TSTP Solution File: NUM376+1.025 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM376+1.025 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n012.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 08:43:48 EDT 2022
% Result : Unsatisfiable 30.58s 11.40s
% Output : Proof 56.69s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM376+1.025 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n012.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 23:47:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.58 ____ _
% 0.19/0.58 ___ / __ \_____(_)___ ________ __________
% 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.88/1.27 Prover 0: Preprocessing ...
% 5.00/1.74 Prover 0: Constructing countermodel ...
% 16.58/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 17.38/6.12 Prover 1: Preprocessing ...
% 17.76/6.26 Prover 1: Constructing countermodel ...
% 24.86/8.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 25.43/8.72 Prover 2: Preprocessing ...
% 26.10/8.83 Prover 2: Warning: ignoring some quantifiers
% 26.10/8.83 Prover 2: Constructing countermodel ...
% 30.58/11.40 Prover 0: proved (5732ms)
% 30.58/11.40 Prover 2: stopped
% 30.58/11.40 Prover 1: stopped
% 30.58/11.40
% 30.58/11.40 No countermodel exists, formula is valid
% 30.58/11.40 % SZS status Unsatisfiable for theBenchmark
% 30.58/11.40
% 30.58/11.40 Generating proof ... found it (size 12209)
% 50.27/19.61
% 50.27/19.61 % SZS output start Proof for theBenchmark
% 50.27/19.61 Assumed formulas after preprocessing and simplification:
% 50.27/19.61 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = v8) & ~ (n25 = n24) & ~ (n25 = n23) & ~ (n25 = n22) & ~ (n25 = n21) & ~ (n25 = n20) & ~ (n25 = n19) & ~ (n25 = n18) & ~ (n25 = n17) & ~ (n25 = n16) & ~ (n25 = n15) & ~ (n25 = n14) & ~ (n25 = n13) & ~ (n25 = n12) & ~ (n25 = n11) & ~ (n25 = n10) & ~ (n25 = n9) & ~ (n25 = n8) & ~ (n25 = n7) & ~ (n25 = n6) & ~ (n25 = n5) & ~ (n25 = n4) & ~ (n25 = n3) & ~ (n25 = n2) & ~ (n25 = n1) & ~ (n25 = n0) & ~ (n24 = n23) & ~ (n24 = n22) & ~ (n24 = n21) & ~ (n24 = n20) & ~ (n24 = n19) & ~ (n24 = n18) & ~ (n24 = n17) & ~ (n24 = n16) & ~ (n24 = n15) & ~ (n24 = n14) & ~ (n24 = n13) & ~ (n24 = n12) & ~ (n24 = n11) & ~ (n24 = n10) & ~ (n24 = n9) & ~ (n24 = n8) & ~ (n24 = n7) & ~ (n24 = n6) & ~ (n24 = n5) & ~ (n24 = n4) & ~ (n24 = n3) & ~ (n24 = n2) & ~ (n24 = n1) & ~ (n24 = n0) & ~ (n23 = n22) & ~ (n23 = n21) & ~ (n23 = n20) & ~ (n23 = n19) & ~ (n23 = n18) & ~ (n23 = n17) & ~ (n23 = n16) & ~ (n23 = n15) & ~ (n23 = n14) & ~ (n23 = n13) & ~ (n23 = n12) & ~ (n23 = n11) & ~ (n23 = n10) & ~ (n23 = n9) & ~ (n23 = n8) & ~ (n23 = n7) & ~ (n23 = n6) & ~ (n23 = n5) & ~ (n23 = n4) & ~ (n23 = n3) & ~ (n23 = n2) & ~ (n23 = n1) & ~ (n23 = n0) & ~ (n22 = n21) & ~ (n22 = n20) & ~ (n22 = n19) & ~ (n22 = n18) & ~ (n22 = n17) & ~ (n22 = n16) & ~ (n22 = n15) & ~ (n22 = n14) & ~ (n22 = n13) & ~ (n22 = n12) & ~ (n22 = n11) & ~ (n22 = n10) & ~ (n22 = n9) & ~ (n22 = n8) & ~ (n22 = n7) & ~ (n22 = n6) & ~ (n22 = n5) & ~ (n22 = n4) & ~ (n22 = n3) & ~ (n22 = n2) & ~ (n22 = n1) & ~ (n22 = n0) & ~ (n21 = n20) & ~ (n21 = n19) & ~ (n21 = n18) & ~ (n21 = n17) & ~ (n21 = n16) & ~ (n21 = n15) & ~ (n21 = n14) & ~ (n21 = n13) & ~ (n21 = n12) & ~ (n21 = n11) & ~ (n21 = n10) & ~ (n21 = n9) & ~ (n21 = n8) & ~ (n21 = n7) & ~ (n21 = n6) & ~ (n21 = n5) & ~ (n21 = n4) & ~ (n21 = n3) & ~ (n21 = n2) & ~ (n21 = n1) & ~ (n21 = n0) & ~ (n20 = n19) & ~ (n20 = n18) & ~ (n20 = n17) & ~ (n20 = n16) & ~ (n20 = n15) & ~ (n20 = n14) & ~ (n20 = n13) & ~ (n20 = n12) & ~ (n20 = n11) & ~ (n20 = n10) & ~ (n20 = n9) & ~ (n20 = n8) & ~ (n20 = n7) & ~ (n20 = n6) & ~ (n20 = n5) & ~ (n20 = n4) & ~ (n20 = n3) & ~ (n20 = n2) & ~ (n20 = n1) & ~ (n20 = n0) & ~ (n19 = n18) & ~ (n19 = n17) & ~ (n19 = n16) & ~ (n19 = n15) & ~ (n19 = n14) & ~ (n19 = n13) & ~ (n19 = n12) & ~ (n19 = n11) & ~ (n19 = n10) & ~ (n19 = n9) & ~ (n19 = n8) & ~ (n19 = n7) & ~ (n19 = n6) & ~ (n19 = n5) & ~ (n19 = n4) & ~ (n19 = n3) & ~ (n19 = n2) & ~ (n19 = n1) & ~ (n19 = n0) & ~ (n18 = n17) & ~ (n18 = n16) & ~ (n18 = n15) & ~ (n18 = n14) & ~ (n18 = n13) & ~ (n18 = n12) & ~ (n18 = n11) & ~ (n18 = n10) & ~ (n18 = n9) & ~ (n18 = n8) & ~ (n18 = n7) & ~ (n18 = n6) & ~ (n18 = n5) & ~ (n18 = n4) & ~ (n18 = n3) & ~ (n18 = n2) & ~ (n18 = n1) & ~ (n18 = n0) & ~ (n17 = n16) & ~ (n17 = n15) & ~ (n17 = n14) & ~ (n17 = n13) & ~ (n17 = n12) & ~ (n17 = n11) & ~ (n17 = n10) & ~ (n17 = n9) & ~ (n17 = n8) & ~ (n17 = n7) & ~ (n17 = n6) & ~ (n17 = n5) & ~ (n17 = n4) & ~ (n17 = n3) & ~ (n17 = n2) & ~ (n17 = n1) & ~ (n17 = n0) & ~ (n16 = n15) & ~ (n16 = n14) & ~ (n16 = n13) & ~ (n16 = n12) & ~ (n16 = n11) & ~ (n16 = n10) & ~ (n16 = n9) & ~ (n16 = n8) & ~ (n16 = n7) & ~ (n16 = n6) & ~ (n16 = n5) & ~ (n16 = n4) & ~ (n16 = n3) & ~ (n16 = n2) & ~ (n16 = n1) & ~ (n16 = n0) & ~ (n15 = n14) & ~ (n15 = n13) & ~ (n15 = n12) & ~ (n15 = n11) & ~ (n15 = n10) & ~ (n15 = n9) & ~ (n15 = n8) & ~ (n15 = n7) & ~ (n15 = n6) & ~ (n15 = n5) & ~ (n15 = n4) & ~ (n15 = n3) & ~ (n15 = n2) & ~ (n15 = n1) & ~ (n15 = n0) & ~ (n14 = n13) & ~ (n14 = n12) & ~ (n14 = n11) & ~ (n14 = n10) & ~ (n14 = n9) & ~ (n14 = n8) & ~ (n14 = n7) & ~ (n14 = n6) & ~ (n14 = n5) & ~ (n14 = n4) & ~ (n14 = n3) & ~ (n14 = n2) & ~ (n14 = n1) & ~ (n14 = n0) & ~ (n13 = n12) & ~ (n13 = n11) & ~ (n13 = n10) & ~ (n13 = n9) & ~ (n13 = n8) & ~ (n13 = n7) & ~ (n13 = n6) & ~ (n13 = n5) & ~ (n13 = n4) & ~ (n13 = n3) & ~ (n13 = n2) & ~ (n13 = n1) & ~ (n13 = n0) & ~ (n12 = n11) & ~ (n12 = n10) & ~ (n12 = n9) & ~ (n12 = n8) & ~ (n12 = n7) & ~ (n12 = n6) & ~ (n12 = n5) & ~ (n12 = n4) & ~ (n12 = n3) & ~ (n12 = n2) & ~ (n12 = n1) & ~ (n12 = n0) & ~ (n11 = n10) & ~ (n11 = n9) & ~ (n11 = n8) & ~ (n11 = n7) & ~ (n11 = n6) & ~ (n11 = n5) & ~ (n11 = n4) & ~ (n11 = n3) & ~ (n11 = n2) & ~ (n11 = n1) & ~ (n11 = n0) & ~ (n10 = n9) & ~ (n10 = n8) & ~ (n10 = n7) & ~ (n10 = n6) & ~ (n10 = n5) & ~ (n10 = n4) & ~ (n10 = n3) & ~ (n10 = n2) & ~ (n10 = n1) & ~ (n10 = n0) & ~ (n9 = n8) & ~ (n9 = n7) & ~ (n9 = n6) & ~ (n9 = n5) & ~ (n9 = n4) & ~ (n9 = n3) & ~ (n9 = n2) & ~ (n9 = n1) & ~ (n9 = n0) & ~ (n8 = n7) & ~ (n8 = n6) & ~ (n8 = n5) & ~ (n8 = n4) & ~ (n8 = n3) & ~ (n8 = n2) & ~ (n8 = n1) & ~ (n8 = n0) & ~ (n7 = n6) & ~ (n7 = n5) & ~ (n7 = n4) & ~ (n7 = n3) & ~ (n7 = n2) & ~ (n7 = n1) & ~ (n7 = n0) & ~ (n6 = n5) & ~ (n6 = n4) & ~ (n6 = n3) & ~ (n6 = n2) & ~ (n6 = n1) & ~ (n6 = n0) & ~ (n5 = n4) & ~ (n5 = n3) & ~ (n5 = n2) & ~ (n5 = n1) & ~ (n5 = n0) & ~ (n4 = n3) & ~ (n4 = n2) & ~ (n4 = n1) & ~ (n4 = n0) & ~ (n3 = n2) & ~ (n3 = n1) & ~ (n3 = n0) & ~ (n2 = n1) & ~ (n2 = n0) & ~ (n1 = n0) & pred(v1) = v5 & pred(v0) = v2 & pred(n25) = n24 & pred(n24) = n23 & pred(n23) = n22 & pred(n22) = n21 & pred(n21) = n20 & 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) = n25 & succ(v1) = v3 & succ(v0) = v6 & succ(n25) = n0 & succ(n24) = n25 & succ(n23) = n24 & succ(n22) = n23 & succ(n21) = n22 & succ(n20) = n21 & 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(n25, n25) = n24 & sum(n25, n24) = n23 & sum(n25, n23) = n22 & sum(n25, n22) = n21 & sum(n25, n21) = n20 & sum(n25, n20) = n19 & sum(n25, n19) = n18 & sum(n25, n18) = n17 & sum(n25, n17) = n16 & sum(n25, n16) = n15 & sum(n25, n15) = n14 & sum(n25, n14) = n13 & sum(n25, n13) = n12 & sum(n25, n12) = n11 & sum(n25, n11) = n10 & sum(n25, n10) = n9 & sum(n25, n9) = n8 & sum(n25, n8) = n7 & sum(n25, n7) = n6 & sum(n25, n6) = n5 & sum(n25, n5) = n4 & sum(n25, n4) = n3 & sum(n25, n3) = n2 & sum(n25, n2) = n1 & sum(n25, n1) = n0 & sum(n25, n0) = n25 & sum(n24, n25) = n23 & sum(n24, n24) = n22 & sum(n24, n23) = n21 & sum(n24, n22) = n20 & sum(n24, n21) = n19 & sum(n24, n20) = n18 & sum(n24, n19) = n17 & sum(n24, n18) = n16 & sum(n24, n17) = n15 & sum(n24, n16) = n14 & sum(n24, n15) = n13 & sum(n24, n14) = n12 & sum(n24, n13) = n11 & sum(n24, n12) = n10 & sum(n24, n11) = n9 & sum(n24, n10) = n8 & sum(n24, n9) = n7 & sum(n24, n8) = n6 & sum(n24, n7) = n5 & sum(n24, n6) = n4 & sum(n24, n5) = n3 & sum(n24, n4) = n2 & sum(n24, n3) = n1 & sum(n24, n2) = n0 & sum(n24, n1) = n25 & sum(n24, n0) = n24 & sum(n23, n25) = n22 & sum(n23, n24) = n21 & sum(n23, n23) = n20 & sum(n23, n22) = n19 & sum(n23, n21) = n18 & sum(n23, n20) = n17 & sum(n23, n19) = n16 & sum(n23, n18) = n15 & sum(n23, n17) = n14 & sum(n23, n16) = n13 & sum(n23, n15) = n12 & sum(n23, n14) = n11 & sum(n23, n13) = n10 & sum(n23, n12) = n9 & sum(n23, n11) = n8 & sum(n23, n10) = n7 & sum(n23, n9) = n6 & sum(n23, n8) = n5 & sum(n23, n7) = n4 & sum(n23, n6) = n3 & sum(n23, n5) = n2 & sum(n23, n4) = n1 & sum(n23, n3) = n0 & sum(n23, n2) = n25 & sum(n23, n1) = n24 & sum(n23, n0) = n23 & sum(n22, n25) = n21 & sum(n22, n24) = n20 & sum(n22, n23) = n19 & sum(n22, n22) = n18 & sum(n22, n21) = n17 & sum(n22, n20) = n16 & sum(n22, n19) = n15 & sum(n22, n18) = n14 & sum(n22, n17) = n13 & sum(n22, n16) = n12 & sum(n22, n15) = n11 & sum(n22, n14) = n10 & sum(n22, n13) = n9 & sum(n22, n12) = n8 & sum(n22, n11) = n7 & sum(n22, n10) = n6 & sum(n22, n9) = n5 & sum(n22, n8) = n4 & sum(n22, n7) = n3 & sum(n22, n6) = n2 & sum(n22, n5) = n1 & sum(n22, n4) = n0 & sum(n22, n3) = n25 & sum(n22, n2) = n24 & sum(n22, n1) = n23 & sum(n22, n0) = n22 & sum(n21, n25) = n20 & sum(n21, n24) = n19 & sum(n21, n23) = n18 & sum(n21, n22) = n17 & sum(n21, n21) = n16 & sum(n21, n20) = n15 & sum(n21, n19) = n14 & sum(n21, n18) = n13 & sum(n21, n17) = n12 & sum(n21, n16) = n11 & sum(n21, n15) = n10 & sum(n21, n14) = n9 & sum(n21, n13) = n8 & sum(n21, n12) = n7 & sum(n21, n11) = n6 & sum(n21, n10) = n5 & sum(n21, n9) = n4 & sum(n21, n8) = n3 & sum(n21, n7) = n2 & sum(n21, n6) = n1 & sum(n21, n5) = n0 & sum(n21, n4) = n25 & sum(n21, n3) = n24 & sum(n21, n2) = n23 & sum(n21, n1) = n22 & sum(n21, n0) = n21 & sum(n20, n25) = n19 & sum(n20, n24) = n18 & sum(n20, n23) = n17 & sum(n20, n22) = n16 & sum(n20, n21) = n15 & sum(n20, n20) = n14 & sum(n20, n19) = n13 & sum(n20, n18) = n12 & sum(n20, n17) = n11 & sum(n20, n16) = n10 & sum(n20, n15) = n9 & sum(n20, n14) = n8 & sum(n20, n13) = n7 & sum(n20, n12) = n6 & sum(n20, n11) = n5 & sum(n20, n10) = n4 & sum(n20, n9) = n3 & sum(n20, n8) = n2 & sum(n20, n7) = n1 & sum(n20, n6) = n0 & sum(n20, n5) = n25 & sum(n20, n4) = n24 & sum(n20, n3) = n23 & sum(n20, n2) = n22 & sum(n20, n1) = n21 & sum(n20, n0) = n20 & sum(n19, n25) = n18 & sum(n19, n24) = n17 & sum(n19, n23) = n16 & sum(n19, n22) = n15 & sum(n19, n21) = n14 & sum(n19, n20) = n13 & sum(n19, n19) = n12 & sum(n19, n18) = n11 & sum(n19, n17) = n10 & sum(n19, n16) = n9 & sum(n19, n15) = n8 & sum(n19, n14) = n7 & sum(n19, n13) = n6 & sum(n19, n12) = n5 & sum(n19, n11) = n4 & sum(n19, n10) = n3 & sum(n19, n9) = n2 & sum(n19, n8) = n1 & sum(n19, n7) = n0 & sum(n19, n6) = n25 & sum(n19, n5) = n24 & sum(n19, n4) = n23 & sum(n19, n3) = n22 & sum(n19, n2) = n21 & sum(n19, n1) = n20 & sum(n19, n0) = n19 & sum(n18, n25) = n17 & sum(n18, n24) = n16 & sum(n18, n23) = n15 & sum(n18, n22) = n14 & sum(n18, n21) = n13 & sum(n18, n20) = n12 & sum(n18, n19) = n11 & sum(n18, n18) = n10 & sum(n18, n17) = n9 & sum(n18, n16) = n8 & sum(n18, n15) = n7 & sum(n18, n14) = n6 & sum(n18, n13) = n5 & sum(n18, n12) = n4 & sum(n18, n11) = n3 & sum(n18, n10) = n2 & sum(n18, n9) = n1 & sum(n18, n8) = n0 & sum(n18, n7) = n25 & sum(n18, n6) = n24 & sum(n18, n5) = n23 & sum(n18, n4) = n22 & sum(n18, n3) = n21 & sum(n18, n2) = n20 & sum(n18, n1) = n19 & sum(n18, n0) = n18 & sum(n17, n25) = n16 & sum(n17, n24) = n15 & sum(n17, n23) = n14 & sum(n17, n22) = n13 & sum(n17, n21) = n12 & sum(n17, n20) = n11 & sum(n17, n19) = n10 & sum(n17, n18) = n9 & sum(n17, n17) = n8 & sum(n17, n16) = n7 & sum(n17, n15) = n6 & sum(n17, n14) = n5 & sum(n17, n13) = n4 & sum(n17, n12) = n3 & sum(n17, n11) = n2 & sum(n17, n10) = n1 & sum(n17, n9) = n0 & sum(n17, n8) = n25 & sum(n17, n7) = n24 & sum(n17, n6) = n23 & sum(n17, n5) = n22 & sum(n17, n4) = n21 & sum(n17, n3) = n20 & sum(n17, n2) = n19 & sum(n17, n1) = n18 & sum(n17, n0) = n17 & sum(n16, n25) = n15 & sum(n16, n24) = n14 & sum(n16, n23) = n13 & sum(n16, n22) = n12 & sum(n16, n21) = n11 & sum(n16, n20) = n10 & sum(n16, n19) = n9 & sum(n16, n18) = n8 & sum(n16, n17) = n7 & sum(n16, n16) = n6 & sum(n16, n15) = n5 & sum(n16, n14) = n4 & sum(n16, n13) = n3 & sum(n16, n12) = n2 & sum(n16, n11) = n1 & sum(n16, n10) = n0 & sum(n16, n9) = n25 & sum(n16, n8) = n24 & sum(n16, n7) = n23 & sum(n16, n6) = n22 & sum(n16, n5) = n21 & sum(n16, n4) = n20 & sum(n16, n3) = n19 & sum(n16, n2) = n18 & sum(n16, n1) = n17 & sum(n16, n0) = n16 & sum(n15, n25) = n14 & sum(n15, n24) = n13 & sum(n15, n23) = n12 & sum(n15, n22) = n11 & sum(n15, n21) = n10 & sum(n15, n20) = n9 & sum(n15, n19) = n8 & sum(n15, n18) = n7 & sum(n15, n17) = n6 & sum(n15, n16) = n5 & sum(n15, n15) = n4 & sum(n15, n14) = n3 & sum(n15, n13) = n2 & sum(n15, n12) = n1 & sum(n15, n11) = n0 & sum(n15, n10) = n25 & sum(n15, n9) = n24 & sum(n15, n8) = n23 & sum(n15, n7) = n22 & sum(n15, n6) = n21 & 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, n25) = n13 & sum(n14, n24) = n12 & sum(n14, n23) = n11 & sum(n14, n22) = n10 & sum(n14, n21) = n9 & sum(n14, n20) = n8 & sum(n14, n19) = n7 & sum(n14, n18) = n6 & sum(n14, n17) = n5 & sum(n14, n16) = n4 & sum(n14, n15) = n3 & sum(n14, n14) = n2 & sum(n14, n13) = n1 & sum(n14, n12) = n0 & sum(n14, n11) = n25 & sum(n14, n10) = n24 & sum(n14, n9) = n23 & sum(n14, n8) = n22 & sum(n14, n7) = n21 & 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, n25) = n12 & sum(n13, n24) = n11 & sum(n13, n23) = n10 & sum(n13, n22) = n9 & sum(n13, n21) = n8 & sum(n13, n20) = n7 & sum(n13, n19) = n6 & sum(n13, n18) = n5 & sum(n13, n17) = n4 & sum(n13, n16) = n3 & sum(n13, n15) = n2 & sum(n13, n14) = n1 & sum(n13, n13) = n0 & sum(n13, n12) = n25 & sum(n13, n11) = n24 & sum(n13, n10) = n23 & sum(n13, n9) = n22 & sum(n13, n8) = n21 & 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, n25) = n11 & sum(n12, n24) = n10 & sum(n12, n23) = n9 & sum(n12, n22) = n8 & sum(n12, n21) = n7 & sum(n12, n20) = n6 & sum(n12, n19) = n5 & sum(n12, n18) = n4 & sum(n12, n17) = n3 & sum(n12, n16) = n2 & sum(n12, n15) = n1 & sum(n12, n14) = n0 & sum(n12, n13) = n25 & sum(n12, n12) = n24 & sum(n12, n11) = n23 & sum(n12, n10) = n22 & sum(n12, n9) = n21 & 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, n25) = n10 & sum(n11, n24) = n9 & sum(n11, n23) = n8 & sum(n11, n22) = n7 & sum(n11, n21) = n6 & sum(n11, n20) = n5 & sum(n11, n19) = n4 & sum(n11, n18) = n3 & sum(n11, n17) = n2 & sum(n11, n16) = n1 & sum(n11, n15) = n0 & sum(n11, n14) = n25 & sum(n11, n13) = n24 & sum(n11, n12) = n23 & sum(n11, n11) = n22 & sum(n11, n10) = n21 & 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, n25) = n9 & sum(n10, n24) = n8 & sum(n10, n23) = n7 & sum(n10, n22) = n6 & sum(n10, n21) = n5 & sum(n10, n20) = n4 & sum(n10, n19) = n3 & sum(n10, n18) = n2 & sum(n10, n17) = n1 & sum(n10, n16) = n0 & sum(n10, n15) = n25 & sum(n10, n14) = n24 & sum(n10, n13) = n23 & sum(n10, n12) = n22 & sum(n10, n11) = n21 & 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, n25) = n8 & sum(n9, n24) = n7 & sum(n9, n23) = n6 & sum(n9, n22) = n5 & sum(n9, n21) = n4 & sum(n9, n20) = n3 & sum(n9, n19) = n2 & sum(n9, n18) = n1 & sum(n9, n17) = n0 & sum(n9, n16) = n25 & sum(n9, n15) = n24 & sum(n9, n14) = n23 & sum(n9, n13) = n22 & sum(n9, n12) = n21 & 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, n25) = n7 & sum(n8, n24) = n6 & sum(n8, n23) = n5 & sum(n8, n22) = n4 & sum(n8, n21) = n3 & sum(n8, n20) = n2 & sum(n8, n19) = n1 & sum(n8, n18) = n0 & sum(n8, n17) = n25 & sum(n8, n16) = n24 & sum(n8, n15) = n23 & sum(n8, n14) = n22 & sum(n8, n13) = n21 & 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, n25) = n6 & sum(n7, n24) = n5 & sum(n7, n23) = n4 & sum(n7, n22) = n3 & sum(n7, n21) = n2 & sum(n7, n20) = n1 & sum(n7, n19) = n0 & sum(n7, n18) = n25 & sum(n7, n17) = n24 & sum(n7, n16) = n23 & sum(n7, n15) = n22 & sum(n7, n14) = n21 & 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, n25) = n5 & sum(n6, n24) = n4 & sum(n6, n23) = n3 & sum(n6, n22) = n2 & sum(n6, n21) = n1 & sum(n6, n20) = n0 & sum(n6, n19) = n25 & sum(n6, n18) = n24 & sum(n6, n17) = n23 & sum(n6, n16) = n22 & sum(n6, n15) = n21 & 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, n25) = n4 & sum(n5, n24) = n3 & sum(n5, n23) = n2 & sum(n5, n22) = n1 & sum(n5, n21) = n0 & sum(n5, n20) = n25 & sum(n5, n19) = n24 & sum(n5, n18) = n23 & sum(n5, n17) = n22 & sum(n5, n16) = n21 & 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, n25) = n3 & sum(n4, n24) = n2 & sum(n4, n23) = n1 & sum(n4, n22) = n0 & sum(n4, n21) = n25 & sum(n4, n20) = n24 & sum(n4, n19) = n23 & sum(n4, n18) = n22 & sum(n4, n17) = n21 & 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, n25) = n2 & sum(n3, n24) = n1 & sum(n3, n23) = n0 & sum(n3, n22) = n25 & sum(n3, n21) = n24 & sum(n3, n20) = n23 & sum(n3, n19) = n22 & sum(n3, n18) = n21 & 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, n25) = n1 & sum(n2, n24) = n0 & sum(n2, n23) = n25 & sum(n2, n22) = n24 & sum(n2, n21) = n23 & sum(n2, n20) = n22 & sum(n2, n19) = n21 & 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, n25) = n0 & sum(n1, n24) = n25 & sum(n1, n23) = n24 & sum(n1, n22) = n23 & sum(n1, n21) = n22 & sum(n1, n20) = n21 & 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, n25) = n25 & sum(n0, n24) = n24 & sum(n0, n23) = n23 & sum(n0, n22) = n22 & sum(n0, n21) = n21 & 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 = n25 | v1 = n24 | v1 = n23 | v1 = n22 | v1 = n21 | 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 = n25 | v0 = n24 | v0 = n23 | v0 = n22 | v0 = n21 | 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))
% 50.80/19.74 | 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:
% 50.80/19.74 | (1) ~ (all_0_0_0 = all_0_3_3) & ~ (n25 = n24) & ~ (n25 = n23) & ~ (n25 = n22) & ~ (n25 = n21) & ~ (n25 = n20) & ~ (n25 = n19) & ~ (n25 = n18) & ~ (n25 = n17) & ~ (n25 = n16) & ~ (n25 = n15) & ~ (n25 = n14) & ~ (n25 = n13) & ~ (n25 = n12) & ~ (n25 = n11) & ~ (n25 = n10) & ~ (n25 = n9) & ~ (n25 = n8) & ~ (n25 = n7) & ~ (n25 = n6) & ~ (n25 = n5) & ~ (n25 = n4) & ~ (n25 = n3) & ~ (n25 = n2) & ~ (n25 = n1) & ~ (n25 = n0) & ~ (n24 = n23) & ~ (n24 = n22) & ~ (n24 = n21) & ~ (n24 = n20) & ~ (n24 = n19) & ~ (n24 = n18) & ~ (n24 = n17) & ~ (n24 = n16) & ~ (n24 = n15) & ~ (n24 = n14) & ~ (n24 = n13) & ~ (n24 = n12) & ~ (n24 = n11) & ~ (n24 = n10) & ~ (n24 = n9) & ~ (n24 = n8) & ~ (n24 = n7) & ~ (n24 = n6) & ~ (n24 = n5) & ~ (n24 = n4) & ~ (n24 = n3) & ~ (n24 = n2) & ~ (n24 = n1) & ~ (n24 = n0) & ~ (n23 = n22) & ~ (n23 = n21) & ~ (n23 = n20) & ~ (n23 = n19) & ~ (n23 = n18) & ~ (n23 = n17) & ~ (n23 = n16) & ~ (n23 = n15) & ~ (n23 = n14) & ~ (n23 = n13) & ~ (n23 = n12) & ~ (n23 = n11) & ~ (n23 = n10) & ~ (n23 = n9) & ~ (n23 = n8) & ~ (n23 = n7) & ~ (n23 = n6) & ~ (n23 = n5) & ~ (n23 = n4) & ~ (n23 = n3) & ~ (n23 = n2) & ~ (n23 = n1) & ~ (n23 = n0) & ~ (n22 = n21) & ~ (n22 = n20) & ~ (n22 = n19) & ~ (n22 = n18) & ~ (n22 = n17) & ~ (n22 = n16) & ~ (n22 = n15) & ~ (n22 = n14) & ~ (n22 = n13) & ~ (n22 = n12) & ~ (n22 = n11) & ~ (n22 = n10) & ~ (n22 = n9) & ~ (n22 = n8) & ~ (n22 = n7) & ~ (n22 = n6) & ~ (n22 = n5) & ~ (n22 = n4) & ~ (n22 = n3) & ~ (n22 = n2) & ~ (n22 = n1) & ~ (n22 = n0) & ~ (n21 = n20) & ~ (n21 = n19) & ~ (n21 = n18) & ~ (n21 = n17) & ~ (n21 = n16) & ~ (n21 = n15) & ~ (n21 = n14) & ~ (n21 = n13) & ~ (n21 = n12) & ~ (n21 = n11) & ~ (n21 = n10) & ~ (n21 = n9) & ~ (n21 = n8) & ~ (n21 = n7) & ~ (n21 = n6) & ~ (n21 = n5) & ~ (n21 = n4) & ~ (n21 = n3) & ~ (n21 = n2) & ~ (n21 = n1) & ~ (n21 = n0) & ~ (n20 = n19) & ~ (n20 = n18) & ~ (n20 = n17) & ~ (n20 = n16) & ~ (n20 = n15) & ~ (n20 = n14) & ~ (n20 = n13) & ~ (n20 = n12) & ~ (n20 = n11) & ~ (n20 = n10) & ~ (n20 = n9) & ~ (n20 = n8) & ~ (n20 = n7) & ~ (n20 = n6) & ~ (n20 = n5) & ~ (n20 = n4) & ~ (n20 = n3) & ~ (n20 = n2) & ~ (n20 = n1) & ~ (n20 = n0) & ~ (n19 = n18) & ~ (n19 = n17) & ~ (n19 = n16) & ~ (n19 = n15) & ~ (n19 = n14) & ~ (n19 = n13) & ~ (n19 = n12) & ~ (n19 = n11) & ~ (n19 = n10) & ~ (n19 = n9) & ~ (n19 = n8) & ~ (n19 = n7) & ~ (n19 = n6) & ~ (n19 = n5) & ~ (n19 = n4) & ~ (n19 = n3) & ~ (n19 = n2) & ~ (n19 = n1) & ~ (n19 = n0) & ~ (n18 = n17) & ~ (n18 = n16) & ~ (n18 = n15) & ~ (n18 = n14) & ~ (n18 = n13) & ~ (n18 = n12) & ~ (n18 = n11) & ~ (n18 = n10) & ~ (n18 = n9) & ~ (n18 = n8) & ~ (n18 = n7) & ~ (n18 = n6) & ~ (n18 = n5) & ~ (n18 = n4) & ~ (n18 = n3) & ~ (n18 = n2) & ~ (n18 = n1) & ~ (n18 = n0) & ~ (n17 = n16) & ~ (n17 = n15) & ~ (n17 = n14) & ~ (n17 = n13) & ~ (n17 = n12) & ~ (n17 = n11) & ~ (n17 = n10) & ~ (n17 = n9) & ~ (n17 = n8) & ~ (n17 = n7) & ~ (n17 = n6) & ~ (n17 = n5) & ~ (n17 = n4) & ~ (n17 = n3) & ~ (n17 = n2) & ~ (n17 = n1) & ~ (n17 = n0) & ~ (n16 = n15) & ~ (n16 = n14) & ~ (n16 = n13) & ~ (n16 = n12) & ~ (n16 = n11) & ~ (n16 = n10) & ~ (n16 = n9) & ~ (n16 = n8) & ~ (n16 = n7) & ~ (n16 = n6) & ~ (n16 = n5) & ~ (n16 = n4) & ~ (n16 = n3) & ~ (n16 = n2) & ~ (n16 = n1) & ~ (n16 = n0) & ~ (n15 = n14) & ~ (n15 = n13) & ~ (n15 = n12) & ~ (n15 = n11) & ~ (n15 = n10) & ~ (n15 = n9) & ~ (n15 = n8) & ~ (n15 = n7) & ~ (n15 = n6) & ~ (n15 = n5) & ~ (n15 = n4) & ~ (n15 = n3) & ~ (n15 = n2) & ~ (n15 = n1) & ~ (n15 = n0) & ~ (n14 = n13) & ~ (n14 = n12) & ~ (n14 = n11) & ~ (n14 = n10) & ~ (n14 = n9) & ~ (n14 = n8) & ~ (n14 = n7) & ~ (n14 = n6) & ~ (n14 = n5) & ~ (n14 = n4) & ~ (n14 = n3) & ~ (n14 = n2) & ~ (n14 = n1) & ~ (n14 = n0) & ~ (n13 = n12) & ~ (n13 = n11) & ~ (n13 = n10) & ~ (n13 = n9) & ~ (n13 = n8) & ~ (n13 = n7) & ~ (n13 = n6) & ~ (n13 = n5) & ~ (n13 = n4) & ~ (n13 = n3) & ~ (n13 = n2) & ~ (n13 = n1) & ~ (n13 = n0) & ~ (n12 = n11) & ~ (n12 = n10) & ~ (n12 = n9) & ~ (n12 = n8) & ~ (n12 = n7) & ~ (n12 = n6) & ~ (n12 = n5) & ~ (n12 = n4) & ~ (n12 = n3) & ~ (n12 = n2) & ~ (n12 = n1) & ~ (n12 = n0) & ~ (n11 = n10) & ~ (n11 = n9) & ~ (n11 = n8) & ~ (n11 = n7) & ~ (n11 = n6) & ~ (n11 = n5) & ~ (n11 = n4) & ~ (n11 = n3) & ~ (n11 = n2) & ~ (n11 = n1) & ~ (n11 = n0) & ~ (n10 = n9) & ~ (n10 = n8) & ~ (n10 = n7) & ~ (n10 = n6) & ~ (n10 = n5) & ~ (n10 = n4) & ~ (n10 = n3) & ~ (n10 = n2) & ~ (n10 = n1) & ~ (n10 = n0) & ~ (n9 = n8) & ~ (n9 = n7) & ~ (n9 = n6) & ~ (n9 = n5) & ~ (n9 = n4) & ~ (n9 = n3) & ~ (n9 = n2) & ~ (n9 = n1) & ~ (n9 = n0) & ~ (n8 = n7) & ~ (n8 = n6) & ~ (n8 = n5) & ~ (n8 = n4) & ~ (n8 = n3) & ~ (n8 = n2) & ~ (n8 = n1) & ~ (n8 = n0) & ~ (n7 = n6) & ~ (n7 = n5) & ~ (n7 = n4) & ~ (n7 = n3) & ~ (n7 = n2) & ~ (n7 = n1) & ~ (n7 = n0) & ~ (n6 = n5) & ~ (n6 = n4) & ~ (n6 = n3) & ~ (n6 = n2) & ~ (n6 = n1) & ~ (n6 = n0) & ~ (n5 = n4) & ~ (n5 = n3) & ~ (n5 = n2) & ~ (n5 = n1) & ~ (n5 = n0) & ~ (n4 = n3) & ~ (n4 = n2) & ~ (n4 = n1) & ~ (n4 = n0) & ~ (n3 = n2) & ~ (n3 = n1) & ~ (n3 = n0) & ~ (n2 = n1) & ~ (n2 = n0) & ~ (n1 = n0) & pred(all_0_10_10) = all_0_6_6 & pred(all_0_11_11) = all_0_9_9 & pred(n25) = n24 & pred(n24) = n23 & pred(n23) = n22 & pred(n22) = n21 & pred(n21) = n20 & 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) = n25 & succ(all_0_10_10) = all_0_8_8 & succ(all_0_11_11) = all_0_5_5 & succ(n25) = n0 & succ(n24) = n25 & succ(n23) = n24 & succ(n22) = n23 & succ(n21) = n22 & succ(n20) = n21 & 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(n25, n25) = n24 & sum(n25, n24) = n23 & sum(n25, n23) = n22 & sum(n25, n22) = n21 & sum(n25, n21) = n20 & sum(n25, n20) = n19 & sum(n25, n19) = n18 & sum(n25, n18) = n17 & sum(n25, n17) = n16 & sum(n25, n16) = n15 & sum(n25, n15) = n14 & sum(n25, n14) = n13 & sum(n25, n13) = n12 & sum(n25, n12) = n11 & sum(n25, n11) = n10 & sum(n25, n10) = n9 & sum(n25, n9) = n8 & sum(n25, n8) = n7 & sum(n25, n7) = n6 & sum(n25, n6) = n5 & sum(n25, n5) = n4 & sum(n25, n4) = n3 & sum(n25, n3) = n2 & sum(n25, n2) = n1 & sum(n25, n1) = n0 & sum(n25, n0) = n25 & sum(n24, n25) = n23 & sum(n24, n24) = n22 & sum(n24, n23) = n21 & sum(n24, n22) = n20 & sum(n24, n21) = n19 & sum(n24, n20) = n18 & sum(n24, n19) = n17 & sum(n24, n18) = n16 & sum(n24, n17) = n15 & sum(n24, n16) = n14 & sum(n24, n15) = n13 & sum(n24, n14) = n12 & sum(n24, n13) = n11 & sum(n24, n12) = n10 & sum(n24, n11) = n9 & sum(n24, n10) = n8 & sum(n24, n9) = n7 & sum(n24, n8) = n6 & sum(n24, n7) = n5 & sum(n24, n6) = n4 & sum(n24, n5) = n3 & sum(n24, n4) = n2 & sum(n24, n3) = n1 & sum(n24, n2) = n0 & sum(n24, n1) = n25 & sum(n24, n0) = n24 & sum(n23, n25) = n22 & sum(n23, n24) = n21 & sum(n23, n23) = n20 & sum(n23, n22) = n19 & sum(n23, n21) = n18 & sum(n23, n20) = n17 & sum(n23, n19) = n16 & sum(n23, n18) = n15 & sum(n23, n17) = n14 & sum(n23, n16) = n13 & sum(n23, n15) = n12 & sum(n23, n14) = n11 & sum(n23, n13) = n10 & sum(n23, n12) = n9 & sum(n23, n11) = n8 & sum(n23, n10) = n7 & sum(n23, n9) = n6 & sum(n23, n8) = n5 & sum(n23, n7) = n4 & sum(n23, n6) = n3 & sum(n23, n5) = n2 & sum(n23, n4) = n1 & sum(n23, n3) = n0 & sum(n23, n2) = n25 & sum(n23, n1) = n24 & sum(n23, n0) = n23 & sum(n22, n25) = n21 & sum(n22, n24) = n20 & sum(n22, n23) = n19 & sum(n22, n22) = n18 & sum(n22, n21) = n17 & sum(n22, n20) = n16 & sum(n22, n19) = n15 & sum(n22, n18) = n14 & sum(n22, n17) = n13 & sum(n22, n16) = n12 & sum(n22, n15) = n11 & sum(n22, n14) = n10 & sum(n22, n13) = n9 & sum(n22, n12) = n8 & sum(n22, n11) = n7 & sum(n22, n10) = n6 & sum(n22, n9) = n5 & sum(n22, n8) = n4 & sum(n22, n7) = n3 & sum(n22, n6) = n2 & sum(n22, n5) = n1 & sum(n22, n4) = n0 & sum(n22, n3) = n25 & sum(n22, n2) = n24 & sum(n22, n1) = n23 & sum(n22, n0) = n22 & sum(n21, n25) = n20 & sum(n21, n24) = n19 & sum(n21, n23) = n18 & sum(n21, n22) = n17 & sum(n21, n21) = n16 & sum(n21, n20) = n15 & sum(n21, n19) = n14 & sum(n21, n18) = n13 & sum(n21, n17) = n12 & sum(n21, n16) = n11 & sum(n21, n15) = n10 & sum(n21, n14) = n9 & sum(n21, n13) = n8 & sum(n21, n12) = n7 & sum(n21, n11) = n6 & sum(n21, n10) = n5 & sum(n21, n9) = n4 & sum(n21, n8) = n3 & sum(n21, n7) = n2 & sum(n21, n6) = n1 & sum(n21, n5) = n0 & sum(n21, n4) = n25 & sum(n21, n3) = n24 & sum(n21, n2) = n23 & sum(n21, n1) = n22 & sum(n21, n0) = n21 & sum(n20, n25) = n19 & sum(n20, n24) = n18 & sum(n20, n23) = n17 & sum(n20, n22) = n16 & sum(n20, n21) = n15 & sum(n20, n20) = n14 & sum(n20, n19) = n13 & sum(n20, n18) = n12 & sum(n20, n17) = n11 & sum(n20, n16) = n10 & sum(n20, n15) = n9 & sum(n20, n14) = n8 & sum(n20, n13) = n7 & sum(n20, n12) = n6 & sum(n20, n11) = n5 & sum(n20, n10) = n4 & sum(n20, n9) = n3 & sum(n20, n8) = n2 & sum(n20, n7) = n1 & sum(n20, n6) = n0 & sum(n20, n5) = n25 & sum(n20, n4) = n24 & sum(n20, n3) = n23 & sum(n20, n2) = n22 & sum(n20, n1) = n21 & sum(n20, n0) = n20 & sum(n19, n25) = n18 & sum(n19, n24) = n17 & sum(n19, n23) = n16 & sum(n19, n22) = n15 & sum(n19, n21) = n14 & sum(n19, n20) = n13 & sum(n19, n19) = n12 & sum(n19, n18) = n11 & sum(n19, n17) = n10 & sum(n19, n16) = n9 & sum(n19, n15) = n8 & sum(n19, n14) = n7 & sum(n19, n13) = n6 & sum(n19, n12) = n5 & sum(n19, n11) = n4 & sum(n19, n10) = n3 & sum(n19, n9) = n2 & sum(n19, n8) = n1 & sum(n19, n7) = n0 & sum(n19, n6) = n25 & sum(n19, n5) = n24 & sum(n19, n4) = n23 & sum(n19, n3) = n22 & sum(n19, n2) = n21 & sum(n19, n1) = n20 & sum(n19, n0) = n19 & sum(n18, n25) = n17 & sum(n18, n24) = n16 & sum(n18, n23) = n15 & sum(n18, n22) = n14 & sum(n18, n21) = n13 & sum(n18, n20) = n12 & sum(n18, n19) = n11 & sum(n18, n18) = n10 & sum(n18, n17) = n9 & sum(n18, n16) = n8 & sum(n18, n15) = n7 & sum(n18, n14) = n6 & sum(n18, n13) = n5 & sum(n18, n12) = n4 & sum(n18, n11) = n3 & sum(n18, n10) = n2 & sum(n18, n9) = n1 & sum(n18, n8) = n0 & sum(n18, n7) = n25 & sum(n18, n6) = n24 & sum(n18, n5) = n23 & sum(n18, n4) = n22 & sum(n18, n3) = n21 & sum(n18, n2) = n20 & sum(n18, n1) = n19 & sum(n18, n0) = n18 & sum(n17, n25) = n16 & sum(n17, n24) = n15 & sum(n17, n23) = n14 & sum(n17, n22) = n13 & sum(n17, n21) = n12 & sum(n17, n20) = n11 & sum(n17, n19) = n10 & sum(n17, n18) = n9 & sum(n17, n17) = n8 & sum(n17, n16) = n7 & sum(n17, n15) = n6 & sum(n17, n14) = n5 & sum(n17, n13) = n4 & sum(n17, n12) = n3 & sum(n17, n11) = n2 & sum(n17, n10) = n1 & sum(n17, n9) = n0 & sum(n17, n8) = n25 & sum(n17, n7) = n24 & sum(n17, n6) = n23 & sum(n17, n5) = n22 & sum(n17, n4) = n21 & sum(n17, n3) = n20 & sum(n17, n2) = n19 & sum(n17, n1) = n18 & sum(n17, n0) = n17 & sum(n16, n25) = n15 & sum(n16, n24) = n14 & sum(n16, n23) = n13 & sum(n16, n22) = n12 & sum(n16, n21) = n11 & sum(n16, n20) = n10 & sum(n16, n19) = n9 & sum(n16, n18) = n8 & sum(n16, n17) = n7 & sum(n16, n16) = n6 & sum(n16, n15) = n5 & sum(n16, n14) = n4 & sum(n16, n13) = n3 & sum(n16, n12) = n2 & sum(n16, n11) = n1 & sum(n16, n10) = n0 & sum(n16, n9) = n25 & sum(n16, n8) = n24 & sum(n16, n7) = n23 & sum(n16, n6) = n22 & sum(n16, n5) = n21 & sum(n16, n4) = n20 & sum(n16, n3) = n19 & sum(n16, n2) = n18 & sum(n16, n1) = n17 & sum(n16, n0) = n16 & sum(n15, n25) = n14 & sum(n15, n24) = n13 & sum(n15, n23) = n12 & sum(n15, n22) = n11 & sum(n15, n21) = n10 & sum(n15, n20) = n9 & sum(n15, n19) = n8 & sum(n15, n18) = n7 & sum(n15, n17) = n6 & sum(n15, n16) = n5 & sum(n15, n15) = n4 & sum(n15, n14) = n3 & sum(n15, n13) = n2 & sum(n15, n12) = n1 & sum(n15, n11) = n0 & sum(n15, n10) = n25 & sum(n15, n9) = n24 & sum(n15, n8) = n23 & sum(n15, n7) = n22 & sum(n15, n6) = n21 & 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, n25) = n13 & sum(n14, n24) = n12 & sum(n14, n23) = n11 & sum(n14, n22) = n10 & sum(n14, n21) = n9 & sum(n14, n20) = n8 & sum(n14, n19) = n7 & sum(n14, n18) = n6 & sum(n14, n17) = n5 & sum(n14, n16) = n4 & sum(n14, n15) = n3 & sum(n14, n14) = n2 & sum(n14, n13) = n1 & sum(n14, n12) = n0 & sum(n14, n11) = n25 & sum(n14, n10) = n24 & sum(n14, n9) = n23 & sum(n14, n8) = n22 & sum(n14, n7) = n21 & 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, n25) = n12 & sum(n13, n24) = n11 & sum(n13, n23) = n10 & sum(n13, n22) = n9 & sum(n13, n21) = n8 & sum(n13, n20) = n7 & sum(n13, n19) = n6 & sum(n13, n18) = n5 & sum(n13, n17) = n4 & sum(n13, n16) = n3 & sum(n13, n15) = n2 & sum(n13, n14) = n1 & sum(n13, n13) = n0 & sum(n13, n12) = n25 & sum(n13, n11) = n24 & sum(n13, n10) = n23 & sum(n13, n9) = n22 & sum(n13, n8) = n21 & 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, n25) = n11 & sum(n12, n24) = n10 & sum(n12, n23) = n9 & sum(n12, n22) = n8 & sum(n12, n21) = n7 & sum(n12, n20) = n6 & sum(n12, n19) = n5 & sum(n12, n18) = n4 & sum(n12, n17) = n3 & sum(n12, n16) = n2 & sum(n12, n15) = n1 & sum(n12, n14) = n0 & sum(n12, n13) = n25 & sum(n12, n12) = n24 & sum(n12, n11) = n23 & sum(n12, n10) = n22 & sum(n12, n9) = n21 & 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, n25) = n10 & sum(n11, n24) = n9 & sum(n11, n23) = n8 & sum(n11, n22) = n7 & sum(n11, n21) = n6 & sum(n11, n20) = n5 & sum(n11, n19) = n4 & sum(n11, n18) = n3 & sum(n11, n17) = n2 & sum(n11, n16) = n1 & sum(n11, n15) = n0 & sum(n11, n14) = n25 & sum(n11, n13) = n24 & sum(n11, n12) = n23 & sum(n11, n11) = n22 & sum(n11, n10) = n21 & 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, n25) = n9 & sum(n10, n24) = n8 & sum(n10, n23) = n7 & sum(n10, n22) = n6 & sum(n10, n21) = n5 & sum(n10, n20) = n4 & sum(n10, n19) = n3 & sum(n10, n18) = n2 & sum(n10, n17) = n1 & sum(n10, n16) = n0 & sum(n10, n15) = n25 & sum(n10, n14) = n24 & sum(n10, n13) = n23 & sum(n10, n12) = n22 & sum(n10, n11) = n21 & 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, n25) = n8 & sum(n9, n24) = n7 & sum(n9, n23) = n6 & sum(n9, n22) = n5 & sum(n9, n21) = n4 & sum(n9, n20) = n3 & sum(n9, n19) = n2 & sum(n9, n18) = n1 & sum(n9, n17) = n0 & sum(n9, n16) = n25 & sum(n9, n15) = n24 & sum(n9, n14) = n23 & sum(n9, n13) = n22 & sum(n9, n12) = n21 & 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, n25) = n7 & sum(n8, n24) = n6 & sum(n8, n23) = n5 & sum(n8, n22) = n4 & sum(n8, n21) = n3 & sum(n8, n20) = n2 & sum(n8, n19) = n1 & sum(n8, n18) = n0 & sum(n8, n17) = n25 & sum(n8, n16) = n24 & sum(n8, n15) = n23 & sum(n8, n14) = n22 & sum(n8, n13) = n21 & 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, n25) = n6 & sum(n7, n24) = n5 & sum(n7, n23) = n4 & sum(n7, n22) = n3 & sum(n7, n21) = n2 & sum(n7, n20) = n1 & sum(n7, n19) = n0 & sum(n7, n18) = n25 & sum(n7, n17) = n24 & sum(n7, n16) = n23 & sum(n7, n15) = n22 & sum(n7, n14) = n21 & 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, n25) = n5 & sum(n6, n24) = n4 & sum(n6, n23) = n3 & sum(n6, n22) = n2 & sum(n6, n21) = n1 & sum(n6, n20) = n0 & sum(n6, n19) = n25 & sum(n6, n18) = n24 & sum(n6, n17) = n23 & sum(n6, n16) = n22 & sum(n6, n15) = n21 & 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, n25) = n4 & sum(n5, n24) = n3 & sum(n5, n23) = n2 & sum(n5, n22) = n1 & sum(n5, n21) = n0 & sum(n5, n20) = n25 & sum(n5, n19) = n24 & sum(n5, n18) = n23 & sum(n5, n17) = n22 & sum(n5, n16) = n21 & 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, n25) = n3 & sum(n4, n24) = n2 & sum(n4, n23) = n1 & sum(n4, n22) = n0 & sum(n4, n21) = n25 & sum(n4, n20) = n24 & sum(n4, n19) = n23 & sum(n4, n18) = n22 & sum(n4, n17) = n21 & 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, n25) = n2 & sum(n3, n24) = n1 & sum(n3, n23) = n0 & sum(n3, n22) = n25 & sum(n3, n21) = n24 & sum(n3, n20) = n23 & sum(n3, n19) = n22 & sum(n3, n18) = n21 & 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, n25) = n1 & sum(n2, n24) = n0 & sum(n2, n23) = n25 & sum(n2, n22) = n24 & sum(n2, n21) = n23 & sum(n2, n20) = n22 & sum(n2, n19) = n21 & 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, n25) = n0 & sum(n1, n24) = n25 & sum(n1, n23) = n24 & sum(n1, n22) = n23 & sum(n1, n21) = n22 & sum(n1, n20) = n21 & 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, n25) = n25 & sum(n0, n24) = n24 & sum(n0, n23) = n23 & sum(n0, n22) = n22 & sum(n0, n21) = n21 & 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 = n25 | all_0_10_10 = n24 | all_0_10_10 = n23 | all_0_10_10 = n22 | all_0_10_10 = n21 | 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 = n25 | all_0_11_11 = n24 | all_0_11_11 = n23 | all_0_11_11 = n22 | all_0_11_11 = n21 | 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)
% 50.80/19.78 |
% 50.80/19.78 | Applying alpha-rule on (1) yields:
% 50.80/19.78 | (2) sum(n15, n0) = n15
% 50.80/19.78 | (3) sum(n8, n0) = n8
% 50.80/19.78 | (4) sum(n11, n19) = n4
% 50.80/19.78 | (5) sum(n15, n25) = n14
% 50.80/19.78 | (6) sum(n17, n5) = n22
% 50.80/19.78 | (7) sum(n15, n10) = n25
% 50.80/19.78 | (8) sum(n20, n16) = n10
% 50.80/19.78 | (9) sum(n20, n11) = n5
% 50.80/19.78 | (10) succ(n1) = n2
% 50.80/19.78 | (11) sum(n7, n7) = n14
% 50.80/19.78 | (12) sum(n17, n9) = n0
% 50.80/19.78 | (13) sum(n12, n25) = n11
% 50.80/19.78 | (14) sum(n4, n16) = n20
% 50.80/19.78 | (15) sum(n10, n7) = n17
% 50.80/19.78 | (16) sum(n10, n8) = n18
% 50.80/19.78 | (17) sum(n19, n1) = n20
% 50.80/19.78 | (18) sum(n17, n18) = n9
% 50.80/19.78 | (19) sum(n4, n23) = n1
% 50.80/19.78 | (20) sum(n24, n19) = n17
% 50.80/19.78 | (21) sum(n17, n23) = n14
% 50.80/19.78 | (22) sum(n16, n13) = n3
% 50.80/19.78 | (23) sum(n4, n22) = n0
% 50.80/19.78 | (24) sum(n16, n19) = n9
% 50.80/19.78 | (25) sum(n8, n6) = n14
% 50.80/19.78 | (26) pred(n14) = n13
% 50.80/19.78 | (27) sum(n6, n25) = n5
% 50.80/19.78 | (28) sum(n23, n16) = n13
% 50.80/19.78 | (29) sum(n18, n7) = n25
% 50.80/19.78 | (30) ~ (n25 = n9)
% 50.80/19.79 | (31) sum(n0, n18) = n18
% 50.80/19.79 | (32) sum(n3, n5) = n8
% 50.80/19.79 | (33) ~ (n6 = n3)
% 50.80/19.79 | (34) ~ (n19 = n5)
% 50.80/19.79 | (35) sum(n4, n9) = n13
% 50.80/19.79 | (36) ~ (n14 = n0)
% 50.80/19.79 | (37) sum(n19, n13) = n6
% 50.80/19.79 | (38) sum(n11, n13) = n24
% 50.80/19.79 | (39) sum(n22, n21) = n17
% 50.80/19.79 | (40) pred(n22) = n21
% 50.80/19.79 | (41) ~ (n15 = n12)
% 50.80/19.79 | (42) sum(n18, n18) = n10
% 50.80/19.79 | (43) sum(n11, n12) = n23
% 50.80/19.79 | (44) ~ (n17 = n6)
% 50.80/19.79 | (45) ~ (n16 = n10)
% 50.80/19.79 | (46) ~ (n12 = n8)
% 50.80/19.79 | (47) ~ (n2 = n0)
% 50.80/19.79 | (48) sum(n4, n3) = n7
% 50.80/19.79 | (49) ~ (n11 = n6)
% 50.80/19.79 | (50) sum(n19, n5) = n24
% 50.80/19.79 | (51) sum(n20, n17) = n11
% 50.80/19.79 | (52) ~ (n22 = n0)
% 50.80/19.79 | (53) ~ (n24 = n0)
% 50.80/19.79 | (54) ~ (n23 = n2)
% 50.80/19.79 | (55) sum(n21, n11) = n6
% 50.80/19.79 | (56) ~ (n3 = n1)
% 50.80/19.79 | (57) sum(n4, n17) = n21
% 50.80/19.79 | (58) sum(n22, n11) = n7
% 50.80/19.79 | (59) ~ (n19 = n2)
% 50.80/19.79 | (60) sum(n18, n20) = n12
% 50.80/19.79 | (61) sum(n21, n20) = n15
% 50.80/19.79 | (62) sum(n25, n10) = n9
% 50.80/19.79 | (63) sum(n21, n25) = n20
% 50.80/19.79 | (64) sum(n0, n21) = n21
% 50.80/19.79 | (65) sum(n2, n1) = n3
% 50.80/19.79 | (66) ~ (n15 = n4)
% 50.80/19.79 | (67) sum(n19, n22) = n15
% 50.80/19.79 | (68) ~ (n3 = n2)
% 50.80/19.79 | (69) ~ (n8 = n6)
% 50.80/19.79 | (70) sum(n12, n22) = n8
% 50.80/19.79 | (71) ~ (n24 = n5)
% 50.80/19.79 | (72) sum(n9, n3) = n12
% 50.80/19.79 | (73) sum(n8, n2) = n10
% 50.80/19.79 | (74) succ(n2) = n3
% 50.80/19.79 | (75) ~ (n9 = n4)
% 50.80/19.79 | (76) sum(n12, n1) = n13
% 50.80/19.79 | (77) sum(n8, n17) = n25
% 50.80/19.79 | (78) sum(n0, n8) = n8
% 50.80/19.79 | (79) ~ (n1 = n0)
% 50.80/19.79 | (80) sum(n14, n19) = n7
% 50.80/19.79 | (81) ~ (n23 = n11)
% 50.80/19.79 | (82) sum(n5, n25) = n4
% 50.80/19.79 | (83) sum(n21, n24) = n19
% 50.80/19.79 | (84) sum(n13, n0) = n13
% 50.80/19.79 | (85) sum(n10, n15) = n25
% 50.80/19.79 | (86) ~ (n20 = n7)
% 50.80/19.79 | (87) sum(n25, n7) = n6
% 50.80/19.79 | (88) ~ (n25 = n18)
% 50.80/19.79 | (89) sum(n9, n25) = n8
% 50.80/19.79 | (90) sum(n2, n11) = n13
% 50.80/19.79 | (91) sum(n6, n20) = n0
% 50.80/19.79 | (92) pred(n8) = n7
% 50.80/19.79 | (93) sum(n23, n20) = n17
% 50.80/19.79 | (94) sum(n17, n19) = n10
% 50.80/19.79 | (95) ~ (n25 = n24)
% 50.80/19.79 | (96) sum(n25, n23) = n22
% 50.80/19.79 | (97) sum(n0, n6) = n6
% 50.80/19.79 | (98) sum(n22, n17) = n13
% 50.80/19.79 | (99) ~ (n17 = n14)
% 50.80/19.79 | (100) ~ (n13 = n7)
% 50.80/19.79 | (101) sum(n19, n23) = n16
% 50.80/19.79 | (102) sum(n1, n15) = n16
% 50.80/19.79 | (103) ~ (n23 = n16)
% 50.80/19.79 | (104) sum(n18, n23) = n15
% 50.80/19.79 | (105) sum(n6, n6) = n12
% 50.80/19.79 | (106) sum(n6, n1) = n7
% 50.80/19.79 | (107) ~ (n21 = n4)
% 50.80/19.79 | (108) ~ (n23 = n21)
% 50.80/19.79 | (109) sum(n3, n23) = n0
% 50.80/19.79 | (110) sum(n18, n15) = n7
% 50.80/19.79 | (111) sum(n1, n3) = n4
% 50.80/19.79 | (112) ~ (n6 = n2)
% 50.80/19.79 | (113) ~ (n12 = n9)
% 50.80/19.79 | (114) sum(n18, n2) = n20
% 50.80/19.79 | (115) sum(n19, n8) = n1
% 50.80/19.79 | (116) sum(n15, n16) = n5
% 50.80/19.79 | (117) ~ (n10 = n6)
% 50.80/19.79 | (118) sum(n14, n20) = n8
% 50.80/19.79 | (119) ~ (n11 = n3)
% 50.80/19.79 | (120) sum(n2, n24) = n0
% 50.80/19.79 | (121) ~ (n18 = n7)
% 50.80/19.79 | (122) ~ (n6 = n1)
% 50.80/19.79 | (123) sum(n25, n3) = n2
% 50.80/19.79 | (124) ~ (n6 = n4)
% 50.80/19.79 | (125) sum(n21, n21) = n16
% 50.80/19.79 | (126) sum(n11, n25) = n10
% 50.80/19.79 | (127) sum(n20, n15) = n9
% 50.80/19.79 | (128) sum(n4, n15) = n19
% 50.80/19.79 | (129) sum(n1, n18) = n19
% 50.80/19.79 | (130) sum(n5, n24) = n3
% 50.80/19.79 | (131) ~ (n22 = n3)
% 50.80/19.79 | (132) sum(n7, n25) = n6
% 50.80/19.79 | (133) sum(n4, n8) = n12
% 50.80/19.79 | (134) succ(n10) = n11
% 50.80/19.79 | (135) pred(n12) = n11
% 50.80/19.79 | (136) ~ (n7 = n1)
% 50.80/19.79 | (137) sum(n16, n8) = n24
% 50.80/19.79 | (138) ~ (n21 = n8)
% 50.80/19.79 | (139) ~ (n19 = n8)
% 50.80/19.79 | (140) sum(n5, n22) = n1
% 50.80/19.79 | (141) ~ (n21 = n7)
% 50.80/19.79 | (142) sum(n25, n25) = n24
% 50.80/19.79 | (143) sum(n12, n17) = n3
% 50.80/19.80 | (144) sum(n4, n7) = n11
% 50.80/19.80 | (145) sum(n23, n25) = n22
% 50.80/19.80 | (146) sum(n7, n13) = n20
% 50.80/19.80 | (147) sum(n15, n14) = n3
% 50.80/19.80 | (148) sum(n17, n10) = n1
% 50.80/19.80 | (149) ~ (n25 = n5)
% 50.80/19.80 | (150) sum(n7, n14) = n21
% 50.80/19.80 | (151) sum(n17, n22) = n13
% 50.80/19.80 | (152) pred(n1) = n0
% 50.80/19.80 | (153) ~ (n16 = n11)
% 50.80/19.80 | (154) ~ (n16 = n13)
% 50.80/19.80 | (155) ~ (n22 = n12)
% 50.80/19.80 | (156) sum(n6, n3) = n9
% 50.80/19.80 | (157) sum(n1, n2) = n3
% 50.80/19.80 | (158) ~ (n14 = n5)
% 50.80/19.80 | (159) pred(n2) = n1
% 50.80/19.80 | (160) sum(n18, n11) = n3
% 50.80/19.80 | (161) ~ (n21 = n10)
% 50.80/19.80 | (162) sum(n22, n15) = n11
% 50.80/19.80 | (163) sum(n1, n14) = n15
% 50.80/19.80 | (164) ~ (n9 = n1)
% 50.80/19.80 | (165) sum(n23, n18) = n15
% 50.80/19.80 | (166) sum(n25, n20) = n19
% 50.80/19.80 | (167) ~ (n12 = n0)
% 50.80/19.80 | (168) sum(n13, n1) = n14
% 50.80/19.80 | (169) sum(n6, n9) = n15
% 50.80/19.80 | (170) ~ (n25 = n7)
% 50.80/19.80 | (171) ~ (n19 = n15)
% 50.80/19.80 | (172) sum(n23, n7) = n4
% 50.80/19.80 | (173) ~ (n16 = n15)
% 50.80/19.80 | (174) ~ (n21 = n20)
% 50.80/19.80 | (175) ~ (n8 = n2)
% 50.80/19.80 | (176) ~ (n21 = n18)
% 50.80/19.80 | (177) ~ (n23 = n15)
% 50.80/19.80 | (178) ~ (n5 = n1)
% 50.80/19.80 | (179) sum(n25, n12) = n11
% 50.80/19.80 | (180) sum(n24, n11) = n9
% 50.80/19.80 | (181) sum(n21, n3) = n24
% 50.80/19.80 | (182) ~ (n18 = n15)
% 50.80/19.80 | (183) sum(n17, n13) = n4
% 50.80/19.80 | (184) sum(n1, n23) = n24
% 50.80/19.80 | (185) sum(n0, n24) = n24
% 50.80/19.80 | (186) ~ (n22 = n17)
% 50.80/19.80 | (187) sum(n10, n2) = n12
% 50.80/19.80 | (188) sum(n25, n24) = n23
% 50.80/19.80 | (189) sum(n1, n6) = n7
% 50.80/19.80 | (190) sum(n1, n10) = n11
% 50.80/19.80 | (191) sum(n4, n2) = n6
% 50.80/19.80 | (192) ~ (n13 = n4)
% 50.80/19.80 | (193) sum(n16, n7) = n23
% 50.80/19.80 | (194) ~ (n24 = n13)
% 50.80/19.80 | (195) ~ (n24 = n15)
% 50.80/19.80 | (196) ~ (n11 = n8)
% 50.80/19.80 | (197) sum(n9, n24) = n7
% 50.80/19.80 | (198) sum(n6, n24) = n4
% 50.80/19.80 | (199) ~ (n7 = n3)
% 50.80/19.80 | (200) sum(n20, n22) = n16
% 50.80/19.80 | (201) ~ (n25 = n21)
% 50.80/19.80 | (202) ~ (n17 = n15)
% 50.80/19.80 | (203) sum(n9, n5) = n14
% 50.80/19.80 | (204) ~ (n16 = n3)
% 50.80/19.80 | (205) sum(n22, n5) = n1
% 50.80/19.80 | (206) sum(n15, n7) = n22
% 50.80/19.80 | (207) sum(n3, n14) = n17
% 50.80/19.80 | (208) sum(n0, n0) = n0
% 50.80/19.80 | (209) ~ (n4 = n1)
% 50.80/19.80 | (210) sum(n18, n0) = n18
% 50.80/19.80 | (211) ~ (n25 = n15)
% 50.80/19.80 | (212) sum(n2, n3) = n5
% 50.80/19.80 | (213) ~ (n16 = n6)
% 50.80/19.80 | (214) ~ (n23 = n12)
% 50.80/19.80 | (215) sum(n14, n13) = n1
% 50.80/19.80 | (216) ~ (n17 = n3)
% 50.80/19.80 | (217) sum(n5, n19) = n24
% 50.80/19.80 | (218) ~ (n22 = n5)
% 50.80/19.80 | (219) ~ (n20 = n13)
% 50.80/19.80 | (220) sum(n25, n6) = n5
% 50.80/19.80 | (221) sum(n3, n21) = n24
% 50.80/19.80 | (222) ~ (n11 = n10)
% 50.80/19.80 | (223) sum(n7, n17) = n24
% 50.80/19.80 | (224) sum(n16, n23) = n13
% 50.80/19.80 | (225) sum(n0, n16) = n16
% 50.80/19.80 | (226) sum(n1, n8) = n9
% 50.80/19.80 | (227) sum(n20, n19) = n13
% 50.80/19.80 | (228) ~ (n20 = n5)
% 50.80/19.80 | (229) ~ (n21 = n1)
% 50.80/19.80 | (230) ~ (n25 = n4)
% 50.80/19.80 | (231) sum(n18, n12) = n4
% 50.80/19.80 | (232) ~ (n17 = n10)
% 50.80/19.80 | (233) sum(n16, n21) = n11
% 50.80/19.80 | (234) sum(n11, n8) = n19
% 50.80/19.80 | (235) ~ (n14 = n1)
% 50.80/19.80 | (236) sum(n23, n14) = n11
% 50.80/19.80 | (237) sum(n9, n8) = n17
% 50.80/19.80 | (238) sum(n6, n14) = n20
% 50.80/19.80 | (239) sum(n16, n24) = n14
% 50.80/19.80 | (240) sum(n16, n2) = n18
% 50.80/19.80 | (241) ~ (n22 = n15)
% 50.80/19.80 | (242) sum(n13, n8) = n21
% 50.80/19.80 | (243) sum(n11, n10) = n21
% 50.80/19.80 | (244) ~ (n19 = n10)
% 50.80/19.80 | (245) sum(n3, n15) = n18
% 50.80/19.80 | (246) sum(n5, n10) = n15
% 50.80/19.80 | (247) sum(n14, n8) = n22
% 50.80/19.80 | (248) ~ (n25 = n0)
% 50.80/19.80 | (249) sum(n6, n23) = n3
% 50.80/19.80 | (250) ~ (n12 = n5)
% 50.80/19.80 | (251) sum(n16, n18) = n8
% 50.80/19.80 | (252) succ(n11) = n12
% 50.80/19.80 | (253) sum(n8, n8) = n16
% 50.80/19.80 | (254) sum(n16, n20) = n10
% 50.80/19.80 | (255) sum(n20, n1) = n21
% 50.80/19.80 | (256) sum(n21, n23) = n18
% 50.80/19.80 | (257) sum(n20, n0) = n20
% 50.80/19.80 | (258) sum(n21, n18) = n13
% 50.80/19.80 | (259) sum(n23, n12) = n9
% 50.80/19.80 | (260) all_0_10_10 = n25 | all_0_10_10 = n24 | all_0_10_10 = n23 | all_0_10_10 = n22 | all_0_10_10 = n21 | 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
% 50.80/19.80 | (261) ~ (n16 = n7)
% 50.80/19.80 | (262) sum(n1, n7) = n8
% 50.80/19.80 | (263) ~ (n22 = n20)
% 50.80/19.80 | (264) sum(n23, n0) = n23
% 50.80/19.80 | (265) sum(n7, n15) = n22
% 50.80/19.80 | (266) sum(n14, n4) = n18
% 50.80/19.80 | (267) sum(n3, n12) = n15
% 50.80/19.80 | (268) sum(n20, n9) = n3
% 50.80/19.80 | (269) sum(n2, n19) = n21
% 50.80/19.80 | (270) sum(n4, n19) = n23
% 50.80/19.80 | (271) sum(n21, n7) = n2
% 50.80/19.80 | (272) sum(n2, n23) = n25
% 50.80/19.80 | (273) ~ (n16 = n5)
% 50.80/19.80 | (274) sum(n5, n2) = n7
% 50.80/19.81 | (275) pred(n16) = n15
% 50.80/19.81 | (276) sum(n25, n0) = n25
% 50.80/19.81 | (277) sum(n25, n2) = n1
% 50.80/19.81 | (278) sum(n11, n16) = n1
% 50.80/19.81 | (279) sum(n7, n8) = n15
% 50.80/19.81 | (280) succ(n3) = n4
% 50.80/19.81 | (281) sum(n8, n18) = n0
% 50.80/19.81 | (282) sum(n7, n1) = n8
% 50.80/19.81 | (283) sum(n8, n19) = n1
% 50.80/19.81 | (284) ~ (n10 = n5)
% 50.80/19.81 | (285) sum(n14, n2) = n16
% 50.80/19.81 | (286) sum(n8, n1) = n9
% 50.80/19.81 | (287) ~ (n10 = n7)
% 50.80/19.81 | (288) sum(n0, n20) = n20
% 50.80/19.81 | (289) sum(n0, n19) = n19
% 50.80/19.81 | (290) sum(n21, n12) = n7
% 50.80/19.81 | (291) ~ (n22 = n1)
% 50.80/19.81 | (292) pred(all_0_10_10) = all_0_6_6
% 50.80/19.81 | (293) sum(n19, n0) = n19
% 50.80/19.81 | (294) ~ (n19 = n4)
% 50.80/19.81 | (295) ~ (n8 = n0)
% 50.80/19.81 | (296) sum(n14, n21) = n9
% 50.80/19.81 | (297) sum(n19, n7) = n0
% 50.80/19.81 | (298) sum(n13, n14) = n1
% 50.80/19.81 | (299) sum(n11, n23) = n8
% 50.80/19.81 | (300) sum(n6, n21) = n1
% 50.80/19.81 | (301) ~ (n24 = n2)
% 50.80/19.81 | (302) ~ (n15 = n1)
% 50.80/19.81 | (303) sum(n24, n12) = n10
% 50.80/19.81 | (304) ~ (n14 = n3)
% 50.80/19.81 | (305) ~ (n12 = n1)
% 50.80/19.81 | (306) ~ (n25 = n6)
% 50.80/19.81 | (307) sum(n10, n4) = n14
% 50.80/19.81 | (308) succ(n12) = n13
% 50.80/19.81 | (309) sum(n12, n6) = n18
% 50.80/19.81 | (310) sum(n17, n17) = n8
% 50.80/19.81 | (311) sum(n23, n13) = n10
% 50.80/19.81 | (312) sum(n0, n25) = n25
% 50.80/19.81 | (313) sum(n22, n3) = n25
% 50.80/19.81 | (314) sum(n24, n13) = n11
% 50.80/19.81 | (315) ~ (n16 = n8)
% 50.80/19.81 | (316) ~ (n4 = n3)
% 50.80/19.81 | (317) ~ (n13 = n10)
% 50.80/19.81 | (318) sum(n20, n3) = n23
% 50.80/19.81 | (319) sum(n0, n13) = n13
% 50.80/19.81 | (320) sum(n19, n2) = n21
% 50.80/19.81 | (321) pred(n21) = n20
% 50.80/19.81 | (322) sum(n9, n19) = n2
% 50.80/19.81 | (323) sum(n19, n3) = n22
% 50.80/19.81 | (324) sum(n18, n3) = n21
% 50.80/19.81 | (325) ~ (n21 = n2)
% 50.80/19.81 | (326) sum(n12, n10) = n22
% 50.80/19.81 | (327) sum(n0, n2) = n2
% 50.80/19.81 | (328) ~ (n14 = n11)
% 50.80/19.81 | (329) sum(n17, n25) = n16
% 50.80/19.81 | (330) ~ (n20 = n15)
% 50.80/19.81 | (331) sum(n7, n0) = n7
% 50.80/19.81 | (332) sum(n2, n4) = n6
% 50.80/19.81 | (333) ~ (n21 = n13)
% 50.80/19.81 | (334) ~ (n25 = n2)
% 50.80/19.81 | (335) sum(n24, n23) = n21
% 50.80/19.81 | (336) sum(n3, n6) = n9
% 50.80/19.81 | (337) succ(n15) = n16
% 50.80/19.81 | (338) sum(n20, n8) = n2
% 50.80/19.81 | (339) sum(n9, n15) = n24
% 50.80/19.81 | (340) sum(n16, n0) = n16
% 50.80/19.81 | (341) ~ (n22 = n7)
% 50.80/19.81 | (342) sum(n12, n19) = n5
% 50.80/19.81 | (343) ~ (n11 = n0)
% 50.80/19.81 | (344) sum(n5, n7) = n12
% 50.80/19.81 | (345) sum(n7, n23) = n4
% 50.80/19.81 | (346) sum(n1, n4) = n5
% 50.80/19.81 | (347) sum(n10, n18) = n2
% 50.80/19.81 | (348) sum(n5, n13) = n18
% 50.80/19.81 | (349) sum(n24, n1) = n25
% 50.80/19.81 | (350) sum(n3, n8) = n11
% 50.80/19.81 | (351) sum(n13, n5) = n18
% 50.80/19.81 | (352) ~ (n19 = n7)
% 50.80/19.81 | (353) ~ (n24 = n22)
% 50.80/19.81 | (354) ~ (n25 = n14)
% 50.80/19.81 | (355) sum(n2, n0) = n2
% 50.80/19.81 | (356) sum(n10, n24) = n8
% 50.80/19.81 | (357) ~ (n15 = n6)
% 50.80/19.81 | (358) sum(n1, n12) = n13
% 50.80/19.81 | (359) ~ (n8 = n7)
% 50.80/19.81 | (360) sum(n15, n23) = n12
% 50.80/19.81 | (361) all_0_11_11 = n25 | all_0_11_11 = n24 | all_0_11_11 = n23 | all_0_11_11 = n22 | all_0_11_11 = n21 | 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
% 50.80/19.81 | (362) sum(n11, n3) = n14
% 50.80/19.81 | (363) sum(n10, n25) = n9
% 50.80/19.81 | (364) sum(n5, n15) = n20
% 50.80/19.81 | (365) ~ (n13 = n11)
% 50.80/19.81 | (366) sum(n15, n12) = n1
% 50.80/19.81 | (367) sum(n12, n16) = n2
% 50.80/19.81 | (368) sum(n14, n6) = n20
% 50.80/19.81 | (369) sum(n24, n10) = n8
% 50.80/19.81 | (370) ~ (n8 = n1)
% 50.80/19.81 | (371) ~ (n13 = n9)
% 50.80/19.81 | (372) sum(n17, n6) = n23
% 50.80/19.81 | (373) sum(n19, n10) = n3
% 50.80/19.81 | (374) ~ (n12 = n4)
% 50.80/19.81 | (375) sum(n5, n3) = n8
% 51.20/19.81 | (376) sum(n9, n16) = n25
% 51.20/19.81 | (377) sum(n12, n18) = n4
% 51.20/19.81 | (378) sum(n13, n23) = n10
% 51.20/19.81 | (379) ~ (n18 = n1)
% 51.20/19.81 | (380) ~ (n23 = n7)
% 51.20/19.81 | (381) sum(n17, n16) = n7
% 51.20/19.81 | (382) sum(n20, n6) = n0
% 51.20/19.81 | (383) sum(n5, n8) = n13
% 51.20/19.81 | (384) sum(n3, n20) = n23
% 51.20/19.81 | (385) sum(n11, n18) = n3
% 51.20/19.81 | (386) sum(n4, n1) = n5
% 51.20/19.81 | (387) pred(n25) = n24
% 51.20/19.81 | (388) ~ (n14 = n13)
% 51.20/19.81 | (389) succ(n13) = n14
% 51.20/19.81 | (390) ~ (n5 = n4)
% 51.20/19.81 | (391) sum(n24, n5) = n3
% 51.20/19.81 | (392) sum(n0, n12) = n12
% 51.20/19.81 | (393) sum(n16, n9) = n25
% 51.20/19.81 | (394) ~ (n20 = n1)
% 51.20/19.81 | (395) sum(n7, n22) = n3
% 51.20/19.81 | (396) ~ (n19 = n3)
% 51.20/19.81 | (397) sum(n6, n4) = n10
% 51.20/19.81 | (398) sum(n4, n20) = n24
% 51.20/19.81 | (399) ~ (n17 = n2)
% 51.20/19.81 | (400) ~ (n17 = n13)
% 51.20/19.81 | (401) ~ (n18 = n5)
% 51.20/19.81 | (402) sum(n23, n19) = n16
% 51.20/19.81 | (403) sum(n19, n12) = n5
% 51.20/19.82 | (404) ~ (n25 = n1)
% 51.20/19.82 | (405) pred(n10) = n9
% 51.20/19.82 | (406) sum(n15, n3) = n18
% 51.20/19.82 | (407) sum(n12, n2) = n14
% 51.20/19.82 | (408) sum(n5, n20) = n25
% 51.20/19.82 | (409) ~ (n3 = n0)
% 51.20/19.82 | (410) ~ (n13 = n12)
% 51.20/19.82 | (411) sum(all_0_6_6, all_0_8_8) = all_0_1_1
% 51.20/19.82 | (412) sum(n1, n13) = n14
% 51.20/19.82 | (413) sum(n17, n12) = n3
% 51.20/19.82 | (414) sum(n8, n14) = n22
% 51.20/19.82 | (415) ~ (n7 = n5)
% 51.20/19.82 | (416) ~ (n25 = n10)
% 51.20/19.82 | (417) sum(n0, n3) = n3
% 51.20/19.82 | (418) ~ (n23 = n3)
% 51.20/19.82 | (419) sum(n8, n16) = n24
% 51.20/19.82 | (420) sum(n24, n17) = n15
% 51.20/19.82 | (421) ~ (n23 = n5)
% 51.20/19.82 | (422) succ(n25) = n0
% 51.20/19.82 | (423) pred(n4) = n3
% 51.20/19.82 | (424) ~ (n15 = n11)
% 51.20/19.82 | (425) ~ (n14 = n7)
% 51.20/19.82 | (426) sum(n2, n12) = n14
% 51.20/19.82 | (427) sum(all_0_9_9, all_0_8_8) = all_0_7_7
% 51.20/19.82 | (428) sum(n15, n24) = n13
% 51.20/19.82 | (429) ~ (n20 = n16)
% 51.20/19.82 | (430) sum(n15, n8) = n23
% 51.20/19.82 | (431) ~ (n23 = n17)
% 51.20/19.82 | (432) ~ (n20 = n0)
% 51.20/19.82 | (433) sum(n14, n16) = n4
% 51.20/19.82 | (434) sum(n13, n7) = n20
% 51.20/19.82 | (435) sum(n14, n0) = n14
% 51.20/19.82 | (436) sum(n4, n10) = n14
% 51.20/19.82 | (437) sum(n20, n2) = n22
% 51.20/19.82 | (438) sum(n8, n25) = n7
% 51.20/19.82 | (439) ~ (n11 = n1)
% 51.20/19.82 | (440) ~ (n12 = n6)
% 51.20/19.82 | (441) ~ (n24 = n1)
% 51.20/19.82 | (442) sum(n13, n12) = n25
% 51.20/19.82 | (443) ~ (n18 = n12)
% 51.20/19.82 | (444) sum(n0, n5) = n5
% 51.20/19.82 | (445) sum(n19, n19) = n12
% 51.20/19.82 | (446) sum(n3, n2) = n5
% 51.20/19.82 | (447) ~ (n12 = n3)
% 51.20/19.82 | (448) sum(n25, n18) = n17
% 51.20/19.82 | (449) sum(n12, n5) = n17
% 51.20/19.82 | (450) sum(n12, n20) = n6
% 51.20/19.82 | (451) sum(n24, n4) = n2
% 51.20/19.82 | (452) sum(n3, n0) = n3
% 51.20/19.82 | (453) sum(n12, n0) = n12
% 51.20/19.82 | (454) ~ (n4 = n2)
% 51.20/19.82 | (455) sum(n10, n5) = n15
% 51.20/19.82 | (456) sum(n8, n21) = n3
% 51.20/19.82 | (457) sum(n5, n14) = n19
% 51.20/19.82 | (458) ~ (n23 = n9)
% 51.20/19.82 | (459) sum(n6, n16) = n22
% 51.20/19.82 | (460) sum(n22, n20) = n16
% 51.20/19.82 | (461) sum(n19, n16) = n9
% 51.20/19.82 | (462) ~ (n5 = n2)
% 51.20/19.82 | (463) ~ (n22 = n13)
% 51.20/19.82 | (464) sum(n8, n5) = n13
% 51.20/19.82 | (465) sum(n17, n8) = n25
% 51.20/19.82 | (466) sum(n10, n11) = n21
% 51.20/19.82 | (467) ~ (n21 = n16)
% 51.20/19.82 | (468) sum(n8, n3) = n11
% 51.20/19.82 | (469) sum(n10, n0) = n10
% 51.20/19.82 | (470) sum(n8, n7) = n15
% 51.20/19.82 | (471) ~ (n23 = n18)
% 51.20/19.82 | (472) sum(n2, n14) = n16
% 51.20/19.82 | (473) ~ (n7 = n2)
% 51.20/19.82 | (474) ~ (n22 = n16)
% 51.20/19.82 | (475) succ(n8) = n9
% 51.20/19.82 | (476) ~ (n10 = n0)
% 51.20/19.82 | (477) sum(n7, n20) = n1
% 51.20/19.82 | (478) ~ (n15 = n2)
% 51.20/19.82 | (479) ~ (n9 = n7)
% 51.20/19.82 | (480) ~ (n19 = n1)
% 51.20/19.82 | (481) sum(n6, n10) = n16
% 51.20/19.82 | (482) sum(n6, n15) = n21
% 51.20/19.82 | (483) sum(n12, n4) = n16
% 51.20/19.82 | (484) sum(n13, n19) = n6
% 51.20/19.82 | (485) sum(n24, n21) = n19
% 51.20/19.82 | (486) ~ (n24 = n11)
% 51.20/19.82 | (487) sum(n12, n12) = n24
% 51.20/19.82 | (488) sum(n18, n19) = n11
% 51.20/19.82 | (489) ~ (n18 = n10)
% 51.20/19.82 | (490) ~ (n21 = n6)
% 51.20/19.82 | (491) ~ (n6 = n5)
% 51.20/19.82 | (492) sum(n19, n15) = n8
% 51.20/19.82 | (493) ~ (n23 = n6)
% 51.20/19.82 | (494) ~ (n13 = n2)
% 51.20/19.82 | (495) sum(n3, n16) = n19
% 51.20/19.82 | (496) sum(n15, n6) = n21
% 51.20/19.82 | (497) sum(n9, n4) = n13
% 51.20/19.82 | (498) sum(n8, n10) = n18
% 51.20/19.82 | (499) sum(n14, n10) = n24
% 51.20/19.82 | (500) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 51.20/19.82 | (501) sum(n13, n2) = n15
% 51.20/19.82 | (502) sum(n18, n14) = n6
% 51.20/19.82 | (503) sum(n14, n11) = n25
% 51.20/19.82 | (504) sum(n9, n13) = n22
% 51.20/19.82 | (505) sum(n1, n21) = n22
% 51.20/19.82 | (506) ~ (n16 = n9)
% 51.20/19.82 | (507) ~ (n11 = n7)
% 51.20/19.82 | (508) sum(n4, n13) = n17
% 51.20/19.82 | (509) ~ (n22 = n21)
% 51.20/19.82 | (510) sum(n15, n18) = n7
% 51.20/19.82 | (511) ~ (n25 = n13)
% 51.20/19.82 | (512) sum(n5, n4) = n9
% 51.20/19.82 | (513) sum(n5, n12) = n17
% 51.20/19.82 | (514) sum(n18, n10) = n2
% 51.20/19.82 | (515) ~ (n22 = n18)
% 51.20/19.82 | (516) sum(n11, n11) = n22
% 51.20/19.82 | (517) pred(n13) = n12
% 51.20/19.82 | (518) ~ (n19 = n16)
% 51.20/19.82 | (519) sum(n25, n8) = n7
% 51.20/19.82 | (520) ~ (n21 = n17)
% 51.20/19.82 | (521) ~ (n6 = n0)
% 51.20/19.82 | (522) pred(n20) = n19
% 51.20/19.83 | (523) pred(n19) = n18
% 51.20/19.83 | (524) sum(n5, n17) = n22
% 51.20/19.83 | (525) sum(n3, n10) = n13
% 51.20/19.83 | (526) ~ (n9 = n8)
% 51.20/19.83 | (527) sum(n8, n4) = n12
% 51.20/19.83 | (528) sum(n18, n25) = n17
% 51.20/19.83 | (529) ~ (n11 = n4)
% 51.20/19.83 | (530) sum(n17, n3) = n20
% 51.20/19.83 | (531) sum(n3, n1) = n4
% 51.20/19.83 | (532) sum(n17, n20) = n11
% 51.20/19.83 | (533) sum(n2, n22) = n24
% 51.20/19.83 | (534) sum(n22, n24) = n20
% 51.20/19.83 | (535) sum(n4, n12) = n16
% 51.20/19.83 | (536) sum(n15, n13) = n2
% 51.20/19.83 | (537) sum(n20, n25) = n19
% 51.20/19.83 | (538) sum(all_0_9_9, all_0_5_5) = all_0_2_2
% 51.20/19.83 | (539) ~ (n19 = n9)
% 51.20/19.83 | (540) sum(n24, n9) = n7
% 51.20/19.83 | (541) sum(all_0_6_6, all_0_5_5) = all_0_4_4
% 51.20/19.83 | (542) sum(n2, n6) = n8
% 51.20/19.83 | (543) sum(n24, n6) = n4
% 51.20/19.83 | (544) sum(n17, n21) = n12
% 51.20/19.83 | (545) sum(n17, n0) = n17
% 51.20/19.83 | (546) sum(n21, n5) = n0
% 51.20/19.83 | (547) sum(n19, n9) = n2
% 51.20/19.83 | (548) ~ (n22 = n8)
% 51.20/19.83 | (549) sum(n19, n20) = n13
% 51.20/19.83 | (550) sum(n14, n17) = n5
% 51.20/19.83 | (551) sum(n21, n1) = n22
% 51.20/19.83 | (552) ~ (n10 = n3)
% 51.20/19.83 | (553) sum(n1, n19) = n20
% 51.20/19.83 | (554) sum(n1, n16) = n17
% 51.20/19.83 | (555) sum(n9, n7) = n16
% 51.20/19.83 | (556) ~ (n21 = n3)
% 51.20/19.83 | (557) sum(n2, n2) = n4
% 51.20/19.83 | (558) sum(n0, n9) = n9
% 51.20/19.83 | (559) pred(all_0_11_11) = all_0_9_9
% 51.20/19.83 | (560) ~ (n24 = n12)
% 51.20/19.83 | (561) ~ (n19 = n17)
% 51.20/19.83 | (562) sum(n11, n15) = n0
% 51.20/19.83 | (563) sum(n20, n12) = n6
% 51.20/19.83 | (564) sum(n18, n13) = n5
% 51.20/19.83 | (565) sum(n5, n11) = n16
% 51.20/19.83 | (566) ~ (n20 = n10)
% 51.20/19.83 | (567) sum(n22, n6) = n2
% 51.20/19.83 | (568) sum(n3, n24) = n1
% 51.20/19.83 | (569) sum(n8, n20) = n2
% 51.20/19.83 | (570) ~ (n18 = n13)
% 51.20/19.83 | (571) succ(n19) = n20
% 51.20/19.83 | (572) sum(n5, n5) = n10
% 51.20/19.83 | (573) ~ (n25 = n17)
% 51.20/19.83 | (574) sum(n21, n16) = n11
% 51.20/19.83 | (575) sum(n11, n4) = n15
% 51.20/19.83 | (576) succ(n16) = n17
% 51.20/19.83 | (577) sum(n10, n17) = n1
% 51.20/19.83 | (578) ~ (n2 = n1)
% 51.20/19.83 | (579) ~ (n24 = n20)
% 51.20/19.83 | (580) sum(n13, n3) = n16
% 51.20/19.83 | (581) ~ (n23 = n19)
% 51.20/19.83 | (582) ~ (n15 = n14)
% 51.20/19.83 | (583) sum(n5, n21) = n0
% 51.20/19.83 | (584) sum(n13, n6) = n19
% 51.20/19.83 | (585) ~ (n24 = n16)
% 51.20/19.83 | (586) sum(n4, n11) = n15
% 51.20/19.83 | (587) sum(n11, n2) = n13
% 51.20/19.83 | (588) sum(n4, n0) = n4
% 51.20/19.83 | (589) pred(n11) = n10
% 51.20/19.83 | (590) sum(all_0_7_7, all_0_4_4) = all_0_3_3
% 51.20/19.83 | (591) ~ (n17 = n0)
% 51.20/19.83 | (592) sum(n7, n21) = n2
% 51.20/19.83 | (593) sum(n14, n24) = n12
% 51.20/19.83 | (594) ~ (n19 = n14)
% 51.20/19.83 | (595) sum(n4, n24) = n2
% 51.20/19.83 | (596) sum(n20, n7) = n1
% 51.20/19.83 | (597) sum(n14, n7) = n21
% 51.20/19.83 | (598) sum(n24, n20) = n18
% 51.20/19.83 | (599) sum(n8, n23) = n5
% 51.20/19.83 | (600) sum(n22, n18) = n14
% 51.20/19.83 | (601) sum(n10, n12) = n22
% 51.20/19.83 | (602) ~ (n18 = n11)
% 51.20/19.83 | (603) sum(n4, n6) = n10
% 51.20/19.83 | (604) sum(n13, n13) = n0
% 51.20/19.83 | (605) ~ (n13 = n0)
% 51.20/19.83 | (606) sum(n5, n0) = n5
% 51.20/19.83 | (607) sum(n22, n16) = n12
% 51.20/19.83 | (608) sum(n16, n12) = n2
% 51.20/19.83 | (609) pred(n15) = n14
% 51.20/19.83 | (610) pred(n9) = n8
% 51.20/19.83 | (611) sum(n10, n6) = n16
% 51.20/19.83 | (612) ~ (n24 = n23)
% 51.20/19.83 | (613) sum(n8, n22) = n4
% 51.20/19.83 | (614) sum(n14, n22) = n10
% 51.20/19.83 | (615) ~ (n9 = n2)
% 51.20/19.83 | (616) sum(n19, n14) = n7
% 51.20/19.83 | (617) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0))
% 51.20/19.83 | (618) sum(n20, n18) = n12
% 51.20/19.83 | (619) sum(n16, n15) = n5
% 51.20/19.83 | (620) sum(n11, n7) = n18
% 51.20/19.83 | (621) sum(n25, n5) = n4
% 51.20/19.83 | (622) succ(n18) = n19
% 51.20/19.83 | (623) sum(n1, n24) = n25
% 51.20/19.83 | (624) sum(n0, n23) = n23
% 51.20/19.83 | (625) ~ (n22 = n6)
% 51.20/19.83 | (626) sum(n13, n20) = n7
% 51.20/19.83 | (627) sum(n18, n17) = n9
% 51.20/19.83 | (628) ~ (n13 = n8)
% 51.20/19.83 | (629) sum(n16, n6) = n22
% 51.20/19.83 | (630) sum(all_0_2_2, all_0_1_1) = all_0_0_0
% 51.20/19.83 | (631) sum(n7, n11) = n18
% 51.20/19.84 | (632) ~ (n19 = n6)
% 51.20/19.84 | (633) sum(n9, n17) = n0
% 51.20/19.84 | (634) ~ (n10 = n4)
% 51.20/19.84 | (635) ~ (n11 = n5)
% 51.20/19.84 | (636) sum(n21, n6) = n1
% 51.20/19.84 | (637) sum(n22, n10) = n6
% 51.20/19.84 | (638) sum(n24, n3) = n1
% 51.20/19.84 | (639) sum(n24, n15) = n13
% 51.20/19.84 | (640) ~ (n22 = n11)
% 51.20/19.84 | (641) sum(n23, n5) = n2
% 51.20/19.84 | (642) ~ (n15 = n13)
% 51.20/19.84 | (643) sum(n3, n17) = n20
% 51.20/19.84 | (644) ~ (n16 = n14)
% 51.20/19.84 | (645) sum(n19, n6) = n25
% 51.20/19.84 | (646) sum(n24, n24) = n22
% 51.20/19.84 | (647) ~ (n22 = n9)
% 51.20/19.84 | (648) sum(n2, n7) = n9
% 51.20/19.84 | (649) ~ (n23 = n22)
% 51.20/19.84 | (650) sum(n23, n2) = n25
% 51.20/19.84 | (651) sum(n3, n22) = n25
% 51.20/19.84 | (652) sum(n14, n1) = n15
% 51.20/19.84 | (653) sum(n12, n13) = n25
% 51.20/19.84 | (654) sum(n2, n20) = n22
% 51.20/19.84 | (655) sum(n21, n9) = n4
% 51.20/19.84 | (656) sum(n3, n4) = n7
% 51.20/19.84 | (657) ~ (n19 = n12)
% 51.20/19.84 | (658) sum(n14, n18) = n6
% 51.20/19.84 | (659) ~ (n14 = n2)
% 51.20/19.84 | (660) sum(n6, n5) = n11
% 51.20/19.84 | (661) ~ (n18 = n17)
% 51.20/19.84 | (662) sum(n18, n5) = n23
% 51.20/19.84 | (663) sum(n11, n21) = n6
% 51.20/19.84 | (664) sum(n20, n24) = n18
% 51.20/19.84 | (665) sum(n24, n18) = n16
% 51.20/19.84 | (666) ~ (n20 = n19)
% 51.20/19.84 | (667) ~ (n10 = n1)
% 51.20/19.84 | (668) ~ (n12 = n10)
% 51.20/19.84 | (669) ~ (n15 = n10)
% 51.20/19.84 | (670) sum(n12, n3) = n15
% 51.20/19.84 | (671) ~ (n18 = n3)
% 51.20/19.84 | (672) sum(n4, n4) = n8
% 51.20/19.84 | (673) sum(n14, n23) = n11
% 51.20/19.84 | (674) sum(n12, n21) = n7
% 51.20/19.84 | (675) ~ (n13 = n6)
% 51.20/19.84 | (676) sum(n2, n18) = n20
% 51.20/19.84 | (677) sum(n12, n24) = n10
% 51.20/19.84 | (678) ~ (n21 = n9)
% 51.20/19.84 | (679) ~ (all_0_0_0 = all_0_3_3)
% 51.20/19.84 | (680) ~ (n24 = n9)
% 51.20/19.84 | (681) sum(n2, n25) = n1
% 51.20/19.84 | (682) sum(n11, n17) = n2
% 51.20/19.84 | (683) sum(n22, n2) = n24
% 51.20/19.84 | (684) sum(n14, n5) = n19
% 51.20/19.84 | (685) ~ (n14 = n4)
% 51.20/19.84 | (686) ~ (n17 = n1)
% 51.20/19.84 | (687) sum(n16, n17) = n7
% 51.20/19.84 | (688) sum(n12, n8) = n20
% 51.20/19.84 | (689) sum(n9, n9) = n18
% 51.20/19.84 | (690) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0))
% 51.20/19.84 | (691) sum(n5, n23) = n2
% 51.20/19.84 | (692) sum(n1, n20) = n21
% 51.20/19.84 | (693) sum(n8, n9) = n17
% 51.20/19.84 | (694) sum(n11, n24) = n9
% 51.20/19.84 | (695) sum(n10, n14) = n24
% 51.20/19.84 | (696) sum(n9, n18) = n1
% 51.20/19.84 | (697) ~ (n14 = n6)
% 51.20/19.84 | (698) sum(n5, n1) = n6
% 51.20/19.84 | (699) sum(n11, n20) = n5
% 51.20/19.84 | (700) sum(n17, n11) = n2
% 51.20/19.84 | (701) ~ (n18 = n9)
% 51.20/19.84 | (702) ~ (n12 = n11)
% 51.20/19.84 | (703) sum(n14, n25) = n13
% 51.20/19.84 | (704) sum(n21, n13) = n8
% 51.20/19.84 | (705) sum(n1, n25) = n0
% 51.20/19.84 | (706) ~ (n22 = n2)
% 51.20/19.84 | (707) ~ (n20 = n17)
% 51.20/19.84 | (708) sum(n0, n15) = n15
% 51.20/19.84 | (709) ~ (n21 = n14)
% 51.20/19.84 | (710) ~ (n23 = n13)
% 51.20/19.84 | (711) sum(n22, n14) = n10
% 51.20/19.84 | (712) sum(n11, n6) = n17
% 51.20/19.84 | (713) ~ (n15 = n7)
% 51.20/19.84 | (714) sum(n0, n17) = n17
% 51.20/19.84 | (715) ~ (n5 = n3)
% 51.20/19.84 | (716) sum(n14, n12) = n0
% 51.20/19.84 | (717) ~ (n17 = n5)
% 51.20/19.84 | (718) sum(n19, n18) = n11
% 51.20/19.84 | (719) sum(n22, n22) = n18
% 51.20/19.84 | (720) ~ (n20 = n9)
% 51.20/19.84 | (721) sum(n18, n22) = n14
% 51.20/19.84 | (722) ~ (n17 = n7)
% 51.20/19.84 | (723) sum(n20, n20) = n14
% 51.20/19.84 | (724) sum(n4, n5) = n9
% 51.20/19.84 | (725) sum(n10, n20) = n4
% 51.20/19.84 | (726) ~ (n21 = n12)
% 51.20/19.84 | (727) ~ (n8 = n3)
% 51.20/19.84 | (728) sum(n10, n9) = n19
% 51.20/19.84 | (729) ~ (n25 = n22)
% 51.20/19.84 | (730) sum(n2, n9) = n11
% 51.20/19.84 | (731) sum(n15, n4) = n19
% 51.20/19.84 | (732) sum(n0, n14) = n14
% 51.20/19.84 | (733) sum(n22, n19) = n15
% 51.20/19.84 | (734) sum(n25, n9) = n8
% 51.20/19.84 | (735) sum(n19, n4) = n23
% 51.20/19.84 | (736) sum(n3, n25) = n2
% 51.20/19.84 | (737) sum(n7, n4) = n11
% 51.20/19.84 | (738) sum(n20, n14) = n8
% 51.20/19.84 | (739) sum(n8, n15) = n23
% 51.20/19.84 | (740) sum(n13, n18) = n5
% 51.20/19.84 | (741) ~ (n21 = n15)
% 51.20/19.84 | (742) sum(n22, n8) = n4
% 51.20/19.84 | (743) ~ (n15 = n0)
% 51.20/19.84 | (744) sum(n23, n22) = n19
% 51.20/19.85 | (745) sum(n8, n13) = n21
% 51.20/19.85 | (746) sum(n13, n24) = n11
% 51.20/19.85 | (747) sum(n22, n1) = n23
% 51.20/19.85 | (748) sum(n19, n24) = n17
% 51.20/19.85 | (749) ~ (n19 = n13)
% 51.20/19.85 | (750) ~ (n13 = n1)
% 51.20/19.85 | (751) sum(n25, n11) = n10
% 51.20/19.85 | (752) ~ (n25 = n16)
% 51.20/19.85 | (753) sum(n0, n4) = n4
% 51.20/19.85 | (754) sum(n7, n9) = n16
% 51.20/19.85 | (755) sum(n24, n7) = n5
% 51.20/19.85 | (756) sum(n12, n14) = n0
% 51.20/19.85 | (757) ~ (n15 = n9)
% 51.20/19.85 | (758) succ(n24) = n25
% 51.20/19.85 | (759) succ(n5) = n6
% 51.20/19.85 | (760) succ(all_0_10_10) = all_0_8_8
% 51.20/19.85 | (761) ~ (n14 = n10)
% 51.20/19.85 | (762) sum(n20, n23) = n17
% 51.20/19.85 | (763) sum(n0, n1) = n1
% 51.20/19.85 | (764) ~ (n24 = n3)
% 51.20/19.85 | (765) sum(n21, n15) = n10
% 51.20/19.85 | (766) ~ (n16 = n4)
% 51.20/19.85 | (767) sum(n18, n1) = n19
% 51.20/19.85 | (768) sum(n19, n17) = n10
% 51.20/19.85 | (769) ~ (n13 = n3)
% 51.20/19.85 | (770) sum(n21, n2) = n23
% 51.20/19.85 | (771) sum(n25, n13) = n12
% 51.20/19.85 | (772) sum(n4, n14) = n18
% 51.20/19.85 | (773) sum(n23, n23) = n20
% 51.20/19.85 | (774) sum(n19, n11) = n4
% 51.20/19.85 | (775) sum(n17, n15) = n6
% 51.20/19.85 | (776) ~ (n24 = n17)
% 51.20/19.85 | (777) sum(n25, n1) = n0
% 51.20/19.85 | (778) sum(n3, n7) = n10
% 51.20/19.85 | (779) ~ (n24 = n7)
% 51.20/19.85 | (780) sum(n2, n15) = n17
% 51.20/19.85 | (781) sum(n14, n3) = n17
% 51.20/19.85 | (782) ~ (n18 = n16)
% 51.20/19.85 | (783) sum(n16, n16) = n6
% 51.20/19.85 | (784) succ(n23) = n24
% 51.20/19.85 | (785) ~ (n25 = n19)
% 51.20/19.85 | (786) sum(n0, n7) = n7
% 51.20/19.85 | (787) sum(n22, n12) = n8
% 51.20/19.85 | (788) sum(n17, n1) = n18
% 51.20/19.85 | (789) ~ (n20 = n6)
% 51.20/19.85 | (790) sum(n16, n10) = n0
% 51.20/19.85 | (791) sum(n15, n5) = n20
% 51.20/19.85 | (792) sum(n4, n21) = n25
% 51.20/19.85 | (793) pred(n0) = n25
% 51.20/19.85 | (794) ~ (n8 = n4)
% 51.20/19.85 | (795) sum(n24, n16) = n14
% 51.20/19.85 | (796) succ(n4) = n5
% 51.20/19.85 | (797) ~ (n24 = n21)
% 51.20/19.85 | (798) sum(n1, n5) = n6
% 51.20/19.85 | (799) sum(n13, n10) = n23
% 51.20/19.85 | (800) ~ (n17 = n11)
% 51.20/19.85 | (801) sum(n4, n25) = n3
% 51.20/19.85 | (802) sum(n13, n4) = n17
% 51.20/19.85 | (803) sum(n22, n13) = n9
% 51.20/19.85 | (804) sum(n23, n3) = n0
% 51.20/19.85 | (805) ~ (n20 = n4)
% 51.20/19.85 | (806) ~ (n17 = n8)
% 51.20/19.85 | (807) sum(n15, n2) = n17
% 51.20/19.85 | (808) sum(n21, n17) = n12
% 51.20/19.85 | (809) sum(n21, n0) = n21
% 51.20/19.85 | (810) sum(n10, n19) = n3
% 51.20/19.85 | (811) ~ (n20 = n11)
% 51.20/19.85 | (812) sum(n15, n22) = n11
% 51.20/19.85 | (813) sum(n0, n10) = n10
% 51.20/19.85 | (814) ~ (n25 = n3)
% 51.20/19.85 | (815) ~ (n19 = n0)
% 51.20/19.85 | (816) sum(n13, n17) = n4
% 51.20/19.85 | (817) sum(n8, n11) = n19
% 51.20/19.85 | (818) sum(n25, n15) = n14
% 51.20/19.85 | (819) sum(n10, n1) = n11
% 51.20/19.85 | (820) sum(n10, n10) = n20
% 51.20/19.85 | (821) ~ (n9 = n0)
% 51.20/19.85 | (822) sum(n9, n12) = n21
% 51.20/19.85 | (823) sum(n2, n10) = n12
% 51.20/19.85 | (824) succ(n9) = n10
% 51.20/19.85 | (825) succ(n6) = n7
% 51.20/19.85 | (826) sum(n18, n6) = n24
% 51.20/19.85 | (827) ~ (n18 = n0)
% 51.20/19.85 | (828) sum(n6, n8) = n14
% 51.20/19.85 | (829) sum(n13, n11) = n24
% 51.20/19.85 | (830) sum(n6, n13) = n19
% 51.20/19.85 | (831) pred(n24) = n23
% 51.20/19.85 | (832) ~ (n22 = n10)
% 51.20/19.85 | (833) sum(n6, n12) = n18
% 51.20/19.85 | (834) sum(n24, n8) = n6
% 51.20/19.85 | (835) succ(n0) = n1
% 51.20/19.85 | (836) ~ (n20 = n18)
% 51.20/19.85 | (837) sum(n12, n7) = n19
% 51.20/19.85 | (838) sum(n22, n7) = n3
% 51.20/19.85 | (839) ~ (n12 = n2)
% 51.20/19.85 | (840) sum(n21, n10) = n5
% 51.20/19.85 | (841) sum(n13, n15) = n2
% 51.20/19.85 | (842) sum(n15, n20) = n9
% 51.20/19.85 | (843) ~ (n23 = n0)
% 51.20/19.85 | (844) ~ (n17 = n4)
% 51.20/19.85 | (845) ~ (n25 = n8)
% 51.20/19.85 | (846) ~ (n19 = n18)
% 51.20/19.85 | (847) sum(n23, n4) = n1
% 51.20/19.85 | (848) sum(n22, n23) = n19
% 51.20/19.85 | (849) ~ (n24 = n8)
% 51.20/19.85 | (850) ~ (n7 = n6)
% 51.20/19.85 | (851) sum(n0, n22) = n22
% 51.20/19.85 | (852) ~ (n13 = n5)
% 51.20/19.85 | (853) sum(n1, n11) = n12
% 51.20/19.85 | (854) sum(n23, n17) = n14
% 51.20/19.85 | (855) sum(n16, n1) = n17
% 51.20/19.85 | (856) sum(n17, n14) = n5
% 51.20/19.85 | (857) sum(n20, n4) = n24
% 51.20/19.85 | (858) ~ (n23 = n20)
% 51.20/19.85 | (859) ~ (n10 = n2)
% 51.20/19.85 | (860) sum(n18, n24) = n16
% 51.20/19.85 | (861) sum(n7, n2) = n9
% 51.20/19.85 | (862) ~ (n7 = n0)
% 51.20/19.85 | (863) ~ (n7 = n4)
% 51.20/19.85 | (864) sum(n2, n17) = n19
% 51.20/19.85 | (865) sum(n9, n0) = n9
% 51.20/19.85 | (866) pred(n6) = n5
% 51.20/19.86 | (867) sum(n22, n9) = n5
% 51.20/19.86 | (868) ~ (n23 = n1)
% 51.20/19.86 | (869) ~ (n4 = n0)
% 51.20/19.86 | (870) ~ (n18 = n6)
% 51.20/19.86 | (871) sum(n2, n13) = n15
% 51.20/19.86 | (872) sum(n16, n14) = n4
% 51.20/19.86 | (873) sum(n17, n4) = n21
% 51.20/19.86 | (874) sum(n23, n10) = n7
% 51.20/19.86 | (875) ~ (n9 = n5)
% 51.20/19.86 | (876) sum(n10, n13) = n23
% 51.20/19.86 | (877) sum(n19, n21) = n14
% 51.20/19.86 | (878) ~ (n16 = n0)
% 51.20/19.86 | (879) sum(n21, n14) = n9
% 51.20/19.86 | (880) ~ (n22 = n19)
% 51.20/19.86 | (881) sum(n8, n12) = n20
% 51.20/19.86 | (882) sum(n22, n25) = n21
% 51.20/19.86 | (883) succ(n20) = n21
% 51.20/19.86 | (884) sum(n11, n1) = n12
% 51.20/19.86 | (885) ~ (n24 = n4)
% 51.20/19.86 | (886) sum(n2, n8) = n10
% 51.20/19.86 | (887) sum(n14, n9) = n23
% 51.20/19.86 | (888) sum(n1, n0) = n1
% 51.20/19.86 | (889) sum(n12, n23) = n9
% 51.20/19.86 | (890) pred(n7) = n6
% 51.20/19.86 | (891) sum(n25, n14) = n13
% 51.20/19.86 | (892) sum(n3, n13) = n16
% 51.20/19.86 | (893) sum(n13, n9) = n22
% 51.20/19.86 | (894) ~ (n23 = n10)
% 51.20/19.86 | (895) sum(n9, n10) = n19
% 51.20/19.86 | (896) ~ (n11 = n2)
% 51.20/19.86 | (897) ~ (n20 = n14)
% 51.20/19.86 | (898) sum(n20, n13) = n7
% 51.20/19.86 | (899) sum(n0, n11) = n11
% 51.20/19.86 | (900) sum(n24, n22) = n20
% 51.20/19.86 | (901) ~ (n21 = n19)
% 51.20/19.86 | (902) ~ (n21 = n11)
% 51.20/19.86 | (903) sum(n23, n8) = n5
% 51.20/19.86 | (904) sum(n12, n11) = n23
% 51.20/19.86 | (905) sum(n25, n17) = n16
% 51.20/19.86 | (906) ~ (n8 = n5)
% 51.20/19.86 | (907) sum(n20, n21) = n15
% 51.20/19.86 | (908) sum(n9, n22) = n5
% 51.20/19.86 | (909) sum(n5, n16) = n21
% 51.20/19.86 | (910) sum(n9, n1) = n10
% 51.20/19.86 | (911) ~ (n14 = n8)
% 51.20/19.86 | (912) sum(n23, n15) = n12
% 51.20/19.86 | (913) sum(n3, n11) = n14
% 51.20/19.86 | (914) succ(n17) = n18
% 51.20/19.86 | (915) sum(n9, n21) = n4
% 51.20/19.86 | (916) sum(n6, n22) = n2
% 51.20/19.86 | (917) ~ (n25 = n20)
% 51.20/19.86 | (918) succ(n22) = n23
% 51.20/19.86 | (919) sum(n20, n5) = n25
% 51.20/19.86 | (920) sum(n3, n18) = n21
% 51.20/19.86 | (921) sum(n16, n3) = n19
% 51.20/19.86 | (922) sum(n11, n5) = n16
% 51.20/19.86 | (923) sum(n11, n14) = n25
% 51.20/19.86 | (924) succ(n14) = n15
% 51.20/19.86 | (925) sum(n21, n4) = n25
% 51.20/19.86 | (926) sum(n9, n11) = n20
% 51.20/19.86 | (927) sum(n16, n11) = n1
% 51.20/19.86 | (928) ~ (n24 = n6)
% 51.20/19.86 | (929) ~ (n20 = n2)
% 51.20/19.86 | (930) ~ (n25 = n12)
% 51.20/19.86 | (931) pred(n18) = n17
% 51.20/19.86 | (932) sum(n5, n18) = n23
% 51.20/19.86 | (933) ~ (n18 = n4)
% 51.20/19.86 | (934) sum(n7, n18) = n25
% 51.20/19.86 | (935) ~ (n14 = n9)
% 51.20/19.86 | (936) sum(n1, n1) = n2
% 51.20/19.86 | (937) sum(n9, n20) = n3
% 51.20/19.86 | (938) sum(n6, n0) = n6
% 51.20/19.86 | (939) sum(n23, n11) = n8
% 51.20/19.86 | (940) sum(n6, n17) = n23
% 51.20/19.86 | (941) sum(n7, n12) = n19
% 51.20/19.86 | (942) ~ (n23 = n14)
% 51.20/19.86 | (943) sum(n10, n23) = n7
% 51.20/19.86 | (944) sum(n9, n23) = n6
% 51.20/19.86 | (945) sum(n25, n4) = n3
% 51.20/19.86 | (946) ~ (n24 = n14)
% 51.20/19.86 | (947) sum(n24, n14) = n12
% 51.20/19.86 | (948) ~ (n19 = n11)
% 51.20/19.86 | (949) sum(n25, n19) = n18
% 51.20/19.86 | (950) sum(n9, n14) = n23
% 51.20/19.86 | (951) ~ (n16 = n1)
% 51.20/19.86 | (952) sum(n17, n7) = n24
% 51.20/19.86 | (953) pred(n3) = n2
% 51.20/19.86 | (954) sum(n19, n25) = n18
% 51.20/19.86 | (955) sum(n25, n22) = n21
% 51.20/19.86 | (956) sum(n21, n19) = n14
% 51.20/19.86 | (957) sum(n10, n3) = n13
% 51.20/19.86 | (958) ~ (n5 = n0)
% 51.20/19.86 | (959) sum(n1, n9) = n10
% 51.20/19.86 | (960) succ(n21) = n22
% 51.20/19.86 | (961) sum(n10, n16) = n0
% 51.20/19.86 | (962) sum(n24, n25) = n23
% 51.20/19.86 | (963) sum(n1, n17) = n18
% 51.20/19.86 | (964) sum(n23, n1) = n24
% 51.20/19.86 | (965) sum(n24, n0) = n24
% 51.20/19.86 | (966) sum(n7, n19) = n0
% 51.20/19.86 | (967) sum(n11, n22) = n7
% 51.20/19.86 | (968) sum(n6, n7) = n13
% 51.20/19.86 | (969) sum(n21, n8) = n3
% 51.20/19.86 | (970) pred(n5) = n4
% 51.20/19.86 | (971) ~ (n18 = n14)
% 51.20/19.86 | (972) sum(n18, n16) = n8
% 51.20/19.86 | (973) sum(n24, n2) = n0
% 51.20/19.86 | (974) sum(n14, n15) = n3
% 51.20/19.87 | (975) sum(n13, n25) = n12
% 51.20/19.87 | (976) sum(n22, n0) = n22
% 51.20/19.87 | (977) sum(n2, n16) = n18
% 51.20/19.87 | (978) sum(n6, n18) = n24
% 51.20/19.87 | (979) ~ (n15 = n5)
% 51.20/19.87 | (980) sum(n2, n21) = n23
% 51.20/19.87 | (981) sum(n3, n19) = n22
% 51.20/19.87 | (982) ~ (n10 = n8)
% 51.20/19.87 | (983) sum(n23, n21) = n18
% 51.20/19.87 | (984) sum(n3, n3) = n6
% 51.20/19.87 | (985) sum(n18, n4) = n22
% 51.20/19.87 | (986) sum(n6, n11) = n17
% 51.20/19.87 | (987) sum(n18, n21) = n13
% 51.20/19.87 | (988) ~ (n14 = n12)
% 51.20/19.87 | (989) sum(n18, n9) = n1
% 51.20/19.87 | (990) ~ (n17 = n9)
% 51.20/19.87 | (991) sum(n15, n15) = n4
% 51.20/19.87 | (992) succ(all_0_11_11) = all_0_5_5
% 51.20/19.87 | (993) sum(n15, n11) = n0
% 51.20/19.87 | (994) ~ (n15 = n8)
% 51.20/19.87 | (995) sum(n8, n24) = n6
% 51.20/19.87 | (996) ~ (n15 = n3)
% 51.20/19.87 | (997) ~ (n21 = n5)
% 51.20/19.87 | (998) pred(n17) = n16
% 51.20/19.87 | (999) sum(n6, n2) = n8
% 51.20/19.87 | (1000) sum(n5, n6) = n11
% 51.20/19.87 | (1001) ~ (n24 = n19)
% 51.20/19.87 | (1002) succ(n7) = n8
% 51.20/19.87 | (1003) sum(n14, n14) = n2
% 51.20/19.87 | (1004) ~ (n10 = n9)
% 51.20/19.87 | (1005) sum(n7, n24) = n5
% 51.20/19.87 | (1006) ~ (n18 = n2)
% 51.20/19.87 | (1007) ~ (n21 = n0)
% 51.20/19.87 | (1008) sum(n13, n21) = n8
% 51.20/19.87 | (1009) sum(n17, n24) = n15
% 51.20/19.87 | (1010) sum(n17, n2) = n19
% 51.20/19.87 | (1011) ~ (n17 = n16)
% 51.20/19.87 | (1012) pred(n23) = n22
% 51.20/19.87 | (1013) ~ (n23 = n4)
% 51.20/19.87 | (1014) sum(n9, n2) = n11
% 51.20/19.87 | (1015) sum(n12, n15) = n1
% 51.20/19.87 | (1016) sum(n13, n22) = n9
% 51.20/19.87 | (1017) sum(n16, n4) = n20
% 51.20/19.87 | (1018) sum(n15, n21) = n10
% 51.20/19.87 | (1019) sum(n2, n5) = n7
% 51.20/19.87 | (1020) sum(n20, n10) = n4
% 51.20/19.87 | (1021) sum(n9, n6) = n15
% 51.20/19.87 | (1022) sum(n11, n0) = n11
% 51.20/19.87 | (1023) sum(n7, n5) = n12
% 51.20/19.87 | (1024) sum(n15, n17) = n6
% 51.20/19.87 | (1025) ~ (n17 = n12)
% 51.20/19.87 | (1026) ~ (n20 = n12)
% 51.20/19.87 | (1027) sum(n11, n9) = n20
% 51.20/19.87 | (1028) ~ (n23 = n8)
% 51.20/19.87 | (1029) ~ (n11 = n9)
% 51.20/19.87 | (1030) ~ (n25 = n23)
% 51.20/19.87 | (1031) sum(n7, n3) = n10
% 51.20/19.87 | (1032) ~ (n12 = n7)
% 51.20/19.87 | (1033) ~ (n9 = n6)
% 51.20/19.87 | (1034) ~ (n22 = n14)
% 51.20/19.87 | (1035) sum(n10, n21) = n5
% 51.20/19.87 | (1036) sum(n16, n5) = n21
% 51.20/19.87 | (1037) ~ (n22 = n4)
% 51.20/19.87 | (1038) sum(n7, n16) = n23
% 51.20/19.87 | (1039) ~ (n20 = n3)
% 51.20/19.87 | (1040) sum(n6, n19) = n25
% 51.20/19.87 | (1041) sum(n21, n22) = n17
% 51.20/19.87 | (1042) sum(n15, n19) = n8
% 51.20/19.87 | (1043) ~ (n16 = n2)
% 51.20/19.87 | (1044) sum(n13, n16) = n3
% 51.20/19.87 | (1045) ~ (n9 = n3)
% 51.20/19.87 | (1046) sum(n25, n16) = n15
% 51.20/19.87 | (1047) sum(n23, n9) = n6
% 51.20/19.87 | (1048) sum(n10, n22) = n6
% 51.20/19.87 | (1049) sum(n1, n22) = n23
% 51.20/19.87 | (1050) sum(n4, n18) = n22
% 51.20/19.87 | (1051) sum(n16, n25) = n15
% 51.20/19.87 | (1052) sum(n15, n9) = n24
% 51.20/19.87 | (1053) ~ (n18 = n8)
% 51.20/19.87 | (1054) ~ (n25 = n11)
% 51.20/19.87 | (1055) sum(n7, n10) = n17
% 51.20/19.87 | (1056) sum(n23, n6) = n3
% 51.20/19.87 | (1057) sum(n25, n21) = n20
% 51.20/19.87 | (1058) sum(n16, n22) = n12
% 51.20/19.87 | (1059) sum(n22, n4) = n0
% 51.20/19.87 | (1060) ~ (n24 = n18)
% 51.20/19.87 | (1061) ~ (n16 = n12)
% 51.20/19.87 | (1062) sum(n3, n9) = n12
% 51.20/19.87 | (1063) sum(n15, n1) = n16
% 51.20/19.87 | (1064) sum(n18, n8) = n0
% 51.20/19.87 | (1065) sum(n7, n6) = n13
% 51.20/19.87 | (1066) sum(n23, n24) = n21
% 51.20/19.87 | (1067) ~ (n24 = n10)
% 51.20/19.87 | (1068) sum(n12, n9) = n21
% 51.20/19.87 | (1069) ~ (n20 = n8)
% 51.20/19.87 | (1070) sum(n5, n9) = n14
% 51.20/19.87 |
% 51.20/19.87 +-Applying beta-rule and splitting (260), into two cases.
% 51.20/19.87 |-Branch one:
% 51.20/19.87 | (1071) all_0_10_10 = n25
% 51.20/19.87 |
% 51.20/19.87 | From (1071) and (292) follows:
% 51.20/19.88 | (1072) pred(n25) = all_0_6_6
% 51.20/19.88 |
% 51.20/19.88 | From (1071) and (760) follows:
% 51.20/19.88 | (1073) succ(n25) = all_0_8_8
% 51.20/19.88 |
% 51.20/19.88 | Instantiating formula (500) with n25, all_0_6_6, n24 and discharging atoms pred(n25) = all_0_6_6, pred(n25) = n24, yields:
% 51.20/19.88 | (1074) all_0_6_6 = n24
% 51.20/19.88 |
% 51.20/19.88 | Instantiating formula (617) with n25, all_0_8_8, n0 and discharging atoms succ(n25) = all_0_8_8, succ(n25) = n0, yields:
% 51.20/19.88 | (1075) all_0_8_8 = n0
% 51.20/19.88 |
% 51.20/19.88 | From (1074) and (1072) follows:
% 51.20/19.88 | (387) pred(n25) = n24
% 51.20/19.88 |
% 51.20/19.88 | From (1075) and (1073) follows:
% 51.20/19.88 | (422) succ(n25) = n0
% 51.20/19.88 |
% 51.20/19.88 | From (1074) and (541) follows:
% 51.20/19.88 | (1078) sum(n24, all_0_5_5) = all_0_4_4
% 51.20/19.88 |
% 51.20/19.88 | From (1074)(1075) and (411) follows:
% 51.20/19.88 | (1079) sum(n24, n0) = all_0_1_1
% 51.20/19.88 |
% 51.20/19.88 | From (1075) and (427) follows:
% 51.20/19.88 | (1080) sum(all_0_9_9, n0) = all_0_7_7
% 51.20/19.88 |
% 51.20/19.88 | Instantiating formula (690) with n24, n0, all_0_1_1, n24 and discharging atoms sum(n24, n0) = all_0_1_1, sum(n24, n0) = n24, yields:
% 51.20/19.88 | (1081) all_0_1_1 = n24
% 51.20/19.88 |
% 51.20/19.88 | From (1081) and (630) follows:
% 51.20/19.88 | (1082) sum(all_0_2_2, n24) = all_0_0_0
% 51.20/19.88 |
% 51.20/19.88 | From (1081) and (1079) follows:
% 51.20/19.88 | (965) sum(n24, n0) = n24
% 51.20/19.88 |
% 51.20/19.88 +-Applying beta-rule and splitting (361), into two cases.
% 51.20/19.88 |-Branch one:
% 51.20/19.88 | (1084) all_0_11_11 = n25
% 51.20/19.88 |
% 51.20/19.88 | From (1084) and (559) follows:
% 51.20/19.88 | (1085) pred(n25) = all_0_9_9
% 51.20/19.88 |
% 51.20/19.88 | From (1084) and (992) follows:
% 51.20/19.88 | (1086) succ(n25) = all_0_5_5
% 51.20/19.88 |
% 51.20/19.88 | Instantiating formula (500) with n25, all_0_9_9, n24 and discharging atoms pred(n25) = all_0_9_9, pred(n25) = n24, yields:
% 51.20/19.88 | (1087) all_0_9_9 = n24
% 51.20/19.88 |
% 51.20/19.88 | Instantiating formula (617) with n25, all_0_5_5, n0 and discharging atoms succ(n25) = all_0_5_5, succ(n25) = n0, yields:
% 51.20/19.88 | (1088) all_0_5_5 = n0
% 51.20/19.88 |
% 51.20/19.88 | From (1087)(1088) and (538) follows:
% 51.20/19.88 | (1089) sum(n24, n0) = all_0_2_2
% 51.20/19.88 |
% 51.20/19.88 | From (1087) and (1080) follows:
% 51.20/19.88 | (1090) sum(n24, n0) = all_0_7_7
% 51.20/19.88 |
% 51.20/19.88 | From (1088) and (1078) follows:
% 51.20/19.88 | (1091) sum(n24, n0) = all_0_4_4
% 51.20/19.88 |
% 51.20/19.88 | Instantiating formula (690) with n24, n0, all_0_2_2, n24 and discharging atoms sum(n24, n0) = all_0_2_2, sum(n24, n0) = n24, yields:
% 51.20/19.88 | (1092) all_0_2_2 = n24
% 51.20/19.88 |
% 51.20/19.88 | Instantiating formula (690) with n24, n0, all_0_4_4, all_0_2_2 and discharging atoms sum(n24, n0) = all_0_2_2, sum(n24, n0) = all_0_4_4, yields:
% 51.20/19.88 | (1093) all_0_2_2 = all_0_4_4
% 51.20/19.88 |
% 51.20/19.88 | Instantiating formula (690) with n24, n0, all_0_7_7, all_0_2_2 and discharging atoms sum(n24, n0) = all_0_2_2, sum(n24, n0) = all_0_7_7, yields:
% 51.20/19.88 | (1094) all_0_2_2 = all_0_7_7
% 51.20/19.88 |
% 51.20/19.88 | Combining equations (1094,1093) yields a new equation:
% 51.20/19.88 | (1095) all_0_4_4 = all_0_7_7
% 51.20/19.88 |
% 51.20/19.88 | Combining equations (1092,1093) yields a new equation:
% 51.20/19.88 | (1096) all_0_4_4 = n24
% 51.20/19.88 |
% 51.20/19.88 | Combining equations (1096,1095) yields a new equation:
% 51.20/19.88 | (1097) all_0_7_7 = n24
% 51.20/19.88 |
% 51.20/19.88 | Combining equations (1097,1095) yields a new equation:
% 51.20/19.88 | (1096) all_0_4_4 = n24
% 51.20/19.88 |
% 51.20/19.88 | Combining equations (1096,1093) yields a new equation:
% 51.20/19.88 | (1092) all_0_2_2 = n24
% 51.20/19.88 |
% 51.20/19.88 | From (1092) and (1082) follows:
% 51.20/19.88 | (1100) sum(n24, n24) = all_0_0_0
% 51.20/19.88 |
% 51.20/19.88 | From (1097)(1096) and (590) follows:
% 51.20/19.88 | (1101) sum(n24, n24) = all_0_3_3
% 51.20/19.88 |
% 51.20/19.88 | Instantiating formula (690) with n24, n24, all_0_0_0, n22 and discharging atoms sum(n24, n24) = all_0_0_0, sum(n24, n24) = n22, yields:
% 51.20/19.88 | (1102) all_0_0_0 = n22
% 51.20/19.88 |
% 51.20/19.88 | Instantiating formula (690) with n24, n24, all_0_3_3, all_0_0_0 and discharging atoms sum(n24, n24) = all_0_0_0, sum(n24, n24) = all_0_3_3, yields:
% 51.20/19.88 | (1103) all_0_0_0 = all_0_3_3
% 51.20/19.88 |
% 51.20/19.88 | Combining equations (1102,1103) yields a new equation:
% 51.20/19.88 | (1104) all_0_3_3 = n22
% 51.20/19.88 |
% 51.20/19.88 | Combining equations (1104,1103) yields a new equation:
% 51.20/19.88 | (1102) all_0_0_0 = n22
% 51.20/19.88 |
% 51.20/19.88 | Equations (1102,1104) can reduce 679 to:
% 51.20/19.88 | (1106) $false
% 51.20/19.88 |
% 51.20/19.88 |-The branch is then unsatisfiable
% 51.20/19.88 |-Branch two:
% 51.20/19.88 | (1107) ~ (all_0_11_11 = n25)
% 51.20/19.88 | (1108) all_0_11_11 = n24 | all_0_11_11 = n23 | all_0_11_11 = n22 | all_0_11_11 = n21 | 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
% 51.20/19.88 |
% 51.20/19.88 +-Applying beta-rule and splitting (1108), into two cases.
% 51.20/19.88 |-Branch one:
% 51.20/19.88 | (1109) all_0_11_11 = n24
% 51.20/19.88 |
% 51.20/19.88 | From (1109) and (559) follows:
% 51.20/19.88 | (1110) pred(n24) = all_0_9_9
% 51.20/19.88 |
% 51.20/19.88 | From (1109) and (992) follows:
% 51.20/19.88 | (1111) succ(n24) = all_0_5_5
% 51.20/19.88 |
% 51.20/19.88 | Instantiating formula (500) with n24, all_0_9_9, n23 and discharging atoms pred(n24) = all_0_9_9, pred(n24) = n23, yields:
% 51.20/19.88 | (1112) all_0_9_9 = n23
% 51.20/19.88 |
% 51.20/19.88 | Instantiating formula (617) with n24, all_0_5_5, n25 and discharging atoms succ(n24) = all_0_5_5, succ(n24) = n25, yields:
% 51.20/19.88 | (1113) all_0_5_5 = n25
% 51.20/19.88 |
% 51.20/19.88 | From (1112)(1113) and (538) follows:
% 51.20/19.88 | (1114) sum(n23, n25) = all_0_2_2
% 51.20/19.88 |
% 51.20/19.88 | From (1112) and (1080) follows:
% 51.20/19.88 | (1115) sum(n23, n0) = all_0_7_7
% 51.20/19.88 |
% 51.20/19.88 | From (1113) and (1078) follows:
% 51.20/19.89 | (1116) sum(n24, n25) = all_0_4_4
% 51.20/19.89 |
% 51.20/19.89 | Instantiating formula (690) with n24, n25, all_0_4_4, n23 and discharging atoms sum(n24, n25) = all_0_4_4, sum(n24, n25) = n23, yields:
% 51.20/19.89 | (1117) all_0_4_4 = n23
% 51.20/19.89 |
% 51.20/19.89 | Instantiating formula (690) with n23, n25, all_0_2_2, n22 and discharging atoms sum(n23, n25) = all_0_2_2, sum(n23, n25) = n22, yields:
% 51.20/19.89 | (1118) all_0_2_2 = n22
% 51.20/19.89 |
% 51.20/19.89 | Instantiating formula (690) with n23, n0, all_0_7_7, n23 and discharging atoms sum(n23, n0) = all_0_7_7, sum(n23, n0) = n23, yields:
% 51.20/19.89 | (1119) all_0_7_7 = n23
% 51.20/19.89 |
% 51.20/19.89 | From (1118) and (1082) follows:
% 51.20/19.89 | (1120) sum(n22, n24) = all_0_0_0
% 51.20/19.89 |
% 51.20/19.89 | From (1119)(1117) and (590) follows:
% 51.51/19.89 | (1121) sum(n23, n23) = all_0_3_3
% 51.51/19.89 |
% 51.51/19.89 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 51.51/19.89 | (1122) all_0_3_3 = n20
% 51.51/19.89 |
% 51.51/19.89 | Instantiating formula (690) with n22, n24, all_0_0_0, n20 and discharging atoms sum(n22, n24) = all_0_0_0, sum(n22, n24) = n20, yields:
% 51.51/19.89 | (1123) all_0_0_0 = n20
% 51.51/19.89 |
% 51.51/19.89 | Equations (1123,1122) can reduce 679 to:
% 51.51/19.89 | (1106) $false
% 51.51/19.89 |
% 51.51/19.89 |-The branch is then unsatisfiable
% 51.51/19.89 |-Branch two:
% 51.51/19.89 | (1125) ~ (all_0_11_11 = n24)
% 51.51/19.89 | (1126) all_0_11_11 = n23 | all_0_11_11 = n22 | all_0_11_11 = n21 | 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
% 51.51/19.89 |
% 51.51/19.89 +-Applying beta-rule and splitting (1126), into two cases.
% 51.51/19.89 |-Branch one:
% 51.51/19.89 | (1127) all_0_11_11 = n23
% 51.51/19.89 |
% 51.51/19.89 | From (1127) and (559) follows:
% 51.51/19.89 | (1128) pred(n23) = all_0_9_9
% 51.51/19.89 |
% 51.51/19.89 | From (1127) and (992) follows:
% 51.51/19.89 | (1129) succ(n23) = all_0_5_5
% 51.51/19.89 |
% 51.51/19.89 | Instantiating formula (500) with n23, all_0_9_9, n22 and discharging atoms pred(n23) = all_0_9_9, pred(n23) = n22, yields:
% 51.51/19.89 | (1130) all_0_9_9 = n22
% 51.51/19.89 |
% 51.51/19.89 | Instantiating formula (617) with n23, all_0_5_5, n24 and discharging atoms succ(n23) = all_0_5_5, succ(n23) = n24, yields:
% 51.51/19.89 | (1131) all_0_5_5 = n24
% 51.51/19.89 |
% 51.51/19.89 | From (1130)(1131) and (538) follows:
% 51.51/19.89 | (1132) sum(n22, n24) = all_0_2_2
% 51.51/19.89 |
% 51.51/19.89 | From (1130) and (1080) follows:
% 51.51/19.89 | (1133) sum(n22, n0) = all_0_7_7
% 51.51/19.89 |
% 51.51/19.89 | From (1131) and (1078) follows:
% 51.51/19.89 | (1134) sum(n24, n24) = all_0_4_4
% 51.51/19.89 |
% 51.51/19.89 | Instantiating formula (690) with n24, n24, all_0_4_4, n22 and discharging atoms sum(n24, n24) = all_0_4_4, sum(n24, n24) = n22, yields:
% 51.51/19.89 | (1135) all_0_4_4 = n22
% 51.51/19.89 |
% 51.51/19.89 | Instantiating formula (690) with n22, n24, all_0_2_2, n20 and discharging atoms sum(n22, n24) = all_0_2_2, sum(n22, n24) = n20, yields:
% 51.51/19.89 | (1136) all_0_2_2 = n20
% 51.51/19.89 |
% 51.51/19.89 | Instantiating formula (690) with n22, n0, all_0_7_7, n22 and discharging atoms sum(n22, n0) = all_0_7_7, sum(n22, n0) = n22, yields:
% 51.51/19.89 | (1137) all_0_7_7 = n22
% 51.51/19.89 |
% 51.51/19.89 | From (1136) and (1082) follows:
% 51.51/19.89 | (1138) sum(n20, n24) = all_0_0_0
% 51.51/19.89 |
% 51.51/19.89 | From (1137)(1135) and (590) follows:
% 51.51/19.89 | (1139) sum(n22, n22) = all_0_3_3
% 51.51/19.89 |
% 51.51/19.89 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 51.51/19.89 | (1140) all_0_3_3 = n18
% 51.51/19.89 |
% 51.51/19.89 | Instantiating formula (690) with n20, n24, all_0_0_0, n18 and discharging atoms sum(n20, n24) = all_0_0_0, sum(n20, n24) = n18, yields:
% 51.51/19.89 | (1141) all_0_0_0 = n18
% 51.51/19.89 |
% 51.51/19.89 | Equations (1141,1140) can reduce 679 to:
% 51.51/19.89 | (1106) $false
% 51.51/19.89 |
% 51.51/19.89 |-The branch is then unsatisfiable
% 51.51/19.89 |-Branch two:
% 51.51/19.89 | (1143) ~ (all_0_11_11 = n23)
% 51.51/19.89 | (1144) all_0_11_11 = n22 | all_0_11_11 = n21 | 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
% 51.51/19.89 |
% 51.51/19.89 +-Applying beta-rule and splitting (1144), into two cases.
