2, sum(n4, n10) = n14, yields:
% 31.80/10.52 | (822) all_0_2_2 = n14
% 31.80/10.52 |
% 31.80/10.52 | From (822) and (473) follows:
% 31.80/10.52 | (824) pred(n14) = all_0_1_1
% 31.80/10.52 |
% 31.80/10.52 | From (823) and (716) follows:
% 31.80/10.52 | (825) pred(n15) = all_0_3_3
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 31.80/10.52 | (826) all_0_3_3 = n14
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 31.80/10.52 | (827) all_0_1_1 = n13
% 31.80/10.52 |
% 31.80/10.52 | From (826) and (232) follows:
% 31.80/10.52 | (828) sum(n14, all_0_0_0) = all_0_6_6
% 31.80/10.52 |
% 31.80/10.52 | From (827) and (1266) follows:
% 31.80/10.52 | (6666) sum(n10, n13) = all_0_0_0
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (619) with n10, n13, all_0_0_0, n2 and discharging atoms sum(n10, n13) = all_0_0_0, sum(n10, n13) = n2, yields:
% 31.80/10.52 | (1000) all_0_0_0 = n2
% 31.80/10.52 |
% 31.80/10.52 | From (1000) and (828) follows:
% 31.80/10.52 | (6668) sum(n14, n2) = all_0_6_6
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (619) with n14, n2, all_0_6_6, n16 and discharging atoms sum(n14, n2) = all_0_6_6, sum(n14, n2) = n16, yields:
% 31.80/10.52 | (917) all_0_6_6 = n16
% 31.80/10.52 |
% 31.80/10.52 | Equations (917) can reduce 163 to:
% 31.80/10.52 | (748) $false
% 31.80/10.52 |
% 31.80/10.52 |-The branch is then unsatisfiable
% 31.80/10.52 |-Branch two:
% 31.80/10.52 | (1021) ~ (all_0_8_8 = n4)
% 31.80/10.52 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.52 |
% 31.80/10.52 +-Applying beta-rule and splitting (1022), into two cases.
% 31.80/10.52 |-Branch one:
% 31.80/10.52 | (1023) all_0_8_8 = n3
% 31.80/10.52 |
% 31.80/10.52 | From (1023) and (6553) follows:
% 31.80/10.52 | (6674) sum(n3, n11) = all_0_4_4
% 31.80/10.52 |
% 31.80/10.52 | From (1023) and (6551) follows:
% 31.80/10.52 | (6675) sum(n3, n10) = all_0_2_2
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (619) with n3, n11, all_0_4_4, n14 and discharging atoms sum(n3, n11) = all_0_4_4, sum(n3, n11) = n14, yields:
% 31.80/10.52 | (840) all_0_4_4 = n14
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (619) with n3, n10, all_0_2_2, n13 and discharging atoms sum(n3, n10) = all_0_2_2, sum(n3, n10) = n13, yields:
% 31.80/10.52 | (839) all_0_2_2 = n13
% 31.80/10.52 |
% 31.80/10.52 | From (839) and (473) follows:
% 31.80/10.52 | (841) pred(n13) = all_0_1_1
% 31.80/10.52 |
% 31.80/10.52 | From (840) and (716) follows:
% 31.80/10.52 | (842) pred(n14) = all_0_3_3
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 31.80/10.52 | (843) all_0_3_3 = n13
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 31.80/10.52 | (844) all_0_1_1 = n12
% 31.80/10.52 |
% 31.80/10.52 | From (843) and (232) follows:
% 31.80/10.52 | (845) sum(n13, all_0_0_0) = all_0_6_6
% 31.80/10.52 |
% 31.80/10.52 | From (844) and (1266) follows:
% 31.80/10.52 | (6683) sum(n10, n12) = all_0_0_0
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (619) with n10, n12, all_0_0_0, n1 and discharging atoms sum(n10, n12) = all_0_0_0, sum(n10, n12) = n1, yields:
% 31.80/10.52 | (1017) all_0_0_0 = n1
% 31.80/10.52 |
% 31.80/10.52 | From (1017) and (845) follows:
% 31.80/10.52 | (6685) sum(n13, n1) = all_0_6_6
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (619) with n13, n1, all_0_6_6, n14 and discharging atoms sum(n13, n1) = all_0_6_6, sum(n13, n1) = n14, yields:
% 31.80/10.52 | (934) all_0_6_6 = n14
% 31.80/10.52 |
% 31.80/10.52 | Equations (934) can reduce 353 to:
% 31.80/10.52 | (748) $false
% 31.80/10.52 |
% 31.80/10.52 |-The branch is then unsatisfiable
% 31.80/10.52 |-Branch two:
% 31.80/10.52 | (1038) ~ (all_0_8_8 = n3)
% 31.80/10.52 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.52 |
% 31.80/10.52 +-Applying beta-rule and splitting (1039), into two cases.
% 31.80/10.52 |-Branch one:
% 31.80/10.52 | (1040) all_0_8_8 = n2
% 31.80/10.52 |
% 31.80/10.52 | From (1040) and (6553) follows:
% 31.80/10.52 | (6691) sum(n2, n11) = all_0_4_4
% 31.80/10.52 |
% 31.80/10.52 | From (1040) and (6551) follows:
% 31.80/10.52 | (6692) sum(n2, n10) = all_0_2_2
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (619) with n2, n11, all_0_4_4, n13 and discharging atoms sum(n2, n11) = all_0_4_4, sum(n2, n11) = n13, yields:
% 31.80/10.52 | (857) all_0_4_4 = n13
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (619) with n2, n10, all_0_2_2, n12 and discharging atoms sum(n2, n10) = all_0_2_2, sum(n2, n10) = n12, yields:
% 31.80/10.52 | (856) all_0_2_2 = n12
% 31.80/10.52 |
% 31.80/10.52 | From (856) and (473) follows:
% 31.80/10.52 | (858) pred(n12) = all_0_1_1
% 31.80/10.52 |
% 31.80/10.52 | From (857) and (716) follows:
% 31.80/10.52 | (859) pred(n13) = all_0_3_3
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 31.80/10.52 | (860) all_0_3_3 = n12
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 31.80/10.52 | (861) all_0_1_1 = n11
% 31.80/10.52 |
% 31.80/10.52 | From (860) and (232) follows:
% 31.80/10.52 | (862) sum(n12, all_0_0_0) = all_0_6_6
% 31.80/10.52 |
% 31.80/10.52 | From (861) and (1266) follows:
% 31.80/10.52 | (6700) sum(n10, n11) = all_0_0_0
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (619) with n10, n11, all_0_0_0, n0 and discharging atoms sum(n10, n11) = all_0_0_0, sum(n10, n11) = n0, yields:
% 31.80/10.52 | (1034) all_0_0_0 = n0
% 31.80/10.52 |
% 31.80/10.52 | From (1034) and (862) follows:
% 31.80/10.52 | (6702) sum(n12, n0) = all_0_6_6
% 31.80/10.52 |
% 31.80/10.52 | Instantiating formula (619) with n12, n0, all_0_6_6, n12 and discharging atoms sum(n12, n0) = all_0_6_6, sum(n12, n0) = n12, yields:
% 31.80/10.52 | (951) all_0_6_6 = n12
% 31.80/10.52 |
% 31.80/10.52 | Equations (951) can reduce 76 to:
% 31.80/10.52 | (748) $false
% 31.80/10.52 |
% 31.80/10.52 |-The branch is then unsatisfiable
% 31.80/10.52 |-Branch two:
% 31.80/10.52 | (1055) ~ (all_0_8_8 = n2)
% 31.80/10.52 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.52 |
% 31.80/10.52 +-Applying beta-rule and splitting (1056), into two cases.
% 31.80/10.52 |-Branch one:
% 31.80/10.52 | (1057) all_0_8_8 = n1
% 31.80/10.52 |
% 31.80/10.52 | From (1057) and (6553) follows:
% 31.80/10.52 | (6708) sum(n1, n11) = all_0_4_4
% 31.80/10.52 |
% 31.80/10.52 | From (1057) and (6551) follows:
% 31.80/10.53 | (6709) sum(n1, n10) = all_0_2_2
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (619) with n1, n11, all_0_4_4, n12 and discharging atoms sum(n1, n11) = all_0_4_4, sum(n1, n11) = n12, yields:
% 31.80/10.53 | (874) all_0_4_4 = n12
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (619) with n1, n10, all_0_2_2, n11 and discharging atoms sum(n1, n10) = all_0_2_2, sum(n1, n10) = n11, yields:
% 31.80/10.53 | (873) all_0_2_2 = n11
% 31.80/10.53 |
% 31.80/10.53 | From (873) and (473) follows:
% 31.80/10.53 | (875) pred(n11) = all_0_1_1
% 31.80/10.53 |
% 31.80/10.53 | From (874) and (716) follows:
% 31.80/10.53 | (876) pred(n12) = all_0_3_3
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 31.80/10.53 | (877) all_0_3_3 = n11
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 31.80/10.53 | (878) all_0_1_1 = n10
% 31.80/10.53 |
% 31.80/10.53 | From (877) and (232) follows:
% 31.80/10.53 | (879) sum(n11, all_0_0_0) = all_0_6_6
% 31.80/10.53 |
% 31.80/10.53 | From (878) and (1266) follows:
% 31.80/10.53 | (6717) sum(n10, n10) = all_0_0_0
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (619) with n10, n10, all_0_0_0, n20 and discharging atoms sum(n10, n10) = all_0_0_0, sum(n10, n10) = n20, yields:
% 31.80/10.53 | (1051) all_0_0_0 = n20
% 31.80/10.53 |
% 31.80/10.53 | From (1051) and (879) follows:
% 31.80/10.53 | (6719) sum(n11, n20) = all_0_6_6
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (619) with n11, n20, all_0_6_6, n10 and discharging atoms sum(n11, n20) = all_0_6_6, sum(n11, n20) = n10, yields:
% 31.80/10.53 | (968) all_0_6_6 = n10
% 31.80/10.53 |
% 31.80/10.53 | Equations (968) can reduce 176 to:
% 31.80/10.53 | (748) $false
% 31.80/10.53 |
% 31.80/10.53 |-The branch is then unsatisfiable
% 31.80/10.53 |-Branch two:
% 31.80/10.53 | (1072) ~ (all_0_8_8 = n1)
% 31.80/10.53 | (1073) all_0_8_8 = n0
% 31.80/10.53 |
% 31.80/10.53 | From (1073) and (6553) follows:
% 31.80/10.53 | (6724) sum(n0, n11) = all_0_4_4
% 31.80/10.53 |
% 31.80/10.53 | From (1073) and (6551) follows:
% 31.80/10.53 | (6725) sum(n0, n10) = all_0_2_2
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (619) with n0, n11, all_0_4_4, n11 and discharging atoms sum(n0, n11) = all_0_4_4, sum(n0, n11) = n11, yields:
% 31.80/10.53 | (891) all_0_4_4 = n11
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (619) with n0, n10, all_0_2_2, n10 and discharging atoms sum(n0, n10) = all_0_2_2, sum(n0, n10) = n10, yields:
% 31.80/10.53 | (890) all_0_2_2 = n10
% 31.80/10.53 |
% 31.80/10.53 | From (890) and (473) follows:
% 31.80/10.53 | (892) pred(n10) = all_0_1_1
% 31.80/10.53 |
% 31.80/10.53 | From (891) and (716) follows:
% 31.80/10.53 | (893) pred(n11) = all_0_3_3
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 31.80/10.53 | (894) all_0_3_3 = n10
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 31.80/10.53 | (895) all_0_1_1 = n9
% 31.80/10.53 |
% 31.80/10.53 | From (894) and (232) follows:
% 31.80/10.53 | (896) sum(n10, all_0_0_0) = all_0_6_6
% 31.80/10.53 |
% 31.80/10.53 | From (895) and (1266) follows:
% 31.80/10.53 | (6733) sum(n10, n9) = all_0_0_0
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (619) with n10, n9, all_0_0_0, n19 and discharging atoms sum(n10, n9) = all_0_0_0, sum(n10, n9) = n19, yields:
% 31.80/10.53 | (1068) all_0_0_0 = n19
% 31.80/10.53 |
% 31.80/10.53 | From (1068) and (896) follows:
% 31.80/10.53 | (6735) sum(n10, n19) = all_0_6_6
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (619) with n10, n19, all_0_6_6, n8 and discharging atoms sum(n10, n19) = all_0_6_6, sum(n10, n19) = n8, yields:
% 31.80/10.53 | (985) all_0_6_6 = n8
% 31.80/10.53 |
% 31.80/10.53 | Equations (985) can reduce 357 to:
% 31.80/10.53 | (748) $false
% 31.80/10.53 |
% 31.80/10.53 |-The branch is then unsatisfiable
% 31.80/10.53 |-Branch two:
% 31.80/10.53 | (1281) ~ (all_0_7_7 = n10)
% 31.80/10.53 | (1282) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.80/10.53 |
% 31.80/10.53 +-Applying beta-rule and splitting (903), into two cases.
% 31.80/10.53 |-Branch one:
% 31.80/10.53 | (904) all_0_8_8 = n10
% 31.80/10.53 |
% 31.80/10.53 | From (904) and (708) follows:
% 31.80/10.53 | (6741) sum(n10, all_0_5_5) = all_0_4_4
% 31.80/10.53 |
% 31.80/10.53 | From (904) and (378) follows:
% 31.80/10.53 | (6742) sum(n10, all_0_7_7) = all_0_2_2
% 31.80/10.53 |
% 31.80/10.53 +-Applying beta-rule and splitting (1282), into two cases.
% 31.80/10.53 |-Branch one:
% 31.80/10.53 | (1283) all_0_7_7 = n9
% 31.80/10.53 |
% 31.80/10.53 | From (1283) and (683) follows:
% 31.80/10.53 | (1284) succ(n9) = all_0_5_5
% 31.80/10.53 |
% 31.80/10.53 | From (1283) and (8) follows:
% 31.80/10.53 | (1285) sum(n9, all_0_1_1) = all_0_0_0
% 31.80/10.53 |
% 31.80/10.53 | From (1283) and (6742) follows:
% 31.80/10.53 | (6746) sum(n10, n9) = all_0_2_2
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (388) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 31.80/10.53 | (1287) all_0_5_5 = n10
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (619) with n10, n9, all_0_2_2, n19 and discharging atoms sum(n10, n9) = all_0_2_2, sum(n10, n9) = n19, yields:
% 31.80/10.53 | (737) all_0_2_2 = n19
% 31.80/10.53 |
% 31.80/10.53 | From (737) and (473) follows:
% 31.80/10.53 | (739) pred(n19) = all_0_1_1
% 31.80/10.53 |
% 31.80/10.53 | From (1287) and (6741) follows:
% 31.80/10.53 | (6750) sum(n10, n10) = all_0_4_4
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (244) with n19, all_0_1_1, n18 and discharging atoms pred(n19) = all_0_1_1, pred(n19) = n18, yields:
% 31.80/10.53 | (742) all_0_1_1 = n18
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (619) with n10, n10, all_0_4_4, n20 and discharging atoms sum(n10, n10) = all_0_4_4, sum(n10, n10) = n20, yields:
% 31.80/10.53 | (738) all_0_4_4 = n20
% 31.80/10.53 |
% 31.80/10.53 | From (738) and (716) follows:
% 31.80/10.53 | (740) pred(n20) = all_0_3_3
% 31.80/10.53 |
% 31.80/10.53 | From (742) and (1285) follows:
% 31.80/10.53 | (6754) sum(n9, n18) = all_0_0_0
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (244) with n20, all_0_3_3, n19 and discharging atoms pred(n20) = all_0_3_3, pred(n20) = n19, yields:
% 31.80/10.53 | (741) all_0_3_3 = n19
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (619) with n9, n18, all_0_0_0, n6 and discharging atoms sum(n9, n18) = all_0_0_0, sum(n9, n18) = n6, yields:
% 31.80/10.53 | (932) all_0_0_0 = n6
% 31.80/10.53 |
% 31.80/10.53 | From (741)(932) and (232) follows:
% 31.80/10.53 | (6757) sum(n19, n6) = all_0_6_6
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (619) with n19, n6, all_0_6_6, n4 and discharging atoms sum(n19, n6) = all_0_6_6, sum(n19, n6) = n4, yields:
% 31.80/10.53 | (1019) all_0_6_6 = n4
% 31.80/10.53 |
% 31.80/10.53 | Equations (1019) can reduce 48 to:
% 31.80/10.53 | (748) $false
% 31.80/10.53 |
% 31.80/10.53 |-The branch is then unsatisfiable
% 31.80/10.53 |-Branch two:
% 31.80/10.53 | (1300) ~ (all_0_7_7 = n9)
% 31.80/10.53 | (1301) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.80/10.53 |
% 31.80/10.53 +-Applying beta-rule and splitting (1301), into two cases.
% 31.80/10.53 |-Branch one:
% 31.80/10.53 | (1302) all_0_7_7 = n8
% 31.80/10.53 |
% 31.80/10.53 | From (1302) and (683) follows:
% 31.80/10.53 | (1303) succ(n8) = all_0_5_5
% 31.80/10.53 |
% 31.80/10.53 | From (1302) and (8) follows:
% 31.80/10.53 | (1304) sum(n8, all_0_1_1) = all_0_0_0
% 31.80/10.53 |
% 31.80/10.53 | From (1302) and (6742) follows:
% 31.80/10.53 | (6765) sum(n10, n8) = all_0_2_2
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (388) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 31.80/10.53 | (1306) all_0_5_5 = n9
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (619) with n10, n8, all_0_2_2, n18 and discharging atoms sum(n10, n8) = all_0_2_2, sum(n10, n8) = n18, yields:
% 31.80/10.53 | (754) all_0_2_2 = n18
% 31.80/10.53 |
% 31.80/10.53 | From (754) and (473) follows:
% 31.80/10.53 | (756) pred(n18) = all_0_1_1
% 31.80/10.53 |
% 31.80/10.53 | From (1306) and (6741) follows:
% 31.80/10.53 | (6769) sum(n10, n9) = all_0_4_4
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 31.80/10.53 | (759) all_0_1_1 = n17
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (619) with n10, n9, all_0_4_4, n19 and discharging atoms sum(n10, n9) = all_0_4_4, sum(n10, n9) = n19, yields:
% 31.80/10.53 | (755) all_0_4_4 = n19
% 31.80/10.53 |
% 31.80/10.53 | From (755) and (716) follows:
% 31.80/10.53 | (757) pred(n19) = all_0_3_3
% 31.80/10.53 |
% 31.80/10.53 | From (759) and (1304) follows:
% 31.80/10.53 | (6773) sum(n8, n17) = all_0_0_0
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 31.80/10.53 | (758) all_0_3_3 = n18
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (619) with n8, n17, all_0_0_0, n4 and discharging atoms sum(n8, n17) = all_0_0_0, sum(n8, n17) = n4, yields:
% 31.80/10.53 | (966) all_0_0_0 = n4
% 31.80/10.53 |
% 31.80/10.53 | From (758)(966) and (232) follows:
% 31.80/10.53 | (6776) sum(n18, n4) = all_0_6_6
% 31.80/10.53 |
% 31.80/10.53 | Instantiating formula (619) with n18, n4, all_0_6_6, n1 and discharging atoms sum(n18, n4) = all_0_6_6, sum(n18, n4) = n1, yields:
% 31.80/10.53 | (866) all_0_6_6 = n1
% 31.80/10.53 |
% 31.80/10.53 | Equations (866) can reduce 28 to:
% 31.80/10.53 | (748) $false
% 31.80/10.53 |
% 31.80/10.53 |-The branch is then unsatisfiable
% 31.80/10.53 |-Branch two:
% 31.80/10.53 | (1319) ~ (all_0_7_7 = n8)
% 31.80/10.53 | (1320) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.80/10.53 |
% 31.80/10.53 +-Applying beta-rule and splitting (1320), into two cases.
% 31.80/10.53 |-Branch one:
% 31.80/10.53 | (1321) all_0_7_7 = n7
% 31.80/10.53 |
% 31.80/10.53 | From (1321) and (683) follows:
% 31.80/10.53 | (1322) succ(n7) = all_0_5_5
% 31.80/10.53 |
% 31.80/10.53 | From (1321) and (8) follows:
% 31.80/10.53 | (1323) sum(n7, all_0_1_1) = all_0_0_0
% 31.80/10.53 |
% 31.80/10.53 | From (1321) and (6742) follows:
% 31.80/10.54 | (6784) sum(n10, n7) = all_0_2_2
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (388) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 31.80/10.54 | (1325) all_0_5_5 = n8
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (619) with n10, n7, all_0_2_2, n17 and discharging atoms sum(n10, n7) = all_0_2_2, sum(n10, n7) = n17, yields:
% 31.80/10.54 | (771) all_0_2_2 = n17
% 31.80/10.54 |
% 31.80/10.54 | From (771) and (473) follows:
% 31.80/10.54 | (773) pred(n17) = all_0_1_1
% 31.80/10.54 |
% 31.80/10.54 | From (1325) and (6741) follows:
% 31.80/10.54 | (6788) sum(n10, n8) = all_0_4_4
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 31.80/10.54 | (776) all_0_1_1 = n16
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (619) with n10, n8, all_0_4_4, n18 and discharging atoms sum(n10, n8) = all_0_4_4, sum(n10, n8) = n18, yields:
% 31.80/10.54 | (772) all_0_4_4 = n18
% 31.80/10.54 |
% 31.80/10.54 | From (772) and (716) follows:
% 31.80/10.54 | (774) pred(n18) = all_0_3_3
% 31.80/10.54 |
% 31.80/10.54 | From (776) and (1323) follows:
% 31.80/10.54 | (6792) sum(n7, n16) = all_0_0_0
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 31.80/10.54 | (775) all_0_3_3 = n17
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (619) with n7, n16, all_0_0_0, n2 and discharging atoms sum(n7, n16) = all_0_0_0, sum(n7, n16) = n2, yields:
% 31.80/10.54 | (1000) all_0_0_0 = n2
% 31.80/10.54 |
% 31.80/10.54 | From (775)(1000) and (232) follows:
% 31.80/10.54 | (6795) sum(n17, n2) = all_0_6_6
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (619) with n17, n2, all_0_6_6, n19 and discharging atoms sum(n17, n2) = all_0_6_6, sum(n17, n2) = n19, yields:
% 31.80/10.54 | (1070) all_0_6_6 = n19
% 31.80/10.54 |
% 31.80/10.54 | Equations (1070) can reduce 31 to:
% 31.80/10.54 | (748) $false
% 31.80/10.54 |
% 31.80/10.54 |-The branch is then unsatisfiable
% 31.80/10.54 |-Branch two:
% 31.80/10.54 | (1338) ~ (all_0_7_7 = n7)
% 31.80/10.54 | (1339) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.80/10.54 |
% 31.80/10.54 +-Applying beta-rule and splitting (1339), into two cases.
% 31.80/10.54 |-Branch one:
% 31.80/10.54 | (1340) all_0_7_7 = n6
% 31.80/10.54 |
% 31.80/10.54 | From (1340) and (683) follows:
% 31.80/10.54 | (1341) succ(n6) = all_0_5_5
% 31.80/10.54 |
% 31.80/10.54 | From (1340) and (8) follows:
% 31.80/10.54 | (1342) sum(n6, all_0_1_1) = all_0_0_0
% 31.80/10.54 |
% 31.80/10.54 | From (1340) and (6742) follows:
% 31.80/10.54 | (6803) sum(n10, n6) = all_0_2_2
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (388) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 31.80/10.54 | (1344) all_0_5_5 = n7
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (619) with n10, n6, all_0_2_2, n16 and discharging atoms sum(n10, n6) = all_0_2_2, sum(n10, n6) = n16, yields:
% 31.80/10.54 | (788) all_0_2_2 = n16
% 31.80/10.54 |
% 31.80/10.54 | From (788) and (473) follows:
% 31.80/10.54 | (790) pred(n16) = all_0_1_1
% 31.80/10.54 |
% 31.80/10.54 | From (1344) and (6741) follows:
% 31.80/10.54 | (6807) sum(n10, n7) = all_0_4_4
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 31.80/10.54 | (793) all_0_1_1 = n15
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (619) with n10, n7, all_0_4_4, n17 and discharging atoms sum(n10, n7) = all_0_4_4, sum(n10, n7) = n17, yields:
% 31.80/10.54 | (789) all_0_4_4 = n17
% 31.80/10.54 |
% 31.80/10.54 | From (789) and (716) follows:
% 31.80/10.54 | (791) pred(n17) = all_0_3_3
% 31.80/10.54 |
% 31.80/10.54 | From (793) and (1342) follows:
% 31.80/10.54 | (6811) sum(n6, n15) = all_0_0_0
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 31.80/10.54 | (792) all_0_3_3 = n16
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (619) with n6, n15, all_0_0_0, n0 and discharging atoms sum(n6, n15) = all_0_0_0, sum(n6, n15) = n0, yields:
% 31.80/10.54 | (1034) all_0_0_0 = n0
% 31.80/10.54 |
% 31.80/10.54 | From (792)(1034) and (232) follows:
% 31.80/10.54 | (6814) sum(n16, n0) = all_0_6_6
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (619) with n16, n0, all_0_6_6, n16 and discharging atoms sum(n16, n0) = all_0_6_6, sum(n16, n0) = n16, yields:
% 31.80/10.54 | (917) all_0_6_6 = n16
% 31.80/10.54 |
% 31.80/10.54 | Equations (917) can reduce 163 to:
% 31.80/10.54 | (748) $false
% 31.80/10.54 |
% 31.80/10.54 |-The branch is then unsatisfiable
% 31.80/10.54 |-Branch two:
% 31.80/10.54 | (1357) ~ (all_0_7_7 = n6)
% 31.80/10.54 | (1358) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.80/10.54 |
% 31.80/10.54 +-Applying beta-rule and splitting (1358), into two cases.
% 31.80/10.54 |-Branch one:
% 31.80/10.54 | (1359) all_0_7_7 = n5
% 31.80/10.54 |
% 31.80/10.54 | From (1359) and (683) follows:
% 31.80/10.54 | (1360) succ(n5) = all_0_5_5
% 31.80/10.54 |
% 31.80/10.54 | From (1359) and (8) follows:
% 31.80/10.54 | (1361) sum(n5, all_0_1_1) = all_0_0_0
% 31.80/10.54 |
% 31.80/10.54 | From (1359) and (6742) follows:
% 31.80/10.54 | (6822) sum(n10, n5) = all_0_2_2
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (388) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 31.80/10.54 | (1363) all_0_5_5 = n6
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (619) with n10, n5, all_0_2_2, n15 and discharging atoms sum(n10, n5) = all_0_2_2, sum(n10, n5) = n15, yields:
% 31.80/10.54 | (805) all_0_2_2 = n15
% 31.80/10.54 |
% 31.80/10.54 | From (805) and (473) follows:
% 31.80/10.54 | (807) pred(n15) = all_0_1_1
% 31.80/10.54 |
% 31.80/10.54 | From (1363) and (6741) follows:
% 31.80/10.54 | (6826) sum(n10, n6) = all_0_4_4
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 31.80/10.54 | (810) all_0_1_1 = n14
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (619) with n10, n6, all_0_4_4, n16 and discharging atoms sum(n10, n6) = all_0_4_4, sum(n10, n6) = n16, yields:
% 31.80/10.54 | (806) all_0_4_4 = n16
% 31.80/10.54 |
% 31.80/10.54 | From (806) and (716) follows:
% 31.80/10.54 | (808) pred(n16) = all_0_3_3
% 31.80/10.54 |
% 31.80/10.54 | From (810) and (1361) follows:
% 31.80/10.54 | (6830) sum(n5, n14) = all_0_0_0
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 31.80/10.54 | (809) all_0_3_3 = n15
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (619) with n5, n14, all_0_0_0, n19 and discharging atoms sum(n5, n14) = all_0_0_0, sum(n5, n14) = n19, yields:
% 31.80/10.54 | (1068) all_0_0_0 = n19
% 31.80/10.54 |
% 31.80/10.54 | From (809)(1068) and (232) follows:
% 31.80/10.54 | (6833) sum(n15, n19) = all_0_6_6
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (619) with n15, n19, all_0_6_6, n13 and discharging atoms sum(n15, n19) = all_0_6_6, sum(n15, n19) = n13, yields:
% 31.80/10.54 | (764) all_0_6_6 = n13
% 31.80/10.54 |
% 31.80/10.54 | Equations (764) can reduce 293 to:
% 31.80/10.54 | (748) $false
% 31.80/10.54 |
% 31.80/10.54 |-The branch is then unsatisfiable
% 31.80/10.54 |-Branch two:
% 31.80/10.54 | (1376) ~ (all_0_7_7 = n5)
% 31.80/10.54 | (1377) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.80/10.54 |
% 31.80/10.54 +-Applying beta-rule and splitting (1377), into two cases.
% 31.80/10.54 |-Branch one:
% 31.80/10.54 | (1378) all_0_7_7 = n4
% 31.80/10.54 |
% 31.80/10.54 | From (1378) and (683) follows:
% 31.80/10.54 | (1379) succ(n4) = all_0_5_5
% 31.80/10.54 |
% 31.80/10.54 | From (1378) and (8) follows:
% 31.80/10.54 | (1380) sum(n4, all_0_1_1) = all_0_0_0
% 31.80/10.54 |
% 31.80/10.54 | From (1378) and (6742) follows:
% 31.80/10.54 | (6841) sum(n10, n4) = all_0_2_2
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (388) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 31.80/10.54 | (1382) all_0_5_5 = n5
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (619) with n10, n4, all_0_2_2, n14 and discharging atoms sum(n10, n4) = all_0_2_2, sum(n10, n4) = n14, yields:
% 31.80/10.54 | (822) all_0_2_2 = n14
% 31.80/10.54 |
% 31.80/10.54 | From (822) and (473) follows:
% 31.80/10.54 | (824) pred(n14) = all_0_1_1
% 31.80/10.54 |
% 31.80/10.54 | From (1382) and (6741) follows:
% 31.80/10.54 | (6845) sum(n10, n5) = all_0_4_4
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 31.80/10.54 | (827) all_0_1_1 = n13
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (619) with n10, n5, all_0_4_4, n15 and discharging atoms sum(n10, n5) = all_0_4_4, sum(n10, n5) = n15, yields:
% 31.80/10.54 | (823) all_0_4_4 = n15
% 31.80/10.54 |
% 31.80/10.54 | From (823) and (716) follows:
% 31.80/10.54 | (825) pred(n15) = all_0_3_3
% 31.80/10.54 |
% 31.80/10.54 | From (827) and (1380) follows:
% 31.80/10.54 | (6849) sum(n4, n13) = all_0_0_0
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 31.80/10.54 | (826) all_0_3_3 = n14
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (619) with n4, n13, all_0_0_0, n17 and discharging atoms sum(n4, n13) = all_0_0_0, sum(n4, n13) = n17, yields:
% 31.80/10.54 | (745) all_0_0_0 = n17
% 31.80/10.54 |
% 31.80/10.54 | From (826)(745) and (232) follows:
% 31.80/10.54 | (6852) sum(n14, n17) = all_0_6_6
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (619) with n14, n17, all_0_6_6, n10 and discharging atoms sum(n14, n17) = all_0_6_6, sum(n14, n17) = n10, yields:
% 31.80/10.54 | (968) all_0_6_6 = n10
% 31.80/10.54 |
% 31.80/10.54 | Equations (968) can reduce 176 to:
% 31.80/10.54 | (748) $false
% 31.80/10.54 |
% 31.80/10.54 |-The branch is then unsatisfiable
% 31.80/10.54 |-Branch two:
% 31.80/10.54 | (1395) ~ (all_0_7_7 = n4)
% 31.80/10.54 | (1396) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.80/10.54 |
% 31.80/10.54 +-Applying beta-rule and splitting (1396), into two cases.
% 31.80/10.54 |-Branch one:
% 31.80/10.54 | (1397) all_0_7_7 = n3
% 31.80/10.54 |
% 31.80/10.54 | From (1397) and (683) follows:
% 31.80/10.54 | (1398) succ(n3) = all_0_5_5
% 31.80/10.54 |
% 31.80/10.54 | From (1397) and (8) follows:
% 31.80/10.54 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 31.80/10.54 |
% 31.80/10.54 | From (1397) and (6742) follows:
% 31.80/10.54 | (6860) sum(n10, n3) = all_0_2_2
% 31.80/10.54 |
% 31.80/10.54 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 31.80/10.55 | (1401) all_0_5_5 = n4
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (619) with n10, n3, all_0_2_2, n13 and discharging atoms sum(n10, n3) = all_0_2_2, sum(n10, n3) = n13, yields:
% 31.80/10.55 | (839) all_0_2_2 = n13
% 31.80/10.55 |
% 31.80/10.55 | From (839) and (473) follows:
% 31.80/10.55 | (841) pred(n13) = all_0_1_1
% 31.80/10.55 |
% 31.80/10.55 | From (1401) and (6741) follows:
% 31.80/10.55 | (6864) sum(n10, n4) = all_0_4_4
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 31.80/10.55 | (844) all_0_1_1 = n12
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (619) with n10, n4, all_0_4_4, n14 and discharging atoms sum(n10, n4) = all_0_4_4, sum(n10, n4) = n14, yields:
% 31.80/10.55 | (840) all_0_4_4 = n14
% 31.80/10.55 |
% 31.80/10.55 | From (840) and (716) follows:
% 31.80/10.55 | (842) pred(n14) = all_0_3_3
% 31.80/10.55 |
% 31.80/10.55 | From (844) and (1399) follows:
% 31.80/10.55 | (6868) sum(n3, n12) = all_0_0_0
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 31.80/10.55 | (843) all_0_3_3 = n13
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (619) with n3, n12, all_0_0_0, n15 and discharging atoms sum(n3, n12) = all_0_0_0, sum(n3, n12) = n15, yields:
% 31.80/10.55 | (779) all_0_0_0 = n15
% 31.80/10.55 |
% 31.80/10.55 | From (843)(779) and (232) follows:
% 31.80/10.55 | (6871) sum(n13, n15) = all_0_6_6
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (619) with n13, n15, all_0_6_6, n7 and discharging atoms sum(n13, n15) = all_0_6_6, sum(n13, n15) = n7, yields:
% 31.80/10.55 | (815) all_0_6_6 = n7
% 31.80/10.55 |
% 31.80/10.55 | Equations (815) can reduce 557 to:
% 31.80/10.55 | (748) $false
% 31.80/10.55 |
% 31.80/10.55 |-The branch is then unsatisfiable
% 31.80/10.55 |-Branch two:
% 31.80/10.55 | (1414) ~ (all_0_7_7 = n3)
% 31.80/10.55 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.80/10.55 |
% 31.80/10.55 +-Applying beta-rule and splitting (1415), into two cases.
% 31.80/10.55 |-Branch one:
% 31.80/10.55 | (1416) all_0_7_7 = n2
% 31.80/10.55 |
% 31.80/10.55 | From (1416) and (683) follows:
% 31.80/10.55 | (1417) succ(n2) = all_0_5_5
% 31.80/10.55 |
% 31.80/10.55 | From (1416) and (8) follows:
% 31.80/10.55 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 31.80/10.55 |
% 31.80/10.55 | From (1416) and (6742) follows:
% 31.80/10.55 | (6879) sum(n10, n2) = all_0_2_2
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.80/10.55 | (1420) all_0_5_5 = n3
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (619) with n10, n2, all_0_2_2, n12 and discharging atoms sum(n10, n2) = all_0_2_2, sum(n10, n2) = n12, yields:
% 31.80/10.55 | (856) all_0_2_2 = n12
% 31.80/10.55 |
% 31.80/10.55 | From (856) and (473) follows:
% 31.80/10.55 | (858) pred(n12) = all_0_1_1
% 31.80/10.55 |
% 31.80/10.55 | From (1420) and (6741) follows:
% 31.80/10.55 | (6883) sum(n10, n3) = all_0_4_4
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 31.80/10.55 | (861) all_0_1_1 = n11
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (619) with n10, n3, all_0_4_4, n13 and discharging atoms sum(n10, n3) = all_0_4_4, sum(n10, n3) = n13, yields:
% 31.80/10.55 | (857) all_0_4_4 = n13
% 31.80/10.55 |
% 31.80/10.55 | From (857) and (716) follows:
% 31.80/10.55 | (859) pred(n13) = all_0_3_3
% 31.80/10.55 |
% 31.80/10.55 | From (861) and (1418) follows:
% 31.80/10.55 | (6887) sum(n2, n11) = all_0_0_0
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 31.80/10.55 | (860) all_0_3_3 = n12
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (619) with n2, n11, all_0_0_0, n13 and discharging atoms sum(n2, n11) = all_0_0_0, sum(n2, n11) = n13, yields:
% 31.80/10.55 | (813) all_0_0_0 = n13
% 31.80/10.55 |
% 31.80/10.55 | From (860)(813) and (232) follows:
% 31.80/10.55 | (6890) sum(n12, n13) = all_0_6_6
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (619) with n12, n13, all_0_6_6, n4 and discharging atoms sum(n12, n13) = all_0_6_6, sum(n12, n13) = n4, yields:
% 31.80/10.55 | (1019) all_0_6_6 = n4
% 31.80/10.55 |
% 31.80/10.55 | Equations (1019) can reduce 48 to:
% 31.80/10.55 | (748) $false
% 31.80/10.55 |
% 31.80/10.55 |-The branch is then unsatisfiable
% 31.80/10.55 |-Branch two:
% 31.80/10.55 | (1433) ~ (all_0_7_7 = n2)
% 31.80/10.55 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 31.80/10.55 |
% 31.80/10.55 +-Applying beta-rule and splitting (1434), into two cases.
% 31.80/10.55 |-Branch one:
% 31.80/10.55 | (1435) all_0_7_7 = n1
% 31.80/10.55 |
% 31.80/10.55 | From (1435) and (683) follows:
% 31.80/10.55 | (1436) succ(n1) = all_0_5_5
% 31.80/10.55 |
% 31.80/10.55 | From (1435) and (8) follows:
% 31.80/10.55 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 31.80/10.55 |
% 31.80/10.55 | From (1435) and (6742) follows:
% 31.80/10.55 | (6898) sum(n10, n1) = all_0_2_2
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.80/10.55 | (1439) all_0_5_5 = n2
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (619) with n10, n1, all_0_2_2, n11 and discharging atoms sum(n10, n1) = all_0_2_2, sum(n10, n1) = n11, yields:
% 31.80/10.55 | (873) all_0_2_2 = n11
% 31.80/10.55 |
% 31.80/10.55 | From (873) and (473) follows:
% 31.80/10.55 | (875) pred(n11) = all_0_1_1
% 31.80/10.55 |
% 31.80/10.55 | From (1439) and (6741) follows:
% 31.80/10.55 | (6902) sum(n10, n2) = all_0_4_4
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 31.80/10.55 | (878) all_0_1_1 = n10
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (619) with n10, n2, all_0_4_4, n12 and discharging atoms sum(n10, n2) = all_0_4_4, sum(n10, n2) = n12, yields:
% 31.80/10.55 | (874) all_0_4_4 = n12
% 31.80/10.55 |
% 31.80/10.55 | From (874) and (716) follows:
% 31.80/10.55 | (876) pred(n12) = all_0_3_3
% 31.80/10.55 |
% 31.80/10.55 | From (878) and (1437) follows:
% 31.80/10.55 | (6906) sum(n1, n10) = all_0_0_0
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 31.80/10.55 | (877) all_0_3_3 = n11
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (619) with n1, n10, all_0_0_0, n11 and discharging atoms sum(n1, n10) = all_0_0_0, sum(n1, n10) = n11, yields:
% 31.80/10.55 | (847) all_0_0_0 = n11
% 31.80/10.55 |
% 31.80/10.55 | From (877)(847) and (232) follows:
% 31.80/10.55 | (6909) sum(n11, n11) = all_0_6_6
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (619) with n11, n11, all_0_6_6, n1 and discharging atoms sum(n11, n11) = all_0_6_6, sum(n11, n11) = n1, yields:
% 31.80/10.55 | (866) all_0_6_6 = n1
% 31.80/10.55 |
% 31.80/10.55 | Equations (866) can reduce 28 to:
% 31.80/10.55 | (748) $false
% 31.80/10.55 |
% 31.80/10.55 |-The branch is then unsatisfiable
% 31.80/10.55 |-Branch two:
% 31.80/10.55 | (1452) ~ (all_0_7_7 = n1)
% 31.80/10.55 | (1453) all_0_7_7 = n0
% 31.80/10.55 |
% 31.80/10.55 | From (1453) and (683) follows:
% 31.80/10.55 | (1454) succ(n0) = all_0_5_5
% 31.80/10.55 |
% 31.80/10.55 | From (1453) and (8) follows:
% 31.80/10.55 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 31.80/10.55 |
% 31.80/10.55 | From (1453) and (6742) follows:
% 31.80/10.55 | (6916) sum(n10, n0) = all_0_2_2
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.80/10.55 | (1457) all_0_5_5 = n1
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (619) with n10, n0, all_0_2_2, n10 and discharging atoms sum(n10, n0) = all_0_2_2, sum(n10, n0) = n10, yields:
% 31.80/10.55 | (890) all_0_2_2 = n10
% 31.80/10.55 |
% 31.80/10.55 | From (890) and (473) follows:
% 31.80/10.55 | (892) pred(n10) = all_0_1_1
% 31.80/10.55 |
% 31.80/10.55 | From (1457) and (6741) follows:
% 31.80/10.55 | (6920) sum(n10, n1) = all_0_4_4
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 31.80/10.55 | (895) all_0_1_1 = n9
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (619) with n10, n1, all_0_4_4, n11 and discharging atoms sum(n10, n1) = all_0_4_4, sum(n10, n1) = n11, yields:
% 31.80/10.55 | (891) all_0_4_4 = n11
% 31.80/10.55 |
% 31.80/10.55 | From (891) and (716) follows:
% 31.80/10.55 | (893) pred(n11) = all_0_3_3
% 31.80/10.55 |
% 31.80/10.55 | From (895) and (1455) follows:
% 31.80/10.55 | (6924) sum(n0, n9) = all_0_0_0
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 31.80/10.55 | (894) all_0_3_3 = n10
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (619) with n0, n9, all_0_0_0, n9 and discharging atoms sum(n0, n9) = all_0_0_0, sum(n0, n9) = n9, yields:
% 31.80/10.55 | (881) all_0_0_0 = n9
% 31.80/10.55 |
% 31.80/10.55 | From (894)(881) and (232) follows:
% 31.80/10.55 | (6927) sum(n10, n9) = all_0_6_6
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (619) with n10, n9, all_0_6_6, n19 and discharging atoms sum(n10, n9) = all_0_6_6, sum(n10, n9) = n19, yields:
% 31.80/10.55 | (1070) all_0_6_6 = n19
% 31.80/10.55 |
% 31.80/10.55 | Equations (1070) can reduce 31 to:
% 31.80/10.55 | (748) $false
% 31.80/10.55 |
% 31.80/10.55 |-The branch is then unsatisfiable
% 31.80/10.55 |-Branch two:
% 31.80/10.55 | (919) ~ (all_0_8_8 = n10)
% 31.80/10.55 | (920) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.55 |
% 31.80/10.55 +-Applying beta-rule and splitting (1282), into two cases.
