TSTP Solution File: NUM376+1.020 by ePrincess---1.0
View Problem
- Process Solution
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% File : ePrincess---1.0
% Problem : NUM376+1.020 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n009.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 08:43:47 EDT 2022
% Result : Unsatisfiable 12.40s 4.04s
% Output : Proof 31.97s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM376+1.020 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jul 6 22:07:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.63/0.64 ____ _
% 0.63/0.64 ___ / __ \_____(_)___ ________ __________
% 0.63/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.64
% 0.63/0.64 A Theorem Prover for First-Order Logic
% 0.63/0.64 (ePrincess v.1.0)
% 0.63/0.64
% 0.63/0.64 (c) Philipp Rümmer, 2009-2015
% 0.63/0.64 (c) Peter Backeman, 2014-2015
% 0.63/0.64 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.64 Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.64 Bug reports to peter@backeman.se
% 0.63/0.64
% 0.63/0.64 For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.64
% 0.63/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.80/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.54/1.21 Prover 0: Preprocessing ...
% 4.36/1.59 Prover 0: Constructing countermodel ...
% 12.40/4.04 Prover 0: proved (3351ms)
% 12.40/4.04
% 12.40/4.04 No countermodel exists, formula is valid
% 12.40/4.04 % SZS status Unsatisfiable for theBenchmark
% 12.40/4.04
% 12.40/4.04 Generating proof ... found it (size 8072)
% 27.19/8.96
% 27.19/8.96 % SZS output start Proof for theBenchmark
% 27.19/8.97 Assumed formulas after preprocessing and simplification:
% 27.19/8.97 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = v8) & ~ (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) & pred(v1) = v5 & pred(v0) = v2 & 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 & succ(v1) = v3 & succ(v0) = v6 & 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 & sum(v9, v10) = v11 & sum(v5, v6) = v7 & sum(v5, v3) = v10 & sum(v4, v7) = v8 & sum(v2, v6) = v9 & sum(v2, v3) = v4 & 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 & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (sum(v15, v14) = v13) | ~ (sum(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (pred(v14) = v13) | ~ (pred(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (succ(v14) = v13) | ~ (succ(v14) = v12)) & (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))
% 27.31/9.06 | 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, all_0_9_9, all_0_10_10, all_0_11_11 yields:
% 27.31/9.06 | (1) ~ (all_0_0_0 = all_0_3_3) & ~ (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) & pred(all_0_10_10) = all_0_6_6 & pred(all_0_11_11) = all_0_9_9 & 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 & succ(all_0_10_10) = all_0_8_8 & succ(all_0_11_11) = 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 & sum(all_0_2_2, all_0_1_1) = all_0_0_0 & sum(all_0_6_6, all_0_5_5) = all_0_4_4 & sum(all_0_6_6, all_0_8_8) = all_0_1_1 & sum(all_0_7_7, all_0_4_4) = all_0_3_3 & sum(all_0_9_9, all_0_5_5) = all_0_2_2 & sum(all_0_9_9, all_0_8_8) = all_0_7_7 & 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 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & (all_0_10_10 = n20 | all_0_10_10 = n19 | all_0_10_10 = n18 | all_0_10_10 = n17 | all_0_10_10 = n16 | all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0) & (all_0_11_11 = n20 | all_0_11_11 = n19 | all_0_11_11 = n18 | all_0_11_11 = n17 | all_0_11_11 = n16 | all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0)
% 27.98/9.11 |
% 27.98/9.11 | Applying alpha-rule on (1) yields:
% 27.98/9.11 | (2) sum(n1, n4) = n5
% 27.98/9.11 | (3) sum(n14, n17) = n10
% 27.98/9.11 | (4) ~ (n20 = n18)
% 27.98/9.11 | (5) sum(n1, n6) = n7
% 27.98/9.11 | (6) sum(n19, n8) = n6
% 27.98/9.11 | (7) ~ (n15 = n3)
% 27.98/9.11 | (8) sum(n0, n10) = n10
% 27.98/9.11 | (9) ~ (n17 = n2)
% 27.98/9.11 | (10) sum(n11, n14) = n4
% 27.98/9.11 | (11) sum(n9, n10) = n19
% 27.98/9.11 | (12) ~ (n17 = n16)
% 27.98/9.11 | (13) sum(n3, n18) = n0
% 27.98/9.11 | (14) ~ (n9 = n6)
% 27.98/9.11 | (15) sum(n6, n2) = n8
% 27.98/9.11 | (16) sum(n4, n9) = n13
% 27.98/9.11 | (17) sum(n17, n2) = n19
% 27.98/9.11 | (18) ~ (n6 = n0)
% 27.98/9.11 | (19) sum(n19, n3) = n1
% 27.98/9.11 | (20) sum(n15, n9) = n3
% 27.98/9.11 | (21) sum(n5, n7) = n12
% 27.98/9.11 | (22) ~ (n12 = n1)
% 27.98/9.11 | (23) sum(n10, n13) = n2
% 27.98/9.11 | (24) ~ (n10 = n5)
% 27.98/9.11 | (25) sum(n4, n3) = n7
% 27.98/9.11 | (26) sum(n2, n4) = n6
% 27.98/9.12 | (27) sum(n3, n14) = n17
% 27.98/9.12 | (28) ~ (n10 = n8)
% 27.98/9.12 | (29) sum(n12, n19) = n10
% 27.98/9.12 | (30) sum(n12, n3) = n15
% 27.98/9.12 | (31) ~ (n15 = n0)
% 27.98/9.12 | (32) sum(n3, n7) = n10
% 27.98/9.12 | (33) sum(n2, n12) = n14
% 27.98/9.12 | (34) sum(n2, n19) = n0
% 27.98/9.12 | (35) ~ (n16 = n1)
% 27.98/9.12 | (36) sum(n19, n18) = n16
% 27.98/9.12 | (37) ~ (n10 = n2)
% 27.98/9.12 | (38) sum(n13, n8) = n0
% 27.98/9.12 | (39) sum(n1, n12) = n13
% 27.98/9.12 | (40) sum(n3, n15) = n18
% 27.98/9.12 | (41) sum(n4, n14) = n18
% 27.98/9.12 | (42) ~ (n15 = n4)
% 27.98/9.12 | (43) ~ (n17 = n10)
% 27.98/9.12 | (44) sum(n1, n1) = n2
% 27.98/9.12 | (45) ~ (n12 = n8)
% 27.98/9.12 | (46) ~ (n10 = n1)
% 27.98/9.12 | (47) ~ (n13 = n5)
% 27.98/9.12 | (48) ~ (n16 = n11)
% 27.98/9.12 | (49) sum(n15, n6) = n0
% 27.98/9.12 | (50) ~ (n17 = n11)
% 27.98/9.12 | (51) sum(n8, n2) = n10
% 27.98/9.12 | (52) ~ (n15 = n1)
% 27.98/9.12 | (53) ~ (n13 = n4)
% 27.98/9.12 | (54) sum(n6, n1) = n7
% 27.98/9.12 | (55) sum(n17, n6) = n2
% 27.98/9.12 | (56) ~ (n20 = n12)
% 27.98/9.12 | (57) pred(all_0_10_10) = all_0_6_6
% 27.98/9.12 | (58) sum(n8, n13) = n0
% 27.98/9.12 | (59) sum(n2, n14) = n16
% 27.98/9.12 | (60) ~ (n14 = n2)
% 27.98/9.12 | (61) sum(n20, n6) = n5
% 27.98/9.12 | (62) sum(n9, n13) = n1
% 27.98/9.12 | (63) sum(n4, n0) = n4
% 27.98/9.12 | (64) sum(n12, n15) = n6
% 27.98/9.12 | (65) sum(n7, n15) = n1
% 27.98/9.12 | (66) succ(n11) = n12
% 27.98/9.12 | (67) ~ (n18 = n15)
% 27.98/9.12 | (68) ~ (n12 = n5)
% 27.98/9.12 | (69) sum(n3, n11) = n14
% 27.98/9.12 | (70) sum(n17, n3) = n20
% 27.98/9.12 | (71) sum(n16, n2) = n18
% 27.98/9.12 | (72) ~ (n4 = n0)
% 27.98/9.12 | (73) sum(n20, n15) = n14
% 27.98/9.12 | (74) sum(all_0_9_9, all_0_8_8) = all_0_7_7
% 27.98/9.12 | (75) ~ (n8 = n2)
% 27.98/9.12 | (76) sum(n17, n5) = n1
% 27.98/9.12 | (77) sum(n6, n18) = n3
% 27.98/9.12 | (78) ~ (n11 = n6)
% 27.98/9.12 | (79) sum(n14, n5) = n19
% 27.98/9.12 | (80) sum(n15, n7) = n1
% 27.98/9.12 | (81) sum(n0, n2) = n2
% 27.98/9.12 | (82) sum(n19, n12) = n10
% 27.98/9.12 | (83) sum(n20, n2) = n1
% 27.98/9.12 | (84) sum(n10, n2) = n12
% 27.98/9.12 | (85) sum(all_0_2_2, all_0_1_1) = all_0_0_0
% 27.98/9.12 | (86) ~ (n8 = n0)
% 27.98/9.12 | (87) all_0_10_10 = n20 | all_0_10_10 = n19 | all_0_10_10 = n18 | all_0_10_10 = n17 | all_0_10_10 = n16 | all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 27.98/9.12 | (88) sum(n8, n12) = n20
% 27.98/9.13 | (89) sum(n19, n16) = n14
% 27.98/9.13 | (90) sum(n13, n16) = n8
% 27.98/9.13 | (91) sum(n10, n1) = n11
% 27.98/9.13 | (92) sum(n2, n2) = n4
% 27.98/9.13 | (93) sum(n16, n6) = n1
% 27.98/9.13 | (94) sum(n3, n8) = n11
% 27.98/9.13 | (95) sum(n18, n3) = n0
% 27.98/9.13 | (96) sum(n9, n12) = n0
% 27.98/9.13 | (97) sum(n8, n19) = n6
% 27.98/9.13 | (98) sum(n1, n19) = n20
% 27.98/9.13 | (99) sum(n11, n2) = n13
% 27.98/9.13 | (100) sum(n13, n2) = n15
% 27.98/9.13 | (101) sum(n5, n2) = n7
% 27.98/9.13 | (102) ~ (n20 = n7)
% 27.98/9.13 | (103) ~ (n17 = n4)
% 27.98/9.13 | (104) sum(n5, n13) = n18
% 27.98/9.13 | (105) ~ (n19 = n10)
% 27.98/9.13 | (106) sum(n9, n16) = n4
% 27.98/9.13 | (107) sum(n5, n4) = n9
% 27.98/9.13 | (108) sum(n2, n6) = n8
% 27.98/9.13 | (109) ~ (n20 = n1)
% 27.98/9.13 | (110) sum(n14, n8) = n1
% 27.98/9.13 | (111) succ(n9) = n10
% 27.98/9.13 | (112) ~ (n16 = n5)
% 27.98/9.13 | (113) ~ (n18 = n4)
% 27.98/9.13 | (114) sum(n14, n9) = n2
% 27.98/9.13 | (115) pred(n7) = n6
% 27.98/9.13 | (116) pred(n13) = n12
% 27.98/9.13 | (117) sum(n5, n3) = n8
% 27.98/9.13 | (118) sum(n6, n3) = n9
% 27.98/9.13 | (119) succ(n15) = n16
% 27.98/9.13 | (120) sum(n9, n2) = n11
% 27.98/9.13 | (121) sum(n8, n9) = n17
% 27.98/9.13 | (122) sum(n16, n13) = n8
% 27.98/9.13 | (123) sum(n2, n1) = n3
% 27.98/9.13 | (124) sum(n16, n12) = n7
% 27.98/9.13 | (125) pred(n6) = n5
% 27.98/9.13 | (126) sum(n19, n1) = n20
% 27.98/9.13 | (127) ~ (n12 = n7)
% 27.98/9.13 | (128) sum(n10, n19) = n8
% 27.98/9.13 | (129) sum(n9, n3) = n12
% 27.98/9.13 | (130) sum(n11, n15) = n5
% 27.98/9.13 | (131) sum(n18, n13) = n10
% 27.98/9.13 | (132) sum(n9, n15) = n3
% 27.98/9.13 | (133) sum(n1, n2) = n3
% 27.98/9.13 | (134) sum(n15, n20) = n14
% 27.98/9.13 | (135) sum(n16, n4) = n20
% 27.98/9.13 | (136) ~ (n13 = n10)
% 27.98/9.13 | (137) sum(n12, n7) = n19
% 27.98/9.13 | (138) sum(n15, n13) = n7
% 27.98/9.13 | (139) ~ (n8 = n1)
% 27.98/9.13 | (140) sum(n6, n8) = n14
% 27.98/9.13 | (141) pred(n8) = n7
% 27.98/9.13 | (142) sum(n0, n16) = n16
% 27.98/9.13 | (143) sum(n6, n4) = n10
% 27.98/9.13 | (144) ~ (n13 = n3)
% 27.98/9.13 | (145) sum(n9, n9) = n18
% 27.98/9.13 | (146) sum(n8, n0) = n8
% 27.98/9.13 | (147) succ(n19) = n20
% 27.98/9.13 | (148) ~ (n19 = n8)
% 27.98/9.13 | (149) sum(n7, n18) = n4
% 27.98/9.13 | (150) sum(n11, n0) = n11
% 27.98/9.13 | (151) ~ (n12 = n4)
% 27.98/9.13 | (152) sum(n5, n9) = n14
% 27.98/9.13 | (153) sum(n12, n4) = n16
% 27.98/9.13 | (154) ~ (n13 = n8)
% 27.98/9.13 | (155) sum(n10, n12) = n1
% 27.98/9.13 | (156) sum(all_0_9_9, all_0_5_5) = all_0_2_2
% 27.98/9.13 | (157) sum(n15, n17) = n11
% 27.98/9.13 | (158) ~ (n12 = n11)
% 27.98/9.13 | (159) sum(n8, n7) = n15
% 27.98/9.13 | (160) ~ (n7 = n2)
% 27.98/9.13 | (161) sum(n17, n0) = n17
% 27.98/9.13 | (162) ~ (n14 = n13)
% 27.98/9.13 | (163) sum(n14, n3) = n17
% 27.98/9.14 | (164) sum(n5, n5) = n10
% 27.98/9.14 | (165) sum(n0, n14) = n14
% 27.98/9.14 | (166) sum(n14, n11) = n4
% 27.98/9.14 | (167) ~ (n17 = n7)
% 27.98/9.14 | (168) sum(n8, n6) = n14
% 27.98/9.14 | (169) ~ (n12 = n10)
% 27.98/9.14 | (170) ~ (n20 = n6)
% 27.98/9.14 | (171) ~ (n17 = n0)
% 27.98/9.14 | (172) ~ (n3 = n0)
% 27.98/9.14 | (173) ~ (n16 = n3)
% 27.98/9.14 | (174) sum(n12, n17) = n8
% 27.98/9.14 | (175) succ(n8) = n9
% 27.98/9.14 | (176) ~ (n19 = n17)
% 27.98/9.14 | (177) sum(n10, n3) = n13
% 27.98/9.14 | (178) sum(n19, n7) = n5
% 27.98/9.14 | (179) ~ (n7 = n6)
% 27.98/9.14 | (180) sum(n15, n5) = n20
% 27.98/9.14 | (181) ~ (n11 = n7)
% 27.98/9.14 | (182) sum(n20, n13) = n12
% 27.98/9.14 | (183) sum(n3, n19) = n1
% 27.98/9.14 | (184) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0))
% 27.98/9.14 | (185) ~ (n16 = n7)
% 27.98/9.14 | (186) sum(n11, n1) = n12
% 27.98/9.14 | (187) sum(n12, n12) = n3
% 27.98/9.14 | (188) sum(n7, n2) = n9
% 27.98/9.14 | (189) ~ (n13 = n11)
% 27.98/9.14 | (190) pred(all_0_11_11) = all_0_9_9
% 27.98/9.14 | (191) ~ (n18 = n9)
% 27.98/9.14 | (192) sum(n8, n14) = n1
% 27.98/9.14 | (193) sum(n3, n6) = n9
% 27.98/9.14 | (194) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0))
% 27.98/9.14 | (195) sum(n15, n10) = n4
% 27.98/9.14 | (196) ~ (n13 = n9)
% 27.98/9.14 | (197) pred(n11) = n10
% 27.98/9.14 | (198) sum(n11, n7) = n18
% 27.98/9.14 | (199) ~ (n15 = n11)
% 27.98/9.14 | (200) sum(n5, n11) = n16
% 27.98/9.14 | (201) ~ (all_0_0_0 = all_0_3_3)
% 27.98/9.14 | (202) ~ (n10 = n4)
% 27.98/9.14 | (203) sum(n8, n4) = n12
% 27.98/9.14 | (204) ~ (n17 = n15)
% 27.98/9.14 | (205) sum(n18, n11) = n8
% 27.98/9.14 | (206) sum(n4, n5) = n9
% 27.98/9.14 | (207) sum(n19, n11) = n9
% 27.98/9.14 | (208) sum(n19, n13) = n11
% 27.98/9.14 | (209) sum(n13, n1) = n14
% 27.98/9.14 | (210) ~ (n20 = n17)
% 27.98/9.14 | (211) sum(n11, n6) = n17
% 27.98/9.14 | (212) ~ (n20 = n14)
% 27.98/9.14 | (213) ~ (n4 = n1)
% 27.98/9.14 | (214) pred(n16) = n15
% 27.98/9.14 | (215) ~ (n16 = n8)
% 27.98/9.14 | (216) ~ (n19 = n3)
% 27.98/9.14 | (217) succ(n2) = n3
% 27.98/9.14 | (218) sum(n11, n5) = n16
% 27.98/9.14 | (219) sum(n10, n5) = n15
% 27.98/9.14 | (220) sum(n12, n6) = n18
% 28.18/9.14 | (221) sum(n7, n7) = n14
% 28.18/9.14 | (222) sum(n4, n20) = n3
% 28.18/9.14 | (223) sum(n3, n16) = n19
% 28.18/9.14 | (224) sum(n18, n0) = n18
% 28.18/9.14 | (225) ~ (n18 = n16)
% 28.18/9.14 | (226) sum(n12, n9) = n0
% 28.18/9.14 | (227) sum(n18, n9) = n6
% 28.18/9.14 | (228) sum(n5, n18) = n2
% 28.18/9.14 | (229) sum(n2, n17) = n19
% 28.18/9.14 | (230) ~ (n14 = n7)
% 28.18/9.14 | (231) pred(n5) = n4
% 28.18/9.14 | (232) pred(n4) = n3
% 28.18/9.14 | (233) sum(n3, n13) = n16
% 28.18/9.14 | (234) ~ (n19 = n13)
% 28.18/9.14 | (235) sum(n7, n5) = n12
% 28.18/9.14 | (236) ~ (n14 = n1)
% 28.18/9.14 | (237) sum(n17, n13) = n9
% 28.18/9.14 | (238) sum(n16, n16) = n11
% 28.18/9.14 | (239) sum(n3, n1) = n4
% 28.18/9.14 | (240) sum(n8, n3) = n11
% 28.18/9.14 | (241) ~ (n18 = n5)
% 28.18/9.14 | (242) sum(n11, n20) = n10
% 28.18/9.14 | (243) sum(n10, n15) = n4
% 28.18/9.15 | (244) sum(n20, n1) = n0
% 28.18/9.15 | (245) sum(n9, n19) = n7
% 28.18/9.15 | (246) sum(n4, n18) = n1
% 28.18/9.15 | (247) ~ (n19 = n12)
% 28.18/9.15 | (248) ~ (n6 = n4)
% 28.18/9.15 | (249) sum(n14, n15) = n8
% 28.18/9.15 | (250) ~ (n8 = n6)
% 28.18/9.15 | (251) sum(n14, n12) = n5
% 28.18/9.15 | (252) ~ (n19 = n6)
% 28.18/9.15 | (253) sum(n13, n14) = n6
% 28.18/9.15 | (254) ~ (n5 = n4)
% 28.18/9.15 | (255) sum(n4, n15) = n19
% 28.18/9.15 | (256) sum(n18, n7) = n4
% 28.18/9.15 | (257) sum(n19, n9) = n7
% 28.18/9.15 | (258) sum(n10, n14) = n3
% 28.18/9.15 | (259) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 28.18/9.15 | (260) ~ (n7 = n1)
% 28.18/9.15 | (261) ~ (n7 = n5)
% 28.18/9.15 | (262) sum(n8, n16) = n3
% 28.18/9.15 | (263) sum(n17, n18) = n14
% 28.18/9.15 | (264) ~ (n9 = n0)
% 28.18/9.15 | (265) sum(n19, n6) = n4
% 28.18/9.15 | (266) sum(n17, n4) = n0
% 28.18/9.15 | (267) ~ (n12 = n9)
% 28.18/9.15 | (268) sum(n20, n8) = n7
% 28.18/9.15 | (269) ~ (n18 = n6)
% 28.18/9.15 | (270) sum(n18, n18) = n15
% 28.18/9.15 | (271) sum(n8, n11) = n19
% 28.18/9.15 | (272) sum(n13, n4) = n17
% 28.18/9.15 | (273) ~ (n11 = n8)
% 28.18/9.15 | (274) sum(n12, n0) = n12
% 28.18/9.15 | (275) sum(n5, n10) = n15
% 28.18/9.15 | (276) sum(n3, n10) = n13
% 28.18/9.15 | (277) sum(n7, n20) = n6
% 28.18/9.15 | (278) pred(n17) = n16
% 28.18/9.15 | (279) sum(n1, n0) = n1
% 28.18/9.15 | (280) sum(n3, n4) = n7
% 28.18/9.15 | (281) ~ (n19 = n5)
% 28.18/9.15 | (282) ~ (n15 = n2)
% 28.18/9.15 | (283) sum(n0, n18) = n18
% 28.18/9.15 | (284) sum(n0, n9) = n9
% 28.18/9.15 | (285) ~ (n12 = n2)
% 28.18/9.15 | (286) sum(n12, n11) = n2
% 28.18/9.15 | (287) sum(n18, n10) = n7
% 28.18/9.15 | (288) sum(n19, n0) = n19
% 28.18/9.15 | (289) sum(n6, n14) = n20
% 28.18/9.15 | (290) sum(n18, n4) = n1
% 28.18/9.15 | (291) ~ (n11 = n10)
% 28.18/9.15 | (292) sum(n13, n11) = n3
% 28.18/9.15 | (293) sum(n13, n5) = n18
% 28.18/9.15 | (294) sum(n14, n1) = n15
% 28.18/9.15 | (295) ~ (n20 = n16)
% 28.18/9.15 | (296) ~ (n18 = n7)
% 28.18/9.15 | (297) sum(n0, n7) = n7
% 28.18/9.15 | (298) ~ (n9 = n3)
% 28.18/9.15 | (299) sum(n3, n0) = n3
% 28.18/9.15 | (300) sum(n4, n13) = n17
% 28.18/9.15 | (301) sum(n17, n17) = n13
% 28.18/9.15 | (302) ~ (n14 = n0)
% 28.18/9.15 | (303) sum(n16, n17) = n12
% 28.18/9.15 | (304) all_0_11_11 = n20 | all_0_11_11 = n19 | all_0_11_11 = n18 | all_0_11_11 = n17 | all_0_11_11 = n16 | all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.18/9.15 | (305) sum(n11, n11) = n1
% 28.18/9.15 | (306) succ(n3) = n4
% 28.18/9.15 | (307) sum(n20, n0) = n20
% 28.18/9.15 | (308) sum(n19, n2) = n0
% 28.18/9.15 | (309) ~ (n20 = n0)
% 28.18/9.15 | (310) ~ (n13 = n12)
% 28.18/9.15 | (311) sum(n3, n9) = n12
% 28.18/9.15 | (312) sum(n4, n19) = n2
% 28.18/9.15 | (313) sum(n0, n3) = n3
% 28.18/9.15 | (314) ~ (n19 = n4)
% 28.18/9.15 | (315) sum(n14, n6) = n20
% 28.18/9.15 | (316) sum(n4, n12) = n16
% 28.18/9.15 | (317) sum(n2, n10) = n12
% 28.18/9.15 | (318) sum(n16, n11) = n6
% 28.18/9.15 | (319) sum(n13, n3) = n16
% 28.18/9.15 | (320) ~ (n5 = n2)
% 28.18/9.15 | (321) ~ (n19 = n9)
% 28.18/9.15 | (322) sum(n11, n18) = n8
% 28.18/9.15 | (323) ~ (n16 = n6)
% 28.18/9.15 | (324) pred(n9) = n8
% 28.18/9.15 | (325) sum(n16, n3) = n19
% 28.18/9.15 | (326) pred(n0) = n20
% 28.18/9.15 | (327) sum(n4, n16) = n20
% 28.18/9.15 | (328) sum(n12, n13) = n4
% 28.18/9.15 | (329) sum(n2, n20) = n1
% 28.18/9.15 | (330) ~ (n18 = n14)
% 28.18/9.15 | (331) ~ (n19 = n2)
% 28.18/9.15 | (332) sum(n7, n13) = n20
% 28.18/9.15 | (333) sum(n10, n17) = n6
% 28.18/9.15 | (334) sum(n1, n11) = n12
% 28.18/9.15 | (335) sum(n3, n2) = n5
% 28.18/9.15 | (336) sum(n6, n10) = n16
% 28.18/9.15 | (337) sum(n17, n15) = n11
% 28.18/9.15 | (338) sum(n9, n7) = n16
% 28.18/9.15 | (339) sum(n14, n16) = n9
% 28.18/9.16 | (340) ~ (n10 = n6)
% 28.18/9.16 | (341) sum(n19, n14) = n12
% 28.18/9.16 | (342) sum(n9, n5) = n14
% 28.18/9.16 | (343) sum(n12, n16) = n7
% 28.18/9.16 | (344) sum(n14, n7) = n0
% 28.18/9.16 | (345) ~ (n13 = n1)
% 28.18/9.16 | (346) ~ (n3 = n2)
% 28.18/9.16 | (347) sum(n19, n4) = n2
% 28.18/9.16 | (348) succ(n6) = n7
% 28.18/9.16 | (349) sum(n16, n10) = n5
% 28.18/9.16 | (350) sum(n2, n8) = n10
% 28.18/9.16 | (351) succ(n18) = n19
% 28.18/9.16 | (352) ~ (n18 = n1)
% 28.18/9.16 | (353) sum(n2, n0) = n2
% 28.18/9.16 | (354) sum(n18, n6) = n3
% 28.18/9.16 | (355) sum(n3, n3) = n6
% 28.18/9.16 | (356) sum(n11, n4) = n15
% 28.18/9.16 | (357) sum(n18, n19) = n16
% 28.18/9.16 | (358) ~ (n13 = n2)
% 28.18/9.16 | (359) pred(n20) = n19
% 28.18/9.16 | (360) ~ (n9 = n2)
% 28.18/9.16 | (361) sum(n5, n15) = n20
% 28.18/9.16 | (362) sum(n16, n20) = n15
% 28.18/9.16 | (363) sum(n5, n6) = n11
% 28.18/9.16 | (364) sum(n17, n12) = n8
% 28.18/9.16 | (365) ~ (n5 = n1)
% 28.18/9.16 | (366) ~ (n19 = n18)
% 28.18/9.16 | (367) succ(n20) = n0
% 28.18/9.16 | (368) ~ (n1 = n0)
% 28.18/9.16 | (369) sum(n4, n1) = n5
% 28.18/9.16 | (370) sum(n11, n10) = n0
% 28.18/9.16 | (371) sum(n8, n18) = n5
% 28.18/9.16 | (372) ~ (n3 = n1)
% 28.18/9.16 | (373) sum(n2, n15) = n17
% 28.18/9.16 | (374) ~ (n18 = n12)
% 28.18/9.16 | (375) ~ (n11 = n5)
% 28.18/9.16 | (376) sum(n5, n14) = n19
% 28.18/9.16 | (377) sum(n10, n18) = n7
% 28.18/9.16 | (378) sum(n7, n4) = n11
% 28.18/9.16 | (379) sum(n11, n17) = n7
% 28.18/9.16 | (380) ~ (n11 = n3)
% 28.18/9.16 | (381) succ(all_0_10_10) = all_0_8_8
% 28.18/9.16 | (382) ~ (n12 = n3)
% 28.18/9.16 | (383) ~ (n20 = n2)
% 28.18/9.16 | (384) ~ (n11 = n2)
% 28.18/9.16 | (385) sum(n13, n6) = n19
% 28.18/9.16 | (386) sum(all_0_6_6, all_0_5_5) = all_0_4_4
% 28.18/9.16 | (387) ~ (n8 = n5)
% 28.18/9.16 | (388) sum(n12, n14) = n5
% 28.18/9.16 | (389) sum(n12, n18) = n9
% 28.18/9.16 | (390) sum(n17, n16) = n12
% 28.18/9.16 | (391) sum(n4, n4) = n8
% 28.18/9.16 | (392) sum(n9, n14) = n2
% 28.18/9.16 | (393) sum(n8, n10) = n18
% 28.18/9.16 | (394) sum(n13, n13) = n5
% 28.18/9.16 | (395) ~ (n10 = n3)
% 28.18/9.16 | (396) ~ (n20 = n9)
% 28.18/9.16 | (397) sum(n15, n4) = n19
% 28.18/9.16 | (398) ~ (n12 = n6)
% 28.18/9.16 | (399) ~ (n20 = n13)
% 28.18/9.16 | (400) sum(n15, n16) = n10
% 28.18/9.16 | (401) ~ (n16 = n0)
% 28.18/9.16 | (402) sum(n11, n8) = n19
% 28.18/9.16 | (403) sum(n2, n9) = n11
% 28.18/9.16 | (404) sum(n0, n20) = n20
% 28.18/9.16 | (405) sum(n16, n8) = n3
% 28.18/9.16 | (406) sum(n6, n20) = n5
% 28.18/9.16 | (407) sum(n13, n15) = n7
% 28.18/9.16 | (408) ~ (n15 = n6)
% 28.18/9.16 | (409) sum(n7, n10) = n17
% 28.18/9.16 | (410) succ(n4) = n5
% 28.18/9.16 | (411) sum(n11, n3) = n14
% 28.18/9.16 | (412) succ(n13) = n14
% 28.18/9.16 | (413) ~ (n19 = n0)
% 28.18/9.16 | (414) sum(n16, n1) = n17
% 28.18/9.16 | (415) ~ (n14 = n3)
% 28.18/9.16 | (416) sum(n12, n20) = n11
% 28.18/9.16 | (417) ~ (n15 = n14)
% 28.18/9.16 | (418) sum(n15, n18) = n12
% 28.18/9.16 | (419) sum(n16, n18) = n13
% 28.18/9.16 | (420) sum(n7, n12) = n19
% 28.18/9.16 | (421) ~ (n20 = n11)
% 28.18/9.16 | (422) sum(n0, n1) = n1
% 28.18/9.16 | (423) sum(n15, n3) = n18
% 28.18/9.16 | (424) sum(n8, n5) = n13
% 28.18/9.16 | (425) sum(n20, n20) = n19
% 28.18/9.16 | (426) ~ (n12 = n0)
% 28.18/9.16 | (427) sum(n13, n7) = n20
% 28.18/9.16 | (428) sum(n0, n17) = n17
% 28.18/9.16 | (429) ~ (n14 = n5)
% 28.18/9.16 | (430) sum(n17, n20) = n16
% 28.18/9.16 | (431) ~ (n17 = n6)
% 28.18/9.16 | (432) ~ (n16 = n4)
% 28.18/9.16 | (433) sum(n7, n6) = n13
% 28.18/9.16 | (434) ~ (n15 = n9)
% 28.18/9.16 | (435) sum(all_0_7_7, all_0_4_4) = all_0_3_3
% 28.18/9.16 | (436) succ(n1) = n2
% 28.18/9.16 | (437) sum(n14, n4) = n18
% 28.18/9.16 | (438) pred(n3) = n2
% 28.18/9.16 | (439) sum(n6, n16) = n1
% 28.18/9.17 | (440) sum(n19, n17) = n15
% 28.18/9.17 | (441) ~ (n9 = n5)
% 28.18/9.17 | (442) sum(n3, n20) = n2
% 28.18/9.17 | (443) sum(n17, n9) = n5
% 28.18/9.17 | (444) sum(n14, n13) = n6
% 28.18/9.17 | (445) ~ (n11 = n0)
% 28.18/9.17 | (446) ~ (n20 = n5)
% 28.18/9.17 | (447) sum(n15, n2) = n17
% 28.18/9.17 | (448) sum(n9, n18) = n6
% 28.18/9.17 | (449) sum(n5, n19) = n3
% 28.18/9.17 | (450) sum(n14, n2) = n16
% 28.18/9.17 | (451) sum(n10, n0) = n10
% 28.18/9.17 | (452) sum(n15, n15) = n9
% 28.18/9.17 | (453) sum(n5, n1) = n6
% 28.18/9.17 | (454) sum(n12, n5) = n17
% 28.18/9.17 | (455) ~ (n13 = n0)
% 28.18/9.17 | (456) sum(n2, n5) = n7
% 28.18/9.17 | (457) sum(n9, n11) = n20
% 28.18/9.17 | (458) sum(n16, n9) = n4
% 28.18/9.17 | (459) sum(n0, n5) = n5
% 28.18/9.17 | (460) sum(n16, n7) = n2
% 28.18/9.17 | (461) sum(n7, n9) = n16
% 28.18/9.17 | (462) sum(n18, n14) = n11
% 28.18/9.17 | (463) ~ (n17 = n3)
% 28.18/9.17 | (464) ~ (n9 = n7)
% 28.18/9.17 | (465) sum(n10, n6) = n16
% 28.18/9.17 | (466) sum(n9, n1) = n10
% 28.18/9.17 | (467) ~ (n20 = n4)
% 28.18/9.17 | (468) sum(n19, n19) = n17
% 28.18/9.17 | (469) sum(n13, n20) = n12
% 28.18/9.17 | (470) sum(n1, n9) = n10
% 28.18/9.17 | (471) ~ (n15 = n8)
% 28.18/9.17 | (472) sum(n12, n8) = n20
% 28.18/9.17 | (473) pred(n10) = n9
% 28.18/9.17 | (474) sum(n15, n8) = n2
% 28.18/9.17 | (475) sum(n13, n17) = n9
% 28.18/9.17 | (476) ~ (n6 = n2)
% 28.18/9.17 | (477) ~ (n14 = n6)
% 28.18/9.17 | (478) sum(n2, n3) = n5
% 28.18/9.17 | (479) sum(n4, n8) = n12
% 28.18/9.17 | (480) sum(n1, n7) = n8
% 28.18/9.17 | (481) ~ (n13 = n6)
% 28.18/9.17 | (482) sum(n20, n19) = n18
% 28.18/9.17 | (483) sum(n4, n6) = n10
% 28.18/9.17 | (484) sum(n0, n11) = n11
% 28.18/9.17 | (485) ~ (n20 = n3)
% 28.18/9.17 | (486) sum(n15, n12) = n6
% 28.18/9.17 | (487) sum(n8, n8) = n16
% 28.18/9.17 | (488) ~ (n14 = n9)
% 28.18/9.17 | (489) ~ (n5 = n0)
% 28.18/9.17 | (490) sum(n7, n3) = n10
% 28.18/9.17 | (491) ~ (n16 = n12)
% 28.18/9.17 | (492) sum(n0, n6) = n6
% 28.18/9.17 | (493) sum(n6, n17) = n2
% 28.18/9.17 | (494) sum(n14, n14) = n7
% 28.18/9.17 | (495) ~ (n19 = n7)
% 28.18/9.17 | (496) ~ (n17 = n8)
% 28.18/9.17 | (497) sum(n18, n2) = n20
% 28.18/9.17 | (498) sum(n2, n11) = n13
% 28.18/9.17 | (499) sum(n17, n14) = n10
% 28.18/9.17 | (500) sum(n1, n3) = n4
% 28.18/9.17 | (501) ~ (n18 = n3)
% 28.18/9.17 | (502) sum(n4, n17) = n0
% 28.18/9.17 | (503) sum(n20, n3) = n2
% 28.18/9.17 | (504) pred(n1) = n0
% 28.18/9.17 | (505) succ(all_0_11_11) = all_0_5_5
% 28.18/9.17 | (506) ~ (n19 = n14)
% 28.18/9.17 | (507) sum(n9, n20) = n8
% 28.18/9.17 | (508) sum(n10, n7) = n17
% 28.18/9.17 | (509) ~ (n10 = n7)
% 28.18/9.17 | (510) sum(n1, n15) = n16
% 28.18/9.17 | (511) pred(n2) = n1
% 28.18/9.17 | (512) ~ (n7 = n0)
% 28.18/9.17 | (513) sum(n6, n11) = n17
% 28.18/9.17 | (514) ~ (n11 = n1)
% 28.18/9.17 | (515) sum(n10, n4) = n14
% 28.18/9.17 | (516) ~ (n19 = n1)
% 28.18/9.17 | (517) ~ (n16 = n10)
% 28.18/9.17 | (518) sum(n10, n9) = n19
% 28.18/9.17 | (519) ~ (n16 = n15)
% 28.18/9.17 | (520) ~ (n5 = n3)
% 28.18/9.17 | (521) sum(n5, n16) = n0
% 28.18/9.17 | (522) sum(n9, n0) = n9
% 28.18/9.17 | (523) ~ (n6 = n3)
% 28.18/9.17 | (524) sum(n19, n20) = n18
% 28.18/9.17 | (525) ~ (n17 = n9)
% 28.18/9.17 | (526) ~ (n19 = n11)
% 28.18/9.17 | (527) sum(n0, n0) = n0
% 28.18/9.17 | (528) sum(n19, n5) = n3
% 28.18/9.17 | (529) sum(n15, n0) = n15
% 28.18/9.17 | (530) sum(n20, n14) = n13
% 28.18/9.17 | (531) sum(n20, n4) = n3
% 28.18/9.17 | (532) sum(n14, n20) = n13
% 28.18/9.17 | (533) sum(n15, n1) = n16
% 28.18/9.17 | (534) sum(n3, n17) = n20
% 28.18/9.18 | (535) sum(n14, n0) = n14
% 28.18/9.18 | (536) succ(n0) = n1
% 28.18/9.18 | (537) sum(n2, n7) = n9
% 28.18/9.18 | (538) sum(n11, n19) = n9
% 28.18/9.18 | (539) sum(n7, n0) = n7
% 28.18/9.18 | (540) ~ (n9 = n8)
% 28.18/9.18 | (541) ~ (n7 = n3)
% 28.18/9.18 | (542) sum(n18, n15) = n12
% 28.18/9.18 | (543) ~ (n20 = n15)
% 28.18/9.18 | (544) ~ (n8 = n3)
% 28.18/9.18 | (545) succ(n7) = n8
% 28.18/9.18 | (546) sum(n11, n16) = n6
% 28.18/9.18 | (547) sum(n3, n12) = n15
% 28.18/9.18 | (548) sum(n13, n12) = n4
% 28.18/9.18 | (549) ~ (n16 = n14)
% 28.18/9.18 | (550) ~ (n16 = n9)
% 28.18/9.18 | (551) sum(n7, n19) = n5
% 28.18/9.18 | (552) sum(n20, n10) = n9
% 28.18/9.18 | (553) sum(n7, n14) = n0
% 28.18/9.18 | (554) succ(n14) = n15
% 28.18/9.18 | (555) sum(n12, n2) = n14
% 28.18/9.18 | (556) sum(n5, n8) = n13
% 28.18/9.18 | (557) sum(n1, n5) = n6
% 28.18/9.18 | (558) sum(n1, n8) = n9
% 28.18/9.18 | (559) sum(n2, n16) = n18
% 28.18/9.18 | (560) sum(n1, n18) = n19
% 28.18/9.18 | (561) ~ (n18 = n10)
% 28.18/9.18 | (562) ~ (n17 = n1)
% 28.18/9.18 | (563) ~ (n17 = n14)
% 28.18/9.18 | (564) sum(n5, n0) = n5
% 28.18/9.18 | (565) ~ (n14 = n4)
% 28.18/9.18 | (566) sum(n10, n8) = n18
% 28.18/9.18 | (567) sum(n17, n8) = n4
% 28.18/9.18 | (568) sum(n10, n11) = n0
% 28.18/9.18 | (569) ~ (n17 = n12)
% 28.18/9.18 | (570) sum(n6, n15) = n0
% 28.18/9.18 | (571) sum(n18, n12) = n9
% 28.18/9.18 | (572) succ(n12) = n13
% 28.18/9.18 | (573) ~ (n17 = n5)
% 28.18/9.18 | (574) sum(n5, n12) = n17
% 28.18/9.18 | (575) sum(n0, n4) = n4
% 28.18/9.18 | (576) ~ (n10 = n9)
% 28.18/9.18 | (577) sum(n20, n17) = n16
% 28.18/9.18 | (578) sum(n10, n10) = n20
% 28.18/9.18 | (579) ~ (n18 = n13)
% 28.18/9.18 | (580) sum(n18, n1) = n19
% 28.18/9.18 | (581) sum(n7, n17) = n3
% 28.18/9.18 | (582) sum(n15, n14) = n8
% 28.18/9.18 | (583) pred(n18) = n17
% 28.18/9.18 | (584) ~ (n20 = n8)
% 28.18/9.18 | (585) ~ (n17 = n13)
% 28.18/9.18 | (586) sum(n12, n1) = n13
% 28.18/9.18 | (587) ~ (n13 = n7)
% 28.18/9.18 | (588) pred(n19) = n18
% 28.18/9.18 | (589) sum(n2, n18) = n20
% 28.18/9.18 | (590) ~ (n18 = n0)
% 28.18/9.18 | (591) sum(n0, n13) = n13
% 28.18/9.18 | (592) sum(n4, n7) = n11
% 28.18/9.18 | (593) sum(n6, n9) = n15
% 28.18/9.18 | (594) sum(n9, n8) = n17
% 28.18/9.18 | (595) sum(n15, n19) = n13
% 28.18/9.18 | (596) sum(n4, n11) = n15
% 28.18/9.18 | (597) ~ (n16 = n2)
% 28.18/9.18 | (598) sum(n6, n12) = n18
% 28.18/9.18 | (599) sum(n12, n10) = n1
% 28.18/9.18 | (600) sum(n6, n5) = n11
% 28.18/9.18 | (601) sum(n18, n5) = n2
% 28.18/9.18 | (602) sum(n7, n11) = n18
% 28.18/9.18 | (603) succ(n16) = n17
% 28.18/9.18 | (604) ~ (n14 = n10)
% 28.18/9.18 | (605) sum(n3, n5) = n8
% 28.18/9.18 | (606) ~ (n7 = n4)
% 28.18/9.18 | (607) ~ (n14 = n8)
% 28.18/9.18 | (608) ~ (n20 = n19)
% 28.18/9.18 | (609) ~ (n15 = n13)
% 28.18/9.18 | (610) sum(n20, n11) = n10
% 28.18/9.18 | (611) sum(n16, n15) = n10
% 28.18/9.18 | (612) ~ (n19 = n16)
% 28.18/9.18 | (613) sum(n6, n6) = n12
% 28.18/9.18 | (614) ~ (n4 = n3)
% 28.18/9.18 | (615) ~ (n8 = n4)
% 28.18/9.18 | (616) sum(n0, n19) = n19
% 28.18/9.18 | (617) ~ (n18 = n2)
% 28.18/9.18 | (618) ~ (n4 = n2)
% 28.18/9.18 | (619) sum(n13, n18) = n10
% 28.18/9.18 | (620) sum(n16, n0) = n16
% 28.18/9.18 | (621) sum(n0, n15) = n15
% 28.18/9.18 | (622) sum(n20, n7) = n6
% 28.18/9.18 | (623) sum(n1, n20) = n0
% 28.18/9.18 | (624) sum(n20, n5) = n4
% 28.18/9.18 | (625) sum(n1, n13) = n14
% 28.18/9.18 | (626) sum(n20, n16) = n15
% 28.18/9.18 | (627) sum(n8, n1) = n9
% 28.18/9.18 | (628) sum(all_0_6_6, all_0_8_8) = all_0_1_1
% 28.18/9.18 | (629) sum(n6, n0) = n6
% 28.18/9.18 | (630) pred(n14) = n13
% 28.18/9.18 | (631) succ(n17) = n18
% 28.18/9.18 | (632) sum(n11, n12) = n2
% 28.18/9.18 | (633) sum(n13, n19) = n11
% 28.18/9.18 | (634) sum(n1, n14) = n15
% 28.18/9.18 | (635) sum(n5, n17) = n1
% 28.18/9.18 | (636) ~ (n6 = n5)
% 28.18/9.18 | (637) sum(n5, n20) = n4
% 28.18/9.18 | (638) sum(n17, n7) = n3
% 28.18/9.18 | (639) sum(n20, n9) = n8
% 28.18/9.19 | (640) sum(n18, n8) = n5
% 28.18/9.19 | (641) sum(n18, n17) = n14
% 28.18/9.19 | (642) ~ (n18 = n17)
% 28.18/9.19 | (643) sum(n1, n16) = n17
% 28.18/9.19 | (644) sum(n13, n9) = n1
% 28.18/9.19 | (645) sum(n18, n20) = n17
% 28.18/9.19 | (646) sum(n13, n10) = n2
% 28.18/9.19 | (647) sum(n11, n9) = n20
% 28.18/9.19 | (648) sum(n17, n19) = n15
% 28.18/9.19 | (649) sum(n15, n11) = n5
% 28.18/9.19 | (650) ~ (n11 = n9)
% 28.18/9.19 | (651) sum(n17, n1) = n18
% 28.18/9.19 | (652) sum(n7, n8) = n15
% 28.18/9.19 | (653) ~ (n18 = n11)
% 28.18/9.19 | (654) ~ (n11 = n4)
% 28.18/9.19 | (655) sum(n16, n5) = n0
% 28.18/9.19 | (656) sum(n9, n17) = n5
% 28.18/9.19 | (657) sum(n6, n19) = n4
% 28.18/9.19 | (658) sum(n14, n10) = n3
% 28.18/9.19 | (659) sum(n19, n10) = n8
% 28.18/9.19 | (660) sum(n7, n1) = n8
% 28.18/9.19 | (661) ~ (n9 = n4)
% 28.18/9.19 | (662) sum(n13, n0) = n13
% 28.18/9.19 | (663) ~ (n19 = n15)
% 28.18/9.19 | (664) sum(n18, n16) = n13
% 28.18/9.19 | (665) sum(n2, n13) = n15
% 28.18/9.19 | (666) sum(n11, n13) = n3
% 28.18/9.19 | (667) sum(n19, n15) = n13
% 28.18/9.19 | (668) sum(n20, n12) = n11
% 28.18/9.19 | (669) sum(n1, n17) = n18
% 28.18/9.19 | (670) ~ (n9 = n1)
% 28.18/9.19 | (671) sum(n20, n18) = n17
% 28.18/9.19 | (672) sum(n8, n17) = n4
% 28.18/9.19 | (673) ~ (n20 = n10)
% 28.18/9.19 | (674) sum(n6, n13) = n19
% 28.18/9.19 | (675) succ(n5) = n6
% 28.18/9.19 | (676) ~ (n2 = n1)
% 28.18/9.19 | (677) sum(n14, n19) = n12
% 28.18/9.19 | (678) sum(n4, n10) = n14
% 28.18/9.19 | (679) sum(n0, n8) = n8
% 28.18/9.19 | (680) ~ (n10 = n0)
% 28.18/9.19 | (681) sum(n16, n19) = n14
% 28.18/9.19 | (682) succ(n10) = n11
% 28.18/9.19 | (683) sum(n9, n4) = n13
% 28.18/9.19 | (684) ~ (n14 = n12)
% 28.18/9.19 | (685) ~ (n8 = n7)
% 28.18/9.19 | (686) ~ (n15 = n7)
% 28.18/9.19 | (687) ~ (n2 = n0)
% 28.18/9.19 | (688) ~ (n6 = n1)
% 28.18/9.19 | (689) sum(n17, n10) = n6
% 28.18/9.19 | (690) ~ (n14 = n11)
% 28.18/9.19 | (691) sum(n6, n7) = n13
% 28.18/9.19 | (692) ~ (n15 = n12)
% 28.18/9.19 | (693) sum(n0, n12) = n12
% 28.18/9.19 | (694) sum(n9, n6) = n15
% 28.18/9.19 | (695) sum(n4, n2) = n6
% 28.18/9.19 | (696) ~ (n15 = n5)
% 28.18/9.19 | (697) sum(n16, n14) = n9
% 28.18/9.19 | (698) ~ (n18 = n8)
% 28.18/9.19 | (699) pred(n12) = n11
% 28.18/9.19 | (700) ~ (n16 = n13)
% 28.18/9.19 | (701) sum(n8, n20) = n7
% 28.18/9.19 | (702) sum(n14, n18) = n11
% 28.18/9.19 | (703) sum(n10, n16) = n5
% 28.18/9.19 | (704) sum(n7, n16) = n2
% 28.18/9.19 | (705) ~ (n15 = n10)
% 28.18/9.19 | (706) sum(n8, n15) = n2
% 28.18/9.19 | (707) sum(n1, n10) = n11
% 28.18/9.19 | (708) sum(n17, n11) = n7
% 28.18/9.19 | (709) pred(n15) = n14
% 28.18/9.19 | (710) sum(n10, n20) = n9
% 28.18/9.19 |
% 28.18/9.19 +-Applying beta-rule and splitting (87), into two cases.
% 28.18/9.19 |-Branch one:
% 28.18/9.19 | (711) all_0_10_10 = n20
% 28.18/9.19 |
% 28.18/9.19 | From (711) and (57) follows:
% 28.18/9.19 | (712) pred(n20) = all_0_6_6
% 28.18/9.19 |
% 28.18/9.19 | From (711) and (381) follows:
% 28.18/9.19 | (713) succ(n20) = all_0_8_8
% 28.18/9.19 |
% 28.18/9.19 | Instantiating formula (259) with n20, all_0_6_6, n19 and discharging atoms pred(n20) = all_0_6_6, pred(n20) = n19, yields:
% 28.18/9.19 | (714) all_0_6_6 = n19
% 28.18/9.19 |
% 28.18/9.19 | Instantiating formula (184) with n20, all_0_8_8, n0 and discharging atoms succ(n20) = all_0_8_8, succ(n20) = n0, yields:
% 28.18/9.19 | (715) all_0_8_8 = n0
% 28.18/9.19 |
% 28.18/9.19 | From (714) and (712) follows:
% 28.18/9.19 | (359) pred(n20) = n19
% 28.18/9.19 |
% 28.18/9.19 | From (715) and (713) follows:
% 28.18/9.19 | (367) succ(n20) = n0
% 28.18/9.19 |
% 28.18/9.19 | From (714) and (386) follows:
% 28.18/9.19 | (718) sum(n19, all_0_5_5) = all_0_4_4
% 28.18/9.19 |
% 28.18/9.19 | From (714)(715) and (628) follows:
% 28.18/9.19 | (719) sum(n19, n0) = all_0_1_1
% 28.18/9.19 |
% 28.18/9.19 | From (715) and (74) follows:
% 28.18/9.19 | (720) sum(all_0_9_9, n0) = all_0_7_7
% 28.18/9.19 |
% 28.18/9.19 | Instantiating formula (194) with n19, n0, all_0_1_1, n19 and discharging atoms sum(n19, n0) = all_0_1_1, sum(n19, n0) = n19, yields:
% 28.18/9.19 | (721) all_0_1_1 = n19
% 28.18/9.19 |
% 28.18/9.19 | From (721) and (85) follows:
% 28.18/9.19 | (722) sum(all_0_2_2, n19) = all_0_0_0
% 28.18/9.19 |
% 28.18/9.19 | From (721) and (719) follows:
% 28.18/9.19 | (288) sum(n19, n0) = n19
% 28.18/9.19 |
% 28.18/9.19 +-Applying beta-rule and splitting (304), into two cases.
% 28.18/9.19 |-Branch one:
% 28.18/9.19 | (724) all_0_11_11 = n20
% 28.18/9.19 |
% 28.18/9.19 | From (724) and (190) follows:
% 28.18/9.19 | (725) pred(n20) = all_0_9_9
% 28.18/9.19 |
% 28.18/9.19 | From (724) and (505) follows:
% 28.18/9.19 | (726) succ(n20) = all_0_5_5
% 28.18/9.19 |
% 28.18/9.20 | Instantiating formula (259) with n20, all_0_9_9, n19 and discharging atoms pred(n20) = all_0_9_9, pred(n20) = n19, yields:
% 28.18/9.20 | (727) all_0_9_9 = n19
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (184) with n20, all_0_5_5, n0 and discharging atoms succ(n20) = all_0_5_5, succ(n20) = n0, yields:
% 28.18/9.20 | (728) all_0_5_5 = n0
% 28.18/9.20 |
% 28.18/9.20 | From (727)(728) and (156) follows:
% 28.18/9.20 | (729) sum(n19, n0) = all_0_2_2
% 28.18/9.20 |
% 28.18/9.20 | From (727) and (720) follows:
% 28.18/9.20 | (730) sum(n19, n0) = all_0_7_7
% 28.18/9.20 |
% 28.18/9.20 | From (728) and (718) follows:
% 28.18/9.20 | (731) sum(n19, n0) = all_0_4_4
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (194) with n19, n0, all_0_2_2, n19 and discharging atoms sum(n19, n0) = all_0_2_2, sum(n19, n0) = n19, yields:
% 28.18/9.20 | (732) all_0_2_2 = n19
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (194) with n19, n0, all_0_4_4, all_0_2_2 and discharging atoms sum(n19, n0) = all_0_2_2, sum(n19, n0) = all_0_4_4, yields:
% 28.18/9.20 | (733) all_0_2_2 = all_0_4_4
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (194) with n19, n0, all_0_7_7, all_0_2_2 and discharging atoms sum(n19, n0) = all_0_2_2, sum(n19, n0) = all_0_7_7, yields:
% 28.18/9.20 | (734) all_0_2_2 = all_0_7_7
% 28.18/9.20 |
% 28.18/9.20 | Combining equations (734,733) yields a new equation:
% 28.18/9.20 | (735) all_0_4_4 = all_0_7_7
% 28.18/9.20 |
% 28.18/9.20 | Combining equations (732,733) yields a new equation:
% 28.18/9.20 | (736) all_0_4_4 = n19
% 28.18/9.20 |
% 28.18/9.20 | Combining equations (736,735) yields a new equation:
% 28.18/9.20 | (737) all_0_7_7 = n19
% 28.18/9.20 |
% 28.18/9.20 | Combining equations (737,735) yields a new equation:
% 28.18/9.20 | (736) all_0_4_4 = n19
% 28.18/9.20 |
% 28.18/9.20 | Combining equations (736,733) yields a new equation:
% 28.18/9.20 | (732) all_0_2_2 = n19
% 28.18/9.20 |
% 28.18/9.20 | From (732) and (722) follows:
% 28.18/9.20 | (740) sum(n19, n19) = all_0_0_0
% 28.18/9.20 |
% 28.18/9.20 | From (737)(736) and (435) follows:
% 28.18/9.20 | (741) sum(n19, n19) = all_0_3_3
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (194) with n19, n19, all_0_0_0, n17 and discharging atoms sum(n19, n19) = all_0_0_0, sum(n19, n19) = n17, yields:
% 28.18/9.20 | (742) all_0_0_0 = n17
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (194) with n19, n19, all_0_3_3, all_0_0_0 and discharging atoms sum(n19, n19) = all_0_0_0, sum(n19, n19) = all_0_3_3, yields:
% 28.18/9.20 | (743) all_0_0_0 = all_0_3_3
% 28.18/9.20 |
% 28.18/9.20 | Combining equations (742,743) yields a new equation:
% 28.18/9.20 | (744) all_0_3_3 = n17
% 28.18/9.20 |
% 28.18/9.20 | Combining equations (744,743) yields a new equation:
% 28.18/9.20 | (742) all_0_0_0 = n17
% 28.18/9.20 |
% 28.18/9.20 | Equations (742,744) can reduce 201 to:
% 28.18/9.20 | (746) $false
% 28.18/9.20 |
% 28.18/9.20 |-The branch is then unsatisfiable
% 28.18/9.20 |-Branch two:
% 28.18/9.20 | (747) ~ (all_0_11_11 = n20)
% 28.18/9.20 | (748) all_0_11_11 = n19 | all_0_11_11 = n18 | all_0_11_11 = n17 | all_0_11_11 = n16 | all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.18/9.20 |
% 28.18/9.20 +-Applying beta-rule and splitting (748), into two cases.
% 28.18/9.20 |-Branch one:
% 28.18/9.20 | (749) all_0_11_11 = n19
% 28.18/9.20 |
% 28.18/9.20 | From (749) and (190) follows:
% 28.18/9.20 | (750) pred(n19) = all_0_9_9
% 28.18/9.20 |
% 28.18/9.20 | From (749) and (505) follows:
% 28.18/9.20 | (751) succ(n19) = all_0_5_5
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (259) with n19, all_0_9_9, n18 and discharging atoms pred(n19) = all_0_9_9, pred(n19) = n18, yields:
% 28.18/9.20 | (752) all_0_9_9 = n18
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (184) with n19, all_0_5_5, n20 and discharging atoms succ(n19) = all_0_5_5, succ(n19) = n20, yields:
% 28.18/9.20 | (753) all_0_5_5 = n20
% 28.18/9.20 |
% 28.18/9.20 | From (752)(753) and (156) follows:
% 28.18/9.20 | (754) sum(n18, n20) = all_0_2_2
% 28.18/9.20 |
% 28.18/9.20 | From (752) and (720) follows:
% 28.18/9.20 | (755) sum(n18, n0) = all_0_7_7
% 28.18/9.20 |
% 28.18/9.20 | From (753) and (718) follows:
% 28.18/9.20 | (756) sum(n19, n20) = all_0_4_4
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (194) with n19, n20, all_0_4_4, n18 and discharging atoms sum(n19, n20) = all_0_4_4, sum(n19, n20) = n18, yields:
% 28.18/9.20 | (757) all_0_4_4 = n18
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (194) with n18, n20, all_0_2_2, n17 and discharging atoms sum(n18, n20) = all_0_2_2, sum(n18, n20) = n17, yields:
% 28.18/9.20 | (758) all_0_2_2 = n17
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (194) with n18, n0, all_0_7_7, n18 and discharging atoms sum(n18, n0) = all_0_7_7, sum(n18, n0) = n18, yields:
% 28.18/9.20 | (759) all_0_7_7 = n18
% 28.18/9.20 |
% 28.18/9.20 | From (758) and (722) follows:
% 28.18/9.20 | (760) sum(n17, n19) = all_0_0_0
% 28.18/9.20 |
% 28.18/9.20 | From (759)(757) and (435) follows:
% 28.18/9.20 | (761) sum(n18, n18) = all_0_3_3
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 28.18/9.20 | (762) all_0_3_3 = n15
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (194) with n17, n19, all_0_0_0, n15 and discharging atoms sum(n17, n19) = all_0_0_0, sum(n17, n19) = n15, yields:
% 28.18/9.20 | (763) all_0_0_0 = n15
% 28.18/9.20 |
% 28.18/9.20 | Equations (763,762) can reduce 201 to:
% 28.18/9.20 | (746) $false
% 28.18/9.20 |
% 28.18/9.20 |-The branch is then unsatisfiable
% 28.18/9.20 |-Branch two:
% 28.18/9.20 | (765) ~ (all_0_11_11 = n19)
% 28.18/9.20 | (766) all_0_11_11 = n18 | all_0_11_11 = n17 | all_0_11_11 = n16 | all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.18/9.20 |
% 28.18/9.20 +-Applying beta-rule and splitting (766), into two cases.
% 28.18/9.20 |-Branch one:
% 28.18/9.20 | (767) all_0_11_11 = n18
% 28.18/9.20 |
% 28.18/9.20 | From (767) and (190) follows:
% 28.18/9.20 | (768) pred(n18) = all_0_9_9
% 28.18/9.20 |
% 28.18/9.20 | From (767) and (505) follows:
% 28.18/9.20 | (769) succ(n18) = all_0_5_5
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (259) with n18, all_0_9_9, n17 and discharging atoms pred(n18) = all_0_9_9, pred(n18) = n17, yields:
% 28.18/9.20 | (770) all_0_9_9 = n17
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (184) with n18, all_0_5_5, n19 and discharging atoms succ(n18) = all_0_5_5, succ(n18) = n19, yields:
% 28.18/9.20 | (771) all_0_5_5 = n19
% 28.18/9.20 |
% 28.18/9.20 | From (770)(771) and (156) follows:
% 28.18/9.20 | (772) sum(n17, n19) = all_0_2_2
% 28.18/9.20 |
% 28.18/9.20 | From (770) and (720) follows:
% 28.18/9.20 | (773) sum(n17, n0) = all_0_7_7
% 28.18/9.20 |
% 28.18/9.20 | From (771) and (718) follows:
% 28.18/9.20 | (774) sum(n19, n19) = all_0_4_4
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (194) with n19, n19, all_0_4_4, n17 and discharging atoms sum(n19, n19) = all_0_4_4, sum(n19, n19) = n17, yields:
% 28.18/9.20 | (775) all_0_4_4 = n17
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (194) with n17, n19, all_0_2_2, n15 and discharging atoms sum(n17, n19) = all_0_2_2, sum(n17, n19) = n15, yields:
% 28.18/9.20 | (776) all_0_2_2 = n15
% 28.18/9.20 |
% 28.18/9.20 | Instantiating formula (194) with n17, n0, all_0_7_7, n17 and discharging atoms sum(n17, n0) = all_0_7_7, sum(n17, n0) = n17, yields:
% 28.18/9.20 | (777) all_0_7_7 = n17
% 28.18/9.20 |
% 28.18/9.20 | From (776) and (722) follows:
% 28.18/9.20 | (778) sum(n15, n19) = all_0_0_0
% 28.18/9.20 |
% 28.18/9.20 | From (777)(775) and (435) follows:
% 28.18/9.20 | (779) sum(n17, n17) = all_0_3_3
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 28.18/9.21 | (780) all_0_3_3 = n13
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (194) with n15, n19, all_0_0_0, n13 and discharging atoms sum(n15, n19) = all_0_0_0, sum(n15, n19) = n13, yields:
% 28.18/9.21 | (781) all_0_0_0 = n13
% 28.18/9.21 |
% 28.18/9.21 | Equations (781,780) can reduce 201 to:
% 28.18/9.21 | (746) $false
% 28.18/9.21 |
% 28.18/9.21 |-The branch is then unsatisfiable
% 28.18/9.21 |-Branch two:
% 28.18/9.21 | (783) ~ (all_0_11_11 = n18)
% 28.18/9.21 | (784) all_0_11_11 = n17 | all_0_11_11 = n16 | all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.18/9.21 |
% 28.18/9.21 +-Applying beta-rule and splitting (784), into two cases.
% 28.18/9.21 |-Branch one:
% 28.18/9.21 | (785) all_0_11_11 = n17
% 28.18/9.21 |
% 28.18/9.21 | From (785) and (190) follows:
% 28.18/9.21 | (786) pred(n17) = all_0_9_9
% 28.18/9.21 |
% 28.18/9.21 | From (785) and (505) follows:
% 28.18/9.21 | (787) succ(n17) = all_0_5_5
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (259) with n17, all_0_9_9, n16 and discharging atoms pred(n17) = all_0_9_9, pred(n17) = n16, yields:
% 28.18/9.21 | (788) all_0_9_9 = n16
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (184) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 28.18/9.21 | (789) all_0_5_5 = n18
% 28.18/9.21 |
% 28.18/9.21 | From (788)(789) and (156) follows:
% 28.18/9.21 | (790) sum(n16, n18) = all_0_2_2
% 28.18/9.21 |
% 28.18/9.21 | From (788) and (720) follows:
% 28.18/9.21 | (791) sum(n16, n0) = all_0_7_7
% 28.18/9.21 |
% 28.18/9.21 | From (789) and (718) follows:
% 28.18/9.21 | (792) sum(n19, n18) = all_0_4_4
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (194) with n19, n18, all_0_4_4, n16 and discharging atoms sum(n19, n18) = all_0_4_4, sum(n19, n18) = n16, yields:
% 28.18/9.21 | (793) all_0_4_4 = n16
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (194) with n16, n18, all_0_2_2, n13 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = n13, yields:
% 28.18/9.21 | (794) all_0_2_2 = n13
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (194) with n16, n0, all_0_7_7, n16 and discharging atoms sum(n16, n0) = all_0_7_7, sum(n16, n0) = n16, yields:
% 28.18/9.21 | (795) all_0_7_7 = n16
% 28.18/9.21 |
% 28.18/9.21 | From (794) and (722) follows:
% 28.18/9.21 | (796) sum(n13, n19) = all_0_0_0
% 28.18/9.21 |
% 28.18/9.21 | From (795)(793) and (435) follows:
% 28.18/9.21 | (797) sum(n16, n16) = all_0_3_3
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 28.18/9.21 | (798) all_0_3_3 = n11
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (194) with n13, n19, all_0_0_0, n11 and discharging atoms sum(n13, n19) = all_0_0_0, sum(n13, n19) = n11, yields:
% 28.18/9.21 | (799) all_0_0_0 = n11
% 28.18/9.21 |
% 28.18/9.21 | Equations (799,798) can reduce 201 to:
% 28.18/9.21 | (746) $false
% 28.18/9.21 |
% 28.18/9.21 |-The branch is then unsatisfiable
% 28.18/9.21 |-Branch two:
% 28.18/9.21 | (801) ~ (all_0_11_11 = n17)
% 28.18/9.21 | (802) all_0_11_11 = n16 | all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.18/9.21 |
% 28.18/9.21 +-Applying beta-rule and splitting (802), into two cases.
% 28.18/9.21 |-Branch one:
% 28.18/9.21 | (803) all_0_11_11 = n16
% 28.18/9.21 |
% 28.18/9.21 | From (803) and (190) follows:
% 28.18/9.21 | (804) pred(n16) = all_0_9_9
% 28.18/9.21 |
% 28.18/9.21 | From (803) and (505) follows:
% 28.18/9.21 | (805) succ(n16) = all_0_5_5
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (259) with n16, all_0_9_9, n15 and discharging atoms pred(n16) = all_0_9_9, pred(n16) = n15, yields:
% 28.18/9.21 | (806) all_0_9_9 = n15
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (184) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 28.18/9.21 | (807) all_0_5_5 = n17
% 28.18/9.21 |
% 28.18/9.21 | From (806)(807) and (156) follows:
% 28.18/9.21 | (808) sum(n15, n17) = all_0_2_2
% 28.18/9.21 |
% 28.18/9.21 | From (806) and (720) follows:
% 28.18/9.21 | (809) sum(n15, n0) = all_0_7_7
% 28.18/9.21 |
% 28.18/9.21 | From (807) and (718) follows:
% 28.18/9.21 | (810) sum(n19, n17) = all_0_4_4
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (194) with n19, n17, all_0_4_4, n15 and discharging atoms sum(n19, n17) = all_0_4_4, sum(n19, n17) = n15, yields:
% 28.18/9.21 | (811) all_0_4_4 = n15
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (194) with n15, n17, all_0_2_2, n11 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n11, yields:
% 28.18/9.21 | (812) all_0_2_2 = n11
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (194) with n15, n0, all_0_7_7, n15 and discharging atoms sum(n15, n0) = all_0_7_7, sum(n15, n0) = n15, yields:
% 28.18/9.21 | (813) all_0_7_7 = n15
% 28.18/9.21 |
% 28.18/9.21 | From (812) and (722) follows:
% 28.18/9.21 | (814) sum(n11, n19) = all_0_0_0
% 28.18/9.21 |
% 28.18/9.21 | From (813)(811) and (435) follows:
% 28.18/9.21 | (815) sum(n15, n15) = all_0_3_3
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 28.18/9.21 | (816) all_0_3_3 = n9
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (194) with n11, n19, all_0_0_0, n9 and discharging atoms sum(n11, n19) = all_0_0_0, sum(n11, n19) = n9, yields:
% 28.18/9.21 | (817) all_0_0_0 = n9
% 28.18/9.21 |
% 28.18/9.21 | Equations (817,816) can reduce 201 to:
% 28.18/9.21 | (746) $false
% 28.18/9.21 |
% 28.18/9.21 |-The branch is then unsatisfiable
% 28.18/9.21 |-Branch two:
% 28.18/9.21 | (819) ~ (all_0_11_11 = n16)
% 28.18/9.21 | (820) all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.18/9.21 |
% 28.18/9.21 +-Applying beta-rule and splitting (820), into two cases.
% 28.18/9.21 |-Branch one:
% 28.18/9.21 | (821) all_0_11_11 = n15
% 28.18/9.21 |
% 28.18/9.21 | From (821) and (190) follows:
% 28.18/9.21 | (822) pred(n15) = all_0_9_9
% 28.18/9.21 |
% 28.18/9.21 | From (821) and (505) follows:
% 28.18/9.21 | (823) succ(n15) = all_0_5_5
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (259) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 28.18/9.21 | (824) all_0_9_9 = n14
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (184) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 28.18/9.21 | (825) all_0_5_5 = n16
% 28.18/9.21 |
% 28.18/9.21 | From (824)(825) and (156) follows:
% 28.18/9.21 | (826) sum(n14, n16) = all_0_2_2
% 28.18/9.21 |
% 28.18/9.21 | From (824) and (720) follows:
% 28.18/9.21 | (827) sum(n14, n0) = all_0_7_7
% 28.18/9.21 |
% 28.18/9.21 | From (825) and (718) follows:
% 28.18/9.21 | (828) sum(n19, n16) = all_0_4_4
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (194) with n19, n16, all_0_4_4, n14 and discharging atoms sum(n19, n16) = all_0_4_4, sum(n19, n16) = n14, yields:
% 28.18/9.21 | (829) all_0_4_4 = n14
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (194) with n14, n16, all_0_2_2, n9 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n9, yields:
% 28.18/9.21 | (830) all_0_2_2 = n9
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (194) with n14, n0, all_0_7_7, n14 and discharging atoms sum(n14, n0) = all_0_7_7, sum(n14, n0) = n14, yields:
% 28.18/9.21 | (831) all_0_7_7 = n14
% 28.18/9.21 |
% 28.18/9.21 | From (830) and (722) follows:
% 28.18/9.21 | (832) sum(n9, n19) = all_0_0_0
% 28.18/9.21 |
% 28.18/9.21 | From (831)(829) and (435) follows:
% 28.18/9.21 | (833) sum(n14, n14) = all_0_3_3
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 28.18/9.21 | (834) all_0_3_3 = n7
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (194) with n9, n19, all_0_0_0, n7 and discharging atoms sum(n9, n19) = all_0_0_0, sum(n9, n19) = n7, yields:
% 28.18/9.21 | (835) all_0_0_0 = n7
% 28.18/9.21 |
% 28.18/9.21 | Equations (835,834) can reduce 201 to:
% 28.18/9.21 | (746) $false
% 28.18/9.21 |
% 28.18/9.21 |-The branch is then unsatisfiable
% 28.18/9.21 |-Branch two:
% 28.18/9.21 | (837) ~ (all_0_11_11 = n15)
% 28.18/9.21 | (838) all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.18/9.21 |
% 28.18/9.21 +-Applying beta-rule and splitting (838), into two cases.
% 28.18/9.21 |-Branch one:
% 28.18/9.21 | (839) all_0_11_11 = n14
% 28.18/9.21 |
% 28.18/9.21 | From (839) and (190) follows:
% 28.18/9.21 | (840) pred(n14) = all_0_9_9
% 28.18/9.21 |
% 28.18/9.21 | From (839) and (505) follows:
% 28.18/9.21 | (841) succ(n14) = all_0_5_5
% 28.18/9.21 |
% 28.18/9.21 | Instantiating formula (259) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 28.18/9.22 | (842) all_0_9_9 = n13
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (184) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 28.18/9.22 | (843) all_0_5_5 = n15
% 28.18/9.22 |
% 28.18/9.22 | From (842)(843) and (156) follows:
% 28.18/9.22 | (844) sum(n13, n15) = all_0_2_2
% 28.18/9.22 |
% 28.18/9.22 | From (842) and (720) follows:
% 28.18/9.22 | (845) sum(n13, n0) = all_0_7_7
% 28.18/9.22 |
% 28.18/9.22 | From (843) and (718) follows:
% 28.18/9.22 | (846) sum(n19, n15) = all_0_4_4
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n19, n15, all_0_4_4, n13 and discharging atoms sum(n19, n15) = all_0_4_4, sum(n19, n15) = n13, yields:
% 28.18/9.22 | (847) all_0_4_4 = n13
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n13, n15, all_0_2_2, n7 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n7, yields:
% 28.18/9.22 | (848) all_0_2_2 = n7
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n13, n0, all_0_7_7, n13 and discharging atoms sum(n13, n0) = all_0_7_7, sum(n13, n0) = n13, yields:
% 28.18/9.22 | (849) all_0_7_7 = n13
% 28.18/9.22 |
% 28.18/9.22 | From (848) and (722) follows:
% 28.18/9.22 | (850) sum(n7, n19) = all_0_0_0
% 28.18/9.22 |
% 28.18/9.22 | From (849)(847) and (435) follows:
% 28.18/9.22 | (851) sum(n13, n13) = all_0_3_3
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 28.18/9.22 | (852) all_0_3_3 = n5
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n7, n19, all_0_0_0, n5 and discharging atoms sum(n7, n19) = all_0_0_0, sum(n7, n19) = n5, yields:
% 28.18/9.22 | (853) all_0_0_0 = n5
% 28.18/9.22 |
% 28.18/9.22 | Equations (853,852) can reduce 201 to:
% 28.18/9.22 | (746) $false
% 28.18/9.22 |
% 28.18/9.22 |-The branch is then unsatisfiable
% 28.18/9.22 |-Branch two:
% 28.18/9.22 | (855) ~ (all_0_11_11 = n14)
% 28.18/9.22 | (856) all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.18/9.22 |
% 28.18/9.22 +-Applying beta-rule and splitting (856), into two cases.
% 28.18/9.22 |-Branch one:
% 28.18/9.22 | (857) all_0_11_11 = n13
% 28.18/9.22 |
% 28.18/9.22 | From (857) and (190) follows:
% 28.18/9.22 | (858) pred(n13) = all_0_9_9
% 28.18/9.22 |
% 28.18/9.22 | From (857) and (505) follows:
% 28.18/9.22 | (859) succ(n13) = all_0_5_5
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (259) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 28.18/9.22 | (860) all_0_9_9 = n12
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (184) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 28.18/9.22 | (861) all_0_5_5 = n14
% 28.18/9.22 |
% 28.18/9.22 | From (860)(861) and (156) follows:
% 28.18/9.22 | (862) sum(n12, n14) = all_0_2_2
% 28.18/9.22 |
% 28.18/9.22 | From (860) and (720) follows:
% 28.18/9.22 | (863) sum(n12, n0) = all_0_7_7
% 28.18/9.22 |
% 28.18/9.22 | From (861) and (718) follows:
% 28.18/9.22 | (864) sum(n19, n14) = all_0_4_4
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n19, n14, all_0_4_4, n12 and discharging atoms sum(n19, n14) = all_0_4_4, sum(n19, n14) = n12, yields:
% 28.18/9.22 | (865) all_0_4_4 = n12
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n12, n14, all_0_2_2, n5 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n5, yields:
% 28.18/9.22 | (866) all_0_2_2 = n5
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n12, n0, all_0_7_7, n12 and discharging atoms sum(n12, n0) = all_0_7_7, sum(n12, n0) = n12, yields:
% 28.18/9.22 | (867) all_0_7_7 = n12
% 28.18/9.22 |
% 28.18/9.22 | From (866) and (722) follows:
% 28.18/9.22 | (868) sum(n5, n19) = all_0_0_0
% 28.18/9.22 |
% 28.18/9.22 | From (867)(865) and (435) follows:
% 28.18/9.22 | (869) sum(n12, n12) = all_0_3_3
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 28.18/9.22 | (870) all_0_3_3 = n3
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n5, n19, all_0_0_0, n3 and discharging atoms sum(n5, n19) = all_0_0_0, sum(n5, n19) = n3, yields:
% 28.18/9.22 | (871) all_0_0_0 = n3
% 28.18/9.22 |
% 28.18/9.22 | Equations (871,870) can reduce 201 to:
% 28.18/9.22 | (746) $false
% 28.18/9.22 |
% 28.18/9.22 |-The branch is then unsatisfiable
% 28.18/9.22 |-Branch two:
% 28.18/9.22 | (873) ~ (all_0_11_11 = n13)
% 28.18/9.22 | (874) all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.18/9.22 |
% 28.18/9.22 +-Applying beta-rule and splitting (874), into two cases.
% 28.18/9.22 |-Branch one:
% 28.18/9.22 | (875) all_0_11_11 = n12
% 28.18/9.22 |
% 28.18/9.22 | From (875) and (190) follows:
% 28.18/9.22 | (876) pred(n12) = all_0_9_9
% 28.18/9.22 |
% 28.18/9.22 | From (875) and (505) follows:
% 28.18/9.22 | (877) succ(n12) = all_0_5_5
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (259) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 28.18/9.22 | (878) all_0_9_9 = n11
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (184) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 28.18/9.22 | (879) all_0_5_5 = n13
% 28.18/9.22 |
% 28.18/9.22 | From (878)(879) and (156) follows:
% 28.18/9.22 | (880) sum(n11, n13) = all_0_2_2
% 28.18/9.22 |
% 28.18/9.22 | From (878) and (720) follows:
% 28.18/9.22 | (881) sum(n11, n0) = all_0_7_7
% 28.18/9.22 |
% 28.18/9.22 | From (879) and (718) follows:
% 28.18/9.22 | (882) sum(n19, n13) = all_0_4_4
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n19, n13, all_0_4_4, n11 and discharging atoms sum(n19, n13) = all_0_4_4, sum(n19, n13) = n11, yields:
% 28.18/9.22 | (883) all_0_4_4 = n11
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n11, n13, all_0_2_2, n3 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n3, yields:
% 28.18/9.22 | (884) all_0_2_2 = n3
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n11, n0, all_0_7_7, n11 and discharging atoms sum(n11, n0) = all_0_7_7, sum(n11, n0) = n11, yields:
% 28.18/9.22 | (885) all_0_7_7 = n11
% 28.18/9.22 |
% 28.18/9.22 | From (884) and (722) follows:
% 28.18/9.22 | (886) sum(n3, n19) = all_0_0_0
% 28.18/9.22 |
% 28.18/9.22 | From (885)(883) and (435) follows:
% 28.18/9.22 | (887) sum(n11, n11) = all_0_3_3
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 28.18/9.22 | (888) all_0_3_3 = n1
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n3, n19, all_0_0_0, n1 and discharging atoms sum(n3, n19) = all_0_0_0, sum(n3, n19) = n1, yields:
% 28.18/9.22 | (889) all_0_0_0 = n1
% 28.18/9.22 |
% 28.18/9.22 | Equations (889,888) can reduce 201 to:
% 28.18/9.22 | (746) $false
% 28.18/9.22 |
% 28.18/9.22 |-The branch is then unsatisfiable
% 28.18/9.22 |-Branch two:
% 28.18/9.22 | (891) ~ (all_0_11_11 = n12)
% 28.18/9.22 | (892) all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.18/9.22 |
% 28.18/9.22 +-Applying beta-rule and splitting (892), into two cases.
% 28.18/9.22 |-Branch one:
% 28.18/9.22 | (893) all_0_11_11 = n11
% 28.18/9.22 |
% 28.18/9.22 | From (893) and (190) follows:
% 28.18/9.22 | (894) pred(n11) = all_0_9_9
% 28.18/9.22 |
% 28.18/9.22 | From (893) and (505) follows:
% 28.18/9.22 | (895) succ(n11) = all_0_5_5
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (259) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 28.18/9.22 | (896) all_0_9_9 = n10
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (184) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 28.18/9.22 | (897) all_0_5_5 = n12
% 28.18/9.22 |
% 28.18/9.22 | From (896)(897) and (156) follows:
% 28.18/9.22 | (898) sum(n10, n12) = all_0_2_2
% 28.18/9.22 |
% 28.18/9.22 | From (896) and (720) follows:
% 28.18/9.22 | (899) sum(n10, n0) = all_0_7_7
% 28.18/9.22 |
% 28.18/9.22 | From (897) and (718) follows:
% 28.18/9.22 | (900) sum(n19, n12) = all_0_4_4
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n19, n12, all_0_4_4, n10 and discharging atoms sum(n19, n12) = all_0_4_4, sum(n19, n12) = n10, yields:
% 28.18/9.22 | (901) all_0_4_4 = n10
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n10, n12, all_0_2_2, n1 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n1, yields:
% 28.18/9.22 | (902) all_0_2_2 = n1
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n10, n0, all_0_7_7, n10 and discharging atoms sum(n10, n0) = all_0_7_7, sum(n10, n0) = n10, yields:
% 28.18/9.22 | (903) all_0_7_7 = n10
% 28.18/9.22 |
% 28.18/9.22 | From (902) and (722) follows:
% 28.18/9.22 | (904) sum(n1, n19) = all_0_0_0
% 28.18/9.22 |
% 28.18/9.22 | From (903)(901) and (435) follows:
% 28.18/9.22 | (905) sum(n10, n10) = all_0_3_3
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 28.18/9.22 | (906) all_0_3_3 = n20
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (194) with n1, n19, all_0_0_0, n20 and discharging atoms sum(n1, n19) = all_0_0_0, sum(n1, n19) = n20, yields:
% 28.18/9.22 | (907) all_0_0_0 = n20
% 28.18/9.22 |
% 28.18/9.22 | Equations (907,906) can reduce 201 to:
% 28.18/9.22 | (746) $false
% 28.18/9.22 |
% 28.18/9.22 |-The branch is then unsatisfiable
% 28.18/9.22 |-Branch two:
% 28.18/9.22 | (909) ~ (all_0_11_11 = n11)
% 28.18/9.22 | (910) all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.18/9.22 |
% 28.18/9.22 +-Applying beta-rule and splitting (910), into two cases.
% 28.18/9.22 |-Branch one:
% 28.18/9.22 | (911) all_0_11_11 = n10
% 28.18/9.22 |
% 28.18/9.22 | From (911) and (190) follows:
% 28.18/9.22 | (912) pred(n10) = all_0_9_9
% 28.18/9.22 |
% 28.18/9.22 | From (911) and (505) follows:
% 28.18/9.22 | (913) succ(n10) = all_0_5_5
% 28.18/9.22 |
% 28.18/9.22 | Instantiating formula (259) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 28.18/9.22 | (914) all_0_9_9 = n9
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (184) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 28.18/9.23 | (915) all_0_5_5 = n11
% 28.18/9.23 |
% 28.18/9.23 | From (914)(915) and (156) follows:
% 28.18/9.23 | (916) sum(n9, n11) = all_0_2_2
% 28.18/9.23 |
% 28.18/9.23 | From (914) and (720) follows:
% 28.18/9.23 | (917) sum(n9, n0) = all_0_7_7
% 28.18/9.23 |
% 28.18/9.23 | From (915) and (718) follows:
% 28.18/9.23 | (918) sum(n19, n11) = all_0_4_4
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n19, n11, all_0_4_4, n9 and discharging atoms sum(n19, n11) = all_0_4_4, sum(n19, n11) = n9, yields:
% 28.18/9.23 | (919) all_0_4_4 = n9
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 28.18/9.23 | (920) all_0_2_2 = n20
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n9, n0, all_0_7_7, n9 and discharging atoms sum(n9, n0) = all_0_7_7, sum(n9, n0) = n9, yields:
% 28.18/9.23 | (921) all_0_7_7 = n9
% 28.18/9.23 |
% 28.18/9.23 | From (920) and (722) follows:
% 28.18/9.23 | (922) sum(n20, n19) = all_0_0_0
% 28.18/9.23 |
% 28.18/9.23 | From (921)(919) and (435) follows:
% 28.18/9.23 | (923) sum(n9, n9) = all_0_3_3
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n20, n19, all_0_0_0, n18 and discharging atoms sum(n20, n19) = all_0_0_0, sum(n20, n19) = n18, yields:
% 28.18/9.23 | (924) all_0_0_0 = n18
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 28.18/9.23 | (925) all_0_3_3 = n18
% 28.18/9.23 |
% 28.18/9.23 | Equations (924,925) can reduce 201 to:
% 28.18/9.23 | (746) $false
% 28.18/9.23 |
% 28.18/9.23 |-The branch is then unsatisfiable
% 28.18/9.23 |-Branch two:
% 28.18/9.23 | (927) ~ (all_0_11_11 = n10)
% 28.18/9.23 | (928) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.18/9.23 |
% 28.18/9.23 +-Applying beta-rule and splitting (928), into two cases.
% 28.18/9.23 |-Branch one:
% 28.18/9.23 | (929) all_0_11_11 = n9
% 28.18/9.23 |
% 28.18/9.23 | From (929) and (190) follows:
% 28.18/9.23 | (930) pred(n9) = all_0_9_9
% 28.18/9.23 |
% 28.18/9.23 | From (929) and (505) follows:
% 28.18/9.23 | (931) succ(n9) = all_0_5_5
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (259) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 28.18/9.23 | (932) all_0_9_9 = n8
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (184) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 28.18/9.23 | (933) all_0_5_5 = n10
% 28.18/9.23 |
% 28.18/9.23 | From (932)(933) and (156) follows:
% 28.18/9.23 | (934) sum(n8, n10) = all_0_2_2
% 28.18/9.23 |
% 28.18/9.23 | From (932) and (720) follows:
% 28.18/9.23 | (935) sum(n8, n0) = all_0_7_7
% 28.18/9.23 |
% 28.18/9.23 | From (933) and (718) follows:
% 28.18/9.23 | (936) sum(n19, n10) = all_0_4_4
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n19, n10, all_0_4_4, n8 and discharging atoms sum(n19, n10) = all_0_4_4, sum(n19, n10) = n8, yields:
% 28.18/9.23 | (937) all_0_4_4 = n8
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 28.18/9.23 | (938) all_0_2_2 = n18
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n8, n0, all_0_7_7, n8 and discharging atoms sum(n8, n0) = all_0_7_7, sum(n8, n0) = n8, yields:
% 28.18/9.23 | (939) all_0_7_7 = n8
% 28.18/9.23 |
% 28.18/9.23 | From (938) and (722) follows:
% 28.18/9.23 | (940) sum(n18, n19) = all_0_0_0
% 28.18/9.23 |
% 28.18/9.23 | From (939)(937) and (435) follows:
% 28.18/9.23 | (941) sum(n8, n8) = all_0_3_3
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n18, n19, all_0_0_0, n16 and discharging atoms sum(n18, n19) = all_0_0_0, sum(n18, n19) = n16, yields:
% 28.18/9.23 | (942) all_0_0_0 = n16
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 28.18/9.23 | (943) all_0_3_3 = n16
% 28.18/9.23 |
% 28.18/9.23 | Equations (942,943) can reduce 201 to:
% 28.18/9.23 | (746) $false
% 28.18/9.23 |
% 28.18/9.23 |-The branch is then unsatisfiable
% 28.18/9.23 |-Branch two:
% 28.18/9.23 | (945) ~ (all_0_11_11 = n9)
% 28.18/9.23 | (946) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.18/9.23 |
% 28.18/9.23 +-Applying beta-rule and splitting (946), into two cases.
% 28.18/9.23 |-Branch one:
% 28.18/9.23 | (947) all_0_11_11 = n8
% 28.18/9.23 |
% 28.18/9.23 | From (947) and (190) follows:
% 28.18/9.23 | (948) pred(n8) = all_0_9_9
% 28.18/9.23 |
% 28.18/9.23 | From (947) and (505) follows:
% 28.18/9.23 | (949) succ(n8) = all_0_5_5
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (259) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 28.18/9.23 | (950) all_0_9_9 = n7
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (184) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 28.18/9.23 | (951) all_0_5_5 = n9
% 28.18/9.23 |
% 28.18/9.23 | From (950)(951) and (156) follows:
% 28.18/9.23 | (952) sum(n7, n9) = all_0_2_2
% 28.18/9.23 |
% 28.18/9.23 | From (950) and (720) follows:
% 28.18/9.23 | (953) sum(n7, n0) = all_0_7_7
% 28.18/9.23 |
% 28.18/9.23 | From (951) and (718) follows:
% 28.18/9.23 | (954) sum(n19, n9) = all_0_4_4
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n19, n9, all_0_4_4, n7 and discharging atoms sum(n19, n9) = all_0_4_4, sum(n19, n9) = n7, yields:
% 28.18/9.23 | (955) all_0_4_4 = n7
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 28.18/9.23 | (956) all_0_2_2 = n16
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n7, n0, all_0_7_7, n7 and discharging atoms sum(n7, n0) = all_0_7_7, sum(n7, n0) = n7, yields:
% 28.18/9.23 | (957) all_0_7_7 = n7
% 28.18/9.23 |
% 28.18/9.23 | From (956) and (722) follows:
% 28.18/9.23 | (958) sum(n16, n19) = all_0_0_0
% 28.18/9.23 |
% 28.18/9.23 | From (957)(955) and (435) follows:
% 28.18/9.23 | (959) sum(n7, n7) = all_0_3_3
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n16, n19, all_0_0_0, n14 and discharging atoms sum(n16, n19) = all_0_0_0, sum(n16, n19) = n14, yields:
% 28.18/9.23 | (960) all_0_0_0 = n14
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 28.18/9.23 | (961) all_0_3_3 = n14
% 28.18/9.23 |
% 28.18/9.23 | Equations (960,961) can reduce 201 to:
% 28.18/9.23 | (746) $false
% 28.18/9.23 |
% 28.18/9.23 |-The branch is then unsatisfiable
% 28.18/9.23 |-Branch two:
% 28.18/9.23 | (963) ~ (all_0_11_11 = n8)
% 28.18/9.23 | (964) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.18/9.23 |
% 28.18/9.23 +-Applying beta-rule and splitting (964), into two cases.
% 28.18/9.23 |-Branch one:
% 28.18/9.23 | (965) all_0_11_11 = n7
% 28.18/9.23 |
% 28.18/9.23 | From (965) and (190) follows:
% 28.18/9.23 | (966) pred(n7) = all_0_9_9
% 28.18/9.23 |
% 28.18/9.23 | From (965) and (505) follows:
% 28.18/9.23 | (967) succ(n7) = all_0_5_5
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (259) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 28.18/9.23 | (968) all_0_9_9 = n6
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (184) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 28.18/9.23 | (969) all_0_5_5 = n8
% 28.18/9.23 |
% 28.18/9.23 | From (968)(969) and (156) follows:
% 28.18/9.23 | (970) sum(n6, n8) = all_0_2_2
% 28.18/9.23 |
% 28.18/9.23 | From (968) and (720) follows:
% 28.18/9.23 | (971) sum(n6, n0) = all_0_7_7
% 28.18/9.23 |
% 28.18/9.23 | From (969) and (718) follows:
% 28.18/9.23 | (972) sum(n19, n8) = all_0_4_4
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n19, n8, all_0_4_4, n6 and discharging atoms sum(n19, n8) = all_0_4_4, sum(n19, n8) = n6, yields:
% 28.18/9.23 | (973) all_0_4_4 = n6
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 28.18/9.23 | (974) all_0_2_2 = n14
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n6, n0, all_0_7_7, n6 and discharging atoms sum(n6, n0) = all_0_7_7, sum(n6, n0) = n6, yields:
% 28.18/9.23 | (975) all_0_7_7 = n6
% 28.18/9.23 |
% 28.18/9.23 | From (974) and (722) follows:
% 28.18/9.23 | (976) sum(n14, n19) = all_0_0_0
% 28.18/9.23 |
% 28.18/9.23 | From (975)(973) and (435) follows:
% 28.18/9.23 | (977) sum(n6, n6) = all_0_3_3
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n14, n19, all_0_0_0, n12 and discharging atoms sum(n14, n19) = all_0_0_0, sum(n14, n19) = n12, yields:
% 28.18/9.23 | (978) all_0_0_0 = n12
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 28.18/9.23 | (979) all_0_3_3 = n12
% 28.18/9.23 |
% 28.18/9.23 | Equations (978,979) can reduce 201 to:
% 28.18/9.23 | (746) $false
% 28.18/9.23 |
% 28.18/9.23 |-The branch is then unsatisfiable
% 28.18/9.23 |-Branch two:
% 28.18/9.23 | (981) ~ (all_0_11_11 = n7)
% 28.18/9.23 | (982) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.18/9.23 |
% 28.18/9.23 +-Applying beta-rule and splitting (982), into two cases.
% 28.18/9.23 |-Branch one:
% 28.18/9.23 | (983) all_0_11_11 = n6
% 28.18/9.23 |
% 28.18/9.23 | From (983) and (190) follows:
% 28.18/9.23 | (984) pred(n6) = all_0_9_9
% 28.18/9.23 |
% 28.18/9.23 | From (983) and (505) follows:
% 28.18/9.23 | (985) succ(n6) = all_0_5_5
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (259) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 28.18/9.23 | (986) all_0_9_9 = n5
% 28.18/9.23 |
% 28.18/9.23 | Instantiating formula (184) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 28.18/9.23 | (987) all_0_5_5 = n7
% 28.18/9.23 |
% 28.18/9.23 | From (986)(987) and (156) follows:
% 28.18/9.23 | (988) sum(n5, n7) = all_0_2_2
% 28.18/9.23 |
% 28.18/9.23 | From (986) and (720) follows:
% 28.18/9.23 | (989) sum(n5, n0) = all_0_7_7
% 28.18/9.23 |
% 28.18/9.23 | From (987) and (718) follows:
% 28.18/9.24 | (990) sum(n19, n7) = all_0_4_4
% 28.18/9.24 |
% 28.18/9.24 | Instantiating formula (194) with n19, n7, all_0_4_4, n5 and discharging atoms sum(n19, n7) = all_0_4_4, sum(n19, n7) = n5, yields:
% 28.18/9.24 | (991) all_0_4_4 = n5
% 28.18/9.24 |
% 28.18/9.24 | Instantiating formula (194) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 28.18/9.24 | (992) all_0_2_2 = n12
% 28.18/9.24 |
% 28.18/9.24 | Instantiating formula (194) with n5, n0, all_0_7_7, n5 and discharging atoms sum(n5, n0) = all_0_7_7, sum(n5, n0) = n5, yields:
% 28.18/9.24 | (993) all_0_7_7 = n5
% 28.18/9.24 |
% 28.18/9.24 | From (992) and (722) follows:
% 28.18/9.24 | (994) sum(n12, n19) = all_0_0_0
% 28.18/9.24 |
% 28.18/9.24 | From (993)(991) and (435) follows:
% 28.18/9.24 | (995) sum(n5, n5) = all_0_3_3
% 28.18/9.24 |
% 28.18/9.24 | Instantiating formula (194) with n12, n19, all_0_0_0, n10 and discharging atoms sum(n12, n19) = all_0_0_0, sum(n12, n19) = n10, yields:
% 28.18/9.24 | (996) all_0_0_0 = n10
% 28.18/9.24 |
% 28.18/9.24 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 28.18/9.24 | (997) all_0_3_3 = n10
% 28.18/9.24 |
% 28.18/9.24 | Equations (996,997) can reduce 201 to:
% 28.18/9.24 | (746) $false
% 28.18/9.24 |
% 28.18/9.24 |-The branch is then unsatisfiable
% 28.18/9.24 |-Branch two:
% 28.18/9.24 | (999) ~ (all_0_11_11 = n6)
% 28.18/9.24 | (1000) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.18/9.24 |
% 28.18/9.24 +-Applying beta-rule and splitting (1000), into two cases.
% 28.18/9.24 |-Branch one:
% 28.18/9.24 | (1001) all_0_11_11 = n5
% 28.18/9.24 |
% 28.18/9.24 | From (1001) and (190) follows:
% 28.18/9.24 | (1002) pred(n5) = all_0_9_9
% 28.18/9.24 |
% 28.18/9.24 | From (1001) and (505) follows:
% 28.59/9.24 | (1003) succ(n5) = all_0_5_5
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (259) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 28.59/9.24 | (1004) all_0_9_9 = n4
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (184) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 28.59/9.24 | (1005) all_0_5_5 = n6
% 28.59/9.24 |
% 28.59/9.24 | From (1004)(1005) and (156) follows:
% 28.59/9.24 | (1006) sum(n4, n6) = all_0_2_2
% 28.59/9.24 |
% 28.59/9.24 | From (1004) and (720) follows:
% 28.59/9.24 | (1007) sum(n4, n0) = all_0_7_7
% 28.59/9.24 |
% 28.59/9.24 | From (1005) and (718) follows:
% 28.59/9.24 | (1008) sum(n19, n6) = all_0_4_4
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (194) with n19, n6, all_0_4_4, n4 and discharging atoms sum(n19, n6) = all_0_4_4, sum(n19, n6) = n4, yields:
% 28.59/9.24 | (1009) all_0_4_4 = n4
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (194) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 28.59/9.24 | (1010) all_0_2_2 = n10
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (194) with n4, n0, all_0_7_7, n4 and discharging atoms sum(n4, n0) = all_0_7_7, sum(n4, n0) = n4, yields:
% 28.59/9.24 | (1011) all_0_7_7 = n4
% 28.59/9.24 |
% 28.59/9.24 | From (1010) and (722) follows:
% 28.59/9.24 | (1012) sum(n10, n19) = all_0_0_0
% 28.59/9.24 |
% 28.59/9.24 | From (1011)(1009) and (435) follows:
% 28.59/9.24 | (1013) sum(n4, n4) = all_0_3_3
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (194) with n10, n19, all_0_0_0, n8 and discharging atoms sum(n10, n19) = all_0_0_0, sum(n10, n19) = n8, yields:
% 28.59/9.24 | (1014) all_0_0_0 = n8
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 28.59/9.24 | (1015) all_0_3_3 = n8
% 28.59/9.24 |
% 28.59/9.24 | Equations (1014,1015) can reduce 201 to:
% 28.59/9.24 | (746) $false
% 28.59/9.24 |
% 28.59/9.24 |-The branch is then unsatisfiable
% 28.59/9.24 |-Branch two:
% 28.59/9.24 | (1017) ~ (all_0_11_11 = n5)
% 28.59/9.24 | (1018) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.59/9.24 |
% 28.59/9.24 +-Applying beta-rule and splitting (1018), into two cases.
% 28.59/9.24 |-Branch one:
% 28.59/9.24 | (1019) all_0_11_11 = n4
% 28.59/9.24 |
% 28.59/9.24 | From (1019) and (190) follows:
% 28.59/9.24 | (1020) pred(n4) = all_0_9_9
% 28.59/9.24 |
% 28.59/9.24 | From (1019) and (505) follows:
% 28.59/9.24 | (1021) succ(n4) = all_0_5_5
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 28.59/9.24 | (1022) all_0_9_9 = n3
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 28.59/9.24 | (1023) all_0_5_5 = n5
% 28.59/9.24 |
% 28.59/9.24 | From (1022)(1023) and (156) follows:
% 28.59/9.24 | (1024) sum(n3, n5) = all_0_2_2
% 28.59/9.24 |
% 28.59/9.24 | From (1022) and (720) follows:
% 28.59/9.24 | (1025) sum(n3, n0) = all_0_7_7
% 28.59/9.24 |
% 28.59/9.24 | From (1023) and (718) follows:
% 28.59/9.24 | (1026) sum(n19, n5) = all_0_4_4
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (194) with n19, n5, all_0_4_4, n3 and discharging atoms sum(n19, n5) = all_0_4_4, sum(n19, n5) = n3, yields:
% 28.59/9.24 | (1027) all_0_4_4 = n3
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 28.59/9.24 | (1028) all_0_2_2 = n8
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (194) with n3, n0, all_0_7_7, n3 and discharging atoms sum(n3, n0) = all_0_7_7, sum(n3, n0) = n3, yields:
% 28.59/9.24 | (1029) all_0_7_7 = n3
% 28.59/9.24 |
% 28.59/9.24 | From (1028) and (722) follows:
% 28.59/9.24 | (1030) sum(n8, n19) = all_0_0_0
% 28.59/9.24 |
% 28.59/9.24 | From (1029)(1027) and (435) follows:
% 28.59/9.24 | (1031) sum(n3, n3) = all_0_3_3
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (194) with n8, n19, all_0_0_0, n6 and discharging atoms sum(n8, n19) = all_0_0_0, sum(n8, n19) = n6, yields:
% 28.59/9.24 | (1032) all_0_0_0 = n6
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 28.59/9.24 | (1033) all_0_3_3 = n6
% 28.59/9.24 |
% 28.59/9.24 | Equations (1032,1033) can reduce 201 to:
% 28.59/9.24 | (746) $false
% 28.59/9.24 |
% 28.59/9.24 |-The branch is then unsatisfiable
% 28.59/9.24 |-Branch two:
% 28.59/9.24 | (1035) ~ (all_0_11_11 = n4)
% 28.59/9.24 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.59/9.24 |
% 28.59/9.24 +-Applying beta-rule and splitting (1036), into two cases.
% 28.59/9.24 |-Branch one:
% 28.59/9.24 | (1037) all_0_11_11 = n3
% 28.59/9.24 |
% 28.59/9.24 | From (1037) and (190) follows:
% 28.59/9.24 | (1038) pred(n3) = all_0_9_9
% 28.59/9.24 |
% 28.59/9.24 | From (1037) and (505) follows:
% 28.59/9.24 | (1039) succ(n3) = all_0_5_5
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 28.59/9.24 | (1040) all_0_9_9 = n2
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 28.59/9.24 | (1041) all_0_5_5 = n4
% 28.59/9.24 |
% 28.59/9.24 | From (1040)(1041) and (156) follows:
% 28.59/9.24 | (1042) sum(n2, n4) = all_0_2_2
% 28.59/9.24 |
% 28.59/9.24 | From (1040) and (720) follows:
% 28.59/9.24 | (1043) sum(n2, n0) = all_0_7_7
% 28.59/9.24 |
% 28.59/9.24 | From (1041) and (718) follows:
% 28.59/9.24 | (1044) sum(n19, n4) = all_0_4_4
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (194) with n19, n4, all_0_4_4, n2 and discharging atoms sum(n19, n4) = all_0_4_4, sum(n19, n4) = n2, yields:
% 28.59/9.24 | (1045) all_0_4_4 = n2
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 28.59/9.24 | (1046) all_0_2_2 = n6
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (194) with n2, n0, all_0_7_7, n2 and discharging atoms sum(n2, n0) = all_0_7_7, sum(n2, n0) = n2, yields:
% 28.59/9.24 | (1047) all_0_7_7 = n2
% 28.59/9.24 |
% 28.59/9.24 | From (1046) and (722) follows:
% 28.59/9.24 | (1048) sum(n6, n19) = all_0_0_0
% 28.59/9.24 |
% 28.59/9.24 | From (1047)(1045) and (435) follows:
% 28.59/9.24 | (1049) sum(n2, n2) = all_0_3_3
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (194) with n6, n19, all_0_0_0, n4 and discharging atoms sum(n6, n19) = all_0_0_0, sum(n6, n19) = n4, yields:
% 28.59/9.24 | (1050) all_0_0_0 = n4
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 28.59/9.24 | (1051) all_0_3_3 = n4
% 28.59/9.24 |
% 28.59/9.24 | Equations (1050,1051) can reduce 201 to:
% 28.59/9.24 | (746) $false
% 28.59/9.24 |
% 28.59/9.24 |-The branch is then unsatisfiable
% 28.59/9.24 |-Branch two:
% 28.59/9.24 | (1053) ~ (all_0_11_11 = n3)
% 28.59/9.24 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.59/9.24 |
% 28.59/9.24 +-Applying beta-rule and splitting (1054), into two cases.
% 28.59/9.24 |-Branch one:
% 28.59/9.24 | (1055) all_0_11_11 = n2
% 28.59/9.24 |
% 28.59/9.24 | From (1055) and (190) follows:
% 28.59/9.24 | (1056) pred(n2) = all_0_9_9
% 28.59/9.24 |
% 28.59/9.24 | From (1055) and (505) follows:
% 28.59/9.24 | (1057) succ(n2) = all_0_5_5
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 28.59/9.24 | (1058) all_0_9_9 = n1
% 28.59/9.24 |
% 28.59/9.24 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 28.59/9.24 | (1059) all_0_5_5 = n3
% 28.59/9.24 |
% 28.59/9.24 | From (1058)(1059) and (156) follows:
% 28.59/9.24 | (1060) sum(n1, n3) = all_0_2_2
% 28.59/9.24 |
% 28.59/9.24 | From (1058) and (720) follows:
% 28.59/9.25 | (1061) sum(n1, n0) = all_0_7_7
% 28.59/9.25 |
% 28.59/9.25 | From (1059) and (718) follows:
% 28.59/9.25 | (1062) sum(n19, n3) = all_0_4_4
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n19, n3, all_0_4_4, n1 and discharging atoms sum(n19, n3) = all_0_4_4, sum(n19, n3) = n1, yields:
% 28.59/9.25 | (1063) all_0_4_4 = n1
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 28.59/9.25 | (1064) all_0_2_2 = n4
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n1, n0, all_0_7_7, n1 and discharging atoms sum(n1, n0) = all_0_7_7, sum(n1, n0) = n1, yields:
% 28.59/9.25 | (1065) all_0_7_7 = n1
% 28.59/9.25 |
% 28.59/9.25 | From (1064) and (722) follows:
% 28.59/9.25 | (1066) sum(n4, n19) = all_0_0_0
% 28.59/9.25 |
% 28.59/9.25 | From (1065)(1063) and (435) follows:
% 28.59/9.25 | (1067) sum(n1, n1) = all_0_3_3
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n4, n19, all_0_0_0, n2 and discharging atoms sum(n4, n19) = all_0_0_0, sum(n4, n19) = n2, yields:
% 28.59/9.25 | (1068) all_0_0_0 = n2
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 28.59/9.25 | (1069) all_0_3_3 = n2
% 28.59/9.25 |
% 28.59/9.25 | Equations (1068,1069) can reduce 201 to:
% 28.59/9.25 | (746) $false
% 28.59/9.25 |
% 28.59/9.25 |-The branch is then unsatisfiable
% 28.59/9.25 |-Branch two:
% 28.59/9.25 | (1071) ~ (all_0_11_11 = n2)
% 28.59/9.25 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 28.59/9.25 |
% 28.59/9.25 +-Applying beta-rule and splitting (1072), into two cases.
% 28.59/9.25 |-Branch one:
% 28.59/9.25 | (1073) all_0_11_11 = n1
% 28.59/9.25 |
% 28.59/9.25 | From (1073) and (190) follows:
% 28.59/9.25 | (1074) pred(n1) = all_0_9_9
% 28.59/9.25 |
% 28.59/9.25 | From (1073) and (505) follows:
% 28.59/9.25 | (1075) succ(n1) = all_0_5_5
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 28.59/9.25 | (1076) all_0_9_9 = n0
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 28.59/9.25 | (1077) all_0_5_5 = n2
% 28.59/9.25 |
% 28.59/9.25 | From (1076)(1077) and (156) follows:
% 28.59/9.25 | (1078) sum(n0, n2) = all_0_2_2
% 28.59/9.25 |
% 28.59/9.25 | From (1076) and (720) follows:
% 28.59/9.25 | (1079) sum(n0, n0) = all_0_7_7
% 28.59/9.25 |
% 28.59/9.25 | From (1077) and (718) follows:
% 28.59/9.25 | (1080) sum(n19, n2) = all_0_4_4
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n19, n2, all_0_4_4, n0 and discharging atoms sum(n19, n2) = all_0_4_4, sum(n19, n2) = n0, yields:
% 28.59/9.25 | (1081) all_0_4_4 = n0
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 28.59/9.25 | (1082) all_0_2_2 = n2
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n0, n0, all_0_7_7, n0 and discharging atoms sum(n0, n0) = all_0_7_7, sum(n0, n0) = n0, yields:
% 28.59/9.25 | (1083) all_0_7_7 = n0
% 28.59/9.25 |
% 28.59/9.25 | From (1082) and (722) follows:
% 28.59/9.25 | (1084) sum(n2, n19) = all_0_0_0
% 28.59/9.25 |
% 28.59/9.25 | From (1083)(1081) and (435) follows:
% 28.59/9.25 | (1085) sum(n0, n0) = all_0_3_3
% 28.59/9.25 |
% 28.59/9.25 | From (1083) and (1079) follows:
% 28.59/9.25 | (527) sum(n0, n0) = n0
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n2, n19, all_0_0_0, n0 and discharging atoms sum(n2, n19) = all_0_0_0, sum(n2, n19) = n0, yields:
% 28.59/9.25 | (1087) all_0_0_0 = n0
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 28.59/9.25 | (1088) all_0_3_3 = n0
% 28.59/9.25 |
% 28.59/9.25 | Equations (1087,1088) can reduce 201 to:
% 28.59/9.25 | (746) $false
% 28.59/9.25 |
% 28.59/9.25 |-The branch is then unsatisfiable
% 28.59/9.25 |-Branch two:
% 28.59/9.25 | (1090) ~ (all_0_11_11 = n1)
% 28.59/9.25 | (1091) all_0_11_11 = n0
% 28.59/9.25 |
% 28.59/9.25 | From (1091) and (190) follows:
% 28.59/9.25 | (1092) pred(n0) = all_0_9_9
% 28.59/9.25 |
% 28.59/9.25 | From (1091) and (505) follows:
% 28.59/9.25 | (1093) succ(n0) = all_0_5_5
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 28.59/9.25 | (1094) all_0_9_9 = n20
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 28.59/9.25 | (1095) all_0_5_5 = n1
% 28.59/9.25 |
% 28.59/9.25 | From (1094)(1095) and (156) follows:
% 28.59/9.25 | (1096) sum(n20, n1) = all_0_2_2
% 28.59/9.25 |
% 28.59/9.25 | From (1094) and (720) follows:
% 28.59/9.25 | (1097) sum(n20, n0) = all_0_7_7
% 28.59/9.25 |
% 28.59/9.25 | From (1095) and (718) follows:
% 28.59/9.25 | (1098) sum(n19, n1) = all_0_4_4
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 28.59/9.25 | (1099) all_0_2_2 = n0
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n20, n0, all_0_7_7, n20 and discharging atoms sum(n20, n0) = all_0_7_7, sum(n20, n0) = n20, yields:
% 28.59/9.25 | (1100) all_0_7_7 = n20
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n19, n1, all_0_4_4, n20 and discharging atoms sum(n19, n1) = all_0_4_4, sum(n19, n1) = n20, yields:
% 28.59/9.25 | (1101) all_0_4_4 = n20
% 28.59/9.25 |
% 28.59/9.25 | From (1099) and (722) follows:
% 28.59/9.25 | (1102) sum(n0, n19) = all_0_0_0
% 28.59/9.25 |
% 28.59/9.25 | From (1100)(1101) and (435) follows:
% 28.59/9.25 | (1103) sum(n20, n20) = all_0_3_3
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 28.59/9.25 | (1104) all_0_3_3 = n19
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n0, n19, all_0_0_0, n19 and discharging atoms sum(n0, n19) = all_0_0_0, sum(n0, n19) = n19, yields:
% 28.59/9.25 | (1105) all_0_0_0 = n19
% 28.59/9.25 |
% 28.59/9.25 | Equations (1105,1104) can reduce 201 to:
% 28.59/9.25 | (746) $false
% 28.59/9.25 |
% 28.59/9.25 |-The branch is then unsatisfiable
% 28.59/9.25 |-Branch two:
% 28.59/9.25 | (1107) ~ (all_0_10_10 = n20)
% 28.59/9.25 | (1108) all_0_10_10 = n19 | all_0_10_10 = n18 | all_0_10_10 = n17 | all_0_10_10 = n16 | all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.59/9.25 |
% 28.59/9.25 +-Applying beta-rule and splitting (304), into two cases.
% 28.59/9.25 |-Branch one:
% 28.59/9.25 | (724) all_0_11_11 = n20
% 28.59/9.25 |
% 28.59/9.25 | From (724) and (190) follows:
% 28.59/9.25 | (725) pred(n20) = all_0_9_9
% 28.59/9.25 |
% 28.59/9.25 | From (724) and (505) follows:
% 28.59/9.25 | (726) succ(n20) = all_0_5_5
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (259) with n20, all_0_9_9, n19 and discharging atoms pred(n20) = all_0_9_9, pred(n20) = n19, yields:
% 28.59/9.25 | (727) all_0_9_9 = n19
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (184) with n20, all_0_5_5, n0 and discharging atoms succ(n20) = all_0_5_5, succ(n20) = n0, yields:
% 28.59/9.25 | (728) all_0_5_5 = n0
% 28.59/9.25 |
% 28.59/9.25 | From (728) and (386) follows:
% 28.59/9.25 | (1114) sum(all_0_6_6, n0) = all_0_4_4
% 28.59/9.25 |
% 28.59/9.25 | From (727)(728) and (156) follows:
% 28.59/9.25 | (729) sum(n19, n0) = all_0_2_2
% 28.59/9.25 |
% 28.59/9.25 | From (727) and (74) follows:
% 28.59/9.25 | (1116) sum(n19, all_0_8_8) = all_0_7_7
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n19, n0, all_0_2_2, n19 and discharging atoms sum(n19, n0) = all_0_2_2, sum(n19, n0) = n19, yields:
% 28.59/9.25 | (732) all_0_2_2 = n19
% 28.59/9.25 |
% 28.59/9.25 | From (732) and (85) follows:
% 28.59/9.25 | (1118) sum(n19, all_0_1_1) = all_0_0_0
% 28.59/9.25 |
% 28.59/9.25 | From (732) and (729) follows:
% 28.59/9.25 | (288) sum(n19, n0) = n19
% 28.59/9.25 |
% 28.59/9.25 +-Applying beta-rule and splitting (1108), into two cases.
% 28.59/9.25 |-Branch one:
% 28.59/9.25 | (1120) all_0_10_10 = n19
% 28.59/9.25 |
% 28.59/9.25 | From (1120) and (57) follows:
% 28.59/9.25 | (1121) pred(n19) = all_0_6_6
% 28.59/9.25 |
% 28.59/9.25 | From (1120) and (381) follows:
% 28.59/9.25 | (1122) succ(n19) = all_0_8_8
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (259) with n19, all_0_6_6, n18 and discharging atoms pred(n19) = all_0_6_6, pred(n19) = n18, yields:
% 28.59/9.25 | (1123) all_0_6_6 = n18
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (184) with n19, all_0_8_8, n20 and discharging atoms succ(n19) = all_0_8_8, succ(n19) = n20, yields:
% 28.59/9.25 | (1124) all_0_8_8 = n20
% 28.59/9.25 |
% 28.59/9.25 | From (1123)(1124) and (628) follows:
% 28.59/9.25 | (1125) sum(n18, n20) = all_0_1_1
% 28.59/9.25 |
% 28.59/9.25 | From (1123) and (1114) follows:
% 28.59/9.25 | (1126) sum(n18, n0) = all_0_4_4
% 28.59/9.25 |
% 28.59/9.25 | From (1124) and (1116) follows:
% 28.59/9.25 | (1127) sum(n19, n20) = all_0_7_7
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n19, n20, all_0_7_7, n18 and discharging atoms sum(n19, n20) = all_0_7_7, sum(n19, n20) = n18, yields:
% 28.59/9.25 | (759) all_0_7_7 = n18
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n18, n20, all_0_1_1, n17 and discharging atoms sum(n18, n20) = all_0_1_1, sum(n18, n20) = n17, yields:
% 28.59/9.25 | (1129) all_0_1_1 = n17
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n18, n0, all_0_4_4, n18 and discharging atoms sum(n18, n0) = all_0_4_4, sum(n18, n0) = n18, yields:
% 28.59/9.25 | (757) all_0_4_4 = n18
% 28.59/9.25 |
% 28.59/9.25 | From (759)(757) and (435) follows:
% 28.59/9.25 | (761) sum(n18, n18) = all_0_3_3
% 28.59/9.25 |
% 28.59/9.25 | From (1129) and (1118) follows:
% 28.59/9.25 | (1132) sum(n19, n17) = all_0_0_0
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n19, n17, all_0_0_0, n15 and discharging atoms sum(n19, n17) = all_0_0_0, sum(n19, n17) = n15, yields:
% 28.59/9.25 | (763) all_0_0_0 = n15
% 28.59/9.25 |
% 28.59/9.25 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 28.59/9.26 | (762) all_0_3_3 = n15
% 28.59/9.26 |
% 28.59/9.26 | Equations (763,762) can reduce 201 to:
% 28.59/9.26 | (746) $false
% 28.59/9.26 |
% 28.59/9.26 |-The branch is then unsatisfiable
% 28.59/9.26 |-Branch two:
% 28.59/9.26 | (1136) ~ (all_0_10_10 = n19)
% 28.59/9.26 | (1137) all_0_10_10 = n18 | all_0_10_10 = n17 | all_0_10_10 = n16 | all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.59/9.26 |
% 28.59/9.26 +-Applying beta-rule and splitting (1137), into two cases.
% 28.59/9.26 |-Branch one:
% 28.59/9.26 | (1138) all_0_10_10 = n18
% 28.59/9.26 |
% 28.59/9.26 | From (1138) and (57) follows:
% 28.59/9.26 | (1139) pred(n18) = all_0_6_6
% 28.59/9.26 |
% 28.59/9.26 | From (1138) and (381) follows:
% 28.59/9.26 | (1140) succ(n18) = all_0_8_8
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (259) with n18, all_0_6_6, n17 and discharging atoms pred(n18) = all_0_6_6, pred(n18) = n17, yields:
% 28.59/9.26 | (1141) all_0_6_6 = n17
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (184) with n18, all_0_8_8, n19 and discharging atoms succ(n18) = all_0_8_8, succ(n18) = n19, yields:
% 28.59/9.26 | (1142) all_0_8_8 = n19
% 28.59/9.26 |
% 28.59/9.26 | From (1141)(1142) and (628) follows:
% 28.59/9.26 | (1143) sum(n17, n19) = all_0_1_1
% 28.59/9.26 |
% 28.59/9.26 | From (1141) and (1114) follows:
% 28.59/9.26 | (1144) sum(n17, n0) = all_0_4_4
% 28.59/9.26 |
% 28.59/9.26 | From (1142) and (1116) follows:
% 28.59/9.26 | (1145) sum(n19, n19) = all_0_7_7
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n19, n19, all_0_7_7, n17 and discharging atoms sum(n19, n19) = all_0_7_7, sum(n19, n19) = n17, yields:
% 28.59/9.26 | (777) all_0_7_7 = n17
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n17, n19, all_0_1_1, n15 and discharging atoms sum(n17, n19) = all_0_1_1, sum(n17, n19) = n15, yields:
% 28.59/9.26 | (1147) all_0_1_1 = n15
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n17, n0, all_0_4_4, n17 and discharging atoms sum(n17, n0) = all_0_4_4, sum(n17, n0) = n17, yields:
% 28.59/9.26 | (775) all_0_4_4 = n17
% 28.59/9.26 |
% 28.59/9.26 | From (777)(775) and (435) follows:
% 28.59/9.26 | (779) sum(n17, n17) = all_0_3_3
% 28.59/9.26 |
% 28.59/9.26 | From (1147) and (1118) follows:
% 28.59/9.26 | (1150) sum(n19, n15) = all_0_0_0
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n19, n15, all_0_0_0, n13 and discharging atoms sum(n19, n15) = all_0_0_0, sum(n19, n15) = n13, yields:
% 28.59/9.26 | (781) all_0_0_0 = n13
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 28.59/9.26 | (780) all_0_3_3 = n13
% 28.59/9.26 |
% 28.59/9.26 | Equations (781,780) can reduce 201 to:
% 28.59/9.26 | (746) $false
% 28.59/9.26 |
% 28.59/9.26 |-The branch is then unsatisfiable
% 28.59/9.26 |-Branch two:
% 28.59/9.26 | (1154) ~ (all_0_10_10 = n18)
% 28.59/9.26 | (1155) all_0_10_10 = n17 | all_0_10_10 = n16 | all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.59/9.26 |
% 28.59/9.26 +-Applying beta-rule and splitting (1155), into two cases.
% 28.59/9.26 |-Branch one:
% 28.59/9.26 | (1156) all_0_10_10 = n17
% 28.59/9.26 |
% 28.59/9.26 | From (1156) and (57) follows:
% 28.59/9.26 | (1157) pred(n17) = all_0_6_6
% 28.59/9.26 |
% 28.59/9.26 | From (1156) and (381) follows:
% 28.59/9.26 | (1158) succ(n17) = all_0_8_8
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (259) with n17, all_0_6_6, n16 and discharging atoms pred(n17) = all_0_6_6, pred(n17) = n16, yields:
% 28.59/9.26 | (1159) all_0_6_6 = n16
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (184) with n17, all_0_8_8, n18 and discharging atoms succ(n17) = all_0_8_8, succ(n17) = n18, yields:
% 28.59/9.26 | (1160) all_0_8_8 = n18
% 28.59/9.26 |
% 28.59/9.26 | From (1159)(1160) and (628) follows:
% 28.59/9.26 | (1161) sum(n16, n18) = all_0_1_1
% 28.59/9.26 |
% 28.59/9.26 | From (1159) and (1114) follows:
% 28.59/9.26 | (1162) sum(n16, n0) = all_0_4_4
% 28.59/9.26 |
% 28.59/9.26 | From (1160) and (1116) follows:
% 28.59/9.26 | (1163) sum(n19, n18) = all_0_7_7
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n19, n18, all_0_7_7, n16 and discharging atoms sum(n19, n18) = all_0_7_7, sum(n19, n18) = n16, yields:
% 28.59/9.26 | (795) all_0_7_7 = n16
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n16, n18, all_0_1_1, n13 and discharging atoms sum(n16, n18) = all_0_1_1, sum(n16, n18) = n13, yields:
% 28.59/9.26 | (1165) all_0_1_1 = n13
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n16, n0, all_0_4_4, n16 and discharging atoms sum(n16, n0) = all_0_4_4, sum(n16, n0) = n16, yields:
% 28.59/9.26 | (793) all_0_4_4 = n16
% 28.59/9.26 |
% 28.59/9.26 | From (795)(793) and (435) follows:
% 28.59/9.26 | (797) sum(n16, n16) = all_0_3_3
% 28.59/9.26 |
% 28.59/9.26 | From (1165) and (1118) follows:
% 28.59/9.26 | (1168) sum(n19, n13) = all_0_0_0
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n19, n13, all_0_0_0, n11 and discharging atoms sum(n19, n13) = all_0_0_0, sum(n19, n13) = n11, yields:
% 28.59/9.26 | (799) all_0_0_0 = n11
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 28.59/9.26 | (798) all_0_3_3 = n11
% 28.59/9.26 |
% 28.59/9.26 | Equations (799,798) can reduce 201 to:
% 28.59/9.26 | (746) $false
% 28.59/9.26 |
% 28.59/9.26 |-The branch is then unsatisfiable
% 28.59/9.26 |-Branch two:
% 28.59/9.26 | (1172) ~ (all_0_10_10 = n17)
% 28.59/9.26 | (1173) all_0_10_10 = n16 | all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.59/9.26 |
% 28.59/9.26 +-Applying beta-rule and splitting (1173), into two cases.
% 28.59/9.26 |-Branch one:
% 28.59/9.26 | (1174) all_0_10_10 = n16
% 28.59/9.26 |
% 28.59/9.26 | From (1174) and (57) follows:
% 28.59/9.26 | (1175) pred(n16) = all_0_6_6
% 28.59/9.26 |
% 28.59/9.26 | From (1174) and (381) follows:
% 28.59/9.26 | (1176) succ(n16) = all_0_8_8
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (259) with n16, all_0_6_6, n15 and discharging atoms pred(n16) = all_0_6_6, pred(n16) = n15, yields:
% 28.59/9.26 | (1177) all_0_6_6 = n15
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (184) with n16, all_0_8_8, n17 and discharging atoms succ(n16) = all_0_8_8, succ(n16) = n17, yields:
% 28.59/9.26 | (1178) all_0_8_8 = n17
% 28.59/9.26 |
% 28.59/9.26 | From (1177)(1178) and (628) follows:
% 28.59/9.26 | (1179) sum(n15, n17) = all_0_1_1
% 28.59/9.26 |
% 28.59/9.26 | From (1177) and (1114) follows:
% 28.59/9.26 | (1180) sum(n15, n0) = all_0_4_4
% 28.59/9.26 |
% 28.59/9.26 | From (1178) and (1116) follows:
% 28.59/9.26 | (1181) sum(n19, n17) = all_0_7_7
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n19, n17, all_0_7_7, n15 and discharging atoms sum(n19, n17) = all_0_7_7, sum(n19, n17) = n15, yields:
% 28.59/9.26 | (813) all_0_7_7 = n15
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n15, n17, all_0_1_1, n11 and discharging atoms sum(n15, n17) = all_0_1_1, sum(n15, n17) = n11, yields:
% 28.59/9.26 | (1183) all_0_1_1 = n11
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n15, n0, all_0_4_4, n15 and discharging atoms sum(n15, n0) = all_0_4_4, sum(n15, n0) = n15, yields:
% 28.59/9.26 | (811) all_0_4_4 = n15
% 28.59/9.26 |
% 28.59/9.26 | From (813)(811) and (435) follows:
% 28.59/9.26 | (815) sum(n15, n15) = all_0_3_3
% 28.59/9.26 |
% 28.59/9.26 | From (1183) and (1118) follows:
% 28.59/9.26 | (1186) sum(n19, n11) = all_0_0_0
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n19, n11, all_0_0_0, n9 and discharging atoms sum(n19, n11) = all_0_0_0, sum(n19, n11) = n9, yields:
% 28.59/9.26 | (817) all_0_0_0 = n9
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 28.59/9.26 | (816) all_0_3_3 = n9
% 28.59/9.26 |
% 28.59/9.26 | Equations (817,816) can reduce 201 to:
% 28.59/9.26 | (746) $false
% 28.59/9.26 |
% 28.59/9.26 |-The branch is then unsatisfiable
% 28.59/9.26 |-Branch two:
% 28.59/9.26 | (1190) ~ (all_0_10_10 = n16)
% 28.59/9.26 | (1191) all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.59/9.26 |
% 28.59/9.26 +-Applying beta-rule and splitting (1191), into two cases.
% 28.59/9.26 |-Branch one:
% 28.59/9.26 | (1192) all_0_10_10 = n15
% 28.59/9.26 |
% 28.59/9.26 | From (1192) and (57) follows:
% 28.59/9.26 | (1193) pred(n15) = all_0_6_6
% 28.59/9.26 |
% 28.59/9.26 | From (1192) and (381) follows:
% 28.59/9.26 | (1194) succ(n15) = all_0_8_8
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (259) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 28.59/9.26 | (1195) all_0_6_6 = n14
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (184) with n15, all_0_8_8, n16 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n16, yields:
% 28.59/9.26 | (1196) all_0_8_8 = n16
% 28.59/9.26 |
% 28.59/9.26 | From (1195)(1196) and (628) follows:
% 28.59/9.26 | (1197) sum(n14, n16) = all_0_1_1
% 28.59/9.26 |
% 28.59/9.26 | From (1195) and (1114) follows:
% 28.59/9.26 | (1198) sum(n14, n0) = all_0_4_4
% 28.59/9.26 |
% 28.59/9.26 | From (1196) and (1116) follows:
% 28.59/9.26 | (1199) sum(n19, n16) = all_0_7_7
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n19, n16, all_0_7_7, n14 and discharging atoms sum(n19, n16) = all_0_7_7, sum(n19, n16) = n14, yields:
% 28.59/9.26 | (831) all_0_7_7 = n14
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n14, n16, all_0_1_1, n9 and discharging atoms sum(n14, n16) = all_0_1_1, sum(n14, n16) = n9, yields:
% 28.59/9.26 | (1201) all_0_1_1 = n9
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n14, n0, all_0_4_4, n14 and discharging atoms sum(n14, n0) = all_0_4_4, sum(n14, n0) = n14, yields:
% 28.59/9.26 | (829) all_0_4_4 = n14
% 28.59/9.26 |
% 28.59/9.26 | From (831)(829) and (435) follows:
% 28.59/9.26 | (833) sum(n14, n14) = all_0_3_3
% 28.59/9.26 |
% 28.59/9.26 | From (1201) and (1118) follows:
% 28.59/9.26 | (1204) sum(n19, n9) = all_0_0_0
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n19, n9, all_0_0_0, n7 and discharging atoms sum(n19, n9) = all_0_0_0, sum(n19, n9) = n7, yields:
% 28.59/9.26 | (835) all_0_0_0 = n7
% 28.59/9.26 |
% 28.59/9.26 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 28.59/9.27 | (834) all_0_3_3 = n7
% 28.59/9.27 |
% 28.59/9.27 | Equations (835,834) can reduce 201 to:
% 28.59/9.27 | (746) $false
% 28.59/9.27 |
% 28.59/9.27 |-The branch is then unsatisfiable
% 28.59/9.27 |-Branch two:
% 28.59/9.27 | (1208) ~ (all_0_10_10 = n15)
% 28.59/9.27 | (1209) all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.59/9.27 |
% 28.59/9.27 +-Applying beta-rule and splitting (1209), into two cases.
% 28.59/9.27 |-Branch one:
% 28.59/9.27 | (1210) all_0_10_10 = n14
% 28.59/9.27 |
% 28.59/9.27 | From (1210) and (57) follows:
% 28.59/9.27 | (1211) pred(n14) = all_0_6_6
% 28.59/9.27 |
% 28.59/9.27 | From (1210) and (381) follows:
% 28.59/9.27 | (1212) succ(n14) = all_0_8_8
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (259) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 28.59/9.27 | (1213) all_0_6_6 = n13
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (184) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 28.59/9.27 | (1214) all_0_8_8 = n15
% 28.59/9.27 |
% 28.59/9.27 | From (1213)(1214) and (628) follows:
% 28.59/9.27 | (1215) sum(n13, n15) = all_0_1_1
% 28.59/9.27 |
% 28.59/9.27 | From (1213) and (1114) follows:
% 28.59/9.27 | (1216) sum(n13, n0) = all_0_4_4
% 28.59/9.27 |
% 28.59/9.27 | From (1214) and (1116) follows:
% 28.59/9.27 | (1217) sum(n19, n15) = all_0_7_7
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n19, n15, all_0_7_7, n13 and discharging atoms sum(n19, n15) = all_0_7_7, sum(n19, n15) = n13, yields:
% 28.59/9.27 | (849) all_0_7_7 = n13
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n13, n15, all_0_1_1, n7 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n7, yields:
% 28.59/9.27 | (1219) all_0_1_1 = n7
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n13, n0, all_0_4_4, n13 and discharging atoms sum(n13, n0) = all_0_4_4, sum(n13, n0) = n13, yields:
% 28.59/9.27 | (847) all_0_4_4 = n13
% 28.59/9.27 |
% 28.59/9.27 | From (849)(847) and (435) follows:
% 28.59/9.27 | (851) sum(n13, n13) = all_0_3_3
% 28.59/9.27 |
% 28.59/9.27 | From (1219) and (1118) follows:
% 28.59/9.27 | (1222) sum(n19, n7) = all_0_0_0
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n19, n7, all_0_0_0, n5 and discharging atoms sum(n19, n7) = all_0_0_0, sum(n19, n7) = n5, yields:
% 28.59/9.27 | (853) all_0_0_0 = n5
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 28.59/9.27 | (852) all_0_3_3 = n5
% 28.59/9.27 |
% 28.59/9.27 | Equations (853,852) can reduce 201 to:
% 28.59/9.27 | (746) $false
% 28.59/9.27 |
% 28.59/9.27 |-The branch is then unsatisfiable
% 28.59/9.27 |-Branch two:
% 28.59/9.27 | (1226) ~ (all_0_10_10 = n14)
% 28.59/9.27 | (1227) all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.59/9.27 |
% 28.59/9.27 +-Applying beta-rule and splitting (1227), into two cases.
% 28.59/9.27 |-Branch one:
% 28.59/9.27 | (1228) all_0_10_10 = n13
% 28.59/9.27 |
% 28.59/9.27 | From (1228) and (57) follows:
% 28.59/9.27 | (1229) pred(n13) = all_0_6_6
% 28.59/9.27 |
% 28.59/9.27 | From (1228) and (381) follows:
% 28.59/9.27 | (1230) succ(n13) = all_0_8_8
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (259) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 28.59/9.27 | (1231) all_0_6_6 = n12
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (184) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 28.59/9.27 | (1232) all_0_8_8 = n14
% 28.59/9.27 |
% 28.59/9.27 | From (1231)(1232) and (628) follows:
% 28.59/9.27 | (1233) sum(n12, n14) = all_0_1_1
% 28.59/9.27 |
% 28.59/9.27 | From (1231) and (1114) follows:
% 28.59/9.27 | (1234) sum(n12, n0) = all_0_4_4
% 28.59/9.27 |
% 28.59/9.27 | From (1232) and (1116) follows:
% 28.59/9.27 | (1235) sum(n19, n14) = all_0_7_7
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n19, n14, all_0_7_7, n12 and discharging atoms sum(n19, n14) = all_0_7_7, sum(n19, n14) = n12, yields:
% 28.59/9.27 | (867) all_0_7_7 = n12
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n12, n14, all_0_1_1, n5 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n5, yields:
% 28.59/9.27 | (1237) all_0_1_1 = n5
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n12, n0, all_0_4_4, n12 and discharging atoms sum(n12, n0) = all_0_4_4, sum(n12, n0) = n12, yields:
% 28.59/9.27 | (865) all_0_4_4 = n12
% 28.59/9.27 |
% 28.59/9.27 | From (867)(865) and (435) follows:
% 28.59/9.27 | (869) sum(n12, n12) = all_0_3_3
% 28.59/9.27 |
% 28.59/9.27 | From (1237) and (1118) follows:
% 28.59/9.27 | (1240) sum(n19, n5) = all_0_0_0
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n19, n5, all_0_0_0, n3 and discharging atoms sum(n19, n5) = all_0_0_0, sum(n19, n5) = n3, yields:
% 28.59/9.27 | (871) all_0_0_0 = n3
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 28.59/9.27 | (870) all_0_3_3 = n3
% 28.59/9.27 |
% 28.59/9.27 | Equations (871,870) can reduce 201 to:
% 28.59/9.27 | (746) $false
% 28.59/9.27 |
% 28.59/9.27 |-The branch is then unsatisfiable
% 28.59/9.27 |-Branch two:
% 28.59/9.27 | (1244) ~ (all_0_10_10 = n13)
% 28.59/9.27 | (1245) all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.59/9.27 |
% 28.59/9.27 +-Applying beta-rule and splitting (1245), into two cases.
% 28.59/9.27 |-Branch one:
% 28.59/9.27 | (1246) all_0_10_10 = n12
% 28.59/9.27 |
% 28.59/9.27 | From (1246) and (57) follows:
% 28.59/9.27 | (1247) pred(n12) = all_0_6_6
% 28.59/9.27 |
% 28.59/9.27 | From (1246) and (381) follows:
% 28.59/9.27 | (1248) succ(n12) = all_0_8_8
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (259) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 28.59/9.27 | (1249) all_0_6_6 = n11
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (184) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 28.59/9.27 | (1250) all_0_8_8 = n13
% 28.59/9.27 |
% 28.59/9.27 | From (1249)(1250) and (628) follows:
% 28.59/9.27 | (1251) sum(n11, n13) = all_0_1_1
% 28.59/9.27 |
% 28.59/9.27 | From (1249) and (1114) follows:
% 28.59/9.27 | (1252) sum(n11, n0) = all_0_4_4
% 28.59/9.27 |
% 28.59/9.27 | From (1250) and (1116) follows:
% 28.59/9.27 | (1253) sum(n19, n13) = all_0_7_7
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n19, n13, all_0_7_7, n11 and discharging atoms sum(n19, n13) = all_0_7_7, sum(n19, n13) = n11, yields:
% 28.59/9.27 | (885) all_0_7_7 = n11
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n11, n13, all_0_1_1, n3 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n3, yields:
% 28.59/9.27 | (1255) all_0_1_1 = n3
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n11, n0, all_0_4_4, n11 and discharging atoms sum(n11, n0) = all_0_4_4, sum(n11, n0) = n11, yields:
% 28.59/9.27 | (883) all_0_4_4 = n11
% 28.59/9.27 |
% 28.59/9.27 | From (885)(883) and (435) follows:
% 28.59/9.27 | (887) sum(n11, n11) = all_0_3_3
% 28.59/9.27 |
% 28.59/9.27 | From (1255) and (1118) follows:
% 28.59/9.27 | (1258) sum(n19, n3) = all_0_0_0
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n19, n3, all_0_0_0, n1 and discharging atoms sum(n19, n3) = all_0_0_0, sum(n19, n3) = n1, yields:
% 28.59/9.27 | (889) all_0_0_0 = n1
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 28.59/9.27 | (888) all_0_3_3 = n1
% 28.59/9.27 |
% 28.59/9.27 | Equations (889,888) can reduce 201 to:
% 28.59/9.27 | (746) $false
% 28.59/9.27 |
% 28.59/9.27 |-The branch is then unsatisfiable
% 28.59/9.27 |-Branch two:
% 28.59/9.27 | (1262) ~ (all_0_10_10 = n12)
% 28.59/9.27 | (1263) all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.59/9.27 |
% 28.59/9.27 +-Applying beta-rule and splitting (1263), into two cases.
% 28.59/9.27 |-Branch one:
% 28.59/9.27 | (1264) all_0_10_10 = n11
% 28.59/9.27 |
% 28.59/9.27 | From (1264) and (57) follows:
% 28.59/9.27 | (1265) pred(n11) = all_0_6_6
% 28.59/9.27 |
% 28.59/9.27 | From (1264) and (381) follows:
% 28.59/9.27 | (1266) succ(n11) = all_0_8_8
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (259) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 28.59/9.27 | (1267) all_0_6_6 = n10
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (184) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 28.59/9.27 | (1268) all_0_8_8 = n12
% 28.59/9.27 |
% 28.59/9.27 | From (1267)(1268) and (628) follows:
% 28.59/9.27 | (1269) sum(n10, n12) = all_0_1_1
% 28.59/9.27 |
% 28.59/9.27 | From (1267) and (1114) follows:
% 28.59/9.27 | (1270) sum(n10, n0) = all_0_4_4
% 28.59/9.27 |
% 28.59/9.27 | From (1268) and (1116) follows:
% 28.59/9.27 | (1271) sum(n19, n12) = all_0_7_7
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n19, n12, all_0_7_7, n10 and discharging atoms sum(n19, n12) = all_0_7_7, sum(n19, n12) = n10, yields:
% 28.59/9.27 | (903) all_0_7_7 = n10
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n10, n12, all_0_1_1, n1 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n1, yields:
% 28.59/9.27 | (1273) all_0_1_1 = n1
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n10, n0, all_0_4_4, n10 and discharging atoms sum(n10, n0) = all_0_4_4, sum(n10, n0) = n10, yields:
% 28.59/9.27 | (901) all_0_4_4 = n10
% 28.59/9.27 |
% 28.59/9.27 | From (903)(901) and (435) follows:
% 28.59/9.27 | (905) sum(n10, n10) = all_0_3_3
% 28.59/9.27 |
% 28.59/9.27 | From (1273) and (1118) follows:
% 28.59/9.27 | (1276) sum(n19, n1) = all_0_0_0
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n19, n1, all_0_0_0, n20 and discharging atoms sum(n19, n1) = all_0_0_0, sum(n19, n1) = n20, yields:
% 28.59/9.27 | (907) all_0_0_0 = n20
% 28.59/9.27 |
% 28.59/9.27 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 28.59/9.27 | (906) all_0_3_3 = n20
% 28.59/9.27 |
% 28.59/9.27 | Equations (907,906) can reduce 201 to:
% 28.59/9.27 | (746) $false
% 28.59/9.28 |
% 28.59/9.28 |-The branch is then unsatisfiable
% 28.59/9.28 |-Branch two:
% 28.59/9.28 | (1280) ~ (all_0_10_10 = n11)
% 28.59/9.28 | (1281) all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.59/9.28 |
% 28.59/9.28 +-Applying beta-rule and splitting (1281), into two cases.
% 28.59/9.28 |-Branch one:
% 28.59/9.28 | (1282) all_0_10_10 = n10
% 28.59/9.28 |
% 28.59/9.28 | From (1282) and (57) follows:
% 28.59/9.28 | (1283) pred(n10) = all_0_6_6
% 28.59/9.28 |
% 28.59/9.28 | From (1282) and (381) follows:
% 28.59/9.28 | (1284) succ(n10) = all_0_8_8
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (259) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 28.59/9.28 | (1285) all_0_6_6 = n9
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (184) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 28.59/9.28 | (1286) all_0_8_8 = n11
% 28.59/9.28 |
% 28.59/9.28 | From (1285)(1286) and (628) follows:
% 28.59/9.28 | (1287) sum(n9, n11) = all_0_1_1
% 28.59/9.28 |
% 28.59/9.28 | From (1285) and (1114) follows:
% 28.59/9.28 | (1288) sum(n9, n0) = all_0_4_4
% 28.59/9.28 |
% 28.59/9.28 | From (1286) and (1116) follows:
% 28.59/9.28 | (1289) sum(n19, n11) = all_0_7_7
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n19, n11, all_0_7_7, n9 and discharging atoms sum(n19, n11) = all_0_7_7, sum(n19, n11) = n9, yields:
% 28.59/9.28 | (921) all_0_7_7 = n9
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 28.59/9.28 | (1291) all_0_1_1 = n20
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n9, n0, all_0_4_4, n9 and discharging atoms sum(n9, n0) = all_0_4_4, sum(n9, n0) = n9, yields:
% 28.59/9.28 | (919) all_0_4_4 = n9
% 28.59/9.28 |
% 28.59/9.28 | From (921)(919) and (435) follows:
% 28.59/9.28 | (923) sum(n9, n9) = all_0_3_3
% 28.59/9.28 |
% 28.59/9.28 | From (1291) and (1118) follows:
% 28.59/9.28 | (1294) sum(n19, n20) = all_0_0_0
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n19, n20, all_0_0_0, n18 and discharging atoms sum(n19, n20) = all_0_0_0, sum(n19, n20) = n18, yields:
% 28.59/9.28 | (924) all_0_0_0 = n18
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 28.59/9.28 | (925) all_0_3_3 = n18
% 28.59/9.28 |
% 28.59/9.28 | Equations (924,925) can reduce 201 to:
% 28.59/9.28 | (746) $false
% 28.59/9.28 |
% 28.59/9.28 |-The branch is then unsatisfiable
% 28.59/9.28 |-Branch two:
% 28.59/9.28 | (1298) ~ (all_0_10_10 = n10)
% 28.59/9.28 | (1299) all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.59/9.28 |
% 28.59/9.28 +-Applying beta-rule and splitting (1299), into two cases.
% 28.59/9.28 |-Branch one:
% 28.59/9.28 | (1300) all_0_10_10 = n9
% 28.59/9.28 |
% 28.59/9.28 | From (1300) and (57) follows:
% 28.59/9.28 | (1301) pred(n9) = all_0_6_6
% 28.59/9.28 |
% 28.59/9.28 | From (1300) and (381) follows:
% 28.59/9.28 | (1302) succ(n9) = all_0_8_8
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (259) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 28.59/9.28 | (1303) all_0_6_6 = n8
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (184) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 28.59/9.28 | (1304) all_0_8_8 = n10
% 28.59/9.28 |
% 28.59/9.28 | From (1303)(1304) and (628) follows:
% 28.59/9.28 | (1305) sum(n8, n10) = all_0_1_1
% 28.59/9.28 |
% 28.59/9.28 | From (1303) and (1114) follows:
% 28.59/9.28 | (1306) sum(n8, n0) = all_0_4_4
% 28.59/9.28 |
% 28.59/9.28 | From (1304) and (1116) follows:
% 28.59/9.28 | (1307) sum(n19, n10) = all_0_7_7
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n19, n10, all_0_7_7, n8 and discharging atoms sum(n19, n10) = all_0_7_7, sum(n19, n10) = n8, yields:
% 28.59/9.28 | (939) all_0_7_7 = n8
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 28.59/9.28 | (1309) all_0_1_1 = n18
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n8, n0, all_0_4_4, n8 and discharging atoms sum(n8, n0) = all_0_4_4, sum(n8, n0) = n8, yields:
% 28.59/9.28 | (937) all_0_4_4 = n8
% 28.59/9.28 |
% 28.59/9.28 | From (939)(937) and (435) follows:
% 28.59/9.28 | (941) sum(n8, n8) = all_0_3_3
% 28.59/9.28 |
% 28.59/9.28 | From (1309) and (1118) follows:
% 28.59/9.28 | (1312) sum(n19, n18) = all_0_0_0
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n19, n18, all_0_0_0, n16 and discharging atoms sum(n19, n18) = all_0_0_0, sum(n19, n18) = n16, yields:
% 28.59/9.28 | (942) all_0_0_0 = n16
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 28.59/9.28 | (943) all_0_3_3 = n16
% 28.59/9.28 |
% 28.59/9.28 | Equations (942,943) can reduce 201 to:
% 28.59/9.28 | (746) $false
% 28.59/9.28 |
% 28.59/9.28 |-The branch is then unsatisfiable
% 28.59/9.28 |-Branch two:
% 28.59/9.28 | (1316) ~ (all_0_10_10 = n9)
% 28.59/9.28 | (1317) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.59/9.28 |
% 28.59/9.28 +-Applying beta-rule and splitting (1317), into two cases.
% 28.59/9.28 |-Branch one:
% 28.59/9.28 | (1318) all_0_10_10 = n8
% 28.59/9.28 |
% 28.59/9.28 | From (1318) and (57) follows:
% 28.59/9.28 | (1319) pred(n8) = all_0_6_6
% 28.59/9.28 |
% 28.59/9.28 | From (1318) and (381) follows:
% 28.59/9.28 | (1320) succ(n8) = all_0_8_8
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (259) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 28.59/9.28 | (1321) all_0_6_6 = n7
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (184) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 28.59/9.28 | (1322) all_0_8_8 = n9
% 28.59/9.28 |
% 28.59/9.28 | From (1321)(1322) and (628) follows:
% 28.59/9.28 | (1323) sum(n7, n9) = all_0_1_1
% 28.59/9.28 |
% 28.59/9.28 | From (1321) and (1114) follows:
% 28.59/9.28 | (1324) sum(n7, n0) = all_0_4_4
% 28.59/9.28 |
% 28.59/9.28 | From (1322) and (1116) follows:
% 28.59/9.28 | (1325) sum(n19, n9) = all_0_7_7
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n19, n9, all_0_7_7, n7 and discharging atoms sum(n19, n9) = all_0_7_7, sum(n19, n9) = n7, yields:
% 28.59/9.28 | (957) all_0_7_7 = n7
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 28.59/9.28 | (1327) all_0_1_1 = n16
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n7, n0, all_0_4_4, n7 and discharging atoms sum(n7, n0) = all_0_4_4, sum(n7, n0) = n7, yields:
% 28.59/9.28 | (955) all_0_4_4 = n7
% 28.59/9.28 |
% 28.59/9.28 | From (957)(955) and (435) follows:
% 28.59/9.28 | (959) sum(n7, n7) = all_0_3_3
% 28.59/9.28 |
% 28.59/9.28 | From (1327) and (1118) follows:
% 28.59/9.28 | (1330) sum(n19, n16) = all_0_0_0
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n19, n16, all_0_0_0, n14 and discharging atoms sum(n19, n16) = all_0_0_0, sum(n19, n16) = n14, yields:
% 28.59/9.28 | (960) all_0_0_0 = n14
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 28.59/9.28 | (961) all_0_3_3 = n14
% 28.59/9.28 |
% 28.59/9.28 | Equations (960,961) can reduce 201 to:
% 28.59/9.28 | (746) $false
% 28.59/9.28 |
% 28.59/9.28 |-The branch is then unsatisfiable
% 28.59/9.28 |-Branch two:
% 28.59/9.28 | (1334) ~ (all_0_10_10 = n8)
% 28.59/9.28 | (1335) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.59/9.28 |
% 28.59/9.28 +-Applying beta-rule and splitting (1335), into two cases.
% 28.59/9.28 |-Branch one:
% 28.59/9.28 | (1336) all_0_10_10 = n7
% 28.59/9.28 |
% 28.59/9.28 | From (1336) and (57) follows:
% 28.59/9.28 | (1337) pred(n7) = all_0_6_6
% 28.59/9.28 |
% 28.59/9.28 | From (1336) and (381) follows:
% 28.59/9.28 | (1338) succ(n7) = all_0_8_8
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (259) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 28.59/9.28 | (1339) all_0_6_6 = n6
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (184) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 28.59/9.28 | (1340) all_0_8_8 = n8
% 28.59/9.28 |
% 28.59/9.28 | From (1339)(1340) and (628) follows:
% 28.59/9.28 | (1341) sum(n6, n8) = all_0_1_1
% 28.59/9.28 |
% 28.59/9.28 | From (1339) and (1114) follows:
% 28.59/9.28 | (1342) sum(n6, n0) = all_0_4_4
% 28.59/9.28 |
% 28.59/9.28 | From (1340) and (1116) follows:
% 28.59/9.28 | (1343) sum(n19, n8) = all_0_7_7
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n19, n8, all_0_7_7, n6 and discharging atoms sum(n19, n8) = all_0_7_7, sum(n19, n8) = n6, yields:
% 28.59/9.28 | (975) all_0_7_7 = n6
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 28.59/9.28 | (1345) all_0_1_1 = n14
% 28.59/9.28 |
% 28.59/9.28 | Instantiating formula (194) with n6, n0, all_0_4_4, n6 and discharging atoms sum(n6, n0) = all_0_4_4, sum(n6, n0) = n6, yields:
% 28.59/9.28 | (973) all_0_4_4 = n6
% 28.59/9.28 |
% 28.59/9.28 | From (975)(973) and (435) follows:
% 28.59/9.29 | (977) sum(n6, n6) = all_0_3_3
% 28.59/9.29 |
% 28.59/9.29 | From (1345) and (1118) follows:
% 28.59/9.29 | (1348) sum(n19, n14) = all_0_0_0
% 28.59/9.29 |
% 28.59/9.29 | Instantiating formula (194) with n19, n14, all_0_0_0, n12 and discharging atoms sum(n19, n14) = all_0_0_0, sum(n19, n14) = n12, yields:
% 28.59/9.29 | (978) all_0_0_0 = n12
% 28.59/9.29 |
% 28.59/9.29 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 28.59/9.29 | (979) all_0_3_3 = n12
% 28.59/9.29 |
% 28.59/9.29 | Equations (978,979) can reduce 201 to:
% 28.59/9.29 | (746) $false
% 28.59/9.29 |
% 28.59/9.29 |-The branch is then unsatisfiable
% 28.59/9.29 |-Branch two:
% 28.59/9.29 | (1352) ~ (all_0_10_10 = n7)
% 28.59/9.29 | (1353) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.59/9.29 |
% 28.59/9.29 +-Applying beta-rule and splitting (1353), into two cases.
% 28.59/9.29 |-Branch one:
% 28.59/9.29 | (1354) all_0_10_10 = n6
% 28.59/9.29 |
% 28.59/9.29 | From (1354) and (57) follows:
% 28.59/9.29 | (1355) pred(n6) = all_0_6_6
% 28.59/9.29 |
% 28.59/9.29 | From (1354) and (381) follows:
% 28.59/9.29 | (1356) succ(n6) = all_0_8_8
% 28.59/9.29 |
% 28.59/9.29 | Instantiating formula (259) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 28.59/9.29 | (1357) all_0_6_6 = n5
% 28.59/9.29 |
% 28.59/9.29 | Instantiating formula (184) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 28.59/9.29 | (1358) all_0_8_8 = n7
% 28.59/9.29 |
% 28.59/9.29 | From (1357)(1358) and (628) follows:
% 28.59/9.29 | (1359) sum(n5, n7) = all_0_1_1
% 28.59/9.29 |
% 28.59/9.29 | From (1357) and (1114) follows:
% 28.59/9.29 | (1360) sum(n5, n0) = all_0_4_4
% 28.59/9.29 |
% 28.59/9.29 | From (1358) and (1116) follows:
% 28.59/9.29 | (1361) sum(n19, n7) = all_0_7_7
% 28.59/9.29 |
% 28.59/9.29 | Instantiating formula (194) with n19, n7, all_0_7_7, n5 and discharging atoms sum(n19, n7) = all_0_7_7, sum(n19, n7) = n5, yields:
% 28.59/9.29 | (993) all_0_7_7 = n5
% 28.59/9.29 |
% 28.59/9.29 | Instantiating formula (194) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 28.59/9.29 | (1363) all_0_1_1 = n12
% 28.59/9.29 |
% 28.59/9.29 | Instantiating formula (194) with n5, n0, all_0_4_4, n5 and discharging atoms sum(n5, n0) = all_0_4_4, sum(n5, n0) = n5, yields:
% 28.59/9.29 | (991) all_0_4_4 = n5
% 28.59/9.29 |
% 28.59/9.29 | From (993)(991) and (435) follows:
% 28.59/9.29 | (995) sum(n5, n5) = all_0_3_3
% 28.59/9.29 |
% 28.59/9.29 | From (1363) and (1118) follows:
% 28.59/9.29 | (1366) sum(n19, n12) = all_0_0_0
% 28.59/9.29 |
% 28.59/9.29 | Instantiating formula (194) with n19, n12, all_0_0_0, n10 and discharging atoms sum(n19, n12) = all_0_0_0, sum(n19, n12) = n10, yields:
% 28.59/9.29 | (996) all_0_0_0 = n10
% 28.59/9.29 |
% 28.59/9.29 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 28.59/9.29 | (997) all_0_3_3 = n10
% 28.59/9.29 |
% 28.59/9.29 | Equations (996,997) can reduce 201 to:
% 28.59/9.29 | (746) $false
% 28.59/9.29 |
% 28.59/9.29 |-The branch is then unsatisfiable
% 28.59/9.29 |-Branch two:
% 28.59/9.29 | (1370) ~ (all_0_10_10 = n6)
% 28.59/9.29 | (1371) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.59/9.29 |
% 28.59/9.29 +-Applying beta-rule and splitting (1371), into two cases.
% 28.59/9.29 |-Branch one:
% 28.59/9.29 | (1372) all_0_10_10 = n5
% 28.59/9.29 |
% 28.59/9.29 | From (1372) and (57) follows:
% 28.59/9.29 | (1373) pred(n5) = all_0_6_6
% 28.59/9.29 |
% 28.59/9.29 | From (1372) and (381) follows:
% 28.59/9.29 | (1374) succ(n5) = all_0_8_8
% 28.59/9.29 |
% 28.59/9.29 | Instantiating formula (259) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 28.59/9.29 | (1375) all_0_6_6 = n4
% 28.59/9.29 |
% 28.59/9.29 | Instantiating formula (184) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 28.59/9.29 | (1376) all_0_8_8 = n6
% 28.59/9.29 |
% 28.59/9.29 | From (1375)(1376) and (628) follows:
% 28.59/9.29 | (1377) sum(n4, n6) = all_0_1_1
% 28.59/9.29 |
% 28.59/9.29 | From (1375) and (1114) follows:
% 28.59/9.29 | (1378) sum(n4, n0) = all_0_4_4
% 28.59/9.29 |
% 28.59/9.29 | From (1376) and (1116) follows:
% 28.59/9.29 | (1379) sum(n19, n6) = all_0_7_7
% 28.59/9.29 |
% 28.59/9.29 | Instantiating formula (194) with n19, n6, all_0_7_7, n4 and discharging atoms sum(n19, n6) = all_0_7_7, sum(n19, n6) = n4, yields:
% 28.59/9.29 | (1011) all_0_7_7 = n4
% 28.59/9.29 |
% 28.59/9.29 | Instantiating formula (194) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 28.59/9.29 | (1381) all_0_1_1 = n10
% 28.59/9.29 |
% 28.59/9.29 | Instantiating formula (194) with n4, n0, all_0_4_4, n4 and discharging atoms sum(n4, n0) = all_0_4_4, sum(n4, n0) = n4, yields:
% 28.59/9.29 | (1009) all_0_4_4 = n4
% 28.59/9.29 |
% 28.59/9.29 | From (1011)(1009) and (435) follows:
% 28.59/9.29 | (1013) sum(n4, n4) = all_0_3_3
% 28.59/9.29 |
% 28.59/9.29 | From (1381) and (1118) follows:
% 28.59/9.29 | (1384) sum(n19, n10) = all_0_0_0
% 28.59/9.29 |
% 28.59/9.29 | Instantiating formula (194) with n19, n10, all_0_0_0, n8 and discharging atoms sum(n19, n10) = all_0_0_0, sum(n19, n10) = n8, yields:
% 28.59/9.29 | (1014) all_0_0_0 = n8
% 28.59/9.29 |
% 28.59/9.29 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 28.59/9.29 | (1015) all_0_3_3 = n8
% 28.59/9.29 |
% 28.59/9.29 | Equations (1014,1015) can reduce 201 to:
% 28.59/9.29 | (746) $false
% 28.59/9.29 |
% 28.59/9.29 |-The branch is then unsatisfiable
% 28.59/9.29 |-Branch two:
% 28.59/9.29 | (1388) ~ (all_0_10_10 = n5)
% 28.59/9.29 | (1389) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.59/9.29 |
% 28.59/9.29 +-Applying beta-rule and splitting (1389), into two cases.
% 28.59/9.29 |-Branch one:
% 28.59/9.29 | (1390) all_0_10_10 = n4
% 28.59/9.29 |
% 28.59/9.29 | From (1390) and (57) follows:
% 28.59/9.29 | (1391) pred(n4) = all_0_6_6
% 28.59/9.29 |
% 28.59/9.29 | From (1390) and (381) follows:
% 28.59/9.29 | (1392) succ(n4) = all_0_8_8
% 28.59/9.29 |
% 28.59/9.29 | Instantiating formula (259) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 28.59/9.29 | (1393) all_0_6_6 = n3
% 28.81/9.29 |
% 28.81/9.29 | Instantiating formula (184) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 28.81/9.29 | (1394) all_0_8_8 = n5
% 28.81/9.29 |
% 28.81/9.29 | From (1393)(1394) and (628) follows:
% 28.81/9.29 | (1395) sum(n3, n5) = all_0_1_1
% 28.81/9.29 |
% 28.81/9.29 | From (1393) and (1114) follows:
% 28.81/9.29 | (1396) sum(n3, n0) = all_0_4_4
% 28.81/9.29 |
% 28.81/9.29 | From (1394) and (1116) follows:
% 28.81/9.29 | (1397) sum(n19, n5) = all_0_7_7
% 28.81/9.29 |
% 28.81/9.29 | Instantiating formula (194) with n19, n5, all_0_7_7, n3 and discharging atoms sum(n19, n5) = all_0_7_7, sum(n19, n5) = n3, yields:
% 28.81/9.29 | (1029) all_0_7_7 = n3
% 28.81/9.29 |
% 28.81/9.29 | Instantiating formula (194) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 28.81/9.29 | (1399) all_0_1_1 = n8
% 28.81/9.29 |
% 28.81/9.29 | Instantiating formula (194) with n3, n0, all_0_4_4, n3 and discharging atoms sum(n3, n0) = all_0_4_4, sum(n3, n0) = n3, yields:
% 28.81/9.29 | (1027) all_0_4_4 = n3
% 28.81/9.29 |
% 28.81/9.29 | From (1029)(1027) and (435) follows:
% 28.81/9.29 | (1031) sum(n3, n3) = all_0_3_3
% 28.81/9.29 |
% 28.81/9.29 | From (1399) and (1118) follows:
% 28.81/9.29 | (1402) sum(n19, n8) = all_0_0_0
% 28.81/9.29 |
% 28.81/9.29 | Instantiating formula (194) with n19, n8, all_0_0_0, n6 and discharging atoms sum(n19, n8) = all_0_0_0, sum(n19, n8) = n6, yields:
% 28.81/9.29 | (1032) all_0_0_0 = n6
% 28.81/9.29 |
% 28.81/9.29 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 28.81/9.29 | (1033) all_0_3_3 = n6
% 28.81/9.29 |
% 28.81/9.29 | Equations (1032,1033) can reduce 201 to:
% 28.81/9.29 | (746) $false
% 28.81/9.29 |
% 28.81/9.29 |-The branch is then unsatisfiable
% 28.81/9.29 |-Branch two:
% 28.81/9.29 | (1406) ~ (all_0_10_10 = n4)
% 28.81/9.29 | (1407) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.81/9.29 |
% 28.81/9.29 +-Applying beta-rule and splitting (1407), into two cases.
% 28.81/9.29 |-Branch one:
% 28.81/9.29 | (1408) all_0_10_10 = n3
% 28.81/9.29 |
% 28.81/9.29 | From (1408) and (57) follows:
% 28.81/9.29 | (1409) pred(n3) = all_0_6_6
% 28.81/9.29 |
% 28.81/9.29 | From (1408) and (381) follows:
% 28.81/9.29 | (1410) succ(n3) = all_0_8_8
% 28.81/9.29 |
% 28.81/9.29 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 28.81/9.29 | (1411) all_0_6_6 = n2
% 28.81/9.29 |
% 28.81/9.29 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 28.81/9.29 | (1412) all_0_8_8 = n4
% 28.81/9.29 |
% 28.81/9.29 | From (1411)(1412) and (628) follows:
% 28.81/9.29 | (1413) sum(n2, n4) = all_0_1_1
% 28.81/9.29 |
% 28.81/9.29 | From (1411) and (1114) follows:
% 28.81/9.29 | (1414) sum(n2, n0) = all_0_4_4
% 28.81/9.29 |
% 28.81/9.29 | From (1412) and (1116) follows:
% 28.81/9.29 | (1415) sum(n19, n4) = all_0_7_7
% 28.81/9.29 |
% 28.81/9.29 | Instantiating formula (194) with n19, n4, all_0_7_7, n2 and discharging atoms sum(n19, n4) = all_0_7_7, sum(n19, n4) = n2, yields:
% 28.81/9.29 | (1047) all_0_7_7 = n2
% 28.81/9.29 |
% 28.81/9.29 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 28.81/9.29 | (1417) all_0_1_1 = n6
% 28.81/9.29 |
% 28.81/9.29 | Instantiating formula (194) with n2, n0, all_0_4_4, n2 and discharging atoms sum(n2, n0) = all_0_4_4, sum(n2, n0) = n2, yields:
% 28.81/9.30 | (1045) all_0_4_4 = n2
% 28.81/9.30 |
% 28.81/9.30 | From (1047)(1045) and (435) follows:
% 28.81/9.30 | (1049) sum(n2, n2) = all_0_3_3
% 28.81/9.30 |
% 28.81/9.30 | From (1417) and (1118) follows:
% 28.81/9.30 | (1420) sum(n19, n6) = all_0_0_0
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (194) with n19, n6, all_0_0_0, n4 and discharging atoms sum(n19, n6) = all_0_0_0, sum(n19, n6) = n4, yields:
% 28.81/9.30 | (1050) all_0_0_0 = n4
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 28.81/9.30 | (1051) all_0_3_3 = n4
% 28.81/9.30 |
% 28.81/9.30 | Equations (1050,1051) can reduce 201 to:
% 28.81/9.30 | (746) $false
% 28.81/9.30 |
% 28.81/9.30 |-The branch is then unsatisfiable
% 28.81/9.30 |-Branch two:
% 28.81/9.30 | (1424) ~ (all_0_10_10 = n3)
% 28.81/9.30 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 28.81/9.30 |
% 28.81/9.30 +-Applying beta-rule and splitting (1425), into two cases.
% 28.81/9.30 |-Branch one:
% 28.81/9.30 | (1426) all_0_10_10 = n2
% 28.81/9.30 |
% 28.81/9.30 | From (1426) and (57) follows:
% 28.81/9.30 | (1427) pred(n2) = all_0_6_6
% 28.81/9.30 |
% 28.81/9.30 | From (1426) and (381) follows:
% 28.81/9.30 | (1428) succ(n2) = all_0_8_8
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 28.81/9.30 | (1429) all_0_6_6 = n1
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 28.81/9.30 | (1430) all_0_8_8 = n3
% 28.81/9.30 |
% 28.81/9.30 | From (1429)(1430) and (628) follows:
% 28.81/9.30 | (1431) sum(n1, n3) = all_0_1_1
% 28.81/9.30 |
% 28.81/9.30 | From (1429) and (1114) follows:
% 28.81/9.30 | (1432) sum(n1, n0) = all_0_4_4
% 28.81/9.30 |
% 28.81/9.30 | From (1430) and (1116) follows:
% 28.81/9.30 | (1433) sum(n19, n3) = all_0_7_7
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (194) with n19, n3, all_0_7_7, n1 and discharging atoms sum(n19, n3) = all_0_7_7, sum(n19, n3) = n1, yields:
% 28.81/9.30 | (1065) all_0_7_7 = n1
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 28.81/9.30 | (1435) all_0_1_1 = n4
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (194) with n1, n0, all_0_4_4, n1 and discharging atoms sum(n1, n0) = all_0_4_4, sum(n1, n0) = n1, yields:
% 28.81/9.30 | (1063) all_0_4_4 = n1
% 28.81/9.30 |
% 28.81/9.30 | From (1065)(1063) and (435) follows:
% 28.81/9.30 | (1067) sum(n1, n1) = all_0_3_3
% 28.81/9.30 |
% 28.81/9.30 | From (1435) and (1118) follows:
% 28.81/9.30 | (1438) sum(n19, n4) = all_0_0_0
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (194) with n19, n4, all_0_0_0, n2 and discharging atoms sum(n19, n4) = all_0_0_0, sum(n19, n4) = n2, yields:
% 28.81/9.30 | (1068) all_0_0_0 = n2
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 28.81/9.30 | (1069) all_0_3_3 = n2
% 28.81/9.30 |
% 28.81/9.30 | Equations (1068,1069) can reduce 201 to:
% 28.81/9.30 | (746) $false
% 28.81/9.30 |
% 28.81/9.30 |-The branch is then unsatisfiable
% 28.81/9.30 |-Branch two:
% 28.81/9.30 | (1442) ~ (all_0_10_10 = n2)
% 28.81/9.30 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 28.81/9.30 |
% 28.81/9.30 +-Applying beta-rule and splitting (1443), into two cases.
% 28.81/9.30 |-Branch one:
% 28.81/9.30 | (1444) all_0_10_10 = n1
% 28.81/9.30 |
% 28.81/9.30 | From (1444) and (57) follows:
% 28.81/9.30 | (1445) pred(n1) = all_0_6_6
% 28.81/9.30 |
% 28.81/9.30 | From (1444) and (381) follows:
% 28.81/9.30 | (1446) succ(n1) = all_0_8_8
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 28.81/9.30 | (1447) all_0_6_6 = n0
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 28.81/9.30 | (1448) all_0_8_8 = n2
% 28.81/9.30 |
% 28.81/9.30 | From (1447)(1448) and (628) follows:
% 28.81/9.30 | (1449) sum(n0, n2) = all_0_1_1
% 28.81/9.30 |
% 28.81/9.30 | From (1447) and (1114) follows:
% 28.81/9.30 | (1450) sum(n0, n0) = all_0_4_4
% 28.81/9.30 |
% 28.81/9.30 | From (1448) and (1116) follows:
% 28.81/9.30 | (1451) sum(n19, n2) = all_0_7_7
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (194) with n19, n2, all_0_7_7, n0 and discharging atoms sum(n19, n2) = all_0_7_7, sum(n19, n2) = n0, yields:
% 28.81/9.30 | (1083) all_0_7_7 = n0
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 28.81/9.30 | (1453) all_0_1_1 = n2
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (194) with n0, n0, all_0_4_4, n0 and discharging atoms sum(n0, n0) = all_0_4_4, sum(n0, n0) = n0, yields:
% 28.81/9.30 | (1081) all_0_4_4 = n0
% 28.81/9.30 |
% 28.81/9.30 | From (1083)(1081) and (435) follows:
% 28.81/9.30 | (1085) sum(n0, n0) = all_0_3_3
% 28.81/9.30 |
% 28.81/9.30 | From (1453) and (1118) follows:
% 28.81/9.30 | (1456) sum(n19, n2) = all_0_0_0
% 28.81/9.30 |
% 28.81/9.30 | From (1083) and (1451) follows:
% 28.81/9.30 | (308) sum(n19, n2) = n0
% 28.81/9.30 |
% 28.81/9.30 | From (1081) and (1450) follows:
% 28.81/9.30 | (527) sum(n0, n0) = n0
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (194) with n19, n2, all_0_0_0, n0 and discharging atoms sum(n19, n2) = all_0_0_0, sum(n19, n2) = n0, yields:
% 28.81/9.30 | (1087) all_0_0_0 = n0
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 28.81/9.30 | (1088) all_0_3_3 = n0
% 28.81/9.30 |
% 28.81/9.30 | Equations (1087,1088) can reduce 201 to:
% 28.81/9.30 | (746) $false
% 28.81/9.30 |
% 28.81/9.30 |-The branch is then unsatisfiable
% 28.81/9.30 |-Branch two:
% 28.81/9.30 | (1462) ~ (all_0_10_10 = n1)
% 28.81/9.30 | (1463) all_0_10_10 = n0
% 28.81/9.30 |
% 28.81/9.30 | From (1463) and (57) follows:
% 28.81/9.30 | (1464) pred(n0) = all_0_6_6
% 28.81/9.30 |
% 28.81/9.30 | From (1463) and (381) follows:
% 28.81/9.30 | (1465) succ(n0) = all_0_8_8
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 28.81/9.30 | (1466) all_0_6_6 = n20
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 28.81/9.30 | (1467) all_0_8_8 = n1
% 28.81/9.30 |
% 28.81/9.30 | From (1466)(1467) and (628) follows:
% 28.81/9.30 | (1468) sum(n20, n1) = all_0_1_1
% 28.81/9.30 |
% 28.81/9.30 | From (1466) and (1114) follows:
% 28.81/9.30 | (1469) sum(n20, n0) = all_0_4_4
% 28.81/9.30 |
% 28.81/9.30 | From (1467) and (1116) follows:
% 28.81/9.30 | (1470) sum(n19, n1) = all_0_7_7
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 28.81/9.30 | (1471) all_0_1_1 = n0
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (194) with n20, n0, all_0_4_4, n20 and discharging atoms sum(n20, n0) = all_0_4_4, sum(n20, n0) = n20, yields:
% 28.81/9.30 | (1101) all_0_4_4 = n20
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (194) with n19, n1, all_0_7_7, n20 and discharging atoms sum(n19, n1) = all_0_7_7, sum(n19, n1) = n20, yields:
% 28.81/9.30 | (1100) all_0_7_7 = n20
% 28.81/9.30 |
% 28.81/9.30 | From (1100)(1101) and (435) follows:
% 28.81/9.30 | (1103) sum(n20, n20) = all_0_3_3
% 28.81/9.30 |
% 28.81/9.30 | From (1471) and (1118) follows:
% 28.81/9.30 | (1475) sum(n19, n0) = all_0_0_0
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 28.81/9.30 | (1104) all_0_3_3 = n19
% 28.81/9.30 |
% 28.81/9.30 | Instantiating formula (194) with n19, n0, all_0_0_0, n19 and discharging atoms sum(n19, n0) = all_0_0_0, sum(n19, n0) = n19, yields:
% 28.81/9.30 | (1105) all_0_0_0 = n19
% 28.81/9.30 |
% 28.81/9.30 | Equations (1105,1104) can reduce 201 to:
% 28.81/9.30 | (746) $false
% 28.81/9.30 |
% 28.81/9.30 |-The branch is then unsatisfiable
% 28.81/9.30 |-Branch two:
% 28.81/9.30 | (747) ~ (all_0_11_11 = n20)
% 28.81/9.30 | (748) all_0_11_11 = n19 | all_0_11_11 = n18 | all_0_11_11 = n17 | all_0_11_11 = n16 | all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.30 |
% 28.81/9.30 +-Applying beta-rule and splitting (1108), into two cases.