% 51.51/19.89 |-Branch one:
% 51.51/19.89 | (1145) all_0_11_11 = n22
% 51.51/19.89 |
% 51.51/19.89 | From (1145) and (559) follows:
% 51.51/19.89 | (1146) pred(n22) = all_0_9_9
% 51.51/19.89 |
% 51.51/19.89 | From (1145) and (992) follows:
% 51.51/19.89 | (1147) succ(n22) = all_0_5_5
% 51.51/19.89 |
% 51.51/19.89 | Instantiating formula (500) with n22, all_0_9_9, n21 and discharging atoms pred(n22) = all_0_9_9, pred(n22) = n21, yields:
% 51.51/19.89 | (1148) all_0_9_9 = n21
% 51.51/19.89 |
% 51.51/19.89 | Instantiating formula (617) with n22, all_0_5_5, n23 and discharging atoms succ(n22) = all_0_5_5, succ(n22) = n23, yields:
% 51.51/19.89 | (1149) all_0_5_5 = n23
% 51.51/19.89 |
% 51.51/19.89 | From (1148)(1149) and (538) follows:
% 51.51/19.89 | (1150) sum(n21, n23) = all_0_2_2
% 51.51/19.89 |
% 51.51/19.89 | From (1148) and (1080) follows:
% 51.51/19.89 | (1151) sum(n21, n0) = all_0_7_7
% 51.51/19.89 |
% 51.51/19.89 | From (1149) and (1078) follows:
% 51.51/19.89 | (1152) sum(n24, n23) = all_0_4_4
% 51.51/19.89 |
% 51.51/19.89 | Instantiating formula (690) with n24, n23, all_0_4_4, n21 and discharging atoms sum(n24, n23) = all_0_4_4, sum(n24, n23) = n21, yields:
% 51.51/19.89 | (1153) all_0_4_4 = n21
% 51.51/19.89 |
% 51.51/19.89 | Instantiating formula (690) with n21, n23, all_0_2_2, n18 and discharging atoms sum(n21, n23) = all_0_2_2, sum(n21, n23) = n18, yields:
% 51.51/19.89 | (1154) all_0_2_2 = n18
% 51.51/19.89 |
% 51.51/19.89 | Instantiating formula (690) with n21, n0, all_0_7_7, n21 and discharging atoms sum(n21, n0) = all_0_7_7, sum(n21, n0) = n21, yields:
% 51.51/19.89 | (1155) all_0_7_7 = n21
% 51.51/19.89 |
% 51.51/19.89 | From (1154) and (1082) follows:
% 51.51/19.89 | (1156) sum(n18, n24) = all_0_0_0
% 51.51/19.89 |
% 51.51/19.89 | From (1155)(1153) and (590) follows:
% 51.51/19.89 | (1157) sum(n21, n21) = all_0_3_3
% 51.51/19.89 |
% 51.51/19.89 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 51.51/19.89 | (1158) all_0_3_3 = n16
% 51.51/19.89 |
% 51.51/19.89 | Instantiating formula (690) with n18, n24, all_0_0_0, n16 and discharging atoms sum(n18, n24) = all_0_0_0, sum(n18, n24) = n16, yields:
% 51.51/19.89 | (1159) all_0_0_0 = n16
% 51.51/19.89 |
% 51.51/19.89 | Equations (1159,1158) can reduce 679 to:
% 51.51/19.89 | (1106) $false
% 51.51/19.89 |
% 51.51/19.89 |-The branch is then unsatisfiable
% 51.51/19.89 |-Branch two:
% 51.51/19.89 | (1161) ~ (all_0_11_11 = n22)
% 51.51/19.89 | (1162) all_0_11_11 = n21 | 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
% 51.51/19.89 |
% 51.51/19.89 +-Applying beta-rule and splitting (1162), into two cases.
% 51.51/19.89 |-Branch one:
% 51.51/19.89 | (1163) all_0_11_11 = n21
% 51.51/19.89 |
% 51.51/19.89 | From (1163) and (559) follows:
% 51.51/19.89 | (1164) pred(n21) = all_0_9_9
% 51.51/19.89 |
% 51.51/19.89 | From (1163) and (992) follows:
% 51.51/19.89 | (1165) succ(n21) = all_0_5_5
% 51.51/19.89 |
% 51.51/19.89 | Instantiating formula (500) with n21, all_0_9_9, n20 and discharging atoms pred(n21) = all_0_9_9, pred(n21) = n20, yields:
% 51.51/19.90 | (1166) all_0_9_9 = n20
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (617) with n21, all_0_5_5, n22 and discharging atoms succ(n21) = all_0_5_5, succ(n21) = n22, yields:
% 51.51/19.90 | (1167) all_0_5_5 = n22
% 51.51/19.90 |
% 51.51/19.90 | From (1166)(1167) and (538) follows:
% 51.51/19.90 | (1168) sum(n20, n22) = all_0_2_2
% 51.51/19.90 |
% 51.51/19.90 | From (1166) and (1080) follows:
% 51.51/19.90 | (1169) sum(n20, n0) = all_0_7_7
% 51.51/19.90 |
% 51.51/19.90 | From (1167) and (1078) follows:
% 51.51/19.90 | (1170) sum(n24, n22) = all_0_4_4
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (690) with n24, n22, all_0_4_4, n20 and discharging atoms sum(n24, n22) = all_0_4_4, sum(n24, n22) = n20, yields:
% 51.51/19.90 | (1171) all_0_4_4 = n20
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (690) with n20, n22, all_0_2_2, n16 and discharging atoms sum(n20, n22) = all_0_2_2, sum(n20, n22) = n16, yields:
% 51.51/19.90 | (1172) all_0_2_2 = n16
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (690) with n20, n0, all_0_7_7, n20 and discharging atoms sum(n20, n0) = all_0_7_7, sum(n20, n0) = n20, yields:
% 51.51/19.90 | (1173) all_0_7_7 = n20
% 51.51/19.90 |
% 51.51/19.90 | From (1172) and (1082) follows:
% 51.51/19.90 | (1174) sum(n16, n24) = all_0_0_0
% 51.51/19.90 |
% 51.51/19.90 | From (1173)(1171) and (590) follows:
% 51.51/19.90 | (1175) sum(n20, n20) = all_0_3_3
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 51.51/19.90 | (1176) all_0_3_3 = n14
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (690) with n16, n24, all_0_0_0, n14 and discharging atoms sum(n16, n24) = all_0_0_0, sum(n16, n24) = n14, yields:
% 51.51/19.90 | (1177) all_0_0_0 = n14
% 51.51/19.90 |
% 51.51/19.90 | Equations (1177,1176) can reduce 679 to:
% 51.51/19.90 | (1106) $false
% 51.51/19.90 |
% 51.51/19.90 |-The branch is then unsatisfiable
% 51.51/19.90 |-Branch two:
% 51.51/19.90 | (1179) ~ (all_0_11_11 = n21)
% 51.51/19.90 | (1180) 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
% 51.51/19.90 |
% 51.51/19.90 +-Applying beta-rule and splitting (1180), into two cases.
% 51.51/19.90 |-Branch one:
% 51.51/19.90 | (1181) all_0_11_11 = n20
% 51.51/19.90 |
% 51.51/19.90 | From (1181) and (559) follows:
% 51.51/19.90 | (1182) pred(n20) = all_0_9_9
% 51.51/19.90 |
% 51.51/19.90 | From (1181) and (992) follows:
% 51.51/19.90 | (1183) succ(n20) = all_0_5_5
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (500) with n20, all_0_9_9, n19 and discharging atoms pred(n20) = all_0_9_9, pred(n20) = n19, yields:
% 51.51/19.90 | (1184) all_0_9_9 = n19
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (617) with n20, all_0_5_5, n21 and discharging atoms succ(n20) = all_0_5_5, succ(n20) = n21, yields:
% 51.51/19.90 | (1185) all_0_5_5 = n21
% 51.51/19.90 |
% 51.51/19.90 | From (1184)(1185) and (538) follows:
% 51.51/19.90 | (1186) sum(n19, n21) = all_0_2_2
% 51.51/19.90 |
% 51.51/19.90 | From (1184) and (1080) follows:
% 51.51/19.90 | (1187) sum(n19, n0) = all_0_7_7
% 51.51/19.90 |
% 51.51/19.90 | From (1185) and (1078) follows:
% 51.51/19.90 | (1188) sum(n24, n21) = all_0_4_4
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (690) with n24, n21, all_0_4_4, n19 and discharging atoms sum(n24, n21) = all_0_4_4, sum(n24, n21) = n19, yields:
% 51.51/19.90 | (1189) all_0_4_4 = n19
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (690) with n19, n21, all_0_2_2, n14 and discharging atoms sum(n19, n21) = all_0_2_2, sum(n19, n21) = n14, yields:
% 51.51/19.90 | (1190) all_0_2_2 = n14
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (690) with n19, n0, all_0_7_7, n19 and discharging atoms sum(n19, n0) = all_0_7_7, sum(n19, n0) = n19, yields:
% 51.51/19.90 | (1191) all_0_7_7 = n19
% 51.51/19.90 |
% 51.51/19.90 | From (1190) and (1082) follows:
% 51.51/19.90 | (1192) sum(n14, n24) = all_0_0_0
% 51.51/19.90 |
% 51.51/19.90 | From (1191)(1189) and (590) follows:
% 51.51/19.90 | (1193) sum(n19, n19) = all_0_3_3
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 51.51/19.90 | (1194) all_0_3_3 = n12
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (690) with n14, n24, all_0_0_0, n12 and discharging atoms sum(n14, n24) = all_0_0_0, sum(n14, n24) = n12, yields:
% 51.51/19.90 | (1195) all_0_0_0 = n12
% 51.51/19.90 |
% 51.51/19.90 | Equations (1195,1194) can reduce 679 to:
% 51.51/19.90 | (1106) $false
% 51.51/19.90 |
% 51.51/19.90 |-The branch is then unsatisfiable
% 51.51/19.90 |-Branch two:
% 51.51/19.90 | (1197) ~ (all_0_11_11 = n20)
% 51.51/19.90 | (1198) 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
% 51.51/19.90 |
% 51.51/19.90 +-Applying beta-rule and splitting (1198), into two cases.
% 51.51/19.90 |-Branch one:
% 51.51/19.90 | (1199) all_0_11_11 = n19
% 51.51/19.90 |
% 51.51/19.90 | From (1199) and (559) follows:
% 51.51/19.90 | (1200) pred(n19) = all_0_9_9
% 51.51/19.90 |
% 51.51/19.90 | From (1199) and (992) follows:
% 51.51/19.90 | (1201) succ(n19) = all_0_5_5
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (500) with n19, all_0_9_9, n18 and discharging atoms pred(n19) = all_0_9_9, pred(n19) = n18, yields:
% 51.51/19.90 | (1202) all_0_9_9 = n18
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (617) with n19, all_0_5_5, n20 and discharging atoms succ(n19) = all_0_5_5, succ(n19) = n20, yields:
% 51.51/19.90 | (1203) all_0_5_5 = n20
% 51.51/19.90 |
% 51.51/19.90 | From (1202)(1203) and (538) follows:
% 51.51/19.90 | (1204) sum(n18, n20) = all_0_2_2
% 51.51/19.90 |
% 51.51/19.90 | From (1202) and (1080) follows:
% 51.51/19.90 | (1205) sum(n18, n0) = all_0_7_7
% 51.51/19.90 |
% 51.51/19.90 | From (1203) and (1078) follows:
% 51.51/19.90 | (1206) sum(n24, n20) = all_0_4_4
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (690) with n24, n20, all_0_4_4, n18 and discharging atoms sum(n24, n20) = all_0_4_4, sum(n24, n20) = n18, yields:
% 51.51/19.90 | (1207) all_0_4_4 = n18
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (690) with n18, n20, all_0_2_2, n12 and discharging atoms sum(n18, n20) = all_0_2_2, sum(n18, n20) = n12, yields:
% 51.51/19.90 | (1208) all_0_2_2 = n12
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (690) with n18, n0, all_0_7_7, n18 and discharging atoms sum(n18, n0) = all_0_7_7, sum(n18, n0) = n18, yields:
% 51.51/19.90 | (1209) all_0_7_7 = n18
% 51.51/19.90 |
% 51.51/19.90 | From (1208) and (1082) follows:
% 51.51/19.90 | (1210) sum(n12, n24) = all_0_0_0
% 51.51/19.90 |
% 51.51/19.90 | From (1209)(1207) and (590) follows:
% 51.51/19.90 | (1211) sum(n18, n18) = all_0_3_3
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 51.51/19.90 | (1212) all_0_3_3 = n10
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (690) with n12, n24, all_0_0_0, n10 and discharging atoms sum(n12, n24) = all_0_0_0, sum(n12, n24) = n10, yields:
% 51.51/19.90 | (1213) all_0_0_0 = n10
% 51.51/19.90 |
% 51.51/19.90 | Equations (1213,1212) can reduce 679 to:
% 51.51/19.90 | (1106) $false
% 51.51/19.90 |
% 51.51/19.90 |-The branch is then unsatisfiable
% 51.51/19.90 |-Branch two:
% 51.51/19.90 | (1215) ~ (all_0_11_11 = n19)
% 51.51/19.90 | (1216) 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
% 51.51/19.90 |
% 51.51/19.90 +-Applying beta-rule and splitting (1216), into two cases.
% 51.51/19.90 |-Branch one:
% 51.51/19.90 | (1217) all_0_11_11 = n18
% 51.51/19.90 |
% 51.51/19.90 | From (1217) and (559) follows:
% 51.51/19.90 | (1218) pred(n18) = all_0_9_9
% 51.51/19.90 |
% 51.51/19.90 | From (1217) and (992) follows:
% 51.51/19.90 | (1219) succ(n18) = all_0_5_5
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (500) with n18, all_0_9_9, n17 and discharging atoms pred(n18) = all_0_9_9, pred(n18) = n17, yields:
% 51.51/19.90 | (1220) all_0_9_9 = n17
% 51.51/19.90 |
% 51.51/19.90 | Instantiating formula (617) with n18, all_0_5_5, n19 and discharging atoms succ(n18) = all_0_5_5, succ(n18) = n19, yields:
% 51.51/19.90 | (1221) all_0_5_5 = n19
% 51.51/19.90 |
% 51.51/19.90 | From (1220)(1221) and (538) follows:
% 51.51/19.90 | (1222) sum(n17, n19) = all_0_2_2
% 51.51/19.90 |
% 51.51/19.90 | From (1220) and (1080) follows:
% 51.51/19.91 | (1223) sum(n17, n0) = all_0_7_7
% 51.51/19.91 |
% 51.51/19.91 | From (1221) and (1078) follows:
% 51.51/19.91 | (1224) sum(n24, n19) = all_0_4_4
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (690) with n24, n19, all_0_4_4, n17 and discharging atoms sum(n24, n19) = all_0_4_4, sum(n24, n19) = n17, yields:
% 51.51/19.91 | (1225) all_0_4_4 = n17
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (690) with n17, n19, all_0_2_2, n10 and discharging atoms sum(n17, n19) = all_0_2_2, sum(n17, n19) = n10, yields:
% 51.51/19.91 | (1226) all_0_2_2 = n10
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (690) with n17, n0, all_0_7_7, n17 and discharging atoms sum(n17, n0) = all_0_7_7, sum(n17, n0) = n17, yields:
% 51.51/19.91 | (1227) all_0_7_7 = n17
% 51.51/19.91 |
% 51.51/19.91 | From (1226) and (1082) follows:
% 51.51/19.91 | (1228) sum(n10, n24) = all_0_0_0
% 51.51/19.91 |
% 51.51/19.91 | From (1227)(1225) and (590) follows:
% 51.51/19.91 | (1229) sum(n17, n17) = all_0_3_3
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 51.51/19.91 | (1230) all_0_3_3 = n8
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (690) with n10, n24, all_0_0_0, n8 and discharging atoms sum(n10, n24) = all_0_0_0, sum(n10, n24) = n8, yields:
% 51.51/19.91 | (1231) all_0_0_0 = n8
% 51.51/19.91 |
% 51.51/19.91 | Equations (1231,1230) can reduce 679 to:
% 51.51/19.91 | (1106) $false
% 51.51/19.91 |
% 51.51/19.91 |-The branch is then unsatisfiable
% 51.51/19.91 |-Branch two:
% 51.51/19.91 | (1233) ~ (all_0_11_11 = n18)
% 51.51/19.91 | (1234) 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
% 51.51/19.91 |
% 51.51/19.91 +-Applying beta-rule and splitting (1234), into two cases.
% 51.51/19.91 |-Branch one:
% 51.51/19.91 | (1235) all_0_11_11 = n17
% 51.51/19.91 |
% 51.51/19.91 | From (1235) and (559) follows:
% 51.51/19.91 | (1236) pred(n17) = all_0_9_9
% 51.51/19.91 |
% 51.51/19.91 | From (1235) and (992) follows:
% 51.51/19.91 | (1237) succ(n17) = all_0_5_5
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (500) with n17, all_0_9_9, n16 and discharging atoms pred(n17) = all_0_9_9, pred(n17) = n16, yields:
% 51.51/19.91 | (1238) all_0_9_9 = n16
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (617) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 51.51/19.91 | (1239) all_0_5_5 = n18
% 51.51/19.91 |
% 51.51/19.91 | From (1238)(1239) and (538) follows:
% 51.51/19.91 | (1240) sum(n16, n18) = all_0_2_2
% 51.51/19.91 |
% 51.51/19.91 | From (1238) and (1080) follows:
% 51.51/19.91 | (1241) sum(n16, n0) = all_0_7_7
% 51.51/19.91 |
% 51.51/19.91 | From (1239) and (1078) follows:
% 51.51/19.91 | (1242) sum(n24, n18) = all_0_4_4
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (690) with n24, n18, all_0_4_4, n16 and discharging atoms sum(n24, n18) = all_0_4_4, sum(n24, n18) = n16, yields:
% 51.51/19.91 | (1243) all_0_4_4 = n16
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (690) with n16, n18, all_0_2_2, n8 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = n8, yields:
% 51.51/19.91 | (1244) all_0_2_2 = n8
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (690) with n16, n0, all_0_7_7, n16 and discharging atoms sum(n16, n0) = all_0_7_7, sum(n16, n0) = n16, yields:
% 51.51/19.91 | (1245) all_0_7_7 = n16
% 51.51/19.91 |
% 51.51/19.91 | From (1244) and (1082) follows:
% 51.51/19.91 | (1246) sum(n8, n24) = all_0_0_0
% 51.51/19.91 |
% 51.51/19.91 | From (1245)(1243) and (590) follows:
% 51.51/19.91 | (1247) sum(n16, n16) = all_0_3_3
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 51.51/19.91 | (1248) all_0_3_3 = n6
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (690) with n8, n24, all_0_0_0, n6 and discharging atoms sum(n8, n24) = all_0_0_0, sum(n8, n24) = n6, yields:
% 51.51/19.91 | (1249) all_0_0_0 = n6
% 51.51/19.91 |
% 51.51/19.91 | Equations (1249,1248) can reduce 679 to:
% 51.51/19.91 | (1106) $false
% 51.51/19.91 |
% 51.51/19.91 |-The branch is then unsatisfiable
% 51.51/19.91 |-Branch two:
% 51.51/19.91 | (1251) ~ (all_0_11_11 = n17)
% 51.51/19.91 | (1252) 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
% 51.51/19.91 |
% 51.51/19.91 +-Applying beta-rule and splitting (1252), into two cases.
% 51.51/19.91 |-Branch one:
% 51.51/19.91 | (1253) all_0_11_11 = n16
% 51.51/19.91 |
% 51.51/19.91 | From (1253) and (559) follows:
% 51.51/19.91 | (1254) pred(n16) = all_0_9_9
% 51.51/19.91 |
% 51.51/19.91 | From (1253) and (992) follows:
% 51.51/19.91 | (1255) succ(n16) = all_0_5_5
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (500) with n16, all_0_9_9, n15 and discharging atoms pred(n16) = all_0_9_9, pred(n16) = n15, yields:
% 51.51/19.91 | (1256) all_0_9_9 = n15
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (617) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 51.51/19.91 | (1257) all_0_5_5 = n17
% 51.51/19.91 |
% 51.51/19.91 | From (1256)(1257) and (538) follows:
% 51.51/19.91 | (1258) sum(n15, n17) = all_0_2_2
% 51.51/19.91 |
% 51.51/19.91 | From (1256) and (1080) follows:
% 51.51/19.91 | (1259) sum(n15, n0) = all_0_7_7
% 51.51/19.91 |
% 51.51/19.91 | From (1257) and (1078) follows:
% 51.51/19.91 | (1260) sum(n24, n17) = all_0_4_4
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (690) with n24, n17, all_0_4_4, n15 and discharging atoms sum(n24, n17) = all_0_4_4, sum(n24, n17) = n15, yields:
% 51.51/19.91 | (1261) all_0_4_4 = n15
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (690) with n15, n17, all_0_2_2, n6 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n6, yields:
% 51.51/19.91 | (1262) all_0_2_2 = n6
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (690) with n15, n0, all_0_7_7, n15 and discharging atoms sum(n15, n0) = all_0_7_7, sum(n15, n0) = n15, yields:
% 51.51/19.91 | (1263) all_0_7_7 = n15
% 51.51/19.91 |
% 51.51/19.91 | From (1262) and (1082) follows:
% 51.51/19.91 | (1264) sum(n6, n24) = all_0_0_0
% 51.51/19.91 |
% 51.51/19.91 | From (1263)(1261) and (590) follows:
% 51.51/19.91 | (1265) sum(n15, n15) = all_0_3_3
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 51.51/19.91 | (1266) all_0_3_3 = n4
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (690) with n6, n24, all_0_0_0, n4 and discharging atoms sum(n6, n24) = all_0_0_0, sum(n6, n24) = n4, yields:
% 51.51/19.91 | (1267) all_0_0_0 = n4
% 51.51/19.91 |
% 51.51/19.91 | Equations (1267,1266) can reduce 679 to:
% 51.51/19.91 | (1106) $false
% 51.51/19.91 |
% 51.51/19.91 |-The branch is then unsatisfiable
% 51.51/19.91 |-Branch two:
% 51.51/19.91 | (1269) ~ (all_0_11_11 = n16)
% 51.51/19.91 | (1270) 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
% 51.51/19.91 |
% 51.51/19.91 +-Applying beta-rule and splitting (1270), into two cases.
% 51.51/19.91 |-Branch one:
% 51.51/19.91 | (1271) all_0_11_11 = n15
% 51.51/19.91 |
% 51.51/19.91 | From (1271) and (559) follows:
% 51.51/19.91 | (1272) pred(n15) = all_0_9_9
% 51.51/19.91 |
% 51.51/19.91 | From (1271) and (992) follows:
% 51.51/19.91 | (1273) succ(n15) = all_0_5_5
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (500) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 51.51/19.91 | (1274) all_0_9_9 = n14
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (617) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 51.51/19.91 | (1275) all_0_5_5 = n16
% 51.51/19.91 |
% 51.51/19.91 | From (1274)(1275) and (538) follows:
% 51.51/19.91 | (1276) sum(n14, n16) = all_0_2_2
% 51.51/19.91 |
% 51.51/19.91 | From (1274) and (1080) follows:
% 51.51/19.91 | (1277) sum(n14, n0) = all_0_7_7
% 51.51/19.91 |
% 51.51/19.91 | From (1275) and (1078) follows:
% 51.51/19.91 | (1278) sum(n24, n16) = all_0_4_4
% 51.51/19.91 |
% 51.51/19.91 | Instantiating formula (690) with n24, n16, all_0_4_4, n14 and discharging atoms sum(n24, n16) = all_0_4_4, sum(n24, n16) = n14, yields:
% 51.51/19.92 | (1279) all_0_4_4 = n14
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (690) with n14, n16, all_0_2_2, n4 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n4, yields:
% 51.51/19.92 | (1280) all_0_2_2 = n4
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (690) with n14, n0, all_0_7_7, n14 and discharging atoms sum(n14, n0) = all_0_7_7, sum(n14, n0) = n14, yields:
% 51.51/19.92 | (1281) all_0_7_7 = n14
% 51.51/19.92 |
% 51.51/19.92 | From (1280) and (1082) follows:
% 51.51/19.92 | (1282) sum(n4, n24) = all_0_0_0
% 51.51/19.92 |
% 51.51/19.92 | From (1281)(1279) and (590) follows:
% 51.51/19.92 | (1283) sum(n14, n14) = all_0_3_3
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 51.51/19.92 | (1284) all_0_3_3 = n2
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (690) with n4, n24, all_0_0_0, n2 and discharging atoms sum(n4, n24) = all_0_0_0, sum(n4, n24) = n2, yields:
% 51.51/19.92 | (1285) all_0_0_0 = n2
% 51.51/19.92 |
% 51.51/19.92 | Equations (1285,1284) can reduce 679 to:
% 51.51/19.92 | (1106) $false
% 51.51/19.92 |
% 51.51/19.92 |-The branch is then unsatisfiable
% 51.51/19.92 |-Branch two:
% 51.51/19.92 | (1287) ~ (all_0_11_11 = n15)
% 51.51/19.92 | (1288) 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
% 51.51/19.92 |
% 51.51/19.92 +-Applying beta-rule and splitting (1288), into two cases.
% 51.51/19.92 |-Branch one:
% 51.51/19.92 | (1289) all_0_11_11 = n14
% 51.51/19.92 |
% 51.51/19.92 | From (1289) and (559) follows:
% 51.51/19.92 | (1290) pred(n14) = all_0_9_9
% 51.51/19.92 |
% 51.51/19.92 | From (1289) and (992) follows:
% 51.51/19.92 | (1291) succ(n14) = all_0_5_5
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (500) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 51.51/19.92 | (1292) all_0_9_9 = n13
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (617) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 51.51/19.92 | (1293) all_0_5_5 = n15
% 51.51/19.92 |
% 51.51/19.92 | From (1292)(1293) and (538) follows:
% 51.51/19.92 | (1294) sum(n13, n15) = all_0_2_2
% 51.51/19.92 |
% 51.51/19.92 | From (1292) and (1080) follows:
% 51.51/19.92 | (1295) sum(n13, n0) = all_0_7_7
% 51.51/19.92 |
% 51.51/19.92 | From (1293) and (1078) follows:
% 51.51/19.92 | (1296) sum(n24, n15) = all_0_4_4
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (690) with n24, n15, all_0_4_4, n13 and discharging atoms sum(n24, n15) = all_0_4_4, sum(n24, n15) = n13, yields:
% 51.51/19.92 | (1297) all_0_4_4 = n13
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (690) with n13, n15, all_0_2_2, n2 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n2, yields:
% 51.51/19.92 | (1298) all_0_2_2 = n2
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (690) with n13, n0, all_0_7_7, n13 and discharging atoms sum(n13, n0) = all_0_7_7, sum(n13, n0) = n13, yields:
% 51.51/19.92 | (1299) all_0_7_7 = n13
% 51.51/19.92 |
% 51.51/19.92 | From (1298) and (1082) follows:
% 51.51/19.92 | (1300) sum(n2, n24) = all_0_0_0
% 51.51/19.92 |
% 51.51/19.92 | From (1299)(1297) and (590) follows:
% 51.51/19.92 | (1301) sum(n13, n13) = all_0_3_3
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 51.51/19.92 | (1302) all_0_3_3 = n0
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (690) with n2, n24, all_0_0_0, n0 and discharging atoms sum(n2, n24) = all_0_0_0, sum(n2, n24) = n0, yields:
% 51.51/19.92 | (1303) all_0_0_0 = n0
% 51.51/19.92 |
% 51.51/19.92 | Equations (1303,1302) can reduce 679 to:
% 51.51/19.92 | (1106) $false
% 51.51/19.92 |
% 51.51/19.92 |-The branch is then unsatisfiable
% 51.51/19.92 |-Branch two:
% 51.51/19.92 | (1305) ~ (all_0_11_11 = n14)
% 51.51/19.92 | (1306) 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
% 51.51/19.92 |
% 51.51/19.92 +-Applying beta-rule and splitting (1306), into two cases.
% 51.51/19.92 |-Branch one:
% 51.51/19.92 | (1307) all_0_11_11 = n13
% 51.51/19.92 |
% 51.51/19.92 | From (1307) and (559) follows:
% 51.51/19.92 | (1308) pred(n13) = all_0_9_9
% 51.51/19.92 |
% 51.51/19.92 | From (1307) and (992) follows:
% 51.51/19.92 | (1309) succ(n13) = all_0_5_5
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (500) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 51.51/19.92 | (1310) all_0_9_9 = n12
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (617) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 51.51/19.92 | (1311) all_0_5_5 = n14
% 51.51/19.92 |
% 51.51/19.92 | From (1310)(1311) and (538) follows:
% 51.51/19.92 | (1312) sum(n12, n14) = all_0_2_2
% 51.51/19.92 |
% 51.51/19.92 | From (1310) and (1080) follows:
% 51.51/19.92 | (1313) sum(n12, n0) = all_0_7_7
% 51.51/19.92 |
% 51.51/19.92 | From (1311) and (1078) follows:
% 51.51/19.92 | (1314) sum(n24, n14) = all_0_4_4
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (690) with n24, n14, all_0_4_4, n12 and discharging atoms sum(n24, n14) = all_0_4_4, sum(n24, n14) = n12, yields:
% 51.51/19.92 | (1315) all_0_4_4 = n12
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (690) with n12, n14, all_0_2_2, n0 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n0, yields:
% 51.51/19.92 | (1316) all_0_2_2 = n0
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (690) with n12, n0, all_0_7_7, n12 and discharging atoms sum(n12, n0) = all_0_7_7, sum(n12, n0) = n12, yields:
% 51.51/19.92 | (1317) all_0_7_7 = n12
% 51.51/19.92 |
% 51.51/19.92 | From (1316) and (1082) follows:
% 51.51/19.92 | (1318) sum(n0, n24) = all_0_0_0
% 51.51/19.92 |
% 51.51/19.92 | From (1317)(1315) and (590) follows:
% 51.51/19.92 | (1319) sum(n12, n12) = all_0_3_3
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 51.51/19.92 | (1320) all_0_3_3 = n24
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (690) with n0, n24, all_0_0_0, n24 and discharging atoms sum(n0, n24) = all_0_0_0, sum(n0, n24) = n24, yields:
% 51.51/19.92 | (1321) all_0_0_0 = n24
% 51.51/19.92 |
% 51.51/19.92 | Equations (1321,1320) can reduce 679 to:
% 51.51/19.92 | (1106) $false
% 51.51/19.92 |
% 51.51/19.92 |-The branch is then unsatisfiable
% 51.51/19.92 |-Branch two:
% 51.51/19.92 | (1323) ~ (all_0_11_11 = n13)
% 51.51/19.92 | (1324) 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
% 51.51/19.92 |
% 51.51/19.92 +-Applying beta-rule and splitting (1324), into two cases.
% 51.51/19.92 |-Branch one:
% 51.51/19.92 | (1325) all_0_11_11 = n12
% 51.51/19.92 |
% 51.51/19.92 | From (1325) and (559) follows:
% 51.51/19.92 | (1326) pred(n12) = all_0_9_9
% 51.51/19.92 |
% 51.51/19.92 | From (1325) and (992) follows:
% 51.51/19.92 | (1327) succ(n12) = all_0_5_5
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (500) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 51.51/19.92 | (1328) all_0_9_9 = n11
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (617) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 51.51/19.92 | (1329) all_0_5_5 = n13
% 51.51/19.92 |
% 51.51/19.92 | From (1328)(1329) and (538) follows:
% 51.51/19.92 | (1330) sum(n11, n13) = all_0_2_2
% 51.51/19.92 |
% 51.51/19.92 | From (1328) and (1080) follows:
% 51.51/19.92 | (1331) sum(n11, n0) = all_0_7_7
% 51.51/19.92 |
% 51.51/19.92 | From (1329) and (1078) follows:
% 51.51/19.92 | (1332) sum(n24, n13) = all_0_4_4
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (690) with n24, n13, all_0_4_4, n11 and discharging atoms sum(n24, n13) = all_0_4_4, sum(n24, n13) = n11, yields:
% 51.51/19.92 | (1333) all_0_4_4 = n11
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (690) with n11, n13, all_0_2_2, n24 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n24, yields:
% 51.51/19.92 | (1092) all_0_2_2 = n24
% 51.51/19.92 |
% 51.51/19.92 | Instantiating formula (690) with n11, n0, all_0_7_7, n11 and discharging atoms sum(n11, n0) = all_0_7_7, sum(n11, n0) = n11, yields:
% 51.51/19.92 | (1335) all_0_7_7 = n11
% 51.51/19.92 |
% 51.51/19.92 | From (1092) and (1082) follows:
% 51.51/19.92 | (1100) sum(n24, n24) = all_0_0_0
% 51.51/19.92 |
% 51.51/19.92 | From (1335)(1333) and (590) follows:
% 51.51/19.93 | (1337) sum(n11, n11) = all_0_3_3
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (690) with n24, n24, all_0_0_0, n22 and discharging atoms sum(n24, n24) = all_0_0_0, sum(n24, n24) = n22, yields:
% 51.51/19.93 | (1102) all_0_0_0 = n22
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 51.51/19.93 | (1104) all_0_3_3 = n22
% 51.51/19.93 |
% 51.51/19.93 | Equations (1102,1104) can reduce 679 to:
% 51.51/19.93 | (1106) $false
% 51.51/19.93 |
% 51.51/19.93 |-The branch is then unsatisfiable
% 51.51/19.93 |-Branch two:
% 51.51/19.93 | (1341) ~ (all_0_11_11 = n12)
% 51.51/19.93 | (1342) 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
% 51.51/19.93 |
% 51.51/19.93 +-Applying beta-rule and splitting (1342), into two cases.
% 51.51/19.93 |-Branch one:
% 51.51/19.93 | (1343) all_0_11_11 = n11
% 51.51/19.93 |
% 51.51/19.93 | From (1343) and (559) follows:
% 51.51/19.93 | (1344) pred(n11) = all_0_9_9
% 51.51/19.93 |
% 51.51/19.93 | From (1343) and (992) follows:
% 51.51/19.93 | (1345) succ(n11) = all_0_5_5
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (500) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 51.51/19.93 | (1346) all_0_9_9 = n10
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (617) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 51.51/19.93 | (1347) all_0_5_5 = n12
% 51.51/19.93 |
% 51.51/19.93 | From (1346)(1347) and (538) follows:
% 51.51/19.93 | (1348) sum(n10, n12) = all_0_2_2
% 51.51/19.93 |
% 51.51/19.93 | From (1346) and (1080) follows:
% 51.51/19.93 | (1349) sum(n10, n0) = all_0_7_7
% 51.51/19.93 |
% 51.51/19.93 | From (1347) and (1078) follows:
% 51.51/19.93 | (1350) sum(n24, n12) = all_0_4_4
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (690) with n24, n12, all_0_4_4, n10 and discharging atoms sum(n24, n12) = all_0_4_4, sum(n24, n12) = n10, yields:
% 51.51/19.93 | (1351) all_0_4_4 = n10
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (690) with n10, n12, all_0_2_2, n22 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n22, yields:
% 51.51/19.93 | (1118) all_0_2_2 = n22
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (690) with n10, n0, all_0_7_7, n10 and discharging atoms sum(n10, n0) = all_0_7_7, sum(n10, n0) = n10, yields:
% 51.51/19.93 | (1353) all_0_7_7 = n10
% 51.51/19.93 |
% 51.51/19.93 | From (1118) and (1082) follows:
% 51.51/19.93 | (1120) sum(n22, n24) = all_0_0_0
% 51.51/19.93 |
% 51.51/19.93 | From (1353)(1351) and (590) follows:
% 51.51/19.93 | (1355) sum(n10, n10) = all_0_3_3
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (690) with n22, n24, all_0_0_0, n20 and discharging atoms sum(n22, n24) = all_0_0_0, sum(n22, n24) = n20, yields:
% 51.51/19.93 | (1123) all_0_0_0 = n20
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 51.51/19.93 | (1122) all_0_3_3 = n20
% 51.51/19.93 |
% 51.51/19.93 | Equations (1123,1122) can reduce 679 to:
% 51.51/19.93 | (1106) $false
% 51.51/19.93 |
% 51.51/19.93 |-The branch is then unsatisfiable
% 51.51/19.93 |-Branch two:
% 51.51/19.93 | (1359) ~ (all_0_11_11 = n11)
% 51.51/19.93 | (1360) 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
% 51.51/19.93 |
% 51.51/19.93 +-Applying beta-rule and splitting (1360), into two cases.
% 51.51/19.93 |-Branch one:
% 51.51/19.93 | (1361) all_0_11_11 = n10
% 51.51/19.93 |
% 51.51/19.93 | From (1361) and (559) follows:
% 51.51/19.93 | (1362) pred(n10) = all_0_9_9
% 51.51/19.93 |
% 51.51/19.93 | From (1361) and (992) follows:
% 51.51/19.93 | (1363) succ(n10) = all_0_5_5
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (500) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 51.51/19.93 | (1364) all_0_9_9 = n9
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (617) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 51.51/19.93 | (1365) all_0_5_5 = n11
% 51.51/19.93 |
% 51.51/19.93 | From (1364)(1365) and (538) follows:
% 51.51/19.93 | (1366) sum(n9, n11) = all_0_2_2
% 51.51/19.93 |
% 51.51/19.93 | From (1364) and (1080) follows:
% 51.51/19.93 | (1367) sum(n9, n0) = all_0_7_7
% 51.51/19.93 |
% 51.51/19.93 | From (1365) and (1078) follows:
% 51.51/19.93 | (1368) sum(n24, n11) = all_0_4_4
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (690) with n24, n11, all_0_4_4, n9 and discharging atoms sum(n24, n11) = all_0_4_4, sum(n24, n11) = n9, yields:
% 51.51/19.93 | (1369) all_0_4_4 = n9
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (690) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 51.51/19.93 | (1136) all_0_2_2 = n20
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (690) with n9, n0, all_0_7_7, n9 and discharging atoms sum(n9, n0) = all_0_7_7, sum(n9, n0) = n9, yields:
% 51.51/19.93 | (1371) all_0_7_7 = n9
% 51.51/19.93 |
% 51.51/19.93 | From (1136) and (1082) follows:
% 51.51/19.93 | (1138) sum(n20, n24) = all_0_0_0
% 51.51/19.93 |
% 51.51/19.93 | From (1371)(1369) and (590) follows:
% 51.51/19.93 | (1373) sum(n9, n9) = all_0_3_3
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (690) with n20, n24, all_0_0_0, n18 and discharging atoms sum(n20, n24) = all_0_0_0, sum(n20, n24) = n18, yields:
% 51.51/19.93 | (1141) all_0_0_0 = n18
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 51.51/19.93 | (1140) all_0_3_3 = n18
% 51.51/19.93 |
% 51.51/19.93 | Equations (1141,1140) can reduce 679 to:
% 51.51/19.93 | (1106) $false
% 51.51/19.93 |
% 51.51/19.93 |-The branch is then unsatisfiable
% 51.51/19.93 |-Branch two:
% 51.51/19.93 | (1377) ~ (all_0_11_11 = n10)
% 51.51/19.93 | (1378) 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
% 51.51/19.93 |
% 51.51/19.93 +-Applying beta-rule and splitting (1378), into two cases.
% 51.51/19.93 |-Branch one:
% 51.51/19.93 | (1379) all_0_11_11 = n9
% 51.51/19.93 |
% 51.51/19.93 | From (1379) and (559) follows:
% 51.51/19.93 | (1380) pred(n9) = all_0_9_9
% 51.51/19.93 |
% 51.51/19.93 | From (1379) and (992) follows:
% 51.51/19.93 | (1381) succ(n9) = all_0_5_5
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 51.51/19.93 | (1382) all_0_9_9 = n8
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 51.51/19.93 | (1383) all_0_5_5 = n10
% 51.51/19.93 |
% 51.51/19.93 | From (1382)(1383) and (538) follows:
% 51.51/19.93 | (1384) sum(n8, n10) = all_0_2_2
% 51.51/19.93 |
% 51.51/19.93 | From (1382) and (1080) follows:
% 51.51/19.93 | (1385) sum(n8, n0) = all_0_7_7
% 51.51/19.93 |
% 51.51/19.93 | From (1383) and (1078) follows:
% 51.51/19.93 | (1386) sum(n24, n10) = all_0_4_4
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (690) with n24, n10, all_0_4_4, n8 and discharging atoms sum(n24, n10) = all_0_4_4, sum(n24, n10) = n8, yields:
% 51.51/19.93 | (1387) all_0_4_4 = n8
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 51.51/19.93 | (1154) all_0_2_2 = n18
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (690) with n8, n0, all_0_7_7, n8 and discharging atoms sum(n8, n0) = all_0_7_7, sum(n8, n0) = n8, yields:
% 51.51/19.93 | (1389) all_0_7_7 = n8
% 51.51/19.93 |
% 51.51/19.93 | From (1154) and (1082) follows:
% 51.51/19.93 | (1156) sum(n18, n24) = all_0_0_0
% 51.51/19.93 |
% 51.51/19.93 | From (1389)(1387) and (590) follows:
% 51.51/19.93 | (1391) sum(n8, n8) = all_0_3_3
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (690) with n18, n24, all_0_0_0, n16 and discharging atoms sum(n18, n24) = all_0_0_0, sum(n18, n24) = n16, yields:
% 51.51/19.93 | (1159) all_0_0_0 = n16
% 51.51/19.93 |
% 51.51/19.93 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 51.51/19.93 | (1158) all_0_3_3 = n16
% 51.51/19.93 |
% 51.51/19.93 | Equations (1159,1158) can reduce 679 to:
% 51.51/19.93 | (1106) $false
% 51.51/19.93 |
% 51.51/19.93 |-The branch is then unsatisfiable
% 51.51/19.93 |-Branch two:
% 51.51/19.93 | (1395) ~ (all_0_11_11 = n9)
% 51.51/19.94 | (1396) 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
% 51.51/19.94 |
% 51.51/19.94 +-Applying beta-rule and splitting (1396), into two cases.
% 51.51/19.94 |-Branch one:
% 51.51/19.94 | (1397) all_0_11_11 = n8
% 51.51/19.94 |
% 51.51/19.94 | From (1397) and (559) follows:
% 51.51/19.94 | (1398) pred(n8) = all_0_9_9
% 51.51/19.94 |
% 51.51/19.94 | From (1397) and (992) follows:
% 51.51/19.94 | (1399) succ(n8) = all_0_5_5
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 51.51/19.94 | (1400) all_0_9_9 = n7
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 51.51/19.94 | (1401) all_0_5_5 = n9
% 51.51/19.94 |
% 51.51/19.94 | From (1400)(1401) and (538) follows:
% 51.51/19.94 | (1402) sum(n7, n9) = all_0_2_2
% 51.51/19.94 |
% 51.51/19.94 | From (1400) and (1080) follows:
% 51.51/19.94 | (1403) sum(n7, n0) = all_0_7_7
% 51.51/19.94 |
% 51.51/19.94 | From (1401) and (1078) follows:
% 51.51/19.94 | (1404) sum(n24, n9) = all_0_4_4
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (690) with n24, n9, all_0_4_4, n7 and discharging atoms sum(n24, n9) = all_0_4_4, sum(n24, n9) = n7, yields:
% 51.51/19.94 | (1405) all_0_4_4 = n7
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 51.51/19.94 | (1172) all_0_2_2 = n16
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (690) with n7, n0, all_0_7_7, n7 and discharging atoms sum(n7, n0) = all_0_7_7, sum(n7, n0) = n7, yields:
% 51.51/19.94 | (1407) all_0_7_7 = n7
% 51.51/19.94 |
% 51.51/19.94 | From (1172) and (1082) follows:
% 51.51/19.94 | (1174) sum(n16, n24) = all_0_0_0
% 51.51/19.94 |
% 51.51/19.94 | From (1407)(1405) and (590) follows:
% 51.51/19.94 | (1409) sum(n7, n7) = all_0_3_3
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (690) with n16, n24, all_0_0_0, n14 and discharging atoms sum(n16, n24) = all_0_0_0, sum(n16, n24) = n14, yields:
% 51.51/19.94 | (1177) all_0_0_0 = n14
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 51.51/19.94 | (1176) all_0_3_3 = n14
% 51.51/19.94 |
% 51.51/19.94 | Equations (1177,1176) can reduce 679 to:
% 51.51/19.94 | (1106) $false
% 51.51/19.94 |
% 51.51/19.94 |-The branch is then unsatisfiable
% 51.51/19.94 |-Branch two:
% 51.51/19.94 | (1413) ~ (all_0_11_11 = n8)
% 51.51/19.94 | (1414) 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
% 51.51/19.94 |
% 51.51/19.94 +-Applying beta-rule and splitting (1414), into two cases.
% 51.51/19.94 |-Branch one:
% 51.51/19.94 | (1415) all_0_11_11 = n7
% 51.51/19.94 |
% 51.51/19.94 | From (1415) and (559) follows:
% 51.51/19.94 | (1416) pred(n7) = all_0_9_9
% 51.51/19.94 |
% 51.51/19.94 | From (1415) and (992) follows:
% 51.51/19.94 | (1417) succ(n7) = all_0_5_5
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 51.51/19.94 | (1418) all_0_9_9 = n6
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 51.51/19.94 | (1419) all_0_5_5 = n8
% 51.51/19.94 |
% 51.51/19.94 | From (1418)(1419) and (538) follows:
% 51.51/19.94 | (1420) sum(n6, n8) = all_0_2_2
% 51.51/19.94 |
% 51.51/19.94 | From (1418) and (1080) follows:
% 51.51/19.94 | (1421) sum(n6, n0) = all_0_7_7
% 51.51/19.94 |
% 51.51/19.94 | From (1419) and (1078) follows:
% 51.51/19.94 | (1422) sum(n24, n8) = all_0_4_4
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (690) with n24, n8, all_0_4_4, n6 and discharging atoms sum(n24, n8) = all_0_4_4, sum(n24, n8) = n6, yields:
% 51.51/19.94 | (1423) all_0_4_4 = n6
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 51.51/19.94 | (1190) all_0_2_2 = n14
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (690) with n6, n0, all_0_7_7, n6 and discharging atoms sum(n6, n0) = all_0_7_7, sum(n6, n0) = n6, yields:
% 51.51/19.94 | (1425) all_0_7_7 = n6
% 51.51/19.94 |
% 51.51/19.94 | From (1190) and (1082) follows:
% 51.51/19.94 | (1192) sum(n14, n24) = all_0_0_0
% 51.51/19.94 |
% 51.51/19.94 | From (1425)(1423) and (590) follows:
% 51.51/19.94 | (1427) sum(n6, n6) = all_0_3_3
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (690) with n14, n24, all_0_0_0, n12 and discharging atoms sum(n14, n24) = all_0_0_0, sum(n14, n24) = n12, yields:
% 51.51/19.94 | (1195) all_0_0_0 = n12
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 51.51/19.94 | (1194) all_0_3_3 = n12
% 51.51/19.94 |
% 51.51/19.94 | Equations (1195,1194) can reduce 679 to:
% 51.51/19.94 | (1106) $false
% 51.51/19.94 |
% 51.51/19.94 |-The branch is then unsatisfiable
% 51.51/19.94 |-Branch two:
% 51.51/19.94 | (1431) ~ (all_0_11_11 = n7)
% 51.51/19.94 | (1432) 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
% 51.51/19.94 |
% 51.51/19.94 +-Applying beta-rule and splitting (1432), into two cases.
% 51.51/19.94 |-Branch one:
% 51.51/19.94 | (1433) all_0_11_11 = n6
% 51.51/19.94 |
% 51.51/19.94 | From (1433) and (559) follows:
% 51.51/19.94 | (1434) pred(n6) = all_0_9_9
% 51.51/19.94 |
% 51.51/19.94 | From (1433) and (992) follows:
% 51.51/19.94 | (1435) succ(n6) = all_0_5_5
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 51.51/19.94 | (1436) all_0_9_9 = n5
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 51.51/19.94 | (1437) all_0_5_5 = n7
% 51.51/19.94 |
% 51.51/19.94 | From (1436)(1437) and (538) follows:
% 51.51/19.94 | (1438) sum(n5, n7) = all_0_2_2
% 51.51/19.94 |
% 51.51/19.94 | From (1436) and (1080) follows:
% 51.51/19.94 | (1439) sum(n5, n0) = all_0_7_7
% 51.51/19.94 |
% 51.51/19.94 | From (1437) and (1078) follows:
% 51.51/19.94 | (1440) sum(n24, n7) = all_0_4_4
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (690) with n24, n7, all_0_4_4, n5 and discharging atoms sum(n24, n7) = all_0_4_4, sum(n24, n7) = n5, yields:
% 51.51/19.94 | (1441) all_0_4_4 = n5
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 51.51/19.94 | (1208) all_0_2_2 = n12
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (690) with n5, n0, all_0_7_7, n5 and discharging atoms sum(n5, n0) = all_0_7_7, sum(n5, n0) = n5, yields:
% 51.51/19.94 | (1443) all_0_7_7 = n5
% 51.51/19.94 |
% 51.51/19.94 | From (1208) and (1082) follows:
% 51.51/19.94 | (1210) sum(n12, n24) = all_0_0_0
% 51.51/19.94 |
% 51.51/19.94 | From (1443)(1441) and (590) follows:
% 51.51/19.94 | (1445) sum(n5, n5) = all_0_3_3
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (690) with n12, n24, all_0_0_0, n10 and discharging atoms sum(n12, n24) = all_0_0_0, sum(n12, n24) = n10, yields:
% 51.51/19.94 | (1213) all_0_0_0 = n10
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 51.51/19.94 | (1212) all_0_3_3 = n10
% 51.51/19.94 |
% 51.51/19.94 | Equations (1213,1212) can reduce 679 to:
% 51.51/19.94 | (1106) $false
% 51.51/19.94 |
% 51.51/19.94 |-The branch is then unsatisfiable
% 51.51/19.94 |-Branch two:
% 51.51/19.94 | (1449) ~ (all_0_11_11 = n6)
% 51.51/19.94 | (1450) 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
% 51.51/19.94 |
% 51.51/19.94 +-Applying beta-rule and splitting (1450), into two cases.
% 51.51/19.94 |-Branch one:
% 51.51/19.94 | (1451) all_0_11_11 = n5
% 51.51/19.94 |
% 51.51/19.94 | From (1451) and (559) follows:
% 51.51/19.94 | (1452) pred(n5) = all_0_9_9
% 51.51/19.94 |
% 51.51/19.94 | From (1451) and (992) follows:
% 51.51/19.94 | (1453) succ(n5) = all_0_5_5
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 51.51/19.94 | (1454) all_0_9_9 = n4
% 51.51/19.94 |
% 51.51/19.94 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 51.51/19.95 | (1455) all_0_5_5 = n6
% 51.51/19.95 |
% 51.51/19.95 | From (1454)(1455) and (538) follows:
% 51.51/19.95 | (1456) sum(n4, n6) = all_0_2_2
% 51.51/19.95 |
% 51.51/19.95 | From (1454) and (1080) follows:
% 51.51/19.95 | (1457) sum(n4, n0) = all_0_7_7
% 51.51/19.95 |
% 51.51/19.95 | From (1455) and (1078) follows:
% 51.51/19.95 | (1458) sum(n24, n6) = all_0_4_4
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (690) with n24, n6, all_0_4_4, n4 and discharging atoms sum(n24, n6) = all_0_4_4, sum(n24, n6) = n4, yields:
% 51.51/19.95 | (1459) all_0_4_4 = n4
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 51.51/19.95 | (1226) all_0_2_2 = n10
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (690) with n4, n0, all_0_7_7, n4 and discharging atoms sum(n4, n0) = all_0_7_7, sum(n4, n0) = n4, yields:
% 51.51/19.95 | (1461) all_0_7_7 = n4
% 51.51/19.95 |
% 51.51/19.95 | From (1226) and (1082) follows:
% 51.51/19.95 | (1228) sum(n10, n24) = all_0_0_0
% 51.51/19.95 |
% 51.51/19.95 | From (1461)(1459) and (590) follows:
% 51.51/19.95 | (1463) sum(n4, n4) = all_0_3_3
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (690) with n10, n24, all_0_0_0, n8 and discharging atoms sum(n10, n24) = all_0_0_0, sum(n10, n24) = n8, yields:
% 51.51/19.95 | (1231) all_0_0_0 = n8
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 51.51/19.95 | (1230) all_0_3_3 = n8
% 51.51/19.95 |
% 51.51/19.95 | Equations (1231,1230) can reduce 679 to:
% 51.51/19.95 | (1106) $false
% 51.51/19.95 |
% 51.51/19.95 |-The branch is then unsatisfiable
% 51.51/19.95 |-Branch two:
% 51.51/19.95 | (1467) ~ (all_0_11_11 = n5)
% 51.51/19.95 | (1468) 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
% 51.51/19.95 |
% 51.51/19.95 +-Applying beta-rule and splitting (1468), into two cases.
% 51.51/19.95 |-Branch one:
% 51.51/19.95 | (1469) all_0_11_11 = n4
% 51.51/19.95 |
% 51.51/19.95 | From (1469) and (559) follows:
% 51.51/19.95 | (1470) pred(n4) = all_0_9_9
% 51.51/19.95 |
% 51.51/19.95 | From (1469) and (992) follows:
% 51.51/19.95 | (1471) succ(n4) = all_0_5_5
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 51.51/19.95 | (1472) all_0_9_9 = n3
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 51.51/19.95 | (1473) all_0_5_5 = n5
% 51.51/19.95 |
% 51.51/19.95 | From (1472)(1473) and (538) follows:
% 51.51/19.95 | (1474) sum(n3, n5) = all_0_2_2
% 51.51/19.95 |
% 51.51/19.95 | From (1472) and (1080) follows:
% 51.51/19.95 | (1475) sum(n3, n0) = all_0_7_7
% 51.51/19.95 |
% 51.51/19.95 | From (1473) and (1078) follows:
% 51.51/19.95 | (1476) sum(n24, n5) = all_0_4_4
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (690) with n24, n5, all_0_4_4, n3 and discharging atoms sum(n24, n5) = all_0_4_4, sum(n24, n5) = n3, yields:
% 51.51/19.95 | (1477) all_0_4_4 = n3
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 51.51/19.95 | (1244) all_0_2_2 = n8
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (690) with n3, n0, all_0_7_7, n3 and discharging atoms sum(n3, n0) = all_0_7_7, sum(n3, n0) = n3, yields:
% 51.51/19.95 | (1479) all_0_7_7 = n3
% 51.51/19.95 |
% 51.51/19.95 | From (1244) and (1082) follows:
% 51.51/19.95 | (1246) sum(n8, n24) = all_0_0_0
% 51.51/19.95 |
% 51.51/19.95 | From (1479)(1477) and (590) follows:
% 51.51/19.95 | (1481) sum(n3, n3) = all_0_3_3
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (690) with n8, n24, all_0_0_0, n6 and discharging atoms sum(n8, n24) = all_0_0_0, sum(n8, n24) = n6, yields:
% 51.51/19.95 | (1249) all_0_0_0 = n6
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 51.51/19.95 | (1248) all_0_3_3 = n6
% 51.51/19.95 |
% 51.51/19.95 | Equations (1249,1248) can reduce 679 to:
% 51.51/19.95 | (1106) $false
% 51.51/19.95 |
% 51.51/19.95 |-The branch is then unsatisfiable
% 51.51/19.95 |-Branch two:
% 51.51/19.95 | (1485) ~ (all_0_11_11 = n4)
% 51.51/19.95 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 51.51/19.95 |
% 51.51/19.95 +-Applying beta-rule and splitting (1486), into two cases.
% 51.51/19.95 |-Branch one:
% 51.51/19.95 | (1487) all_0_11_11 = n3
% 51.51/19.95 |
% 51.51/19.95 | From (1487) and (559) follows:
% 51.51/19.95 | (1488) pred(n3) = all_0_9_9
% 51.51/19.95 |
% 51.51/19.95 | From (1487) and (992) follows:
% 51.51/19.95 | (1489) succ(n3) = all_0_5_5
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 51.51/19.95 | (1490) all_0_9_9 = n2
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 51.51/19.95 | (1491) all_0_5_5 = n4
% 51.51/19.95 |
% 51.51/19.95 | From (1490)(1491) and (538) follows:
% 51.51/19.95 | (1492) sum(n2, n4) = all_0_2_2
% 51.51/19.95 |
% 51.51/19.95 | From (1490) and (1080) follows:
% 51.51/19.95 | (1493) sum(n2, n0) = all_0_7_7
% 51.51/19.95 |
% 51.51/19.95 | From (1491) and (1078) follows:
% 51.51/19.95 | (1494) sum(n24, n4) = all_0_4_4
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (690) with n24, n4, all_0_4_4, n2 and discharging atoms sum(n24, n4) = all_0_4_4, sum(n24, n4) = n2, yields:
% 51.51/19.95 | (1495) all_0_4_4 = n2
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 51.51/19.95 | (1262) all_0_2_2 = n6
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (690) with n2, n0, all_0_7_7, n2 and discharging atoms sum(n2, n0) = all_0_7_7, sum(n2, n0) = n2, yields:
% 51.51/19.95 | (1497) all_0_7_7 = n2
% 51.51/19.95 |
% 51.51/19.95 | From (1262) and (1082) follows:
% 51.51/19.95 | (1264) sum(n6, n24) = all_0_0_0
% 51.51/19.95 |
% 51.51/19.95 | From (1497)(1495) and (590) follows:
% 51.51/19.95 | (1499) sum(n2, n2) = all_0_3_3
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (690) with n6, n24, all_0_0_0, n4 and discharging atoms sum(n6, n24) = all_0_0_0, sum(n6, n24) = n4, yields:
% 51.51/19.95 | (1267) all_0_0_0 = n4
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 51.51/19.95 | (1266) all_0_3_3 = n4
% 51.51/19.95 |
% 51.51/19.95 | Equations (1267,1266) can reduce 679 to:
% 51.51/19.95 | (1106) $false
% 51.51/19.95 |
% 51.51/19.95 |-The branch is then unsatisfiable
% 51.51/19.95 |-Branch two:
% 51.51/19.95 | (1503) ~ (all_0_11_11 = n3)
% 51.51/19.95 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 51.51/19.95 |
% 51.51/19.95 +-Applying beta-rule and splitting (1504), into two cases.
% 51.51/19.95 |-Branch one:
% 51.51/19.95 | (1505) all_0_11_11 = n2
% 51.51/19.95 |
% 51.51/19.95 | From (1505) and (559) follows:
% 51.51/19.95 | (1506) pred(n2) = all_0_9_9
% 51.51/19.95 |
% 51.51/19.95 | From (1505) and (992) follows:
% 51.51/19.95 | (1507) succ(n2) = all_0_5_5
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 51.51/19.95 | (1508) all_0_9_9 = n1
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 51.51/19.95 | (1509) all_0_5_5 = n3
% 51.51/19.95 |
% 51.51/19.95 | From (1508)(1509) and (538) follows:
% 51.51/19.95 | (1510) sum(n1, n3) = all_0_2_2
% 51.51/19.95 |
% 51.51/19.95 | From (1508) and (1080) follows:
% 51.51/19.95 | (1511) sum(n1, n0) = all_0_7_7
% 51.51/19.95 |
% 51.51/19.95 | From (1509) and (1078) follows:
% 51.51/19.95 | (1512) sum(n24, n3) = all_0_4_4
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (690) with n24, n3, all_0_4_4, n1 and discharging atoms sum(n24, n3) = all_0_4_4, sum(n24, n3) = n1, yields:
% 51.51/19.95 | (1513) all_0_4_4 = n1
% 51.51/19.95 |
% 51.51/19.95 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 51.51/19.95 | (1280) all_0_2_2 = n4
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (690) with n1, n0, all_0_7_7, n1 and discharging atoms sum(n1, n0) = all_0_7_7, sum(n1, n0) = n1, yields:
% 51.51/19.96 | (1515) all_0_7_7 = n1
% 51.51/19.96 |
% 51.51/19.96 | From (1280) and (1082) follows:
% 51.51/19.96 | (1282) sum(n4, n24) = all_0_0_0
% 51.51/19.96 |
% 51.51/19.96 | From (1515)(1513) and (590) follows:
% 51.51/19.96 | (1517) sum(n1, n1) = all_0_3_3
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (690) with n4, n24, all_0_0_0, n2 and discharging atoms sum(n4, n24) = all_0_0_0, sum(n4, n24) = n2, yields:
% 51.51/19.96 | (1285) all_0_0_0 = n2
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 51.51/19.96 | (1284) all_0_3_3 = n2
% 51.51/19.96 |
% 51.51/19.96 | Equations (1285,1284) can reduce 679 to:
% 51.51/19.96 | (1106) $false
% 51.51/19.96 |
% 51.51/19.96 |-The branch is then unsatisfiable
% 51.51/19.96 |-Branch two:
% 51.51/19.96 | (1521) ~ (all_0_11_11 = n2)
% 51.51/19.96 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 51.51/19.96 |
% 51.51/19.96 +-Applying beta-rule and splitting (1522), into two cases.
% 51.51/19.96 |-Branch one:
% 51.51/19.96 | (1523) all_0_11_11 = n1
% 51.51/19.96 |
% 51.51/19.96 | From (1523) and (559) follows:
% 51.51/19.96 | (1524) pred(n1) = all_0_9_9
% 51.51/19.96 |
% 51.51/19.96 | From (1523) and (992) follows:
% 51.51/19.96 | (1525) succ(n1) = all_0_5_5
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 51.51/19.96 | (1526) all_0_9_9 = n0
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 51.51/19.96 | (1527) all_0_5_5 = n2
% 51.51/19.96 |
% 51.51/19.96 | From (1526)(1527) and (538) follows:
% 51.51/19.96 | (1528) sum(n0, n2) = all_0_2_2
% 51.51/19.96 |
% 51.51/19.96 | From (1526) and (1080) follows:
% 51.51/19.96 | (1529) sum(n0, n0) = all_0_7_7
% 51.51/19.96 |
% 51.51/19.96 | From (1527) and (1078) follows:
% 51.51/19.96 | (1530) sum(n24, n2) = all_0_4_4
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (690) with n24, n2, all_0_4_4, n0 and discharging atoms sum(n24, n2) = all_0_4_4, sum(n24, n2) = n0, yields:
% 51.51/19.96 | (1531) all_0_4_4 = n0
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 51.51/19.96 | (1298) all_0_2_2 = n2
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (690) with n0, n0, all_0_7_7, n0 and discharging atoms sum(n0, n0) = all_0_7_7, sum(n0, n0) = n0, yields:
% 51.51/19.96 | (1533) all_0_7_7 = n0
% 51.51/19.96 |
% 51.51/19.96 | From (1298) and (1082) follows:
% 51.51/19.96 | (1300) sum(n2, n24) = all_0_0_0
% 51.51/19.96 |
% 51.51/19.96 | From (1533)(1531) and (590) follows:
% 51.51/19.96 | (1535) sum(n0, n0) = all_0_3_3
% 51.51/19.96 |
% 51.51/19.96 | From (1533) and (1529) follows:
% 51.51/19.96 | (208) sum(n0, n0) = n0
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (690) with n2, n24, all_0_0_0, n0 and discharging atoms sum(n2, n24) = all_0_0_0, sum(n2, n24) = n0, yields:
% 51.51/19.96 | (1303) all_0_0_0 = n0
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 51.51/19.96 | (1302) all_0_3_3 = n0
% 51.51/19.96 |
% 51.51/19.96 | Equations (1303,1302) can reduce 679 to:
% 51.51/19.96 | (1106) $false
% 51.51/19.96 |
% 51.51/19.96 |-The branch is then unsatisfiable
% 51.51/19.96 |-Branch two:
% 51.51/19.96 | (1540) ~ (all_0_11_11 = n1)
% 51.51/19.96 | (1541) all_0_11_11 = n0
% 51.51/19.96 |
% 51.51/19.96 | From (1541) and (559) follows:
% 51.51/19.96 | (1542) pred(n0) = all_0_9_9
% 51.51/19.96 |
% 51.51/19.96 | From (1541) and (992) follows:
% 51.51/19.96 | (1543) succ(n0) = all_0_5_5
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 51.51/19.96 | (1544) all_0_9_9 = n25
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 51.51/19.96 | (1545) all_0_5_5 = n1
% 51.51/19.96 |
% 51.51/19.96 | From (1544)(1545) and (538) follows:
% 51.51/19.96 | (1546) sum(n25, n1) = all_0_2_2
% 51.51/19.96 |
% 51.51/19.96 | From (1544) and (1080) follows:
% 51.51/19.96 | (1547) sum(n25, n0) = all_0_7_7
% 51.51/19.96 |
% 51.51/19.96 | From (1545) and (1078) follows:
% 51.51/19.96 | (1548) sum(n24, n1) = all_0_4_4
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 51.51/19.96 | (1316) all_0_2_2 = n0
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (690) with n25, n0, all_0_7_7, n25 and discharging atoms sum(n25, n0) = all_0_7_7, sum(n25, n0) = n25, yields:
% 51.51/19.96 | (1550) all_0_7_7 = n25
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (690) with n24, n1, all_0_4_4, n25 and discharging atoms sum(n24, n1) = all_0_4_4, sum(n24, n1) = n25, yields:
% 51.51/19.96 | (1551) all_0_4_4 = n25
% 51.51/19.96 |
% 51.51/19.96 | From (1316) and (1082) follows:
% 51.51/19.96 | (1318) sum(n0, n24) = all_0_0_0
% 51.51/19.96 |
% 51.51/19.96 | From (1550)(1551) and (590) follows:
% 51.51/19.96 | (1553) sum(n25, n25) = all_0_3_3
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 51.51/19.96 | (1320) all_0_3_3 = n24
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (690) with n0, n24, all_0_0_0, n24 and discharging atoms sum(n0, n24) = all_0_0_0, sum(n0, n24) = n24, yields:
% 51.51/19.96 | (1321) all_0_0_0 = n24
% 51.51/19.96 |
% 51.51/19.96 | Equations (1321,1320) can reduce 679 to:
% 51.51/19.96 | (1106) $false
% 51.51/19.96 |
% 51.51/19.96 |-The branch is then unsatisfiable
% 51.51/19.96 |-Branch two:
% 51.51/19.96 | (1557) ~ (all_0_10_10 = n25)
% 51.51/19.96 | (1558) all_0_10_10 = n24 | all_0_10_10 = n23 | all_0_10_10 = n22 | all_0_10_10 = n21 | 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
% 51.51/19.96 |
% 51.51/19.96 +-Applying beta-rule and splitting (361), into two cases.
% 51.51/19.96 |-Branch one:
% 51.51/19.96 | (1084) all_0_11_11 = n25
% 51.51/19.96 |
% 51.51/19.96 | From (1084) and (559) follows:
% 51.51/19.96 | (1085) pred(n25) = all_0_9_9
% 51.51/19.96 |
% 51.51/19.96 | From (1084) and (992) follows:
% 51.51/19.96 | (1086) succ(n25) = all_0_5_5
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (500) with n25, all_0_9_9, n24 and discharging atoms pred(n25) = all_0_9_9, pred(n25) = n24, yields:
% 51.51/19.96 | (1087) all_0_9_9 = n24
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (617) with n25, all_0_5_5, n0 and discharging atoms succ(n25) = all_0_5_5, succ(n25) = n0, yields:
% 51.51/19.96 | (1088) all_0_5_5 = n0
% 51.51/19.96 |
% 51.51/19.96 | From (1088) and (541) follows:
% 51.51/19.96 | (1564) sum(all_0_6_6, n0) = all_0_4_4
% 51.51/19.96 |
% 51.51/19.96 | From (1087)(1088) and (538) follows:
% 51.51/19.96 | (1089) sum(n24, n0) = all_0_2_2
% 51.51/19.96 |
% 51.51/19.96 | From (1087) and (427) follows:
% 51.51/19.96 | (1566) sum(n24, all_0_8_8) = all_0_7_7
% 51.51/19.96 |
% 51.51/19.96 | Instantiating formula (690) with n24, n0, all_0_2_2, n24 and discharging atoms sum(n24, n0) = all_0_2_2, sum(n24, n0) = n24, yields:
% 51.51/19.96 | (1092) all_0_2_2 = n24
% 51.51/19.96 |
% 51.51/19.96 | From (1092) and (630) follows:
% 51.51/19.97 | (1568) sum(n24, all_0_1_1) = all_0_0_0
% 51.51/19.97 |
% 51.51/19.97 | From (1092) and (1089) follows:
% 51.51/19.97 | (965) sum(n24, n0) = n24
% 51.51/19.97 |
% 51.51/19.97 +-Applying beta-rule and splitting (1558), into two cases.
% 51.51/19.97 |-Branch one:
% 51.51/19.97 | (1570) all_0_10_10 = n24
% 51.51/19.97 |
% 51.51/19.97 | From (1570) and (292) follows:
% 51.51/19.97 | (1571) pred(n24) = all_0_6_6
% 51.51/19.97 |
% 51.51/19.97 | From (1570) and (760) follows:
% 51.51/19.97 | (1572) succ(n24) = all_0_8_8
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (500) with n24, all_0_6_6, n23 and discharging atoms pred(n24) = all_0_6_6, pred(n24) = n23, yields:
% 51.51/19.97 | (1573) all_0_6_6 = n23
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (617) with n24, all_0_8_8, n25 and discharging atoms succ(n24) = all_0_8_8, succ(n24) = n25, yields:
% 51.51/19.97 | (1574) all_0_8_8 = n25
% 51.51/19.97 |
% 51.51/19.97 | From (1573)(1574) and (411) follows:
% 51.51/19.97 | (1575) sum(n23, n25) = all_0_1_1
% 51.51/19.97 |
% 51.51/19.97 | From (1573) and (1564) follows:
% 51.51/19.97 | (1576) sum(n23, n0) = all_0_4_4
% 51.51/19.97 |
% 51.51/19.97 | From (1574) and (1566) follows:
% 51.51/19.97 | (1577) sum(n24, n25) = all_0_7_7
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (690) with n24, n25, all_0_7_7, n23 and discharging atoms sum(n24, n25) = all_0_7_7, sum(n24, n25) = n23, yields:
% 51.51/19.97 | (1119) all_0_7_7 = n23
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (690) with n23, n25, all_0_1_1, n22 and discharging atoms sum(n23, n25) = all_0_1_1, sum(n23, n25) = n22, yields:
% 51.51/19.97 | (1579) all_0_1_1 = n22
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (690) with n23, n0, all_0_4_4, n23 and discharging atoms sum(n23, n0) = all_0_4_4, sum(n23, n0) = n23, yields:
% 51.51/19.97 | (1117) all_0_4_4 = n23
% 51.51/19.97 |
% 51.51/19.97 | From (1119)(1117) and (590) follows:
% 51.51/19.97 | (1121) sum(n23, n23) = all_0_3_3
% 51.51/19.97 |
% 51.51/19.97 | From (1579) and (1568) follows:
% 51.51/19.97 | (1582) sum(n24, n22) = all_0_0_0
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (690) with n24, n22, all_0_0_0, n20 and discharging atoms sum(n24, n22) = all_0_0_0, sum(n24, n22) = n20, yields:
% 51.51/19.97 | (1123) all_0_0_0 = n20
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 51.51/19.97 | (1122) all_0_3_3 = n20
% 51.51/19.97 |
% 51.51/19.97 | Equations (1123,1122) can reduce 679 to:
% 51.51/19.97 | (1106) $false
% 51.51/19.97 |
% 51.51/19.97 |-The branch is then unsatisfiable
% 51.51/19.97 |-Branch two:
% 51.51/19.97 | (1586) ~ (all_0_10_10 = n24)
% 51.51/19.97 | (1587) all_0_10_10 = n23 | all_0_10_10 = n22 | all_0_10_10 = n21 | 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
% 51.51/19.97 |
% 51.51/19.97 +-Applying beta-rule and splitting (1587), into two cases.
% 51.51/19.97 |-Branch one:
% 51.51/19.97 | (1588) all_0_10_10 = n23
% 51.51/19.97 |
% 51.51/19.97 | From (1588) and (292) follows:
% 51.51/19.97 | (1589) pred(n23) = all_0_6_6
% 51.51/19.97 |
% 51.51/19.97 | From (1588) and (760) follows:
% 51.51/19.97 | (1590) succ(n23) = all_0_8_8
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (500) with n23, all_0_6_6, n22 and discharging atoms pred(n23) = all_0_6_6, pred(n23) = n22, yields:
% 51.51/19.97 | (1591) all_0_6_6 = n22
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (617) with n23, all_0_8_8, n24 and discharging atoms succ(n23) = all_0_8_8, succ(n23) = n24, yields:
% 51.51/19.97 | (1592) all_0_8_8 = n24
% 51.51/19.97 |
% 51.51/19.97 | From (1591)(1592) and (411) follows:
% 51.51/19.97 | (1593) sum(n22, n24) = all_0_1_1
% 51.51/19.97 |
% 51.51/19.97 | From (1591) and (1564) follows:
% 51.51/19.97 | (1594) sum(n22, n0) = all_0_4_4
% 51.51/19.97 |
% 51.51/19.97 | From (1592) and (1566) follows:
% 51.51/19.97 | (1595) sum(n24, n24) = all_0_7_7
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (690) with n24, n24, all_0_7_7, n22 and discharging atoms sum(n24, n24) = all_0_7_7, sum(n24, n24) = n22, yields:
% 51.51/19.97 | (1137) all_0_7_7 = n22
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (690) with n22, n24, all_0_1_1, n20 and discharging atoms sum(n22, n24) = all_0_1_1, sum(n22, n24) = n20, yields:
% 51.51/19.97 | (1597) all_0_1_1 = n20
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (690) with n22, n0, all_0_4_4, n22 and discharging atoms sum(n22, n0) = all_0_4_4, sum(n22, n0) = n22, yields:
% 51.51/19.97 | (1135) all_0_4_4 = n22
% 51.51/19.97 |
% 51.51/19.97 | From (1137)(1135) and (590) follows:
% 51.51/19.97 | (1139) sum(n22, n22) = all_0_3_3
% 51.51/19.97 |
% 51.51/19.97 | From (1597) and (1568) follows:
% 51.51/19.97 | (1600) sum(n24, n20) = all_0_0_0
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (690) with n24, n20, all_0_0_0, n18 and discharging atoms sum(n24, n20) = all_0_0_0, sum(n24, n20) = n18, yields:
% 51.51/19.97 | (1141) all_0_0_0 = n18
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 51.51/19.97 | (1140) all_0_3_3 = n18
% 51.51/19.97 |
% 51.51/19.97 | Equations (1141,1140) can reduce 679 to:
% 51.51/19.97 | (1106) $false
% 51.51/19.97 |
% 51.51/19.97 |-The branch is then unsatisfiable
% 51.51/19.97 |-Branch two:
% 51.51/19.97 | (1604) ~ (all_0_10_10 = n23)
% 51.51/19.97 | (1605) all_0_10_10 = n22 | all_0_10_10 = n21 | 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
% 51.51/19.97 |
% 51.51/19.97 +-Applying beta-rule and splitting (1605), into two cases.
% 51.51/19.97 |-Branch one:
% 51.51/19.97 | (1606) all_0_10_10 = n22
% 51.51/19.97 |
% 51.51/19.97 | From (1606) and (292) follows:
% 51.51/19.97 | (1607) pred(n22) = all_0_6_6
% 51.51/19.97 |
% 51.51/19.97 | From (1606) and (760) follows:
% 51.51/19.97 | (1608) succ(n22) = all_0_8_8
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (500) with n22, all_0_6_6, n21 and discharging atoms pred(n22) = all_0_6_6, pred(n22) = n21, yields:
% 51.51/19.97 | (1609) all_0_6_6 = n21
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (617) with n22, all_0_8_8, n23 and discharging atoms succ(n22) = all_0_8_8, succ(n22) = n23, yields:
% 51.51/19.97 | (1610) all_0_8_8 = n23
% 51.51/19.97 |
% 51.51/19.97 | From (1609)(1610) and (411) follows:
% 51.51/19.97 | (1611) sum(n21, n23) = all_0_1_1
% 51.51/19.97 |
% 51.51/19.97 | From (1609) and (1564) follows:
% 51.51/19.97 | (1612) sum(n21, n0) = all_0_4_4
% 51.51/19.97 |
% 51.51/19.97 | From (1610) and (1566) follows:
% 51.51/19.97 | (1613) sum(n24, n23) = all_0_7_7
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (690) with n24, n23, all_0_7_7, n21 and discharging atoms sum(n24, n23) = all_0_7_7, sum(n24, n23) = n21, yields:
% 51.51/19.97 | (1155) all_0_7_7 = n21
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (690) with n21, n23, all_0_1_1, n18 and discharging atoms sum(n21, n23) = all_0_1_1, sum(n21, n23) = n18, yields:
% 51.51/19.97 | (1615) all_0_1_1 = n18
% 51.51/19.97 |
% 51.51/19.97 | Instantiating formula (690) with n21, n0, all_0_4_4, n21 and discharging atoms sum(n21, n0) = all_0_4_4, sum(n21, n0) = n21, yields:
% 51.51/19.97 | (1153) all_0_4_4 = n21
% 51.51/19.97 |
% 51.51/19.97 | From (1155)(1153) and (590) follows:
% 51.51/19.97 | (1157) sum(n21, n21) = all_0_3_3
% 51.51/19.97 |
% 51.51/19.97 | From (1615) and (1568) follows:
% 51.51/19.98 | (1618) sum(n24, n18) = all_0_0_0
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (690) with n24, n18, all_0_0_0, n16 and discharging atoms sum(n24, n18) = all_0_0_0, sum(n24, n18) = n16, yields:
% 51.51/19.98 | (1159) all_0_0_0 = n16
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 51.51/19.98 | (1158) all_0_3_3 = n16
% 51.51/19.98 |
% 51.51/19.98 | Equations (1159,1158) can reduce 679 to:
% 51.51/19.98 | (1106) $false
% 51.51/19.98 |
% 51.51/19.98 |-The branch is then unsatisfiable
% 51.51/19.98 |-Branch two:
% 51.51/19.98 | (1622) ~ (all_0_10_10 = n22)
% 51.51/19.98 | (1623) all_0_10_10 = n21 | 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
% 51.51/19.98 |
% 51.51/19.98 +-Applying beta-rule and splitting (1623), into two cases.
% 51.51/19.98 |-Branch one:
% 51.51/19.98 | (1624) all_0_10_10 = n21
% 51.51/19.98 |
% 51.51/19.98 | From (1624) and (292) follows:
% 51.51/19.98 | (1625) pred(n21) = all_0_6_6
% 51.51/19.98 |
% 51.51/19.98 | From (1624) and (760) follows:
% 51.51/19.98 | (1626) succ(n21) = all_0_8_8
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (500) with n21, all_0_6_6, n20 and discharging atoms pred(n21) = all_0_6_6, pred(n21) = n20, yields:
% 51.51/19.98 | (1627) all_0_6_6 = n20
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (617) with n21, all_0_8_8, n22 and discharging atoms succ(n21) = all_0_8_8, succ(n21) = n22, yields:
% 51.51/19.98 | (1628) all_0_8_8 = n22
% 51.51/19.98 |
% 51.51/19.98 | From (1627)(1628) and (411) follows:
% 51.51/19.98 | (1629) sum(n20, n22) = all_0_1_1
% 51.51/19.98 |
% 51.51/19.98 | From (1627) and (1564) follows:
% 51.51/19.98 | (1630) sum(n20, n0) = all_0_4_4
% 51.51/19.98 |
% 51.51/19.98 | From (1628) and (1566) follows:
% 51.51/19.98 | (1631) sum(n24, n22) = all_0_7_7
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (690) with n24, n22, all_0_7_7, n20 and discharging atoms sum(n24, n22) = all_0_7_7, sum(n24, n22) = n20, yields:
% 51.51/19.98 | (1173) all_0_7_7 = n20
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (690) with n20, n22, all_0_1_1, n16 and discharging atoms sum(n20, n22) = all_0_1_1, sum(n20, n22) = n16, yields:
% 51.51/19.98 | (1633) all_0_1_1 = n16
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (690) with n20, n0, all_0_4_4, n20 and discharging atoms sum(n20, n0) = all_0_4_4, sum(n20, n0) = n20, yields:
% 51.51/19.98 | (1171) all_0_4_4 = n20
% 51.51/19.98 |
% 51.51/19.98 | From (1173)(1171) and (590) follows:
% 51.51/19.98 | (1175) sum(n20, n20) = all_0_3_3
% 51.51/19.98 |
% 51.51/19.98 | From (1633) and (1568) follows:
% 51.51/19.98 | (1636) sum(n24, n16) = all_0_0_0
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (690) with n24, n16, all_0_0_0, n14 and discharging atoms sum(n24, n16) = all_0_0_0, sum(n24, n16) = n14, yields:
% 51.51/19.98 | (1177) all_0_0_0 = n14
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 51.51/19.98 | (1176) all_0_3_3 = n14
% 51.51/19.98 |
% 51.51/19.98 | Equations (1177,1176) can reduce 679 to:
% 51.51/19.98 | (1106) $false
% 51.51/19.98 |
% 51.51/19.98 |-The branch is then unsatisfiable
% 51.51/19.98 |-Branch two:
% 51.51/19.98 | (1640) ~ (all_0_10_10 = n21)
% 51.51/19.98 | (1641) 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
% 51.51/19.98 |
% 51.51/19.98 +-Applying beta-rule and splitting (1641), into two cases.
% 51.51/19.98 |-Branch one:
% 51.51/19.98 | (1642) all_0_10_10 = n20
% 51.51/19.98 |
% 51.51/19.98 | From (1642) and (292) follows:
% 51.51/19.98 | (1643) pred(n20) = all_0_6_6
% 51.51/19.98 |
% 51.51/19.98 | From (1642) and (760) follows:
% 51.51/19.98 | (1644) succ(n20) = all_0_8_8
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (500) with n20, all_0_6_6, n19 and discharging atoms pred(n20) = all_0_6_6, pred(n20) = n19, yields:
% 51.51/19.98 | (1645) all_0_6_6 = n19
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (617) with n20, all_0_8_8, n21 and discharging atoms succ(n20) = all_0_8_8, succ(n20) = n21, yields:
% 51.51/19.98 | (1646) all_0_8_8 = n21
% 51.51/19.98 |
% 51.51/19.98 | From (1645)(1646) and (411) follows:
% 51.51/19.98 | (1647) sum(n19, n21) = all_0_1_1
% 51.51/19.98 |
% 51.51/19.98 | From (1645) and (1564) follows:
% 51.51/19.98 | (1648) sum(n19, n0) = all_0_4_4
% 51.51/19.98 |
% 51.51/19.98 | From (1646) and (1566) follows:
% 51.51/19.98 | (1649) sum(n24, n21) = all_0_7_7
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (690) with n24, n21, all_0_7_7, n19 and discharging atoms sum(n24, n21) = all_0_7_7, sum(n24, n21) = n19, yields:
% 51.51/19.98 | (1191) all_0_7_7 = n19
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (690) with n19, n21, all_0_1_1, n14 and discharging atoms sum(n19, n21) = all_0_1_1, sum(n19, n21) = n14, yields:
% 51.51/19.98 | (1651) all_0_1_1 = n14
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (690) with n19, n0, all_0_4_4, n19 and discharging atoms sum(n19, n0) = all_0_4_4, sum(n19, n0) = n19, yields:
% 51.51/19.98 | (1189) all_0_4_4 = n19
% 51.51/19.98 |
% 51.51/19.98 | From (1191)(1189) and (590) follows:
% 51.51/19.98 | (1193) sum(n19, n19) = all_0_3_3
% 51.51/19.98 |
% 51.51/19.98 | From (1651) and (1568) follows:
% 51.51/19.98 | (1654) sum(n24, n14) = all_0_0_0
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (690) with n24, n14, all_0_0_0, n12 and discharging atoms sum(n24, n14) = all_0_0_0, sum(n24, n14) = n12, yields:
% 51.51/19.98 | (1195) all_0_0_0 = n12
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 51.51/19.98 | (1194) all_0_3_3 = n12
% 51.51/19.98 |
% 51.51/19.98 | Equations (1195,1194) can reduce 679 to:
% 51.51/19.98 | (1106) $false
% 51.51/19.98 |
% 51.51/19.98 |-The branch is then unsatisfiable
% 51.51/19.98 |-Branch two:
% 51.51/19.98 | (1658) ~ (all_0_10_10 = n20)
% 51.51/19.98 | (1659) 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
% 51.51/19.98 |
% 51.51/19.98 +-Applying beta-rule and splitting (1659), into two cases.
% 51.51/19.98 |-Branch one:
% 51.51/19.98 | (1660) all_0_10_10 = n19
% 51.51/19.98 |
% 51.51/19.98 | From (1660) and (292) follows:
% 51.51/19.98 | (1661) pred(n19) = all_0_6_6
% 51.51/19.98 |
% 51.51/19.98 | From (1660) and (760) follows:
% 51.51/19.98 | (1662) succ(n19) = all_0_8_8
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (500) with n19, all_0_6_6, n18 and discharging atoms pred(n19) = all_0_6_6, pred(n19) = n18, yields:
% 51.51/19.98 | (1663) all_0_6_6 = n18
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (617) with n19, all_0_8_8, n20 and discharging atoms succ(n19) = all_0_8_8, succ(n19) = n20, yields:
% 51.51/19.98 | (1664) all_0_8_8 = n20
% 51.51/19.98 |
% 51.51/19.98 | From (1663)(1664) and (411) follows:
% 51.51/19.98 | (1665) sum(n18, n20) = all_0_1_1
% 51.51/19.98 |
% 51.51/19.98 | From (1663) and (1564) follows:
% 51.51/19.98 | (1666) sum(n18, n0) = all_0_4_4
% 51.51/19.98 |
% 51.51/19.98 | From (1664) and (1566) follows:
% 51.51/19.98 | (1667) sum(n24, n20) = all_0_7_7
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (690) with n24, n20, all_0_7_7, n18 and discharging atoms sum(n24, n20) = all_0_7_7, sum(n24, n20) = n18, yields:
% 51.51/19.98 | (1209) all_0_7_7 = n18
% 51.51/19.98 |
% 51.51/19.98 | Instantiating formula (690) with n18, n20, all_0_1_1, n12 and discharging atoms sum(n18, n20) = all_0_1_1, sum(n18, n20) = n12, yields:
% 51.51/19.99 | (1669) all_0_1_1 = n12
% 51.51/19.99 |
% 51.51/19.99 | Instantiating formula (690) with n18, n0, all_0_4_4, n18 and discharging atoms sum(n18, n0) = all_0_4_4, sum(n18, n0) = n18, yields:
% 51.51/19.99 | (1207) all_0_4_4 = n18
% 51.51/19.99 |
% 51.51/19.99 | From (1209)(1207) and (590) follows:
% 51.51/19.99 | (1211) sum(n18, n18) = all_0_3_3
% 51.51/19.99 |
% 51.51/19.99 | From (1669) and (1568) follows:
% 51.51/19.99 | (1672) sum(n24, n12) = all_0_0_0
% 51.51/19.99 |
% 51.51/19.99 | Instantiating formula (690) with n24, n12, all_0_0_0, n10 and discharging atoms sum(n24, n12) = all_0_0_0, sum(n24, n12) = n10, yields:
% 51.51/19.99 | (1213) all_0_0_0 = n10
% 51.51/19.99 |
% 51.51/19.99 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 51.51/19.99 | (1212) all_0_3_3 = n10
% 51.51/19.99 |
% 51.51/19.99 | Equations (1213,1212) can reduce 679 to:
% 51.51/19.99 | (1106) $false
% 51.51/19.99 |
% 51.51/19.99 |-The branch is then unsatisfiable
% 51.51/19.99 |-Branch two:
% 51.51/19.99 | (1676) ~ (all_0_10_10 = n19)
% 51.51/19.99 | (1677) 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
% 51.51/19.99 |
% 51.51/19.99 +-Applying beta-rule and splitting (1677), into two cases.
% 51.51/19.99 |-Branch one:
% 51.51/19.99 | (1678) all_0_10_10 = n18
% 51.51/19.99 |
% 51.51/19.99 | From (1678) and (292) follows:
% 51.51/19.99 | (1679) pred(n18) = all_0_6_6
% 51.51/19.99 |
% 51.51/19.99 | From (1678) and (760) follows:
% 51.51/19.99 | (1680) succ(n18) = all_0_8_8
% 51.51/19.99 |
% 51.51/19.99 | Instantiating formula (500) with n18, all_0_6_6, n17 and discharging atoms pred(n18) = all_0_6_6, pred(n18) = n17, yields:
% 51.93/19.99 | (1681) all_0_6_6 = n17
% 51.93/19.99 |
% 51.93/19.99 | Instantiating formula (617) with n18, all_0_8_8, n19 and discharging atoms succ(n18) = all_0_8_8, succ(n18) = n19, yields:
% 51.93/19.99 | (1682) all_0_8_8 = n19
% 51.93/19.99 |
% 51.93/19.99 | From (1681)(1682) and (411) follows:
% 51.93/19.99 | (1683) sum(n17, n19) = all_0_1_1
% 51.93/19.99 |
% 51.93/19.99 | From (1681) and (1564) follows:
% 51.93/19.99 | (1684) sum(n17, n0) = all_0_4_4
% 51.93/19.99 |
% 51.93/19.99 | From (1682) and (1566) follows:
% 51.93/19.99 | (1685) sum(n24, n19) = all_0_7_7
% 51.93/19.99 |
% 51.93/19.99 | Instantiating formula (690) with n24, n19, all_0_7_7, n17 and discharging atoms sum(n24, n19) = all_0_7_7, sum(n24, n19) = n17, yields:
% 51.93/19.99 | (1227) all_0_7_7 = n17
% 51.93/19.99 |
% 51.93/19.99 | Instantiating formula (690) with n17, n19, all_0_1_1, n10 and discharging atoms sum(n17, n19) = all_0_1_1, sum(n17, n19) = n10, yields:
% 51.93/19.99 | (1687) all_0_1_1 = n10
% 51.93/19.99 |
% 51.93/19.99 | Instantiating formula (690) with n17, n0, all_0_4_4, n17 and discharging atoms sum(n17, n0) = all_0_4_4, sum(n17, n0) = n17, yields:
% 51.93/19.99 | (1225) all_0_4_4 = n17
% 51.93/19.99 |
% 51.93/19.99 | From (1227)(1225) and (590) follows:
% 51.93/19.99 | (1229) sum(n17, n17) = all_0_3_3
% 51.93/19.99 |
% 51.93/19.99 | From (1687) and (1568) follows:
% 51.93/19.99 | (1690) sum(n24, n10) = all_0_0_0
% 51.93/19.99 |
% 51.93/19.99 | Instantiating formula (690) with n24, n10, all_0_0_0, n8 and discharging atoms sum(n24, n10) = all_0_0_0, sum(n24, n10) = n8, yields:
% 51.93/19.99 | (1231) all_0_0_0 = n8
% 51.93/19.99 |
% 51.93/19.99 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 51.93/19.99 | (1230) all_0_3_3 = n8
% 51.93/19.99 |
% 51.93/19.99 | Equations (1231,1230) can reduce 679 to:
% 51.93/19.99 | (1106) $false
% 51.93/19.99 |
% 51.93/19.99 |-The branch is then unsatisfiable
% 51.93/19.99 |-Branch two:
% 51.93/19.99 | (1694) ~ (all_0_10_10 = n18)
% 51.93/19.99 | (1695) 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
% 51.93/19.99 |
% 51.93/19.99 +-Applying beta-rule and splitting (1695), into two cases.
% 51.93/19.99 |-Branch one:
% 51.93/19.99 | (1696) all_0_10_10 = n17
% 51.93/19.99 |
% 51.93/19.99 | From (1696) and (292) follows:
% 51.93/19.99 | (1697) pred(n17) = all_0_6_6
% 51.93/19.99 |
% 51.93/19.99 | From (1696) and (760) follows:
% 51.93/19.99 | (1698) succ(n17) = all_0_8_8
% 51.93/19.99 |
% 51.93/19.99 | Instantiating formula (500) with n17, all_0_6_6, n16 and discharging atoms pred(n17) = all_0_6_6, pred(n17) = n16, yields:
% 51.93/19.99 | (1699) all_0_6_6 = n16
% 51.93/19.99 |
% 51.93/19.99 | Instantiating formula (617) with n17, all_0_8_8, n18 and discharging atoms succ(n17) = all_0_8_8, succ(n17) = n18, yields:
% 51.93/19.99 | (1700) all_0_8_8 = n18
% 51.93/19.99 |
% 51.93/19.99 | From (1699)(1700) and (411) follows:
% 51.93/19.99 | (1701) sum(n16, n18) = all_0_1_1
% 51.93/19.99 |
% 51.93/19.99 | From (1699) and (1564) follows:
% 51.93/19.99 | (1702) sum(n16, n0) = all_0_4_4
% 51.93/19.99 |
% 51.93/19.99 | From (1700) and (1566) follows:
% 51.93/19.99 | (1703) sum(n24, n18) = all_0_7_7
% 51.93/19.99 |
% 51.93/19.99 | Instantiating formula (690) with n24, n18, all_0_7_7, n16 and discharging atoms sum(n24, n18) = all_0_7_7, sum(n24, n18) = n16, yields:
% 51.93/19.99 | (1245) all_0_7_7 = n16
% 51.93/19.99 |
% 51.93/19.99 | Instantiating formula (690) with n16, n18, all_0_1_1, n8 and discharging atoms sum(n16, n18) = all_0_1_1, sum(n16, n18) = n8, yields:
% 51.93/19.99 | (1705) all_0_1_1 = n8
% 51.93/19.99 |
% 51.93/19.99 | Instantiating formula (690) with n16, n0, all_0_4_4, n16 and discharging atoms sum(n16, n0) = all_0_4_4, sum(n16, n0) = n16, yields:
% 51.93/19.99 | (1243) all_0_4_4 = n16
% 51.93/19.99 |
% 51.93/19.99 | From (1245)(1243) and (590) follows:
% 51.93/19.99 | (1247) sum(n16, n16) = all_0_3_3
% 51.93/19.99 |
% 51.93/19.99 | From (1705) and (1568) follows:
% 51.93/19.99 | (1708) sum(n24, n8) = all_0_0_0
% 51.93/19.99 |
% 51.93/19.99 | Instantiating formula (690) with n24, n8, all_0_0_0, n6 and discharging atoms sum(n24, n8) = all_0_0_0, sum(n24, n8) = n6, yields:
% 51.93/19.99 | (1249) all_0_0_0 = n6
% 51.93/19.99 |
% 51.93/19.99 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 51.93/19.99 | (1248) all_0_3_3 = n6
% 51.93/19.99 |
% 51.93/19.99 | Equations (1249,1248) can reduce 679 to:
% 51.93/19.99 | (1106) $false
% 51.93/19.99 |
% 51.93/19.99 |-The branch is then unsatisfiable
% 51.93/19.99 |-Branch two:
% 51.93/19.99 | (1712) ~ (all_0_10_10 = n17)
% 51.93/19.99 | (1713) 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
% 51.93/19.99 |
% 51.93/19.99 +-Applying beta-rule and splitting (1713), into two cases.
% 51.93/19.99 |-Branch one:
% 51.93/19.99 | (1714) all_0_10_10 = n16
% 51.93/19.99 |
% 51.93/19.99 | From (1714) and (292) follows:
% 51.93/19.99 | (1715) pred(n16) = all_0_6_6
% 51.93/19.99 |
% 51.93/19.99 | From (1714) and (760) follows:
% 51.93/19.99 | (1716) succ(n16) = all_0_8_8
% 51.93/19.99 |
% 51.93/19.99 | Instantiating formula (500) with n16, all_0_6_6, n15 and discharging atoms pred(n16) = all_0_6_6, pred(n16) = n15, yields:
% 51.93/19.99 | (1717) all_0_6_6 = n15
% 51.93/19.99 |
% 51.93/19.99 | Instantiating formula (617) with n16, all_0_8_8, n17 and discharging atoms succ(n16) = all_0_8_8, succ(n16) = n17, yields:
% 51.93/19.99 | (1718) all_0_8_8 = n17
% 51.93/19.99 |
% 51.93/19.99 | From (1717)(1718) and (411) follows:
% 51.93/19.99 | (1719) sum(n15, n17) = all_0_1_1
% 51.93/19.99 |
% 51.93/19.99 | From (1717) and (1564) follows:
% 51.93/19.99 | (1720) sum(n15, n0) = all_0_4_4
% 51.93/20.00 |
% 51.93/20.00 | From (1718) and (1566) follows:
% 51.93/20.00 | (1721) sum(n24, n17) = all_0_7_7
% 51.93/20.00 |
% 51.93/20.00 | Instantiating formula (690) with n24, n17, all_0_7_7, n15 and discharging atoms sum(n24, n17) = all_0_7_7, sum(n24, n17) = n15, yields:
% 51.93/20.00 | (1263) all_0_7_7 = n15
% 51.93/20.00 |
% 51.93/20.00 | Instantiating formula (690) with n15, n17, all_0_1_1, n6 and discharging atoms sum(n15, n17) = all_0_1_1, sum(n15, n17) = n6, yields:
% 51.93/20.00 | (1723) all_0_1_1 = n6
% 51.93/20.00 |
% 51.93/20.00 | Instantiating formula (690) with n15, n0, all_0_4_4, n15 and discharging atoms sum(n15, n0) = all_0_4_4, sum(n15, n0) = n15, yields:
% 51.93/20.00 | (1261) all_0_4_4 = n15
% 51.93/20.00 |
% 51.93/20.00 | From (1263)(1261) and (590) follows:
% 51.93/20.00 | (1265) sum(n15, n15) = all_0_3_3
% 51.93/20.00 |
% 51.93/20.00 | From (1723) and (1568) follows:
% 51.93/20.00 | (1726) sum(n24, n6) = all_0_0_0
% 51.93/20.00 |
% 51.93/20.00 | Instantiating formula (690) with n24, n6, all_0_0_0, n4 and discharging atoms sum(n24, n6) = all_0_0_0, sum(n24, n6) = n4, yields:
% 51.93/20.00 | (1267) all_0_0_0 = n4
% 51.93/20.00 |
% 51.93/20.00 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 51.93/20.00 | (1266) all_0_3_3 = n4
% 51.93/20.00 |
% 51.93/20.00 | Equations (1267,1266) can reduce 679 to:
% 51.93/20.00 | (1106) $false
% 51.93/20.00 |
% 51.93/20.00 |-The branch is then unsatisfiable
% 51.93/20.00 |-Branch two:
% 51.93/20.00 | (1730) ~ (all_0_10_10 = n16)
% 51.93/20.00 | (1731) 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
% 51.93/20.00 |
% 51.93/20.00 +-Applying beta-rule and splitting (1731), into two cases.
% 51.93/20.00 |-Branch one:
% 51.93/20.00 | (1732) all_0_10_10 = n15
% 51.93/20.00 |
% 51.93/20.00 | From (1732) and (292) follows:
% 51.93/20.00 | (1733) pred(n15) = all_0_6_6
% 51.93/20.00 |
% 51.93/20.00 | From (1732) and (760) follows:
% 51.93/20.00 | (1734) succ(n15) = all_0_8_8
% 51.93/20.00 |
% 51.93/20.00 | Instantiating formula (500) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 51.93/20.00 | (1735) all_0_6_6 = n14
% 51.93/20.00 |
% 51.93/20.00 | Instantiating formula (617) with n15, all_0_8_8, n16 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n16, yields:
% 51.93/20.00 | (1736) all_0_8_8 = n16
% 51.93/20.00 |
% 51.93/20.00 | From (1735)(1736) and (411) follows:
% 51.99/20.00 | (1737) sum(n14, n16) = all_0_1_1
% 51.99/20.00 |
% 51.99/20.00 | From (1735) and (1564) follows:
% 51.99/20.00 | (1738) sum(n14, n0) = all_0_4_4
% 51.99/20.00 |
% 51.99/20.00 | From (1736) and (1566) follows:
% 51.99/20.00 | (1739) sum(n24, n16) = all_0_7_7
% 51.99/20.00 |
% 51.99/20.00 | Instantiating formula (690) with n24, n16, all_0_7_7, n14 and discharging atoms sum(n24, n16) = all_0_7_7, sum(n24, n16) = n14, yields:
% 51.99/20.00 | (1281) all_0_7_7 = n14
% 51.99/20.00 |
% 51.99/20.00 | Instantiating formula (690) with n14, n16, all_0_1_1, n4 and discharging atoms sum(n14, n16) = all_0_1_1, sum(n14, n16) = n4, yields:
% 51.99/20.00 | (1741) all_0_1_1 = n4
% 51.99/20.00 |
% 51.99/20.00 | Instantiating formula (690) with n14, n0, all_0_4_4, n14 and discharging atoms sum(n14, n0) = all_0_4_4, sum(n14, n0) = n14, yields:
% 51.99/20.00 | (1279) all_0_4_4 = n14
% 51.99/20.00 |
% 51.99/20.00 | From (1281)(1279) and (590) follows:
% 51.99/20.00 | (1283) sum(n14, n14) = all_0_3_3
% 51.99/20.00 |
% 51.99/20.00 | From (1741) and (1568) follows:
% 51.99/20.00 | (1744) sum(n24, n4) = all_0_0_0
% 51.99/20.00 |
% 51.99/20.00 | Instantiating formula (690) with n24, n4, all_0_0_0, n2 and discharging atoms sum(n24, n4) = all_0_0_0, sum(n24, n4) = n2, yields:
% 51.99/20.00 | (1285) all_0_0_0 = n2
% 51.99/20.00 |
% 51.99/20.00 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 51.99/20.00 | (1284) all_0_3_3 = n2
% 51.99/20.00 |
% 51.99/20.00 | Equations (1285,1284) can reduce 679 to:
% 51.99/20.00 | (1106) $false
% 51.99/20.00 |
% 51.99/20.00 |-The branch is then unsatisfiable
% 51.99/20.00 |-Branch two:
% 51.99/20.00 | (1748) ~ (all_0_10_10 = n15)
% 51.99/20.00 | (1749) 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
% 51.99/20.00 |
% 51.99/20.00 +-Applying beta-rule and splitting (1749), into two cases.
% 51.99/20.00 |-Branch one:
% 51.99/20.00 | (1750) all_0_10_10 = n14
% 51.99/20.00 |
% 51.99/20.00 | From (1750) and (292) follows:
% 51.99/20.00 | (1751) pred(n14) = all_0_6_6
% 51.99/20.00 |
% 51.99/20.00 | From (1750) and (760) follows:
% 51.99/20.00 | (1752) succ(n14) = all_0_8_8
% 51.99/20.00 |
% 51.99/20.00 | Instantiating formula (500) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 51.99/20.00 | (1753) all_0_6_6 = n13
% 51.99/20.00 |
% 51.99/20.00 | Instantiating formula (617) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 51.99/20.00 | (1754) all_0_8_8 = n15
% 51.99/20.00 |
% 51.99/20.00 | From (1753)(1754) and (411) follows:
% 51.99/20.00 | (1755) sum(n13, n15) = all_0_1_1
% 51.99/20.00 |
% 51.99/20.00 | From (1753) and (1564) follows:
% 51.99/20.00 | (1756) sum(n13, n0) = all_0_4_4
% 51.99/20.00 |
% 51.99/20.00 | From (1754) and (1566) follows:
% 51.99/20.00 | (1757) sum(n24, n15) = all_0_7_7
% 51.99/20.00 |
% 51.99/20.00 | Instantiating formula (690) with n24, n15, all_0_7_7, n13 and discharging atoms sum(n24, n15) = all_0_7_7, sum(n24, n15) = n13, yields:
% 51.99/20.00 | (1299) all_0_7_7 = n13
% 51.99/20.00 |
% 51.99/20.00 | Instantiating formula (690) with n13, n15, all_0_1_1, n2 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n2, yields:
% 51.99/20.00 | (1759) all_0_1_1 = n2
% 51.99/20.00 |
% 51.99/20.00 | Instantiating formula (690) with n13, n0, all_0_4_4, n13 and discharging atoms sum(n13, n0) = all_0_4_4, sum(n13, n0) = n13, yields:
% 51.99/20.00 | (1297) all_0_4_4 = n13
% 51.99/20.00 |
% 51.99/20.00 | From (1299)(1297) and (590) follows:
% 51.99/20.00 | (1301) sum(n13, n13) = all_0_3_3
% 51.99/20.00 |
% 51.99/20.00 | From (1759) and (1568) follows:
% 51.99/20.00 | (1762) sum(n24, n2) = all_0_0_0
% 51.99/20.00 |
% 51.99/20.00 | Instantiating formula (690) with n24, n2, all_0_0_0, n0 and discharging atoms sum(n24, n2) = all_0_0_0, sum(n24, n2) = n0, yields:
% 51.99/20.00 | (1303) all_0_0_0 = n0
% 51.99/20.00 |
% 51.99/20.00 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 51.99/20.00 | (1302) all_0_3_3 = n0
% 51.99/20.00 |
% 51.99/20.00 | Equations (1303,1302) can reduce 679 to:
% 51.99/20.00 | (1106) $false
% 51.99/20.00 |
% 51.99/20.00 |-The branch is then unsatisfiable
% 51.99/20.00 |-Branch two:
% 51.99/20.00 | (1766) ~ (all_0_10_10 = n14)
% 51.99/20.00 | (1767) 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
% 51.99/20.00 |
% 51.99/20.00 +-Applying beta-rule and splitting (1767), into two cases.
% 51.99/20.00 |-Branch one:
% 51.99/20.00 | (1768) all_0_10_10 = n13
% 51.99/20.00 |
% 51.99/20.00 | From (1768) and (292) follows:
% 51.99/20.00 | (1769) pred(n13) = all_0_6_6
% 51.99/20.00 |
% 51.99/20.00 | From (1768) and (760) follows:
% 51.99/20.00 | (1770) succ(n13) = all_0_8_8
% 51.99/20.00 |
% 51.99/20.00 | Instantiating formula (500) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 51.99/20.00 | (1771) all_0_6_6 = n12
% 51.99/20.00 |
% 51.99/20.00 | Instantiating formula (617) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 51.99/20.00 | (1772) all_0_8_8 = n14
% 51.99/20.00 |
% 51.99/20.00 | From (1771)(1772) and (411) follows:
% 51.99/20.01 | (1773) sum(n12, n14) = all_0_1_1
% 51.99/20.01 |
% 51.99/20.01 | From (1771) and (1564) follows:
% 51.99/20.01 | (1774) sum(n12, n0) = all_0_4_4
% 51.99/20.01 |
% 51.99/20.01 | From (1772) and (1566) follows:
% 51.99/20.01 | (1775) sum(n24, n14) = all_0_7_7
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (690) with n24, n14, all_0_7_7, n12 and discharging atoms sum(n24, n14) = all_0_7_7, sum(n24, n14) = n12, yields:
% 51.99/20.01 | (1317) all_0_7_7 = n12
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (690) with n12, n14, all_0_1_1, n0 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n0, yields:
% 51.99/20.01 | (1777) all_0_1_1 = n0
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (690) with n12, n0, all_0_4_4, n12 and discharging atoms sum(n12, n0) = all_0_4_4, sum(n12, n0) = n12, yields:
% 51.99/20.01 | (1315) all_0_4_4 = n12
% 51.99/20.01 |
% 51.99/20.01 | From (1317)(1315) and (590) follows:
% 51.99/20.01 | (1319) sum(n12, n12) = all_0_3_3
% 51.99/20.01 |
% 51.99/20.01 | From (1777) and (1568) follows:
% 51.99/20.01 | (1780) sum(n24, n0) = all_0_0_0
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (690) with n24, n0, all_0_0_0, n24 and discharging atoms sum(n24, n0) = all_0_0_0, sum(n24, n0) = n24, yields:
% 51.99/20.01 | (1321) all_0_0_0 = n24
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 51.99/20.01 | (1320) all_0_3_3 = n24
% 51.99/20.01 |
% 51.99/20.01 | Equations (1321,1320) can reduce 679 to:
% 51.99/20.01 | (1106) $false
% 51.99/20.01 |
% 51.99/20.01 |-The branch is then unsatisfiable
% 51.99/20.01 |-Branch two:
% 51.99/20.01 | (1784) ~ (all_0_10_10 = n13)
% 51.99/20.01 | (1785) 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
% 51.99/20.01 |
% 51.99/20.01 +-Applying beta-rule and splitting (1785), into two cases.
% 51.99/20.01 |-Branch one:
% 51.99/20.01 | (1786) all_0_10_10 = n12
% 51.99/20.01 |
% 51.99/20.01 | From (1786) and (292) follows:
% 51.99/20.01 | (1787) pred(n12) = all_0_6_6
% 51.99/20.01 |
% 51.99/20.01 | From (1786) and (760) follows:
% 51.99/20.01 | (1788) succ(n12) = all_0_8_8
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (500) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 51.99/20.01 | (1789) all_0_6_6 = n11
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (617) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 51.99/20.01 | (1790) all_0_8_8 = n13
% 51.99/20.01 |
% 51.99/20.01 | From (1789)(1790) and (411) follows:
% 51.99/20.01 | (1791) sum(n11, n13) = all_0_1_1
% 51.99/20.01 |
% 51.99/20.01 | From (1789) and (1564) follows:
% 51.99/20.01 | (1792) sum(n11, n0) = all_0_4_4
% 51.99/20.01 |
% 51.99/20.01 | From (1790) and (1566) follows:
% 51.99/20.01 | (1793) sum(n24, n13) = all_0_7_7
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (690) with n24, n13, all_0_7_7, n11 and discharging atoms sum(n24, n13) = all_0_7_7, sum(n24, n13) = n11, yields:
% 51.99/20.01 | (1335) all_0_7_7 = n11
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (690) with n11, n13, all_0_1_1, n24 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n24, yields:
% 51.99/20.01 | (1081) all_0_1_1 = n24
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (690) with n11, n0, all_0_4_4, n11 and discharging atoms sum(n11, n0) = all_0_4_4, sum(n11, n0) = n11, yields:
% 51.99/20.01 | (1333) all_0_4_4 = n11
% 51.99/20.01 |
% 51.99/20.01 | From (1335)(1333) and (590) follows:
% 51.99/20.01 | (1337) sum(n11, n11) = all_0_3_3
% 51.99/20.01 |
% 51.99/20.01 | From (1081) and (1568) follows:
% 51.99/20.01 | (1100) sum(n24, n24) = all_0_0_0
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (690) with n24, n24, all_0_0_0, n22 and discharging atoms sum(n24, n24) = all_0_0_0, sum(n24, n24) = n22, yields:
% 51.99/20.01 | (1102) all_0_0_0 = n22
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 51.99/20.01 | (1104) all_0_3_3 = n22
% 51.99/20.01 |
% 51.99/20.01 | Equations (1102,1104) can reduce 679 to:
% 51.99/20.01 | (1106) $false
% 51.99/20.01 |
% 51.99/20.01 |-The branch is then unsatisfiable
% 51.99/20.01 |-Branch two:
% 51.99/20.01 | (1802) ~ (all_0_10_10 = n12)
% 51.99/20.01 | (1803) 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
% 51.99/20.01 |
% 51.99/20.01 +-Applying beta-rule and splitting (1803), into two cases.
% 51.99/20.01 |-Branch one:
% 51.99/20.01 | (1804) all_0_10_10 = n11
% 51.99/20.01 |
% 51.99/20.01 | From (1804) and (292) follows:
% 51.99/20.01 | (1805) pred(n11) = all_0_6_6
% 51.99/20.01 |
% 51.99/20.01 | From (1804) and (760) follows:
% 51.99/20.01 | (1806) succ(n11) = all_0_8_8
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (500) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 51.99/20.01 | (1807) all_0_6_6 = n10
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (617) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 51.99/20.01 | (1808) all_0_8_8 = n12
% 51.99/20.01 |
% 51.99/20.01 | From (1807)(1808) and (411) follows:
% 51.99/20.01 | (1809) sum(n10, n12) = all_0_1_1
% 51.99/20.01 |
% 51.99/20.01 | From (1807) and (1564) follows:
% 51.99/20.01 | (1810) sum(n10, n0) = all_0_4_4
% 51.99/20.01 |
% 51.99/20.01 | From (1808) and (1566) follows:
% 51.99/20.01 | (1811) sum(n24, n12) = all_0_7_7
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (690) with n24, n12, all_0_7_7, n10 and discharging atoms sum(n24, n12) = all_0_7_7, sum(n24, n12) = n10, yields:
% 51.99/20.01 | (1353) all_0_7_7 = n10
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (690) with n10, n12, all_0_1_1, n22 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n22, yields:
% 51.99/20.01 | (1579) all_0_1_1 = n22
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (690) with n10, n0, all_0_4_4, n10 and discharging atoms sum(n10, n0) = all_0_4_4, sum(n10, n0) = n10, yields:
% 51.99/20.01 | (1351) all_0_4_4 = n10
% 51.99/20.01 |
% 51.99/20.01 | From (1353)(1351) and (590) follows:
% 51.99/20.01 | (1355) sum(n10, n10) = all_0_3_3
% 51.99/20.01 |
% 51.99/20.01 | From (1579) and (1568) follows:
% 51.99/20.01 | (1582) sum(n24, n22) = all_0_0_0
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (690) with n24, n22, all_0_0_0, n20 and discharging atoms sum(n24, n22) = all_0_0_0, sum(n24, n22) = n20, yields:
% 51.99/20.01 | (1123) all_0_0_0 = n20
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 51.99/20.01 | (1122) all_0_3_3 = n20
% 51.99/20.01 |
% 51.99/20.01 | Equations (1123,1122) can reduce 679 to:
% 51.99/20.01 | (1106) $false
% 51.99/20.01 |
% 51.99/20.01 |-The branch is then unsatisfiable
% 51.99/20.01 |-Branch two:
% 51.99/20.01 | (1820) ~ (all_0_10_10 = n11)
% 51.99/20.01 | (1821) 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
% 51.99/20.01 |
% 51.99/20.01 +-Applying beta-rule and splitting (1821), into two cases.
% 51.99/20.01 |-Branch one:
% 51.99/20.01 | (1822) all_0_10_10 = n10
% 51.99/20.01 |
% 51.99/20.01 | From (1822) and (292) follows:
% 51.99/20.01 | (1823) pred(n10) = all_0_6_6
% 51.99/20.01 |
% 51.99/20.01 | From (1822) and (760) follows:
% 51.99/20.01 | (1824) succ(n10) = all_0_8_8
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (500) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 51.99/20.01 | (1825) all_0_6_6 = n9
% 51.99/20.01 |
% 51.99/20.01 | Instantiating formula (617) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 51.99/20.01 | (1826) all_0_8_8 = n11
% 51.99/20.01 |
% 51.99/20.01 | From (1825)(1826) and (411) follows:
% 51.99/20.02 | (1827) sum(n9, n11) = all_0_1_1
% 51.99/20.02 |
% 51.99/20.02 | From (1825) and (1564) follows:
% 51.99/20.02 | (1828) sum(n9, n0) = all_0_4_4
% 51.99/20.02 |
% 51.99/20.02 | From (1826) and (1566) follows:
% 51.99/20.02 | (1829) sum(n24, n11) = all_0_7_7
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (690) with n24, n11, all_0_7_7, n9 and discharging atoms sum(n24, n11) = all_0_7_7, sum(n24, n11) = n9, yields:
% 51.99/20.02 | (1371) all_0_7_7 = n9
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (690) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 51.99/20.02 | (1597) all_0_1_1 = n20
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (690) with n9, n0, all_0_4_4, n9 and discharging atoms sum(n9, n0) = all_0_4_4, sum(n9, n0) = n9, yields:
% 51.99/20.02 | (1369) all_0_4_4 = n9
% 51.99/20.02 |
% 51.99/20.02 | From (1371)(1369) and (590) follows:
% 51.99/20.02 | (1373) sum(n9, n9) = all_0_3_3
% 51.99/20.02 |
% 51.99/20.02 | From (1597) and (1568) follows:
% 51.99/20.02 | (1600) sum(n24, n20) = all_0_0_0
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (690) with n24, n20, all_0_0_0, n18 and discharging atoms sum(n24, n20) = all_0_0_0, sum(n24, n20) = n18, yields:
% 51.99/20.02 | (1141) all_0_0_0 = n18
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 51.99/20.02 | (1140) all_0_3_3 = n18
% 51.99/20.02 |
% 51.99/20.02 | Equations (1141,1140) can reduce 679 to:
% 51.99/20.02 | (1106) $false
% 51.99/20.02 |
% 51.99/20.02 |-The branch is then unsatisfiable
% 51.99/20.02 |-Branch two:
% 51.99/20.02 | (1838) ~ (all_0_10_10 = n10)
% 51.99/20.02 | (1839) 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
% 51.99/20.02 |
% 51.99/20.02 +-Applying beta-rule and splitting (1839), into two cases.
% 51.99/20.02 |-Branch one:
% 51.99/20.02 | (1840) all_0_10_10 = n9
% 51.99/20.02 |
% 51.99/20.02 | From (1840) and (292) follows:
% 51.99/20.02 | (1841) pred(n9) = all_0_6_6
% 51.99/20.02 |
% 51.99/20.02 | From (1840) and (760) follows:
% 51.99/20.02 | (1842) succ(n9) = all_0_8_8
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (500) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 51.99/20.02 | (1843) all_0_6_6 = n8
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (617) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 51.99/20.02 | (1844) all_0_8_8 = n10
% 51.99/20.02 |
% 51.99/20.02 | From (1843)(1844) and (411) follows:
% 51.99/20.02 | (1845) sum(n8, n10) = all_0_1_1
% 51.99/20.02 |
% 51.99/20.02 | From (1843) and (1564) follows:
% 51.99/20.02 | (1846) sum(n8, n0) = all_0_4_4
% 51.99/20.02 |
% 51.99/20.02 | From (1844) and (1566) follows:
% 51.99/20.02 | (1847) sum(n24, n10) = all_0_7_7
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (690) with n24, n10, all_0_7_7, n8 and discharging atoms sum(n24, n10) = all_0_7_7, sum(n24, n10) = n8, yields:
% 51.99/20.02 | (1389) all_0_7_7 = n8
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (690) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 51.99/20.02 | (1615) all_0_1_1 = n18
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (690) with n8, n0, all_0_4_4, n8 and discharging atoms sum(n8, n0) = all_0_4_4, sum(n8, n0) = n8, yields:
% 51.99/20.02 | (1387) all_0_4_4 = n8
% 51.99/20.02 |
% 51.99/20.02 | From (1389)(1387) and (590) follows:
% 51.99/20.02 | (1391) sum(n8, n8) = all_0_3_3
% 51.99/20.02 |
% 51.99/20.02 | From (1615) and (1568) follows:
% 51.99/20.02 | (1618) sum(n24, n18) = all_0_0_0
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (690) with n24, n18, all_0_0_0, n16 and discharging atoms sum(n24, n18) = all_0_0_0, sum(n24, n18) = n16, yields:
% 51.99/20.02 | (1159) all_0_0_0 = n16
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 51.99/20.02 | (1158) all_0_3_3 = n16
% 51.99/20.02 |
% 51.99/20.02 | Equations (1159,1158) can reduce 679 to:
% 51.99/20.02 | (1106) $false
% 51.99/20.02 |
% 51.99/20.02 |-The branch is then unsatisfiable
% 51.99/20.02 |-Branch two:
% 51.99/20.02 | (1856) ~ (all_0_10_10 = n9)
% 51.99/20.02 | (1857) 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
% 51.99/20.02 |
% 51.99/20.02 +-Applying beta-rule and splitting (1857), into two cases.
% 51.99/20.02 |-Branch one:
% 51.99/20.02 | (1858) all_0_10_10 = n8
% 51.99/20.02 |
% 51.99/20.02 | From (1858) and (292) follows:
% 51.99/20.02 | (1859) pred(n8) = all_0_6_6
% 51.99/20.02 |
% 51.99/20.02 | From (1858) and (760) follows:
% 51.99/20.02 | (1860) succ(n8) = all_0_8_8
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 51.99/20.02 | (1861) all_0_6_6 = n7
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 51.99/20.02 | (1862) all_0_8_8 = n9
% 51.99/20.02 |
% 51.99/20.02 | From (1861)(1862) and (411) follows:
% 51.99/20.02 | (1863) sum(n7, n9) = all_0_1_1
% 51.99/20.02 |
% 51.99/20.02 | From (1861) and (1564) follows:
% 51.99/20.02 | (1864) sum(n7, n0) = all_0_4_4
% 51.99/20.02 |
% 51.99/20.02 | From (1862) and (1566) follows:
% 51.99/20.02 | (1865) sum(n24, n9) = all_0_7_7
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (690) with n24, n9, all_0_7_7, n7 and discharging atoms sum(n24, n9) = all_0_7_7, sum(n24, n9) = n7, yields:
% 51.99/20.02 | (1407) all_0_7_7 = n7
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 51.99/20.02 | (1633) all_0_1_1 = n16
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (690) with n7, n0, all_0_4_4, n7 and discharging atoms sum(n7, n0) = all_0_4_4, sum(n7, n0) = n7, yields:
% 51.99/20.02 | (1405) all_0_4_4 = n7
% 51.99/20.02 |
% 51.99/20.02 | From (1407)(1405) and (590) follows:
% 51.99/20.02 | (1409) sum(n7, n7) = all_0_3_3
% 51.99/20.02 |
% 51.99/20.02 | From (1633) and (1568) follows:
% 51.99/20.02 | (1636) sum(n24, n16) = all_0_0_0
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (690) with n24, n16, all_0_0_0, n14 and discharging atoms sum(n24, n16) = all_0_0_0, sum(n24, n16) = n14, yields:
% 51.99/20.02 | (1177) all_0_0_0 = n14
% 51.99/20.02 |
% 51.99/20.02 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 51.99/20.02 | (1176) all_0_3_3 = n14
% 51.99/20.02 |
% 51.99/20.02 | Equations (1177,1176) can reduce 679 to:
% 51.99/20.02 | (1106) $false
% 51.99/20.02 |
% 51.99/20.02 |-The branch is then unsatisfiable
% 51.99/20.02 |-Branch two:
% 51.99/20.02 | (1874) ~ (all_0_10_10 = n8)
% 51.99/20.02 | (1875) 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
% 52.10/20.02 |
% 52.10/20.02 +-Applying beta-rule and splitting (1875), into two cases.
% 52.10/20.02 |-Branch one:
% 52.10/20.02 | (1876) all_0_10_10 = n7
% 52.10/20.02 |
% 52.10/20.02 | From (1876) and (292) follows:
% 52.10/20.03 | (1877) pred(n7) = all_0_6_6
% 52.10/20.03 |
% 52.10/20.03 | From (1876) and (760) follows:
% 52.10/20.03 | (1878) succ(n7) = all_0_8_8
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 52.10/20.03 | (1879) all_0_6_6 = n6
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 52.10/20.03 | (1880) all_0_8_8 = n8
% 52.10/20.03 |
% 52.10/20.03 | From (1879)(1880) and (411) follows:
% 52.10/20.03 | (1881) sum(n6, n8) = all_0_1_1
% 52.10/20.03 |
% 52.10/20.03 | From (1879) and (1564) follows:
% 52.10/20.03 | (1882) sum(n6, n0) = all_0_4_4
% 52.10/20.03 |
% 52.10/20.03 | From (1880) and (1566) follows:
% 52.10/20.03 | (1883) sum(n24, n8) = all_0_7_7
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (690) with n24, n8, all_0_7_7, n6 and discharging atoms sum(n24, n8) = all_0_7_7, sum(n24, n8) = n6, yields:
% 52.10/20.03 | (1425) all_0_7_7 = n6
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 52.10/20.03 | (1651) all_0_1_1 = n14
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (690) with n6, n0, all_0_4_4, n6 and discharging atoms sum(n6, n0) = all_0_4_4, sum(n6, n0) = n6, yields:
% 52.10/20.03 | (1423) all_0_4_4 = n6
% 52.10/20.03 |
% 52.10/20.03 | From (1425)(1423) and (590) follows:
% 52.10/20.03 | (1427) sum(n6, n6) = all_0_3_3
% 52.10/20.03 |
% 52.10/20.03 | From (1651) and (1568) follows:
% 52.10/20.03 | (1654) sum(n24, n14) = all_0_0_0
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (690) with n24, n14, all_0_0_0, n12 and discharging atoms sum(n24, n14) = all_0_0_0, sum(n24, n14) = n12, yields:
% 52.10/20.03 | (1195) all_0_0_0 = n12
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 52.10/20.03 | (1194) all_0_3_3 = n12
% 52.10/20.03 |
% 52.10/20.03 | Equations (1195,1194) can reduce 679 to:
% 52.10/20.03 | (1106) $false
% 52.10/20.03 |
% 52.10/20.03 |-The branch is then unsatisfiable
% 52.10/20.03 |-Branch two:
% 52.10/20.03 | (1892) ~ (all_0_10_10 = n7)
% 52.10/20.03 | (1893) 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
% 52.10/20.03 |
% 52.10/20.03 +-Applying beta-rule and splitting (1893), into two cases.
% 52.10/20.03 |-Branch one:
% 52.10/20.03 | (1894) all_0_10_10 = n6
% 52.10/20.03 |
% 52.10/20.03 | From (1894) and (292) follows:
% 52.10/20.03 | (1895) pred(n6) = all_0_6_6
% 52.10/20.03 |
% 52.10/20.03 | From (1894) and (760) follows:
% 52.10/20.03 | (1896) succ(n6) = all_0_8_8
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 52.10/20.03 | (1897) all_0_6_6 = n5
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 52.10/20.03 | (1898) all_0_8_8 = n7
% 52.10/20.03 |
% 52.10/20.03 | From (1897)(1898) and (411) follows:
% 52.10/20.03 | (1899) sum(n5, n7) = all_0_1_1
% 52.10/20.03 |
% 52.10/20.03 | From (1897) and (1564) follows:
% 52.10/20.03 | (1900) sum(n5, n0) = all_0_4_4
% 52.10/20.03 |
% 52.10/20.03 | From (1898) and (1566) follows:
% 52.10/20.03 | (1901) sum(n24, n7) = all_0_7_7
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (690) with n24, n7, all_0_7_7, n5 and discharging atoms sum(n24, n7) = all_0_7_7, sum(n24, n7) = n5, yields:
% 52.10/20.03 | (1443) all_0_7_7 = n5
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 52.10/20.03 | (1669) all_0_1_1 = n12
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (690) with n5, n0, all_0_4_4, n5 and discharging atoms sum(n5, n0) = all_0_4_4, sum(n5, n0) = n5, yields:
% 52.10/20.03 | (1441) all_0_4_4 = n5
% 52.10/20.03 |
% 52.10/20.03 | From (1443)(1441) and (590) follows:
% 52.10/20.03 | (1445) sum(n5, n5) = all_0_3_3
% 52.10/20.03 |
% 52.10/20.03 | From (1669) and (1568) follows:
% 52.10/20.03 | (1672) sum(n24, n12) = all_0_0_0
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (690) with n24, n12, all_0_0_0, n10 and discharging atoms sum(n24, n12) = all_0_0_0, sum(n24, n12) = n10, yields:
% 52.10/20.03 | (1213) all_0_0_0 = n10
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 52.10/20.03 | (1212) all_0_3_3 = n10
% 52.10/20.03 |
% 52.10/20.03 | Equations (1213,1212) can reduce 679 to:
% 52.10/20.03 | (1106) $false
% 52.10/20.03 |
% 52.10/20.03 |-The branch is then unsatisfiable
% 52.10/20.03 |-Branch two:
% 52.10/20.03 | (1910) ~ (all_0_10_10 = n6)
% 52.10/20.03 | (1911) 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
% 52.10/20.03 |
% 52.10/20.03 +-Applying beta-rule and splitting (1911), into two cases.
% 52.10/20.03 |-Branch one:
% 52.10/20.03 | (1912) all_0_10_10 = n5
% 52.10/20.03 |
% 52.10/20.03 | From (1912) and (292) follows:
% 52.10/20.03 | (1913) pred(n5) = all_0_6_6
% 52.10/20.03 |
% 52.10/20.03 | From (1912) and (760) follows:
% 52.10/20.03 | (1914) succ(n5) = all_0_8_8
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 52.10/20.03 | (1915) all_0_6_6 = n4
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 52.10/20.03 | (1916) all_0_8_8 = n6
% 52.10/20.03 |
% 52.10/20.03 | From (1915)(1916) and (411) follows:
% 52.10/20.03 | (1917) sum(n4, n6) = all_0_1_1
% 52.10/20.03 |
% 52.10/20.03 | From (1915) and (1564) follows:
% 52.10/20.03 | (1918) sum(n4, n0) = all_0_4_4
% 52.10/20.03 |
% 52.10/20.03 | From (1916) and (1566) follows:
% 52.10/20.03 | (1919) sum(n24, n6) = all_0_7_7
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (690) with n24, n6, all_0_7_7, n4 and discharging atoms sum(n24, n6) = all_0_7_7, sum(n24, n6) = n4, yields:
% 52.10/20.03 | (1461) all_0_7_7 = n4
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 52.10/20.03 | (1687) all_0_1_1 = n10
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (690) with n4, n0, all_0_4_4, n4 and discharging atoms sum(n4, n0) = all_0_4_4, sum(n4, n0) = n4, yields:
% 52.10/20.03 | (1459) all_0_4_4 = n4
% 52.10/20.03 |
% 52.10/20.03 | From (1461)(1459) and (590) follows:
% 52.10/20.03 | (1463) sum(n4, n4) = all_0_3_3
% 52.10/20.03 |
% 52.10/20.03 | From (1687) and (1568) follows:
% 52.10/20.03 | (1690) sum(n24, n10) = all_0_0_0
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (690) with n24, n10, all_0_0_0, n8 and discharging atoms sum(n24, n10) = all_0_0_0, sum(n24, n10) = n8, yields:
% 52.10/20.03 | (1231) all_0_0_0 = n8
% 52.10/20.03 |
% 52.10/20.03 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 52.10/20.03 | (1230) all_0_3_3 = n8
% 52.10/20.03 |
% 52.10/20.04 | Equations (1231,1230) can reduce 679 to:
% 52.10/20.04 | (1106) $false
% 52.10/20.04 |
% 52.10/20.04 |-The branch is then unsatisfiable
% 52.10/20.04 |-Branch two:
% 52.10/20.04 | (1928) ~ (all_0_10_10 = n5)
% 52.10/20.04 | (1929) 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
% 52.10/20.04 |
% 52.10/20.04 +-Applying beta-rule and splitting (1929), into two cases.
% 52.10/20.04 |-Branch one:
% 52.10/20.04 | (1930) all_0_10_10 = n4
% 52.10/20.04 |
% 52.10/20.04 | From (1930) and (292) follows:
% 52.10/20.04 | (1931) pred(n4) = all_0_6_6
% 52.10/20.04 |
% 52.10/20.04 | From (1930) and (760) follows:
% 52.10/20.04 | (1932) succ(n4) = all_0_8_8
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 52.10/20.04 | (1933) all_0_6_6 = n3
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 52.10/20.04 | (1934) all_0_8_8 = n5
% 52.10/20.04 |
% 52.10/20.04 | From (1933)(1934) and (411) follows:
% 52.10/20.04 | (1935) sum(n3, n5) = all_0_1_1
% 52.10/20.04 |
% 52.10/20.04 | From (1933) and (1564) follows:
% 52.10/20.04 | (1936) sum(n3, n0) = all_0_4_4
% 52.10/20.04 |
% 52.10/20.04 | From (1934) and (1566) follows:
% 52.10/20.04 | (1937) sum(n24, n5) = all_0_7_7
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (690) with n24, n5, all_0_7_7, n3 and discharging atoms sum(n24, n5) = all_0_7_7, sum(n24, n5) = n3, yields:
% 52.10/20.04 | (1479) all_0_7_7 = n3
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 52.10/20.04 | (1705) all_0_1_1 = n8
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (690) with n3, n0, all_0_4_4, n3 and discharging atoms sum(n3, n0) = all_0_4_4, sum(n3, n0) = n3, yields:
% 52.10/20.04 | (1477) all_0_4_4 = n3
% 52.10/20.04 |
% 52.10/20.04 | From (1479)(1477) and (590) follows:
% 52.10/20.04 | (1481) sum(n3, n3) = all_0_3_3
% 52.10/20.04 |
% 52.10/20.04 | From (1705) and (1568) follows:
% 52.10/20.04 | (1708) sum(n24, n8) = all_0_0_0
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (690) with n24, n8, all_0_0_0, n6 and discharging atoms sum(n24, n8) = all_0_0_0, sum(n24, n8) = n6, yields:
% 52.10/20.04 | (1249) all_0_0_0 = n6
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 52.10/20.04 | (1248) all_0_3_3 = n6
% 52.10/20.04 |
% 52.10/20.04 | Equations (1249,1248) can reduce 679 to:
% 52.10/20.04 | (1106) $false
% 52.10/20.04 |
% 52.10/20.04 |-The branch is then unsatisfiable
% 52.10/20.04 |-Branch two:
% 52.10/20.04 | (1946) ~ (all_0_10_10 = n4)
% 52.10/20.04 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 52.10/20.04 |
% 52.10/20.04 +-Applying beta-rule and splitting (1947), into two cases.
% 52.10/20.04 |-Branch one:
% 52.10/20.04 | (1948) all_0_10_10 = n3
% 52.10/20.04 |
% 52.10/20.04 | From (1948) and (292) follows:
% 52.10/20.04 | (1949) pred(n3) = all_0_6_6
% 52.10/20.04 |
% 52.10/20.04 | From (1948) and (760) follows:
% 52.10/20.04 | (1950) succ(n3) = all_0_8_8
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 52.10/20.04 | (1951) all_0_6_6 = n2
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 52.10/20.04 | (1952) all_0_8_8 = n4
% 52.10/20.04 |
% 52.10/20.04 | From (1951)(1952) and (411) follows:
% 52.10/20.04 | (1953) sum(n2, n4) = all_0_1_1
% 52.10/20.04 |
% 52.10/20.04 | From (1951) and (1564) follows:
% 52.10/20.04 | (1954) sum(n2, n0) = all_0_4_4
% 52.10/20.04 |
% 52.10/20.04 | From (1952) and (1566) follows:
% 52.10/20.04 | (1955) sum(n24, n4) = all_0_7_7
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (690) with n24, n4, all_0_7_7, n2 and discharging atoms sum(n24, n4) = all_0_7_7, sum(n24, n4) = n2, yields:
% 52.10/20.04 | (1497) all_0_7_7 = n2
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 52.10/20.04 | (1723) all_0_1_1 = n6
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (690) with n2, n0, all_0_4_4, n2 and discharging atoms sum(n2, n0) = all_0_4_4, sum(n2, n0) = n2, yields:
% 52.10/20.04 | (1495) all_0_4_4 = n2
% 52.10/20.04 |
% 52.10/20.04 | From (1497)(1495) and (590) follows:
% 52.10/20.04 | (1499) sum(n2, n2) = all_0_3_3
% 52.10/20.04 |
% 52.10/20.04 | From (1723) and (1568) follows:
% 52.10/20.04 | (1726) sum(n24, n6) = all_0_0_0
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (690) with n24, n6, all_0_0_0, n4 and discharging atoms sum(n24, n6) = all_0_0_0, sum(n24, n6) = n4, yields:
% 52.10/20.04 | (1267) all_0_0_0 = n4
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 52.10/20.04 | (1266) all_0_3_3 = n4
% 52.10/20.04 |
% 52.10/20.04 | Equations (1267,1266) can reduce 679 to:
% 52.10/20.04 | (1106) $false
% 52.10/20.04 |
% 52.10/20.04 |-The branch is then unsatisfiable
% 52.10/20.04 |-Branch two:
% 52.10/20.04 | (1964) ~ (all_0_10_10 = n3)
% 52.10/20.04 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 52.10/20.04 |
% 52.10/20.04 +-Applying beta-rule and splitting (1965), into two cases.