% 31.80/10.55 |-Branch one:
% 31.80/10.55 | (1283) all_0_7_7 = n9
% 31.80/10.55 |
% 31.80/10.55 | From (1283) and (683) follows:
% 31.80/10.55 | (1284) succ(n9) = all_0_5_5
% 31.80/10.55 |
% 31.80/10.55 | From (1283) and (8) follows:
% 31.80/10.55 | (1285) sum(n9, all_0_1_1) = all_0_0_0
% 31.80/10.55 |
% 31.80/10.55 | From (1283) and (378) follows:
% 31.80/10.55 | (6935) sum(all_0_8_8, n9) = all_0_2_2
% 31.80/10.55 |
% 31.80/10.55 | Instantiating formula (388) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 31.80/10.55 | (1287) all_0_5_5 = n10
% 31.80/10.55 |
% 31.80/10.55 | From (1287) and (708) follows:
% 31.80/10.55 | (6937) sum(all_0_8_8, n10) = all_0_4_4
% 31.80/10.55 |
% 31.80/10.55 +-Applying beta-rule and splitting (920), into two cases.
% 31.80/10.55 |-Branch one:
% 31.80/10.55 | (921) all_0_8_8 = n9
% 31.80/10.55 |
% 31.80/10.55 | From (921) and (6937) follows:
% 31.80/10.56 | (6939) sum(n9, n10) = all_0_4_4
% 31.80/10.56 |
% 31.80/10.56 | From (921) and (6935) follows:
% 31.80/10.56 | (6940) sum(n9, n9) = all_0_2_2
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n9, n10, all_0_4_4, n19 and discharging atoms sum(n9, n10) = all_0_4_4, sum(n9, n10) = n19, yields:
% 31.80/10.56 | (755) all_0_4_4 = n19
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n9, n9, all_0_2_2, n18 and discharging atoms sum(n9, n9) = all_0_2_2, sum(n9, n9) = n18, yields:
% 31.80/10.56 | (754) all_0_2_2 = n18
% 31.80/10.56 |
% 31.80/10.56 | From (754) and (473) follows:
% 31.80/10.56 | (756) pred(n18) = all_0_1_1
% 31.80/10.56 |
% 31.80/10.56 | From (755) and (716) follows:
% 31.80/10.56 | (757) pred(n19) = all_0_3_3
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (244) with n19, all_0_3_3, n18 and discharging atoms pred(n19) = all_0_3_3, pred(n19) = n18, yields:
% 31.80/10.56 | (758) all_0_3_3 = n18
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (244) with n18, all_0_1_1, n17 and discharging atoms pred(n18) = all_0_1_1, pred(n18) = n17, yields:
% 31.80/10.56 | (759) all_0_1_1 = n17
% 31.80/10.56 |
% 31.80/10.56 | From (758) and (232) follows:
% 31.80/10.56 | (760) sum(n18, all_0_0_0) = all_0_6_6
% 31.80/10.56 |
% 31.80/10.56 | From (759) and (1285) follows:
% 31.80/10.56 | (6948) sum(n9, n17) = all_0_0_0
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n9, n17, all_0_0_0, n5 and discharging atoms sum(n9, n17) = all_0_0_0, sum(n9, n17) = n5, yields:
% 31.80/10.56 | (949) all_0_0_0 = n5
% 31.80/10.56 |
% 31.80/10.56 | From (949) and (760) follows:
% 31.80/10.56 | (6950) sum(n18, n5) = all_0_6_6
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n18, n5, all_0_6_6, n2 and discharging atoms sum(n18, n5) = all_0_6_6, sum(n18, n5) = n2, yields:
% 31.80/10.56 | (1036) all_0_6_6 = n2
% 31.80/10.56 |
% 31.80/10.56 | Equations (1036) can reduce 56 to:
% 31.80/10.56 | (748) $false
% 31.80/10.56 |
% 31.80/10.56 |-The branch is then unsatisfiable
% 31.80/10.56 |-Branch two:
% 31.80/10.56 | (936) ~ (all_0_8_8 = n9)
% 31.80/10.56 | (937) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.56 |
% 31.80/10.56 +-Applying beta-rule and splitting (937), into two cases.
% 31.80/10.56 |-Branch one:
% 31.80/10.56 | (938) all_0_8_8 = n8
% 31.80/10.56 |
% 31.80/10.56 | From (938) and (6937) follows:
% 31.80/10.56 | (6956) sum(n8, n10) = all_0_4_4
% 31.80/10.56 |
% 31.80/10.56 | From (938) and (6935) follows:
% 31.80/10.56 | (6957) sum(n8, n9) = all_0_2_2
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n8, n10, all_0_4_4, n18 and discharging atoms sum(n8, n10) = all_0_4_4, sum(n8, n10) = n18, yields:
% 31.80/10.56 | (772) all_0_4_4 = n18
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n8, n9, all_0_2_2, n17 and discharging atoms sum(n8, n9) = all_0_2_2, sum(n8, n9) = n17, yields:
% 31.80/10.56 | (771) all_0_2_2 = n17
% 31.80/10.56 |
% 31.80/10.56 | From (771) and (473) follows:
% 31.80/10.56 | (773) pred(n17) = all_0_1_1
% 31.80/10.56 |
% 31.80/10.56 | From (772) and (716) follows:
% 31.80/10.56 | (774) pred(n18) = all_0_3_3
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 31.80/10.56 | (775) all_0_3_3 = n17
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 31.80/10.56 | (776) all_0_1_1 = n16
% 31.80/10.56 |
% 31.80/10.56 | From (775) and (232) follows:
% 31.80/10.56 | (777) sum(n17, all_0_0_0) = all_0_6_6
% 31.80/10.56 |
% 31.80/10.56 | From (776) and (1285) follows:
% 31.80/10.56 | (6965) sum(n9, n16) = all_0_0_0
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n9, n16, all_0_0_0, n4 and discharging atoms sum(n9, n16) = all_0_0_0, sum(n9, n16) = n4, yields:
% 31.80/10.56 | (966) all_0_0_0 = n4
% 31.80/10.56 |
% 31.80/10.56 | From (966) and (777) follows:
% 31.80/10.56 | (6967) sum(n17, n4) = all_0_6_6
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n17, n4, all_0_6_6, n0 and discharging atoms sum(n17, n4) = all_0_6_6, sum(n17, n4) = n0, yields:
% 31.80/10.56 | (1053) all_0_6_6 = n0
% 31.80/10.56 |
% 31.80/10.56 | Equations (1053) can reduce 676 to:
% 31.80/10.56 | (748) $false
% 31.80/10.56 |
% 31.80/10.56 |-The branch is then unsatisfiable
% 31.80/10.56 |-Branch two:
% 31.80/10.56 | (953) ~ (all_0_8_8 = n8)
% 31.80/10.56 | (954) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.56 |
% 31.80/10.56 +-Applying beta-rule and splitting (954), into two cases.
% 31.80/10.56 |-Branch one:
% 31.80/10.56 | (955) all_0_8_8 = n7
% 31.80/10.56 |
% 31.80/10.56 | From (955) and (6937) follows:
% 31.80/10.56 | (6973) sum(n7, n10) = all_0_4_4
% 31.80/10.56 |
% 31.80/10.56 | From (955) and (6935) follows:
% 31.80/10.56 | (6974) sum(n7, n9) = all_0_2_2
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n7, n10, all_0_4_4, n17 and discharging atoms sum(n7, n10) = all_0_4_4, sum(n7, n10) = n17, yields:
% 31.80/10.56 | (789) all_0_4_4 = n17
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 31.80/10.56 | (788) all_0_2_2 = n16
% 31.80/10.56 |
% 31.80/10.56 | From (788) and (473) follows:
% 31.80/10.56 | (790) pred(n16) = all_0_1_1
% 31.80/10.56 |
% 31.80/10.56 | From (789) and (716) follows:
% 31.80/10.56 | (791) pred(n17) = all_0_3_3
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 31.80/10.56 | (792) all_0_3_3 = n16
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 31.80/10.56 | (793) all_0_1_1 = n15
% 31.80/10.56 |
% 31.80/10.56 | From (792) and (232) follows:
% 31.80/10.56 | (794) sum(n16, all_0_0_0) = all_0_6_6
% 31.80/10.56 |
% 31.80/10.56 | From (793) and (1285) follows:
% 31.80/10.56 | (6982) sum(n9, n15) = all_0_0_0
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n9, n15, all_0_0_0, n3 and discharging atoms sum(n9, n15) = all_0_0_0, sum(n9, n15) = n3, yields:
% 31.80/10.56 | (983) all_0_0_0 = n3
% 31.80/10.56 |
% 31.80/10.56 | From (983) and (794) follows:
% 31.80/10.56 | (6984) sum(n16, n3) = all_0_6_6
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n16, n3, all_0_6_6, n19 and discharging atoms sum(n16, n3) = all_0_6_6, sum(n16, n3) = n19, yields:
% 31.80/10.56 | (1070) all_0_6_6 = n19
% 31.80/10.56 |
% 31.80/10.56 | Equations (1070) can reduce 31 to:
% 31.80/10.56 | (748) $false
% 31.80/10.56 |
% 31.80/10.56 |-The branch is then unsatisfiable
% 31.80/10.56 |-Branch two:
% 31.80/10.56 | (970) ~ (all_0_8_8 = n7)
% 31.80/10.56 | (971) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.56 |
% 31.80/10.56 +-Applying beta-rule and splitting (971), into two cases.
% 31.80/10.56 |-Branch one:
% 31.80/10.56 | (972) all_0_8_8 = n6
% 31.80/10.56 |
% 31.80/10.56 | From (972) and (6937) follows:
% 31.80/10.56 | (6990) sum(n6, n10) = all_0_4_4
% 31.80/10.56 |
% 31.80/10.56 | From (972) and (6935) follows:
% 31.80/10.56 | (6991) sum(n6, n9) = all_0_2_2
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n6, n10, all_0_4_4, n16 and discharging atoms sum(n6, n10) = all_0_4_4, sum(n6, n10) = n16, yields:
% 31.80/10.56 | (806) all_0_4_4 = n16
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n6, n9, all_0_2_2, n15 and discharging atoms sum(n6, n9) = all_0_2_2, sum(n6, n9) = n15, yields:
% 31.80/10.56 | (805) all_0_2_2 = n15
% 31.80/10.56 |
% 31.80/10.56 | From (805) and (473) follows:
% 31.80/10.56 | (807) pred(n15) = all_0_1_1
% 31.80/10.56 |
% 31.80/10.56 | From (806) and (716) follows:
% 31.80/10.56 | (808) pred(n16) = all_0_3_3
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 31.80/10.56 | (809) all_0_3_3 = n15
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 31.80/10.56 | (810) all_0_1_1 = n14
% 31.80/10.56 |
% 31.80/10.56 | From (809) and (232) follows:
% 31.80/10.56 | (811) sum(n15, all_0_0_0) = all_0_6_6
% 31.80/10.56 |
% 31.80/10.56 | From (810) and (1285) follows:
% 31.80/10.56 | (6999) sum(n9, n14) = all_0_0_0
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n9, n14, all_0_0_0, n2 and discharging atoms sum(n9, n14) = all_0_0_0, sum(n9, n14) = n2, yields:
% 31.80/10.56 | (1000) all_0_0_0 = n2
% 31.80/10.56 |
% 31.80/10.56 | From (1000) and (811) follows:
% 31.80/10.56 | (7001) sum(n15, n2) = all_0_6_6
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n15, n2, all_0_6_6, n17 and discharging atoms sum(n15, n2) = all_0_6_6, sum(n15, n2) = n17, yields:
% 31.80/10.56 | (1086) all_0_6_6 = n17
% 31.80/10.56 |
% 31.80/10.56 | Equations (1086) can reduce 669 to:
% 31.80/10.56 | (748) $false
% 31.80/10.56 |
% 31.80/10.56 |-The branch is then unsatisfiable
% 31.80/10.56 |-Branch two:
% 31.80/10.56 | (987) ~ (all_0_8_8 = n6)
% 31.80/10.56 | (988) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.56 |
% 31.80/10.56 +-Applying beta-rule and splitting (988), into two cases.
% 31.80/10.56 |-Branch one:
% 31.80/10.56 | (989) all_0_8_8 = n5
% 31.80/10.56 |
% 31.80/10.56 | From (989) and (6937) follows:
% 31.80/10.56 | (7007) sum(n5, n10) = all_0_4_4
% 31.80/10.56 |
% 31.80/10.56 | From (989) and (6935) follows:
% 31.80/10.56 | (7008) sum(n5, n9) = all_0_2_2
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n5, n10, all_0_4_4, n15 and discharging atoms sum(n5, n10) = all_0_4_4, sum(n5, n10) = n15, yields:
% 31.80/10.56 | (823) all_0_4_4 = n15
% 31.80/10.56 |
% 31.80/10.56 | Instantiating formula (619) with n5, n9, all_0_2_2, n14 and discharging atoms sum(n5, n9) = all_0_2_2, sum(n5, n9) = n14, yields:
% 31.80/10.56 | (822) all_0_2_2 = n14
% 31.80/10.56 |
% 31.80/10.56 | From (822) and (473) follows:
% 31.80/10.57 | (824) pred(n14) = all_0_1_1
% 31.80/10.57 |
% 31.80/10.57 | From (823) and (716) follows:
% 31.80/10.57 | (825) pred(n15) = all_0_3_3
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 31.80/10.57 | (826) all_0_3_3 = n14
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 31.80/10.57 | (827) all_0_1_1 = n13
% 31.80/10.57 |
% 31.80/10.57 | From (826) and (232) follows:
% 31.80/10.57 | (828) sum(n14, all_0_0_0) = all_0_6_6
% 31.80/10.57 |
% 31.80/10.57 | From (827) and (1285) follows:
% 31.80/10.57 | (7016) sum(n9, n13) = all_0_0_0
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (619) with n9, n13, all_0_0_0, n1 and discharging atoms sum(n9, n13) = all_0_0_0, sum(n9, n13) = n1, yields:
% 31.80/10.57 | (1017) all_0_0_0 = n1
% 31.80/10.57 |
% 31.80/10.57 | From (1017) and (828) follows:
% 31.80/10.57 | (7018) sum(n14, n1) = all_0_6_6
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (619) with n14, n1, all_0_6_6, n15 and discharging atoms sum(n14, n1) = all_0_6_6, sum(n14, n1) = n15, yields:
% 31.80/10.57 | (747) all_0_6_6 = n15
% 31.80/10.57 |
% 31.80/10.57 | Equations (747) can reduce 456 to:
% 31.80/10.57 | (748) $false
% 31.80/10.57 |
% 31.80/10.57 |-The branch is then unsatisfiable
% 31.80/10.57 |-Branch two:
% 31.80/10.57 | (1004) ~ (all_0_8_8 = n5)
% 31.80/10.57 | (1005) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.57 |
% 31.80/10.57 +-Applying beta-rule and splitting (1005), into two cases.
% 31.80/10.57 |-Branch one:
% 31.80/10.57 | (1006) all_0_8_8 = n4
% 31.80/10.57 |
% 31.80/10.57 | From (1006) and (6937) follows:
% 31.80/10.57 | (7024) sum(n4, n10) = all_0_4_4
% 31.80/10.57 |
% 31.80/10.57 | From (1006) and (6935) follows:
% 31.80/10.57 | (7025) sum(n4, n9) = all_0_2_2
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (619) with n4, n10, all_0_4_4, n14 and discharging atoms sum(n4, n10) = all_0_4_4, sum(n4, n10) = n14, yields:
% 31.80/10.57 | (840) all_0_4_4 = n14
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (619) with n4, n9, all_0_2_2, n13 and discharging atoms sum(n4, n9) = all_0_2_2, sum(n4, n9) = n13, yields:
% 31.80/10.57 | (839) all_0_2_2 = n13
% 31.80/10.57 |
% 31.80/10.57 | From (839) and (473) follows:
% 31.80/10.57 | (841) pred(n13) = all_0_1_1
% 31.80/10.57 |
% 31.80/10.57 | From (840) and (716) follows:
% 31.80/10.57 | (842) pred(n14) = all_0_3_3
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 31.80/10.57 | (843) all_0_3_3 = n13
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 31.80/10.57 | (844) all_0_1_1 = n12
% 31.80/10.57 |
% 31.80/10.57 | From (843) and (232) follows:
% 31.80/10.57 | (845) sum(n13, all_0_0_0) = all_0_6_6
% 31.80/10.57 |
% 31.80/10.57 | From (844) and (1285) follows:
% 31.80/10.57 | (7033) sum(n9, n12) = all_0_0_0
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (619) with n9, n12, all_0_0_0, n0 and discharging atoms sum(n9, n12) = all_0_0_0, sum(n9, n12) = n0, yields:
% 31.80/10.57 | (1034) all_0_0_0 = n0
% 31.80/10.57 |
% 31.80/10.57 | From (1034) and (845) follows:
% 31.80/10.57 | (7035) sum(n13, n0) = all_0_6_6
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (619) with n13, n0, all_0_6_6, n13 and discharging atoms sum(n13, n0) = all_0_6_6, sum(n13, n0) = n13, yields:
% 31.80/10.57 | (764) all_0_6_6 = n13
% 31.80/10.57 |
% 31.80/10.57 | Equations (764) can reduce 293 to:
% 31.80/10.57 | (748) $false
% 31.80/10.57 |
% 31.80/10.57 |-The branch is then unsatisfiable
% 31.80/10.57 |-Branch two:
% 31.80/10.57 | (1021) ~ (all_0_8_8 = n4)
% 31.80/10.57 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.57 |
% 31.80/10.57 +-Applying beta-rule and splitting (1022), into two cases.
% 31.80/10.57 |-Branch one:
% 31.80/10.57 | (1023) all_0_8_8 = n3
% 31.80/10.57 |
% 31.80/10.57 | From (1023) and (6937) follows:
% 31.80/10.57 | (7041) sum(n3, n10) = all_0_4_4
% 31.80/10.57 |
% 31.80/10.57 | From (1023) and (6935) follows:
% 31.80/10.57 | (7042) sum(n3, n9) = all_0_2_2
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (619) with n3, n10, all_0_4_4, n13 and discharging atoms sum(n3, n10) = all_0_4_4, sum(n3, n10) = n13, yields:
% 31.80/10.57 | (857) all_0_4_4 = n13
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (619) with n3, n9, all_0_2_2, n12 and discharging atoms sum(n3, n9) = all_0_2_2, sum(n3, n9) = n12, yields:
% 31.80/10.57 | (856) all_0_2_2 = n12
% 31.80/10.57 |
% 31.80/10.57 | From (856) and (473) follows:
% 31.80/10.57 | (858) pred(n12) = all_0_1_1
% 31.80/10.57 |
% 31.80/10.57 | From (857) and (716) follows:
% 31.80/10.57 | (859) pred(n13) = all_0_3_3
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 31.80/10.57 | (860) all_0_3_3 = n12
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 31.80/10.57 | (861) all_0_1_1 = n11
% 31.80/10.57 |
% 31.80/10.57 | From (860) and (232) follows:
% 31.80/10.57 | (862) sum(n12, all_0_0_0) = all_0_6_6
% 31.80/10.57 |
% 31.80/10.57 | From (861) and (1285) follows:
% 31.80/10.57 | (7050) sum(n9, n11) = all_0_0_0
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (619) with n9, n11, all_0_0_0, n20 and discharging atoms sum(n9, n11) = all_0_0_0, sum(n9, n11) = n20, yields:
% 31.80/10.57 | (1051) all_0_0_0 = n20
% 31.80/10.57 |
% 31.80/10.57 | From (1051) and (862) follows:
% 31.80/10.57 | (7052) sum(n12, n20) = all_0_6_6
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (619) with n12, n20, all_0_6_6, n11 and discharging atoms sum(n12, n20) = all_0_6_6, sum(n12, n20) = n11, yields:
% 31.80/10.57 | (781) all_0_6_6 = n11
% 31.80/10.57 |
% 31.80/10.57 | Equations (781) can reduce 2 to:
% 31.80/10.57 | (748) $false
% 31.80/10.57 |
% 31.80/10.57 |-The branch is then unsatisfiable
% 31.80/10.57 |-Branch two:
% 31.80/10.57 | (1038) ~ (all_0_8_8 = n3)
% 31.80/10.57 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.57 |
% 31.80/10.57 +-Applying beta-rule and splitting (1039), into two cases.
% 31.80/10.57 |-Branch one:
% 31.80/10.57 | (1040) all_0_8_8 = n2
% 31.80/10.57 |
% 31.80/10.57 | From (1040) and (6937) follows:
% 31.80/10.57 | (7058) sum(n2, n10) = all_0_4_4
% 31.80/10.57 |
% 31.80/10.57 | From (1040) and (6935) follows:
% 31.80/10.57 | (7059) sum(n2, n9) = all_0_2_2
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (619) with n2, n10, all_0_4_4, n12 and discharging atoms sum(n2, n10) = all_0_4_4, sum(n2, n10) = n12, yields:
% 31.80/10.57 | (874) all_0_4_4 = n12
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (619) with n2, n9, all_0_2_2, n11 and discharging atoms sum(n2, n9) = all_0_2_2, sum(n2, n9) = n11, yields:
% 31.80/10.57 | (873) all_0_2_2 = n11
% 31.80/10.57 |
% 31.80/10.57 | From (873) and (473) follows:
% 31.80/10.57 | (875) pred(n11) = all_0_1_1
% 31.80/10.57 |
% 31.80/10.57 | From (874) and (716) follows:
% 31.80/10.57 | (876) pred(n12) = all_0_3_3
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 31.80/10.57 | (877) all_0_3_3 = n11
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 31.80/10.57 | (878) all_0_1_1 = n10
% 31.80/10.57 |
% 31.80/10.57 | From (877) and (232) follows:
% 31.80/10.57 | (879) sum(n11, all_0_0_0) = all_0_6_6
% 31.80/10.57 |
% 31.80/10.57 | From (878) and (1285) follows:
% 31.80/10.57 | (7067) sum(n9, n10) = all_0_0_0
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (619) with n9, n10, all_0_0_0, n19 and discharging atoms sum(n9, n10) = all_0_0_0, sum(n9, n10) = n19, yields:
% 31.80/10.57 | (1068) all_0_0_0 = n19
% 31.80/10.57 |
% 31.80/10.57 | From (1068) and (879) follows:
% 31.80/10.57 | (7069) sum(n11, n19) = all_0_6_6
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (619) with n11, n19, all_0_6_6, n9 and discharging atoms sum(n11, n19) = all_0_6_6, sum(n11, n19) = n9, yields:
% 31.80/10.57 | (798) all_0_6_6 = n9
% 31.80/10.57 |
% 31.80/10.57 | Equations (798) can reduce 593 to:
% 31.80/10.57 | (748) $false
% 31.80/10.57 |
% 31.80/10.57 |-The branch is then unsatisfiable
% 31.80/10.57 |-Branch two:
% 31.80/10.57 | (1055) ~ (all_0_8_8 = n2)
% 31.80/10.57 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.57 |
% 31.80/10.57 +-Applying beta-rule and splitting (1056), into two cases.
% 31.80/10.57 |-Branch one:
% 31.80/10.57 | (1057) all_0_8_8 = n1
% 31.80/10.57 |
% 31.80/10.57 | From (1057) and (6937) follows:
% 31.80/10.57 | (7075) sum(n1, n10) = all_0_4_4
% 31.80/10.57 |
% 31.80/10.57 | From (1057) and (6935) follows:
% 31.80/10.57 | (7076) sum(n1, n9) = all_0_2_2
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (619) with n1, n10, all_0_4_4, n11 and discharging atoms sum(n1, n10) = all_0_4_4, sum(n1, n10) = n11, yields:
% 31.80/10.57 | (891) all_0_4_4 = n11
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (619) with n1, n9, all_0_2_2, n10 and discharging atoms sum(n1, n9) = all_0_2_2, sum(n1, n9) = n10, yields:
% 31.80/10.57 | (890) all_0_2_2 = n10
% 31.80/10.57 |
% 31.80/10.57 | From (890) and (473) follows:
% 31.80/10.57 | (892) pred(n10) = all_0_1_1
% 31.80/10.57 |
% 31.80/10.57 | From (891) and (716) follows:
% 31.80/10.57 | (893) pred(n11) = all_0_3_3
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 31.80/10.57 | (894) all_0_3_3 = n10
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 31.80/10.57 | (895) all_0_1_1 = n9
% 31.80/10.57 |
% 31.80/10.57 | From (894) and (232) follows:
% 31.80/10.57 | (896) sum(n10, all_0_0_0) = all_0_6_6
% 31.80/10.57 |
% 31.80/10.57 | From (895) and (1285) follows:
% 31.80/10.57 | (7084) sum(n9, n9) = all_0_0_0
% 31.80/10.57 |
% 31.80/10.57 | Instantiating formula (619) with n9, n9, all_0_0_0, n18 and discharging atoms sum(n9, n9) = all_0_0_0, sum(n9, n9) = n18, yields:
% 31.80/10.57 | (1084) all_0_0_0 = n18
% 31.80/10.57 |
% 31.80/10.57 | From (1084) and (896) follows:
% 31.80/10.58 | (7086) sum(n10, n18) = all_0_6_6
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (619) with n10, n18, all_0_6_6, n7 and discharging atoms sum(n10, n18) = all_0_6_6, sum(n10, n18) = n7, yields:
% 31.80/10.58 | (815) all_0_6_6 = n7
% 31.80/10.58 |
% 31.80/10.58 | Equations (815) can reduce 557 to:
% 31.80/10.58 | (748) $false
% 31.80/10.58 |
% 31.80/10.58 |-The branch is then unsatisfiable
% 31.80/10.58 |-Branch two:
% 31.80/10.58 | (1072) ~ (all_0_8_8 = n1)
% 31.80/10.58 | (1073) all_0_8_8 = n0
% 31.80/10.58 |
% 31.80/10.58 | From (1073) and (6937) follows:
% 31.80/10.58 | (7091) sum(n0, n10) = all_0_4_4
% 31.80/10.58 |
% 31.80/10.58 | From (1073) and (6935) follows:
% 31.80/10.58 | (7092) sum(n0, n9) = all_0_2_2
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (619) with n0, n10, all_0_4_4, n10 and discharging atoms sum(n0, n10) = all_0_4_4, sum(n0, n10) = n10, yields:
% 31.80/10.58 | (908) all_0_4_4 = n10
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (619) with n0, n9, all_0_2_2, n9 and discharging atoms sum(n0, n9) = all_0_2_2, sum(n0, n9) = n9, yields:
% 31.80/10.58 | (907) all_0_2_2 = n9
% 31.80/10.58 |
% 31.80/10.58 | From (907) and (473) follows:
% 31.80/10.58 | (909) pred(n9) = all_0_1_1
% 31.80/10.58 |
% 31.80/10.58 | From (908) and (716) follows:
% 31.80/10.58 | (910) pred(n10) = all_0_3_3
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 31.80/10.58 | (911) all_0_3_3 = n9
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 31.80/10.58 | (912) all_0_1_1 = n8
% 31.80/10.58 |
% 31.80/10.58 | From (911) and (232) follows:
% 31.80/10.58 | (913) sum(n9, all_0_0_0) = all_0_6_6
% 31.80/10.58 |
% 31.80/10.58 | From (912) and (1285) follows:
% 31.80/10.58 | (7100) sum(n9, n8) = all_0_0_0
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (619) with n9, n8, all_0_0_0, n17 and discharging atoms sum(n9, n8) = all_0_0_0, sum(n9, n8) = n17, yields:
% 31.80/10.58 | (745) all_0_0_0 = n17
% 31.80/10.58 |
% 31.80/10.58 | From (745) and (913) follows:
% 31.80/10.58 | (7102) sum(n9, n17) = all_0_6_6
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (619) with n9, n17, all_0_6_6, n5 and discharging atoms sum(n9, n17) = all_0_6_6, sum(n9, n17) = n5, yields:
% 31.80/10.58 | (832) all_0_6_6 = n5
% 31.80/10.58 |
% 31.80/10.58 | Equations (832) can reduce 462 to:
% 31.80/10.58 | (748) $false
% 31.80/10.58 |
% 31.80/10.58 |-The branch is then unsatisfiable
% 31.80/10.58 |-Branch two:
% 31.80/10.58 | (1300) ~ (all_0_7_7 = n9)
% 31.80/10.58 | (1301) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.80/10.58 |
% 31.80/10.58 +-Applying beta-rule and splitting (920), into two cases.
% 31.80/10.58 |-Branch one:
% 31.80/10.58 | (921) all_0_8_8 = n9
% 31.80/10.58 |
% 31.80/10.58 | From (921) and (708) follows:
% 31.80/10.58 | (7108) sum(n9, all_0_5_5) = all_0_4_4
% 31.80/10.58 |
% 31.80/10.58 | From (921) and (378) follows:
% 31.80/10.58 | (7109) sum(n9, all_0_7_7) = all_0_2_2
% 31.80/10.58 |
% 31.80/10.58 +-Applying beta-rule and splitting (1301), into two cases.
% 31.80/10.58 |-Branch one:
% 31.80/10.58 | (1302) all_0_7_7 = n8
% 31.80/10.58 |
% 31.80/10.58 | From (1302) and (683) follows:
% 31.80/10.58 | (1303) succ(n8) = all_0_5_5
% 31.80/10.58 |
% 31.80/10.58 | From (1302) and (8) follows:
% 31.80/10.58 | (1304) sum(n8, all_0_1_1) = all_0_0_0
% 31.80/10.58 |
% 31.80/10.58 | From (1302) and (7109) follows:
% 31.80/10.58 | (7113) sum(n9, n8) = all_0_2_2
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (388) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 31.80/10.58 | (1306) all_0_5_5 = n9
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (619) with n9, n8, all_0_2_2, n17 and discharging atoms sum(n9, n8) = all_0_2_2, sum(n9, n8) = n17, yields:
% 31.80/10.58 | (771) all_0_2_2 = n17
% 31.80/10.58 |
% 31.80/10.58 | From (771) and (473) follows:
% 31.80/10.58 | (773) pred(n17) = all_0_1_1
% 31.80/10.58 |
% 31.80/10.58 | From (1306) and (7108) follows:
% 31.80/10.58 | (7117) sum(n9, n9) = all_0_4_4
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (244) with n17, all_0_1_1, n16 and discharging atoms pred(n17) = all_0_1_1, pred(n17) = n16, yields:
% 31.80/10.58 | (776) all_0_1_1 = n16
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (619) with n9, n9, all_0_4_4, n18 and discharging atoms sum(n9, n9) = all_0_4_4, sum(n9, n9) = n18, yields:
% 31.80/10.58 | (772) all_0_4_4 = n18
% 31.80/10.58 |
% 31.80/10.58 | From (772) and (716) follows:
% 31.80/10.58 | (774) pred(n18) = all_0_3_3
% 31.80/10.58 |
% 31.80/10.58 | From (776) and (1304) follows:
% 31.80/10.58 | (7121) sum(n8, n16) = all_0_0_0
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (244) with n18, all_0_3_3, n17 and discharging atoms pred(n18) = all_0_3_3, pred(n18) = n17, yields:
% 31.80/10.58 | (775) all_0_3_3 = n17
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (619) with n8, n16, all_0_0_0, n3 and discharging atoms sum(n8, n16) = all_0_0_0, sum(n8, n16) = n3, yields:
% 31.80/10.58 | (983) all_0_0_0 = n3
% 31.80/10.58 |
% 31.80/10.58 | From (775)(983) and (232) follows:
% 31.80/10.58 | (7124) sum(n17, n3) = all_0_6_6
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (619) with n17, n3, all_0_6_6, n20 and discharging atoms sum(n17, n3) = all_0_6_6, sum(n17, n3) = n20, yields:
% 31.80/10.58 | (883) all_0_6_6 = n20
% 31.80/10.58 |
% 31.80/10.58 | Equations (883) can reduce 381 to:
% 31.80/10.58 | (748) $false
% 31.80/10.58 |
% 31.80/10.58 |-The branch is then unsatisfiable
% 31.80/10.58 |-Branch two:
% 31.80/10.58 | (1319) ~ (all_0_7_7 = n8)
% 31.80/10.58 | (1320) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.80/10.58 |
% 31.80/10.58 +-Applying beta-rule and splitting (1320), into two cases.
% 31.80/10.58 |-Branch one:
% 31.80/10.58 | (1321) all_0_7_7 = n7
% 31.80/10.58 |
% 31.80/10.58 | From (1321) and (683) follows:
% 31.80/10.58 | (1322) succ(n7) = all_0_5_5
% 31.80/10.58 |
% 31.80/10.58 | From (1321) and (8) follows:
% 31.80/10.58 | (1323) sum(n7, all_0_1_1) = all_0_0_0
% 31.80/10.58 |
% 31.80/10.58 | From (1321) and (7109) follows:
% 31.80/10.58 | (7132) sum(n9, n7) = all_0_2_2
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (388) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 31.80/10.58 | (1325) all_0_5_5 = n8
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (619) with n9, n7, all_0_2_2, n16 and discharging atoms sum(n9, n7) = all_0_2_2, sum(n9, n7) = n16, yields:
% 31.80/10.58 | (788) all_0_2_2 = n16
% 31.80/10.58 |
% 31.80/10.58 | From (788) and (473) follows:
% 31.80/10.58 | (790) pred(n16) = all_0_1_1
% 31.80/10.58 |
% 31.80/10.58 | From (1325) and (7108) follows:
% 31.80/10.58 | (7136) sum(n9, n8) = all_0_4_4
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 31.80/10.58 | (793) all_0_1_1 = n15
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (619) with n9, n8, all_0_4_4, n17 and discharging atoms sum(n9, n8) = all_0_4_4, sum(n9, n8) = n17, yields:
% 31.80/10.58 | (789) all_0_4_4 = n17
% 31.80/10.58 |
% 31.80/10.58 | From (789) and (716) follows:
% 31.80/10.58 | (791) pred(n17) = all_0_3_3
% 31.80/10.58 |
% 31.80/10.58 | From (793) and (1323) follows:
% 31.80/10.58 | (7140) sum(n7, n15) = all_0_0_0
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 31.80/10.58 | (792) all_0_3_3 = n16
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (619) with n7, n15, all_0_0_0, n1 and discharging atoms sum(n7, n15) = all_0_0_0, sum(n7, n15) = n1, yields:
% 31.80/10.58 | (1017) all_0_0_0 = n1
% 31.80/10.58 |
% 31.80/10.58 | From (792)(1017) and (232) follows:
% 31.80/10.58 | (7143) sum(n16, n1) = all_0_6_6
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (619) with n16, n1, all_0_6_6, n17 and discharging atoms sum(n16, n1) = all_0_6_6, sum(n16, n1) = n17, yields:
% 31.80/10.58 | (1086) all_0_6_6 = n17
% 31.80/10.58 |
% 31.80/10.58 | Equations (1086) can reduce 669 to:
% 31.80/10.58 | (748) $false
% 31.80/10.58 |
% 31.80/10.58 |-The branch is then unsatisfiable
% 31.80/10.58 |-Branch two:
% 31.80/10.58 | (1338) ~ (all_0_7_7 = n7)
% 31.80/10.58 | (1339) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.80/10.58 |
% 31.80/10.58 +-Applying beta-rule and splitting (1339), into two cases.
% 31.80/10.58 |-Branch one:
% 31.80/10.58 | (1340) all_0_7_7 = n6
% 31.80/10.58 |
% 31.80/10.58 | From (1340) and (683) follows:
% 31.80/10.58 | (1341) succ(n6) = all_0_5_5
% 31.80/10.58 |
% 31.80/10.58 | From (1340) and (8) follows:
% 31.80/10.58 | (1342) sum(n6, all_0_1_1) = all_0_0_0
% 31.80/10.58 |
% 31.80/10.58 | From (1340) and (7109) follows:
% 31.80/10.58 | (7151) sum(n9, n6) = all_0_2_2
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (388) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 31.80/10.58 | (1344) all_0_5_5 = n7
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (619) with n9, n6, all_0_2_2, n15 and discharging atoms sum(n9, n6) = all_0_2_2, sum(n9, n6) = n15, yields:
% 31.80/10.58 | (805) all_0_2_2 = n15
% 31.80/10.58 |
% 31.80/10.58 | From (805) and (473) follows:
% 31.80/10.58 | (807) pred(n15) = all_0_1_1
% 31.80/10.58 |
% 31.80/10.58 | From (1344) and (7108) follows:
% 31.80/10.58 | (7155) sum(n9, n7) = all_0_4_4
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 31.80/10.58 | (810) all_0_1_1 = n14
% 31.80/10.58 |
% 31.80/10.58 | Instantiating formula (619) with n9, n7, all_0_4_4, n16 and discharging atoms sum(n9, n7) = all_0_4_4, sum(n9, n7) = n16, yields:
% 31.80/10.58 | (806) all_0_4_4 = n16
% 31.80/10.58 |
% 31.80/10.58 | From (806) and (716) follows:
% 31.80/10.58 | (808) pred(n16) = all_0_3_3
% 31.80/10.58 |
% 31.80/10.58 | From (810) and (1342) follows:
% 31.80/10.59 | (7159) sum(n6, n14) = all_0_0_0
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 31.80/10.59 | (809) all_0_3_3 = n15
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (619) with n6, n14, all_0_0_0, n20 and discharging atoms sum(n6, n14) = all_0_0_0, sum(n6, n14) = n20, yields:
% 31.80/10.59 | (1051) all_0_0_0 = n20
% 31.80/10.59 |
% 31.80/10.59 | From (809)(1051) and (232) follows:
% 31.80/10.59 | (7162) sum(n15, n20) = all_0_6_6
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (619) with n15, n20, all_0_6_6, n14 and discharging atoms sum(n15, n20) = all_0_6_6, sum(n15, n20) = n14, yields:
% 31.80/10.59 | (934) all_0_6_6 = n14
% 31.80/10.59 |
% 31.80/10.59 | Equations (934) can reduce 353 to:
% 31.80/10.59 | (748) $false
% 31.80/10.59 |
% 31.80/10.59 |-The branch is then unsatisfiable
% 31.80/10.59 |-Branch two:
% 31.80/10.59 | (1357) ~ (all_0_7_7 = n6)
% 31.80/10.59 | (1358) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.80/10.59 |
% 31.80/10.59 +-Applying beta-rule and splitting (1358), into two cases.
% 31.80/10.59 |-Branch one:
% 31.80/10.59 | (1359) all_0_7_7 = n5
% 31.80/10.59 |
% 31.80/10.59 | From (1359) and (683) follows:
% 31.80/10.59 | (1360) succ(n5) = all_0_5_5
% 31.80/10.59 |
% 31.80/10.59 | From (1359) and (8) follows:
% 31.80/10.59 | (1361) sum(n5, all_0_1_1) = all_0_0_0
% 31.80/10.59 |
% 31.80/10.59 | From (1359) and (7109) follows:
% 31.80/10.59 | (7170) sum(n9, n5) = all_0_2_2
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (388) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 31.80/10.59 | (1363) all_0_5_5 = n6
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (619) with n9, n5, all_0_2_2, n14 and discharging atoms sum(n9, n5) = all_0_2_2, sum(n9, n5) = n14, yields:
% 31.80/10.59 | (822) all_0_2_2 = n14
% 31.80/10.59 |
% 31.80/10.59 | From (822) and (473) follows:
% 31.80/10.59 | (824) pred(n14) = all_0_1_1
% 31.80/10.59 |
% 31.80/10.59 | From (1363) and (7108) follows:
% 31.80/10.59 | (7174) sum(n9, n6) = all_0_4_4
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 31.80/10.59 | (827) all_0_1_1 = n13
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (619) with n9, n6, all_0_4_4, n15 and discharging atoms sum(n9, n6) = all_0_4_4, sum(n9, n6) = n15, yields:
% 31.80/10.59 | (823) all_0_4_4 = n15
% 31.80/10.59 |
% 31.80/10.59 | From (823) and (716) follows:
% 31.80/10.59 | (825) pred(n15) = all_0_3_3
% 31.80/10.59 |
% 31.80/10.59 | From (827) and (1361) follows:
% 31.80/10.59 | (7178) sum(n5, n13) = all_0_0_0
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 31.80/10.59 | (826) all_0_3_3 = n14
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (619) with n5, n13, all_0_0_0, n18 and discharging atoms sum(n5, n13) = all_0_0_0, sum(n5, n13) = n18, yields:
% 31.80/10.59 | (1084) all_0_0_0 = n18
% 31.80/10.59 |
% 31.80/10.59 | From (826)(1084) and (232) follows:
% 31.80/10.59 | (7181) sum(n14, n18) = all_0_6_6
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (619) with n14, n18, all_0_6_6, n11 and discharging atoms sum(n14, n18) = all_0_6_6, sum(n14, n18) = n11, yields:
% 31.80/10.59 | (781) all_0_6_6 = n11
% 31.80/10.59 |
% 31.80/10.59 | Equations (781) can reduce 2 to:
% 31.80/10.59 | (748) $false
% 31.80/10.59 |
% 31.80/10.59 |-The branch is then unsatisfiable
% 31.80/10.59 |-Branch two:
% 31.80/10.59 | (1376) ~ (all_0_7_7 = n5)
% 31.80/10.59 | (1377) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.80/10.59 |
% 31.80/10.59 +-Applying beta-rule and splitting (1377), into two cases.
% 31.80/10.59 |-Branch one:
% 31.80/10.59 | (1378) all_0_7_7 = n4
% 31.80/10.59 |
% 31.80/10.59 | From (1378) and (683) follows:
% 31.80/10.59 | (1379) succ(n4) = all_0_5_5
% 31.80/10.59 |
% 31.80/10.59 | From (1378) and (8) follows:
% 31.80/10.59 | (1380) sum(n4, all_0_1_1) = all_0_0_0
% 31.80/10.59 |
% 31.80/10.59 | From (1378) and (7109) follows:
% 31.80/10.59 | (7189) sum(n9, n4) = all_0_2_2
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (388) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 31.80/10.59 | (1382) all_0_5_5 = n5
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (619) with n9, n4, all_0_2_2, n13 and discharging atoms sum(n9, n4) = all_0_2_2, sum(n9, n4) = n13, yields:
% 31.80/10.59 | (839) all_0_2_2 = n13
% 31.80/10.59 |
% 31.80/10.59 | From (839) and (473) follows:
% 31.80/10.59 | (841) pred(n13) = all_0_1_1
% 31.80/10.59 |
% 31.80/10.59 | From (1382) and (7108) follows:
% 31.80/10.59 | (7193) sum(n9, n5) = all_0_4_4
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 31.80/10.59 | (844) all_0_1_1 = n12
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (619) with n9, n5, all_0_4_4, n14 and discharging atoms sum(n9, n5) = all_0_4_4, sum(n9, n5) = n14, yields:
% 31.80/10.59 | (840) all_0_4_4 = n14
% 31.80/10.59 |
% 31.80/10.59 | From (840) and (716) follows:
% 31.80/10.59 | (842) pred(n14) = all_0_3_3
% 31.80/10.59 |
% 31.80/10.59 | From (844) and (1380) follows:
% 31.80/10.59 | (7197) sum(n4, n12) = all_0_0_0
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 31.80/10.59 | (843) all_0_3_3 = n13
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (619) with n4, n12, all_0_0_0, n16 and discharging atoms sum(n4, n12) = all_0_0_0, sum(n4, n12) = n16, yields:
% 31.80/10.59 | (762) all_0_0_0 = n16
% 31.80/10.59 |
% 31.80/10.59 | From (843)(762) and (232) follows:
% 31.80/10.59 | (7200) sum(n13, n16) = all_0_6_6
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (619) with n13, n16, all_0_6_6, n8 and discharging atoms sum(n13, n16) = all_0_6_6, sum(n13, n16) = n8, yields:
% 31.80/10.59 | (985) all_0_6_6 = n8
% 31.80/10.59 |
% 31.80/10.59 | Equations (985) can reduce 357 to:
% 31.80/10.59 | (748) $false
% 31.80/10.59 |
% 31.80/10.59 |-The branch is then unsatisfiable
% 31.80/10.59 |-Branch two:
% 31.80/10.59 | (1395) ~ (all_0_7_7 = n4)
% 31.80/10.59 | (1396) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.80/10.59 |
% 31.80/10.59 +-Applying beta-rule and splitting (1396), into two cases.