% 28.81/9.30 |-Branch one:
% 28.81/9.30 | (1120) all_0_10_10 = n19
% 28.81/9.31 |
% 28.81/9.31 | From (1120) and (57) follows:
% 28.81/9.31 | (1121) pred(n19) = all_0_6_6
% 28.81/9.31 |
% 28.81/9.31 | From (1120) and (381) follows:
% 28.81/9.31 | (1122) succ(n19) = all_0_8_8
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (259) with n19, all_0_6_6, n18 and discharging atoms pred(n19) = all_0_6_6, pred(n19) = n18, yields:
% 28.81/9.31 | (1123) all_0_6_6 = n18
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (184) with n19, all_0_8_8, n20 and discharging atoms succ(n19) = all_0_8_8, succ(n19) = n20, yields:
% 28.81/9.31 | (1124) all_0_8_8 = n20
% 28.81/9.31 |
% 28.81/9.31 | From (1123) and (1121) follows:
% 28.81/9.31 | (588) pred(n19) = n18
% 28.81/9.31 |
% 28.81/9.31 | From (1124) and (1122) follows:
% 28.81/9.31 | (147) succ(n19) = n20
% 28.81/9.31 |
% 28.81/9.31 | From (1123) and (386) follows:
% 28.81/9.31 | (1488) sum(n18, all_0_5_5) = all_0_4_4
% 28.81/9.31 |
% 28.81/9.31 | From (1123)(1124) and (628) follows:
% 28.81/9.31 | (1125) sum(n18, n20) = all_0_1_1
% 28.81/9.31 |
% 28.81/9.31 | From (1124) and (74) follows:
% 28.81/9.31 | (1490) sum(all_0_9_9, n20) = all_0_7_7
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (194) with n18, n20, all_0_1_1, n17 and discharging atoms sum(n18, n20) = all_0_1_1, sum(n18, n20) = n17, yields:
% 28.81/9.31 | (1129) all_0_1_1 = n17
% 28.81/9.31 |
% 28.81/9.31 | From (1129) and (85) follows:
% 28.81/9.31 | (1492) sum(all_0_2_2, n17) = all_0_0_0
% 28.81/9.31 |
% 28.81/9.31 | From (1129) and (1125) follows:
% 28.81/9.31 | (645) sum(n18, n20) = n17
% 28.81/9.31 |
% 28.81/9.31 +-Applying beta-rule and splitting (748), into two cases.
% 28.81/9.31 |-Branch one:
% 28.81/9.31 | (749) all_0_11_11 = n19
% 28.81/9.31 |
% 28.81/9.31 | From (749) and (190) follows:
% 28.81/9.31 | (750) pred(n19) = all_0_9_9
% 28.81/9.31 |
% 28.81/9.31 | From (749) and (505) follows:
% 28.81/9.31 | (751) succ(n19) = all_0_5_5
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (259) with n19, all_0_9_9, n18 and discharging atoms pred(n19) = all_0_9_9, pred(n19) = n18, yields:
% 28.81/9.31 | (752) all_0_9_9 = n18
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (184) with n19, all_0_5_5, n20 and discharging atoms succ(n19) = all_0_5_5, succ(n19) = n20, yields:
% 28.81/9.31 | (753) all_0_5_5 = n20
% 28.81/9.31 |
% 28.81/9.31 | From (752)(753) and (156) follows:
% 28.81/9.31 | (754) sum(n18, n20) = all_0_2_2
% 28.81/9.31 |
% 28.81/9.31 | From (752) and (1490) follows:
% 28.81/9.31 | (1500) sum(n18, n20) = all_0_7_7
% 28.81/9.31 |
% 28.81/9.31 | From (753) and (1488) follows:
% 28.81/9.31 | (1501) sum(n18, n20) = all_0_4_4
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (194) with n18, n20, all_0_2_2, n17 and discharging atoms sum(n18, n20) = all_0_2_2, sum(n18, n20) = n17, yields:
% 28.81/9.31 | (758) all_0_2_2 = n17
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (194) with n18, n20, all_0_4_4, all_0_2_2 and discharging atoms sum(n18, n20) = all_0_2_2, sum(n18, n20) = all_0_4_4, yields:
% 28.81/9.31 | (733) all_0_2_2 = all_0_4_4
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (194) with n18, n20, all_0_7_7, all_0_2_2 and discharging atoms sum(n18, n20) = all_0_2_2, sum(n18, n20) = all_0_7_7, yields:
% 28.81/9.31 | (734) all_0_2_2 = all_0_7_7
% 28.81/9.31 |
% 28.81/9.31 | Combining equations (734,733) yields a new equation:
% 28.81/9.31 | (735) all_0_4_4 = all_0_7_7
% 28.81/9.31 |
% 28.81/9.31 | Combining equations (758,733) yields a new equation:
% 28.81/9.31 | (775) all_0_4_4 = n17
% 28.81/9.31 |
% 28.81/9.31 | Combining equations (775,735) yields a new equation:
% 28.81/9.31 | (777) all_0_7_7 = n17
% 28.81/9.31 |
% 28.81/9.31 | Combining equations (777,735) yields a new equation:
% 28.81/9.31 | (775) all_0_4_4 = n17
% 28.81/9.31 |
% 28.81/9.31 | Combining equations (775,733) yields a new equation:
% 28.81/9.31 | (758) all_0_2_2 = n17
% 28.81/9.31 |
% 28.81/9.31 | From (758) and (1492) follows:
% 28.81/9.31 | (1510) sum(n17, n17) = all_0_0_0
% 28.81/9.31 |
% 28.81/9.31 | From (777)(775) and (435) follows:
% 28.81/9.31 | (779) sum(n17, n17) = all_0_3_3
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (194) with n17, n17, all_0_0_0, n13 and discharging atoms sum(n17, n17) = all_0_0_0, sum(n17, n17) = n13, yields:
% 28.81/9.31 | (781) all_0_0_0 = n13
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (194) with n17, n17, all_0_3_3, all_0_0_0 and discharging atoms sum(n17, n17) = all_0_0_0, sum(n17, n17) = all_0_3_3, yields:
% 28.81/9.31 | (743) all_0_0_0 = all_0_3_3
% 28.81/9.31 |
% 28.81/9.31 | Combining equations (781,743) yields a new equation:
% 28.81/9.31 | (780) all_0_3_3 = n13
% 28.81/9.31 |
% 28.81/9.31 | Combining equations (780,743) yields a new equation:
% 28.81/9.31 | (781) all_0_0_0 = n13
% 28.81/9.31 |
% 28.81/9.31 | Equations (781,780) can reduce 201 to:
% 28.81/9.31 | (746) $false
% 28.81/9.31 |
% 28.81/9.31 |-The branch is then unsatisfiable
% 28.81/9.31 |-Branch two:
% 28.81/9.31 | (765) ~ (all_0_11_11 = n19)
% 28.81/9.31 | (766) all_0_11_11 = n18 | all_0_11_11 = n17 | all_0_11_11 = n16 | all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.31 |
% 28.81/9.31 +-Applying beta-rule and splitting (766), into two cases.
% 28.81/9.31 |-Branch one:
% 28.81/9.31 | (767) all_0_11_11 = n18
% 28.81/9.31 |
% 28.81/9.31 | From (767) and (190) follows:
% 28.81/9.31 | (768) pred(n18) = all_0_9_9
% 28.81/9.31 |
% 28.81/9.31 | From (767) and (505) follows:
% 28.81/9.31 | (769) succ(n18) = all_0_5_5
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (259) with n18, all_0_9_9, n17 and discharging atoms pred(n18) = all_0_9_9, pred(n18) = n17, yields:
% 28.81/9.31 | (770) all_0_9_9 = n17
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (184) with n18, all_0_5_5, n19 and discharging atoms succ(n18) = all_0_5_5, succ(n18) = n19, yields:
% 28.81/9.31 | (771) all_0_5_5 = n19
% 28.81/9.31 |
% 28.81/9.31 | From (770)(771) and (156) follows:
% 28.81/9.31 | (772) sum(n17, n19) = all_0_2_2
% 28.81/9.31 |
% 28.81/9.31 | From (770) and (1490) follows:
% 28.81/9.31 | (1525) sum(n17, n20) = all_0_7_7
% 28.81/9.31 |
% 28.81/9.31 | From (771) and (1488) follows:
% 28.81/9.31 | (1526) sum(n18, n19) = all_0_4_4
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (194) with n18, n19, all_0_4_4, n16 and discharging atoms sum(n18, n19) = all_0_4_4, sum(n18, n19) = n16, yields:
% 28.81/9.31 | (793) all_0_4_4 = n16
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (194) with n17, n20, all_0_7_7, n16 and discharging atoms sum(n17, n20) = all_0_7_7, sum(n17, n20) = n16, yields:
% 28.81/9.31 | (795) all_0_7_7 = n16
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (194) with n17, n19, all_0_2_2, n15 and discharging atoms sum(n17, n19) = all_0_2_2, sum(n17, n19) = n15, yields:
% 28.81/9.31 | (776) all_0_2_2 = n15
% 28.81/9.31 |
% 28.81/9.31 | From (776) and (1492) follows:
% 28.81/9.31 | (1530) sum(n15, n17) = all_0_0_0
% 28.81/9.31 |
% 28.81/9.31 | From (795)(793) and (435) follows:
% 28.81/9.31 | (797) sum(n16, n16) = all_0_3_3
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 28.81/9.31 | (798) all_0_3_3 = n11
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (194) with n15, n17, all_0_0_0, n11 and discharging atoms sum(n15, n17) = all_0_0_0, sum(n15, n17) = n11, yields:
% 28.81/9.31 | (799) all_0_0_0 = n11
% 28.81/9.31 |
% 28.81/9.31 | Equations (799,798) can reduce 201 to:
% 28.81/9.31 | (746) $false
% 28.81/9.31 |
% 28.81/9.31 |-The branch is then unsatisfiable
% 28.81/9.31 |-Branch two:
% 28.81/9.31 | (783) ~ (all_0_11_11 = n18)
% 28.81/9.31 | (784) all_0_11_11 = n17 | all_0_11_11 = n16 | all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.31 |
% 28.81/9.31 +-Applying beta-rule and splitting (784), into two cases.
% 28.81/9.31 |-Branch one:
% 28.81/9.31 | (785) all_0_11_11 = n17
% 28.81/9.31 |
% 28.81/9.31 | From (785) and (190) follows:
% 28.81/9.31 | (786) pred(n17) = all_0_9_9
% 28.81/9.31 |
% 28.81/9.31 | From (785) and (505) follows:
% 28.81/9.31 | (787) succ(n17) = all_0_5_5
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (259) with n17, all_0_9_9, n16 and discharging atoms pred(n17) = all_0_9_9, pred(n17) = n16, yields:
% 28.81/9.31 | (788) all_0_9_9 = n16
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (184) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 28.81/9.31 | (789) all_0_5_5 = n18
% 28.81/9.31 |
% 28.81/9.31 | From (788)(789) and (156) follows:
% 28.81/9.31 | (790) sum(n16, n18) = all_0_2_2
% 28.81/9.31 |
% 28.81/9.31 | From (788) and (1490) follows:
% 28.81/9.31 | (1543) sum(n16, n20) = all_0_7_7
% 28.81/9.31 |
% 28.81/9.31 | From (789) and (1488) follows:
% 28.81/9.31 | (1544) sum(n18, n18) = all_0_4_4
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (194) with n18, n18, all_0_4_4, n15 and discharging atoms sum(n18, n18) = all_0_4_4, sum(n18, n18) = n15, yields:
% 28.81/9.31 | (811) all_0_4_4 = n15
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (194) with n16, n20, all_0_7_7, n15 and discharging atoms sum(n16, n20) = all_0_7_7, sum(n16, n20) = n15, yields:
% 28.81/9.31 | (813) all_0_7_7 = n15
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (194) with n16, n18, all_0_2_2, n13 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = n13, yields:
% 28.81/9.31 | (794) all_0_2_2 = n13
% 28.81/9.31 |
% 28.81/9.31 | From (794) and (1492) follows:
% 28.81/9.31 | (1548) sum(n13, n17) = all_0_0_0
% 28.81/9.31 |
% 28.81/9.31 | From (813)(811) and (435) follows:
% 28.81/9.31 | (815) sum(n15, n15) = all_0_3_3
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 28.81/9.31 | (816) all_0_3_3 = n9
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (194) with n13, n17, all_0_0_0, n9 and discharging atoms sum(n13, n17) = all_0_0_0, sum(n13, n17) = n9, yields:
% 28.81/9.31 | (817) all_0_0_0 = n9
% 28.81/9.31 |
% 28.81/9.31 | Equations (817,816) can reduce 201 to:
% 28.81/9.31 | (746) $false
% 28.81/9.31 |
% 28.81/9.31 |-The branch is then unsatisfiable
% 28.81/9.31 |-Branch two:
% 28.81/9.31 | (801) ~ (all_0_11_11 = n17)
% 28.81/9.31 | (802) all_0_11_11 = n16 | all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.31 |
% 28.81/9.31 +-Applying beta-rule and splitting (802), into two cases.
% 28.81/9.31 |-Branch one:
% 28.81/9.31 | (803) all_0_11_11 = n16
% 28.81/9.31 |
% 28.81/9.31 | From (803) and (190) follows:
% 28.81/9.31 | (804) pred(n16) = all_0_9_9
% 28.81/9.31 |
% 28.81/9.31 | From (803) and (505) follows:
% 28.81/9.31 | (805) succ(n16) = all_0_5_5
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (259) with n16, all_0_9_9, n15 and discharging atoms pred(n16) = all_0_9_9, pred(n16) = n15, yields:
% 28.81/9.31 | (806) all_0_9_9 = n15
% 28.81/9.31 |
% 28.81/9.31 | Instantiating formula (184) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 28.81/9.31 | (807) all_0_5_5 = n17
% 28.81/9.31 |
% 28.81/9.31 | From (806)(807) and (156) follows:
% 28.81/9.31 | (808) sum(n15, n17) = all_0_2_2
% 28.81/9.31 |
% 28.81/9.31 | From (806) and (1490) follows:
% 28.81/9.31 | (1561) sum(n15, n20) = all_0_7_7
% 28.81/9.32 |
% 28.81/9.32 | From (807) and (1488) follows:
% 28.81/9.32 | (1562) sum(n18, n17) = all_0_4_4
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n18, n17, all_0_4_4, n14 and discharging atoms sum(n18, n17) = all_0_4_4, sum(n18, n17) = n14, yields:
% 28.81/9.32 | (829) all_0_4_4 = n14
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n15, n20, all_0_7_7, n14 and discharging atoms sum(n15, n20) = all_0_7_7, sum(n15, n20) = n14, yields:
% 28.81/9.32 | (831) all_0_7_7 = n14
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n15, n17, all_0_2_2, n11 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n11, yields:
% 28.81/9.32 | (812) all_0_2_2 = n11
% 28.81/9.32 |
% 28.81/9.32 | From (812) and (1492) follows:
% 28.81/9.32 | (1566) sum(n11, n17) = all_0_0_0
% 28.81/9.32 |
% 28.81/9.32 | From (831)(829) and (435) follows:
% 28.81/9.32 | (833) sum(n14, n14) = all_0_3_3
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 28.81/9.32 | (834) all_0_3_3 = n7
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n11, n17, all_0_0_0, n7 and discharging atoms sum(n11, n17) = all_0_0_0, sum(n11, n17) = n7, yields:
% 28.81/9.32 | (835) all_0_0_0 = n7
% 28.81/9.32 |
% 28.81/9.32 | Equations (835,834) can reduce 201 to:
% 28.81/9.32 | (746) $false
% 28.81/9.32 |
% 28.81/9.32 |-The branch is then unsatisfiable
% 28.81/9.32 |-Branch two:
% 28.81/9.32 | (819) ~ (all_0_11_11 = n16)
% 28.81/9.32 | (820) all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.32 |
% 28.81/9.32 +-Applying beta-rule and splitting (820), into two cases.
% 28.81/9.32 |-Branch one:
% 28.81/9.32 | (821) all_0_11_11 = n15
% 28.81/9.32 |
% 28.81/9.32 | From (821) and (190) follows:
% 28.81/9.32 | (822) pred(n15) = all_0_9_9
% 28.81/9.32 |
% 28.81/9.32 | From (821) and (505) follows:
% 28.81/9.32 | (823) succ(n15) = all_0_5_5
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (259) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 28.81/9.32 | (824) all_0_9_9 = n14
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (184) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 28.81/9.32 | (825) all_0_5_5 = n16
% 28.81/9.32 |
% 28.81/9.32 | From (824)(825) and (156) follows:
% 28.81/9.32 | (826) sum(n14, n16) = all_0_2_2
% 28.81/9.32 |
% 28.81/9.32 | From (824) and (1490) follows:
% 28.81/9.32 | (1579) sum(n14, n20) = all_0_7_7
% 28.81/9.32 |
% 28.81/9.32 | From (825) and (1488) follows:
% 28.81/9.32 | (1580) sum(n18, n16) = all_0_4_4
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n18, n16, all_0_4_4, n13 and discharging atoms sum(n18, n16) = all_0_4_4, sum(n18, n16) = n13, yields:
% 28.81/9.32 | (847) all_0_4_4 = n13
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n14, n20, all_0_7_7, n13 and discharging atoms sum(n14, n20) = all_0_7_7, sum(n14, n20) = n13, yields:
% 28.81/9.32 | (849) all_0_7_7 = n13
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n14, n16, all_0_2_2, n9 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n9, yields:
% 28.81/9.32 | (830) all_0_2_2 = n9
% 28.81/9.32 |
% 28.81/9.32 | From (830) and (1492) follows:
% 28.81/9.32 | (1584) sum(n9, n17) = all_0_0_0
% 28.81/9.32 |
% 28.81/9.32 | From (849)(847) and (435) follows:
% 28.81/9.32 | (851) sum(n13, n13) = all_0_3_3
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 28.81/9.32 | (852) all_0_3_3 = n5
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n9, n17, all_0_0_0, n5 and discharging atoms sum(n9, n17) = all_0_0_0, sum(n9, n17) = n5, yields:
% 28.81/9.32 | (853) all_0_0_0 = n5
% 28.81/9.32 |
% 28.81/9.32 | Equations (853,852) can reduce 201 to:
% 28.81/9.32 | (746) $false
% 28.81/9.32 |
% 28.81/9.32 |-The branch is then unsatisfiable
% 28.81/9.32 |-Branch two:
% 28.81/9.32 | (837) ~ (all_0_11_11 = n15)
% 28.81/9.32 | (838) all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.32 |
% 28.81/9.32 +-Applying beta-rule and splitting (838), into two cases.
% 28.81/9.32 |-Branch one:
% 28.81/9.32 | (839) all_0_11_11 = n14
% 28.81/9.32 |
% 28.81/9.32 | From (839) and (190) follows:
% 28.81/9.32 | (840) pred(n14) = all_0_9_9
% 28.81/9.32 |
% 28.81/9.32 | From (839) and (505) follows:
% 28.81/9.32 | (841) succ(n14) = all_0_5_5
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (259) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 28.81/9.32 | (842) all_0_9_9 = n13
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (184) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 28.81/9.32 | (843) all_0_5_5 = n15
% 28.81/9.32 |
% 28.81/9.32 | From (842)(843) and (156) follows:
% 28.81/9.32 | (844) sum(n13, n15) = all_0_2_2
% 28.81/9.32 |
% 28.81/9.32 | From (842) and (1490) follows:
% 28.81/9.32 | (1597) sum(n13, n20) = all_0_7_7
% 28.81/9.32 |
% 28.81/9.32 | From (843) and (1488) follows:
% 28.81/9.32 | (1598) sum(n18, n15) = all_0_4_4
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n18, n15, all_0_4_4, n12 and discharging atoms sum(n18, n15) = all_0_4_4, sum(n18, n15) = n12, yields:
% 28.81/9.32 | (865) all_0_4_4 = n12
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n13, n20, all_0_7_7, n12 and discharging atoms sum(n13, n20) = all_0_7_7, sum(n13, n20) = n12, yields:
% 28.81/9.32 | (867) all_0_7_7 = n12
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n13, n15, all_0_2_2, n7 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n7, yields:
% 28.81/9.32 | (848) all_0_2_2 = n7
% 28.81/9.32 |
% 28.81/9.32 | From (848) and (1492) follows:
% 28.81/9.32 | (1602) sum(n7, n17) = all_0_0_0
% 28.81/9.32 |
% 28.81/9.32 | From (867)(865) and (435) follows:
% 28.81/9.32 | (869) sum(n12, n12) = all_0_3_3
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 28.81/9.32 | (870) all_0_3_3 = n3
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n7, n17, all_0_0_0, n3 and discharging atoms sum(n7, n17) = all_0_0_0, sum(n7, n17) = n3, yields:
% 28.81/9.32 | (871) all_0_0_0 = n3
% 28.81/9.32 |
% 28.81/9.32 | Equations (871,870) can reduce 201 to:
% 28.81/9.32 | (746) $false
% 28.81/9.32 |
% 28.81/9.32 |-The branch is then unsatisfiable
% 28.81/9.32 |-Branch two:
% 28.81/9.32 | (855) ~ (all_0_11_11 = n14)
% 28.81/9.32 | (856) all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.32 |
% 28.81/9.32 +-Applying beta-rule and splitting (856), into two cases.
% 28.81/9.32 |-Branch one:
% 28.81/9.32 | (857) all_0_11_11 = n13
% 28.81/9.32 |
% 28.81/9.32 | From (857) and (190) follows:
% 28.81/9.32 | (858) pred(n13) = all_0_9_9
% 28.81/9.32 |
% 28.81/9.32 | From (857) and (505) follows:
% 28.81/9.32 | (859) succ(n13) = all_0_5_5
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (259) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 28.81/9.32 | (860) all_0_9_9 = n12
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (184) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 28.81/9.32 | (861) all_0_5_5 = n14
% 28.81/9.32 |
% 28.81/9.32 | From (860)(861) and (156) follows:
% 28.81/9.32 | (862) sum(n12, n14) = all_0_2_2
% 28.81/9.32 |
% 28.81/9.32 | From (860) and (1490) follows:
% 28.81/9.32 | (1615) sum(n12, n20) = all_0_7_7
% 28.81/9.32 |
% 28.81/9.32 | From (861) and (1488) follows:
% 28.81/9.32 | (1616) sum(n18, n14) = all_0_4_4
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n18, n14, all_0_4_4, n11 and discharging atoms sum(n18, n14) = all_0_4_4, sum(n18, n14) = n11, yields:
% 28.81/9.32 | (883) all_0_4_4 = n11
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n12, n20, all_0_7_7, n11 and discharging atoms sum(n12, n20) = all_0_7_7, sum(n12, n20) = n11, yields:
% 28.81/9.32 | (885) all_0_7_7 = n11
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n12, n14, all_0_2_2, n5 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n5, yields:
% 28.81/9.32 | (866) all_0_2_2 = n5
% 28.81/9.32 |
% 28.81/9.32 | From (866) and (1492) follows:
% 28.81/9.32 | (1620) sum(n5, n17) = all_0_0_0
% 28.81/9.32 |
% 28.81/9.32 | From (885)(883) and (435) follows:
% 28.81/9.32 | (887) sum(n11, n11) = all_0_3_3
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 28.81/9.32 | (888) all_0_3_3 = n1
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n5, n17, all_0_0_0, n1 and discharging atoms sum(n5, n17) = all_0_0_0, sum(n5, n17) = n1, yields:
% 28.81/9.32 | (889) all_0_0_0 = n1
% 28.81/9.32 |
% 28.81/9.32 | Equations (889,888) can reduce 201 to:
% 28.81/9.32 | (746) $false
% 28.81/9.32 |
% 28.81/9.32 |-The branch is then unsatisfiable
% 28.81/9.32 |-Branch two:
% 28.81/9.32 | (873) ~ (all_0_11_11 = n13)
% 28.81/9.32 | (874) all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.32 |
% 28.81/9.32 +-Applying beta-rule and splitting (874), into two cases.
% 28.81/9.32 |-Branch one:
% 28.81/9.32 | (875) all_0_11_11 = n12
% 28.81/9.32 |
% 28.81/9.32 | From (875) and (190) follows:
% 28.81/9.32 | (876) pred(n12) = all_0_9_9
% 28.81/9.32 |
% 28.81/9.32 | From (875) and (505) follows:
% 28.81/9.32 | (877) succ(n12) = all_0_5_5
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (259) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 28.81/9.32 | (878) all_0_9_9 = n11
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (184) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 28.81/9.32 | (879) all_0_5_5 = n13
% 28.81/9.32 |
% 28.81/9.32 | From (878)(879) and (156) follows:
% 28.81/9.32 | (880) sum(n11, n13) = all_0_2_2
% 28.81/9.32 |
% 28.81/9.32 | From (878) and (1490) follows:
% 28.81/9.32 | (1633) sum(n11, n20) = all_0_7_7
% 28.81/9.32 |
% 28.81/9.32 | From (879) and (1488) follows:
% 28.81/9.32 | (1634) sum(n18, n13) = all_0_4_4
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n18, n13, all_0_4_4, n10 and discharging atoms sum(n18, n13) = all_0_4_4, sum(n18, n13) = n10, yields:
% 28.81/9.32 | (901) all_0_4_4 = n10
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n11, n20, all_0_7_7, n10 and discharging atoms sum(n11, n20) = all_0_7_7, sum(n11, n20) = n10, yields:
% 28.81/9.32 | (903) all_0_7_7 = n10
% 28.81/9.32 |
% 28.81/9.32 | Instantiating formula (194) with n11, n13, all_0_2_2, n3 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n3, yields:
% 28.81/9.32 | (884) all_0_2_2 = n3
% 28.81/9.32 |
% 28.81/9.32 | From (884) and (1492) follows:
% 28.81/9.32 | (1638) sum(n3, n17) = all_0_0_0
% 28.81/9.32 |
% 28.81/9.32 | From (903)(901) and (435) follows:
% 28.81/9.33 | (905) sum(n10, n10) = all_0_3_3
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 28.81/9.33 | (906) all_0_3_3 = n20
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n3, n17, all_0_0_0, n20 and discharging atoms sum(n3, n17) = all_0_0_0, sum(n3, n17) = n20, yields:
% 28.81/9.33 | (907) all_0_0_0 = n20
% 28.81/9.33 |
% 28.81/9.33 | Equations (907,906) can reduce 201 to:
% 28.81/9.33 | (746) $false
% 28.81/9.33 |
% 28.81/9.33 |-The branch is then unsatisfiable
% 28.81/9.33 |-Branch two:
% 28.81/9.33 | (891) ~ (all_0_11_11 = n12)
% 28.81/9.33 | (892) all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.33 |
% 28.81/9.33 +-Applying beta-rule and splitting (892), into two cases.
% 28.81/9.33 |-Branch one:
% 28.81/9.33 | (893) all_0_11_11 = n11
% 28.81/9.33 |
% 28.81/9.33 | From (893) and (190) follows:
% 28.81/9.33 | (894) pred(n11) = all_0_9_9
% 28.81/9.33 |
% 28.81/9.33 | From (893) and (505) follows:
% 28.81/9.33 | (895) succ(n11) = all_0_5_5
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (259) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 28.81/9.33 | (896) all_0_9_9 = n10
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (184) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 28.81/9.33 | (897) all_0_5_5 = n12
% 28.81/9.33 |
% 28.81/9.33 | From (896)(897) and (156) follows:
% 28.81/9.33 | (898) sum(n10, n12) = all_0_2_2
% 28.81/9.33 |
% 28.81/9.33 | From (896) and (1490) follows:
% 28.81/9.33 | (1651) sum(n10, n20) = all_0_7_7
% 28.81/9.33 |
% 28.81/9.33 | From (897) and (1488) follows:
% 28.81/9.33 | (1652) sum(n18, n12) = all_0_4_4
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n18, n12, all_0_4_4, n9 and discharging atoms sum(n18, n12) = all_0_4_4, sum(n18, n12) = n9, yields:
% 28.81/9.33 | (919) all_0_4_4 = n9
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n10, n20, all_0_7_7, n9 and discharging atoms sum(n10, n20) = all_0_7_7, sum(n10, n20) = n9, yields:
% 28.81/9.33 | (921) all_0_7_7 = n9
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n10, n12, all_0_2_2, n1 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n1, yields:
% 28.81/9.33 | (902) all_0_2_2 = n1
% 28.81/9.33 |
% 28.81/9.33 | From (902) and (1492) follows:
% 28.81/9.33 | (1656) sum(n1, n17) = all_0_0_0
% 28.81/9.33 |
% 28.81/9.33 | From (921)(919) and (435) follows:
% 28.81/9.33 | (923) sum(n9, n9) = all_0_3_3
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 28.81/9.33 | (925) all_0_3_3 = n18
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n1, n17, all_0_0_0, n18 and discharging atoms sum(n1, n17) = all_0_0_0, sum(n1, n17) = n18, yields:
% 28.81/9.33 | (924) all_0_0_0 = n18
% 28.81/9.33 |
% 28.81/9.33 | Equations (924,925) can reduce 201 to:
% 28.81/9.33 | (746) $false
% 28.81/9.33 |
% 28.81/9.33 |-The branch is then unsatisfiable
% 28.81/9.33 |-Branch two:
% 28.81/9.33 | (909) ~ (all_0_11_11 = n11)
% 28.81/9.33 | (910) all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.33 |
% 28.81/9.33 +-Applying beta-rule and splitting (910), into two cases.
% 28.81/9.33 |-Branch one:
% 28.81/9.33 | (911) all_0_11_11 = n10
% 28.81/9.33 |
% 28.81/9.33 | From (911) and (190) follows:
% 28.81/9.33 | (912) pred(n10) = all_0_9_9
% 28.81/9.33 |
% 28.81/9.33 | From (911) and (505) follows:
% 28.81/9.33 | (913) succ(n10) = all_0_5_5
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (259) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 28.81/9.33 | (914) all_0_9_9 = n9
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (184) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 28.81/9.33 | (915) all_0_5_5 = n11
% 28.81/9.33 |
% 28.81/9.33 | From (914)(915) and (156) follows:
% 28.81/9.33 | (916) sum(n9, n11) = all_0_2_2
% 28.81/9.33 |
% 28.81/9.33 | From (914) and (1490) follows:
% 28.81/9.33 | (1669) sum(n9, n20) = all_0_7_7
% 28.81/9.33 |
% 28.81/9.33 | From (915) and (1488) follows:
% 28.81/9.33 | (1670) sum(n18, n11) = all_0_4_4
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n18, n11, all_0_4_4, n8 and discharging atoms sum(n18, n11) = all_0_4_4, sum(n18, n11) = n8, yields:
% 28.81/9.33 | (937) all_0_4_4 = n8
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n9, n20, all_0_7_7, n8 and discharging atoms sum(n9, n20) = all_0_7_7, sum(n9, n20) = n8, yields:
% 28.81/9.33 | (939) all_0_7_7 = n8
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 28.81/9.33 | (920) all_0_2_2 = n20
% 28.81/9.33 |
% 28.81/9.33 | From (920) and (1492) follows:
% 28.81/9.33 | (1674) sum(n20, n17) = all_0_0_0
% 28.81/9.33 |
% 28.81/9.33 | From (939)(937) and (435) follows:
% 28.81/9.33 | (941) sum(n8, n8) = all_0_3_3
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n20, n17, all_0_0_0, n16 and discharging atoms sum(n20, n17) = all_0_0_0, sum(n20, n17) = n16, yields:
% 28.81/9.33 | (942) all_0_0_0 = n16
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 28.81/9.33 | (943) all_0_3_3 = n16
% 28.81/9.33 |
% 28.81/9.33 | Equations (942,943) can reduce 201 to:
% 28.81/9.33 | (746) $false
% 28.81/9.33 |
% 28.81/9.33 |-The branch is then unsatisfiable
% 28.81/9.33 |-Branch two:
% 28.81/9.33 | (927) ~ (all_0_11_11 = n10)
% 28.81/9.33 | (928) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.33 |
% 28.81/9.33 +-Applying beta-rule and splitting (928), into two cases.
% 28.81/9.33 |-Branch one:
% 28.81/9.33 | (929) all_0_11_11 = n9
% 28.81/9.33 |
% 28.81/9.33 | From (929) and (190) follows:
% 28.81/9.33 | (930) pred(n9) = all_0_9_9
% 28.81/9.33 |
% 28.81/9.33 | From (929) and (505) follows:
% 28.81/9.33 | (931) succ(n9) = all_0_5_5
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (259) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 28.81/9.33 | (932) all_0_9_9 = n8
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (184) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 28.81/9.33 | (933) all_0_5_5 = n10
% 28.81/9.33 |
% 28.81/9.33 | From (932)(933) and (156) follows:
% 28.81/9.33 | (934) sum(n8, n10) = all_0_2_2
% 28.81/9.33 |
% 28.81/9.33 | From (932) and (1490) follows:
% 28.81/9.33 | (1687) sum(n8, n20) = all_0_7_7
% 28.81/9.33 |
% 28.81/9.33 | From (933) and (1488) follows:
% 28.81/9.33 | (1688) sum(n18, n10) = all_0_4_4
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n18, n10, all_0_4_4, n7 and discharging atoms sum(n18, n10) = all_0_4_4, sum(n18, n10) = n7, yields:
% 28.81/9.33 | (955) all_0_4_4 = n7
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n8, n20, all_0_7_7, n7 and discharging atoms sum(n8, n20) = all_0_7_7, sum(n8, n20) = n7, yields:
% 28.81/9.33 | (957) all_0_7_7 = n7
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 28.81/9.33 | (938) all_0_2_2 = n18
% 28.81/9.33 |
% 28.81/9.33 | From (938) and (1492) follows:
% 28.81/9.33 | (1692) sum(n18, n17) = all_0_0_0
% 28.81/9.33 |
% 28.81/9.33 | From (957)(955) and (435) follows:
% 28.81/9.33 | (959) sum(n7, n7) = all_0_3_3
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n18, n17, all_0_0_0, n14 and discharging atoms sum(n18, n17) = all_0_0_0, sum(n18, n17) = n14, yields:
% 28.81/9.33 | (960) all_0_0_0 = n14
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 28.81/9.33 | (961) all_0_3_3 = n14
% 28.81/9.33 |
% 28.81/9.33 | Equations (960,961) can reduce 201 to:
% 28.81/9.33 | (746) $false
% 28.81/9.33 |
% 28.81/9.33 |-The branch is then unsatisfiable
% 28.81/9.33 |-Branch two:
% 28.81/9.33 | (945) ~ (all_0_11_11 = n9)
% 28.81/9.33 | (946) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.33 |
% 28.81/9.33 +-Applying beta-rule and splitting (946), into two cases.
% 28.81/9.33 |-Branch one:
% 28.81/9.33 | (947) all_0_11_11 = n8
% 28.81/9.33 |
% 28.81/9.33 | From (947) and (190) follows:
% 28.81/9.33 | (948) pred(n8) = all_0_9_9
% 28.81/9.33 |
% 28.81/9.33 | From (947) and (505) follows:
% 28.81/9.33 | (949) succ(n8) = all_0_5_5
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (259) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 28.81/9.33 | (950) all_0_9_9 = n7
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (184) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 28.81/9.33 | (951) all_0_5_5 = n9
% 28.81/9.33 |
% 28.81/9.33 | From (950)(951) and (156) follows:
% 28.81/9.33 | (952) sum(n7, n9) = all_0_2_2
% 28.81/9.33 |
% 28.81/9.33 | From (950) and (1490) follows:
% 28.81/9.33 | (1705) sum(n7, n20) = all_0_7_7
% 28.81/9.33 |
% 28.81/9.33 | From (951) and (1488) follows:
% 28.81/9.33 | (1706) sum(n18, n9) = all_0_4_4
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n18, n9, all_0_4_4, n6 and discharging atoms sum(n18, n9) = all_0_4_4, sum(n18, n9) = n6, yields:
% 28.81/9.33 | (973) all_0_4_4 = n6
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n7, n20, all_0_7_7, n6 and discharging atoms sum(n7, n20) = all_0_7_7, sum(n7, n20) = n6, yields:
% 28.81/9.33 | (975) all_0_7_7 = n6
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 28.81/9.33 | (956) all_0_2_2 = n16
% 28.81/9.33 |
% 28.81/9.33 | From (956) and (1492) follows:
% 28.81/9.33 | (1710) sum(n16, n17) = all_0_0_0
% 28.81/9.33 |
% 28.81/9.33 | From (975)(973) and (435) follows:
% 28.81/9.33 | (977) sum(n6, n6) = all_0_3_3
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n16, n17, all_0_0_0, n12 and discharging atoms sum(n16, n17) = all_0_0_0, sum(n16, n17) = n12, yields:
% 28.81/9.33 | (978) all_0_0_0 = n12
% 28.81/9.33 |
% 28.81/9.33 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 28.81/9.33 | (979) all_0_3_3 = n12
% 28.81/9.33 |
% 28.81/9.33 | Equations (978,979) can reduce 201 to:
% 28.81/9.33 | (746) $false
% 28.81/9.33 |
% 28.81/9.33 |-The branch is then unsatisfiable
% 28.81/9.33 |-Branch two:
% 28.81/9.33 | (963) ~ (all_0_11_11 = n8)
% 28.81/9.33 | (964) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.34 |
% 28.81/9.34 +-Applying beta-rule and splitting (964), into two cases.
% 28.81/9.34 |-Branch one:
% 28.81/9.34 | (965) all_0_11_11 = n7
% 28.81/9.34 |
% 28.81/9.34 | From (965) and (190) follows:
% 28.81/9.34 | (966) pred(n7) = all_0_9_9
% 28.81/9.34 |
% 28.81/9.34 | From (965) and (505) follows:
% 28.81/9.34 | (967) succ(n7) = all_0_5_5
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (259) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 28.81/9.34 | (968) all_0_9_9 = n6
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (184) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 28.81/9.34 | (969) all_0_5_5 = n8
% 28.81/9.34 |
% 28.81/9.34 | From (968)(969) and (156) follows:
% 28.81/9.34 | (970) sum(n6, n8) = all_0_2_2
% 28.81/9.34 |
% 28.81/9.34 | From (968) and (1490) follows:
% 28.81/9.34 | (1723) sum(n6, n20) = all_0_7_7
% 28.81/9.34 |
% 28.81/9.34 | From (969) and (1488) follows:
% 28.81/9.34 | (1724) sum(n18, n8) = all_0_4_4
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n18, n8, all_0_4_4, n5 and discharging atoms sum(n18, n8) = all_0_4_4, sum(n18, n8) = n5, yields:
% 28.81/9.34 | (991) all_0_4_4 = n5
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n6, n20, all_0_7_7, n5 and discharging atoms sum(n6, n20) = all_0_7_7, sum(n6, n20) = n5, yields:
% 28.81/9.34 | (993) all_0_7_7 = n5
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 28.81/9.34 | (974) all_0_2_2 = n14
% 28.81/9.34 |
% 28.81/9.34 | From (974) and (1492) follows:
% 28.81/9.34 | (1728) sum(n14, n17) = all_0_0_0
% 28.81/9.34 |
% 28.81/9.34 | From (993)(991) and (435) follows:
% 28.81/9.34 | (995) sum(n5, n5) = all_0_3_3
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n14, n17, all_0_0_0, n10 and discharging atoms sum(n14, n17) = all_0_0_0, sum(n14, n17) = n10, yields:
% 28.81/9.34 | (996) all_0_0_0 = n10
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 28.81/9.34 | (997) all_0_3_3 = n10
% 28.81/9.34 |
% 28.81/9.34 | Equations (996,997) can reduce 201 to:
% 28.81/9.34 | (746) $false
% 28.81/9.34 |
% 28.81/9.34 |-The branch is then unsatisfiable
% 28.81/9.34 |-Branch two:
% 28.81/9.34 | (981) ~ (all_0_11_11 = n7)
% 28.81/9.34 | (982) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.34 |
% 28.81/9.34 +-Applying beta-rule and splitting (982), into two cases.
% 28.81/9.34 |-Branch one:
% 28.81/9.34 | (983) all_0_11_11 = n6
% 28.81/9.34 |
% 28.81/9.34 | From (983) and (190) follows:
% 28.81/9.34 | (984) pred(n6) = all_0_9_9
% 28.81/9.34 |
% 28.81/9.34 | From (983) and (505) follows:
% 28.81/9.34 | (985) succ(n6) = all_0_5_5
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (259) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 28.81/9.34 | (986) all_0_9_9 = n5
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (184) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 28.81/9.34 | (987) all_0_5_5 = n7
% 28.81/9.34 |
% 28.81/9.34 | From (986)(987) and (156) follows:
% 28.81/9.34 | (988) sum(n5, n7) = all_0_2_2
% 28.81/9.34 |
% 28.81/9.34 | From (986) and (1490) follows:
% 28.81/9.34 | (1741) sum(n5, n20) = all_0_7_7
% 28.81/9.34 |
% 28.81/9.34 | From (987) and (1488) follows:
% 28.81/9.34 | (1742) sum(n18, n7) = all_0_4_4
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n18, n7, all_0_4_4, n4 and discharging atoms sum(n18, n7) = all_0_4_4, sum(n18, n7) = n4, yields:
% 28.81/9.34 | (1009) all_0_4_4 = n4
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n5, n20, all_0_7_7, n4 and discharging atoms sum(n5, n20) = all_0_7_7, sum(n5, n20) = n4, yields:
% 28.81/9.34 | (1011) all_0_7_7 = n4
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 28.81/9.34 | (992) all_0_2_2 = n12
% 28.81/9.34 |
% 28.81/9.34 | From (992) and (1492) follows:
% 28.81/9.34 | (1746) sum(n12, n17) = all_0_0_0
% 28.81/9.34 |
% 28.81/9.34 | From (1011)(1009) and (435) follows:
% 28.81/9.34 | (1013) sum(n4, n4) = all_0_3_3
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n12, n17, all_0_0_0, n8 and discharging atoms sum(n12, n17) = all_0_0_0, sum(n12, n17) = n8, yields:
% 28.81/9.34 | (1014) all_0_0_0 = n8
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 28.81/9.34 | (1015) all_0_3_3 = n8
% 28.81/9.34 |
% 28.81/9.34 | Equations (1014,1015) can reduce 201 to:
% 28.81/9.34 | (746) $false
% 28.81/9.34 |
% 28.81/9.34 |-The branch is then unsatisfiable
% 28.81/9.34 |-Branch two:
% 28.81/9.34 | (999) ~ (all_0_11_11 = n6)
% 28.81/9.34 | (1000) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.34 |
% 28.81/9.34 +-Applying beta-rule and splitting (1000), into two cases.
% 28.81/9.34 |-Branch one:
% 28.81/9.34 | (1001) all_0_11_11 = n5
% 28.81/9.34 |
% 28.81/9.34 | From (1001) and (190) follows:
% 28.81/9.34 | (1002) pred(n5) = all_0_9_9
% 28.81/9.34 |
% 28.81/9.34 | From (1001) and (505) follows:
% 28.81/9.34 | (1003) succ(n5) = all_0_5_5
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (259) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 28.81/9.34 | (1004) all_0_9_9 = n4
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (184) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 28.81/9.34 | (1005) all_0_5_5 = n6
% 28.81/9.34 |
% 28.81/9.34 | From (1004)(1005) and (156) follows:
% 28.81/9.34 | (1006) sum(n4, n6) = all_0_2_2
% 28.81/9.34 |
% 28.81/9.34 | From (1004) and (1490) follows:
% 28.81/9.34 | (1759) sum(n4, n20) = all_0_7_7
% 28.81/9.34 |
% 28.81/9.34 | From (1005) and (1488) follows:
% 28.81/9.34 | (1760) sum(n18, n6) = all_0_4_4
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n18, n6, all_0_4_4, n3 and discharging atoms sum(n18, n6) = all_0_4_4, sum(n18, n6) = n3, yields:
% 28.81/9.34 | (1027) all_0_4_4 = n3
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n4, n20, all_0_7_7, n3 and discharging atoms sum(n4, n20) = all_0_7_7, sum(n4, n20) = n3, yields:
% 28.81/9.34 | (1029) all_0_7_7 = n3
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 28.81/9.34 | (1010) all_0_2_2 = n10
% 28.81/9.34 |
% 28.81/9.34 | From (1010) and (1492) follows:
% 28.81/9.34 | (1764) sum(n10, n17) = all_0_0_0
% 28.81/9.34 |
% 28.81/9.34 | From (1029)(1027) and (435) follows:
% 28.81/9.34 | (1031) sum(n3, n3) = all_0_3_3
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n10, n17, all_0_0_0, n6 and discharging atoms sum(n10, n17) = all_0_0_0, sum(n10, n17) = n6, yields:
% 28.81/9.34 | (1032) all_0_0_0 = n6
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 28.81/9.34 | (1033) all_0_3_3 = n6
% 28.81/9.34 |
% 28.81/9.34 | Equations (1032,1033) can reduce 201 to:
% 28.81/9.34 | (746) $false
% 28.81/9.34 |
% 28.81/9.34 |-The branch is then unsatisfiable
% 28.81/9.34 |-Branch two:
% 28.81/9.34 | (1017) ~ (all_0_11_11 = n5)
% 28.81/9.34 | (1018) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.34 |
% 28.81/9.34 +-Applying beta-rule and splitting (1018), into two cases.
% 28.81/9.34 |-Branch one:
% 28.81/9.34 | (1019) all_0_11_11 = n4
% 28.81/9.34 |
% 28.81/9.34 | From (1019) and (190) follows:
% 28.81/9.34 | (1020) pred(n4) = all_0_9_9
% 28.81/9.34 |
% 28.81/9.34 | From (1019) and (505) follows:
% 28.81/9.34 | (1021) succ(n4) = all_0_5_5
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 28.81/9.34 | (1022) all_0_9_9 = n3
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 28.81/9.34 | (1023) all_0_5_5 = n5
% 28.81/9.34 |
% 28.81/9.34 | From (1022)(1023) and (156) follows:
% 28.81/9.34 | (1024) sum(n3, n5) = all_0_2_2
% 28.81/9.34 |
% 28.81/9.34 | From (1022) and (1490) follows:
% 28.81/9.34 | (1777) sum(n3, n20) = all_0_7_7
% 28.81/9.34 |
% 28.81/9.34 | From (1023) and (1488) follows:
% 28.81/9.34 | (1778) sum(n18, n5) = all_0_4_4
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n18, n5, all_0_4_4, n2 and discharging atoms sum(n18, n5) = all_0_4_4, sum(n18, n5) = n2, yields:
% 28.81/9.34 | (1045) all_0_4_4 = n2
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n3, n20, all_0_7_7, n2 and discharging atoms sum(n3, n20) = all_0_7_7, sum(n3, n20) = n2, yields:
% 28.81/9.34 | (1047) all_0_7_7 = n2
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 28.81/9.34 | (1028) all_0_2_2 = n8
% 28.81/9.34 |
% 28.81/9.34 | From (1028) and (1492) follows:
% 28.81/9.34 | (1782) sum(n8, n17) = all_0_0_0
% 28.81/9.34 |
% 28.81/9.34 | From (1047)(1045) and (435) follows:
% 28.81/9.34 | (1049) sum(n2, n2) = all_0_3_3
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n8, n17, all_0_0_0, n4 and discharging atoms sum(n8, n17) = all_0_0_0, sum(n8, n17) = n4, yields:
% 28.81/9.34 | (1050) all_0_0_0 = n4
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 28.81/9.34 | (1051) all_0_3_3 = n4
% 28.81/9.34 |
% 28.81/9.34 | Equations (1050,1051) can reduce 201 to:
% 28.81/9.34 | (746) $false
% 28.81/9.34 |
% 28.81/9.34 |-The branch is then unsatisfiable
% 28.81/9.34 |-Branch two:
% 28.81/9.34 | (1035) ~ (all_0_11_11 = n4)
% 28.81/9.34 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.34 |
% 28.81/9.34 +-Applying beta-rule and splitting (1036), into two cases.
% 28.81/9.34 |-Branch one:
% 28.81/9.34 | (1037) all_0_11_11 = n3
% 28.81/9.34 |
% 28.81/9.34 | From (1037) and (190) follows:
% 28.81/9.34 | (1038) pred(n3) = all_0_9_9
% 28.81/9.34 |
% 28.81/9.34 | From (1037) and (505) follows:
% 28.81/9.34 | (1039) succ(n3) = all_0_5_5
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 28.81/9.34 | (1040) all_0_9_9 = n2
% 28.81/9.34 |
% 28.81/9.34 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 28.81/9.34 | (1041) all_0_5_5 = n4
% 28.81/9.34 |
% 28.81/9.34 | From (1040)(1041) and (156) follows:
% 28.81/9.35 | (1042) sum(n2, n4) = all_0_2_2
% 28.81/9.35 |
% 28.81/9.35 | From (1040) and (1490) follows:
% 28.81/9.35 | (1795) sum(n2, n20) = all_0_7_7
% 28.81/9.35 |
% 28.81/9.35 | From (1041) and (1488) follows:
% 28.81/9.35 | (1796) sum(n18, n4) = all_0_4_4
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (194) with n18, n4, all_0_4_4, n1 and discharging atoms sum(n18, n4) = all_0_4_4, sum(n18, n4) = n1, yields:
% 28.81/9.35 | (1063) all_0_4_4 = n1
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (194) with n2, n20, all_0_7_7, n1 and discharging atoms sum(n2, n20) = all_0_7_7, sum(n2, n20) = n1, yields:
% 28.81/9.35 | (1065) all_0_7_7 = n1
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 28.81/9.35 | (1046) all_0_2_2 = n6
% 28.81/9.35 |
% 28.81/9.35 | From (1046) and (1492) follows:
% 28.81/9.35 | (1800) sum(n6, n17) = all_0_0_0
% 28.81/9.35 |
% 28.81/9.35 | From (1065)(1063) and (435) follows:
% 28.81/9.35 | (1067) sum(n1, n1) = all_0_3_3
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (194) with n6, n17, all_0_0_0, n2 and discharging atoms sum(n6, n17) = all_0_0_0, sum(n6, n17) = n2, yields:
% 28.81/9.35 | (1068) all_0_0_0 = n2
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 28.81/9.35 | (1069) all_0_3_3 = n2
% 28.81/9.35 |
% 28.81/9.35 | Equations (1068,1069) can reduce 201 to:
% 28.81/9.35 | (746) $false
% 28.81/9.35 |
% 28.81/9.35 |-The branch is then unsatisfiable
% 28.81/9.35 |-Branch two:
% 28.81/9.35 | (1053) ~ (all_0_11_11 = n3)
% 28.81/9.35 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.35 |
% 28.81/9.35 +-Applying beta-rule and splitting (1054), into two cases.
% 28.81/9.35 |-Branch one:
% 28.81/9.35 | (1055) all_0_11_11 = n2
% 28.81/9.35 |
% 28.81/9.35 | From (1055) and (190) follows:
% 28.81/9.35 | (1056) pred(n2) = all_0_9_9
% 28.81/9.35 |
% 28.81/9.35 | From (1055) and (505) follows:
% 28.81/9.35 | (1057) succ(n2) = all_0_5_5
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 28.81/9.35 | (1058) all_0_9_9 = n1
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 28.81/9.35 | (1059) all_0_5_5 = n3
% 28.81/9.35 |
% 28.81/9.35 | From (1058)(1059) and (156) follows:
% 28.81/9.35 | (1060) sum(n1, n3) = all_0_2_2
% 28.81/9.35 |
% 28.81/9.35 | From (1058) and (1490) follows:
% 28.81/9.35 | (1813) sum(n1, n20) = all_0_7_7
% 28.81/9.35 |
% 28.81/9.35 | From (1059) and (1488) follows:
% 28.81/9.35 | (1814) sum(n18, n3) = all_0_4_4
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (194) with n18, n3, all_0_4_4, n0 and discharging atoms sum(n18, n3) = all_0_4_4, sum(n18, n3) = n0, yields:
% 28.81/9.35 | (1081) all_0_4_4 = n0
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (194) with n1, n20, all_0_7_7, n0 and discharging atoms sum(n1, n20) = all_0_7_7, sum(n1, n20) = n0, yields:
% 28.81/9.35 | (1083) all_0_7_7 = n0
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 28.81/9.35 | (1064) all_0_2_2 = n4
% 28.81/9.35 |
% 28.81/9.35 | From (1064) and (1492) follows:
% 28.81/9.35 | (1818) sum(n4, n17) = all_0_0_0
% 28.81/9.35 |
% 28.81/9.35 | From (1083)(1081) and (435) follows:
% 28.81/9.35 | (1085) sum(n0, n0) = all_0_3_3
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (194) with n4, n17, all_0_0_0, n0 and discharging atoms sum(n4, n17) = all_0_0_0, sum(n4, n17) = n0, yields:
% 28.81/9.35 | (1087) all_0_0_0 = n0
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 28.81/9.35 | (1088) all_0_3_3 = n0
% 28.81/9.35 |
% 28.81/9.35 | Equations (1087,1088) can reduce 201 to:
% 28.81/9.35 | (746) $false
% 28.81/9.35 |
% 28.81/9.35 |-The branch is then unsatisfiable
% 28.81/9.35 |-Branch two:
% 28.81/9.35 | (1071) ~ (all_0_11_11 = n2)
% 28.81/9.35 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 28.81/9.35 |
% 28.81/9.35 +-Applying beta-rule and splitting (1072), into two cases.
% 28.81/9.35 |-Branch one:
% 28.81/9.35 | (1073) all_0_11_11 = n1
% 28.81/9.35 |
% 28.81/9.35 | From (1073) and (190) follows:
% 28.81/9.35 | (1074) pred(n1) = all_0_9_9
% 28.81/9.35 |
% 28.81/9.35 | From (1073) and (505) follows:
% 28.81/9.35 | (1075) succ(n1) = all_0_5_5
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 28.81/9.35 | (1076) all_0_9_9 = n0
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 28.81/9.35 | (1077) all_0_5_5 = n2
% 28.81/9.35 |
% 28.81/9.35 | From (1076)(1077) and (156) follows:
% 28.81/9.35 | (1078) sum(n0, n2) = all_0_2_2
% 28.81/9.35 |
% 28.81/9.35 | From (1076) and (1490) follows:
% 28.81/9.35 | (1831) sum(n0, n20) = all_0_7_7
% 28.81/9.35 |
% 28.81/9.35 | From (1077) and (1488) follows:
% 28.81/9.35 | (1832) sum(n18, n2) = all_0_4_4
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (194) with n18, n2, all_0_4_4, n20 and discharging atoms sum(n18, n2) = all_0_4_4, sum(n18, n2) = n20, yields:
% 28.81/9.35 | (1101) all_0_4_4 = n20
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (194) with n0, n20, all_0_7_7, n20 and discharging atoms sum(n0, n20) = all_0_7_7, sum(n0, n20) = n20, yields:
% 28.81/9.35 | (1100) all_0_7_7 = n20
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 28.81/9.35 | (1082) all_0_2_2 = n2
% 28.81/9.35 |
% 28.81/9.35 | From (1082) and (1492) follows:
% 28.81/9.35 | (1836) sum(n2, n17) = all_0_0_0
% 28.81/9.35 |
% 28.81/9.35 | From (1100)(1101) and (435) follows:
% 28.81/9.35 | (1103) sum(n20, n20) = all_0_3_3
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 28.81/9.35 | (1104) all_0_3_3 = n19
% 28.81/9.35 |
% 28.81/9.35 | Instantiating formula (194) with n2, n17, all_0_0_0, n19 and discharging atoms sum(n2, n17) = all_0_0_0, sum(n2, n17) = n19, yields:
% 28.81/9.35 | (1105) all_0_0_0 = n19
% 28.81/9.35 |
% 29.05/9.35 | Equations (1105,1104) can reduce 201 to:
% 29.05/9.35 | (746) $false
% 29.05/9.35 |
% 29.05/9.35 |-The branch is then unsatisfiable
% 29.05/9.35 |-Branch two:
% 29.05/9.35 | (1090) ~ (all_0_11_11 = n1)
% 29.05/9.35 | (1091) all_0_11_11 = n0
% 29.05/9.35 |
% 29.05/9.35 | From (1091) and (190) follows:
% 29.05/9.35 | (1092) pred(n0) = all_0_9_9
% 29.05/9.35 |
% 29.05/9.35 | From (1091) and (505) follows:
% 29.05/9.35 | (1093) succ(n0) = all_0_5_5
% 29.05/9.35 |
% 29.05/9.35 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 29.05/9.35 | (1094) all_0_9_9 = n20
% 29.05/9.35 |
% 29.05/9.35 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 29.05/9.35 | (1095) all_0_5_5 = n1
% 29.05/9.35 |
% 29.05/9.35 | From (1094)(1095) and (156) follows:
% 29.05/9.35 | (1096) sum(n20, n1) = all_0_2_2
% 29.05/9.35 |
% 29.05/9.35 | From (1094) and (1490) follows:
% 29.05/9.35 | (1848) sum(n20, n20) = all_0_7_7
% 29.05/9.35 |
% 29.05/9.35 | From (1095) and (1488) follows:
% 29.05/9.35 | (1849) sum(n18, n1) = all_0_4_4
% 29.05/9.35 |
% 29.05/9.35 | Instantiating formula (194) with n20, n20, all_0_7_7, n19 and discharging atoms sum(n20, n20) = all_0_7_7, sum(n20, n20) = n19, yields:
% 29.05/9.35 | (737) all_0_7_7 = n19
% 29.05/9.35 |
% 29.05/9.35 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 29.05/9.35 | (1099) all_0_2_2 = n0
% 29.05/9.35 |
% 29.05/9.35 | Instantiating formula (194) with n18, n1, all_0_4_4, n19 and discharging atoms sum(n18, n1) = all_0_4_4, sum(n18, n1) = n19, yields:
% 29.05/9.35 | (736) all_0_4_4 = n19
% 29.05/9.35 |
% 29.05/9.35 | From (1099) and (1492) follows:
% 29.05/9.35 | (1853) sum(n0, n17) = all_0_0_0
% 29.05/9.35 |
% 29.05/9.35 | From (737)(736) and (435) follows:
% 29.05/9.35 | (741) sum(n19, n19) = all_0_3_3
% 29.05/9.35 |
% 29.05/9.35 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 29.05/9.35 | (744) all_0_3_3 = n17
% 29.05/9.35 |
% 29.05/9.35 | Instantiating formula (194) with n0, n17, all_0_0_0, n17 and discharging atoms sum(n0, n17) = all_0_0_0, sum(n0, n17) = n17, yields:
% 29.05/9.35 | (742) all_0_0_0 = n17
% 29.05/9.35 |
% 29.05/9.35 | Equations (742,744) can reduce 201 to:
% 29.05/9.35 | (746) $false
% 29.05/9.35 |
% 29.05/9.35 |-The branch is then unsatisfiable
% 29.05/9.35 |-Branch two:
% 29.05/9.35 | (1136) ~ (all_0_10_10 = n19)
% 29.05/9.35 | (1137) all_0_10_10 = n18 | all_0_10_10 = n17 | all_0_10_10 = n16 | all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.05/9.35 |
% 29.05/9.35 +-Applying beta-rule and splitting (748), into two cases.
% 29.05/9.35 |-Branch one:
% 29.05/9.35 | (749) all_0_11_11 = n19
% 29.05/9.35 |
% 29.05/9.35 | From (749) and (190) follows:
% 29.05/9.35 | (750) pred(n19) = all_0_9_9
% 29.05/9.35 |
% 29.05/9.35 | From (749) and (505) follows:
% 29.05/9.35 | (751) succ(n19) = all_0_5_5
% 29.05/9.35 |
% 29.05/9.35 | Instantiating formula (259) with n19, all_0_9_9, n18 and discharging atoms pred(n19) = all_0_9_9, pred(n19) = n18, yields:
% 29.05/9.35 | (752) all_0_9_9 = n18
% 29.05/9.35 |
% 29.05/9.35 | Instantiating formula (184) with n19, all_0_5_5, n20 and discharging atoms succ(n19) = all_0_5_5, succ(n19) = n20, yields:
% 29.05/9.35 | (753) all_0_5_5 = n20
% 29.05/9.35 |
% 29.05/9.35 | From (753) and (386) follows:
% 29.05/9.35 | (1865) sum(all_0_6_6, n20) = all_0_4_4
% 29.05/9.36 |
% 29.05/9.36 | From (752)(753) and (156) follows:
% 29.05/9.36 | (754) sum(n18, n20) = all_0_2_2
% 29.05/9.36 |
% 29.05/9.36 | From (752) and (74) follows:
% 29.05/9.36 | (1867) sum(n18, all_0_8_8) = all_0_7_7
% 29.05/9.36 |
% 29.05/9.36 | Instantiating formula (194) with n18, n20, all_0_2_2, n17 and discharging atoms sum(n18, n20) = all_0_2_2, sum(n18, n20) = n17, yields:
% 29.05/9.36 | (758) all_0_2_2 = n17
% 29.05/9.36 |
% 29.05/9.36 | From (758) and (85) follows:
% 29.05/9.36 | (1869) sum(n17, all_0_1_1) = all_0_0_0
% 29.05/9.36 |
% 29.05/9.36 +-Applying beta-rule and splitting (1137), into two cases.
% 29.05/9.36 |-Branch one:
% 29.05/9.36 | (1138) all_0_10_10 = n18
% 29.05/9.36 |
% 29.05/9.36 | From (1138) and (57) follows:
% 29.05/9.36 | (1139) pred(n18) = all_0_6_6
% 29.05/9.36 |
% 29.05/9.36 | From (1138) and (381) follows:
% 29.05/9.36 | (1140) succ(n18) = all_0_8_8
% 29.05/9.36 |
% 29.05/9.36 | Instantiating formula (259) with n18, all_0_6_6, n17 and discharging atoms pred(n18) = all_0_6_6, pred(n18) = n17, yields:
% 29.05/9.36 | (1141) all_0_6_6 = n17
% 29.05/9.36 |
% 29.05/9.36 | Instantiating formula (184) with n18, all_0_8_8, n19 and discharging atoms succ(n18) = all_0_8_8, succ(n18) = n19, yields:
% 29.05/9.36 | (1142) all_0_8_8 = n19
% 29.05/9.36 |
% 29.05/9.36 | From (1141)(1142) and (628) follows:
% 29.05/9.36 | (1143) sum(n17, n19) = all_0_1_1
% 29.05/9.36 |
% 29.05/9.36 | From (1141) and (1865) follows:
% 29.05/9.36 | (1876) sum(n17, n20) = all_0_4_4
% 29.05/9.36 |
% 29.05/9.36 | From (1142) and (1867) follows:
% 29.05/9.36 | (1877) sum(n18, n19) = all_0_7_7
% 29.05/9.36 |
% 29.05/9.36 | Instantiating formula (194) with n18, n19, all_0_7_7, n16 and discharging atoms sum(n18, n19) = all_0_7_7, sum(n18, n19) = n16, yields:
% 29.05/9.36 | (795) all_0_7_7 = n16
% 29.05/9.36 |
% 29.05/9.36 | Instantiating formula (194) with n17, n20, all_0_4_4, n16 and discharging atoms sum(n17, n20) = all_0_4_4, sum(n17, n20) = n16, yields:
% 29.07/9.36 | (793) all_0_4_4 = n16
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (194) with n17, n19, all_0_1_1, n15 and discharging atoms sum(n17, n19) = all_0_1_1, sum(n17, n19) = n15, yields:
% 29.07/9.36 | (1147) all_0_1_1 = n15
% 29.07/9.36 |
% 29.07/9.36 | From (795)(793) and (435) follows:
% 29.07/9.36 | (797) sum(n16, n16) = all_0_3_3
% 29.07/9.36 |
% 29.07/9.36 | From (1147) and (1869) follows:
% 29.07/9.36 | (1882) sum(n17, n15) = all_0_0_0
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (194) with n17, n15, all_0_0_0, n11 and discharging atoms sum(n17, n15) = all_0_0_0, sum(n17, n15) = n11, yields:
% 29.07/9.36 | (799) all_0_0_0 = n11
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 29.07/9.36 | (798) all_0_3_3 = n11
% 29.07/9.36 |
% 29.07/9.36 | Equations (799,798) can reduce 201 to:
% 29.07/9.36 | (746) $false
% 29.07/9.36 |
% 29.07/9.36 |-The branch is then unsatisfiable
% 29.07/9.36 |-Branch two:
% 29.07/9.36 | (1154) ~ (all_0_10_10 = n18)
% 29.07/9.36 | (1155) all_0_10_10 = n17 | all_0_10_10 = n16 | all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.07/9.36 |
% 29.07/9.36 +-Applying beta-rule and splitting (1155), into two cases.
% 29.07/9.36 |-Branch one:
% 29.07/9.36 | (1156) all_0_10_10 = n17
% 29.07/9.36 |
% 29.07/9.36 | From (1156) and (57) follows:
% 29.07/9.36 | (1157) pred(n17) = all_0_6_6
% 29.07/9.36 |
% 29.07/9.36 | From (1156) and (381) follows:
% 29.07/9.36 | (1158) succ(n17) = all_0_8_8
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (259) with n17, all_0_6_6, n16 and discharging atoms pred(n17) = all_0_6_6, pred(n17) = n16, yields:
% 29.07/9.36 | (1159) all_0_6_6 = n16
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (184) with n17, all_0_8_8, n18 and discharging atoms succ(n17) = all_0_8_8, succ(n17) = n18, yields:
% 29.07/9.36 | (1160) all_0_8_8 = n18
% 29.07/9.36 |
% 29.07/9.36 | From (1159)(1160) and (628) follows:
% 29.07/9.36 | (1161) sum(n16, n18) = all_0_1_1
% 29.07/9.36 |
% 29.07/9.36 | From (1159) and (1865) follows:
% 29.07/9.36 | (1894) sum(n16, n20) = all_0_4_4
% 29.07/9.36 |
% 29.07/9.36 | From (1160) and (1867) follows:
% 29.07/9.36 | (1895) sum(n18, n18) = all_0_7_7
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (194) with n18, n18, all_0_7_7, n15 and discharging atoms sum(n18, n18) = all_0_7_7, sum(n18, n18) = n15, yields:
% 29.07/9.36 | (813) all_0_7_7 = n15
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (194) with n16, n20, all_0_4_4, n15 and discharging atoms sum(n16, n20) = all_0_4_4, sum(n16, n20) = n15, yields:
% 29.07/9.36 | (811) all_0_4_4 = n15
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (194) with n16, n18, all_0_1_1, n13 and discharging atoms sum(n16, n18) = all_0_1_1, sum(n16, n18) = n13, yields:
% 29.07/9.36 | (1165) all_0_1_1 = n13
% 29.07/9.36 |
% 29.07/9.36 | From (813)(811) and (435) follows:
% 29.07/9.36 | (815) sum(n15, n15) = all_0_3_3
% 29.07/9.36 |
% 29.07/9.36 | From (1165) and (1869) follows:
% 29.07/9.36 | (1900) sum(n17, n13) = all_0_0_0
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (194) with n17, n13, all_0_0_0, n9 and discharging atoms sum(n17, n13) = all_0_0_0, sum(n17, n13) = n9, yields:
% 29.07/9.36 | (817) all_0_0_0 = n9
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 29.07/9.36 | (816) all_0_3_3 = n9
% 29.07/9.36 |
% 29.07/9.36 | Equations (817,816) can reduce 201 to:
% 29.07/9.36 | (746) $false
% 29.07/9.36 |
% 29.07/9.36 |-The branch is then unsatisfiable
% 29.07/9.36 |-Branch two:
% 29.07/9.36 | (1172) ~ (all_0_10_10 = n17)
% 29.07/9.36 | (1173) all_0_10_10 = n16 | all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.07/9.36 |
% 29.07/9.36 +-Applying beta-rule and splitting (1173), into two cases.
% 29.07/9.36 |-Branch one:
% 29.07/9.36 | (1174) all_0_10_10 = n16
% 29.07/9.36 |
% 29.07/9.36 | From (1174) and (57) follows:
% 29.07/9.36 | (1175) pred(n16) = all_0_6_6
% 29.07/9.36 |
% 29.07/9.36 | From (1174) and (381) follows:
% 29.07/9.36 | (1176) succ(n16) = all_0_8_8
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (259) with n16, all_0_6_6, n15 and discharging atoms pred(n16) = all_0_6_6, pred(n16) = n15, yields:
% 29.07/9.36 | (1177) all_0_6_6 = n15
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (184) with n16, all_0_8_8, n17 and discharging atoms succ(n16) = all_0_8_8, succ(n16) = n17, yields:
% 29.07/9.36 | (1178) all_0_8_8 = n17
% 29.07/9.36 |
% 29.07/9.36 | From (1177)(1178) and (628) follows:
% 29.07/9.36 | (1179) sum(n15, n17) = all_0_1_1
% 29.07/9.36 |
% 29.07/9.36 | From (1177) and (1865) follows:
% 29.07/9.36 | (1912) sum(n15, n20) = all_0_4_4
% 29.07/9.36 |
% 29.07/9.36 | From (1178) and (1867) follows:
% 29.07/9.36 | (1913) sum(n18, n17) = all_0_7_7
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (194) with n18, n17, all_0_7_7, n14 and discharging atoms sum(n18, n17) = all_0_7_7, sum(n18, n17) = n14, yields:
% 29.07/9.36 | (831) all_0_7_7 = n14
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (194) with n15, n20, all_0_4_4, n14 and discharging atoms sum(n15, n20) = all_0_4_4, sum(n15, n20) = n14, yields:
% 29.07/9.36 | (829) all_0_4_4 = n14
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (194) with n15, n17, all_0_1_1, n11 and discharging atoms sum(n15, n17) = all_0_1_1, sum(n15, n17) = n11, yields:
% 29.07/9.36 | (1183) all_0_1_1 = n11
% 29.07/9.36 |
% 29.07/9.36 | From (831)(829) and (435) follows:
% 29.07/9.36 | (833) sum(n14, n14) = all_0_3_3
% 29.07/9.36 |
% 29.07/9.36 | From (1183) and (1869) follows:
% 29.07/9.36 | (1918) sum(n17, n11) = all_0_0_0
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (194) with n17, n11, all_0_0_0, n7 and discharging atoms sum(n17, n11) = all_0_0_0, sum(n17, n11) = n7, yields:
% 29.07/9.36 | (835) all_0_0_0 = n7
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 29.07/9.36 | (834) all_0_3_3 = n7
% 29.07/9.36 |
% 29.07/9.36 | Equations (835,834) can reduce 201 to:
% 29.07/9.36 | (746) $false
% 29.07/9.36 |
% 29.07/9.36 |-The branch is then unsatisfiable
% 29.07/9.36 |-Branch two:
% 29.07/9.36 | (1190) ~ (all_0_10_10 = n16)
% 29.07/9.36 | (1191) all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.07/9.36 |
% 29.07/9.36 +-Applying beta-rule and splitting (1191), into two cases.
% 29.07/9.36 |-Branch one:
% 29.07/9.36 | (1192) all_0_10_10 = n15
% 29.07/9.36 |
% 29.07/9.36 | From (1192) and (57) follows:
% 29.07/9.36 | (1193) pred(n15) = all_0_6_6
% 29.07/9.36 |
% 29.07/9.36 | From (1192) and (381) follows:
% 29.07/9.36 | (1194) succ(n15) = all_0_8_8
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (259) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 29.07/9.36 | (1195) all_0_6_6 = n14
% 29.07/9.36 |
% 29.07/9.36 | Instantiating formula (184) with n15, all_0_8_8, n16 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n16, yields:
% 29.07/9.36 | (1196) all_0_8_8 = n16
% 29.07/9.36 |
% 29.07/9.36 | From (1195)(1196) and (628) follows:
% 29.07/9.36 | (1197) sum(n14, n16) = all_0_1_1
% 29.07/9.36 |
% 29.07/9.36 | From (1195) and (1865) follows:
% 29.07/9.36 | (1930) sum(n14, n20) = all_0_4_4
% 29.07/9.36 |
% 29.07/9.36 | From (1196) and (1867) follows:
% 29.07/9.37 | (1931) sum(n18, n16) = all_0_7_7
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n18, n16, all_0_7_7, n13 and discharging atoms sum(n18, n16) = all_0_7_7, sum(n18, n16) = n13, yields:
% 29.07/9.37 | (849) all_0_7_7 = n13
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n14, n20, all_0_4_4, n13 and discharging atoms sum(n14, n20) = all_0_4_4, sum(n14, n20) = n13, yields:
% 29.07/9.37 | (847) all_0_4_4 = n13
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n14, n16, all_0_1_1, n9 and discharging atoms sum(n14, n16) = all_0_1_1, sum(n14, n16) = n9, yields:
% 29.07/9.37 | (1201) all_0_1_1 = n9
% 29.07/9.37 |
% 29.07/9.37 | From (849)(847) and (435) follows:
% 29.07/9.37 | (851) sum(n13, n13) = all_0_3_3
% 29.07/9.37 |
% 29.07/9.37 | From (1201) and (1869) follows:
% 29.07/9.37 | (1936) sum(n17, n9) = all_0_0_0
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n17, n9, all_0_0_0, n5 and discharging atoms sum(n17, n9) = all_0_0_0, sum(n17, n9) = n5, yields:
% 29.07/9.37 | (853) all_0_0_0 = n5
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 29.07/9.37 | (852) all_0_3_3 = n5
% 29.07/9.37 |
% 29.07/9.37 | Equations (853,852) can reduce 201 to:
% 29.07/9.37 | (746) $false
% 29.07/9.37 |
% 29.07/9.37 |-The branch is then unsatisfiable
% 29.07/9.37 |-Branch two:
% 29.07/9.37 | (1208) ~ (all_0_10_10 = n15)
% 29.07/9.37 | (1209) all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.07/9.37 |
% 29.07/9.37 +-Applying beta-rule and splitting (1209), into two cases.
% 29.07/9.37 |-Branch one:
% 29.07/9.37 | (1210) all_0_10_10 = n14
% 29.07/9.37 |
% 29.07/9.37 | From (1210) and (57) follows:
% 29.07/9.37 | (1211) pred(n14) = all_0_6_6
% 29.07/9.37 |
% 29.07/9.37 | From (1210) and (381) follows:
% 29.07/9.37 | (1212) succ(n14) = all_0_8_8
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (259) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 29.07/9.37 | (1213) all_0_6_6 = n13
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (184) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 29.07/9.37 | (1214) all_0_8_8 = n15
% 29.07/9.37 |
% 29.07/9.37 | From (1213)(1214) and (628) follows:
% 29.07/9.37 | (1215) sum(n13, n15) = all_0_1_1
% 29.07/9.37 |
% 29.07/9.37 | From (1213) and (1865) follows:
% 29.07/9.37 | (1948) sum(n13, n20) = all_0_4_4
% 29.07/9.37 |
% 29.07/9.37 | From (1214) and (1867) follows:
% 29.07/9.37 | (1949) sum(n18, n15) = all_0_7_7
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n18, n15, all_0_7_7, n12 and discharging atoms sum(n18, n15) = all_0_7_7, sum(n18, n15) = n12, yields:
% 29.07/9.37 | (867) all_0_7_7 = n12
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n13, n20, all_0_4_4, n12 and discharging atoms sum(n13, n20) = all_0_4_4, sum(n13, n20) = n12, yields:
% 29.07/9.37 | (865) all_0_4_4 = n12
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n13, n15, all_0_1_1, n7 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n7, yields:
% 29.07/9.37 | (1219) all_0_1_1 = n7
% 29.07/9.37 |
% 29.07/9.37 | From (867)(865) and (435) follows:
% 29.07/9.37 | (869) sum(n12, n12) = all_0_3_3
% 29.07/9.37 |
% 29.07/9.37 | From (1219) and (1869) follows:
% 29.07/9.37 | (1954) sum(n17, n7) = all_0_0_0
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n17, n7, all_0_0_0, n3 and discharging atoms sum(n17, n7) = all_0_0_0, sum(n17, n7) = n3, yields:
% 29.07/9.37 | (871) all_0_0_0 = n3
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 29.07/9.37 | (870) all_0_3_3 = n3
% 29.07/9.37 |
% 29.07/9.37 | Equations (871,870) can reduce 201 to:
% 29.07/9.37 | (746) $false
% 29.07/9.37 |
% 29.07/9.37 |-The branch is then unsatisfiable
% 29.07/9.37 |-Branch two:
% 29.07/9.37 | (1226) ~ (all_0_10_10 = n14)
% 29.07/9.37 | (1227) all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.07/9.37 |
% 29.07/9.37 +-Applying beta-rule and splitting (1227), into two cases.
% 29.07/9.37 |-Branch one:
% 29.07/9.37 | (1228) all_0_10_10 = n13
% 29.07/9.37 |
% 29.07/9.37 | From (1228) and (57) follows:
% 29.07/9.37 | (1229) pred(n13) = all_0_6_6
% 29.07/9.37 |
% 29.07/9.37 | From (1228) and (381) follows:
% 29.07/9.37 | (1230) succ(n13) = all_0_8_8
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (259) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 29.07/9.37 | (1231) all_0_6_6 = n12
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (184) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 29.07/9.37 | (1232) all_0_8_8 = n14
% 29.07/9.37 |
% 29.07/9.37 | From (1231)(1232) and (628) follows:
% 29.07/9.37 | (1233) sum(n12, n14) = all_0_1_1
% 29.07/9.37 |
% 29.07/9.37 | From (1231) and (1865) follows:
% 29.07/9.37 | (1966) sum(n12, n20) = all_0_4_4
% 29.07/9.37 |
% 29.07/9.37 | From (1232) and (1867) follows:
% 29.07/9.37 | (1967) sum(n18, n14) = all_0_7_7
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n18, n14, all_0_7_7, n11 and discharging atoms sum(n18, n14) = all_0_7_7, sum(n18, n14) = n11, yields:
% 29.07/9.37 | (885) all_0_7_7 = n11
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n12, n20, all_0_4_4, n11 and discharging atoms sum(n12, n20) = all_0_4_4, sum(n12, n20) = n11, yields:
% 29.07/9.37 | (883) all_0_4_4 = n11
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n12, n14, all_0_1_1, n5 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n5, yields:
% 29.07/9.37 | (1237) all_0_1_1 = n5
% 29.07/9.37 |
% 29.07/9.37 | From (885)(883) and (435) follows:
% 29.07/9.37 | (887) sum(n11, n11) = all_0_3_3
% 29.07/9.37 |
% 29.07/9.37 | From (1237) and (1869) follows:
% 29.07/9.37 | (1972) sum(n17, n5) = all_0_0_0
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n17, n5, all_0_0_0, n1 and discharging atoms sum(n17, n5) = all_0_0_0, sum(n17, n5) = n1, yields:
% 29.07/9.37 | (889) all_0_0_0 = n1
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 29.07/9.37 | (888) all_0_3_3 = n1
% 29.07/9.37 |
% 29.07/9.37 | Equations (889,888) can reduce 201 to:
% 29.07/9.37 | (746) $false
% 29.07/9.37 |
% 29.07/9.37 |-The branch is then unsatisfiable
% 29.07/9.37 |-Branch two:
% 29.07/9.37 | (1244) ~ (all_0_10_10 = n13)
% 29.07/9.37 | (1245) all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.07/9.37 |
% 29.07/9.37 +-Applying beta-rule and splitting (1245), into two cases.
% 29.07/9.37 |-Branch one:
% 29.07/9.37 | (1246) all_0_10_10 = n12
% 29.07/9.37 |
% 29.07/9.37 | From (1246) and (57) follows:
% 29.07/9.37 | (1247) pred(n12) = all_0_6_6
% 29.07/9.37 |
% 29.07/9.37 | From (1246) and (381) follows:
% 29.07/9.37 | (1248) succ(n12) = all_0_8_8
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (259) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 29.07/9.37 | (1249) all_0_6_6 = n11
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (184) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 29.07/9.37 | (1250) all_0_8_8 = n13
% 29.07/9.37 |
% 29.07/9.37 | From (1249)(1250) and (628) follows:
% 29.07/9.37 | (1251) sum(n11, n13) = all_0_1_1
% 29.07/9.37 |
% 29.07/9.37 | From (1249) and (1865) follows:
% 29.07/9.37 | (1984) sum(n11, n20) = all_0_4_4
% 29.07/9.37 |
% 29.07/9.37 | From (1250) and (1867) follows:
% 29.07/9.37 | (1985) sum(n18, n13) = all_0_7_7
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n18, n13, all_0_7_7, n10 and discharging atoms sum(n18, n13) = all_0_7_7, sum(n18, n13) = n10, yields:
% 29.07/9.37 | (903) all_0_7_7 = n10
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n11, n20, all_0_4_4, n10 and discharging atoms sum(n11, n20) = all_0_4_4, sum(n11, n20) = n10, yields:
% 29.07/9.37 | (901) all_0_4_4 = n10
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n11, n13, all_0_1_1, n3 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n3, yields:
% 29.07/9.37 | (1255) all_0_1_1 = n3
% 29.07/9.37 |
% 29.07/9.37 | From (903)(901) and (435) follows:
% 29.07/9.37 | (905) sum(n10, n10) = all_0_3_3
% 29.07/9.37 |
% 29.07/9.37 | From (1255) and (1869) follows:
% 29.07/9.37 | (1990) sum(n17, n3) = all_0_0_0
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n17, n3, all_0_0_0, n20 and discharging atoms sum(n17, n3) = all_0_0_0, sum(n17, n3) = n20, yields:
% 29.07/9.37 | (907) all_0_0_0 = n20
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 29.07/9.37 | (906) all_0_3_3 = n20
% 29.07/9.37 |
% 29.07/9.37 | Equations (907,906) can reduce 201 to:
% 29.07/9.37 | (746) $false
% 29.07/9.37 |
% 29.07/9.37 |-The branch is then unsatisfiable
% 29.07/9.37 |-Branch two:
% 29.07/9.37 | (1262) ~ (all_0_10_10 = n12)
% 29.07/9.37 | (1263) all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.07/9.37 |
% 29.07/9.37 +-Applying beta-rule and splitting (1263), into two cases.
% 29.07/9.37 |-Branch one:
% 29.07/9.37 | (1264) all_0_10_10 = n11
% 29.07/9.37 |
% 29.07/9.37 | From (1264) and (57) follows:
% 29.07/9.37 | (1265) pred(n11) = all_0_6_6
% 29.07/9.37 |
% 29.07/9.37 | From (1264) and (381) follows:
% 29.07/9.37 | (1266) succ(n11) = all_0_8_8
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (259) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 29.07/9.37 | (1267) all_0_6_6 = n10
% 29.07/9.37 |
% 29.07/9.37 | Instantiating formula (184) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 29.07/9.37 | (1268) all_0_8_8 = n12
% 29.07/9.37 |
% 29.07/9.37 | From (1267)(1268) and (628) follows:
% 29.07/9.37 | (1269) sum(n10, n12) = all_0_1_1
% 29.07/9.37 |
% 29.07/9.37 | From (1267) and (1865) follows:
% 29.07/9.37 | (2002) sum(n10, n20) = all_0_4_4
% 29.07/9.37 |
% 29.07/9.37 | From (1268) and (1867) follows:
% 29.07/9.38 | (2003) sum(n18, n12) = all_0_7_7
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n18, n12, all_0_7_7, n9 and discharging atoms sum(n18, n12) = all_0_7_7, sum(n18, n12) = n9, yields:
% 29.07/9.38 | (921) all_0_7_7 = n9
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n10, n20, all_0_4_4, n9 and discharging atoms sum(n10, n20) = all_0_4_4, sum(n10, n20) = n9, yields:
% 29.07/9.38 | (919) all_0_4_4 = n9
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n10, n12, all_0_1_1, n1 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n1, yields:
% 29.07/9.38 | (1273) all_0_1_1 = n1
% 29.07/9.38 |
% 29.07/9.38 | From (921)(919) and (435) follows:
% 29.07/9.38 | (923) sum(n9, n9) = all_0_3_3
% 29.07/9.38 |
% 29.07/9.38 | From (1273) and (1869) follows:
% 29.07/9.38 | (2008) sum(n17, n1) = all_0_0_0
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n17, n1, all_0_0_0, n18 and discharging atoms sum(n17, n1) = all_0_0_0, sum(n17, n1) = n18, yields:
% 29.07/9.38 | (924) all_0_0_0 = n18
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 29.07/9.38 | (925) all_0_3_3 = n18
% 29.07/9.38 |
% 29.07/9.38 | Equations (924,925) can reduce 201 to:
% 29.07/9.38 | (746) $false
% 29.07/9.38 |
% 29.07/9.38 |-The branch is then unsatisfiable
% 29.07/9.38 |-Branch two:
% 29.07/9.38 | (1280) ~ (all_0_10_10 = n11)
% 29.07/9.38 | (1281) all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.07/9.38 |
% 29.07/9.38 +-Applying beta-rule and splitting (1281), into two cases.
% 29.07/9.38 |-Branch one:
% 29.07/9.38 | (1282) all_0_10_10 = n10
% 29.07/9.38 |
% 29.07/9.38 | From (1282) and (57) follows:
% 29.07/9.38 | (1283) pred(n10) = all_0_6_6
% 29.07/9.38 |
% 29.07/9.38 | From (1282) and (381) follows:
% 29.07/9.38 | (1284) succ(n10) = all_0_8_8
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (259) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 29.07/9.38 | (1285) all_0_6_6 = n9
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (184) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 29.07/9.38 | (1286) all_0_8_8 = n11
% 29.07/9.38 |
% 29.07/9.38 | From (1285)(1286) and (628) follows:
% 29.07/9.38 | (1287) sum(n9, n11) = all_0_1_1
% 29.07/9.38 |
% 29.07/9.38 | From (1285) and (1865) follows:
% 29.07/9.38 | (2020) sum(n9, n20) = all_0_4_4
% 29.07/9.38 |
% 29.07/9.38 | From (1286) and (1867) follows:
% 29.07/9.38 | (2021) sum(n18, n11) = all_0_7_7
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n18, n11, all_0_7_7, n8 and discharging atoms sum(n18, n11) = all_0_7_7, sum(n18, n11) = n8, yields:
% 29.07/9.38 | (939) all_0_7_7 = n8
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n9, n20, all_0_4_4, n8 and discharging atoms sum(n9, n20) = all_0_4_4, sum(n9, n20) = n8, yields:
% 29.07/9.38 | (937) all_0_4_4 = n8
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 29.07/9.38 | (1291) all_0_1_1 = n20
% 29.07/9.38 |
% 29.07/9.38 | From (939)(937) and (435) follows:
% 29.07/9.38 | (941) sum(n8, n8) = all_0_3_3
% 29.07/9.38 |
% 29.07/9.38 | From (1291) and (1869) follows:
% 29.07/9.38 | (2026) sum(n17, n20) = all_0_0_0
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n17, n20, all_0_0_0, n16 and discharging atoms sum(n17, n20) = all_0_0_0, sum(n17, n20) = n16, yields:
% 29.07/9.38 | (942) all_0_0_0 = n16
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 29.07/9.38 | (943) all_0_3_3 = n16
% 29.07/9.38 |
% 29.07/9.38 | Equations (942,943) can reduce 201 to:
% 29.07/9.38 | (746) $false
% 29.07/9.38 |
% 29.07/9.38 |-The branch is then unsatisfiable
% 29.07/9.38 |-Branch two:
% 29.07/9.38 | (1298) ~ (all_0_10_10 = n10)
% 29.07/9.38 | (1299) all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.07/9.38 |
% 29.07/9.38 +-Applying beta-rule and splitting (1299), into two cases.
% 29.07/9.38 |-Branch one:
% 29.07/9.38 | (1300) all_0_10_10 = n9
% 29.07/9.38 |
% 29.07/9.38 | From (1300) and (57) follows:
% 29.07/9.38 | (1301) pred(n9) = all_0_6_6
% 29.07/9.38 |
% 29.07/9.38 | From (1300) and (381) follows:
% 29.07/9.38 | (1302) succ(n9) = all_0_8_8
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (259) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 29.07/9.38 | (1303) all_0_6_6 = n8
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (184) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 29.07/9.38 | (1304) all_0_8_8 = n10
% 29.07/9.38 |
% 29.07/9.38 | From (1303)(1304) and (628) follows:
% 29.07/9.38 | (1305) sum(n8, n10) = all_0_1_1
% 29.07/9.38 |
% 29.07/9.38 | From (1303) and (1865) follows:
% 29.07/9.38 | (2038) sum(n8, n20) = all_0_4_4
% 29.07/9.38 |
% 29.07/9.38 | From (1304) and (1867) follows:
% 29.07/9.38 | (2039) sum(n18, n10) = all_0_7_7
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n18, n10, all_0_7_7, n7 and discharging atoms sum(n18, n10) = all_0_7_7, sum(n18, n10) = n7, yields:
% 29.07/9.38 | (957) all_0_7_7 = n7
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n8, n20, all_0_4_4, n7 and discharging atoms sum(n8, n20) = all_0_4_4, sum(n8, n20) = n7, yields:
% 29.07/9.38 | (955) all_0_4_4 = n7
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 29.07/9.38 | (1309) all_0_1_1 = n18
% 29.07/9.38 |
% 29.07/9.38 | From (957)(955) and (435) follows:
% 29.07/9.38 | (959) sum(n7, n7) = all_0_3_3
% 29.07/9.38 |
% 29.07/9.38 | From (1309) and (1869) follows:
% 29.07/9.38 | (2044) sum(n17, n18) = all_0_0_0
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n17, n18, all_0_0_0, n14 and discharging atoms sum(n17, n18) = all_0_0_0, sum(n17, n18) = n14, yields:
% 29.07/9.38 | (960) all_0_0_0 = n14
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 29.07/9.38 | (961) all_0_3_3 = n14
% 29.07/9.38 |
% 29.07/9.38 | Equations (960,961) can reduce 201 to:
% 29.07/9.38 | (746) $false
% 29.07/9.38 |
% 29.07/9.38 |-The branch is then unsatisfiable
% 29.07/9.38 |-Branch two:
% 29.07/9.38 | (1316) ~ (all_0_10_10 = n9)
% 29.07/9.38 | (1317) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.07/9.38 |
% 29.07/9.38 +-Applying beta-rule and splitting (1317), into two cases.
% 29.07/9.38 |-Branch one:
% 29.07/9.38 | (1318) all_0_10_10 = n8
% 29.07/9.38 |
% 29.07/9.38 | From (1318) and (57) follows:
% 29.07/9.38 | (1319) pred(n8) = all_0_6_6
% 29.07/9.38 |
% 29.07/9.38 | From (1318) and (381) follows:
% 29.07/9.38 | (1320) succ(n8) = all_0_8_8
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (259) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 29.07/9.38 | (1321) all_0_6_6 = n7
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (184) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 29.07/9.38 | (1322) all_0_8_8 = n9
% 29.07/9.38 |
% 29.07/9.38 | From (1321)(1322) and (628) follows:
% 29.07/9.38 | (1323) sum(n7, n9) = all_0_1_1
% 29.07/9.38 |
% 29.07/9.38 | From (1321) and (1865) follows:
% 29.07/9.38 | (2056) sum(n7, n20) = all_0_4_4
% 29.07/9.38 |
% 29.07/9.38 | From (1322) and (1867) follows:
% 29.07/9.38 | (2057) sum(n18, n9) = all_0_7_7
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n18, n9, all_0_7_7, n6 and discharging atoms sum(n18, n9) = all_0_7_7, sum(n18, n9) = n6, yields:
% 29.07/9.38 | (975) all_0_7_7 = n6
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n7, n20, all_0_4_4, n6 and discharging atoms sum(n7, n20) = all_0_4_4, sum(n7, n20) = n6, yields:
% 29.07/9.38 | (973) all_0_4_4 = n6
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 29.07/9.38 | (1327) all_0_1_1 = n16
% 29.07/9.38 |
% 29.07/9.38 | From (975)(973) and (435) follows:
% 29.07/9.38 | (977) sum(n6, n6) = all_0_3_3
% 29.07/9.38 |
% 29.07/9.38 | From (1327) and (1869) follows:
% 29.07/9.38 | (2062) sum(n17, n16) = all_0_0_0
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n17, n16, all_0_0_0, n12 and discharging atoms sum(n17, n16) = all_0_0_0, sum(n17, n16) = n12, yields:
% 29.07/9.38 | (978) all_0_0_0 = n12
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 29.07/9.38 | (979) all_0_3_3 = n12
% 29.07/9.38 |
% 29.07/9.38 | Equations (978,979) can reduce 201 to:
% 29.07/9.38 | (746) $false
% 29.07/9.38 |
% 29.07/9.38 |-The branch is then unsatisfiable
% 29.07/9.38 |-Branch two:
% 29.07/9.38 | (1334) ~ (all_0_10_10 = n8)
% 29.07/9.38 | (1335) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.07/9.38 |
% 29.07/9.38 +-Applying beta-rule and splitting (1335), into two cases.
% 29.07/9.38 |-Branch one:
% 29.07/9.38 | (1336) all_0_10_10 = n7
% 29.07/9.38 |
% 29.07/9.38 | From (1336) and (57) follows:
% 29.07/9.38 | (1337) pred(n7) = all_0_6_6
% 29.07/9.38 |
% 29.07/9.38 | From (1336) and (381) follows:
% 29.07/9.38 | (1338) succ(n7) = all_0_8_8
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (259) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 29.07/9.38 | (1339) all_0_6_6 = n6
% 29.07/9.38 |
% 29.07/9.38 | Instantiating formula (184) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 29.07/9.38 | (1340) all_0_8_8 = n8
% 29.07/9.38 |
% 29.07/9.38 | From (1339)(1340) and (628) follows:
% 29.07/9.38 | (1341) sum(n6, n8) = all_0_1_1
% 29.07/9.38 |
% 29.07/9.38 | From (1339) and (1865) follows:
% 29.07/9.39 | (2074) sum(n6, n20) = all_0_4_4
% 29.07/9.39 |
% 29.07/9.39 | From (1340) and (1867) follows:
% 29.07/9.39 | (2075) sum(n18, n8) = all_0_7_7
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n18, n8, all_0_7_7, n5 and discharging atoms sum(n18, n8) = all_0_7_7, sum(n18, n8) = n5, yields:
% 29.07/9.39 | (993) all_0_7_7 = n5
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n6, n20, all_0_4_4, n5 and discharging atoms sum(n6, n20) = all_0_4_4, sum(n6, n20) = n5, yields:
% 29.07/9.39 | (991) all_0_4_4 = n5
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 29.07/9.39 | (1345) all_0_1_1 = n14
% 29.07/9.39 |
% 29.07/9.39 | From (993)(991) and (435) follows:
% 29.07/9.39 | (995) sum(n5, n5) = all_0_3_3
% 29.07/9.39 |
% 29.07/9.39 | From (1345) and (1869) follows:
% 29.07/9.39 | (2080) sum(n17, n14) = all_0_0_0
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n17, n14, all_0_0_0, n10 and discharging atoms sum(n17, n14) = all_0_0_0, sum(n17, n14) = n10, yields:
% 29.07/9.39 | (996) all_0_0_0 = n10
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 29.07/9.39 | (997) all_0_3_3 = n10
% 29.07/9.39 |
% 29.07/9.39 | Equations (996,997) can reduce 201 to:
% 29.07/9.39 | (746) $false
% 29.07/9.39 |
% 29.07/9.39 |-The branch is then unsatisfiable
% 29.07/9.39 |-Branch two:
% 29.07/9.39 | (1352) ~ (all_0_10_10 = n7)
% 29.07/9.39 | (1353) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.07/9.39 |
% 29.07/9.39 +-Applying beta-rule and splitting (1353), into two cases.
% 29.07/9.39 |-Branch one:
% 29.07/9.39 | (1354) all_0_10_10 = n6
% 29.07/9.39 |
% 29.07/9.39 | From (1354) and (57) follows:
% 29.07/9.39 | (1355) pred(n6) = all_0_6_6
% 29.07/9.39 |
% 29.07/9.39 | From (1354) and (381) follows:
% 29.07/9.39 | (1356) succ(n6) = all_0_8_8
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (259) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 29.07/9.39 | (1357) all_0_6_6 = n5
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (184) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 29.07/9.39 | (1358) all_0_8_8 = n7
% 29.07/9.39 |
% 29.07/9.39 | From (1357)(1358) and (628) follows:
% 29.07/9.39 | (1359) sum(n5, n7) = all_0_1_1
% 29.07/9.39 |
% 29.07/9.39 | From (1357) and (1865) follows:
% 29.07/9.39 | (2092) sum(n5, n20) = all_0_4_4
% 29.07/9.39 |
% 29.07/9.39 | From (1358) and (1867) follows:
% 29.07/9.39 | (2093) sum(n18, n7) = all_0_7_7
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n18, n7, all_0_7_7, n4 and discharging atoms sum(n18, n7) = all_0_7_7, sum(n18, n7) = n4, yields:
% 29.07/9.39 | (1011) all_0_7_7 = n4
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n5, n20, all_0_4_4, n4 and discharging atoms sum(n5, n20) = all_0_4_4, sum(n5, n20) = n4, yields:
% 29.07/9.39 | (1009) all_0_4_4 = n4
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 29.07/9.39 | (1363) all_0_1_1 = n12
% 29.07/9.39 |
% 29.07/9.39 | From (1011)(1009) and (435) follows:
% 29.07/9.39 | (1013) sum(n4, n4) = all_0_3_3
% 29.07/9.39 |
% 29.07/9.39 | From (1363) and (1869) follows:
% 29.07/9.39 | (2098) sum(n17, n12) = all_0_0_0
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n17, n12, all_0_0_0, n8 and discharging atoms sum(n17, n12) = all_0_0_0, sum(n17, n12) = n8, yields:
% 29.07/9.39 | (1014) all_0_0_0 = n8
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 29.07/9.39 | (1015) all_0_3_3 = n8
% 29.07/9.39 |
% 29.07/9.39 | Equations (1014,1015) can reduce 201 to:
% 29.07/9.39 | (746) $false
% 29.07/9.39 |
% 29.07/9.39 |-The branch is then unsatisfiable
% 29.07/9.39 |-Branch two:
% 29.07/9.39 | (1370) ~ (all_0_10_10 = n6)
% 29.07/9.39 | (1371) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.07/9.39 |
% 29.07/9.39 +-Applying beta-rule and splitting (1371), into two cases.
% 29.07/9.39 |-Branch one:
% 29.07/9.39 | (1372) all_0_10_10 = n5
% 29.07/9.39 |
% 29.07/9.39 | From (1372) and (57) follows:
% 29.07/9.39 | (1373) pred(n5) = all_0_6_6
% 29.07/9.39 |
% 29.07/9.39 | From (1372) and (381) follows:
% 29.07/9.39 | (1374) succ(n5) = all_0_8_8
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (259) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 29.07/9.39 | (1375) all_0_6_6 = n4
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (184) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 29.07/9.39 | (1376) all_0_8_8 = n6
% 29.07/9.39 |
% 29.07/9.39 | From (1375)(1376) and (628) follows:
% 29.07/9.39 | (1377) sum(n4, n6) = all_0_1_1
% 29.07/9.39 |
% 29.07/9.39 | From (1375) and (1865) follows:
% 29.07/9.39 | (2110) sum(n4, n20) = all_0_4_4
% 29.07/9.39 |
% 29.07/9.39 | From (1376) and (1867) follows:
% 29.07/9.39 | (2111) sum(n18, n6) = all_0_7_7
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n18, n6, all_0_7_7, n3 and discharging atoms sum(n18, n6) = all_0_7_7, sum(n18, n6) = n3, yields:
% 29.07/9.39 | (1029) all_0_7_7 = n3
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n4, n20, all_0_4_4, n3 and discharging atoms sum(n4, n20) = all_0_4_4, sum(n4, n20) = n3, yields:
% 29.07/9.39 | (1027) all_0_4_4 = n3
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 29.07/9.39 | (1381) all_0_1_1 = n10
% 29.07/9.39 |
% 29.07/9.39 | From (1029)(1027) and (435) follows:
% 29.07/9.39 | (1031) sum(n3, n3) = all_0_3_3
% 29.07/9.39 |
% 29.07/9.39 | From (1381) and (1869) follows:
% 29.07/9.39 | (2116) sum(n17, n10) = all_0_0_0
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n17, n10, all_0_0_0, n6 and discharging atoms sum(n17, n10) = all_0_0_0, sum(n17, n10) = n6, yields:
% 29.07/9.39 | (1032) all_0_0_0 = n6
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 29.07/9.39 | (1033) all_0_3_3 = n6
% 29.07/9.39 |
% 29.07/9.39 | Equations (1032,1033) can reduce 201 to:
% 29.07/9.39 | (746) $false
% 29.07/9.39 |
% 29.07/9.39 |-The branch is then unsatisfiable
% 29.07/9.39 |-Branch two:
% 29.07/9.39 | (1388) ~ (all_0_10_10 = n5)
% 29.07/9.39 | (1389) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.07/9.39 |
% 29.07/9.39 +-Applying beta-rule and splitting (1389), into two cases.
% 29.07/9.39 |-Branch one:
% 29.07/9.39 | (1390) all_0_10_10 = n4
% 29.07/9.39 |
% 29.07/9.39 | From (1390) and (57) follows:
% 29.07/9.39 | (1391) pred(n4) = all_0_6_6
% 29.07/9.39 |
% 29.07/9.39 | From (1390) and (381) follows:
% 29.07/9.39 | (1392) succ(n4) = all_0_8_8
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (259) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 29.07/9.39 | (1393) all_0_6_6 = n3
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (184) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 29.07/9.39 | (1394) all_0_8_8 = n5
% 29.07/9.39 |
% 29.07/9.39 | From (1393)(1394) and (628) follows:
% 29.07/9.39 | (1395) sum(n3, n5) = all_0_1_1
% 29.07/9.39 |
% 29.07/9.39 | From (1393) and (1865) follows:
% 29.07/9.39 | (2128) sum(n3, n20) = all_0_4_4
% 29.07/9.39 |
% 29.07/9.39 | From (1394) and (1867) follows:
% 29.07/9.39 | (2129) sum(n18, n5) = all_0_7_7
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n18, n5, all_0_7_7, n2 and discharging atoms sum(n18, n5) = all_0_7_7, sum(n18, n5) = n2, yields:
% 29.07/9.39 | (1047) all_0_7_7 = n2
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n3, n20, all_0_4_4, n2 and discharging atoms sum(n3, n20) = all_0_4_4, sum(n3, n20) = n2, yields:
% 29.07/9.39 | (1045) all_0_4_4 = n2
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 29.07/9.39 | (1399) all_0_1_1 = n8
% 29.07/9.39 |
% 29.07/9.39 | From (1047)(1045) and (435) follows:
% 29.07/9.39 | (1049) sum(n2, n2) = all_0_3_3
% 29.07/9.39 |
% 29.07/9.39 | From (1399) and (1869) follows:
% 29.07/9.39 | (2134) sum(n17, n8) = all_0_0_0
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n17, n8, all_0_0_0, n4 and discharging atoms sum(n17, n8) = all_0_0_0, sum(n17, n8) = n4, yields:
% 29.07/9.39 | (1050) all_0_0_0 = n4
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 29.07/9.39 | (1051) all_0_3_3 = n4
% 29.07/9.39 |
% 29.07/9.39 | Equations (1050,1051) can reduce 201 to:
% 29.07/9.39 | (746) $false
% 29.07/9.39 |
% 29.07/9.39 |-The branch is then unsatisfiable
% 29.07/9.39 |-Branch two:
% 29.07/9.39 | (1406) ~ (all_0_10_10 = n4)
% 29.07/9.39 | (1407) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.07/9.39 |
% 29.07/9.39 +-Applying beta-rule and splitting (1407), into two cases.
% 29.07/9.39 |-Branch one:
% 29.07/9.39 | (1408) all_0_10_10 = n3
% 29.07/9.39 |
% 29.07/9.39 | From (1408) and (57) follows:
% 29.07/9.39 | (1409) pred(n3) = all_0_6_6
% 29.07/9.39 |
% 29.07/9.39 | From (1408) and (381) follows:
% 29.07/9.39 | (1410) succ(n3) = all_0_8_8
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 29.07/9.39 | (1411) all_0_6_6 = n2
% 29.07/9.39 |
% 29.07/9.39 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 29.07/9.39 | (1412) all_0_8_8 = n4
% 29.07/9.39 |
% 29.07/9.39 | From (1411)(1412) and (628) follows:
% 29.07/9.39 | (1413) sum(n2, n4) = all_0_1_1
% 29.07/9.39 |
% 29.07/9.39 | From (1411) and (1865) follows:
% 29.07/9.40 | (2146) sum(n2, n20) = all_0_4_4
% 29.07/9.40 |
% 29.07/9.40 | From (1412) and (1867) follows:
% 29.07/9.40 | (2147) sum(n18, n4) = all_0_7_7
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (194) with n18, n4, all_0_7_7, n1 and discharging atoms sum(n18, n4) = all_0_7_7, sum(n18, n4) = n1, yields:
% 29.07/9.40 | (1065) all_0_7_7 = n1
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (194) with n2, n20, all_0_4_4, n1 and discharging atoms sum(n2, n20) = all_0_4_4, sum(n2, n20) = n1, yields:
% 29.07/9.40 | (1063) all_0_4_4 = n1
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 29.07/9.40 | (1417) all_0_1_1 = n6
% 29.07/9.40 |
% 29.07/9.40 | From (1065)(1063) and (435) follows:
% 29.07/9.40 | (1067) sum(n1, n1) = all_0_3_3
% 29.07/9.40 |
% 29.07/9.40 | From (1417) and (1869) follows:
% 29.07/9.40 | (2152) sum(n17, n6) = all_0_0_0
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (194) with n17, n6, all_0_0_0, n2 and discharging atoms sum(n17, n6) = all_0_0_0, sum(n17, n6) = n2, yields:
% 29.07/9.40 | (1068) all_0_0_0 = n2
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 29.07/9.40 | (1069) all_0_3_3 = n2
% 29.07/9.40 |
% 29.07/9.40 | Equations (1068,1069) can reduce 201 to:
% 29.07/9.40 | (746) $false
% 29.07/9.40 |
% 29.07/9.40 |-The branch is then unsatisfiable
% 29.07/9.40 |-Branch two:
% 29.07/9.40 | (1424) ~ (all_0_10_10 = n3)
% 29.07/9.40 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.07/9.40 |
% 29.07/9.40 +-Applying beta-rule and splitting (1425), into two cases.
% 29.07/9.40 |-Branch one:
% 29.07/9.40 | (1426) all_0_10_10 = n2
% 29.07/9.40 |
% 29.07/9.40 | From (1426) and (57) follows:
% 29.07/9.40 | (1427) pred(n2) = all_0_6_6
% 29.07/9.40 |
% 29.07/9.40 | From (1426) and (381) follows:
% 29.07/9.40 | (1428) succ(n2) = all_0_8_8
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 29.07/9.40 | (1429) all_0_6_6 = n1
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 29.07/9.40 | (1430) all_0_8_8 = n3
% 29.07/9.40 |
% 29.07/9.40 | From (1429)(1430) and (628) follows:
% 29.07/9.40 | (1431) sum(n1, n3) = all_0_1_1
% 29.07/9.40 |
% 29.07/9.40 | From (1429) and (1865) follows:
% 29.07/9.40 | (2164) sum(n1, n20) = all_0_4_4
% 29.07/9.40 |
% 29.07/9.40 | From (1430) and (1867) follows:
% 29.07/9.40 | (2165) sum(n18, n3) = all_0_7_7
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (194) with n18, n3, all_0_7_7, n0 and discharging atoms sum(n18, n3) = all_0_7_7, sum(n18, n3) = n0, yields:
% 29.07/9.40 | (1083) all_0_7_7 = n0
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (194) with n1, n20, all_0_4_4, n0 and discharging atoms sum(n1, n20) = all_0_4_4, sum(n1, n20) = n0, yields:
% 29.07/9.40 | (1081) all_0_4_4 = n0
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 29.07/9.40 | (1435) all_0_1_1 = n4
% 29.07/9.40 |
% 29.07/9.40 | From (1083)(1081) and (435) follows:
% 29.07/9.40 | (1085) sum(n0, n0) = all_0_3_3
% 29.07/9.40 |
% 29.07/9.40 | From (1435) and (1869) follows:
% 29.07/9.40 | (2170) sum(n17, n4) = all_0_0_0
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (194) with n17, n4, all_0_0_0, n0 and discharging atoms sum(n17, n4) = all_0_0_0, sum(n17, n4) = n0, yields:
% 29.07/9.40 | (1087) all_0_0_0 = n0
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 29.07/9.40 | (1088) all_0_3_3 = n0
% 29.07/9.40 |
% 29.07/9.40 | Equations (1087,1088) can reduce 201 to:
% 29.07/9.40 | (746) $false
% 29.07/9.40 |
% 29.07/9.40 |-The branch is then unsatisfiable
% 29.07/9.40 |-Branch two:
% 29.07/9.40 | (1442) ~ (all_0_10_10 = n2)
% 29.07/9.40 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 29.07/9.40 |
% 29.07/9.40 +-Applying beta-rule and splitting (1443), into two cases.
% 29.07/9.40 |-Branch one:
% 29.07/9.40 | (1444) all_0_10_10 = n1
% 29.07/9.40 |
% 29.07/9.40 | From (1444) and (57) follows:
% 29.07/9.40 | (1445) pred(n1) = all_0_6_6
% 29.07/9.40 |
% 29.07/9.40 | From (1444) and (381) follows:
% 29.07/9.40 | (1446) succ(n1) = all_0_8_8
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 29.07/9.40 | (1447) all_0_6_6 = n0
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 29.07/9.40 | (1448) all_0_8_8 = n2
% 29.07/9.40 |
% 29.07/9.40 | From (1447)(1448) and (628) follows:
% 29.07/9.40 | (1449) sum(n0, n2) = all_0_1_1
% 29.07/9.40 |
% 29.07/9.40 | From (1447) and (1865) follows:
% 29.07/9.40 | (2182) sum(n0, n20) = all_0_4_4
% 29.07/9.40 |
% 29.07/9.40 | From (1448) and (1867) follows:
% 29.07/9.40 | (2183) sum(n18, n2) = all_0_7_7
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (194) with n18, n2, all_0_7_7, n20 and discharging atoms sum(n18, n2) = all_0_7_7, sum(n18, n2) = n20, yields:
% 29.07/9.40 | (1100) all_0_7_7 = n20
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (194) with n0, n20, all_0_4_4, n20 and discharging atoms sum(n0, n20) = all_0_4_4, sum(n0, n20) = n20, yields:
% 29.07/9.40 | (1101) all_0_4_4 = n20
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 29.07/9.40 | (1453) all_0_1_1 = n2
% 29.07/9.40 |
% 29.07/9.40 | From (1100)(1101) and (435) follows:
% 29.07/9.40 | (1103) sum(n20, n20) = all_0_3_3
% 29.07/9.40 |
% 29.07/9.40 | From (1453) and (1869) follows:
% 29.07/9.40 | (2188) sum(n17, n2) = all_0_0_0
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 29.07/9.40 | (1104) all_0_3_3 = n19
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (194) with n17, n2, all_0_0_0, n19 and discharging atoms sum(n17, n2) = all_0_0_0, sum(n17, n2) = n19, yields:
% 29.07/9.40 | (1105) all_0_0_0 = n19
% 29.07/9.40 |
% 29.07/9.40 | Equations (1105,1104) can reduce 201 to:
% 29.07/9.40 | (746) $false
% 29.07/9.40 |
% 29.07/9.40 |-The branch is then unsatisfiable
% 29.07/9.40 |-Branch two:
% 29.07/9.40 | (1462) ~ (all_0_10_10 = n1)
% 29.07/9.40 | (1463) all_0_10_10 = n0
% 29.07/9.40 |
% 29.07/9.40 | From (1463) and (57) follows:
% 29.07/9.40 | (1464) pred(n0) = all_0_6_6
% 29.07/9.40 |
% 29.07/9.40 | From (1463) and (381) follows:
% 29.07/9.40 | (1465) succ(n0) = all_0_8_8
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 29.07/9.40 | (1466) all_0_6_6 = n20
% 29.07/9.40 |
% 29.07/9.40 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 29.07/9.40 | (1467) all_0_8_8 = n1
% 29.07/9.40 |
% 29.07/9.40 | From (1466)(1467) and (628) follows:
% 29.07/9.40 | (1468) sum(n20, n1) = all_0_1_1
% 29.26/9.40 |
% 29.26/9.40 | From (1466) and (1865) follows:
% 29.26/9.40 | (2199) sum(n20, n20) = all_0_4_4
% 29.26/9.40 |
% 29.26/9.40 | From (1467) and (1867) follows:
% 29.26/9.40 | (2200) sum(n18, n1) = all_0_7_7
% 29.26/9.40 |
% 29.26/9.40 | Instantiating formula (194) with n20, n20, all_0_4_4, n19 and discharging atoms sum(n20, n20) = all_0_4_4, sum(n20, n20) = n19, yields:
% 29.26/9.40 | (736) all_0_4_4 = n19
% 29.26/9.40 |
% 29.26/9.40 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 29.26/9.40 | (1471) all_0_1_1 = n0
% 29.26/9.40 |
% 29.26/9.40 | Instantiating formula (194) with n18, n1, all_0_7_7, n19 and discharging atoms sum(n18, n1) = all_0_7_7, sum(n18, n1) = n19, yields:
% 29.26/9.40 | (737) all_0_7_7 = n19
% 29.26/9.40 |
% 29.26/9.40 | From (737)(736) and (435) follows:
% 29.26/9.40 | (741) sum(n19, n19) = all_0_3_3
% 29.26/9.40 |
% 29.26/9.40 | From (1471) and (1869) follows:
% 29.26/9.40 | (2205) sum(n17, n0) = all_0_0_0
% 29.26/9.40 |
% 29.26/9.40 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 29.26/9.40 | (744) all_0_3_3 = n17
% 29.26/9.40 |
% 29.26/9.40 | Instantiating formula (194) with n17, n0, all_0_0_0, n17 and discharging atoms sum(n17, n0) = all_0_0_0, sum(n17, n0) = n17, yields:
% 29.26/9.40 | (742) all_0_0_0 = n17
% 29.26/9.40 |
% 29.26/9.40 | Equations (742,744) can reduce 201 to:
% 29.26/9.40 | (746) $false
% 29.26/9.40 |
% 29.26/9.40 |-The branch is then unsatisfiable
% 29.26/9.41 |-Branch two:
% 29.26/9.41 | (765) ~ (all_0_11_11 = n19)
% 29.26/9.41 | (766) all_0_11_11 = n18 | all_0_11_11 = n17 | all_0_11_11 = n16 | all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.26/9.41 |
% 29.26/9.41 +-Applying beta-rule and splitting (1137), into two cases.
% 29.26/9.41 |-Branch one:
% 29.26/9.41 | (1138) all_0_10_10 = n18
% 29.26/9.41 |
% 29.26/9.41 | From (1138) and (57) follows:
% 29.26/9.41 | (1139) pred(n18) = all_0_6_6
% 29.26/9.41 |
% 29.26/9.41 | From (1138) and (381) follows:
% 29.26/9.41 | (1140) succ(n18) = all_0_8_8
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (259) with n18, all_0_6_6, n17 and discharging atoms pred(n18) = all_0_6_6, pred(n18) = n17, yields:
% 29.26/9.41 | (1141) all_0_6_6 = n17
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (184) with n18, all_0_8_8, n19 and discharging atoms succ(n18) = all_0_8_8, succ(n18) = n19, yields:
% 29.26/9.41 | (1142) all_0_8_8 = n19
% 29.26/9.41 |
% 29.26/9.41 | From (1141) and (1139) follows:
% 29.26/9.41 | (583) pred(n18) = n17
% 29.26/9.41 |
% 29.26/9.41 | From (1142) and (1140) follows:
% 29.26/9.41 | (351) succ(n18) = n19
% 29.26/9.41 |
% 29.26/9.41 | From (1141) and (386) follows:
% 29.26/9.41 | (2218) sum(n17, all_0_5_5) = all_0_4_4
% 29.26/9.41 |
% 29.26/9.41 | From (1141)(1142) and (628) follows:
% 29.26/9.41 | (1143) sum(n17, n19) = all_0_1_1
% 29.26/9.41 |
% 29.26/9.41 | From (1142) and (74) follows:
% 29.26/9.41 | (2220) sum(all_0_9_9, n19) = all_0_7_7
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (194) with n17, n19, all_0_1_1, n15 and discharging atoms sum(n17, n19) = all_0_1_1, sum(n17, n19) = n15, yields:
% 29.26/9.41 | (1147) all_0_1_1 = n15
% 29.26/9.41 |
% 29.26/9.41 | From (1147) and (85) follows:
% 29.26/9.41 | (2222) sum(all_0_2_2, n15) = all_0_0_0
% 29.26/9.41 |
% 29.26/9.41 | From (1147) and (1143) follows:
% 29.26/9.41 | (648) sum(n17, n19) = n15
% 29.26/9.41 |
% 29.26/9.41 +-Applying beta-rule and splitting (766), into two cases.
% 29.26/9.41 |-Branch one:
% 29.26/9.41 | (767) all_0_11_11 = n18
% 29.26/9.41 |
% 29.26/9.41 | From (767) and (190) follows:
% 29.26/9.41 | (768) pred(n18) = all_0_9_9
% 29.26/9.41 |
% 29.26/9.41 | From (767) and (505) follows:
% 29.26/9.41 | (769) succ(n18) = all_0_5_5
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (259) with n18, all_0_9_9, n17 and discharging atoms pred(n18) = all_0_9_9, pred(n18) = n17, yields:
% 29.26/9.41 | (770) all_0_9_9 = n17
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (184) with n18, all_0_5_5, n19 and discharging atoms succ(n18) = all_0_5_5, succ(n18) = n19, yields:
% 29.26/9.41 | (771) all_0_5_5 = n19
% 29.26/9.41 |
% 29.26/9.41 | From (770)(771) and (156) follows:
% 29.26/9.41 | (772) sum(n17, n19) = all_0_2_2
% 29.26/9.41 |
% 29.26/9.41 | From (770) and (2220) follows:
% 29.26/9.41 | (2230) sum(n17, n19) = all_0_7_7
% 29.26/9.41 |
% 29.26/9.41 | From (771) and (2218) follows:
% 29.26/9.41 | (2231) sum(n17, n19) = all_0_4_4
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (194) with n17, n19, all_0_2_2, n15 and discharging atoms sum(n17, n19) = all_0_2_2, sum(n17, n19) = n15, yields:
% 29.26/9.41 | (776) all_0_2_2 = n15
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (194) with n17, n19, all_0_4_4, all_0_2_2 and discharging atoms sum(n17, n19) = all_0_2_2, sum(n17, n19) = all_0_4_4, yields:
% 29.26/9.41 | (733) all_0_2_2 = all_0_4_4
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (194) with n17, n19, all_0_7_7, all_0_2_2 and discharging atoms sum(n17, n19) = all_0_2_2, sum(n17, n19) = all_0_7_7, yields:
% 29.26/9.41 | (734) all_0_2_2 = all_0_7_7
% 29.26/9.41 |
% 29.26/9.41 | Combining equations (734,733) yields a new equation:
% 29.26/9.41 | (735) all_0_4_4 = all_0_7_7
% 29.26/9.41 |
% 29.26/9.41 | Combining equations (776,733) yields a new equation:
% 29.26/9.41 | (811) all_0_4_4 = n15
% 29.26/9.41 |
% 29.26/9.41 | Combining equations (811,735) yields a new equation:
% 29.26/9.41 | (813) all_0_7_7 = n15
% 29.26/9.41 |
% 29.26/9.41 | Combining equations (813,735) yields a new equation:
% 29.26/9.41 | (811) all_0_4_4 = n15
% 29.26/9.41 |
% 29.26/9.41 | Combining equations (811,733) yields a new equation:
% 29.26/9.41 | (776) all_0_2_2 = n15
% 29.26/9.41 |
% 29.26/9.41 | From (776) and (2222) follows:
% 29.26/9.41 | (2240) sum(n15, n15) = all_0_0_0
% 29.26/9.41 |
% 29.26/9.41 | From (813)(811) and (435) follows:
% 29.26/9.41 | (815) sum(n15, n15) = all_0_3_3
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (194) with n15, n15, all_0_0_0, n9 and discharging atoms sum(n15, n15) = all_0_0_0, sum(n15, n15) = n9, yields:
% 29.26/9.41 | (817) all_0_0_0 = n9
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (194) with n15, n15, all_0_3_3, all_0_0_0 and discharging atoms sum(n15, n15) = all_0_0_0, sum(n15, n15) = all_0_3_3, yields:
% 29.26/9.41 | (743) all_0_0_0 = all_0_3_3
% 29.26/9.41 |
% 29.26/9.41 | Combining equations (817,743) yields a new equation:
% 29.26/9.41 | (816) all_0_3_3 = n9
% 29.26/9.41 |
% 29.26/9.41 | Combining equations (816,743) yields a new equation:
% 29.26/9.41 | (817) all_0_0_0 = n9
% 29.26/9.41 |
% 29.26/9.41 | Equations (817,816) can reduce 201 to:
% 29.26/9.41 | (746) $false
% 29.26/9.41 |
% 29.26/9.41 |-The branch is then unsatisfiable
% 29.26/9.41 |-Branch two:
% 29.26/9.41 | (783) ~ (all_0_11_11 = n18)
% 29.26/9.41 | (784) all_0_11_11 = n17 | all_0_11_11 = n16 | all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.26/9.41 |
% 29.26/9.41 +-Applying beta-rule and splitting (784), into two cases.
% 29.26/9.41 |-Branch one:
% 29.26/9.41 | (785) all_0_11_11 = n17
% 29.26/9.41 |
% 29.26/9.41 | From (785) and (190) follows:
% 29.26/9.41 | (786) pred(n17) = all_0_9_9
% 29.26/9.41 |
% 29.26/9.41 | From (785) and (505) follows:
% 29.26/9.41 | (787) succ(n17) = all_0_5_5
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (259) with n17, all_0_9_9, n16 and discharging atoms pred(n17) = all_0_9_9, pred(n17) = n16, yields:
% 29.26/9.41 | (788) all_0_9_9 = n16
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (184) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 29.26/9.41 | (789) all_0_5_5 = n18
% 29.26/9.41 |
% 29.26/9.41 | From (788)(789) and (156) follows:
% 29.26/9.41 | (790) sum(n16, n18) = all_0_2_2
% 29.26/9.41 |
% 29.26/9.41 | From (788) and (2220) follows:
% 29.26/9.41 | (2255) sum(n16, n19) = all_0_7_7
% 29.26/9.41 |
% 29.26/9.41 | From (789) and (2218) follows:
% 29.26/9.41 | (2256) sum(n17, n18) = all_0_4_4
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (194) with n17, n18, all_0_4_4, n14 and discharging atoms sum(n17, n18) = all_0_4_4, sum(n17, n18) = n14, yields:
% 29.26/9.41 | (829) all_0_4_4 = n14
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (194) with n16, n19, all_0_7_7, n14 and discharging atoms sum(n16, n19) = all_0_7_7, sum(n16, n19) = n14, yields:
% 29.26/9.41 | (831) all_0_7_7 = n14
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (194) with n16, n18, all_0_2_2, n13 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = n13, yields:
% 29.26/9.41 | (794) all_0_2_2 = n13
% 29.26/9.41 |
% 29.26/9.41 | From (794) and (2222) follows:
% 29.26/9.41 | (2260) sum(n13, n15) = all_0_0_0
% 29.26/9.41 |
% 29.26/9.41 | From (831)(829) and (435) follows:
% 29.26/9.41 | (833) sum(n14, n14) = all_0_3_3
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 29.26/9.41 | (834) all_0_3_3 = n7
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (194) with n13, n15, all_0_0_0, n7 and discharging atoms sum(n13, n15) = all_0_0_0, sum(n13, n15) = n7, yields:
% 29.26/9.41 | (835) all_0_0_0 = n7
% 29.26/9.41 |
% 29.26/9.41 | Equations (835,834) can reduce 201 to:
% 29.26/9.41 | (746) $false
% 29.26/9.41 |
% 29.26/9.41 |-The branch is then unsatisfiable
% 29.26/9.41 |-Branch two:
% 29.26/9.41 | (801) ~ (all_0_11_11 = n17)
% 29.26/9.41 | (802) all_0_11_11 = n16 | all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.26/9.41 |
% 29.26/9.41 +-Applying beta-rule and splitting (802), into two cases.
% 29.26/9.41 |-Branch one:
% 29.26/9.41 | (803) all_0_11_11 = n16
% 29.26/9.41 |
% 29.26/9.41 | From (803) and (190) follows:
% 29.26/9.41 | (804) pred(n16) = all_0_9_9
% 29.26/9.41 |
% 29.26/9.41 | From (803) and (505) follows:
% 29.26/9.41 | (805) succ(n16) = all_0_5_5
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (259) with n16, all_0_9_9, n15 and discharging atoms pred(n16) = all_0_9_9, pred(n16) = n15, yields:
% 29.26/9.41 | (806) all_0_9_9 = n15
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (184) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 29.26/9.41 | (807) all_0_5_5 = n17
% 29.26/9.41 |
% 29.26/9.41 | From (806)(807) and (156) follows:
% 29.26/9.41 | (808) sum(n15, n17) = all_0_2_2
% 29.26/9.41 |
% 29.26/9.41 | From (806) and (2220) follows:
% 29.26/9.41 | (2273) sum(n15, n19) = all_0_7_7
% 29.26/9.41 |
% 29.26/9.41 | From (807) and (2218) follows:
% 29.26/9.41 | (2274) sum(n17, n17) = all_0_4_4
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (194) with n17, n17, all_0_4_4, n13 and discharging atoms sum(n17, n17) = all_0_4_4, sum(n17, n17) = n13, yields:
% 29.26/9.41 | (847) all_0_4_4 = n13
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (194) with n15, n19, all_0_7_7, n13 and discharging atoms sum(n15, n19) = all_0_7_7, sum(n15, n19) = n13, yields:
% 29.26/9.41 | (849) all_0_7_7 = n13
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (194) with n15, n17, all_0_2_2, n11 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n11, yields:
% 29.26/9.41 | (812) all_0_2_2 = n11
% 29.26/9.41 |
% 29.26/9.41 | From (812) and (2222) follows:
% 29.26/9.41 | (2278) sum(n11, n15) = all_0_0_0
% 29.26/9.41 |
% 29.26/9.41 | From (849)(847) and (435) follows:
% 29.26/9.41 | (851) sum(n13, n13) = all_0_3_3
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 29.26/9.41 | (852) all_0_3_3 = n5
% 29.26/9.41 |
% 29.26/9.41 | Instantiating formula (194) with n11, n15, all_0_0_0, n5 and discharging atoms sum(n11, n15) = all_0_0_0, sum(n11, n15) = n5, yields:
% 29.26/9.41 | (853) all_0_0_0 = n5
% 29.26/9.41 |
% 29.26/9.41 | Equations (853,852) can reduce 201 to:
% 29.26/9.41 | (746) $false
% 29.26/9.41 |
% 29.26/9.41 |-The branch is then unsatisfiable
% 29.26/9.41 |-Branch two:
% 29.26/9.41 | (819) ~ (all_0_11_11 = n16)
% 29.26/9.41 | (820) all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.26/9.41 |
% 29.26/9.41 +-Applying beta-rule and splitting (820), into two cases.
% 29.26/9.41 |-Branch one:
% 29.26/9.41 | (821) all_0_11_11 = n15
% 29.26/9.41 |
% 29.26/9.41 | From (821) and (190) follows:
% 29.26/9.41 | (822) pred(n15) = all_0_9_9
% 29.26/9.41 |
% 29.26/9.41 | From (821) and (505) follows:
% 29.26/9.41 | (823) succ(n15) = all_0_5_5
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (259) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 29.26/9.42 | (824) all_0_9_9 = n14
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (184) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 29.26/9.42 | (825) all_0_5_5 = n16
% 29.26/9.42 |
% 29.26/9.42 | From (824)(825) and (156) follows:
% 29.26/9.42 | (826) sum(n14, n16) = all_0_2_2
% 29.26/9.42 |
% 29.26/9.42 | From (824) and (2220) follows:
% 29.26/9.42 | (2291) sum(n14, n19) = all_0_7_7
% 29.26/9.42 |
% 29.26/9.42 | From (825) and (2218) follows:
% 29.26/9.42 | (2292) sum(n17, n16) = all_0_4_4
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n17, n16, all_0_4_4, n12 and discharging atoms sum(n17, n16) = all_0_4_4, sum(n17, n16) = n12, yields:
% 29.26/9.42 | (865) all_0_4_4 = n12
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n14, n19, all_0_7_7, n12 and discharging atoms sum(n14, n19) = all_0_7_7, sum(n14, n19) = n12, yields:
% 29.26/9.42 | (867) all_0_7_7 = n12
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n14, n16, all_0_2_2, n9 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n9, yields:
% 29.26/9.42 | (830) all_0_2_2 = n9
% 29.26/9.42 |
% 29.26/9.42 | From (830) and (2222) follows:
% 29.26/9.42 | (2296) sum(n9, n15) = all_0_0_0
% 29.26/9.42 |
% 29.26/9.42 | From (867)(865) and (435) follows:
% 29.26/9.42 | (869) sum(n12, n12) = all_0_3_3
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 29.26/9.42 | (870) all_0_3_3 = n3
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n9, n15, all_0_0_0, n3 and discharging atoms sum(n9, n15) = all_0_0_0, sum(n9, n15) = n3, yields:
% 29.26/9.42 | (871) all_0_0_0 = n3
% 29.26/9.42 |
% 29.26/9.42 | Equations (871,870) can reduce 201 to:
% 29.26/9.42 | (746) $false
% 29.26/9.42 |
% 29.26/9.42 |-The branch is then unsatisfiable
% 29.26/9.42 |-Branch two:
% 29.26/9.42 | (837) ~ (all_0_11_11 = n15)
% 29.26/9.42 | (838) all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.26/9.42 |
% 29.26/9.42 +-Applying beta-rule and splitting (838), into two cases.
% 29.26/9.42 |-Branch one:
% 29.26/9.42 | (839) all_0_11_11 = n14
% 29.26/9.42 |
% 29.26/9.42 | From (839) and (190) follows:
% 29.26/9.42 | (840) pred(n14) = all_0_9_9
% 29.26/9.42 |
% 29.26/9.42 | From (839) and (505) follows:
% 29.26/9.42 | (841) succ(n14) = all_0_5_5
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (259) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 29.26/9.42 | (842) all_0_9_9 = n13
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (184) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 29.26/9.42 | (843) all_0_5_5 = n15
% 29.26/9.42 |
% 29.26/9.42 | From (842)(843) and (156) follows:
% 29.26/9.42 | (844) sum(n13, n15) = all_0_2_2
% 29.26/9.42 |
% 29.26/9.42 | From (842) and (2220) follows:
% 29.26/9.42 | (2309) sum(n13, n19) = all_0_7_7
% 29.26/9.42 |
% 29.26/9.42 | From (843) and (2218) follows:
% 29.26/9.42 | (2310) sum(n17, n15) = all_0_4_4
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n17, n15, all_0_4_4, n11 and discharging atoms sum(n17, n15) = all_0_4_4, sum(n17, n15) = n11, yields:
% 29.26/9.42 | (883) all_0_4_4 = n11
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n13, n19, all_0_7_7, n11 and discharging atoms sum(n13, n19) = all_0_7_7, sum(n13, n19) = n11, yields:
% 29.26/9.42 | (885) all_0_7_7 = n11
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n13, n15, all_0_2_2, n7 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n7, yields:
% 29.26/9.42 | (848) all_0_2_2 = n7
% 29.26/9.42 |
% 29.26/9.42 | From (848) and (2222) follows:
% 29.26/9.42 | (2314) sum(n7, n15) = all_0_0_0
% 29.26/9.42 |
% 29.26/9.42 | From (885)(883) and (435) follows:
% 29.26/9.42 | (887) sum(n11, n11) = all_0_3_3
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 29.26/9.42 | (888) all_0_3_3 = n1
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n7, n15, all_0_0_0, n1 and discharging atoms sum(n7, n15) = all_0_0_0, sum(n7, n15) = n1, yields:
% 29.26/9.42 | (889) all_0_0_0 = n1
% 29.26/9.42 |
% 29.26/9.42 | Equations (889,888) can reduce 201 to:
% 29.26/9.42 | (746) $false
% 29.26/9.42 |
% 29.26/9.42 |-The branch is then unsatisfiable
% 29.26/9.42 |-Branch two:
% 29.26/9.42 | (855) ~ (all_0_11_11 = n14)
% 29.26/9.42 | (856) all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.26/9.42 |
% 29.26/9.42 +-Applying beta-rule and splitting (856), into two cases.
% 29.26/9.42 |-Branch one:
% 29.26/9.42 | (857) all_0_11_11 = n13
% 29.26/9.42 |
% 29.26/9.42 | From (857) and (190) follows:
% 29.26/9.42 | (858) pred(n13) = all_0_9_9
% 29.26/9.42 |
% 29.26/9.42 | From (857) and (505) follows:
% 29.26/9.42 | (859) succ(n13) = all_0_5_5
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (259) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 29.26/9.42 | (860) all_0_9_9 = n12
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (184) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 29.26/9.42 | (861) all_0_5_5 = n14
% 29.26/9.42 |
% 29.26/9.42 | From (860)(861) and (156) follows:
% 29.26/9.42 | (862) sum(n12, n14) = all_0_2_2
% 29.26/9.42 |
% 29.26/9.42 | From (860) and (2220) follows:
% 29.26/9.42 | (2327) sum(n12, n19) = all_0_7_7
% 29.26/9.42 |
% 29.26/9.42 | From (861) and (2218) follows:
% 29.26/9.42 | (2328) sum(n17, n14) = all_0_4_4
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n17, n14, all_0_4_4, n10 and discharging atoms sum(n17, n14) = all_0_4_4, sum(n17, n14) = n10, yields:
% 29.26/9.42 | (901) all_0_4_4 = n10
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n12, n19, all_0_7_7, n10 and discharging atoms sum(n12, n19) = all_0_7_7, sum(n12, n19) = n10, yields:
% 29.26/9.42 | (903) all_0_7_7 = n10
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n12, n14, all_0_2_2, n5 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n5, yields:
% 29.26/9.42 | (866) all_0_2_2 = n5
% 29.26/9.42 |
% 29.26/9.42 | From (866) and (2222) follows:
% 29.26/9.42 | (2332) sum(n5, n15) = all_0_0_0
% 29.26/9.42 |
% 29.26/9.42 | From (903)(901) and (435) follows:
% 29.26/9.42 | (905) sum(n10, n10) = all_0_3_3
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 29.26/9.42 | (906) all_0_3_3 = n20
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n5, n15, all_0_0_0, n20 and discharging atoms sum(n5, n15) = all_0_0_0, sum(n5, n15) = n20, yields:
% 29.26/9.42 | (907) all_0_0_0 = n20
% 29.26/9.42 |
% 29.26/9.42 | Equations (907,906) can reduce 201 to:
% 29.26/9.42 | (746) $false
% 29.26/9.42 |
% 29.26/9.42 |-The branch is then unsatisfiable
% 29.26/9.42 |-Branch two:
% 29.26/9.42 | (873) ~ (all_0_11_11 = n13)
% 29.26/9.42 | (874) all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.26/9.42 |
% 29.26/9.42 +-Applying beta-rule and splitting (874), into two cases.
% 29.26/9.42 |-Branch one:
% 29.26/9.42 | (875) all_0_11_11 = n12
% 29.26/9.42 |
% 29.26/9.42 | From (875) and (190) follows:
% 29.26/9.42 | (876) pred(n12) = all_0_9_9
% 29.26/9.42 |
% 29.26/9.42 | From (875) and (505) follows:
% 29.26/9.42 | (877) succ(n12) = all_0_5_5
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (259) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 29.26/9.42 | (878) all_0_9_9 = n11
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (184) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 29.26/9.42 | (879) all_0_5_5 = n13
% 29.26/9.42 |
% 29.26/9.42 | From (878)(879) and (156) follows:
% 29.26/9.42 | (880) sum(n11, n13) = all_0_2_2
% 29.26/9.42 |
% 29.26/9.42 | From (878) and (2220) follows:
% 29.26/9.42 | (2345) sum(n11, n19) = all_0_7_7
% 29.26/9.42 |
% 29.26/9.42 | From (879) and (2218) follows:
% 29.26/9.42 | (2346) sum(n17, n13) = all_0_4_4
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n17, n13, all_0_4_4, n9 and discharging atoms sum(n17, n13) = all_0_4_4, sum(n17, n13) = n9, yields:
% 29.26/9.42 | (919) all_0_4_4 = n9
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n11, n19, all_0_7_7, n9 and discharging atoms sum(n11, n19) = all_0_7_7, sum(n11, n19) = n9, yields:
% 29.26/9.42 | (921) all_0_7_7 = n9
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n11, n13, all_0_2_2, n3 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n3, yields:
% 29.26/9.42 | (884) all_0_2_2 = n3
% 29.26/9.42 |
% 29.26/9.42 | From (884) and (2222) follows:
% 29.26/9.42 | (2350) sum(n3, n15) = all_0_0_0
% 29.26/9.42 |
% 29.26/9.42 | From (921)(919) and (435) follows:
% 29.26/9.42 | (923) sum(n9, n9) = all_0_3_3
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 29.26/9.42 | (925) all_0_3_3 = n18
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (194) with n3, n15, all_0_0_0, n18 and discharging atoms sum(n3, n15) = all_0_0_0, sum(n3, n15) = n18, yields:
% 29.26/9.42 | (924) all_0_0_0 = n18
% 29.26/9.42 |
% 29.26/9.42 | Equations (924,925) can reduce 201 to:
% 29.26/9.42 | (746) $false
% 29.26/9.42 |
% 29.26/9.42 |-The branch is then unsatisfiable
% 29.26/9.42 |-Branch two:
% 29.26/9.42 | (891) ~ (all_0_11_11 = n12)
% 29.26/9.42 | (892) all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.26/9.42 |
% 29.26/9.42 +-Applying beta-rule and splitting (892), into two cases.
% 29.26/9.42 |-Branch one:
% 29.26/9.42 | (893) all_0_11_11 = n11
% 29.26/9.42 |
% 29.26/9.42 | From (893) and (190) follows:
% 29.26/9.42 | (894) pred(n11) = all_0_9_9
% 29.26/9.42 |
% 29.26/9.42 | From (893) and (505) follows:
% 29.26/9.42 | (895) succ(n11) = all_0_5_5
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (259) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 29.26/9.42 | (896) all_0_9_9 = n10
% 29.26/9.42 |
% 29.26/9.42 | Instantiating formula (184) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 29.26/9.42 | (897) all_0_5_5 = n12
% 29.26/9.42 |
% 29.26/9.42 | From (896)(897) and (156) follows:
% 29.26/9.42 | (898) sum(n10, n12) = all_0_2_2
% 29.26/9.43 |
% 29.26/9.43 | From (896) and (2220) follows:
% 29.26/9.43 | (2363) sum(n10, n19) = all_0_7_7
% 29.26/9.43 |
% 29.26/9.43 | From (897) and (2218) follows:
% 29.26/9.43 | (2364) sum(n17, n12) = all_0_4_4
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n17, n12, all_0_4_4, n8 and discharging atoms sum(n17, n12) = all_0_4_4, sum(n17, n12) = n8, yields:
% 29.26/9.43 | (937) all_0_4_4 = n8
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n10, n19, all_0_7_7, n8 and discharging atoms sum(n10, n19) = all_0_7_7, sum(n10, n19) = n8, yields:
% 29.26/9.43 | (939) all_0_7_7 = n8
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n10, n12, all_0_2_2, n1 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n1, yields:
% 29.26/9.43 | (902) all_0_2_2 = n1
% 29.26/9.43 |
% 29.26/9.43 | From (902) and (2222) follows:
% 29.26/9.43 | (2368) sum(n1, n15) = all_0_0_0
% 29.26/9.43 |
% 29.26/9.43 | From (939)(937) and (435) follows:
% 29.26/9.43 | (941) sum(n8, n8) = all_0_3_3
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 29.26/9.43 | (943) all_0_3_3 = n16
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n1, n15, all_0_0_0, n16 and discharging atoms sum(n1, n15) = all_0_0_0, sum(n1, n15) = n16, yields:
% 29.26/9.43 | (942) all_0_0_0 = n16
% 29.26/9.43 |
% 29.26/9.43 | Equations (942,943) can reduce 201 to:
% 29.26/9.43 | (746) $false
% 29.26/9.43 |
% 29.26/9.43 |-The branch is then unsatisfiable
% 29.26/9.43 |-Branch two:
% 29.26/9.43 | (909) ~ (all_0_11_11 = n11)
% 29.26/9.43 | (910) all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.26/9.43 |
% 29.26/9.43 +-Applying beta-rule and splitting (910), into two cases.
% 29.26/9.43 |-Branch one:
% 29.26/9.43 | (911) all_0_11_11 = n10
% 29.26/9.43 |
% 29.26/9.43 | From (911) and (190) follows:
% 29.26/9.43 | (912) pred(n10) = all_0_9_9
% 29.26/9.43 |
% 29.26/9.43 | From (911) and (505) follows:
% 29.26/9.43 | (913) succ(n10) = all_0_5_5
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (259) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 29.26/9.43 | (914) all_0_9_9 = n9
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (184) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 29.26/9.43 | (915) all_0_5_5 = n11
% 29.26/9.43 |
% 29.26/9.43 | From (914)(915) and (156) follows:
% 29.26/9.43 | (916) sum(n9, n11) = all_0_2_2
% 29.26/9.43 |
% 29.26/9.43 | From (914) and (2220) follows:
% 29.26/9.43 | (2381) sum(n9, n19) = all_0_7_7
% 29.26/9.43 |
% 29.26/9.43 | From (915) and (2218) follows:
% 29.26/9.43 | (2382) sum(n17, n11) = all_0_4_4
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n17, n11, all_0_4_4, n7 and discharging atoms sum(n17, n11) = all_0_4_4, sum(n17, n11) = n7, yields:
% 29.26/9.43 | (955) all_0_4_4 = n7
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n9, n19, all_0_7_7, n7 and discharging atoms sum(n9, n19) = all_0_7_7, sum(n9, n19) = n7, yields:
% 29.26/9.43 | (957) all_0_7_7 = n7
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 29.26/9.43 | (920) all_0_2_2 = n20
% 29.26/9.43 |
% 29.26/9.43 | From (920) and (2222) follows:
% 29.26/9.43 | (2386) sum(n20, n15) = all_0_0_0
% 29.26/9.43 |
% 29.26/9.43 | From (957)(955) and (435) follows:
% 29.26/9.43 | (959) sum(n7, n7) = all_0_3_3
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n20, n15, all_0_0_0, n14 and discharging atoms sum(n20, n15) = all_0_0_0, sum(n20, n15) = n14, yields:
% 29.26/9.43 | (960) all_0_0_0 = n14
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 29.26/9.43 | (961) all_0_3_3 = n14
% 29.26/9.43 |
% 29.26/9.43 | Equations (960,961) can reduce 201 to:
% 29.26/9.43 | (746) $false
% 29.26/9.43 |
% 29.26/9.43 |-The branch is then unsatisfiable
% 29.26/9.43 |-Branch two:
% 29.26/9.43 | (927) ~ (all_0_11_11 = n10)
% 29.26/9.43 | (928) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.26/9.43 |
% 29.26/9.43 +-Applying beta-rule and splitting (928), into two cases.
% 29.26/9.43 |-Branch one:
% 29.26/9.43 | (929) all_0_11_11 = n9
% 29.26/9.43 |
% 29.26/9.43 | From (929) and (190) follows:
% 29.26/9.43 | (930) pred(n9) = all_0_9_9
% 29.26/9.43 |
% 29.26/9.43 | From (929) and (505) follows:
% 29.26/9.43 | (931) succ(n9) = all_0_5_5
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (259) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 29.26/9.43 | (932) all_0_9_9 = n8
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (184) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 29.26/9.43 | (933) all_0_5_5 = n10
% 29.26/9.43 |
% 29.26/9.43 | From (932)(933) and (156) follows:
% 29.26/9.43 | (934) sum(n8, n10) = all_0_2_2
% 29.26/9.43 |
% 29.26/9.43 | From (932) and (2220) follows:
% 29.26/9.43 | (2399) sum(n8, n19) = all_0_7_7
% 29.26/9.43 |
% 29.26/9.43 | From (933) and (2218) follows:
% 29.26/9.43 | (2400) sum(n17, n10) = all_0_4_4
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n17, n10, all_0_4_4, n6 and discharging atoms sum(n17, n10) = all_0_4_4, sum(n17, n10) = n6, yields:
% 29.26/9.43 | (973) all_0_4_4 = n6
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n8, n19, all_0_7_7, n6 and discharging atoms sum(n8, n19) = all_0_7_7, sum(n8, n19) = n6, yields:
% 29.26/9.43 | (975) all_0_7_7 = n6
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 29.26/9.43 | (938) all_0_2_2 = n18
% 29.26/9.43 |
% 29.26/9.43 | From (938) and (2222) follows:
% 29.26/9.43 | (2404) sum(n18, n15) = all_0_0_0
% 29.26/9.43 |
% 29.26/9.43 | From (975)(973) and (435) follows:
% 29.26/9.43 | (977) sum(n6, n6) = all_0_3_3
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n18, n15, all_0_0_0, n12 and discharging atoms sum(n18, n15) = all_0_0_0, sum(n18, n15) = n12, yields:
% 29.26/9.43 | (978) all_0_0_0 = n12
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 29.26/9.43 | (979) all_0_3_3 = n12
% 29.26/9.43 |
% 29.26/9.43 | Equations (978,979) can reduce 201 to:
% 29.26/9.43 | (746) $false
% 29.26/9.43 |
% 29.26/9.43 |-The branch is then unsatisfiable
% 29.26/9.43 |-Branch two:
% 29.26/9.43 | (945) ~ (all_0_11_11 = n9)
% 29.26/9.43 | (946) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.26/9.43 |
% 29.26/9.43 +-Applying beta-rule and splitting (946), into two cases.
% 29.26/9.43 |-Branch one:
% 29.26/9.43 | (947) all_0_11_11 = n8
% 29.26/9.43 |
% 29.26/9.43 | From (947) and (190) follows:
% 29.26/9.43 | (948) pred(n8) = all_0_9_9
% 29.26/9.43 |
% 29.26/9.43 | From (947) and (505) follows:
% 29.26/9.43 | (949) succ(n8) = all_0_5_5
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (259) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 29.26/9.43 | (950) all_0_9_9 = n7
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (184) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 29.26/9.43 | (951) all_0_5_5 = n9
% 29.26/9.43 |
% 29.26/9.43 | From (950)(951) and (156) follows:
% 29.26/9.43 | (952) sum(n7, n9) = all_0_2_2
% 29.26/9.43 |
% 29.26/9.43 | From (950) and (2220) follows:
% 29.26/9.43 | (2417) sum(n7, n19) = all_0_7_7
% 29.26/9.43 |
% 29.26/9.43 | From (951) and (2218) follows:
% 29.26/9.43 | (2418) sum(n17, n9) = all_0_4_4
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n17, n9, all_0_4_4, n5 and discharging atoms sum(n17, n9) = all_0_4_4, sum(n17, n9) = n5, yields:
% 29.26/9.43 | (991) all_0_4_4 = n5
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n7, n19, all_0_7_7, n5 and discharging atoms sum(n7, n19) = all_0_7_7, sum(n7, n19) = n5, yields:
% 29.26/9.43 | (993) all_0_7_7 = n5
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 29.26/9.43 | (956) all_0_2_2 = n16
% 29.26/9.43 |
% 29.26/9.43 | From (956) and (2222) follows:
% 29.26/9.43 | (2422) sum(n16, n15) = all_0_0_0
% 29.26/9.43 |
% 29.26/9.43 | From (993)(991) and (435) follows:
% 29.26/9.43 | (995) sum(n5, n5) = all_0_3_3
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n16, n15, all_0_0_0, n10 and discharging atoms sum(n16, n15) = all_0_0_0, sum(n16, n15) = n10, yields:
% 29.26/9.43 | (996) all_0_0_0 = n10
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 29.26/9.43 | (997) all_0_3_3 = n10
% 29.26/9.43 |
% 29.26/9.43 | Equations (996,997) can reduce 201 to:
% 29.26/9.43 | (746) $false
% 29.26/9.43 |
% 29.26/9.43 |-The branch is then unsatisfiable
% 29.26/9.43 |-Branch two:
% 29.26/9.43 | (963) ~ (all_0_11_11 = n8)
% 29.26/9.43 | (964) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.26/9.43 |
% 29.26/9.43 +-Applying beta-rule and splitting (964), into two cases.
% 29.26/9.43 |-Branch one:
% 29.26/9.43 | (965) all_0_11_11 = n7
% 29.26/9.43 |
% 29.26/9.43 | From (965) and (190) follows:
% 29.26/9.43 | (966) pred(n7) = all_0_9_9
% 29.26/9.43 |
% 29.26/9.43 | From (965) and (505) follows:
% 29.26/9.43 | (967) succ(n7) = all_0_5_5
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (259) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 29.26/9.43 | (968) all_0_9_9 = n6
% 29.26/9.43 |
% 29.26/9.43 | Instantiating formula (184) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 29.26/9.43 | (969) all_0_5_5 = n8
% 29.26/9.43 |
% 29.26/9.43 | From (968)(969) and (156) follows:
% 29.26/9.43 | (970) sum(n6, n8) = all_0_2_2
% 29.26/9.43 |
% 29.26/9.43 | From (968) and (2220) follows:
% 29.26/9.43 | (2435) sum(n6, n19) = all_0_7_7
% 29.26/9.43 |
% 29.26/9.43 | From (969) and (2218) follows:
% 29.26/9.44 | (2436) sum(n17, n8) = all_0_4_4
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n17, n8, all_0_4_4, n4 and discharging atoms sum(n17, n8) = all_0_4_4, sum(n17, n8) = n4, yields:
% 29.26/9.44 | (1009) all_0_4_4 = n4
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n6, n19, all_0_7_7, n4 and discharging atoms sum(n6, n19) = all_0_7_7, sum(n6, n19) = n4, yields:
% 29.26/9.44 | (1011) all_0_7_7 = n4
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 29.26/9.44 | (974) all_0_2_2 = n14
% 29.26/9.44 |
% 29.26/9.44 | From (974) and (2222) follows:
% 29.26/9.44 | (2440) sum(n14, n15) = all_0_0_0
% 29.26/9.44 |
% 29.26/9.44 | From (1011)(1009) and (435) follows:
% 29.26/9.44 | (1013) sum(n4, n4) = all_0_3_3
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n14, n15, all_0_0_0, n8 and discharging atoms sum(n14, n15) = all_0_0_0, sum(n14, n15) = n8, yields:
% 29.26/9.44 | (1014) all_0_0_0 = n8
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 29.26/9.44 | (1015) all_0_3_3 = n8
% 29.26/9.44 |
% 29.26/9.44 | Equations (1014,1015) can reduce 201 to:
% 29.26/9.44 | (746) $false
% 29.26/9.44 |
% 29.26/9.44 |-The branch is then unsatisfiable
% 29.26/9.44 |-Branch two:
% 29.26/9.44 | (981) ~ (all_0_11_11 = n7)
% 29.26/9.44 | (982) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.26/9.44 |
% 29.26/9.44 +-Applying beta-rule and splitting (982), into two cases.
% 29.26/9.44 |-Branch one:
% 29.26/9.44 | (983) all_0_11_11 = n6
% 29.26/9.44 |
% 29.26/9.44 | From (983) and (190) follows:
% 29.26/9.44 | (984) pred(n6) = all_0_9_9
% 29.26/9.44 |
% 29.26/9.44 | From (983) and (505) follows:
% 29.26/9.44 | (985) succ(n6) = all_0_5_5
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (259) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 29.26/9.44 | (986) all_0_9_9 = n5
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (184) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 29.26/9.44 | (987) all_0_5_5 = n7
% 29.26/9.44 |
% 29.26/9.44 | From (986)(987) and (156) follows:
% 29.26/9.44 | (988) sum(n5, n7) = all_0_2_2
% 29.26/9.44 |
% 29.26/9.44 | From (986) and (2220) follows:
% 29.26/9.44 | (2453) sum(n5, n19) = all_0_7_7
% 29.26/9.44 |
% 29.26/9.44 | From (987) and (2218) follows:
% 29.26/9.44 | (2454) sum(n17, n7) = all_0_4_4
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n17, n7, all_0_4_4, n3 and discharging atoms sum(n17, n7) = all_0_4_4, sum(n17, n7) = n3, yields:
% 29.26/9.44 | (1027) all_0_4_4 = n3
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n5, n19, all_0_7_7, n3 and discharging atoms sum(n5, n19) = all_0_7_7, sum(n5, n19) = n3, yields:
% 29.26/9.44 | (1029) all_0_7_7 = n3
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 29.26/9.44 | (992) all_0_2_2 = n12
% 29.26/9.44 |
% 29.26/9.44 | From (992) and (2222) follows:
% 29.26/9.44 | (2458) sum(n12, n15) = all_0_0_0
% 29.26/9.44 |
% 29.26/9.44 | From (1029)(1027) and (435) follows:
% 29.26/9.44 | (1031) sum(n3, n3) = all_0_3_3
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n12, n15, all_0_0_0, n6 and discharging atoms sum(n12, n15) = all_0_0_0, sum(n12, n15) = n6, yields:
% 29.26/9.44 | (1032) all_0_0_0 = n6
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 29.26/9.44 | (1033) all_0_3_3 = n6
% 29.26/9.44 |
% 29.26/9.44 | Equations (1032,1033) can reduce 201 to:
% 29.26/9.44 | (746) $false
% 29.26/9.44 |
% 29.26/9.44 |-The branch is then unsatisfiable
% 29.26/9.44 |-Branch two:
% 29.26/9.44 | (999) ~ (all_0_11_11 = n6)
% 29.26/9.44 | (1000) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.26/9.44 |
% 29.26/9.44 +-Applying beta-rule and splitting (1000), into two cases.
% 29.26/9.44 |-Branch one:
% 29.26/9.44 | (1001) all_0_11_11 = n5
% 29.26/9.44 |
% 29.26/9.44 | From (1001) and (190) follows:
% 29.26/9.44 | (1002) pred(n5) = all_0_9_9
% 29.26/9.44 |
% 29.26/9.44 | From (1001) and (505) follows:
% 29.26/9.44 | (1003) succ(n5) = all_0_5_5
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (259) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 29.26/9.44 | (1004) all_0_9_9 = n4
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (184) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 29.26/9.44 | (1005) all_0_5_5 = n6
% 29.26/9.44 |
% 29.26/9.44 | From (1004)(1005) and (156) follows:
% 29.26/9.44 | (1006) sum(n4, n6) = all_0_2_2
% 29.26/9.44 |
% 29.26/9.44 | From (1004) and (2220) follows:
% 29.26/9.44 | (2471) sum(n4, n19) = all_0_7_7
% 29.26/9.44 |
% 29.26/9.44 | From (1005) and (2218) follows:
% 29.26/9.44 | (2472) sum(n17, n6) = all_0_4_4
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n17, n6, all_0_4_4, n2 and discharging atoms sum(n17, n6) = all_0_4_4, sum(n17, n6) = n2, yields:
% 29.26/9.44 | (1045) all_0_4_4 = n2
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n4, n19, all_0_7_7, n2 and discharging atoms sum(n4, n19) = all_0_7_7, sum(n4, n19) = n2, yields:
% 29.26/9.44 | (1047) all_0_7_7 = n2
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 29.26/9.44 | (1010) all_0_2_2 = n10
% 29.26/9.44 |
% 29.26/9.44 | From (1010) and (2222) follows:
% 29.26/9.44 | (2476) sum(n10, n15) = all_0_0_0
% 29.26/9.44 |
% 29.26/9.44 | From (1047)(1045) and (435) follows:
% 29.26/9.44 | (1049) sum(n2, n2) = all_0_3_3
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n10, n15, all_0_0_0, n4 and discharging atoms sum(n10, n15) = all_0_0_0, sum(n10, n15) = n4, yields:
% 29.26/9.44 | (1050) all_0_0_0 = n4
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 29.26/9.44 | (1051) all_0_3_3 = n4
% 29.26/9.44 |
% 29.26/9.44 | Equations (1050,1051) can reduce 201 to:
% 29.26/9.44 | (746) $false
% 29.26/9.44 |
% 29.26/9.44 |-The branch is then unsatisfiable
% 29.26/9.44 |-Branch two:
% 29.26/9.44 | (1017) ~ (all_0_11_11 = n5)
% 29.26/9.44 | (1018) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.26/9.44 |
% 29.26/9.44 +-Applying beta-rule and splitting (1018), into two cases.
% 29.26/9.44 |-Branch one:
% 29.26/9.44 | (1019) all_0_11_11 = n4
% 29.26/9.44 |
% 29.26/9.44 | From (1019) and (190) follows:
% 29.26/9.44 | (1020) pred(n4) = all_0_9_9
% 29.26/9.44 |
% 29.26/9.44 | From (1019) and (505) follows:
% 29.26/9.44 | (1021) succ(n4) = all_0_5_5
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 29.26/9.44 | (1022) all_0_9_9 = n3
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 29.26/9.44 | (1023) all_0_5_5 = n5
% 29.26/9.44 |
% 29.26/9.44 | From (1022)(1023) and (156) follows:
% 29.26/9.44 | (1024) sum(n3, n5) = all_0_2_2
% 29.26/9.44 |
% 29.26/9.44 | From (1022) and (2220) follows:
% 29.26/9.44 | (2489) sum(n3, n19) = all_0_7_7
% 29.26/9.44 |
% 29.26/9.44 | From (1023) and (2218) follows:
% 29.26/9.44 | (2490) sum(n17, n5) = all_0_4_4
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n17, n5, all_0_4_4, n1 and discharging atoms sum(n17, n5) = all_0_4_4, sum(n17, n5) = n1, yields:
% 29.26/9.44 | (1063) all_0_4_4 = n1
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n3, n19, all_0_7_7, n1 and discharging atoms sum(n3, n19) = all_0_7_7, sum(n3, n19) = n1, yields:
% 29.26/9.44 | (1065) all_0_7_7 = n1
% 29.26/9.44 |
% 29.26/9.44 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 29.40/9.44 | (1028) all_0_2_2 = n8
% 29.40/9.44 |
% 29.40/9.44 | From (1028) and (2222) follows:
% 29.40/9.44 | (2494) sum(n8, n15) = all_0_0_0
% 29.40/9.44 |
% 29.40/9.44 | From (1065)(1063) and (435) follows:
% 29.40/9.44 | (1067) sum(n1, n1) = all_0_3_3
% 29.40/9.44 |
% 29.40/9.44 | Instantiating formula (194) with n8, n15, all_0_0_0, n2 and discharging atoms sum(n8, n15) = all_0_0_0, sum(n8, n15) = n2, yields:
% 29.40/9.44 | (1068) all_0_0_0 = n2
% 29.40/9.44 |
% 29.40/9.44 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 29.40/9.44 | (1069) all_0_3_3 = n2
% 29.40/9.44 |
% 29.40/9.44 | Equations (1068,1069) can reduce 201 to:
% 29.40/9.44 | (746) $false
% 29.40/9.44 |
% 29.40/9.44 |-The branch is then unsatisfiable
% 29.40/9.44 |-Branch two:
% 29.40/9.44 | (1035) ~ (all_0_11_11 = n4)
% 29.40/9.44 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.44 |
% 29.40/9.44 +-Applying beta-rule and splitting (1036), into two cases.
% 29.40/9.44 |-Branch one:
% 29.40/9.44 | (1037) all_0_11_11 = n3
% 29.40/9.44 |
% 29.40/9.44 | From (1037) and (190) follows:
% 29.40/9.44 | (1038) pred(n3) = all_0_9_9
% 29.40/9.44 |
% 29.40/9.44 | From (1037) and (505) follows:
% 29.40/9.44 | (1039) succ(n3) = all_0_5_5
% 29.40/9.44 |
% 29.40/9.44 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 29.40/9.44 | (1040) all_0_9_9 = n2
% 29.40/9.44 |
% 29.40/9.44 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 29.40/9.44 | (1041) all_0_5_5 = n4
% 29.40/9.44 |
% 29.40/9.44 | From (1040)(1041) and (156) follows:
% 29.40/9.44 | (1042) sum(n2, n4) = all_0_2_2
% 29.40/9.44 |
% 29.40/9.44 | From (1040) and (2220) follows:
% 29.40/9.44 | (2507) sum(n2, n19) = all_0_7_7
% 29.40/9.44 |
% 29.40/9.44 | From (1041) and (2218) follows:
% 29.40/9.44 | (2508) sum(n17, n4) = all_0_4_4
% 29.40/9.44 |
% 29.40/9.44 | Instantiating formula (194) with n17, n4, all_0_4_4, n0 and discharging atoms sum(n17, n4) = all_0_4_4, sum(n17, n4) = n0, yields:
% 29.40/9.44 | (1081) all_0_4_4 = n0
% 29.40/9.44 |
% 29.40/9.44 | Instantiating formula (194) with n2, n19, all_0_7_7, n0 and discharging atoms sum(n2, n19) = all_0_7_7, sum(n2, n19) = n0, yields:
% 29.40/9.44 | (1083) all_0_7_7 = n0
% 29.40/9.44 |
% 29.40/9.44 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 29.40/9.44 | (1046) all_0_2_2 = n6
% 29.40/9.44 |
% 29.40/9.44 | From (1046) and (2222) follows:
% 29.40/9.45 | (2512) sum(n6, n15) = all_0_0_0
% 29.40/9.45 |
% 29.40/9.45 | From (1083)(1081) and (435) follows:
% 29.40/9.45 | (1085) sum(n0, n0) = all_0_3_3
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n6, n15, all_0_0_0, n0 and discharging atoms sum(n6, n15) = all_0_0_0, sum(n6, n15) = n0, yields:
% 29.40/9.45 | (1087) all_0_0_0 = n0
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 29.40/9.45 | (1088) all_0_3_3 = n0
% 29.40/9.45 |
% 29.40/9.45 | Equations (1087,1088) can reduce 201 to:
% 29.40/9.45 | (746) $false
% 29.40/9.45 |
% 29.40/9.45 |-The branch is then unsatisfiable
% 29.40/9.45 |-Branch two:
% 29.40/9.45 | (1053) ~ (all_0_11_11 = n3)
% 29.40/9.45 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.45 |
% 29.40/9.45 +-Applying beta-rule and splitting (1054), into two cases.
% 29.40/9.45 |-Branch one:
% 29.40/9.45 | (1055) all_0_11_11 = n2
% 29.40/9.45 |
% 29.40/9.45 | From (1055) and (190) follows:
% 29.40/9.45 | (1056) pred(n2) = all_0_9_9
% 29.40/9.45 |
% 29.40/9.45 | From (1055) and (505) follows:
% 29.40/9.45 | (1057) succ(n2) = all_0_5_5
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 29.40/9.45 | (1058) all_0_9_9 = n1
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 29.40/9.45 | (1059) all_0_5_5 = n3
% 29.40/9.45 |
% 29.40/9.45 | From (1058)(1059) and (156) follows:
% 29.40/9.45 | (1060) sum(n1, n3) = all_0_2_2
% 29.40/9.45 |
% 29.40/9.45 | From (1058) and (2220) follows:
% 29.40/9.45 | (2525) sum(n1, n19) = all_0_7_7
% 29.40/9.45 |
% 29.40/9.45 | From (1059) and (2218) follows:
% 29.40/9.45 | (2526) sum(n17, n3) = all_0_4_4
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n17, n3, all_0_4_4, n20 and discharging atoms sum(n17, n3) = all_0_4_4, sum(n17, n3) = n20, yields:
% 29.40/9.45 | (1101) all_0_4_4 = n20
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n1, n19, all_0_7_7, n20 and discharging atoms sum(n1, n19) = all_0_7_7, sum(n1, n19) = n20, yields:
% 29.40/9.45 | (1100) all_0_7_7 = n20
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 29.40/9.45 | (1064) all_0_2_2 = n4
% 29.40/9.45 |
% 29.40/9.45 | From (1064) and (2222) follows:
% 29.40/9.45 | (2530) sum(n4, n15) = all_0_0_0
% 29.40/9.45 |
% 29.40/9.45 | From (1100)(1101) and (435) follows:
% 29.40/9.45 | (1103) sum(n20, n20) = all_0_3_3
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 29.40/9.45 | (1104) all_0_3_3 = n19
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n4, n15, all_0_0_0, n19 and discharging atoms sum(n4, n15) = all_0_0_0, sum(n4, n15) = n19, yields:
% 29.40/9.45 | (1105) all_0_0_0 = n19
% 29.40/9.45 |
% 29.40/9.45 | Equations (1105,1104) can reduce 201 to:
% 29.40/9.45 | (746) $false
% 29.40/9.45 |
% 29.40/9.45 |-The branch is then unsatisfiable
% 29.40/9.45 |-Branch two:
% 29.40/9.45 | (1071) ~ (all_0_11_11 = n2)
% 29.40/9.45 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.45 |
% 29.40/9.45 +-Applying beta-rule and splitting (1072), into two cases.
% 29.40/9.45 |-Branch one:
% 29.40/9.45 | (1073) all_0_11_11 = n1
% 29.40/9.45 |
% 29.40/9.45 | From (1073) and (190) follows:
% 29.40/9.45 | (1074) pred(n1) = all_0_9_9
% 29.40/9.45 |
% 29.40/9.45 | From (1073) and (505) follows:
% 29.40/9.45 | (1075) succ(n1) = all_0_5_5
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 29.40/9.45 | (1076) all_0_9_9 = n0
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 29.40/9.45 | (1077) all_0_5_5 = n2
% 29.40/9.45 |
% 29.40/9.45 | From (1076)(1077) and (156) follows:
% 29.40/9.45 | (1078) sum(n0, n2) = all_0_2_2
% 29.40/9.45 |
% 29.40/9.45 | From (1076) and (2220) follows:
% 29.40/9.45 | (2543) sum(n0, n19) = all_0_7_7
% 29.40/9.45 |
% 29.40/9.45 | From (1077) and (2218) follows:
% 29.40/9.45 | (2544) sum(n17, n2) = all_0_4_4
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n17, n2, all_0_4_4, n19 and discharging atoms sum(n17, n2) = all_0_4_4, sum(n17, n2) = n19, yields:
% 29.40/9.45 | (736) all_0_4_4 = n19
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n0, n19, all_0_7_7, n19 and discharging atoms sum(n0, n19) = all_0_7_7, sum(n0, n19) = n19, yields:
% 29.40/9.45 | (737) all_0_7_7 = n19
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 29.40/9.45 | (1082) all_0_2_2 = n2
% 29.40/9.45 |
% 29.40/9.45 | From (1082) and (2222) follows:
% 29.40/9.45 | (2548) sum(n2, n15) = all_0_0_0
% 29.40/9.45 |
% 29.40/9.45 | From (737)(736) and (435) follows:
% 29.40/9.45 | (741) sum(n19, n19) = all_0_3_3
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 29.40/9.45 | (744) all_0_3_3 = n17
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n2, n15, all_0_0_0, n17 and discharging atoms sum(n2, n15) = all_0_0_0, sum(n2, n15) = n17, yields:
% 29.40/9.45 | (742) all_0_0_0 = n17
% 29.40/9.45 |
% 29.40/9.45 | Equations (742,744) can reduce 201 to:
% 29.40/9.45 | (746) $false
% 29.40/9.45 |
% 29.40/9.45 |-The branch is then unsatisfiable
% 29.40/9.45 |-Branch two:
% 29.40/9.45 | (1090) ~ (all_0_11_11 = n1)
% 29.40/9.45 | (1091) all_0_11_11 = n0
% 29.40/9.45 |
% 29.40/9.45 | From (1091) and (190) follows:
% 29.40/9.45 | (1092) pred(n0) = all_0_9_9
% 29.40/9.45 |
% 29.40/9.45 | From (1091) and (505) follows:
% 29.40/9.45 | (1093) succ(n0) = all_0_5_5
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 29.40/9.45 | (1094) all_0_9_9 = n20
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 29.40/9.45 | (1095) all_0_5_5 = n1
% 29.40/9.45 |
% 29.40/9.45 | From (1094)(1095) and (156) follows:
% 29.40/9.45 | (1096) sum(n20, n1) = all_0_2_2
% 29.40/9.45 |
% 29.40/9.45 | From (1094) and (2220) follows:
% 29.40/9.45 | (2560) sum(n20, n19) = all_0_7_7
% 29.40/9.45 |
% 29.40/9.45 | From (1095) and (2218) follows:
% 29.40/9.45 | (2561) sum(n17, n1) = all_0_4_4
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n20, n19, all_0_7_7, n18 and discharging atoms sum(n20, n19) = all_0_7_7, sum(n20, n19) = n18, yields:
% 29.40/9.45 | (759) all_0_7_7 = n18
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 29.40/9.45 | (1099) all_0_2_2 = n0
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n17, n1, all_0_4_4, n18 and discharging atoms sum(n17, n1) = all_0_4_4, sum(n17, n1) = n18, yields:
% 29.40/9.45 | (757) all_0_4_4 = n18
% 29.40/9.45 |
% 29.40/9.45 | From (1099) and (2222) follows:
% 29.40/9.45 | (2565) sum(n0, n15) = all_0_0_0
% 29.40/9.45 |
% 29.40/9.45 | From (759)(757) and (435) follows:
% 29.40/9.45 | (761) sum(n18, n18) = all_0_3_3
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 29.40/9.45 | (762) all_0_3_3 = n15
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n0, n15, all_0_0_0, n15 and discharging atoms sum(n0, n15) = all_0_0_0, sum(n0, n15) = n15, yields:
% 29.40/9.45 | (763) all_0_0_0 = n15
% 29.40/9.45 |
% 29.40/9.45 | Equations (763,762) can reduce 201 to:
% 29.40/9.45 | (746) $false
% 29.40/9.45 |
% 29.40/9.45 |-The branch is then unsatisfiable
% 29.40/9.45 |-Branch two:
% 29.40/9.45 | (1154) ~ (all_0_10_10 = n18)
% 29.40/9.45 | (1155) all_0_10_10 = n17 | all_0_10_10 = n16 | all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.40/9.45 |
% 29.40/9.45 +-Applying beta-rule and splitting (766), into two cases.