% 52.10/20.04 |-Branch one:
% 52.10/20.04 | (1966) all_0_10_10 = n2
% 52.10/20.04 |
% 52.10/20.04 | From (1966) and (292) follows:
% 52.10/20.04 | (1967) pred(n2) = all_0_6_6
% 52.10/20.04 |
% 52.10/20.04 | From (1966) and (760) follows:
% 52.10/20.04 | (1968) succ(n2) = all_0_8_8
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 52.10/20.04 | (1969) all_0_6_6 = n1
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 52.10/20.04 | (1970) all_0_8_8 = n3
% 52.10/20.04 |
% 52.10/20.04 | From (1969)(1970) and (411) follows:
% 52.10/20.04 | (1971) sum(n1, n3) = all_0_1_1
% 52.10/20.04 |
% 52.10/20.04 | From (1969) and (1564) follows:
% 52.10/20.04 | (1972) sum(n1, n0) = all_0_4_4
% 52.10/20.04 |
% 52.10/20.04 | From (1970) and (1566) follows:
% 52.10/20.04 | (1973) sum(n24, n3) = all_0_7_7
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (690) with n24, n3, all_0_7_7, n1 and discharging atoms sum(n24, n3) = all_0_7_7, sum(n24, n3) = n1, yields:
% 52.10/20.04 | (1515) all_0_7_7 = n1
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 52.10/20.04 | (1741) all_0_1_1 = n4
% 52.10/20.04 |
% 52.10/20.04 | Instantiating formula (690) with n1, n0, all_0_4_4, n1 and discharging atoms sum(n1, n0) = all_0_4_4, sum(n1, n0) = n1, yields:
% 52.10/20.04 | (1513) all_0_4_4 = n1
% 52.10/20.04 |
% 52.10/20.04 | From (1515)(1513) and (590) follows:
% 52.10/20.04 | (1517) sum(n1, n1) = all_0_3_3
% 52.10/20.04 |
% 52.10/20.04 | From (1741) and (1568) follows:
% 52.10/20.04 | (1744) sum(n24, n4) = all_0_0_0
% 52.10/20.05 |
% 52.10/20.05 | Instantiating formula (690) with n24, n4, all_0_0_0, n2 and discharging atoms sum(n24, n4) = all_0_0_0, sum(n24, n4) = n2, yields:
% 52.10/20.05 | (1285) all_0_0_0 = n2
% 52.10/20.05 |
% 52.10/20.05 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 52.10/20.05 | (1284) all_0_3_3 = n2
% 52.10/20.05 |
% 52.10/20.05 | Equations (1285,1284) can reduce 679 to:
% 52.10/20.05 | (1106) $false
% 52.10/20.05 |
% 52.10/20.05 |-The branch is then unsatisfiable
% 52.10/20.05 |-Branch two:
% 52.10/20.05 | (1982) ~ (all_0_10_10 = n2)
% 52.10/20.05 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 52.10/20.05 |
% 52.10/20.05 +-Applying beta-rule and splitting (1983), into two cases.
% 52.10/20.05 |-Branch one:
% 52.10/20.05 | (1984) all_0_10_10 = n1
% 52.10/20.05 |
% 52.10/20.05 | From (1984) and (292) follows:
% 52.10/20.05 | (1985) pred(n1) = all_0_6_6
% 52.10/20.05 |
% 52.10/20.05 | From (1984) and (760) follows:
% 52.10/20.05 | (1986) succ(n1) = all_0_8_8
% 52.10/20.05 |
% 52.10/20.05 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 52.10/20.05 | (1987) all_0_6_6 = n0
% 52.10/20.05 |
% 52.10/20.05 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 52.10/20.05 | (1988) all_0_8_8 = n2
% 52.10/20.05 |
% 52.10/20.05 | From (1987)(1988) and (411) follows:
% 52.10/20.05 | (1989) sum(n0, n2) = all_0_1_1
% 52.10/20.05 |
% 52.10/20.05 | From (1987) and (1564) follows:
% 52.10/20.05 | (1990) sum(n0, n0) = all_0_4_4
% 52.10/20.05 |
% 52.10/20.05 | From (1988) and (1566) follows:
% 52.10/20.05 | (1991) sum(n24, n2) = all_0_7_7
% 52.10/20.05 |
% 52.10/20.05 | Instantiating formula (690) with n24, n2, all_0_7_7, n0 and discharging atoms sum(n24, n2) = all_0_7_7, sum(n24, n2) = n0, yields:
% 52.10/20.05 | (1533) all_0_7_7 = n0
% 52.10/20.05 |
% 52.10/20.05 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 52.10/20.05 | (1759) all_0_1_1 = n2
% 52.10/20.05 |
% 52.10/20.05 | Instantiating formula (690) with n0, n0, all_0_4_4, n0 and discharging atoms sum(n0, n0) = all_0_4_4, sum(n0, n0) = n0, yields:
% 52.10/20.05 | (1531) all_0_4_4 = n0
% 52.10/20.05 |
% 52.10/20.05 | From (1533)(1531) and (590) follows:
% 52.10/20.05 | (1535) sum(n0, n0) = all_0_3_3
% 52.10/20.05 |
% 52.10/20.05 | From (1759) and (1568) follows:
% 52.10/20.05 | (1762) sum(n24, n2) = all_0_0_0
% 52.10/20.05 |
% 52.10/20.05 | From (1533) and (1991) follows:
% 52.10/20.05 | (973) sum(n24, n2) = n0
% 52.10/20.05 |
% 52.10/20.05 | From (1531) and (1990) follows:
% 52.10/20.05 | (208) sum(n0, n0) = n0
% 52.10/20.05 |
% 52.10/20.05 | Instantiating formula (690) with n24, n2, all_0_0_0, n0 and discharging atoms sum(n24, n2) = all_0_0_0, sum(n24, n2) = n0, yields:
% 52.10/20.05 | (1303) all_0_0_0 = n0
% 52.10/20.05 |
% 52.10/20.05 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 52.10/20.05 | (1302) all_0_3_3 = n0
% 52.10/20.05 |
% 52.10/20.05 | Equations (1303,1302) can reduce 679 to:
% 52.10/20.05 | (1106) $false
% 52.10/20.05 |
% 52.10/20.05 |-The branch is then unsatisfiable
% 52.10/20.05 |-Branch two:
% 52.10/20.05 | (2002) ~ (all_0_10_10 = n1)
% 52.10/20.05 | (2003) all_0_10_10 = n0
% 52.10/20.05 |
% 52.10/20.05 | From (2003) and (292) follows:
% 52.10/20.05 | (2004) pred(n0) = all_0_6_6
% 52.10/20.05 |
% 52.10/20.05 | From (2003) and (760) follows:
% 52.10/20.05 | (2005) succ(n0) = all_0_8_8
% 52.10/20.05 |
% 52.10/20.05 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 52.10/20.05 | (2006) all_0_6_6 = n25
% 52.10/20.05 |
% 52.10/20.05 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 52.10/20.05 | (2007) all_0_8_8 = n1
% 52.10/20.05 |
% 52.10/20.05 | From (2006)(2007) and (411) follows:
% 52.10/20.05 | (2008) sum(n25, n1) = all_0_1_1
% 52.10/20.05 |
% 52.10/20.05 | From (2006) and (1564) follows:
% 52.10/20.05 | (2009) sum(n25, n0) = all_0_4_4
% 52.10/20.05 |
% 52.10/20.05 | From (2007) and (1566) follows:
% 52.10/20.05 | (2010) sum(n24, n1) = all_0_7_7
% 52.10/20.05 |
% 52.10/20.05 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 52.10/20.05 | (1777) all_0_1_1 = n0
% 52.10/20.05 |
% 52.10/20.05 | Instantiating formula (690) with n25, n0, all_0_4_4, n25 and discharging atoms sum(n25, n0) = all_0_4_4, sum(n25, n0) = n25, yields:
% 52.10/20.05 | (1551) all_0_4_4 = n25
% 52.10/20.05 |
% 52.10/20.05 | Instantiating formula (690) with n24, n1, all_0_7_7, n25 and discharging atoms sum(n24, n1) = all_0_7_7, sum(n24, n1) = n25, yields:
% 52.10/20.05 | (1550) all_0_7_7 = n25
% 52.10/20.05 |
% 52.10/20.05 | From (1550)(1551) and (590) follows:
% 52.10/20.05 | (1553) sum(n25, n25) = all_0_3_3
% 52.10/20.05 |
% 52.10/20.05 | From (1777) and (1568) follows:
% 52.10/20.05 | (1780) sum(n24, n0) = all_0_0_0
% 52.10/20.05 |
% 52.10/20.05 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 52.10/20.05 | (1320) all_0_3_3 = n24
% 52.10/20.05 |
% 52.10/20.05 | Instantiating formula (690) with n24, n0, all_0_0_0, n24 and discharging atoms sum(n24, n0) = all_0_0_0, sum(n24, n0) = n24, yields:
% 52.10/20.05 | (1321) all_0_0_0 = n24
% 52.10/20.05 |
% 52.10/20.05 | Equations (1321,1320) can reduce 679 to:
% 52.10/20.05 | (1106) $false
% 52.10/20.05 |
% 52.10/20.05 |-The branch is then unsatisfiable
% 52.10/20.05 |-Branch two:
% 52.10/20.05 | (1107) ~ (all_0_11_11 = n25)
% 52.10/20.05 | (1108) all_0_11_11 = n24 | all_0_11_11 = n23 | all_0_11_11 = n22 | all_0_11_11 = n21 | 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
% 52.10/20.05 |
% 52.10/20.05 +-Applying beta-rule and splitting (1558), into two cases.
% 52.10/20.05 |-Branch one:
% 52.10/20.05 | (1570) all_0_10_10 = n24
% 52.10/20.05 |
% 52.10/20.05 | From (1570) and (292) follows:
% 52.10/20.06 | (1571) pred(n24) = all_0_6_6
% 52.10/20.06 |
% 52.10/20.06 | From (1570) and (760) follows:
% 52.10/20.06 | (1572) succ(n24) = all_0_8_8
% 52.10/20.06 |
% 52.10/20.06 | Instantiating formula (500) with n24, all_0_6_6, n23 and discharging atoms pred(n24) = all_0_6_6, pred(n24) = n23, yields:
% 52.10/20.06 | (1573) all_0_6_6 = n23
% 52.10/20.06 |
% 52.10/20.06 | Instantiating formula (617) with n24, all_0_8_8, n25 and discharging atoms succ(n24) = all_0_8_8, succ(n24) = n25, yields:
% 52.10/20.06 | (1574) all_0_8_8 = n25
% 52.10/20.06 |
% 52.10/20.06 | From (1573) and (1571) follows:
% 52.10/20.06 | (831) pred(n24) = n23
% 52.10/20.06 |
% 52.10/20.06 | From (1574) and (1572) follows:
% 52.10/20.06 | (758) succ(n24) = n25
% 52.10/20.06 |
% 52.10/20.06 | From (1573) and (541) follows:
% 52.10/20.06 | (2028) sum(n23, all_0_5_5) = all_0_4_4
% 52.10/20.06 |
% 52.10/20.06 | From (1573)(1574) and (411) follows:
% 52.10/20.06 | (1575) sum(n23, n25) = all_0_1_1
% 52.10/20.06 |
% 52.10/20.06 | From (1574) and (427) follows:
% 52.10/20.06 | (2030) sum(all_0_9_9, n25) = all_0_7_7
% 52.10/20.06 |
% 52.10/20.06 | Instantiating formula (690) with n23, n25, all_0_1_1, n22 and discharging atoms sum(n23, n25) = all_0_1_1, sum(n23, n25) = n22, yields:
% 52.10/20.06 | (1579) all_0_1_1 = n22
% 52.10/20.06 |
% 52.10/20.06 | From (1579) and (630) follows:
% 52.10/20.06 | (2032) sum(all_0_2_2, n22) = all_0_0_0
% 52.10/20.06 |
% 52.10/20.06 | From (1579) and (1575) follows:
% 52.10/20.06 | (145) sum(n23, n25) = n22
% 52.10/20.06 |
% 52.10/20.06 +-Applying beta-rule and splitting (1108), into two cases.
% 52.10/20.06 |-Branch one:
% 52.10/20.06 | (1109) all_0_11_11 = n24
% 52.10/20.06 |
% 52.10/20.06 | From (1109) and (559) follows:
% 52.10/20.06 | (1110) pred(n24) = all_0_9_9
% 52.10/20.06 |
% 52.10/20.06 | From (1109) and (992) follows:
% 52.10/20.06 | (1111) succ(n24) = all_0_5_5
% 52.10/20.06 |
% 52.10/20.06 | Instantiating formula (500) with n24, all_0_9_9, n23 and discharging atoms pred(n24) = all_0_9_9, pred(n24) = n23, yields:
% 52.10/20.06 | (1112) all_0_9_9 = n23
% 52.10/20.06 |
% 52.10/20.06 | Instantiating formula (617) with n24, all_0_5_5, n25 and discharging atoms succ(n24) = all_0_5_5, succ(n24) = n25, yields:
% 52.10/20.06 | (1113) all_0_5_5 = n25
% 52.10/20.06 |
% 52.10/20.06 | From (1112)(1113) and (538) follows:
% 52.10/20.06 | (1114) sum(n23, n25) = all_0_2_2
% 52.10/20.06 |
% 52.10/20.06 | From (1112) and (2030) follows:
% 52.10/20.06 | (2040) sum(n23, n25) = all_0_7_7
% 52.10/20.06 |
% 52.10/20.06 | From (1113) and (2028) follows:
% 52.10/20.06 | (2041) sum(n23, n25) = all_0_4_4
% 52.10/20.06 |
% 52.10/20.06 | Instantiating formula (690) with n23, n25, all_0_2_2, n22 and discharging atoms sum(n23, n25) = all_0_2_2, sum(n23, n25) = n22, yields:
% 52.10/20.06 | (1118) all_0_2_2 = n22
% 52.10/20.06 |
% 52.10/20.06 | Instantiating formula (690) with n23, n25, all_0_4_4, all_0_2_2 and discharging atoms sum(n23, n25) = all_0_2_2, sum(n23, n25) = all_0_4_4, yields:
% 52.10/20.06 | (1093) all_0_2_2 = all_0_4_4
% 52.10/20.06 |
% 52.10/20.06 | Instantiating formula (690) with n23, n25, all_0_7_7, all_0_2_2 and discharging atoms sum(n23, n25) = all_0_2_2, sum(n23, n25) = all_0_7_7, yields:
% 52.10/20.06 | (1094) all_0_2_2 = all_0_7_7
% 52.10/20.06 |
% 52.10/20.06 | Combining equations (1094,1093) yields a new equation:
% 52.10/20.06 | (1095) all_0_4_4 = all_0_7_7
% 52.10/20.06 |
% 52.10/20.06 | Combining equations (1118,1093) yields a new equation:
% 52.10/20.06 | (1135) all_0_4_4 = n22
% 52.10/20.06 |
% 52.10/20.06 | Combining equations (1135,1095) yields a new equation:
% 52.10/20.06 | (1137) all_0_7_7 = n22
% 52.10/20.06 |
% 52.10/20.06 | Combining equations (1137,1095) yields a new equation:
% 52.10/20.06 | (1135) all_0_4_4 = n22
% 52.10/20.06 |
% 52.10/20.06 | Combining equations (1135,1093) yields a new equation:
% 52.10/20.06 | (1118) all_0_2_2 = n22
% 52.10/20.06 |
% 52.10/20.06 | From (1118) and (2032) follows:
% 52.10/20.06 | (2050) sum(n22, n22) = all_0_0_0
% 52.10/20.06 |
% 52.10/20.06 | From (1137)(1135) and (590) follows:
% 52.10/20.06 | (1139) sum(n22, n22) = all_0_3_3
% 52.10/20.06 |
% 52.10/20.06 | Instantiating formula (690) with n22, n22, all_0_0_0, n18 and discharging atoms sum(n22, n22) = all_0_0_0, sum(n22, n22) = n18, yields:
% 52.10/20.06 | (1141) all_0_0_0 = n18
% 52.10/20.06 |
% 52.10/20.06 | Instantiating formula (690) with n22, n22, all_0_3_3, all_0_0_0 and discharging atoms sum(n22, n22) = all_0_0_0, sum(n22, n22) = all_0_3_3, yields:
% 52.10/20.06 | (1103) all_0_0_0 = all_0_3_3
% 52.10/20.06 |
% 52.10/20.06 | Combining equations (1141,1103) yields a new equation:
% 52.10/20.06 | (1140) all_0_3_3 = n18
% 52.10/20.06 |
% 52.10/20.06 | Combining equations (1140,1103) yields a new equation:
% 52.10/20.06 | (1141) all_0_0_0 = n18
% 52.10/20.06 |
% 52.10/20.06 | Equations (1141,1140) can reduce 679 to:
% 52.10/20.06 | (1106) $false
% 52.10/20.06 |
% 52.10/20.06 |-The branch is then unsatisfiable
% 52.10/20.06 |-Branch two:
% 52.10/20.06 | (1125) ~ (all_0_11_11 = n24)
% 52.10/20.06 | (1126) all_0_11_11 = n23 | all_0_11_11 = n22 | all_0_11_11 = n21 | 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
% 52.10/20.06 |
% 52.10/20.06 +-Applying beta-rule and splitting (1126), into two cases.
% 52.10/20.06 |-Branch one:
% 52.10/20.06 | (1127) all_0_11_11 = n23
% 52.10/20.06 |
% 52.10/20.06 | From (1127) and (559) follows:
% 52.10/20.06 | (1128) pred(n23) = all_0_9_9
% 52.10/20.06 |
% 52.10/20.06 | From (1127) and (992) follows:
% 52.10/20.06 | (1129) succ(n23) = all_0_5_5
% 52.10/20.06 |
% 52.10/20.06 | Instantiating formula (500) with n23, all_0_9_9, n22 and discharging atoms pred(n23) = all_0_9_9, pred(n23) = n22, yields:
% 52.10/20.06 | (1130) all_0_9_9 = n22
% 52.10/20.06 |
% 52.10/20.06 | Instantiating formula (617) with n23, all_0_5_5, n24 and discharging atoms succ(n23) = all_0_5_5, succ(n23) = n24, yields:
% 52.10/20.06 | (1131) all_0_5_5 = n24
% 52.10/20.06 |
% 52.10/20.06 | From (1130)(1131) and (538) follows:
% 52.10/20.06 | (1132) sum(n22, n24) = all_0_2_2
% 52.10/20.06 |
% 52.10/20.06 | From (1130) and (2030) follows:
% 52.10/20.06 | (2065) sum(n22, n25) = all_0_7_7
% 52.10/20.06 |
% 52.10/20.06 | From (1131) and (2028) follows:
% 52.10/20.06 | (2066) sum(n23, n24) = all_0_4_4
% 52.10/20.06 |
% 52.10/20.06 | Instantiating formula (690) with n23, n24, all_0_4_4, n21 and discharging atoms sum(n23, n24) = all_0_4_4, sum(n23, n24) = n21, yields:
% 52.10/20.06 | (1153) all_0_4_4 = n21
% 52.10/20.06 |
% 52.10/20.06 | Instantiating formula (690) with n22, n25, all_0_7_7, n21 and discharging atoms sum(n22, n25) = all_0_7_7, sum(n22, n25) = n21, yields:
% 52.10/20.06 | (1155) all_0_7_7 = n21
% 52.10/20.06 |
% 52.10/20.06 | Instantiating formula (690) with n22, n24, all_0_2_2, n20 and discharging atoms sum(n22, n24) = all_0_2_2, sum(n22, n24) = n20, yields:
% 52.10/20.06 | (1136) all_0_2_2 = n20
% 52.10/20.06 |
% 52.10/20.06 | From (1136) and (2032) follows:
% 52.10/20.06 | (2070) sum(n20, n22) = all_0_0_0
% 52.10/20.06 |
% 52.10/20.06 | From (1155)(1153) and (590) follows:
% 52.10/20.06 | (1157) sum(n21, n21) = all_0_3_3
% 52.10/20.06 |
% 52.10/20.06 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 52.10/20.06 | (1158) all_0_3_3 = n16
% 52.10/20.06 |
% 52.10/20.06 | Instantiating formula (690) with n20, n22, all_0_0_0, n16 and discharging atoms sum(n20, n22) = all_0_0_0, sum(n20, n22) = n16, yields:
% 52.10/20.06 | (1159) all_0_0_0 = n16
% 52.10/20.06 |
% 52.10/20.06 | Equations (1159,1158) can reduce 679 to:
% 52.10/20.06 | (1106) $false
% 52.10/20.06 |
% 52.10/20.06 |-The branch is then unsatisfiable
% 52.10/20.06 |-Branch two:
% 52.10/20.06 | (1143) ~ (all_0_11_11 = n23)
% 52.10/20.06 | (1144) all_0_11_11 = n22 | all_0_11_11 = n21 | 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
% 52.10/20.06 |
% 52.10/20.06 +-Applying beta-rule and splitting (1144), into two cases.
% 52.10/20.06 |-Branch one:
% 52.10/20.06 | (1145) all_0_11_11 = n22
% 52.10/20.07 |
% 52.10/20.07 | From (1145) and (559) follows:
% 52.10/20.07 | (1146) pred(n22) = all_0_9_9
% 52.10/20.07 |
% 52.10/20.07 | From (1145) and (992) follows:
% 52.10/20.07 | (1147) succ(n22) = all_0_5_5
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (500) with n22, all_0_9_9, n21 and discharging atoms pred(n22) = all_0_9_9, pred(n22) = n21, yields:
% 52.10/20.07 | (1148) all_0_9_9 = n21
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (617) with n22, all_0_5_5, n23 and discharging atoms succ(n22) = all_0_5_5, succ(n22) = n23, yields:
% 52.10/20.07 | (1149) all_0_5_5 = n23
% 52.10/20.07 |
% 52.10/20.07 | From (1148)(1149) and (538) follows:
% 52.10/20.07 | (1150) sum(n21, n23) = all_0_2_2
% 52.10/20.07 |
% 52.10/20.07 | From (1148) and (2030) follows:
% 52.10/20.07 | (2083) sum(n21, n25) = all_0_7_7
% 52.10/20.07 |
% 52.10/20.07 | From (1149) and (2028) follows:
% 52.10/20.07 | (2084) sum(n23, n23) = all_0_4_4
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (690) with n23, n23, all_0_4_4, n20 and discharging atoms sum(n23, n23) = all_0_4_4, sum(n23, n23) = n20, yields:
% 52.10/20.07 | (1171) all_0_4_4 = n20
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (690) with n21, n25, all_0_7_7, n20 and discharging atoms sum(n21, n25) = all_0_7_7, sum(n21, n25) = n20, yields:
% 52.10/20.07 | (1173) all_0_7_7 = n20
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (690) with n21, n23, all_0_2_2, n18 and discharging atoms sum(n21, n23) = all_0_2_2, sum(n21, n23) = n18, yields:
% 52.10/20.07 | (1154) all_0_2_2 = n18
% 52.10/20.07 |
% 52.10/20.07 | From (1154) and (2032) follows:
% 52.10/20.07 | (2088) sum(n18, n22) = all_0_0_0
% 52.10/20.07 |
% 52.10/20.07 | From (1173)(1171) and (590) follows:
% 52.10/20.07 | (1175) sum(n20, n20) = all_0_3_3
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 52.10/20.07 | (1176) all_0_3_3 = n14
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (690) with n18, n22, all_0_0_0, n14 and discharging atoms sum(n18, n22) = all_0_0_0, sum(n18, n22) = n14, yields:
% 52.10/20.07 | (1177) all_0_0_0 = n14
% 52.10/20.07 |
% 52.10/20.07 | Equations (1177,1176) can reduce 679 to:
% 52.10/20.07 | (1106) $false
% 52.10/20.07 |
% 52.10/20.07 |-The branch is then unsatisfiable
% 52.10/20.07 |-Branch two:
% 52.10/20.07 | (1161) ~ (all_0_11_11 = n22)
% 52.10/20.07 | (1162) all_0_11_11 = n21 | 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
% 52.10/20.07 |
% 52.10/20.07 +-Applying beta-rule and splitting (1162), into two cases.
% 52.10/20.07 |-Branch one:
% 52.10/20.07 | (1163) all_0_11_11 = n21
% 52.10/20.07 |
% 52.10/20.07 | From (1163) and (559) follows:
% 52.10/20.07 | (1164) pred(n21) = all_0_9_9
% 52.10/20.07 |
% 52.10/20.07 | From (1163) and (992) follows:
% 52.10/20.07 | (1165) succ(n21) = all_0_5_5
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (500) with n21, all_0_9_9, n20 and discharging atoms pred(n21) = all_0_9_9, pred(n21) = n20, yields:
% 52.10/20.07 | (1166) all_0_9_9 = n20
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (617) with n21, all_0_5_5, n22 and discharging atoms succ(n21) = all_0_5_5, succ(n21) = n22, yields:
% 52.10/20.07 | (1167) all_0_5_5 = n22
% 52.10/20.07 |
% 52.10/20.07 | From (1166)(1167) and (538) follows:
% 52.10/20.07 | (1168) sum(n20, n22) = all_0_2_2
% 52.10/20.07 |
% 52.10/20.07 | From (1166) and (2030) follows:
% 52.10/20.07 | (2101) sum(n20, n25) = all_0_7_7
% 52.10/20.07 |
% 52.10/20.07 | From (1167) and (2028) follows:
% 52.10/20.07 | (2102) sum(n23, n22) = all_0_4_4
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (690) with n23, n22, all_0_4_4, n19 and discharging atoms sum(n23, n22) = all_0_4_4, sum(n23, n22) = n19, yields:
% 52.10/20.07 | (1189) all_0_4_4 = n19
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (690) with n20, n25, all_0_7_7, n19 and discharging atoms sum(n20, n25) = all_0_7_7, sum(n20, n25) = n19, yields:
% 52.10/20.07 | (1191) all_0_7_7 = n19
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (690) with n20, n22, all_0_2_2, n16 and discharging atoms sum(n20, n22) = all_0_2_2, sum(n20, n22) = n16, yields:
% 52.10/20.07 | (1172) all_0_2_2 = n16
% 52.10/20.07 |
% 52.10/20.07 | From (1172) and (2032) follows:
% 52.10/20.07 | (2106) sum(n16, n22) = all_0_0_0
% 52.10/20.07 |
% 52.10/20.07 | From (1191)(1189) and (590) follows:
% 52.10/20.07 | (1193) sum(n19, n19) = all_0_3_3
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 52.10/20.07 | (1194) all_0_3_3 = n12
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (690) with n16, n22, all_0_0_0, n12 and discharging atoms sum(n16, n22) = all_0_0_0, sum(n16, n22) = n12, yields:
% 52.10/20.07 | (1195) all_0_0_0 = n12
% 52.10/20.07 |
% 52.10/20.07 | Equations (1195,1194) can reduce 679 to:
% 52.10/20.07 | (1106) $false
% 52.10/20.07 |
% 52.10/20.07 |-The branch is then unsatisfiable
% 52.10/20.07 |-Branch two:
% 52.10/20.07 | (1179) ~ (all_0_11_11 = n21)
% 52.10/20.07 | (1180) 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
% 52.10/20.07 |
% 52.10/20.07 +-Applying beta-rule and splitting (1180), into two cases.
% 52.10/20.07 |-Branch one:
% 52.10/20.07 | (1181) all_0_11_11 = n20
% 52.10/20.07 |
% 52.10/20.07 | From (1181) and (559) follows:
% 52.10/20.07 | (1182) pred(n20) = all_0_9_9
% 52.10/20.07 |
% 52.10/20.07 | From (1181) and (992) follows:
% 52.10/20.07 | (1183) succ(n20) = all_0_5_5
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (500) with n20, all_0_9_9, n19 and discharging atoms pred(n20) = all_0_9_9, pred(n20) = n19, yields:
% 52.10/20.07 | (1184) all_0_9_9 = n19
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (617) with n20, all_0_5_5, n21 and discharging atoms succ(n20) = all_0_5_5, succ(n20) = n21, yields:
% 52.10/20.07 | (1185) all_0_5_5 = n21
% 52.10/20.07 |
% 52.10/20.07 | From (1184)(1185) and (538) follows:
% 52.10/20.07 | (1186) sum(n19, n21) = all_0_2_2
% 52.10/20.07 |
% 52.10/20.07 | From (1184) and (2030) follows:
% 52.10/20.07 | (2119) sum(n19, n25) = all_0_7_7
% 52.10/20.07 |
% 52.10/20.07 | From (1185) and (2028) follows:
% 52.10/20.07 | (2120) sum(n23, n21) = all_0_4_4
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (690) with n23, n21, all_0_4_4, n18 and discharging atoms sum(n23, n21) = all_0_4_4, sum(n23, n21) = n18, yields:
% 52.10/20.07 | (1207) all_0_4_4 = n18
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (690) with n19, n25, all_0_7_7, n18 and discharging atoms sum(n19, n25) = all_0_7_7, sum(n19, n25) = n18, yields:
% 52.10/20.07 | (1209) all_0_7_7 = n18
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (690) with n19, n21, all_0_2_2, n14 and discharging atoms sum(n19, n21) = all_0_2_2, sum(n19, n21) = n14, yields:
% 52.10/20.07 | (1190) all_0_2_2 = n14
% 52.10/20.07 |
% 52.10/20.07 | From (1190) and (2032) follows:
% 52.10/20.07 | (2124) sum(n14, n22) = all_0_0_0
% 52.10/20.07 |
% 52.10/20.07 | From (1209)(1207) and (590) follows:
% 52.10/20.07 | (1211) sum(n18, n18) = all_0_3_3
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 52.10/20.07 | (1212) all_0_3_3 = n10
% 52.10/20.07 |
% 52.10/20.07 | Instantiating formula (690) with n14, n22, all_0_0_0, n10 and discharging atoms sum(n14, n22) = all_0_0_0, sum(n14, n22) = n10, yields:
% 52.10/20.07 | (1213) all_0_0_0 = n10
% 52.10/20.07 |
% 52.10/20.07 | Equations (1213,1212) can reduce 679 to:
% 52.10/20.07 | (1106) $false
% 52.10/20.07 |
% 52.10/20.07 |-The branch is then unsatisfiable
% 52.10/20.07 |-Branch two:
% 52.10/20.07 | (1197) ~ (all_0_11_11 = n20)
% 52.10/20.07 | (1198) 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
% 52.10/20.08 |
% 52.10/20.08 +-Applying beta-rule and splitting (1198), into two cases.
% 52.10/20.08 |-Branch one:
% 52.10/20.08 | (1199) all_0_11_11 = n19
% 52.10/20.08 |
% 52.10/20.08 | From (1199) and (559) follows:
% 52.10/20.08 | (1200) pred(n19) = all_0_9_9
% 52.10/20.08 |
% 52.10/20.08 | From (1199) and (992) follows:
% 52.10/20.08 | (1201) succ(n19) = all_0_5_5
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (500) with n19, all_0_9_9, n18 and discharging atoms pred(n19) = all_0_9_9, pred(n19) = n18, yields:
% 52.10/20.08 | (1202) all_0_9_9 = n18
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (617) with n19, all_0_5_5, n20 and discharging atoms succ(n19) = all_0_5_5, succ(n19) = n20, yields:
% 52.10/20.08 | (1203) all_0_5_5 = n20
% 52.10/20.08 |
% 52.10/20.08 | From (1202)(1203) and (538) follows:
% 52.10/20.08 | (1204) sum(n18, n20) = all_0_2_2
% 52.10/20.08 |
% 52.10/20.08 | From (1202) and (2030) follows:
% 52.10/20.08 | (2137) sum(n18, n25) = all_0_7_7
% 52.10/20.08 |
% 52.10/20.08 | From (1203) and (2028) follows:
% 52.10/20.08 | (2138) sum(n23, n20) = all_0_4_4
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (690) with n23, n20, all_0_4_4, n17 and discharging atoms sum(n23, n20) = all_0_4_4, sum(n23, n20) = n17, yields:
% 52.10/20.08 | (1225) all_0_4_4 = n17
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (690) with n18, n25, all_0_7_7, n17 and discharging atoms sum(n18, n25) = all_0_7_7, sum(n18, n25) = n17, yields:
% 52.10/20.08 | (1227) all_0_7_7 = n17
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (690) with n18, n20, all_0_2_2, n12 and discharging atoms sum(n18, n20) = all_0_2_2, sum(n18, n20) = n12, yields:
% 52.10/20.08 | (1208) all_0_2_2 = n12
% 52.10/20.08 |
% 52.10/20.08 | From (1208) and (2032) follows:
% 52.10/20.08 | (2142) sum(n12, n22) = all_0_0_0
% 52.10/20.08 |
% 52.10/20.08 | From (1227)(1225) and (590) follows:
% 52.10/20.08 | (1229) sum(n17, n17) = all_0_3_3
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 52.10/20.08 | (1230) all_0_3_3 = n8
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (690) with n12, n22, all_0_0_0, n8 and discharging atoms sum(n12, n22) = all_0_0_0, sum(n12, n22) = n8, yields:
% 52.10/20.08 | (1231) all_0_0_0 = n8
% 52.10/20.08 |
% 52.10/20.08 | Equations (1231,1230) can reduce 679 to:
% 52.10/20.08 | (1106) $false
% 52.10/20.08 |
% 52.10/20.08 |-The branch is then unsatisfiable
% 52.10/20.08 |-Branch two:
% 52.10/20.08 | (1215) ~ (all_0_11_11 = n19)
% 52.10/20.08 | (1216) 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
% 52.10/20.08 |
% 52.10/20.08 +-Applying beta-rule and splitting (1216), into two cases.
% 52.10/20.08 |-Branch one:
% 52.10/20.08 | (1217) all_0_11_11 = n18
% 52.10/20.08 |
% 52.10/20.08 | From (1217) and (559) follows:
% 52.10/20.08 | (1218) pred(n18) = all_0_9_9
% 52.10/20.08 |
% 52.10/20.08 | From (1217) and (992) follows:
% 52.10/20.08 | (1219) succ(n18) = all_0_5_5
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (500) with n18, all_0_9_9, n17 and discharging atoms pred(n18) = all_0_9_9, pred(n18) = n17, yields:
% 52.10/20.08 | (1220) all_0_9_9 = n17
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (617) with n18, all_0_5_5, n19 and discharging atoms succ(n18) = all_0_5_5, succ(n18) = n19, yields:
% 52.10/20.08 | (1221) all_0_5_5 = n19
% 52.10/20.08 |
% 52.10/20.08 | From (1220)(1221) and (538) follows:
% 52.10/20.08 | (1222) sum(n17, n19) = all_0_2_2
% 52.10/20.08 |
% 52.10/20.08 | From (1220) and (2030) follows:
% 52.10/20.08 | (2155) sum(n17, n25) = all_0_7_7
% 52.10/20.08 |
% 52.10/20.08 | From (1221) and (2028) follows:
% 52.10/20.08 | (2156) sum(n23, n19) = all_0_4_4
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (690) with n23, n19, all_0_4_4, n16 and discharging atoms sum(n23, n19) = all_0_4_4, sum(n23, n19) = n16, yields:
% 52.10/20.08 | (1243) all_0_4_4 = n16
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (690) with n17, n25, all_0_7_7, n16 and discharging atoms sum(n17, n25) = all_0_7_7, sum(n17, n25) = n16, yields:
% 52.10/20.08 | (1245) all_0_7_7 = n16
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (690) with n17, n19, all_0_2_2, n10 and discharging atoms sum(n17, n19) = all_0_2_2, sum(n17, n19) = n10, yields:
% 52.10/20.08 | (1226) all_0_2_2 = n10
% 52.10/20.08 |
% 52.10/20.08 | From (1226) and (2032) follows:
% 52.10/20.08 | (2160) sum(n10, n22) = all_0_0_0
% 52.10/20.08 |
% 52.10/20.08 | From (1245)(1243) and (590) follows:
% 52.10/20.08 | (1247) sum(n16, n16) = all_0_3_3
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 52.10/20.08 | (1248) all_0_3_3 = n6
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (690) with n10, n22, all_0_0_0, n6 and discharging atoms sum(n10, n22) = all_0_0_0, sum(n10, n22) = n6, yields:
% 52.10/20.08 | (1249) all_0_0_0 = n6
% 52.10/20.08 |
% 52.10/20.08 | Equations (1249,1248) can reduce 679 to:
% 52.10/20.08 | (1106) $false
% 52.10/20.08 |
% 52.10/20.08 |-The branch is then unsatisfiable
% 52.10/20.08 |-Branch two:
% 52.10/20.08 | (1233) ~ (all_0_11_11 = n18)
% 52.10/20.08 | (1234) 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
% 52.10/20.08 |
% 52.10/20.08 +-Applying beta-rule and splitting (1234), into two cases.
% 52.10/20.08 |-Branch one:
% 52.10/20.08 | (1235) all_0_11_11 = n17
% 52.10/20.08 |
% 52.10/20.08 | From (1235) and (559) follows:
% 52.10/20.08 | (1236) pred(n17) = all_0_9_9
% 52.10/20.08 |
% 52.10/20.08 | From (1235) and (992) follows:
% 52.10/20.08 | (1237) succ(n17) = all_0_5_5
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (500) with n17, all_0_9_9, n16 and discharging atoms pred(n17) = all_0_9_9, pred(n17) = n16, yields:
% 52.10/20.08 | (1238) all_0_9_9 = n16
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (617) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 52.10/20.08 | (1239) all_0_5_5 = n18
% 52.10/20.08 |
% 52.10/20.08 | From (1238)(1239) and (538) follows:
% 52.10/20.08 | (1240) sum(n16, n18) = all_0_2_2
% 52.10/20.08 |
% 52.10/20.08 | From (1238) and (2030) follows:
% 52.10/20.08 | (2173) sum(n16, n25) = all_0_7_7
% 52.10/20.08 |
% 52.10/20.08 | From (1239) and (2028) follows:
% 52.10/20.08 | (2174) sum(n23, n18) = all_0_4_4
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (690) with n23, n18, all_0_4_4, n15 and discharging atoms sum(n23, n18) = all_0_4_4, sum(n23, n18) = n15, yields:
% 52.10/20.08 | (1261) all_0_4_4 = n15
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (690) with n16, n25, all_0_7_7, n15 and discharging atoms sum(n16, n25) = all_0_7_7, sum(n16, n25) = n15, yields:
% 52.10/20.08 | (1263) all_0_7_7 = n15
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (690) with n16, n18, all_0_2_2, n8 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = n8, yields:
% 52.10/20.08 | (1244) all_0_2_2 = n8
% 52.10/20.08 |
% 52.10/20.08 | From (1244) and (2032) follows:
% 52.10/20.08 | (2178) sum(n8, n22) = all_0_0_0
% 52.10/20.08 |
% 52.10/20.08 | From (1263)(1261) and (590) follows:
% 52.10/20.08 | (1265) sum(n15, n15) = all_0_3_3
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 52.10/20.08 | (1266) all_0_3_3 = n4
% 52.10/20.08 |
% 52.10/20.08 | Instantiating formula (690) with n8, n22, all_0_0_0, n4 and discharging atoms sum(n8, n22) = all_0_0_0, sum(n8, n22) = n4, yields:
% 52.10/20.08 | (1267) all_0_0_0 = n4
% 52.10/20.08 |
% 52.10/20.08 | Equations (1267,1266) can reduce 679 to:
% 52.10/20.08 | (1106) $false
% 52.10/20.08 |
% 52.10/20.08 |-The branch is then unsatisfiable
% 52.10/20.08 |-Branch two:
% 52.10/20.08 | (1251) ~ (all_0_11_11 = n17)
% 52.10/20.09 | (1252) 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
% 52.10/20.09 |
% 52.10/20.09 +-Applying beta-rule and splitting (1252), into two cases.
% 52.10/20.09 |-Branch one:
% 52.10/20.09 | (1253) all_0_11_11 = n16
% 52.10/20.09 |
% 52.10/20.09 | From (1253) and (559) follows:
% 52.10/20.09 | (1254) pred(n16) = all_0_9_9
% 52.10/20.09 |
% 52.10/20.09 | From (1253) and (992) follows:
% 52.10/20.09 | (1255) succ(n16) = all_0_5_5
% 52.10/20.09 |
% 52.10/20.09 | Instantiating formula (500) with n16, all_0_9_9, n15 and discharging atoms pred(n16) = all_0_9_9, pred(n16) = n15, yields:
% 52.10/20.09 | (1256) all_0_9_9 = n15
% 52.10/20.09 |
% 52.10/20.09 | Instantiating formula (617) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 52.10/20.09 | (1257) all_0_5_5 = n17
% 52.10/20.09 |
% 52.10/20.09 | From (1256)(1257) and (538) follows:
% 52.10/20.09 | (1258) sum(n15, n17) = all_0_2_2
% 52.10/20.09 |
% 52.10/20.09 | From (1256) and (2030) follows:
% 52.10/20.09 | (2191) sum(n15, n25) = all_0_7_7
% 52.10/20.09 |
% 52.10/20.09 | From (1257) and (2028) follows:
% 52.10/20.09 | (2192) sum(n23, n17) = all_0_4_4
% 52.10/20.09 |
% 52.10/20.09 | Instantiating formula (690) with n23, n17, all_0_4_4, n14 and discharging atoms sum(n23, n17) = all_0_4_4, sum(n23, n17) = n14, yields:
% 52.10/20.09 | (1279) all_0_4_4 = n14
% 52.10/20.09 |
% 52.10/20.09 | Instantiating formula (690) with n15, n25, all_0_7_7, n14 and discharging atoms sum(n15, n25) = all_0_7_7, sum(n15, n25) = n14, yields:
% 52.10/20.09 | (1281) all_0_7_7 = n14
% 52.10/20.09 |
% 52.10/20.09 | Instantiating formula (690) with n15, n17, all_0_2_2, n6 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n6, yields:
% 52.10/20.09 | (1262) all_0_2_2 = n6
% 52.10/20.09 |
% 52.10/20.09 | From (1262) and (2032) follows:
% 52.10/20.09 | (2196) sum(n6, n22) = all_0_0_0
% 52.10/20.09 |
% 52.10/20.09 | From (1281)(1279) and (590) follows:
% 52.10/20.09 | (1283) sum(n14, n14) = all_0_3_3
% 52.10/20.09 |
% 52.10/20.09 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 52.10/20.09 | (1284) all_0_3_3 = n2
% 52.10/20.09 |
% 52.10/20.09 | Instantiating formula (690) with n6, n22, all_0_0_0, n2 and discharging atoms sum(n6, n22) = all_0_0_0, sum(n6, n22) = n2, yields:
% 52.10/20.09 | (1285) all_0_0_0 = n2
% 52.10/20.09 |
% 52.10/20.09 | Equations (1285,1284) can reduce 679 to:
% 52.10/20.09 | (1106) $false
% 52.10/20.09 |
% 52.10/20.09 |-The branch is then unsatisfiable
% 52.10/20.09 |-Branch two:
% 52.10/20.09 | (1269) ~ (all_0_11_11 = n16)
% 52.10/20.09 | (1270) 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
% 52.10/20.09 |
% 52.10/20.09 +-Applying beta-rule and splitting (1270), into two cases.
% 52.10/20.09 |-Branch one:
% 52.10/20.09 | (1271) all_0_11_11 = n15
% 52.10/20.09 |
% 52.10/20.09 | From (1271) and (559) follows:
% 52.10/20.09 | (1272) pred(n15) = all_0_9_9
% 52.10/20.09 |
% 52.10/20.09 | From (1271) and (992) follows:
% 52.10/20.09 | (1273) succ(n15) = all_0_5_5
% 52.10/20.09 |
% 52.10/20.09 | Instantiating formula (500) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 52.10/20.09 | (1274) all_0_9_9 = n14
% 52.10/20.09 |
% 52.10/20.09 | Instantiating formula (617) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 52.10/20.09 | (1275) all_0_5_5 = n16
% 52.10/20.09 |
% 52.10/20.09 | From (1274)(1275) and (538) follows:
% 52.10/20.09 | (1276) sum(n14, n16) = all_0_2_2
% 52.10/20.09 |
% 52.10/20.09 | From (1274) and (2030) follows:
% 52.10/20.09 | (2209) sum(n14, n25) = all_0_7_7
% 52.10/20.09 |
% 52.10/20.09 | From (1275) and (2028) follows:
% 52.10/20.09 | (2210) sum(n23, n16) = all_0_4_4
% 52.10/20.09 |
% 52.10/20.09 | Instantiating formula (690) with n23, n16, all_0_4_4, n13 and discharging atoms sum(n23, n16) = all_0_4_4, sum(n23, n16) = n13, yields:
% 52.10/20.09 | (1297) all_0_4_4 = n13
% 52.10/20.09 |
% 52.10/20.09 | Instantiating formula (690) with n14, n25, all_0_7_7, n13 and discharging atoms sum(n14, n25) = all_0_7_7, sum(n14, n25) = n13, yields:
% 52.10/20.09 | (1299) all_0_7_7 = n13
% 52.10/20.09 |
% 52.10/20.09 | Instantiating formula (690) with n14, n16, all_0_2_2, n4 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n4, yields:
% 52.10/20.09 | (1280) all_0_2_2 = n4
% 52.10/20.09 |
% 52.10/20.09 | From (1280) and (2032) follows:
% 52.10/20.09 | (2214) sum(n4, n22) = all_0_0_0
% 52.10/20.09 |
% 52.10/20.09 | From (1299)(1297) and (590) follows:
% 52.10/20.09 | (1301) sum(n13, n13) = all_0_3_3
% 52.10/20.09 |
% 52.10/20.09 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 52.10/20.09 | (1302) all_0_3_3 = n0
% 52.10/20.09 |
% 52.10/20.09 | Instantiating formula (690) with n4, n22, all_0_0_0, n0 and discharging atoms sum(n4, n22) = all_0_0_0, sum(n4, n22) = n0, yields:
% 52.10/20.09 | (1303) all_0_0_0 = n0
% 52.10/20.09 |
% 52.10/20.09 | Equations (1303,1302) can reduce 679 to:
% 52.10/20.09 | (1106) $false
% 52.10/20.09 |
% 52.10/20.09 |-The branch is then unsatisfiable
% 52.10/20.09 |-Branch two:
% 52.10/20.09 | (1287) ~ (all_0_11_11 = n15)
% 52.10/20.09 | (1288) 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
% 52.10/20.09 |
% 52.10/20.09 +-Applying beta-rule and splitting (1288), into two cases.
% 52.10/20.09 |-Branch one:
% 52.10/20.09 | (1289) all_0_11_11 = n14
% 52.10/20.09 |
% 52.10/20.09 | From (1289) and (559) follows:
% 52.10/20.09 | (1290) pred(n14) = all_0_9_9
% 52.10/20.09 |
% 52.10/20.09 | From (1289) and (992) follows:
% 52.10/20.10 | (1291) succ(n14) = all_0_5_5
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (500) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 52.10/20.10 | (1292) all_0_9_9 = n13
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (617) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 52.10/20.10 | (1293) all_0_5_5 = n15
% 52.10/20.10 |
% 52.10/20.10 | From (1292)(1293) and (538) follows:
% 52.10/20.10 | (1294) sum(n13, n15) = all_0_2_2
% 52.10/20.10 |
% 52.10/20.10 | From (1292) and (2030) follows:
% 52.10/20.10 | (2227) sum(n13, n25) = all_0_7_7
% 52.10/20.10 |
% 52.10/20.10 | From (1293) and (2028) follows:
% 52.10/20.10 | (2228) sum(n23, n15) = all_0_4_4
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (690) with n23, n15, all_0_4_4, n12 and discharging atoms sum(n23, n15) = all_0_4_4, sum(n23, n15) = n12, yields:
% 52.10/20.10 | (1315) all_0_4_4 = n12
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (690) with n13, n25, all_0_7_7, n12 and discharging atoms sum(n13, n25) = all_0_7_7, sum(n13, n25) = n12, yields:
% 52.10/20.10 | (1317) all_0_7_7 = n12
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (690) with n13, n15, all_0_2_2, n2 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n2, yields:
% 52.10/20.10 | (1298) all_0_2_2 = n2
% 52.10/20.10 |
% 52.10/20.10 | From (1298) and (2032) follows:
% 52.10/20.10 | (2232) sum(n2, n22) = all_0_0_0
% 52.10/20.10 |
% 52.10/20.10 | From (1317)(1315) and (590) follows:
% 52.10/20.10 | (1319) sum(n12, n12) = all_0_3_3
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 52.10/20.10 | (1320) all_0_3_3 = n24
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (690) with n2, n22, all_0_0_0, n24 and discharging atoms sum(n2, n22) = all_0_0_0, sum(n2, n22) = n24, yields:
% 52.10/20.10 | (1321) all_0_0_0 = n24
% 52.10/20.10 |
% 52.10/20.10 | Equations (1321,1320) can reduce 679 to:
% 52.10/20.10 | (1106) $false
% 52.10/20.10 |
% 52.10/20.10 |-The branch is then unsatisfiable
% 52.10/20.10 |-Branch two:
% 52.10/20.10 | (1305) ~ (all_0_11_11 = n14)
% 52.10/20.10 | (1306) 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
% 52.10/20.10 |
% 52.10/20.10 +-Applying beta-rule and splitting (1306), into two cases.
% 52.10/20.10 |-Branch one:
% 52.10/20.10 | (1307) all_0_11_11 = n13
% 52.10/20.10 |
% 52.10/20.10 | From (1307) and (559) follows:
% 52.10/20.10 | (1308) pred(n13) = all_0_9_9
% 52.10/20.10 |
% 52.10/20.10 | From (1307) and (992) follows:
% 52.10/20.10 | (1309) succ(n13) = all_0_5_5
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (500) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 52.10/20.10 | (1310) all_0_9_9 = n12
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (617) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 52.10/20.10 | (1311) all_0_5_5 = n14
% 52.10/20.10 |
% 52.10/20.10 | From (1310)(1311) and (538) follows:
% 52.10/20.10 | (1312) sum(n12, n14) = all_0_2_2
% 52.10/20.10 |
% 52.10/20.10 | From (1310) and (2030) follows:
% 52.10/20.10 | (2245) sum(n12, n25) = all_0_7_7
% 52.10/20.10 |
% 52.10/20.10 | From (1311) and (2028) follows:
% 52.10/20.10 | (2246) sum(n23, n14) = all_0_4_4
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (690) with n23, n14, all_0_4_4, n11 and discharging atoms sum(n23, n14) = all_0_4_4, sum(n23, n14) = n11, yields:
% 52.10/20.10 | (1333) all_0_4_4 = n11
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (690) with n12, n25, all_0_7_7, n11 and discharging atoms sum(n12, n25) = all_0_7_7, sum(n12, n25) = n11, yields:
% 52.10/20.10 | (1335) all_0_7_7 = n11
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (690) with n12, n14, all_0_2_2, n0 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n0, yields:
% 52.10/20.10 | (1316) all_0_2_2 = n0
% 52.10/20.10 |
% 52.10/20.10 | From (1316) and (2032) follows:
% 52.10/20.10 | (2250) sum(n0, n22) = all_0_0_0
% 52.10/20.10 |
% 52.10/20.10 | From (1335)(1333) and (590) follows:
% 52.10/20.10 | (1337) sum(n11, n11) = all_0_3_3
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 52.10/20.10 | (1104) all_0_3_3 = n22
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (690) with n0, n22, all_0_0_0, n22 and discharging atoms sum(n0, n22) = all_0_0_0, sum(n0, n22) = n22, yields:
% 52.10/20.10 | (1102) all_0_0_0 = n22
% 52.10/20.10 |
% 52.10/20.10 | Equations (1102,1104) can reduce 679 to:
% 52.10/20.10 | (1106) $false
% 52.10/20.10 |
% 52.10/20.10 |-The branch is then unsatisfiable
% 52.10/20.10 |-Branch two:
% 52.10/20.10 | (1323) ~ (all_0_11_11 = n13)
% 52.10/20.10 | (1324) 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
% 52.10/20.10 |
% 52.10/20.10 +-Applying beta-rule and splitting (1324), into two cases.
% 52.10/20.10 |-Branch one:
% 52.10/20.10 | (1325) all_0_11_11 = n12
% 52.10/20.10 |
% 52.10/20.10 | From (1325) and (559) follows:
% 52.10/20.10 | (1326) pred(n12) = all_0_9_9
% 52.10/20.10 |
% 52.10/20.10 | From (1325) and (992) follows:
% 52.10/20.10 | (1327) succ(n12) = all_0_5_5
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (500) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 52.10/20.10 | (1328) all_0_9_9 = n11
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (617) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 52.10/20.10 | (1329) all_0_5_5 = n13
% 52.10/20.10 |
% 52.10/20.10 | From (1328)(1329) and (538) follows:
% 52.10/20.10 | (1330) sum(n11, n13) = all_0_2_2
% 52.10/20.10 |
% 52.10/20.10 | From (1328) and (2030) follows:
% 52.10/20.10 | (2263) sum(n11, n25) = all_0_7_7
% 52.10/20.10 |
% 52.10/20.10 | From (1329) and (2028) follows:
% 52.10/20.10 | (2264) sum(n23, n13) = all_0_4_4
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (690) with n23, n13, all_0_4_4, n10 and discharging atoms sum(n23, n13) = all_0_4_4, sum(n23, n13) = n10, yields:
% 52.10/20.10 | (1351) all_0_4_4 = n10
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (690) with n11, n25, all_0_7_7, n10 and discharging atoms sum(n11, n25) = all_0_7_7, sum(n11, n25) = n10, yields:
% 52.10/20.10 | (1353) all_0_7_7 = n10
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (690) with n11, n13, all_0_2_2, n24 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n24, yields:
% 52.10/20.10 | (1092) all_0_2_2 = n24
% 52.10/20.10 |
% 52.10/20.10 | From (1092) and (2032) follows:
% 52.10/20.10 | (1582) sum(n24, n22) = all_0_0_0
% 52.10/20.10 |
% 52.10/20.10 | From (1353)(1351) and (590) follows:
% 52.10/20.10 | (1355) sum(n10, n10) = all_0_3_3
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (690) with n24, n22, all_0_0_0, n20 and discharging atoms sum(n24, n22) = all_0_0_0, sum(n24, n22) = n20, yields:
% 52.10/20.10 | (1123) all_0_0_0 = n20
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 52.10/20.10 | (1122) all_0_3_3 = n20
% 52.10/20.10 |
% 52.10/20.10 | Equations (1123,1122) can reduce 679 to:
% 52.10/20.10 | (1106) $false
% 52.10/20.10 |
% 52.10/20.10 |-The branch is then unsatisfiable
% 52.10/20.10 |-Branch two:
% 52.10/20.10 | (1341) ~ (all_0_11_11 = n12)
% 52.10/20.10 | (1342) 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
% 52.10/20.10 |
% 52.10/20.10 +-Applying beta-rule and splitting (1342), into two cases.
% 52.10/20.10 |-Branch one:
% 52.10/20.10 | (1343) all_0_11_11 = n11
% 52.10/20.10 |
% 52.10/20.10 | From (1343) and (559) follows:
% 52.10/20.10 | (1344) pred(n11) = all_0_9_9
% 52.10/20.10 |
% 52.10/20.10 | From (1343) and (992) follows:
% 52.10/20.10 | (1345) succ(n11) = all_0_5_5
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (500) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 52.10/20.10 | (1346) all_0_9_9 = n10
% 52.10/20.10 |
% 52.10/20.10 | Instantiating formula (617) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 52.10/20.10 | (1347) all_0_5_5 = n12
% 52.10/20.10 |
% 52.10/20.10 | From (1346)(1347) and (538) follows:
% 52.10/20.10 | (1348) sum(n10, n12) = all_0_2_2
% 52.10/20.10 |
% 52.10/20.10 | From (1346) and (2030) follows:
% 52.10/20.10 | (2281) sum(n10, n25) = all_0_7_7
% 52.10/20.11 |
% 52.10/20.11 | From (1347) and (2028) follows:
% 52.10/20.11 | (2282) sum(n23, n12) = all_0_4_4
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n23, n12, all_0_4_4, n9 and discharging atoms sum(n23, n12) = all_0_4_4, sum(n23, n12) = n9, yields:
% 52.10/20.11 | (1369) all_0_4_4 = n9
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n10, n25, all_0_7_7, n9 and discharging atoms sum(n10, n25) = all_0_7_7, sum(n10, n25) = n9, yields:
% 52.10/20.11 | (1371) all_0_7_7 = n9
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n10, n12, all_0_2_2, n22 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n22, yields:
% 52.10/20.11 | (1118) all_0_2_2 = n22
% 52.10/20.11 |
% 52.10/20.11 | From (1118) and (2032) follows:
% 52.10/20.11 | (2050) sum(n22, n22) = all_0_0_0
% 52.10/20.11 |
% 52.10/20.11 | From (1371)(1369) and (590) follows:
% 52.10/20.11 | (1373) sum(n9, n9) = all_0_3_3
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n22, n22, all_0_0_0, n18 and discharging atoms sum(n22, n22) = all_0_0_0, sum(n22, n22) = n18, yields:
% 52.10/20.11 | (1141) all_0_0_0 = n18
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 52.10/20.11 | (1140) all_0_3_3 = n18
% 52.10/20.11 |
% 52.10/20.11 | Equations (1141,1140) can reduce 679 to:
% 52.10/20.11 | (1106) $false
% 52.10/20.11 |
% 52.10/20.11 |-The branch is then unsatisfiable
% 52.10/20.11 |-Branch two:
% 52.10/20.11 | (1359) ~ (all_0_11_11 = n11)
% 52.10/20.11 | (1360) 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
% 52.10/20.11 |
% 52.10/20.11 +-Applying beta-rule and splitting (1360), into two cases.
% 52.10/20.11 |-Branch one:
% 52.10/20.11 | (1361) all_0_11_11 = n10
% 52.10/20.11 |
% 52.10/20.11 | From (1361) and (559) follows:
% 52.10/20.11 | (1362) pred(n10) = all_0_9_9
% 52.10/20.11 |
% 52.10/20.11 | From (1361) and (992) follows:
% 52.10/20.11 | (1363) succ(n10) = all_0_5_5
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (500) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 52.10/20.11 | (1364) all_0_9_9 = n9
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (617) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 52.10/20.11 | (1365) all_0_5_5 = n11
% 52.10/20.11 |
% 52.10/20.11 | From (1364)(1365) and (538) follows:
% 52.10/20.11 | (1366) sum(n9, n11) = all_0_2_2
% 52.10/20.11 |
% 52.10/20.11 | From (1364) and (2030) follows:
% 52.10/20.11 | (2299) sum(n9, n25) = all_0_7_7
% 52.10/20.11 |
% 52.10/20.11 | From (1365) and (2028) follows:
% 52.10/20.11 | (2300) sum(n23, n11) = all_0_4_4
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n23, n11, all_0_4_4, n8 and discharging atoms sum(n23, n11) = all_0_4_4, sum(n23, n11) = n8, yields:
% 52.10/20.11 | (1387) all_0_4_4 = n8
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n9, n25, all_0_7_7, n8 and discharging atoms sum(n9, n25) = all_0_7_7, sum(n9, n25) = n8, yields:
% 52.10/20.11 | (1389) all_0_7_7 = n8
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 52.10/20.11 | (1136) all_0_2_2 = n20
% 52.10/20.11 |
% 52.10/20.11 | From (1136) and (2032) follows:
% 52.10/20.11 | (2070) sum(n20, n22) = all_0_0_0
% 52.10/20.11 |
% 52.10/20.11 | From (1389)(1387) and (590) follows:
% 52.10/20.11 | (1391) sum(n8, n8) = all_0_3_3
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n20, n22, all_0_0_0, n16 and discharging atoms sum(n20, n22) = all_0_0_0, sum(n20, n22) = n16, yields:
% 52.10/20.11 | (1159) all_0_0_0 = n16
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 52.10/20.11 | (1158) all_0_3_3 = n16
% 52.10/20.11 |
% 52.10/20.11 | Equations (1159,1158) can reduce 679 to:
% 52.10/20.11 | (1106) $false
% 52.10/20.11 |
% 52.10/20.11 |-The branch is then unsatisfiable
% 52.10/20.11 |-Branch two:
% 52.10/20.11 | (1377) ~ (all_0_11_11 = n10)
% 52.10/20.11 | (1378) 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
% 52.10/20.11 |
% 52.10/20.11 +-Applying beta-rule and splitting (1378), into two cases.
% 52.10/20.11 |-Branch one:
% 52.10/20.11 | (1379) all_0_11_11 = n9
% 52.10/20.11 |
% 52.10/20.11 | From (1379) and (559) follows:
% 52.10/20.11 | (1380) pred(n9) = all_0_9_9
% 52.10/20.11 |
% 52.10/20.11 | From (1379) and (992) follows:
% 52.10/20.11 | (1381) succ(n9) = all_0_5_5
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 52.10/20.11 | (1382) all_0_9_9 = n8
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 52.10/20.11 | (1383) all_0_5_5 = n10
% 52.10/20.11 |
% 52.10/20.11 | From (1382)(1383) and (538) follows:
% 52.10/20.11 | (1384) sum(n8, n10) = all_0_2_2
% 52.10/20.11 |
% 52.10/20.11 | From (1382) and (2030) follows:
% 52.10/20.11 | (2317) sum(n8, n25) = all_0_7_7
% 52.10/20.11 |
% 52.10/20.11 | From (1383) and (2028) follows:
% 52.10/20.11 | (2318) sum(n23, n10) = all_0_4_4
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n23, n10, all_0_4_4, n7 and discharging atoms sum(n23, n10) = all_0_4_4, sum(n23, n10) = n7, yields:
% 52.10/20.11 | (1405) all_0_4_4 = n7
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n8, n25, all_0_7_7, n7 and discharging atoms sum(n8, n25) = all_0_7_7, sum(n8, n25) = n7, yields:
% 52.10/20.11 | (1407) all_0_7_7 = n7
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 52.10/20.11 | (1154) all_0_2_2 = n18
% 52.10/20.11 |
% 52.10/20.11 | From (1154) and (2032) follows:
% 52.10/20.11 | (2088) sum(n18, n22) = all_0_0_0
% 52.10/20.11 |
% 52.10/20.11 | From (1407)(1405) and (590) follows:
% 52.10/20.11 | (1409) sum(n7, n7) = all_0_3_3
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n18, n22, all_0_0_0, n14 and discharging atoms sum(n18, n22) = all_0_0_0, sum(n18, n22) = n14, yields:
% 52.10/20.11 | (1177) all_0_0_0 = n14
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 52.10/20.11 | (1176) all_0_3_3 = n14
% 52.10/20.11 |
% 52.10/20.11 | Equations (1177,1176) can reduce 679 to:
% 52.10/20.11 | (1106) $false
% 52.10/20.11 |
% 52.10/20.11 |-The branch is then unsatisfiable
% 52.10/20.11 |-Branch two:
% 52.10/20.11 | (1395) ~ (all_0_11_11 = n9)
% 52.10/20.11 | (1396) 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
% 52.10/20.11 |
% 52.10/20.11 +-Applying beta-rule and splitting (1396), into two cases.
% 52.10/20.11 |-Branch one:
% 52.10/20.11 | (1397) all_0_11_11 = n8
% 52.10/20.11 |
% 52.10/20.11 | From (1397) and (559) follows:
% 52.10/20.11 | (1398) pred(n8) = all_0_9_9
% 52.10/20.11 |
% 52.10/20.11 | From (1397) and (992) follows:
% 52.10/20.11 | (1399) succ(n8) = all_0_5_5
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 52.10/20.11 | (1400) all_0_9_9 = n7
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 52.10/20.11 | (1401) all_0_5_5 = n9
% 52.10/20.11 |
% 52.10/20.11 | From (1400)(1401) and (538) follows:
% 52.10/20.11 | (1402) sum(n7, n9) = all_0_2_2
% 52.10/20.11 |
% 52.10/20.11 | From (1400) and (2030) follows:
% 52.10/20.11 | (2335) sum(n7, n25) = all_0_7_7
% 52.10/20.11 |
% 52.10/20.11 | From (1401) and (2028) follows:
% 52.10/20.11 | (2336) sum(n23, n9) = all_0_4_4
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n23, n9, all_0_4_4, n6 and discharging atoms sum(n23, n9) = all_0_4_4, sum(n23, n9) = n6, yields:
% 52.10/20.11 | (1423) all_0_4_4 = n6
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n7, n25, all_0_7_7, n6 and discharging atoms sum(n7, n25) = all_0_7_7, sum(n7, n25) = n6, yields:
% 52.10/20.11 | (1425) all_0_7_7 = n6
% 52.10/20.11 |
% 52.10/20.11 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 52.10/20.11 | (1172) all_0_2_2 = n16
% 52.10/20.11 |
% 52.10/20.11 | From (1172) and (2032) follows:
% 52.10/20.11 | (2106) sum(n16, n22) = all_0_0_0
% 52.10/20.11 |
% 52.10/20.11 | From (1425)(1423) and (590) follows:
% 52.10/20.12 | (1427) sum(n6, n6) = all_0_3_3
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (690) with n16, n22, all_0_0_0, n12 and discharging atoms sum(n16, n22) = all_0_0_0, sum(n16, n22) = n12, yields:
% 52.10/20.12 | (1195) all_0_0_0 = n12
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 52.10/20.12 | (1194) all_0_3_3 = n12
% 52.10/20.12 |
% 52.10/20.12 | Equations (1195,1194) can reduce 679 to:
% 52.10/20.12 | (1106) $false
% 52.10/20.12 |
% 52.10/20.12 |-The branch is then unsatisfiable
% 52.10/20.12 |-Branch two:
% 52.10/20.12 | (1413) ~ (all_0_11_11 = n8)
% 52.10/20.12 | (1414) 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
% 52.10/20.12 |
% 52.10/20.12 +-Applying beta-rule and splitting (1414), into two cases.
% 52.10/20.12 |-Branch one:
% 52.10/20.12 | (1415) all_0_11_11 = n7
% 52.10/20.12 |
% 52.10/20.12 | From (1415) and (559) follows:
% 52.10/20.12 | (1416) pred(n7) = all_0_9_9
% 52.10/20.12 |
% 52.10/20.12 | From (1415) and (992) follows:
% 52.10/20.12 | (1417) succ(n7) = all_0_5_5
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 52.10/20.12 | (1418) all_0_9_9 = n6
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 52.10/20.12 | (1419) all_0_5_5 = n8
% 52.10/20.12 |
% 52.10/20.12 | From (1418)(1419) and (538) follows:
% 52.10/20.12 | (1420) sum(n6, n8) = all_0_2_2
% 52.10/20.12 |
% 52.10/20.12 | From (1418) and (2030) follows:
% 52.10/20.12 | (2353) sum(n6, n25) = all_0_7_7
% 52.10/20.12 |
% 52.10/20.12 | From (1419) and (2028) follows:
% 52.10/20.12 | (2354) sum(n23, n8) = all_0_4_4
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (690) with n23, n8, all_0_4_4, n5 and discharging atoms sum(n23, n8) = all_0_4_4, sum(n23, n8) = n5, yields:
% 52.10/20.12 | (1441) all_0_4_4 = n5
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (690) with n6, n25, all_0_7_7, n5 and discharging atoms sum(n6, n25) = all_0_7_7, sum(n6, n25) = n5, yields:
% 52.10/20.12 | (1443) all_0_7_7 = n5
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 52.10/20.12 | (1190) all_0_2_2 = n14
% 52.10/20.12 |
% 52.10/20.12 | From (1190) and (2032) follows:
% 52.10/20.12 | (2124) sum(n14, n22) = all_0_0_0
% 52.10/20.12 |
% 52.10/20.12 | From (1443)(1441) and (590) follows:
% 52.10/20.12 | (1445) sum(n5, n5) = all_0_3_3
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (690) with n14, n22, all_0_0_0, n10 and discharging atoms sum(n14, n22) = all_0_0_0, sum(n14, n22) = n10, yields:
% 52.10/20.12 | (1213) all_0_0_0 = n10
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 52.10/20.12 | (1212) all_0_3_3 = n10
% 52.10/20.12 |
% 52.10/20.12 | Equations (1213,1212) can reduce 679 to:
% 52.10/20.12 | (1106) $false
% 52.10/20.12 |
% 52.10/20.12 |-The branch is then unsatisfiable
% 52.10/20.12 |-Branch two:
% 52.10/20.12 | (1431) ~ (all_0_11_11 = n7)
% 52.10/20.12 | (1432) 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
% 52.10/20.12 |
% 52.10/20.12 +-Applying beta-rule and splitting (1432), into two cases.
% 52.10/20.12 |-Branch one:
% 52.10/20.12 | (1433) all_0_11_11 = n6
% 52.10/20.12 |
% 52.10/20.12 | From (1433) and (559) follows:
% 52.10/20.12 | (1434) pred(n6) = all_0_9_9
% 52.10/20.12 |
% 52.10/20.12 | From (1433) and (992) follows:
% 52.10/20.12 | (1435) succ(n6) = all_0_5_5
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 52.10/20.12 | (1436) all_0_9_9 = n5
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 52.10/20.12 | (1437) all_0_5_5 = n7
% 52.10/20.12 |
% 52.10/20.12 | From (1436)(1437) and (538) follows:
% 52.10/20.12 | (1438) sum(n5, n7) = all_0_2_2
% 52.10/20.12 |
% 52.10/20.12 | From (1436) and (2030) follows:
% 52.10/20.12 | (2371) sum(n5, n25) = all_0_7_7
% 52.10/20.12 |
% 52.10/20.12 | From (1437) and (2028) follows:
% 52.10/20.12 | (2372) sum(n23, n7) = all_0_4_4
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (690) with n23, n7, all_0_4_4, n4 and discharging atoms sum(n23, n7) = all_0_4_4, sum(n23, n7) = n4, yields:
% 52.10/20.12 | (1459) all_0_4_4 = n4
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (690) with n5, n25, all_0_7_7, n4 and discharging atoms sum(n5, n25) = all_0_7_7, sum(n5, n25) = n4, yields:
% 52.10/20.12 | (1461) all_0_7_7 = n4
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 52.10/20.12 | (1208) all_0_2_2 = n12
% 52.10/20.12 |
% 52.10/20.12 | From (1208) and (2032) follows:
% 52.10/20.12 | (2142) sum(n12, n22) = all_0_0_0
% 52.10/20.12 |
% 52.10/20.12 | From (1461)(1459) and (590) follows:
% 52.10/20.12 | (1463) sum(n4, n4) = all_0_3_3
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (690) with n12, n22, all_0_0_0, n8 and discharging atoms sum(n12, n22) = all_0_0_0, sum(n12, n22) = n8, yields:
% 52.10/20.12 | (1231) all_0_0_0 = n8
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 52.10/20.12 | (1230) all_0_3_3 = n8
% 52.10/20.12 |
% 52.10/20.12 | Equations (1231,1230) can reduce 679 to:
% 52.10/20.12 | (1106) $false
% 52.10/20.12 |
% 52.10/20.12 |-The branch is then unsatisfiable
% 52.10/20.12 |-Branch two:
% 52.10/20.12 | (1449) ~ (all_0_11_11 = n6)
% 52.10/20.12 | (1450) 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
% 52.10/20.12 |
% 52.10/20.12 +-Applying beta-rule and splitting (1450), into two cases.
% 52.10/20.12 |-Branch one:
% 52.10/20.12 | (1451) all_0_11_11 = n5
% 52.10/20.12 |
% 52.10/20.12 | From (1451) and (559) follows:
% 52.10/20.12 | (1452) pred(n5) = all_0_9_9
% 52.10/20.12 |
% 52.10/20.12 | From (1451) and (992) follows:
% 52.10/20.12 | (1453) succ(n5) = all_0_5_5
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 52.10/20.12 | (1454) all_0_9_9 = n4
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 52.10/20.12 | (1455) all_0_5_5 = n6
% 52.10/20.12 |
% 52.10/20.12 | From (1454)(1455) and (538) follows:
% 52.10/20.12 | (1456) sum(n4, n6) = all_0_2_2
% 52.10/20.12 |
% 52.10/20.12 | From (1454) and (2030) follows:
% 52.10/20.12 | (2389) sum(n4, n25) = all_0_7_7
% 52.10/20.12 |
% 52.10/20.12 | From (1455) and (2028) follows:
% 52.10/20.12 | (2390) sum(n23, n6) = all_0_4_4
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (690) with n23, n6, all_0_4_4, n3 and discharging atoms sum(n23, n6) = all_0_4_4, sum(n23, n6) = n3, yields:
% 52.10/20.12 | (1477) all_0_4_4 = n3
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (690) with n4, n25, all_0_7_7, n3 and discharging atoms sum(n4, n25) = all_0_7_7, sum(n4, n25) = n3, yields:
% 52.10/20.12 | (1479) all_0_7_7 = n3
% 52.10/20.12 |
% 52.10/20.12 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 52.10/20.12 | (1226) all_0_2_2 = n10
% 52.10/20.12 |
% 52.10/20.12 | From (1226) and (2032) follows:
% 52.48/20.12 | (2160) sum(n10, n22) = all_0_0_0
% 52.48/20.12 |
% 52.48/20.12 | From (1479)(1477) and (590) follows:
% 52.48/20.12 | (1481) sum(n3, n3) = all_0_3_3
% 52.48/20.12 |
% 52.48/20.12 | Instantiating formula (690) with n10, n22, all_0_0_0, n6 and discharging atoms sum(n10, n22) = all_0_0_0, sum(n10, n22) = n6, yields:
% 52.48/20.12 | (1249) all_0_0_0 = n6
% 52.48/20.12 |
% 52.48/20.12 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 52.48/20.12 | (1248) all_0_3_3 = n6
% 52.48/20.12 |
% 52.48/20.12 | Equations (1249,1248) can reduce 679 to:
% 52.48/20.12 | (1106) $false
% 52.48/20.12 |
% 52.48/20.12 |-The branch is then unsatisfiable
% 52.48/20.12 |-Branch two:
% 52.48/20.12 | (1467) ~ (all_0_11_11 = n5)
% 52.48/20.12 | (1468) 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
% 52.48/20.12 |
% 52.48/20.12 +-Applying beta-rule and splitting (1468), into two cases.
% 52.48/20.12 |-Branch one:
% 52.48/20.12 | (1469) all_0_11_11 = n4
% 52.48/20.12 |
% 52.48/20.12 | From (1469) and (559) follows:
% 52.48/20.12 | (1470) pred(n4) = all_0_9_9
% 52.48/20.12 |
% 52.48/20.12 | From (1469) and (992) follows:
% 52.48/20.12 | (1471) succ(n4) = all_0_5_5
% 52.48/20.12 |
% 52.48/20.12 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 52.48/20.13 | (1472) all_0_9_9 = n3
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 52.48/20.13 | (1473) all_0_5_5 = n5
% 52.48/20.13 |
% 52.48/20.13 | From (1472)(1473) and (538) follows:
% 52.48/20.13 | (1474) sum(n3, n5) = all_0_2_2
% 52.48/20.13 |
% 52.48/20.13 | From (1472) and (2030) follows:
% 52.48/20.13 | (2407) sum(n3, n25) = all_0_7_7
% 52.48/20.13 |
% 52.48/20.13 | From (1473) and (2028) follows:
% 52.48/20.13 | (2408) sum(n23, n5) = all_0_4_4
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (690) with n23, n5, all_0_4_4, n2 and discharging atoms sum(n23, n5) = all_0_4_4, sum(n23, n5) = n2, yields:
% 52.48/20.13 | (1495) all_0_4_4 = n2
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (690) with n3, n25, all_0_7_7, n2 and discharging atoms sum(n3, n25) = all_0_7_7, sum(n3, n25) = n2, yields:
% 52.48/20.13 | (1497) all_0_7_7 = n2
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 52.48/20.13 | (1244) all_0_2_2 = n8
% 52.48/20.13 |
% 52.48/20.13 | From (1244) and (2032) follows:
% 52.48/20.13 | (2178) sum(n8, n22) = all_0_0_0
% 52.48/20.13 |
% 52.48/20.13 | From (1497)(1495) and (590) follows:
% 52.48/20.13 | (1499) sum(n2, n2) = all_0_3_3
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (690) with n8, n22, all_0_0_0, n4 and discharging atoms sum(n8, n22) = all_0_0_0, sum(n8, n22) = n4, yields:
% 52.48/20.13 | (1267) all_0_0_0 = n4
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 52.48/20.13 | (1266) all_0_3_3 = n4
% 52.48/20.13 |
% 52.48/20.13 | Equations (1267,1266) can reduce 679 to:
% 52.48/20.13 | (1106) $false
% 52.48/20.13 |
% 52.48/20.13 |-The branch is then unsatisfiable
% 52.48/20.13 |-Branch two:
% 52.48/20.13 | (1485) ~ (all_0_11_11 = n4)
% 52.48/20.13 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 52.48/20.13 |
% 52.48/20.13 +-Applying beta-rule and splitting (1486), into two cases.
% 52.48/20.13 |-Branch one:
% 52.48/20.13 | (1487) all_0_11_11 = n3
% 52.48/20.13 |
% 52.48/20.13 | From (1487) and (559) follows:
% 52.48/20.13 | (1488) pred(n3) = all_0_9_9
% 52.48/20.13 |
% 52.48/20.13 | From (1487) and (992) follows:
% 52.48/20.13 | (1489) succ(n3) = all_0_5_5
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 52.48/20.13 | (1490) all_0_9_9 = n2
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 52.48/20.13 | (1491) all_0_5_5 = n4
% 52.48/20.13 |
% 52.48/20.13 | From (1490)(1491) and (538) follows:
% 52.48/20.13 | (1492) sum(n2, n4) = all_0_2_2
% 52.48/20.13 |
% 52.48/20.13 | From (1490) and (2030) follows:
% 52.48/20.13 | (2425) sum(n2, n25) = all_0_7_7
% 52.48/20.13 |
% 52.48/20.13 | From (1491) and (2028) follows:
% 52.48/20.13 | (2426) sum(n23, n4) = all_0_4_4
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (690) with n23, n4, all_0_4_4, n1 and discharging atoms sum(n23, n4) = all_0_4_4, sum(n23, n4) = n1, yields:
% 52.48/20.13 | (1513) all_0_4_4 = n1
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (690) with n2, n25, all_0_7_7, n1 and discharging atoms sum(n2, n25) = all_0_7_7, sum(n2, n25) = n1, yields:
% 52.48/20.13 | (1515) all_0_7_7 = n1
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 52.48/20.13 | (1262) all_0_2_2 = n6
% 52.48/20.13 |
% 52.48/20.13 | From (1262) and (2032) follows:
% 52.48/20.13 | (2196) sum(n6, n22) = all_0_0_0
% 52.48/20.13 |
% 52.48/20.13 | From (1515)(1513) and (590) follows:
% 52.48/20.13 | (1517) sum(n1, n1) = all_0_3_3
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (690) with n6, n22, all_0_0_0, n2 and discharging atoms sum(n6, n22) = all_0_0_0, sum(n6, n22) = n2, yields:
% 52.48/20.13 | (1285) all_0_0_0 = n2
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 52.48/20.13 | (1284) all_0_3_3 = n2
% 52.48/20.13 |
% 52.48/20.13 | Equations (1285,1284) can reduce 679 to:
% 52.48/20.13 | (1106) $false
% 52.48/20.13 |
% 52.48/20.13 |-The branch is then unsatisfiable
% 52.48/20.13 |-Branch two:
% 52.48/20.13 | (1503) ~ (all_0_11_11 = n3)
% 52.48/20.13 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 52.48/20.13 |
% 52.48/20.13 +-Applying beta-rule and splitting (1504), into two cases.
% 52.48/20.13 |-Branch one:
% 52.48/20.13 | (1505) all_0_11_11 = n2
% 52.48/20.13 |
% 52.48/20.13 | From (1505) and (559) follows:
% 52.48/20.13 | (1506) pred(n2) = all_0_9_9
% 52.48/20.13 |
% 52.48/20.13 | From (1505) and (992) follows:
% 52.48/20.13 | (1507) succ(n2) = all_0_5_5
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 52.48/20.13 | (1508) all_0_9_9 = n1
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 52.48/20.13 | (1509) all_0_5_5 = n3
% 52.48/20.13 |
% 52.48/20.13 | From (1508)(1509) and (538) follows:
% 52.48/20.13 | (1510) sum(n1, n3) = all_0_2_2
% 52.48/20.13 |
% 52.48/20.13 | From (1508) and (2030) follows:
% 52.48/20.13 | (2443) sum(n1, n25) = all_0_7_7
% 52.48/20.13 |
% 52.48/20.13 | From (1509) and (2028) follows:
% 52.48/20.13 | (2444) sum(n23, n3) = all_0_4_4
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (690) with n23, n3, all_0_4_4, n0 and discharging atoms sum(n23, n3) = all_0_4_4, sum(n23, n3) = n0, yields:
% 52.48/20.13 | (1531) all_0_4_4 = n0
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (690) with n1, n25, all_0_7_7, n0 and discharging atoms sum(n1, n25) = all_0_7_7, sum(n1, n25) = n0, yields:
% 52.48/20.13 | (1533) all_0_7_7 = n0
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 52.48/20.13 | (1280) all_0_2_2 = n4
% 52.48/20.13 |
% 52.48/20.13 | From (1280) and (2032) follows:
% 52.48/20.13 | (2214) sum(n4, n22) = all_0_0_0
% 52.48/20.13 |
% 52.48/20.13 | From (1533)(1531) and (590) follows:
% 52.48/20.13 | (1535) sum(n0, n0) = all_0_3_3
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (690) with n4, n22, all_0_0_0, n0 and discharging atoms sum(n4, n22) = all_0_0_0, sum(n4, n22) = n0, yields:
% 52.48/20.13 | (1303) all_0_0_0 = n0
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 52.48/20.13 | (1302) all_0_3_3 = n0
% 52.48/20.13 |
% 52.48/20.13 | Equations (1303,1302) can reduce 679 to:
% 52.48/20.13 | (1106) $false
% 52.48/20.13 |
% 52.48/20.13 |-The branch is then unsatisfiable
% 52.48/20.13 |-Branch two:
% 52.48/20.13 | (1521) ~ (all_0_11_11 = n2)
% 52.48/20.13 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 52.48/20.13 |
% 52.48/20.13 +-Applying beta-rule and splitting (1522), into two cases.
% 52.48/20.13 |-Branch one:
% 52.48/20.13 | (1523) all_0_11_11 = n1
% 52.48/20.13 |
% 52.48/20.13 | From (1523) and (559) follows:
% 52.48/20.13 | (1524) pred(n1) = all_0_9_9
% 52.48/20.13 |
% 52.48/20.13 | From (1523) and (992) follows:
% 52.48/20.13 | (1525) succ(n1) = all_0_5_5
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 52.48/20.13 | (1526) all_0_9_9 = n0
% 52.48/20.13 |
% 52.48/20.13 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 52.48/20.13 | (1527) all_0_5_5 = n2
% 52.48/20.13 |
% 52.48/20.13 | From (1526)(1527) and (538) follows:
% 52.48/20.13 | (1528) sum(n0, n2) = all_0_2_2
% 52.48/20.13 |
% 52.48/20.13 | From (1526) and (2030) follows:
% 52.48/20.13 | (2461) sum(n0, n25) = all_0_7_7
% 52.48/20.13 |
% 52.48/20.13 | From (1527) and (2028) follows:
% 52.48/20.14 | (2462) sum(n23, n2) = all_0_4_4
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (690) with n23, n2, all_0_4_4, n25 and discharging atoms sum(n23, n2) = all_0_4_4, sum(n23, n2) = n25, yields:
% 52.48/20.14 | (1551) all_0_4_4 = n25
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (690) with n0, n25, all_0_7_7, n25 and discharging atoms sum(n0, n25) = all_0_7_7, sum(n0, n25) = n25, yields:
% 52.48/20.14 | (1550) all_0_7_7 = n25
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 52.48/20.14 | (1298) all_0_2_2 = n2
% 52.48/20.14 |
% 52.48/20.14 | From (1298) and (2032) follows:
% 52.48/20.14 | (2232) sum(n2, n22) = all_0_0_0
% 52.48/20.14 |
% 52.48/20.14 | From (1550)(1551) and (590) follows:
% 52.48/20.14 | (1553) sum(n25, n25) = all_0_3_3
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 52.48/20.14 | (1320) all_0_3_3 = n24
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (690) with n2, n22, all_0_0_0, n24 and discharging atoms sum(n2, n22) = all_0_0_0, sum(n2, n22) = n24, yields:
% 52.48/20.14 | (1321) all_0_0_0 = n24
% 52.48/20.14 |
% 52.48/20.14 | Equations (1321,1320) can reduce 679 to:
% 52.48/20.14 | (1106) $false
% 52.48/20.14 |
% 52.48/20.14 |-The branch is then unsatisfiable
% 52.48/20.14 |-Branch two:
% 52.48/20.14 | (1540) ~ (all_0_11_11 = n1)
% 52.48/20.14 | (1541) all_0_11_11 = n0
% 52.48/20.14 |
% 52.48/20.14 | From (1541) and (559) follows:
% 52.48/20.14 | (1542) pred(n0) = all_0_9_9
% 52.48/20.14 |
% 52.48/20.14 | From (1541) and (992) follows:
% 52.48/20.14 | (1543) succ(n0) = all_0_5_5
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 52.48/20.14 | (1544) all_0_9_9 = n25
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 52.48/20.14 | (1545) all_0_5_5 = n1
% 52.48/20.14 |
% 52.48/20.14 | From (1544)(1545) and (538) follows:
% 52.48/20.14 | (1546) sum(n25, n1) = all_0_2_2
% 52.48/20.14 |
% 52.48/20.14 | From (1544) and (2030) follows:
% 52.48/20.14 | (2478) sum(n25, n25) = all_0_7_7
% 52.48/20.14 |
% 52.48/20.14 | From (1545) and (2028) follows:
% 52.48/20.14 | (2479) sum(n23, n1) = all_0_4_4
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (690) with n25, n25, all_0_7_7, n24 and discharging atoms sum(n25, n25) = all_0_7_7, sum(n25, n25) = n24, yields:
% 52.48/20.14 | (1097) all_0_7_7 = n24
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 52.48/20.14 | (1316) all_0_2_2 = n0
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (690) with n23, n1, all_0_4_4, n24 and discharging atoms sum(n23, n1) = all_0_4_4, sum(n23, n1) = n24, yields:
% 52.48/20.14 | (1096) all_0_4_4 = n24
% 52.48/20.14 |
% 52.48/20.14 | From (1316) and (2032) follows:
% 52.48/20.14 | (2250) sum(n0, n22) = all_0_0_0
% 52.48/20.14 |
% 52.48/20.14 | From (1097)(1096) and (590) follows:
% 52.48/20.14 | (1101) sum(n24, n24) = all_0_3_3
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 52.48/20.14 | (1104) all_0_3_3 = n22
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (690) with n0, n22, all_0_0_0, n22 and discharging atoms sum(n0, n22) = all_0_0_0, sum(n0, n22) = n22, yields:
% 52.48/20.14 | (1102) all_0_0_0 = n22
% 52.48/20.14 |
% 52.48/20.14 | Equations (1102,1104) can reduce 679 to:
% 52.48/20.14 | (1106) $false
% 52.48/20.14 |
% 52.48/20.14 |-The branch is then unsatisfiable
% 52.48/20.14 |-Branch two:
% 52.48/20.14 | (1586) ~ (all_0_10_10 = n24)
% 52.48/20.14 | (1587) all_0_10_10 = n23 | all_0_10_10 = n22 | all_0_10_10 = n21 | 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
% 52.48/20.14 |
% 52.48/20.14 +-Applying beta-rule and splitting (1108), into two cases.
% 52.48/20.14 |-Branch one:
% 52.48/20.14 | (1109) all_0_11_11 = n24
% 52.48/20.14 |
% 52.48/20.14 | From (1109) and (559) follows:
% 52.48/20.14 | (1110) pred(n24) = all_0_9_9
% 52.48/20.14 |
% 52.48/20.14 | From (1109) and (992) follows:
% 52.48/20.14 | (1111) succ(n24) = all_0_5_5
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (500) with n24, all_0_9_9, n23 and discharging atoms pred(n24) = all_0_9_9, pred(n24) = n23, yields:
% 52.48/20.14 | (1112) all_0_9_9 = n23
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (617) with n24, all_0_5_5, n25 and discharging atoms succ(n24) = all_0_5_5, succ(n24) = n25, yields:
% 52.48/20.14 | (1113) all_0_5_5 = n25
% 52.48/20.14 |
% 52.48/20.14 | From (1113) and (541) follows:
% 52.48/20.14 | (2495) sum(all_0_6_6, n25) = all_0_4_4
% 52.48/20.14 |
% 52.48/20.14 | From (1112)(1113) and (538) follows:
% 52.48/20.14 | (1114) sum(n23, n25) = all_0_2_2
% 52.48/20.14 |
% 52.48/20.14 | From (1112) and (427) follows:
% 52.48/20.14 | (2497) sum(n23, all_0_8_8) = all_0_7_7
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (690) with n23, n25, all_0_2_2, n22 and discharging atoms sum(n23, n25) = all_0_2_2, sum(n23, n25) = n22, yields:
% 52.48/20.14 | (1118) all_0_2_2 = n22
% 52.48/20.14 |
% 52.48/20.14 | From (1118) and (630) follows:
% 52.48/20.14 | (2499) sum(n22, all_0_1_1) = all_0_0_0
% 52.48/20.14 |
% 52.48/20.14 +-Applying beta-rule and splitting (1587), into two cases.
% 52.48/20.14 |-Branch one:
% 52.48/20.14 | (1588) all_0_10_10 = n23
% 52.48/20.14 |
% 52.48/20.14 | From (1588) and (292) follows:
% 52.48/20.14 | (1589) pred(n23) = all_0_6_6
% 52.48/20.14 |
% 52.48/20.14 | From (1588) and (760) follows:
% 52.48/20.14 | (1590) succ(n23) = all_0_8_8
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (500) with n23, all_0_6_6, n22 and discharging atoms pred(n23) = all_0_6_6, pred(n23) = n22, yields:
% 52.48/20.14 | (1591) all_0_6_6 = n22
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (617) with n23, all_0_8_8, n24 and discharging atoms succ(n23) = all_0_8_8, succ(n23) = n24, yields:
% 52.48/20.14 | (1592) all_0_8_8 = n24
% 52.48/20.14 |
% 52.48/20.14 | From (1591)(1592) and (411) follows:
% 52.48/20.14 | (1593) sum(n22, n24) = all_0_1_1
% 52.48/20.14 |
% 52.48/20.14 | From (1591) and (2495) follows:
% 52.48/20.14 | (2506) sum(n22, n25) = all_0_4_4
% 52.48/20.14 |
% 52.48/20.14 | From (1592) and (2497) follows:
% 52.48/20.14 | (2507) sum(n23, n24) = all_0_7_7
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (690) with n23, n24, all_0_7_7, n21 and discharging atoms sum(n23, n24) = all_0_7_7, sum(n23, n24) = n21, yields:
% 52.48/20.14 | (1155) all_0_7_7 = n21
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (690) with n22, n25, all_0_4_4, n21 and discharging atoms sum(n22, n25) = all_0_4_4, sum(n22, n25) = n21, yields:
% 52.48/20.14 | (1153) all_0_4_4 = n21
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (690) with n22, n24, all_0_1_1, n20 and discharging atoms sum(n22, n24) = all_0_1_1, sum(n22, n24) = n20, yields:
% 52.48/20.14 | (1597) all_0_1_1 = n20
% 52.48/20.14 |
% 52.48/20.14 | From (1155)(1153) and (590) follows:
% 52.48/20.14 | (1157) sum(n21, n21) = all_0_3_3
% 52.48/20.14 |
% 52.48/20.14 | From (1597) and (2499) follows:
% 52.48/20.14 | (2512) sum(n22, n20) = all_0_0_0
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (690) with n22, n20, all_0_0_0, n16 and discharging atoms sum(n22, n20) = all_0_0_0, sum(n22, n20) = n16, yields:
% 52.48/20.14 | (1159) all_0_0_0 = n16
% 52.48/20.14 |
% 52.48/20.14 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 52.48/20.14 | (1158) all_0_3_3 = n16
% 52.48/20.14 |
% 52.48/20.14 | Equations (1159,1158) can reduce 679 to:
% 52.48/20.14 | (1106) $false
% 52.48/20.14 |
% 52.48/20.14 |-The branch is then unsatisfiable
% 52.48/20.14 |-Branch two:
% 52.48/20.14 | (1604) ~ (all_0_10_10 = n23)
% 52.48/20.15 | (1605) all_0_10_10 = n22 | all_0_10_10 = n21 | 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
% 52.48/20.15 |
% 52.48/20.15 +-Applying beta-rule and splitting (1605), into two cases.
% 52.48/20.15 |-Branch one:
% 52.48/20.15 | (1606) all_0_10_10 = n22
% 52.48/20.15 |
% 52.48/20.15 | From (1606) and (292) follows:
% 52.48/20.15 | (1607) pred(n22) = all_0_6_6
% 52.48/20.15 |
% 52.48/20.15 | From (1606) and (760) follows:
% 52.48/20.15 | (1608) succ(n22) = all_0_8_8
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (500) with n22, all_0_6_6, n21 and discharging atoms pred(n22) = all_0_6_6, pred(n22) = n21, yields:
% 52.48/20.15 | (1609) all_0_6_6 = n21
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (617) with n22, all_0_8_8, n23 and discharging atoms succ(n22) = all_0_8_8, succ(n22) = n23, yields:
% 52.48/20.15 | (1610) all_0_8_8 = n23
% 52.48/20.15 |
% 52.48/20.15 | From (1609)(1610) and (411) follows:
% 52.48/20.15 | (1611) sum(n21, n23) = all_0_1_1
% 52.48/20.15 |
% 52.48/20.15 | From (1609) and (2495) follows:
% 52.48/20.15 | (2524) sum(n21, n25) = all_0_4_4
% 52.48/20.15 |
% 52.48/20.15 | From (1610) and (2497) follows:
% 52.48/20.15 | (2525) sum(n23, n23) = all_0_7_7
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (690) with n23, n23, all_0_7_7, n20 and discharging atoms sum(n23, n23) = all_0_7_7, sum(n23, n23) = n20, yields:
% 52.48/20.15 | (1173) all_0_7_7 = n20
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (690) with n21, n25, all_0_4_4, n20 and discharging atoms sum(n21, n25) = all_0_4_4, sum(n21, n25) = n20, yields:
% 52.48/20.15 | (1171) all_0_4_4 = n20
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (690) with n21, n23, all_0_1_1, n18 and discharging atoms sum(n21, n23) = all_0_1_1, sum(n21, n23) = n18, yields:
% 52.48/20.15 | (1615) all_0_1_1 = n18
% 52.48/20.15 |
% 52.48/20.15 | From (1173)(1171) and (590) follows:
% 52.48/20.15 | (1175) sum(n20, n20) = all_0_3_3
% 52.48/20.15 |
% 52.48/20.15 | From (1615) and (2499) follows:
% 52.48/20.15 | (2530) sum(n22, n18) = all_0_0_0
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (690) with n22, n18, all_0_0_0, n14 and discharging atoms sum(n22, n18) = all_0_0_0, sum(n22, n18) = n14, yields:
% 52.48/20.15 | (1177) all_0_0_0 = n14
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 52.48/20.15 | (1176) all_0_3_3 = n14
% 52.48/20.15 |
% 52.48/20.15 | Equations (1177,1176) can reduce 679 to:
% 52.48/20.15 | (1106) $false
% 52.48/20.15 |
% 52.48/20.15 |-The branch is then unsatisfiable
% 52.48/20.15 |-Branch two:
% 52.48/20.15 | (1622) ~ (all_0_10_10 = n22)
% 52.48/20.15 | (1623) all_0_10_10 = n21 | 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
% 52.48/20.15 |
% 52.48/20.15 +-Applying beta-rule and splitting (1623), into two cases.
% 52.48/20.15 |-Branch one:
% 52.48/20.15 | (1624) all_0_10_10 = n21
% 52.48/20.15 |
% 52.48/20.15 | From (1624) and (292) follows:
% 52.48/20.15 | (1625) pred(n21) = all_0_6_6
% 52.48/20.15 |
% 52.48/20.15 | From (1624) and (760) follows:
% 52.48/20.15 | (1626) succ(n21) = all_0_8_8
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (500) with n21, all_0_6_6, n20 and discharging atoms pred(n21) = all_0_6_6, pred(n21) = n20, yields:
% 52.48/20.15 | (1627) all_0_6_6 = n20
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (617) with n21, all_0_8_8, n22 and discharging atoms succ(n21) = all_0_8_8, succ(n21) = n22, yields:
% 52.48/20.15 | (1628) all_0_8_8 = n22
% 52.48/20.15 |
% 52.48/20.15 | From (1627)(1628) and (411) follows:
% 52.48/20.15 | (1629) sum(n20, n22) = all_0_1_1
% 52.48/20.15 |
% 52.48/20.15 | From (1627) and (2495) follows:
% 52.48/20.15 | (2542) sum(n20, n25) = all_0_4_4
% 52.48/20.15 |
% 52.48/20.15 | From (1628) and (2497) follows:
% 52.48/20.15 | (2543) sum(n23, n22) = all_0_7_7
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (690) with n23, n22, all_0_7_7, n19 and discharging atoms sum(n23, n22) = all_0_7_7, sum(n23, n22) = n19, yields:
% 52.48/20.15 | (1191) all_0_7_7 = n19
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (690) with n20, n25, all_0_4_4, n19 and discharging atoms sum(n20, n25) = all_0_4_4, sum(n20, n25) = n19, yields:
% 52.48/20.15 | (1189) all_0_4_4 = n19
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (690) with n20, n22, all_0_1_1, n16 and discharging atoms sum(n20, n22) = all_0_1_1, sum(n20, n22) = n16, yields:
% 52.48/20.15 | (1633) all_0_1_1 = n16
% 52.48/20.15 |
% 52.48/20.15 | From (1191)(1189) and (590) follows:
% 52.48/20.15 | (1193) sum(n19, n19) = all_0_3_3
% 52.48/20.15 |
% 52.48/20.15 | From (1633) and (2499) follows:
% 52.48/20.15 | (2548) sum(n22, n16) = all_0_0_0
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (690) with n22, n16, all_0_0_0, n12 and discharging atoms sum(n22, n16) = all_0_0_0, sum(n22, n16) = n12, yields:
% 52.48/20.15 | (1195) all_0_0_0 = n12
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 52.48/20.15 | (1194) all_0_3_3 = n12
% 52.48/20.15 |
% 52.48/20.15 | Equations (1195,1194) can reduce 679 to:
% 52.48/20.15 | (1106) $false
% 52.48/20.15 |
% 52.48/20.15 |-The branch is then unsatisfiable
% 52.48/20.15 |-Branch two:
% 52.48/20.15 | (1640) ~ (all_0_10_10 = n21)
% 52.48/20.15 | (1641) 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
% 52.48/20.15 |
% 52.48/20.15 +-Applying beta-rule and splitting (1641), into two cases.
% 52.48/20.15 |-Branch one:
% 52.48/20.15 | (1642) all_0_10_10 = n20
% 52.48/20.15 |
% 52.48/20.15 | From (1642) and (292) follows:
% 52.48/20.15 | (1643) pred(n20) = all_0_6_6
% 52.48/20.15 |
% 52.48/20.15 | From (1642) and (760) follows:
% 52.48/20.15 | (1644) succ(n20) = all_0_8_8
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (500) with n20, all_0_6_6, n19 and discharging atoms pred(n20) = all_0_6_6, pred(n20) = n19, yields:
% 52.48/20.15 | (1645) all_0_6_6 = n19
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (617) with n20, all_0_8_8, n21 and discharging atoms succ(n20) = all_0_8_8, succ(n20) = n21, yields:
% 52.48/20.15 | (1646) all_0_8_8 = n21
% 52.48/20.15 |
% 52.48/20.15 | From (1645)(1646) and (411) follows:
% 52.48/20.15 | (1647) sum(n19, n21) = all_0_1_1
% 52.48/20.15 |
% 52.48/20.15 | From (1645) and (2495) follows:
% 52.48/20.15 | (2560) sum(n19, n25) = all_0_4_4
% 52.48/20.15 |
% 52.48/20.15 | From (1646) and (2497) follows:
% 52.48/20.15 | (2561) sum(n23, n21) = all_0_7_7
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (690) with n23, n21, all_0_7_7, n18 and discharging atoms sum(n23, n21) = all_0_7_7, sum(n23, n21) = n18, yields:
% 52.48/20.15 | (1209) all_0_7_7 = n18
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (690) with n19, n25, all_0_4_4, n18 and discharging atoms sum(n19, n25) = all_0_4_4, sum(n19, n25) = n18, yields:
% 52.48/20.15 | (1207) all_0_4_4 = n18
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (690) with n19, n21, all_0_1_1, n14 and discharging atoms sum(n19, n21) = all_0_1_1, sum(n19, n21) = n14, yields:
% 52.48/20.15 | (1651) all_0_1_1 = n14
% 52.48/20.15 |
% 52.48/20.15 | From (1209)(1207) and (590) follows:
% 52.48/20.15 | (1211) sum(n18, n18) = all_0_3_3
% 52.48/20.15 |
% 52.48/20.15 | From (1651) and (2499) follows:
% 52.48/20.15 | (2566) sum(n22, n14) = all_0_0_0
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (690) with n22, n14, all_0_0_0, n10 and discharging atoms sum(n22, n14) = all_0_0_0, sum(n22, n14) = n10, yields:
% 52.48/20.15 | (1213) all_0_0_0 = n10
% 52.48/20.15 |
% 52.48/20.15 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 52.48/20.15 | (1212) all_0_3_3 = n10
% 52.48/20.15 |
% 52.48/20.15 | Equations (1213,1212) can reduce 679 to:
% 52.48/20.15 | (1106) $false
% 52.48/20.15 |
% 52.48/20.15 |-The branch is then unsatisfiable
% 52.48/20.15 |-Branch two:
% 52.48/20.15 | (1658) ~ (all_0_10_10 = n20)
% 52.48/20.15 | (1659) 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
% 52.48/20.15 |
% 52.48/20.15 +-Applying beta-rule and splitting (1659), into two cases.
% 52.48/20.15 |-Branch one:
% 52.48/20.15 | (1660) all_0_10_10 = n19
% 52.48/20.15 |
% 52.48/20.15 | From (1660) and (292) follows:
% 52.48/20.16 | (1661) pred(n19) = all_0_6_6
% 52.48/20.16 |
% 52.48/20.16 | From (1660) and (760) follows:
% 52.48/20.16 | (1662) succ(n19) = all_0_8_8
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (500) with n19, all_0_6_6, n18 and discharging atoms pred(n19) = all_0_6_6, pred(n19) = n18, yields:
% 52.48/20.16 | (1663) all_0_6_6 = n18
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (617) with n19, all_0_8_8, n20 and discharging atoms succ(n19) = all_0_8_8, succ(n19) = n20, yields:
% 52.48/20.16 | (1664) all_0_8_8 = n20
% 52.48/20.16 |
% 52.48/20.16 | From (1663)(1664) and (411) follows:
% 52.48/20.16 | (1665) sum(n18, n20) = all_0_1_1
% 52.48/20.16 |
% 52.48/20.16 | From (1663) and (2495) follows:
% 52.48/20.16 | (2578) sum(n18, n25) = all_0_4_4
% 52.48/20.16 |
% 52.48/20.16 | From (1664) and (2497) follows:
% 52.48/20.16 | (2579) sum(n23, n20) = all_0_7_7
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (690) with n23, n20, all_0_7_7, n17 and discharging atoms sum(n23, n20) = all_0_7_7, sum(n23, n20) = n17, yields:
% 52.48/20.16 | (1227) all_0_7_7 = n17
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (690) with n18, n25, all_0_4_4, n17 and discharging atoms sum(n18, n25) = all_0_4_4, sum(n18, n25) = n17, yields:
% 52.48/20.16 | (1225) all_0_4_4 = n17
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (690) with n18, n20, all_0_1_1, n12 and discharging atoms sum(n18, n20) = all_0_1_1, sum(n18, n20) = n12, yields:
% 52.48/20.16 | (1669) all_0_1_1 = n12
% 52.48/20.16 |
% 52.48/20.16 | From (1227)(1225) and (590) follows:
% 52.48/20.16 | (1229) sum(n17, n17) = all_0_3_3
% 52.48/20.16 |
% 52.48/20.16 | From (1669) and (2499) follows:
% 52.48/20.16 | (2584) sum(n22, n12) = all_0_0_0
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (690) with n22, n12, all_0_0_0, n8 and discharging atoms sum(n22, n12) = all_0_0_0, sum(n22, n12) = n8, yields:
% 52.48/20.16 | (1231) all_0_0_0 = n8
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 52.48/20.16 | (1230) all_0_3_3 = n8
% 52.48/20.16 |
% 52.48/20.16 | Equations (1231,1230) can reduce 679 to:
% 52.48/20.16 | (1106) $false
% 52.48/20.16 |
% 52.48/20.16 |-The branch is then unsatisfiable
% 52.48/20.16 |-Branch two:
% 52.48/20.16 | (1676) ~ (all_0_10_10 = n19)
% 52.48/20.16 | (1677) 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
% 52.48/20.16 |
% 52.48/20.16 +-Applying beta-rule and splitting (1677), into two cases.
% 52.48/20.16 |-Branch one:
% 52.48/20.16 | (1678) all_0_10_10 = n18
% 52.48/20.16 |
% 52.48/20.16 | From (1678) and (292) follows:
% 52.48/20.16 | (1679) pred(n18) = all_0_6_6
% 52.48/20.16 |
% 52.48/20.16 | From (1678) and (760) follows:
% 52.48/20.16 | (1680) succ(n18) = all_0_8_8
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (500) with n18, all_0_6_6, n17 and discharging atoms pred(n18) = all_0_6_6, pred(n18) = n17, yields:
% 52.48/20.16 | (1681) all_0_6_6 = n17
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (617) with n18, all_0_8_8, n19 and discharging atoms succ(n18) = all_0_8_8, succ(n18) = n19, yields:
% 52.48/20.16 | (1682) all_0_8_8 = n19
% 52.48/20.16 |
% 52.48/20.16 | From (1681)(1682) and (411) follows:
% 52.48/20.16 | (1683) sum(n17, n19) = all_0_1_1
% 52.48/20.16 |
% 52.48/20.16 | From (1681) and (2495) follows:
% 52.48/20.16 | (2596) sum(n17, n25) = all_0_4_4
% 52.48/20.16 |
% 52.48/20.16 | From (1682) and (2497) follows:
% 52.48/20.16 | (2597) sum(n23, n19) = all_0_7_7
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (690) with n23, n19, all_0_7_7, n16 and discharging atoms sum(n23, n19) = all_0_7_7, sum(n23, n19) = n16, yields:
% 52.48/20.16 | (1245) all_0_7_7 = n16
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (690) with n17, n25, all_0_4_4, n16 and discharging atoms sum(n17, n25) = all_0_4_4, sum(n17, n25) = n16, yields:
% 52.48/20.16 | (1243) all_0_4_4 = n16
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (690) with n17, n19, all_0_1_1, n10 and discharging atoms sum(n17, n19) = all_0_1_1, sum(n17, n19) = n10, yields:
% 52.48/20.16 | (1687) all_0_1_1 = n10
% 52.48/20.16 |
% 52.48/20.16 | From (1245)(1243) and (590) follows:
% 52.48/20.16 | (1247) sum(n16, n16) = all_0_3_3
% 52.48/20.16 |
% 52.48/20.16 | From (1687) and (2499) follows:
% 52.48/20.16 | (2602) sum(n22, n10) = all_0_0_0
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (690) with n22, n10, all_0_0_0, n6 and discharging atoms sum(n22, n10) = all_0_0_0, sum(n22, n10) = n6, yields:
% 52.48/20.16 | (1249) all_0_0_0 = n6
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 52.48/20.16 | (1248) all_0_3_3 = n6
% 52.48/20.16 |
% 52.48/20.16 | Equations (1249,1248) can reduce 679 to:
% 52.48/20.16 | (1106) $false
% 52.48/20.16 |
% 52.48/20.16 |-The branch is then unsatisfiable
% 52.48/20.16 |-Branch two:
% 52.48/20.16 | (1694) ~ (all_0_10_10 = n18)
% 52.48/20.16 | (1695) 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
% 52.48/20.16 |
% 52.48/20.16 +-Applying beta-rule and splitting (1695), into two cases.
% 52.48/20.16 |-Branch one:
% 52.48/20.16 | (1696) all_0_10_10 = n17
% 52.48/20.16 |
% 52.48/20.16 | From (1696) and (292) follows:
% 52.48/20.16 | (1697) pred(n17) = all_0_6_6
% 52.48/20.16 |
% 52.48/20.16 | From (1696) and (760) follows:
% 52.48/20.16 | (1698) succ(n17) = all_0_8_8
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (500) with n17, all_0_6_6, n16 and discharging atoms pred(n17) = all_0_6_6, pred(n17) = n16, yields:
% 52.48/20.16 | (1699) all_0_6_6 = n16
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (617) with n17, all_0_8_8, n18 and discharging atoms succ(n17) = all_0_8_8, succ(n17) = n18, yields:
% 52.48/20.16 | (1700) all_0_8_8 = n18
% 52.48/20.16 |
% 52.48/20.16 | From (1699)(1700) and (411) follows:
% 52.48/20.16 | (1701) sum(n16, n18) = all_0_1_1
% 52.48/20.16 |
% 52.48/20.16 | From (1699) and (2495) follows:
% 52.48/20.16 | (2614) sum(n16, n25) = all_0_4_4
% 52.48/20.16 |
% 52.48/20.16 | From (1700) and (2497) follows:
% 52.48/20.16 | (2615) sum(n23, n18) = all_0_7_7
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (690) with n23, n18, all_0_7_7, n15 and discharging atoms sum(n23, n18) = all_0_7_7, sum(n23, n18) = n15, yields:
% 52.48/20.16 | (1263) all_0_7_7 = n15
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (690) with n16, n25, all_0_4_4, n15 and discharging atoms sum(n16, n25) = all_0_4_4, sum(n16, n25) = n15, yields:
% 52.48/20.16 | (1261) all_0_4_4 = n15
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (690) with n16, n18, all_0_1_1, n8 and discharging atoms sum(n16, n18) = all_0_1_1, sum(n16, n18) = n8, yields:
% 52.48/20.16 | (1705) all_0_1_1 = n8
% 52.48/20.16 |
% 52.48/20.16 | From (1263)(1261) and (590) follows:
% 52.48/20.16 | (1265) sum(n15, n15) = all_0_3_3
% 52.48/20.16 |
% 52.48/20.16 | From (1705) and (2499) follows:
% 52.48/20.16 | (2620) sum(n22, n8) = all_0_0_0
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (690) with n22, n8, all_0_0_0, n4 and discharging atoms sum(n22, n8) = all_0_0_0, sum(n22, n8) = n4, yields:
% 52.48/20.16 | (1267) all_0_0_0 = n4
% 52.48/20.16 |
% 52.48/20.16 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 52.48/20.16 | (1266) all_0_3_3 = n4
% 52.48/20.16 |
% 52.48/20.16 | Equations (1267,1266) can reduce 679 to:
% 52.48/20.16 | (1106) $false
% 52.48/20.16 |
% 52.48/20.16 |-The branch is then unsatisfiable
% 52.48/20.16 |-Branch two:
% 52.48/20.16 | (1712) ~ (all_0_10_10 = n17)
% 52.48/20.16 | (1713) 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
% 52.48/20.16 |
% 52.48/20.16 +-Applying beta-rule and splitting (1713), into two cases.
% 52.48/20.16 |-Branch one:
% 52.48/20.16 | (1714) all_0_10_10 = n16
% 52.48/20.16 |
% 52.48/20.16 | From (1714) and (292) follows:
% 52.48/20.16 | (1715) pred(n16) = all_0_6_6
% 52.48/20.16 |
% 52.48/20.16 | From (1714) and (760) follows:
% 52.48/20.17 | (1716) succ(n16) = all_0_8_8
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (500) with n16, all_0_6_6, n15 and discharging atoms pred(n16) = all_0_6_6, pred(n16) = n15, yields:
% 52.48/20.17 | (1717) all_0_6_6 = n15
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (617) with n16, all_0_8_8, n17 and discharging atoms succ(n16) = all_0_8_8, succ(n16) = n17, yields:
% 52.48/20.17 | (1718) all_0_8_8 = n17
% 52.48/20.17 |
% 52.48/20.17 | From (1717)(1718) and (411) follows:
% 52.48/20.17 | (1719) sum(n15, n17) = all_0_1_1
% 52.48/20.17 |
% 52.48/20.17 | From (1717) and (2495) follows:
% 52.48/20.17 | (2632) sum(n15, n25) = all_0_4_4
% 52.48/20.17 |
% 52.48/20.17 | From (1718) and (2497) follows:
% 52.48/20.17 | (2633) sum(n23, n17) = all_0_7_7
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (690) with n23, n17, all_0_7_7, n14 and discharging atoms sum(n23, n17) = all_0_7_7, sum(n23, n17) = n14, yields:
% 52.48/20.17 | (1281) all_0_7_7 = n14
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (690) with n15, n25, all_0_4_4, n14 and discharging atoms sum(n15, n25) = all_0_4_4, sum(n15, n25) = n14, yields:
% 52.48/20.17 | (1279) all_0_4_4 = n14
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (690) with n15, n17, all_0_1_1, n6 and discharging atoms sum(n15, n17) = all_0_1_1, sum(n15, n17) = n6, yields:
% 52.48/20.17 | (1723) all_0_1_1 = n6
% 52.48/20.17 |
% 52.48/20.17 | From (1281)(1279) and (590) follows:
% 52.48/20.17 | (1283) sum(n14, n14) = all_0_3_3
% 52.48/20.17 |
% 52.48/20.17 | From (1723) and (2499) follows:
% 52.48/20.17 | (2638) sum(n22, n6) = all_0_0_0
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (690) with n22, n6, all_0_0_0, n2 and discharging atoms sum(n22, n6) = all_0_0_0, sum(n22, n6) = n2, yields:
% 52.48/20.17 | (1285) all_0_0_0 = n2
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 52.48/20.17 | (1284) all_0_3_3 = n2
% 52.48/20.17 |
% 52.48/20.17 | Equations (1285,1284) can reduce 679 to:
% 52.48/20.17 | (1106) $false
% 52.48/20.17 |
% 52.48/20.17 |-The branch is then unsatisfiable
% 52.48/20.17 |-Branch two:
% 52.48/20.17 | (1730) ~ (all_0_10_10 = n16)
% 52.48/20.17 | (1731) 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
% 52.48/20.17 |
% 52.48/20.17 +-Applying beta-rule and splitting (1731), into two cases.
% 52.48/20.17 |-Branch one:
% 52.48/20.17 | (1732) all_0_10_10 = n15
% 52.48/20.17 |
% 52.48/20.17 | From (1732) and (292) follows:
% 52.48/20.17 | (1733) pred(n15) = all_0_6_6
% 52.48/20.17 |
% 52.48/20.17 | From (1732) and (760) follows:
% 52.48/20.17 | (1734) succ(n15) = all_0_8_8
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (500) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 52.48/20.17 | (1735) all_0_6_6 = n14
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (617) with n15, all_0_8_8, n16 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n16, yields:
% 52.48/20.17 | (1736) all_0_8_8 = n16
% 52.48/20.17 |
% 52.48/20.17 | From (1735)(1736) and (411) follows:
% 52.48/20.17 | (1737) sum(n14, n16) = all_0_1_1
% 52.48/20.17 |
% 52.48/20.17 | From (1735) and (2495) follows:
% 52.48/20.17 | (2650) sum(n14, n25) = all_0_4_4
% 52.48/20.17 |
% 52.48/20.17 | From (1736) and (2497) follows:
% 52.48/20.17 | (2651) sum(n23, n16) = all_0_7_7
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (690) with n23, n16, all_0_7_7, n13 and discharging atoms sum(n23, n16) = all_0_7_7, sum(n23, n16) = n13, yields:
% 52.48/20.17 | (1299) all_0_7_7 = n13
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (690) with n14, n25, all_0_4_4, n13 and discharging atoms sum(n14, n25) = all_0_4_4, sum(n14, n25) = n13, yields:
% 52.48/20.17 | (1297) all_0_4_4 = n13
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (690) with n14, n16, all_0_1_1, n4 and discharging atoms sum(n14, n16) = all_0_1_1, sum(n14, n16) = n4, yields:
% 52.48/20.17 | (1741) all_0_1_1 = n4
% 52.48/20.17 |
% 52.48/20.17 | From (1299)(1297) and (590) follows:
% 52.48/20.17 | (1301) sum(n13, n13) = all_0_3_3
% 52.48/20.17 |
% 52.48/20.17 | From (1741) and (2499) follows:
% 52.48/20.17 | (2656) sum(n22, n4) = all_0_0_0
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (690) with n22, n4, all_0_0_0, n0 and discharging atoms sum(n22, n4) = all_0_0_0, sum(n22, n4) = n0, yields:
% 52.48/20.17 | (1303) all_0_0_0 = n0
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 52.48/20.17 | (1302) all_0_3_3 = n0
% 52.48/20.17 |
% 52.48/20.17 | Equations (1303,1302) can reduce 679 to:
% 52.48/20.17 | (1106) $false
% 52.48/20.17 |
% 52.48/20.17 |-The branch is then unsatisfiable
% 52.48/20.17 |-Branch two:
% 52.48/20.17 | (1748) ~ (all_0_10_10 = n15)
% 52.48/20.17 | (1749) 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
% 52.48/20.17 |
% 52.48/20.17 +-Applying beta-rule and splitting (1749), into two cases.
% 52.48/20.17 |-Branch one:
% 52.48/20.17 | (1750) all_0_10_10 = n14
% 52.48/20.17 |
% 52.48/20.17 | From (1750) and (292) follows:
% 52.48/20.17 | (1751) pred(n14) = all_0_6_6
% 52.48/20.17 |
% 52.48/20.17 | From (1750) and (760) follows:
% 52.48/20.17 | (1752) succ(n14) = all_0_8_8
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (500) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 52.48/20.17 | (1753) all_0_6_6 = n13
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (617) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 52.48/20.17 | (1754) all_0_8_8 = n15
% 52.48/20.17 |
% 52.48/20.17 | From (1753)(1754) and (411) follows:
% 52.48/20.17 | (1755) sum(n13, n15) = all_0_1_1
% 52.48/20.17 |
% 52.48/20.17 | From (1753) and (2495) follows:
% 52.48/20.17 | (2668) sum(n13, n25) = all_0_4_4
% 52.48/20.17 |
% 52.48/20.17 | From (1754) and (2497) follows:
% 52.48/20.17 | (2669) sum(n23, n15) = all_0_7_7
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (690) with n23, n15, all_0_7_7, n12 and discharging atoms sum(n23, n15) = all_0_7_7, sum(n23, n15) = n12, yields:
% 52.48/20.17 | (1317) all_0_7_7 = n12
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (690) with n13, n25, all_0_4_4, n12 and discharging atoms sum(n13, n25) = all_0_4_4, sum(n13, n25) = n12, yields:
% 52.48/20.17 | (1315) all_0_4_4 = n12
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (690) with n13, n15, all_0_1_1, n2 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n2, yields:
% 52.48/20.17 | (1759) all_0_1_1 = n2
% 52.48/20.17 |
% 52.48/20.17 | From (1317)(1315) and (590) follows:
% 52.48/20.17 | (1319) sum(n12, n12) = all_0_3_3
% 52.48/20.17 |
% 52.48/20.17 | From (1759) and (2499) follows:
% 52.48/20.17 | (2674) sum(n22, n2) = all_0_0_0
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (690) with n22, n2, all_0_0_0, n24 and discharging atoms sum(n22, n2) = all_0_0_0, sum(n22, n2) = n24, yields:
% 52.48/20.17 | (1321) all_0_0_0 = n24
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 52.48/20.17 | (1320) all_0_3_3 = n24
% 52.48/20.17 |
% 52.48/20.17 | Equations (1321,1320) can reduce 679 to:
% 52.48/20.17 | (1106) $false
% 52.48/20.17 |
% 52.48/20.17 |-The branch is then unsatisfiable
% 52.48/20.17 |-Branch two:
% 52.48/20.17 | (1766) ~ (all_0_10_10 = n14)
% 52.48/20.17 | (1767) 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
% 52.48/20.17 |
% 52.48/20.17 +-Applying beta-rule and splitting (1767), into two cases.
% 52.48/20.17 |-Branch one:
% 52.48/20.17 | (1768) all_0_10_10 = n13
% 52.48/20.17 |
% 52.48/20.17 | From (1768) and (292) follows:
% 52.48/20.17 | (1769) pred(n13) = all_0_6_6
% 52.48/20.17 |
% 52.48/20.17 | From (1768) and (760) follows:
% 52.48/20.17 | (1770) succ(n13) = all_0_8_8
% 52.48/20.17 |
% 52.48/20.17 | Instantiating formula (500) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 52.48/20.17 | (1771) all_0_6_6 = n12
% 52.48/20.17 |
% 52.48/20.18 | Instantiating formula (617) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 52.48/20.18 | (1772) all_0_8_8 = n14
% 52.48/20.18 |
% 52.48/20.18 | From (1771)(1772) and (411) follows:
% 52.48/20.18 | (1773) sum(n12, n14) = all_0_1_1
% 52.48/20.18 |
% 52.48/20.18 | From (1771) and (2495) follows:
% 52.48/20.18 | (2686) sum(n12, n25) = all_0_4_4
% 52.48/20.18 |
% 52.48/20.18 | From (1772) and (2497) follows:
% 52.48/20.18 | (2687) sum(n23, n14) = all_0_7_7
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (690) with n23, n14, all_0_7_7, n11 and discharging atoms sum(n23, n14) = all_0_7_7, sum(n23, n14) = n11, yields:
% 52.48/20.18 | (1335) all_0_7_7 = n11
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (690) with n12, n25, all_0_4_4, n11 and discharging atoms sum(n12, n25) = all_0_4_4, sum(n12, n25) = n11, yields:
% 52.48/20.18 | (1333) all_0_4_4 = n11
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (690) with n12, n14, all_0_1_1, n0 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n0, yields:
% 52.48/20.18 | (1777) all_0_1_1 = n0
% 52.48/20.18 |
% 52.48/20.18 | From (1335)(1333) and (590) follows:
% 52.48/20.18 | (1337) sum(n11, n11) = all_0_3_3
% 52.48/20.18 |
% 52.48/20.18 | From (1777) and (2499) follows:
% 52.48/20.18 | (2692) sum(n22, n0) = all_0_0_0
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (690) with n22, n0, all_0_0_0, n22 and discharging atoms sum(n22, n0) = all_0_0_0, sum(n22, n0) = n22, yields:
% 52.48/20.18 | (1102) all_0_0_0 = n22
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 52.48/20.18 | (1104) all_0_3_3 = n22
% 52.48/20.18 |
% 52.48/20.18 | Equations (1102,1104) can reduce 679 to:
% 52.48/20.18 | (1106) $false
% 52.48/20.18 |
% 52.48/20.18 |-The branch is then unsatisfiable
% 52.48/20.18 |-Branch two:
% 52.48/20.18 | (1784) ~ (all_0_10_10 = n13)
% 52.48/20.18 | (1785) 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
% 52.48/20.18 |
% 52.48/20.18 +-Applying beta-rule and splitting (1785), into two cases.
% 52.48/20.18 |-Branch one:
% 52.48/20.18 | (1786) all_0_10_10 = n12
% 52.48/20.18 |
% 52.48/20.18 | From (1786) and (292) follows:
% 52.48/20.18 | (1787) pred(n12) = all_0_6_6
% 52.48/20.18 |
% 52.48/20.18 | From (1786) and (760) follows:
% 52.48/20.18 | (1788) succ(n12) = all_0_8_8
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (500) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 52.48/20.18 | (1789) all_0_6_6 = n11
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (617) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 52.48/20.18 | (1790) all_0_8_8 = n13
% 52.48/20.18 |
% 52.48/20.18 | From (1789)(1790) and (411) follows:
% 52.48/20.18 | (1791) sum(n11, n13) = all_0_1_1
% 52.48/20.18 |
% 52.48/20.18 | From (1789) and (2495) follows:
% 52.48/20.18 | (2704) sum(n11, n25) = all_0_4_4
% 52.48/20.18 |
% 52.48/20.18 | From (1790) and (2497) follows:
% 52.48/20.18 | (2705) sum(n23, n13) = all_0_7_7
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (690) with n23, n13, all_0_7_7, n10 and discharging atoms sum(n23, n13) = all_0_7_7, sum(n23, n13) = n10, yields:
% 52.48/20.18 | (1353) all_0_7_7 = n10
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (690) with n11, n25, all_0_4_4, n10 and discharging atoms sum(n11, n25) = all_0_4_4, sum(n11, n25) = n10, yields:
% 52.48/20.18 | (1351) all_0_4_4 = n10
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (690) with n11, n13, all_0_1_1, n24 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n24, yields:
% 52.48/20.18 | (1081) all_0_1_1 = n24
% 52.48/20.18 |
% 52.48/20.18 | From (1353)(1351) and (590) follows:
% 52.48/20.18 | (1355) sum(n10, n10) = all_0_3_3
% 52.48/20.18 |
% 52.48/20.18 | From (1081) and (2499) follows:
% 52.48/20.18 | (1120) sum(n22, n24) = all_0_0_0
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (690) with n22, n24, all_0_0_0, n20 and discharging atoms sum(n22, n24) = all_0_0_0, sum(n22, n24) = n20, yields:
% 52.48/20.18 | (1123) all_0_0_0 = n20
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 52.48/20.18 | (1122) all_0_3_3 = n20
% 52.48/20.18 |
% 52.48/20.18 | Equations (1123,1122) can reduce 679 to:
% 52.48/20.18 | (1106) $false
% 52.48/20.18 |
% 52.48/20.18 |-The branch is then unsatisfiable
% 52.48/20.18 |-Branch two:
% 52.48/20.18 | (1802) ~ (all_0_10_10 = n12)
% 52.48/20.18 | (1803) 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
% 52.48/20.18 |
% 52.48/20.18 +-Applying beta-rule and splitting (1803), into two cases.
% 52.48/20.18 |-Branch one:
% 52.48/20.18 | (1804) all_0_10_10 = n11
% 52.48/20.18 |
% 52.48/20.18 | From (1804) and (292) follows:
% 52.48/20.18 | (1805) pred(n11) = all_0_6_6
% 52.48/20.18 |
% 52.48/20.18 | From (1804) and (760) follows:
% 52.48/20.18 | (1806) succ(n11) = all_0_8_8
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (500) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 52.48/20.18 | (1807) all_0_6_6 = n10
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (617) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 52.48/20.18 | (1808) all_0_8_8 = n12
% 52.48/20.18 |
% 52.48/20.18 | From (1807)(1808) and (411) follows:
% 52.48/20.18 | (1809) sum(n10, n12) = all_0_1_1
% 52.48/20.18 |
% 52.48/20.18 | From (1807) and (2495) follows:
% 52.48/20.18 | (2722) sum(n10, n25) = all_0_4_4
% 52.48/20.18 |
% 52.48/20.18 | From (1808) and (2497) follows:
% 52.48/20.18 | (2723) sum(n23, n12) = all_0_7_7
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (690) with n23, n12, all_0_7_7, n9 and discharging atoms sum(n23, n12) = all_0_7_7, sum(n23, n12) = n9, yields:
% 52.48/20.18 | (1371) all_0_7_7 = n9
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (690) with n10, n25, all_0_4_4, n9 and discharging atoms sum(n10, n25) = all_0_4_4, sum(n10, n25) = n9, yields:
% 52.48/20.18 | (1369) all_0_4_4 = n9
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (690) with n10, n12, all_0_1_1, n22 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n22, yields:
% 52.48/20.18 | (1579) all_0_1_1 = n22
% 52.48/20.18 |
% 52.48/20.18 | From (1371)(1369) and (590) follows:
% 52.48/20.18 | (1373) sum(n9, n9) = all_0_3_3
% 52.48/20.18 |
% 52.48/20.18 | From (1579) and (2499) follows:
% 52.48/20.18 | (2050) sum(n22, n22) = all_0_0_0
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (690) with n22, n22, all_0_0_0, n18 and discharging atoms sum(n22, n22) = all_0_0_0, sum(n22, n22) = n18, yields:
% 52.48/20.18 | (1141) all_0_0_0 = n18
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 52.48/20.18 | (1140) all_0_3_3 = n18
% 52.48/20.18 |
% 52.48/20.18 | Equations (1141,1140) can reduce 679 to:
% 52.48/20.18 | (1106) $false
% 52.48/20.18 |
% 52.48/20.18 |-The branch is then unsatisfiable
% 52.48/20.18 |-Branch two:
% 52.48/20.18 | (1820) ~ (all_0_10_10 = n11)
% 52.48/20.18 | (1821) 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
% 52.48/20.18 |
% 52.48/20.18 +-Applying beta-rule and splitting (1821), into two cases.
% 52.48/20.18 |-Branch one:
% 52.48/20.18 | (1822) all_0_10_10 = n10
% 52.48/20.18 |
% 52.48/20.18 | From (1822) and (292) follows:
% 52.48/20.18 | (1823) pred(n10) = all_0_6_6
% 52.48/20.18 |
% 52.48/20.18 | From (1822) and (760) follows:
% 52.48/20.18 | (1824) succ(n10) = all_0_8_8
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (500) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 52.48/20.18 | (1825) all_0_6_6 = n9
% 52.48/20.18 |
% 52.48/20.18 | Instantiating formula (617) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 52.48/20.18 | (1826) all_0_8_8 = n11
% 52.48/20.18 |
% 52.48/20.18 | From (1825)(1826) and (411) follows:
% 52.48/20.18 | (1827) sum(n9, n11) = all_0_1_1
% 52.48/20.18 |
% 52.48/20.18 | From (1825) and (2495) follows:
% 52.48/20.19 | (2740) sum(n9, n25) = all_0_4_4
% 52.48/20.19 |
% 52.48/20.19 | From (1826) and (2497) follows:
% 52.48/20.19 | (2741) sum(n23, n11) = all_0_7_7
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (690) with n23, n11, all_0_7_7, n8 and discharging atoms sum(n23, n11) = all_0_7_7, sum(n23, n11) = n8, yields:
% 52.48/20.19 | (1389) all_0_7_7 = n8
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (690) with n9, n25, all_0_4_4, n8 and discharging atoms sum(n9, n25) = all_0_4_4, sum(n9, n25) = n8, yields:
% 52.48/20.19 | (1387) all_0_4_4 = n8
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (690) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 52.48/20.19 | (1597) all_0_1_1 = n20
% 52.48/20.19 |
% 52.48/20.19 | From (1389)(1387) and (590) follows:
% 52.48/20.19 | (1391) sum(n8, n8) = all_0_3_3
% 52.48/20.19 |
% 52.48/20.19 | From (1597) and (2499) follows:
% 52.48/20.19 | (2512) sum(n22, n20) = all_0_0_0
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (690) with n22, n20, all_0_0_0, n16 and discharging atoms sum(n22, n20) = all_0_0_0, sum(n22, n20) = n16, yields:
% 52.48/20.19 | (1159) all_0_0_0 = n16
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 52.48/20.19 | (1158) all_0_3_3 = n16
% 52.48/20.19 |
% 52.48/20.19 | Equations (1159,1158) can reduce 679 to:
% 52.48/20.19 | (1106) $false
% 52.48/20.19 |
% 52.48/20.19 |-The branch is then unsatisfiable
% 52.48/20.19 |-Branch two:
% 52.48/20.19 | (1838) ~ (all_0_10_10 = n10)
% 52.48/20.19 | (1839) 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
% 52.48/20.19 |
% 52.48/20.19 +-Applying beta-rule and splitting (1839), into two cases.
% 52.48/20.19 |-Branch one:
% 52.48/20.19 | (1840) all_0_10_10 = n9
% 52.48/20.19 |
% 52.48/20.19 | From (1840) and (292) follows:
% 52.48/20.19 | (1841) pred(n9) = all_0_6_6
% 52.48/20.19 |
% 52.48/20.19 | From (1840) and (760) follows:
% 52.48/20.19 | (1842) succ(n9) = all_0_8_8
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (500) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 52.48/20.19 | (1843) all_0_6_6 = n8
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (617) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 52.48/20.19 | (1844) all_0_8_8 = n10
% 52.48/20.19 |
% 52.48/20.19 | From (1843)(1844) and (411) follows:
% 52.48/20.19 | (1845) sum(n8, n10) = all_0_1_1
% 52.48/20.19 |
% 52.48/20.19 | From (1843) and (2495) follows:
% 52.48/20.19 | (2758) sum(n8, n25) = all_0_4_4
% 52.48/20.19 |
% 52.48/20.19 | From (1844) and (2497) follows:
% 52.48/20.19 | (2759) sum(n23, n10) = all_0_7_7
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (690) with n23, n10, all_0_7_7, n7 and discharging atoms sum(n23, n10) = all_0_7_7, sum(n23, n10) = n7, yields:
% 52.48/20.19 | (1407) all_0_7_7 = n7
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (690) with n8, n25, all_0_4_4, n7 and discharging atoms sum(n8, n25) = all_0_4_4, sum(n8, n25) = n7, yields:
% 52.48/20.19 | (1405) all_0_4_4 = n7
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (690) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 52.48/20.19 | (1615) all_0_1_1 = n18
% 52.48/20.19 |
% 52.48/20.19 | From (1407)(1405) and (590) follows:
% 52.48/20.19 | (1409) sum(n7, n7) = all_0_3_3
% 52.48/20.19 |
% 52.48/20.19 | From (1615) and (2499) follows:
% 52.48/20.19 | (2530) sum(n22, n18) = all_0_0_0
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (690) with n22, n18, all_0_0_0, n14 and discharging atoms sum(n22, n18) = all_0_0_0, sum(n22, n18) = n14, yields:
% 52.48/20.19 | (1177) all_0_0_0 = n14
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 52.48/20.19 | (1176) all_0_3_3 = n14
% 52.48/20.19 |
% 52.48/20.19 | Equations (1177,1176) can reduce 679 to:
% 52.48/20.19 | (1106) $false
% 52.48/20.19 |
% 52.48/20.19 |-The branch is then unsatisfiable
% 52.48/20.19 |-Branch two:
% 52.48/20.19 | (1856) ~ (all_0_10_10 = n9)
% 52.48/20.19 | (1857) 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
% 52.48/20.19 |
% 52.48/20.19 +-Applying beta-rule and splitting (1857), into two cases.
% 52.48/20.19 |-Branch one:
% 52.48/20.19 | (1858) all_0_10_10 = n8
% 52.48/20.19 |
% 52.48/20.19 | From (1858) and (292) follows:
% 52.48/20.19 | (1859) pred(n8) = all_0_6_6
% 52.48/20.19 |
% 52.48/20.19 | From (1858) and (760) follows:
% 52.48/20.19 | (1860) succ(n8) = all_0_8_8
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 52.48/20.19 | (1861) all_0_6_6 = n7
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 52.48/20.19 | (1862) all_0_8_8 = n9
% 52.48/20.19 |
% 52.48/20.19 | From (1861)(1862) and (411) follows:
% 52.48/20.19 | (1863) sum(n7, n9) = all_0_1_1
% 52.48/20.19 |
% 52.48/20.19 | From (1861) and (2495) follows:
% 52.48/20.19 | (2776) sum(n7, n25) = all_0_4_4
% 52.48/20.19 |
% 52.48/20.19 | From (1862) and (2497) follows:
% 52.48/20.19 | (2777) sum(n23, n9) = all_0_7_7
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (690) with n23, n9, all_0_7_7, n6 and discharging atoms sum(n23, n9) = all_0_7_7, sum(n23, n9) = n6, yields:
% 52.48/20.19 | (1425) all_0_7_7 = n6
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (690) with n7, n25, all_0_4_4, n6 and discharging atoms sum(n7, n25) = all_0_4_4, sum(n7, n25) = n6, yields:
% 52.48/20.19 | (1423) all_0_4_4 = n6
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 52.48/20.19 | (1633) all_0_1_1 = n16
% 52.48/20.19 |
% 52.48/20.19 | From (1425)(1423) and (590) follows:
% 52.48/20.19 | (1427) sum(n6, n6) = all_0_3_3
% 52.48/20.19 |
% 52.48/20.19 | From (1633) and (2499) follows:
% 52.48/20.19 | (2548) sum(n22, n16) = all_0_0_0
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (690) with n22, n16, all_0_0_0, n12 and discharging atoms sum(n22, n16) = all_0_0_0, sum(n22, n16) = n12, yields:
% 52.48/20.19 | (1195) all_0_0_0 = n12
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 52.48/20.19 | (1194) all_0_3_3 = n12
% 52.48/20.19 |
% 52.48/20.19 | Equations (1195,1194) can reduce 679 to:
% 52.48/20.19 | (1106) $false
% 52.48/20.19 |
% 52.48/20.19 |-The branch is then unsatisfiable
% 52.48/20.19 |-Branch two:
% 52.48/20.19 | (1874) ~ (all_0_10_10 = n8)
% 52.48/20.19 | (1875) 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
% 52.48/20.19 |
% 52.48/20.19 +-Applying beta-rule and splitting (1875), into two cases.