% 31.80/10.59 |-Branch one:
% 31.80/10.59 | (1397) all_0_7_7 = n3
% 31.80/10.59 |
% 31.80/10.59 | From (1397) and (683) follows:
% 31.80/10.59 | (1398) succ(n3) = all_0_5_5
% 31.80/10.59 |
% 31.80/10.59 | From (1397) and (8) follows:
% 31.80/10.59 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 31.80/10.59 |
% 31.80/10.59 | From (1397) and (7109) follows:
% 31.80/10.59 | (7208) sum(n9, n3) = all_0_2_2
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 31.80/10.59 | (1401) all_0_5_5 = n4
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (619) with n9, n3, all_0_2_2, n12 and discharging atoms sum(n9, n3) = all_0_2_2, sum(n9, n3) = n12, yields:
% 31.80/10.59 | (856) all_0_2_2 = n12
% 31.80/10.59 |
% 31.80/10.59 | From (856) and (473) follows:
% 31.80/10.59 | (858) pred(n12) = all_0_1_1
% 31.80/10.59 |
% 31.80/10.59 | From (1401) and (7108) follows:
% 31.80/10.59 | (7212) sum(n9, n4) = all_0_4_4
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 31.80/10.59 | (861) all_0_1_1 = n11
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (619) with n9, n4, all_0_4_4, n13 and discharging atoms sum(n9, n4) = all_0_4_4, sum(n9, n4) = n13, yields:
% 31.80/10.59 | (857) all_0_4_4 = n13
% 31.80/10.59 |
% 31.80/10.59 | From (857) and (716) follows:
% 31.80/10.59 | (859) pred(n13) = all_0_3_3
% 31.80/10.59 |
% 31.80/10.59 | From (861) and (1399) follows:
% 31.80/10.59 | (7216) sum(n3, n11) = all_0_0_0
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 31.80/10.59 | (860) all_0_3_3 = n12
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (619) with n3, n11, all_0_0_0, n14 and discharging atoms sum(n3, n11) = all_0_0_0, sum(n3, n11) = n14, yields:
% 31.80/10.59 | (796) all_0_0_0 = n14
% 31.80/10.59 |
% 31.80/10.59 | From (860)(796) and (232) follows:
% 31.80/10.59 | (7219) sum(n12, n14) = all_0_6_6
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (619) with n12, n14, all_0_6_6, n5 and discharging atoms sum(n12, n14) = all_0_6_6, sum(n12, n14) = n5, yields:
% 31.80/10.59 | (832) all_0_6_6 = n5
% 31.80/10.59 |
% 31.80/10.59 | Equations (832) can reduce 462 to:
% 31.80/10.59 | (748) $false
% 31.80/10.59 |
% 31.80/10.59 |-The branch is then unsatisfiable
% 31.80/10.59 |-Branch two:
% 31.80/10.59 | (1414) ~ (all_0_7_7 = n3)
% 31.80/10.59 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 31.80/10.59 |
% 31.80/10.59 +-Applying beta-rule and splitting (1415), into two cases.
% 31.80/10.59 |-Branch one:
% 31.80/10.59 | (1416) all_0_7_7 = n2
% 31.80/10.59 |
% 31.80/10.59 | From (1416) and (683) follows:
% 31.80/10.59 | (1417) succ(n2) = all_0_5_5
% 31.80/10.59 |
% 31.80/10.59 | From (1416) and (8) follows:
% 31.80/10.59 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 31.80/10.59 |
% 31.80/10.59 | From (1416) and (7109) follows:
% 31.80/10.59 | (7227) sum(n9, n2) = all_0_2_2
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.80/10.59 | (1420) all_0_5_5 = n3
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (619) with n9, n2, all_0_2_2, n11 and discharging atoms sum(n9, n2) = all_0_2_2, sum(n9, n2) = n11, yields:
% 31.80/10.59 | (873) all_0_2_2 = n11
% 31.80/10.59 |
% 31.80/10.59 | From (873) and (473) follows:
% 31.80/10.59 | (875) pred(n11) = all_0_1_1
% 31.80/10.59 |
% 31.80/10.59 | From (1420) and (7108) follows:
% 31.80/10.59 | (7231) sum(n9, n3) = all_0_4_4
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 31.80/10.59 | (878) all_0_1_1 = n10
% 31.80/10.59 |
% 31.80/10.59 | Instantiating formula (619) with n9, n3, all_0_4_4, n12 and discharging atoms sum(n9, n3) = all_0_4_4, sum(n9, n3) = n12, yields:
% 31.80/10.59 | (874) all_0_4_4 = n12
% 31.80/10.59 |
% 31.80/10.59 | From (874) and (716) follows:
% 31.80/10.59 | (876) pred(n12) = all_0_3_3
% 31.80/10.59 |
% 31.80/10.59 | From (878) and (1418) follows:
% 31.80/10.60 | (7235) sum(n2, n10) = all_0_0_0
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 31.80/10.60 | (877) all_0_3_3 = n11
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (619) with n2, n10, all_0_0_0, n12 and discharging atoms sum(n2, n10) = all_0_0_0, sum(n2, n10) = n12, yields:
% 31.80/10.60 | (830) all_0_0_0 = n12
% 31.80/10.60 |
% 31.80/10.60 | From (877)(830) and (232) follows:
% 31.80/10.60 | (7238) sum(n11, n12) = all_0_6_6
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (619) with n11, n12, all_0_6_6, n2 and discharging atoms sum(n11, n12) = all_0_6_6, sum(n11, n12) = n2, yields:
% 31.80/10.60 | (1036) all_0_6_6 = n2
% 31.80/10.60 |
% 31.80/10.60 | Equations (1036) can reduce 56 to:
% 31.80/10.60 | (748) $false
% 31.80/10.60 |
% 31.80/10.60 |-The branch is then unsatisfiable
% 31.80/10.60 |-Branch two:
% 31.80/10.60 | (1433) ~ (all_0_7_7 = n2)
% 31.80/10.60 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 31.80/10.60 |
% 31.80/10.60 +-Applying beta-rule and splitting (1434), into two cases.
% 31.80/10.60 |-Branch one:
% 31.80/10.60 | (1435) all_0_7_7 = n1
% 31.80/10.60 |
% 31.80/10.60 | From (1435) and (683) follows:
% 31.80/10.60 | (1436) succ(n1) = all_0_5_5
% 31.80/10.60 |
% 31.80/10.60 | From (1435) and (8) follows:
% 31.80/10.60 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 31.80/10.60 |
% 31.80/10.60 | From (1435) and (7109) follows:
% 31.80/10.60 | (7246) sum(n9, n1) = all_0_2_2
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.80/10.60 | (1439) all_0_5_5 = n2
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (619) with n9, n1, all_0_2_2, n10 and discharging atoms sum(n9, n1) = all_0_2_2, sum(n9, n1) = n10, yields:
% 31.80/10.60 | (890) all_0_2_2 = n10
% 31.80/10.60 |
% 31.80/10.60 | From (890) and (473) follows:
% 31.80/10.60 | (892) pred(n10) = all_0_1_1
% 31.80/10.60 |
% 31.80/10.60 | From (1439) and (7108) follows:
% 31.80/10.60 | (7250) sum(n9, n2) = all_0_4_4
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 31.80/10.60 | (895) all_0_1_1 = n9
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (619) with n9, n2, all_0_4_4, n11 and discharging atoms sum(n9, n2) = all_0_4_4, sum(n9, n2) = n11, yields:
% 31.80/10.60 | (891) all_0_4_4 = n11
% 31.80/10.60 |
% 31.80/10.60 | From (891) and (716) follows:
% 31.80/10.60 | (893) pred(n11) = all_0_3_3
% 31.80/10.60 |
% 31.80/10.60 | From (895) and (1437) follows:
% 31.80/10.60 | (7254) sum(n1, n9) = all_0_0_0
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 31.80/10.60 | (894) all_0_3_3 = n10
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (619) with n1, n9, all_0_0_0, n10 and discharging atoms sum(n1, n9) = all_0_0_0, sum(n1, n9) = n10, yields:
% 31.80/10.60 | (864) all_0_0_0 = n10
% 31.80/10.60 |
% 31.80/10.60 | From (894)(864) and (232) follows:
% 31.80/10.60 | (7257) sum(n10, n10) = all_0_6_6
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (619) with n10, n10, all_0_6_6, n20 and discharging atoms sum(n10, n10) = all_0_6_6, sum(n10, n10) = n20, yields:
% 31.80/10.60 | (883) all_0_6_6 = n20
% 31.80/10.60 |
% 31.80/10.60 | Equations (883) can reduce 381 to:
% 31.80/10.60 | (748) $false
% 31.80/10.60 |
% 31.80/10.60 |-The branch is then unsatisfiable
% 31.80/10.60 |-Branch two:
% 31.80/10.60 | (1452) ~ (all_0_7_7 = n1)
% 31.80/10.60 | (1453) all_0_7_7 = n0
% 31.80/10.60 |
% 31.80/10.60 | From (1453) and (683) follows:
% 31.80/10.60 | (1454) succ(n0) = all_0_5_5
% 31.80/10.60 |
% 31.80/10.60 | From (1453) and (8) follows:
% 31.80/10.60 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 31.80/10.60 |
% 31.80/10.60 | From (1453) and (7109) follows:
% 31.80/10.60 | (7264) sum(n9, n0) = all_0_2_2
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.80/10.60 | (1457) all_0_5_5 = n1
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (619) with n9, n0, all_0_2_2, n9 and discharging atoms sum(n9, n0) = all_0_2_2, sum(n9, n0) = n9, yields:
% 31.80/10.60 | (907) all_0_2_2 = n9
% 31.80/10.60 |
% 31.80/10.60 | From (907) and (473) follows:
% 31.80/10.60 | (909) pred(n9) = all_0_1_1
% 31.80/10.60 |
% 31.80/10.60 | From (1457) and (7108) follows:
% 31.80/10.60 | (7268) sum(n9, n1) = all_0_4_4
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 31.80/10.60 | (912) all_0_1_1 = n8
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (619) with n9, n1, all_0_4_4, n10 and discharging atoms sum(n9, n1) = all_0_4_4, sum(n9, n1) = n10, yields:
% 31.80/10.60 | (908) all_0_4_4 = n10
% 31.80/10.60 |
% 31.80/10.60 | From (908) and (716) follows:
% 31.80/10.60 | (910) pred(n10) = all_0_3_3
% 31.80/10.60 |
% 31.80/10.60 | From (912) and (1455) follows:
% 31.80/10.60 | (7272) sum(n0, n8) = all_0_0_0
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 31.80/10.60 | (911) all_0_3_3 = n9
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (619) with n0, n8, all_0_0_0, n8 and discharging atoms sum(n0, n8) = all_0_0_0, sum(n0, n8) = n8, yields:
% 31.80/10.60 | (898) all_0_0_0 = n8
% 31.80/10.60 |
% 31.80/10.60 | From (911)(898) and (232) follows:
% 31.80/10.60 | (7275) sum(n9, n8) = all_0_6_6
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (619) with n9, n8, all_0_6_6, n17 and discharging atoms sum(n9, n8) = all_0_6_6, sum(n9, n8) = n17, yields:
% 31.80/10.60 | (1086) all_0_6_6 = n17
% 31.80/10.60 |
% 31.80/10.60 | Equations (1086) can reduce 669 to:
% 31.80/10.60 | (748) $false
% 31.80/10.60 |
% 31.80/10.60 |-The branch is then unsatisfiable
% 31.80/10.60 |-Branch two:
% 31.80/10.60 | (936) ~ (all_0_8_8 = n9)
% 31.80/10.60 | (937) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.60 |
% 31.80/10.60 +-Applying beta-rule and splitting (1301), into two cases.
% 31.80/10.60 |-Branch one:
% 31.80/10.60 | (1302) all_0_7_7 = n8
% 31.80/10.60 |
% 31.80/10.60 | From (1302) and (683) follows:
% 31.80/10.60 | (1303) succ(n8) = all_0_5_5
% 31.80/10.60 |
% 31.80/10.60 | From (1302) and (8) follows:
% 31.80/10.60 | (1304) sum(n8, all_0_1_1) = all_0_0_0
% 31.80/10.60 |
% 31.80/10.60 | From (1302) and (378) follows:
% 31.80/10.60 | (7283) sum(all_0_8_8, n8) = all_0_2_2
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (388) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 31.80/10.60 | (1306) all_0_5_5 = n9
% 31.80/10.60 |
% 31.80/10.60 | From (1306) and (708) follows:
% 31.80/10.60 | (7285) sum(all_0_8_8, n9) = all_0_4_4
% 31.80/10.60 |
% 31.80/10.60 +-Applying beta-rule and splitting (937), into two cases.
% 31.80/10.60 |-Branch one:
% 31.80/10.60 | (938) all_0_8_8 = n8
% 31.80/10.60 |
% 31.80/10.60 | From (938) and (7285) follows:
% 31.80/10.60 | (7287) sum(n8, n9) = all_0_4_4
% 31.80/10.60 |
% 31.80/10.60 | From (938) and (7283) follows:
% 31.80/10.60 | (7288) sum(n8, n8) = all_0_2_2
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (619) with n8, n9, all_0_4_4, n17 and discharging atoms sum(n8, n9) = all_0_4_4, sum(n8, n9) = n17, yields:
% 31.80/10.60 | (789) all_0_4_4 = n17
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (619) with n8, n8, all_0_2_2, n16 and discharging atoms sum(n8, n8) = all_0_2_2, sum(n8, n8) = n16, yields:
% 31.80/10.60 | (788) all_0_2_2 = n16
% 31.80/10.60 |
% 31.80/10.60 | From (788) and (473) follows:
% 31.80/10.60 | (790) pred(n16) = all_0_1_1
% 31.80/10.60 |
% 31.80/10.60 | From (789) and (716) follows:
% 31.80/10.60 | (791) pred(n17) = all_0_3_3
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (244) with n17, all_0_3_3, n16 and discharging atoms pred(n17) = all_0_3_3, pred(n17) = n16, yields:
% 31.80/10.60 | (792) all_0_3_3 = n16
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (244) with n16, all_0_1_1, n15 and discharging atoms pred(n16) = all_0_1_1, pred(n16) = n15, yields:
% 31.80/10.60 | (793) all_0_1_1 = n15
% 31.80/10.60 |
% 31.80/10.60 | From (792) and (232) follows:
% 31.80/10.60 | (794) sum(n16, all_0_0_0) = all_0_6_6
% 31.80/10.60 |
% 31.80/10.60 | From (793) and (1304) follows:
% 31.80/10.60 | (7296) sum(n8, n15) = all_0_0_0
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (619) with n8, n15, all_0_0_0, n2 and discharging atoms sum(n8, n15) = all_0_0_0, sum(n8, n15) = n2, yields:
% 31.80/10.60 | (1000) all_0_0_0 = n2
% 31.80/10.60 |
% 31.80/10.60 | From (1000) and (794) follows:
% 31.80/10.60 | (7298) sum(n16, n2) = all_0_6_6
% 31.80/10.60 |
% 31.80/10.60 | Instantiating formula (619) with n16, n2, all_0_6_6, n18 and discharging atoms sum(n16, n2) = all_0_6_6, sum(n16, n2) = n18, yields:
% 31.80/10.60 | (900) all_0_6_6 = n18
% 31.80/10.60 |
% 31.80/10.60 | Equations (900) can reduce 622 to:
% 31.80/10.60 | (748) $false
% 31.80/10.60 |
% 31.80/10.60 |-The branch is then unsatisfiable
% 31.80/10.60 |-Branch two:
% 31.80/10.60 | (953) ~ (all_0_8_8 = n8)
% 31.80/10.60 | (954) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.60 |
% 31.80/10.60 +-Applying beta-rule and splitting (954), into two cases.
% 31.80/10.60 |-Branch one:
% 31.80/10.60 | (955) all_0_8_8 = n7
% 31.80/10.60 |
% 31.80/10.60 | From (955) and (7285) follows:
% 31.80/10.60 | (7304) sum(n7, n9) = all_0_4_4
% 31.80/10.60 |
% 31.80/10.60 | From (955) and (7283) follows:
% 31.80/10.61 | (7305) sum(n7, n8) = all_0_2_2
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (619) with n7, n9, all_0_4_4, n16 and discharging atoms sum(n7, n9) = all_0_4_4, sum(n7, n9) = n16, yields:
% 31.80/10.61 | (806) all_0_4_4 = n16
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (619) with n7, n8, all_0_2_2, n15 and discharging atoms sum(n7, n8) = all_0_2_2, sum(n7, n8) = n15, yields:
% 31.80/10.61 | (805) all_0_2_2 = n15
% 31.80/10.61 |
% 31.80/10.61 | From (805) and (473) follows:
% 31.80/10.61 | (807) pred(n15) = all_0_1_1
% 31.80/10.61 |
% 31.80/10.61 | From (806) and (716) follows:
% 31.80/10.61 | (808) pred(n16) = all_0_3_3
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 31.80/10.61 | (809) all_0_3_3 = n15
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 31.80/10.61 | (810) all_0_1_1 = n14
% 31.80/10.61 |
% 31.80/10.61 | From (809) and (232) follows:
% 31.80/10.61 | (811) sum(n15, all_0_0_0) = all_0_6_6
% 31.80/10.61 |
% 31.80/10.61 | From (810) and (1304) follows:
% 31.80/10.61 | (7313) sum(n8, n14) = all_0_0_0
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (619) with n8, n14, all_0_0_0, n1 and discharging atoms sum(n8, n14) = all_0_0_0, sum(n8, n14) = n1, yields:
% 31.80/10.61 | (1017) all_0_0_0 = n1
% 31.80/10.61 |
% 31.80/10.61 | From (1017) and (811) follows:
% 31.80/10.61 | (7315) sum(n15, n1) = all_0_6_6
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (619) with n15, n1, all_0_6_6, n16 and discharging atoms sum(n15, n1) = all_0_6_6, sum(n15, n1) = n16, yields:
% 31.80/10.61 | (917) all_0_6_6 = n16
% 31.80/10.61 |
% 31.80/10.61 | Equations (917) can reduce 163 to:
% 31.80/10.61 | (748) $false
% 31.80/10.61 |
% 31.80/10.61 |-The branch is then unsatisfiable
% 31.80/10.61 |-Branch two:
% 31.80/10.61 | (970) ~ (all_0_8_8 = n7)
% 31.80/10.61 | (971) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.61 |
% 31.80/10.61 +-Applying beta-rule and splitting (971), into two cases.
% 31.80/10.61 |-Branch one:
% 31.80/10.61 | (972) all_0_8_8 = n6
% 31.80/10.61 |
% 31.80/10.61 | From (972) and (7285) follows:
% 31.80/10.61 | (7321) sum(n6, n9) = all_0_4_4
% 31.80/10.61 |
% 31.80/10.61 | From (972) and (7283) follows:
% 31.80/10.61 | (7322) sum(n6, n8) = all_0_2_2
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (619) with n6, n9, all_0_4_4, n15 and discharging atoms sum(n6, n9) = all_0_4_4, sum(n6, n9) = n15, yields:
% 31.80/10.61 | (823) all_0_4_4 = n15
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (619) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 31.80/10.61 | (822) all_0_2_2 = n14
% 31.80/10.61 |
% 31.80/10.61 | From (822) and (473) follows:
% 31.80/10.61 | (824) pred(n14) = all_0_1_1
% 31.80/10.61 |
% 31.80/10.61 | From (823) and (716) follows:
% 31.80/10.61 | (825) pred(n15) = all_0_3_3
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 31.80/10.61 | (826) all_0_3_3 = n14
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 31.80/10.61 | (827) all_0_1_1 = n13
% 31.80/10.61 |
% 31.80/10.61 | From (826) and (232) follows:
% 31.80/10.61 | (828) sum(n14, all_0_0_0) = all_0_6_6
% 31.80/10.61 |
% 31.80/10.61 | From (827) and (1304) follows:
% 31.80/10.61 | (7330) sum(n8, n13) = all_0_0_0
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (619) with n8, n13, all_0_0_0, n0 and discharging atoms sum(n8, n13) = all_0_0_0, sum(n8, n13) = n0, yields:
% 31.80/10.61 | (1034) all_0_0_0 = n0
% 31.80/10.61 |
% 31.80/10.61 | From (1034) and (828) follows:
% 31.80/10.61 | (7332) sum(n14, n0) = all_0_6_6
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (619) with n14, n0, all_0_6_6, n14 and discharging atoms sum(n14, n0) = all_0_6_6, sum(n14, n0) = n14, yields:
% 31.80/10.61 | (934) all_0_6_6 = n14
% 31.80/10.61 |
% 31.80/10.61 | Equations (934) can reduce 353 to:
% 31.80/10.61 | (748) $false
% 31.80/10.61 |
% 31.80/10.61 |-The branch is then unsatisfiable
% 31.80/10.61 |-Branch two:
% 31.80/10.61 | (987) ~ (all_0_8_8 = n6)
% 31.80/10.61 | (988) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.61 |
% 31.80/10.61 +-Applying beta-rule and splitting (988), into two cases.
% 31.80/10.61 |-Branch one:
% 31.80/10.61 | (989) all_0_8_8 = n5
% 31.80/10.61 |
% 31.80/10.61 | From (989) and (7285) follows:
% 31.80/10.61 | (7338) sum(n5, n9) = all_0_4_4
% 31.80/10.61 |
% 31.80/10.61 | From (989) and (7283) follows:
% 31.80/10.61 | (7339) sum(n5, n8) = all_0_2_2
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (619) with n5, n9, all_0_4_4, n14 and discharging atoms sum(n5, n9) = all_0_4_4, sum(n5, n9) = n14, yields:
% 31.80/10.61 | (840) all_0_4_4 = n14
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (619) with n5, n8, all_0_2_2, n13 and discharging atoms sum(n5, n8) = all_0_2_2, sum(n5, n8) = n13, yields:
% 31.80/10.61 | (839) all_0_2_2 = n13
% 31.80/10.61 |
% 31.80/10.61 | From (839) and (473) follows:
% 31.80/10.61 | (841) pred(n13) = all_0_1_1
% 31.80/10.61 |
% 31.80/10.61 | From (840) and (716) follows:
% 31.80/10.61 | (842) pred(n14) = all_0_3_3
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 31.80/10.61 | (843) all_0_3_3 = n13
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 31.80/10.61 | (844) all_0_1_1 = n12
% 31.80/10.61 |
% 31.80/10.61 | From (843) and (232) follows:
% 31.80/10.61 | (845) sum(n13, all_0_0_0) = all_0_6_6
% 31.80/10.61 |
% 31.80/10.61 | From (844) and (1304) follows:
% 31.80/10.61 | (7347) sum(n8, n12) = all_0_0_0
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (619) with n8, n12, all_0_0_0, n20 and discharging atoms sum(n8, n12) = all_0_0_0, sum(n8, n12) = n20, yields:
% 31.80/10.61 | (1051) all_0_0_0 = n20
% 31.80/10.61 |
% 31.80/10.61 | From (1051) and (845) follows:
% 31.80/10.61 | (7349) sum(n13, n20) = all_0_6_6
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (619) with n13, n20, all_0_6_6, n12 and discharging atoms sum(n13, n20) = all_0_6_6, sum(n13, n20) = n12, yields:
% 31.80/10.61 | (951) all_0_6_6 = n12
% 31.80/10.61 |
% 31.80/10.61 | Equations (951) can reduce 76 to:
% 31.80/10.61 | (748) $false
% 31.80/10.61 |
% 31.80/10.61 |-The branch is then unsatisfiable
% 31.80/10.61 |-Branch two:
% 31.80/10.61 | (1004) ~ (all_0_8_8 = n5)
% 31.80/10.61 | (1005) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 31.80/10.61 |
% 31.80/10.61 +-Applying beta-rule and splitting (1005), into two cases.
% 31.80/10.61 |-Branch one:
% 31.80/10.61 | (1006) all_0_8_8 = n4
% 31.80/10.61 |
% 31.80/10.61 | From (1006) and (7285) follows:
% 31.80/10.61 | (7355) sum(n4, n9) = all_0_4_4
% 31.80/10.61 |
% 31.80/10.61 | From (1006) and (7283) follows:
% 31.80/10.61 | (7356) sum(n4, n8) = all_0_2_2
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (619) with n4, n9, all_0_4_4, n13 and discharging atoms sum(n4, n9) = all_0_4_4, sum(n4, n9) = n13, yields:
% 31.80/10.61 | (857) all_0_4_4 = n13
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (619) with n4, n8, all_0_2_2, n12 and discharging atoms sum(n4, n8) = all_0_2_2, sum(n4, n8) = n12, yields:
% 31.80/10.61 | (856) all_0_2_2 = n12
% 31.80/10.61 |
% 31.80/10.61 | From (856) and (473) follows:
% 31.80/10.61 | (858) pred(n12) = all_0_1_1
% 31.80/10.61 |
% 31.80/10.61 | From (857) and (716) follows:
% 31.80/10.61 | (859) pred(n13) = all_0_3_3
% 31.80/10.61 |
% 31.80/10.61 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 32.19/10.61 | (860) all_0_3_3 = n12
% 32.19/10.61 |
% 32.19/10.61 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 32.19/10.61 | (861) all_0_1_1 = n11
% 32.19/10.61 |
% 32.19/10.61 | From (860) and (232) follows:
% 32.19/10.61 | (862) sum(n12, all_0_0_0) = all_0_6_6
% 32.19/10.61 |
% 32.19/10.61 | From (861) and (1304) follows:
% 32.19/10.61 | (7364) sum(n8, n11) = all_0_0_0
% 32.19/10.61 |
% 32.19/10.61 | Instantiating formula (619) with n8, n11, all_0_0_0, n19 and discharging atoms sum(n8, n11) = all_0_0_0, sum(n8, n11) = n19, yields:
% 32.19/10.61 | (1068) all_0_0_0 = n19
% 32.19/10.61 |
% 32.19/10.61 | From (1068) and (862) follows:
% 32.19/10.61 | (7366) sum(n12, n19) = all_0_6_6
% 32.19/10.61 |
% 32.19/10.61 | Instantiating formula (619) with n12, n19, all_0_6_6, n10 and discharging atoms sum(n12, n19) = all_0_6_6, sum(n12, n19) = n10, yields:
% 32.19/10.61 | (968) all_0_6_6 = n10
% 32.19/10.61 |
% 32.19/10.61 | Equations (968) can reduce 176 to:
% 32.19/10.61 | (748) $false
% 32.19/10.61 |
% 32.19/10.61 |-The branch is then unsatisfiable
% 32.19/10.61 |-Branch two:
% 32.19/10.61 | (1021) ~ (all_0_8_8 = n4)
% 32.19/10.61 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.19/10.61 |
% 32.19/10.61 +-Applying beta-rule and splitting (1022), into two cases.
% 32.19/10.61 |-Branch one:
% 32.19/10.61 | (1023) all_0_8_8 = n3
% 32.19/10.61 |
% 32.19/10.61 | From (1023) and (7285) follows:
% 32.19/10.61 | (7372) sum(n3, n9) = all_0_4_4
% 32.19/10.61 |
% 32.19/10.61 | From (1023) and (7283) follows:
% 32.19/10.61 | (7373) sum(n3, n8) = all_0_2_2
% 32.19/10.61 |
% 32.19/10.61 | Instantiating formula (619) with n3, n9, all_0_4_4, n12 and discharging atoms sum(n3, n9) = all_0_4_4, sum(n3, n9) = n12, yields:
% 32.19/10.61 | (874) all_0_4_4 = n12
% 32.19/10.61 |
% 32.19/10.61 | Instantiating formula (619) with n3, n8, all_0_2_2, n11 and discharging atoms sum(n3, n8) = all_0_2_2, sum(n3, n8) = n11, yields:
% 32.19/10.61 | (873) all_0_2_2 = n11
% 32.19/10.61 |
% 32.19/10.61 | From (873) and (473) follows:
% 32.19/10.61 | (875) pred(n11) = all_0_1_1
% 32.19/10.61 |
% 32.19/10.61 | From (874) and (716) follows:
% 32.19/10.61 | (876) pred(n12) = all_0_3_3
% 32.19/10.61 |
% 32.19/10.61 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 32.19/10.61 | (877) all_0_3_3 = n11
% 32.19/10.61 |
% 32.19/10.61 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 32.19/10.61 | (878) all_0_1_1 = n10
% 32.19/10.61 |
% 32.19/10.61 | From (877) and (232) follows:
% 32.19/10.61 | (879) sum(n11, all_0_0_0) = all_0_6_6
% 32.19/10.61 |
% 32.19/10.61 | From (878) and (1304) follows:
% 32.19/10.62 | (7381) sum(n8, n10) = all_0_0_0
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (619) with n8, n10, all_0_0_0, n18 and discharging atoms sum(n8, n10) = all_0_0_0, sum(n8, n10) = n18, yields:
% 32.19/10.62 | (1084) all_0_0_0 = n18
% 32.19/10.62 |
% 32.19/10.62 | From (1084) and (879) follows:
% 32.19/10.62 | (7383) sum(n11, n18) = all_0_6_6
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (619) with n11, n18, all_0_6_6, n8 and discharging atoms sum(n11, n18) = all_0_6_6, sum(n11, n18) = n8, yields:
% 32.19/10.62 | (985) all_0_6_6 = n8
% 32.19/10.62 |
% 32.19/10.62 | Equations (985) can reduce 357 to:
% 32.19/10.62 | (748) $false
% 32.19/10.62 |
% 32.19/10.62 |-The branch is then unsatisfiable
% 32.19/10.62 |-Branch two:
% 32.19/10.62 | (1038) ~ (all_0_8_8 = n3)
% 32.19/10.62 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.19/10.62 |
% 32.19/10.62 +-Applying beta-rule and splitting (1039), into two cases.
% 32.19/10.62 |-Branch one:
% 32.19/10.62 | (1040) all_0_8_8 = n2
% 32.19/10.62 |
% 32.19/10.62 | From (1040) and (7285) follows:
% 32.19/10.62 | (7389) sum(n2, n9) = all_0_4_4
% 32.19/10.62 |
% 32.19/10.62 | From (1040) and (7283) follows:
% 32.19/10.62 | (7390) sum(n2, n8) = all_0_2_2
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (619) with n2, n9, all_0_4_4, n11 and discharging atoms sum(n2, n9) = all_0_4_4, sum(n2, n9) = n11, yields:
% 32.19/10.62 | (891) all_0_4_4 = n11
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (619) with n2, n8, all_0_2_2, n10 and discharging atoms sum(n2, n8) = all_0_2_2, sum(n2, n8) = n10, yields:
% 32.19/10.62 | (890) all_0_2_2 = n10
% 32.19/10.62 |
% 32.19/10.62 | From (890) and (473) follows:
% 32.19/10.62 | (892) pred(n10) = all_0_1_1
% 32.19/10.62 |
% 32.19/10.62 | From (891) and (716) follows:
% 32.19/10.62 | (893) pred(n11) = all_0_3_3
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 32.19/10.62 | (894) all_0_3_3 = n10
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 32.19/10.62 | (895) all_0_1_1 = n9
% 32.19/10.62 |
% 32.19/10.62 | From (894) and (232) follows:
% 32.19/10.62 | (896) sum(n10, all_0_0_0) = all_0_6_6
% 32.19/10.62 |
% 32.19/10.62 | From (895) and (1304) follows:
% 32.19/10.62 | (7398) sum(n8, n9) = all_0_0_0
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (619) with n8, n9, all_0_0_0, n17 and discharging atoms sum(n8, n9) = all_0_0_0, sum(n8, n9) = n17, yields:
% 32.19/10.62 | (745) all_0_0_0 = n17
% 32.19/10.62 |
% 32.19/10.62 | From (745) and (896) follows:
% 32.19/10.62 | (7400) sum(n10, n17) = all_0_6_6
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (619) with n10, n17, all_0_6_6, n6 and discharging atoms sum(n10, n17) = all_0_6_6, sum(n10, n17) = n6, yields:
% 32.19/10.62 | (1002) all_0_6_6 = n6
% 32.19/10.62 |
% 32.19/10.62 | Equations (1002) can reduce 498 to:
% 32.19/10.62 | (748) $false
% 32.19/10.62 |
% 32.19/10.62 |-The branch is then unsatisfiable
% 32.19/10.62 |-Branch two:
% 32.19/10.62 | (1055) ~ (all_0_8_8 = n2)
% 32.19/10.62 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 32.19/10.62 |
% 32.19/10.62 +-Applying beta-rule and splitting (1056), into two cases.
% 32.19/10.62 |-Branch one:
% 32.19/10.62 | (1057) all_0_8_8 = n1
% 32.19/10.62 |
% 32.19/10.62 | From (1057) and (7285) follows:
% 32.19/10.62 | (7406) sum(n1, n9) = all_0_4_4
% 32.19/10.62 |
% 32.19/10.62 | From (1057) and (7283) follows:
% 32.19/10.62 | (7407) sum(n1, n8) = all_0_2_2
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (619) with n1, n9, all_0_4_4, n10 and discharging atoms sum(n1, n9) = all_0_4_4, sum(n1, n9) = n10, yields:
% 32.19/10.62 | (908) all_0_4_4 = n10
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (619) with n1, n8, all_0_2_2, n9 and discharging atoms sum(n1, n8) = all_0_2_2, sum(n1, n8) = n9, yields:
% 32.19/10.62 | (907) all_0_2_2 = n9
% 32.19/10.62 |
% 32.19/10.62 | From (907) and (473) follows:
% 32.19/10.62 | (909) pred(n9) = all_0_1_1
% 32.19/10.62 |
% 32.19/10.62 | From (908) and (716) follows:
% 32.19/10.62 | (910) pred(n10) = all_0_3_3
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 32.19/10.62 | (911) all_0_3_3 = n9
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 32.19/10.62 | (912) all_0_1_1 = n8
% 32.19/10.62 |
% 32.19/10.62 | From (911) and (232) follows:
% 32.19/10.62 | (913) sum(n9, all_0_0_0) = all_0_6_6
% 32.19/10.62 |
% 32.19/10.62 | From (912) and (1304) follows:
% 32.19/10.62 | (7415) sum(n8, n8) = all_0_0_0
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (619) with n8, n8, all_0_0_0, n16 and discharging atoms sum(n8, n8) = all_0_0_0, sum(n8, n8) = n16, yields:
% 32.19/10.62 | (762) all_0_0_0 = n16
% 32.19/10.62 |
% 32.19/10.62 | From (762) and (913) follows:
% 32.19/10.62 | (7417) sum(n9, n16) = all_0_6_6
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (619) with n9, n16, all_0_6_6, n4 and discharging atoms sum(n9, n16) = all_0_6_6, sum(n9, n16) = n4, yields:
% 32.19/10.62 | (1019) all_0_6_6 = n4
% 32.19/10.62 |
% 32.19/10.62 | Equations (1019) can reduce 48 to:
% 32.19/10.62 | (748) $false
% 32.19/10.62 |
% 32.19/10.62 |-The branch is then unsatisfiable
% 32.19/10.62 |-Branch two:
% 32.19/10.62 | (1072) ~ (all_0_8_8 = n1)
% 32.19/10.62 | (1073) all_0_8_8 = n0
% 32.19/10.62 |
% 32.19/10.62 | From (1073) and (7285) follows:
% 32.19/10.62 | (7422) sum(n0, n9) = all_0_4_4
% 32.19/10.62 |
% 32.19/10.62 | From (1073) and (7283) follows:
% 32.19/10.62 | (7423) sum(n0, n8) = all_0_2_2
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (619) with n0, n9, all_0_4_4, n9 and discharging atoms sum(n0, n9) = all_0_4_4, sum(n0, n9) = n9, yields:
% 32.19/10.62 | (925) all_0_4_4 = n9
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (619) with n0, n8, all_0_2_2, n8 and discharging atoms sum(n0, n8) = all_0_2_2, sum(n0, n8) = n8, yields:
% 32.19/10.62 | (924) all_0_2_2 = n8
% 32.19/10.62 |
% 32.19/10.62 | From (924) and (473) follows:
% 32.19/10.62 | (926) pred(n8) = all_0_1_1
% 32.19/10.62 |
% 32.19/10.62 | From (925) and (716) follows:
% 32.19/10.62 | (927) pred(n9) = all_0_3_3
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 32.19/10.62 | (928) all_0_3_3 = n8
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 32.19/10.62 | (929) all_0_1_1 = n7
% 32.19/10.62 |
% 32.19/10.62 | From (928) and (232) follows:
% 32.19/10.62 | (930) sum(n8, all_0_0_0) = all_0_6_6
% 32.19/10.62 |
% 32.19/10.62 | From (929) and (1304) follows:
% 32.19/10.62 | (7431) sum(n8, n7) = all_0_0_0
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (619) with n8, n7, all_0_0_0, n15 and discharging atoms sum(n8, n7) = all_0_0_0, sum(n8, n7) = n15, yields:
% 32.19/10.62 | (779) all_0_0_0 = n15
% 32.19/10.62 |
% 32.19/10.62 | From (779) and (930) follows:
% 32.19/10.62 | (7433) sum(n8, n15) = all_0_6_6
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (619) with n8, n15, all_0_6_6, n2 and discharging atoms sum(n8, n15) = all_0_6_6, sum(n8, n15) = n2, yields:
% 32.19/10.62 | (1036) all_0_6_6 = n2
% 32.19/10.62 |
% 32.19/10.62 | Equations (1036) can reduce 56 to:
% 32.19/10.62 | (748) $false
% 32.19/10.62 |
% 32.19/10.62 |-The branch is then unsatisfiable
% 32.19/10.62 |-Branch two:
% 32.19/10.62 | (1319) ~ (all_0_7_7 = n8)
% 32.19/10.62 | (1320) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.19/10.62 |
% 32.19/10.62 +-Applying beta-rule and splitting (937), into two cases.
% 32.19/10.62 |-Branch one:
% 32.19/10.62 | (938) all_0_8_8 = n8
% 32.19/10.62 |
% 32.19/10.62 | From (938) and (708) follows:
% 32.19/10.62 | (7439) sum(n8, all_0_5_5) = all_0_4_4
% 32.19/10.62 |
% 32.19/10.62 | From (938) and (378) follows:
% 32.19/10.62 | (7440) sum(n8, all_0_7_7) = all_0_2_2
% 32.19/10.62 |
% 32.19/10.62 +-Applying beta-rule and splitting (1320), into two cases.
% 32.19/10.62 |-Branch one:
% 32.19/10.62 | (1321) all_0_7_7 = n7
% 32.19/10.62 |
% 32.19/10.62 | From (1321) and (683) follows:
% 32.19/10.62 | (1322) succ(n7) = all_0_5_5
% 32.19/10.62 |
% 32.19/10.62 | From (1321) and (8) follows:
% 32.19/10.62 | (1323) sum(n7, all_0_1_1) = all_0_0_0
% 32.19/10.62 |
% 32.19/10.62 | From (1321) and (7440) follows:
% 32.19/10.62 | (7444) sum(n8, n7) = all_0_2_2
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (388) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 32.19/10.62 | (1325) all_0_5_5 = n8
% 32.19/10.62 |
% 32.19/10.62 | Instantiating formula (619) with n8, n7, all_0_2_2, n15 and discharging atoms sum(n8, n7) = all_0_2_2, sum(n8, n7) = n15, yields:
% 32.19/10.62 | (805) all_0_2_2 = n15
% 32.19/10.62 |
% 32.19/10.62 | From (805) and (473) follows:
% 32.19/10.62 | (807) pred(n15) = all_0_1_1
% 32.19/10.62 |
% 32.19/10.62 | From (1325) and (7439) follows:
% 32.19/10.62 | (7448) sum(n8, n8) = all_0_4_4
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (244) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 32.19/10.63 | (810) all_0_1_1 = n14
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (619) with n8, n8, all_0_4_4, n16 and discharging atoms sum(n8, n8) = all_0_4_4, sum(n8, n8) = n16, yields:
% 32.19/10.63 | (806) all_0_4_4 = n16
% 32.19/10.63 |
% 32.19/10.63 | From (806) and (716) follows:
% 32.19/10.63 | (808) pred(n16) = all_0_3_3
% 32.19/10.63 |
% 32.19/10.63 | From (810) and (1323) follows:
% 32.19/10.63 | (7452) sum(n7, n14) = all_0_0_0
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (244) with n16, all_0_3_3, n15 and discharging atoms pred(n16) = all_0_3_3, pred(n16) = n15, yields:
% 32.19/10.63 | (809) all_0_3_3 = n15
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (619) with n7, n14, all_0_0_0, n0 and discharging atoms sum(n7, n14) = all_0_0_0, sum(n7, n14) = n0, yields:
% 32.19/10.63 | (1034) all_0_0_0 = n0
% 32.19/10.63 |
% 32.19/10.63 | From (809)(1034) and (232) follows:
% 32.19/10.63 | (7455) sum(n15, n0) = all_0_6_6
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (619) with n15, n0, all_0_6_6, n15 and discharging atoms sum(n15, n0) = all_0_6_6, sum(n15, n0) = n15, yields:
% 32.19/10.63 | (747) all_0_6_6 = n15
% 32.19/10.63 |
% 32.19/10.63 | Equations (747) can reduce 456 to:
% 32.19/10.63 | (748) $false
% 32.19/10.63 |
% 32.19/10.63 |-The branch is then unsatisfiable
% 32.19/10.63 |-Branch two:
% 32.19/10.63 | (1338) ~ (all_0_7_7 = n7)
% 32.19/10.63 | (1339) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.19/10.63 |
% 32.19/10.63 +-Applying beta-rule and splitting (1339), into two cases.