% 29.40/9.45 |-Branch one:
% 29.40/9.45 | (767) all_0_11_11 = n18
% 29.40/9.45 |
% 29.40/9.45 | From (767) and (190) follows:
% 29.40/9.45 | (768) pred(n18) = all_0_9_9
% 29.40/9.45 |
% 29.40/9.45 | From (767) and (505) follows:
% 29.40/9.45 | (769) succ(n18) = all_0_5_5
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (259) with n18, all_0_9_9, n17 and discharging atoms pred(n18) = all_0_9_9, pred(n18) = n17, yields:
% 29.40/9.45 | (770) all_0_9_9 = n17
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (184) with n18, all_0_5_5, n19 and discharging atoms succ(n18) = all_0_5_5, succ(n18) = n19, yields:
% 29.40/9.45 | (771) all_0_5_5 = n19
% 29.40/9.45 |
% 29.40/9.45 | From (771) and (386) follows:
% 29.40/9.45 | (2577) sum(all_0_6_6, n19) = all_0_4_4
% 29.40/9.45 |
% 29.40/9.45 | From (770)(771) and (156) follows:
% 29.40/9.45 | (772) sum(n17, n19) = all_0_2_2
% 29.40/9.45 |
% 29.40/9.45 | From (770) and (74) follows:
% 29.40/9.45 | (2579) sum(n17, all_0_8_8) = all_0_7_7
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (194) with n17, n19, all_0_2_2, n15 and discharging atoms sum(n17, n19) = all_0_2_2, sum(n17, n19) = n15, yields:
% 29.40/9.45 | (776) all_0_2_2 = n15
% 29.40/9.45 |
% 29.40/9.45 | From (776) and (85) follows:
% 29.40/9.45 | (2581) sum(n15, all_0_1_1) = all_0_0_0
% 29.40/9.45 |
% 29.40/9.45 +-Applying beta-rule and splitting (1155), into two cases.
% 29.40/9.45 |-Branch one:
% 29.40/9.45 | (1156) all_0_10_10 = n17
% 29.40/9.45 |
% 29.40/9.45 | From (1156) and (57) follows:
% 29.40/9.45 | (1157) pred(n17) = all_0_6_6
% 29.40/9.45 |
% 29.40/9.45 | From (1156) and (381) follows:
% 29.40/9.45 | (1158) succ(n17) = all_0_8_8
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (259) with n17, all_0_6_6, n16 and discharging atoms pred(n17) = all_0_6_6, pred(n17) = n16, yields:
% 29.40/9.45 | (1159) all_0_6_6 = n16
% 29.40/9.45 |
% 29.40/9.45 | Instantiating formula (184) with n17, all_0_8_8, n18 and discharging atoms succ(n17) = all_0_8_8, succ(n17) = n18, yields:
% 29.40/9.45 | (1160) all_0_8_8 = n18
% 29.40/9.45 |
% 29.40/9.45 | From (1159)(1160) and (628) follows:
% 29.40/9.45 | (1161) sum(n16, n18) = all_0_1_1
% 29.40/9.45 |
% 29.40/9.45 | From (1159) and (2577) follows:
% 29.40/9.46 | (2588) sum(n16, n19) = all_0_4_4
% 29.40/9.46 |
% 29.40/9.46 | From (1160) and (2579) follows:
% 29.40/9.46 | (2589) sum(n17, n18) = all_0_7_7
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n17, n18, all_0_7_7, n14 and discharging atoms sum(n17, n18) = all_0_7_7, sum(n17, n18) = n14, yields:
% 29.40/9.46 | (831) all_0_7_7 = n14
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n16, n19, all_0_4_4, n14 and discharging atoms sum(n16, n19) = all_0_4_4, sum(n16, n19) = n14, yields:
% 29.40/9.46 | (829) all_0_4_4 = n14
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n16, n18, all_0_1_1, n13 and discharging atoms sum(n16, n18) = all_0_1_1, sum(n16, n18) = n13, yields:
% 29.40/9.46 | (1165) all_0_1_1 = n13
% 29.40/9.46 |
% 29.40/9.46 | From (831)(829) and (435) follows:
% 29.40/9.46 | (833) sum(n14, n14) = all_0_3_3
% 29.40/9.46 |
% 29.40/9.46 | From (1165) and (2581) follows:
% 29.40/9.46 | (2594) sum(n15, n13) = all_0_0_0
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n15, n13, all_0_0_0, n7 and discharging atoms sum(n15, n13) = all_0_0_0, sum(n15, n13) = n7, yields:
% 29.40/9.46 | (835) all_0_0_0 = n7
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 29.40/9.46 | (834) all_0_3_3 = n7
% 29.40/9.46 |
% 29.40/9.46 | Equations (835,834) can reduce 201 to:
% 29.40/9.46 | (746) $false
% 29.40/9.46 |
% 29.40/9.46 |-The branch is then unsatisfiable
% 29.40/9.46 |-Branch two:
% 29.40/9.46 | (1172) ~ (all_0_10_10 = n17)
% 29.40/9.46 | (1173) all_0_10_10 = n16 | all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.40/9.46 |
% 29.40/9.46 +-Applying beta-rule and splitting (1173), into two cases.
% 29.40/9.46 |-Branch one:
% 29.40/9.46 | (1174) all_0_10_10 = n16
% 29.40/9.46 |
% 29.40/9.46 | From (1174) and (57) follows:
% 29.40/9.46 | (1175) pred(n16) = all_0_6_6
% 29.40/9.46 |
% 29.40/9.46 | From (1174) and (381) follows:
% 29.40/9.46 | (1176) succ(n16) = all_0_8_8
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (259) with n16, all_0_6_6, n15 and discharging atoms pred(n16) = all_0_6_6, pred(n16) = n15, yields:
% 29.40/9.46 | (1177) all_0_6_6 = n15
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (184) with n16, all_0_8_8, n17 and discharging atoms succ(n16) = all_0_8_8, succ(n16) = n17, yields:
% 29.40/9.46 | (1178) all_0_8_8 = n17
% 29.40/9.46 |
% 29.40/9.46 | From (1177)(1178) and (628) follows:
% 29.40/9.46 | (1179) sum(n15, n17) = all_0_1_1
% 29.40/9.46 |
% 29.40/9.46 | From (1177) and (2577) follows:
% 29.40/9.46 | (2606) sum(n15, n19) = all_0_4_4
% 29.40/9.46 |
% 29.40/9.46 | From (1178) and (2579) follows:
% 29.40/9.46 | (2607) sum(n17, n17) = all_0_7_7
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n17, n17, all_0_7_7, n13 and discharging atoms sum(n17, n17) = all_0_7_7, sum(n17, n17) = n13, yields:
% 29.40/9.46 | (849) all_0_7_7 = n13
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n15, n19, all_0_4_4, n13 and discharging atoms sum(n15, n19) = all_0_4_4, sum(n15, n19) = n13, yields:
% 29.40/9.46 | (847) all_0_4_4 = n13
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n15, n17, all_0_1_1, n11 and discharging atoms sum(n15, n17) = all_0_1_1, sum(n15, n17) = n11, yields:
% 29.40/9.46 | (1183) all_0_1_1 = n11
% 29.40/9.46 |
% 29.40/9.46 | From (849)(847) and (435) follows:
% 29.40/9.46 | (851) sum(n13, n13) = all_0_3_3
% 29.40/9.46 |
% 29.40/9.46 | From (1183) and (2581) follows:
% 29.40/9.46 | (2612) sum(n15, n11) = all_0_0_0
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n15, n11, all_0_0_0, n5 and discharging atoms sum(n15, n11) = all_0_0_0, sum(n15, n11) = n5, yields:
% 29.40/9.46 | (853) all_0_0_0 = n5
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 29.40/9.46 | (852) all_0_3_3 = n5
% 29.40/9.46 |
% 29.40/9.46 | Equations (853,852) can reduce 201 to:
% 29.40/9.46 | (746) $false
% 29.40/9.46 |
% 29.40/9.46 |-The branch is then unsatisfiable
% 29.40/9.46 |-Branch two:
% 29.40/9.46 | (1190) ~ (all_0_10_10 = n16)
% 29.40/9.46 | (1191) all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.40/9.46 |
% 29.40/9.46 +-Applying beta-rule and splitting (1191), into two cases.
% 29.40/9.46 |-Branch one:
% 29.40/9.46 | (1192) all_0_10_10 = n15
% 29.40/9.46 |
% 29.40/9.46 | From (1192) and (57) follows:
% 29.40/9.46 | (1193) pred(n15) = all_0_6_6
% 29.40/9.46 |
% 29.40/9.46 | From (1192) and (381) follows:
% 29.40/9.46 | (1194) succ(n15) = all_0_8_8
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (259) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 29.40/9.46 | (1195) all_0_6_6 = n14
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (184) with n15, all_0_8_8, n16 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n16, yields:
% 29.40/9.46 | (1196) all_0_8_8 = n16
% 29.40/9.46 |
% 29.40/9.46 | From (1195)(1196) and (628) follows:
% 29.40/9.46 | (1197) sum(n14, n16) = all_0_1_1
% 29.40/9.46 |
% 29.40/9.46 | From (1195) and (2577) follows:
% 29.40/9.46 | (2624) sum(n14, n19) = all_0_4_4
% 29.40/9.46 |
% 29.40/9.46 | From (1196) and (2579) follows:
% 29.40/9.46 | (2625) sum(n17, n16) = all_0_7_7
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n17, n16, all_0_7_7, n12 and discharging atoms sum(n17, n16) = all_0_7_7, sum(n17, n16) = n12, yields:
% 29.40/9.46 | (867) all_0_7_7 = n12
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n14, n19, all_0_4_4, n12 and discharging atoms sum(n14, n19) = all_0_4_4, sum(n14, n19) = n12, yields:
% 29.40/9.46 | (865) all_0_4_4 = n12
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n14, n16, all_0_1_1, n9 and discharging atoms sum(n14, n16) = all_0_1_1, sum(n14, n16) = n9, yields:
% 29.40/9.46 | (1201) all_0_1_1 = n9
% 29.40/9.46 |
% 29.40/9.46 | From (867)(865) and (435) follows:
% 29.40/9.46 | (869) sum(n12, n12) = all_0_3_3
% 29.40/9.46 |
% 29.40/9.46 | From (1201) and (2581) follows:
% 29.40/9.46 | (2630) sum(n15, n9) = all_0_0_0
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n15, n9, all_0_0_0, n3 and discharging atoms sum(n15, n9) = all_0_0_0, sum(n15, n9) = n3, yields:
% 29.40/9.46 | (871) all_0_0_0 = n3
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 29.40/9.46 | (870) all_0_3_3 = n3
% 29.40/9.46 |
% 29.40/9.46 | Equations (871,870) can reduce 201 to:
% 29.40/9.46 | (746) $false
% 29.40/9.46 |
% 29.40/9.46 |-The branch is then unsatisfiable
% 29.40/9.46 |-Branch two:
% 29.40/9.46 | (1208) ~ (all_0_10_10 = n15)
% 29.40/9.46 | (1209) all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.40/9.46 |
% 29.40/9.46 +-Applying beta-rule and splitting (1209), into two cases.
% 29.40/9.46 |-Branch one:
% 29.40/9.46 | (1210) all_0_10_10 = n14
% 29.40/9.46 |
% 29.40/9.46 | From (1210) and (57) follows:
% 29.40/9.46 | (1211) pred(n14) = all_0_6_6
% 29.40/9.46 |
% 29.40/9.46 | From (1210) and (381) follows:
% 29.40/9.46 | (1212) succ(n14) = all_0_8_8
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (259) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 29.40/9.46 | (1213) all_0_6_6 = n13
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (184) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 29.40/9.46 | (1214) all_0_8_8 = n15
% 29.40/9.46 |
% 29.40/9.46 | From (1213)(1214) and (628) follows:
% 29.40/9.46 | (1215) sum(n13, n15) = all_0_1_1
% 29.40/9.46 |
% 29.40/9.46 | From (1213) and (2577) follows:
% 29.40/9.46 | (2642) sum(n13, n19) = all_0_4_4
% 29.40/9.46 |
% 29.40/9.46 | From (1214) and (2579) follows:
% 29.40/9.46 | (2643) sum(n17, n15) = all_0_7_7
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n17, n15, all_0_7_7, n11 and discharging atoms sum(n17, n15) = all_0_7_7, sum(n17, n15) = n11, yields:
% 29.40/9.46 | (885) all_0_7_7 = n11
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n13, n19, all_0_4_4, n11 and discharging atoms sum(n13, n19) = all_0_4_4, sum(n13, n19) = n11, yields:
% 29.40/9.46 | (883) all_0_4_4 = n11
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n13, n15, all_0_1_1, n7 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n7, yields:
% 29.40/9.46 | (1219) all_0_1_1 = n7
% 29.40/9.46 |
% 29.40/9.46 | From (885)(883) and (435) follows:
% 29.40/9.46 | (887) sum(n11, n11) = all_0_3_3
% 29.40/9.46 |
% 29.40/9.46 | From (1219) and (2581) follows:
% 29.40/9.46 | (2648) sum(n15, n7) = all_0_0_0
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n15, n7, all_0_0_0, n1 and discharging atoms sum(n15, n7) = all_0_0_0, sum(n15, n7) = n1, yields:
% 29.40/9.46 | (889) all_0_0_0 = n1
% 29.40/9.46 |
% 29.40/9.46 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 29.40/9.46 | (888) all_0_3_3 = n1
% 29.40/9.46 |
% 29.40/9.46 | Equations (889,888) can reduce 201 to:
% 29.40/9.46 | (746) $false
% 29.40/9.46 |
% 29.40/9.46 |-The branch is then unsatisfiable
% 29.40/9.46 |-Branch two:
% 29.40/9.46 | (1226) ~ (all_0_10_10 = n14)
% 29.40/9.46 | (1227) all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.40/9.46 |
% 29.40/9.46 +-Applying beta-rule and splitting (1227), into two cases.
% 29.40/9.46 |-Branch one:
% 29.40/9.46 | (1228) all_0_10_10 = n13
% 29.40/9.46 |
% 29.40/9.46 | From (1228) and (57) follows:
% 29.40/9.46 | (1229) pred(n13) = all_0_6_6
% 29.40/9.46 |
% 29.40/9.46 | From (1228) and (381) follows:
% 29.40/9.47 | (1230) succ(n13) = all_0_8_8
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (259) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 29.40/9.47 | (1231) all_0_6_6 = n12
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (184) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 29.40/9.47 | (1232) all_0_8_8 = n14
% 29.40/9.47 |
% 29.40/9.47 | From (1231)(1232) and (628) follows:
% 29.40/9.47 | (1233) sum(n12, n14) = all_0_1_1
% 29.40/9.47 |
% 29.40/9.47 | From (1231) and (2577) follows:
% 29.40/9.47 | (2660) sum(n12, n19) = all_0_4_4
% 29.40/9.47 |
% 29.40/9.47 | From (1232) and (2579) follows:
% 29.40/9.47 | (2661) sum(n17, n14) = all_0_7_7
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n17, n14, all_0_7_7, n10 and discharging atoms sum(n17, n14) = all_0_7_7, sum(n17, n14) = n10, yields:
% 29.40/9.47 | (903) all_0_7_7 = n10
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n12, n19, all_0_4_4, n10 and discharging atoms sum(n12, n19) = all_0_4_4, sum(n12, n19) = n10, yields:
% 29.40/9.47 | (901) all_0_4_4 = n10
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n12, n14, all_0_1_1, n5 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n5, yields:
% 29.40/9.47 | (1237) all_0_1_1 = n5
% 29.40/9.47 |
% 29.40/9.47 | From (903)(901) and (435) follows:
% 29.40/9.47 | (905) sum(n10, n10) = all_0_3_3
% 29.40/9.47 |
% 29.40/9.47 | From (1237) and (2581) follows:
% 29.40/9.47 | (2666) sum(n15, n5) = all_0_0_0
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n15, n5, all_0_0_0, n20 and discharging atoms sum(n15, n5) = all_0_0_0, sum(n15, n5) = n20, yields:
% 29.40/9.47 | (907) all_0_0_0 = n20
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 29.40/9.47 | (906) all_0_3_3 = n20
% 29.40/9.47 |
% 29.40/9.47 | Equations (907,906) can reduce 201 to:
% 29.40/9.47 | (746) $false
% 29.40/9.47 |
% 29.40/9.47 |-The branch is then unsatisfiable
% 29.40/9.47 |-Branch two:
% 29.40/9.47 | (1244) ~ (all_0_10_10 = n13)
% 29.40/9.47 | (1245) all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.40/9.47 |
% 29.40/9.47 +-Applying beta-rule and splitting (1245), into two cases.
% 29.40/9.47 |-Branch one:
% 29.40/9.47 | (1246) all_0_10_10 = n12
% 29.40/9.47 |
% 29.40/9.47 | From (1246) and (57) follows:
% 29.40/9.47 | (1247) pred(n12) = all_0_6_6
% 29.40/9.47 |
% 29.40/9.47 | From (1246) and (381) follows:
% 29.40/9.47 | (1248) succ(n12) = all_0_8_8
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (259) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 29.40/9.47 | (1249) all_0_6_6 = n11
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (184) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 29.40/9.47 | (1250) all_0_8_8 = n13
% 29.40/9.47 |
% 29.40/9.47 | From (1249)(1250) and (628) follows:
% 29.40/9.47 | (1251) sum(n11, n13) = all_0_1_1
% 29.40/9.47 |
% 29.40/9.47 | From (1249) and (2577) follows:
% 29.40/9.47 | (2678) sum(n11, n19) = all_0_4_4
% 29.40/9.47 |
% 29.40/9.47 | From (1250) and (2579) follows:
% 29.40/9.47 | (2679) sum(n17, n13) = all_0_7_7
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n17, n13, all_0_7_7, n9 and discharging atoms sum(n17, n13) = all_0_7_7, sum(n17, n13) = n9, yields:
% 29.40/9.47 | (921) all_0_7_7 = n9
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n11, n19, all_0_4_4, n9 and discharging atoms sum(n11, n19) = all_0_4_4, sum(n11, n19) = n9, yields:
% 29.40/9.47 | (919) all_0_4_4 = n9
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n11, n13, all_0_1_1, n3 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n3, yields:
% 29.40/9.47 | (1255) all_0_1_1 = n3
% 29.40/9.47 |
% 29.40/9.47 | From (921)(919) and (435) follows:
% 29.40/9.47 | (923) sum(n9, n9) = all_0_3_3
% 29.40/9.47 |
% 29.40/9.47 | From (1255) and (2581) follows:
% 29.40/9.47 | (2684) sum(n15, n3) = all_0_0_0
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n15, n3, all_0_0_0, n18 and discharging atoms sum(n15, n3) = all_0_0_0, sum(n15, n3) = n18, yields:
% 29.40/9.47 | (924) all_0_0_0 = n18
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 29.40/9.47 | (925) all_0_3_3 = n18
% 29.40/9.47 |
% 29.40/9.47 | Equations (924,925) can reduce 201 to:
% 29.40/9.47 | (746) $false
% 29.40/9.47 |
% 29.40/9.47 |-The branch is then unsatisfiable
% 29.40/9.47 |-Branch two:
% 29.40/9.47 | (1262) ~ (all_0_10_10 = n12)
% 29.40/9.47 | (1263) all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.40/9.47 |
% 29.40/9.47 +-Applying beta-rule and splitting (1263), into two cases.
% 29.40/9.47 |-Branch one:
% 29.40/9.47 | (1264) all_0_10_10 = n11
% 29.40/9.47 |
% 29.40/9.47 | From (1264) and (57) follows:
% 29.40/9.47 | (1265) pred(n11) = all_0_6_6
% 29.40/9.47 |
% 29.40/9.47 | From (1264) and (381) follows:
% 29.40/9.47 | (1266) succ(n11) = all_0_8_8
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (259) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 29.40/9.47 | (1267) all_0_6_6 = n10
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (184) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 29.40/9.47 | (1268) all_0_8_8 = n12
% 29.40/9.47 |
% 29.40/9.47 | From (1267)(1268) and (628) follows:
% 29.40/9.47 | (1269) sum(n10, n12) = all_0_1_1
% 29.40/9.47 |
% 29.40/9.47 | From (1267) and (2577) follows:
% 29.40/9.47 | (2696) sum(n10, n19) = all_0_4_4
% 29.40/9.47 |
% 29.40/9.47 | From (1268) and (2579) follows:
% 29.40/9.47 | (2697) sum(n17, n12) = all_0_7_7
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n17, n12, all_0_7_7, n8 and discharging atoms sum(n17, n12) = all_0_7_7, sum(n17, n12) = n8, yields:
% 29.40/9.47 | (939) all_0_7_7 = n8
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n10, n19, all_0_4_4, n8 and discharging atoms sum(n10, n19) = all_0_4_4, sum(n10, n19) = n8, yields:
% 29.40/9.47 | (937) all_0_4_4 = n8
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n10, n12, all_0_1_1, n1 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n1, yields:
% 29.40/9.47 | (1273) all_0_1_1 = n1
% 29.40/9.47 |
% 29.40/9.47 | From (939)(937) and (435) follows:
% 29.40/9.47 | (941) sum(n8, n8) = all_0_3_3
% 29.40/9.47 |
% 29.40/9.47 | From (1273) and (2581) follows:
% 29.40/9.47 | (2702) sum(n15, n1) = all_0_0_0
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n15, n1, all_0_0_0, n16 and discharging atoms sum(n15, n1) = all_0_0_0, sum(n15, n1) = n16, yields:
% 29.40/9.47 | (942) all_0_0_0 = n16
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 29.40/9.47 | (943) all_0_3_3 = n16
% 29.40/9.47 |
% 29.40/9.47 | Equations (942,943) can reduce 201 to:
% 29.40/9.47 | (746) $false
% 29.40/9.47 |
% 29.40/9.47 |-The branch is then unsatisfiable
% 29.40/9.47 |-Branch two:
% 29.40/9.47 | (1280) ~ (all_0_10_10 = n11)
% 29.40/9.47 | (1281) all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.40/9.47 |
% 29.40/9.47 +-Applying beta-rule and splitting (1281), into two cases.
% 29.40/9.47 |-Branch one:
% 29.40/9.47 | (1282) all_0_10_10 = n10
% 29.40/9.47 |
% 29.40/9.47 | From (1282) and (57) follows:
% 29.40/9.47 | (1283) pred(n10) = all_0_6_6
% 29.40/9.47 |
% 29.40/9.47 | From (1282) and (381) follows:
% 29.40/9.47 | (1284) succ(n10) = all_0_8_8
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (259) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 29.40/9.47 | (1285) all_0_6_6 = n9
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (184) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 29.40/9.47 | (1286) all_0_8_8 = n11
% 29.40/9.47 |
% 29.40/9.47 | From (1285)(1286) and (628) follows:
% 29.40/9.47 | (1287) sum(n9, n11) = all_0_1_1
% 29.40/9.47 |
% 29.40/9.47 | From (1285) and (2577) follows:
% 29.40/9.47 | (2714) sum(n9, n19) = all_0_4_4
% 29.40/9.47 |
% 29.40/9.47 | From (1286) and (2579) follows:
% 29.40/9.47 | (2715) sum(n17, n11) = all_0_7_7
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n17, n11, all_0_7_7, n7 and discharging atoms sum(n17, n11) = all_0_7_7, sum(n17, n11) = n7, yields:
% 29.40/9.47 | (957) all_0_7_7 = n7
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n9, n19, all_0_4_4, n7 and discharging atoms sum(n9, n19) = all_0_4_4, sum(n9, n19) = n7, yields:
% 29.40/9.47 | (955) all_0_4_4 = n7
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 29.40/9.47 | (1291) all_0_1_1 = n20
% 29.40/9.47 |
% 29.40/9.47 | From (957)(955) and (435) follows:
% 29.40/9.47 | (959) sum(n7, n7) = all_0_3_3
% 29.40/9.47 |
% 29.40/9.47 | From (1291) and (2581) follows:
% 29.40/9.47 | (2720) sum(n15, n20) = all_0_0_0
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n15, n20, all_0_0_0, n14 and discharging atoms sum(n15, n20) = all_0_0_0, sum(n15, n20) = n14, yields:
% 29.40/9.47 | (960) all_0_0_0 = n14
% 29.40/9.47 |
% 29.40/9.47 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 29.40/9.47 | (961) all_0_3_3 = n14
% 29.40/9.47 |
% 29.40/9.47 | Equations (960,961) can reduce 201 to:
% 29.40/9.47 | (746) $false
% 29.40/9.47 |
% 29.40/9.47 |-The branch is then unsatisfiable
% 29.40/9.47 |-Branch two:
% 29.40/9.47 | (1298) ~ (all_0_10_10 = n10)
% 29.40/9.47 | (1299) all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.40/9.47 |
% 29.40/9.47 +-Applying beta-rule and splitting (1299), into two cases.
% 29.40/9.47 |-Branch one:
% 29.40/9.47 | (1300) all_0_10_10 = n9
% 29.40/9.47 |
% 29.40/9.47 | From (1300) and (57) follows:
% 29.40/9.48 | (1301) pred(n9) = all_0_6_6
% 29.40/9.48 |
% 29.40/9.48 | From (1300) and (381) follows:
% 29.40/9.48 | (1302) succ(n9) = all_0_8_8
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (259) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 29.40/9.48 | (1303) all_0_6_6 = n8
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (184) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 29.40/9.48 | (1304) all_0_8_8 = n10
% 29.40/9.48 |
% 29.40/9.48 | From (1303)(1304) and (628) follows:
% 29.40/9.48 | (1305) sum(n8, n10) = all_0_1_1
% 29.40/9.48 |
% 29.40/9.48 | From (1303) and (2577) follows:
% 29.40/9.48 | (2732) sum(n8, n19) = all_0_4_4
% 29.40/9.48 |
% 29.40/9.48 | From (1304) and (2579) follows:
% 29.40/9.48 | (2733) sum(n17, n10) = all_0_7_7
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n17, n10, all_0_7_7, n6 and discharging atoms sum(n17, n10) = all_0_7_7, sum(n17, n10) = n6, yields:
% 29.40/9.48 | (975) all_0_7_7 = n6
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n8, n19, all_0_4_4, n6 and discharging atoms sum(n8, n19) = all_0_4_4, sum(n8, n19) = n6, yields:
% 29.40/9.48 | (973) all_0_4_4 = n6
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 29.40/9.48 | (1309) all_0_1_1 = n18
% 29.40/9.48 |
% 29.40/9.48 | From (975)(973) and (435) follows:
% 29.40/9.48 | (977) sum(n6, n6) = all_0_3_3
% 29.40/9.48 |
% 29.40/9.48 | From (1309) and (2581) follows:
% 29.40/9.48 | (2738) sum(n15, n18) = all_0_0_0
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n15, n18, all_0_0_0, n12 and discharging atoms sum(n15, n18) = all_0_0_0, sum(n15, n18) = n12, yields:
% 29.40/9.48 | (978) all_0_0_0 = n12
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 29.40/9.48 | (979) all_0_3_3 = n12
% 29.40/9.48 |
% 29.40/9.48 | Equations (978,979) can reduce 201 to:
% 29.40/9.48 | (746) $false
% 29.40/9.48 |
% 29.40/9.48 |-The branch is then unsatisfiable
% 29.40/9.48 |-Branch two:
% 29.40/9.48 | (1316) ~ (all_0_10_10 = n9)
% 29.40/9.48 | (1317) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.40/9.48 |
% 29.40/9.48 +-Applying beta-rule and splitting (1317), into two cases.
% 29.40/9.48 |-Branch one:
% 29.40/9.48 | (1318) all_0_10_10 = n8
% 29.40/9.48 |
% 29.40/9.48 | From (1318) and (57) follows:
% 29.40/9.48 | (1319) pred(n8) = all_0_6_6
% 29.40/9.48 |
% 29.40/9.48 | From (1318) and (381) follows:
% 29.40/9.48 | (1320) succ(n8) = all_0_8_8
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (259) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 29.40/9.48 | (1321) all_0_6_6 = n7
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (184) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 29.40/9.48 | (1322) all_0_8_8 = n9
% 29.40/9.48 |
% 29.40/9.48 | From (1321)(1322) and (628) follows:
% 29.40/9.48 | (1323) sum(n7, n9) = all_0_1_1
% 29.40/9.48 |
% 29.40/9.48 | From (1321) and (2577) follows:
% 29.40/9.48 | (2750) sum(n7, n19) = all_0_4_4
% 29.40/9.48 |
% 29.40/9.48 | From (1322) and (2579) follows:
% 29.40/9.48 | (2751) sum(n17, n9) = all_0_7_7
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n17, n9, all_0_7_7, n5 and discharging atoms sum(n17, n9) = all_0_7_7, sum(n17, n9) = n5, yields:
% 29.40/9.48 | (993) all_0_7_7 = n5
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n7, n19, all_0_4_4, n5 and discharging atoms sum(n7, n19) = all_0_4_4, sum(n7, n19) = n5, yields:
% 29.40/9.48 | (991) all_0_4_4 = n5
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 29.40/9.48 | (1327) all_0_1_1 = n16
% 29.40/9.48 |
% 29.40/9.48 | From (993)(991) and (435) follows:
% 29.40/9.48 | (995) sum(n5, n5) = all_0_3_3
% 29.40/9.48 |
% 29.40/9.48 | From (1327) and (2581) follows:
% 29.40/9.48 | (2756) sum(n15, n16) = all_0_0_0
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n15, n16, all_0_0_0, n10 and discharging atoms sum(n15, n16) = all_0_0_0, sum(n15, n16) = n10, yields:
% 29.40/9.48 | (996) all_0_0_0 = n10
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 29.40/9.48 | (997) all_0_3_3 = n10
% 29.40/9.48 |
% 29.40/9.48 | Equations (996,997) can reduce 201 to:
% 29.40/9.48 | (746) $false
% 29.40/9.48 |
% 29.40/9.48 |-The branch is then unsatisfiable
% 29.40/9.48 |-Branch two:
% 29.40/9.48 | (1334) ~ (all_0_10_10 = n8)
% 29.40/9.48 | (1335) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.40/9.48 |
% 29.40/9.48 +-Applying beta-rule and splitting (1335), into two cases.
% 29.40/9.48 |-Branch one:
% 29.40/9.48 | (1336) all_0_10_10 = n7
% 29.40/9.48 |
% 29.40/9.48 | From (1336) and (57) follows:
% 29.40/9.48 | (1337) pred(n7) = all_0_6_6
% 29.40/9.48 |
% 29.40/9.48 | From (1336) and (381) follows:
% 29.40/9.48 | (1338) succ(n7) = all_0_8_8
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (259) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 29.40/9.48 | (1339) all_0_6_6 = n6
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (184) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 29.40/9.48 | (1340) all_0_8_8 = n8
% 29.40/9.48 |
% 29.40/9.48 | From (1339)(1340) and (628) follows:
% 29.40/9.48 | (1341) sum(n6, n8) = all_0_1_1
% 29.40/9.48 |
% 29.40/9.48 | From (1339) and (2577) follows:
% 29.40/9.48 | (2768) sum(n6, n19) = all_0_4_4
% 29.40/9.48 |
% 29.40/9.48 | From (1340) and (2579) follows:
% 29.40/9.48 | (2769) sum(n17, n8) = all_0_7_7
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n17, n8, all_0_7_7, n4 and discharging atoms sum(n17, n8) = all_0_7_7, sum(n17, n8) = n4, yields:
% 29.40/9.48 | (1011) all_0_7_7 = n4
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n6, n19, all_0_4_4, n4 and discharging atoms sum(n6, n19) = all_0_4_4, sum(n6, n19) = n4, yields:
% 29.40/9.48 | (1009) all_0_4_4 = n4
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 29.40/9.48 | (1345) all_0_1_1 = n14
% 29.40/9.48 |
% 29.40/9.48 | From (1011)(1009) and (435) follows:
% 29.40/9.48 | (1013) sum(n4, n4) = all_0_3_3
% 29.40/9.48 |
% 29.40/9.48 | From (1345) and (2581) follows:
% 29.40/9.48 | (2774) sum(n15, n14) = all_0_0_0
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n15, n14, all_0_0_0, n8 and discharging atoms sum(n15, n14) = all_0_0_0, sum(n15, n14) = n8, yields:
% 29.40/9.48 | (1014) all_0_0_0 = n8
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 29.40/9.48 | (1015) all_0_3_3 = n8
% 29.40/9.48 |
% 29.40/9.48 | Equations (1014,1015) can reduce 201 to:
% 29.40/9.48 | (746) $false
% 29.40/9.48 |
% 29.40/9.48 |-The branch is then unsatisfiable
% 29.40/9.48 |-Branch two:
% 29.40/9.48 | (1352) ~ (all_0_10_10 = n7)
% 29.40/9.48 | (1353) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.40/9.48 |
% 29.40/9.48 +-Applying beta-rule and splitting (1353), into two cases.
% 29.40/9.48 |-Branch one:
% 29.40/9.48 | (1354) all_0_10_10 = n6
% 29.40/9.48 |
% 29.40/9.48 | From (1354) and (57) follows:
% 29.40/9.48 | (1355) pred(n6) = all_0_6_6
% 29.40/9.48 |
% 29.40/9.48 | From (1354) and (381) follows:
% 29.40/9.48 | (1356) succ(n6) = all_0_8_8
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (259) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 29.40/9.48 | (1357) all_0_6_6 = n5
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (184) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 29.40/9.48 | (1358) all_0_8_8 = n7
% 29.40/9.48 |
% 29.40/9.48 | From (1357)(1358) and (628) follows:
% 29.40/9.48 | (1359) sum(n5, n7) = all_0_1_1
% 29.40/9.48 |
% 29.40/9.48 | From (1357) and (2577) follows:
% 29.40/9.48 | (2786) sum(n5, n19) = all_0_4_4
% 29.40/9.48 |
% 29.40/9.48 | From (1358) and (2579) follows:
% 29.40/9.48 | (2787) sum(n17, n7) = all_0_7_7
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n17, n7, all_0_7_7, n3 and discharging atoms sum(n17, n7) = all_0_7_7, sum(n17, n7) = n3, yields:
% 29.40/9.48 | (1029) all_0_7_7 = n3
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n5, n19, all_0_4_4, n3 and discharging atoms sum(n5, n19) = all_0_4_4, sum(n5, n19) = n3, yields:
% 29.40/9.48 | (1027) all_0_4_4 = n3
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 29.40/9.48 | (1363) all_0_1_1 = n12
% 29.40/9.48 |
% 29.40/9.48 | From (1029)(1027) and (435) follows:
% 29.40/9.48 | (1031) sum(n3, n3) = all_0_3_3
% 29.40/9.48 |
% 29.40/9.48 | From (1363) and (2581) follows:
% 29.40/9.48 | (2792) sum(n15, n12) = all_0_0_0
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n15, n12, all_0_0_0, n6 and discharging atoms sum(n15, n12) = all_0_0_0, sum(n15, n12) = n6, yields:
% 29.40/9.48 | (1032) all_0_0_0 = n6
% 29.40/9.48 |
% 29.40/9.48 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 29.40/9.48 | (1033) all_0_3_3 = n6
% 29.40/9.48 |
% 29.40/9.48 | Equations (1032,1033) can reduce 201 to:
% 29.40/9.48 | (746) $false
% 29.40/9.48 |
% 29.40/9.48 |-The branch is then unsatisfiable
% 29.40/9.48 |-Branch two:
% 29.40/9.48 | (1370) ~ (all_0_10_10 = n6)
% 29.40/9.48 | (1371) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.40/9.48 |
% 29.40/9.48 +-Applying beta-rule and splitting (1371), into two cases.
% 29.40/9.48 |-Branch one:
% 29.40/9.48 | (1372) all_0_10_10 = n5
% 29.40/9.48 |
% 29.40/9.48 | From (1372) and (57) follows:
% 29.40/9.48 | (1373) pred(n5) = all_0_6_6
% 29.40/9.48 |
% 29.40/9.48 | From (1372) and (381) follows:
% 29.40/9.49 | (1374) succ(n5) = all_0_8_8
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (259) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 29.40/9.49 | (1375) all_0_6_6 = n4
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (184) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 29.40/9.49 | (1376) all_0_8_8 = n6
% 29.40/9.49 |
% 29.40/9.49 | From (1375)(1376) and (628) follows:
% 29.40/9.49 | (1377) sum(n4, n6) = all_0_1_1
% 29.40/9.49 |
% 29.40/9.49 | From (1375) and (2577) follows:
% 29.40/9.49 | (2804) sum(n4, n19) = all_0_4_4
% 29.40/9.49 |
% 29.40/9.49 | From (1376) and (2579) follows:
% 29.40/9.49 | (2805) sum(n17, n6) = all_0_7_7
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n17, n6, all_0_7_7, n2 and discharging atoms sum(n17, n6) = all_0_7_7, sum(n17, n6) = n2, yields:
% 29.40/9.49 | (1047) all_0_7_7 = n2
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n4, n19, all_0_4_4, n2 and discharging atoms sum(n4, n19) = all_0_4_4, sum(n4, n19) = n2, yields:
% 29.40/9.49 | (1045) all_0_4_4 = n2
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 29.40/9.49 | (1381) all_0_1_1 = n10
% 29.40/9.49 |
% 29.40/9.49 | From (1047)(1045) and (435) follows:
% 29.40/9.49 | (1049) sum(n2, n2) = all_0_3_3
% 29.40/9.49 |
% 29.40/9.49 | From (1381) and (2581) follows:
% 29.40/9.49 | (2810) sum(n15, n10) = all_0_0_0
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n15, n10, all_0_0_0, n4 and discharging atoms sum(n15, n10) = all_0_0_0, sum(n15, n10) = n4, yields:
% 29.40/9.49 | (1050) all_0_0_0 = n4
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 29.40/9.49 | (1051) all_0_3_3 = n4
% 29.40/9.49 |
% 29.40/9.49 | Equations (1050,1051) can reduce 201 to:
% 29.40/9.49 | (746) $false
% 29.40/9.49 |
% 29.40/9.49 |-The branch is then unsatisfiable
% 29.40/9.49 |-Branch two:
% 29.40/9.49 | (1388) ~ (all_0_10_10 = n5)
% 29.40/9.49 | (1389) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.40/9.49 |
% 29.40/9.49 +-Applying beta-rule and splitting (1389), into two cases.
% 29.40/9.49 |-Branch one:
% 29.40/9.49 | (1390) all_0_10_10 = n4
% 29.40/9.49 |
% 29.40/9.49 | From (1390) and (57) follows:
% 29.40/9.49 | (1391) pred(n4) = all_0_6_6
% 29.40/9.49 |
% 29.40/9.49 | From (1390) and (381) follows:
% 29.40/9.49 | (1392) succ(n4) = all_0_8_8
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (259) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 29.40/9.49 | (1393) all_0_6_6 = n3
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (184) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 29.40/9.49 | (1394) all_0_8_8 = n5
% 29.40/9.49 |
% 29.40/9.49 | From (1393)(1394) and (628) follows:
% 29.40/9.49 | (1395) sum(n3, n5) = all_0_1_1
% 29.40/9.49 |
% 29.40/9.49 | From (1393) and (2577) follows:
% 29.40/9.49 | (2822) sum(n3, n19) = all_0_4_4
% 29.40/9.49 |
% 29.40/9.49 | From (1394) and (2579) follows:
% 29.40/9.49 | (2823) sum(n17, n5) = all_0_7_7
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n17, n5, all_0_7_7, n1 and discharging atoms sum(n17, n5) = all_0_7_7, sum(n17, n5) = n1, yields:
% 29.40/9.49 | (1065) all_0_7_7 = n1
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n3, n19, all_0_4_4, n1 and discharging atoms sum(n3, n19) = all_0_4_4, sum(n3, n19) = n1, yields:
% 29.40/9.49 | (1063) all_0_4_4 = n1
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 29.40/9.49 | (1399) all_0_1_1 = n8
% 29.40/9.49 |
% 29.40/9.49 | From (1065)(1063) and (435) follows:
% 29.40/9.49 | (1067) sum(n1, n1) = all_0_3_3
% 29.40/9.49 |
% 29.40/9.49 | From (1399) and (2581) follows:
% 29.40/9.49 | (2828) sum(n15, n8) = all_0_0_0
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n15, n8, all_0_0_0, n2 and discharging atoms sum(n15, n8) = all_0_0_0, sum(n15, n8) = n2, yields:
% 29.40/9.49 | (1068) all_0_0_0 = n2
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 29.40/9.49 | (1069) all_0_3_3 = n2
% 29.40/9.49 |
% 29.40/9.49 | Equations (1068,1069) can reduce 201 to:
% 29.40/9.49 | (746) $false
% 29.40/9.49 |
% 29.40/9.49 |-The branch is then unsatisfiable
% 29.40/9.49 |-Branch two:
% 29.40/9.49 | (1406) ~ (all_0_10_10 = n4)
% 29.40/9.49 | (1407) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.40/9.49 |
% 29.40/9.49 +-Applying beta-rule and splitting (1407), into two cases.
% 29.40/9.49 |-Branch one:
% 29.40/9.49 | (1408) all_0_10_10 = n3
% 29.40/9.49 |
% 29.40/9.49 | From (1408) and (57) follows:
% 29.40/9.49 | (1409) pred(n3) = all_0_6_6
% 29.40/9.49 |
% 29.40/9.49 | From (1408) and (381) follows:
% 29.40/9.49 | (1410) succ(n3) = all_0_8_8
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 29.40/9.49 | (1411) all_0_6_6 = n2
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 29.40/9.49 | (1412) all_0_8_8 = n4
% 29.40/9.49 |
% 29.40/9.49 | From (1411)(1412) and (628) follows:
% 29.40/9.49 | (1413) sum(n2, n4) = all_0_1_1
% 29.40/9.49 |
% 29.40/9.49 | From (1411) and (2577) follows:
% 29.40/9.49 | (2840) sum(n2, n19) = all_0_4_4
% 29.40/9.49 |
% 29.40/9.49 | From (1412) and (2579) follows:
% 29.40/9.49 | (2841) sum(n17, n4) = all_0_7_7
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n17, n4, all_0_7_7, n0 and discharging atoms sum(n17, n4) = all_0_7_7, sum(n17, n4) = n0, yields:
% 29.40/9.49 | (1083) all_0_7_7 = n0
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n2, n19, all_0_4_4, n0 and discharging atoms sum(n2, n19) = all_0_4_4, sum(n2, n19) = n0, yields:
% 29.40/9.49 | (1081) all_0_4_4 = n0
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 29.40/9.49 | (1417) all_0_1_1 = n6
% 29.40/9.49 |
% 29.40/9.49 | From (1083)(1081) and (435) follows:
% 29.40/9.49 | (1085) sum(n0, n0) = all_0_3_3
% 29.40/9.49 |
% 29.40/9.49 | From (1417) and (2581) follows:
% 29.40/9.49 | (2846) sum(n15, n6) = all_0_0_0
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n15, n6, all_0_0_0, n0 and discharging atoms sum(n15, n6) = all_0_0_0, sum(n15, n6) = n0, yields:
% 29.40/9.49 | (1087) all_0_0_0 = n0
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 29.40/9.49 | (1088) all_0_3_3 = n0
% 29.40/9.49 |
% 29.40/9.49 | Equations (1087,1088) can reduce 201 to:
% 29.40/9.49 | (746) $false
% 29.40/9.49 |
% 29.40/9.49 |-The branch is then unsatisfiable
% 29.40/9.49 |-Branch two:
% 29.40/9.49 | (1424) ~ (all_0_10_10 = n3)
% 29.40/9.49 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.40/9.49 |
% 29.40/9.49 +-Applying beta-rule and splitting (1425), into two cases.
% 29.40/9.49 |-Branch one:
% 29.40/9.49 | (1426) all_0_10_10 = n2
% 29.40/9.49 |
% 29.40/9.49 | From (1426) and (57) follows:
% 29.40/9.49 | (1427) pred(n2) = all_0_6_6
% 29.40/9.49 |
% 29.40/9.49 | From (1426) and (381) follows:
% 29.40/9.49 | (1428) succ(n2) = all_0_8_8
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 29.40/9.49 | (1429) all_0_6_6 = n1
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 29.40/9.49 | (1430) all_0_8_8 = n3
% 29.40/9.49 |
% 29.40/9.49 | From (1429)(1430) and (628) follows:
% 29.40/9.49 | (1431) sum(n1, n3) = all_0_1_1
% 29.40/9.49 |
% 29.40/9.49 | From (1429) and (2577) follows:
% 29.40/9.49 | (2858) sum(n1, n19) = all_0_4_4
% 29.40/9.49 |
% 29.40/9.49 | From (1430) and (2579) follows:
% 29.40/9.49 | (2859) sum(n17, n3) = all_0_7_7
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n17, n3, all_0_7_7, n20 and discharging atoms sum(n17, n3) = all_0_7_7, sum(n17, n3) = n20, yields:
% 29.40/9.49 | (1100) all_0_7_7 = n20
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n1, n19, all_0_4_4, n20 and discharging atoms sum(n1, n19) = all_0_4_4, sum(n1, n19) = n20, yields:
% 29.40/9.49 | (1101) all_0_4_4 = n20
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 29.40/9.49 | (1435) all_0_1_1 = n4
% 29.40/9.49 |
% 29.40/9.49 | From (1100)(1101) and (435) follows:
% 29.40/9.49 | (1103) sum(n20, n20) = all_0_3_3
% 29.40/9.49 |
% 29.40/9.49 | From (1435) and (2581) follows:
% 29.40/9.49 | (2864) sum(n15, n4) = all_0_0_0
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 29.40/9.49 | (1104) all_0_3_3 = n19
% 29.40/9.49 |
% 29.40/9.49 | Instantiating formula (194) with n15, n4, all_0_0_0, n19 and discharging atoms sum(n15, n4) = all_0_0_0, sum(n15, n4) = n19, yields:
% 29.40/9.49 | (1105) all_0_0_0 = n19
% 29.40/9.49 |
% 29.40/9.49 | Equations (1105,1104) can reduce 201 to:
% 29.40/9.49 | (746) $false
% 29.40/9.49 |
% 29.40/9.49 |-The branch is then unsatisfiable
% 29.40/9.49 |-Branch two:
% 29.40/9.49 | (1442) ~ (all_0_10_10 = n2)
% 29.40/9.49 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 29.40/9.49 |
% 29.40/9.49 +-Applying beta-rule and splitting (1443), into two cases.
% 29.40/9.49 |-Branch one:
% 29.40/9.49 | (1444) all_0_10_10 = n1
% 29.40/9.49 |
% 29.40/9.49 | From (1444) and (57) follows:
% 29.40/9.50 | (1445) pred(n1) = all_0_6_6
% 29.40/9.50 |
% 29.40/9.50 | From (1444) and (381) follows:
% 29.40/9.50 | (1446) succ(n1) = all_0_8_8
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 29.40/9.50 | (1447) all_0_6_6 = n0
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 29.40/9.50 | (1448) all_0_8_8 = n2
% 29.40/9.50 |
% 29.40/9.50 | From (1447)(1448) and (628) follows:
% 29.40/9.50 | (1449) sum(n0, n2) = all_0_1_1
% 29.40/9.50 |
% 29.40/9.50 | From (1447) and (2577) follows:
% 29.40/9.50 | (2876) sum(n0, n19) = all_0_4_4
% 29.40/9.50 |
% 29.40/9.50 | From (1448) and (2579) follows:
% 29.40/9.50 | (2877) sum(n17, n2) = all_0_7_7
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (194) with n17, n2, all_0_7_7, n19 and discharging atoms sum(n17, n2) = all_0_7_7, sum(n17, n2) = n19, yields:
% 29.40/9.50 | (737) all_0_7_7 = n19
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (194) with n0, n19, all_0_4_4, n19 and discharging atoms sum(n0, n19) = all_0_4_4, sum(n0, n19) = n19, yields:
% 29.40/9.50 | (736) all_0_4_4 = n19
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 29.40/9.50 | (1453) all_0_1_1 = n2
% 29.40/9.50 |
% 29.40/9.50 | From (737)(736) and (435) follows:
% 29.40/9.50 | (741) sum(n19, n19) = all_0_3_3
% 29.40/9.50 |
% 29.40/9.50 | From (1453) and (2581) follows:
% 29.40/9.50 | (2882) sum(n15, n2) = all_0_0_0
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 29.40/9.50 | (744) all_0_3_3 = n17
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (194) with n15, n2, all_0_0_0, n17 and discharging atoms sum(n15, n2) = all_0_0_0, sum(n15, n2) = n17, yields:
% 29.40/9.50 | (742) all_0_0_0 = n17
% 29.40/9.50 |
% 29.40/9.50 | Equations (742,744) can reduce 201 to:
% 29.40/9.50 | (746) $false
% 29.40/9.50 |
% 29.40/9.50 |-The branch is then unsatisfiable
% 29.40/9.50 |-Branch two:
% 29.40/9.50 | (1462) ~ (all_0_10_10 = n1)
% 29.40/9.50 | (1463) all_0_10_10 = n0
% 29.40/9.50 |
% 29.40/9.50 | From (1463) and (57) follows:
% 29.40/9.50 | (1464) pred(n0) = all_0_6_6
% 29.40/9.50 |
% 29.40/9.50 | From (1463) and (381) follows:
% 29.40/9.50 | (1465) succ(n0) = all_0_8_8
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 29.40/9.50 | (1466) all_0_6_6 = n20
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 29.40/9.50 | (1467) all_0_8_8 = n1
% 29.40/9.50 |
% 29.40/9.50 | From (1466)(1467) and (628) follows:
% 29.40/9.50 | (1468) sum(n20, n1) = all_0_1_1
% 29.40/9.50 |
% 29.40/9.50 | From (1466) and (2577) follows:
% 29.40/9.50 | (2893) sum(n20, n19) = all_0_4_4
% 29.40/9.50 |
% 29.40/9.50 | From (1467) and (2579) follows:
% 29.40/9.50 | (2894) sum(n17, n1) = all_0_7_7
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (194) with n20, n19, all_0_4_4, n18 and discharging atoms sum(n20, n19) = all_0_4_4, sum(n20, n19) = n18, yields:
% 29.40/9.50 | (757) all_0_4_4 = n18
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 29.40/9.50 | (1471) all_0_1_1 = n0
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (194) with n17, n1, all_0_7_7, n18 and discharging atoms sum(n17, n1) = all_0_7_7, sum(n17, n1) = n18, yields:
% 29.40/9.50 | (759) all_0_7_7 = n18
% 29.40/9.50 |
% 29.40/9.50 | From (759)(757) and (435) follows:
% 29.40/9.50 | (761) sum(n18, n18) = all_0_3_3
% 29.40/9.50 |
% 29.40/9.50 | From (1471) and (2581) follows:
% 29.40/9.50 | (2899) sum(n15, n0) = all_0_0_0
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 29.40/9.50 | (762) all_0_3_3 = n15
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (194) with n15, n0, all_0_0_0, n15 and discharging atoms sum(n15, n0) = all_0_0_0, sum(n15, n0) = n15, yields:
% 29.40/9.50 | (763) all_0_0_0 = n15
% 29.40/9.50 |
% 29.40/9.50 | Equations (763,762) can reduce 201 to:
% 29.40/9.50 | (746) $false
% 29.40/9.50 |
% 29.40/9.50 |-The branch is then unsatisfiable
% 29.40/9.50 |-Branch two:
% 29.40/9.50 | (783) ~ (all_0_11_11 = n18)
% 29.40/9.50 | (784) all_0_11_11 = n17 | all_0_11_11 = n16 | all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.50 |
% 29.40/9.50 +-Applying beta-rule and splitting (1155), into two cases.
% 29.40/9.50 |-Branch one:
% 29.40/9.50 | (1156) all_0_10_10 = n17
% 29.40/9.50 |
% 29.40/9.50 | From (1156) and (57) follows:
% 29.40/9.50 | (1157) pred(n17) = all_0_6_6
% 29.40/9.50 |
% 29.40/9.50 | From (1156) and (381) follows:
% 29.40/9.50 | (1158) succ(n17) = all_0_8_8
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (259) with n17, all_0_6_6, n16 and discharging atoms pred(n17) = all_0_6_6, pred(n17) = n16, yields:
% 29.40/9.50 | (1159) all_0_6_6 = n16
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (184) with n17, all_0_8_8, n18 and discharging atoms succ(n17) = all_0_8_8, succ(n17) = n18, yields:
% 29.40/9.50 | (1160) all_0_8_8 = n18
% 29.40/9.50 |
% 29.40/9.50 | From (1159) and (1157) follows:
% 29.40/9.50 | (278) pred(n17) = n16
% 29.40/9.50 |
% 29.40/9.50 | From (1160) and (1158) follows:
% 29.40/9.50 | (631) succ(n17) = n18
% 29.40/9.50 |
% 29.40/9.50 | From (1159) and (386) follows:
% 29.40/9.50 | (2912) sum(n16, all_0_5_5) = all_0_4_4
% 29.40/9.50 |
% 29.40/9.50 | From (1159)(1160) and (628) follows:
% 29.40/9.50 | (1161) sum(n16, n18) = all_0_1_1
% 29.40/9.50 |
% 29.40/9.50 | From (1160) and (74) follows:
% 29.40/9.50 | (2914) sum(all_0_9_9, n18) = all_0_7_7
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (194) with n16, n18, all_0_1_1, n13 and discharging atoms sum(n16, n18) = all_0_1_1, sum(n16, n18) = n13, yields:
% 29.40/9.50 | (1165) all_0_1_1 = n13
% 29.40/9.50 |
% 29.40/9.50 | From (1165) and (85) follows:
% 29.40/9.50 | (2916) sum(all_0_2_2, n13) = all_0_0_0
% 29.40/9.50 |
% 29.40/9.50 | From (1165) and (1161) follows:
% 29.40/9.50 | (419) sum(n16, n18) = n13
% 29.40/9.50 |
% 29.40/9.50 +-Applying beta-rule and splitting (784), into two cases.
% 29.40/9.50 |-Branch one:
% 29.40/9.50 | (785) all_0_11_11 = n17
% 29.40/9.50 |
% 29.40/9.50 | From (785) and (190) follows:
% 29.40/9.50 | (786) pred(n17) = all_0_9_9
% 29.40/9.50 |
% 29.40/9.50 | From (785) and (505) follows:
% 29.40/9.50 | (787) succ(n17) = all_0_5_5
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (259) with n17, all_0_9_9, n16 and discharging atoms pred(n17) = all_0_9_9, pred(n17) = n16, yields:
% 29.40/9.50 | (788) all_0_9_9 = n16
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (184) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 29.40/9.50 | (789) all_0_5_5 = n18
% 29.40/9.50 |
% 29.40/9.50 | From (788)(789) and (156) follows:
% 29.40/9.50 | (790) sum(n16, n18) = all_0_2_2
% 29.40/9.50 |
% 29.40/9.50 | From (788) and (2914) follows:
% 29.40/9.50 | (2924) sum(n16, n18) = all_0_7_7
% 29.40/9.50 |
% 29.40/9.50 | From (789) and (2912) follows:
% 29.40/9.50 | (2925) sum(n16, n18) = all_0_4_4
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (194) with n16, n18, all_0_2_2, n13 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = n13, yields:
% 29.40/9.50 | (794) all_0_2_2 = n13
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (194) with n16, n18, all_0_4_4, all_0_2_2 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = all_0_4_4, yields:
% 29.40/9.50 | (733) all_0_2_2 = all_0_4_4
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (194) with n16, n18, all_0_7_7, all_0_2_2 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = all_0_7_7, yields:
% 29.40/9.50 | (734) all_0_2_2 = all_0_7_7
% 29.40/9.50 |
% 29.40/9.50 | Combining equations (734,733) yields a new equation:
% 29.40/9.50 | (735) all_0_4_4 = all_0_7_7
% 29.40/9.50 |
% 29.40/9.50 | Combining equations (794,733) yields a new equation:
% 29.40/9.50 | (847) all_0_4_4 = n13
% 29.40/9.50 |
% 29.40/9.50 | Combining equations (847,735) yields a new equation:
% 29.40/9.50 | (849) all_0_7_7 = n13
% 29.40/9.50 |
% 29.40/9.50 | Combining equations (849,735) yields a new equation:
% 29.40/9.50 | (847) all_0_4_4 = n13
% 29.40/9.50 |
% 29.40/9.50 | Combining equations (847,733) yields a new equation:
% 29.40/9.50 | (794) all_0_2_2 = n13
% 29.40/9.50 |
% 29.40/9.50 | From (794) and (2916) follows:
% 29.40/9.50 | (2934) sum(n13, n13) = all_0_0_0
% 29.40/9.50 |
% 29.40/9.50 | From (849)(847) and (435) follows:
% 29.40/9.50 | (851) sum(n13, n13) = all_0_3_3
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (194) with n13, n13, all_0_0_0, n5 and discharging atoms sum(n13, n13) = all_0_0_0, sum(n13, n13) = n5, yields:
% 29.40/9.50 | (853) all_0_0_0 = n5
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (194) with n13, n13, all_0_3_3, all_0_0_0 and discharging atoms sum(n13, n13) = all_0_0_0, sum(n13, n13) = all_0_3_3, yields:
% 29.40/9.50 | (743) all_0_0_0 = all_0_3_3
% 29.40/9.50 |
% 29.40/9.50 | Combining equations (853,743) yields a new equation:
% 29.40/9.50 | (852) all_0_3_3 = n5
% 29.40/9.50 |
% 29.40/9.50 | Combining equations (852,743) yields a new equation:
% 29.40/9.50 | (853) all_0_0_0 = n5
% 29.40/9.50 |
% 29.40/9.50 | Equations (853,852) can reduce 201 to:
% 29.40/9.50 | (746) $false
% 29.40/9.50 |
% 29.40/9.50 |-The branch is then unsatisfiable
% 29.40/9.50 |-Branch two:
% 29.40/9.50 | (801) ~ (all_0_11_11 = n17)
% 29.40/9.50 | (802) all_0_11_11 = n16 | all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.50 |
% 29.40/9.50 +-Applying beta-rule and splitting (802), into two cases.
% 29.40/9.50 |-Branch one:
% 29.40/9.50 | (803) all_0_11_11 = n16
% 29.40/9.50 |
% 29.40/9.50 | From (803) and (190) follows:
% 29.40/9.50 | (804) pred(n16) = all_0_9_9
% 29.40/9.50 |
% 29.40/9.50 | From (803) and (505) follows:
% 29.40/9.50 | (805) succ(n16) = all_0_5_5
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (259) with n16, all_0_9_9, n15 and discharging atoms pred(n16) = all_0_9_9, pred(n16) = n15, yields:
% 29.40/9.50 | (806) all_0_9_9 = n15
% 29.40/9.50 |
% 29.40/9.50 | Instantiating formula (184) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 29.40/9.50 | (807) all_0_5_5 = n17
% 29.40/9.50 |
% 29.40/9.50 | From (806)(807) and (156) follows:
% 29.40/9.51 | (808) sum(n15, n17) = all_0_2_2
% 29.40/9.51 |
% 29.40/9.51 | From (806) and (2914) follows:
% 29.40/9.51 | (2949) sum(n15, n18) = all_0_7_7
% 29.40/9.51 |
% 29.40/9.51 | From (807) and (2912) follows:
% 29.40/9.51 | (2950) sum(n16, n17) = all_0_4_4
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n16, n17, all_0_4_4, n12 and discharging atoms sum(n16, n17) = all_0_4_4, sum(n16, n17) = n12, yields:
% 29.40/9.51 | (865) all_0_4_4 = n12
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n15, n18, all_0_7_7, n12 and discharging atoms sum(n15, n18) = all_0_7_7, sum(n15, n18) = n12, yields:
% 29.40/9.51 | (867) all_0_7_7 = n12
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n15, n17, all_0_2_2, n11 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n11, yields:
% 29.40/9.51 | (812) all_0_2_2 = n11
% 29.40/9.51 |
% 29.40/9.51 | From (812) and (2916) follows:
% 29.40/9.51 | (2954) sum(n11, n13) = all_0_0_0
% 29.40/9.51 |
% 29.40/9.51 | From (867)(865) and (435) follows:
% 29.40/9.51 | (869) sum(n12, n12) = all_0_3_3
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 29.40/9.51 | (870) all_0_3_3 = n3
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n11, n13, all_0_0_0, n3 and discharging atoms sum(n11, n13) = all_0_0_0, sum(n11, n13) = n3, yields:
% 29.40/9.51 | (871) all_0_0_0 = n3
% 29.40/9.51 |
% 29.40/9.51 | Equations (871,870) can reduce 201 to:
% 29.40/9.51 | (746) $false
% 29.40/9.51 |
% 29.40/9.51 |-The branch is then unsatisfiable
% 29.40/9.51 |-Branch two:
% 29.40/9.51 | (819) ~ (all_0_11_11 = n16)
% 29.40/9.51 | (820) all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.51 |
% 29.40/9.51 +-Applying beta-rule and splitting (820), into two cases.
% 29.40/9.51 |-Branch one:
% 29.40/9.51 | (821) all_0_11_11 = n15
% 29.40/9.51 |
% 29.40/9.51 | From (821) and (190) follows:
% 29.40/9.51 | (822) pred(n15) = all_0_9_9
% 29.40/9.51 |
% 29.40/9.51 | From (821) and (505) follows:
% 29.40/9.51 | (823) succ(n15) = all_0_5_5
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (259) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 29.40/9.51 | (824) all_0_9_9 = n14
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (184) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 29.40/9.51 | (825) all_0_5_5 = n16
% 29.40/9.51 |
% 29.40/9.51 | From (824)(825) and (156) follows:
% 29.40/9.51 | (826) sum(n14, n16) = all_0_2_2
% 29.40/9.51 |
% 29.40/9.51 | From (824) and (2914) follows:
% 29.40/9.51 | (2967) sum(n14, n18) = all_0_7_7
% 29.40/9.51 |
% 29.40/9.51 | From (825) and (2912) follows:
% 29.40/9.51 | (2968) sum(n16, n16) = all_0_4_4
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n16, n16, all_0_4_4, n11 and discharging atoms sum(n16, n16) = all_0_4_4, sum(n16, n16) = n11, yields:
% 29.40/9.51 | (883) all_0_4_4 = n11
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n14, n18, all_0_7_7, n11 and discharging atoms sum(n14, n18) = all_0_7_7, sum(n14, n18) = n11, yields:
% 29.40/9.51 | (885) all_0_7_7 = n11
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n14, n16, all_0_2_2, n9 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n9, yields:
% 29.40/9.51 | (830) all_0_2_2 = n9
% 29.40/9.51 |
% 29.40/9.51 | From (830) and (2916) follows:
% 29.40/9.51 | (2972) sum(n9, n13) = all_0_0_0
% 29.40/9.51 |
% 29.40/9.51 | From (885)(883) and (435) follows:
% 29.40/9.51 | (887) sum(n11, n11) = all_0_3_3
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 29.40/9.51 | (888) all_0_3_3 = n1
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n9, n13, all_0_0_0, n1 and discharging atoms sum(n9, n13) = all_0_0_0, sum(n9, n13) = n1, yields:
% 29.40/9.51 | (889) all_0_0_0 = n1
% 29.40/9.51 |
% 29.40/9.51 | Equations (889,888) can reduce 201 to:
% 29.40/9.51 | (746) $false
% 29.40/9.51 |
% 29.40/9.51 |-The branch is then unsatisfiable
% 29.40/9.51 |-Branch two:
% 29.40/9.51 | (837) ~ (all_0_11_11 = n15)
% 29.40/9.51 | (838) all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.51 |
% 29.40/9.51 +-Applying beta-rule and splitting (838), into two cases.
% 29.40/9.51 |-Branch one:
% 29.40/9.51 | (839) all_0_11_11 = n14
% 29.40/9.51 |
% 29.40/9.51 | From (839) and (190) follows:
% 29.40/9.51 | (840) pred(n14) = all_0_9_9
% 29.40/9.51 |
% 29.40/9.51 | From (839) and (505) follows:
% 29.40/9.51 | (841) succ(n14) = all_0_5_5
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (259) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 29.40/9.51 | (842) all_0_9_9 = n13
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (184) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 29.40/9.51 | (843) all_0_5_5 = n15
% 29.40/9.51 |
% 29.40/9.51 | From (842)(843) and (156) follows:
% 29.40/9.51 | (844) sum(n13, n15) = all_0_2_2
% 29.40/9.51 |
% 29.40/9.51 | From (842) and (2914) follows:
% 29.40/9.51 | (2985) sum(n13, n18) = all_0_7_7
% 29.40/9.51 |
% 29.40/9.51 | From (843) and (2912) follows:
% 29.40/9.51 | (2986) sum(n16, n15) = all_0_4_4
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n16, n15, all_0_4_4, n10 and discharging atoms sum(n16, n15) = all_0_4_4, sum(n16, n15) = n10, yields:
% 29.40/9.51 | (901) all_0_4_4 = n10
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n13, n18, all_0_7_7, n10 and discharging atoms sum(n13, n18) = all_0_7_7, sum(n13, n18) = n10, yields:
% 29.40/9.51 | (903) all_0_7_7 = n10
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n13, n15, all_0_2_2, n7 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n7, yields:
% 29.40/9.51 | (848) all_0_2_2 = n7
% 29.40/9.51 |
% 29.40/9.51 | From (848) and (2916) follows:
% 29.40/9.51 | (2990) sum(n7, n13) = all_0_0_0
% 29.40/9.51 |
% 29.40/9.51 | From (903)(901) and (435) follows:
% 29.40/9.51 | (905) sum(n10, n10) = all_0_3_3
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 29.40/9.51 | (906) all_0_3_3 = n20
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n7, n13, all_0_0_0, n20 and discharging atoms sum(n7, n13) = all_0_0_0, sum(n7, n13) = n20, yields:
% 29.40/9.51 | (907) all_0_0_0 = n20
% 29.40/9.51 |
% 29.40/9.51 | Equations (907,906) can reduce 201 to:
% 29.40/9.51 | (746) $false
% 29.40/9.51 |
% 29.40/9.51 |-The branch is then unsatisfiable
% 29.40/9.51 |-Branch two:
% 29.40/9.51 | (855) ~ (all_0_11_11 = n14)
% 29.40/9.51 | (856) all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.51 |
% 29.40/9.51 +-Applying beta-rule and splitting (856), into two cases.
% 29.40/9.51 |-Branch one:
% 29.40/9.51 | (857) all_0_11_11 = n13
% 29.40/9.51 |
% 29.40/9.51 | From (857) and (190) follows:
% 29.40/9.51 | (858) pred(n13) = all_0_9_9
% 29.40/9.51 |
% 29.40/9.51 | From (857) and (505) follows:
% 29.40/9.51 | (859) succ(n13) = all_0_5_5
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (259) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 29.40/9.51 | (860) all_0_9_9 = n12
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (184) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 29.40/9.51 | (861) all_0_5_5 = n14
% 29.40/9.51 |
% 29.40/9.51 | From (860)(861) and (156) follows:
% 29.40/9.51 | (862) sum(n12, n14) = all_0_2_2
% 29.40/9.51 |
% 29.40/9.51 | From (860) and (2914) follows:
% 29.40/9.51 | (3003) sum(n12, n18) = all_0_7_7
% 29.40/9.51 |
% 29.40/9.51 | From (861) and (2912) follows:
% 29.40/9.51 | (3004) sum(n16, n14) = all_0_4_4
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n16, n14, all_0_4_4, n9 and discharging atoms sum(n16, n14) = all_0_4_4, sum(n16, n14) = n9, yields:
% 29.40/9.51 | (919) all_0_4_4 = n9
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n12, n18, all_0_7_7, n9 and discharging atoms sum(n12, n18) = all_0_7_7, sum(n12, n18) = n9, yields:
% 29.40/9.51 | (921) all_0_7_7 = n9
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n12, n14, all_0_2_2, n5 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n5, yields:
% 29.40/9.51 | (866) all_0_2_2 = n5
% 29.40/9.51 |
% 29.40/9.51 | From (866) and (2916) follows:
% 29.40/9.51 | (3008) sum(n5, n13) = all_0_0_0
% 29.40/9.51 |
% 29.40/9.51 | From (921)(919) and (435) follows:
% 29.40/9.51 | (923) sum(n9, n9) = all_0_3_3
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 29.40/9.51 | (925) all_0_3_3 = n18
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n5, n13, all_0_0_0, n18 and discharging atoms sum(n5, n13) = all_0_0_0, sum(n5, n13) = n18, yields:
% 29.40/9.51 | (924) all_0_0_0 = n18
% 29.40/9.51 |
% 29.40/9.51 | Equations (924,925) can reduce 201 to:
% 29.40/9.51 | (746) $false
% 29.40/9.51 |
% 29.40/9.51 |-The branch is then unsatisfiable
% 29.40/9.51 |-Branch two:
% 29.40/9.51 | (873) ~ (all_0_11_11 = n13)
% 29.40/9.51 | (874) all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.51 |
% 29.40/9.51 +-Applying beta-rule and splitting (874), into two cases.
% 29.40/9.51 |-Branch one:
% 29.40/9.51 | (875) all_0_11_11 = n12
% 29.40/9.51 |
% 29.40/9.51 | From (875) and (190) follows:
% 29.40/9.51 | (876) pred(n12) = all_0_9_9
% 29.40/9.51 |
% 29.40/9.51 | From (875) and (505) follows:
% 29.40/9.51 | (877) succ(n12) = all_0_5_5
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (259) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 29.40/9.51 | (878) all_0_9_9 = n11
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (184) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 29.40/9.51 | (879) all_0_5_5 = n13
% 29.40/9.51 |
% 29.40/9.51 | From (878)(879) and (156) follows:
% 29.40/9.51 | (880) sum(n11, n13) = all_0_2_2
% 29.40/9.51 |
% 29.40/9.51 | From (878) and (2914) follows:
% 29.40/9.51 | (3021) sum(n11, n18) = all_0_7_7
% 29.40/9.51 |
% 29.40/9.51 | From (879) and (2912) follows:
% 29.40/9.51 | (3022) sum(n16, n13) = all_0_4_4
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n16, n13, all_0_4_4, n8 and discharging atoms sum(n16, n13) = all_0_4_4, sum(n16, n13) = n8, yields:
% 29.40/9.51 | (937) all_0_4_4 = n8
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n11, n18, all_0_7_7, n8 and discharging atoms sum(n11, n18) = all_0_7_7, sum(n11, n18) = n8, yields:
% 29.40/9.51 | (939) all_0_7_7 = n8
% 29.40/9.51 |
% 29.40/9.51 | Instantiating formula (194) with n11, n13, all_0_2_2, n3 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n3, yields:
% 29.40/9.51 | (884) all_0_2_2 = n3
% 29.40/9.51 |
% 29.40/9.51 | From (884) and (2916) follows:
% 29.40/9.52 | (3026) sum(n3, n13) = all_0_0_0
% 29.40/9.52 |
% 29.40/9.52 | From (939)(937) and (435) follows:
% 29.40/9.52 | (941) sum(n8, n8) = all_0_3_3
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 29.40/9.52 | (943) all_0_3_3 = n16
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n3, n13, all_0_0_0, n16 and discharging atoms sum(n3, n13) = all_0_0_0, sum(n3, n13) = n16, yields:
% 29.40/9.52 | (942) all_0_0_0 = n16
% 29.40/9.52 |
% 29.40/9.52 | Equations (942,943) can reduce 201 to:
% 29.40/9.52 | (746) $false
% 29.40/9.52 |
% 29.40/9.52 |-The branch is then unsatisfiable
% 29.40/9.52 |-Branch two:
% 29.40/9.52 | (891) ~ (all_0_11_11 = n12)
% 29.40/9.52 | (892) all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.52 |
% 29.40/9.52 +-Applying beta-rule and splitting (892), into two cases.
% 29.40/9.52 |-Branch one:
% 29.40/9.52 | (893) all_0_11_11 = n11
% 29.40/9.52 |
% 29.40/9.52 | From (893) and (190) follows:
% 29.40/9.52 | (894) pred(n11) = all_0_9_9
% 29.40/9.52 |
% 29.40/9.52 | From (893) and (505) follows:
% 29.40/9.52 | (895) succ(n11) = all_0_5_5
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (259) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 29.40/9.52 | (896) all_0_9_9 = n10
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (184) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 29.40/9.52 | (897) all_0_5_5 = n12
% 29.40/9.52 |
% 29.40/9.52 | From (896)(897) and (156) follows:
% 29.40/9.52 | (898) sum(n10, n12) = all_0_2_2
% 29.40/9.52 |
% 29.40/9.52 | From (896) and (2914) follows:
% 29.40/9.52 | (3039) sum(n10, n18) = all_0_7_7
% 29.40/9.52 |
% 29.40/9.52 | From (897) and (2912) follows:
% 29.40/9.52 | (3040) sum(n16, n12) = all_0_4_4
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n16, n12, all_0_4_4, n7 and discharging atoms sum(n16, n12) = all_0_4_4, sum(n16, n12) = n7, yields:
% 29.40/9.52 | (955) all_0_4_4 = n7
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n10, n18, all_0_7_7, n7 and discharging atoms sum(n10, n18) = all_0_7_7, sum(n10, n18) = n7, yields:
% 29.40/9.52 | (957) all_0_7_7 = n7
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n10, n12, all_0_2_2, n1 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n1, yields:
% 29.40/9.52 | (902) all_0_2_2 = n1
% 29.40/9.52 |
% 29.40/9.52 | From (902) and (2916) follows:
% 29.40/9.52 | (3044) sum(n1, n13) = all_0_0_0
% 29.40/9.52 |
% 29.40/9.52 | From (957)(955) and (435) follows:
% 29.40/9.52 | (959) sum(n7, n7) = all_0_3_3
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 29.40/9.52 | (961) all_0_3_3 = n14
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n1, n13, all_0_0_0, n14 and discharging atoms sum(n1, n13) = all_0_0_0, sum(n1, n13) = n14, yields:
% 29.40/9.52 | (960) all_0_0_0 = n14
% 29.40/9.52 |
% 29.40/9.52 | Equations (960,961) can reduce 201 to:
% 29.40/9.52 | (746) $false
% 29.40/9.52 |
% 29.40/9.52 |-The branch is then unsatisfiable
% 29.40/9.52 |-Branch two:
% 29.40/9.52 | (909) ~ (all_0_11_11 = n11)
% 29.40/9.52 | (910) all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.52 |
% 29.40/9.52 +-Applying beta-rule and splitting (910), into two cases.
% 29.40/9.52 |-Branch one:
% 29.40/9.52 | (911) all_0_11_11 = n10
% 29.40/9.52 |
% 29.40/9.52 | From (911) and (190) follows:
% 29.40/9.52 | (912) pred(n10) = all_0_9_9
% 29.40/9.52 |
% 29.40/9.52 | From (911) and (505) follows:
% 29.40/9.52 | (913) succ(n10) = all_0_5_5
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (259) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 29.40/9.52 | (914) all_0_9_9 = n9
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (184) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 29.40/9.52 | (915) all_0_5_5 = n11
% 29.40/9.52 |
% 29.40/9.52 | From (914)(915) and (156) follows:
% 29.40/9.52 | (916) sum(n9, n11) = all_0_2_2
% 29.40/9.52 |
% 29.40/9.52 | From (914) and (2914) follows:
% 29.40/9.52 | (3057) sum(n9, n18) = all_0_7_7
% 29.40/9.52 |
% 29.40/9.52 | From (915) and (2912) follows:
% 29.40/9.52 | (3058) sum(n16, n11) = all_0_4_4
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n16, n11, all_0_4_4, n6 and discharging atoms sum(n16, n11) = all_0_4_4, sum(n16, n11) = n6, yields:
% 29.40/9.52 | (973) all_0_4_4 = n6
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n9, n18, all_0_7_7, n6 and discharging atoms sum(n9, n18) = all_0_7_7, sum(n9, n18) = n6, yields:
% 29.40/9.52 | (975) all_0_7_7 = n6
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 29.40/9.52 | (920) all_0_2_2 = n20
% 29.40/9.52 |
% 29.40/9.52 | From (920) and (2916) follows:
% 29.40/9.52 | (3062) sum(n20, n13) = all_0_0_0
% 29.40/9.52 |
% 29.40/9.52 | From (975)(973) and (435) follows:
% 29.40/9.52 | (977) sum(n6, n6) = all_0_3_3
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n20, n13, all_0_0_0, n12 and discharging atoms sum(n20, n13) = all_0_0_0, sum(n20, n13) = n12, yields:
% 29.40/9.52 | (978) all_0_0_0 = n12
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 29.40/9.52 | (979) all_0_3_3 = n12
% 29.40/9.52 |
% 29.40/9.52 | Equations (978,979) can reduce 201 to:
% 29.40/9.52 | (746) $false
% 29.40/9.52 |
% 29.40/9.52 |-The branch is then unsatisfiable
% 29.40/9.52 |-Branch two:
% 29.40/9.52 | (927) ~ (all_0_11_11 = n10)
% 29.40/9.52 | (928) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.52 |
% 29.40/9.52 +-Applying beta-rule and splitting (928), into two cases.
% 29.40/9.52 |-Branch one:
% 29.40/9.52 | (929) all_0_11_11 = n9
% 29.40/9.52 |
% 29.40/9.52 | From (929) and (190) follows:
% 29.40/9.52 | (930) pred(n9) = all_0_9_9
% 29.40/9.52 |
% 29.40/9.52 | From (929) and (505) follows:
% 29.40/9.52 | (931) succ(n9) = all_0_5_5
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (259) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 29.40/9.52 | (932) all_0_9_9 = n8
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (184) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 29.40/9.52 | (933) all_0_5_5 = n10
% 29.40/9.52 |
% 29.40/9.52 | From (932)(933) and (156) follows:
% 29.40/9.52 | (934) sum(n8, n10) = all_0_2_2
% 29.40/9.52 |
% 29.40/9.52 | From (932) and (2914) follows:
% 29.40/9.52 | (3075) sum(n8, n18) = all_0_7_7
% 29.40/9.52 |
% 29.40/9.52 | From (933) and (2912) follows:
% 29.40/9.52 | (3076) sum(n16, n10) = all_0_4_4
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n16, n10, all_0_4_4, n5 and discharging atoms sum(n16, n10) = all_0_4_4, sum(n16, n10) = n5, yields:
% 29.40/9.52 | (991) all_0_4_4 = n5
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n8, n18, all_0_7_7, n5 and discharging atoms sum(n8, n18) = all_0_7_7, sum(n8, n18) = n5, yields:
% 29.40/9.52 | (993) all_0_7_7 = n5
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 29.40/9.52 | (938) all_0_2_2 = n18
% 29.40/9.52 |
% 29.40/9.52 | From (938) and (2916) follows:
% 29.40/9.52 | (3080) sum(n18, n13) = all_0_0_0
% 29.40/9.52 |
% 29.40/9.52 | From (993)(991) and (435) follows:
% 29.40/9.52 | (995) sum(n5, n5) = all_0_3_3
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n18, n13, all_0_0_0, n10 and discharging atoms sum(n18, n13) = all_0_0_0, sum(n18, n13) = n10, yields:
% 29.40/9.52 | (996) all_0_0_0 = n10
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 29.40/9.52 | (997) all_0_3_3 = n10
% 29.40/9.52 |
% 29.40/9.52 | Equations (996,997) can reduce 201 to:
% 29.40/9.52 | (746) $false
% 29.40/9.52 |
% 29.40/9.52 |-The branch is then unsatisfiable
% 29.40/9.52 |-Branch two:
% 29.40/9.52 | (945) ~ (all_0_11_11 = n9)
% 29.40/9.52 | (946) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.52 |
% 29.40/9.52 +-Applying beta-rule and splitting (946), into two cases.
% 29.40/9.52 |-Branch one:
% 29.40/9.52 | (947) all_0_11_11 = n8
% 29.40/9.52 |
% 29.40/9.52 | From (947) and (190) follows:
% 29.40/9.52 | (948) pred(n8) = all_0_9_9
% 29.40/9.52 |
% 29.40/9.52 | From (947) and (505) follows:
% 29.40/9.52 | (949) succ(n8) = all_0_5_5
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (259) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 29.40/9.52 | (950) all_0_9_9 = n7
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (184) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 29.40/9.52 | (951) all_0_5_5 = n9
% 29.40/9.52 |
% 29.40/9.52 | From (950)(951) and (156) follows:
% 29.40/9.52 | (952) sum(n7, n9) = all_0_2_2
% 29.40/9.52 |
% 29.40/9.52 | From (950) and (2914) follows:
% 29.40/9.52 | (3093) sum(n7, n18) = all_0_7_7
% 29.40/9.52 |
% 29.40/9.52 | From (951) and (2912) follows:
% 29.40/9.52 | (3094) sum(n16, n9) = all_0_4_4
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n16, n9, all_0_4_4, n4 and discharging atoms sum(n16, n9) = all_0_4_4, sum(n16, n9) = n4, yields:
% 29.40/9.52 | (1009) all_0_4_4 = n4
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n7, n18, all_0_7_7, n4 and discharging atoms sum(n7, n18) = all_0_7_7, sum(n7, n18) = n4, yields:
% 29.40/9.52 | (1011) all_0_7_7 = n4
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 29.40/9.52 | (956) all_0_2_2 = n16
% 29.40/9.52 |
% 29.40/9.52 | From (956) and (2916) follows:
% 29.40/9.52 | (3098) sum(n16, n13) = all_0_0_0
% 29.40/9.52 |
% 29.40/9.52 | From (1011)(1009) and (435) follows:
% 29.40/9.52 | (1013) sum(n4, n4) = all_0_3_3
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n16, n13, all_0_0_0, n8 and discharging atoms sum(n16, n13) = all_0_0_0, sum(n16, n13) = n8, yields:
% 29.40/9.52 | (1014) all_0_0_0 = n8
% 29.40/9.52 |
% 29.40/9.52 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 29.40/9.52 | (1015) all_0_3_3 = n8
% 29.40/9.52 |
% 29.40/9.52 | Equations (1014,1015) can reduce 201 to:
% 29.40/9.52 | (746) $false
% 29.40/9.52 |
% 29.40/9.52 |-The branch is then unsatisfiable
% 29.40/9.52 |-Branch two:
% 29.40/9.52 | (963) ~ (all_0_11_11 = n8)
% 29.40/9.52 | (964) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.52 |
% 29.40/9.52 +-Applying beta-rule and splitting (964), into two cases.
% 29.40/9.52 |-Branch one:
% 29.40/9.52 | (965) all_0_11_11 = n7
% 29.40/9.52 |
% 29.40/9.52 | From (965) and (190) follows:
% 29.40/9.52 | (966) pred(n7) = all_0_9_9
% 29.40/9.53 |
% 29.40/9.53 | From (965) and (505) follows:
% 29.40/9.53 | (967) succ(n7) = all_0_5_5
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (259) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 29.40/9.53 | (968) all_0_9_9 = n6
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (184) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 29.40/9.53 | (969) all_0_5_5 = n8
% 29.40/9.53 |
% 29.40/9.53 | From (968)(969) and (156) follows:
% 29.40/9.53 | (970) sum(n6, n8) = all_0_2_2
% 29.40/9.53 |
% 29.40/9.53 | From (968) and (2914) follows:
% 29.40/9.53 | (3111) sum(n6, n18) = all_0_7_7
% 29.40/9.53 |
% 29.40/9.53 | From (969) and (2912) follows:
% 29.40/9.53 | (3112) sum(n16, n8) = all_0_4_4
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n16, n8, all_0_4_4, n3 and discharging atoms sum(n16, n8) = all_0_4_4, sum(n16, n8) = n3, yields:
% 29.40/9.53 | (1027) all_0_4_4 = n3
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n6, n18, all_0_7_7, n3 and discharging atoms sum(n6, n18) = all_0_7_7, sum(n6, n18) = n3, yields:
% 29.40/9.53 | (1029) all_0_7_7 = n3
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 29.40/9.53 | (974) all_0_2_2 = n14
% 29.40/9.53 |
% 29.40/9.53 | From (974) and (2916) follows:
% 29.40/9.53 | (3116) sum(n14, n13) = all_0_0_0
% 29.40/9.53 |
% 29.40/9.53 | From (1029)(1027) and (435) follows:
% 29.40/9.53 | (1031) sum(n3, n3) = all_0_3_3
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n14, n13, all_0_0_0, n6 and discharging atoms sum(n14, n13) = all_0_0_0, sum(n14, n13) = n6, yields:
% 29.40/9.53 | (1032) all_0_0_0 = n6
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 29.40/9.53 | (1033) all_0_3_3 = n6
% 29.40/9.53 |
% 29.40/9.53 | Equations (1032,1033) can reduce 201 to:
% 29.40/9.53 | (746) $false
% 29.40/9.53 |
% 29.40/9.53 |-The branch is then unsatisfiable
% 29.40/9.53 |-Branch two:
% 29.40/9.53 | (981) ~ (all_0_11_11 = n7)
% 29.40/9.53 | (982) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.53 |
% 29.40/9.53 +-Applying beta-rule and splitting (982), into two cases.
% 29.40/9.53 |-Branch one:
% 29.40/9.53 | (983) all_0_11_11 = n6
% 29.40/9.53 |
% 29.40/9.53 | From (983) and (190) follows:
% 29.40/9.53 | (984) pred(n6) = all_0_9_9
% 29.40/9.53 |
% 29.40/9.53 | From (983) and (505) follows:
% 29.40/9.53 | (985) succ(n6) = all_0_5_5
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (259) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 29.40/9.53 | (986) all_0_9_9 = n5
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (184) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 29.40/9.53 | (987) all_0_5_5 = n7
% 29.40/9.53 |
% 29.40/9.53 | From (986)(987) and (156) follows:
% 29.40/9.53 | (988) sum(n5, n7) = all_0_2_2
% 29.40/9.53 |
% 29.40/9.53 | From (986) and (2914) follows:
% 29.40/9.53 | (3129) sum(n5, n18) = all_0_7_7
% 29.40/9.53 |
% 29.40/9.53 | From (987) and (2912) follows:
% 29.40/9.53 | (3130) sum(n16, n7) = all_0_4_4
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n16, n7, all_0_4_4, n2 and discharging atoms sum(n16, n7) = all_0_4_4, sum(n16, n7) = n2, yields:
% 29.40/9.53 | (1045) all_0_4_4 = n2
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n5, n18, all_0_7_7, n2 and discharging atoms sum(n5, n18) = all_0_7_7, sum(n5, n18) = n2, yields:
% 29.40/9.53 | (1047) all_0_7_7 = n2
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 29.40/9.53 | (992) all_0_2_2 = n12
% 29.40/9.53 |
% 29.40/9.53 | From (992) and (2916) follows:
% 29.40/9.53 | (3134) sum(n12, n13) = all_0_0_0
% 29.40/9.53 |
% 29.40/9.53 | From (1047)(1045) and (435) follows:
% 29.40/9.53 | (1049) sum(n2, n2) = all_0_3_3
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n12, n13, all_0_0_0, n4 and discharging atoms sum(n12, n13) = all_0_0_0, sum(n12, n13) = n4, yields:
% 29.40/9.53 | (1050) all_0_0_0 = n4
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 29.40/9.53 | (1051) all_0_3_3 = n4
% 29.40/9.53 |
% 29.40/9.53 | Equations (1050,1051) can reduce 201 to:
% 29.40/9.53 | (746) $false
% 29.40/9.53 |
% 29.40/9.53 |-The branch is then unsatisfiable
% 29.40/9.53 |-Branch two:
% 29.40/9.53 | (999) ~ (all_0_11_11 = n6)
% 29.40/9.53 | (1000) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.53 |
% 29.40/9.53 +-Applying beta-rule and splitting (1000), into two cases.
% 29.40/9.53 |-Branch one:
% 29.40/9.53 | (1001) all_0_11_11 = n5
% 29.40/9.53 |
% 29.40/9.53 | From (1001) and (190) follows:
% 29.40/9.53 | (1002) pred(n5) = all_0_9_9
% 29.40/9.53 |
% 29.40/9.53 | From (1001) and (505) follows:
% 29.40/9.53 | (1003) succ(n5) = all_0_5_5
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (259) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 29.40/9.53 | (1004) all_0_9_9 = n4
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (184) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 29.40/9.53 | (1005) all_0_5_5 = n6
% 29.40/9.53 |
% 29.40/9.53 | From (1004)(1005) and (156) follows:
% 29.40/9.53 | (1006) sum(n4, n6) = all_0_2_2
% 29.40/9.53 |
% 29.40/9.53 | From (1004) and (2914) follows:
% 29.40/9.53 | (3147) sum(n4, n18) = all_0_7_7
% 29.40/9.53 |
% 29.40/9.53 | From (1005) and (2912) follows:
% 29.40/9.53 | (3148) sum(n16, n6) = all_0_4_4
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n16, n6, all_0_4_4, n1 and discharging atoms sum(n16, n6) = all_0_4_4, sum(n16, n6) = n1, yields:
% 29.40/9.53 | (1063) all_0_4_4 = n1
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n4, n18, all_0_7_7, n1 and discharging atoms sum(n4, n18) = all_0_7_7, sum(n4, n18) = n1, yields:
% 29.40/9.53 | (1065) all_0_7_7 = n1
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 29.40/9.53 | (1010) all_0_2_2 = n10
% 29.40/9.53 |
% 29.40/9.53 | From (1010) and (2916) follows:
% 29.40/9.53 | (3152) sum(n10, n13) = all_0_0_0
% 29.40/9.53 |
% 29.40/9.53 | From (1065)(1063) and (435) follows:
% 29.40/9.53 | (1067) sum(n1, n1) = all_0_3_3
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n10, n13, all_0_0_0, n2 and discharging atoms sum(n10, n13) = all_0_0_0, sum(n10, n13) = n2, yields:
% 29.40/9.53 | (1068) all_0_0_0 = n2
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 29.40/9.53 | (1069) all_0_3_3 = n2
% 29.40/9.53 |
% 29.40/9.53 | Equations (1068,1069) can reduce 201 to:
% 29.40/9.53 | (746) $false
% 29.40/9.53 |
% 29.40/9.53 |-The branch is then unsatisfiable
% 29.40/9.53 |-Branch two:
% 29.40/9.53 | (1017) ~ (all_0_11_11 = n5)
% 29.40/9.53 | (1018) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.53 |
% 29.40/9.53 +-Applying beta-rule and splitting (1018), into two cases.
% 29.40/9.53 |-Branch one:
% 29.40/9.53 | (1019) all_0_11_11 = n4
% 29.40/9.53 |
% 29.40/9.53 | From (1019) and (190) follows:
% 29.40/9.53 | (1020) pred(n4) = all_0_9_9
% 29.40/9.53 |
% 29.40/9.53 | From (1019) and (505) follows:
% 29.40/9.53 | (1021) succ(n4) = all_0_5_5
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 29.40/9.53 | (1022) all_0_9_9 = n3
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 29.40/9.53 | (1023) all_0_5_5 = n5
% 29.40/9.53 |
% 29.40/9.53 | From (1022)(1023) and (156) follows:
% 29.40/9.53 | (1024) sum(n3, n5) = all_0_2_2
% 29.40/9.53 |
% 29.40/9.53 | From (1022) and (2914) follows:
% 29.40/9.53 | (3165) sum(n3, n18) = all_0_7_7
% 29.40/9.53 |
% 29.40/9.53 | From (1023) and (2912) follows:
% 29.40/9.53 | (3166) sum(n16, n5) = all_0_4_4
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n16, n5, all_0_4_4, n0 and discharging atoms sum(n16, n5) = all_0_4_4, sum(n16, n5) = n0, yields:
% 29.40/9.53 | (1081) all_0_4_4 = n0
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n3, n18, all_0_7_7, n0 and discharging atoms sum(n3, n18) = all_0_7_7, sum(n3, n18) = n0, yields:
% 29.40/9.53 | (1083) all_0_7_7 = n0
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 29.40/9.53 | (1028) all_0_2_2 = n8
% 29.40/9.53 |
% 29.40/9.53 | From (1028) and (2916) follows:
% 29.40/9.53 | (3170) sum(n8, n13) = all_0_0_0
% 29.40/9.53 |
% 29.40/9.53 | From (1083)(1081) and (435) follows:
% 29.40/9.53 | (1085) sum(n0, n0) = all_0_3_3
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n8, n13, all_0_0_0, n0 and discharging atoms sum(n8, n13) = all_0_0_0, sum(n8, n13) = n0, yields:
% 29.40/9.53 | (1087) all_0_0_0 = n0
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 29.40/9.53 | (1088) all_0_3_3 = n0
% 29.40/9.53 |
% 29.40/9.53 | Equations (1087,1088) can reduce 201 to:
% 29.40/9.53 | (746) $false
% 29.40/9.53 |
% 29.40/9.53 |-The branch is then unsatisfiable
% 29.40/9.53 |-Branch two:
% 29.40/9.53 | (1035) ~ (all_0_11_11 = n4)
% 29.40/9.53 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.40/9.53 |
% 29.40/9.53 +-Applying beta-rule and splitting (1036), into two cases.
% 29.40/9.53 |-Branch one:
% 29.40/9.53 | (1037) all_0_11_11 = n3
% 29.40/9.53 |
% 29.40/9.53 | From (1037) and (190) follows:
% 29.40/9.53 | (1038) pred(n3) = all_0_9_9
% 29.40/9.53 |
% 29.40/9.53 | From (1037) and (505) follows:
% 29.40/9.53 | (1039) succ(n3) = all_0_5_5
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 29.40/9.53 | (1040) all_0_9_9 = n2
% 29.40/9.53 |
% 29.40/9.53 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 29.40/9.53 | (1041) all_0_5_5 = n4
% 29.40/9.53 |
% 29.40/9.53 | From (1040)(1041) and (156) follows:
% 29.40/9.54 | (1042) sum(n2, n4) = all_0_2_2
% 29.40/9.54 |
% 29.40/9.54 | From (1040) and (2914) follows:
% 29.40/9.54 | (3183) sum(n2, n18) = all_0_7_7
% 29.40/9.54 |
% 29.40/9.54 | From (1041) and (2912) follows:
% 29.40/9.54 | (3184) sum(n16, n4) = all_0_4_4
% 29.40/9.54 |
% 29.40/9.54 | Instantiating formula (194) with n16, n4, all_0_4_4, n20 and discharging atoms sum(n16, n4) = all_0_4_4, sum(n16, n4) = n20, yields:
% 29.40/9.54 | (1101) all_0_4_4 = n20
% 29.40/9.54 |
% 29.40/9.54 | Instantiating formula (194) with n2, n18, all_0_7_7, n20 and discharging atoms sum(n2, n18) = all_0_7_7, sum(n2, n18) = n20, yields:
% 29.40/9.54 | (1100) all_0_7_7 = n20
% 29.40/9.54 |
% 29.40/9.54 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 29.40/9.54 | (1046) all_0_2_2 = n6
% 29.40/9.54 |
% 29.40/9.54 | From (1046) and (2916) follows:
% 29.40/9.54 | (3188) sum(n6, n13) = all_0_0_0
% 29.40/9.54 |
% 29.40/9.54 | From (1100)(1101) and (435) follows:
% 29.40/9.54 | (1103) sum(n20, n20) = all_0_3_3
% 29.40/9.54 |
% 29.40/9.54 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 29.59/9.54 | (1104) all_0_3_3 = n19
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (194) with n6, n13, all_0_0_0, n19 and discharging atoms sum(n6, n13) = all_0_0_0, sum(n6, n13) = n19, yields:
% 29.59/9.54 | (1105) all_0_0_0 = n19
% 29.59/9.54 |
% 29.59/9.54 | Equations (1105,1104) can reduce 201 to:
% 29.59/9.54 | (746) $false
% 29.59/9.54 |
% 29.59/9.54 |-The branch is then unsatisfiable
% 29.59/9.54 |-Branch two:
% 29.59/9.54 | (1053) ~ (all_0_11_11 = n3)
% 29.59/9.54 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.59/9.54 |
% 29.59/9.54 +-Applying beta-rule and splitting (1054), into two cases.
% 29.59/9.54 |-Branch one:
% 29.59/9.54 | (1055) all_0_11_11 = n2
% 29.59/9.54 |
% 29.59/9.54 | From (1055) and (190) follows:
% 29.59/9.54 | (1056) pred(n2) = all_0_9_9
% 29.59/9.54 |
% 29.59/9.54 | From (1055) and (505) follows:
% 29.59/9.54 | (1057) succ(n2) = all_0_5_5
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 29.59/9.54 | (1058) all_0_9_9 = n1
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 29.59/9.54 | (1059) all_0_5_5 = n3
% 29.59/9.54 |
% 29.59/9.54 | From (1058)(1059) and (156) follows:
% 29.59/9.54 | (1060) sum(n1, n3) = all_0_2_2
% 29.59/9.54 |
% 29.59/9.54 | From (1058) and (2914) follows:
% 29.59/9.54 | (3201) sum(n1, n18) = all_0_7_7
% 29.59/9.54 |
% 29.59/9.54 | From (1059) and (2912) follows:
% 29.59/9.54 | (3202) sum(n16, n3) = all_0_4_4
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (194) with n16, n3, all_0_4_4, n19 and discharging atoms sum(n16, n3) = all_0_4_4, sum(n16, n3) = n19, yields:
% 29.59/9.54 | (736) all_0_4_4 = n19
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (194) with n1, n18, all_0_7_7, n19 and discharging atoms sum(n1, n18) = all_0_7_7, sum(n1, n18) = n19, yields:
% 29.59/9.54 | (737) all_0_7_7 = n19
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 29.59/9.54 | (1064) all_0_2_2 = n4
% 29.59/9.54 |
% 29.59/9.54 | From (1064) and (2916) follows:
% 29.59/9.54 | (3206) sum(n4, n13) = all_0_0_0
% 29.59/9.54 |
% 29.59/9.54 | From (737)(736) and (435) follows:
% 29.59/9.54 | (741) sum(n19, n19) = all_0_3_3
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 29.59/9.54 | (744) all_0_3_3 = n17
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (194) with n4, n13, all_0_0_0, n17 and discharging atoms sum(n4, n13) = all_0_0_0, sum(n4, n13) = n17, yields:
% 29.59/9.54 | (742) all_0_0_0 = n17
% 29.59/9.54 |
% 29.59/9.54 | Equations (742,744) can reduce 201 to:
% 29.59/9.54 | (746) $false
% 29.59/9.54 |
% 29.59/9.54 |-The branch is then unsatisfiable
% 29.59/9.54 |-Branch two:
% 29.59/9.54 | (1071) ~ (all_0_11_11 = n2)
% 29.59/9.54 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 29.59/9.54 |
% 29.59/9.54 +-Applying beta-rule and splitting (1072), into two cases.
% 29.59/9.54 |-Branch one:
% 29.59/9.54 | (1073) all_0_11_11 = n1
% 29.59/9.54 |
% 29.59/9.54 | From (1073) and (190) follows:
% 29.59/9.54 | (1074) pred(n1) = all_0_9_9
% 29.59/9.54 |
% 29.59/9.54 | From (1073) and (505) follows:
% 29.59/9.54 | (1075) succ(n1) = all_0_5_5
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 29.59/9.54 | (1076) all_0_9_9 = n0
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 29.59/9.54 | (1077) all_0_5_5 = n2
% 29.59/9.54 |
% 29.59/9.54 | From (1076)(1077) and (156) follows:
% 29.59/9.54 | (1078) sum(n0, n2) = all_0_2_2
% 29.59/9.54 |
% 29.59/9.54 | From (1076) and (2914) follows:
% 29.59/9.54 | (3219) sum(n0, n18) = all_0_7_7
% 29.59/9.54 |
% 29.59/9.54 | From (1077) and (2912) follows:
% 29.59/9.54 | (3220) sum(n16, n2) = all_0_4_4
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (194) with n16, n2, all_0_4_4, n18 and discharging atoms sum(n16, n2) = all_0_4_4, sum(n16, n2) = n18, yields:
% 29.59/9.54 | (757) all_0_4_4 = n18
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (194) with n0, n18, all_0_7_7, n18 and discharging atoms sum(n0, n18) = all_0_7_7, sum(n0, n18) = n18, yields:
% 29.59/9.54 | (759) all_0_7_7 = n18
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 29.59/9.54 | (1082) all_0_2_2 = n2
% 29.59/9.54 |
% 29.59/9.54 | From (1082) and (2916) follows:
% 29.59/9.54 | (3224) sum(n2, n13) = all_0_0_0
% 29.59/9.54 |
% 29.59/9.54 | From (759)(757) and (435) follows:
% 29.59/9.54 | (761) sum(n18, n18) = all_0_3_3
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 29.59/9.54 | (762) all_0_3_3 = n15
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (194) with n2, n13, all_0_0_0, n15 and discharging atoms sum(n2, n13) = all_0_0_0, sum(n2, n13) = n15, yields:
% 29.59/9.54 | (763) all_0_0_0 = n15
% 29.59/9.54 |
% 29.59/9.54 | Equations (763,762) can reduce 201 to:
% 29.59/9.54 | (746) $false
% 29.59/9.54 |
% 29.59/9.54 |-The branch is then unsatisfiable
% 29.59/9.54 |-Branch two:
% 29.59/9.54 | (1090) ~ (all_0_11_11 = n1)
% 29.59/9.54 | (1091) all_0_11_11 = n0
% 29.59/9.54 |
% 29.59/9.54 | From (1091) and (190) follows:
% 29.59/9.54 | (1092) pred(n0) = all_0_9_9
% 29.59/9.54 |
% 29.59/9.54 | From (1091) and (505) follows:
% 29.59/9.54 | (1093) succ(n0) = all_0_5_5
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 29.59/9.54 | (1094) all_0_9_9 = n20
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 29.59/9.54 | (1095) all_0_5_5 = n1
% 29.59/9.54 |
% 29.59/9.54 | From (1094)(1095) and (156) follows:
% 29.59/9.54 | (1096) sum(n20, n1) = all_0_2_2
% 29.59/9.54 |
% 29.59/9.54 | From (1094) and (2914) follows:
% 29.59/9.54 | (3236) sum(n20, n18) = all_0_7_7
% 29.59/9.54 |
% 29.59/9.54 | From (1095) and (2912) follows:
% 29.59/9.54 | (3237) sum(n16, n1) = all_0_4_4
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (194) with n20, n18, all_0_7_7, n17 and discharging atoms sum(n20, n18) = all_0_7_7, sum(n20, n18) = n17, yields:
% 29.59/9.54 | (777) all_0_7_7 = n17
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 29.59/9.54 | (1099) all_0_2_2 = n0
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (194) with n16, n1, all_0_4_4, n17 and discharging atoms sum(n16, n1) = all_0_4_4, sum(n16, n1) = n17, yields:
% 29.59/9.54 | (775) all_0_4_4 = n17
% 29.59/9.54 |
% 29.59/9.54 | From (1099) and (2916) follows:
% 29.59/9.54 | (3241) sum(n0, n13) = all_0_0_0
% 29.59/9.54 |
% 29.59/9.54 | From (777)(775) and (435) follows:
% 29.59/9.54 | (779) sum(n17, n17) = all_0_3_3
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 29.59/9.54 | (780) all_0_3_3 = n13
% 29.59/9.54 |
% 29.59/9.54 | Instantiating formula (194) with n0, n13, all_0_0_0, n13 and discharging atoms sum(n0, n13) = all_0_0_0, sum(n0, n13) = n13, yields:
% 29.59/9.54 | (781) all_0_0_0 = n13
% 29.59/9.54 |
% 29.59/9.54 | Equations (781,780) can reduce 201 to:
% 29.59/9.54 | (746) $false
% 29.59/9.54 |
% 29.59/9.54 |-The branch is then unsatisfiable
% 29.59/9.54 |-Branch two:
% 29.59/9.54 | (1172) ~ (all_0_10_10 = n17)
% 29.59/9.54 | (1173) all_0_10_10 = n16 | all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.59/9.54 |
% 29.59/9.54 +-Applying beta-rule and splitting (784), into two cases.
% 29.59/9.54 |-Branch one:
% 29.59/9.54 | (785) all_0_11_11 = n17
% 29.59/9.54 |
% 29.59/9.55 | From (785) and (190) follows:
% 29.59/9.55 | (786) pred(n17) = all_0_9_9
% 29.59/9.55 |
% 29.59/9.55 | From (785) and (505) follows:
% 29.59/9.55 | (787) succ(n17) = all_0_5_5
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (259) with n17, all_0_9_9, n16 and discharging atoms pred(n17) = all_0_9_9, pred(n17) = n16, yields:
% 29.59/9.55 | (788) all_0_9_9 = n16
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (184) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 29.59/9.55 | (789) all_0_5_5 = n18
% 29.59/9.55 |
% 29.59/9.55 | From (789) and (386) follows:
% 29.59/9.55 | (3253) sum(all_0_6_6, n18) = all_0_4_4
% 29.59/9.55 |
% 29.59/9.55 | From (788)(789) and (156) follows:
% 29.59/9.55 | (790) sum(n16, n18) = all_0_2_2
% 29.59/9.55 |
% 29.59/9.55 | From (788) and (74) follows:
% 29.59/9.55 | (3255) sum(n16, all_0_8_8) = all_0_7_7
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (194) with n16, n18, all_0_2_2, n13 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = n13, yields:
% 29.59/9.55 | (794) all_0_2_2 = n13
% 29.59/9.55 |
% 29.59/9.55 | From (794) and (85) follows:
% 29.59/9.55 | (3257) sum(n13, all_0_1_1) = all_0_0_0
% 29.59/9.55 |
% 29.59/9.55 +-Applying beta-rule and splitting (1173), into two cases.
% 29.59/9.55 |-Branch one:
% 29.59/9.55 | (1174) all_0_10_10 = n16
% 29.59/9.55 |
% 29.59/9.55 | From (1174) and (57) follows:
% 29.59/9.55 | (1175) pred(n16) = all_0_6_6
% 29.59/9.55 |
% 29.59/9.55 | From (1174) and (381) follows:
% 29.59/9.55 | (1176) succ(n16) = all_0_8_8
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (259) with n16, all_0_6_6, n15 and discharging atoms pred(n16) = all_0_6_6, pred(n16) = n15, yields:
% 29.59/9.55 | (1177) all_0_6_6 = n15
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (184) with n16, all_0_8_8, n17 and discharging atoms succ(n16) = all_0_8_8, succ(n16) = n17, yields:
% 29.59/9.55 | (1178) all_0_8_8 = n17
% 29.59/9.55 |
% 29.59/9.55 | From (1177)(1178) and (628) follows:
% 29.59/9.55 | (1179) sum(n15, n17) = all_0_1_1
% 29.59/9.55 |
% 29.59/9.55 | From (1177) and (3253) follows:
% 29.59/9.55 | (3264) sum(n15, n18) = all_0_4_4
% 29.59/9.55 |
% 29.59/9.55 | From (1178) and (3255) follows:
% 29.59/9.55 | (3265) sum(n16, n17) = all_0_7_7
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (194) with n16, n17, all_0_7_7, n12 and discharging atoms sum(n16, n17) = all_0_7_7, sum(n16, n17) = n12, yields:
% 29.59/9.55 | (867) all_0_7_7 = n12
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (194) with n15, n18, all_0_4_4, n12 and discharging atoms sum(n15, n18) = all_0_4_4, sum(n15, n18) = n12, yields:
% 29.59/9.55 | (865) all_0_4_4 = n12
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (194) with n15, n17, all_0_1_1, n11 and discharging atoms sum(n15, n17) = all_0_1_1, sum(n15, n17) = n11, yields:
% 29.59/9.55 | (1183) all_0_1_1 = n11
% 29.59/9.55 |
% 29.59/9.55 | From (867)(865) and (435) follows:
% 29.59/9.55 | (869) sum(n12, n12) = all_0_3_3
% 29.59/9.55 |
% 29.59/9.55 | From (1183) and (3257) follows:
% 29.59/9.55 | (3270) sum(n13, n11) = all_0_0_0
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (194) with n13, n11, all_0_0_0, n3 and discharging atoms sum(n13, n11) = all_0_0_0, sum(n13, n11) = n3, yields:
% 29.59/9.55 | (871) all_0_0_0 = n3
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 29.59/9.55 | (870) all_0_3_3 = n3
% 29.59/9.55 |
% 29.59/9.55 | Equations (871,870) can reduce 201 to:
% 29.59/9.55 | (746) $false
% 29.59/9.55 |
% 29.59/9.55 |-The branch is then unsatisfiable
% 29.59/9.55 |-Branch two:
% 29.59/9.55 | (1190) ~ (all_0_10_10 = n16)
% 29.59/9.55 | (1191) all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.59/9.55 |
% 29.59/9.55 +-Applying beta-rule and splitting (1191), into two cases.
% 29.59/9.55 |-Branch one:
% 29.59/9.55 | (1192) all_0_10_10 = n15
% 29.59/9.55 |
% 29.59/9.55 | From (1192) and (57) follows:
% 29.59/9.55 | (1193) pred(n15) = all_0_6_6
% 29.59/9.55 |
% 29.59/9.55 | From (1192) and (381) follows:
% 29.59/9.55 | (1194) succ(n15) = all_0_8_8
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (259) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 29.59/9.55 | (1195) all_0_6_6 = n14
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (184) with n15, all_0_8_8, n16 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n16, yields:
% 29.59/9.55 | (1196) all_0_8_8 = n16
% 29.59/9.55 |
% 29.59/9.55 | From (1195)(1196) and (628) follows:
% 29.59/9.55 | (1197) sum(n14, n16) = all_0_1_1
% 29.59/9.55 |
% 29.59/9.55 | From (1195) and (3253) follows:
% 29.59/9.55 | (3282) sum(n14, n18) = all_0_4_4
% 29.59/9.55 |
% 29.59/9.55 | From (1196) and (3255) follows:
% 29.59/9.55 | (3283) sum(n16, n16) = all_0_7_7
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (194) with n16, n16, all_0_7_7, n11 and discharging atoms sum(n16, n16) = all_0_7_7, sum(n16, n16) = n11, yields:
% 29.59/9.55 | (885) all_0_7_7 = n11
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (194) with n14, n18, all_0_4_4, n11 and discharging atoms sum(n14, n18) = all_0_4_4, sum(n14, n18) = n11, yields:
% 29.59/9.55 | (883) all_0_4_4 = n11
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (194) with n14, n16, all_0_1_1, n9 and discharging atoms sum(n14, n16) = all_0_1_1, sum(n14, n16) = n9, yields:
% 29.59/9.55 | (1201) all_0_1_1 = n9
% 29.59/9.55 |
% 29.59/9.55 | From (885)(883) and (435) follows:
% 29.59/9.55 | (887) sum(n11, n11) = all_0_3_3
% 29.59/9.55 |
% 29.59/9.55 | From (1201) and (3257) follows:
% 29.59/9.55 | (3288) sum(n13, n9) = all_0_0_0
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (194) with n13, n9, all_0_0_0, n1 and discharging atoms sum(n13, n9) = all_0_0_0, sum(n13, n9) = n1, yields:
% 29.59/9.55 | (889) all_0_0_0 = n1
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 29.59/9.55 | (888) all_0_3_3 = n1
% 29.59/9.55 |
% 29.59/9.55 | Equations (889,888) can reduce 201 to:
% 29.59/9.55 | (746) $false
% 29.59/9.55 |
% 29.59/9.55 |-The branch is then unsatisfiable
% 29.59/9.55 |-Branch two:
% 29.59/9.55 | (1208) ~ (all_0_10_10 = n15)
% 29.59/9.55 | (1209) all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.59/9.55 |
% 29.59/9.55 +-Applying beta-rule and splitting (1209), into two cases.
% 29.59/9.55 |-Branch one:
% 29.59/9.55 | (1210) all_0_10_10 = n14
% 29.59/9.55 |
% 29.59/9.55 | From (1210) and (57) follows:
% 29.59/9.55 | (1211) pred(n14) = all_0_6_6
% 29.59/9.55 |
% 29.59/9.55 | From (1210) and (381) follows:
% 29.59/9.55 | (1212) succ(n14) = all_0_8_8
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (259) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 29.59/9.55 | (1213) all_0_6_6 = n13
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (184) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 29.59/9.55 | (1214) all_0_8_8 = n15
% 29.59/9.55 |
% 29.59/9.55 | From (1213)(1214) and (628) follows:
% 29.59/9.55 | (1215) sum(n13, n15) = all_0_1_1
% 29.59/9.55 |
% 29.59/9.55 | From (1213) and (3253) follows:
% 29.59/9.55 | (3300) sum(n13, n18) = all_0_4_4
% 29.59/9.55 |
% 29.59/9.55 | From (1214) and (3255) follows:
% 29.59/9.55 | (3301) sum(n16, n15) = all_0_7_7
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (194) with n16, n15, all_0_7_7, n10 and discharging atoms sum(n16, n15) = all_0_7_7, sum(n16, n15) = n10, yields:
% 29.59/9.55 | (903) all_0_7_7 = n10
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (194) with n13, n18, all_0_4_4, n10 and discharging atoms sum(n13, n18) = all_0_4_4, sum(n13, n18) = n10, yields:
% 29.59/9.55 | (901) all_0_4_4 = n10
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (194) with n13, n15, all_0_1_1, n7 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n7, yields:
% 29.59/9.55 | (1219) all_0_1_1 = n7
% 29.59/9.55 |
% 29.59/9.55 | From (903)(901) and (435) follows:
% 29.59/9.55 | (905) sum(n10, n10) = all_0_3_3
% 29.59/9.55 |
% 29.59/9.55 | From (1219) and (3257) follows:
% 29.59/9.55 | (3306) sum(n13, n7) = all_0_0_0
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (194) with n13, n7, all_0_0_0, n20 and discharging atoms sum(n13, n7) = all_0_0_0, sum(n13, n7) = n20, yields:
% 29.59/9.55 | (907) all_0_0_0 = n20
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 29.59/9.55 | (906) all_0_3_3 = n20
% 29.59/9.55 |
% 29.59/9.55 | Equations (907,906) can reduce 201 to:
% 29.59/9.55 | (746) $false
% 29.59/9.55 |
% 29.59/9.55 |-The branch is then unsatisfiable
% 29.59/9.55 |-Branch two:
% 29.59/9.55 | (1226) ~ (all_0_10_10 = n14)
% 29.59/9.55 | (1227) all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.59/9.55 |
% 29.59/9.55 +-Applying beta-rule and splitting (1227), into two cases.
% 29.59/9.55 |-Branch one:
% 29.59/9.55 | (1228) all_0_10_10 = n13
% 29.59/9.55 |
% 29.59/9.55 | From (1228) and (57) follows:
% 29.59/9.55 | (1229) pred(n13) = all_0_6_6
% 29.59/9.55 |
% 29.59/9.55 | From (1228) and (381) follows:
% 29.59/9.55 | (1230) succ(n13) = all_0_8_8
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (259) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 29.59/9.55 | (1231) all_0_6_6 = n12
% 29.59/9.55 |
% 29.59/9.55 | Instantiating formula (184) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 29.59/9.55 | (1232) all_0_8_8 = n14
% 29.59/9.55 |
% 29.59/9.55 | From (1231)(1232) and (628) follows:
% 29.59/9.55 | (1233) sum(n12, n14) = all_0_1_1
% 29.59/9.55 |
% 29.59/9.55 | From (1231) and (3253) follows:
% 29.59/9.55 | (3318) sum(n12, n18) = all_0_4_4
% 29.59/9.55 |
% 29.59/9.55 | From (1232) and (3255) follows:
% 29.59/9.56 | (3319) sum(n16, n14) = all_0_7_7
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n16, n14, all_0_7_7, n9 and discharging atoms sum(n16, n14) = all_0_7_7, sum(n16, n14) = n9, yields:
% 29.59/9.56 | (921) all_0_7_7 = n9
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n12, n18, all_0_4_4, n9 and discharging atoms sum(n12, n18) = all_0_4_4, sum(n12, n18) = n9, yields:
% 29.59/9.56 | (919) all_0_4_4 = n9
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n12, n14, all_0_1_1, n5 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n5, yields:
% 29.59/9.56 | (1237) all_0_1_1 = n5
% 29.59/9.56 |
% 29.59/9.56 | From (921)(919) and (435) follows:
% 29.59/9.56 | (923) sum(n9, n9) = all_0_3_3
% 29.59/9.56 |
% 29.59/9.56 | From (1237) and (3257) follows:
% 29.59/9.56 | (3324) sum(n13, n5) = all_0_0_0
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n13, n5, all_0_0_0, n18 and discharging atoms sum(n13, n5) = all_0_0_0, sum(n13, n5) = n18, yields:
% 29.59/9.56 | (924) all_0_0_0 = n18
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 29.59/9.56 | (925) all_0_3_3 = n18
% 29.59/9.56 |
% 29.59/9.56 | Equations (924,925) can reduce 201 to:
% 29.59/9.56 | (746) $false
% 29.59/9.56 |
% 29.59/9.56 |-The branch is then unsatisfiable
% 29.59/9.56 |-Branch two:
% 29.59/9.56 | (1244) ~ (all_0_10_10 = n13)
% 29.59/9.56 | (1245) all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.59/9.56 |
% 29.59/9.56 +-Applying beta-rule and splitting (1245), into two cases.
% 29.59/9.56 |-Branch one:
% 29.59/9.56 | (1246) all_0_10_10 = n12
% 29.59/9.56 |
% 29.59/9.56 | From (1246) and (57) follows:
% 29.59/9.56 | (1247) pred(n12) = all_0_6_6
% 29.59/9.56 |
% 29.59/9.56 | From (1246) and (381) follows:
% 29.59/9.56 | (1248) succ(n12) = all_0_8_8
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (259) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 29.59/9.56 | (1249) all_0_6_6 = n11
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (184) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 29.59/9.56 | (1250) all_0_8_8 = n13
% 29.59/9.56 |
% 29.59/9.56 | From (1249)(1250) and (628) follows:
% 29.59/9.56 | (1251) sum(n11, n13) = all_0_1_1
% 29.59/9.56 |
% 29.59/9.56 | From (1249) and (3253) follows:
% 29.59/9.56 | (3336) sum(n11, n18) = all_0_4_4
% 29.59/9.56 |
% 29.59/9.56 | From (1250) and (3255) follows:
% 29.59/9.56 | (3337) sum(n16, n13) = all_0_7_7
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n16, n13, all_0_7_7, n8 and discharging atoms sum(n16, n13) = all_0_7_7, sum(n16, n13) = n8, yields:
% 29.59/9.56 | (939) all_0_7_7 = n8
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n11, n18, all_0_4_4, n8 and discharging atoms sum(n11, n18) = all_0_4_4, sum(n11, n18) = n8, yields:
% 29.59/9.56 | (937) all_0_4_4 = n8
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n11, n13, all_0_1_1, n3 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n3, yields:
% 29.59/9.56 | (1255) all_0_1_1 = n3
% 29.59/9.56 |
% 29.59/9.56 | From (939)(937) and (435) follows:
% 29.59/9.56 | (941) sum(n8, n8) = all_0_3_3
% 29.59/9.56 |
% 29.59/9.56 | From (1255) and (3257) follows:
% 29.59/9.56 | (3342) sum(n13, n3) = all_0_0_0
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n13, n3, all_0_0_0, n16 and discharging atoms sum(n13, n3) = all_0_0_0, sum(n13, n3) = n16, yields:
% 29.59/9.56 | (942) all_0_0_0 = n16
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 29.59/9.56 | (943) all_0_3_3 = n16
% 29.59/9.56 |
% 29.59/9.56 | Equations (942,943) can reduce 201 to:
% 29.59/9.56 | (746) $false
% 29.59/9.56 |
% 29.59/9.56 |-The branch is then unsatisfiable
% 29.59/9.56 |-Branch two:
% 29.59/9.56 | (1262) ~ (all_0_10_10 = n12)
% 29.59/9.56 | (1263) all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.59/9.56 |
% 29.59/9.56 +-Applying beta-rule and splitting (1263), into two cases.
% 29.59/9.56 |-Branch one:
% 29.59/9.56 | (1264) all_0_10_10 = n11
% 29.59/9.56 |
% 29.59/9.56 | From (1264) and (57) follows:
% 29.59/9.56 | (1265) pred(n11) = all_0_6_6
% 29.59/9.56 |
% 29.59/9.56 | From (1264) and (381) follows:
% 29.59/9.56 | (1266) succ(n11) = all_0_8_8
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (259) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 29.59/9.56 | (1267) all_0_6_6 = n10
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (184) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 29.59/9.56 | (1268) all_0_8_8 = n12
% 29.59/9.56 |
% 29.59/9.56 | From (1267)(1268) and (628) follows:
% 29.59/9.56 | (1269) sum(n10, n12) = all_0_1_1
% 29.59/9.56 |
% 29.59/9.56 | From (1267) and (3253) follows:
% 29.59/9.56 | (3354) sum(n10, n18) = all_0_4_4
% 29.59/9.56 |
% 29.59/9.56 | From (1268) and (3255) follows:
% 29.59/9.56 | (3355) sum(n16, n12) = all_0_7_7
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n16, n12, all_0_7_7, n7 and discharging atoms sum(n16, n12) = all_0_7_7, sum(n16, n12) = n7, yields:
% 29.59/9.56 | (957) all_0_7_7 = n7
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n10, n18, all_0_4_4, n7 and discharging atoms sum(n10, n18) = all_0_4_4, sum(n10, n18) = n7, yields:
% 29.59/9.56 | (955) all_0_4_4 = n7
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n10, n12, all_0_1_1, n1 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n1, yields:
% 29.59/9.56 | (1273) all_0_1_1 = n1
% 29.59/9.56 |
% 29.59/9.56 | From (957)(955) and (435) follows:
% 29.59/9.56 | (959) sum(n7, n7) = all_0_3_3
% 29.59/9.56 |
% 29.59/9.56 | From (1273) and (3257) follows:
% 29.59/9.56 | (3360) sum(n13, n1) = all_0_0_0
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n13, n1, all_0_0_0, n14 and discharging atoms sum(n13, n1) = all_0_0_0, sum(n13, n1) = n14, yields:
% 29.59/9.56 | (960) all_0_0_0 = n14
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 29.59/9.56 | (961) all_0_3_3 = n14
% 29.59/9.56 |
% 29.59/9.56 | Equations (960,961) can reduce 201 to:
% 29.59/9.56 | (746) $false
% 29.59/9.56 |
% 29.59/9.56 |-The branch is then unsatisfiable
% 29.59/9.56 |-Branch two:
% 29.59/9.56 | (1280) ~ (all_0_10_10 = n11)
% 29.59/9.56 | (1281) all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.59/9.56 |
% 29.59/9.56 +-Applying beta-rule and splitting (1281), into two cases.
% 29.59/9.56 |-Branch one:
% 29.59/9.56 | (1282) all_0_10_10 = n10
% 29.59/9.56 |
% 29.59/9.56 | From (1282) and (57) follows:
% 29.59/9.56 | (1283) pred(n10) = all_0_6_6
% 29.59/9.56 |
% 29.59/9.56 | From (1282) and (381) follows:
% 29.59/9.56 | (1284) succ(n10) = all_0_8_8
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (259) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 29.59/9.56 | (1285) all_0_6_6 = n9
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (184) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 29.59/9.56 | (1286) all_0_8_8 = n11
% 29.59/9.56 |
% 29.59/9.56 | From (1285)(1286) and (628) follows:
% 29.59/9.56 | (1287) sum(n9, n11) = all_0_1_1
% 29.59/9.56 |
% 29.59/9.56 | From (1285) and (3253) follows:
% 29.59/9.56 | (3372) sum(n9, n18) = all_0_4_4
% 29.59/9.56 |
% 29.59/9.56 | From (1286) and (3255) follows:
% 29.59/9.56 | (3373) sum(n16, n11) = all_0_7_7
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n16, n11, all_0_7_7, n6 and discharging atoms sum(n16, n11) = all_0_7_7, sum(n16, n11) = n6, yields:
% 29.59/9.56 | (975) all_0_7_7 = n6
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n9, n18, all_0_4_4, n6 and discharging atoms sum(n9, n18) = all_0_4_4, sum(n9, n18) = n6, yields:
% 29.59/9.56 | (973) all_0_4_4 = n6
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 29.59/9.56 | (1291) all_0_1_1 = n20
% 29.59/9.56 |
% 29.59/9.56 | From (975)(973) and (435) follows:
% 29.59/9.56 | (977) sum(n6, n6) = all_0_3_3
% 29.59/9.56 |
% 29.59/9.56 | From (1291) and (3257) follows:
% 29.59/9.56 | (3378) sum(n13, n20) = all_0_0_0
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n13, n20, all_0_0_0, n12 and discharging atoms sum(n13, n20) = all_0_0_0, sum(n13, n20) = n12, yields:
% 29.59/9.56 | (978) all_0_0_0 = n12
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 29.59/9.56 | (979) all_0_3_3 = n12
% 29.59/9.56 |
% 29.59/9.56 | Equations (978,979) can reduce 201 to:
% 29.59/9.56 | (746) $false
% 29.59/9.56 |
% 29.59/9.56 |-The branch is then unsatisfiable
% 29.59/9.56 |-Branch two:
% 29.59/9.56 | (1298) ~ (all_0_10_10 = n10)
% 29.59/9.56 | (1299) all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.59/9.56 |
% 29.59/9.56 +-Applying beta-rule and splitting (1299), into two cases.
% 29.59/9.56 |-Branch one:
% 29.59/9.56 | (1300) all_0_10_10 = n9
% 29.59/9.56 |
% 29.59/9.56 | From (1300) and (57) follows:
% 29.59/9.56 | (1301) pred(n9) = all_0_6_6
% 29.59/9.56 |
% 29.59/9.56 | From (1300) and (381) follows:
% 29.59/9.56 | (1302) succ(n9) = all_0_8_8
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (259) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 29.59/9.56 | (1303) all_0_6_6 = n8
% 29.59/9.56 |
% 29.59/9.56 | Instantiating formula (184) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 29.59/9.56 | (1304) all_0_8_8 = n10
% 29.59/9.56 |
% 29.59/9.56 | From (1303)(1304) and (628) follows:
% 29.59/9.56 | (1305) sum(n8, n10) = all_0_1_1
% 29.59/9.56 |
% 29.59/9.56 | From (1303) and (3253) follows:
% 29.59/9.57 | (3390) sum(n8, n18) = all_0_4_4
% 29.59/9.57 |
% 29.59/9.57 | From (1304) and (3255) follows:
% 29.59/9.57 | (3391) sum(n16, n10) = all_0_7_7
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n16, n10, all_0_7_7, n5 and discharging atoms sum(n16, n10) = all_0_7_7, sum(n16, n10) = n5, yields:
% 29.59/9.57 | (993) all_0_7_7 = n5
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n8, n18, all_0_4_4, n5 and discharging atoms sum(n8, n18) = all_0_4_4, sum(n8, n18) = n5, yields:
% 29.59/9.57 | (991) all_0_4_4 = n5
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 29.59/9.57 | (1309) all_0_1_1 = n18
% 29.59/9.57 |
% 29.59/9.57 | From (993)(991) and (435) follows:
% 29.59/9.57 | (995) sum(n5, n5) = all_0_3_3
% 29.59/9.57 |
% 29.59/9.57 | From (1309) and (3257) follows:
% 29.59/9.57 | (3396) sum(n13, n18) = all_0_0_0
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n13, n18, all_0_0_0, n10 and discharging atoms sum(n13, n18) = all_0_0_0, sum(n13, n18) = n10, yields:
% 29.59/9.57 | (996) all_0_0_0 = n10
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 29.59/9.57 | (997) all_0_3_3 = n10
% 29.59/9.57 |
% 29.59/9.57 | Equations (996,997) can reduce 201 to:
% 29.59/9.57 | (746) $false
% 29.59/9.57 |
% 29.59/9.57 |-The branch is then unsatisfiable
% 29.59/9.57 |-Branch two:
% 29.59/9.57 | (1316) ~ (all_0_10_10 = n9)
% 29.59/9.57 | (1317) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.59/9.57 |
% 29.59/9.57 +-Applying beta-rule and splitting (1317), into two cases.
% 29.59/9.57 |-Branch one:
% 29.59/9.57 | (1318) all_0_10_10 = n8
% 29.59/9.57 |
% 29.59/9.57 | From (1318) and (57) follows:
% 29.59/9.57 | (1319) pred(n8) = all_0_6_6
% 29.59/9.57 |
% 29.59/9.57 | From (1318) and (381) follows:
% 29.59/9.57 | (1320) succ(n8) = all_0_8_8
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (259) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 29.59/9.57 | (1321) all_0_6_6 = n7
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (184) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 29.59/9.57 | (1322) all_0_8_8 = n9
% 29.59/9.57 |
% 29.59/9.57 | From (1321)(1322) and (628) follows:
% 29.59/9.57 | (1323) sum(n7, n9) = all_0_1_1
% 29.59/9.57 |
% 29.59/9.57 | From (1321) and (3253) follows:
% 29.59/9.57 | (3408) sum(n7, n18) = all_0_4_4
% 29.59/9.57 |
% 29.59/9.57 | From (1322) and (3255) follows:
% 29.59/9.57 | (3409) sum(n16, n9) = all_0_7_7
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n16, n9, all_0_7_7, n4 and discharging atoms sum(n16, n9) = all_0_7_7, sum(n16, n9) = n4, yields:
% 29.59/9.57 | (1011) all_0_7_7 = n4
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n7, n18, all_0_4_4, n4 and discharging atoms sum(n7, n18) = all_0_4_4, sum(n7, n18) = n4, yields:
% 29.59/9.57 | (1009) all_0_4_4 = n4
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 29.59/9.57 | (1327) all_0_1_1 = n16
% 29.59/9.57 |
% 29.59/9.57 | From (1011)(1009) and (435) follows:
% 29.59/9.57 | (1013) sum(n4, n4) = all_0_3_3
% 29.59/9.57 |
% 29.59/9.57 | From (1327) and (3257) follows:
% 29.59/9.57 | (3414) sum(n13, n16) = all_0_0_0
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n13, n16, all_0_0_0, n8 and discharging atoms sum(n13, n16) = all_0_0_0, sum(n13, n16) = n8, yields:
% 29.59/9.57 | (1014) all_0_0_0 = n8
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 29.59/9.57 | (1015) all_0_3_3 = n8
% 29.59/9.57 |
% 29.59/9.57 | Equations (1014,1015) can reduce 201 to:
% 29.59/9.57 | (746) $false
% 29.59/9.57 |
% 29.59/9.57 |-The branch is then unsatisfiable
% 29.59/9.57 |-Branch two:
% 29.59/9.57 | (1334) ~ (all_0_10_10 = n8)
% 29.59/9.57 | (1335) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.59/9.57 |
% 29.59/9.57 +-Applying beta-rule and splitting (1335), into two cases.
% 29.59/9.57 |-Branch one:
% 29.59/9.57 | (1336) all_0_10_10 = n7
% 29.59/9.57 |
% 29.59/9.57 | From (1336) and (57) follows:
% 29.59/9.57 | (1337) pred(n7) = all_0_6_6
% 29.59/9.57 |
% 29.59/9.57 | From (1336) and (381) follows:
% 29.59/9.57 | (1338) succ(n7) = all_0_8_8
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (259) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 29.59/9.57 | (1339) all_0_6_6 = n6
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (184) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 29.59/9.57 | (1340) all_0_8_8 = n8
% 29.59/9.57 |
% 29.59/9.57 | From (1339)(1340) and (628) follows:
% 29.59/9.57 | (1341) sum(n6, n8) = all_0_1_1
% 29.59/9.57 |
% 29.59/9.57 | From (1339) and (3253) follows:
% 29.59/9.57 | (3426) sum(n6, n18) = all_0_4_4
% 29.59/9.57 |
% 29.59/9.57 | From (1340) and (3255) follows:
% 29.59/9.57 | (3427) sum(n16, n8) = all_0_7_7
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n16, n8, all_0_7_7, n3 and discharging atoms sum(n16, n8) = all_0_7_7, sum(n16, n8) = n3, yields:
% 29.59/9.57 | (1029) all_0_7_7 = n3
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n6, n18, all_0_4_4, n3 and discharging atoms sum(n6, n18) = all_0_4_4, sum(n6, n18) = n3, yields:
% 29.59/9.57 | (1027) all_0_4_4 = n3
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 29.59/9.57 | (1345) all_0_1_1 = n14
% 29.59/9.57 |
% 29.59/9.57 | From (1029)(1027) and (435) follows:
% 29.59/9.57 | (1031) sum(n3, n3) = all_0_3_3
% 29.59/9.57 |
% 29.59/9.57 | From (1345) and (3257) follows:
% 29.59/9.57 | (3432) sum(n13, n14) = all_0_0_0
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n13, n14, all_0_0_0, n6 and discharging atoms sum(n13, n14) = all_0_0_0, sum(n13, n14) = n6, yields:
% 29.59/9.57 | (1032) all_0_0_0 = n6
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 29.59/9.57 | (1033) all_0_3_3 = n6
% 29.59/9.57 |
% 29.59/9.57 | Equations (1032,1033) can reduce 201 to:
% 29.59/9.57 | (746) $false
% 29.59/9.57 |
% 29.59/9.57 |-The branch is then unsatisfiable
% 29.59/9.57 |-Branch two:
% 29.59/9.57 | (1352) ~ (all_0_10_10 = n7)
% 29.59/9.57 | (1353) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.59/9.57 |
% 29.59/9.57 +-Applying beta-rule and splitting (1353), into two cases.
% 29.59/9.57 |-Branch one:
% 29.59/9.57 | (1354) all_0_10_10 = n6
% 29.59/9.57 |
% 29.59/9.57 | From (1354) and (57) follows:
% 29.59/9.57 | (1355) pred(n6) = all_0_6_6
% 29.59/9.57 |
% 29.59/9.57 | From (1354) and (381) follows:
% 29.59/9.57 | (1356) succ(n6) = all_0_8_8
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (259) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 29.59/9.57 | (1357) all_0_6_6 = n5
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (184) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 29.59/9.57 | (1358) all_0_8_8 = n7
% 29.59/9.57 |
% 29.59/9.57 | From (1357)(1358) and (628) follows:
% 29.59/9.57 | (1359) sum(n5, n7) = all_0_1_1
% 29.59/9.57 |
% 29.59/9.57 | From (1357) and (3253) follows:
% 29.59/9.57 | (3444) sum(n5, n18) = all_0_4_4
% 29.59/9.57 |
% 29.59/9.57 | From (1358) and (3255) follows:
% 29.59/9.57 | (3445) sum(n16, n7) = all_0_7_7
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n16, n7, all_0_7_7, n2 and discharging atoms sum(n16, n7) = all_0_7_7, sum(n16, n7) = n2, yields:
% 29.59/9.57 | (1047) all_0_7_7 = n2
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n5, n18, all_0_4_4, n2 and discharging atoms sum(n5, n18) = all_0_4_4, sum(n5, n18) = n2, yields:
% 29.59/9.57 | (1045) all_0_4_4 = n2
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 29.59/9.57 | (1363) all_0_1_1 = n12
% 29.59/9.57 |
% 29.59/9.57 | From (1047)(1045) and (435) follows:
% 29.59/9.57 | (1049) sum(n2, n2) = all_0_3_3
% 29.59/9.57 |
% 29.59/9.57 | From (1363) and (3257) follows:
% 29.59/9.57 | (3450) sum(n13, n12) = all_0_0_0
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n13, n12, all_0_0_0, n4 and discharging atoms sum(n13, n12) = all_0_0_0, sum(n13, n12) = n4, yields:
% 29.59/9.57 | (1050) all_0_0_0 = n4
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 29.59/9.57 | (1051) all_0_3_3 = n4
% 29.59/9.57 |
% 29.59/9.57 | Equations (1050,1051) can reduce 201 to:
% 29.59/9.57 | (746) $false
% 29.59/9.57 |
% 29.59/9.57 |-The branch is then unsatisfiable
% 29.59/9.57 |-Branch two:
% 29.59/9.57 | (1370) ~ (all_0_10_10 = n6)
% 29.59/9.57 | (1371) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.59/9.57 |
% 29.59/9.57 +-Applying beta-rule and splitting (1371), into two cases.
% 29.59/9.57 |-Branch one:
% 29.59/9.57 | (1372) all_0_10_10 = n5
% 29.59/9.57 |
% 29.59/9.57 | From (1372) and (57) follows:
% 29.59/9.57 | (1373) pred(n5) = all_0_6_6
% 29.59/9.57 |
% 29.59/9.57 | From (1372) and (381) follows:
% 29.59/9.57 | (1374) succ(n5) = all_0_8_8
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (259) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 29.59/9.57 | (1375) all_0_6_6 = n4
% 29.59/9.57 |
% 29.59/9.57 | Instantiating formula (184) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 29.59/9.58 | (1376) all_0_8_8 = n6
% 29.59/9.58 |
% 29.59/9.58 | From (1375)(1376) and (628) follows:
% 29.59/9.58 | (1377) sum(n4, n6) = all_0_1_1
% 29.59/9.58 |
% 29.59/9.58 | From (1375) and (3253) follows:
% 29.59/9.58 | (3462) sum(n4, n18) = all_0_4_4
% 29.59/9.58 |
% 29.59/9.58 | From (1376) and (3255) follows:
% 29.59/9.58 | (3463) sum(n16, n6) = all_0_7_7
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n16, n6, all_0_7_7, n1 and discharging atoms sum(n16, n6) = all_0_7_7, sum(n16, n6) = n1, yields:
% 29.59/9.58 | (1065) all_0_7_7 = n1
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n4, n18, all_0_4_4, n1 and discharging atoms sum(n4, n18) = all_0_4_4, sum(n4, n18) = n1, yields:
% 29.59/9.58 | (1063) all_0_4_4 = n1
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 29.59/9.58 | (1381) all_0_1_1 = n10
% 29.59/9.58 |
% 29.59/9.58 | From (1065)(1063) and (435) follows:
% 29.59/9.58 | (1067) sum(n1, n1) = all_0_3_3
% 29.59/9.58 |
% 29.59/9.58 | From (1381) and (3257) follows:
% 29.59/9.58 | (3468) sum(n13, n10) = all_0_0_0
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n13, n10, all_0_0_0, n2 and discharging atoms sum(n13, n10) = all_0_0_0, sum(n13, n10) = n2, yields:
% 29.59/9.58 | (1068) all_0_0_0 = n2
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 29.59/9.58 | (1069) all_0_3_3 = n2
% 29.59/9.58 |
% 29.59/9.58 | Equations (1068,1069) can reduce 201 to:
% 29.59/9.58 | (746) $false
% 29.59/9.58 |
% 29.59/9.58 |-The branch is then unsatisfiable
% 29.59/9.58 |-Branch two:
% 29.59/9.58 | (1388) ~ (all_0_10_10 = n5)
% 29.59/9.58 | (1389) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.59/9.58 |
% 29.59/9.58 +-Applying beta-rule and splitting (1389), into two cases.
% 29.59/9.58 |-Branch one:
% 29.59/9.58 | (1390) all_0_10_10 = n4
% 29.59/9.58 |
% 29.59/9.58 | From (1390) and (57) follows:
% 29.59/9.58 | (1391) pred(n4) = all_0_6_6
% 29.59/9.58 |
% 29.59/9.58 | From (1390) and (381) follows:
% 29.59/9.58 | (1392) succ(n4) = all_0_8_8
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (259) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 29.59/9.58 | (1393) all_0_6_6 = n3
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (184) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 29.59/9.58 | (1394) all_0_8_8 = n5
% 29.59/9.58 |
% 29.59/9.58 | From (1393)(1394) and (628) follows:
% 29.59/9.58 | (1395) sum(n3, n5) = all_0_1_1
% 29.59/9.58 |
% 29.59/9.58 | From (1393) and (3253) follows:
% 29.59/9.58 | (3480) sum(n3, n18) = all_0_4_4
% 29.59/9.58 |
% 29.59/9.58 | From (1394) and (3255) follows:
% 29.59/9.58 | (3481) sum(n16, n5) = all_0_7_7
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n16, n5, all_0_7_7, n0 and discharging atoms sum(n16, n5) = all_0_7_7, sum(n16, n5) = n0, yields:
% 29.59/9.58 | (1083) all_0_7_7 = n0
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n3, n18, all_0_4_4, n0 and discharging atoms sum(n3, n18) = all_0_4_4, sum(n3, n18) = n0, yields:
% 29.59/9.58 | (1081) all_0_4_4 = n0
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 29.59/9.58 | (1399) all_0_1_1 = n8
% 29.59/9.58 |
% 29.59/9.58 | From (1083)(1081) and (435) follows:
% 29.59/9.58 | (1085) sum(n0, n0) = all_0_3_3
% 29.59/9.58 |
% 29.59/9.58 | From (1399) and (3257) follows:
% 29.59/9.58 | (3486) sum(n13, n8) = all_0_0_0
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n13, n8, all_0_0_0, n0 and discharging atoms sum(n13, n8) = all_0_0_0, sum(n13, n8) = n0, yields:
% 29.59/9.58 | (1087) all_0_0_0 = n0
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 29.59/9.58 | (1088) all_0_3_3 = n0
% 29.59/9.58 |
% 29.59/9.58 | Equations (1087,1088) can reduce 201 to:
% 29.59/9.58 | (746) $false
% 29.59/9.58 |
% 29.59/9.58 |-The branch is then unsatisfiable
% 29.59/9.58 |-Branch two:
% 29.59/9.58 | (1406) ~ (all_0_10_10 = n4)
% 29.59/9.58 | (1407) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.59/9.58 |
% 29.59/9.58 +-Applying beta-rule and splitting (1407), into two cases.
% 29.59/9.58 |-Branch one:
% 29.59/9.58 | (1408) all_0_10_10 = n3
% 29.59/9.58 |
% 29.59/9.58 | From (1408) and (57) follows:
% 29.59/9.58 | (1409) pred(n3) = all_0_6_6
% 29.59/9.58 |
% 29.59/9.58 | From (1408) and (381) follows:
% 29.59/9.58 | (1410) succ(n3) = all_0_8_8
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 29.59/9.58 | (1411) all_0_6_6 = n2
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 29.59/9.58 | (1412) all_0_8_8 = n4
% 29.59/9.58 |
% 29.59/9.58 | From (1411)(1412) and (628) follows:
% 29.59/9.58 | (1413) sum(n2, n4) = all_0_1_1
% 29.59/9.58 |
% 29.59/9.58 | From (1411) and (3253) follows:
% 29.59/9.58 | (3498) sum(n2, n18) = all_0_4_4
% 29.59/9.58 |
% 29.59/9.58 | From (1412) and (3255) follows:
% 29.59/9.58 | (3499) sum(n16, n4) = all_0_7_7
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n16, n4, all_0_7_7, n20 and discharging atoms sum(n16, n4) = all_0_7_7, sum(n16, n4) = n20, yields:
% 29.59/9.58 | (1100) all_0_7_7 = n20
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n2, n18, all_0_4_4, n20 and discharging atoms sum(n2, n18) = all_0_4_4, sum(n2, n18) = n20, yields:
% 29.59/9.58 | (1101) all_0_4_4 = n20
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 29.59/9.58 | (1417) all_0_1_1 = n6
% 29.59/9.58 |
% 29.59/9.58 | From (1100)(1101) and (435) follows:
% 29.59/9.58 | (1103) sum(n20, n20) = all_0_3_3
% 29.59/9.58 |
% 29.59/9.58 | From (1417) and (3257) follows:
% 29.59/9.58 | (3504) sum(n13, n6) = all_0_0_0
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 29.59/9.58 | (1104) all_0_3_3 = n19
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n13, n6, all_0_0_0, n19 and discharging atoms sum(n13, n6) = all_0_0_0, sum(n13, n6) = n19, yields:
% 29.59/9.58 | (1105) all_0_0_0 = n19
% 29.59/9.58 |
% 29.59/9.58 | Equations (1105,1104) can reduce 201 to:
% 29.59/9.58 | (746) $false
% 29.59/9.58 |
% 29.59/9.58 |-The branch is then unsatisfiable
% 29.59/9.58 |-Branch two:
% 29.59/9.58 | (1424) ~ (all_0_10_10 = n3)
% 29.59/9.58 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.59/9.58 |
% 29.59/9.58 +-Applying beta-rule and splitting (1425), into two cases.
% 29.59/9.58 |-Branch one:
% 29.59/9.58 | (1426) all_0_10_10 = n2
% 29.59/9.58 |
% 29.59/9.58 | From (1426) and (57) follows:
% 29.59/9.58 | (1427) pred(n2) = all_0_6_6
% 29.59/9.58 |
% 29.59/9.58 | From (1426) and (381) follows:
% 29.59/9.58 | (1428) succ(n2) = all_0_8_8
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 29.59/9.58 | (1429) all_0_6_6 = n1
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 29.59/9.58 | (1430) all_0_8_8 = n3
% 29.59/9.58 |
% 29.59/9.58 | From (1429)(1430) and (628) follows:
% 29.59/9.58 | (1431) sum(n1, n3) = all_0_1_1
% 29.59/9.58 |
% 29.59/9.58 | From (1429) and (3253) follows:
% 29.59/9.58 | (3516) sum(n1, n18) = all_0_4_4
% 29.59/9.58 |
% 29.59/9.58 | From (1430) and (3255) follows:
% 29.59/9.58 | (3517) sum(n16, n3) = all_0_7_7
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n16, n3, all_0_7_7, n19 and discharging atoms sum(n16, n3) = all_0_7_7, sum(n16, n3) = n19, yields:
% 29.59/9.58 | (737) all_0_7_7 = n19
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n1, n18, all_0_4_4, n19 and discharging atoms sum(n1, n18) = all_0_4_4, sum(n1, n18) = n19, yields:
% 29.59/9.58 | (736) all_0_4_4 = n19
% 29.59/9.58 |
% 29.59/9.58 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 29.59/9.58 | (1435) all_0_1_1 = n4
% 29.59/9.58 |
% 29.59/9.58 | From (737)(736) and (435) follows:
% 29.59/9.58 | (741) sum(n19, n19) = all_0_3_3
% 29.59/9.58 |
% 29.59/9.58 | From (1435) and (3257) follows:
% 29.59/9.58 | (3522) sum(n13, n4) = all_0_0_0
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 29.59/9.59 | (744) all_0_3_3 = n17
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (194) with n13, n4, all_0_0_0, n17 and discharging atoms sum(n13, n4) = all_0_0_0, sum(n13, n4) = n17, yields:
% 29.59/9.59 | (742) all_0_0_0 = n17
% 29.59/9.59 |
% 29.59/9.59 | Equations (742,744) can reduce 201 to:
% 29.59/9.59 | (746) $false
% 29.59/9.59 |
% 29.59/9.59 |-The branch is then unsatisfiable
% 29.59/9.59 |-Branch two:
% 29.59/9.59 | (1442) ~ (all_0_10_10 = n2)
% 29.59/9.59 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 29.59/9.59 |
% 29.59/9.59 +-Applying beta-rule and splitting (1443), into two cases.
% 29.59/9.59 |-Branch one:
% 29.59/9.59 | (1444) all_0_10_10 = n1
% 29.59/9.59 |
% 29.59/9.59 | From (1444) and (57) follows:
% 29.59/9.59 | (1445) pred(n1) = all_0_6_6
% 29.59/9.59 |
% 29.59/9.59 | From (1444) and (381) follows:
% 29.59/9.59 | (1446) succ(n1) = all_0_8_8
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 29.59/9.59 | (1447) all_0_6_6 = n0
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 29.59/9.59 | (1448) all_0_8_8 = n2
% 29.59/9.59 |
% 29.59/9.59 | From (1447)(1448) and (628) follows:
% 29.59/9.59 | (1449) sum(n0, n2) = all_0_1_1
% 29.59/9.59 |
% 29.59/9.59 | From (1447) and (3253) follows:
% 29.59/9.59 | (3534) sum(n0, n18) = all_0_4_4
% 29.59/9.59 |
% 29.59/9.59 | From (1448) and (3255) follows:
% 29.59/9.59 | (3535) sum(n16, n2) = all_0_7_7
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (194) with n16, n2, all_0_7_7, n18 and discharging atoms sum(n16, n2) = all_0_7_7, sum(n16, n2) = n18, yields:
% 29.59/9.59 | (759) all_0_7_7 = n18
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (194) with n0, n18, all_0_4_4, n18 and discharging atoms sum(n0, n18) = all_0_4_4, sum(n0, n18) = n18, yields:
% 29.59/9.59 | (757) all_0_4_4 = n18
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 29.59/9.59 | (1453) all_0_1_1 = n2
% 29.59/9.59 |
% 29.59/9.59 | From (759)(757) and (435) follows:
% 29.59/9.59 | (761) sum(n18, n18) = all_0_3_3
% 29.59/9.59 |
% 29.59/9.59 | From (1453) and (3257) follows:
% 29.59/9.59 | (3540) sum(n13, n2) = all_0_0_0
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 29.59/9.59 | (762) all_0_3_3 = n15
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (194) with n13, n2, all_0_0_0, n15 and discharging atoms sum(n13, n2) = all_0_0_0, sum(n13, n2) = n15, yields:
% 29.59/9.59 | (763) all_0_0_0 = n15
% 29.59/9.59 |
% 29.59/9.59 | Equations (763,762) can reduce 201 to:
% 29.59/9.59 | (746) $false
% 29.59/9.59 |
% 29.59/9.59 |-The branch is then unsatisfiable
% 29.59/9.59 |-Branch two:
% 29.59/9.59 | (1462) ~ (all_0_10_10 = n1)
% 29.59/9.59 | (1463) all_0_10_10 = n0
% 29.59/9.59 |
% 29.59/9.59 | From (1463) and (57) follows:
% 29.59/9.59 | (1464) pred(n0) = all_0_6_6
% 29.59/9.59 |
% 29.59/9.59 | From (1463) and (381) follows:
% 29.59/9.59 | (1465) succ(n0) = all_0_8_8
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 29.59/9.59 | (1466) all_0_6_6 = n20
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 29.59/9.59 | (1467) all_0_8_8 = n1
% 29.59/9.59 |
% 29.59/9.59 | From (1466)(1467) and (628) follows:
% 29.59/9.59 | (1468) sum(n20, n1) = all_0_1_1
% 29.59/9.59 |
% 29.59/9.59 | From (1466) and (3253) follows:
% 29.59/9.59 | (3551) sum(n20, n18) = all_0_4_4
% 29.59/9.59 |
% 29.59/9.59 | From (1467) and (3255) follows:
% 29.59/9.59 | (3552) sum(n16, n1) = all_0_7_7
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (194) with n20, n18, all_0_4_4, n17 and discharging atoms sum(n20, n18) = all_0_4_4, sum(n20, n18) = n17, yields:
% 29.59/9.59 | (775) all_0_4_4 = n17
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 29.59/9.59 | (1471) all_0_1_1 = n0
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (194) with n16, n1, all_0_7_7, n17 and discharging atoms sum(n16, n1) = all_0_7_7, sum(n16, n1) = n17, yields:
% 29.59/9.59 | (777) all_0_7_7 = n17
% 29.59/9.59 |
% 29.59/9.59 | From (777)(775) and (435) follows:
% 29.59/9.59 | (779) sum(n17, n17) = all_0_3_3
% 29.59/9.59 |
% 29.59/9.59 | From (1471) and (3257) follows:
% 29.59/9.59 | (3557) sum(n13, n0) = all_0_0_0
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 29.59/9.59 | (780) all_0_3_3 = n13
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (194) with n13, n0, all_0_0_0, n13 and discharging atoms sum(n13, n0) = all_0_0_0, sum(n13, n0) = n13, yields:
% 29.59/9.59 | (781) all_0_0_0 = n13
% 29.59/9.59 |
% 29.59/9.59 | Equations (781,780) can reduce 201 to:
% 29.59/9.59 | (746) $false
% 29.59/9.59 |
% 29.59/9.59 |-The branch is then unsatisfiable
% 29.59/9.59 |-Branch two:
% 29.59/9.59 | (801) ~ (all_0_11_11 = n17)
% 29.59/9.59 | (802) all_0_11_11 = n16 | all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.59/9.59 |
% 29.59/9.59 +-Applying beta-rule and splitting (1173), into two cases.
% 29.59/9.59 |-Branch one:
% 29.59/9.59 | (1174) all_0_10_10 = n16
% 29.59/9.59 |
% 29.59/9.59 | From (1174) and (57) follows:
% 29.59/9.59 | (1175) pred(n16) = all_0_6_6
% 29.59/9.59 |
% 29.59/9.59 | From (1174) and (381) follows:
% 29.59/9.59 | (1176) succ(n16) = all_0_8_8
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (259) with n16, all_0_6_6, n15 and discharging atoms pred(n16) = all_0_6_6, pred(n16) = n15, yields:
% 29.59/9.59 | (1177) all_0_6_6 = n15
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (184) with n16, all_0_8_8, n17 and discharging atoms succ(n16) = all_0_8_8, succ(n16) = n17, yields:
% 29.59/9.59 | (1178) all_0_8_8 = n17
% 29.59/9.59 |
% 29.59/9.59 | From (1177) and (1175) follows:
% 29.59/9.59 | (214) pred(n16) = n15
% 29.59/9.59 |
% 29.59/9.59 | From (1178) and (1176) follows:
% 29.59/9.59 | (603) succ(n16) = n17
% 29.59/9.59 |
% 29.59/9.59 | From (1177) and (386) follows:
% 29.59/9.59 | (3570) sum(n15, all_0_5_5) = all_0_4_4
% 29.59/9.59 |
% 29.59/9.59 | From (1177)(1178) and (628) follows:
% 29.59/9.59 | (1179) sum(n15, n17) = all_0_1_1
% 29.59/9.59 |
% 29.59/9.59 | From (1178) and (74) follows:
% 29.59/9.59 | (3572) sum(all_0_9_9, n17) = all_0_7_7
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (194) with n15, n17, all_0_1_1, n11 and discharging atoms sum(n15, n17) = all_0_1_1, sum(n15, n17) = n11, yields:
% 29.59/9.59 | (1183) all_0_1_1 = n11
% 29.59/9.59 |
% 29.59/9.59 | From (1183) and (85) follows:
% 29.59/9.59 | (3574) sum(all_0_2_2, n11) = all_0_0_0
% 29.59/9.59 |
% 29.59/9.59 | From (1183) and (1179) follows:
% 29.59/9.59 | (157) sum(n15, n17) = n11
% 29.59/9.59 |
% 29.59/9.59 +-Applying beta-rule and splitting (802), into two cases.
% 29.59/9.59 |-Branch one:
% 29.59/9.59 | (803) all_0_11_11 = n16
% 29.59/9.59 |
% 29.59/9.59 | From (803) and (190) follows:
% 29.59/9.59 | (804) pred(n16) = all_0_9_9
% 29.59/9.59 |
% 29.59/9.59 | From (803) and (505) follows:
% 29.59/9.59 | (805) succ(n16) = all_0_5_5
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (259) with n16, all_0_9_9, n15 and discharging atoms pred(n16) = all_0_9_9, pred(n16) = n15, yields:
% 29.59/9.59 | (806) all_0_9_9 = n15
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (184) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 29.59/9.59 | (807) all_0_5_5 = n17
% 29.59/9.59 |
% 29.59/9.59 | From (806)(807) and (156) follows:
% 29.59/9.59 | (808) sum(n15, n17) = all_0_2_2
% 29.59/9.59 |
% 29.59/9.59 | From (806) and (3572) follows:
% 29.59/9.59 | (3582) sum(n15, n17) = all_0_7_7
% 29.59/9.59 |
% 29.59/9.59 | From (807) and (3570) follows:
% 29.59/9.59 | (3583) sum(n15, n17) = all_0_4_4
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (194) with n15, n17, all_0_2_2, n11 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n11, yields:
% 29.59/9.59 | (812) all_0_2_2 = n11
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (194) with n15, n17, all_0_4_4, all_0_2_2 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = all_0_4_4, yields:
% 29.59/9.59 | (733) all_0_2_2 = all_0_4_4
% 29.59/9.59 |
% 29.59/9.59 | Instantiating formula (194) with n15, n17, all_0_7_7, all_0_2_2 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = all_0_7_7, yields:
% 29.59/9.59 | (734) all_0_2_2 = all_0_7_7
% 29.59/9.59 |
% 29.59/9.60 | Combining equations (734,733) yields a new equation:
% 29.59/9.60 | (735) all_0_4_4 = all_0_7_7
% 29.59/9.60 |
% 29.59/9.60 | Combining equations (812,733) yields a new equation:
% 29.59/9.60 | (883) all_0_4_4 = n11
% 29.59/9.60 |
% 29.59/9.60 | Combining equations (883,735) yields a new equation:
% 29.59/9.60 | (885) all_0_7_7 = n11
% 29.59/9.60 |
% 29.59/9.60 | Combining equations (885,735) yields a new equation:
% 29.59/9.60 | (883) all_0_4_4 = n11
% 29.59/9.60 |
% 29.59/9.60 | Combining equations (883,733) yields a new equation:
% 29.59/9.60 | (812) all_0_2_2 = n11
% 29.59/9.60 |
% 29.59/9.60 | From (812) and (3574) follows:
% 29.59/9.60 | (3592) sum(n11, n11) = all_0_0_0
% 29.59/9.60 |
% 29.59/9.60 | From (885)(883) and (435) follows:
% 29.59/9.60 | (887) sum(n11, n11) = all_0_3_3
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (194) with n11, n11, all_0_0_0, n1 and discharging atoms sum(n11, n11) = all_0_0_0, sum(n11, n11) = n1, yields:
% 29.59/9.60 | (889) all_0_0_0 = n1
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (194) with n11, n11, all_0_3_3, all_0_0_0 and discharging atoms sum(n11, n11) = all_0_0_0, sum(n11, n11) = all_0_3_3, yields:
% 29.59/9.60 | (743) all_0_0_0 = all_0_3_3
% 29.59/9.60 |
% 29.59/9.60 | Combining equations (889,743) yields a new equation:
% 29.59/9.60 | (888) all_0_3_3 = n1
% 29.59/9.60 |
% 29.59/9.60 | Combining equations (888,743) yields a new equation:
% 29.59/9.60 | (889) all_0_0_0 = n1
% 29.59/9.60 |
% 29.59/9.60 | Equations (889,888) can reduce 201 to:
% 29.59/9.60 | (746) $false
% 29.59/9.60 |
% 29.59/9.60 |-The branch is then unsatisfiable
% 29.59/9.60 |-Branch two:
% 29.59/9.60 | (819) ~ (all_0_11_11 = n16)
% 29.59/9.60 | (820) all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.59/9.60 |
% 29.59/9.60 +-Applying beta-rule and splitting (820), into two cases.
% 29.59/9.60 |-Branch one:
% 29.59/9.60 | (821) all_0_11_11 = n15
% 29.59/9.60 |
% 29.59/9.60 | From (821) and (190) follows:
% 29.59/9.60 | (822) pred(n15) = all_0_9_9
% 29.59/9.60 |
% 29.59/9.60 | From (821) and (505) follows:
% 29.59/9.60 | (823) succ(n15) = all_0_5_5
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (259) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 29.59/9.60 | (824) all_0_9_9 = n14
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (184) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 29.59/9.60 | (825) all_0_5_5 = n16
% 29.59/9.60 |
% 29.59/9.60 | From (824)(825) and (156) follows:
% 29.59/9.60 | (826) sum(n14, n16) = all_0_2_2
% 29.59/9.60 |
% 29.59/9.60 | From (824) and (3572) follows:
% 29.59/9.60 | (3607) sum(n14, n17) = all_0_7_7
% 29.59/9.60 |
% 29.59/9.60 | From (825) and (3570) follows:
% 29.59/9.60 | (3608) sum(n15, n16) = all_0_4_4
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (194) with n15, n16, all_0_4_4, n10 and discharging atoms sum(n15, n16) = all_0_4_4, sum(n15, n16) = n10, yields:
% 29.59/9.60 | (901) all_0_4_4 = n10
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (194) with n14, n17, all_0_7_7, n10 and discharging atoms sum(n14, n17) = all_0_7_7, sum(n14, n17) = n10, yields:
% 29.59/9.60 | (903) all_0_7_7 = n10
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (194) with n14, n16, all_0_2_2, n9 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n9, yields:
% 29.59/9.60 | (830) all_0_2_2 = n9
% 29.59/9.60 |
% 29.59/9.60 | From (830) and (3574) follows:
% 29.59/9.60 | (3612) sum(n9, n11) = all_0_0_0
% 29.59/9.60 |
% 29.59/9.60 | From (903)(901) and (435) follows:
% 29.59/9.60 | (905) sum(n10, n10) = all_0_3_3
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 29.59/9.60 | (906) all_0_3_3 = n20
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (194) with n9, n11, all_0_0_0, n20 and discharging atoms sum(n9, n11) = all_0_0_0, sum(n9, n11) = n20, yields:
% 29.59/9.60 | (907) all_0_0_0 = n20
% 29.59/9.60 |
% 29.59/9.60 | Equations (907,906) can reduce 201 to:
% 29.59/9.60 | (746) $false
% 29.59/9.60 |
% 29.59/9.60 |-The branch is then unsatisfiable
% 29.59/9.60 |-Branch two:
% 29.59/9.60 | (837) ~ (all_0_11_11 = n15)
% 29.59/9.60 | (838) all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.59/9.60 |
% 29.59/9.60 +-Applying beta-rule and splitting (838), into two cases.
% 29.59/9.60 |-Branch one:
% 29.59/9.60 | (839) all_0_11_11 = n14
% 29.59/9.60 |
% 29.59/9.60 | From (839) and (190) follows:
% 29.59/9.60 | (840) pred(n14) = all_0_9_9
% 29.59/9.60 |
% 29.59/9.60 | From (839) and (505) follows:
% 29.59/9.60 | (841) succ(n14) = all_0_5_5
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (259) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 29.59/9.60 | (842) all_0_9_9 = n13
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (184) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 29.59/9.60 | (843) all_0_5_5 = n15
% 29.59/9.60 |
% 29.59/9.60 | From (842)(843) and (156) follows:
% 29.59/9.60 | (844) sum(n13, n15) = all_0_2_2
% 29.59/9.60 |
% 29.59/9.60 | From (842) and (3572) follows:
% 29.59/9.60 | (3625) sum(n13, n17) = all_0_7_7
% 29.59/9.60 |
% 29.59/9.60 | From (843) and (3570) follows:
% 29.59/9.60 | (3626) sum(n15, n15) = all_0_4_4
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (194) with n15, n15, all_0_4_4, n9 and discharging atoms sum(n15, n15) = all_0_4_4, sum(n15, n15) = n9, yields:
% 29.59/9.60 | (919) all_0_4_4 = n9
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (194) with n13, n17, all_0_7_7, n9 and discharging atoms sum(n13, n17) = all_0_7_7, sum(n13, n17) = n9, yields:
% 29.59/9.60 | (921) all_0_7_7 = n9
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (194) with n13, n15, all_0_2_2, n7 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n7, yields:
% 29.59/9.60 | (848) all_0_2_2 = n7
% 29.59/9.60 |
% 29.59/9.60 | From (848) and (3574) follows:
% 29.59/9.60 | (3630) sum(n7, n11) = all_0_0_0
% 29.59/9.60 |
% 29.59/9.60 | From (921)(919) and (435) follows:
% 29.59/9.60 | (923) sum(n9, n9) = all_0_3_3
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 29.59/9.60 | (925) all_0_3_3 = n18
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (194) with n7, n11, all_0_0_0, n18 and discharging atoms sum(n7, n11) = all_0_0_0, sum(n7, n11) = n18, yields:
% 29.59/9.60 | (924) all_0_0_0 = n18
% 29.59/9.60 |
% 29.59/9.60 | Equations (924,925) can reduce 201 to:
% 29.59/9.60 | (746) $false
% 29.59/9.60 |
% 29.59/9.60 |-The branch is then unsatisfiable
% 29.59/9.60 |-Branch two:
% 29.59/9.60 | (855) ~ (all_0_11_11 = n14)
% 29.59/9.60 | (856) all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.59/9.60 |
% 29.59/9.60 +-Applying beta-rule and splitting (856), into two cases.
% 29.59/9.60 |-Branch one:
% 29.59/9.60 | (857) all_0_11_11 = n13
% 29.59/9.60 |
% 29.59/9.60 | From (857) and (190) follows:
% 29.59/9.60 | (858) pred(n13) = all_0_9_9
% 29.59/9.60 |
% 29.59/9.60 | From (857) and (505) follows:
% 29.59/9.60 | (859) succ(n13) = all_0_5_5
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (259) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 29.59/9.60 | (860) all_0_9_9 = n12
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (184) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 29.59/9.60 | (861) all_0_5_5 = n14
% 29.59/9.60 |
% 29.59/9.60 | From (860)(861) and (156) follows:
% 29.59/9.60 | (862) sum(n12, n14) = all_0_2_2
% 29.59/9.60 |
% 29.59/9.60 | From (860) and (3572) follows:
% 29.59/9.60 | (3643) sum(n12, n17) = all_0_7_7
% 29.59/9.60 |
% 29.59/9.60 | From (861) and (3570) follows:
% 29.59/9.60 | (3644) sum(n15, n14) = all_0_4_4
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (194) with n15, n14, all_0_4_4, n8 and discharging atoms sum(n15, n14) = all_0_4_4, sum(n15, n14) = n8, yields:
% 29.59/9.60 | (937) all_0_4_4 = n8
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (194) with n12, n17, all_0_7_7, n8 and discharging atoms sum(n12, n17) = all_0_7_7, sum(n12, n17) = n8, yields:
% 29.59/9.60 | (939) all_0_7_7 = n8
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (194) with n12, n14, all_0_2_2, n5 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n5, yields:
% 29.59/9.60 | (866) all_0_2_2 = n5
% 29.59/9.60 |
% 29.59/9.60 | From (866) and (3574) follows:
% 29.59/9.60 | (3648) sum(n5, n11) = all_0_0_0
% 29.59/9.60 |
% 29.59/9.60 | From (939)(937) and (435) follows:
% 29.59/9.60 | (941) sum(n8, n8) = all_0_3_3
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 29.59/9.60 | (943) all_0_3_3 = n16
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (194) with n5, n11, all_0_0_0, n16 and discharging atoms sum(n5, n11) = all_0_0_0, sum(n5, n11) = n16, yields:
% 29.59/9.60 | (942) all_0_0_0 = n16
% 29.59/9.60 |
% 29.59/9.60 | Equations (942,943) can reduce 201 to:
% 29.59/9.60 | (746) $false
% 29.59/9.60 |
% 29.59/9.60 |-The branch is then unsatisfiable
% 29.59/9.60 |-Branch two:
% 29.59/9.60 | (873) ~ (all_0_11_11 = n13)
% 29.59/9.60 | (874) all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.59/9.60 |
% 29.59/9.60 +-Applying beta-rule and splitting (874), into two cases.
% 29.59/9.60 |-Branch one:
% 29.59/9.60 | (875) all_0_11_11 = n12
% 29.59/9.60 |
% 29.59/9.60 | From (875) and (190) follows:
% 29.59/9.60 | (876) pred(n12) = all_0_9_9
% 29.59/9.60 |
% 29.59/9.60 | From (875) and (505) follows:
% 29.59/9.60 | (877) succ(n12) = all_0_5_5
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (259) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 29.59/9.60 | (878) all_0_9_9 = n11
% 29.59/9.60 |
% 29.59/9.60 | Instantiating formula (184) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 29.59/9.60 | (879) all_0_5_5 = n13
% 29.59/9.60 |
% 29.59/9.60 | From (878)(879) and (156) follows:
% 29.59/9.60 | (880) sum(n11, n13) = all_0_2_2
% 29.59/9.60 |
% 29.59/9.60 | From (878) and (3572) follows:
% 29.59/9.61 | (3661) sum(n11, n17) = all_0_7_7
% 29.59/9.61 |
% 29.59/9.61 | From (879) and (3570) follows:
% 29.59/9.61 | (3662) sum(n15, n13) = all_0_4_4
% 29.59/9.61 |
% 29.59/9.61 | Instantiating formula (194) with n15, n13, all_0_4_4, n7 and discharging atoms sum(n15, n13) = all_0_4_4, sum(n15, n13) = n7, yields:
% 29.59/9.61 | (955) all_0_4_4 = n7
% 29.59/9.61 |
% 29.59/9.61 | Instantiating formula (194) with n11, n17, all_0_7_7, n7 and discharging atoms sum(n11, n17) = all_0_7_7, sum(n11, n17) = n7, yields:
% 29.59/9.61 | (957) all_0_7_7 = n7
% 29.59/9.61 |
% 29.59/9.61 | Instantiating formula (194) with n11, n13, all_0_2_2, n3 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n3, yields:
% 29.59/9.61 | (884) all_0_2_2 = n3
% 29.59/9.61 |
% 29.59/9.61 | From (884) and (3574) follows:
% 29.59/9.61 | (3666) sum(n3, n11) = all_0_0_0
% 29.59/9.61 |
% 29.59/9.61 | From (957)(955) and (435) follows:
% 29.59/9.61 | (959) sum(n7, n7) = all_0_3_3
% 29.59/9.61 |
% 29.59/9.61 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 29.59/9.61 | (961) all_0_3_3 = n14
% 29.59/9.61 |
% 29.59/9.61 | Instantiating formula (194) with n3, n11, all_0_0_0, n14 and discharging atoms sum(n3, n11) = all_0_0_0, sum(n3, n11) = n14, yields:
% 29.59/9.61 | (960) all_0_0_0 = n14
% 29.59/9.61 |
% 29.59/9.61 | Equations (960,961) can reduce 201 to:
% 29.59/9.61 | (746) $false
% 29.59/9.61 |
% 29.59/9.61 |-The branch is then unsatisfiable
% 29.59/9.61 |-Branch two:
% 29.59/9.61 | (891) ~ (all_0_11_11 = n12)
% 29.59/9.61 | (892) all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.59/9.61 |
% 29.59/9.61 +-Applying beta-rule and splitting (892), into two cases.