% 52.48/20.19 |-Branch one:
% 52.48/20.19 | (1876) all_0_10_10 = n7
% 52.48/20.19 |
% 52.48/20.19 | From (1876) and (292) follows:
% 52.48/20.19 | (1877) pred(n7) = all_0_6_6
% 52.48/20.19 |
% 52.48/20.19 | From (1876) and (760) follows:
% 52.48/20.19 | (1878) succ(n7) = all_0_8_8
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 52.48/20.19 | (1879) all_0_6_6 = n6
% 52.48/20.19 |
% 52.48/20.19 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 52.48/20.19 | (1880) all_0_8_8 = n8
% 52.48/20.19 |
% 52.48/20.19 | From (1879)(1880) and (411) follows:
% 52.48/20.19 | (1881) sum(n6, n8) = all_0_1_1
% 52.48/20.19 |
% 52.48/20.19 | From (1879) and (2495) follows:
% 52.48/20.19 | (2794) sum(n6, n25) = all_0_4_4
% 52.48/20.19 |
% 52.48/20.19 | From (1880) and (2497) follows:
% 52.48/20.20 | (2795) sum(n23, n8) = all_0_7_7
% 52.48/20.20 |
% 52.48/20.20 | Instantiating formula (690) with n23, n8, all_0_7_7, n5 and discharging atoms sum(n23, n8) = all_0_7_7, sum(n23, n8) = n5, yields:
% 52.48/20.20 | (1443) all_0_7_7 = n5
% 52.48/20.20 |
% 52.48/20.20 | Instantiating formula (690) with n6, n25, all_0_4_4, n5 and discharging atoms sum(n6, n25) = all_0_4_4, sum(n6, n25) = n5, yields:
% 52.48/20.20 | (1441) all_0_4_4 = n5
% 52.48/20.20 |
% 52.66/20.20 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 52.66/20.20 | (1651) all_0_1_1 = n14
% 52.66/20.20 |
% 52.66/20.20 | From (1443)(1441) and (590) follows:
% 52.66/20.20 | (1445) sum(n5, n5) = all_0_3_3
% 52.66/20.20 |
% 52.66/20.20 | From (1651) and (2499) follows:
% 52.66/20.20 | (2566) sum(n22, n14) = all_0_0_0
% 52.66/20.20 |
% 52.66/20.20 | Instantiating formula (690) with n22, n14, all_0_0_0, n10 and discharging atoms sum(n22, n14) = all_0_0_0, sum(n22, n14) = n10, yields:
% 52.66/20.20 | (1213) all_0_0_0 = n10
% 52.66/20.20 |
% 52.66/20.20 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 52.66/20.20 | (1212) all_0_3_3 = n10
% 52.66/20.20 |
% 52.66/20.20 | Equations (1213,1212) can reduce 679 to:
% 52.66/20.20 | (1106) $false
% 52.66/20.20 |
% 52.66/20.20 |-The branch is then unsatisfiable
% 52.66/20.20 |-Branch two:
% 52.66/20.20 | (1892) ~ (all_0_10_10 = n7)
% 52.66/20.20 | (1893) 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
% 52.66/20.20 |
% 52.66/20.20 +-Applying beta-rule and splitting (1893), into two cases.
% 52.66/20.20 |-Branch one:
% 52.66/20.20 | (1894) all_0_10_10 = n6
% 52.66/20.20 |
% 52.66/20.20 | From (1894) and (292) follows:
% 52.66/20.20 | (1895) pred(n6) = all_0_6_6
% 52.66/20.20 |
% 52.66/20.20 | From (1894) and (760) follows:
% 52.66/20.20 | (1896) succ(n6) = all_0_8_8
% 52.66/20.20 |
% 52.66/20.20 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 52.66/20.20 | (1897) all_0_6_6 = n5
% 52.66/20.20 |
% 52.66/20.20 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 52.66/20.20 | (1898) all_0_8_8 = n7
% 52.66/20.20 |
% 52.66/20.20 | From (1897)(1898) and (411) follows:
% 52.66/20.20 | (1899) sum(n5, n7) = all_0_1_1
% 52.66/20.20 |
% 52.66/20.20 | From (1897) and (2495) follows:
% 52.66/20.20 | (2812) sum(n5, n25) = all_0_4_4
% 52.66/20.20 |
% 52.66/20.20 | From (1898) and (2497) follows:
% 52.66/20.20 | (2813) sum(n23, n7) = all_0_7_7
% 52.66/20.20 |
% 52.66/20.20 | Instantiating formula (690) with n23, n7, all_0_7_7, n4 and discharging atoms sum(n23, n7) = all_0_7_7, sum(n23, n7) = n4, yields:
% 52.66/20.20 | (1461) all_0_7_7 = n4
% 52.66/20.20 |
% 52.66/20.20 | Instantiating formula (690) with n5, n25, all_0_4_4, n4 and discharging atoms sum(n5, n25) = all_0_4_4, sum(n5, n25) = n4, yields:
% 52.66/20.20 | (1459) all_0_4_4 = n4
% 52.66/20.20 |
% 52.66/20.20 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 52.66/20.20 | (1669) all_0_1_1 = n12
% 52.66/20.20 |
% 52.66/20.20 | From (1461)(1459) and (590) follows:
% 52.66/20.20 | (1463) sum(n4, n4) = all_0_3_3
% 52.66/20.20 |
% 52.66/20.20 | From (1669) and (2499) follows:
% 52.66/20.20 | (2584) sum(n22, n12) = all_0_0_0
% 52.66/20.20 |
% 52.66/20.20 | Instantiating formula (690) with n22, n12, all_0_0_0, n8 and discharging atoms sum(n22, n12) = all_0_0_0, sum(n22, n12) = n8, yields:
% 52.66/20.20 | (1231) all_0_0_0 = n8
% 52.66/20.20 |
% 52.66/20.20 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 52.66/20.20 | (1230) all_0_3_3 = n8
% 52.66/20.20 |
% 52.66/20.20 | Equations (1231,1230) can reduce 679 to:
% 52.66/20.20 | (1106) $false
% 52.66/20.20 |
% 52.66/20.20 |-The branch is then unsatisfiable
% 52.66/20.20 |-Branch two:
% 52.66/20.20 | (1910) ~ (all_0_10_10 = n6)
% 52.66/20.20 | (1911) 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
% 52.66/20.20 |
% 52.66/20.20 +-Applying beta-rule and splitting (1911), into two cases.
% 52.66/20.20 |-Branch one:
% 52.66/20.20 | (1912) all_0_10_10 = n5
% 52.66/20.20 |
% 52.66/20.20 | From (1912) and (292) follows:
% 52.66/20.20 | (1913) pred(n5) = all_0_6_6
% 52.66/20.20 |
% 52.66/20.20 | From (1912) and (760) follows:
% 52.66/20.20 | (1914) succ(n5) = all_0_8_8
% 52.66/20.20 |
% 52.66/20.20 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 52.66/20.20 | (1915) all_0_6_6 = n4
% 52.66/20.20 |
% 52.66/20.20 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 52.66/20.20 | (1916) all_0_8_8 = n6
% 52.66/20.20 |
% 52.66/20.20 | From (1915)(1916) and (411) follows:
% 52.66/20.20 | (1917) sum(n4, n6) = all_0_1_1
% 52.66/20.20 |
% 52.66/20.20 | From (1915) and (2495) follows:
% 52.66/20.20 | (2830) sum(n4, n25) = all_0_4_4
% 52.66/20.20 |
% 52.66/20.20 | From (1916) and (2497) follows:
% 52.66/20.20 | (2831) sum(n23, n6) = all_0_7_7
% 52.66/20.20 |
% 52.66/20.20 | Instantiating formula (690) with n23, n6, all_0_7_7, n3 and discharging atoms sum(n23, n6) = all_0_7_7, sum(n23, n6) = n3, yields:
% 52.66/20.20 | (1479) all_0_7_7 = n3
% 52.66/20.20 |
% 52.66/20.20 | Instantiating formula (690) with n4, n25, all_0_4_4, n3 and discharging atoms sum(n4, n25) = all_0_4_4, sum(n4, n25) = n3, yields:
% 52.66/20.20 | (1477) all_0_4_4 = n3
% 52.66/20.20 |
% 52.66/20.20 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 52.66/20.20 | (1687) all_0_1_1 = n10
% 52.66/20.20 |
% 52.66/20.20 | From (1479)(1477) and (590) follows:
% 52.66/20.20 | (1481) sum(n3, n3) = all_0_3_3
% 52.66/20.20 |
% 52.66/20.20 | From (1687) and (2499) follows:
% 52.66/20.20 | (2602) sum(n22, n10) = all_0_0_0
% 52.66/20.20 |
% 52.66/20.20 | Instantiating formula (690) with n22, n10, all_0_0_0, n6 and discharging atoms sum(n22, n10) = all_0_0_0, sum(n22, n10) = n6, yields:
% 52.66/20.20 | (1249) all_0_0_0 = n6
% 52.66/20.20 |
% 52.66/20.20 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 52.66/20.20 | (1248) all_0_3_3 = n6
% 52.66/20.20 |
% 52.66/20.20 | Equations (1249,1248) can reduce 679 to:
% 52.66/20.20 | (1106) $false
% 52.66/20.20 |
% 52.66/20.20 |-The branch is then unsatisfiable
% 52.66/20.20 |-Branch two:
% 52.66/20.20 | (1928) ~ (all_0_10_10 = n5)
% 52.66/20.20 | (1929) 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
% 52.66/20.20 |
% 52.66/20.20 +-Applying beta-rule and splitting (1929), into two cases.
% 52.66/20.20 |-Branch one:
% 52.66/20.20 | (1930) all_0_10_10 = n4
% 52.66/20.20 |
% 52.66/20.20 | From (1930) and (292) follows:
% 52.66/20.20 | (1931) pred(n4) = all_0_6_6
% 52.66/20.20 |
% 52.66/20.20 | From (1930) and (760) follows:
% 52.66/20.20 | (1932) succ(n4) = all_0_8_8
% 52.66/20.20 |
% 52.66/20.20 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 52.66/20.21 | (1933) all_0_6_6 = n3
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 52.66/20.21 | (1934) all_0_8_8 = n5
% 52.66/20.21 |
% 52.66/20.21 | From (1933)(1934) and (411) follows:
% 52.66/20.21 | (1935) sum(n3, n5) = all_0_1_1
% 52.66/20.21 |
% 52.66/20.21 | From (1933) and (2495) follows:
% 52.66/20.21 | (2848) sum(n3, n25) = all_0_4_4
% 52.66/20.21 |
% 52.66/20.21 | From (1934) and (2497) follows:
% 52.66/20.21 | (2849) sum(n23, n5) = all_0_7_7
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (690) with n23, n5, all_0_7_7, n2 and discharging atoms sum(n23, n5) = all_0_7_7, sum(n23, n5) = n2, yields:
% 52.66/20.21 | (1497) all_0_7_7 = n2
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (690) with n3, n25, all_0_4_4, n2 and discharging atoms sum(n3, n25) = all_0_4_4, sum(n3, n25) = n2, yields:
% 52.66/20.21 | (1495) all_0_4_4 = n2
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 52.66/20.21 | (1705) all_0_1_1 = n8
% 52.66/20.21 |
% 52.66/20.21 | From (1497)(1495) and (590) follows:
% 52.66/20.21 | (1499) sum(n2, n2) = all_0_3_3
% 52.66/20.21 |
% 52.66/20.21 | From (1705) and (2499) follows:
% 52.66/20.21 | (2620) sum(n22, n8) = all_0_0_0
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (690) with n22, n8, all_0_0_0, n4 and discharging atoms sum(n22, n8) = all_0_0_0, sum(n22, n8) = n4, yields:
% 52.66/20.21 | (1267) all_0_0_0 = n4
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 52.66/20.21 | (1266) all_0_3_3 = n4
% 52.66/20.21 |
% 52.66/20.21 | Equations (1267,1266) can reduce 679 to:
% 52.66/20.21 | (1106) $false
% 52.66/20.21 |
% 52.66/20.21 |-The branch is then unsatisfiable
% 52.66/20.21 |-Branch two:
% 52.66/20.21 | (1946) ~ (all_0_10_10 = n4)
% 52.66/20.21 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 52.66/20.21 |
% 52.66/20.21 +-Applying beta-rule and splitting (1947), into two cases.
% 52.66/20.21 |-Branch one:
% 52.66/20.21 | (1948) all_0_10_10 = n3
% 52.66/20.21 |
% 52.66/20.21 | From (1948) and (292) follows:
% 52.66/20.21 | (1949) pred(n3) = all_0_6_6
% 52.66/20.21 |
% 52.66/20.21 | From (1948) and (760) follows:
% 52.66/20.21 | (1950) succ(n3) = all_0_8_8
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 52.66/20.21 | (1951) all_0_6_6 = n2
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 52.66/20.21 | (1952) all_0_8_8 = n4
% 52.66/20.21 |
% 52.66/20.21 | From (1951)(1952) and (411) follows:
% 52.66/20.21 | (1953) sum(n2, n4) = all_0_1_1
% 52.66/20.21 |
% 52.66/20.21 | From (1951) and (2495) follows:
% 52.66/20.21 | (2866) sum(n2, n25) = all_0_4_4
% 52.66/20.21 |
% 52.66/20.21 | From (1952) and (2497) follows:
% 52.66/20.21 | (2867) sum(n23, n4) = all_0_7_7
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (690) with n23, n4, all_0_7_7, n1 and discharging atoms sum(n23, n4) = all_0_7_7, sum(n23, n4) = n1, yields:
% 52.66/20.21 | (1515) all_0_7_7 = n1
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (690) with n2, n25, all_0_4_4, n1 and discharging atoms sum(n2, n25) = all_0_4_4, sum(n2, n25) = n1, yields:
% 52.66/20.21 | (1513) all_0_4_4 = n1
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 52.66/20.21 | (1723) all_0_1_1 = n6
% 52.66/20.21 |
% 52.66/20.21 | From (1515)(1513) and (590) follows:
% 52.66/20.21 | (1517) sum(n1, n1) = all_0_3_3
% 52.66/20.21 |
% 52.66/20.21 | From (1723) and (2499) follows:
% 52.66/20.21 | (2638) sum(n22, n6) = all_0_0_0
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (690) with n22, n6, all_0_0_0, n2 and discharging atoms sum(n22, n6) = all_0_0_0, sum(n22, n6) = n2, yields:
% 52.66/20.21 | (1285) all_0_0_0 = n2
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 52.66/20.21 | (1284) all_0_3_3 = n2
% 52.66/20.21 |
% 52.66/20.21 | Equations (1285,1284) can reduce 679 to:
% 52.66/20.21 | (1106) $false
% 52.66/20.21 |
% 52.66/20.21 |-The branch is then unsatisfiable
% 52.66/20.21 |-Branch two:
% 52.66/20.21 | (1964) ~ (all_0_10_10 = n3)
% 52.66/20.21 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 52.66/20.21 |
% 52.66/20.21 +-Applying beta-rule and splitting (1965), into two cases.
% 52.66/20.21 |-Branch one:
% 52.66/20.21 | (1966) all_0_10_10 = n2
% 52.66/20.21 |
% 52.66/20.21 | From (1966) and (292) follows:
% 52.66/20.21 | (1967) pred(n2) = all_0_6_6
% 52.66/20.21 |
% 52.66/20.21 | From (1966) and (760) follows:
% 52.66/20.21 | (1968) succ(n2) = all_0_8_8
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 52.66/20.21 | (1969) all_0_6_6 = n1
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 52.66/20.21 | (1970) all_0_8_8 = n3
% 52.66/20.21 |
% 52.66/20.21 | From (1969)(1970) and (411) follows:
% 52.66/20.21 | (1971) sum(n1, n3) = all_0_1_1
% 52.66/20.21 |
% 52.66/20.21 | From (1969) and (2495) follows:
% 52.66/20.21 | (2884) sum(n1, n25) = all_0_4_4
% 52.66/20.21 |
% 52.66/20.21 | From (1970) and (2497) follows:
% 52.66/20.21 | (2885) sum(n23, n3) = all_0_7_7
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (690) with n23, n3, all_0_7_7, n0 and discharging atoms sum(n23, n3) = all_0_7_7, sum(n23, n3) = n0, yields:
% 52.66/20.21 | (1533) all_0_7_7 = n0
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (690) with n1, n25, all_0_4_4, n0 and discharging atoms sum(n1, n25) = all_0_4_4, sum(n1, n25) = n0, yields:
% 52.66/20.21 | (1531) all_0_4_4 = n0
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 52.66/20.21 | (1741) all_0_1_1 = n4
% 52.66/20.21 |
% 52.66/20.21 | From (1533)(1531) and (590) follows:
% 52.66/20.21 | (1535) sum(n0, n0) = all_0_3_3
% 52.66/20.21 |
% 52.66/20.21 | From (1741) and (2499) follows:
% 52.66/20.21 | (2656) sum(n22, n4) = all_0_0_0
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (690) with n22, n4, all_0_0_0, n0 and discharging atoms sum(n22, n4) = all_0_0_0, sum(n22, n4) = n0, yields:
% 52.66/20.21 | (1303) all_0_0_0 = n0
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 52.66/20.21 | (1302) all_0_3_3 = n0
% 52.66/20.21 |
% 52.66/20.21 | Equations (1303,1302) can reduce 679 to:
% 52.66/20.21 | (1106) $false
% 52.66/20.21 |
% 52.66/20.21 |-The branch is then unsatisfiable
% 52.66/20.21 |-Branch two:
% 52.66/20.21 | (1982) ~ (all_0_10_10 = n2)
% 52.66/20.21 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 52.66/20.21 |
% 52.66/20.21 +-Applying beta-rule and splitting (1983), into two cases.
% 52.66/20.21 |-Branch one:
% 52.66/20.21 | (1984) all_0_10_10 = n1
% 52.66/20.21 |
% 52.66/20.21 | From (1984) and (292) follows:
% 52.66/20.21 | (1985) pred(n1) = all_0_6_6
% 52.66/20.21 |
% 52.66/20.21 | From (1984) and (760) follows:
% 52.66/20.21 | (1986) succ(n1) = all_0_8_8
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 52.66/20.21 | (1987) all_0_6_6 = n0
% 52.66/20.21 |
% 52.66/20.21 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 52.66/20.21 | (1988) all_0_8_8 = n2
% 52.66/20.21 |
% 52.66/20.21 | From (1987)(1988) and (411) follows:
% 52.66/20.22 | (1989) sum(n0, n2) = all_0_1_1
% 52.66/20.22 |
% 52.66/20.22 | From (1987) and (2495) follows:
% 52.66/20.22 | (2902) sum(n0, n25) = all_0_4_4
% 52.66/20.22 |
% 52.66/20.22 | From (1988) and (2497) follows:
% 52.66/20.22 | (2903) sum(n23, n2) = all_0_7_7
% 52.66/20.22 |
% 52.66/20.22 | Instantiating formula (690) with n23, n2, all_0_7_7, n25 and discharging atoms sum(n23, n2) = all_0_7_7, sum(n23, n2) = n25, yields:
% 52.66/20.22 | (1550) all_0_7_7 = n25
% 52.66/20.22 |
% 52.66/20.22 | Instantiating formula (690) with n0, n25, all_0_4_4, n25 and discharging atoms sum(n0, n25) = all_0_4_4, sum(n0, n25) = n25, yields:
% 52.66/20.22 | (1551) all_0_4_4 = n25
% 52.66/20.22 |
% 52.66/20.22 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 52.66/20.22 | (1759) all_0_1_1 = n2
% 52.66/20.22 |
% 52.66/20.22 | From (1550)(1551) and (590) follows:
% 52.66/20.22 | (1553) sum(n25, n25) = all_0_3_3
% 52.66/20.22 |
% 52.66/20.22 | From (1759) and (2499) follows:
% 52.66/20.22 | (2674) sum(n22, n2) = all_0_0_0
% 52.66/20.22 |
% 52.66/20.22 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 52.66/20.22 | (1320) all_0_3_3 = n24
% 52.66/20.22 |
% 52.66/20.22 | Instantiating formula (690) with n22, n2, all_0_0_0, n24 and discharging atoms sum(n22, n2) = all_0_0_0, sum(n22, n2) = n24, yields:
% 52.66/20.22 | (1321) all_0_0_0 = n24
% 52.66/20.22 |
% 52.66/20.22 | Equations (1321,1320) can reduce 679 to:
% 52.66/20.22 | (1106) $false
% 52.66/20.22 |
% 52.66/20.22 |-The branch is then unsatisfiable
% 52.66/20.22 |-Branch two:
% 52.66/20.22 | (2002) ~ (all_0_10_10 = n1)
% 52.66/20.22 | (2003) all_0_10_10 = n0
% 52.66/20.22 |
% 52.66/20.22 | From (2003) and (292) follows:
% 52.66/20.22 | (2004) pred(n0) = all_0_6_6
% 52.66/20.22 |
% 52.66/20.22 | From (2003) and (760) follows:
% 52.66/20.22 | (2005) succ(n0) = all_0_8_8
% 52.66/20.22 |
% 52.66/20.22 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 52.66/20.22 | (2006) all_0_6_6 = n25
% 52.66/20.22 |
% 52.66/20.22 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 52.66/20.22 | (2007) all_0_8_8 = n1
% 52.66/20.22 |
% 52.66/20.22 | From (2006)(2007) and (411) follows:
% 52.66/20.22 | (2008) sum(n25, n1) = all_0_1_1
% 52.66/20.22 |
% 52.66/20.22 | From (2006) and (2495) follows:
% 52.66/20.22 | (2919) sum(n25, n25) = all_0_4_4
% 52.66/20.22 |
% 52.66/20.22 | From (2007) and (2497) follows:
% 52.66/20.22 | (2920) sum(n23, n1) = all_0_7_7
% 52.66/20.22 |
% 52.66/20.22 | Instantiating formula (690) with n25, n25, all_0_4_4, n24 and discharging atoms sum(n25, n25) = all_0_4_4, sum(n25, n25) = n24, yields:
% 52.66/20.22 | (1096) all_0_4_4 = n24
% 52.66/20.22 |
% 52.66/20.22 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 52.66/20.22 | (1777) all_0_1_1 = n0
% 52.66/20.22 |
% 52.66/20.22 | Instantiating formula (690) with n23, n1, all_0_7_7, n24 and discharging atoms sum(n23, n1) = all_0_7_7, sum(n23, n1) = n24, yields:
% 52.66/20.22 | (1097) all_0_7_7 = n24
% 52.66/20.22 |
% 52.66/20.22 | From (1097)(1096) and (590) follows:
% 52.66/20.22 | (1101) sum(n24, n24) = all_0_3_3
% 52.66/20.22 |
% 52.66/20.22 | From (1777) and (2499) follows:
% 52.66/20.22 | (2692) sum(n22, n0) = all_0_0_0
% 52.66/20.22 |
% 52.66/20.22 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 52.66/20.22 | (1104) all_0_3_3 = n22
% 52.66/20.22 |
% 52.66/20.22 | Instantiating formula (690) with n22, n0, all_0_0_0, n22 and discharging atoms sum(n22, n0) = all_0_0_0, sum(n22, n0) = n22, yields:
% 52.66/20.22 | (1102) all_0_0_0 = n22
% 52.66/20.22 |
% 52.66/20.22 | Equations (1102,1104) can reduce 679 to:
% 52.66/20.22 | (1106) $false
% 52.66/20.22 |
% 52.66/20.22 |-The branch is then unsatisfiable
% 52.66/20.22 |-Branch two:
% 52.66/20.22 | (1125) ~ (all_0_11_11 = n24)
% 52.66/20.22 | (1126) all_0_11_11 = n23 | all_0_11_11 = n22 | all_0_11_11 = n21 | 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
% 52.66/20.22 |
% 52.66/20.22 +-Applying beta-rule and splitting (1587), into two cases.
% 52.66/20.22 |-Branch one:
% 52.66/20.22 | (1588) all_0_10_10 = n23
% 52.66/20.22 |
% 52.66/20.22 | From (1588) and (292) follows:
% 52.66/20.22 | (1589) pred(n23) = all_0_6_6
% 52.66/20.22 |
% 52.66/20.22 | From (1588) and (760) follows:
% 52.66/20.22 | (1590) succ(n23) = all_0_8_8
% 52.66/20.22 |
% 52.66/20.22 | Instantiating formula (500) with n23, all_0_6_6, n22 and discharging atoms pred(n23) = all_0_6_6, pred(n23) = n22, yields:
% 52.66/20.22 | (1591) all_0_6_6 = n22
% 52.66/20.22 |
% 52.66/20.22 | Instantiating formula (617) with n23, all_0_8_8, n24 and discharging atoms succ(n23) = all_0_8_8, succ(n23) = n24, yields:
% 52.66/20.22 | (1592) all_0_8_8 = n24
% 52.66/20.22 |
% 52.66/20.22 | From (1591) and (1589) follows:
% 52.66/20.22 | (1012) pred(n23) = n22
% 52.66/20.22 |
% 52.66/20.22 | From (1592) and (1590) follows:
% 52.66/20.22 | (784) succ(n23) = n24
% 52.66/20.22 |
% 52.66/20.22 | From (1591) and (541) follows:
% 52.66/20.22 | (2938) sum(n22, all_0_5_5) = all_0_4_4
% 52.66/20.22 |
% 52.66/20.22 | From (1591)(1592) and (411) follows:
% 52.66/20.22 | (1593) sum(n22, n24) = all_0_1_1
% 52.66/20.22 |
% 52.66/20.22 | From (1592) and (427) follows:
% 52.66/20.22 | (2940) sum(all_0_9_9, n24) = all_0_7_7
% 52.66/20.22 |
% 52.66/20.22 | Instantiating formula (690) with n22, n24, all_0_1_1, n20 and discharging atoms sum(n22, n24) = all_0_1_1, sum(n22, n24) = n20, yields:
% 52.66/20.22 | (1597) all_0_1_1 = n20
% 52.66/20.22 |
% 52.66/20.22 | From (1597) and (630) follows:
% 52.66/20.22 | (2942) sum(all_0_2_2, n20) = all_0_0_0
% 52.66/20.22 |
% 52.66/20.22 | From (1597) and (1593) follows:
% 52.66/20.22 | (534) sum(n22, n24) = n20
% 52.66/20.22 |
% 52.66/20.22 +-Applying beta-rule and splitting (1126), into two cases.
% 52.66/20.22 |-Branch one:
% 52.66/20.22 | (1127) all_0_11_11 = n23
% 52.66/20.22 |
% 52.66/20.22 | From (1127) and (559) follows:
% 52.66/20.22 | (1128) pred(n23) = all_0_9_9
% 52.66/20.22 |
% 52.66/20.22 | From (1127) and (992) follows:
% 52.66/20.22 | (1129) succ(n23) = all_0_5_5
% 52.66/20.22 |
% 52.66/20.22 | Instantiating formula (500) with n23, all_0_9_9, n22 and discharging atoms pred(n23) = all_0_9_9, pred(n23) = n22, yields:
% 52.66/20.22 | (1130) all_0_9_9 = n22
% 52.66/20.22 |
% 52.66/20.22 | Instantiating formula (617) with n23, all_0_5_5, n24 and discharging atoms succ(n23) = all_0_5_5, succ(n23) = n24, yields:
% 52.66/20.22 | (1131) all_0_5_5 = n24
% 52.66/20.22 |
% 52.66/20.22 | From (1130)(1131) and (538) follows:
% 52.66/20.22 | (1132) sum(n22, n24) = all_0_2_2
% 52.66/20.22 |
% 52.66/20.22 | From (1130) and (2940) follows:
% 52.66/20.23 | (2950) sum(n22, n24) = all_0_7_7
% 52.66/20.23 |
% 52.66/20.23 | From (1131) and (2938) follows:
% 52.66/20.23 | (2951) sum(n22, n24) = all_0_4_4
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (690) with n22, n24, all_0_2_2, n20 and discharging atoms sum(n22, n24) = all_0_2_2, sum(n22, n24) = n20, yields:
% 52.66/20.23 | (1136) all_0_2_2 = n20
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (690) with n22, n24, all_0_4_4, all_0_2_2 and discharging atoms sum(n22, n24) = all_0_2_2, sum(n22, n24) = all_0_4_4, yields:
% 52.66/20.23 | (1093) all_0_2_2 = all_0_4_4
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (690) with n22, n24, all_0_7_7, all_0_2_2 and discharging atoms sum(n22, n24) = all_0_2_2, sum(n22, n24) = all_0_7_7, yields:
% 52.66/20.23 | (1094) all_0_2_2 = all_0_7_7
% 52.66/20.23 |
% 52.66/20.23 | Combining equations (1094,1093) yields a new equation:
% 52.66/20.23 | (1095) all_0_4_4 = all_0_7_7
% 52.66/20.23 |
% 52.66/20.23 | Combining equations (1136,1093) yields a new equation:
% 52.66/20.23 | (1171) all_0_4_4 = n20
% 52.66/20.23 |
% 52.66/20.23 | Combining equations (1171,1095) yields a new equation:
% 52.66/20.23 | (1173) all_0_7_7 = n20
% 52.66/20.23 |
% 52.66/20.23 | Combining equations (1173,1095) yields a new equation:
% 52.66/20.23 | (1171) all_0_4_4 = n20
% 52.66/20.23 |
% 52.66/20.23 | Combining equations (1171,1093) yields a new equation:
% 52.66/20.23 | (1136) all_0_2_2 = n20
% 52.66/20.23 |
% 52.66/20.23 | From (1136) and (2942) follows:
% 52.66/20.23 | (2960) sum(n20, n20) = all_0_0_0
% 52.66/20.23 |
% 52.66/20.23 | From (1173)(1171) and (590) follows:
% 52.66/20.23 | (1175) sum(n20, n20) = all_0_3_3
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (690) with n20, n20, all_0_0_0, n14 and discharging atoms sum(n20, n20) = all_0_0_0, sum(n20, n20) = n14, yields:
% 52.66/20.23 | (1177) all_0_0_0 = n14
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (690) 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:
% 52.66/20.23 | (1103) all_0_0_0 = all_0_3_3
% 52.66/20.23 |
% 52.66/20.23 | Combining equations (1177,1103) yields a new equation:
% 52.66/20.23 | (1176) all_0_3_3 = n14
% 52.66/20.23 |
% 52.66/20.23 | Combining equations (1176,1103) yields a new equation:
% 52.66/20.23 | (1177) all_0_0_0 = n14
% 52.66/20.23 |
% 52.66/20.23 | Equations (1177,1176) can reduce 679 to:
% 52.66/20.23 | (1106) $false
% 52.66/20.23 |
% 52.66/20.23 |-The branch is then unsatisfiable
% 52.66/20.23 |-Branch two:
% 52.66/20.23 | (1143) ~ (all_0_11_11 = n23)
% 52.66/20.23 | (1144) all_0_11_11 = n22 | all_0_11_11 = n21 | 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
% 52.66/20.23 |
% 52.66/20.23 +-Applying beta-rule and splitting (1144), into two cases.
% 52.66/20.23 |-Branch one:
% 52.66/20.23 | (1145) all_0_11_11 = n22
% 52.66/20.23 |
% 52.66/20.23 | From (1145) and (559) follows:
% 52.66/20.23 | (1146) pred(n22) = all_0_9_9
% 52.66/20.23 |
% 52.66/20.23 | From (1145) and (992) follows:
% 52.66/20.23 | (1147) succ(n22) = all_0_5_5
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (500) with n22, all_0_9_9, n21 and discharging atoms pred(n22) = all_0_9_9, pred(n22) = n21, yields:
% 52.66/20.23 | (1148) all_0_9_9 = n21
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (617) with n22, all_0_5_5, n23 and discharging atoms succ(n22) = all_0_5_5, succ(n22) = n23, yields:
% 52.66/20.23 | (1149) all_0_5_5 = n23
% 52.66/20.23 |
% 52.66/20.23 | From (1148)(1149) and (538) follows:
% 52.66/20.23 | (1150) sum(n21, n23) = all_0_2_2
% 52.66/20.23 |
% 52.66/20.23 | From (1148) and (2940) follows:
% 52.66/20.23 | (2975) sum(n21, n24) = all_0_7_7
% 52.66/20.23 |
% 52.66/20.23 | From (1149) and (2938) follows:
% 52.66/20.23 | (2976) sum(n22, n23) = all_0_4_4
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (690) with n22, n23, all_0_4_4, n19 and discharging atoms sum(n22, n23) = all_0_4_4, sum(n22, n23) = n19, yields:
% 52.66/20.23 | (1189) all_0_4_4 = n19
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (690) with n21, n24, all_0_7_7, n19 and discharging atoms sum(n21, n24) = all_0_7_7, sum(n21, n24) = n19, yields:
% 52.66/20.23 | (1191) all_0_7_7 = n19
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (690) with n21, n23, all_0_2_2, n18 and discharging atoms sum(n21, n23) = all_0_2_2, sum(n21, n23) = n18, yields:
% 52.66/20.23 | (1154) all_0_2_2 = n18
% 52.66/20.23 |
% 52.66/20.23 | From (1154) and (2942) follows:
% 52.66/20.23 | (2980) sum(n18, n20) = all_0_0_0
% 52.66/20.23 |
% 52.66/20.23 | From (1191)(1189) and (590) follows:
% 52.66/20.23 | (1193) sum(n19, n19) = all_0_3_3
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 52.66/20.23 | (1194) all_0_3_3 = n12
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (690) with n18, n20, all_0_0_0, n12 and discharging atoms sum(n18, n20) = all_0_0_0, sum(n18, n20) = n12, yields:
% 52.66/20.23 | (1195) all_0_0_0 = n12
% 52.66/20.23 |
% 52.66/20.23 | Equations (1195,1194) can reduce 679 to:
% 52.66/20.23 | (1106) $false
% 52.66/20.23 |
% 52.66/20.23 |-The branch is then unsatisfiable
% 52.66/20.23 |-Branch two:
% 52.66/20.23 | (1161) ~ (all_0_11_11 = n22)
% 52.66/20.23 | (1162) all_0_11_11 = n21 | 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
% 52.66/20.23 |
% 52.66/20.23 +-Applying beta-rule and splitting (1162), into two cases.
% 52.66/20.23 |-Branch one:
% 52.66/20.23 | (1163) all_0_11_11 = n21
% 52.66/20.23 |
% 52.66/20.23 | From (1163) and (559) follows:
% 52.66/20.23 | (1164) pred(n21) = all_0_9_9
% 52.66/20.23 |
% 52.66/20.23 | From (1163) and (992) follows:
% 52.66/20.23 | (1165) succ(n21) = all_0_5_5
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (500) with n21, all_0_9_9, n20 and discharging atoms pred(n21) = all_0_9_9, pred(n21) = n20, yields:
% 52.66/20.23 | (1166) all_0_9_9 = n20
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (617) with n21, all_0_5_5, n22 and discharging atoms succ(n21) = all_0_5_5, succ(n21) = n22, yields:
% 52.66/20.23 | (1167) all_0_5_5 = n22
% 52.66/20.23 |
% 52.66/20.23 | From (1166)(1167) and (538) follows:
% 52.66/20.23 | (1168) sum(n20, n22) = all_0_2_2
% 52.66/20.23 |
% 52.66/20.23 | From (1166) and (2940) follows:
% 52.66/20.23 | (2993) sum(n20, n24) = all_0_7_7
% 52.66/20.23 |
% 52.66/20.23 | From (1167) and (2938) follows:
% 52.66/20.23 | (2994) sum(n22, n22) = all_0_4_4
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (690) with n22, n22, all_0_4_4, n18 and discharging atoms sum(n22, n22) = all_0_4_4, sum(n22, n22) = n18, yields:
% 52.66/20.23 | (1207) all_0_4_4 = n18
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (690) with n20, n24, all_0_7_7, n18 and discharging atoms sum(n20, n24) = all_0_7_7, sum(n20, n24) = n18, yields:
% 52.66/20.23 | (1209) all_0_7_7 = n18
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (690) with n20, n22, all_0_2_2, n16 and discharging atoms sum(n20, n22) = all_0_2_2, sum(n20, n22) = n16, yields:
% 52.66/20.23 | (1172) all_0_2_2 = n16
% 52.66/20.23 |
% 52.66/20.23 | From (1172) and (2942) follows:
% 52.66/20.23 | (2998) sum(n16, n20) = all_0_0_0
% 52.66/20.23 |
% 52.66/20.23 | From (1209)(1207) and (590) follows:
% 52.66/20.23 | (1211) sum(n18, n18) = all_0_3_3
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 52.66/20.23 | (1212) all_0_3_3 = n10
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (690) with n16, n20, all_0_0_0, n10 and discharging atoms sum(n16, n20) = all_0_0_0, sum(n16, n20) = n10, yields:
% 52.66/20.23 | (1213) all_0_0_0 = n10
% 52.66/20.23 |
% 52.66/20.23 | Equations (1213,1212) can reduce 679 to:
% 52.66/20.23 | (1106) $false
% 52.66/20.23 |
% 52.66/20.23 |-The branch is then unsatisfiable
% 52.66/20.23 |-Branch two:
% 52.66/20.23 | (1179) ~ (all_0_11_11 = n21)
% 52.66/20.23 | (1180) 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
% 52.66/20.23 |
% 52.66/20.23 +-Applying beta-rule and splitting (1180), into two cases.
% 52.66/20.23 |-Branch one:
% 52.66/20.23 | (1181) all_0_11_11 = n20
% 52.66/20.23 |
% 52.66/20.23 | From (1181) and (559) follows:
% 52.66/20.23 | (1182) pred(n20) = all_0_9_9
% 52.66/20.23 |
% 52.66/20.23 | From (1181) and (992) follows:
% 52.66/20.23 | (1183) succ(n20) = all_0_5_5
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (500) with n20, all_0_9_9, n19 and discharging atoms pred(n20) = all_0_9_9, pred(n20) = n19, yields:
% 52.66/20.23 | (1184) all_0_9_9 = n19
% 52.66/20.23 |
% 52.66/20.23 | Instantiating formula (617) with n20, all_0_5_5, n21 and discharging atoms succ(n20) = all_0_5_5, succ(n20) = n21, yields:
% 52.66/20.23 | (1185) all_0_5_5 = n21
% 52.66/20.23 |
% 52.66/20.23 | From (1184)(1185) and (538) follows:
% 52.66/20.23 | (1186) sum(n19, n21) = all_0_2_2
% 52.66/20.23 |
% 52.66/20.23 | From (1184) and (2940) follows:
% 52.66/20.24 | (3011) sum(n19, n24) = all_0_7_7
% 52.66/20.24 |
% 52.66/20.24 | From (1185) and (2938) follows:
% 52.66/20.24 | (3012) sum(n22, n21) = all_0_4_4
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (690) with n22, n21, all_0_4_4, n17 and discharging atoms sum(n22, n21) = all_0_4_4, sum(n22, n21) = n17, yields:
% 52.66/20.24 | (1225) all_0_4_4 = n17
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (690) with n19, n24, all_0_7_7, n17 and discharging atoms sum(n19, n24) = all_0_7_7, sum(n19, n24) = n17, yields:
% 52.66/20.24 | (1227) all_0_7_7 = n17
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (690) with n19, n21, all_0_2_2, n14 and discharging atoms sum(n19, n21) = all_0_2_2, sum(n19, n21) = n14, yields:
% 52.66/20.24 | (1190) all_0_2_2 = n14
% 52.66/20.24 |
% 52.66/20.24 | From (1190) and (2942) follows:
% 52.66/20.24 | (3016) sum(n14, n20) = all_0_0_0
% 52.66/20.24 |
% 52.66/20.24 | From (1227)(1225) and (590) follows:
% 52.66/20.24 | (1229) sum(n17, n17) = all_0_3_3
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 52.66/20.24 | (1230) all_0_3_3 = n8
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (690) with n14, n20, all_0_0_0, n8 and discharging atoms sum(n14, n20) = all_0_0_0, sum(n14, n20) = n8, yields:
% 52.66/20.24 | (1231) all_0_0_0 = n8
% 52.66/20.24 |
% 52.66/20.24 | Equations (1231,1230) can reduce 679 to:
% 52.66/20.24 | (1106) $false
% 52.66/20.24 |
% 52.66/20.24 |-The branch is then unsatisfiable
% 52.66/20.24 |-Branch two:
% 52.66/20.24 | (1197) ~ (all_0_11_11 = n20)
% 52.66/20.24 | (1198) 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
% 52.66/20.24 |
% 52.66/20.24 +-Applying beta-rule and splitting (1198), into two cases.
% 52.66/20.24 |-Branch one:
% 52.66/20.24 | (1199) all_0_11_11 = n19
% 52.66/20.24 |
% 52.66/20.24 | From (1199) and (559) follows:
% 52.66/20.24 | (1200) pred(n19) = all_0_9_9
% 52.66/20.24 |
% 52.66/20.24 | From (1199) and (992) follows:
% 52.66/20.24 | (1201) succ(n19) = all_0_5_5
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (500) with n19, all_0_9_9, n18 and discharging atoms pred(n19) = all_0_9_9, pred(n19) = n18, yields:
% 52.66/20.24 | (1202) all_0_9_9 = n18
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (617) with n19, all_0_5_5, n20 and discharging atoms succ(n19) = all_0_5_5, succ(n19) = n20, yields:
% 52.66/20.24 | (1203) all_0_5_5 = n20
% 52.66/20.24 |
% 52.66/20.24 | From (1202)(1203) and (538) follows:
% 52.66/20.24 | (1204) sum(n18, n20) = all_0_2_2
% 52.66/20.24 |
% 52.66/20.24 | From (1202) and (2940) follows:
% 52.66/20.24 | (3029) sum(n18, n24) = all_0_7_7
% 52.66/20.24 |
% 52.66/20.24 | From (1203) and (2938) follows:
% 52.66/20.24 | (3030) sum(n22, n20) = all_0_4_4
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (690) with n22, n20, all_0_4_4, n16 and discharging atoms sum(n22, n20) = all_0_4_4, sum(n22, n20) = n16, yields:
% 52.66/20.24 | (1243) all_0_4_4 = n16
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (690) with n18, n24, all_0_7_7, n16 and discharging atoms sum(n18, n24) = all_0_7_7, sum(n18, n24) = n16, yields:
% 52.66/20.24 | (1245) all_0_7_7 = n16
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (690) with n18, n20, all_0_2_2, n12 and discharging atoms sum(n18, n20) = all_0_2_2, sum(n18, n20) = n12, yields:
% 52.66/20.24 | (1208) all_0_2_2 = n12
% 52.66/20.24 |
% 52.66/20.24 | From (1208) and (2942) follows:
% 52.66/20.24 | (3034) sum(n12, n20) = all_0_0_0
% 52.66/20.24 |
% 52.66/20.24 | From (1245)(1243) and (590) follows:
% 52.66/20.24 | (1247) sum(n16, n16) = all_0_3_3
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 52.66/20.24 | (1248) all_0_3_3 = n6
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (690) with n12, n20, all_0_0_0, n6 and discharging atoms sum(n12, n20) = all_0_0_0, sum(n12, n20) = n6, yields:
% 52.66/20.24 | (1249) all_0_0_0 = n6
% 52.66/20.24 |
% 52.66/20.24 | Equations (1249,1248) can reduce 679 to:
% 52.66/20.24 | (1106) $false
% 52.66/20.24 |
% 52.66/20.24 |-The branch is then unsatisfiable
% 52.66/20.24 |-Branch two:
% 52.66/20.24 | (1215) ~ (all_0_11_11 = n19)
% 52.66/20.24 | (1216) 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
% 52.66/20.24 |
% 52.66/20.24 +-Applying beta-rule and splitting (1216), into two cases.
% 52.66/20.24 |-Branch one:
% 52.66/20.24 | (1217) all_0_11_11 = n18
% 52.66/20.24 |
% 52.66/20.24 | From (1217) and (559) follows:
% 52.66/20.24 | (1218) pred(n18) = all_0_9_9
% 52.66/20.24 |
% 52.66/20.24 | From (1217) and (992) follows:
% 52.66/20.24 | (1219) succ(n18) = all_0_5_5
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (500) with n18, all_0_9_9, n17 and discharging atoms pred(n18) = all_0_9_9, pred(n18) = n17, yields:
% 52.66/20.24 | (1220) all_0_9_9 = n17
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (617) with n18, all_0_5_5, n19 and discharging atoms succ(n18) = all_0_5_5, succ(n18) = n19, yields:
% 52.66/20.24 | (1221) all_0_5_5 = n19
% 52.66/20.24 |
% 52.66/20.24 | From (1220)(1221) and (538) follows:
% 52.66/20.24 | (1222) sum(n17, n19) = all_0_2_2
% 52.66/20.24 |
% 52.66/20.24 | From (1220) and (2940) follows:
% 52.66/20.24 | (3047) sum(n17, n24) = all_0_7_7
% 52.66/20.24 |
% 52.66/20.24 | From (1221) and (2938) follows:
% 52.66/20.24 | (3048) sum(n22, n19) = all_0_4_4
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (690) with n22, n19, all_0_4_4, n15 and discharging atoms sum(n22, n19) = all_0_4_4, sum(n22, n19) = n15, yields:
% 52.66/20.24 | (1261) all_0_4_4 = n15
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (690) with n17, n24, all_0_7_7, n15 and discharging atoms sum(n17, n24) = all_0_7_7, sum(n17, n24) = n15, yields:
% 52.66/20.24 | (1263) all_0_7_7 = n15
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (690) with n17, n19, all_0_2_2, n10 and discharging atoms sum(n17, n19) = all_0_2_2, sum(n17, n19) = n10, yields:
% 52.66/20.24 | (1226) all_0_2_2 = n10
% 52.66/20.24 |
% 52.66/20.24 | From (1226) and (2942) follows:
% 52.66/20.24 | (3052) sum(n10, n20) = all_0_0_0
% 52.66/20.24 |
% 52.66/20.24 | From (1263)(1261) and (590) follows:
% 52.66/20.24 | (1265) sum(n15, n15) = all_0_3_3
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 52.66/20.24 | (1266) all_0_3_3 = n4
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (690) with n10, n20, all_0_0_0, n4 and discharging atoms sum(n10, n20) = all_0_0_0, sum(n10, n20) = n4, yields:
% 52.66/20.24 | (1267) all_0_0_0 = n4
% 52.66/20.24 |
% 52.66/20.24 | Equations (1267,1266) can reduce 679 to:
% 52.66/20.24 | (1106) $false
% 52.66/20.24 |
% 52.66/20.24 |-The branch is then unsatisfiable
% 52.66/20.24 |-Branch two:
% 52.66/20.24 | (1233) ~ (all_0_11_11 = n18)
% 52.66/20.24 | (1234) 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
% 52.66/20.24 |
% 52.66/20.24 +-Applying beta-rule and splitting (1234), into two cases.
% 52.66/20.24 |-Branch one:
% 52.66/20.24 | (1235) all_0_11_11 = n17
% 52.66/20.24 |
% 52.66/20.24 | From (1235) and (559) follows:
% 52.66/20.24 | (1236) pred(n17) = all_0_9_9
% 52.66/20.24 |
% 52.66/20.24 | From (1235) and (992) follows:
% 52.66/20.24 | (1237) succ(n17) = all_0_5_5
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (500) with n17, all_0_9_9, n16 and discharging atoms pred(n17) = all_0_9_9, pred(n17) = n16, yields:
% 52.66/20.24 | (1238) all_0_9_9 = n16
% 52.66/20.24 |
% 52.66/20.24 | Instantiating formula (617) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 52.66/20.24 | (1239) all_0_5_5 = n18
% 52.66/20.24 |
% 52.66/20.24 | From (1238)(1239) and (538) follows:
% 52.66/20.24 | (1240) sum(n16, n18) = all_0_2_2
% 52.66/20.24 |
% 52.66/20.24 | From (1238) and (2940) follows:
% 52.66/20.24 | (3065) sum(n16, n24) = all_0_7_7
% 52.66/20.24 |
% 52.66/20.24 | From (1239) and (2938) follows:
% 52.66/20.25 | (3066) sum(n22, n18) = all_0_4_4
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (690) with n22, n18, all_0_4_4, n14 and discharging atoms sum(n22, n18) = all_0_4_4, sum(n22, n18) = n14, yields:
% 52.66/20.25 | (1279) all_0_4_4 = n14
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (690) with n16, n24, all_0_7_7, n14 and discharging atoms sum(n16, n24) = all_0_7_7, sum(n16, n24) = n14, yields:
% 52.66/20.25 | (1281) all_0_7_7 = n14
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (690) with n16, n18, all_0_2_2, n8 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = n8, yields:
% 52.66/20.25 | (1244) all_0_2_2 = n8
% 52.66/20.25 |
% 52.66/20.25 | From (1244) and (2942) follows:
% 52.66/20.25 | (3070) sum(n8, n20) = all_0_0_0
% 52.66/20.25 |
% 52.66/20.25 | From (1281)(1279) and (590) follows:
% 52.66/20.25 | (1283) sum(n14, n14) = all_0_3_3
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 52.66/20.25 | (1284) all_0_3_3 = n2
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (690) with n8, n20, all_0_0_0, n2 and discharging atoms sum(n8, n20) = all_0_0_0, sum(n8, n20) = n2, yields:
% 52.66/20.25 | (1285) all_0_0_0 = n2
% 52.66/20.25 |
% 52.66/20.25 | Equations (1285,1284) can reduce 679 to:
% 52.66/20.25 | (1106) $false
% 52.66/20.25 |
% 52.66/20.25 |-The branch is then unsatisfiable
% 52.66/20.25 |-Branch two:
% 52.66/20.25 | (1251) ~ (all_0_11_11 = n17)
% 52.66/20.25 | (1252) 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
% 52.66/20.25 |
% 52.66/20.25 +-Applying beta-rule and splitting (1252), into two cases.
% 52.66/20.25 |-Branch one:
% 52.66/20.25 | (1253) all_0_11_11 = n16
% 52.66/20.25 |
% 52.66/20.25 | From (1253) and (559) follows:
% 52.66/20.25 | (1254) pred(n16) = all_0_9_9
% 52.66/20.25 |
% 52.66/20.25 | From (1253) and (992) follows:
% 52.66/20.25 | (1255) succ(n16) = all_0_5_5
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (500) with n16, all_0_9_9, n15 and discharging atoms pred(n16) = all_0_9_9, pred(n16) = n15, yields:
% 52.66/20.25 | (1256) all_0_9_9 = n15
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (617) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 52.66/20.25 | (1257) all_0_5_5 = n17
% 52.66/20.25 |
% 52.66/20.25 | From (1256)(1257) and (538) follows:
% 52.66/20.25 | (1258) sum(n15, n17) = all_0_2_2
% 52.66/20.25 |
% 52.66/20.25 | From (1256) and (2940) follows:
% 52.66/20.25 | (3083) sum(n15, n24) = all_0_7_7
% 52.66/20.25 |
% 52.66/20.25 | From (1257) and (2938) follows:
% 52.66/20.25 | (3084) sum(n22, n17) = all_0_4_4
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (690) with n22, n17, all_0_4_4, n13 and discharging atoms sum(n22, n17) = all_0_4_4, sum(n22, n17) = n13, yields:
% 52.66/20.25 | (1297) all_0_4_4 = n13
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (690) with n15, n24, all_0_7_7, n13 and discharging atoms sum(n15, n24) = all_0_7_7, sum(n15, n24) = n13, yields:
% 52.66/20.25 | (1299) all_0_7_7 = n13
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (690) with n15, n17, all_0_2_2, n6 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n6, yields:
% 52.66/20.25 | (1262) all_0_2_2 = n6
% 52.66/20.25 |
% 52.66/20.25 | From (1262) and (2942) follows:
% 52.66/20.25 | (3088) sum(n6, n20) = all_0_0_0
% 52.66/20.25 |
% 52.66/20.25 | From (1299)(1297) and (590) follows:
% 52.66/20.25 | (1301) sum(n13, n13) = all_0_3_3
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 52.66/20.25 | (1302) all_0_3_3 = n0
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (690) with n6, n20, all_0_0_0, n0 and discharging atoms sum(n6, n20) = all_0_0_0, sum(n6, n20) = n0, yields:
% 52.66/20.25 | (1303) all_0_0_0 = n0
% 52.66/20.25 |
% 52.66/20.25 | Equations (1303,1302) can reduce 679 to:
% 52.66/20.25 | (1106) $false
% 52.66/20.25 |
% 52.66/20.25 |-The branch is then unsatisfiable
% 52.66/20.25 |-Branch two:
% 52.66/20.25 | (1269) ~ (all_0_11_11 = n16)
% 52.66/20.25 | (1270) 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
% 52.66/20.25 |
% 52.66/20.25 +-Applying beta-rule and splitting (1270), into two cases.
% 52.66/20.25 |-Branch one:
% 52.66/20.25 | (1271) all_0_11_11 = n15
% 52.66/20.25 |
% 52.66/20.25 | From (1271) and (559) follows:
% 52.66/20.25 | (1272) pred(n15) = all_0_9_9
% 52.66/20.25 |
% 52.66/20.25 | From (1271) and (992) follows:
% 52.66/20.25 | (1273) succ(n15) = all_0_5_5
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (500) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 52.66/20.25 | (1274) all_0_9_9 = n14
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (617) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 52.66/20.25 | (1275) all_0_5_5 = n16
% 52.66/20.25 |
% 52.66/20.25 | From (1274)(1275) and (538) follows:
% 52.66/20.25 | (1276) sum(n14, n16) = all_0_2_2
% 52.66/20.25 |
% 52.66/20.25 | From (1274) and (2940) follows:
% 52.66/20.25 | (3101) sum(n14, n24) = all_0_7_7
% 52.66/20.25 |
% 52.66/20.25 | From (1275) and (2938) follows:
% 52.66/20.25 | (3102) sum(n22, n16) = all_0_4_4
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (690) with n22, n16, all_0_4_4, n12 and discharging atoms sum(n22, n16) = all_0_4_4, sum(n22, n16) = n12, yields:
% 52.66/20.25 | (1315) all_0_4_4 = n12
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (690) with n14, n24, all_0_7_7, n12 and discharging atoms sum(n14, n24) = all_0_7_7, sum(n14, n24) = n12, yields:
% 52.66/20.25 | (1317) all_0_7_7 = n12
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (690) with n14, n16, all_0_2_2, n4 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n4, yields:
% 52.66/20.25 | (1280) all_0_2_2 = n4
% 52.66/20.25 |
% 52.66/20.25 | From (1280) and (2942) follows:
% 52.66/20.25 | (3106) sum(n4, n20) = all_0_0_0
% 52.66/20.25 |
% 52.66/20.25 | From (1317)(1315) and (590) follows:
% 52.66/20.25 | (1319) sum(n12, n12) = all_0_3_3
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 52.66/20.25 | (1320) all_0_3_3 = n24
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (690) with n4, n20, all_0_0_0, n24 and discharging atoms sum(n4, n20) = all_0_0_0, sum(n4, n20) = n24, yields:
% 52.66/20.25 | (1321) all_0_0_0 = n24
% 52.66/20.25 |
% 52.66/20.25 | Equations (1321,1320) can reduce 679 to:
% 52.66/20.25 | (1106) $false
% 52.66/20.25 |
% 52.66/20.25 |-The branch is then unsatisfiable
% 52.66/20.25 |-Branch two:
% 52.66/20.25 | (1287) ~ (all_0_11_11 = n15)
% 52.66/20.25 | (1288) 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
% 52.66/20.25 |
% 52.66/20.25 +-Applying beta-rule and splitting (1288), into two cases.
% 52.66/20.25 |-Branch one:
% 52.66/20.25 | (1289) all_0_11_11 = n14
% 52.66/20.25 |
% 52.66/20.25 | From (1289) and (559) follows:
% 52.66/20.25 | (1290) pred(n14) = all_0_9_9
% 52.66/20.25 |
% 52.66/20.25 | From (1289) and (992) follows:
% 52.66/20.25 | (1291) succ(n14) = all_0_5_5
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (500) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 52.66/20.25 | (1292) all_0_9_9 = n13
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (617) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 52.66/20.25 | (1293) all_0_5_5 = n15
% 52.66/20.25 |
% 52.66/20.25 | From (1292)(1293) and (538) follows:
% 52.66/20.25 | (1294) sum(n13, n15) = all_0_2_2
% 52.66/20.25 |
% 52.66/20.25 | From (1292) and (2940) follows:
% 52.66/20.25 | (3119) sum(n13, n24) = all_0_7_7
% 52.66/20.25 |
% 52.66/20.25 | From (1293) and (2938) follows:
% 52.66/20.25 | (3120) sum(n22, n15) = all_0_4_4
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (690) with n22, n15, all_0_4_4, n11 and discharging atoms sum(n22, n15) = all_0_4_4, sum(n22, n15) = n11, yields:
% 52.66/20.25 | (1333) all_0_4_4 = n11
% 52.66/20.25 |
% 52.66/20.25 | Instantiating formula (690) with n13, n24, all_0_7_7, n11 and discharging atoms sum(n13, n24) = all_0_7_7, sum(n13, n24) = n11, yields:
% 52.66/20.26 | (1335) all_0_7_7 = n11
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (690) with n13, n15, all_0_2_2, n2 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n2, yields:
% 52.66/20.26 | (1298) all_0_2_2 = n2
% 52.66/20.26 |
% 52.66/20.26 | From (1298) and (2942) follows:
% 52.66/20.26 | (3124) sum(n2, n20) = all_0_0_0
% 52.66/20.26 |
% 52.66/20.26 | From (1335)(1333) and (590) follows:
% 52.66/20.26 | (1337) sum(n11, n11) = all_0_3_3
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 52.66/20.26 | (1104) all_0_3_3 = n22
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (690) with n2, n20, all_0_0_0, n22 and discharging atoms sum(n2, n20) = all_0_0_0, sum(n2, n20) = n22, yields:
% 52.66/20.26 | (1102) all_0_0_0 = n22
% 52.66/20.26 |
% 52.66/20.26 | Equations (1102,1104) can reduce 679 to:
% 52.66/20.26 | (1106) $false
% 52.66/20.26 |
% 52.66/20.26 |-The branch is then unsatisfiable
% 52.66/20.26 |-Branch two:
% 52.66/20.26 | (1305) ~ (all_0_11_11 = n14)
% 52.66/20.26 | (1306) 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
% 52.66/20.26 |
% 52.66/20.26 +-Applying beta-rule and splitting (1306), into two cases.
% 52.66/20.26 |-Branch one:
% 52.66/20.26 | (1307) all_0_11_11 = n13
% 52.66/20.26 |
% 52.66/20.26 | From (1307) and (559) follows:
% 52.66/20.26 | (1308) pred(n13) = all_0_9_9
% 52.66/20.26 |
% 52.66/20.26 | From (1307) and (992) follows:
% 52.66/20.26 | (1309) succ(n13) = all_0_5_5
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (500) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 52.66/20.26 | (1310) all_0_9_9 = n12
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (617) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 52.66/20.26 | (1311) all_0_5_5 = n14
% 52.66/20.26 |
% 52.66/20.26 | From (1310)(1311) and (538) follows:
% 52.66/20.26 | (1312) sum(n12, n14) = all_0_2_2
% 52.66/20.26 |
% 52.66/20.26 | From (1310) and (2940) follows:
% 52.66/20.26 | (3137) sum(n12, n24) = all_0_7_7
% 52.66/20.26 |
% 52.66/20.26 | From (1311) and (2938) follows:
% 52.66/20.26 | (3138) sum(n22, n14) = all_0_4_4
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (690) with n22, n14, all_0_4_4, n10 and discharging atoms sum(n22, n14) = all_0_4_4, sum(n22, n14) = n10, yields:
% 52.66/20.26 | (1351) all_0_4_4 = n10
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (690) with n12, n24, all_0_7_7, n10 and discharging atoms sum(n12, n24) = all_0_7_7, sum(n12, n24) = n10, yields:
% 52.66/20.26 | (1353) all_0_7_7 = n10
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (690) with n12, n14, all_0_2_2, n0 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n0, yields:
% 52.66/20.26 | (1316) all_0_2_2 = n0
% 52.66/20.26 |
% 52.66/20.26 | From (1316) and (2942) follows:
% 52.66/20.26 | (3142) sum(n0, n20) = all_0_0_0
% 52.66/20.26 |
% 52.66/20.26 | From (1353)(1351) and (590) follows:
% 52.66/20.26 | (1355) sum(n10, n10) = all_0_3_3
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 52.66/20.26 | (1122) all_0_3_3 = n20
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (690) with n0, n20, all_0_0_0, n20 and discharging atoms sum(n0, n20) = all_0_0_0, sum(n0, n20) = n20, yields:
% 52.66/20.26 | (1123) all_0_0_0 = n20
% 52.66/20.26 |
% 52.66/20.26 | Equations (1123,1122) can reduce 679 to:
% 52.66/20.26 | (1106) $false
% 52.66/20.26 |
% 52.66/20.26 |-The branch is then unsatisfiable
% 52.66/20.26 |-Branch two:
% 52.66/20.26 | (1323) ~ (all_0_11_11 = n13)
% 52.66/20.26 | (1324) 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
% 52.66/20.26 |
% 52.66/20.26 +-Applying beta-rule and splitting (1324), into two cases.
% 52.66/20.26 |-Branch one:
% 52.66/20.26 | (1325) all_0_11_11 = n12
% 52.66/20.26 |
% 52.66/20.26 | From (1325) and (559) follows:
% 52.66/20.26 | (1326) pred(n12) = all_0_9_9
% 52.66/20.26 |
% 52.66/20.26 | From (1325) and (992) follows:
% 52.66/20.26 | (1327) succ(n12) = all_0_5_5
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (500) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 52.66/20.26 | (1328) all_0_9_9 = n11
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (617) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 52.66/20.26 | (1329) all_0_5_5 = n13
% 52.66/20.26 |
% 52.66/20.26 | From (1328)(1329) and (538) follows:
% 52.66/20.26 | (1330) sum(n11, n13) = all_0_2_2
% 52.66/20.26 |
% 52.66/20.26 | From (1328) and (2940) follows:
% 52.66/20.26 | (3155) sum(n11, n24) = all_0_7_7
% 52.66/20.26 |
% 52.66/20.26 | From (1329) and (2938) follows:
% 52.66/20.26 | (3156) sum(n22, n13) = all_0_4_4
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (690) with n22, n13, all_0_4_4, n9 and discharging atoms sum(n22, n13) = all_0_4_4, sum(n22, n13) = n9, yields:
% 52.66/20.26 | (1369) all_0_4_4 = n9
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (690) with n11, n24, all_0_7_7, n9 and discharging atoms sum(n11, n24) = all_0_7_7, sum(n11, n24) = n9, yields:
% 52.66/20.26 | (1371) all_0_7_7 = n9
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (690) with n11, n13, all_0_2_2, n24 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n24, yields:
% 52.66/20.26 | (1092) all_0_2_2 = n24
% 52.66/20.26 |
% 52.66/20.26 | From (1092) and (2942) follows:
% 52.66/20.26 | (1600) sum(n24, n20) = all_0_0_0
% 52.66/20.26 |
% 52.66/20.26 | From (1371)(1369) and (590) follows:
% 52.66/20.26 | (1373) sum(n9, n9) = all_0_3_3
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (690) with n24, n20, all_0_0_0, n18 and discharging atoms sum(n24, n20) = all_0_0_0, sum(n24, n20) = n18, yields:
% 52.66/20.26 | (1141) all_0_0_0 = n18
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 52.66/20.26 | (1140) all_0_3_3 = n18
% 52.66/20.26 |
% 52.66/20.26 | Equations (1141,1140) can reduce 679 to:
% 52.66/20.26 | (1106) $false
% 52.66/20.26 |
% 52.66/20.26 |-The branch is then unsatisfiable
% 52.66/20.26 |-Branch two:
% 52.66/20.26 | (1341) ~ (all_0_11_11 = n12)
% 52.66/20.26 | (1342) 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
% 52.66/20.26 |
% 52.66/20.26 +-Applying beta-rule and splitting (1342), into two cases.
% 52.66/20.26 |-Branch one:
% 52.66/20.26 | (1343) all_0_11_11 = n11
% 52.66/20.26 |
% 52.66/20.26 | From (1343) and (559) follows:
% 52.66/20.26 | (1344) pred(n11) = all_0_9_9
% 52.66/20.26 |
% 52.66/20.26 | From (1343) and (992) follows:
% 52.66/20.26 | (1345) succ(n11) = all_0_5_5
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (500) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 52.66/20.26 | (1346) all_0_9_9 = n10
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (617) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 52.66/20.26 | (1347) all_0_5_5 = n12
% 52.66/20.26 |
% 52.66/20.26 | From (1346)(1347) and (538) follows:
% 52.66/20.26 | (1348) sum(n10, n12) = all_0_2_2
% 52.66/20.26 |
% 52.66/20.26 | From (1346) and (2940) follows:
% 52.66/20.26 | (3173) sum(n10, n24) = all_0_7_7
% 52.66/20.26 |
% 52.66/20.26 | From (1347) and (2938) follows:
% 52.66/20.26 | (3174) sum(n22, n12) = all_0_4_4
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (690) with n22, n12, all_0_4_4, n8 and discharging atoms sum(n22, n12) = all_0_4_4, sum(n22, n12) = n8, yields:
% 52.66/20.26 | (1387) all_0_4_4 = n8
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (690) with n10, n24, all_0_7_7, n8 and discharging atoms sum(n10, n24) = all_0_7_7, sum(n10, n24) = n8, yields:
% 52.66/20.26 | (1389) all_0_7_7 = n8
% 52.66/20.26 |
% 52.66/20.26 | Instantiating formula (690) with n10, n12, all_0_2_2, n22 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n22, yields:
% 52.66/20.26 | (1118) all_0_2_2 = n22
% 52.66/20.26 |
% 52.66/20.26 | From (1118) and (2942) follows:
% 52.66/20.27 | (2512) sum(n22, n20) = all_0_0_0
% 52.66/20.27 |
% 52.66/20.27 | From (1389)(1387) and (590) follows:
% 52.66/20.27 | (1391) sum(n8, n8) = all_0_3_3
% 52.66/20.27 |
% 52.66/20.27 | Instantiating formula (690) with n22, n20, all_0_0_0, n16 and discharging atoms sum(n22, n20) = all_0_0_0, sum(n22, n20) = n16, yields:
% 52.66/20.27 | (1159) all_0_0_0 = n16
% 52.66/20.27 |
% 52.66/20.27 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 52.66/20.27 | (1158) all_0_3_3 = n16
% 52.66/20.27 |
% 52.66/20.27 | Equations (1159,1158) can reduce 679 to:
% 52.66/20.27 | (1106) $false
% 52.66/20.27 |
% 52.66/20.27 |-The branch is then unsatisfiable
% 52.66/20.27 |-Branch two:
% 52.66/20.27 | (1359) ~ (all_0_11_11 = n11)
% 52.66/20.27 | (1360) 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
% 52.66/20.27 |
% 52.66/20.27 +-Applying beta-rule and splitting (1360), into two cases.
% 52.66/20.27 |-Branch one:
% 52.66/20.27 | (1361) all_0_11_11 = n10
% 52.66/20.27 |
% 52.66/20.27 | From (1361) and (559) follows:
% 52.66/20.27 | (1362) pred(n10) = all_0_9_9
% 52.66/20.27 |
% 52.66/20.27 | From (1361) and (992) follows:
% 52.66/20.27 | (1363) succ(n10) = all_0_5_5
% 52.66/20.27 |
% 52.66/20.27 | Instantiating formula (500) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 52.66/20.27 | (1364) all_0_9_9 = n9
% 52.66/20.27 |
% 52.66/20.27 | Instantiating formula (617) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 52.66/20.27 | (1365) all_0_5_5 = n11
% 52.66/20.27 |
% 52.66/20.27 | From (1364)(1365) and (538) follows:
% 52.66/20.27 | (1366) sum(n9, n11) = all_0_2_2
% 52.66/20.27 |
% 52.66/20.27 | From (1364) and (2940) follows:
% 52.66/20.27 | (3191) sum(n9, n24) = all_0_7_7
% 52.66/20.27 |
% 52.66/20.27 | From (1365) and (2938) follows:
% 52.66/20.27 | (3192) sum(n22, n11) = all_0_4_4
% 52.66/20.27 |
% 52.66/20.27 | Instantiating formula (690) with n22, n11, all_0_4_4, n7 and discharging atoms sum(n22, n11) = all_0_4_4, sum(n22, n11) = n7, yields:
% 52.66/20.27 | (1405) all_0_4_4 = n7
% 52.66/20.27 |
% 52.66/20.27 | Instantiating formula (690) with n9, n24, all_0_7_7, n7 and discharging atoms sum(n9, n24) = all_0_7_7, sum(n9, n24) = n7, yields:
% 52.66/20.27 | (1407) all_0_7_7 = n7
% 52.66/20.27 |
% 52.66/20.27 | Instantiating formula (690) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 52.66/20.27 | (1136) all_0_2_2 = n20
% 52.66/20.27 |
% 52.66/20.27 | From (1136) and (2942) follows:
% 52.66/20.27 | (2960) sum(n20, n20) = all_0_0_0
% 52.66/20.27 |
% 52.66/20.27 | From (1407)(1405) and (590) follows:
% 52.66/20.27 | (1409) sum(n7, n7) = all_0_3_3
% 52.66/20.27 |
% 52.66/20.27 | Instantiating formula (690) with n20, n20, all_0_0_0, n14 and discharging atoms sum(n20, n20) = all_0_0_0, sum(n20, n20) = n14, yields:
% 52.66/20.27 | (1177) all_0_0_0 = n14
% 52.66/20.27 |
% 52.91/20.27 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 52.91/20.27 | (1176) all_0_3_3 = n14
% 52.91/20.27 |
% 52.91/20.27 | Equations (1177,1176) can reduce 679 to:
% 52.91/20.27 | (1106) $false
% 52.91/20.27 |
% 52.91/20.27 |-The branch is then unsatisfiable
% 52.91/20.27 |-Branch two:
% 52.91/20.27 | (1377) ~ (all_0_11_11 = n10)
% 52.91/20.27 | (1378) 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
% 52.91/20.27 |
% 52.91/20.27 +-Applying beta-rule and splitting (1378), into two cases.
% 52.91/20.27 |-Branch one:
% 52.91/20.27 | (1379) all_0_11_11 = n9
% 52.91/20.27 |
% 52.91/20.27 | From (1379) and (559) follows:
% 52.91/20.27 | (1380) pred(n9) = all_0_9_9
% 52.91/20.27 |
% 52.91/20.27 | From (1379) and (992) follows:
% 52.91/20.27 | (1381) succ(n9) = all_0_5_5
% 52.91/20.27 |
% 52.91/20.27 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 52.91/20.27 | (1382) all_0_9_9 = n8
% 52.91/20.27 |
% 52.91/20.27 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 52.91/20.27 | (1383) all_0_5_5 = n10
% 52.91/20.27 |
% 52.91/20.27 | From (1382)(1383) and (538) follows:
% 52.91/20.27 | (1384) sum(n8, n10) = all_0_2_2
% 52.91/20.27 |
% 52.91/20.27 | From (1382) and (2940) follows:
% 52.91/20.27 | (3209) sum(n8, n24) = all_0_7_7
% 52.91/20.27 |
% 52.91/20.27 | From (1383) and (2938) follows:
% 52.91/20.27 | (3210) sum(n22, n10) = all_0_4_4
% 52.91/20.27 |
% 52.91/20.27 | Instantiating formula (690) with n22, n10, all_0_4_4, n6 and discharging atoms sum(n22, n10) = all_0_4_4, sum(n22, n10) = n6, yields:
% 52.91/20.27 | (1423) all_0_4_4 = n6
% 52.91/20.27 |
% 52.91/20.27 | Instantiating formula (690) with n8, n24, all_0_7_7, n6 and discharging atoms sum(n8, n24) = all_0_7_7, sum(n8, n24) = n6, yields:
% 52.91/20.27 | (1425) all_0_7_7 = n6
% 52.91/20.27 |
% 52.91/20.27 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 52.91/20.27 | (1154) all_0_2_2 = n18
% 52.91/20.27 |
% 52.91/20.27 | From (1154) and (2942) follows:
% 52.91/20.27 | (2980) sum(n18, n20) = all_0_0_0
% 52.91/20.27 |
% 52.91/20.27 | From (1425)(1423) and (590) follows:
% 52.91/20.27 | (1427) sum(n6, n6) = all_0_3_3
% 52.91/20.27 |
% 52.91/20.27 | Instantiating formula (690) with n18, n20, all_0_0_0, n12 and discharging atoms sum(n18, n20) = all_0_0_0, sum(n18, n20) = n12, yields:
% 52.91/20.27 | (1195) all_0_0_0 = n12
% 52.91/20.27 |
% 52.91/20.27 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 52.91/20.27 | (1194) all_0_3_3 = n12
% 52.91/20.27 |
% 52.91/20.27 | Equations (1195,1194) can reduce 679 to:
% 52.91/20.27 | (1106) $false
% 52.91/20.27 |
% 52.91/20.27 |-The branch is then unsatisfiable
% 52.91/20.27 |-Branch two:
% 52.91/20.27 | (1395) ~ (all_0_11_11 = n9)
% 52.91/20.27 | (1396) 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
% 52.91/20.27 |
% 52.91/20.27 +-Applying beta-rule and splitting (1396), into two cases.
% 52.91/20.27 |-Branch one:
% 52.91/20.27 | (1397) all_0_11_11 = n8
% 52.91/20.27 |
% 52.91/20.27 | From (1397) and (559) follows:
% 52.91/20.27 | (1398) pred(n8) = all_0_9_9
% 52.91/20.27 |
% 52.91/20.27 | From (1397) and (992) follows:
% 52.91/20.27 | (1399) succ(n8) = all_0_5_5
% 52.91/20.27 |
% 52.91/20.27 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 52.91/20.27 | (1400) all_0_9_9 = n7
% 52.91/20.27 |
% 52.91/20.27 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 52.91/20.27 | (1401) all_0_5_5 = n9
% 52.91/20.27 |
% 52.91/20.27 | From (1400)(1401) and (538) follows:
% 52.91/20.27 | (1402) sum(n7, n9) = all_0_2_2
% 52.91/20.27 |
% 52.91/20.27 | From (1400) and (2940) follows:
% 52.91/20.27 | (3227) sum(n7, n24) = all_0_7_7
% 52.91/20.27 |
% 52.91/20.27 | From (1401) and (2938) follows:
% 52.91/20.27 | (3228) sum(n22, n9) = all_0_4_4
% 52.91/20.27 |
% 52.91/20.27 | Instantiating formula (690) with n22, n9, all_0_4_4, n5 and discharging atoms sum(n22, n9) = all_0_4_4, sum(n22, n9) = n5, yields:
% 52.91/20.27 | (1441) all_0_4_4 = n5
% 52.91/20.27 |
% 52.91/20.27 | Instantiating formula (690) with n7, n24, all_0_7_7, n5 and discharging atoms sum(n7, n24) = all_0_7_7, sum(n7, n24) = n5, yields:
% 52.91/20.27 | (1443) all_0_7_7 = n5
% 52.91/20.27 |
% 52.91/20.27 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 52.91/20.27 | (1172) all_0_2_2 = n16
% 52.91/20.27 |
% 52.91/20.27 | From (1172) and (2942) follows:
% 52.91/20.28 | (2998) sum(n16, n20) = all_0_0_0
% 52.91/20.28 |
% 52.91/20.28 | From (1443)(1441) and (590) follows:
% 52.91/20.28 | (1445) sum(n5, n5) = all_0_3_3
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (690) with n16, n20, all_0_0_0, n10 and discharging atoms sum(n16, n20) = all_0_0_0, sum(n16, n20) = n10, yields:
% 52.91/20.28 | (1213) all_0_0_0 = n10
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 52.91/20.28 | (1212) all_0_3_3 = n10
% 52.91/20.28 |
% 52.91/20.28 | Equations (1213,1212) can reduce 679 to:
% 52.91/20.28 | (1106) $false
% 52.91/20.28 |
% 52.91/20.28 |-The branch is then unsatisfiable
% 52.91/20.28 |-Branch two:
% 52.91/20.28 | (1413) ~ (all_0_11_11 = n8)
% 52.91/20.28 | (1414) 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
% 52.91/20.28 |
% 52.91/20.28 +-Applying beta-rule and splitting (1414), into two cases.
% 52.91/20.28 |-Branch one:
% 52.91/20.28 | (1415) all_0_11_11 = n7
% 52.91/20.28 |
% 52.91/20.28 | From (1415) and (559) follows:
% 52.91/20.28 | (1416) pred(n7) = all_0_9_9
% 52.91/20.28 |
% 52.91/20.28 | From (1415) and (992) follows:
% 52.91/20.28 | (1417) succ(n7) = all_0_5_5
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 52.91/20.28 | (1418) all_0_9_9 = n6
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 52.91/20.28 | (1419) all_0_5_5 = n8
% 52.91/20.28 |
% 52.91/20.28 | From (1418)(1419) and (538) follows:
% 52.91/20.28 | (1420) sum(n6, n8) = all_0_2_2
% 52.91/20.28 |
% 52.91/20.28 | From (1418) and (2940) follows:
% 52.91/20.28 | (3245) sum(n6, n24) = all_0_7_7
% 52.91/20.28 |
% 52.91/20.28 | From (1419) and (2938) follows:
% 52.91/20.28 | (3246) sum(n22, n8) = all_0_4_4
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (690) with n22, n8, all_0_4_4, n4 and discharging atoms sum(n22, n8) = all_0_4_4, sum(n22, n8) = n4, yields:
% 52.91/20.28 | (1459) all_0_4_4 = n4
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (690) with n6, n24, all_0_7_7, n4 and discharging atoms sum(n6, n24) = all_0_7_7, sum(n6, n24) = n4, yields:
% 52.91/20.28 | (1461) all_0_7_7 = n4
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 52.91/20.28 | (1190) all_0_2_2 = n14
% 52.91/20.28 |
% 52.91/20.28 | From (1190) and (2942) follows:
% 52.91/20.28 | (3016) sum(n14, n20) = all_0_0_0
% 52.91/20.28 |
% 52.91/20.28 | From (1461)(1459) and (590) follows:
% 52.91/20.28 | (1463) sum(n4, n4) = all_0_3_3
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (690) with n14, n20, all_0_0_0, n8 and discharging atoms sum(n14, n20) = all_0_0_0, sum(n14, n20) = n8, yields:
% 52.91/20.28 | (1231) all_0_0_0 = n8
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 52.91/20.28 | (1230) all_0_3_3 = n8
% 52.91/20.28 |
% 52.91/20.28 | Equations (1231,1230) can reduce 679 to:
% 52.91/20.28 | (1106) $false
% 52.91/20.28 |
% 52.91/20.28 |-The branch is then unsatisfiable
% 52.91/20.28 |-Branch two:
% 52.91/20.28 | (1431) ~ (all_0_11_11 = n7)
% 52.91/20.28 | (1432) 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
% 52.91/20.28 |
% 52.91/20.28 +-Applying beta-rule and splitting (1432), into two cases.
% 52.91/20.28 |-Branch one:
% 52.91/20.28 | (1433) all_0_11_11 = n6
% 52.91/20.28 |
% 52.91/20.28 | From (1433) and (559) follows:
% 52.91/20.28 | (1434) pred(n6) = all_0_9_9
% 52.91/20.28 |
% 52.91/20.28 | From (1433) and (992) follows:
% 52.91/20.28 | (1435) succ(n6) = all_0_5_5
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 52.91/20.28 | (1436) all_0_9_9 = n5
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 52.91/20.28 | (1437) all_0_5_5 = n7
% 52.91/20.28 |
% 52.91/20.28 | From (1436)(1437) and (538) follows:
% 52.91/20.28 | (1438) sum(n5, n7) = all_0_2_2
% 52.91/20.28 |
% 52.91/20.28 | From (1436) and (2940) follows:
% 52.91/20.28 | (3263) sum(n5, n24) = all_0_7_7
% 52.91/20.28 |
% 52.91/20.28 | From (1437) and (2938) follows:
% 52.91/20.28 | (3264) sum(n22, n7) = all_0_4_4
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (690) with n22, n7, all_0_4_4, n3 and discharging atoms sum(n22, n7) = all_0_4_4, sum(n22, n7) = n3, yields:
% 52.91/20.28 | (1477) all_0_4_4 = n3
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (690) with n5, n24, all_0_7_7, n3 and discharging atoms sum(n5, n24) = all_0_7_7, sum(n5, n24) = n3, yields:
% 52.91/20.28 | (1479) all_0_7_7 = n3
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 52.91/20.28 | (1208) all_0_2_2 = n12
% 52.91/20.28 |
% 52.91/20.28 | From (1208) and (2942) follows:
% 52.91/20.28 | (3034) sum(n12, n20) = all_0_0_0
% 52.91/20.28 |
% 52.91/20.28 | From (1479)(1477) and (590) follows:
% 52.91/20.28 | (1481) sum(n3, n3) = all_0_3_3
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (690) with n12, n20, all_0_0_0, n6 and discharging atoms sum(n12, n20) = all_0_0_0, sum(n12, n20) = n6, yields:
% 52.91/20.28 | (1249) all_0_0_0 = n6
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 52.91/20.28 | (1248) all_0_3_3 = n6
% 52.91/20.28 |
% 52.91/20.28 | Equations (1249,1248) can reduce 679 to:
% 52.91/20.28 | (1106) $false
% 52.91/20.28 |
% 52.91/20.28 |-The branch is then unsatisfiable
% 52.91/20.28 |-Branch two:
% 52.91/20.28 | (1449) ~ (all_0_11_11 = n6)
% 52.91/20.28 | (1450) 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
% 52.91/20.28 |
% 52.91/20.28 +-Applying beta-rule and splitting (1450), into two cases.
% 52.91/20.28 |-Branch one:
% 52.91/20.28 | (1451) all_0_11_11 = n5
% 52.91/20.28 |
% 52.91/20.28 | From (1451) and (559) follows:
% 52.91/20.28 | (1452) pred(n5) = all_0_9_9
% 52.91/20.28 |
% 52.91/20.28 | From (1451) and (992) follows:
% 52.91/20.28 | (1453) succ(n5) = all_0_5_5
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 52.91/20.28 | (1454) all_0_9_9 = n4
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 52.91/20.28 | (1455) all_0_5_5 = n6
% 52.91/20.28 |
% 52.91/20.28 | From (1454)(1455) and (538) follows:
% 52.91/20.28 | (1456) sum(n4, n6) = all_0_2_2
% 52.91/20.28 |
% 52.91/20.28 | From (1454) and (2940) follows:
% 52.91/20.28 | (3281) sum(n4, n24) = all_0_7_7
% 52.91/20.28 |
% 52.91/20.28 | From (1455) and (2938) follows:
% 52.91/20.28 | (3282) sum(n22, n6) = all_0_4_4
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (690) with n22, n6, all_0_4_4, n2 and discharging atoms sum(n22, n6) = all_0_4_4, sum(n22, n6) = n2, yields:
% 52.91/20.28 | (1495) all_0_4_4 = n2
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (690) with n4, n24, all_0_7_7, n2 and discharging atoms sum(n4, n24) = all_0_7_7, sum(n4, n24) = n2, yields:
% 52.91/20.28 | (1497) all_0_7_7 = n2
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 52.91/20.28 | (1226) all_0_2_2 = n10
% 52.91/20.28 |
% 52.91/20.28 | From (1226) and (2942) follows:
% 52.91/20.28 | (3052) sum(n10, n20) = all_0_0_0
% 52.91/20.28 |
% 52.91/20.28 | From (1497)(1495) and (590) follows:
% 52.91/20.28 | (1499) sum(n2, n2) = all_0_3_3
% 52.91/20.28 |
% 52.91/20.28 | Instantiating formula (690) with n10, n20, all_0_0_0, n4 and discharging atoms sum(n10, n20) = all_0_0_0, sum(n10, n20) = n4, yields:
% 52.91/20.29 | (1267) all_0_0_0 = n4
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 52.91/20.29 | (1266) all_0_3_3 = n4
% 52.91/20.29 |
% 52.91/20.29 | Equations (1267,1266) can reduce 679 to:
% 52.91/20.29 | (1106) $false
% 52.91/20.29 |
% 52.91/20.29 |-The branch is then unsatisfiable
% 52.91/20.29 |-Branch two:
% 52.91/20.29 | (1467) ~ (all_0_11_11 = n5)
% 52.91/20.29 | (1468) 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
% 52.91/20.29 |
% 52.91/20.29 +-Applying beta-rule and splitting (1468), into two cases.
% 52.91/20.29 |-Branch one:
% 52.91/20.29 | (1469) all_0_11_11 = n4
% 52.91/20.29 |
% 52.91/20.29 | From (1469) and (559) follows:
% 52.91/20.29 | (1470) pred(n4) = all_0_9_9
% 52.91/20.29 |
% 52.91/20.29 | From (1469) and (992) follows:
% 52.91/20.29 | (1471) succ(n4) = all_0_5_5
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 52.91/20.29 | (1472) all_0_9_9 = n3
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 52.91/20.29 | (1473) all_0_5_5 = n5
% 52.91/20.29 |
% 52.91/20.29 | From (1472)(1473) and (538) follows:
% 52.91/20.29 | (1474) sum(n3, n5) = all_0_2_2
% 52.91/20.29 |
% 52.91/20.29 | From (1472) and (2940) follows:
% 52.91/20.29 | (3299) sum(n3, n24) = all_0_7_7
% 52.91/20.29 |
% 52.91/20.29 | From (1473) and (2938) follows:
% 52.91/20.29 | (3300) sum(n22, n5) = all_0_4_4
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (690) with n22, n5, all_0_4_4, n1 and discharging atoms sum(n22, n5) = all_0_4_4, sum(n22, n5) = n1, yields:
% 52.91/20.29 | (1513) all_0_4_4 = n1
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (690) with n3, n24, all_0_7_7, n1 and discharging atoms sum(n3, n24) = all_0_7_7, sum(n3, n24) = n1, yields:
% 52.91/20.29 | (1515) all_0_7_7 = n1
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 52.91/20.29 | (1244) all_0_2_2 = n8
% 52.91/20.29 |
% 52.91/20.29 | From (1244) and (2942) follows:
% 52.91/20.29 | (3070) sum(n8, n20) = all_0_0_0
% 52.91/20.29 |
% 52.91/20.29 | From (1515)(1513) and (590) follows:
% 52.91/20.29 | (1517) sum(n1, n1) = all_0_3_3
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (690) with n8, n20, all_0_0_0, n2 and discharging atoms sum(n8, n20) = all_0_0_0, sum(n8, n20) = n2, yields:
% 52.91/20.29 | (1285) all_0_0_0 = n2
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 52.91/20.29 | (1284) all_0_3_3 = n2
% 52.91/20.29 |
% 52.91/20.29 | Equations (1285,1284) can reduce 679 to:
% 52.91/20.29 | (1106) $false
% 52.91/20.29 |
% 52.91/20.29 |-The branch is then unsatisfiable
% 52.91/20.29 |-Branch two:
% 52.91/20.29 | (1485) ~ (all_0_11_11 = n4)
% 52.91/20.29 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 52.91/20.29 |
% 52.91/20.29 +-Applying beta-rule and splitting (1486), into two cases.
% 52.91/20.29 |-Branch one:
% 52.91/20.29 | (1487) all_0_11_11 = n3
% 52.91/20.29 |
% 52.91/20.29 | From (1487) and (559) follows:
% 52.91/20.29 | (1488) pred(n3) = all_0_9_9
% 52.91/20.29 |
% 52.91/20.29 | From (1487) and (992) follows:
% 52.91/20.29 | (1489) succ(n3) = all_0_5_5
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 52.91/20.29 | (1490) all_0_9_9 = n2
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 52.91/20.29 | (1491) all_0_5_5 = n4
% 52.91/20.29 |
% 52.91/20.29 | From (1490)(1491) and (538) follows:
% 52.91/20.29 | (1492) sum(n2, n4) = all_0_2_2
% 52.91/20.29 |
% 52.91/20.29 | From (1490) and (2940) follows:
% 52.91/20.29 | (3317) sum(n2, n24) = all_0_7_7
% 52.91/20.29 |
% 52.91/20.29 | From (1491) and (2938) follows:
% 52.91/20.29 | (3318) sum(n22, n4) = all_0_4_4
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (690) with n22, n4, all_0_4_4, n0 and discharging atoms sum(n22, n4) = all_0_4_4, sum(n22, n4) = n0, yields:
% 52.91/20.29 | (1531) all_0_4_4 = n0
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (690) with n2, n24, all_0_7_7, n0 and discharging atoms sum(n2, n24) = all_0_7_7, sum(n2, n24) = n0, yields:
% 52.91/20.29 | (1533) all_0_7_7 = n0
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 52.91/20.29 | (1262) all_0_2_2 = n6
% 52.91/20.29 |
% 52.91/20.29 | From (1262) and (2942) follows:
% 52.91/20.29 | (3088) sum(n6, n20) = all_0_0_0
% 52.91/20.29 |
% 52.91/20.29 | From (1533)(1531) and (590) follows:
% 52.91/20.29 | (1535) sum(n0, n0) = all_0_3_3
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (690) with n6, n20, all_0_0_0, n0 and discharging atoms sum(n6, n20) = all_0_0_0, sum(n6, n20) = n0, yields:
% 52.91/20.29 | (1303) all_0_0_0 = n0
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 52.91/20.29 | (1302) all_0_3_3 = n0
% 52.91/20.29 |
% 52.91/20.29 | Equations (1303,1302) can reduce 679 to:
% 52.91/20.29 | (1106) $false
% 52.91/20.29 |
% 52.91/20.29 |-The branch is then unsatisfiable
% 52.91/20.29 |-Branch two:
% 52.91/20.29 | (1503) ~ (all_0_11_11 = n3)
% 52.91/20.29 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 52.91/20.29 |
% 52.91/20.29 +-Applying beta-rule and splitting (1504), into two cases.
% 52.91/20.29 |-Branch one:
% 52.91/20.29 | (1505) all_0_11_11 = n2
% 52.91/20.29 |
% 52.91/20.29 | From (1505) and (559) follows:
% 52.91/20.29 | (1506) pred(n2) = all_0_9_9
% 52.91/20.29 |
% 52.91/20.29 | From (1505) and (992) follows:
% 52.91/20.29 | (1507) succ(n2) = all_0_5_5
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 52.91/20.29 | (1508) all_0_9_9 = n1
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 52.91/20.29 | (1509) all_0_5_5 = n3
% 52.91/20.29 |
% 52.91/20.29 | From (1508)(1509) and (538) follows:
% 52.91/20.29 | (1510) sum(n1, n3) = all_0_2_2
% 52.91/20.29 |
% 52.91/20.29 | From (1508) and (2940) follows:
% 52.91/20.29 | (3335) sum(n1, n24) = all_0_7_7
% 52.91/20.29 |
% 52.91/20.29 | From (1509) and (2938) follows:
% 52.91/20.29 | (3336) sum(n22, n3) = all_0_4_4
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (690) with n22, n3, all_0_4_4, n25 and discharging atoms sum(n22, n3) = all_0_4_4, sum(n22, n3) = n25, yields:
% 52.91/20.29 | (1551) all_0_4_4 = n25
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (690) with n1, n24, all_0_7_7, n25 and discharging atoms sum(n1, n24) = all_0_7_7, sum(n1, n24) = n25, yields:
% 52.91/20.29 | (1550) all_0_7_7 = n25
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 52.91/20.29 | (1280) all_0_2_2 = n4
% 52.91/20.29 |
% 52.91/20.29 | From (1280) and (2942) follows:
% 52.91/20.29 | (3106) sum(n4, n20) = all_0_0_0
% 52.91/20.29 |
% 52.91/20.29 | From (1550)(1551) and (590) follows:
% 52.91/20.29 | (1553) sum(n25, n25) = all_0_3_3
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 52.91/20.29 | (1320) all_0_3_3 = n24
% 52.91/20.29 |
% 52.91/20.29 | Instantiating formula (690) with n4, n20, all_0_0_0, n24 and discharging atoms sum(n4, n20) = all_0_0_0, sum(n4, n20) = n24, yields:
% 52.91/20.29 | (1321) all_0_0_0 = n24
% 52.91/20.29 |
% 52.91/20.29 | Equations (1321,1320) can reduce 679 to:
% 52.91/20.29 | (1106) $false
% 52.91/20.29 |
% 52.91/20.29 |-The branch is then unsatisfiable
% 52.91/20.29 |-Branch two:
% 52.91/20.29 | (1521) ~ (all_0_11_11 = n2)
% 52.91/20.29 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 52.91/20.30 |
% 52.91/20.30 +-Applying beta-rule and splitting (1522), into two cases.
% 52.91/20.30 |-Branch one:
% 52.91/20.30 | (1523) all_0_11_11 = n1
% 52.91/20.30 |
% 52.91/20.30 | From (1523) and (559) follows:
% 52.91/20.30 | (1524) pred(n1) = all_0_9_9
% 52.91/20.30 |
% 52.91/20.30 | From (1523) and (992) follows:
% 52.91/20.30 | (1525) succ(n1) = all_0_5_5
% 52.91/20.30 |
% 52.91/20.30 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 52.91/20.30 | (1526) all_0_9_9 = n0
% 52.91/20.30 |
% 52.91/20.30 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 52.91/20.30 | (1527) all_0_5_5 = n2
% 52.91/20.30 |
% 52.91/20.30 | From (1526)(1527) and (538) follows:
% 52.91/20.30 | (1528) sum(n0, n2) = all_0_2_2
% 52.91/20.30 |
% 52.91/20.30 | From (1526) and (2940) follows:
% 52.91/20.30 | (3353) sum(n0, n24) = all_0_7_7
% 52.91/20.30 |
% 52.91/20.30 | From (1527) and (2938) follows:
% 52.91/20.30 | (3354) sum(n22, n2) = all_0_4_4
% 52.91/20.30 |
% 52.91/20.30 | Instantiating formula (690) with n22, n2, all_0_4_4, n24 and discharging atoms sum(n22, n2) = all_0_4_4, sum(n22, n2) = n24, yields:
% 52.91/20.30 | (1096) all_0_4_4 = n24
% 52.91/20.30 |
% 52.91/20.30 | Instantiating formula (690) with n0, n24, all_0_7_7, n24 and discharging atoms sum(n0, n24) = all_0_7_7, sum(n0, n24) = n24, yields:
% 52.91/20.30 | (1097) all_0_7_7 = n24
% 52.91/20.30 |
% 52.91/20.30 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 52.91/20.30 | (1298) all_0_2_2 = n2
% 52.91/20.30 |
% 52.91/20.30 | From (1298) and (2942) follows:
% 52.91/20.30 | (3124) sum(n2, n20) = all_0_0_0
% 52.91/20.30 |
% 52.91/20.30 | From (1097)(1096) and (590) follows:
% 52.91/20.30 | (1101) sum(n24, n24) = all_0_3_3
% 52.91/20.30 |
% 52.91/20.30 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 52.91/20.30 | (1104) all_0_3_3 = n22
% 52.91/20.30 |
% 53.01/20.30 | Instantiating formula (690) with n2, n20, all_0_0_0, n22 and discharging atoms sum(n2, n20) = all_0_0_0, sum(n2, n20) = n22, yields:
% 53.01/20.30 | (1102) all_0_0_0 = n22
% 53.01/20.30 |
% 53.01/20.30 | Equations (1102,1104) can reduce 679 to:
% 53.01/20.30 | (1106) $false
% 53.01/20.30 |
% 53.01/20.30 |-The branch is then unsatisfiable
% 53.01/20.30 |-Branch two:
% 53.01/20.30 | (1540) ~ (all_0_11_11 = n1)
% 53.01/20.30 | (1541) all_0_11_11 = n0
% 53.01/20.30 |
% 53.01/20.30 | From (1541) and (559) follows:
% 53.01/20.30 | (1542) pred(n0) = all_0_9_9
% 53.01/20.30 |
% 53.01/20.30 | From (1541) and (992) follows:
% 53.01/20.30 | (1543) succ(n0) = all_0_5_5
% 53.01/20.30 |
% 53.01/20.30 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 53.01/20.30 | (1544) all_0_9_9 = n25
% 53.01/20.30 |
% 53.01/20.30 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 53.01/20.30 | (1545) all_0_5_5 = n1
% 53.01/20.30 |
% 53.01/20.30 | From (1544)(1545) and (538) follows:
% 53.01/20.30 | (1546) sum(n25, n1) = all_0_2_2
% 53.01/20.30 |
% 53.01/20.30 | From (1544) and (2940) follows:
% 53.01/20.30 | (3370) sum(n25, n24) = all_0_7_7
% 53.01/20.30 |
% 53.01/20.30 | From (1545) and (2938) follows:
% 53.01/20.30 | (3371) sum(n22, n1) = all_0_4_4
% 53.01/20.30 |
% 53.01/20.30 | Instantiating formula (690) with n25, n24, all_0_7_7, n23 and discharging atoms sum(n25, n24) = all_0_7_7, sum(n25, n24) = n23, yields:
% 53.01/20.30 | (1119) all_0_7_7 = n23
% 53.01/20.30 |
% 53.01/20.30 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 53.01/20.30 | (1316) all_0_2_2 = n0
% 53.01/20.30 |
% 53.01/20.30 | Instantiating formula (690) with n22, n1, all_0_4_4, n23 and discharging atoms sum(n22, n1) = all_0_4_4, sum(n22, n1) = n23, yields:
% 53.01/20.30 | (1117) all_0_4_4 = n23
% 53.01/20.30 |
% 53.01/20.30 | From (1316) and (2942) follows:
% 53.01/20.30 | (3142) sum(n0, n20) = all_0_0_0
% 53.01/20.30 |
% 53.01/20.30 | From (1119)(1117) and (590) follows:
% 53.01/20.30 | (1121) sum(n23, n23) = all_0_3_3
% 53.01/20.30 |
% 53.01/20.30 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 53.01/20.30 | (1122) all_0_3_3 = n20
% 53.01/20.30 |
% 53.01/20.30 | Instantiating formula (690) with n0, n20, all_0_0_0, n20 and discharging atoms sum(n0, n20) = all_0_0_0, sum(n0, n20) = n20, yields:
% 53.01/20.30 | (1123) all_0_0_0 = n20
% 53.01/20.30 |
% 53.01/20.30 | Equations (1123,1122) can reduce 679 to:
% 53.01/20.30 | (1106) $false
% 53.01/20.30 |
% 53.01/20.30 |-The branch is then unsatisfiable
% 53.01/20.30 |-Branch two:
% 53.01/20.30 | (1604) ~ (all_0_10_10 = n23)
% 53.01/20.30 | (1605) all_0_10_10 = n22 | all_0_10_10 = n21 | 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
% 53.01/20.30 |
% 53.01/20.30 +-Applying beta-rule and splitting (1126), into two cases.
% 53.01/20.30 |-Branch one:
% 53.01/20.30 | (1127) all_0_11_11 = n23
% 53.01/20.30 |
% 53.01/20.30 | From (1127) and (559) follows:
% 53.01/20.30 | (1128) pred(n23) = all_0_9_9
% 53.01/20.30 |
% 53.01/20.30 | From (1127) and (992) follows:
% 53.01/20.30 | (1129) succ(n23) = all_0_5_5
% 53.01/20.30 |
% 53.01/20.30 | Instantiating formula (500) with n23, all_0_9_9, n22 and discharging atoms pred(n23) = all_0_9_9, pred(n23) = n22, yields:
% 53.01/20.30 | (1130) all_0_9_9 = n22
% 53.01/20.30 |
% 53.01/20.30 | Instantiating formula (617) with n23, all_0_5_5, n24 and discharging atoms succ(n23) = all_0_5_5, succ(n23) = n24, yields:
% 53.01/20.30 | (1131) all_0_5_5 = n24
% 53.01/20.30 |
% 53.01/20.30 | From (1131) and (541) follows:
% 53.01/20.30 | (3387) sum(all_0_6_6, n24) = all_0_4_4
% 53.01/20.30 |
% 53.01/20.30 | From (1130)(1131) and (538) follows:
% 53.01/20.30 | (1132) sum(n22, n24) = all_0_2_2
% 53.01/20.30 |
% 53.01/20.30 | From (1130) and (427) follows:
% 53.01/20.30 | (3389) sum(n22, all_0_8_8) = all_0_7_7
% 53.01/20.30 |
% 53.01/20.30 | Instantiating formula (690) with n22, n24, all_0_2_2, n20 and discharging atoms sum(n22, n24) = all_0_2_2, sum(n22, n24) = n20, yields:
% 53.01/20.30 | (1136) all_0_2_2 = n20
% 53.01/20.30 |
% 53.01/20.30 | From (1136) and (630) follows:
% 53.01/20.30 | (3391) sum(n20, all_0_1_1) = all_0_0_0
% 53.01/20.30 |
% 53.01/20.30 +-Applying beta-rule and splitting (1605), into two cases.
% 53.01/20.30 |-Branch one:
% 53.01/20.30 | (1606) all_0_10_10 = n22
% 53.01/20.30 |
% 53.01/20.30 | From (1606) and (292) follows:
% 53.01/20.30 | (1607) pred(n22) = all_0_6_6
% 53.01/20.30 |
% 53.01/20.30 | From (1606) and (760) follows:
% 53.01/20.30 | (1608) succ(n22) = all_0_8_8
% 53.01/20.30 |
% 53.01/20.30 | Instantiating formula (500) with n22, all_0_6_6, n21 and discharging atoms pred(n22) = all_0_6_6, pred(n22) = n21, yields:
% 53.01/20.30 | (1609) all_0_6_6 = n21
% 53.01/20.30 |
% 53.01/20.30 | Instantiating formula (617) with n22, all_0_8_8, n23 and discharging atoms succ(n22) = all_0_8_8, succ(n22) = n23, yields:
% 53.01/20.30 | (1610) all_0_8_8 = n23
% 53.01/20.30 |
% 53.01/20.30 | From (1609)(1610) and (411) follows:
% 53.01/20.30 | (1611) sum(n21, n23) = all_0_1_1
% 53.01/20.30 |
% 53.01/20.30 | From (1609) and (3387) follows:
% 53.01/20.31 | (3398) sum(n21, n24) = all_0_4_4
% 53.01/20.31 |
% 53.01/20.31 | From (1610) and (3389) follows:
% 53.01/20.31 | (3399) sum(n22, n23) = all_0_7_7
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (690) with n22, n23, all_0_7_7, n19 and discharging atoms sum(n22, n23) = all_0_7_7, sum(n22, n23) = n19, yields:
% 53.01/20.31 | (1191) all_0_7_7 = n19
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (690) with n21, n24, all_0_4_4, n19 and discharging atoms sum(n21, n24) = all_0_4_4, sum(n21, n24) = n19, yields:
% 53.01/20.31 | (1189) all_0_4_4 = n19
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (690) with n21, n23, all_0_1_1, n18 and discharging atoms sum(n21, n23) = all_0_1_1, sum(n21, n23) = n18, yields:
% 53.01/20.31 | (1615) all_0_1_1 = n18
% 53.01/20.31 |
% 53.01/20.31 | From (1191)(1189) and (590) follows:
% 53.01/20.31 | (1193) sum(n19, n19) = all_0_3_3
% 53.01/20.31 |
% 53.01/20.31 | From (1615) and (3391) follows:
% 53.01/20.31 | (3404) sum(n20, n18) = all_0_0_0
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (690) with n20, n18, all_0_0_0, n12 and discharging atoms sum(n20, n18) = all_0_0_0, sum(n20, n18) = n12, yields:
% 53.01/20.31 | (1195) all_0_0_0 = n12
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 53.01/20.31 | (1194) all_0_3_3 = n12
% 53.01/20.31 |
% 53.01/20.31 | Equations (1195,1194) can reduce 679 to:
% 53.01/20.31 | (1106) $false
% 53.01/20.31 |
% 53.01/20.31 |-The branch is then unsatisfiable
% 53.01/20.31 |-Branch two:
% 53.01/20.31 | (1622) ~ (all_0_10_10 = n22)
% 53.01/20.31 | (1623) all_0_10_10 = n21 | 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
% 53.01/20.31 |
% 53.01/20.31 +-Applying beta-rule and splitting (1623), into two cases.
% 53.01/20.31 |-Branch one:
% 53.01/20.31 | (1624) all_0_10_10 = n21
% 53.01/20.31 |
% 53.01/20.31 | From (1624) and (292) follows:
% 53.01/20.31 | (1625) pred(n21) = all_0_6_6
% 53.01/20.31 |
% 53.01/20.31 | From (1624) and (760) follows:
% 53.01/20.31 | (1626) succ(n21) = all_0_8_8
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (500) with n21, all_0_6_6, n20 and discharging atoms pred(n21) = all_0_6_6, pred(n21) = n20, yields:
% 53.01/20.31 | (1627) all_0_6_6 = n20
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (617) with n21, all_0_8_8, n22 and discharging atoms succ(n21) = all_0_8_8, succ(n21) = n22, yields:
% 53.01/20.31 | (1628) all_0_8_8 = n22
% 53.01/20.31 |
% 53.01/20.31 | From (1627)(1628) and (411) follows:
% 53.01/20.31 | (1629) sum(n20, n22) = all_0_1_1
% 53.01/20.31 |
% 53.01/20.31 | From (1627) and (3387) follows:
% 53.01/20.31 | (3416) sum(n20, n24) = all_0_4_4
% 53.01/20.31 |
% 53.01/20.31 | From (1628) and (3389) follows:
% 53.01/20.31 | (3417) sum(n22, n22) = all_0_7_7
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (690) with n22, n22, all_0_7_7, n18 and discharging atoms sum(n22, n22) = all_0_7_7, sum(n22, n22) = n18, yields:
% 53.01/20.31 | (1209) all_0_7_7 = n18
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (690) with n20, n24, all_0_4_4, n18 and discharging atoms sum(n20, n24) = all_0_4_4, sum(n20, n24) = n18, yields:
% 53.01/20.31 | (1207) all_0_4_4 = n18
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (690) with n20, n22, all_0_1_1, n16 and discharging atoms sum(n20, n22) = all_0_1_1, sum(n20, n22) = n16, yields:
% 53.01/20.31 | (1633) all_0_1_1 = n16
% 53.01/20.31 |
% 53.01/20.31 | From (1209)(1207) and (590) follows:
% 53.01/20.31 | (1211) sum(n18, n18) = all_0_3_3
% 53.01/20.31 |
% 53.01/20.31 | From (1633) and (3391) follows:
% 53.01/20.31 | (3422) sum(n20, n16) = all_0_0_0
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (690) with n20, n16, all_0_0_0, n10 and discharging atoms sum(n20, n16) = all_0_0_0, sum(n20, n16) = n10, yields:
% 53.01/20.31 | (1213) all_0_0_0 = n10
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 53.01/20.31 | (1212) all_0_3_3 = n10
% 53.01/20.31 |
% 53.01/20.31 | Equations (1213,1212) can reduce 679 to:
% 53.01/20.31 | (1106) $false
% 53.01/20.31 |
% 53.01/20.31 |-The branch is then unsatisfiable
% 53.01/20.31 |-Branch two:
% 53.01/20.31 | (1640) ~ (all_0_10_10 = n21)
% 53.01/20.31 | (1641) 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
% 53.01/20.31 |
% 53.01/20.31 +-Applying beta-rule and splitting (1641), into two cases.
% 53.01/20.31 |-Branch one:
% 53.01/20.31 | (1642) all_0_10_10 = n20
% 53.01/20.31 |
% 53.01/20.31 | From (1642) and (292) follows:
% 53.01/20.31 | (1643) pred(n20) = all_0_6_6
% 53.01/20.31 |
% 53.01/20.31 | From (1642) and (760) follows:
% 53.01/20.31 | (1644) succ(n20) = all_0_8_8
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (500) with n20, all_0_6_6, n19 and discharging atoms pred(n20) = all_0_6_6, pred(n20) = n19, yields:
% 53.01/20.31 | (1645) all_0_6_6 = n19
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (617) with n20, all_0_8_8, n21 and discharging atoms succ(n20) = all_0_8_8, succ(n20) = n21, yields:
% 53.01/20.31 | (1646) all_0_8_8 = n21
% 53.01/20.31 |
% 53.01/20.31 | From (1645)(1646) and (411) follows:
% 53.01/20.31 | (1647) sum(n19, n21) = all_0_1_1
% 53.01/20.31 |
% 53.01/20.31 | From (1645) and (3387) follows:
% 53.01/20.31 | (3434) sum(n19, n24) = all_0_4_4
% 53.01/20.31 |
% 53.01/20.31 | From (1646) and (3389) follows:
% 53.01/20.31 | (3435) sum(n22, n21) = all_0_7_7
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (690) with n22, n21, all_0_7_7, n17 and discharging atoms sum(n22, n21) = all_0_7_7, sum(n22, n21) = n17, yields:
% 53.01/20.31 | (1227) all_0_7_7 = n17
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (690) with n19, n24, all_0_4_4, n17 and discharging atoms sum(n19, n24) = all_0_4_4, sum(n19, n24) = n17, yields:
% 53.01/20.31 | (1225) all_0_4_4 = n17
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (690) with n19, n21, all_0_1_1, n14 and discharging atoms sum(n19, n21) = all_0_1_1, sum(n19, n21) = n14, yields:
% 53.01/20.31 | (1651) all_0_1_1 = n14
% 53.01/20.31 |
% 53.01/20.31 | From (1227)(1225) and (590) follows:
% 53.01/20.31 | (1229) sum(n17, n17) = all_0_3_3
% 53.01/20.31 |
% 53.01/20.31 | From (1651) and (3391) follows:
% 53.01/20.31 | (3440) sum(n20, n14) = all_0_0_0
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (690) with n20, n14, all_0_0_0, n8 and discharging atoms sum(n20, n14) = all_0_0_0, sum(n20, n14) = n8, yields:
% 53.01/20.31 | (1231) all_0_0_0 = n8
% 53.01/20.31 |
% 53.01/20.31 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 53.01/20.31 | (1230) all_0_3_3 = n8
% 53.01/20.31 |
% 53.01/20.31 | Equations (1231,1230) can reduce 679 to:
% 53.01/20.31 | (1106) $false
% 53.01/20.31 |
% 53.01/20.31 |-The branch is then unsatisfiable
% 53.01/20.31 |-Branch two:
% 53.01/20.31 | (1658) ~ (all_0_10_10 = n20)
% 53.01/20.31 | (1659) 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
% 53.01/20.31 |
% 53.01/20.31 +-Applying beta-rule and splitting (1659), into two cases.
% 53.01/20.31 |-Branch one:
% 53.01/20.31 | (1660) all_0_10_10 = n19
% 53.01/20.31 |
% 53.01/20.31 | From (1660) and (292) follows:
% 53.01/20.31 | (1661) pred(n19) = all_0_6_6
% 53.01/20.31 |
% 53.01/20.31 | From (1660) and (760) follows:
% 53.01/20.32 | (1662) succ(n19) = all_0_8_8
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (500) with n19, all_0_6_6, n18 and discharging atoms pred(n19) = all_0_6_6, pred(n19) = n18, yields:
% 53.01/20.32 | (1663) all_0_6_6 = n18
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (617) with n19, all_0_8_8, n20 and discharging atoms succ(n19) = all_0_8_8, succ(n19) = n20, yields:
% 53.01/20.32 | (1664) all_0_8_8 = n20
% 53.01/20.32 |
% 53.01/20.32 | From (1663)(1664) and (411) follows:
% 53.01/20.32 | (1665) sum(n18, n20) = all_0_1_1
% 53.01/20.32 |
% 53.01/20.32 | From (1663) and (3387) follows:
% 53.01/20.32 | (3452) sum(n18, n24) = all_0_4_4
% 53.01/20.32 |
% 53.01/20.32 | From (1664) and (3389) follows:
% 53.01/20.32 | (3453) sum(n22, n20) = all_0_7_7
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (690) with n22, n20, all_0_7_7, n16 and discharging atoms sum(n22, n20) = all_0_7_7, sum(n22, n20) = n16, yields:
% 53.01/20.32 | (1245) all_0_7_7 = n16
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (690) with n18, n24, all_0_4_4, n16 and discharging atoms sum(n18, n24) = all_0_4_4, sum(n18, n24) = n16, yields:
% 53.01/20.32 | (1243) all_0_4_4 = n16
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (690) with n18, n20, all_0_1_1, n12 and discharging atoms sum(n18, n20) = all_0_1_1, sum(n18, n20) = n12, yields:
% 53.01/20.32 | (1669) all_0_1_1 = n12
% 53.01/20.32 |
% 53.01/20.32 | From (1245)(1243) and (590) follows:
% 53.01/20.32 | (1247) sum(n16, n16) = all_0_3_3
% 53.01/20.32 |
% 53.01/20.32 | From (1669) and (3391) follows:
% 53.01/20.32 | (3458) sum(n20, n12) = all_0_0_0
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (690) with n20, n12, all_0_0_0, n6 and discharging atoms sum(n20, n12) = all_0_0_0, sum(n20, n12) = n6, yields:
% 53.01/20.32 | (1249) all_0_0_0 = n6
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 53.01/20.32 | (1248) all_0_3_3 = n6
% 53.01/20.32 |
% 53.01/20.32 | Equations (1249,1248) can reduce 679 to:
% 53.01/20.32 | (1106) $false
% 53.01/20.32 |
% 53.01/20.32 |-The branch is then unsatisfiable
% 53.01/20.32 |-Branch two:
% 53.01/20.32 | (1676) ~ (all_0_10_10 = n19)
% 53.01/20.32 | (1677) 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
% 53.01/20.32 |
% 53.01/20.32 +-Applying beta-rule and splitting (1677), into two cases.
% 53.01/20.32 |-Branch one:
% 53.01/20.32 | (1678) all_0_10_10 = n18
% 53.01/20.32 |
% 53.01/20.32 | From (1678) and (292) follows:
% 53.01/20.32 | (1679) pred(n18) = all_0_6_6
% 53.01/20.32 |
% 53.01/20.32 | From (1678) and (760) follows:
% 53.01/20.32 | (1680) succ(n18) = all_0_8_8
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (500) with n18, all_0_6_6, n17 and discharging atoms pred(n18) = all_0_6_6, pred(n18) = n17, yields:
% 53.01/20.32 | (1681) all_0_6_6 = n17
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (617) with n18, all_0_8_8, n19 and discharging atoms succ(n18) = all_0_8_8, succ(n18) = n19, yields:
% 53.01/20.32 | (1682) all_0_8_8 = n19
% 53.01/20.32 |
% 53.01/20.32 | From (1681)(1682) and (411) follows:
% 53.01/20.32 | (1683) sum(n17, n19) = all_0_1_1
% 53.01/20.32 |
% 53.01/20.32 | From (1681) and (3387) follows:
% 53.01/20.32 | (3470) sum(n17, n24) = all_0_4_4
% 53.01/20.32 |
% 53.01/20.32 | From (1682) and (3389) follows:
% 53.01/20.32 | (3471) sum(n22, n19) = all_0_7_7
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (690) with n22, n19, all_0_7_7, n15 and discharging atoms sum(n22, n19) = all_0_7_7, sum(n22, n19) = n15, yields:
% 53.01/20.32 | (1263) all_0_7_7 = n15
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (690) with n17, n24, all_0_4_4, n15 and discharging atoms sum(n17, n24) = all_0_4_4, sum(n17, n24) = n15, yields:
% 53.01/20.32 | (1261) all_0_4_4 = n15
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (690) with n17, n19, all_0_1_1, n10 and discharging atoms sum(n17, n19) = all_0_1_1, sum(n17, n19) = n10, yields:
% 53.01/20.32 | (1687) all_0_1_1 = n10
% 53.01/20.32 |
% 53.01/20.32 | From (1263)(1261) and (590) follows:
% 53.01/20.32 | (1265) sum(n15, n15) = all_0_3_3
% 53.01/20.32 |
% 53.01/20.32 | From (1687) and (3391) follows:
% 53.01/20.32 | (3476) sum(n20, n10) = all_0_0_0
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (690) with n20, n10, all_0_0_0, n4 and discharging atoms sum(n20, n10) = all_0_0_0, sum(n20, n10) = n4, yields:
% 53.01/20.32 | (1267) all_0_0_0 = n4
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 53.01/20.32 | (1266) all_0_3_3 = n4
% 53.01/20.32 |
% 53.01/20.32 | Equations (1267,1266) can reduce 679 to:
% 53.01/20.32 | (1106) $false
% 53.01/20.32 |
% 53.01/20.32 |-The branch is then unsatisfiable
% 53.01/20.32 |-Branch two:
% 53.01/20.32 | (1694) ~ (all_0_10_10 = n18)
% 53.01/20.32 | (1695) 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
% 53.01/20.32 |
% 53.01/20.32 +-Applying beta-rule and splitting (1695), into two cases.
% 53.01/20.32 |-Branch one:
% 53.01/20.32 | (1696) all_0_10_10 = n17
% 53.01/20.32 |
% 53.01/20.32 | From (1696) and (292) follows:
% 53.01/20.32 | (1697) pred(n17) = all_0_6_6
% 53.01/20.32 |
% 53.01/20.32 | From (1696) and (760) follows:
% 53.01/20.32 | (1698) succ(n17) = all_0_8_8
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (500) with n17, all_0_6_6, n16 and discharging atoms pred(n17) = all_0_6_6, pred(n17) = n16, yields:
% 53.01/20.32 | (1699) all_0_6_6 = n16
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (617) with n17, all_0_8_8, n18 and discharging atoms succ(n17) = all_0_8_8, succ(n17) = n18, yields:
% 53.01/20.32 | (1700) all_0_8_8 = n18
% 53.01/20.32 |
% 53.01/20.32 | From (1699)(1700) and (411) follows:
% 53.01/20.32 | (1701) sum(n16, n18) = all_0_1_1
% 53.01/20.32 |
% 53.01/20.32 | From (1699) and (3387) follows:
% 53.01/20.32 | (3488) sum(n16, n24) = all_0_4_4
% 53.01/20.32 |
% 53.01/20.32 | From (1700) and (3389) follows:
% 53.01/20.32 | (3489) sum(n22, n18) = all_0_7_7
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (690) with n22, n18, all_0_7_7, n14 and discharging atoms sum(n22, n18) = all_0_7_7, sum(n22, n18) = n14, yields:
% 53.01/20.32 | (1281) all_0_7_7 = n14
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (690) with n16, n24, all_0_4_4, n14 and discharging atoms sum(n16, n24) = all_0_4_4, sum(n16, n24) = n14, yields:
% 53.01/20.32 | (1279) all_0_4_4 = n14
% 53.01/20.32 |
% 53.01/20.32 | Instantiating formula (690) with n16, n18, all_0_1_1, n8 and discharging atoms sum(n16, n18) = all_0_1_1, sum(n16, n18) = n8, yields:
% 53.01/20.32 | (1705) all_0_1_1 = n8
% 53.01/20.32 |
% 53.01/20.32 | From (1281)(1279) and (590) follows:
% 53.01/20.32 | (1283) sum(n14, n14) = all_0_3_3
% 53.01/20.32 |
% 53.01/20.32 | From (1705) and (3391) follows:
% 53.08/20.32 | (3494) sum(n20, n8) = all_0_0_0
% 53.08/20.32 |
% 53.08/20.32 | Instantiating formula (690) with n20, n8, all_0_0_0, n2 and discharging atoms sum(n20, n8) = all_0_0_0, sum(n20, n8) = n2, yields:
% 53.08/20.32 | (1285) all_0_0_0 = n2
% 53.08/20.32 |
% 53.08/20.32 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 53.08/20.32 | (1284) all_0_3_3 = n2
% 53.08/20.32 |
% 53.08/20.32 | Equations (1285,1284) can reduce 679 to:
% 53.08/20.33 | (1106) $false
% 53.08/20.33 |
% 53.08/20.33 |-The branch is then unsatisfiable
% 53.08/20.33 |-Branch two:
% 53.08/20.33 | (1712) ~ (all_0_10_10 = n17)
% 53.08/20.33 | (1713) 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
% 53.08/20.33 |
% 53.08/20.33 +-Applying beta-rule and splitting (1713), into two cases.
% 53.08/20.33 |-Branch one:
% 53.08/20.33 | (1714) all_0_10_10 = n16
% 53.08/20.33 |
% 53.08/20.33 | From (1714) and (292) follows:
% 53.08/20.33 | (1715) pred(n16) = all_0_6_6
% 53.08/20.33 |
% 53.08/20.33 | From (1714) and (760) follows:
% 53.08/20.33 | (1716) succ(n16) = all_0_8_8
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (500) with n16, all_0_6_6, n15 and discharging atoms pred(n16) = all_0_6_6, pred(n16) = n15, yields:
% 53.08/20.33 | (1717) all_0_6_6 = n15
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (617) with n16, all_0_8_8, n17 and discharging atoms succ(n16) = all_0_8_8, succ(n16) = n17, yields:
% 53.08/20.33 | (1718) all_0_8_8 = n17
% 53.08/20.33 |
% 53.08/20.33 | From (1717)(1718) and (411) follows:
% 53.08/20.33 | (1719) sum(n15, n17) = all_0_1_1
% 53.08/20.33 |
% 53.08/20.33 | From (1717) and (3387) follows:
% 53.08/20.33 | (3506) sum(n15, n24) = all_0_4_4
% 53.08/20.33 |
% 53.08/20.33 | From (1718) and (3389) follows:
% 53.08/20.33 | (3507) sum(n22, n17) = all_0_7_7
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (690) with n22, n17, all_0_7_7, n13 and discharging atoms sum(n22, n17) = all_0_7_7, sum(n22, n17) = n13, yields:
% 53.08/20.33 | (1299) all_0_7_7 = n13
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (690) with n15, n24, all_0_4_4, n13 and discharging atoms sum(n15, n24) = all_0_4_4, sum(n15, n24) = n13, yields:
% 53.08/20.33 | (1297) all_0_4_4 = n13
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (690) with n15, n17, all_0_1_1, n6 and discharging atoms sum(n15, n17) = all_0_1_1, sum(n15, n17) = n6, yields:
% 53.08/20.33 | (1723) all_0_1_1 = n6
% 53.08/20.33 |
% 53.08/20.33 | From (1299)(1297) and (590) follows:
% 53.08/20.33 | (1301) sum(n13, n13) = all_0_3_3
% 53.08/20.33 |
% 53.08/20.33 | From (1723) and (3391) follows:
% 53.08/20.33 | (3512) sum(n20, n6) = all_0_0_0
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (690) with n20, n6, all_0_0_0, n0 and discharging atoms sum(n20, n6) = all_0_0_0, sum(n20, n6) = n0, yields:
% 53.08/20.33 | (1303) all_0_0_0 = n0
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 53.08/20.33 | (1302) all_0_3_3 = n0
% 53.08/20.33 |
% 53.08/20.33 | Equations (1303,1302) can reduce 679 to:
% 53.08/20.33 | (1106) $false
% 53.08/20.33 |
% 53.08/20.33 |-The branch is then unsatisfiable
% 53.08/20.33 |-Branch two:
% 53.08/20.33 | (1730) ~ (all_0_10_10 = n16)
% 53.08/20.33 | (1731) 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
% 53.08/20.33 |
% 53.08/20.33 +-Applying beta-rule and splitting (1731), into two cases.
% 53.08/20.33 |-Branch one:
% 53.08/20.33 | (1732) all_0_10_10 = n15
% 53.08/20.33 |
% 53.08/20.33 | From (1732) and (292) follows:
% 53.08/20.33 | (1733) pred(n15) = all_0_6_6
% 53.08/20.33 |
% 53.08/20.33 | From (1732) and (760) follows:
% 53.08/20.33 | (1734) succ(n15) = all_0_8_8
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (500) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 53.08/20.33 | (1735) all_0_6_6 = n14
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (617) with n15, all_0_8_8, n16 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n16, yields:
% 53.08/20.33 | (1736) all_0_8_8 = n16
% 53.08/20.33 |
% 53.08/20.33 | From (1735)(1736) and (411) follows:
% 53.08/20.33 | (1737) sum(n14, n16) = all_0_1_1
% 53.08/20.33 |
% 53.08/20.33 | From (1735) and (3387) follows:
% 53.08/20.33 | (3524) sum(n14, n24) = all_0_4_4
% 53.08/20.33 |
% 53.08/20.33 | From (1736) and (3389) follows:
% 53.08/20.33 | (3525) sum(n22, n16) = all_0_7_7
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (690) with n22, n16, all_0_7_7, n12 and discharging atoms sum(n22, n16) = all_0_7_7, sum(n22, n16) = n12, yields:
% 53.08/20.33 | (1317) all_0_7_7 = n12
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (690) with n14, n24, all_0_4_4, n12 and discharging atoms sum(n14, n24) = all_0_4_4, sum(n14, n24) = n12, yields:
% 53.08/20.33 | (1315) all_0_4_4 = n12
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (690) with n14, n16, all_0_1_1, n4 and discharging atoms sum(n14, n16) = all_0_1_1, sum(n14, n16) = n4, yields:
% 53.08/20.33 | (1741) all_0_1_1 = n4
% 53.08/20.33 |
% 53.08/20.33 | From (1317)(1315) and (590) follows:
% 53.08/20.33 | (1319) sum(n12, n12) = all_0_3_3
% 53.08/20.33 |
% 53.08/20.33 | From (1741) and (3391) follows:
% 53.08/20.33 | (3530) sum(n20, n4) = all_0_0_0
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (690) with n20, n4, all_0_0_0, n24 and discharging atoms sum(n20, n4) = all_0_0_0, sum(n20, n4) = n24, yields:
% 53.08/20.33 | (1321) all_0_0_0 = n24
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 53.08/20.33 | (1320) all_0_3_3 = n24
% 53.08/20.33 |
% 53.08/20.33 | Equations (1321,1320) can reduce 679 to:
% 53.08/20.33 | (1106) $false
% 53.08/20.33 |
% 53.08/20.33 |-The branch is then unsatisfiable
% 53.08/20.33 |-Branch two:
% 53.08/20.33 | (1748) ~ (all_0_10_10 = n15)
% 53.08/20.33 | (1749) 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
% 53.08/20.33 |
% 53.08/20.33 +-Applying beta-rule and splitting (1749), into two cases.
% 53.08/20.33 |-Branch one:
% 53.08/20.33 | (1750) all_0_10_10 = n14
% 53.08/20.33 |
% 53.08/20.33 | From (1750) and (292) follows:
% 53.08/20.33 | (1751) pred(n14) = all_0_6_6
% 53.08/20.33 |
% 53.08/20.33 | From (1750) and (760) follows:
% 53.08/20.33 | (1752) succ(n14) = all_0_8_8
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (500) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 53.08/20.33 | (1753) all_0_6_6 = n13
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (617) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 53.08/20.33 | (1754) all_0_8_8 = n15
% 53.08/20.33 |
% 53.08/20.33 | From (1753)(1754) and (411) follows:
% 53.08/20.33 | (1755) sum(n13, n15) = all_0_1_1
% 53.08/20.33 |
% 53.08/20.33 | From (1753) and (3387) follows:
% 53.08/20.33 | (3542) sum(n13, n24) = all_0_4_4
% 53.08/20.33 |
% 53.08/20.33 | From (1754) and (3389) follows:
% 53.08/20.33 | (3543) sum(n22, n15) = all_0_7_7
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (690) with n22, n15, all_0_7_7, n11 and discharging atoms sum(n22, n15) = all_0_7_7, sum(n22, n15) = n11, yields:
% 53.08/20.33 | (1335) all_0_7_7 = n11
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (690) with n13, n24, all_0_4_4, n11 and discharging atoms sum(n13, n24) = all_0_4_4, sum(n13, n24) = n11, yields:
% 53.08/20.33 | (1333) all_0_4_4 = n11
% 53.08/20.33 |
% 53.08/20.33 | Instantiating formula (690) with n13, n15, all_0_1_1, n2 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n2, yields:
% 53.08/20.34 | (1759) all_0_1_1 = n2
% 53.08/20.34 |
% 53.08/20.34 | From (1335)(1333) and (590) follows:
% 53.08/20.34 | (1337) sum(n11, n11) = all_0_3_3
% 53.08/20.34 |
% 53.08/20.34 | From (1759) and (3391) follows:
% 53.08/20.34 | (3548) sum(n20, n2) = all_0_0_0
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (690) with n20, n2, all_0_0_0, n22 and discharging atoms sum(n20, n2) = all_0_0_0, sum(n20, n2) = n22, yields:
% 53.08/20.34 | (1102) all_0_0_0 = n22
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 53.08/20.34 | (1104) all_0_3_3 = n22
% 53.08/20.34 |
% 53.08/20.34 | Equations (1102,1104) can reduce 679 to:
% 53.08/20.34 | (1106) $false
% 53.08/20.34 |
% 53.08/20.34 |-The branch is then unsatisfiable
% 53.08/20.34 |-Branch two:
% 53.08/20.34 | (1766) ~ (all_0_10_10 = n14)
% 53.08/20.34 | (1767) 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
% 53.08/20.34 |
% 53.08/20.34 +-Applying beta-rule and splitting (1767), into two cases.
% 53.08/20.34 |-Branch one:
% 53.08/20.34 | (1768) all_0_10_10 = n13
% 53.08/20.34 |
% 53.08/20.34 | From (1768) and (292) follows:
% 53.08/20.34 | (1769) pred(n13) = all_0_6_6
% 53.08/20.34 |
% 53.08/20.34 | From (1768) and (760) follows:
% 53.08/20.34 | (1770) succ(n13) = all_0_8_8
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (500) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 53.08/20.34 | (1771) all_0_6_6 = n12
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (617) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 53.08/20.34 | (1772) all_0_8_8 = n14
% 53.08/20.34 |
% 53.08/20.34 | From (1771)(1772) and (411) follows:
% 53.08/20.34 | (1773) sum(n12, n14) = all_0_1_1
% 53.08/20.34 |
% 53.08/20.34 | From (1771) and (3387) follows:
% 53.08/20.34 | (3560) sum(n12, n24) = all_0_4_4
% 53.08/20.34 |
% 53.08/20.34 | From (1772) and (3389) follows:
% 53.08/20.34 | (3561) sum(n22, n14) = all_0_7_7
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (690) with n22, n14, all_0_7_7, n10 and discharging atoms sum(n22, n14) = all_0_7_7, sum(n22, n14) = n10, yields:
% 53.08/20.34 | (1353) all_0_7_7 = n10
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (690) with n12, n24, all_0_4_4, n10 and discharging atoms sum(n12, n24) = all_0_4_4, sum(n12, n24) = n10, yields:
% 53.08/20.34 | (1351) all_0_4_4 = n10
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (690) with n12, n14, all_0_1_1, n0 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n0, yields:
% 53.08/20.34 | (1777) all_0_1_1 = n0
% 53.08/20.34 |
% 53.08/20.34 | From (1353)(1351) and (590) follows:
% 53.08/20.34 | (1355) sum(n10, n10) = all_0_3_3
% 53.08/20.34 |
% 53.08/20.34 | From (1777) and (3391) follows:
% 53.08/20.34 | (3566) sum(n20, n0) = all_0_0_0
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (690) with n20, n0, all_0_0_0, n20 and discharging atoms sum(n20, n0) = all_0_0_0, sum(n20, n0) = n20, yields:
% 53.08/20.34 | (1123) all_0_0_0 = n20
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 53.08/20.34 | (1122) all_0_3_3 = n20
% 53.08/20.34 |
% 53.08/20.34 | Equations (1123,1122) can reduce 679 to:
% 53.08/20.34 | (1106) $false
% 53.08/20.34 |
% 53.08/20.34 |-The branch is then unsatisfiable
% 53.08/20.34 |-Branch two:
% 53.08/20.34 | (1784) ~ (all_0_10_10 = n13)
% 53.08/20.34 | (1785) 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
% 53.08/20.34 |
% 53.08/20.34 +-Applying beta-rule and splitting (1785), into two cases.
% 53.08/20.34 |-Branch one:
% 53.08/20.34 | (1786) all_0_10_10 = n12
% 53.08/20.34 |
% 53.08/20.34 | From (1786) and (292) follows:
% 53.08/20.34 | (1787) pred(n12) = all_0_6_6
% 53.08/20.34 |
% 53.08/20.34 | From (1786) and (760) follows:
% 53.08/20.34 | (1788) succ(n12) = all_0_8_8
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (500) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 53.08/20.34 | (1789) all_0_6_6 = n11
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (617) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 53.08/20.34 | (1790) all_0_8_8 = n13
% 53.08/20.34 |
% 53.08/20.34 | From (1789)(1790) and (411) follows:
% 53.08/20.34 | (1791) sum(n11, n13) = all_0_1_1
% 53.08/20.34 |
% 53.08/20.34 | From (1789) and (3387) follows:
% 53.08/20.34 | (3578) sum(n11, n24) = all_0_4_4
% 53.08/20.34 |
% 53.08/20.34 | From (1790) and (3389) follows:
% 53.08/20.34 | (3579) sum(n22, n13) = all_0_7_7
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (690) with n22, n13, all_0_7_7, n9 and discharging atoms sum(n22, n13) = all_0_7_7, sum(n22, n13) = n9, yields:
% 53.08/20.34 | (1371) all_0_7_7 = n9
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (690) with n11, n24, all_0_4_4, n9 and discharging atoms sum(n11, n24) = all_0_4_4, sum(n11, n24) = n9, yields:
% 53.08/20.34 | (1369) all_0_4_4 = n9
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (690) with n11, n13, all_0_1_1, n24 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n24, yields:
% 53.08/20.34 | (1081) all_0_1_1 = n24
% 53.08/20.34 |
% 53.08/20.34 | From (1371)(1369) and (590) follows:
% 53.08/20.34 | (1373) sum(n9, n9) = all_0_3_3
% 53.08/20.34 |
% 53.08/20.34 | From (1081) and (3391) follows:
% 53.08/20.34 | (1138) sum(n20, n24) = all_0_0_0
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (690) with n20, n24, all_0_0_0, n18 and discharging atoms sum(n20, n24) = all_0_0_0, sum(n20, n24) = n18, yields:
% 53.08/20.34 | (1141) all_0_0_0 = n18
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 53.08/20.34 | (1140) all_0_3_3 = n18
% 53.08/20.34 |
% 53.08/20.34 | Equations (1141,1140) can reduce 679 to:
% 53.08/20.34 | (1106) $false
% 53.08/20.34 |
% 53.08/20.34 |-The branch is then unsatisfiable
% 53.08/20.34 |-Branch two:
% 53.08/20.34 | (1802) ~ (all_0_10_10 = n12)
% 53.08/20.34 | (1803) 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
% 53.08/20.34 |
% 53.08/20.34 +-Applying beta-rule and splitting (1803), into two cases.
% 53.08/20.34 |-Branch one:
% 53.08/20.34 | (1804) all_0_10_10 = n11
% 53.08/20.34 |
% 53.08/20.34 | From (1804) and (292) follows:
% 53.08/20.34 | (1805) pred(n11) = all_0_6_6
% 53.08/20.34 |
% 53.08/20.34 | From (1804) and (760) follows:
% 53.08/20.34 | (1806) succ(n11) = all_0_8_8
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (500) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 53.08/20.34 | (1807) all_0_6_6 = n10
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (617) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 53.08/20.34 | (1808) all_0_8_8 = n12
% 53.08/20.34 |
% 53.08/20.34 | From (1807)(1808) and (411) follows:
% 53.08/20.34 | (1809) sum(n10, n12) = all_0_1_1
% 53.08/20.34 |
% 53.08/20.34 | From (1807) and (3387) follows:
% 53.08/20.34 | (3596) sum(n10, n24) = all_0_4_4
% 53.08/20.34 |
% 53.08/20.34 | From (1808) and (3389) follows:
% 53.08/20.34 | (3597) sum(n22, n12) = all_0_7_7
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (690) with n22, n12, all_0_7_7, n8 and discharging atoms sum(n22, n12) = all_0_7_7, sum(n22, n12) = n8, yields:
% 53.08/20.34 | (1389) all_0_7_7 = n8
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (690) with n10, n24, all_0_4_4, n8 and discharging atoms sum(n10, n24) = all_0_4_4, sum(n10, n24) = n8, yields:
% 53.08/20.34 | (1387) all_0_4_4 = n8
% 53.08/20.34 |
% 53.08/20.34 | Instantiating formula (690) with n10, n12, all_0_1_1, n22 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n22, yields:
% 53.08/20.35 | (1579) all_0_1_1 = n22
% 53.08/20.35 |
% 53.08/20.35 | From (1389)(1387) and (590) follows:
% 53.08/20.35 | (1391) sum(n8, n8) = all_0_3_3
% 53.08/20.35 |
% 53.08/20.35 | From (1579) and (3391) follows:
% 53.08/20.35 | (2070) sum(n20, n22) = all_0_0_0
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (690) with n20, n22, all_0_0_0, n16 and discharging atoms sum(n20, n22) = all_0_0_0, sum(n20, n22) = n16, yields:
% 53.08/20.35 | (1159) all_0_0_0 = n16
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 53.08/20.35 | (1158) all_0_3_3 = n16
% 53.08/20.35 |
% 53.08/20.35 | Equations (1159,1158) can reduce 679 to:
% 53.08/20.35 | (1106) $false
% 53.08/20.35 |
% 53.08/20.35 |-The branch is then unsatisfiable
% 53.08/20.35 |-Branch two:
% 53.08/20.35 | (1820) ~ (all_0_10_10 = n11)
% 53.08/20.35 | (1821) 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
% 53.08/20.35 |
% 53.08/20.35 +-Applying beta-rule and splitting (1821), into two cases.