% 32.19/10.63 |-Branch one:
% 32.19/10.63 | (1340) all_0_7_7 = n6
% 32.19/10.63 |
% 32.19/10.63 | From (1340) and (683) follows:
% 32.19/10.63 | (1341) succ(n6) = all_0_5_5
% 32.19/10.63 |
% 32.19/10.63 | From (1340) and (8) follows:
% 32.19/10.63 | (1342) sum(n6, all_0_1_1) = all_0_0_0
% 32.19/10.63 |
% 32.19/10.63 | From (1340) and (7440) follows:
% 32.19/10.63 | (7463) sum(n8, n6) = all_0_2_2
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (388) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 32.19/10.63 | (1344) all_0_5_5 = n7
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (619) with n8, n6, all_0_2_2, n14 and discharging atoms sum(n8, n6) = all_0_2_2, sum(n8, n6) = n14, yields:
% 32.19/10.63 | (822) all_0_2_2 = n14
% 32.19/10.63 |
% 32.19/10.63 | From (822) and (473) follows:
% 32.19/10.63 | (824) pred(n14) = all_0_1_1
% 32.19/10.63 |
% 32.19/10.63 | From (1344) and (7439) follows:
% 32.19/10.63 | (7467) sum(n8, n7) = all_0_4_4
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 32.19/10.63 | (827) all_0_1_1 = n13
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (619) with n8, n7, all_0_4_4, n15 and discharging atoms sum(n8, n7) = all_0_4_4, sum(n8, n7) = n15, yields:
% 32.19/10.63 | (823) all_0_4_4 = n15
% 32.19/10.63 |
% 32.19/10.63 | From (823) and (716) follows:
% 32.19/10.63 | (825) pred(n15) = all_0_3_3
% 32.19/10.63 |
% 32.19/10.63 | From (827) and (1342) follows:
% 32.19/10.63 | (7471) sum(n6, n13) = all_0_0_0
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 32.19/10.63 | (826) all_0_3_3 = n14
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (619) with n6, n13, all_0_0_0, n19 and discharging atoms sum(n6, n13) = all_0_0_0, sum(n6, n13) = n19, yields:
% 32.19/10.63 | (1068) all_0_0_0 = n19
% 32.19/10.63 |
% 32.19/10.63 | From (826)(1068) and (232) follows:
% 32.19/10.63 | (7474) sum(n14, n19) = all_0_6_6
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (619) with n14, n19, all_0_6_6, n12 and discharging atoms sum(n14, n19) = all_0_6_6, sum(n14, n19) = n12, yields:
% 32.19/10.63 | (951) all_0_6_6 = n12
% 32.19/10.63 |
% 32.19/10.63 | Equations (951) can reduce 76 to:
% 32.19/10.63 | (748) $false
% 32.19/10.63 |
% 32.19/10.63 |-The branch is then unsatisfiable
% 32.19/10.63 |-Branch two:
% 32.19/10.63 | (1357) ~ (all_0_7_7 = n6)
% 32.19/10.63 | (1358) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.19/10.63 |
% 32.19/10.63 +-Applying beta-rule and splitting (1358), into two cases.
% 32.19/10.63 |-Branch one:
% 32.19/10.63 | (1359) all_0_7_7 = n5
% 32.19/10.63 |
% 32.19/10.63 | From (1359) and (683) follows:
% 32.19/10.63 | (1360) succ(n5) = all_0_5_5
% 32.19/10.63 |
% 32.19/10.63 | From (1359) and (8) follows:
% 32.19/10.63 | (1361) sum(n5, all_0_1_1) = all_0_0_0
% 32.19/10.63 |
% 32.19/10.63 | From (1359) and (7440) follows:
% 32.19/10.63 | (7482) sum(n8, n5) = all_0_2_2
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (388) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 32.19/10.63 | (1363) all_0_5_5 = n6
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (619) with n8, n5, all_0_2_2, n13 and discharging atoms sum(n8, n5) = all_0_2_2, sum(n8, n5) = n13, yields:
% 32.19/10.63 | (839) all_0_2_2 = n13
% 32.19/10.63 |
% 32.19/10.63 | From (839) and (473) follows:
% 32.19/10.63 | (841) pred(n13) = all_0_1_1
% 32.19/10.63 |
% 32.19/10.63 | From (1363) and (7439) follows:
% 32.19/10.63 | (7486) sum(n8, n6) = all_0_4_4
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 32.19/10.63 | (844) all_0_1_1 = n12
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (619) with n8, n6, all_0_4_4, n14 and discharging atoms sum(n8, n6) = all_0_4_4, sum(n8, n6) = n14, yields:
% 32.19/10.63 | (840) all_0_4_4 = n14
% 32.19/10.63 |
% 32.19/10.63 | From (840) and (716) follows:
% 32.19/10.63 | (842) pred(n14) = all_0_3_3
% 32.19/10.63 |
% 32.19/10.63 | From (844) and (1361) follows:
% 32.19/10.63 | (7490) sum(n5, n12) = all_0_0_0
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 32.19/10.63 | (843) all_0_3_3 = n13
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (619) with n5, n12, all_0_0_0, n17 and discharging atoms sum(n5, n12) = all_0_0_0, sum(n5, n12) = n17, yields:
% 32.19/10.63 | (745) all_0_0_0 = n17
% 32.19/10.63 |
% 32.19/10.63 | From (843)(745) and (232) follows:
% 32.19/10.63 | (7493) sum(n13, n17) = all_0_6_6
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (619) with n13, n17, all_0_6_6, n9 and discharging atoms sum(n13, n17) = all_0_6_6, sum(n13, n17) = n9, yields:
% 32.19/10.63 | (798) all_0_6_6 = n9
% 32.19/10.63 |
% 32.19/10.63 | Equations (798) can reduce 593 to:
% 32.19/10.63 | (748) $false
% 32.19/10.63 |
% 32.19/10.63 |-The branch is then unsatisfiable
% 32.19/10.63 |-Branch two:
% 32.19/10.63 | (1376) ~ (all_0_7_7 = n5)
% 32.19/10.63 | (1377) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.19/10.63 |
% 32.19/10.63 +-Applying beta-rule and splitting (1377), into two cases.
% 32.19/10.63 |-Branch one:
% 32.19/10.63 | (1378) all_0_7_7 = n4
% 32.19/10.63 |
% 32.19/10.63 | From (1378) and (683) follows:
% 32.19/10.63 | (1379) succ(n4) = all_0_5_5
% 32.19/10.63 |
% 32.19/10.63 | From (1378) and (8) follows:
% 32.19/10.63 | (1380) sum(n4, all_0_1_1) = all_0_0_0
% 32.19/10.63 |
% 32.19/10.63 | From (1378) and (7440) follows:
% 32.19/10.63 | (7501) sum(n8, n4) = all_0_2_2
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (388) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 32.19/10.63 | (1382) all_0_5_5 = n5
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (619) with n8, n4, all_0_2_2, n12 and discharging atoms sum(n8, n4) = all_0_2_2, sum(n8, n4) = n12, yields:
% 32.19/10.63 | (856) all_0_2_2 = n12
% 32.19/10.63 |
% 32.19/10.63 | From (856) and (473) follows:
% 32.19/10.63 | (858) pred(n12) = all_0_1_1
% 32.19/10.63 |
% 32.19/10.63 | From (1382) and (7439) follows:
% 32.19/10.63 | (7505) sum(n8, n5) = all_0_4_4
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 32.19/10.63 | (861) all_0_1_1 = n11
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (619) with n8, n5, all_0_4_4, n13 and discharging atoms sum(n8, n5) = all_0_4_4, sum(n8, n5) = n13, yields:
% 32.19/10.63 | (857) all_0_4_4 = n13
% 32.19/10.63 |
% 32.19/10.63 | From (857) and (716) follows:
% 32.19/10.63 | (859) pred(n13) = all_0_3_3
% 32.19/10.63 |
% 32.19/10.63 | From (861) and (1380) follows:
% 32.19/10.63 | (7509) sum(n4, n11) = all_0_0_0
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 32.19/10.63 | (860) all_0_3_3 = n12
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (619) with n4, n11, all_0_0_0, n15 and discharging atoms sum(n4, n11) = all_0_0_0, sum(n4, n11) = n15, yields:
% 32.19/10.63 | (779) all_0_0_0 = n15
% 32.19/10.63 |
% 32.19/10.63 | From (860)(779) and (232) follows:
% 32.19/10.63 | (7512) sum(n12, n15) = all_0_6_6
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (619) with n12, n15, all_0_6_6, n6 and discharging atoms sum(n12, n15) = all_0_6_6, sum(n12, n15) = n6, yields:
% 32.19/10.63 | (1002) all_0_6_6 = n6
% 32.19/10.63 |
% 32.19/10.63 | Equations (1002) can reduce 498 to:
% 32.19/10.63 | (748) $false
% 32.19/10.63 |
% 32.19/10.63 |-The branch is then unsatisfiable
% 32.19/10.63 |-Branch two:
% 32.19/10.63 | (1395) ~ (all_0_7_7 = n4)
% 32.19/10.63 | (1396) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.19/10.63 |
% 32.19/10.63 +-Applying beta-rule and splitting (1396), into two cases.
% 32.19/10.63 |-Branch one:
% 32.19/10.63 | (1397) all_0_7_7 = n3
% 32.19/10.63 |
% 32.19/10.63 | From (1397) and (683) follows:
% 32.19/10.63 | (1398) succ(n3) = all_0_5_5
% 32.19/10.63 |
% 32.19/10.63 | From (1397) and (8) follows:
% 32.19/10.63 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 32.19/10.63 |
% 32.19/10.63 | From (1397) and (7440) follows:
% 32.19/10.63 | (7520) sum(n8, n3) = all_0_2_2
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 32.19/10.63 | (1401) all_0_5_5 = n4
% 32.19/10.63 |
% 32.19/10.63 | Instantiating formula (619) with n8, n3, all_0_2_2, n11 and discharging atoms sum(n8, n3) = all_0_2_2, sum(n8, n3) = n11, yields:
% 32.19/10.63 | (873) all_0_2_2 = n11
% 32.19/10.63 |
% 32.19/10.63 | From (873) and (473) follows:
% 32.19/10.63 | (875) pred(n11) = all_0_1_1
% 32.19/10.63 |
% 32.19/10.63 | From (1401) and (7439) follows:
% 32.19/10.64 | (7524) sum(n8, n4) = all_0_4_4
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 32.19/10.64 | (878) all_0_1_1 = n10
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (619) with n8, n4, all_0_4_4, n12 and discharging atoms sum(n8, n4) = all_0_4_4, sum(n8, n4) = n12, yields:
% 32.19/10.64 | (874) all_0_4_4 = n12
% 32.19/10.64 |
% 32.19/10.64 | From (874) and (716) follows:
% 32.19/10.64 | (876) pred(n12) = all_0_3_3
% 32.19/10.64 |
% 32.19/10.64 | From (878) and (1399) follows:
% 32.19/10.64 | (7528) sum(n3, n10) = all_0_0_0
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 32.19/10.64 | (877) all_0_3_3 = n11
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (619) with n3, n10, all_0_0_0, n13 and discharging atoms sum(n3, n10) = all_0_0_0, sum(n3, n10) = n13, yields:
% 32.19/10.64 | (813) all_0_0_0 = n13
% 32.19/10.64 |
% 32.19/10.64 | From (877)(813) and (232) follows:
% 32.19/10.64 | (7531) sum(n11, n13) = all_0_6_6
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (619) with n11, n13, all_0_6_6, n3 and discharging atoms sum(n11, n13) = all_0_6_6, sum(n11, n13) = n3, yields:
% 32.19/10.64 | (849) all_0_6_6 = n3
% 32.19/10.64 |
% 32.19/10.64 | Equations (849) can reduce 416 to:
% 32.19/10.64 | (748) $false
% 32.19/10.64 |
% 32.19/10.64 |-The branch is then unsatisfiable
% 32.19/10.64 |-Branch two:
% 32.19/10.64 | (1414) ~ (all_0_7_7 = n3)
% 32.19/10.64 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.19/10.64 |
% 32.19/10.64 +-Applying beta-rule and splitting (1415), into two cases.
% 32.19/10.64 |-Branch one:
% 32.19/10.64 | (1416) all_0_7_7 = n2
% 32.19/10.64 |
% 32.19/10.64 | From (1416) and (683) follows:
% 32.19/10.64 | (1417) succ(n2) = all_0_5_5
% 32.19/10.64 |
% 32.19/10.64 | From (1416) and (8) follows:
% 32.19/10.64 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 32.19/10.64 |
% 32.19/10.64 | From (1416) and (7440) follows:
% 32.19/10.64 | (7539) sum(n8, n2) = all_0_2_2
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 32.19/10.64 | (1420) all_0_5_5 = n3
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (619) with n8, n2, all_0_2_2, n10 and discharging atoms sum(n8, n2) = all_0_2_2, sum(n8, n2) = n10, yields:
% 32.19/10.64 | (890) all_0_2_2 = n10
% 32.19/10.64 |
% 32.19/10.64 | From (890) and (473) follows:
% 32.19/10.64 | (892) pred(n10) = all_0_1_1
% 32.19/10.64 |
% 32.19/10.64 | From (1420) and (7439) follows:
% 32.19/10.64 | (7543) sum(n8, n3) = all_0_4_4
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 32.19/10.64 | (895) all_0_1_1 = n9
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (619) with n8, n3, all_0_4_4, n11 and discharging atoms sum(n8, n3) = all_0_4_4, sum(n8, n3) = n11, yields:
% 32.19/10.64 | (891) all_0_4_4 = n11
% 32.19/10.64 |
% 32.19/10.64 | From (891) and (716) follows:
% 32.19/10.64 | (893) pred(n11) = all_0_3_3
% 32.19/10.64 |
% 32.19/10.64 | From (895) and (1418) follows:
% 32.19/10.64 | (7547) sum(n2, n9) = all_0_0_0
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 32.19/10.64 | (894) all_0_3_3 = n10
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (619) with n2, n9, all_0_0_0, n11 and discharging atoms sum(n2, n9) = all_0_0_0, sum(n2, n9) = n11, yields:
% 32.19/10.64 | (847) all_0_0_0 = n11
% 32.19/10.64 |
% 32.19/10.64 | From (894)(847) and (232) follows:
% 32.19/10.64 | (7550) sum(n10, n11) = all_0_6_6
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (619) with n10, n11, all_0_6_6, n0 and discharging atoms sum(n10, n11) = all_0_6_6, sum(n10, n11) = n0, yields:
% 32.19/10.64 | (1053) all_0_6_6 = n0
% 32.19/10.64 |
% 32.19/10.64 | Equations (1053) can reduce 676 to:
% 32.19/10.64 | (748) $false
% 32.19/10.64 |
% 32.19/10.64 |-The branch is then unsatisfiable
% 32.19/10.64 |-Branch two:
% 32.19/10.64 | (1433) ~ (all_0_7_7 = n2)
% 32.19/10.64 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 32.19/10.64 |
% 32.19/10.64 +-Applying beta-rule and splitting (1434), into two cases.
% 32.19/10.64 |-Branch one:
% 32.19/10.64 | (1435) all_0_7_7 = n1
% 32.19/10.64 |
% 32.19/10.64 | From (1435) and (683) follows:
% 32.19/10.64 | (1436) succ(n1) = all_0_5_5
% 32.19/10.64 |
% 32.19/10.64 | From (1435) and (8) follows:
% 32.19/10.64 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 32.19/10.64 |
% 32.19/10.64 | From (1435) and (7440) follows:
% 32.19/10.64 | (7558) sum(n8, n1) = all_0_2_2
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 32.19/10.64 | (1439) all_0_5_5 = n2
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (619) with n8, n1, all_0_2_2, n9 and discharging atoms sum(n8, n1) = all_0_2_2, sum(n8, n1) = n9, yields:
% 32.19/10.64 | (907) all_0_2_2 = n9
% 32.19/10.64 |
% 32.19/10.64 | From (907) and (473) follows:
% 32.19/10.64 | (909) pred(n9) = all_0_1_1
% 32.19/10.64 |
% 32.19/10.64 | From (1439) and (7439) follows:
% 32.19/10.64 | (7562) sum(n8, n2) = all_0_4_4
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 32.19/10.64 | (912) all_0_1_1 = n8
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (619) with n8, n2, all_0_4_4, n10 and discharging atoms sum(n8, n2) = all_0_4_4, sum(n8, n2) = n10, yields:
% 32.19/10.64 | (908) all_0_4_4 = n10
% 32.19/10.64 |
% 32.19/10.64 | From (908) and (716) follows:
% 32.19/10.64 | (910) pred(n10) = all_0_3_3
% 32.19/10.64 |
% 32.19/10.64 | From (912) and (1437) follows:
% 32.19/10.64 | (7566) sum(n1, n8) = all_0_0_0
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 32.19/10.64 | (911) all_0_3_3 = n9
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (619) with n1, n8, all_0_0_0, n9 and discharging atoms sum(n1, n8) = all_0_0_0, sum(n1, n8) = n9, yields:
% 32.19/10.64 | (881) all_0_0_0 = n9
% 32.19/10.64 |
% 32.19/10.64 | From (911)(881) and (232) follows:
% 32.19/10.64 | (7569) sum(n9, n9) = all_0_6_6
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (619) with n9, n9, all_0_6_6, n18 and discharging atoms sum(n9, n9) = all_0_6_6, sum(n9, n9) = n18, yields:
% 32.19/10.64 | (900) all_0_6_6 = n18
% 32.19/10.64 |
% 32.19/10.64 | Equations (900) can reduce 622 to:
% 32.19/10.64 | (748) $false
% 32.19/10.64 |
% 32.19/10.64 |-The branch is then unsatisfiable
% 32.19/10.64 |-Branch two:
% 32.19/10.64 | (1452) ~ (all_0_7_7 = n1)
% 32.19/10.64 | (1453) all_0_7_7 = n0
% 32.19/10.64 |
% 32.19/10.64 | From (1453) and (683) follows:
% 32.19/10.64 | (1454) succ(n0) = all_0_5_5
% 32.19/10.64 |
% 32.19/10.64 | From (1453) and (8) follows:
% 32.19/10.64 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 32.19/10.64 |
% 32.19/10.64 | From (1453) and (7440) follows:
% 32.19/10.64 | (7576) sum(n8, n0) = all_0_2_2
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 32.19/10.64 | (1457) all_0_5_5 = n1
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (619) with n8, n0, all_0_2_2, n8 and discharging atoms sum(n8, n0) = all_0_2_2, sum(n8, n0) = n8, yields:
% 32.19/10.64 | (924) all_0_2_2 = n8
% 32.19/10.64 |
% 32.19/10.64 | From (924) and (473) follows:
% 32.19/10.64 | (926) pred(n8) = all_0_1_1
% 32.19/10.64 |
% 32.19/10.64 | From (1457) and (7439) follows:
% 32.19/10.64 | (7580) sum(n8, n1) = all_0_4_4
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 32.19/10.64 | (929) all_0_1_1 = n7
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (619) with n8, n1, all_0_4_4, n9 and discharging atoms sum(n8, n1) = all_0_4_4, sum(n8, n1) = n9, yields:
% 32.19/10.64 | (925) all_0_4_4 = n9
% 32.19/10.64 |
% 32.19/10.64 | From (925) and (716) follows:
% 32.19/10.64 | (927) pred(n9) = all_0_3_3
% 32.19/10.64 |
% 32.19/10.64 | From (929) and (1455) follows:
% 32.19/10.64 | (7584) sum(n0, n7) = all_0_0_0
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 32.19/10.64 | (928) all_0_3_3 = n8
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (619) with n0, n7, all_0_0_0, n7 and discharging atoms sum(n0, n7) = all_0_0_0, sum(n0, n7) = n7, yields:
% 32.19/10.64 | (915) all_0_0_0 = n7
% 32.19/10.64 |
% 32.19/10.64 | From (928)(915) and (232) follows:
% 32.19/10.64 | (7587) sum(n8, n7) = all_0_6_6
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (619) with n8, n7, all_0_6_6, n15 and discharging atoms sum(n8, n7) = all_0_6_6, sum(n8, n7) = n15, yields:
% 32.19/10.64 | (747) all_0_6_6 = n15
% 32.19/10.64 |
% 32.19/10.64 | Equations (747) can reduce 456 to:
% 32.19/10.64 | (748) $false
% 32.19/10.64 |
% 32.19/10.64 |-The branch is then unsatisfiable
% 32.19/10.64 |-Branch two:
% 32.19/10.64 | (953) ~ (all_0_8_8 = n8)
% 32.19/10.64 | (954) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.19/10.64 |
% 32.19/10.64 +-Applying beta-rule and splitting (1320), into two cases.
% 32.19/10.64 |-Branch one:
% 32.19/10.64 | (1321) all_0_7_7 = n7
% 32.19/10.64 |
% 32.19/10.64 | From (1321) and (683) follows:
% 32.19/10.64 | (1322) succ(n7) = all_0_5_5
% 32.19/10.64 |
% 32.19/10.64 | From (1321) and (8) follows:
% 32.19/10.64 | (1323) sum(n7, all_0_1_1) = all_0_0_0
% 32.19/10.64 |
% 32.19/10.64 | From (1321) and (378) follows:
% 32.19/10.64 | (7595) sum(all_0_8_8, n7) = all_0_2_2
% 32.19/10.64 |
% 32.19/10.64 | Instantiating formula (388) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 32.19/10.64 | (1325) all_0_5_5 = n8
% 32.19/10.64 |
% 32.19/10.64 | From (1325) and (708) follows:
% 32.19/10.64 | (7597) sum(all_0_8_8, n8) = all_0_4_4
% 32.19/10.64 |
% 32.19/10.64 +-Applying beta-rule and splitting (954), into two cases.
% 32.19/10.64 |-Branch one:
% 32.19/10.64 | (955) all_0_8_8 = n7
% 32.19/10.64 |
% 32.19/10.64 | From (955) and (7597) follows:
% 32.19/10.65 | (7599) sum(n7, n8) = all_0_4_4
% 32.19/10.65 |
% 32.19/10.65 | From (955) and (7595) follows:
% 32.19/10.65 | (7600) sum(n7, n7) = all_0_2_2
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (619) with n7, n8, all_0_4_4, n15 and discharging atoms sum(n7, n8) = all_0_4_4, sum(n7, n8) = n15, yields:
% 32.19/10.65 | (823) all_0_4_4 = n15
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (619) with n7, n7, all_0_2_2, n14 and discharging atoms sum(n7, n7) = all_0_2_2, sum(n7, n7) = n14, yields:
% 32.19/10.65 | (822) all_0_2_2 = n14
% 32.19/10.65 |
% 32.19/10.65 | From (822) and (473) follows:
% 32.19/10.65 | (824) pred(n14) = all_0_1_1
% 32.19/10.65 |
% 32.19/10.65 | From (823) and (716) follows:
% 32.19/10.65 | (825) pred(n15) = all_0_3_3
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (244) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 32.19/10.65 | (826) all_0_3_3 = n14
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (244) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 32.19/10.65 | (827) all_0_1_1 = n13
% 32.19/10.65 |
% 32.19/10.65 | From (826) and (232) follows:
% 32.19/10.65 | (828) sum(n14, all_0_0_0) = all_0_6_6
% 32.19/10.65 |
% 32.19/10.65 | From (827) and (1323) follows:
% 32.19/10.65 | (7608) sum(n7, n13) = all_0_0_0
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (619) with n7, n13, all_0_0_0, n20 and discharging atoms sum(n7, n13) = all_0_0_0, sum(n7, n13) = n20, yields:
% 32.19/10.65 | (1051) all_0_0_0 = n20
% 32.19/10.65 |
% 32.19/10.65 | From (1051) and (828) follows:
% 32.19/10.65 | (7610) sum(n14, n20) = all_0_6_6
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (619) with n14, n20, all_0_6_6, n13 and discharging atoms sum(n14, n20) = all_0_6_6, sum(n14, n20) = n13, yields:
% 32.19/10.65 | (764) all_0_6_6 = n13
% 32.19/10.65 |
% 32.19/10.65 | Equations (764) can reduce 293 to:
% 32.19/10.65 | (748) $false
% 32.19/10.65 |
% 32.19/10.65 |-The branch is then unsatisfiable
% 32.19/10.65 |-Branch two:
% 32.19/10.65 | (970) ~ (all_0_8_8 = n7)
% 32.19/10.65 | (971) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.19/10.65 |
% 32.19/10.65 +-Applying beta-rule and splitting (971), into two cases.
% 32.19/10.65 |-Branch one:
% 32.19/10.65 | (972) all_0_8_8 = n6
% 32.19/10.65 |
% 32.19/10.65 | From (972) and (7597) follows:
% 32.19/10.65 | (7616) sum(n6, n8) = all_0_4_4
% 32.19/10.65 |
% 32.19/10.65 | From (972) and (7595) follows:
% 32.19/10.65 | (7617) sum(n6, n7) = all_0_2_2
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (619) with n6, n8, all_0_4_4, n14 and discharging atoms sum(n6, n8) = all_0_4_4, sum(n6, n8) = n14, yields:
% 32.19/10.65 | (840) all_0_4_4 = n14
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (619) with n6, n7, all_0_2_2, n13 and discharging atoms sum(n6, n7) = all_0_2_2, sum(n6, n7) = n13, yields:
% 32.19/10.65 | (839) all_0_2_2 = n13
% 32.19/10.65 |
% 32.19/10.65 | From (839) and (473) follows:
% 32.19/10.65 | (841) pred(n13) = all_0_1_1
% 32.19/10.65 |
% 32.19/10.65 | From (840) and (716) follows:
% 32.19/10.65 | (842) pred(n14) = all_0_3_3
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 32.19/10.65 | (843) all_0_3_3 = n13
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 32.19/10.65 | (844) all_0_1_1 = n12
% 32.19/10.65 |
% 32.19/10.65 | From (843) and (232) follows:
% 32.19/10.65 | (845) sum(n13, all_0_0_0) = all_0_6_6
% 32.19/10.65 |
% 32.19/10.65 | From (844) and (1323) follows:
% 32.19/10.65 | (7625) sum(n7, n12) = all_0_0_0
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (619) with n7, n12, all_0_0_0, n19 and discharging atoms sum(n7, n12) = all_0_0_0, sum(n7, n12) = n19, yields:
% 32.19/10.65 | (1068) all_0_0_0 = n19
% 32.19/10.65 |
% 32.19/10.65 | From (1068) and (845) follows:
% 32.19/10.65 | (7627) sum(n13, n19) = all_0_6_6
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (619) with n13, n19, all_0_6_6, n11 and discharging atoms sum(n13, n19) = all_0_6_6, sum(n13, n19) = n11, yields:
% 32.19/10.65 | (781) all_0_6_6 = n11
% 32.19/10.65 |
% 32.19/10.65 | Equations (781) can reduce 2 to:
% 32.19/10.65 | (748) $false
% 32.19/10.65 |
% 32.19/10.65 |-The branch is then unsatisfiable
% 32.19/10.65 |-Branch two:
% 32.19/10.65 | (987) ~ (all_0_8_8 = n6)
% 32.19/10.65 | (988) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.19/10.65 |
% 32.19/10.65 +-Applying beta-rule and splitting (988), into two cases.
% 32.19/10.65 |-Branch one:
% 32.19/10.65 | (989) all_0_8_8 = n5
% 32.19/10.65 |
% 32.19/10.65 | From (989) and (7597) follows:
% 32.19/10.65 | (7633) sum(n5, n8) = all_0_4_4
% 32.19/10.65 |
% 32.19/10.65 | From (989) and (7595) follows:
% 32.19/10.65 | (7634) sum(n5, n7) = all_0_2_2
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (619) with n5, n8, all_0_4_4, n13 and discharging atoms sum(n5, n8) = all_0_4_4, sum(n5, n8) = n13, yields:
% 32.19/10.65 | (857) all_0_4_4 = n13
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (619) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 32.19/10.65 | (856) all_0_2_2 = n12
% 32.19/10.65 |
% 32.19/10.65 | From (856) and (473) follows:
% 32.19/10.65 | (858) pred(n12) = all_0_1_1
% 32.19/10.65 |
% 32.19/10.65 | From (857) and (716) follows:
% 32.19/10.65 | (859) pred(n13) = all_0_3_3
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 32.19/10.65 | (860) all_0_3_3 = n12
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 32.19/10.65 | (861) all_0_1_1 = n11
% 32.19/10.65 |
% 32.19/10.65 | From (860) and (232) follows:
% 32.19/10.65 | (862) sum(n12, all_0_0_0) = all_0_6_6
% 32.19/10.65 |
% 32.19/10.65 | From (861) and (1323) follows:
% 32.19/10.65 | (7642) sum(n7, n11) = all_0_0_0
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (619) with n7, n11, all_0_0_0, n18 and discharging atoms sum(n7, n11) = all_0_0_0, sum(n7, n11) = n18, yields:
% 32.19/10.65 | (1084) all_0_0_0 = n18
% 32.19/10.65 |
% 32.19/10.65 | From (1084) and (862) follows:
% 32.19/10.65 | (7644) sum(n12, n18) = all_0_6_6
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (619) with n12, n18, all_0_6_6, n9 and discharging atoms sum(n12, n18) = all_0_6_6, sum(n12, n18) = n9, yields:
% 32.19/10.65 | (798) all_0_6_6 = n9
% 32.19/10.65 |
% 32.19/10.65 | Equations (798) can reduce 593 to:
% 32.19/10.65 | (748) $false
% 32.19/10.65 |
% 32.19/10.65 |-The branch is then unsatisfiable
% 32.19/10.65 |-Branch two:
% 32.19/10.65 | (1004) ~ (all_0_8_8 = n5)
% 32.19/10.65 | (1005) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.19/10.65 |
% 32.19/10.65 +-Applying beta-rule and splitting (1005), into two cases.
% 32.19/10.65 |-Branch one:
% 32.19/10.65 | (1006) all_0_8_8 = n4
% 32.19/10.65 |
% 32.19/10.65 | From (1006) and (7597) follows:
% 32.19/10.65 | (7650) sum(n4, n8) = all_0_4_4
% 32.19/10.65 |
% 32.19/10.65 | From (1006) and (7595) follows:
% 32.19/10.65 | (7651) sum(n4, n7) = all_0_2_2
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (619) with n4, n8, all_0_4_4, n12 and discharging atoms sum(n4, n8) = all_0_4_4, sum(n4, n8) = n12, yields:
% 32.19/10.65 | (874) all_0_4_4 = n12
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (619) with n4, n7, all_0_2_2, n11 and discharging atoms sum(n4, n7) = all_0_2_2, sum(n4, n7) = n11, yields:
% 32.19/10.65 | (873) all_0_2_2 = n11
% 32.19/10.65 |
% 32.19/10.65 | From (873) and (473) follows:
% 32.19/10.65 | (875) pred(n11) = all_0_1_1
% 32.19/10.65 |
% 32.19/10.65 | From (874) and (716) follows:
% 32.19/10.65 | (876) pred(n12) = all_0_3_3
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 32.19/10.65 | (877) all_0_3_3 = n11
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 32.19/10.65 | (878) all_0_1_1 = n10
% 32.19/10.65 |
% 32.19/10.65 | From (877) and (232) follows:
% 32.19/10.65 | (879) sum(n11, all_0_0_0) = all_0_6_6
% 32.19/10.65 |
% 32.19/10.65 | From (878) and (1323) follows:
% 32.19/10.65 | (7659) sum(n7, n10) = all_0_0_0
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (619) with n7, n10, all_0_0_0, n17 and discharging atoms sum(n7, n10) = all_0_0_0, sum(n7, n10) = n17, yields:
% 32.19/10.65 | (745) all_0_0_0 = n17
% 32.19/10.65 |
% 32.19/10.65 | From (745) and (879) follows:
% 32.19/10.65 | (7661) sum(n11, n17) = all_0_6_6
% 32.19/10.65 |
% 32.19/10.65 | Instantiating formula (619) with n11, n17, all_0_6_6, n7 and discharging atoms sum(n11, n17) = all_0_6_6, sum(n11, n17) = n7, yields:
% 32.19/10.65 | (815) all_0_6_6 = n7
% 32.19/10.65 |
% 32.19/10.65 | Equations (815) can reduce 557 to:
% 32.19/10.65 | (748) $false
% 32.19/10.65 |
% 32.19/10.65 |-The branch is then unsatisfiable
% 32.19/10.65 |-Branch two:
% 32.19/10.65 | (1021) ~ (all_0_8_8 = n4)
% 32.19/10.65 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.19/10.65 |
% 32.19/10.65 +-Applying beta-rule and splitting (1022), into two cases.
% 32.19/10.65 |-Branch one:
% 32.19/10.65 | (1023) all_0_8_8 = n3
% 32.19/10.65 |
% 32.19/10.65 | From (1023) and (7597) follows:
% 32.19/10.65 | (7667) sum(n3, n8) = all_0_4_4
% 32.19/10.65 |
% 32.19/10.65 | From (1023) and (7595) follows:
% 32.19/10.66 | (7668) sum(n3, n7) = all_0_2_2
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (619) with n3, n8, all_0_4_4, n11 and discharging atoms sum(n3, n8) = all_0_4_4, sum(n3, n8) = n11, yields:
% 32.19/10.66 | (891) all_0_4_4 = n11
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (619) with n3, n7, all_0_2_2, n10 and discharging atoms sum(n3, n7) = all_0_2_2, sum(n3, n7) = n10, yields:
% 32.19/10.66 | (890) all_0_2_2 = n10
% 32.19/10.66 |
% 32.19/10.66 | From (890) and (473) follows:
% 32.19/10.66 | (892) pred(n10) = all_0_1_1
% 32.19/10.66 |
% 32.19/10.66 | From (891) and (716) follows:
% 32.19/10.66 | (893) pred(n11) = all_0_3_3
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 32.19/10.66 | (894) all_0_3_3 = n10
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 32.19/10.66 | (895) all_0_1_1 = n9
% 32.19/10.66 |
% 32.19/10.66 | From (894) and (232) follows:
% 32.19/10.66 | (896) sum(n10, all_0_0_0) = all_0_6_6
% 32.19/10.66 |
% 32.19/10.66 | From (895) and (1323) follows:
% 32.19/10.66 | (7676) sum(n7, n9) = all_0_0_0
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (619) with n7, n9, all_0_0_0, n16 and discharging atoms sum(n7, n9) = all_0_0_0, sum(n7, n9) = n16, yields:
% 32.19/10.66 | (762) all_0_0_0 = n16
% 32.19/10.66 |
% 32.19/10.66 | From (762) and (896) follows:
% 32.19/10.66 | (7678) sum(n10, n16) = all_0_6_6
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (619) with n10, n16, all_0_6_6, n5 and discharging atoms sum(n10, n16) = all_0_6_6, sum(n10, n16) = n5, yields:
% 32.19/10.66 | (832) all_0_6_6 = n5
% 32.19/10.66 |
% 32.19/10.66 | Equations (832) can reduce 462 to:
% 32.19/10.66 | (748) $false
% 32.19/10.66 |
% 32.19/10.66 |-The branch is then unsatisfiable
% 32.19/10.66 |-Branch two:
% 32.19/10.66 | (1038) ~ (all_0_8_8 = n3)
% 32.19/10.66 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.19/10.66 |
% 32.19/10.66 +-Applying beta-rule and splitting (1039), into two cases.
% 32.19/10.66 |-Branch one:
% 32.19/10.66 | (1040) all_0_8_8 = n2
% 32.19/10.66 |
% 32.19/10.66 | From (1040) and (7597) follows:
% 32.19/10.66 | (7684) sum(n2, n8) = all_0_4_4
% 32.19/10.66 |
% 32.19/10.66 | From (1040) and (7595) follows:
% 32.19/10.66 | (7685) sum(n2, n7) = all_0_2_2
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (619) with n2, n8, all_0_4_4, n10 and discharging atoms sum(n2, n8) = all_0_4_4, sum(n2, n8) = n10, yields:
% 32.19/10.66 | (908) all_0_4_4 = n10
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (619) with n2, n7, all_0_2_2, n9 and discharging atoms sum(n2, n7) = all_0_2_2, sum(n2, n7) = n9, yields:
% 32.19/10.66 | (907) all_0_2_2 = n9
% 32.19/10.66 |
% 32.19/10.66 | From (907) and (473) follows:
% 32.19/10.66 | (909) pred(n9) = all_0_1_1
% 32.19/10.66 |
% 32.19/10.66 | From (908) and (716) follows:
% 32.19/10.66 | (910) pred(n10) = all_0_3_3
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 32.19/10.66 | (911) all_0_3_3 = n9
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 32.19/10.66 | (912) all_0_1_1 = n8
% 32.19/10.66 |
% 32.19/10.66 | From (911) and (232) follows:
% 32.19/10.66 | (913) sum(n9, all_0_0_0) = all_0_6_6
% 32.19/10.66 |
% 32.19/10.66 | From (912) and (1323) follows:
% 32.19/10.66 | (7693) sum(n7, n8) = all_0_0_0
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (619) with n7, n8, all_0_0_0, n15 and discharging atoms sum(n7, n8) = all_0_0_0, sum(n7, n8) = n15, yields:
% 32.19/10.66 | (779) all_0_0_0 = n15
% 32.19/10.66 |
% 32.19/10.66 | From (779) and (913) follows:
% 32.19/10.66 | (7695) sum(n9, n15) = all_0_6_6
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (619) with n9, n15, all_0_6_6, n3 and discharging atoms sum(n9, n15) = all_0_6_6, sum(n9, n15) = n3, yields:
% 32.19/10.66 | (849) all_0_6_6 = n3
% 32.19/10.66 |
% 32.19/10.66 | Equations (849) can reduce 416 to:
% 32.19/10.66 | (748) $false
% 32.19/10.66 |
% 32.19/10.66 |-The branch is then unsatisfiable
% 32.19/10.66 |-Branch two:
% 32.19/10.66 | (1055) ~ (all_0_8_8 = n2)
% 32.19/10.66 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 32.19/10.66 |
% 32.19/10.66 +-Applying beta-rule and splitting (1056), into two cases.
% 32.19/10.66 |-Branch one:
% 32.19/10.66 | (1057) all_0_8_8 = n1
% 32.19/10.66 |
% 32.19/10.66 | From (1057) and (7597) follows:
% 32.19/10.66 | (7701) sum(n1, n8) = all_0_4_4
% 32.19/10.66 |
% 32.19/10.66 | From (1057) and (7595) follows:
% 32.19/10.66 | (7702) sum(n1, n7) = all_0_2_2
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (619) with n1, n8, all_0_4_4, n9 and discharging atoms sum(n1, n8) = all_0_4_4, sum(n1, n8) = n9, yields:
% 32.19/10.66 | (925) all_0_4_4 = n9
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (619) with n1, n7, all_0_2_2, n8 and discharging atoms sum(n1, n7) = all_0_2_2, sum(n1, n7) = n8, yields:
% 32.19/10.66 | (924) all_0_2_2 = n8
% 32.19/10.66 |
% 32.19/10.66 | From (924) and (473) follows:
% 32.19/10.66 | (926) pred(n8) = all_0_1_1
% 32.19/10.66 |
% 32.19/10.66 | From (925) and (716) follows:
% 32.19/10.66 | (927) pred(n9) = all_0_3_3
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 32.19/10.66 | (928) all_0_3_3 = n8
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 32.19/10.66 | (929) all_0_1_1 = n7
% 32.19/10.66 |
% 32.19/10.66 | From (928) and (232) follows:
% 32.19/10.66 | (930) sum(n8, all_0_0_0) = all_0_6_6
% 32.19/10.66 |
% 32.19/10.66 | From (929) and (1323) follows:
% 32.19/10.66 | (7710) sum(n7, n7) = all_0_0_0
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (619) with n7, n7, all_0_0_0, n14 and discharging atoms sum(n7, n7) = all_0_0_0, sum(n7, n7) = n14, yields:
% 32.19/10.66 | (796) all_0_0_0 = n14
% 32.19/10.66 |
% 32.19/10.66 | From (796) and (930) follows:
% 32.19/10.66 | (7712) sum(n8, n14) = all_0_6_6
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (619) with n8, n14, all_0_6_6, n1 and discharging atoms sum(n8, n14) = all_0_6_6, sum(n8, n14) = n1, yields:
% 32.19/10.66 | (866) all_0_6_6 = n1
% 32.19/10.66 |
% 32.19/10.66 | Equations (866) can reduce 28 to:
% 32.19/10.66 | (748) $false
% 32.19/10.66 |
% 32.19/10.66 |-The branch is then unsatisfiable
% 32.19/10.66 |-Branch two:
% 32.19/10.66 | (1072) ~ (all_0_8_8 = n1)
% 32.19/10.66 | (1073) all_0_8_8 = n0
% 32.19/10.66 |
% 32.19/10.66 | From (1073) and (7597) follows:
% 32.19/10.66 | (7717) sum(n0, n8) = all_0_4_4
% 32.19/10.66 |
% 32.19/10.66 | From (1073) and (7595) follows:
% 32.19/10.66 | (7718) sum(n0, n7) = all_0_2_2
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (619) with n0, n8, all_0_4_4, n8 and discharging atoms sum(n0, n8) = all_0_4_4, sum(n0, n8) = n8, yields:
% 32.19/10.66 | (942) all_0_4_4 = n8
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (619) with n0, n7, all_0_2_2, n7 and discharging atoms sum(n0, n7) = all_0_2_2, sum(n0, n7) = n7, yields:
% 32.19/10.66 | (941) all_0_2_2 = n7
% 32.19/10.66 |
% 32.19/10.66 | From (941) and (473) follows:
% 32.19/10.66 | (943) pred(n7) = all_0_1_1
% 32.19/10.66 |
% 32.19/10.66 | From (942) and (716) follows:
% 32.19/10.66 | (944) pred(n8) = all_0_3_3
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 32.19/10.66 | (945) all_0_3_3 = n7
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 32.19/10.66 | (946) all_0_1_1 = n6
% 32.19/10.66 |
% 32.19/10.66 | From (945) and (232) follows:
% 32.19/10.66 | (947) sum(n7, all_0_0_0) = all_0_6_6
% 32.19/10.66 |
% 32.19/10.66 | From (946) and (1323) follows:
% 32.19/10.66 | (7726) sum(n7, n6) = all_0_0_0
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (619) with n7, n6, all_0_0_0, n13 and discharging atoms sum(n7, n6) = all_0_0_0, sum(n7, n6) = n13, yields:
% 32.19/10.66 | (813) all_0_0_0 = n13
% 32.19/10.66 |
% 32.19/10.66 | From (813) and (947) follows:
% 32.19/10.66 | (7728) sum(n7, n13) = all_0_6_6
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (619) with n7, n13, all_0_6_6, n20 and discharging atoms sum(n7, n13) = all_0_6_6, sum(n7, n13) = n20, yields:
% 32.19/10.66 | (883) all_0_6_6 = n20
% 32.19/10.66 |
% 32.19/10.66 | Equations (883) can reduce 381 to:
% 32.19/10.66 | (748) $false
% 32.19/10.66 |
% 32.19/10.66 |-The branch is then unsatisfiable
% 32.19/10.66 |-Branch two:
% 32.19/10.66 | (1338) ~ (all_0_7_7 = n7)
% 32.19/10.66 | (1339) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.19/10.66 |
% 32.19/10.66 +-Applying beta-rule and splitting (954), into two cases.
% 32.19/10.66 |-Branch one:
% 32.19/10.66 | (955) all_0_8_8 = n7
% 32.19/10.66 |
% 32.19/10.66 | From (955) and (708) follows:
% 32.19/10.66 | (7734) sum(n7, all_0_5_5) = all_0_4_4
% 32.19/10.66 |
% 32.19/10.66 | From (955) and (378) follows:
% 32.19/10.66 | (7735) sum(n7, all_0_7_7) = all_0_2_2
% 32.19/10.66 |
% 32.19/10.66 +-Applying beta-rule and splitting (1339), into two cases.