% 29.59/9.61 |-Branch one:
% 29.59/9.61 | (893) all_0_11_11 = n11
% 29.59/9.61 |
% 29.59/9.61 | From (893) and (190) follows:
% 29.59/9.61 | (894) pred(n11) = all_0_9_9
% 29.59/9.61 |
% 29.59/9.61 | From (893) and (505) follows:
% 29.59/9.61 | (895) succ(n11) = all_0_5_5
% 29.59/9.61 |
% 29.59/9.61 | Instantiating formula (259) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 29.59/9.61 | (896) all_0_9_9 = n10
% 29.59/9.61 |
% 29.59/9.61 | Instantiating formula (184) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 29.59/9.61 | (897) all_0_5_5 = n12
% 29.59/9.61 |
% 29.59/9.61 | From (896)(897) and (156) follows:
% 29.59/9.61 | (898) sum(n10, n12) = all_0_2_2
% 29.59/9.61 |
% 29.59/9.61 | From (896) and (3572) follows:
% 29.59/9.61 | (3679) sum(n10, n17) = all_0_7_7
% 29.59/9.61 |
% 29.59/9.61 | From (897) and (3570) follows:
% 29.81/9.61 | (3680) sum(n15, n12) = all_0_4_4
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (194) with n15, n12, all_0_4_4, n6 and discharging atoms sum(n15, n12) = all_0_4_4, sum(n15, n12) = n6, yields:
% 29.81/9.61 | (973) all_0_4_4 = n6
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (194) with n10, n17, all_0_7_7, n6 and discharging atoms sum(n10, n17) = all_0_7_7, sum(n10, n17) = n6, yields:
% 29.81/9.61 | (975) all_0_7_7 = n6
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (194) with n10, n12, all_0_2_2, n1 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n1, yields:
% 29.81/9.61 | (902) all_0_2_2 = n1
% 29.81/9.61 |
% 29.81/9.61 | From (902) and (3574) follows:
% 29.81/9.61 | (3684) sum(n1, n11) = all_0_0_0
% 29.81/9.61 |
% 29.81/9.61 | From (975)(973) and (435) follows:
% 29.81/9.61 | (977) sum(n6, n6) = all_0_3_3
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 29.81/9.61 | (979) all_0_3_3 = n12
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (194) with n1, n11, all_0_0_0, n12 and discharging atoms sum(n1, n11) = all_0_0_0, sum(n1, n11) = n12, yields:
% 29.81/9.61 | (978) all_0_0_0 = n12
% 29.81/9.61 |
% 29.81/9.61 | Equations (978,979) can reduce 201 to:
% 29.81/9.61 | (746) $false
% 29.81/9.61 |
% 29.81/9.61 |-The branch is then unsatisfiable
% 29.81/9.61 |-Branch two:
% 29.81/9.61 | (909) ~ (all_0_11_11 = n11)
% 29.81/9.61 | (910) all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.81/9.61 |
% 29.81/9.61 +-Applying beta-rule and splitting (910), into two cases.
% 29.81/9.61 |-Branch one:
% 29.81/9.61 | (911) all_0_11_11 = n10
% 29.81/9.61 |
% 29.81/9.61 | From (911) and (190) follows:
% 29.81/9.61 | (912) pred(n10) = all_0_9_9
% 29.81/9.61 |
% 29.81/9.61 | From (911) and (505) follows:
% 29.81/9.61 | (913) succ(n10) = all_0_5_5
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (259) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 29.81/9.61 | (914) all_0_9_9 = n9
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (184) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 29.81/9.61 | (915) all_0_5_5 = n11
% 29.81/9.61 |
% 29.81/9.61 | From (914)(915) and (156) follows:
% 29.81/9.61 | (916) sum(n9, n11) = all_0_2_2
% 29.81/9.61 |
% 29.81/9.61 | From (914) and (3572) follows:
% 29.81/9.61 | (3697) sum(n9, n17) = all_0_7_7
% 29.81/9.61 |
% 29.81/9.61 | From (915) and (3570) follows:
% 29.81/9.61 | (3698) sum(n15, n11) = all_0_4_4
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (194) with n15, n11, all_0_4_4, n5 and discharging atoms sum(n15, n11) = all_0_4_4, sum(n15, n11) = n5, yields:
% 29.81/9.61 | (991) all_0_4_4 = n5
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (194) with n9, n17, all_0_7_7, n5 and discharging atoms sum(n9, n17) = all_0_7_7, sum(n9, n17) = n5, yields:
% 29.81/9.61 | (993) all_0_7_7 = n5
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (194) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 29.81/9.61 | (920) all_0_2_2 = n20
% 29.81/9.61 |
% 29.81/9.61 | From (920) and (3574) follows:
% 29.81/9.61 | (3702) sum(n20, n11) = all_0_0_0
% 29.81/9.61 |
% 29.81/9.61 | From (993)(991) and (435) follows:
% 29.81/9.61 | (995) sum(n5, n5) = all_0_3_3
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (194) with n20, n11, all_0_0_0, n10 and discharging atoms sum(n20, n11) = all_0_0_0, sum(n20, n11) = n10, yields:
% 29.81/9.61 | (996) all_0_0_0 = n10
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 29.81/9.61 | (997) all_0_3_3 = n10
% 29.81/9.61 |
% 29.81/9.61 | Equations (996,997) can reduce 201 to:
% 29.81/9.61 | (746) $false
% 29.81/9.61 |
% 29.81/9.61 |-The branch is then unsatisfiable
% 29.81/9.61 |-Branch two:
% 29.81/9.61 | (927) ~ (all_0_11_11 = n10)
% 29.81/9.61 | (928) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.81/9.61 |
% 29.81/9.61 +-Applying beta-rule and splitting (928), into two cases.
% 29.81/9.61 |-Branch one:
% 29.81/9.61 | (929) all_0_11_11 = n9
% 29.81/9.61 |
% 29.81/9.61 | From (929) and (190) follows:
% 29.81/9.61 | (930) pred(n9) = all_0_9_9
% 29.81/9.61 |
% 29.81/9.61 | From (929) and (505) follows:
% 29.81/9.61 | (931) succ(n9) = all_0_5_5
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (259) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 29.81/9.61 | (932) all_0_9_9 = n8
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (184) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 29.81/9.61 | (933) all_0_5_5 = n10
% 29.81/9.61 |
% 29.81/9.61 | From (932)(933) and (156) follows:
% 29.81/9.61 | (934) sum(n8, n10) = all_0_2_2
% 29.81/9.61 |
% 29.81/9.61 | From (932) and (3572) follows:
% 29.81/9.61 | (3715) sum(n8, n17) = all_0_7_7
% 29.81/9.61 |
% 29.81/9.61 | From (933) and (3570) follows:
% 29.81/9.61 | (3716) sum(n15, n10) = all_0_4_4
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (194) with n15, n10, all_0_4_4, n4 and discharging atoms sum(n15, n10) = all_0_4_4, sum(n15, n10) = n4, yields:
% 29.81/9.61 | (1009) all_0_4_4 = n4
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (194) with n8, n17, all_0_7_7, n4 and discharging atoms sum(n8, n17) = all_0_7_7, sum(n8, n17) = n4, yields:
% 29.81/9.61 | (1011) all_0_7_7 = n4
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (194) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 29.81/9.61 | (938) all_0_2_2 = n18
% 29.81/9.61 |
% 29.81/9.61 | From (938) and (3574) follows:
% 29.81/9.61 | (3720) sum(n18, n11) = all_0_0_0
% 29.81/9.61 |
% 29.81/9.61 | From (1011)(1009) and (435) follows:
% 29.81/9.61 | (1013) sum(n4, n4) = all_0_3_3
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (194) with n18, n11, all_0_0_0, n8 and discharging atoms sum(n18, n11) = all_0_0_0, sum(n18, n11) = n8, yields:
% 29.81/9.61 | (1014) all_0_0_0 = n8
% 29.81/9.61 |
% 29.81/9.61 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 29.81/9.61 | (1015) all_0_3_3 = n8
% 29.81/9.61 |
% 29.81/9.61 | Equations (1014,1015) can reduce 201 to:
% 29.81/9.61 | (746) $false
% 29.81/9.61 |
% 29.81/9.61 |-The branch is then unsatisfiable
% 29.81/9.61 |-Branch two:
% 29.81/9.61 | (945) ~ (all_0_11_11 = n9)
% 29.81/9.61 | (946) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.81/9.61 |
% 29.81/9.61 +-Applying beta-rule and splitting (946), into two cases.
% 29.81/9.61 |-Branch one:
% 29.81/9.62 | (947) all_0_11_11 = n8
% 29.81/9.62 |
% 29.81/9.62 | From (947) and (190) follows:
% 29.81/9.62 | (948) pred(n8) = all_0_9_9
% 29.81/9.62 |
% 29.81/9.62 | From (947) and (505) follows:
% 29.81/9.62 | (949) succ(n8) = all_0_5_5
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (259) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 29.81/9.62 | (950) all_0_9_9 = n7
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (184) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 29.81/9.62 | (951) all_0_5_5 = n9
% 29.81/9.62 |
% 29.81/9.62 | From (950)(951) and (156) follows:
% 29.81/9.62 | (952) sum(n7, n9) = all_0_2_2
% 29.81/9.62 |
% 29.81/9.62 | From (950) and (3572) follows:
% 29.81/9.62 | (3733) sum(n7, n17) = all_0_7_7
% 29.81/9.62 |
% 29.81/9.62 | From (951) and (3570) follows:
% 29.81/9.62 | (3734) sum(n15, n9) = all_0_4_4
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n15, n9, all_0_4_4, n3 and discharging atoms sum(n15, n9) = all_0_4_4, sum(n15, n9) = n3, yields:
% 29.81/9.62 | (1027) all_0_4_4 = n3
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n7, n17, all_0_7_7, n3 and discharging atoms sum(n7, n17) = all_0_7_7, sum(n7, n17) = n3, yields:
% 29.81/9.62 | (1029) all_0_7_7 = n3
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 29.81/9.62 | (956) all_0_2_2 = n16
% 29.81/9.62 |
% 29.81/9.62 | From (956) and (3574) follows:
% 29.81/9.62 | (3738) sum(n16, n11) = all_0_0_0
% 29.81/9.62 |
% 29.81/9.62 | From (1029)(1027) and (435) follows:
% 29.81/9.62 | (1031) sum(n3, n3) = all_0_3_3
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n16, n11, all_0_0_0, n6 and discharging atoms sum(n16, n11) = all_0_0_0, sum(n16, n11) = n6, yields:
% 29.81/9.62 | (1032) all_0_0_0 = n6
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 29.81/9.62 | (1033) all_0_3_3 = n6
% 29.81/9.62 |
% 29.81/9.62 | Equations (1032,1033) can reduce 201 to:
% 29.81/9.62 | (746) $false
% 29.81/9.62 |
% 29.81/9.62 |-The branch is then unsatisfiable
% 29.81/9.62 |-Branch two:
% 29.81/9.62 | (963) ~ (all_0_11_11 = n8)
% 29.81/9.62 | (964) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.81/9.62 |
% 29.81/9.62 +-Applying beta-rule and splitting (964), into two cases.
% 29.81/9.62 |-Branch one:
% 29.81/9.62 | (965) all_0_11_11 = n7
% 29.81/9.62 |
% 29.81/9.62 | From (965) and (190) follows:
% 29.81/9.62 | (966) pred(n7) = all_0_9_9
% 29.81/9.62 |
% 29.81/9.62 | From (965) and (505) follows:
% 29.81/9.62 | (967) succ(n7) = all_0_5_5
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (259) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 29.81/9.62 | (968) all_0_9_9 = n6
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (184) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 29.81/9.62 | (969) all_0_5_5 = n8
% 29.81/9.62 |
% 29.81/9.62 | From (968)(969) and (156) follows:
% 29.81/9.62 | (970) sum(n6, n8) = all_0_2_2
% 29.81/9.62 |
% 29.81/9.62 | From (968) and (3572) follows:
% 29.81/9.62 | (3751) sum(n6, n17) = all_0_7_7
% 29.81/9.62 |
% 29.81/9.62 | From (969) and (3570) follows:
% 29.81/9.62 | (3752) sum(n15, n8) = all_0_4_4
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n15, n8, all_0_4_4, n2 and discharging atoms sum(n15, n8) = all_0_4_4, sum(n15, n8) = n2, yields:
% 29.81/9.62 | (1045) all_0_4_4 = n2
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n6, n17, all_0_7_7, n2 and discharging atoms sum(n6, n17) = all_0_7_7, sum(n6, n17) = n2, yields:
% 29.81/9.62 | (1047) all_0_7_7 = n2
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 29.81/9.62 | (974) all_0_2_2 = n14
% 29.81/9.62 |
% 29.81/9.62 | From (974) and (3574) follows:
% 29.81/9.62 | (3756) sum(n14, n11) = all_0_0_0
% 29.81/9.62 |
% 29.81/9.62 | From (1047)(1045) and (435) follows:
% 29.81/9.62 | (1049) sum(n2, n2) = all_0_3_3
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n14, n11, all_0_0_0, n4 and discharging atoms sum(n14, n11) = all_0_0_0, sum(n14, n11) = n4, yields:
% 29.81/9.62 | (1050) all_0_0_0 = n4
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 29.81/9.62 | (1051) all_0_3_3 = n4
% 29.81/9.62 |
% 29.81/9.62 | Equations (1050,1051) can reduce 201 to:
% 29.81/9.62 | (746) $false
% 29.81/9.62 |
% 29.81/9.62 |-The branch is then unsatisfiable
% 29.81/9.62 |-Branch two:
% 29.81/9.62 | (981) ~ (all_0_11_11 = n7)
% 29.81/9.62 | (982) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.81/9.62 |
% 29.81/9.62 +-Applying beta-rule and splitting (982), into two cases.
% 29.81/9.62 |-Branch one:
% 29.81/9.62 | (983) all_0_11_11 = n6
% 29.81/9.62 |
% 29.81/9.62 | From (983) and (190) follows:
% 29.81/9.62 | (984) pred(n6) = all_0_9_9
% 29.81/9.62 |
% 29.81/9.62 | From (983) and (505) follows:
% 29.81/9.62 | (985) succ(n6) = all_0_5_5
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (259) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 29.81/9.62 | (986) all_0_9_9 = n5
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (184) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 29.81/9.62 | (987) all_0_5_5 = n7
% 29.81/9.62 |
% 29.81/9.62 | From (986)(987) and (156) follows:
% 29.81/9.62 | (988) sum(n5, n7) = all_0_2_2
% 29.81/9.62 |
% 29.81/9.62 | From (986) and (3572) follows:
% 29.81/9.62 | (3769) sum(n5, n17) = all_0_7_7
% 29.81/9.62 |
% 29.81/9.62 | From (987) and (3570) follows:
% 29.81/9.62 | (3770) sum(n15, n7) = all_0_4_4
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n15, n7, all_0_4_4, n1 and discharging atoms sum(n15, n7) = all_0_4_4, sum(n15, n7) = n1, yields:
% 29.81/9.62 | (1063) all_0_4_4 = n1
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n5, n17, all_0_7_7, n1 and discharging atoms sum(n5, n17) = all_0_7_7, sum(n5, n17) = n1, yields:
% 29.81/9.62 | (1065) all_0_7_7 = n1
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 29.81/9.62 | (992) all_0_2_2 = n12
% 29.81/9.62 |
% 29.81/9.62 | From (992) and (3574) follows:
% 29.81/9.62 | (3774) sum(n12, n11) = all_0_0_0
% 29.81/9.62 |
% 29.81/9.62 | From (1065)(1063) and (435) follows:
% 29.81/9.62 | (1067) sum(n1, n1) = all_0_3_3
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n12, n11, all_0_0_0, n2 and discharging atoms sum(n12, n11) = all_0_0_0, sum(n12, n11) = n2, yields:
% 29.81/9.62 | (1068) all_0_0_0 = n2
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 29.81/9.62 | (1069) all_0_3_3 = n2
% 29.81/9.62 |
% 29.81/9.62 | Equations (1068,1069) can reduce 201 to:
% 29.81/9.62 | (746) $false
% 29.81/9.62 |
% 29.81/9.62 |-The branch is then unsatisfiable
% 29.81/9.62 |-Branch two:
% 29.81/9.62 | (999) ~ (all_0_11_11 = n6)
% 29.81/9.62 | (1000) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.81/9.62 |
% 29.81/9.62 +-Applying beta-rule and splitting (1000), into two cases.
% 29.81/9.62 |-Branch one:
% 29.81/9.62 | (1001) all_0_11_11 = n5
% 29.81/9.62 |
% 29.81/9.62 | From (1001) and (190) follows:
% 29.81/9.62 | (1002) pred(n5) = all_0_9_9
% 29.81/9.62 |
% 29.81/9.62 | From (1001) and (505) follows:
% 29.81/9.62 | (1003) succ(n5) = all_0_5_5
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (259) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 29.81/9.62 | (1004) all_0_9_9 = n4
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (184) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 29.81/9.62 | (1005) all_0_5_5 = n6
% 29.81/9.62 |
% 29.81/9.62 | From (1004)(1005) and (156) follows:
% 29.81/9.62 | (1006) sum(n4, n6) = all_0_2_2
% 29.81/9.62 |
% 29.81/9.62 | From (1004) and (3572) follows:
% 29.81/9.62 | (3787) sum(n4, n17) = all_0_7_7
% 29.81/9.62 |
% 29.81/9.62 | From (1005) and (3570) follows:
% 29.81/9.62 | (3788) sum(n15, n6) = all_0_4_4
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n15, n6, all_0_4_4, n0 and discharging atoms sum(n15, n6) = all_0_4_4, sum(n15, n6) = n0, yields:
% 29.81/9.62 | (1081) all_0_4_4 = n0
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n4, n17, all_0_7_7, n0 and discharging atoms sum(n4, n17) = all_0_7_7, sum(n4, n17) = n0, yields:
% 29.81/9.62 | (1083) all_0_7_7 = n0
% 29.81/9.62 |
% 29.81/9.62 | Instantiating formula (194) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 29.81/9.62 | (1010) all_0_2_2 = n10
% 29.81/9.62 |
% 29.81/9.62 | From (1010) and (3574) follows:
% 29.81/9.63 | (3792) sum(n10, n11) = all_0_0_0
% 29.81/9.63 |
% 29.81/9.63 | From (1083)(1081) and (435) follows:
% 29.81/9.63 | (1085) sum(n0, n0) = all_0_3_3
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n10, n11, all_0_0_0, n0 and discharging atoms sum(n10, n11) = all_0_0_0, sum(n10, n11) = n0, yields:
% 29.81/9.63 | (1087) all_0_0_0 = n0
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 29.81/9.63 | (1088) all_0_3_3 = n0
% 29.81/9.63 |
% 29.81/9.63 | Equations (1087,1088) can reduce 201 to:
% 29.81/9.63 | (746) $false
% 29.81/9.63 |
% 29.81/9.63 |-The branch is then unsatisfiable
% 29.81/9.63 |-Branch two:
% 29.81/9.63 | (1017) ~ (all_0_11_11 = n5)
% 29.81/9.63 | (1018) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.81/9.63 |
% 29.81/9.63 +-Applying beta-rule and splitting (1018), into two cases.
% 29.81/9.63 |-Branch one:
% 29.81/9.63 | (1019) all_0_11_11 = n4
% 29.81/9.63 |
% 29.81/9.63 | From (1019) and (190) follows:
% 29.81/9.63 | (1020) pred(n4) = all_0_9_9
% 29.81/9.63 |
% 29.81/9.63 | From (1019) and (505) follows:
% 29.81/9.63 | (1021) succ(n4) = all_0_5_5
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 29.81/9.63 | (1022) all_0_9_9 = n3
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 29.81/9.63 | (1023) all_0_5_5 = n5
% 29.81/9.63 |
% 29.81/9.63 | From (1022)(1023) and (156) follows:
% 29.81/9.63 | (1024) sum(n3, n5) = all_0_2_2
% 29.81/9.63 |
% 29.81/9.63 | From (1022) and (3572) follows:
% 29.81/9.63 | (3805) sum(n3, n17) = all_0_7_7
% 29.81/9.63 |
% 29.81/9.63 | From (1023) and (3570) follows:
% 29.81/9.63 | (3806) sum(n15, n5) = all_0_4_4
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n15, n5, all_0_4_4, n20 and discharging atoms sum(n15, n5) = all_0_4_4, sum(n15, n5) = n20, yields:
% 29.81/9.63 | (1101) all_0_4_4 = n20
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n3, n17, all_0_7_7, n20 and discharging atoms sum(n3, n17) = all_0_7_7, sum(n3, n17) = n20, yields:
% 29.81/9.63 | (1100) all_0_7_7 = n20
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 29.81/9.63 | (1028) all_0_2_2 = n8
% 29.81/9.63 |
% 29.81/9.63 | From (1028) and (3574) follows:
% 29.81/9.63 | (3810) sum(n8, n11) = all_0_0_0
% 29.81/9.63 |
% 29.81/9.63 | From (1100)(1101) and (435) follows:
% 29.81/9.63 | (1103) sum(n20, n20) = all_0_3_3
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 29.81/9.63 | (1104) all_0_3_3 = n19
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n8, n11, all_0_0_0, n19 and discharging atoms sum(n8, n11) = all_0_0_0, sum(n8, n11) = n19, yields:
% 29.81/9.63 | (1105) all_0_0_0 = n19
% 29.81/9.63 |
% 29.81/9.63 | Equations (1105,1104) can reduce 201 to:
% 29.81/9.63 | (746) $false
% 29.81/9.63 |
% 29.81/9.63 |-The branch is then unsatisfiable
% 29.81/9.63 |-Branch two:
% 29.81/9.63 | (1035) ~ (all_0_11_11 = n4)
% 29.81/9.63 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.81/9.63 |
% 29.81/9.63 +-Applying beta-rule and splitting (1036), into two cases.
% 29.81/9.63 |-Branch one:
% 29.81/9.63 | (1037) all_0_11_11 = n3
% 29.81/9.63 |
% 29.81/9.63 | From (1037) and (190) follows:
% 29.81/9.63 | (1038) pred(n3) = all_0_9_9
% 29.81/9.63 |
% 29.81/9.63 | From (1037) and (505) follows:
% 29.81/9.63 | (1039) succ(n3) = all_0_5_5
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 29.81/9.63 | (1040) all_0_9_9 = n2
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 29.81/9.63 | (1041) all_0_5_5 = n4
% 29.81/9.63 |
% 29.81/9.63 | From (1040)(1041) and (156) follows:
% 29.81/9.63 | (1042) sum(n2, n4) = all_0_2_2
% 29.81/9.63 |
% 29.81/9.63 | From (1040) and (3572) follows:
% 29.81/9.63 | (3823) sum(n2, n17) = all_0_7_7
% 29.81/9.63 |
% 29.81/9.63 | From (1041) and (3570) follows:
% 29.81/9.63 | (3824) sum(n15, n4) = all_0_4_4
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n15, n4, all_0_4_4, n19 and discharging atoms sum(n15, n4) = all_0_4_4, sum(n15, n4) = n19, yields:
% 29.81/9.63 | (736) all_0_4_4 = n19
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n2, n17, all_0_7_7, n19 and discharging atoms sum(n2, n17) = all_0_7_7, sum(n2, n17) = n19, yields:
% 29.81/9.63 | (737) all_0_7_7 = n19
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 29.81/9.63 | (1046) all_0_2_2 = n6
% 29.81/9.63 |
% 29.81/9.63 | From (1046) and (3574) follows:
% 29.81/9.63 | (3828) sum(n6, n11) = all_0_0_0
% 29.81/9.63 |
% 29.81/9.63 | From (737)(736) and (435) follows:
% 29.81/9.63 | (741) sum(n19, n19) = all_0_3_3
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 29.81/9.63 | (744) all_0_3_3 = n17
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n6, n11, all_0_0_0, n17 and discharging atoms sum(n6, n11) = all_0_0_0, sum(n6, n11) = n17, yields:
% 29.81/9.63 | (742) all_0_0_0 = n17
% 29.81/9.63 |
% 29.81/9.63 | Equations (742,744) can reduce 201 to:
% 29.81/9.63 | (746) $false
% 29.81/9.63 |
% 29.81/9.63 |-The branch is then unsatisfiable
% 29.81/9.63 |-Branch two:
% 29.81/9.63 | (1053) ~ (all_0_11_11 = n3)
% 29.81/9.63 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 29.81/9.63 |
% 29.81/9.63 +-Applying beta-rule and splitting (1054), into two cases.
% 29.81/9.63 |-Branch one:
% 29.81/9.63 | (1055) all_0_11_11 = n2
% 29.81/9.63 |
% 29.81/9.63 | From (1055) and (190) follows:
% 29.81/9.63 | (1056) pred(n2) = all_0_9_9
% 29.81/9.63 |
% 29.81/9.63 | From (1055) and (505) follows:
% 29.81/9.63 | (1057) succ(n2) = all_0_5_5
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 29.81/9.63 | (1058) all_0_9_9 = n1
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 29.81/9.63 | (1059) all_0_5_5 = n3
% 29.81/9.63 |
% 29.81/9.63 | From (1058)(1059) and (156) follows:
% 29.81/9.63 | (1060) sum(n1, n3) = all_0_2_2
% 29.81/9.63 |
% 29.81/9.63 | From (1058) and (3572) follows:
% 29.81/9.63 | (3841) sum(n1, n17) = all_0_7_7
% 29.81/9.63 |
% 29.81/9.63 | From (1059) and (3570) follows:
% 29.81/9.63 | (3842) sum(n15, n3) = all_0_4_4
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n15, n3, all_0_4_4, n18 and discharging atoms sum(n15, n3) = all_0_4_4, sum(n15, n3) = n18, yields:
% 29.81/9.63 | (757) all_0_4_4 = n18
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n1, n17, all_0_7_7, n18 and discharging atoms sum(n1, n17) = all_0_7_7, sum(n1, n17) = n18, yields:
% 29.81/9.63 | (759) all_0_7_7 = n18
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 29.81/9.63 | (1064) all_0_2_2 = n4
% 29.81/9.63 |
% 29.81/9.63 | From (1064) and (3574) follows:
% 29.81/9.63 | (3846) sum(n4, n11) = all_0_0_0
% 29.81/9.63 |
% 29.81/9.63 | From (759)(757) and (435) follows:
% 29.81/9.63 | (761) sum(n18, n18) = all_0_3_3
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 29.81/9.63 | (762) all_0_3_3 = n15
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n4, n11, all_0_0_0, n15 and discharging atoms sum(n4, n11) = all_0_0_0, sum(n4, n11) = n15, yields:
% 29.81/9.63 | (763) all_0_0_0 = n15
% 29.81/9.63 |
% 29.81/9.63 | Equations (763,762) can reduce 201 to:
% 29.81/9.63 | (746) $false
% 29.81/9.63 |
% 29.81/9.63 |-The branch is then unsatisfiable
% 29.81/9.63 |-Branch two:
% 29.81/9.63 | (1071) ~ (all_0_11_11 = n2)
% 29.81/9.63 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 29.81/9.63 |
% 29.81/9.63 +-Applying beta-rule and splitting (1072), into two cases.
% 29.81/9.63 |-Branch one:
% 29.81/9.63 | (1073) all_0_11_11 = n1
% 29.81/9.63 |
% 29.81/9.63 | From (1073) and (190) follows:
% 29.81/9.63 | (1074) pred(n1) = all_0_9_9
% 29.81/9.63 |
% 29.81/9.63 | From (1073) and (505) follows:
% 29.81/9.63 | (1075) succ(n1) = all_0_5_5
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 29.81/9.63 | (1076) all_0_9_9 = n0
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 29.81/9.63 | (1077) all_0_5_5 = n2
% 29.81/9.63 |
% 29.81/9.63 | From (1076)(1077) and (156) follows:
% 29.81/9.63 | (1078) sum(n0, n2) = all_0_2_2
% 29.81/9.63 |
% 29.81/9.63 | From (1076) and (3572) follows:
% 29.81/9.63 | (3859) sum(n0, n17) = all_0_7_7
% 29.81/9.63 |
% 29.81/9.63 | From (1077) and (3570) follows:
% 29.81/9.63 | (3860) sum(n15, n2) = all_0_4_4
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n15, n2, all_0_4_4, n17 and discharging atoms sum(n15, n2) = all_0_4_4, sum(n15, n2) = n17, yields:
% 29.81/9.63 | (775) all_0_4_4 = n17
% 29.81/9.63 |
% 29.81/9.63 | Instantiating formula (194) with n0, n17, all_0_7_7, n17 and discharging atoms sum(n0, n17) = all_0_7_7, sum(n0, n17) = n17, yields:
% 29.81/9.64 | (777) all_0_7_7 = n17
% 29.81/9.64 |
% 29.81/9.64 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 29.81/9.64 | (1082) all_0_2_2 = n2
% 29.81/9.64 |
% 29.81/9.64 | From (1082) and (3574) follows:
% 29.81/9.64 | (3864) sum(n2, n11) = all_0_0_0
% 29.81/9.64 |
% 29.81/9.64 | From (777)(775) and (435) follows:
% 29.81/9.64 | (779) sum(n17, n17) = all_0_3_3
% 29.81/9.64 |
% 29.81/9.64 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 29.81/9.64 | (780) all_0_3_3 = n13
% 29.81/9.64 |
% 29.81/9.64 | Instantiating formula (194) with n2, n11, all_0_0_0, n13 and discharging atoms sum(n2, n11) = all_0_0_0, sum(n2, n11) = n13, yields:
% 29.81/9.64 | (781) all_0_0_0 = n13
% 29.81/9.64 |
% 29.81/9.64 | Equations (781,780) can reduce 201 to:
% 29.81/9.64 | (746) $false
% 29.81/9.64 |
% 29.81/9.64 |-The branch is then unsatisfiable
% 29.81/9.64 |-Branch two:
% 29.81/9.64 | (1090) ~ (all_0_11_11 = n1)
% 29.81/9.64 | (1091) all_0_11_11 = n0
% 29.81/9.64 |
% 29.81/9.64 | From (1091) and (190) follows:
% 29.81/9.64 | (1092) pred(n0) = all_0_9_9
% 29.81/9.64 |
% 29.81/9.64 | From (1091) and (505) follows:
% 29.81/9.64 | (1093) succ(n0) = all_0_5_5
% 29.81/9.64 |
% 29.81/9.64 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 29.81/9.64 | (1094) all_0_9_9 = n20
% 29.81/9.64 |
% 29.81/9.64 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 29.81/9.64 | (1095) all_0_5_5 = n1
% 29.81/9.64 |
% 29.81/9.64 | From (1094)(1095) and (156) follows:
% 29.81/9.64 | (1096) sum(n20, n1) = all_0_2_2
% 29.81/9.64 |
% 29.81/9.64 | From (1094) and (3572) follows:
% 29.81/9.64 | (3876) sum(n20, n17) = all_0_7_7
% 29.81/9.64 |
% 29.81/9.64 | From (1095) and (3570) follows:
% 29.81/9.64 | (3877) sum(n15, n1) = all_0_4_4
% 29.81/9.64 |
% 29.81/9.64 | Instantiating formula (194) with n20, n17, all_0_7_7, n16 and discharging atoms sum(n20, n17) = all_0_7_7, sum(n20, n17) = n16, yields:
% 29.81/9.64 | (795) all_0_7_7 = n16
% 29.81/9.64 |
% 29.81/9.64 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 29.81/9.65 | (1099) all_0_2_2 = n0
% 29.81/9.65 |
% 29.81/9.65 | Instantiating formula (194) with n15, n1, all_0_4_4, n16 and discharging atoms sum(n15, n1) = all_0_4_4, sum(n15, n1) = n16, yields:
% 29.81/9.65 | (793) all_0_4_4 = n16
% 29.81/9.65 |
% 29.81/9.65 | From (1099) and (3574) follows:
% 29.81/9.66 | (3881) sum(n0, n11) = all_0_0_0
% 29.81/9.66 |
% 29.81/9.66 | From (795)(793) and (435) follows:
% 29.81/9.66 | (797) sum(n16, n16) = all_0_3_3
% 29.81/9.66 |
% 29.81/9.66 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 29.81/9.66 | (798) all_0_3_3 = n11
% 29.81/9.66 |
% 29.81/9.66 | Instantiating formula (194) with n0, n11, all_0_0_0, n11 and discharging atoms sum(n0, n11) = all_0_0_0, sum(n0, n11) = n11, yields:
% 29.81/9.66 | (799) all_0_0_0 = n11
% 29.81/9.66 |
% 29.81/9.66 | Equations (799,798) can reduce 201 to:
% 29.81/9.66 | (746) $false
% 29.81/9.66 |
% 29.81/9.66 |-The branch is then unsatisfiable
% 29.81/9.66 |-Branch two:
% 29.81/9.66 | (1190) ~ (all_0_10_10 = n16)
% 29.81/9.66 | (1191) all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.81/9.66 |
% 29.81/9.66 +-Applying beta-rule and splitting (802), into two cases.
% 29.81/9.66 |-Branch one:
% 29.81/9.66 | (803) all_0_11_11 = n16
% 29.81/9.66 |
% 29.81/9.66 | From (803) and (190) follows:
% 29.81/9.66 | (804) pred(n16) = all_0_9_9
% 29.81/9.66 |
% 29.81/9.66 | From (803) and (505) follows:
% 29.81/9.66 | (805) succ(n16) = all_0_5_5
% 29.81/9.66 |
% 29.81/9.66 | Instantiating formula (259) with n16, all_0_9_9, n15 and discharging atoms pred(n16) = all_0_9_9, pred(n16) = n15, yields:
% 29.81/9.66 | (806) all_0_9_9 = n15
% 29.81/9.66 |
% 29.81/9.66 | Instantiating formula (184) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 29.81/9.66 | (807) all_0_5_5 = n17
% 29.81/9.66 |
% 29.81/9.66 | From (807) and (386) follows:
% 29.81/9.66 | (3893) sum(all_0_6_6, n17) = all_0_4_4
% 29.81/9.66 |
% 29.81/9.66 | From (806)(807) and (156) follows:
% 29.81/9.66 | (808) sum(n15, n17) = all_0_2_2
% 29.81/9.66 |
% 29.81/9.66 | From (806) and (74) follows:
% 29.81/9.66 | (3895) sum(n15, all_0_8_8) = all_0_7_7
% 29.81/9.66 |
% 29.81/9.66 | Instantiating formula (194) with n15, n17, all_0_2_2, n11 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n11, yields:
% 29.81/9.66 | (812) all_0_2_2 = n11
% 29.81/9.66 |
% 29.81/9.66 | From (812) and (85) follows:
% 29.81/9.66 | (3897) sum(n11, all_0_1_1) = all_0_0_0
% 29.81/9.66 |
% 29.81/9.66 +-Applying beta-rule and splitting (1191), into two cases.
% 29.81/9.66 |-Branch one:
% 29.81/9.66 | (1192) all_0_10_10 = n15
% 29.81/9.66 |
% 29.81/9.66 | From (1192) and (57) follows:
% 29.81/9.66 | (1193) pred(n15) = all_0_6_6
% 29.81/9.66 |
% 29.81/9.66 | From (1192) and (381) follows:
% 29.81/9.66 | (1194) succ(n15) = all_0_8_8
% 29.81/9.66 |
% 29.81/9.66 | Instantiating formula (259) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 29.81/9.66 | (1195) all_0_6_6 = n14
% 29.81/9.66 |
% 29.81/9.66 | Instantiating formula (184) with n15, all_0_8_8, n16 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n16, yields:
% 29.81/9.66 | (1196) all_0_8_8 = n16
% 29.81/9.66 |
% 29.81/9.66 | From (1195)(1196) and (628) follows:
% 29.81/9.66 | (1197) sum(n14, n16) = all_0_1_1
% 29.81/9.66 |
% 29.81/9.66 | From (1195) and (3893) follows:
% 29.81/9.66 | (3904) sum(n14, n17) = all_0_4_4
% 29.81/9.66 |
% 29.81/9.66 | From (1196) and (3895) follows:
% 29.81/9.66 | (3905) sum(n15, n16) = all_0_7_7
% 29.81/9.66 |
% 29.81/9.66 | Instantiating formula (194) with n15, n16, all_0_7_7, n10 and discharging atoms sum(n15, n16) = all_0_7_7, sum(n15, n16) = n10, yields:
% 29.81/9.66 | (903) all_0_7_7 = n10
% 29.81/9.66 |
% 29.81/9.66 | Instantiating formula (194) with n14, n17, all_0_4_4, n10 and discharging atoms sum(n14, n17) = all_0_4_4, sum(n14, n17) = n10, yields:
% 29.81/9.66 | (901) all_0_4_4 = n10
% 29.81/9.66 |
% 29.81/9.66 | Instantiating formula (194) with n14, n16, all_0_1_1, n9 and discharging atoms sum(n14, n16) = all_0_1_1, sum(n14, n16) = n9, yields:
% 29.81/9.66 | (1201) all_0_1_1 = n9
% 29.81/9.66 |
% 29.81/9.66 | From (903)(901) and (435) follows:
% 29.81/9.66 | (905) sum(n10, n10) = all_0_3_3
% 29.81/9.66 |
% 29.81/9.66 | From (1201) and (3897) follows:
% 29.81/9.66 | (3910) sum(n11, n9) = all_0_0_0
% 29.81/9.66 |
% 29.81/9.66 | Instantiating formula (194) with n11, n9, all_0_0_0, n20 and discharging atoms sum(n11, n9) = all_0_0_0, sum(n11, n9) = n20, yields:
% 29.81/9.66 | (907) all_0_0_0 = n20
% 29.81/9.66 |
% 29.81/9.66 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 29.81/9.66 | (906) all_0_3_3 = n20
% 29.81/9.66 |
% 29.81/9.66 | Equations (907,906) can reduce 201 to:
% 29.81/9.66 | (746) $false
% 29.81/9.66 |
% 29.81/9.66 |-The branch is then unsatisfiable
% 29.81/9.66 |-Branch two:
% 29.81/9.66 | (1208) ~ (all_0_10_10 = n15)
% 29.81/9.66 | (1209) all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.81/9.66 |
% 29.81/9.66 +-Applying beta-rule and splitting (1209), into two cases.
% 29.81/9.66 |-Branch one:
% 29.81/9.66 | (1210) all_0_10_10 = n14
% 29.81/9.66 |
% 29.81/9.66 | From (1210) and (57) follows:
% 29.81/9.66 | (1211) pred(n14) = all_0_6_6
% 29.81/9.66 |
% 29.81/9.66 | From (1210) and (381) follows:
% 29.81/9.66 | (1212) succ(n14) = all_0_8_8
% 29.81/9.66 |
% 29.81/9.66 | Instantiating formula (259) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 29.81/9.66 | (1213) all_0_6_6 = n13
% 29.81/9.66 |
% 29.81/9.66 | Instantiating formula (184) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 29.81/9.66 | (1214) all_0_8_8 = n15
% 29.81/9.66 |
% 29.81/9.66 | From (1213)(1214) and (628) follows:
% 29.81/9.66 | (1215) sum(n13, n15) = all_0_1_1
% 29.81/9.66 |
% 29.81/9.66 | From (1213) and (3893) follows:
% 29.81/9.66 | (3922) sum(n13, n17) = all_0_4_4
% 29.81/9.66 |
% 29.81/9.66 | From (1214) and (3895) follows:
% 29.81/9.66 | (3923) sum(n15, n15) = all_0_7_7
% 29.81/9.66 |
% 29.81/9.66 | Instantiating formula (194) with n15, n15, all_0_7_7, n9 and discharging atoms sum(n15, n15) = all_0_7_7, sum(n15, n15) = n9, yields:
% 29.81/9.66 | (921) all_0_7_7 = n9
% 29.81/9.66 |
% 29.81/9.66 | Instantiating formula (194) with n13, n17, all_0_4_4, n9 and discharging atoms sum(n13, n17) = all_0_4_4, sum(n13, n17) = n9, yields:
% 29.81/9.66 | (919) all_0_4_4 = n9
% 29.81/9.66 |
% 29.81/9.66 | Instantiating formula (194) with n13, n15, all_0_1_1, n7 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n7, yields:
% 29.81/9.66 | (1219) all_0_1_1 = n7
% 29.81/9.66 |
% 29.81/9.66 | From (921)(919) and (435) follows:
% 29.81/9.66 | (923) sum(n9, n9) = all_0_3_3
% 29.81/9.66 |
% 29.81/9.66 | From (1219) and (3897) follows:
% 29.81/9.67 | (3928) sum(n11, n7) = all_0_0_0
% 29.81/9.67 |
% 29.81/9.67 | Instantiating formula (194) with n11, n7, all_0_0_0, n18 and discharging atoms sum(n11, n7) = all_0_0_0, sum(n11, n7) = n18, yields:
% 29.81/9.67 | (924) all_0_0_0 = n18
% 29.81/9.67 |
% 29.81/9.67 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 29.81/9.67 | (925) all_0_3_3 = n18
% 29.81/9.67 |
% 29.81/9.67 | Equations (924,925) can reduce 201 to:
% 29.81/9.67 | (746) $false
% 29.81/9.67 |
% 29.81/9.67 |-The branch is then unsatisfiable
% 29.81/9.67 |-Branch two:
% 29.81/9.67 | (1226) ~ (all_0_10_10 = n14)
% 29.81/9.67 | (1227) all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 29.81/9.67 |
% 29.81/9.67 +-Applying beta-rule and splitting (1227), into two cases.
% 29.81/9.67 |-Branch one:
% 29.81/9.67 | (1228) all_0_10_10 = n13
% 29.81/9.67 |
% 29.81/9.67 | From (1228) and (57) follows:
% 29.81/9.67 | (1229) pred(n13) = all_0_6_6
% 29.81/9.67 |
% 29.81/9.67 | From (1228) and (381) follows:
% 29.81/9.67 | (1230) succ(n13) = all_0_8_8
% 29.81/9.67 |
% 29.81/9.67 | Instantiating formula (259) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 29.81/9.67 | (1231) all_0_6_6 = n12
% 29.81/9.67 |
% 29.81/9.67 | Instantiating formula (184) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 29.81/9.67 | (1232) all_0_8_8 = n14
% 29.81/9.67 |
% 29.81/9.67 | From (1231)(1232) and (628) follows:
% 29.81/9.67 | (1233) sum(n12, n14) = all_0_1_1
% 29.81/9.67 |
% 29.81/9.67 | From (1231) and (3893) follows:
% 29.81/9.67 | (3940) sum(n12, n17) = all_0_4_4
% 29.81/9.67 |
% 29.81/9.67 | From (1232) and (3895) follows:
% 29.81/9.67 | (3941) sum(n15, n14) = all_0_7_7
% 29.81/9.67 |
% 29.81/9.67 | Instantiating formula (194) with n15, n14, all_0_7_7, n8 and discharging atoms sum(n15, n14) = all_0_7_7, sum(n15, n14) = n8, yields:
% 29.81/9.67 | (939) all_0_7_7 = n8
% 29.81/9.67 |
% 29.81/9.67 | Instantiating formula (194) with n12, n17, all_0_4_4, n8 and discharging atoms sum(n12, n17) = all_0_4_4, sum(n12, n17) = n8, yields:
% 29.81/9.67 | (937) all_0_4_4 = n8
% 29.81/9.67 |
% 29.81/9.67 | Instantiating formula (194) with n12, n14, all_0_1_1, n5 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n5, yields:
% 29.81/9.67 | (1237) all_0_1_1 = n5
% 29.81/9.67 |
% 29.81/9.67 | From (939)(937) and (435) follows:
% 29.81/9.67 | (941) sum(n8, n8) = all_0_3_3
% 29.81/9.67 |
% 29.81/9.67 | From (1237) and (3897) follows:
% 30.09/9.67 | (3946) sum(n11, n5) = all_0_0_0
% 30.09/9.67 |
% 30.09/9.67 | Instantiating formula (194) with n11, n5, all_0_0_0, n16 and discharging atoms sum(n11, n5) = all_0_0_0, sum(n11, n5) = n16, yields:
% 30.09/9.67 | (942) all_0_0_0 = n16
% 30.09/9.67 |
% 30.09/9.67 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 30.09/9.67 | (943) all_0_3_3 = n16
% 30.09/9.67 |
% 30.09/9.67 | Equations (942,943) can reduce 201 to:
% 30.09/9.67 | (746) $false
% 30.09/9.67 |
% 30.09/9.67 |-The branch is then unsatisfiable
% 30.09/9.67 |-Branch two:
% 30.09/9.67 | (1244) ~ (all_0_10_10 = n13)
% 30.09/9.67 | (1245) all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.09/9.67 |
% 30.09/9.67 +-Applying beta-rule and splitting (1245), into two cases.
% 30.09/9.67 |-Branch one:
% 30.09/9.67 | (1246) all_0_10_10 = n12
% 30.09/9.67 |
% 30.09/9.67 | From (1246) and (57) follows:
% 30.09/9.67 | (1247) pred(n12) = all_0_6_6
% 30.09/9.67 |
% 30.09/9.67 | From (1246) and (381) follows:
% 30.09/9.67 | (1248) succ(n12) = all_0_8_8
% 30.09/9.67 |
% 30.09/9.67 | Instantiating formula (259) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 30.09/9.67 | (1249) all_0_6_6 = n11
% 30.09/9.67 |
% 30.09/9.67 | Instantiating formula (184) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 30.09/9.67 | (1250) all_0_8_8 = n13
% 30.09/9.67 |
% 30.09/9.67 | From (1249)(1250) and (628) follows:
% 30.09/9.67 | (1251) sum(n11, n13) = all_0_1_1
% 30.09/9.67 |
% 30.09/9.67 | From (1249) and (3893) follows:
% 30.09/9.67 | (3958) sum(n11, n17) = all_0_4_4
% 30.09/9.67 |
% 30.09/9.67 | From (1250) and (3895) follows:
% 30.09/9.67 | (3959) sum(n15, n13) = all_0_7_7
% 30.09/9.67 |
% 30.09/9.67 | Instantiating formula (194) with n15, n13, all_0_7_7, n7 and discharging atoms sum(n15, n13) = all_0_7_7, sum(n15, n13) = n7, yields:
% 30.09/9.67 | (957) all_0_7_7 = n7
% 30.09/9.67 |
% 30.09/9.67 | Instantiating formula (194) with n11, n17, all_0_4_4, n7 and discharging atoms sum(n11, n17) = all_0_4_4, sum(n11, n17) = n7, yields:
% 30.09/9.67 | (955) all_0_4_4 = n7
% 30.09/9.67 |
% 30.09/9.67 | Instantiating formula (194) with n11, n13, all_0_1_1, n3 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n3, yields:
% 30.09/9.67 | (1255) all_0_1_1 = n3
% 30.09/9.67 |
% 30.09/9.67 | From (957)(955) and (435) follows:
% 30.09/9.67 | (959) sum(n7, n7) = all_0_3_3
% 30.09/9.67 |
% 30.09/9.67 | From (1255) and (3897) follows:
% 30.09/9.67 | (3964) sum(n11, n3) = all_0_0_0
% 30.09/9.67 |
% 30.09/9.67 | Instantiating formula (194) with n11, n3, all_0_0_0, n14 and discharging atoms sum(n11, n3) = all_0_0_0, sum(n11, n3) = n14, yields:
% 30.09/9.67 | (960) all_0_0_0 = n14
% 30.09/9.67 |
% 30.09/9.67 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 30.09/9.67 | (961) all_0_3_3 = n14
% 30.09/9.67 |
% 30.09/9.67 | Equations (960,961) can reduce 201 to:
% 30.09/9.67 | (746) $false
% 30.09/9.67 |
% 30.09/9.67 |-The branch is then unsatisfiable
% 30.09/9.67 |-Branch two:
% 30.09/9.67 | (1262) ~ (all_0_10_10 = n12)
% 30.09/9.67 | (1263) all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.09/9.67 |
% 30.09/9.67 +-Applying beta-rule and splitting (1263), into two cases.
% 30.09/9.67 |-Branch one:
% 30.09/9.67 | (1264) all_0_10_10 = n11
% 30.09/9.67 |
% 30.09/9.67 | From (1264) and (57) follows:
% 30.09/9.67 | (1265) pred(n11) = all_0_6_6
% 30.09/9.67 |
% 30.09/9.67 | From (1264) and (381) follows:
% 30.09/9.67 | (1266) succ(n11) = all_0_8_8
% 30.09/9.67 |
% 30.09/9.67 | Instantiating formula (259) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 30.09/9.67 | (1267) all_0_6_6 = n10
% 30.09/9.67 |
% 30.09/9.67 | Instantiating formula (184) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 30.09/9.67 | (1268) all_0_8_8 = n12
% 30.09/9.67 |
% 30.09/9.67 | From (1267)(1268) and (628) follows:
% 30.09/9.67 | (1269) sum(n10, n12) = all_0_1_1
% 30.09/9.67 |
% 30.09/9.67 | From (1267) and (3893) follows:
% 30.09/9.67 | (3976) sum(n10, n17) = all_0_4_4
% 30.09/9.67 |
% 30.09/9.67 | From (1268) and (3895) follows:
% 30.11/9.67 | (3977) sum(n15, n12) = all_0_7_7
% 30.11/9.67 |
% 30.11/9.67 | Instantiating formula (194) with n15, n12, all_0_7_7, n6 and discharging atoms sum(n15, n12) = all_0_7_7, sum(n15, n12) = n6, yields:
% 30.11/9.67 | (975) all_0_7_7 = n6
% 30.11/9.67 |
% 30.11/9.67 | Instantiating formula (194) with n10, n17, all_0_4_4, n6 and discharging atoms sum(n10, n17) = all_0_4_4, sum(n10, n17) = n6, yields:
% 30.11/9.67 | (973) all_0_4_4 = n6
% 30.11/9.67 |
% 30.11/9.67 | Instantiating formula (194) with n10, n12, all_0_1_1, n1 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n1, yields:
% 30.11/9.67 | (1273) all_0_1_1 = n1
% 30.11/9.67 |
% 30.11/9.67 | From (975)(973) and (435) follows:
% 30.11/9.67 | (977) sum(n6, n6) = all_0_3_3
% 30.11/9.67 |
% 30.11/9.67 | From (1273) and (3897) follows:
% 30.11/9.68 | (3982) sum(n11, n1) = all_0_0_0
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n11, n1, all_0_0_0, n12 and discharging atoms sum(n11, n1) = all_0_0_0, sum(n11, n1) = n12, yields:
% 30.11/9.68 | (978) all_0_0_0 = n12
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 30.11/9.68 | (979) all_0_3_3 = n12
% 30.11/9.68 |
% 30.11/9.68 | Equations (978,979) can reduce 201 to:
% 30.11/9.68 | (746) $false
% 30.11/9.68 |
% 30.11/9.68 |-The branch is then unsatisfiable
% 30.11/9.68 |-Branch two:
% 30.11/9.68 | (1280) ~ (all_0_10_10 = n11)
% 30.11/9.68 | (1281) all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.11/9.68 |
% 30.11/9.68 +-Applying beta-rule and splitting (1281), into two cases.
% 30.11/9.68 |-Branch one:
% 30.11/9.68 | (1282) all_0_10_10 = n10
% 30.11/9.68 |
% 30.11/9.68 | From (1282) and (57) follows:
% 30.11/9.68 | (1283) pred(n10) = all_0_6_6
% 30.11/9.68 |
% 30.11/9.68 | From (1282) and (381) follows:
% 30.11/9.68 | (1284) succ(n10) = all_0_8_8
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (259) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 30.11/9.68 | (1285) all_0_6_6 = n9
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (184) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 30.11/9.68 | (1286) all_0_8_8 = n11
% 30.11/9.68 |
% 30.11/9.68 | From (1285)(1286) and (628) follows:
% 30.11/9.68 | (1287) sum(n9, n11) = all_0_1_1
% 30.11/9.68 |
% 30.11/9.68 | From (1285) and (3893) follows:
% 30.11/9.68 | (3994) sum(n9, n17) = all_0_4_4
% 30.11/9.68 |
% 30.11/9.68 | From (1286) and (3895) follows:
% 30.11/9.68 | (3995) sum(n15, n11) = all_0_7_7
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n15, n11, all_0_7_7, n5 and discharging atoms sum(n15, n11) = all_0_7_7, sum(n15, n11) = n5, yields:
% 30.11/9.68 | (993) all_0_7_7 = n5
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n9, n17, all_0_4_4, n5 and discharging atoms sum(n9, n17) = all_0_4_4, sum(n9, n17) = n5, yields:
% 30.11/9.68 | (991) all_0_4_4 = n5
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 30.11/9.68 | (1291) all_0_1_1 = n20
% 30.11/9.68 |
% 30.11/9.68 | From (993)(991) and (435) follows:
% 30.11/9.68 | (995) sum(n5, n5) = all_0_3_3
% 30.11/9.68 |
% 30.11/9.68 | From (1291) and (3897) follows:
% 30.11/9.68 | (4000) sum(n11, n20) = all_0_0_0
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n11, n20, all_0_0_0, n10 and discharging atoms sum(n11, n20) = all_0_0_0, sum(n11, n20) = n10, yields:
% 30.11/9.68 | (996) all_0_0_0 = n10
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 30.11/9.68 | (997) all_0_3_3 = n10
% 30.11/9.68 |
% 30.11/9.68 | Equations (996,997) can reduce 201 to:
% 30.11/9.68 | (746) $false
% 30.11/9.68 |
% 30.11/9.68 |-The branch is then unsatisfiable
% 30.11/9.68 |-Branch two:
% 30.11/9.68 | (1298) ~ (all_0_10_10 = n10)
% 30.11/9.68 | (1299) all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.11/9.68 |
% 30.11/9.68 +-Applying beta-rule and splitting (1299), into two cases.
% 30.11/9.68 |-Branch one:
% 30.11/9.68 | (1300) all_0_10_10 = n9
% 30.11/9.68 |
% 30.11/9.68 | From (1300) and (57) follows:
% 30.11/9.68 | (1301) pred(n9) = all_0_6_6
% 30.11/9.68 |
% 30.11/9.68 | From (1300) and (381) follows:
% 30.11/9.68 | (1302) succ(n9) = all_0_8_8
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (259) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 30.11/9.68 | (1303) all_0_6_6 = n8
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (184) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 30.11/9.68 | (1304) all_0_8_8 = n10
% 30.11/9.68 |
% 30.11/9.68 | From (1303)(1304) and (628) follows:
% 30.11/9.68 | (1305) sum(n8, n10) = all_0_1_1
% 30.11/9.68 |
% 30.11/9.68 | From (1303) and (3893) follows:
% 30.11/9.68 | (4012) sum(n8, n17) = all_0_4_4
% 30.11/9.68 |
% 30.11/9.68 | From (1304) and (3895) follows:
% 30.11/9.68 | (4013) sum(n15, n10) = all_0_7_7
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n15, n10, all_0_7_7, n4 and discharging atoms sum(n15, n10) = all_0_7_7, sum(n15, n10) = n4, yields:
% 30.11/9.68 | (1011) all_0_7_7 = n4
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n8, n17, all_0_4_4, n4 and discharging atoms sum(n8, n17) = all_0_4_4, sum(n8, n17) = n4, yields:
% 30.11/9.68 | (1009) all_0_4_4 = n4
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 30.11/9.68 | (1309) all_0_1_1 = n18
% 30.11/9.68 |
% 30.11/9.68 | From (1011)(1009) and (435) follows:
% 30.11/9.68 | (1013) sum(n4, n4) = all_0_3_3
% 30.11/9.68 |
% 30.11/9.68 | From (1309) and (3897) follows:
% 30.11/9.68 | (4018) sum(n11, n18) = all_0_0_0
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n11, n18, all_0_0_0, n8 and discharging atoms sum(n11, n18) = all_0_0_0, sum(n11, n18) = n8, yields:
% 30.11/9.68 | (1014) all_0_0_0 = n8
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 30.11/9.68 | (1015) all_0_3_3 = n8
% 30.11/9.68 |
% 30.11/9.68 | Equations (1014,1015) can reduce 201 to:
% 30.11/9.68 | (746) $false
% 30.11/9.68 |
% 30.11/9.68 |-The branch is then unsatisfiable
% 30.11/9.68 |-Branch two:
% 30.11/9.68 | (1316) ~ (all_0_10_10 = n9)
% 30.11/9.68 | (1317) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.11/9.68 |
% 30.11/9.68 +-Applying beta-rule and splitting (1317), into two cases.
% 30.11/9.68 |-Branch one:
% 30.11/9.68 | (1318) all_0_10_10 = n8
% 30.11/9.68 |
% 30.11/9.68 | From (1318) and (57) follows:
% 30.11/9.68 | (1319) pred(n8) = all_0_6_6
% 30.11/9.68 |
% 30.11/9.68 | From (1318) and (381) follows:
% 30.11/9.68 | (1320) succ(n8) = all_0_8_8
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (259) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 30.11/9.68 | (1321) all_0_6_6 = n7
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (184) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 30.11/9.68 | (1322) all_0_8_8 = n9
% 30.11/9.68 |
% 30.11/9.68 | From (1321)(1322) and (628) follows:
% 30.11/9.68 | (1323) sum(n7, n9) = all_0_1_1
% 30.11/9.68 |
% 30.11/9.68 | From (1321) and (3893) follows:
% 30.11/9.68 | (4030) sum(n7, n17) = all_0_4_4
% 30.11/9.68 |
% 30.11/9.68 | From (1322) and (3895) follows:
% 30.11/9.68 | (4031) sum(n15, n9) = all_0_7_7
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n15, n9, all_0_7_7, n3 and discharging atoms sum(n15, n9) = all_0_7_7, sum(n15, n9) = n3, yields:
% 30.11/9.68 | (1029) all_0_7_7 = n3
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n7, n17, all_0_4_4, n3 and discharging atoms sum(n7, n17) = all_0_4_4, sum(n7, n17) = n3, yields:
% 30.11/9.68 | (1027) all_0_4_4 = n3
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 30.11/9.68 | (1327) all_0_1_1 = n16
% 30.11/9.68 |
% 30.11/9.68 | From (1029)(1027) and (435) follows:
% 30.11/9.68 | (1031) sum(n3, n3) = all_0_3_3
% 30.11/9.68 |
% 30.11/9.68 | From (1327) and (3897) follows:
% 30.11/9.68 | (4036) sum(n11, n16) = all_0_0_0
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n11, n16, all_0_0_0, n6 and discharging atoms sum(n11, n16) = all_0_0_0, sum(n11, n16) = n6, yields:
% 30.11/9.68 | (1032) all_0_0_0 = n6
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 30.11/9.68 | (1033) all_0_3_3 = n6
% 30.11/9.68 |
% 30.11/9.68 | Equations (1032,1033) can reduce 201 to:
% 30.11/9.68 | (746) $false
% 30.11/9.68 |
% 30.11/9.68 |-The branch is then unsatisfiable
% 30.11/9.68 |-Branch two:
% 30.11/9.68 | (1334) ~ (all_0_10_10 = n8)
% 30.11/9.68 | (1335) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.11/9.68 |
% 30.11/9.68 +-Applying beta-rule and splitting (1335), into two cases.
% 30.11/9.68 |-Branch one:
% 30.11/9.68 | (1336) all_0_10_10 = n7
% 30.11/9.68 |
% 30.11/9.68 | From (1336) and (57) follows:
% 30.11/9.68 | (1337) pred(n7) = all_0_6_6
% 30.11/9.68 |
% 30.11/9.68 | From (1336) and (381) follows:
% 30.11/9.68 | (1338) succ(n7) = all_0_8_8
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (259) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 30.11/9.68 | (1339) all_0_6_6 = n6
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (184) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 30.11/9.68 | (1340) all_0_8_8 = n8
% 30.11/9.68 |
% 30.11/9.68 | From (1339)(1340) and (628) follows:
% 30.11/9.68 | (1341) sum(n6, n8) = all_0_1_1
% 30.11/9.68 |
% 30.11/9.68 | From (1339) and (3893) follows:
% 30.11/9.68 | (4048) sum(n6, n17) = all_0_4_4
% 30.11/9.68 |
% 30.11/9.68 | From (1340) and (3895) follows:
% 30.11/9.68 | (4049) sum(n15, n8) = all_0_7_7
% 30.11/9.68 |
% 30.11/9.68 | Instantiating formula (194) with n15, n8, all_0_7_7, n2 and discharging atoms sum(n15, n8) = all_0_7_7, sum(n15, n8) = n2, yields:
% 30.11/9.69 | (1047) all_0_7_7 = n2
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n6, n17, all_0_4_4, n2 and discharging atoms sum(n6, n17) = all_0_4_4, sum(n6, n17) = n2, yields:
% 30.11/9.69 | (1045) all_0_4_4 = n2
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 30.11/9.69 | (1345) all_0_1_1 = n14
% 30.11/9.69 |
% 30.11/9.69 | From (1047)(1045) and (435) follows:
% 30.11/9.69 | (1049) sum(n2, n2) = all_0_3_3
% 30.11/9.69 |
% 30.11/9.69 | From (1345) and (3897) follows:
% 30.11/9.69 | (4054) sum(n11, n14) = all_0_0_0
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n11, n14, all_0_0_0, n4 and discharging atoms sum(n11, n14) = all_0_0_0, sum(n11, n14) = n4, yields:
% 30.11/9.69 | (1050) all_0_0_0 = n4
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 30.11/9.69 | (1051) all_0_3_3 = n4
% 30.11/9.69 |
% 30.11/9.69 | Equations (1050,1051) can reduce 201 to:
% 30.11/9.69 | (746) $false
% 30.11/9.69 |
% 30.11/9.69 |-The branch is then unsatisfiable
% 30.11/9.69 |-Branch two:
% 30.11/9.69 | (1352) ~ (all_0_10_10 = n7)
% 30.11/9.69 | (1353) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.11/9.69 |
% 30.11/9.69 +-Applying beta-rule and splitting (1353), into two cases.
% 30.11/9.69 |-Branch one:
% 30.11/9.69 | (1354) all_0_10_10 = n6
% 30.11/9.69 |
% 30.11/9.69 | From (1354) and (57) follows:
% 30.11/9.69 | (1355) pred(n6) = all_0_6_6
% 30.11/9.69 |
% 30.11/9.69 | From (1354) and (381) follows:
% 30.11/9.69 | (1356) succ(n6) = all_0_8_8
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (259) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 30.11/9.69 | (1357) all_0_6_6 = n5
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (184) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 30.11/9.69 | (1358) all_0_8_8 = n7
% 30.11/9.69 |
% 30.11/9.69 | From (1357)(1358) and (628) follows:
% 30.11/9.69 | (1359) sum(n5, n7) = all_0_1_1
% 30.11/9.69 |
% 30.11/9.69 | From (1357) and (3893) follows:
% 30.11/9.69 | (4066) sum(n5, n17) = all_0_4_4
% 30.11/9.69 |
% 30.11/9.69 | From (1358) and (3895) follows:
% 30.11/9.69 | (4067) sum(n15, n7) = all_0_7_7
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n15, n7, all_0_7_7, n1 and discharging atoms sum(n15, n7) = all_0_7_7, sum(n15, n7) = n1, yields:
% 30.11/9.69 | (1065) all_0_7_7 = n1
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n5, n17, all_0_4_4, n1 and discharging atoms sum(n5, n17) = all_0_4_4, sum(n5, n17) = n1, yields:
% 30.11/9.69 | (1063) all_0_4_4 = n1
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 30.11/9.69 | (1363) all_0_1_1 = n12
% 30.11/9.69 |
% 30.11/9.69 | From (1065)(1063) and (435) follows:
% 30.11/9.69 | (1067) sum(n1, n1) = all_0_3_3
% 30.11/9.69 |
% 30.11/9.69 | From (1363) and (3897) follows:
% 30.11/9.69 | (4072) sum(n11, n12) = all_0_0_0
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n11, n12, all_0_0_0, n2 and discharging atoms sum(n11, n12) = all_0_0_0, sum(n11, n12) = n2, yields:
% 30.11/9.69 | (1068) all_0_0_0 = n2
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 30.11/9.69 | (1069) all_0_3_3 = n2
% 30.11/9.69 |
% 30.11/9.69 | Equations (1068,1069) can reduce 201 to:
% 30.11/9.69 | (746) $false
% 30.11/9.69 |
% 30.11/9.69 |-The branch is then unsatisfiable
% 30.11/9.69 |-Branch two:
% 30.11/9.69 | (1370) ~ (all_0_10_10 = n6)
% 30.11/9.69 | (1371) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.11/9.69 |
% 30.11/9.69 +-Applying beta-rule and splitting (1371), into two cases.
% 30.11/9.69 |-Branch one:
% 30.11/9.69 | (1372) all_0_10_10 = n5
% 30.11/9.69 |
% 30.11/9.69 | From (1372) and (57) follows:
% 30.11/9.69 | (1373) pred(n5) = all_0_6_6
% 30.11/9.69 |
% 30.11/9.69 | From (1372) and (381) follows:
% 30.11/9.69 | (1374) succ(n5) = all_0_8_8
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (259) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 30.11/9.69 | (1375) all_0_6_6 = n4
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (184) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 30.11/9.69 | (1376) all_0_8_8 = n6
% 30.11/9.69 |
% 30.11/9.69 | From (1375)(1376) and (628) follows:
% 30.11/9.69 | (1377) sum(n4, n6) = all_0_1_1
% 30.11/9.69 |
% 30.11/9.69 | From (1375) and (3893) follows:
% 30.11/9.69 | (4084) sum(n4, n17) = all_0_4_4
% 30.11/9.69 |
% 30.11/9.69 | From (1376) and (3895) follows:
% 30.11/9.69 | (4085) sum(n15, n6) = all_0_7_7
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n15, n6, all_0_7_7, n0 and discharging atoms sum(n15, n6) = all_0_7_7, sum(n15, n6) = n0, yields:
% 30.11/9.69 | (1083) all_0_7_7 = n0
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n4, n17, all_0_4_4, n0 and discharging atoms sum(n4, n17) = all_0_4_4, sum(n4, n17) = n0, yields:
% 30.11/9.69 | (1081) all_0_4_4 = n0
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 30.11/9.69 | (1381) all_0_1_1 = n10
% 30.11/9.69 |
% 30.11/9.69 | From (1083)(1081) and (435) follows:
% 30.11/9.69 | (1085) sum(n0, n0) = all_0_3_3
% 30.11/9.69 |
% 30.11/9.69 | From (1381) and (3897) follows:
% 30.11/9.69 | (4090) sum(n11, n10) = all_0_0_0
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n11, n10, all_0_0_0, n0 and discharging atoms sum(n11, n10) = all_0_0_0, sum(n11, n10) = n0, yields:
% 30.11/9.69 | (1087) all_0_0_0 = n0
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 30.11/9.69 | (1088) all_0_3_3 = n0
% 30.11/9.69 |
% 30.11/9.69 | Equations (1087,1088) can reduce 201 to:
% 30.11/9.69 | (746) $false
% 30.11/9.69 |
% 30.11/9.69 |-The branch is then unsatisfiable
% 30.11/9.69 |-Branch two:
% 30.11/9.69 | (1388) ~ (all_0_10_10 = n5)
% 30.11/9.69 | (1389) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.11/9.69 |
% 30.11/9.69 +-Applying beta-rule and splitting (1389), into two cases.
% 30.11/9.69 |-Branch one:
% 30.11/9.69 | (1390) all_0_10_10 = n4
% 30.11/9.69 |
% 30.11/9.69 | From (1390) and (57) follows:
% 30.11/9.69 | (1391) pred(n4) = all_0_6_6
% 30.11/9.69 |
% 30.11/9.69 | From (1390) and (381) follows:
% 30.11/9.69 | (1392) succ(n4) = all_0_8_8
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (259) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 30.11/9.69 | (1393) all_0_6_6 = n3
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (184) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 30.11/9.69 | (1394) all_0_8_8 = n5
% 30.11/9.69 |
% 30.11/9.69 | From (1393)(1394) and (628) follows:
% 30.11/9.69 | (1395) sum(n3, n5) = all_0_1_1
% 30.11/9.69 |
% 30.11/9.69 | From (1393) and (3893) follows:
% 30.11/9.69 | (4102) sum(n3, n17) = all_0_4_4
% 30.11/9.69 |
% 30.11/9.69 | From (1394) and (3895) follows:
% 30.11/9.69 | (4103) sum(n15, n5) = all_0_7_7
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n15, n5, all_0_7_7, n20 and discharging atoms sum(n15, n5) = all_0_7_7, sum(n15, n5) = n20, yields:
% 30.11/9.69 | (1100) all_0_7_7 = n20
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n3, n17, all_0_4_4, n20 and discharging atoms sum(n3, n17) = all_0_4_4, sum(n3, n17) = n20, yields:
% 30.11/9.69 | (1101) all_0_4_4 = n20
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 30.11/9.69 | (1399) all_0_1_1 = n8
% 30.11/9.69 |
% 30.11/9.69 | From (1100)(1101) and (435) follows:
% 30.11/9.69 | (1103) sum(n20, n20) = all_0_3_3
% 30.11/9.69 |
% 30.11/9.69 | From (1399) and (3897) follows:
% 30.11/9.69 | (4108) sum(n11, n8) = all_0_0_0
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 30.11/9.69 | (1104) all_0_3_3 = n19
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (194) with n11, n8, all_0_0_0, n19 and discharging atoms sum(n11, n8) = all_0_0_0, sum(n11, n8) = n19, yields:
% 30.11/9.69 | (1105) all_0_0_0 = n19
% 30.11/9.69 |
% 30.11/9.69 | Equations (1105,1104) can reduce 201 to:
% 30.11/9.69 | (746) $false
% 30.11/9.69 |
% 30.11/9.69 |-The branch is then unsatisfiable
% 30.11/9.69 |-Branch two:
% 30.11/9.69 | (1406) ~ (all_0_10_10 = n4)
% 30.11/9.69 | (1407) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.11/9.69 |
% 30.11/9.69 +-Applying beta-rule and splitting (1407), into two cases.
% 30.11/9.69 |-Branch one:
% 30.11/9.69 | (1408) all_0_10_10 = n3
% 30.11/9.69 |
% 30.11/9.69 | From (1408) and (57) follows:
% 30.11/9.69 | (1409) pred(n3) = all_0_6_6
% 30.11/9.69 |
% 30.11/9.69 | From (1408) and (381) follows:
% 30.11/9.69 | (1410) succ(n3) = all_0_8_8
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 30.11/9.69 | (1411) all_0_6_6 = n2
% 30.11/9.69 |
% 30.11/9.69 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 30.11/9.69 | (1412) all_0_8_8 = n4
% 30.11/9.69 |
% 30.11/9.69 | From (1411)(1412) and (628) follows:
% 30.11/9.69 | (1413) sum(n2, n4) = all_0_1_1
% 30.11/9.69 |
% 30.11/9.69 | From (1411) and (3893) follows:
% 30.11/9.70 | (4120) sum(n2, n17) = all_0_4_4
% 30.11/9.70 |
% 30.11/9.70 | From (1412) and (3895) follows:
% 30.11/9.70 | (4121) sum(n15, n4) = all_0_7_7
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (194) with n15, n4, all_0_7_7, n19 and discharging atoms sum(n15, n4) = all_0_7_7, sum(n15, n4) = n19, yields:
% 30.11/9.70 | (737) all_0_7_7 = n19
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (194) with n2, n17, all_0_4_4, n19 and discharging atoms sum(n2, n17) = all_0_4_4, sum(n2, n17) = n19, yields:
% 30.11/9.70 | (736) all_0_4_4 = n19
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 30.11/9.70 | (1417) all_0_1_1 = n6
% 30.11/9.70 |
% 30.11/9.70 | From (737)(736) and (435) follows:
% 30.11/9.70 | (741) sum(n19, n19) = all_0_3_3
% 30.11/9.70 |
% 30.11/9.70 | From (1417) and (3897) follows:
% 30.11/9.70 | (4126) sum(n11, n6) = all_0_0_0
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 30.11/9.70 | (744) all_0_3_3 = n17
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (194) with n11, n6, all_0_0_0, n17 and discharging atoms sum(n11, n6) = all_0_0_0, sum(n11, n6) = n17, yields:
% 30.11/9.70 | (742) all_0_0_0 = n17
% 30.11/9.70 |
% 30.11/9.70 | Equations (742,744) can reduce 201 to:
% 30.11/9.70 | (746) $false
% 30.11/9.70 |
% 30.11/9.70 |-The branch is then unsatisfiable
% 30.11/9.70 |-Branch two:
% 30.11/9.70 | (1424) ~ (all_0_10_10 = n3)
% 30.11/9.70 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.11/9.70 |
% 30.11/9.70 +-Applying beta-rule and splitting (1425), into two cases.
% 30.11/9.70 |-Branch one:
% 30.11/9.70 | (1426) all_0_10_10 = n2
% 30.11/9.70 |
% 30.11/9.70 | From (1426) and (57) follows:
% 30.11/9.70 | (1427) pred(n2) = all_0_6_6
% 30.11/9.70 |
% 30.11/9.70 | From (1426) and (381) follows:
% 30.11/9.70 | (1428) succ(n2) = all_0_8_8
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 30.11/9.70 | (1429) all_0_6_6 = n1
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 30.11/9.70 | (1430) all_0_8_8 = n3
% 30.11/9.70 |
% 30.11/9.70 | From (1429)(1430) and (628) follows:
% 30.11/9.70 | (1431) sum(n1, n3) = all_0_1_1
% 30.11/9.70 |
% 30.11/9.70 | From (1429) and (3893) follows:
% 30.11/9.70 | (4138) sum(n1, n17) = all_0_4_4
% 30.11/9.70 |
% 30.11/9.70 | From (1430) and (3895) follows:
% 30.11/9.70 | (4139) sum(n15, n3) = all_0_7_7
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (194) with n15, n3, all_0_7_7, n18 and discharging atoms sum(n15, n3) = all_0_7_7, sum(n15, n3) = n18, yields:
% 30.11/9.70 | (759) all_0_7_7 = n18
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (194) with n1, n17, all_0_4_4, n18 and discharging atoms sum(n1, n17) = all_0_4_4, sum(n1, n17) = n18, yields:
% 30.11/9.70 | (757) all_0_4_4 = n18
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 30.11/9.70 | (1435) all_0_1_1 = n4
% 30.11/9.70 |
% 30.11/9.70 | From (759)(757) and (435) follows:
% 30.11/9.70 | (761) sum(n18, n18) = all_0_3_3
% 30.11/9.70 |
% 30.11/9.70 | From (1435) and (3897) follows:
% 30.11/9.70 | (4144) sum(n11, n4) = all_0_0_0
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 30.11/9.70 | (762) all_0_3_3 = n15
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (194) with n11, n4, all_0_0_0, n15 and discharging atoms sum(n11, n4) = all_0_0_0, sum(n11, n4) = n15, yields:
% 30.11/9.70 | (763) all_0_0_0 = n15
% 30.11/9.70 |
% 30.11/9.70 | Equations (763,762) can reduce 201 to:
% 30.11/9.70 | (746) $false
% 30.11/9.70 |
% 30.11/9.70 |-The branch is then unsatisfiable
% 30.11/9.70 |-Branch two:
% 30.11/9.70 | (1442) ~ (all_0_10_10 = n2)
% 30.11/9.70 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 30.11/9.70 |
% 30.11/9.70 +-Applying beta-rule and splitting (1443), into two cases.
% 30.11/9.70 |-Branch one:
% 30.11/9.70 | (1444) all_0_10_10 = n1
% 30.11/9.70 |
% 30.11/9.70 | From (1444) and (57) follows:
% 30.11/9.70 | (1445) pred(n1) = all_0_6_6
% 30.11/9.70 |
% 30.11/9.70 | From (1444) and (381) follows:
% 30.11/9.70 | (1446) succ(n1) = all_0_8_8
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 30.11/9.70 | (1447) all_0_6_6 = n0
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 30.11/9.70 | (1448) all_0_8_8 = n2
% 30.11/9.70 |
% 30.11/9.70 | From (1447)(1448) and (628) follows:
% 30.11/9.70 | (1449) sum(n0, n2) = all_0_1_1
% 30.11/9.70 |
% 30.11/9.70 | From (1447) and (3893) follows:
% 30.11/9.70 | (4156) sum(n0, n17) = all_0_4_4
% 30.11/9.70 |
% 30.11/9.70 | From (1448) and (3895) follows:
% 30.11/9.70 | (4157) sum(n15, n2) = all_0_7_7
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (194) with n15, n2, all_0_7_7, n17 and discharging atoms sum(n15, n2) = all_0_7_7, sum(n15, n2) = n17, yields:
% 30.11/9.70 | (777) all_0_7_7 = n17
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (194) with n0, n17, all_0_4_4, n17 and discharging atoms sum(n0, n17) = all_0_4_4, sum(n0, n17) = n17, yields:
% 30.11/9.70 | (775) all_0_4_4 = n17
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 30.11/9.70 | (1453) all_0_1_1 = n2
% 30.11/9.70 |
% 30.11/9.70 | From (777)(775) and (435) follows:
% 30.11/9.70 | (779) sum(n17, n17) = all_0_3_3
% 30.11/9.70 |
% 30.11/9.70 | From (1453) and (3897) follows:
% 30.11/9.70 | (4162) sum(n11, n2) = all_0_0_0
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 30.11/9.70 | (780) all_0_3_3 = n13
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (194) with n11, n2, all_0_0_0, n13 and discharging atoms sum(n11, n2) = all_0_0_0, sum(n11, n2) = n13, yields:
% 30.11/9.70 | (781) all_0_0_0 = n13
% 30.11/9.70 |
% 30.11/9.70 | Equations (781,780) can reduce 201 to:
% 30.11/9.70 | (746) $false
% 30.11/9.70 |
% 30.11/9.70 |-The branch is then unsatisfiable
% 30.11/9.70 |-Branch two:
% 30.11/9.70 | (1462) ~ (all_0_10_10 = n1)
% 30.11/9.70 | (1463) all_0_10_10 = n0
% 30.11/9.70 |
% 30.11/9.70 | From (1463) and (57) follows:
% 30.11/9.70 | (1464) pred(n0) = all_0_6_6
% 30.11/9.70 |
% 30.11/9.70 | From (1463) and (381) follows:
% 30.11/9.70 | (1465) succ(n0) = all_0_8_8
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 30.11/9.70 | (1466) all_0_6_6 = n20
% 30.11/9.70 |
% 30.11/9.70 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 30.11/9.70 | (1467) all_0_8_8 = n1
% 30.11/9.70 |
% 30.11/9.70 | From (1466)(1467) and (628) follows:
% 30.11/9.70 | (1468) sum(n20, n1) = all_0_1_1
% 30.11/9.70 |
% 30.11/9.70 | From (1466) and (3893) follows:
% 30.22/9.70 | (4173) sum(n20, n17) = all_0_4_4
% 30.22/9.70 |
% 30.22/9.70 | From (1467) and (3895) follows:
% 30.22/9.70 | (4174) sum(n15, n1) = all_0_7_7
% 30.22/9.70 |
% 30.22/9.70 | Instantiating formula (194) with n20, n17, all_0_4_4, n16 and discharging atoms sum(n20, n17) = all_0_4_4, sum(n20, n17) = n16, yields:
% 30.22/9.70 | (793) all_0_4_4 = n16
% 30.22/9.70 |
% 30.22/9.70 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 30.22/9.70 | (1471) all_0_1_1 = n0
% 30.22/9.70 |
% 30.22/9.70 | Instantiating formula (194) with n15, n1, all_0_7_7, n16 and discharging atoms sum(n15, n1) = all_0_7_7, sum(n15, n1) = n16, yields:
% 30.22/9.70 | (795) all_0_7_7 = n16
% 30.22/9.70 |
% 30.22/9.70 | From (795)(793) and (435) follows:
% 30.22/9.70 | (797) sum(n16, n16) = all_0_3_3
% 30.22/9.70 |
% 30.22/9.70 | From (1471) and (3897) follows:
% 30.22/9.70 | (4179) sum(n11, n0) = all_0_0_0
% 30.22/9.70 |
% 30.22/9.70 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 30.22/9.70 | (798) all_0_3_3 = n11
% 30.22/9.70 |
% 30.22/9.70 | Instantiating formula (194) with n11, n0, all_0_0_0, n11 and discharging atoms sum(n11, n0) = all_0_0_0, sum(n11, n0) = n11, yields:
% 30.22/9.70 | (799) all_0_0_0 = n11
% 30.22/9.70 |
% 30.22/9.70 | Equations (799,798) can reduce 201 to:
% 30.22/9.70 | (746) $false
% 30.22/9.70 |
% 30.22/9.70 |-The branch is then unsatisfiable
% 30.22/9.70 |-Branch two:
% 30.22/9.70 | (819) ~ (all_0_11_11 = n16)
% 30.22/9.70 | (820) all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.22/9.71 |
% 30.22/9.71 +-Applying beta-rule and splitting (1191), into two cases.
% 30.22/9.71 |-Branch one:
% 30.22/9.71 | (1192) all_0_10_10 = n15
% 30.22/9.71 |
% 30.22/9.71 | From (1192) and (57) follows:
% 30.22/9.71 | (1193) pred(n15) = all_0_6_6
% 30.22/9.71 |
% 30.22/9.71 | From (1192) and (381) follows:
% 30.22/9.71 | (1194) succ(n15) = all_0_8_8
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (259) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 30.22/9.71 | (1195) all_0_6_6 = n14
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (184) with n15, all_0_8_8, n16 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n16, yields:
% 30.22/9.71 | (1196) all_0_8_8 = n16
% 30.22/9.71 |
% 30.22/9.71 | From (1195) and (1193) follows:
% 30.22/9.71 | (709) pred(n15) = n14
% 30.22/9.71 |
% 30.22/9.71 | From (1196) and (1194) follows:
% 30.22/9.71 | (119) succ(n15) = n16
% 30.22/9.71 |
% 30.22/9.71 | From (1195) and (386) follows:
% 30.22/9.71 | (4192) sum(n14, all_0_5_5) = all_0_4_4
% 30.22/9.71 |
% 30.22/9.71 | From (1195)(1196) and (628) follows:
% 30.22/9.71 | (1197) sum(n14, n16) = all_0_1_1
% 30.22/9.71 |
% 30.22/9.71 | From (1196) and (74) follows:
% 30.22/9.71 | (4194) sum(all_0_9_9, n16) = all_0_7_7
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (194) with n14, n16, all_0_1_1, n9 and discharging atoms sum(n14, n16) = all_0_1_1, sum(n14, n16) = n9, yields:
% 30.22/9.71 | (1201) all_0_1_1 = n9
% 30.22/9.71 |
% 30.22/9.71 | From (1201) and (85) follows:
% 30.22/9.71 | (4196) sum(all_0_2_2, n9) = all_0_0_0
% 30.22/9.71 |
% 30.22/9.71 | From (1201) and (1197) follows:
% 30.22/9.71 | (339) sum(n14, n16) = n9
% 30.22/9.71 |
% 30.22/9.71 +-Applying beta-rule and splitting (820), into two cases.
% 30.22/9.71 |-Branch one:
% 30.22/9.71 | (821) all_0_11_11 = n15
% 30.22/9.71 |
% 30.22/9.71 | From (821) and (190) follows:
% 30.22/9.71 | (822) pred(n15) = all_0_9_9
% 30.22/9.71 |
% 30.22/9.71 | From (821) and (505) follows:
% 30.22/9.71 | (823) succ(n15) = all_0_5_5
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (259) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 30.22/9.71 | (824) all_0_9_9 = n14
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (184) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 30.22/9.71 | (825) all_0_5_5 = n16
% 30.22/9.71 |
% 30.22/9.71 | From (824)(825) and (156) follows:
% 30.22/9.71 | (826) sum(n14, n16) = all_0_2_2
% 30.22/9.71 |
% 30.22/9.71 | From (824) and (4194) follows:
% 30.22/9.71 | (4204) sum(n14, n16) = all_0_7_7
% 30.22/9.71 |
% 30.22/9.71 | From (825) and (4192) follows:
% 30.22/9.71 | (4205) sum(n14, n16) = all_0_4_4
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (194) with n14, n16, all_0_2_2, n9 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n9, yields:
% 30.22/9.71 | (830) all_0_2_2 = n9
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (194) with n14, n16, all_0_4_4, all_0_2_2 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = all_0_4_4, yields:
% 30.22/9.71 | (733) all_0_2_2 = all_0_4_4
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (194) with n14, n16, all_0_7_7, all_0_2_2 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = all_0_7_7, yields:
% 30.22/9.71 | (734) all_0_2_2 = all_0_7_7
% 30.22/9.71 |
% 30.22/9.71 | Combining equations (734,733) yields a new equation:
% 30.22/9.71 | (735) all_0_4_4 = all_0_7_7
% 30.22/9.71 |
% 30.22/9.71 | Combining equations (830,733) yields a new equation:
% 30.22/9.71 | (919) all_0_4_4 = n9
% 30.22/9.71 |
% 30.22/9.71 | Combining equations (919,735) yields a new equation:
% 30.22/9.71 | (921) all_0_7_7 = n9
% 30.22/9.71 |
% 30.22/9.71 | Combining equations (921,735) yields a new equation:
% 30.22/9.71 | (919) all_0_4_4 = n9
% 30.22/9.71 |
% 30.22/9.71 | Combining equations (919,733) yields a new equation:
% 30.22/9.71 | (830) all_0_2_2 = n9
% 30.22/9.71 |
% 30.22/9.71 | From (830) and (4196) follows:
% 30.22/9.71 | (4214) sum(n9, n9) = all_0_0_0
% 30.22/9.71 |
% 30.22/9.71 | From (921)(919) and (435) follows:
% 30.22/9.71 | (923) sum(n9, n9) = all_0_3_3
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (194) with n9, n9, all_0_0_0, n18 and discharging atoms sum(n9, n9) = all_0_0_0, sum(n9, n9) = n18, yields:
% 30.22/9.71 | (924) all_0_0_0 = n18
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (194) with n9, n9, all_0_3_3, all_0_0_0 and discharging atoms sum(n9, n9) = all_0_0_0, sum(n9, n9) = all_0_3_3, yields:
% 30.22/9.71 | (743) all_0_0_0 = all_0_3_3
% 30.22/9.71 |
% 30.22/9.71 | Combining equations (924,743) yields a new equation:
% 30.22/9.71 | (925) all_0_3_3 = n18
% 30.22/9.71 |
% 30.22/9.71 | Combining equations (925,743) yields a new equation:
% 30.22/9.71 | (924) all_0_0_0 = n18
% 30.22/9.71 |
% 30.22/9.71 | Equations (924,925) can reduce 201 to:
% 30.22/9.71 | (746) $false
% 30.22/9.71 |
% 30.22/9.71 |-The branch is then unsatisfiable
% 30.22/9.71 |-Branch two:
% 30.22/9.71 | (837) ~ (all_0_11_11 = n15)
% 30.22/9.71 | (838) all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.22/9.71 |
% 30.22/9.71 +-Applying beta-rule and splitting (838), into two cases.
% 30.22/9.71 |-Branch one:
% 30.22/9.71 | (839) all_0_11_11 = n14
% 30.22/9.71 |
% 30.22/9.71 | From (839) and (190) follows:
% 30.22/9.71 | (840) pred(n14) = all_0_9_9
% 30.22/9.71 |
% 30.22/9.71 | From (839) and (505) follows:
% 30.22/9.71 | (841) succ(n14) = all_0_5_5
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (259) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 30.22/9.71 | (842) all_0_9_9 = n13
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (184) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 30.22/9.71 | (843) all_0_5_5 = n15
% 30.22/9.71 |
% 30.22/9.71 | From (842)(843) and (156) follows:
% 30.22/9.71 | (844) sum(n13, n15) = all_0_2_2
% 30.22/9.71 |
% 30.22/9.71 | From (842) and (4194) follows:
% 30.22/9.71 | (4229) sum(n13, n16) = all_0_7_7
% 30.22/9.71 |
% 30.22/9.71 | From (843) and (4192) follows:
% 30.22/9.71 | (4230) sum(n14, n15) = all_0_4_4
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (194) with n14, n15, all_0_4_4, n8 and discharging atoms sum(n14, n15) = all_0_4_4, sum(n14, n15) = n8, yields:
% 30.22/9.71 | (937) all_0_4_4 = n8
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (194) with n13, n16, all_0_7_7, n8 and discharging atoms sum(n13, n16) = all_0_7_7, sum(n13, n16) = n8, yields:
% 30.22/9.71 | (939) all_0_7_7 = n8
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (194) with n13, n15, all_0_2_2, n7 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n7, yields:
% 30.22/9.71 | (848) all_0_2_2 = n7
% 30.22/9.71 |
% 30.22/9.71 | From (848) and (4196) follows:
% 30.22/9.71 | (4234) sum(n7, n9) = all_0_0_0
% 30.22/9.71 |
% 30.22/9.71 | From (939)(937) and (435) follows:
% 30.22/9.71 | (941) sum(n8, n8) = all_0_3_3
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 30.22/9.71 | (943) all_0_3_3 = n16
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (194) with n7, n9, all_0_0_0, n16 and discharging atoms sum(n7, n9) = all_0_0_0, sum(n7, n9) = n16, yields:
% 30.22/9.71 | (942) all_0_0_0 = n16
% 30.22/9.71 |
% 30.22/9.71 | Equations (942,943) can reduce 201 to:
% 30.22/9.71 | (746) $false
% 30.22/9.71 |
% 30.22/9.71 |-The branch is then unsatisfiable
% 30.22/9.71 |-Branch two:
% 30.22/9.71 | (855) ~ (all_0_11_11 = n14)
% 30.22/9.71 | (856) all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.22/9.71 |
% 30.22/9.71 +-Applying beta-rule and splitting (856), into two cases.
% 30.22/9.71 |-Branch one:
% 30.22/9.71 | (857) all_0_11_11 = n13
% 30.22/9.71 |
% 30.22/9.71 | From (857) and (190) follows:
% 30.22/9.71 | (858) pred(n13) = all_0_9_9
% 30.22/9.71 |
% 30.22/9.71 | From (857) and (505) follows:
% 30.22/9.71 | (859) succ(n13) = all_0_5_5
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (259) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 30.22/9.71 | (860) all_0_9_9 = n12
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (184) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 30.22/9.71 | (861) all_0_5_5 = n14
% 30.22/9.71 |
% 30.22/9.71 | From (860)(861) and (156) follows:
% 30.22/9.71 | (862) sum(n12, n14) = all_0_2_2
% 30.22/9.71 |
% 30.22/9.71 | From (860) and (4194) follows:
% 30.22/9.71 | (4247) sum(n12, n16) = all_0_7_7
% 30.22/9.71 |
% 30.22/9.71 | From (861) and (4192) follows:
% 30.22/9.71 | (4248) sum(n14, n14) = all_0_4_4
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (194) with n14, n14, all_0_4_4, n7 and discharging atoms sum(n14, n14) = all_0_4_4, sum(n14, n14) = n7, yields:
% 30.22/9.71 | (955) all_0_4_4 = n7
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (194) with n12, n16, all_0_7_7, n7 and discharging atoms sum(n12, n16) = all_0_7_7, sum(n12, n16) = n7, yields:
% 30.22/9.71 | (957) all_0_7_7 = n7
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (194) with n12, n14, all_0_2_2, n5 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n5, yields:
% 30.22/9.71 | (866) all_0_2_2 = n5
% 30.22/9.71 |
% 30.22/9.71 | From (866) and (4196) follows:
% 30.22/9.71 | (4252) sum(n5, n9) = all_0_0_0
% 30.22/9.71 |
% 30.22/9.71 | From (957)(955) and (435) follows:
% 30.22/9.71 | (959) sum(n7, n7) = all_0_3_3
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 30.22/9.71 | (961) all_0_3_3 = n14
% 30.22/9.71 |
% 30.22/9.71 | Instantiating formula (194) with n5, n9, all_0_0_0, n14 and discharging atoms sum(n5, n9) = all_0_0_0, sum(n5, n9) = n14, yields:
% 30.22/9.71 | (960) all_0_0_0 = n14
% 30.22/9.71 |
% 30.22/9.71 | Equations (960,961) can reduce 201 to:
% 30.22/9.71 | (746) $false
% 30.22/9.71 |
% 30.22/9.71 |-The branch is then unsatisfiable
% 30.22/9.71 |-Branch two:
% 30.22/9.71 | (873) ~ (all_0_11_11 = n13)
% 30.22/9.71 | (874) all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.22/9.71 |
% 30.22/9.71 +-Applying beta-rule and splitting (874), into two cases.
% 30.22/9.71 |-Branch one:
% 30.22/9.71 | (875) all_0_11_11 = n12
% 30.22/9.71 |
% 30.22/9.71 | From (875) and (190) follows:
% 30.22/9.71 | (876) pred(n12) = all_0_9_9
% 30.22/9.71 |
% 30.22/9.71 | From (875) and (505) follows:
% 30.22/9.72 | (877) succ(n12) = all_0_5_5
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (259) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 30.22/9.72 | (878) all_0_9_9 = n11
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (184) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 30.22/9.72 | (879) all_0_5_5 = n13
% 30.22/9.72 |
% 30.22/9.72 | From (878)(879) and (156) follows:
% 30.22/9.72 | (880) sum(n11, n13) = all_0_2_2
% 30.22/9.72 |
% 30.22/9.72 | From (878) and (4194) follows:
% 30.22/9.72 | (4265) sum(n11, n16) = all_0_7_7
% 30.22/9.72 |
% 30.22/9.72 | From (879) and (4192) follows:
% 30.22/9.72 | (4266) sum(n14, n13) = all_0_4_4
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n14, n13, all_0_4_4, n6 and discharging atoms sum(n14, n13) = all_0_4_4, sum(n14, n13) = n6, yields:
% 30.22/9.72 | (973) all_0_4_4 = n6
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n11, n16, all_0_7_7, n6 and discharging atoms sum(n11, n16) = all_0_7_7, sum(n11, n16) = n6, yields:
% 30.22/9.72 | (975) all_0_7_7 = n6
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n11, n13, all_0_2_2, n3 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n3, yields:
% 30.22/9.72 | (884) all_0_2_2 = n3
% 30.22/9.72 |
% 30.22/9.72 | From (884) and (4196) follows:
% 30.22/9.72 | (4270) sum(n3, n9) = all_0_0_0
% 30.22/9.72 |
% 30.22/9.72 | From (975)(973) and (435) follows:
% 30.22/9.72 | (977) sum(n6, n6) = all_0_3_3
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 30.22/9.72 | (979) all_0_3_3 = n12
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n3, n9, all_0_0_0, n12 and discharging atoms sum(n3, n9) = all_0_0_0, sum(n3, n9) = n12, yields:
% 30.22/9.72 | (978) all_0_0_0 = n12
% 30.22/9.72 |
% 30.22/9.72 | Equations (978,979) can reduce 201 to:
% 30.22/9.72 | (746) $false
% 30.22/9.72 |
% 30.22/9.72 |-The branch is then unsatisfiable
% 30.22/9.72 |-Branch two:
% 30.22/9.72 | (891) ~ (all_0_11_11 = n12)
% 30.22/9.72 | (892) all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.22/9.72 |
% 30.22/9.72 +-Applying beta-rule and splitting (892), into two cases.
% 30.22/9.72 |-Branch one:
% 30.22/9.72 | (893) all_0_11_11 = n11
% 30.22/9.72 |
% 30.22/9.72 | From (893) and (190) follows:
% 30.22/9.72 | (894) pred(n11) = all_0_9_9
% 30.22/9.72 |
% 30.22/9.72 | From (893) and (505) follows:
% 30.22/9.72 | (895) succ(n11) = all_0_5_5
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (259) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 30.22/9.72 | (896) all_0_9_9 = n10
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (184) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 30.22/9.72 | (897) all_0_5_5 = n12
% 30.22/9.72 |
% 30.22/9.72 | From (896)(897) and (156) follows:
% 30.22/9.72 | (898) sum(n10, n12) = all_0_2_2
% 30.22/9.72 |
% 30.22/9.72 | From (896) and (4194) follows:
% 30.22/9.72 | (4283) sum(n10, n16) = all_0_7_7
% 30.22/9.72 |
% 30.22/9.72 | From (897) and (4192) follows:
% 30.22/9.72 | (4284) sum(n14, n12) = all_0_4_4
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n14, n12, all_0_4_4, n5 and discharging atoms sum(n14, n12) = all_0_4_4, sum(n14, n12) = n5, yields:
% 30.22/9.72 | (991) all_0_4_4 = n5
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n10, n16, all_0_7_7, n5 and discharging atoms sum(n10, n16) = all_0_7_7, sum(n10, n16) = n5, yields:
% 30.22/9.72 | (993) all_0_7_7 = n5
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n10, n12, all_0_2_2, n1 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n1, yields:
% 30.22/9.72 | (902) all_0_2_2 = n1
% 30.22/9.72 |
% 30.22/9.72 | From (902) and (4196) follows:
% 30.22/9.72 | (4288) sum(n1, n9) = all_0_0_0
% 30.22/9.72 |
% 30.22/9.72 | From (993)(991) and (435) follows:
% 30.22/9.72 | (995) sum(n5, n5) = all_0_3_3
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 30.22/9.72 | (997) all_0_3_3 = n10
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n1, n9, all_0_0_0, n10 and discharging atoms sum(n1, n9) = all_0_0_0, sum(n1, n9) = n10, yields:
% 30.22/9.72 | (996) all_0_0_0 = n10
% 30.22/9.72 |
% 30.22/9.72 | Equations (996,997) can reduce 201 to:
% 30.22/9.72 | (746) $false
% 30.22/9.72 |
% 30.22/9.72 |-The branch is then unsatisfiable
% 30.22/9.72 |-Branch two:
% 30.22/9.72 | (909) ~ (all_0_11_11 = n11)
% 30.22/9.72 | (910) all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.22/9.72 |
% 30.22/9.72 +-Applying beta-rule and splitting (910), into two cases.
% 30.22/9.72 |-Branch one:
% 30.22/9.72 | (911) all_0_11_11 = n10
% 30.22/9.72 |
% 30.22/9.72 | From (911) and (190) follows:
% 30.22/9.72 | (912) pred(n10) = all_0_9_9
% 30.22/9.72 |
% 30.22/9.72 | From (911) and (505) follows:
% 30.22/9.72 | (913) succ(n10) = all_0_5_5
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (259) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 30.22/9.72 | (914) all_0_9_9 = n9
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (184) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 30.22/9.72 | (915) all_0_5_5 = n11
% 30.22/9.72 |
% 30.22/9.72 | From (914)(915) and (156) follows:
% 30.22/9.72 | (916) sum(n9, n11) = all_0_2_2
% 30.22/9.72 |
% 30.22/9.72 | From (914) and (4194) follows:
% 30.22/9.72 | (4301) sum(n9, n16) = all_0_7_7
% 30.22/9.72 |
% 30.22/9.72 | From (915) and (4192) follows:
% 30.22/9.72 | (4302) sum(n14, n11) = all_0_4_4
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n14, n11, all_0_4_4, n4 and discharging atoms sum(n14, n11) = all_0_4_4, sum(n14, n11) = n4, yields:
% 30.22/9.72 | (1009) all_0_4_4 = n4
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n9, n16, all_0_7_7, n4 and discharging atoms sum(n9, n16) = all_0_7_7, sum(n9, n16) = n4, yields:
% 30.22/9.72 | (1011) all_0_7_7 = n4
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 30.22/9.72 | (920) all_0_2_2 = n20
% 30.22/9.72 |
% 30.22/9.72 | From (920) and (4196) follows:
% 30.22/9.72 | (4306) sum(n20, n9) = all_0_0_0
% 30.22/9.72 |
% 30.22/9.72 | From (1011)(1009) and (435) follows:
% 30.22/9.72 | (1013) sum(n4, n4) = all_0_3_3
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n20, n9, all_0_0_0, n8 and discharging atoms sum(n20, n9) = all_0_0_0, sum(n20, n9) = n8, yields:
% 30.22/9.72 | (1014) all_0_0_0 = n8
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 30.22/9.72 | (1015) all_0_3_3 = n8
% 30.22/9.72 |
% 30.22/9.72 | Equations (1014,1015) can reduce 201 to:
% 30.22/9.72 | (746) $false
% 30.22/9.72 |
% 30.22/9.72 |-The branch is then unsatisfiable
% 30.22/9.72 |-Branch two:
% 30.22/9.72 | (927) ~ (all_0_11_11 = n10)
% 30.22/9.72 | (928) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.22/9.72 |
% 30.22/9.72 +-Applying beta-rule and splitting (928), into two cases.
% 30.22/9.72 |-Branch one:
% 30.22/9.72 | (929) all_0_11_11 = n9
% 30.22/9.72 |
% 30.22/9.72 | From (929) and (190) follows:
% 30.22/9.72 | (930) pred(n9) = all_0_9_9
% 30.22/9.72 |
% 30.22/9.72 | From (929) and (505) follows:
% 30.22/9.72 | (931) succ(n9) = all_0_5_5
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (259) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 30.22/9.72 | (932) all_0_9_9 = n8
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (184) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 30.22/9.72 | (933) all_0_5_5 = n10
% 30.22/9.72 |
% 30.22/9.72 | From (932)(933) and (156) follows:
% 30.22/9.72 | (934) sum(n8, n10) = all_0_2_2
% 30.22/9.72 |
% 30.22/9.72 | From (932) and (4194) follows:
% 30.22/9.72 | (4319) sum(n8, n16) = all_0_7_7
% 30.22/9.72 |
% 30.22/9.72 | From (933) and (4192) follows:
% 30.22/9.72 | (4320) sum(n14, n10) = all_0_4_4
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n14, n10, all_0_4_4, n3 and discharging atoms sum(n14, n10) = all_0_4_4, sum(n14, n10) = n3, yields:
% 30.22/9.72 | (1027) all_0_4_4 = n3
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n8, n16, all_0_7_7, n3 and discharging atoms sum(n8, n16) = all_0_7_7, sum(n8, n16) = n3, yields:
% 30.22/9.72 | (1029) all_0_7_7 = n3
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 30.22/9.72 | (938) all_0_2_2 = n18
% 30.22/9.72 |
% 30.22/9.72 | From (938) and (4196) follows:
% 30.22/9.72 | (4324) sum(n18, n9) = all_0_0_0
% 30.22/9.72 |
% 30.22/9.72 | From (1029)(1027) and (435) follows:
% 30.22/9.72 | (1031) sum(n3, n3) = all_0_3_3
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n18, n9, all_0_0_0, n6 and discharging atoms sum(n18, n9) = all_0_0_0, sum(n18, n9) = n6, yields:
% 30.22/9.72 | (1032) all_0_0_0 = n6
% 30.22/9.72 |
% 30.22/9.72 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 30.22/9.72 | (1033) all_0_3_3 = n6
% 30.22/9.72 |
% 30.22/9.72 | Equations (1032,1033) can reduce 201 to:
% 30.22/9.72 | (746) $false
% 30.22/9.72 |
% 30.22/9.72 |-The branch is then unsatisfiable
% 30.22/9.72 |-Branch two:
% 30.22/9.72 | (945) ~ (all_0_11_11 = n9)
% 30.22/9.73 | (946) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.22/9.73 |
% 30.22/9.73 +-Applying beta-rule and splitting (946), into two cases.
% 30.22/9.73 |-Branch one:
% 30.22/9.73 | (947) all_0_11_11 = n8
% 30.22/9.73 |
% 30.22/9.73 | From (947) and (190) follows:
% 30.22/9.73 | (948) pred(n8) = all_0_9_9
% 30.22/9.73 |
% 30.22/9.73 | From (947) and (505) follows:
% 30.31/9.73 | (949) succ(n8) = all_0_5_5
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (259) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 30.31/9.73 | (950) all_0_9_9 = n7
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (184) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 30.31/9.73 | (951) all_0_5_5 = n9
% 30.31/9.73 |
% 30.31/9.73 | From (950)(951) and (156) follows:
% 30.31/9.73 | (952) sum(n7, n9) = all_0_2_2
% 30.31/9.73 |
% 30.31/9.73 | From (950) and (4194) follows:
% 30.31/9.73 | (4337) sum(n7, n16) = all_0_7_7
% 30.31/9.73 |
% 30.31/9.73 | From (951) and (4192) follows:
% 30.31/9.73 | (4338) sum(n14, n9) = all_0_4_4
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n14, n9, all_0_4_4, n2 and discharging atoms sum(n14, n9) = all_0_4_4, sum(n14, n9) = n2, yields:
% 30.31/9.73 | (1045) all_0_4_4 = n2
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n7, n16, all_0_7_7, n2 and discharging atoms sum(n7, n16) = all_0_7_7, sum(n7, n16) = n2, yields:
% 30.31/9.73 | (1047) all_0_7_7 = n2
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 30.31/9.73 | (956) all_0_2_2 = n16
% 30.31/9.73 |
% 30.31/9.73 | From (956) and (4196) follows:
% 30.31/9.73 | (4342) sum(n16, n9) = all_0_0_0
% 30.31/9.73 |
% 30.31/9.73 | From (1047)(1045) and (435) follows:
% 30.31/9.73 | (1049) sum(n2, n2) = all_0_3_3
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n16, n9, all_0_0_0, n4 and discharging atoms sum(n16, n9) = all_0_0_0, sum(n16, n9) = n4, yields:
% 30.31/9.73 | (1050) all_0_0_0 = n4
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 30.31/9.73 | (1051) all_0_3_3 = n4
% 30.31/9.73 |
% 30.31/9.73 | Equations (1050,1051) can reduce 201 to:
% 30.31/9.73 | (746) $false
% 30.31/9.73 |
% 30.31/9.73 |-The branch is then unsatisfiable
% 30.31/9.73 |-Branch two:
% 30.31/9.73 | (963) ~ (all_0_11_11 = n8)
% 30.31/9.73 | (964) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.31/9.73 |
% 30.31/9.73 +-Applying beta-rule and splitting (964), into two cases.
% 30.31/9.73 |-Branch one:
% 30.31/9.73 | (965) all_0_11_11 = n7
% 30.31/9.73 |
% 30.31/9.73 | From (965) and (190) follows:
% 30.31/9.73 | (966) pred(n7) = all_0_9_9
% 30.31/9.73 |
% 30.31/9.73 | From (965) and (505) follows:
% 30.31/9.73 | (967) succ(n7) = all_0_5_5
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (259) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 30.31/9.73 | (968) all_0_9_9 = n6
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (184) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 30.31/9.73 | (969) all_0_5_5 = n8
% 30.31/9.73 |
% 30.31/9.73 | From (968)(969) and (156) follows:
% 30.31/9.73 | (970) sum(n6, n8) = all_0_2_2
% 30.31/9.73 |
% 30.31/9.73 | From (968) and (4194) follows:
% 30.31/9.73 | (4355) sum(n6, n16) = all_0_7_7
% 30.31/9.73 |
% 30.31/9.73 | From (969) and (4192) follows:
% 30.31/9.73 | (4356) sum(n14, n8) = all_0_4_4
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n14, n8, all_0_4_4, n1 and discharging atoms sum(n14, n8) = all_0_4_4, sum(n14, n8) = n1, yields:
% 30.31/9.73 | (1063) all_0_4_4 = n1
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n6, n16, all_0_7_7, n1 and discharging atoms sum(n6, n16) = all_0_7_7, sum(n6, n16) = n1, yields:
% 30.31/9.73 | (1065) all_0_7_7 = n1
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 30.31/9.73 | (974) all_0_2_2 = n14
% 30.31/9.73 |
% 30.31/9.73 | From (974) and (4196) follows:
% 30.31/9.73 | (4360) sum(n14, n9) = all_0_0_0
% 30.31/9.73 |
% 30.31/9.73 | From (1065)(1063) and (435) follows:
% 30.31/9.73 | (1067) sum(n1, n1) = all_0_3_3
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n14, n9, all_0_0_0, n2 and discharging atoms sum(n14, n9) = all_0_0_0, sum(n14, n9) = n2, yields:
% 30.31/9.73 | (1068) all_0_0_0 = n2
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 30.31/9.73 | (1069) all_0_3_3 = n2
% 30.31/9.73 |
% 30.31/9.73 | Equations (1068,1069) can reduce 201 to:
% 30.31/9.73 | (746) $false
% 30.31/9.73 |
% 30.31/9.73 |-The branch is then unsatisfiable
% 30.31/9.73 |-Branch two:
% 30.31/9.73 | (981) ~ (all_0_11_11 = n7)
% 30.31/9.73 | (982) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.31/9.73 |
% 30.31/9.73 +-Applying beta-rule and splitting (982), into two cases.
% 30.31/9.73 |-Branch one:
% 30.31/9.73 | (983) all_0_11_11 = n6
% 30.31/9.73 |
% 30.31/9.73 | From (983) and (190) follows:
% 30.31/9.73 | (984) pred(n6) = all_0_9_9
% 30.31/9.73 |
% 30.31/9.73 | From (983) and (505) follows:
% 30.31/9.73 | (985) succ(n6) = all_0_5_5
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (259) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 30.31/9.73 | (986) all_0_9_9 = n5
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (184) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 30.31/9.73 | (987) all_0_5_5 = n7
% 30.31/9.73 |
% 30.31/9.73 | From (986)(987) and (156) follows:
% 30.31/9.73 | (988) sum(n5, n7) = all_0_2_2
% 30.31/9.73 |
% 30.31/9.73 | From (986) and (4194) follows:
% 30.31/9.73 | (4373) sum(n5, n16) = all_0_7_7
% 30.31/9.73 |
% 30.31/9.73 | From (987) and (4192) follows:
% 30.31/9.73 | (4374) sum(n14, n7) = all_0_4_4
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n14, n7, all_0_4_4, n0 and discharging atoms sum(n14, n7) = all_0_4_4, sum(n14, n7) = n0, yields:
% 30.31/9.73 | (1081) all_0_4_4 = n0
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n5, n16, all_0_7_7, n0 and discharging atoms sum(n5, n16) = all_0_7_7, sum(n5, n16) = n0, yields:
% 30.31/9.73 | (1083) all_0_7_7 = n0
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 30.31/9.73 | (992) all_0_2_2 = n12
% 30.31/9.73 |
% 30.31/9.73 | From (992) and (4196) follows:
% 30.31/9.73 | (4378) sum(n12, n9) = all_0_0_0
% 30.31/9.73 |
% 30.31/9.73 | From (1083)(1081) and (435) follows:
% 30.31/9.73 | (1085) sum(n0, n0) = all_0_3_3
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n12, n9, all_0_0_0, n0 and discharging atoms sum(n12, n9) = all_0_0_0, sum(n12, n9) = n0, yields:
% 30.31/9.73 | (1087) all_0_0_0 = n0
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 30.31/9.73 | (1088) all_0_3_3 = n0
% 30.31/9.73 |
% 30.31/9.73 | Equations (1087,1088) can reduce 201 to:
% 30.31/9.73 | (746) $false
% 30.31/9.73 |
% 30.31/9.73 |-The branch is then unsatisfiable
% 30.31/9.73 |-Branch two:
% 30.31/9.73 | (999) ~ (all_0_11_11 = n6)
% 30.31/9.73 | (1000) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.31/9.73 |
% 30.31/9.73 +-Applying beta-rule and splitting (1000), into two cases.
% 30.31/9.73 |-Branch one:
% 30.31/9.73 | (1001) all_0_11_11 = n5
% 30.31/9.73 |
% 30.31/9.73 | From (1001) and (190) follows:
% 30.31/9.73 | (1002) pred(n5) = all_0_9_9
% 30.31/9.73 |
% 30.31/9.73 | From (1001) and (505) follows:
% 30.31/9.73 | (1003) succ(n5) = all_0_5_5
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (259) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 30.31/9.73 | (1004) all_0_9_9 = n4
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (184) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 30.31/9.73 | (1005) all_0_5_5 = n6
% 30.31/9.73 |
% 30.31/9.73 | From (1004)(1005) and (156) follows:
% 30.31/9.73 | (1006) sum(n4, n6) = all_0_2_2
% 30.31/9.73 |
% 30.31/9.73 | From (1004) and (4194) follows:
% 30.31/9.73 | (4391) sum(n4, n16) = all_0_7_7
% 30.31/9.73 |
% 30.31/9.73 | From (1005) and (4192) follows:
% 30.31/9.73 | (4392) sum(n14, n6) = all_0_4_4
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n14, n6, all_0_4_4, n20 and discharging atoms sum(n14, n6) = all_0_4_4, sum(n14, n6) = n20, yields:
% 30.31/9.73 | (1101) all_0_4_4 = n20
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n4, n16, all_0_7_7, n20 and discharging atoms sum(n4, n16) = all_0_7_7, sum(n4, n16) = n20, yields:
% 30.31/9.73 | (1100) all_0_7_7 = n20
% 30.31/9.73 |
% 30.31/9.73 | Instantiating formula (194) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 30.31/9.73 | (1010) all_0_2_2 = n10
% 30.31/9.73 |
% 30.31/9.73 | From (1010) and (4196) follows:
% 30.31/9.73 | (4396) sum(n10, n9) = all_0_0_0
% 30.31/9.73 |
% 30.31/9.73 | From (1100)(1101) and (435) follows:
% 30.31/9.74 | (1103) sum(n20, n20) = all_0_3_3
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 30.31/9.74 | (1104) all_0_3_3 = n19
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n10, n9, all_0_0_0, n19 and discharging atoms sum(n10, n9) = all_0_0_0, sum(n10, n9) = n19, yields:
% 30.31/9.74 | (1105) all_0_0_0 = n19
% 30.31/9.74 |
% 30.31/9.74 | Equations (1105,1104) can reduce 201 to:
% 30.31/9.74 | (746) $false
% 30.31/9.74 |
% 30.31/9.74 |-The branch is then unsatisfiable
% 30.31/9.74 |-Branch two:
% 30.31/9.74 | (1017) ~ (all_0_11_11 = n5)
% 30.31/9.74 | (1018) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.31/9.74 |
% 30.31/9.74 +-Applying beta-rule and splitting (1018), into two cases.
% 30.31/9.74 |-Branch one:
% 30.31/9.74 | (1019) all_0_11_11 = n4
% 30.31/9.74 |
% 30.31/9.74 | From (1019) and (190) follows:
% 30.31/9.74 | (1020) pred(n4) = all_0_9_9
% 30.31/9.74 |
% 30.31/9.74 | From (1019) and (505) follows:
% 30.31/9.74 | (1021) succ(n4) = all_0_5_5
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 30.31/9.74 | (1022) all_0_9_9 = n3
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 30.31/9.74 | (1023) all_0_5_5 = n5
% 30.31/9.74 |
% 30.31/9.74 | From (1022)(1023) and (156) follows:
% 30.31/9.74 | (1024) sum(n3, n5) = all_0_2_2
% 30.31/9.74 |
% 30.31/9.74 | From (1022) and (4194) follows:
% 30.31/9.74 | (4409) sum(n3, n16) = all_0_7_7
% 30.31/9.74 |
% 30.31/9.74 | From (1023) and (4192) follows:
% 30.31/9.74 | (4410) sum(n14, n5) = all_0_4_4
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n14, n5, all_0_4_4, n19 and discharging atoms sum(n14, n5) = all_0_4_4, sum(n14, n5) = n19, yields:
% 30.31/9.74 | (736) all_0_4_4 = n19
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n3, n16, all_0_7_7, n19 and discharging atoms sum(n3, n16) = all_0_7_7, sum(n3, n16) = n19, yields:
% 30.31/9.74 | (737) all_0_7_7 = n19
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 30.31/9.74 | (1028) all_0_2_2 = n8
% 30.31/9.74 |
% 30.31/9.74 | From (1028) and (4196) follows:
% 30.31/9.74 | (4414) sum(n8, n9) = all_0_0_0
% 30.31/9.74 |
% 30.31/9.74 | From (737)(736) and (435) follows:
% 30.31/9.74 | (741) sum(n19, n19) = all_0_3_3
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 30.31/9.74 | (744) all_0_3_3 = n17
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n8, n9, all_0_0_0, n17 and discharging atoms sum(n8, n9) = all_0_0_0, sum(n8, n9) = n17, yields:
% 30.31/9.74 | (742) all_0_0_0 = n17
% 30.31/9.74 |
% 30.31/9.74 | Equations (742,744) can reduce 201 to:
% 30.31/9.74 | (746) $false
% 30.31/9.74 |
% 30.31/9.74 |-The branch is then unsatisfiable
% 30.31/9.74 |-Branch two:
% 30.31/9.74 | (1035) ~ (all_0_11_11 = n4)
% 30.31/9.74 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.31/9.74 |
% 30.31/9.74 +-Applying beta-rule and splitting (1036), into two cases.
% 30.31/9.74 |-Branch one:
% 30.31/9.74 | (1037) all_0_11_11 = n3
% 30.31/9.74 |
% 30.31/9.74 | From (1037) and (190) follows:
% 30.31/9.74 | (1038) pred(n3) = all_0_9_9
% 30.31/9.74 |
% 30.31/9.74 | From (1037) and (505) follows:
% 30.31/9.74 | (1039) succ(n3) = all_0_5_5
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 30.31/9.74 | (1040) all_0_9_9 = n2
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 30.31/9.74 | (1041) all_0_5_5 = n4
% 30.31/9.74 |
% 30.31/9.74 | From (1040)(1041) and (156) follows:
% 30.31/9.74 | (1042) sum(n2, n4) = all_0_2_2
% 30.31/9.74 |
% 30.31/9.74 | From (1040) and (4194) follows:
% 30.31/9.74 | (4427) sum(n2, n16) = all_0_7_7
% 30.31/9.74 |
% 30.31/9.74 | From (1041) and (4192) follows:
% 30.31/9.74 | (4428) sum(n14, n4) = all_0_4_4
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n14, n4, all_0_4_4, n18 and discharging atoms sum(n14, n4) = all_0_4_4, sum(n14, n4) = n18, yields:
% 30.31/9.74 | (757) all_0_4_4 = n18
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n2, n16, all_0_7_7, n18 and discharging atoms sum(n2, n16) = all_0_7_7, sum(n2, n16) = n18, yields:
% 30.31/9.74 | (759) all_0_7_7 = n18
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 30.31/9.74 | (1046) all_0_2_2 = n6
% 30.31/9.74 |
% 30.31/9.74 | From (1046) and (4196) follows:
% 30.31/9.74 | (4432) sum(n6, n9) = all_0_0_0
% 30.31/9.74 |
% 30.31/9.74 | From (759)(757) and (435) follows:
% 30.31/9.74 | (761) sum(n18, n18) = all_0_3_3
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 30.31/9.74 | (762) all_0_3_3 = n15
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n6, n9, all_0_0_0, n15 and discharging atoms sum(n6, n9) = all_0_0_0, sum(n6, n9) = n15, yields:
% 30.31/9.74 | (763) all_0_0_0 = n15
% 30.31/9.74 |
% 30.31/9.74 | Equations (763,762) can reduce 201 to:
% 30.31/9.74 | (746) $false
% 30.31/9.74 |
% 30.31/9.74 |-The branch is then unsatisfiable
% 30.31/9.74 |-Branch two:
% 30.31/9.74 | (1053) ~ (all_0_11_11 = n3)
% 30.31/9.74 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.31/9.74 |
% 30.31/9.74 +-Applying beta-rule and splitting (1054), into two cases.
% 30.31/9.74 |-Branch one:
% 30.31/9.74 | (1055) all_0_11_11 = n2
% 30.31/9.74 |
% 30.31/9.74 | From (1055) and (190) follows:
% 30.31/9.74 | (1056) pred(n2) = all_0_9_9
% 30.31/9.74 |
% 30.31/9.74 | From (1055) and (505) follows:
% 30.31/9.74 | (1057) succ(n2) = all_0_5_5
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 30.31/9.74 | (1058) all_0_9_9 = n1
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 30.31/9.74 | (1059) all_0_5_5 = n3
% 30.31/9.74 |
% 30.31/9.74 | From (1058)(1059) and (156) follows:
% 30.31/9.74 | (1060) sum(n1, n3) = all_0_2_2
% 30.31/9.74 |
% 30.31/9.74 | From (1058) and (4194) follows:
% 30.31/9.74 | (4445) sum(n1, n16) = all_0_7_7
% 30.31/9.74 |
% 30.31/9.74 | From (1059) and (4192) follows:
% 30.31/9.74 | (4446) sum(n14, n3) = all_0_4_4
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n14, n3, all_0_4_4, n17 and discharging atoms sum(n14, n3) = all_0_4_4, sum(n14, n3) = n17, yields:
% 30.31/9.74 | (775) all_0_4_4 = n17
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n1, n16, all_0_7_7, n17 and discharging atoms sum(n1, n16) = all_0_7_7, sum(n1, n16) = n17, yields:
% 30.31/9.74 | (777) all_0_7_7 = n17
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 30.31/9.74 | (1064) all_0_2_2 = n4
% 30.31/9.74 |
% 30.31/9.74 | From (1064) and (4196) follows:
% 30.31/9.74 | (4450) sum(n4, n9) = all_0_0_0
% 30.31/9.74 |
% 30.31/9.74 | From (777)(775) and (435) follows:
% 30.31/9.74 | (779) sum(n17, n17) = all_0_3_3
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 30.31/9.74 | (780) all_0_3_3 = n13
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n4, n9, all_0_0_0, n13 and discharging atoms sum(n4, n9) = all_0_0_0, sum(n4, n9) = n13, yields:
% 30.31/9.74 | (781) all_0_0_0 = n13
% 30.31/9.74 |
% 30.31/9.74 | Equations (781,780) can reduce 201 to:
% 30.31/9.74 | (746) $false
% 30.31/9.74 |
% 30.31/9.74 |-The branch is then unsatisfiable
% 30.31/9.74 |-Branch two:
% 30.31/9.74 | (1071) ~ (all_0_11_11 = n2)
% 30.31/9.74 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 30.31/9.74 |
% 30.31/9.74 +-Applying beta-rule and splitting (1072), into two cases.
% 30.31/9.74 |-Branch one:
% 30.31/9.74 | (1073) all_0_11_11 = n1
% 30.31/9.74 |
% 30.31/9.74 | From (1073) and (190) follows:
% 30.31/9.74 | (1074) pred(n1) = all_0_9_9
% 30.31/9.74 |
% 30.31/9.74 | From (1073) and (505) follows:
% 30.31/9.74 | (1075) succ(n1) = all_0_5_5
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 30.31/9.74 | (1076) all_0_9_9 = n0
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 30.31/9.74 | (1077) all_0_5_5 = n2
% 30.31/9.74 |
% 30.31/9.74 | From (1076)(1077) and (156) follows:
% 30.31/9.74 | (1078) sum(n0, n2) = all_0_2_2
% 30.31/9.74 |
% 30.31/9.74 | From (1076) and (4194) follows:
% 30.31/9.74 | (4463) sum(n0, n16) = all_0_7_7
% 30.31/9.74 |
% 30.31/9.74 | From (1077) and (4192) follows:
% 30.31/9.74 | (4464) sum(n14, n2) = all_0_4_4
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n14, n2, all_0_4_4, n16 and discharging atoms sum(n14, n2) = all_0_4_4, sum(n14, n2) = n16, yields:
% 30.31/9.74 | (793) all_0_4_4 = n16
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n0, n16, all_0_7_7, n16 and discharging atoms sum(n0, n16) = all_0_7_7, sum(n0, n16) = n16, yields:
% 30.31/9.74 | (795) all_0_7_7 = n16
% 30.31/9.74 |
% 30.31/9.74 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 30.31/9.74 | (1082) all_0_2_2 = n2
% 30.31/9.74 |
% 30.31/9.74 | From (1082) and (4196) follows:
% 30.31/9.75 | (4468) sum(n2, n9) = all_0_0_0
% 30.31/9.75 |
% 30.31/9.75 | From (795)(793) and (435) follows:
% 30.31/9.75 | (797) sum(n16, n16) = all_0_3_3
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 30.31/9.75 | (798) all_0_3_3 = n11
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (194) with n2, n9, all_0_0_0, n11 and discharging atoms sum(n2, n9) = all_0_0_0, sum(n2, n9) = n11, yields:
% 30.31/9.75 | (799) all_0_0_0 = n11
% 30.31/9.75 |
% 30.31/9.75 | Equations (799,798) can reduce 201 to:
% 30.31/9.75 | (746) $false
% 30.31/9.75 |
% 30.31/9.75 |-The branch is then unsatisfiable
% 30.31/9.75 |-Branch two:
% 30.31/9.75 | (1090) ~ (all_0_11_11 = n1)
% 30.31/9.75 | (1091) all_0_11_11 = n0
% 30.31/9.75 |
% 30.31/9.75 | From (1091) and (190) follows:
% 30.31/9.75 | (1092) pred(n0) = all_0_9_9
% 30.31/9.75 |
% 30.31/9.75 | From (1091) and (505) follows:
% 30.31/9.75 | (1093) succ(n0) = all_0_5_5
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 30.31/9.75 | (1094) all_0_9_9 = n20
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 30.31/9.75 | (1095) all_0_5_5 = n1
% 30.31/9.75 |
% 30.31/9.75 | From (1094)(1095) and (156) follows:
% 30.31/9.75 | (1096) sum(n20, n1) = all_0_2_2
% 30.31/9.75 |
% 30.31/9.75 | From (1094) and (4194) follows:
% 30.31/9.75 | (4480) sum(n20, n16) = all_0_7_7
% 30.31/9.75 |
% 30.31/9.75 | From (1095) and (4192) follows:
% 30.31/9.75 | (4481) sum(n14, n1) = all_0_4_4
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (194) with n20, n16, all_0_7_7, n15 and discharging atoms sum(n20, n16) = all_0_7_7, sum(n20, n16) = n15, yields:
% 30.31/9.75 | (813) all_0_7_7 = n15
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 30.31/9.75 | (1099) all_0_2_2 = n0
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (194) with n14, n1, all_0_4_4, n15 and discharging atoms sum(n14, n1) = all_0_4_4, sum(n14, n1) = n15, yields:
% 30.31/9.75 | (811) all_0_4_4 = n15
% 30.31/9.75 |
% 30.31/9.75 | From (1099) and (4196) follows:
% 30.31/9.75 | (4485) sum(n0, n9) = all_0_0_0
% 30.31/9.75 |
% 30.31/9.75 | From (813)(811) and (435) follows:
% 30.31/9.75 | (815) sum(n15, n15) = all_0_3_3
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 30.31/9.75 | (816) all_0_3_3 = n9
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (194) with n0, n9, all_0_0_0, n9 and discharging atoms sum(n0, n9) = all_0_0_0, sum(n0, n9) = n9, yields:
% 30.31/9.75 | (817) all_0_0_0 = n9
% 30.31/9.75 |
% 30.31/9.75 | Equations (817,816) can reduce 201 to:
% 30.31/9.75 | (746) $false
% 30.31/9.75 |
% 30.31/9.75 |-The branch is then unsatisfiable
% 30.31/9.75 |-Branch two:
% 30.31/9.75 | (1208) ~ (all_0_10_10 = n15)
% 30.31/9.75 | (1209) all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.31/9.75 |
% 30.31/9.75 +-Applying beta-rule and splitting (820), into two cases.
% 30.31/9.75 |-Branch one:
% 30.31/9.75 | (821) all_0_11_11 = n15
% 30.31/9.75 |
% 30.31/9.75 | From (821) and (190) follows:
% 30.31/9.75 | (822) pred(n15) = all_0_9_9
% 30.31/9.75 |
% 30.31/9.75 | From (821) and (505) follows:
% 30.31/9.75 | (823) succ(n15) = all_0_5_5
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (259) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 30.31/9.75 | (824) all_0_9_9 = n14
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (184) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 30.31/9.75 | (825) all_0_5_5 = n16
% 30.31/9.75 |
% 30.31/9.75 | From (825) and (386) follows:
% 30.31/9.75 | (4497) sum(all_0_6_6, n16) = all_0_4_4
% 30.31/9.75 |
% 30.31/9.75 | From (824)(825) and (156) follows:
% 30.31/9.75 | (826) sum(n14, n16) = all_0_2_2
% 30.31/9.75 |
% 30.31/9.75 | From (824) and (74) follows:
% 30.31/9.75 | (4499) sum(n14, all_0_8_8) = all_0_7_7
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (194) with n14, n16, all_0_2_2, n9 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n9, yields:
% 30.31/9.75 | (830) all_0_2_2 = n9
% 30.31/9.75 |
% 30.31/9.75 | From (830) and (85) follows:
% 30.31/9.75 | (4501) sum(n9, all_0_1_1) = all_0_0_0
% 30.31/9.75 |
% 30.31/9.75 +-Applying beta-rule and splitting (1209), into two cases.
% 30.31/9.75 |-Branch one:
% 30.31/9.75 | (1210) all_0_10_10 = n14
% 30.31/9.75 |
% 30.31/9.75 | From (1210) and (57) follows:
% 30.31/9.75 | (1211) pred(n14) = all_0_6_6
% 30.31/9.75 |
% 30.31/9.75 | From (1210) and (381) follows:
% 30.31/9.75 | (1212) succ(n14) = all_0_8_8
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (259) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 30.31/9.75 | (1213) all_0_6_6 = n13
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (184) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 30.31/9.75 | (1214) all_0_8_8 = n15
% 30.31/9.75 |
% 30.31/9.75 | From (1213)(1214) and (628) follows:
% 30.31/9.75 | (1215) sum(n13, n15) = all_0_1_1
% 30.31/9.75 |
% 30.31/9.75 | From (1213) and (4497) follows:
% 30.31/9.75 | (4508) sum(n13, n16) = all_0_4_4
% 30.31/9.75 |
% 30.31/9.75 | From (1214) and (4499) follows:
% 30.31/9.75 | (4509) sum(n14, n15) = all_0_7_7
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (194) with n14, n15, all_0_7_7, n8 and discharging atoms sum(n14, n15) = all_0_7_7, sum(n14, n15) = n8, yields:
% 30.31/9.75 | (939) all_0_7_7 = n8
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (194) with n13, n16, all_0_4_4, n8 and discharging atoms sum(n13, n16) = all_0_4_4, sum(n13, n16) = n8, yields:
% 30.31/9.75 | (937) all_0_4_4 = n8
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (194) with n13, n15, all_0_1_1, n7 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n7, yields:
% 30.31/9.75 | (1219) all_0_1_1 = n7
% 30.31/9.75 |
% 30.31/9.75 | From (939)(937) and (435) follows:
% 30.31/9.75 | (941) sum(n8, n8) = all_0_3_3
% 30.31/9.75 |
% 30.31/9.75 | From (1219) and (4501) follows:
% 30.31/9.75 | (4514) sum(n9, n7) = all_0_0_0
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (194) with n9, n7, all_0_0_0, n16 and discharging atoms sum(n9, n7) = all_0_0_0, sum(n9, n7) = n16, yields:
% 30.31/9.75 | (942) all_0_0_0 = n16
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 30.31/9.75 | (943) all_0_3_3 = n16
% 30.31/9.75 |
% 30.31/9.75 | Equations (942,943) can reduce 201 to:
% 30.31/9.75 | (746) $false
% 30.31/9.75 |
% 30.31/9.75 |-The branch is then unsatisfiable
% 30.31/9.75 |-Branch two:
% 30.31/9.75 | (1226) ~ (all_0_10_10 = n14)
% 30.31/9.75 | (1227) all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.31/9.75 |
% 30.31/9.75 +-Applying beta-rule and splitting (1227), into two cases.
% 30.31/9.75 |-Branch one:
% 30.31/9.75 | (1228) all_0_10_10 = n13
% 30.31/9.75 |
% 30.31/9.75 | From (1228) and (57) follows:
% 30.31/9.75 | (1229) pred(n13) = all_0_6_6
% 30.31/9.75 |
% 30.31/9.75 | From (1228) and (381) follows:
% 30.31/9.75 | (1230) succ(n13) = all_0_8_8
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (259) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 30.31/9.75 | (1231) all_0_6_6 = n12
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (184) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 30.31/9.75 | (1232) all_0_8_8 = n14
% 30.31/9.75 |
% 30.31/9.75 | From (1231)(1232) and (628) follows:
% 30.31/9.75 | (1233) sum(n12, n14) = all_0_1_1
% 30.31/9.75 |
% 30.31/9.75 | From (1231) and (4497) follows:
% 30.31/9.75 | (4526) sum(n12, n16) = all_0_4_4
% 30.31/9.75 |
% 30.31/9.75 | From (1232) and (4499) follows:
% 30.31/9.75 | (4527) sum(n14, n14) = all_0_7_7
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (194) with n14, n14, all_0_7_7, n7 and discharging atoms sum(n14, n14) = all_0_7_7, sum(n14, n14) = n7, yields:
% 30.31/9.75 | (957) all_0_7_7 = n7
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (194) with n12, n16, all_0_4_4, n7 and discharging atoms sum(n12, n16) = all_0_4_4, sum(n12, n16) = n7, yields:
% 30.31/9.75 | (955) all_0_4_4 = n7
% 30.31/9.75 |
% 30.31/9.75 | Instantiating formula (194) with n12, n14, all_0_1_1, n5 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n5, yields:
% 30.31/9.75 | (1237) all_0_1_1 = n5
% 30.31/9.75 |
% 30.31/9.75 | From (957)(955) and (435) follows:
% 30.31/9.75 | (959) sum(n7, n7) = all_0_3_3
% 30.31/9.75 |
% 30.31/9.75 | From (1237) and (4501) follows:
% 30.31/9.76 | (4532) sum(n9, n5) = all_0_0_0
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (194) with n9, n5, all_0_0_0, n14 and discharging atoms sum(n9, n5) = all_0_0_0, sum(n9, n5) = n14, yields:
% 30.31/9.76 | (960) all_0_0_0 = n14
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 30.31/9.76 | (961) all_0_3_3 = n14
% 30.31/9.76 |
% 30.31/9.76 | Equations (960,961) can reduce 201 to:
% 30.31/9.76 | (746) $false
% 30.31/9.76 |
% 30.31/9.76 |-The branch is then unsatisfiable
% 30.31/9.76 |-Branch two:
% 30.31/9.76 | (1244) ~ (all_0_10_10 = n13)
% 30.31/9.76 | (1245) all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.31/9.76 |
% 30.31/9.76 +-Applying beta-rule and splitting (1245), into two cases.
% 30.31/9.76 |-Branch one:
% 30.31/9.76 | (1246) all_0_10_10 = n12
% 30.31/9.76 |
% 30.31/9.76 | From (1246) and (57) follows:
% 30.31/9.76 | (1247) pred(n12) = all_0_6_6
% 30.31/9.76 |
% 30.31/9.76 | From (1246) and (381) follows:
% 30.31/9.76 | (1248) succ(n12) = all_0_8_8
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (259) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 30.31/9.76 | (1249) all_0_6_6 = n11
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (184) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 30.31/9.76 | (1250) all_0_8_8 = n13
% 30.31/9.76 |
% 30.31/9.76 | From (1249)(1250) and (628) follows:
% 30.31/9.76 | (1251) sum(n11, n13) = all_0_1_1
% 30.31/9.76 |
% 30.31/9.76 | From (1249) and (4497) follows:
% 30.31/9.76 | (4544) sum(n11, n16) = all_0_4_4
% 30.31/9.76 |
% 30.31/9.76 | From (1250) and (4499) follows:
% 30.31/9.76 | (4545) sum(n14, n13) = all_0_7_7
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (194) with n14, n13, all_0_7_7, n6 and discharging atoms sum(n14, n13) = all_0_7_7, sum(n14, n13) = n6, yields:
% 30.31/9.76 | (975) all_0_7_7 = n6
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (194) with n11, n16, all_0_4_4, n6 and discharging atoms sum(n11, n16) = all_0_4_4, sum(n11, n16) = n6, yields:
% 30.31/9.76 | (973) all_0_4_4 = n6
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (194) with n11, n13, all_0_1_1, n3 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n3, yields:
% 30.31/9.76 | (1255) all_0_1_1 = n3
% 30.31/9.76 |
% 30.31/9.76 | From (975)(973) and (435) follows:
% 30.31/9.76 | (977) sum(n6, n6) = all_0_3_3
% 30.31/9.76 |
% 30.31/9.76 | From (1255) and (4501) follows:
% 30.31/9.76 | (4550) sum(n9, n3) = all_0_0_0
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (194) with n9, n3, all_0_0_0, n12 and discharging atoms sum(n9, n3) = all_0_0_0, sum(n9, n3) = n12, yields:
% 30.31/9.76 | (978) all_0_0_0 = n12
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 30.31/9.76 | (979) all_0_3_3 = n12
% 30.31/9.76 |
% 30.31/9.76 | Equations (978,979) can reduce 201 to:
% 30.31/9.76 | (746) $false
% 30.31/9.76 |
% 30.31/9.76 |-The branch is then unsatisfiable
% 30.31/9.76 |-Branch two:
% 30.31/9.76 | (1262) ~ (all_0_10_10 = n12)
% 30.31/9.76 | (1263) all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.31/9.76 |
% 30.31/9.76 +-Applying beta-rule and splitting (1263), into two cases.
% 30.31/9.76 |-Branch one:
% 30.31/9.76 | (1264) all_0_10_10 = n11
% 30.31/9.76 |
% 30.31/9.76 | From (1264) and (57) follows:
% 30.31/9.76 | (1265) pred(n11) = all_0_6_6
% 30.31/9.76 |
% 30.31/9.76 | From (1264) and (381) follows:
% 30.31/9.76 | (1266) succ(n11) = all_0_8_8
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (259) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 30.31/9.76 | (1267) all_0_6_6 = n10
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (184) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 30.31/9.76 | (1268) all_0_8_8 = n12
% 30.31/9.76 |
% 30.31/9.76 | From (1267)(1268) and (628) follows:
% 30.31/9.76 | (1269) sum(n10, n12) = all_0_1_1
% 30.31/9.76 |
% 30.31/9.76 | From (1267) and (4497) follows:
% 30.31/9.76 | (4562) sum(n10, n16) = all_0_4_4
% 30.31/9.76 |
% 30.31/9.76 | From (1268) and (4499) follows:
% 30.31/9.76 | (4563) sum(n14, n12) = all_0_7_7
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (194) with n14, n12, all_0_7_7, n5 and discharging atoms sum(n14, n12) = all_0_7_7, sum(n14, n12) = n5, yields:
% 30.31/9.76 | (993) all_0_7_7 = n5
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (194) with n10, n16, all_0_4_4, n5 and discharging atoms sum(n10, n16) = all_0_4_4, sum(n10, n16) = n5, yields:
% 30.31/9.76 | (991) all_0_4_4 = n5
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (194) with n10, n12, all_0_1_1, n1 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n1, yields:
% 30.31/9.76 | (1273) all_0_1_1 = n1
% 30.31/9.76 |
% 30.31/9.76 | From (993)(991) and (435) follows:
% 30.31/9.76 | (995) sum(n5, n5) = all_0_3_3
% 30.31/9.76 |
% 30.31/9.76 | From (1273) and (4501) follows:
% 30.31/9.76 | (4568) sum(n9, n1) = all_0_0_0
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (194) with n9, n1, all_0_0_0, n10 and discharging atoms sum(n9, n1) = all_0_0_0, sum(n9, n1) = n10, yields:
% 30.31/9.76 | (996) all_0_0_0 = n10
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 30.31/9.76 | (997) all_0_3_3 = n10
% 30.31/9.76 |
% 30.31/9.76 | Equations (996,997) can reduce 201 to:
% 30.31/9.76 | (746) $false
% 30.31/9.76 |
% 30.31/9.76 |-The branch is then unsatisfiable
% 30.31/9.76 |-Branch two:
% 30.31/9.76 | (1280) ~ (all_0_10_10 = n11)
% 30.31/9.76 | (1281) all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.31/9.76 |
% 30.31/9.76 +-Applying beta-rule and splitting (1281), into two cases.
% 30.31/9.76 |-Branch one:
% 30.31/9.76 | (1282) all_0_10_10 = n10
% 30.31/9.76 |
% 30.31/9.76 | From (1282) and (57) follows:
% 30.31/9.76 | (1283) pred(n10) = all_0_6_6
% 30.31/9.76 |
% 30.31/9.76 | From (1282) and (381) follows:
% 30.31/9.76 | (1284) succ(n10) = all_0_8_8
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (259) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 30.31/9.76 | (1285) all_0_6_6 = n9
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (184) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 30.31/9.76 | (1286) all_0_8_8 = n11
% 30.31/9.76 |
% 30.31/9.76 | From (1285)(1286) and (628) follows:
% 30.31/9.76 | (1287) sum(n9, n11) = all_0_1_1
% 30.31/9.76 |
% 30.31/9.76 | From (1285) and (4497) follows:
% 30.31/9.76 | (4580) sum(n9, n16) = all_0_4_4
% 30.31/9.76 |
% 30.31/9.76 | From (1286) and (4499) follows:
% 30.31/9.76 | (4581) sum(n14, n11) = all_0_7_7
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (194) with n14, n11, all_0_7_7, n4 and discharging atoms sum(n14, n11) = all_0_7_7, sum(n14, n11) = n4, yields:
% 30.31/9.76 | (1011) all_0_7_7 = n4
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (194) with n9, n16, all_0_4_4, n4 and discharging atoms sum(n9, n16) = all_0_4_4, sum(n9, n16) = n4, yields:
% 30.31/9.76 | (1009) all_0_4_4 = n4
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (194) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 30.31/9.76 | (1291) all_0_1_1 = n20
% 30.31/9.76 |
% 30.31/9.76 | From (1011)(1009) and (435) follows:
% 30.31/9.76 | (1013) sum(n4, n4) = all_0_3_3
% 30.31/9.76 |
% 30.31/9.76 | From (1291) and (4501) follows:
% 30.31/9.76 | (4586) sum(n9, n20) = all_0_0_0
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (194) with n9, n20, all_0_0_0, n8 and discharging atoms sum(n9, n20) = all_0_0_0, sum(n9, n20) = n8, yields:
% 30.31/9.76 | (1014) all_0_0_0 = n8
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 30.31/9.76 | (1015) all_0_3_3 = n8
% 30.31/9.76 |
% 30.31/9.76 | Equations (1014,1015) can reduce 201 to:
% 30.31/9.76 | (746) $false
% 30.31/9.76 |
% 30.31/9.76 |-The branch is then unsatisfiable
% 30.31/9.76 |-Branch two:
% 30.31/9.76 | (1298) ~ (all_0_10_10 = n10)
% 30.31/9.76 | (1299) all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.31/9.76 |
% 30.31/9.76 +-Applying beta-rule and splitting (1299), into two cases.
% 30.31/9.76 |-Branch one:
% 30.31/9.76 | (1300) all_0_10_10 = n9
% 30.31/9.76 |
% 30.31/9.76 | From (1300) and (57) follows:
% 30.31/9.76 | (1301) pred(n9) = all_0_6_6
% 30.31/9.76 |
% 30.31/9.76 | From (1300) and (381) follows:
% 30.31/9.76 | (1302) succ(n9) = all_0_8_8
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (259) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 30.31/9.76 | (1303) all_0_6_6 = n8
% 30.31/9.76 |
% 30.31/9.76 | Instantiating formula (184) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 30.31/9.76 | (1304) all_0_8_8 = n10
% 30.31/9.76 |
% 30.31/9.76 | From (1303)(1304) and (628) follows:
% 30.31/9.76 | (1305) sum(n8, n10) = all_0_1_1
% 30.31/9.76 |
% 30.31/9.76 | From (1303) and (4497) follows:
% 30.31/9.77 | (4598) sum(n8, n16) = all_0_4_4
% 30.31/9.77 |
% 30.31/9.77 | From (1304) and (4499) follows:
% 30.31/9.77 | (4599) sum(n14, n10) = all_0_7_7
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n14, n10, all_0_7_7, n3 and discharging atoms sum(n14, n10) = all_0_7_7, sum(n14, n10) = n3, yields:
% 30.31/9.77 | (1029) all_0_7_7 = n3
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n8, n16, all_0_4_4, n3 and discharging atoms sum(n8, n16) = all_0_4_4, sum(n8, n16) = n3, yields:
% 30.31/9.77 | (1027) all_0_4_4 = n3
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 30.31/9.77 | (1309) all_0_1_1 = n18
% 30.31/9.77 |
% 30.31/9.77 | From (1029)(1027) and (435) follows:
% 30.31/9.77 | (1031) sum(n3, n3) = all_0_3_3
% 30.31/9.77 |
% 30.31/9.77 | From (1309) and (4501) follows:
% 30.31/9.77 | (4604) sum(n9, n18) = all_0_0_0
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n9, n18, all_0_0_0, n6 and discharging atoms sum(n9, n18) = all_0_0_0, sum(n9, n18) = n6, yields:
% 30.31/9.77 | (1032) all_0_0_0 = n6
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 30.31/9.77 | (1033) all_0_3_3 = n6
% 30.31/9.77 |
% 30.31/9.77 | Equations (1032,1033) can reduce 201 to:
% 30.31/9.77 | (746) $false
% 30.31/9.77 |
% 30.31/9.77 |-The branch is then unsatisfiable
% 30.31/9.77 |-Branch two:
% 30.31/9.77 | (1316) ~ (all_0_10_10 = n9)
% 30.31/9.77 | (1317) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.31/9.77 |
% 30.31/9.77 +-Applying beta-rule and splitting (1317), into two cases.
% 30.31/9.77 |-Branch one:
% 30.31/9.77 | (1318) all_0_10_10 = n8
% 30.31/9.77 |
% 30.31/9.77 | From (1318) and (57) follows:
% 30.31/9.77 | (1319) pred(n8) = all_0_6_6
% 30.31/9.77 |
% 30.31/9.77 | From (1318) and (381) follows:
% 30.31/9.77 | (1320) succ(n8) = all_0_8_8
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (259) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 30.31/9.77 | (1321) all_0_6_6 = n7
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (184) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 30.31/9.77 | (1322) all_0_8_8 = n9
% 30.31/9.77 |
% 30.31/9.77 | From (1321)(1322) and (628) follows:
% 30.31/9.77 | (1323) sum(n7, n9) = all_0_1_1
% 30.31/9.77 |
% 30.31/9.77 | From (1321) and (4497) follows:
% 30.31/9.77 | (4616) sum(n7, n16) = all_0_4_4
% 30.31/9.77 |
% 30.31/9.77 | From (1322) and (4499) follows:
% 30.31/9.77 | (4617) sum(n14, n9) = all_0_7_7
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n14, n9, all_0_7_7, n2 and discharging atoms sum(n14, n9) = all_0_7_7, sum(n14, n9) = n2, yields:
% 30.31/9.77 | (1047) all_0_7_7 = n2
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n7, n16, all_0_4_4, n2 and discharging atoms sum(n7, n16) = all_0_4_4, sum(n7, n16) = n2, yields:
% 30.31/9.77 | (1045) all_0_4_4 = n2
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 30.31/9.77 | (1327) all_0_1_1 = n16
% 30.31/9.77 |
% 30.31/9.77 | From (1047)(1045) and (435) follows:
% 30.31/9.77 | (1049) sum(n2, n2) = all_0_3_3
% 30.31/9.77 |
% 30.31/9.77 | From (1327) and (4501) follows:
% 30.31/9.77 | (4622) sum(n9, n16) = all_0_0_0
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n9, n16, all_0_0_0, n4 and discharging atoms sum(n9, n16) = all_0_0_0, sum(n9, n16) = n4, yields:
% 30.31/9.77 | (1050) all_0_0_0 = n4
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 30.31/9.77 | (1051) all_0_3_3 = n4
% 30.31/9.77 |
% 30.31/9.77 | Equations (1050,1051) can reduce 201 to:
% 30.31/9.77 | (746) $false
% 30.31/9.77 |
% 30.31/9.77 |-The branch is then unsatisfiable
% 30.31/9.77 |-Branch two:
% 30.31/9.77 | (1334) ~ (all_0_10_10 = n8)
% 30.31/9.77 | (1335) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.31/9.77 |
% 30.31/9.77 +-Applying beta-rule and splitting (1335), into two cases.
% 30.31/9.77 |-Branch one:
% 30.31/9.77 | (1336) all_0_10_10 = n7
% 30.31/9.77 |
% 30.31/9.77 | From (1336) and (57) follows:
% 30.31/9.77 | (1337) pred(n7) = all_0_6_6
% 30.31/9.77 |
% 30.31/9.77 | From (1336) and (381) follows:
% 30.31/9.77 | (1338) succ(n7) = all_0_8_8
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (259) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 30.31/9.77 | (1339) all_0_6_6 = n6
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (184) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 30.31/9.77 | (1340) all_0_8_8 = n8
% 30.31/9.77 |
% 30.31/9.77 | From (1339)(1340) and (628) follows:
% 30.31/9.77 | (1341) sum(n6, n8) = all_0_1_1
% 30.31/9.77 |
% 30.31/9.77 | From (1339) and (4497) follows:
% 30.31/9.77 | (4634) sum(n6, n16) = all_0_4_4
% 30.31/9.77 |
% 30.31/9.77 | From (1340) and (4499) follows:
% 30.31/9.77 | (4635) sum(n14, n8) = all_0_7_7
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n14, n8, all_0_7_7, n1 and discharging atoms sum(n14, n8) = all_0_7_7, sum(n14, n8) = n1, yields:
% 30.31/9.77 | (1065) all_0_7_7 = n1
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n6, n16, all_0_4_4, n1 and discharging atoms sum(n6, n16) = all_0_4_4, sum(n6, n16) = n1, yields:
% 30.31/9.77 | (1063) all_0_4_4 = n1
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 30.31/9.77 | (1345) all_0_1_1 = n14
% 30.31/9.77 |
% 30.31/9.77 | From (1065)(1063) and (435) follows:
% 30.31/9.77 | (1067) sum(n1, n1) = all_0_3_3
% 30.31/9.77 |
% 30.31/9.77 | From (1345) and (4501) follows:
% 30.31/9.77 | (4640) sum(n9, n14) = all_0_0_0
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n9, n14, all_0_0_0, n2 and discharging atoms sum(n9, n14) = all_0_0_0, sum(n9, n14) = n2, yields:
% 30.31/9.77 | (1068) all_0_0_0 = n2
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 30.31/9.77 | (1069) all_0_3_3 = n2
% 30.31/9.77 |
% 30.31/9.77 | Equations (1068,1069) can reduce 201 to:
% 30.31/9.77 | (746) $false
% 30.31/9.77 |
% 30.31/9.77 |-The branch is then unsatisfiable
% 30.31/9.77 |-Branch two:
% 30.31/9.77 | (1352) ~ (all_0_10_10 = n7)
% 30.31/9.77 | (1353) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.31/9.77 |
% 30.31/9.77 +-Applying beta-rule and splitting (1353), into two cases.
% 30.31/9.77 |-Branch one:
% 30.31/9.77 | (1354) all_0_10_10 = n6
% 30.31/9.77 |
% 30.31/9.77 | From (1354) and (57) follows:
% 30.31/9.77 | (1355) pred(n6) = all_0_6_6
% 30.31/9.77 |
% 30.31/9.77 | From (1354) and (381) follows:
% 30.31/9.77 | (1356) succ(n6) = all_0_8_8
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (259) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 30.31/9.77 | (1357) all_0_6_6 = n5
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (184) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 30.31/9.77 | (1358) all_0_8_8 = n7
% 30.31/9.77 |
% 30.31/9.77 | From (1357)(1358) and (628) follows:
% 30.31/9.77 | (1359) sum(n5, n7) = all_0_1_1
% 30.31/9.77 |
% 30.31/9.77 | From (1357) and (4497) follows:
% 30.31/9.77 | (4652) sum(n5, n16) = all_0_4_4
% 30.31/9.77 |
% 30.31/9.77 | From (1358) and (4499) follows:
% 30.31/9.77 | (4653) sum(n14, n7) = all_0_7_7
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n14, n7, all_0_7_7, n0 and discharging atoms sum(n14, n7) = all_0_7_7, sum(n14, n7) = n0, yields:
% 30.31/9.77 | (1083) all_0_7_7 = n0
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n5, n16, all_0_4_4, n0 and discharging atoms sum(n5, n16) = all_0_4_4, sum(n5, n16) = n0, yields:
% 30.31/9.77 | (1081) all_0_4_4 = n0
% 30.31/9.77 |
% 30.31/9.77 | Instantiating formula (194) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 30.31/9.77 | (1363) all_0_1_1 = n12
% 30.31/9.77 |
% 30.31/9.77 | From (1083)(1081) and (435) follows:
% 30.31/9.77 | (1085) sum(n0, n0) = all_0_3_3
% 30.31/9.77 |
% 30.31/9.77 | From (1363) and (4501) follows:
% 30.31/9.78 | (4658) sum(n9, n12) = all_0_0_0
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (194) with n9, n12, all_0_0_0, n0 and discharging atoms sum(n9, n12) = all_0_0_0, sum(n9, n12) = n0, yields:
% 30.31/9.78 | (1087) all_0_0_0 = n0
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 30.31/9.78 | (1088) all_0_3_3 = n0
% 30.31/9.78 |
% 30.31/9.78 | Equations (1087,1088) can reduce 201 to:
% 30.31/9.78 | (746) $false
% 30.31/9.78 |
% 30.31/9.78 |-The branch is then unsatisfiable
% 30.31/9.78 |-Branch two:
% 30.31/9.78 | (1370) ~ (all_0_10_10 = n6)
% 30.31/9.78 | (1371) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.31/9.78 |
% 30.31/9.78 +-Applying beta-rule and splitting (1371), into two cases.
% 30.31/9.78 |-Branch one:
% 30.31/9.78 | (1372) all_0_10_10 = n5
% 30.31/9.78 |
% 30.31/9.78 | From (1372) and (57) follows:
% 30.31/9.78 | (1373) pred(n5) = all_0_6_6
% 30.31/9.78 |
% 30.31/9.78 | From (1372) and (381) follows:
% 30.31/9.78 | (1374) succ(n5) = all_0_8_8
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (259) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 30.31/9.78 | (1375) all_0_6_6 = n4
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (184) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 30.31/9.78 | (1376) all_0_8_8 = n6
% 30.31/9.78 |
% 30.31/9.78 | From (1375)(1376) and (628) follows:
% 30.31/9.78 | (1377) sum(n4, n6) = all_0_1_1
% 30.31/9.78 |
% 30.31/9.78 | From (1375) and (4497) follows:
% 30.31/9.78 | (4670) sum(n4, n16) = all_0_4_4
% 30.31/9.78 |
% 30.31/9.78 | From (1376) and (4499) follows:
% 30.31/9.78 | (4671) sum(n14, n6) = all_0_7_7
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (194) with n14, n6, all_0_7_7, n20 and discharging atoms sum(n14, n6) = all_0_7_7, sum(n14, n6) = n20, yields:
% 30.31/9.78 | (1100) all_0_7_7 = n20
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (194) with n4, n16, all_0_4_4, n20 and discharging atoms sum(n4, n16) = all_0_4_4, sum(n4, n16) = n20, yields:
% 30.31/9.78 | (1101) all_0_4_4 = n20
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (194) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 30.31/9.78 | (1381) all_0_1_1 = n10
% 30.31/9.78 |
% 30.31/9.78 | From (1100)(1101) and (435) follows:
% 30.31/9.78 | (1103) sum(n20, n20) = all_0_3_3
% 30.31/9.78 |
% 30.31/9.78 | From (1381) and (4501) follows:
% 30.31/9.78 | (4676) sum(n9, n10) = all_0_0_0
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 30.31/9.78 | (1104) all_0_3_3 = n19
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (194) with n9, n10, all_0_0_0, n19 and discharging atoms sum(n9, n10) = all_0_0_0, sum(n9, n10) = n19, yields:
% 30.31/9.78 | (1105) all_0_0_0 = n19
% 30.31/9.78 |
% 30.31/9.78 | Equations (1105,1104) can reduce 201 to:
% 30.31/9.78 | (746) $false
% 30.31/9.78 |
% 30.31/9.78 |-The branch is then unsatisfiable
% 30.31/9.78 |-Branch two:
% 30.31/9.78 | (1388) ~ (all_0_10_10 = n5)
% 30.31/9.78 | (1389) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.31/9.78 |
% 30.31/9.78 +-Applying beta-rule and splitting (1389), into two cases.
% 30.31/9.78 |-Branch one:
% 30.31/9.78 | (1390) all_0_10_10 = n4
% 30.31/9.78 |
% 30.31/9.78 | From (1390) and (57) follows:
% 30.31/9.78 | (1391) pred(n4) = all_0_6_6
% 30.31/9.78 |
% 30.31/9.78 | From (1390) and (381) follows:
% 30.31/9.78 | (1392) succ(n4) = all_0_8_8
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (259) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 30.31/9.78 | (1393) all_0_6_6 = n3
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (184) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 30.31/9.78 | (1394) all_0_8_8 = n5
% 30.31/9.78 |
% 30.31/9.78 | From (1393)(1394) and (628) follows:
% 30.31/9.78 | (1395) sum(n3, n5) = all_0_1_1
% 30.31/9.78 |
% 30.31/9.78 | From (1393) and (4497) follows:
% 30.31/9.78 | (4688) sum(n3, n16) = all_0_4_4
% 30.31/9.78 |
% 30.31/9.78 | From (1394) and (4499) follows:
% 30.31/9.78 | (4689) sum(n14, n5) = all_0_7_7
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (194) with n14, n5, all_0_7_7, n19 and discharging atoms sum(n14, n5) = all_0_7_7, sum(n14, n5) = n19, yields:
% 30.31/9.78 | (737) all_0_7_7 = n19
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (194) with n3, n16, all_0_4_4, n19 and discharging atoms sum(n3, n16) = all_0_4_4, sum(n3, n16) = n19, yields:
% 30.31/9.78 | (736) all_0_4_4 = n19
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (194) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 30.31/9.78 | (1399) all_0_1_1 = n8
% 30.31/9.78 |
% 30.31/9.78 | From (737)(736) and (435) follows:
% 30.31/9.78 | (741) sum(n19, n19) = all_0_3_3
% 30.31/9.78 |
% 30.31/9.78 | From (1399) and (4501) follows:
% 30.31/9.78 | (4694) sum(n9, n8) = all_0_0_0
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 30.31/9.78 | (744) all_0_3_3 = n17
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (194) with n9, n8, all_0_0_0, n17 and discharging atoms sum(n9, n8) = all_0_0_0, sum(n9, n8) = n17, yields:
% 30.31/9.78 | (742) all_0_0_0 = n17
% 30.31/9.78 |
% 30.31/9.78 | Equations (742,744) can reduce 201 to:
% 30.31/9.78 | (746) $false
% 30.31/9.78 |
% 30.31/9.78 |-The branch is then unsatisfiable
% 30.31/9.78 |-Branch two:
% 30.31/9.78 | (1406) ~ (all_0_10_10 = n4)
% 30.31/9.78 | (1407) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.31/9.78 |
% 30.31/9.78 +-Applying beta-rule and splitting (1407), into two cases.
% 30.31/9.78 |-Branch one:
% 30.31/9.78 | (1408) all_0_10_10 = n3
% 30.31/9.78 |
% 30.31/9.78 | From (1408) and (57) follows:
% 30.31/9.78 | (1409) pred(n3) = all_0_6_6
% 30.31/9.78 |
% 30.31/9.78 | From (1408) and (381) follows:
% 30.31/9.78 | (1410) succ(n3) = all_0_8_8
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 30.31/9.78 | (1411) all_0_6_6 = n2
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 30.31/9.78 | (1412) all_0_8_8 = n4
% 30.31/9.78 |
% 30.31/9.78 | From (1411)(1412) and (628) follows:
% 30.31/9.78 | (1413) sum(n2, n4) = all_0_1_1
% 30.31/9.78 |
% 30.31/9.78 | From (1411) and (4497) follows:
% 30.31/9.78 | (4706) sum(n2, n16) = all_0_4_4
% 30.31/9.78 |
% 30.31/9.78 | From (1412) and (4499) follows:
% 30.31/9.78 | (4707) sum(n14, n4) = all_0_7_7
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (194) with n14, n4, all_0_7_7, n18 and discharging atoms sum(n14, n4) = all_0_7_7, sum(n14, n4) = n18, yields:
% 30.31/9.78 | (759) all_0_7_7 = n18
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (194) with n2, n16, all_0_4_4, n18 and discharging atoms sum(n2, n16) = all_0_4_4, sum(n2, n16) = n18, yields:
% 30.31/9.78 | (757) all_0_4_4 = n18
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 30.31/9.78 | (1417) all_0_1_1 = n6
% 30.31/9.78 |
% 30.31/9.78 | From (759)(757) and (435) follows:
% 30.31/9.78 | (761) sum(n18, n18) = all_0_3_3
% 30.31/9.78 |
% 30.31/9.78 | From (1417) and (4501) follows:
% 30.31/9.78 | (4712) sum(n9, n6) = all_0_0_0
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 30.31/9.78 | (762) all_0_3_3 = n15
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (194) with n9, n6, all_0_0_0, n15 and discharging atoms sum(n9, n6) = all_0_0_0, sum(n9, n6) = n15, yields:
% 30.31/9.78 | (763) all_0_0_0 = n15
% 30.31/9.78 |
% 30.31/9.78 | Equations (763,762) can reduce 201 to:
% 30.31/9.78 | (746) $false
% 30.31/9.78 |
% 30.31/9.78 |-The branch is then unsatisfiable
% 30.31/9.78 |-Branch two:
% 30.31/9.78 | (1424) ~ (all_0_10_10 = n3)
% 30.31/9.78 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.31/9.78 |
% 30.31/9.78 +-Applying beta-rule and splitting (1425), into two cases.
% 30.31/9.78 |-Branch one:
% 30.31/9.78 | (1426) all_0_10_10 = n2
% 30.31/9.78 |
% 30.31/9.78 | From (1426) and (57) follows:
% 30.31/9.78 | (1427) pred(n2) = all_0_6_6
% 30.31/9.78 |
% 30.31/9.78 | From (1426) and (381) follows:
% 30.31/9.78 | (1428) succ(n2) = all_0_8_8
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 30.31/9.78 | (1429) all_0_6_6 = n1
% 30.31/9.78 |
% 30.31/9.78 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 30.31/9.78 | (1430) all_0_8_8 = n3
% 30.31/9.78 |
% 30.31/9.78 | From (1429)(1430) and (628) follows:
% 30.31/9.78 | (1431) sum(n1, n3) = all_0_1_1
% 30.31/9.78 |
% 30.31/9.78 | From (1429) and (4497) follows:
% 30.31/9.78 | (4724) sum(n1, n16) = all_0_4_4
% 30.31/9.78 |
% 30.31/9.78 | From (1430) and (4499) follows:
% 30.31/9.79 | (4725) sum(n14, n3) = all_0_7_7
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (194) with n14, n3, all_0_7_7, n17 and discharging atoms sum(n14, n3) = all_0_7_7, sum(n14, n3) = n17, yields:
% 30.31/9.79 | (777) all_0_7_7 = n17
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (194) with n1, n16, all_0_4_4, n17 and discharging atoms sum(n1, n16) = all_0_4_4, sum(n1, n16) = n17, yields:
% 30.31/9.79 | (775) all_0_4_4 = n17
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 30.31/9.79 | (1435) all_0_1_1 = n4
% 30.31/9.79 |
% 30.31/9.79 | From (777)(775) and (435) follows:
% 30.31/9.79 | (779) sum(n17, n17) = all_0_3_3
% 30.31/9.79 |
% 30.31/9.79 | From (1435) and (4501) follows:
% 30.31/9.79 | (4730) sum(n9, n4) = all_0_0_0
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 30.31/9.79 | (780) all_0_3_3 = n13
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (194) with n9, n4, all_0_0_0, n13 and discharging atoms sum(n9, n4) = all_0_0_0, sum(n9, n4) = n13, yields:
% 30.31/9.79 | (781) all_0_0_0 = n13
% 30.31/9.79 |
% 30.31/9.79 | Equations (781,780) can reduce 201 to:
% 30.31/9.79 | (746) $false
% 30.31/9.79 |
% 30.31/9.79 |-The branch is then unsatisfiable
% 30.31/9.79 |-Branch two:
% 30.31/9.79 | (1442) ~ (all_0_10_10 = n2)
% 30.31/9.79 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 30.31/9.79 |
% 30.31/9.79 +-Applying beta-rule and splitting (1443), into two cases.
% 30.31/9.79 |-Branch one:
% 30.31/9.79 | (1444) all_0_10_10 = n1
% 30.31/9.79 |
% 30.31/9.79 | From (1444) and (57) follows:
% 30.31/9.79 | (1445) pred(n1) = all_0_6_6
% 30.31/9.79 |
% 30.31/9.79 | From (1444) and (381) follows:
% 30.31/9.79 | (1446) succ(n1) = all_0_8_8
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 30.31/9.79 | (1447) all_0_6_6 = n0
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 30.31/9.79 | (1448) all_0_8_8 = n2
% 30.31/9.79 |
% 30.31/9.79 | From (1447)(1448) and (628) follows:
% 30.31/9.79 | (1449) sum(n0, n2) = all_0_1_1
% 30.31/9.79 |
% 30.31/9.79 | From (1447) and (4497) follows:
% 30.31/9.79 | (4742) sum(n0, n16) = all_0_4_4
% 30.31/9.79 |
% 30.31/9.79 | From (1448) and (4499) follows:
% 30.31/9.79 | (4743) sum(n14, n2) = all_0_7_7
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (194) with n14, n2, all_0_7_7, n16 and discharging atoms sum(n14, n2) = all_0_7_7, sum(n14, n2) = n16, yields:
% 30.31/9.79 | (795) all_0_7_7 = n16
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (194) with n0, n16, all_0_4_4, n16 and discharging atoms sum(n0, n16) = all_0_4_4, sum(n0, n16) = n16, yields:
% 30.31/9.79 | (793) all_0_4_4 = n16
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 30.31/9.79 | (1453) all_0_1_1 = n2
% 30.31/9.79 |
% 30.31/9.79 | From (795)(793) and (435) follows:
% 30.31/9.79 | (797) sum(n16, n16) = all_0_3_3
% 30.31/9.79 |
% 30.31/9.79 | From (1453) and (4501) follows:
% 30.31/9.79 | (4748) sum(n9, n2) = all_0_0_0
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 30.31/9.79 | (798) all_0_3_3 = n11
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (194) with n9, n2, all_0_0_0, n11 and discharging atoms sum(n9, n2) = all_0_0_0, sum(n9, n2) = n11, yields:
% 30.31/9.79 | (799) all_0_0_0 = n11
% 30.31/9.79 |
% 30.31/9.79 | Equations (799,798) can reduce 201 to:
% 30.31/9.79 | (746) $false
% 30.31/9.79 |
% 30.31/9.79 |-The branch is then unsatisfiable
% 30.31/9.79 |-Branch two:
% 30.31/9.79 | (1462) ~ (all_0_10_10 = n1)
% 30.31/9.79 | (1463) all_0_10_10 = n0
% 30.31/9.79 |
% 30.31/9.79 | From (1463) and (57) follows:
% 30.31/9.79 | (1464) pred(n0) = all_0_6_6
% 30.31/9.79 |
% 30.31/9.79 | From (1463) and (381) follows:
% 30.31/9.79 | (1465) succ(n0) = all_0_8_8
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 30.31/9.79 | (1466) all_0_6_6 = n20
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 30.31/9.79 | (1467) all_0_8_8 = n1
% 30.31/9.79 |
% 30.31/9.79 | From (1466)(1467) and (628) follows:
% 30.31/9.79 | (1468) sum(n20, n1) = all_0_1_1
% 30.31/9.79 |
% 30.31/9.79 | From (1466) and (4497) follows:
% 30.31/9.79 | (4759) sum(n20, n16) = all_0_4_4
% 30.31/9.79 |
% 30.31/9.79 | From (1467) and (4499) follows:
% 30.31/9.79 | (4760) sum(n14, n1) = all_0_7_7
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (194) with n20, n16, all_0_4_4, n15 and discharging atoms sum(n20, n16) = all_0_4_4, sum(n20, n16) = n15, yields:
% 30.31/9.79 | (811) all_0_4_4 = n15
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 30.31/9.79 | (1471) all_0_1_1 = n0
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (194) with n14, n1, all_0_7_7, n15 and discharging atoms sum(n14, n1) = all_0_7_7, sum(n14, n1) = n15, yields:
% 30.31/9.79 | (813) all_0_7_7 = n15
% 30.31/9.79 |
% 30.31/9.79 | From (813)(811) and (435) follows:
% 30.31/9.79 | (815) sum(n15, n15) = all_0_3_3
% 30.31/9.79 |
% 30.31/9.79 | From (1471) and (4501) follows:
% 30.31/9.79 | (4765) sum(n9, n0) = all_0_0_0
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 30.31/9.79 | (816) all_0_3_3 = n9
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (194) with n9, n0, all_0_0_0, n9 and discharging atoms sum(n9, n0) = all_0_0_0, sum(n9, n0) = n9, yields:
% 30.31/9.79 | (817) all_0_0_0 = n9
% 30.31/9.79 |
% 30.31/9.79 | Equations (817,816) can reduce 201 to:
% 30.31/9.79 | (746) $false
% 30.31/9.79 |
% 30.31/9.79 |-The branch is then unsatisfiable
% 30.31/9.79 |-Branch two:
% 30.31/9.79 | (837) ~ (all_0_11_11 = n15)
% 30.31/9.79 | (838) all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.31/9.79 |
% 30.31/9.79 +-Applying beta-rule and splitting (1209), into two cases.