% 53.08/20.35 |-Branch one:
% 53.08/20.35 | (1822) all_0_10_10 = n10
% 53.08/20.35 |
% 53.08/20.35 | From (1822) and (292) follows:
% 53.08/20.35 | (1823) pred(n10) = all_0_6_6
% 53.08/20.35 |
% 53.08/20.35 | From (1822) and (760) follows:
% 53.08/20.35 | (1824) succ(n10) = all_0_8_8
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (500) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 53.08/20.35 | (1825) all_0_6_6 = n9
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (617) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 53.08/20.35 | (1826) all_0_8_8 = n11
% 53.08/20.35 |
% 53.08/20.35 | From (1825)(1826) and (411) follows:
% 53.08/20.35 | (1827) sum(n9, n11) = all_0_1_1
% 53.08/20.35 |
% 53.08/20.35 | From (1825) and (3387) follows:
% 53.08/20.35 | (3614) sum(n9, n24) = all_0_4_4
% 53.08/20.35 |
% 53.08/20.35 | From (1826) and (3389) follows:
% 53.08/20.35 | (3615) sum(n22, n11) = all_0_7_7
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (690) with n22, n11, all_0_7_7, n7 and discharging atoms sum(n22, n11) = all_0_7_7, sum(n22, n11) = n7, yields:
% 53.08/20.35 | (1407) all_0_7_7 = n7
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (690) with n9, n24, all_0_4_4, n7 and discharging atoms sum(n9, n24) = all_0_4_4, sum(n9, n24) = n7, yields:
% 53.08/20.35 | (1405) all_0_4_4 = n7
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (690) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 53.08/20.35 | (1597) all_0_1_1 = n20
% 53.08/20.35 |
% 53.08/20.35 | From (1407)(1405) and (590) follows:
% 53.08/20.35 | (1409) sum(n7, n7) = all_0_3_3
% 53.08/20.35 |
% 53.08/20.35 | From (1597) and (3391) follows:
% 53.08/20.35 | (2960) sum(n20, n20) = all_0_0_0
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (690) with n20, n20, all_0_0_0, n14 and discharging atoms sum(n20, n20) = all_0_0_0, sum(n20, n20) = n14, yields:
% 53.08/20.35 | (1177) all_0_0_0 = n14
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 53.08/20.35 | (1176) all_0_3_3 = n14
% 53.08/20.35 |
% 53.08/20.35 | Equations (1177,1176) can reduce 679 to:
% 53.08/20.35 | (1106) $false
% 53.08/20.35 |
% 53.08/20.35 |-The branch is then unsatisfiable
% 53.08/20.35 |-Branch two:
% 53.08/20.35 | (1838) ~ (all_0_10_10 = n10)
% 53.08/20.35 | (1839) 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
% 53.08/20.35 |
% 53.08/20.35 +-Applying beta-rule and splitting (1839), into two cases.
% 53.08/20.35 |-Branch one:
% 53.08/20.35 | (1840) all_0_10_10 = n9
% 53.08/20.35 |
% 53.08/20.35 | From (1840) and (292) follows:
% 53.08/20.35 | (1841) pred(n9) = all_0_6_6
% 53.08/20.35 |
% 53.08/20.35 | From (1840) and (760) follows:
% 53.08/20.35 | (1842) succ(n9) = all_0_8_8
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (500) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 53.08/20.35 | (1843) all_0_6_6 = n8
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (617) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 53.08/20.35 | (1844) all_0_8_8 = n10
% 53.08/20.35 |
% 53.08/20.35 | From (1843)(1844) and (411) follows:
% 53.08/20.35 | (1845) sum(n8, n10) = all_0_1_1
% 53.08/20.35 |
% 53.08/20.35 | From (1843) and (3387) follows:
% 53.08/20.35 | (3632) sum(n8, n24) = all_0_4_4
% 53.08/20.35 |
% 53.08/20.35 | From (1844) and (3389) follows:
% 53.08/20.35 | (3633) sum(n22, n10) = all_0_7_7
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (690) with n22, n10, all_0_7_7, n6 and discharging atoms sum(n22, n10) = all_0_7_7, sum(n22, n10) = n6, yields:
% 53.08/20.35 | (1425) all_0_7_7 = n6
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (690) with n8, n24, all_0_4_4, n6 and discharging atoms sum(n8, n24) = all_0_4_4, sum(n8, n24) = n6, yields:
% 53.08/20.35 | (1423) all_0_4_4 = n6
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (690) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 53.08/20.35 | (1615) all_0_1_1 = n18
% 53.08/20.35 |
% 53.08/20.35 | From (1425)(1423) and (590) follows:
% 53.08/20.35 | (1427) sum(n6, n6) = all_0_3_3
% 53.08/20.35 |
% 53.08/20.35 | From (1615) and (3391) follows:
% 53.08/20.35 | (3404) sum(n20, n18) = all_0_0_0
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (690) with n20, n18, all_0_0_0, n12 and discharging atoms sum(n20, n18) = all_0_0_0, sum(n20, n18) = n12, yields:
% 53.08/20.35 | (1195) all_0_0_0 = n12
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 53.08/20.35 | (1194) all_0_3_3 = n12
% 53.08/20.35 |
% 53.08/20.35 | Equations (1195,1194) can reduce 679 to:
% 53.08/20.35 | (1106) $false
% 53.08/20.35 |
% 53.08/20.35 |-The branch is then unsatisfiable
% 53.08/20.35 |-Branch two:
% 53.08/20.35 | (1856) ~ (all_0_10_10 = n9)
% 53.08/20.35 | (1857) 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
% 53.08/20.35 |
% 53.08/20.35 +-Applying beta-rule and splitting (1857), into two cases.
% 53.08/20.35 |-Branch one:
% 53.08/20.35 | (1858) all_0_10_10 = n8
% 53.08/20.35 |
% 53.08/20.35 | From (1858) and (292) follows:
% 53.08/20.35 | (1859) pred(n8) = all_0_6_6
% 53.08/20.35 |
% 53.08/20.35 | From (1858) and (760) follows:
% 53.08/20.35 | (1860) succ(n8) = all_0_8_8
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 53.08/20.35 | (1861) all_0_6_6 = n7
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 53.08/20.35 | (1862) all_0_8_8 = n9
% 53.08/20.35 |
% 53.08/20.35 | From (1861)(1862) and (411) follows:
% 53.08/20.35 | (1863) sum(n7, n9) = all_0_1_1
% 53.08/20.35 |
% 53.08/20.35 | From (1861) and (3387) follows:
% 53.08/20.35 | (3650) sum(n7, n24) = all_0_4_4
% 53.08/20.35 |
% 53.08/20.35 | From (1862) and (3389) follows:
% 53.08/20.35 | (3651) sum(n22, n9) = all_0_7_7
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (690) with n22, n9, all_0_7_7, n5 and discharging atoms sum(n22, n9) = all_0_7_7, sum(n22, n9) = n5, yields:
% 53.08/20.35 | (1443) all_0_7_7 = n5
% 53.08/20.35 |
% 53.08/20.35 | Instantiating formula (690) with n7, n24, all_0_4_4, n5 and discharging atoms sum(n7, n24) = all_0_4_4, sum(n7, n24) = n5, yields:
% 53.08/20.35 | (1441) all_0_4_4 = n5
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 53.08/20.36 | (1633) all_0_1_1 = n16
% 53.08/20.36 |
% 53.08/20.36 | From (1443)(1441) and (590) follows:
% 53.08/20.36 | (1445) sum(n5, n5) = all_0_3_3
% 53.08/20.36 |
% 53.08/20.36 | From (1633) and (3391) follows:
% 53.08/20.36 | (3422) sum(n20, n16) = all_0_0_0
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (690) with n20, n16, all_0_0_0, n10 and discharging atoms sum(n20, n16) = all_0_0_0, sum(n20, n16) = n10, yields:
% 53.08/20.36 | (1213) all_0_0_0 = n10
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 53.08/20.36 | (1212) all_0_3_3 = n10
% 53.08/20.36 |
% 53.08/20.36 | Equations (1213,1212) can reduce 679 to:
% 53.08/20.36 | (1106) $false
% 53.08/20.36 |
% 53.08/20.36 |-The branch is then unsatisfiable
% 53.08/20.36 |-Branch two:
% 53.08/20.36 | (1874) ~ (all_0_10_10 = n8)
% 53.08/20.36 | (1875) 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
% 53.08/20.36 |
% 53.08/20.36 +-Applying beta-rule and splitting (1875), into two cases.
% 53.08/20.36 |-Branch one:
% 53.08/20.36 | (1876) all_0_10_10 = n7
% 53.08/20.36 |
% 53.08/20.36 | From (1876) and (292) follows:
% 53.08/20.36 | (1877) pred(n7) = all_0_6_6
% 53.08/20.36 |
% 53.08/20.36 | From (1876) and (760) follows:
% 53.08/20.36 | (1878) succ(n7) = all_0_8_8
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 53.08/20.36 | (1879) all_0_6_6 = n6
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 53.08/20.36 | (1880) all_0_8_8 = n8
% 53.08/20.36 |
% 53.08/20.36 | From (1879)(1880) and (411) follows:
% 53.08/20.36 | (1881) sum(n6, n8) = all_0_1_1
% 53.08/20.36 |
% 53.08/20.36 | From (1879) and (3387) follows:
% 53.08/20.36 | (3668) sum(n6, n24) = all_0_4_4
% 53.08/20.36 |
% 53.08/20.36 | From (1880) and (3389) follows:
% 53.08/20.36 | (3669) sum(n22, n8) = all_0_7_7
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (690) with n22, n8, all_0_7_7, n4 and discharging atoms sum(n22, n8) = all_0_7_7, sum(n22, n8) = n4, yields:
% 53.08/20.36 | (1461) all_0_7_7 = n4
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (690) with n6, n24, all_0_4_4, n4 and discharging atoms sum(n6, n24) = all_0_4_4, sum(n6, n24) = n4, yields:
% 53.08/20.36 | (1459) all_0_4_4 = n4
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 53.08/20.36 | (1651) all_0_1_1 = n14
% 53.08/20.36 |
% 53.08/20.36 | From (1461)(1459) and (590) follows:
% 53.08/20.36 | (1463) sum(n4, n4) = all_0_3_3
% 53.08/20.36 |
% 53.08/20.36 | From (1651) and (3391) follows:
% 53.08/20.36 | (3440) sum(n20, n14) = all_0_0_0
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (690) with n20, n14, all_0_0_0, n8 and discharging atoms sum(n20, n14) = all_0_0_0, sum(n20, n14) = n8, yields:
% 53.08/20.36 | (1231) all_0_0_0 = n8
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 53.08/20.36 | (1230) all_0_3_3 = n8
% 53.08/20.36 |
% 53.08/20.36 | Equations (1231,1230) can reduce 679 to:
% 53.08/20.36 | (1106) $false
% 53.08/20.36 |
% 53.08/20.36 |-The branch is then unsatisfiable
% 53.08/20.36 |-Branch two:
% 53.08/20.36 | (1892) ~ (all_0_10_10 = n7)
% 53.08/20.36 | (1893) 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
% 53.08/20.36 |
% 53.08/20.36 +-Applying beta-rule and splitting (1893), into two cases.
% 53.08/20.36 |-Branch one:
% 53.08/20.36 | (1894) all_0_10_10 = n6
% 53.08/20.36 |
% 53.08/20.36 | From (1894) and (292) follows:
% 53.08/20.36 | (1895) pred(n6) = all_0_6_6
% 53.08/20.36 |
% 53.08/20.36 | From (1894) and (760) follows:
% 53.08/20.36 | (1896) succ(n6) = all_0_8_8
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 53.08/20.36 | (1897) all_0_6_6 = n5
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 53.08/20.36 | (1898) all_0_8_8 = n7
% 53.08/20.36 |
% 53.08/20.36 | From (1897)(1898) and (411) follows:
% 53.08/20.36 | (1899) sum(n5, n7) = all_0_1_1
% 53.08/20.36 |
% 53.08/20.36 | From (1897) and (3387) follows:
% 53.08/20.36 | (3686) sum(n5, n24) = all_0_4_4
% 53.08/20.36 |
% 53.08/20.36 | From (1898) and (3389) follows:
% 53.08/20.36 | (3687) sum(n22, n7) = all_0_7_7
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (690) with n22, n7, all_0_7_7, n3 and discharging atoms sum(n22, n7) = all_0_7_7, sum(n22, n7) = n3, yields:
% 53.08/20.36 | (1479) all_0_7_7 = n3
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (690) with n5, n24, all_0_4_4, n3 and discharging atoms sum(n5, n24) = all_0_4_4, sum(n5, n24) = n3, yields:
% 53.08/20.36 | (1477) all_0_4_4 = n3
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 53.08/20.36 | (1669) all_0_1_1 = n12
% 53.08/20.36 |
% 53.08/20.36 | From (1479)(1477) and (590) follows:
% 53.08/20.36 | (1481) sum(n3, n3) = all_0_3_3
% 53.08/20.36 |
% 53.08/20.36 | From (1669) and (3391) follows:
% 53.08/20.36 | (3458) sum(n20, n12) = all_0_0_0
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (690) with n20, n12, all_0_0_0, n6 and discharging atoms sum(n20, n12) = all_0_0_0, sum(n20, n12) = n6, yields:
% 53.08/20.36 | (1249) all_0_0_0 = n6
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 53.08/20.36 | (1248) all_0_3_3 = n6
% 53.08/20.36 |
% 53.08/20.36 | Equations (1249,1248) can reduce 679 to:
% 53.08/20.36 | (1106) $false
% 53.08/20.36 |
% 53.08/20.36 |-The branch is then unsatisfiable
% 53.08/20.36 |-Branch two:
% 53.08/20.36 | (1910) ~ (all_0_10_10 = n6)
% 53.08/20.36 | (1911) 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
% 53.08/20.36 |
% 53.08/20.36 +-Applying beta-rule and splitting (1911), into two cases.
% 53.08/20.36 |-Branch one:
% 53.08/20.36 | (1912) all_0_10_10 = n5
% 53.08/20.36 |
% 53.08/20.36 | From (1912) and (292) follows:
% 53.08/20.36 | (1913) pred(n5) = all_0_6_6
% 53.08/20.36 |
% 53.08/20.36 | From (1912) and (760) follows:
% 53.08/20.36 | (1914) succ(n5) = all_0_8_8
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 53.08/20.36 | (1915) all_0_6_6 = n4
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 53.08/20.36 | (1916) all_0_8_8 = n6
% 53.08/20.36 |
% 53.08/20.36 | From (1915)(1916) and (411) follows:
% 53.08/20.36 | (1917) sum(n4, n6) = all_0_1_1
% 53.08/20.36 |
% 53.08/20.36 | From (1915) and (3387) follows:
% 53.08/20.36 | (3704) sum(n4, n24) = all_0_4_4
% 53.08/20.36 |
% 53.08/20.36 | From (1916) and (3389) follows:
% 53.08/20.36 | (3705) sum(n22, n6) = all_0_7_7
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (690) with n22, n6, all_0_7_7, n2 and discharging atoms sum(n22, n6) = all_0_7_7, sum(n22, n6) = n2, yields:
% 53.08/20.36 | (1497) all_0_7_7 = n2
% 53.08/20.36 |
% 53.08/20.36 | Instantiating formula (690) with n4, n24, all_0_4_4, n2 and discharging atoms sum(n4, n24) = all_0_4_4, sum(n4, n24) = n2, yields:
% 53.08/20.37 | (1495) all_0_4_4 = n2
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 53.08/20.37 | (1687) all_0_1_1 = n10
% 53.08/20.37 |
% 53.08/20.37 | From (1497)(1495) and (590) follows:
% 53.08/20.37 | (1499) sum(n2, n2) = all_0_3_3
% 53.08/20.37 |
% 53.08/20.37 | From (1687) and (3391) follows:
% 53.08/20.37 | (3476) sum(n20, n10) = all_0_0_0
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (690) with n20, n10, all_0_0_0, n4 and discharging atoms sum(n20, n10) = all_0_0_0, sum(n20, n10) = n4, yields:
% 53.08/20.37 | (1267) all_0_0_0 = n4
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 53.08/20.37 | (1266) all_0_3_3 = n4
% 53.08/20.37 |
% 53.08/20.37 | Equations (1267,1266) can reduce 679 to:
% 53.08/20.37 | (1106) $false
% 53.08/20.37 |
% 53.08/20.37 |-The branch is then unsatisfiable
% 53.08/20.37 |-Branch two:
% 53.08/20.37 | (1928) ~ (all_0_10_10 = n5)
% 53.08/20.37 | (1929) 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
% 53.08/20.37 |
% 53.08/20.37 +-Applying beta-rule and splitting (1929), into two cases.
% 53.08/20.37 |-Branch one:
% 53.08/20.37 | (1930) all_0_10_10 = n4
% 53.08/20.37 |
% 53.08/20.37 | From (1930) and (292) follows:
% 53.08/20.37 | (1931) pred(n4) = all_0_6_6
% 53.08/20.37 |
% 53.08/20.37 | From (1930) and (760) follows:
% 53.08/20.37 | (1932) succ(n4) = all_0_8_8
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 53.08/20.37 | (1933) all_0_6_6 = n3
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 53.08/20.37 | (1934) all_0_8_8 = n5
% 53.08/20.37 |
% 53.08/20.37 | From (1933)(1934) and (411) follows:
% 53.08/20.37 | (1935) sum(n3, n5) = all_0_1_1
% 53.08/20.37 |
% 53.08/20.37 | From (1933) and (3387) follows:
% 53.08/20.37 | (3722) sum(n3, n24) = all_0_4_4
% 53.08/20.37 |
% 53.08/20.37 | From (1934) and (3389) follows:
% 53.08/20.37 | (3723) sum(n22, n5) = all_0_7_7
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (690) with n22, n5, all_0_7_7, n1 and discharging atoms sum(n22, n5) = all_0_7_7, sum(n22, n5) = n1, yields:
% 53.08/20.37 | (1515) all_0_7_7 = n1
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (690) with n3, n24, all_0_4_4, n1 and discharging atoms sum(n3, n24) = all_0_4_4, sum(n3, n24) = n1, yields:
% 53.08/20.37 | (1513) all_0_4_4 = n1
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 53.08/20.37 | (1705) all_0_1_1 = n8
% 53.08/20.37 |
% 53.08/20.37 | From (1515)(1513) and (590) follows:
% 53.08/20.37 | (1517) sum(n1, n1) = all_0_3_3
% 53.08/20.37 |
% 53.08/20.37 | From (1705) and (3391) follows:
% 53.08/20.37 | (3494) sum(n20, n8) = all_0_0_0
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (690) with n20, n8, all_0_0_0, n2 and discharging atoms sum(n20, n8) = all_0_0_0, sum(n20, n8) = n2, yields:
% 53.08/20.37 | (1285) all_0_0_0 = n2
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 53.08/20.37 | (1284) all_0_3_3 = n2
% 53.08/20.37 |
% 53.08/20.37 | Equations (1285,1284) can reduce 679 to:
% 53.08/20.37 | (1106) $false
% 53.08/20.37 |
% 53.08/20.37 |-The branch is then unsatisfiable
% 53.08/20.37 |-Branch two:
% 53.08/20.37 | (1946) ~ (all_0_10_10 = n4)
% 53.08/20.37 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 53.08/20.37 |
% 53.08/20.37 +-Applying beta-rule and splitting (1947), into two cases.
% 53.08/20.37 |-Branch one:
% 53.08/20.37 | (1948) all_0_10_10 = n3
% 53.08/20.37 |
% 53.08/20.37 | From (1948) and (292) follows:
% 53.08/20.37 | (1949) pred(n3) = all_0_6_6
% 53.08/20.37 |
% 53.08/20.37 | From (1948) and (760) follows:
% 53.08/20.37 | (1950) succ(n3) = all_0_8_8
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 53.08/20.37 | (1951) all_0_6_6 = n2
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 53.08/20.37 | (1952) all_0_8_8 = n4
% 53.08/20.37 |
% 53.08/20.37 | From (1951)(1952) and (411) follows:
% 53.08/20.37 | (1953) sum(n2, n4) = all_0_1_1
% 53.08/20.37 |
% 53.08/20.37 | From (1951) and (3387) follows:
% 53.08/20.37 | (3740) sum(n2, n24) = all_0_4_4
% 53.08/20.37 |
% 53.08/20.37 | From (1952) and (3389) follows:
% 53.08/20.37 | (3741) sum(n22, n4) = all_0_7_7
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (690) with n22, n4, all_0_7_7, n0 and discharging atoms sum(n22, n4) = all_0_7_7, sum(n22, n4) = n0, yields:
% 53.08/20.37 | (1533) all_0_7_7 = n0
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (690) with n2, n24, all_0_4_4, n0 and discharging atoms sum(n2, n24) = all_0_4_4, sum(n2, n24) = n0, yields:
% 53.08/20.37 | (1531) all_0_4_4 = n0
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 53.08/20.37 | (1723) all_0_1_1 = n6
% 53.08/20.37 |
% 53.08/20.37 | From (1533)(1531) and (590) follows:
% 53.08/20.37 | (1535) sum(n0, n0) = all_0_3_3
% 53.08/20.37 |
% 53.08/20.37 | From (1723) and (3391) follows:
% 53.08/20.37 | (3512) sum(n20, n6) = all_0_0_0
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (690) with n20, n6, all_0_0_0, n0 and discharging atoms sum(n20, n6) = all_0_0_0, sum(n20, n6) = n0, yields:
% 53.08/20.37 | (1303) all_0_0_0 = n0
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 53.08/20.37 | (1302) all_0_3_3 = n0
% 53.08/20.37 |
% 53.08/20.37 | Equations (1303,1302) can reduce 679 to:
% 53.08/20.37 | (1106) $false
% 53.08/20.37 |
% 53.08/20.37 |-The branch is then unsatisfiable
% 53.08/20.37 |-Branch two:
% 53.08/20.37 | (1964) ~ (all_0_10_10 = n3)
% 53.08/20.37 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 53.08/20.37 |
% 53.08/20.37 +-Applying beta-rule and splitting (1965), into two cases.
% 53.08/20.37 |-Branch one:
% 53.08/20.37 | (1966) all_0_10_10 = n2
% 53.08/20.37 |
% 53.08/20.37 | From (1966) and (292) follows:
% 53.08/20.37 | (1967) pred(n2) = all_0_6_6
% 53.08/20.37 |
% 53.08/20.37 | From (1966) and (760) follows:
% 53.08/20.37 | (1968) succ(n2) = all_0_8_8
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 53.08/20.37 | (1969) all_0_6_6 = n1
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 53.08/20.37 | (1970) all_0_8_8 = n3
% 53.08/20.37 |
% 53.08/20.37 | From (1969)(1970) and (411) follows:
% 53.08/20.37 | (1971) sum(n1, n3) = all_0_1_1
% 53.08/20.37 |
% 53.08/20.37 | From (1969) and (3387) follows:
% 53.08/20.37 | (3758) sum(n1, n24) = all_0_4_4
% 53.08/20.37 |
% 53.08/20.37 | From (1970) and (3389) follows:
% 53.08/20.37 | (3759) sum(n22, n3) = all_0_7_7
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (690) with n22, n3, all_0_7_7, n25 and discharging atoms sum(n22, n3) = all_0_7_7, sum(n22, n3) = n25, yields:
% 53.08/20.37 | (1550) all_0_7_7 = n25
% 53.08/20.37 |
% 53.08/20.37 | Instantiating formula (690) with n1, n24, all_0_4_4, n25 and discharging atoms sum(n1, n24) = all_0_4_4, sum(n1, n24) = n25, yields:
% 53.08/20.38 | (1551) all_0_4_4 = n25
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 53.08/20.38 | (1741) all_0_1_1 = n4
% 53.08/20.38 |
% 53.08/20.38 | From (1550)(1551) and (590) follows:
% 53.08/20.38 | (1553) sum(n25, n25) = all_0_3_3
% 53.08/20.38 |
% 53.08/20.38 | From (1741) and (3391) follows:
% 53.08/20.38 | (3530) sum(n20, n4) = all_0_0_0
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 53.08/20.38 | (1320) all_0_3_3 = n24
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (690) with n20, n4, all_0_0_0, n24 and discharging atoms sum(n20, n4) = all_0_0_0, sum(n20, n4) = n24, yields:
% 53.08/20.38 | (1321) all_0_0_0 = n24
% 53.08/20.38 |
% 53.08/20.38 | Equations (1321,1320) can reduce 679 to:
% 53.08/20.38 | (1106) $false
% 53.08/20.38 |
% 53.08/20.38 |-The branch is then unsatisfiable
% 53.08/20.38 |-Branch two:
% 53.08/20.38 | (1982) ~ (all_0_10_10 = n2)
% 53.08/20.38 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 53.08/20.38 |
% 53.08/20.38 +-Applying beta-rule and splitting (1983), into two cases.
% 53.08/20.38 |-Branch one:
% 53.08/20.38 | (1984) all_0_10_10 = n1
% 53.08/20.38 |
% 53.08/20.38 | From (1984) and (292) follows:
% 53.08/20.38 | (1985) pred(n1) = all_0_6_6
% 53.08/20.38 |
% 53.08/20.38 | From (1984) and (760) follows:
% 53.08/20.38 | (1986) succ(n1) = all_0_8_8
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 53.08/20.38 | (1987) all_0_6_6 = n0
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 53.08/20.38 | (1988) all_0_8_8 = n2
% 53.08/20.38 |
% 53.08/20.38 | From (1987)(1988) and (411) follows:
% 53.08/20.38 | (1989) sum(n0, n2) = all_0_1_1
% 53.08/20.38 |
% 53.08/20.38 | From (1987) and (3387) follows:
% 53.08/20.38 | (3776) sum(n0, n24) = all_0_4_4
% 53.08/20.38 |
% 53.08/20.38 | From (1988) and (3389) follows:
% 53.08/20.38 | (3777) sum(n22, n2) = all_0_7_7
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (690) with n22, n2, all_0_7_7, n24 and discharging atoms sum(n22, n2) = all_0_7_7, sum(n22, n2) = n24, yields:
% 53.08/20.38 | (1097) all_0_7_7 = n24
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (690) with n0, n24, all_0_4_4, n24 and discharging atoms sum(n0, n24) = all_0_4_4, sum(n0, n24) = n24, yields:
% 53.08/20.38 | (1096) all_0_4_4 = n24
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 53.08/20.38 | (1759) all_0_1_1 = n2
% 53.08/20.38 |
% 53.08/20.38 | From (1097)(1096) and (590) follows:
% 53.08/20.38 | (1101) sum(n24, n24) = all_0_3_3
% 53.08/20.38 |
% 53.08/20.38 | From (1759) and (3391) follows:
% 53.08/20.38 | (3548) sum(n20, n2) = all_0_0_0
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 53.08/20.38 | (1104) all_0_3_3 = n22
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (690) with n20, n2, all_0_0_0, n22 and discharging atoms sum(n20, n2) = all_0_0_0, sum(n20, n2) = n22, yields:
% 53.08/20.38 | (1102) all_0_0_0 = n22
% 53.08/20.38 |
% 53.08/20.38 | Equations (1102,1104) can reduce 679 to:
% 53.08/20.38 | (1106) $false
% 53.08/20.38 |
% 53.08/20.38 |-The branch is then unsatisfiable
% 53.08/20.38 |-Branch two:
% 53.08/20.38 | (2002) ~ (all_0_10_10 = n1)
% 53.08/20.38 | (2003) all_0_10_10 = n0
% 53.08/20.38 |
% 53.08/20.38 | From (2003) and (292) follows:
% 53.08/20.38 | (2004) pred(n0) = all_0_6_6
% 53.08/20.38 |
% 53.08/20.38 | From (2003) and (760) follows:
% 53.08/20.38 | (2005) succ(n0) = all_0_8_8
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 53.08/20.38 | (2006) all_0_6_6 = n25
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 53.08/20.38 | (2007) all_0_8_8 = n1
% 53.08/20.38 |
% 53.08/20.38 | From (2006)(2007) and (411) follows:
% 53.08/20.38 | (2008) sum(n25, n1) = all_0_1_1
% 53.08/20.38 |
% 53.08/20.38 | From (2006) and (3387) follows:
% 53.08/20.38 | (3793) sum(n25, n24) = all_0_4_4
% 53.08/20.38 |
% 53.08/20.38 | From (2007) and (3389) follows:
% 53.08/20.38 | (3794) sum(n22, n1) = all_0_7_7
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (690) with n25, n24, all_0_4_4, n23 and discharging atoms sum(n25, n24) = all_0_4_4, sum(n25, n24) = n23, yields:
% 53.08/20.38 | (1117) all_0_4_4 = n23
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 53.08/20.38 | (1777) all_0_1_1 = n0
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (690) with n22, n1, all_0_7_7, n23 and discharging atoms sum(n22, n1) = all_0_7_7, sum(n22, n1) = n23, yields:
% 53.08/20.38 | (1119) all_0_7_7 = n23
% 53.08/20.38 |
% 53.08/20.38 | From (1119)(1117) and (590) follows:
% 53.08/20.38 | (1121) sum(n23, n23) = all_0_3_3
% 53.08/20.38 |
% 53.08/20.38 | From (1777) and (3391) follows:
% 53.08/20.38 | (3566) sum(n20, n0) = all_0_0_0
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 53.08/20.38 | (1122) all_0_3_3 = n20
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (690) with n20, n0, all_0_0_0, n20 and discharging atoms sum(n20, n0) = all_0_0_0, sum(n20, n0) = n20, yields:
% 53.08/20.38 | (1123) all_0_0_0 = n20
% 53.08/20.38 |
% 53.08/20.38 | Equations (1123,1122) can reduce 679 to:
% 53.08/20.38 | (1106) $false
% 53.08/20.38 |
% 53.08/20.38 |-The branch is then unsatisfiable
% 53.08/20.38 |-Branch two:
% 53.08/20.38 | (1143) ~ (all_0_11_11 = n23)
% 53.08/20.38 | (1144) all_0_11_11 = n22 | all_0_11_11 = n21 | 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
% 53.08/20.38 |
% 53.08/20.38 +-Applying beta-rule and splitting (1605), into two cases.
% 53.08/20.38 |-Branch one:
% 53.08/20.38 | (1606) all_0_10_10 = n22
% 53.08/20.38 |
% 53.08/20.38 | From (1606) and (292) follows:
% 53.08/20.38 | (1607) pred(n22) = all_0_6_6
% 53.08/20.38 |
% 53.08/20.38 | From (1606) and (760) follows:
% 53.08/20.38 | (1608) succ(n22) = all_0_8_8
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (500) with n22, all_0_6_6, n21 and discharging atoms pred(n22) = all_0_6_6, pred(n22) = n21, yields:
% 53.08/20.38 | (1609) all_0_6_6 = n21
% 53.08/20.38 |
% 53.08/20.38 | Instantiating formula (617) with n22, all_0_8_8, n23 and discharging atoms succ(n22) = all_0_8_8, succ(n22) = n23, yields:
% 53.08/20.38 | (1610) all_0_8_8 = n23
% 53.08/20.38 |
% 53.08/20.38 | From (1609) and (1607) follows:
% 53.08/20.38 | (40) pred(n22) = n21
% 53.08/20.38 |
% 53.08/20.38 | From (1610) and (1608) follows:
% 53.08/20.39 | (918) succ(n22) = n23
% 53.08/20.39 |
% 53.08/20.39 | From (1609) and (541) follows:
% 53.08/20.39 | (3812) sum(n21, all_0_5_5) = all_0_4_4
% 53.08/20.39 |
% 53.08/20.39 | From (1609)(1610) and (411) follows:
% 53.08/20.39 | (1611) sum(n21, n23) = all_0_1_1
% 53.08/20.39 |
% 53.08/20.39 | From (1610) and (427) follows:
% 53.08/20.39 | (3814) sum(all_0_9_9, n23) = all_0_7_7
% 53.08/20.39 |
% 53.08/20.39 | Instantiating formula (690) with n21, n23, all_0_1_1, n18 and discharging atoms sum(n21, n23) = all_0_1_1, sum(n21, n23) = n18, yields:
% 53.08/20.39 | (1615) all_0_1_1 = n18
% 53.08/20.39 |
% 53.08/20.39 | From (1615) and (630) follows:
% 53.08/20.39 | (3816) sum(all_0_2_2, n18) = all_0_0_0
% 53.08/20.39 |
% 53.08/20.39 | From (1615) and (1611) follows:
% 53.08/20.39 | (256) sum(n21, n23) = n18
% 53.08/20.39 |
% 53.08/20.39 +-Applying beta-rule and splitting (1144), into two cases.
% 53.08/20.39 |-Branch one:
% 53.08/20.39 | (1145) all_0_11_11 = n22
% 53.08/20.39 |
% 53.08/20.39 | From (1145) and (559) follows:
% 53.08/20.39 | (1146) pred(n22) = all_0_9_9
% 53.08/20.39 |
% 53.08/20.39 | From (1145) and (992) follows:
% 53.08/20.39 | (1147) succ(n22) = all_0_5_5
% 53.08/20.39 |
% 53.08/20.39 | Instantiating formula (500) with n22, all_0_9_9, n21 and discharging atoms pred(n22) = all_0_9_9, pred(n22) = n21, yields:
% 53.08/20.39 | (1148) all_0_9_9 = n21
% 53.08/20.39 |
% 53.08/20.39 | Instantiating formula (617) with n22, all_0_5_5, n23 and discharging atoms succ(n22) = all_0_5_5, succ(n22) = n23, yields:
% 53.08/20.39 | (1149) all_0_5_5 = n23
% 53.08/20.39 |
% 53.08/20.39 | From (1148)(1149) and (538) follows:
% 53.08/20.39 | (1150) sum(n21, n23) = all_0_2_2
% 53.08/20.39 |
% 53.08/20.39 | From (1148) and (3814) follows:
% 53.08/20.39 | (3824) sum(n21, n23) = all_0_7_7
% 53.08/20.39 |
% 53.08/20.39 | From (1149) and (3812) follows:
% 53.08/20.39 | (3825) sum(n21, n23) = all_0_4_4
% 53.08/20.39 |
% 53.08/20.39 | Instantiating formula (690) with n21, n23, all_0_2_2, n18 and discharging atoms sum(n21, n23) = all_0_2_2, sum(n21, n23) = n18, yields:
% 53.08/20.39 | (1154) all_0_2_2 = n18
% 53.08/20.39 |
% 53.08/20.39 | Instantiating formula (690) with n21, n23, all_0_4_4, all_0_2_2 and discharging atoms sum(n21, n23) = all_0_2_2, sum(n21, n23) = all_0_4_4, yields:
% 53.08/20.39 | (1093) all_0_2_2 = all_0_4_4
% 53.08/20.39 |
% 53.08/20.39 | Instantiating formula (690) with n21, n23, all_0_7_7, all_0_2_2 and discharging atoms sum(n21, n23) = all_0_2_2, sum(n21, n23) = all_0_7_7, yields:
% 53.08/20.39 | (1094) all_0_2_2 = all_0_7_7
% 53.08/20.39 |
% 53.08/20.39 | Combining equations (1094,1093) yields a new equation:
% 53.08/20.39 | (1095) all_0_4_4 = all_0_7_7
% 53.08/20.39 |
% 53.08/20.39 | Combining equations (1154,1093) yields a new equation:
% 53.08/20.39 | (1207) all_0_4_4 = n18
% 53.08/20.39 |
% 53.08/20.39 | Combining equations (1207,1095) yields a new equation:
% 53.08/20.39 | (1209) all_0_7_7 = n18
% 53.08/20.39 |
% 53.08/20.39 | Combining equations (1209,1095) yields a new equation:
% 53.08/20.39 | (1207) all_0_4_4 = n18
% 53.08/20.39 |
% 53.08/20.39 | Combining equations (1207,1093) yields a new equation:
% 53.08/20.39 | (1154) all_0_2_2 = n18
% 53.08/20.39 |
% 53.08/20.39 | From (1154) and (3816) follows:
% 53.08/20.39 | (3834) sum(n18, n18) = all_0_0_0
% 53.08/20.39 |
% 53.08/20.39 | From (1209)(1207) and (590) follows:
% 53.08/20.39 | (1211) sum(n18, n18) = all_0_3_3
% 53.08/20.39 |
% 53.08/20.39 | Instantiating formula (690) with n18, n18, all_0_0_0, n10 and discharging atoms sum(n18, n18) = all_0_0_0, sum(n18, n18) = n10, yields:
% 53.08/20.39 | (1213) all_0_0_0 = n10
% 53.08/20.39 |
% 53.08/20.39 | Instantiating formula (690) 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:
% 53.08/20.39 | (1103) all_0_0_0 = all_0_3_3
% 53.08/20.39 |
% 53.08/20.39 | Combining equations (1213,1103) yields a new equation:
% 53.08/20.39 | (1212) all_0_3_3 = n10
% 53.08/20.39 |
% 53.08/20.39 | Combining equations (1212,1103) yields a new equation:
% 53.08/20.39 | (1213) all_0_0_0 = n10
% 53.08/20.39 |
% 53.08/20.39 | Equations (1213,1212) can reduce 679 to:
% 53.08/20.39 | (1106) $false
% 53.08/20.39 |
% 53.08/20.39 |-The branch is then unsatisfiable
% 53.08/20.39 |-Branch two:
% 53.08/20.39 | (1161) ~ (all_0_11_11 = n22)
% 53.08/20.39 | (1162) all_0_11_11 = n21 | 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
% 53.08/20.39 |
% 53.08/20.39 +-Applying beta-rule and splitting (1162), into two cases.
% 53.08/20.39 |-Branch one:
% 53.08/20.39 | (1163) all_0_11_11 = n21
% 53.08/20.39 |
% 53.08/20.39 | From (1163) and (559) follows:
% 53.08/20.39 | (1164) pred(n21) = all_0_9_9
% 53.08/20.39 |
% 53.08/20.39 | From (1163) and (992) follows:
% 53.08/20.39 | (1165) succ(n21) = all_0_5_5
% 53.08/20.39 |
% 53.08/20.39 | Instantiating formula (500) with n21, all_0_9_9, n20 and discharging atoms pred(n21) = all_0_9_9, pred(n21) = n20, yields:
% 53.08/20.39 | (1166) all_0_9_9 = n20
% 53.08/20.39 |
% 53.08/20.39 | Instantiating formula (617) with n21, all_0_5_5, n22 and discharging atoms succ(n21) = all_0_5_5, succ(n21) = n22, yields:
% 53.08/20.39 | (1167) all_0_5_5 = n22
% 53.08/20.39 |
% 53.08/20.39 | From (1166)(1167) and (538) follows:
% 53.08/20.39 | (1168) sum(n20, n22) = all_0_2_2
% 53.08/20.39 |
% 53.08/20.39 | From (1166) and (3814) follows:
% 53.08/20.39 | (3849) sum(n20, n23) = all_0_7_7
% 53.08/20.39 |
% 53.08/20.39 | From (1167) and (3812) follows:
% 53.08/20.39 | (3850) sum(n21, n22) = all_0_4_4
% 53.08/20.39 |
% 53.08/20.39 | Instantiating formula (690) with n21, n22, all_0_4_4, n17 and discharging atoms sum(n21, n22) = all_0_4_4, sum(n21, n22) = n17, yields:
% 53.08/20.39 | (1225) all_0_4_4 = n17
% 53.08/20.39 |
% 53.08/20.39 | Instantiating formula (690) with n20, n23, all_0_7_7, n17 and discharging atoms sum(n20, n23) = all_0_7_7, sum(n20, n23) = n17, yields:
% 53.08/20.39 | (1227) all_0_7_7 = n17
% 53.08/20.39 |
% 53.08/20.39 | Instantiating formula (690) with n20, n22, all_0_2_2, n16 and discharging atoms sum(n20, n22) = all_0_2_2, sum(n20, n22) = n16, yields:
% 53.08/20.39 | (1172) all_0_2_2 = n16
% 53.08/20.39 |
% 53.08/20.39 | From (1172) and (3816) follows:
% 53.08/20.39 | (3854) sum(n16, n18) = all_0_0_0
% 53.08/20.39 |
% 53.08/20.39 | From (1227)(1225) and (590) follows:
% 53.08/20.39 | (1229) sum(n17, n17) = all_0_3_3
% 53.08/20.39 |
% 53.08/20.39 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 53.08/20.39 | (1230) all_0_3_3 = n8
% 53.08/20.39 |
% 53.08/20.39 | Instantiating formula (690) with n16, n18, all_0_0_0, n8 and discharging atoms sum(n16, n18) = all_0_0_0, sum(n16, n18) = n8, yields:
% 53.08/20.39 | (1231) all_0_0_0 = n8
% 53.08/20.39 |
% 53.08/20.39 | Equations (1231,1230) can reduce 679 to:
% 53.08/20.39 | (1106) $false
% 53.08/20.39 |
% 53.08/20.39 |-The branch is then unsatisfiable
% 53.08/20.39 |-Branch two:
% 53.08/20.39 | (1179) ~ (all_0_11_11 = n21)
% 53.08/20.39 | (1180) 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
% 53.08/20.39 |
% 53.08/20.39 +-Applying beta-rule and splitting (1180), into two cases.
% 53.08/20.39 |-Branch one:
% 53.08/20.39 | (1181) all_0_11_11 = n20
% 53.08/20.39 |
% 53.08/20.39 | From (1181) and (559) follows:
% 53.08/20.39 | (1182) pred(n20) = all_0_9_9
% 53.08/20.39 |
% 53.08/20.39 | From (1181) and (992) follows:
% 53.08/20.39 | (1183) succ(n20) = all_0_5_5
% 53.08/20.39 |
% 53.08/20.39 | Instantiating formula (500) with n20, all_0_9_9, n19 and discharging atoms pred(n20) = all_0_9_9, pred(n20) = n19, yields:
% 53.08/20.39 | (1184) all_0_9_9 = n19
% 53.08/20.39 |
% 53.08/20.39 | Instantiating formula (617) with n20, all_0_5_5, n21 and discharging atoms succ(n20) = all_0_5_5, succ(n20) = n21, yields:
% 53.08/20.39 | (1185) all_0_5_5 = n21
% 53.08/20.39 |
% 53.08/20.39 | From (1184)(1185) and (538) follows:
% 53.08/20.39 | (1186) sum(n19, n21) = all_0_2_2
% 53.08/20.39 |
% 53.08/20.39 | From (1184) and (3814) follows:
% 53.08/20.39 | (3867) sum(n19, n23) = all_0_7_7
% 53.08/20.39 |
% 53.08/20.39 | From (1185) and (3812) follows:
% 53.08/20.40 | (3868) sum(n21, n21) = all_0_4_4
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (690) with n21, n21, all_0_4_4, n16 and discharging atoms sum(n21, n21) = all_0_4_4, sum(n21, n21) = n16, yields:
% 53.08/20.40 | (1243) all_0_4_4 = n16
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (690) with n19, n23, all_0_7_7, n16 and discharging atoms sum(n19, n23) = all_0_7_7, sum(n19, n23) = n16, yields:
% 53.08/20.40 | (1245) all_0_7_7 = n16
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (690) with n19, n21, all_0_2_2, n14 and discharging atoms sum(n19, n21) = all_0_2_2, sum(n19, n21) = n14, yields:
% 53.08/20.40 | (1190) all_0_2_2 = n14
% 53.08/20.40 |
% 53.08/20.40 | From (1190) and (3816) follows:
% 53.08/20.40 | (3872) sum(n14, n18) = all_0_0_0
% 53.08/20.40 |
% 53.08/20.40 | From (1245)(1243) and (590) follows:
% 53.08/20.40 | (1247) sum(n16, n16) = all_0_3_3
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 53.08/20.40 | (1248) all_0_3_3 = n6
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (690) with n14, n18, all_0_0_0, n6 and discharging atoms sum(n14, n18) = all_0_0_0, sum(n14, n18) = n6, yields:
% 53.08/20.40 | (1249) all_0_0_0 = n6
% 53.08/20.40 |
% 53.08/20.40 | Equations (1249,1248) can reduce 679 to:
% 53.08/20.40 | (1106) $false
% 53.08/20.40 |
% 53.08/20.40 |-The branch is then unsatisfiable
% 53.08/20.40 |-Branch two:
% 53.08/20.40 | (1197) ~ (all_0_11_11 = n20)
% 53.08/20.40 | (1198) 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
% 53.08/20.40 |
% 53.08/20.40 +-Applying beta-rule and splitting (1198), into two cases.
% 53.08/20.40 |-Branch one:
% 53.08/20.40 | (1199) all_0_11_11 = n19
% 53.08/20.40 |
% 53.08/20.40 | From (1199) and (559) follows:
% 53.08/20.40 | (1200) pred(n19) = all_0_9_9
% 53.08/20.40 |
% 53.08/20.40 | From (1199) and (992) follows:
% 53.08/20.40 | (1201) succ(n19) = all_0_5_5
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (500) with n19, all_0_9_9, n18 and discharging atoms pred(n19) = all_0_9_9, pred(n19) = n18, yields:
% 53.08/20.40 | (1202) all_0_9_9 = n18
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (617) with n19, all_0_5_5, n20 and discharging atoms succ(n19) = all_0_5_5, succ(n19) = n20, yields:
% 53.08/20.40 | (1203) all_0_5_5 = n20
% 53.08/20.40 |
% 53.08/20.40 | From (1202)(1203) and (538) follows:
% 53.08/20.40 | (1204) sum(n18, n20) = all_0_2_2
% 53.08/20.40 |
% 53.08/20.40 | From (1202) and (3814) follows:
% 53.08/20.40 | (3885) sum(n18, n23) = all_0_7_7
% 53.08/20.40 |
% 53.08/20.40 | From (1203) and (3812) follows:
% 53.08/20.40 | (3886) sum(n21, n20) = all_0_4_4
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (690) with n21, n20, all_0_4_4, n15 and discharging atoms sum(n21, n20) = all_0_4_4, sum(n21, n20) = n15, yields:
% 53.08/20.40 | (1261) all_0_4_4 = n15
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (690) with n18, n23, all_0_7_7, n15 and discharging atoms sum(n18, n23) = all_0_7_7, sum(n18, n23) = n15, yields:
% 53.08/20.40 | (1263) all_0_7_7 = n15
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (690) with n18, n20, all_0_2_2, n12 and discharging atoms sum(n18, n20) = all_0_2_2, sum(n18, n20) = n12, yields:
% 53.08/20.40 | (1208) all_0_2_2 = n12
% 53.08/20.40 |
% 53.08/20.40 | From (1208) and (3816) follows:
% 53.08/20.40 | (3890) sum(n12, n18) = all_0_0_0
% 53.08/20.40 |
% 53.08/20.40 | From (1263)(1261) and (590) follows:
% 53.08/20.40 | (1265) sum(n15, n15) = all_0_3_3
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 53.08/20.40 | (1266) all_0_3_3 = n4
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (690) with n12, n18, all_0_0_0, n4 and discharging atoms sum(n12, n18) = all_0_0_0, sum(n12, n18) = n4, yields:
% 53.08/20.40 | (1267) all_0_0_0 = n4
% 53.08/20.40 |
% 53.08/20.40 | Equations (1267,1266) can reduce 679 to:
% 53.08/20.40 | (1106) $false
% 53.08/20.40 |
% 53.08/20.40 |-The branch is then unsatisfiable
% 53.08/20.40 |-Branch two:
% 53.08/20.40 | (1215) ~ (all_0_11_11 = n19)
% 53.08/20.40 | (1216) 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
% 53.08/20.40 |
% 53.08/20.40 +-Applying beta-rule and splitting (1216), into two cases.
% 53.08/20.40 |-Branch one:
% 53.08/20.40 | (1217) all_0_11_11 = n18
% 53.08/20.40 |
% 53.08/20.40 | From (1217) and (559) follows:
% 53.08/20.40 | (1218) pred(n18) = all_0_9_9
% 53.08/20.40 |
% 53.08/20.40 | From (1217) and (992) follows:
% 53.08/20.40 | (1219) succ(n18) = all_0_5_5
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (500) with n18, all_0_9_9, n17 and discharging atoms pred(n18) = all_0_9_9, pred(n18) = n17, yields:
% 53.08/20.40 | (1220) all_0_9_9 = n17
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (617) with n18, all_0_5_5, n19 and discharging atoms succ(n18) = all_0_5_5, succ(n18) = n19, yields:
% 53.08/20.40 | (1221) all_0_5_5 = n19
% 53.08/20.40 |
% 53.08/20.40 | From (1220)(1221) and (538) follows:
% 53.08/20.40 | (1222) sum(n17, n19) = all_0_2_2
% 53.08/20.40 |
% 53.08/20.40 | From (1220) and (3814) follows:
% 53.08/20.40 | (3903) sum(n17, n23) = all_0_7_7
% 53.08/20.40 |
% 53.08/20.40 | From (1221) and (3812) follows:
% 53.08/20.40 | (3904) sum(n21, n19) = all_0_4_4
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (690) with n21, n19, all_0_4_4, n14 and discharging atoms sum(n21, n19) = all_0_4_4, sum(n21, n19) = n14, yields:
% 53.08/20.40 | (1279) all_0_4_4 = n14
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (690) with n17, n23, all_0_7_7, n14 and discharging atoms sum(n17, n23) = all_0_7_7, sum(n17, n23) = n14, yields:
% 53.08/20.40 | (1281) all_0_7_7 = n14
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (690) with n17, n19, all_0_2_2, n10 and discharging atoms sum(n17, n19) = all_0_2_2, sum(n17, n19) = n10, yields:
% 53.08/20.40 | (1226) all_0_2_2 = n10
% 53.08/20.40 |
% 53.08/20.40 | From (1226) and (3816) follows:
% 53.08/20.40 | (3908) sum(n10, n18) = all_0_0_0
% 53.08/20.40 |
% 53.08/20.40 | From (1281)(1279) and (590) follows:
% 53.08/20.40 | (1283) sum(n14, n14) = all_0_3_3
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 53.08/20.40 | (1284) all_0_3_3 = n2
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (690) with n10, n18, all_0_0_0, n2 and discharging atoms sum(n10, n18) = all_0_0_0, sum(n10, n18) = n2, yields:
% 53.08/20.40 | (1285) all_0_0_0 = n2
% 53.08/20.40 |
% 53.08/20.40 | Equations (1285,1284) can reduce 679 to:
% 53.08/20.40 | (1106) $false
% 53.08/20.40 |
% 53.08/20.40 |-The branch is then unsatisfiable
% 53.08/20.40 |-Branch two:
% 53.08/20.40 | (1233) ~ (all_0_11_11 = n18)
% 53.08/20.40 | (1234) 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
% 53.08/20.40 |
% 53.08/20.40 +-Applying beta-rule and splitting (1234), into two cases.
% 53.08/20.40 |-Branch one:
% 53.08/20.40 | (1235) all_0_11_11 = n17
% 53.08/20.40 |
% 53.08/20.40 | From (1235) and (559) follows:
% 53.08/20.40 | (1236) pred(n17) = all_0_9_9
% 53.08/20.40 |
% 53.08/20.40 | From (1235) and (992) follows:
% 53.08/20.40 | (1237) succ(n17) = all_0_5_5
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (500) with n17, all_0_9_9, n16 and discharging atoms pred(n17) = all_0_9_9, pred(n17) = n16, yields:
% 53.08/20.40 | (1238) all_0_9_9 = n16
% 53.08/20.40 |
% 53.08/20.40 | Instantiating formula (617) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 53.08/20.40 | (1239) all_0_5_5 = n18
% 53.08/20.40 |
% 53.08/20.40 | From (1238)(1239) and (538) follows:
% 53.08/20.40 | (1240) sum(n16, n18) = all_0_2_2
% 53.08/20.40 |
% 53.08/20.40 | From (1238) and (3814) follows:
% 53.08/20.40 | (3921) sum(n16, n23) = all_0_7_7
% 53.08/20.40 |
% 53.08/20.40 | From (1239) and (3812) follows:
% 53.08/20.41 | (3922) sum(n21, n18) = all_0_4_4
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (690) with n21, n18, all_0_4_4, n13 and discharging atoms sum(n21, n18) = all_0_4_4, sum(n21, n18) = n13, yields:
% 53.08/20.41 | (1297) all_0_4_4 = n13
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (690) with n16, n23, all_0_7_7, n13 and discharging atoms sum(n16, n23) = all_0_7_7, sum(n16, n23) = n13, yields:
% 53.08/20.41 | (1299) all_0_7_7 = n13
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (690) with n16, n18, all_0_2_2, n8 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = n8, yields:
% 53.08/20.41 | (1244) all_0_2_2 = n8
% 53.08/20.41 |
% 53.08/20.41 | From (1244) and (3816) follows:
% 53.08/20.41 | (3926) sum(n8, n18) = all_0_0_0
% 53.08/20.41 |
% 53.08/20.41 | From (1299)(1297) and (590) follows:
% 53.08/20.41 | (1301) sum(n13, n13) = all_0_3_3
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 53.08/20.41 | (1302) all_0_3_3 = n0
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (690) with n8, n18, all_0_0_0, n0 and discharging atoms sum(n8, n18) = all_0_0_0, sum(n8, n18) = n0, yields:
% 53.08/20.41 | (1303) all_0_0_0 = n0
% 53.08/20.41 |
% 53.08/20.41 | Equations (1303,1302) can reduce 679 to:
% 53.08/20.41 | (1106) $false
% 53.08/20.41 |
% 53.08/20.41 |-The branch is then unsatisfiable
% 53.08/20.41 |-Branch two:
% 53.08/20.41 | (1251) ~ (all_0_11_11 = n17)
% 53.08/20.41 | (1252) 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
% 53.08/20.41 |
% 53.08/20.41 +-Applying beta-rule and splitting (1252), into two cases.
% 53.08/20.41 |-Branch one:
% 53.08/20.41 | (1253) all_0_11_11 = n16
% 53.08/20.41 |
% 53.08/20.41 | From (1253) and (559) follows:
% 53.08/20.41 | (1254) pred(n16) = all_0_9_9
% 53.08/20.41 |
% 53.08/20.41 | From (1253) and (992) follows:
% 53.08/20.41 | (1255) succ(n16) = all_0_5_5
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (500) with n16, all_0_9_9, n15 and discharging atoms pred(n16) = all_0_9_9, pred(n16) = n15, yields:
% 53.08/20.41 | (1256) all_0_9_9 = n15
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (617) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 53.08/20.41 | (1257) all_0_5_5 = n17
% 53.08/20.41 |
% 53.08/20.41 | From (1256)(1257) and (538) follows:
% 53.08/20.41 | (1258) sum(n15, n17) = all_0_2_2
% 53.08/20.41 |
% 53.08/20.41 | From (1256) and (3814) follows:
% 53.08/20.41 | (3939) sum(n15, n23) = all_0_7_7
% 53.08/20.41 |
% 53.08/20.41 | From (1257) and (3812) follows:
% 53.08/20.41 | (3940) sum(n21, n17) = all_0_4_4
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (690) with n21, n17, all_0_4_4, n12 and discharging atoms sum(n21, n17) = all_0_4_4, sum(n21, n17) = n12, yields:
% 53.08/20.41 | (1315) all_0_4_4 = n12
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (690) with n15, n23, all_0_7_7, n12 and discharging atoms sum(n15, n23) = all_0_7_7, sum(n15, n23) = n12, yields:
% 53.08/20.41 | (1317) all_0_7_7 = n12
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (690) with n15, n17, all_0_2_2, n6 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n6, yields:
% 53.08/20.41 | (1262) all_0_2_2 = n6
% 53.08/20.41 |
% 53.08/20.41 | From (1262) and (3816) follows:
% 53.08/20.41 | (3944) sum(n6, n18) = all_0_0_0
% 53.08/20.41 |
% 53.08/20.41 | From (1317)(1315) and (590) follows:
% 53.08/20.41 | (1319) sum(n12, n12) = all_0_3_3
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 53.08/20.41 | (1320) all_0_3_3 = n24
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (690) with n6, n18, all_0_0_0, n24 and discharging atoms sum(n6, n18) = all_0_0_0, sum(n6, n18) = n24, yields:
% 53.08/20.41 | (1321) all_0_0_0 = n24
% 53.08/20.41 |
% 53.08/20.41 | Equations (1321,1320) can reduce 679 to:
% 53.08/20.41 | (1106) $false
% 53.08/20.41 |
% 53.08/20.41 |-The branch is then unsatisfiable
% 53.08/20.41 |-Branch two:
% 53.08/20.41 | (1269) ~ (all_0_11_11 = n16)
% 53.08/20.41 | (1270) 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
% 53.08/20.41 |
% 53.08/20.41 +-Applying beta-rule and splitting (1270), into two cases.
% 53.08/20.41 |-Branch one:
% 53.08/20.41 | (1271) all_0_11_11 = n15
% 53.08/20.41 |
% 53.08/20.41 | From (1271) and (559) follows:
% 53.08/20.41 | (1272) pred(n15) = all_0_9_9
% 53.08/20.41 |
% 53.08/20.41 | From (1271) and (992) follows:
% 53.08/20.41 | (1273) succ(n15) = all_0_5_5
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (500) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 53.08/20.41 | (1274) all_0_9_9 = n14
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (617) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 53.08/20.41 | (1275) all_0_5_5 = n16
% 53.08/20.41 |
% 53.08/20.41 | From (1274)(1275) and (538) follows:
% 53.08/20.41 | (1276) sum(n14, n16) = all_0_2_2
% 53.08/20.41 |
% 53.08/20.41 | From (1274) and (3814) follows:
% 53.08/20.41 | (3957) sum(n14, n23) = all_0_7_7
% 53.08/20.41 |
% 53.08/20.41 | From (1275) and (3812) follows:
% 53.08/20.41 | (3958) sum(n21, n16) = all_0_4_4
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (690) with n21, n16, all_0_4_4, n11 and discharging atoms sum(n21, n16) = all_0_4_4, sum(n21, n16) = n11, yields:
% 53.08/20.41 | (1333) all_0_4_4 = n11
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (690) with n14, n23, all_0_7_7, n11 and discharging atoms sum(n14, n23) = all_0_7_7, sum(n14, n23) = n11, yields:
% 53.08/20.41 | (1335) all_0_7_7 = n11
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (690) with n14, n16, all_0_2_2, n4 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n4, yields:
% 53.08/20.41 | (1280) all_0_2_2 = n4
% 53.08/20.41 |
% 53.08/20.41 | From (1280) and (3816) follows:
% 53.08/20.41 | (3962) sum(n4, n18) = all_0_0_0
% 53.08/20.41 |
% 53.08/20.41 | From (1335)(1333) and (590) follows:
% 53.08/20.41 | (1337) sum(n11, n11) = all_0_3_3
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 53.08/20.41 | (1104) all_0_3_3 = n22
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (690) with n4, n18, all_0_0_0, n22 and discharging atoms sum(n4, n18) = all_0_0_0, sum(n4, n18) = n22, yields:
% 53.08/20.41 | (1102) all_0_0_0 = n22
% 53.08/20.41 |
% 53.08/20.41 | Equations (1102,1104) can reduce 679 to:
% 53.08/20.41 | (1106) $false
% 53.08/20.41 |
% 53.08/20.41 |-The branch is then unsatisfiable
% 53.08/20.41 |-Branch two:
% 53.08/20.41 | (1287) ~ (all_0_11_11 = n15)
% 53.08/20.41 | (1288) 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
% 53.08/20.41 |
% 53.08/20.41 +-Applying beta-rule and splitting (1288), into two cases.
% 53.08/20.41 |-Branch one:
% 53.08/20.41 | (1289) all_0_11_11 = n14
% 53.08/20.41 |
% 53.08/20.41 | From (1289) and (559) follows:
% 53.08/20.41 | (1290) pred(n14) = all_0_9_9
% 53.08/20.41 |
% 53.08/20.41 | From (1289) and (992) follows:
% 53.08/20.41 | (1291) succ(n14) = all_0_5_5
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (500) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 53.08/20.41 | (1292) all_0_9_9 = n13
% 53.08/20.41 |
% 53.08/20.41 | Instantiating formula (617) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 53.08/20.41 | (1293) all_0_5_5 = n15
% 53.08/20.41 |
% 53.08/20.41 | From (1292)(1293) and (538) follows:
% 53.08/20.42 | (1294) sum(n13, n15) = all_0_2_2
% 53.08/20.42 |
% 53.08/20.42 | From (1292) and (3814) follows:
% 53.08/20.42 | (3975) sum(n13, n23) = all_0_7_7
% 53.08/20.42 |
% 53.08/20.42 | From (1293) and (3812) follows:
% 53.08/20.42 | (3976) sum(n21, n15) = all_0_4_4
% 53.08/20.42 |
% 53.08/20.42 | Instantiating formula (690) with n21, n15, all_0_4_4, n10 and discharging atoms sum(n21, n15) = all_0_4_4, sum(n21, n15) = n10, yields:
% 53.08/20.42 | (1351) all_0_4_4 = n10
% 53.08/20.42 |
% 53.08/20.42 | Instantiating formula (690) with n13, n23, all_0_7_7, n10 and discharging atoms sum(n13, n23) = all_0_7_7, sum(n13, n23) = n10, yields:
% 53.08/20.42 | (1353) all_0_7_7 = n10
% 53.08/20.42 |
% 53.08/20.42 | Instantiating formula (690) with n13, n15, all_0_2_2, n2 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n2, yields:
% 53.08/20.42 | (1298) all_0_2_2 = n2
% 53.08/20.42 |
% 53.08/20.42 | From (1298) and (3816) follows:
% 53.08/20.42 | (3980) sum(n2, n18) = all_0_0_0
% 53.08/20.42 |
% 53.08/20.42 | From (1353)(1351) and (590) follows:
% 53.08/20.42 | (1355) sum(n10, n10) = all_0_3_3
% 53.08/20.42 |
% 53.08/20.42 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 53.08/20.42 | (1122) all_0_3_3 = n20
% 53.08/20.42 |
% 53.08/20.42 | Instantiating formula (690) with n2, n18, all_0_0_0, n20 and discharging atoms sum(n2, n18) = all_0_0_0, sum(n2, n18) = n20, yields:
% 53.08/20.42 | (1123) all_0_0_0 = n20
% 53.08/20.42 |
% 53.08/20.42 | Equations (1123,1122) can reduce 679 to:
% 53.08/20.42 | (1106) $false
% 53.08/20.42 |
% 53.08/20.42 |-The branch is then unsatisfiable
% 53.08/20.42 |-Branch two:
% 53.08/20.42 | (1305) ~ (all_0_11_11 = n14)
% 53.08/20.42 | (1306) 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
% 53.08/20.42 |
% 53.08/20.42 +-Applying beta-rule and splitting (1306), into two cases.
% 53.08/20.42 |-Branch one:
% 53.08/20.42 | (1307) all_0_11_11 = n13
% 53.08/20.42 |
% 53.08/20.42 | From (1307) and (559) follows:
% 53.08/20.42 | (1308) pred(n13) = all_0_9_9
% 53.08/20.42 |
% 53.08/20.42 | From (1307) and (992) follows:
% 53.08/20.42 | (1309) succ(n13) = all_0_5_5
% 53.08/20.42 |
% 53.08/20.42 | Instantiating formula (500) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 53.08/20.42 | (1310) all_0_9_9 = n12
% 53.08/20.42 |
% 53.08/20.42 | Instantiating formula (617) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 53.08/20.42 | (1311) all_0_5_5 = n14
% 53.08/20.42 |
% 53.08/20.42 | From (1310)(1311) and (538) follows:
% 53.08/20.42 | (1312) sum(n12, n14) = all_0_2_2
% 53.08/20.42 |
% 53.08/20.42 | From (1310) and (3814) follows:
% 53.08/20.42 | (3993) sum(n12, n23) = all_0_7_7
% 53.08/20.42 |
% 53.08/20.42 | From (1311) and (3812) follows:
% 53.08/20.42 | (3994) sum(n21, n14) = all_0_4_4
% 53.08/20.42 |
% 53.08/20.42 | Instantiating formula (690) with n21, n14, all_0_4_4, n9 and discharging atoms sum(n21, n14) = all_0_4_4, sum(n21, n14) = n9, yields:
% 53.08/20.42 | (1369) all_0_4_4 = n9
% 53.08/20.42 |
% 53.08/20.42 | Instantiating formula (690) with n12, n23, all_0_7_7, n9 and discharging atoms sum(n12, n23) = all_0_7_7, sum(n12, n23) = n9, yields:
% 53.08/20.42 | (1371) all_0_7_7 = n9
% 53.08/20.42 |
% 53.08/20.42 | Instantiating formula (690) with n12, n14, all_0_2_2, n0 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n0, yields:
% 53.08/20.42 | (1316) all_0_2_2 = n0
% 53.08/20.42 |
% 53.08/20.42 | From (1316) and (3816) follows:
% 53.08/20.42 | (3998) sum(n0, n18) = all_0_0_0
% 53.08/20.42 |
% 53.08/20.42 | From (1371)(1369) and (590) follows:
% 53.08/20.42 | (1373) sum(n9, n9) = all_0_3_3
% 53.08/20.42 |
% 53.08/20.42 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 53.08/20.42 | (1140) all_0_3_3 = n18
% 53.08/20.42 |
% 53.08/20.42 | Instantiating formula (690) with n0, n18, all_0_0_0, n18 and discharging atoms sum(n0, n18) = all_0_0_0, sum(n0, n18) = n18, yields:
% 53.08/20.42 | (1141) all_0_0_0 = n18
% 53.08/20.42 |
% 53.08/20.42 | Equations (1141,1140) can reduce 679 to:
% 53.08/20.42 | (1106) $false
% 53.08/20.42 |
% 53.08/20.42 |-The branch is then unsatisfiable
% 53.08/20.42 |-Branch two:
% 53.08/20.42 | (1323) ~ (all_0_11_11 = n13)
% 53.08/20.42 | (1324) 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
% 53.08/20.42 |
% 53.08/20.42 +-Applying beta-rule and splitting (1324), into two cases.
% 53.08/20.42 |-Branch one:
% 53.08/20.42 | (1325) all_0_11_11 = n12
% 53.08/20.42 |
% 53.08/20.42 | From (1325) and (559) follows:
% 53.08/20.42 | (1326) pred(n12) = all_0_9_9
% 53.08/20.42 |
% 53.08/20.42 | From (1325) and (992) follows:
% 53.08/20.42 | (1327) succ(n12) = all_0_5_5
% 53.08/20.42 |
% 53.08/20.42 | Instantiating formula (500) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 53.08/20.42 | (1328) all_0_9_9 = n11
% 53.08/20.42 |
% 53.08/20.42 | Instantiating formula (617) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 53.08/20.42 | (1329) all_0_5_5 = n13
% 53.08/20.42 |
% 53.08/20.42 | From (1328)(1329) and (538) follows:
% 53.08/20.42 | (1330) sum(n11, n13) = all_0_2_2
% 53.08/20.42 |
% 53.08/20.42 | From (1328) and (3814) follows:
% 53.08/20.42 | (4011) sum(n11, n23) = all_0_7_7
% 53.08/20.42 |
% 53.08/20.42 | From (1329) and (3812) follows:
% 53.08/20.42 | (4012) sum(n21, n13) = all_0_4_4
% 53.08/20.42 |
% 53.08/20.42 | Instantiating formula (690) with n21, n13, all_0_4_4, n8 and discharging atoms sum(n21, n13) = all_0_4_4, sum(n21, n13) = n8, yields:
% 53.08/20.42 | (1387) all_0_4_4 = n8
% 53.08/20.42 |
% 53.08/20.42 | Instantiating formula (690) with n11, n23, all_0_7_7, n8 and discharging atoms sum(n11, n23) = all_0_7_7, sum(n11, n23) = n8, yields:
% 53.08/20.42 | (1389) all_0_7_7 = n8
% 53.08/20.42 |
% 53.08/20.42 | Instantiating formula (690) with n11, n13, all_0_2_2, n24 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n24, yields:
% 53.08/20.42 | (1092) all_0_2_2 = n24
% 53.08/20.42 |
% 53.08/20.42 | From (1092) and (3816) follows:
% 53.37/20.42 | (1618) sum(n24, n18) = all_0_0_0
% 53.37/20.42 |
% 53.37/20.42 | From (1389)(1387) and (590) follows:
% 53.37/20.42 | (1391) sum(n8, n8) = all_0_3_3
% 53.37/20.42 |
% 53.37/20.42 | Instantiating formula (690) with n24, n18, all_0_0_0, n16 and discharging atoms sum(n24, n18) = all_0_0_0, sum(n24, n18) = n16, yields:
% 53.37/20.42 | (1159) all_0_0_0 = n16
% 53.37/20.42 |
% 53.37/20.42 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 53.37/20.42 | (1158) all_0_3_3 = n16
% 53.37/20.42 |
% 53.37/20.42 | Equations (1159,1158) can reduce 679 to:
% 53.37/20.42 | (1106) $false
% 53.37/20.42 |
% 53.37/20.42 |-The branch is then unsatisfiable
% 53.37/20.42 |-Branch two:
% 53.37/20.42 | (1341) ~ (all_0_11_11 = n12)
% 53.37/20.42 | (1342) 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
% 53.37/20.42 |
% 53.37/20.42 +-Applying beta-rule and splitting (1342), into two cases.
% 53.37/20.42 |-Branch one:
% 53.37/20.42 | (1343) all_0_11_11 = n11
% 53.37/20.42 |
% 53.37/20.42 | From (1343) and (559) follows:
% 53.37/20.42 | (1344) pred(n11) = all_0_9_9
% 53.37/20.42 |
% 53.37/20.42 | From (1343) and (992) follows:
% 53.37/20.42 | (1345) succ(n11) = all_0_5_5
% 53.37/20.42 |
% 53.37/20.42 | Instantiating formula (500) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 53.37/20.42 | (1346) all_0_9_9 = n10
% 53.37/20.42 |
% 53.37/20.42 | Instantiating formula (617) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 53.37/20.43 | (1347) all_0_5_5 = n12
% 53.37/20.43 |
% 53.37/20.43 | From (1346)(1347) and (538) follows:
% 53.37/20.43 | (1348) sum(n10, n12) = all_0_2_2
% 53.37/20.43 |
% 53.37/20.43 | From (1346) and (3814) follows:
% 53.37/20.43 | (4029) sum(n10, n23) = all_0_7_7
% 53.37/20.43 |
% 53.37/20.43 | From (1347) and (3812) follows:
% 53.37/20.43 | (4030) sum(n21, n12) = all_0_4_4
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (690) with n21, n12, all_0_4_4, n7 and discharging atoms sum(n21, n12) = all_0_4_4, sum(n21, n12) = n7, yields:
% 53.37/20.43 | (1405) all_0_4_4 = n7
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (690) with n10, n23, all_0_7_7, n7 and discharging atoms sum(n10, n23) = all_0_7_7, sum(n10, n23) = n7, yields:
% 53.37/20.43 | (1407) all_0_7_7 = n7
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (690) with n10, n12, all_0_2_2, n22 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n22, yields:
% 53.37/20.43 | (1118) all_0_2_2 = n22
% 53.37/20.43 |
% 53.37/20.43 | From (1118) and (3816) follows:
% 53.37/20.43 | (2530) sum(n22, n18) = all_0_0_0
% 53.37/20.43 |
% 53.37/20.43 | From (1407)(1405) and (590) follows:
% 53.37/20.43 | (1409) sum(n7, n7) = all_0_3_3
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (690) with n22, n18, all_0_0_0, n14 and discharging atoms sum(n22, n18) = all_0_0_0, sum(n22, n18) = n14, yields:
% 53.37/20.43 | (1177) all_0_0_0 = n14
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 53.37/20.43 | (1176) all_0_3_3 = n14
% 53.37/20.43 |
% 53.37/20.43 | Equations (1177,1176) can reduce 679 to:
% 53.37/20.43 | (1106) $false
% 53.37/20.43 |
% 53.37/20.43 |-The branch is then unsatisfiable
% 53.37/20.43 |-Branch two:
% 53.37/20.43 | (1359) ~ (all_0_11_11 = n11)
% 53.37/20.43 | (1360) 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
% 53.37/20.43 |
% 53.37/20.43 +-Applying beta-rule and splitting (1360), into two cases.
% 53.37/20.43 |-Branch one:
% 53.37/20.43 | (1361) all_0_11_11 = n10
% 53.37/20.43 |
% 53.37/20.43 | From (1361) and (559) follows:
% 53.37/20.43 | (1362) pred(n10) = all_0_9_9
% 53.37/20.43 |
% 53.37/20.43 | From (1361) and (992) follows:
% 53.37/20.43 | (1363) succ(n10) = all_0_5_5
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (500) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 53.37/20.43 | (1364) all_0_9_9 = n9
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (617) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 53.37/20.43 | (1365) all_0_5_5 = n11
% 53.37/20.43 |
% 53.37/20.43 | From (1364)(1365) and (538) follows:
% 53.37/20.43 | (1366) sum(n9, n11) = all_0_2_2
% 53.37/20.43 |
% 53.37/20.43 | From (1364) and (3814) follows:
% 53.37/20.43 | (4047) sum(n9, n23) = all_0_7_7
% 53.37/20.43 |
% 53.37/20.43 | From (1365) and (3812) follows:
% 53.37/20.43 | (4048) sum(n21, n11) = all_0_4_4
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (690) with n21, n11, all_0_4_4, n6 and discharging atoms sum(n21, n11) = all_0_4_4, sum(n21, n11) = n6, yields:
% 53.37/20.43 | (1423) all_0_4_4 = n6
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (690) with n9, n23, all_0_7_7, n6 and discharging atoms sum(n9, n23) = all_0_7_7, sum(n9, n23) = n6, yields:
% 53.37/20.43 | (1425) all_0_7_7 = n6
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (690) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 53.37/20.43 | (1136) all_0_2_2 = n20
% 53.37/20.43 |
% 53.37/20.43 | From (1136) and (3816) follows:
% 53.37/20.43 | (3404) sum(n20, n18) = all_0_0_0
% 53.37/20.43 |
% 53.37/20.43 | From (1425)(1423) and (590) follows:
% 53.37/20.43 | (1427) sum(n6, n6) = all_0_3_3
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (690) with n20, n18, all_0_0_0, n12 and discharging atoms sum(n20, n18) = all_0_0_0, sum(n20, n18) = n12, yields:
% 53.37/20.43 | (1195) all_0_0_0 = n12
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 53.37/20.43 | (1194) all_0_3_3 = n12
% 53.37/20.43 |
% 53.37/20.43 | Equations (1195,1194) can reduce 679 to:
% 53.37/20.43 | (1106) $false
% 53.37/20.43 |
% 53.37/20.43 |-The branch is then unsatisfiable
% 53.37/20.43 |-Branch two:
% 53.37/20.43 | (1377) ~ (all_0_11_11 = n10)
% 53.37/20.43 | (1378) 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
% 53.37/20.43 |
% 53.37/20.43 +-Applying beta-rule and splitting (1378), into two cases.
% 53.37/20.43 |-Branch one:
% 53.37/20.43 | (1379) all_0_11_11 = n9
% 53.37/20.43 |
% 53.37/20.43 | From (1379) and (559) follows:
% 53.37/20.43 | (1380) pred(n9) = all_0_9_9
% 53.37/20.43 |
% 53.37/20.43 | From (1379) and (992) follows:
% 53.37/20.43 | (1381) succ(n9) = all_0_5_5
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 53.37/20.43 | (1382) all_0_9_9 = n8
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 53.37/20.43 | (1383) all_0_5_5 = n10
% 53.37/20.43 |
% 53.37/20.43 | From (1382)(1383) and (538) follows:
% 53.37/20.43 | (1384) sum(n8, n10) = all_0_2_2
% 53.37/20.43 |
% 53.37/20.43 | From (1382) and (3814) follows:
% 53.37/20.43 | (4065) sum(n8, n23) = all_0_7_7
% 53.37/20.43 |
% 53.37/20.43 | From (1383) and (3812) follows:
% 53.37/20.43 | (4066) sum(n21, n10) = all_0_4_4
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (690) with n21, n10, all_0_4_4, n5 and discharging atoms sum(n21, n10) = all_0_4_4, sum(n21, n10) = n5, yields:
% 53.37/20.43 | (1441) all_0_4_4 = n5
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (690) with n8, n23, all_0_7_7, n5 and discharging atoms sum(n8, n23) = all_0_7_7, sum(n8, n23) = n5, yields:
% 53.37/20.43 | (1443) all_0_7_7 = n5
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 53.37/20.43 | (1154) all_0_2_2 = n18
% 53.37/20.43 |
% 53.37/20.43 | From (1154) and (3816) follows:
% 53.37/20.43 | (3834) sum(n18, n18) = all_0_0_0
% 53.37/20.43 |
% 53.37/20.43 | From (1443)(1441) and (590) follows:
% 53.37/20.43 | (1445) sum(n5, n5) = all_0_3_3
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (690) with n18, n18, all_0_0_0, n10 and discharging atoms sum(n18, n18) = all_0_0_0, sum(n18, n18) = n10, yields:
% 53.37/20.43 | (1213) all_0_0_0 = n10
% 53.37/20.43 |
% 53.37/20.43 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 53.37/20.43 | (1212) all_0_3_3 = n10
% 53.37/20.43 |
% 53.37/20.43 | Equations (1213,1212) can reduce 679 to:
% 53.37/20.43 | (1106) $false
% 53.37/20.43 |
% 53.37/20.43 |-The branch is then unsatisfiable
% 53.37/20.43 |-Branch two:
% 53.37/20.43 | (1395) ~ (all_0_11_11 = n9)
% 53.37/20.43 | (1396) 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
% 53.37/20.43 |
% 53.37/20.43 +-Applying beta-rule and splitting (1396), into two cases.
% 53.37/20.43 |-Branch one:
% 53.37/20.43 | (1397) all_0_11_11 = n8
% 53.37/20.43 |
% 53.37/20.43 | From (1397) and (559) follows:
% 53.37/20.43 | (1398) pred(n8) = all_0_9_9
% 53.37/20.43 |
% 53.37/20.43 | From (1397) and (992) follows:
% 53.37/20.43 | (1399) succ(n8) = all_0_5_5
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 53.37/20.44 | (1400) all_0_9_9 = n7
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 53.37/20.44 | (1401) all_0_5_5 = n9
% 53.37/20.44 |
% 53.37/20.44 | From (1400)(1401) and (538) follows:
% 53.37/20.44 | (1402) sum(n7, n9) = all_0_2_2
% 53.37/20.44 |
% 53.37/20.44 | From (1400) and (3814) follows:
% 53.37/20.44 | (4083) sum(n7, n23) = all_0_7_7
% 53.37/20.44 |
% 53.37/20.44 | From (1401) and (3812) follows:
% 53.37/20.44 | (4084) sum(n21, n9) = all_0_4_4
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (690) with n21, n9, all_0_4_4, n4 and discharging atoms sum(n21, n9) = all_0_4_4, sum(n21, n9) = n4, yields:
% 53.37/20.44 | (1459) all_0_4_4 = n4
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (690) with n7, n23, all_0_7_7, n4 and discharging atoms sum(n7, n23) = all_0_7_7, sum(n7, n23) = n4, yields:
% 53.37/20.44 | (1461) all_0_7_7 = n4
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 53.37/20.44 | (1172) all_0_2_2 = n16
% 53.37/20.44 |
% 53.37/20.44 | From (1172) and (3816) follows:
% 53.37/20.44 | (3854) sum(n16, n18) = all_0_0_0
% 53.37/20.44 |
% 53.37/20.44 | From (1461)(1459) and (590) follows:
% 53.37/20.44 | (1463) sum(n4, n4) = all_0_3_3
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (690) with n16, n18, all_0_0_0, n8 and discharging atoms sum(n16, n18) = all_0_0_0, sum(n16, n18) = n8, yields:
% 53.37/20.44 | (1231) all_0_0_0 = n8
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 53.37/20.44 | (1230) all_0_3_3 = n8
% 53.37/20.44 |
% 53.37/20.44 | Equations (1231,1230) can reduce 679 to:
% 53.37/20.44 | (1106) $false
% 53.37/20.44 |
% 53.37/20.44 |-The branch is then unsatisfiable
% 53.37/20.44 |-Branch two:
% 53.37/20.44 | (1413) ~ (all_0_11_11 = n8)
% 53.37/20.44 | (1414) 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
% 53.37/20.44 |
% 53.37/20.44 +-Applying beta-rule and splitting (1414), into two cases.
% 53.37/20.44 |-Branch one:
% 53.37/20.44 | (1415) all_0_11_11 = n7
% 53.37/20.44 |
% 53.37/20.44 | From (1415) and (559) follows:
% 53.37/20.44 | (1416) pred(n7) = all_0_9_9
% 53.37/20.44 |
% 53.37/20.44 | From (1415) and (992) follows:
% 53.37/20.44 | (1417) succ(n7) = all_0_5_5
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 53.37/20.44 | (1418) all_0_9_9 = n6
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 53.37/20.44 | (1419) all_0_5_5 = n8
% 53.37/20.44 |
% 53.37/20.44 | From (1418)(1419) and (538) follows:
% 53.37/20.44 | (1420) sum(n6, n8) = all_0_2_2
% 53.37/20.44 |
% 53.37/20.44 | From (1418) and (3814) follows:
% 53.37/20.44 | (4101) sum(n6, n23) = all_0_7_7
% 53.37/20.44 |
% 53.37/20.44 | From (1419) and (3812) follows:
% 53.37/20.44 | (4102) sum(n21, n8) = all_0_4_4
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (690) with n21, n8, all_0_4_4, n3 and discharging atoms sum(n21, n8) = all_0_4_4, sum(n21, n8) = n3, yields:
% 53.37/20.44 | (1477) all_0_4_4 = n3
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (690) with n6, n23, all_0_7_7, n3 and discharging atoms sum(n6, n23) = all_0_7_7, sum(n6, n23) = n3, yields:
% 53.37/20.44 | (1479) all_0_7_7 = n3
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 53.37/20.44 | (1190) all_0_2_2 = n14
% 53.37/20.44 |
% 53.37/20.44 | From (1190) and (3816) follows:
% 53.37/20.44 | (3872) sum(n14, n18) = all_0_0_0
% 53.37/20.44 |
% 53.37/20.44 | From (1479)(1477) and (590) follows:
% 53.37/20.44 | (1481) sum(n3, n3) = all_0_3_3
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (690) with n14, n18, all_0_0_0, n6 and discharging atoms sum(n14, n18) = all_0_0_0, sum(n14, n18) = n6, yields:
% 53.37/20.44 | (1249) all_0_0_0 = n6
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 53.37/20.44 | (1248) all_0_3_3 = n6
% 53.37/20.44 |
% 53.37/20.44 | Equations (1249,1248) can reduce 679 to:
% 53.37/20.44 | (1106) $false
% 53.37/20.44 |
% 53.37/20.44 |-The branch is then unsatisfiable
% 53.37/20.44 |-Branch two:
% 53.37/20.44 | (1431) ~ (all_0_11_11 = n7)
% 53.37/20.44 | (1432) 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
% 53.37/20.44 |
% 53.37/20.44 +-Applying beta-rule and splitting (1432), into two cases.
% 53.37/20.44 |-Branch one:
% 53.37/20.44 | (1433) all_0_11_11 = n6
% 53.37/20.44 |
% 53.37/20.44 | From (1433) and (559) follows:
% 53.37/20.44 | (1434) pred(n6) = all_0_9_9
% 53.37/20.44 |
% 53.37/20.44 | From (1433) and (992) follows:
% 53.37/20.44 | (1435) succ(n6) = all_0_5_5
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 53.37/20.44 | (1436) all_0_9_9 = n5
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 53.37/20.44 | (1437) all_0_5_5 = n7
% 53.37/20.44 |
% 53.37/20.44 | From (1436)(1437) and (538) follows:
% 53.37/20.44 | (1438) sum(n5, n7) = all_0_2_2
% 53.37/20.44 |
% 53.37/20.44 | From (1436) and (3814) follows:
% 53.37/20.44 | (4119) sum(n5, n23) = all_0_7_7
% 53.37/20.44 |
% 53.37/20.44 | From (1437) and (3812) follows:
% 53.37/20.44 | (4120) sum(n21, n7) = all_0_4_4
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (690) with n21, n7, all_0_4_4, n2 and discharging atoms sum(n21, n7) = all_0_4_4, sum(n21, n7) = n2, yields:
% 53.37/20.44 | (1495) all_0_4_4 = n2
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (690) with n5, n23, all_0_7_7, n2 and discharging atoms sum(n5, n23) = all_0_7_7, sum(n5, n23) = n2, yields:
% 53.37/20.44 | (1497) all_0_7_7 = n2
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 53.37/20.44 | (1208) all_0_2_2 = n12
% 53.37/20.44 |
% 53.37/20.44 | From (1208) and (3816) follows:
% 53.37/20.44 | (3890) sum(n12, n18) = all_0_0_0
% 53.37/20.44 |
% 53.37/20.44 | From (1497)(1495) and (590) follows:
% 53.37/20.44 | (1499) sum(n2, n2) = all_0_3_3
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (690) with n12, n18, all_0_0_0, n4 and discharging atoms sum(n12, n18) = all_0_0_0, sum(n12, n18) = n4, yields:
% 53.37/20.44 | (1267) all_0_0_0 = n4
% 53.37/20.44 |
% 53.37/20.44 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 53.37/20.44 | (1266) all_0_3_3 = n4
% 53.37/20.44 |
% 53.37/20.44 | Equations (1267,1266) can reduce 679 to:
% 53.37/20.44 | (1106) $false
% 53.37/20.44 |
% 53.37/20.44 |-The branch is then unsatisfiable
% 53.37/20.44 |-Branch two:
% 53.37/20.44 | (1449) ~ (all_0_11_11 = n6)
% 53.37/20.44 | (1450) 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
% 53.37/20.44 |
% 53.37/20.44 +-Applying beta-rule and splitting (1450), into two cases.
% 53.37/20.44 |-Branch one:
% 53.37/20.44 | (1451) all_0_11_11 = n5
% 53.37/20.44 |
% 53.37/20.44 | From (1451) and (559) follows:
% 53.37/20.45 | (1452) pred(n5) = all_0_9_9
% 53.37/20.45 |
% 53.37/20.45 | From (1451) and (992) follows:
% 53.37/20.45 | (1453) succ(n5) = all_0_5_5
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 53.37/20.45 | (1454) all_0_9_9 = n4
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 53.37/20.45 | (1455) all_0_5_5 = n6
% 53.37/20.45 |
% 53.37/20.45 | From (1454)(1455) and (538) follows:
% 53.37/20.45 | (1456) sum(n4, n6) = all_0_2_2
% 53.37/20.45 |
% 53.37/20.45 | From (1454) and (3814) follows:
% 53.37/20.45 | (4137) sum(n4, n23) = all_0_7_7
% 53.37/20.45 |
% 53.37/20.45 | From (1455) and (3812) follows:
% 53.37/20.45 | (4138) sum(n21, n6) = all_0_4_4
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (690) with n21, n6, all_0_4_4, n1 and discharging atoms sum(n21, n6) = all_0_4_4, sum(n21, n6) = n1, yields:
% 53.37/20.45 | (1513) all_0_4_4 = n1
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (690) with n4, n23, all_0_7_7, n1 and discharging atoms sum(n4, n23) = all_0_7_7, sum(n4, n23) = n1, yields:
% 53.37/20.45 | (1515) all_0_7_7 = n1
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 53.37/20.45 | (1226) all_0_2_2 = n10
% 53.37/20.45 |
% 53.37/20.45 | From (1226) and (3816) follows:
% 53.37/20.45 | (3908) sum(n10, n18) = all_0_0_0
% 53.37/20.45 |
% 53.37/20.45 | From (1515)(1513) and (590) follows:
% 53.37/20.45 | (1517) sum(n1, n1) = all_0_3_3
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (690) with n10, n18, all_0_0_0, n2 and discharging atoms sum(n10, n18) = all_0_0_0, sum(n10, n18) = n2, yields:
% 53.37/20.45 | (1285) all_0_0_0 = n2
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 53.37/20.45 | (1284) all_0_3_3 = n2
% 53.37/20.45 |
% 53.37/20.45 | Equations (1285,1284) can reduce 679 to:
% 53.37/20.45 | (1106) $false
% 53.37/20.45 |
% 53.37/20.45 |-The branch is then unsatisfiable
% 53.37/20.45 |-Branch two:
% 53.37/20.45 | (1467) ~ (all_0_11_11 = n5)
% 53.37/20.45 | (1468) 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
% 53.37/20.45 |
% 53.37/20.45 +-Applying beta-rule and splitting (1468), into two cases.
% 53.37/20.45 |-Branch one:
% 53.37/20.45 | (1469) all_0_11_11 = n4
% 53.37/20.45 |
% 53.37/20.45 | From (1469) and (559) follows:
% 53.37/20.45 | (1470) pred(n4) = all_0_9_9
% 53.37/20.45 |
% 53.37/20.45 | From (1469) and (992) follows:
% 53.37/20.45 | (1471) succ(n4) = all_0_5_5
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 53.37/20.45 | (1472) all_0_9_9 = n3
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 53.37/20.45 | (1473) all_0_5_5 = n5
% 53.37/20.45 |
% 53.37/20.45 | From (1472)(1473) and (538) follows:
% 53.37/20.45 | (1474) sum(n3, n5) = all_0_2_2
% 53.37/20.45 |
% 53.37/20.45 | From (1472) and (3814) follows:
% 53.37/20.45 | (4155) sum(n3, n23) = all_0_7_7
% 53.37/20.45 |
% 53.37/20.45 | From (1473) and (3812) follows:
% 53.37/20.45 | (4156) sum(n21, n5) = all_0_4_4
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (690) with n21, n5, all_0_4_4, n0 and discharging atoms sum(n21, n5) = all_0_4_4, sum(n21, n5) = n0, yields:
% 53.37/20.45 | (1531) all_0_4_4 = n0
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (690) with n3, n23, all_0_7_7, n0 and discharging atoms sum(n3, n23) = all_0_7_7, sum(n3, n23) = n0, yields:
% 53.37/20.45 | (1533) all_0_7_7 = n0
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 53.37/20.45 | (1244) all_0_2_2 = n8
% 53.37/20.45 |
% 53.37/20.45 | From (1244) and (3816) follows:
% 53.37/20.45 | (3926) sum(n8, n18) = all_0_0_0
% 53.37/20.45 |
% 53.37/20.45 | From (1533)(1531) and (590) follows:
% 53.37/20.45 | (1535) sum(n0, n0) = all_0_3_3
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (690) with n8, n18, all_0_0_0, n0 and discharging atoms sum(n8, n18) = all_0_0_0, sum(n8, n18) = n0, yields:
% 53.37/20.45 | (1303) all_0_0_0 = n0
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 53.37/20.45 | (1302) all_0_3_3 = n0
% 53.37/20.45 |
% 53.37/20.45 | Equations (1303,1302) can reduce 679 to:
% 53.37/20.45 | (1106) $false
% 53.37/20.45 |
% 53.37/20.45 |-The branch is then unsatisfiable
% 53.37/20.45 |-Branch two:
% 53.37/20.45 | (1485) ~ (all_0_11_11 = n4)
% 53.37/20.45 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 53.37/20.45 |
% 53.37/20.45 +-Applying beta-rule and splitting (1486), into two cases.
% 53.37/20.45 |-Branch one:
% 53.37/20.45 | (1487) all_0_11_11 = n3
% 53.37/20.45 |
% 53.37/20.45 | From (1487) and (559) follows:
% 53.37/20.45 | (1488) pred(n3) = all_0_9_9
% 53.37/20.45 |
% 53.37/20.45 | From (1487) and (992) follows:
% 53.37/20.45 | (1489) succ(n3) = all_0_5_5
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 53.37/20.45 | (1490) all_0_9_9 = n2
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 53.37/20.45 | (1491) all_0_5_5 = n4
% 53.37/20.45 |
% 53.37/20.45 | From (1490)(1491) and (538) follows:
% 53.37/20.45 | (1492) sum(n2, n4) = all_0_2_2
% 53.37/20.45 |
% 53.37/20.45 | From (1490) and (3814) follows:
% 53.37/20.45 | (4173) sum(n2, n23) = all_0_7_7
% 53.37/20.45 |
% 53.37/20.45 | From (1491) and (3812) follows:
% 53.37/20.45 | (4174) sum(n21, n4) = all_0_4_4
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (690) with n21, n4, all_0_4_4, n25 and discharging atoms sum(n21, n4) = all_0_4_4, sum(n21, n4) = n25, yields:
% 53.37/20.45 | (1551) all_0_4_4 = n25
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (690) with n2, n23, all_0_7_7, n25 and discharging atoms sum(n2, n23) = all_0_7_7, sum(n2, n23) = n25, yields:
% 53.37/20.45 | (1550) all_0_7_7 = n25
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 53.37/20.45 | (1262) all_0_2_2 = n6
% 53.37/20.45 |
% 53.37/20.45 | From (1262) and (3816) follows:
% 53.37/20.45 | (3944) sum(n6, n18) = all_0_0_0
% 53.37/20.45 |
% 53.37/20.45 | From (1550)(1551) and (590) follows:
% 53.37/20.45 | (1553) sum(n25, n25) = all_0_3_3
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 53.37/20.45 | (1320) all_0_3_3 = n24
% 53.37/20.45 |
% 53.37/20.45 | Instantiating formula (690) with n6, n18, all_0_0_0, n24 and discharging atoms sum(n6, n18) = all_0_0_0, sum(n6, n18) = n24, yields:
% 53.37/20.45 | (1321) all_0_0_0 = n24
% 53.37/20.45 |
% 53.37/20.45 | Equations (1321,1320) can reduce 679 to:
% 53.37/20.45 | (1106) $false
% 53.37/20.45 |
% 53.37/20.45 |-The branch is then unsatisfiable
% 53.37/20.45 |-Branch two:
% 53.37/20.45 | (1503) ~ (all_0_11_11 = n3)
% 53.37/20.45 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 53.37/20.45 |
% 53.37/20.45 +-Applying beta-rule and splitting (1504), into two cases.
% 53.37/20.45 |-Branch one:
% 53.37/20.46 | (1505) all_0_11_11 = n2
% 53.37/20.46 |
% 53.37/20.46 | From (1505) and (559) follows:
% 53.37/20.46 | (1506) pred(n2) = all_0_9_9
% 53.37/20.46 |
% 53.37/20.46 | From (1505) and (992) follows:
% 53.37/20.46 | (1507) succ(n2) = all_0_5_5
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 53.37/20.46 | (1508) all_0_9_9 = n1
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 53.37/20.46 | (1509) all_0_5_5 = n3
% 53.37/20.46 |
% 53.37/20.46 | From (1508)(1509) and (538) follows:
% 53.37/20.46 | (1510) sum(n1, n3) = all_0_2_2
% 53.37/20.46 |
% 53.37/20.46 | From (1508) and (3814) follows:
% 53.37/20.46 | (4191) sum(n1, n23) = all_0_7_7
% 53.37/20.46 |
% 53.37/20.46 | From (1509) and (3812) follows:
% 53.37/20.46 | (4192) sum(n21, n3) = all_0_4_4
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (690) with n21, n3, all_0_4_4, n24 and discharging atoms sum(n21, n3) = all_0_4_4, sum(n21, n3) = n24, yields:
% 53.37/20.46 | (1096) all_0_4_4 = n24
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (690) with n1, n23, all_0_7_7, n24 and discharging atoms sum(n1, n23) = all_0_7_7, sum(n1, n23) = n24, yields:
% 53.37/20.46 | (1097) all_0_7_7 = n24
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 53.37/20.46 | (1280) all_0_2_2 = n4
% 53.37/20.46 |
% 53.37/20.46 | From (1280) and (3816) follows:
% 53.37/20.46 | (3962) sum(n4, n18) = all_0_0_0
% 53.37/20.46 |
% 53.37/20.46 | From (1097)(1096) and (590) follows:
% 53.37/20.46 | (1101) sum(n24, n24) = all_0_3_3
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 53.37/20.46 | (1104) all_0_3_3 = n22
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (690) with n4, n18, all_0_0_0, n22 and discharging atoms sum(n4, n18) = all_0_0_0, sum(n4, n18) = n22, yields:
% 53.37/20.46 | (1102) all_0_0_0 = n22
% 53.37/20.46 |
% 53.37/20.46 | Equations (1102,1104) can reduce 679 to:
% 53.37/20.46 | (1106) $false
% 53.37/20.46 |
% 53.37/20.46 |-The branch is then unsatisfiable
% 53.37/20.46 |-Branch two:
% 53.37/20.46 | (1521) ~ (all_0_11_11 = n2)
% 53.37/20.46 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 53.37/20.46 |
% 53.37/20.46 +-Applying beta-rule and splitting (1522), into two cases.
% 53.37/20.46 |-Branch one:
% 53.37/20.46 | (1523) all_0_11_11 = n1
% 53.37/20.46 |
% 53.37/20.46 | From (1523) and (559) follows:
% 53.37/20.46 | (1524) pred(n1) = all_0_9_9
% 53.37/20.46 |
% 53.37/20.46 | From (1523) and (992) follows:
% 53.37/20.46 | (1525) succ(n1) = all_0_5_5
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 53.37/20.46 | (1526) all_0_9_9 = n0
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 53.37/20.46 | (1527) all_0_5_5 = n2
% 53.37/20.46 |
% 53.37/20.46 | From (1526)(1527) and (538) follows:
% 53.37/20.46 | (1528) sum(n0, n2) = all_0_2_2
% 53.37/20.46 |
% 53.37/20.46 | From (1526) and (3814) follows:
% 53.37/20.46 | (4209) sum(n0, n23) = all_0_7_7
% 53.37/20.46 |
% 53.37/20.46 | From (1527) and (3812) follows:
% 53.37/20.46 | (4210) sum(n21, n2) = all_0_4_4
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (690) with n21, n2, all_0_4_4, n23 and discharging atoms sum(n21, n2) = all_0_4_4, sum(n21, n2) = n23, yields:
% 53.37/20.46 | (1117) all_0_4_4 = n23
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (690) with n0, n23, all_0_7_7, n23 and discharging atoms sum(n0, n23) = all_0_7_7, sum(n0, n23) = n23, yields:
% 53.37/20.46 | (1119) all_0_7_7 = n23
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 53.37/20.46 | (1298) all_0_2_2 = n2
% 53.37/20.46 |
% 53.37/20.46 | From (1298) and (3816) follows:
% 53.37/20.46 | (3980) sum(n2, n18) = all_0_0_0
% 53.37/20.46 |
% 53.37/20.46 | From (1119)(1117) and (590) follows:
% 53.37/20.46 | (1121) sum(n23, n23) = all_0_3_3
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 53.37/20.46 | (1122) all_0_3_3 = n20
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (690) with n2, n18, all_0_0_0, n20 and discharging atoms sum(n2, n18) = all_0_0_0, sum(n2, n18) = n20, yields:
% 53.37/20.46 | (1123) all_0_0_0 = n20
% 53.37/20.46 |
% 53.37/20.46 | Equations (1123,1122) can reduce 679 to:
% 53.37/20.46 | (1106) $false
% 53.37/20.46 |
% 53.37/20.46 |-The branch is then unsatisfiable
% 53.37/20.46 |-Branch two:
% 53.37/20.46 | (1540) ~ (all_0_11_11 = n1)
% 53.37/20.46 | (1541) all_0_11_11 = n0
% 53.37/20.46 |
% 53.37/20.46 | From (1541) and (559) follows:
% 53.37/20.46 | (1542) pred(n0) = all_0_9_9
% 53.37/20.46 |
% 53.37/20.46 | From (1541) and (992) follows:
% 53.37/20.46 | (1543) succ(n0) = all_0_5_5
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 53.37/20.46 | (1544) all_0_9_9 = n25
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 53.37/20.46 | (1545) all_0_5_5 = n1
% 53.37/20.46 |
% 53.37/20.46 | From (1544)(1545) and (538) follows:
% 53.37/20.46 | (1546) sum(n25, n1) = all_0_2_2
% 53.37/20.46 |
% 53.37/20.46 | From (1544) and (3814) follows:
% 53.37/20.46 | (4226) sum(n25, n23) = all_0_7_7
% 53.37/20.46 |
% 53.37/20.46 | From (1545) and (3812) follows:
% 53.37/20.46 | (4227) sum(n21, n1) = all_0_4_4
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (690) with n25, n23, all_0_7_7, n22 and discharging atoms sum(n25, n23) = all_0_7_7, sum(n25, n23) = n22, yields:
% 53.37/20.46 | (1137) all_0_7_7 = n22
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 53.37/20.46 | (1316) all_0_2_2 = n0
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (690) with n21, n1, all_0_4_4, n22 and discharging atoms sum(n21, n1) = all_0_4_4, sum(n21, n1) = n22, yields:
% 53.37/20.46 | (1135) all_0_4_4 = n22
% 53.37/20.46 |
% 53.37/20.46 | From (1316) and (3816) follows:
% 53.37/20.46 | (3998) sum(n0, n18) = all_0_0_0
% 53.37/20.46 |
% 53.37/20.46 | From (1137)(1135) and (590) follows:
% 53.37/20.46 | (1139) sum(n22, n22) = all_0_3_3
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 53.37/20.46 | (1140) all_0_3_3 = n18
% 53.37/20.46 |
% 53.37/20.46 | Instantiating formula (690) with n0, n18, all_0_0_0, n18 and discharging atoms sum(n0, n18) = all_0_0_0, sum(n0, n18) = n18, yields:
% 53.37/20.46 | (1141) all_0_0_0 = n18
% 53.37/20.46 |
% 53.37/20.46 | Equations (1141,1140) can reduce 679 to:
% 53.37/20.46 | (1106) $false
% 53.37/20.46 |
% 53.37/20.46 |-The branch is then unsatisfiable
% 53.37/20.47 |-Branch two:
% 53.37/20.47 | (1622) ~ (all_0_10_10 = n22)
% 53.37/20.47 | (1623) all_0_10_10 = n21 | 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
% 53.37/20.47 |
% 53.37/20.47 +-Applying beta-rule and splitting (1144), into two cases.
% 53.37/20.47 |-Branch one:
% 53.37/20.47 | (1145) all_0_11_11 = n22
% 53.37/20.47 |
% 53.37/20.47 | From (1145) and (559) follows:
% 53.37/20.47 | (1146) pred(n22) = all_0_9_9
% 53.37/20.47 |
% 53.37/20.47 | From (1145) and (992) follows:
% 53.37/20.47 | (1147) succ(n22) = all_0_5_5
% 53.37/20.47 |
% 53.37/20.47 | Instantiating formula (500) with n22, all_0_9_9, n21 and discharging atoms pred(n22) = all_0_9_9, pred(n22) = n21, yields:
% 53.37/20.47 | (1148) all_0_9_9 = n21
% 53.37/20.47 |
% 53.37/20.47 | Instantiating formula (617) with n22, all_0_5_5, n23 and discharging atoms succ(n22) = all_0_5_5, succ(n22) = n23, yields:
% 53.37/20.47 | (1149) all_0_5_5 = n23
% 53.37/20.47 |
% 53.37/20.47 | From (1149) and (541) follows:
% 53.37/20.47 | (4243) sum(all_0_6_6, n23) = all_0_4_4
% 53.37/20.47 |
% 53.37/20.47 | From (1148)(1149) and (538) follows:
% 53.37/20.47 | (1150) sum(n21, n23) = all_0_2_2
% 53.37/20.47 |
% 53.37/20.47 | From (1148) and (427) follows:
% 53.37/20.47 | (4245) sum(n21, all_0_8_8) = all_0_7_7
% 53.37/20.47 |
% 53.37/20.47 | Instantiating formula (690) with n21, n23, all_0_2_2, n18 and discharging atoms sum(n21, n23) = all_0_2_2, sum(n21, n23) = n18, yields:
% 53.37/20.47 | (1154) all_0_2_2 = n18
% 53.37/20.47 |
% 53.37/20.47 | From (1154) and (630) follows:
% 53.37/20.47 | (4247) sum(n18, all_0_1_1) = all_0_0_0
% 53.37/20.47 |
% 53.37/20.47 +-Applying beta-rule and splitting (1623), into two cases.
% 53.37/20.47 |-Branch one:
% 53.37/20.47 | (1624) all_0_10_10 = n21
% 53.37/20.47 |
% 53.37/20.47 | From (1624) and (292) follows:
% 53.37/20.47 | (1625) pred(n21) = all_0_6_6
% 53.37/20.47 |
% 53.37/20.47 | From (1624) and (760) follows:
% 53.37/20.47 | (1626) succ(n21) = all_0_8_8
% 53.37/20.47 |
% 53.37/20.47 | Instantiating formula (500) with n21, all_0_6_6, n20 and discharging atoms pred(n21) = all_0_6_6, pred(n21) = n20, yields:
% 53.37/20.47 | (1627) all_0_6_6 = n20
% 53.37/20.47 |
% 53.37/20.47 | Instantiating formula (617) with n21, all_0_8_8, n22 and discharging atoms succ(n21) = all_0_8_8, succ(n21) = n22, yields:
% 53.37/20.47 | (1628) all_0_8_8 = n22
% 53.37/20.47 |
% 53.37/20.47 | From (1627)(1628) and (411) follows:
% 53.37/20.47 | (1629) sum(n20, n22) = all_0_1_1
% 53.37/20.47 |
% 53.37/20.47 | From (1627) and (4243) follows:
% 53.37/20.47 | (4254) sum(n20, n23) = all_0_4_4
% 53.37/20.47 |
% 53.37/20.47 | From (1628) and (4245) follows:
% 53.37/20.47 | (4255) sum(n21, n22) = all_0_7_7
% 53.37/20.47 |
% 53.37/20.47 | Instantiating formula (690) with n21, n22, all_0_7_7, n17 and discharging atoms sum(n21, n22) = all_0_7_7, sum(n21, n22) = n17, yields:
% 53.37/20.47 | (1227) all_0_7_7 = n17
% 53.37/20.47 |
% 53.37/20.47 | Instantiating formula (690) with n20, n23, all_0_4_4, n17 and discharging atoms sum(n20, n23) = all_0_4_4, sum(n20, n23) = n17, yields:
% 53.37/20.47 | (1225) all_0_4_4 = n17
% 53.37/20.47 |
% 53.37/20.47 | Instantiating formula (690) with n20, n22, all_0_1_1, n16 and discharging atoms sum(n20, n22) = all_0_1_1, sum(n20, n22) = n16, yields:
% 53.37/20.47 | (1633) all_0_1_1 = n16
% 53.37/20.47 |
% 53.37/20.47 | From (1227)(1225) and (590) follows:
% 53.37/20.47 | (1229) sum(n17, n17) = all_0_3_3
% 53.37/20.47 |
% 53.37/20.47 | From (1633) and (4247) follows:
% 53.37/20.47 | (4260) sum(n18, n16) = all_0_0_0
% 53.37/20.47 |
% 53.37/20.47 | Instantiating formula (690) with n18, n16, all_0_0_0, n8 and discharging atoms sum(n18, n16) = all_0_0_0, sum(n18, n16) = n8, yields:
% 53.37/20.47 | (1231) all_0_0_0 = n8
% 53.37/20.47 |
% 53.37/20.47 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 53.37/20.47 | (1230) all_0_3_3 = n8
% 53.37/20.47 |
% 53.37/20.47 | Equations (1231,1230) can reduce 679 to:
% 53.37/20.47 | (1106) $false
% 53.37/20.47 |
% 53.37/20.47 |-The branch is then unsatisfiable
% 53.37/20.47 |-Branch two:
% 53.37/20.47 | (1640) ~ (all_0_10_10 = n21)
% 53.37/20.47 | (1641) 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
% 53.37/20.47 |
% 53.37/20.47 +-Applying beta-rule and splitting (1641), into two cases.
% 53.37/20.47 |-Branch one:
% 53.37/20.47 | (1642) all_0_10_10 = n20
% 53.37/20.47 |
% 53.37/20.47 | From (1642) and (292) follows:
% 53.37/20.47 | (1643) pred(n20) = all_0_6_6
% 53.37/20.47 |
% 53.37/20.47 | From (1642) and (760) follows:
% 53.37/20.47 | (1644) succ(n20) = all_0_8_8
% 53.37/20.47 |
% 53.37/20.47 | Instantiating formula (500) with n20, all_0_6_6, n19 and discharging atoms pred(n20) = all_0_6_6, pred(n20) = n19, yields:
% 53.37/20.47 | (1645) all_0_6_6 = n19
% 53.37/20.47 |
% 53.37/20.47 | Instantiating formula (617) with n20, all_0_8_8, n21 and discharging atoms succ(n20) = all_0_8_8, succ(n20) = n21, yields:
% 53.37/20.47 | (1646) all_0_8_8 = n21
% 53.37/20.47 |
% 53.37/20.47 | From (1645)(1646) and (411) follows:
% 53.37/20.47 | (1647) sum(n19, n21) = all_0_1_1
% 53.37/20.47 |
% 53.37/20.47 | From (1645) and (4243) follows:
% 53.37/20.47 | (4272) sum(n19, n23) = all_0_4_4
% 53.37/20.47 |
% 53.37/20.47 | From (1646) and (4245) follows:
% 53.37/20.47 | (4273) sum(n21, n21) = all_0_7_7
% 53.37/20.47 |
% 53.37/20.47 | Instantiating formula (690) with n21, n21, all_0_7_7, n16 and discharging atoms sum(n21, n21) = all_0_7_7, sum(n21, n21) = n16, yields:
% 53.37/20.47 | (1245) all_0_7_7 = n16
% 53.37/20.47 |
% 53.37/20.47 | Instantiating formula (690) with n19, n23, all_0_4_4, n16 and discharging atoms sum(n19, n23) = all_0_4_4, sum(n19, n23) = n16, yields:
% 53.37/20.47 | (1243) all_0_4_4 = n16
% 53.37/20.47 |
% 53.37/20.47 | Instantiating formula (690) with n19, n21, all_0_1_1, n14 and discharging atoms sum(n19, n21) = all_0_1_1, sum(n19, n21) = n14, yields:
% 53.37/20.47 | (1651) all_0_1_1 = n14
% 53.37/20.47 |
% 53.37/20.47 | From (1245)(1243) and (590) follows:
% 53.37/20.47 | (1247) sum(n16, n16) = all_0_3_3
% 53.37/20.47 |
% 53.37/20.47 | From (1651) and (4247) follows:
% 53.37/20.47 | (4278) sum(n18, n14) = all_0_0_0
% 53.37/20.47 |
% 53.37/20.47 | Instantiating formula (690) with n18, n14, all_0_0_0, n6 and discharging atoms sum(n18, n14) = all_0_0_0, sum(n18, n14) = n6, yields:
% 53.37/20.47 | (1249) all_0_0_0 = n6
% 53.37/20.47 |
% 53.37/20.47 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 53.37/20.47 | (1248) all_0_3_3 = n6
% 53.37/20.47 |
% 53.37/20.47 | Equations (1249,1248) can reduce 679 to:
% 53.37/20.47 | (1106) $false
% 53.37/20.47 |
% 53.37/20.47 |-The branch is then unsatisfiable
% 53.37/20.47 |-Branch two:
% 53.37/20.47 | (1658) ~ (all_0_10_10 = n20)
% 53.37/20.47 | (1659) 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
% 53.37/20.47 |
% 53.37/20.47 +-Applying beta-rule and splitting (1659), into two cases.
% 53.37/20.47 |-Branch one:
% 53.37/20.48 | (1660) all_0_10_10 = n19
% 53.37/20.48 |
% 53.37/20.48 | From (1660) and (292) follows:
% 53.37/20.48 | (1661) pred(n19) = all_0_6_6
% 53.37/20.48 |
% 53.37/20.48 | From (1660) and (760) follows:
% 53.37/20.48 | (1662) succ(n19) = all_0_8_8
% 53.37/20.48 |
% 53.37/20.48 | Instantiating formula (500) with n19, all_0_6_6, n18 and discharging atoms pred(n19) = all_0_6_6, pred(n19) = n18, yields:
% 53.37/20.48 | (1663) all_0_6_6 = n18
% 53.37/20.48 |
% 53.37/20.48 | Instantiating formula (617) with n19, all_0_8_8, n20 and discharging atoms succ(n19) = all_0_8_8, succ(n19) = n20, yields:
% 53.37/20.48 | (1664) all_0_8_8 = n20
% 53.37/20.48 |
% 53.37/20.48 | From (1663)(1664) and (411) follows:
% 53.37/20.48 | (1665) sum(n18, n20) = all_0_1_1
% 53.37/20.48 |
% 53.37/20.48 | From (1663) and (4243) follows:
% 53.37/20.48 | (4290) sum(n18, n23) = all_0_4_4
% 53.37/20.48 |
% 53.37/20.48 | From (1664) and (4245) follows:
% 53.37/20.48 | (4291) sum(n21, n20) = all_0_7_7
% 53.37/20.48 |
% 53.37/20.48 | Instantiating formula (690) with n21, n20, all_0_7_7, n15 and discharging atoms sum(n21, n20) = all_0_7_7, sum(n21, n20) = n15, yields:
% 53.37/20.48 | (1263) all_0_7_7 = n15
% 53.37/20.48 |
% 53.37/20.48 | Instantiating formula (690) with n18, n23, all_0_4_4, n15 and discharging atoms sum(n18, n23) = all_0_4_4, sum(n18, n23) = n15, yields:
% 53.37/20.48 | (1261) all_0_4_4 = n15
% 53.37/20.48 |
% 53.37/20.48 | Instantiating formula (690) with n18, n20, all_0_1_1, n12 and discharging atoms sum(n18, n20) = all_0_1_1, sum(n18, n20) = n12, yields:
% 53.37/20.48 | (1669) all_0_1_1 = n12
% 53.37/20.48 |
% 53.37/20.48 | From (1263)(1261) and (590) follows:
% 53.37/20.48 | (1265) sum(n15, n15) = all_0_3_3
% 53.37/20.48 |
% 53.37/20.48 | From (1669) and (4247) follows:
% 53.37/20.49 | (4296) sum(n18, n12) = all_0_0_0
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (690) with n18, n12, all_0_0_0, n4 and discharging atoms sum(n18, n12) = all_0_0_0, sum(n18, n12) = n4, yields:
% 53.37/20.49 | (1267) all_0_0_0 = n4
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 53.37/20.49 | (1266) all_0_3_3 = n4
% 53.37/20.49 |
% 53.37/20.49 | Equations (1267,1266) can reduce 679 to:
% 53.37/20.49 | (1106) $false
% 53.37/20.49 |
% 53.37/20.49 |-The branch is then unsatisfiable
% 53.37/20.49 |-Branch two:
% 53.37/20.49 | (1676) ~ (all_0_10_10 = n19)
% 53.37/20.49 | (1677) 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
% 53.37/20.49 |
% 53.37/20.49 +-Applying beta-rule and splitting (1677), into two cases.
% 53.37/20.49 |-Branch one:
% 53.37/20.49 | (1678) all_0_10_10 = n18
% 53.37/20.49 |
% 53.37/20.49 | From (1678) and (292) follows:
% 53.37/20.49 | (1679) pred(n18) = all_0_6_6
% 53.37/20.49 |
% 53.37/20.49 | From (1678) and (760) follows:
% 53.37/20.49 | (1680) succ(n18) = all_0_8_8
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (500) with n18, all_0_6_6, n17 and discharging atoms pred(n18) = all_0_6_6, pred(n18) = n17, yields:
% 53.37/20.49 | (1681) all_0_6_6 = n17
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (617) with n18, all_0_8_8, n19 and discharging atoms succ(n18) = all_0_8_8, succ(n18) = n19, yields:
% 53.37/20.49 | (1682) all_0_8_8 = n19
% 53.37/20.49 |
% 53.37/20.49 | From (1681)(1682) and (411) follows:
% 53.37/20.49 | (1683) sum(n17, n19) = all_0_1_1
% 53.37/20.49 |
% 53.37/20.49 | From (1681) and (4243) follows:
% 53.37/20.49 | (4308) sum(n17, n23) = all_0_4_4
% 53.37/20.49 |
% 53.37/20.49 | From (1682) and (4245) follows:
% 53.37/20.49 | (4309) sum(n21, n19) = all_0_7_7
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (690) with n21, n19, all_0_7_7, n14 and discharging atoms sum(n21, n19) = all_0_7_7, sum(n21, n19) = n14, yields:
% 53.37/20.49 | (1281) all_0_7_7 = n14
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (690) with n17, n23, all_0_4_4, n14 and discharging atoms sum(n17, n23) = all_0_4_4, sum(n17, n23) = n14, yields:
% 53.37/20.49 | (1279) all_0_4_4 = n14
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (690) with n17, n19, all_0_1_1, n10 and discharging atoms sum(n17, n19) = all_0_1_1, sum(n17, n19) = n10, yields:
% 53.37/20.49 | (1687) all_0_1_1 = n10
% 53.37/20.49 |
% 53.37/20.49 | From (1281)(1279) and (590) follows:
% 53.37/20.49 | (1283) sum(n14, n14) = all_0_3_3
% 53.37/20.49 |
% 53.37/20.49 | From (1687) and (4247) follows:
% 53.37/20.49 | (4314) sum(n18, n10) = all_0_0_0
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (690) with n18, n10, all_0_0_0, n2 and discharging atoms sum(n18, n10) = all_0_0_0, sum(n18, n10) = n2, yields:
% 53.37/20.49 | (1285) all_0_0_0 = n2
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 53.37/20.49 | (1284) all_0_3_3 = n2
% 53.37/20.49 |
% 53.37/20.49 | Equations (1285,1284) can reduce 679 to:
% 53.37/20.49 | (1106) $false
% 53.37/20.49 |
% 53.37/20.49 |-The branch is then unsatisfiable
% 53.37/20.49 |-Branch two:
% 53.37/20.49 | (1694) ~ (all_0_10_10 = n18)
% 53.37/20.49 | (1695) 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
% 53.37/20.49 |
% 53.37/20.49 +-Applying beta-rule and splitting (1695), into two cases.
% 53.37/20.49 |-Branch one:
% 53.37/20.49 | (1696) all_0_10_10 = n17
% 53.37/20.49 |
% 53.37/20.49 | From (1696) and (292) follows:
% 53.37/20.49 | (1697) pred(n17) = all_0_6_6
% 53.37/20.49 |
% 53.37/20.49 | From (1696) and (760) follows:
% 53.37/20.49 | (1698) succ(n17) = all_0_8_8
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (500) with n17, all_0_6_6, n16 and discharging atoms pred(n17) = all_0_6_6, pred(n17) = n16, yields:
% 53.37/20.49 | (1699) all_0_6_6 = n16
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (617) with n17, all_0_8_8, n18 and discharging atoms succ(n17) = all_0_8_8, succ(n17) = n18, yields:
% 53.37/20.49 | (1700) all_0_8_8 = n18
% 53.37/20.49 |
% 53.37/20.49 | From (1699)(1700) and (411) follows:
% 53.37/20.49 | (1701) sum(n16, n18) = all_0_1_1
% 53.37/20.49 |
% 53.37/20.49 | From (1699) and (4243) follows:
% 53.37/20.49 | (4326) sum(n16, n23) = all_0_4_4
% 53.37/20.49 |
% 53.37/20.49 | From (1700) and (4245) follows:
% 53.37/20.49 | (4327) sum(n21, n18) = all_0_7_7
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (690) with n21, n18, all_0_7_7, n13 and discharging atoms sum(n21, n18) = all_0_7_7, sum(n21, n18) = n13, yields:
% 53.37/20.49 | (1299) all_0_7_7 = n13
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (690) with n16, n23, all_0_4_4, n13 and discharging atoms sum(n16, n23) = all_0_4_4, sum(n16, n23) = n13, yields:
% 53.37/20.49 | (1297) all_0_4_4 = n13
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (690) with n16, n18, all_0_1_1, n8 and discharging atoms sum(n16, n18) = all_0_1_1, sum(n16, n18) = n8, yields:
% 53.37/20.49 | (1705) all_0_1_1 = n8
% 53.37/20.49 |
% 53.37/20.49 | From (1299)(1297) and (590) follows:
% 53.37/20.49 | (1301) sum(n13, n13) = all_0_3_3
% 53.37/20.49 |
% 53.37/20.49 | From (1705) and (4247) follows:
% 53.37/20.49 | (4332) sum(n18, n8) = all_0_0_0
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (690) with n18, n8, all_0_0_0, n0 and discharging atoms sum(n18, n8) = all_0_0_0, sum(n18, n8) = n0, yields:
% 53.37/20.49 | (1303) all_0_0_0 = n0
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 53.37/20.49 | (1302) all_0_3_3 = n0
% 53.37/20.49 |
% 53.37/20.49 | Equations (1303,1302) can reduce 679 to:
% 53.37/20.49 | (1106) $false
% 53.37/20.49 |
% 53.37/20.49 |-The branch is then unsatisfiable
% 53.37/20.49 |-Branch two:
% 53.37/20.49 | (1712) ~ (all_0_10_10 = n17)
% 53.37/20.49 | (1713) 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
% 53.37/20.49 |
% 53.37/20.49 +-Applying beta-rule and splitting (1713), into two cases.
% 53.37/20.49 |-Branch one:
% 53.37/20.49 | (1714) all_0_10_10 = n16
% 53.37/20.49 |
% 53.37/20.49 | From (1714) and (292) follows:
% 53.37/20.49 | (1715) pred(n16) = all_0_6_6
% 53.37/20.49 |
% 53.37/20.49 | From (1714) and (760) follows:
% 53.37/20.49 | (1716) succ(n16) = all_0_8_8
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (500) with n16, all_0_6_6, n15 and discharging atoms pred(n16) = all_0_6_6, pred(n16) = n15, yields:
% 53.37/20.49 | (1717) all_0_6_6 = n15
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (617) with n16, all_0_8_8, n17 and discharging atoms succ(n16) = all_0_8_8, succ(n16) = n17, yields:
% 53.37/20.49 | (1718) all_0_8_8 = n17
% 53.37/20.49 |
% 53.37/20.49 | From (1717)(1718) and (411) follows:
% 53.37/20.49 | (1719) sum(n15, n17) = all_0_1_1
% 53.37/20.49 |
% 53.37/20.49 | From (1717) and (4243) follows:
% 53.37/20.49 | (4344) sum(n15, n23) = all_0_4_4
% 53.37/20.49 |
% 53.37/20.49 | From (1718) and (4245) follows:
% 53.37/20.49 | (4345) sum(n21, n17) = all_0_7_7
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (690) with n21, n17, all_0_7_7, n12 and discharging atoms sum(n21, n17) = all_0_7_7, sum(n21, n17) = n12, yields:
% 53.37/20.49 | (1317) all_0_7_7 = n12
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (690) with n15, n23, all_0_4_4, n12 and discharging atoms sum(n15, n23) = all_0_4_4, sum(n15, n23) = n12, yields:
% 53.37/20.49 | (1315) all_0_4_4 = n12
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (690) with n15, n17, all_0_1_1, n6 and discharging atoms sum(n15, n17) = all_0_1_1, sum(n15, n17) = n6, yields:
% 53.37/20.49 | (1723) all_0_1_1 = n6
% 53.37/20.49 |
% 53.37/20.49 | From (1317)(1315) and (590) follows:
% 53.37/20.49 | (1319) sum(n12, n12) = all_0_3_3
% 53.37/20.49 |
% 53.37/20.49 | From (1723) and (4247) follows:
% 53.37/20.49 | (4350) sum(n18, n6) = all_0_0_0
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (690) with n18, n6, all_0_0_0, n24 and discharging atoms sum(n18, n6) = all_0_0_0, sum(n18, n6) = n24, yields:
% 53.37/20.49 | (1321) all_0_0_0 = n24
% 53.37/20.49 |
% 53.37/20.49 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 53.37/20.49 | (1320) all_0_3_3 = n24
% 53.37/20.49 |
% 53.37/20.49 | Equations (1321,1320) can reduce 679 to:
% 53.37/20.49 | (1106) $false
% 53.37/20.49 |
% 53.37/20.49 |-The branch is then unsatisfiable
% 53.37/20.49 |-Branch two:
% 53.37/20.49 | (1730) ~ (all_0_10_10 = n16)
% 53.37/20.49 | (1731) 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
% 53.37/20.49 |
% 53.64/20.50 +-Applying beta-rule and splitting (1731), into two cases.
% 53.64/20.50 |-Branch one:
% 53.64/20.50 | (1732) all_0_10_10 = n15
% 53.64/20.50 |
% 53.64/20.50 | From (1732) and (292) follows:
% 53.64/20.50 | (1733) pred(n15) = all_0_6_6
% 53.64/20.50 |
% 53.64/20.50 | From (1732) and (760) follows:
% 53.64/20.50 | (1734) succ(n15) = all_0_8_8
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (500) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 53.64/20.50 | (1735) all_0_6_6 = n14
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (617) with n15, all_0_8_8, n16 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n16, yields:
% 53.64/20.50 | (1736) all_0_8_8 = n16
% 53.64/20.50 |
% 53.64/20.50 | From (1735)(1736) and (411) follows:
% 53.64/20.50 | (1737) sum(n14, n16) = all_0_1_1
% 53.64/20.50 |
% 53.64/20.50 | From (1735) and (4243) follows:
% 53.64/20.50 | (4362) sum(n14, n23) = all_0_4_4
% 53.64/20.50 |
% 53.64/20.50 | From (1736) and (4245) follows:
% 53.64/20.50 | (4363) sum(n21, n16) = all_0_7_7
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (690) with n21, n16, all_0_7_7, n11 and discharging atoms sum(n21, n16) = all_0_7_7, sum(n21, n16) = n11, yields:
% 53.64/20.50 | (1335) all_0_7_7 = n11
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (690) with n14, n23, all_0_4_4, n11 and discharging atoms sum(n14, n23) = all_0_4_4, sum(n14, n23) = n11, yields:
% 53.64/20.50 | (1333) all_0_4_4 = n11
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (690) with n14, n16, all_0_1_1, n4 and discharging atoms sum(n14, n16) = all_0_1_1, sum(n14, n16) = n4, yields:
% 53.64/20.50 | (1741) all_0_1_1 = n4
% 53.64/20.50 |
% 53.64/20.50 | From (1335)(1333) and (590) follows:
% 53.64/20.50 | (1337) sum(n11, n11) = all_0_3_3
% 53.64/20.50 |
% 53.64/20.50 | From (1741) and (4247) follows:
% 53.64/20.50 | (4368) sum(n18, n4) = all_0_0_0
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (690) with n18, n4, all_0_0_0, n22 and discharging atoms sum(n18, n4) = all_0_0_0, sum(n18, n4) = n22, yields:
% 53.64/20.50 | (1102) all_0_0_0 = n22
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 53.64/20.50 | (1104) all_0_3_3 = n22
% 53.64/20.50 |
% 53.64/20.50 | Equations (1102,1104) can reduce 679 to:
% 53.64/20.50 | (1106) $false
% 53.64/20.50 |
% 53.64/20.50 |-The branch is then unsatisfiable
% 53.64/20.50 |-Branch two:
% 53.64/20.50 | (1748) ~ (all_0_10_10 = n15)
% 53.64/20.50 | (1749) 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
% 53.64/20.50 |
% 53.64/20.50 +-Applying beta-rule and splitting (1749), into two cases.
% 53.64/20.50 |-Branch one:
% 53.64/20.50 | (1750) all_0_10_10 = n14
% 53.64/20.50 |
% 53.64/20.50 | From (1750) and (292) follows:
% 53.64/20.50 | (1751) pred(n14) = all_0_6_6
% 53.64/20.50 |
% 53.64/20.50 | From (1750) and (760) follows:
% 53.64/20.50 | (1752) succ(n14) = all_0_8_8
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (500) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 53.64/20.50 | (1753) all_0_6_6 = n13
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (617) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 53.64/20.50 | (1754) all_0_8_8 = n15
% 53.64/20.50 |
% 53.64/20.50 | From (1753)(1754) and (411) follows:
% 53.64/20.50 | (1755) sum(n13, n15) = all_0_1_1
% 53.64/20.50 |
% 53.64/20.50 | From (1753) and (4243) follows:
% 53.64/20.50 | (4380) sum(n13, n23) = all_0_4_4
% 53.64/20.50 |
% 53.64/20.50 | From (1754) and (4245) follows:
% 53.64/20.50 | (4381) sum(n21, n15) = all_0_7_7
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (690) with n21, n15, all_0_7_7, n10 and discharging atoms sum(n21, n15) = all_0_7_7, sum(n21, n15) = n10, yields:
% 53.64/20.50 | (1353) all_0_7_7 = n10
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (690) with n13, n23, all_0_4_4, n10 and discharging atoms sum(n13, n23) = all_0_4_4, sum(n13, n23) = n10, yields:
% 53.64/20.50 | (1351) all_0_4_4 = n10
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (690) with n13, n15, all_0_1_1, n2 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n2, yields:
% 53.64/20.50 | (1759) all_0_1_1 = n2
% 53.64/20.50 |
% 53.64/20.50 | From (1353)(1351) and (590) follows:
% 53.64/20.50 | (1355) sum(n10, n10) = all_0_3_3
% 53.64/20.50 |
% 53.64/20.50 | From (1759) and (4247) follows:
% 53.64/20.50 | (4386) sum(n18, n2) = all_0_0_0
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (690) with n18, n2, all_0_0_0, n20 and discharging atoms sum(n18, n2) = all_0_0_0, sum(n18, n2) = n20, yields:
% 53.64/20.50 | (1123) all_0_0_0 = n20
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 53.64/20.50 | (1122) all_0_3_3 = n20
% 53.64/20.50 |
% 53.64/20.50 | Equations (1123,1122) can reduce 679 to:
% 53.64/20.50 | (1106) $false
% 53.64/20.50 |
% 53.64/20.50 |-The branch is then unsatisfiable
% 53.64/20.50 |-Branch two:
% 53.64/20.50 | (1766) ~ (all_0_10_10 = n14)
% 53.64/20.50 | (1767) 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
% 53.64/20.50 |
% 53.64/20.50 +-Applying beta-rule and splitting (1767), into two cases.
% 53.64/20.50 |-Branch one:
% 53.64/20.50 | (1768) all_0_10_10 = n13
% 53.64/20.50 |
% 53.64/20.50 | From (1768) and (292) follows:
% 53.64/20.50 | (1769) pred(n13) = all_0_6_6
% 53.64/20.50 |
% 53.64/20.50 | From (1768) and (760) follows:
% 53.64/20.50 | (1770) succ(n13) = all_0_8_8
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (500) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 53.64/20.50 | (1771) all_0_6_6 = n12
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (617) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 53.64/20.50 | (1772) all_0_8_8 = n14
% 53.64/20.50 |
% 53.64/20.50 | From (1771)(1772) and (411) follows:
% 53.64/20.50 | (1773) sum(n12, n14) = all_0_1_1
% 53.64/20.50 |
% 53.64/20.50 | From (1771) and (4243) follows:
% 53.64/20.50 | (4398) sum(n12, n23) = all_0_4_4
% 53.64/20.50 |
% 53.64/20.50 | From (1772) and (4245) follows:
% 53.64/20.50 | (4399) sum(n21, n14) = all_0_7_7
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (690) with n21, n14, all_0_7_7, n9 and discharging atoms sum(n21, n14) = all_0_7_7, sum(n21, n14) = n9, yields:
% 53.64/20.50 | (1371) all_0_7_7 = n9
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (690) with n12, n23, all_0_4_4, n9 and discharging atoms sum(n12, n23) = all_0_4_4, sum(n12, n23) = n9, yields:
% 53.64/20.50 | (1369) all_0_4_4 = n9
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (690) with n12, n14, all_0_1_1, n0 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n0, yields:
% 53.64/20.50 | (1777) all_0_1_1 = n0
% 53.64/20.50 |
% 53.64/20.50 | From (1371)(1369) and (590) follows:
% 53.64/20.50 | (1373) sum(n9, n9) = all_0_3_3
% 53.64/20.50 |
% 53.64/20.50 | From (1777) and (4247) follows:
% 53.64/20.50 | (4404) sum(n18, n0) = all_0_0_0
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (690) with n18, n0, all_0_0_0, n18 and discharging atoms sum(n18, n0) = all_0_0_0, sum(n18, n0) = n18, yields:
% 53.64/20.50 | (1141) all_0_0_0 = n18
% 53.64/20.50 |
% 53.64/20.50 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 53.64/20.50 | (1140) all_0_3_3 = n18
% 53.64/20.50 |
% 53.64/20.50 | Equations (1141,1140) can reduce 679 to:
% 53.64/20.50 | (1106) $false
% 53.64/20.50 |
% 53.64/20.50 |-The branch is then unsatisfiable
% 53.64/20.50 |-Branch two:
% 53.64/20.50 | (1784) ~ (all_0_10_10 = n13)
% 53.64/20.50 | (1785) 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
% 53.64/20.50 |
% 53.64/20.50 +-Applying beta-rule and splitting (1785), into two cases.
% 53.64/20.50 |-Branch one:
% 53.64/20.50 | (1786) all_0_10_10 = n12
% 53.64/20.50 |
% 53.64/20.50 | From (1786) and (292) follows:
% 53.64/20.50 | (1787) pred(n12) = all_0_6_6
% 53.64/20.50 |
% 53.64/20.50 | From (1786) and (760) follows:
% 53.64/20.51 | (1788) succ(n12) = all_0_8_8
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (500) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 53.64/20.51 | (1789) all_0_6_6 = n11
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (617) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 53.64/20.51 | (1790) all_0_8_8 = n13
% 53.64/20.51 |
% 53.64/20.51 | From (1789)(1790) and (411) follows:
% 53.64/20.51 | (1791) sum(n11, n13) = all_0_1_1
% 53.64/20.51 |
% 53.64/20.51 | From (1789) and (4243) follows:
% 53.64/20.51 | (4416) sum(n11, n23) = all_0_4_4
% 53.64/20.51 |
% 53.64/20.51 | From (1790) and (4245) follows:
% 53.64/20.51 | (4417) sum(n21, n13) = all_0_7_7
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (690) with n21, n13, all_0_7_7, n8 and discharging atoms sum(n21, n13) = all_0_7_7, sum(n21, n13) = n8, yields:
% 53.64/20.51 | (1389) all_0_7_7 = n8
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (690) with n11, n23, all_0_4_4, n8 and discharging atoms sum(n11, n23) = all_0_4_4, sum(n11, n23) = n8, yields:
% 53.64/20.51 | (1387) all_0_4_4 = n8
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (690) with n11, n13, all_0_1_1, n24 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n24, yields:
% 53.64/20.51 | (1081) all_0_1_1 = n24
% 53.64/20.51 |
% 53.64/20.51 | From (1389)(1387) and (590) follows:
% 53.64/20.51 | (1391) sum(n8, n8) = all_0_3_3
% 53.64/20.51 |
% 53.64/20.51 | From (1081) and (4247) follows:
% 53.64/20.51 | (1156) sum(n18, n24) = all_0_0_0
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (690) with n18, n24, all_0_0_0, n16 and discharging atoms sum(n18, n24) = all_0_0_0, sum(n18, n24) = n16, yields:
% 53.64/20.51 | (1159) all_0_0_0 = n16
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 53.64/20.51 | (1158) all_0_3_3 = n16
% 53.64/20.51 |
% 53.64/20.51 | Equations (1159,1158) can reduce 679 to:
% 53.64/20.51 | (1106) $false
% 53.64/20.51 |
% 53.64/20.51 |-The branch is then unsatisfiable
% 53.64/20.51 |-Branch two:
% 53.64/20.51 | (1802) ~ (all_0_10_10 = n12)
% 53.64/20.51 | (1803) 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
% 53.64/20.51 |
% 53.64/20.51 +-Applying beta-rule and splitting (1803), into two cases.