% 32.19/10.66 |-Branch one:
% 32.19/10.66 | (1340) all_0_7_7 = n6
% 32.19/10.66 |
% 32.19/10.66 | From (1340) and (683) follows:
% 32.19/10.66 | (1341) succ(n6) = all_0_5_5
% 32.19/10.66 |
% 32.19/10.66 | From (1340) and (8) follows:
% 32.19/10.66 | (1342) sum(n6, all_0_1_1) = all_0_0_0
% 32.19/10.66 |
% 32.19/10.66 | From (1340) and (7735) follows:
% 32.19/10.66 | (7739) sum(n7, n6) = all_0_2_2
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (388) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 32.19/10.66 | (1344) all_0_5_5 = n7
% 32.19/10.66 |
% 32.19/10.66 | Instantiating formula (619) with n7, n6, all_0_2_2, n13 and discharging atoms sum(n7, n6) = all_0_2_2, sum(n7, n6) = n13, yields:
% 32.19/10.67 | (839) all_0_2_2 = n13
% 32.19/10.67 |
% 32.19/10.67 | From (839) and (473) follows:
% 32.19/10.67 | (841) pred(n13) = all_0_1_1
% 32.19/10.67 |
% 32.19/10.67 | From (1344) and (7734) follows:
% 32.19/10.67 | (7743) sum(n7, n7) = all_0_4_4
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (244) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 32.19/10.67 | (844) all_0_1_1 = n12
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (619) with n7, n7, all_0_4_4, n14 and discharging atoms sum(n7, n7) = all_0_4_4, sum(n7, n7) = n14, yields:
% 32.19/10.67 | (840) all_0_4_4 = n14
% 32.19/10.67 |
% 32.19/10.67 | From (840) and (716) follows:
% 32.19/10.67 | (842) pred(n14) = all_0_3_3
% 32.19/10.67 |
% 32.19/10.67 | From (844) and (1342) follows:
% 32.19/10.67 | (7747) sum(n6, n12) = all_0_0_0
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (244) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 32.19/10.67 | (843) all_0_3_3 = n13
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (619) with n6, n12, all_0_0_0, n18 and discharging atoms sum(n6, n12) = all_0_0_0, sum(n6, n12) = n18, yields:
% 32.19/10.67 | (1084) all_0_0_0 = n18
% 32.19/10.67 |
% 32.19/10.67 | From (843)(1084) and (232) follows:
% 32.19/10.67 | (7750) sum(n13, n18) = all_0_6_6
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (619) with n13, n18, all_0_6_6, n10 and discharging atoms sum(n13, n18) = all_0_6_6, sum(n13, n18) = n10, yields:
% 32.19/10.67 | (968) all_0_6_6 = n10
% 32.19/10.67 |
% 32.19/10.67 | Equations (968) can reduce 176 to:
% 32.19/10.67 | (748) $false
% 32.19/10.67 |
% 32.19/10.67 |-The branch is then unsatisfiable
% 32.19/10.67 |-Branch two:
% 32.19/10.67 | (1357) ~ (all_0_7_7 = n6)
% 32.19/10.67 | (1358) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.19/10.67 |
% 32.19/10.67 +-Applying beta-rule and splitting (1358), into two cases.
% 32.19/10.67 |-Branch one:
% 32.19/10.67 | (1359) all_0_7_7 = n5
% 32.19/10.67 |
% 32.19/10.67 | From (1359) and (683) follows:
% 32.19/10.67 | (1360) succ(n5) = all_0_5_5
% 32.19/10.67 |
% 32.19/10.67 | From (1359) and (8) follows:
% 32.19/10.67 | (1361) sum(n5, all_0_1_1) = all_0_0_0
% 32.19/10.67 |
% 32.19/10.67 | From (1359) and (7735) follows:
% 32.19/10.67 | (7758) sum(n7, n5) = all_0_2_2
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (388) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 32.19/10.67 | (1363) all_0_5_5 = n6
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (619) with n7, n5, all_0_2_2, n12 and discharging atoms sum(n7, n5) = all_0_2_2, sum(n7, n5) = n12, yields:
% 32.19/10.67 | (856) all_0_2_2 = n12
% 32.19/10.67 |
% 32.19/10.67 | From (856) and (473) follows:
% 32.19/10.67 | (858) pred(n12) = all_0_1_1
% 32.19/10.67 |
% 32.19/10.67 | From (1363) and (7734) follows:
% 32.19/10.67 | (7762) sum(n7, n6) = all_0_4_4
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 32.19/10.67 | (861) all_0_1_1 = n11
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (619) with n7, n6, all_0_4_4, n13 and discharging atoms sum(n7, n6) = all_0_4_4, sum(n7, n6) = n13, yields:
% 32.19/10.67 | (857) all_0_4_4 = n13
% 32.19/10.67 |
% 32.19/10.67 | From (857) and (716) follows:
% 32.19/10.67 | (859) pred(n13) = all_0_3_3
% 32.19/10.67 |
% 32.19/10.67 | From (861) and (1361) follows:
% 32.19/10.67 | (7766) sum(n5, n11) = all_0_0_0
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 32.19/10.67 | (860) all_0_3_3 = n12
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (619) with n5, n11, all_0_0_0, n16 and discharging atoms sum(n5, n11) = all_0_0_0, sum(n5, n11) = n16, yields:
% 32.19/10.67 | (762) all_0_0_0 = n16
% 32.19/10.67 |
% 32.19/10.67 | From (860)(762) and (232) follows:
% 32.19/10.67 | (7769) sum(n12, n16) = all_0_6_6
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (619) with n12, n16, all_0_6_6, n7 and discharging atoms sum(n12, n16) = all_0_6_6, sum(n12, n16) = n7, yields:
% 32.19/10.67 | (815) all_0_6_6 = n7
% 32.19/10.67 |
% 32.19/10.67 | Equations (815) can reduce 557 to:
% 32.19/10.67 | (748) $false
% 32.19/10.67 |
% 32.19/10.67 |-The branch is then unsatisfiable
% 32.19/10.67 |-Branch two:
% 32.19/10.67 | (1376) ~ (all_0_7_7 = n5)
% 32.19/10.67 | (1377) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.19/10.67 |
% 32.19/10.67 +-Applying beta-rule and splitting (1377), into two cases.
% 32.19/10.67 |-Branch one:
% 32.19/10.67 | (1378) all_0_7_7 = n4
% 32.19/10.67 |
% 32.19/10.67 | From (1378) and (683) follows:
% 32.19/10.67 | (1379) succ(n4) = all_0_5_5
% 32.19/10.67 |
% 32.19/10.67 | From (1378) and (8) follows:
% 32.19/10.67 | (1380) sum(n4, all_0_1_1) = all_0_0_0
% 32.19/10.67 |
% 32.19/10.67 | From (1378) and (7735) follows:
% 32.19/10.67 | (7777) sum(n7, n4) = all_0_2_2
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (388) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 32.19/10.67 | (1382) all_0_5_5 = n5
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (619) with n7, n4, all_0_2_2, n11 and discharging atoms sum(n7, n4) = all_0_2_2, sum(n7, n4) = n11, yields:
% 32.19/10.67 | (873) all_0_2_2 = n11
% 32.19/10.67 |
% 32.19/10.67 | From (873) and (473) follows:
% 32.19/10.67 | (875) pred(n11) = all_0_1_1
% 32.19/10.67 |
% 32.19/10.67 | From (1382) and (7734) follows:
% 32.19/10.67 | (7781) sum(n7, n5) = all_0_4_4
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 32.19/10.67 | (878) all_0_1_1 = n10
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (619) with n7, n5, all_0_4_4, n12 and discharging atoms sum(n7, n5) = all_0_4_4, sum(n7, n5) = n12, yields:
% 32.19/10.67 | (874) all_0_4_4 = n12
% 32.19/10.67 |
% 32.19/10.67 | From (874) and (716) follows:
% 32.19/10.67 | (876) pred(n12) = all_0_3_3
% 32.19/10.67 |
% 32.19/10.67 | From (878) and (1380) follows:
% 32.19/10.67 | (7785) sum(n4, n10) = all_0_0_0
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 32.19/10.67 | (877) all_0_3_3 = n11
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (619) with n4, n10, all_0_0_0, n14 and discharging atoms sum(n4, n10) = all_0_0_0, sum(n4, n10) = n14, yields:
% 32.19/10.67 | (796) all_0_0_0 = n14
% 32.19/10.67 |
% 32.19/10.67 | From (877)(796) and (232) follows:
% 32.19/10.67 | (7788) sum(n11, n14) = all_0_6_6
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (619) with n11, n14, all_0_6_6, n4 and discharging atoms sum(n11, n14) = all_0_6_6, sum(n11, n14) = n4, yields:
% 32.19/10.67 | (1019) all_0_6_6 = n4
% 32.19/10.67 |
% 32.19/10.67 | Equations (1019) can reduce 48 to:
% 32.19/10.67 | (748) $false
% 32.19/10.67 |
% 32.19/10.67 |-The branch is then unsatisfiable
% 32.19/10.67 |-Branch two:
% 32.19/10.67 | (1395) ~ (all_0_7_7 = n4)
% 32.19/10.67 | (1396) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.19/10.67 |
% 32.19/10.67 +-Applying beta-rule and splitting (1396), into two cases.
% 32.19/10.67 |-Branch one:
% 32.19/10.67 | (1397) all_0_7_7 = n3
% 32.19/10.67 |
% 32.19/10.67 | From (1397) and (683) follows:
% 32.19/10.67 | (1398) succ(n3) = all_0_5_5
% 32.19/10.67 |
% 32.19/10.67 | From (1397) and (8) follows:
% 32.19/10.67 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 32.19/10.67 |
% 32.19/10.67 | From (1397) and (7735) follows:
% 32.19/10.67 | (7796) sum(n7, n3) = all_0_2_2
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 32.19/10.67 | (1401) all_0_5_5 = n4
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (619) with n7, n3, all_0_2_2, n10 and discharging atoms sum(n7, n3) = all_0_2_2, sum(n7, n3) = n10, yields:
% 32.19/10.67 | (890) all_0_2_2 = n10
% 32.19/10.67 |
% 32.19/10.67 | From (890) and (473) follows:
% 32.19/10.67 | (892) pred(n10) = all_0_1_1
% 32.19/10.67 |
% 32.19/10.67 | From (1401) and (7734) follows:
% 32.19/10.67 | (7800) sum(n7, n4) = all_0_4_4
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 32.19/10.67 | (895) all_0_1_1 = n9
% 32.19/10.67 |
% 32.19/10.67 | Instantiating formula (619) with n7, n4, all_0_4_4, n11 and discharging atoms sum(n7, n4) = all_0_4_4, sum(n7, n4) = n11, yields:
% 32.19/10.67 | (891) all_0_4_4 = n11
% 32.19/10.67 |
% 32.19/10.67 | From (891) and (716) follows:
% 32.19/10.67 | (893) pred(n11) = all_0_3_3
% 32.19/10.67 |
% 32.19/10.67 | From (895) and (1399) follows:
% 32.19/10.68 | (7804) sum(n3, n9) = all_0_0_0
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 32.19/10.68 | (894) all_0_3_3 = n10
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (619) with n3, n9, all_0_0_0, n12 and discharging atoms sum(n3, n9) = all_0_0_0, sum(n3, n9) = n12, yields:
% 32.19/10.68 | (830) all_0_0_0 = n12
% 32.19/10.68 |
% 32.19/10.68 | From (894)(830) and (232) follows:
% 32.19/10.68 | (7807) sum(n10, n12) = all_0_6_6
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (619) with n10, n12, all_0_6_6, n1 and discharging atoms sum(n10, n12) = all_0_6_6, sum(n10, n12) = n1, yields:
% 32.19/10.68 | (866) all_0_6_6 = n1
% 32.19/10.68 |
% 32.19/10.68 | Equations (866) can reduce 28 to:
% 32.19/10.68 | (748) $false
% 32.19/10.68 |
% 32.19/10.68 |-The branch is then unsatisfiable
% 32.19/10.68 |-Branch two:
% 32.19/10.68 | (1414) ~ (all_0_7_7 = n3)
% 32.19/10.68 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.19/10.68 |
% 32.19/10.68 +-Applying beta-rule and splitting (1415), into two cases.
% 32.19/10.68 |-Branch one:
% 32.19/10.68 | (1416) all_0_7_7 = n2
% 32.19/10.68 |
% 32.19/10.68 | From (1416) and (683) follows:
% 32.19/10.68 | (1417) succ(n2) = all_0_5_5
% 32.19/10.68 |
% 32.19/10.68 | From (1416) and (8) follows:
% 32.19/10.68 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 32.19/10.68 |
% 32.19/10.68 | From (1416) and (7735) follows:
% 32.19/10.68 | (7815) sum(n7, n2) = all_0_2_2
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 32.19/10.68 | (1420) all_0_5_5 = n3
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (619) with n7, n2, all_0_2_2, n9 and discharging atoms sum(n7, n2) = all_0_2_2, sum(n7, n2) = n9, yields:
% 32.19/10.68 | (907) all_0_2_2 = n9
% 32.19/10.68 |
% 32.19/10.68 | From (907) and (473) follows:
% 32.19/10.68 | (909) pred(n9) = all_0_1_1
% 32.19/10.68 |
% 32.19/10.68 | From (1420) and (7734) follows:
% 32.19/10.68 | (7819) sum(n7, n3) = all_0_4_4
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 32.19/10.68 | (912) all_0_1_1 = n8
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (619) with n7, n3, all_0_4_4, n10 and discharging atoms sum(n7, n3) = all_0_4_4, sum(n7, n3) = n10, yields:
% 32.19/10.68 | (908) all_0_4_4 = n10
% 32.19/10.68 |
% 32.19/10.68 | From (908) and (716) follows:
% 32.19/10.68 | (910) pred(n10) = all_0_3_3
% 32.19/10.68 |
% 32.19/10.68 | From (912) and (1418) follows:
% 32.19/10.68 | (7823) sum(n2, n8) = all_0_0_0
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 32.19/10.68 | (911) all_0_3_3 = n9
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (619) with n2, n8, all_0_0_0, n10 and discharging atoms sum(n2, n8) = all_0_0_0, sum(n2, n8) = n10, yields:
% 32.19/10.68 | (864) all_0_0_0 = n10
% 32.19/10.68 |
% 32.19/10.68 | From (911)(864) and (232) follows:
% 32.19/10.68 | (7826) sum(n9, n10) = all_0_6_6
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (619) with n9, n10, all_0_6_6, n19 and discharging atoms sum(n9, n10) = all_0_6_6, sum(n9, n10) = n19, yields:
% 32.19/10.68 | (1070) all_0_6_6 = n19
% 32.19/10.68 |
% 32.19/10.68 | Equations (1070) can reduce 31 to:
% 32.19/10.68 | (748) $false
% 32.19/10.68 |
% 32.19/10.68 |-The branch is then unsatisfiable
% 32.19/10.68 |-Branch two:
% 32.19/10.68 | (1433) ~ (all_0_7_7 = n2)
% 32.19/10.68 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 32.19/10.68 |
% 32.19/10.68 +-Applying beta-rule and splitting (1434), into two cases.
% 32.19/10.68 |-Branch one:
% 32.19/10.68 | (1435) all_0_7_7 = n1
% 32.19/10.68 |
% 32.19/10.68 | From (1435) and (683) follows:
% 32.19/10.68 | (1436) succ(n1) = all_0_5_5
% 32.19/10.68 |
% 32.19/10.68 | From (1435) and (8) follows:
% 32.19/10.68 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 32.19/10.68 |
% 32.19/10.68 | From (1435) and (7735) follows:
% 32.19/10.68 | (7834) sum(n7, n1) = all_0_2_2
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 32.19/10.68 | (1439) all_0_5_5 = n2
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (619) with n7, n1, all_0_2_2, n8 and discharging atoms sum(n7, n1) = all_0_2_2, sum(n7, n1) = n8, yields:
% 32.19/10.68 | (924) all_0_2_2 = n8
% 32.19/10.68 |
% 32.19/10.68 | From (924) and (473) follows:
% 32.19/10.68 | (926) pred(n8) = all_0_1_1
% 32.19/10.68 |
% 32.19/10.68 | From (1439) and (7734) follows:
% 32.19/10.68 | (7838) sum(n7, n2) = all_0_4_4
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 32.19/10.68 | (929) all_0_1_1 = n7
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (619) with n7, n2, all_0_4_4, n9 and discharging atoms sum(n7, n2) = all_0_4_4, sum(n7, n2) = n9, yields:
% 32.19/10.68 | (925) all_0_4_4 = n9
% 32.19/10.68 |
% 32.19/10.68 | From (925) and (716) follows:
% 32.19/10.68 | (927) pred(n9) = all_0_3_3
% 32.19/10.68 |
% 32.19/10.68 | From (929) and (1437) follows:
% 32.19/10.68 | (7842) sum(n1, n7) = all_0_0_0
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 32.19/10.68 | (928) all_0_3_3 = n8
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (619) with n1, n7, all_0_0_0, n8 and discharging atoms sum(n1, n7) = all_0_0_0, sum(n1, n7) = n8, yields:
% 32.19/10.68 | (898) all_0_0_0 = n8
% 32.19/10.68 |
% 32.19/10.68 | From (928)(898) and (232) follows:
% 32.19/10.68 | (7845) sum(n8, n8) = all_0_6_6
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (619) with n8, n8, all_0_6_6, n16 and discharging atoms sum(n8, n8) = all_0_6_6, sum(n8, n8) = n16, yields:
% 32.19/10.68 | (917) all_0_6_6 = n16
% 32.19/10.68 |
% 32.19/10.68 | Equations (917) can reduce 163 to:
% 32.19/10.68 | (748) $false
% 32.19/10.68 |
% 32.19/10.68 |-The branch is then unsatisfiable
% 32.19/10.68 |-Branch two:
% 32.19/10.68 | (1452) ~ (all_0_7_7 = n1)
% 32.19/10.68 | (1453) all_0_7_7 = n0
% 32.19/10.68 |
% 32.19/10.68 | From (1453) and (683) follows:
% 32.19/10.68 | (1454) succ(n0) = all_0_5_5
% 32.19/10.68 |
% 32.19/10.68 | From (1453) and (8) follows:
% 32.19/10.68 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 32.19/10.68 |
% 32.19/10.68 | From (1453) and (7735) follows:
% 32.19/10.68 | (7852) sum(n7, n0) = all_0_2_2
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 32.19/10.68 | (1457) all_0_5_5 = n1
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (619) with n7, n0, all_0_2_2, n7 and discharging atoms sum(n7, n0) = all_0_2_2, sum(n7, n0) = n7, yields:
% 32.19/10.68 | (941) all_0_2_2 = n7
% 32.19/10.68 |
% 32.19/10.68 | From (941) and (473) follows:
% 32.19/10.68 | (943) pred(n7) = all_0_1_1
% 32.19/10.68 |
% 32.19/10.68 | From (1457) and (7734) follows:
% 32.19/10.68 | (7856) sum(n7, n1) = all_0_4_4
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 32.19/10.68 | (946) all_0_1_1 = n6
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (619) with n7, n1, all_0_4_4, n8 and discharging atoms sum(n7, n1) = all_0_4_4, sum(n7, n1) = n8, yields:
% 32.19/10.68 | (942) all_0_4_4 = n8
% 32.19/10.68 |
% 32.19/10.68 | From (942) and (716) follows:
% 32.19/10.68 | (944) pred(n8) = all_0_3_3
% 32.19/10.68 |
% 32.19/10.68 | From (946) and (1455) follows:
% 32.19/10.68 | (7860) sum(n0, n6) = all_0_0_0
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 32.19/10.68 | (945) all_0_3_3 = n7
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (619) with n0, n6, all_0_0_0, n6 and discharging atoms sum(n0, n6) = all_0_0_0, sum(n0, n6) = n6, yields:
% 32.19/10.68 | (932) all_0_0_0 = n6
% 32.19/10.68 |
% 32.19/10.68 | From (945)(932) and (232) follows:
% 32.19/10.68 | (7863) sum(n7, n6) = all_0_6_6
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (619) with n7, n6, all_0_6_6, n13 and discharging atoms sum(n7, n6) = all_0_6_6, sum(n7, n6) = n13, yields:
% 32.19/10.68 | (764) all_0_6_6 = n13
% 32.19/10.68 |
% 32.19/10.68 | Equations (764) can reduce 293 to:
% 32.19/10.68 | (748) $false
% 32.19/10.68 |
% 32.19/10.68 |-The branch is then unsatisfiable
% 32.19/10.68 |-Branch two:
% 32.19/10.68 | (970) ~ (all_0_8_8 = n7)
% 32.19/10.68 | (971) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.19/10.68 |
% 32.19/10.68 +-Applying beta-rule and splitting (1339), into two cases.
% 32.19/10.68 |-Branch one:
% 32.19/10.68 | (1340) all_0_7_7 = n6
% 32.19/10.68 |
% 32.19/10.68 | From (1340) and (683) follows:
% 32.19/10.68 | (1341) succ(n6) = all_0_5_5
% 32.19/10.68 |
% 32.19/10.68 | From (1340) and (8) follows:
% 32.19/10.68 | (1342) sum(n6, all_0_1_1) = all_0_0_0
% 32.19/10.68 |
% 32.19/10.68 | From (1340) and (378) follows:
% 32.19/10.68 | (7871) sum(all_0_8_8, n6) = all_0_2_2
% 32.19/10.68 |
% 32.19/10.68 | Instantiating formula (388) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 32.19/10.68 | (1344) all_0_5_5 = n7
% 32.19/10.68 |
% 32.19/10.68 | From (1344) and (708) follows:
% 32.19/10.68 | (7873) sum(all_0_8_8, n7) = all_0_4_4
% 32.19/10.68 |
% 32.19/10.68 +-Applying beta-rule and splitting (971), into two cases.
% 32.19/10.68 |-Branch one:
% 32.19/10.68 | (972) all_0_8_8 = n6
% 32.19/10.68 |
% 32.19/10.68 | From (972) and (7873) follows:
% 32.19/10.69 | (7875) sum(n6, n7) = all_0_4_4
% 32.19/10.69 |
% 32.19/10.69 | From (972) and (7871) follows:
% 32.19/10.69 | (7876) sum(n6, n6) = all_0_2_2
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (619) with n6, n7, all_0_4_4, n13 and discharging atoms sum(n6, n7) = all_0_4_4, sum(n6, n7) = n13, yields:
% 32.19/10.69 | (857) all_0_4_4 = n13
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (619) with n6, n6, all_0_2_2, n12 and discharging atoms sum(n6, n6) = all_0_2_2, sum(n6, n6) = n12, yields:
% 32.19/10.69 | (856) all_0_2_2 = n12
% 32.19/10.69 |
% 32.19/10.69 | From (856) and (473) follows:
% 32.19/10.69 | (858) pred(n12) = all_0_1_1
% 32.19/10.69 |
% 32.19/10.69 | From (857) and (716) follows:
% 32.19/10.69 | (859) pred(n13) = all_0_3_3
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (244) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 32.19/10.69 | (860) all_0_3_3 = n12
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (244) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 32.19/10.69 | (861) all_0_1_1 = n11
% 32.19/10.69 |
% 32.19/10.69 | From (860) and (232) follows:
% 32.19/10.69 | (862) sum(n12, all_0_0_0) = all_0_6_6
% 32.19/10.69 |
% 32.19/10.69 | From (861) and (1342) follows:
% 32.19/10.69 | (7884) sum(n6, n11) = all_0_0_0
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (619) with n6, n11, all_0_0_0, n17 and discharging atoms sum(n6, n11) = all_0_0_0, sum(n6, n11) = n17, yields:
% 32.19/10.69 | (745) all_0_0_0 = n17
% 32.19/10.69 |
% 32.19/10.69 | From (745) and (862) follows:
% 32.19/10.69 | (7886) sum(n12, n17) = all_0_6_6
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (619) with n12, n17, all_0_6_6, n8 and discharging atoms sum(n12, n17) = all_0_6_6, sum(n12, n17) = n8, yields:
% 32.19/10.69 | (985) all_0_6_6 = n8
% 32.19/10.69 |
% 32.19/10.69 | Equations (985) can reduce 357 to:
% 32.19/10.69 | (748) $false
% 32.19/10.69 |
% 32.19/10.69 |-The branch is then unsatisfiable
% 32.19/10.69 |-Branch two:
% 32.19/10.69 | (987) ~ (all_0_8_8 = n6)
% 32.19/10.69 | (988) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.19/10.69 |
% 32.19/10.69 +-Applying beta-rule and splitting (988), into two cases.
% 32.19/10.69 |-Branch one:
% 32.19/10.69 | (989) all_0_8_8 = n5
% 32.19/10.69 |
% 32.19/10.69 | From (989) and (7873) follows:
% 32.19/10.69 | (7892) sum(n5, n7) = all_0_4_4
% 32.19/10.69 |
% 32.19/10.69 | From (989) and (7871) follows:
% 32.19/10.69 | (7893) sum(n5, n6) = all_0_2_2
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (619) with n5, n7, all_0_4_4, n12 and discharging atoms sum(n5, n7) = all_0_4_4, sum(n5, n7) = n12, yields:
% 32.19/10.69 | (874) all_0_4_4 = n12
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (619) with n5, n6, all_0_2_2, n11 and discharging atoms sum(n5, n6) = all_0_2_2, sum(n5, n6) = n11, yields:
% 32.19/10.69 | (873) all_0_2_2 = n11
% 32.19/10.69 |
% 32.19/10.69 | From (873) and (473) follows:
% 32.19/10.69 | (875) pred(n11) = all_0_1_1
% 32.19/10.69 |
% 32.19/10.69 | From (874) and (716) follows:
% 32.19/10.69 | (876) pred(n12) = all_0_3_3
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 32.19/10.69 | (877) all_0_3_3 = n11
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 32.19/10.69 | (878) all_0_1_1 = n10
% 32.19/10.69 |
% 32.19/10.69 | From (877) and (232) follows:
% 32.19/10.69 | (879) sum(n11, all_0_0_0) = all_0_6_6
% 32.19/10.69 |
% 32.19/10.69 | From (878) and (1342) follows:
% 32.19/10.69 | (7901) sum(n6, n10) = all_0_0_0
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (619) with n6, n10, all_0_0_0, n16 and discharging atoms sum(n6, n10) = all_0_0_0, sum(n6, n10) = n16, yields:
% 32.19/10.69 | (762) all_0_0_0 = n16
% 32.19/10.69 |
% 32.19/10.69 | From (762) and (879) follows:
% 32.19/10.69 | (7903) sum(n11, n16) = all_0_6_6
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (619) with n11, n16, all_0_6_6, n6 and discharging atoms sum(n11, n16) = all_0_6_6, sum(n11, n16) = n6, yields:
% 32.19/10.69 | (1002) all_0_6_6 = n6
% 32.19/10.69 |
% 32.19/10.69 | Equations (1002) can reduce 498 to:
% 32.19/10.69 | (748) $false
% 32.19/10.69 |
% 32.19/10.69 |-The branch is then unsatisfiable
% 32.19/10.69 |-Branch two:
% 32.19/10.69 | (1004) ~ (all_0_8_8 = n5)
% 32.19/10.69 | (1005) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.19/10.69 |
% 32.19/10.69 +-Applying beta-rule and splitting (1005), into two cases.
% 32.19/10.69 |-Branch one:
% 32.19/10.69 | (1006) all_0_8_8 = n4
% 32.19/10.69 |
% 32.19/10.69 | From (1006) and (7873) follows:
% 32.19/10.69 | (7909) sum(n4, n7) = all_0_4_4
% 32.19/10.69 |
% 32.19/10.69 | From (1006) and (7871) follows:
% 32.19/10.69 | (7910) sum(n4, n6) = all_0_2_2
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (619) with n4, n7, all_0_4_4, n11 and discharging atoms sum(n4, n7) = all_0_4_4, sum(n4, n7) = n11, yields:
% 32.19/10.69 | (891) all_0_4_4 = n11
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (619) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 32.19/10.69 | (890) all_0_2_2 = n10
% 32.19/10.69 |
% 32.19/10.69 | From (890) and (473) follows:
% 32.19/10.69 | (892) pred(n10) = all_0_1_1
% 32.19/10.69 |
% 32.19/10.69 | From (891) and (716) follows:
% 32.19/10.69 | (893) pred(n11) = all_0_3_3
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 32.19/10.69 | (894) all_0_3_3 = n10
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 32.19/10.69 | (895) all_0_1_1 = n9
% 32.19/10.69 |
% 32.19/10.69 | From (894) and (232) follows:
% 32.19/10.69 | (896) sum(n10, all_0_0_0) = all_0_6_6
% 32.19/10.69 |
% 32.19/10.69 | From (895) and (1342) follows:
% 32.19/10.69 | (7918) sum(n6, n9) = all_0_0_0
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (619) with n6, n9, all_0_0_0, n15 and discharging atoms sum(n6, n9) = all_0_0_0, sum(n6, n9) = n15, yields:
% 32.19/10.69 | (779) all_0_0_0 = n15
% 32.19/10.69 |
% 32.19/10.69 | From (779) and (896) follows:
% 32.19/10.69 | (7920) sum(n10, n15) = all_0_6_6
% 32.19/10.69 |
% 32.19/10.69 | Instantiating formula (619) with n10, n15, all_0_6_6, n4 and discharging atoms sum(n10, n15) = all_0_6_6, sum(n10, n15) = n4, yields:
% 32.19/10.69 | (1019) all_0_6_6 = n4
% 32.19/10.69 |
% 32.19/10.69 | Equations (1019) can reduce 48 to:
% 32.19/10.69 | (748) $false
% 32.19/10.69 |
% 32.19/10.69 |-The branch is then unsatisfiable
% 32.19/10.69 |-Branch two:
% 32.19/10.69 | (1021) ~ (all_0_8_8 = n4)
% 32.19/10.69 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.19/10.69 |
% 32.19/10.69 +-Applying beta-rule and splitting (1022), into two cases.
% 32.19/10.69 |-Branch one:
% 32.19/10.69 | (1023) all_0_8_8 = n3
% 32.19/10.69 |
% 32.19/10.69 | From (1023) and (7873) follows:
% 32.19/10.69 | (7926) sum(n3, n7) = all_0_4_4
% 32.19/10.69 |
% 32.19/10.69 | From (1023) and (7871) follows:
% 32.45/10.69 | (7927) sum(n3, n6) = all_0_2_2
% 32.45/10.69 |
% 32.45/10.69 | Instantiating formula (619) with n3, n7, all_0_4_4, n10 and discharging atoms sum(n3, n7) = all_0_4_4, sum(n3, n7) = n10, yields:
% 32.45/10.69 | (908) all_0_4_4 = n10
% 32.45/10.69 |
% 32.45/10.69 | Instantiating formula (619) with n3, n6, all_0_2_2, n9 and discharging atoms sum(n3, n6) = all_0_2_2, sum(n3, n6) = n9, yields:
% 32.45/10.69 | (907) all_0_2_2 = n9
% 32.45/10.69 |
% 32.45/10.69 | From (907) and (473) follows:
% 32.45/10.69 | (909) pred(n9) = all_0_1_1
% 32.45/10.69 |
% 32.45/10.69 | From (908) and (716) follows:
% 32.45/10.69 | (910) pred(n10) = all_0_3_3
% 32.45/10.69 |
% 32.45/10.69 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 32.45/10.69 | (911) all_0_3_3 = n9
% 32.45/10.69 |
% 32.45/10.69 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 32.45/10.69 | (912) all_0_1_1 = n8
% 32.45/10.69 |
% 32.45/10.69 | From (911) and (232) follows:
% 32.45/10.69 | (913) sum(n9, all_0_0_0) = all_0_6_6
% 32.45/10.69 |
% 32.45/10.69 | From (912) and (1342) follows:
% 32.45/10.69 | (7935) sum(n6, n8) = all_0_0_0
% 32.45/10.69 |
% 32.45/10.69 | Instantiating formula (619) with n6, n8, all_0_0_0, n14 and discharging atoms sum(n6, n8) = all_0_0_0, sum(n6, n8) = n14, yields:
% 32.45/10.69 | (796) all_0_0_0 = n14
% 32.45/10.69 |
% 32.45/10.69 | From (796) and (913) follows:
% 32.45/10.69 | (7937) sum(n9, n14) = all_0_6_6
% 32.45/10.69 |
% 32.45/10.69 | Instantiating formula (619) with n9, n14, all_0_6_6, n2 and discharging atoms sum(n9, n14) = all_0_6_6, sum(n9, n14) = n2, yields:
% 32.45/10.70 | (1036) all_0_6_6 = n2
% 32.45/10.70 |
% 32.45/10.70 | Equations (1036) can reduce 56 to:
% 32.45/10.70 | (748) $false
% 32.45/10.70 |
% 32.45/10.70 |-The branch is then unsatisfiable
% 32.45/10.70 |-Branch two:
% 32.45/10.70 | (1038) ~ (all_0_8_8 = n3)
% 32.45/10.70 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.45/10.70 |
% 32.45/10.70 +-Applying beta-rule and splitting (1039), into two cases.
% 32.45/10.70 |-Branch one:
% 32.45/10.70 | (1040) all_0_8_8 = n2
% 32.45/10.70 |
% 32.45/10.70 | From (1040) and (7873) follows:
% 32.45/10.70 | (7943) sum(n2, n7) = all_0_4_4
% 32.45/10.70 |
% 32.45/10.70 | From (1040) and (7871) follows:
% 32.45/10.70 | (7944) sum(n2, n6) = all_0_2_2
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (619) with n2, n7, all_0_4_4, n9 and discharging atoms sum(n2, n7) = all_0_4_4, sum(n2, n7) = n9, yields:
% 32.45/10.70 | (925) all_0_4_4 = n9
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (619) with n2, n6, all_0_2_2, n8 and discharging atoms sum(n2, n6) = all_0_2_2, sum(n2, n6) = n8, yields:
% 32.45/10.70 | (924) all_0_2_2 = n8
% 32.45/10.70 |
% 32.45/10.70 | From (924) and (473) follows:
% 32.45/10.70 | (926) pred(n8) = all_0_1_1
% 32.45/10.70 |
% 32.45/10.70 | From (925) and (716) follows:
% 32.45/10.70 | (927) pred(n9) = all_0_3_3
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 32.45/10.70 | (928) all_0_3_3 = n8
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 32.45/10.70 | (929) all_0_1_1 = n7
% 32.45/10.70 |
% 32.45/10.70 | From (928) and (232) follows:
% 32.45/10.70 | (930) sum(n8, all_0_0_0) = all_0_6_6
% 32.45/10.70 |
% 32.45/10.70 | From (929) and (1342) follows:
% 32.45/10.70 | (7952) sum(n6, n7) = all_0_0_0
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (619) with n6, n7, all_0_0_0, n13 and discharging atoms sum(n6, n7) = all_0_0_0, sum(n6, n7) = n13, yields:
% 32.45/10.70 | (813) all_0_0_0 = n13
% 32.45/10.70 |
% 32.45/10.70 | From (813) and (930) follows:
% 32.45/10.70 | (7954) sum(n8, n13) = all_0_6_6
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (619) with n8, n13, all_0_6_6, n0 and discharging atoms sum(n8, n13) = all_0_6_6, sum(n8, n13) = n0, yields:
% 32.45/10.70 | (1053) all_0_6_6 = n0
% 32.45/10.70 |
% 32.45/10.70 | Equations (1053) can reduce 676 to:
% 32.45/10.70 | (748) $false
% 32.45/10.70 |
% 32.45/10.70 |-The branch is then unsatisfiable
% 32.45/10.70 |-Branch two:
% 32.45/10.70 | (1055) ~ (all_0_8_8 = n2)
% 32.45/10.70 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 32.45/10.70 |
% 32.45/10.70 +-Applying beta-rule and splitting (1056), into two cases.
% 32.45/10.70 |-Branch one:
% 32.45/10.70 | (1057) all_0_8_8 = n1
% 32.45/10.70 |
% 32.45/10.70 | From (1057) and (7873) follows:
% 32.45/10.70 | (7960) sum(n1, n7) = all_0_4_4
% 32.45/10.70 |
% 32.45/10.70 | From (1057) and (7871) follows:
% 32.45/10.70 | (7961) sum(n1, n6) = all_0_2_2
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (619) with n1, n7, all_0_4_4, n8 and discharging atoms sum(n1, n7) = all_0_4_4, sum(n1, n7) = n8, yields:
% 32.45/10.70 | (942) all_0_4_4 = n8
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (619) with n1, n6, all_0_2_2, n7 and discharging atoms sum(n1, n6) = all_0_2_2, sum(n1, n6) = n7, yields:
% 32.45/10.70 | (941) all_0_2_2 = n7
% 32.45/10.70 |
% 32.45/10.70 | From (941) and (473) follows:
% 32.45/10.70 | (943) pred(n7) = all_0_1_1
% 32.45/10.70 |
% 32.45/10.70 | From (942) and (716) follows:
% 32.45/10.70 | (944) pred(n8) = all_0_3_3
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 32.45/10.70 | (945) all_0_3_3 = n7
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 32.45/10.70 | (946) all_0_1_1 = n6
% 32.45/10.70 |
% 32.45/10.70 | From (945) and (232) follows:
% 32.45/10.70 | (947) sum(n7, all_0_0_0) = all_0_6_6
% 32.45/10.70 |
% 32.45/10.70 | From (946) and (1342) follows:
% 32.45/10.70 | (7969) sum(n6, n6) = all_0_0_0
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (619) with n6, n6, all_0_0_0, n12 and discharging atoms sum(n6, n6) = all_0_0_0, sum(n6, n6) = n12, yields:
% 32.45/10.70 | (830) all_0_0_0 = n12
% 32.45/10.70 |
% 32.45/10.70 | From (830) and (947) follows:
% 32.45/10.70 | (7971) sum(n7, n12) = all_0_6_6
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (619) with n7, n12, all_0_6_6, n19 and discharging atoms sum(n7, n12) = all_0_6_6, sum(n7, n12) = n19, yields:
% 32.45/10.70 | (1070) all_0_6_6 = n19
% 32.45/10.70 |
% 32.45/10.70 | Equations (1070) can reduce 31 to:
% 32.45/10.70 | (748) $false
% 32.45/10.70 |
% 32.45/10.70 |-The branch is then unsatisfiable
% 32.45/10.70 |-Branch two:
% 32.45/10.70 | (1072) ~ (all_0_8_8 = n1)
% 32.45/10.70 | (1073) all_0_8_8 = n0
% 32.45/10.70 |
% 32.45/10.70 | From (1073) and (7873) follows:
% 32.45/10.70 | (7976) sum(n0, n7) = all_0_4_4
% 32.45/10.70 |
% 32.45/10.70 | From (1073) and (7871) follows:
% 32.45/10.70 | (7977) sum(n0, n6) = all_0_2_2
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (619) with n0, n7, all_0_4_4, n7 and discharging atoms sum(n0, n7) = all_0_4_4, sum(n0, n7) = n7, yields:
% 32.45/10.70 | (959) all_0_4_4 = n7
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (619) with n0, n6, all_0_2_2, n6 and discharging atoms sum(n0, n6) = all_0_2_2, sum(n0, n6) = n6, yields:
% 32.45/10.70 | (958) all_0_2_2 = n6
% 32.45/10.70 |
% 32.45/10.70 | From (958) and (473) follows:
% 32.45/10.70 | (960) pred(n6) = all_0_1_1
% 32.45/10.70 |
% 32.45/10.70 | From (959) and (716) follows:
% 32.45/10.70 | (961) pred(n7) = all_0_3_3
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 32.45/10.70 | (962) all_0_3_3 = n6
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 32.45/10.70 | (963) all_0_1_1 = n5
% 32.45/10.70 |
% 32.45/10.70 | From (962) and (232) follows:
% 32.45/10.70 | (964) sum(n6, all_0_0_0) = all_0_6_6
% 32.45/10.70 |
% 32.45/10.70 | From (963) and (1342) follows:
% 32.45/10.70 | (7985) sum(n6, n5) = all_0_0_0
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (619) with n6, n5, all_0_0_0, n11 and discharging atoms sum(n6, n5) = all_0_0_0, sum(n6, n5) = n11, yields:
% 32.45/10.70 | (847) all_0_0_0 = n11
% 32.45/10.70 |
% 32.45/10.70 | From (847) and (964) follows:
% 32.45/10.70 | (7987) sum(n6, n11) = all_0_6_6
% 32.45/10.70 |
% 32.45/10.70 | Instantiating formula (619) with n6, n11, all_0_6_6, n17 and discharging atoms sum(n6, n11) = all_0_6_6, sum(n6, n11) = n17, yields:
% 32.45/10.70 | (1086) all_0_6_6 = n17
% 32.45/10.70 |
% 32.45/10.70 | Equations (1086) can reduce 669 to:
% 32.45/10.70 | (748) $false
% 32.45/10.70 |
% 32.45/10.70 |-The branch is then unsatisfiable
% 32.45/10.70 |-Branch two:
% 32.45/10.70 | (1357) ~ (all_0_7_7 = n6)
% 32.45/10.70 | (1358) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.45/10.70 |
% 32.45/10.70 +-Applying beta-rule and splitting (971), into two cases.
% 32.45/10.70 |-Branch one:
% 32.45/10.70 | (972) all_0_8_8 = n6
% 32.45/10.70 |
% 32.45/10.70 | From (972) and (708) follows:
% 32.45/10.70 | (7993) sum(n6, all_0_5_5) = all_0_4_4
% 32.45/10.70 |
% 32.45/10.70 | From (972) and (378) follows:
% 32.45/10.70 | (7994) sum(n6, all_0_7_7) = all_0_2_2
% 32.45/10.70 |
% 32.45/10.70 +-Applying beta-rule and splitting (1358), into two cases.
% 32.45/10.70 |-Branch one:
% 32.45/10.70 | (1359) all_0_7_7 = n5
% 32.45/10.70 |
% 32.45/10.70 | From (1359) and (683) follows:
% 32.45/10.70 | (1360) succ(n5) = all_0_5_5
% 32.45/10.70 |
% 32.45/10.70 | From (1359) and (8) follows:
% 32.45/10.70 | (1361) sum(n5, all_0_1_1) = all_0_0_0
% 32.45/10.70 |
% 32.45/10.70 | From (1359) and (7994) follows:
% 32.45/10.71 | (7998) sum(n6, n5) = all_0_2_2
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (388) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 32.45/10.71 | (1363) all_0_5_5 = n6
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (619) with n6, n5, all_0_2_2, n11 and discharging atoms sum(n6, n5) = all_0_2_2, sum(n6, n5) = n11, yields:
% 32.45/10.71 | (873) all_0_2_2 = n11
% 32.45/10.71 |
% 32.45/10.71 | From (873) and (473) follows:
% 32.45/10.71 | (875) pred(n11) = all_0_1_1
% 32.45/10.71 |
% 32.45/10.71 | From (1363) and (7993) follows:
% 32.45/10.71 | (8002) sum(n6, n6) = all_0_4_4
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (244) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 32.45/10.71 | (878) all_0_1_1 = n10
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (619) with n6, n6, all_0_4_4, n12 and discharging atoms sum(n6, n6) = all_0_4_4, sum(n6, n6) = n12, yields:
% 32.45/10.71 | (874) all_0_4_4 = n12
% 32.45/10.71 |
% 32.45/10.71 | From (874) and (716) follows:
% 32.45/10.71 | (876) pred(n12) = all_0_3_3
% 32.45/10.71 |
% 32.45/10.71 | From (878) and (1361) follows:
% 32.45/10.71 | (8006) sum(n5, n10) = all_0_0_0
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (244) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 32.45/10.71 | (877) all_0_3_3 = n11
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (619) with n5, n10, all_0_0_0, n15 and discharging atoms sum(n5, n10) = all_0_0_0, sum(n5, n10) = n15, yields:
% 32.45/10.71 | (779) all_0_0_0 = n15
% 32.45/10.71 |
% 32.45/10.71 | From (877)(779) and (232) follows:
% 32.45/10.71 | (8009) sum(n11, n15) = all_0_6_6
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (619) with n11, n15, all_0_6_6, n5 and discharging atoms sum(n11, n15) = all_0_6_6, sum(n11, n15) = n5, yields:
% 32.45/10.71 | (832) all_0_6_6 = n5
% 32.45/10.71 |
% 32.45/10.71 | Equations (832) can reduce 462 to:
% 32.45/10.71 | (748) $false
% 32.45/10.71 |
% 32.45/10.71 |-The branch is then unsatisfiable
% 32.45/10.71 |-Branch two:
% 32.45/10.71 | (1376) ~ (all_0_7_7 = n5)
% 32.45/10.71 | (1377) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.45/10.71 |
% 32.45/10.71 +-Applying beta-rule and splitting (1377), into two cases.