% 30.31/9.79 |-Branch one:
% 30.31/9.79 | (1210) all_0_10_10 = n14
% 30.31/9.79 |
% 30.31/9.79 | From (1210) and (57) follows:
% 30.31/9.79 | (1211) pred(n14) = all_0_6_6
% 30.31/9.79 |
% 30.31/9.79 | From (1210) and (381) follows:
% 30.31/9.79 | (1212) succ(n14) = all_0_8_8
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (259) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 30.31/9.79 | (1213) all_0_6_6 = n13
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (184) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 30.31/9.79 | (1214) all_0_8_8 = n15
% 30.31/9.79 |
% 30.31/9.79 | From (1213) and (1211) follows:
% 30.31/9.79 | (630) pred(n14) = n13
% 30.31/9.79 |
% 30.31/9.79 | From (1214) and (1212) follows:
% 30.31/9.79 | (554) succ(n14) = n15
% 30.31/9.79 |
% 30.31/9.79 | From (1213) and (386) follows:
% 30.31/9.79 | (4778) sum(n13, all_0_5_5) = all_0_4_4
% 30.31/9.79 |
% 30.31/9.79 | From (1213)(1214) and (628) follows:
% 30.31/9.79 | (1215) sum(n13, n15) = all_0_1_1
% 30.31/9.79 |
% 30.31/9.79 | From (1214) and (74) follows:
% 30.31/9.79 | (4780) sum(all_0_9_9, n15) = all_0_7_7
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (194) with n13, n15, all_0_1_1, n7 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n7, yields:
% 30.31/9.79 | (1219) all_0_1_1 = n7
% 30.31/9.79 |
% 30.31/9.79 | From (1219) and (85) follows:
% 30.31/9.79 | (4782) sum(all_0_2_2, n7) = all_0_0_0
% 30.31/9.79 |
% 30.31/9.79 | From (1219) and (1215) follows:
% 30.31/9.79 | (407) sum(n13, n15) = n7
% 30.31/9.79 |
% 30.31/9.79 +-Applying beta-rule and splitting (838), into two cases.
% 30.31/9.79 |-Branch one:
% 30.31/9.79 | (839) all_0_11_11 = n14
% 30.31/9.79 |
% 30.31/9.79 | From (839) and (190) follows:
% 30.31/9.79 | (840) pred(n14) = all_0_9_9
% 30.31/9.79 |
% 30.31/9.79 | From (839) and (505) follows:
% 30.31/9.79 | (841) succ(n14) = all_0_5_5
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (259) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 30.31/9.79 | (842) all_0_9_9 = n13
% 30.31/9.79 |
% 30.31/9.79 | Instantiating formula (184) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 30.31/9.79 | (843) all_0_5_5 = n15
% 30.31/9.79 |
% 30.31/9.79 | From (842)(843) and (156) follows:
% 30.31/9.79 | (844) sum(n13, n15) = all_0_2_2
% 30.31/9.79 |
% 30.31/9.79 | From (842) and (4780) follows:
% 30.31/9.80 | (4790) sum(n13, n15) = all_0_7_7
% 30.31/9.80 |
% 30.31/9.80 | From (843) and (4778) follows:
% 30.31/9.80 | (4791) sum(n13, n15) = all_0_4_4
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n13, n15, all_0_2_2, n7 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n7, yields:
% 30.31/9.80 | (848) all_0_2_2 = n7
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n13, n15, all_0_4_4, all_0_2_2 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = all_0_4_4, yields:
% 30.31/9.80 | (733) all_0_2_2 = all_0_4_4
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n13, n15, all_0_7_7, all_0_2_2 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = all_0_7_7, yields:
% 30.31/9.80 | (734) all_0_2_2 = all_0_7_7
% 30.31/9.80 |
% 30.31/9.80 | Combining equations (734,733) yields a new equation:
% 30.31/9.80 | (735) all_0_4_4 = all_0_7_7
% 30.31/9.80 |
% 30.31/9.80 | Combining equations (848,733) yields a new equation:
% 30.31/9.80 | (955) all_0_4_4 = n7
% 30.31/9.80 |
% 30.31/9.80 | Combining equations (955,735) yields a new equation:
% 30.31/9.80 | (957) all_0_7_7 = n7
% 30.31/9.80 |
% 30.31/9.80 | Combining equations (957,735) yields a new equation:
% 30.31/9.80 | (955) all_0_4_4 = n7
% 30.31/9.80 |
% 30.31/9.80 | Combining equations (955,733) yields a new equation:
% 30.31/9.80 | (848) all_0_2_2 = n7
% 30.31/9.80 |
% 30.31/9.80 | From (848) and (4782) follows:
% 30.31/9.80 | (4800) sum(n7, n7) = all_0_0_0
% 30.31/9.80 |
% 30.31/9.80 | From (957)(955) and (435) follows:
% 30.31/9.80 | (959) sum(n7, n7) = all_0_3_3
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n7, n7, all_0_0_0, n14 and discharging atoms sum(n7, n7) = all_0_0_0, sum(n7, n7) = n14, yields:
% 30.31/9.80 | (960) all_0_0_0 = n14
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n7, n7, all_0_3_3, all_0_0_0 and discharging atoms sum(n7, n7) = all_0_0_0, sum(n7, n7) = all_0_3_3, yields:
% 30.31/9.80 | (743) all_0_0_0 = all_0_3_3
% 30.31/9.80 |
% 30.31/9.80 | Combining equations (960,743) yields a new equation:
% 30.31/9.80 | (961) all_0_3_3 = n14
% 30.31/9.80 |
% 30.31/9.80 | Combining equations (961,743) yields a new equation:
% 30.31/9.80 | (960) all_0_0_0 = n14
% 30.31/9.80 |
% 30.31/9.80 | Equations (960,961) can reduce 201 to:
% 30.31/9.80 | (746) $false
% 30.31/9.80 |
% 30.31/9.80 |-The branch is then unsatisfiable
% 30.31/9.80 |-Branch two:
% 30.31/9.80 | (855) ~ (all_0_11_11 = n14)
% 30.31/9.80 | (856) all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.31/9.80 |
% 30.31/9.80 +-Applying beta-rule and splitting (856), into two cases.
% 30.31/9.80 |-Branch one:
% 30.31/9.80 | (857) all_0_11_11 = n13
% 30.31/9.80 |
% 30.31/9.80 | From (857) and (190) follows:
% 30.31/9.80 | (858) pred(n13) = all_0_9_9
% 30.31/9.80 |
% 30.31/9.80 | From (857) and (505) follows:
% 30.31/9.80 | (859) succ(n13) = all_0_5_5
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (259) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 30.31/9.80 | (860) all_0_9_9 = n12
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (184) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 30.31/9.80 | (861) all_0_5_5 = n14
% 30.31/9.80 |
% 30.31/9.80 | From (860)(861) and (156) follows:
% 30.31/9.80 | (862) sum(n12, n14) = all_0_2_2
% 30.31/9.80 |
% 30.31/9.80 | From (860) and (4780) follows:
% 30.31/9.80 | (4815) sum(n12, n15) = all_0_7_7
% 30.31/9.80 |
% 30.31/9.80 | From (861) and (4778) follows:
% 30.31/9.80 | (4816) sum(n13, n14) = all_0_4_4
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n13, n14, all_0_4_4, n6 and discharging atoms sum(n13, n14) = all_0_4_4, sum(n13, n14) = n6, yields:
% 30.31/9.80 | (973) all_0_4_4 = n6
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n12, n15, all_0_7_7, n6 and discharging atoms sum(n12, n15) = all_0_7_7, sum(n12, n15) = n6, yields:
% 30.31/9.80 | (975) all_0_7_7 = n6
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n12, n14, all_0_2_2, n5 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n5, yields:
% 30.31/9.80 | (866) all_0_2_2 = n5
% 30.31/9.80 |
% 30.31/9.80 | From (866) and (4782) follows:
% 30.31/9.80 | (4820) sum(n5, n7) = all_0_0_0
% 30.31/9.80 |
% 30.31/9.80 | From (975)(973) and (435) follows:
% 30.31/9.80 | (977) sum(n6, n6) = all_0_3_3
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 30.31/9.80 | (979) all_0_3_3 = n12
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n5, n7, all_0_0_0, n12 and discharging atoms sum(n5, n7) = all_0_0_0, sum(n5, n7) = n12, yields:
% 30.31/9.80 | (978) all_0_0_0 = n12
% 30.31/9.80 |
% 30.31/9.80 | Equations (978,979) can reduce 201 to:
% 30.31/9.80 | (746) $false
% 30.31/9.80 |
% 30.31/9.80 |-The branch is then unsatisfiable
% 30.31/9.80 |-Branch two:
% 30.31/9.80 | (873) ~ (all_0_11_11 = n13)
% 30.31/9.80 | (874) all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.31/9.80 |
% 30.31/9.80 +-Applying beta-rule and splitting (874), into two cases.
% 30.31/9.80 |-Branch one:
% 30.31/9.80 | (875) all_0_11_11 = n12
% 30.31/9.80 |
% 30.31/9.80 | From (875) and (190) follows:
% 30.31/9.80 | (876) pred(n12) = all_0_9_9
% 30.31/9.80 |
% 30.31/9.80 | From (875) and (505) follows:
% 30.31/9.80 | (877) succ(n12) = all_0_5_5
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (259) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 30.31/9.80 | (878) all_0_9_9 = n11
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (184) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 30.31/9.80 | (879) all_0_5_5 = n13
% 30.31/9.80 |
% 30.31/9.80 | From (878)(879) and (156) follows:
% 30.31/9.80 | (880) sum(n11, n13) = all_0_2_2
% 30.31/9.80 |
% 30.31/9.80 | From (878) and (4780) follows:
% 30.31/9.80 | (4833) sum(n11, n15) = all_0_7_7
% 30.31/9.80 |
% 30.31/9.80 | From (879) and (4778) follows:
% 30.31/9.80 | (4834) sum(n13, n13) = all_0_4_4
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n13, n13, all_0_4_4, n5 and discharging atoms sum(n13, n13) = all_0_4_4, sum(n13, n13) = n5, yields:
% 30.31/9.80 | (991) all_0_4_4 = n5
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n11, n15, all_0_7_7, n5 and discharging atoms sum(n11, n15) = all_0_7_7, sum(n11, n15) = n5, yields:
% 30.31/9.80 | (993) all_0_7_7 = n5
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n11, n13, all_0_2_2, n3 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n3, yields:
% 30.31/9.80 | (884) all_0_2_2 = n3
% 30.31/9.80 |
% 30.31/9.80 | From (884) and (4782) follows:
% 30.31/9.80 | (4838) sum(n3, n7) = all_0_0_0
% 30.31/9.80 |
% 30.31/9.80 | From (993)(991) and (435) follows:
% 30.31/9.80 | (995) sum(n5, n5) = all_0_3_3
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 30.31/9.80 | (997) all_0_3_3 = n10
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n3, n7, all_0_0_0, n10 and discharging atoms sum(n3, n7) = all_0_0_0, sum(n3, n7) = n10, yields:
% 30.31/9.80 | (996) all_0_0_0 = n10
% 30.31/9.80 |
% 30.31/9.80 | Equations (996,997) can reduce 201 to:
% 30.31/9.80 | (746) $false
% 30.31/9.80 |
% 30.31/9.80 |-The branch is then unsatisfiable
% 30.31/9.80 |-Branch two:
% 30.31/9.80 | (891) ~ (all_0_11_11 = n12)
% 30.31/9.80 | (892) all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.31/9.80 |
% 30.31/9.80 +-Applying beta-rule and splitting (892), into two cases.
% 30.31/9.80 |-Branch one:
% 30.31/9.80 | (893) all_0_11_11 = n11
% 30.31/9.80 |
% 30.31/9.80 | From (893) and (190) follows:
% 30.31/9.80 | (894) pred(n11) = all_0_9_9
% 30.31/9.80 |
% 30.31/9.80 | From (893) and (505) follows:
% 30.31/9.80 | (895) succ(n11) = all_0_5_5
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (259) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 30.31/9.80 | (896) all_0_9_9 = n10
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (184) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 30.31/9.80 | (897) all_0_5_5 = n12
% 30.31/9.80 |
% 30.31/9.80 | From (896)(897) and (156) follows:
% 30.31/9.80 | (898) sum(n10, n12) = all_0_2_2
% 30.31/9.80 |
% 30.31/9.80 | From (896) and (4780) follows:
% 30.31/9.80 | (4851) sum(n10, n15) = all_0_7_7
% 30.31/9.80 |
% 30.31/9.80 | From (897) and (4778) follows:
% 30.31/9.80 | (4852) sum(n13, n12) = all_0_4_4
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n13, n12, all_0_4_4, n4 and discharging atoms sum(n13, n12) = all_0_4_4, sum(n13, n12) = n4, yields:
% 30.31/9.80 | (1009) all_0_4_4 = n4
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n10, n15, all_0_7_7, n4 and discharging atoms sum(n10, n15) = all_0_7_7, sum(n10, n15) = n4, yields:
% 30.31/9.80 | (1011) all_0_7_7 = n4
% 30.31/9.80 |
% 30.31/9.80 | Instantiating formula (194) with n10, n12, all_0_2_2, n1 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n1, yields:
% 30.31/9.80 | (902) all_0_2_2 = n1
% 30.31/9.80 |
% 30.31/9.80 | From (902) and (4782) follows:
% 30.31/9.81 | (4856) sum(n1, n7) = all_0_0_0
% 30.31/9.81 |
% 30.31/9.81 | From (1011)(1009) and (435) follows:
% 30.31/9.81 | (1013) sum(n4, n4) = all_0_3_3
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 30.31/9.81 | (1015) all_0_3_3 = n8
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (194) with n1, n7, all_0_0_0, n8 and discharging atoms sum(n1, n7) = all_0_0_0, sum(n1, n7) = n8, yields:
% 30.31/9.81 | (1014) all_0_0_0 = n8
% 30.31/9.81 |
% 30.31/9.81 | Equations (1014,1015) can reduce 201 to:
% 30.31/9.81 | (746) $false
% 30.31/9.81 |
% 30.31/9.81 |-The branch is then unsatisfiable
% 30.31/9.81 |-Branch two:
% 30.31/9.81 | (909) ~ (all_0_11_11 = n11)
% 30.31/9.81 | (910) all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.31/9.81 |
% 30.31/9.81 +-Applying beta-rule and splitting (910), into two cases.
% 30.31/9.81 |-Branch one:
% 30.31/9.81 | (911) all_0_11_11 = n10
% 30.31/9.81 |
% 30.31/9.81 | From (911) and (190) follows:
% 30.31/9.81 | (912) pred(n10) = all_0_9_9
% 30.31/9.81 |
% 30.31/9.81 | From (911) and (505) follows:
% 30.31/9.81 | (913) succ(n10) = all_0_5_5
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (259) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 30.31/9.81 | (914) all_0_9_9 = n9
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (184) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 30.31/9.81 | (915) all_0_5_5 = n11
% 30.31/9.81 |
% 30.31/9.81 | From (914)(915) and (156) follows:
% 30.31/9.81 | (916) sum(n9, n11) = all_0_2_2
% 30.31/9.81 |
% 30.31/9.81 | From (914) and (4780) follows:
% 30.31/9.81 | (4869) sum(n9, n15) = all_0_7_7
% 30.31/9.81 |
% 30.31/9.81 | From (915) and (4778) follows:
% 30.31/9.81 | (4870) sum(n13, n11) = all_0_4_4
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (194) with n13, n11, all_0_4_4, n3 and discharging atoms sum(n13, n11) = all_0_4_4, sum(n13, n11) = n3, yields:
% 30.31/9.81 | (1027) all_0_4_4 = n3
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (194) with n9, n15, all_0_7_7, n3 and discharging atoms sum(n9, n15) = all_0_7_7, sum(n9, n15) = n3, yields:
% 30.31/9.81 | (1029) all_0_7_7 = n3
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (194) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 30.31/9.81 | (920) all_0_2_2 = n20
% 30.31/9.81 |
% 30.31/9.81 | From (920) and (4782) follows:
% 30.31/9.81 | (4874) sum(n20, n7) = all_0_0_0
% 30.31/9.81 |
% 30.31/9.81 | From (1029)(1027) and (435) follows:
% 30.31/9.81 | (1031) sum(n3, n3) = all_0_3_3
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (194) with n20, n7, all_0_0_0, n6 and discharging atoms sum(n20, n7) = all_0_0_0, sum(n20, n7) = n6, yields:
% 30.31/9.81 | (1032) all_0_0_0 = n6
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 30.31/9.81 | (1033) all_0_3_3 = n6
% 30.31/9.81 |
% 30.31/9.81 | Equations (1032,1033) can reduce 201 to:
% 30.31/9.81 | (746) $false
% 30.31/9.81 |
% 30.31/9.81 |-The branch is then unsatisfiable
% 30.31/9.81 |-Branch two:
% 30.31/9.81 | (927) ~ (all_0_11_11 = n10)
% 30.31/9.81 | (928) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.31/9.81 |
% 30.31/9.81 +-Applying beta-rule and splitting (928), into two cases.
% 30.31/9.81 |-Branch one:
% 30.31/9.81 | (929) all_0_11_11 = n9
% 30.31/9.81 |
% 30.31/9.81 | From (929) and (190) follows:
% 30.31/9.81 | (930) pred(n9) = all_0_9_9
% 30.31/9.81 |
% 30.31/9.81 | From (929) and (505) follows:
% 30.31/9.81 | (931) succ(n9) = all_0_5_5
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (259) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 30.31/9.81 | (932) all_0_9_9 = n8
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (184) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 30.31/9.81 | (933) all_0_5_5 = n10
% 30.31/9.81 |
% 30.31/9.81 | From (932)(933) and (156) follows:
% 30.31/9.81 | (934) sum(n8, n10) = all_0_2_2
% 30.31/9.81 |
% 30.31/9.81 | From (932) and (4780) follows:
% 30.31/9.81 | (4887) sum(n8, n15) = all_0_7_7
% 30.31/9.81 |
% 30.31/9.81 | From (933) and (4778) follows:
% 30.31/9.81 | (4888) sum(n13, n10) = all_0_4_4
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (194) with n13, n10, all_0_4_4, n2 and discharging atoms sum(n13, n10) = all_0_4_4, sum(n13, n10) = n2, yields:
% 30.31/9.81 | (1045) all_0_4_4 = n2
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (194) with n8, n15, all_0_7_7, n2 and discharging atoms sum(n8, n15) = all_0_7_7, sum(n8, n15) = n2, yields:
% 30.31/9.81 | (1047) all_0_7_7 = n2
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (194) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 30.31/9.81 | (938) all_0_2_2 = n18
% 30.31/9.81 |
% 30.31/9.81 | From (938) and (4782) follows:
% 30.31/9.81 | (4892) sum(n18, n7) = all_0_0_0
% 30.31/9.81 |
% 30.31/9.81 | From (1047)(1045) and (435) follows:
% 30.31/9.81 | (1049) sum(n2, n2) = all_0_3_3
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (194) with n18, n7, all_0_0_0, n4 and discharging atoms sum(n18, n7) = all_0_0_0, sum(n18, n7) = n4, yields:
% 30.31/9.81 | (1050) all_0_0_0 = n4
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 30.31/9.81 | (1051) all_0_3_3 = n4
% 30.31/9.81 |
% 30.31/9.81 | Equations (1050,1051) can reduce 201 to:
% 30.31/9.81 | (746) $false
% 30.31/9.81 |
% 30.31/9.81 |-The branch is then unsatisfiable
% 30.31/9.81 |-Branch two:
% 30.31/9.81 | (945) ~ (all_0_11_11 = n9)
% 30.31/9.81 | (946) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.31/9.81 |
% 30.31/9.81 +-Applying beta-rule and splitting (946), into two cases.
% 30.31/9.81 |-Branch one:
% 30.31/9.81 | (947) all_0_11_11 = n8
% 30.31/9.81 |
% 30.31/9.81 | From (947) and (190) follows:
% 30.31/9.81 | (948) pred(n8) = all_0_9_9
% 30.31/9.81 |
% 30.31/9.81 | From (947) and (505) follows:
% 30.31/9.81 | (949) succ(n8) = all_0_5_5
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (259) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 30.31/9.81 | (950) all_0_9_9 = n7
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (184) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 30.31/9.81 | (951) all_0_5_5 = n9
% 30.31/9.81 |
% 30.31/9.81 | From (950)(951) and (156) follows:
% 30.31/9.81 | (952) sum(n7, n9) = all_0_2_2
% 30.31/9.81 |
% 30.31/9.81 | From (950) and (4780) follows:
% 30.31/9.81 | (4905) sum(n7, n15) = all_0_7_7
% 30.31/9.81 |
% 30.31/9.81 | From (951) and (4778) follows:
% 30.31/9.81 | (4906) sum(n13, n9) = all_0_4_4
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (194) with n13, n9, all_0_4_4, n1 and discharging atoms sum(n13, n9) = all_0_4_4, sum(n13, n9) = n1, yields:
% 30.31/9.81 | (1063) all_0_4_4 = n1
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (194) with n7, n15, all_0_7_7, n1 and discharging atoms sum(n7, n15) = all_0_7_7, sum(n7, n15) = n1, yields:
% 30.31/9.81 | (1065) all_0_7_7 = n1
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (194) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 30.31/9.81 | (956) all_0_2_2 = n16
% 30.31/9.81 |
% 30.31/9.81 | From (956) and (4782) follows:
% 30.31/9.81 | (4910) sum(n16, n7) = all_0_0_0
% 30.31/9.81 |
% 30.31/9.81 | From (1065)(1063) and (435) follows:
% 30.31/9.81 | (1067) sum(n1, n1) = all_0_3_3
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (194) with n16, n7, all_0_0_0, n2 and discharging atoms sum(n16, n7) = all_0_0_0, sum(n16, n7) = n2, yields:
% 30.31/9.81 | (1068) all_0_0_0 = n2
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 30.31/9.81 | (1069) all_0_3_3 = n2
% 30.31/9.81 |
% 30.31/9.81 | Equations (1068,1069) can reduce 201 to:
% 30.31/9.81 | (746) $false
% 30.31/9.81 |
% 30.31/9.81 |-The branch is then unsatisfiable
% 30.31/9.81 |-Branch two:
% 30.31/9.81 | (963) ~ (all_0_11_11 = n8)
% 30.31/9.81 | (964) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.31/9.81 |
% 30.31/9.81 +-Applying beta-rule and splitting (964), into two cases.
% 30.31/9.81 |-Branch one:
% 30.31/9.81 | (965) all_0_11_11 = n7
% 30.31/9.81 |
% 30.31/9.81 | From (965) and (190) follows:
% 30.31/9.81 | (966) pred(n7) = all_0_9_9
% 30.31/9.81 |
% 30.31/9.81 | From (965) and (505) follows:
% 30.31/9.81 | (967) succ(n7) = all_0_5_5
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (259) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 30.31/9.81 | (968) all_0_9_9 = n6
% 30.31/9.81 |
% 30.31/9.81 | Instantiating formula (184) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 30.31/9.81 | (969) all_0_5_5 = n8
% 30.31/9.81 |
% 30.31/9.81 | From (968)(969) and (156) follows:
% 30.31/9.81 | (970) sum(n6, n8) = all_0_2_2
% 30.31/9.81 |
% 30.31/9.81 | From (968) and (4780) follows:
% 30.31/9.81 | (4923) sum(n6, n15) = all_0_7_7
% 30.31/9.81 |
% 30.31/9.81 | From (969) and (4778) follows:
% 30.31/9.82 | (4924) sum(n13, n8) = all_0_4_4
% 30.31/9.82 |
% 30.31/9.82 | Instantiating formula (194) with n13, n8, all_0_4_4, n0 and discharging atoms sum(n13, n8) = all_0_4_4, sum(n13, n8) = n0, yields:
% 30.31/9.82 | (1081) all_0_4_4 = n0
% 30.31/9.82 |
% 30.31/9.82 | Instantiating formula (194) with n6, n15, all_0_7_7, n0 and discharging atoms sum(n6, n15) = all_0_7_7, sum(n6, n15) = n0, yields:
% 30.31/9.82 | (1083) all_0_7_7 = n0
% 30.31/9.82 |
% 30.31/9.82 | Instantiating formula (194) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 30.31/9.82 | (974) all_0_2_2 = n14
% 30.31/9.82 |
% 30.31/9.82 | From (974) and (4782) follows:
% 30.31/9.82 | (4928) sum(n14, n7) = all_0_0_0
% 30.31/9.82 |
% 30.31/9.82 | From (1083)(1081) and (435) follows:
% 30.31/9.82 | (1085) sum(n0, n0) = all_0_3_3
% 30.31/9.82 |
% 30.31/9.82 | Instantiating formula (194) with n14, n7, all_0_0_0, n0 and discharging atoms sum(n14, n7) = all_0_0_0, sum(n14, n7) = n0, yields:
% 30.31/9.82 | (1087) all_0_0_0 = n0
% 30.31/9.82 |
% 30.31/9.82 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 30.31/9.82 | (1088) all_0_3_3 = n0
% 30.31/9.82 |
% 30.31/9.82 | Equations (1087,1088) can reduce 201 to:
% 30.31/9.82 | (746) $false
% 30.31/9.82 |
% 30.31/9.82 |-The branch is then unsatisfiable
% 30.31/9.82 |-Branch two:
% 30.31/9.82 | (981) ~ (all_0_11_11 = n7)
% 30.31/9.82 | (982) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.31/9.82 |
% 30.31/9.82 +-Applying beta-rule and splitting (982), into two cases.
% 30.31/9.82 |-Branch one:
% 30.31/9.82 | (983) all_0_11_11 = n6
% 30.31/9.82 |
% 30.31/9.82 | From (983) and (190) follows:
% 30.31/9.82 | (984) pred(n6) = all_0_9_9
% 30.31/9.82 |
% 30.31/9.82 | From (983) and (505) follows:
% 30.31/9.82 | (985) succ(n6) = all_0_5_5
% 30.31/9.82 |
% 30.31/9.82 | Instantiating formula (259) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 30.31/9.82 | (986) all_0_9_9 = n5
% 30.31/9.82 |
% 30.31/9.82 | Instantiating formula (184) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 30.31/9.82 | (987) all_0_5_5 = n7
% 30.31/9.82 |
% 30.31/9.82 | From (986)(987) and (156) follows:
% 30.31/9.82 | (988) sum(n5, n7) = all_0_2_2
% 30.31/9.82 |
% 30.31/9.82 | From (986) and (4780) follows:
% 30.31/9.82 | (4941) sum(n5, n15) = all_0_7_7
% 30.31/9.82 |
% 30.31/9.82 | From (987) and (4778) follows:
% 30.31/9.82 | (4942) sum(n13, n7) = all_0_4_4
% 30.31/9.82 |
% 30.31/9.82 | Instantiating formula (194) with n13, n7, all_0_4_4, n20 and discharging atoms sum(n13, n7) = all_0_4_4, sum(n13, n7) = n20, yields:
% 30.31/9.82 | (1101) all_0_4_4 = n20
% 30.31/9.82 |
% 30.31/9.82 | Instantiating formula (194) with n5, n15, all_0_7_7, n20 and discharging atoms sum(n5, n15) = all_0_7_7, sum(n5, n15) = n20, yields:
% 30.31/9.82 | (1100) all_0_7_7 = n20
% 30.31/9.82 |
% 30.31/9.82 | Instantiating formula (194) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 30.31/9.82 | (992) all_0_2_2 = n12
% 30.31/9.82 |
% 30.31/9.82 | From (992) and (4782) follows:
% 30.31/9.82 | (4946) sum(n12, n7) = all_0_0_0
% 30.31/9.82 |
% 30.31/9.82 | From (1100)(1101) and (435) follows:
% 30.31/9.82 | (1103) sum(n20, n20) = all_0_3_3
% 30.31/9.82 |
% 30.31/9.82 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 30.31/9.82 | (1104) all_0_3_3 = n19
% 30.31/9.82 |
% 30.31/9.82 | Instantiating formula (194) with n12, n7, all_0_0_0, n19 and discharging atoms sum(n12, n7) = all_0_0_0, sum(n12, n7) = n19, yields:
% 30.31/9.82 | (1105) all_0_0_0 = n19
% 30.69/9.82 |
% 30.69/9.82 | Equations (1105,1104) can reduce 201 to:
% 30.69/9.82 | (746) $false
% 30.69/9.82 |
% 30.69/9.82 |-The branch is then unsatisfiable
% 30.69/9.82 |-Branch two:
% 30.69/9.82 | (999) ~ (all_0_11_11 = n6)
% 30.69/9.82 | (1000) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.69/9.82 |
% 30.69/9.82 +-Applying beta-rule and splitting (1000), into two cases.
% 30.69/9.82 |-Branch one:
% 30.69/9.82 | (1001) all_0_11_11 = n5
% 30.69/9.82 |
% 30.69/9.82 | From (1001) and (190) follows:
% 30.69/9.82 | (1002) pred(n5) = all_0_9_9
% 30.69/9.82 |
% 30.69/9.82 | From (1001) and (505) follows:
% 30.69/9.82 | (1003) succ(n5) = all_0_5_5
% 30.69/9.82 |
% 30.69/9.82 | Instantiating formula (259) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 30.69/9.82 | (1004) all_0_9_9 = n4
% 30.69/9.82 |
% 30.69/9.82 | Instantiating formula (184) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 30.69/9.82 | (1005) all_0_5_5 = n6
% 30.69/9.82 |
% 30.69/9.82 | From (1004)(1005) and (156) follows:
% 30.69/9.82 | (1006) sum(n4, n6) = all_0_2_2
% 30.69/9.82 |
% 30.69/9.82 | From (1004) and (4780) follows:
% 30.69/9.82 | (4959) sum(n4, n15) = all_0_7_7
% 30.69/9.82 |
% 30.69/9.82 | From (1005) and (4778) follows:
% 30.69/9.82 | (4960) sum(n13, n6) = all_0_4_4
% 30.69/9.82 |
% 30.69/9.82 | Instantiating formula (194) with n13, n6, all_0_4_4, n19 and discharging atoms sum(n13, n6) = all_0_4_4, sum(n13, n6) = n19, yields:
% 30.69/9.82 | (736) all_0_4_4 = n19
% 30.69/9.82 |
% 30.69/9.82 | Instantiating formula (194) with n4, n15, all_0_7_7, n19 and discharging atoms sum(n4, n15) = all_0_7_7, sum(n4, n15) = n19, yields:
% 30.69/9.82 | (737) all_0_7_7 = n19
% 30.69/9.82 |
% 30.69/9.82 | Instantiating formula (194) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 30.69/9.82 | (1010) all_0_2_2 = n10
% 30.69/9.82 |
% 30.69/9.82 | From (1010) and (4782) follows:
% 30.69/9.82 | (4964) sum(n10, n7) = all_0_0_0
% 30.69/9.82 |
% 30.69/9.82 | From (737)(736) and (435) follows:
% 30.69/9.82 | (741) sum(n19, n19) = all_0_3_3
% 30.69/9.82 |
% 30.69/9.82 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 30.69/9.82 | (744) all_0_3_3 = n17
% 30.69/9.82 |
% 30.69/9.82 | Instantiating formula (194) with n10, n7, all_0_0_0, n17 and discharging atoms sum(n10, n7) = all_0_0_0, sum(n10, n7) = n17, yields:
% 30.69/9.82 | (742) all_0_0_0 = n17
% 30.69/9.82 |
% 30.69/9.82 | Equations (742,744) can reduce 201 to:
% 30.69/9.82 | (746) $false
% 30.69/9.82 |
% 30.69/9.82 |-The branch is then unsatisfiable
% 30.69/9.82 |-Branch two:
% 30.69/9.82 | (1017) ~ (all_0_11_11 = n5)
% 30.69/9.82 | (1018) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.69/9.82 |
% 30.69/9.82 +-Applying beta-rule and splitting (1018), into two cases.
% 30.69/9.82 |-Branch one:
% 30.69/9.82 | (1019) all_0_11_11 = n4
% 30.69/9.82 |
% 30.69/9.82 | From (1019) and (190) follows:
% 30.69/9.82 | (1020) pred(n4) = all_0_9_9
% 30.69/9.82 |
% 30.69/9.82 | From (1019) and (505) follows:
% 30.69/9.82 | (1021) succ(n4) = all_0_5_5
% 30.69/9.82 |
% 30.69/9.82 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 30.69/9.82 | (1022) all_0_9_9 = n3
% 30.69/9.82 |
% 30.69/9.82 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 30.69/9.82 | (1023) all_0_5_5 = n5
% 30.69/9.82 |
% 30.69/9.82 | From (1022)(1023) and (156) follows:
% 30.69/9.82 | (1024) sum(n3, n5) = all_0_2_2
% 30.69/9.82 |
% 30.69/9.82 | From (1022) and (4780) follows:
% 30.69/9.82 | (4977) sum(n3, n15) = all_0_7_7
% 30.69/9.82 |
% 30.69/9.82 | From (1023) and (4778) follows:
% 30.69/9.82 | (4978) sum(n13, n5) = all_0_4_4
% 30.69/9.82 |
% 30.69/9.82 | Instantiating formula (194) with n13, n5, all_0_4_4, n18 and discharging atoms sum(n13, n5) = all_0_4_4, sum(n13, n5) = n18, yields:
% 30.69/9.82 | (757) all_0_4_4 = n18
% 30.69/9.82 |
% 30.69/9.82 | Instantiating formula (194) with n3, n15, all_0_7_7, n18 and discharging atoms sum(n3, n15) = all_0_7_7, sum(n3, n15) = n18, yields:
% 30.69/9.82 | (759) all_0_7_7 = n18
% 30.69/9.82 |
% 30.69/9.82 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 30.69/9.82 | (1028) all_0_2_2 = n8
% 30.69/9.82 |
% 30.69/9.82 | From (1028) and (4782) follows:
% 30.69/9.82 | (4982) sum(n8, n7) = all_0_0_0
% 30.69/9.82 |
% 30.69/9.82 | From (759)(757) and (435) follows:
% 30.69/9.82 | (761) sum(n18, n18) = all_0_3_3
% 30.69/9.82 |
% 30.69/9.82 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 30.69/9.82 | (762) all_0_3_3 = n15
% 30.69/9.82 |
% 30.69/9.82 | Instantiating formula (194) with n8, n7, all_0_0_0, n15 and discharging atoms sum(n8, n7) = all_0_0_0, sum(n8, n7) = n15, yields:
% 30.69/9.82 | (763) all_0_0_0 = n15
% 30.69/9.82 |
% 30.69/9.82 | Equations (763,762) can reduce 201 to:
% 30.69/9.82 | (746) $false
% 30.69/9.82 |
% 30.69/9.82 |-The branch is then unsatisfiable
% 30.69/9.82 |-Branch two:
% 30.69/9.82 | (1035) ~ (all_0_11_11 = n4)
% 30.69/9.82 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.69/9.82 |
% 30.69/9.82 +-Applying beta-rule and splitting (1036), into two cases.
% 30.69/9.82 |-Branch one:
% 30.69/9.82 | (1037) all_0_11_11 = n3
% 30.69/9.82 |
% 30.69/9.82 | From (1037) and (190) follows:
% 30.69/9.82 | (1038) pred(n3) = all_0_9_9
% 30.69/9.82 |
% 30.69/9.82 | From (1037) and (505) follows:
% 30.69/9.83 | (1039) succ(n3) = all_0_5_5
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 30.69/9.83 | (1040) all_0_9_9 = n2
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 30.69/9.83 | (1041) all_0_5_5 = n4
% 30.69/9.83 |
% 30.69/9.83 | From (1040)(1041) and (156) follows:
% 30.69/9.83 | (1042) sum(n2, n4) = all_0_2_2
% 30.69/9.83 |
% 30.69/9.83 | From (1040) and (4780) follows:
% 30.69/9.83 | (4995) sum(n2, n15) = all_0_7_7
% 30.69/9.83 |
% 30.69/9.83 | From (1041) and (4778) follows:
% 30.69/9.83 | (4996) sum(n13, n4) = all_0_4_4
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (194) with n13, n4, all_0_4_4, n17 and discharging atoms sum(n13, n4) = all_0_4_4, sum(n13, n4) = n17, yields:
% 30.69/9.83 | (775) all_0_4_4 = n17
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (194) with n2, n15, all_0_7_7, n17 and discharging atoms sum(n2, n15) = all_0_7_7, sum(n2, n15) = n17, yields:
% 30.69/9.83 | (777) all_0_7_7 = n17
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 30.69/9.83 | (1046) all_0_2_2 = n6
% 30.69/9.83 |
% 30.69/9.83 | From (1046) and (4782) follows:
% 30.69/9.83 | (5000) sum(n6, n7) = all_0_0_0
% 30.69/9.83 |
% 30.69/9.83 | From (777)(775) and (435) follows:
% 30.69/9.83 | (779) sum(n17, n17) = all_0_3_3
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 30.69/9.83 | (780) all_0_3_3 = n13
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (194) with n6, n7, all_0_0_0, n13 and discharging atoms sum(n6, n7) = all_0_0_0, sum(n6, n7) = n13, yields:
% 30.69/9.83 | (781) all_0_0_0 = n13
% 30.69/9.83 |
% 30.69/9.83 | Equations (781,780) can reduce 201 to:
% 30.69/9.83 | (746) $false
% 30.69/9.83 |
% 30.69/9.83 |-The branch is then unsatisfiable
% 30.69/9.83 |-Branch two:
% 30.69/9.83 | (1053) ~ (all_0_11_11 = n3)
% 30.69/9.83 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.69/9.83 |
% 30.69/9.83 +-Applying beta-rule and splitting (1054), into two cases.
% 30.69/9.83 |-Branch one:
% 30.69/9.83 | (1055) all_0_11_11 = n2
% 30.69/9.83 |
% 30.69/9.83 | From (1055) and (190) follows:
% 30.69/9.83 | (1056) pred(n2) = all_0_9_9
% 30.69/9.83 |
% 30.69/9.83 | From (1055) and (505) follows:
% 30.69/9.83 | (1057) succ(n2) = all_0_5_5
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 30.69/9.83 | (1058) all_0_9_9 = n1
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 30.69/9.83 | (1059) all_0_5_5 = n3
% 30.69/9.83 |
% 30.69/9.83 | From (1058)(1059) and (156) follows:
% 30.69/9.83 | (1060) sum(n1, n3) = all_0_2_2
% 30.69/9.83 |
% 30.69/9.83 | From (1058) and (4780) follows:
% 30.69/9.83 | (5013) sum(n1, n15) = all_0_7_7
% 30.69/9.83 |
% 30.69/9.83 | From (1059) and (4778) follows:
% 30.69/9.83 | (5014) sum(n13, n3) = all_0_4_4
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (194) with n13, n3, all_0_4_4, n16 and discharging atoms sum(n13, n3) = all_0_4_4, sum(n13, n3) = n16, yields:
% 30.69/9.83 | (793) all_0_4_4 = n16
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (194) with n1, n15, all_0_7_7, n16 and discharging atoms sum(n1, n15) = all_0_7_7, sum(n1, n15) = n16, yields:
% 30.69/9.83 | (795) all_0_7_7 = n16
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 30.69/9.83 | (1064) all_0_2_2 = n4
% 30.69/9.83 |
% 30.69/9.83 | From (1064) and (4782) follows:
% 30.69/9.83 | (5018) sum(n4, n7) = all_0_0_0
% 30.69/9.83 |
% 30.69/9.83 | From (795)(793) and (435) follows:
% 30.69/9.83 | (797) sum(n16, n16) = all_0_3_3
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 30.69/9.83 | (798) all_0_3_3 = n11
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (194) with n4, n7, all_0_0_0, n11 and discharging atoms sum(n4, n7) = all_0_0_0, sum(n4, n7) = n11, yields:
% 30.69/9.83 | (799) all_0_0_0 = n11
% 30.69/9.83 |
% 30.69/9.83 | Equations (799,798) can reduce 201 to:
% 30.69/9.83 | (746) $false
% 30.69/9.83 |
% 30.69/9.83 |-The branch is then unsatisfiable
% 30.69/9.83 |-Branch two:
% 30.69/9.83 | (1071) ~ (all_0_11_11 = n2)
% 30.69/9.83 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 30.69/9.83 |
% 30.69/9.83 +-Applying beta-rule and splitting (1072), into two cases.
% 30.69/9.83 |-Branch one:
% 30.69/9.83 | (1073) all_0_11_11 = n1
% 30.69/9.83 |
% 30.69/9.83 | From (1073) and (190) follows:
% 30.69/9.83 | (1074) pred(n1) = all_0_9_9
% 30.69/9.83 |
% 30.69/9.83 | From (1073) and (505) follows:
% 30.69/9.83 | (1075) succ(n1) = all_0_5_5
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 30.69/9.83 | (1076) all_0_9_9 = n0
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 30.69/9.83 | (1077) all_0_5_5 = n2
% 30.69/9.83 |
% 30.69/9.83 | From (1076)(1077) and (156) follows:
% 30.69/9.83 | (1078) sum(n0, n2) = all_0_2_2
% 30.69/9.83 |
% 30.69/9.83 | From (1076) and (4780) follows:
% 30.69/9.83 | (5031) sum(n0, n15) = all_0_7_7
% 30.69/9.83 |
% 30.69/9.83 | From (1077) and (4778) follows:
% 30.69/9.83 | (5032) sum(n13, n2) = all_0_4_4
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (194) with n13, n2, all_0_4_4, n15 and discharging atoms sum(n13, n2) = all_0_4_4, sum(n13, n2) = n15, yields:
% 30.69/9.83 | (811) all_0_4_4 = n15
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (194) with n0, n15, all_0_7_7, n15 and discharging atoms sum(n0, n15) = all_0_7_7, sum(n0, n15) = n15, yields:
% 30.69/9.83 | (813) all_0_7_7 = n15
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 30.69/9.83 | (1082) all_0_2_2 = n2
% 30.69/9.83 |
% 30.69/9.83 | From (1082) and (4782) follows:
% 30.69/9.83 | (5036) sum(n2, n7) = all_0_0_0
% 30.69/9.83 |
% 30.69/9.83 | From (813)(811) and (435) follows:
% 30.69/9.83 | (815) sum(n15, n15) = all_0_3_3
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 30.69/9.83 | (816) all_0_3_3 = n9
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (194) with n2, n7, all_0_0_0, n9 and discharging atoms sum(n2, n7) = all_0_0_0, sum(n2, n7) = n9, yields:
% 30.69/9.83 | (817) all_0_0_0 = n9
% 30.69/9.83 |
% 30.69/9.83 | Equations (817,816) can reduce 201 to:
% 30.69/9.83 | (746) $false
% 30.69/9.83 |
% 30.69/9.83 |-The branch is then unsatisfiable
% 30.69/9.83 |-Branch two:
% 30.69/9.83 | (1090) ~ (all_0_11_11 = n1)
% 30.69/9.83 | (1091) all_0_11_11 = n0
% 30.69/9.83 |
% 30.69/9.83 | From (1091) and (190) follows:
% 30.69/9.83 | (1092) pred(n0) = all_0_9_9
% 30.69/9.83 |
% 30.69/9.83 | From (1091) and (505) follows:
% 30.69/9.83 | (1093) succ(n0) = all_0_5_5
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 30.69/9.83 | (1094) all_0_9_9 = n20
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 30.69/9.83 | (1095) all_0_5_5 = n1
% 30.69/9.83 |
% 30.69/9.83 | From (1094)(1095) and (156) follows:
% 30.69/9.83 | (1096) sum(n20, n1) = all_0_2_2
% 30.69/9.83 |
% 30.69/9.83 | From (1094) and (4780) follows:
% 30.69/9.83 | (5048) sum(n20, n15) = all_0_7_7
% 30.69/9.83 |
% 30.69/9.83 | From (1095) and (4778) follows:
% 30.69/9.83 | (5049) sum(n13, n1) = all_0_4_4
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (194) with n20, n15, all_0_7_7, n14 and discharging atoms sum(n20, n15) = all_0_7_7, sum(n20, n15) = n14, yields:
% 30.69/9.83 | (831) all_0_7_7 = n14
% 30.69/9.83 |
% 30.69/9.83 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 30.69/9.83 | (1099) all_0_2_2 = n0
% 30.69/9.83 |
% 30.69/9.84 | Instantiating formula (194) with n13, n1, all_0_4_4, n14 and discharging atoms sum(n13, n1) = all_0_4_4, sum(n13, n1) = n14, yields:
% 30.69/9.84 | (829) all_0_4_4 = n14
% 30.69/9.84 |
% 30.69/9.84 | From (1099) and (4782) follows:
% 30.69/9.84 | (5053) sum(n0, n7) = all_0_0_0
% 30.69/9.84 |
% 30.69/9.84 | From (831)(829) and (435) follows:
% 30.69/9.84 | (833) sum(n14, n14) = all_0_3_3
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 30.69/9.84 | (834) all_0_3_3 = n7
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (194) with n0, n7, all_0_0_0, n7 and discharging atoms sum(n0, n7) = all_0_0_0, sum(n0, n7) = n7, yields:
% 30.69/9.84 | (835) all_0_0_0 = n7
% 30.69/9.84 |
% 30.69/9.84 | Equations (835,834) can reduce 201 to:
% 30.69/9.84 | (746) $false
% 30.69/9.84 |
% 30.69/9.84 |-The branch is then unsatisfiable
% 30.69/9.84 |-Branch two:
% 30.69/9.84 | (1226) ~ (all_0_10_10 = n14)
% 30.69/9.84 | (1227) all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.69/9.84 |
% 30.69/9.84 +-Applying beta-rule and splitting (838), into two cases.
% 30.69/9.84 |-Branch one:
% 30.69/9.84 | (839) all_0_11_11 = n14
% 30.69/9.84 |
% 30.69/9.84 | From (839) and (190) follows:
% 30.69/9.84 | (840) pred(n14) = all_0_9_9
% 30.69/9.84 |
% 30.69/9.84 | From (839) and (505) follows:
% 30.69/9.84 | (841) succ(n14) = all_0_5_5
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (259) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 30.69/9.84 | (842) all_0_9_9 = n13
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (184) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 30.69/9.84 | (843) all_0_5_5 = n15
% 30.69/9.84 |
% 30.69/9.84 | From (843) and (386) follows:
% 30.69/9.84 | (5065) sum(all_0_6_6, n15) = all_0_4_4
% 30.69/9.84 |
% 30.69/9.84 | From (842)(843) and (156) follows:
% 30.69/9.84 | (844) sum(n13, n15) = all_0_2_2
% 30.69/9.84 |
% 30.69/9.84 | From (842) and (74) follows:
% 30.69/9.84 | (5067) sum(n13, all_0_8_8) = all_0_7_7
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (194) with n13, n15, all_0_2_2, n7 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n7, yields:
% 30.69/9.84 | (848) all_0_2_2 = n7
% 30.69/9.84 |
% 30.69/9.84 | From (848) and (85) follows:
% 30.69/9.84 | (5069) sum(n7, all_0_1_1) = all_0_0_0
% 30.69/9.84 |
% 30.69/9.84 +-Applying beta-rule and splitting (1227), into two cases.
% 30.69/9.84 |-Branch one:
% 30.69/9.84 | (1228) all_0_10_10 = n13
% 30.69/9.84 |
% 30.69/9.84 | From (1228) and (57) follows:
% 30.69/9.84 | (1229) pred(n13) = all_0_6_6
% 30.69/9.84 |
% 30.69/9.84 | From (1228) and (381) follows:
% 30.69/9.84 | (1230) succ(n13) = all_0_8_8
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (259) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 30.69/9.84 | (1231) all_0_6_6 = n12
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (184) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 30.69/9.84 | (1232) all_0_8_8 = n14
% 30.69/9.84 |
% 30.69/9.84 | From (1231)(1232) and (628) follows:
% 30.69/9.84 | (1233) sum(n12, n14) = all_0_1_1
% 30.69/9.84 |
% 30.69/9.84 | From (1231) and (5065) follows:
% 30.69/9.84 | (5076) sum(n12, n15) = all_0_4_4
% 30.69/9.84 |
% 30.69/9.84 | From (1232) and (5067) follows:
% 30.69/9.84 | (5077) sum(n13, n14) = all_0_7_7
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (194) with n13, n14, all_0_7_7, n6 and discharging atoms sum(n13, n14) = all_0_7_7, sum(n13, n14) = n6, yields:
% 30.69/9.84 | (975) all_0_7_7 = n6
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (194) with n12, n15, all_0_4_4, n6 and discharging atoms sum(n12, n15) = all_0_4_4, sum(n12, n15) = n6, yields:
% 30.69/9.84 | (973) all_0_4_4 = n6
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (194) with n12, n14, all_0_1_1, n5 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n5, yields:
% 30.69/9.84 | (1237) all_0_1_1 = n5
% 30.69/9.84 |
% 30.69/9.84 | From (975)(973) and (435) follows:
% 30.69/9.84 | (977) sum(n6, n6) = all_0_3_3
% 30.69/9.84 |
% 30.69/9.84 | From (1237) and (5069) follows:
% 30.69/9.84 | (5082) sum(n7, n5) = all_0_0_0
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (194) with n7, n5, all_0_0_0, n12 and discharging atoms sum(n7, n5) = all_0_0_0, sum(n7, n5) = n12, yields:
% 30.69/9.84 | (978) all_0_0_0 = n12
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 30.69/9.84 | (979) all_0_3_3 = n12
% 30.69/9.84 |
% 30.69/9.84 | Equations (978,979) can reduce 201 to:
% 30.69/9.84 | (746) $false
% 30.69/9.84 |
% 30.69/9.84 |-The branch is then unsatisfiable
% 30.69/9.84 |-Branch two:
% 30.69/9.84 | (1244) ~ (all_0_10_10 = n13)
% 30.69/9.84 | (1245) all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.69/9.84 |
% 30.69/9.84 +-Applying beta-rule and splitting (1245), into two cases.
% 30.69/9.84 |-Branch one:
% 30.69/9.84 | (1246) all_0_10_10 = n12
% 30.69/9.84 |
% 30.69/9.84 | From (1246) and (57) follows:
% 30.69/9.84 | (1247) pred(n12) = all_0_6_6
% 30.69/9.84 |
% 30.69/9.84 | From (1246) and (381) follows:
% 30.69/9.84 | (1248) succ(n12) = all_0_8_8
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (259) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 30.69/9.84 | (1249) all_0_6_6 = n11
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (184) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 30.69/9.84 | (1250) all_0_8_8 = n13
% 30.69/9.84 |
% 30.69/9.84 | From (1249)(1250) and (628) follows:
% 30.69/9.84 | (1251) sum(n11, n13) = all_0_1_1
% 30.69/9.84 |
% 30.69/9.84 | From (1249) and (5065) follows:
% 30.69/9.84 | (5094) sum(n11, n15) = all_0_4_4
% 30.69/9.84 |
% 30.69/9.84 | From (1250) and (5067) follows:
% 30.69/9.84 | (5095) sum(n13, n13) = all_0_7_7
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (194) with n13, n13, all_0_7_7, n5 and discharging atoms sum(n13, n13) = all_0_7_7, sum(n13, n13) = n5, yields:
% 30.69/9.84 | (993) all_0_7_7 = n5
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (194) with n11, n15, all_0_4_4, n5 and discharging atoms sum(n11, n15) = all_0_4_4, sum(n11, n15) = n5, yields:
% 30.69/9.84 | (991) all_0_4_4 = n5
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (194) with n11, n13, all_0_1_1, n3 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n3, yields:
% 30.69/9.84 | (1255) all_0_1_1 = n3
% 30.69/9.84 |
% 30.69/9.84 | From (993)(991) and (435) follows:
% 30.69/9.84 | (995) sum(n5, n5) = all_0_3_3
% 30.69/9.84 |
% 30.69/9.84 | From (1255) and (5069) follows:
% 30.69/9.84 | (5100) sum(n7, n3) = all_0_0_0
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (194) with n7, n3, all_0_0_0, n10 and discharging atoms sum(n7, n3) = all_0_0_0, sum(n7, n3) = n10, yields:
% 30.69/9.84 | (996) all_0_0_0 = n10
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 30.69/9.84 | (997) all_0_3_3 = n10
% 30.69/9.84 |
% 30.69/9.84 | Equations (996,997) can reduce 201 to:
% 30.69/9.84 | (746) $false
% 30.69/9.84 |
% 30.69/9.84 |-The branch is then unsatisfiable
% 30.69/9.84 |-Branch two:
% 30.69/9.84 | (1262) ~ (all_0_10_10 = n12)
% 30.69/9.84 | (1263) all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.69/9.84 |
% 30.69/9.84 +-Applying beta-rule and splitting (1263), into two cases.
% 30.69/9.84 |-Branch one:
% 30.69/9.84 | (1264) all_0_10_10 = n11
% 30.69/9.84 |
% 30.69/9.84 | From (1264) and (57) follows:
% 30.69/9.84 | (1265) pred(n11) = all_0_6_6
% 30.69/9.84 |
% 30.69/9.84 | From (1264) and (381) follows:
% 30.69/9.84 | (1266) succ(n11) = all_0_8_8
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (259) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 30.69/9.84 | (1267) all_0_6_6 = n10
% 30.69/9.84 |
% 30.69/9.84 | Instantiating formula (184) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 30.69/9.84 | (1268) all_0_8_8 = n12
% 30.69/9.84 |
% 30.69/9.84 | From (1267)(1268) and (628) follows:
% 30.69/9.84 | (1269) sum(n10, n12) = all_0_1_1
% 30.69/9.84 |
% 30.69/9.84 | From (1267) and (5065) follows:
% 30.69/9.84 | (5112) sum(n10, n15) = all_0_4_4
% 30.69/9.84 |
% 30.69/9.84 | From (1268) and (5067) follows:
% 30.69/9.85 | (5113) sum(n13, n12) = all_0_7_7
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n13, n12, all_0_7_7, n4 and discharging atoms sum(n13, n12) = all_0_7_7, sum(n13, n12) = n4, yields:
% 30.69/9.85 | (1011) all_0_7_7 = n4
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n10, n15, all_0_4_4, n4 and discharging atoms sum(n10, n15) = all_0_4_4, sum(n10, n15) = n4, yields:
% 30.69/9.85 | (1009) all_0_4_4 = n4
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n10, n12, all_0_1_1, n1 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n1, yields:
% 30.69/9.85 | (1273) all_0_1_1 = n1
% 30.69/9.85 |
% 30.69/9.85 | From (1011)(1009) and (435) follows:
% 30.69/9.85 | (1013) sum(n4, n4) = all_0_3_3
% 30.69/9.85 |
% 30.69/9.85 | From (1273) and (5069) follows:
% 30.69/9.85 | (5118) sum(n7, n1) = all_0_0_0
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n7, n1, all_0_0_0, n8 and discharging atoms sum(n7, n1) = all_0_0_0, sum(n7, n1) = n8, yields:
% 30.69/9.85 | (1014) all_0_0_0 = n8
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 30.69/9.85 | (1015) all_0_3_3 = n8
% 30.69/9.85 |
% 30.69/9.85 | Equations (1014,1015) can reduce 201 to:
% 30.69/9.85 | (746) $false
% 30.69/9.85 |
% 30.69/9.85 |-The branch is then unsatisfiable
% 30.69/9.85 |-Branch two:
% 30.69/9.85 | (1280) ~ (all_0_10_10 = n11)
% 30.69/9.85 | (1281) all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.69/9.85 |
% 30.69/9.85 +-Applying beta-rule and splitting (1281), into two cases.
% 30.69/9.85 |-Branch one:
% 30.69/9.85 | (1282) all_0_10_10 = n10
% 30.69/9.85 |
% 30.69/9.85 | From (1282) and (57) follows:
% 30.69/9.85 | (1283) pred(n10) = all_0_6_6
% 30.69/9.85 |
% 30.69/9.85 | From (1282) and (381) follows:
% 30.69/9.85 | (1284) succ(n10) = all_0_8_8
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (259) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 30.69/9.85 | (1285) all_0_6_6 = n9
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (184) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 30.69/9.85 | (1286) all_0_8_8 = n11
% 30.69/9.85 |
% 30.69/9.85 | From (1285)(1286) and (628) follows:
% 30.69/9.85 | (1287) sum(n9, n11) = all_0_1_1
% 30.69/9.85 |
% 30.69/9.85 | From (1285) and (5065) follows:
% 30.69/9.85 | (5130) sum(n9, n15) = all_0_4_4
% 30.69/9.85 |
% 30.69/9.85 | From (1286) and (5067) follows:
% 30.69/9.85 | (5131) sum(n13, n11) = all_0_7_7
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n13, n11, all_0_7_7, n3 and discharging atoms sum(n13, n11) = all_0_7_7, sum(n13, n11) = n3, yields:
% 30.69/9.85 | (1029) all_0_7_7 = n3
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n9, n15, all_0_4_4, n3 and discharging atoms sum(n9, n15) = all_0_4_4, sum(n9, n15) = n3, yields:
% 30.69/9.85 | (1027) all_0_4_4 = n3
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 30.69/9.85 | (1291) all_0_1_1 = n20
% 30.69/9.85 |
% 30.69/9.85 | From (1029)(1027) and (435) follows:
% 30.69/9.85 | (1031) sum(n3, n3) = all_0_3_3
% 30.69/9.85 |
% 30.69/9.85 | From (1291) and (5069) follows:
% 30.69/9.85 | (5136) sum(n7, n20) = all_0_0_0
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n7, n20, all_0_0_0, n6 and discharging atoms sum(n7, n20) = all_0_0_0, sum(n7, n20) = n6, yields:
% 30.69/9.85 | (1032) all_0_0_0 = n6
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 30.69/9.85 | (1033) all_0_3_3 = n6
% 30.69/9.85 |
% 30.69/9.85 | Equations (1032,1033) can reduce 201 to:
% 30.69/9.85 | (746) $false
% 30.69/9.85 |
% 30.69/9.85 |-The branch is then unsatisfiable
% 30.69/9.85 |-Branch two:
% 30.69/9.85 | (1298) ~ (all_0_10_10 = n10)
% 30.69/9.85 | (1299) all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.69/9.85 |
% 30.69/9.85 +-Applying beta-rule and splitting (1299), into two cases.
% 30.69/9.85 |-Branch one:
% 30.69/9.85 | (1300) all_0_10_10 = n9
% 30.69/9.85 |
% 30.69/9.85 | From (1300) and (57) follows:
% 30.69/9.85 | (1301) pred(n9) = all_0_6_6
% 30.69/9.85 |
% 30.69/9.85 | From (1300) and (381) follows:
% 30.69/9.85 | (1302) succ(n9) = all_0_8_8
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (259) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 30.69/9.85 | (1303) all_0_6_6 = n8
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (184) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 30.69/9.85 | (1304) all_0_8_8 = n10
% 30.69/9.85 |
% 30.69/9.85 | From (1303)(1304) and (628) follows:
% 30.69/9.85 | (1305) sum(n8, n10) = all_0_1_1
% 30.69/9.85 |
% 30.69/9.85 | From (1303) and (5065) follows:
% 30.69/9.85 | (5148) sum(n8, n15) = all_0_4_4
% 30.69/9.85 |
% 30.69/9.85 | From (1304) and (5067) follows:
% 30.69/9.85 | (5149) sum(n13, n10) = all_0_7_7
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n13, n10, all_0_7_7, n2 and discharging atoms sum(n13, n10) = all_0_7_7, sum(n13, n10) = n2, yields:
% 30.69/9.85 | (1047) all_0_7_7 = n2
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n8, n15, all_0_4_4, n2 and discharging atoms sum(n8, n15) = all_0_4_4, sum(n8, n15) = n2, yields:
% 30.69/9.85 | (1045) all_0_4_4 = n2
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 30.69/9.85 | (1309) all_0_1_1 = n18
% 30.69/9.85 |
% 30.69/9.85 | From (1047)(1045) and (435) follows:
% 30.69/9.85 | (1049) sum(n2, n2) = all_0_3_3
% 30.69/9.85 |
% 30.69/9.85 | From (1309) and (5069) follows:
% 30.69/9.85 | (5154) sum(n7, n18) = all_0_0_0
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n7, n18, all_0_0_0, n4 and discharging atoms sum(n7, n18) = all_0_0_0, sum(n7, n18) = n4, yields:
% 30.69/9.85 | (1050) all_0_0_0 = n4
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 30.69/9.85 | (1051) all_0_3_3 = n4
% 30.69/9.85 |
% 30.69/9.85 | Equations (1050,1051) can reduce 201 to:
% 30.69/9.85 | (746) $false
% 30.69/9.85 |
% 30.69/9.85 |-The branch is then unsatisfiable
% 30.69/9.85 |-Branch two:
% 30.69/9.85 | (1316) ~ (all_0_10_10 = n9)
% 30.69/9.85 | (1317) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.69/9.85 |
% 30.69/9.85 +-Applying beta-rule and splitting (1317), into two cases.
% 30.69/9.85 |-Branch one:
% 30.69/9.85 | (1318) all_0_10_10 = n8
% 30.69/9.85 |
% 30.69/9.85 | From (1318) and (57) follows:
% 30.69/9.85 | (1319) pred(n8) = all_0_6_6
% 30.69/9.85 |
% 30.69/9.85 | From (1318) and (381) follows:
% 30.69/9.85 | (1320) succ(n8) = all_0_8_8
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (259) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 30.69/9.85 | (1321) all_0_6_6 = n7
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (184) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 30.69/9.85 | (1322) all_0_8_8 = n9
% 30.69/9.85 |
% 30.69/9.85 | From (1321)(1322) and (628) follows:
% 30.69/9.85 | (1323) sum(n7, n9) = all_0_1_1
% 30.69/9.85 |
% 30.69/9.85 | From (1321) and (5065) follows:
% 30.69/9.85 | (5166) sum(n7, n15) = all_0_4_4
% 30.69/9.85 |
% 30.69/9.85 | From (1322) and (5067) follows:
% 30.69/9.85 | (5167) sum(n13, n9) = all_0_7_7
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n13, n9, all_0_7_7, n1 and discharging atoms sum(n13, n9) = all_0_7_7, sum(n13, n9) = n1, yields:
% 30.69/9.85 | (1065) all_0_7_7 = n1
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n7, n15, all_0_4_4, n1 and discharging atoms sum(n7, n15) = all_0_4_4, sum(n7, n15) = n1, yields:
% 30.69/9.85 | (1063) all_0_4_4 = n1
% 30.69/9.85 |
% 30.69/9.85 | Instantiating formula (194) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 30.69/9.85 | (1327) all_0_1_1 = n16
% 30.69/9.85 |
% 30.69/9.85 | From (1065)(1063) and (435) follows:
% 30.69/9.85 | (1067) sum(n1, n1) = all_0_3_3
% 30.69/9.85 |
% 30.69/9.85 | From (1327) and (5069) follows:
% 30.69/9.86 | (5172) sum(n7, n16) = all_0_0_0
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (194) with n7, n16, all_0_0_0, n2 and discharging atoms sum(n7, n16) = all_0_0_0, sum(n7, n16) = n2, yields:
% 30.69/9.86 | (1068) all_0_0_0 = n2
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 30.69/9.86 | (1069) all_0_3_3 = n2
% 30.69/9.86 |
% 30.69/9.86 | Equations (1068,1069) can reduce 201 to:
% 30.69/9.86 | (746) $false
% 30.69/9.86 |
% 30.69/9.86 |-The branch is then unsatisfiable
% 30.69/9.86 |-Branch two:
% 30.69/9.86 | (1334) ~ (all_0_10_10 = n8)
% 30.69/9.86 | (1335) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.69/9.86 |
% 30.69/9.86 +-Applying beta-rule and splitting (1335), into two cases.
% 30.69/9.86 |-Branch one:
% 30.69/9.86 | (1336) all_0_10_10 = n7
% 30.69/9.86 |
% 30.69/9.86 | From (1336) and (57) follows:
% 30.69/9.86 | (1337) pred(n7) = all_0_6_6
% 30.69/9.86 |
% 30.69/9.86 | From (1336) and (381) follows:
% 30.69/9.86 | (1338) succ(n7) = all_0_8_8
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (259) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 30.69/9.86 | (1339) all_0_6_6 = n6
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (184) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 30.69/9.86 | (1340) all_0_8_8 = n8
% 30.69/9.86 |
% 30.69/9.86 | From (1339)(1340) and (628) follows:
% 30.69/9.86 | (1341) sum(n6, n8) = all_0_1_1
% 30.69/9.86 |
% 30.69/9.86 | From (1339) and (5065) follows:
% 30.69/9.86 | (5184) sum(n6, n15) = all_0_4_4
% 30.69/9.86 |
% 30.69/9.86 | From (1340) and (5067) follows:
% 30.69/9.86 | (5185) sum(n13, n8) = all_0_7_7
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (194) with n13, n8, all_0_7_7, n0 and discharging atoms sum(n13, n8) = all_0_7_7, sum(n13, n8) = n0, yields:
% 30.69/9.86 | (1083) all_0_7_7 = n0
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (194) with n6, n15, all_0_4_4, n0 and discharging atoms sum(n6, n15) = all_0_4_4, sum(n6, n15) = n0, yields:
% 30.69/9.86 | (1081) all_0_4_4 = n0
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (194) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 30.69/9.86 | (1345) all_0_1_1 = n14
% 30.69/9.86 |
% 30.69/9.86 | From (1083)(1081) and (435) follows:
% 30.69/9.86 | (1085) sum(n0, n0) = all_0_3_3
% 30.69/9.86 |
% 30.69/9.86 | From (1345) and (5069) follows:
% 30.69/9.86 | (5190) sum(n7, n14) = all_0_0_0
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (194) with n7, n14, all_0_0_0, n0 and discharging atoms sum(n7, n14) = all_0_0_0, sum(n7, n14) = n0, yields:
% 30.69/9.86 | (1087) all_0_0_0 = n0
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 30.69/9.86 | (1088) all_0_3_3 = n0
% 30.69/9.86 |
% 30.69/9.86 | Equations (1087,1088) can reduce 201 to:
% 30.69/9.86 | (746) $false
% 30.69/9.86 |
% 30.69/9.86 |-The branch is then unsatisfiable
% 30.69/9.86 |-Branch two:
% 30.69/9.86 | (1352) ~ (all_0_10_10 = n7)
% 30.69/9.86 | (1353) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.69/9.86 |
% 30.69/9.86 +-Applying beta-rule and splitting (1353), into two cases.
% 30.69/9.86 |-Branch one:
% 30.69/9.86 | (1354) all_0_10_10 = n6
% 30.69/9.86 |
% 30.69/9.86 | From (1354) and (57) follows:
% 30.69/9.86 | (1355) pred(n6) = all_0_6_6
% 30.69/9.86 |
% 30.69/9.86 | From (1354) and (381) follows:
% 30.69/9.86 | (1356) succ(n6) = all_0_8_8
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (259) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 30.69/9.86 | (1357) all_0_6_6 = n5
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (184) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 30.69/9.86 | (1358) all_0_8_8 = n7
% 30.69/9.86 |
% 30.69/9.86 | From (1357)(1358) and (628) follows:
% 30.69/9.86 | (1359) sum(n5, n7) = all_0_1_1
% 30.69/9.86 |
% 30.69/9.86 | From (1357) and (5065) follows:
% 30.69/9.86 | (5202) sum(n5, n15) = all_0_4_4
% 30.69/9.86 |
% 30.69/9.86 | From (1358) and (5067) follows:
% 30.69/9.86 | (5203) sum(n13, n7) = all_0_7_7
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (194) with n13, n7, all_0_7_7, n20 and discharging atoms sum(n13, n7) = all_0_7_7, sum(n13, n7) = n20, yields:
% 30.69/9.86 | (1100) all_0_7_7 = n20
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (194) with n5, n15, all_0_4_4, n20 and discharging atoms sum(n5, n15) = all_0_4_4, sum(n5, n15) = n20, yields:
% 30.69/9.86 | (1101) all_0_4_4 = n20
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (194) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 30.69/9.86 | (1363) all_0_1_1 = n12
% 30.69/9.86 |
% 30.69/9.86 | From (1100)(1101) and (435) follows:
% 30.69/9.86 | (1103) sum(n20, n20) = all_0_3_3
% 30.69/9.86 |
% 30.69/9.86 | From (1363) and (5069) follows:
% 30.69/9.86 | (5208) sum(n7, n12) = all_0_0_0
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 30.69/9.86 | (1104) all_0_3_3 = n19
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (194) with n7, n12, all_0_0_0, n19 and discharging atoms sum(n7, n12) = all_0_0_0, sum(n7, n12) = n19, yields:
% 30.69/9.86 | (1105) all_0_0_0 = n19
% 30.69/9.86 |
% 30.69/9.86 | Equations (1105,1104) can reduce 201 to:
% 30.69/9.86 | (746) $false
% 30.69/9.86 |
% 30.69/9.86 |-The branch is then unsatisfiable
% 30.69/9.86 |-Branch two:
% 30.69/9.86 | (1370) ~ (all_0_10_10 = n6)
% 30.69/9.86 | (1371) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.69/9.86 |
% 30.69/9.86 +-Applying beta-rule and splitting (1371), into two cases.
% 30.69/9.86 |-Branch one:
% 30.69/9.86 | (1372) all_0_10_10 = n5
% 30.69/9.86 |
% 30.69/9.86 | From (1372) and (57) follows:
% 30.69/9.86 | (1373) pred(n5) = all_0_6_6
% 30.69/9.86 |
% 30.69/9.86 | From (1372) and (381) follows:
% 30.69/9.86 | (1374) succ(n5) = all_0_8_8
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (259) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 30.69/9.86 | (1375) all_0_6_6 = n4
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (184) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 30.69/9.86 | (1376) all_0_8_8 = n6
% 30.69/9.86 |
% 30.69/9.86 | From (1375)(1376) and (628) follows:
% 30.69/9.86 | (1377) sum(n4, n6) = all_0_1_1
% 30.69/9.86 |
% 30.69/9.86 | From (1375) and (5065) follows:
% 30.69/9.86 | (5220) sum(n4, n15) = all_0_4_4
% 30.69/9.86 |
% 30.69/9.86 | From (1376) and (5067) follows:
% 30.69/9.86 | (5221) sum(n13, n6) = all_0_7_7
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (194) with n13, n6, all_0_7_7, n19 and discharging atoms sum(n13, n6) = all_0_7_7, sum(n13, n6) = n19, yields:
% 30.69/9.86 | (737) all_0_7_7 = n19
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (194) with n4, n15, all_0_4_4, n19 and discharging atoms sum(n4, n15) = all_0_4_4, sum(n4, n15) = n19, yields:
% 30.69/9.86 | (736) all_0_4_4 = n19
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (194) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 30.69/9.86 | (1381) all_0_1_1 = n10
% 30.69/9.86 |
% 30.69/9.86 | From (737)(736) and (435) follows:
% 30.69/9.86 | (741) sum(n19, n19) = all_0_3_3
% 30.69/9.86 |
% 30.69/9.86 | From (1381) and (5069) follows:
% 30.69/9.86 | (5226) sum(n7, n10) = all_0_0_0
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 30.69/9.86 | (744) all_0_3_3 = n17
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (194) with n7, n10, all_0_0_0, n17 and discharging atoms sum(n7, n10) = all_0_0_0, sum(n7, n10) = n17, yields:
% 30.69/9.86 | (742) all_0_0_0 = n17
% 30.69/9.86 |
% 30.69/9.86 | Equations (742,744) can reduce 201 to:
% 30.69/9.86 | (746) $false
% 30.69/9.86 |
% 30.69/9.86 |-The branch is then unsatisfiable
% 30.69/9.86 |-Branch two:
% 30.69/9.86 | (1388) ~ (all_0_10_10 = n5)
% 30.69/9.86 | (1389) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.69/9.86 |
% 30.69/9.86 +-Applying beta-rule and splitting (1389), into two cases.
% 30.69/9.86 |-Branch one:
% 30.69/9.86 | (1390) all_0_10_10 = n4
% 30.69/9.86 |
% 30.69/9.86 | From (1390) and (57) follows:
% 30.69/9.86 | (1391) pred(n4) = all_0_6_6
% 30.69/9.86 |
% 30.69/9.86 | From (1390) and (381) follows:
% 30.69/9.86 | (1392) succ(n4) = all_0_8_8
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (259) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 30.69/9.86 | (1393) all_0_6_6 = n3
% 30.69/9.86 |
% 30.69/9.86 | Instantiating formula (184) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 30.69/9.86 | (1394) all_0_8_8 = n5
% 30.69/9.86 |
% 30.69/9.86 | From (1393)(1394) and (628) follows:
% 30.69/9.87 | (1395) sum(n3, n5) = all_0_1_1
% 30.69/9.87 |
% 30.69/9.87 | From (1393) and (5065) follows:
% 30.69/9.87 | (5238) sum(n3, n15) = all_0_4_4
% 30.69/9.87 |
% 30.69/9.87 | From (1394) and (5067) follows:
% 30.69/9.87 | (5239) sum(n13, n5) = all_0_7_7
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (194) with n13, n5, all_0_7_7, n18 and discharging atoms sum(n13, n5) = all_0_7_7, sum(n13, n5) = n18, yields:
% 30.69/9.87 | (759) all_0_7_7 = n18
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (194) with n3, n15, all_0_4_4, n18 and discharging atoms sum(n3, n15) = all_0_4_4, sum(n3, n15) = n18, yields:
% 30.69/9.87 | (757) all_0_4_4 = n18
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (194) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 30.69/9.87 | (1399) all_0_1_1 = n8
% 30.69/9.87 |
% 30.69/9.87 | From (759)(757) and (435) follows:
% 30.69/9.87 | (761) sum(n18, n18) = all_0_3_3
% 30.69/9.87 |
% 30.69/9.87 | From (1399) and (5069) follows:
% 30.69/9.87 | (5244) sum(n7, n8) = all_0_0_0
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 30.69/9.87 | (762) all_0_3_3 = n15
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (194) with n7, n8, all_0_0_0, n15 and discharging atoms sum(n7, n8) = all_0_0_0, sum(n7, n8) = n15, yields:
% 30.69/9.87 | (763) all_0_0_0 = n15
% 30.69/9.87 |
% 30.69/9.87 | Equations (763,762) can reduce 201 to:
% 30.69/9.87 | (746) $false
% 30.69/9.87 |
% 30.69/9.87 |-The branch is then unsatisfiable
% 30.69/9.87 |-Branch two:
% 30.69/9.87 | (1406) ~ (all_0_10_10 = n4)
% 30.69/9.87 | (1407) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.69/9.87 |
% 30.69/9.87 +-Applying beta-rule and splitting (1407), into two cases.
% 30.69/9.87 |-Branch one:
% 30.69/9.87 | (1408) all_0_10_10 = n3
% 30.69/9.87 |
% 30.69/9.87 | From (1408) and (57) follows:
% 30.69/9.87 | (1409) pred(n3) = all_0_6_6
% 30.69/9.87 |
% 30.69/9.87 | From (1408) and (381) follows:
% 30.69/9.87 | (1410) succ(n3) = all_0_8_8
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 30.69/9.87 | (1411) all_0_6_6 = n2
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 30.69/9.87 | (1412) all_0_8_8 = n4
% 30.69/9.87 |
% 30.69/9.87 | From (1411)(1412) and (628) follows:
% 30.69/9.87 | (1413) sum(n2, n4) = all_0_1_1
% 30.69/9.87 |
% 30.69/9.87 | From (1411) and (5065) follows:
% 30.69/9.87 | (5256) sum(n2, n15) = all_0_4_4
% 30.69/9.87 |
% 30.69/9.87 | From (1412) and (5067) follows:
% 30.69/9.87 | (5257) sum(n13, n4) = all_0_7_7
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (194) with n13, n4, all_0_7_7, n17 and discharging atoms sum(n13, n4) = all_0_7_7, sum(n13, n4) = n17, yields:
% 30.69/9.87 | (777) all_0_7_7 = n17
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (194) with n2, n15, all_0_4_4, n17 and discharging atoms sum(n2, n15) = all_0_4_4, sum(n2, n15) = n17, yields:
% 30.69/9.87 | (775) all_0_4_4 = n17
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 30.69/9.87 | (1417) all_0_1_1 = n6
% 30.69/9.87 |
% 30.69/9.87 | From (777)(775) and (435) follows:
% 30.69/9.87 | (779) sum(n17, n17) = all_0_3_3
% 30.69/9.87 |
% 30.69/9.87 | From (1417) and (5069) follows:
% 30.69/9.87 | (5262) sum(n7, n6) = all_0_0_0
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 30.69/9.87 | (780) all_0_3_3 = n13
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (194) with n7, n6, all_0_0_0, n13 and discharging atoms sum(n7, n6) = all_0_0_0, sum(n7, n6) = n13, yields:
% 30.69/9.87 | (781) all_0_0_0 = n13
% 30.69/9.87 |
% 30.69/9.87 | Equations (781,780) can reduce 201 to:
% 30.69/9.87 | (746) $false
% 30.69/9.87 |
% 30.69/9.87 |-The branch is then unsatisfiable
% 30.69/9.87 |-Branch two:
% 30.69/9.87 | (1424) ~ (all_0_10_10 = n3)
% 30.69/9.87 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.69/9.87 |
% 30.69/9.87 +-Applying beta-rule and splitting (1425), into two cases.
% 30.69/9.87 |-Branch one:
% 30.69/9.87 | (1426) all_0_10_10 = n2
% 30.69/9.87 |
% 30.69/9.87 | From (1426) and (57) follows:
% 30.69/9.87 | (1427) pred(n2) = all_0_6_6
% 30.69/9.87 |
% 30.69/9.87 | From (1426) and (381) follows:
% 30.69/9.87 | (1428) succ(n2) = all_0_8_8
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 30.69/9.87 | (1429) all_0_6_6 = n1
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 30.69/9.87 | (1430) all_0_8_8 = n3
% 30.69/9.87 |
% 30.69/9.87 | From (1429)(1430) and (628) follows:
% 30.69/9.87 | (1431) sum(n1, n3) = all_0_1_1
% 30.69/9.87 |
% 30.69/9.87 | From (1429) and (5065) follows:
% 30.69/9.87 | (5274) sum(n1, n15) = all_0_4_4
% 30.69/9.87 |
% 30.69/9.87 | From (1430) and (5067) follows:
% 30.69/9.87 | (5275) sum(n13, n3) = all_0_7_7
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (194) with n13, n3, all_0_7_7, n16 and discharging atoms sum(n13, n3) = all_0_7_7, sum(n13, n3) = n16, yields:
% 30.69/9.87 | (795) all_0_7_7 = n16
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (194) with n1, n15, all_0_4_4, n16 and discharging atoms sum(n1, n15) = all_0_4_4, sum(n1, n15) = n16, yields:
% 30.69/9.87 | (793) all_0_4_4 = n16
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 30.69/9.87 | (1435) all_0_1_1 = n4
% 30.69/9.87 |
% 30.69/9.87 | From (795)(793) and (435) follows:
% 30.69/9.87 | (797) sum(n16, n16) = all_0_3_3
% 30.69/9.87 |
% 30.69/9.87 | From (1435) and (5069) follows:
% 30.69/9.87 | (5280) sum(n7, n4) = all_0_0_0
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 30.69/9.87 | (798) all_0_3_3 = n11
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (194) with n7, n4, all_0_0_0, n11 and discharging atoms sum(n7, n4) = all_0_0_0, sum(n7, n4) = n11, yields:
% 30.69/9.87 | (799) all_0_0_0 = n11
% 30.69/9.87 |
% 30.69/9.87 | Equations (799,798) can reduce 201 to:
% 30.69/9.87 | (746) $false
% 30.69/9.87 |
% 30.69/9.87 |-The branch is then unsatisfiable
% 30.69/9.87 |-Branch two:
% 30.69/9.87 | (1442) ~ (all_0_10_10 = n2)
% 30.69/9.87 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 30.69/9.87 |
% 30.69/9.87 +-Applying beta-rule and splitting (1443), into two cases.
% 30.69/9.87 |-Branch one:
% 30.69/9.87 | (1444) all_0_10_10 = n1
% 30.69/9.87 |
% 30.69/9.87 | From (1444) and (57) follows:
% 30.69/9.87 | (1445) pred(n1) = all_0_6_6
% 30.69/9.87 |
% 30.69/9.87 | From (1444) and (381) follows:
% 30.69/9.87 | (1446) succ(n1) = all_0_8_8
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 30.69/9.87 | (1447) all_0_6_6 = n0
% 30.69/9.87 |
% 30.69/9.87 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 30.69/9.87 | (1448) all_0_8_8 = n2
% 30.69/9.87 |
% 30.69/9.87 | From (1447)(1448) and (628) follows:
% 30.69/9.87 | (1449) sum(n0, n2) = all_0_1_1
% 30.69/9.87 |
% 30.69/9.87 | From (1447) and (5065) follows:
% 30.69/9.87 | (5292) sum(n0, n15) = all_0_4_4
% 30.69/9.87 |
% 30.69/9.87 | From (1448) and (5067) follows:
% 30.69/9.88 | (5293) sum(n13, n2) = all_0_7_7
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (194) with n13, n2, all_0_7_7, n15 and discharging atoms sum(n13, n2) = all_0_7_7, sum(n13, n2) = n15, yields:
% 30.69/9.88 | (813) all_0_7_7 = n15
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (194) with n0, n15, all_0_4_4, n15 and discharging atoms sum(n0, n15) = all_0_4_4, sum(n0, n15) = n15, yields:
% 30.69/9.88 | (811) all_0_4_4 = n15
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 30.69/9.88 | (1453) all_0_1_1 = n2
% 30.69/9.88 |
% 30.69/9.88 | From (813)(811) and (435) follows:
% 30.69/9.88 | (815) sum(n15, n15) = all_0_3_3
% 30.69/9.88 |
% 30.69/9.88 | From (1453) and (5069) follows:
% 30.69/9.88 | (5298) sum(n7, n2) = all_0_0_0
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 30.69/9.88 | (816) all_0_3_3 = n9
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (194) with n7, n2, all_0_0_0, n9 and discharging atoms sum(n7, n2) = all_0_0_0, sum(n7, n2) = n9, yields:
% 30.69/9.88 | (817) all_0_0_0 = n9
% 30.69/9.88 |
% 30.69/9.88 | Equations (817,816) can reduce 201 to:
% 30.69/9.88 | (746) $false
% 30.69/9.88 |
% 30.69/9.88 |-The branch is then unsatisfiable
% 30.69/9.88 |-Branch two:
% 30.69/9.88 | (1462) ~ (all_0_10_10 = n1)
% 30.69/9.88 | (1463) all_0_10_10 = n0
% 30.69/9.88 |
% 30.69/9.88 | From (1463) and (57) follows:
% 30.69/9.88 | (1464) pred(n0) = all_0_6_6
% 30.69/9.88 |
% 30.69/9.88 | From (1463) and (381) follows:
% 30.69/9.88 | (1465) succ(n0) = all_0_8_8
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 30.69/9.88 | (1466) all_0_6_6 = n20
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 30.69/9.88 | (1467) all_0_8_8 = n1
% 30.69/9.88 |
% 30.69/9.88 | From (1466)(1467) and (628) follows:
% 30.69/9.88 | (1468) sum(n20, n1) = all_0_1_1
% 30.69/9.88 |
% 30.69/9.88 | From (1466) and (5065) follows:
% 30.69/9.88 | (5309) sum(n20, n15) = all_0_4_4
% 30.69/9.88 |
% 30.69/9.88 | From (1467) and (5067) follows:
% 30.69/9.88 | (5310) sum(n13, n1) = all_0_7_7
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (194) with n20, n15, all_0_4_4, n14 and discharging atoms sum(n20, n15) = all_0_4_4, sum(n20, n15) = n14, yields:
% 30.69/9.88 | (829) all_0_4_4 = n14
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 30.69/9.88 | (1471) all_0_1_1 = n0
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (194) with n13, n1, all_0_7_7, n14 and discharging atoms sum(n13, n1) = all_0_7_7, sum(n13, n1) = n14, yields:
% 30.69/9.88 | (831) all_0_7_7 = n14
% 30.69/9.88 |
% 30.69/9.88 | From (831)(829) and (435) follows:
% 30.69/9.88 | (833) sum(n14, n14) = all_0_3_3
% 30.69/9.88 |
% 30.69/9.88 | From (1471) and (5069) follows:
% 30.69/9.88 | (5315) sum(n7, n0) = all_0_0_0
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 30.69/9.88 | (834) all_0_3_3 = n7
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (194) with n7, n0, all_0_0_0, n7 and discharging atoms sum(n7, n0) = all_0_0_0, sum(n7, n0) = n7, yields:
% 30.69/9.88 | (835) all_0_0_0 = n7
% 30.69/9.88 |
% 30.69/9.88 | Equations (835,834) can reduce 201 to:
% 30.69/9.88 | (746) $false
% 30.69/9.88 |
% 30.69/9.88 |-The branch is then unsatisfiable
% 30.69/9.88 |-Branch two:
% 30.69/9.88 | (855) ~ (all_0_11_11 = n14)
% 30.69/9.88 | (856) all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.69/9.88 |
% 30.69/9.88 +-Applying beta-rule and splitting (1227), into two cases.
% 30.69/9.88 |-Branch one:
% 30.69/9.88 | (1228) all_0_10_10 = n13
% 30.69/9.88 |
% 30.69/9.88 | From (1228) and (57) follows:
% 30.69/9.88 | (1229) pred(n13) = all_0_6_6
% 30.69/9.88 |
% 30.69/9.88 | From (1228) and (381) follows:
% 30.69/9.88 | (1230) succ(n13) = all_0_8_8
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (259) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 30.69/9.88 | (1231) all_0_6_6 = n12
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (184) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 30.69/9.88 | (1232) all_0_8_8 = n14
% 30.69/9.88 |
% 30.69/9.88 | From (1231) and (1229) follows:
% 30.69/9.88 | (116) pred(n13) = n12
% 30.69/9.88 |
% 30.69/9.88 | From (1232) and (1230) follows:
% 30.69/9.88 | (412) succ(n13) = n14
% 30.69/9.88 |
% 30.69/9.88 | From (1231) and (386) follows:
% 30.69/9.88 | (5328) sum(n12, all_0_5_5) = all_0_4_4
% 30.69/9.88 |
% 30.69/9.88 | From (1231)(1232) and (628) follows:
% 30.69/9.88 | (1233) sum(n12, n14) = all_0_1_1
% 30.69/9.88 |
% 30.69/9.88 | From (1232) and (74) follows:
% 30.69/9.88 | (5330) sum(all_0_9_9, n14) = all_0_7_7
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (194) with n12, n14, all_0_1_1, n5 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n5, yields:
% 30.69/9.88 | (1237) all_0_1_1 = n5
% 30.69/9.88 |
% 30.69/9.88 | From (1237) and (85) follows:
% 30.69/9.88 | (5332) sum(all_0_2_2, n5) = all_0_0_0
% 30.69/9.88 |
% 30.69/9.88 | From (1237) and (1233) follows:
% 30.69/9.88 | (388) sum(n12, n14) = n5
% 30.69/9.88 |
% 30.69/9.88 +-Applying beta-rule and splitting (856), into two cases.
% 30.69/9.88 |-Branch one:
% 30.69/9.88 | (857) all_0_11_11 = n13
% 30.69/9.88 |
% 30.69/9.88 | From (857) and (190) follows:
% 30.69/9.88 | (858) pred(n13) = all_0_9_9
% 30.69/9.88 |
% 30.69/9.88 | From (857) and (505) follows:
% 30.69/9.88 | (859) succ(n13) = all_0_5_5
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (259) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 30.69/9.88 | (860) all_0_9_9 = n12
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (184) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 30.69/9.88 | (861) all_0_5_5 = n14
% 30.69/9.88 |
% 30.69/9.88 | From (860)(861) and (156) follows:
% 30.69/9.88 | (862) sum(n12, n14) = all_0_2_2
% 30.69/9.88 |
% 30.69/9.88 | From (860) and (5330) follows:
% 30.69/9.88 | (5340) sum(n12, n14) = all_0_7_7
% 30.69/9.88 |
% 30.69/9.88 | From (861) and (5328) follows:
% 30.69/9.88 | (5341) sum(n12, n14) = all_0_4_4
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (194) with n12, n14, all_0_2_2, n5 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n5, yields:
% 30.69/9.88 | (866) all_0_2_2 = n5
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (194) with n12, n14, all_0_4_4, all_0_2_2 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = all_0_4_4, yields:
% 30.69/9.88 | (733) all_0_2_2 = all_0_4_4
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (194) with n12, n14, all_0_7_7, all_0_2_2 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = all_0_7_7, yields:
% 30.69/9.88 | (734) all_0_2_2 = all_0_7_7
% 30.69/9.88 |
% 30.69/9.88 | Combining equations (734,733) yields a new equation:
% 30.69/9.88 | (735) all_0_4_4 = all_0_7_7
% 30.69/9.88 |
% 30.69/9.88 | Combining equations (866,733) yields a new equation:
% 30.69/9.88 | (991) all_0_4_4 = n5
% 30.69/9.88 |
% 30.69/9.88 | Combining equations (991,735) yields a new equation:
% 30.69/9.88 | (993) all_0_7_7 = n5
% 30.69/9.88 |
% 30.69/9.88 | Combining equations (993,735) yields a new equation:
% 30.69/9.88 | (991) all_0_4_4 = n5
% 30.69/9.88 |
% 30.69/9.88 | Combining equations (991,733) yields a new equation:
% 30.69/9.88 | (866) all_0_2_2 = n5
% 30.69/9.88 |
% 30.69/9.88 | From (866) and (5332) follows:
% 30.69/9.88 | (5350) sum(n5, n5) = all_0_0_0
% 30.69/9.88 |
% 30.69/9.88 | From (993)(991) and (435) follows:
% 30.69/9.88 | (995) sum(n5, n5) = all_0_3_3
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (194) with n5, n5, all_0_0_0, n10 and discharging atoms sum(n5, n5) = all_0_0_0, sum(n5, n5) = n10, yields:
% 30.69/9.88 | (996) all_0_0_0 = n10
% 30.69/9.88 |
% 30.69/9.88 | Instantiating formula (194) with n5, n5, all_0_3_3, all_0_0_0 and discharging atoms sum(n5, n5) = all_0_0_0, sum(n5, n5) = all_0_3_3, yields:
% 30.69/9.88 | (743) all_0_0_0 = all_0_3_3
% 30.69/9.88 |
% 30.69/9.88 | Combining equations (996,743) yields a new equation:
% 30.69/9.88 | (997) all_0_3_3 = n10
% 30.69/9.88 |
% 30.69/9.88 | Combining equations (997,743) yields a new equation:
% 30.69/9.88 | (996) all_0_0_0 = n10
% 30.69/9.88 |
% 30.69/9.88 | Equations (996,997) can reduce 201 to:
% 30.69/9.88 | (746) $false
% 30.69/9.88 |
% 30.69/9.88 |-The branch is then unsatisfiable
% 30.69/9.88 |-Branch two:
% 30.69/9.88 | (873) ~ (all_0_11_11 = n13)
% 30.69/9.88 | (874) all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.69/9.88 |
% 30.69/9.88 +-Applying beta-rule and splitting (874), into two cases.
% 30.69/9.88 |-Branch one:
% 30.69/9.88 | (875) all_0_11_11 = n12
% 30.69/9.88 |
% 30.69/9.88 | From (875) and (190) follows:
% 30.69/9.88 | (876) pred(n12) = all_0_9_9
% 30.69/9.88 |
% 30.69/9.88 | From (875) and (505) follows:
% 30.69/9.89 | (877) succ(n12) = all_0_5_5
% 30.69/9.89 |
% 30.69/9.89 | Instantiating formula (259) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 30.69/9.89 | (878) all_0_9_9 = n11
% 30.69/9.89 |
% 30.69/9.89 | Instantiating formula (184) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 30.69/9.89 | (879) all_0_5_5 = n13
% 30.69/9.89 |
% 30.69/9.89 | From (878)(879) and (156) follows:
% 30.69/9.89 | (880) sum(n11, n13) = all_0_2_2
% 30.69/9.89 |
% 30.69/9.89 | From (878) and (5330) follows:
% 30.69/9.89 | (5365) sum(n11, n14) = all_0_7_7
% 30.69/9.89 |
% 30.69/9.89 | From (879) and (5328) follows:
% 30.69/9.89 | (5366) sum(n12, n13) = all_0_4_4
% 30.69/9.89 |
% 30.69/9.89 | Instantiating formula (194) with n12, n13, all_0_4_4, n4 and discharging atoms sum(n12, n13) = all_0_4_4, sum(n12, n13) = n4, yields:
% 30.69/9.89 | (1009) all_0_4_4 = n4
% 30.69/9.89 |
% 30.69/9.89 | Instantiating formula (194) with n11, n14, all_0_7_7, n4 and discharging atoms sum(n11, n14) = all_0_7_7, sum(n11, n14) = n4, yields:
% 30.69/9.89 | (1011) all_0_7_7 = n4
% 30.69/9.89 |
% 30.69/9.89 | Instantiating formula (194) with n11, n13, all_0_2_2, n3 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n3, yields:
% 30.69/9.89 | (884) all_0_2_2 = n3
% 30.69/9.89 |
% 30.69/9.89 | From (884) and (5332) follows:
% 30.69/9.89 | (5370) sum(n3, n5) = all_0_0_0
% 30.69/9.89 |
% 30.69/9.89 | From (1011)(1009) and (435) follows:
% 30.69/9.89 | (1013) sum(n4, n4) = all_0_3_3
% 30.69/9.89 |
% 30.69/9.89 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 30.69/9.89 | (1015) all_0_3_3 = n8
% 30.69/9.89 |
% 30.69/9.89 | Instantiating formula (194) with n3, n5, all_0_0_0, n8 and discharging atoms sum(n3, n5) = all_0_0_0, sum(n3, n5) = n8, yields:
% 30.69/9.89 | (1014) all_0_0_0 = n8
% 30.69/9.89 |
% 30.69/9.89 | Equations (1014,1015) can reduce 201 to:
% 30.69/9.89 | (746) $false
% 30.69/9.89 |
% 30.69/9.89 |-The branch is then unsatisfiable
% 30.69/9.89 |-Branch two:
% 30.69/9.89 | (891) ~ (all_0_11_11 = n12)
% 30.69/9.89 | (892) all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.69/9.89 |
% 30.69/9.89 +-Applying beta-rule and splitting (892), into two cases.
% 30.69/9.89 |-Branch one:
% 30.69/9.89 | (893) all_0_11_11 = n11
% 30.69/9.89 |
% 30.69/9.89 | From (893) and (190) follows:
% 30.69/9.89 | (894) pred(n11) = all_0_9_9
% 30.69/9.89 |
% 30.69/9.89 | From (893) and (505) follows:
% 30.69/9.89 | (895) succ(n11) = all_0_5_5
% 30.69/9.89 |
% 30.69/9.89 | Instantiating formula (259) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 30.69/9.89 | (896) all_0_9_9 = n10
% 30.69/9.89 |
% 30.69/9.89 | Instantiating formula (184) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 30.69/9.89 | (897) all_0_5_5 = n12
% 30.69/9.89 |
% 30.69/9.89 | From (896)(897) and (156) follows:
% 30.69/9.89 | (898) sum(n10, n12) = all_0_2_2
% 30.69/9.89 |
% 30.69/9.89 | From (896) and (5330) follows:
% 30.69/9.89 | (5383) sum(n10, n14) = all_0_7_7
% 30.69/9.89 |
% 30.69/9.89 | From (897) and (5328) follows:
% 30.69/9.89 | (5384) sum(n12, n12) = all_0_4_4
% 30.69/9.89 |
% 30.69/9.89 | Instantiating formula (194) with n12, n12, all_0_4_4, n3 and discharging atoms sum(n12, n12) = all_0_4_4, sum(n12, n12) = n3, yields:
% 30.69/9.89 | (1027) all_0_4_4 = n3
% 30.69/9.89 |
% 30.69/9.89 | Instantiating formula (194) with n10, n14, all_0_7_7, n3 and discharging atoms sum(n10, n14) = all_0_7_7, sum(n10, n14) = n3, yields:
% 30.69/9.89 | (1029) all_0_7_7 = n3
% 30.69/9.89 |
% 30.69/9.89 | Instantiating formula (194) with n10, n12, all_0_2_2, n1 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n1, yields:
% 30.69/9.89 | (902) all_0_2_2 = n1
% 30.69/9.89 |
% 30.69/9.89 | From (902) and (5332) follows:
% 30.69/9.89 | (5388) sum(n1, n5) = all_0_0_0
% 30.69/9.89 |
% 30.69/9.89 | From (1029)(1027) and (435) follows:
% 30.69/9.89 | (1031) sum(n3, n3) = all_0_3_3
% 30.69/9.89 |
% 30.69/9.89 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 30.69/9.89 | (1033) all_0_3_3 = n6
% 30.97/9.89 |
% 30.97/9.89 | Instantiating formula (194) with n1, n5, all_0_0_0, n6 and discharging atoms sum(n1, n5) = all_0_0_0, sum(n1, n5) = n6, yields:
% 30.97/9.89 | (1032) all_0_0_0 = n6
% 30.97/9.89 |
% 30.97/9.89 | Equations (1032,1033) can reduce 201 to:
% 30.97/9.89 | (746) $false
% 30.97/9.89 |
% 30.97/9.89 |-The branch is then unsatisfiable
% 30.97/9.89 |-Branch two:
% 30.97/9.89 | (909) ~ (all_0_11_11 = n11)
% 30.97/9.89 | (910) all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.97/9.89 |
% 30.97/9.89 +-Applying beta-rule and splitting (910), into two cases.
% 30.97/9.89 |-Branch one:
% 30.97/9.89 | (911) all_0_11_11 = n10
% 30.97/9.89 |
% 30.97/9.89 | From (911) and (190) follows:
% 30.97/9.89 | (912) pred(n10) = all_0_9_9
% 30.97/9.89 |
% 30.97/9.89 | From (911) and (505) follows:
% 30.97/9.89 | (913) succ(n10) = all_0_5_5
% 30.97/9.89 |
% 30.97/9.89 | Instantiating formula (259) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 30.97/9.89 | (914) all_0_9_9 = n9
% 30.97/9.89 |
% 30.97/9.89 | Instantiating formula (184) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 30.97/9.89 | (915) all_0_5_5 = n11
% 30.97/9.89 |
% 30.97/9.89 | From (914)(915) and (156) follows:
% 30.97/9.89 | (916) sum(n9, n11) = all_0_2_2
% 30.97/9.89 |
% 30.97/9.89 | From (914) and (5330) follows:
% 30.97/9.89 | (5401) sum(n9, n14) = all_0_7_7
% 30.97/9.89 |
% 30.97/9.89 | From (915) and (5328) follows:
% 30.97/9.89 | (5402) sum(n12, n11) = all_0_4_4
% 30.97/9.89 |
% 30.97/9.89 | Instantiating formula (194) with n12, n11, all_0_4_4, n2 and discharging atoms sum(n12, n11) = all_0_4_4, sum(n12, n11) = n2, yields:
% 30.97/9.89 | (1045) all_0_4_4 = n2
% 30.97/9.89 |
% 30.97/9.89 | Instantiating formula (194) with n9, n14, all_0_7_7, n2 and discharging atoms sum(n9, n14) = all_0_7_7, sum(n9, n14) = n2, yields:
% 30.97/9.89 | (1047) all_0_7_7 = n2
% 30.97/9.89 |
% 30.97/9.89 | Instantiating formula (194) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 30.97/9.89 | (920) all_0_2_2 = n20
% 30.97/9.89 |
% 30.97/9.89 | From (920) and (5332) follows:
% 30.97/9.89 | (5406) sum(n20, n5) = all_0_0_0
% 30.97/9.89 |
% 30.97/9.89 | From (1047)(1045) and (435) follows:
% 30.97/9.89 | (1049) sum(n2, n2) = all_0_3_3
% 30.97/9.89 |
% 30.97/9.89 | Instantiating formula (194) with n20, n5, all_0_0_0, n4 and discharging atoms sum(n20, n5) = all_0_0_0, sum(n20, n5) = n4, yields:
% 30.97/9.89 | (1050) all_0_0_0 = n4
% 30.97/9.89 |
% 30.97/9.89 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 30.97/9.89 | (1051) all_0_3_3 = n4
% 30.97/9.89 |
% 30.97/9.89 | Equations (1050,1051) can reduce 201 to:
% 30.97/9.89 | (746) $false
% 30.97/9.89 |
% 30.97/9.89 |-The branch is then unsatisfiable
% 30.97/9.89 |-Branch two:
% 30.97/9.89 | (927) ~ (all_0_11_11 = n10)
% 30.97/9.89 | (928) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.97/9.89 |
% 30.97/9.89 +-Applying beta-rule and splitting (928), into two cases.
% 30.97/9.89 |-Branch one:
% 30.97/9.89 | (929) all_0_11_11 = n9
% 30.97/9.89 |
% 30.97/9.89 | From (929) and (190) follows:
% 30.97/9.89 | (930) pred(n9) = all_0_9_9
% 30.97/9.89 |
% 30.97/9.89 | From (929) and (505) follows:
% 30.97/9.89 | (931) succ(n9) = all_0_5_5
% 30.97/9.89 |
% 30.97/9.89 | Instantiating formula (259) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 30.97/9.89 | (932) all_0_9_9 = n8
% 30.97/9.89 |
% 30.97/9.89 | Instantiating formula (184) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 30.97/9.89 | (933) all_0_5_5 = n10
% 30.97/9.89 |
% 30.97/9.89 | From (932)(933) and (156) follows:
% 30.97/9.89 | (934) sum(n8, n10) = all_0_2_2
% 30.97/9.89 |
% 30.97/9.89 | From (932) and (5330) follows:
% 30.97/9.89 | (5419) sum(n8, n14) = all_0_7_7
% 30.97/9.89 |
% 30.97/9.89 | From (933) and (5328) follows:
% 30.97/9.90 | (5420) sum(n12, n10) = all_0_4_4
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n12, n10, all_0_4_4, n1 and discharging atoms sum(n12, n10) = all_0_4_4, sum(n12, n10) = n1, yields:
% 30.97/9.90 | (1063) all_0_4_4 = n1
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n8, n14, all_0_7_7, n1 and discharging atoms sum(n8, n14) = all_0_7_7, sum(n8, n14) = n1, yields:
% 30.97/9.90 | (1065) all_0_7_7 = n1
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 30.97/9.90 | (938) all_0_2_2 = n18
% 30.97/9.90 |
% 30.97/9.90 | From (938) and (5332) follows:
% 30.97/9.90 | (5424) sum(n18, n5) = all_0_0_0
% 30.97/9.90 |
% 30.97/9.90 | From (1065)(1063) and (435) follows:
% 30.97/9.90 | (1067) sum(n1, n1) = all_0_3_3
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n18, n5, all_0_0_0, n2 and discharging atoms sum(n18, n5) = all_0_0_0, sum(n18, n5) = n2, yields:
% 30.97/9.90 | (1068) all_0_0_0 = n2
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 30.97/9.90 | (1069) all_0_3_3 = n2
% 30.97/9.90 |
% 30.97/9.90 | Equations (1068,1069) can reduce 201 to:
% 30.97/9.90 | (746) $false
% 30.97/9.90 |
% 30.97/9.90 |-The branch is then unsatisfiable
% 30.97/9.90 |-Branch two:
% 30.97/9.90 | (945) ~ (all_0_11_11 = n9)
% 30.97/9.90 | (946) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.97/9.90 |
% 30.97/9.90 +-Applying beta-rule and splitting (946), into two cases.
% 30.97/9.90 |-Branch one:
% 30.97/9.90 | (947) all_0_11_11 = n8
% 30.97/9.90 |
% 30.97/9.90 | From (947) and (190) follows:
% 30.97/9.90 | (948) pred(n8) = all_0_9_9
% 30.97/9.90 |
% 30.97/9.90 | From (947) and (505) follows:
% 30.97/9.90 | (949) succ(n8) = all_0_5_5
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (259) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 30.97/9.90 | (950) all_0_9_9 = n7
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (184) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 30.97/9.90 | (951) all_0_5_5 = n9
% 30.97/9.90 |
% 30.97/9.90 | From (950)(951) and (156) follows:
% 30.97/9.90 | (952) sum(n7, n9) = all_0_2_2
% 30.97/9.90 |
% 30.97/9.90 | From (950) and (5330) follows:
% 30.97/9.90 | (5437) sum(n7, n14) = all_0_7_7
% 30.97/9.90 |
% 30.97/9.90 | From (951) and (5328) follows:
% 30.97/9.90 | (5438) sum(n12, n9) = all_0_4_4
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n12, n9, all_0_4_4, n0 and discharging atoms sum(n12, n9) = all_0_4_4, sum(n12, n9) = n0, yields:
% 30.97/9.90 | (1081) all_0_4_4 = n0
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n7, n14, all_0_7_7, n0 and discharging atoms sum(n7, n14) = all_0_7_7, sum(n7, n14) = n0, yields:
% 30.97/9.90 | (1083) all_0_7_7 = n0
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 30.97/9.90 | (956) all_0_2_2 = n16
% 30.97/9.90 |
% 30.97/9.90 | From (956) and (5332) follows:
% 30.97/9.90 | (5442) sum(n16, n5) = all_0_0_0
% 30.97/9.90 |
% 30.97/9.90 | From (1083)(1081) and (435) follows:
% 30.97/9.90 | (1085) sum(n0, n0) = all_0_3_3
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n16, n5, all_0_0_0, n0 and discharging atoms sum(n16, n5) = all_0_0_0, sum(n16, n5) = n0, yields:
% 30.97/9.90 | (1087) all_0_0_0 = n0
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 30.97/9.90 | (1088) all_0_3_3 = n0
% 30.97/9.90 |
% 30.97/9.90 | Equations (1087,1088) can reduce 201 to:
% 30.97/9.90 | (746) $false
% 30.97/9.90 |
% 30.97/9.90 |-The branch is then unsatisfiable
% 30.97/9.90 |-Branch two:
% 30.97/9.90 | (963) ~ (all_0_11_11 = n8)
% 30.97/9.90 | (964) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.97/9.90 |
% 30.97/9.90 +-Applying beta-rule and splitting (964), into two cases.
% 30.97/9.90 |-Branch one:
% 30.97/9.90 | (965) all_0_11_11 = n7
% 30.97/9.90 |
% 30.97/9.90 | From (965) and (190) follows:
% 30.97/9.90 | (966) pred(n7) = all_0_9_9
% 30.97/9.90 |
% 30.97/9.90 | From (965) and (505) follows:
% 30.97/9.90 | (967) succ(n7) = all_0_5_5
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (259) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 30.97/9.90 | (968) all_0_9_9 = n6
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (184) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 30.97/9.90 | (969) all_0_5_5 = n8
% 30.97/9.90 |
% 30.97/9.90 | From (968)(969) and (156) follows:
% 30.97/9.90 | (970) sum(n6, n8) = all_0_2_2
% 30.97/9.90 |
% 30.97/9.90 | From (968) and (5330) follows:
% 30.97/9.90 | (5455) sum(n6, n14) = all_0_7_7
% 30.97/9.90 |
% 30.97/9.90 | From (969) and (5328) follows:
% 30.97/9.90 | (5456) sum(n12, n8) = all_0_4_4
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n12, n8, all_0_4_4, n20 and discharging atoms sum(n12, n8) = all_0_4_4, sum(n12, n8) = n20, yields:
% 30.97/9.90 | (1101) all_0_4_4 = n20
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n6, n14, all_0_7_7, n20 and discharging atoms sum(n6, n14) = all_0_7_7, sum(n6, n14) = n20, yields:
% 30.97/9.90 | (1100) all_0_7_7 = n20
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 30.97/9.90 | (974) all_0_2_2 = n14
% 30.97/9.90 |
% 30.97/9.90 | From (974) and (5332) follows:
% 30.97/9.90 | (5460) sum(n14, n5) = all_0_0_0
% 30.97/9.90 |
% 30.97/9.90 | From (1100)(1101) and (435) follows:
% 30.97/9.90 | (1103) sum(n20, n20) = all_0_3_3
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 30.97/9.90 | (1104) all_0_3_3 = n19
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n14, n5, all_0_0_0, n19 and discharging atoms sum(n14, n5) = all_0_0_0, sum(n14, n5) = n19, yields:
% 30.97/9.90 | (1105) all_0_0_0 = n19
% 30.97/9.90 |
% 30.97/9.90 | Equations (1105,1104) can reduce 201 to:
% 30.97/9.90 | (746) $false
% 30.97/9.90 |
% 30.97/9.90 |-The branch is then unsatisfiable
% 30.97/9.90 |-Branch two:
% 30.97/9.90 | (981) ~ (all_0_11_11 = n7)
% 30.97/9.90 | (982) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.97/9.90 |
% 30.97/9.90 +-Applying beta-rule and splitting (982), into two cases.
% 30.97/9.90 |-Branch one:
% 30.97/9.90 | (983) all_0_11_11 = n6
% 30.97/9.90 |
% 30.97/9.90 | From (983) and (190) follows:
% 30.97/9.90 | (984) pred(n6) = all_0_9_9
% 30.97/9.90 |
% 30.97/9.90 | From (983) and (505) follows:
% 30.97/9.90 | (985) succ(n6) = all_0_5_5
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (259) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 30.97/9.90 | (986) all_0_9_9 = n5
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (184) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 30.97/9.90 | (987) all_0_5_5 = n7
% 30.97/9.90 |
% 30.97/9.90 | From (986)(987) and (156) follows:
% 30.97/9.90 | (988) sum(n5, n7) = all_0_2_2
% 30.97/9.90 |
% 30.97/9.90 | From (986) and (5330) follows:
% 30.97/9.90 | (5473) sum(n5, n14) = all_0_7_7
% 30.97/9.90 |
% 30.97/9.90 | From (987) and (5328) follows:
% 30.97/9.90 | (5474) sum(n12, n7) = all_0_4_4
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n12, n7, all_0_4_4, n19 and discharging atoms sum(n12, n7) = all_0_4_4, sum(n12, n7) = n19, yields:
% 30.97/9.90 | (736) all_0_4_4 = n19
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n5, n14, all_0_7_7, n19 and discharging atoms sum(n5, n14) = all_0_7_7, sum(n5, n14) = n19, yields:
% 30.97/9.90 | (737) all_0_7_7 = n19
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 30.97/9.90 | (992) all_0_2_2 = n12
% 30.97/9.90 |
% 30.97/9.90 | From (992) and (5332) follows:
% 30.97/9.90 | (5478) sum(n12, n5) = all_0_0_0
% 30.97/9.90 |
% 30.97/9.90 | From (737)(736) and (435) follows:
% 30.97/9.90 | (741) sum(n19, n19) = all_0_3_3
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 30.97/9.90 | (744) all_0_3_3 = n17
% 30.97/9.90 |
% 30.97/9.90 | Instantiating formula (194) with n12, n5, all_0_0_0, n17 and discharging atoms sum(n12, n5) = all_0_0_0, sum(n12, n5) = n17, yields:
% 30.97/9.90 | (742) all_0_0_0 = n17
% 30.97/9.90 |
% 30.97/9.90 | Equations (742,744) can reduce 201 to:
% 30.97/9.90 | (746) $false
% 30.97/9.90 |
% 30.97/9.90 |-The branch is then unsatisfiable
% 30.97/9.90 |-Branch two:
% 30.97/9.90 | (999) ~ (all_0_11_11 = n6)
% 30.97/9.90 | (1000) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.97/9.90 |
% 30.97/9.90 +-Applying beta-rule and splitting (1000), into two cases.
% 30.97/9.90 |-Branch one:
% 30.97/9.90 | (1001) all_0_11_11 = n5
% 30.97/9.90 |
% 30.97/9.90 | From (1001) and (190) follows:
% 30.97/9.90 | (1002) pred(n5) = all_0_9_9
% 30.97/9.90 |
% 30.97/9.90 | From (1001) and (505) follows:
% 30.97/9.91 | (1003) succ(n5) = all_0_5_5
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (259) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 30.97/9.91 | (1004) all_0_9_9 = n4
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (184) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 30.97/9.91 | (1005) all_0_5_5 = n6
% 30.97/9.91 |
% 30.97/9.91 | From (1004)(1005) and (156) follows:
% 30.97/9.91 | (1006) sum(n4, n6) = all_0_2_2
% 30.97/9.91 |
% 30.97/9.91 | From (1004) and (5330) follows:
% 30.97/9.91 | (5491) sum(n4, n14) = all_0_7_7
% 30.97/9.91 |
% 30.97/9.91 | From (1005) and (5328) follows:
% 30.97/9.91 | (5492) sum(n12, n6) = all_0_4_4
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (194) with n12, n6, all_0_4_4, n18 and discharging atoms sum(n12, n6) = all_0_4_4, sum(n12, n6) = n18, yields:
% 30.97/9.91 | (757) all_0_4_4 = n18
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (194) with n4, n14, all_0_7_7, n18 and discharging atoms sum(n4, n14) = all_0_7_7, sum(n4, n14) = n18, yields:
% 30.97/9.91 | (759) all_0_7_7 = n18
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (194) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 30.97/9.91 | (1010) all_0_2_2 = n10
% 30.97/9.91 |
% 30.97/9.91 | From (1010) and (5332) follows:
% 30.97/9.91 | (5496) sum(n10, n5) = all_0_0_0
% 30.97/9.91 |
% 30.97/9.91 | From (759)(757) and (435) follows:
% 30.97/9.91 | (761) sum(n18, n18) = all_0_3_3
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 30.97/9.91 | (762) all_0_3_3 = n15
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (194) with n10, n5, all_0_0_0, n15 and discharging atoms sum(n10, n5) = all_0_0_0, sum(n10, n5) = n15, yields:
% 30.97/9.91 | (763) all_0_0_0 = n15
% 30.97/9.91 |
% 30.97/9.91 | Equations (763,762) can reduce 201 to:
% 30.97/9.91 | (746) $false
% 30.97/9.91 |
% 30.97/9.91 |-The branch is then unsatisfiable
% 30.97/9.91 |-Branch two:
% 30.97/9.91 | (1017) ~ (all_0_11_11 = n5)
% 30.97/9.91 | (1018) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.97/9.91 |
% 30.97/9.91 +-Applying beta-rule and splitting (1018), into two cases.
% 30.97/9.91 |-Branch one:
% 30.97/9.91 | (1019) all_0_11_11 = n4
% 30.97/9.91 |
% 30.97/9.91 | From (1019) and (190) follows:
% 30.97/9.91 | (1020) pred(n4) = all_0_9_9
% 30.97/9.91 |
% 30.97/9.91 | From (1019) and (505) follows:
% 30.97/9.91 | (1021) succ(n4) = all_0_5_5
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 30.97/9.91 | (1022) all_0_9_9 = n3
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 30.97/9.91 | (1023) all_0_5_5 = n5
% 30.97/9.91 |
% 30.97/9.91 | From (1022)(1023) and (156) follows:
% 30.97/9.91 | (1024) sum(n3, n5) = all_0_2_2
% 30.97/9.91 |
% 30.97/9.91 | From (1022) and (5330) follows:
% 30.97/9.91 | (5509) sum(n3, n14) = all_0_7_7
% 30.97/9.91 |
% 30.97/9.91 | From (1023) and (5328) follows:
% 30.97/9.91 | (5510) sum(n12, n5) = all_0_4_4
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (194) with n12, n5, all_0_4_4, n17 and discharging atoms sum(n12, n5) = all_0_4_4, sum(n12, n5) = n17, yields:
% 30.97/9.91 | (775) all_0_4_4 = n17
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (194) with n3, n14, all_0_7_7, n17 and discharging atoms sum(n3, n14) = all_0_7_7, sum(n3, n14) = n17, yields:
% 30.97/9.91 | (777) all_0_7_7 = n17
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 30.97/9.91 | (1028) all_0_2_2 = n8
% 30.97/9.91 |
% 30.97/9.91 | From (1028) and (5332) follows:
% 30.97/9.91 | (5514) sum(n8, n5) = all_0_0_0
% 30.97/9.91 |
% 30.97/9.91 | From (777)(775) and (435) follows:
% 30.97/9.91 | (779) sum(n17, n17) = all_0_3_3
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 30.97/9.91 | (780) all_0_3_3 = n13
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (194) with n8, n5, all_0_0_0, n13 and discharging atoms sum(n8, n5) = all_0_0_0, sum(n8, n5) = n13, yields:
% 30.97/9.91 | (781) all_0_0_0 = n13
% 30.97/9.91 |
% 30.97/9.91 | Equations (781,780) can reduce 201 to:
% 30.97/9.91 | (746) $false
% 30.97/9.91 |
% 30.97/9.91 |-The branch is then unsatisfiable
% 30.97/9.91 |-Branch two:
% 30.97/9.91 | (1035) ~ (all_0_11_11 = n4)
% 30.97/9.91 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.97/9.91 |
% 30.97/9.91 +-Applying beta-rule and splitting (1036), into two cases.
% 30.97/9.91 |-Branch one:
% 30.97/9.91 | (1037) all_0_11_11 = n3
% 30.97/9.91 |
% 30.97/9.91 | From (1037) and (190) follows:
% 30.97/9.91 | (1038) pred(n3) = all_0_9_9
% 30.97/9.91 |
% 30.97/9.91 | From (1037) and (505) follows:
% 30.97/9.91 | (1039) succ(n3) = all_0_5_5
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 30.97/9.91 | (1040) all_0_9_9 = n2
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 30.97/9.91 | (1041) all_0_5_5 = n4
% 30.97/9.91 |
% 30.97/9.91 | From (1040)(1041) and (156) follows:
% 30.97/9.91 | (1042) sum(n2, n4) = all_0_2_2
% 30.97/9.91 |
% 30.97/9.91 | From (1040) and (5330) follows:
% 30.97/9.91 | (5527) sum(n2, n14) = all_0_7_7
% 30.97/9.91 |
% 30.97/9.91 | From (1041) and (5328) follows:
% 30.97/9.91 | (5528) sum(n12, n4) = all_0_4_4
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (194) with n12, n4, all_0_4_4, n16 and discharging atoms sum(n12, n4) = all_0_4_4, sum(n12, n4) = n16, yields:
% 30.97/9.91 | (793) all_0_4_4 = n16
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (194) with n2, n14, all_0_7_7, n16 and discharging atoms sum(n2, n14) = all_0_7_7, sum(n2, n14) = n16, yields:
% 30.97/9.91 | (795) all_0_7_7 = n16
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 30.97/9.91 | (1046) all_0_2_2 = n6
% 30.97/9.91 |
% 30.97/9.91 | From (1046) and (5332) follows:
% 30.97/9.91 | (5532) sum(n6, n5) = all_0_0_0
% 30.97/9.91 |
% 30.97/9.91 | From (795)(793) and (435) follows:
% 30.97/9.91 | (797) sum(n16, n16) = all_0_3_3
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 30.97/9.91 | (798) all_0_3_3 = n11
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (194) with n6, n5, all_0_0_0, n11 and discharging atoms sum(n6, n5) = all_0_0_0, sum(n6, n5) = n11, yields:
% 30.97/9.91 | (799) all_0_0_0 = n11
% 30.97/9.91 |
% 30.97/9.91 | Equations (799,798) can reduce 201 to:
% 30.97/9.91 | (746) $false
% 30.97/9.91 |
% 30.97/9.91 |-The branch is then unsatisfiable
% 30.97/9.91 |-Branch two:
% 30.97/9.91 | (1053) ~ (all_0_11_11 = n3)
% 30.97/9.91 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.97/9.91 |
% 30.97/9.91 +-Applying beta-rule and splitting (1054), into two cases.
% 30.97/9.91 |-Branch one:
% 30.97/9.91 | (1055) all_0_11_11 = n2
% 30.97/9.91 |
% 30.97/9.91 | From (1055) and (190) follows:
% 30.97/9.91 | (1056) pred(n2) = all_0_9_9
% 30.97/9.91 |
% 30.97/9.91 | From (1055) and (505) follows:
% 30.97/9.91 | (1057) succ(n2) = all_0_5_5
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 30.97/9.91 | (1058) all_0_9_9 = n1
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 30.97/9.91 | (1059) all_0_5_5 = n3
% 30.97/9.91 |
% 30.97/9.91 | From (1058)(1059) and (156) follows:
% 30.97/9.91 | (1060) sum(n1, n3) = all_0_2_2
% 30.97/9.91 |
% 30.97/9.91 | From (1058) and (5330) follows:
% 30.97/9.91 | (5545) sum(n1, n14) = all_0_7_7
% 30.97/9.91 |
% 30.97/9.91 | From (1059) and (5328) follows:
% 30.97/9.91 | (5546) sum(n12, n3) = all_0_4_4
% 30.97/9.91 |
% 30.97/9.91 | Instantiating formula (194) with n12, n3, all_0_4_4, n15 and discharging atoms sum(n12, n3) = all_0_4_4, sum(n12, n3) = n15, yields:
% 30.97/9.91 | (811) all_0_4_4 = n15
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (194) with n1, n14, all_0_7_7, n15 and discharging atoms sum(n1, n14) = all_0_7_7, sum(n1, n14) = n15, yields:
% 30.97/9.92 | (813) all_0_7_7 = n15
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 30.97/9.92 | (1064) all_0_2_2 = n4
% 30.97/9.92 |
% 30.97/9.92 | From (1064) and (5332) follows:
% 30.97/9.92 | (5550) sum(n4, n5) = all_0_0_0
% 30.97/9.92 |
% 30.97/9.92 | From (813)(811) and (435) follows:
% 30.97/9.92 | (815) sum(n15, n15) = all_0_3_3
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 30.97/9.92 | (816) all_0_3_3 = n9
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (194) with n4, n5, all_0_0_0, n9 and discharging atoms sum(n4, n5) = all_0_0_0, sum(n4, n5) = n9, yields:
% 30.97/9.92 | (817) all_0_0_0 = n9
% 30.97/9.92 |
% 30.97/9.92 | Equations (817,816) can reduce 201 to:
% 30.97/9.92 | (746) $false
% 30.97/9.92 |
% 30.97/9.92 |-The branch is then unsatisfiable
% 30.97/9.92 |-Branch two:
% 30.97/9.92 | (1071) ~ (all_0_11_11 = n2)
% 30.97/9.92 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 30.97/9.92 |
% 30.97/9.92 +-Applying beta-rule and splitting (1072), into two cases.
% 30.97/9.92 |-Branch one:
% 30.97/9.92 | (1073) all_0_11_11 = n1
% 30.97/9.92 |
% 30.97/9.92 | From (1073) and (190) follows:
% 30.97/9.92 | (1074) pred(n1) = all_0_9_9
% 30.97/9.92 |
% 30.97/9.92 | From (1073) and (505) follows:
% 30.97/9.92 | (1075) succ(n1) = all_0_5_5
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 30.97/9.92 | (1076) all_0_9_9 = n0
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 30.97/9.92 | (1077) all_0_5_5 = n2
% 30.97/9.92 |
% 30.97/9.92 | From (1076)(1077) and (156) follows:
% 30.97/9.92 | (1078) sum(n0, n2) = all_0_2_2
% 30.97/9.92 |
% 30.97/9.92 | From (1076) and (5330) follows:
% 30.97/9.92 | (5563) sum(n0, n14) = all_0_7_7
% 30.97/9.92 |
% 30.97/9.92 | From (1077) and (5328) follows:
% 30.97/9.92 | (5564) sum(n12, n2) = all_0_4_4
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (194) with n12, n2, all_0_4_4, n14 and discharging atoms sum(n12, n2) = all_0_4_4, sum(n12, n2) = n14, yields:
% 30.97/9.92 | (829) all_0_4_4 = n14
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (194) with n0, n14, all_0_7_7, n14 and discharging atoms sum(n0, n14) = all_0_7_7, sum(n0, n14) = n14, yields:
% 30.97/9.92 | (831) all_0_7_7 = n14
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 30.97/9.92 | (1082) all_0_2_2 = n2
% 30.97/9.92 |
% 30.97/9.92 | From (1082) and (5332) follows:
% 30.97/9.92 | (5568) sum(n2, n5) = all_0_0_0
% 30.97/9.92 |
% 30.97/9.92 | From (831)(829) and (435) follows:
% 30.97/9.92 | (833) sum(n14, n14) = all_0_3_3
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 30.97/9.92 | (834) all_0_3_3 = n7
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (194) with n2, n5, all_0_0_0, n7 and discharging atoms sum(n2, n5) = all_0_0_0, sum(n2, n5) = n7, yields:
% 30.97/9.92 | (835) all_0_0_0 = n7
% 30.97/9.92 |
% 30.97/9.92 | Equations (835,834) can reduce 201 to:
% 30.97/9.92 | (746) $false
% 30.97/9.92 |
% 30.97/9.92 |-The branch is then unsatisfiable
% 30.97/9.92 |-Branch two:
% 30.97/9.92 | (1090) ~ (all_0_11_11 = n1)
% 30.97/9.92 | (1091) all_0_11_11 = n0
% 30.97/9.92 |
% 30.97/9.92 | From (1091) and (190) follows:
% 30.97/9.92 | (1092) pred(n0) = all_0_9_9
% 30.97/9.92 |
% 30.97/9.92 | From (1091) and (505) follows:
% 30.97/9.92 | (1093) succ(n0) = all_0_5_5
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 30.97/9.92 | (1094) all_0_9_9 = n20
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 30.97/9.92 | (1095) all_0_5_5 = n1
% 30.97/9.92 |
% 30.97/9.92 | From (1094)(1095) and (156) follows:
% 30.97/9.92 | (1096) sum(n20, n1) = all_0_2_2
% 30.97/9.92 |
% 30.97/9.92 | From (1094) and (5330) follows:
% 30.97/9.92 | (5580) sum(n20, n14) = all_0_7_7
% 30.97/9.92 |
% 30.97/9.92 | From (1095) and (5328) follows:
% 30.97/9.92 | (5581) sum(n12, n1) = all_0_4_4
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (194) with n20, n14, all_0_7_7, n13 and discharging atoms sum(n20, n14) = all_0_7_7, sum(n20, n14) = n13, yields:
% 30.97/9.92 | (849) all_0_7_7 = n13
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 30.97/9.92 | (1099) all_0_2_2 = n0
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (194) with n12, n1, all_0_4_4, n13 and discharging atoms sum(n12, n1) = all_0_4_4, sum(n12, n1) = n13, yields:
% 30.97/9.92 | (847) all_0_4_4 = n13
% 30.97/9.92 |
% 30.97/9.92 | From (1099) and (5332) follows:
% 30.97/9.92 | (5585) sum(n0, n5) = all_0_0_0
% 30.97/9.92 |
% 30.97/9.92 | From (849)(847) and (435) follows:
% 30.97/9.92 | (851) sum(n13, n13) = all_0_3_3
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 30.97/9.92 | (852) all_0_3_3 = n5
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (194) with n0, n5, all_0_0_0, n5 and discharging atoms sum(n0, n5) = all_0_0_0, sum(n0, n5) = n5, yields:
% 30.97/9.92 | (853) all_0_0_0 = n5
% 30.97/9.92 |
% 30.97/9.92 | Equations (853,852) can reduce 201 to:
% 30.97/9.92 | (746) $false
% 30.97/9.92 |
% 30.97/9.92 |-The branch is then unsatisfiable
% 30.97/9.92 |-Branch two:
% 30.97/9.92 | (1244) ~ (all_0_10_10 = n13)
% 30.97/9.92 | (1245) all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.97/9.92 |
% 30.97/9.92 +-Applying beta-rule and splitting (856), into two cases.
% 30.97/9.92 |-Branch one:
% 30.97/9.92 | (857) all_0_11_11 = n13
% 30.97/9.92 |
% 30.97/9.92 | From (857) and (190) follows:
% 30.97/9.92 | (858) pred(n13) = all_0_9_9
% 30.97/9.92 |
% 30.97/9.92 | From (857) and (505) follows:
% 30.97/9.92 | (859) succ(n13) = all_0_5_5
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (259) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 30.97/9.92 | (860) all_0_9_9 = n12
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (184) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 30.97/9.92 | (861) all_0_5_5 = n14
% 30.97/9.92 |
% 30.97/9.92 | From (861) and (386) follows:
% 30.97/9.92 | (5597) sum(all_0_6_6, n14) = all_0_4_4
% 30.97/9.92 |
% 30.97/9.92 | From (860)(861) and (156) follows:
% 30.97/9.92 | (862) sum(n12, n14) = all_0_2_2
% 30.97/9.92 |
% 30.97/9.92 | From (860) and (74) follows:
% 30.97/9.92 | (5599) sum(n12, all_0_8_8) = all_0_7_7
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (194) with n12, n14, all_0_2_2, n5 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n5, yields:
% 30.97/9.92 | (866) all_0_2_2 = n5
% 30.97/9.92 |
% 30.97/9.92 | From (866) and (85) follows:
% 30.97/9.92 | (5601) sum(n5, all_0_1_1) = all_0_0_0
% 30.97/9.92 |
% 30.97/9.92 +-Applying beta-rule and splitting (1245), into two cases.
% 30.97/9.92 |-Branch one:
% 30.97/9.92 | (1246) all_0_10_10 = n12
% 30.97/9.92 |
% 30.97/9.92 | From (1246) and (57) follows:
% 30.97/9.92 | (1247) pred(n12) = all_0_6_6
% 30.97/9.92 |
% 30.97/9.92 | From (1246) and (381) follows:
% 30.97/9.92 | (1248) succ(n12) = all_0_8_8
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (259) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 30.97/9.92 | (1249) all_0_6_6 = n11
% 30.97/9.92 |
% 30.97/9.92 | Instantiating formula (184) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 30.97/9.92 | (1250) all_0_8_8 = n13
% 30.97/9.92 |
% 30.97/9.92 | From (1249)(1250) and (628) follows:
% 30.97/9.92 | (1251) sum(n11, n13) = all_0_1_1
% 30.97/9.92 |
% 30.97/9.92 | From (1249) and (5597) follows:
% 30.97/9.92 | (5608) sum(n11, n14) = all_0_4_4
% 30.97/9.92 |
% 30.97/9.92 | From (1250) and (5599) follows:
% 30.97/9.93 | (5609) sum(n12, n13) = all_0_7_7
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n12, n13, all_0_7_7, n4 and discharging atoms sum(n12, n13) = all_0_7_7, sum(n12, n13) = n4, yields:
% 30.97/9.93 | (1011) all_0_7_7 = n4
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n11, n14, all_0_4_4, n4 and discharging atoms sum(n11, n14) = all_0_4_4, sum(n11, n14) = n4, yields:
% 30.97/9.93 | (1009) all_0_4_4 = n4
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n11, n13, all_0_1_1, n3 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n3, yields:
% 30.97/9.93 | (1255) all_0_1_1 = n3
% 30.97/9.93 |
% 30.97/9.93 | From (1011)(1009) and (435) follows:
% 30.97/9.93 | (1013) sum(n4, n4) = all_0_3_3
% 30.97/9.93 |
% 30.97/9.93 | From (1255) and (5601) follows:
% 30.97/9.93 | (5614) sum(n5, n3) = all_0_0_0
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n5, n3, all_0_0_0, n8 and discharging atoms sum(n5, n3) = all_0_0_0, sum(n5, n3) = n8, yields:
% 30.97/9.93 | (1014) all_0_0_0 = n8
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 30.97/9.93 | (1015) all_0_3_3 = n8
% 30.97/9.93 |
% 30.97/9.93 | Equations (1014,1015) can reduce 201 to:
% 30.97/9.93 | (746) $false
% 30.97/9.93 |
% 30.97/9.93 |-The branch is then unsatisfiable
% 30.97/9.93 |-Branch two:
% 30.97/9.93 | (1262) ~ (all_0_10_10 = n12)
% 30.97/9.93 | (1263) all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.97/9.93 |
% 30.97/9.93 +-Applying beta-rule and splitting (1263), into two cases.
% 30.97/9.93 |-Branch one:
% 30.97/9.93 | (1264) all_0_10_10 = n11
% 30.97/9.93 |
% 30.97/9.93 | From (1264) and (57) follows:
% 30.97/9.93 | (1265) pred(n11) = all_0_6_6
% 30.97/9.93 |
% 30.97/9.93 | From (1264) and (381) follows:
% 30.97/9.93 | (1266) succ(n11) = all_0_8_8
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (259) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 30.97/9.93 | (1267) all_0_6_6 = n10
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (184) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 30.97/9.93 | (1268) all_0_8_8 = n12
% 30.97/9.93 |
% 30.97/9.93 | From (1267)(1268) and (628) follows:
% 30.97/9.93 | (1269) sum(n10, n12) = all_0_1_1
% 30.97/9.93 |
% 30.97/9.93 | From (1267) and (5597) follows:
% 30.97/9.93 | (5626) sum(n10, n14) = all_0_4_4
% 30.97/9.93 |
% 30.97/9.93 | From (1268) and (5599) follows:
% 30.97/9.93 | (5627) sum(n12, n12) = all_0_7_7
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n12, n12, all_0_7_7, n3 and discharging atoms sum(n12, n12) = all_0_7_7, sum(n12, n12) = n3, yields:
% 30.97/9.93 | (1029) all_0_7_7 = n3
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n10, n14, all_0_4_4, n3 and discharging atoms sum(n10, n14) = all_0_4_4, sum(n10, n14) = n3, yields:
% 30.97/9.93 | (1027) all_0_4_4 = n3
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n10, n12, all_0_1_1, n1 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n1, yields:
% 30.97/9.93 | (1273) all_0_1_1 = n1
% 30.97/9.93 |
% 30.97/9.93 | From (1029)(1027) and (435) follows:
% 30.97/9.93 | (1031) sum(n3, n3) = all_0_3_3
% 30.97/9.93 |
% 30.97/9.93 | From (1273) and (5601) follows:
% 30.97/9.93 | (5632) sum(n5, n1) = all_0_0_0
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n5, n1, all_0_0_0, n6 and discharging atoms sum(n5, n1) = all_0_0_0, sum(n5, n1) = n6, yields:
% 30.97/9.93 | (1032) all_0_0_0 = n6
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 30.97/9.93 | (1033) all_0_3_3 = n6
% 30.97/9.93 |
% 30.97/9.93 | Equations (1032,1033) can reduce 201 to:
% 30.97/9.93 | (746) $false
% 30.97/9.93 |
% 30.97/9.93 |-The branch is then unsatisfiable
% 30.97/9.93 |-Branch two:
% 30.97/9.93 | (1280) ~ (all_0_10_10 = n11)
% 30.97/9.93 | (1281) all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.97/9.93 |
% 30.97/9.93 +-Applying beta-rule and splitting (1281), into two cases.
% 30.97/9.93 |-Branch one:
% 30.97/9.93 | (1282) all_0_10_10 = n10
% 30.97/9.93 |
% 30.97/9.93 | From (1282) and (57) follows:
% 30.97/9.93 | (1283) pred(n10) = all_0_6_6
% 30.97/9.93 |
% 30.97/9.93 | From (1282) and (381) follows:
% 30.97/9.93 | (1284) succ(n10) = all_0_8_8
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (259) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 30.97/9.93 | (1285) all_0_6_6 = n9
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (184) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 30.97/9.93 | (1286) all_0_8_8 = n11
% 30.97/9.93 |
% 30.97/9.93 | From (1285)(1286) and (628) follows:
% 30.97/9.93 | (1287) sum(n9, n11) = all_0_1_1
% 30.97/9.93 |
% 30.97/9.93 | From (1285) and (5597) follows:
% 30.97/9.93 | (5644) sum(n9, n14) = all_0_4_4
% 30.97/9.93 |
% 30.97/9.93 | From (1286) and (5599) follows:
% 30.97/9.93 | (5645) sum(n12, n11) = all_0_7_7
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n12, n11, all_0_7_7, n2 and discharging atoms sum(n12, n11) = all_0_7_7, sum(n12, n11) = n2, yields:
% 30.97/9.93 | (1047) all_0_7_7 = n2
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n9, n14, all_0_4_4, n2 and discharging atoms sum(n9, n14) = all_0_4_4, sum(n9, n14) = n2, yields:
% 30.97/9.93 | (1045) all_0_4_4 = n2
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 30.97/9.93 | (1291) all_0_1_1 = n20
% 30.97/9.93 |
% 30.97/9.93 | From (1047)(1045) and (435) follows:
% 30.97/9.93 | (1049) sum(n2, n2) = all_0_3_3
% 30.97/9.93 |
% 30.97/9.93 | From (1291) and (5601) follows:
% 30.97/9.93 | (5650) sum(n5, n20) = all_0_0_0
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n5, n20, all_0_0_0, n4 and discharging atoms sum(n5, n20) = all_0_0_0, sum(n5, n20) = n4, yields:
% 30.97/9.93 | (1050) all_0_0_0 = n4
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 30.97/9.93 | (1051) all_0_3_3 = n4
% 30.97/9.93 |
% 30.97/9.93 | Equations (1050,1051) can reduce 201 to:
% 30.97/9.93 | (746) $false
% 30.97/9.93 |
% 30.97/9.93 |-The branch is then unsatisfiable
% 30.97/9.93 |-Branch two:
% 30.97/9.93 | (1298) ~ (all_0_10_10 = n10)
% 30.97/9.93 | (1299) all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.97/9.93 |
% 30.97/9.93 +-Applying beta-rule and splitting (1299), into two cases.
% 30.97/9.93 |-Branch one:
% 30.97/9.93 | (1300) all_0_10_10 = n9
% 30.97/9.93 |
% 30.97/9.93 | From (1300) and (57) follows:
% 30.97/9.93 | (1301) pred(n9) = all_0_6_6
% 30.97/9.93 |
% 30.97/9.93 | From (1300) and (381) follows:
% 30.97/9.93 | (1302) succ(n9) = all_0_8_8
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (259) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 30.97/9.93 | (1303) all_0_6_6 = n8
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (184) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 30.97/9.93 | (1304) all_0_8_8 = n10
% 30.97/9.93 |
% 30.97/9.93 | From (1303)(1304) and (628) follows:
% 30.97/9.93 | (1305) sum(n8, n10) = all_0_1_1
% 30.97/9.93 |
% 30.97/9.93 | From (1303) and (5597) follows:
% 30.97/9.93 | (5662) sum(n8, n14) = all_0_4_4
% 30.97/9.93 |
% 30.97/9.93 | From (1304) and (5599) follows:
% 30.97/9.93 | (5663) sum(n12, n10) = all_0_7_7
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n12, n10, all_0_7_7, n1 and discharging atoms sum(n12, n10) = all_0_7_7, sum(n12, n10) = n1, yields:
% 30.97/9.93 | (1065) all_0_7_7 = n1
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n8, n14, all_0_4_4, n1 and discharging atoms sum(n8, n14) = all_0_4_4, sum(n8, n14) = n1, yields:
% 30.97/9.93 | (1063) all_0_4_4 = n1
% 30.97/9.93 |
% 30.97/9.93 | Instantiating formula (194) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 30.97/9.93 | (1309) all_0_1_1 = n18
% 30.97/9.93 |
% 30.97/9.93 | From (1065)(1063) and (435) follows:
% 30.97/9.93 | (1067) sum(n1, n1) = all_0_3_3
% 30.97/9.93 |
% 30.97/9.93 | From (1309) and (5601) follows:
% 30.97/9.94 | (5668) sum(n5, n18) = all_0_0_0
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (194) with n5, n18, all_0_0_0, n2 and discharging atoms sum(n5, n18) = all_0_0_0, sum(n5, n18) = n2, yields:
% 30.97/9.94 | (1068) all_0_0_0 = n2
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 30.97/9.94 | (1069) all_0_3_3 = n2
% 30.97/9.94 |
% 30.97/9.94 | Equations (1068,1069) can reduce 201 to:
% 30.97/9.94 | (746) $false
% 30.97/9.94 |
% 30.97/9.94 |-The branch is then unsatisfiable
% 30.97/9.94 |-Branch two:
% 30.97/9.94 | (1316) ~ (all_0_10_10 = n9)
% 30.97/9.94 | (1317) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.97/9.94 |
% 30.97/9.94 +-Applying beta-rule and splitting (1317), into two cases.
% 30.97/9.94 |-Branch one:
% 30.97/9.94 | (1318) all_0_10_10 = n8
% 30.97/9.94 |
% 30.97/9.94 | From (1318) and (57) follows:
% 30.97/9.94 | (1319) pred(n8) = all_0_6_6
% 30.97/9.94 |
% 30.97/9.94 | From (1318) and (381) follows:
% 30.97/9.94 | (1320) succ(n8) = all_0_8_8
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (259) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 30.97/9.94 | (1321) all_0_6_6 = n7
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (184) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 30.97/9.94 | (1322) all_0_8_8 = n9
% 30.97/9.94 |
% 30.97/9.94 | From (1321)(1322) and (628) follows:
% 30.97/9.94 | (1323) sum(n7, n9) = all_0_1_1
% 30.97/9.94 |
% 30.97/9.94 | From (1321) and (5597) follows:
% 30.97/9.94 | (5680) sum(n7, n14) = all_0_4_4
% 30.97/9.94 |
% 30.97/9.94 | From (1322) and (5599) follows:
% 30.97/9.94 | (5681) sum(n12, n9) = all_0_7_7
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (194) with n12, n9, all_0_7_7, n0 and discharging atoms sum(n12, n9) = all_0_7_7, sum(n12, n9) = n0, yields:
% 30.97/9.94 | (1083) all_0_7_7 = n0
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (194) with n7, n14, all_0_4_4, n0 and discharging atoms sum(n7, n14) = all_0_4_4, sum(n7, n14) = n0, yields:
% 30.97/9.94 | (1081) all_0_4_4 = n0
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (194) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 30.97/9.94 | (1327) all_0_1_1 = n16
% 30.97/9.94 |
% 30.97/9.94 | From (1083)(1081) and (435) follows:
% 30.97/9.94 | (1085) sum(n0, n0) = all_0_3_3
% 30.97/9.94 |
% 30.97/9.94 | From (1327) and (5601) follows:
% 30.97/9.94 | (5686) sum(n5, n16) = all_0_0_0
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (194) with n5, n16, all_0_0_0, n0 and discharging atoms sum(n5, n16) = all_0_0_0, sum(n5, n16) = n0, yields:
% 30.97/9.94 | (1087) all_0_0_0 = n0
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 30.97/9.94 | (1088) all_0_3_3 = n0
% 30.97/9.94 |
% 30.97/9.94 | Equations (1087,1088) can reduce 201 to:
% 30.97/9.94 | (746) $false
% 30.97/9.94 |
% 30.97/9.94 |-The branch is then unsatisfiable
% 30.97/9.94 |-Branch two:
% 30.97/9.94 | (1334) ~ (all_0_10_10 = n8)
% 30.97/9.94 | (1335) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.97/9.94 |
% 30.97/9.94 +-Applying beta-rule and splitting (1335), into two cases.
% 30.97/9.94 |-Branch one:
% 30.97/9.94 | (1336) all_0_10_10 = n7
% 30.97/9.94 |
% 30.97/9.94 | From (1336) and (57) follows:
% 30.97/9.94 | (1337) pred(n7) = all_0_6_6
% 30.97/9.94 |
% 30.97/9.94 | From (1336) and (381) follows:
% 30.97/9.94 | (1338) succ(n7) = all_0_8_8
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (259) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 30.97/9.94 | (1339) all_0_6_6 = n6
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (184) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 30.97/9.94 | (1340) all_0_8_8 = n8
% 30.97/9.94 |
% 30.97/9.94 | From (1339)(1340) and (628) follows:
% 30.97/9.94 | (1341) sum(n6, n8) = all_0_1_1
% 30.97/9.94 |
% 30.97/9.94 | From (1339) and (5597) follows:
% 30.97/9.94 | (5698) sum(n6, n14) = all_0_4_4
% 30.97/9.94 |
% 30.97/9.94 | From (1340) and (5599) follows:
% 30.97/9.94 | (5699) sum(n12, n8) = all_0_7_7
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (194) with n12, n8, all_0_7_7, n20 and discharging atoms sum(n12, n8) = all_0_7_7, sum(n12, n8) = n20, yields:
% 30.97/9.94 | (1100) all_0_7_7 = n20
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (194) with n6, n14, all_0_4_4, n20 and discharging atoms sum(n6, n14) = all_0_4_4, sum(n6, n14) = n20, yields:
% 30.97/9.94 | (1101) all_0_4_4 = n20
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (194) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 30.97/9.94 | (1345) all_0_1_1 = n14
% 30.97/9.94 |
% 30.97/9.94 | From (1100)(1101) and (435) follows:
% 30.97/9.94 | (1103) sum(n20, n20) = all_0_3_3
% 30.97/9.94 |
% 30.97/9.94 | From (1345) and (5601) follows:
% 30.97/9.94 | (5704) sum(n5, n14) = all_0_0_0
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 30.97/9.94 | (1104) all_0_3_3 = n19
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (194) with n5, n14, all_0_0_0, n19 and discharging atoms sum(n5, n14) = all_0_0_0, sum(n5, n14) = n19, yields:
% 30.97/9.94 | (1105) all_0_0_0 = n19
% 30.97/9.94 |
% 30.97/9.94 | Equations (1105,1104) can reduce 201 to:
% 30.97/9.94 | (746) $false
% 30.97/9.94 |
% 30.97/9.94 |-The branch is then unsatisfiable
% 30.97/9.94 |-Branch two:
% 30.97/9.94 | (1352) ~ (all_0_10_10 = n7)
% 30.97/9.94 | (1353) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.97/9.94 |
% 30.97/9.94 +-Applying beta-rule and splitting (1353), into two cases.
% 30.97/9.94 |-Branch one:
% 30.97/9.94 | (1354) all_0_10_10 = n6
% 30.97/9.94 |
% 30.97/9.94 | From (1354) and (57) follows:
% 30.97/9.94 | (1355) pred(n6) = all_0_6_6
% 30.97/9.94 |
% 30.97/9.94 | From (1354) and (381) follows:
% 30.97/9.94 | (1356) succ(n6) = all_0_8_8
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (259) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 30.97/9.94 | (1357) all_0_6_6 = n5
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (184) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 30.97/9.94 | (1358) all_0_8_8 = n7
% 30.97/9.94 |
% 30.97/9.94 | From (1357)(1358) and (628) follows:
% 30.97/9.94 | (1359) sum(n5, n7) = all_0_1_1
% 30.97/9.94 |
% 30.97/9.94 | From (1357) and (5597) follows:
% 30.97/9.94 | (5716) sum(n5, n14) = all_0_4_4
% 30.97/9.94 |
% 30.97/9.94 | From (1358) and (5599) follows:
% 30.97/9.94 | (5717) sum(n12, n7) = all_0_7_7
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (194) with n12, n7, all_0_7_7, n19 and discharging atoms sum(n12, n7) = all_0_7_7, sum(n12, n7) = n19, yields:
% 30.97/9.94 | (737) all_0_7_7 = n19
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (194) with n5, n14, all_0_4_4, n19 and discharging atoms sum(n5, n14) = all_0_4_4, sum(n5, n14) = n19, yields:
% 30.97/9.94 | (736) all_0_4_4 = n19
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (194) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 30.97/9.94 | (1363) all_0_1_1 = n12
% 30.97/9.94 |
% 30.97/9.94 | From (737)(736) and (435) follows:
% 30.97/9.94 | (741) sum(n19, n19) = all_0_3_3
% 30.97/9.94 |
% 30.97/9.94 | From (1363) and (5601) follows:
% 30.97/9.94 | (5722) sum(n5, n12) = all_0_0_0
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 30.97/9.94 | (744) all_0_3_3 = n17
% 30.97/9.94 |
% 30.97/9.94 | Instantiating formula (194) with n5, n12, all_0_0_0, n17 and discharging atoms sum(n5, n12) = all_0_0_0, sum(n5, n12) = n17, yields:
% 30.97/9.94 | (742) all_0_0_0 = n17
% 30.97/9.94 |
% 30.97/9.94 | Equations (742,744) can reduce 201 to:
% 30.97/9.94 | (746) $false
% 30.97/9.94 |
% 30.97/9.94 |-The branch is then unsatisfiable
% 30.97/9.94 |-Branch two:
% 30.97/9.94 | (1370) ~ (all_0_10_10 = n6)
% 30.97/9.94 | (1371) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.97/9.94 |
% 30.97/9.94 +-Applying beta-rule and splitting (1371), into two cases.
% 30.97/9.94 |-Branch one:
% 30.97/9.94 | (1372) all_0_10_10 = n5
% 30.97/9.94 |
% 30.97/9.94 | From (1372) and (57) follows:
% 30.97/9.94 | (1373) pred(n5) = all_0_6_6
% 30.97/9.95 |
% 30.97/9.95 | From (1372) and (381) follows:
% 30.97/9.95 | (1374) succ(n5) = all_0_8_8
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (259) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 30.97/9.95 | (1375) all_0_6_6 = n4
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (184) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 30.97/9.95 | (1376) all_0_8_8 = n6
% 30.97/9.95 |
% 30.97/9.95 | From (1375)(1376) and (628) follows:
% 30.97/9.95 | (1377) sum(n4, n6) = all_0_1_1
% 30.97/9.95 |
% 30.97/9.95 | From (1375) and (5597) follows:
% 30.97/9.95 | (5734) sum(n4, n14) = all_0_4_4
% 30.97/9.95 |
% 30.97/9.95 | From (1376) and (5599) follows:
% 30.97/9.95 | (5735) sum(n12, n6) = all_0_7_7
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (194) with n12, n6, all_0_7_7, n18 and discharging atoms sum(n12, n6) = all_0_7_7, sum(n12, n6) = n18, yields:
% 30.97/9.95 | (759) all_0_7_7 = n18
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (194) with n4, n14, all_0_4_4, n18 and discharging atoms sum(n4, n14) = all_0_4_4, sum(n4, n14) = n18, yields:
% 30.97/9.95 | (757) all_0_4_4 = n18
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (194) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 30.97/9.95 | (1381) all_0_1_1 = n10
% 30.97/9.95 |
% 30.97/9.95 | From (759)(757) and (435) follows:
% 30.97/9.95 | (761) sum(n18, n18) = all_0_3_3
% 30.97/9.95 |
% 30.97/9.95 | From (1381) and (5601) follows:
% 30.97/9.95 | (5740) sum(n5, n10) = all_0_0_0
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 30.97/9.95 | (762) all_0_3_3 = n15
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (194) with n5, n10, all_0_0_0, n15 and discharging atoms sum(n5, n10) = all_0_0_0, sum(n5, n10) = n15, yields:
% 30.97/9.95 | (763) all_0_0_0 = n15
% 30.97/9.95 |
% 30.97/9.95 | Equations (763,762) can reduce 201 to:
% 30.97/9.95 | (746) $false
% 30.97/9.95 |
% 30.97/9.95 |-The branch is then unsatisfiable
% 30.97/9.95 |-Branch two:
% 30.97/9.95 | (1388) ~ (all_0_10_10 = n5)
% 30.97/9.95 | (1389) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.97/9.95 |
% 30.97/9.95 +-Applying beta-rule and splitting (1389), into two cases.
% 30.97/9.95 |-Branch one:
% 30.97/9.95 | (1390) all_0_10_10 = n4
% 30.97/9.95 |
% 30.97/9.95 | From (1390) and (57) follows:
% 30.97/9.95 | (1391) pred(n4) = all_0_6_6
% 30.97/9.95 |
% 30.97/9.95 | From (1390) and (381) follows:
% 30.97/9.95 | (1392) succ(n4) = all_0_8_8
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (259) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 30.97/9.95 | (1393) all_0_6_6 = n3
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (184) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 30.97/9.95 | (1394) all_0_8_8 = n5
% 30.97/9.95 |
% 30.97/9.95 | From (1393)(1394) and (628) follows:
% 30.97/9.95 | (1395) sum(n3, n5) = all_0_1_1
% 30.97/9.95 |
% 30.97/9.95 | From (1393) and (5597) follows:
% 30.97/9.95 | (5752) sum(n3, n14) = all_0_4_4
% 30.97/9.95 |
% 30.97/9.95 | From (1394) and (5599) follows:
% 30.97/9.95 | (5753) sum(n12, n5) = all_0_7_7
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (194) with n12, n5, all_0_7_7, n17 and discharging atoms sum(n12, n5) = all_0_7_7, sum(n12, n5) = n17, yields:
% 30.97/9.95 | (777) all_0_7_7 = n17
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (194) with n3, n14, all_0_4_4, n17 and discharging atoms sum(n3, n14) = all_0_4_4, sum(n3, n14) = n17, yields:
% 30.97/9.95 | (775) all_0_4_4 = n17
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (194) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 30.97/9.95 | (1399) all_0_1_1 = n8
% 30.97/9.95 |
% 30.97/9.95 | From (777)(775) and (435) follows:
% 30.97/9.95 | (779) sum(n17, n17) = all_0_3_3
% 30.97/9.95 |
% 30.97/9.95 | From (1399) and (5601) follows:
% 30.97/9.95 | (5758) sum(n5, n8) = all_0_0_0
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 30.97/9.95 | (780) all_0_3_3 = n13
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (194) with n5, n8, all_0_0_0, n13 and discharging atoms sum(n5, n8) = all_0_0_0, sum(n5, n8) = n13, yields:
% 30.97/9.95 | (781) all_0_0_0 = n13
% 30.97/9.95 |
% 30.97/9.95 | Equations (781,780) can reduce 201 to:
% 30.97/9.95 | (746) $false
% 30.97/9.95 |
% 30.97/9.95 |-The branch is then unsatisfiable
% 30.97/9.95 |-Branch two:
% 30.97/9.95 | (1406) ~ (all_0_10_10 = n4)
% 30.97/9.95 | (1407) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.97/9.95 |
% 30.97/9.95 +-Applying beta-rule and splitting (1407), into two cases.
% 30.97/9.95 |-Branch one:
% 30.97/9.95 | (1408) all_0_10_10 = n3
% 30.97/9.95 |
% 30.97/9.95 | From (1408) and (57) follows:
% 30.97/9.95 | (1409) pred(n3) = all_0_6_6
% 30.97/9.95 |
% 30.97/9.95 | From (1408) and (381) follows:
% 30.97/9.95 | (1410) succ(n3) = all_0_8_8
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 30.97/9.95 | (1411) all_0_6_6 = n2
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 30.97/9.95 | (1412) all_0_8_8 = n4
% 30.97/9.95 |
% 30.97/9.95 | From (1411)(1412) and (628) follows:
% 30.97/9.95 | (1413) sum(n2, n4) = all_0_1_1
% 30.97/9.95 |
% 30.97/9.95 | From (1411) and (5597) follows:
% 30.97/9.95 | (5770) sum(n2, n14) = all_0_4_4
% 30.97/9.95 |
% 30.97/9.95 | From (1412) and (5599) follows:
% 30.97/9.95 | (5771) sum(n12, n4) = all_0_7_7
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (194) with n12, n4, all_0_7_7, n16 and discharging atoms sum(n12, n4) = all_0_7_7, sum(n12, n4) = n16, yields:
% 30.97/9.95 | (795) all_0_7_7 = n16
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (194) with n2, n14, all_0_4_4, n16 and discharging atoms sum(n2, n14) = all_0_4_4, sum(n2, n14) = n16, yields:
% 30.97/9.95 | (793) all_0_4_4 = n16
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 30.97/9.95 | (1417) all_0_1_1 = n6
% 30.97/9.95 |
% 30.97/9.95 | From (795)(793) and (435) follows:
% 30.97/9.95 | (797) sum(n16, n16) = all_0_3_3
% 30.97/9.95 |
% 30.97/9.95 | From (1417) and (5601) follows:
% 30.97/9.95 | (5776) sum(n5, n6) = all_0_0_0
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 30.97/9.95 | (798) all_0_3_3 = n11
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (194) with n5, n6, all_0_0_0, n11 and discharging atoms sum(n5, n6) = all_0_0_0, sum(n5, n6) = n11, yields:
% 30.97/9.95 | (799) all_0_0_0 = n11
% 30.97/9.95 |
% 30.97/9.95 | Equations (799,798) can reduce 201 to:
% 30.97/9.95 | (746) $false
% 30.97/9.95 |
% 30.97/9.95 |-The branch is then unsatisfiable
% 30.97/9.95 |-Branch two:
% 30.97/9.95 | (1424) ~ (all_0_10_10 = n3)
% 30.97/9.95 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 30.97/9.95 |
% 30.97/9.95 +-Applying beta-rule and splitting (1425), into two cases.
% 30.97/9.95 |-Branch one:
% 30.97/9.95 | (1426) all_0_10_10 = n2
% 30.97/9.95 |
% 30.97/9.95 | From (1426) and (57) follows:
% 30.97/9.95 | (1427) pred(n2) = all_0_6_6
% 30.97/9.95 |
% 30.97/9.95 | From (1426) and (381) follows:
% 30.97/9.95 | (1428) succ(n2) = all_0_8_8
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 30.97/9.95 | (1429) all_0_6_6 = n1
% 30.97/9.95 |
% 30.97/9.95 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 30.97/9.95 | (1430) all_0_8_8 = n3
% 30.97/9.95 |
% 30.97/9.95 | From (1429)(1430) and (628) follows:
% 30.97/9.95 | (1431) sum(n1, n3) = all_0_1_1
% 30.97/9.95 |
% 30.97/9.95 | From (1429) and (5597) follows:
% 30.97/9.95 | (5788) sum(n1, n14) = all_0_4_4
% 30.97/9.95 |
% 30.97/9.95 | From (1430) and (5599) follows:
% 30.97/9.96 | (5789) sum(n12, n3) = all_0_7_7
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (194) with n12, n3, all_0_7_7, n15 and discharging atoms sum(n12, n3) = all_0_7_7, sum(n12, n3) = n15, yields:
% 30.97/9.96 | (813) all_0_7_7 = n15
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (194) with n1, n14, all_0_4_4, n15 and discharging atoms sum(n1, n14) = all_0_4_4, sum(n1, n14) = n15, yields:
% 30.97/9.96 | (811) all_0_4_4 = n15
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 30.97/9.96 | (1435) all_0_1_1 = n4
% 30.97/9.96 |
% 30.97/9.96 | From (813)(811) and (435) follows:
% 30.97/9.96 | (815) sum(n15, n15) = all_0_3_3
% 30.97/9.96 |
% 30.97/9.96 | From (1435) and (5601) follows:
% 30.97/9.96 | (5794) sum(n5, n4) = all_0_0_0
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 30.97/9.96 | (816) all_0_3_3 = n9
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (194) with n5, n4, all_0_0_0, n9 and discharging atoms sum(n5, n4) = all_0_0_0, sum(n5, n4) = n9, yields:
% 30.97/9.96 | (817) all_0_0_0 = n9
% 30.97/9.96 |
% 30.97/9.96 | Equations (817,816) can reduce 201 to:
% 30.97/9.96 | (746) $false
% 30.97/9.96 |
% 30.97/9.96 |-The branch is then unsatisfiable
% 30.97/9.96 |-Branch two:
% 30.97/9.96 | (1442) ~ (all_0_10_10 = n2)
% 30.97/9.96 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 30.97/9.96 |
% 30.97/9.96 +-Applying beta-rule and splitting (1443), into two cases.
% 30.97/9.96 |-Branch one:
% 30.97/9.96 | (1444) all_0_10_10 = n1
% 30.97/9.96 |
% 30.97/9.96 | From (1444) and (57) follows:
% 30.97/9.96 | (1445) pred(n1) = all_0_6_6
% 30.97/9.96 |
% 30.97/9.96 | From (1444) and (381) follows:
% 30.97/9.96 | (1446) succ(n1) = all_0_8_8
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 30.97/9.96 | (1447) all_0_6_6 = n0
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 30.97/9.96 | (1448) all_0_8_8 = n2
% 30.97/9.96 |
% 30.97/9.96 | From (1447)(1448) and (628) follows:
% 30.97/9.96 | (1449) sum(n0, n2) = all_0_1_1
% 30.97/9.96 |
% 30.97/9.96 | From (1447) and (5597) follows:
% 30.97/9.96 | (5806) sum(n0, n14) = all_0_4_4
% 30.97/9.96 |
% 30.97/9.96 | From (1448) and (5599) follows:
% 30.97/9.96 | (5807) sum(n12, n2) = all_0_7_7
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (194) with n12, n2, all_0_7_7, n14 and discharging atoms sum(n12, n2) = all_0_7_7, sum(n12, n2) = n14, yields:
% 30.97/9.96 | (831) all_0_7_7 = n14
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (194) with n0, n14, all_0_4_4, n14 and discharging atoms sum(n0, n14) = all_0_4_4, sum(n0, n14) = n14, yields:
% 30.97/9.96 | (829) all_0_4_4 = n14
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 30.97/9.96 | (1453) all_0_1_1 = n2
% 30.97/9.96 |
% 30.97/9.96 | From (831)(829) and (435) follows:
% 30.97/9.96 | (833) sum(n14, n14) = all_0_3_3
% 30.97/9.96 |
% 30.97/9.96 | From (1453) and (5601) follows:
% 30.97/9.96 | (5812) sum(n5, n2) = all_0_0_0
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 30.97/9.96 | (834) all_0_3_3 = n7
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (194) with n5, n2, all_0_0_0, n7 and discharging atoms sum(n5, n2) = all_0_0_0, sum(n5, n2) = n7, yields:
% 30.97/9.96 | (835) all_0_0_0 = n7
% 30.97/9.96 |
% 30.97/9.96 | Equations (835,834) can reduce 201 to:
% 30.97/9.96 | (746) $false
% 30.97/9.96 |
% 30.97/9.96 |-The branch is then unsatisfiable
% 30.97/9.96 |-Branch two:
% 30.97/9.96 | (1462) ~ (all_0_10_10 = n1)
% 30.97/9.96 | (1463) all_0_10_10 = n0
% 30.97/9.96 |
% 30.97/9.96 | From (1463) and (57) follows:
% 30.97/9.96 | (1464) pred(n0) = all_0_6_6
% 30.97/9.96 |
% 30.97/9.96 | From (1463) and (381) follows:
% 30.97/9.96 | (1465) succ(n0) = all_0_8_8
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 30.97/9.96 | (1466) all_0_6_6 = n20
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 30.97/9.96 | (1467) all_0_8_8 = n1
% 30.97/9.96 |
% 30.97/9.96 | From (1466)(1467) and (628) follows:
% 30.97/9.96 | (1468) sum(n20, n1) = all_0_1_1
% 30.97/9.96 |
% 30.97/9.96 | From (1466) and (5597) follows:
% 30.97/9.96 | (5823) sum(n20, n14) = all_0_4_4
% 30.97/9.96 |
% 30.97/9.96 | From (1467) and (5599) follows:
% 30.97/9.96 | (5824) sum(n12, n1) = all_0_7_7
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (194) with n20, n14, all_0_4_4, n13 and discharging atoms sum(n20, n14) = all_0_4_4, sum(n20, n14) = n13, yields:
% 30.97/9.96 | (847) all_0_4_4 = n13
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 30.97/9.96 | (1471) all_0_1_1 = n0
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (194) with n12, n1, all_0_7_7, n13 and discharging atoms sum(n12, n1) = all_0_7_7, sum(n12, n1) = n13, yields:
% 30.97/9.96 | (849) all_0_7_7 = n13
% 30.97/9.96 |
% 30.97/9.96 | From (849)(847) and (435) follows:
% 30.97/9.96 | (851) sum(n13, n13) = all_0_3_3
% 30.97/9.96 |
% 30.97/9.96 | From (1471) and (5601) follows:
% 30.97/9.96 | (5829) sum(n5, n0) = all_0_0_0
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 30.97/9.96 | (852) all_0_3_3 = n5
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (194) with n5, n0, all_0_0_0, n5 and discharging atoms sum(n5, n0) = all_0_0_0, sum(n5, n0) = n5, yields:
% 30.97/9.96 | (853) all_0_0_0 = n5
% 30.97/9.96 |
% 30.97/9.96 | Equations (853,852) can reduce 201 to:
% 30.97/9.96 | (746) $false
% 30.97/9.96 |
% 30.97/9.96 |-The branch is then unsatisfiable
% 30.97/9.96 |-Branch two:
% 30.97/9.96 | (873) ~ (all_0_11_11 = n13)
% 30.97/9.96 | (874) all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 30.97/9.96 |
% 30.97/9.96 +-Applying beta-rule and splitting (1245), into two cases.
% 30.97/9.96 |-Branch one:
% 30.97/9.96 | (1246) all_0_10_10 = n12
% 30.97/9.96 |
% 30.97/9.96 | From (1246) and (57) follows:
% 30.97/9.96 | (1247) pred(n12) = all_0_6_6
% 30.97/9.96 |
% 30.97/9.96 | From (1246) and (381) follows:
% 30.97/9.96 | (1248) succ(n12) = all_0_8_8
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (259) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 30.97/9.96 | (1249) all_0_6_6 = n11
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (184) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 30.97/9.96 | (1250) all_0_8_8 = n13
% 30.97/9.96 |
% 30.97/9.96 | From (1249) and (1247) follows:
% 30.97/9.96 | (699) pred(n12) = n11
% 30.97/9.96 |
% 30.97/9.96 | From (1250) and (1248) follows:
% 30.97/9.96 | (572) succ(n12) = n13
% 30.97/9.96 |
% 30.97/9.96 | From (1249) and (386) follows:
% 30.97/9.96 | (5842) sum(n11, all_0_5_5) = all_0_4_4
% 30.97/9.96 |
% 30.97/9.96 | From (1249)(1250) and (628) follows:
% 30.97/9.96 | (1251) sum(n11, n13) = all_0_1_1
% 30.97/9.96 |
% 30.97/9.96 | From (1250) and (74) follows:
% 30.97/9.96 | (5844) sum(all_0_9_9, n13) = all_0_7_7
% 30.97/9.96 |
% 30.97/9.96 | Instantiating formula (194) with n11, n13, all_0_1_1, n3 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n3, yields:
% 30.97/9.96 | (1255) all_0_1_1 = n3
% 30.97/9.96 |
% 30.97/9.96 | From (1255) and (85) follows:
% 30.97/9.96 | (5846) sum(all_0_2_2, n3) = all_0_0_0
% 30.97/9.96 |
% 30.97/9.96 | From (1255) and (1251) follows:
% 30.97/9.96 | (666) sum(n11, n13) = n3
% 30.97/9.96 |
% 30.97/9.96 +-Applying beta-rule and splitting (874), into two cases.
% 30.97/9.96 |-Branch one:
% 30.97/9.96 | (875) all_0_11_11 = n12
% 30.97/9.96 |
% 30.97/9.96 | From (875) and (190) follows:
% 30.97/9.96 | (876) pred(n12) = all_0_9_9
% 30.97/9.97 |
% 30.97/9.97 | From (875) and (505) follows:
% 30.97/9.97 | (877) succ(n12) = all_0_5_5
% 30.97/9.97 |
% 30.97/9.97 | Instantiating formula (259) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 30.97/9.97 | (878) all_0_9_9 = n11
% 30.97/9.97 |
% 30.97/9.97 | Instantiating formula (184) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 30.97/9.97 | (879) all_0_5_5 = n13
% 30.97/9.97 |
% 30.97/9.97 | From (878)(879) and (156) follows:
% 30.97/9.97 | (880) sum(n11, n13) = all_0_2_2
% 30.97/9.97 |
% 30.97/9.97 | From (878) and (5844) follows:
% 30.97/9.97 | (5854) sum(n11, n13) = all_0_7_7
% 30.97/9.97 |
% 30.97/9.97 | From (879) and (5842) follows:
% 30.97/9.97 | (5855) sum(n11, n13) = all_0_4_4
% 30.97/9.97 |
% 30.97/9.97 | Instantiating formula (194) with n11, n13, all_0_2_2, n3 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n3, yields:
% 30.97/9.97 | (884) all_0_2_2 = n3
% 30.97/9.97 |
% 30.97/9.97 | Instantiating formula (194) with n11, n13, all_0_4_4, all_0_2_2 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = all_0_4_4, yields:
% 30.97/9.97 | (733) all_0_2_2 = all_0_4_4
% 30.97/9.97 |
% 30.97/9.97 | Instantiating formula (194) with n11, n13, all_0_7_7, all_0_2_2 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = all_0_7_7, yields:
% 30.97/9.97 | (734) all_0_2_2 = all_0_7_7
% 30.97/9.97 |
% 30.97/9.97 | Combining equations (734,733) yields a new equation:
% 30.97/9.97 | (735) all_0_4_4 = all_0_7_7
% 30.97/9.97 |
% 30.97/9.97 | Combining equations (884,733) yields a new equation:
% 30.97/9.97 | (1027) all_0_4_4 = n3
% 30.97/9.97 |
% 30.97/9.97 | Combining equations (1027,735) yields a new equation:
% 30.97/9.97 | (1029) all_0_7_7 = n3
% 30.97/9.97 |
% 30.97/9.97 | Combining equations (1029,735) yields a new equation:
% 30.97/9.97 | (1027) all_0_4_4 = n3
% 30.97/9.97 |
% 30.97/9.97 | Combining equations (1027,733) yields a new equation:
% 30.97/9.97 | (884) all_0_2_2 = n3
% 30.97/9.97 |
% 30.97/9.97 | From (884) and (5846) follows:
% 31.15/9.97 | (5864) sum(n3, n3) = all_0_0_0
% 31.15/9.97 |
% 31.15/9.97 | From (1029)(1027) and (435) follows:
% 31.15/9.97 | (1031) sum(n3, n3) = all_0_3_3
% 31.15/9.97 |
% 31.15/9.97 | Instantiating formula (194) with n3, n3, all_0_0_0, n6 and discharging atoms sum(n3, n3) = all_0_0_0, sum(n3, n3) = n6, yields:
% 31.15/9.97 | (1032) all_0_0_0 = n6
% 31.15/9.97 |
% 31.15/9.97 | Instantiating formula (194) with n3, n3, all_0_3_3, all_0_0_0 and discharging atoms sum(n3, n3) = all_0_0_0, sum(n3, n3) = all_0_3_3, yields:
% 31.15/9.97 | (743) all_0_0_0 = all_0_3_3
% 31.15/9.97 |
% 31.15/9.97 | Combining equations (1032,743) yields a new equation:
% 31.15/9.97 | (1033) all_0_3_3 = n6
% 31.15/9.97 |
% 31.15/9.97 | Combining equations (1033,743) yields a new equation:
% 31.15/9.97 | (1032) all_0_0_0 = n6
% 31.15/9.97 |
% 31.15/9.97 | Equations (1032,1033) can reduce 201 to:
% 31.15/9.97 | (746) $false
% 31.15/9.97 |
% 31.15/9.97 |-The branch is then unsatisfiable
% 31.15/9.97 |-Branch two:
% 31.15/9.97 | (891) ~ (all_0_11_11 = n12)
% 31.15/9.97 | (892) all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.15/9.97 |
% 31.15/9.97 +-Applying beta-rule and splitting (892), into two cases.