% 53.64/20.51 |-Branch one:
% 53.64/20.51 | (1804) all_0_10_10 = n11
% 53.64/20.51 |
% 53.64/20.51 | From (1804) and (292) follows:
% 53.64/20.51 | (1805) pred(n11) = all_0_6_6
% 53.64/20.51 |
% 53.64/20.51 | From (1804) and (760) follows:
% 53.64/20.51 | (1806) succ(n11) = all_0_8_8
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (500) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 53.64/20.51 | (1807) all_0_6_6 = n10
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (617) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 53.64/20.51 | (1808) all_0_8_8 = n12
% 53.64/20.51 |
% 53.64/20.51 | From (1807)(1808) and (411) follows:
% 53.64/20.51 | (1809) sum(n10, n12) = all_0_1_1
% 53.64/20.51 |
% 53.64/20.51 | From (1807) and (4243) follows:
% 53.64/20.51 | (4434) sum(n10, n23) = all_0_4_4
% 53.64/20.51 |
% 53.64/20.51 | From (1808) and (4245) follows:
% 53.64/20.51 | (4435) sum(n21, n12) = all_0_7_7
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (690) with n21, n12, all_0_7_7, n7 and discharging atoms sum(n21, n12) = all_0_7_7, sum(n21, n12) = n7, yields:
% 53.64/20.51 | (1407) all_0_7_7 = n7
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (690) with n10, n23, all_0_4_4, n7 and discharging atoms sum(n10, n23) = all_0_4_4, sum(n10, n23) = n7, yields:
% 53.64/20.51 | (1405) all_0_4_4 = n7
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (690) with n10, n12, all_0_1_1, n22 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n22, yields:
% 53.64/20.51 | (1579) all_0_1_1 = n22
% 53.64/20.51 |
% 53.64/20.51 | From (1407)(1405) and (590) follows:
% 53.64/20.51 | (1409) sum(n7, n7) = all_0_3_3
% 53.64/20.51 |
% 53.64/20.51 | From (1579) and (4247) follows:
% 53.64/20.51 | (2088) sum(n18, n22) = all_0_0_0
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (690) with n18, n22, all_0_0_0, n14 and discharging atoms sum(n18, n22) = all_0_0_0, sum(n18, n22) = n14, yields:
% 53.64/20.51 | (1177) all_0_0_0 = n14
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 53.64/20.51 | (1176) all_0_3_3 = n14
% 53.64/20.51 |
% 53.64/20.51 | Equations (1177,1176) can reduce 679 to:
% 53.64/20.51 | (1106) $false
% 53.64/20.51 |
% 53.64/20.51 |-The branch is then unsatisfiable
% 53.64/20.51 |-Branch two:
% 53.64/20.51 | (1820) ~ (all_0_10_10 = n11)
% 53.64/20.51 | (1821) 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
% 53.64/20.51 |
% 53.64/20.51 +-Applying beta-rule and splitting (1821), into two cases.
% 53.64/20.51 |-Branch one:
% 53.64/20.51 | (1822) all_0_10_10 = n10
% 53.64/20.51 |
% 53.64/20.51 | From (1822) and (292) follows:
% 53.64/20.51 | (1823) pred(n10) = all_0_6_6
% 53.64/20.51 |
% 53.64/20.51 | From (1822) and (760) follows:
% 53.64/20.51 | (1824) succ(n10) = all_0_8_8
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (500) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 53.64/20.51 | (1825) all_0_6_6 = n9
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (617) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 53.64/20.51 | (1826) all_0_8_8 = n11
% 53.64/20.51 |
% 53.64/20.51 | From (1825)(1826) and (411) follows:
% 53.64/20.51 | (1827) sum(n9, n11) = all_0_1_1
% 53.64/20.51 |
% 53.64/20.51 | From (1825) and (4243) follows:
% 53.64/20.51 | (4452) sum(n9, n23) = all_0_4_4
% 53.64/20.51 |
% 53.64/20.51 | From (1826) and (4245) follows:
% 53.64/20.51 | (4453) sum(n21, n11) = all_0_7_7
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (690) with n21, n11, all_0_7_7, n6 and discharging atoms sum(n21, n11) = all_0_7_7, sum(n21, n11) = n6, yields:
% 53.64/20.51 | (1425) all_0_7_7 = n6
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (690) with n9, n23, all_0_4_4, n6 and discharging atoms sum(n9, n23) = all_0_4_4, sum(n9, n23) = n6, yields:
% 53.64/20.51 | (1423) all_0_4_4 = n6
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (690) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 53.64/20.51 | (1597) all_0_1_1 = n20
% 53.64/20.51 |
% 53.64/20.51 | From (1425)(1423) and (590) follows:
% 53.64/20.51 | (1427) sum(n6, n6) = all_0_3_3
% 53.64/20.51 |
% 53.64/20.51 | From (1597) and (4247) follows:
% 53.64/20.51 | (2980) sum(n18, n20) = all_0_0_0
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (690) with n18, n20, all_0_0_0, n12 and discharging atoms sum(n18, n20) = all_0_0_0, sum(n18, n20) = n12, yields:
% 53.64/20.51 | (1195) all_0_0_0 = n12
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 53.64/20.51 | (1194) all_0_3_3 = n12
% 53.64/20.51 |
% 53.64/20.51 | Equations (1195,1194) can reduce 679 to:
% 53.64/20.51 | (1106) $false
% 53.64/20.51 |
% 53.64/20.51 |-The branch is then unsatisfiable
% 53.64/20.51 |-Branch two:
% 53.64/20.51 | (1838) ~ (all_0_10_10 = n10)
% 53.64/20.51 | (1839) 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
% 53.64/20.51 |
% 53.64/20.51 +-Applying beta-rule and splitting (1839), into two cases.
% 53.64/20.51 |-Branch one:
% 53.64/20.51 | (1840) all_0_10_10 = n9
% 53.64/20.51 |
% 53.64/20.51 | From (1840) and (292) follows:
% 53.64/20.51 | (1841) pred(n9) = all_0_6_6
% 53.64/20.51 |
% 53.64/20.51 | From (1840) and (760) follows:
% 53.64/20.51 | (1842) succ(n9) = all_0_8_8
% 53.64/20.51 |
% 53.64/20.51 | Instantiating formula (500) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 53.64/20.52 | (1843) all_0_6_6 = n8
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (617) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 53.64/20.52 | (1844) all_0_8_8 = n10
% 53.64/20.52 |
% 53.64/20.52 | From (1843)(1844) and (411) follows:
% 53.64/20.52 | (1845) sum(n8, n10) = all_0_1_1
% 53.64/20.52 |
% 53.64/20.52 | From (1843) and (4243) follows:
% 53.64/20.52 | (4470) sum(n8, n23) = all_0_4_4
% 53.64/20.52 |
% 53.64/20.52 | From (1844) and (4245) follows:
% 53.64/20.52 | (4471) sum(n21, n10) = all_0_7_7
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (690) with n21, n10, all_0_7_7, n5 and discharging atoms sum(n21, n10) = all_0_7_7, sum(n21, n10) = n5, yields:
% 53.64/20.52 | (1443) all_0_7_7 = n5
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (690) with n8, n23, all_0_4_4, n5 and discharging atoms sum(n8, n23) = all_0_4_4, sum(n8, n23) = n5, yields:
% 53.64/20.52 | (1441) all_0_4_4 = n5
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (690) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 53.64/20.52 | (1615) all_0_1_1 = n18
% 53.64/20.52 |
% 53.64/20.52 | From (1443)(1441) and (590) follows:
% 53.64/20.52 | (1445) sum(n5, n5) = all_0_3_3
% 53.64/20.52 |
% 53.64/20.52 | From (1615) and (4247) follows:
% 53.64/20.52 | (3834) sum(n18, n18) = all_0_0_0
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (690) with n18, n18, all_0_0_0, n10 and discharging atoms sum(n18, n18) = all_0_0_0, sum(n18, n18) = n10, yields:
% 53.64/20.52 | (1213) all_0_0_0 = n10
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 53.64/20.52 | (1212) all_0_3_3 = n10
% 53.64/20.52 |
% 53.64/20.52 | Equations (1213,1212) can reduce 679 to:
% 53.64/20.52 | (1106) $false
% 53.64/20.52 |
% 53.64/20.52 |-The branch is then unsatisfiable
% 53.64/20.52 |-Branch two:
% 53.64/20.52 | (1856) ~ (all_0_10_10 = n9)
% 53.64/20.52 | (1857) 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
% 53.64/20.52 |
% 53.64/20.52 +-Applying beta-rule and splitting (1857), into two cases.
% 53.64/20.52 |-Branch one:
% 53.64/20.52 | (1858) all_0_10_10 = n8
% 53.64/20.52 |
% 53.64/20.52 | From (1858) and (292) follows:
% 53.64/20.52 | (1859) pred(n8) = all_0_6_6
% 53.64/20.52 |
% 53.64/20.52 | From (1858) and (760) follows:
% 53.64/20.52 | (1860) succ(n8) = all_0_8_8
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 53.64/20.52 | (1861) all_0_6_6 = n7
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 53.64/20.52 | (1862) all_0_8_8 = n9
% 53.64/20.52 |
% 53.64/20.52 | From (1861)(1862) and (411) follows:
% 53.64/20.52 | (1863) sum(n7, n9) = all_0_1_1
% 53.64/20.52 |
% 53.64/20.52 | From (1861) and (4243) follows:
% 53.64/20.52 | (4488) sum(n7, n23) = all_0_4_4
% 53.64/20.52 |
% 53.64/20.52 | From (1862) and (4245) follows:
% 53.64/20.52 | (4489) sum(n21, n9) = all_0_7_7
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (690) with n21, n9, all_0_7_7, n4 and discharging atoms sum(n21, n9) = all_0_7_7, sum(n21, n9) = n4, yields:
% 53.64/20.52 | (1461) all_0_7_7 = n4
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (690) with n7, n23, all_0_4_4, n4 and discharging atoms sum(n7, n23) = all_0_4_4, sum(n7, n23) = n4, yields:
% 53.64/20.52 | (1459) all_0_4_4 = n4
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 53.64/20.52 | (1633) all_0_1_1 = n16
% 53.64/20.52 |
% 53.64/20.52 | From (1461)(1459) and (590) follows:
% 53.64/20.52 | (1463) sum(n4, n4) = all_0_3_3
% 53.64/20.52 |
% 53.64/20.52 | From (1633) and (4247) follows:
% 53.64/20.52 | (4260) sum(n18, n16) = all_0_0_0
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (690) with n18, n16, all_0_0_0, n8 and discharging atoms sum(n18, n16) = all_0_0_0, sum(n18, n16) = n8, yields:
% 53.64/20.52 | (1231) all_0_0_0 = n8
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 53.64/20.52 | (1230) all_0_3_3 = n8
% 53.64/20.52 |
% 53.64/20.52 | Equations (1231,1230) can reduce 679 to:
% 53.64/20.52 | (1106) $false
% 53.64/20.52 |
% 53.64/20.52 |-The branch is then unsatisfiable
% 53.64/20.52 |-Branch two:
% 53.64/20.52 | (1874) ~ (all_0_10_10 = n8)
% 53.64/20.52 | (1875) 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
% 53.64/20.52 |
% 53.64/20.52 +-Applying beta-rule and splitting (1875), into two cases.
% 53.64/20.52 |-Branch one:
% 53.64/20.52 | (1876) all_0_10_10 = n7
% 53.64/20.52 |
% 53.64/20.52 | From (1876) and (292) follows:
% 53.64/20.52 | (1877) pred(n7) = all_0_6_6
% 53.64/20.52 |
% 53.64/20.52 | From (1876) and (760) follows:
% 53.64/20.52 | (1878) succ(n7) = all_0_8_8
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 53.64/20.52 | (1879) all_0_6_6 = n6
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 53.64/20.52 | (1880) all_0_8_8 = n8
% 53.64/20.52 |
% 53.64/20.52 | From (1879)(1880) and (411) follows:
% 53.64/20.52 | (1881) sum(n6, n8) = all_0_1_1
% 53.64/20.52 |
% 53.64/20.52 | From (1879) and (4243) follows:
% 53.64/20.52 | (4506) sum(n6, n23) = all_0_4_4
% 53.64/20.52 |
% 53.64/20.52 | From (1880) and (4245) follows:
% 53.64/20.52 | (4507) sum(n21, n8) = all_0_7_7
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (690) with n21, n8, all_0_7_7, n3 and discharging atoms sum(n21, n8) = all_0_7_7, sum(n21, n8) = n3, yields:
% 53.64/20.52 | (1479) all_0_7_7 = n3
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (690) with n6, n23, all_0_4_4, n3 and discharging atoms sum(n6, n23) = all_0_4_4, sum(n6, n23) = n3, yields:
% 53.64/20.52 | (1477) all_0_4_4 = n3
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 53.64/20.52 | (1651) all_0_1_1 = n14
% 53.64/20.52 |
% 53.64/20.52 | From (1479)(1477) and (590) follows:
% 53.64/20.52 | (1481) sum(n3, n3) = all_0_3_3
% 53.64/20.52 |
% 53.64/20.52 | From (1651) and (4247) follows:
% 53.64/20.52 | (4278) sum(n18, n14) = all_0_0_0
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (690) with n18, n14, all_0_0_0, n6 and discharging atoms sum(n18, n14) = all_0_0_0, sum(n18, n14) = n6, yields:
% 53.64/20.52 | (1249) all_0_0_0 = n6
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 53.64/20.52 | (1248) all_0_3_3 = n6
% 53.64/20.52 |
% 53.64/20.52 | Equations (1249,1248) can reduce 679 to:
% 53.64/20.52 | (1106) $false
% 53.64/20.52 |
% 53.64/20.52 |-The branch is then unsatisfiable
% 53.64/20.52 |-Branch two:
% 53.64/20.52 | (1892) ~ (all_0_10_10 = n7)
% 53.64/20.52 | (1893) 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
% 53.64/20.52 |
% 53.64/20.52 +-Applying beta-rule and splitting (1893), into two cases.
% 53.64/20.52 |-Branch one:
% 53.64/20.52 | (1894) all_0_10_10 = n6
% 53.64/20.52 |
% 53.64/20.52 | From (1894) and (292) follows:
% 53.64/20.52 | (1895) pred(n6) = all_0_6_6
% 53.64/20.52 |
% 53.64/20.52 | From (1894) and (760) follows:
% 53.64/20.52 | (1896) succ(n6) = all_0_8_8
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 53.64/20.52 | (1897) all_0_6_6 = n5
% 53.64/20.52 |
% 53.64/20.52 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 53.64/20.52 | (1898) all_0_8_8 = n7
% 53.64/20.52 |
% 53.64/20.52 | From (1897)(1898) and (411) follows:
% 53.64/20.52 | (1899) sum(n5, n7) = all_0_1_1
% 53.64/20.52 |
% 53.64/20.52 | From (1897) and (4243) follows:
% 53.64/20.52 | (4524) sum(n5, n23) = all_0_4_4
% 53.64/20.53 |
% 53.64/20.53 | From (1898) and (4245) follows:
% 53.64/20.53 | (4525) sum(n21, n7) = all_0_7_7
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n21, n7, all_0_7_7, n2 and discharging atoms sum(n21, n7) = all_0_7_7, sum(n21, n7) = n2, yields:
% 53.64/20.53 | (1497) all_0_7_7 = n2
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n5, n23, all_0_4_4, n2 and discharging atoms sum(n5, n23) = all_0_4_4, sum(n5, n23) = n2, yields:
% 53.64/20.53 | (1495) all_0_4_4 = n2
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 53.64/20.53 | (1669) all_0_1_1 = n12
% 53.64/20.53 |
% 53.64/20.53 | From (1497)(1495) and (590) follows:
% 53.64/20.53 | (1499) sum(n2, n2) = all_0_3_3
% 53.64/20.53 |
% 53.64/20.53 | From (1669) and (4247) follows:
% 53.64/20.53 | (4296) sum(n18, n12) = all_0_0_0
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n18, n12, all_0_0_0, n4 and discharging atoms sum(n18, n12) = all_0_0_0, sum(n18, n12) = n4, yields:
% 53.64/20.53 | (1267) all_0_0_0 = n4
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 53.64/20.53 | (1266) all_0_3_3 = n4
% 53.64/20.53 |
% 53.64/20.53 | Equations (1267,1266) can reduce 679 to:
% 53.64/20.53 | (1106) $false
% 53.64/20.53 |
% 53.64/20.53 |-The branch is then unsatisfiable
% 53.64/20.53 |-Branch two:
% 53.64/20.53 | (1910) ~ (all_0_10_10 = n6)
% 53.64/20.53 | (1911) 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
% 53.64/20.53 |
% 53.64/20.53 +-Applying beta-rule and splitting (1911), into two cases.
% 53.64/20.53 |-Branch one:
% 53.64/20.53 | (1912) all_0_10_10 = n5
% 53.64/20.53 |
% 53.64/20.53 | From (1912) and (292) follows:
% 53.64/20.53 | (1913) pred(n5) = all_0_6_6
% 53.64/20.53 |
% 53.64/20.53 | From (1912) and (760) follows:
% 53.64/20.53 | (1914) succ(n5) = all_0_8_8
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 53.64/20.53 | (1915) all_0_6_6 = n4
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 53.64/20.53 | (1916) all_0_8_8 = n6
% 53.64/20.53 |
% 53.64/20.53 | From (1915)(1916) and (411) follows:
% 53.64/20.53 | (1917) sum(n4, n6) = all_0_1_1
% 53.64/20.53 |
% 53.64/20.53 | From (1915) and (4243) follows:
% 53.64/20.53 | (4542) sum(n4, n23) = all_0_4_4
% 53.64/20.53 |
% 53.64/20.53 | From (1916) and (4245) follows:
% 53.64/20.53 | (4543) sum(n21, n6) = all_0_7_7
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n21, n6, all_0_7_7, n1 and discharging atoms sum(n21, n6) = all_0_7_7, sum(n21, n6) = n1, yields:
% 53.64/20.53 | (1515) all_0_7_7 = n1
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n4, n23, all_0_4_4, n1 and discharging atoms sum(n4, n23) = all_0_4_4, sum(n4, n23) = n1, yields:
% 53.64/20.53 | (1513) all_0_4_4 = n1
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 53.64/20.53 | (1687) all_0_1_1 = n10
% 53.64/20.53 |
% 53.64/20.53 | From (1515)(1513) and (590) follows:
% 53.64/20.53 | (1517) sum(n1, n1) = all_0_3_3
% 53.64/20.53 |
% 53.64/20.53 | From (1687) and (4247) follows:
% 53.64/20.53 | (4314) sum(n18, n10) = all_0_0_0
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n18, n10, all_0_0_0, n2 and discharging atoms sum(n18, n10) = all_0_0_0, sum(n18, n10) = n2, yields:
% 53.64/20.53 | (1285) all_0_0_0 = n2
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 53.64/20.53 | (1284) all_0_3_3 = n2
% 53.64/20.53 |
% 53.64/20.53 | Equations (1285,1284) can reduce 679 to:
% 53.64/20.53 | (1106) $false
% 53.64/20.53 |
% 53.64/20.53 |-The branch is then unsatisfiable
% 53.64/20.53 |-Branch two:
% 53.64/20.53 | (1928) ~ (all_0_10_10 = n5)
% 53.64/20.53 | (1929) 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
% 53.64/20.53 |
% 53.64/20.53 +-Applying beta-rule and splitting (1929), into two cases.
% 53.64/20.53 |-Branch one:
% 53.64/20.53 | (1930) all_0_10_10 = n4
% 53.64/20.53 |
% 53.64/20.53 | From (1930) and (292) follows:
% 53.64/20.53 | (1931) pred(n4) = all_0_6_6
% 53.64/20.53 |
% 53.64/20.53 | From (1930) and (760) follows:
% 53.64/20.53 | (1932) succ(n4) = all_0_8_8
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 53.64/20.53 | (1933) all_0_6_6 = n3
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 53.64/20.53 | (1934) all_0_8_8 = n5
% 53.64/20.53 |
% 53.64/20.53 | From (1933)(1934) and (411) follows:
% 53.64/20.53 | (1935) sum(n3, n5) = all_0_1_1
% 53.64/20.53 |
% 53.64/20.53 | From (1933) and (4243) follows:
% 53.64/20.53 | (4560) sum(n3, n23) = all_0_4_4
% 53.64/20.53 |
% 53.64/20.53 | From (1934) and (4245) follows:
% 53.64/20.53 | (4561) sum(n21, n5) = all_0_7_7
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n21, n5, all_0_7_7, n0 and discharging atoms sum(n21, n5) = all_0_7_7, sum(n21, n5) = n0, yields:
% 53.64/20.53 | (1533) all_0_7_7 = n0
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n3, n23, all_0_4_4, n0 and discharging atoms sum(n3, n23) = all_0_4_4, sum(n3, n23) = n0, yields:
% 53.64/20.53 | (1531) all_0_4_4 = n0
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 53.64/20.53 | (1705) all_0_1_1 = n8
% 53.64/20.53 |
% 53.64/20.53 | From (1533)(1531) and (590) follows:
% 53.64/20.53 | (1535) sum(n0, n0) = all_0_3_3
% 53.64/20.53 |
% 53.64/20.53 | From (1705) and (4247) follows:
% 53.64/20.53 | (4332) sum(n18, n8) = all_0_0_0
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n18, n8, all_0_0_0, n0 and discharging atoms sum(n18, n8) = all_0_0_0, sum(n18, n8) = n0, yields:
% 53.64/20.53 | (1303) all_0_0_0 = n0
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 53.64/20.53 | (1302) all_0_3_3 = n0
% 53.64/20.53 |
% 53.64/20.53 | Equations (1303,1302) can reduce 679 to:
% 53.64/20.53 | (1106) $false
% 53.64/20.53 |
% 53.64/20.53 |-The branch is then unsatisfiable
% 53.64/20.53 |-Branch two:
% 53.64/20.53 | (1946) ~ (all_0_10_10 = n4)
% 53.64/20.53 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 53.64/20.53 |
% 53.64/20.53 +-Applying beta-rule and splitting (1947), into two cases.
% 53.64/20.53 |-Branch one:
% 53.64/20.53 | (1948) all_0_10_10 = n3
% 53.64/20.53 |
% 53.64/20.53 | From (1948) and (292) follows:
% 53.64/20.53 | (1949) pred(n3) = all_0_6_6
% 53.64/20.53 |
% 53.64/20.53 | From (1948) and (760) follows:
% 53.64/20.53 | (1950) succ(n3) = all_0_8_8
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 53.64/20.53 | (1951) all_0_6_6 = n2
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 53.64/20.53 | (1952) all_0_8_8 = n4
% 53.64/20.53 |
% 53.64/20.53 | From (1951)(1952) and (411) follows:
% 53.64/20.53 | (1953) sum(n2, n4) = all_0_1_1
% 53.64/20.53 |
% 53.64/20.53 | From (1951) and (4243) follows:
% 53.64/20.53 | (4578) sum(n2, n23) = all_0_4_4
% 53.64/20.53 |
% 53.64/20.53 | From (1952) and (4245) follows:
% 53.64/20.53 | (4579) sum(n21, n4) = all_0_7_7
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n21, n4, all_0_7_7, n25 and discharging atoms sum(n21, n4) = all_0_7_7, sum(n21, n4) = n25, yields:
% 53.64/20.53 | (1550) all_0_7_7 = n25
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n2, n23, all_0_4_4, n25 and discharging atoms sum(n2, n23) = all_0_4_4, sum(n2, n23) = n25, yields:
% 53.64/20.53 | (1551) all_0_4_4 = n25
% 53.64/20.53 |
% 53.64/20.53 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 53.64/20.53 | (1723) all_0_1_1 = n6
% 53.64/20.53 |
% 53.64/20.53 | From (1550)(1551) and (590) follows:
% 53.64/20.53 | (1553) sum(n25, n25) = all_0_3_3
% 53.64/20.53 |
% 53.64/20.53 | From (1723) and (4247) follows:
% 53.64/20.54 | (4350) sum(n18, n6) = all_0_0_0
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 53.64/20.54 | (1320) all_0_3_3 = n24
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (690) with n18, n6, all_0_0_0, n24 and discharging atoms sum(n18, n6) = all_0_0_0, sum(n18, n6) = n24, yields:
% 53.64/20.54 | (1321) all_0_0_0 = n24
% 53.64/20.54 |
% 53.64/20.54 | Equations (1321,1320) can reduce 679 to:
% 53.64/20.54 | (1106) $false
% 53.64/20.54 |
% 53.64/20.54 |-The branch is then unsatisfiable
% 53.64/20.54 |-Branch two:
% 53.64/20.54 | (1964) ~ (all_0_10_10 = n3)
% 53.64/20.54 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 53.64/20.54 |
% 53.64/20.54 +-Applying beta-rule and splitting (1965), into two cases.
% 53.64/20.54 |-Branch one:
% 53.64/20.54 | (1966) all_0_10_10 = n2
% 53.64/20.54 |
% 53.64/20.54 | From (1966) and (292) follows:
% 53.64/20.54 | (1967) pred(n2) = all_0_6_6
% 53.64/20.54 |
% 53.64/20.54 | From (1966) and (760) follows:
% 53.64/20.54 | (1968) succ(n2) = all_0_8_8
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 53.64/20.54 | (1969) all_0_6_6 = n1
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 53.64/20.54 | (1970) all_0_8_8 = n3
% 53.64/20.54 |
% 53.64/20.54 | From (1969)(1970) and (411) follows:
% 53.64/20.54 | (1971) sum(n1, n3) = all_0_1_1
% 53.64/20.54 |
% 53.64/20.54 | From (1969) and (4243) follows:
% 53.64/20.54 | (4596) sum(n1, n23) = all_0_4_4
% 53.64/20.54 |
% 53.64/20.54 | From (1970) and (4245) follows:
% 53.64/20.54 | (4597) sum(n21, n3) = all_0_7_7
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (690) with n21, n3, all_0_7_7, n24 and discharging atoms sum(n21, n3) = all_0_7_7, sum(n21, n3) = n24, yields:
% 53.64/20.54 | (1097) all_0_7_7 = n24
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (690) with n1, n23, all_0_4_4, n24 and discharging atoms sum(n1, n23) = all_0_4_4, sum(n1, n23) = n24, yields:
% 53.64/20.54 | (1096) all_0_4_4 = n24
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 53.64/20.54 | (1741) all_0_1_1 = n4
% 53.64/20.54 |
% 53.64/20.54 | From (1097)(1096) and (590) follows:
% 53.64/20.54 | (1101) sum(n24, n24) = all_0_3_3
% 53.64/20.54 |
% 53.64/20.54 | From (1741) and (4247) follows:
% 53.64/20.54 | (4368) sum(n18, n4) = all_0_0_0
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 53.64/20.54 | (1104) all_0_3_3 = n22
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (690) with n18, n4, all_0_0_0, n22 and discharging atoms sum(n18, n4) = all_0_0_0, sum(n18, n4) = n22, yields:
% 53.64/20.54 | (1102) all_0_0_0 = n22
% 53.64/20.54 |
% 53.64/20.54 | Equations (1102,1104) can reduce 679 to:
% 53.64/20.54 | (1106) $false
% 53.64/20.54 |
% 53.64/20.54 |-The branch is then unsatisfiable
% 53.64/20.54 |-Branch two:
% 53.64/20.54 | (1982) ~ (all_0_10_10 = n2)
% 53.64/20.54 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 53.64/20.54 |
% 53.64/20.54 +-Applying beta-rule and splitting (1983), into two cases.
% 53.64/20.54 |-Branch one:
% 53.64/20.54 | (1984) all_0_10_10 = n1
% 53.64/20.54 |
% 53.64/20.54 | From (1984) and (292) follows:
% 53.64/20.54 | (1985) pred(n1) = all_0_6_6
% 53.64/20.54 |
% 53.64/20.54 | From (1984) and (760) follows:
% 53.64/20.54 | (1986) succ(n1) = all_0_8_8
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 53.64/20.54 | (1987) all_0_6_6 = n0
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 53.64/20.54 | (1988) all_0_8_8 = n2
% 53.64/20.54 |
% 53.64/20.54 | From (1987)(1988) and (411) follows:
% 53.64/20.54 | (1989) sum(n0, n2) = all_0_1_1
% 53.64/20.54 |
% 53.64/20.54 | From (1987) and (4243) follows:
% 53.64/20.54 | (4614) sum(n0, n23) = all_0_4_4
% 53.64/20.54 |
% 53.64/20.54 | From (1988) and (4245) follows:
% 53.64/20.54 | (4615) sum(n21, n2) = all_0_7_7
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (690) with n21, n2, all_0_7_7, n23 and discharging atoms sum(n21, n2) = all_0_7_7, sum(n21, n2) = n23, yields:
% 53.64/20.54 | (1119) all_0_7_7 = n23
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (690) with n0, n23, all_0_4_4, n23 and discharging atoms sum(n0, n23) = all_0_4_4, sum(n0, n23) = n23, yields:
% 53.64/20.54 | (1117) all_0_4_4 = n23
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 53.64/20.54 | (1759) all_0_1_1 = n2
% 53.64/20.54 |
% 53.64/20.54 | From (1119)(1117) and (590) follows:
% 53.64/20.54 | (1121) sum(n23, n23) = all_0_3_3
% 53.64/20.54 |
% 53.64/20.54 | From (1759) and (4247) follows:
% 53.64/20.54 | (4386) sum(n18, n2) = all_0_0_0
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 53.64/20.54 | (1122) all_0_3_3 = n20
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (690) with n18, n2, all_0_0_0, n20 and discharging atoms sum(n18, n2) = all_0_0_0, sum(n18, n2) = n20, yields:
% 53.64/20.54 | (1123) all_0_0_0 = n20
% 53.64/20.54 |
% 53.64/20.54 | Equations (1123,1122) can reduce 679 to:
% 53.64/20.54 | (1106) $false
% 53.64/20.54 |
% 53.64/20.54 |-The branch is then unsatisfiable
% 53.64/20.54 |-Branch two:
% 53.64/20.54 | (2002) ~ (all_0_10_10 = n1)
% 53.64/20.54 | (2003) all_0_10_10 = n0
% 53.64/20.54 |
% 53.64/20.54 | From (2003) and (292) follows:
% 53.64/20.54 | (2004) pred(n0) = all_0_6_6
% 53.64/20.54 |
% 53.64/20.54 | From (2003) and (760) follows:
% 53.64/20.54 | (2005) succ(n0) = all_0_8_8
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 53.64/20.54 | (2006) all_0_6_6 = n25
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 53.64/20.54 | (2007) all_0_8_8 = n1
% 53.64/20.54 |
% 53.64/20.54 | From (2006)(2007) and (411) follows:
% 53.64/20.54 | (2008) sum(n25, n1) = all_0_1_1
% 53.64/20.54 |
% 53.64/20.54 | From (2006) and (4243) follows:
% 53.64/20.54 | (4631) sum(n25, n23) = all_0_4_4
% 53.64/20.54 |
% 53.64/20.54 | From (2007) and (4245) follows:
% 53.64/20.54 | (4632) sum(n21, n1) = all_0_7_7
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (690) with n25, n23, all_0_4_4, n22 and discharging atoms sum(n25, n23) = all_0_4_4, sum(n25, n23) = n22, yields:
% 53.64/20.54 | (1135) all_0_4_4 = n22
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 53.64/20.54 | (1777) all_0_1_1 = n0
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (690) with n21, n1, all_0_7_7, n22 and discharging atoms sum(n21, n1) = all_0_7_7, sum(n21, n1) = n22, yields:
% 53.64/20.54 | (1137) all_0_7_7 = n22
% 53.64/20.54 |
% 53.64/20.54 | From (1137)(1135) and (590) follows:
% 53.64/20.54 | (1139) sum(n22, n22) = all_0_3_3
% 53.64/20.54 |
% 53.64/20.54 | From (1777) and (4247) follows:
% 53.64/20.54 | (4404) sum(n18, n0) = all_0_0_0
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 53.64/20.54 | (1140) all_0_3_3 = n18
% 53.64/20.54 |
% 53.64/20.54 | Instantiating formula (690) with n18, n0, all_0_0_0, n18 and discharging atoms sum(n18, n0) = all_0_0_0, sum(n18, n0) = n18, yields:
% 53.64/20.54 | (1141) all_0_0_0 = n18
% 53.64/20.54 |
% 53.64/20.54 | Equations (1141,1140) can reduce 679 to:
% 53.64/20.54 | (1106) $false
% 53.64/20.54 |
% 53.64/20.54 |-The branch is then unsatisfiable
% 53.64/20.55 |-Branch two:
% 53.64/20.55 | (1161) ~ (all_0_11_11 = n22)
% 53.64/20.55 | (1162) all_0_11_11 = n21 | 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
% 53.64/20.55 |
% 53.64/20.55 +-Applying beta-rule and splitting (1623), into two cases.
% 53.64/20.55 |-Branch one:
% 53.64/20.55 | (1624) all_0_10_10 = n21
% 53.64/20.55 |
% 53.64/20.55 | From (1624) and (292) follows:
% 53.64/20.55 | (1625) pred(n21) = all_0_6_6
% 53.64/20.55 |
% 53.64/20.55 | From (1624) and (760) follows:
% 53.64/20.55 | (1626) succ(n21) = all_0_8_8
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (500) with n21, all_0_6_6, n20 and discharging atoms pred(n21) = all_0_6_6, pred(n21) = n20, yields:
% 53.64/20.55 | (1627) all_0_6_6 = n20
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (617) with n21, all_0_8_8, n22 and discharging atoms succ(n21) = all_0_8_8, succ(n21) = n22, yields:
% 53.64/20.55 | (1628) all_0_8_8 = n22
% 53.64/20.55 |
% 53.64/20.55 | From (1627) and (1625) follows:
% 53.64/20.55 | (321) pred(n21) = n20
% 53.64/20.55 |
% 53.64/20.55 | From (1628) and (1626) follows:
% 53.64/20.55 | (960) succ(n21) = n22
% 53.64/20.55 |
% 53.64/20.55 | From (1627) and (541) follows:
% 53.64/20.55 | (4650) sum(n20, all_0_5_5) = all_0_4_4
% 53.64/20.55 |
% 53.64/20.55 | From (1627)(1628) and (411) follows:
% 53.64/20.55 | (1629) sum(n20, n22) = all_0_1_1
% 53.64/20.55 |
% 53.64/20.55 | From (1628) and (427) follows:
% 53.64/20.55 | (4652) sum(all_0_9_9, n22) = all_0_7_7
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (690) with n20, n22, all_0_1_1, n16 and discharging atoms sum(n20, n22) = all_0_1_1, sum(n20, n22) = n16, yields:
% 53.64/20.55 | (1633) all_0_1_1 = n16
% 53.64/20.55 |
% 53.64/20.55 | From (1633) and (630) follows:
% 53.64/20.55 | (4654) sum(all_0_2_2, n16) = all_0_0_0
% 53.64/20.55 |
% 53.64/20.55 | From (1633) and (1629) follows:
% 53.64/20.55 | (200) sum(n20, n22) = n16
% 53.64/20.55 |
% 53.64/20.55 +-Applying beta-rule and splitting (1162), into two cases.
% 53.64/20.55 |-Branch one:
% 53.64/20.55 | (1163) all_0_11_11 = n21
% 53.64/20.55 |
% 53.64/20.55 | From (1163) and (559) follows:
% 53.64/20.55 | (1164) pred(n21) = all_0_9_9
% 53.64/20.55 |
% 53.64/20.55 | From (1163) and (992) follows:
% 53.64/20.55 | (1165) succ(n21) = all_0_5_5
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (500) with n21, all_0_9_9, n20 and discharging atoms pred(n21) = all_0_9_9, pred(n21) = n20, yields:
% 53.64/20.55 | (1166) all_0_9_9 = n20
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (617) with n21, all_0_5_5, n22 and discharging atoms succ(n21) = all_0_5_5, succ(n21) = n22, yields:
% 53.64/20.55 | (1167) all_0_5_5 = n22
% 53.64/20.55 |
% 53.64/20.55 | From (1166)(1167) and (538) follows:
% 53.64/20.55 | (1168) sum(n20, n22) = all_0_2_2
% 53.64/20.55 |
% 53.64/20.55 | From (1166) and (4652) follows:
% 53.64/20.55 | (4662) sum(n20, n22) = all_0_7_7
% 53.64/20.55 |
% 53.64/20.55 | From (1167) and (4650) follows:
% 53.64/20.55 | (4663) sum(n20, n22) = all_0_4_4
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (690) with n20, n22, all_0_2_2, n16 and discharging atoms sum(n20, n22) = all_0_2_2, sum(n20, n22) = n16, yields:
% 53.64/20.55 | (1172) all_0_2_2 = n16
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (690) with n20, n22, all_0_4_4, all_0_2_2 and discharging atoms sum(n20, n22) = all_0_2_2, sum(n20, n22) = all_0_4_4, yields:
% 53.64/20.55 | (1093) all_0_2_2 = all_0_4_4
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (690) with n20, n22, all_0_7_7, all_0_2_2 and discharging atoms sum(n20, n22) = all_0_2_2, sum(n20, n22) = all_0_7_7, yields:
% 53.64/20.55 | (1094) all_0_2_2 = all_0_7_7
% 53.64/20.55 |
% 53.64/20.55 | Combining equations (1094,1093) yields a new equation:
% 53.64/20.55 | (1095) all_0_4_4 = all_0_7_7
% 53.64/20.55 |
% 53.64/20.55 | Combining equations (1172,1093) yields a new equation:
% 53.64/20.55 | (1243) all_0_4_4 = n16
% 53.64/20.55 |
% 53.64/20.55 | Combining equations (1243,1095) yields a new equation:
% 53.64/20.55 | (1245) all_0_7_7 = n16
% 53.64/20.55 |
% 53.64/20.55 | Combining equations (1245,1095) yields a new equation:
% 53.64/20.55 | (1243) all_0_4_4 = n16
% 53.64/20.55 |
% 53.64/20.55 | Combining equations (1243,1093) yields a new equation:
% 53.64/20.55 | (1172) all_0_2_2 = n16
% 53.64/20.55 |
% 53.64/20.55 | From (1172) and (4654) follows:
% 53.64/20.55 | (4672) sum(n16, n16) = all_0_0_0
% 53.64/20.55 |
% 53.64/20.55 | From (1245)(1243) and (590) follows:
% 53.64/20.55 | (1247) sum(n16, n16) = all_0_3_3
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (690) with n16, n16, all_0_0_0, n6 and discharging atoms sum(n16, n16) = all_0_0_0, sum(n16, n16) = n6, yields:
% 53.64/20.55 | (1249) all_0_0_0 = n6
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (690) 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:
% 53.64/20.55 | (1103) all_0_0_0 = all_0_3_3
% 53.64/20.55 |
% 53.64/20.55 | Combining equations (1249,1103) yields a new equation:
% 53.64/20.55 | (1248) all_0_3_3 = n6
% 53.64/20.55 |
% 53.64/20.55 | Combining equations (1248,1103) yields a new equation:
% 53.64/20.55 | (1249) all_0_0_0 = n6
% 53.64/20.55 |
% 53.64/20.55 | Equations (1249,1248) can reduce 679 to:
% 53.64/20.55 | (1106) $false
% 53.64/20.55 |
% 53.64/20.55 |-The branch is then unsatisfiable
% 53.64/20.55 |-Branch two:
% 53.64/20.55 | (1179) ~ (all_0_11_11 = n21)
% 53.64/20.55 | (1180) 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
% 53.64/20.55 |
% 53.64/20.55 +-Applying beta-rule and splitting (1180), into two cases.
% 53.64/20.55 |-Branch one:
% 53.64/20.55 | (1181) all_0_11_11 = n20
% 53.64/20.55 |
% 53.64/20.55 | From (1181) and (559) follows:
% 53.64/20.55 | (1182) pred(n20) = all_0_9_9
% 53.64/20.55 |
% 53.64/20.55 | From (1181) and (992) follows:
% 53.64/20.55 | (1183) succ(n20) = all_0_5_5
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (500) with n20, all_0_9_9, n19 and discharging atoms pred(n20) = all_0_9_9, pred(n20) = n19, yields:
% 53.64/20.55 | (1184) all_0_9_9 = n19
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (617) with n20, all_0_5_5, n21 and discharging atoms succ(n20) = all_0_5_5, succ(n20) = n21, yields:
% 53.64/20.55 | (1185) all_0_5_5 = n21
% 53.64/20.55 |
% 53.64/20.55 | From (1184)(1185) and (538) follows:
% 53.64/20.55 | (1186) sum(n19, n21) = all_0_2_2
% 53.64/20.55 |
% 53.64/20.55 | From (1184) and (4652) follows:
% 53.64/20.55 | (4687) sum(n19, n22) = all_0_7_7
% 53.64/20.55 |
% 53.64/20.55 | From (1185) and (4650) follows:
% 53.64/20.55 | (4688) sum(n20, n21) = all_0_4_4
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (690) with n20, n21, all_0_4_4, n15 and discharging atoms sum(n20, n21) = all_0_4_4, sum(n20, n21) = n15, yields:
% 53.64/20.55 | (1261) all_0_4_4 = n15
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (690) with n19, n22, all_0_7_7, n15 and discharging atoms sum(n19, n22) = all_0_7_7, sum(n19, n22) = n15, yields:
% 53.64/20.55 | (1263) all_0_7_7 = n15
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (690) with n19, n21, all_0_2_2, n14 and discharging atoms sum(n19, n21) = all_0_2_2, sum(n19, n21) = n14, yields:
% 53.64/20.55 | (1190) all_0_2_2 = n14
% 53.64/20.55 |
% 53.64/20.55 | From (1190) and (4654) follows:
% 53.64/20.55 | (4692) sum(n14, n16) = all_0_0_0
% 53.64/20.55 |
% 53.64/20.55 | From (1263)(1261) and (590) follows:
% 53.64/20.55 | (1265) sum(n15, n15) = all_0_3_3
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 53.64/20.55 | (1266) all_0_3_3 = n4
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (690) with n14, n16, all_0_0_0, n4 and discharging atoms sum(n14, n16) = all_0_0_0, sum(n14, n16) = n4, yields:
% 53.64/20.55 | (1267) all_0_0_0 = n4
% 53.64/20.55 |
% 53.64/20.55 | Equations (1267,1266) can reduce 679 to:
% 53.64/20.55 | (1106) $false
% 53.64/20.55 |
% 53.64/20.55 |-The branch is then unsatisfiable
% 53.64/20.55 |-Branch two:
% 53.64/20.55 | (1197) ~ (all_0_11_11 = n20)
% 53.64/20.55 | (1198) 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
% 53.64/20.55 |
% 53.64/20.55 +-Applying beta-rule and splitting (1198), into two cases.
% 53.64/20.55 |-Branch one:
% 53.64/20.55 | (1199) all_0_11_11 = n19
% 53.64/20.55 |
% 53.64/20.55 | From (1199) and (559) follows:
% 53.64/20.55 | (1200) pred(n19) = all_0_9_9
% 53.64/20.55 |
% 53.64/20.55 | From (1199) and (992) follows:
% 53.64/20.55 | (1201) succ(n19) = all_0_5_5
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (500) with n19, all_0_9_9, n18 and discharging atoms pred(n19) = all_0_9_9, pred(n19) = n18, yields:
% 53.64/20.55 | (1202) all_0_9_9 = n18
% 53.64/20.55 |
% 53.64/20.55 | Instantiating formula (617) with n19, all_0_5_5, n20 and discharging atoms succ(n19) = all_0_5_5, succ(n19) = n20, yields:
% 53.64/20.55 | (1203) all_0_5_5 = n20
% 53.64/20.55 |
% 53.64/20.55 | From (1202)(1203) and (538) follows:
% 53.64/20.56 | (1204) sum(n18, n20) = all_0_2_2
% 53.64/20.56 |
% 53.64/20.56 | From (1202) and (4652) follows:
% 53.64/20.56 | (4705) sum(n18, n22) = all_0_7_7
% 53.64/20.56 |
% 53.64/20.56 | From (1203) and (4650) follows:
% 53.64/20.56 | (4706) sum(n20, n20) = all_0_4_4
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n20, n20, all_0_4_4, n14 and discharging atoms sum(n20, n20) = all_0_4_4, sum(n20, n20) = n14, yields:
% 53.64/20.56 | (1279) all_0_4_4 = n14
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n18, n22, all_0_7_7, n14 and discharging atoms sum(n18, n22) = all_0_7_7, sum(n18, n22) = n14, yields:
% 53.64/20.56 | (1281) all_0_7_7 = n14
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n18, n20, all_0_2_2, n12 and discharging atoms sum(n18, n20) = all_0_2_2, sum(n18, n20) = n12, yields:
% 53.64/20.56 | (1208) all_0_2_2 = n12
% 53.64/20.56 |
% 53.64/20.56 | From (1208) and (4654) follows:
% 53.64/20.56 | (4710) sum(n12, n16) = all_0_0_0
% 53.64/20.56 |
% 53.64/20.56 | From (1281)(1279) and (590) follows:
% 53.64/20.56 | (1283) sum(n14, n14) = all_0_3_3
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 53.64/20.56 | (1284) all_0_3_3 = n2
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n12, n16, all_0_0_0, n2 and discharging atoms sum(n12, n16) = all_0_0_0, sum(n12, n16) = n2, yields:
% 53.64/20.56 | (1285) all_0_0_0 = n2
% 53.64/20.56 |
% 53.64/20.56 | Equations (1285,1284) can reduce 679 to:
% 53.64/20.56 | (1106) $false
% 53.64/20.56 |
% 53.64/20.56 |-The branch is then unsatisfiable
% 53.64/20.56 |-Branch two:
% 53.64/20.56 | (1215) ~ (all_0_11_11 = n19)
% 53.64/20.56 | (1216) 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
% 53.64/20.56 |
% 53.64/20.56 +-Applying beta-rule and splitting (1216), into two cases.
% 53.64/20.56 |-Branch one:
% 53.64/20.56 | (1217) all_0_11_11 = n18
% 53.64/20.56 |
% 53.64/20.56 | From (1217) and (559) follows:
% 53.64/20.56 | (1218) pred(n18) = all_0_9_9
% 53.64/20.56 |
% 53.64/20.56 | From (1217) and (992) follows:
% 53.64/20.56 | (1219) succ(n18) = all_0_5_5
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (500) with n18, all_0_9_9, n17 and discharging atoms pred(n18) = all_0_9_9, pred(n18) = n17, yields:
% 53.64/20.56 | (1220) all_0_9_9 = n17
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (617) with n18, all_0_5_5, n19 and discharging atoms succ(n18) = all_0_5_5, succ(n18) = n19, yields:
% 53.64/20.56 | (1221) all_0_5_5 = n19
% 53.64/20.56 |
% 53.64/20.56 | From (1220)(1221) and (538) follows:
% 53.64/20.56 | (1222) sum(n17, n19) = all_0_2_2
% 53.64/20.56 |
% 53.64/20.56 | From (1220) and (4652) follows:
% 53.64/20.56 | (4723) sum(n17, n22) = all_0_7_7
% 53.64/20.56 |
% 53.64/20.56 | From (1221) and (4650) follows:
% 53.64/20.56 | (4724) sum(n20, n19) = all_0_4_4
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n20, n19, all_0_4_4, n13 and discharging atoms sum(n20, n19) = all_0_4_4, sum(n20, n19) = n13, yields:
% 53.64/20.56 | (1297) all_0_4_4 = n13
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n17, n22, all_0_7_7, n13 and discharging atoms sum(n17, n22) = all_0_7_7, sum(n17, n22) = n13, yields:
% 53.64/20.56 | (1299) all_0_7_7 = n13
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n17, n19, all_0_2_2, n10 and discharging atoms sum(n17, n19) = all_0_2_2, sum(n17, n19) = n10, yields:
% 53.64/20.56 | (1226) all_0_2_2 = n10
% 53.64/20.56 |
% 53.64/20.56 | From (1226) and (4654) follows:
% 53.64/20.56 | (4728) sum(n10, n16) = all_0_0_0
% 53.64/20.56 |
% 53.64/20.56 | From (1299)(1297) and (590) follows:
% 53.64/20.56 | (1301) sum(n13, n13) = all_0_3_3
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 53.64/20.56 | (1302) all_0_3_3 = n0
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n10, n16, all_0_0_0, n0 and discharging atoms sum(n10, n16) = all_0_0_0, sum(n10, n16) = n0, yields:
% 53.64/20.56 | (1303) all_0_0_0 = n0
% 53.64/20.56 |
% 53.64/20.56 | Equations (1303,1302) can reduce 679 to:
% 53.64/20.56 | (1106) $false
% 53.64/20.56 |
% 53.64/20.56 |-The branch is then unsatisfiable
% 53.64/20.56 |-Branch two:
% 53.64/20.56 | (1233) ~ (all_0_11_11 = n18)
% 53.64/20.56 | (1234) 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
% 53.64/20.56 |
% 53.64/20.56 +-Applying beta-rule and splitting (1234), into two cases.
% 53.64/20.56 |-Branch one:
% 53.64/20.56 | (1235) all_0_11_11 = n17
% 53.64/20.56 |
% 53.64/20.56 | From (1235) and (559) follows:
% 53.64/20.56 | (1236) pred(n17) = all_0_9_9
% 53.64/20.56 |
% 53.64/20.56 | From (1235) and (992) follows:
% 53.64/20.56 | (1237) succ(n17) = all_0_5_5
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (500) with n17, all_0_9_9, n16 and discharging atoms pred(n17) = all_0_9_9, pred(n17) = n16, yields:
% 53.64/20.56 | (1238) all_0_9_9 = n16
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (617) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 53.64/20.56 | (1239) all_0_5_5 = n18
% 53.64/20.56 |
% 53.64/20.56 | From (1238)(1239) and (538) follows:
% 53.64/20.56 | (1240) sum(n16, n18) = all_0_2_2
% 53.64/20.56 |
% 53.64/20.56 | From (1238) and (4652) follows:
% 53.64/20.56 | (4741) sum(n16, n22) = all_0_7_7
% 53.64/20.56 |
% 53.64/20.56 | From (1239) and (4650) follows:
% 53.64/20.56 | (4742) sum(n20, n18) = all_0_4_4
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n20, n18, all_0_4_4, n12 and discharging atoms sum(n20, n18) = all_0_4_4, sum(n20, n18) = n12, yields:
% 53.64/20.56 | (1315) all_0_4_4 = n12
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n16, n22, all_0_7_7, n12 and discharging atoms sum(n16, n22) = all_0_7_7, sum(n16, n22) = n12, yields:
% 53.64/20.56 | (1317) all_0_7_7 = n12
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n16, n18, all_0_2_2, n8 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = n8, yields:
% 53.64/20.56 | (1244) all_0_2_2 = n8
% 53.64/20.56 |
% 53.64/20.56 | From (1244) and (4654) follows:
% 53.64/20.56 | (4746) sum(n8, n16) = all_0_0_0
% 53.64/20.56 |
% 53.64/20.56 | From (1317)(1315) and (590) follows:
% 53.64/20.56 | (1319) sum(n12, n12) = all_0_3_3
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 53.64/20.56 | (1320) all_0_3_3 = n24
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n8, n16, all_0_0_0, n24 and discharging atoms sum(n8, n16) = all_0_0_0, sum(n8, n16) = n24, yields:
% 53.64/20.56 | (1321) all_0_0_0 = n24
% 53.64/20.56 |
% 53.64/20.56 | Equations (1321,1320) can reduce 679 to:
% 53.64/20.56 | (1106) $false
% 53.64/20.56 |
% 53.64/20.56 |-The branch is then unsatisfiable
% 53.64/20.56 |-Branch two:
% 53.64/20.56 | (1251) ~ (all_0_11_11 = n17)
% 53.64/20.56 | (1252) 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
% 53.64/20.56 |
% 53.64/20.56 +-Applying beta-rule and splitting (1252), into two cases.
% 53.64/20.56 |-Branch one:
% 53.64/20.56 | (1253) all_0_11_11 = n16
% 53.64/20.56 |
% 53.64/20.56 | From (1253) and (559) follows:
% 53.64/20.56 | (1254) pred(n16) = all_0_9_9
% 53.64/20.56 |
% 53.64/20.56 | From (1253) and (992) follows:
% 53.64/20.56 | (1255) succ(n16) = all_0_5_5
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (500) with n16, all_0_9_9, n15 and discharging atoms pred(n16) = all_0_9_9, pred(n16) = n15, yields:
% 53.64/20.56 | (1256) all_0_9_9 = n15
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (617) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 53.64/20.56 | (1257) all_0_5_5 = n17
% 53.64/20.56 |
% 53.64/20.56 | From (1256)(1257) and (538) follows:
% 53.64/20.56 | (1258) sum(n15, n17) = all_0_2_2
% 53.64/20.56 |
% 53.64/20.56 | From (1256) and (4652) follows:
% 53.64/20.56 | (4759) sum(n15, n22) = all_0_7_7
% 53.64/20.56 |
% 53.64/20.56 | From (1257) and (4650) follows:
% 53.64/20.56 | (4760) sum(n20, n17) = all_0_4_4
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n20, n17, all_0_4_4, n11 and discharging atoms sum(n20, n17) = all_0_4_4, sum(n20, n17) = n11, yields:
% 53.64/20.56 | (1333) all_0_4_4 = n11
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n15, n22, all_0_7_7, n11 and discharging atoms sum(n15, n22) = all_0_7_7, sum(n15, n22) = n11, yields:
% 53.64/20.56 | (1335) all_0_7_7 = n11
% 53.64/20.56 |
% 53.64/20.56 | Instantiating formula (690) with n15, n17, all_0_2_2, n6 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n6, yields:
% 53.64/20.56 | (1262) all_0_2_2 = n6
% 53.64/20.57 |
% 53.64/20.57 | From (1262) and (4654) follows:
% 53.64/20.57 | (4764) sum(n6, n16) = all_0_0_0
% 53.64/20.57 |
% 53.64/20.57 | From (1335)(1333) and (590) follows:
% 53.64/20.57 | (1337) sum(n11, n11) = all_0_3_3
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 53.64/20.57 | (1104) all_0_3_3 = n22
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (690) with n6, n16, all_0_0_0, n22 and discharging atoms sum(n6, n16) = all_0_0_0, sum(n6, n16) = n22, yields:
% 53.64/20.57 | (1102) all_0_0_0 = n22
% 53.64/20.57 |
% 53.64/20.57 | Equations (1102,1104) can reduce 679 to:
% 53.64/20.57 | (1106) $false
% 53.64/20.57 |
% 53.64/20.57 |-The branch is then unsatisfiable
% 53.64/20.57 |-Branch two:
% 53.64/20.57 | (1269) ~ (all_0_11_11 = n16)
% 53.64/20.57 | (1270) 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
% 53.64/20.57 |
% 53.64/20.57 +-Applying beta-rule and splitting (1270), into two cases.
% 53.64/20.57 |-Branch one:
% 53.64/20.57 | (1271) all_0_11_11 = n15
% 53.64/20.57 |
% 53.64/20.57 | From (1271) and (559) follows:
% 53.64/20.57 | (1272) pred(n15) = all_0_9_9
% 53.64/20.57 |
% 53.64/20.57 | From (1271) and (992) follows:
% 53.64/20.57 | (1273) succ(n15) = all_0_5_5
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (500) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 53.64/20.57 | (1274) all_0_9_9 = n14
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (617) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 53.64/20.57 | (1275) all_0_5_5 = n16
% 53.64/20.57 |
% 53.64/20.57 | From (1274)(1275) and (538) follows:
% 53.64/20.57 | (1276) sum(n14, n16) = all_0_2_2
% 53.64/20.57 |
% 53.64/20.57 | From (1274) and (4652) follows:
% 53.64/20.57 | (4777) sum(n14, n22) = all_0_7_7
% 53.64/20.57 |
% 53.64/20.57 | From (1275) and (4650) follows:
% 53.64/20.57 | (4778) sum(n20, n16) = all_0_4_4
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (690) with n20, n16, all_0_4_4, n10 and discharging atoms sum(n20, n16) = all_0_4_4, sum(n20, n16) = n10, yields:
% 53.64/20.57 | (1351) all_0_4_4 = n10
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (690) with n14, n22, all_0_7_7, n10 and discharging atoms sum(n14, n22) = all_0_7_7, sum(n14, n22) = n10, yields:
% 53.64/20.57 | (1353) all_0_7_7 = n10
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (690) with n14, n16, all_0_2_2, n4 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n4, yields:
% 53.64/20.57 | (1280) all_0_2_2 = n4
% 53.64/20.57 |
% 53.64/20.57 | From (1280) and (4654) follows:
% 53.64/20.57 | (4782) sum(n4, n16) = all_0_0_0
% 53.64/20.57 |
% 53.64/20.57 | From (1353)(1351) and (590) follows:
% 53.64/20.57 | (1355) sum(n10, n10) = all_0_3_3
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 53.64/20.57 | (1122) all_0_3_3 = n20
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (690) with n4, n16, all_0_0_0, n20 and discharging atoms sum(n4, n16) = all_0_0_0, sum(n4, n16) = n20, yields:
% 53.64/20.57 | (1123) all_0_0_0 = n20
% 53.64/20.57 |
% 53.64/20.57 | Equations (1123,1122) can reduce 679 to:
% 53.64/20.57 | (1106) $false
% 53.64/20.57 |
% 53.64/20.57 |-The branch is then unsatisfiable
% 53.64/20.57 |-Branch two:
% 53.64/20.57 | (1287) ~ (all_0_11_11 = n15)
% 53.64/20.57 | (1288) 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
% 53.64/20.57 |
% 53.64/20.57 +-Applying beta-rule and splitting (1288), into two cases.
% 53.64/20.57 |-Branch one:
% 53.64/20.57 | (1289) all_0_11_11 = n14
% 53.64/20.57 |
% 53.64/20.57 | From (1289) and (559) follows:
% 53.64/20.57 | (1290) pred(n14) = all_0_9_9
% 53.64/20.57 |
% 53.64/20.57 | From (1289) and (992) follows:
% 53.64/20.57 | (1291) succ(n14) = all_0_5_5
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (500) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 53.64/20.57 | (1292) all_0_9_9 = n13
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (617) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 53.64/20.57 | (1293) all_0_5_5 = n15
% 53.64/20.57 |
% 53.64/20.57 | From (1292)(1293) and (538) follows:
% 53.64/20.57 | (1294) sum(n13, n15) = all_0_2_2
% 53.64/20.57 |
% 53.64/20.57 | From (1292) and (4652) follows:
% 53.64/20.57 | (4795) sum(n13, n22) = all_0_7_7
% 53.64/20.57 |
% 53.64/20.57 | From (1293) and (4650) follows:
% 53.64/20.57 | (4796) sum(n20, n15) = all_0_4_4
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (690) with n20, n15, all_0_4_4, n9 and discharging atoms sum(n20, n15) = all_0_4_4, sum(n20, n15) = n9, yields:
% 53.64/20.57 | (1369) all_0_4_4 = n9
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (690) with n13, n22, all_0_7_7, n9 and discharging atoms sum(n13, n22) = all_0_7_7, sum(n13, n22) = n9, yields:
% 53.64/20.57 | (1371) all_0_7_7 = n9
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (690) with n13, n15, all_0_2_2, n2 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n2, yields:
% 53.64/20.57 | (1298) all_0_2_2 = n2
% 53.64/20.57 |
% 53.64/20.57 | From (1298) and (4654) follows:
% 53.64/20.57 | (4800) sum(n2, n16) = all_0_0_0
% 53.64/20.57 |
% 53.64/20.57 | From (1371)(1369) and (590) follows:
% 53.64/20.57 | (1373) sum(n9, n9) = all_0_3_3
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 53.64/20.57 | (1140) all_0_3_3 = n18
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (690) with n2, n16, all_0_0_0, n18 and discharging atoms sum(n2, n16) = all_0_0_0, sum(n2, n16) = n18, yields:
% 53.64/20.57 | (1141) all_0_0_0 = n18
% 53.64/20.57 |
% 53.64/20.57 | Equations (1141,1140) can reduce 679 to:
% 53.64/20.57 | (1106) $false
% 53.64/20.57 |
% 53.64/20.57 |-The branch is then unsatisfiable
% 53.64/20.57 |-Branch two:
% 53.64/20.57 | (1305) ~ (all_0_11_11 = n14)
% 53.64/20.57 | (1306) 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
% 53.64/20.57 |
% 53.64/20.57 +-Applying beta-rule and splitting (1306), into two cases.
% 53.64/20.57 |-Branch one:
% 53.64/20.57 | (1307) all_0_11_11 = n13
% 53.64/20.57 |
% 53.64/20.57 | From (1307) and (559) follows:
% 53.64/20.57 | (1308) pred(n13) = all_0_9_9
% 53.64/20.57 |
% 53.64/20.57 | From (1307) and (992) follows:
% 53.64/20.57 | (1309) succ(n13) = all_0_5_5
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (500) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 53.64/20.57 | (1310) all_0_9_9 = n12
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (617) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 53.64/20.57 | (1311) all_0_5_5 = n14
% 53.64/20.57 |
% 53.64/20.57 | From (1310)(1311) and (538) follows:
% 53.64/20.57 | (1312) sum(n12, n14) = all_0_2_2
% 53.64/20.57 |
% 53.64/20.57 | From (1310) and (4652) follows:
% 53.64/20.57 | (4813) sum(n12, n22) = all_0_7_7
% 53.64/20.57 |
% 53.64/20.57 | From (1311) and (4650) follows:
% 53.64/20.57 | (4814) sum(n20, n14) = all_0_4_4
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (690) with n20, n14, all_0_4_4, n8 and discharging atoms sum(n20, n14) = all_0_4_4, sum(n20, n14) = n8, yields:
% 53.64/20.57 | (1387) all_0_4_4 = n8
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (690) with n12, n22, all_0_7_7, n8 and discharging atoms sum(n12, n22) = all_0_7_7, sum(n12, n22) = n8, yields:
% 53.64/20.57 | (1389) all_0_7_7 = n8
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (690) with n12, n14, all_0_2_2, n0 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n0, yields:
% 53.64/20.57 | (1316) all_0_2_2 = n0
% 53.64/20.57 |
% 53.64/20.57 | From (1316) and (4654) follows:
% 53.64/20.57 | (4818) sum(n0, n16) = all_0_0_0
% 53.64/20.57 |
% 53.64/20.57 | From (1389)(1387) and (590) follows:
% 53.64/20.57 | (1391) sum(n8, n8) = all_0_3_3
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 53.64/20.57 | (1158) all_0_3_3 = n16
% 53.64/20.57 |
% 53.64/20.57 | Instantiating formula (690) with n0, n16, all_0_0_0, n16 and discharging atoms sum(n0, n16) = all_0_0_0, sum(n0, n16) = n16, yields:
% 53.64/20.57 | (1159) all_0_0_0 = n16
% 53.64/20.57 |
% 53.64/20.58 | Equations (1159,1158) can reduce 679 to:
% 53.64/20.58 | (1106) $false
% 53.64/20.58 |
% 53.64/20.58 |-The branch is then unsatisfiable
% 53.64/20.58 |-Branch two:
% 53.64/20.58 | (1323) ~ (all_0_11_11 = n13)
% 53.64/20.58 | (1324) 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
% 53.64/20.58 |
% 53.64/20.58 +-Applying beta-rule and splitting (1324), into two cases.
% 53.64/20.58 |-Branch one:
% 53.64/20.58 | (1325) all_0_11_11 = n12
% 53.64/20.58 |
% 53.64/20.58 | From (1325) and (559) follows:
% 53.64/20.58 | (1326) pred(n12) = all_0_9_9
% 53.64/20.58 |
% 53.64/20.58 | From (1325) and (992) follows:
% 53.64/20.58 | (1327) succ(n12) = all_0_5_5
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (500) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 53.64/20.58 | (1328) all_0_9_9 = n11
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (617) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 53.64/20.58 | (1329) all_0_5_5 = n13
% 53.64/20.58 |
% 53.64/20.58 | From (1328)(1329) and (538) follows:
% 53.64/20.58 | (1330) sum(n11, n13) = all_0_2_2
% 53.64/20.58 |
% 53.64/20.58 | From (1328) and (4652) follows:
% 53.64/20.58 | (4831) sum(n11, n22) = all_0_7_7
% 53.64/20.58 |
% 53.64/20.58 | From (1329) and (4650) follows:
% 53.64/20.58 | (4832) sum(n20, n13) = all_0_4_4
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (690) with n20, n13, all_0_4_4, n7 and discharging atoms sum(n20, n13) = all_0_4_4, sum(n20, n13) = n7, yields:
% 53.64/20.58 | (1405) all_0_4_4 = n7
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (690) with n11, n22, all_0_7_7, n7 and discharging atoms sum(n11, n22) = all_0_7_7, sum(n11, n22) = n7, yields:
% 53.64/20.58 | (1407) all_0_7_7 = n7
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (690) with n11, n13, all_0_2_2, n24 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n24, yields:
% 53.64/20.58 | (1092) all_0_2_2 = n24
% 53.64/20.58 |
% 53.64/20.58 | From (1092) and (4654) follows:
% 53.64/20.58 | (1636) sum(n24, n16) = all_0_0_0
% 53.64/20.58 |
% 53.64/20.58 | From (1407)(1405) and (590) follows:
% 53.64/20.58 | (1409) sum(n7, n7) = all_0_3_3
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (690) with n24, n16, all_0_0_0, n14 and discharging atoms sum(n24, n16) = all_0_0_0, sum(n24, n16) = n14, yields:
% 53.64/20.58 | (1177) all_0_0_0 = n14
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 53.64/20.58 | (1176) all_0_3_3 = n14
% 53.64/20.58 |
% 53.64/20.58 | Equations (1177,1176) can reduce 679 to:
% 53.64/20.58 | (1106) $false
% 53.64/20.58 |
% 53.64/20.58 |-The branch is then unsatisfiable
% 53.64/20.58 |-Branch two:
% 53.64/20.58 | (1341) ~ (all_0_11_11 = n12)
% 53.64/20.58 | (1342) 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
% 53.64/20.58 |
% 53.64/20.58 +-Applying beta-rule and splitting (1342), into two cases.
% 53.64/20.58 |-Branch one:
% 53.64/20.58 | (1343) all_0_11_11 = n11
% 53.64/20.58 |
% 53.64/20.58 | From (1343) and (559) follows:
% 53.64/20.58 | (1344) pred(n11) = all_0_9_9
% 53.64/20.58 |
% 53.64/20.58 | From (1343) and (992) follows:
% 53.64/20.58 | (1345) succ(n11) = all_0_5_5
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (500) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 53.64/20.58 | (1346) all_0_9_9 = n10
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (617) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 53.64/20.58 | (1347) all_0_5_5 = n12
% 53.64/20.58 |
% 53.64/20.58 | From (1346)(1347) and (538) follows:
% 53.64/20.58 | (1348) sum(n10, n12) = all_0_2_2
% 53.64/20.58 |
% 53.64/20.58 | From (1346) and (4652) follows:
% 53.64/20.58 | (4849) sum(n10, n22) = all_0_7_7
% 53.64/20.58 |
% 53.64/20.58 | From (1347) and (4650) follows:
% 53.64/20.58 | (4850) sum(n20, n12) = all_0_4_4
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (690) with n20, n12, all_0_4_4, n6 and discharging atoms sum(n20, n12) = all_0_4_4, sum(n20, n12) = n6, yields:
% 53.64/20.58 | (1423) all_0_4_4 = n6
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (690) with n10, n22, all_0_7_7, n6 and discharging atoms sum(n10, n22) = all_0_7_7, sum(n10, n22) = n6, yields:
% 53.64/20.58 | (1425) all_0_7_7 = n6
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (690) with n10, n12, all_0_2_2, n22 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n22, yields:
% 53.64/20.58 | (1118) all_0_2_2 = n22
% 53.64/20.58 |
% 53.64/20.58 | From (1118) and (4654) follows:
% 53.64/20.58 | (2548) sum(n22, n16) = all_0_0_0
% 53.64/20.58 |
% 53.64/20.58 | From (1425)(1423) and (590) follows:
% 53.64/20.58 | (1427) sum(n6, n6) = all_0_3_3
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (690) with n22, n16, all_0_0_0, n12 and discharging atoms sum(n22, n16) = all_0_0_0, sum(n22, n16) = n12, yields:
% 53.64/20.58 | (1195) all_0_0_0 = n12
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 53.64/20.58 | (1194) all_0_3_3 = n12
% 53.64/20.58 |
% 53.64/20.58 | Equations (1195,1194) can reduce 679 to:
% 53.64/20.58 | (1106) $false
% 53.64/20.58 |
% 53.64/20.58 |-The branch is then unsatisfiable
% 53.64/20.58 |-Branch two:
% 53.64/20.58 | (1359) ~ (all_0_11_11 = n11)
% 53.64/20.58 | (1360) 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
% 53.64/20.58 |
% 53.64/20.58 +-Applying beta-rule and splitting (1360), into two cases.
% 53.64/20.58 |-Branch one:
% 53.64/20.58 | (1361) all_0_11_11 = n10
% 53.64/20.58 |
% 53.64/20.58 | From (1361) and (559) follows:
% 53.64/20.58 | (1362) pred(n10) = all_0_9_9
% 53.64/20.58 |
% 53.64/20.58 | From (1361) and (992) follows:
% 53.64/20.58 | (1363) succ(n10) = all_0_5_5
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (500) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 53.64/20.58 | (1364) all_0_9_9 = n9
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (617) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 53.64/20.58 | (1365) all_0_5_5 = n11
% 53.64/20.58 |
% 53.64/20.58 | From (1364)(1365) and (538) follows:
% 53.64/20.58 | (1366) sum(n9, n11) = all_0_2_2
% 53.64/20.58 |
% 53.64/20.58 | From (1364) and (4652) follows:
% 53.64/20.58 | (4867) sum(n9, n22) = all_0_7_7
% 53.64/20.58 |
% 53.64/20.58 | From (1365) and (4650) follows:
% 53.64/20.58 | (4868) sum(n20, n11) = all_0_4_4
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (690) with n20, n11, all_0_4_4, n5 and discharging atoms sum(n20, n11) = all_0_4_4, sum(n20, n11) = n5, yields:
% 53.64/20.58 | (1441) all_0_4_4 = n5
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (690) with n9, n22, all_0_7_7, n5 and discharging atoms sum(n9, n22) = all_0_7_7, sum(n9, n22) = n5, yields:
% 53.64/20.58 | (1443) all_0_7_7 = n5
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (690) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 53.64/20.58 | (1136) all_0_2_2 = n20
% 53.64/20.58 |
% 53.64/20.58 | From (1136) and (4654) follows:
% 53.64/20.58 | (3422) sum(n20, n16) = all_0_0_0
% 53.64/20.58 |
% 53.64/20.58 | From (1443)(1441) and (590) follows:
% 53.64/20.58 | (1445) sum(n5, n5) = all_0_3_3
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (690) with n20, n16, all_0_0_0, n10 and discharging atoms sum(n20, n16) = all_0_0_0, sum(n20, n16) = n10, yields:
% 53.64/20.58 | (1213) all_0_0_0 = n10
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 53.64/20.58 | (1212) all_0_3_3 = n10
% 53.64/20.58 |
% 53.64/20.58 | Equations (1213,1212) can reduce 679 to:
% 53.64/20.58 | (1106) $false
% 53.64/20.58 |
% 53.64/20.58 |-The branch is then unsatisfiable
% 53.64/20.58 |-Branch two:
% 53.64/20.58 | (1377) ~ (all_0_11_11 = n10)
% 53.64/20.58 | (1378) 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
% 53.64/20.58 |
% 53.64/20.58 +-Applying beta-rule and splitting (1378), into two cases.
% 53.64/20.58 |-Branch one:
% 53.64/20.58 | (1379) all_0_11_11 = n9
% 53.64/20.58 |
% 53.64/20.58 | From (1379) and (559) follows:
% 53.64/20.58 | (1380) pred(n9) = all_0_9_9
% 53.64/20.58 |
% 53.64/20.58 | From (1379) and (992) follows:
% 53.64/20.58 | (1381) succ(n9) = all_0_5_5
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 53.64/20.58 | (1382) all_0_9_9 = n8
% 53.64/20.58 |
% 53.64/20.58 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 53.64/20.58 | (1383) all_0_5_5 = n10
% 53.64/20.58 |
% 53.64/20.58 | From (1382)(1383) and (538) follows:
% 53.64/20.58 | (1384) sum(n8, n10) = all_0_2_2
% 53.64/20.58 |
% 53.64/20.58 | From (1382) and (4652) follows:
% 53.64/20.59 | (4885) sum(n8, n22) = all_0_7_7
% 53.64/20.59 |
% 53.64/20.59 | From (1383) and (4650) follows:
% 53.64/20.59 | (4886) sum(n20, n10) = all_0_4_4
% 53.64/20.59 |
% 53.64/20.59 | Instantiating formula (690) with n20, n10, all_0_4_4, n4 and discharging atoms sum(n20, n10) = all_0_4_4, sum(n20, n10) = n4, yields:
% 53.64/20.59 | (1459) all_0_4_4 = n4
% 53.64/20.59 |
% 53.64/20.59 | Instantiating formula (690) with n8, n22, all_0_7_7, n4 and discharging atoms sum(n8, n22) = all_0_7_7, sum(n8, n22) = n4, yields:
% 53.98/20.59 | (1461) all_0_7_7 = n4
% 53.98/20.59 |
% 53.98/20.59 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 53.98/20.59 | (1154) all_0_2_2 = n18
% 53.98/20.59 |
% 53.98/20.59 | From (1154) and (4654) follows:
% 53.98/20.59 | (4260) sum(n18, n16) = all_0_0_0
% 53.98/20.59 |
% 53.98/20.59 | From (1461)(1459) and (590) follows:
% 53.98/20.59 | (1463) sum(n4, n4) = all_0_3_3
% 53.98/20.59 |
% 53.98/20.59 | Instantiating formula (690) with n18, n16, all_0_0_0, n8 and discharging atoms sum(n18, n16) = all_0_0_0, sum(n18, n16) = n8, yields:
% 53.98/20.59 | (1231) all_0_0_0 = n8
% 53.98/20.59 |
% 53.98/20.59 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 54.01/20.59 | (1230) all_0_3_3 = n8
% 54.01/20.59 |
% 54.01/20.59 | Equations (1231,1230) can reduce 679 to:
% 54.01/20.59 | (1106) $false
% 54.01/20.59 |
% 54.01/20.59 |-The branch is then unsatisfiable
% 54.01/20.59 |-Branch two:
% 54.01/20.59 | (1395) ~ (all_0_11_11 = n9)
% 54.01/20.59 | (1396) 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
% 54.01/20.59 |
% 54.01/20.59 +-Applying beta-rule and splitting (1396), into two cases.
% 54.01/20.59 |-Branch one:
% 54.01/20.59 | (1397) all_0_11_11 = n8
% 54.01/20.59 |
% 54.01/20.59 | From (1397) and (559) follows:
% 54.01/20.59 | (1398) pred(n8) = all_0_9_9
% 54.01/20.59 |
% 54.01/20.59 | From (1397) and (992) follows:
% 54.01/20.59 | (1399) succ(n8) = all_0_5_5
% 54.01/20.59 |
% 54.01/20.59 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 54.01/20.59 | (1400) all_0_9_9 = n7
% 54.01/20.59 |
% 54.01/20.59 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 54.01/20.59 | (1401) all_0_5_5 = n9
% 54.01/20.59 |
% 54.01/20.59 | From (1400)(1401) and (538) follows:
% 54.01/20.59 | (1402) sum(n7, n9) = all_0_2_2
% 54.01/20.59 |
% 54.01/20.59 | From (1400) and (4652) follows:
% 54.01/20.59 | (4903) sum(n7, n22) = all_0_7_7
% 54.01/20.59 |
% 54.01/20.59 | From (1401) and (4650) follows:
% 54.01/20.59 | (4904) sum(n20, n9) = all_0_4_4
% 54.01/20.59 |
% 54.01/20.59 | Instantiating formula (690) with n20, n9, all_0_4_4, n3 and discharging atoms sum(n20, n9) = all_0_4_4, sum(n20, n9) = n3, yields:
% 54.01/20.59 | (1477) all_0_4_4 = n3
% 54.01/20.59 |
% 54.01/20.59 | Instantiating formula (690) with n7, n22, all_0_7_7, n3 and discharging atoms sum(n7, n22) = all_0_7_7, sum(n7, n22) = n3, yields:
% 54.01/20.59 | (1479) all_0_7_7 = n3
% 54.01/20.59 |
% 54.01/20.59 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 54.01/20.59 | (1172) all_0_2_2 = n16
% 54.01/20.59 |
% 54.01/20.59 | From (1172) and (4654) follows:
% 54.01/20.59 | (4672) sum(n16, n16) = all_0_0_0
% 54.01/20.59 |
% 54.01/20.59 | From (1479)(1477) and (590) follows:
% 54.01/20.59 | (1481) sum(n3, n3) = all_0_3_3
% 54.01/20.59 |
% 54.01/20.59 | Instantiating formula (690) with n16, n16, all_0_0_0, n6 and discharging atoms sum(n16, n16) = all_0_0_0, sum(n16, n16) = n6, yields:
% 54.01/20.59 | (1249) all_0_0_0 = n6
% 54.01/20.59 |
% 54.01/20.59 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 54.01/20.59 | (1248) all_0_3_3 = n6
% 54.01/20.59 |
% 54.01/20.59 | Equations (1249,1248) can reduce 679 to:
% 54.01/20.59 | (1106) $false
% 54.01/20.59 |
% 54.01/20.59 |-The branch is then unsatisfiable
% 54.01/20.59 |-Branch two:
% 54.01/20.59 | (1413) ~ (all_0_11_11 = n8)
% 54.01/20.59 | (1414) 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
% 54.01/20.59 |
% 54.01/20.59 +-Applying beta-rule and splitting (1414), into two cases.
% 54.01/20.59 |-Branch one:
% 54.01/20.59 | (1415) all_0_11_11 = n7
% 54.01/20.59 |
% 54.01/20.59 | From (1415) and (559) follows:
% 54.01/20.59 | (1416) pred(n7) = all_0_9_9
% 54.01/20.59 |
% 54.01/20.59 | From (1415) and (992) follows:
% 54.01/20.59 | (1417) succ(n7) = all_0_5_5
% 54.01/20.59 |
% 54.01/20.59 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 54.01/20.59 | (1418) all_0_9_9 = n6
% 54.01/20.59 |
% 54.01/20.59 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 54.01/20.59 | (1419) all_0_5_5 = n8
% 54.01/20.59 |
% 54.01/20.59 | From (1418)(1419) and (538) follows:
% 54.01/20.59 | (1420) sum(n6, n8) = all_0_2_2
% 54.01/20.59 |
% 54.01/20.59 | From (1418) and (4652) follows:
% 54.01/20.59 | (4921) sum(n6, n22) = all_0_7_7
% 54.01/20.59 |
% 54.01/20.59 | From (1419) and (4650) follows:
% 54.01/20.59 | (4922) sum(n20, n8) = all_0_4_4
% 54.01/20.59 |
% 54.01/20.59 | Instantiating formula (690) with n20, n8, all_0_4_4, n2 and discharging atoms sum(n20, n8) = all_0_4_4, sum(n20, n8) = n2, yields:
% 54.01/20.59 | (1495) all_0_4_4 = n2
% 54.01/20.59 |
% 54.01/20.59 | Instantiating formula (690) with n6, n22, all_0_7_7, n2 and discharging atoms sum(n6, n22) = all_0_7_7, sum(n6, n22) = n2, yields:
% 54.01/20.59 | (1497) all_0_7_7 = n2
% 54.01/20.59 |
% 54.01/20.59 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 54.01/20.59 | (1190) all_0_2_2 = n14
% 54.01/20.59 |
% 54.01/20.59 | From (1190) and (4654) follows:
% 54.01/20.59 | (4692) sum(n14, n16) = all_0_0_0
% 54.01/20.59 |
% 54.01/20.59 | From (1497)(1495) and (590) follows:
% 54.01/20.59 | (1499) sum(n2, n2) = all_0_3_3
% 54.01/20.59 |
% 54.01/20.59 | Instantiating formula (690) with n14, n16, all_0_0_0, n4 and discharging atoms sum(n14, n16) = all_0_0_0, sum(n14, n16) = n4, yields:
% 54.01/20.59 | (1267) all_0_0_0 = n4
% 54.01/20.59 |
% 54.01/20.59 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 54.01/20.59 | (1266) all_0_3_3 = n4
% 54.01/20.59 |
% 54.01/20.59 | Equations (1267,1266) can reduce 679 to:
% 54.01/20.59 | (1106) $false
% 54.01/20.59 |
% 54.01/20.59 |-The branch is then unsatisfiable
% 54.01/20.59 |-Branch two:
% 54.01/20.59 | (1431) ~ (all_0_11_11 = n7)
% 54.01/20.59 | (1432) 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
% 54.01/20.59 |
% 54.01/20.59 +-Applying beta-rule and splitting (1432), into two cases.
% 54.01/20.59 |-Branch one:
% 54.01/20.59 | (1433) all_0_11_11 = n6
% 54.01/20.59 |
% 54.01/20.59 | From (1433) and (559) follows:
% 54.01/20.59 | (1434) pred(n6) = all_0_9_9
% 54.01/20.59 |
% 54.01/20.59 | From (1433) and (992) follows:
% 54.01/20.59 | (1435) succ(n6) = all_0_5_5
% 54.01/20.59 |
% 54.01/20.59 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 54.01/20.59 | (1436) all_0_9_9 = n5
% 54.01/20.59 |
% 54.01/20.59 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 54.01/20.59 | (1437) all_0_5_5 = n7
% 54.01/20.59 |
% 54.01/20.59 | From (1436)(1437) and (538) follows:
% 54.01/20.59 | (1438) sum(n5, n7) = all_0_2_2
% 54.01/20.59 |
% 54.01/20.59 | From (1436) and (4652) follows:
% 54.01/20.59 | (4939) sum(n5, n22) = all_0_7_7
% 54.01/20.59 |
% 54.01/20.59 | From (1437) and (4650) follows:
% 54.01/20.59 | (4940) sum(n20, n7) = all_0_4_4
% 54.01/20.59 |
% 54.01/20.59 | Instantiating formula (690) with n20, n7, all_0_4_4, n1 and discharging atoms sum(n20, n7) = all_0_4_4, sum(n20, n7) = n1, yields:
% 54.01/20.60 | (1513) all_0_4_4 = n1
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n5, n22, all_0_7_7, n1 and discharging atoms sum(n5, n22) = all_0_7_7, sum(n5, n22) = n1, yields:
% 54.01/20.60 | (1515) all_0_7_7 = n1
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 54.01/20.60 | (1208) all_0_2_2 = n12
% 54.01/20.60 |
% 54.01/20.60 | From (1208) and (4654) follows:
% 54.01/20.60 | (4710) sum(n12, n16) = all_0_0_0
% 54.01/20.60 |
% 54.01/20.60 | From (1515)(1513) and (590) follows:
% 54.01/20.60 | (1517) sum(n1, n1) = all_0_3_3
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n12, n16, all_0_0_0, n2 and discharging atoms sum(n12, n16) = all_0_0_0, sum(n12, n16) = n2, yields:
% 54.01/20.60 | (1285) all_0_0_0 = n2
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 54.01/20.60 | (1284) all_0_3_3 = n2
% 54.01/20.60 |
% 54.01/20.60 | Equations (1285,1284) can reduce 679 to:
% 54.01/20.60 | (1106) $false
% 54.01/20.60 |
% 54.01/20.60 |-The branch is then unsatisfiable
% 54.01/20.60 |-Branch two:
% 54.01/20.60 | (1449) ~ (all_0_11_11 = n6)
% 54.01/20.60 | (1450) 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
% 54.01/20.60 |
% 54.01/20.60 +-Applying beta-rule and splitting (1450), into two cases.
% 54.01/20.60 |-Branch one:
% 54.01/20.60 | (1451) all_0_11_11 = n5
% 54.01/20.60 |
% 54.01/20.60 | From (1451) and (559) follows:
% 54.01/20.60 | (1452) pred(n5) = all_0_9_9
% 54.01/20.60 |
% 54.01/20.60 | From (1451) and (992) follows:
% 54.01/20.60 | (1453) succ(n5) = all_0_5_5
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 54.01/20.60 | (1454) all_0_9_9 = n4
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 54.01/20.60 | (1455) all_0_5_5 = n6
% 54.01/20.60 |
% 54.01/20.60 | From (1454)(1455) and (538) follows:
% 54.01/20.60 | (1456) sum(n4, n6) = all_0_2_2
% 54.01/20.60 |
% 54.01/20.60 | From (1454) and (4652) follows:
% 54.01/20.60 | (4957) sum(n4, n22) = all_0_7_7
% 54.01/20.60 |
% 54.01/20.60 | From (1455) and (4650) follows:
% 54.01/20.60 | (4958) sum(n20, n6) = all_0_4_4
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n20, n6, all_0_4_4, n0 and discharging atoms sum(n20, n6) = all_0_4_4, sum(n20, n6) = n0, yields:
% 54.01/20.60 | (1531) all_0_4_4 = n0
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n4, n22, all_0_7_7, n0 and discharging atoms sum(n4, n22) = all_0_7_7, sum(n4, n22) = n0, yields:
% 54.01/20.60 | (1533) all_0_7_7 = n0
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 54.01/20.60 | (1226) all_0_2_2 = n10
% 54.01/20.60 |
% 54.01/20.60 | From (1226) and (4654) follows:
% 54.01/20.60 | (4728) sum(n10, n16) = all_0_0_0
% 54.01/20.60 |
% 54.01/20.60 | From (1533)(1531) and (590) follows:
% 54.01/20.60 | (1535) sum(n0, n0) = all_0_3_3
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n10, n16, all_0_0_0, n0 and discharging atoms sum(n10, n16) = all_0_0_0, sum(n10, n16) = n0, yields:
% 54.01/20.60 | (1303) all_0_0_0 = n0
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 54.01/20.60 | (1302) all_0_3_3 = n0
% 54.01/20.60 |
% 54.01/20.60 | Equations (1303,1302) can reduce 679 to:
% 54.01/20.60 | (1106) $false
% 54.01/20.60 |
% 54.01/20.60 |-The branch is then unsatisfiable
% 54.01/20.60 |-Branch two:
% 54.01/20.60 | (1467) ~ (all_0_11_11 = n5)
% 54.01/20.60 | (1468) 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
% 54.01/20.60 |
% 54.01/20.60 +-Applying beta-rule and splitting (1468), into two cases.
% 54.01/20.60 |-Branch one:
% 54.01/20.60 | (1469) all_0_11_11 = n4
% 54.01/20.60 |
% 54.01/20.60 | From (1469) and (559) follows:
% 54.01/20.60 | (1470) pred(n4) = all_0_9_9
% 54.01/20.60 |
% 54.01/20.60 | From (1469) and (992) follows:
% 54.01/20.60 | (1471) succ(n4) = all_0_5_5
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 54.01/20.60 | (1472) all_0_9_9 = n3
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 54.01/20.60 | (1473) all_0_5_5 = n5
% 54.01/20.60 |
% 54.01/20.60 | From (1472)(1473) and (538) follows:
% 54.01/20.60 | (1474) sum(n3, n5) = all_0_2_2
% 54.01/20.60 |
% 54.01/20.60 | From (1472) and (4652) follows:
% 54.01/20.60 | (4975) sum(n3, n22) = all_0_7_7
% 54.01/20.60 |
% 54.01/20.60 | From (1473) and (4650) follows:
% 54.01/20.60 | (4976) sum(n20, n5) = all_0_4_4
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n20, n5, all_0_4_4, n25 and discharging atoms sum(n20, n5) = all_0_4_4, sum(n20, n5) = n25, yields:
% 54.01/20.60 | (1551) all_0_4_4 = n25
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n3, n22, all_0_7_7, n25 and discharging atoms sum(n3, n22) = all_0_7_7, sum(n3, n22) = n25, yields:
% 54.01/20.60 | (1550) all_0_7_7 = n25
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 54.01/20.60 | (1244) all_0_2_2 = n8
% 54.01/20.60 |
% 54.01/20.60 | From (1244) and (4654) follows:
% 54.01/20.60 | (4746) sum(n8, n16) = all_0_0_0
% 54.01/20.60 |
% 54.01/20.60 | From (1550)(1551) and (590) follows:
% 54.01/20.60 | (1553) sum(n25, n25) = all_0_3_3
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 54.01/20.60 | (1320) all_0_3_3 = n24
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n8, n16, all_0_0_0, n24 and discharging atoms sum(n8, n16) = all_0_0_0, sum(n8, n16) = n24, yields:
% 54.01/20.60 | (1321) all_0_0_0 = n24
% 54.01/20.60 |
% 54.01/20.60 | Equations (1321,1320) can reduce 679 to:
% 54.01/20.60 | (1106) $false
% 54.01/20.60 |
% 54.01/20.60 |-The branch is then unsatisfiable
% 54.01/20.60 |-Branch two:
% 54.01/20.60 | (1485) ~ (all_0_11_11 = n4)
% 54.01/20.60 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 54.01/20.60 |
% 54.01/20.60 +-Applying beta-rule and splitting (1486), into two cases.
% 54.01/20.60 |-Branch one:
% 54.01/20.60 | (1487) all_0_11_11 = n3
% 54.01/20.60 |
% 54.01/20.60 | From (1487) and (559) follows:
% 54.01/20.60 | (1488) pred(n3) = all_0_9_9
% 54.01/20.60 |
% 54.01/20.60 | From (1487) and (992) follows:
% 54.01/20.60 | (1489) succ(n3) = all_0_5_5
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 54.01/20.60 | (1490) all_0_9_9 = n2
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 54.01/20.60 | (1491) all_0_5_5 = n4
% 54.01/20.60 |
% 54.01/20.60 | From (1490)(1491) and (538) follows:
% 54.01/20.60 | (1492) sum(n2, n4) = all_0_2_2
% 54.01/20.60 |
% 54.01/20.60 | From (1490) and (4652) follows:
% 54.01/20.60 | (4993) sum(n2, n22) = all_0_7_7
% 54.01/20.60 |
% 54.01/20.60 | From (1491) and (4650) follows:
% 54.01/20.60 | (4994) sum(n20, n4) = all_0_4_4
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n20, n4, all_0_4_4, n24 and discharging atoms sum(n20, n4) = all_0_4_4, sum(n20, n4) = n24, yields:
% 54.01/20.60 | (1096) all_0_4_4 = n24
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n2, n22, all_0_7_7, n24 and discharging atoms sum(n2, n22) = all_0_7_7, sum(n2, n22) = n24, yields:
% 54.01/20.60 | (1097) all_0_7_7 = n24
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 54.01/20.60 | (1262) all_0_2_2 = n6
% 54.01/20.60 |
% 54.01/20.60 | From (1262) and (4654) follows:
% 54.01/20.60 | (4764) sum(n6, n16) = all_0_0_0
% 54.01/20.60 |
% 54.01/20.60 | From (1097)(1096) and (590) follows:
% 54.01/20.60 | (1101) sum(n24, n24) = all_0_3_3
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 54.01/20.60 | (1104) all_0_3_3 = n22
% 54.01/20.60 |
% 54.01/20.60 | Instantiating formula (690) with n6, n16, all_0_0_0, n22 and discharging atoms sum(n6, n16) = all_0_0_0, sum(n6, n16) = n22, yields:
% 54.01/20.60 | (1102) all_0_0_0 = n22
% 54.01/20.60 |
% 54.01/20.60 | Equations (1102,1104) can reduce 679 to:
% 54.01/20.60 | (1106) $false
% 54.01/20.60 |
% 54.01/20.60 |-The branch is then unsatisfiable
% 54.01/20.60 |-Branch two:
% 54.01/20.60 | (1503) ~ (all_0_11_11 = n3)
% 54.01/20.60 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 54.01/20.60 |
% 54.01/20.61 +-Applying beta-rule and splitting (1504), into two cases.
% 54.01/20.61 |-Branch one:
% 54.01/20.61 | (1505) all_0_11_11 = n2
% 54.01/20.61 |
% 54.01/20.61 | From (1505) and (559) follows:
% 54.01/20.61 | (1506) pred(n2) = all_0_9_9
% 54.01/20.61 |
% 54.01/20.61 | From (1505) and (992) follows:
% 54.01/20.61 | (1507) succ(n2) = all_0_5_5
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 54.01/20.61 | (1508) all_0_9_9 = n1
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 54.01/20.61 | (1509) all_0_5_5 = n3
% 54.01/20.61 |
% 54.01/20.61 | From (1508)(1509) and (538) follows:
% 54.01/20.61 | (1510) sum(n1, n3) = all_0_2_2
% 54.01/20.61 |
% 54.01/20.61 | From (1508) and (4652) follows:
% 54.01/20.61 | (5011) sum(n1, n22) = all_0_7_7
% 54.01/20.61 |
% 54.01/20.61 | From (1509) and (4650) follows:
% 54.01/20.61 | (5012) sum(n20, n3) = all_0_4_4
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (690) with n20, n3, all_0_4_4, n23 and discharging atoms sum(n20, n3) = all_0_4_4, sum(n20, n3) = n23, yields:
% 54.01/20.61 | (1117) all_0_4_4 = n23
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (690) with n1, n22, all_0_7_7, n23 and discharging atoms sum(n1, n22) = all_0_7_7, sum(n1, n22) = n23, yields:
% 54.01/20.61 | (1119) all_0_7_7 = n23
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 54.01/20.61 | (1280) all_0_2_2 = n4
% 54.01/20.61 |
% 54.01/20.61 | From (1280) and (4654) follows:
% 54.01/20.61 | (4782) sum(n4, n16) = all_0_0_0
% 54.01/20.61 |
% 54.01/20.61 | From (1119)(1117) and (590) follows:
% 54.01/20.61 | (1121) sum(n23, n23) = all_0_3_3
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 54.01/20.61 | (1122) all_0_3_3 = n20
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (690) with n4, n16, all_0_0_0, n20 and discharging atoms sum(n4, n16) = all_0_0_0, sum(n4, n16) = n20, yields:
% 54.01/20.61 | (1123) all_0_0_0 = n20
% 54.01/20.61 |
% 54.01/20.61 | Equations (1123,1122) can reduce 679 to:
% 54.01/20.61 | (1106) $false
% 54.01/20.61 |
% 54.01/20.61 |-The branch is then unsatisfiable
% 54.01/20.61 |-Branch two:
% 54.01/20.61 | (1521) ~ (all_0_11_11 = n2)
% 54.01/20.61 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 54.01/20.61 |
% 54.01/20.61 +-Applying beta-rule and splitting (1522), into two cases.
% 54.01/20.61 |-Branch one:
% 54.01/20.61 | (1523) all_0_11_11 = n1
% 54.01/20.61 |
% 54.01/20.61 | From (1523) and (559) follows:
% 54.01/20.61 | (1524) pred(n1) = all_0_9_9
% 54.01/20.61 |
% 54.01/20.61 | From (1523) and (992) follows:
% 54.01/20.61 | (1525) succ(n1) = all_0_5_5
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 54.01/20.61 | (1526) all_0_9_9 = n0
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 54.01/20.61 | (1527) all_0_5_5 = n2
% 54.01/20.61 |
% 54.01/20.61 | From (1526)(1527) and (538) follows:
% 54.01/20.61 | (1528) sum(n0, n2) = all_0_2_2
% 54.01/20.61 |
% 54.01/20.61 | From (1526) and (4652) follows:
% 54.01/20.61 | (5029) sum(n0, n22) = all_0_7_7
% 54.01/20.61 |
% 54.01/20.61 | From (1527) and (4650) follows:
% 54.01/20.61 | (5030) sum(n20, n2) = all_0_4_4
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (690) with n20, n2, all_0_4_4, n22 and discharging atoms sum(n20, n2) = all_0_4_4, sum(n20, n2) = n22, yields:
% 54.01/20.61 | (1135) all_0_4_4 = n22
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (690) with n0, n22, all_0_7_7, n22 and discharging atoms sum(n0, n22) = all_0_7_7, sum(n0, n22) = n22, yields:
% 54.01/20.61 | (1137) all_0_7_7 = n22
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 54.01/20.61 | (1298) all_0_2_2 = n2
% 54.01/20.61 |
% 54.01/20.61 | From (1298) and (4654) follows:
% 54.01/20.61 | (4800) sum(n2, n16) = all_0_0_0
% 54.01/20.61 |
% 54.01/20.61 | From (1137)(1135) and (590) follows:
% 54.01/20.61 | (1139) sum(n22, n22) = all_0_3_3
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 54.01/20.61 | (1140) all_0_3_3 = n18
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (690) with n2, n16, all_0_0_0, n18 and discharging atoms sum(n2, n16) = all_0_0_0, sum(n2, n16) = n18, yields:
% 54.01/20.61 | (1141) all_0_0_0 = n18
% 54.01/20.61 |
% 54.01/20.61 | Equations (1141,1140) can reduce 679 to:
% 54.01/20.61 | (1106) $false
% 54.01/20.61 |
% 54.01/20.61 |-The branch is then unsatisfiable
% 54.01/20.61 |-Branch two:
% 54.01/20.61 | (1540) ~ (all_0_11_11 = n1)
% 54.01/20.61 | (1541) all_0_11_11 = n0
% 54.01/20.61 |
% 54.01/20.61 | From (1541) and (559) follows:
% 54.01/20.61 | (1542) pred(n0) = all_0_9_9
% 54.01/20.61 |
% 54.01/20.61 | From (1541) and (992) follows:
% 54.01/20.61 | (1543) succ(n0) = all_0_5_5
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 54.01/20.61 | (1544) all_0_9_9 = n25
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 54.01/20.61 | (1545) all_0_5_5 = n1
% 54.01/20.61 |
% 54.01/20.61 | From (1544)(1545) and (538) follows:
% 54.01/20.61 | (1546) sum(n25, n1) = all_0_2_2
% 54.01/20.61 |
% 54.01/20.61 | From (1544) and (4652) follows:
% 54.01/20.61 | (5046) sum(n25, n22) = all_0_7_7
% 54.01/20.61 |
% 54.01/20.61 | From (1545) and (4650) follows:
% 54.01/20.61 | (5047) sum(n20, n1) = all_0_4_4
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (690) with n25, n22, all_0_7_7, n21 and discharging atoms sum(n25, n22) = all_0_7_7, sum(n25, n22) = n21, yields:
% 54.01/20.61 | (1155) all_0_7_7 = n21
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 54.01/20.61 | (1316) all_0_2_2 = n0
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (690) with n20, n1, all_0_4_4, n21 and discharging atoms sum(n20, n1) = all_0_4_4, sum(n20, n1) = n21, yields:
% 54.01/20.61 | (1153) all_0_4_4 = n21
% 54.01/20.61 |
% 54.01/20.61 | From (1316) and (4654) follows:
% 54.01/20.61 | (4818) sum(n0, n16) = all_0_0_0
% 54.01/20.61 |
% 54.01/20.61 | From (1155)(1153) and (590) follows:
% 54.01/20.61 | (1157) sum(n21, n21) = all_0_3_3
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 54.01/20.61 | (1158) all_0_3_3 = n16
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (690) with n0, n16, all_0_0_0, n16 and discharging atoms sum(n0, n16) = all_0_0_0, sum(n0, n16) = n16, yields:
% 54.01/20.61 | (1159) all_0_0_0 = n16
% 54.01/20.61 |
% 54.01/20.61 | Equations (1159,1158) can reduce 679 to:
% 54.01/20.61 | (1106) $false
% 54.01/20.61 |
% 54.01/20.61 |-The branch is then unsatisfiable
% 54.01/20.61 |-Branch two:
% 54.01/20.61 | (1640) ~ (all_0_10_10 = n21)
% 54.01/20.61 | (1641) 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
% 54.01/20.61 |
% 54.01/20.61 +-Applying beta-rule and splitting (1162), into two cases.
% 54.01/20.61 |-Branch one:
% 54.01/20.61 | (1163) all_0_11_11 = n21
% 54.01/20.61 |
% 54.01/20.61 | From (1163) and (559) follows:
% 54.01/20.61 | (1164) pred(n21) = all_0_9_9
% 54.01/20.61 |
% 54.01/20.61 | From (1163) and (992) follows:
% 54.01/20.61 | (1165) succ(n21) = all_0_5_5
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (500) with n21, all_0_9_9, n20 and discharging atoms pred(n21) = all_0_9_9, pred(n21) = n20, yields:
% 54.01/20.61 | (1166) all_0_9_9 = n20
% 54.01/20.61 |
% 54.01/20.61 | Instantiating formula (617) with n21, all_0_5_5, n22 and discharging atoms succ(n21) = all_0_5_5, succ(n21) = n22, yields:
% 54.01/20.61 | (1167) all_0_5_5 = n22
% 54.01/20.61 |
% 54.01/20.61 | From (1167) and (541) follows:
% 54.11/20.61 | (5063) sum(all_0_6_6, n22) = all_0_4_4
% 54.11/20.61 |
% 54.11/20.61 | From (1166)(1167) and (538) follows:
% 54.11/20.62 | (1168) sum(n20, n22) = all_0_2_2
% 54.11/20.62 |
% 54.11/20.62 | From (1166) and (427) follows:
% 54.11/20.62 | (5065) sum(n20, all_0_8_8) = all_0_7_7
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (690) with n20, n22, all_0_2_2, n16 and discharging atoms sum(n20, n22) = all_0_2_2, sum(n20, n22) = n16, yields:
% 54.11/20.62 | (1172) all_0_2_2 = n16
% 54.11/20.62 |
% 54.11/20.62 | From (1172) and (630) follows:
% 54.11/20.62 | (5067) sum(n16, all_0_1_1) = all_0_0_0
% 54.11/20.62 |
% 54.11/20.62 +-Applying beta-rule and splitting (1641), into two cases.
% 54.11/20.62 |-Branch one:
% 54.11/20.62 | (1642) all_0_10_10 = n20
% 54.11/20.62 |
% 54.11/20.62 | From (1642) and (292) follows:
% 54.11/20.62 | (1643) pred(n20) = all_0_6_6
% 54.11/20.62 |
% 54.11/20.62 | From (1642) and (760) follows:
% 54.11/20.62 | (1644) succ(n20) = all_0_8_8
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (500) with n20, all_0_6_6, n19 and discharging atoms pred(n20) = all_0_6_6, pred(n20) = n19, yields:
% 54.11/20.62 | (1645) all_0_6_6 = n19
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (617) with n20, all_0_8_8, n21 and discharging atoms succ(n20) = all_0_8_8, succ(n20) = n21, yields:
% 54.11/20.62 | (1646) all_0_8_8 = n21
% 54.11/20.62 |
% 54.11/20.62 | From (1645)(1646) and (411) follows:
% 54.11/20.62 | (1647) sum(n19, n21) = all_0_1_1
% 54.11/20.62 |
% 54.11/20.62 | From (1645) and (5063) follows:
% 54.11/20.62 | (5074) sum(n19, n22) = all_0_4_4
% 54.11/20.62 |
% 54.11/20.62 | From (1646) and (5065) follows:
% 54.11/20.62 | (5075) sum(n20, n21) = all_0_7_7
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (690) with n20, n21, all_0_7_7, n15 and discharging atoms sum(n20, n21) = all_0_7_7, sum(n20, n21) = n15, yields:
% 54.11/20.62 | (1263) all_0_7_7 = n15
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (690) with n19, n22, all_0_4_4, n15 and discharging atoms sum(n19, n22) = all_0_4_4, sum(n19, n22) = n15, yields:
% 54.11/20.62 | (1261) all_0_4_4 = n15
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (690) with n19, n21, all_0_1_1, n14 and discharging atoms sum(n19, n21) = all_0_1_1, sum(n19, n21) = n14, yields:
% 54.11/20.62 | (1651) all_0_1_1 = n14
% 54.11/20.62 |
% 54.11/20.62 | From (1263)(1261) and (590) follows:
% 54.11/20.62 | (1265) sum(n15, n15) = all_0_3_3
% 54.11/20.62 |
% 54.11/20.62 | From (1651) and (5067) follows:
% 54.11/20.62 | (5080) sum(n16, n14) = all_0_0_0
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (690) with n16, n14, all_0_0_0, n4 and discharging atoms sum(n16, n14) = all_0_0_0, sum(n16, n14) = n4, yields:
% 54.11/20.62 | (1267) all_0_0_0 = n4
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 54.11/20.62 | (1266) all_0_3_3 = n4
% 54.11/20.62 |
% 54.11/20.62 | Equations (1267,1266) can reduce 679 to:
% 54.11/20.62 | (1106) $false
% 54.11/20.62 |
% 54.11/20.62 |-The branch is then unsatisfiable
% 54.11/20.62 |-Branch two:
% 54.11/20.62 | (1658) ~ (all_0_10_10 = n20)
% 54.11/20.62 | (1659) 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
% 54.11/20.62 |
% 54.11/20.62 +-Applying beta-rule and splitting (1659), into two cases.
% 54.11/20.62 |-Branch one:
% 54.11/20.62 | (1660) all_0_10_10 = n19
% 54.11/20.62 |
% 54.11/20.62 | From (1660) and (292) follows:
% 54.11/20.62 | (1661) pred(n19) = all_0_6_6
% 54.11/20.62 |
% 54.11/20.62 | From (1660) and (760) follows:
% 54.11/20.62 | (1662) succ(n19) = all_0_8_8
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (500) with n19, all_0_6_6, n18 and discharging atoms pred(n19) = all_0_6_6, pred(n19) = n18, yields:
% 54.11/20.62 | (1663) all_0_6_6 = n18
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (617) with n19, all_0_8_8, n20 and discharging atoms succ(n19) = all_0_8_8, succ(n19) = n20, yields:
% 54.11/20.62 | (1664) all_0_8_8 = n20
% 54.11/20.62 |
% 54.11/20.62 | From (1663)(1664) and (411) follows:
% 54.11/20.62 | (1665) sum(n18, n20) = all_0_1_1
% 54.11/20.62 |
% 54.11/20.62 | From (1663) and (5063) follows:
% 54.11/20.62 | (5092) sum(n18, n22) = all_0_4_4
% 54.11/20.62 |
% 54.11/20.62 | From (1664) and (5065) follows:
% 54.11/20.62 | (5093) sum(n20, n20) = all_0_7_7
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (690) with n20, n20, all_0_7_7, n14 and discharging atoms sum(n20, n20) = all_0_7_7, sum(n20, n20) = n14, yields:
% 54.11/20.62 | (1281) all_0_7_7 = n14
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (690) with n18, n22, all_0_4_4, n14 and discharging atoms sum(n18, n22) = all_0_4_4, sum(n18, n22) = n14, yields:
% 54.11/20.62 | (1279) all_0_4_4 = n14
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (690) with n18, n20, all_0_1_1, n12 and discharging atoms sum(n18, n20) = all_0_1_1, sum(n18, n20) = n12, yields:
% 54.11/20.62 | (1669) all_0_1_1 = n12
% 54.11/20.62 |
% 54.11/20.62 | From (1281)(1279) and (590) follows:
% 54.11/20.62 | (1283) sum(n14, n14) = all_0_3_3
% 54.11/20.62 |
% 54.11/20.62 | From (1669) and (5067) follows:
% 54.11/20.62 | (5098) sum(n16, n12) = all_0_0_0
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (690) with n16, n12, all_0_0_0, n2 and discharging atoms sum(n16, n12) = all_0_0_0, sum(n16, n12) = n2, yields:
% 54.11/20.62 | (1285) all_0_0_0 = n2
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 54.11/20.62 | (1284) all_0_3_3 = n2
% 54.11/20.62 |
% 54.11/20.62 | Equations (1285,1284) can reduce 679 to:
% 54.11/20.62 | (1106) $false
% 54.11/20.62 |
% 54.11/20.62 |-The branch is then unsatisfiable
% 54.11/20.62 |-Branch two:
% 54.11/20.62 | (1676) ~ (all_0_10_10 = n19)
% 54.11/20.62 | (1677) 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
% 54.11/20.62 |
% 54.11/20.62 +-Applying beta-rule and splitting (1677), into two cases.
% 54.11/20.62 |-Branch one:
% 54.11/20.62 | (1678) all_0_10_10 = n18
% 54.11/20.62 |
% 54.11/20.62 | From (1678) and (292) follows:
% 54.11/20.62 | (1679) pred(n18) = all_0_6_6
% 54.11/20.62 |
% 54.11/20.62 | From (1678) and (760) follows:
% 54.11/20.62 | (1680) succ(n18) = all_0_8_8
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (500) with n18, all_0_6_6, n17 and discharging atoms pred(n18) = all_0_6_6, pred(n18) = n17, yields:
% 54.11/20.62 | (1681) all_0_6_6 = n17
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (617) with n18, all_0_8_8, n19 and discharging atoms succ(n18) = all_0_8_8, succ(n18) = n19, yields:
% 54.11/20.62 | (1682) all_0_8_8 = n19
% 54.11/20.62 |
% 54.11/20.62 | From (1681)(1682) and (411) follows:
% 54.11/20.62 | (1683) sum(n17, n19) = all_0_1_1
% 54.11/20.62 |
% 54.11/20.62 | From (1681) and (5063) follows:
% 54.11/20.62 | (5110) sum(n17, n22) = all_0_4_4
% 54.11/20.62 |
% 54.11/20.62 | From (1682) and (5065) follows:
% 54.11/20.62 | (5111) sum(n20, n19) = all_0_7_7
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (690) with n20, n19, all_0_7_7, n13 and discharging atoms sum(n20, n19) = all_0_7_7, sum(n20, n19) = n13, yields:
% 54.11/20.62 | (1299) all_0_7_7 = n13
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (690) with n17, n22, all_0_4_4, n13 and discharging atoms sum(n17, n22) = all_0_4_4, sum(n17, n22) = n13, yields:
% 54.11/20.62 | (1297) all_0_4_4 = n13
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (690) with n17, n19, all_0_1_1, n10 and discharging atoms sum(n17, n19) = all_0_1_1, sum(n17, n19) = n10, yields:
% 54.11/20.62 | (1687) all_0_1_1 = n10
% 54.11/20.62 |
% 54.11/20.62 | From (1299)(1297) and (590) follows:
% 54.11/20.62 | (1301) sum(n13, n13) = all_0_3_3
% 54.11/20.62 |
% 54.11/20.62 | From (1687) and (5067) follows:
% 54.11/20.62 | (5116) sum(n16, n10) = all_0_0_0
% 54.11/20.62 |
% 54.11/20.62 | Instantiating formula (690) with n16, n10, all_0_0_0, n0 and discharging atoms sum(n16, n10) = all_0_0_0, sum(n16, n10) = n0, yields:
% 54.15/20.62 | (1303) all_0_0_0 = n0
% 54.15/20.62 |
% 54.15/20.62 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 54.15/20.62 | (1302) all_0_3_3 = n0
% 54.15/20.62 |
% 54.15/20.62 | Equations (1303,1302) can reduce 679 to:
% 54.15/20.62 | (1106) $false
% 54.15/20.62 |
% 54.15/20.62 |-The branch is then unsatisfiable
% 54.15/20.62 |-Branch two:
% 54.15/20.62 | (1694) ~ (all_0_10_10 = n18)
% 54.15/20.62 | (1695) 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
% 54.15/20.63 |
% 54.15/20.63 +-Applying beta-rule and splitting (1695), into two cases.
% 54.15/20.63 |-Branch one:
% 54.15/20.63 | (1696) all_0_10_10 = n17
% 54.15/20.63 |
% 54.15/20.63 | From (1696) and (292) follows:
% 54.15/20.63 | (1697) pred(n17) = all_0_6_6
% 54.15/20.63 |
% 54.15/20.63 | From (1696) and (760) follows:
% 54.15/20.63 | (1698) succ(n17) = all_0_8_8
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (500) with n17, all_0_6_6, n16 and discharging atoms pred(n17) = all_0_6_6, pred(n17) = n16, yields:
% 54.15/20.63 | (1699) all_0_6_6 = n16
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (617) with n17, all_0_8_8, n18 and discharging atoms succ(n17) = all_0_8_8, succ(n17) = n18, yields:
% 54.15/20.63 | (1700) all_0_8_8 = n18
% 54.15/20.63 |
% 54.15/20.63 | From (1699)(1700) and (411) follows:
% 54.15/20.63 | (1701) sum(n16, n18) = all_0_1_1
% 54.15/20.63 |
% 54.15/20.63 | From (1699) and (5063) follows:
% 54.15/20.63 | (5128) sum(n16, n22) = all_0_4_4
% 54.15/20.63 |
% 54.15/20.63 | From (1700) and (5065) follows:
% 54.15/20.63 | (5129) sum(n20, n18) = all_0_7_7
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (690) with n20, n18, all_0_7_7, n12 and discharging atoms sum(n20, n18) = all_0_7_7, sum(n20, n18) = n12, yields:
% 54.15/20.63 | (1317) all_0_7_7 = n12
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (690) with n16, n22, all_0_4_4, n12 and discharging atoms sum(n16, n22) = all_0_4_4, sum(n16, n22) = n12, yields:
% 54.15/20.63 | (1315) all_0_4_4 = n12
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (690) with n16, n18, all_0_1_1, n8 and discharging atoms sum(n16, n18) = all_0_1_1, sum(n16, n18) = n8, yields:
% 54.15/20.63 | (1705) all_0_1_1 = n8
% 54.15/20.63 |
% 54.15/20.63 | From (1317)(1315) and (590) follows:
% 54.15/20.63 | (1319) sum(n12, n12) = all_0_3_3
% 54.15/20.63 |
% 54.15/20.63 | From (1705) and (5067) follows:
% 54.15/20.63 | (5134) sum(n16, n8) = all_0_0_0
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (690) with n16, n8, all_0_0_0, n24 and discharging atoms sum(n16, n8) = all_0_0_0, sum(n16, n8) = n24, yields:
% 54.15/20.63 | (1321) all_0_0_0 = n24
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 54.15/20.63 | (1320) all_0_3_3 = n24
% 54.15/20.63 |
% 54.15/20.63 | Equations (1321,1320) can reduce 679 to:
% 54.15/20.63 | (1106) $false
% 54.15/20.63 |
% 54.15/20.63 |-The branch is then unsatisfiable
% 54.15/20.63 |-Branch two:
% 54.15/20.63 | (1712) ~ (all_0_10_10 = n17)
% 54.15/20.63 | (1713) 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
% 54.15/20.63 |
% 54.15/20.63 +-Applying beta-rule and splitting (1713), into two cases.
% 54.15/20.63 |-Branch one:
% 54.15/20.63 | (1714) all_0_10_10 = n16
% 54.15/20.63 |
% 54.15/20.63 | From (1714) and (292) follows:
% 54.15/20.63 | (1715) pred(n16) = all_0_6_6
% 54.15/20.63 |
% 54.15/20.63 | From (1714) and (760) follows:
% 54.15/20.63 | (1716) succ(n16) = all_0_8_8
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (500) with n16, all_0_6_6, n15 and discharging atoms pred(n16) = all_0_6_6, pred(n16) = n15, yields:
% 54.15/20.63 | (1717) all_0_6_6 = n15
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (617) with n16, all_0_8_8, n17 and discharging atoms succ(n16) = all_0_8_8, succ(n16) = n17, yields:
% 54.15/20.63 | (1718) all_0_8_8 = n17
% 54.15/20.63 |
% 54.15/20.63 | From (1717)(1718) and (411) follows:
% 54.15/20.63 | (1719) sum(n15, n17) = all_0_1_1
% 54.15/20.63 |
% 54.15/20.63 | From (1717) and (5063) follows:
% 54.15/20.63 | (5146) sum(n15, n22) = all_0_4_4
% 54.15/20.63 |
% 54.15/20.63 | From (1718) and (5065) follows:
% 54.15/20.63 | (5147) sum(n20, n17) = all_0_7_7
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (690) with n20, n17, all_0_7_7, n11 and discharging atoms sum(n20, n17) = all_0_7_7, sum(n20, n17) = n11, yields:
% 54.15/20.63 | (1335) all_0_7_7 = n11
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (690) with n15, n22, all_0_4_4, n11 and discharging atoms sum(n15, n22) = all_0_4_4, sum(n15, n22) = n11, yields:
% 54.15/20.63 | (1333) all_0_4_4 = n11
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (690) with n15, n17, all_0_1_1, n6 and discharging atoms sum(n15, n17) = all_0_1_1, sum(n15, n17) = n6, yields:
% 54.15/20.63 | (1723) all_0_1_1 = n6
% 54.15/20.63 |
% 54.15/20.63 | From (1335)(1333) and (590) follows:
% 54.15/20.63 | (1337) sum(n11, n11) = all_0_3_3
% 54.15/20.63 |
% 54.15/20.63 | From (1723) and (5067) follows:
% 54.15/20.63 | (5152) sum(n16, n6) = all_0_0_0
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (690) with n16, n6, all_0_0_0, n22 and discharging atoms sum(n16, n6) = all_0_0_0, sum(n16, n6) = n22, yields:
% 54.15/20.63 | (1102) all_0_0_0 = n22
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 54.15/20.63 | (1104) all_0_3_3 = n22
% 54.15/20.63 |
% 54.15/20.63 | Equations (1102,1104) can reduce 679 to:
% 54.15/20.63 | (1106) $false
% 54.15/20.63 |
% 54.15/20.63 |-The branch is then unsatisfiable
% 54.15/20.63 |-Branch two:
% 54.15/20.63 | (1730) ~ (all_0_10_10 = n16)
% 54.15/20.63 | (1731) 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
% 54.15/20.63 |
% 54.15/20.63 +-Applying beta-rule and splitting (1731), into two cases.
% 54.15/20.63 |-Branch one:
% 54.15/20.63 | (1732) all_0_10_10 = n15
% 54.15/20.63 |
% 54.15/20.63 | From (1732) and (292) follows:
% 54.15/20.63 | (1733) pred(n15) = all_0_6_6
% 54.15/20.63 |
% 54.15/20.63 | From (1732) and (760) follows:
% 54.15/20.63 | (1734) succ(n15) = all_0_8_8
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (500) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 54.15/20.63 | (1735) all_0_6_6 = n14
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (617) with n15, all_0_8_8, n16 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n16, yields:
% 54.15/20.63 | (1736) all_0_8_8 = n16
% 54.15/20.63 |
% 54.15/20.63 | From (1735)(1736) and (411) follows:
% 54.15/20.63 | (1737) sum(n14, n16) = all_0_1_1
% 54.15/20.63 |
% 54.15/20.63 | From (1735) and (5063) follows:
% 54.15/20.63 | (5164) sum(n14, n22) = all_0_4_4
% 54.15/20.63 |
% 54.15/20.63 | From (1736) and (5065) follows:
% 54.15/20.63 | (5165) sum(n20, n16) = all_0_7_7
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (690) with n20, n16, all_0_7_7, n10 and discharging atoms sum(n20, n16) = all_0_7_7, sum(n20, n16) = n10, yields:
% 54.15/20.63 | (1353) all_0_7_7 = n10
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (690) with n14, n22, all_0_4_4, n10 and discharging atoms sum(n14, n22) = all_0_4_4, sum(n14, n22) = n10, yields:
% 54.15/20.63 | (1351) all_0_4_4 = n10
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (690) with n14, n16, all_0_1_1, n4 and discharging atoms sum(n14, n16) = all_0_1_1, sum(n14, n16) = n4, yields:
% 54.15/20.63 | (1741) all_0_1_1 = n4
% 54.15/20.63 |
% 54.15/20.63 | From (1353)(1351) and (590) follows:
% 54.15/20.63 | (1355) sum(n10, n10) = all_0_3_3
% 54.15/20.63 |
% 54.15/20.63 | From (1741) and (5067) follows:
% 54.15/20.63 | (5170) sum(n16, n4) = all_0_0_0
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (690) with n16, n4, all_0_0_0, n20 and discharging atoms sum(n16, n4) = all_0_0_0, sum(n16, n4) = n20, yields:
% 54.15/20.63 | (1123) all_0_0_0 = n20
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 54.15/20.63 | (1122) all_0_3_3 = n20
% 54.15/20.63 |
% 54.15/20.63 | Equations (1123,1122) can reduce 679 to:
% 54.15/20.63 | (1106) $false
% 54.15/20.63 |
% 54.15/20.63 |-The branch is then unsatisfiable
% 54.15/20.63 |-Branch two:
% 54.15/20.63 | (1748) ~ (all_0_10_10 = n15)
% 54.15/20.63 | (1749) 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
% 54.15/20.63 |
% 54.15/20.63 +-Applying beta-rule and splitting (1749), into two cases.
% 54.15/20.63 |-Branch one:
% 54.15/20.63 | (1750) all_0_10_10 = n14
% 54.15/20.63 |
% 54.15/20.63 | From (1750) and (292) follows:
% 54.15/20.63 | (1751) pred(n14) = all_0_6_6
% 54.15/20.63 |
% 54.15/20.63 | From (1750) and (760) follows:
% 54.15/20.63 | (1752) succ(n14) = all_0_8_8
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (500) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 54.15/20.63 | (1753) all_0_6_6 = n13
% 54.15/20.63 |
% 54.15/20.63 | Instantiating formula (617) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 54.15/20.64 | (1754) all_0_8_8 = n15
% 54.15/20.64 |
% 54.15/20.64 | From (1753)(1754) and (411) follows:
% 54.15/20.64 | (1755) sum(n13, n15) = all_0_1_1
% 54.15/20.64 |
% 54.15/20.64 | From (1753) and (5063) follows:
% 54.15/20.64 | (5182) sum(n13, n22) = all_0_4_4
% 54.15/20.64 |
% 54.15/20.64 | From (1754) and (5065) follows:
% 54.15/20.64 | (5183) sum(n20, n15) = all_0_7_7
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (690) with n20, n15, all_0_7_7, n9 and discharging atoms sum(n20, n15) = all_0_7_7, sum(n20, n15) = n9, yields:
% 54.15/20.64 | (1371) all_0_7_7 = n9
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (690) with n13, n22, all_0_4_4, n9 and discharging atoms sum(n13, n22) = all_0_4_4, sum(n13, n22) = n9, yields:
% 54.15/20.64 | (1369) all_0_4_4 = n9
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (690) with n13, n15, all_0_1_1, n2 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n2, yields:
% 54.15/20.64 | (1759) all_0_1_1 = n2
% 54.15/20.64 |
% 54.15/20.64 | From (1371)(1369) and (590) follows:
% 54.15/20.64 | (1373) sum(n9, n9) = all_0_3_3
% 54.15/20.64 |
% 54.15/20.64 | From (1759) and (5067) follows:
% 54.15/20.64 | (5188) sum(n16, n2) = all_0_0_0
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (690) with n16, n2, all_0_0_0, n18 and discharging atoms sum(n16, n2) = all_0_0_0, sum(n16, n2) = n18, yields:
% 54.15/20.64 | (1141) all_0_0_0 = n18
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 54.15/20.64 | (1140) all_0_3_3 = n18
% 54.15/20.64 |
% 54.15/20.64 | Equations (1141,1140) can reduce 679 to:
% 54.15/20.64 | (1106) $false
% 54.15/20.64 |
% 54.15/20.64 |-The branch is then unsatisfiable
% 54.15/20.64 |-Branch two:
% 54.15/20.64 | (1766) ~ (all_0_10_10 = n14)
% 54.15/20.64 | (1767) 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
% 54.15/20.64 |
% 54.15/20.64 +-Applying beta-rule and splitting (1767), into two cases.
% 54.15/20.64 |-Branch one:
% 54.15/20.64 | (1768) all_0_10_10 = n13
% 54.15/20.64 |
% 54.15/20.64 | From (1768) and (292) follows:
% 54.15/20.64 | (1769) pred(n13) = all_0_6_6
% 54.15/20.64 |
% 54.15/20.64 | From (1768) and (760) follows:
% 54.15/20.64 | (1770) succ(n13) = all_0_8_8
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (500) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 54.15/20.64 | (1771) all_0_6_6 = n12
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (617) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 54.15/20.64 | (1772) all_0_8_8 = n14
% 54.15/20.64 |
% 54.15/20.64 | From (1771)(1772) and (411) follows:
% 54.15/20.64 | (1773) sum(n12, n14) = all_0_1_1
% 54.15/20.64 |
% 54.15/20.64 | From (1771) and (5063) follows:
% 54.15/20.64 | (5200) sum(n12, n22) = all_0_4_4
% 54.15/20.64 |
% 54.15/20.64 | From (1772) and (5065) follows:
% 54.15/20.64 | (5201) sum(n20, n14) = all_0_7_7
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (690) with n20, n14, all_0_7_7, n8 and discharging atoms sum(n20, n14) = all_0_7_7, sum(n20, n14) = n8, yields:
% 54.15/20.64 | (1389) all_0_7_7 = n8
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (690) with n12, n22, all_0_4_4, n8 and discharging atoms sum(n12, n22) = all_0_4_4, sum(n12, n22) = n8, yields:
% 54.15/20.64 | (1387) all_0_4_4 = n8
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (690) with n12, n14, all_0_1_1, n0 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n0, yields:
% 54.15/20.64 | (1777) all_0_1_1 = n0
% 54.15/20.64 |
% 54.15/20.64 | From (1389)(1387) and (590) follows:
% 54.15/20.64 | (1391) sum(n8, n8) = all_0_3_3
% 54.15/20.64 |
% 54.15/20.64 | From (1777) and (5067) follows:
% 54.15/20.64 | (5206) sum(n16, n0) = all_0_0_0
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (690) with n16, n0, all_0_0_0, n16 and discharging atoms sum(n16, n0) = all_0_0_0, sum(n16, n0) = n16, yields:
% 54.15/20.64 | (1159) all_0_0_0 = n16
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 54.15/20.64 | (1158) all_0_3_3 = n16
% 54.15/20.64 |
% 54.15/20.64 | Equations (1159,1158) can reduce 679 to:
% 54.15/20.64 | (1106) $false
% 54.15/20.64 |
% 54.15/20.64 |-The branch is then unsatisfiable
% 54.15/20.64 |-Branch two:
% 54.15/20.64 | (1784) ~ (all_0_10_10 = n13)
% 54.15/20.64 | (1785) 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
% 54.15/20.64 |
% 54.15/20.64 +-Applying beta-rule and splitting (1785), into two cases.
% 54.15/20.64 |-Branch one:
% 54.15/20.64 | (1786) all_0_10_10 = n12
% 54.15/20.64 |
% 54.15/20.64 | From (1786) and (292) follows:
% 54.15/20.64 | (1787) pred(n12) = all_0_6_6
% 54.15/20.64 |
% 54.15/20.64 | From (1786) and (760) follows:
% 54.15/20.64 | (1788) succ(n12) = all_0_8_8
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (500) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 54.15/20.64 | (1789) all_0_6_6 = n11
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (617) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 54.15/20.64 | (1790) all_0_8_8 = n13
% 54.15/20.64 |
% 54.15/20.64 | From (1789)(1790) and (411) follows:
% 54.15/20.64 | (1791) sum(n11, n13) = all_0_1_1
% 54.15/20.64 |
% 54.15/20.64 | From (1789) and (5063) follows:
% 54.15/20.64 | (5218) sum(n11, n22) = all_0_4_4
% 54.15/20.64 |
% 54.15/20.64 | From (1790) and (5065) follows:
% 54.15/20.64 | (5219) sum(n20, n13) = all_0_7_7
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (690) with n20, n13, all_0_7_7, n7 and discharging atoms sum(n20, n13) = all_0_7_7, sum(n20, n13) = n7, yields:
% 54.15/20.64 | (1407) all_0_7_7 = n7
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (690) with n11, n22, all_0_4_4, n7 and discharging atoms sum(n11, n22) = all_0_4_4, sum(n11, n22) = n7, yields:
% 54.15/20.64 | (1405) all_0_4_4 = n7
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (690) with n11, n13, all_0_1_1, n24 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n24, yields:
% 54.15/20.64 | (1081) all_0_1_1 = n24
% 54.15/20.64 |
% 54.15/20.64 | From (1407)(1405) and (590) follows:
% 54.15/20.64 | (1409) sum(n7, n7) = all_0_3_3
% 54.15/20.64 |
% 54.15/20.64 | From (1081) and (5067) follows:
% 54.15/20.64 | (1174) sum(n16, n24) = all_0_0_0
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (690) with n16, n24, all_0_0_0, n14 and discharging atoms sum(n16, n24) = all_0_0_0, sum(n16, n24) = n14, yields:
% 54.15/20.64 | (1177) all_0_0_0 = n14
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 54.15/20.64 | (1176) all_0_3_3 = n14
% 54.15/20.64 |
% 54.15/20.64 | Equations (1177,1176) can reduce 679 to:
% 54.15/20.64 | (1106) $false
% 54.15/20.64 |
% 54.15/20.64 |-The branch is then unsatisfiable
% 54.15/20.64 |-Branch two:
% 54.15/20.64 | (1802) ~ (all_0_10_10 = n12)
% 54.15/20.64 | (1803) 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
% 54.15/20.64 |
% 54.15/20.64 +-Applying beta-rule and splitting (1803), into two cases.
% 54.15/20.64 |-Branch one:
% 54.15/20.64 | (1804) all_0_10_10 = n11
% 54.15/20.64 |
% 54.15/20.64 | From (1804) and (292) follows:
% 54.15/20.64 | (1805) pred(n11) = all_0_6_6
% 54.15/20.64 |
% 54.15/20.64 | From (1804) and (760) follows:
% 54.15/20.64 | (1806) succ(n11) = all_0_8_8
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (500) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 54.15/20.64 | (1807) all_0_6_6 = n10
% 54.15/20.64 |
% 54.15/20.64 | Instantiating formula (617) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 54.15/20.64 | (1808) all_0_8_8 = n12
% 54.15/20.64 |
% 54.15/20.64 | From (1807)(1808) and (411) follows:
% 54.15/20.64 | (1809) sum(n10, n12) = all_0_1_1
% 54.15/20.64 |
% 54.15/20.64 | From (1807) and (5063) follows:
% 54.15/20.64 | (5236) sum(n10, n22) = all_0_4_4
% 54.15/20.64 |
% 54.15/20.64 | From (1808) and (5065) follows:
% 54.15/20.65 | (5237) sum(n20, n12) = all_0_7_7
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n20, n12, all_0_7_7, n6 and discharging atoms sum(n20, n12) = all_0_7_7, sum(n20, n12) = n6, yields:
% 54.15/20.65 | (1425) all_0_7_7 = n6
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n10, n22, all_0_4_4, n6 and discharging atoms sum(n10, n22) = all_0_4_4, sum(n10, n22) = n6, yields:
% 54.15/20.65 | (1423) all_0_4_4 = n6
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n10, n12, all_0_1_1, n22 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n22, yields:
% 54.15/20.65 | (1579) all_0_1_1 = n22
% 54.15/20.65 |
% 54.15/20.65 | From (1425)(1423) and (590) follows:
% 54.15/20.65 | (1427) sum(n6, n6) = all_0_3_3
% 54.15/20.65 |
% 54.15/20.65 | From (1579) and (5067) follows:
% 54.15/20.65 | (2106) sum(n16, n22) = all_0_0_0
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n16, n22, all_0_0_0, n12 and discharging atoms sum(n16, n22) = all_0_0_0, sum(n16, n22) = n12, yields:
% 54.15/20.65 | (1195) all_0_0_0 = n12
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 54.15/20.65 | (1194) all_0_3_3 = n12
% 54.15/20.65 |
% 54.15/20.65 | Equations (1195,1194) can reduce 679 to:
% 54.15/20.65 | (1106) $false
% 54.15/20.65 |
% 54.15/20.65 |-The branch is then unsatisfiable
% 54.15/20.65 |-Branch two:
% 54.15/20.65 | (1820) ~ (all_0_10_10 = n11)
% 54.15/20.65 | (1821) 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
% 54.15/20.65 |
% 54.15/20.65 +-Applying beta-rule and splitting (1821), into two cases.
% 54.15/20.65 |-Branch one:
% 54.15/20.65 | (1822) all_0_10_10 = n10
% 54.15/20.65 |
% 54.15/20.65 | From (1822) and (292) follows:
% 54.15/20.65 | (1823) pred(n10) = all_0_6_6
% 54.15/20.65 |
% 54.15/20.65 | From (1822) and (760) follows:
% 54.15/20.65 | (1824) succ(n10) = all_0_8_8
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (500) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 54.15/20.65 | (1825) all_0_6_6 = n9
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (617) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 54.15/20.65 | (1826) all_0_8_8 = n11
% 54.15/20.65 |
% 54.15/20.65 | From (1825)(1826) and (411) follows:
% 54.15/20.65 | (1827) sum(n9, n11) = all_0_1_1
% 54.15/20.65 |
% 54.15/20.65 | From (1825) and (5063) follows:
% 54.15/20.65 | (5254) sum(n9, n22) = all_0_4_4
% 54.15/20.65 |
% 54.15/20.65 | From (1826) and (5065) follows:
% 54.15/20.65 | (5255) sum(n20, n11) = all_0_7_7
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n20, n11, all_0_7_7, n5 and discharging atoms sum(n20, n11) = all_0_7_7, sum(n20, n11) = n5, yields:
% 54.15/20.65 | (1443) all_0_7_7 = n5
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n9, n22, all_0_4_4, n5 and discharging atoms sum(n9, n22) = all_0_4_4, sum(n9, n22) = n5, yields:
% 54.15/20.65 | (1441) all_0_4_4 = n5
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 54.15/20.65 | (1597) all_0_1_1 = n20
% 54.15/20.65 |
% 54.15/20.65 | From (1443)(1441) and (590) follows:
% 54.15/20.65 | (1445) sum(n5, n5) = all_0_3_3
% 54.15/20.65 |
% 54.15/20.65 | From (1597) and (5067) follows:
% 54.15/20.65 | (2998) sum(n16, n20) = all_0_0_0
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n16, n20, all_0_0_0, n10 and discharging atoms sum(n16, n20) = all_0_0_0, sum(n16, n20) = n10, yields:
% 54.15/20.65 | (1213) all_0_0_0 = n10
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 54.15/20.65 | (1212) all_0_3_3 = n10
% 54.15/20.65 |
% 54.15/20.65 | Equations (1213,1212) can reduce 679 to:
% 54.15/20.65 | (1106) $false
% 54.15/20.65 |
% 54.15/20.65 |-The branch is then unsatisfiable
% 54.15/20.65 |-Branch two:
% 54.15/20.65 | (1838) ~ (all_0_10_10 = n10)
% 54.15/20.65 | (1839) 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
% 54.15/20.65 |
% 54.15/20.65 +-Applying beta-rule and splitting (1839), into two cases.
% 54.15/20.65 |-Branch one:
% 54.15/20.65 | (1840) all_0_10_10 = n9
% 54.15/20.65 |
% 54.15/20.65 | From (1840) and (292) follows:
% 54.15/20.65 | (1841) pred(n9) = all_0_6_6
% 54.15/20.65 |
% 54.15/20.65 | From (1840) and (760) follows:
% 54.15/20.65 | (1842) succ(n9) = all_0_8_8
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (500) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 54.15/20.65 | (1843) all_0_6_6 = n8
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (617) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 54.15/20.65 | (1844) all_0_8_8 = n10
% 54.15/20.65 |
% 54.15/20.65 | From (1843)(1844) and (411) follows:
% 54.15/20.65 | (1845) sum(n8, n10) = all_0_1_1
% 54.15/20.65 |
% 54.15/20.65 | From (1843) and (5063) follows:
% 54.15/20.65 | (5272) sum(n8, n22) = all_0_4_4
% 54.15/20.65 |
% 54.15/20.65 | From (1844) and (5065) follows:
% 54.15/20.65 | (5273) sum(n20, n10) = all_0_7_7
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n20, n10, all_0_7_7, n4 and discharging atoms sum(n20, n10) = all_0_7_7, sum(n20, n10) = n4, yields:
% 54.15/20.65 | (1461) all_0_7_7 = n4
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n8, n22, all_0_4_4, n4 and discharging atoms sum(n8, n22) = all_0_4_4, sum(n8, n22) = n4, yields:
% 54.15/20.65 | (1459) all_0_4_4 = n4
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 54.15/20.65 | (1615) all_0_1_1 = n18
% 54.15/20.65 |
% 54.15/20.65 | From (1461)(1459) and (590) follows:
% 54.15/20.65 | (1463) sum(n4, n4) = all_0_3_3
% 54.15/20.65 |
% 54.15/20.65 | From (1615) and (5067) follows:
% 54.15/20.65 | (3854) sum(n16, n18) = all_0_0_0
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n16, n18, all_0_0_0, n8 and discharging atoms sum(n16, n18) = all_0_0_0, sum(n16, n18) = n8, yields:
% 54.15/20.65 | (1231) all_0_0_0 = n8
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 54.15/20.65 | (1230) all_0_3_3 = n8
% 54.15/20.65 |
% 54.15/20.65 | Equations (1231,1230) can reduce 679 to:
% 54.15/20.65 | (1106) $false
% 54.15/20.65 |
% 54.15/20.65 |-The branch is then unsatisfiable
% 54.15/20.65 |-Branch two:
% 54.15/20.65 | (1856) ~ (all_0_10_10 = n9)
% 54.15/20.65 | (1857) 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
% 54.15/20.65 |
% 54.15/20.65 +-Applying beta-rule and splitting (1857), into two cases.