% 32.45/10.71 |-Branch one:
% 32.45/10.71 | (1378) all_0_7_7 = n4
% 32.45/10.71 |
% 32.45/10.71 | From (1378) and (683) follows:
% 32.45/10.71 | (1379) succ(n4) = all_0_5_5
% 32.45/10.71 |
% 32.45/10.71 | From (1378) and (8) follows:
% 32.45/10.71 | (1380) sum(n4, all_0_1_1) = all_0_0_0
% 32.45/10.71 |
% 32.45/10.71 | From (1378) and (7994) follows:
% 32.45/10.71 | (8017) sum(n6, n4) = all_0_2_2
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (388) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 32.45/10.71 | (1382) all_0_5_5 = n5
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (619) with n6, n4, all_0_2_2, n10 and discharging atoms sum(n6, n4) = all_0_2_2, sum(n6, n4) = n10, yields:
% 32.45/10.71 | (890) all_0_2_2 = n10
% 32.45/10.71 |
% 32.45/10.71 | From (890) and (473) follows:
% 32.45/10.71 | (892) pred(n10) = all_0_1_1
% 32.45/10.71 |
% 32.45/10.71 | From (1382) and (7993) follows:
% 32.45/10.71 | (8021) sum(n6, n5) = all_0_4_4
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 32.45/10.71 | (895) all_0_1_1 = n9
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (619) with n6, n5, all_0_4_4, n11 and discharging atoms sum(n6, n5) = all_0_4_4, sum(n6, n5) = n11, yields:
% 32.45/10.71 | (891) all_0_4_4 = n11
% 32.45/10.71 |
% 32.45/10.71 | From (891) and (716) follows:
% 32.45/10.71 | (893) pred(n11) = all_0_3_3
% 32.45/10.71 |
% 32.45/10.71 | From (895) and (1380) follows:
% 32.45/10.71 | (8025) sum(n4, n9) = all_0_0_0
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 32.45/10.71 | (894) all_0_3_3 = n10
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (619) with n4, n9, all_0_0_0, n13 and discharging atoms sum(n4, n9) = all_0_0_0, sum(n4, n9) = n13, yields:
% 32.45/10.71 | (813) all_0_0_0 = n13
% 32.45/10.71 |
% 32.45/10.71 | From (894)(813) and (232) follows:
% 32.45/10.71 | (8028) sum(n10, n13) = all_0_6_6
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (619) with n10, n13, all_0_6_6, n2 and discharging atoms sum(n10, n13) = all_0_6_6, sum(n10, n13) = n2, yields:
% 32.45/10.71 | (1036) all_0_6_6 = n2
% 32.45/10.71 |
% 32.45/10.71 | Equations (1036) can reduce 56 to:
% 32.45/10.71 | (748) $false
% 32.45/10.71 |
% 32.45/10.71 |-The branch is then unsatisfiable
% 32.45/10.71 |-Branch two:
% 32.45/10.71 | (1395) ~ (all_0_7_7 = n4)
% 32.45/10.71 | (1396) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.45/10.71 |
% 32.45/10.71 +-Applying beta-rule and splitting (1396), into two cases.
% 32.45/10.71 |-Branch one:
% 32.45/10.71 | (1397) all_0_7_7 = n3
% 32.45/10.71 |
% 32.45/10.71 | From (1397) and (683) follows:
% 32.45/10.71 | (1398) succ(n3) = all_0_5_5
% 32.45/10.71 |
% 32.45/10.71 | From (1397) and (8) follows:
% 32.45/10.71 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 32.45/10.71 |
% 32.45/10.71 | From (1397) and (7994) follows:
% 32.45/10.71 | (8036) sum(n6, n3) = all_0_2_2
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 32.45/10.71 | (1401) all_0_5_5 = n4
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (619) with n6, n3, all_0_2_2, n9 and discharging atoms sum(n6, n3) = all_0_2_2, sum(n6, n3) = n9, yields:
% 32.45/10.71 | (907) all_0_2_2 = n9
% 32.45/10.71 |
% 32.45/10.71 | From (907) and (473) follows:
% 32.45/10.71 | (909) pred(n9) = all_0_1_1
% 32.45/10.71 |
% 32.45/10.71 | From (1401) and (7993) follows:
% 32.45/10.71 | (8040) sum(n6, n4) = all_0_4_4
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 32.45/10.71 | (912) all_0_1_1 = n8
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (619) with n6, n4, all_0_4_4, n10 and discharging atoms sum(n6, n4) = all_0_4_4, sum(n6, n4) = n10, yields:
% 32.45/10.71 | (908) all_0_4_4 = n10
% 32.45/10.71 |
% 32.45/10.71 | From (908) and (716) follows:
% 32.45/10.71 | (910) pred(n10) = all_0_3_3
% 32.45/10.71 |
% 32.45/10.71 | From (912) and (1399) follows:
% 32.45/10.71 | (8044) sum(n3, n8) = all_0_0_0
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 32.45/10.71 | (911) all_0_3_3 = n9
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (619) with n3, n8, all_0_0_0, n11 and discharging atoms sum(n3, n8) = all_0_0_0, sum(n3, n8) = n11, yields:
% 32.45/10.71 | (847) all_0_0_0 = n11
% 32.45/10.71 |
% 32.45/10.71 | From (911)(847) and (232) follows:
% 32.45/10.71 | (8047) sum(n9, n11) = all_0_6_6
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (619) with n9, n11, all_0_6_6, n20 and discharging atoms sum(n9, n11) = all_0_6_6, sum(n9, n11) = n20, yields:
% 32.45/10.71 | (883) all_0_6_6 = n20
% 32.45/10.71 |
% 32.45/10.71 | Equations (883) can reduce 381 to:
% 32.45/10.71 | (748) $false
% 32.45/10.71 |
% 32.45/10.71 |-The branch is then unsatisfiable
% 32.45/10.71 |-Branch two:
% 32.45/10.71 | (1414) ~ (all_0_7_7 = n3)
% 32.45/10.71 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.45/10.71 |
% 32.45/10.71 +-Applying beta-rule and splitting (1415), into two cases.
% 32.45/10.71 |-Branch one:
% 32.45/10.71 | (1416) all_0_7_7 = n2
% 32.45/10.71 |
% 32.45/10.71 | From (1416) and (683) follows:
% 32.45/10.71 | (1417) succ(n2) = all_0_5_5
% 32.45/10.71 |
% 32.45/10.71 | From (1416) and (8) follows:
% 32.45/10.71 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 32.45/10.71 |
% 32.45/10.71 | From (1416) and (7994) follows:
% 32.45/10.71 | (8055) sum(n6, n2) = all_0_2_2
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 32.45/10.71 | (1420) all_0_5_5 = n3
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (619) with n6, n2, all_0_2_2, n8 and discharging atoms sum(n6, n2) = all_0_2_2, sum(n6, n2) = n8, yields:
% 32.45/10.71 | (924) all_0_2_2 = n8
% 32.45/10.71 |
% 32.45/10.71 | From (924) and (473) follows:
% 32.45/10.71 | (926) pred(n8) = all_0_1_1
% 32.45/10.71 |
% 32.45/10.71 | From (1420) and (7993) follows:
% 32.45/10.71 | (8059) sum(n6, n3) = all_0_4_4
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 32.45/10.71 | (929) all_0_1_1 = n7
% 32.45/10.71 |
% 32.45/10.71 | Instantiating formula (619) with n6, n3, all_0_4_4, n9 and discharging atoms sum(n6, n3) = all_0_4_4, sum(n6, n3) = n9, yields:
% 32.45/10.71 | (925) all_0_4_4 = n9
% 32.45/10.71 |
% 32.45/10.71 | From (925) and (716) follows:
% 32.45/10.71 | (927) pred(n9) = all_0_3_3
% 32.45/10.71 |
% 32.45/10.71 | From (929) and (1418) follows:
% 32.45/10.72 | (8063) sum(n2, n7) = all_0_0_0
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 32.45/10.72 | (928) all_0_3_3 = n8
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (619) with n2, n7, all_0_0_0, n9 and discharging atoms sum(n2, n7) = all_0_0_0, sum(n2, n7) = n9, yields:
% 32.45/10.72 | (881) all_0_0_0 = n9
% 32.45/10.72 |
% 32.45/10.72 | From (928)(881) and (232) follows:
% 32.45/10.72 | (8066) sum(n8, n9) = all_0_6_6
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (619) with n8, n9, all_0_6_6, n17 and discharging atoms sum(n8, n9) = all_0_6_6, sum(n8, n9) = n17, yields:
% 32.45/10.72 | (1086) all_0_6_6 = n17
% 32.45/10.72 |
% 32.45/10.72 | Equations (1086) can reduce 669 to:
% 32.45/10.72 | (748) $false
% 32.45/10.72 |
% 32.45/10.72 |-The branch is then unsatisfiable
% 32.45/10.72 |-Branch two:
% 32.45/10.72 | (1433) ~ (all_0_7_7 = n2)
% 32.45/10.72 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 32.45/10.72 |
% 32.45/10.72 +-Applying beta-rule and splitting (1434), into two cases.
% 32.45/10.72 |-Branch one:
% 32.45/10.72 | (1435) all_0_7_7 = n1
% 32.45/10.72 |
% 32.45/10.72 | From (1435) and (683) follows:
% 32.45/10.72 | (1436) succ(n1) = all_0_5_5
% 32.45/10.72 |
% 32.45/10.72 | From (1435) and (8) follows:
% 32.45/10.72 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 32.45/10.72 |
% 32.45/10.72 | From (1435) and (7994) follows:
% 32.45/10.72 | (8074) sum(n6, n1) = all_0_2_2
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 32.45/10.72 | (1439) all_0_5_5 = n2
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (619) with n6, n1, all_0_2_2, n7 and discharging atoms sum(n6, n1) = all_0_2_2, sum(n6, n1) = n7, yields:
% 32.45/10.72 | (941) all_0_2_2 = n7
% 32.45/10.72 |
% 32.45/10.72 | From (941) and (473) follows:
% 32.45/10.72 | (943) pred(n7) = all_0_1_1
% 32.45/10.72 |
% 32.45/10.72 | From (1439) and (7993) follows:
% 32.45/10.72 | (8078) sum(n6, n2) = all_0_4_4
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 32.45/10.72 | (946) all_0_1_1 = n6
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (619) with n6, n2, all_0_4_4, n8 and discharging atoms sum(n6, n2) = all_0_4_4, sum(n6, n2) = n8, yields:
% 32.45/10.72 | (942) all_0_4_4 = n8
% 32.45/10.72 |
% 32.45/10.72 | From (942) and (716) follows:
% 32.45/10.72 | (944) pred(n8) = all_0_3_3
% 32.45/10.72 |
% 32.45/10.72 | From (946) and (1437) follows:
% 32.45/10.72 | (8082) sum(n1, n6) = all_0_0_0
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 32.45/10.72 | (945) all_0_3_3 = n7
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (619) with n1, n6, all_0_0_0, n7 and discharging atoms sum(n1, n6) = all_0_0_0, sum(n1, n6) = n7, yields:
% 32.45/10.72 | (915) all_0_0_0 = n7
% 32.45/10.72 |
% 32.45/10.72 | From (945)(915) and (232) follows:
% 32.45/10.72 | (8085) sum(n7, n7) = all_0_6_6
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (619) with n7, n7, all_0_6_6, n14 and discharging atoms sum(n7, n7) = all_0_6_6, sum(n7, n7) = n14, yields:
% 32.45/10.72 | (934) all_0_6_6 = n14
% 32.45/10.72 |
% 32.45/10.72 | Equations (934) can reduce 353 to:
% 32.45/10.72 | (748) $false
% 32.45/10.72 |
% 32.45/10.72 |-The branch is then unsatisfiable
% 32.45/10.72 |-Branch two:
% 32.45/10.72 | (1452) ~ (all_0_7_7 = n1)
% 32.45/10.72 | (1453) all_0_7_7 = n0
% 32.45/10.72 |
% 32.45/10.72 | From (1453) and (683) follows:
% 32.45/10.72 | (1454) succ(n0) = all_0_5_5
% 32.45/10.72 |
% 32.45/10.72 | From (1453) and (8) follows:
% 32.45/10.72 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 32.45/10.72 |
% 32.45/10.72 | From (1453) and (7994) follows:
% 32.45/10.72 | (8092) sum(n6, n0) = all_0_2_2
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 32.45/10.72 | (1457) all_0_5_5 = n1
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (619) with n6, n0, all_0_2_2, n6 and discharging atoms sum(n6, n0) = all_0_2_2, sum(n6, n0) = n6, yields:
% 32.45/10.72 | (958) all_0_2_2 = n6
% 32.45/10.72 |
% 32.45/10.72 | From (958) and (473) follows:
% 32.45/10.72 | (960) pred(n6) = all_0_1_1
% 32.45/10.72 |
% 32.45/10.72 | From (1457) and (7993) follows:
% 32.45/10.72 | (8096) sum(n6, n1) = all_0_4_4
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 32.45/10.72 | (963) all_0_1_1 = n5
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (619) with n6, n1, all_0_4_4, n7 and discharging atoms sum(n6, n1) = all_0_4_4, sum(n6, n1) = n7, yields:
% 32.45/10.72 | (959) all_0_4_4 = n7
% 32.45/10.72 |
% 32.45/10.72 | From (959) and (716) follows:
% 32.45/10.72 | (961) pred(n7) = all_0_3_3
% 32.45/10.72 |
% 32.45/10.72 | From (963) and (1455) follows:
% 32.45/10.72 | (8100) sum(n0, n5) = all_0_0_0
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 32.45/10.72 | (962) all_0_3_3 = n6
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (619) with n0, n5, all_0_0_0, n5 and discharging atoms sum(n0, n5) = all_0_0_0, sum(n0, n5) = n5, yields:
% 32.45/10.72 | (949) all_0_0_0 = n5
% 32.45/10.72 |
% 32.45/10.72 | From (962)(949) and (232) follows:
% 32.45/10.72 | (8103) sum(n6, n5) = all_0_6_6
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (619) with n6, n5, all_0_6_6, n11 and discharging atoms sum(n6, n5) = all_0_6_6, sum(n6, n5) = n11, yields:
% 32.45/10.72 | (781) all_0_6_6 = n11
% 32.45/10.72 |
% 32.45/10.72 | Equations (781) can reduce 2 to:
% 32.45/10.72 | (748) $false
% 32.45/10.72 |
% 32.45/10.72 |-The branch is then unsatisfiable
% 32.45/10.72 |-Branch two:
% 32.45/10.72 | (987) ~ (all_0_8_8 = n6)
% 32.45/10.72 | (988) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.45/10.72 |
% 32.45/10.72 +-Applying beta-rule and splitting (1358), into two cases.
% 32.45/10.72 |-Branch one:
% 32.45/10.72 | (1359) all_0_7_7 = n5
% 32.45/10.72 |
% 32.45/10.72 | From (1359) and (683) follows:
% 32.45/10.72 | (1360) succ(n5) = all_0_5_5
% 32.45/10.72 |
% 32.45/10.72 | From (1359) and (8) follows:
% 32.45/10.72 | (1361) sum(n5, all_0_1_1) = all_0_0_0
% 32.45/10.72 |
% 32.45/10.72 | From (1359) and (378) follows:
% 32.45/10.72 | (8111) sum(all_0_8_8, n5) = all_0_2_2
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (388) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 32.45/10.72 | (1363) all_0_5_5 = n6
% 32.45/10.72 |
% 32.45/10.72 | From (1363) and (708) follows:
% 32.45/10.72 | (8113) sum(all_0_8_8, n6) = all_0_4_4
% 32.45/10.72 |
% 32.45/10.72 +-Applying beta-rule and splitting (988), into two cases.
% 32.45/10.72 |-Branch one:
% 32.45/10.72 | (989) all_0_8_8 = n5
% 32.45/10.72 |
% 32.45/10.72 | From (989) and (8113) follows:
% 32.45/10.72 | (8115) sum(n5, n6) = all_0_4_4
% 32.45/10.72 |
% 32.45/10.72 | From (989) and (8111) follows:
% 32.45/10.72 | (8116) sum(n5, n5) = all_0_2_2
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (619) with n5, n6, all_0_4_4, n11 and discharging atoms sum(n5, n6) = all_0_4_4, sum(n5, n6) = n11, yields:
% 32.45/10.72 | (891) all_0_4_4 = n11
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (619) with n5, n5, all_0_2_2, n10 and discharging atoms sum(n5, n5) = all_0_2_2, sum(n5, n5) = n10, yields:
% 32.45/10.72 | (890) all_0_2_2 = n10
% 32.45/10.72 |
% 32.45/10.72 | From (890) and (473) follows:
% 32.45/10.72 | (892) pred(n10) = all_0_1_1
% 32.45/10.72 |
% 32.45/10.72 | From (891) and (716) follows:
% 32.45/10.72 | (893) pred(n11) = all_0_3_3
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (244) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 32.45/10.72 | (894) all_0_3_3 = n10
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (244) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 32.45/10.72 | (895) all_0_1_1 = n9
% 32.45/10.72 |
% 32.45/10.72 | From (894) and (232) follows:
% 32.45/10.72 | (896) sum(n10, all_0_0_0) = all_0_6_6
% 32.45/10.72 |
% 32.45/10.72 | From (895) and (1361) follows:
% 32.45/10.72 | (8124) sum(n5, n9) = all_0_0_0
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (619) with n5, n9, all_0_0_0, n14 and discharging atoms sum(n5, n9) = all_0_0_0, sum(n5, n9) = n14, yields:
% 32.45/10.72 | (796) all_0_0_0 = n14
% 32.45/10.72 |
% 32.45/10.72 | From (796) and (896) follows:
% 32.45/10.72 | (8126) sum(n10, n14) = all_0_6_6
% 32.45/10.72 |
% 32.45/10.72 | Instantiating formula (619) with n10, n14, all_0_6_6, n3 and discharging atoms sum(n10, n14) = all_0_6_6, sum(n10, n14) = n3, yields:
% 32.45/10.72 | (849) all_0_6_6 = n3
% 32.45/10.72 |
% 32.45/10.72 | Equations (849) can reduce 416 to:
% 32.45/10.72 | (748) $false
% 32.45/10.72 |
% 32.45/10.72 |-The branch is then unsatisfiable
% 32.45/10.72 |-Branch two:
% 32.45/10.72 | (1004) ~ (all_0_8_8 = n5)
% 32.45/10.72 | (1005) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.45/10.72 |
% 32.45/10.72 +-Applying beta-rule and splitting (1005), into two cases.
% 32.45/10.72 |-Branch one:
% 32.45/10.72 | (1006) all_0_8_8 = n4
% 32.45/10.72 |
% 32.45/10.72 | From (1006) and (8113) follows:
% 32.45/10.73 | (8132) sum(n4, n6) = all_0_4_4
% 32.45/10.73 |
% 32.45/10.73 | From (1006) and (8111) follows:
% 32.45/10.73 | (8133) sum(n4, n5) = all_0_2_2
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (619) with n4, n6, all_0_4_4, n10 and discharging atoms sum(n4, n6) = all_0_4_4, sum(n4, n6) = n10, yields:
% 32.45/10.73 | (908) all_0_4_4 = n10
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (619) with n4, n5, all_0_2_2, n9 and discharging atoms sum(n4, n5) = all_0_2_2, sum(n4, n5) = n9, yields:
% 32.45/10.73 | (907) all_0_2_2 = n9
% 32.45/10.73 |
% 32.45/10.73 | From (907) and (473) follows:
% 32.45/10.73 | (909) pred(n9) = all_0_1_1
% 32.45/10.73 |
% 32.45/10.73 | From (908) and (716) follows:
% 32.45/10.73 | (910) pred(n10) = all_0_3_3
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 32.45/10.73 | (911) all_0_3_3 = n9
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 32.45/10.73 | (912) all_0_1_1 = n8
% 32.45/10.73 |
% 32.45/10.73 | From (911) and (232) follows:
% 32.45/10.73 | (913) sum(n9, all_0_0_0) = all_0_6_6
% 32.45/10.73 |
% 32.45/10.73 | From (912) and (1361) follows:
% 32.45/10.73 | (8141) sum(n5, n8) = all_0_0_0
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (619) with n5, n8, all_0_0_0, n13 and discharging atoms sum(n5, n8) = all_0_0_0, sum(n5, n8) = n13, yields:
% 32.45/10.73 | (813) all_0_0_0 = n13
% 32.45/10.73 |
% 32.45/10.73 | From (813) and (913) follows:
% 32.45/10.73 | (8143) sum(n9, n13) = all_0_6_6
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (619) with n9, n13, all_0_6_6, n1 and discharging atoms sum(n9, n13) = all_0_6_6, sum(n9, n13) = n1, yields:
% 32.45/10.73 | (866) all_0_6_6 = n1
% 32.45/10.73 |
% 32.45/10.73 | Equations (866) can reduce 28 to:
% 32.45/10.73 | (748) $false
% 32.45/10.73 |
% 32.45/10.73 |-The branch is then unsatisfiable
% 32.45/10.73 |-Branch two:
% 32.45/10.73 | (1021) ~ (all_0_8_8 = n4)
% 32.45/10.73 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.45/10.73 |
% 32.45/10.73 +-Applying beta-rule and splitting (1022), into two cases.
% 32.45/10.73 |-Branch one:
% 32.45/10.73 | (1023) all_0_8_8 = n3
% 32.45/10.73 |
% 32.45/10.73 | From (1023) and (8113) follows:
% 32.45/10.73 | (8149) sum(n3, n6) = all_0_4_4
% 32.45/10.73 |
% 32.45/10.73 | From (1023) and (8111) follows:
% 32.45/10.73 | (8150) sum(n3, n5) = all_0_2_2
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (619) with n3, n6, all_0_4_4, n9 and discharging atoms sum(n3, n6) = all_0_4_4, sum(n3, n6) = n9, yields:
% 32.45/10.73 | (925) all_0_4_4 = n9
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (619) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 32.45/10.73 | (924) all_0_2_2 = n8
% 32.45/10.73 |
% 32.45/10.73 | From (924) and (473) follows:
% 32.45/10.73 | (926) pred(n8) = all_0_1_1
% 32.45/10.73 |
% 32.45/10.73 | From (925) and (716) follows:
% 32.45/10.73 | (927) pred(n9) = all_0_3_3
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 32.45/10.73 | (928) all_0_3_3 = n8
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 32.45/10.73 | (929) all_0_1_1 = n7
% 32.45/10.73 |
% 32.45/10.73 | From (928) and (232) follows:
% 32.45/10.73 | (930) sum(n8, all_0_0_0) = all_0_6_6
% 32.45/10.73 |
% 32.45/10.73 | From (929) and (1361) follows:
% 32.45/10.73 | (8158) sum(n5, n7) = all_0_0_0
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (619) with n5, n7, all_0_0_0, n12 and discharging atoms sum(n5, n7) = all_0_0_0, sum(n5, n7) = n12, yields:
% 32.45/10.73 | (830) all_0_0_0 = n12
% 32.45/10.73 |
% 32.45/10.73 | From (830) and (930) follows:
% 32.45/10.73 | (8160) sum(n8, n12) = all_0_6_6
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (619) with n8, n12, all_0_6_6, n20 and discharging atoms sum(n8, n12) = all_0_6_6, sum(n8, n12) = n20, yields:
% 32.45/10.73 | (883) all_0_6_6 = n20
% 32.45/10.73 |
% 32.45/10.73 | Equations (883) can reduce 381 to:
% 32.45/10.73 | (748) $false
% 32.45/10.73 |
% 32.45/10.73 |-The branch is then unsatisfiable
% 32.45/10.73 |-Branch two:
% 32.45/10.73 | (1038) ~ (all_0_8_8 = n3)
% 32.45/10.73 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.45/10.73 |
% 32.45/10.73 +-Applying beta-rule and splitting (1039), into two cases.
% 32.45/10.73 |-Branch one:
% 32.45/10.73 | (1040) all_0_8_8 = n2
% 32.45/10.73 |
% 32.45/10.73 | From (1040) and (8113) follows:
% 32.45/10.73 | (8166) sum(n2, n6) = all_0_4_4
% 32.45/10.73 |
% 32.45/10.73 | From (1040) and (8111) follows:
% 32.45/10.73 | (8167) sum(n2, n5) = all_0_2_2
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (619) with n2, n6, all_0_4_4, n8 and discharging atoms sum(n2, n6) = all_0_4_4, sum(n2, n6) = n8, yields:
% 32.45/10.73 | (942) all_0_4_4 = n8
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (619) with n2, n5, all_0_2_2, n7 and discharging atoms sum(n2, n5) = all_0_2_2, sum(n2, n5) = n7, yields:
% 32.45/10.73 | (941) all_0_2_2 = n7
% 32.45/10.73 |
% 32.45/10.73 | From (941) and (473) follows:
% 32.45/10.73 | (943) pred(n7) = all_0_1_1
% 32.45/10.73 |
% 32.45/10.73 | From (942) and (716) follows:
% 32.45/10.73 | (944) pred(n8) = all_0_3_3
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 32.45/10.73 | (945) all_0_3_3 = n7
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 32.45/10.73 | (946) all_0_1_1 = n6
% 32.45/10.73 |
% 32.45/10.73 | From (945) and (232) follows:
% 32.45/10.73 | (947) sum(n7, all_0_0_0) = all_0_6_6
% 32.45/10.73 |
% 32.45/10.73 | From (946) and (1361) follows:
% 32.45/10.73 | (8175) sum(n5, n6) = all_0_0_0
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (619) with n5, n6, all_0_0_0, n11 and discharging atoms sum(n5, n6) = all_0_0_0, sum(n5, n6) = n11, yields:
% 32.45/10.73 | (847) all_0_0_0 = n11
% 32.45/10.73 |
% 32.45/10.73 | From (847) and (947) follows:
% 32.45/10.73 | (8177) sum(n7, n11) = all_0_6_6
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (619) with n7, n11, all_0_6_6, n18 and discharging atoms sum(n7, n11) = all_0_6_6, sum(n7, n11) = n18, yields:
% 32.45/10.73 | (900) all_0_6_6 = n18
% 32.45/10.73 |
% 32.45/10.73 | Equations (900) can reduce 622 to:
% 32.45/10.73 | (748) $false
% 32.45/10.73 |
% 32.45/10.73 |-The branch is then unsatisfiable
% 32.45/10.73 |-Branch two:
% 32.45/10.73 | (1055) ~ (all_0_8_8 = n2)
% 32.45/10.73 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 32.45/10.73 |
% 32.45/10.73 +-Applying beta-rule and splitting (1056), into two cases.
% 32.45/10.73 |-Branch one:
% 32.45/10.73 | (1057) all_0_8_8 = n1
% 32.45/10.73 |
% 32.45/10.73 | From (1057) and (8113) follows:
% 32.45/10.73 | (8183) sum(n1, n6) = all_0_4_4
% 32.45/10.73 |
% 32.45/10.73 | From (1057) and (8111) follows:
% 32.45/10.73 | (8184) sum(n1, n5) = all_0_2_2
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (619) with n1, n6, all_0_4_4, n7 and discharging atoms sum(n1, n6) = all_0_4_4, sum(n1, n6) = n7, yields:
% 32.45/10.73 | (959) all_0_4_4 = n7
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (619) with n1, n5, all_0_2_2, n6 and discharging atoms sum(n1, n5) = all_0_2_2, sum(n1, n5) = n6, yields:
% 32.45/10.73 | (958) all_0_2_2 = n6
% 32.45/10.73 |
% 32.45/10.73 | From (958) and (473) follows:
% 32.45/10.73 | (960) pred(n6) = all_0_1_1
% 32.45/10.73 |
% 32.45/10.73 | From (959) and (716) follows:
% 32.45/10.73 | (961) pred(n7) = all_0_3_3
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 32.45/10.73 | (962) all_0_3_3 = n6
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 32.45/10.73 | (963) all_0_1_1 = n5
% 32.45/10.73 |
% 32.45/10.73 | From (962) and (232) follows:
% 32.45/10.73 | (964) sum(n6, all_0_0_0) = all_0_6_6
% 32.45/10.73 |
% 32.45/10.73 | From (963) and (1361) follows:
% 32.45/10.73 | (8192) sum(n5, n5) = all_0_0_0
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (619) with n5, n5, all_0_0_0, n10 and discharging atoms sum(n5, n5) = all_0_0_0, sum(n5, n5) = n10, yields:
% 32.45/10.73 | (864) all_0_0_0 = n10
% 32.45/10.73 |
% 32.45/10.73 | From (864) and (964) follows:
% 32.45/10.73 | (8194) sum(n6, n10) = all_0_6_6
% 32.45/10.73 |
% 32.45/10.73 | Instantiating formula (619) with n6, n10, all_0_6_6, n16 and discharging atoms sum(n6, n10) = all_0_6_6, sum(n6, n10) = n16, yields:
% 32.45/10.73 | (917) all_0_6_6 = n16
% 32.45/10.73 |
% 32.45/10.73 | Equations (917) can reduce 163 to:
% 32.45/10.73 | (748) $false
% 32.45/10.73 |
% 32.45/10.73 |-The branch is then unsatisfiable
% 32.45/10.73 |-Branch two:
% 32.45/10.73 | (1072) ~ (all_0_8_8 = n1)
% 32.45/10.73 | (1073) all_0_8_8 = n0
% 32.45/10.73 |
% 32.45/10.73 | From (1073) and (8113) follows:
% 32.45/10.73 | (8199) sum(n0, n6) = all_0_4_4
% 32.45/10.73 |
% 32.45/10.73 | From (1073) and (8111) follows:
% 32.45/10.74 | (8200) sum(n0, n5) = all_0_2_2
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (619) with n0, n6, all_0_4_4, n6 and discharging atoms sum(n0, n6) = all_0_4_4, sum(n0, n6) = n6, yields:
% 32.45/10.74 | (976) all_0_4_4 = n6
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (619) with n0, n5, all_0_2_2, n5 and discharging atoms sum(n0, n5) = all_0_2_2, sum(n0, n5) = n5, yields:
% 32.45/10.74 | (975) all_0_2_2 = n5
% 32.45/10.74 |
% 32.45/10.74 | From (975) and (473) follows:
% 32.45/10.74 | (977) pred(n5) = all_0_1_1
% 32.45/10.74 |
% 32.45/10.74 | From (976) and (716) follows:
% 32.45/10.74 | (978) pred(n6) = all_0_3_3
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 32.45/10.74 | (979) all_0_3_3 = n5
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 32.45/10.74 | (980) all_0_1_1 = n4
% 32.45/10.74 |
% 32.45/10.74 | From (979) and (232) follows:
% 32.45/10.74 | (981) sum(n5, all_0_0_0) = all_0_6_6
% 32.45/10.74 |
% 32.45/10.74 | From (980) and (1361) follows:
% 32.45/10.74 | (8208) sum(n5, n4) = all_0_0_0
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (619) with n5, n4, all_0_0_0, n9 and discharging atoms sum(n5, n4) = all_0_0_0, sum(n5, n4) = n9, yields:
% 32.45/10.74 | (881) all_0_0_0 = n9
% 32.45/10.74 |
% 32.45/10.74 | From (881) and (981) follows:
% 32.45/10.74 | (8210) sum(n5, n9) = all_0_6_6
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (619) with n5, n9, all_0_6_6, n14 and discharging atoms sum(n5, n9) = all_0_6_6, sum(n5, n9) = n14, yields:
% 32.45/10.74 | (934) all_0_6_6 = n14
% 32.45/10.74 |
% 32.45/10.74 | Equations (934) can reduce 353 to:
% 32.45/10.74 | (748) $false
% 32.45/10.74 |
% 32.45/10.74 |-The branch is then unsatisfiable
% 32.45/10.74 |-Branch two:
% 32.45/10.74 | (1376) ~ (all_0_7_7 = n5)
% 32.45/10.74 | (1377) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.45/10.74 |
% 32.45/10.74 +-Applying beta-rule and splitting (988), into two cases.
% 32.45/10.74 |-Branch one:
% 32.45/10.74 | (989) all_0_8_8 = n5
% 32.45/10.74 |
% 32.45/10.74 | From (989) and (708) follows:
% 32.45/10.74 | (8216) sum(n5, all_0_5_5) = all_0_4_4
% 32.45/10.74 |
% 32.45/10.74 | From (989) and (378) follows:
% 32.45/10.74 | (8217) sum(n5, all_0_7_7) = all_0_2_2
% 32.45/10.74 |
% 32.45/10.74 +-Applying beta-rule and splitting (1377), into two cases.
% 32.45/10.74 |-Branch one:
% 32.45/10.74 | (1378) all_0_7_7 = n4
% 32.45/10.74 |
% 32.45/10.74 | From (1378) and (683) follows:
% 32.45/10.74 | (1379) succ(n4) = all_0_5_5
% 32.45/10.74 |
% 32.45/10.74 | From (1378) and (8) follows:
% 32.45/10.74 | (1380) sum(n4, all_0_1_1) = all_0_0_0
% 32.45/10.74 |
% 32.45/10.74 | From (1378) and (8217) follows:
% 32.45/10.74 | (8221) sum(n5, n4) = all_0_2_2
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (388) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 32.45/10.74 | (1382) all_0_5_5 = n5
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (619) with n5, n4, all_0_2_2, n9 and discharging atoms sum(n5, n4) = all_0_2_2, sum(n5, n4) = n9, yields:
% 32.45/10.74 | (907) all_0_2_2 = n9
% 32.45/10.74 |
% 32.45/10.74 | From (907) and (473) follows:
% 32.45/10.74 | (909) pred(n9) = all_0_1_1
% 32.45/10.74 |
% 32.45/10.74 | From (1382) and (8216) follows:
% 32.45/10.74 | (8225) sum(n5, n5) = all_0_4_4
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (244) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 32.45/10.74 | (912) all_0_1_1 = n8
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (619) with n5, n5, all_0_4_4, n10 and discharging atoms sum(n5, n5) = all_0_4_4, sum(n5, n5) = n10, yields:
% 32.45/10.74 | (908) all_0_4_4 = n10
% 32.45/10.74 |
% 32.45/10.74 | From (908) and (716) follows:
% 32.45/10.74 | (910) pred(n10) = all_0_3_3
% 32.45/10.74 |
% 32.45/10.74 | From (912) and (1380) follows:
% 32.45/10.74 | (8229) sum(n4, n8) = all_0_0_0
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (244) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 32.45/10.74 | (911) all_0_3_3 = n9
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (619) with n4, n8, all_0_0_0, n12 and discharging atoms sum(n4, n8) = all_0_0_0, sum(n4, n8) = n12, yields:
% 32.45/10.74 | (830) all_0_0_0 = n12
% 32.45/10.74 |
% 32.45/10.74 | From (911)(830) and (232) follows:
% 32.45/10.74 | (8232) sum(n9, n12) = all_0_6_6
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (619) with n9, n12, all_0_6_6, n0 and discharging atoms sum(n9, n12) = all_0_6_6, sum(n9, n12) = n0, yields:
% 32.45/10.74 | (1053) all_0_6_6 = n0
% 32.45/10.74 |
% 32.45/10.74 | Equations (1053) can reduce 676 to:
% 32.45/10.74 | (748) $false
% 32.45/10.74 |
% 32.45/10.74 |-The branch is then unsatisfiable
% 32.45/10.74 |-Branch two:
% 32.45/10.74 | (1395) ~ (all_0_7_7 = n4)
% 32.45/10.74 | (1396) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.45/10.74 |
% 32.45/10.74 +-Applying beta-rule and splitting (1396), into two cases.
% 32.45/10.74 |-Branch one:
% 32.45/10.74 | (1397) all_0_7_7 = n3
% 32.45/10.74 |
% 32.45/10.74 | From (1397) and (683) follows:
% 32.45/10.74 | (1398) succ(n3) = all_0_5_5
% 32.45/10.74 |
% 32.45/10.74 | From (1397) and (8) follows:
% 32.45/10.74 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 32.45/10.74 |
% 32.45/10.74 | From (1397) and (8217) follows:
% 32.45/10.74 | (8240) sum(n5, n3) = all_0_2_2
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 32.45/10.74 | (1401) all_0_5_5 = n4
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (619) with n5, n3, all_0_2_2, n8 and discharging atoms sum(n5, n3) = all_0_2_2, sum(n5, n3) = n8, yields:
% 32.45/10.74 | (924) all_0_2_2 = n8
% 32.45/10.74 |
% 32.45/10.74 | From (924) and (473) follows:
% 32.45/10.74 | (926) pred(n8) = all_0_1_1
% 32.45/10.74 |
% 32.45/10.74 | From (1401) and (8216) follows:
% 32.45/10.74 | (8244) sum(n5, n4) = all_0_4_4
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 32.45/10.74 | (929) all_0_1_1 = n7
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (619) with n5, n4, all_0_4_4, n9 and discharging atoms sum(n5, n4) = all_0_4_4, sum(n5, n4) = n9, yields:
% 32.45/10.74 | (925) all_0_4_4 = n9
% 32.45/10.74 |
% 32.45/10.74 | From (925) and (716) follows:
% 32.45/10.74 | (927) pred(n9) = all_0_3_3
% 32.45/10.74 |
% 32.45/10.74 | From (929) and (1399) follows:
% 32.45/10.74 | (8248) sum(n3, n7) = all_0_0_0
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 32.45/10.74 | (928) all_0_3_3 = n8
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (619) with n3, n7, all_0_0_0, n10 and discharging atoms sum(n3, n7) = all_0_0_0, sum(n3, n7) = n10, yields:
% 32.45/10.74 | (864) all_0_0_0 = n10
% 32.45/10.74 |
% 32.45/10.74 | From (928)(864) and (232) follows:
% 32.45/10.74 | (8251) sum(n8, n10) = all_0_6_6
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (619) with n8, n10, all_0_6_6, n18 and discharging atoms sum(n8, n10) = all_0_6_6, sum(n8, n10) = n18, yields:
% 32.45/10.74 | (900) all_0_6_6 = n18
% 32.45/10.74 |
% 32.45/10.74 | Equations (900) can reduce 622 to:
% 32.45/10.74 | (748) $false
% 32.45/10.74 |
% 32.45/10.74 |-The branch is then unsatisfiable
% 32.45/10.74 |-Branch two:
% 32.45/10.74 | (1414) ~ (all_0_7_7 = n3)
% 32.45/10.74 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.45/10.74 |
% 32.45/10.74 +-Applying beta-rule and splitting (1415), into two cases.
% 32.45/10.74 |-Branch one:
% 32.45/10.74 | (1416) all_0_7_7 = n2
% 32.45/10.74 |
% 32.45/10.74 | From (1416) and (683) follows:
% 32.45/10.74 | (1417) succ(n2) = all_0_5_5
% 32.45/10.74 |
% 32.45/10.74 | From (1416) and (8) follows:
% 32.45/10.74 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 32.45/10.74 |
% 32.45/10.74 | From (1416) and (8217) follows:
% 32.45/10.74 | (8259) sum(n5, n2) = all_0_2_2
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 32.45/10.74 | (1420) all_0_5_5 = n3
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (619) with n5, n2, all_0_2_2, n7 and discharging atoms sum(n5, n2) = all_0_2_2, sum(n5, n2) = n7, yields:
% 32.45/10.74 | (941) all_0_2_2 = n7
% 32.45/10.74 |
% 32.45/10.74 | From (941) and (473) follows:
% 32.45/10.74 | (943) pred(n7) = all_0_1_1
% 32.45/10.74 |
% 32.45/10.74 | From (1420) and (8216) follows:
% 32.45/10.74 | (8263) sum(n5, n3) = all_0_4_4
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 32.45/10.74 | (946) all_0_1_1 = n6
% 32.45/10.74 |
% 32.45/10.74 | Instantiating formula (619) with n5, n3, all_0_4_4, n8 and discharging atoms sum(n5, n3) = all_0_4_4, sum(n5, n3) = n8, yields:
% 32.45/10.74 | (942) all_0_4_4 = n8
% 32.45/10.74 |
% 32.45/10.74 | From (942) and (716) follows:
% 32.45/10.74 | (944) pred(n8) = all_0_3_3
% 32.45/10.74 |
% 32.45/10.74 | From (946) and (1418) follows:
% 32.45/10.75 | (8267) sum(n2, n6) = all_0_0_0
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 32.45/10.75 | (945) all_0_3_3 = n7
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (619) with n2, n6, all_0_0_0, n8 and discharging atoms sum(n2, n6) = all_0_0_0, sum(n2, n6) = n8, yields:
% 32.45/10.75 | (898) all_0_0_0 = n8
% 32.45/10.75 |
% 32.45/10.75 | From (945)(898) and (232) follows:
% 32.45/10.75 | (8270) sum(n7, n8) = all_0_6_6
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (619) with n7, n8, all_0_6_6, n15 and discharging atoms sum(n7, n8) = all_0_6_6, sum(n7, n8) = n15, yields:
% 32.45/10.75 | (747) all_0_6_6 = n15
% 32.45/10.75 |
% 32.45/10.75 | Equations (747) can reduce 456 to:
% 32.45/10.75 | (748) $false
% 32.45/10.75 |
% 32.45/10.75 |-The branch is then unsatisfiable
% 32.45/10.75 |-Branch two:
% 32.45/10.75 | (1433) ~ (all_0_7_7 = n2)
% 32.45/10.75 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 32.45/10.75 |
% 32.45/10.75 +-Applying beta-rule and splitting (1434), into two cases.