% 31.15/9.97 |-Branch one:
% 31.15/9.97 | (893) all_0_11_11 = n11
% 31.15/9.97 |
% 31.15/9.97 | From (893) and (190) follows:
% 31.15/9.97 | (894) pred(n11) = all_0_9_9
% 31.15/9.97 |
% 31.15/9.97 | From (893) and (505) follows:
% 31.15/9.97 | (895) succ(n11) = all_0_5_5
% 31.15/9.97 |
% 31.15/9.97 | Instantiating formula (259) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 31.15/9.97 | (896) all_0_9_9 = n10
% 31.15/9.97 |
% 31.15/9.97 | Instantiating formula (184) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 31.15/9.97 | (897) all_0_5_5 = n12
% 31.15/9.97 |
% 31.15/9.97 | From (896)(897) and (156) follows:
% 31.15/9.97 | (898) sum(n10, n12) = all_0_2_2
% 31.15/9.97 |
% 31.15/9.97 | From (896) and (5844) follows:
% 31.15/9.97 | (5879) sum(n10, n13) = all_0_7_7
% 31.15/9.97 |
% 31.15/9.97 | From (897) and (5842) follows:
% 31.15/9.97 | (5880) sum(n11, n12) = all_0_4_4
% 31.15/9.97 |
% 31.15/9.97 | Instantiating formula (194) with n11, n12, all_0_4_4, n2 and discharging atoms sum(n11, n12) = all_0_4_4, sum(n11, n12) = n2, yields:
% 31.15/9.97 | (1045) all_0_4_4 = n2
% 31.15/9.97 |
% 31.15/9.97 | Instantiating formula (194) with n10, n13, all_0_7_7, n2 and discharging atoms sum(n10, n13) = all_0_7_7, sum(n10, n13) = n2, yields:
% 31.15/9.97 | (1047) all_0_7_7 = n2
% 31.15/9.97 |
% 31.15/9.97 | Instantiating formula (194) with n10, n12, all_0_2_2, n1 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n1, yields:
% 31.15/9.97 | (902) all_0_2_2 = n1
% 31.15/9.97 |
% 31.15/9.97 | From (902) and (5846) follows:
% 31.15/9.97 | (5884) sum(n1, n3) = all_0_0_0
% 31.15/9.97 |
% 31.15/9.97 | From (1047)(1045) and (435) follows:
% 31.15/9.97 | (1049) sum(n2, n2) = all_0_3_3
% 31.15/9.97 |
% 31.15/9.97 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 31.15/9.97 | (1051) all_0_3_3 = n4
% 31.15/9.97 |
% 31.15/9.97 | Instantiating formula (194) with n1, n3, all_0_0_0, n4 and discharging atoms sum(n1, n3) = all_0_0_0, sum(n1, n3) = n4, yields:
% 31.15/9.97 | (1050) all_0_0_0 = n4
% 31.15/9.97 |
% 31.15/9.97 | Equations (1050,1051) can reduce 201 to:
% 31.15/9.97 | (746) $false
% 31.15/9.97 |
% 31.15/9.97 |-The branch is then unsatisfiable
% 31.15/9.97 |-Branch two:
% 31.15/9.97 | (909) ~ (all_0_11_11 = n11)
% 31.15/9.97 | (910) all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.15/9.97 |
% 31.15/9.97 +-Applying beta-rule and splitting (910), into two cases.
% 31.15/9.97 |-Branch one:
% 31.15/9.97 | (911) all_0_11_11 = n10
% 31.15/9.97 |
% 31.15/9.97 | From (911) and (190) follows:
% 31.15/9.97 | (912) pred(n10) = all_0_9_9
% 31.15/9.97 |
% 31.15/9.97 | From (911) and (505) follows:
% 31.15/9.97 | (913) succ(n10) = all_0_5_5
% 31.15/9.97 |
% 31.15/9.97 | Instantiating formula (259) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 31.15/9.97 | (914) all_0_9_9 = n9
% 31.15/9.97 |
% 31.15/9.97 | Instantiating formula (184) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 31.15/9.97 | (915) all_0_5_5 = n11
% 31.15/9.97 |
% 31.15/9.97 | From (914)(915) and (156) follows:
% 31.15/9.97 | (916) sum(n9, n11) = all_0_2_2
% 31.15/9.97 |
% 31.15/9.97 | From (914) and (5844) follows:
% 31.15/9.97 | (5897) sum(n9, n13) = all_0_7_7
% 31.15/9.97 |
% 31.15/9.97 | From (915) and (5842) follows:
% 31.15/9.97 | (5898) sum(n11, n11) = all_0_4_4
% 31.15/9.97 |
% 31.15/9.97 | Instantiating formula (194) with n11, n11, all_0_4_4, n1 and discharging atoms sum(n11, n11) = all_0_4_4, sum(n11, n11) = n1, yields:
% 31.15/9.97 | (1063) all_0_4_4 = n1
% 31.15/9.97 |
% 31.15/9.97 | Instantiating formula (194) with n9, n13, all_0_7_7, n1 and discharging atoms sum(n9, n13) = all_0_7_7, sum(n9, n13) = n1, yields:
% 31.15/9.97 | (1065) all_0_7_7 = n1
% 31.15/9.97 |
% 31.15/9.97 | Instantiating formula (194) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 31.15/9.97 | (920) all_0_2_2 = n20
% 31.15/9.97 |
% 31.15/9.97 | From (920) and (5846) follows:
% 31.16/9.97 | (5902) sum(n20, n3) = all_0_0_0
% 31.16/9.97 |
% 31.16/9.97 | From (1065)(1063) and (435) follows:
% 31.16/9.97 | (1067) sum(n1, n1) = all_0_3_3
% 31.16/9.97 |
% 31.16/9.97 | Instantiating formula (194) with n20, n3, all_0_0_0, n2 and discharging atoms sum(n20, n3) = all_0_0_0, sum(n20, n3) = n2, yields:
% 31.16/9.97 | (1068) all_0_0_0 = n2
% 31.16/9.97 |
% 31.16/9.97 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 31.16/9.97 | (1069) all_0_3_3 = n2
% 31.16/9.97 |
% 31.16/9.97 | Equations (1068,1069) can reduce 201 to:
% 31.16/9.97 | (746) $false
% 31.16/9.97 |
% 31.16/9.97 |-The branch is then unsatisfiable
% 31.16/9.97 |-Branch two:
% 31.16/9.97 | (927) ~ (all_0_11_11 = n10)
% 31.16/9.97 | (928) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.16/9.97 |
% 31.16/9.97 +-Applying beta-rule and splitting (928), into two cases.
% 31.16/9.97 |-Branch one:
% 31.16/9.97 | (929) all_0_11_11 = n9
% 31.16/9.97 |
% 31.16/9.97 | From (929) and (190) follows:
% 31.16/9.97 | (930) pred(n9) = all_0_9_9
% 31.16/9.97 |
% 31.16/9.97 | From (929) and (505) follows:
% 31.16/9.97 | (931) succ(n9) = all_0_5_5
% 31.16/9.97 |
% 31.16/9.97 | Instantiating formula (259) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 31.16/9.97 | (932) all_0_9_9 = n8
% 31.16/9.97 |
% 31.16/9.97 | Instantiating formula (184) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 31.16/9.97 | (933) all_0_5_5 = n10
% 31.16/9.97 |
% 31.16/9.97 | From (932)(933) and (156) follows:
% 31.16/9.97 | (934) sum(n8, n10) = all_0_2_2
% 31.16/9.97 |
% 31.16/9.97 | From (932) and (5844) follows:
% 31.16/9.97 | (5915) sum(n8, n13) = all_0_7_7
% 31.16/9.97 |
% 31.16/9.97 | From (933) and (5842) follows:
% 31.16/9.98 | (5916) sum(n11, n10) = all_0_4_4
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n11, n10, all_0_4_4, n0 and discharging atoms sum(n11, n10) = all_0_4_4, sum(n11, n10) = n0, yields:
% 31.16/9.98 | (1081) all_0_4_4 = n0
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n8, n13, all_0_7_7, n0 and discharging atoms sum(n8, n13) = all_0_7_7, sum(n8, n13) = n0, yields:
% 31.16/9.98 | (1083) all_0_7_7 = n0
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 31.16/9.98 | (938) all_0_2_2 = n18
% 31.16/9.98 |
% 31.16/9.98 | From (938) and (5846) follows:
% 31.16/9.98 | (5920) sum(n18, n3) = all_0_0_0
% 31.16/9.98 |
% 31.16/9.98 | From (1083)(1081) and (435) follows:
% 31.16/9.98 | (1085) sum(n0, n0) = all_0_3_3
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n18, n3, all_0_0_0, n0 and discharging atoms sum(n18, n3) = all_0_0_0, sum(n18, n3) = n0, yields:
% 31.16/9.98 | (1087) all_0_0_0 = n0
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 31.16/9.98 | (1088) all_0_3_3 = n0
% 31.16/9.98 |
% 31.16/9.98 | Equations (1087,1088) can reduce 201 to:
% 31.16/9.98 | (746) $false
% 31.16/9.98 |
% 31.16/9.98 |-The branch is then unsatisfiable
% 31.16/9.98 |-Branch two:
% 31.16/9.98 | (945) ~ (all_0_11_11 = n9)
% 31.16/9.98 | (946) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.16/9.98 |
% 31.16/9.98 +-Applying beta-rule and splitting (946), into two cases.
% 31.16/9.98 |-Branch one:
% 31.16/9.98 | (947) all_0_11_11 = n8
% 31.16/9.98 |
% 31.16/9.98 | From (947) and (190) follows:
% 31.16/9.98 | (948) pred(n8) = all_0_9_9
% 31.16/9.98 |
% 31.16/9.98 | From (947) and (505) follows:
% 31.16/9.98 | (949) succ(n8) = all_0_5_5
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (259) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 31.16/9.98 | (950) all_0_9_9 = n7
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (184) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 31.16/9.98 | (951) all_0_5_5 = n9
% 31.16/9.98 |
% 31.16/9.98 | From (950)(951) and (156) follows:
% 31.16/9.98 | (952) sum(n7, n9) = all_0_2_2
% 31.16/9.98 |
% 31.16/9.98 | From (950) and (5844) follows:
% 31.16/9.98 | (5933) sum(n7, n13) = all_0_7_7
% 31.16/9.98 |
% 31.16/9.98 | From (951) and (5842) follows:
% 31.16/9.98 | (5934) sum(n11, n9) = all_0_4_4
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n11, n9, all_0_4_4, n20 and discharging atoms sum(n11, n9) = all_0_4_4, sum(n11, n9) = n20, yields:
% 31.16/9.98 | (1101) all_0_4_4 = n20
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n7, n13, all_0_7_7, n20 and discharging atoms sum(n7, n13) = all_0_7_7, sum(n7, n13) = n20, yields:
% 31.16/9.98 | (1100) all_0_7_7 = n20
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 31.16/9.98 | (956) all_0_2_2 = n16
% 31.16/9.98 |
% 31.16/9.98 | From (956) and (5846) follows:
% 31.16/9.98 | (5938) sum(n16, n3) = all_0_0_0
% 31.16/9.98 |
% 31.16/9.98 | From (1100)(1101) and (435) follows:
% 31.16/9.98 | (1103) sum(n20, n20) = all_0_3_3
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 31.16/9.98 | (1104) all_0_3_3 = n19
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n16, n3, all_0_0_0, n19 and discharging atoms sum(n16, n3) = all_0_0_0, sum(n16, n3) = n19, yields:
% 31.16/9.98 | (1105) all_0_0_0 = n19
% 31.16/9.98 |
% 31.16/9.98 | Equations (1105,1104) can reduce 201 to:
% 31.16/9.98 | (746) $false
% 31.16/9.98 |
% 31.16/9.98 |-The branch is then unsatisfiable
% 31.16/9.98 |-Branch two:
% 31.16/9.98 | (963) ~ (all_0_11_11 = n8)
% 31.16/9.98 | (964) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.16/9.98 |
% 31.16/9.98 +-Applying beta-rule and splitting (964), into two cases.
% 31.16/9.98 |-Branch one:
% 31.16/9.98 | (965) all_0_11_11 = n7
% 31.16/9.98 |
% 31.16/9.98 | From (965) and (190) follows:
% 31.16/9.98 | (966) pred(n7) = all_0_9_9
% 31.16/9.98 |
% 31.16/9.98 | From (965) and (505) follows:
% 31.16/9.98 | (967) succ(n7) = all_0_5_5
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (259) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 31.16/9.98 | (968) all_0_9_9 = n6
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (184) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 31.16/9.98 | (969) all_0_5_5 = n8
% 31.16/9.98 |
% 31.16/9.98 | From (968)(969) and (156) follows:
% 31.16/9.98 | (970) sum(n6, n8) = all_0_2_2
% 31.16/9.98 |
% 31.16/9.98 | From (968) and (5844) follows:
% 31.16/9.98 | (5951) sum(n6, n13) = all_0_7_7
% 31.16/9.98 |
% 31.16/9.98 | From (969) and (5842) follows:
% 31.16/9.98 | (5952) sum(n11, n8) = all_0_4_4
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n11, n8, all_0_4_4, n19 and discharging atoms sum(n11, n8) = all_0_4_4, sum(n11, n8) = n19, yields:
% 31.16/9.98 | (736) all_0_4_4 = n19
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n6, n13, all_0_7_7, n19 and discharging atoms sum(n6, n13) = all_0_7_7, sum(n6, n13) = n19, yields:
% 31.16/9.98 | (737) all_0_7_7 = n19
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 31.16/9.98 | (974) all_0_2_2 = n14
% 31.16/9.98 |
% 31.16/9.98 | From (974) and (5846) follows:
% 31.16/9.98 | (5956) sum(n14, n3) = all_0_0_0
% 31.16/9.98 |
% 31.16/9.98 | From (737)(736) and (435) follows:
% 31.16/9.98 | (741) sum(n19, n19) = all_0_3_3
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 31.16/9.98 | (744) all_0_3_3 = n17
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n14, n3, all_0_0_0, n17 and discharging atoms sum(n14, n3) = all_0_0_0, sum(n14, n3) = n17, yields:
% 31.16/9.98 | (742) all_0_0_0 = n17
% 31.16/9.98 |
% 31.16/9.98 | Equations (742,744) can reduce 201 to:
% 31.16/9.98 | (746) $false
% 31.16/9.98 |
% 31.16/9.98 |-The branch is then unsatisfiable
% 31.16/9.98 |-Branch two:
% 31.16/9.98 | (981) ~ (all_0_11_11 = n7)
% 31.16/9.98 | (982) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.16/9.98 |
% 31.16/9.98 +-Applying beta-rule and splitting (982), into two cases.
% 31.16/9.98 |-Branch one:
% 31.16/9.98 | (983) all_0_11_11 = n6
% 31.16/9.98 |
% 31.16/9.98 | From (983) and (190) follows:
% 31.16/9.98 | (984) pred(n6) = all_0_9_9
% 31.16/9.98 |
% 31.16/9.98 | From (983) and (505) follows:
% 31.16/9.98 | (985) succ(n6) = all_0_5_5
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (259) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 31.16/9.98 | (986) all_0_9_9 = n5
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (184) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 31.16/9.98 | (987) all_0_5_5 = n7
% 31.16/9.98 |
% 31.16/9.98 | From (986)(987) and (156) follows:
% 31.16/9.98 | (988) sum(n5, n7) = all_0_2_2
% 31.16/9.98 |
% 31.16/9.98 | From (986) and (5844) follows:
% 31.16/9.98 | (5969) sum(n5, n13) = all_0_7_7
% 31.16/9.98 |
% 31.16/9.98 | From (987) and (5842) follows:
% 31.16/9.98 | (5970) sum(n11, n7) = all_0_4_4
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n11, n7, all_0_4_4, n18 and discharging atoms sum(n11, n7) = all_0_4_4, sum(n11, n7) = n18, yields:
% 31.16/9.98 | (757) all_0_4_4 = n18
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n5, n13, all_0_7_7, n18 and discharging atoms sum(n5, n13) = all_0_7_7, sum(n5, n13) = n18, yields:
% 31.16/9.98 | (759) all_0_7_7 = n18
% 31.16/9.98 |
% 31.16/9.98 | Instantiating formula (194) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 31.16/9.98 | (992) all_0_2_2 = n12
% 31.16/9.98 |
% 31.16/9.98 | From (992) and (5846) follows:
% 31.16/9.99 | (5974) sum(n12, n3) = all_0_0_0
% 31.16/9.99 |
% 31.16/9.99 | From (759)(757) and (435) follows:
% 31.16/9.99 | (761) sum(n18, n18) = all_0_3_3
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 31.16/9.99 | (762) all_0_3_3 = n15
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (194) with n12, n3, all_0_0_0, n15 and discharging atoms sum(n12, n3) = all_0_0_0, sum(n12, n3) = n15, yields:
% 31.16/9.99 | (763) all_0_0_0 = n15
% 31.16/9.99 |
% 31.16/9.99 | Equations (763,762) can reduce 201 to:
% 31.16/9.99 | (746) $false
% 31.16/9.99 |
% 31.16/9.99 |-The branch is then unsatisfiable
% 31.16/9.99 |-Branch two:
% 31.16/9.99 | (999) ~ (all_0_11_11 = n6)
% 31.16/9.99 | (1000) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.16/9.99 |
% 31.16/9.99 +-Applying beta-rule and splitting (1000), into two cases.
% 31.16/9.99 |-Branch one:
% 31.16/9.99 | (1001) all_0_11_11 = n5
% 31.16/9.99 |
% 31.16/9.99 | From (1001) and (190) follows:
% 31.16/9.99 | (1002) pred(n5) = all_0_9_9
% 31.16/9.99 |
% 31.16/9.99 | From (1001) and (505) follows:
% 31.16/9.99 | (1003) succ(n5) = all_0_5_5
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (259) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 31.16/9.99 | (1004) all_0_9_9 = n4
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (184) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 31.16/9.99 | (1005) all_0_5_5 = n6
% 31.16/9.99 |
% 31.16/9.99 | From (1004)(1005) and (156) follows:
% 31.16/9.99 | (1006) sum(n4, n6) = all_0_2_2
% 31.16/9.99 |
% 31.16/9.99 | From (1004) and (5844) follows:
% 31.16/9.99 | (5987) sum(n4, n13) = all_0_7_7
% 31.16/9.99 |
% 31.16/9.99 | From (1005) and (5842) follows:
% 31.16/9.99 | (5988) sum(n11, n6) = all_0_4_4
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (194) with n11, n6, all_0_4_4, n17 and discharging atoms sum(n11, n6) = all_0_4_4, sum(n11, n6) = n17, yields:
% 31.16/9.99 | (775) all_0_4_4 = n17
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (194) with n4, n13, all_0_7_7, n17 and discharging atoms sum(n4, n13) = all_0_7_7, sum(n4, n13) = n17, yields:
% 31.16/9.99 | (777) all_0_7_7 = n17
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (194) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 31.16/9.99 | (1010) all_0_2_2 = n10
% 31.16/9.99 |
% 31.16/9.99 | From (1010) and (5846) follows:
% 31.16/9.99 | (5992) sum(n10, n3) = all_0_0_0
% 31.16/9.99 |
% 31.16/9.99 | From (777)(775) and (435) follows:
% 31.16/9.99 | (779) sum(n17, n17) = all_0_3_3
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 31.16/9.99 | (780) all_0_3_3 = n13
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (194) with n10, n3, all_0_0_0, n13 and discharging atoms sum(n10, n3) = all_0_0_0, sum(n10, n3) = n13, yields:
% 31.16/9.99 | (781) all_0_0_0 = n13
% 31.16/9.99 |
% 31.16/9.99 | Equations (781,780) can reduce 201 to:
% 31.16/9.99 | (746) $false
% 31.16/9.99 |
% 31.16/9.99 |-The branch is then unsatisfiable
% 31.16/9.99 |-Branch two:
% 31.16/9.99 | (1017) ~ (all_0_11_11 = n5)
% 31.16/9.99 | (1018) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.16/9.99 |
% 31.16/9.99 +-Applying beta-rule and splitting (1018), into two cases.
% 31.16/9.99 |-Branch one:
% 31.16/9.99 | (1019) all_0_11_11 = n4
% 31.16/9.99 |
% 31.16/9.99 | From (1019) and (190) follows:
% 31.16/9.99 | (1020) pred(n4) = all_0_9_9
% 31.16/9.99 |
% 31.16/9.99 | From (1019) and (505) follows:
% 31.16/9.99 | (1021) succ(n4) = all_0_5_5
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 31.16/9.99 | (1022) all_0_9_9 = n3
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 31.16/9.99 | (1023) all_0_5_5 = n5
% 31.16/9.99 |
% 31.16/9.99 | From (1022)(1023) and (156) follows:
% 31.16/9.99 | (1024) sum(n3, n5) = all_0_2_2
% 31.16/9.99 |
% 31.16/9.99 | From (1022) and (5844) follows:
% 31.16/9.99 | (6005) sum(n3, n13) = all_0_7_7
% 31.16/9.99 |
% 31.16/9.99 | From (1023) and (5842) follows:
% 31.16/9.99 | (6006) sum(n11, n5) = all_0_4_4
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (194) with n11, n5, all_0_4_4, n16 and discharging atoms sum(n11, n5) = all_0_4_4, sum(n11, n5) = n16, yields:
% 31.16/9.99 | (793) all_0_4_4 = n16
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (194) with n3, n13, all_0_7_7, n16 and discharging atoms sum(n3, n13) = all_0_7_7, sum(n3, n13) = n16, yields:
% 31.16/9.99 | (795) all_0_7_7 = n16
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 31.16/9.99 | (1028) all_0_2_2 = n8
% 31.16/9.99 |
% 31.16/9.99 | From (1028) and (5846) follows:
% 31.16/9.99 | (6010) sum(n8, n3) = all_0_0_0
% 31.16/9.99 |
% 31.16/9.99 | From (795)(793) and (435) follows:
% 31.16/9.99 | (797) sum(n16, n16) = all_0_3_3
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 31.16/9.99 | (798) all_0_3_3 = n11
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (194) with n8, n3, all_0_0_0, n11 and discharging atoms sum(n8, n3) = all_0_0_0, sum(n8, n3) = n11, yields:
% 31.16/9.99 | (799) all_0_0_0 = n11
% 31.16/9.99 |
% 31.16/9.99 | Equations (799,798) can reduce 201 to:
% 31.16/9.99 | (746) $false
% 31.16/9.99 |
% 31.16/9.99 |-The branch is then unsatisfiable
% 31.16/9.99 |-Branch two:
% 31.16/9.99 | (1035) ~ (all_0_11_11 = n4)
% 31.16/9.99 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.16/9.99 |
% 31.16/9.99 +-Applying beta-rule and splitting (1036), into two cases.
% 31.16/9.99 |-Branch one:
% 31.16/9.99 | (1037) all_0_11_11 = n3
% 31.16/9.99 |
% 31.16/9.99 | From (1037) and (190) follows:
% 31.16/9.99 | (1038) pred(n3) = all_0_9_9
% 31.16/9.99 |
% 31.16/9.99 | From (1037) and (505) follows:
% 31.16/9.99 | (1039) succ(n3) = all_0_5_5
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 31.16/9.99 | (1040) all_0_9_9 = n2
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 31.16/9.99 | (1041) all_0_5_5 = n4
% 31.16/9.99 |
% 31.16/9.99 | From (1040)(1041) and (156) follows:
% 31.16/9.99 | (1042) sum(n2, n4) = all_0_2_2
% 31.16/9.99 |
% 31.16/9.99 | From (1040) and (5844) follows:
% 31.16/9.99 | (6023) sum(n2, n13) = all_0_7_7
% 31.16/9.99 |
% 31.16/9.99 | From (1041) and (5842) follows:
% 31.16/9.99 | (6024) sum(n11, n4) = all_0_4_4
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (194) with n11, n4, all_0_4_4, n15 and discharging atoms sum(n11, n4) = all_0_4_4, sum(n11, n4) = n15, yields:
% 31.16/9.99 | (811) all_0_4_4 = n15
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (194) with n2, n13, all_0_7_7, n15 and discharging atoms sum(n2, n13) = all_0_7_7, sum(n2, n13) = n15, yields:
% 31.16/9.99 | (813) all_0_7_7 = n15
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 31.16/9.99 | (1046) all_0_2_2 = n6
% 31.16/9.99 |
% 31.16/9.99 | From (1046) and (5846) follows:
% 31.16/9.99 | (6028) sum(n6, n3) = all_0_0_0
% 31.16/9.99 |
% 31.16/9.99 | From (813)(811) and (435) follows:
% 31.16/9.99 | (815) sum(n15, n15) = all_0_3_3
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 31.16/9.99 | (816) all_0_3_3 = n9
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (194) with n6, n3, all_0_0_0, n9 and discharging atoms sum(n6, n3) = all_0_0_0, sum(n6, n3) = n9, yields:
% 31.16/9.99 | (817) all_0_0_0 = n9
% 31.16/9.99 |
% 31.16/9.99 | Equations (817,816) can reduce 201 to:
% 31.16/9.99 | (746) $false
% 31.16/9.99 |
% 31.16/9.99 |-The branch is then unsatisfiable
% 31.16/9.99 |-Branch two:
% 31.16/9.99 | (1053) ~ (all_0_11_11 = n3)
% 31.16/9.99 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.16/9.99 |
% 31.16/9.99 +-Applying beta-rule and splitting (1054), into two cases.
% 31.16/9.99 |-Branch one:
% 31.16/9.99 | (1055) all_0_11_11 = n2
% 31.16/9.99 |
% 31.16/9.99 | From (1055) and (190) follows:
% 31.16/9.99 | (1056) pred(n2) = all_0_9_9
% 31.16/9.99 |
% 31.16/9.99 | From (1055) and (505) follows:
% 31.16/9.99 | (1057) succ(n2) = all_0_5_5
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 31.16/9.99 | (1058) all_0_9_9 = n1
% 31.16/9.99 |
% 31.16/9.99 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.16/9.99 | (1059) all_0_5_5 = n3
% 31.16/9.99 |
% 31.16/9.99 | From (1058)(1059) and (156) follows:
% 31.16/9.99 | (1060) sum(n1, n3) = all_0_2_2
% 31.16/9.99 |
% 31.16/9.99 | From (1058) and (5844) follows:
% 31.16/10.00 | (6041) sum(n1, n13) = all_0_7_7
% 31.16/10.00 |
% 31.16/10.00 | From (1059) and (5842) follows:
% 31.16/10.00 | (6042) sum(n11, n3) = all_0_4_4
% 31.16/10.00 |
% 31.16/10.00 | Instantiating formula (194) with n11, n3, all_0_4_4, n14 and discharging atoms sum(n11, n3) = all_0_4_4, sum(n11, n3) = n14, yields:
% 31.16/10.00 | (829) all_0_4_4 = n14
% 31.16/10.00 |
% 31.16/10.00 | Instantiating formula (194) with n1, n13, all_0_7_7, n14 and discharging atoms sum(n1, n13) = all_0_7_7, sum(n1, n13) = n14, yields:
% 31.16/10.00 | (831) all_0_7_7 = n14
% 31.16/10.00 |
% 31.16/10.00 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 31.16/10.00 | (1064) all_0_2_2 = n4
% 31.16/10.00 |
% 31.16/10.00 | From (1064) and (5846) follows:
% 31.16/10.00 | (6046) sum(n4, n3) = all_0_0_0
% 31.16/10.00 |
% 31.16/10.00 | From (831)(829) and (435) follows:
% 31.16/10.00 | (833) sum(n14, n14) = all_0_3_3
% 31.16/10.00 |
% 31.16/10.00 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 31.16/10.00 | (834) all_0_3_3 = n7
% 31.16/10.00 |
% 31.16/10.00 | Instantiating formula (194) with n4, n3, all_0_0_0, n7 and discharging atoms sum(n4, n3) = all_0_0_0, sum(n4, n3) = n7, yields:
% 31.16/10.00 | (835) all_0_0_0 = n7
% 31.16/10.00 |
% 31.16/10.00 | Equations (835,834) can reduce 201 to:
% 31.16/10.00 | (746) $false
% 31.16/10.00 |
% 31.16/10.00 |-The branch is then unsatisfiable
% 31.16/10.00 |-Branch two:
% 31.16/10.00 | (1071) ~ (all_0_11_11 = n2)
% 31.16/10.00 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 31.16/10.00 |
% 31.16/10.00 +-Applying beta-rule and splitting (1072), into two cases.
% 31.16/10.00 |-Branch one:
% 31.16/10.00 | (1073) all_0_11_11 = n1
% 31.16/10.00 |
% 31.16/10.00 | From (1073) and (190) follows:
% 31.16/10.00 | (1074) pred(n1) = all_0_9_9
% 31.16/10.00 |
% 31.16/10.00 | From (1073) and (505) follows:
% 31.16/10.00 | (1075) succ(n1) = all_0_5_5
% 31.16/10.00 |
% 31.16/10.00 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 31.16/10.00 | (1076) all_0_9_9 = n0
% 31.16/10.00 |
% 31.16/10.00 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.16/10.00 | (1077) all_0_5_5 = n2
% 31.16/10.00 |
% 31.16/10.00 | From (1076)(1077) and (156) follows:
% 31.16/10.00 | (1078) sum(n0, n2) = all_0_2_2
% 31.16/10.00 |
% 31.16/10.00 | From (1076) and (5844) follows:
% 31.16/10.00 | (6059) sum(n0, n13) = all_0_7_7
% 31.16/10.00 |
% 31.16/10.00 | From (1077) and (5842) follows:
% 31.16/10.00 | (6060) sum(n11, n2) = all_0_4_4
% 31.16/10.00 |
% 31.16/10.00 | Instantiating formula (194) with n11, n2, all_0_4_4, n13 and discharging atoms sum(n11, n2) = all_0_4_4, sum(n11, n2) = n13, yields:
% 31.16/10.00 | (847) all_0_4_4 = n13
% 31.16/10.00 |
% 31.16/10.00 | Instantiating formula (194) with n0, n13, all_0_7_7, n13 and discharging atoms sum(n0, n13) = all_0_7_7, sum(n0, n13) = n13, yields:
% 31.16/10.00 | (849) all_0_7_7 = n13
% 31.16/10.00 |
% 31.16/10.00 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 31.16/10.00 | (1082) all_0_2_2 = n2
% 31.16/10.00 |
% 31.16/10.00 | From (1082) and (5846) follows:
% 31.16/10.00 | (6064) sum(n2, n3) = all_0_0_0
% 31.16/10.00 |
% 31.16/10.00 | From (849)(847) and (435) follows:
% 31.16/10.00 | (851) sum(n13, n13) = all_0_3_3
% 31.16/10.00 |
% 31.16/10.00 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 31.16/10.00 | (852) all_0_3_3 = n5
% 31.16/10.00 |
% 31.16/10.00 | Instantiating formula (194) with n2, n3, all_0_0_0, n5 and discharging atoms sum(n2, n3) = all_0_0_0, sum(n2, n3) = n5, yields:
% 31.16/10.00 | (853) all_0_0_0 = n5
% 31.16/10.00 |
% 31.16/10.00 | Equations (853,852) can reduce 201 to:
% 31.16/10.00 | (746) $false
% 31.16/10.00 |
% 31.16/10.00 |-The branch is then unsatisfiable
% 31.16/10.00 |-Branch two:
% 31.16/10.00 | (1090) ~ (all_0_11_11 = n1)
% 31.16/10.00 | (1091) all_0_11_11 = n0
% 31.16/10.00 |
% 31.16/10.00 | From (1091) and (190) follows:
% 31.16/10.00 | (1092) pred(n0) = all_0_9_9
% 31.16/10.00 |
% 31.16/10.00 | From (1091) and (505) follows:
% 31.16/10.00 | (1093) succ(n0) = all_0_5_5
% 31.16/10.00 |
% 31.16/10.00 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 31.16/10.00 | (1094) all_0_9_9 = n20
% 31.16/10.00 |
% 31.16/10.00 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.16/10.00 | (1095) all_0_5_5 = n1
% 31.16/10.00 |
% 31.16/10.00 | From (1094)(1095) and (156) follows:
% 31.16/10.00 | (1096) sum(n20, n1) = all_0_2_2
% 31.16/10.00 |
% 31.16/10.00 | From (1094) and (5844) follows:
% 31.16/10.00 | (6076) sum(n20, n13) = all_0_7_7
% 31.16/10.00 |
% 31.16/10.00 | From (1095) and (5842) follows:
% 31.24/10.00 | (6077) sum(n11, n1) = all_0_4_4
% 31.24/10.00 |
% 31.24/10.00 | Instantiating formula (194) with n20, n13, all_0_7_7, n12 and discharging atoms sum(n20, n13) = all_0_7_7, sum(n20, n13) = n12, yields:
% 31.24/10.00 | (867) all_0_7_7 = n12
% 31.24/10.00 |
% 31.24/10.00 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 31.24/10.00 | (1099) all_0_2_2 = n0
% 31.24/10.00 |
% 31.24/10.00 | Instantiating formula (194) with n11, n1, all_0_4_4, n12 and discharging atoms sum(n11, n1) = all_0_4_4, sum(n11, n1) = n12, yields:
% 31.24/10.00 | (865) all_0_4_4 = n12
% 31.24/10.00 |
% 31.24/10.00 | From (1099) and (5846) follows:
% 31.24/10.00 | (6081) sum(n0, n3) = all_0_0_0
% 31.24/10.00 |
% 31.24/10.00 | From (867)(865) and (435) follows:
% 31.24/10.00 | (869) sum(n12, n12) = all_0_3_3
% 31.24/10.00 |
% 31.24/10.00 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 31.24/10.00 | (870) all_0_3_3 = n3
% 31.24/10.00 |
% 31.24/10.00 | Instantiating formula (194) with n0, n3, all_0_0_0, n3 and discharging atoms sum(n0, n3) = all_0_0_0, sum(n0, n3) = n3, yields:
% 31.24/10.00 | (871) all_0_0_0 = n3
% 31.24/10.00 |
% 31.24/10.00 | Equations (871,870) can reduce 201 to:
% 31.24/10.00 | (746) $false
% 31.24/10.00 |
% 31.24/10.00 |-The branch is then unsatisfiable
% 31.24/10.00 |-Branch two:
% 31.24/10.00 | (1262) ~ (all_0_10_10 = n12)
% 31.24/10.00 | (1263) all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.24/10.00 |
% 31.24/10.00 +-Applying beta-rule and splitting (874), into two cases.
% 31.24/10.00 |-Branch one:
% 31.24/10.00 | (875) all_0_11_11 = n12
% 31.24/10.00 |
% 31.24/10.00 | From (875) and (190) follows:
% 31.24/10.00 | (876) pred(n12) = all_0_9_9
% 31.24/10.00 |
% 31.24/10.00 | From (875) and (505) follows:
% 31.24/10.00 | (877) succ(n12) = all_0_5_5
% 31.24/10.00 |
% 31.24/10.00 | Instantiating formula (259) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 31.24/10.00 | (878) all_0_9_9 = n11
% 31.24/10.00 |
% 31.24/10.00 | Instantiating formula (184) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 31.24/10.00 | (879) all_0_5_5 = n13
% 31.24/10.00 |
% 31.24/10.00 | From (879) and (386) follows:
% 31.24/10.00 | (6093) sum(all_0_6_6, n13) = all_0_4_4
% 31.24/10.00 |
% 31.24/10.00 | From (878)(879) and (156) follows:
% 31.24/10.00 | (880) sum(n11, n13) = all_0_2_2
% 31.24/10.00 |
% 31.24/10.00 | From (878) and (74) follows:
% 31.24/10.00 | (6095) sum(n11, all_0_8_8) = all_0_7_7
% 31.24/10.00 |
% 31.24/10.00 | Instantiating formula (194) with n11, n13, all_0_2_2, n3 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n3, yields:
% 31.24/10.00 | (884) all_0_2_2 = n3
% 31.24/10.00 |
% 31.24/10.00 | From (884) and (85) follows:
% 31.24/10.00 | (6097) sum(n3, all_0_1_1) = all_0_0_0
% 31.24/10.00 |
% 31.24/10.00 +-Applying beta-rule and splitting (1263), into two cases.
% 31.24/10.00 |-Branch one:
% 31.24/10.00 | (1264) all_0_10_10 = n11
% 31.24/10.01 |
% 31.24/10.01 | From (1264) and (57) follows:
% 31.24/10.01 | (1265) pred(n11) = all_0_6_6
% 31.24/10.01 |
% 31.24/10.01 | From (1264) and (381) follows:
% 31.24/10.01 | (1266) succ(n11) = all_0_8_8
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (259) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 31.24/10.01 | (1267) all_0_6_6 = n10
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (184) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 31.24/10.01 | (1268) all_0_8_8 = n12
% 31.24/10.01 |
% 31.24/10.01 | From (1267)(1268) and (628) follows:
% 31.24/10.01 | (1269) sum(n10, n12) = all_0_1_1
% 31.24/10.01 |
% 31.24/10.01 | From (1267) and (6093) follows:
% 31.24/10.01 | (6104) sum(n10, n13) = all_0_4_4
% 31.24/10.01 |
% 31.24/10.01 | From (1268) and (6095) follows:
% 31.24/10.01 | (6105) sum(n11, n12) = all_0_7_7
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (194) with n11, n12, all_0_7_7, n2 and discharging atoms sum(n11, n12) = all_0_7_7, sum(n11, n12) = n2, yields:
% 31.24/10.01 | (1047) all_0_7_7 = n2
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (194) with n10, n13, all_0_4_4, n2 and discharging atoms sum(n10, n13) = all_0_4_4, sum(n10, n13) = n2, yields:
% 31.24/10.01 | (1045) all_0_4_4 = n2
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (194) with n10, n12, all_0_1_1, n1 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n1, yields:
% 31.24/10.01 | (1273) all_0_1_1 = n1
% 31.24/10.01 |
% 31.24/10.01 | From (1047)(1045) and (435) follows:
% 31.24/10.01 | (1049) sum(n2, n2) = all_0_3_3
% 31.24/10.01 |
% 31.24/10.01 | From (1273) and (6097) follows:
% 31.24/10.01 | (6110) sum(n3, n1) = all_0_0_0
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (194) with n3, n1, all_0_0_0, n4 and discharging atoms sum(n3, n1) = all_0_0_0, sum(n3, n1) = n4, yields:
% 31.24/10.01 | (1050) all_0_0_0 = n4
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 31.24/10.01 | (1051) all_0_3_3 = n4
% 31.24/10.01 |
% 31.24/10.01 | Equations (1050,1051) can reduce 201 to:
% 31.24/10.01 | (746) $false
% 31.24/10.01 |
% 31.24/10.01 |-The branch is then unsatisfiable
% 31.24/10.01 |-Branch two:
% 31.24/10.01 | (1280) ~ (all_0_10_10 = n11)
% 31.24/10.01 | (1281) all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.24/10.01 |
% 31.24/10.01 +-Applying beta-rule and splitting (1281), into two cases.
% 31.24/10.01 |-Branch one:
% 31.24/10.01 | (1282) all_0_10_10 = n10
% 31.24/10.01 |
% 31.24/10.01 | From (1282) and (57) follows:
% 31.24/10.01 | (1283) pred(n10) = all_0_6_6
% 31.24/10.01 |
% 31.24/10.01 | From (1282) and (381) follows:
% 31.24/10.01 | (1284) succ(n10) = all_0_8_8
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (259) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 31.24/10.01 | (1285) all_0_6_6 = n9
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (184) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 31.24/10.01 | (1286) all_0_8_8 = n11
% 31.24/10.01 |
% 31.24/10.01 | From (1285)(1286) and (628) follows:
% 31.24/10.01 | (1287) sum(n9, n11) = all_0_1_1
% 31.24/10.01 |
% 31.24/10.01 | From (1285) and (6093) follows:
% 31.24/10.01 | (6122) sum(n9, n13) = all_0_4_4
% 31.24/10.01 |
% 31.24/10.01 | From (1286) and (6095) follows:
% 31.24/10.01 | (6123) sum(n11, n11) = all_0_7_7
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (194) with n11, n11, all_0_7_7, n1 and discharging atoms sum(n11, n11) = all_0_7_7, sum(n11, n11) = n1, yields:
% 31.24/10.01 | (1065) all_0_7_7 = n1
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (194) with n9, n13, all_0_4_4, n1 and discharging atoms sum(n9, n13) = all_0_4_4, sum(n9, n13) = n1, yields:
% 31.24/10.01 | (1063) all_0_4_4 = n1
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (194) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 31.24/10.01 | (1291) all_0_1_1 = n20
% 31.24/10.01 |
% 31.24/10.01 | From (1065)(1063) and (435) follows:
% 31.24/10.01 | (1067) sum(n1, n1) = all_0_3_3
% 31.24/10.01 |
% 31.24/10.01 | From (1291) and (6097) follows:
% 31.24/10.01 | (6128) sum(n3, n20) = all_0_0_0
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (194) with n3, n20, all_0_0_0, n2 and discharging atoms sum(n3, n20) = all_0_0_0, sum(n3, n20) = n2, yields:
% 31.24/10.01 | (1068) all_0_0_0 = n2
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 31.24/10.01 | (1069) all_0_3_3 = n2
% 31.24/10.01 |
% 31.24/10.01 | Equations (1068,1069) can reduce 201 to:
% 31.24/10.01 | (746) $false
% 31.24/10.01 |
% 31.24/10.01 |-The branch is then unsatisfiable
% 31.24/10.01 |-Branch two:
% 31.24/10.01 | (1298) ~ (all_0_10_10 = n10)
% 31.24/10.01 | (1299) all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.24/10.01 |
% 31.24/10.01 +-Applying beta-rule and splitting (1299), into two cases.
% 31.24/10.01 |-Branch one:
% 31.24/10.01 | (1300) all_0_10_10 = n9
% 31.24/10.01 |
% 31.24/10.01 | From (1300) and (57) follows:
% 31.24/10.01 | (1301) pred(n9) = all_0_6_6
% 31.24/10.01 |
% 31.24/10.01 | From (1300) and (381) follows:
% 31.24/10.01 | (1302) succ(n9) = all_0_8_8
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (259) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 31.24/10.01 | (1303) all_0_6_6 = n8
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (184) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 31.24/10.01 | (1304) all_0_8_8 = n10
% 31.24/10.01 |
% 31.24/10.01 | From (1303)(1304) and (628) follows:
% 31.24/10.01 | (1305) sum(n8, n10) = all_0_1_1
% 31.24/10.01 |
% 31.24/10.01 | From (1303) and (6093) follows:
% 31.24/10.01 | (6140) sum(n8, n13) = all_0_4_4
% 31.24/10.01 |
% 31.24/10.01 | From (1304) and (6095) follows:
% 31.24/10.01 | (6141) sum(n11, n10) = all_0_7_7
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (194) with n11, n10, all_0_7_7, n0 and discharging atoms sum(n11, n10) = all_0_7_7, sum(n11, n10) = n0, yields:
% 31.24/10.01 | (1083) all_0_7_7 = n0
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (194) with n8, n13, all_0_4_4, n0 and discharging atoms sum(n8, n13) = all_0_4_4, sum(n8, n13) = n0, yields:
% 31.24/10.01 | (1081) all_0_4_4 = n0
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (194) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 31.24/10.01 | (1309) all_0_1_1 = n18
% 31.24/10.01 |
% 31.24/10.01 | From (1083)(1081) and (435) follows:
% 31.24/10.01 | (1085) sum(n0, n0) = all_0_3_3
% 31.24/10.01 |
% 31.24/10.01 | From (1309) and (6097) follows:
% 31.24/10.01 | (6146) sum(n3, n18) = all_0_0_0
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (194) with n3, n18, all_0_0_0, n0 and discharging atoms sum(n3, n18) = all_0_0_0, sum(n3, n18) = n0, yields:
% 31.24/10.01 | (1087) all_0_0_0 = n0
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 31.24/10.01 | (1088) all_0_3_3 = n0
% 31.24/10.01 |
% 31.24/10.01 | Equations (1087,1088) can reduce 201 to:
% 31.24/10.01 | (746) $false
% 31.24/10.01 |
% 31.24/10.01 |-The branch is then unsatisfiable
% 31.24/10.01 |-Branch two:
% 31.24/10.01 | (1316) ~ (all_0_10_10 = n9)
% 31.24/10.01 | (1317) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.24/10.01 |
% 31.24/10.01 +-Applying beta-rule and splitting (1317), into two cases.
% 31.24/10.01 |-Branch one:
% 31.24/10.01 | (1318) all_0_10_10 = n8
% 31.24/10.01 |
% 31.24/10.01 | From (1318) and (57) follows:
% 31.24/10.01 | (1319) pred(n8) = all_0_6_6
% 31.24/10.01 |
% 31.24/10.01 | From (1318) and (381) follows:
% 31.24/10.01 | (1320) succ(n8) = all_0_8_8
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (259) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 31.24/10.01 | (1321) all_0_6_6 = n7
% 31.24/10.01 |
% 31.24/10.01 | Instantiating formula (184) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 31.24/10.01 | (1322) all_0_8_8 = n9
% 31.24/10.01 |
% 31.24/10.01 | From (1321)(1322) and (628) follows:
% 31.24/10.01 | (1323) sum(n7, n9) = all_0_1_1
% 31.24/10.01 |
% 31.24/10.01 | From (1321) and (6093) follows:
% 31.24/10.02 | (6158) sum(n7, n13) = all_0_4_4
% 31.24/10.02 |
% 31.24/10.02 | From (1322) and (6095) follows:
% 31.24/10.02 | (6159) sum(n11, n9) = all_0_7_7
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n11, n9, all_0_7_7, n20 and discharging atoms sum(n11, n9) = all_0_7_7, sum(n11, n9) = n20, yields:
% 31.24/10.02 | (1100) all_0_7_7 = n20
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n7, n13, all_0_4_4, n20 and discharging atoms sum(n7, n13) = all_0_4_4, sum(n7, n13) = n20, yields:
% 31.24/10.02 | (1101) all_0_4_4 = n20
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 31.24/10.02 | (1327) all_0_1_1 = n16
% 31.24/10.02 |
% 31.24/10.02 | From (1100)(1101) and (435) follows:
% 31.24/10.02 | (1103) sum(n20, n20) = all_0_3_3
% 31.24/10.02 |
% 31.24/10.02 | From (1327) and (6097) follows:
% 31.24/10.02 | (6164) sum(n3, n16) = all_0_0_0
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 31.24/10.02 | (1104) all_0_3_3 = n19
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n3, n16, all_0_0_0, n19 and discharging atoms sum(n3, n16) = all_0_0_0, sum(n3, n16) = n19, yields:
% 31.24/10.02 | (1105) all_0_0_0 = n19
% 31.24/10.02 |
% 31.24/10.02 | Equations (1105,1104) can reduce 201 to:
% 31.24/10.02 | (746) $false
% 31.24/10.02 |
% 31.24/10.02 |-The branch is then unsatisfiable
% 31.24/10.02 |-Branch two:
% 31.24/10.02 | (1334) ~ (all_0_10_10 = n8)
% 31.24/10.02 | (1335) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.24/10.02 |
% 31.24/10.02 +-Applying beta-rule and splitting (1335), into two cases.
% 31.24/10.02 |-Branch one:
% 31.24/10.02 | (1336) all_0_10_10 = n7
% 31.24/10.02 |
% 31.24/10.02 | From (1336) and (57) follows:
% 31.24/10.02 | (1337) pred(n7) = all_0_6_6
% 31.24/10.02 |
% 31.24/10.02 | From (1336) and (381) follows:
% 31.24/10.02 | (1338) succ(n7) = all_0_8_8
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (259) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 31.24/10.02 | (1339) all_0_6_6 = n6
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (184) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 31.24/10.02 | (1340) all_0_8_8 = n8
% 31.24/10.02 |
% 31.24/10.02 | From (1339)(1340) and (628) follows:
% 31.24/10.02 | (1341) sum(n6, n8) = all_0_1_1
% 31.24/10.02 |
% 31.24/10.02 | From (1339) and (6093) follows:
% 31.24/10.02 | (6176) sum(n6, n13) = all_0_4_4
% 31.24/10.02 |
% 31.24/10.02 | From (1340) and (6095) follows:
% 31.24/10.02 | (6177) sum(n11, n8) = all_0_7_7
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n11, n8, all_0_7_7, n19 and discharging atoms sum(n11, n8) = all_0_7_7, sum(n11, n8) = n19, yields:
% 31.24/10.02 | (737) all_0_7_7 = n19
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n6, n13, all_0_4_4, n19 and discharging atoms sum(n6, n13) = all_0_4_4, sum(n6, n13) = n19, yields:
% 31.24/10.02 | (736) all_0_4_4 = n19
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 31.24/10.02 | (1345) all_0_1_1 = n14
% 31.24/10.02 |
% 31.24/10.02 | From (737)(736) and (435) follows:
% 31.24/10.02 | (741) sum(n19, n19) = all_0_3_3
% 31.24/10.02 |
% 31.24/10.02 | From (1345) and (6097) follows:
% 31.24/10.02 | (6182) sum(n3, n14) = all_0_0_0
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 31.24/10.02 | (744) all_0_3_3 = n17
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n3, n14, all_0_0_0, n17 and discharging atoms sum(n3, n14) = all_0_0_0, sum(n3, n14) = n17, yields:
% 31.24/10.02 | (742) all_0_0_0 = n17
% 31.24/10.02 |
% 31.24/10.02 | Equations (742,744) can reduce 201 to:
% 31.24/10.02 | (746) $false
% 31.24/10.02 |
% 31.24/10.02 |-The branch is then unsatisfiable
% 31.24/10.02 |-Branch two:
% 31.24/10.02 | (1352) ~ (all_0_10_10 = n7)
% 31.24/10.02 | (1353) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.24/10.02 |
% 31.24/10.02 +-Applying beta-rule and splitting (1353), into two cases.
% 31.24/10.02 |-Branch one:
% 31.24/10.02 | (1354) all_0_10_10 = n6
% 31.24/10.02 |
% 31.24/10.02 | From (1354) and (57) follows:
% 31.24/10.02 | (1355) pred(n6) = all_0_6_6
% 31.24/10.02 |
% 31.24/10.02 | From (1354) and (381) follows:
% 31.24/10.02 | (1356) succ(n6) = all_0_8_8
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (259) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 31.24/10.02 | (1357) all_0_6_6 = n5
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (184) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 31.24/10.02 | (1358) all_0_8_8 = n7
% 31.24/10.02 |
% 31.24/10.02 | From (1357)(1358) and (628) follows:
% 31.24/10.02 | (1359) sum(n5, n7) = all_0_1_1
% 31.24/10.02 |
% 31.24/10.02 | From (1357) and (6093) follows:
% 31.24/10.02 | (6194) sum(n5, n13) = all_0_4_4
% 31.24/10.02 |
% 31.24/10.02 | From (1358) and (6095) follows:
% 31.24/10.02 | (6195) sum(n11, n7) = all_0_7_7
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n11, n7, all_0_7_7, n18 and discharging atoms sum(n11, n7) = all_0_7_7, sum(n11, n7) = n18, yields:
% 31.24/10.02 | (759) all_0_7_7 = n18
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n5, n13, all_0_4_4, n18 and discharging atoms sum(n5, n13) = all_0_4_4, sum(n5, n13) = n18, yields:
% 31.24/10.02 | (757) all_0_4_4 = n18
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 31.24/10.02 | (1363) all_0_1_1 = n12
% 31.24/10.02 |
% 31.24/10.02 | From (759)(757) and (435) follows:
% 31.24/10.02 | (761) sum(n18, n18) = all_0_3_3
% 31.24/10.02 |
% 31.24/10.02 | From (1363) and (6097) follows:
% 31.24/10.02 | (6200) sum(n3, n12) = all_0_0_0
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 31.24/10.02 | (762) all_0_3_3 = n15
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n3, n12, all_0_0_0, n15 and discharging atoms sum(n3, n12) = all_0_0_0, sum(n3, n12) = n15, yields:
% 31.24/10.02 | (763) all_0_0_0 = n15
% 31.24/10.02 |
% 31.24/10.02 | Equations (763,762) can reduce 201 to:
% 31.24/10.02 | (746) $false
% 31.24/10.02 |
% 31.24/10.02 |-The branch is then unsatisfiable
% 31.24/10.02 |-Branch two:
% 31.24/10.02 | (1370) ~ (all_0_10_10 = n6)
% 31.24/10.02 | (1371) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.24/10.02 |
% 31.24/10.02 +-Applying beta-rule and splitting (1371), into two cases.
% 31.24/10.02 |-Branch one:
% 31.24/10.02 | (1372) all_0_10_10 = n5
% 31.24/10.02 |
% 31.24/10.02 | From (1372) and (57) follows:
% 31.24/10.02 | (1373) pred(n5) = all_0_6_6
% 31.24/10.02 |
% 31.24/10.02 | From (1372) and (381) follows:
% 31.24/10.02 | (1374) succ(n5) = all_0_8_8
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (259) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 31.24/10.02 | (1375) all_0_6_6 = n4
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (184) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 31.24/10.02 | (1376) all_0_8_8 = n6
% 31.24/10.02 |
% 31.24/10.02 | From (1375)(1376) and (628) follows:
% 31.24/10.02 | (1377) sum(n4, n6) = all_0_1_1
% 31.24/10.02 |
% 31.24/10.02 | From (1375) and (6093) follows:
% 31.24/10.02 | (6212) sum(n4, n13) = all_0_4_4
% 31.24/10.02 |
% 31.24/10.02 | From (1376) and (6095) follows:
% 31.24/10.02 | (6213) sum(n11, n6) = all_0_7_7
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n11, n6, all_0_7_7, n17 and discharging atoms sum(n11, n6) = all_0_7_7, sum(n11, n6) = n17, yields:
% 31.24/10.02 | (777) all_0_7_7 = n17
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n4, n13, all_0_4_4, n17 and discharging atoms sum(n4, n13) = all_0_4_4, sum(n4, n13) = n17, yields:
% 31.24/10.02 | (775) all_0_4_4 = n17
% 31.24/10.02 |
% 31.24/10.02 | Instantiating formula (194) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 31.24/10.02 | (1381) all_0_1_1 = n10
% 31.24/10.02 |
% 31.24/10.02 | From (777)(775) and (435) follows:
% 31.34/10.02 | (779) sum(n17, n17) = all_0_3_3
% 31.34/10.02 |
% 31.34/10.02 | From (1381) and (6097) follows:
% 31.34/10.03 | (6218) sum(n3, n10) = all_0_0_0
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 31.34/10.03 | (780) all_0_3_3 = n13
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (194) with n3, n10, all_0_0_0, n13 and discharging atoms sum(n3, n10) = all_0_0_0, sum(n3, n10) = n13, yields:
% 31.34/10.03 | (781) all_0_0_0 = n13
% 31.34/10.03 |
% 31.34/10.03 | Equations (781,780) can reduce 201 to:
% 31.34/10.03 | (746) $false
% 31.34/10.03 |
% 31.34/10.03 |-The branch is then unsatisfiable
% 31.34/10.03 |-Branch two:
% 31.34/10.03 | (1388) ~ (all_0_10_10 = n5)
% 31.34/10.03 | (1389) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.34/10.03 |
% 31.34/10.03 +-Applying beta-rule and splitting (1389), into two cases.
% 31.34/10.03 |-Branch one:
% 31.34/10.03 | (1390) all_0_10_10 = n4
% 31.34/10.03 |
% 31.34/10.03 | From (1390) and (57) follows:
% 31.34/10.03 | (1391) pred(n4) = all_0_6_6
% 31.34/10.03 |
% 31.34/10.03 | From (1390) and (381) follows:
% 31.34/10.03 | (1392) succ(n4) = all_0_8_8
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (259) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 31.34/10.03 | (1393) all_0_6_6 = n3
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (184) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 31.34/10.03 | (1394) all_0_8_8 = n5
% 31.34/10.03 |
% 31.34/10.03 | From (1393)(1394) and (628) follows:
% 31.34/10.03 | (1395) sum(n3, n5) = all_0_1_1
% 31.34/10.03 |
% 31.34/10.03 | From (1393) and (6093) follows:
% 31.34/10.03 | (6230) sum(n3, n13) = all_0_4_4
% 31.34/10.03 |
% 31.34/10.03 | From (1394) and (6095) follows:
% 31.34/10.03 | (6231) sum(n11, n5) = all_0_7_7
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (194) with n11, n5, all_0_7_7, n16 and discharging atoms sum(n11, n5) = all_0_7_7, sum(n11, n5) = n16, yields:
% 31.34/10.03 | (795) all_0_7_7 = n16
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (194) with n3, n13, all_0_4_4, n16 and discharging atoms sum(n3, n13) = all_0_4_4, sum(n3, n13) = n16, yields:
% 31.34/10.03 | (793) all_0_4_4 = n16
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (194) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 31.34/10.03 | (1399) all_0_1_1 = n8
% 31.34/10.03 |
% 31.34/10.03 | From (795)(793) and (435) follows:
% 31.34/10.03 | (797) sum(n16, n16) = all_0_3_3
% 31.34/10.03 |
% 31.34/10.03 | From (1399) and (6097) follows:
% 31.34/10.03 | (6236) sum(n3, n8) = all_0_0_0
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 31.34/10.03 | (798) all_0_3_3 = n11
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (194) with n3, n8, all_0_0_0, n11 and discharging atoms sum(n3, n8) = all_0_0_0, sum(n3, n8) = n11, yields:
% 31.34/10.03 | (799) all_0_0_0 = n11
% 31.34/10.03 |
% 31.34/10.03 | Equations (799,798) can reduce 201 to:
% 31.34/10.03 | (746) $false
% 31.34/10.03 |
% 31.34/10.03 |-The branch is then unsatisfiable
% 31.34/10.03 |-Branch two:
% 31.34/10.03 | (1406) ~ (all_0_10_10 = n4)
% 31.34/10.03 | (1407) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.34/10.03 |
% 31.34/10.03 +-Applying beta-rule and splitting (1407), into two cases.
% 31.34/10.03 |-Branch one:
% 31.34/10.03 | (1408) all_0_10_10 = n3
% 31.34/10.03 |
% 31.34/10.03 | From (1408) and (57) follows:
% 31.34/10.03 | (1409) pred(n3) = all_0_6_6
% 31.34/10.03 |
% 31.34/10.03 | From (1408) and (381) follows:
% 31.34/10.03 | (1410) succ(n3) = all_0_8_8
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 31.34/10.03 | (1411) all_0_6_6 = n2
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 31.34/10.03 | (1412) all_0_8_8 = n4
% 31.34/10.03 |
% 31.34/10.03 | From (1411)(1412) and (628) follows:
% 31.34/10.03 | (1413) sum(n2, n4) = all_0_1_1
% 31.34/10.03 |
% 31.34/10.03 | From (1411) and (6093) follows:
% 31.34/10.03 | (6248) sum(n2, n13) = all_0_4_4
% 31.34/10.03 |
% 31.34/10.03 | From (1412) and (6095) follows:
% 31.34/10.03 | (6249) sum(n11, n4) = all_0_7_7
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (194) with n11, n4, all_0_7_7, n15 and discharging atoms sum(n11, n4) = all_0_7_7, sum(n11, n4) = n15, yields:
% 31.34/10.03 | (813) all_0_7_7 = n15
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (194) with n2, n13, all_0_4_4, n15 and discharging atoms sum(n2, n13) = all_0_4_4, sum(n2, n13) = n15, yields:
% 31.34/10.03 | (811) all_0_4_4 = n15
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 31.34/10.03 | (1417) all_0_1_1 = n6
% 31.34/10.03 |
% 31.34/10.03 | From (813)(811) and (435) follows:
% 31.34/10.03 | (815) sum(n15, n15) = all_0_3_3
% 31.34/10.03 |
% 31.34/10.03 | From (1417) and (6097) follows:
% 31.34/10.03 | (6254) sum(n3, n6) = all_0_0_0
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 31.34/10.03 | (816) all_0_3_3 = n9
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (194) with n3, n6, all_0_0_0, n9 and discharging atoms sum(n3, n6) = all_0_0_0, sum(n3, n6) = n9, yields:
% 31.34/10.03 | (817) all_0_0_0 = n9
% 31.34/10.03 |
% 31.34/10.03 | Equations (817,816) can reduce 201 to:
% 31.34/10.03 | (746) $false
% 31.34/10.03 |
% 31.34/10.03 |-The branch is then unsatisfiable
% 31.34/10.03 |-Branch two:
% 31.34/10.03 | (1424) ~ (all_0_10_10 = n3)
% 31.34/10.03 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.34/10.03 |
% 31.34/10.03 +-Applying beta-rule and splitting (1425), into two cases.
% 31.34/10.03 |-Branch one:
% 31.34/10.03 | (1426) all_0_10_10 = n2
% 31.34/10.03 |
% 31.34/10.03 | From (1426) and (57) follows:
% 31.34/10.03 | (1427) pred(n2) = all_0_6_6
% 31.34/10.03 |
% 31.34/10.03 | From (1426) and (381) follows:
% 31.34/10.03 | (1428) succ(n2) = all_0_8_8
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 31.34/10.03 | (1429) all_0_6_6 = n1
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 31.34/10.03 | (1430) all_0_8_8 = n3
% 31.34/10.03 |
% 31.34/10.03 | From (1429)(1430) and (628) follows:
% 31.34/10.03 | (1431) sum(n1, n3) = all_0_1_1
% 31.34/10.03 |
% 31.34/10.03 | From (1429) and (6093) follows:
% 31.34/10.03 | (6266) sum(n1, n13) = all_0_4_4
% 31.34/10.03 |
% 31.34/10.03 | From (1430) and (6095) follows:
% 31.34/10.03 | (6267) sum(n11, n3) = all_0_7_7
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (194) with n11, n3, all_0_7_7, n14 and discharging atoms sum(n11, n3) = all_0_7_7, sum(n11, n3) = n14, yields:
% 31.34/10.03 | (831) all_0_7_7 = n14
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (194) with n1, n13, all_0_4_4, n14 and discharging atoms sum(n1, n13) = all_0_4_4, sum(n1, n13) = n14, yields:
% 31.34/10.03 | (829) all_0_4_4 = n14
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 31.34/10.03 | (1435) all_0_1_1 = n4
% 31.34/10.03 |
% 31.34/10.03 | From (831)(829) and (435) follows:
% 31.34/10.03 | (833) sum(n14, n14) = all_0_3_3
% 31.34/10.03 |
% 31.34/10.03 | From (1435) and (6097) follows:
% 31.34/10.03 | (6272) sum(n3, n4) = all_0_0_0
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 31.34/10.03 | (834) all_0_3_3 = n7
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (194) with n3, n4, all_0_0_0, n7 and discharging atoms sum(n3, n4) = all_0_0_0, sum(n3, n4) = n7, yields:
% 31.34/10.03 | (835) all_0_0_0 = n7
% 31.34/10.03 |
% 31.34/10.03 | Equations (835,834) can reduce 201 to:
% 31.34/10.03 | (746) $false
% 31.34/10.03 |
% 31.34/10.03 |-The branch is then unsatisfiable
% 31.34/10.03 |-Branch two:
% 31.34/10.03 | (1442) ~ (all_0_10_10 = n2)
% 31.34/10.03 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 31.34/10.03 |
% 31.34/10.03 +-Applying beta-rule and splitting (1443), into two cases.
% 31.34/10.03 |-Branch one:
% 31.34/10.03 | (1444) all_0_10_10 = n1
% 31.34/10.03 |
% 31.34/10.03 | From (1444) and (57) follows:
% 31.34/10.03 | (1445) pred(n1) = all_0_6_6
% 31.34/10.03 |
% 31.34/10.03 | From (1444) and (381) follows:
% 31.34/10.03 | (1446) succ(n1) = all_0_8_8
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 31.34/10.03 | (1447) all_0_6_6 = n0
% 31.34/10.03 |
% 31.34/10.03 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 31.34/10.03 | (1448) all_0_8_8 = n2
% 31.34/10.03 |
% 31.34/10.03 | From (1447)(1448) and (628) follows:
% 31.34/10.03 | (1449) sum(n0, n2) = all_0_1_1
% 31.34/10.03 |
% 31.34/10.03 | From (1447) and (6093) follows:
% 31.34/10.03 | (6284) sum(n0, n13) = all_0_4_4
% 31.34/10.03 |
% 31.34/10.03 | From (1448) and (6095) follows:
% 31.34/10.04 | (6285) sum(n11, n2) = all_0_7_7
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (194) with n11, n2, all_0_7_7, n13 and discharging atoms sum(n11, n2) = all_0_7_7, sum(n11, n2) = n13, yields:
% 31.34/10.04 | (849) all_0_7_7 = n13
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (194) with n0, n13, all_0_4_4, n13 and discharging atoms sum(n0, n13) = all_0_4_4, sum(n0, n13) = n13, yields:
% 31.34/10.04 | (847) all_0_4_4 = n13
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 31.34/10.04 | (1453) all_0_1_1 = n2
% 31.34/10.04 |
% 31.34/10.04 | From (849)(847) and (435) follows:
% 31.34/10.04 | (851) sum(n13, n13) = all_0_3_3
% 31.34/10.04 |
% 31.34/10.04 | From (1453) and (6097) follows:
% 31.34/10.04 | (6290) sum(n3, n2) = all_0_0_0
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 31.34/10.04 | (852) all_0_3_3 = n5
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (194) with n3, n2, all_0_0_0, n5 and discharging atoms sum(n3, n2) = all_0_0_0, sum(n3, n2) = n5, yields:
% 31.34/10.04 | (853) all_0_0_0 = n5
% 31.34/10.04 |
% 31.34/10.04 | Equations (853,852) can reduce 201 to:
% 31.34/10.04 | (746) $false
% 31.34/10.04 |
% 31.34/10.04 |-The branch is then unsatisfiable
% 31.34/10.04 |-Branch two:
% 31.34/10.04 | (1462) ~ (all_0_10_10 = n1)
% 31.34/10.04 | (1463) all_0_10_10 = n0
% 31.34/10.04 |
% 31.34/10.04 | From (1463) and (57) follows:
% 31.34/10.04 | (1464) pred(n0) = all_0_6_6
% 31.34/10.04 |
% 31.34/10.04 | From (1463) and (381) follows:
% 31.34/10.04 | (1465) succ(n0) = all_0_8_8
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 31.34/10.04 | (1466) all_0_6_6 = n20
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 31.34/10.04 | (1467) all_0_8_8 = n1
% 31.34/10.04 |
% 31.34/10.04 | From (1466)(1467) and (628) follows:
% 31.34/10.04 | (1468) sum(n20, n1) = all_0_1_1
% 31.34/10.04 |
% 31.34/10.04 | From (1466) and (6093) follows:
% 31.34/10.04 | (6301) sum(n20, n13) = all_0_4_4
% 31.34/10.04 |
% 31.34/10.04 | From (1467) and (6095) follows:
% 31.34/10.04 | (6302) sum(n11, n1) = all_0_7_7
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (194) with n20, n13, all_0_4_4, n12 and discharging atoms sum(n20, n13) = all_0_4_4, sum(n20, n13) = n12, yields:
% 31.34/10.04 | (865) all_0_4_4 = n12
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 31.34/10.04 | (1471) all_0_1_1 = n0
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (194) with n11, n1, all_0_7_7, n12 and discharging atoms sum(n11, n1) = all_0_7_7, sum(n11, n1) = n12, yields:
% 31.34/10.04 | (867) all_0_7_7 = n12
% 31.34/10.04 |
% 31.34/10.04 | From (867)(865) and (435) follows:
% 31.34/10.04 | (869) sum(n12, n12) = all_0_3_3
% 31.34/10.04 |
% 31.34/10.04 | From (1471) and (6097) follows:
% 31.34/10.04 | (6307) sum(n3, n0) = all_0_0_0
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 31.34/10.04 | (870) all_0_3_3 = n3
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (194) with n3, n0, all_0_0_0, n3 and discharging atoms sum(n3, n0) = all_0_0_0, sum(n3, n0) = n3, yields:
% 31.34/10.04 | (871) all_0_0_0 = n3
% 31.34/10.04 |
% 31.34/10.04 | Equations (871,870) can reduce 201 to:
% 31.34/10.04 | (746) $false
% 31.34/10.04 |
% 31.34/10.04 |-The branch is then unsatisfiable
% 31.34/10.04 |-Branch two:
% 31.34/10.04 | (891) ~ (all_0_11_11 = n12)
% 31.34/10.04 | (892) all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.04 |
% 31.34/10.04 +-Applying beta-rule and splitting (1263), into two cases.
% 31.34/10.04 |-Branch one:
% 31.34/10.04 | (1264) all_0_10_10 = n11
% 31.34/10.04 |
% 31.34/10.04 | From (1264) and (57) follows:
% 31.34/10.04 | (1265) pred(n11) = all_0_6_6
% 31.34/10.04 |
% 31.34/10.04 | From (1264) and (381) follows:
% 31.34/10.04 | (1266) succ(n11) = all_0_8_8
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (259) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 31.34/10.04 | (1267) all_0_6_6 = n10
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (184) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 31.34/10.04 | (1268) all_0_8_8 = n12
% 31.34/10.04 |
% 31.34/10.04 | From (1267) and (1265) follows:
% 31.34/10.04 | (197) pred(n11) = n10
% 31.34/10.04 |
% 31.34/10.04 | From (1268) and (1266) follows:
% 31.34/10.04 | (66) succ(n11) = n12
% 31.34/10.04 |
% 31.34/10.04 | From (1267) and (386) follows:
% 31.34/10.04 | (6320) sum(n10, all_0_5_5) = all_0_4_4
% 31.34/10.04 |
% 31.34/10.04 | From (1267)(1268) and (628) follows:
% 31.34/10.04 | (1269) sum(n10, n12) = all_0_1_1
% 31.34/10.04 |
% 31.34/10.04 | From (1268) and (74) follows:
% 31.34/10.04 | (6322) sum(all_0_9_9, n12) = all_0_7_7
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (194) with n10, n12, all_0_1_1, n1 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n1, yields:
% 31.34/10.04 | (1273) all_0_1_1 = n1
% 31.34/10.04 |
% 31.34/10.04 | From (1273) and (85) follows:
% 31.34/10.04 | (6324) sum(all_0_2_2, n1) = all_0_0_0
% 31.34/10.04 |
% 31.34/10.04 | From (1273) and (1269) follows:
% 31.34/10.04 | (155) sum(n10, n12) = n1
% 31.34/10.04 |
% 31.34/10.04 +-Applying beta-rule and splitting (892), into two cases.
% 31.34/10.04 |-Branch one:
% 31.34/10.04 | (893) all_0_11_11 = n11
% 31.34/10.04 |
% 31.34/10.04 | From (893) and (190) follows:
% 31.34/10.04 | (894) pred(n11) = all_0_9_9
% 31.34/10.04 |
% 31.34/10.04 | From (893) and (505) follows:
% 31.34/10.04 | (895) succ(n11) = all_0_5_5
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (259) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 31.34/10.04 | (896) all_0_9_9 = n10
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (184) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 31.34/10.04 | (897) all_0_5_5 = n12
% 31.34/10.04 |
% 31.34/10.04 | From (896)(897) and (156) follows:
% 31.34/10.04 | (898) sum(n10, n12) = all_0_2_2
% 31.34/10.04 |
% 31.34/10.04 | From (896) and (6322) follows:
% 31.34/10.04 | (6332) sum(n10, n12) = all_0_7_7
% 31.34/10.04 |
% 31.34/10.04 | From (897) and (6320) follows:
% 31.34/10.04 | (6333) sum(n10, n12) = all_0_4_4
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (194) with n10, n12, all_0_2_2, n1 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n1, yields:
% 31.34/10.04 | (902) all_0_2_2 = n1
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (194) with n10, n12, all_0_4_4, all_0_2_2 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = all_0_4_4, yields:
% 31.34/10.04 | (733) all_0_2_2 = all_0_4_4
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (194) with n10, n12, all_0_7_7, all_0_2_2 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = all_0_7_7, yields:
% 31.34/10.04 | (734) all_0_2_2 = all_0_7_7
% 31.34/10.04 |
% 31.34/10.04 | Combining equations (734,733) yields a new equation:
% 31.34/10.04 | (735) all_0_4_4 = all_0_7_7
% 31.34/10.04 |
% 31.34/10.04 | Combining equations (902,733) yields a new equation:
% 31.34/10.04 | (1063) all_0_4_4 = n1
% 31.34/10.04 |
% 31.34/10.04 | Combining equations (1063,735) yields a new equation:
% 31.34/10.04 | (1065) all_0_7_7 = n1
% 31.34/10.04 |
% 31.34/10.04 | Combining equations (1065,735) yields a new equation:
% 31.34/10.04 | (1063) all_0_4_4 = n1
% 31.34/10.04 |
% 31.34/10.04 | Combining equations (1063,733) yields a new equation:
% 31.34/10.04 | (902) all_0_2_2 = n1
% 31.34/10.04 |
% 31.34/10.04 | From (902) and (6324) follows:
% 31.34/10.04 | (6342) sum(n1, n1) = all_0_0_0
% 31.34/10.04 |
% 31.34/10.04 | From (1065)(1063) and (435) follows:
% 31.34/10.04 | (1067) sum(n1, n1) = all_0_3_3
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (194) with n1, n1, all_0_0_0, n2 and discharging atoms sum(n1, n1) = all_0_0_0, sum(n1, n1) = n2, yields:
% 31.34/10.04 | (1068) all_0_0_0 = n2
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (194) with n1, n1, all_0_3_3, all_0_0_0 and discharging atoms sum(n1, n1) = all_0_0_0, sum(n1, n1) = all_0_3_3, yields:
% 31.34/10.04 | (743) all_0_0_0 = all_0_3_3
% 31.34/10.04 |
% 31.34/10.04 | Combining equations (1068,743) yields a new equation:
% 31.34/10.04 | (1069) all_0_3_3 = n2
% 31.34/10.04 |
% 31.34/10.04 | Combining equations (1069,743) yields a new equation:
% 31.34/10.04 | (1068) all_0_0_0 = n2
% 31.34/10.04 |
% 31.34/10.04 | Equations (1068,1069) can reduce 201 to:
% 31.34/10.04 | (746) $false
% 31.34/10.04 |
% 31.34/10.04 |-The branch is then unsatisfiable
% 31.34/10.04 |-Branch two:
% 31.34/10.04 | (909) ~ (all_0_11_11 = n11)
% 31.34/10.04 | (910) all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.04 |
% 31.34/10.04 +-Applying beta-rule and splitting (910), into two cases.
% 31.34/10.04 |-Branch one:
% 31.34/10.04 | (911) all_0_11_11 = n10
% 31.34/10.04 |
% 31.34/10.04 | From (911) and (190) follows:
% 31.34/10.04 | (912) pred(n10) = all_0_9_9
% 31.34/10.04 |
% 31.34/10.04 | From (911) and (505) follows:
% 31.34/10.04 | (913) succ(n10) = all_0_5_5
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (259) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 31.34/10.04 | (914) all_0_9_9 = n9
% 31.34/10.04 |
% 31.34/10.04 | Instantiating formula (184) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 31.34/10.04 | (915) all_0_5_5 = n11
% 31.34/10.04 |
% 31.34/10.04 | From (914)(915) and (156) follows:
% 31.34/10.04 | (916) sum(n9, n11) = all_0_2_2
% 31.34/10.04 |
% 31.34/10.04 | From (914) and (6322) follows:
% 31.34/10.04 | (6357) sum(n9, n12) = all_0_7_7
% 31.34/10.04 |
% 31.34/10.04 | From (915) and (6320) follows:
% 31.34/10.05 | (6358) sum(n10, n11) = all_0_4_4
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n10, n11, all_0_4_4, n0 and discharging atoms sum(n10, n11) = all_0_4_4, sum(n10, n11) = n0, yields:
% 31.34/10.05 | (1081) all_0_4_4 = n0
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n9, n12, all_0_7_7, n0 and discharging atoms sum(n9, n12) = all_0_7_7, sum(n9, n12) = n0, yields:
% 31.34/10.05 | (1083) all_0_7_7 = n0
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 31.34/10.05 | (920) all_0_2_2 = n20
% 31.34/10.05 |
% 31.34/10.05 | From (920) and (6324) follows:
% 31.34/10.05 | (6362) sum(n20, n1) = all_0_0_0
% 31.34/10.05 |
% 31.34/10.05 | From (1083)(1081) and (435) follows:
% 31.34/10.05 | (1085) sum(n0, n0) = all_0_3_3
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n20, n1, all_0_0_0, n0 and discharging atoms sum(n20, n1) = all_0_0_0, sum(n20, n1) = n0, yields:
% 31.34/10.05 | (1087) all_0_0_0 = n0
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 31.34/10.05 | (1088) all_0_3_3 = n0
% 31.34/10.05 |
% 31.34/10.05 | Equations (1087,1088) can reduce 201 to:
% 31.34/10.05 | (746) $false
% 31.34/10.05 |
% 31.34/10.05 |-The branch is then unsatisfiable
% 31.34/10.05 |-Branch two:
% 31.34/10.05 | (927) ~ (all_0_11_11 = n10)
% 31.34/10.05 | (928) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.05 |
% 31.34/10.05 +-Applying beta-rule and splitting (928), into two cases.
% 31.34/10.05 |-Branch one:
% 31.34/10.05 | (929) all_0_11_11 = n9
% 31.34/10.05 |
% 31.34/10.05 | From (929) and (190) follows:
% 31.34/10.05 | (930) pred(n9) = all_0_9_9
% 31.34/10.05 |
% 31.34/10.05 | From (929) and (505) follows:
% 31.34/10.05 | (931) succ(n9) = all_0_5_5
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (259) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 31.34/10.05 | (932) all_0_9_9 = n8
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (184) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 31.34/10.05 | (933) all_0_5_5 = n10
% 31.34/10.05 |
% 31.34/10.05 | From (932)(933) and (156) follows:
% 31.34/10.05 | (934) sum(n8, n10) = all_0_2_2
% 31.34/10.05 |
% 31.34/10.05 | From (932) and (6322) follows:
% 31.34/10.05 | (6375) sum(n8, n12) = all_0_7_7
% 31.34/10.05 |
% 31.34/10.05 | From (933) and (6320) follows:
% 31.34/10.05 | (6376) sum(n10, n10) = all_0_4_4
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n10, n10, all_0_4_4, n20 and discharging atoms sum(n10, n10) = all_0_4_4, sum(n10, n10) = n20, yields:
% 31.34/10.05 | (1101) all_0_4_4 = n20
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n8, n12, all_0_7_7, n20 and discharging atoms sum(n8, n12) = all_0_7_7, sum(n8, n12) = n20, yields:
% 31.34/10.05 | (1100) all_0_7_7 = n20
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 31.34/10.05 | (938) all_0_2_2 = n18
% 31.34/10.05 |
% 31.34/10.05 | From (938) and (6324) follows:
% 31.34/10.05 | (6380) sum(n18, n1) = all_0_0_0
% 31.34/10.05 |
% 31.34/10.05 | From (1100)(1101) and (435) follows:
% 31.34/10.05 | (1103) sum(n20, n20) = all_0_3_3
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 31.34/10.05 | (1104) all_0_3_3 = n19
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n18, n1, all_0_0_0, n19 and discharging atoms sum(n18, n1) = all_0_0_0, sum(n18, n1) = n19, yields:
% 31.34/10.05 | (1105) all_0_0_0 = n19
% 31.34/10.05 |
% 31.34/10.05 | Equations (1105,1104) can reduce 201 to:
% 31.34/10.05 | (746) $false
% 31.34/10.05 |
% 31.34/10.05 |-The branch is then unsatisfiable
% 31.34/10.05 |-Branch two:
% 31.34/10.05 | (945) ~ (all_0_11_11 = n9)
% 31.34/10.05 | (946) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.05 |
% 31.34/10.05 +-Applying beta-rule and splitting (946), into two cases.
% 31.34/10.05 |-Branch one:
% 31.34/10.05 | (947) all_0_11_11 = n8
% 31.34/10.05 |
% 31.34/10.05 | From (947) and (190) follows:
% 31.34/10.05 | (948) pred(n8) = all_0_9_9
% 31.34/10.05 |
% 31.34/10.05 | From (947) and (505) follows:
% 31.34/10.05 | (949) succ(n8) = all_0_5_5
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (259) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 31.34/10.05 | (950) all_0_9_9 = n7
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (184) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 31.34/10.05 | (951) all_0_5_5 = n9
% 31.34/10.05 |
% 31.34/10.05 | From (950)(951) and (156) follows:
% 31.34/10.05 | (952) sum(n7, n9) = all_0_2_2
% 31.34/10.05 |
% 31.34/10.05 | From (950) and (6322) follows:
% 31.34/10.05 | (6393) sum(n7, n12) = all_0_7_7
% 31.34/10.05 |
% 31.34/10.05 | From (951) and (6320) follows:
% 31.34/10.05 | (6394) sum(n10, n9) = all_0_4_4
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n10, n9, all_0_4_4, n19 and discharging atoms sum(n10, n9) = all_0_4_4, sum(n10, n9) = n19, yields:
% 31.34/10.05 | (736) all_0_4_4 = n19
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n7, n12, all_0_7_7, n19 and discharging atoms sum(n7, n12) = all_0_7_7, sum(n7, n12) = n19, yields:
% 31.34/10.05 | (737) all_0_7_7 = n19
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 31.34/10.05 | (956) all_0_2_2 = n16
% 31.34/10.05 |
% 31.34/10.05 | From (956) and (6324) follows:
% 31.34/10.05 | (6398) sum(n16, n1) = all_0_0_0
% 31.34/10.05 |
% 31.34/10.05 | From (737)(736) and (435) follows:
% 31.34/10.05 | (741) sum(n19, n19) = all_0_3_3
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 31.34/10.05 | (744) all_0_3_3 = n17
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n16, n1, all_0_0_0, n17 and discharging atoms sum(n16, n1) = all_0_0_0, sum(n16, n1) = n17, yields:
% 31.34/10.05 | (742) all_0_0_0 = n17
% 31.34/10.05 |
% 31.34/10.05 | Equations (742,744) can reduce 201 to:
% 31.34/10.05 | (746) $false
% 31.34/10.05 |
% 31.34/10.05 |-The branch is then unsatisfiable
% 31.34/10.05 |-Branch two:
% 31.34/10.05 | (963) ~ (all_0_11_11 = n8)
% 31.34/10.05 | (964) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.05 |
% 31.34/10.05 +-Applying beta-rule and splitting (964), into two cases.
% 31.34/10.05 |-Branch one:
% 31.34/10.05 | (965) all_0_11_11 = n7
% 31.34/10.05 |
% 31.34/10.05 | From (965) and (190) follows:
% 31.34/10.05 | (966) pred(n7) = all_0_9_9
% 31.34/10.05 |
% 31.34/10.05 | From (965) and (505) follows:
% 31.34/10.05 | (967) succ(n7) = all_0_5_5
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (259) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 31.34/10.05 | (968) all_0_9_9 = n6
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (184) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 31.34/10.05 | (969) all_0_5_5 = n8
% 31.34/10.05 |
% 31.34/10.05 | From (968)(969) and (156) follows:
% 31.34/10.05 | (970) sum(n6, n8) = all_0_2_2
% 31.34/10.05 |
% 31.34/10.05 | From (968) and (6322) follows:
% 31.34/10.05 | (6411) sum(n6, n12) = all_0_7_7
% 31.34/10.05 |
% 31.34/10.05 | From (969) and (6320) follows:
% 31.34/10.05 | (6412) sum(n10, n8) = all_0_4_4
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n10, n8, all_0_4_4, n18 and discharging atoms sum(n10, n8) = all_0_4_4, sum(n10, n8) = n18, yields:
% 31.34/10.05 | (757) all_0_4_4 = n18
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n6, n12, all_0_7_7, n18 and discharging atoms sum(n6, n12) = all_0_7_7, sum(n6, n12) = n18, yields:
% 31.34/10.05 | (759) all_0_7_7 = n18
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 31.34/10.05 | (974) all_0_2_2 = n14
% 31.34/10.05 |
% 31.34/10.05 | From (974) and (6324) follows:
% 31.34/10.05 | (6416) sum(n14, n1) = all_0_0_0
% 31.34/10.05 |
% 31.34/10.05 | From (759)(757) and (435) follows:
% 31.34/10.05 | (761) sum(n18, n18) = all_0_3_3
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 31.34/10.05 | (762) all_0_3_3 = n15
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n14, n1, all_0_0_0, n15 and discharging atoms sum(n14, n1) = all_0_0_0, sum(n14, n1) = n15, yields:
% 31.34/10.05 | (763) all_0_0_0 = n15
% 31.34/10.05 |
% 31.34/10.05 | Equations (763,762) can reduce 201 to:
% 31.34/10.05 | (746) $false
% 31.34/10.05 |
% 31.34/10.05 |-The branch is then unsatisfiable
% 31.34/10.05 |-Branch two:
% 31.34/10.05 | (981) ~ (all_0_11_11 = n7)
% 31.34/10.05 | (982) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.05 |
% 31.34/10.05 +-Applying beta-rule and splitting (982), into two cases.
% 31.34/10.05 |-Branch one:
% 31.34/10.05 | (983) all_0_11_11 = n6
% 31.34/10.05 |
% 31.34/10.05 | From (983) and (190) follows:
% 31.34/10.05 | (984) pred(n6) = all_0_9_9
% 31.34/10.05 |
% 31.34/10.05 | From (983) and (505) follows:
% 31.34/10.05 | (985) succ(n6) = all_0_5_5
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (259) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 31.34/10.05 | (986) all_0_9_9 = n5
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (184) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 31.34/10.05 | (987) all_0_5_5 = n7
% 31.34/10.05 |
% 31.34/10.05 | From (986)(987) and (156) follows:
% 31.34/10.05 | (988) sum(n5, n7) = all_0_2_2
% 31.34/10.05 |
% 31.34/10.05 | From (986) and (6322) follows:
% 31.34/10.05 | (6429) sum(n5, n12) = all_0_7_7
% 31.34/10.05 |
% 31.34/10.05 | From (987) and (6320) follows:
% 31.34/10.05 | (6430) sum(n10, n7) = all_0_4_4
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n10, n7, all_0_4_4, n17 and discharging atoms sum(n10, n7) = all_0_4_4, sum(n10, n7) = n17, yields:
% 31.34/10.05 | (775) all_0_4_4 = n17
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n5, n12, all_0_7_7, n17 and discharging atoms sum(n5, n12) = all_0_7_7, sum(n5, n12) = n17, yields:
% 31.34/10.05 | (777) all_0_7_7 = n17
% 31.34/10.05 |
% 31.34/10.05 | Instantiating formula (194) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 31.34/10.05 | (992) all_0_2_2 = n12
% 31.34/10.05 |
% 31.34/10.05 | From (992) and (6324) follows:
% 31.34/10.06 | (6434) sum(n12, n1) = all_0_0_0
% 31.34/10.06 |
% 31.34/10.06 | From (777)(775) and (435) follows:
% 31.34/10.06 | (779) sum(n17, n17) = all_0_3_3
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 31.34/10.06 | (780) all_0_3_3 = n13
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n12, n1, all_0_0_0, n13 and discharging atoms sum(n12, n1) = all_0_0_0, sum(n12, n1) = n13, yields:
% 31.34/10.06 | (781) all_0_0_0 = n13
% 31.34/10.06 |
% 31.34/10.06 | Equations (781,780) can reduce 201 to:
% 31.34/10.06 | (746) $false
% 31.34/10.06 |
% 31.34/10.06 |-The branch is then unsatisfiable
% 31.34/10.06 |-Branch two:
% 31.34/10.06 | (999) ~ (all_0_11_11 = n6)
% 31.34/10.06 | (1000) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.06 |
% 31.34/10.06 +-Applying beta-rule and splitting (1000), into two cases.
% 31.34/10.06 |-Branch one:
% 31.34/10.06 | (1001) all_0_11_11 = n5
% 31.34/10.06 |
% 31.34/10.06 | From (1001) and (190) follows:
% 31.34/10.06 | (1002) pred(n5) = all_0_9_9
% 31.34/10.06 |
% 31.34/10.06 | From (1001) and (505) follows:
% 31.34/10.06 | (1003) succ(n5) = all_0_5_5
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (259) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 31.34/10.06 | (1004) all_0_9_9 = n4
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (184) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 31.34/10.06 | (1005) all_0_5_5 = n6
% 31.34/10.06 |
% 31.34/10.06 | From (1004)(1005) and (156) follows:
% 31.34/10.06 | (1006) sum(n4, n6) = all_0_2_2
% 31.34/10.06 |
% 31.34/10.06 | From (1004) and (6322) follows:
% 31.34/10.06 | (6447) sum(n4, n12) = all_0_7_7
% 31.34/10.06 |
% 31.34/10.06 | From (1005) and (6320) follows:
% 31.34/10.06 | (6448) sum(n10, n6) = all_0_4_4
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n10, n6, all_0_4_4, n16 and discharging atoms sum(n10, n6) = all_0_4_4, sum(n10, n6) = n16, yields:
% 31.34/10.06 | (793) all_0_4_4 = n16
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n4, n12, all_0_7_7, n16 and discharging atoms sum(n4, n12) = all_0_7_7, sum(n4, n12) = n16, yields:
% 31.34/10.06 | (795) all_0_7_7 = n16
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 31.34/10.06 | (1010) all_0_2_2 = n10
% 31.34/10.06 |
% 31.34/10.06 | From (1010) and (6324) follows:
% 31.34/10.06 | (6452) sum(n10, n1) = all_0_0_0
% 31.34/10.06 |
% 31.34/10.06 | From (795)(793) and (435) follows:
% 31.34/10.06 | (797) sum(n16, n16) = all_0_3_3
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 31.34/10.06 | (798) all_0_3_3 = n11
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n10, n1, all_0_0_0, n11 and discharging atoms sum(n10, n1) = all_0_0_0, sum(n10, n1) = n11, yields:
% 31.34/10.06 | (799) all_0_0_0 = n11
% 31.34/10.06 |
% 31.34/10.06 | Equations (799,798) can reduce 201 to:
% 31.34/10.06 | (746) $false
% 31.34/10.06 |
% 31.34/10.06 |-The branch is then unsatisfiable
% 31.34/10.06 |-Branch two:
% 31.34/10.06 | (1017) ~ (all_0_11_11 = n5)
% 31.34/10.06 | (1018) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.06 |
% 31.34/10.06 +-Applying beta-rule and splitting (1018), into two cases.
% 31.34/10.06 |-Branch one:
% 31.34/10.06 | (1019) all_0_11_11 = n4
% 31.34/10.06 |
% 31.34/10.06 | From (1019) and (190) follows:
% 31.34/10.06 | (1020) pred(n4) = all_0_9_9
% 31.34/10.06 |
% 31.34/10.06 | From (1019) and (505) follows:
% 31.34/10.06 | (1021) succ(n4) = all_0_5_5
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 31.34/10.06 | (1022) all_0_9_9 = n3
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 31.34/10.06 | (1023) all_0_5_5 = n5
% 31.34/10.06 |
% 31.34/10.06 | From (1022)(1023) and (156) follows:
% 31.34/10.06 | (1024) sum(n3, n5) = all_0_2_2
% 31.34/10.06 |
% 31.34/10.06 | From (1022) and (6322) follows:
% 31.34/10.06 | (6465) sum(n3, n12) = all_0_7_7
% 31.34/10.06 |
% 31.34/10.06 | From (1023) and (6320) follows:
% 31.34/10.06 | (6466) sum(n10, n5) = all_0_4_4
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n10, n5, all_0_4_4, n15 and discharging atoms sum(n10, n5) = all_0_4_4, sum(n10, n5) = n15, yields:
% 31.34/10.06 | (811) all_0_4_4 = n15
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n3, n12, all_0_7_7, n15 and discharging atoms sum(n3, n12) = all_0_7_7, sum(n3, n12) = n15, yields:
% 31.34/10.06 | (813) all_0_7_7 = n15
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 31.34/10.06 | (1028) all_0_2_2 = n8
% 31.34/10.06 |
% 31.34/10.06 | From (1028) and (6324) follows:
% 31.34/10.06 | (6470) sum(n8, n1) = all_0_0_0
% 31.34/10.06 |
% 31.34/10.06 | From (813)(811) and (435) follows:
% 31.34/10.06 | (815) sum(n15, n15) = all_0_3_3
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 31.34/10.06 | (816) all_0_3_3 = n9
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n8, n1, all_0_0_0, n9 and discharging atoms sum(n8, n1) = all_0_0_0, sum(n8, n1) = n9, yields:
% 31.34/10.06 | (817) all_0_0_0 = n9
% 31.34/10.06 |
% 31.34/10.06 | Equations (817,816) can reduce 201 to:
% 31.34/10.06 | (746) $false
% 31.34/10.06 |
% 31.34/10.06 |-The branch is then unsatisfiable
% 31.34/10.06 |-Branch two:
% 31.34/10.06 | (1035) ~ (all_0_11_11 = n4)
% 31.34/10.06 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.06 |
% 31.34/10.06 +-Applying beta-rule and splitting (1036), into two cases.
% 31.34/10.06 |-Branch one:
% 31.34/10.06 | (1037) all_0_11_11 = n3
% 31.34/10.06 |
% 31.34/10.06 | From (1037) and (190) follows:
% 31.34/10.06 | (1038) pred(n3) = all_0_9_9
% 31.34/10.06 |
% 31.34/10.06 | From (1037) and (505) follows:
% 31.34/10.06 | (1039) succ(n3) = all_0_5_5
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 31.34/10.06 | (1040) all_0_9_9 = n2
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 31.34/10.06 | (1041) all_0_5_5 = n4
% 31.34/10.06 |
% 31.34/10.06 | From (1040)(1041) and (156) follows:
% 31.34/10.06 | (1042) sum(n2, n4) = all_0_2_2
% 31.34/10.06 |
% 31.34/10.06 | From (1040) and (6322) follows:
% 31.34/10.06 | (6483) sum(n2, n12) = all_0_7_7
% 31.34/10.06 |
% 31.34/10.06 | From (1041) and (6320) follows:
% 31.34/10.06 | (6484) sum(n10, n4) = all_0_4_4
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n10, n4, all_0_4_4, n14 and discharging atoms sum(n10, n4) = all_0_4_4, sum(n10, n4) = n14, yields:
% 31.34/10.06 | (829) all_0_4_4 = n14
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n2, n12, all_0_7_7, n14 and discharging atoms sum(n2, n12) = all_0_7_7, sum(n2, n12) = n14, yields:
% 31.34/10.06 | (831) all_0_7_7 = n14
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 31.34/10.06 | (1046) all_0_2_2 = n6
% 31.34/10.06 |
% 31.34/10.06 | From (1046) and (6324) follows:
% 31.34/10.06 | (6488) sum(n6, n1) = all_0_0_0
% 31.34/10.06 |
% 31.34/10.06 | From (831)(829) and (435) follows:
% 31.34/10.06 | (833) sum(n14, n14) = all_0_3_3
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 31.34/10.06 | (834) all_0_3_3 = n7
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n6, n1, all_0_0_0, n7 and discharging atoms sum(n6, n1) = all_0_0_0, sum(n6, n1) = n7, yields:
% 31.34/10.06 | (835) all_0_0_0 = n7
% 31.34/10.06 |
% 31.34/10.06 | Equations (835,834) can reduce 201 to:
% 31.34/10.06 | (746) $false
% 31.34/10.06 |
% 31.34/10.06 |-The branch is then unsatisfiable
% 31.34/10.06 |-Branch two:
% 31.34/10.06 | (1053) ~ (all_0_11_11 = n3)
% 31.34/10.06 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.06 |
% 31.34/10.06 +-Applying beta-rule and splitting (1054), into two cases.
% 31.34/10.06 |-Branch one:
% 31.34/10.06 | (1055) all_0_11_11 = n2
% 31.34/10.06 |
% 31.34/10.06 | From (1055) and (190) follows:
% 31.34/10.06 | (1056) pred(n2) = all_0_9_9
% 31.34/10.06 |
% 31.34/10.06 | From (1055) and (505) follows:
% 31.34/10.06 | (1057) succ(n2) = all_0_5_5
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 31.34/10.06 | (1058) all_0_9_9 = n1
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.34/10.06 | (1059) all_0_5_5 = n3
% 31.34/10.06 |
% 31.34/10.06 | From (1058)(1059) and (156) follows:
% 31.34/10.06 | (1060) sum(n1, n3) = all_0_2_2
% 31.34/10.06 |
% 31.34/10.06 | From (1058) and (6322) follows:
% 31.34/10.06 | (6501) sum(n1, n12) = all_0_7_7
% 31.34/10.06 |
% 31.34/10.06 | From (1059) and (6320) follows:
% 31.34/10.06 | (6502) sum(n10, n3) = all_0_4_4
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n10, n3, all_0_4_4, n13 and discharging atoms sum(n10, n3) = all_0_4_4, sum(n10, n3) = n13, yields:
% 31.34/10.06 | (847) all_0_4_4 = n13
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n1, n12, all_0_7_7, n13 and discharging atoms sum(n1, n12) = all_0_7_7, sum(n1, n12) = n13, yields:
% 31.34/10.06 | (849) all_0_7_7 = n13
% 31.34/10.06 |
% 31.34/10.06 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 31.34/10.06 | (1064) all_0_2_2 = n4
% 31.34/10.06 |
% 31.34/10.06 | From (1064) and (6324) follows:
% 31.34/10.06 | (6506) sum(n4, n1) = all_0_0_0
% 31.34/10.06 |
% 31.34/10.06 | From (849)(847) and (435) follows:
% 31.34/10.06 | (851) sum(n13, n13) = all_0_3_3
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 31.34/10.07 | (852) all_0_3_3 = n5
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n4, n1, all_0_0_0, n5 and discharging atoms sum(n4, n1) = all_0_0_0, sum(n4, n1) = n5, yields:
% 31.34/10.07 | (853) all_0_0_0 = n5
% 31.34/10.07 |
% 31.34/10.07 | Equations (853,852) can reduce 201 to:
% 31.34/10.07 | (746) $false
% 31.34/10.07 |
% 31.34/10.07 |-The branch is then unsatisfiable
% 31.34/10.07 |-Branch two:
% 31.34/10.07 | (1071) ~ (all_0_11_11 = n2)
% 31.34/10.07 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.07 |
% 31.34/10.07 +-Applying beta-rule and splitting (1072), into two cases.
% 31.34/10.07 |-Branch one:
% 31.34/10.07 | (1073) all_0_11_11 = n1
% 31.34/10.07 |
% 31.34/10.07 | From (1073) and (190) follows:
% 31.34/10.07 | (1074) pred(n1) = all_0_9_9
% 31.34/10.07 |
% 31.34/10.07 | From (1073) and (505) follows:
% 31.34/10.07 | (1075) succ(n1) = all_0_5_5
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 31.34/10.07 | (1076) all_0_9_9 = n0
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.34/10.07 | (1077) all_0_5_5 = n2
% 31.34/10.07 |
% 31.34/10.07 | From (1076)(1077) and (156) follows:
% 31.34/10.07 | (1078) sum(n0, n2) = all_0_2_2
% 31.34/10.07 |
% 31.34/10.07 | From (1076) and (6322) follows:
% 31.34/10.07 | (6519) sum(n0, n12) = all_0_7_7
% 31.34/10.07 |
% 31.34/10.07 | From (1077) and (6320) follows:
% 31.34/10.07 | (6520) sum(n10, n2) = all_0_4_4
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n10, n2, all_0_4_4, n12 and discharging atoms sum(n10, n2) = all_0_4_4, sum(n10, n2) = n12, yields:
% 31.34/10.07 | (865) all_0_4_4 = n12
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n0, n12, all_0_7_7, n12 and discharging atoms sum(n0, n12) = all_0_7_7, sum(n0, n12) = n12, yields:
% 31.34/10.07 | (867) all_0_7_7 = n12
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 31.34/10.07 | (1082) all_0_2_2 = n2
% 31.34/10.07 |
% 31.34/10.07 | From (1082) and (6324) follows:
% 31.34/10.07 | (6524) sum(n2, n1) = all_0_0_0
% 31.34/10.07 |
% 31.34/10.07 | From (867)(865) and (435) follows:
% 31.34/10.07 | (869) sum(n12, n12) = all_0_3_3
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 31.34/10.07 | (870) all_0_3_3 = n3
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n2, n1, all_0_0_0, n3 and discharging atoms sum(n2, n1) = all_0_0_0, sum(n2, n1) = n3, yields:
% 31.34/10.07 | (871) all_0_0_0 = n3
% 31.34/10.07 |
% 31.34/10.07 | Equations (871,870) can reduce 201 to:
% 31.34/10.07 | (746) $false
% 31.34/10.07 |
% 31.34/10.07 |-The branch is then unsatisfiable
% 31.34/10.07 |-Branch two:
% 31.34/10.07 | (1090) ~ (all_0_11_11 = n1)
% 31.34/10.07 | (1091) all_0_11_11 = n0
% 31.34/10.07 |
% 31.34/10.07 | From (1091) and (190) follows:
% 31.34/10.07 | (1092) pred(n0) = all_0_9_9
% 31.34/10.07 |
% 31.34/10.07 | From (1091) and (505) follows:
% 31.34/10.07 | (1093) succ(n0) = all_0_5_5
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 31.34/10.07 | (1094) all_0_9_9 = n20
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.34/10.07 | (1095) all_0_5_5 = n1
% 31.34/10.07 |
% 31.34/10.07 | From (1094)(1095) and (156) follows:
% 31.34/10.07 | (1096) sum(n20, n1) = all_0_2_2
% 31.34/10.07 |
% 31.34/10.07 | From (1094) and (6322) follows:
% 31.34/10.07 | (6536) sum(n20, n12) = all_0_7_7
% 31.34/10.07 |
% 31.34/10.07 | From (1095) and (6320) follows:
% 31.34/10.07 | (6537) sum(n10, n1) = all_0_4_4
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n20, n12, all_0_7_7, n11 and discharging atoms sum(n20, n12) = all_0_7_7, sum(n20, n12) = n11, yields:
% 31.34/10.07 | (885) all_0_7_7 = n11
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 31.34/10.07 | (1099) all_0_2_2 = n0
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n10, n1, all_0_4_4, n11 and discharging atoms sum(n10, n1) = all_0_4_4, sum(n10, n1) = n11, yields:
% 31.34/10.07 | (883) all_0_4_4 = n11
% 31.34/10.07 |
% 31.34/10.07 | From (1099) and (6324) follows:
% 31.34/10.07 | (6541) sum(n0, n1) = all_0_0_0
% 31.34/10.07 |
% 31.34/10.07 | From (885)(883) and (435) follows:
% 31.34/10.07 | (887) sum(n11, n11) = all_0_3_3
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 31.34/10.07 | (888) all_0_3_3 = n1
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n0, n1, all_0_0_0, n1 and discharging atoms sum(n0, n1) = all_0_0_0, sum(n0, n1) = n1, yields:
% 31.34/10.07 | (889) all_0_0_0 = n1
% 31.34/10.07 |
% 31.34/10.07 | Equations (889,888) can reduce 201 to:
% 31.34/10.07 | (746) $false
% 31.34/10.07 |
% 31.34/10.07 |-The branch is then unsatisfiable
% 31.34/10.07 |-Branch two:
% 31.34/10.07 | (1280) ~ (all_0_10_10 = n11)
% 31.34/10.07 | (1281) all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.34/10.07 |
% 31.34/10.07 +-Applying beta-rule and splitting (892), into two cases.
% 31.34/10.07 |-Branch one:
% 31.34/10.07 | (893) all_0_11_11 = n11
% 31.34/10.07 |
% 31.34/10.07 | From (893) and (190) follows:
% 31.34/10.07 | (894) pred(n11) = all_0_9_9
% 31.34/10.07 |
% 31.34/10.07 | From (893) and (505) follows:
% 31.34/10.07 | (895) succ(n11) = all_0_5_5
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (259) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 31.34/10.07 | (896) all_0_9_9 = n10
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (184) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 31.34/10.07 | (897) all_0_5_5 = n12
% 31.34/10.07 |
% 31.34/10.07 | From (897) and (386) follows:
% 31.34/10.07 | (6553) sum(all_0_6_6, n12) = all_0_4_4
% 31.34/10.07 |
% 31.34/10.07 | From (896)(897) and (156) follows:
% 31.34/10.07 | (898) sum(n10, n12) = all_0_2_2
% 31.34/10.07 |
% 31.34/10.07 | From (896) and (74) follows:
% 31.34/10.07 | (6555) sum(n10, all_0_8_8) = all_0_7_7
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n10, n12, all_0_2_2, n1 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n1, yields:
% 31.34/10.07 | (902) all_0_2_2 = n1
% 31.34/10.07 |
% 31.34/10.07 | From (902) and (85) follows:
% 31.34/10.07 | (6557) sum(n1, all_0_1_1) = all_0_0_0
% 31.34/10.07 |
% 31.34/10.07 +-Applying beta-rule and splitting (1281), into two cases.
% 31.34/10.07 |-Branch one:
% 31.34/10.07 | (1282) all_0_10_10 = n10
% 31.34/10.07 |
% 31.34/10.07 | From (1282) and (57) follows:
% 31.34/10.07 | (1283) pred(n10) = all_0_6_6
% 31.34/10.07 |
% 31.34/10.07 | From (1282) and (381) follows:
% 31.34/10.07 | (1284) succ(n10) = all_0_8_8
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (259) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 31.34/10.07 | (1285) all_0_6_6 = n9
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (184) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 31.34/10.07 | (1286) all_0_8_8 = n11
% 31.34/10.07 |
% 31.34/10.07 | From (1285)(1286) and (628) follows:
% 31.34/10.07 | (1287) sum(n9, n11) = all_0_1_1
% 31.34/10.07 |
% 31.34/10.07 | From (1285) and (6553) follows:
% 31.34/10.07 | (6564) sum(n9, n12) = all_0_4_4
% 31.34/10.07 |
% 31.34/10.07 | From (1286) and (6555) follows:
% 31.34/10.07 | (6565) sum(n10, n11) = all_0_7_7
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n10, n11, all_0_7_7, n0 and discharging atoms sum(n10, n11) = all_0_7_7, sum(n10, n11) = n0, yields:
% 31.34/10.07 | (1083) all_0_7_7 = n0
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n9, n12, all_0_4_4, n0 and discharging atoms sum(n9, n12) = all_0_4_4, sum(n9, n12) = n0, yields:
% 31.34/10.07 | (1081) all_0_4_4 = n0
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 31.34/10.07 | (1291) all_0_1_1 = n20
% 31.34/10.07 |
% 31.34/10.07 | From (1083)(1081) and (435) follows:
% 31.34/10.07 | (1085) sum(n0, n0) = all_0_3_3
% 31.34/10.07 |
% 31.34/10.07 | From (1291) and (6557) follows:
% 31.34/10.07 | (6570) sum(n1, n20) = all_0_0_0
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n1, n20, all_0_0_0, n0 and discharging atoms sum(n1, n20) = all_0_0_0, sum(n1, n20) = n0, yields:
% 31.34/10.07 | (1087) all_0_0_0 = n0
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (194) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 31.34/10.07 | (1088) all_0_3_3 = n0
% 31.34/10.07 |
% 31.34/10.07 | Equations (1087,1088) can reduce 201 to:
% 31.34/10.07 | (746) $false
% 31.34/10.07 |
% 31.34/10.07 |-The branch is then unsatisfiable
% 31.34/10.07 |-Branch two:
% 31.34/10.07 | (1298) ~ (all_0_10_10 = n10)
% 31.34/10.07 | (1299) all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.34/10.07 |
% 31.34/10.07 +-Applying beta-rule and splitting (1299), into two cases.
% 31.34/10.07 |-Branch one:
% 31.34/10.07 | (1300) all_0_10_10 = n9
% 31.34/10.07 |
% 31.34/10.07 | From (1300) and (57) follows:
% 31.34/10.07 | (1301) pred(n9) = all_0_6_6
% 31.34/10.07 |
% 31.34/10.07 | From (1300) and (381) follows:
% 31.34/10.07 | (1302) succ(n9) = all_0_8_8
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (259) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 31.34/10.07 | (1303) all_0_6_6 = n8
% 31.34/10.07 |
% 31.34/10.07 | Instantiating formula (184) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 31.34/10.07 | (1304) all_0_8_8 = n10
% 31.34/10.07 |
% 31.34/10.07 | From (1303)(1304) and (628) follows:
% 31.34/10.07 | (1305) sum(n8, n10) = all_0_1_1
% 31.34/10.07 |
% 31.34/10.07 | From (1303) and (6553) follows:
% 31.34/10.08 | (6582) sum(n8, n12) = all_0_4_4
% 31.34/10.08 |
% 31.34/10.08 | From (1304) and (6555) follows:
% 31.34/10.08 | (6583) sum(n10, n10) = all_0_7_7
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n10, n10, all_0_7_7, n20 and discharging atoms sum(n10, n10) = all_0_7_7, sum(n10, n10) = n20, yields:
% 31.34/10.08 | (1100) all_0_7_7 = n20
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n8, n12, all_0_4_4, n20 and discharging atoms sum(n8, n12) = all_0_4_4, sum(n8, n12) = n20, yields:
% 31.34/10.08 | (1101) all_0_4_4 = n20
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 31.34/10.08 | (1309) all_0_1_1 = n18
% 31.34/10.08 |
% 31.34/10.08 | From (1100)(1101) and (435) follows:
% 31.34/10.08 | (1103) sum(n20, n20) = all_0_3_3
% 31.34/10.08 |
% 31.34/10.08 | From (1309) and (6557) follows:
% 31.34/10.08 | (6588) sum(n1, n18) = all_0_0_0
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n20, n20, all_0_3_3, n19 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n19, yields:
% 31.34/10.08 | (1104) all_0_3_3 = n19
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n1, n18, all_0_0_0, n19 and discharging atoms sum(n1, n18) = all_0_0_0, sum(n1, n18) = n19, yields:
% 31.34/10.08 | (1105) all_0_0_0 = n19
% 31.34/10.08 |
% 31.34/10.08 | Equations (1105,1104) can reduce 201 to:
% 31.34/10.08 | (746) $false
% 31.34/10.08 |
% 31.34/10.08 |-The branch is then unsatisfiable
% 31.34/10.08 |-Branch two:
% 31.34/10.08 | (1316) ~ (all_0_10_10 = n9)
% 31.34/10.08 | (1317) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.34/10.08 |
% 31.34/10.08 +-Applying beta-rule and splitting (1317), into two cases.
% 31.34/10.08 |-Branch one:
% 31.34/10.08 | (1318) all_0_10_10 = n8
% 31.34/10.08 |
% 31.34/10.08 | From (1318) and (57) follows:
% 31.34/10.08 | (1319) pred(n8) = all_0_6_6
% 31.34/10.08 |
% 31.34/10.08 | From (1318) and (381) follows:
% 31.34/10.08 | (1320) succ(n8) = all_0_8_8
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (259) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 31.34/10.08 | (1321) all_0_6_6 = n7
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (184) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 31.34/10.08 | (1322) all_0_8_8 = n9
% 31.34/10.08 |
% 31.34/10.08 | From (1321)(1322) and (628) follows:
% 31.34/10.08 | (1323) sum(n7, n9) = all_0_1_1
% 31.34/10.08 |
% 31.34/10.08 | From (1321) and (6553) follows:
% 31.34/10.08 | (6600) sum(n7, n12) = all_0_4_4
% 31.34/10.08 |
% 31.34/10.08 | From (1322) and (6555) follows:
% 31.34/10.08 | (6601) sum(n10, n9) = all_0_7_7
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n10, n9, all_0_7_7, n19 and discharging atoms sum(n10, n9) = all_0_7_7, sum(n10, n9) = n19, yields:
% 31.34/10.08 | (737) all_0_7_7 = n19
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n7, n12, all_0_4_4, n19 and discharging atoms sum(n7, n12) = all_0_4_4, sum(n7, n12) = n19, yields:
% 31.34/10.08 | (736) all_0_4_4 = n19
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 31.34/10.08 | (1327) all_0_1_1 = n16
% 31.34/10.08 |
% 31.34/10.08 | From (737)(736) and (435) follows:
% 31.34/10.08 | (741) sum(n19, n19) = all_0_3_3
% 31.34/10.08 |
% 31.34/10.08 | From (1327) and (6557) follows:
% 31.34/10.08 | (6606) sum(n1, n16) = all_0_0_0
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 31.34/10.08 | (744) all_0_3_3 = n17
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n1, n16, all_0_0_0, n17 and discharging atoms sum(n1, n16) = all_0_0_0, sum(n1, n16) = n17, yields:
% 31.34/10.08 | (742) all_0_0_0 = n17
% 31.34/10.08 |
% 31.34/10.08 | Equations (742,744) can reduce 201 to:
% 31.34/10.08 | (746) $false
% 31.34/10.08 |
% 31.34/10.08 |-The branch is then unsatisfiable
% 31.34/10.08 |-Branch two:
% 31.34/10.08 | (1334) ~ (all_0_10_10 = n8)
% 31.34/10.08 | (1335) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.34/10.08 |
% 31.34/10.08 +-Applying beta-rule and splitting (1335), into two cases.
% 31.34/10.08 |-Branch one:
% 31.34/10.08 | (1336) all_0_10_10 = n7
% 31.34/10.08 |
% 31.34/10.08 | From (1336) and (57) follows:
% 31.34/10.08 | (1337) pred(n7) = all_0_6_6
% 31.34/10.08 |
% 31.34/10.08 | From (1336) and (381) follows:
% 31.34/10.08 | (1338) succ(n7) = all_0_8_8
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (259) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 31.34/10.08 | (1339) all_0_6_6 = n6
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (184) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 31.34/10.08 | (1340) all_0_8_8 = n8
% 31.34/10.08 |
% 31.34/10.08 | From (1339)(1340) and (628) follows:
% 31.34/10.08 | (1341) sum(n6, n8) = all_0_1_1
% 31.34/10.08 |
% 31.34/10.08 | From (1339) and (6553) follows:
% 31.34/10.08 | (6618) sum(n6, n12) = all_0_4_4
% 31.34/10.08 |
% 31.34/10.08 | From (1340) and (6555) follows:
% 31.34/10.08 | (6619) sum(n10, n8) = all_0_7_7
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n10, n8, all_0_7_7, n18 and discharging atoms sum(n10, n8) = all_0_7_7, sum(n10, n8) = n18, yields:
% 31.34/10.08 | (759) all_0_7_7 = n18
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n6, n12, all_0_4_4, n18 and discharging atoms sum(n6, n12) = all_0_4_4, sum(n6, n12) = n18, yields:
% 31.34/10.08 | (757) all_0_4_4 = n18
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 31.34/10.08 | (1345) all_0_1_1 = n14
% 31.34/10.08 |
% 31.34/10.08 | From (759)(757) and (435) follows:
% 31.34/10.08 | (761) sum(n18, n18) = all_0_3_3
% 31.34/10.08 |
% 31.34/10.08 | From (1345) and (6557) follows:
% 31.34/10.08 | (6624) sum(n1, n14) = all_0_0_0
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 31.34/10.08 | (762) all_0_3_3 = n15
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n1, n14, all_0_0_0, n15 and discharging atoms sum(n1, n14) = all_0_0_0, sum(n1, n14) = n15, yields:
% 31.34/10.08 | (763) all_0_0_0 = n15
% 31.34/10.08 |
% 31.34/10.08 | Equations (763,762) can reduce 201 to:
% 31.34/10.08 | (746) $false
% 31.34/10.08 |
% 31.34/10.08 |-The branch is then unsatisfiable
% 31.34/10.08 |-Branch two:
% 31.34/10.08 | (1352) ~ (all_0_10_10 = n7)
% 31.34/10.08 | (1353) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.34/10.08 |
% 31.34/10.08 +-Applying beta-rule and splitting (1353), into two cases.
% 31.34/10.08 |-Branch one:
% 31.34/10.08 | (1354) all_0_10_10 = n6
% 31.34/10.08 |
% 31.34/10.08 | From (1354) and (57) follows:
% 31.34/10.08 | (1355) pred(n6) = all_0_6_6
% 31.34/10.08 |
% 31.34/10.08 | From (1354) and (381) follows:
% 31.34/10.08 | (1356) succ(n6) = all_0_8_8
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (259) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 31.34/10.08 | (1357) all_0_6_6 = n5
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (184) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 31.34/10.08 | (1358) all_0_8_8 = n7
% 31.34/10.08 |
% 31.34/10.08 | From (1357)(1358) and (628) follows:
% 31.34/10.08 | (1359) sum(n5, n7) = all_0_1_1
% 31.34/10.08 |
% 31.34/10.08 | From (1357) and (6553) follows:
% 31.34/10.08 | (6636) sum(n5, n12) = all_0_4_4
% 31.34/10.08 |
% 31.34/10.08 | From (1358) and (6555) follows:
% 31.34/10.08 | (6637) sum(n10, n7) = all_0_7_7
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n10, n7, all_0_7_7, n17 and discharging atoms sum(n10, n7) = all_0_7_7, sum(n10, n7) = n17, yields:
% 31.34/10.08 | (777) all_0_7_7 = n17
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n5, n12, all_0_4_4, n17 and discharging atoms sum(n5, n12) = all_0_4_4, sum(n5, n12) = n17, yields:
% 31.34/10.08 | (775) all_0_4_4 = n17
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 31.34/10.08 | (1363) all_0_1_1 = n12
% 31.34/10.08 |
% 31.34/10.08 | From (777)(775) and (435) follows:
% 31.34/10.08 | (779) sum(n17, n17) = all_0_3_3
% 31.34/10.08 |
% 31.34/10.08 | From (1363) and (6557) follows:
% 31.34/10.08 | (6642) sum(n1, n12) = all_0_0_0
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 31.34/10.08 | (780) all_0_3_3 = n13
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (194) with n1, n12, all_0_0_0, n13 and discharging atoms sum(n1, n12) = all_0_0_0, sum(n1, n12) = n13, yields:
% 31.34/10.08 | (781) all_0_0_0 = n13
% 31.34/10.08 |
% 31.34/10.08 | Equations (781,780) can reduce 201 to:
% 31.34/10.08 | (746) $false
% 31.34/10.08 |
% 31.34/10.08 |-The branch is then unsatisfiable
% 31.34/10.08 |-Branch two:
% 31.34/10.08 | (1370) ~ (all_0_10_10 = n6)
% 31.34/10.08 | (1371) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.34/10.08 |
% 31.34/10.08 +-Applying beta-rule and splitting (1371), into two cases.
% 31.34/10.08 |-Branch one:
% 31.34/10.08 | (1372) all_0_10_10 = n5
% 31.34/10.08 |
% 31.34/10.08 | From (1372) and (57) follows:
% 31.34/10.08 | (1373) pred(n5) = all_0_6_6
% 31.34/10.08 |
% 31.34/10.08 | From (1372) and (381) follows:
% 31.34/10.08 | (1374) succ(n5) = all_0_8_8
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (259) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 31.34/10.08 | (1375) all_0_6_6 = n4
% 31.34/10.08 |
% 31.34/10.08 | Instantiating formula (184) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 31.34/10.08 | (1376) all_0_8_8 = n6
% 31.34/10.08 |
% 31.34/10.08 | From (1375)(1376) and (628) follows:
% 31.34/10.08 | (1377) sum(n4, n6) = all_0_1_1
% 31.34/10.08 |
% 31.34/10.08 | From (1375) and (6553) follows:
% 31.34/10.09 | (6654) sum(n4, n12) = all_0_4_4
% 31.34/10.09 |
% 31.34/10.09 | From (1376) and (6555) follows:
% 31.34/10.09 | (6655) sum(n10, n6) = all_0_7_7
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n10, n6, all_0_7_7, n16 and discharging atoms sum(n10, n6) = all_0_7_7, sum(n10, n6) = n16, yields:
% 31.34/10.09 | (795) all_0_7_7 = n16
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n4, n12, all_0_4_4, n16 and discharging atoms sum(n4, n12) = all_0_4_4, sum(n4, n12) = n16, yields:
% 31.34/10.09 | (793) all_0_4_4 = n16
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 31.34/10.09 | (1381) all_0_1_1 = n10
% 31.34/10.09 |
% 31.34/10.09 | From (795)(793) and (435) follows:
% 31.34/10.09 | (797) sum(n16, n16) = all_0_3_3
% 31.34/10.09 |
% 31.34/10.09 | From (1381) and (6557) follows:
% 31.34/10.09 | (6660) sum(n1, n10) = all_0_0_0
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 31.34/10.09 | (798) all_0_3_3 = n11
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n1, n10, all_0_0_0, n11 and discharging atoms sum(n1, n10) = all_0_0_0, sum(n1, n10) = n11, yields:
% 31.34/10.09 | (799) all_0_0_0 = n11
% 31.34/10.09 |
% 31.34/10.09 | Equations (799,798) can reduce 201 to:
% 31.34/10.09 | (746) $false
% 31.34/10.09 |
% 31.34/10.09 |-The branch is then unsatisfiable
% 31.34/10.09 |-Branch two:
% 31.34/10.09 | (1388) ~ (all_0_10_10 = n5)
% 31.34/10.09 | (1389) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.34/10.09 |
% 31.34/10.09 +-Applying beta-rule and splitting (1389), into two cases.
% 31.34/10.09 |-Branch one:
% 31.34/10.09 | (1390) all_0_10_10 = n4
% 31.34/10.09 |
% 31.34/10.09 | From (1390) and (57) follows:
% 31.34/10.09 | (1391) pred(n4) = all_0_6_6
% 31.34/10.09 |
% 31.34/10.09 | From (1390) and (381) follows:
% 31.34/10.09 | (1392) succ(n4) = all_0_8_8
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (259) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 31.34/10.09 | (1393) all_0_6_6 = n3
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (184) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 31.34/10.09 | (1394) all_0_8_8 = n5
% 31.34/10.09 |
% 31.34/10.09 | From (1393)(1394) and (628) follows:
% 31.34/10.09 | (1395) sum(n3, n5) = all_0_1_1
% 31.34/10.09 |
% 31.34/10.09 | From (1393) and (6553) follows:
% 31.34/10.09 | (6672) sum(n3, n12) = all_0_4_4
% 31.34/10.09 |
% 31.34/10.09 | From (1394) and (6555) follows:
% 31.34/10.09 | (6673) sum(n10, n5) = all_0_7_7
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n10, n5, all_0_7_7, n15 and discharging atoms sum(n10, n5) = all_0_7_7, sum(n10, n5) = n15, yields:
% 31.34/10.09 | (813) all_0_7_7 = n15
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n3, n12, all_0_4_4, n15 and discharging atoms sum(n3, n12) = all_0_4_4, sum(n3, n12) = n15, yields:
% 31.34/10.09 | (811) all_0_4_4 = n15
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 31.34/10.09 | (1399) all_0_1_1 = n8
% 31.34/10.09 |
% 31.34/10.09 | From (813)(811) and (435) follows:
% 31.34/10.09 | (815) sum(n15, n15) = all_0_3_3
% 31.34/10.09 |
% 31.34/10.09 | From (1399) and (6557) follows:
% 31.34/10.09 | (6678) sum(n1, n8) = all_0_0_0
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 31.34/10.09 | (816) all_0_3_3 = n9
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n1, n8, all_0_0_0, n9 and discharging atoms sum(n1, n8) = all_0_0_0, sum(n1, n8) = n9, yields:
% 31.34/10.09 | (817) all_0_0_0 = n9
% 31.34/10.09 |
% 31.34/10.09 | Equations (817,816) can reduce 201 to:
% 31.34/10.09 | (746) $false
% 31.34/10.09 |
% 31.34/10.09 |-The branch is then unsatisfiable
% 31.34/10.09 |-Branch two:
% 31.34/10.09 | (1406) ~ (all_0_10_10 = n4)
% 31.34/10.09 | (1407) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.34/10.09 |
% 31.34/10.09 +-Applying beta-rule and splitting (1407), into two cases.
% 31.34/10.09 |-Branch one:
% 31.34/10.09 | (1408) all_0_10_10 = n3
% 31.34/10.09 |
% 31.34/10.09 | From (1408) and (57) follows:
% 31.34/10.09 | (1409) pred(n3) = all_0_6_6
% 31.34/10.09 |
% 31.34/10.09 | From (1408) and (381) follows:
% 31.34/10.09 | (1410) succ(n3) = all_0_8_8
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 31.34/10.09 | (1411) all_0_6_6 = n2
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 31.34/10.09 | (1412) all_0_8_8 = n4
% 31.34/10.09 |
% 31.34/10.09 | From (1411)(1412) and (628) follows:
% 31.34/10.09 | (1413) sum(n2, n4) = all_0_1_1
% 31.34/10.09 |
% 31.34/10.09 | From (1411) and (6553) follows:
% 31.34/10.09 | (6690) sum(n2, n12) = all_0_4_4
% 31.34/10.09 |
% 31.34/10.09 | From (1412) and (6555) follows:
% 31.34/10.09 | (6691) sum(n10, n4) = all_0_7_7
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n10, n4, all_0_7_7, n14 and discharging atoms sum(n10, n4) = all_0_7_7, sum(n10, n4) = n14, yields:
% 31.34/10.09 | (831) all_0_7_7 = n14
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n2, n12, all_0_4_4, n14 and discharging atoms sum(n2, n12) = all_0_4_4, sum(n2, n12) = n14, yields:
% 31.34/10.09 | (829) all_0_4_4 = n14
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 31.34/10.09 | (1417) all_0_1_1 = n6
% 31.34/10.09 |
% 31.34/10.09 | From (831)(829) and (435) follows:
% 31.34/10.09 | (833) sum(n14, n14) = all_0_3_3
% 31.34/10.09 |
% 31.34/10.09 | From (1417) and (6557) follows:
% 31.34/10.09 | (6696) sum(n1, n6) = all_0_0_0
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 31.34/10.09 | (834) all_0_3_3 = n7
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n1, n6, all_0_0_0, n7 and discharging atoms sum(n1, n6) = all_0_0_0, sum(n1, n6) = n7, yields:
% 31.34/10.09 | (835) all_0_0_0 = n7
% 31.34/10.09 |
% 31.34/10.09 | Equations (835,834) can reduce 201 to:
% 31.34/10.09 | (746) $false
% 31.34/10.09 |
% 31.34/10.09 |-The branch is then unsatisfiable
% 31.34/10.09 |-Branch two:
% 31.34/10.09 | (1424) ~ (all_0_10_10 = n3)
% 31.34/10.09 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.34/10.09 |
% 31.34/10.09 +-Applying beta-rule and splitting (1425), into two cases.
% 31.34/10.09 |-Branch one:
% 31.34/10.09 | (1426) all_0_10_10 = n2
% 31.34/10.09 |
% 31.34/10.09 | From (1426) and (57) follows:
% 31.34/10.09 | (1427) pred(n2) = all_0_6_6
% 31.34/10.09 |
% 31.34/10.09 | From (1426) and (381) follows:
% 31.34/10.09 | (1428) succ(n2) = all_0_8_8
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 31.34/10.09 | (1429) all_0_6_6 = n1
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 31.34/10.09 | (1430) all_0_8_8 = n3
% 31.34/10.09 |
% 31.34/10.09 | From (1429)(1430) and (628) follows:
% 31.34/10.09 | (1431) sum(n1, n3) = all_0_1_1
% 31.34/10.09 |
% 31.34/10.09 | From (1429) and (6553) follows:
% 31.34/10.09 | (6708) sum(n1, n12) = all_0_4_4
% 31.34/10.09 |
% 31.34/10.09 | From (1430) and (6555) follows:
% 31.34/10.09 | (6709) sum(n10, n3) = all_0_7_7
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n10, n3, all_0_7_7, n13 and discharging atoms sum(n10, n3) = all_0_7_7, sum(n10, n3) = n13, yields:
% 31.34/10.09 | (849) all_0_7_7 = n13
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n1, n12, all_0_4_4, n13 and discharging atoms sum(n1, n12) = all_0_4_4, sum(n1, n12) = n13, yields:
% 31.34/10.09 | (847) all_0_4_4 = n13
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 31.34/10.09 | (1435) all_0_1_1 = n4
% 31.34/10.09 |
% 31.34/10.09 | From (849)(847) and (435) follows:
% 31.34/10.09 | (851) sum(n13, n13) = all_0_3_3
% 31.34/10.09 |
% 31.34/10.09 | From (1435) and (6557) follows:
% 31.34/10.09 | (6714) sum(n1, n4) = all_0_0_0
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 31.34/10.09 | (852) all_0_3_3 = n5
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (194) with n1, n4, all_0_0_0, n5 and discharging atoms sum(n1, n4) = all_0_0_0, sum(n1, n4) = n5, yields:
% 31.34/10.09 | (853) all_0_0_0 = n5
% 31.34/10.09 |
% 31.34/10.09 | Equations (853,852) can reduce 201 to:
% 31.34/10.09 | (746) $false
% 31.34/10.09 |
% 31.34/10.09 |-The branch is then unsatisfiable
% 31.34/10.09 |-Branch two:
% 31.34/10.09 | (1442) ~ (all_0_10_10 = n2)
% 31.34/10.09 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 31.34/10.09 |
% 31.34/10.09 +-Applying beta-rule and splitting (1443), into two cases.
% 31.34/10.09 |-Branch one:
% 31.34/10.09 | (1444) all_0_10_10 = n1
% 31.34/10.09 |
% 31.34/10.09 | From (1444) and (57) follows:
% 31.34/10.09 | (1445) pred(n1) = all_0_6_6
% 31.34/10.09 |
% 31.34/10.09 | From (1444) and (381) follows:
% 31.34/10.09 | (1446) succ(n1) = all_0_8_8
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 31.34/10.09 | (1447) all_0_6_6 = n0
% 31.34/10.09 |
% 31.34/10.09 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 31.34/10.09 | (1448) all_0_8_8 = n2
% 31.34/10.09 |
% 31.34/10.09 | From (1447)(1448) and (628) follows:
% 31.34/10.09 | (1449) sum(n0, n2) = all_0_1_1
% 31.34/10.09 |
% 31.34/10.09 | From (1447) and (6553) follows:
% 31.34/10.10 | (6726) sum(n0, n12) = all_0_4_4
% 31.34/10.10 |
% 31.34/10.10 | From (1448) and (6555) follows:
% 31.34/10.10 | (6727) sum(n10, n2) = all_0_7_7
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (194) with n10, n2, all_0_7_7, n12 and discharging atoms sum(n10, n2) = all_0_7_7, sum(n10, n2) = n12, yields:
% 31.34/10.10 | (867) all_0_7_7 = n12
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (194) with n0, n12, all_0_4_4, n12 and discharging atoms sum(n0, n12) = all_0_4_4, sum(n0, n12) = n12, yields:
% 31.34/10.10 | (865) all_0_4_4 = n12
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 31.34/10.10 | (1453) all_0_1_1 = n2
% 31.34/10.10 |
% 31.34/10.10 | From (867)(865) and (435) follows:
% 31.34/10.10 | (869) sum(n12, n12) = all_0_3_3
% 31.34/10.10 |
% 31.34/10.10 | From (1453) and (6557) follows:
% 31.34/10.10 | (6732) sum(n1, n2) = all_0_0_0
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 31.34/10.10 | (870) all_0_3_3 = n3
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (194) with n1, n2, all_0_0_0, n3 and discharging atoms sum(n1, n2) = all_0_0_0, sum(n1, n2) = n3, yields:
% 31.34/10.10 | (871) all_0_0_0 = n3
% 31.34/10.10 |
% 31.34/10.10 | Equations (871,870) can reduce 201 to:
% 31.34/10.10 | (746) $false
% 31.34/10.10 |
% 31.34/10.10 |-The branch is then unsatisfiable
% 31.34/10.10 |-Branch two:
% 31.34/10.10 | (1462) ~ (all_0_10_10 = n1)
% 31.34/10.10 | (1463) all_0_10_10 = n0
% 31.34/10.10 |
% 31.34/10.10 | From (1463) and (57) follows:
% 31.34/10.10 | (1464) pred(n0) = all_0_6_6
% 31.34/10.10 |
% 31.34/10.10 | From (1463) and (381) follows:
% 31.34/10.10 | (1465) succ(n0) = all_0_8_8
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 31.34/10.10 | (1466) all_0_6_6 = n20
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 31.34/10.10 | (1467) all_0_8_8 = n1
% 31.34/10.10 |
% 31.34/10.10 | From (1466)(1467) and (628) follows:
% 31.34/10.10 | (1468) sum(n20, n1) = all_0_1_1
% 31.34/10.10 |
% 31.34/10.10 | From (1466) and (6553) follows:
% 31.34/10.10 | (6743) sum(n20, n12) = all_0_4_4
% 31.34/10.10 |
% 31.34/10.10 | From (1467) and (6555) follows:
% 31.34/10.10 | (6744) sum(n10, n1) = all_0_7_7
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (194) with n20, n12, all_0_4_4, n11 and discharging atoms sum(n20, n12) = all_0_4_4, sum(n20, n12) = n11, yields:
% 31.34/10.10 | (883) all_0_4_4 = n11
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 31.34/10.10 | (1471) all_0_1_1 = n0
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (194) with n10, n1, all_0_7_7, n11 and discharging atoms sum(n10, n1) = all_0_7_7, sum(n10, n1) = n11, yields:
% 31.34/10.10 | (885) all_0_7_7 = n11
% 31.34/10.10 |
% 31.34/10.10 | From (885)(883) and (435) follows:
% 31.34/10.10 | (887) sum(n11, n11) = all_0_3_3
% 31.34/10.10 |
% 31.34/10.10 | From (1471) and (6557) follows:
% 31.34/10.10 | (6749) sum(n1, n0) = all_0_0_0
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 31.34/10.10 | (888) all_0_3_3 = n1
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (194) with n1, n0, all_0_0_0, n1 and discharging atoms sum(n1, n0) = all_0_0_0, sum(n1, n0) = n1, yields:
% 31.34/10.10 | (889) all_0_0_0 = n1
% 31.34/10.10 |
% 31.34/10.10 | Equations (889,888) can reduce 201 to:
% 31.34/10.10 | (746) $false
% 31.34/10.10 |
% 31.34/10.10 |-The branch is then unsatisfiable
% 31.34/10.10 |-Branch two:
% 31.34/10.10 | (909) ~ (all_0_11_11 = n11)
% 31.34/10.10 | (910) all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.10 |
% 31.34/10.10 +-Applying beta-rule and splitting (1281), into two cases.
% 31.34/10.10 |-Branch one:
% 31.34/10.10 | (1282) all_0_10_10 = n10
% 31.34/10.10 |
% 31.34/10.10 | From (1282) and (57) follows:
% 31.34/10.10 | (1283) pred(n10) = all_0_6_6
% 31.34/10.10 |
% 31.34/10.10 | From (1282) and (381) follows:
% 31.34/10.10 | (1284) succ(n10) = all_0_8_8
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (259) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 31.34/10.10 | (1285) all_0_6_6 = n9
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (184) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 31.34/10.10 | (1286) all_0_8_8 = n11
% 31.34/10.10 |
% 31.34/10.10 | From (1285) and (1283) follows:
% 31.34/10.10 | (473) pred(n10) = n9
% 31.34/10.10 |
% 31.34/10.10 | From (1286) and (1284) follows:
% 31.34/10.10 | (682) succ(n10) = n11
% 31.34/10.10 |
% 31.34/10.10 | From (1285) and (386) follows:
% 31.34/10.10 | (6762) sum(n9, all_0_5_5) = all_0_4_4
% 31.34/10.10 |
% 31.34/10.10 | From (1285)(1286) and (628) follows:
% 31.34/10.10 | (1287) sum(n9, n11) = all_0_1_1
% 31.34/10.10 |
% 31.34/10.10 | From (1286) and (74) follows:
% 31.34/10.10 | (6764) sum(all_0_9_9, n11) = all_0_7_7
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (194) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 31.34/10.10 | (1291) all_0_1_1 = n20
% 31.34/10.10 |
% 31.34/10.10 | From (1291) and (85) follows:
% 31.34/10.10 | (6766) sum(all_0_2_2, n20) = all_0_0_0
% 31.34/10.10 |
% 31.34/10.10 | From (1291) and (1287) follows:
% 31.34/10.10 | (457) sum(n9, n11) = n20
% 31.34/10.10 |
% 31.34/10.10 +-Applying beta-rule and splitting (910), into two cases.
% 31.34/10.10 |-Branch one:
% 31.34/10.10 | (911) all_0_11_11 = n10
% 31.34/10.10 |
% 31.34/10.10 | From (911) and (190) follows:
% 31.34/10.10 | (912) pred(n10) = all_0_9_9
% 31.34/10.10 |
% 31.34/10.10 | From (911) and (505) follows:
% 31.34/10.10 | (913) succ(n10) = all_0_5_5
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (259) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 31.34/10.10 | (914) all_0_9_9 = n9
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (184) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 31.34/10.10 | (915) all_0_5_5 = n11
% 31.34/10.10 |
% 31.34/10.10 | From (914)(915) and (156) follows:
% 31.34/10.10 | (916) sum(n9, n11) = all_0_2_2
% 31.34/10.10 |
% 31.34/10.10 | From (914) and (6764) follows:
% 31.34/10.10 | (6774) sum(n9, n11) = all_0_7_7
% 31.34/10.10 |
% 31.34/10.10 | From (915) and (6762) follows:
% 31.34/10.10 | (6775) sum(n9, n11) = all_0_4_4
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (194) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 31.34/10.10 | (920) all_0_2_2 = n20
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (194) with n9, n11, all_0_4_4, all_0_2_2 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = all_0_4_4, yields:
% 31.34/10.10 | (733) all_0_2_2 = all_0_4_4
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (194) with n9, n11, all_0_7_7, all_0_2_2 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = all_0_7_7, yields:
% 31.34/10.10 | (734) all_0_2_2 = all_0_7_7
% 31.34/10.10 |
% 31.34/10.10 | Combining equations (734,733) yields a new equation:
% 31.34/10.10 | (735) all_0_4_4 = all_0_7_7
% 31.34/10.10 |
% 31.34/10.10 | Combining equations (920,733) yields a new equation:
% 31.34/10.10 | (1101) all_0_4_4 = n20
% 31.34/10.10 |
% 31.34/10.10 | Combining equations (1101,735) yields a new equation:
% 31.34/10.10 | (1100) all_0_7_7 = n20
% 31.34/10.10 |
% 31.34/10.10 | Combining equations (1100,735) yields a new equation:
% 31.34/10.10 | (1101) all_0_4_4 = n20
% 31.34/10.10 |
% 31.34/10.10 | Combining equations (1101,733) yields a new equation:
% 31.34/10.10 | (920) all_0_2_2 = n20
% 31.34/10.10 |
% 31.34/10.10 | From (920) and (6766) follows:
% 31.34/10.10 | (6784) sum(n20, n20) = all_0_0_0
% 31.34/10.10 |
% 31.34/10.10 | From (1100)(1101) and (435) follows:
% 31.34/10.10 | (1103) sum(n20, n20) = all_0_3_3
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (194) with n20, n20, all_0_0_0, n19 and discharging atoms sum(n20, n20) = all_0_0_0, sum(n20, n20) = n19, yields:
% 31.34/10.10 | (1105) all_0_0_0 = n19
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (194) with n20, n20, all_0_3_3, all_0_0_0 and discharging atoms sum(n20, n20) = all_0_0_0, sum(n20, n20) = all_0_3_3, yields:
% 31.34/10.10 | (743) all_0_0_0 = all_0_3_3
% 31.34/10.10 |
% 31.34/10.10 | Combining equations (1105,743) yields a new equation:
% 31.34/10.10 | (1104) all_0_3_3 = n19
% 31.34/10.10 |
% 31.34/10.10 | Combining equations (1104,743) yields a new equation:
% 31.34/10.10 | (1105) all_0_0_0 = n19
% 31.34/10.10 |
% 31.34/10.10 | Equations (1105,1104) can reduce 201 to:
% 31.34/10.10 | (746) $false
% 31.34/10.10 |
% 31.34/10.10 |-The branch is then unsatisfiable
% 31.34/10.10 |-Branch two:
% 31.34/10.10 | (927) ~ (all_0_11_11 = n10)
% 31.34/10.10 | (928) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.10 |
% 31.34/10.10 +-Applying beta-rule and splitting (928), into two cases.
% 31.34/10.10 |-Branch one:
% 31.34/10.10 | (929) all_0_11_11 = n9
% 31.34/10.10 |
% 31.34/10.10 | From (929) and (190) follows:
% 31.34/10.10 | (930) pred(n9) = all_0_9_9
% 31.34/10.10 |
% 31.34/10.10 | From (929) and (505) follows:
% 31.34/10.10 | (931) succ(n9) = all_0_5_5
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (259) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 31.34/10.10 | (932) all_0_9_9 = n8
% 31.34/10.10 |
% 31.34/10.10 | Instantiating formula (184) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 31.34/10.10 | (933) all_0_5_5 = n10
% 31.34/10.10 |
% 31.34/10.10 | From (932)(933) and (156) follows:
% 31.34/10.10 | (934) sum(n8, n10) = all_0_2_2
% 31.34/10.10 |
% 31.34/10.10 | From (932) and (6764) follows:
% 31.34/10.10 | (6799) sum(n8, n11) = all_0_7_7
% 31.34/10.10 |
% 31.34/10.10 | From (933) and (6762) follows:
% 31.34/10.11 | (6800) sum(n9, n10) = all_0_4_4
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n9, n10, all_0_4_4, n19 and discharging atoms sum(n9, n10) = all_0_4_4, sum(n9, n10) = n19, yields:
% 31.34/10.11 | (736) all_0_4_4 = n19
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n8, n11, all_0_7_7, n19 and discharging atoms sum(n8, n11) = all_0_7_7, sum(n8, n11) = n19, yields:
% 31.34/10.11 | (737) all_0_7_7 = n19
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 31.34/10.11 | (938) all_0_2_2 = n18
% 31.34/10.11 |
% 31.34/10.11 | From (938) and (6766) follows:
% 31.34/10.11 | (6804) sum(n18, n20) = all_0_0_0
% 31.34/10.11 |
% 31.34/10.11 | From (737)(736) and (435) follows:
% 31.34/10.11 | (741) sum(n19, n19) = all_0_3_3
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 31.34/10.11 | (744) all_0_3_3 = n17
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n18, n20, all_0_0_0, n17 and discharging atoms sum(n18, n20) = all_0_0_0, sum(n18, n20) = n17, yields:
% 31.34/10.11 | (742) all_0_0_0 = n17
% 31.34/10.11 |
% 31.34/10.11 | Equations (742,744) can reduce 201 to:
% 31.34/10.11 | (746) $false
% 31.34/10.11 |
% 31.34/10.11 |-The branch is then unsatisfiable
% 31.34/10.11 |-Branch two:
% 31.34/10.11 | (945) ~ (all_0_11_11 = n9)
% 31.34/10.11 | (946) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.11 |
% 31.34/10.11 +-Applying beta-rule and splitting (946), into two cases.
% 31.34/10.11 |-Branch one:
% 31.34/10.11 | (947) all_0_11_11 = n8
% 31.34/10.11 |
% 31.34/10.11 | From (947) and (190) follows:
% 31.34/10.11 | (948) pred(n8) = all_0_9_9
% 31.34/10.11 |
% 31.34/10.11 | From (947) and (505) follows:
% 31.34/10.11 | (949) succ(n8) = all_0_5_5
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (259) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 31.34/10.11 | (950) all_0_9_9 = n7
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (184) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 31.34/10.11 | (951) all_0_5_5 = n9
% 31.34/10.11 |
% 31.34/10.11 | From (950)(951) and (156) follows:
% 31.34/10.11 | (952) sum(n7, n9) = all_0_2_2
% 31.34/10.11 |
% 31.34/10.11 | From (950) and (6764) follows:
% 31.34/10.11 | (6817) sum(n7, n11) = all_0_7_7
% 31.34/10.11 |
% 31.34/10.11 | From (951) and (6762) follows:
% 31.34/10.11 | (6818) sum(n9, n9) = all_0_4_4
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n9, n9, all_0_4_4, n18 and discharging atoms sum(n9, n9) = all_0_4_4, sum(n9, n9) = n18, yields:
% 31.34/10.11 | (757) all_0_4_4 = n18
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n7, n11, all_0_7_7, n18 and discharging atoms sum(n7, n11) = all_0_7_7, sum(n7, n11) = n18, yields:
% 31.34/10.11 | (759) all_0_7_7 = n18
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 31.34/10.11 | (956) all_0_2_2 = n16
% 31.34/10.11 |
% 31.34/10.11 | From (956) and (6766) follows:
% 31.34/10.11 | (6822) sum(n16, n20) = all_0_0_0
% 31.34/10.11 |
% 31.34/10.11 | From (759)(757) and (435) follows:
% 31.34/10.11 | (761) sum(n18, n18) = all_0_3_3
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 31.34/10.11 | (762) all_0_3_3 = n15
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n16, n20, all_0_0_0, n15 and discharging atoms sum(n16, n20) = all_0_0_0, sum(n16, n20) = n15, yields:
% 31.34/10.11 | (763) all_0_0_0 = n15
% 31.34/10.11 |
% 31.34/10.11 | Equations (763,762) can reduce 201 to:
% 31.34/10.11 | (746) $false
% 31.34/10.11 |
% 31.34/10.11 |-The branch is then unsatisfiable
% 31.34/10.11 |-Branch two:
% 31.34/10.11 | (963) ~ (all_0_11_11 = n8)
% 31.34/10.11 | (964) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.11 |
% 31.34/10.11 +-Applying beta-rule and splitting (964), into two cases.
% 31.34/10.11 |-Branch one:
% 31.34/10.11 | (965) all_0_11_11 = n7
% 31.34/10.11 |
% 31.34/10.11 | From (965) and (190) follows:
% 31.34/10.11 | (966) pred(n7) = all_0_9_9
% 31.34/10.11 |
% 31.34/10.11 | From (965) and (505) follows:
% 31.34/10.11 | (967) succ(n7) = all_0_5_5
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (259) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 31.34/10.11 | (968) all_0_9_9 = n6
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (184) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 31.34/10.11 | (969) all_0_5_5 = n8
% 31.34/10.11 |
% 31.34/10.11 | From (968)(969) and (156) follows:
% 31.34/10.11 | (970) sum(n6, n8) = all_0_2_2
% 31.34/10.11 |
% 31.34/10.11 | From (968) and (6764) follows:
% 31.34/10.11 | (6835) sum(n6, n11) = all_0_7_7
% 31.34/10.11 |
% 31.34/10.11 | From (969) and (6762) follows:
% 31.34/10.11 | (6836) sum(n9, n8) = all_0_4_4
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n9, n8, all_0_4_4, n17 and discharging atoms sum(n9, n8) = all_0_4_4, sum(n9, n8) = n17, yields:
% 31.34/10.11 | (775) all_0_4_4 = n17
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n6, n11, all_0_7_7, n17 and discharging atoms sum(n6, n11) = all_0_7_7, sum(n6, n11) = n17, yields:
% 31.34/10.11 | (777) all_0_7_7 = n17
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 31.34/10.11 | (974) all_0_2_2 = n14
% 31.34/10.11 |
% 31.34/10.11 | From (974) and (6766) follows:
% 31.34/10.11 | (6840) sum(n14, n20) = all_0_0_0
% 31.34/10.11 |
% 31.34/10.11 | From (777)(775) and (435) follows:
% 31.34/10.11 | (779) sum(n17, n17) = all_0_3_3
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 31.34/10.11 | (780) all_0_3_3 = n13
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n14, n20, all_0_0_0, n13 and discharging atoms sum(n14, n20) = all_0_0_0, sum(n14, n20) = n13, yields:
% 31.34/10.11 | (781) all_0_0_0 = n13
% 31.34/10.11 |
% 31.34/10.11 | Equations (781,780) can reduce 201 to:
% 31.34/10.11 | (746) $false
% 31.34/10.11 |
% 31.34/10.11 |-The branch is then unsatisfiable
% 31.34/10.11 |-Branch two:
% 31.34/10.11 | (981) ~ (all_0_11_11 = n7)
% 31.34/10.11 | (982) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.11 |
% 31.34/10.11 +-Applying beta-rule and splitting (982), into two cases.
% 31.34/10.11 |-Branch one:
% 31.34/10.11 | (983) all_0_11_11 = n6
% 31.34/10.11 |
% 31.34/10.11 | From (983) and (190) follows:
% 31.34/10.11 | (984) pred(n6) = all_0_9_9
% 31.34/10.11 |
% 31.34/10.11 | From (983) and (505) follows:
% 31.34/10.11 | (985) succ(n6) = all_0_5_5
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (259) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 31.34/10.11 | (986) all_0_9_9 = n5
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (184) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 31.34/10.11 | (987) all_0_5_5 = n7
% 31.34/10.11 |
% 31.34/10.11 | From (986)(987) and (156) follows:
% 31.34/10.11 | (988) sum(n5, n7) = all_0_2_2
% 31.34/10.11 |
% 31.34/10.11 | From (986) and (6764) follows:
% 31.34/10.11 | (6853) sum(n5, n11) = all_0_7_7
% 31.34/10.11 |
% 31.34/10.11 | From (987) and (6762) follows:
% 31.34/10.11 | (6854) sum(n9, n7) = all_0_4_4
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n9, n7, all_0_4_4, n16 and discharging atoms sum(n9, n7) = all_0_4_4, sum(n9, n7) = n16, yields:
% 31.34/10.11 | (793) all_0_4_4 = n16
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n5, n11, all_0_7_7, n16 and discharging atoms sum(n5, n11) = all_0_7_7, sum(n5, n11) = n16, yields:
% 31.34/10.11 | (795) all_0_7_7 = n16
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 31.34/10.11 | (992) all_0_2_2 = n12
% 31.34/10.11 |
% 31.34/10.11 | From (992) and (6766) follows:
% 31.34/10.11 | (6858) sum(n12, n20) = all_0_0_0
% 31.34/10.11 |
% 31.34/10.11 | From (795)(793) and (435) follows:
% 31.34/10.11 | (797) sum(n16, n16) = all_0_3_3
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 31.34/10.11 | (798) all_0_3_3 = n11
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (194) with n12, n20, all_0_0_0, n11 and discharging atoms sum(n12, n20) = all_0_0_0, sum(n12, n20) = n11, yields:
% 31.34/10.11 | (799) all_0_0_0 = n11
% 31.34/10.11 |
% 31.34/10.11 | Equations (799,798) can reduce 201 to:
% 31.34/10.11 | (746) $false
% 31.34/10.11 |
% 31.34/10.11 |-The branch is then unsatisfiable
% 31.34/10.11 |-Branch two:
% 31.34/10.11 | (999) ~ (all_0_11_11 = n6)
% 31.34/10.11 | (1000) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.11 |
% 31.34/10.11 +-Applying beta-rule and splitting (1000), into two cases.
% 31.34/10.11 |-Branch one:
% 31.34/10.11 | (1001) all_0_11_11 = n5
% 31.34/10.11 |
% 31.34/10.11 | From (1001) and (190) follows:
% 31.34/10.11 | (1002) pred(n5) = all_0_9_9
% 31.34/10.11 |
% 31.34/10.11 | From (1001) and (505) follows:
% 31.34/10.11 | (1003) succ(n5) = all_0_5_5
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (259) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 31.34/10.11 | (1004) all_0_9_9 = n4
% 31.34/10.11 |
% 31.34/10.11 | Instantiating formula (184) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 31.34/10.11 | (1005) all_0_5_5 = n6
% 31.34/10.11 |
% 31.34/10.11 | From (1004)(1005) and (156) follows:
% 31.34/10.11 | (1006) sum(n4, n6) = all_0_2_2
% 31.34/10.11 |
% 31.34/10.11 | From (1004) and (6764) follows:
% 31.34/10.11 | (6871) sum(n4, n11) = all_0_7_7
% 31.34/10.11 |
% 31.34/10.11 | From (1005) and (6762) follows:
% 31.34/10.12 | (6872) sum(n9, n6) = all_0_4_4
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n9, n6, all_0_4_4, n15 and discharging atoms sum(n9, n6) = all_0_4_4, sum(n9, n6) = n15, yields:
% 31.34/10.12 | (811) all_0_4_4 = n15
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n4, n11, all_0_7_7, n15 and discharging atoms sum(n4, n11) = all_0_7_7, sum(n4, n11) = n15, yields:
% 31.34/10.12 | (813) all_0_7_7 = n15
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 31.34/10.12 | (1010) all_0_2_2 = n10
% 31.34/10.12 |
% 31.34/10.12 | From (1010) and (6766) follows:
% 31.34/10.12 | (6876) sum(n10, n20) = all_0_0_0
% 31.34/10.12 |
% 31.34/10.12 | From (813)(811) and (435) follows:
% 31.34/10.12 | (815) sum(n15, n15) = all_0_3_3
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 31.34/10.12 | (816) all_0_3_3 = n9
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n10, n20, all_0_0_0, n9 and discharging atoms sum(n10, n20) = all_0_0_0, sum(n10, n20) = n9, yields:
% 31.34/10.12 | (817) all_0_0_0 = n9
% 31.34/10.12 |
% 31.34/10.12 | Equations (817,816) can reduce 201 to:
% 31.34/10.12 | (746) $false
% 31.34/10.12 |
% 31.34/10.12 |-The branch is then unsatisfiable
% 31.34/10.12 |-Branch two:
% 31.34/10.12 | (1017) ~ (all_0_11_11 = n5)
% 31.34/10.12 | (1018) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.12 |
% 31.34/10.12 +-Applying beta-rule and splitting (1018), into two cases.
% 31.34/10.12 |-Branch one:
% 31.34/10.12 | (1019) all_0_11_11 = n4
% 31.34/10.12 |
% 31.34/10.12 | From (1019) and (190) follows:
% 31.34/10.12 | (1020) pred(n4) = all_0_9_9
% 31.34/10.12 |
% 31.34/10.12 | From (1019) and (505) follows:
% 31.34/10.12 | (1021) succ(n4) = all_0_5_5
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 31.34/10.12 | (1022) all_0_9_9 = n3
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 31.34/10.12 | (1023) all_0_5_5 = n5
% 31.34/10.12 |
% 31.34/10.12 | From (1022)(1023) and (156) follows:
% 31.34/10.12 | (1024) sum(n3, n5) = all_0_2_2
% 31.34/10.12 |
% 31.34/10.12 | From (1022) and (6764) follows:
% 31.34/10.12 | (6889) sum(n3, n11) = all_0_7_7
% 31.34/10.12 |
% 31.34/10.12 | From (1023) and (6762) follows:
% 31.34/10.12 | (6890) sum(n9, n5) = all_0_4_4
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n9, n5, all_0_4_4, n14 and discharging atoms sum(n9, n5) = all_0_4_4, sum(n9, n5) = n14, yields:
% 31.34/10.12 | (829) all_0_4_4 = n14
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n3, n11, all_0_7_7, n14 and discharging atoms sum(n3, n11) = all_0_7_7, sum(n3, n11) = n14, yields:
% 31.34/10.12 | (831) all_0_7_7 = n14
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 31.34/10.12 | (1028) all_0_2_2 = n8
% 31.34/10.12 |
% 31.34/10.12 | From (1028) and (6766) follows:
% 31.34/10.12 | (6894) sum(n8, n20) = all_0_0_0
% 31.34/10.12 |
% 31.34/10.12 | From (831)(829) and (435) follows:
% 31.34/10.12 | (833) sum(n14, n14) = all_0_3_3
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 31.34/10.12 | (834) all_0_3_3 = n7
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n8, n20, all_0_0_0, n7 and discharging atoms sum(n8, n20) = all_0_0_0, sum(n8, n20) = n7, yields:
% 31.34/10.12 | (835) all_0_0_0 = n7
% 31.34/10.12 |
% 31.34/10.12 | Equations (835,834) can reduce 201 to:
% 31.34/10.12 | (746) $false
% 31.34/10.12 |
% 31.34/10.12 |-The branch is then unsatisfiable
% 31.34/10.12 |-Branch two:
% 31.34/10.12 | (1035) ~ (all_0_11_11 = n4)
% 31.34/10.12 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.12 |
% 31.34/10.12 +-Applying beta-rule and splitting (1036), into two cases.
% 31.34/10.12 |-Branch one:
% 31.34/10.12 | (1037) all_0_11_11 = n3
% 31.34/10.12 |
% 31.34/10.12 | From (1037) and (190) follows:
% 31.34/10.12 | (1038) pred(n3) = all_0_9_9
% 31.34/10.12 |
% 31.34/10.12 | From (1037) and (505) follows:
% 31.34/10.12 | (1039) succ(n3) = all_0_5_5
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 31.34/10.12 | (1040) all_0_9_9 = n2
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 31.34/10.12 | (1041) all_0_5_5 = n4
% 31.34/10.12 |
% 31.34/10.12 | From (1040)(1041) and (156) follows:
% 31.34/10.12 | (1042) sum(n2, n4) = all_0_2_2
% 31.34/10.12 |
% 31.34/10.12 | From (1040) and (6764) follows:
% 31.34/10.12 | (6907) sum(n2, n11) = all_0_7_7
% 31.34/10.12 |
% 31.34/10.12 | From (1041) and (6762) follows:
% 31.34/10.12 | (6908) sum(n9, n4) = all_0_4_4
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n9, n4, all_0_4_4, n13 and discharging atoms sum(n9, n4) = all_0_4_4, sum(n9, n4) = n13, yields:
% 31.34/10.12 | (847) all_0_4_4 = n13
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n2, n11, all_0_7_7, n13 and discharging atoms sum(n2, n11) = all_0_7_7, sum(n2, n11) = n13, yields:
% 31.34/10.12 | (849) all_0_7_7 = n13
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 31.34/10.12 | (1046) all_0_2_2 = n6
% 31.34/10.12 |
% 31.34/10.12 | From (1046) and (6766) follows:
% 31.34/10.12 | (6912) sum(n6, n20) = all_0_0_0
% 31.34/10.12 |
% 31.34/10.12 | From (849)(847) and (435) follows:
% 31.34/10.12 | (851) sum(n13, n13) = all_0_3_3
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 31.34/10.12 | (852) all_0_3_3 = n5
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n6, n20, all_0_0_0, n5 and discharging atoms sum(n6, n20) = all_0_0_0, sum(n6, n20) = n5, yields:
% 31.34/10.12 | (853) all_0_0_0 = n5
% 31.34/10.12 |
% 31.34/10.12 | Equations (853,852) can reduce 201 to:
% 31.34/10.12 | (746) $false
% 31.34/10.12 |
% 31.34/10.12 |-The branch is then unsatisfiable
% 31.34/10.12 |-Branch two:
% 31.34/10.12 | (1053) ~ (all_0_11_11 = n3)
% 31.34/10.12 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.12 |
% 31.34/10.12 +-Applying beta-rule and splitting (1054), into two cases.
% 31.34/10.12 |-Branch one:
% 31.34/10.12 | (1055) all_0_11_11 = n2
% 31.34/10.12 |
% 31.34/10.12 | From (1055) and (190) follows:
% 31.34/10.12 | (1056) pred(n2) = all_0_9_9
% 31.34/10.12 |
% 31.34/10.12 | From (1055) and (505) follows:
% 31.34/10.12 | (1057) succ(n2) = all_0_5_5
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 31.34/10.12 | (1058) all_0_9_9 = n1
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.34/10.12 | (1059) all_0_5_5 = n3
% 31.34/10.12 |
% 31.34/10.12 | From (1058)(1059) and (156) follows:
% 31.34/10.12 | (1060) sum(n1, n3) = all_0_2_2
% 31.34/10.12 |
% 31.34/10.12 | From (1058) and (6764) follows:
% 31.34/10.12 | (6925) sum(n1, n11) = all_0_7_7
% 31.34/10.12 |
% 31.34/10.12 | From (1059) and (6762) follows:
% 31.34/10.12 | (6926) sum(n9, n3) = all_0_4_4
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n9, n3, all_0_4_4, n12 and discharging atoms sum(n9, n3) = all_0_4_4, sum(n9, n3) = n12, yields:
% 31.34/10.12 | (865) all_0_4_4 = n12
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n1, n11, all_0_7_7, n12 and discharging atoms sum(n1, n11) = all_0_7_7, sum(n1, n11) = n12, yields:
% 31.34/10.12 | (867) all_0_7_7 = n12
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 31.34/10.12 | (1064) all_0_2_2 = n4
% 31.34/10.12 |
% 31.34/10.12 | From (1064) and (6766) follows:
% 31.34/10.12 | (6930) sum(n4, n20) = all_0_0_0
% 31.34/10.12 |
% 31.34/10.12 | From (867)(865) and (435) follows:
% 31.34/10.12 | (869) sum(n12, n12) = all_0_3_3
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 31.34/10.12 | (870) all_0_3_3 = n3
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (194) with n4, n20, all_0_0_0, n3 and discharging atoms sum(n4, n20) = all_0_0_0, sum(n4, n20) = n3, yields:
% 31.34/10.12 | (871) all_0_0_0 = n3
% 31.34/10.12 |
% 31.34/10.12 | Equations (871,870) can reduce 201 to:
% 31.34/10.12 | (746) $false
% 31.34/10.12 |
% 31.34/10.12 |-The branch is then unsatisfiable
% 31.34/10.12 |-Branch two:
% 31.34/10.12 | (1071) ~ (all_0_11_11 = n2)
% 31.34/10.12 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 31.34/10.12 |
% 31.34/10.12 +-Applying beta-rule and splitting (1072), into two cases.
% 31.34/10.12 |-Branch one:
% 31.34/10.12 | (1073) all_0_11_11 = n1
% 31.34/10.12 |
% 31.34/10.12 | From (1073) and (190) follows:
% 31.34/10.12 | (1074) pred(n1) = all_0_9_9
% 31.34/10.12 |
% 31.34/10.12 | From (1073) and (505) follows:
% 31.34/10.12 | (1075) succ(n1) = all_0_5_5
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 31.34/10.12 | (1076) all_0_9_9 = n0
% 31.34/10.12 |
% 31.34/10.12 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.34/10.12 | (1077) all_0_5_5 = n2
% 31.34/10.12 |
% 31.34/10.12 | From (1076)(1077) and (156) follows:
% 31.34/10.12 | (1078) sum(n0, n2) = all_0_2_2
% 31.34/10.12 |
% 31.34/10.12 | From (1076) and (6764) follows:
% 31.34/10.13 | (6943) sum(n0, n11) = all_0_7_7
% 31.34/10.13 |
% 31.34/10.13 | From (1077) and (6762) follows:
% 31.34/10.13 | (6944) sum(n9, n2) = all_0_4_4
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (194) with n9, n2, all_0_4_4, n11 and discharging atoms sum(n9, n2) = all_0_4_4, sum(n9, n2) = n11, yields:
% 31.34/10.13 | (883) all_0_4_4 = n11
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (194) with n0, n11, all_0_7_7, n11 and discharging atoms sum(n0, n11) = all_0_7_7, sum(n0, n11) = n11, yields:
% 31.34/10.13 | (885) all_0_7_7 = n11
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 31.34/10.13 | (1082) all_0_2_2 = n2
% 31.34/10.13 |
% 31.34/10.13 | From (1082) and (6766) follows:
% 31.34/10.13 | (6948) sum(n2, n20) = all_0_0_0
% 31.34/10.13 |
% 31.34/10.13 | From (885)(883) and (435) follows:
% 31.34/10.13 | (887) sum(n11, n11) = all_0_3_3
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 31.34/10.13 | (888) all_0_3_3 = n1
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (194) with n2, n20, all_0_0_0, n1 and discharging atoms sum(n2, n20) = all_0_0_0, sum(n2, n20) = n1, yields:
% 31.34/10.13 | (889) all_0_0_0 = n1
% 31.34/10.13 |
% 31.34/10.13 | Equations (889,888) can reduce 201 to:
% 31.34/10.13 | (746) $false
% 31.34/10.13 |
% 31.34/10.13 |-The branch is then unsatisfiable
% 31.34/10.13 |-Branch two:
% 31.34/10.13 | (1090) ~ (all_0_11_11 = n1)
% 31.34/10.13 | (1091) all_0_11_11 = n0
% 31.34/10.13 |
% 31.34/10.13 | From (1091) and (190) follows:
% 31.34/10.13 | (1092) pred(n0) = all_0_9_9
% 31.34/10.13 |
% 31.34/10.13 | From (1091) and (505) follows:
% 31.34/10.13 | (1093) succ(n0) = all_0_5_5
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 31.34/10.13 | (1094) all_0_9_9 = n20
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.34/10.13 | (1095) all_0_5_5 = n1
% 31.34/10.13 |
% 31.34/10.13 | From (1094)(1095) and (156) follows:
% 31.34/10.13 | (1096) sum(n20, n1) = all_0_2_2
% 31.34/10.13 |
% 31.34/10.13 | From (1094) and (6764) follows:
% 31.34/10.13 | (6960) sum(n20, n11) = all_0_7_7
% 31.34/10.13 |
% 31.34/10.13 | From (1095) and (6762) follows:
% 31.34/10.13 | (6961) sum(n9, n1) = all_0_4_4
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (194) with n20, n11, all_0_7_7, n10 and discharging atoms sum(n20, n11) = all_0_7_7, sum(n20, n11) = n10, yields:
% 31.34/10.13 | (903) all_0_7_7 = n10
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 31.34/10.13 | (1099) all_0_2_2 = n0
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (194) with n9, n1, all_0_4_4, n10 and discharging atoms sum(n9, n1) = all_0_4_4, sum(n9, n1) = n10, yields:
% 31.34/10.13 | (901) all_0_4_4 = n10
% 31.34/10.13 |
% 31.34/10.13 | From (1099) and (6766) follows:
% 31.34/10.13 | (6965) sum(n0, n20) = all_0_0_0
% 31.34/10.13 |
% 31.34/10.13 | From (903)(901) and (435) follows:
% 31.34/10.13 | (905) sum(n10, n10) = all_0_3_3
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 31.34/10.13 | (906) all_0_3_3 = n20
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (194) with n0, n20, all_0_0_0, n20 and discharging atoms sum(n0, n20) = all_0_0_0, sum(n0, n20) = n20, yields:
% 31.34/10.13 | (907) all_0_0_0 = n20
% 31.34/10.13 |
% 31.34/10.13 | Equations (907,906) can reduce 201 to:
% 31.34/10.13 | (746) $false
% 31.34/10.13 |
% 31.34/10.13 |-The branch is then unsatisfiable
% 31.34/10.13 |-Branch two:
% 31.34/10.13 | (1298) ~ (all_0_10_10 = n10)
% 31.34/10.13 | (1299) all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.34/10.13 |
% 31.34/10.13 +-Applying beta-rule and splitting (910), into two cases.
% 31.34/10.13 |-Branch one:
% 31.34/10.13 | (911) all_0_11_11 = n10
% 31.34/10.13 |
% 31.34/10.13 | From (911) and (190) follows:
% 31.34/10.13 | (912) pred(n10) = all_0_9_9
% 31.34/10.13 |
% 31.34/10.13 | From (911) and (505) follows:
% 31.34/10.13 | (913) succ(n10) = all_0_5_5
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (259) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 31.34/10.13 | (914) all_0_9_9 = n9
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (184) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 31.34/10.13 | (915) all_0_5_5 = n11
% 31.34/10.13 |
% 31.34/10.13 | From (915) and (386) follows:
% 31.34/10.13 | (6977) sum(all_0_6_6, n11) = all_0_4_4
% 31.34/10.13 |
% 31.34/10.13 | From (914)(915) and (156) follows:
% 31.34/10.13 | (916) sum(n9, n11) = all_0_2_2
% 31.34/10.13 |
% 31.34/10.13 | From (914) and (74) follows:
% 31.34/10.13 | (6979) sum(n9, all_0_8_8) = all_0_7_7
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (194) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 31.34/10.13 | (920) all_0_2_2 = n20
% 31.34/10.13 |
% 31.34/10.13 | From (920) and (85) follows:
% 31.34/10.13 | (6981) sum(n20, all_0_1_1) = all_0_0_0
% 31.34/10.13 |
% 31.34/10.13 +-Applying beta-rule and splitting (1299), into two cases.
% 31.34/10.13 |-Branch one:
% 31.34/10.13 | (1300) all_0_10_10 = n9
% 31.34/10.13 |
% 31.34/10.13 | From (1300) and (57) follows:
% 31.34/10.13 | (1301) pred(n9) = all_0_6_6
% 31.34/10.13 |
% 31.34/10.13 | From (1300) and (381) follows:
% 31.34/10.13 | (1302) succ(n9) = all_0_8_8
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (259) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 31.34/10.13 | (1303) all_0_6_6 = n8
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (184) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 31.34/10.13 | (1304) all_0_8_8 = n10
% 31.34/10.13 |
% 31.34/10.13 | From (1303)(1304) and (628) follows:
% 31.34/10.13 | (1305) sum(n8, n10) = all_0_1_1
% 31.34/10.13 |
% 31.34/10.13 | From (1303) and (6977) follows:
% 31.34/10.13 | (6988) sum(n8, n11) = all_0_4_4
% 31.34/10.13 |
% 31.34/10.13 | From (1304) and (6979) follows:
% 31.34/10.13 | (6989) sum(n9, n10) = all_0_7_7
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (194) with n9, n10, all_0_7_7, n19 and discharging atoms sum(n9, n10) = all_0_7_7, sum(n9, n10) = n19, yields:
% 31.34/10.13 | (737) all_0_7_7 = n19
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (194) with n8, n11, all_0_4_4, n19 and discharging atoms sum(n8, n11) = all_0_4_4, sum(n8, n11) = n19, yields:
% 31.34/10.13 | (736) all_0_4_4 = n19
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (194) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 31.34/10.13 | (1309) all_0_1_1 = n18
% 31.34/10.13 |
% 31.34/10.13 | From (737)(736) and (435) follows:
% 31.34/10.13 | (741) sum(n19, n19) = all_0_3_3
% 31.34/10.13 |
% 31.34/10.13 | From (1309) and (6981) follows:
% 31.34/10.13 | (6994) sum(n20, n18) = all_0_0_0
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (194) with n20, n18, all_0_0_0, n17 and discharging atoms sum(n20, n18) = all_0_0_0, sum(n20, n18) = n17, yields:
% 31.34/10.13 | (742) all_0_0_0 = n17
% 31.34/10.13 |
% 31.34/10.13 | Instantiating formula (194) with n19, n19, all_0_3_3, n17 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n17, yields:
% 31.44/10.13 | (744) all_0_3_3 = n17
% 31.44/10.13 |
% 31.44/10.13 | Equations (742,744) can reduce 201 to:
% 31.44/10.13 | (746) $false
% 31.44/10.13 |
% 31.44/10.13 |-The branch is then unsatisfiable
% 31.44/10.13 |-Branch two:
% 31.44/10.13 | (1316) ~ (all_0_10_10 = n9)
% 31.44/10.13 | (1317) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.44/10.13 |
% 31.44/10.13 +-Applying beta-rule and splitting (1317), into two cases.