% 54.15/20.65 |-Branch one:
% 54.15/20.65 | (1858) all_0_10_10 = n8
% 54.15/20.65 |
% 54.15/20.65 | From (1858) and (292) follows:
% 54.15/20.65 | (1859) pred(n8) = all_0_6_6
% 54.15/20.65 |
% 54.15/20.65 | From (1858) and (760) follows:
% 54.15/20.65 | (1860) succ(n8) = all_0_8_8
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 54.15/20.65 | (1861) all_0_6_6 = n7
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 54.15/20.65 | (1862) all_0_8_8 = n9
% 54.15/20.65 |
% 54.15/20.65 | From (1861)(1862) and (411) follows:
% 54.15/20.65 | (1863) sum(n7, n9) = all_0_1_1
% 54.15/20.65 |
% 54.15/20.65 | From (1861) and (5063) follows:
% 54.15/20.65 | (5290) sum(n7, n22) = all_0_4_4
% 54.15/20.65 |
% 54.15/20.65 | From (1862) and (5065) follows:
% 54.15/20.65 | (5291) sum(n20, n9) = all_0_7_7
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n20, n9, all_0_7_7, n3 and discharging atoms sum(n20, n9) = all_0_7_7, sum(n20, n9) = n3, yields:
% 54.15/20.65 | (1479) all_0_7_7 = n3
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n7, n22, all_0_4_4, n3 and discharging atoms sum(n7, n22) = all_0_4_4, sum(n7, n22) = n3, yields:
% 54.15/20.65 | (1477) all_0_4_4 = n3
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 54.15/20.65 | (1633) all_0_1_1 = n16
% 54.15/20.65 |
% 54.15/20.65 | From (1479)(1477) and (590) follows:
% 54.15/20.65 | (1481) sum(n3, n3) = all_0_3_3
% 54.15/20.65 |
% 54.15/20.65 | From (1633) and (5067) follows:
% 54.15/20.65 | (4672) sum(n16, n16) = all_0_0_0
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n16, n16, all_0_0_0, n6 and discharging atoms sum(n16, n16) = all_0_0_0, sum(n16, n16) = n6, yields:
% 54.15/20.65 | (1249) all_0_0_0 = n6
% 54.15/20.65 |
% 54.15/20.65 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 54.15/20.65 | (1248) all_0_3_3 = n6
% 54.15/20.65 |
% 54.15/20.66 | Equations (1249,1248) can reduce 679 to:
% 54.15/20.66 | (1106) $false
% 54.15/20.66 |
% 54.15/20.66 |-The branch is then unsatisfiable
% 54.15/20.66 |-Branch two:
% 54.15/20.66 | (1874) ~ (all_0_10_10 = n8)
% 54.15/20.66 | (1875) 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
% 54.15/20.66 |
% 54.15/20.66 +-Applying beta-rule and splitting (1875), into two cases.
% 54.15/20.66 |-Branch one:
% 54.15/20.66 | (1876) all_0_10_10 = n7
% 54.15/20.66 |
% 54.15/20.66 | From (1876) and (292) follows:
% 54.15/20.66 | (1877) pred(n7) = all_0_6_6
% 54.15/20.66 |
% 54.15/20.66 | From (1876) and (760) follows:
% 54.15/20.66 | (1878) succ(n7) = all_0_8_8
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 54.15/20.66 | (1879) all_0_6_6 = n6
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 54.15/20.66 | (1880) all_0_8_8 = n8
% 54.15/20.66 |
% 54.15/20.66 | From (1879)(1880) and (411) follows:
% 54.15/20.66 | (1881) sum(n6, n8) = all_0_1_1
% 54.15/20.66 |
% 54.15/20.66 | From (1879) and (5063) follows:
% 54.15/20.66 | (5308) sum(n6, n22) = all_0_4_4
% 54.15/20.66 |
% 54.15/20.66 | From (1880) and (5065) follows:
% 54.15/20.66 | (5309) sum(n20, n8) = all_0_7_7
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (690) with n20, n8, all_0_7_7, n2 and discharging atoms sum(n20, n8) = all_0_7_7, sum(n20, n8) = n2, yields:
% 54.15/20.66 | (1497) all_0_7_7 = n2
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (690) with n6, n22, all_0_4_4, n2 and discharging atoms sum(n6, n22) = all_0_4_4, sum(n6, n22) = n2, yields:
% 54.15/20.66 | (1495) all_0_4_4 = n2
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 54.15/20.66 | (1651) all_0_1_1 = n14
% 54.15/20.66 |
% 54.15/20.66 | From (1497)(1495) and (590) follows:
% 54.15/20.66 | (1499) sum(n2, n2) = all_0_3_3
% 54.15/20.66 |
% 54.15/20.66 | From (1651) and (5067) follows:
% 54.15/20.66 | (5080) sum(n16, n14) = all_0_0_0
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (690) with n16, n14, all_0_0_0, n4 and discharging atoms sum(n16, n14) = all_0_0_0, sum(n16, n14) = n4, yields:
% 54.15/20.66 | (1267) all_0_0_0 = n4
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 54.15/20.66 | (1266) all_0_3_3 = n4
% 54.15/20.66 |
% 54.15/20.66 | Equations (1267,1266) can reduce 679 to:
% 54.15/20.66 | (1106) $false
% 54.15/20.66 |
% 54.15/20.66 |-The branch is then unsatisfiable
% 54.15/20.66 |-Branch two:
% 54.15/20.66 | (1892) ~ (all_0_10_10 = n7)
% 54.15/20.66 | (1893) 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
% 54.15/20.66 |
% 54.15/20.66 +-Applying beta-rule and splitting (1893), into two cases.
% 54.15/20.66 |-Branch one:
% 54.15/20.66 | (1894) all_0_10_10 = n6
% 54.15/20.66 |
% 54.15/20.66 | From (1894) and (292) follows:
% 54.15/20.66 | (1895) pred(n6) = all_0_6_6
% 54.15/20.66 |
% 54.15/20.66 | From (1894) and (760) follows:
% 54.15/20.66 | (1896) succ(n6) = all_0_8_8
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 54.15/20.66 | (1897) all_0_6_6 = n5
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 54.15/20.66 | (1898) all_0_8_8 = n7
% 54.15/20.66 |
% 54.15/20.66 | From (1897)(1898) and (411) follows:
% 54.15/20.66 | (1899) sum(n5, n7) = all_0_1_1
% 54.15/20.66 |
% 54.15/20.66 | From (1897) and (5063) follows:
% 54.15/20.66 | (5326) sum(n5, n22) = all_0_4_4
% 54.15/20.66 |
% 54.15/20.66 | From (1898) and (5065) follows:
% 54.15/20.66 | (5327) sum(n20, n7) = all_0_7_7
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (690) with n20, n7, all_0_7_7, n1 and discharging atoms sum(n20, n7) = all_0_7_7, sum(n20, n7) = n1, yields:
% 54.15/20.66 | (1515) all_0_7_7 = n1
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (690) with n5, n22, all_0_4_4, n1 and discharging atoms sum(n5, n22) = all_0_4_4, sum(n5, n22) = n1, yields:
% 54.15/20.66 | (1513) all_0_4_4 = n1
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 54.15/20.66 | (1669) all_0_1_1 = n12
% 54.15/20.66 |
% 54.15/20.66 | From (1515)(1513) and (590) follows:
% 54.15/20.66 | (1517) sum(n1, n1) = all_0_3_3
% 54.15/20.66 |
% 54.15/20.66 | From (1669) and (5067) follows:
% 54.15/20.66 | (5098) sum(n16, n12) = all_0_0_0
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (690) with n16, n12, all_0_0_0, n2 and discharging atoms sum(n16, n12) = all_0_0_0, sum(n16, n12) = n2, yields:
% 54.15/20.66 | (1285) all_0_0_0 = n2
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 54.15/20.66 | (1284) all_0_3_3 = n2
% 54.15/20.66 |
% 54.15/20.66 | Equations (1285,1284) can reduce 679 to:
% 54.15/20.66 | (1106) $false
% 54.15/20.66 |
% 54.15/20.66 |-The branch is then unsatisfiable
% 54.15/20.66 |-Branch two:
% 54.15/20.66 | (1910) ~ (all_0_10_10 = n6)
% 54.15/20.66 | (1911) 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
% 54.15/20.66 |
% 54.15/20.66 +-Applying beta-rule and splitting (1911), into two cases.
% 54.15/20.66 |-Branch one:
% 54.15/20.66 | (1912) all_0_10_10 = n5
% 54.15/20.66 |
% 54.15/20.66 | From (1912) and (292) follows:
% 54.15/20.66 | (1913) pred(n5) = all_0_6_6
% 54.15/20.66 |
% 54.15/20.66 | From (1912) and (760) follows:
% 54.15/20.66 | (1914) succ(n5) = all_0_8_8
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 54.15/20.66 | (1915) all_0_6_6 = n4
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 54.15/20.66 | (1916) all_0_8_8 = n6
% 54.15/20.66 |
% 54.15/20.66 | From (1915)(1916) and (411) follows:
% 54.15/20.66 | (1917) sum(n4, n6) = all_0_1_1
% 54.15/20.66 |
% 54.15/20.66 | From (1915) and (5063) follows:
% 54.15/20.66 | (5344) sum(n4, n22) = all_0_4_4
% 54.15/20.66 |
% 54.15/20.66 | From (1916) and (5065) follows:
% 54.15/20.66 | (5345) sum(n20, n6) = all_0_7_7
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (690) with n20, n6, all_0_7_7, n0 and discharging atoms sum(n20, n6) = all_0_7_7, sum(n20, n6) = n0, yields:
% 54.15/20.66 | (1533) all_0_7_7 = n0
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (690) with n4, n22, all_0_4_4, n0 and discharging atoms sum(n4, n22) = all_0_4_4, sum(n4, n22) = n0, yields:
% 54.15/20.66 | (1531) all_0_4_4 = n0
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 54.15/20.66 | (1687) all_0_1_1 = n10
% 54.15/20.66 |
% 54.15/20.66 | From (1533)(1531) and (590) follows:
% 54.15/20.66 | (1535) sum(n0, n0) = all_0_3_3
% 54.15/20.66 |
% 54.15/20.66 | From (1687) and (5067) follows:
% 54.15/20.66 | (5116) sum(n16, n10) = all_0_0_0
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (690) with n16, n10, all_0_0_0, n0 and discharging atoms sum(n16, n10) = all_0_0_0, sum(n16, n10) = n0, yields:
% 54.15/20.66 | (1303) all_0_0_0 = n0
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 54.15/20.66 | (1302) all_0_3_3 = n0
% 54.15/20.66 |
% 54.15/20.66 | Equations (1303,1302) can reduce 679 to:
% 54.15/20.66 | (1106) $false
% 54.15/20.66 |
% 54.15/20.66 |-The branch is then unsatisfiable
% 54.15/20.66 |-Branch two:
% 54.15/20.66 | (1928) ~ (all_0_10_10 = n5)
% 54.15/20.66 | (1929) 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
% 54.15/20.66 |
% 54.15/20.66 +-Applying beta-rule and splitting (1929), into two cases.
% 54.15/20.66 |-Branch one:
% 54.15/20.66 | (1930) all_0_10_10 = n4
% 54.15/20.66 |
% 54.15/20.66 | From (1930) and (292) follows:
% 54.15/20.66 | (1931) pred(n4) = all_0_6_6
% 54.15/20.66 |
% 54.15/20.66 | From (1930) and (760) follows:
% 54.15/20.66 | (1932) succ(n4) = all_0_8_8
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 54.15/20.66 | (1933) all_0_6_6 = n3
% 54.15/20.66 |
% 54.15/20.66 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 54.15/20.66 | (1934) all_0_8_8 = n5
% 54.15/20.66 |
% 54.15/20.66 | From (1933)(1934) and (411) follows:
% 54.15/20.67 | (1935) sum(n3, n5) = all_0_1_1
% 54.15/20.67 |
% 54.15/20.67 | From (1933) and (5063) follows:
% 54.15/20.67 | (5362) sum(n3, n22) = all_0_4_4
% 54.15/20.67 |
% 54.15/20.67 | From (1934) and (5065) follows:
% 54.15/20.67 | (5363) sum(n20, n5) = all_0_7_7
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (690) with n20, n5, all_0_7_7, n25 and discharging atoms sum(n20, n5) = all_0_7_7, sum(n20, n5) = n25, yields:
% 54.15/20.67 | (1550) all_0_7_7 = n25
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (690) with n3, n22, all_0_4_4, n25 and discharging atoms sum(n3, n22) = all_0_4_4, sum(n3, n22) = n25, yields:
% 54.15/20.67 | (1551) all_0_4_4 = n25
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 54.15/20.67 | (1705) all_0_1_1 = n8
% 54.15/20.67 |
% 54.15/20.67 | From (1550)(1551) and (590) follows:
% 54.15/20.67 | (1553) sum(n25, n25) = all_0_3_3
% 54.15/20.67 |
% 54.15/20.67 | From (1705) and (5067) follows:
% 54.15/20.67 | (5134) sum(n16, n8) = all_0_0_0
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 54.15/20.67 | (1320) all_0_3_3 = n24
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (690) with n16, n8, all_0_0_0, n24 and discharging atoms sum(n16, n8) = all_0_0_0, sum(n16, n8) = n24, yields:
% 54.15/20.67 | (1321) all_0_0_0 = n24
% 54.15/20.67 |
% 54.15/20.67 | Equations (1321,1320) can reduce 679 to:
% 54.15/20.67 | (1106) $false
% 54.15/20.67 |
% 54.15/20.67 |-The branch is then unsatisfiable
% 54.15/20.67 |-Branch two:
% 54.15/20.67 | (1946) ~ (all_0_10_10 = n4)
% 54.15/20.67 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 54.15/20.67 |
% 54.15/20.67 +-Applying beta-rule and splitting (1947), into two cases.
% 54.15/20.67 |-Branch one:
% 54.15/20.67 | (1948) all_0_10_10 = n3
% 54.15/20.67 |
% 54.15/20.67 | From (1948) and (292) follows:
% 54.15/20.67 | (1949) pred(n3) = all_0_6_6
% 54.15/20.67 |
% 54.15/20.67 | From (1948) and (760) follows:
% 54.15/20.67 | (1950) succ(n3) = all_0_8_8
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 54.15/20.67 | (1951) all_0_6_6 = n2
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 54.15/20.67 | (1952) all_0_8_8 = n4
% 54.15/20.67 |
% 54.15/20.67 | From (1951)(1952) and (411) follows:
% 54.15/20.67 | (1953) sum(n2, n4) = all_0_1_1
% 54.15/20.67 |
% 54.15/20.67 | From (1951) and (5063) follows:
% 54.15/20.67 | (5380) sum(n2, n22) = all_0_4_4
% 54.15/20.67 |
% 54.15/20.67 | From (1952) and (5065) follows:
% 54.15/20.67 | (5381) sum(n20, n4) = all_0_7_7
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (690) with n20, n4, all_0_7_7, n24 and discharging atoms sum(n20, n4) = all_0_7_7, sum(n20, n4) = n24, yields:
% 54.15/20.67 | (1097) all_0_7_7 = n24
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (690) with n2, n22, all_0_4_4, n24 and discharging atoms sum(n2, n22) = all_0_4_4, sum(n2, n22) = n24, yields:
% 54.15/20.67 | (1096) all_0_4_4 = n24
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 54.15/20.67 | (1723) all_0_1_1 = n6
% 54.15/20.67 |
% 54.15/20.67 | From (1097)(1096) and (590) follows:
% 54.15/20.67 | (1101) sum(n24, n24) = all_0_3_3
% 54.15/20.67 |
% 54.15/20.67 | From (1723) and (5067) follows:
% 54.15/20.67 | (5152) sum(n16, n6) = all_0_0_0
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 54.15/20.67 | (1104) all_0_3_3 = n22
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (690) with n16, n6, all_0_0_0, n22 and discharging atoms sum(n16, n6) = all_0_0_0, sum(n16, n6) = n22, yields:
% 54.15/20.67 | (1102) all_0_0_0 = n22
% 54.15/20.67 |
% 54.15/20.67 | Equations (1102,1104) can reduce 679 to:
% 54.15/20.67 | (1106) $false
% 54.15/20.67 |
% 54.15/20.67 |-The branch is then unsatisfiable
% 54.15/20.67 |-Branch two:
% 54.15/20.67 | (1964) ~ (all_0_10_10 = n3)
% 54.15/20.67 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 54.15/20.67 |
% 54.15/20.67 +-Applying beta-rule and splitting (1965), into two cases.
% 54.15/20.67 |-Branch one:
% 54.15/20.67 | (1966) all_0_10_10 = n2
% 54.15/20.67 |
% 54.15/20.67 | From (1966) and (292) follows:
% 54.15/20.67 | (1967) pred(n2) = all_0_6_6
% 54.15/20.67 |
% 54.15/20.67 | From (1966) and (760) follows:
% 54.15/20.67 | (1968) succ(n2) = all_0_8_8
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 54.15/20.67 | (1969) all_0_6_6 = n1
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 54.15/20.67 | (1970) all_0_8_8 = n3
% 54.15/20.67 |
% 54.15/20.67 | From (1969)(1970) and (411) follows:
% 54.15/20.67 | (1971) sum(n1, n3) = all_0_1_1
% 54.15/20.67 |
% 54.15/20.67 | From (1969) and (5063) follows:
% 54.15/20.67 | (5398) sum(n1, n22) = all_0_4_4
% 54.15/20.67 |
% 54.15/20.67 | From (1970) and (5065) follows:
% 54.15/20.67 | (5399) sum(n20, n3) = all_0_7_7
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (690) with n20, n3, all_0_7_7, n23 and discharging atoms sum(n20, n3) = all_0_7_7, sum(n20, n3) = n23, yields:
% 54.15/20.67 | (1119) all_0_7_7 = n23
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (690) with n1, n22, all_0_4_4, n23 and discharging atoms sum(n1, n22) = all_0_4_4, sum(n1, n22) = n23, yields:
% 54.15/20.67 | (1117) all_0_4_4 = n23
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 54.15/20.67 | (1741) all_0_1_1 = n4
% 54.15/20.67 |
% 54.15/20.67 | From (1119)(1117) and (590) follows:
% 54.15/20.67 | (1121) sum(n23, n23) = all_0_3_3
% 54.15/20.67 |
% 54.15/20.67 | From (1741) and (5067) follows:
% 54.15/20.67 | (5170) sum(n16, n4) = all_0_0_0
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 54.15/20.67 | (1122) all_0_3_3 = n20
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (690) with n16, n4, all_0_0_0, n20 and discharging atoms sum(n16, n4) = all_0_0_0, sum(n16, n4) = n20, yields:
% 54.15/20.67 | (1123) all_0_0_0 = n20
% 54.15/20.67 |
% 54.15/20.67 | Equations (1123,1122) can reduce 679 to:
% 54.15/20.67 | (1106) $false
% 54.15/20.67 |
% 54.15/20.67 |-The branch is then unsatisfiable
% 54.15/20.67 |-Branch two:
% 54.15/20.67 | (1982) ~ (all_0_10_10 = n2)
% 54.15/20.67 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 54.15/20.67 |
% 54.15/20.67 +-Applying beta-rule and splitting (1983), into two cases.
% 54.15/20.67 |-Branch one:
% 54.15/20.67 | (1984) all_0_10_10 = n1
% 54.15/20.67 |
% 54.15/20.67 | From (1984) and (292) follows:
% 54.15/20.67 | (1985) pred(n1) = all_0_6_6
% 54.15/20.67 |
% 54.15/20.67 | From (1984) and (760) follows:
% 54.15/20.67 | (1986) succ(n1) = all_0_8_8
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 54.15/20.67 | (1987) all_0_6_6 = n0
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 54.15/20.67 | (1988) all_0_8_8 = n2
% 54.15/20.67 |
% 54.15/20.67 | From (1987)(1988) and (411) follows:
% 54.15/20.67 | (1989) sum(n0, n2) = all_0_1_1
% 54.15/20.67 |
% 54.15/20.67 | From (1987) and (5063) follows:
% 54.15/20.67 | (5416) sum(n0, n22) = all_0_4_4
% 54.15/20.67 |
% 54.15/20.67 | From (1988) and (5065) follows:
% 54.15/20.67 | (5417) sum(n20, n2) = all_0_7_7
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (690) with n20, n2, all_0_7_7, n22 and discharging atoms sum(n20, n2) = all_0_7_7, sum(n20, n2) = n22, yields:
% 54.15/20.67 | (1137) all_0_7_7 = n22
% 54.15/20.67 |
% 54.15/20.67 | Instantiating formula (690) with n0, n22, all_0_4_4, n22 and discharging atoms sum(n0, n22) = all_0_4_4, sum(n0, n22) = n22, yields:
% 54.15/20.67 | (1135) all_0_4_4 = n22
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 54.15/20.68 | (1759) all_0_1_1 = n2
% 54.15/20.68 |
% 54.15/20.68 | From (1137)(1135) and (590) follows:
% 54.15/20.68 | (1139) sum(n22, n22) = all_0_3_3
% 54.15/20.68 |
% 54.15/20.68 | From (1759) and (5067) follows:
% 54.15/20.68 | (5188) sum(n16, n2) = all_0_0_0
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 54.15/20.68 | (1140) all_0_3_3 = n18
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (690) with n16, n2, all_0_0_0, n18 and discharging atoms sum(n16, n2) = all_0_0_0, sum(n16, n2) = n18, yields:
% 54.15/20.68 | (1141) all_0_0_0 = n18
% 54.15/20.68 |
% 54.15/20.68 | Equations (1141,1140) can reduce 679 to:
% 54.15/20.68 | (1106) $false
% 54.15/20.68 |
% 54.15/20.68 |-The branch is then unsatisfiable
% 54.15/20.68 |-Branch two:
% 54.15/20.68 | (2002) ~ (all_0_10_10 = n1)
% 54.15/20.68 | (2003) all_0_10_10 = n0
% 54.15/20.68 |
% 54.15/20.68 | From (2003) and (292) follows:
% 54.15/20.68 | (2004) pred(n0) = all_0_6_6
% 54.15/20.68 |
% 54.15/20.68 | From (2003) and (760) follows:
% 54.15/20.68 | (2005) succ(n0) = all_0_8_8
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 54.15/20.68 | (2006) all_0_6_6 = n25
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 54.15/20.68 | (2007) all_0_8_8 = n1
% 54.15/20.68 |
% 54.15/20.68 | From (2006)(2007) and (411) follows:
% 54.15/20.68 | (2008) sum(n25, n1) = all_0_1_1
% 54.15/20.68 |
% 54.15/20.68 | From (2006) and (5063) follows:
% 54.15/20.68 | (5433) sum(n25, n22) = all_0_4_4
% 54.15/20.68 |
% 54.15/20.68 | From (2007) and (5065) follows:
% 54.15/20.68 | (5434) sum(n20, n1) = all_0_7_7
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (690) with n25, n22, all_0_4_4, n21 and discharging atoms sum(n25, n22) = all_0_4_4, sum(n25, n22) = n21, yields:
% 54.15/20.68 | (1153) all_0_4_4 = n21
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 54.15/20.68 | (1777) all_0_1_1 = n0
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (690) with n20, n1, all_0_7_7, n21 and discharging atoms sum(n20, n1) = all_0_7_7, sum(n20, n1) = n21, yields:
% 54.15/20.68 | (1155) all_0_7_7 = n21
% 54.15/20.68 |
% 54.15/20.68 | From (1155)(1153) and (590) follows:
% 54.15/20.68 | (1157) sum(n21, n21) = all_0_3_3
% 54.15/20.68 |
% 54.15/20.68 | From (1777) and (5067) follows:
% 54.15/20.68 | (5206) sum(n16, n0) = all_0_0_0
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 54.15/20.68 | (1158) all_0_3_3 = n16
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (690) with n16, n0, all_0_0_0, n16 and discharging atoms sum(n16, n0) = all_0_0_0, sum(n16, n0) = n16, yields:
% 54.15/20.68 | (1159) all_0_0_0 = n16
% 54.15/20.68 |
% 54.15/20.68 | Equations (1159,1158) can reduce 679 to:
% 54.15/20.68 | (1106) $false
% 54.15/20.68 |
% 54.15/20.68 |-The branch is then unsatisfiable
% 54.15/20.68 |-Branch two:
% 54.15/20.68 | (1179) ~ (all_0_11_11 = n21)
% 54.15/20.68 | (1180) 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
% 54.15/20.68 |
% 54.15/20.68 +-Applying beta-rule and splitting (1641), into two cases.
% 54.15/20.68 |-Branch one:
% 54.15/20.68 | (1642) all_0_10_10 = n20
% 54.15/20.68 |
% 54.15/20.68 | From (1642) and (292) follows:
% 54.15/20.68 | (1643) pred(n20) = all_0_6_6
% 54.15/20.68 |
% 54.15/20.68 | From (1642) and (760) follows:
% 54.15/20.68 | (1644) succ(n20) = all_0_8_8
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (500) with n20, all_0_6_6, n19 and discharging atoms pred(n20) = all_0_6_6, pred(n20) = n19, yields:
% 54.15/20.68 | (1645) all_0_6_6 = n19
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (617) with n20, all_0_8_8, n21 and discharging atoms succ(n20) = all_0_8_8, succ(n20) = n21, yields:
% 54.15/20.68 | (1646) all_0_8_8 = n21
% 54.15/20.68 |
% 54.15/20.68 | From (1645) and (1643) follows:
% 54.15/20.68 | (522) pred(n20) = n19
% 54.15/20.68 |
% 54.15/20.68 | From (1646) and (1644) follows:
% 54.15/20.68 | (883) succ(n20) = n21
% 54.15/20.68 |
% 54.15/20.68 | From (1645) and (541) follows:
% 54.15/20.68 | (5452) sum(n19, all_0_5_5) = all_0_4_4
% 54.15/20.68 |
% 54.15/20.68 | From (1645)(1646) and (411) follows:
% 54.15/20.68 | (1647) sum(n19, n21) = all_0_1_1
% 54.15/20.68 |
% 54.15/20.68 | From (1646) and (427) follows:
% 54.15/20.68 | (5454) sum(all_0_9_9, n21) = all_0_7_7
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (690) with n19, n21, all_0_1_1, n14 and discharging atoms sum(n19, n21) = all_0_1_1, sum(n19, n21) = n14, yields:
% 54.15/20.68 | (1651) all_0_1_1 = n14
% 54.15/20.68 |
% 54.15/20.68 | From (1651) and (630) follows:
% 54.15/20.68 | (5456) sum(all_0_2_2, n14) = all_0_0_0
% 54.15/20.68 |
% 54.15/20.68 | From (1651) and (1647) follows:
% 54.15/20.68 | (877) sum(n19, n21) = n14
% 54.15/20.68 |
% 54.15/20.68 +-Applying beta-rule and splitting (1180), into two cases.
% 54.15/20.68 |-Branch one:
% 54.15/20.68 | (1181) all_0_11_11 = n20
% 54.15/20.68 |
% 54.15/20.68 | From (1181) and (559) follows:
% 54.15/20.68 | (1182) pred(n20) = all_0_9_9
% 54.15/20.68 |
% 54.15/20.68 | From (1181) and (992) follows:
% 54.15/20.68 | (1183) succ(n20) = all_0_5_5
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (500) with n20, all_0_9_9, n19 and discharging atoms pred(n20) = all_0_9_9, pred(n20) = n19, yields:
% 54.15/20.68 | (1184) all_0_9_9 = n19
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (617) with n20, all_0_5_5, n21 and discharging atoms succ(n20) = all_0_5_5, succ(n20) = n21, yields:
% 54.15/20.68 | (1185) all_0_5_5 = n21
% 54.15/20.68 |
% 54.15/20.68 | From (1184)(1185) and (538) follows:
% 54.15/20.68 | (1186) sum(n19, n21) = all_0_2_2
% 54.15/20.68 |
% 54.15/20.68 | From (1184) and (5454) follows:
% 54.15/20.68 | (5464) sum(n19, n21) = all_0_7_7
% 54.15/20.68 |
% 54.15/20.68 | From (1185) and (5452) follows:
% 54.15/20.68 | (5465) sum(n19, n21) = all_0_4_4
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (690) with n19, n21, all_0_2_2, n14 and discharging atoms sum(n19, n21) = all_0_2_2, sum(n19, n21) = n14, yields:
% 54.15/20.68 | (1190) all_0_2_2 = n14
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (690) with n19, n21, all_0_4_4, all_0_2_2 and discharging atoms sum(n19, n21) = all_0_2_2, sum(n19, n21) = all_0_4_4, yields:
% 54.15/20.68 | (1093) all_0_2_2 = all_0_4_4
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (690) with n19, n21, all_0_7_7, all_0_2_2 and discharging atoms sum(n19, n21) = all_0_2_2, sum(n19, n21) = all_0_7_7, yields:
% 54.15/20.68 | (1094) all_0_2_2 = all_0_7_7
% 54.15/20.68 |
% 54.15/20.68 | Combining equations (1094,1093) yields a new equation:
% 54.15/20.68 | (1095) all_0_4_4 = all_0_7_7
% 54.15/20.68 |
% 54.15/20.68 | Combining equations (1190,1093) yields a new equation:
% 54.15/20.68 | (1279) all_0_4_4 = n14
% 54.15/20.68 |
% 54.15/20.68 | Combining equations (1279,1095) yields a new equation:
% 54.15/20.68 | (1281) all_0_7_7 = n14
% 54.15/20.68 |
% 54.15/20.68 | Combining equations (1281,1095) yields a new equation:
% 54.15/20.68 | (1279) all_0_4_4 = n14
% 54.15/20.68 |
% 54.15/20.68 | Combining equations (1279,1093) yields a new equation:
% 54.15/20.68 | (1190) all_0_2_2 = n14
% 54.15/20.68 |
% 54.15/20.68 | From (1190) and (5456) follows:
% 54.15/20.68 | (5474) sum(n14, n14) = all_0_0_0
% 54.15/20.68 |
% 54.15/20.68 | From (1281)(1279) and (590) follows:
% 54.15/20.68 | (1283) sum(n14, n14) = all_0_3_3
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (690) with n14, n14, all_0_0_0, n2 and discharging atoms sum(n14, n14) = all_0_0_0, sum(n14, n14) = n2, yields:
% 54.15/20.68 | (1285) all_0_0_0 = n2
% 54.15/20.68 |
% 54.15/20.68 | Instantiating formula (690) 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:
% 54.15/20.69 | (1103) all_0_0_0 = all_0_3_3
% 54.15/20.69 |
% 54.15/20.69 | Combining equations (1285,1103) yields a new equation:
% 54.15/20.69 | (1284) all_0_3_3 = n2
% 54.15/20.69 |
% 54.15/20.69 | Combining equations (1284,1103) yields a new equation:
% 54.15/20.69 | (1285) all_0_0_0 = n2
% 54.15/20.69 |
% 54.15/20.69 | Equations (1285,1284) can reduce 679 to:
% 54.15/20.69 | (1106) $false
% 54.15/20.69 |
% 54.15/20.69 |-The branch is then unsatisfiable
% 54.15/20.69 |-Branch two:
% 54.15/20.69 | (1197) ~ (all_0_11_11 = n20)
% 54.15/20.69 | (1198) 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
% 54.15/20.69 |
% 54.15/20.69 +-Applying beta-rule and splitting (1198), into two cases.
% 54.15/20.69 |-Branch one:
% 54.15/20.69 | (1199) all_0_11_11 = n19
% 54.15/20.69 |
% 54.15/20.69 | From (1199) and (559) follows:
% 54.15/20.69 | (1200) pred(n19) = all_0_9_9
% 54.15/20.69 |
% 54.15/20.69 | From (1199) and (992) follows:
% 54.15/20.69 | (1201) succ(n19) = all_0_5_5
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (500) with n19, all_0_9_9, n18 and discharging atoms pred(n19) = all_0_9_9, pred(n19) = n18, yields:
% 54.15/20.69 | (1202) all_0_9_9 = n18
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (617) with n19, all_0_5_5, n20 and discharging atoms succ(n19) = all_0_5_5, succ(n19) = n20, yields:
% 54.15/20.69 | (1203) all_0_5_5 = n20
% 54.15/20.69 |
% 54.15/20.69 | From (1202)(1203) and (538) follows:
% 54.15/20.69 | (1204) sum(n18, n20) = all_0_2_2
% 54.15/20.69 |
% 54.15/20.69 | From (1202) and (5454) follows:
% 54.15/20.69 | (5489) sum(n18, n21) = all_0_7_7
% 54.15/20.69 |
% 54.15/20.69 | From (1203) and (5452) follows:
% 54.15/20.69 | (5490) sum(n19, n20) = all_0_4_4
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (690) with n19, n20, all_0_4_4, n13 and discharging atoms sum(n19, n20) = all_0_4_4, sum(n19, n20) = n13, yields:
% 54.15/20.69 | (1297) all_0_4_4 = n13
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (690) with n18, n21, all_0_7_7, n13 and discharging atoms sum(n18, n21) = all_0_7_7, sum(n18, n21) = n13, yields:
% 54.15/20.69 | (1299) all_0_7_7 = n13
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (690) with n18, n20, all_0_2_2, n12 and discharging atoms sum(n18, n20) = all_0_2_2, sum(n18, n20) = n12, yields:
% 54.15/20.69 | (1208) all_0_2_2 = n12
% 54.15/20.69 |
% 54.15/20.69 | From (1208) and (5456) follows:
% 54.15/20.69 | (5494) sum(n12, n14) = all_0_0_0
% 54.15/20.69 |
% 54.15/20.69 | From (1299)(1297) and (590) follows:
% 54.15/20.69 | (1301) sum(n13, n13) = all_0_3_3
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 54.15/20.69 | (1302) all_0_3_3 = n0
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (690) with n12, n14, all_0_0_0, n0 and discharging atoms sum(n12, n14) = all_0_0_0, sum(n12, n14) = n0, yields:
% 54.15/20.69 | (1303) all_0_0_0 = n0
% 54.15/20.69 |
% 54.15/20.69 | Equations (1303,1302) can reduce 679 to:
% 54.15/20.69 | (1106) $false
% 54.15/20.69 |
% 54.15/20.69 |-The branch is then unsatisfiable
% 54.15/20.69 |-Branch two:
% 54.15/20.69 | (1215) ~ (all_0_11_11 = n19)
% 54.15/20.69 | (1216) 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
% 54.15/20.69 |
% 54.15/20.69 +-Applying beta-rule and splitting (1216), into two cases.
% 54.15/20.69 |-Branch one:
% 54.15/20.69 | (1217) all_0_11_11 = n18
% 54.15/20.69 |
% 54.15/20.69 | From (1217) and (559) follows:
% 54.15/20.69 | (1218) pred(n18) = all_0_9_9
% 54.15/20.69 |
% 54.15/20.69 | From (1217) and (992) follows:
% 54.15/20.69 | (1219) succ(n18) = all_0_5_5
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (500) with n18, all_0_9_9, n17 and discharging atoms pred(n18) = all_0_9_9, pred(n18) = n17, yields:
% 54.15/20.69 | (1220) all_0_9_9 = n17
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (617) with n18, all_0_5_5, n19 and discharging atoms succ(n18) = all_0_5_5, succ(n18) = n19, yields:
% 54.15/20.69 | (1221) all_0_5_5 = n19
% 54.15/20.69 |
% 54.15/20.69 | From (1220)(1221) and (538) follows:
% 54.15/20.69 | (1222) sum(n17, n19) = all_0_2_2
% 54.15/20.69 |
% 54.15/20.69 | From (1220) and (5454) follows:
% 54.15/20.69 | (5507) sum(n17, n21) = all_0_7_7
% 54.15/20.69 |
% 54.15/20.69 | From (1221) and (5452) follows:
% 54.15/20.69 | (5508) sum(n19, n19) = all_0_4_4
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (690) with n19, n19, all_0_4_4, n12 and discharging atoms sum(n19, n19) = all_0_4_4, sum(n19, n19) = n12, yields:
% 54.15/20.69 | (1315) all_0_4_4 = n12
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (690) with n17, n21, all_0_7_7, n12 and discharging atoms sum(n17, n21) = all_0_7_7, sum(n17, n21) = n12, yields:
% 54.15/20.69 | (1317) all_0_7_7 = n12
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (690) with n17, n19, all_0_2_2, n10 and discharging atoms sum(n17, n19) = all_0_2_2, sum(n17, n19) = n10, yields:
% 54.15/20.69 | (1226) all_0_2_2 = n10
% 54.15/20.69 |
% 54.15/20.69 | From (1226) and (5456) follows:
% 54.15/20.69 | (5512) sum(n10, n14) = all_0_0_0
% 54.15/20.69 |
% 54.15/20.69 | From (1317)(1315) and (590) follows:
% 54.15/20.69 | (1319) sum(n12, n12) = all_0_3_3
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 54.15/20.69 | (1320) all_0_3_3 = n24
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (690) with n10, n14, all_0_0_0, n24 and discharging atoms sum(n10, n14) = all_0_0_0, sum(n10, n14) = n24, yields:
% 54.15/20.69 | (1321) all_0_0_0 = n24
% 54.15/20.69 |
% 54.15/20.69 | Equations (1321,1320) can reduce 679 to:
% 54.15/20.69 | (1106) $false
% 54.15/20.69 |
% 54.15/20.69 |-The branch is then unsatisfiable
% 54.15/20.69 |-Branch two:
% 54.15/20.69 | (1233) ~ (all_0_11_11 = n18)
% 54.15/20.69 | (1234) 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
% 54.15/20.69 |
% 54.15/20.69 +-Applying beta-rule and splitting (1234), into two cases.
% 54.15/20.69 |-Branch one:
% 54.15/20.69 | (1235) all_0_11_11 = n17
% 54.15/20.69 |
% 54.15/20.69 | From (1235) and (559) follows:
% 54.15/20.69 | (1236) pred(n17) = all_0_9_9
% 54.15/20.69 |
% 54.15/20.69 | From (1235) and (992) follows:
% 54.15/20.69 | (1237) succ(n17) = all_0_5_5
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (500) with n17, all_0_9_9, n16 and discharging atoms pred(n17) = all_0_9_9, pred(n17) = n16, yields:
% 54.15/20.69 | (1238) all_0_9_9 = n16
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (617) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 54.15/20.69 | (1239) all_0_5_5 = n18
% 54.15/20.69 |
% 54.15/20.69 | From (1238)(1239) and (538) follows:
% 54.15/20.69 | (1240) sum(n16, n18) = all_0_2_2
% 54.15/20.69 |
% 54.15/20.69 | From (1238) and (5454) follows:
% 54.15/20.69 | (5525) sum(n16, n21) = all_0_7_7
% 54.15/20.69 |
% 54.15/20.69 | From (1239) and (5452) follows:
% 54.15/20.69 | (5526) sum(n19, n18) = all_0_4_4
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (690) with n19, n18, all_0_4_4, n11 and discharging atoms sum(n19, n18) = all_0_4_4, sum(n19, n18) = n11, yields:
% 54.15/20.69 | (1333) all_0_4_4 = n11
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (690) with n16, n21, all_0_7_7, n11 and discharging atoms sum(n16, n21) = all_0_7_7, sum(n16, n21) = n11, yields:
% 54.15/20.69 | (1335) all_0_7_7 = n11
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (690) with n16, n18, all_0_2_2, n8 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = n8, yields:
% 54.15/20.69 | (1244) all_0_2_2 = n8
% 54.15/20.69 |
% 54.15/20.69 | From (1244) and (5456) follows:
% 54.15/20.69 | (5530) sum(n8, n14) = all_0_0_0
% 54.15/20.69 |
% 54.15/20.69 | From (1335)(1333) and (590) follows:
% 54.15/20.69 | (1337) sum(n11, n11) = all_0_3_3
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 54.15/20.69 | (1104) all_0_3_3 = n22
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (690) with n8, n14, all_0_0_0, n22 and discharging atoms sum(n8, n14) = all_0_0_0, sum(n8, n14) = n22, yields:
% 54.15/20.69 | (1102) all_0_0_0 = n22
% 54.15/20.69 |
% 54.15/20.69 | Equations (1102,1104) can reduce 679 to:
% 54.15/20.69 | (1106) $false
% 54.15/20.69 |
% 54.15/20.69 |-The branch is then unsatisfiable
% 54.15/20.69 |-Branch two:
% 54.15/20.69 | (1251) ~ (all_0_11_11 = n17)
% 54.15/20.69 | (1252) 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
% 54.15/20.69 |
% 54.15/20.69 +-Applying beta-rule and splitting (1252), into two cases.
% 54.15/20.69 |-Branch one:
% 54.15/20.69 | (1253) all_0_11_11 = n16
% 54.15/20.69 |
% 54.15/20.69 | From (1253) and (559) follows:
% 54.15/20.69 | (1254) pred(n16) = all_0_9_9
% 54.15/20.69 |
% 54.15/20.69 | From (1253) and (992) follows:
% 54.15/20.69 | (1255) succ(n16) = all_0_5_5
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (500) with n16, all_0_9_9, n15 and discharging atoms pred(n16) = all_0_9_9, pred(n16) = n15, yields:
% 54.15/20.69 | (1256) all_0_9_9 = n15
% 54.15/20.69 |
% 54.15/20.69 | Instantiating formula (617) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 54.15/20.69 | (1257) all_0_5_5 = n17
% 54.15/20.69 |
% 54.15/20.69 | From (1256)(1257) and (538) follows:
% 54.15/20.70 | (1258) sum(n15, n17) = all_0_2_2
% 54.15/20.70 |
% 54.15/20.70 | From (1256) and (5454) follows:
% 54.15/20.70 | (5543) sum(n15, n21) = all_0_7_7
% 54.15/20.70 |
% 54.15/20.70 | From (1257) and (5452) follows:
% 54.15/20.70 | (5544) sum(n19, n17) = all_0_4_4
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (690) with n19, n17, all_0_4_4, n10 and discharging atoms sum(n19, n17) = all_0_4_4, sum(n19, n17) = n10, yields:
% 54.15/20.70 | (1351) all_0_4_4 = n10
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (690) with n15, n21, all_0_7_7, n10 and discharging atoms sum(n15, n21) = all_0_7_7, sum(n15, n21) = n10, yields:
% 54.15/20.70 | (1353) all_0_7_7 = n10
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (690) with n15, n17, all_0_2_2, n6 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n6, yields:
% 54.15/20.70 | (1262) all_0_2_2 = n6
% 54.15/20.70 |
% 54.15/20.70 | From (1262) and (5456) follows:
% 54.15/20.70 | (5548) sum(n6, n14) = all_0_0_0
% 54.15/20.70 |
% 54.15/20.70 | From (1353)(1351) and (590) follows:
% 54.15/20.70 | (1355) sum(n10, n10) = all_0_3_3
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 54.15/20.70 | (1122) all_0_3_3 = n20
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (690) with n6, n14, all_0_0_0, n20 and discharging atoms sum(n6, n14) = all_0_0_0, sum(n6, n14) = n20, yields:
% 54.15/20.70 | (1123) all_0_0_0 = n20
% 54.15/20.70 |
% 54.15/20.70 | Equations (1123,1122) can reduce 679 to:
% 54.15/20.70 | (1106) $false
% 54.15/20.70 |
% 54.15/20.70 |-The branch is then unsatisfiable
% 54.15/20.70 |-Branch two:
% 54.15/20.70 | (1269) ~ (all_0_11_11 = n16)
% 54.15/20.70 | (1270) 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
% 54.15/20.70 |
% 54.15/20.70 +-Applying beta-rule and splitting (1270), into two cases.
% 54.15/20.70 |-Branch one:
% 54.15/20.70 | (1271) all_0_11_11 = n15
% 54.15/20.70 |
% 54.15/20.70 | From (1271) and (559) follows:
% 54.15/20.70 | (1272) pred(n15) = all_0_9_9
% 54.15/20.70 |
% 54.15/20.70 | From (1271) and (992) follows:
% 54.15/20.70 | (1273) succ(n15) = all_0_5_5
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (500) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 54.15/20.70 | (1274) all_0_9_9 = n14
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (617) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 54.15/20.70 | (1275) all_0_5_5 = n16
% 54.15/20.70 |
% 54.15/20.70 | From (1274)(1275) and (538) follows:
% 54.15/20.70 | (1276) sum(n14, n16) = all_0_2_2
% 54.15/20.70 |
% 54.15/20.70 | From (1274) and (5454) follows:
% 54.15/20.70 | (5561) sum(n14, n21) = all_0_7_7
% 54.15/20.70 |
% 54.15/20.70 | From (1275) and (5452) follows:
% 54.15/20.70 | (5562) sum(n19, n16) = all_0_4_4
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (690) with n19, n16, all_0_4_4, n9 and discharging atoms sum(n19, n16) = all_0_4_4, sum(n19, n16) = n9, yields:
% 54.15/20.70 | (1369) all_0_4_4 = n9
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (690) with n14, n21, all_0_7_7, n9 and discharging atoms sum(n14, n21) = all_0_7_7, sum(n14, n21) = n9, yields:
% 54.15/20.70 | (1371) all_0_7_7 = n9
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (690) with n14, n16, all_0_2_2, n4 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n4, yields:
% 54.15/20.70 | (1280) all_0_2_2 = n4
% 54.15/20.70 |
% 54.15/20.70 | From (1280) and (5456) follows:
% 54.15/20.70 | (5566) sum(n4, n14) = all_0_0_0
% 54.15/20.70 |
% 54.15/20.70 | From (1371)(1369) and (590) follows:
% 54.15/20.70 | (1373) sum(n9, n9) = all_0_3_3
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 54.15/20.70 | (1140) all_0_3_3 = n18
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (690) with n4, n14, all_0_0_0, n18 and discharging atoms sum(n4, n14) = all_0_0_0, sum(n4, n14) = n18, yields:
% 54.15/20.70 | (1141) all_0_0_0 = n18
% 54.15/20.70 |
% 54.15/20.70 | Equations (1141,1140) can reduce 679 to:
% 54.15/20.70 | (1106) $false
% 54.15/20.70 |
% 54.15/20.70 |-The branch is then unsatisfiable
% 54.15/20.70 |-Branch two:
% 54.15/20.70 | (1287) ~ (all_0_11_11 = n15)
% 54.15/20.70 | (1288) 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
% 54.15/20.70 |
% 54.15/20.70 +-Applying beta-rule and splitting (1288), into two cases.
% 54.15/20.70 |-Branch one:
% 54.15/20.70 | (1289) all_0_11_11 = n14
% 54.15/20.70 |
% 54.15/20.70 | From (1289) and (559) follows:
% 54.15/20.70 | (1290) pred(n14) = all_0_9_9
% 54.15/20.70 |
% 54.15/20.70 | From (1289) and (992) follows:
% 54.15/20.70 | (1291) succ(n14) = all_0_5_5
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (500) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 54.15/20.70 | (1292) all_0_9_9 = n13
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (617) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 54.15/20.70 | (1293) all_0_5_5 = n15
% 54.15/20.70 |
% 54.15/20.70 | From (1292)(1293) and (538) follows:
% 54.15/20.70 | (1294) sum(n13, n15) = all_0_2_2
% 54.15/20.70 |
% 54.15/20.70 | From (1292) and (5454) follows:
% 54.15/20.70 | (5579) sum(n13, n21) = all_0_7_7
% 54.15/20.70 |
% 54.15/20.70 | From (1293) and (5452) follows:
% 54.15/20.70 | (5580) sum(n19, n15) = all_0_4_4
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (690) with n19, n15, all_0_4_4, n8 and discharging atoms sum(n19, n15) = all_0_4_4, sum(n19, n15) = n8, yields:
% 54.15/20.70 | (1387) all_0_4_4 = n8
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (690) with n13, n21, all_0_7_7, n8 and discharging atoms sum(n13, n21) = all_0_7_7, sum(n13, n21) = n8, yields:
% 54.15/20.70 | (1389) all_0_7_7 = n8
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (690) with n13, n15, all_0_2_2, n2 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n2, yields:
% 54.15/20.70 | (1298) all_0_2_2 = n2
% 54.15/20.70 |
% 54.15/20.70 | From (1298) and (5456) follows:
% 54.15/20.70 | (5584) sum(n2, n14) = all_0_0_0
% 54.15/20.70 |
% 54.15/20.70 | From (1389)(1387) and (590) follows:
% 54.15/20.70 | (1391) sum(n8, n8) = all_0_3_3
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 54.15/20.70 | (1158) all_0_3_3 = n16
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (690) with n2, n14, all_0_0_0, n16 and discharging atoms sum(n2, n14) = all_0_0_0, sum(n2, n14) = n16, yields:
% 54.15/20.70 | (1159) all_0_0_0 = n16
% 54.15/20.70 |
% 54.15/20.70 | Equations (1159,1158) can reduce 679 to:
% 54.15/20.70 | (1106) $false
% 54.15/20.70 |
% 54.15/20.70 |-The branch is then unsatisfiable
% 54.15/20.70 |-Branch two:
% 54.15/20.70 | (1305) ~ (all_0_11_11 = n14)
% 54.15/20.70 | (1306) 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
% 54.15/20.70 |
% 54.15/20.70 +-Applying beta-rule and splitting (1306), into two cases.
% 54.15/20.70 |-Branch one:
% 54.15/20.70 | (1307) all_0_11_11 = n13
% 54.15/20.70 |
% 54.15/20.70 | From (1307) and (559) follows:
% 54.15/20.70 | (1308) pred(n13) = all_0_9_9
% 54.15/20.70 |
% 54.15/20.70 | From (1307) and (992) follows:
% 54.15/20.70 | (1309) succ(n13) = all_0_5_5
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (500) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 54.15/20.70 | (1310) all_0_9_9 = n12
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (617) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 54.15/20.70 | (1311) all_0_5_5 = n14
% 54.15/20.70 |
% 54.15/20.70 | From (1310)(1311) and (538) follows:
% 54.15/20.70 | (1312) sum(n12, n14) = all_0_2_2
% 54.15/20.70 |
% 54.15/20.70 | From (1310) and (5454) follows:
% 54.15/20.70 | (5597) sum(n12, n21) = all_0_7_7
% 54.15/20.70 |
% 54.15/20.70 | From (1311) and (5452) follows:
% 54.15/20.70 | (5598) sum(n19, n14) = all_0_4_4
% 54.15/20.70 |
% 54.15/20.70 | Instantiating formula (690) with n19, n14, all_0_4_4, n7 and discharging atoms sum(n19, n14) = all_0_4_4, sum(n19, n14) = n7, yields:
% 54.15/20.71 | (1405) all_0_4_4 = n7
% 54.15/20.71 |
% 54.15/20.71 | Instantiating formula (690) with n12, n21, all_0_7_7, n7 and discharging atoms sum(n12, n21) = all_0_7_7, sum(n12, n21) = n7, yields:
% 54.15/20.71 | (1407) all_0_7_7 = n7
% 54.15/20.71 |
% 54.15/20.71 | Instantiating formula (690) with n12, n14, all_0_2_2, n0 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n0, yields:
% 54.15/20.71 | (1316) all_0_2_2 = n0
% 54.15/20.71 |
% 54.15/20.71 | From (1316) and (5456) follows:
% 54.15/20.71 | (5602) sum(n0, n14) = all_0_0_0
% 54.15/20.71 |
% 54.15/20.71 | From (1407)(1405) and (590) follows:
% 54.15/20.71 | (1409) sum(n7, n7) = all_0_3_3
% 54.15/20.71 |
% 54.15/20.71 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 54.15/20.71 | (1176) all_0_3_3 = n14
% 54.15/20.71 |
% 54.15/20.71 | Instantiating formula (690) with n0, n14, all_0_0_0, n14 and discharging atoms sum(n0, n14) = all_0_0_0, sum(n0, n14) = n14, yields:
% 54.15/20.71 | (1177) all_0_0_0 = n14
% 54.15/20.71 |
% 54.15/20.71 | Equations (1177,1176) can reduce 679 to:
% 54.15/20.71 | (1106) $false
% 54.15/20.71 |
% 54.15/20.71 |-The branch is then unsatisfiable
% 54.15/20.71 |-Branch two:
% 54.15/20.71 | (1323) ~ (all_0_11_11 = n13)
% 54.15/20.71 | (1324) 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
% 54.15/20.71 |
% 54.15/20.71 +-Applying beta-rule and splitting (1324), into two cases.
% 54.15/20.71 |-Branch one:
% 54.15/20.71 | (1325) all_0_11_11 = n12
% 54.15/20.71 |
% 54.15/20.71 | From (1325) and (559) follows:
% 54.15/20.71 | (1326) pred(n12) = all_0_9_9
% 54.15/20.71 |
% 54.15/20.71 | From (1325) and (992) follows:
% 54.47/20.71 | (1327) succ(n12) = all_0_5_5
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (500) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 54.47/20.71 | (1328) all_0_9_9 = n11
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (617) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 54.47/20.71 | (1329) all_0_5_5 = n13
% 54.47/20.71 |
% 54.47/20.71 | From (1328)(1329) and (538) follows:
% 54.47/20.71 | (1330) sum(n11, n13) = all_0_2_2
% 54.47/20.71 |
% 54.47/20.71 | From (1328) and (5454) follows:
% 54.47/20.71 | (5615) sum(n11, n21) = all_0_7_7
% 54.47/20.71 |
% 54.47/20.71 | From (1329) and (5452) follows:
% 54.47/20.71 | (5616) sum(n19, n13) = all_0_4_4
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (690) with n19, n13, all_0_4_4, n6 and discharging atoms sum(n19, n13) = all_0_4_4, sum(n19, n13) = n6, yields:
% 54.47/20.71 | (1423) all_0_4_4 = n6
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (690) with n11, n21, all_0_7_7, n6 and discharging atoms sum(n11, n21) = all_0_7_7, sum(n11, n21) = n6, yields:
% 54.47/20.71 | (1425) all_0_7_7 = n6
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (690) with n11, n13, all_0_2_2, n24 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n24, yields:
% 54.47/20.71 | (1092) all_0_2_2 = n24
% 54.47/20.71 |
% 54.47/20.71 | From (1092) and (5456) follows:
% 54.47/20.71 | (1654) sum(n24, n14) = all_0_0_0
% 54.47/20.71 |
% 54.47/20.71 | From (1425)(1423) and (590) follows:
% 54.47/20.71 | (1427) sum(n6, n6) = all_0_3_3
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (690) with n24, n14, all_0_0_0, n12 and discharging atoms sum(n24, n14) = all_0_0_0, sum(n24, n14) = n12, yields:
% 54.47/20.71 | (1195) all_0_0_0 = n12
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 54.47/20.71 | (1194) all_0_3_3 = n12
% 54.47/20.71 |
% 54.47/20.71 | Equations (1195,1194) can reduce 679 to:
% 54.47/20.71 | (1106) $false
% 54.47/20.71 |
% 54.47/20.71 |-The branch is then unsatisfiable
% 54.47/20.71 |-Branch two:
% 54.47/20.71 | (1341) ~ (all_0_11_11 = n12)
% 54.47/20.71 | (1342) 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
% 54.47/20.71 |
% 54.47/20.71 +-Applying beta-rule and splitting (1342), into two cases.
% 54.47/20.71 |-Branch one:
% 54.47/20.71 | (1343) all_0_11_11 = n11
% 54.47/20.71 |
% 54.47/20.71 | From (1343) and (559) follows:
% 54.47/20.71 | (1344) pred(n11) = all_0_9_9
% 54.47/20.71 |
% 54.47/20.71 | From (1343) and (992) follows:
% 54.47/20.71 | (1345) succ(n11) = all_0_5_5
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (500) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 54.47/20.71 | (1346) all_0_9_9 = n10
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (617) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 54.47/20.71 | (1347) all_0_5_5 = n12
% 54.47/20.71 |
% 54.47/20.71 | From (1346)(1347) and (538) follows:
% 54.47/20.71 | (1348) sum(n10, n12) = all_0_2_2
% 54.47/20.71 |
% 54.47/20.71 | From (1346) and (5454) follows:
% 54.47/20.71 | (5633) sum(n10, n21) = all_0_7_7
% 54.47/20.71 |
% 54.47/20.71 | From (1347) and (5452) follows:
% 54.47/20.71 | (5634) sum(n19, n12) = all_0_4_4
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (690) with n19, n12, all_0_4_4, n5 and discharging atoms sum(n19, n12) = all_0_4_4, sum(n19, n12) = n5, yields:
% 54.47/20.71 | (1441) all_0_4_4 = n5
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (690) with n10, n21, all_0_7_7, n5 and discharging atoms sum(n10, n21) = all_0_7_7, sum(n10, n21) = n5, yields:
% 54.47/20.71 | (1443) all_0_7_7 = n5
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (690) with n10, n12, all_0_2_2, n22 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n22, yields:
% 54.47/20.71 | (1118) all_0_2_2 = n22
% 54.47/20.71 |
% 54.47/20.71 | From (1118) and (5456) follows:
% 54.47/20.71 | (2566) sum(n22, n14) = all_0_0_0
% 54.47/20.71 |
% 54.47/20.71 | From (1443)(1441) and (590) follows:
% 54.47/20.71 | (1445) sum(n5, n5) = all_0_3_3
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (690) with n22, n14, all_0_0_0, n10 and discharging atoms sum(n22, n14) = all_0_0_0, sum(n22, n14) = n10, yields:
% 54.47/20.71 | (1213) all_0_0_0 = n10
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 54.47/20.71 | (1212) all_0_3_3 = n10
% 54.47/20.71 |
% 54.47/20.71 | Equations (1213,1212) can reduce 679 to:
% 54.47/20.71 | (1106) $false
% 54.47/20.71 |
% 54.47/20.71 |-The branch is then unsatisfiable
% 54.47/20.71 |-Branch two:
% 54.47/20.71 | (1359) ~ (all_0_11_11 = n11)
% 54.47/20.71 | (1360) 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
% 54.47/20.71 |
% 54.47/20.71 +-Applying beta-rule and splitting (1360), into two cases.
% 54.47/20.71 |-Branch one:
% 54.47/20.71 | (1361) all_0_11_11 = n10
% 54.47/20.71 |
% 54.47/20.71 | From (1361) and (559) follows:
% 54.47/20.71 | (1362) pred(n10) = all_0_9_9
% 54.47/20.71 |
% 54.47/20.71 | From (1361) and (992) follows:
% 54.47/20.71 | (1363) succ(n10) = all_0_5_5
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (500) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 54.47/20.71 | (1364) all_0_9_9 = n9
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (617) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 54.47/20.71 | (1365) all_0_5_5 = n11
% 54.47/20.71 |
% 54.47/20.71 | From (1364)(1365) and (538) follows:
% 54.47/20.71 | (1366) sum(n9, n11) = all_0_2_2
% 54.47/20.71 |
% 54.47/20.71 | From (1364) and (5454) follows:
% 54.47/20.71 | (5651) sum(n9, n21) = all_0_7_7
% 54.47/20.71 |
% 54.47/20.71 | From (1365) and (5452) follows:
% 54.47/20.71 | (5652) sum(n19, n11) = all_0_4_4
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (690) with n19, n11, all_0_4_4, n4 and discharging atoms sum(n19, n11) = all_0_4_4, sum(n19, n11) = n4, yields:
% 54.47/20.71 | (1459) all_0_4_4 = n4
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (690) with n9, n21, all_0_7_7, n4 and discharging atoms sum(n9, n21) = all_0_7_7, sum(n9, n21) = n4, yields:
% 54.47/20.71 | (1461) all_0_7_7 = n4
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (690) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 54.47/20.71 | (1136) all_0_2_2 = n20
% 54.47/20.71 |
% 54.47/20.71 | From (1136) and (5456) follows:
% 54.47/20.71 | (3440) sum(n20, n14) = all_0_0_0
% 54.47/20.71 |
% 54.47/20.71 | From (1461)(1459) and (590) follows:
% 54.47/20.71 | (1463) sum(n4, n4) = all_0_3_3
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (690) with n20, n14, all_0_0_0, n8 and discharging atoms sum(n20, n14) = all_0_0_0, sum(n20, n14) = n8, yields:
% 54.47/20.71 | (1231) all_0_0_0 = n8
% 54.47/20.71 |
% 54.47/20.71 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 54.47/20.71 | (1230) all_0_3_3 = n8
% 54.47/20.72 |
% 54.47/20.72 | Equations (1231,1230) can reduce 679 to:
% 54.47/20.72 | (1106) $false
% 54.47/20.72 |
% 54.47/20.72 |-The branch is then unsatisfiable
% 54.47/20.72 |-Branch two:
% 54.47/20.72 | (1377) ~ (all_0_11_11 = n10)
% 54.47/20.72 | (1378) 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
% 54.47/20.72 |
% 54.47/20.72 +-Applying beta-rule and splitting (1378), into two cases.
% 54.47/20.72 |-Branch one:
% 54.47/20.72 | (1379) all_0_11_11 = n9
% 54.47/20.72 |
% 54.47/20.72 | From (1379) and (559) follows:
% 54.47/20.72 | (1380) pred(n9) = all_0_9_9
% 54.47/20.72 |
% 54.47/20.72 | From (1379) and (992) follows:
% 54.47/20.72 | (1381) succ(n9) = all_0_5_5
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 54.47/20.72 | (1382) all_0_9_9 = n8
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 54.47/20.72 | (1383) all_0_5_5 = n10
% 54.47/20.72 |
% 54.47/20.72 | From (1382)(1383) and (538) follows:
% 54.47/20.72 | (1384) sum(n8, n10) = all_0_2_2
% 54.47/20.72 |
% 54.47/20.72 | From (1382) and (5454) follows:
% 54.47/20.72 | (5669) sum(n8, n21) = all_0_7_7
% 54.47/20.72 |
% 54.47/20.72 | From (1383) and (5452) follows:
% 54.47/20.72 | (5670) sum(n19, n10) = all_0_4_4
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (690) with n19, n10, all_0_4_4, n3 and discharging atoms sum(n19, n10) = all_0_4_4, sum(n19, n10) = n3, yields:
% 54.47/20.72 | (1477) all_0_4_4 = n3
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (690) with n8, n21, all_0_7_7, n3 and discharging atoms sum(n8, n21) = all_0_7_7, sum(n8, n21) = n3, yields:
% 54.47/20.72 | (1479) all_0_7_7 = n3
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 54.47/20.72 | (1154) all_0_2_2 = n18
% 54.47/20.72 |
% 54.47/20.72 | From (1154) and (5456) follows:
% 54.47/20.72 | (4278) sum(n18, n14) = all_0_0_0
% 54.47/20.72 |
% 54.47/20.72 | From (1479)(1477) and (590) follows:
% 54.47/20.72 | (1481) sum(n3, n3) = all_0_3_3
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (690) with n18, n14, all_0_0_0, n6 and discharging atoms sum(n18, n14) = all_0_0_0, sum(n18, n14) = n6, yields:
% 54.47/20.72 | (1249) all_0_0_0 = n6
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 54.47/20.72 | (1248) all_0_3_3 = n6
% 54.47/20.72 |
% 54.47/20.72 | Equations (1249,1248) can reduce 679 to:
% 54.47/20.72 | (1106) $false
% 54.47/20.72 |
% 54.47/20.72 |-The branch is then unsatisfiable
% 54.47/20.72 |-Branch two:
% 54.47/20.72 | (1395) ~ (all_0_11_11 = n9)
% 54.47/20.72 | (1396) 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
% 54.47/20.72 |
% 54.47/20.72 +-Applying beta-rule and splitting (1396), into two cases.
% 54.47/20.72 |-Branch one:
% 54.47/20.72 | (1397) all_0_11_11 = n8
% 54.47/20.72 |
% 54.47/20.72 | From (1397) and (559) follows:
% 54.47/20.72 | (1398) pred(n8) = all_0_9_9
% 54.47/20.72 |
% 54.47/20.72 | From (1397) and (992) follows:
% 54.47/20.72 | (1399) succ(n8) = all_0_5_5
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 54.47/20.72 | (1400) all_0_9_9 = n7
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 54.47/20.72 | (1401) all_0_5_5 = n9
% 54.47/20.72 |
% 54.47/20.72 | From (1400)(1401) and (538) follows:
% 54.47/20.72 | (1402) sum(n7, n9) = all_0_2_2
% 54.47/20.72 |
% 54.47/20.72 | From (1400) and (5454) follows:
% 54.47/20.72 | (5687) sum(n7, n21) = all_0_7_7
% 54.47/20.72 |
% 54.47/20.72 | From (1401) and (5452) follows:
% 54.47/20.72 | (5688) sum(n19, n9) = all_0_4_4
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (690) with n19, n9, all_0_4_4, n2 and discharging atoms sum(n19, n9) = all_0_4_4, sum(n19, n9) = n2, yields:
% 54.47/20.72 | (1495) all_0_4_4 = n2
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (690) with n7, n21, all_0_7_7, n2 and discharging atoms sum(n7, n21) = all_0_7_7, sum(n7, n21) = n2, yields:
% 54.47/20.72 | (1497) all_0_7_7 = n2
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 54.47/20.72 | (1172) all_0_2_2 = n16
% 54.47/20.72 |
% 54.47/20.72 | From (1172) and (5456) follows:
% 54.47/20.72 | (5080) sum(n16, n14) = all_0_0_0
% 54.47/20.72 |
% 54.47/20.72 | From (1497)(1495) and (590) follows:
% 54.47/20.72 | (1499) sum(n2, n2) = all_0_3_3
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (690) with n16, n14, all_0_0_0, n4 and discharging atoms sum(n16, n14) = all_0_0_0, sum(n16, n14) = n4, yields:
% 54.47/20.72 | (1267) all_0_0_0 = n4
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 54.47/20.72 | (1266) all_0_3_3 = n4
% 54.47/20.72 |
% 54.47/20.72 | Equations (1267,1266) can reduce 679 to:
% 54.47/20.72 | (1106) $false
% 54.47/20.72 |
% 54.47/20.72 |-The branch is then unsatisfiable
% 54.47/20.72 |-Branch two:
% 54.47/20.72 | (1413) ~ (all_0_11_11 = n8)
% 54.47/20.72 | (1414) 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
% 54.47/20.72 |
% 54.47/20.72 +-Applying beta-rule and splitting (1414), into two cases.
% 54.47/20.72 |-Branch one:
% 54.47/20.72 | (1415) all_0_11_11 = n7
% 54.47/20.72 |
% 54.47/20.72 | From (1415) and (559) follows:
% 54.47/20.72 | (1416) pred(n7) = all_0_9_9
% 54.47/20.72 |
% 54.47/20.72 | From (1415) and (992) follows:
% 54.47/20.72 | (1417) succ(n7) = all_0_5_5
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 54.47/20.72 | (1418) all_0_9_9 = n6
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 54.47/20.72 | (1419) all_0_5_5 = n8
% 54.47/20.72 |
% 54.47/20.72 | From (1418)(1419) and (538) follows:
% 54.47/20.72 | (1420) sum(n6, n8) = all_0_2_2
% 54.47/20.72 |
% 54.47/20.72 | From (1418) and (5454) follows:
% 54.47/20.72 | (5705) sum(n6, n21) = all_0_7_7
% 54.47/20.72 |
% 54.47/20.72 | From (1419) and (5452) follows:
% 54.47/20.72 | (5706) sum(n19, n8) = all_0_4_4
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (690) with n19, n8, all_0_4_4, n1 and discharging atoms sum(n19, n8) = all_0_4_4, sum(n19, n8) = n1, yields:
% 54.47/20.72 | (1513) all_0_4_4 = n1
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (690) with n6, n21, all_0_7_7, n1 and discharging atoms sum(n6, n21) = all_0_7_7, sum(n6, n21) = n1, yields:
% 54.47/20.72 | (1515) all_0_7_7 = n1
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 54.47/20.72 | (1190) all_0_2_2 = n14
% 54.47/20.72 |
% 54.47/20.72 | From (1190) and (5456) follows:
% 54.47/20.72 | (5474) sum(n14, n14) = all_0_0_0
% 54.47/20.72 |
% 54.47/20.72 | From (1515)(1513) and (590) follows:
% 54.47/20.72 | (1517) sum(n1, n1) = all_0_3_3
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (690) with n14, n14, all_0_0_0, n2 and discharging atoms sum(n14, n14) = all_0_0_0, sum(n14, n14) = n2, yields:
% 54.47/20.72 | (1285) all_0_0_0 = n2
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 54.47/20.72 | (1284) all_0_3_3 = n2
% 54.47/20.72 |
% 54.47/20.72 | Equations (1285,1284) can reduce 679 to:
% 54.47/20.72 | (1106) $false
% 54.47/20.72 |
% 54.47/20.72 |-The branch is then unsatisfiable
% 54.47/20.72 |-Branch two:
% 54.47/20.72 | (1431) ~ (all_0_11_11 = n7)
% 54.47/20.72 | (1432) 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
% 54.47/20.72 |
% 54.47/20.72 +-Applying beta-rule and splitting (1432), into two cases.
% 54.47/20.72 |-Branch one:
% 54.47/20.72 | (1433) all_0_11_11 = n6
% 54.47/20.72 |
% 54.47/20.72 | From (1433) and (559) follows:
% 54.47/20.72 | (1434) pred(n6) = all_0_9_9
% 54.47/20.72 |
% 54.47/20.72 | From (1433) and (992) follows:
% 54.47/20.72 | (1435) succ(n6) = all_0_5_5
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 54.47/20.72 | (1436) all_0_9_9 = n5
% 54.47/20.72 |
% 54.47/20.72 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 54.47/20.72 | (1437) all_0_5_5 = n7
% 54.47/20.72 |
% 54.47/20.72 | From (1436)(1437) and (538) follows:
% 54.47/20.72 | (1438) sum(n5, n7) = all_0_2_2
% 54.47/20.72 |
% 54.47/20.72 | From (1436) and (5454) follows:
% 54.47/20.73 | (5723) sum(n5, n21) = all_0_7_7
% 54.47/20.73 |
% 54.47/20.73 | From (1437) and (5452) follows:
% 54.47/20.73 | (5724) sum(n19, n7) = all_0_4_4
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (690) with n19, n7, all_0_4_4, n0 and discharging atoms sum(n19, n7) = all_0_4_4, sum(n19, n7) = n0, yields:
% 54.47/20.73 | (1531) all_0_4_4 = n0
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (690) with n5, n21, all_0_7_7, n0 and discharging atoms sum(n5, n21) = all_0_7_7, sum(n5, n21) = n0, yields:
% 54.47/20.73 | (1533) all_0_7_7 = n0
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 54.47/20.73 | (1208) all_0_2_2 = n12
% 54.47/20.73 |
% 54.47/20.73 | From (1208) and (5456) follows:
% 54.47/20.73 | (5494) sum(n12, n14) = all_0_0_0
% 54.47/20.73 |
% 54.47/20.73 | From (1533)(1531) and (590) follows:
% 54.47/20.73 | (1535) sum(n0, n0) = all_0_3_3
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (690) with n12, n14, all_0_0_0, n0 and discharging atoms sum(n12, n14) = all_0_0_0, sum(n12, n14) = n0, yields:
% 54.47/20.73 | (1303) all_0_0_0 = n0
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 54.47/20.73 | (1302) all_0_3_3 = n0
% 54.47/20.73 |
% 54.47/20.73 | Equations (1303,1302) can reduce 679 to:
% 54.47/20.73 | (1106) $false
% 54.47/20.73 |
% 54.47/20.73 |-The branch is then unsatisfiable
% 54.47/20.73 |-Branch two:
% 54.47/20.73 | (1449) ~ (all_0_11_11 = n6)
% 54.47/20.73 | (1450) 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
% 54.47/20.73 |
% 54.47/20.73 +-Applying beta-rule and splitting (1450), into two cases.
% 54.47/20.73 |-Branch one:
% 54.47/20.73 | (1451) all_0_11_11 = n5
% 54.47/20.73 |
% 54.47/20.73 | From (1451) and (559) follows:
% 54.47/20.73 | (1452) pred(n5) = all_0_9_9
% 54.47/20.73 |
% 54.47/20.73 | From (1451) and (992) follows:
% 54.47/20.73 | (1453) succ(n5) = all_0_5_5
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 54.47/20.73 | (1454) all_0_9_9 = n4
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 54.47/20.73 | (1455) all_0_5_5 = n6
% 54.47/20.73 |
% 54.47/20.73 | From (1454)(1455) and (538) follows:
% 54.47/20.73 | (1456) sum(n4, n6) = all_0_2_2
% 54.47/20.73 |
% 54.47/20.73 | From (1454) and (5454) follows:
% 54.47/20.73 | (5741) sum(n4, n21) = all_0_7_7
% 54.47/20.73 |
% 54.47/20.73 | From (1455) and (5452) follows:
% 54.47/20.73 | (5742) sum(n19, n6) = all_0_4_4
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (690) with n19, n6, all_0_4_4, n25 and discharging atoms sum(n19, n6) = all_0_4_4, sum(n19, n6) = n25, yields:
% 54.47/20.73 | (1551) all_0_4_4 = n25
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (690) with n4, n21, all_0_7_7, n25 and discharging atoms sum(n4, n21) = all_0_7_7, sum(n4, n21) = n25, yields:
% 54.47/20.73 | (1550) all_0_7_7 = n25
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 54.47/20.73 | (1226) all_0_2_2 = n10
% 54.47/20.73 |
% 54.47/20.73 | From (1226) and (5456) follows:
% 54.47/20.73 | (5512) sum(n10, n14) = all_0_0_0
% 54.47/20.73 |
% 54.47/20.73 | From (1550)(1551) and (590) follows:
% 54.47/20.73 | (1553) sum(n25, n25) = all_0_3_3
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 54.47/20.73 | (1320) all_0_3_3 = n24
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (690) with n10, n14, all_0_0_0, n24 and discharging atoms sum(n10, n14) = all_0_0_0, sum(n10, n14) = n24, yields:
% 54.47/20.73 | (1321) all_0_0_0 = n24
% 54.47/20.73 |
% 54.47/20.73 | Equations (1321,1320) can reduce 679 to:
% 54.47/20.73 | (1106) $false
% 54.47/20.73 |
% 54.47/20.73 |-The branch is then unsatisfiable
% 54.47/20.73 |-Branch two:
% 54.47/20.73 | (1467) ~ (all_0_11_11 = n5)
% 54.47/20.73 | (1468) 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
% 54.47/20.73 |
% 54.47/20.73 +-Applying beta-rule and splitting (1468), into two cases.
% 54.47/20.73 |-Branch one:
% 54.47/20.73 | (1469) all_0_11_11 = n4
% 54.47/20.73 |
% 54.47/20.73 | From (1469) and (559) follows:
% 54.47/20.73 | (1470) pred(n4) = all_0_9_9
% 54.47/20.73 |
% 54.47/20.73 | From (1469) and (992) follows:
% 54.47/20.73 | (1471) succ(n4) = all_0_5_5
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 54.47/20.73 | (1472) all_0_9_9 = n3
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 54.47/20.73 | (1473) all_0_5_5 = n5
% 54.47/20.73 |
% 54.47/20.73 | From (1472)(1473) and (538) follows:
% 54.47/20.73 | (1474) sum(n3, n5) = all_0_2_2
% 54.47/20.73 |
% 54.47/20.73 | From (1472) and (5454) follows:
% 54.47/20.73 | (5759) sum(n3, n21) = all_0_7_7
% 54.47/20.73 |
% 54.47/20.73 | From (1473) and (5452) follows:
% 54.47/20.73 | (5760) sum(n19, n5) = all_0_4_4
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (690) with n19, n5, all_0_4_4, n24 and discharging atoms sum(n19, n5) = all_0_4_4, sum(n19, n5) = n24, yields:
% 54.47/20.73 | (1096) all_0_4_4 = n24
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (690) with n3, n21, all_0_7_7, n24 and discharging atoms sum(n3, n21) = all_0_7_7, sum(n3, n21) = n24, yields:
% 54.47/20.73 | (1097) all_0_7_7 = n24
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 54.47/20.73 | (1244) all_0_2_2 = n8
% 54.47/20.73 |
% 54.47/20.73 | From (1244) and (5456) follows:
% 54.47/20.73 | (5530) sum(n8, n14) = all_0_0_0
% 54.47/20.73 |
% 54.47/20.73 | From (1097)(1096) and (590) follows:
% 54.47/20.73 | (1101) sum(n24, n24) = all_0_3_3
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 54.47/20.73 | (1104) all_0_3_3 = n22
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (690) with n8, n14, all_0_0_0, n22 and discharging atoms sum(n8, n14) = all_0_0_0, sum(n8, n14) = n22, yields:
% 54.47/20.73 | (1102) all_0_0_0 = n22
% 54.47/20.73 |
% 54.47/20.73 | Equations (1102,1104) can reduce 679 to:
% 54.47/20.73 | (1106) $false
% 54.47/20.73 |
% 54.47/20.73 |-The branch is then unsatisfiable
% 54.47/20.73 |-Branch two:
% 54.47/20.73 | (1485) ~ (all_0_11_11 = n4)
% 54.47/20.73 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 54.47/20.73 |
% 54.47/20.73 +-Applying beta-rule and splitting (1486), into two cases.
% 54.47/20.73 |-Branch one:
% 54.47/20.73 | (1487) all_0_11_11 = n3
% 54.47/20.73 |
% 54.47/20.73 | From (1487) and (559) follows:
% 54.47/20.73 | (1488) pred(n3) = all_0_9_9
% 54.47/20.73 |
% 54.47/20.73 | From (1487) and (992) follows:
% 54.47/20.73 | (1489) succ(n3) = all_0_5_5
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 54.47/20.73 | (1490) all_0_9_9 = n2
% 54.47/20.73 |
% 54.47/20.73 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 54.47/20.73 | (1491) all_0_5_5 = n4
% 54.47/20.73 |
% 54.47/20.73 | From (1490)(1491) and (538) follows:
% 54.47/20.73 | (1492) sum(n2, n4) = all_0_2_2
% 54.47/20.73 |
% 54.47/20.73 | From (1490) and (5454) follows:
% 54.47/20.73 | (5777) sum(n2, n21) = all_0_7_7
% 54.47/20.73 |
% 54.47/20.73 | From (1491) and (5452) follows:
% 54.47/20.74 | (5778) sum(n19, n4) = all_0_4_4
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n19, n4, all_0_4_4, n23 and discharging atoms sum(n19, n4) = all_0_4_4, sum(n19, n4) = n23, yields:
% 54.47/20.74 | (1117) all_0_4_4 = n23
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n2, n21, all_0_7_7, n23 and discharging atoms sum(n2, n21) = all_0_7_7, sum(n2, n21) = n23, yields:
% 54.47/20.74 | (1119) all_0_7_7 = n23
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 54.47/20.74 | (1262) all_0_2_2 = n6
% 54.47/20.74 |
% 54.47/20.74 | From (1262) and (5456) follows:
% 54.47/20.74 | (5548) sum(n6, n14) = all_0_0_0
% 54.47/20.74 |
% 54.47/20.74 | From (1119)(1117) and (590) follows:
% 54.47/20.74 | (1121) sum(n23, n23) = all_0_3_3
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 54.47/20.74 | (1122) all_0_3_3 = n20
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n6, n14, all_0_0_0, n20 and discharging atoms sum(n6, n14) = all_0_0_0, sum(n6, n14) = n20, yields:
% 54.47/20.74 | (1123) all_0_0_0 = n20
% 54.47/20.74 |
% 54.47/20.74 | Equations (1123,1122) can reduce 679 to:
% 54.47/20.74 | (1106) $false
% 54.47/20.74 |
% 54.47/20.74 |-The branch is then unsatisfiable
% 54.47/20.74 |-Branch two:
% 54.47/20.74 | (1503) ~ (all_0_11_11 = n3)
% 54.47/20.74 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 54.47/20.74 |
% 54.47/20.74 +-Applying beta-rule and splitting (1504), into two cases.
% 54.47/20.74 |-Branch one:
% 54.47/20.74 | (1505) all_0_11_11 = n2
% 54.47/20.74 |
% 54.47/20.74 | From (1505) and (559) follows:
% 54.47/20.74 | (1506) pred(n2) = all_0_9_9
% 54.47/20.74 |
% 54.47/20.74 | From (1505) and (992) follows:
% 54.47/20.74 | (1507) succ(n2) = all_0_5_5
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 54.47/20.74 | (1508) all_0_9_9 = n1
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 54.47/20.74 | (1509) all_0_5_5 = n3
% 54.47/20.74 |
% 54.47/20.74 | From (1508)(1509) and (538) follows:
% 54.47/20.74 | (1510) sum(n1, n3) = all_0_2_2
% 54.47/20.74 |
% 54.47/20.74 | From (1508) and (5454) follows:
% 54.47/20.74 | (5795) sum(n1, n21) = all_0_7_7
% 54.47/20.74 |
% 54.47/20.74 | From (1509) and (5452) follows:
% 54.47/20.74 | (5796) sum(n19, n3) = all_0_4_4
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n19, n3, all_0_4_4, n22 and discharging atoms sum(n19, n3) = all_0_4_4, sum(n19, n3) = n22, yields:
% 54.47/20.74 | (1135) all_0_4_4 = n22
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n1, n21, all_0_7_7, n22 and discharging atoms sum(n1, n21) = all_0_7_7, sum(n1, n21) = n22, yields:
% 54.47/20.74 | (1137) all_0_7_7 = n22
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 54.47/20.74 | (1280) all_0_2_2 = n4
% 54.47/20.74 |
% 54.47/20.74 | From (1280) and (5456) follows:
% 54.47/20.74 | (5566) sum(n4, n14) = all_0_0_0
% 54.47/20.74 |
% 54.47/20.74 | From (1137)(1135) and (590) follows:
% 54.47/20.74 | (1139) sum(n22, n22) = all_0_3_3
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 54.47/20.74 | (1140) all_0_3_3 = n18
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n4, n14, all_0_0_0, n18 and discharging atoms sum(n4, n14) = all_0_0_0, sum(n4, n14) = n18, yields:
% 54.47/20.74 | (1141) all_0_0_0 = n18
% 54.47/20.74 |
% 54.47/20.74 | Equations (1141,1140) can reduce 679 to:
% 54.47/20.74 | (1106) $false
% 54.47/20.74 |
% 54.47/20.74 |-The branch is then unsatisfiable
% 54.47/20.74 |-Branch two:
% 54.47/20.74 | (1521) ~ (all_0_11_11 = n2)
% 54.47/20.74 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 54.47/20.74 |
% 54.47/20.74 +-Applying beta-rule and splitting (1522), into two cases.
% 54.47/20.74 |-Branch one:
% 54.47/20.74 | (1523) all_0_11_11 = n1
% 54.47/20.74 |
% 54.47/20.74 | From (1523) and (559) follows:
% 54.47/20.74 | (1524) pred(n1) = all_0_9_9
% 54.47/20.74 |
% 54.47/20.74 | From (1523) and (992) follows:
% 54.47/20.74 | (1525) succ(n1) = all_0_5_5
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 54.47/20.74 | (1526) all_0_9_9 = n0
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 54.47/20.74 | (1527) all_0_5_5 = n2
% 54.47/20.74 |
% 54.47/20.74 | From (1526)(1527) and (538) follows:
% 54.47/20.74 | (1528) sum(n0, n2) = all_0_2_2
% 54.47/20.74 |
% 54.47/20.74 | From (1526) and (5454) follows:
% 54.47/20.74 | (5813) sum(n0, n21) = all_0_7_7
% 54.47/20.74 |
% 54.47/20.74 | From (1527) and (5452) follows:
% 54.47/20.74 | (5814) sum(n19, n2) = all_0_4_4
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n19, n2, all_0_4_4, n21 and discharging atoms sum(n19, n2) = all_0_4_4, sum(n19, n2) = n21, yields:
% 54.47/20.74 | (1153) all_0_4_4 = n21
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n0, n21, all_0_7_7, n21 and discharging atoms sum(n0, n21) = all_0_7_7, sum(n0, n21) = n21, yields:
% 54.47/20.74 | (1155) all_0_7_7 = n21
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 54.47/20.74 | (1298) all_0_2_2 = n2
% 54.47/20.74 |
% 54.47/20.74 | From (1298) and (5456) follows:
% 54.47/20.74 | (5584) sum(n2, n14) = all_0_0_0
% 54.47/20.74 |
% 54.47/20.74 | From (1155)(1153) and (590) follows:
% 54.47/20.74 | (1157) sum(n21, n21) = all_0_3_3
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 54.47/20.74 | (1158) all_0_3_3 = n16
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n2, n14, all_0_0_0, n16 and discharging atoms sum(n2, n14) = all_0_0_0, sum(n2, n14) = n16, yields:
% 54.47/20.74 | (1159) all_0_0_0 = n16
% 54.47/20.74 |
% 54.47/20.74 | Equations (1159,1158) can reduce 679 to:
% 54.47/20.74 | (1106) $false
% 54.47/20.74 |
% 54.47/20.74 |-The branch is then unsatisfiable
% 54.47/20.74 |-Branch two:
% 54.47/20.74 | (1540) ~ (all_0_11_11 = n1)
% 54.47/20.74 | (1541) all_0_11_11 = n0
% 54.47/20.74 |
% 54.47/20.74 | From (1541) and (559) follows:
% 54.47/20.74 | (1542) pred(n0) = all_0_9_9
% 54.47/20.74 |
% 54.47/20.74 | From (1541) and (992) follows:
% 54.47/20.74 | (1543) succ(n0) = all_0_5_5
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 54.47/20.74 | (1544) all_0_9_9 = n25
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 54.47/20.74 | (1545) all_0_5_5 = n1
% 54.47/20.74 |
% 54.47/20.74 | From (1544)(1545) and (538) follows:
% 54.47/20.74 | (1546) sum(n25, n1) = all_0_2_2
% 54.47/20.74 |
% 54.47/20.74 | From (1544) and (5454) follows:
% 54.47/20.74 | (5830) sum(n25, n21) = all_0_7_7
% 54.47/20.74 |
% 54.47/20.74 | From (1545) and (5452) follows:
% 54.47/20.74 | (5831) sum(n19, n1) = all_0_4_4
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n25, n21, all_0_7_7, n20 and discharging atoms sum(n25, n21) = all_0_7_7, sum(n25, n21) = n20, yields:
% 54.47/20.74 | (1173) all_0_7_7 = n20
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 54.47/20.74 | (1316) all_0_2_2 = n0
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n19, n1, all_0_4_4, n20 and discharging atoms sum(n19, n1) = all_0_4_4, sum(n19, n1) = n20, yields:
% 54.47/20.74 | (1171) all_0_4_4 = n20
% 54.47/20.74 |
% 54.47/20.74 | From (1316) and (5456) follows:
% 54.47/20.74 | (5602) sum(n0, n14) = all_0_0_0
% 54.47/20.74 |
% 54.47/20.74 | From (1173)(1171) and (590) follows:
% 54.47/20.74 | (1175) sum(n20, n20) = all_0_3_3
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 54.47/20.74 | (1176) all_0_3_3 = n14
% 54.47/20.74 |
% 54.47/20.74 | Instantiating formula (690) with n0, n14, all_0_0_0, n14 and discharging atoms sum(n0, n14) = all_0_0_0, sum(n0, n14) = n14, yields:
% 54.47/20.74 | (1177) all_0_0_0 = n14
% 54.47/20.74 |
% 54.47/20.74 | Equations (1177,1176) can reduce 679 to:
% 54.47/20.74 | (1106) $false
% 54.47/20.74 |
% 54.47/20.74 |-The branch is then unsatisfiable
% 54.47/20.75 |-Branch two:
% 54.47/20.75 | (1658) ~ (all_0_10_10 = n20)
% 54.47/20.75 | (1659) 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
% 54.47/20.75 |
% 54.47/20.75 +-Applying beta-rule and splitting (1180), into two cases.
% 54.47/20.75 |-Branch one:
% 54.47/20.75 | (1181) all_0_11_11 = n20
% 54.47/20.75 |
% 54.47/20.75 | From (1181) and (559) follows:
% 54.47/20.75 | (1182) pred(n20) = all_0_9_9
% 54.47/20.75 |
% 54.47/20.75 | From (1181) and (992) follows:
% 54.47/20.75 | (1183) succ(n20) = all_0_5_5
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (500) with n20, all_0_9_9, n19 and discharging atoms pred(n20) = all_0_9_9, pred(n20) = n19, yields:
% 54.47/20.75 | (1184) all_0_9_9 = n19
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (617) with n20, all_0_5_5, n21 and discharging atoms succ(n20) = all_0_5_5, succ(n20) = n21, yields:
% 54.47/20.75 | (1185) all_0_5_5 = n21
% 54.47/20.75 |
% 54.47/20.75 | From (1185) and (541) follows:
% 54.47/20.75 | (5847) sum(all_0_6_6, n21) = all_0_4_4
% 54.47/20.75 |
% 54.47/20.75 | From (1184)(1185) and (538) follows:
% 54.47/20.75 | (1186) sum(n19, n21) = all_0_2_2
% 54.47/20.75 |
% 54.47/20.75 | From (1184) and (427) follows:
% 54.47/20.75 | (5849) sum(n19, all_0_8_8) = all_0_7_7
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (690) with n19, n21, all_0_2_2, n14 and discharging atoms sum(n19, n21) = all_0_2_2, sum(n19, n21) = n14, yields:
% 54.47/20.75 | (1190) all_0_2_2 = n14
% 54.47/20.75 |
% 54.47/20.75 | From (1190) and (630) follows:
% 54.47/20.75 | (5851) sum(n14, all_0_1_1) = all_0_0_0
% 54.47/20.75 |
% 54.47/20.75 +-Applying beta-rule and splitting (1659), into two cases.
% 54.47/20.75 |-Branch one:
% 54.47/20.75 | (1660) all_0_10_10 = n19
% 54.47/20.75 |
% 54.47/20.75 | From (1660) and (292) follows:
% 54.47/20.75 | (1661) pred(n19) = all_0_6_6
% 54.47/20.75 |
% 54.47/20.75 | From (1660) and (760) follows:
% 54.47/20.75 | (1662) succ(n19) = all_0_8_8
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (500) with n19, all_0_6_6, n18 and discharging atoms pred(n19) = all_0_6_6, pred(n19) = n18, yields:
% 54.47/20.75 | (1663) all_0_6_6 = n18
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (617) with n19, all_0_8_8, n20 and discharging atoms succ(n19) = all_0_8_8, succ(n19) = n20, yields:
% 54.47/20.75 | (1664) all_0_8_8 = n20
% 54.47/20.75 |
% 54.47/20.75 | From (1663)(1664) and (411) follows:
% 54.47/20.75 | (1665) sum(n18, n20) = all_0_1_1
% 54.47/20.75 |
% 54.47/20.75 | From (1663) and (5847) follows:
% 54.47/20.75 | (5858) sum(n18, n21) = all_0_4_4
% 54.47/20.75 |
% 54.47/20.75 | From (1664) and (5849) follows:
% 54.47/20.75 | (5859) sum(n19, n20) = all_0_7_7
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (690) with n19, n20, all_0_7_7, n13 and discharging atoms sum(n19, n20) = all_0_7_7, sum(n19, n20) = n13, yields:
% 54.47/20.75 | (1299) all_0_7_7 = n13
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (690) with n18, n21, all_0_4_4, n13 and discharging atoms sum(n18, n21) = all_0_4_4, sum(n18, n21) = n13, yields:
% 54.47/20.75 | (1297) all_0_4_4 = n13
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (690) with n18, n20, all_0_1_1, n12 and discharging atoms sum(n18, n20) = all_0_1_1, sum(n18, n20) = n12, yields:
% 54.47/20.75 | (1669) all_0_1_1 = n12
% 54.47/20.75 |
% 54.47/20.75 | From (1299)(1297) and (590) follows:
% 54.47/20.75 | (1301) sum(n13, n13) = all_0_3_3
% 54.47/20.75 |
% 54.47/20.75 | From (1669) and (5851) follows:
% 54.47/20.75 | (5864) sum(n14, n12) = all_0_0_0
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (690) with n14, n12, all_0_0_0, n0 and discharging atoms sum(n14, n12) = all_0_0_0, sum(n14, n12) = n0, yields:
% 54.47/20.75 | (1303) all_0_0_0 = n0
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 54.47/20.75 | (1302) all_0_3_3 = n0
% 54.47/20.75 |
% 54.47/20.75 | Equations (1303,1302) can reduce 679 to:
% 54.47/20.75 | (1106) $false
% 54.47/20.75 |
% 54.47/20.75 |-The branch is then unsatisfiable
% 54.47/20.75 |-Branch two:
% 54.47/20.75 | (1676) ~ (all_0_10_10 = n19)
% 54.47/20.75 | (1677) 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
% 54.47/20.75 |
% 54.47/20.75 +-Applying beta-rule and splitting (1677), into two cases.
% 54.47/20.75 |-Branch one:
% 54.47/20.75 | (1678) all_0_10_10 = n18
% 54.47/20.75 |
% 54.47/20.75 | From (1678) and (292) follows:
% 54.47/20.75 | (1679) pred(n18) = all_0_6_6
% 54.47/20.75 |
% 54.47/20.75 | From (1678) and (760) follows:
% 54.47/20.75 | (1680) succ(n18) = all_0_8_8
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (500) with n18, all_0_6_6, n17 and discharging atoms pred(n18) = all_0_6_6, pred(n18) = n17, yields:
% 54.47/20.75 | (1681) all_0_6_6 = n17
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (617) with n18, all_0_8_8, n19 and discharging atoms succ(n18) = all_0_8_8, succ(n18) = n19, yields:
% 54.47/20.75 | (1682) all_0_8_8 = n19
% 54.47/20.75 |
% 54.47/20.75 | From (1681)(1682) and (411) follows:
% 54.47/20.75 | (1683) sum(n17, n19) = all_0_1_1
% 54.47/20.75 |
% 54.47/20.75 | From (1681) and (5847) follows:
% 54.47/20.75 | (5876) sum(n17, n21) = all_0_4_4
% 54.47/20.75 |
% 54.47/20.75 | From (1682) and (5849) follows:
% 54.47/20.75 | (5877) sum(n19, n19) = all_0_7_7
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (690) with n19, n19, all_0_7_7, n12 and discharging atoms sum(n19, n19) = all_0_7_7, sum(n19, n19) = n12, yields:
% 54.47/20.75 | (1317) all_0_7_7 = n12
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (690) with n17, n21, all_0_4_4, n12 and discharging atoms sum(n17, n21) = all_0_4_4, sum(n17, n21) = n12, yields:
% 54.47/20.75 | (1315) all_0_4_4 = n12
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (690) with n17, n19, all_0_1_1, n10 and discharging atoms sum(n17, n19) = all_0_1_1, sum(n17, n19) = n10, yields:
% 54.47/20.75 | (1687) all_0_1_1 = n10
% 54.47/20.75 |
% 54.47/20.75 | From (1317)(1315) and (590) follows:
% 54.47/20.75 | (1319) sum(n12, n12) = all_0_3_3
% 54.47/20.75 |
% 54.47/20.75 | From (1687) and (5851) follows:
% 54.47/20.75 | (5882) sum(n14, n10) = all_0_0_0
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (690) with n14, n10, all_0_0_0, n24 and discharging atoms sum(n14, n10) = all_0_0_0, sum(n14, n10) = n24, yields:
% 54.47/20.75 | (1321) all_0_0_0 = n24
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 54.47/20.75 | (1320) all_0_3_3 = n24
% 54.47/20.75 |
% 54.47/20.75 | Equations (1321,1320) can reduce 679 to:
% 54.47/20.75 | (1106) $false
% 54.47/20.75 |
% 54.47/20.75 |-The branch is then unsatisfiable
% 54.47/20.75 |-Branch two:
% 54.47/20.75 | (1694) ~ (all_0_10_10 = n18)
% 54.47/20.75 | (1695) 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
% 54.47/20.75 |
% 54.47/20.75 +-Applying beta-rule and splitting (1695), into two cases.
% 54.47/20.75 |-Branch one:
% 54.47/20.75 | (1696) all_0_10_10 = n17
% 54.47/20.75 |
% 54.47/20.75 | From (1696) and (292) follows:
% 54.47/20.75 | (1697) pred(n17) = all_0_6_6
% 54.47/20.75 |
% 54.47/20.75 | From (1696) and (760) follows:
% 54.47/20.75 | (1698) succ(n17) = all_0_8_8
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (500) with n17, all_0_6_6, n16 and discharging atoms pred(n17) = all_0_6_6, pred(n17) = n16, yields:
% 54.47/20.75 | (1699) all_0_6_6 = n16
% 54.47/20.75 |
% 54.47/20.75 | Instantiating formula (617) with n17, all_0_8_8, n18 and discharging atoms succ(n17) = all_0_8_8, succ(n17) = n18, yields:
% 54.47/20.75 | (1700) all_0_8_8 = n18
% 54.47/20.75 |
% 54.47/20.75 | From (1699)(1700) and (411) follows:
% 54.47/20.75 | (1701) sum(n16, n18) = all_0_1_1
% 54.47/20.75 |
% 54.47/20.75 | From (1699) and (5847) follows:
% 54.47/20.75 | (5894) sum(n16, n21) = all_0_4_4
% 54.47/20.75 |
% 54.47/20.75 | From (1700) and (5849) follows:
% 54.47/20.76 | (5895) sum(n19, n18) = all_0_7_7
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n19, n18, all_0_7_7, n11 and discharging atoms sum(n19, n18) = all_0_7_7, sum(n19, n18) = n11, yields:
% 54.47/20.76 | (1335) all_0_7_7 = n11
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n16, n21, all_0_4_4, n11 and discharging atoms sum(n16, n21) = all_0_4_4, sum(n16, n21) = n11, yields:
% 54.47/20.76 | (1333) all_0_4_4 = n11
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n16, n18, all_0_1_1, n8 and discharging atoms sum(n16, n18) = all_0_1_1, sum(n16, n18) = n8, yields:
% 54.47/20.76 | (1705) all_0_1_1 = n8
% 54.47/20.76 |
% 54.47/20.76 | From (1335)(1333) and (590) follows:
% 54.47/20.76 | (1337) sum(n11, n11) = all_0_3_3
% 54.47/20.76 |
% 54.47/20.76 | From (1705) and (5851) follows:
% 54.47/20.76 | (5900) sum(n14, n8) = all_0_0_0
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n14, n8, all_0_0_0, n22 and discharging atoms sum(n14, n8) = all_0_0_0, sum(n14, n8) = n22, yields:
% 54.47/20.76 | (1102) all_0_0_0 = n22
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 54.47/20.76 | (1104) all_0_3_3 = n22
% 54.47/20.76 |
% 54.47/20.76 | Equations (1102,1104) can reduce 679 to:
% 54.47/20.76 | (1106) $false
% 54.47/20.76 |
% 54.47/20.76 |-The branch is then unsatisfiable
% 54.47/20.76 |-Branch two:
% 54.47/20.76 | (1712) ~ (all_0_10_10 = n17)
% 54.47/20.76 | (1713) 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
% 54.47/20.76 |
% 54.47/20.76 +-Applying beta-rule and splitting (1713), into two cases.
% 54.47/20.76 |-Branch one:
% 54.47/20.76 | (1714) all_0_10_10 = n16
% 54.47/20.76 |
% 54.47/20.76 | From (1714) and (292) follows:
% 54.47/20.76 | (1715) pred(n16) = all_0_6_6
% 54.47/20.76 |
% 54.47/20.76 | From (1714) and (760) follows:
% 54.47/20.76 | (1716) succ(n16) = all_0_8_8
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (500) with n16, all_0_6_6, n15 and discharging atoms pred(n16) = all_0_6_6, pred(n16) = n15, yields:
% 54.47/20.76 | (1717) all_0_6_6 = n15
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (617) with n16, all_0_8_8, n17 and discharging atoms succ(n16) = all_0_8_8, succ(n16) = n17, yields:
% 54.47/20.76 | (1718) all_0_8_8 = n17
% 54.47/20.76 |
% 54.47/20.76 | From (1717)(1718) and (411) follows:
% 54.47/20.76 | (1719) sum(n15, n17) = all_0_1_1
% 54.47/20.76 |
% 54.47/20.76 | From (1717) and (5847) follows:
% 54.47/20.76 | (5912) sum(n15, n21) = all_0_4_4
% 54.47/20.76 |
% 54.47/20.76 | From (1718) and (5849) follows:
% 54.47/20.76 | (5913) sum(n19, n17) = all_0_7_7
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n19, n17, all_0_7_7, n10 and discharging atoms sum(n19, n17) = all_0_7_7, sum(n19, n17) = n10, yields:
% 54.47/20.76 | (1353) all_0_7_7 = n10
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n15, n21, all_0_4_4, n10 and discharging atoms sum(n15, n21) = all_0_4_4, sum(n15, n21) = n10, yields:
% 54.47/20.76 | (1351) all_0_4_4 = n10
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n15, n17, all_0_1_1, n6 and discharging atoms sum(n15, n17) = all_0_1_1, sum(n15, n17) = n6, yields:
% 54.47/20.76 | (1723) all_0_1_1 = n6
% 54.47/20.76 |
% 54.47/20.76 | From (1353)(1351) and (590) follows:
% 54.47/20.76 | (1355) sum(n10, n10) = all_0_3_3
% 54.47/20.76 |
% 54.47/20.76 | From (1723) and (5851) follows:
% 54.47/20.76 | (5918) sum(n14, n6) = all_0_0_0
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n14, n6, all_0_0_0, n20 and discharging atoms sum(n14, n6) = all_0_0_0, sum(n14, n6) = n20, yields:
% 54.47/20.76 | (1123) all_0_0_0 = n20
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 54.47/20.76 | (1122) all_0_3_3 = n20
% 54.47/20.76 |
% 54.47/20.76 | Equations (1123,1122) can reduce 679 to:
% 54.47/20.76 | (1106) $false
% 54.47/20.76 |
% 54.47/20.76 |-The branch is then unsatisfiable
% 54.47/20.76 |-Branch two:
% 54.47/20.76 | (1730) ~ (all_0_10_10 = n16)
% 54.47/20.76 | (1731) 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
% 54.47/20.76 |
% 54.47/20.76 +-Applying beta-rule and splitting (1731), into two cases.
% 54.47/20.76 |-Branch one:
% 54.47/20.76 | (1732) all_0_10_10 = n15
% 54.47/20.76 |
% 54.47/20.76 | From (1732) and (292) follows:
% 54.47/20.76 | (1733) pred(n15) = all_0_6_6
% 54.47/20.76 |
% 54.47/20.76 | From (1732) and (760) follows:
% 54.47/20.76 | (1734) succ(n15) = all_0_8_8
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (500) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 54.47/20.76 | (1735) all_0_6_6 = n14
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (617) with n15, all_0_8_8, n16 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n16, yields:
% 54.47/20.76 | (1736) all_0_8_8 = n16
% 54.47/20.76 |
% 54.47/20.76 | From (1735)(1736) and (411) follows:
% 54.47/20.76 | (1737) sum(n14, n16) = all_0_1_1
% 54.47/20.76 |
% 54.47/20.76 | From (1735) and (5847) follows:
% 54.47/20.76 | (5930) sum(n14, n21) = all_0_4_4
% 54.47/20.76 |
% 54.47/20.76 | From (1736) and (5849) follows:
% 54.47/20.76 | (5931) sum(n19, n16) = all_0_7_7
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n19, n16, all_0_7_7, n9 and discharging atoms sum(n19, n16) = all_0_7_7, sum(n19, n16) = n9, yields:
% 54.47/20.76 | (1371) all_0_7_7 = n9
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n14, n21, all_0_4_4, n9 and discharging atoms sum(n14, n21) = all_0_4_4, sum(n14, n21) = n9, yields:
% 54.47/20.76 | (1369) all_0_4_4 = n9
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n14, n16, all_0_1_1, n4 and discharging atoms sum(n14, n16) = all_0_1_1, sum(n14, n16) = n4, yields:
% 54.47/20.76 | (1741) all_0_1_1 = n4
% 54.47/20.76 |
% 54.47/20.76 | From (1371)(1369) and (590) follows:
% 54.47/20.76 | (1373) sum(n9, n9) = all_0_3_3
% 54.47/20.76 |
% 54.47/20.76 | From (1741) and (5851) follows:
% 54.47/20.76 | (5936) sum(n14, n4) = all_0_0_0
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n14, n4, all_0_0_0, n18 and discharging atoms sum(n14, n4) = all_0_0_0, sum(n14, n4) = n18, yields:
% 54.47/20.76 | (1141) all_0_0_0 = n18
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 54.47/20.76 | (1140) all_0_3_3 = n18
% 54.47/20.76 |
% 54.47/20.76 | Equations (1141,1140) can reduce 679 to:
% 54.47/20.76 | (1106) $false
% 54.47/20.76 |
% 54.47/20.76 |-The branch is then unsatisfiable
% 54.47/20.76 |-Branch two:
% 54.47/20.76 | (1748) ~ (all_0_10_10 = n15)
% 54.47/20.76 | (1749) 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
% 54.47/20.76 |
% 54.47/20.76 +-Applying beta-rule and splitting (1749), into two cases.
% 54.47/20.76 |-Branch one:
% 54.47/20.76 | (1750) all_0_10_10 = n14
% 54.47/20.76 |
% 54.47/20.76 | From (1750) and (292) follows:
% 54.47/20.76 | (1751) pred(n14) = all_0_6_6
% 54.47/20.76 |
% 54.47/20.76 | From (1750) and (760) follows:
% 54.47/20.76 | (1752) succ(n14) = all_0_8_8
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (500) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 54.47/20.76 | (1753) all_0_6_6 = n13
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (617) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 54.47/20.76 | (1754) all_0_8_8 = n15
% 54.47/20.76 |
% 54.47/20.76 | From (1753)(1754) and (411) follows:
% 54.47/20.76 | (1755) sum(n13, n15) = all_0_1_1
% 54.47/20.76 |
% 54.47/20.76 | From (1753) and (5847) follows:
% 54.47/20.76 | (5948) sum(n13, n21) = all_0_4_4
% 54.47/20.76 |
% 54.47/20.76 | From (1754) and (5849) follows:
% 54.47/20.76 | (5949) sum(n19, n15) = all_0_7_7
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n19, n15, all_0_7_7, n8 and discharging atoms sum(n19, n15) = all_0_7_7, sum(n19, n15) = n8, yields:
% 54.47/20.76 | (1389) all_0_7_7 = n8
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n13, n21, all_0_4_4, n8 and discharging atoms sum(n13, n21) = all_0_4_4, sum(n13, n21) = n8, yields:
% 54.47/20.76 | (1387) all_0_4_4 = n8
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n13, n15, all_0_1_1, n2 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n2, yields:
% 54.47/20.76 | (1759) all_0_1_1 = n2
% 54.47/20.76 |
% 54.47/20.76 | From (1389)(1387) and (590) follows:
% 54.47/20.76 | (1391) sum(n8, n8) = all_0_3_3
% 54.47/20.76 |
% 54.47/20.76 | From (1759) and (5851) follows:
% 54.47/20.76 | (5954) sum(n14, n2) = all_0_0_0
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n14, n2, all_0_0_0, n16 and discharging atoms sum(n14, n2) = all_0_0_0, sum(n14, n2) = n16, yields:
% 54.47/20.76 | (1159) all_0_0_0 = n16
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 54.47/20.76 | (1158) all_0_3_3 = n16
% 54.47/20.76 |
% 54.47/20.76 | Equations (1159,1158) can reduce 679 to:
% 54.47/20.76 | (1106) $false
% 54.47/20.76 |
% 54.47/20.76 |-The branch is then unsatisfiable
% 54.47/20.76 |-Branch two:
% 54.47/20.76 | (1766) ~ (all_0_10_10 = n14)
% 54.47/20.76 | (1767) 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
% 54.47/20.76 |
% 54.47/20.76 +-Applying beta-rule and splitting (1767), into two cases.
% 54.47/20.76 |-Branch one:
% 54.47/20.76 | (1768) all_0_10_10 = n13
% 54.47/20.76 |
% 54.47/20.76 | From (1768) and (292) follows:
% 54.47/20.76 | (1769) pred(n13) = all_0_6_6
% 54.47/20.76 |
% 54.47/20.76 | From (1768) and (760) follows:
% 54.47/20.76 | (1770) succ(n13) = all_0_8_8
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (500) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 54.47/20.76 | (1771) all_0_6_6 = n12
% 54.47/20.76 |
% 54.47/20.76 | Instantiating formula (617) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 54.47/20.76 | (1772) all_0_8_8 = n14
% 54.47/20.76 |
% 54.47/20.76 | From (1771)(1772) and (411) follows:
% 54.47/20.77 | (1773) sum(n12, n14) = all_0_1_1
% 54.47/20.77 |
% 54.47/20.77 | From (1771) and (5847) follows:
% 54.47/20.77 | (5966) sum(n12, n21) = all_0_4_4
% 54.47/20.77 |
% 54.47/20.77 | From (1772) and (5849) follows:
% 54.47/20.77 | (5967) sum(n19, n14) = all_0_7_7
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n19, n14, all_0_7_7, n7 and discharging atoms sum(n19, n14) = all_0_7_7, sum(n19, n14) = n7, yields:
% 54.47/20.77 | (1407) all_0_7_7 = n7
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n12, n21, all_0_4_4, n7 and discharging atoms sum(n12, n21) = all_0_4_4, sum(n12, n21) = n7, yields:
% 54.47/20.77 | (1405) all_0_4_4 = n7
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n12, n14, all_0_1_1, n0 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n0, yields:
% 54.47/20.77 | (1777) all_0_1_1 = n0
% 54.47/20.77 |
% 54.47/20.77 | From (1407)(1405) and (590) follows:
% 54.47/20.77 | (1409) sum(n7, n7) = all_0_3_3
% 54.47/20.77 |
% 54.47/20.77 | From (1777) and (5851) follows:
% 54.47/20.77 | (5972) sum(n14, n0) = all_0_0_0
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n14, n0, all_0_0_0, n14 and discharging atoms sum(n14, n0) = all_0_0_0, sum(n14, n0) = n14, yields:
% 54.47/20.77 | (1177) all_0_0_0 = n14
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 54.47/20.77 | (1176) all_0_3_3 = n14
% 54.47/20.77 |
% 54.47/20.77 | Equations (1177,1176) can reduce 679 to:
% 54.47/20.77 | (1106) $false
% 54.47/20.77 |
% 54.47/20.77 |-The branch is then unsatisfiable
% 54.47/20.77 |-Branch two:
% 54.47/20.77 | (1784) ~ (all_0_10_10 = n13)
% 54.47/20.77 | (1785) 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
% 54.47/20.77 |
% 54.47/20.77 +-Applying beta-rule and splitting (1785), into two cases.
% 54.47/20.77 |-Branch one:
% 54.47/20.77 | (1786) all_0_10_10 = n12
% 54.47/20.77 |
% 54.47/20.77 | From (1786) and (292) follows:
% 54.47/20.77 | (1787) pred(n12) = all_0_6_6
% 54.47/20.77 |
% 54.47/20.77 | From (1786) and (760) follows:
% 54.47/20.77 | (1788) succ(n12) = all_0_8_8
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (500) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 54.47/20.77 | (1789) all_0_6_6 = n11
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (617) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 54.47/20.77 | (1790) all_0_8_8 = n13
% 54.47/20.77 |
% 54.47/20.77 | From (1789)(1790) and (411) follows:
% 54.47/20.77 | (1791) sum(n11, n13) = all_0_1_1
% 54.47/20.77 |
% 54.47/20.77 | From (1789) and (5847) follows:
% 54.47/20.77 | (5984) sum(n11, n21) = all_0_4_4
% 54.47/20.77 |
% 54.47/20.77 | From (1790) and (5849) follows:
% 54.47/20.77 | (5985) sum(n19, n13) = all_0_7_7
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n19, n13, all_0_7_7, n6 and discharging atoms sum(n19, n13) = all_0_7_7, sum(n19, n13) = n6, yields:
% 54.47/20.77 | (1425) all_0_7_7 = n6
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n11, n21, all_0_4_4, n6 and discharging atoms sum(n11, n21) = all_0_4_4, sum(n11, n21) = n6, yields:
% 54.47/20.77 | (1423) all_0_4_4 = n6
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n11, n13, all_0_1_1, n24 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n24, yields:
% 54.47/20.77 | (1081) all_0_1_1 = n24
% 54.47/20.77 |
% 54.47/20.77 | From (1425)(1423) and (590) follows:
% 54.47/20.77 | (1427) sum(n6, n6) = all_0_3_3
% 54.47/20.77 |
% 54.47/20.77 | From (1081) and (5851) follows:
% 54.47/20.77 | (1192) sum(n14, n24) = all_0_0_0
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n14, n24, all_0_0_0, n12 and discharging atoms sum(n14, n24) = all_0_0_0, sum(n14, n24) = n12, yields:
% 54.47/20.77 | (1195) all_0_0_0 = n12
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 54.47/20.77 | (1194) all_0_3_3 = n12
% 54.47/20.77 |
% 54.47/20.77 | Equations (1195,1194) can reduce 679 to:
% 54.47/20.77 | (1106) $false
% 54.47/20.77 |
% 54.47/20.77 |-The branch is then unsatisfiable
% 54.47/20.77 |-Branch two:
% 54.47/20.77 | (1802) ~ (all_0_10_10 = n12)
% 54.47/20.77 | (1803) 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
% 54.47/20.77 |
% 54.47/20.77 +-Applying beta-rule and splitting (1803), into two cases.
% 54.47/20.77 |-Branch one:
% 54.47/20.77 | (1804) all_0_10_10 = n11
% 54.47/20.77 |
% 54.47/20.77 | From (1804) and (292) follows:
% 54.47/20.77 | (1805) pred(n11) = all_0_6_6
% 54.47/20.77 |
% 54.47/20.77 | From (1804) and (760) follows:
% 54.47/20.77 | (1806) succ(n11) = all_0_8_8
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (500) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 54.47/20.77 | (1807) all_0_6_6 = n10
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (617) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 54.47/20.77 | (1808) all_0_8_8 = n12
% 54.47/20.77 |
% 54.47/20.77 | From (1807)(1808) and (411) follows:
% 54.47/20.77 | (1809) sum(n10, n12) = all_0_1_1
% 54.47/20.77 |
% 54.47/20.77 | From (1807) and (5847) follows:
% 54.47/20.77 | (6002) sum(n10, n21) = all_0_4_4
% 54.47/20.77 |
% 54.47/20.77 | From (1808) and (5849) follows:
% 54.47/20.77 | (6003) sum(n19, n12) = all_0_7_7
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n19, n12, all_0_7_7, n5 and discharging atoms sum(n19, n12) = all_0_7_7, sum(n19, n12) = n5, yields:
% 54.47/20.77 | (1443) all_0_7_7 = n5
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n10, n21, all_0_4_4, n5 and discharging atoms sum(n10, n21) = all_0_4_4, sum(n10, n21) = n5, yields:
% 54.47/20.77 | (1441) all_0_4_4 = n5
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n10, n12, all_0_1_1, n22 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n22, yields:
% 54.47/20.77 | (1579) all_0_1_1 = n22
% 54.47/20.77 |
% 54.47/20.77 | From (1443)(1441) and (590) follows:
% 54.47/20.77 | (1445) sum(n5, n5) = all_0_3_3
% 54.47/20.77 |
% 54.47/20.77 | From (1579) and (5851) follows:
% 54.47/20.77 | (2124) sum(n14, n22) = all_0_0_0
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n14, n22, all_0_0_0, n10 and discharging atoms sum(n14, n22) = all_0_0_0, sum(n14, n22) = n10, yields:
% 54.47/20.77 | (1213) all_0_0_0 = n10
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 54.47/20.77 | (1212) all_0_3_3 = n10
% 54.47/20.77 |
% 54.47/20.77 | Equations (1213,1212) can reduce 679 to:
% 54.47/20.77 | (1106) $false
% 54.47/20.77 |
% 54.47/20.77 |-The branch is then unsatisfiable
% 54.47/20.77 |-Branch two:
% 54.47/20.77 | (1820) ~ (all_0_10_10 = n11)
% 54.47/20.77 | (1821) 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
% 54.47/20.77 |
% 54.47/20.77 +-Applying beta-rule and splitting (1821), into two cases.
% 54.47/20.77 |-Branch one:
% 54.47/20.77 | (1822) all_0_10_10 = n10
% 54.47/20.77 |
% 54.47/20.77 | From (1822) and (292) follows:
% 54.47/20.77 | (1823) pred(n10) = all_0_6_6
% 54.47/20.77 |
% 54.47/20.77 | From (1822) and (760) follows:
% 54.47/20.77 | (1824) succ(n10) = all_0_8_8
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (500) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 54.47/20.77 | (1825) all_0_6_6 = n9
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (617) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 54.47/20.77 | (1826) all_0_8_8 = n11
% 54.47/20.77 |
% 54.47/20.77 | From (1825)(1826) and (411) follows:
% 54.47/20.77 | (1827) sum(n9, n11) = all_0_1_1
% 54.47/20.77 |
% 54.47/20.77 | From (1825) and (5847) follows:
% 54.47/20.77 | (6020) sum(n9, n21) = all_0_4_4
% 54.47/20.77 |
% 54.47/20.77 | From (1826) and (5849) follows:
% 54.47/20.77 | (6021) sum(n19, n11) = all_0_7_7
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n19, n11, all_0_7_7, n4 and discharging atoms sum(n19, n11) = all_0_7_7, sum(n19, n11) = n4, yields:
% 54.47/20.77 | (1461) all_0_7_7 = n4
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n9, n21, all_0_4_4, n4 and discharging atoms sum(n9, n21) = all_0_4_4, sum(n9, n21) = n4, yields:
% 54.47/20.77 | (1459) all_0_4_4 = n4
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 54.47/20.77 | (1597) all_0_1_1 = n20
% 54.47/20.77 |
% 54.47/20.77 | From (1461)(1459) and (590) follows:
% 54.47/20.77 | (1463) sum(n4, n4) = all_0_3_3
% 54.47/20.77 |
% 54.47/20.77 | From (1597) and (5851) follows:
% 54.47/20.77 | (3016) sum(n14, n20) = all_0_0_0
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n14, n20, all_0_0_0, n8 and discharging atoms sum(n14, n20) = all_0_0_0, sum(n14, n20) = n8, yields:
% 54.47/20.77 | (1231) all_0_0_0 = n8
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 54.47/20.77 | (1230) all_0_3_3 = n8
% 54.47/20.77 |
% 54.47/20.77 | Equations (1231,1230) can reduce 679 to:
% 54.47/20.77 | (1106) $false
% 54.47/20.77 |
% 54.47/20.77 |-The branch is then unsatisfiable
% 54.47/20.77 |-Branch two:
% 54.47/20.77 | (1838) ~ (all_0_10_10 = n10)
% 54.47/20.77 | (1839) 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
% 54.47/20.77 |
% 54.47/20.77 +-Applying beta-rule and splitting (1839), into two cases.
% 54.47/20.77 |-Branch one:
% 54.47/20.77 | (1840) all_0_10_10 = n9
% 54.47/20.77 |
% 54.47/20.77 | From (1840) and (292) follows:
% 54.47/20.77 | (1841) pred(n9) = all_0_6_6
% 54.47/20.77 |
% 54.47/20.77 | From (1840) and (760) follows:
% 54.47/20.77 | (1842) succ(n9) = all_0_8_8
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (500) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 54.47/20.77 | (1843) all_0_6_6 = n8
% 54.47/20.77 |
% 54.47/20.77 | Instantiating formula (617) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 54.47/20.77 | (1844) all_0_8_8 = n10
% 54.47/20.77 |
% 54.47/20.77 | From (1843)(1844) and (411) follows:
% 54.47/20.77 | (1845) sum(n8, n10) = all_0_1_1
% 54.47/20.77 |
% 54.47/20.77 | From (1843) and (5847) follows:
% 54.47/20.78 | (6038) sum(n8, n21) = all_0_4_4
% 54.47/20.78 |
% 54.47/20.78 | From (1844) and (5849) follows:
% 54.47/20.78 | (6039) sum(n19, n10) = all_0_7_7
% 54.47/20.78 |
% 54.47/20.78 | Instantiating formula (690) with n19, n10, all_0_7_7, n3 and discharging atoms sum(n19, n10) = all_0_7_7, sum(n19, n10) = n3, yields:
% 54.47/20.78 | (1479) all_0_7_7 = n3
% 54.47/20.78 |
% 54.47/20.78 | Instantiating formula (690) with n8, n21, all_0_4_4, n3 and discharging atoms sum(n8, n21) = all_0_4_4, sum(n8, n21) = n3, yields:
% 54.47/20.78 | (1477) all_0_4_4 = n3
% 54.47/20.78 |
% 54.47/20.78 | Instantiating formula (690) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 54.47/20.78 | (1615) all_0_1_1 = n18
% 54.47/20.78 |
% 54.47/20.78 | From (1479)(1477) and (590) follows:
% 54.47/20.78 | (1481) sum(n3, n3) = all_0_3_3
% 54.47/20.78 |
% 54.47/20.78 | From (1615) and (5851) follows:
% 54.47/20.78 | (3872) sum(n14, n18) = all_0_0_0
% 54.47/20.78 |
% 54.47/20.78 | Instantiating formula (690) with n14, n18, all_0_0_0, n6 and discharging atoms sum(n14, n18) = all_0_0_0, sum(n14, n18) = n6, yields:
% 54.47/20.78 | (1249) all_0_0_0 = n6
% 54.47/20.78 |
% 54.47/20.78 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 54.47/20.78 | (1248) all_0_3_3 = n6
% 54.47/20.78 |
% 54.47/20.78 | Equations (1249,1248) can reduce 679 to:
% 54.47/20.78 | (1106) $false
% 54.47/20.78 |
% 54.47/20.78 |-The branch is then unsatisfiable
% 54.47/20.78 |-Branch two:
% 54.47/20.78 | (1856) ~ (all_0_10_10 = n9)
% 54.47/20.78 | (1857) 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
% 54.47/20.78 |
% 54.47/20.78 +-Applying beta-rule and splitting (1857), into two cases.
% 54.47/20.78 |-Branch one:
% 54.47/20.78 | (1858) all_0_10_10 = n8
% 54.47/20.78 |
% 54.47/20.78 | From (1858) and (292) follows:
% 54.47/20.78 | (1859) pred(n8) = all_0_6_6
% 54.47/20.78 |
% 54.47/20.78 | From (1858) and (760) follows:
% 54.47/20.78 | (1860) succ(n8) = all_0_8_8
% 54.47/20.78 |
% 54.47/20.78 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 54.47/20.78 | (1861) all_0_6_6 = n7
% 54.47/20.78 |
% 54.47/20.78 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 54.47/20.78 | (1862) all_0_8_8 = n9
% 54.47/20.78 |
% 54.47/20.78 | From (1861)(1862) and (411) follows:
% 54.47/20.78 | (1863) sum(n7, n9) = all_0_1_1
% 54.47/20.78 |
% 54.47/20.78 | From (1861) and (5847) follows:
% 54.47/20.78 | (6056) sum(n7, n21) = all_0_4_4
% 54.47/20.78 |
% 54.47/20.78 | From (1862) and (5849) follows:
% 54.47/20.78 | (6057) sum(n19, n9) = all_0_7_7
% 54.47/20.78 |
% 54.47/20.78 | Instantiating formula (690) with n19, n9, all_0_7_7, n2 and discharging atoms sum(n19, n9) = all_0_7_7, sum(n19, n9) = n2, yields:
% 54.47/20.78 | (1497) all_0_7_7 = n2
% 54.47/20.78 |
% 54.47/20.78 | Instantiating formula (690) with n7, n21, all_0_4_4, n2 and discharging atoms sum(n7, n21) = all_0_4_4, sum(n7, n21) = n2, yields:
% 54.47/20.78 | (1495) all_0_4_4 = n2
% 54.47/20.78 |
% 54.47/20.78 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 54.47/20.78 | (1633) all_0_1_1 = n16
% 54.47/20.78 |
% 54.47/20.78 | From (1497)(1495) and (590) follows:
% 54.47/20.78 | (1499) sum(n2, n2) = all_0_3_3
% 54.47/20.78 |
% 54.47/20.78 | From (1633) and (5851) follows:
% 54.47/20.78 | (4692) sum(n14, n16) = all_0_0_0
% 54.47/20.78 |
% 54.47/20.78 | Instantiating formula (690) with n14, n16, all_0_0_0, n4 and discharging atoms sum(n14, n16) = all_0_0_0, sum(n14, n16) = n4, yields:
% 54.47/20.78 | (1267) all_0_0_0 = n4
% 54.47/20.78 |
% 54.47/20.78 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 54.47/20.78 | (1266) all_0_3_3 = n4
% 54.47/20.78 |
% 54.68/20.78 | Equations (1267,1266) can reduce 679 to:
% 54.68/20.78 | (1106) $false
% 54.68/20.78 |
% 54.68/20.78 |-The branch is then unsatisfiable
% 54.68/20.78 |-Branch two:
% 54.68/20.78 | (1874) ~ (all_0_10_10 = n8)
% 54.68/20.78 | (1875) 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
% 54.68/20.78 |
% 54.68/20.78 +-Applying beta-rule and splitting (1875), into two cases.
% 54.68/20.78 |-Branch one:
% 54.68/20.78 | (1876) all_0_10_10 = n7
% 54.68/20.78 |
% 54.68/20.78 | From (1876) and (292) follows:
% 54.68/20.78 | (1877) pred(n7) = all_0_6_6
% 54.68/20.78 |
% 54.68/20.78 | From (1876) and (760) follows:
% 54.68/20.78 | (1878) succ(n7) = all_0_8_8
% 54.68/20.78 |
% 54.68/20.78 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 54.68/20.78 | (1879) all_0_6_6 = n6
% 54.68/20.78 |
% 54.68/20.78 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 54.68/20.78 | (1880) all_0_8_8 = n8
% 54.68/20.78 |
% 54.68/20.78 | From (1879)(1880) and (411) follows:
% 54.68/20.78 | (1881) sum(n6, n8) = all_0_1_1
% 54.68/20.78 |
% 54.68/20.78 | From (1879) and (5847) follows:
% 54.68/20.78 | (6074) sum(n6, n21) = all_0_4_4
% 54.68/20.78 |
% 54.68/20.78 | From (1880) and (5849) follows:
% 54.68/20.78 | (6075) sum(n19, n8) = all_0_7_7
% 54.68/20.78 |
% 54.68/20.78 | Instantiating formula (690) with n19, n8, all_0_7_7, n1 and discharging atoms sum(n19, n8) = all_0_7_7, sum(n19, n8) = n1, yields:
% 54.68/20.78 | (1515) all_0_7_7 = n1
% 54.68/20.78 |
% 54.68/20.78 | Instantiating formula (690) with n6, n21, all_0_4_4, n1 and discharging atoms sum(n6, n21) = all_0_4_4, sum(n6, n21) = n1, yields:
% 54.68/20.78 | (1513) all_0_4_4 = n1
% 54.68/20.78 |
% 54.68/20.78 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 54.68/20.78 | (1651) all_0_1_1 = n14
% 54.68/20.78 |
% 54.68/20.78 | From (1515)(1513) and (590) follows:
% 54.68/20.78 | (1517) sum(n1, n1) = all_0_3_3
% 54.68/20.78 |
% 54.68/20.78 | From (1651) and (5851) follows:
% 54.68/20.78 | (5474) sum(n14, n14) = all_0_0_0
% 54.68/20.78 |
% 54.68/20.78 | Instantiating formula (690) with n14, n14, all_0_0_0, n2 and discharging atoms sum(n14, n14) = all_0_0_0, sum(n14, n14) = n2, yields:
% 54.68/20.78 | (1285) all_0_0_0 = n2
% 54.68/20.78 |
% 54.68/20.78 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 54.68/20.78 | (1284) all_0_3_3 = n2
% 54.68/20.78 |
% 54.68/20.78 | Equations (1285,1284) can reduce 679 to:
% 54.68/20.78 | (1106) $false
% 54.68/20.78 |
% 54.68/20.78 |-The branch is then unsatisfiable
% 54.68/20.78 |-Branch two:
% 54.68/20.78 | (1892) ~ (all_0_10_10 = n7)
% 54.68/20.78 | (1893) 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
% 54.68/20.78 |
% 54.68/20.78 +-Applying beta-rule and splitting (1893), into two cases.
% 54.68/20.78 |-Branch one:
% 54.68/20.78 | (1894) all_0_10_10 = n6
% 54.68/20.78 |
% 54.68/20.78 | From (1894) and (292) follows:
% 54.68/20.78 | (1895) pred(n6) = all_0_6_6
% 54.68/20.78 |
% 54.68/20.78 | From (1894) and (760) follows:
% 54.68/20.78 | (1896) succ(n6) = all_0_8_8
% 54.68/20.78 |
% 54.68/20.78 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 54.68/20.78 | (1897) all_0_6_6 = n5
% 54.68/20.78 |
% 54.68/20.78 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 54.68/20.78 | (1898) all_0_8_8 = n7
% 54.68/20.78 |
% 54.68/20.78 | From (1897)(1898) and (411) follows:
% 54.68/20.78 | (1899) sum(n5, n7) = all_0_1_1
% 54.68/20.78 |
% 54.68/20.78 | From (1897) and (5847) follows:
% 54.68/20.78 | (6092) sum(n5, n21) = all_0_4_4
% 54.68/20.78 |
% 54.68/20.78 | From (1898) and (5849) follows:
% 54.68/20.78 | (6093) sum(n19, n7) = all_0_7_7
% 54.68/20.78 |
% 54.68/20.78 | Instantiating formula (690) with n19, n7, all_0_7_7, n0 and discharging atoms sum(n19, n7) = all_0_7_7, sum(n19, n7) = n0, yields:
% 54.68/20.78 | (1533) all_0_7_7 = n0
% 54.68/20.78 |
% 54.68/20.78 | Instantiating formula (690) with n5, n21, all_0_4_4, n0 and discharging atoms sum(n5, n21) = all_0_4_4, sum(n5, n21) = n0, yields:
% 54.68/20.78 | (1531) all_0_4_4 = n0
% 54.68/20.78 |
% 54.68/20.78 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 54.68/20.78 | (1669) all_0_1_1 = n12
% 54.68/20.78 |
% 54.68/20.78 | From (1533)(1531) and (590) follows:
% 54.68/20.78 | (1535) sum(n0, n0) = all_0_3_3
% 54.68/20.78 |
% 54.68/20.78 | From (1669) and (5851) follows:
% 54.68/20.78 | (5864) sum(n14, n12) = all_0_0_0
% 54.68/20.78 |
% 54.68/20.78 | Instantiating formula (690) with n14, n12, all_0_0_0, n0 and discharging atoms sum(n14, n12) = all_0_0_0, sum(n14, n12) = n0, yields:
% 54.68/20.78 | (1303) all_0_0_0 = n0
% 54.68/20.78 |
% 54.68/20.78 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 54.68/20.78 | (1302) all_0_3_3 = n0
% 54.68/20.78 |
% 54.68/20.78 | Equations (1303,1302) can reduce 679 to:
% 54.68/20.78 | (1106) $false
% 54.68/20.78 |
% 54.68/20.78 |-The branch is then unsatisfiable
% 54.68/20.78 |-Branch two:
% 54.68/20.78 | (1910) ~ (all_0_10_10 = n6)
% 54.68/20.78 | (1911) 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
% 54.68/20.78 |
% 54.68/20.78 +-Applying beta-rule and splitting (1911), into two cases.
% 54.68/20.78 |-Branch one:
% 54.68/20.78 | (1912) all_0_10_10 = n5
% 54.68/20.78 |
% 54.68/20.78 | From (1912) and (292) follows:
% 54.68/20.78 | (1913) pred(n5) = all_0_6_6
% 54.68/20.78 |
% 54.68/20.78 | From (1912) and (760) follows:
% 54.68/20.78 | (1914) succ(n5) = all_0_8_8
% 54.68/20.78 |
% 54.68/20.78 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 54.68/20.78 | (1915) all_0_6_6 = n4
% 54.68/20.78 |
% 54.68/20.78 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 54.68/20.78 | (1916) all_0_8_8 = n6
% 54.68/20.78 |
% 54.68/20.78 | From (1915)(1916) and (411) follows:
% 54.68/20.79 | (1917) sum(n4, n6) = all_0_1_1
% 54.68/20.79 |
% 54.68/20.79 | From (1915) and (5847) follows:
% 54.68/20.79 | (6110) sum(n4, n21) = all_0_4_4
% 54.68/20.79 |
% 54.68/20.79 | From (1916) and (5849) follows:
% 54.68/20.79 | (6111) sum(n19, n6) = all_0_7_7
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n19, n6, all_0_7_7, n25 and discharging atoms sum(n19, n6) = all_0_7_7, sum(n19, n6) = n25, yields:
% 54.68/20.79 | (1550) all_0_7_7 = n25
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n4, n21, all_0_4_4, n25 and discharging atoms sum(n4, n21) = all_0_4_4, sum(n4, n21) = n25, yields:
% 54.68/20.79 | (1551) all_0_4_4 = n25
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 54.68/20.79 | (1687) all_0_1_1 = n10
% 54.68/20.79 |
% 54.68/20.79 | From (1550)(1551) and (590) follows:
% 54.68/20.79 | (1553) sum(n25, n25) = all_0_3_3
% 54.68/20.79 |
% 54.68/20.79 | From (1687) and (5851) follows:
% 54.68/20.79 | (5882) sum(n14, n10) = all_0_0_0
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 54.68/20.79 | (1320) all_0_3_3 = n24
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n14, n10, all_0_0_0, n24 and discharging atoms sum(n14, n10) = all_0_0_0, sum(n14, n10) = n24, yields:
% 54.68/20.79 | (1321) all_0_0_0 = n24
% 54.68/20.79 |
% 54.68/20.79 | Equations (1321,1320) can reduce 679 to:
% 54.68/20.79 | (1106) $false
% 54.68/20.79 |
% 54.68/20.79 |-The branch is then unsatisfiable
% 54.68/20.79 |-Branch two:
% 54.68/20.79 | (1928) ~ (all_0_10_10 = n5)
% 54.68/20.79 | (1929) 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
% 54.68/20.79 |
% 54.68/20.79 +-Applying beta-rule and splitting (1929), into two cases.
% 54.68/20.79 |-Branch one:
% 54.68/20.79 | (1930) all_0_10_10 = n4
% 54.68/20.79 |
% 54.68/20.79 | From (1930) and (292) follows:
% 54.68/20.79 | (1931) pred(n4) = all_0_6_6
% 54.68/20.79 |
% 54.68/20.79 | From (1930) and (760) follows:
% 54.68/20.79 | (1932) succ(n4) = all_0_8_8
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 54.68/20.79 | (1933) all_0_6_6 = n3
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 54.68/20.79 | (1934) all_0_8_8 = n5
% 54.68/20.79 |
% 54.68/20.79 | From (1933)(1934) and (411) follows:
% 54.68/20.79 | (1935) sum(n3, n5) = all_0_1_1
% 54.68/20.79 |
% 54.68/20.79 | From (1933) and (5847) follows:
% 54.68/20.79 | (6128) sum(n3, n21) = all_0_4_4
% 54.68/20.79 |
% 54.68/20.79 | From (1934) and (5849) follows:
% 54.68/20.79 | (6129) sum(n19, n5) = all_0_7_7
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n19, n5, all_0_7_7, n24 and discharging atoms sum(n19, n5) = all_0_7_7, sum(n19, n5) = n24, yields:
% 54.68/20.79 | (1097) all_0_7_7 = n24
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n3, n21, all_0_4_4, n24 and discharging atoms sum(n3, n21) = all_0_4_4, sum(n3, n21) = n24, yields:
% 54.68/20.79 | (1096) all_0_4_4 = n24
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 54.68/20.79 | (1705) all_0_1_1 = n8
% 54.68/20.79 |
% 54.68/20.79 | From (1097)(1096) and (590) follows:
% 54.68/20.79 | (1101) sum(n24, n24) = all_0_3_3
% 54.68/20.79 |
% 54.68/20.79 | From (1705) and (5851) follows:
% 54.68/20.79 | (5900) sum(n14, n8) = all_0_0_0
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 54.68/20.79 | (1104) all_0_3_3 = n22
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n14, n8, all_0_0_0, n22 and discharging atoms sum(n14, n8) = all_0_0_0, sum(n14, n8) = n22, yields:
% 54.68/20.79 | (1102) all_0_0_0 = n22
% 54.68/20.79 |
% 54.68/20.79 | Equations (1102,1104) can reduce 679 to:
% 54.68/20.79 | (1106) $false
% 54.68/20.79 |
% 54.68/20.79 |-The branch is then unsatisfiable
% 54.68/20.79 |-Branch two:
% 54.68/20.79 | (1946) ~ (all_0_10_10 = n4)
% 54.68/20.79 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 54.68/20.79 |
% 54.68/20.79 +-Applying beta-rule and splitting (1947), into two cases.