% 32.45/10.75 |-Branch one:
% 32.45/10.75 | (1435) all_0_7_7 = n1
% 32.45/10.75 |
% 32.45/10.75 | From (1435) and (683) follows:
% 32.45/10.75 | (1436) succ(n1) = all_0_5_5
% 32.45/10.75 |
% 32.45/10.75 | From (1435) and (8) follows:
% 32.45/10.75 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 32.45/10.75 |
% 32.45/10.75 | From (1435) and (8217) follows:
% 32.45/10.75 | (8278) sum(n5, n1) = all_0_2_2
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 32.45/10.75 | (1439) all_0_5_5 = n2
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (619) with n5, n1, all_0_2_2, n6 and discharging atoms sum(n5, n1) = all_0_2_2, sum(n5, n1) = n6, yields:
% 32.45/10.75 | (958) all_0_2_2 = n6
% 32.45/10.75 |
% 32.45/10.75 | From (958) and (473) follows:
% 32.45/10.75 | (960) pred(n6) = all_0_1_1
% 32.45/10.75 |
% 32.45/10.75 | From (1439) and (8216) follows:
% 32.45/10.75 | (8282) sum(n5, n2) = all_0_4_4
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 32.45/10.75 | (963) all_0_1_1 = n5
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (619) with n5, n2, all_0_4_4, n7 and discharging atoms sum(n5, n2) = all_0_4_4, sum(n5, n2) = n7, yields:
% 32.45/10.75 | (959) all_0_4_4 = n7
% 32.45/10.75 |
% 32.45/10.75 | From (959) and (716) follows:
% 32.45/10.75 | (961) pred(n7) = all_0_3_3
% 32.45/10.75 |
% 32.45/10.75 | From (963) and (1437) follows:
% 32.45/10.75 | (8286) sum(n1, n5) = all_0_0_0
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 32.45/10.75 | (962) all_0_3_3 = n6
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (619) with n1, n5, all_0_0_0, n6 and discharging atoms sum(n1, n5) = all_0_0_0, sum(n1, n5) = n6, yields:
% 32.45/10.75 | (932) all_0_0_0 = n6
% 32.45/10.75 |
% 32.45/10.75 | From (962)(932) and (232) follows:
% 32.45/10.75 | (8289) sum(n6, n6) = all_0_6_6
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (619) with n6, n6, all_0_6_6, n12 and discharging atoms sum(n6, n6) = all_0_6_6, sum(n6, n6) = n12, yields:
% 32.45/10.75 | (951) all_0_6_6 = n12
% 32.45/10.75 |
% 32.45/10.75 | Equations (951) can reduce 76 to:
% 32.45/10.75 | (748) $false
% 32.45/10.75 |
% 32.45/10.75 |-The branch is then unsatisfiable
% 32.45/10.75 |-Branch two:
% 32.45/10.75 | (1452) ~ (all_0_7_7 = n1)
% 32.45/10.75 | (1453) all_0_7_7 = n0
% 32.45/10.75 |
% 32.45/10.75 | From (1453) and (683) follows:
% 32.45/10.75 | (1454) succ(n0) = all_0_5_5
% 32.45/10.75 |
% 32.45/10.75 | From (1453) and (8) follows:
% 32.45/10.75 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 32.45/10.75 |
% 32.45/10.75 | From (1453) and (8217) follows:
% 32.45/10.75 | (8296) sum(n5, n0) = all_0_2_2
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 32.45/10.75 | (1457) all_0_5_5 = n1
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (619) with n5, n0, all_0_2_2, n5 and discharging atoms sum(n5, n0) = all_0_2_2, sum(n5, n0) = n5, yields:
% 32.45/10.75 | (975) all_0_2_2 = n5
% 32.45/10.75 |
% 32.45/10.75 | From (975) and (473) follows:
% 32.45/10.75 | (977) pred(n5) = all_0_1_1
% 32.45/10.75 |
% 32.45/10.75 | From (1457) and (8216) follows:
% 32.45/10.75 | (8300) sum(n5, n1) = all_0_4_4
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 32.45/10.75 | (980) all_0_1_1 = n4
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (619) with n5, n1, all_0_4_4, n6 and discharging atoms sum(n5, n1) = all_0_4_4, sum(n5, n1) = n6, yields:
% 32.45/10.75 | (976) all_0_4_4 = n6
% 32.45/10.75 |
% 32.45/10.75 | From (976) and (716) follows:
% 32.45/10.75 | (978) pred(n6) = all_0_3_3
% 32.45/10.75 |
% 32.45/10.75 | From (980) and (1455) follows:
% 32.45/10.75 | (8304) sum(n0, n4) = all_0_0_0
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 32.45/10.75 | (979) all_0_3_3 = n5
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (619) with n0, n4, all_0_0_0, n4 and discharging atoms sum(n0, n4) = all_0_0_0, sum(n0, n4) = n4, yields:
% 32.45/10.75 | (966) all_0_0_0 = n4
% 32.45/10.75 |
% 32.45/10.75 | From (979)(966) and (232) follows:
% 32.45/10.75 | (8307) sum(n5, n4) = all_0_6_6
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (619) with n5, n4, all_0_6_6, n9 and discharging atoms sum(n5, n4) = all_0_6_6, sum(n5, n4) = n9, yields:
% 32.45/10.75 | (798) all_0_6_6 = n9
% 32.45/10.75 |
% 32.45/10.75 | Equations (798) can reduce 593 to:
% 32.45/10.75 | (748) $false
% 32.45/10.75 |
% 32.45/10.75 |-The branch is then unsatisfiable
% 32.45/10.75 |-Branch two:
% 32.45/10.75 | (1004) ~ (all_0_8_8 = n5)
% 32.45/10.75 | (1005) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.45/10.75 |
% 32.45/10.75 +-Applying beta-rule and splitting (1377), into two cases.
% 32.45/10.75 |-Branch one:
% 32.45/10.75 | (1378) all_0_7_7 = n4
% 32.45/10.75 |
% 32.45/10.75 | From (1378) and (683) follows:
% 32.45/10.75 | (1379) succ(n4) = all_0_5_5
% 32.45/10.75 |
% 32.45/10.75 | From (1378) and (8) follows:
% 32.45/10.75 | (1380) sum(n4, all_0_1_1) = all_0_0_0
% 32.45/10.75 |
% 32.45/10.75 | From (1378) and (378) follows:
% 32.45/10.75 | (8315) sum(all_0_8_8, n4) = all_0_2_2
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (388) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 32.45/10.75 | (1382) all_0_5_5 = n5
% 32.45/10.75 |
% 32.45/10.75 | From (1382) and (708) follows:
% 32.45/10.75 | (8317) sum(all_0_8_8, n5) = all_0_4_4
% 32.45/10.75 |
% 32.45/10.75 +-Applying beta-rule and splitting (1005), into two cases.
% 32.45/10.75 |-Branch one:
% 32.45/10.75 | (1006) all_0_8_8 = n4
% 32.45/10.75 |
% 32.45/10.75 | From (1006) and (8317) follows:
% 32.45/10.75 | (8319) sum(n4, n5) = all_0_4_4
% 32.45/10.75 |
% 32.45/10.75 | From (1006) and (8315) follows:
% 32.45/10.75 | (8320) sum(n4, n4) = all_0_2_2
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (619) with n4, n5, all_0_4_4, n9 and discharging atoms sum(n4, n5) = all_0_4_4, sum(n4, n5) = n9, yields:
% 32.45/10.75 | (925) all_0_4_4 = n9
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (619) with n4, n4, all_0_2_2, n8 and discharging atoms sum(n4, n4) = all_0_2_2, sum(n4, n4) = n8, yields:
% 32.45/10.75 | (924) all_0_2_2 = n8
% 32.45/10.75 |
% 32.45/10.75 | From (924) and (473) follows:
% 32.45/10.75 | (926) pred(n8) = all_0_1_1
% 32.45/10.75 |
% 32.45/10.75 | From (925) and (716) follows:
% 32.45/10.75 | (927) pred(n9) = all_0_3_3
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (244) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 32.45/10.75 | (928) all_0_3_3 = n8
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (244) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 32.45/10.75 | (929) all_0_1_1 = n7
% 32.45/10.75 |
% 32.45/10.75 | From (928) and (232) follows:
% 32.45/10.75 | (930) sum(n8, all_0_0_0) = all_0_6_6
% 32.45/10.75 |
% 32.45/10.75 | From (929) and (1380) follows:
% 32.45/10.75 | (8328) sum(n4, n7) = all_0_0_0
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (619) with n4, n7, all_0_0_0, n11 and discharging atoms sum(n4, n7) = all_0_0_0, sum(n4, n7) = n11, yields:
% 32.45/10.75 | (847) all_0_0_0 = n11
% 32.45/10.75 |
% 32.45/10.75 | From (847) and (930) follows:
% 32.45/10.75 | (8330) sum(n8, n11) = all_0_6_6
% 32.45/10.75 |
% 32.45/10.75 | Instantiating formula (619) with n8, n11, all_0_6_6, n19 and discharging atoms sum(n8, n11) = all_0_6_6, sum(n8, n11) = n19, yields:
% 32.45/10.75 | (1070) all_0_6_6 = n19
% 32.45/10.75 |
% 32.45/10.76 | Equations (1070) can reduce 31 to:
% 32.45/10.76 | (748) $false
% 32.45/10.76 |
% 32.45/10.76 |-The branch is then unsatisfiable
% 32.45/10.76 |-Branch two:
% 32.45/10.76 | (1021) ~ (all_0_8_8 = n4)
% 32.45/10.76 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.45/10.76 |
% 32.45/10.76 +-Applying beta-rule and splitting (1022), into two cases.
% 32.45/10.76 |-Branch one:
% 32.45/10.76 | (1023) all_0_8_8 = n3
% 32.45/10.76 |
% 32.45/10.76 | From (1023) and (8317) follows:
% 32.45/10.76 | (8336) sum(n3, n5) = all_0_4_4
% 32.45/10.76 |
% 32.45/10.76 | From (1023) and (8315) follows:
% 32.45/10.76 | (8337) sum(n3, n4) = all_0_2_2
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (619) with n3, n5, all_0_4_4, n8 and discharging atoms sum(n3, n5) = all_0_4_4, sum(n3, n5) = n8, yields:
% 32.45/10.76 | (942) all_0_4_4 = n8
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (619) with n3, n4, all_0_2_2, n7 and discharging atoms sum(n3, n4) = all_0_2_2, sum(n3, n4) = n7, yields:
% 32.45/10.76 | (941) all_0_2_2 = n7
% 32.45/10.76 |
% 32.45/10.76 | From (941) and (473) follows:
% 32.45/10.76 | (943) pred(n7) = all_0_1_1
% 32.45/10.76 |
% 32.45/10.76 | From (942) and (716) follows:
% 32.45/10.76 | (944) pred(n8) = all_0_3_3
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 32.45/10.76 | (945) all_0_3_3 = n7
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 32.45/10.76 | (946) all_0_1_1 = n6
% 32.45/10.76 |
% 32.45/10.76 | From (945) and (232) follows:
% 32.45/10.76 | (947) sum(n7, all_0_0_0) = all_0_6_6
% 32.45/10.76 |
% 32.45/10.76 | From (946) and (1380) follows:
% 32.45/10.76 | (8345) sum(n4, n6) = all_0_0_0
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (619) with n4, n6, all_0_0_0, n10 and discharging atoms sum(n4, n6) = all_0_0_0, sum(n4, n6) = n10, yields:
% 32.45/10.76 | (864) all_0_0_0 = n10
% 32.45/10.76 |
% 32.45/10.76 | From (864) and (947) follows:
% 32.45/10.76 | (8347) sum(n7, n10) = all_0_6_6
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (619) with n7, n10, all_0_6_6, n17 and discharging atoms sum(n7, n10) = all_0_6_6, sum(n7, n10) = n17, yields:
% 32.45/10.76 | (1086) all_0_6_6 = n17
% 32.45/10.76 |
% 32.45/10.76 | Equations (1086) can reduce 669 to:
% 32.45/10.76 | (748) $false
% 32.45/10.76 |
% 32.45/10.76 |-The branch is then unsatisfiable
% 32.45/10.76 |-Branch two:
% 32.45/10.76 | (1038) ~ (all_0_8_8 = n3)
% 32.45/10.76 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.45/10.76 |
% 32.45/10.76 +-Applying beta-rule and splitting (1039), into two cases.
% 32.45/10.76 |-Branch one:
% 32.45/10.76 | (1040) all_0_8_8 = n2
% 32.45/10.76 |
% 32.45/10.76 | From (1040) and (8317) follows:
% 32.45/10.76 | (8353) sum(n2, n5) = all_0_4_4
% 32.45/10.76 |
% 32.45/10.76 | From (1040) and (8315) follows:
% 32.45/10.76 | (8354) sum(n2, n4) = all_0_2_2
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (619) with n2, n5, all_0_4_4, n7 and discharging atoms sum(n2, n5) = all_0_4_4, sum(n2, n5) = n7, yields:
% 32.45/10.76 | (959) all_0_4_4 = n7
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (619) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 32.45/10.76 | (958) all_0_2_2 = n6
% 32.45/10.76 |
% 32.45/10.76 | From (958) and (473) follows:
% 32.45/10.76 | (960) pred(n6) = all_0_1_1
% 32.45/10.76 |
% 32.45/10.76 | From (959) and (716) follows:
% 32.45/10.76 | (961) pred(n7) = all_0_3_3
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 32.45/10.76 | (962) all_0_3_3 = n6
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 32.45/10.76 | (963) all_0_1_1 = n5
% 32.45/10.76 |
% 32.45/10.76 | From (962) and (232) follows:
% 32.45/10.76 | (964) sum(n6, all_0_0_0) = all_0_6_6
% 32.45/10.76 |
% 32.45/10.76 | From (963) and (1380) follows:
% 32.45/10.76 | (8362) sum(n4, n5) = all_0_0_0
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (619) with n4, n5, all_0_0_0, n9 and discharging atoms sum(n4, n5) = all_0_0_0, sum(n4, n5) = n9, yields:
% 32.45/10.76 | (881) all_0_0_0 = n9
% 32.45/10.76 |
% 32.45/10.76 | From (881) and (964) follows:
% 32.45/10.76 | (8364) sum(n6, n9) = all_0_6_6
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (619) with n6, n9, all_0_6_6, n15 and discharging atoms sum(n6, n9) = all_0_6_6, sum(n6, n9) = n15, yields:
% 32.45/10.76 | (747) all_0_6_6 = n15
% 32.45/10.76 |
% 32.45/10.76 | Equations (747) can reduce 456 to:
% 32.45/10.76 | (748) $false
% 32.45/10.76 |
% 32.45/10.76 |-The branch is then unsatisfiable
% 32.45/10.76 |-Branch two:
% 32.45/10.76 | (1055) ~ (all_0_8_8 = n2)
% 32.45/10.76 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 32.45/10.76 |
% 32.45/10.76 +-Applying beta-rule and splitting (1056), into two cases.
% 32.45/10.76 |-Branch one:
% 32.45/10.76 | (1057) all_0_8_8 = n1
% 32.45/10.76 |
% 32.45/10.76 | From (1057) and (8317) follows:
% 32.45/10.76 | (8370) sum(n1, n5) = all_0_4_4
% 32.45/10.76 |
% 32.45/10.76 | From (1057) and (8315) follows:
% 32.45/10.76 | (8371) sum(n1, n4) = all_0_2_2
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (619) with n1, n5, all_0_4_4, n6 and discharging atoms sum(n1, n5) = all_0_4_4, sum(n1, n5) = n6, yields:
% 32.45/10.76 | (976) all_0_4_4 = n6
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (619) with n1, n4, all_0_2_2, n5 and discharging atoms sum(n1, n4) = all_0_2_2, sum(n1, n4) = n5, yields:
% 32.45/10.76 | (975) all_0_2_2 = n5
% 32.45/10.76 |
% 32.45/10.76 | From (975) and (473) follows:
% 32.45/10.76 | (977) pred(n5) = all_0_1_1
% 32.45/10.76 |
% 32.45/10.76 | From (976) and (716) follows:
% 32.45/10.76 | (978) pred(n6) = all_0_3_3
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 32.45/10.76 | (979) all_0_3_3 = n5
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 32.45/10.76 | (980) all_0_1_1 = n4
% 32.45/10.76 |
% 32.45/10.76 | From (979) and (232) follows:
% 32.45/10.76 | (981) sum(n5, all_0_0_0) = all_0_6_6
% 32.45/10.76 |
% 32.45/10.76 | From (980) and (1380) follows:
% 32.45/10.76 | (8379) sum(n4, n4) = all_0_0_0
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (619) with n4, n4, all_0_0_0, n8 and discharging atoms sum(n4, n4) = all_0_0_0, sum(n4, n4) = n8, yields:
% 32.45/10.76 | (898) all_0_0_0 = n8
% 32.45/10.76 |
% 32.45/10.76 | From (898) and (981) follows:
% 32.45/10.76 | (8381) sum(n5, n8) = all_0_6_6
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (619) with n5, n8, all_0_6_6, n13 and discharging atoms sum(n5, n8) = all_0_6_6, sum(n5, n8) = n13, yields:
% 32.45/10.76 | (764) all_0_6_6 = n13
% 32.45/10.76 |
% 32.45/10.76 | Equations (764) can reduce 293 to:
% 32.45/10.76 | (748) $false
% 32.45/10.76 |
% 32.45/10.76 |-The branch is then unsatisfiable
% 32.45/10.76 |-Branch two:
% 32.45/10.76 | (1072) ~ (all_0_8_8 = n1)
% 32.45/10.76 | (1073) all_0_8_8 = n0
% 32.45/10.76 |
% 32.45/10.76 | From (1073) and (8317) follows:
% 32.45/10.76 | (8386) sum(n0, n5) = all_0_4_4
% 32.45/10.76 |
% 32.45/10.76 | From (1073) and (8315) follows:
% 32.45/10.76 | (8387) sum(n0, n4) = all_0_2_2
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (619) with n0, n5, all_0_4_4, n5 and discharging atoms sum(n0, n5) = all_0_4_4, sum(n0, n5) = n5, yields:
% 32.45/10.76 | (993) all_0_4_4 = n5
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (619) with n0, n4, all_0_2_2, n4 and discharging atoms sum(n0, n4) = all_0_2_2, sum(n0, n4) = n4, yields:
% 32.45/10.76 | (992) all_0_2_2 = n4
% 32.45/10.76 |
% 32.45/10.76 | From (992) and (473) follows:
% 32.45/10.76 | (994) pred(n4) = all_0_1_1
% 32.45/10.76 |
% 32.45/10.76 | From (993) and (716) follows:
% 32.45/10.76 | (995) pred(n5) = all_0_3_3
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 32.45/10.76 | (996) all_0_3_3 = n4
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 32.45/10.76 | (997) all_0_1_1 = n3
% 32.45/10.76 |
% 32.45/10.76 | From (996) and (232) follows:
% 32.45/10.76 | (998) sum(n4, all_0_0_0) = all_0_6_6
% 32.45/10.76 |
% 32.45/10.76 | From (997) and (1380) follows:
% 32.45/10.76 | (8395) sum(n4, n3) = all_0_0_0
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (619) with n4, n3, all_0_0_0, n7 and discharging atoms sum(n4, n3) = all_0_0_0, sum(n4, n3) = n7, yields:
% 32.45/10.76 | (915) all_0_0_0 = n7
% 32.45/10.76 |
% 32.45/10.76 | From (915) and (998) follows:
% 32.45/10.76 | (8397) sum(n4, n7) = all_0_6_6
% 32.45/10.76 |
% 32.45/10.76 | Instantiating formula (619) with n4, n7, all_0_6_6, n11 and discharging atoms sum(n4, n7) = all_0_6_6, sum(n4, n7) = n11, yields:
% 32.45/10.76 | (781) all_0_6_6 = n11
% 32.45/10.76 |
% 32.45/10.76 | Equations (781) can reduce 2 to:
% 32.45/10.76 | (748) $false
% 32.45/10.76 |
% 32.45/10.76 |-The branch is then unsatisfiable
% 32.45/10.77 |-Branch two:
% 32.45/10.77 | (1395) ~ (all_0_7_7 = n4)
% 32.45/10.77 | (1396) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.45/10.77 |
% 32.45/10.77 +-Applying beta-rule and splitting (1005), into two cases.
% 32.45/10.77 |-Branch one:
% 32.45/10.77 | (1006) all_0_8_8 = n4
% 32.45/10.77 |
% 32.45/10.77 | From (1006) and (708) follows:
% 32.45/10.77 | (8403) sum(n4, all_0_5_5) = all_0_4_4
% 32.45/10.77 |
% 32.45/10.77 | From (1006) and (378) follows:
% 32.45/10.77 | (8404) sum(n4, all_0_7_7) = all_0_2_2
% 32.45/10.77 |
% 32.45/10.77 +-Applying beta-rule and splitting (1396), into two cases.
% 32.45/10.77 |-Branch one:
% 32.45/10.77 | (1397) all_0_7_7 = n3
% 32.45/10.77 |
% 32.45/10.77 | From (1397) and (683) follows:
% 32.45/10.77 | (1398) succ(n3) = all_0_5_5
% 32.45/10.77 |
% 32.45/10.77 | From (1397) and (8) follows:
% 32.45/10.77 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 32.45/10.77 |
% 32.45/10.77 | From (1397) and (8404) follows:
% 32.45/10.77 | (8408) sum(n4, n3) = all_0_2_2
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 32.45/10.77 | (1401) all_0_5_5 = n4
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (619) with n4, n3, all_0_2_2, n7 and discharging atoms sum(n4, n3) = all_0_2_2, sum(n4, n3) = n7, yields:
% 32.45/10.77 | (941) all_0_2_2 = n7
% 32.45/10.77 |
% 32.45/10.77 | From (941) and (473) follows:
% 32.45/10.77 | (943) pred(n7) = all_0_1_1
% 32.45/10.77 |
% 32.45/10.77 | From (1401) and (8403) follows:
% 32.45/10.77 | (8412) sum(n4, n4) = all_0_4_4
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (244) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 32.45/10.77 | (946) all_0_1_1 = n6
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (619) with n4, n4, all_0_4_4, n8 and discharging atoms sum(n4, n4) = all_0_4_4, sum(n4, n4) = n8, yields:
% 32.45/10.77 | (942) all_0_4_4 = n8
% 32.45/10.77 |
% 32.45/10.77 | From (942) and (716) follows:
% 32.45/10.77 | (944) pred(n8) = all_0_3_3
% 32.45/10.77 |
% 32.45/10.77 | From (946) and (1399) follows:
% 32.45/10.77 | (8416) sum(n3, n6) = all_0_0_0
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (244) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 32.45/10.77 | (945) all_0_3_3 = n7
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (619) with n3, n6, all_0_0_0, n9 and discharging atoms sum(n3, n6) = all_0_0_0, sum(n3, n6) = n9, yields:
% 32.45/10.77 | (881) all_0_0_0 = n9
% 32.45/10.77 |
% 32.45/10.77 | From (945)(881) and (232) follows:
% 32.45/10.77 | (8419) sum(n7, n9) = all_0_6_6
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (619) with n7, n9, all_0_6_6, n16 and discharging atoms sum(n7, n9) = all_0_6_6, sum(n7, n9) = n16, yields:
% 32.45/10.77 | (917) all_0_6_6 = n16
% 32.45/10.77 |
% 32.45/10.77 | Equations (917) can reduce 163 to:
% 32.45/10.77 | (748) $false
% 32.45/10.77 |
% 32.45/10.77 |-The branch is then unsatisfiable
% 32.45/10.77 |-Branch two:
% 32.45/10.77 | (1414) ~ (all_0_7_7 = n3)
% 32.45/10.77 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.45/10.77 |
% 32.45/10.77 +-Applying beta-rule and splitting (1415), into two cases.
% 32.45/10.77 |-Branch one:
% 32.45/10.77 | (1416) all_0_7_7 = n2
% 32.45/10.77 |
% 32.45/10.77 | From (1416) and (683) follows:
% 32.45/10.77 | (1417) succ(n2) = all_0_5_5
% 32.45/10.77 |
% 32.45/10.77 | From (1416) and (8) follows:
% 32.45/10.77 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 32.45/10.77 |
% 32.45/10.77 | From (1416) and (8404) follows:
% 32.45/10.77 | (8427) sum(n4, n2) = all_0_2_2
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 32.45/10.77 | (1420) all_0_5_5 = n3
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (619) with n4, n2, all_0_2_2, n6 and discharging atoms sum(n4, n2) = all_0_2_2, sum(n4, n2) = n6, yields:
% 32.45/10.77 | (958) all_0_2_2 = n6
% 32.45/10.77 |
% 32.45/10.77 | From (958) and (473) follows:
% 32.45/10.77 | (960) pred(n6) = all_0_1_1
% 32.45/10.77 |
% 32.45/10.77 | From (1420) and (8403) follows:
% 32.45/10.77 | (8431) sum(n4, n3) = all_0_4_4
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 32.45/10.77 | (963) all_0_1_1 = n5
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (619) with n4, n3, all_0_4_4, n7 and discharging atoms sum(n4, n3) = all_0_4_4, sum(n4, n3) = n7, yields:
% 32.45/10.77 | (959) all_0_4_4 = n7
% 32.45/10.77 |
% 32.45/10.77 | From (959) and (716) follows:
% 32.45/10.77 | (961) pred(n7) = all_0_3_3
% 32.45/10.77 |
% 32.45/10.77 | From (963) and (1418) follows:
% 32.45/10.77 | (8435) sum(n2, n5) = all_0_0_0
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 32.45/10.77 | (962) all_0_3_3 = n6
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (619) with n2, n5, all_0_0_0, n7 and discharging atoms sum(n2, n5) = all_0_0_0, sum(n2, n5) = n7, yields:
% 32.45/10.77 | (915) all_0_0_0 = n7
% 32.45/10.77 |
% 32.45/10.77 | From (962)(915) and (232) follows:
% 32.45/10.77 | (8438) sum(n6, n7) = all_0_6_6
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (619) with n6, n7, all_0_6_6, n13 and discharging atoms sum(n6, n7) = all_0_6_6, sum(n6, n7) = n13, yields:
% 32.45/10.77 | (764) all_0_6_6 = n13
% 32.45/10.77 |
% 32.45/10.77 | Equations (764) can reduce 293 to:
% 32.45/10.77 | (748) $false
% 32.45/10.77 |
% 32.45/10.77 |-The branch is then unsatisfiable
% 32.45/10.77 |-Branch two:
% 32.45/10.77 | (1433) ~ (all_0_7_7 = n2)
% 32.45/10.77 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 32.45/10.77 |
% 32.45/10.77 +-Applying beta-rule and splitting (1434), into two cases.
% 32.45/10.77 |-Branch one:
% 32.45/10.77 | (1435) all_0_7_7 = n1
% 32.45/10.77 |
% 32.45/10.77 | From (1435) and (683) follows:
% 32.45/10.77 | (1436) succ(n1) = all_0_5_5
% 32.45/10.77 |
% 32.45/10.77 | From (1435) and (8) follows:
% 32.45/10.77 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 32.45/10.77 |
% 32.45/10.77 | From (1435) and (8404) follows:
% 32.45/10.77 | (8446) sum(n4, n1) = all_0_2_2
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 32.45/10.77 | (1439) all_0_5_5 = n2
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (619) with n4, n1, all_0_2_2, n5 and discharging atoms sum(n4, n1) = all_0_2_2, sum(n4, n1) = n5, yields:
% 32.45/10.77 | (975) all_0_2_2 = n5
% 32.45/10.77 |
% 32.45/10.77 | From (975) and (473) follows:
% 32.45/10.77 | (977) pred(n5) = all_0_1_1
% 32.45/10.77 |
% 32.45/10.77 | From (1439) and (8403) follows:
% 32.45/10.77 | (8450) sum(n4, n2) = all_0_4_4
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 32.45/10.77 | (980) all_0_1_1 = n4
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (619) with n4, n2, all_0_4_4, n6 and discharging atoms sum(n4, n2) = all_0_4_4, sum(n4, n2) = n6, yields:
% 32.45/10.77 | (976) all_0_4_4 = n6
% 32.45/10.77 |
% 32.45/10.77 | From (976) and (716) follows:
% 32.45/10.77 | (978) pred(n6) = all_0_3_3
% 32.45/10.77 |
% 32.45/10.77 | From (980) and (1437) follows:
% 32.45/10.77 | (8454) sum(n1, n4) = all_0_0_0
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 32.45/10.77 | (979) all_0_3_3 = n5
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (619) with n1, n4, all_0_0_0, n5 and discharging atoms sum(n1, n4) = all_0_0_0, sum(n1, n4) = n5, yields:
% 32.45/10.77 | (949) all_0_0_0 = n5
% 32.45/10.77 |
% 32.45/10.77 | From (979)(949) and (232) follows:
% 32.45/10.77 | (8457) sum(n5, n5) = all_0_6_6
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (619) with n5, n5, all_0_6_6, n10 and discharging atoms sum(n5, n5) = all_0_6_6, sum(n5, n5) = n10, yields:
% 32.45/10.77 | (968) all_0_6_6 = n10
% 32.45/10.77 |
% 32.45/10.77 | Equations (968) can reduce 176 to:
% 32.45/10.77 | (748) $false
% 32.45/10.77 |
% 32.45/10.77 |-The branch is then unsatisfiable
% 32.45/10.77 |-Branch two:
% 32.45/10.77 | (1452) ~ (all_0_7_7 = n1)
% 32.45/10.77 | (1453) all_0_7_7 = n0
% 32.45/10.77 |
% 32.45/10.77 | From (1453) and (683) follows:
% 32.45/10.77 | (1454) succ(n0) = all_0_5_5
% 32.45/10.77 |
% 32.45/10.77 | From (1453) and (8) follows:
% 32.45/10.77 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 32.45/10.77 |
% 32.45/10.77 | From (1453) and (8404) follows:
% 32.45/10.77 | (8464) sum(n4, n0) = all_0_2_2
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 32.45/10.77 | (1457) all_0_5_5 = n1
% 32.45/10.77 |
% 32.45/10.77 | Instantiating formula (619) with n4, n0, all_0_2_2, n4 and discharging atoms sum(n4, n0) = all_0_2_2, sum(n4, n0) = n4, yields:
% 32.45/10.77 | (992) all_0_2_2 = n4
% 32.45/10.77 |
% 32.45/10.77 | From (992) and (473) follows:
% 32.45/10.77 | (994) pred(n4) = all_0_1_1
% 32.45/10.77 |
% 32.45/10.77 | From (1457) and (8403) follows:
% 32.45/10.78 | (8468) sum(n4, n1) = all_0_4_4
% 32.45/10.78 |
% 32.45/10.78 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 32.45/10.78 | (997) all_0_1_1 = n3
% 32.45/10.78 |
% 32.45/10.78 | Instantiating formula (619) with n4, n1, all_0_4_4, n5 and discharging atoms sum(n4, n1) = all_0_4_4, sum(n4, n1) = n5, yields:
% 32.45/10.78 | (993) all_0_4_4 = n5
% 32.45/10.78 |
% 32.45/10.78 | From (993) and (716) follows:
% 32.45/10.78 | (995) pred(n5) = all_0_3_3
% 32.45/10.78 |
% 32.45/10.78 | From (997) and (1455) follows:
% 32.45/10.78 | (8472) sum(n0, n3) = all_0_0_0
% 32.45/10.78 |
% 32.45/10.78 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 32.45/10.78 | (996) all_0_3_3 = n4
% 32.45/10.78 |
% 32.45/10.78 | Instantiating formula (619) with n0, n3, all_0_0_0, n3 and discharging atoms sum(n0, n3) = all_0_0_0, sum(n0, n3) = n3, yields:
% 32.45/10.78 | (983) all_0_0_0 = n3
% 32.45/10.78 |
% 32.45/10.78 | From (996)(983) and (232) follows:
% 32.45/10.78 | (8475) sum(n4, n3) = all_0_6_6
% 32.45/10.78 |
% 32.45/10.78 | Instantiating formula (619) with n4, n3, all_0_6_6, n7 and discharging atoms sum(n4, n3) = all_0_6_6, sum(n4, n3) = n7, yields:
% 32.45/10.78 | (815) all_0_6_6 = n7
% 32.45/10.78 |
% 32.45/10.78 | Equations (815) can reduce 557 to:
% 32.45/10.78 | (748) $false
% 32.45/10.78 |
% 32.45/10.78 |-The branch is then unsatisfiable
% 32.45/10.78 |-Branch two:
% 32.45/10.78 | (1021) ~ (all_0_8_8 = n4)
% 32.45/10.78 | (1022) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.45/10.78 |
% 32.45/10.78 +-Applying beta-rule and splitting (1396), into two cases.
% 32.45/10.78 |-Branch one:
% 32.45/10.78 | (1397) all_0_7_7 = n3
% 32.45/10.78 |
% 32.45/10.78 | From (1397) and (683) follows:
% 32.45/10.78 | (1398) succ(n3) = all_0_5_5
% 32.45/10.78 |
% 32.45/10.78 | From (1397) and (8) follows:
% 32.45/10.78 | (1399) sum(n3, all_0_1_1) = all_0_0_0
% 32.45/10.78 |
% 32.45/10.78 | From (1397) and (378) follows:
% 32.56/10.78 | (8483) sum(all_0_8_8, n3) = all_0_2_2
% 32.56/10.78 |
% 32.56/10.78 | Instantiating formula (388) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 32.56/10.78 | (1401) all_0_5_5 = n4
% 32.56/10.78 |
% 32.56/10.78 | From (1401) and (708) follows:
% 32.56/10.78 | (8485) sum(all_0_8_8, n4) = all_0_4_4
% 32.56/10.78 |
% 32.56/10.78 +-Applying beta-rule and splitting (1022), into two cases.
% 32.56/10.78 |-Branch one:
% 32.56/10.78 | (1023) all_0_8_8 = n3
% 32.56/10.78 |
% 32.56/10.78 | From (1023) and (8485) follows:
% 32.56/10.78 | (8487) sum(n3, n4) = all_0_4_4
% 32.56/10.78 |
% 32.56/10.78 | From (1023) and (8483) follows:
% 32.56/10.78 | (8488) sum(n3, n3) = all_0_2_2
% 32.56/10.78 |
% 32.56/10.78 | Instantiating formula (619) with n3, n4, all_0_4_4, n7 and discharging atoms sum(n3, n4) = all_0_4_4, sum(n3, n4) = n7, yields:
% 32.56/10.78 | (959) all_0_4_4 = n7
% 32.56/10.78 |
% 32.56/10.78 | Instantiating formula (619) with n3, n3, all_0_2_2, n6 and discharging atoms sum(n3, n3) = all_0_2_2, sum(n3, n3) = n6, yields:
% 32.56/10.78 | (958) all_0_2_2 = n6
% 32.56/10.78 |
% 32.56/10.78 | From (958) and (473) follows:
% 32.56/10.78 | (960) pred(n6) = all_0_1_1
% 32.56/10.78 |
% 32.56/10.78 | From (959) and (716) follows:
% 32.56/10.78 | (961) pred(n7) = all_0_3_3
% 32.56/10.78 |
% 32.56/10.78 | Instantiating formula (244) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 32.56/10.78 | (962) all_0_3_3 = n6
% 32.56/10.78 |
% 32.56/10.78 | Instantiating formula (244) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 32.56/10.78 | (963) all_0_1_1 = n5
% 32.56/10.78 |
% 32.56/10.78 | From (962) and (232) follows:
% 32.56/10.78 | (964) sum(n6, all_0_0_0) = all_0_6_6
% 32.56/10.78 |
% 32.56/10.78 | From (963) and (1399) follows:
% 32.56/10.78 | (8496) sum(n3, n5) = all_0_0_0
% 32.56/10.78 |
% 32.56/10.78 | Instantiating formula (619) with n3, n5, all_0_0_0, n8 and discharging atoms sum(n3, n5) = all_0_0_0, sum(n3, n5) = n8, yields:
% 32.56/10.78 | (898) all_0_0_0 = n8
% 32.56/10.78 |
% 32.56/10.78 | From (898) and (964) follows:
% 32.56/10.78 | (8498) sum(n6, n8) = all_0_6_6
% 32.56/10.78 |
% 32.56/10.78 | Instantiating formula (619) with n6, n8, all_0_6_6, n14 and discharging atoms sum(n6, n8) = all_0_6_6, sum(n6, n8) = n14, yields:
% 32.57/10.78 | (934) all_0_6_6 = n14
% 32.57/10.78 |
% 32.57/10.78 | Equations (934) can reduce 353 to:
% 32.57/10.78 | (748) $false
% 32.57/10.78 |
% 32.57/10.78 |-The branch is then unsatisfiable
% 32.57/10.78 |-Branch two:
% 32.57/10.78 | (1038) ~ (all_0_8_8 = n3)
% 32.57/10.78 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.57/10.78 |
% 32.57/10.78 +-Applying beta-rule and splitting (1039), into two cases.
% 32.57/10.78 |-Branch one:
% 32.57/10.78 | (1040) all_0_8_8 = n2
% 32.57/10.78 |
% 32.57/10.78 | From (1040) and (8485) follows:
% 32.57/10.78 | (8504) sum(n2, n4) = all_0_4_4
% 32.57/10.78 |
% 32.57/10.78 | From (1040) and (8483) follows:
% 32.57/10.78 | (8505) sum(n2, n3) = all_0_2_2
% 32.57/10.78 |
% 32.57/10.78 | Instantiating formula (619) with n2, n4, all_0_4_4, n6 and discharging atoms sum(n2, n4) = all_0_4_4, sum(n2, n4) = n6, yields:
% 32.57/10.78 | (976) all_0_4_4 = n6
% 32.57/10.78 |
% 32.57/10.78 | Instantiating formula (619) with n2, n3, all_0_2_2, n5 and discharging atoms sum(n2, n3) = all_0_2_2, sum(n2, n3) = n5, yields:
% 32.57/10.78 | (975) all_0_2_2 = n5
% 32.57/10.78 |
% 32.57/10.78 | From (975) and (473) follows:
% 32.57/10.78 | (977) pred(n5) = all_0_1_1
% 32.57/10.78 |
% 32.57/10.78 | From (976) and (716) follows:
% 32.57/10.78 | (978) pred(n6) = all_0_3_3
% 32.57/10.78 |
% 32.57/10.78 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 32.57/10.78 | (979) all_0_3_3 = n5
% 32.57/10.78 |
% 32.57/10.78 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 32.57/10.78 | (980) all_0_1_1 = n4
% 32.57/10.78 |
% 32.57/10.78 | From (979) and (232) follows:
% 32.57/10.78 | (981) sum(n5, all_0_0_0) = all_0_6_6
% 32.57/10.78 |
% 32.57/10.78 | From (980) and (1399) follows:
% 32.57/10.78 | (8513) sum(n3, n4) = all_0_0_0
% 32.57/10.78 |
% 32.57/10.78 | Instantiating formula (619) with n3, n4, all_0_0_0, n7 and discharging atoms sum(n3, n4) = all_0_0_0, sum(n3, n4) = n7, yields:
% 32.57/10.78 | (915) all_0_0_0 = n7
% 32.57/10.78 |
% 32.57/10.78 | From (915) and (981) follows:
% 32.57/10.78 | (8515) sum(n5, n7) = all_0_6_6
% 32.57/10.78 |
% 32.57/10.78 | Instantiating formula (619) with n5, n7, all_0_6_6, n12 and discharging atoms sum(n5, n7) = all_0_6_6, sum(n5, n7) = n12, yields:
% 32.57/10.78 | (951) all_0_6_6 = n12
% 32.57/10.78 |
% 32.57/10.78 | Equations (951) can reduce 76 to:
% 32.57/10.78 | (748) $false
% 32.57/10.78 |
% 32.57/10.78 |-The branch is then unsatisfiable
% 32.57/10.78 |-Branch two:
% 32.57/10.78 | (1055) ~ (all_0_8_8 = n2)
% 32.57/10.78 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 32.57/10.78 |
% 32.57/10.78 +-Applying beta-rule and splitting (1056), into two cases.
% 32.57/10.78 |-Branch one:
% 32.57/10.78 | (1057) all_0_8_8 = n1
% 32.57/10.78 |
% 32.57/10.78 | From (1057) and (8485) follows:
% 32.57/10.78 | (8521) sum(n1, n4) = all_0_4_4
% 32.57/10.78 |
% 32.57/10.78 | From (1057) and (8483) follows:
% 32.57/10.78 | (8522) sum(n1, n3) = all_0_2_2
% 32.57/10.78 |
% 32.57/10.78 | Instantiating formula (619) with n1, n4, all_0_4_4, n5 and discharging atoms sum(n1, n4) = all_0_4_4, sum(n1, n4) = n5, yields:
% 32.57/10.78 | (993) all_0_4_4 = n5
% 32.57/10.78 |
% 32.57/10.78 | Instantiating formula (619) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 32.57/10.78 | (992) all_0_2_2 = n4
% 32.57/10.78 |
% 32.57/10.78 | From (992) and (473) follows:
% 32.57/10.78 | (994) pred(n4) = all_0_1_1
% 32.57/10.78 |
% 32.57/10.78 | From (993) and (716) follows:
% 32.57/10.78 | (995) pred(n5) = all_0_3_3
% 32.57/10.78 |
% 32.57/10.78 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 32.57/10.78 | (996) all_0_3_3 = n4
% 32.57/10.78 |
% 32.57/10.79 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 32.57/10.79 | (997) all_0_1_1 = n3
% 32.57/10.79 |
% 32.57/10.79 | From (996) and (232) follows:
% 32.57/10.79 | (998) sum(n4, all_0_0_0) = all_0_6_6
% 32.57/10.79 |
% 32.57/10.79 | From (997) and (1399) follows:
% 32.57/10.79 | (8530) sum(n3, n3) = all_0_0_0
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (619) with n3, n3, all_0_0_0, n6 and discharging atoms sum(n3, n3) = all_0_0_0, sum(n3, n3) = n6, yields:
% 32.57/10.79 | (932) all_0_0_0 = n6
% 32.57/10.79 |
% 32.57/10.79 | From (932) and (998) follows:
% 32.57/10.79 | (8532) sum(n4, n6) = all_0_6_6
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (619) with n4, n6, all_0_6_6, n10 and discharging atoms sum(n4, n6) = all_0_6_6, sum(n4, n6) = n10, yields:
% 32.57/10.79 | (968) all_0_6_6 = n10
% 32.57/10.79 |
% 32.57/10.79 | Equations (968) can reduce 176 to:
% 32.57/10.79 | (748) $false
% 32.57/10.79 |
% 32.57/10.79 |-The branch is then unsatisfiable
% 32.57/10.79 |-Branch two:
% 32.57/10.79 | (1072) ~ (all_0_8_8 = n1)
% 32.57/10.79 | (1073) all_0_8_8 = n0
% 32.57/10.79 |
% 32.57/10.79 | From (1073) and (8485) follows:
% 32.57/10.79 | (8537) sum(n0, n4) = all_0_4_4
% 32.57/10.79 |
% 32.57/10.79 | From (1073) and (8483) follows:
% 32.57/10.79 | (8538) sum(n0, n3) = all_0_2_2
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (619) with n0, n4, all_0_4_4, n4 and discharging atoms sum(n0, n4) = all_0_4_4, sum(n0, n4) = n4, yields:
% 32.57/10.79 | (1010) all_0_4_4 = n4
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (619) with n0, n3, all_0_2_2, n3 and discharging atoms sum(n0, n3) = all_0_2_2, sum(n0, n3) = n3, yields:
% 32.57/10.79 | (1009) all_0_2_2 = n3
% 32.57/10.79 |
% 32.57/10.79 | From (1009) and (473) follows:
% 32.57/10.79 | (1011) pred(n3) = all_0_1_1
% 32.57/10.79 |
% 32.57/10.79 | From (1010) and (716) follows:
% 32.57/10.79 | (1012) pred(n4) = all_0_3_3
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 32.57/10.79 | (1013) all_0_3_3 = n3
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 32.57/10.79 | (1014) all_0_1_1 = n2
% 32.57/10.79 |
% 32.57/10.79 | From (1013) and (232) follows:
% 32.57/10.79 | (1015) sum(n3, all_0_0_0) = all_0_6_6
% 32.57/10.79 |
% 32.57/10.79 | From (1014) and (1399) follows:
% 32.57/10.79 | (8546) sum(n3, n2) = all_0_0_0
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (619) with n3, n2, all_0_0_0, n5 and discharging atoms sum(n3, n2) = all_0_0_0, sum(n3, n2) = n5, yields:
% 32.57/10.79 | (949) all_0_0_0 = n5
% 32.57/10.79 |
% 32.57/10.79 | From (949) and (1015) follows:
% 32.57/10.79 | (8548) sum(n3, n5) = all_0_6_6
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (619) with n3, n5, all_0_6_6, n8 and discharging atoms sum(n3, n5) = all_0_6_6, sum(n3, n5) = n8, yields:
% 32.57/10.79 | (985) all_0_6_6 = n8
% 32.57/10.79 |
% 32.57/10.79 | Equations (985) can reduce 357 to:
% 32.57/10.79 | (748) $false
% 32.57/10.79 |
% 32.57/10.79 |-The branch is then unsatisfiable
% 32.57/10.79 |-Branch two:
% 32.57/10.79 | (1414) ~ (all_0_7_7 = n3)
% 32.57/10.79 | (1415) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 32.57/10.79 |
% 32.57/10.79 +-Applying beta-rule and splitting (1022), into two cases.