% 31.44/10.13 |-Branch one:
% 31.44/10.13 | (1318) all_0_10_10 = n8
% 31.44/10.13 |
% 31.44/10.13 | From (1318) and (57) follows:
% 31.44/10.13 | (1319) pred(n8) = all_0_6_6
% 31.44/10.13 |
% 31.44/10.13 | From (1318) and (381) follows:
% 31.44/10.13 | (1320) succ(n8) = all_0_8_8
% 31.44/10.13 |
% 31.44/10.13 | Instantiating formula (259) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 31.44/10.13 | (1321) all_0_6_6 = n7
% 31.44/10.13 |
% 31.44/10.13 | Instantiating formula (184) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 31.44/10.13 | (1322) all_0_8_8 = n9
% 31.44/10.13 |
% 31.44/10.13 | From (1321)(1322) and (628) follows:
% 31.44/10.13 | (1323) sum(n7, n9) = all_0_1_1
% 31.44/10.13 |
% 31.44/10.13 | From (1321) and (6977) follows:
% 31.44/10.14 | (7006) sum(n7, n11) = all_0_4_4
% 31.44/10.14 |
% 31.44/10.14 | From (1322) and (6979) follows:
% 31.44/10.14 | (7007) sum(n9, n9) = all_0_7_7
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n9, n9, all_0_7_7, n18 and discharging atoms sum(n9, n9) = all_0_7_7, sum(n9, n9) = n18, yields:
% 31.44/10.14 | (759) all_0_7_7 = n18
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n7, n11, all_0_4_4, n18 and discharging atoms sum(n7, n11) = all_0_4_4, sum(n7, n11) = n18, yields:
% 31.44/10.14 | (757) all_0_4_4 = n18
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 31.44/10.14 | (1327) all_0_1_1 = n16
% 31.44/10.14 |
% 31.44/10.14 | From (759)(757) and (435) follows:
% 31.44/10.14 | (761) sum(n18, n18) = all_0_3_3
% 31.44/10.14 |
% 31.44/10.14 | From (1327) and (6981) follows:
% 31.44/10.14 | (7012) sum(n20, n16) = all_0_0_0
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n20, n16, all_0_0_0, n15 and discharging atoms sum(n20, n16) = all_0_0_0, sum(n20, n16) = n15, yields:
% 31.44/10.14 | (763) all_0_0_0 = n15
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n18, n18, all_0_3_3, n15 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n15, yields:
% 31.44/10.14 | (762) all_0_3_3 = n15
% 31.44/10.14 |
% 31.44/10.14 | Equations (763,762) can reduce 201 to:
% 31.44/10.14 | (746) $false
% 31.44/10.14 |
% 31.44/10.14 |-The branch is then unsatisfiable
% 31.44/10.14 |-Branch two:
% 31.44/10.14 | (1334) ~ (all_0_10_10 = n8)
% 31.44/10.14 | (1335) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.44/10.14 |
% 31.44/10.14 +-Applying beta-rule and splitting (1335), into two cases.
% 31.44/10.14 |-Branch one:
% 31.44/10.14 | (1336) all_0_10_10 = n7
% 31.44/10.14 |
% 31.44/10.14 | From (1336) and (57) follows:
% 31.44/10.14 | (1337) pred(n7) = all_0_6_6
% 31.44/10.14 |
% 31.44/10.14 | From (1336) and (381) follows:
% 31.44/10.14 | (1338) succ(n7) = all_0_8_8
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (259) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 31.44/10.14 | (1339) all_0_6_6 = n6
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (184) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 31.44/10.14 | (1340) all_0_8_8 = n8
% 31.44/10.14 |
% 31.44/10.14 | From (1339)(1340) and (628) follows:
% 31.44/10.14 | (1341) sum(n6, n8) = all_0_1_1
% 31.44/10.14 |
% 31.44/10.14 | From (1339) and (6977) follows:
% 31.44/10.14 | (7024) sum(n6, n11) = all_0_4_4
% 31.44/10.14 |
% 31.44/10.14 | From (1340) and (6979) follows:
% 31.44/10.14 | (7025) sum(n9, n8) = all_0_7_7
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n9, n8, all_0_7_7, n17 and discharging atoms sum(n9, n8) = all_0_7_7, sum(n9, n8) = n17, yields:
% 31.44/10.14 | (777) all_0_7_7 = n17
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n6, n11, all_0_4_4, n17 and discharging atoms sum(n6, n11) = all_0_4_4, sum(n6, n11) = n17, yields:
% 31.44/10.14 | (775) all_0_4_4 = n17
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 31.44/10.14 | (1345) all_0_1_1 = n14
% 31.44/10.14 |
% 31.44/10.14 | From (777)(775) and (435) follows:
% 31.44/10.14 | (779) sum(n17, n17) = all_0_3_3
% 31.44/10.14 |
% 31.44/10.14 | From (1345) and (6981) follows:
% 31.44/10.14 | (7030) sum(n20, n14) = all_0_0_0
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n20, n14, all_0_0_0, n13 and discharging atoms sum(n20, n14) = all_0_0_0, sum(n20, n14) = n13, yields:
% 31.44/10.14 | (781) all_0_0_0 = n13
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 31.44/10.14 | (780) all_0_3_3 = n13
% 31.44/10.14 |
% 31.44/10.14 | Equations (781,780) can reduce 201 to:
% 31.44/10.14 | (746) $false
% 31.44/10.14 |
% 31.44/10.14 |-The branch is then unsatisfiable
% 31.44/10.14 |-Branch two:
% 31.44/10.14 | (1352) ~ (all_0_10_10 = n7)
% 31.44/10.14 | (1353) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.44/10.14 |
% 31.44/10.14 +-Applying beta-rule and splitting (1353), into two cases.
% 31.44/10.14 |-Branch one:
% 31.44/10.14 | (1354) all_0_10_10 = n6
% 31.44/10.14 |
% 31.44/10.14 | From (1354) and (57) follows:
% 31.44/10.14 | (1355) pred(n6) = all_0_6_6
% 31.44/10.14 |
% 31.44/10.14 | From (1354) and (381) follows:
% 31.44/10.14 | (1356) succ(n6) = all_0_8_8
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (259) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 31.44/10.14 | (1357) all_0_6_6 = n5
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (184) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 31.44/10.14 | (1358) all_0_8_8 = n7
% 31.44/10.14 |
% 31.44/10.14 | From (1357)(1358) and (628) follows:
% 31.44/10.14 | (1359) sum(n5, n7) = all_0_1_1
% 31.44/10.14 |
% 31.44/10.14 | From (1357) and (6977) follows:
% 31.44/10.14 | (7042) sum(n5, n11) = all_0_4_4
% 31.44/10.14 |
% 31.44/10.14 | From (1358) and (6979) follows:
% 31.44/10.14 | (7043) sum(n9, n7) = all_0_7_7
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n9, n7, all_0_7_7, n16 and discharging atoms sum(n9, n7) = all_0_7_7, sum(n9, n7) = n16, yields:
% 31.44/10.14 | (795) all_0_7_7 = n16
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n5, n11, all_0_4_4, n16 and discharging atoms sum(n5, n11) = all_0_4_4, sum(n5, n11) = n16, yields:
% 31.44/10.14 | (793) all_0_4_4 = n16
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 31.44/10.14 | (1363) all_0_1_1 = n12
% 31.44/10.14 |
% 31.44/10.14 | From (795)(793) and (435) follows:
% 31.44/10.14 | (797) sum(n16, n16) = all_0_3_3
% 31.44/10.14 |
% 31.44/10.14 | From (1363) and (6981) follows:
% 31.44/10.14 | (7048) sum(n20, n12) = all_0_0_0
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n20, n12, all_0_0_0, n11 and discharging atoms sum(n20, n12) = all_0_0_0, sum(n20, n12) = n11, yields:
% 31.44/10.14 | (799) all_0_0_0 = n11
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 31.44/10.14 | (798) all_0_3_3 = n11
% 31.44/10.14 |
% 31.44/10.14 | Equations (799,798) can reduce 201 to:
% 31.44/10.14 | (746) $false
% 31.44/10.14 |
% 31.44/10.14 |-The branch is then unsatisfiable
% 31.44/10.14 |-Branch two:
% 31.44/10.14 | (1370) ~ (all_0_10_10 = n6)
% 31.44/10.14 | (1371) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.44/10.14 |
% 31.44/10.14 +-Applying beta-rule and splitting (1371), into two cases.
% 31.44/10.14 |-Branch one:
% 31.44/10.14 | (1372) all_0_10_10 = n5
% 31.44/10.14 |
% 31.44/10.14 | From (1372) and (57) follows:
% 31.44/10.14 | (1373) pred(n5) = all_0_6_6
% 31.44/10.14 |
% 31.44/10.14 | From (1372) and (381) follows:
% 31.44/10.14 | (1374) succ(n5) = all_0_8_8
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (259) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 31.44/10.14 | (1375) all_0_6_6 = n4
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (184) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 31.44/10.14 | (1376) all_0_8_8 = n6
% 31.44/10.14 |
% 31.44/10.14 | From (1375)(1376) and (628) follows:
% 31.44/10.14 | (1377) sum(n4, n6) = all_0_1_1
% 31.44/10.14 |
% 31.44/10.14 | From (1375) and (6977) follows:
% 31.44/10.14 | (7060) sum(n4, n11) = all_0_4_4
% 31.44/10.14 |
% 31.44/10.14 | From (1376) and (6979) follows:
% 31.44/10.14 | (7061) sum(n9, n6) = all_0_7_7
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n9, n6, all_0_7_7, n15 and discharging atoms sum(n9, n6) = all_0_7_7, sum(n9, n6) = n15, yields:
% 31.44/10.14 | (813) all_0_7_7 = n15
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n4, n11, all_0_4_4, n15 and discharging atoms sum(n4, n11) = all_0_4_4, sum(n4, n11) = n15, yields:
% 31.44/10.14 | (811) all_0_4_4 = n15
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 31.44/10.14 | (1381) all_0_1_1 = n10
% 31.44/10.14 |
% 31.44/10.14 | From (813)(811) and (435) follows:
% 31.44/10.14 | (815) sum(n15, n15) = all_0_3_3
% 31.44/10.14 |
% 31.44/10.14 | From (1381) and (6981) follows:
% 31.44/10.14 | (7066) sum(n20, n10) = all_0_0_0
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n20, n10, all_0_0_0, n9 and discharging atoms sum(n20, n10) = all_0_0_0, sum(n20, n10) = n9, yields:
% 31.44/10.14 | (817) all_0_0_0 = n9
% 31.44/10.14 |
% 31.44/10.14 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 31.44/10.14 | (816) all_0_3_3 = n9
% 31.44/10.14 |
% 31.44/10.15 | Equations (817,816) can reduce 201 to:
% 31.44/10.15 | (746) $false
% 31.44/10.15 |
% 31.44/10.15 |-The branch is then unsatisfiable
% 31.44/10.15 |-Branch two:
% 31.44/10.15 | (1388) ~ (all_0_10_10 = n5)
% 31.44/10.15 | (1389) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.44/10.15 |
% 31.44/10.15 +-Applying beta-rule and splitting (1389), into two cases.
% 31.44/10.15 |-Branch one:
% 31.44/10.15 | (1390) all_0_10_10 = n4
% 31.44/10.15 |
% 31.44/10.15 | From (1390) and (57) follows:
% 31.44/10.15 | (1391) pred(n4) = all_0_6_6
% 31.44/10.15 |
% 31.44/10.15 | From (1390) and (381) follows:
% 31.44/10.15 | (1392) succ(n4) = all_0_8_8
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (259) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 31.44/10.15 | (1393) all_0_6_6 = n3
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (184) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 31.44/10.15 | (1394) all_0_8_8 = n5
% 31.44/10.15 |
% 31.44/10.15 | From (1393)(1394) and (628) follows:
% 31.44/10.15 | (1395) sum(n3, n5) = all_0_1_1
% 31.44/10.15 |
% 31.44/10.15 | From (1393) and (6977) follows:
% 31.44/10.15 | (7078) sum(n3, n11) = all_0_4_4
% 31.44/10.15 |
% 31.44/10.15 | From (1394) and (6979) follows:
% 31.44/10.15 | (7079) sum(n9, n5) = all_0_7_7
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (194) with n9, n5, all_0_7_7, n14 and discharging atoms sum(n9, n5) = all_0_7_7, sum(n9, n5) = n14, yields:
% 31.44/10.15 | (831) all_0_7_7 = n14
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (194) with n3, n11, all_0_4_4, n14 and discharging atoms sum(n3, n11) = all_0_4_4, sum(n3, n11) = n14, yields:
% 31.44/10.15 | (829) all_0_4_4 = n14
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (194) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 31.44/10.15 | (1399) all_0_1_1 = n8
% 31.44/10.15 |
% 31.44/10.15 | From (831)(829) and (435) follows:
% 31.44/10.15 | (833) sum(n14, n14) = all_0_3_3
% 31.44/10.15 |
% 31.44/10.15 | From (1399) and (6981) follows:
% 31.44/10.15 | (7084) sum(n20, n8) = all_0_0_0
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (194) with n20, n8, all_0_0_0, n7 and discharging atoms sum(n20, n8) = all_0_0_0, sum(n20, n8) = n7, yields:
% 31.44/10.15 | (835) all_0_0_0 = n7
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 31.44/10.15 | (834) all_0_3_3 = n7
% 31.44/10.15 |
% 31.44/10.15 | Equations (835,834) can reduce 201 to:
% 31.44/10.15 | (746) $false
% 31.44/10.15 |
% 31.44/10.15 |-The branch is then unsatisfiable
% 31.44/10.15 |-Branch two:
% 31.44/10.15 | (1406) ~ (all_0_10_10 = n4)
% 31.44/10.15 | (1407) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.44/10.15 |
% 31.44/10.15 +-Applying beta-rule and splitting (1407), into two cases.
% 31.44/10.15 |-Branch one:
% 31.44/10.15 | (1408) all_0_10_10 = n3
% 31.44/10.15 |
% 31.44/10.15 | From (1408) and (57) follows:
% 31.44/10.15 | (1409) pred(n3) = all_0_6_6
% 31.44/10.15 |
% 31.44/10.15 | From (1408) and (381) follows:
% 31.44/10.15 | (1410) succ(n3) = all_0_8_8
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 31.44/10.15 | (1411) all_0_6_6 = n2
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 31.44/10.15 | (1412) all_0_8_8 = n4
% 31.44/10.15 |
% 31.44/10.15 | From (1411)(1412) and (628) follows:
% 31.44/10.15 | (1413) sum(n2, n4) = all_0_1_1
% 31.44/10.15 |
% 31.44/10.15 | From (1411) and (6977) follows:
% 31.44/10.15 | (7096) sum(n2, n11) = all_0_4_4
% 31.44/10.15 |
% 31.44/10.15 | From (1412) and (6979) follows:
% 31.44/10.15 | (7097) sum(n9, n4) = all_0_7_7
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (194) with n9, n4, all_0_7_7, n13 and discharging atoms sum(n9, n4) = all_0_7_7, sum(n9, n4) = n13, yields:
% 31.44/10.15 | (849) all_0_7_7 = n13
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (194) with n2, n11, all_0_4_4, n13 and discharging atoms sum(n2, n11) = all_0_4_4, sum(n2, n11) = n13, yields:
% 31.44/10.15 | (847) all_0_4_4 = n13
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 31.44/10.15 | (1417) all_0_1_1 = n6
% 31.44/10.15 |
% 31.44/10.15 | From (849)(847) and (435) follows:
% 31.44/10.15 | (851) sum(n13, n13) = all_0_3_3
% 31.44/10.15 |
% 31.44/10.15 | From (1417) and (6981) follows:
% 31.44/10.15 | (7102) sum(n20, n6) = all_0_0_0
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (194) with n20, n6, all_0_0_0, n5 and discharging atoms sum(n20, n6) = all_0_0_0, sum(n20, n6) = n5, yields:
% 31.44/10.15 | (853) all_0_0_0 = n5
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 31.44/10.15 | (852) all_0_3_3 = n5
% 31.44/10.15 |
% 31.44/10.15 | Equations (853,852) can reduce 201 to:
% 31.44/10.15 | (746) $false
% 31.44/10.15 |
% 31.44/10.15 |-The branch is then unsatisfiable
% 31.44/10.15 |-Branch two:
% 31.44/10.15 | (1424) ~ (all_0_10_10 = n3)
% 31.44/10.15 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.44/10.15 |
% 31.44/10.15 +-Applying beta-rule and splitting (1425), into two cases.
% 31.44/10.15 |-Branch one:
% 31.44/10.15 | (1426) all_0_10_10 = n2
% 31.44/10.15 |
% 31.44/10.15 | From (1426) and (57) follows:
% 31.44/10.15 | (1427) pred(n2) = all_0_6_6
% 31.44/10.15 |
% 31.44/10.15 | From (1426) and (381) follows:
% 31.44/10.15 | (1428) succ(n2) = all_0_8_8
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 31.44/10.15 | (1429) all_0_6_6 = n1
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 31.44/10.15 | (1430) all_0_8_8 = n3
% 31.44/10.15 |
% 31.44/10.15 | From (1429)(1430) and (628) follows:
% 31.44/10.15 | (1431) sum(n1, n3) = all_0_1_1
% 31.44/10.15 |
% 31.44/10.15 | From (1429) and (6977) follows:
% 31.44/10.15 | (7114) sum(n1, n11) = all_0_4_4
% 31.44/10.15 |
% 31.44/10.15 | From (1430) and (6979) follows:
% 31.44/10.15 | (7115) sum(n9, n3) = all_0_7_7
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (194) with n9, n3, all_0_7_7, n12 and discharging atoms sum(n9, n3) = all_0_7_7, sum(n9, n3) = n12, yields:
% 31.44/10.15 | (867) all_0_7_7 = n12
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (194) with n1, n11, all_0_4_4, n12 and discharging atoms sum(n1, n11) = all_0_4_4, sum(n1, n11) = n12, yields:
% 31.44/10.15 | (865) all_0_4_4 = n12
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 31.44/10.15 | (1435) all_0_1_1 = n4
% 31.44/10.15 |
% 31.44/10.15 | From (867)(865) and (435) follows:
% 31.44/10.15 | (869) sum(n12, n12) = all_0_3_3
% 31.44/10.15 |
% 31.44/10.15 | From (1435) and (6981) follows:
% 31.44/10.15 | (7120) sum(n20, n4) = all_0_0_0
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (194) with n20, n4, all_0_0_0, n3 and discharging atoms sum(n20, n4) = all_0_0_0, sum(n20, n4) = n3, yields:
% 31.44/10.15 | (871) all_0_0_0 = n3
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 31.44/10.15 | (870) all_0_3_3 = n3
% 31.44/10.15 |
% 31.44/10.15 | Equations (871,870) can reduce 201 to:
% 31.44/10.15 | (746) $false
% 31.44/10.15 |
% 31.44/10.15 |-The branch is then unsatisfiable
% 31.44/10.15 |-Branch two:
% 31.44/10.15 | (1442) ~ (all_0_10_10 = n2)
% 31.44/10.15 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 31.44/10.15 |
% 31.44/10.15 +-Applying beta-rule and splitting (1443), into two cases.
% 31.44/10.15 |-Branch one:
% 31.44/10.15 | (1444) all_0_10_10 = n1
% 31.44/10.15 |
% 31.44/10.15 | From (1444) and (57) follows:
% 31.44/10.15 | (1445) pred(n1) = all_0_6_6
% 31.44/10.15 |
% 31.44/10.15 | From (1444) and (381) follows:
% 31.44/10.15 | (1446) succ(n1) = all_0_8_8
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 31.44/10.15 | (1447) all_0_6_6 = n0
% 31.44/10.15 |
% 31.44/10.15 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 31.44/10.15 | (1448) all_0_8_8 = n2
% 31.44/10.15 |
% 31.44/10.15 | From (1447)(1448) and (628) follows:
% 31.44/10.15 | (1449) sum(n0, n2) = all_0_1_1
% 31.44/10.15 |
% 31.44/10.15 | From (1447) and (6977) follows:
% 31.44/10.15 | (7132) sum(n0, n11) = all_0_4_4
% 31.44/10.15 |
% 31.44/10.15 | From (1448) and (6979) follows:
% 31.44/10.16 | (7133) sum(n9, n2) = all_0_7_7
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (194) with n9, n2, all_0_7_7, n11 and discharging atoms sum(n9, n2) = all_0_7_7, sum(n9, n2) = n11, yields:
% 31.44/10.16 | (885) all_0_7_7 = n11
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (194) with n0, n11, all_0_4_4, n11 and discharging atoms sum(n0, n11) = all_0_4_4, sum(n0, n11) = n11, yields:
% 31.44/10.16 | (883) all_0_4_4 = n11
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 31.44/10.16 | (1453) all_0_1_1 = n2
% 31.44/10.16 |
% 31.44/10.16 | From (885)(883) and (435) follows:
% 31.44/10.16 | (887) sum(n11, n11) = all_0_3_3
% 31.44/10.16 |
% 31.44/10.16 | From (1453) and (6981) follows:
% 31.44/10.16 | (7138) sum(n20, n2) = all_0_0_0
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (194) with n20, n2, all_0_0_0, n1 and discharging atoms sum(n20, n2) = all_0_0_0, sum(n20, n2) = n1, yields:
% 31.44/10.16 | (889) all_0_0_0 = n1
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 31.44/10.16 | (888) all_0_3_3 = n1
% 31.44/10.16 |
% 31.44/10.16 | Equations (889,888) can reduce 201 to:
% 31.44/10.16 | (746) $false
% 31.44/10.16 |
% 31.44/10.16 |-The branch is then unsatisfiable
% 31.44/10.16 |-Branch two:
% 31.44/10.16 | (1462) ~ (all_0_10_10 = n1)
% 31.44/10.16 | (1463) all_0_10_10 = n0
% 31.44/10.16 |
% 31.44/10.16 | From (1463) and (57) follows:
% 31.44/10.16 | (1464) pred(n0) = all_0_6_6
% 31.44/10.16 |
% 31.44/10.16 | From (1463) and (381) follows:
% 31.44/10.16 | (1465) succ(n0) = all_0_8_8
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 31.44/10.16 | (1466) all_0_6_6 = n20
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 31.44/10.16 | (1467) all_0_8_8 = n1
% 31.44/10.16 |
% 31.44/10.16 | From (1466)(1467) and (628) follows:
% 31.44/10.16 | (1468) sum(n20, n1) = all_0_1_1
% 31.44/10.16 |
% 31.44/10.16 | From (1466) and (6977) follows:
% 31.44/10.16 | (7149) sum(n20, n11) = all_0_4_4
% 31.44/10.16 |
% 31.44/10.16 | From (1467) and (6979) follows:
% 31.44/10.16 | (7150) sum(n9, n1) = all_0_7_7
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (194) with n20, n11, all_0_4_4, n10 and discharging atoms sum(n20, n11) = all_0_4_4, sum(n20, n11) = n10, yields:
% 31.44/10.16 | (901) all_0_4_4 = n10
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 31.44/10.16 | (1471) all_0_1_1 = n0
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (194) with n9, n1, all_0_7_7, n10 and discharging atoms sum(n9, n1) = all_0_7_7, sum(n9, n1) = n10, yields:
% 31.44/10.16 | (903) all_0_7_7 = n10
% 31.44/10.16 |
% 31.44/10.16 | From (903)(901) and (435) follows:
% 31.44/10.16 | (905) sum(n10, n10) = all_0_3_3
% 31.44/10.16 |
% 31.44/10.16 | From (1471) and (6981) follows:
% 31.44/10.16 | (7155) sum(n20, n0) = all_0_0_0
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (194) with n20, n0, all_0_0_0, n20 and discharging atoms sum(n20, n0) = all_0_0_0, sum(n20, n0) = n20, yields:
% 31.44/10.16 | (907) all_0_0_0 = n20
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 31.44/10.16 | (906) all_0_3_3 = n20
% 31.44/10.16 |
% 31.44/10.16 | Equations (907,906) can reduce 201 to:
% 31.44/10.16 | (746) $false
% 31.44/10.16 |
% 31.44/10.16 |-The branch is then unsatisfiable
% 31.44/10.16 |-Branch two:
% 31.44/10.16 | (927) ~ (all_0_11_11 = n10)
% 31.44/10.16 | (928) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.44/10.16 |
% 31.44/10.16 +-Applying beta-rule and splitting (1299), into two cases.
% 31.44/10.16 |-Branch one:
% 31.44/10.16 | (1300) all_0_10_10 = n9
% 31.44/10.16 |
% 31.44/10.16 | From (1300) and (57) follows:
% 31.44/10.16 | (1301) pred(n9) = all_0_6_6
% 31.44/10.16 |
% 31.44/10.16 | From (1300) and (381) follows:
% 31.44/10.16 | (1302) succ(n9) = all_0_8_8
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (259) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 31.44/10.16 | (1303) all_0_6_6 = n8
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (184) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 31.44/10.16 | (1304) all_0_8_8 = n10
% 31.44/10.16 |
% 31.44/10.16 | From (1303) and (1301) follows:
% 31.44/10.16 | (324) pred(n9) = n8
% 31.44/10.16 |
% 31.44/10.16 | From (1304) and (1302) follows:
% 31.44/10.16 | (111) succ(n9) = n10
% 31.44/10.16 |
% 31.44/10.16 | From (1303) and (386) follows:
% 31.44/10.16 | (7168) sum(n8, all_0_5_5) = all_0_4_4
% 31.44/10.16 |
% 31.44/10.16 | From (1303)(1304) and (628) follows:
% 31.44/10.16 | (1305) sum(n8, n10) = all_0_1_1
% 31.44/10.16 |
% 31.44/10.16 | From (1304) and (74) follows:
% 31.44/10.16 | (7170) sum(all_0_9_9, n10) = all_0_7_7
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (194) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 31.44/10.16 | (1309) all_0_1_1 = n18
% 31.44/10.16 |
% 31.44/10.16 | From (1309) and (85) follows:
% 31.44/10.16 | (7172) sum(all_0_2_2, n18) = all_0_0_0
% 31.44/10.16 |
% 31.44/10.16 | From (1309) and (1305) follows:
% 31.44/10.16 | (393) sum(n8, n10) = n18
% 31.44/10.16 |
% 31.44/10.16 +-Applying beta-rule and splitting (928), into two cases.
% 31.44/10.16 |-Branch one:
% 31.44/10.16 | (929) all_0_11_11 = n9
% 31.44/10.16 |
% 31.44/10.16 | From (929) and (190) follows:
% 31.44/10.16 | (930) pred(n9) = all_0_9_9
% 31.44/10.16 |
% 31.44/10.16 | From (929) and (505) follows:
% 31.44/10.16 | (931) succ(n9) = all_0_5_5
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (259) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 31.44/10.16 | (932) all_0_9_9 = n8
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (184) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 31.44/10.16 | (933) all_0_5_5 = n10
% 31.44/10.16 |
% 31.44/10.16 | From (932)(933) and (156) follows:
% 31.44/10.16 | (934) sum(n8, n10) = all_0_2_2
% 31.44/10.16 |
% 31.44/10.16 | From (932) and (7170) follows:
% 31.44/10.16 | (7180) sum(n8, n10) = all_0_7_7
% 31.44/10.16 |
% 31.44/10.16 | From (933) and (7168) follows:
% 31.44/10.16 | (7181) sum(n8, n10) = all_0_4_4
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (194) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 31.44/10.16 | (938) all_0_2_2 = n18
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (194) with n8, n10, all_0_4_4, all_0_2_2 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = all_0_4_4, yields:
% 31.44/10.16 | (733) all_0_2_2 = all_0_4_4
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (194) with n8, n10, all_0_7_7, all_0_2_2 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = all_0_7_7, yields:
% 31.44/10.16 | (734) all_0_2_2 = all_0_7_7
% 31.44/10.16 |
% 31.44/10.16 | Combining equations (734,733) yields a new equation:
% 31.44/10.16 | (735) all_0_4_4 = all_0_7_7
% 31.44/10.16 |
% 31.44/10.16 | Combining equations (938,733) yields a new equation:
% 31.44/10.16 | (757) all_0_4_4 = n18
% 31.44/10.16 |
% 31.44/10.16 | Combining equations (757,735) yields a new equation:
% 31.44/10.16 | (759) all_0_7_7 = n18
% 31.44/10.16 |
% 31.44/10.16 | Combining equations (759,735) yields a new equation:
% 31.44/10.16 | (757) all_0_4_4 = n18
% 31.44/10.16 |
% 31.44/10.16 | Combining equations (757,733) yields a new equation:
% 31.44/10.16 | (938) all_0_2_2 = n18
% 31.44/10.16 |
% 31.44/10.16 | From (938) and (7172) follows:
% 31.44/10.16 | (7190) sum(n18, n18) = all_0_0_0
% 31.44/10.16 |
% 31.44/10.16 | From (759)(757) and (435) follows:
% 31.44/10.16 | (761) sum(n18, n18) = all_0_3_3
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (194) with n18, n18, all_0_0_0, n15 and discharging atoms sum(n18, n18) = all_0_0_0, sum(n18, n18) = n15, yields:
% 31.44/10.16 | (763) all_0_0_0 = n15
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (194) with n18, n18, all_0_3_3, all_0_0_0 and discharging atoms sum(n18, n18) = all_0_0_0, sum(n18, n18) = all_0_3_3, yields:
% 31.44/10.16 | (743) all_0_0_0 = all_0_3_3
% 31.44/10.16 |
% 31.44/10.16 | Combining equations (763,743) yields a new equation:
% 31.44/10.16 | (762) all_0_3_3 = n15
% 31.44/10.16 |
% 31.44/10.16 | Combining equations (762,743) yields a new equation:
% 31.44/10.16 | (763) all_0_0_0 = n15
% 31.44/10.16 |
% 31.44/10.16 | Equations (763,762) can reduce 201 to:
% 31.44/10.16 | (746) $false
% 31.44/10.16 |
% 31.44/10.16 |-The branch is then unsatisfiable
% 31.44/10.16 |-Branch two:
% 31.44/10.16 | (945) ~ (all_0_11_11 = n9)
% 31.44/10.16 | (946) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.44/10.16 |
% 31.44/10.16 +-Applying beta-rule and splitting (946), into two cases.
% 31.44/10.16 |-Branch one:
% 31.44/10.16 | (947) all_0_11_11 = n8
% 31.44/10.16 |
% 31.44/10.16 | From (947) and (190) follows:
% 31.44/10.16 | (948) pred(n8) = all_0_9_9
% 31.44/10.16 |
% 31.44/10.16 | From (947) and (505) follows:
% 31.44/10.16 | (949) succ(n8) = all_0_5_5
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (259) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 31.44/10.16 | (950) all_0_9_9 = n7
% 31.44/10.16 |
% 31.44/10.16 | Instantiating formula (184) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 31.44/10.16 | (951) all_0_5_5 = n9
% 31.44/10.16 |
% 31.44/10.16 | From (950)(951) and (156) follows:
% 31.44/10.17 | (952) sum(n7, n9) = all_0_2_2
% 31.44/10.17 |
% 31.44/10.17 | From (950) and (7170) follows:
% 31.44/10.17 | (7205) sum(n7, n10) = all_0_7_7
% 31.44/10.17 |
% 31.44/10.17 | From (951) and (7168) follows:
% 31.44/10.17 | (7206) sum(n8, n9) = all_0_4_4
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n8, n9, all_0_4_4, n17 and discharging atoms sum(n8, n9) = all_0_4_4, sum(n8, n9) = n17, yields:
% 31.44/10.17 | (775) all_0_4_4 = n17
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n7, n10, all_0_7_7, n17 and discharging atoms sum(n7, n10) = all_0_7_7, sum(n7, n10) = n17, yields:
% 31.44/10.17 | (777) all_0_7_7 = n17
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 31.44/10.17 | (956) all_0_2_2 = n16
% 31.44/10.17 |
% 31.44/10.17 | From (956) and (7172) follows:
% 31.44/10.17 | (7210) sum(n16, n18) = all_0_0_0
% 31.44/10.17 |
% 31.44/10.17 | From (777)(775) and (435) follows:
% 31.44/10.17 | (779) sum(n17, n17) = all_0_3_3
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 31.44/10.17 | (780) all_0_3_3 = n13
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n16, n18, all_0_0_0, n13 and discharging atoms sum(n16, n18) = all_0_0_0, sum(n16, n18) = n13, yields:
% 31.44/10.17 | (781) all_0_0_0 = n13
% 31.44/10.17 |
% 31.44/10.17 | Equations (781,780) can reduce 201 to:
% 31.44/10.17 | (746) $false
% 31.44/10.17 |
% 31.44/10.17 |-The branch is then unsatisfiable
% 31.44/10.17 |-Branch two:
% 31.44/10.17 | (963) ~ (all_0_11_11 = n8)
% 31.44/10.17 | (964) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.44/10.17 |
% 31.44/10.17 +-Applying beta-rule and splitting (964), into two cases.
% 31.44/10.17 |-Branch one:
% 31.44/10.17 | (965) all_0_11_11 = n7
% 31.44/10.17 |
% 31.44/10.17 | From (965) and (190) follows:
% 31.44/10.17 | (966) pred(n7) = all_0_9_9
% 31.44/10.17 |
% 31.44/10.17 | From (965) and (505) follows:
% 31.44/10.17 | (967) succ(n7) = all_0_5_5
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (259) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 31.44/10.17 | (968) all_0_9_9 = n6
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (184) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 31.44/10.17 | (969) all_0_5_5 = n8
% 31.44/10.17 |
% 31.44/10.17 | From (968)(969) and (156) follows:
% 31.44/10.17 | (970) sum(n6, n8) = all_0_2_2
% 31.44/10.17 |
% 31.44/10.17 | From (968) and (7170) follows:
% 31.44/10.17 | (7223) sum(n6, n10) = all_0_7_7
% 31.44/10.17 |
% 31.44/10.17 | From (969) and (7168) follows:
% 31.44/10.17 | (7224) sum(n8, n8) = all_0_4_4
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n8, n8, all_0_4_4, n16 and discharging atoms sum(n8, n8) = all_0_4_4, sum(n8, n8) = n16, yields:
% 31.44/10.17 | (793) all_0_4_4 = n16
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n6, n10, all_0_7_7, n16 and discharging atoms sum(n6, n10) = all_0_7_7, sum(n6, n10) = n16, yields:
% 31.44/10.17 | (795) all_0_7_7 = n16
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 31.44/10.17 | (974) all_0_2_2 = n14
% 31.44/10.17 |
% 31.44/10.17 | From (974) and (7172) follows:
% 31.44/10.17 | (7228) sum(n14, n18) = all_0_0_0
% 31.44/10.17 |
% 31.44/10.17 | From (795)(793) and (435) follows:
% 31.44/10.17 | (797) sum(n16, n16) = all_0_3_3
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 31.44/10.17 | (798) all_0_3_3 = n11
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n14, n18, all_0_0_0, n11 and discharging atoms sum(n14, n18) = all_0_0_0, sum(n14, n18) = n11, yields:
% 31.44/10.17 | (799) all_0_0_0 = n11
% 31.44/10.17 |
% 31.44/10.17 | Equations (799,798) can reduce 201 to:
% 31.44/10.17 | (746) $false
% 31.44/10.17 |
% 31.44/10.17 |-The branch is then unsatisfiable
% 31.44/10.17 |-Branch two:
% 31.44/10.17 | (981) ~ (all_0_11_11 = n7)
% 31.44/10.17 | (982) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.44/10.17 |
% 31.44/10.17 +-Applying beta-rule and splitting (982), into two cases.
% 31.44/10.17 |-Branch one:
% 31.44/10.17 | (983) all_0_11_11 = n6
% 31.44/10.17 |
% 31.44/10.17 | From (983) and (190) follows:
% 31.44/10.17 | (984) pred(n6) = all_0_9_9
% 31.44/10.17 |
% 31.44/10.17 | From (983) and (505) follows:
% 31.44/10.17 | (985) succ(n6) = all_0_5_5
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (259) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 31.44/10.17 | (986) all_0_9_9 = n5
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (184) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 31.44/10.17 | (987) all_0_5_5 = n7
% 31.44/10.17 |
% 31.44/10.17 | From (986)(987) and (156) follows:
% 31.44/10.17 | (988) sum(n5, n7) = all_0_2_2
% 31.44/10.17 |
% 31.44/10.17 | From (986) and (7170) follows:
% 31.44/10.17 | (7241) sum(n5, n10) = all_0_7_7
% 31.44/10.17 |
% 31.44/10.17 | From (987) and (7168) follows:
% 31.44/10.17 | (7242) sum(n8, n7) = all_0_4_4
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n8, n7, all_0_4_4, n15 and discharging atoms sum(n8, n7) = all_0_4_4, sum(n8, n7) = n15, yields:
% 31.44/10.17 | (811) all_0_4_4 = n15
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n5, n10, all_0_7_7, n15 and discharging atoms sum(n5, n10) = all_0_7_7, sum(n5, n10) = n15, yields:
% 31.44/10.17 | (813) all_0_7_7 = n15
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 31.44/10.17 | (992) all_0_2_2 = n12
% 31.44/10.17 |
% 31.44/10.17 | From (992) and (7172) follows:
% 31.44/10.17 | (7246) sum(n12, n18) = all_0_0_0
% 31.44/10.17 |
% 31.44/10.17 | From (813)(811) and (435) follows:
% 31.44/10.17 | (815) sum(n15, n15) = all_0_3_3
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 31.44/10.17 | (816) all_0_3_3 = n9
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n12, n18, all_0_0_0, n9 and discharging atoms sum(n12, n18) = all_0_0_0, sum(n12, n18) = n9, yields:
% 31.44/10.17 | (817) all_0_0_0 = n9
% 31.44/10.17 |
% 31.44/10.17 | Equations (817,816) can reduce 201 to:
% 31.44/10.17 | (746) $false
% 31.44/10.17 |
% 31.44/10.17 |-The branch is then unsatisfiable
% 31.44/10.17 |-Branch two:
% 31.44/10.17 | (999) ~ (all_0_11_11 = n6)
% 31.44/10.17 | (1000) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.44/10.17 |
% 31.44/10.17 +-Applying beta-rule and splitting (1000), into two cases.
% 31.44/10.17 |-Branch one:
% 31.44/10.17 | (1001) all_0_11_11 = n5
% 31.44/10.17 |
% 31.44/10.17 | From (1001) and (190) follows:
% 31.44/10.17 | (1002) pred(n5) = all_0_9_9
% 31.44/10.17 |
% 31.44/10.17 | From (1001) and (505) follows:
% 31.44/10.17 | (1003) succ(n5) = all_0_5_5
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (259) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 31.44/10.17 | (1004) all_0_9_9 = n4
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (184) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 31.44/10.17 | (1005) all_0_5_5 = n6
% 31.44/10.17 |
% 31.44/10.17 | From (1004)(1005) and (156) follows:
% 31.44/10.17 | (1006) sum(n4, n6) = all_0_2_2
% 31.44/10.17 |
% 31.44/10.17 | From (1004) and (7170) follows:
% 31.44/10.17 | (7259) sum(n4, n10) = all_0_7_7
% 31.44/10.17 |
% 31.44/10.17 | From (1005) and (7168) follows:
% 31.44/10.17 | (7260) sum(n8, n6) = all_0_4_4
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n8, n6, all_0_4_4, n14 and discharging atoms sum(n8, n6) = all_0_4_4, sum(n8, n6) = n14, yields:
% 31.44/10.17 | (829) all_0_4_4 = n14
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n4, n10, all_0_7_7, n14 and discharging atoms sum(n4, n10) = all_0_7_7, sum(n4, n10) = n14, yields:
% 31.44/10.17 | (831) all_0_7_7 = n14
% 31.44/10.17 |
% 31.44/10.17 | Instantiating formula (194) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 31.44/10.17 | (1010) all_0_2_2 = n10
% 31.44/10.17 |
% 31.44/10.17 | From (1010) and (7172) follows:
% 31.44/10.18 | (7264) sum(n10, n18) = all_0_0_0
% 31.44/10.18 |
% 31.44/10.18 | From (831)(829) and (435) follows:
% 31.44/10.18 | (833) sum(n14, n14) = all_0_3_3
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 31.44/10.18 | (834) all_0_3_3 = n7
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (194) with n10, n18, all_0_0_0, n7 and discharging atoms sum(n10, n18) = all_0_0_0, sum(n10, n18) = n7, yields:
% 31.44/10.18 | (835) all_0_0_0 = n7
% 31.44/10.18 |
% 31.44/10.18 | Equations (835,834) can reduce 201 to:
% 31.44/10.18 | (746) $false
% 31.44/10.18 |
% 31.44/10.18 |-The branch is then unsatisfiable
% 31.44/10.18 |-Branch two:
% 31.44/10.18 | (1017) ~ (all_0_11_11 = n5)
% 31.44/10.18 | (1018) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.44/10.18 |
% 31.44/10.18 +-Applying beta-rule and splitting (1018), into two cases.
% 31.44/10.18 |-Branch one:
% 31.44/10.18 | (1019) all_0_11_11 = n4
% 31.44/10.18 |
% 31.44/10.18 | From (1019) and (190) follows:
% 31.44/10.18 | (1020) pred(n4) = all_0_9_9
% 31.44/10.18 |
% 31.44/10.18 | From (1019) and (505) follows:
% 31.44/10.18 | (1021) succ(n4) = all_0_5_5
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 31.44/10.18 | (1022) all_0_9_9 = n3
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 31.44/10.18 | (1023) all_0_5_5 = n5
% 31.44/10.18 |
% 31.44/10.18 | From (1022)(1023) and (156) follows:
% 31.44/10.18 | (1024) sum(n3, n5) = all_0_2_2
% 31.44/10.18 |
% 31.44/10.18 | From (1022) and (7170) follows:
% 31.44/10.18 | (7277) sum(n3, n10) = all_0_7_7
% 31.44/10.18 |
% 31.44/10.18 | From (1023) and (7168) follows:
% 31.44/10.18 | (7278) sum(n8, n5) = all_0_4_4
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (194) with n8, n5, all_0_4_4, n13 and discharging atoms sum(n8, n5) = all_0_4_4, sum(n8, n5) = n13, yields:
% 31.44/10.18 | (847) all_0_4_4 = n13
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (194) with n3, n10, all_0_7_7, n13 and discharging atoms sum(n3, n10) = all_0_7_7, sum(n3, n10) = n13, yields:
% 31.44/10.18 | (849) all_0_7_7 = n13
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 31.44/10.18 | (1028) all_0_2_2 = n8
% 31.44/10.18 |
% 31.44/10.18 | From (1028) and (7172) follows:
% 31.44/10.18 | (7282) sum(n8, n18) = all_0_0_0
% 31.44/10.18 |
% 31.44/10.18 | From (849)(847) and (435) follows:
% 31.44/10.18 | (851) sum(n13, n13) = all_0_3_3
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 31.44/10.18 | (852) all_0_3_3 = n5
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (194) with n8, n18, all_0_0_0, n5 and discharging atoms sum(n8, n18) = all_0_0_0, sum(n8, n18) = n5, yields:
% 31.44/10.18 | (853) all_0_0_0 = n5
% 31.44/10.18 |
% 31.44/10.18 | Equations (853,852) can reduce 201 to:
% 31.44/10.18 | (746) $false
% 31.44/10.18 |
% 31.44/10.18 |-The branch is then unsatisfiable
% 31.44/10.18 |-Branch two:
% 31.44/10.18 | (1035) ~ (all_0_11_11 = n4)
% 31.44/10.18 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.44/10.18 |
% 31.44/10.18 +-Applying beta-rule and splitting (1036), into two cases.
% 31.44/10.18 |-Branch one:
% 31.44/10.18 | (1037) all_0_11_11 = n3
% 31.44/10.18 |
% 31.44/10.18 | From (1037) and (190) follows:
% 31.44/10.18 | (1038) pred(n3) = all_0_9_9
% 31.44/10.18 |
% 31.44/10.18 | From (1037) and (505) follows:
% 31.44/10.18 | (1039) succ(n3) = all_0_5_5
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 31.44/10.18 | (1040) all_0_9_9 = n2
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 31.44/10.18 | (1041) all_0_5_5 = n4
% 31.44/10.18 |
% 31.44/10.18 | From (1040)(1041) and (156) follows:
% 31.44/10.18 | (1042) sum(n2, n4) = all_0_2_2
% 31.44/10.18 |
% 31.44/10.18 | From (1040) and (7170) follows:
% 31.44/10.18 | (7295) sum(n2, n10) = all_0_7_7
% 31.44/10.18 |
% 31.44/10.18 | From (1041) and (7168) follows:
% 31.44/10.18 | (7296) sum(n8, n4) = all_0_4_4
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (194) with n8, n4, all_0_4_4, n12 and discharging atoms sum(n8, n4) = all_0_4_4, sum(n8, n4) = n12, yields:
% 31.44/10.18 | (865) all_0_4_4 = n12
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (194) with n2, n10, all_0_7_7, n12 and discharging atoms sum(n2, n10) = all_0_7_7, sum(n2, n10) = n12, yields:
% 31.44/10.18 | (867) all_0_7_7 = n12
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 31.44/10.18 | (1046) all_0_2_2 = n6
% 31.44/10.18 |
% 31.44/10.18 | From (1046) and (7172) follows:
% 31.44/10.18 | (7300) sum(n6, n18) = all_0_0_0
% 31.44/10.18 |
% 31.44/10.18 | From (867)(865) and (435) follows:
% 31.44/10.18 | (869) sum(n12, n12) = all_0_3_3
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 31.44/10.18 | (870) all_0_3_3 = n3
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (194) with n6, n18, all_0_0_0, n3 and discharging atoms sum(n6, n18) = all_0_0_0, sum(n6, n18) = n3, yields:
% 31.44/10.18 | (871) all_0_0_0 = n3
% 31.44/10.18 |
% 31.44/10.18 | Equations (871,870) can reduce 201 to:
% 31.44/10.18 | (746) $false
% 31.44/10.18 |
% 31.44/10.18 |-The branch is then unsatisfiable
% 31.44/10.18 |-Branch two:
% 31.44/10.18 | (1053) ~ (all_0_11_11 = n3)
% 31.44/10.18 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.44/10.18 |
% 31.44/10.18 +-Applying beta-rule and splitting (1054), into two cases.
% 31.44/10.18 |-Branch one:
% 31.44/10.18 | (1055) all_0_11_11 = n2
% 31.44/10.18 |
% 31.44/10.18 | From (1055) and (190) follows:
% 31.44/10.18 | (1056) pred(n2) = all_0_9_9
% 31.44/10.18 |
% 31.44/10.18 | From (1055) and (505) follows:
% 31.44/10.18 | (1057) succ(n2) = all_0_5_5
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 31.44/10.18 | (1058) all_0_9_9 = n1
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.44/10.18 | (1059) all_0_5_5 = n3
% 31.44/10.18 |
% 31.44/10.18 | From (1058)(1059) and (156) follows:
% 31.44/10.18 | (1060) sum(n1, n3) = all_0_2_2
% 31.44/10.18 |
% 31.44/10.18 | From (1058) and (7170) follows:
% 31.44/10.18 | (7313) sum(n1, n10) = all_0_7_7
% 31.44/10.18 |
% 31.44/10.18 | From (1059) and (7168) follows:
% 31.44/10.18 | (7314) sum(n8, n3) = all_0_4_4
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (194) with n8, n3, all_0_4_4, n11 and discharging atoms sum(n8, n3) = all_0_4_4, sum(n8, n3) = n11, yields:
% 31.44/10.18 | (883) all_0_4_4 = n11
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (194) with n1, n10, all_0_7_7, n11 and discharging atoms sum(n1, n10) = all_0_7_7, sum(n1, n10) = n11, yields:
% 31.44/10.18 | (885) all_0_7_7 = n11
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 31.44/10.18 | (1064) all_0_2_2 = n4
% 31.44/10.18 |
% 31.44/10.18 | From (1064) and (7172) follows:
% 31.44/10.18 | (7318) sum(n4, n18) = all_0_0_0
% 31.44/10.18 |
% 31.44/10.18 | From (885)(883) and (435) follows:
% 31.44/10.18 | (887) sum(n11, n11) = all_0_3_3
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 31.44/10.18 | (888) all_0_3_3 = n1
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (194) with n4, n18, all_0_0_0, n1 and discharging atoms sum(n4, n18) = all_0_0_0, sum(n4, n18) = n1, yields:
% 31.44/10.18 | (889) all_0_0_0 = n1
% 31.44/10.18 |
% 31.44/10.18 | Equations (889,888) can reduce 201 to:
% 31.44/10.18 | (746) $false
% 31.44/10.18 |
% 31.44/10.18 |-The branch is then unsatisfiable
% 31.44/10.18 |-Branch two:
% 31.44/10.18 | (1071) ~ (all_0_11_11 = n2)
% 31.44/10.18 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 31.44/10.18 |
% 31.44/10.18 +-Applying beta-rule and splitting (1072), into two cases.
% 31.44/10.18 |-Branch one:
% 31.44/10.18 | (1073) all_0_11_11 = n1
% 31.44/10.18 |
% 31.44/10.18 | From (1073) and (190) follows:
% 31.44/10.18 | (1074) pred(n1) = all_0_9_9
% 31.44/10.18 |
% 31.44/10.18 | From (1073) and (505) follows:
% 31.44/10.18 | (1075) succ(n1) = all_0_5_5
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 31.44/10.18 | (1076) all_0_9_9 = n0
% 31.44/10.18 |
% 31.44/10.18 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.44/10.18 | (1077) all_0_5_5 = n2
% 31.44/10.18 |
% 31.44/10.18 | From (1076)(1077) and (156) follows:
% 31.44/10.18 | (1078) sum(n0, n2) = all_0_2_2
% 31.44/10.18 |
% 31.44/10.18 | From (1076) and (7170) follows:
% 31.44/10.18 | (7331) sum(n0, n10) = all_0_7_7
% 31.44/10.18 |
% 31.44/10.18 | From (1077) and (7168) follows:
% 31.44/10.19 | (7332) sum(n8, n2) = all_0_4_4
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (194) with n8, n2, all_0_4_4, n10 and discharging atoms sum(n8, n2) = all_0_4_4, sum(n8, n2) = n10, yields:
% 31.44/10.19 | (901) all_0_4_4 = n10
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (194) with n0, n10, all_0_7_7, n10 and discharging atoms sum(n0, n10) = all_0_7_7, sum(n0, n10) = n10, yields:
% 31.44/10.19 | (903) all_0_7_7 = n10
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 31.44/10.19 | (1082) all_0_2_2 = n2
% 31.44/10.19 |
% 31.44/10.19 | From (1082) and (7172) follows:
% 31.44/10.19 | (7336) sum(n2, n18) = all_0_0_0
% 31.44/10.19 |
% 31.44/10.19 | From (903)(901) and (435) follows:
% 31.44/10.19 | (905) sum(n10, n10) = all_0_3_3
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 31.44/10.19 | (906) all_0_3_3 = n20
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (194) with n2, n18, all_0_0_0, n20 and discharging atoms sum(n2, n18) = all_0_0_0, sum(n2, n18) = n20, yields:
% 31.44/10.19 | (907) all_0_0_0 = n20
% 31.44/10.19 |
% 31.44/10.19 | Equations (907,906) can reduce 201 to:
% 31.44/10.19 | (746) $false
% 31.44/10.19 |
% 31.44/10.19 |-The branch is then unsatisfiable
% 31.44/10.19 |-Branch two:
% 31.44/10.19 | (1090) ~ (all_0_11_11 = n1)
% 31.44/10.19 | (1091) all_0_11_11 = n0
% 31.44/10.19 |
% 31.44/10.19 | From (1091) and (190) follows:
% 31.44/10.19 | (1092) pred(n0) = all_0_9_9
% 31.44/10.19 |
% 31.44/10.19 | From (1091) and (505) follows:
% 31.44/10.19 | (1093) succ(n0) = all_0_5_5
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 31.44/10.19 | (1094) all_0_9_9 = n20
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.44/10.19 | (1095) all_0_5_5 = n1
% 31.44/10.19 |
% 31.44/10.19 | From (1094)(1095) and (156) follows:
% 31.44/10.19 | (1096) sum(n20, n1) = all_0_2_2
% 31.44/10.19 |
% 31.44/10.19 | From (1094) and (7170) follows:
% 31.44/10.19 | (7348) sum(n20, n10) = all_0_7_7
% 31.44/10.19 |
% 31.44/10.19 | From (1095) and (7168) follows:
% 31.44/10.19 | (7349) sum(n8, n1) = all_0_4_4
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (194) with n20, n10, all_0_7_7, n9 and discharging atoms sum(n20, n10) = all_0_7_7, sum(n20, n10) = n9, yields:
% 31.44/10.19 | (921) all_0_7_7 = n9
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 31.44/10.19 | (1099) all_0_2_2 = n0
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (194) with n8, n1, all_0_4_4, n9 and discharging atoms sum(n8, n1) = all_0_4_4, sum(n8, n1) = n9, yields:
% 31.44/10.19 | (919) all_0_4_4 = n9
% 31.44/10.19 |
% 31.44/10.19 | From (1099) and (7172) follows:
% 31.44/10.19 | (7353) sum(n0, n18) = all_0_0_0
% 31.44/10.19 |
% 31.44/10.19 | From (921)(919) and (435) follows:
% 31.44/10.19 | (923) sum(n9, n9) = all_0_3_3
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 31.44/10.19 | (925) all_0_3_3 = n18
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (194) with n0, n18, all_0_0_0, n18 and discharging atoms sum(n0, n18) = all_0_0_0, sum(n0, n18) = n18, yields:
% 31.44/10.19 | (924) all_0_0_0 = n18
% 31.44/10.19 |
% 31.44/10.19 | Equations (924,925) can reduce 201 to:
% 31.44/10.19 | (746) $false
% 31.44/10.19 |
% 31.44/10.19 |-The branch is then unsatisfiable
% 31.44/10.19 |-Branch two:
% 31.44/10.19 | (1316) ~ (all_0_10_10 = n9)
% 31.44/10.19 | (1317) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.44/10.19 |
% 31.44/10.19 +-Applying beta-rule and splitting (928), into two cases.
% 31.44/10.19 |-Branch one:
% 31.44/10.19 | (929) all_0_11_11 = n9
% 31.44/10.19 |
% 31.44/10.19 | From (929) and (190) follows:
% 31.44/10.19 | (930) pred(n9) = all_0_9_9
% 31.44/10.19 |
% 31.44/10.19 | From (929) and (505) follows:
% 31.44/10.19 | (931) succ(n9) = all_0_5_5
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (259) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 31.44/10.19 | (932) all_0_9_9 = n8
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (184) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 31.44/10.19 | (933) all_0_5_5 = n10
% 31.44/10.19 |
% 31.44/10.19 | From (933) and (386) follows:
% 31.44/10.19 | (7365) sum(all_0_6_6, n10) = all_0_4_4
% 31.44/10.19 |
% 31.44/10.19 | From (932)(933) and (156) follows:
% 31.44/10.19 | (934) sum(n8, n10) = all_0_2_2
% 31.44/10.19 |
% 31.44/10.19 | From (932) and (74) follows:
% 31.44/10.19 | (7367) sum(n8, all_0_8_8) = all_0_7_7
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (194) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 31.44/10.19 | (938) all_0_2_2 = n18
% 31.44/10.19 |
% 31.44/10.19 | From (938) and (85) follows:
% 31.44/10.19 | (7369) sum(n18, all_0_1_1) = all_0_0_0
% 31.44/10.19 |
% 31.44/10.19 +-Applying beta-rule and splitting (1317), into two cases.
% 31.44/10.19 |-Branch one:
% 31.44/10.19 | (1318) all_0_10_10 = n8
% 31.44/10.19 |
% 31.44/10.19 | From (1318) and (57) follows:
% 31.44/10.19 | (1319) pred(n8) = all_0_6_6
% 31.44/10.19 |
% 31.44/10.19 | From (1318) and (381) follows:
% 31.44/10.19 | (1320) succ(n8) = all_0_8_8
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (259) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 31.44/10.19 | (1321) all_0_6_6 = n7
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (184) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 31.44/10.19 | (1322) all_0_8_8 = n9
% 31.44/10.19 |
% 31.44/10.19 | From (1321)(1322) and (628) follows:
% 31.44/10.19 | (1323) sum(n7, n9) = all_0_1_1
% 31.44/10.19 |
% 31.44/10.19 | From (1321) and (7365) follows:
% 31.44/10.19 | (7376) sum(n7, n10) = all_0_4_4
% 31.44/10.19 |
% 31.44/10.19 | From (1322) and (7367) follows:
% 31.44/10.19 | (7377) sum(n8, n9) = all_0_7_7
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (194) with n8, n9, all_0_7_7, n17 and discharging atoms sum(n8, n9) = all_0_7_7, sum(n8, n9) = n17, yields:
% 31.44/10.19 | (777) all_0_7_7 = n17
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (194) with n7, n10, all_0_4_4, n17 and discharging atoms sum(n7, n10) = all_0_4_4, sum(n7, n10) = n17, yields:
% 31.44/10.19 | (775) all_0_4_4 = n17
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (194) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 31.44/10.19 | (1327) all_0_1_1 = n16
% 31.44/10.19 |
% 31.44/10.19 | From (777)(775) and (435) follows:
% 31.44/10.19 | (779) sum(n17, n17) = all_0_3_3
% 31.44/10.19 |
% 31.44/10.19 | From (1327) and (7369) follows:
% 31.44/10.19 | (7382) sum(n18, n16) = all_0_0_0
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (194) with n18, n16, all_0_0_0, n13 and discharging atoms sum(n18, n16) = all_0_0_0, sum(n18, n16) = n13, yields:
% 31.44/10.19 | (781) all_0_0_0 = n13
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (194) with n17, n17, all_0_3_3, n13 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n13, yields:
% 31.44/10.19 | (780) all_0_3_3 = n13
% 31.44/10.19 |
% 31.44/10.19 | Equations (781,780) can reduce 201 to:
% 31.44/10.19 | (746) $false
% 31.44/10.19 |
% 31.44/10.19 |-The branch is then unsatisfiable
% 31.44/10.19 |-Branch two:
% 31.44/10.19 | (1334) ~ (all_0_10_10 = n8)
% 31.44/10.19 | (1335) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.44/10.19 |
% 31.44/10.19 +-Applying beta-rule and splitting (1335), into two cases.
% 31.44/10.19 |-Branch one:
% 31.44/10.19 | (1336) all_0_10_10 = n7
% 31.44/10.19 |
% 31.44/10.19 | From (1336) and (57) follows:
% 31.44/10.19 | (1337) pred(n7) = all_0_6_6
% 31.44/10.19 |
% 31.44/10.19 | From (1336) and (381) follows:
% 31.44/10.19 | (1338) succ(n7) = all_0_8_8
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (259) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 31.44/10.19 | (1339) all_0_6_6 = n6
% 31.44/10.19 |
% 31.44/10.19 | Instantiating formula (184) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 31.44/10.19 | (1340) all_0_8_8 = n8
% 31.44/10.19 |
% 31.44/10.19 | From (1339)(1340) and (628) follows:
% 31.44/10.19 | (1341) sum(n6, n8) = all_0_1_1
% 31.44/10.19 |
% 31.44/10.19 | From (1339) and (7365) follows:
% 31.44/10.20 | (7394) sum(n6, n10) = all_0_4_4
% 31.44/10.20 |
% 31.44/10.20 | From (1340) and (7367) follows:
% 31.44/10.20 | (7395) sum(n8, n8) = all_0_7_7
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n8, n8, all_0_7_7, n16 and discharging atoms sum(n8, n8) = all_0_7_7, sum(n8, n8) = n16, yields:
% 31.44/10.20 | (795) all_0_7_7 = n16
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n6, n10, all_0_4_4, n16 and discharging atoms sum(n6, n10) = all_0_4_4, sum(n6, n10) = n16, yields:
% 31.44/10.20 | (793) all_0_4_4 = n16
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 31.44/10.20 | (1345) all_0_1_1 = n14
% 31.44/10.20 |
% 31.44/10.20 | From (795)(793) and (435) follows:
% 31.44/10.20 | (797) sum(n16, n16) = all_0_3_3
% 31.44/10.20 |
% 31.44/10.20 | From (1345) and (7369) follows:
% 31.44/10.20 | (7400) sum(n18, n14) = all_0_0_0
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n18, n14, all_0_0_0, n11 and discharging atoms sum(n18, n14) = all_0_0_0, sum(n18, n14) = n11, yields:
% 31.44/10.20 | (799) all_0_0_0 = n11
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n16, n16, all_0_3_3, n11 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n11, yields:
% 31.44/10.20 | (798) all_0_3_3 = n11
% 31.44/10.20 |
% 31.44/10.20 | Equations (799,798) can reduce 201 to:
% 31.44/10.20 | (746) $false
% 31.44/10.20 |
% 31.44/10.20 |-The branch is then unsatisfiable
% 31.44/10.20 |-Branch two:
% 31.44/10.20 | (1352) ~ (all_0_10_10 = n7)
% 31.44/10.20 | (1353) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.44/10.20 |
% 31.44/10.20 +-Applying beta-rule and splitting (1353), into two cases.
% 31.44/10.20 |-Branch one:
% 31.44/10.20 | (1354) all_0_10_10 = n6
% 31.44/10.20 |
% 31.44/10.20 | From (1354) and (57) follows:
% 31.44/10.20 | (1355) pred(n6) = all_0_6_6
% 31.44/10.20 |
% 31.44/10.20 | From (1354) and (381) follows:
% 31.44/10.20 | (1356) succ(n6) = all_0_8_8
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (259) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 31.44/10.20 | (1357) all_0_6_6 = n5
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (184) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 31.44/10.20 | (1358) all_0_8_8 = n7
% 31.44/10.20 |
% 31.44/10.20 | From (1357)(1358) and (628) follows:
% 31.44/10.20 | (1359) sum(n5, n7) = all_0_1_1
% 31.44/10.20 |
% 31.44/10.20 | From (1357) and (7365) follows:
% 31.44/10.20 | (7412) sum(n5, n10) = all_0_4_4
% 31.44/10.20 |
% 31.44/10.20 | From (1358) and (7367) follows:
% 31.44/10.20 | (7413) sum(n8, n7) = all_0_7_7
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n8, n7, all_0_7_7, n15 and discharging atoms sum(n8, n7) = all_0_7_7, sum(n8, n7) = n15, yields:
% 31.44/10.20 | (813) all_0_7_7 = n15
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n5, n10, all_0_4_4, n15 and discharging atoms sum(n5, n10) = all_0_4_4, sum(n5, n10) = n15, yields:
% 31.44/10.20 | (811) all_0_4_4 = n15
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 31.44/10.20 | (1363) all_0_1_1 = n12
% 31.44/10.20 |
% 31.44/10.20 | From (813)(811) and (435) follows:
% 31.44/10.20 | (815) sum(n15, n15) = all_0_3_3
% 31.44/10.20 |
% 31.44/10.20 | From (1363) and (7369) follows:
% 31.44/10.20 | (7418) sum(n18, n12) = all_0_0_0
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n18, n12, all_0_0_0, n9 and discharging atoms sum(n18, n12) = all_0_0_0, sum(n18, n12) = n9, yields:
% 31.44/10.20 | (817) all_0_0_0 = n9
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 31.44/10.20 | (816) all_0_3_3 = n9
% 31.44/10.20 |
% 31.44/10.20 | Equations (817,816) can reduce 201 to:
% 31.44/10.20 | (746) $false
% 31.44/10.20 |
% 31.44/10.20 |-The branch is then unsatisfiable
% 31.44/10.20 |-Branch two:
% 31.44/10.20 | (1370) ~ (all_0_10_10 = n6)
% 31.44/10.20 | (1371) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.44/10.20 |
% 31.44/10.20 +-Applying beta-rule and splitting (1371), into two cases.
% 31.44/10.20 |-Branch one:
% 31.44/10.20 | (1372) all_0_10_10 = n5
% 31.44/10.20 |
% 31.44/10.20 | From (1372) and (57) follows:
% 31.44/10.20 | (1373) pred(n5) = all_0_6_6
% 31.44/10.20 |
% 31.44/10.20 | From (1372) and (381) follows:
% 31.44/10.20 | (1374) succ(n5) = all_0_8_8
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (259) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 31.44/10.20 | (1375) all_0_6_6 = n4
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (184) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 31.44/10.20 | (1376) all_0_8_8 = n6
% 31.44/10.20 |
% 31.44/10.20 | From (1375)(1376) and (628) follows:
% 31.44/10.20 | (1377) sum(n4, n6) = all_0_1_1
% 31.44/10.20 |
% 31.44/10.20 | From (1375) and (7365) follows:
% 31.44/10.20 | (7430) sum(n4, n10) = all_0_4_4
% 31.44/10.20 |
% 31.44/10.20 | From (1376) and (7367) follows:
% 31.44/10.20 | (7431) sum(n8, n6) = all_0_7_7
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n8, n6, all_0_7_7, n14 and discharging atoms sum(n8, n6) = all_0_7_7, sum(n8, n6) = n14, yields:
% 31.44/10.20 | (831) all_0_7_7 = n14
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n4, n10, all_0_4_4, n14 and discharging atoms sum(n4, n10) = all_0_4_4, sum(n4, n10) = n14, yields:
% 31.44/10.20 | (829) all_0_4_4 = n14
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 31.44/10.20 | (1381) all_0_1_1 = n10
% 31.44/10.20 |
% 31.44/10.20 | From (831)(829) and (435) follows:
% 31.44/10.20 | (833) sum(n14, n14) = all_0_3_3
% 31.44/10.20 |
% 31.44/10.20 | From (1381) and (7369) follows:
% 31.44/10.20 | (7436) sum(n18, n10) = all_0_0_0
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n18, n10, all_0_0_0, n7 and discharging atoms sum(n18, n10) = all_0_0_0, sum(n18, n10) = n7, yields:
% 31.44/10.20 | (835) all_0_0_0 = n7
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 31.44/10.20 | (834) all_0_3_3 = n7
% 31.44/10.20 |
% 31.44/10.20 | Equations (835,834) can reduce 201 to:
% 31.44/10.20 | (746) $false
% 31.44/10.20 |
% 31.44/10.20 |-The branch is then unsatisfiable
% 31.44/10.20 |-Branch two:
% 31.44/10.20 | (1388) ~ (all_0_10_10 = n5)
% 31.44/10.20 | (1389) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.44/10.20 |
% 31.44/10.20 +-Applying beta-rule and splitting (1389), into two cases.
% 31.44/10.20 |-Branch one:
% 31.44/10.20 | (1390) all_0_10_10 = n4
% 31.44/10.20 |
% 31.44/10.20 | From (1390) and (57) follows:
% 31.44/10.20 | (1391) pred(n4) = all_0_6_6
% 31.44/10.20 |
% 31.44/10.20 | From (1390) and (381) follows:
% 31.44/10.20 | (1392) succ(n4) = all_0_8_8
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (259) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 31.44/10.20 | (1393) all_0_6_6 = n3
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (184) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 31.44/10.20 | (1394) all_0_8_8 = n5
% 31.44/10.20 |
% 31.44/10.20 | From (1393)(1394) and (628) follows:
% 31.44/10.20 | (1395) sum(n3, n5) = all_0_1_1
% 31.44/10.20 |
% 31.44/10.20 | From (1393) and (7365) follows:
% 31.44/10.20 | (7448) sum(n3, n10) = all_0_4_4
% 31.44/10.20 |
% 31.44/10.20 | From (1394) and (7367) follows:
% 31.44/10.20 | (7449) sum(n8, n5) = all_0_7_7
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n8, n5, all_0_7_7, n13 and discharging atoms sum(n8, n5) = all_0_7_7, sum(n8, n5) = n13, yields:
% 31.44/10.20 | (849) all_0_7_7 = n13
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n3, n10, all_0_4_4, n13 and discharging atoms sum(n3, n10) = all_0_4_4, sum(n3, n10) = n13, yields:
% 31.44/10.20 | (847) all_0_4_4 = n13
% 31.44/10.20 |
% 31.44/10.20 | Instantiating formula (194) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 31.44/10.20 | (1399) all_0_1_1 = n8
% 31.44/10.20 |
% 31.44/10.20 | From (849)(847) and (435) follows:
% 31.44/10.20 | (851) sum(n13, n13) = all_0_3_3
% 31.44/10.20 |
% 31.44/10.20 | From (1399) and (7369) follows:
% 31.44/10.21 | (7454) sum(n18, n8) = all_0_0_0
% 31.44/10.21 |
% 31.44/10.21 | Instantiating formula (194) with n18, n8, all_0_0_0, n5 and discharging atoms sum(n18, n8) = all_0_0_0, sum(n18, n8) = n5, yields:
% 31.44/10.21 | (853) all_0_0_0 = n5
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 31.58/10.21 | (852) all_0_3_3 = n5
% 31.58/10.21 |
% 31.58/10.21 | Equations (853,852) can reduce 201 to:
% 31.58/10.21 | (746) $false
% 31.58/10.21 |
% 31.58/10.21 |-The branch is then unsatisfiable
% 31.58/10.21 |-Branch two:
% 31.58/10.21 | (1406) ~ (all_0_10_10 = n4)
% 31.58/10.21 | (1407) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.58/10.21 |
% 31.58/10.21 +-Applying beta-rule and splitting (1407), into two cases.
% 31.58/10.21 |-Branch one:
% 31.58/10.21 | (1408) all_0_10_10 = n3
% 31.58/10.21 |
% 31.58/10.21 | From (1408) and (57) follows:
% 31.58/10.21 | (1409) pred(n3) = all_0_6_6
% 31.58/10.21 |
% 31.58/10.21 | From (1408) and (381) follows:
% 31.58/10.21 | (1410) succ(n3) = all_0_8_8
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 31.58/10.21 | (1411) all_0_6_6 = n2
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 31.58/10.21 | (1412) all_0_8_8 = n4
% 31.58/10.21 |
% 31.58/10.21 | From (1411)(1412) and (628) follows:
% 31.58/10.21 | (1413) sum(n2, n4) = all_0_1_1
% 31.58/10.21 |
% 31.58/10.21 | From (1411) and (7365) follows:
% 31.58/10.21 | (7466) sum(n2, n10) = all_0_4_4
% 31.58/10.21 |
% 31.58/10.21 | From (1412) and (7367) follows:
% 31.58/10.21 | (7467) sum(n8, n4) = all_0_7_7
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (194) with n8, n4, all_0_7_7, n12 and discharging atoms sum(n8, n4) = all_0_7_7, sum(n8, n4) = n12, yields:
% 31.58/10.21 | (867) all_0_7_7 = n12
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (194) with n2, n10, all_0_4_4, n12 and discharging atoms sum(n2, n10) = all_0_4_4, sum(n2, n10) = n12, yields:
% 31.58/10.21 | (865) all_0_4_4 = n12
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 31.58/10.21 | (1417) all_0_1_1 = n6
% 31.58/10.21 |
% 31.58/10.21 | From (867)(865) and (435) follows:
% 31.58/10.21 | (869) sum(n12, n12) = all_0_3_3
% 31.58/10.21 |
% 31.58/10.21 | From (1417) and (7369) follows:
% 31.58/10.21 | (7472) sum(n18, n6) = all_0_0_0
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (194) with n18, n6, all_0_0_0, n3 and discharging atoms sum(n18, n6) = all_0_0_0, sum(n18, n6) = n3, yields:
% 31.58/10.21 | (871) all_0_0_0 = n3
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 31.58/10.21 | (870) all_0_3_3 = n3
% 31.58/10.21 |
% 31.58/10.21 | Equations (871,870) can reduce 201 to:
% 31.58/10.21 | (746) $false
% 31.58/10.21 |
% 31.58/10.21 |-The branch is then unsatisfiable
% 31.58/10.21 |-Branch two:
% 31.58/10.21 | (1424) ~ (all_0_10_10 = n3)
% 31.58/10.21 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.58/10.21 |
% 31.58/10.21 +-Applying beta-rule and splitting (1425), into two cases.
% 31.58/10.21 |-Branch one:
% 31.58/10.21 | (1426) all_0_10_10 = n2
% 31.58/10.21 |
% 31.58/10.21 | From (1426) and (57) follows:
% 31.58/10.21 | (1427) pred(n2) = all_0_6_6
% 31.58/10.21 |
% 31.58/10.21 | From (1426) and (381) follows:
% 31.58/10.21 | (1428) succ(n2) = all_0_8_8
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 31.58/10.21 | (1429) all_0_6_6 = n1
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 31.58/10.21 | (1430) all_0_8_8 = n3
% 31.58/10.21 |
% 31.58/10.21 | From (1429)(1430) and (628) follows:
% 31.58/10.21 | (1431) sum(n1, n3) = all_0_1_1
% 31.58/10.21 |
% 31.58/10.21 | From (1429) and (7365) follows:
% 31.58/10.21 | (7484) sum(n1, n10) = all_0_4_4
% 31.58/10.21 |
% 31.58/10.21 | From (1430) and (7367) follows:
% 31.58/10.21 | (7485) sum(n8, n3) = all_0_7_7
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (194) with n8, n3, all_0_7_7, n11 and discharging atoms sum(n8, n3) = all_0_7_7, sum(n8, n3) = n11, yields:
% 31.58/10.21 | (885) all_0_7_7 = n11
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (194) with n1, n10, all_0_4_4, n11 and discharging atoms sum(n1, n10) = all_0_4_4, sum(n1, n10) = n11, yields:
% 31.58/10.21 | (883) all_0_4_4 = n11
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 31.58/10.21 | (1435) all_0_1_1 = n4
% 31.58/10.21 |
% 31.58/10.21 | From (885)(883) and (435) follows:
% 31.58/10.21 | (887) sum(n11, n11) = all_0_3_3
% 31.58/10.21 |
% 31.58/10.21 | From (1435) and (7369) follows:
% 31.58/10.21 | (7490) sum(n18, n4) = all_0_0_0
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (194) with n18, n4, all_0_0_0, n1 and discharging atoms sum(n18, n4) = all_0_0_0, sum(n18, n4) = n1, yields:
% 31.58/10.21 | (889) all_0_0_0 = n1
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 31.58/10.21 | (888) all_0_3_3 = n1
% 31.58/10.21 |
% 31.58/10.21 | Equations (889,888) can reduce 201 to:
% 31.58/10.21 | (746) $false
% 31.58/10.21 |
% 31.58/10.21 |-The branch is then unsatisfiable
% 31.58/10.21 |-Branch two:
% 31.58/10.21 | (1442) ~ (all_0_10_10 = n2)
% 31.58/10.21 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 31.58/10.21 |
% 31.58/10.21 +-Applying beta-rule and splitting (1443), into two cases.
% 31.58/10.21 |-Branch one:
% 31.58/10.21 | (1444) all_0_10_10 = n1
% 31.58/10.21 |
% 31.58/10.21 | From (1444) and (57) follows:
% 31.58/10.21 | (1445) pred(n1) = all_0_6_6
% 31.58/10.21 |
% 31.58/10.21 | From (1444) and (381) follows:
% 31.58/10.21 | (1446) succ(n1) = all_0_8_8
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 31.58/10.21 | (1447) all_0_6_6 = n0
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 31.58/10.21 | (1448) all_0_8_8 = n2
% 31.58/10.21 |
% 31.58/10.21 | From (1447)(1448) and (628) follows:
% 31.58/10.21 | (1449) sum(n0, n2) = all_0_1_1
% 31.58/10.21 |
% 31.58/10.21 | From (1447) and (7365) follows:
% 31.58/10.21 | (7502) sum(n0, n10) = all_0_4_4
% 31.58/10.21 |
% 31.58/10.21 | From (1448) and (7367) follows:
% 31.58/10.21 | (7503) sum(n8, n2) = all_0_7_7
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (194) with n8, n2, all_0_7_7, n10 and discharging atoms sum(n8, n2) = all_0_7_7, sum(n8, n2) = n10, yields:
% 31.58/10.21 | (903) all_0_7_7 = n10
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (194) with n0, n10, all_0_4_4, n10 and discharging atoms sum(n0, n10) = all_0_4_4, sum(n0, n10) = n10, yields:
% 31.58/10.21 | (901) all_0_4_4 = n10
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 31.58/10.21 | (1453) all_0_1_1 = n2
% 31.58/10.21 |
% 31.58/10.21 | From (903)(901) and (435) follows:
% 31.58/10.21 | (905) sum(n10, n10) = all_0_3_3
% 31.58/10.21 |
% 31.58/10.21 | From (1453) and (7369) follows:
% 31.58/10.21 | (7508) sum(n18, n2) = all_0_0_0
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (194) with n18, n2, all_0_0_0, n20 and discharging atoms sum(n18, n2) = all_0_0_0, sum(n18, n2) = n20, yields:
% 31.58/10.21 | (907) all_0_0_0 = n20
% 31.58/10.21 |
% 31.58/10.21 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 31.58/10.22 | (906) all_0_3_3 = n20
% 31.58/10.22 |
% 31.58/10.22 | Equations (907,906) can reduce 201 to:
% 31.58/10.22 | (746) $false
% 31.58/10.22 |
% 31.58/10.22 |-The branch is then unsatisfiable
% 31.58/10.22 |-Branch two:
% 31.58/10.22 | (1462) ~ (all_0_10_10 = n1)
% 31.58/10.22 | (1463) all_0_10_10 = n0
% 31.58/10.22 |
% 31.58/10.22 | From (1463) and (57) follows:
% 31.58/10.22 | (1464) pred(n0) = all_0_6_6
% 31.58/10.22 |
% 31.58/10.22 | From (1463) and (381) follows:
% 31.58/10.22 | (1465) succ(n0) = all_0_8_8
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 31.58/10.22 | (1466) all_0_6_6 = n20
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 31.58/10.22 | (1467) all_0_8_8 = n1
% 31.58/10.22 |
% 31.58/10.22 | From (1466)(1467) and (628) follows:
% 31.58/10.22 | (1468) sum(n20, n1) = all_0_1_1
% 31.58/10.22 |
% 31.58/10.22 | From (1466) and (7365) follows:
% 31.58/10.22 | (7519) sum(n20, n10) = all_0_4_4
% 31.58/10.22 |
% 31.58/10.22 | From (1467) and (7367) follows:
% 31.58/10.22 | (7520) sum(n8, n1) = all_0_7_7
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (194) with n20, n10, all_0_4_4, n9 and discharging atoms sum(n20, n10) = all_0_4_4, sum(n20, n10) = n9, yields:
% 31.58/10.22 | (919) all_0_4_4 = n9
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 31.58/10.22 | (1471) all_0_1_1 = n0
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (194) with n8, n1, all_0_7_7, n9 and discharging atoms sum(n8, n1) = all_0_7_7, sum(n8, n1) = n9, yields:
% 31.58/10.22 | (921) all_0_7_7 = n9
% 31.58/10.22 |
% 31.58/10.22 | From (921)(919) and (435) follows:
% 31.58/10.22 | (923) sum(n9, n9) = all_0_3_3
% 31.58/10.22 |
% 31.58/10.22 | From (1471) and (7369) follows:
% 31.58/10.22 | (7525) sum(n18, n0) = all_0_0_0
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (194) with n18, n0, all_0_0_0, n18 and discharging atoms sum(n18, n0) = all_0_0_0, sum(n18, n0) = n18, yields:
% 31.58/10.22 | (924) all_0_0_0 = n18
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 31.58/10.22 | (925) all_0_3_3 = n18
% 31.58/10.22 |
% 31.58/10.22 | Equations (924,925) can reduce 201 to:
% 31.58/10.22 | (746) $false
% 31.58/10.22 |
% 31.58/10.22 |-The branch is then unsatisfiable
% 31.58/10.22 |-Branch two:
% 31.58/10.22 | (945) ~ (all_0_11_11 = n9)
% 31.58/10.22 | (946) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.58/10.22 |
% 31.58/10.22 +-Applying beta-rule and splitting (1317), into two cases.
% 31.58/10.22 |-Branch one:
% 31.58/10.22 | (1318) all_0_10_10 = n8
% 31.58/10.22 |
% 31.58/10.22 | From (1318) and (57) follows:
% 31.58/10.22 | (1319) pred(n8) = all_0_6_6
% 31.58/10.22 |
% 31.58/10.22 | From (1318) and (381) follows:
% 31.58/10.22 | (1320) succ(n8) = all_0_8_8
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (259) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 31.58/10.22 | (1321) all_0_6_6 = n7
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (184) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 31.58/10.22 | (1322) all_0_8_8 = n9
% 31.58/10.22 |
% 31.58/10.22 | From (1321) and (1319) follows:
% 31.58/10.22 | (141) pred(n8) = n7
% 31.58/10.22 |
% 31.58/10.22 | From (1322) and (1320) follows:
% 31.58/10.22 | (175) succ(n8) = n9
% 31.58/10.22 |
% 31.58/10.22 | From (1321) and (386) follows:
% 31.58/10.22 | (7538) sum(n7, all_0_5_5) = all_0_4_4
% 31.58/10.22 |
% 31.58/10.22 | From (1321)(1322) and (628) follows:
% 31.58/10.22 | (1323) sum(n7, n9) = all_0_1_1
% 31.58/10.22 |
% 31.58/10.22 | From (1322) and (74) follows:
% 31.58/10.22 | (7540) sum(all_0_9_9, n9) = all_0_7_7
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (194) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 31.58/10.22 | (1327) all_0_1_1 = n16
% 31.58/10.22 |
% 31.58/10.22 | From (1327) and (85) follows:
% 31.58/10.22 | (7542) sum(all_0_2_2, n16) = all_0_0_0
% 31.58/10.22 |
% 31.58/10.22 | From (1327) and (1323) follows:
% 31.58/10.22 | (461) sum(n7, n9) = n16
% 31.58/10.22 |
% 31.58/10.22 +-Applying beta-rule and splitting (946), into two cases.
% 31.58/10.22 |-Branch one:
% 31.58/10.22 | (947) all_0_11_11 = n8
% 31.58/10.22 |
% 31.58/10.22 | From (947) and (190) follows:
% 31.58/10.22 | (948) pred(n8) = all_0_9_9
% 31.58/10.22 |
% 31.58/10.22 | From (947) and (505) follows:
% 31.58/10.22 | (949) succ(n8) = all_0_5_5
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (259) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 31.58/10.22 | (950) all_0_9_9 = n7
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (184) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 31.58/10.22 | (951) all_0_5_5 = n9
% 31.58/10.22 |
% 31.58/10.22 | From (950)(951) and (156) follows:
% 31.58/10.22 | (952) sum(n7, n9) = all_0_2_2
% 31.58/10.22 |
% 31.58/10.22 | From (950) and (7540) follows:
% 31.58/10.22 | (7550) sum(n7, n9) = all_0_7_7
% 31.58/10.22 |
% 31.58/10.22 | From (951) and (7538) follows:
% 31.58/10.22 | (7551) sum(n7, n9) = all_0_4_4
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (194) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 31.58/10.22 | (956) all_0_2_2 = n16
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (194) with n7, n9, all_0_4_4, all_0_2_2 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = all_0_4_4, yields:
% 31.58/10.22 | (733) all_0_2_2 = all_0_4_4
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (194) with n7, n9, all_0_7_7, all_0_2_2 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = all_0_7_7, yields:
% 31.58/10.22 | (734) all_0_2_2 = all_0_7_7
% 31.58/10.22 |
% 31.58/10.22 | Combining equations (734,733) yields a new equation:
% 31.58/10.22 | (735) all_0_4_4 = all_0_7_7
% 31.58/10.22 |
% 31.58/10.22 | Combining equations (956,733) yields a new equation:
% 31.58/10.22 | (793) all_0_4_4 = n16
% 31.58/10.22 |
% 31.58/10.22 | Combining equations (793,735) yields a new equation:
% 31.58/10.22 | (795) all_0_7_7 = n16
% 31.58/10.22 |
% 31.58/10.22 | Combining equations (795,735) yields a new equation:
% 31.58/10.22 | (793) all_0_4_4 = n16
% 31.58/10.22 |
% 31.58/10.22 | Combining equations (793,733) yields a new equation:
% 31.58/10.22 | (956) all_0_2_2 = n16
% 31.58/10.22 |
% 31.58/10.22 | From (956) and (7542) follows:
% 31.58/10.22 | (7560) sum(n16, n16) = all_0_0_0
% 31.58/10.22 |
% 31.58/10.22 | From (795)(793) and (435) follows:
% 31.58/10.22 | (797) sum(n16, n16) = all_0_3_3
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (194) with n16, n16, all_0_0_0, n11 and discharging atoms sum(n16, n16) = all_0_0_0, sum(n16, n16) = n11, yields:
% 31.58/10.22 | (799) all_0_0_0 = n11
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (194) with n16, n16, all_0_3_3, all_0_0_0 and discharging atoms sum(n16, n16) = all_0_0_0, sum(n16, n16) = all_0_3_3, yields:
% 31.58/10.22 | (743) all_0_0_0 = all_0_3_3
% 31.58/10.22 |
% 31.58/10.22 | Combining equations (799,743) yields a new equation:
% 31.58/10.22 | (798) all_0_3_3 = n11
% 31.58/10.22 |
% 31.58/10.22 | Combining equations (798,743) yields a new equation:
% 31.58/10.22 | (799) all_0_0_0 = n11
% 31.58/10.22 |
% 31.58/10.22 | Equations (799,798) can reduce 201 to:
% 31.58/10.22 | (746) $false
% 31.58/10.22 |
% 31.58/10.22 |-The branch is then unsatisfiable
% 31.58/10.22 |-Branch two:
% 31.58/10.22 | (963) ~ (all_0_11_11 = n8)
% 31.58/10.22 | (964) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.58/10.22 |
% 31.58/10.22 +-Applying beta-rule and splitting (964), into two cases.
% 31.58/10.22 |-Branch one:
% 31.58/10.22 | (965) all_0_11_11 = n7
% 31.58/10.22 |
% 31.58/10.22 | From (965) and (190) follows:
% 31.58/10.22 | (966) pred(n7) = all_0_9_9
% 31.58/10.22 |
% 31.58/10.22 | From (965) and (505) follows:
% 31.58/10.22 | (967) succ(n7) = all_0_5_5
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (259) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 31.58/10.22 | (968) all_0_9_9 = n6
% 31.58/10.22 |
% 31.58/10.22 | Instantiating formula (184) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 31.58/10.22 | (969) all_0_5_5 = n8
% 31.58/10.22 |
% 31.58/10.22 | From (968)(969) and (156) follows:
% 31.58/10.22 | (970) sum(n6, n8) = all_0_2_2
% 31.58/10.22 |
% 31.58/10.22 | From (968) and (7540) follows:
% 31.58/10.22 | (7575) sum(n6, n9) = all_0_7_7
% 31.58/10.22 |
% 31.58/10.22 | From (969) and (7538) follows:
% 31.58/10.23 | (7576) sum(n7, n8) = all_0_4_4
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n7, n8, all_0_4_4, n15 and discharging atoms sum(n7, n8) = all_0_4_4, sum(n7, n8) = n15, yields:
% 31.58/10.23 | (811) all_0_4_4 = n15
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n6, n9, all_0_7_7, n15 and discharging atoms sum(n6, n9) = all_0_7_7, sum(n6, n9) = n15, yields:
% 31.58/10.23 | (813) all_0_7_7 = n15
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 31.58/10.23 | (974) all_0_2_2 = n14
% 31.58/10.23 |
% 31.58/10.23 | From (974) and (7542) follows:
% 31.58/10.23 | (7580) sum(n14, n16) = all_0_0_0
% 31.58/10.23 |
% 31.58/10.23 | From (813)(811) and (435) follows:
% 31.58/10.23 | (815) sum(n15, n15) = all_0_3_3
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 31.58/10.23 | (816) all_0_3_3 = n9
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n14, n16, all_0_0_0, n9 and discharging atoms sum(n14, n16) = all_0_0_0, sum(n14, n16) = n9, yields:
% 31.58/10.23 | (817) all_0_0_0 = n9
% 31.58/10.23 |
% 31.58/10.23 | Equations (817,816) can reduce 201 to:
% 31.58/10.23 | (746) $false
% 31.58/10.23 |
% 31.58/10.23 |-The branch is then unsatisfiable
% 31.58/10.23 |-Branch two:
% 31.58/10.23 | (981) ~ (all_0_11_11 = n7)
% 31.58/10.23 | (982) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.58/10.23 |
% 31.58/10.23 +-Applying beta-rule and splitting (982), into two cases.
% 31.58/10.23 |-Branch one:
% 31.58/10.23 | (983) all_0_11_11 = n6
% 31.58/10.23 |
% 31.58/10.23 | From (983) and (190) follows:
% 31.58/10.23 | (984) pred(n6) = all_0_9_9
% 31.58/10.23 |
% 31.58/10.23 | From (983) and (505) follows:
% 31.58/10.23 | (985) succ(n6) = all_0_5_5
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (259) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 31.58/10.23 | (986) all_0_9_9 = n5
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (184) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 31.58/10.23 | (987) all_0_5_5 = n7
% 31.58/10.23 |
% 31.58/10.23 | From (986)(987) and (156) follows:
% 31.58/10.23 | (988) sum(n5, n7) = all_0_2_2
% 31.58/10.23 |
% 31.58/10.23 | From (986) and (7540) follows:
% 31.58/10.23 | (7593) sum(n5, n9) = all_0_7_7
% 31.58/10.23 |
% 31.58/10.23 | From (987) and (7538) follows:
% 31.58/10.23 | (7594) sum(n7, n7) = all_0_4_4
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n7, n7, all_0_4_4, n14 and discharging atoms sum(n7, n7) = all_0_4_4, sum(n7, n7) = n14, yields:
% 31.58/10.23 | (829) all_0_4_4 = n14
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n5, n9, all_0_7_7, n14 and discharging atoms sum(n5, n9) = all_0_7_7, sum(n5, n9) = n14, yields:
% 31.58/10.23 | (831) all_0_7_7 = n14
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 31.58/10.23 | (992) all_0_2_2 = n12
% 31.58/10.23 |
% 31.58/10.23 | From (992) and (7542) follows:
% 31.58/10.23 | (7598) sum(n12, n16) = all_0_0_0
% 31.58/10.23 |
% 31.58/10.23 | From (831)(829) and (435) follows:
% 31.58/10.23 | (833) sum(n14, n14) = all_0_3_3
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 31.58/10.23 | (834) all_0_3_3 = n7
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n12, n16, all_0_0_0, n7 and discharging atoms sum(n12, n16) = all_0_0_0, sum(n12, n16) = n7, yields:
% 31.58/10.23 | (835) all_0_0_0 = n7
% 31.58/10.23 |
% 31.58/10.23 | Equations (835,834) can reduce 201 to:
% 31.58/10.23 | (746) $false
% 31.58/10.23 |
% 31.58/10.23 |-The branch is then unsatisfiable
% 31.58/10.23 |-Branch two:
% 31.58/10.23 | (999) ~ (all_0_11_11 = n6)
% 31.58/10.23 | (1000) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.58/10.23 |
% 31.58/10.23 +-Applying beta-rule and splitting (1000), into two cases.
% 31.58/10.23 |-Branch one:
% 31.58/10.23 | (1001) all_0_11_11 = n5
% 31.58/10.23 |
% 31.58/10.23 | From (1001) and (190) follows:
% 31.58/10.23 | (1002) pred(n5) = all_0_9_9
% 31.58/10.23 |
% 31.58/10.23 | From (1001) and (505) follows:
% 31.58/10.23 | (1003) succ(n5) = all_0_5_5
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (259) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 31.58/10.23 | (1004) all_0_9_9 = n4
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (184) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 31.58/10.23 | (1005) all_0_5_5 = n6
% 31.58/10.23 |
% 31.58/10.23 | From (1004)(1005) and (156) follows:
% 31.58/10.23 | (1006) sum(n4, n6) = all_0_2_2
% 31.58/10.23 |
% 31.58/10.23 | From (1004) and (7540) follows:
% 31.58/10.23 | (7611) sum(n4, n9) = all_0_7_7
% 31.58/10.23 |
% 31.58/10.23 | From (1005) and (7538) follows:
% 31.58/10.23 | (7612) sum(n7, n6) = all_0_4_4
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n7, n6, all_0_4_4, n13 and discharging atoms sum(n7, n6) = all_0_4_4, sum(n7, n6) = n13, yields:
% 31.58/10.23 | (847) all_0_4_4 = n13
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n4, n9, all_0_7_7, n13 and discharging atoms sum(n4, n9) = all_0_7_7, sum(n4, n9) = n13, yields:
% 31.58/10.23 | (849) all_0_7_7 = n13
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 31.58/10.23 | (1010) all_0_2_2 = n10
% 31.58/10.23 |
% 31.58/10.23 | From (1010) and (7542) follows:
% 31.58/10.23 | (7616) sum(n10, n16) = all_0_0_0
% 31.58/10.23 |
% 31.58/10.23 | From (849)(847) and (435) follows:
% 31.58/10.23 | (851) sum(n13, n13) = all_0_3_3
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 31.58/10.23 | (852) all_0_3_3 = n5
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n10, n16, all_0_0_0, n5 and discharging atoms sum(n10, n16) = all_0_0_0, sum(n10, n16) = n5, yields:
% 31.58/10.23 | (853) all_0_0_0 = n5
% 31.58/10.23 |
% 31.58/10.23 | Equations (853,852) can reduce 201 to:
% 31.58/10.23 | (746) $false
% 31.58/10.23 |
% 31.58/10.23 |-The branch is then unsatisfiable
% 31.58/10.23 |-Branch two:
% 31.58/10.23 | (1017) ~ (all_0_11_11 = n5)
% 31.58/10.23 | (1018) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.58/10.23 |
% 31.58/10.23 +-Applying beta-rule and splitting (1018), into two cases.
% 31.58/10.23 |-Branch one:
% 31.58/10.23 | (1019) all_0_11_11 = n4
% 31.58/10.23 |
% 31.58/10.23 | From (1019) and (190) follows:
% 31.58/10.23 | (1020) pred(n4) = all_0_9_9
% 31.58/10.23 |
% 31.58/10.23 | From (1019) and (505) follows:
% 31.58/10.23 | (1021) succ(n4) = all_0_5_5
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 31.58/10.23 | (1022) all_0_9_9 = n3
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 31.58/10.23 | (1023) all_0_5_5 = n5
% 31.58/10.23 |
% 31.58/10.23 | From (1022)(1023) and (156) follows:
% 31.58/10.23 | (1024) sum(n3, n5) = all_0_2_2
% 31.58/10.23 |
% 31.58/10.23 | From (1022) and (7540) follows:
% 31.58/10.23 | (7629) sum(n3, n9) = all_0_7_7
% 31.58/10.23 |
% 31.58/10.23 | From (1023) and (7538) follows:
% 31.58/10.23 | (7630) sum(n7, n5) = all_0_4_4
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n7, n5, all_0_4_4, n12 and discharging atoms sum(n7, n5) = all_0_4_4, sum(n7, n5) = n12, yields:
% 31.58/10.23 | (865) all_0_4_4 = n12
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n3, n9, all_0_7_7, n12 and discharging atoms sum(n3, n9) = all_0_7_7, sum(n3, n9) = n12, yields:
% 31.58/10.23 | (867) all_0_7_7 = n12
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 31.58/10.23 | (1028) all_0_2_2 = n8
% 31.58/10.23 |
% 31.58/10.23 | From (1028) and (7542) follows:
% 31.58/10.23 | (7634) sum(n8, n16) = all_0_0_0
% 31.58/10.23 |
% 31.58/10.23 | From (867)(865) and (435) follows:
% 31.58/10.23 | (869) sum(n12, n12) = all_0_3_3
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 31.58/10.23 | (870) all_0_3_3 = n3
% 31.58/10.23 |
% 31.58/10.23 | Instantiating formula (194) with n8, n16, all_0_0_0, n3 and discharging atoms sum(n8, n16) = all_0_0_0, sum(n8, n16) = n3, yields:
% 31.58/10.23 | (871) all_0_0_0 = n3
% 31.58/10.23 |
% 31.58/10.23 | Equations (871,870) can reduce 201 to:
% 31.58/10.23 | (746) $false
% 31.58/10.23 |
% 31.58/10.23 |-The branch is then unsatisfiable
% 31.58/10.23 |-Branch two:
% 31.58/10.23 | (1035) ~ (all_0_11_11 = n4)
% 31.58/10.23 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.58/10.23 |
% 31.58/10.23 +-Applying beta-rule and splitting (1036), into two cases.
% 31.58/10.23 |-Branch one:
% 31.58/10.23 | (1037) all_0_11_11 = n3
% 31.58/10.24 |
% 31.58/10.24 | From (1037) and (190) follows:
% 31.58/10.24 | (1038) pred(n3) = all_0_9_9
% 31.58/10.24 |
% 31.58/10.24 | From (1037) and (505) follows:
% 31.58/10.24 | (1039) succ(n3) = all_0_5_5
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 31.58/10.24 | (1040) all_0_9_9 = n2
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 31.58/10.24 | (1041) all_0_5_5 = n4
% 31.58/10.24 |
% 31.58/10.24 | From (1040)(1041) and (156) follows:
% 31.58/10.24 | (1042) sum(n2, n4) = all_0_2_2
% 31.58/10.24 |
% 31.58/10.24 | From (1040) and (7540) follows:
% 31.58/10.24 | (7647) sum(n2, n9) = all_0_7_7
% 31.58/10.24 |
% 31.58/10.24 | From (1041) and (7538) follows:
% 31.58/10.24 | (7648) sum(n7, n4) = all_0_4_4
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (194) with n7, n4, all_0_4_4, n11 and discharging atoms sum(n7, n4) = all_0_4_4, sum(n7, n4) = n11, yields:
% 31.58/10.24 | (883) all_0_4_4 = n11
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (194) with n2, n9, all_0_7_7, n11 and discharging atoms sum(n2, n9) = all_0_7_7, sum(n2, n9) = n11, yields:
% 31.58/10.24 | (885) all_0_7_7 = n11
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 31.58/10.24 | (1046) all_0_2_2 = n6
% 31.58/10.24 |
% 31.58/10.24 | From (1046) and (7542) follows:
% 31.58/10.24 | (7652) sum(n6, n16) = all_0_0_0
% 31.58/10.24 |
% 31.58/10.24 | From (885)(883) and (435) follows:
% 31.58/10.24 | (887) sum(n11, n11) = all_0_3_3
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 31.58/10.24 | (888) all_0_3_3 = n1
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (194) with n6, n16, all_0_0_0, n1 and discharging atoms sum(n6, n16) = all_0_0_0, sum(n6, n16) = n1, yields:
% 31.58/10.24 | (889) all_0_0_0 = n1
% 31.58/10.24 |
% 31.58/10.24 | Equations (889,888) can reduce 201 to:
% 31.58/10.24 | (746) $false
% 31.58/10.24 |
% 31.58/10.24 |-The branch is then unsatisfiable
% 31.58/10.24 |-Branch two:
% 31.58/10.24 | (1053) ~ (all_0_11_11 = n3)
% 31.58/10.24 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.58/10.24 |
% 31.58/10.24 +-Applying beta-rule and splitting (1054), into two cases.
% 31.58/10.24 |-Branch one:
% 31.58/10.24 | (1055) all_0_11_11 = n2
% 31.58/10.24 |
% 31.58/10.24 | From (1055) and (190) follows:
% 31.58/10.24 | (1056) pred(n2) = all_0_9_9
% 31.58/10.24 |
% 31.58/10.24 | From (1055) and (505) follows:
% 31.58/10.24 | (1057) succ(n2) = all_0_5_5
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 31.58/10.24 | (1058) all_0_9_9 = n1
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.58/10.24 | (1059) all_0_5_5 = n3
% 31.58/10.24 |
% 31.58/10.24 | From (1058)(1059) and (156) follows:
% 31.58/10.24 | (1060) sum(n1, n3) = all_0_2_2
% 31.58/10.24 |
% 31.58/10.24 | From (1058) and (7540) follows:
% 31.58/10.24 | (7665) sum(n1, n9) = all_0_7_7
% 31.58/10.24 |
% 31.58/10.24 | From (1059) and (7538) follows:
% 31.58/10.24 | (7666) sum(n7, n3) = all_0_4_4
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (194) with n7, n3, all_0_4_4, n10 and discharging atoms sum(n7, n3) = all_0_4_4, sum(n7, n3) = n10, yields:
% 31.58/10.24 | (901) all_0_4_4 = n10
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (194) with n1, n9, all_0_7_7, n10 and discharging atoms sum(n1, n9) = all_0_7_7, sum(n1, n9) = n10, yields:
% 31.58/10.24 | (903) all_0_7_7 = n10
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 31.58/10.24 | (1064) all_0_2_2 = n4
% 31.58/10.24 |
% 31.58/10.24 | From (1064) and (7542) follows:
% 31.58/10.24 | (7670) sum(n4, n16) = all_0_0_0
% 31.58/10.24 |
% 31.58/10.24 | From (903)(901) and (435) follows:
% 31.58/10.24 | (905) sum(n10, n10) = all_0_3_3
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 31.58/10.24 | (906) all_0_3_3 = n20
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (194) with n4, n16, all_0_0_0, n20 and discharging atoms sum(n4, n16) = all_0_0_0, sum(n4, n16) = n20, yields:
% 31.58/10.24 | (907) all_0_0_0 = n20
% 31.58/10.24 |
% 31.58/10.24 | Equations (907,906) can reduce 201 to:
% 31.58/10.24 | (746) $false
% 31.58/10.24 |
% 31.58/10.24 |-The branch is then unsatisfiable
% 31.58/10.24 |-Branch two:
% 31.58/10.24 | (1071) ~ (all_0_11_11 = n2)
% 31.58/10.24 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 31.58/10.24 |
% 31.58/10.24 +-Applying beta-rule and splitting (1072), into two cases.
% 31.58/10.24 |-Branch one:
% 31.58/10.24 | (1073) all_0_11_11 = n1
% 31.58/10.24 |
% 31.58/10.24 | From (1073) and (190) follows:
% 31.58/10.24 | (1074) pred(n1) = all_0_9_9
% 31.58/10.24 |
% 31.58/10.24 | From (1073) and (505) follows:
% 31.58/10.24 | (1075) succ(n1) = all_0_5_5
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 31.58/10.24 | (1076) all_0_9_9 = n0
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.58/10.24 | (1077) all_0_5_5 = n2
% 31.58/10.24 |
% 31.58/10.24 | From (1076)(1077) and (156) follows:
% 31.58/10.24 | (1078) sum(n0, n2) = all_0_2_2
% 31.58/10.24 |
% 31.58/10.24 | From (1076) and (7540) follows:
% 31.58/10.24 | (7683) sum(n0, n9) = all_0_7_7
% 31.58/10.24 |
% 31.58/10.24 | From (1077) and (7538) follows:
% 31.58/10.24 | (7684) sum(n7, n2) = all_0_4_4
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (194) with n7, n2, all_0_4_4, n9 and discharging atoms sum(n7, n2) = all_0_4_4, sum(n7, n2) = n9, yields:
% 31.58/10.24 | (919) all_0_4_4 = n9
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (194) with n0, n9, all_0_7_7, n9 and discharging atoms sum(n0, n9) = all_0_7_7, sum(n0, n9) = n9, yields:
% 31.58/10.24 | (921) all_0_7_7 = n9
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 31.58/10.24 | (1082) all_0_2_2 = n2
% 31.58/10.24 |
% 31.58/10.24 | From (1082) and (7542) follows:
% 31.58/10.24 | (7688) sum(n2, n16) = all_0_0_0
% 31.58/10.24 |
% 31.58/10.24 | From (921)(919) and (435) follows:
% 31.58/10.24 | (923) sum(n9, n9) = all_0_3_3
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 31.58/10.24 | (925) all_0_3_3 = n18
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (194) with n2, n16, all_0_0_0, n18 and discharging atoms sum(n2, n16) = all_0_0_0, sum(n2, n16) = n18, yields:
% 31.58/10.24 | (924) all_0_0_0 = n18
% 31.58/10.24 |
% 31.58/10.24 | Equations (924,925) can reduce 201 to:
% 31.58/10.24 | (746) $false
% 31.58/10.24 |
% 31.58/10.24 |-The branch is then unsatisfiable
% 31.58/10.24 |-Branch two:
% 31.58/10.24 | (1090) ~ (all_0_11_11 = n1)
% 31.58/10.24 | (1091) all_0_11_11 = n0
% 31.58/10.24 |
% 31.58/10.24 | From (1091) and (190) follows:
% 31.58/10.24 | (1092) pred(n0) = all_0_9_9
% 31.58/10.24 |
% 31.58/10.24 | From (1091) and (505) follows:
% 31.58/10.24 | (1093) succ(n0) = all_0_5_5
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 31.58/10.24 | (1094) all_0_9_9 = n20
% 31.58/10.24 |
% 31.58/10.24 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.58/10.24 | (1095) all_0_5_5 = n1
% 31.58/10.24 |
% 31.58/10.24 | From (1094)(1095) and (156) follows:
% 31.58/10.24 | (1096) sum(n20, n1) = all_0_2_2
% 31.58/10.24 |
% 31.58/10.24 | From (1094) and (7540) follows:
% 31.58/10.24 | (7700) sum(n20, n9) = all_0_7_7
% 31.58/10.24 |
% 31.58/10.24 | From (1095) and (7538) follows:
% 31.58/10.25 | (7701) sum(n7, n1) = all_0_4_4
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (194) with n20, n9, all_0_7_7, n8 and discharging atoms sum(n20, n9) = all_0_7_7, sum(n20, n9) = n8, yields:
% 31.58/10.25 | (939) all_0_7_7 = n8
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 31.58/10.25 | (1099) all_0_2_2 = n0
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (194) with n7, n1, all_0_4_4, n8 and discharging atoms sum(n7, n1) = all_0_4_4, sum(n7, n1) = n8, yields:
% 31.58/10.25 | (937) all_0_4_4 = n8
% 31.58/10.25 |
% 31.58/10.25 | From (1099) and (7542) follows:
% 31.58/10.25 | (7705) sum(n0, n16) = all_0_0_0
% 31.58/10.25 |
% 31.58/10.25 | From (939)(937) and (435) follows:
% 31.58/10.25 | (941) sum(n8, n8) = all_0_3_3
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 31.58/10.25 | (943) all_0_3_3 = n16
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (194) with n0, n16, all_0_0_0, n16 and discharging atoms sum(n0, n16) = all_0_0_0, sum(n0, n16) = n16, yields:
% 31.58/10.25 | (942) all_0_0_0 = n16
% 31.58/10.25 |
% 31.58/10.25 | Equations (942,943) can reduce 201 to:
% 31.58/10.25 | (746) $false
% 31.58/10.25 |
% 31.58/10.25 |-The branch is then unsatisfiable
% 31.58/10.25 |-Branch two:
% 31.58/10.25 | (1334) ~ (all_0_10_10 = n8)
% 31.58/10.25 | (1335) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.58/10.25 |
% 31.58/10.25 +-Applying beta-rule and splitting (946), into two cases.
% 31.58/10.25 |-Branch one:
% 31.58/10.25 | (947) all_0_11_11 = n8
% 31.58/10.25 |
% 31.58/10.25 | From (947) and (190) follows:
% 31.58/10.25 | (948) pred(n8) = all_0_9_9
% 31.58/10.25 |
% 31.58/10.25 | From (947) and (505) follows:
% 31.58/10.25 | (949) succ(n8) = all_0_5_5
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (259) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 31.58/10.25 | (950) all_0_9_9 = n7
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (184) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 31.58/10.25 | (951) all_0_5_5 = n9
% 31.58/10.25 |
% 31.58/10.25 | From (951) and (386) follows:
% 31.58/10.25 | (7717) sum(all_0_6_6, n9) = all_0_4_4
% 31.58/10.25 |
% 31.58/10.25 | From (950)(951) and (156) follows:
% 31.58/10.25 | (952) sum(n7, n9) = all_0_2_2
% 31.58/10.25 |
% 31.58/10.25 | From (950) and (74) follows:
% 31.58/10.25 | (7719) sum(n7, all_0_8_8) = all_0_7_7
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (194) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 31.58/10.25 | (956) all_0_2_2 = n16
% 31.58/10.25 |
% 31.58/10.25 | From (956) and (85) follows:
% 31.58/10.25 | (7721) sum(n16, all_0_1_1) = all_0_0_0
% 31.58/10.25 |
% 31.58/10.25 +-Applying beta-rule and splitting (1335), into two cases.
% 31.58/10.25 |-Branch one:
% 31.58/10.25 | (1336) all_0_10_10 = n7
% 31.58/10.25 |
% 31.58/10.25 | From (1336) and (57) follows:
% 31.58/10.25 | (1337) pred(n7) = all_0_6_6
% 31.58/10.25 |
% 31.58/10.25 | From (1336) and (381) follows:
% 31.58/10.25 | (1338) succ(n7) = all_0_8_8
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (259) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 31.58/10.25 | (1339) all_0_6_6 = n6
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (184) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 31.58/10.25 | (1340) all_0_8_8 = n8
% 31.58/10.25 |
% 31.58/10.25 | From (1339)(1340) and (628) follows:
% 31.58/10.25 | (1341) sum(n6, n8) = all_0_1_1
% 31.58/10.25 |
% 31.58/10.25 | From (1339) and (7717) follows:
% 31.58/10.25 | (7728) sum(n6, n9) = all_0_4_4
% 31.58/10.25 |
% 31.58/10.25 | From (1340) and (7719) follows:
% 31.58/10.25 | (7729) sum(n7, n8) = all_0_7_7
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (194) with n7, n8, all_0_7_7, n15 and discharging atoms sum(n7, n8) = all_0_7_7, sum(n7, n8) = n15, yields:
% 31.58/10.25 | (813) all_0_7_7 = n15
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (194) with n6, n9, all_0_4_4, n15 and discharging atoms sum(n6, n9) = all_0_4_4, sum(n6, n9) = n15, yields:
% 31.58/10.25 | (811) all_0_4_4 = n15
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (194) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 31.58/10.25 | (1345) all_0_1_1 = n14
% 31.58/10.25 |
% 31.58/10.25 | From (813)(811) and (435) follows:
% 31.58/10.25 | (815) sum(n15, n15) = all_0_3_3
% 31.58/10.25 |
% 31.58/10.25 | From (1345) and (7721) follows:
% 31.58/10.25 | (7734) sum(n16, n14) = all_0_0_0
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (194) with n16, n14, all_0_0_0, n9 and discharging atoms sum(n16, n14) = all_0_0_0, sum(n16, n14) = n9, yields:
% 31.58/10.25 | (817) all_0_0_0 = n9
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (194) with n15, n15, all_0_3_3, n9 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n9, yields:
% 31.58/10.25 | (816) all_0_3_3 = n9
% 31.58/10.25 |
% 31.58/10.25 | Equations (817,816) can reduce 201 to:
% 31.58/10.25 | (746) $false
% 31.58/10.25 |
% 31.58/10.25 |-The branch is then unsatisfiable
% 31.58/10.25 |-Branch two:
% 31.58/10.25 | (1352) ~ (all_0_10_10 = n7)
% 31.58/10.25 | (1353) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.58/10.25 |
% 31.58/10.25 +-Applying beta-rule and splitting (1353), into two cases.
% 31.58/10.25 |-Branch one:
% 31.58/10.25 | (1354) all_0_10_10 = n6
% 31.58/10.25 |
% 31.58/10.25 | From (1354) and (57) follows:
% 31.58/10.25 | (1355) pred(n6) = all_0_6_6
% 31.58/10.25 |
% 31.58/10.25 | From (1354) and (381) follows:
% 31.58/10.25 | (1356) succ(n6) = all_0_8_8
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (259) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 31.58/10.25 | (1357) all_0_6_6 = n5
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (184) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 31.58/10.25 | (1358) all_0_8_8 = n7
% 31.58/10.25 |
% 31.58/10.25 | From (1357)(1358) and (628) follows:
% 31.58/10.25 | (1359) sum(n5, n7) = all_0_1_1
% 31.58/10.25 |
% 31.58/10.25 | From (1357) and (7717) follows:
% 31.58/10.25 | (7746) sum(n5, n9) = all_0_4_4
% 31.58/10.25 |
% 31.58/10.25 | From (1358) and (7719) follows:
% 31.58/10.25 | (7747) sum(n7, n7) = all_0_7_7
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (194) with n7, n7, all_0_7_7, n14 and discharging atoms sum(n7, n7) = all_0_7_7, sum(n7, n7) = n14, yields:
% 31.58/10.25 | (831) all_0_7_7 = n14
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (194) with n5, n9, all_0_4_4, n14 and discharging atoms sum(n5, n9) = all_0_4_4, sum(n5, n9) = n14, yields:
% 31.58/10.25 | (829) all_0_4_4 = n14
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (194) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 31.58/10.25 | (1363) all_0_1_1 = n12
% 31.58/10.25 |
% 31.58/10.25 | From (831)(829) and (435) follows:
% 31.58/10.25 | (833) sum(n14, n14) = all_0_3_3
% 31.58/10.25 |
% 31.58/10.25 | From (1363) and (7721) follows:
% 31.58/10.25 | (7752) sum(n16, n12) = all_0_0_0
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (194) with n16, n12, all_0_0_0, n7 and discharging atoms sum(n16, n12) = all_0_0_0, sum(n16, n12) = n7, yields:
% 31.58/10.25 | (835) all_0_0_0 = n7
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (194) with n14, n14, all_0_3_3, n7 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n7, yields:
% 31.58/10.25 | (834) all_0_3_3 = n7
% 31.58/10.25 |
% 31.58/10.25 | Equations (835,834) can reduce 201 to:
% 31.58/10.25 | (746) $false
% 31.58/10.25 |
% 31.58/10.25 |-The branch is then unsatisfiable
% 31.58/10.25 |-Branch two:
% 31.58/10.25 | (1370) ~ (all_0_10_10 = n6)
% 31.58/10.25 | (1371) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.58/10.25 |
% 31.58/10.25 +-Applying beta-rule and splitting (1371), into two cases.
% 31.58/10.25 |-Branch one:
% 31.58/10.25 | (1372) all_0_10_10 = n5
% 31.58/10.25 |
% 31.58/10.25 | From (1372) and (57) follows:
% 31.58/10.25 | (1373) pred(n5) = all_0_6_6
% 31.58/10.25 |
% 31.58/10.25 | From (1372) and (381) follows:
% 31.58/10.25 | (1374) succ(n5) = all_0_8_8
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (259) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 31.58/10.25 | (1375) all_0_6_6 = n4
% 31.58/10.25 |
% 31.58/10.25 | Instantiating formula (184) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 31.58/10.25 | (1376) all_0_8_8 = n6
% 31.58/10.25 |
% 31.58/10.25 | From (1375)(1376) and (628) follows:
% 31.58/10.25 | (1377) sum(n4, n6) = all_0_1_1
% 31.58/10.25 |
% 31.58/10.25 | From (1375) and (7717) follows:
% 31.58/10.26 | (7764) sum(n4, n9) = all_0_4_4
% 31.58/10.26 |
% 31.58/10.26 | From (1376) and (7719) follows:
% 31.58/10.26 | (7765) sum(n7, n6) = all_0_7_7
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (194) with n7, n6, all_0_7_7, n13 and discharging atoms sum(n7, n6) = all_0_7_7, sum(n7, n6) = n13, yields:
% 31.58/10.26 | (849) all_0_7_7 = n13
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (194) with n4, n9, all_0_4_4, n13 and discharging atoms sum(n4, n9) = all_0_4_4, sum(n4, n9) = n13, yields:
% 31.58/10.26 | (847) all_0_4_4 = n13
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (194) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 31.58/10.26 | (1381) all_0_1_1 = n10
% 31.58/10.26 |
% 31.58/10.26 | From (849)(847) and (435) follows:
% 31.58/10.26 | (851) sum(n13, n13) = all_0_3_3
% 31.58/10.26 |
% 31.58/10.26 | From (1381) and (7721) follows:
% 31.58/10.26 | (7770) sum(n16, n10) = all_0_0_0
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (194) with n16, n10, all_0_0_0, n5 and discharging atoms sum(n16, n10) = all_0_0_0, sum(n16, n10) = n5, yields:
% 31.58/10.26 | (853) all_0_0_0 = n5
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 31.58/10.26 | (852) all_0_3_3 = n5
% 31.58/10.26 |
% 31.58/10.26 | Equations (853,852) can reduce 201 to:
% 31.58/10.26 | (746) $false
% 31.58/10.26 |
% 31.58/10.26 |-The branch is then unsatisfiable
% 31.58/10.26 |-Branch two:
% 31.58/10.26 | (1388) ~ (all_0_10_10 = n5)
% 31.58/10.26 | (1389) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.58/10.26 |
% 31.58/10.26 +-Applying beta-rule and splitting (1389), into two cases.
% 31.58/10.26 |-Branch one:
% 31.58/10.26 | (1390) all_0_10_10 = n4
% 31.58/10.26 |
% 31.58/10.26 | From (1390) and (57) follows:
% 31.58/10.26 | (1391) pred(n4) = all_0_6_6
% 31.58/10.26 |
% 31.58/10.26 | From (1390) and (381) follows:
% 31.58/10.26 | (1392) succ(n4) = all_0_8_8
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (259) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 31.58/10.26 | (1393) all_0_6_6 = n3
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (184) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 31.58/10.26 | (1394) all_0_8_8 = n5
% 31.58/10.26 |
% 31.58/10.26 | From (1393)(1394) and (628) follows:
% 31.58/10.26 | (1395) sum(n3, n5) = all_0_1_1
% 31.58/10.26 |
% 31.58/10.26 | From (1393) and (7717) follows:
% 31.58/10.26 | (7782) sum(n3, n9) = all_0_4_4
% 31.58/10.26 |
% 31.58/10.26 | From (1394) and (7719) follows:
% 31.58/10.26 | (7783) sum(n7, n5) = all_0_7_7
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (194) with n7, n5, all_0_7_7, n12 and discharging atoms sum(n7, n5) = all_0_7_7, sum(n7, n5) = n12, yields:
% 31.58/10.26 | (867) all_0_7_7 = n12
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (194) with n3, n9, all_0_4_4, n12 and discharging atoms sum(n3, n9) = all_0_4_4, sum(n3, n9) = n12, yields:
% 31.58/10.26 | (865) all_0_4_4 = n12
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (194) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 31.58/10.26 | (1399) all_0_1_1 = n8
% 31.58/10.26 |
% 31.58/10.26 | From (867)(865) and (435) follows:
% 31.58/10.26 | (869) sum(n12, n12) = all_0_3_3
% 31.58/10.26 |
% 31.58/10.26 | From (1399) and (7721) follows:
% 31.58/10.26 | (7788) sum(n16, n8) = all_0_0_0
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (194) with n16, n8, all_0_0_0, n3 and discharging atoms sum(n16, n8) = all_0_0_0, sum(n16, n8) = n3, yields:
% 31.58/10.26 | (871) all_0_0_0 = n3
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 31.58/10.26 | (870) all_0_3_3 = n3
% 31.58/10.26 |
% 31.58/10.26 | Equations (871,870) can reduce 201 to:
% 31.58/10.26 | (746) $false
% 31.58/10.26 |
% 31.58/10.26 |-The branch is then unsatisfiable
% 31.58/10.26 |-Branch two:
% 31.58/10.26 | (1406) ~ (all_0_10_10 = n4)
% 31.58/10.26 | (1407) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.58/10.26 |
% 31.58/10.26 +-Applying beta-rule and splitting (1407), into two cases.
% 31.58/10.26 |-Branch one:
% 31.58/10.26 | (1408) all_0_10_10 = n3
% 31.58/10.26 |
% 31.58/10.26 | From (1408) and (57) follows:
% 31.58/10.26 | (1409) pred(n3) = all_0_6_6
% 31.58/10.26 |
% 31.58/10.26 | From (1408) and (381) follows:
% 31.58/10.26 | (1410) succ(n3) = all_0_8_8
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 31.58/10.26 | (1411) all_0_6_6 = n2
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 31.58/10.26 | (1412) all_0_8_8 = n4
% 31.58/10.26 |
% 31.58/10.26 | From (1411)(1412) and (628) follows:
% 31.58/10.26 | (1413) sum(n2, n4) = all_0_1_1
% 31.58/10.26 |
% 31.58/10.26 | From (1411) and (7717) follows:
% 31.58/10.26 | (7800) sum(n2, n9) = all_0_4_4
% 31.58/10.26 |
% 31.58/10.26 | From (1412) and (7719) follows:
% 31.58/10.26 | (7801) sum(n7, n4) = all_0_7_7
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (194) with n7, n4, all_0_7_7, n11 and discharging atoms sum(n7, n4) = all_0_7_7, sum(n7, n4) = n11, yields:
% 31.58/10.26 | (885) all_0_7_7 = n11
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (194) with n2, n9, all_0_4_4, n11 and discharging atoms sum(n2, n9) = all_0_4_4, sum(n2, n9) = n11, yields:
% 31.58/10.26 | (883) all_0_4_4 = n11
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 31.58/10.26 | (1417) all_0_1_1 = n6
% 31.58/10.26 |
% 31.58/10.26 | From (885)(883) and (435) follows:
% 31.58/10.26 | (887) sum(n11, n11) = all_0_3_3
% 31.58/10.26 |
% 31.58/10.26 | From (1417) and (7721) follows:
% 31.58/10.26 | (7806) sum(n16, n6) = all_0_0_0
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (194) with n16, n6, all_0_0_0, n1 and discharging atoms sum(n16, n6) = all_0_0_0, sum(n16, n6) = n1, yields:
% 31.58/10.26 | (889) all_0_0_0 = n1
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 31.58/10.26 | (888) all_0_3_3 = n1
% 31.58/10.26 |
% 31.58/10.26 | Equations (889,888) can reduce 201 to:
% 31.58/10.26 | (746) $false
% 31.58/10.26 |
% 31.58/10.26 |-The branch is then unsatisfiable
% 31.58/10.26 |-Branch two:
% 31.58/10.26 | (1424) ~ (all_0_10_10 = n3)
% 31.58/10.26 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.58/10.26 |
% 31.58/10.26 +-Applying beta-rule and splitting (1425), into two cases.
% 31.58/10.26 |-Branch one:
% 31.58/10.26 | (1426) all_0_10_10 = n2
% 31.58/10.26 |
% 31.58/10.26 | From (1426) and (57) follows:
% 31.58/10.26 | (1427) pred(n2) = all_0_6_6
% 31.58/10.26 |
% 31.58/10.26 | From (1426) and (381) follows:
% 31.58/10.26 | (1428) succ(n2) = all_0_8_8
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 31.58/10.26 | (1429) all_0_6_6 = n1
% 31.58/10.26 |
% 31.58/10.26 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 31.58/10.26 | (1430) all_0_8_8 = n3
% 31.58/10.26 |
% 31.58/10.26 | From (1429)(1430) and (628) follows:
% 31.58/10.26 | (1431) sum(n1, n3) = all_0_1_1
% 31.58/10.26 |
% 31.58/10.26 | From (1429) and (7717) follows:
% 31.58/10.27 | (7818) sum(n1, n9) = all_0_4_4
% 31.58/10.27 |
% 31.58/10.27 | From (1430) and (7719) follows:
% 31.58/10.27 | (7819) sum(n7, n3) = all_0_7_7
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (194) with n7, n3, all_0_7_7, n10 and discharging atoms sum(n7, n3) = all_0_7_7, sum(n7, n3) = n10, yields:
% 31.58/10.27 | (903) all_0_7_7 = n10
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (194) with n1, n9, all_0_4_4, n10 and discharging atoms sum(n1, n9) = all_0_4_4, sum(n1, n9) = n10, yields:
% 31.58/10.27 | (901) all_0_4_4 = n10
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 31.58/10.27 | (1435) all_0_1_1 = n4
% 31.58/10.27 |
% 31.58/10.27 | From (903)(901) and (435) follows:
% 31.58/10.27 | (905) sum(n10, n10) = all_0_3_3
% 31.58/10.27 |
% 31.58/10.27 | From (1435) and (7721) follows:
% 31.58/10.27 | (7824) sum(n16, n4) = all_0_0_0
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (194) with n16, n4, all_0_0_0, n20 and discharging atoms sum(n16, n4) = all_0_0_0, sum(n16, n4) = n20, yields:
% 31.58/10.27 | (907) all_0_0_0 = n20
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 31.58/10.27 | (906) all_0_3_3 = n20
% 31.58/10.27 |
% 31.58/10.27 | Equations (907,906) can reduce 201 to:
% 31.58/10.27 | (746) $false
% 31.58/10.27 |
% 31.58/10.27 |-The branch is then unsatisfiable
% 31.58/10.27 |-Branch two:
% 31.58/10.27 | (1442) ~ (all_0_10_10 = n2)
% 31.58/10.27 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 31.58/10.27 |
% 31.58/10.27 +-Applying beta-rule and splitting (1443), into two cases.
% 31.58/10.27 |-Branch one:
% 31.58/10.27 | (1444) all_0_10_10 = n1
% 31.58/10.27 |
% 31.58/10.27 | From (1444) and (57) follows:
% 31.58/10.27 | (1445) pred(n1) = all_0_6_6
% 31.58/10.27 |
% 31.58/10.27 | From (1444) and (381) follows:
% 31.58/10.27 | (1446) succ(n1) = all_0_8_8
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 31.58/10.27 | (1447) all_0_6_6 = n0
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 31.58/10.27 | (1448) all_0_8_8 = n2
% 31.58/10.27 |
% 31.58/10.27 | From (1447)(1448) and (628) follows:
% 31.58/10.27 | (1449) sum(n0, n2) = all_0_1_1
% 31.58/10.27 |
% 31.58/10.27 | From (1447) and (7717) follows:
% 31.58/10.27 | (7836) sum(n0, n9) = all_0_4_4
% 31.58/10.27 |
% 31.58/10.27 | From (1448) and (7719) follows:
% 31.58/10.27 | (7837) sum(n7, n2) = all_0_7_7
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (194) with n7, n2, all_0_7_7, n9 and discharging atoms sum(n7, n2) = all_0_7_7, sum(n7, n2) = n9, yields:
% 31.58/10.27 | (921) all_0_7_7 = n9
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (194) with n0, n9, all_0_4_4, n9 and discharging atoms sum(n0, n9) = all_0_4_4, sum(n0, n9) = n9, yields:
% 31.58/10.27 | (919) all_0_4_4 = n9
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 31.58/10.27 | (1453) all_0_1_1 = n2
% 31.58/10.27 |
% 31.58/10.27 | From (921)(919) and (435) follows:
% 31.58/10.27 | (923) sum(n9, n9) = all_0_3_3
% 31.58/10.27 |
% 31.58/10.27 | From (1453) and (7721) follows:
% 31.58/10.27 | (7842) sum(n16, n2) = all_0_0_0
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (194) with n16, n2, all_0_0_0, n18 and discharging atoms sum(n16, n2) = all_0_0_0, sum(n16, n2) = n18, yields:
% 31.58/10.27 | (924) all_0_0_0 = n18
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 31.58/10.27 | (925) all_0_3_3 = n18
% 31.58/10.27 |
% 31.58/10.27 | Equations (924,925) can reduce 201 to:
% 31.58/10.27 | (746) $false
% 31.58/10.27 |
% 31.58/10.27 |-The branch is then unsatisfiable
% 31.58/10.27 |-Branch two:
% 31.58/10.27 | (1462) ~ (all_0_10_10 = n1)
% 31.58/10.27 | (1463) all_0_10_10 = n0
% 31.58/10.27 |
% 31.58/10.27 | From (1463) and (57) follows:
% 31.58/10.27 | (1464) pred(n0) = all_0_6_6
% 31.58/10.27 |
% 31.58/10.27 | From (1463) and (381) follows:
% 31.58/10.27 | (1465) succ(n0) = all_0_8_8
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 31.58/10.27 | (1466) all_0_6_6 = n20
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 31.58/10.27 | (1467) all_0_8_8 = n1
% 31.58/10.27 |
% 31.58/10.27 | From (1466)(1467) and (628) follows:
% 31.58/10.27 | (1468) sum(n20, n1) = all_0_1_1
% 31.58/10.27 |
% 31.58/10.27 | From (1466) and (7717) follows:
% 31.58/10.27 | (7853) sum(n20, n9) = all_0_4_4
% 31.58/10.27 |
% 31.58/10.27 | From (1467) and (7719) follows:
% 31.58/10.27 | (7854) sum(n7, n1) = all_0_7_7
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (194) with n20, n9, all_0_4_4, n8 and discharging atoms sum(n20, n9) = all_0_4_4, sum(n20, n9) = n8, yields:
% 31.58/10.27 | (937) all_0_4_4 = n8
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 31.58/10.27 | (1471) all_0_1_1 = n0
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (194) with n7, n1, all_0_7_7, n8 and discharging atoms sum(n7, n1) = all_0_7_7, sum(n7, n1) = n8, yields:
% 31.58/10.27 | (939) all_0_7_7 = n8
% 31.58/10.27 |
% 31.58/10.27 | From (939)(937) and (435) follows:
% 31.58/10.27 | (941) sum(n8, n8) = all_0_3_3
% 31.58/10.27 |
% 31.58/10.27 | From (1471) and (7721) follows:
% 31.58/10.27 | (7859) sum(n16, n0) = all_0_0_0
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (194) with n16, n0, all_0_0_0, n16 and discharging atoms sum(n16, n0) = all_0_0_0, sum(n16, n0) = n16, yields:
% 31.58/10.27 | (942) all_0_0_0 = n16
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 31.58/10.27 | (943) all_0_3_3 = n16
% 31.58/10.27 |
% 31.58/10.27 | Equations (942,943) can reduce 201 to:
% 31.58/10.27 | (746) $false
% 31.58/10.27 |
% 31.58/10.27 |-The branch is then unsatisfiable
% 31.58/10.27 |-Branch two:
% 31.58/10.27 | (963) ~ (all_0_11_11 = n8)
% 31.58/10.27 | (964) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.58/10.27 |
% 31.58/10.27 +-Applying beta-rule and splitting (1335), into two cases.
% 31.58/10.27 |-Branch one:
% 31.58/10.27 | (1336) all_0_10_10 = n7
% 31.58/10.27 |
% 31.58/10.27 | From (1336) and (57) follows:
% 31.58/10.27 | (1337) pred(n7) = all_0_6_6
% 31.58/10.27 |
% 31.58/10.27 | From (1336) and (381) follows:
% 31.58/10.27 | (1338) succ(n7) = all_0_8_8
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (259) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 31.58/10.27 | (1339) all_0_6_6 = n6
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (184) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 31.58/10.27 | (1340) all_0_8_8 = n8
% 31.58/10.27 |
% 31.58/10.27 | From (1339) and (1337) follows:
% 31.58/10.27 | (115) pred(n7) = n6
% 31.58/10.27 |
% 31.58/10.27 | From (1340) and (1338) follows:
% 31.58/10.27 | (545) succ(n7) = n8
% 31.58/10.27 |
% 31.58/10.27 | From (1339) and (386) follows:
% 31.58/10.27 | (7872) sum(n6, all_0_5_5) = all_0_4_4
% 31.58/10.27 |
% 31.58/10.27 | From (1339)(1340) and (628) follows:
% 31.58/10.27 | (1341) sum(n6, n8) = all_0_1_1
% 31.58/10.27 |
% 31.58/10.27 | From (1340) and (74) follows:
% 31.58/10.27 | (7874) sum(all_0_9_9, n8) = all_0_7_7
% 31.58/10.27 |
% 31.58/10.27 | Instantiating formula (194) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 31.58/10.27 | (1345) all_0_1_1 = n14
% 31.58/10.27 |
% 31.58/10.27 | From (1345) and (85) follows:
% 31.58/10.28 | (7876) sum(all_0_2_2, n14) = all_0_0_0
% 31.58/10.28 |
% 31.58/10.28 | From (1345) and (1341) follows:
% 31.58/10.28 | (140) sum(n6, n8) = n14
% 31.58/10.28 |
% 31.58/10.28 +-Applying beta-rule and splitting (964), into two cases.
% 31.58/10.28 |-Branch one:
% 31.58/10.28 | (965) all_0_11_11 = n7
% 31.58/10.28 |
% 31.58/10.28 | From (965) and (190) follows:
% 31.58/10.28 | (966) pred(n7) = all_0_9_9
% 31.58/10.28 |
% 31.58/10.28 | From (965) and (505) follows:
% 31.58/10.28 | (967) succ(n7) = all_0_5_5
% 31.58/10.28 |
% 31.58/10.28 | Instantiating formula (259) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 31.58/10.28 | (968) all_0_9_9 = n6
% 31.58/10.28 |
% 31.58/10.28 | Instantiating formula (184) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 31.58/10.28 | (969) all_0_5_5 = n8
% 31.58/10.28 |
% 31.58/10.28 | From (968)(969) and (156) follows:
% 31.58/10.28 | (970) sum(n6, n8) = all_0_2_2
% 31.58/10.28 |
% 31.58/10.28 | From (968) and (7874) follows:
% 31.58/10.28 | (7884) sum(n6, n8) = all_0_7_7
% 31.58/10.28 |
% 31.58/10.28 | From (969) and (7872) follows:
% 31.58/10.28 | (7885) sum(n6, n8) = all_0_4_4
% 31.58/10.28 |
% 31.58/10.28 | Instantiating formula (194) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 31.58/10.28 | (974) all_0_2_2 = n14
% 31.58/10.28 |
% 31.58/10.28 | Instantiating formula (194) with n6, n8, all_0_4_4, all_0_2_2 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = all_0_4_4, yields:
% 31.58/10.28 | (733) all_0_2_2 = all_0_4_4
% 31.58/10.28 |
% 31.58/10.28 | Instantiating formula (194) with n6, n8, all_0_7_7, all_0_2_2 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = all_0_7_7, yields:
% 31.58/10.28 | (734) all_0_2_2 = all_0_7_7
% 31.58/10.28 |
% 31.58/10.28 | Combining equations (734,733) yields a new equation:
% 31.58/10.28 | (735) all_0_4_4 = all_0_7_7
% 31.58/10.28 |
% 31.58/10.28 | Combining equations (974,733) yields a new equation:
% 31.58/10.28 | (829) all_0_4_4 = n14
% 31.58/10.28 |
% 31.58/10.28 | Combining equations (829,735) yields a new equation:
% 31.58/10.28 | (831) all_0_7_7 = n14
% 31.58/10.28 |
% 31.58/10.28 | Combining equations (831,735) yields a new equation:
% 31.58/10.28 | (829) all_0_4_4 = n14
% 31.58/10.28 |
% 31.58/10.28 | Combining equations (829,733) yields a new equation:
% 31.58/10.28 | (974) all_0_2_2 = n14
% 31.58/10.28 |
% 31.58/10.28 | From (974) and (7876) follows:
% 31.58/10.28 | (7894) sum(n14, n14) = all_0_0_0
% 31.58/10.28 |
% 31.58/10.28 | From (831)(829) and (435) follows:
% 31.58/10.28 | (833) sum(n14, n14) = all_0_3_3
% 31.58/10.28 |
% 31.58/10.28 | Instantiating formula (194) with n14, n14, all_0_0_0, n7 and discharging atoms sum(n14, n14) = all_0_0_0, sum(n14, n14) = n7, yields:
% 31.58/10.28 | (835) all_0_0_0 = n7
% 31.58/10.28 |
% 31.58/10.28 | Instantiating formula (194) with n14, n14, all_0_3_3, all_0_0_0 and discharging atoms sum(n14, n14) = all_0_0_0, sum(n14, n14) = all_0_3_3, yields:
% 31.58/10.28 | (743) all_0_0_0 = all_0_3_3
% 31.58/10.28 |
% 31.58/10.28 | Combining equations (835,743) yields a new equation:
% 31.58/10.28 | (834) all_0_3_3 = n7
% 31.58/10.28 |
% 31.58/10.28 | Combining equations (834,743) yields a new equation:
% 31.58/10.28 | (835) all_0_0_0 = n7
% 31.58/10.28 |
% 31.58/10.28 | Equations (835,834) can reduce 201 to:
% 31.58/10.28 | (746) $false
% 31.58/10.28 |
% 31.58/10.28 |-The branch is then unsatisfiable
% 31.58/10.28 |-Branch two:
% 31.58/10.28 | (981) ~ (all_0_11_11 = n7)
% 31.58/10.28 | (982) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.58/10.28 |
% 31.58/10.28 +-Applying beta-rule and splitting (982), into two cases.
% 31.58/10.28 |-Branch one:
% 31.58/10.28 | (983) all_0_11_11 = n6
% 31.58/10.28 |
% 31.58/10.28 | From (983) and (190) follows:
% 31.58/10.28 | (984) pred(n6) = all_0_9_9
% 31.58/10.28 |
% 31.58/10.28 | From (983) and (505) follows:
% 31.58/10.28 | (985) succ(n6) = all_0_5_5
% 31.58/10.28 |
% 31.58/10.28 | Instantiating formula (259) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 31.58/10.28 | (986) all_0_9_9 = n5
% 31.58/10.28 |
% 31.58/10.28 | Instantiating formula (184) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 31.58/10.28 | (987) all_0_5_5 = n7
% 31.58/10.28 |
% 31.58/10.28 | From (986)(987) and (156) follows:
% 31.58/10.28 | (988) sum(n5, n7) = all_0_2_2
% 31.58/10.28 |
% 31.58/10.28 | From (986) and (7874) follows:
% 31.58/10.28 | (7909) sum(n5, n8) = all_0_7_7
% 31.58/10.28 |
% 31.58/10.28 | From (987) and (7872) follows:
% 31.58/10.28 | (7910) sum(n6, n7) = all_0_4_4
% 31.58/10.28 |
% 31.58/10.28 | Instantiating formula (194) with n6, n7, all_0_4_4, n13 and discharging atoms sum(n6, n7) = all_0_4_4, sum(n6, n7) = n13, yields:
% 31.58/10.28 | (847) all_0_4_4 = n13
% 31.58/10.28 |
% 31.58/10.28 | Instantiating formula (194) with n5, n8, all_0_7_7, n13 and discharging atoms sum(n5, n8) = all_0_7_7, sum(n5, n8) = n13, yields:
% 31.58/10.28 | (849) all_0_7_7 = n13
% 31.58/10.28 |
% 31.58/10.28 | Instantiating formula (194) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 31.58/10.28 | (992) all_0_2_2 = n12
% 31.58/10.28 |
% 31.58/10.28 | From (992) and (7876) follows:
% 31.58/10.28 | (7914) sum(n12, n14) = all_0_0_0
% 31.58/10.28 |
% 31.58/10.28 | From (849)(847) and (435) follows:
% 31.58/10.28 | (851) sum(n13, n13) = all_0_3_3
% 31.58/10.28 |
% 31.58/10.28 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 31.58/10.28 | (852) all_0_3_3 = n5
% 31.58/10.28 |
% 31.58/10.28 | Instantiating formula (194) with n12, n14, all_0_0_0, n5 and discharging atoms sum(n12, n14) = all_0_0_0, sum(n12, n14) = n5, yields:
% 31.58/10.28 | (853) all_0_0_0 = n5
% 31.58/10.28 |
% 31.58/10.28 | Equations (853,852) can reduce 201 to:
% 31.58/10.28 | (746) $false
% 31.58/10.28 |
% 31.58/10.28 |-The branch is then unsatisfiable
% 31.58/10.28 |-Branch two:
% 31.58/10.28 | (999) ~ (all_0_11_11 = n6)
% 31.58/10.28 | (1000) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.58/10.28 |
% 31.58/10.28 +-Applying beta-rule and splitting (1000), into two cases.
% 31.58/10.28 |-Branch one:
% 31.58/10.28 | (1001) all_0_11_11 = n5
% 31.58/10.28 |
% 31.58/10.28 | From (1001) and (190) follows:
% 31.58/10.28 | (1002) pred(n5) = all_0_9_9
% 31.58/10.28 |
% 31.58/10.28 | From (1001) and (505) follows:
% 31.58/10.28 | (1003) succ(n5) = all_0_5_5
% 31.58/10.28 |
% 31.58/10.28 | Instantiating formula (259) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 31.58/10.28 | (1004) all_0_9_9 = n4
% 31.58/10.28 |
% 31.58/10.28 | Instantiating formula (184) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 31.58/10.28 | (1005) all_0_5_5 = n6
% 31.58/10.28 |
% 31.58/10.28 | From (1004)(1005) and (156) follows:
% 31.58/10.28 | (1006) sum(n4, n6) = all_0_2_2
% 31.58/10.28 |
% 31.58/10.28 | From (1004) and (7874) follows:
% 31.76/10.28 | (7927) sum(n4, n8) = all_0_7_7
% 31.76/10.28 |
% 31.76/10.28 | From (1005) and (7872) follows:
% 31.76/10.28 | (7928) sum(n6, n6) = all_0_4_4
% 31.76/10.28 |
% 31.76/10.28 | Instantiating formula (194) with n6, n6, all_0_4_4, n12 and discharging atoms sum(n6, n6) = all_0_4_4, sum(n6, n6) = n12, yields:
% 31.76/10.28 | (865) all_0_4_4 = n12
% 31.76/10.28 |
% 31.76/10.28 | Instantiating formula (194) with n4, n8, all_0_7_7, n12 and discharging atoms sum(n4, n8) = all_0_7_7, sum(n4, n8) = n12, yields:
% 31.76/10.28 | (867) all_0_7_7 = n12
% 31.76/10.28 |
% 31.76/10.28 | Instantiating formula (194) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 31.76/10.28 | (1010) all_0_2_2 = n10
% 31.76/10.28 |
% 31.76/10.28 | From (1010) and (7876) follows:
% 31.76/10.28 | (7932) sum(n10, n14) = all_0_0_0
% 31.76/10.28 |
% 31.76/10.28 | From (867)(865) and (435) follows:
% 31.76/10.28 | (869) sum(n12, n12) = all_0_3_3
% 31.76/10.28 |
% 31.76/10.28 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 31.76/10.28 | (870) all_0_3_3 = n3
% 31.76/10.28 |
% 31.76/10.28 | Instantiating formula (194) with n10, n14, all_0_0_0, n3 and discharging atoms sum(n10, n14) = all_0_0_0, sum(n10, n14) = n3, yields:
% 31.76/10.29 | (871) all_0_0_0 = n3
% 31.76/10.29 |
% 31.76/10.29 | Equations (871,870) can reduce 201 to:
% 31.76/10.29 | (746) $false
% 31.76/10.29 |
% 31.76/10.29 |-The branch is then unsatisfiable
% 31.76/10.29 |-Branch two:
% 31.76/10.29 | (1017) ~ (all_0_11_11 = n5)
% 31.76/10.29 | (1018) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.76/10.29 |
% 31.76/10.29 +-Applying beta-rule and splitting (1018), into two cases.
% 31.76/10.29 |-Branch one:
% 31.76/10.29 | (1019) all_0_11_11 = n4
% 31.76/10.29 |
% 31.76/10.29 | From (1019) and (190) follows:
% 31.76/10.29 | (1020) pred(n4) = all_0_9_9
% 31.76/10.29 |
% 31.76/10.29 | From (1019) and (505) follows:
% 31.76/10.29 | (1021) succ(n4) = all_0_5_5
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 31.76/10.29 | (1022) all_0_9_9 = n3
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 31.76/10.29 | (1023) all_0_5_5 = n5
% 31.76/10.29 |
% 31.76/10.29 | From (1022)(1023) and (156) follows:
% 31.76/10.29 | (1024) sum(n3, n5) = all_0_2_2
% 31.76/10.29 |
% 31.76/10.29 | From (1022) and (7874) follows:
% 31.76/10.29 | (7945) sum(n3, n8) = all_0_7_7
% 31.76/10.29 |
% 31.76/10.29 | From (1023) and (7872) follows:
% 31.76/10.29 | (7946) sum(n6, n5) = all_0_4_4
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (194) with n6, n5, all_0_4_4, n11 and discharging atoms sum(n6, n5) = all_0_4_4, sum(n6, n5) = n11, yields:
% 31.76/10.29 | (883) all_0_4_4 = n11
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (194) with n3, n8, all_0_7_7, n11 and discharging atoms sum(n3, n8) = all_0_7_7, sum(n3, n8) = n11, yields:
% 31.76/10.29 | (885) all_0_7_7 = n11
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 31.76/10.29 | (1028) all_0_2_2 = n8
% 31.76/10.29 |
% 31.76/10.29 | From (1028) and (7876) follows:
% 31.76/10.29 | (7950) sum(n8, n14) = all_0_0_0
% 31.76/10.29 |
% 31.76/10.29 | From (885)(883) and (435) follows:
% 31.76/10.29 | (887) sum(n11, n11) = all_0_3_3
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 31.76/10.29 | (888) all_0_3_3 = n1
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (194) with n8, n14, all_0_0_0, n1 and discharging atoms sum(n8, n14) = all_0_0_0, sum(n8, n14) = n1, yields:
% 31.76/10.29 | (889) all_0_0_0 = n1
% 31.76/10.29 |
% 31.76/10.29 | Equations (889,888) can reduce 201 to:
% 31.76/10.29 | (746) $false
% 31.76/10.29 |
% 31.76/10.29 |-The branch is then unsatisfiable
% 31.76/10.29 |-Branch two:
% 31.76/10.29 | (1035) ~ (all_0_11_11 = n4)
% 31.76/10.29 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.76/10.29 |
% 31.76/10.29 +-Applying beta-rule and splitting (1036), into two cases.
% 31.76/10.29 |-Branch one:
% 31.76/10.29 | (1037) all_0_11_11 = n3
% 31.76/10.29 |
% 31.76/10.29 | From (1037) and (190) follows:
% 31.76/10.29 | (1038) pred(n3) = all_0_9_9
% 31.76/10.29 |
% 31.76/10.29 | From (1037) and (505) follows:
% 31.76/10.29 | (1039) succ(n3) = all_0_5_5
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 31.76/10.29 | (1040) all_0_9_9 = n2
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 31.76/10.29 | (1041) all_0_5_5 = n4
% 31.76/10.29 |
% 31.76/10.29 | From (1040)(1041) and (156) follows:
% 31.76/10.29 | (1042) sum(n2, n4) = all_0_2_2
% 31.76/10.29 |
% 31.76/10.29 | From (1040) and (7874) follows:
% 31.76/10.29 | (7963) sum(n2, n8) = all_0_7_7
% 31.76/10.29 |
% 31.76/10.29 | From (1041) and (7872) follows:
% 31.76/10.29 | (7964) sum(n6, n4) = all_0_4_4
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (194) with n6, n4, all_0_4_4, n10 and discharging atoms sum(n6, n4) = all_0_4_4, sum(n6, n4) = n10, yields:
% 31.76/10.29 | (901) all_0_4_4 = n10
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (194) with n2, n8, all_0_7_7, n10 and discharging atoms sum(n2, n8) = all_0_7_7, sum(n2, n8) = n10, yields:
% 31.76/10.29 | (903) all_0_7_7 = n10
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 31.76/10.29 | (1046) all_0_2_2 = n6
% 31.76/10.29 |
% 31.76/10.29 | From (1046) and (7876) follows:
% 31.76/10.29 | (7968) sum(n6, n14) = all_0_0_0
% 31.76/10.29 |
% 31.76/10.29 | From (903)(901) and (435) follows:
% 31.76/10.29 | (905) sum(n10, n10) = all_0_3_3
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 31.76/10.29 | (906) all_0_3_3 = n20
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (194) with n6, n14, all_0_0_0, n20 and discharging atoms sum(n6, n14) = all_0_0_0, sum(n6, n14) = n20, yields:
% 31.76/10.29 | (907) all_0_0_0 = n20
% 31.76/10.29 |
% 31.76/10.29 | Equations (907,906) can reduce 201 to:
% 31.76/10.29 | (746) $false
% 31.76/10.29 |
% 31.76/10.29 |-The branch is then unsatisfiable
% 31.76/10.29 |-Branch two:
% 31.76/10.29 | (1053) ~ (all_0_11_11 = n3)
% 31.76/10.29 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.76/10.29 |
% 31.76/10.29 +-Applying beta-rule and splitting (1054), into two cases.
% 31.76/10.29 |-Branch one:
% 31.76/10.29 | (1055) all_0_11_11 = n2
% 31.76/10.29 |
% 31.76/10.29 | From (1055) and (190) follows:
% 31.76/10.29 | (1056) pred(n2) = all_0_9_9
% 31.76/10.29 |
% 31.76/10.29 | From (1055) and (505) follows:
% 31.76/10.29 | (1057) succ(n2) = all_0_5_5
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 31.76/10.29 | (1058) all_0_9_9 = n1
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.76/10.29 | (1059) all_0_5_5 = n3
% 31.76/10.29 |
% 31.76/10.29 | From (1058)(1059) and (156) follows:
% 31.76/10.29 | (1060) sum(n1, n3) = all_0_2_2
% 31.76/10.29 |
% 31.76/10.29 | From (1058) and (7874) follows:
% 31.76/10.29 | (7981) sum(n1, n8) = all_0_7_7
% 31.76/10.29 |
% 31.76/10.29 | From (1059) and (7872) follows:
% 31.76/10.29 | (7982) sum(n6, n3) = all_0_4_4
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (194) with n6, n3, all_0_4_4, n9 and discharging atoms sum(n6, n3) = all_0_4_4, sum(n6, n3) = n9, yields:
% 31.76/10.29 | (919) all_0_4_4 = n9
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (194) with n1, n8, all_0_7_7, n9 and discharging atoms sum(n1, n8) = all_0_7_7, sum(n1, n8) = n9, yields:
% 31.76/10.29 | (921) all_0_7_7 = n9
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 31.76/10.29 | (1064) all_0_2_2 = n4
% 31.76/10.29 |
% 31.76/10.29 | From (1064) and (7876) follows:
% 31.76/10.29 | (7986) sum(n4, n14) = all_0_0_0
% 31.76/10.29 |
% 31.76/10.29 | From (921)(919) and (435) follows:
% 31.76/10.29 | (923) sum(n9, n9) = all_0_3_3
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 31.76/10.29 | (925) all_0_3_3 = n18
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (194) with n4, n14, all_0_0_0, n18 and discharging atoms sum(n4, n14) = all_0_0_0, sum(n4, n14) = n18, yields:
% 31.76/10.29 | (924) all_0_0_0 = n18
% 31.76/10.29 |
% 31.76/10.29 | Equations (924,925) can reduce 201 to:
% 31.76/10.29 | (746) $false
% 31.76/10.29 |
% 31.76/10.29 |-The branch is then unsatisfiable
% 31.76/10.29 |-Branch two:
% 31.76/10.29 | (1071) ~ (all_0_11_11 = n2)
% 31.76/10.29 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 31.76/10.29 |
% 31.76/10.29 +-Applying beta-rule and splitting (1072), into two cases.
% 31.76/10.29 |-Branch one:
% 31.76/10.29 | (1073) all_0_11_11 = n1
% 31.76/10.29 |
% 31.76/10.29 | From (1073) and (190) follows:
% 31.76/10.29 | (1074) pred(n1) = all_0_9_9
% 31.76/10.29 |
% 31.76/10.29 | From (1073) and (505) follows:
% 31.76/10.29 | (1075) succ(n1) = all_0_5_5
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 31.76/10.29 | (1076) all_0_9_9 = n0
% 31.76/10.29 |
% 31.76/10.29 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.76/10.29 | (1077) all_0_5_5 = n2
% 31.76/10.29 |
% 31.76/10.29 | From (1076)(1077) and (156) follows:
% 31.76/10.29 | (1078) sum(n0, n2) = all_0_2_2
% 31.76/10.29 |
% 31.76/10.29 | From (1076) and (7874) follows:
% 31.76/10.30 | (7999) sum(n0, n8) = all_0_7_7
% 31.76/10.30 |
% 31.76/10.30 | From (1077) and (7872) follows:
% 31.76/10.30 | (8000) sum(n6, n2) = all_0_4_4
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (194) with n6, n2, all_0_4_4, n8 and discharging atoms sum(n6, n2) = all_0_4_4, sum(n6, n2) = n8, yields:
% 31.76/10.30 | (937) all_0_4_4 = n8
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (194) with n0, n8, all_0_7_7, n8 and discharging atoms sum(n0, n8) = all_0_7_7, sum(n0, n8) = n8, yields:
% 31.76/10.30 | (939) all_0_7_7 = n8
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 31.76/10.30 | (1082) all_0_2_2 = n2
% 31.76/10.30 |
% 31.76/10.30 | From (1082) and (7876) follows:
% 31.76/10.30 | (8004) sum(n2, n14) = all_0_0_0
% 31.76/10.30 |
% 31.76/10.30 | From (939)(937) and (435) follows:
% 31.76/10.30 | (941) sum(n8, n8) = all_0_3_3
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 31.76/10.30 | (943) all_0_3_3 = n16
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (194) with n2, n14, all_0_0_0, n16 and discharging atoms sum(n2, n14) = all_0_0_0, sum(n2, n14) = n16, yields:
% 31.76/10.30 | (942) all_0_0_0 = n16
% 31.76/10.30 |
% 31.76/10.30 | Equations (942,943) can reduce 201 to:
% 31.76/10.30 | (746) $false
% 31.76/10.30 |
% 31.76/10.30 |-The branch is then unsatisfiable
% 31.76/10.30 |-Branch two:
% 31.76/10.30 | (1090) ~ (all_0_11_11 = n1)
% 31.76/10.30 | (1091) all_0_11_11 = n0
% 31.76/10.30 |
% 31.76/10.30 | From (1091) and (190) follows:
% 31.76/10.30 | (1092) pred(n0) = all_0_9_9
% 31.76/10.30 |
% 31.76/10.30 | From (1091) and (505) follows:
% 31.76/10.30 | (1093) succ(n0) = all_0_5_5
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 31.76/10.30 | (1094) all_0_9_9 = n20
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.76/10.30 | (1095) all_0_5_5 = n1
% 31.76/10.30 |
% 31.76/10.30 | From (1094)(1095) and (156) follows:
% 31.76/10.30 | (1096) sum(n20, n1) = all_0_2_2
% 31.76/10.30 |
% 31.76/10.30 | From (1094) and (7874) follows:
% 31.76/10.30 | (8016) sum(n20, n8) = all_0_7_7
% 31.76/10.30 |
% 31.76/10.30 | From (1095) and (7872) follows:
% 31.76/10.30 | (8017) sum(n6, n1) = all_0_4_4
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (194) with n20, n8, all_0_7_7, n7 and discharging atoms sum(n20, n8) = all_0_7_7, sum(n20, n8) = n7, yields:
% 31.76/10.30 | (957) all_0_7_7 = n7
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 31.76/10.30 | (1099) all_0_2_2 = n0
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (194) with n6, n1, all_0_4_4, n7 and discharging atoms sum(n6, n1) = all_0_4_4, sum(n6, n1) = n7, yields:
% 31.76/10.30 | (955) all_0_4_4 = n7
% 31.76/10.30 |
% 31.76/10.30 | From (1099) and (7876) follows:
% 31.76/10.30 | (8021) sum(n0, n14) = all_0_0_0
% 31.76/10.30 |
% 31.76/10.30 | From (957)(955) and (435) follows:
% 31.76/10.30 | (959) sum(n7, n7) = all_0_3_3
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 31.76/10.30 | (961) all_0_3_3 = n14
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (194) with n0, n14, all_0_0_0, n14 and discharging atoms sum(n0, n14) = all_0_0_0, sum(n0, n14) = n14, yields:
% 31.76/10.30 | (960) all_0_0_0 = n14
% 31.76/10.30 |
% 31.76/10.30 | Equations (960,961) can reduce 201 to:
% 31.76/10.30 | (746) $false
% 31.76/10.30 |
% 31.76/10.30 |-The branch is then unsatisfiable
% 31.76/10.30 |-Branch two:
% 31.76/10.30 | (1352) ~ (all_0_10_10 = n7)
% 31.76/10.30 | (1353) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.76/10.30 |
% 31.76/10.30 +-Applying beta-rule and splitting (964), into two cases.
% 31.76/10.30 |-Branch one:
% 31.76/10.30 | (965) all_0_11_11 = n7
% 31.76/10.30 |
% 31.76/10.30 | From (965) and (190) follows:
% 31.76/10.30 | (966) pred(n7) = all_0_9_9
% 31.76/10.30 |
% 31.76/10.30 | From (965) and (505) follows:
% 31.76/10.30 | (967) succ(n7) = all_0_5_5
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (259) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 31.76/10.30 | (968) all_0_9_9 = n6
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (184) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 31.76/10.30 | (969) all_0_5_5 = n8
% 31.76/10.30 |
% 31.76/10.30 | From (969) and (386) follows:
% 31.76/10.30 | (8033) sum(all_0_6_6, n8) = all_0_4_4
% 31.76/10.30 |
% 31.76/10.30 | From (968)(969) and (156) follows:
% 31.76/10.30 | (970) sum(n6, n8) = all_0_2_2
% 31.76/10.30 |
% 31.76/10.30 | From (968) and (74) follows:
% 31.76/10.30 | (8035) sum(n6, all_0_8_8) = all_0_7_7
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (194) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 31.76/10.30 | (974) all_0_2_2 = n14
% 31.76/10.30 |
% 31.76/10.30 | From (974) and (85) follows:
% 31.76/10.30 | (8037) sum(n14, all_0_1_1) = all_0_0_0
% 31.76/10.30 |
% 31.76/10.30 +-Applying beta-rule and splitting (1353), into two cases.
% 31.76/10.30 |-Branch one:
% 31.76/10.30 | (1354) all_0_10_10 = n6
% 31.76/10.30 |
% 31.76/10.30 | From (1354) and (57) follows:
% 31.76/10.30 | (1355) pred(n6) = all_0_6_6
% 31.76/10.30 |
% 31.76/10.30 | From (1354) and (381) follows:
% 31.76/10.30 | (1356) succ(n6) = all_0_8_8
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (259) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 31.76/10.30 | (1357) all_0_6_6 = n5
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (184) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 31.76/10.30 | (1358) all_0_8_8 = n7
% 31.76/10.30 |
% 31.76/10.30 | From (1357)(1358) and (628) follows:
% 31.76/10.30 | (1359) sum(n5, n7) = all_0_1_1
% 31.76/10.30 |
% 31.76/10.30 | From (1357) and (8033) follows:
% 31.76/10.30 | (8044) sum(n5, n8) = all_0_4_4
% 31.76/10.30 |
% 31.76/10.30 | From (1358) and (8035) follows:
% 31.76/10.30 | (8045) sum(n6, n7) = all_0_7_7
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (194) with n6, n7, all_0_7_7, n13 and discharging atoms sum(n6, n7) = all_0_7_7, sum(n6, n7) = n13, yields:
% 31.76/10.30 | (849) all_0_7_7 = n13
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (194) with n5, n8, all_0_4_4, n13 and discharging atoms sum(n5, n8) = all_0_4_4, sum(n5, n8) = n13, yields:
% 31.76/10.30 | (847) all_0_4_4 = n13
% 31.76/10.30 |
% 31.76/10.30 | Instantiating formula (194) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 31.76/10.30 | (1363) all_0_1_1 = n12
% 31.76/10.30 |
% 31.76/10.30 | From (849)(847) and (435) follows:
% 31.76/10.30 | (851) sum(n13, n13) = all_0_3_3
% 31.76/10.30 |
% 31.76/10.30 | From (1363) and (8037) follows:
% 31.76/10.31 | (8050) sum(n14, n12) = all_0_0_0
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (194) with n14, n12, all_0_0_0, n5 and discharging atoms sum(n14, n12) = all_0_0_0, sum(n14, n12) = n5, yields:
% 31.76/10.31 | (853) all_0_0_0 = n5
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (194) with n13, n13, all_0_3_3, n5 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n5, yields:
% 31.76/10.31 | (852) all_0_3_3 = n5
% 31.76/10.31 |
% 31.76/10.31 | Equations (853,852) can reduce 201 to:
% 31.76/10.31 | (746) $false
% 31.76/10.31 |
% 31.76/10.31 |-The branch is then unsatisfiable
% 31.76/10.31 |-Branch two:
% 31.76/10.31 | (1370) ~ (all_0_10_10 = n6)
% 31.76/10.31 | (1371) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.76/10.31 |
% 31.76/10.31 +-Applying beta-rule and splitting (1371), into two cases.
% 31.76/10.31 |-Branch one:
% 31.76/10.31 | (1372) all_0_10_10 = n5
% 31.76/10.31 |
% 31.76/10.31 | From (1372) and (57) follows:
% 31.76/10.31 | (1373) pred(n5) = all_0_6_6
% 31.76/10.31 |
% 31.76/10.31 | From (1372) and (381) follows:
% 31.76/10.31 | (1374) succ(n5) = all_0_8_8
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (259) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 31.76/10.31 | (1375) all_0_6_6 = n4
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (184) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 31.76/10.31 | (1376) all_0_8_8 = n6
% 31.76/10.31 |
% 31.76/10.31 | From (1375)(1376) and (628) follows:
% 31.76/10.31 | (1377) sum(n4, n6) = all_0_1_1
% 31.76/10.31 |
% 31.76/10.31 | From (1375) and (8033) follows:
% 31.76/10.31 | (8062) sum(n4, n8) = all_0_4_4
% 31.76/10.31 |
% 31.76/10.31 | From (1376) and (8035) follows:
% 31.76/10.31 | (8063) sum(n6, n6) = all_0_7_7
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (194) with n6, n6, all_0_7_7, n12 and discharging atoms sum(n6, n6) = all_0_7_7, sum(n6, n6) = n12, yields:
% 31.76/10.31 | (867) all_0_7_7 = n12
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (194) with n4, n8, all_0_4_4, n12 and discharging atoms sum(n4, n8) = all_0_4_4, sum(n4, n8) = n12, yields:
% 31.76/10.31 | (865) all_0_4_4 = n12
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (194) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 31.76/10.31 | (1381) all_0_1_1 = n10
% 31.76/10.31 |
% 31.76/10.31 | From (867)(865) and (435) follows:
% 31.76/10.31 | (869) sum(n12, n12) = all_0_3_3
% 31.76/10.31 |
% 31.76/10.31 | From (1381) and (8037) follows:
% 31.76/10.31 | (8068) sum(n14, n10) = all_0_0_0
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (194) with n14, n10, all_0_0_0, n3 and discharging atoms sum(n14, n10) = all_0_0_0, sum(n14, n10) = n3, yields:
% 31.76/10.31 | (871) all_0_0_0 = n3
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (194) with n12, n12, all_0_3_3, n3 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n3, yields:
% 31.76/10.31 | (870) all_0_3_3 = n3
% 31.76/10.31 |
% 31.76/10.31 | Equations (871,870) can reduce 201 to:
% 31.76/10.31 | (746) $false
% 31.76/10.31 |
% 31.76/10.31 |-The branch is then unsatisfiable
% 31.76/10.31 |-Branch two:
% 31.76/10.31 | (1388) ~ (all_0_10_10 = n5)
% 31.76/10.31 | (1389) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.76/10.31 |
% 31.76/10.31 +-Applying beta-rule and splitting (1389), into two cases.
% 31.76/10.31 |-Branch one:
% 31.76/10.31 | (1390) all_0_10_10 = n4
% 31.76/10.31 |
% 31.76/10.31 | From (1390) and (57) follows:
% 31.76/10.31 | (1391) pred(n4) = all_0_6_6
% 31.76/10.31 |
% 31.76/10.31 | From (1390) and (381) follows:
% 31.76/10.31 | (1392) succ(n4) = all_0_8_8
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (259) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 31.76/10.31 | (1393) all_0_6_6 = n3
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (184) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 31.76/10.31 | (1394) all_0_8_8 = n5
% 31.76/10.31 |
% 31.76/10.31 | From (1393)(1394) and (628) follows:
% 31.76/10.31 | (1395) sum(n3, n5) = all_0_1_1
% 31.76/10.31 |
% 31.76/10.31 | From (1393) and (8033) follows:
% 31.76/10.31 | (8080) sum(n3, n8) = all_0_4_4
% 31.76/10.31 |
% 31.76/10.31 | From (1394) and (8035) follows:
% 31.76/10.31 | (8081) sum(n6, n5) = all_0_7_7
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (194) with n6, n5, all_0_7_7, n11 and discharging atoms sum(n6, n5) = all_0_7_7, sum(n6, n5) = n11, yields:
% 31.76/10.31 | (885) all_0_7_7 = n11
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (194) with n3, n8, all_0_4_4, n11 and discharging atoms sum(n3, n8) = all_0_4_4, sum(n3, n8) = n11, yields:
% 31.76/10.31 | (883) all_0_4_4 = n11
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (194) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 31.76/10.31 | (1399) all_0_1_1 = n8
% 31.76/10.31 |
% 31.76/10.31 | From (885)(883) and (435) follows:
% 31.76/10.31 | (887) sum(n11, n11) = all_0_3_3
% 31.76/10.31 |
% 31.76/10.31 | From (1399) and (8037) follows:
% 31.76/10.31 | (8086) sum(n14, n8) = all_0_0_0
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (194) with n14, n8, all_0_0_0, n1 and discharging atoms sum(n14, n8) = all_0_0_0, sum(n14, n8) = n1, yields:
% 31.76/10.31 | (889) all_0_0_0 = n1
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 31.76/10.31 | (888) all_0_3_3 = n1
% 31.76/10.31 |
% 31.76/10.31 | Equations (889,888) can reduce 201 to:
% 31.76/10.31 | (746) $false
% 31.76/10.31 |
% 31.76/10.31 |-The branch is then unsatisfiable
% 31.76/10.31 |-Branch two:
% 31.76/10.31 | (1406) ~ (all_0_10_10 = n4)
% 31.76/10.31 | (1407) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.76/10.31 |
% 31.76/10.31 +-Applying beta-rule and splitting (1407), into two cases.
% 31.76/10.31 |-Branch one:
% 31.76/10.31 | (1408) all_0_10_10 = n3
% 31.76/10.31 |
% 31.76/10.31 | From (1408) and (57) follows:
% 31.76/10.31 | (1409) pred(n3) = all_0_6_6
% 31.76/10.31 |
% 31.76/10.31 | From (1408) and (381) follows:
% 31.76/10.31 | (1410) succ(n3) = all_0_8_8
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 31.76/10.31 | (1411) all_0_6_6 = n2
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 31.76/10.31 | (1412) all_0_8_8 = n4
% 31.76/10.31 |
% 31.76/10.31 | From (1411)(1412) and (628) follows:
% 31.76/10.31 | (1413) sum(n2, n4) = all_0_1_1
% 31.76/10.31 |
% 31.76/10.31 | From (1411) and (8033) follows:
% 31.76/10.31 | (8098) sum(n2, n8) = all_0_4_4
% 31.76/10.31 |
% 31.76/10.31 | From (1412) and (8035) follows:
% 31.76/10.31 | (8099) sum(n6, n4) = all_0_7_7
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (194) with n6, n4, all_0_7_7, n10 and discharging atoms sum(n6, n4) = all_0_7_7, sum(n6, n4) = n10, yields:
% 31.76/10.31 | (903) all_0_7_7 = n10
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (194) with n2, n8, all_0_4_4, n10 and discharging atoms sum(n2, n8) = all_0_4_4, sum(n2, n8) = n10, yields:
% 31.76/10.31 | (901) all_0_4_4 = n10
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 31.76/10.31 | (1417) all_0_1_1 = n6
% 31.76/10.31 |
% 31.76/10.31 | From (903)(901) and (435) follows:
% 31.76/10.31 | (905) sum(n10, n10) = all_0_3_3
% 31.76/10.31 |
% 31.76/10.31 | From (1417) and (8037) follows:
% 31.76/10.31 | (8104) sum(n14, n6) = all_0_0_0
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (194) with n14, n6, all_0_0_0, n20 and discharging atoms sum(n14, n6) = all_0_0_0, sum(n14, n6) = n20, yields:
% 31.76/10.31 | (907) all_0_0_0 = n20
% 31.76/10.31 |
% 31.76/10.31 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 31.76/10.31 | (906) all_0_3_3 = n20
% 31.76/10.31 |
% 31.76/10.31 | Equations (907,906) can reduce 201 to:
% 31.76/10.31 | (746) $false
% 31.76/10.31 |
% 31.76/10.31 |-The branch is then unsatisfiable
% 31.76/10.31 |-Branch two:
% 31.76/10.31 | (1424) ~ (all_0_10_10 = n3)
% 31.76/10.31 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.76/10.32 |
% 31.76/10.32 +-Applying beta-rule and splitting (1425), into two cases.