% 32.57/10.79 |-Branch one:
% 32.57/10.79 | (1023) all_0_8_8 = n3
% 32.57/10.79 |
% 32.57/10.79 | From (1023) and (708) follows:
% 32.57/10.79 | (8554) sum(n3, all_0_5_5) = all_0_4_4
% 32.57/10.79 |
% 32.57/10.79 | From (1023) and (378) follows:
% 32.57/10.79 | (8555) sum(n3, all_0_7_7) = all_0_2_2
% 32.57/10.79 |
% 32.57/10.79 +-Applying beta-rule and splitting (1415), into two cases.
% 32.57/10.79 |-Branch one:
% 32.57/10.79 | (1416) all_0_7_7 = n2
% 32.57/10.79 |
% 32.57/10.79 | From (1416) and (683) follows:
% 32.57/10.79 | (1417) succ(n2) = all_0_5_5
% 32.57/10.79 |
% 32.57/10.79 | From (1416) and (8) follows:
% 32.57/10.79 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 32.57/10.79 |
% 32.57/10.79 | From (1416) and (8555) follows:
% 32.57/10.79 | (8559) sum(n3, n2) = all_0_2_2
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 32.57/10.79 | (1420) all_0_5_5 = n3
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (619) with n3, n2, all_0_2_2, n5 and discharging atoms sum(n3, n2) = all_0_2_2, sum(n3, n2) = n5, yields:
% 32.57/10.79 | (975) all_0_2_2 = n5
% 32.57/10.79 |
% 32.57/10.79 | From (975) and (473) follows:
% 32.57/10.79 | (977) pred(n5) = all_0_1_1
% 32.57/10.79 |
% 32.57/10.79 | From (1420) and (8554) follows:
% 32.57/10.79 | (8563) sum(n3, n3) = all_0_4_4
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (244) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 32.57/10.79 | (980) all_0_1_1 = n4
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (619) with n3, n3, all_0_4_4, n6 and discharging atoms sum(n3, n3) = all_0_4_4, sum(n3, n3) = n6, yields:
% 32.57/10.79 | (976) all_0_4_4 = n6
% 32.57/10.79 |
% 32.57/10.79 | From (976) and (716) follows:
% 32.57/10.79 | (978) pred(n6) = all_0_3_3
% 32.57/10.79 |
% 32.57/10.79 | From (980) and (1418) follows:
% 32.57/10.79 | (8567) sum(n2, n4) = all_0_0_0
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (244) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 32.57/10.79 | (979) all_0_3_3 = n5
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (619) with n2, n4, all_0_0_0, n6 and discharging atoms sum(n2, n4) = all_0_0_0, sum(n2, n4) = n6, yields:
% 32.57/10.79 | (932) all_0_0_0 = n6
% 32.57/10.79 |
% 32.57/10.79 | From (979)(932) and (232) follows:
% 32.57/10.79 | (8570) sum(n5, n6) = all_0_6_6
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (619) with n5, n6, all_0_6_6, n11 and discharging atoms sum(n5, n6) = all_0_6_6, sum(n5, n6) = n11, yields:
% 32.57/10.79 | (781) all_0_6_6 = n11
% 32.57/10.79 |
% 32.57/10.79 | Equations (781) can reduce 2 to:
% 32.57/10.79 | (748) $false
% 32.57/10.79 |
% 32.57/10.79 |-The branch is then unsatisfiable
% 32.57/10.79 |-Branch two:
% 32.57/10.79 | (1433) ~ (all_0_7_7 = n2)
% 32.57/10.79 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 32.57/10.79 |
% 32.57/10.79 +-Applying beta-rule and splitting (1434), into two cases.
% 32.57/10.79 |-Branch one:
% 32.57/10.79 | (1435) all_0_7_7 = n1
% 32.57/10.79 |
% 32.57/10.79 | From (1435) and (683) follows:
% 32.57/10.79 | (1436) succ(n1) = all_0_5_5
% 32.57/10.79 |
% 32.57/10.79 | From (1435) and (8) follows:
% 32.57/10.79 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 32.57/10.79 |
% 32.57/10.79 | From (1435) and (8555) follows:
% 32.57/10.79 | (8578) sum(n3, n1) = all_0_2_2
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 32.57/10.79 | (1439) all_0_5_5 = n2
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (619) with n3, n1, all_0_2_2, n4 and discharging atoms sum(n3, n1) = all_0_2_2, sum(n3, n1) = n4, yields:
% 32.57/10.79 | (992) all_0_2_2 = n4
% 32.57/10.79 |
% 32.57/10.79 | From (992) and (473) follows:
% 32.57/10.79 | (994) pred(n4) = all_0_1_1
% 32.57/10.79 |
% 32.57/10.79 | From (1439) and (8554) follows:
% 32.57/10.79 | (8582) sum(n3, n2) = all_0_4_4
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 32.57/10.79 | (997) all_0_1_1 = n3
% 32.57/10.79 |
% 32.57/10.79 | Instantiating formula (619) with n3, n2, all_0_4_4, n5 and discharging atoms sum(n3, n2) = all_0_4_4, sum(n3, n2) = n5, yields:
% 32.57/10.79 | (993) all_0_4_4 = n5
% 32.57/10.79 |
% 32.57/10.79 | From (993) and (716) follows:
% 32.57/10.80 | (995) pred(n5) = all_0_3_3
% 32.57/10.80 |
% 32.57/10.80 | From (997) and (1437) follows:
% 32.57/10.80 | (8586) sum(n1, n3) = all_0_0_0
% 32.57/10.80 |
% 32.57/10.80 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 32.57/10.80 | (996) all_0_3_3 = n4
% 32.57/10.80 |
% 32.57/10.80 | Instantiating formula (619) with n1, n3, all_0_0_0, n4 and discharging atoms sum(n1, n3) = all_0_0_0, sum(n1, n3) = n4, yields:
% 32.57/10.80 | (966) all_0_0_0 = n4
% 32.57/10.80 |
% 32.57/10.80 | From (996)(966) and (232) follows:
% 32.57/10.80 | (8589) sum(n4, n4) = all_0_6_6
% 32.57/10.80 |
% 32.57/10.80 | Instantiating formula (619) with n4, n4, all_0_6_6, n8 and discharging atoms sum(n4, n4) = all_0_6_6, sum(n4, n4) = n8, yields:
% 32.57/10.80 | (985) all_0_6_6 = n8
% 32.57/10.80 |
% 32.57/10.80 | Equations (985) can reduce 357 to:
% 32.57/10.80 | (748) $false
% 32.57/10.80 |
% 32.57/10.80 |-The branch is then unsatisfiable
% 32.57/10.80 |-Branch two:
% 32.57/10.80 | (1452) ~ (all_0_7_7 = n1)
% 32.57/10.80 | (1453) all_0_7_7 = n0
% 32.57/10.80 |
% 32.57/10.80 | From (1453) and (683) follows:
% 32.57/10.80 | (1454) succ(n0) = all_0_5_5
% 32.57/10.80 |
% 32.57/10.80 | From (1453) and (8) follows:
% 32.57/10.80 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 32.57/10.80 |
% 32.57/10.80 | From (1453) and (8555) follows:
% 32.57/10.80 | (8596) sum(n3, n0) = all_0_2_2
% 32.57/10.80 |
% 32.57/10.80 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 32.57/10.80 | (1457) all_0_5_5 = n1
% 32.57/10.80 |
% 32.57/10.80 | Instantiating formula (619) with n3, n0, all_0_2_2, n3 and discharging atoms sum(n3, n0) = all_0_2_2, sum(n3, n0) = n3, yields:
% 32.57/10.80 | (1009) all_0_2_2 = n3
% 32.57/10.80 |
% 32.57/10.80 | From (1009) and (473) follows:
% 32.57/10.80 | (1011) pred(n3) = all_0_1_1
% 32.57/10.80 |
% 32.57/10.80 | From (1457) and (8554) follows:
% 32.57/10.80 | (8600) sum(n3, n1) = all_0_4_4
% 32.57/10.80 |
% 32.57/10.80 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 32.57/10.80 | (1014) all_0_1_1 = n2
% 32.57/10.80 |
% 32.57/10.80 | Instantiating formula (619) with n3, n1, all_0_4_4, n4 and discharging atoms sum(n3, n1) = all_0_4_4, sum(n3, n1) = n4, yields:
% 32.57/10.80 | (1010) all_0_4_4 = n4
% 32.57/10.80 |
% 32.57/10.80 | From (1010) and (716) follows:
% 32.57/10.80 | (1012) pred(n4) = all_0_3_3
% 32.57/10.80 |
% 32.57/10.80 | From (1014) and (1455) follows:
% 32.57/10.80 | (8604) sum(n0, n2) = all_0_0_0
% 32.57/10.80 |
% 32.57/10.80 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 32.57/10.80 | (1013) all_0_3_3 = n3
% 32.57/10.80 |
% 32.57/10.80 | Instantiating formula (619) with n0, n2, all_0_0_0, n2 and discharging atoms sum(n0, n2) = all_0_0_0, sum(n0, n2) = n2, yields:
% 32.57/10.80 | (1000) all_0_0_0 = n2
% 32.57/10.80 |
% 32.57/10.80 | From (1013)(1000) and (232) follows:
% 32.57/10.80 | (8607) sum(n3, n2) = all_0_6_6
% 32.57/10.80 |
% 32.57/10.80 | Instantiating formula (619) with n3, n2, all_0_6_6, n5 and discharging atoms sum(n3, n2) = all_0_6_6, sum(n3, n2) = n5, yields:
% 32.57/10.80 | (832) all_0_6_6 = n5
% 32.57/10.80 |
% 32.57/10.80 | Equations (832) can reduce 462 to:
% 32.57/10.80 | (748) $false
% 32.57/10.80 |
% 32.57/10.80 |-The branch is then unsatisfiable
% 32.57/10.80 |-Branch two:
% 32.57/10.80 | (1038) ~ (all_0_8_8 = n3)
% 32.57/10.80 | (1039) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 32.57/10.80 |
% 32.57/10.80 +-Applying beta-rule and splitting (1415), into two cases.
% 32.57/10.80 |-Branch one:
% 32.57/10.80 | (1416) all_0_7_7 = n2
% 32.57/10.80 |
% 32.57/10.80 | From (1416) and (683) follows:
% 32.57/10.80 | (1417) succ(n2) = all_0_5_5
% 32.57/10.80 |
% 32.57/10.80 | From (1416) and (8) follows:
% 32.57/10.80 | (1418) sum(n2, all_0_1_1) = all_0_0_0
% 32.57/10.80 |
% 32.57/10.80 | From (1416) and (378) follows:
% 32.57/10.80 | (8615) sum(all_0_8_8, n2) = all_0_2_2
% 32.57/10.80 |
% 32.57/10.80 | Instantiating formula (388) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 32.60/10.80 | (1420) all_0_5_5 = n3
% 32.60/10.80 |
% 32.60/10.80 | From (1420) and (708) follows:
% 32.60/10.80 | (8617) sum(all_0_8_8, n3) = all_0_4_4
% 32.60/10.80 |
% 32.60/10.80 +-Applying beta-rule and splitting (1039), into two cases.
% 32.60/10.80 |-Branch one:
% 32.60/10.80 | (1040) all_0_8_8 = n2
% 32.60/10.80 |
% 32.60/10.80 | From (1040) and (8617) follows:
% 32.60/10.80 | (8619) sum(n2, n3) = all_0_4_4
% 32.60/10.80 |
% 32.60/10.80 | From (1040) and (8615) follows:
% 32.60/10.80 | (8620) sum(n2, n2) = all_0_2_2
% 32.60/10.80 |
% 32.60/10.80 | Instantiating formula (619) with n2, n3, all_0_4_4, n5 and discharging atoms sum(n2, n3) = all_0_4_4, sum(n2, n3) = n5, yields:
% 32.60/10.80 | (993) all_0_4_4 = n5
% 32.60/10.80 |
% 32.60/10.80 | Instantiating formula (619) with n2, n2, all_0_2_2, n4 and discharging atoms sum(n2, n2) = all_0_2_2, sum(n2, n2) = n4, yields:
% 32.60/10.80 | (992) all_0_2_2 = n4
% 32.60/10.80 |
% 32.60/10.80 | From (992) and (473) follows:
% 32.60/10.80 | (994) pred(n4) = all_0_1_1
% 32.60/10.80 |
% 32.60/10.80 | From (993) and (716) follows:
% 32.60/10.80 | (995) pred(n5) = all_0_3_3
% 32.60/10.80 |
% 32.60/10.80 | From (993) and (8619) follows:
% 32.60/10.80 | (705) sum(n2, n3) = n5
% 32.60/10.80 |
% 32.60/10.80 | Instantiating formula (244) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 32.60/10.80 | (996) all_0_3_3 = n4
% 32.60/10.80 |
% 32.60/10.80 | Instantiating formula (244) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 32.60/10.80 | (997) all_0_1_1 = n3
% 32.60/10.80 |
% 32.60/10.80 | From (996) and (232) follows:
% 32.60/10.80 | (998) sum(n4, all_0_0_0) = all_0_6_6
% 32.60/10.80 |
% 32.60/10.80 | From (997) and (1418) follows:
% 32.60/10.80 | (8629) sum(n2, n3) = all_0_0_0
% 32.60/10.80 |
% 32.60/10.80 | Instantiating formula (619) with n2, n3, all_0_0_0, n5 and discharging atoms sum(n2, n3) = all_0_0_0, sum(n2, n3) = n5, yields:
% 32.60/10.80 | (949) all_0_0_0 = n5
% 32.60/10.80 |
% 32.60/10.80 | From (949) and (998) follows:
% 32.60/10.80 | (8631) sum(n4, n5) = all_0_6_6
% 32.60/10.80 |
% 32.60/10.80 | Instantiating formula (619) with n4, n5, all_0_6_6, n9 and discharging atoms sum(n4, n5) = all_0_6_6, sum(n4, n5) = n9, yields:
% 32.60/10.80 | (798) all_0_6_6 = n9
% 32.60/10.80 |
% 32.60/10.80 | Equations (798) can reduce 593 to:
% 32.60/10.80 | (748) $false
% 32.60/10.80 |
% 32.60/10.80 |-The branch is then unsatisfiable
% 32.60/10.80 |-Branch two:
% 32.60/10.80 | (1055) ~ (all_0_8_8 = n2)
% 32.60/10.80 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 32.60/10.80 |
% 32.60/10.80 +-Applying beta-rule and splitting (1056), into two cases.
% 32.60/10.80 |-Branch one:
% 32.60/10.80 | (1057) all_0_8_8 = n1
% 32.60/10.80 |
% 32.60/10.80 | From (1057) and (8617) follows:
% 32.60/10.80 | (8637) sum(n1, n3) = all_0_4_4
% 32.60/10.80 |
% 32.60/10.80 | From (1057) and (8615) follows:
% 32.60/10.80 | (8638) sum(n1, n2) = all_0_2_2
% 32.60/10.80 |
% 32.60/10.80 | Instantiating formula (619) with n1, n3, all_0_4_4, n4 and discharging atoms sum(n1, n3) = all_0_4_4, sum(n1, n3) = n4, yields:
% 32.60/10.81 | (1010) all_0_4_4 = n4
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (619) with n1, n2, all_0_2_2, n3 and discharging atoms sum(n1, n2) = all_0_2_2, sum(n1, n2) = n3, yields:
% 32.60/10.81 | (1009) all_0_2_2 = n3
% 32.60/10.81 |
% 32.60/10.81 | From (1009) and (473) follows:
% 32.60/10.81 | (1011) pred(n3) = all_0_1_1
% 32.60/10.81 |
% 32.60/10.81 | From (1010) and (716) follows:
% 32.60/10.81 | (1012) pred(n4) = all_0_3_3
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 32.60/10.81 | (1013) all_0_3_3 = n3
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 32.60/10.81 | (1014) all_0_1_1 = n2
% 32.60/10.81 |
% 32.60/10.81 | From (1013) and (232) follows:
% 32.60/10.81 | (1015) sum(n3, all_0_0_0) = all_0_6_6
% 32.60/10.81 |
% 32.60/10.81 | From (1014) and (1418) follows:
% 32.60/10.81 | (8646) sum(n2, n2) = all_0_0_0
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (619) with n2, n2, all_0_0_0, n4 and discharging atoms sum(n2, n2) = all_0_0_0, sum(n2, n2) = n4, yields:
% 32.60/10.81 | (966) all_0_0_0 = n4
% 32.60/10.81 |
% 32.60/10.81 | From (966) and (1015) follows:
% 32.60/10.81 | (8648) sum(n3, n4) = all_0_6_6
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (619) with n3, n4, all_0_6_6, n7 and discharging atoms sum(n3, n4) = all_0_6_6, sum(n3, n4) = n7, yields:
% 32.60/10.81 | (815) all_0_6_6 = n7
% 32.60/10.81 |
% 32.60/10.81 | Equations (815) can reduce 557 to:
% 32.60/10.81 | (748) $false
% 32.60/10.81 |
% 32.60/10.81 |-The branch is then unsatisfiable
% 32.60/10.81 |-Branch two:
% 32.60/10.81 | (1072) ~ (all_0_8_8 = n1)
% 32.60/10.81 | (1073) all_0_8_8 = n0
% 32.60/10.81 |
% 32.60/10.81 | From (1073) and (8617) follows:
% 32.60/10.81 | (8653) sum(n0, n3) = all_0_4_4
% 32.60/10.81 |
% 32.60/10.81 | From (1073) and (8615) follows:
% 32.60/10.81 | (8654) sum(n0, n2) = all_0_2_2
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (619) with n0, n3, all_0_4_4, n3 and discharging atoms sum(n0, n3) = all_0_4_4, sum(n0, n3) = n3, yields:
% 32.60/10.81 | (1027) all_0_4_4 = n3
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (619) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 32.60/10.81 | (1026) all_0_2_2 = n2
% 32.60/10.81 |
% 32.60/10.81 | From (1026) and (473) follows:
% 32.60/10.81 | (1028) pred(n2) = all_0_1_1
% 32.60/10.81 |
% 32.60/10.81 | From (1027) and (716) follows:
% 32.60/10.81 | (1029) pred(n3) = all_0_3_3
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 32.60/10.81 | (1030) all_0_3_3 = n2
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 32.60/10.81 | (1031) all_0_1_1 = n1
% 32.60/10.81 |
% 32.60/10.81 | From (1030) and (232) follows:
% 32.60/10.81 | (1032) sum(n2, all_0_0_0) = all_0_6_6
% 32.60/10.81 |
% 32.60/10.81 | From (1031) and (1418) follows:
% 32.60/10.81 | (8662) sum(n2, n1) = all_0_0_0
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (619) with n2, n1, all_0_0_0, n3 and discharging atoms sum(n2, n1) = all_0_0_0, sum(n2, n1) = n3, yields:
% 32.60/10.81 | (983) all_0_0_0 = n3
% 32.60/10.81 |
% 32.60/10.81 | From (983) and (1032) follows:
% 32.60/10.81 | (8664) sum(n2, n3) = all_0_6_6
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (619) with n2, n3, all_0_6_6, n5 and discharging atoms sum(n2, n3) = all_0_6_6, sum(n2, n3) = n5, yields:
% 32.60/10.81 | (832) all_0_6_6 = n5
% 32.60/10.81 |
% 32.60/10.81 | Equations (832) can reduce 462 to:
% 32.60/10.81 | (748) $false
% 32.60/10.81 |
% 32.60/10.81 |-The branch is then unsatisfiable
% 32.60/10.81 |-Branch two:
% 32.60/10.81 | (1433) ~ (all_0_7_7 = n2)
% 32.60/10.81 | (1434) all_0_7_7 = n1 | all_0_7_7 = n0
% 32.60/10.81 |
% 32.60/10.81 +-Applying beta-rule and splitting (1039), into two cases.
% 32.60/10.81 |-Branch one:
% 32.60/10.81 | (1040) all_0_8_8 = n2
% 32.60/10.81 |
% 32.60/10.81 | From (1040) and (708) follows:
% 32.60/10.81 | (8670) sum(n2, all_0_5_5) = all_0_4_4
% 32.60/10.81 |
% 32.60/10.81 | From (1040) and (378) follows:
% 32.60/10.81 | (8671) sum(n2, all_0_7_7) = all_0_2_2
% 32.60/10.81 |
% 32.60/10.81 +-Applying beta-rule and splitting (1434), into two cases.
% 32.60/10.81 |-Branch one:
% 32.60/10.81 | (1435) all_0_7_7 = n1
% 32.60/10.81 |
% 32.60/10.81 | From (1435) and (683) follows:
% 32.60/10.81 | (1436) succ(n1) = all_0_5_5
% 32.60/10.81 |
% 32.60/10.81 | From (1435) and (8) follows:
% 32.60/10.81 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 32.60/10.81 |
% 32.60/10.81 | From (1435) and (8671) follows:
% 32.60/10.81 | (8675) sum(n2, n1) = all_0_2_2
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 32.60/10.81 | (1439) all_0_5_5 = n2
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (619) with n2, n1, all_0_2_2, n3 and discharging atoms sum(n2, n1) = all_0_2_2, sum(n2, n1) = n3, yields:
% 32.60/10.81 | (1009) all_0_2_2 = n3
% 32.60/10.81 |
% 32.60/10.81 | From (1009) and (473) follows:
% 32.60/10.81 | (1011) pred(n3) = all_0_1_1
% 32.60/10.81 |
% 32.60/10.81 | From (1439) and (8670) follows:
% 32.60/10.81 | (8679) sum(n2, n2) = all_0_4_4
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (244) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 32.60/10.81 | (1014) all_0_1_1 = n2
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (619) with n2, n2, all_0_4_4, n4 and discharging atoms sum(n2, n2) = all_0_4_4, sum(n2, n2) = n4, yields:
% 32.60/10.81 | (1010) all_0_4_4 = n4
% 32.60/10.81 |
% 32.60/10.81 | From (1010) and (716) follows:
% 32.60/10.81 | (1012) pred(n4) = all_0_3_3
% 32.60/10.81 |
% 32.60/10.81 | From (1014) and (1437) follows:
% 32.60/10.81 | (8683) sum(n1, n2) = all_0_0_0
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (244) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 32.60/10.81 | (1013) all_0_3_3 = n3
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (619) with n1, n2, all_0_0_0, n3 and discharging atoms sum(n1, n2) = all_0_0_0, sum(n1, n2) = n3, yields:
% 32.60/10.81 | (983) all_0_0_0 = n3
% 32.60/10.81 |
% 32.60/10.81 | From (1013)(983) and (232) follows:
% 32.60/10.81 | (8686) sum(n3, n3) = all_0_6_6
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (619) with n3, n3, all_0_6_6, n6 and discharging atoms sum(n3, n3) = all_0_6_6, sum(n3, n3) = n6, yields:
% 32.60/10.81 | (1002) all_0_6_6 = n6
% 32.60/10.81 |
% 32.60/10.81 | Equations (1002) can reduce 498 to:
% 32.60/10.81 | (748) $false
% 32.60/10.81 |
% 32.60/10.81 |-The branch is then unsatisfiable
% 32.60/10.81 |-Branch two:
% 32.60/10.81 | (1452) ~ (all_0_7_7 = n1)
% 32.60/10.81 | (1453) all_0_7_7 = n0
% 32.60/10.81 |
% 32.60/10.81 | From (1453) and (683) follows:
% 32.60/10.81 | (1454) succ(n0) = all_0_5_5
% 32.60/10.81 |
% 32.60/10.81 | From (1453) and (8) follows:
% 32.60/10.81 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 32.60/10.81 |
% 32.60/10.81 | From (1453) and (8671) follows:
% 32.60/10.81 | (8693) sum(n2, n0) = all_0_2_2
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 32.60/10.81 | (1457) all_0_5_5 = n1
% 32.60/10.81 |
% 32.60/10.81 | Instantiating formula (619) with n2, n0, all_0_2_2, n2 and discharging atoms sum(n2, n0) = all_0_2_2, sum(n2, n0) = n2, yields:
% 32.60/10.81 | (1026) all_0_2_2 = n2
% 32.60/10.81 |
% 32.60/10.81 | From (1026) and (473) follows:
% 32.60/10.81 | (1028) pred(n2) = all_0_1_1
% 32.60/10.81 |
% 32.60/10.81 | From (1457) and (8670) follows:
% 32.60/10.82 | (8697) sum(n2, n1) = all_0_4_4
% 32.60/10.82 |
% 32.60/10.82 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 32.60/10.82 | (1031) all_0_1_1 = n1
% 32.60/10.82 |
% 32.60/10.82 | Instantiating formula (619) with n2, n1, all_0_4_4, n3 and discharging atoms sum(n2, n1) = all_0_4_4, sum(n2, n1) = n3, yields:
% 32.60/10.82 | (1027) all_0_4_4 = n3
% 32.60/10.82 |
% 32.60/10.82 | From (1027) and (716) follows:
% 32.60/10.82 | (1029) pred(n3) = all_0_3_3
% 32.60/10.82 |
% 32.60/10.82 | From (1027) and (8697) follows:
% 32.60/10.82 | (582) sum(n2, n1) = n3
% 32.60/10.82 |
% 32.60/10.82 | From (1031) and (1455) follows:
% 32.60/10.82 | (8702) sum(n0, n1) = all_0_0_0
% 32.60/10.82 |
% 32.60/10.82 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 32.60/10.82 | (1030) all_0_3_3 = n2
% 32.60/10.82 |
% 32.60/10.82 | Instantiating formula (619) with n0, n1, all_0_0_0, n1 and discharging atoms sum(n0, n1) = all_0_0_0, sum(n0, n1) = n1, yields:
% 32.63/10.82 | (1017) all_0_0_0 = n1
% 32.63/10.82 |
% 32.63/10.82 | From (1030)(1017) and (232) follows:
% 32.63/10.82 | (8705) sum(n2, n1) = all_0_6_6
% 32.63/10.82 |
% 32.63/10.82 | Instantiating formula (619) with n2, n1, all_0_6_6, n3 and discharging atoms sum(n2, n1) = all_0_6_6, sum(n2, n1) = n3, yields:
% 32.63/10.82 | (849) all_0_6_6 = n3
% 32.63/10.82 |
% 32.63/10.82 | Equations (849) can reduce 416 to:
% 32.63/10.82 | (748) $false
% 32.63/10.82 |
% 32.63/10.82 |-The branch is then unsatisfiable
% 32.63/10.82 |-Branch two:
% 32.63/10.82 | (1055) ~ (all_0_8_8 = n2)
% 32.63/10.82 | (1056) all_0_8_8 = n1 | all_0_8_8 = n0
% 32.63/10.82 |
% 32.63/10.82 +-Applying beta-rule and splitting (1434), into two cases.
% 32.63/10.82 |-Branch one:
% 32.63/10.82 | (1435) all_0_7_7 = n1
% 32.63/10.82 |
% 32.63/10.82 | From (1435) and (683) follows:
% 32.63/10.82 | (1436) succ(n1) = all_0_5_5
% 32.63/10.82 |
% 32.63/10.82 | From (1435) and (8) follows:
% 32.63/10.82 | (1437) sum(n1, all_0_1_1) = all_0_0_0
% 32.63/10.82 |
% 32.63/10.82 | From (1435) and (378) follows:
% 32.63/10.82 | (8713) sum(all_0_8_8, n1) = all_0_2_2
% 32.63/10.82 |
% 32.63/10.82 | Instantiating formula (388) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 32.63/10.82 | (1439) all_0_5_5 = n2
% 32.63/10.82 |
% 32.63/10.82 | From (1439) and (708) follows:
% 32.63/10.82 | (8715) sum(all_0_8_8, n2) = all_0_4_4
% 32.63/10.82 |
% 32.63/10.82 +-Applying beta-rule and splitting (1056), into two cases.
% 32.63/10.82 |-Branch one:
% 32.63/10.82 | (1057) all_0_8_8 = n1
% 32.63/10.82 |
% 32.63/10.82 | From (1057) and (8715) follows:
% 32.63/10.82 | (8717) sum(n1, n2) = all_0_4_4
% 32.63/10.82 |
% 32.63/10.82 | From (1057) and (8713) follows:
% 32.63/10.82 | (8718) sum(n1, n1) = all_0_2_2
% 32.63/10.82 |
% 32.63/10.82 | Instantiating formula (619) with n1, n2, all_0_4_4, n3 and discharging atoms sum(n1, n2) = all_0_4_4, sum(n1, n2) = n3, yields:
% 32.63/10.82 | (1027) all_0_4_4 = n3
% 32.63/10.82 |
% 32.63/10.82 | Instantiating formula (619) with n1, n1, all_0_2_2, n2 and discharging atoms sum(n1, n1) = all_0_2_2, sum(n1, n1) = n2, yields:
% 32.63/10.82 | (1026) all_0_2_2 = n2
% 32.63/10.82 |
% 32.63/10.82 | From (1026) and (473) follows:
% 32.63/10.82 | (1028) pred(n2) = all_0_1_1
% 32.63/10.82 |
% 32.63/10.82 | From (1027) and (716) follows:
% 32.63/10.82 | (1029) pred(n3) = all_0_3_3
% 32.63/10.82 |
% 32.63/10.82 | From (1026) and (8718) follows:
% 32.63/10.82 | (140) sum(n1, n1) = n2
% 32.63/10.82 |
% 32.63/10.82 | Instantiating formula (244) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 32.63/10.82 | (1030) all_0_3_3 = n2
% 32.63/10.82 |
% 32.63/10.82 | Instantiating formula (244) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 32.63/10.82 | (1031) all_0_1_1 = n1
% 32.63/10.82 |
% 32.63/10.82 | From (1030) and (232) follows:
% 32.63/10.82 | (1032) sum(n2, all_0_0_0) = all_0_6_6
% 32.63/10.82 |
% 32.63/10.82 | From (1031) and (1437) follows:
% 32.63/10.82 | (8727) sum(n1, n1) = all_0_0_0
% 32.63/10.82 |
% 32.63/10.82 | Instantiating formula (619) with n1, n1, all_0_0_0, n2 and discharging atoms sum(n1, n1) = all_0_0_0, sum(n1, n1) = n2, yields:
% 32.63/10.82 | (1000) all_0_0_0 = n2
% 32.63/10.82 |
% 32.63/10.82 | From (1000) and (1032) follows:
% 32.63/10.82 | (8729) sum(n2, n2) = all_0_6_6
% 32.63/10.82 |
% 32.63/10.82 | Instantiating formula (619) with n2, n2, all_0_6_6, n4 and discharging atoms sum(n2, n2) = all_0_6_6, sum(n2, n2) = n4, yields:
% 32.63/10.82 | (1019) all_0_6_6 = n4
% 32.63/10.82 |
% 32.63/10.82 | Equations (1019) can reduce 48 to:
% 32.63/10.82 | (748) $false
% 32.63/10.82 |
% 32.63/10.82 |-The branch is then unsatisfiable
% 32.63/10.82 |-Branch two:
% 32.63/10.82 | (1072) ~ (all_0_8_8 = n1)
% 32.63/10.82 | (1073) all_0_8_8 = n0
% 32.63/10.82 |
% 32.63/10.82 | From (1073) and (8715) follows:
% 32.63/10.82 | (8734) sum(n0, n2) = all_0_4_4
% 32.63/10.82 |
% 32.63/10.82 | From (1073) and (8713) follows:
% 32.63/10.82 | (8735) sum(n0, n1) = all_0_2_2
% 32.63/10.82 |
% 32.63/10.82 | Instantiating formula (619) with n0, n2, all_0_4_4, n2 and discharging atoms sum(n0, n2) = all_0_4_4, sum(n0, n2) = n2, yields:
% 32.63/10.82 | (1044) all_0_4_4 = n2
% 32.63/10.82 |
% 32.63/10.82 | Instantiating formula (619) with n0, n1, all_0_2_2, n1 and discharging atoms sum(n0, n1) = all_0_2_2, sum(n0, n1) = n1, yields:
% 32.63/10.82 | (1043) all_0_2_2 = n1
% 32.63/10.82 |
% 32.63/10.82 | From (1043) and (473) follows:
% 32.63/10.82 | (1045) pred(n1) = all_0_1_1
% 32.63/10.82 |
% 32.63/10.82 | From (1044) and (716) follows:
% 32.63/10.82 | (1046) pred(n2) = all_0_3_3
% 32.63/10.82 |
% 32.63/10.82 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 32.63/10.82 | (1047) all_0_3_3 = n1
% 32.63/10.82 |
% 32.63/10.82 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 32.63/10.82 | (1048) all_0_1_1 = n0
% 32.63/10.82 |
% 32.63/10.82 | From (1047) and (232) follows:
% 32.63/10.82 | (1049) sum(n1, all_0_0_0) = all_0_6_6
% 32.63/10.82 |
% 32.63/10.82 | From (1048) and (1437) follows:
% 32.63/10.82 | (8743) sum(n1, n0) = all_0_0_0
% 32.63/10.82 |
% 32.63/10.82 | Instantiating formula (619) with n1, n0, all_0_0_0, n1 and discharging atoms sum(n1, n0) = all_0_0_0, sum(n1, n0) = n1, yields:
% 32.63/10.82 | (1017) all_0_0_0 = n1
% 32.63/10.82 |
% 32.63/10.82 | From (1017) and (1049) follows:
% 32.63/10.82 | (8745) sum(n1, n1) = all_0_6_6
% 32.63/10.82 |
% 32.63/10.82 | Instantiating formula (619) with n1, n1, all_0_6_6, n2 and discharging atoms sum(n1, n1) = all_0_6_6, sum(n1, n1) = n2, yields:
% 32.63/10.82 | (1036) all_0_6_6 = n2
% 32.63/10.82 |
% 32.63/10.82 | Equations (1036) can reduce 56 to:
% 32.63/10.82 | (748) $false
% 32.63/10.82 |
% 32.63/10.82 |-The branch is then unsatisfiable
% 32.63/10.82 |-Branch two:
% 32.63/10.82 | (1452) ~ (all_0_7_7 = n1)
% 32.63/10.82 | (1453) all_0_7_7 = n0
% 32.63/10.82 |
% 32.63/10.82 | From (1453) and (683) follows:
% 32.63/10.82 | (1454) succ(n0) = all_0_5_5
% 32.63/10.82 |
% 32.63/10.82 | From (1453) and (8) follows:
% 32.63/10.82 | (1455) sum(n0, all_0_1_1) = all_0_0_0
% 32.63/10.82 |
% 32.63/10.82 | From (1453) and (378) follows:
% 32.63/10.82 | (8752) sum(all_0_8_8, n0) = all_0_2_2
% 32.63/10.82 |
% 32.63/10.82 | Instantiating formula (388) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 32.63/10.82 | (1457) all_0_5_5 = n1
% 32.63/10.82 |
% 32.63/10.82 | From (1457) and (708) follows:
% 32.63/10.83 | (8754) sum(all_0_8_8, n1) = all_0_4_4
% 32.63/10.83 |
% 32.63/10.83 +-Applying beta-rule and splitting (1056), into two cases.
% 32.63/10.83 |-Branch one:
% 32.63/10.83 | (1057) all_0_8_8 = n1
% 32.63/10.83 |
% 32.63/10.83 | From (1057) and (8754) follows:
% 32.63/10.83 | (8756) sum(n1, n1) = all_0_4_4
% 32.63/10.83 |
% 32.63/10.83 | From (1057) and (8752) follows:
% 32.63/10.83 | (8757) sum(n1, n0) = all_0_2_2
% 32.63/10.83 |
% 32.63/10.83 | Instantiating formula (619) with n1, n1, all_0_4_4, n2 and discharging atoms sum(n1, n1) = all_0_4_4, sum(n1, n1) = n2, yields:
% 32.63/10.83 | (1044) all_0_4_4 = n2
% 32.63/10.83 |
% 32.63/10.83 | Instantiating formula (619) with n1, n0, all_0_2_2, n1 and discharging atoms sum(n1, n0) = all_0_2_2, sum(n1, n0) = n1, yields:
% 32.63/10.83 | (1043) all_0_2_2 = n1
% 32.63/10.83 |
% 32.63/10.83 | From (1043) and (473) follows:
% 32.63/10.83 | (1045) pred(n1) = all_0_1_1
% 32.63/10.83 |
% 32.63/10.83 | From (1044) and (716) follows:
% 32.63/10.83 | (1046) pred(n2) = all_0_3_3
% 32.63/10.83 |
% 32.63/10.83 | From (1043) and (8757) follows:
% 32.63/10.83 | (658) sum(n1, n0) = n1
% 32.63/10.83 |
% 32.63/10.83 | Instantiating formula (244) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 32.63/10.83 | (1047) all_0_3_3 = n1
% 32.63/10.83 |
% 32.63/10.83 | Instantiating formula (244) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 32.63/10.83 | (1048) all_0_1_1 = n0
% 32.63/10.83 |
% 32.63/10.83 | From (1047) and (232) follows:
% 32.63/10.83 | (1049) sum(n1, all_0_0_0) = all_0_6_6
% 32.63/10.83 |
% 32.63/10.83 | From (1048) and (1455) follows:
% 32.63/10.83 | (8766) sum(n0, n0) = all_0_0_0
% 32.63/10.83 |
% 32.63/10.83 | Instantiating formula (619) with n0, n0, all_0_0_0, n0 and discharging atoms sum(n0, n0) = all_0_0_0, sum(n0, n0) = n0, yields:
% 32.63/10.83 | (1034) all_0_0_0 = n0
% 32.63/10.83 |
% 32.63/10.83 | From (1034) and (1049) follows:
% 32.63/10.83 | (8768) sum(n1, n0) = all_0_6_6
% 32.63/10.83 |
% 32.63/10.83 | Instantiating formula (619) with n1, n0, all_0_6_6, n1 and discharging atoms sum(n1, n0) = all_0_6_6, sum(n1, n0) = n1, yields:
% 32.63/10.83 | (866) all_0_6_6 = n1
% 32.63/10.83 |
% 32.63/10.83 | Equations (866) can reduce 28 to:
% 32.63/10.83 | (748) $false
% 32.63/10.83 |
% 32.63/10.83 |-The branch is then unsatisfiable
% 32.63/10.83 |-Branch two:
% 32.63/10.83 | (1072) ~ (all_0_8_8 = n1)
% 32.63/10.83 | (1073) all_0_8_8 = n0
% 32.63/10.83 |
% 32.63/10.83 | From (1073) and (8754) follows:
% 32.63/10.83 | (8773) sum(n0, n1) = all_0_4_4
% 32.63/10.83 |
% 32.63/10.83 | From (1073) and (8752) follows:
% 32.63/10.83 | (8774) sum(n0, n0) = all_0_2_2
% 32.63/10.83 |
% 32.63/10.83 | Instantiating formula (619) with n0, n1, all_0_4_4, n1 and discharging atoms sum(n0, n1) = all_0_4_4, sum(n0, n1) = n1, yields:
% 32.63/10.83 | (1061) all_0_4_4 = n1
% 32.63/10.83 |
% 32.63/10.83 | Instantiating formula (619) with n0, n0, all_0_2_2, n0 and discharging atoms sum(n0, n0) = all_0_2_2, sum(n0, n0) = n0, yields:
% 32.63/10.83 | (1060) all_0_2_2 = n0
% 32.63/10.83 |
% 32.63/10.83 | From (1060) and (473) follows:
% 32.63/10.83 | (1062) pred(n0) = all_0_1_1
% 32.63/10.83 |
% 32.63/10.83 | From (1061) and (716) follows:
% 32.63/10.83 | (1063) pred(n1) = all_0_3_3
% 32.63/10.83 |
% 32.63/10.83 | Instantiating formula (244) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 32.63/10.83 | (1064) all_0_3_3 = n0
% 32.63/10.83 |
% 32.63/10.83 | Instantiating formula (244) with n0, all_0_1_1, n20 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n20, yields:
% 32.63/10.83 | (1065) all_0_1_1 = n20
% 32.63/10.83 |
% 32.63/10.83 | From (1064) and (232) follows:
% 32.63/10.83 | (1066) sum(n0, all_0_0_0) = all_0_6_6
% 32.63/10.83 |
% 32.63/10.83 | From (1065) and (1455) follows:
% 32.63/10.83 | (8782) sum(n0, n20) = all_0_0_0
% 32.63/10.83 |
% 32.63/10.83 | Instantiating formula (619) with n0, n20, all_0_0_0, n20 and discharging atoms sum(n0, n20) = all_0_0_0, sum(n0, n20) = n20, yields:
% 32.63/10.83 | (1051) all_0_0_0 = n20
% 32.63/10.83 |
% 32.63/10.83 | From (1051) and (1066) follows:
% 32.63/10.83 | (8784) sum(n0, n20) = all_0_6_6
% 32.63/10.83 |
% 32.63/10.83 | From (1051) and (8782) follows:
% 32.63/10.83 | (575) sum(n0, n20) = n20
% 32.63/10.83 |
% 32.63/10.83 | Instantiating formula (619) with n0, n20, all_0_6_6, n20 and discharging atoms sum(n0, n20) = all_0_6_6, sum(n0, n20) = n20, yields:
% 32.63/10.83 | (883) all_0_6_6 = n20
% 32.63/10.83 |
% 32.63/10.83 | Equations (883) can reduce 381 to:
% 32.63/10.83 | (748) $false
% 32.63/10.83 |
% 32.63/10.83 |-The branch is then unsatisfiable
% 32.63/10.83 % SZS output end Proof for theBenchmark
% 32.63/10.83
% 32.63/10.83 10224ms
%------------------------------------------------------------------------------