% 31.76/10.32 |-Branch one:
% 31.76/10.32 | (1426) all_0_10_10 = n2
% 31.76/10.32 |
% 31.76/10.32 | From (1426) and (57) follows:
% 31.76/10.32 | (1427) pred(n2) = all_0_6_6
% 31.76/10.32 |
% 31.76/10.32 | From (1426) and (381) follows:
% 31.76/10.32 | (1428) succ(n2) = all_0_8_8
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 31.76/10.32 | (1429) all_0_6_6 = n1
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 31.76/10.32 | (1430) all_0_8_8 = n3
% 31.76/10.32 |
% 31.76/10.32 | From (1429)(1430) and (628) follows:
% 31.76/10.32 | (1431) sum(n1, n3) = all_0_1_1
% 31.76/10.32 |
% 31.76/10.32 | From (1429) and (8033) follows:
% 31.76/10.32 | (8116) sum(n1, n8) = all_0_4_4
% 31.76/10.32 |
% 31.76/10.32 | From (1430) and (8035) follows:
% 31.76/10.32 | (8117) sum(n6, n3) = all_0_7_7
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (194) with n6, n3, all_0_7_7, n9 and discharging atoms sum(n6, n3) = all_0_7_7, sum(n6, n3) = n9, yields:
% 31.76/10.32 | (921) all_0_7_7 = n9
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (194) with n1, n8, all_0_4_4, n9 and discharging atoms sum(n1, n8) = all_0_4_4, sum(n1, n8) = n9, yields:
% 31.76/10.32 | (919) all_0_4_4 = n9
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 31.76/10.32 | (1435) all_0_1_1 = n4
% 31.76/10.32 |
% 31.76/10.32 | From (921)(919) and (435) follows:
% 31.76/10.32 | (923) sum(n9, n9) = all_0_3_3
% 31.76/10.32 |
% 31.76/10.32 | From (1435) and (8037) follows:
% 31.76/10.32 | (8122) sum(n14, n4) = all_0_0_0
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (194) with n14, n4, all_0_0_0, n18 and discharging atoms sum(n14, n4) = all_0_0_0, sum(n14, n4) = n18, yields:
% 31.76/10.32 | (924) all_0_0_0 = n18
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 31.76/10.32 | (925) all_0_3_3 = n18
% 31.76/10.32 |
% 31.76/10.32 | Equations (924,925) can reduce 201 to:
% 31.76/10.32 | (746) $false
% 31.76/10.32 |
% 31.76/10.32 |-The branch is then unsatisfiable
% 31.76/10.32 |-Branch two:
% 31.76/10.32 | (1442) ~ (all_0_10_10 = n2)
% 31.76/10.32 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 31.76/10.32 |
% 31.76/10.32 +-Applying beta-rule and splitting (1443), into two cases.
% 31.76/10.32 |-Branch one:
% 31.76/10.32 | (1444) all_0_10_10 = n1
% 31.76/10.32 |
% 31.76/10.32 | From (1444) and (57) follows:
% 31.76/10.32 | (1445) pred(n1) = all_0_6_6
% 31.76/10.32 |
% 31.76/10.32 | From (1444) and (381) follows:
% 31.76/10.32 | (1446) succ(n1) = all_0_8_8
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 31.76/10.32 | (1447) all_0_6_6 = n0
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 31.76/10.32 | (1448) all_0_8_8 = n2
% 31.76/10.32 |
% 31.76/10.32 | From (1447)(1448) and (628) follows:
% 31.76/10.32 | (1449) sum(n0, n2) = all_0_1_1
% 31.76/10.32 |
% 31.76/10.32 | From (1447) and (8033) follows:
% 31.76/10.32 | (8134) sum(n0, n8) = all_0_4_4
% 31.76/10.32 |
% 31.76/10.32 | From (1448) and (8035) follows:
% 31.76/10.32 | (8135) sum(n6, n2) = all_0_7_7
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (194) with n6, n2, all_0_7_7, n8 and discharging atoms sum(n6, n2) = all_0_7_7, sum(n6, n2) = n8, yields:
% 31.76/10.32 | (939) all_0_7_7 = n8
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (194) with n0, n8, all_0_4_4, n8 and discharging atoms sum(n0, n8) = all_0_4_4, sum(n0, n8) = n8, yields:
% 31.76/10.32 | (937) all_0_4_4 = n8
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 31.76/10.32 | (1453) all_0_1_1 = n2
% 31.76/10.32 |
% 31.76/10.32 | From (939)(937) and (435) follows:
% 31.76/10.32 | (941) sum(n8, n8) = all_0_3_3
% 31.76/10.32 |
% 31.76/10.32 | From (1453) and (8037) follows:
% 31.76/10.32 | (8140) sum(n14, n2) = all_0_0_0
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (194) with n14, n2, all_0_0_0, n16 and discharging atoms sum(n14, n2) = all_0_0_0, sum(n14, n2) = n16, yields:
% 31.76/10.32 | (942) all_0_0_0 = n16
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 31.76/10.32 | (943) all_0_3_3 = n16
% 31.76/10.32 |
% 31.76/10.32 | Equations (942,943) can reduce 201 to:
% 31.76/10.32 | (746) $false
% 31.76/10.32 |
% 31.76/10.32 |-The branch is then unsatisfiable
% 31.76/10.32 |-Branch two:
% 31.76/10.32 | (1462) ~ (all_0_10_10 = n1)
% 31.76/10.32 | (1463) all_0_10_10 = n0
% 31.76/10.32 |
% 31.76/10.32 | From (1463) and (57) follows:
% 31.76/10.32 | (1464) pred(n0) = all_0_6_6
% 31.76/10.32 |
% 31.76/10.32 | From (1463) and (381) follows:
% 31.76/10.32 | (1465) succ(n0) = all_0_8_8
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 31.76/10.32 | (1466) all_0_6_6 = n20
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 31.76/10.32 | (1467) all_0_8_8 = n1
% 31.76/10.32 |
% 31.76/10.32 | From (1466)(1467) and (628) follows:
% 31.76/10.32 | (1468) sum(n20, n1) = all_0_1_1
% 31.76/10.32 |
% 31.76/10.32 | From (1466) and (8033) follows:
% 31.76/10.32 | (8151) sum(n20, n8) = all_0_4_4
% 31.76/10.32 |
% 31.76/10.32 | From (1467) and (8035) follows:
% 31.76/10.32 | (8152) sum(n6, n1) = all_0_7_7
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (194) with n20, n8, all_0_4_4, n7 and discharging atoms sum(n20, n8) = all_0_4_4, sum(n20, n8) = n7, yields:
% 31.76/10.32 | (955) all_0_4_4 = n7
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 31.76/10.32 | (1471) all_0_1_1 = n0
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (194) with n6, n1, all_0_7_7, n7 and discharging atoms sum(n6, n1) = all_0_7_7, sum(n6, n1) = n7, yields:
% 31.76/10.32 | (957) all_0_7_7 = n7
% 31.76/10.32 |
% 31.76/10.32 | From (957)(955) and (435) follows:
% 31.76/10.32 | (959) sum(n7, n7) = all_0_3_3
% 31.76/10.32 |
% 31.76/10.32 | From (1471) and (8037) follows:
% 31.76/10.32 | (8157) sum(n14, n0) = all_0_0_0
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (194) with n14, n0, all_0_0_0, n14 and discharging atoms sum(n14, n0) = all_0_0_0, sum(n14, n0) = n14, yields:
% 31.76/10.32 | (960) all_0_0_0 = n14
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 31.76/10.32 | (961) all_0_3_3 = n14
% 31.76/10.32 |
% 31.76/10.32 | Equations (960,961) can reduce 201 to:
% 31.76/10.32 | (746) $false
% 31.76/10.32 |
% 31.76/10.32 |-The branch is then unsatisfiable
% 31.76/10.32 |-Branch two:
% 31.76/10.32 | (981) ~ (all_0_11_11 = n7)
% 31.76/10.32 | (982) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.76/10.32 |
% 31.76/10.32 +-Applying beta-rule and splitting (1353), into two cases.
% 31.76/10.32 |-Branch one:
% 31.76/10.32 | (1354) all_0_10_10 = n6
% 31.76/10.32 |
% 31.76/10.32 | From (1354) and (57) follows:
% 31.76/10.32 | (1355) pred(n6) = all_0_6_6
% 31.76/10.32 |
% 31.76/10.32 | From (1354) and (381) follows:
% 31.76/10.32 | (1356) succ(n6) = all_0_8_8
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (259) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 31.76/10.32 | (1357) all_0_6_6 = n5
% 31.76/10.32 |
% 31.76/10.32 | Instantiating formula (184) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 31.76/10.32 | (1358) all_0_8_8 = n7
% 31.76/10.32 |
% 31.76/10.32 | From (1357) and (1355) follows:
% 31.76/10.33 | (125) pred(n6) = n5
% 31.76/10.33 |
% 31.76/10.33 | From (1358) and (1356) follows:
% 31.76/10.33 | (348) succ(n6) = n7
% 31.76/10.33 |
% 31.76/10.33 | From (1357) and (386) follows:
% 31.76/10.33 | (8170) sum(n5, all_0_5_5) = all_0_4_4
% 31.76/10.33 |
% 31.76/10.33 | From (1357)(1358) and (628) follows:
% 31.76/10.33 | (1359) sum(n5, n7) = all_0_1_1
% 31.76/10.33 |
% 31.76/10.33 | From (1358) and (74) follows:
% 31.76/10.33 | (8172) sum(all_0_9_9, n7) = all_0_7_7
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (194) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 31.76/10.33 | (1363) all_0_1_1 = n12
% 31.76/10.33 |
% 31.76/10.33 | From (1363) and (85) follows:
% 31.76/10.33 | (8174) sum(all_0_2_2, n12) = all_0_0_0
% 31.76/10.33 |
% 31.76/10.33 | From (1363) and (1359) follows:
% 31.76/10.33 | (21) sum(n5, n7) = n12
% 31.76/10.33 |
% 31.76/10.33 +-Applying beta-rule and splitting (982), into two cases.
% 31.76/10.33 |-Branch one:
% 31.76/10.33 | (983) all_0_11_11 = n6
% 31.76/10.33 |
% 31.76/10.33 | From (983) and (190) follows:
% 31.76/10.33 | (984) pred(n6) = all_0_9_9
% 31.76/10.33 |
% 31.76/10.33 | From (983) and (505) follows:
% 31.76/10.33 | (985) succ(n6) = all_0_5_5
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (259) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 31.76/10.33 | (986) all_0_9_9 = n5
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (184) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 31.76/10.33 | (987) all_0_5_5 = n7
% 31.76/10.33 |
% 31.76/10.33 | From (986)(987) and (156) follows:
% 31.76/10.33 | (988) sum(n5, n7) = all_0_2_2
% 31.76/10.33 |
% 31.76/10.33 | From (986) and (8172) follows:
% 31.76/10.33 | (8182) sum(n5, n7) = all_0_7_7
% 31.76/10.33 |
% 31.76/10.33 | From (987) and (8170) follows:
% 31.76/10.33 | (8183) sum(n5, n7) = all_0_4_4
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (194) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 31.76/10.33 | (992) all_0_2_2 = n12
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (194) with n5, n7, all_0_4_4, all_0_2_2 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = all_0_4_4, yields:
% 31.76/10.33 | (733) all_0_2_2 = all_0_4_4
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (194) with n5, n7, all_0_7_7, all_0_2_2 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = all_0_7_7, yields:
% 31.76/10.33 | (734) all_0_2_2 = all_0_7_7
% 31.76/10.33 |
% 31.76/10.33 | Combining equations (734,733) yields a new equation:
% 31.76/10.33 | (735) all_0_4_4 = all_0_7_7
% 31.76/10.33 |
% 31.76/10.33 | Combining equations (992,733) yields a new equation:
% 31.76/10.33 | (865) all_0_4_4 = n12
% 31.76/10.33 |
% 31.76/10.33 | Combining equations (865,735) yields a new equation:
% 31.76/10.33 | (867) all_0_7_7 = n12
% 31.76/10.33 |
% 31.76/10.33 | Combining equations (867,735) yields a new equation:
% 31.76/10.33 | (865) all_0_4_4 = n12
% 31.76/10.33 |
% 31.76/10.33 | Combining equations (865,733) yields a new equation:
% 31.76/10.33 | (992) all_0_2_2 = n12
% 31.76/10.33 |
% 31.76/10.33 | From (992) and (8174) follows:
% 31.76/10.33 | (8192) sum(n12, n12) = all_0_0_0
% 31.76/10.33 |
% 31.76/10.33 | From (867)(865) and (435) follows:
% 31.76/10.33 | (869) sum(n12, n12) = all_0_3_3
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (194) with n12, n12, all_0_0_0, n3 and discharging atoms sum(n12, n12) = all_0_0_0, sum(n12, n12) = n3, yields:
% 31.76/10.33 | (871) all_0_0_0 = n3
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (194) with n12, n12, all_0_3_3, all_0_0_0 and discharging atoms sum(n12, n12) = all_0_0_0, sum(n12, n12) = all_0_3_3, yields:
% 31.76/10.33 | (743) all_0_0_0 = all_0_3_3
% 31.76/10.33 |
% 31.76/10.33 | Combining equations (871,743) yields a new equation:
% 31.76/10.33 | (870) all_0_3_3 = n3
% 31.76/10.33 |
% 31.76/10.33 | Combining equations (870,743) yields a new equation:
% 31.76/10.33 | (871) all_0_0_0 = n3
% 31.76/10.33 |
% 31.76/10.33 | Equations (871,870) can reduce 201 to:
% 31.76/10.33 | (746) $false
% 31.76/10.33 |
% 31.76/10.33 |-The branch is then unsatisfiable
% 31.76/10.33 |-Branch two:
% 31.76/10.33 | (999) ~ (all_0_11_11 = n6)
% 31.76/10.33 | (1000) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.76/10.33 |
% 31.76/10.33 +-Applying beta-rule and splitting (1000), into two cases.
% 31.76/10.33 |-Branch one:
% 31.76/10.33 | (1001) all_0_11_11 = n5
% 31.76/10.33 |
% 31.76/10.33 | From (1001) and (190) follows:
% 31.76/10.33 | (1002) pred(n5) = all_0_9_9
% 31.76/10.33 |
% 31.76/10.33 | From (1001) and (505) follows:
% 31.76/10.33 | (1003) succ(n5) = all_0_5_5
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (259) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 31.76/10.33 | (1004) all_0_9_9 = n4
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (184) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 31.76/10.33 | (1005) all_0_5_5 = n6
% 31.76/10.33 |
% 31.76/10.33 | From (1004)(1005) and (156) follows:
% 31.76/10.33 | (1006) sum(n4, n6) = all_0_2_2
% 31.76/10.33 |
% 31.76/10.33 | From (1004) and (8172) follows:
% 31.76/10.33 | (8207) sum(n4, n7) = all_0_7_7
% 31.76/10.33 |
% 31.76/10.33 | From (1005) and (8170) follows:
% 31.76/10.33 | (8208) sum(n5, n6) = all_0_4_4
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (194) with n5, n6, all_0_4_4, n11 and discharging atoms sum(n5, n6) = all_0_4_4, sum(n5, n6) = n11, yields:
% 31.76/10.33 | (883) all_0_4_4 = n11
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (194) with n4, n7, all_0_7_7, n11 and discharging atoms sum(n4, n7) = all_0_7_7, sum(n4, n7) = n11, yields:
% 31.76/10.33 | (885) all_0_7_7 = n11
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (194) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 31.76/10.33 | (1010) all_0_2_2 = n10
% 31.76/10.33 |
% 31.76/10.33 | From (1010) and (8174) follows:
% 31.76/10.33 | (8212) sum(n10, n12) = all_0_0_0
% 31.76/10.33 |
% 31.76/10.33 | From (885)(883) and (435) follows:
% 31.76/10.33 | (887) sum(n11, n11) = all_0_3_3
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 31.76/10.33 | (888) all_0_3_3 = n1
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (194) with n10, n12, all_0_0_0, n1 and discharging atoms sum(n10, n12) = all_0_0_0, sum(n10, n12) = n1, yields:
% 31.76/10.33 | (889) all_0_0_0 = n1
% 31.76/10.33 |
% 31.76/10.33 | Equations (889,888) can reduce 201 to:
% 31.76/10.33 | (746) $false
% 31.76/10.33 |
% 31.76/10.33 |-The branch is then unsatisfiable
% 31.76/10.33 |-Branch two:
% 31.76/10.33 | (1017) ~ (all_0_11_11 = n5)
% 31.76/10.33 | (1018) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.76/10.33 |
% 31.76/10.33 +-Applying beta-rule and splitting (1018), into two cases.
% 31.76/10.33 |-Branch one:
% 31.76/10.33 | (1019) all_0_11_11 = n4
% 31.76/10.33 |
% 31.76/10.33 | From (1019) and (190) follows:
% 31.76/10.33 | (1020) pred(n4) = all_0_9_9
% 31.76/10.33 |
% 31.76/10.33 | From (1019) and (505) follows:
% 31.76/10.33 | (1021) succ(n4) = all_0_5_5
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 31.76/10.33 | (1022) all_0_9_9 = n3
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 31.76/10.33 | (1023) all_0_5_5 = n5
% 31.76/10.33 |
% 31.76/10.33 | From (1022)(1023) and (156) follows:
% 31.76/10.33 | (1024) sum(n3, n5) = all_0_2_2
% 31.76/10.33 |
% 31.76/10.33 | From (1022) and (8172) follows:
% 31.76/10.33 | (8225) sum(n3, n7) = all_0_7_7
% 31.76/10.33 |
% 31.76/10.33 | From (1023) and (8170) follows:
% 31.76/10.33 | (8226) sum(n5, n5) = all_0_4_4
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (194) with n5, n5, all_0_4_4, n10 and discharging atoms sum(n5, n5) = all_0_4_4, sum(n5, n5) = n10, yields:
% 31.76/10.33 | (901) all_0_4_4 = n10
% 31.76/10.33 |
% 31.76/10.33 | Instantiating formula (194) with n3, n7, all_0_7_7, n10 and discharging atoms sum(n3, n7) = all_0_7_7, sum(n3, n7) = n10, yields:
% 31.76/10.33 | (903) all_0_7_7 = n10
% 31.76/10.33 |
% 31.76/10.34 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 31.76/10.34 | (1028) all_0_2_2 = n8
% 31.76/10.34 |
% 31.76/10.34 | From (1028) and (8174) follows:
% 31.76/10.34 | (8230) sum(n8, n12) = all_0_0_0
% 31.76/10.34 |
% 31.76/10.34 | From (903)(901) and (435) follows:
% 31.76/10.34 | (905) sum(n10, n10) = all_0_3_3
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 31.76/10.34 | (906) all_0_3_3 = n20
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (194) with n8, n12, all_0_0_0, n20 and discharging atoms sum(n8, n12) = all_0_0_0, sum(n8, n12) = n20, yields:
% 31.76/10.34 | (907) all_0_0_0 = n20
% 31.76/10.34 |
% 31.76/10.34 | Equations (907,906) can reduce 201 to:
% 31.76/10.34 | (746) $false
% 31.76/10.34 |
% 31.76/10.34 |-The branch is then unsatisfiable
% 31.76/10.34 |-Branch two:
% 31.76/10.34 | (1035) ~ (all_0_11_11 = n4)
% 31.76/10.34 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.76/10.34 |
% 31.76/10.34 +-Applying beta-rule and splitting (1036), into two cases.
% 31.76/10.34 |-Branch one:
% 31.76/10.34 | (1037) all_0_11_11 = n3
% 31.76/10.34 |
% 31.76/10.34 | From (1037) and (190) follows:
% 31.76/10.34 | (1038) pred(n3) = all_0_9_9
% 31.76/10.34 |
% 31.76/10.34 | From (1037) and (505) follows:
% 31.76/10.34 | (1039) succ(n3) = all_0_5_5
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 31.76/10.34 | (1040) all_0_9_9 = n2
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 31.76/10.34 | (1041) all_0_5_5 = n4
% 31.76/10.34 |
% 31.76/10.34 | From (1040)(1041) and (156) follows:
% 31.76/10.34 | (1042) sum(n2, n4) = all_0_2_2
% 31.76/10.34 |
% 31.76/10.34 | From (1040) and (8172) follows:
% 31.76/10.34 | (8243) sum(n2, n7) = all_0_7_7
% 31.76/10.34 |
% 31.76/10.34 | From (1041) and (8170) follows:
% 31.76/10.34 | (8244) sum(n5, n4) = all_0_4_4
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (194) with n5, n4, all_0_4_4, n9 and discharging atoms sum(n5, n4) = all_0_4_4, sum(n5, n4) = n9, yields:
% 31.76/10.34 | (919) all_0_4_4 = n9
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (194) with n2, n7, all_0_7_7, n9 and discharging atoms sum(n2, n7) = all_0_7_7, sum(n2, n7) = n9, yields:
% 31.76/10.34 | (921) all_0_7_7 = n9
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 31.76/10.34 | (1046) all_0_2_2 = n6
% 31.76/10.34 |
% 31.76/10.34 | From (1046) and (8174) follows:
% 31.76/10.34 | (8248) sum(n6, n12) = all_0_0_0
% 31.76/10.34 |
% 31.76/10.34 | From (921)(919) and (435) follows:
% 31.76/10.34 | (923) sum(n9, n9) = all_0_3_3
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 31.76/10.34 | (925) all_0_3_3 = n18
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (194) with n6, n12, all_0_0_0, n18 and discharging atoms sum(n6, n12) = all_0_0_0, sum(n6, n12) = n18, yields:
% 31.76/10.34 | (924) all_0_0_0 = n18
% 31.76/10.34 |
% 31.76/10.34 | Equations (924,925) can reduce 201 to:
% 31.76/10.34 | (746) $false
% 31.76/10.34 |
% 31.76/10.34 |-The branch is then unsatisfiable
% 31.76/10.34 |-Branch two:
% 31.76/10.34 | (1053) ~ (all_0_11_11 = n3)
% 31.76/10.34 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.76/10.34 |
% 31.76/10.34 +-Applying beta-rule and splitting (1054), into two cases.
% 31.76/10.34 |-Branch one:
% 31.76/10.34 | (1055) all_0_11_11 = n2
% 31.76/10.34 |
% 31.76/10.34 | From (1055) and (190) follows:
% 31.76/10.34 | (1056) pred(n2) = all_0_9_9
% 31.76/10.34 |
% 31.76/10.34 | From (1055) and (505) follows:
% 31.76/10.34 | (1057) succ(n2) = all_0_5_5
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 31.76/10.34 | (1058) all_0_9_9 = n1
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.76/10.34 | (1059) all_0_5_5 = n3
% 31.76/10.34 |
% 31.76/10.34 | From (1058)(1059) and (156) follows:
% 31.76/10.34 | (1060) sum(n1, n3) = all_0_2_2
% 31.76/10.34 |
% 31.76/10.34 | From (1058) and (8172) follows:
% 31.76/10.34 | (8261) sum(n1, n7) = all_0_7_7
% 31.76/10.34 |
% 31.76/10.34 | From (1059) and (8170) follows:
% 31.76/10.34 | (8262) sum(n5, n3) = all_0_4_4
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (194) with n5, n3, all_0_4_4, n8 and discharging atoms sum(n5, n3) = all_0_4_4, sum(n5, n3) = n8, yields:
% 31.76/10.34 | (937) all_0_4_4 = n8
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (194) with n1, n7, all_0_7_7, n8 and discharging atoms sum(n1, n7) = all_0_7_7, sum(n1, n7) = n8, yields:
% 31.76/10.34 | (939) all_0_7_7 = n8
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 31.76/10.34 | (1064) all_0_2_2 = n4
% 31.76/10.34 |
% 31.76/10.34 | From (1064) and (8174) follows:
% 31.76/10.34 | (8266) sum(n4, n12) = all_0_0_0
% 31.76/10.34 |
% 31.76/10.34 | From (939)(937) and (435) follows:
% 31.76/10.34 | (941) sum(n8, n8) = all_0_3_3
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 31.76/10.34 | (943) all_0_3_3 = n16
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (194) with n4, n12, all_0_0_0, n16 and discharging atoms sum(n4, n12) = all_0_0_0, sum(n4, n12) = n16, yields:
% 31.76/10.34 | (942) all_0_0_0 = n16
% 31.76/10.34 |
% 31.76/10.34 | Equations (942,943) can reduce 201 to:
% 31.76/10.34 | (746) $false
% 31.76/10.34 |
% 31.76/10.34 |-The branch is then unsatisfiable
% 31.76/10.34 |-Branch two:
% 31.76/10.34 | (1071) ~ (all_0_11_11 = n2)
% 31.76/10.34 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 31.76/10.34 |
% 31.76/10.34 +-Applying beta-rule and splitting (1072), into two cases.
% 31.76/10.34 |-Branch one:
% 31.76/10.34 | (1073) all_0_11_11 = n1
% 31.76/10.34 |
% 31.76/10.34 | From (1073) and (190) follows:
% 31.76/10.34 | (1074) pred(n1) = all_0_9_9
% 31.76/10.34 |
% 31.76/10.34 | From (1073) and (505) follows:
% 31.76/10.34 | (1075) succ(n1) = all_0_5_5
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 31.76/10.34 | (1076) all_0_9_9 = n0
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.76/10.34 | (1077) all_0_5_5 = n2
% 31.76/10.34 |
% 31.76/10.34 | From (1076)(1077) and (156) follows:
% 31.76/10.34 | (1078) sum(n0, n2) = all_0_2_2
% 31.76/10.34 |
% 31.76/10.34 | From (1076) and (8172) follows:
% 31.76/10.34 | (8279) sum(n0, n7) = all_0_7_7
% 31.76/10.34 |
% 31.76/10.34 | From (1077) and (8170) follows:
% 31.76/10.34 | (8280) sum(n5, n2) = all_0_4_4
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (194) with n5, n2, all_0_4_4, n7 and discharging atoms sum(n5, n2) = all_0_4_4, sum(n5, n2) = n7, yields:
% 31.76/10.34 | (955) all_0_4_4 = n7
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (194) with n0, n7, all_0_7_7, n7 and discharging atoms sum(n0, n7) = all_0_7_7, sum(n0, n7) = n7, yields:
% 31.76/10.34 | (957) all_0_7_7 = n7
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 31.76/10.34 | (1082) all_0_2_2 = n2
% 31.76/10.34 |
% 31.76/10.34 | From (1082) and (8174) follows:
% 31.76/10.34 | (8284) sum(n2, n12) = all_0_0_0
% 31.76/10.34 |
% 31.76/10.34 | From (957)(955) and (435) follows:
% 31.76/10.34 | (959) sum(n7, n7) = all_0_3_3
% 31.76/10.34 |
% 31.76/10.34 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 31.76/10.34 | (961) all_0_3_3 = n14
% 31.76/10.34 |
% 31.76/10.35 | Instantiating formula (194) with n2, n12, all_0_0_0, n14 and discharging atoms sum(n2, n12) = all_0_0_0, sum(n2, n12) = n14, yields:
% 31.76/10.35 | (960) all_0_0_0 = n14
% 31.76/10.35 |
% 31.76/10.35 | Equations (960,961) can reduce 201 to:
% 31.76/10.35 | (746) $false
% 31.76/10.35 |
% 31.76/10.35 |-The branch is then unsatisfiable
% 31.76/10.35 |-Branch two:
% 31.76/10.35 | (1090) ~ (all_0_11_11 = n1)
% 31.76/10.35 | (1091) all_0_11_11 = n0
% 31.76/10.35 |
% 31.76/10.35 | From (1091) and (190) follows:
% 31.76/10.35 | (1092) pred(n0) = all_0_9_9
% 31.76/10.35 |
% 31.76/10.35 | From (1091) and (505) follows:
% 31.76/10.35 | (1093) succ(n0) = all_0_5_5
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 31.76/10.35 | (1094) all_0_9_9 = n20
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.76/10.35 | (1095) all_0_5_5 = n1
% 31.76/10.35 |
% 31.76/10.35 | From (1094)(1095) and (156) follows:
% 31.76/10.35 | (1096) sum(n20, n1) = all_0_2_2
% 31.76/10.35 |
% 31.76/10.35 | From (1094) and (8172) follows:
% 31.76/10.35 | (8296) sum(n20, n7) = all_0_7_7
% 31.76/10.35 |
% 31.76/10.35 | From (1095) and (8170) follows:
% 31.76/10.35 | (8297) sum(n5, n1) = all_0_4_4
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (194) with n20, n7, all_0_7_7, n6 and discharging atoms sum(n20, n7) = all_0_7_7, sum(n20, n7) = n6, yields:
% 31.76/10.35 | (975) all_0_7_7 = n6
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 31.76/10.35 | (1099) all_0_2_2 = n0
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (194) with n5, n1, all_0_4_4, n6 and discharging atoms sum(n5, n1) = all_0_4_4, sum(n5, n1) = n6, yields:
% 31.76/10.35 | (973) all_0_4_4 = n6
% 31.76/10.35 |
% 31.76/10.35 | From (1099) and (8174) follows:
% 31.76/10.35 | (8301) sum(n0, n12) = all_0_0_0
% 31.76/10.35 |
% 31.76/10.35 | From (975)(973) and (435) follows:
% 31.76/10.35 | (977) sum(n6, n6) = all_0_3_3
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 31.76/10.35 | (979) all_0_3_3 = n12
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (194) with n0, n12, all_0_0_0, n12 and discharging atoms sum(n0, n12) = all_0_0_0, sum(n0, n12) = n12, yields:
% 31.76/10.35 | (978) all_0_0_0 = n12
% 31.76/10.35 |
% 31.76/10.35 | Equations (978,979) can reduce 201 to:
% 31.76/10.35 | (746) $false
% 31.76/10.35 |
% 31.76/10.35 |-The branch is then unsatisfiable
% 31.76/10.35 |-Branch two:
% 31.76/10.35 | (1370) ~ (all_0_10_10 = n6)
% 31.76/10.35 | (1371) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.76/10.35 |
% 31.76/10.35 +-Applying beta-rule and splitting (982), into two cases.
% 31.76/10.35 |-Branch one:
% 31.76/10.35 | (983) all_0_11_11 = n6
% 31.76/10.35 |
% 31.76/10.35 | From (983) and (190) follows:
% 31.76/10.35 | (984) pred(n6) = all_0_9_9
% 31.76/10.35 |
% 31.76/10.35 | From (983) and (505) follows:
% 31.76/10.35 | (985) succ(n6) = all_0_5_5
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (259) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 31.76/10.35 | (986) all_0_9_9 = n5
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (184) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 31.76/10.35 | (987) all_0_5_5 = n7
% 31.76/10.35 |
% 31.76/10.35 | From (987) and (386) follows:
% 31.76/10.35 | (8313) sum(all_0_6_6, n7) = all_0_4_4
% 31.76/10.35 |
% 31.76/10.35 | From (986)(987) and (156) follows:
% 31.76/10.35 | (988) sum(n5, n7) = all_0_2_2
% 31.76/10.35 |
% 31.76/10.35 | From (986) and (74) follows:
% 31.76/10.35 | (8315) sum(n5, all_0_8_8) = all_0_7_7
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (194) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 31.76/10.35 | (992) all_0_2_2 = n12
% 31.76/10.35 |
% 31.76/10.35 | From (992) and (85) follows:
% 31.76/10.35 | (8317) sum(n12, all_0_1_1) = all_0_0_0
% 31.76/10.35 |
% 31.76/10.35 +-Applying beta-rule and splitting (1371), into two cases.
% 31.76/10.35 |-Branch one:
% 31.76/10.35 | (1372) all_0_10_10 = n5
% 31.76/10.35 |
% 31.76/10.35 | From (1372) and (57) follows:
% 31.76/10.35 | (1373) pred(n5) = all_0_6_6
% 31.76/10.35 |
% 31.76/10.35 | From (1372) and (381) follows:
% 31.76/10.35 | (1374) succ(n5) = all_0_8_8
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (259) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 31.76/10.35 | (1375) all_0_6_6 = n4
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (184) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 31.76/10.35 | (1376) all_0_8_8 = n6
% 31.76/10.35 |
% 31.76/10.35 | From (1375)(1376) and (628) follows:
% 31.76/10.35 | (1377) sum(n4, n6) = all_0_1_1
% 31.76/10.35 |
% 31.76/10.35 | From (1375) and (8313) follows:
% 31.76/10.35 | (8324) sum(n4, n7) = all_0_4_4
% 31.76/10.35 |
% 31.76/10.35 | From (1376) and (8315) follows:
% 31.76/10.35 | (8325) sum(n5, n6) = all_0_7_7
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (194) with n5, n6, all_0_7_7, n11 and discharging atoms sum(n5, n6) = all_0_7_7, sum(n5, n6) = n11, yields:
% 31.76/10.35 | (885) all_0_7_7 = n11
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (194) with n4, n7, all_0_4_4, n11 and discharging atoms sum(n4, n7) = all_0_4_4, sum(n4, n7) = n11, yields:
% 31.76/10.35 | (883) all_0_4_4 = n11
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (194) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 31.76/10.35 | (1381) all_0_1_1 = n10
% 31.76/10.35 |
% 31.76/10.35 | From (885)(883) and (435) follows:
% 31.76/10.35 | (887) sum(n11, n11) = all_0_3_3
% 31.76/10.35 |
% 31.76/10.35 | From (1381) and (8317) follows:
% 31.76/10.35 | (8330) sum(n12, n10) = all_0_0_0
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (194) with n12, n10, all_0_0_0, n1 and discharging atoms sum(n12, n10) = all_0_0_0, sum(n12, n10) = n1, yields:
% 31.76/10.35 | (889) all_0_0_0 = n1
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (194) with n11, n11, all_0_3_3, n1 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n1, yields:
% 31.76/10.35 | (888) all_0_3_3 = n1
% 31.76/10.35 |
% 31.76/10.35 | Equations (889,888) can reduce 201 to:
% 31.76/10.35 | (746) $false
% 31.76/10.35 |
% 31.76/10.35 |-The branch is then unsatisfiable
% 31.76/10.35 |-Branch two:
% 31.76/10.35 | (1388) ~ (all_0_10_10 = n5)
% 31.76/10.35 | (1389) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.76/10.35 |
% 31.76/10.35 +-Applying beta-rule and splitting (1389), into two cases.
% 31.76/10.35 |-Branch one:
% 31.76/10.35 | (1390) all_0_10_10 = n4
% 31.76/10.35 |
% 31.76/10.35 | From (1390) and (57) follows:
% 31.76/10.35 | (1391) pred(n4) = all_0_6_6
% 31.76/10.35 |
% 31.76/10.35 | From (1390) and (381) follows:
% 31.76/10.35 | (1392) succ(n4) = all_0_8_8
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (259) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 31.76/10.35 | (1393) all_0_6_6 = n3
% 31.76/10.35 |
% 31.76/10.35 | Instantiating formula (184) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 31.76/10.35 | (1394) all_0_8_8 = n5
% 31.76/10.35 |
% 31.76/10.35 | From (1393)(1394) and (628) follows:
% 31.76/10.35 | (1395) sum(n3, n5) = all_0_1_1
% 31.76/10.35 |
% 31.76/10.35 | From (1393) and (8313) follows:
% 31.76/10.35 | (8342) sum(n3, n7) = all_0_4_4
% 31.76/10.35 |
% 31.76/10.35 | From (1394) and (8315) follows:
% 31.76/10.36 | (8343) sum(n5, n5) = all_0_7_7
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (194) with n5, n5, all_0_7_7, n10 and discharging atoms sum(n5, n5) = all_0_7_7, sum(n5, n5) = n10, yields:
% 31.76/10.36 | (903) all_0_7_7 = n10
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (194) with n3, n7, all_0_4_4, n10 and discharging atoms sum(n3, n7) = all_0_4_4, sum(n3, n7) = n10, yields:
% 31.76/10.36 | (901) all_0_4_4 = n10
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (194) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 31.76/10.36 | (1399) all_0_1_1 = n8
% 31.76/10.36 |
% 31.76/10.36 | From (903)(901) and (435) follows:
% 31.76/10.36 | (905) sum(n10, n10) = all_0_3_3
% 31.76/10.36 |
% 31.76/10.36 | From (1399) and (8317) follows:
% 31.76/10.36 | (8348) sum(n12, n8) = all_0_0_0
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (194) with n12, n8, all_0_0_0, n20 and discharging atoms sum(n12, n8) = all_0_0_0, sum(n12, n8) = n20, yields:
% 31.76/10.36 | (907) all_0_0_0 = n20
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (194) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 31.76/10.36 | (906) all_0_3_3 = n20
% 31.76/10.36 |
% 31.76/10.36 | Equations (907,906) can reduce 201 to:
% 31.76/10.36 | (746) $false
% 31.76/10.36 |
% 31.76/10.36 |-The branch is then unsatisfiable
% 31.76/10.36 |-Branch two:
% 31.76/10.36 | (1406) ~ (all_0_10_10 = n4)
% 31.76/10.36 | (1407) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.76/10.36 |
% 31.76/10.36 +-Applying beta-rule and splitting (1407), into two cases.
% 31.76/10.36 |-Branch one:
% 31.76/10.36 | (1408) all_0_10_10 = n3
% 31.76/10.36 |
% 31.76/10.36 | From (1408) and (57) follows:
% 31.76/10.36 | (1409) pred(n3) = all_0_6_6
% 31.76/10.36 |
% 31.76/10.36 | From (1408) and (381) follows:
% 31.76/10.36 | (1410) succ(n3) = all_0_8_8
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 31.76/10.36 | (1411) all_0_6_6 = n2
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 31.76/10.36 | (1412) all_0_8_8 = n4
% 31.76/10.36 |
% 31.76/10.36 | From (1411)(1412) and (628) follows:
% 31.76/10.36 | (1413) sum(n2, n4) = all_0_1_1
% 31.76/10.36 |
% 31.76/10.36 | From (1411) and (8313) follows:
% 31.76/10.36 | (8360) sum(n2, n7) = all_0_4_4
% 31.76/10.36 |
% 31.76/10.36 | From (1412) and (8315) follows:
% 31.76/10.36 | (8361) sum(n5, n4) = all_0_7_7
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (194) with n5, n4, all_0_7_7, n9 and discharging atoms sum(n5, n4) = all_0_7_7, sum(n5, n4) = n9, yields:
% 31.76/10.36 | (921) all_0_7_7 = n9
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (194) with n2, n7, all_0_4_4, n9 and discharging atoms sum(n2, n7) = all_0_4_4, sum(n2, n7) = n9, yields:
% 31.76/10.36 | (919) all_0_4_4 = n9
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 31.76/10.36 | (1417) all_0_1_1 = n6
% 31.76/10.36 |
% 31.76/10.36 | From (921)(919) and (435) follows:
% 31.76/10.36 | (923) sum(n9, n9) = all_0_3_3
% 31.76/10.36 |
% 31.76/10.36 | From (1417) and (8317) follows:
% 31.76/10.36 | (8366) sum(n12, n6) = all_0_0_0
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (194) with n12, n6, all_0_0_0, n18 and discharging atoms sum(n12, n6) = all_0_0_0, sum(n12, n6) = n18, yields:
% 31.76/10.36 | (924) all_0_0_0 = n18
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 31.76/10.36 | (925) all_0_3_3 = n18
% 31.76/10.36 |
% 31.76/10.36 | Equations (924,925) can reduce 201 to:
% 31.76/10.36 | (746) $false
% 31.76/10.36 |
% 31.76/10.36 |-The branch is then unsatisfiable
% 31.76/10.36 |-Branch two:
% 31.76/10.36 | (1424) ~ (all_0_10_10 = n3)
% 31.76/10.36 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.76/10.36 |
% 31.76/10.36 +-Applying beta-rule and splitting (1425), into two cases.
% 31.76/10.36 |-Branch one:
% 31.76/10.36 | (1426) all_0_10_10 = n2
% 31.76/10.36 |
% 31.76/10.36 | From (1426) and (57) follows:
% 31.76/10.36 | (1427) pred(n2) = all_0_6_6
% 31.76/10.36 |
% 31.76/10.36 | From (1426) and (381) follows:
% 31.76/10.36 | (1428) succ(n2) = all_0_8_8
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 31.76/10.36 | (1429) all_0_6_6 = n1
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 31.76/10.36 | (1430) all_0_8_8 = n3
% 31.76/10.36 |
% 31.76/10.36 | From (1429)(1430) and (628) follows:
% 31.76/10.36 | (1431) sum(n1, n3) = all_0_1_1
% 31.76/10.36 |
% 31.76/10.36 | From (1429) and (8313) follows:
% 31.76/10.36 | (8378) sum(n1, n7) = all_0_4_4
% 31.76/10.36 |
% 31.76/10.36 | From (1430) and (8315) follows:
% 31.76/10.36 | (8379) sum(n5, n3) = all_0_7_7
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (194) with n5, n3, all_0_7_7, n8 and discharging atoms sum(n5, n3) = all_0_7_7, sum(n5, n3) = n8, yields:
% 31.76/10.36 | (939) all_0_7_7 = n8
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (194) with n1, n7, all_0_4_4, n8 and discharging atoms sum(n1, n7) = all_0_4_4, sum(n1, n7) = n8, yields:
% 31.76/10.36 | (937) all_0_4_4 = n8
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 31.76/10.36 | (1435) all_0_1_1 = n4
% 31.76/10.36 |
% 31.76/10.36 | From (939)(937) and (435) follows:
% 31.76/10.36 | (941) sum(n8, n8) = all_0_3_3
% 31.76/10.36 |
% 31.76/10.36 | From (1435) and (8317) follows:
% 31.76/10.36 | (8384) sum(n12, n4) = all_0_0_0
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (194) with n12, n4, all_0_0_0, n16 and discharging atoms sum(n12, n4) = all_0_0_0, sum(n12, n4) = n16, yields:
% 31.76/10.36 | (942) all_0_0_0 = n16
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 31.76/10.36 | (943) all_0_3_3 = n16
% 31.76/10.36 |
% 31.76/10.36 | Equations (942,943) can reduce 201 to:
% 31.76/10.36 | (746) $false
% 31.76/10.36 |
% 31.76/10.36 |-The branch is then unsatisfiable
% 31.76/10.36 |-Branch two:
% 31.76/10.36 | (1442) ~ (all_0_10_10 = n2)
% 31.76/10.36 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 31.76/10.36 |
% 31.76/10.36 +-Applying beta-rule and splitting (1443), into two cases.
% 31.76/10.36 |-Branch one:
% 31.76/10.36 | (1444) all_0_10_10 = n1
% 31.76/10.36 |
% 31.76/10.36 | From (1444) and (57) follows:
% 31.76/10.36 | (1445) pred(n1) = all_0_6_6
% 31.76/10.36 |
% 31.76/10.36 | From (1444) and (381) follows:
% 31.76/10.36 | (1446) succ(n1) = all_0_8_8
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 31.76/10.36 | (1447) all_0_6_6 = n0
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 31.76/10.36 | (1448) all_0_8_8 = n2
% 31.76/10.36 |
% 31.76/10.36 | From (1447)(1448) and (628) follows:
% 31.76/10.36 | (1449) sum(n0, n2) = all_0_1_1
% 31.76/10.36 |
% 31.76/10.36 | From (1447) and (8313) follows:
% 31.76/10.36 | (8396) sum(n0, n7) = all_0_4_4
% 31.76/10.36 |
% 31.76/10.36 | From (1448) and (8315) follows:
% 31.76/10.36 | (8397) sum(n5, n2) = all_0_7_7
% 31.76/10.36 |
% 31.76/10.36 | Instantiating formula (194) with n5, n2, all_0_7_7, n7 and discharging atoms sum(n5, n2) = all_0_7_7, sum(n5, n2) = n7, yields:
% 31.76/10.37 | (957) all_0_7_7 = n7
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (194) with n0, n7, all_0_4_4, n7 and discharging atoms sum(n0, n7) = all_0_4_4, sum(n0, n7) = n7, yields:
% 31.76/10.37 | (955) all_0_4_4 = n7
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 31.76/10.37 | (1453) all_0_1_1 = n2
% 31.76/10.37 |
% 31.76/10.37 | From (957)(955) and (435) follows:
% 31.76/10.37 | (959) sum(n7, n7) = all_0_3_3
% 31.76/10.37 |
% 31.76/10.37 | From (1453) and (8317) follows:
% 31.76/10.37 | (8402) sum(n12, n2) = all_0_0_0
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (194) with n12, n2, all_0_0_0, n14 and discharging atoms sum(n12, n2) = all_0_0_0, sum(n12, n2) = n14, yields:
% 31.76/10.37 | (960) all_0_0_0 = n14
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 31.76/10.37 | (961) all_0_3_3 = n14
% 31.76/10.37 |
% 31.76/10.37 | Equations (960,961) can reduce 201 to:
% 31.76/10.37 | (746) $false
% 31.76/10.37 |
% 31.76/10.37 |-The branch is then unsatisfiable
% 31.76/10.37 |-Branch two:
% 31.76/10.37 | (1462) ~ (all_0_10_10 = n1)
% 31.76/10.37 | (1463) all_0_10_10 = n0
% 31.76/10.37 |
% 31.76/10.37 | From (1463) and (57) follows:
% 31.76/10.37 | (1464) pred(n0) = all_0_6_6
% 31.76/10.37 |
% 31.76/10.37 | From (1463) and (381) follows:
% 31.76/10.37 | (1465) succ(n0) = all_0_8_8
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 31.76/10.37 | (1466) all_0_6_6 = n20
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 31.76/10.37 | (1467) all_0_8_8 = n1
% 31.76/10.37 |
% 31.76/10.37 | From (1466)(1467) and (628) follows:
% 31.76/10.37 | (1468) sum(n20, n1) = all_0_1_1
% 31.76/10.37 |
% 31.76/10.37 | From (1466) and (8313) follows:
% 31.76/10.37 | (8413) sum(n20, n7) = all_0_4_4
% 31.76/10.37 |
% 31.76/10.37 | From (1467) and (8315) follows:
% 31.76/10.37 | (8414) sum(n5, n1) = all_0_7_7
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (194) with n20, n7, all_0_4_4, n6 and discharging atoms sum(n20, n7) = all_0_4_4, sum(n20, n7) = n6, yields:
% 31.76/10.37 | (973) all_0_4_4 = n6
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 31.76/10.37 | (1471) all_0_1_1 = n0
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (194) with n5, n1, all_0_7_7, n6 and discharging atoms sum(n5, n1) = all_0_7_7, sum(n5, n1) = n6, yields:
% 31.76/10.37 | (975) all_0_7_7 = n6
% 31.76/10.37 |
% 31.76/10.37 | From (975)(973) and (435) follows:
% 31.76/10.37 | (977) sum(n6, n6) = all_0_3_3
% 31.76/10.37 |
% 31.76/10.37 | From (1471) and (8317) follows:
% 31.76/10.37 | (8419) sum(n12, n0) = all_0_0_0
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (194) with n12, n0, all_0_0_0, n12 and discharging atoms sum(n12, n0) = all_0_0_0, sum(n12, n0) = n12, yields:
% 31.76/10.37 | (978) all_0_0_0 = n12
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 31.76/10.37 | (979) all_0_3_3 = n12
% 31.76/10.37 |
% 31.76/10.37 | Equations (978,979) can reduce 201 to:
% 31.76/10.37 | (746) $false
% 31.76/10.37 |
% 31.76/10.37 |-The branch is then unsatisfiable
% 31.76/10.37 |-Branch two:
% 31.76/10.37 | (999) ~ (all_0_11_11 = n6)
% 31.76/10.37 | (1000) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.76/10.37 |
% 31.76/10.37 +-Applying beta-rule and splitting (1371), into two cases.
% 31.76/10.37 |-Branch one:
% 31.76/10.37 | (1372) all_0_10_10 = n5
% 31.76/10.37 |
% 31.76/10.37 | From (1372) and (57) follows:
% 31.76/10.37 | (1373) pred(n5) = all_0_6_6
% 31.76/10.37 |
% 31.76/10.37 | From (1372) and (381) follows:
% 31.76/10.37 | (1374) succ(n5) = all_0_8_8
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (259) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 31.76/10.37 | (1375) all_0_6_6 = n4
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (184) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 31.76/10.37 | (1376) all_0_8_8 = n6
% 31.76/10.37 |
% 31.76/10.37 | From (1375) and (1373) follows:
% 31.76/10.37 | (231) pred(n5) = n4
% 31.76/10.37 |
% 31.76/10.37 | From (1376) and (1374) follows:
% 31.76/10.37 | (675) succ(n5) = n6
% 31.76/10.37 |
% 31.76/10.37 | From (1375) and (386) follows:
% 31.76/10.37 | (8432) sum(n4, all_0_5_5) = all_0_4_4
% 31.76/10.37 |
% 31.76/10.37 | From (1375)(1376) and (628) follows:
% 31.76/10.37 | (1377) sum(n4, n6) = all_0_1_1
% 31.76/10.37 |
% 31.76/10.37 | From (1376) and (74) follows:
% 31.76/10.37 | (8434) sum(all_0_9_9, n6) = all_0_7_7
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (194) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 31.76/10.37 | (1381) all_0_1_1 = n10
% 31.76/10.37 |
% 31.76/10.37 | From (1381) and (85) follows:
% 31.76/10.37 | (8436) sum(all_0_2_2, n10) = all_0_0_0
% 31.76/10.37 |
% 31.76/10.37 | From (1381) and (1377) follows:
% 31.76/10.37 | (483) sum(n4, n6) = n10
% 31.76/10.37 |
% 31.76/10.37 +-Applying beta-rule and splitting (1000), into two cases.
% 31.76/10.37 |-Branch one:
% 31.76/10.37 | (1001) all_0_11_11 = n5
% 31.76/10.37 |
% 31.76/10.37 | From (1001) and (190) follows:
% 31.76/10.37 | (1002) pred(n5) = all_0_9_9
% 31.76/10.37 |
% 31.76/10.37 | From (1001) and (505) follows:
% 31.76/10.37 | (1003) succ(n5) = all_0_5_5
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (259) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 31.76/10.37 | (1004) all_0_9_9 = n4
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (184) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 31.76/10.37 | (1005) all_0_5_5 = n6
% 31.76/10.37 |
% 31.76/10.37 | From (1004)(1005) and (156) follows:
% 31.76/10.37 | (1006) sum(n4, n6) = all_0_2_2
% 31.76/10.37 |
% 31.76/10.37 | From (1004) and (8434) follows:
% 31.76/10.37 | (8444) sum(n4, n6) = all_0_7_7
% 31.76/10.37 |
% 31.76/10.37 | From (1005) and (8432) follows:
% 31.76/10.37 | (8445) sum(n4, n6) = all_0_4_4
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (194) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 31.76/10.37 | (1010) all_0_2_2 = n10
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (194) with n4, n6, all_0_4_4, all_0_2_2 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = all_0_4_4, yields:
% 31.76/10.37 | (733) all_0_2_2 = all_0_4_4
% 31.76/10.37 |
% 31.76/10.37 | Instantiating formula (194) with n4, n6, all_0_7_7, all_0_2_2 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = all_0_7_7, yields:
% 31.76/10.37 | (734) all_0_2_2 = all_0_7_7
% 31.76/10.37 |
% 31.76/10.37 | Combining equations (734,733) yields a new equation:
% 31.76/10.37 | (735) all_0_4_4 = all_0_7_7
% 31.76/10.37 |
% 31.76/10.37 | Combining equations (1010,733) yields a new equation:
% 31.76/10.37 | (901) all_0_4_4 = n10
% 31.76/10.37 |
% 31.76/10.37 | Combining equations (901,735) yields a new equation:
% 31.76/10.37 | (903) all_0_7_7 = n10
% 31.76/10.37 |
% 31.76/10.37 | Combining equations (903,735) yields a new equation:
% 31.76/10.37 | (901) all_0_4_4 = n10
% 31.76/10.37 |
% 31.76/10.37 | Combining equations (901,733) yields a new equation:
% 31.76/10.37 | (1010) all_0_2_2 = n10
% 31.76/10.37 |
% 31.76/10.37 | From (1010) and (8436) follows:
% 31.93/10.37 | (8454) sum(n10, n10) = all_0_0_0
% 31.93/10.37 |
% 31.93/10.37 | From (903)(901) and (435) follows:
% 31.93/10.37 | (905) sum(n10, n10) = all_0_3_3
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (194) with n10, n10, all_0_0_0, n20 and discharging atoms sum(n10, n10) = all_0_0_0, sum(n10, n10) = n20, yields:
% 31.93/10.38 | (907) all_0_0_0 = n20
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (194) with n10, n10, all_0_3_3, all_0_0_0 and discharging atoms sum(n10, n10) = all_0_0_0, sum(n10, n10) = all_0_3_3, yields:
% 31.93/10.38 | (743) all_0_0_0 = all_0_3_3
% 31.93/10.38 |
% 31.93/10.38 | Combining equations (907,743) yields a new equation:
% 31.93/10.38 | (906) all_0_3_3 = n20
% 31.93/10.38 |
% 31.93/10.38 | Combining equations (906,743) yields a new equation:
% 31.93/10.38 | (907) all_0_0_0 = n20
% 31.93/10.38 |
% 31.93/10.38 | Equations (907,906) can reduce 201 to:
% 31.93/10.38 | (746) $false
% 31.93/10.38 |
% 31.93/10.38 |-The branch is then unsatisfiable
% 31.93/10.38 |-Branch two:
% 31.93/10.38 | (1017) ~ (all_0_11_11 = n5)
% 31.93/10.38 | (1018) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.93/10.38 |
% 31.93/10.38 +-Applying beta-rule and splitting (1018), into two cases.
% 31.93/10.38 |-Branch one:
% 31.93/10.38 | (1019) all_0_11_11 = n4
% 31.93/10.38 |
% 31.93/10.38 | From (1019) and (190) follows:
% 31.93/10.38 | (1020) pred(n4) = all_0_9_9
% 31.93/10.38 |
% 31.93/10.38 | From (1019) and (505) follows:
% 31.93/10.38 | (1021) succ(n4) = all_0_5_5
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 31.93/10.38 | (1022) all_0_9_9 = n3
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 31.93/10.38 | (1023) all_0_5_5 = n5
% 31.93/10.38 |
% 31.93/10.38 | From (1022)(1023) and (156) follows:
% 31.93/10.38 | (1024) sum(n3, n5) = all_0_2_2
% 31.93/10.38 |
% 31.93/10.38 | From (1022) and (8434) follows:
% 31.93/10.38 | (8469) sum(n3, n6) = all_0_7_7
% 31.93/10.38 |
% 31.93/10.38 | From (1023) and (8432) follows:
% 31.93/10.38 | (8470) sum(n4, n5) = all_0_4_4
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (194) with n4, n5, all_0_4_4, n9 and discharging atoms sum(n4, n5) = all_0_4_4, sum(n4, n5) = n9, yields:
% 31.93/10.38 | (919) all_0_4_4 = n9
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (194) with n3, n6, all_0_7_7, n9 and discharging atoms sum(n3, n6) = all_0_7_7, sum(n3, n6) = n9, yields:
% 31.93/10.38 | (921) all_0_7_7 = n9
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 31.93/10.38 | (1028) all_0_2_2 = n8
% 31.93/10.38 |
% 31.93/10.38 | From (1028) and (8436) follows:
% 31.93/10.38 | (8474) sum(n8, n10) = all_0_0_0
% 31.93/10.38 |
% 31.93/10.38 | From (921)(919) and (435) follows:
% 31.93/10.38 | (923) sum(n9, n9) = all_0_3_3
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 31.93/10.38 | (925) all_0_3_3 = n18
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (194) with n8, n10, all_0_0_0, n18 and discharging atoms sum(n8, n10) = all_0_0_0, sum(n8, n10) = n18, yields:
% 31.93/10.38 | (924) all_0_0_0 = n18
% 31.93/10.38 |
% 31.93/10.38 | Equations (924,925) can reduce 201 to:
% 31.93/10.38 | (746) $false
% 31.93/10.38 |
% 31.93/10.38 |-The branch is then unsatisfiable
% 31.93/10.38 |-Branch two:
% 31.93/10.38 | (1035) ~ (all_0_11_11 = n4)
% 31.93/10.38 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.93/10.38 |
% 31.93/10.38 +-Applying beta-rule and splitting (1036), into two cases.
% 31.93/10.38 |-Branch one:
% 31.93/10.38 | (1037) all_0_11_11 = n3
% 31.93/10.38 |
% 31.93/10.38 | From (1037) and (190) follows:
% 31.93/10.38 | (1038) pred(n3) = all_0_9_9
% 31.93/10.38 |
% 31.93/10.38 | From (1037) and (505) follows:
% 31.93/10.38 | (1039) succ(n3) = all_0_5_5
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 31.93/10.38 | (1040) all_0_9_9 = n2
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 31.93/10.38 | (1041) all_0_5_5 = n4
% 31.93/10.38 |
% 31.93/10.38 | From (1040)(1041) and (156) follows:
% 31.93/10.38 | (1042) sum(n2, n4) = all_0_2_2
% 31.93/10.38 |
% 31.93/10.38 | From (1040) and (8434) follows:
% 31.93/10.38 | (8487) sum(n2, n6) = all_0_7_7
% 31.93/10.38 |
% 31.93/10.38 | From (1041) and (8432) follows:
% 31.93/10.38 | (8488) sum(n4, n4) = all_0_4_4
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (194) with n4, n4, all_0_4_4, n8 and discharging atoms sum(n4, n4) = all_0_4_4, sum(n4, n4) = n8, yields:
% 31.93/10.38 | (937) all_0_4_4 = n8
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (194) with n2, n6, all_0_7_7, n8 and discharging atoms sum(n2, n6) = all_0_7_7, sum(n2, n6) = n8, yields:
% 31.93/10.38 | (939) all_0_7_7 = n8
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 31.93/10.38 | (1046) all_0_2_2 = n6
% 31.93/10.38 |
% 31.93/10.38 | From (1046) and (8436) follows:
% 31.93/10.38 | (8492) sum(n6, n10) = all_0_0_0
% 31.93/10.38 |
% 31.93/10.38 | From (939)(937) and (435) follows:
% 31.93/10.38 | (941) sum(n8, n8) = all_0_3_3
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 31.93/10.38 | (943) all_0_3_3 = n16
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (194) with n6, n10, all_0_0_0, n16 and discharging atoms sum(n6, n10) = all_0_0_0, sum(n6, n10) = n16, yields:
% 31.93/10.38 | (942) all_0_0_0 = n16
% 31.93/10.38 |
% 31.93/10.38 | Equations (942,943) can reduce 201 to:
% 31.93/10.38 | (746) $false
% 31.93/10.38 |
% 31.93/10.38 |-The branch is then unsatisfiable
% 31.93/10.38 |-Branch two:
% 31.93/10.38 | (1053) ~ (all_0_11_11 = n3)
% 31.93/10.38 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.93/10.38 |
% 31.93/10.38 +-Applying beta-rule and splitting (1054), into two cases.
% 31.93/10.38 |-Branch one:
% 31.93/10.38 | (1055) all_0_11_11 = n2
% 31.93/10.38 |
% 31.93/10.38 | From (1055) and (190) follows:
% 31.93/10.38 | (1056) pred(n2) = all_0_9_9
% 31.93/10.38 |
% 31.93/10.38 | From (1055) and (505) follows:
% 31.93/10.38 | (1057) succ(n2) = all_0_5_5
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 31.93/10.38 | (1058) all_0_9_9 = n1
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.93/10.38 | (1059) all_0_5_5 = n3
% 31.93/10.38 |
% 31.93/10.38 | From (1058)(1059) and (156) follows:
% 31.93/10.38 | (1060) sum(n1, n3) = all_0_2_2
% 31.93/10.38 |
% 31.93/10.38 | From (1058) and (8434) follows:
% 31.93/10.38 | (8505) sum(n1, n6) = all_0_7_7
% 31.93/10.38 |
% 31.93/10.38 | From (1059) and (8432) follows:
% 31.93/10.38 | (8506) sum(n4, n3) = all_0_4_4
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (194) with n4, n3, all_0_4_4, n7 and discharging atoms sum(n4, n3) = all_0_4_4, sum(n4, n3) = n7, yields:
% 31.93/10.38 | (955) all_0_4_4 = n7
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (194) with n1, n6, all_0_7_7, n7 and discharging atoms sum(n1, n6) = all_0_7_7, sum(n1, n6) = n7, yields:
% 31.93/10.38 | (957) all_0_7_7 = n7
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 31.93/10.38 | (1064) all_0_2_2 = n4
% 31.93/10.38 |
% 31.93/10.38 | From (1064) and (8436) follows:
% 31.93/10.38 | (8510) sum(n4, n10) = all_0_0_0
% 31.93/10.38 |
% 31.93/10.38 | From (957)(955) and (435) follows:
% 31.93/10.38 | (959) sum(n7, n7) = all_0_3_3
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 31.93/10.38 | (961) all_0_3_3 = n14
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (194) with n4, n10, all_0_0_0, n14 and discharging atoms sum(n4, n10) = all_0_0_0, sum(n4, n10) = n14, yields:
% 31.93/10.38 | (960) all_0_0_0 = n14
% 31.93/10.38 |
% 31.93/10.38 | Equations (960,961) can reduce 201 to:
% 31.93/10.38 | (746) $false
% 31.93/10.38 |
% 31.93/10.38 |-The branch is then unsatisfiable
% 31.93/10.38 |-Branch two:
% 31.93/10.38 | (1071) ~ (all_0_11_11 = n2)
% 31.93/10.38 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 31.93/10.38 |
% 31.93/10.38 +-Applying beta-rule and splitting (1072), into two cases.
% 31.93/10.38 |-Branch one:
% 31.93/10.38 | (1073) all_0_11_11 = n1
% 31.93/10.38 |
% 31.93/10.38 | From (1073) and (190) follows:
% 31.93/10.38 | (1074) pred(n1) = all_0_9_9
% 31.93/10.38 |
% 31.93/10.38 | From (1073) and (505) follows:
% 31.93/10.38 | (1075) succ(n1) = all_0_5_5
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 31.93/10.38 | (1076) all_0_9_9 = n0
% 31.93/10.38 |
% 31.93/10.38 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.93/10.39 | (1077) all_0_5_5 = n2
% 31.93/10.39 |
% 31.93/10.39 | From (1076)(1077) and (156) follows:
% 31.93/10.39 | (1078) sum(n0, n2) = all_0_2_2
% 31.93/10.39 |
% 31.93/10.39 | From (1076) and (8434) follows:
% 31.93/10.39 | (8523) sum(n0, n6) = all_0_7_7
% 31.93/10.39 |
% 31.93/10.39 | From (1077) and (8432) follows:
% 31.93/10.39 | (8524) sum(n4, n2) = all_0_4_4
% 31.93/10.39 |
% 31.93/10.39 | Instantiating formula (194) with n4, n2, all_0_4_4, n6 and discharging atoms sum(n4, n2) = all_0_4_4, sum(n4, n2) = n6, yields:
% 31.93/10.39 | (973) all_0_4_4 = n6
% 31.93/10.39 |
% 31.93/10.39 | Instantiating formula (194) with n0, n6, all_0_7_7, n6 and discharging atoms sum(n0, n6) = all_0_7_7, sum(n0, n6) = n6, yields:
% 31.93/10.39 | (975) all_0_7_7 = n6
% 31.93/10.39 |
% 31.93/10.39 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 31.93/10.39 | (1082) all_0_2_2 = n2
% 31.93/10.39 |
% 31.93/10.39 | From (1082) and (8436) follows:
% 31.93/10.39 | (8528) sum(n2, n10) = all_0_0_0
% 31.93/10.39 |
% 31.93/10.39 | From (975)(973) and (435) follows:
% 31.93/10.39 | (977) sum(n6, n6) = all_0_3_3
% 31.93/10.39 |
% 31.93/10.39 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 31.93/10.39 | (979) all_0_3_3 = n12
% 31.93/10.39 |
% 31.93/10.39 | Instantiating formula (194) with n2, n10, all_0_0_0, n12 and discharging atoms sum(n2, n10) = all_0_0_0, sum(n2, n10) = n12, yields:
% 31.93/10.39 | (978) all_0_0_0 = n12
% 31.93/10.39 |
% 31.93/10.39 | Equations (978,979) can reduce 201 to:
% 31.93/10.39 | (746) $false
% 31.93/10.39 |
% 31.93/10.39 |-The branch is then unsatisfiable
% 31.93/10.39 |-Branch two:
% 31.93/10.39 | (1090) ~ (all_0_11_11 = n1)
% 31.93/10.39 | (1091) all_0_11_11 = n0
% 31.93/10.39 |
% 31.93/10.39 | From (1091) and (190) follows:
% 31.93/10.39 | (1092) pred(n0) = all_0_9_9
% 31.93/10.39 |
% 31.93/10.39 | From (1091) and (505) follows:
% 31.93/10.39 | (1093) succ(n0) = all_0_5_5
% 31.93/10.39 |
% 31.93/10.39 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 31.93/10.39 | (1094) all_0_9_9 = n20
% 31.93/10.39 |
% 31.93/10.39 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.93/10.39 | (1095) all_0_5_5 = n1
% 31.93/10.39 |
% 31.93/10.39 | From (1094)(1095) and (156) follows:
% 31.93/10.39 | (1096) sum(n20, n1) = all_0_2_2
% 31.93/10.39 |
% 31.93/10.39 | From (1094) and (8434) follows:
% 31.95/10.39 | (8540) sum(n20, n6) = all_0_7_7
% 31.95/10.39 |
% 31.95/10.39 | From (1095) and (8432) follows:
% 31.95/10.39 | (8541) sum(n4, n1) = all_0_4_4
% 31.95/10.39 |
% 31.95/10.39 | Instantiating formula (194) with n20, n6, all_0_7_7, n5 and discharging atoms sum(n20, n6) = all_0_7_7, sum(n20, n6) = n5, yields:
% 31.95/10.39 | (993) all_0_7_7 = n5
% 31.95/10.39 |
% 31.95/10.39 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 31.95/10.39 | (1099) all_0_2_2 = n0
% 31.95/10.39 |
% 31.95/10.39 | Instantiating formula (194) with n4, n1, all_0_4_4, n5 and discharging atoms sum(n4, n1) = all_0_4_4, sum(n4, n1) = n5, yields:
% 31.95/10.39 | (991) all_0_4_4 = n5
% 31.95/10.39 |
% 31.95/10.39 | From (1099) and (8436) follows:
% 31.95/10.39 | (8545) sum(n0, n10) = all_0_0_0
% 31.95/10.39 |
% 31.95/10.39 | From (993)(991) and (435) follows:
% 31.95/10.39 | (995) sum(n5, n5) = all_0_3_3
% 31.95/10.39 |
% 31.95/10.39 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 31.95/10.39 | (997) all_0_3_3 = n10
% 31.95/10.39 |
% 31.95/10.39 | Instantiating formula (194) with n0, n10, all_0_0_0, n10 and discharging atoms sum(n0, n10) = all_0_0_0, sum(n0, n10) = n10, yields:
% 31.95/10.39 | (996) all_0_0_0 = n10
% 31.95/10.39 |
% 31.95/10.39 | Equations (996,997) can reduce 201 to:
% 31.95/10.39 | (746) $false
% 31.95/10.39 |
% 31.95/10.39 |-The branch is then unsatisfiable
% 31.95/10.39 |-Branch two:
% 31.95/10.39 | (1388) ~ (all_0_10_10 = n5)
% 31.95/10.39 | (1389) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.95/10.39 |
% 31.95/10.39 +-Applying beta-rule and splitting (1000), into two cases.
% 31.95/10.39 |-Branch one:
% 31.95/10.39 | (1001) all_0_11_11 = n5
% 31.95/10.39 |
% 31.95/10.39 | From (1001) and (190) follows:
% 31.95/10.39 | (1002) pred(n5) = all_0_9_9
% 31.95/10.39 |
% 31.95/10.39 | From (1001) and (505) follows:
% 31.95/10.39 | (1003) succ(n5) = all_0_5_5
% 31.95/10.39 |
% 31.95/10.39 | Instantiating formula (259) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 31.95/10.39 | (1004) all_0_9_9 = n4
% 31.95/10.39 |
% 31.95/10.39 | Instantiating formula (184) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 31.95/10.39 | (1005) all_0_5_5 = n6
% 31.95/10.39 |
% 31.95/10.39 | From (1005) and (386) follows:
% 31.95/10.39 | (8557) sum(all_0_6_6, n6) = all_0_4_4
% 31.95/10.39 |
% 31.95/10.39 | From (1004)(1005) and (156) follows:
% 31.95/10.39 | (1006) sum(n4, n6) = all_0_2_2
% 31.95/10.39 |
% 31.95/10.39 | From (1004) and (74) follows:
% 31.95/10.39 | (8559) sum(n4, all_0_8_8) = all_0_7_7
% 31.95/10.39 |
% 31.95/10.39 | Instantiating formula (194) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 31.95/10.39 | (1010) all_0_2_2 = n10
% 31.95/10.39 |
% 31.95/10.39 | From (1010) and (85) follows:
% 31.95/10.39 | (8561) sum(n10, all_0_1_1) = all_0_0_0
% 31.95/10.39 |
% 31.95/10.39 +-Applying beta-rule and splitting (1389), into two cases.
% 31.95/10.39 |-Branch one:
% 31.95/10.39 | (1390) all_0_10_10 = n4
% 31.95/10.39 |
% 31.95/10.39 | From (1390) and (57) follows:
% 31.95/10.39 | (1391) pred(n4) = all_0_6_6
% 31.95/10.39 |
% 31.95/10.39 | From (1390) and (381) follows:
% 31.95/10.39 | (1392) succ(n4) = all_0_8_8
% 31.95/10.39 |
% 31.95/10.39 | Instantiating formula (259) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 31.95/10.39 | (1393) all_0_6_6 = n3
% 31.95/10.39 |
% 31.95/10.39 | Instantiating formula (184) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 31.95/10.39 | (1394) all_0_8_8 = n5
% 31.95/10.39 |
% 31.95/10.39 | From (1393)(1394) and (628) follows:
% 31.95/10.39 | (1395) sum(n3, n5) = all_0_1_1
% 31.95/10.39 |
% 31.95/10.39 | From (1393) and (8557) follows:
% 31.95/10.39 | (8568) sum(n3, n6) = all_0_4_4
% 31.95/10.39 |
% 31.95/10.39 | From (1394) and (8559) follows:
% 31.95/10.39 | (8569) sum(n4, n5) = all_0_7_7
% 31.95/10.39 |
% 31.95/10.39 | Instantiating formula (194) with n4, n5, all_0_7_7, n9 and discharging atoms sum(n4, n5) = all_0_7_7, sum(n4, n5) = n9, yields:
% 31.95/10.39 | (921) all_0_7_7 = n9
% 31.95/10.39 |
% 31.95/10.39 | Instantiating formula (194) with n3, n6, all_0_4_4, n9 and discharging atoms sum(n3, n6) = all_0_4_4, sum(n3, n6) = n9, yields:
% 31.95/10.39 | (919) all_0_4_4 = n9
% 31.95/10.39 |
% 31.95/10.39 | Instantiating formula (194) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 31.95/10.39 | (1399) all_0_1_1 = n8
% 31.95/10.39 |
% 31.95/10.39 | From (921)(919) and (435) follows:
% 31.95/10.39 | (923) sum(n9, n9) = all_0_3_3
% 31.95/10.39 |
% 31.95/10.39 | From (1399) and (8561) follows:
% 31.95/10.40 | (8574) sum(n10, n8) = all_0_0_0
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (194) with n10, n8, all_0_0_0, n18 and discharging atoms sum(n10, n8) = all_0_0_0, sum(n10, n8) = n18, yields:
% 31.95/10.40 | (924) all_0_0_0 = n18
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (194) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 31.95/10.40 | (925) all_0_3_3 = n18
% 31.95/10.40 |
% 31.95/10.40 | Equations (924,925) can reduce 201 to:
% 31.95/10.40 | (746) $false
% 31.95/10.40 |
% 31.95/10.40 |-The branch is then unsatisfiable
% 31.95/10.40 |-Branch two:
% 31.95/10.40 | (1406) ~ (all_0_10_10 = n4)
% 31.95/10.40 | (1407) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.95/10.40 |
% 31.95/10.40 +-Applying beta-rule and splitting (1407), into two cases.
% 31.95/10.40 |-Branch one:
% 31.95/10.40 | (1408) all_0_10_10 = n3
% 31.95/10.40 |
% 31.95/10.40 | From (1408) and (57) follows:
% 31.95/10.40 | (1409) pred(n3) = all_0_6_6
% 31.95/10.40 |
% 31.95/10.40 | From (1408) and (381) follows:
% 31.95/10.40 | (1410) succ(n3) = all_0_8_8
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 31.95/10.40 | (1411) all_0_6_6 = n2
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 31.95/10.40 | (1412) all_0_8_8 = n4
% 31.95/10.40 |
% 31.95/10.40 | From (1411)(1412) and (628) follows:
% 31.95/10.40 | (1413) sum(n2, n4) = all_0_1_1
% 31.95/10.40 |
% 31.95/10.40 | From (1411) and (8557) follows:
% 31.95/10.40 | (8586) sum(n2, n6) = all_0_4_4
% 31.95/10.40 |
% 31.95/10.40 | From (1412) and (8559) follows:
% 31.95/10.40 | (8587) sum(n4, n4) = all_0_7_7
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (194) with n4, n4, all_0_7_7, n8 and discharging atoms sum(n4, n4) = all_0_7_7, sum(n4, n4) = n8, yields:
% 31.95/10.40 | (939) all_0_7_7 = n8
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (194) with n2, n6, all_0_4_4, n8 and discharging atoms sum(n2, n6) = all_0_4_4, sum(n2, n6) = n8, yields:
% 31.95/10.40 | (937) all_0_4_4 = n8
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 31.95/10.40 | (1417) all_0_1_1 = n6
% 31.95/10.40 |
% 31.95/10.40 | From (939)(937) and (435) follows:
% 31.95/10.40 | (941) sum(n8, n8) = all_0_3_3
% 31.95/10.40 |
% 31.95/10.40 | From (1417) and (8561) follows:
% 31.95/10.40 | (8592) sum(n10, n6) = all_0_0_0
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (194) with n10, n6, all_0_0_0, n16 and discharging atoms sum(n10, n6) = all_0_0_0, sum(n10, n6) = n16, yields:
% 31.95/10.40 | (942) all_0_0_0 = n16
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (194) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 31.95/10.40 | (943) all_0_3_3 = n16
% 31.95/10.40 |
% 31.95/10.40 | Equations (942,943) can reduce 201 to:
% 31.95/10.40 | (746) $false
% 31.95/10.40 |
% 31.95/10.40 |-The branch is then unsatisfiable
% 31.95/10.40 |-Branch two:
% 31.95/10.40 | (1424) ~ (all_0_10_10 = n3)
% 31.95/10.40 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.95/10.40 |
% 31.95/10.40 +-Applying beta-rule and splitting (1425), into two cases.
% 31.95/10.40 |-Branch one:
% 31.95/10.40 | (1426) all_0_10_10 = n2
% 31.95/10.40 |
% 31.95/10.40 | From (1426) and (57) follows:
% 31.95/10.40 | (1427) pred(n2) = all_0_6_6
% 31.95/10.40 |
% 31.95/10.40 | From (1426) and (381) follows:
% 31.95/10.40 | (1428) succ(n2) = all_0_8_8
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 31.95/10.40 | (1429) all_0_6_6 = n1
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 31.95/10.40 | (1430) all_0_8_8 = n3
% 31.95/10.40 |
% 31.95/10.40 | From (1429)(1430) and (628) follows:
% 31.95/10.40 | (1431) sum(n1, n3) = all_0_1_1
% 31.95/10.40 |
% 31.95/10.40 | From (1429) and (8557) follows:
% 31.95/10.40 | (8604) sum(n1, n6) = all_0_4_4
% 31.95/10.40 |
% 31.95/10.40 | From (1430) and (8559) follows:
% 31.95/10.40 | (8605) sum(n4, n3) = all_0_7_7
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (194) with n4, n3, all_0_7_7, n7 and discharging atoms sum(n4, n3) = all_0_7_7, sum(n4, n3) = n7, yields:
% 31.95/10.40 | (957) all_0_7_7 = n7
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (194) with n1, n6, all_0_4_4, n7 and discharging atoms sum(n1, n6) = all_0_4_4, sum(n1, n6) = n7, yields:
% 31.95/10.40 | (955) all_0_4_4 = n7
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 31.95/10.40 | (1435) all_0_1_1 = n4
% 31.95/10.40 |
% 31.95/10.40 | From (957)(955) and (435) follows:
% 31.95/10.40 | (959) sum(n7, n7) = all_0_3_3
% 31.95/10.40 |
% 31.95/10.40 | From (1435) and (8561) follows:
% 31.95/10.40 | (8610) sum(n10, n4) = all_0_0_0
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (194) with n10, n4, all_0_0_0, n14 and discharging atoms sum(n10, n4) = all_0_0_0, sum(n10, n4) = n14, yields:
% 31.95/10.40 | (960) all_0_0_0 = n14
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 31.95/10.40 | (961) all_0_3_3 = n14
% 31.95/10.40 |
% 31.95/10.40 | Equations (960,961) can reduce 201 to:
% 31.95/10.40 | (746) $false
% 31.95/10.40 |
% 31.95/10.40 |-The branch is then unsatisfiable
% 31.95/10.40 |-Branch two:
% 31.95/10.40 | (1442) ~ (all_0_10_10 = n2)
% 31.95/10.40 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 31.95/10.40 |
% 31.95/10.40 +-Applying beta-rule and splitting (1443), into two cases.
% 31.95/10.40 |-Branch one:
% 31.95/10.40 | (1444) all_0_10_10 = n1
% 31.95/10.40 |
% 31.95/10.40 | From (1444) and (57) follows:
% 31.95/10.40 | (1445) pred(n1) = all_0_6_6
% 31.95/10.40 |
% 31.95/10.40 | From (1444) and (381) follows:
% 31.95/10.40 | (1446) succ(n1) = all_0_8_8
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 31.95/10.40 | (1447) all_0_6_6 = n0
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 31.95/10.40 | (1448) all_0_8_8 = n2
% 31.95/10.40 |
% 31.95/10.40 | From (1447)(1448) and (628) follows:
% 31.95/10.40 | (1449) sum(n0, n2) = all_0_1_1
% 31.95/10.40 |
% 31.95/10.40 | From (1447) and (8557) follows:
% 31.95/10.40 | (8622) sum(n0, n6) = all_0_4_4
% 31.95/10.40 |
% 31.95/10.40 | From (1448) and (8559) follows:
% 31.95/10.40 | (8623) sum(n4, n2) = all_0_7_7
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (194) with n4, n2, all_0_7_7, n6 and discharging atoms sum(n4, n2) = all_0_7_7, sum(n4, n2) = n6, yields:
% 31.95/10.40 | (975) all_0_7_7 = n6
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (194) with n0, n6, all_0_4_4, n6 and discharging atoms sum(n0, n6) = all_0_4_4, sum(n0, n6) = n6, yields:
% 31.95/10.40 | (973) all_0_4_4 = n6
% 31.95/10.40 |
% 31.95/10.40 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 31.95/10.40 | (1453) all_0_1_1 = n2
% 31.95/10.40 |
% 31.95/10.40 | From (975)(973) and (435) follows:
% 31.95/10.40 | (977) sum(n6, n6) = all_0_3_3
% 31.95/10.40 |
% 31.95/10.40 | From (1453) and (8561) follows:
% 31.95/10.41 | (8628) sum(n10, n2) = all_0_0_0
% 31.95/10.41 |
% 31.95/10.41 | Instantiating formula (194) with n10, n2, all_0_0_0, n12 and discharging atoms sum(n10, n2) = all_0_0_0, sum(n10, n2) = n12, yields:
% 31.95/10.41 | (978) all_0_0_0 = n12
% 31.95/10.41 |
% 31.95/10.41 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 31.95/10.41 | (979) all_0_3_3 = n12
% 31.95/10.41 |
% 31.95/10.41 | Equations (978,979) can reduce 201 to:
% 31.95/10.41 | (746) $false
% 31.95/10.41 |
% 31.95/10.41 |-The branch is then unsatisfiable
% 31.95/10.41 |-Branch two:
% 31.95/10.41 | (1462) ~ (all_0_10_10 = n1)
% 31.95/10.41 | (1463) all_0_10_10 = n0
% 31.95/10.41 |
% 31.95/10.41 | From (1463) and (57) follows:
% 31.95/10.41 | (1464) pred(n0) = all_0_6_6
% 31.95/10.41 |
% 31.95/10.41 | From (1463) and (381) follows:
% 31.95/10.41 | (1465) succ(n0) = all_0_8_8
% 31.95/10.41 |
% 31.95/10.41 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 31.95/10.41 | (1466) all_0_6_6 = n20
% 31.95/10.41 |
% 31.95/10.41 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 31.95/10.41 | (1467) all_0_8_8 = n1
% 31.95/10.41 |
% 31.95/10.41 | From (1466)(1467) and (628) follows:
% 31.95/10.41 | (1468) sum(n20, n1) = all_0_1_1
% 31.95/10.41 |
% 31.95/10.41 | From (1466) and (8557) follows:
% 31.95/10.41 | (8639) sum(n20, n6) = all_0_4_4
% 31.95/10.41 |
% 31.95/10.41 | From (1467) and (8559) follows:
% 31.95/10.41 | (8640) sum(n4, n1) = all_0_7_7
% 31.95/10.41 |
% 31.95/10.41 | Instantiating formula (194) with n20, n6, all_0_4_4, n5 and discharging atoms sum(n20, n6) = all_0_4_4, sum(n20, n6) = n5, yields:
% 31.95/10.41 | (991) all_0_4_4 = n5
% 31.95/10.41 |
% 31.95/10.41 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 31.95/10.41 | (1471) all_0_1_1 = n0
% 31.95/10.41 |
% 31.95/10.41 | Instantiating formula (194) with n4, n1, all_0_7_7, n5 and discharging atoms sum(n4, n1) = all_0_7_7, sum(n4, n1) = n5, yields:
% 31.95/10.41 | (993) all_0_7_7 = n5
% 31.95/10.41 |
% 31.95/10.41 | From (993)(991) and (435) follows:
% 31.95/10.41 | (995) sum(n5, n5) = all_0_3_3
% 31.95/10.41 |
% 31.95/10.41 | From (1471) and (8561) follows:
% 31.95/10.41 | (8645) sum(n10, n0) = all_0_0_0
% 31.95/10.41 |
% 31.95/10.41 | Instantiating formula (194) with n10, n0, all_0_0_0, n10 and discharging atoms sum(n10, n0) = all_0_0_0, sum(n10, n0) = n10, yields:
% 31.95/10.41 | (996) all_0_0_0 = n10
% 31.95/10.41 |
% 31.95/10.41 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 31.95/10.41 | (997) all_0_3_3 = n10
% 31.95/10.41 |
% 31.95/10.41 | Equations (996,997) can reduce 201 to:
% 31.95/10.41 | (746) $false
% 31.95/10.41 |
% 31.95/10.41 |-The branch is then unsatisfiable
% 31.95/10.41 |-Branch two:
% 31.95/10.41 | (1017) ~ (all_0_11_11 = n5)
% 31.95/10.41 | (1018) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.95/10.41 |
% 31.95/10.41 +-Applying beta-rule and splitting (1389), into two cases.
% 31.95/10.41 |-Branch one:
% 31.95/10.41 | (1390) all_0_10_10 = n4
% 31.95/10.41 |
% 31.95/10.41 | From (1390) and (57) follows:
% 31.95/10.41 | (1391) pred(n4) = all_0_6_6
% 31.95/10.41 |
% 31.95/10.41 | From (1390) and (381) follows:
% 31.95/10.41 | (1392) succ(n4) = all_0_8_8
% 31.95/10.41 |
% 31.95/10.41 | Instantiating formula (259) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 31.95/10.41 | (1393) all_0_6_6 = n3
% 31.95/10.41 |
% 31.95/10.41 | Instantiating formula (184) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 31.95/10.41 | (1394) all_0_8_8 = n5
% 31.95/10.41 |
% 31.95/10.41 | From (1393) and (1391) follows:
% 31.95/10.41 | (232) pred(n4) = n3
% 31.95/10.41 |
% 31.95/10.41 | From (1394) and (1392) follows:
% 31.95/10.41 | (410) succ(n4) = n5
% 31.95/10.41 |
% 31.95/10.41 | From (1393) and (386) follows:
% 31.95/10.41 | (8658) sum(n3, all_0_5_5) = all_0_4_4
% 31.95/10.41 |
% 31.95/10.41 | From (1393)(1394) and (628) follows:
% 31.95/10.41 | (1395) sum(n3, n5) = all_0_1_1
% 31.95/10.41 |
% 31.95/10.41 | From (1394) and (74) follows:
% 31.95/10.41 | (8660) sum(all_0_9_9, n5) = all_0_7_7
% 31.95/10.41 |
% 31.95/10.41 | Instantiating formula (194) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 31.95/10.41 | (1399) all_0_1_1 = n8
% 31.95/10.41 |
% 31.95/10.41 | From (1399) and (85) follows:
% 31.95/10.41 | (8662) sum(all_0_2_2, n8) = all_0_0_0
% 31.95/10.41 |
% 31.95/10.41 | From (1399) and (1395) follows:
% 31.95/10.41 | (605) sum(n3, n5) = n8
% 31.95/10.41 |
% 31.95/10.41 +-Applying beta-rule and splitting (1018), into two cases.
% 31.95/10.41 |-Branch one:
% 31.95/10.41 | (1019) all_0_11_11 = n4
% 31.97/10.41 |
% 31.97/10.41 | From (1019) and (190) follows:
% 31.97/10.41 | (1020) pred(n4) = all_0_9_9
% 31.97/10.41 |
% 31.97/10.41 | From (1019) and (505) follows:
% 31.97/10.41 | (1021) succ(n4) = all_0_5_5
% 31.97/10.41 |
% 31.97/10.41 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 31.97/10.41 | (1022) all_0_9_9 = n3
% 31.97/10.41 |
% 31.97/10.41 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 31.97/10.41 | (1023) all_0_5_5 = n5
% 31.97/10.41 |
% 31.97/10.41 | From (1022)(1023) and (156) follows:
% 31.97/10.41 | (1024) sum(n3, n5) = all_0_2_2
% 31.97/10.41 |
% 31.97/10.41 | From (1022) and (8660) follows:
% 31.97/10.41 | (8670) sum(n3, n5) = all_0_7_7
% 31.97/10.41 |
% 31.97/10.41 | From (1023) and (8658) follows:
% 31.97/10.41 | (8671) sum(n3, n5) = all_0_4_4
% 31.97/10.41 |
% 31.97/10.41 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 31.97/10.41 | (1028) all_0_2_2 = n8
% 31.97/10.41 |
% 31.97/10.41 | Instantiating formula (194) with n3, n5, all_0_4_4, all_0_2_2 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = all_0_4_4, yields:
% 31.97/10.41 | (733) all_0_2_2 = all_0_4_4
% 31.97/10.41 |
% 31.97/10.41 | Instantiating formula (194) with n3, n5, all_0_7_7, all_0_2_2 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = all_0_7_7, yields:
% 31.97/10.41 | (734) all_0_2_2 = all_0_7_7
% 31.97/10.41 |
% 31.97/10.41 | Combining equations (734,733) yields a new equation:
% 31.97/10.41 | (735) all_0_4_4 = all_0_7_7
% 31.97/10.41 |
% 31.97/10.41 | Combining equations (1028,733) yields a new equation:
% 31.97/10.41 | (937) all_0_4_4 = n8
% 31.97/10.41 |
% 31.97/10.41 | Combining equations (937,735) yields a new equation:
% 31.97/10.41 | (939) all_0_7_7 = n8
% 31.97/10.41 |
% 31.97/10.41 | Combining equations (939,735) yields a new equation:
% 31.97/10.41 | (937) all_0_4_4 = n8
% 31.97/10.41 |
% 31.97/10.41 | Combining equations (937,733) yields a new equation:
% 31.97/10.41 | (1028) all_0_2_2 = n8
% 31.97/10.41 |
% 31.97/10.41 | From (1028) and (8662) follows:
% 31.97/10.41 | (8680) sum(n8, n8) = all_0_0_0
% 31.97/10.41 |
% 31.97/10.41 | From (939)(937) and (435) follows:
% 31.97/10.41 | (941) sum(n8, n8) = all_0_3_3
% 31.97/10.41 |
% 31.97/10.41 | Instantiating formula (194) with n8, n8, all_0_0_0, n16 and discharging atoms sum(n8, n8) = all_0_0_0, sum(n8, n8) = n16, yields:
% 31.97/10.41 | (942) all_0_0_0 = n16
% 31.97/10.41 |
% 31.97/10.41 | Instantiating formula (194) with n8, n8, all_0_3_3, all_0_0_0 and discharging atoms sum(n8, n8) = all_0_0_0, sum(n8, n8) = all_0_3_3, yields:
% 31.97/10.41 | (743) all_0_0_0 = all_0_3_3
% 31.97/10.41 |
% 31.97/10.41 | Combining equations (942,743) yields a new equation:
% 31.97/10.41 | (943) all_0_3_3 = n16
% 31.97/10.41 |
% 31.97/10.41 | Combining equations (943,743) yields a new equation:
% 31.97/10.41 | (942) all_0_0_0 = n16
% 31.97/10.41 |
% 31.97/10.41 | Equations (942,943) can reduce 201 to:
% 31.97/10.41 | (746) $false
% 31.97/10.41 |
% 31.97/10.41 |-The branch is then unsatisfiable
% 31.97/10.41 |-Branch two:
% 31.97/10.41 | (1035) ~ (all_0_11_11 = n4)
% 31.97/10.41 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.97/10.41 |
% 31.97/10.41 +-Applying beta-rule and splitting (1036), into two cases.
% 31.97/10.41 |-Branch one:
% 31.97/10.41 | (1037) all_0_11_11 = n3
% 31.97/10.41 |
% 31.97/10.41 | From (1037) and (190) follows:
% 31.97/10.41 | (1038) pred(n3) = all_0_9_9
% 31.97/10.41 |
% 31.97/10.41 | From (1037) and (505) follows:
% 31.97/10.41 | (1039) succ(n3) = all_0_5_5
% 31.97/10.41 |
% 31.97/10.41 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 31.97/10.41 | (1040) all_0_9_9 = n2
% 31.97/10.41 |
% 31.97/10.41 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 31.97/10.41 | (1041) all_0_5_5 = n4
% 31.97/10.41 |
% 31.97/10.41 | From (1040)(1041) and (156) follows:
% 31.97/10.41 | (1042) sum(n2, n4) = all_0_2_2
% 31.97/10.41 |
% 31.97/10.41 | From (1040) and (8660) follows:
% 31.97/10.42 | (8695) sum(n2, n5) = all_0_7_7
% 31.97/10.42 |
% 31.97/10.42 | From (1041) and (8658) follows:
% 31.97/10.42 | (8696) sum(n3, n4) = all_0_4_4
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (194) with n3, n4, all_0_4_4, n7 and discharging atoms sum(n3, n4) = all_0_4_4, sum(n3, n4) = n7, yields:
% 31.97/10.42 | (955) all_0_4_4 = n7
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (194) with n2, n5, all_0_7_7, n7 and discharging atoms sum(n2, n5) = all_0_7_7, sum(n2, n5) = n7, yields:
% 31.97/10.42 | (957) all_0_7_7 = n7
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 31.97/10.42 | (1046) all_0_2_2 = n6
% 31.97/10.42 |
% 31.97/10.42 | From (1046) and (8662) follows:
% 31.97/10.42 | (8700) sum(n6, n8) = all_0_0_0
% 31.97/10.42 |
% 31.97/10.42 | From (957)(955) and (435) follows:
% 31.97/10.42 | (959) sum(n7, n7) = all_0_3_3
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 31.97/10.42 | (961) all_0_3_3 = n14
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (194) with n6, n8, all_0_0_0, n14 and discharging atoms sum(n6, n8) = all_0_0_0, sum(n6, n8) = n14, yields:
% 31.97/10.42 | (960) all_0_0_0 = n14
% 31.97/10.42 |
% 31.97/10.42 | Equations (960,961) can reduce 201 to:
% 31.97/10.42 | (746) $false
% 31.97/10.42 |
% 31.97/10.42 |-The branch is then unsatisfiable
% 31.97/10.42 |-Branch two:
% 31.97/10.42 | (1053) ~ (all_0_11_11 = n3)
% 31.97/10.42 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.97/10.42 |
% 31.97/10.42 +-Applying beta-rule and splitting (1054), into two cases.
% 31.97/10.42 |-Branch one:
% 31.97/10.42 | (1055) all_0_11_11 = n2
% 31.97/10.42 |
% 31.97/10.42 | From (1055) and (190) follows:
% 31.97/10.42 | (1056) pred(n2) = all_0_9_9
% 31.97/10.42 |
% 31.97/10.42 | From (1055) and (505) follows:
% 31.97/10.42 | (1057) succ(n2) = all_0_5_5
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 31.97/10.42 | (1058) all_0_9_9 = n1
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.97/10.42 | (1059) all_0_5_5 = n3
% 31.97/10.42 |
% 31.97/10.42 | From (1058)(1059) and (156) follows:
% 31.97/10.42 | (1060) sum(n1, n3) = all_0_2_2
% 31.97/10.42 |
% 31.97/10.42 | From (1058) and (8660) follows:
% 31.97/10.42 | (8713) sum(n1, n5) = all_0_7_7
% 31.97/10.42 |
% 31.97/10.42 | From (1059) and (8658) follows:
% 31.97/10.42 | (8714) sum(n3, n3) = all_0_4_4
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (194) with n3, n3, all_0_4_4, n6 and discharging atoms sum(n3, n3) = all_0_4_4, sum(n3, n3) = n6, yields:
% 31.97/10.42 | (973) all_0_4_4 = n6
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (194) with n1, n5, all_0_7_7, n6 and discharging atoms sum(n1, n5) = all_0_7_7, sum(n1, n5) = n6, yields:
% 31.97/10.42 | (975) all_0_7_7 = n6
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 31.97/10.42 | (1064) all_0_2_2 = n4
% 31.97/10.42 |
% 31.97/10.42 | From (1064) and (8662) follows:
% 31.97/10.42 | (8718) sum(n4, n8) = all_0_0_0
% 31.97/10.42 |
% 31.97/10.42 | From (975)(973) and (435) follows:
% 31.97/10.42 | (977) sum(n6, n6) = all_0_3_3
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 31.97/10.42 | (979) all_0_3_3 = n12
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (194) with n4, n8, all_0_0_0, n12 and discharging atoms sum(n4, n8) = all_0_0_0, sum(n4, n8) = n12, yields:
% 31.97/10.42 | (978) all_0_0_0 = n12
% 31.97/10.42 |
% 31.97/10.42 | Equations (978,979) can reduce 201 to:
% 31.97/10.42 | (746) $false
% 31.97/10.42 |
% 31.97/10.42 |-The branch is then unsatisfiable
% 31.97/10.42 |-Branch two:
% 31.97/10.42 | (1071) ~ (all_0_11_11 = n2)
% 31.97/10.42 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 31.97/10.42 |
% 31.97/10.42 +-Applying beta-rule and splitting (1072), into two cases.
% 31.97/10.42 |-Branch one:
% 31.97/10.42 | (1073) all_0_11_11 = n1
% 31.97/10.42 |
% 31.97/10.42 | From (1073) and (190) follows:
% 31.97/10.42 | (1074) pred(n1) = all_0_9_9
% 31.97/10.42 |
% 31.97/10.42 | From (1073) and (505) follows:
% 31.97/10.42 | (1075) succ(n1) = all_0_5_5
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 31.97/10.42 | (1076) all_0_9_9 = n0
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.97/10.42 | (1077) all_0_5_5 = n2
% 31.97/10.42 |
% 31.97/10.42 | From (1076)(1077) and (156) follows:
% 31.97/10.42 | (1078) sum(n0, n2) = all_0_2_2
% 31.97/10.42 |
% 31.97/10.42 | From (1076) and (8660) follows:
% 31.97/10.42 | (8731) sum(n0, n5) = all_0_7_7
% 31.97/10.42 |
% 31.97/10.42 | From (1077) and (8658) follows:
% 31.97/10.42 | (8732) sum(n3, n2) = all_0_4_4
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (194) with n3, n2, all_0_4_4, n5 and discharging atoms sum(n3, n2) = all_0_4_4, sum(n3, n2) = n5, yields:
% 31.97/10.42 | (991) all_0_4_4 = n5
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (194) with n0, n5, all_0_7_7, n5 and discharging atoms sum(n0, n5) = all_0_7_7, sum(n0, n5) = n5, yields:
% 31.97/10.42 | (993) all_0_7_7 = n5
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 31.97/10.42 | (1082) all_0_2_2 = n2
% 31.97/10.42 |
% 31.97/10.42 | From (1082) and (8662) follows:
% 31.97/10.42 | (8736) sum(n2, n8) = all_0_0_0
% 31.97/10.42 |
% 31.97/10.42 | From (993)(991) and (435) follows:
% 31.97/10.42 | (995) sum(n5, n5) = all_0_3_3
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 31.97/10.42 | (997) all_0_3_3 = n10
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (194) with n2, n8, all_0_0_0, n10 and discharging atoms sum(n2, n8) = all_0_0_0, sum(n2, n8) = n10, yields:
% 31.97/10.42 | (996) all_0_0_0 = n10
% 31.97/10.42 |
% 31.97/10.42 | Equations (996,997) can reduce 201 to:
% 31.97/10.42 | (746) $false
% 31.97/10.42 |
% 31.97/10.42 |-The branch is then unsatisfiable
% 31.97/10.42 |-Branch two:
% 31.97/10.42 | (1090) ~ (all_0_11_11 = n1)
% 31.97/10.42 | (1091) all_0_11_11 = n0
% 31.97/10.42 |
% 31.97/10.42 | From (1091) and (190) follows:
% 31.97/10.42 | (1092) pred(n0) = all_0_9_9
% 31.97/10.42 |
% 31.97/10.42 | From (1091) and (505) follows:
% 31.97/10.42 | (1093) succ(n0) = all_0_5_5
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 31.97/10.42 | (1094) all_0_9_9 = n20
% 31.97/10.42 |
% 31.97/10.42 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.97/10.42 | (1095) all_0_5_5 = n1
% 31.97/10.42 |
% 31.97/10.42 | From (1094)(1095) and (156) follows:
% 31.97/10.42 | (1096) sum(n20, n1) = all_0_2_2
% 31.97/10.42 |
% 31.97/10.42 | From (1094) and (8660) follows:
% 31.97/10.43 | (8748) sum(n20, n5) = all_0_7_7
% 31.97/10.43 |
% 31.97/10.43 | From (1095) and (8658) follows:
% 31.97/10.43 | (8749) sum(n3, n1) = all_0_4_4
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (194) with n20, n5, all_0_7_7, n4 and discharging atoms sum(n20, n5) = all_0_7_7, sum(n20, n5) = n4, yields:
% 31.97/10.43 | (1011) all_0_7_7 = n4
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 31.97/10.43 | (1099) all_0_2_2 = n0
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (194) with n3, n1, all_0_4_4, n4 and discharging atoms sum(n3, n1) = all_0_4_4, sum(n3, n1) = n4, yields:
% 31.97/10.43 | (1009) all_0_4_4 = n4
% 31.97/10.43 |
% 31.97/10.43 | From (1099) and (8662) follows:
% 31.97/10.43 | (8753) sum(n0, n8) = all_0_0_0
% 31.97/10.43 |
% 31.97/10.43 | From (1011)(1009) and (435) follows:
% 31.97/10.43 | (1013) sum(n4, n4) = all_0_3_3
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 31.97/10.43 | (1015) all_0_3_3 = n8
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (194) with n0, n8, all_0_0_0, n8 and discharging atoms sum(n0, n8) = all_0_0_0, sum(n0, n8) = n8, yields:
% 31.97/10.43 | (1014) all_0_0_0 = n8
% 31.97/10.43 |
% 31.97/10.43 | Equations (1014,1015) can reduce 201 to:
% 31.97/10.43 | (746) $false
% 31.97/10.43 |
% 31.97/10.43 |-The branch is then unsatisfiable
% 31.97/10.43 |-Branch two:
% 31.97/10.43 | (1406) ~ (all_0_10_10 = n4)
% 31.97/10.43 | (1407) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.97/10.43 |
% 31.97/10.43 +-Applying beta-rule and splitting (1018), into two cases.
% 31.97/10.43 |-Branch one:
% 31.97/10.43 | (1019) all_0_11_11 = n4
% 31.97/10.43 |
% 31.97/10.43 | From (1019) and (190) follows:
% 31.97/10.43 | (1020) pred(n4) = all_0_9_9
% 31.97/10.43 |
% 31.97/10.43 | From (1019) and (505) follows:
% 31.97/10.43 | (1021) succ(n4) = all_0_5_5
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (259) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 31.97/10.43 | (1022) all_0_9_9 = n3
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (184) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 31.97/10.43 | (1023) all_0_5_5 = n5
% 31.97/10.43 |
% 31.97/10.43 | From (1023) and (386) follows:
% 31.97/10.43 | (8765) sum(all_0_6_6, n5) = all_0_4_4
% 31.97/10.43 |
% 31.97/10.43 | From (1022)(1023) and (156) follows:
% 31.97/10.43 | (1024) sum(n3, n5) = all_0_2_2
% 31.97/10.43 |
% 31.97/10.43 | From (1022) and (74) follows:
% 31.97/10.43 | (8767) sum(n3, all_0_8_8) = all_0_7_7
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (194) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 31.97/10.43 | (1028) all_0_2_2 = n8
% 31.97/10.43 |
% 31.97/10.43 | From (1028) and (85) follows:
% 31.97/10.43 | (8769) sum(n8, all_0_1_1) = all_0_0_0
% 31.97/10.43 |
% 31.97/10.43 +-Applying beta-rule and splitting (1407), into two cases.
% 31.97/10.43 |-Branch one:
% 31.97/10.43 | (1408) all_0_10_10 = n3
% 31.97/10.43 |
% 31.97/10.43 | From (1408) and (57) follows:
% 31.97/10.43 | (1409) pred(n3) = all_0_6_6
% 31.97/10.43 |
% 31.97/10.43 | From (1408) and (381) follows:
% 31.97/10.43 | (1410) succ(n3) = all_0_8_8
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 31.97/10.43 | (1411) all_0_6_6 = n2
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 31.97/10.43 | (1412) all_0_8_8 = n4
% 31.97/10.43 |
% 31.97/10.43 | From (1411)(1412) and (628) follows:
% 31.97/10.43 | (1413) sum(n2, n4) = all_0_1_1
% 31.97/10.43 |
% 31.97/10.43 | From (1411) and (8765) follows:
% 31.97/10.43 | (8776) sum(n2, n5) = all_0_4_4
% 31.97/10.43 |
% 31.97/10.43 | From (1412) and (8767) follows:
% 31.97/10.43 | (8777) sum(n3, n4) = all_0_7_7
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (194) with n3, n4, all_0_7_7, n7 and discharging atoms sum(n3, n4) = all_0_7_7, sum(n3, n4) = n7, yields:
% 31.97/10.43 | (957) all_0_7_7 = n7
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (194) with n2, n5, all_0_4_4, n7 and discharging atoms sum(n2, n5) = all_0_4_4, sum(n2, n5) = n7, yields:
% 31.97/10.43 | (955) all_0_4_4 = n7
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 31.97/10.43 | (1417) all_0_1_1 = n6
% 31.97/10.43 |
% 31.97/10.43 | From (957)(955) and (435) follows:
% 31.97/10.43 | (959) sum(n7, n7) = all_0_3_3
% 31.97/10.43 |
% 31.97/10.43 | From (1417) and (8769) follows:
% 31.97/10.43 | (8782) sum(n8, n6) = all_0_0_0
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (194) with n8, n6, all_0_0_0, n14 and discharging atoms sum(n8, n6) = all_0_0_0, sum(n8, n6) = n14, yields:
% 31.97/10.43 | (960) all_0_0_0 = n14
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (194) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 31.97/10.43 | (961) all_0_3_3 = n14
% 31.97/10.43 |
% 31.97/10.43 | Equations (960,961) can reduce 201 to:
% 31.97/10.43 | (746) $false
% 31.97/10.43 |
% 31.97/10.43 |-The branch is then unsatisfiable
% 31.97/10.43 |-Branch two:
% 31.97/10.43 | (1424) ~ (all_0_10_10 = n3)
% 31.97/10.43 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.97/10.43 |
% 31.97/10.43 +-Applying beta-rule and splitting (1425), into two cases.
% 31.97/10.43 |-Branch one:
% 31.97/10.43 | (1426) all_0_10_10 = n2
% 31.97/10.43 |
% 31.97/10.43 | From (1426) and (57) follows:
% 31.97/10.43 | (1427) pred(n2) = all_0_6_6
% 31.97/10.43 |
% 31.97/10.43 | From (1426) and (381) follows:
% 31.97/10.43 | (1428) succ(n2) = all_0_8_8
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 31.97/10.43 | (1429) all_0_6_6 = n1
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 31.97/10.43 | (1430) all_0_8_8 = n3
% 31.97/10.43 |
% 31.97/10.43 | From (1429)(1430) and (628) follows:
% 31.97/10.43 | (1431) sum(n1, n3) = all_0_1_1
% 31.97/10.43 |
% 31.97/10.43 | From (1429) and (8765) follows:
% 31.97/10.43 | (8794) sum(n1, n5) = all_0_4_4
% 31.97/10.43 |
% 31.97/10.43 | From (1430) and (8767) follows:
% 31.97/10.43 | (8795) sum(n3, n3) = all_0_7_7
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (194) with n3, n3, all_0_7_7, n6 and discharging atoms sum(n3, n3) = all_0_7_7, sum(n3, n3) = n6, yields:
% 31.97/10.43 | (975) all_0_7_7 = n6
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (194) with n1, n5, all_0_4_4, n6 and discharging atoms sum(n1, n5) = all_0_4_4, sum(n1, n5) = n6, yields:
% 31.97/10.43 | (973) all_0_4_4 = n6
% 31.97/10.43 |
% 31.97/10.43 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 31.97/10.43 | (1435) all_0_1_1 = n4
% 31.97/10.43 |
% 31.97/10.43 | From (975)(973) and (435) follows:
% 31.97/10.43 | (977) sum(n6, n6) = all_0_3_3
% 31.97/10.43 |
% 31.97/10.43 | From (1435) and (8769) follows:
% 31.97/10.44 | (8800) sum(n8, n4) = all_0_0_0
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (194) with n8, n4, all_0_0_0, n12 and discharging atoms sum(n8, n4) = all_0_0_0, sum(n8, n4) = n12, yields:
% 31.97/10.44 | (978) all_0_0_0 = n12
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (194) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 31.97/10.44 | (979) all_0_3_3 = n12
% 31.97/10.44 |
% 31.97/10.44 | Equations (978,979) can reduce 201 to:
% 31.97/10.44 | (746) $false
% 31.97/10.44 |
% 31.97/10.44 |-The branch is then unsatisfiable
% 31.97/10.44 |-Branch two:
% 31.97/10.44 | (1442) ~ (all_0_10_10 = n2)
% 31.97/10.44 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 31.97/10.44 |
% 31.97/10.44 +-Applying beta-rule and splitting (1443), into two cases.
% 31.97/10.44 |-Branch one:
% 31.97/10.44 | (1444) all_0_10_10 = n1
% 31.97/10.44 |
% 31.97/10.44 | From (1444) and (57) follows:
% 31.97/10.44 | (1445) pred(n1) = all_0_6_6
% 31.97/10.44 |
% 31.97/10.44 | From (1444) and (381) follows:
% 31.97/10.44 | (1446) succ(n1) = all_0_8_8
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 31.97/10.44 | (1447) all_0_6_6 = n0
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 31.97/10.44 | (1448) all_0_8_8 = n2
% 31.97/10.44 |
% 31.97/10.44 | From (1447)(1448) and (628) follows:
% 31.97/10.44 | (1449) sum(n0, n2) = all_0_1_1
% 31.97/10.44 |
% 31.97/10.44 | From (1447) and (8765) follows:
% 31.97/10.44 | (8812) sum(n0, n5) = all_0_4_4
% 31.97/10.44 |
% 31.97/10.44 | From (1448) and (8767) follows:
% 31.97/10.44 | (8813) sum(n3, n2) = all_0_7_7
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (194) with n3, n2, all_0_7_7, n5 and discharging atoms sum(n3, n2) = all_0_7_7, sum(n3, n2) = n5, yields:
% 31.97/10.44 | (993) all_0_7_7 = n5
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (194) with n0, n5, all_0_4_4, n5 and discharging atoms sum(n0, n5) = all_0_4_4, sum(n0, n5) = n5, yields:
% 31.97/10.44 | (991) all_0_4_4 = n5
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 31.97/10.44 | (1453) all_0_1_1 = n2
% 31.97/10.44 |
% 31.97/10.44 | From (993)(991) and (435) follows:
% 31.97/10.44 | (995) sum(n5, n5) = all_0_3_3
% 31.97/10.44 |
% 31.97/10.44 | From (1453) and (8769) follows:
% 31.97/10.44 | (8818) sum(n8, n2) = all_0_0_0
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (194) with n8, n2, all_0_0_0, n10 and discharging atoms sum(n8, n2) = all_0_0_0, sum(n8, n2) = n10, yields:
% 31.97/10.44 | (996) all_0_0_0 = n10
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 31.97/10.44 | (997) all_0_3_3 = n10
% 31.97/10.44 |
% 31.97/10.44 | Equations (996,997) can reduce 201 to:
% 31.97/10.44 | (746) $false
% 31.97/10.44 |
% 31.97/10.44 |-The branch is then unsatisfiable
% 31.97/10.44 |-Branch two:
% 31.97/10.44 | (1462) ~ (all_0_10_10 = n1)
% 31.97/10.44 | (1463) all_0_10_10 = n0
% 31.97/10.44 |
% 31.97/10.44 | From (1463) and (57) follows:
% 31.97/10.44 | (1464) pred(n0) = all_0_6_6
% 31.97/10.44 |
% 31.97/10.44 | From (1463) and (381) follows:
% 31.97/10.44 | (1465) succ(n0) = all_0_8_8
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 31.97/10.44 | (1466) all_0_6_6 = n20
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 31.97/10.44 | (1467) all_0_8_8 = n1
% 31.97/10.44 |
% 31.97/10.44 | From (1466)(1467) and (628) follows:
% 31.97/10.44 | (1468) sum(n20, n1) = all_0_1_1
% 31.97/10.44 |
% 31.97/10.44 | From (1466) and (8765) follows:
% 31.97/10.44 | (8829) sum(n20, n5) = all_0_4_4
% 31.97/10.44 |
% 31.97/10.44 | From (1467) and (8767) follows:
% 31.97/10.44 | (8830) sum(n3, n1) = all_0_7_7
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (194) with n20, n5, all_0_4_4, n4 and discharging atoms sum(n20, n5) = all_0_4_4, sum(n20, n5) = n4, yields:
% 31.97/10.44 | (1009) all_0_4_4 = n4
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 31.97/10.44 | (1471) all_0_1_1 = n0
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (194) with n3, n1, all_0_7_7, n4 and discharging atoms sum(n3, n1) = all_0_7_7, sum(n3, n1) = n4, yields:
% 31.97/10.44 | (1011) all_0_7_7 = n4
% 31.97/10.44 |
% 31.97/10.44 | From (1011)(1009) and (435) follows:
% 31.97/10.44 | (1013) sum(n4, n4) = all_0_3_3
% 31.97/10.44 |
% 31.97/10.44 | From (1471) and (8769) follows:
% 31.97/10.44 | (8835) sum(n8, n0) = all_0_0_0
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (194) with n8, n0, all_0_0_0, n8 and discharging atoms sum(n8, n0) = all_0_0_0, sum(n8, n0) = n8, yields:
% 31.97/10.44 | (1014) all_0_0_0 = n8
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 31.97/10.44 | (1015) all_0_3_3 = n8
% 31.97/10.44 |
% 31.97/10.44 | Equations (1014,1015) can reduce 201 to:
% 31.97/10.44 | (746) $false
% 31.97/10.44 |
% 31.97/10.44 |-The branch is then unsatisfiable
% 31.97/10.44 |-Branch two:
% 31.97/10.44 | (1035) ~ (all_0_11_11 = n4)
% 31.97/10.44 | (1036) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.97/10.44 |
% 31.97/10.44 +-Applying beta-rule and splitting (1407), into two cases.
% 31.97/10.44 |-Branch one:
% 31.97/10.44 | (1408) all_0_10_10 = n3
% 31.97/10.44 |
% 31.97/10.44 | From (1408) and (57) follows:
% 31.97/10.44 | (1409) pred(n3) = all_0_6_6
% 31.97/10.44 |
% 31.97/10.44 | From (1408) and (381) follows:
% 31.97/10.44 | (1410) succ(n3) = all_0_8_8
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (259) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 31.97/10.44 | (1411) all_0_6_6 = n2
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (184) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 31.97/10.44 | (1412) all_0_8_8 = n4
% 31.97/10.44 |
% 31.97/10.44 | From (1411) and (1409) follows:
% 31.97/10.44 | (438) pred(n3) = n2
% 31.97/10.44 |
% 31.97/10.44 | From (1412) and (1410) follows:
% 31.97/10.44 | (306) succ(n3) = n4
% 31.97/10.44 |
% 31.97/10.44 | From (1411) and (386) follows:
% 31.97/10.44 | (8848) sum(n2, all_0_5_5) = all_0_4_4
% 31.97/10.44 |
% 31.97/10.44 | From (1411)(1412) and (628) follows:
% 31.97/10.44 | (1413) sum(n2, n4) = all_0_1_1
% 31.97/10.44 |
% 31.97/10.44 | From (1412) and (74) follows:
% 31.97/10.44 | (8850) sum(all_0_9_9, n4) = all_0_7_7
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (194) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 31.97/10.44 | (1417) all_0_1_1 = n6
% 31.97/10.44 |
% 31.97/10.44 | From (1417) and (85) follows:
% 31.97/10.44 | (8852) sum(all_0_2_2, n6) = all_0_0_0
% 31.97/10.44 |
% 31.97/10.44 | From (1417) and (1413) follows:
% 31.97/10.44 | (26) sum(n2, n4) = n6
% 31.97/10.44 |
% 31.97/10.44 +-Applying beta-rule and splitting (1036), into two cases.
% 31.97/10.44 |-Branch one:
% 31.97/10.44 | (1037) all_0_11_11 = n3
% 31.97/10.44 |
% 31.97/10.44 | From (1037) and (190) follows:
% 31.97/10.44 | (1038) pred(n3) = all_0_9_9
% 31.97/10.44 |
% 31.97/10.44 | From (1037) and (505) follows:
% 31.97/10.44 | (1039) succ(n3) = all_0_5_5
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 31.97/10.44 | (1040) all_0_9_9 = n2
% 31.97/10.44 |
% 31.97/10.44 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 31.97/10.44 | (1041) all_0_5_5 = n4
% 31.97/10.44 |
% 31.97/10.44 | From (1040)(1041) and (156) follows:
% 31.97/10.44 | (1042) sum(n2, n4) = all_0_2_2
% 31.97/10.44 |
% 31.97/10.44 | From (1040) and (8850) follows:
% 31.97/10.44 | (8860) sum(n2, n4) = all_0_7_7
% 31.97/10.44 |
% 31.97/10.44 | From (1041) and (8848) follows:
% 31.97/10.45 | (8861) sum(n2, n4) = all_0_4_4
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 31.97/10.45 | (1046) all_0_2_2 = n6
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n2, n4, all_0_4_4, all_0_2_2 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = all_0_4_4, yields:
% 31.97/10.45 | (733) all_0_2_2 = all_0_4_4
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n2, n4, all_0_7_7, all_0_2_2 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = all_0_7_7, yields:
% 31.97/10.45 | (734) all_0_2_2 = all_0_7_7
% 31.97/10.45 |
% 31.97/10.45 | Combining equations (734,733) yields a new equation:
% 31.97/10.45 | (735) all_0_4_4 = all_0_7_7
% 31.97/10.45 |
% 31.97/10.45 | Combining equations (1046,733) yields a new equation:
% 31.97/10.45 | (973) all_0_4_4 = n6
% 31.97/10.45 |
% 31.97/10.45 | Combining equations (973,735) yields a new equation:
% 31.97/10.45 | (975) all_0_7_7 = n6
% 31.97/10.45 |
% 31.97/10.45 | Combining equations (975,735) yields a new equation:
% 31.97/10.45 | (973) all_0_4_4 = n6
% 31.97/10.45 |
% 31.97/10.45 | Combining equations (973,733) yields a new equation:
% 31.97/10.45 | (1046) all_0_2_2 = n6
% 31.97/10.45 |
% 31.97/10.45 | From (1046) and (8852) follows:
% 31.97/10.45 | (8870) sum(n6, n6) = all_0_0_0
% 31.97/10.45 |
% 31.97/10.45 | From (975)(973) and (435) follows:
% 31.97/10.45 | (977) sum(n6, n6) = all_0_3_3
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n6, n6, all_0_0_0, n12 and discharging atoms sum(n6, n6) = all_0_0_0, sum(n6, n6) = n12, yields:
% 31.97/10.45 | (978) all_0_0_0 = n12
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n6, n6, all_0_3_3, all_0_0_0 and discharging atoms sum(n6, n6) = all_0_0_0, sum(n6, n6) = all_0_3_3, yields:
% 31.97/10.45 | (743) all_0_0_0 = all_0_3_3
% 31.97/10.45 |
% 31.97/10.45 | Combining equations (978,743) yields a new equation:
% 31.97/10.45 | (979) all_0_3_3 = n12
% 31.97/10.45 |
% 31.97/10.45 | Combining equations (979,743) yields a new equation:
% 31.97/10.45 | (978) all_0_0_0 = n12
% 31.97/10.45 |
% 31.97/10.45 | Equations (978,979) can reduce 201 to:
% 31.97/10.45 | (746) $false
% 31.97/10.45 |
% 31.97/10.45 |-The branch is then unsatisfiable
% 31.97/10.45 |-Branch two:
% 31.97/10.45 | (1053) ~ (all_0_11_11 = n3)
% 31.97/10.45 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.97/10.45 |
% 31.97/10.45 +-Applying beta-rule and splitting (1054), into two cases.
% 31.97/10.45 |-Branch one:
% 31.97/10.45 | (1055) all_0_11_11 = n2
% 31.97/10.45 |
% 31.97/10.45 | From (1055) and (190) follows:
% 31.97/10.45 | (1056) pred(n2) = all_0_9_9
% 31.97/10.45 |
% 31.97/10.45 | From (1055) and (505) follows:
% 31.97/10.45 | (1057) succ(n2) = all_0_5_5
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 31.97/10.45 | (1058) all_0_9_9 = n1
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.97/10.45 | (1059) all_0_5_5 = n3
% 31.97/10.45 |
% 31.97/10.45 | From (1058)(1059) and (156) follows:
% 31.97/10.45 | (1060) sum(n1, n3) = all_0_2_2
% 31.97/10.45 |
% 31.97/10.45 | From (1058) and (8850) follows:
% 31.97/10.45 | (8885) sum(n1, n4) = all_0_7_7
% 31.97/10.45 |
% 31.97/10.45 | From (1059) and (8848) follows:
% 31.97/10.45 | (8886) sum(n2, n3) = all_0_4_4
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n2, n3, all_0_4_4, n5 and discharging atoms sum(n2, n3) = all_0_4_4, sum(n2, n3) = n5, yields:
% 31.97/10.45 | (991) all_0_4_4 = n5
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n1, n4, all_0_7_7, n5 and discharging atoms sum(n1, n4) = all_0_7_7, sum(n1, n4) = n5, yields:
% 31.97/10.45 | (993) all_0_7_7 = n5
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 31.97/10.45 | (1064) all_0_2_2 = n4
% 31.97/10.45 |
% 31.97/10.45 | From (1064) and (8852) follows:
% 31.97/10.45 | (8890) sum(n4, n6) = all_0_0_0
% 31.97/10.45 |
% 31.97/10.45 | From (993)(991) and (435) follows:
% 31.97/10.45 | (995) sum(n5, n5) = all_0_3_3
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 31.97/10.45 | (997) all_0_3_3 = n10
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n4, n6, all_0_0_0, n10 and discharging atoms sum(n4, n6) = all_0_0_0, sum(n4, n6) = n10, yields:
% 31.97/10.45 | (996) all_0_0_0 = n10
% 31.97/10.45 |
% 31.97/10.45 | Equations (996,997) can reduce 201 to:
% 31.97/10.45 | (746) $false
% 31.97/10.45 |
% 31.97/10.45 |-The branch is then unsatisfiable
% 31.97/10.45 |-Branch two:
% 31.97/10.45 | (1071) ~ (all_0_11_11 = n2)
% 31.97/10.45 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 31.97/10.45 |
% 31.97/10.45 +-Applying beta-rule and splitting (1072), into two cases.
% 31.97/10.45 |-Branch one:
% 31.97/10.45 | (1073) all_0_11_11 = n1
% 31.97/10.45 |
% 31.97/10.45 | From (1073) and (190) follows:
% 31.97/10.45 | (1074) pred(n1) = all_0_9_9
% 31.97/10.45 |
% 31.97/10.45 | From (1073) and (505) follows:
% 31.97/10.45 | (1075) succ(n1) = all_0_5_5
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 31.97/10.45 | (1076) all_0_9_9 = n0
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.97/10.45 | (1077) all_0_5_5 = n2
% 31.97/10.45 |
% 31.97/10.45 | From (1076)(1077) and (156) follows:
% 31.97/10.45 | (1078) sum(n0, n2) = all_0_2_2
% 31.97/10.45 |
% 31.97/10.45 | From (1076) and (8850) follows:
% 31.97/10.45 | (8903) sum(n0, n4) = all_0_7_7
% 31.97/10.45 |
% 31.97/10.45 | From (1077) and (8848) follows:
% 31.97/10.45 | (8904) sum(n2, n2) = all_0_4_4
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n2, n2, all_0_4_4, n4 and discharging atoms sum(n2, n2) = all_0_4_4, sum(n2, n2) = n4, yields:
% 31.97/10.45 | (1009) all_0_4_4 = n4
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n0, n4, all_0_7_7, n4 and discharging atoms sum(n0, n4) = all_0_7_7, sum(n0, n4) = n4, yields:
% 31.97/10.45 | (1011) all_0_7_7 = n4
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 31.97/10.45 | (1082) all_0_2_2 = n2
% 31.97/10.45 |
% 31.97/10.45 | From (1082) and (8852) follows:
% 31.97/10.45 | (8908) sum(n2, n6) = all_0_0_0
% 31.97/10.45 |
% 31.97/10.45 | From (1011)(1009) and (435) follows:
% 31.97/10.45 | (1013) sum(n4, n4) = all_0_3_3
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 31.97/10.45 | (1015) all_0_3_3 = n8
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n2, n6, all_0_0_0, n8 and discharging atoms sum(n2, n6) = all_0_0_0, sum(n2, n6) = n8, yields:
% 31.97/10.45 | (1014) all_0_0_0 = n8
% 31.97/10.45 |
% 31.97/10.45 | Equations (1014,1015) can reduce 201 to:
% 31.97/10.45 | (746) $false
% 31.97/10.45 |
% 31.97/10.45 |-The branch is then unsatisfiable
% 31.97/10.45 |-Branch two:
% 31.97/10.45 | (1090) ~ (all_0_11_11 = n1)
% 31.97/10.45 | (1091) all_0_11_11 = n0
% 31.97/10.45 |
% 31.97/10.45 | From (1091) and (190) follows:
% 31.97/10.45 | (1092) pred(n0) = all_0_9_9
% 31.97/10.45 |
% 31.97/10.45 | From (1091) and (505) follows:
% 31.97/10.45 | (1093) succ(n0) = all_0_5_5
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 31.97/10.45 | (1094) all_0_9_9 = n20
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.97/10.45 | (1095) all_0_5_5 = n1
% 31.97/10.45 |
% 31.97/10.45 | From (1094)(1095) and (156) follows:
% 31.97/10.45 | (1096) sum(n20, n1) = all_0_2_2
% 31.97/10.45 |
% 31.97/10.45 | From (1094) and (8850) follows:
% 31.97/10.45 | (8920) sum(n20, n4) = all_0_7_7
% 31.97/10.45 |
% 31.97/10.45 | From (1095) and (8848) follows:
% 31.97/10.45 | (8921) sum(n2, n1) = all_0_4_4
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n20, n4, all_0_7_7, n3 and discharging atoms sum(n20, n4) = all_0_7_7, sum(n20, n4) = n3, yields:
% 31.97/10.45 | (1029) all_0_7_7 = n3
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 31.97/10.45 | (1099) all_0_2_2 = n0
% 31.97/10.45 |
% 31.97/10.45 | Instantiating formula (194) with n2, n1, all_0_4_4, n3 and discharging atoms sum(n2, n1) = all_0_4_4, sum(n2, n1) = n3, yields:
% 31.97/10.45 | (1027) all_0_4_4 = n3
% 31.97/10.45 |
% 31.97/10.45 | From (1099) and (8852) follows:
% 31.97/10.46 | (8925) sum(n0, n6) = all_0_0_0
% 31.97/10.46 |
% 31.97/10.46 | From (1029)(1027) and (435) follows:
% 31.97/10.46 | (1031) sum(n3, n3) = all_0_3_3
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 31.97/10.46 | (1033) all_0_3_3 = n6
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (194) with n0, n6, all_0_0_0, n6 and discharging atoms sum(n0, n6) = all_0_0_0, sum(n0, n6) = n6, yields:
% 31.97/10.46 | (1032) all_0_0_0 = n6
% 31.97/10.46 |
% 31.97/10.46 | Equations (1032,1033) can reduce 201 to:
% 31.97/10.46 | (746) $false
% 31.97/10.46 |
% 31.97/10.46 |-The branch is then unsatisfiable
% 31.97/10.46 |-Branch two:
% 31.97/10.46 | (1424) ~ (all_0_10_10 = n3)
% 31.97/10.46 | (1425) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 31.97/10.46 |
% 31.97/10.46 +-Applying beta-rule and splitting (1036), into two cases.
% 31.97/10.46 |-Branch one:
% 31.97/10.46 | (1037) all_0_11_11 = n3
% 31.97/10.46 |
% 31.97/10.46 | From (1037) and (190) follows:
% 31.97/10.46 | (1038) pred(n3) = all_0_9_9
% 31.97/10.46 |
% 31.97/10.46 | From (1037) and (505) follows:
% 31.97/10.46 | (1039) succ(n3) = all_0_5_5
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (259) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 31.97/10.46 | (1040) all_0_9_9 = n2
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (184) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 31.97/10.46 | (1041) all_0_5_5 = n4
% 31.97/10.46 |
% 31.97/10.46 | From (1041) and (386) follows:
% 31.97/10.46 | (8937) sum(all_0_6_6, n4) = all_0_4_4
% 31.97/10.46 |
% 31.97/10.46 | From (1040)(1041) and (156) follows:
% 31.97/10.46 | (1042) sum(n2, n4) = all_0_2_2
% 31.97/10.46 |
% 31.97/10.46 | From (1040) and (74) follows:
% 31.97/10.46 | (8939) sum(n2, all_0_8_8) = all_0_7_7
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (194) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 31.97/10.46 | (1046) all_0_2_2 = n6
% 31.97/10.46 |
% 31.97/10.46 | From (1046) and (85) follows:
% 31.97/10.46 | (8941) sum(n6, all_0_1_1) = all_0_0_0
% 31.97/10.46 |
% 31.97/10.46 +-Applying beta-rule and splitting (1425), into two cases.
% 31.97/10.46 |-Branch one:
% 31.97/10.46 | (1426) all_0_10_10 = n2
% 31.97/10.46 |
% 31.97/10.46 | From (1426) and (57) follows:
% 31.97/10.46 | (1427) pred(n2) = all_0_6_6
% 31.97/10.46 |
% 31.97/10.46 | From (1426) and (381) follows:
% 31.97/10.46 | (1428) succ(n2) = all_0_8_8
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 31.97/10.46 | (1429) all_0_6_6 = n1
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 31.97/10.46 | (1430) all_0_8_8 = n3
% 31.97/10.46 |
% 31.97/10.46 | From (1429)(1430) and (628) follows:
% 31.97/10.46 | (1431) sum(n1, n3) = all_0_1_1
% 31.97/10.46 |
% 31.97/10.46 | From (1429) and (8937) follows:
% 31.97/10.46 | (8948) sum(n1, n4) = all_0_4_4
% 31.97/10.46 |
% 31.97/10.46 | From (1430) and (8939) follows:
% 31.97/10.46 | (8949) sum(n2, n3) = all_0_7_7
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (194) with n2, n3, all_0_7_7, n5 and discharging atoms sum(n2, n3) = all_0_7_7, sum(n2, n3) = n5, yields:
% 31.97/10.46 | (993) all_0_7_7 = n5
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (194) with n1, n4, all_0_4_4, n5 and discharging atoms sum(n1, n4) = all_0_4_4, sum(n1, n4) = n5, yields:
% 31.97/10.46 | (991) all_0_4_4 = n5
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 31.97/10.46 | (1435) all_0_1_1 = n4
% 31.97/10.46 |
% 31.97/10.46 | From (993)(991) and (435) follows:
% 31.97/10.46 | (995) sum(n5, n5) = all_0_3_3
% 31.97/10.46 |
% 31.97/10.46 | From (1435) and (8941) follows:
% 31.97/10.46 | (8954) sum(n6, n4) = all_0_0_0
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (194) with n6, n4, all_0_0_0, n10 and discharging atoms sum(n6, n4) = all_0_0_0, sum(n6, n4) = n10, yields:
% 31.97/10.46 | (996) all_0_0_0 = n10
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (194) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 31.97/10.46 | (997) all_0_3_3 = n10
% 31.97/10.46 |
% 31.97/10.46 | Equations (996,997) can reduce 201 to:
% 31.97/10.46 | (746) $false
% 31.97/10.46 |
% 31.97/10.46 |-The branch is then unsatisfiable
% 31.97/10.46 |-Branch two:
% 31.97/10.46 | (1442) ~ (all_0_10_10 = n2)
% 31.97/10.46 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 31.97/10.46 |
% 31.97/10.46 +-Applying beta-rule and splitting (1443), into two cases.
% 31.97/10.46 |-Branch one:
% 31.97/10.46 | (1444) all_0_10_10 = n1
% 31.97/10.46 |
% 31.97/10.46 | From (1444) and (57) follows:
% 31.97/10.46 | (1445) pred(n1) = all_0_6_6
% 31.97/10.46 |
% 31.97/10.46 | From (1444) and (381) follows:
% 31.97/10.46 | (1446) succ(n1) = all_0_8_8
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 31.97/10.46 | (1447) all_0_6_6 = n0
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 31.97/10.46 | (1448) all_0_8_8 = n2
% 31.97/10.46 |
% 31.97/10.46 | From (1447)(1448) and (628) follows:
% 31.97/10.46 | (1449) sum(n0, n2) = all_0_1_1
% 31.97/10.46 |
% 31.97/10.46 | From (1447) and (8937) follows:
% 31.97/10.46 | (8966) sum(n0, n4) = all_0_4_4
% 31.97/10.46 |
% 31.97/10.46 | From (1448) and (8939) follows:
% 31.97/10.46 | (8967) sum(n2, n2) = all_0_7_7
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (194) with n2, n2, all_0_7_7, n4 and discharging atoms sum(n2, n2) = all_0_7_7, sum(n2, n2) = n4, yields:
% 31.97/10.46 | (1011) all_0_7_7 = n4
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (194) with n0, n4, all_0_4_4, n4 and discharging atoms sum(n0, n4) = all_0_4_4, sum(n0, n4) = n4, yields:
% 31.97/10.46 | (1009) all_0_4_4 = n4
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 31.97/10.46 | (1453) all_0_1_1 = n2
% 31.97/10.46 |
% 31.97/10.46 | From (1011)(1009) and (435) follows:
% 31.97/10.46 | (1013) sum(n4, n4) = all_0_3_3
% 31.97/10.46 |
% 31.97/10.46 | From (1453) and (8941) follows:
% 31.97/10.46 | (8972) sum(n6, n2) = all_0_0_0
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (194) with n6, n2, all_0_0_0, n8 and discharging atoms sum(n6, n2) = all_0_0_0, sum(n6, n2) = n8, yields:
% 31.97/10.46 | (1014) all_0_0_0 = n8
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (194) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 31.97/10.46 | (1015) all_0_3_3 = n8
% 31.97/10.46 |
% 31.97/10.46 | Equations (1014,1015) can reduce 201 to:
% 31.97/10.46 | (746) $false
% 31.97/10.46 |
% 31.97/10.46 |-The branch is then unsatisfiable
% 31.97/10.46 |-Branch two:
% 31.97/10.46 | (1462) ~ (all_0_10_10 = n1)
% 31.97/10.46 | (1463) all_0_10_10 = n0
% 31.97/10.46 |
% 31.97/10.46 | From (1463) and (57) follows:
% 31.97/10.46 | (1464) pred(n0) = all_0_6_6
% 31.97/10.46 |
% 31.97/10.46 | From (1463) and (381) follows:
% 31.97/10.46 | (1465) succ(n0) = all_0_8_8
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 31.97/10.46 | (1466) all_0_6_6 = n20
% 31.97/10.46 |
% 31.97/10.46 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 31.97/10.46 | (1467) all_0_8_8 = n1
% 31.97/10.46 |
% 31.97/10.46 | From (1466)(1467) and (628) follows:
% 31.97/10.46 | (1468) sum(n20, n1) = all_0_1_1
% 31.97/10.46 |
% 31.97/10.46 | From (1466) and (8937) follows:
% 31.97/10.47 | (8983) sum(n20, n4) = all_0_4_4
% 31.97/10.47 |
% 31.97/10.47 | From (1467) and (8939) follows:
% 31.97/10.47 | (8984) sum(n2, n1) = all_0_7_7
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (194) with n20, n4, all_0_4_4, n3 and discharging atoms sum(n20, n4) = all_0_4_4, sum(n20, n4) = n3, yields:
% 31.97/10.47 | (1027) all_0_4_4 = n3
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 31.97/10.47 | (1471) all_0_1_1 = n0
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (194) with n2, n1, all_0_7_7, n3 and discharging atoms sum(n2, n1) = all_0_7_7, sum(n2, n1) = n3, yields:
% 31.97/10.47 | (1029) all_0_7_7 = n3
% 31.97/10.47 |
% 31.97/10.47 | From (1029)(1027) and (435) follows:
% 31.97/10.47 | (1031) sum(n3, n3) = all_0_3_3
% 31.97/10.47 |
% 31.97/10.47 | From (1471) and (8941) follows:
% 31.97/10.47 | (8989) sum(n6, n0) = all_0_0_0
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (194) with n6, n0, all_0_0_0, n6 and discharging atoms sum(n6, n0) = all_0_0_0, sum(n6, n0) = n6, yields:
% 31.97/10.47 | (1032) all_0_0_0 = n6
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 31.97/10.47 | (1033) all_0_3_3 = n6
% 31.97/10.47 |
% 31.97/10.47 | Equations (1032,1033) can reduce 201 to:
% 31.97/10.47 | (746) $false
% 31.97/10.47 |
% 31.97/10.47 |-The branch is then unsatisfiable
% 31.97/10.47 |-Branch two:
% 31.97/10.47 | (1053) ~ (all_0_11_11 = n3)
% 31.97/10.47 | (1054) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 31.97/10.47 |
% 31.97/10.47 +-Applying beta-rule and splitting (1425), into two cases.
% 31.97/10.47 |-Branch one:
% 31.97/10.47 | (1426) all_0_10_10 = n2
% 31.97/10.47 |
% 31.97/10.47 | From (1426) and (57) follows:
% 31.97/10.47 | (1427) pred(n2) = all_0_6_6
% 31.97/10.47 |
% 31.97/10.47 | From (1426) and (381) follows:
% 31.97/10.47 | (1428) succ(n2) = all_0_8_8
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (259) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 31.97/10.47 | (1429) all_0_6_6 = n1
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (184) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 31.97/10.47 | (1430) all_0_8_8 = n3
% 31.97/10.47 |
% 31.97/10.47 | From (1429) and (1427) follows:
% 31.97/10.47 | (511) pred(n2) = n1
% 31.97/10.47 |
% 31.97/10.47 | From (1430) and (1428) follows:
% 31.97/10.47 | (217) succ(n2) = n3
% 31.97/10.47 |
% 31.97/10.47 | From (1429) and (386) follows:
% 31.97/10.47 | (9002) sum(n1, all_0_5_5) = all_0_4_4
% 31.97/10.47 |
% 31.97/10.47 | From (1429)(1430) and (628) follows:
% 31.97/10.47 | (1431) sum(n1, n3) = all_0_1_1
% 31.97/10.47 |
% 31.97/10.47 | From (1430) and (74) follows:
% 31.97/10.47 | (9004) sum(all_0_9_9, n3) = all_0_7_7
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (194) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 31.97/10.47 | (1435) all_0_1_1 = n4
% 31.97/10.47 |
% 31.97/10.47 | From (1435) and (85) follows:
% 31.97/10.47 | (9006) sum(all_0_2_2, n4) = all_0_0_0
% 31.97/10.47 |
% 31.97/10.47 | From (1435) and (1431) follows:
% 31.97/10.47 | (500) sum(n1, n3) = n4
% 31.97/10.47 |
% 31.97/10.47 +-Applying beta-rule and splitting (1054), into two cases.
% 31.97/10.47 |-Branch one:
% 31.97/10.47 | (1055) all_0_11_11 = n2
% 31.97/10.47 |
% 31.97/10.47 | From (1055) and (190) follows:
% 31.97/10.47 | (1056) pred(n2) = all_0_9_9
% 31.97/10.47 |
% 31.97/10.47 | From (1055) and (505) follows:
% 31.97/10.47 | (1057) succ(n2) = all_0_5_5
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 31.97/10.47 | (1058) all_0_9_9 = n1
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.97/10.47 | (1059) all_0_5_5 = n3
% 31.97/10.47 |
% 31.97/10.47 | From (1058)(1059) and (156) follows:
% 31.97/10.47 | (1060) sum(n1, n3) = all_0_2_2
% 31.97/10.47 |
% 31.97/10.47 | From (1058) and (9004) follows:
% 31.97/10.47 | (9014) sum(n1, n3) = all_0_7_7
% 31.97/10.47 |
% 31.97/10.47 | From (1059) and (9002) follows:
% 31.97/10.47 | (9015) sum(n1, n3) = all_0_4_4
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 31.97/10.47 | (1064) all_0_2_2 = n4
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (194) with n1, n3, all_0_4_4, all_0_2_2 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = all_0_4_4, yields:
% 31.97/10.47 | (733) all_0_2_2 = all_0_4_4
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (194) with n1, n3, all_0_7_7, all_0_2_2 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = all_0_7_7, yields:
% 31.97/10.47 | (734) all_0_2_2 = all_0_7_7
% 31.97/10.47 |
% 31.97/10.47 | Combining equations (734,733) yields a new equation:
% 31.97/10.47 | (735) all_0_4_4 = all_0_7_7
% 31.97/10.47 |
% 31.97/10.47 | Combining equations (1064,733) yields a new equation:
% 31.97/10.47 | (1009) all_0_4_4 = n4
% 31.97/10.47 |
% 31.97/10.47 | Combining equations (1009,735) yields a new equation:
% 31.97/10.47 | (1011) all_0_7_7 = n4
% 31.97/10.47 |
% 31.97/10.47 | Combining equations (1011,735) yields a new equation:
% 31.97/10.47 | (1009) all_0_4_4 = n4
% 31.97/10.47 |
% 31.97/10.47 | Combining equations (1009,733) yields a new equation:
% 31.97/10.47 | (1064) all_0_2_2 = n4
% 31.97/10.47 |
% 31.97/10.47 | From (1064) and (9006) follows:
% 31.97/10.47 | (9024) sum(n4, n4) = all_0_0_0
% 31.97/10.47 |
% 31.97/10.47 | From (1011)(1009) and (435) follows:
% 31.97/10.47 | (1013) sum(n4, n4) = all_0_3_3
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (194) with n4, n4, all_0_0_0, n8 and discharging atoms sum(n4, n4) = all_0_0_0, sum(n4, n4) = n8, yields:
% 31.97/10.47 | (1014) all_0_0_0 = n8
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (194) with n4, n4, all_0_3_3, all_0_0_0 and discharging atoms sum(n4, n4) = all_0_0_0, sum(n4, n4) = all_0_3_3, yields:
% 31.97/10.47 | (743) all_0_0_0 = all_0_3_3
% 31.97/10.47 |
% 31.97/10.47 | Combining equations (1014,743) yields a new equation:
% 31.97/10.47 | (1015) all_0_3_3 = n8
% 31.97/10.47 |
% 31.97/10.47 | Combining equations (1015,743) yields a new equation:
% 31.97/10.47 | (1014) all_0_0_0 = n8
% 31.97/10.47 |
% 31.97/10.47 | Equations (1014,1015) can reduce 201 to:
% 31.97/10.47 | (746) $false
% 31.97/10.47 |
% 31.97/10.47 |-The branch is then unsatisfiable
% 31.97/10.47 |-Branch two:
% 31.97/10.47 | (1071) ~ (all_0_11_11 = n2)
% 31.97/10.47 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 31.97/10.47 |
% 31.97/10.47 +-Applying beta-rule and splitting (1072), into two cases.
% 31.97/10.47 |-Branch one:
% 31.97/10.47 | (1073) all_0_11_11 = n1
% 31.97/10.47 |
% 31.97/10.47 | From (1073) and (190) follows:
% 31.97/10.47 | (1074) pred(n1) = all_0_9_9
% 31.97/10.47 |
% 31.97/10.47 | From (1073) and (505) follows:
% 31.97/10.47 | (1075) succ(n1) = all_0_5_5
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 31.97/10.47 | (1076) all_0_9_9 = n0
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.97/10.47 | (1077) all_0_5_5 = n2
% 31.97/10.47 |
% 31.97/10.47 | From (1076)(1077) and (156) follows:
% 31.97/10.47 | (1078) sum(n0, n2) = all_0_2_2
% 31.97/10.47 |
% 31.97/10.47 | From (1076) and (9004) follows:
% 31.97/10.47 | (9039) sum(n0, n3) = all_0_7_7
% 31.97/10.47 |
% 31.97/10.47 | From (1077) and (9002) follows:
% 31.97/10.47 | (9040) sum(n1, n2) = all_0_4_4
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (194) with n1, n2, all_0_4_4, n3 and discharging atoms sum(n1, n2) = all_0_4_4, sum(n1, n2) = n3, yields:
% 31.97/10.47 | (1027) all_0_4_4 = n3
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (194) with n0, n3, all_0_7_7, n3 and discharging atoms sum(n0, n3) = all_0_7_7, sum(n0, n3) = n3, yields:
% 31.97/10.47 | (1029) all_0_7_7 = n3
% 31.97/10.47 |
% 31.97/10.47 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 31.97/10.47 | (1082) all_0_2_2 = n2
% 31.97/10.47 |
% 31.97/10.47 | From (1082) and (9006) follows:
% 31.97/10.48 | (9044) sum(n2, n4) = all_0_0_0
% 31.97/10.48 |
% 31.97/10.48 | From (1029)(1027) and (435) follows:
% 31.97/10.48 | (1031) sum(n3, n3) = all_0_3_3
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 31.97/10.48 | (1033) all_0_3_3 = n6
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (194) with n2, n4, all_0_0_0, n6 and discharging atoms sum(n2, n4) = all_0_0_0, sum(n2, n4) = n6, yields:
% 31.97/10.48 | (1032) all_0_0_0 = n6
% 31.97/10.48 |
% 31.97/10.48 | Equations (1032,1033) can reduce 201 to:
% 31.97/10.48 | (746) $false
% 31.97/10.48 |
% 31.97/10.48 |-The branch is then unsatisfiable
% 31.97/10.48 |-Branch two:
% 31.97/10.48 | (1090) ~ (all_0_11_11 = n1)
% 31.97/10.48 | (1091) all_0_11_11 = n0
% 31.97/10.48 |
% 31.97/10.48 | From (1091) and (190) follows:
% 31.97/10.48 | (1092) pred(n0) = all_0_9_9
% 31.97/10.48 |
% 31.97/10.48 | From (1091) and (505) follows:
% 31.97/10.48 | (1093) succ(n0) = all_0_5_5
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 31.97/10.48 | (1094) all_0_9_9 = n20
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.97/10.48 | (1095) all_0_5_5 = n1
% 31.97/10.48 |
% 31.97/10.48 | From (1094)(1095) and (156) follows:
% 31.97/10.48 | (1096) sum(n20, n1) = all_0_2_2
% 31.97/10.48 |
% 31.97/10.48 | From (1094) and (9004) follows:
% 31.97/10.48 | (9056) sum(n20, n3) = all_0_7_7
% 31.97/10.48 |
% 31.97/10.48 | From (1095) and (9002) follows:
% 31.97/10.48 | (9057) sum(n1, n1) = all_0_4_4
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (194) with n20, n3, all_0_7_7, n2 and discharging atoms sum(n20, n3) = all_0_7_7, sum(n20, n3) = n2, yields:
% 31.97/10.48 | (1047) all_0_7_7 = n2
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 31.97/10.48 | (1099) all_0_2_2 = n0
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (194) with n1, n1, all_0_4_4, n2 and discharging atoms sum(n1, n1) = all_0_4_4, sum(n1, n1) = n2, yields:
% 31.97/10.48 | (1045) all_0_4_4 = n2
% 31.97/10.48 |
% 31.97/10.48 | From (1099) and (9006) follows:
% 31.97/10.48 | (9061) sum(n0, n4) = all_0_0_0
% 31.97/10.48 |
% 31.97/10.48 | From (1047)(1045) and (435) follows:
% 31.97/10.48 | (1049) sum(n2, n2) = all_0_3_3
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 31.97/10.48 | (1051) all_0_3_3 = n4
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (194) with n0, n4, all_0_0_0, n4 and discharging atoms sum(n0, n4) = all_0_0_0, sum(n0, n4) = n4, yields:
% 31.97/10.48 | (1050) all_0_0_0 = n4
% 31.97/10.48 |
% 31.97/10.48 | Equations (1050,1051) can reduce 201 to:
% 31.97/10.48 | (746) $false
% 31.97/10.48 |
% 31.97/10.48 |-The branch is then unsatisfiable
% 31.97/10.48 |-Branch two:
% 31.97/10.48 | (1442) ~ (all_0_10_10 = n2)
% 31.97/10.48 | (1443) all_0_10_10 = n1 | all_0_10_10 = n0
% 31.97/10.48 |
% 31.97/10.48 +-Applying beta-rule and splitting (1054), into two cases.
% 31.97/10.48 |-Branch one:
% 31.97/10.48 | (1055) all_0_11_11 = n2
% 31.97/10.48 |
% 31.97/10.48 | From (1055) and (190) follows:
% 31.97/10.48 | (1056) pred(n2) = all_0_9_9
% 31.97/10.48 |
% 31.97/10.48 | From (1055) and (505) follows:
% 31.97/10.48 | (1057) succ(n2) = all_0_5_5
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (259) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 31.97/10.48 | (1058) all_0_9_9 = n1
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (184) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 31.97/10.48 | (1059) all_0_5_5 = n3
% 31.97/10.48 |
% 31.97/10.48 | From (1059) and (386) follows:
% 31.97/10.48 | (9073) sum(all_0_6_6, n3) = all_0_4_4
% 31.97/10.48 |
% 31.97/10.48 | From (1058)(1059) and (156) follows:
% 31.97/10.48 | (1060) sum(n1, n3) = all_0_2_2
% 31.97/10.48 |
% 31.97/10.48 | From (1058) and (74) follows:
% 31.97/10.48 | (9075) sum(n1, all_0_8_8) = all_0_7_7
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (194) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 31.97/10.48 | (1064) all_0_2_2 = n4
% 31.97/10.48 |
% 31.97/10.48 | From (1064) and (85) follows:
% 31.97/10.48 | (9077) sum(n4, all_0_1_1) = all_0_0_0
% 31.97/10.48 |
% 31.97/10.48 +-Applying beta-rule and splitting (1443), into two cases.
% 31.97/10.48 |-Branch one:
% 31.97/10.48 | (1444) all_0_10_10 = n1
% 31.97/10.48 |
% 31.97/10.48 | From (1444) and (57) follows:
% 31.97/10.48 | (1445) pred(n1) = all_0_6_6
% 31.97/10.48 |
% 31.97/10.48 | From (1444) and (381) follows:
% 31.97/10.48 | (1446) succ(n1) = all_0_8_8
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 31.97/10.48 | (1447) all_0_6_6 = n0
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 31.97/10.48 | (1448) all_0_8_8 = n2
% 31.97/10.48 |
% 31.97/10.48 | From (1447)(1448) and (628) follows:
% 31.97/10.48 | (1449) sum(n0, n2) = all_0_1_1
% 31.97/10.48 |
% 31.97/10.48 | From (1447) and (9073) follows:
% 31.97/10.48 | (9084) sum(n0, n3) = all_0_4_4
% 31.97/10.48 |
% 31.97/10.48 | From (1448) and (9075) follows:
% 31.97/10.48 | (9085) sum(n1, n2) = all_0_7_7
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (194) with n1, n2, all_0_7_7, n3 and discharging atoms sum(n1, n2) = all_0_7_7, sum(n1, n2) = n3, yields:
% 31.97/10.48 | (1029) all_0_7_7 = n3
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (194) with n0, n3, all_0_4_4, n3 and discharging atoms sum(n0, n3) = all_0_4_4, sum(n0, n3) = n3, yields:
% 31.97/10.48 | (1027) all_0_4_4 = n3
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 31.97/10.48 | (1453) all_0_1_1 = n2
% 31.97/10.48 |
% 31.97/10.48 | From (1029)(1027) and (435) follows:
% 31.97/10.48 | (1031) sum(n3, n3) = all_0_3_3
% 31.97/10.48 |
% 31.97/10.48 | From (1453) and (9077) follows:
% 31.97/10.48 | (9090) sum(n4, n2) = all_0_0_0
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (194) with n4, n2, all_0_0_0, n6 and discharging atoms sum(n4, n2) = all_0_0_0, sum(n4, n2) = n6, yields:
% 31.97/10.48 | (1032) all_0_0_0 = n6
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (194) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 31.97/10.48 | (1033) all_0_3_3 = n6
% 31.97/10.48 |
% 31.97/10.48 | Equations (1032,1033) can reduce 201 to:
% 31.97/10.48 | (746) $false
% 31.97/10.48 |
% 31.97/10.48 |-The branch is then unsatisfiable
% 31.97/10.48 |-Branch two:
% 31.97/10.48 | (1462) ~ (all_0_10_10 = n1)
% 31.97/10.48 | (1463) all_0_10_10 = n0
% 31.97/10.48 |
% 31.97/10.48 | From (1463) and (57) follows:
% 31.97/10.48 | (1464) pred(n0) = all_0_6_6
% 31.97/10.48 |
% 31.97/10.48 | From (1463) and (381) follows:
% 31.97/10.48 | (1465) succ(n0) = all_0_8_8
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 31.97/10.48 | (1466) all_0_6_6 = n20
% 31.97/10.48 |
% 31.97/10.48 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 31.97/10.48 | (1467) all_0_8_8 = n1
% 31.97/10.48 |
% 31.97/10.48 | From (1466)(1467) and (628) follows:
% 31.97/10.48 | (1468) sum(n20, n1) = all_0_1_1
% 31.97/10.48 |
% 31.97/10.48 | From (1466) and (9073) follows:
% 31.97/10.49 | (9101) sum(n20, n3) = all_0_4_4
% 31.97/10.49 |
% 31.97/10.49 | From (1467) and (9075) follows:
% 31.97/10.49 | (9102) sum(n1, n1) = all_0_7_7
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (194) with n20, n3, all_0_4_4, n2 and discharging atoms sum(n20, n3) = all_0_4_4, sum(n20, n3) = n2, yields:
% 31.97/10.49 | (1045) all_0_4_4 = n2
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 31.97/10.49 | (1471) all_0_1_1 = n0
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (194) with n1, n1, all_0_7_7, n2 and discharging atoms sum(n1, n1) = all_0_7_7, sum(n1, n1) = n2, yields:
% 31.97/10.49 | (1047) all_0_7_7 = n2
% 31.97/10.49 |
% 31.97/10.49 | From (1047)(1045) and (435) follows:
% 31.97/10.49 | (1049) sum(n2, n2) = all_0_3_3
% 31.97/10.49 |
% 31.97/10.49 | From (1471) and (9077) follows:
% 31.97/10.49 | (9107) sum(n4, n0) = all_0_0_0
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (194) with n4, n0, all_0_0_0, n4 and discharging atoms sum(n4, n0) = all_0_0_0, sum(n4, n0) = n4, yields:
% 31.97/10.49 | (1050) all_0_0_0 = n4
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (194) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 31.97/10.49 | (1051) all_0_3_3 = n4
% 31.97/10.49 |
% 31.97/10.49 | Equations (1050,1051) can reduce 201 to:
% 31.97/10.49 | (746) $false
% 31.97/10.49 |
% 31.97/10.49 |-The branch is then unsatisfiable
% 31.97/10.49 |-Branch two:
% 31.97/10.49 | (1071) ~ (all_0_11_11 = n2)
% 31.97/10.49 | (1072) all_0_11_11 = n1 | all_0_11_11 = n0
% 31.97/10.49 |
% 31.97/10.49 +-Applying beta-rule and splitting (1443), into two cases.
% 31.97/10.49 |-Branch one:
% 31.97/10.49 | (1444) all_0_10_10 = n1
% 31.97/10.49 |
% 31.97/10.49 | From (1444) and (57) follows:
% 31.97/10.49 | (1445) pred(n1) = all_0_6_6
% 31.97/10.49 |
% 31.97/10.49 | From (1444) and (381) follows:
% 31.97/10.49 | (1446) succ(n1) = all_0_8_8
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (259) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 31.97/10.49 | (1447) all_0_6_6 = n0
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (184) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 31.97/10.49 | (1448) all_0_8_8 = n2
% 31.97/10.49 |
% 31.97/10.49 | From (1447) and (1445) follows:
% 31.97/10.49 | (504) pred(n1) = n0
% 31.97/10.49 |
% 31.97/10.49 | From (1448) and (1446) follows:
% 31.97/10.49 | (436) succ(n1) = n2
% 31.97/10.49 |
% 31.97/10.49 | From (1447) and (386) follows:
% 31.97/10.49 | (9120) sum(n0, all_0_5_5) = all_0_4_4
% 31.97/10.49 |
% 31.97/10.49 | From (1447)(1448) and (628) follows:
% 31.97/10.49 | (1449) sum(n0, n2) = all_0_1_1
% 31.97/10.49 |
% 31.97/10.49 | From (1448) and (74) follows:
% 31.97/10.49 | (9122) sum(all_0_9_9, n2) = all_0_7_7
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (194) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 31.97/10.49 | (1453) all_0_1_1 = n2
% 31.97/10.49 |
% 31.97/10.49 | From (1453) and (85) follows:
% 31.97/10.49 | (9124) sum(all_0_2_2, n2) = all_0_0_0
% 31.97/10.49 |
% 31.97/10.49 | From (1453) and (1449) follows:
% 31.97/10.49 | (81) sum(n0, n2) = n2
% 31.97/10.49 |
% 31.97/10.49 +-Applying beta-rule and splitting (1072), into two cases.
% 31.97/10.49 |-Branch one:
% 31.97/10.49 | (1073) all_0_11_11 = n1
% 31.97/10.49 |
% 31.97/10.49 | From (1073) and (190) follows:
% 31.97/10.49 | (1074) pred(n1) = all_0_9_9
% 31.97/10.49 |
% 31.97/10.49 | From (1073) and (505) follows:
% 31.97/10.49 | (1075) succ(n1) = all_0_5_5
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 31.97/10.49 | (1076) all_0_9_9 = n0
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.97/10.49 | (1077) all_0_5_5 = n2
% 31.97/10.49 |
% 31.97/10.49 | From (1076)(1077) and (156) follows:
% 31.97/10.49 | (1078) sum(n0, n2) = all_0_2_2
% 31.97/10.49 |
% 31.97/10.49 | From (1076) and (9122) follows:
% 31.97/10.49 | (9132) sum(n0, n2) = all_0_7_7
% 31.97/10.49 |
% 31.97/10.49 | From (1077) and (9120) follows:
% 31.97/10.49 | (9133) sum(n0, n2) = all_0_4_4
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 31.97/10.49 | (1082) all_0_2_2 = n2
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (194) with n0, n2, all_0_4_4, all_0_2_2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = all_0_4_4, yields:
% 31.97/10.49 | (733) all_0_2_2 = all_0_4_4
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (194) with n0, n2, all_0_7_7, all_0_2_2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = all_0_7_7, yields:
% 31.97/10.49 | (734) all_0_2_2 = all_0_7_7
% 31.97/10.49 |
% 31.97/10.49 | Combining equations (734,733) yields a new equation:
% 31.97/10.49 | (735) all_0_4_4 = all_0_7_7
% 31.97/10.49 |
% 31.97/10.49 | Combining equations (1082,733) yields a new equation:
% 31.97/10.49 | (1045) all_0_4_4 = n2
% 31.97/10.49 |
% 31.97/10.49 | Combining equations (1045,735) yields a new equation:
% 31.97/10.49 | (1047) all_0_7_7 = n2
% 31.97/10.49 |
% 31.97/10.49 | Combining equations (1047,735) yields a new equation:
% 31.97/10.49 | (1045) all_0_4_4 = n2
% 31.97/10.49 |
% 31.97/10.49 | Combining equations (1045,733) yields a new equation:
% 31.97/10.49 | (1082) all_0_2_2 = n2
% 31.97/10.49 |
% 31.97/10.49 | From (1082) and (9124) follows:
% 31.97/10.49 | (9142) sum(n2, n2) = all_0_0_0
% 31.97/10.49 |
% 31.97/10.49 | From (1047)(1045) and (435) follows:
% 31.97/10.49 | (1049) sum(n2, n2) = all_0_3_3
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (194) with n2, n2, all_0_0_0, n4 and discharging atoms sum(n2, n2) = all_0_0_0, sum(n2, n2) = n4, yields:
% 31.97/10.49 | (1050) all_0_0_0 = n4
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (194) with n2, n2, all_0_3_3, all_0_0_0 and discharging atoms sum(n2, n2) = all_0_0_0, sum(n2, n2) = all_0_3_3, yields:
% 31.97/10.49 | (743) all_0_0_0 = all_0_3_3
% 31.97/10.49 |
% 31.97/10.49 | Combining equations (1050,743) yields a new equation:
% 31.97/10.49 | (1051) all_0_3_3 = n4
% 31.97/10.49 |
% 31.97/10.49 | Combining equations (1051,743) yields a new equation:
% 31.97/10.49 | (1050) all_0_0_0 = n4
% 31.97/10.49 |
% 31.97/10.49 | Equations (1050,1051) can reduce 201 to:
% 31.97/10.49 | (746) $false
% 31.97/10.49 |
% 31.97/10.49 |-The branch is then unsatisfiable
% 31.97/10.49 |-Branch two:
% 31.97/10.49 | (1090) ~ (all_0_11_11 = n1)
% 31.97/10.49 | (1091) all_0_11_11 = n0
% 31.97/10.49 |
% 31.97/10.49 | From (1091) and (190) follows:
% 31.97/10.49 | (1092) pred(n0) = all_0_9_9
% 31.97/10.49 |
% 31.97/10.49 | From (1091) and (505) follows:
% 31.97/10.49 | (1093) succ(n0) = all_0_5_5
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 31.97/10.49 | (1094) all_0_9_9 = n20
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.97/10.49 | (1095) all_0_5_5 = n1
% 31.97/10.49 |
% 31.97/10.49 | From (1094)(1095) and (156) follows:
% 31.97/10.49 | (1096) sum(n20, n1) = all_0_2_2
% 31.97/10.49 |
% 31.97/10.49 | From (1094) and (9122) follows:
% 31.97/10.49 | (9156) sum(n20, n2) = all_0_7_7
% 31.97/10.49 |
% 31.97/10.49 | From (1095) and (9120) follows:
% 31.97/10.49 | (9157) sum(n0, n1) = all_0_4_4
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (194) with n20, n2, all_0_7_7, n1 and discharging atoms sum(n20, n2) = all_0_7_7, sum(n20, n2) = n1, yields:
% 31.97/10.49 | (1065) all_0_7_7 = n1
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 31.97/10.49 | (1099) all_0_2_2 = n0
% 31.97/10.49 |
% 31.97/10.49 | Instantiating formula (194) with n0, n1, all_0_4_4, n1 and discharging atoms sum(n0, n1) = all_0_4_4, sum(n0, n1) = n1, yields:
% 31.97/10.49 | (1063) all_0_4_4 = n1
% 31.97/10.49 |
% 31.97/10.49 | From (1099) and (9124) follows:
% 31.97/10.49 | (9161) sum(n0, n2) = all_0_0_0
% 31.97/10.49 |
% 31.97/10.49 | From (1065)(1063) and (435) follows:
% 31.97/10.50 | (1067) sum(n1, n1) = all_0_3_3
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 31.97/10.50 | (1069) all_0_3_3 = n2
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (194) with n0, n2, all_0_0_0, n2 and discharging atoms sum(n0, n2) = all_0_0_0, sum(n0, n2) = n2, yields:
% 31.97/10.50 | (1068) all_0_0_0 = n2
% 31.97/10.50 |
% 31.97/10.50 | Equations (1068,1069) can reduce 201 to:
% 31.97/10.50 | (746) $false
% 31.97/10.50 |
% 31.97/10.50 |-The branch is then unsatisfiable
% 31.97/10.50 |-Branch two:
% 31.97/10.50 | (1462) ~ (all_0_10_10 = n1)
% 31.97/10.50 | (1463) all_0_10_10 = n0
% 31.97/10.50 |
% 31.97/10.50 | From (1463) and (57) follows:
% 31.97/10.50 | (1464) pred(n0) = all_0_6_6
% 31.97/10.50 |
% 31.97/10.50 | From (1463) and (381) follows:
% 31.97/10.50 | (1465) succ(n0) = all_0_8_8
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (259) with n0, all_0_6_6, n20 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n20, yields:
% 31.97/10.50 | (1466) all_0_6_6 = n20
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (184) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 31.97/10.50 | (1467) all_0_8_8 = n1
% 31.97/10.50 |
% 31.97/10.50 | From (1466) and (1464) follows:
% 31.97/10.50 | (326) pred(n0) = n20
% 31.97/10.50 |
% 31.97/10.50 | From (1467) and (1465) follows:
% 31.97/10.50 | (536) succ(n0) = n1
% 31.97/10.50 |
% 31.97/10.50 | From (1466) and (386) follows:
% 31.97/10.50 | (9174) sum(n20, all_0_5_5) = all_0_4_4
% 31.97/10.50 |
% 31.97/10.50 | From (1466)(1467) and (628) follows:
% 31.97/10.50 | (1468) sum(n20, n1) = all_0_1_1
% 31.97/10.50 |
% 31.97/10.50 | From (1467) and (74) follows:
% 31.97/10.50 | (9176) sum(all_0_9_9, n1) = all_0_7_7
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (194) with n20, n1, all_0_1_1, n0 and discharging atoms sum(n20, n1) = all_0_1_1, sum(n20, n1) = n0, yields:
% 31.97/10.50 | (1471) all_0_1_1 = n0
% 31.97/10.50 |
% 31.97/10.50 | From (1471) and (85) follows:
% 31.97/10.50 | (9178) sum(all_0_2_2, n0) = all_0_0_0
% 31.97/10.50 |
% 31.97/10.50 | From (1471) and (1468) follows:
% 31.97/10.50 | (244) sum(n20, n1) = n0
% 31.97/10.50 |
% 31.97/10.50 +-Applying beta-rule and splitting (1072), into two cases.
% 31.97/10.50 |-Branch one:
% 31.97/10.50 | (1073) all_0_11_11 = n1
% 31.97/10.50 |
% 31.97/10.50 | From (1073) and (190) follows:
% 31.97/10.50 | (1074) pred(n1) = all_0_9_9
% 31.97/10.50 |
% 31.97/10.50 | From (1073) and (505) follows:
% 31.97/10.50 | (1075) succ(n1) = all_0_5_5
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (259) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 31.97/10.50 | (1076) all_0_9_9 = n0
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (184) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 31.97/10.50 | (1077) all_0_5_5 = n2
% 31.97/10.50 |
% 31.97/10.50 | From (1076)(1077) and (156) follows:
% 31.97/10.50 | (1078) sum(n0, n2) = all_0_2_2
% 31.97/10.50 |
% 31.97/10.50 | From (1076) and (9176) follows:
% 31.97/10.50 | (9186) sum(n0, n1) = all_0_7_7
% 31.97/10.50 |
% 31.97/10.50 | From (1077) and (9174) follows:
% 31.97/10.50 | (9187) sum(n20, n2) = all_0_4_4
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (194) with n20, n2, all_0_4_4, n1 and discharging atoms sum(n20, n2) = all_0_4_4, sum(n20, n2) = n1, yields:
% 31.97/10.50 | (1063) all_0_4_4 = n1
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (194) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 31.97/10.50 | (1082) all_0_2_2 = n2
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (194) with n0, n1, all_0_7_7, n1 and discharging atoms sum(n0, n1) = all_0_7_7, sum(n0, n1) = n1, yields:
% 31.97/10.50 | (1065) all_0_7_7 = n1
% 31.97/10.50 |
% 31.97/10.50 | From (1082) and (9178) follows:
% 31.97/10.50 | (9191) sum(n2, n0) = all_0_0_0
% 31.97/10.50 |
% 31.97/10.50 | From (1065)(1063) and (435) follows:
% 31.97/10.50 | (1067) sum(n1, n1) = all_0_3_3
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (194) with n2, n0, all_0_0_0, n2 and discharging atoms sum(n2, n0) = all_0_0_0, sum(n2, n0) = n2, yields:
% 31.97/10.50 | (1068) all_0_0_0 = n2
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (194) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 31.97/10.50 | (1069) all_0_3_3 = n2
% 31.97/10.50 |
% 31.97/10.50 | Equations (1068,1069) can reduce 201 to:
% 31.97/10.50 | (746) $false
% 31.97/10.50 |
% 31.97/10.50 |-The branch is then unsatisfiable
% 31.97/10.50 |-Branch two:
% 31.97/10.50 | (1090) ~ (all_0_11_11 = n1)
% 31.97/10.50 | (1091) all_0_11_11 = n0
% 31.97/10.50 |
% 31.97/10.50 | From (1091) and (190) follows:
% 31.97/10.50 | (1092) pred(n0) = all_0_9_9
% 31.97/10.50 |
% 31.97/10.50 | From (1091) and (505) follows:
% 31.97/10.50 | (1093) succ(n0) = all_0_5_5
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (259) with n0, all_0_9_9, n20 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n20, yields:
% 31.97/10.50 | (1094) all_0_9_9 = n20
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (184) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 31.97/10.50 | (1095) all_0_5_5 = n1
% 31.97/10.50 |
% 31.97/10.50 | From (1094)(1095) and (156) follows:
% 31.97/10.50 | (1096) sum(n20, n1) = all_0_2_2
% 31.97/10.50 |
% 31.97/10.50 | From (1094) and (9176) follows:
% 31.97/10.50 | (9203) sum(n20, n1) = all_0_7_7
% 31.97/10.50 |
% 31.97/10.50 | From (1095) and (9174) follows:
% 31.97/10.50 | (9204) sum(n20, n1) = all_0_4_4
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (194) with n20, n1, all_0_2_2, n0 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = n0, yields:
% 31.97/10.50 | (1099) all_0_2_2 = n0
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (194) with n20, n1, all_0_4_4, all_0_2_2 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = all_0_4_4, yields:
% 31.97/10.50 | (733) all_0_2_2 = all_0_4_4
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (194) with n20, n1, all_0_7_7, all_0_2_2 and discharging atoms sum(n20, n1) = all_0_2_2, sum(n20, n1) = all_0_7_7, yields:
% 31.97/10.50 | (734) all_0_2_2 = all_0_7_7
% 31.97/10.50 |
% 31.97/10.50 | Combining equations (734,733) yields a new equation:
% 31.97/10.50 | (735) all_0_4_4 = all_0_7_7
% 31.97/10.50 |
% 31.97/10.50 | Combining equations (1099,733) yields a new equation:
% 31.97/10.50 | (1081) all_0_4_4 = n0
% 31.97/10.50 |
% 31.97/10.50 | Combining equations (1081,735) yields a new equation:
% 31.97/10.50 | (1083) all_0_7_7 = n0
% 31.97/10.50 |
% 31.97/10.50 | Combining equations (1083,735) yields a new equation:
% 31.97/10.50 | (1081) all_0_4_4 = n0
% 31.97/10.50 |
% 31.97/10.50 | Combining equations (1081,733) yields a new equation:
% 31.97/10.50 | (1099) all_0_2_2 = n0
% 31.97/10.50 |
% 31.97/10.50 | From (1099) and (9178) follows:
% 31.97/10.50 | (9213) sum(n0, n0) = all_0_0_0
% 31.97/10.50 |
% 31.97/10.50 | From (1083)(1081) and (435) follows:
% 31.97/10.50 | (1085) sum(n0, n0) = all_0_3_3
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (194) with n0, n0, all_0_0_0, n0 and discharging atoms sum(n0, n0) = all_0_0_0, sum(n0, n0) = n0, yields:
% 31.97/10.50 | (1087) all_0_0_0 = n0
% 31.97/10.50 |
% 31.97/10.50 | Instantiating formula (194) with n0, n0, all_0_3_3, all_0_0_0 and discharging atoms sum(n0, n0) = all_0_0_0, sum(n0, n0) = all_0_3_3, yields:
% 31.97/10.50 | (743) all_0_0_0 = all_0_3_3
% 31.97/10.50 |
% 31.97/10.50 | Combining equations (1087,743) yields a new equation:
% 31.97/10.50 | (1088) all_0_3_3 = n0
% 31.97/10.50 |
% 31.97/10.50 | Combining equations (1088,743) yields a new equation:
% 31.97/10.50 | (1087) all_0_0_0 = n0
% 31.97/10.50 |
% 31.97/10.50 | Equations (1087,1088) can reduce 201 to:
% 31.97/10.50 | (746) $false
% 31.97/10.50 |
% 31.97/10.50 |-The branch is then unsatisfiable
% 31.97/10.50 % SZS output end Proof for theBenchmark
% 31.97/10.51
% 31.97/10.51 9856ms
%------------------------------------------------------------------------------