% 54.68/20.79 |-Branch one:
% 54.68/20.79 | (1948) all_0_10_10 = n3
% 54.68/20.79 |
% 54.68/20.79 | From (1948) and (292) follows:
% 54.68/20.79 | (1949) pred(n3) = all_0_6_6
% 54.68/20.79 |
% 54.68/20.79 | From (1948) and (760) follows:
% 54.68/20.79 | (1950) succ(n3) = all_0_8_8
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 54.68/20.79 | (1951) all_0_6_6 = n2
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 54.68/20.79 | (1952) all_0_8_8 = n4
% 54.68/20.79 |
% 54.68/20.79 | From (1951)(1952) and (411) follows:
% 54.68/20.79 | (1953) sum(n2, n4) = all_0_1_1
% 54.68/20.79 |
% 54.68/20.79 | From (1951) and (5847) follows:
% 54.68/20.79 | (6146) sum(n2, n21) = all_0_4_4
% 54.68/20.79 |
% 54.68/20.79 | From (1952) and (5849) follows:
% 54.68/20.79 | (6147) sum(n19, n4) = all_0_7_7
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n19, n4, all_0_7_7, n23 and discharging atoms sum(n19, n4) = all_0_7_7, sum(n19, n4) = n23, yields:
% 54.68/20.79 | (1119) all_0_7_7 = n23
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n2, n21, all_0_4_4, n23 and discharging atoms sum(n2, n21) = all_0_4_4, sum(n2, n21) = n23, yields:
% 54.68/20.79 | (1117) all_0_4_4 = n23
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 54.68/20.79 | (1723) all_0_1_1 = n6
% 54.68/20.79 |
% 54.68/20.79 | From (1119)(1117) and (590) follows:
% 54.68/20.79 | (1121) sum(n23, n23) = all_0_3_3
% 54.68/20.79 |
% 54.68/20.79 | From (1723) and (5851) follows:
% 54.68/20.79 | (5918) sum(n14, n6) = all_0_0_0
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 54.68/20.79 | (1122) all_0_3_3 = n20
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n14, n6, all_0_0_0, n20 and discharging atoms sum(n14, n6) = all_0_0_0, sum(n14, n6) = n20, yields:
% 54.68/20.79 | (1123) all_0_0_0 = n20
% 54.68/20.79 |
% 54.68/20.79 | Equations (1123,1122) can reduce 679 to:
% 54.68/20.79 | (1106) $false
% 54.68/20.79 |
% 54.68/20.79 |-The branch is then unsatisfiable
% 54.68/20.79 |-Branch two:
% 54.68/20.79 | (1964) ~ (all_0_10_10 = n3)
% 54.68/20.79 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 54.68/20.79 |
% 54.68/20.79 +-Applying beta-rule and splitting (1965), into two cases.
% 54.68/20.79 |-Branch one:
% 54.68/20.79 | (1966) all_0_10_10 = n2
% 54.68/20.79 |
% 54.68/20.79 | From (1966) and (292) follows:
% 54.68/20.79 | (1967) pred(n2) = all_0_6_6
% 54.68/20.79 |
% 54.68/20.79 | From (1966) and (760) follows:
% 54.68/20.79 | (1968) succ(n2) = all_0_8_8
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 54.68/20.79 | (1969) all_0_6_6 = n1
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 54.68/20.79 | (1970) all_0_8_8 = n3
% 54.68/20.79 |
% 54.68/20.79 | From (1969)(1970) and (411) follows:
% 54.68/20.79 | (1971) sum(n1, n3) = all_0_1_1
% 54.68/20.79 |
% 54.68/20.79 | From (1969) and (5847) follows:
% 54.68/20.79 | (6164) sum(n1, n21) = all_0_4_4
% 54.68/20.79 |
% 54.68/20.79 | From (1970) and (5849) follows:
% 54.68/20.79 | (6165) sum(n19, n3) = all_0_7_7
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n19, n3, all_0_7_7, n22 and discharging atoms sum(n19, n3) = all_0_7_7, sum(n19, n3) = n22, yields:
% 54.68/20.79 | (1137) all_0_7_7 = n22
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n1, n21, all_0_4_4, n22 and discharging atoms sum(n1, n21) = all_0_4_4, sum(n1, n21) = n22, yields:
% 54.68/20.79 | (1135) all_0_4_4 = n22
% 54.68/20.79 |
% 54.68/20.79 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 54.68/20.79 | (1741) all_0_1_1 = n4
% 54.68/20.79 |
% 54.68/20.79 | From (1137)(1135) and (590) follows:
% 54.68/20.79 | (1139) sum(n22, n22) = all_0_3_3
% 54.68/20.79 |
% 54.68/20.79 | From (1741) and (5851) follows:
% 54.68/20.80 | (5936) sum(n14, n4) = all_0_0_0
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 54.68/20.80 | (1140) all_0_3_3 = n18
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (690) with n14, n4, all_0_0_0, n18 and discharging atoms sum(n14, n4) = all_0_0_0, sum(n14, n4) = n18, yields:
% 54.68/20.80 | (1141) all_0_0_0 = n18
% 54.68/20.80 |
% 54.68/20.80 | Equations (1141,1140) can reduce 679 to:
% 54.68/20.80 | (1106) $false
% 54.68/20.80 |
% 54.68/20.80 |-The branch is then unsatisfiable
% 54.68/20.80 |-Branch two:
% 54.68/20.80 | (1982) ~ (all_0_10_10 = n2)
% 54.68/20.80 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 54.68/20.80 |
% 54.68/20.80 +-Applying beta-rule and splitting (1983), into two cases.
% 54.68/20.80 |-Branch one:
% 54.68/20.80 | (1984) all_0_10_10 = n1
% 54.68/20.80 |
% 54.68/20.80 | From (1984) and (292) follows:
% 54.68/20.80 | (1985) pred(n1) = all_0_6_6
% 54.68/20.80 |
% 54.68/20.80 | From (1984) and (760) follows:
% 54.68/20.80 | (1986) succ(n1) = all_0_8_8
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 54.68/20.80 | (1987) all_0_6_6 = n0
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 54.68/20.80 | (1988) all_0_8_8 = n2
% 54.68/20.80 |
% 54.68/20.80 | From (1987)(1988) and (411) follows:
% 54.68/20.80 | (1989) sum(n0, n2) = all_0_1_1
% 54.68/20.80 |
% 54.68/20.80 | From (1987) and (5847) follows:
% 54.68/20.80 | (6182) sum(n0, n21) = all_0_4_4
% 54.68/20.80 |
% 54.68/20.80 | From (1988) and (5849) follows:
% 54.68/20.80 | (6183) sum(n19, n2) = all_0_7_7
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (690) with n19, n2, all_0_7_7, n21 and discharging atoms sum(n19, n2) = all_0_7_7, sum(n19, n2) = n21, yields:
% 54.68/20.80 | (1155) all_0_7_7 = n21
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (690) with n0, n21, all_0_4_4, n21 and discharging atoms sum(n0, n21) = all_0_4_4, sum(n0, n21) = n21, yields:
% 54.68/20.80 | (1153) all_0_4_4 = n21
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 54.68/20.80 | (1759) all_0_1_1 = n2
% 54.68/20.80 |
% 54.68/20.80 | From (1155)(1153) and (590) follows:
% 54.68/20.80 | (1157) sum(n21, n21) = all_0_3_3
% 54.68/20.80 |
% 54.68/20.80 | From (1759) and (5851) follows:
% 54.68/20.80 | (5954) sum(n14, n2) = all_0_0_0
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 54.68/20.80 | (1158) all_0_3_3 = n16
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (690) with n14, n2, all_0_0_0, n16 and discharging atoms sum(n14, n2) = all_0_0_0, sum(n14, n2) = n16, yields:
% 54.68/20.80 | (1159) all_0_0_0 = n16
% 54.68/20.80 |
% 54.68/20.80 | Equations (1159,1158) can reduce 679 to:
% 54.68/20.80 | (1106) $false
% 54.68/20.80 |
% 54.68/20.80 |-The branch is then unsatisfiable
% 54.68/20.80 |-Branch two:
% 54.68/20.80 | (2002) ~ (all_0_10_10 = n1)
% 54.68/20.80 | (2003) all_0_10_10 = n0
% 54.68/20.80 |
% 54.68/20.80 | From (2003) and (292) follows:
% 54.68/20.80 | (2004) pred(n0) = all_0_6_6
% 54.68/20.80 |
% 54.68/20.80 | From (2003) and (760) follows:
% 54.68/20.80 | (2005) succ(n0) = all_0_8_8
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 54.68/20.80 | (2006) all_0_6_6 = n25
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 54.68/20.80 | (2007) all_0_8_8 = n1
% 54.68/20.80 |
% 54.68/20.80 | From (2006)(2007) and (411) follows:
% 54.68/20.80 | (2008) sum(n25, n1) = all_0_1_1
% 54.68/20.80 |
% 54.68/20.80 | From (2006) and (5847) follows:
% 54.68/20.80 | (6199) sum(n25, n21) = all_0_4_4
% 54.68/20.80 |
% 54.68/20.80 | From (2007) and (5849) follows:
% 54.68/20.80 | (6200) sum(n19, n1) = all_0_7_7
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (690) with n25, n21, all_0_4_4, n20 and discharging atoms sum(n25, n21) = all_0_4_4, sum(n25, n21) = n20, yields:
% 54.68/20.80 | (1171) all_0_4_4 = n20
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 54.68/20.80 | (1777) all_0_1_1 = n0
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (690) with n19, n1, all_0_7_7, n20 and discharging atoms sum(n19, n1) = all_0_7_7, sum(n19, n1) = n20, yields:
% 54.68/20.80 | (1173) all_0_7_7 = n20
% 54.68/20.80 |
% 54.68/20.80 | From (1173)(1171) and (590) follows:
% 54.68/20.80 | (1175) sum(n20, n20) = all_0_3_3
% 54.68/20.80 |
% 54.68/20.80 | From (1777) and (5851) follows:
% 54.68/20.80 | (5972) sum(n14, n0) = all_0_0_0
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 54.68/20.80 | (1176) all_0_3_3 = n14
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (690) with n14, n0, all_0_0_0, n14 and discharging atoms sum(n14, n0) = all_0_0_0, sum(n14, n0) = n14, yields:
% 54.68/20.80 | (1177) all_0_0_0 = n14
% 54.68/20.80 |
% 54.68/20.80 | Equations (1177,1176) can reduce 679 to:
% 54.68/20.80 | (1106) $false
% 54.68/20.80 |
% 54.68/20.80 |-The branch is then unsatisfiable
% 54.68/20.80 |-Branch two:
% 54.68/20.80 | (1197) ~ (all_0_11_11 = n20)
% 54.68/20.80 | (1198) 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
% 54.68/20.80 |
% 54.68/20.80 +-Applying beta-rule and splitting (1659), into two cases.
% 54.68/20.80 |-Branch one:
% 54.68/20.80 | (1660) all_0_10_10 = n19
% 54.68/20.80 |
% 54.68/20.80 | From (1660) and (292) follows:
% 54.68/20.80 | (1661) pred(n19) = all_0_6_6
% 54.68/20.80 |
% 54.68/20.80 | From (1660) and (760) follows:
% 54.68/20.80 | (1662) succ(n19) = all_0_8_8
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (500) with n19, all_0_6_6, n18 and discharging atoms pred(n19) = all_0_6_6, pred(n19) = n18, yields:
% 54.68/20.80 | (1663) all_0_6_6 = n18
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (617) with n19, all_0_8_8, n20 and discharging atoms succ(n19) = all_0_8_8, succ(n19) = n20, yields:
% 54.68/20.80 | (1664) all_0_8_8 = n20
% 54.68/20.80 |
% 54.68/20.80 | From (1663) and (1661) follows:
% 54.68/20.80 | (523) pred(n19) = n18
% 54.68/20.80 |
% 54.68/20.80 | From (1664) and (1662) follows:
% 54.68/20.80 | (571) succ(n19) = n20
% 54.68/20.80 |
% 54.68/20.80 | From (1663) and (541) follows:
% 54.68/20.80 | (6218) sum(n18, all_0_5_5) = all_0_4_4
% 54.68/20.80 |
% 54.68/20.80 | From (1663)(1664) and (411) follows:
% 54.68/20.80 | (1665) sum(n18, n20) = all_0_1_1
% 54.68/20.80 |
% 54.68/20.80 | From (1664) and (427) follows:
% 54.68/20.80 | (6220) sum(all_0_9_9, n20) = all_0_7_7
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (690) with n18, n20, all_0_1_1, n12 and discharging atoms sum(n18, n20) = all_0_1_1, sum(n18, n20) = n12, yields:
% 54.68/20.80 | (1669) all_0_1_1 = n12
% 54.68/20.80 |
% 54.68/20.80 | From (1669) and (630) follows:
% 54.68/20.80 | (6222) sum(all_0_2_2, n12) = all_0_0_0
% 54.68/20.80 |
% 54.68/20.80 | From (1669) and (1665) follows:
% 54.68/20.80 | (60) sum(n18, n20) = n12
% 54.68/20.80 |
% 54.68/20.80 +-Applying beta-rule and splitting (1198), into two cases.
% 54.68/20.80 |-Branch one:
% 54.68/20.80 | (1199) all_0_11_11 = n19
% 54.68/20.80 |
% 54.68/20.80 | From (1199) and (559) follows:
% 54.68/20.80 | (1200) pred(n19) = all_0_9_9
% 54.68/20.80 |
% 54.68/20.80 | From (1199) and (992) follows:
% 54.68/20.80 | (1201) succ(n19) = all_0_5_5
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (500) with n19, all_0_9_9, n18 and discharging atoms pred(n19) = all_0_9_9, pred(n19) = n18, yields:
% 54.68/20.80 | (1202) all_0_9_9 = n18
% 54.68/20.80 |
% 54.68/20.80 | Instantiating formula (617) with n19, all_0_5_5, n20 and discharging atoms succ(n19) = all_0_5_5, succ(n19) = n20, yields:
% 54.68/20.80 | (1203) all_0_5_5 = n20
% 54.68/20.80 |
% 54.68/20.80 | From (1202)(1203) and (538) follows:
% 54.68/20.80 | (1204) sum(n18, n20) = all_0_2_2
% 54.68/20.80 |
% 54.68/20.80 | From (1202) and (6220) follows:
% 54.68/20.81 | (6230) sum(n18, n20) = all_0_7_7
% 54.68/20.81 |
% 54.68/20.81 | From (1203) and (6218) follows:
% 54.68/20.81 | (6231) sum(n18, n20) = all_0_4_4
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) with n18, n20, all_0_2_2, n12 and discharging atoms sum(n18, n20) = all_0_2_2, sum(n18, n20) = n12, yields:
% 54.68/20.81 | (1208) all_0_2_2 = n12
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) 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:
% 54.68/20.81 | (1093) all_0_2_2 = all_0_4_4
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) 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:
% 54.68/20.81 | (1094) all_0_2_2 = all_0_7_7
% 54.68/20.81 |
% 54.68/20.81 | Combining equations (1094,1093) yields a new equation:
% 54.68/20.81 | (1095) all_0_4_4 = all_0_7_7
% 54.68/20.81 |
% 54.68/20.81 | Combining equations (1208,1093) yields a new equation:
% 54.68/20.81 | (1315) all_0_4_4 = n12
% 54.68/20.81 |
% 54.68/20.81 | Combining equations (1315,1095) yields a new equation:
% 54.68/20.81 | (1317) all_0_7_7 = n12
% 54.68/20.81 |
% 54.68/20.81 | Combining equations (1317,1095) yields a new equation:
% 54.68/20.81 | (1315) all_0_4_4 = n12
% 54.68/20.81 |
% 54.68/20.81 | Combining equations (1315,1093) yields a new equation:
% 54.68/20.81 | (1208) all_0_2_2 = n12
% 54.68/20.81 |
% 54.68/20.81 | From (1208) and (6222) follows:
% 54.68/20.81 | (6240) sum(n12, n12) = all_0_0_0
% 54.68/20.81 |
% 54.68/20.81 | From (1317)(1315) and (590) follows:
% 54.68/20.81 | (1319) sum(n12, n12) = all_0_3_3
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) with n12, n12, all_0_0_0, n24 and discharging atoms sum(n12, n12) = all_0_0_0, sum(n12, n12) = n24, yields:
% 54.68/20.81 | (1321) all_0_0_0 = n24
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) 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:
% 54.68/20.81 | (1103) all_0_0_0 = all_0_3_3
% 54.68/20.81 |
% 54.68/20.81 | Combining equations (1321,1103) yields a new equation:
% 54.68/20.81 | (1320) all_0_3_3 = n24
% 54.68/20.81 |
% 54.68/20.81 | Combining equations (1320,1103) yields a new equation:
% 54.68/20.81 | (1321) all_0_0_0 = n24
% 54.68/20.81 |
% 54.68/20.81 | Equations (1321,1320) can reduce 679 to:
% 54.68/20.81 | (1106) $false
% 54.68/20.81 |
% 54.68/20.81 |-The branch is then unsatisfiable
% 54.68/20.81 |-Branch two:
% 54.68/20.81 | (1215) ~ (all_0_11_11 = n19)
% 54.68/20.81 | (1216) 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
% 54.68/20.81 |
% 54.68/20.81 +-Applying beta-rule and splitting (1216), into two cases.
% 54.68/20.81 |-Branch one:
% 54.68/20.81 | (1217) all_0_11_11 = n18
% 54.68/20.81 |
% 54.68/20.81 | From (1217) and (559) follows:
% 54.68/20.81 | (1218) pred(n18) = all_0_9_9
% 54.68/20.81 |
% 54.68/20.81 | From (1217) and (992) follows:
% 54.68/20.81 | (1219) succ(n18) = all_0_5_5
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (500) with n18, all_0_9_9, n17 and discharging atoms pred(n18) = all_0_9_9, pred(n18) = n17, yields:
% 54.68/20.81 | (1220) all_0_9_9 = n17
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (617) with n18, all_0_5_5, n19 and discharging atoms succ(n18) = all_0_5_5, succ(n18) = n19, yields:
% 54.68/20.81 | (1221) all_0_5_5 = n19
% 54.68/20.81 |
% 54.68/20.81 | From (1220)(1221) and (538) follows:
% 54.68/20.81 | (1222) sum(n17, n19) = all_0_2_2
% 54.68/20.81 |
% 54.68/20.81 | From (1220) and (6220) follows:
% 54.68/20.81 | (6255) sum(n17, n20) = all_0_7_7
% 54.68/20.81 |
% 54.68/20.81 | From (1221) and (6218) follows:
% 54.68/20.81 | (6256) sum(n18, n19) = all_0_4_4
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) with n18, n19, all_0_4_4, n11 and discharging atoms sum(n18, n19) = all_0_4_4, sum(n18, n19) = n11, yields:
% 54.68/20.81 | (1333) all_0_4_4 = n11
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) with n17, n20, all_0_7_7, n11 and discharging atoms sum(n17, n20) = all_0_7_7, sum(n17, n20) = n11, yields:
% 54.68/20.81 | (1335) all_0_7_7 = n11
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) with n17, n19, all_0_2_2, n10 and discharging atoms sum(n17, n19) = all_0_2_2, sum(n17, n19) = n10, yields:
% 54.68/20.81 | (1226) all_0_2_2 = n10
% 54.68/20.81 |
% 54.68/20.81 | From (1226) and (6222) follows:
% 54.68/20.81 | (6260) sum(n10, n12) = all_0_0_0
% 54.68/20.81 |
% 54.68/20.81 | From (1335)(1333) and (590) follows:
% 54.68/20.81 | (1337) sum(n11, n11) = all_0_3_3
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 54.68/20.81 | (1104) all_0_3_3 = n22
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) with n10, n12, all_0_0_0, n22 and discharging atoms sum(n10, n12) = all_0_0_0, sum(n10, n12) = n22, yields:
% 54.68/20.81 | (1102) all_0_0_0 = n22
% 54.68/20.81 |
% 54.68/20.81 | Equations (1102,1104) can reduce 679 to:
% 54.68/20.81 | (1106) $false
% 54.68/20.81 |
% 54.68/20.81 |-The branch is then unsatisfiable
% 54.68/20.81 |-Branch two:
% 54.68/20.81 | (1233) ~ (all_0_11_11 = n18)
% 54.68/20.81 | (1234) 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
% 54.68/20.81 |
% 54.68/20.81 +-Applying beta-rule and splitting (1234), into two cases.
% 54.68/20.81 |-Branch one:
% 54.68/20.81 | (1235) all_0_11_11 = n17
% 54.68/20.81 |
% 54.68/20.81 | From (1235) and (559) follows:
% 54.68/20.81 | (1236) pred(n17) = all_0_9_9
% 54.68/20.81 |
% 54.68/20.81 | From (1235) and (992) follows:
% 54.68/20.81 | (1237) succ(n17) = all_0_5_5
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (500) with n17, all_0_9_9, n16 and discharging atoms pred(n17) = all_0_9_9, pred(n17) = n16, yields:
% 54.68/20.81 | (1238) all_0_9_9 = n16
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (617) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 54.68/20.81 | (1239) all_0_5_5 = n18
% 54.68/20.81 |
% 54.68/20.81 | From (1238)(1239) and (538) follows:
% 54.68/20.81 | (1240) sum(n16, n18) = all_0_2_2
% 54.68/20.81 |
% 54.68/20.81 | From (1238) and (6220) follows:
% 54.68/20.81 | (6273) sum(n16, n20) = all_0_7_7
% 54.68/20.81 |
% 54.68/20.81 | From (1239) and (6218) follows:
% 54.68/20.81 | (6274) sum(n18, n18) = all_0_4_4
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) with n18, n18, all_0_4_4, n10 and discharging atoms sum(n18, n18) = all_0_4_4, sum(n18, n18) = n10, yields:
% 54.68/20.81 | (1351) all_0_4_4 = n10
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) with n16, n20, all_0_7_7, n10 and discharging atoms sum(n16, n20) = all_0_7_7, sum(n16, n20) = n10, yields:
% 54.68/20.81 | (1353) all_0_7_7 = n10
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) with n16, n18, all_0_2_2, n8 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = n8, yields:
% 54.68/20.81 | (1244) all_0_2_2 = n8
% 54.68/20.81 |
% 54.68/20.81 | From (1244) and (6222) follows:
% 54.68/20.81 | (6278) sum(n8, n12) = all_0_0_0
% 54.68/20.81 |
% 54.68/20.81 | From (1353)(1351) and (590) follows:
% 54.68/20.81 | (1355) sum(n10, n10) = all_0_3_3
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 54.68/20.81 | (1122) all_0_3_3 = n20
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) with n8, n12, all_0_0_0, n20 and discharging atoms sum(n8, n12) = all_0_0_0, sum(n8, n12) = n20, yields:
% 54.68/20.81 | (1123) all_0_0_0 = n20
% 54.68/20.81 |
% 54.68/20.81 | Equations (1123,1122) can reduce 679 to:
% 54.68/20.81 | (1106) $false
% 54.68/20.81 |
% 54.68/20.81 |-The branch is then unsatisfiable
% 54.68/20.81 |-Branch two:
% 54.68/20.81 | (1251) ~ (all_0_11_11 = n17)
% 54.68/20.81 | (1252) 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
% 54.68/20.81 |
% 54.68/20.81 +-Applying beta-rule and splitting (1252), into two cases.
% 54.68/20.81 |-Branch one:
% 54.68/20.81 | (1253) all_0_11_11 = n16
% 54.68/20.81 |
% 54.68/20.81 | From (1253) and (559) follows:
% 54.68/20.81 | (1254) pred(n16) = all_0_9_9
% 54.68/20.81 |
% 54.68/20.81 | From (1253) and (992) follows:
% 54.68/20.81 | (1255) succ(n16) = all_0_5_5
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (500) with n16, all_0_9_9, n15 and discharging atoms pred(n16) = all_0_9_9, pred(n16) = n15, yields:
% 54.68/20.81 | (1256) all_0_9_9 = n15
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (617) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 54.68/20.81 | (1257) all_0_5_5 = n17
% 54.68/20.81 |
% 54.68/20.81 | From (1256)(1257) and (538) follows:
% 54.68/20.81 | (1258) sum(n15, n17) = all_0_2_2
% 54.68/20.81 |
% 54.68/20.81 | From (1256) and (6220) follows:
% 54.68/20.81 | (6291) sum(n15, n20) = all_0_7_7
% 54.68/20.81 |
% 54.68/20.81 | From (1257) and (6218) follows:
% 54.68/20.81 | (6292) sum(n18, n17) = all_0_4_4
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) with n18, n17, all_0_4_4, n9 and discharging atoms sum(n18, n17) = all_0_4_4, sum(n18, n17) = n9, yields:
% 54.68/20.81 | (1369) all_0_4_4 = n9
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) with n15, n20, all_0_7_7, n9 and discharging atoms sum(n15, n20) = all_0_7_7, sum(n15, n20) = n9, yields:
% 54.68/20.81 | (1371) all_0_7_7 = n9
% 54.68/20.81 |
% 54.68/20.81 | Instantiating formula (690) with n15, n17, all_0_2_2, n6 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n6, yields:
% 54.68/20.81 | (1262) all_0_2_2 = n6
% 54.68/20.81 |
% 54.68/20.81 | From (1262) and (6222) follows:
% 54.68/20.82 | (6296) sum(n6, n12) = all_0_0_0
% 54.68/20.82 |
% 54.68/20.82 | From (1371)(1369) and (590) follows:
% 54.68/20.82 | (1373) sum(n9, n9) = all_0_3_3
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 54.68/20.82 | (1140) all_0_3_3 = n18
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (690) with n6, n12, all_0_0_0, n18 and discharging atoms sum(n6, n12) = all_0_0_0, sum(n6, n12) = n18, yields:
% 54.68/20.82 | (1141) all_0_0_0 = n18
% 54.68/20.82 |
% 54.68/20.82 | Equations (1141,1140) can reduce 679 to:
% 54.68/20.82 | (1106) $false
% 54.68/20.82 |
% 54.68/20.82 |-The branch is then unsatisfiable
% 54.68/20.82 |-Branch two:
% 54.68/20.82 | (1269) ~ (all_0_11_11 = n16)
% 54.68/20.82 | (1270) 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
% 54.68/20.82 |
% 54.68/20.82 +-Applying beta-rule and splitting (1270), into two cases.
% 54.68/20.82 |-Branch one:
% 54.68/20.82 | (1271) all_0_11_11 = n15
% 54.68/20.82 |
% 54.68/20.82 | From (1271) and (559) follows:
% 54.68/20.82 | (1272) pred(n15) = all_0_9_9
% 54.68/20.82 |
% 54.68/20.82 | From (1271) and (992) follows:
% 54.68/20.82 | (1273) succ(n15) = all_0_5_5
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (500) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 54.68/20.82 | (1274) all_0_9_9 = n14
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (617) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 54.68/20.82 | (1275) all_0_5_5 = n16
% 54.68/20.82 |
% 54.68/20.82 | From (1274)(1275) and (538) follows:
% 54.68/20.82 | (1276) sum(n14, n16) = all_0_2_2
% 54.68/20.82 |
% 54.68/20.82 | From (1274) and (6220) follows:
% 54.68/20.82 | (6309) sum(n14, n20) = all_0_7_7
% 54.68/20.82 |
% 54.68/20.82 | From (1275) and (6218) follows:
% 54.68/20.82 | (6310) sum(n18, n16) = all_0_4_4
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (690) with n18, n16, all_0_4_4, n8 and discharging atoms sum(n18, n16) = all_0_4_4, sum(n18, n16) = n8, yields:
% 54.68/20.82 | (1387) all_0_4_4 = n8
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (690) with n14, n20, all_0_7_7, n8 and discharging atoms sum(n14, n20) = all_0_7_7, sum(n14, n20) = n8, yields:
% 54.68/20.82 | (1389) all_0_7_7 = n8
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (690) with n14, n16, all_0_2_2, n4 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n4, yields:
% 54.68/20.82 | (1280) all_0_2_2 = n4
% 54.68/20.82 |
% 54.68/20.82 | From (1280) and (6222) follows:
% 54.68/20.82 | (6314) sum(n4, n12) = all_0_0_0
% 54.68/20.82 |
% 54.68/20.82 | From (1389)(1387) and (590) follows:
% 54.68/20.82 | (1391) sum(n8, n8) = all_0_3_3
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 54.68/20.82 | (1158) all_0_3_3 = n16
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (690) with n4, n12, all_0_0_0, n16 and discharging atoms sum(n4, n12) = all_0_0_0, sum(n4, n12) = n16, yields:
% 54.68/20.82 | (1159) all_0_0_0 = n16
% 54.68/20.82 |
% 54.68/20.82 | Equations (1159,1158) can reduce 679 to:
% 54.68/20.82 | (1106) $false
% 54.68/20.82 |
% 54.68/20.82 |-The branch is then unsatisfiable
% 54.68/20.82 |-Branch two:
% 54.68/20.82 | (1287) ~ (all_0_11_11 = n15)
% 54.68/20.82 | (1288) 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
% 54.68/20.82 |
% 54.68/20.82 +-Applying beta-rule and splitting (1288), into two cases.
% 54.68/20.82 |-Branch one:
% 54.68/20.82 | (1289) all_0_11_11 = n14
% 54.68/20.82 |
% 54.68/20.82 | From (1289) and (559) follows:
% 54.68/20.82 | (1290) pred(n14) = all_0_9_9
% 54.68/20.82 |
% 54.68/20.82 | From (1289) and (992) follows:
% 54.68/20.82 | (1291) succ(n14) = all_0_5_5
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (500) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 54.68/20.82 | (1292) all_0_9_9 = n13
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (617) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 54.68/20.82 | (1293) all_0_5_5 = n15
% 54.68/20.82 |
% 54.68/20.82 | From (1292)(1293) and (538) follows:
% 54.68/20.82 | (1294) sum(n13, n15) = all_0_2_2
% 54.68/20.82 |
% 54.68/20.82 | From (1292) and (6220) follows:
% 54.68/20.82 | (6327) sum(n13, n20) = all_0_7_7
% 54.68/20.82 |
% 54.68/20.82 | From (1293) and (6218) follows:
% 54.68/20.82 | (6328) sum(n18, n15) = all_0_4_4
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (690) with n18, n15, all_0_4_4, n7 and discharging atoms sum(n18, n15) = all_0_4_4, sum(n18, n15) = n7, yields:
% 54.68/20.82 | (1405) all_0_4_4 = n7
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (690) with n13, n20, all_0_7_7, n7 and discharging atoms sum(n13, n20) = all_0_7_7, sum(n13, n20) = n7, yields:
% 54.68/20.82 | (1407) all_0_7_7 = n7
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (690) with n13, n15, all_0_2_2, n2 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n2, yields:
% 54.68/20.82 | (1298) all_0_2_2 = n2
% 54.68/20.82 |
% 54.68/20.82 | From (1298) and (6222) follows:
% 54.68/20.82 | (6332) sum(n2, n12) = all_0_0_0
% 54.68/20.82 |
% 54.68/20.82 | From (1407)(1405) and (590) follows:
% 54.68/20.82 | (1409) sum(n7, n7) = all_0_3_3
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 54.68/20.82 | (1176) all_0_3_3 = n14
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (690) with n2, n12, all_0_0_0, n14 and discharging atoms sum(n2, n12) = all_0_0_0, sum(n2, n12) = n14, yields:
% 54.68/20.82 | (1177) all_0_0_0 = n14
% 54.68/20.82 |
% 54.68/20.82 | Equations (1177,1176) can reduce 679 to:
% 54.68/20.82 | (1106) $false
% 54.68/20.82 |
% 54.68/20.82 |-The branch is then unsatisfiable
% 54.68/20.82 |-Branch two:
% 54.68/20.82 | (1305) ~ (all_0_11_11 = n14)
% 54.68/20.82 | (1306) 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
% 54.68/20.82 |
% 54.68/20.82 +-Applying beta-rule and splitting (1306), into two cases.
% 54.68/20.82 |-Branch one:
% 54.68/20.82 | (1307) all_0_11_11 = n13
% 54.68/20.82 |
% 54.68/20.82 | From (1307) and (559) follows:
% 54.68/20.82 | (1308) pred(n13) = all_0_9_9
% 54.68/20.82 |
% 54.68/20.82 | From (1307) and (992) follows:
% 54.68/20.82 | (1309) succ(n13) = all_0_5_5
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (500) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 54.68/20.82 | (1310) all_0_9_9 = n12
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (617) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 54.68/20.82 | (1311) all_0_5_5 = n14
% 54.68/20.82 |
% 54.68/20.82 | From (1310)(1311) and (538) follows:
% 54.68/20.82 | (1312) sum(n12, n14) = all_0_2_2
% 54.68/20.82 |
% 54.68/20.82 | From (1310) and (6220) follows:
% 54.68/20.82 | (6345) sum(n12, n20) = all_0_7_7
% 54.68/20.82 |
% 54.68/20.82 | From (1311) and (6218) follows:
% 54.68/20.82 | (6346) sum(n18, n14) = all_0_4_4
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (690) with n18, n14, all_0_4_4, n6 and discharging atoms sum(n18, n14) = all_0_4_4, sum(n18, n14) = n6, yields:
% 54.68/20.82 | (1423) all_0_4_4 = n6
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (690) with n12, n20, all_0_7_7, n6 and discharging atoms sum(n12, n20) = all_0_7_7, sum(n12, n20) = n6, yields:
% 54.68/20.82 | (1425) all_0_7_7 = n6
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (690) with n12, n14, all_0_2_2, n0 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n0, yields:
% 54.68/20.82 | (1316) all_0_2_2 = n0
% 54.68/20.82 |
% 54.68/20.82 | From (1316) and (6222) follows:
% 54.68/20.82 | (6350) sum(n0, n12) = all_0_0_0
% 54.68/20.82 |
% 54.68/20.82 | From (1425)(1423) and (590) follows:
% 54.68/20.82 | (1427) sum(n6, n6) = all_0_3_3
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 54.68/20.82 | (1194) all_0_3_3 = n12
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (690) with n0, n12, all_0_0_0, n12 and discharging atoms sum(n0, n12) = all_0_0_0, sum(n0, n12) = n12, yields:
% 54.68/20.82 | (1195) all_0_0_0 = n12
% 54.68/20.82 |
% 54.68/20.82 | Equations (1195,1194) can reduce 679 to:
% 54.68/20.82 | (1106) $false
% 54.68/20.82 |
% 54.68/20.82 |-The branch is then unsatisfiable
% 54.68/20.82 |-Branch two:
% 54.68/20.82 | (1323) ~ (all_0_11_11 = n13)
% 54.68/20.82 | (1324) 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
% 54.68/20.82 |
% 54.68/20.82 +-Applying beta-rule and splitting (1324), into two cases.
% 54.68/20.82 |-Branch one:
% 54.68/20.82 | (1325) all_0_11_11 = n12
% 54.68/20.82 |
% 54.68/20.82 | From (1325) and (559) follows:
% 54.68/20.82 | (1326) pred(n12) = all_0_9_9
% 54.68/20.82 |
% 54.68/20.82 | From (1325) and (992) follows:
% 54.68/20.82 | (1327) succ(n12) = all_0_5_5
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (500) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 54.68/20.82 | (1328) all_0_9_9 = n11
% 54.68/20.82 |
% 54.68/20.82 | Instantiating formula (617) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 54.68/20.82 | (1329) all_0_5_5 = n13
% 54.68/20.82 |
% 54.68/20.82 | From (1328)(1329) and (538) follows:
% 54.68/20.82 | (1330) sum(n11, n13) = all_0_2_2
% 54.68/20.82 |
% 54.68/20.82 | From (1328) and (6220) follows:
% 54.68/20.83 | (6363) sum(n11, n20) = all_0_7_7
% 54.68/20.83 |
% 54.68/20.83 | From (1329) and (6218) follows:
% 54.68/20.83 | (6364) sum(n18, n13) = all_0_4_4
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n18, n13, all_0_4_4, n5 and discharging atoms sum(n18, n13) = all_0_4_4, sum(n18, n13) = n5, yields:
% 54.68/20.83 | (1441) all_0_4_4 = n5
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n11, n20, all_0_7_7, n5 and discharging atoms sum(n11, n20) = all_0_7_7, sum(n11, n20) = n5, yields:
% 54.68/20.83 | (1443) all_0_7_7 = n5
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n11, n13, all_0_2_2, n24 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n24, yields:
% 54.68/20.83 | (1092) all_0_2_2 = n24
% 54.68/20.83 |
% 54.68/20.83 | From (1092) and (6222) follows:
% 54.68/20.83 | (1672) sum(n24, n12) = all_0_0_0
% 54.68/20.83 |
% 54.68/20.83 | From (1443)(1441) and (590) follows:
% 54.68/20.83 | (1445) sum(n5, n5) = all_0_3_3
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n24, n12, all_0_0_0, n10 and discharging atoms sum(n24, n12) = all_0_0_0, sum(n24, n12) = n10, yields:
% 54.68/20.83 | (1213) all_0_0_0 = n10
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 54.68/20.83 | (1212) all_0_3_3 = n10
% 54.68/20.83 |
% 54.68/20.83 | Equations (1213,1212) can reduce 679 to:
% 54.68/20.83 | (1106) $false
% 54.68/20.83 |
% 54.68/20.83 |-The branch is then unsatisfiable
% 54.68/20.83 |-Branch two:
% 54.68/20.83 | (1341) ~ (all_0_11_11 = n12)
% 54.68/20.83 | (1342) 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
% 54.68/20.83 |
% 54.68/20.83 +-Applying beta-rule and splitting (1342), into two cases.
% 54.68/20.83 |-Branch one:
% 54.68/20.83 | (1343) all_0_11_11 = n11
% 54.68/20.83 |
% 54.68/20.83 | From (1343) and (559) follows:
% 54.68/20.83 | (1344) pred(n11) = all_0_9_9
% 54.68/20.83 |
% 54.68/20.83 | From (1343) and (992) follows:
% 54.68/20.83 | (1345) succ(n11) = all_0_5_5
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (500) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 54.68/20.83 | (1346) all_0_9_9 = n10
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (617) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 54.68/20.83 | (1347) all_0_5_5 = n12
% 54.68/20.83 |
% 54.68/20.83 | From (1346)(1347) and (538) follows:
% 54.68/20.83 | (1348) sum(n10, n12) = all_0_2_2
% 54.68/20.83 |
% 54.68/20.83 | From (1346) and (6220) follows:
% 54.68/20.83 | (6381) sum(n10, n20) = all_0_7_7
% 54.68/20.83 |
% 54.68/20.83 | From (1347) and (6218) follows:
% 54.68/20.83 | (6382) sum(n18, n12) = all_0_4_4
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n18, n12, all_0_4_4, n4 and discharging atoms sum(n18, n12) = all_0_4_4, sum(n18, n12) = n4, yields:
% 54.68/20.83 | (1459) all_0_4_4 = n4
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n10, n20, all_0_7_7, n4 and discharging atoms sum(n10, n20) = all_0_7_7, sum(n10, n20) = n4, yields:
% 54.68/20.83 | (1461) all_0_7_7 = n4
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n10, n12, all_0_2_2, n22 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n22, yields:
% 54.68/20.83 | (1118) all_0_2_2 = n22
% 54.68/20.83 |
% 54.68/20.83 | From (1118) and (6222) follows:
% 54.68/20.83 | (2584) sum(n22, n12) = all_0_0_0
% 54.68/20.83 |
% 54.68/20.83 | From (1461)(1459) and (590) follows:
% 54.68/20.83 | (1463) sum(n4, n4) = all_0_3_3
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n22, n12, all_0_0_0, n8 and discharging atoms sum(n22, n12) = all_0_0_0, sum(n22, n12) = n8, yields:
% 54.68/20.83 | (1231) all_0_0_0 = n8
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 54.68/20.83 | (1230) all_0_3_3 = n8
% 54.68/20.83 |
% 54.68/20.83 | Equations (1231,1230) can reduce 679 to:
% 54.68/20.83 | (1106) $false
% 54.68/20.83 |
% 54.68/20.83 |-The branch is then unsatisfiable
% 54.68/20.83 |-Branch two:
% 54.68/20.83 | (1359) ~ (all_0_11_11 = n11)
% 54.68/20.83 | (1360) 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
% 54.68/20.83 |
% 54.68/20.83 +-Applying beta-rule and splitting (1360), into two cases.
% 54.68/20.83 |-Branch one:
% 54.68/20.83 | (1361) all_0_11_11 = n10
% 54.68/20.83 |
% 54.68/20.83 | From (1361) and (559) follows:
% 54.68/20.83 | (1362) pred(n10) = all_0_9_9
% 54.68/20.83 |
% 54.68/20.83 | From (1361) and (992) follows:
% 54.68/20.83 | (1363) succ(n10) = all_0_5_5
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (500) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 54.68/20.83 | (1364) all_0_9_9 = n9
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (617) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 54.68/20.83 | (1365) all_0_5_5 = n11
% 54.68/20.83 |
% 54.68/20.83 | From (1364)(1365) and (538) follows:
% 54.68/20.83 | (1366) sum(n9, n11) = all_0_2_2
% 54.68/20.83 |
% 54.68/20.83 | From (1364) and (6220) follows:
% 54.68/20.83 | (6399) sum(n9, n20) = all_0_7_7
% 54.68/20.83 |
% 54.68/20.83 | From (1365) and (6218) follows:
% 54.68/20.83 | (6400) sum(n18, n11) = all_0_4_4
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n18, n11, all_0_4_4, n3 and discharging atoms sum(n18, n11) = all_0_4_4, sum(n18, n11) = n3, yields:
% 54.68/20.83 | (1477) all_0_4_4 = n3
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n9, n20, all_0_7_7, n3 and discharging atoms sum(n9, n20) = all_0_7_7, sum(n9, n20) = n3, yields:
% 54.68/20.83 | (1479) all_0_7_7 = n3
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 54.68/20.83 | (1136) all_0_2_2 = n20
% 54.68/20.83 |
% 54.68/20.83 | From (1136) and (6222) follows:
% 54.68/20.83 | (3458) sum(n20, n12) = all_0_0_0
% 54.68/20.83 |
% 54.68/20.83 | From (1479)(1477) and (590) follows:
% 54.68/20.83 | (1481) sum(n3, n3) = all_0_3_3
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n20, n12, all_0_0_0, n6 and discharging atoms sum(n20, n12) = all_0_0_0, sum(n20, n12) = n6, yields:
% 54.68/20.83 | (1249) all_0_0_0 = n6
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 54.68/20.83 | (1248) all_0_3_3 = n6
% 54.68/20.83 |
% 54.68/20.83 | Equations (1249,1248) can reduce 679 to:
% 54.68/20.83 | (1106) $false
% 54.68/20.83 |
% 54.68/20.83 |-The branch is then unsatisfiable
% 54.68/20.83 |-Branch two:
% 54.68/20.83 | (1377) ~ (all_0_11_11 = n10)
% 54.68/20.83 | (1378) 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
% 54.68/20.83 |
% 54.68/20.83 +-Applying beta-rule and splitting (1378), into two cases.
% 54.68/20.83 |-Branch one:
% 54.68/20.83 | (1379) all_0_11_11 = n9
% 54.68/20.83 |
% 54.68/20.83 | From (1379) and (559) follows:
% 54.68/20.83 | (1380) pred(n9) = all_0_9_9
% 54.68/20.83 |
% 54.68/20.83 | From (1379) and (992) follows:
% 54.68/20.83 | (1381) succ(n9) = all_0_5_5
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 54.68/20.83 | (1382) all_0_9_9 = n8
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 54.68/20.83 | (1383) all_0_5_5 = n10
% 54.68/20.83 |
% 54.68/20.83 | From (1382)(1383) and (538) follows:
% 54.68/20.83 | (1384) sum(n8, n10) = all_0_2_2
% 54.68/20.83 |
% 54.68/20.83 | From (1382) and (6220) follows:
% 54.68/20.83 | (6417) sum(n8, n20) = all_0_7_7
% 54.68/20.83 |
% 54.68/20.83 | From (1383) and (6218) follows:
% 54.68/20.83 | (6418) sum(n18, n10) = all_0_4_4
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n18, n10, all_0_4_4, n2 and discharging atoms sum(n18, n10) = all_0_4_4, sum(n18, n10) = n2, yields:
% 54.68/20.83 | (1495) all_0_4_4 = n2
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n8, n20, all_0_7_7, n2 and discharging atoms sum(n8, n20) = all_0_7_7, sum(n8, n20) = n2, yields:
% 54.68/20.83 | (1497) all_0_7_7 = n2
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 54.68/20.83 | (1154) all_0_2_2 = n18
% 54.68/20.83 |
% 54.68/20.83 | From (1154) and (6222) follows:
% 54.68/20.83 | (4296) sum(n18, n12) = all_0_0_0
% 54.68/20.83 |
% 54.68/20.83 | From (1497)(1495) and (590) follows:
% 54.68/20.83 | (1499) sum(n2, n2) = all_0_3_3
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n18, n12, all_0_0_0, n4 and discharging atoms sum(n18, n12) = all_0_0_0, sum(n18, n12) = n4, yields:
% 54.68/20.83 | (1267) all_0_0_0 = n4
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 54.68/20.83 | (1266) all_0_3_3 = n4
% 54.68/20.83 |
% 54.68/20.83 | Equations (1267,1266) can reduce 679 to:
% 54.68/20.83 | (1106) $false
% 54.68/20.83 |
% 54.68/20.83 |-The branch is then unsatisfiable
% 54.68/20.83 |-Branch two:
% 54.68/20.83 | (1395) ~ (all_0_11_11 = n9)
% 54.68/20.83 | (1396) 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
% 54.68/20.83 |
% 54.68/20.83 +-Applying beta-rule and splitting (1396), into two cases.
% 54.68/20.83 |-Branch one:
% 54.68/20.83 | (1397) all_0_11_11 = n8
% 54.68/20.83 |
% 54.68/20.83 | From (1397) and (559) follows:
% 54.68/20.83 | (1398) pred(n8) = all_0_9_9
% 54.68/20.83 |
% 54.68/20.83 | From (1397) and (992) follows:
% 54.68/20.83 | (1399) succ(n8) = all_0_5_5
% 54.68/20.83 |
% 54.68/20.83 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 54.68/20.84 | (1400) all_0_9_9 = n7
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 54.68/20.84 | (1401) all_0_5_5 = n9
% 54.68/20.84 |
% 54.68/20.84 | From (1400)(1401) and (538) follows:
% 54.68/20.84 | (1402) sum(n7, n9) = all_0_2_2
% 54.68/20.84 |
% 54.68/20.84 | From (1400) and (6220) follows:
% 54.68/20.84 | (6435) sum(n7, n20) = all_0_7_7
% 54.68/20.84 |
% 54.68/20.84 | From (1401) and (6218) follows:
% 54.68/20.84 | (6436) sum(n18, n9) = all_0_4_4
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n18, n9, all_0_4_4, n1 and discharging atoms sum(n18, n9) = all_0_4_4, sum(n18, n9) = n1, yields:
% 54.68/20.84 | (1513) all_0_4_4 = n1
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n7, n20, all_0_7_7, n1 and discharging atoms sum(n7, n20) = all_0_7_7, sum(n7, n20) = n1, yields:
% 54.68/20.84 | (1515) all_0_7_7 = n1
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 54.68/20.84 | (1172) all_0_2_2 = n16
% 54.68/20.84 |
% 54.68/20.84 | From (1172) and (6222) follows:
% 54.68/20.84 | (5098) sum(n16, n12) = all_0_0_0
% 54.68/20.84 |
% 54.68/20.84 | From (1515)(1513) and (590) follows:
% 54.68/20.84 | (1517) sum(n1, n1) = all_0_3_3
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n16, n12, all_0_0_0, n2 and discharging atoms sum(n16, n12) = all_0_0_0, sum(n16, n12) = n2, yields:
% 54.68/20.84 | (1285) all_0_0_0 = n2
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 54.68/20.84 | (1284) all_0_3_3 = n2
% 54.68/20.84 |
% 54.68/20.84 | Equations (1285,1284) can reduce 679 to:
% 54.68/20.84 | (1106) $false
% 54.68/20.84 |
% 54.68/20.84 |-The branch is then unsatisfiable
% 54.68/20.84 |-Branch two:
% 54.68/20.84 | (1413) ~ (all_0_11_11 = n8)
% 54.68/20.84 | (1414) 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
% 54.68/20.84 |
% 54.68/20.84 +-Applying beta-rule and splitting (1414), into two cases.
% 54.68/20.84 |-Branch one:
% 54.68/20.84 | (1415) all_0_11_11 = n7
% 54.68/20.84 |
% 54.68/20.84 | From (1415) and (559) follows:
% 54.68/20.84 | (1416) pred(n7) = all_0_9_9
% 54.68/20.84 |
% 54.68/20.84 | From (1415) and (992) follows:
% 54.68/20.84 | (1417) succ(n7) = all_0_5_5
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 54.68/20.84 | (1418) all_0_9_9 = n6
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 54.68/20.84 | (1419) all_0_5_5 = n8
% 54.68/20.84 |
% 54.68/20.84 | From (1418)(1419) and (538) follows:
% 54.68/20.84 | (1420) sum(n6, n8) = all_0_2_2
% 54.68/20.84 |
% 54.68/20.84 | From (1418) and (6220) follows:
% 54.68/20.84 | (6453) sum(n6, n20) = all_0_7_7
% 54.68/20.84 |
% 54.68/20.84 | From (1419) and (6218) follows:
% 54.68/20.84 | (6454) sum(n18, n8) = all_0_4_4
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n18, n8, all_0_4_4, n0 and discharging atoms sum(n18, n8) = all_0_4_4, sum(n18, n8) = n0, yields:
% 54.68/20.84 | (1531) all_0_4_4 = n0
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n6, n20, all_0_7_7, n0 and discharging atoms sum(n6, n20) = all_0_7_7, sum(n6, n20) = n0, yields:
% 54.68/20.84 | (1533) all_0_7_7 = n0
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 54.68/20.84 | (1190) all_0_2_2 = n14
% 54.68/20.84 |
% 54.68/20.84 | From (1190) and (6222) follows:
% 54.68/20.84 | (5864) sum(n14, n12) = all_0_0_0
% 54.68/20.84 |
% 54.68/20.84 | From (1533)(1531) and (590) follows:
% 54.68/20.84 | (1535) sum(n0, n0) = all_0_3_3
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n14, n12, all_0_0_0, n0 and discharging atoms sum(n14, n12) = all_0_0_0, sum(n14, n12) = n0, yields:
% 54.68/20.84 | (1303) all_0_0_0 = n0
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 54.68/20.84 | (1302) all_0_3_3 = n0
% 54.68/20.84 |
% 54.68/20.84 | Equations (1303,1302) can reduce 679 to:
% 54.68/20.84 | (1106) $false
% 54.68/20.84 |
% 54.68/20.84 |-The branch is then unsatisfiable
% 54.68/20.84 |-Branch two:
% 54.68/20.84 | (1431) ~ (all_0_11_11 = n7)
% 54.68/20.84 | (1432) 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
% 54.68/20.84 |
% 54.68/20.84 +-Applying beta-rule and splitting (1432), into two cases.
% 54.68/20.84 |-Branch one:
% 54.68/20.84 | (1433) all_0_11_11 = n6
% 54.68/20.84 |
% 54.68/20.84 | From (1433) and (559) follows:
% 54.68/20.84 | (1434) pred(n6) = all_0_9_9
% 54.68/20.84 |
% 54.68/20.84 | From (1433) and (992) follows:
% 54.68/20.84 | (1435) succ(n6) = all_0_5_5
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 54.68/20.84 | (1436) all_0_9_9 = n5
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 54.68/20.84 | (1437) all_0_5_5 = n7
% 54.68/20.84 |
% 54.68/20.84 | From (1436)(1437) and (538) follows:
% 54.68/20.84 | (1438) sum(n5, n7) = all_0_2_2
% 54.68/20.84 |
% 54.68/20.84 | From (1436) and (6220) follows:
% 54.68/20.84 | (6471) sum(n5, n20) = all_0_7_7
% 54.68/20.84 |
% 54.68/20.84 | From (1437) and (6218) follows:
% 54.68/20.84 | (6472) sum(n18, n7) = all_0_4_4
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n18, n7, all_0_4_4, n25 and discharging atoms sum(n18, n7) = all_0_4_4, sum(n18, n7) = n25, yields:
% 54.68/20.84 | (1551) all_0_4_4 = n25
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n5, n20, all_0_7_7, n25 and discharging atoms sum(n5, n20) = all_0_7_7, sum(n5, n20) = n25, yields:
% 54.68/20.84 | (1550) all_0_7_7 = n25
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 54.68/20.84 | (1208) all_0_2_2 = n12
% 54.68/20.84 |
% 54.68/20.84 | From (1208) and (6222) follows:
% 54.68/20.84 | (6240) sum(n12, n12) = all_0_0_0
% 54.68/20.84 |
% 54.68/20.84 | From (1550)(1551) and (590) follows:
% 54.68/20.84 | (1553) sum(n25, n25) = all_0_3_3
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 54.68/20.84 | (1320) all_0_3_3 = n24
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n12, n12, all_0_0_0, n24 and discharging atoms sum(n12, n12) = all_0_0_0, sum(n12, n12) = n24, yields:
% 54.68/20.84 | (1321) all_0_0_0 = n24
% 54.68/20.84 |
% 54.68/20.84 | Equations (1321,1320) can reduce 679 to:
% 54.68/20.84 | (1106) $false
% 54.68/20.84 |
% 54.68/20.84 |-The branch is then unsatisfiable
% 54.68/20.84 |-Branch two:
% 54.68/20.84 | (1449) ~ (all_0_11_11 = n6)
% 54.68/20.84 | (1450) 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
% 54.68/20.84 |
% 54.68/20.84 +-Applying beta-rule and splitting (1450), into two cases.
% 54.68/20.84 |-Branch one:
% 54.68/20.84 | (1451) all_0_11_11 = n5
% 54.68/20.84 |
% 54.68/20.84 | From (1451) and (559) follows:
% 54.68/20.84 | (1452) pred(n5) = all_0_9_9
% 54.68/20.84 |
% 54.68/20.84 | From (1451) and (992) follows:
% 54.68/20.84 | (1453) succ(n5) = all_0_5_5
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 54.68/20.84 | (1454) all_0_9_9 = n4
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 54.68/20.84 | (1455) all_0_5_5 = n6
% 54.68/20.84 |
% 54.68/20.84 | From (1454)(1455) and (538) follows:
% 54.68/20.84 | (1456) sum(n4, n6) = all_0_2_2
% 54.68/20.84 |
% 54.68/20.84 | From (1454) and (6220) follows:
% 54.68/20.84 | (6489) sum(n4, n20) = all_0_7_7
% 54.68/20.84 |
% 54.68/20.84 | From (1455) and (6218) follows:
% 54.68/20.84 | (6490) sum(n18, n6) = all_0_4_4
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n18, n6, all_0_4_4, n24 and discharging atoms sum(n18, n6) = all_0_4_4, sum(n18, n6) = n24, yields:
% 54.68/20.84 | (1096) all_0_4_4 = n24
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n4, n20, all_0_7_7, n24 and discharging atoms sum(n4, n20) = all_0_7_7, sum(n4, n20) = n24, yields:
% 54.68/20.84 | (1097) all_0_7_7 = n24
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 54.68/20.84 | (1226) all_0_2_2 = n10
% 54.68/20.84 |
% 54.68/20.84 | From (1226) and (6222) follows:
% 54.68/20.84 | (6260) sum(n10, n12) = all_0_0_0
% 54.68/20.84 |
% 54.68/20.84 | From (1097)(1096) and (590) follows:
% 54.68/20.84 | (1101) sum(n24, n24) = all_0_3_3
% 54.68/20.84 |
% 54.68/20.84 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 54.68/20.85 | (1104) all_0_3_3 = n22
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n10, n12, all_0_0_0, n22 and discharging atoms sum(n10, n12) = all_0_0_0, sum(n10, n12) = n22, yields:
% 54.68/20.85 | (1102) all_0_0_0 = n22
% 54.68/20.85 |
% 54.68/20.85 | Equations (1102,1104) can reduce 679 to:
% 54.68/20.85 | (1106) $false
% 54.68/20.85 |
% 54.68/20.85 |-The branch is then unsatisfiable
% 54.68/20.85 |-Branch two:
% 54.68/20.85 | (1467) ~ (all_0_11_11 = n5)
% 54.68/20.85 | (1468) 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
% 54.68/20.85 |
% 54.68/20.85 +-Applying beta-rule and splitting (1468), into two cases.
% 54.68/20.85 |-Branch one:
% 54.68/20.85 | (1469) all_0_11_11 = n4
% 54.68/20.85 |
% 54.68/20.85 | From (1469) and (559) follows:
% 54.68/20.85 | (1470) pred(n4) = all_0_9_9
% 54.68/20.85 |
% 54.68/20.85 | From (1469) and (992) follows:
% 54.68/20.85 | (1471) succ(n4) = all_0_5_5
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 54.68/20.85 | (1472) all_0_9_9 = n3
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 54.68/20.85 | (1473) all_0_5_5 = n5
% 54.68/20.85 |
% 54.68/20.85 | From (1472)(1473) and (538) follows:
% 54.68/20.85 | (1474) sum(n3, n5) = all_0_2_2
% 54.68/20.85 |
% 54.68/20.85 | From (1472) and (6220) follows:
% 54.68/20.85 | (6507) sum(n3, n20) = all_0_7_7
% 54.68/20.85 |
% 54.68/20.85 | From (1473) and (6218) follows:
% 54.68/20.85 | (6508) sum(n18, n5) = all_0_4_4
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n18, n5, all_0_4_4, n23 and discharging atoms sum(n18, n5) = all_0_4_4, sum(n18, n5) = n23, yields:
% 54.68/20.85 | (1117) all_0_4_4 = n23
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n3, n20, all_0_7_7, n23 and discharging atoms sum(n3, n20) = all_0_7_7, sum(n3, n20) = n23, yields:
% 54.68/20.85 | (1119) all_0_7_7 = n23
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 54.68/20.85 | (1244) all_0_2_2 = n8
% 54.68/20.85 |
% 54.68/20.85 | From (1244) and (6222) follows:
% 54.68/20.85 | (6278) sum(n8, n12) = all_0_0_0
% 54.68/20.85 |
% 54.68/20.85 | From (1119)(1117) and (590) follows:
% 54.68/20.85 | (1121) sum(n23, n23) = all_0_3_3
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 54.68/20.85 | (1122) all_0_3_3 = n20
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n8, n12, all_0_0_0, n20 and discharging atoms sum(n8, n12) = all_0_0_0, sum(n8, n12) = n20, yields:
% 54.68/20.85 | (1123) all_0_0_0 = n20
% 54.68/20.85 |
% 54.68/20.85 | Equations (1123,1122) can reduce 679 to:
% 54.68/20.85 | (1106) $false
% 54.68/20.85 |
% 54.68/20.85 |-The branch is then unsatisfiable
% 54.68/20.85 |-Branch two:
% 54.68/20.85 | (1485) ~ (all_0_11_11 = n4)
% 54.68/20.85 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 54.68/20.85 |
% 54.68/20.85 +-Applying beta-rule and splitting (1486), into two cases.
% 54.68/20.85 |-Branch one:
% 54.68/20.85 | (1487) all_0_11_11 = n3
% 54.68/20.85 |
% 54.68/20.85 | From (1487) and (559) follows:
% 54.68/20.85 | (1488) pred(n3) = all_0_9_9
% 54.68/20.85 |
% 54.68/20.85 | From (1487) and (992) follows:
% 54.68/20.85 | (1489) succ(n3) = all_0_5_5
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 54.68/20.85 | (1490) all_0_9_9 = n2
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 54.68/20.85 | (1491) all_0_5_5 = n4
% 54.68/20.85 |
% 54.68/20.85 | From (1490)(1491) and (538) follows:
% 54.68/20.85 | (1492) sum(n2, n4) = all_0_2_2
% 54.68/20.85 |
% 54.68/20.85 | From (1490) and (6220) follows:
% 54.68/20.85 | (6525) sum(n2, n20) = all_0_7_7
% 54.68/20.85 |
% 54.68/20.85 | From (1491) and (6218) follows:
% 54.68/20.85 | (6526) sum(n18, n4) = all_0_4_4
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n18, n4, all_0_4_4, n22 and discharging atoms sum(n18, n4) = all_0_4_4, sum(n18, n4) = n22, yields:
% 54.68/20.85 | (1135) all_0_4_4 = n22
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n2, n20, all_0_7_7, n22 and discharging atoms sum(n2, n20) = all_0_7_7, sum(n2, n20) = n22, yields:
% 54.68/20.85 | (1137) all_0_7_7 = n22
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 54.68/20.85 | (1262) all_0_2_2 = n6
% 54.68/20.85 |
% 54.68/20.85 | From (1262) and (6222) follows:
% 54.68/20.85 | (6296) sum(n6, n12) = all_0_0_0
% 54.68/20.85 |
% 54.68/20.85 | From (1137)(1135) and (590) follows:
% 54.68/20.85 | (1139) sum(n22, n22) = all_0_3_3
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 54.68/20.85 | (1140) all_0_3_3 = n18
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n6, n12, all_0_0_0, n18 and discharging atoms sum(n6, n12) = all_0_0_0, sum(n6, n12) = n18, yields:
% 54.68/20.85 | (1141) all_0_0_0 = n18
% 54.68/20.85 |
% 54.68/20.85 | Equations (1141,1140) can reduce 679 to:
% 54.68/20.85 | (1106) $false
% 54.68/20.85 |
% 54.68/20.85 |-The branch is then unsatisfiable
% 54.68/20.85 |-Branch two:
% 54.68/20.85 | (1503) ~ (all_0_11_11 = n3)
% 54.68/20.85 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 54.68/20.85 |
% 54.68/20.85 +-Applying beta-rule and splitting (1504), into two cases.
% 54.68/20.85 |-Branch one:
% 54.68/20.85 | (1505) all_0_11_11 = n2
% 54.68/20.85 |
% 54.68/20.85 | From (1505) and (559) follows:
% 54.68/20.85 | (1506) pred(n2) = all_0_9_9
% 54.68/20.85 |
% 54.68/20.85 | From (1505) and (992) follows:
% 54.68/20.85 | (1507) succ(n2) = all_0_5_5
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 54.68/20.85 | (1508) all_0_9_9 = n1
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 54.68/20.85 | (1509) all_0_5_5 = n3
% 54.68/20.85 |
% 54.68/20.85 | From (1508)(1509) and (538) follows:
% 54.68/20.85 | (1510) sum(n1, n3) = all_0_2_2
% 54.68/20.85 |
% 54.68/20.85 | From (1508) and (6220) follows:
% 54.68/20.85 | (6543) sum(n1, n20) = all_0_7_7
% 54.68/20.85 |
% 54.68/20.85 | From (1509) and (6218) follows:
% 54.68/20.85 | (6544) sum(n18, n3) = all_0_4_4
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n18, n3, all_0_4_4, n21 and discharging atoms sum(n18, n3) = all_0_4_4, sum(n18, n3) = n21, yields:
% 54.68/20.85 | (1153) all_0_4_4 = n21
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n1, n20, all_0_7_7, n21 and discharging atoms sum(n1, n20) = all_0_7_7, sum(n1, n20) = n21, yields:
% 54.68/20.85 | (1155) all_0_7_7 = n21
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 54.68/20.85 | (1280) all_0_2_2 = n4
% 54.68/20.85 |
% 54.68/20.85 | From (1280) and (6222) follows:
% 54.68/20.85 | (6314) sum(n4, n12) = all_0_0_0
% 54.68/20.85 |
% 54.68/20.85 | From (1155)(1153) and (590) follows:
% 54.68/20.85 | (1157) sum(n21, n21) = all_0_3_3
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 54.68/20.85 | (1158) all_0_3_3 = n16
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n4, n12, all_0_0_0, n16 and discharging atoms sum(n4, n12) = all_0_0_0, sum(n4, n12) = n16, yields:
% 54.68/20.85 | (1159) all_0_0_0 = n16
% 54.68/20.85 |
% 54.68/20.85 | Equations (1159,1158) can reduce 679 to:
% 54.68/20.85 | (1106) $false
% 54.68/20.85 |
% 54.68/20.85 |-The branch is then unsatisfiable
% 54.68/20.85 |-Branch two:
% 54.68/20.85 | (1521) ~ (all_0_11_11 = n2)
% 54.68/20.85 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 54.68/20.85 |
% 54.68/20.85 +-Applying beta-rule and splitting (1522), into two cases.
% 54.68/20.85 |-Branch one:
% 54.68/20.85 | (1523) all_0_11_11 = n1
% 54.68/20.85 |
% 54.68/20.85 | From (1523) and (559) follows:
% 54.68/20.85 | (1524) pred(n1) = all_0_9_9
% 54.68/20.85 |
% 54.68/20.85 | From (1523) and (992) follows:
% 54.68/20.85 | (1525) succ(n1) = all_0_5_5
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 54.68/20.85 | (1526) all_0_9_9 = n0
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 54.68/20.85 | (1527) all_0_5_5 = n2
% 54.68/20.85 |
% 54.68/20.85 | From (1526)(1527) and (538) follows:
% 54.68/20.85 | (1528) sum(n0, n2) = all_0_2_2
% 54.68/20.85 |
% 54.68/20.85 | From (1526) and (6220) follows:
% 54.68/20.85 | (6561) sum(n0, n20) = all_0_7_7
% 54.68/20.85 |
% 54.68/20.85 | From (1527) and (6218) follows:
% 54.68/20.85 | (6562) sum(n18, n2) = all_0_4_4
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n18, n2, all_0_4_4, n20 and discharging atoms sum(n18, n2) = all_0_4_4, sum(n18, n2) = n20, yields:
% 54.68/20.85 | (1171) all_0_4_4 = n20
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n0, n20, all_0_7_7, n20 and discharging atoms sum(n0, n20) = all_0_7_7, sum(n0, n20) = n20, yields:
% 54.68/20.85 | (1173) all_0_7_7 = n20
% 54.68/20.85 |
% 54.68/20.85 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 54.68/20.86 | (1298) all_0_2_2 = n2
% 54.68/20.86 |
% 54.68/20.86 | From (1298) and (6222) follows:
% 54.68/20.86 | (6332) sum(n2, n12) = all_0_0_0
% 54.68/20.86 |
% 54.68/20.86 | From (1173)(1171) and (590) follows:
% 54.68/20.86 | (1175) sum(n20, n20) = all_0_3_3
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 54.68/20.86 | (1176) all_0_3_3 = n14
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (690) with n2, n12, all_0_0_0, n14 and discharging atoms sum(n2, n12) = all_0_0_0, sum(n2, n12) = n14, yields:
% 54.68/20.86 | (1177) all_0_0_0 = n14
% 54.68/20.86 |
% 54.68/20.86 | Equations (1177,1176) can reduce 679 to:
% 54.68/20.86 | (1106) $false
% 54.68/20.86 |
% 54.68/20.86 |-The branch is then unsatisfiable
% 54.68/20.86 |-Branch two:
% 54.68/20.86 | (1540) ~ (all_0_11_11 = n1)
% 54.68/20.86 | (1541) all_0_11_11 = n0
% 54.68/20.86 |
% 54.68/20.86 | From (1541) and (559) follows:
% 54.68/20.86 | (1542) pred(n0) = all_0_9_9
% 54.68/20.86 |
% 54.68/20.86 | From (1541) and (992) follows:
% 54.68/20.86 | (1543) succ(n0) = all_0_5_5
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 54.68/20.86 | (1544) all_0_9_9 = n25
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 54.68/20.86 | (1545) all_0_5_5 = n1
% 54.68/20.86 |
% 54.68/20.86 | From (1544)(1545) and (538) follows:
% 54.68/20.86 | (1546) sum(n25, n1) = all_0_2_2
% 54.68/20.86 |
% 54.68/20.86 | From (1544) and (6220) follows:
% 54.68/20.86 | (6578) sum(n25, n20) = all_0_7_7
% 54.68/20.86 |
% 54.68/20.86 | From (1545) and (6218) follows:
% 54.68/20.86 | (6579) sum(n18, n1) = all_0_4_4
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (690) with n25, n20, all_0_7_7, n19 and discharging atoms sum(n25, n20) = all_0_7_7, sum(n25, n20) = n19, yields:
% 54.68/20.86 | (1191) all_0_7_7 = n19
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 54.68/20.86 | (1316) all_0_2_2 = n0
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (690) with n18, n1, all_0_4_4, n19 and discharging atoms sum(n18, n1) = all_0_4_4, sum(n18, n1) = n19, yields:
% 54.68/20.86 | (1189) all_0_4_4 = n19
% 54.68/20.86 |
% 54.68/20.86 | From (1316) and (6222) follows:
% 54.68/20.86 | (6350) sum(n0, n12) = all_0_0_0
% 54.68/20.86 |
% 54.68/20.86 | From (1191)(1189) and (590) follows:
% 54.68/20.86 | (1193) sum(n19, n19) = all_0_3_3
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 54.68/20.86 | (1194) all_0_3_3 = n12
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (690) with n0, n12, all_0_0_0, n12 and discharging atoms sum(n0, n12) = all_0_0_0, sum(n0, n12) = n12, yields:
% 54.68/20.86 | (1195) all_0_0_0 = n12
% 54.68/20.86 |
% 54.68/20.86 | Equations (1195,1194) can reduce 679 to:
% 54.68/20.86 | (1106) $false
% 54.68/20.86 |
% 54.68/20.86 |-The branch is then unsatisfiable
% 54.68/20.86 |-Branch two:
% 54.68/20.86 | (1676) ~ (all_0_10_10 = n19)
% 54.68/20.86 | (1677) 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
% 54.68/20.86 |
% 54.68/20.86 +-Applying beta-rule and splitting (1198), into two cases.
% 54.68/20.86 |-Branch one:
% 54.68/20.86 | (1199) all_0_11_11 = n19
% 54.68/20.86 |
% 54.68/20.86 | From (1199) and (559) follows:
% 54.68/20.86 | (1200) pred(n19) = all_0_9_9
% 54.68/20.86 |
% 54.68/20.86 | From (1199) and (992) follows:
% 54.68/20.86 | (1201) succ(n19) = all_0_5_5
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (500) with n19, all_0_9_9, n18 and discharging atoms pred(n19) = all_0_9_9, pred(n19) = n18, yields:
% 54.68/20.86 | (1202) all_0_9_9 = n18
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (617) with n19, all_0_5_5, n20 and discharging atoms succ(n19) = all_0_5_5, succ(n19) = n20, yields:
% 54.68/20.86 | (1203) all_0_5_5 = n20
% 54.68/20.86 |
% 54.68/20.86 | From (1203) and (541) follows:
% 54.68/20.86 | (6595) sum(all_0_6_6, n20) = all_0_4_4
% 54.68/20.86 |
% 54.68/20.86 | From (1202)(1203) and (538) follows:
% 54.68/20.86 | (1204) sum(n18, n20) = all_0_2_2
% 54.68/20.86 |
% 54.68/20.86 | From (1202) and (427) follows:
% 54.68/20.86 | (6597) sum(n18, all_0_8_8) = all_0_7_7
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (690) with n18, n20, all_0_2_2, n12 and discharging atoms sum(n18, n20) = all_0_2_2, sum(n18, n20) = n12, yields:
% 54.68/20.86 | (1208) all_0_2_2 = n12
% 54.68/20.86 |
% 54.68/20.86 | From (1208) and (630) follows:
% 54.68/20.86 | (6599) sum(n12, all_0_1_1) = all_0_0_0
% 54.68/20.86 |
% 54.68/20.86 +-Applying beta-rule and splitting (1677), into two cases.
% 54.68/20.86 |-Branch one:
% 54.68/20.86 | (1678) all_0_10_10 = n18
% 54.68/20.86 |
% 54.68/20.86 | From (1678) and (292) follows:
% 54.68/20.86 | (1679) pred(n18) = all_0_6_6
% 54.68/20.86 |
% 54.68/20.86 | From (1678) and (760) follows:
% 54.68/20.86 | (1680) succ(n18) = all_0_8_8
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (500) with n18, all_0_6_6, n17 and discharging atoms pred(n18) = all_0_6_6, pred(n18) = n17, yields:
% 54.68/20.86 | (1681) all_0_6_6 = n17
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (617) with n18, all_0_8_8, n19 and discharging atoms succ(n18) = all_0_8_8, succ(n18) = n19, yields:
% 54.68/20.86 | (1682) all_0_8_8 = n19
% 54.68/20.86 |
% 54.68/20.86 | From (1681)(1682) and (411) follows:
% 54.68/20.86 | (1683) sum(n17, n19) = all_0_1_1
% 54.68/20.86 |
% 54.68/20.86 | From (1681) and (6595) follows:
% 54.68/20.86 | (6606) sum(n17, n20) = all_0_4_4
% 54.68/20.86 |
% 54.68/20.86 | From (1682) and (6597) follows:
% 54.68/20.86 | (6607) sum(n18, n19) = all_0_7_7
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (690) with n18, n19, all_0_7_7, n11 and discharging atoms sum(n18, n19) = all_0_7_7, sum(n18, n19) = n11, yields:
% 54.68/20.86 | (1335) all_0_7_7 = n11
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (690) with n17, n20, all_0_4_4, n11 and discharging atoms sum(n17, n20) = all_0_4_4, sum(n17, n20) = n11, yields:
% 54.68/20.86 | (1333) all_0_4_4 = n11
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (690) with n17, n19, all_0_1_1, n10 and discharging atoms sum(n17, n19) = all_0_1_1, sum(n17, n19) = n10, yields:
% 54.68/20.86 | (1687) all_0_1_1 = n10
% 54.68/20.86 |
% 54.68/20.86 | From (1335)(1333) and (590) follows:
% 54.68/20.86 | (1337) sum(n11, n11) = all_0_3_3
% 54.68/20.86 |
% 54.68/20.86 | From (1687) and (6599) follows:
% 54.68/20.86 | (6612) sum(n12, n10) = all_0_0_0
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (690) with n12, n10, all_0_0_0, n22 and discharging atoms sum(n12, n10) = all_0_0_0, sum(n12, n10) = n22, yields:
% 54.68/20.86 | (1102) all_0_0_0 = n22
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 54.68/20.86 | (1104) all_0_3_3 = n22
% 54.68/20.86 |
% 54.68/20.86 | Equations (1102,1104) can reduce 679 to:
% 54.68/20.86 | (1106) $false
% 54.68/20.86 |
% 54.68/20.86 |-The branch is then unsatisfiable
% 54.68/20.86 |-Branch two:
% 54.68/20.86 | (1694) ~ (all_0_10_10 = n18)
% 54.68/20.86 | (1695) 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
% 54.68/20.86 |
% 54.68/20.86 +-Applying beta-rule and splitting (1695), into two cases.
% 54.68/20.86 |-Branch one:
% 54.68/20.86 | (1696) all_0_10_10 = n17
% 54.68/20.86 |
% 54.68/20.86 | From (1696) and (292) follows:
% 54.68/20.86 | (1697) pred(n17) = all_0_6_6
% 54.68/20.86 |
% 54.68/20.86 | From (1696) and (760) follows:
% 54.68/20.86 | (1698) succ(n17) = all_0_8_8
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (500) with n17, all_0_6_6, n16 and discharging atoms pred(n17) = all_0_6_6, pred(n17) = n16, yields:
% 54.68/20.86 | (1699) all_0_6_6 = n16
% 54.68/20.86 |
% 54.68/20.86 | Instantiating formula (617) with n17, all_0_8_8, n18 and discharging atoms succ(n17) = all_0_8_8, succ(n17) = n18, yields:
% 54.68/20.86 | (1700) all_0_8_8 = n18
% 54.68/20.86 |
% 54.68/20.86 | From (1699)(1700) and (411) follows:
% 54.68/20.86 | (1701) sum(n16, n18) = all_0_1_1
% 54.68/20.86 |
% 54.68/20.86 | From (1699) and (6595) follows:
% 54.68/20.86 | (6624) sum(n16, n20) = all_0_4_4
% 54.68/20.86 |
% 54.68/20.86 | From (1700) and (6597) follows:
% 54.68/20.87 | (6625) sum(n18, n18) = all_0_7_7
% 54.68/20.87 |
% 54.68/20.87 | Instantiating formula (690) with n18, n18, all_0_7_7, n10 and discharging atoms sum(n18, n18) = all_0_7_7, sum(n18, n18) = n10, yields:
% 54.68/20.87 | (1353) all_0_7_7 = n10
% 54.68/20.87 |
% 54.68/20.87 | Instantiating formula (690) with n16, n20, all_0_4_4, n10 and discharging atoms sum(n16, n20) = all_0_4_4, sum(n16, n20) = n10, yields:
% 54.68/20.87 | (1351) all_0_4_4 = n10
% 54.68/20.87 |
% 54.68/20.87 | Instantiating formula (690) with n16, n18, all_0_1_1, n8 and discharging atoms sum(n16, n18) = all_0_1_1, sum(n16, n18) = n8, yields:
% 54.68/20.87 | (1705) all_0_1_1 = n8
% 54.68/20.87 |
% 54.68/20.87 | From (1353)(1351) and (590) follows:
% 54.68/20.87 | (1355) sum(n10, n10) = all_0_3_3
% 54.68/20.87 |
% 54.68/20.87 | From (1705) and (6599) follows:
% 54.68/20.87 | (6630) sum(n12, n8) = all_0_0_0
% 54.68/20.87 |
% 54.68/20.87 | Instantiating formula (690) with n12, n8, all_0_0_0, n20 and discharging atoms sum(n12, n8) = all_0_0_0, sum(n12, n8) = n20, yields:
% 54.68/20.87 | (1123) all_0_0_0 = n20
% 54.68/20.87 |
% 54.68/20.87 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 54.68/20.87 | (1122) all_0_3_3 = n20
% 54.68/20.87 |
% 54.68/20.87 | Equations (1123,1122) can reduce 679 to:
% 54.68/20.87 | (1106) $false
% 54.68/20.87 |
% 54.68/20.87 |-The branch is then unsatisfiable
% 54.68/20.87 |-Branch two:
% 54.68/20.87 | (1712) ~ (all_0_10_10 = n17)
% 54.68/20.87 | (1713) 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
% 54.68/20.87 |
% 54.68/20.87 +-Applying beta-rule and splitting (1713), into two cases.
% 54.68/20.87 |-Branch one:
% 54.68/20.87 | (1714) all_0_10_10 = n16
% 54.68/20.87 |
% 54.68/20.87 | From (1714) and (292) follows:
% 54.68/20.87 | (1715) pred(n16) = all_0_6_6
% 54.68/20.87 |
% 54.68/20.87 | From (1714) and (760) follows:
% 54.68/20.87 | (1716) succ(n16) = all_0_8_8
% 54.68/20.87 |
% 54.68/20.87 | Instantiating formula (500) with n16, all_0_6_6, n15 and discharging atoms pred(n16) = all_0_6_6, pred(n16) = n15, yields:
% 54.68/20.87 | (1717) all_0_6_6 = n15
% 54.68/20.87 |
% 54.68/20.87 | Instantiating formula (617) with n16, all_0_8_8, n17 and discharging atoms succ(n16) = all_0_8_8, succ(n16) = n17, yields:
% 54.68/20.87 | (1718) all_0_8_8 = n17
% 54.68/20.87 |
% 54.68/20.87 | From (1717)(1718) and (411) follows:
% 54.68/20.87 | (1719) sum(n15, n17) = all_0_1_1
% 54.68/20.87 |
% 54.68/20.87 | From (1717) and (6595) follows:
% 54.68/20.87 | (6642) sum(n15, n20) = all_0_4_4
% 54.68/20.87 |
% 54.68/20.87 | From (1718) and (6597) follows:
% 54.68/20.87 | (6643) sum(n18, n17) = all_0_7_7
% 54.68/20.87 |
% 54.68/20.87 | Instantiating formula (690) with n18, n17, all_0_7_7, n9 and discharging atoms sum(n18, n17) = all_0_7_7, sum(n18, n17) = n9, yields:
% 54.68/20.87 | (1371) all_0_7_7 = n9
% 54.68/20.87 |
% 54.68/20.87 | Instantiating formula (690) with n15, n20, all_0_4_4, n9 and discharging atoms sum(n15, n20) = all_0_4_4, sum(n15, n20) = n9, yields:
% 54.68/20.87 | (1369) all_0_4_4 = n9
% 54.68/20.87 |
% 54.68/20.87 | Instantiating formula (690) with n15, n17, all_0_1_1, n6 and discharging atoms sum(n15, n17) = all_0_1_1, sum(n15, n17) = n6, yields:
% 54.68/20.87 | (1723) all_0_1_1 = n6
% 54.68/20.87 |
% 54.68/20.87 | From (1371)(1369) and (590) follows:
% 54.68/20.87 | (1373) sum(n9, n9) = all_0_3_3
% 54.68/20.87 |
% 54.68/20.87 | From (1723) and (6599) follows:
% 54.98/20.87 | (6648) sum(n12, n6) = all_0_0_0
% 54.98/20.87 |
% 54.98/20.87 | Instantiating formula (690) with n12, n6, all_0_0_0, n18 and discharging atoms sum(n12, n6) = all_0_0_0, sum(n12, n6) = n18, yields:
% 54.98/20.87 | (1141) all_0_0_0 = n18
% 54.98/20.87 |
% 54.98/20.87 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 54.98/20.87 | (1140) all_0_3_3 = n18
% 54.98/20.87 |
% 54.98/20.87 | Equations (1141,1140) can reduce 679 to:
% 54.98/20.87 | (1106) $false
% 54.98/20.87 |
% 54.98/20.87 |-The branch is then unsatisfiable
% 54.98/20.87 |-Branch two:
% 54.98/20.87 | (1730) ~ (all_0_10_10 = n16)
% 54.98/20.87 | (1731) 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
% 54.98/20.87 |
% 54.98/20.87 +-Applying beta-rule and splitting (1731), into two cases.
% 54.98/20.87 |-Branch one:
% 54.98/20.87 | (1732) all_0_10_10 = n15
% 54.98/20.87 |
% 54.98/20.87 | From (1732) and (292) follows:
% 54.98/20.87 | (1733) pred(n15) = all_0_6_6
% 54.98/20.87 |
% 54.98/20.87 | From (1732) and (760) follows:
% 54.98/20.87 | (1734) succ(n15) = all_0_8_8
% 54.98/20.87 |
% 54.98/20.87 | Instantiating formula (500) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 54.98/20.87 | (1735) all_0_6_6 = n14
% 54.98/20.87 |
% 54.98/20.87 | Instantiating formula (617) with n15, all_0_8_8, n16 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n16, yields:
% 54.98/20.87 | (1736) all_0_8_8 = n16
% 54.98/20.87 |
% 54.98/20.87 | From (1735)(1736) and (411) follows:
% 54.98/20.87 | (1737) sum(n14, n16) = all_0_1_1
% 54.98/20.87 |
% 54.98/20.87 | From (1735) and (6595) follows:
% 54.98/20.87 | (6660) sum(n14, n20) = all_0_4_4
% 54.98/20.87 |
% 54.98/20.87 | From (1736) and (6597) follows:
% 54.98/20.87 | (6661) sum(n18, n16) = all_0_7_7
% 54.98/20.87 |
% 54.98/20.87 | Instantiating formula (690) with n18, n16, all_0_7_7, n8 and discharging atoms sum(n18, n16) = all_0_7_7, sum(n18, n16) = n8, yields:
% 54.98/20.87 | (1389) all_0_7_7 = n8
% 54.98/20.87 |
% 54.98/20.87 | Instantiating formula (690) with n14, n20, all_0_4_4, n8 and discharging atoms sum(n14, n20) = all_0_4_4, sum(n14, n20) = n8, yields:
% 54.98/20.87 | (1387) all_0_4_4 = n8
% 54.98/20.87 |
% 54.98/20.87 | Instantiating formula (690) with n14, n16, all_0_1_1, n4 and discharging atoms sum(n14, n16) = all_0_1_1, sum(n14, n16) = n4, yields:
% 54.98/20.87 | (1741) all_0_1_1 = n4
% 54.98/20.87 |
% 54.98/20.87 | From (1389)(1387) and (590) follows:
% 54.98/20.87 | (1391) sum(n8, n8) = all_0_3_3
% 54.98/20.87 |
% 54.98/20.87 | From (1741) and (6599) follows:
% 54.98/20.87 | (6666) sum(n12, n4) = all_0_0_0
% 54.98/20.87 |
% 54.98/20.87 | Instantiating formula (690) with n12, n4, all_0_0_0, n16 and discharging atoms sum(n12, n4) = all_0_0_0, sum(n12, n4) = n16, yields:
% 54.98/20.87 | (1159) all_0_0_0 = n16
% 54.98/20.87 |
% 54.98/20.87 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 54.98/20.87 | (1158) all_0_3_3 = n16
% 54.98/20.87 |
% 54.98/20.87 | Equations (1159,1158) can reduce 679 to:
% 54.98/20.87 | (1106) $false
% 54.98/20.87 |
% 54.98/20.87 |-The branch is then unsatisfiable
% 54.98/20.87 |-Branch two:
% 54.98/20.87 | (1748) ~ (all_0_10_10 = n15)
% 54.98/20.87 | (1749) 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
% 54.98/20.87 |
% 54.98/20.87 +-Applying beta-rule and splitting (1749), into two cases.
% 54.98/20.87 |-Branch one:
% 54.98/20.87 | (1750) all_0_10_10 = n14
% 54.98/20.87 |
% 54.98/20.87 | From (1750) and (292) follows:
% 54.98/20.87 | (1751) pred(n14) = all_0_6_6
% 54.98/20.87 |
% 54.98/20.87 | From (1750) and (760) follows:
% 54.98/20.87 | (1752) succ(n14) = all_0_8_8
% 54.98/20.87 |
% 54.98/20.87 | Instantiating formula (500) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 54.98/20.87 | (1753) all_0_6_6 = n13
% 54.98/20.87 |
% 54.98/20.87 | Instantiating formula (617) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 54.98/20.87 | (1754) all_0_8_8 = n15
% 54.98/20.87 |
% 54.98/20.87 | From (1753)(1754) and (411) follows:
% 54.98/20.87 | (1755) sum(n13, n15) = all_0_1_1
% 54.98/20.87 |
% 54.98/20.87 | From (1753) and (6595) follows:
% 54.98/20.87 | (6678) sum(n13, n20) = all_0_4_4
% 54.98/20.87 |
% 54.98/20.87 | From (1754) and (6597) follows:
% 54.98/20.87 | (6679) sum(n18, n15) = all_0_7_7
% 54.98/20.87 |
% 54.98/20.87 | Instantiating formula (690) with n18, n15, all_0_7_7, n7 and discharging atoms sum(n18, n15) = all_0_7_7, sum(n18, n15) = n7, yields:
% 54.98/20.87 | (1407) all_0_7_7 = n7
% 54.98/20.87 |
% 54.98/20.87 | Instantiating formula (690) with n13, n20, all_0_4_4, n7 and discharging atoms sum(n13, n20) = all_0_4_4, sum(n13, n20) = n7, yields:
% 54.98/20.87 | (1405) all_0_4_4 = n7
% 54.98/20.87 |
% 54.98/20.87 | Instantiating formula (690) with n13, n15, all_0_1_1, n2 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n2, yields:
% 54.98/20.87 | (1759) all_0_1_1 = n2
% 54.98/20.87 |
% 54.98/20.87 | From (1407)(1405) and (590) follows:
% 54.98/20.87 | (1409) sum(n7, n7) = all_0_3_3
% 54.98/20.87 |
% 54.98/20.87 | From (1759) and (6599) follows:
% 54.98/20.88 | (6684) sum(n12, n2) = all_0_0_0
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (690) with n12, n2, all_0_0_0, n14 and discharging atoms sum(n12, n2) = all_0_0_0, sum(n12, n2) = n14, yields:
% 54.98/20.88 | (1177) all_0_0_0 = n14
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 54.98/20.88 | (1176) all_0_3_3 = n14
% 54.98/20.88 |
% 54.98/20.88 | Equations (1177,1176) can reduce 679 to:
% 54.98/20.88 | (1106) $false
% 54.98/20.88 |
% 54.98/20.88 |-The branch is then unsatisfiable
% 54.98/20.88 |-Branch two:
% 54.98/20.88 | (1766) ~ (all_0_10_10 = n14)
% 54.98/20.88 | (1767) 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
% 54.98/20.88 |
% 54.98/20.88 +-Applying beta-rule and splitting (1767), into two cases.
% 54.98/20.88 |-Branch one:
% 54.98/20.88 | (1768) all_0_10_10 = n13
% 54.98/20.88 |
% 54.98/20.88 | From (1768) and (292) follows:
% 54.98/20.88 | (1769) pred(n13) = all_0_6_6
% 54.98/20.88 |
% 54.98/20.88 | From (1768) and (760) follows:
% 54.98/20.88 | (1770) succ(n13) = all_0_8_8
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (500) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 54.98/20.88 | (1771) all_0_6_6 = n12
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (617) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 54.98/20.88 | (1772) all_0_8_8 = n14
% 54.98/20.88 |
% 54.98/20.88 | From (1771)(1772) and (411) follows:
% 54.98/20.88 | (1773) sum(n12, n14) = all_0_1_1
% 54.98/20.88 |
% 54.98/20.88 | From (1771) and (6595) follows:
% 54.98/20.88 | (6696) sum(n12, n20) = all_0_4_4
% 54.98/20.88 |
% 54.98/20.88 | From (1772) and (6597) follows:
% 54.98/20.88 | (6697) sum(n18, n14) = all_0_7_7
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (690) with n18, n14, all_0_7_7, n6 and discharging atoms sum(n18, n14) = all_0_7_7, sum(n18, n14) = n6, yields:
% 54.98/20.88 | (1425) all_0_7_7 = n6
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (690) with n12, n20, all_0_4_4, n6 and discharging atoms sum(n12, n20) = all_0_4_4, sum(n12, n20) = n6, yields:
% 54.98/20.88 | (1423) all_0_4_4 = n6
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (690) with n12, n14, all_0_1_1, n0 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n0, yields:
% 54.98/20.88 | (1777) all_0_1_1 = n0
% 54.98/20.88 |
% 54.98/20.88 | From (1425)(1423) and (590) follows:
% 54.98/20.88 | (1427) sum(n6, n6) = all_0_3_3
% 54.98/20.88 |
% 54.98/20.88 | From (1777) and (6599) follows:
% 54.98/20.88 | (6702) sum(n12, n0) = all_0_0_0
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (690) with n12, n0, all_0_0_0, n12 and discharging atoms sum(n12, n0) = all_0_0_0, sum(n12, n0) = n12, yields:
% 54.98/20.88 | (1195) all_0_0_0 = n12
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 54.98/20.88 | (1194) all_0_3_3 = n12
% 54.98/20.88 |
% 54.98/20.88 | Equations (1195,1194) can reduce 679 to:
% 54.98/20.88 | (1106) $false
% 54.98/20.88 |
% 54.98/20.88 |-The branch is then unsatisfiable
% 54.98/20.88 |-Branch two:
% 54.98/20.88 | (1784) ~ (all_0_10_10 = n13)
% 54.98/20.88 | (1785) 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
% 54.98/20.88 |
% 54.98/20.88 +-Applying beta-rule and splitting (1785), into two cases.
% 54.98/20.88 |-Branch one:
% 54.98/20.88 | (1786) all_0_10_10 = n12
% 54.98/20.88 |
% 54.98/20.88 | From (1786) and (292) follows:
% 54.98/20.88 | (1787) pred(n12) = all_0_6_6
% 54.98/20.88 |
% 54.98/20.88 | From (1786) and (760) follows:
% 54.98/20.88 | (1788) succ(n12) = all_0_8_8
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (500) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 54.98/20.88 | (1789) all_0_6_6 = n11
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (617) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 54.98/20.88 | (1790) all_0_8_8 = n13
% 54.98/20.88 |
% 54.98/20.88 | From (1789)(1790) and (411) follows:
% 54.98/20.88 | (1791) sum(n11, n13) = all_0_1_1
% 54.98/20.88 |
% 54.98/20.88 | From (1789) and (6595) follows:
% 54.98/20.88 | (6714) sum(n11, n20) = all_0_4_4
% 54.98/20.88 |
% 54.98/20.88 | From (1790) and (6597) follows:
% 54.98/20.88 | (6715) sum(n18, n13) = all_0_7_7
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (690) with n18, n13, all_0_7_7, n5 and discharging atoms sum(n18, n13) = all_0_7_7, sum(n18, n13) = n5, yields:
% 54.98/20.88 | (1443) all_0_7_7 = n5
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (690) with n11, n20, all_0_4_4, n5 and discharging atoms sum(n11, n20) = all_0_4_4, sum(n11, n20) = n5, yields:
% 54.98/20.88 | (1441) all_0_4_4 = n5
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (690) with n11, n13, all_0_1_1, n24 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n24, yields:
% 54.98/20.88 | (1081) all_0_1_1 = n24
% 54.98/20.88 |
% 54.98/20.88 | From (1443)(1441) and (590) follows:
% 54.98/20.88 | (1445) sum(n5, n5) = all_0_3_3
% 54.98/20.88 |
% 54.98/20.88 | From (1081) and (6599) follows:
% 54.98/20.88 | (1210) sum(n12, n24) = all_0_0_0
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (690) with n12, n24, all_0_0_0, n10 and discharging atoms sum(n12, n24) = all_0_0_0, sum(n12, n24) = n10, yields:
% 54.98/20.88 | (1213) all_0_0_0 = n10
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 54.98/20.88 | (1212) all_0_3_3 = n10
% 54.98/20.88 |
% 54.98/20.88 | Equations (1213,1212) can reduce 679 to:
% 54.98/20.88 | (1106) $false
% 54.98/20.88 |
% 54.98/20.88 |-The branch is then unsatisfiable
% 54.98/20.88 |-Branch two:
% 54.98/20.88 | (1802) ~ (all_0_10_10 = n12)
% 54.98/20.88 | (1803) 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
% 54.98/20.88 |
% 54.98/20.88 +-Applying beta-rule and splitting (1803), into two cases.
% 54.98/20.88 |-Branch one:
% 54.98/20.88 | (1804) all_0_10_10 = n11
% 54.98/20.88 |
% 54.98/20.88 | From (1804) and (292) follows:
% 54.98/20.88 | (1805) pred(n11) = all_0_6_6
% 54.98/20.88 |
% 54.98/20.88 | From (1804) and (760) follows:
% 54.98/20.88 | (1806) succ(n11) = all_0_8_8
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (500) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 54.98/20.88 | (1807) all_0_6_6 = n10
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (617) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 54.98/20.88 | (1808) all_0_8_8 = n12
% 54.98/20.88 |
% 54.98/20.88 | From (1807)(1808) and (411) follows:
% 54.98/20.88 | (1809) sum(n10, n12) = all_0_1_1
% 54.98/20.88 |
% 54.98/20.88 | From (1807) and (6595) follows:
% 54.98/20.88 | (6732) sum(n10, n20) = all_0_4_4
% 54.98/20.88 |
% 54.98/20.88 | From (1808) and (6597) follows:
% 54.98/20.88 | (6733) sum(n18, n12) = all_0_7_7
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (690) with n18, n12, all_0_7_7, n4 and discharging atoms sum(n18, n12) = all_0_7_7, sum(n18, n12) = n4, yields:
% 54.98/20.88 | (1461) all_0_7_7 = n4
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (690) with n10, n20, all_0_4_4, n4 and discharging atoms sum(n10, n20) = all_0_4_4, sum(n10, n20) = n4, yields:
% 54.98/20.88 | (1459) all_0_4_4 = n4
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (690) with n10, n12, all_0_1_1, n22 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n22, yields:
% 54.98/20.88 | (1579) all_0_1_1 = n22
% 54.98/20.88 |
% 54.98/20.88 | From (1461)(1459) and (590) follows:
% 54.98/20.88 | (1463) sum(n4, n4) = all_0_3_3
% 54.98/20.88 |
% 54.98/20.88 | From (1579) and (6599) follows:
% 54.98/20.88 | (2142) sum(n12, n22) = all_0_0_0
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (690) with n12, n22, all_0_0_0, n8 and discharging atoms sum(n12, n22) = all_0_0_0, sum(n12, n22) = n8, yields:
% 54.98/20.88 | (1231) all_0_0_0 = n8
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 54.98/20.88 | (1230) all_0_3_3 = n8
% 54.98/20.88 |
% 54.98/20.88 | Equations (1231,1230) can reduce 679 to:
% 54.98/20.88 | (1106) $false
% 54.98/20.88 |
% 54.98/20.88 |-The branch is then unsatisfiable
% 54.98/20.88 |-Branch two:
% 54.98/20.88 | (1820) ~ (all_0_10_10 = n11)
% 54.98/20.88 | (1821) 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
% 54.98/20.88 |
% 54.98/20.88 +-Applying beta-rule and splitting (1821), into two cases.
% 54.98/20.88 |-Branch one:
% 54.98/20.88 | (1822) all_0_10_10 = n10
% 54.98/20.88 |
% 54.98/20.88 | From (1822) and (292) follows:
% 54.98/20.88 | (1823) pred(n10) = all_0_6_6
% 54.98/20.88 |
% 54.98/20.88 | From (1822) and (760) follows:
% 54.98/20.88 | (1824) succ(n10) = all_0_8_8
% 54.98/20.88 |
% 54.98/20.88 | Instantiating formula (500) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 54.98/20.89 | (1825) all_0_6_6 = n9
% 54.98/20.89 |
% 54.98/20.89 | Instantiating formula (617) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 54.98/20.89 | (1826) all_0_8_8 = n11
% 54.98/20.89 |
% 54.98/20.89 | From (1825)(1826) and (411) follows:
% 54.98/20.89 | (1827) sum(n9, n11) = all_0_1_1
% 54.98/20.89 |
% 54.98/20.89 | From (1825) and (6595) follows:
% 54.98/20.89 | (6750) sum(n9, n20) = all_0_4_4
% 54.98/20.89 |
% 54.98/20.89 | From (1826) and (6597) follows:
% 54.98/20.89 | (6751) sum(n18, n11) = all_0_7_7
% 54.98/20.89 |
% 54.98/20.89 | Instantiating formula (690) with n18, n11, all_0_7_7, n3 and discharging atoms sum(n18, n11) = all_0_7_7, sum(n18, n11) = n3, yields:
% 54.98/20.89 | (1479) all_0_7_7 = n3
% 54.98/20.89 |
% 54.98/20.89 | Instantiating formula (690) with n9, n20, all_0_4_4, n3 and discharging atoms sum(n9, n20) = all_0_4_4, sum(n9, n20) = n3, yields:
% 54.98/20.89 | (1477) all_0_4_4 = n3
% 54.98/20.89 |
% 54.98/20.89 | Instantiating formula (690) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 54.98/20.89 | (1597) all_0_1_1 = n20
% 54.98/20.89 |
% 54.98/20.89 | From (1479)(1477) and (590) follows:
% 54.98/20.89 | (1481) sum(n3, n3) = all_0_3_3
% 54.98/20.89 |
% 54.98/20.89 | From (1597) and (6599) follows:
% 55.05/20.89 | (3034) sum(n12, n20) = all_0_0_0
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (690) with n12, n20, all_0_0_0, n6 and discharging atoms sum(n12, n20) = all_0_0_0, sum(n12, n20) = n6, yields:
% 55.05/20.89 | (1249) all_0_0_0 = n6
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 55.05/20.89 | (1248) all_0_3_3 = n6
% 55.05/20.89 |
% 55.05/20.89 | Equations (1249,1248) can reduce 679 to:
% 55.05/20.89 | (1106) $false
% 55.05/20.89 |
% 55.05/20.89 |-The branch is then unsatisfiable
% 55.05/20.89 |-Branch two:
% 55.05/20.89 | (1838) ~ (all_0_10_10 = n10)
% 55.05/20.89 | (1839) 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
% 55.05/20.89 |
% 55.05/20.89 +-Applying beta-rule and splitting (1839), into two cases.
% 55.05/20.89 |-Branch one:
% 55.05/20.89 | (1840) all_0_10_10 = n9
% 55.05/20.89 |
% 55.05/20.89 | From (1840) and (292) follows:
% 55.05/20.89 | (1841) pred(n9) = all_0_6_6
% 55.05/20.89 |
% 55.05/20.89 | From (1840) and (760) follows:
% 55.05/20.89 | (1842) succ(n9) = all_0_8_8
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (500) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 55.05/20.89 | (1843) all_0_6_6 = n8
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (617) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 55.05/20.89 | (1844) all_0_8_8 = n10
% 55.05/20.89 |
% 55.05/20.89 | From (1843)(1844) and (411) follows:
% 55.05/20.89 | (1845) sum(n8, n10) = all_0_1_1
% 55.05/20.89 |
% 55.05/20.89 | From (1843) and (6595) follows:
% 55.05/20.89 | (6768) sum(n8, n20) = all_0_4_4
% 55.05/20.89 |
% 55.05/20.89 | From (1844) and (6597) follows:
% 55.05/20.89 | (6769) sum(n18, n10) = all_0_7_7
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (690) with n18, n10, all_0_7_7, n2 and discharging atoms sum(n18, n10) = all_0_7_7, sum(n18, n10) = n2, yields:
% 55.05/20.89 | (1497) all_0_7_7 = n2
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (690) with n8, n20, all_0_4_4, n2 and discharging atoms sum(n8, n20) = all_0_4_4, sum(n8, n20) = n2, yields:
% 55.05/20.89 | (1495) all_0_4_4 = n2
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (690) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 55.05/20.89 | (1615) all_0_1_1 = n18
% 55.05/20.89 |
% 55.05/20.89 | From (1497)(1495) and (590) follows:
% 55.05/20.89 | (1499) sum(n2, n2) = all_0_3_3
% 55.05/20.89 |
% 55.05/20.89 | From (1615) and (6599) follows:
% 55.05/20.89 | (3890) sum(n12, n18) = all_0_0_0
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (690) with n12, n18, all_0_0_0, n4 and discharging atoms sum(n12, n18) = all_0_0_0, sum(n12, n18) = n4, yields:
% 55.05/20.89 | (1267) all_0_0_0 = n4
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 55.05/20.89 | (1266) all_0_3_3 = n4
% 55.05/20.89 |
% 55.05/20.89 | Equations (1267,1266) can reduce 679 to:
% 55.05/20.89 | (1106) $false
% 55.05/20.89 |
% 55.05/20.89 |-The branch is then unsatisfiable
% 55.05/20.89 |-Branch two:
% 55.05/20.89 | (1856) ~ (all_0_10_10 = n9)
% 55.05/20.89 | (1857) 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
% 55.05/20.89 |
% 55.05/20.89 +-Applying beta-rule and splitting (1857), into two cases.
% 55.05/20.89 |-Branch one:
% 55.05/20.89 | (1858) all_0_10_10 = n8
% 55.05/20.89 |
% 55.05/20.89 | From (1858) and (292) follows:
% 55.05/20.89 | (1859) pred(n8) = all_0_6_6
% 55.05/20.89 |
% 55.05/20.89 | From (1858) and (760) follows:
% 55.05/20.89 | (1860) succ(n8) = all_0_8_8
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 55.05/20.89 | (1861) all_0_6_6 = n7
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 55.05/20.89 | (1862) all_0_8_8 = n9
% 55.05/20.89 |
% 55.05/20.89 | From (1861)(1862) and (411) follows:
% 55.05/20.89 | (1863) sum(n7, n9) = all_0_1_1
% 55.05/20.89 |
% 55.05/20.89 | From (1861) and (6595) follows:
% 55.05/20.89 | (6786) sum(n7, n20) = all_0_4_4
% 55.05/20.89 |
% 55.05/20.89 | From (1862) and (6597) follows:
% 55.05/20.89 | (6787) sum(n18, n9) = all_0_7_7
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (690) with n18, n9, all_0_7_7, n1 and discharging atoms sum(n18, n9) = all_0_7_7, sum(n18, n9) = n1, yields:
% 55.05/20.89 | (1515) all_0_7_7 = n1
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (690) with n7, n20, all_0_4_4, n1 and discharging atoms sum(n7, n20) = all_0_4_4, sum(n7, n20) = n1, yields:
% 55.05/20.89 | (1513) all_0_4_4 = n1
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 55.05/20.89 | (1633) all_0_1_1 = n16
% 55.05/20.89 |
% 55.05/20.89 | From (1515)(1513) and (590) follows:
% 55.05/20.89 | (1517) sum(n1, n1) = all_0_3_3
% 55.05/20.89 |
% 55.05/20.89 | From (1633) and (6599) follows:
% 55.05/20.89 | (4710) sum(n12, n16) = all_0_0_0
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (690) with n12, n16, all_0_0_0, n2 and discharging atoms sum(n12, n16) = all_0_0_0, sum(n12, n16) = n2, yields:
% 55.05/20.89 | (1285) all_0_0_0 = n2
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 55.05/20.89 | (1284) all_0_3_3 = n2
% 55.05/20.89 |
% 55.05/20.89 | Equations (1285,1284) can reduce 679 to:
% 55.05/20.89 | (1106) $false
% 55.05/20.89 |
% 55.05/20.89 |-The branch is then unsatisfiable
% 55.05/20.89 |-Branch two:
% 55.05/20.89 | (1874) ~ (all_0_10_10 = n8)
% 55.05/20.89 | (1875) 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
% 55.05/20.89 |
% 55.05/20.89 +-Applying beta-rule and splitting (1875), into two cases.
% 55.05/20.89 |-Branch one:
% 55.05/20.89 | (1876) all_0_10_10 = n7
% 55.05/20.89 |
% 55.05/20.89 | From (1876) and (292) follows:
% 55.05/20.89 | (1877) pred(n7) = all_0_6_6
% 55.05/20.89 |
% 55.05/20.89 | From (1876) and (760) follows:
% 55.05/20.89 | (1878) succ(n7) = all_0_8_8
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 55.05/20.89 | (1879) all_0_6_6 = n6
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 55.05/20.89 | (1880) all_0_8_8 = n8
% 55.05/20.89 |
% 55.05/20.89 | From (1879)(1880) and (411) follows:
% 55.05/20.89 | (1881) sum(n6, n8) = all_0_1_1
% 55.05/20.89 |
% 55.05/20.89 | From (1879) and (6595) follows:
% 55.05/20.89 | (6804) sum(n6, n20) = all_0_4_4
% 55.05/20.89 |
% 55.05/20.89 | From (1880) and (6597) follows:
% 55.05/20.89 | (6805) sum(n18, n8) = all_0_7_7
% 55.05/20.89 |
% 55.05/20.89 | Instantiating formula (690) with n18, n8, all_0_7_7, n0 and discharging atoms sum(n18, n8) = all_0_7_7, sum(n18, n8) = n0, yields:
% 55.05/20.90 | (1533) all_0_7_7 = n0
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n6, n20, all_0_4_4, n0 and discharging atoms sum(n6, n20) = all_0_4_4, sum(n6, n20) = n0, yields:
% 55.05/20.90 | (1531) all_0_4_4 = n0
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 55.05/20.90 | (1651) all_0_1_1 = n14
% 55.05/20.90 |
% 55.05/20.90 | From (1533)(1531) and (590) follows:
% 55.05/20.90 | (1535) sum(n0, n0) = all_0_3_3
% 55.05/20.90 |
% 55.05/20.90 | From (1651) and (6599) follows:
% 55.05/20.90 | (5494) sum(n12, n14) = all_0_0_0
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n12, n14, all_0_0_0, n0 and discharging atoms sum(n12, n14) = all_0_0_0, sum(n12, n14) = n0, yields:
% 55.05/20.90 | (1303) all_0_0_0 = n0
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 55.05/20.90 | (1302) all_0_3_3 = n0
% 55.05/20.90 |
% 55.05/20.90 | Equations (1303,1302) can reduce 679 to:
% 55.05/20.90 | (1106) $false
% 55.05/20.90 |
% 55.05/20.90 |-The branch is then unsatisfiable
% 55.05/20.90 |-Branch two:
% 55.05/20.90 | (1892) ~ (all_0_10_10 = n7)
% 55.05/20.90 | (1893) 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
% 55.05/20.90 |
% 55.05/20.90 +-Applying beta-rule and splitting (1893), into two cases.
% 55.05/20.90 |-Branch one:
% 55.05/20.90 | (1894) all_0_10_10 = n6
% 55.05/20.90 |
% 55.05/20.90 | From (1894) and (292) follows:
% 55.05/20.90 | (1895) pred(n6) = all_0_6_6
% 55.05/20.90 |
% 55.05/20.90 | From (1894) and (760) follows:
% 55.05/20.90 | (1896) succ(n6) = all_0_8_8
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 55.05/20.90 | (1897) all_0_6_6 = n5
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 55.05/20.90 | (1898) all_0_8_8 = n7
% 55.05/20.90 |
% 55.05/20.90 | From (1897)(1898) and (411) follows:
% 55.05/20.90 | (1899) sum(n5, n7) = all_0_1_1
% 55.05/20.90 |
% 55.05/20.90 | From (1897) and (6595) follows:
% 55.05/20.90 | (6822) sum(n5, n20) = all_0_4_4
% 55.05/20.90 |
% 55.05/20.90 | From (1898) and (6597) follows:
% 55.05/20.90 | (6823) sum(n18, n7) = all_0_7_7
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n18, n7, all_0_7_7, n25 and discharging atoms sum(n18, n7) = all_0_7_7, sum(n18, n7) = n25, yields:
% 55.05/20.90 | (1550) all_0_7_7 = n25
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n5, n20, all_0_4_4, n25 and discharging atoms sum(n5, n20) = all_0_4_4, sum(n5, n20) = n25, yields:
% 55.05/20.90 | (1551) all_0_4_4 = n25
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 55.05/20.90 | (1669) all_0_1_1 = n12
% 55.05/20.90 |
% 55.05/20.90 | From (1550)(1551) and (590) follows:
% 55.05/20.90 | (1553) sum(n25, n25) = all_0_3_3
% 55.05/20.90 |
% 55.05/20.90 | From (1669) and (6599) follows:
% 55.05/20.90 | (6240) sum(n12, n12) = all_0_0_0
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 55.05/20.90 | (1320) all_0_3_3 = n24
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n12, n12, all_0_0_0, n24 and discharging atoms sum(n12, n12) = all_0_0_0, sum(n12, n12) = n24, yields:
% 55.05/20.90 | (1321) all_0_0_0 = n24
% 55.05/20.90 |
% 55.05/20.90 | Equations (1321,1320) can reduce 679 to:
% 55.05/20.90 | (1106) $false
% 55.05/20.90 |
% 55.05/20.90 |-The branch is then unsatisfiable
% 55.05/20.90 |-Branch two:
% 55.05/20.90 | (1910) ~ (all_0_10_10 = n6)
% 55.05/20.90 | (1911) 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
% 55.05/20.90 |
% 55.05/20.90 +-Applying beta-rule and splitting (1911), into two cases.
% 55.05/20.90 |-Branch one:
% 55.05/20.90 | (1912) all_0_10_10 = n5
% 55.05/20.90 |
% 55.05/20.90 | From (1912) and (292) follows:
% 55.05/20.90 | (1913) pred(n5) = all_0_6_6
% 55.05/20.90 |
% 55.05/20.90 | From (1912) and (760) follows:
% 55.05/20.90 | (1914) succ(n5) = all_0_8_8
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 55.05/20.90 | (1915) all_0_6_6 = n4
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 55.05/20.90 | (1916) all_0_8_8 = n6
% 55.05/20.90 |
% 55.05/20.90 | From (1915)(1916) and (411) follows:
% 55.05/20.90 | (1917) sum(n4, n6) = all_0_1_1
% 55.05/20.90 |
% 55.05/20.90 | From (1915) and (6595) follows:
% 55.05/20.90 | (6840) sum(n4, n20) = all_0_4_4
% 55.05/20.90 |
% 55.05/20.90 | From (1916) and (6597) follows:
% 55.05/20.90 | (6841) sum(n18, n6) = all_0_7_7
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n18, n6, all_0_7_7, n24 and discharging atoms sum(n18, n6) = all_0_7_7, sum(n18, n6) = n24, yields:
% 55.05/20.90 | (1097) all_0_7_7 = n24
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n4, n20, all_0_4_4, n24 and discharging atoms sum(n4, n20) = all_0_4_4, sum(n4, n20) = n24, yields:
% 55.05/20.90 | (1096) all_0_4_4 = n24
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 55.05/20.90 | (1687) all_0_1_1 = n10
% 55.05/20.90 |
% 55.05/20.90 | From (1097)(1096) and (590) follows:
% 55.05/20.90 | (1101) sum(n24, n24) = all_0_3_3
% 55.05/20.90 |
% 55.05/20.90 | From (1687) and (6599) follows:
% 55.05/20.90 | (6612) sum(n12, n10) = all_0_0_0
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 55.05/20.90 | (1104) all_0_3_3 = n22
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n12, n10, all_0_0_0, n22 and discharging atoms sum(n12, n10) = all_0_0_0, sum(n12, n10) = n22, yields:
% 55.05/20.90 | (1102) all_0_0_0 = n22
% 55.05/20.90 |
% 55.05/20.90 | Equations (1102,1104) can reduce 679 to:
% 55.05/20.90 | (1106) $false
% 55.05/20.90 |
% 55.05/20.90 |-The branch is then unsatisfiable
% 55.05/20.90 |-Branch two:
% 55.05/20.90 | (1928) ~ (all_0_10_10 = n5)
% 55.05/20.90 | (1929) 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
% 55.05/20.90 |
% 55.05/20.90 +-Applying beta-rule and splitting (1929), into two cases.
% 55.05/20.90 |-Branch one:
% 55.05/20.90 | (1930) all_0_10_10 = n4
% 55.05/20.90 |
% 55.05/20.90 | From (1930) and (292) follows:
% 55.05/20.90 | (1931) pred(n4) = all_0_6_6
% 55.05/20.90 |
% 55.05/20.90 | From (1930) and (760) follows:
% 55.05/20.90 | (1932) succ(n4) = all_0_8_8
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 55.05/20.90 | (1933) all_0_6_6 = n3
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 55.05/20.90 | (1934) all_0_8_8 = n5
% 55.05/20.90 |
% 55.05/20.90 | From (1933)(1934) and (411) follows:
% 55.05/20.90 | (1935) sum(n3, n5) = all_0_1_1
% 55.05/20.90 |
% 55.05/20.90 | From (1933) and (6595) follows:
% 55.05/20.90 | (6858) sum(n3, n20) = all_0_4_4
% 55.05/20.90 |
% 55.05/20.90 | From (1934) and (6597) follows:
% 55.05/20.90 | (6859) sum(n18, n5) = all_0_7_7
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n18, n5, all_0_7_7, n23 and discharging atoms sum(n18, n5) = all_0_7_7, sum(n18, n5) = n23, yields:
% 55.05/20.90 | (1119) all_0_7_7 = n23
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n3, n20, all_0_4_4, n23 and discharging atoms sum(n3, n20) = all_0_4_4, sum(n3, n20) = n23, yields:
% 55.05/20.90 | (1117) all_0_4_4 = n23
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 55.05/20.90 | (1705) all_0_1_1 = n8
% 55.05/20.90 |
% 55.05/20.90 | From (1119)(1117) and (590) follows:
% 55.05/20.90 | (1121) sum(n23, n23) = all_0_3_3
% 55.05/20.90 |
% 55.05/20.90 | From (1705) and (6599) follows:
% 55.05/20.90 | (6630) sum(n12, n8) = all_0_0_0
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 55.05/20.90 | (1122) all_0_3_3 = n20
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (690) with n12, n8, all_0_0_0, n20 and discharging atoms sum(n12, n8) = all_0_0_0, sum(n12, n8) = n20, yields:
% 55.05/20.90 | (1123) all_0_0_0 = n20
% 55.05/20.90 |
% 55.05/20.90 | Equations (1123,1122) can reduce 679 to:
% 55.05/20.90 | (1106) $false
% 55.05/20.90 |
% 55.05/20.90 |-The branch is then unsatisfiable
% 55.05/20.90 |-Branch two:
% 55.05/20.90 | (1946) ~ (all_0_10_10 = n4)
% 55.05/20.90 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 55.05/20.90 |
% 55.05/20.90 +-Applying beta-rule and splitting (1947), into two cases.
% 55.05/20.90 |-Branch one:
% 55.05/20.90 | (1948) all_0_10_10 = n3
% 55.05/20.90 |
% 55.05/20.90 | From (1948) and (292) follows:
% 55.05/20.90 | (1949) pred(n3) = all_0_6_6
% 55.05/20.90 |
% 55.05/20.90 | From (1948) and (760) follows:
% 55.05/20.90 | (1950) succ(n3) = all_0_8_8
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 55.05/20.90 | (1951) all_0_6_6 = n2
% 55.05/20.90 |
% 55.05/20.90 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 55.05/20.91 | (1952) all_0_8_8 = n4
% 55.05/20.91 |
% 55.05/20.91 | From (1951)(1952) and (411) follows:
% 55.05/20.91 | (1953) sum(n2, n4) = all_0_1_1
% 55.05/20.91 |
% 55.05/20.91 | From (1951) and (6595) follows:
% 55.05/20.91 | (6876) sum(n2, n20) = all_0_4_4
% 55.05/20.91 |
% 55.05/20.91 | From (1952) and (6597) follows:
% 55.05/20.91 | (6877) sum(n18, n4) = all_0_7_7
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n18, n4, all_0_7_7, n22 and discharging atoms sum(n18, n4) = all_0_7_7, sum(n18, n4) = n22, yields:
% 55.05/20.91 | (1137) all_0_7_7 = n22
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n2, n20, all_0_4_4, n22 and discharging atoms sum(n2, n20) = all_0_4_4, sum(n2, n20) = n22, yields:
% 55.05/20.91 | (1135) all_0_4_4 = n22
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 55.05/20.91 | (1723) all_0_1_1 = n6
% 55.05/20.91 |
% 55.05/20.91 | From (1137)(1135) and (590) follows:
% 55.05/20.91 | (1139) sum(n22, n22) = all_0_3_3
% 55.05/20.91 |
% 55.05/20.91 | From (1723) and (6599) follows:
% 55.05/20.91 | (6648) sum(n12, n6) = all_0_0_0
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 55.05/20.91 | (1140) all_0_3_3 = n18
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n12, n6, all_0_0_0, n18 and discharging atoms sum(n12, n6) = all_0_0_0, sum(n12, n6) = n18, yields:
% 55.05/20.91 | (1141) all_0_0_0 = n18
% 55.05/20.91 |
% 55.05/20.91 | Equations (1141,1140) can reduce 679 to:
% 55.05/20.91 | (1106) $false
% 55.05/20.91 |
% 55.05/20.91 |-The branch is then unsatisfiable
% 55.05/20.91 |-Branch two:
% 55.05/20.91 | (1964) ~ (all_0_10_10 = n3)
% 55.05/20.91 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 55.05/20.91 |
% 55.05/20.91 +-Applying beta-rule and splitting (1965), into two cases.
% 55.05/20.91 |-Branch one:
% 55.05/20.91 | (1966) all_0_10_10 = n2
% 55.05/20.91 |
% 55.05/20.91 | From (1966) and (292) follows:
% 55.05/20.91 | (1967) pred(n2) = all_0_6_6
% 55.05/20.91 |
% 55.05/20.91 | From (1966) and (760) follows:
% 55.05/20.91 | (1968) succ(n2) = all_0_8_8
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 55.05/20.91 | (1969) all_0_6_6 = n1
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 55.05/20.91 | (1970) all_0_8_8 = n3
% 55.05/20.91 |
% 55.05/20.91 | From (1969)(1970) and (411) follows:
% 55.05/20.91 | (1971) sum(n1, n3) = all_0_1_1
% 55.05/20.91 |
% 55.05/20.91 | From (1969) and (6595) follows:
% 55.05/20.91 | (6894) sum(n1, n20) = all_0_4_4
% 55.05/20.91 |
% 55.05/20.91 | From (1970) and (6597) follows:
% 55.05/20.91 | (6895) sum(n18, n3) = all_0_7_7
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n18, n3, all_0_7_7, n21 and discharging atoms sum(n18, n3) = all_0_7_7, sum(n18, n3) = n21, yields:
% 55.05/20.91 | (1155) all_0_7_7 = n21
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n1, n20, all_0_4_4, n21 and discharging atoms sum(n1, n20) = all_0_4_4, sum(n1, n20) = n21, yields:
% 55.05/20.91 | (1153) all_0_4_4 = n21
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 55.05/20.91 | (1741) all_0_1_1 = n4
% 55.05/20.91 |
% 55.05/20.91 | From (1155)(1153) and (590) follows:
% 55.05/20.91 | (1157) sum(n21, n21) = all_0_3_3
% 55.05/20.91 |
% 55.05/20.91 | From (1741) and (6599) follows:
% 55.05/20.91 | (6666) sum(n12, n4) = all_0_0_0
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 55.05/20.91 | (1158) all_0_3_3 = n16
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n12, n4, all_0_0_0, n16 and discharging atoms sum(n12, n4) = all_0_0_0, sum(n12, n4) = n16, yields:
% 55.05/20.91 | (1159) all_0_0_0 = n16
% 55.05/20.91 |
% 55.05/20.91 | Equations (1159,1158) can reduce 679 to:
% 55.05/20.91 | (1106) $false
% 55.05/20.91 |
% 55.05/20.91 |-The branch is then unsatisfiable
% 55.05/20.91 |-Branch two:
% 55.05/20.91 | (1982) ~ (all_0_10_10 = n2)
% 55.05/20.91 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 55.05/20.91 |
% 55.05/20.91 +-Applying beta-rule and splitting (1983), into two cases.
% 55.05/20.91 |-Branch one:
% 55.05/20.91 | (1984) all_0_10_10 = n1
% 55.05/20.91 |
% 55.05/20.91 | From (1984) and (292) follows:
% 55.05/20.91 | (1985) pred(n1) = all_0_6_6
% 55.05/20.91 |
% 55.05/20.91 | From (1984) and (760) follows:
% 55.05/20.91 | (1986) succ(n1) = all_0_8_8
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 55.05/20.91 | (1987) all_0_6_6 = n0
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 55.05/20.91 | (1988) all_0_8_8 = n2
% 55.05/20.91 |
% 55.05/20.91 | From (1987)(1988) and (411) follows:
% 55.05/20.91 | (1989) sum(n0, n2) = all_0_1_1
% 55.05/20.91 |
% 55.05/20.91 | From (1987) and (6595) follows:
% 55.05/20.91 | (6912) sum(n0, n20) = all_0_4_4
% 55.05/20.91 |
% 55.05/20.91 | From (1988) and (6597) follows:
% 55.05/20.91 | (6913) sum(n18, n2) = all_0_7_7
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n18, n2, all_0_7_7, n20 and discharging atoms sum(n18, n2) = all_0_7_7, sum(n18, n2) = n20, yields:
% 55.05/20.91 | (1173) all_0_7_7 = n20
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n0, n20, all_0_4_4, n20 and discharging atoms sum(n0, n20) = all_0_4_4, sum(n0, n20) = n20, yields:
% 55.05/20.91 | (1171) all_0_4_4 = n20
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 55.05/20.91 | (1759) all_0_1_1 = n2
% 55.05/20.91 |
% 55.05/20.91 | From (1173)(1171) and (590) follows:
% 55.05/20.91 | (1175) sum(n20, n20) = all_0_3_3
% 55.05/20.91 |
% 55.05/20.91 | From (1759) and (6599) follows:
% 55.05/20.91 | (6684) sum(n12, n2) = all_0_0_0
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 55.05/20.91 | (1176) all_0_3_3 = n14
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n12, n2, all_0_0_0, n14 and discharging atoms sum(n12, n2) = all_0_0_0, sum(n12, n2) = n14, yields:
% 55.05/20.91 | (1177) all_0_0_0 = n14
% 55.05/20.91 |
% 55.05/20.91 | Equations (1177,1176) can reduce 679 to:
% 55.05/20.91 | (1106) $false
% 55.05/20.91 |
% 55.05/20.91 |-The branch is then unsatisfiable
% 55.05/20.91 |-Branch two:
% 55.05/20.91 | (2002) ~ (all_0_10_10 = n1)
% 55.05/20.91 | (2003) all_0_10_10 = n0
% 55.05/20.91 |
% 55.05/20.91 | From (2003) and (292) follows:
% 55.05/20.91 | (2004) pred(n0) = all_0_6_6
% 55.05/20.91 |
% 55.05/20.91 | From (2003) and (760) follows:
% 55.05/20.91 | (2005) succ(n0) = all_0_8_8
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 55.05/20.91 | (2006) all_0_6_6 = n25
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 55.05/20.91 | (2007) all_0_8_8 = n1
% 55.05/20.91 |
% 55.05/20.91 | From (2006)(2007) and (411) follows:
% 55.05/20.91 | (2008) sum(n25, n1) = all_0_1_1
% 55.05/20.91 |
% 55.05/20.91 | From (2006) and (6595) follows:
% 55.05/20.91 | (6929) sum(n25, n20) = all_0_4_4
% 55.05/20.91 |
% 55.05/20.91 | From (2007) and (6597) follows:
% 55.05/20.91 | (6930) sum(n18, n1) = all_0_7_7
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n25, n20, all_0_4_4, n19 and discharging atoms sum(n25, n20) = all_0_4_4, sum(n25, n20) = n19, yields:
% 55.05/20.91 | (1189) all_0_4_4 = n19
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 55.05/20.91 | (1777) all_0_1_1 = n0
% 55.05/20.91 |
% 55.05/20.91 | Instantiating formula (690) with n18, n1, all_0_7_7, n19 and discharging atoms sum(n18, n1) = all_0_7_7, sum(n18, n1) = n19, yields:
% 55.05/20.91 | (1191) all_0_7_7 = n19
% 55.05/20.91 |
% 55.05/20.91 | From (1191)(1189) and (590) follows:
% 55.05/20.91 | (1193) sum(n19, n19) = all_0_3_3
% 55.11/20.91 |
% 55.11/20.91 | From (1777) and (6599) follows:
% 55.11/20.92 | (6702) sum(n12, n0) = all_0_0_0
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 55.11/20.92 | (1194) all_0_3_3 = n12
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (690) with n12, n0, all_0_0_0, n12 and discharging atoms sum(n12, n0) = all_0_0_0, sum(n12, n0) = n12, yields:
% 55.11/20.92 | (1195) all_0_0_0 = n12
% 55.11/20.92 |
% 55.11/20.92 | Equations (1195,1194) can reduce 679 to:
% 55.11/20.92 | (1106) $false
% 55.11/20.92 |
% 55.11/20.92 |-The branch is then unsatisfiable
% 55.11/20.92 |-Branch two:
% 55.11/20.92 | (1215) ~ (all_0_11_11 = n19)
% 55.11/20.92 | (1216) 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
% 55.11/20.92 |
% 55.11/20.92 +-Applying beta-rule and splitting (1677), into two cases.
% 55.11/20.92 |-Branch one:
% 55.11/20.92 | (1678) all_0_10_10 = n18
% 55.11/20.92 |
% 55.11/20.92 | From (1678) and (292) follows:
% 55.11/20.92 | (1679) pred(n18) = all_0_6_6
% 55.11/20.92 |
% 55.11/20.92 | From (1678) and (760) follows:
% 55.11/20.92 | (1680) succ(n18) = all_0_8_8
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (500) with n18, all_0_6_6, n17 and discharging atoms pred(n18) = all_0_6_6, pred(n18) = n17, yields:
% 55.11/20.92 | (1681) all_0_6_6 = n17
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (617) with n18, all_0_8_8, n19 and discharging atoms succ(n18) = all_0_8_8, succ(n18) = n19, yields:
% 55.11/20.92 | (1682) all_0_8_8 = n19
% 55.11/20.92 |
% 55.11/20.92 | From (1681) and (1679) follows:
% 55.11/20.92 | (931) pred(n18) = n17
% 55.11/20.92 |
% 55.11/20.92 | From (1682) and (1680) follows:
% 55.11/20.92 | (622) succ(n18) = n19
% 55.11/20.92 |
% 55.11/20.92 | From (1681) and (541) follows:
% 55.11/20.92 | (6948) sum(n17, all_0_5_5) = all_0_4_4
% 55.11/20.92 |
% 55.11/20.92 | From (1681)(1682) and (411) follows:
% 55.11/20.92 | (1683) sum(n17, n19) = all_0_1_1
% 55.11/20.92 |
% 55.11/20.92 | From (1682) and (427) follows:
% 55.11/20.92 | (6950) sum(all_0_9_9, n19) = all_0_7_7
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (690) with n17, n19, all_0_1_1, n10 and discharging atoms sum(n17, n19) = all_0_1_1, sum(n17, n19) = n10, yields:
% 55.11/20.92 | (1687) all_0_1_1 = n10
% 55.11/20.92 |
% 55.11/20.92 | From (1687) and (630) follows:
% 55.11/20.92 | (6952) sum(all_0_2_2, n10) = all_0_0_0
% 55.11/20.92 |
% 55.11/20.92 | From (1687) and (1683) follows:
% 55.11/20.92 | (94) sum(n17, n19) = n10
% 55.11/20.92 |
% 55.11/20.92 +-Applying beta-rule and splitting (1216), into two cases.
% 55.11/20.92 |-Branch one:
% 55.11/20.92 | (1217) all_0_11_11 = n18
% 55.11/20.92 |
% 55.11/20.92 | From (1217) and (559) follows:
% 55.11/20.92 | (1218) pred(n18) = all_0_9_9
% 55.11/20.92 |
% 55.11/20.92 | From (1217) and (992) follows:
% 55.11/20.92 | (1219) succ(n18) = all_0_5_5
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (500) with n18, all_0_9_9, n17 and discharging atoms pred(n18) = all_0_9_9, pred(n18) = n17, yields:
% 55.11/20.92 | (1220) all_0_9_9 = n17
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (617) with n18, all_0_5_5, n19 and discharging atoms succ(n18) = all_0_5_5, succ(n18) = n19, yields:
% 55.11/20.92 | (1221) all_0_5_5 = n19
% 55.11/20.92 |
% 55.11/20.92 | From (1220)(1221) and (538) follows:
% 55.11/20.92 | (1222) sum(n17, n19) = all_0_2_2
% 55.11/20.92 |
% 55.11/20.92 | From (1220) and (6950) follows:
% 55.11/20.92 | (6960) sum(n17, n19) = all_0_7_7
% 55.11/20.92 |
% 55.11/20.92 | From (1221) and (6948) follows:
% 55.11/20.92 | (6961) sum(n17, n19) = all_0_4_4
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (690) with n17, n19, all_0_2_2, n10 and discharging atoms sum(n17, n19) = all_0_2_2, sum(n17, n19) = n10, yields:
% 55.11/20.92 | (1226) all_0_2_2 = n10
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (690) 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:
% 55.11/20.92 | (1093) all_0_2_2 = all_0_4_4
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (690) 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:
% 55.11/20.92 | (1094) all_0_2_2 = all_0_7_7
% 55.11/20.92 |
% 55.11/20.92 | Combining equations (1094,1093) yields a new equation:
% 55.11/20.92 | (1095) all_0_4_4 = all_0_7_7
% 55.11/20.92 |
% 55.11/20.92 | Combining equations (1226,1093) yields a new equation:
% 55.11/20.92 | (1351) all_0_4_4 = n10
% 55.11/20.92 |
% 55.11/20.92 | Combining equations (1351,1095) yields a new equation:
% 55.11/20.92 | (1353) all_0_7_7 = n10
% 55.11/20.92 |
% 55.11/20.92 | Combining equations (1353,1095) yields a new equation:
% 55.11/20.92 | (1351) all_0_4_4 = n10
% 55.11/20.92 |
% 55.11/20.92 | Combining equations (1351,1093) yields a new equation:
% 55.11/20.92 | (1226) all_0_2_2 = n10
% 55.11/20.92 |
% 55.11/20.92 | From (1226) and (6952) follows:
% 55.11/20.92 | (6970) sum(n10, n10) = all_0_0_0
% 55.11/20.92 |
% 55.11/20.92 | From (1353)(1351) and (590) follows:
% 55.11/20.92 | (1355) sum(n10, n10) = all_0_3_3
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (690) with n10, n10, all_0_0_0, n20 and discharging atoms sum(n10, n10) = all_0_0_0, sum(n10, n10) = n20, yields:
% 55.11/20.92 | (1123) all_0_0_0 = n20
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (690) 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:
% 55.11/20.92 | (1103) all_0_0_0 = all_0_3_3
% 55.11/20.92 |
% 55.11/20.92 | Combining equations (1123,1103) yields a new equation:
% 55.11/20.92 | (1122) all_0_3_3 = n20
% 55.11/20.92 |
% 55.11/20.92 | Combining equations (1122,1103) yields a new equation:
% 55.11/20.92 | (1123) all_0_0_0 = n20
% 55.11/20.92 |
% 55.11/20.92 | Equations (1123,1122) can reduce 679 to:
% 55.11/20.92 | (1106) $false
% 55.11/20.92 |
% 55.11/20.92 |-The branch is then unsatisfiable
% 55.11/20.92 |-Branch two:
% 55.11/20.92 | (1233) ~ (all_0_11_11 = n18)
% 55.11/20.92 | (1234) 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
% 55.11/20.92 |
% 55.11/20.92 +-Applying beta-rule and splitting (1234), into two cases.
% 55.11/20.92 |-Branch one:
% 55.11/20.92 | (1235) all_0_11_11 = n17
% 55.11/20.92 |
% 55.11/20.92 | From (1235) and (559) follows:
% 55.11/20.92 | (1236) pred(n17) = all_0_9_9
% 55.11/20.92 |
% 55.11/20.92 | From (1235) and (992) follows:
% 55.11/20.92 | (1237) succ(n17) = all_0_5_5
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (500) with n17, all_0_9_9, n16 and discharging atoms pred(n17) = all_0_9_9, pred(n17) = n16, yields:
% 55.11/20.92 | (1238) all_0_9_9 = n16
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (617) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 55.11/20.92 | (1239) all_0_5_5 = n18
% 55.11/20.92 |
% 55.11/20.92 | From (1238)(1239) and (538) follows:
% 55.11/20.92 | (1240) sum(n16, n18) = all_0_2_2
% 55.11/20.92 |
% 55.11/20.92 | From (1238) and (6950) follows:
% 55.11/20.92 | (6985) sum(n16, n19) = all_0_7_7
% 55.11/20.92 |
% 55.11/20.92 | From (1239) and (6948) follows:
% 55.11/20.92 | (6986) sum(n17, n18) = all_0_4_4
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (690) with n17, n18, all_0_4_4, n9 and discharging atoms sum(n17, n18) = all_0_4_4, sum(n17, n18) = n9, yields:
% 55.11/20.92 | (1369) all_0_4_4 = n9
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (690) with n16, n19, all_0_7_7, n9 and discharging atoms sum(n16, n19) = all_0_7_7, sum(n16, n19) = n9, yields:
% 55.11/20.92 | (1371) all_0_7_7 = n9
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (690) with n16, n18, all_0_2_2, n8 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = n8, yields:
% 55.11/20.92 | (1244) all_0_2_2 = n8
% 55.11/20.92 |
% 55.11/20.92 | From (1244) and (6952) follows:
% 55.11/20.92 | (6990) sum(n8, n10) = all_0_0_0
% 55.11/20.92 |
% 55.11/20.92 | From (1371)(1369) and (590) follows:
% 55.11/20.92 | (1373) sum(n9, n9) = all_0_3_3
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 55.11/20.92 | (1140) all_0_3_3 = n18
% 55.11/20.92 |
% 55.11/20.92 | Instantiating formula (690) with n8, n10, all_0_0_0, n18 and discharging atoms sum(n8, n10) = all_0_0_0, sum(n8, n10) = n18, yields:
% 55.11/20.92 | (1141) all_0_0_0 = n18
% 55.11/20.92 |
% 55.11/20.92 | Equations (1141,1140) can reduce 679 to:
% 55.11/20.92 | (1106) $false
% 55.11/20.92 |
% 55.11/20.92 |-The branch is then unsatisfiable
% 55.11/20.92 |-Branch two:
% 55.11/20.92 | (1251) ~ (all_0_11_11 = n17)
% 55.11/20.92 | (1252) 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
% 55.11/20.92 |
% 55.13/20.92 +-Applying beta-rule and splitting (1252), into two cases.
% 55.13/20.92 |-Branch one:
% 55.13/20.92 | (1253) all_0_11_11 = n16
% 55.13/20.92 |
% 55.13/20.92 | From (1253) and (559) follows:
% 55.13/20.92 | (1254) pred(n16) = all_0_9_9
% 55.13/20.92 |
% 55.13/20.92 | From (1253) and (992) follows:
% 55.13/20.92 | (1255) succ(n16) = all_0_5_5
% 55.13/20.92 |
% 55.13/20.92 | Instantiating formula (500) with n16, all_0_9_9, n15 and discharging atoms pred(n16) = all_0_9_9, pred(n16) = n15, yields:
% 55.13/20.92 | (1256) all_0_9_9 = n15
% 55.13/20.92 |
% 55.13/20.92 | Instantiating formula (617) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 55.13/20.92 | (1257) all_0_5_5 = n17
% 55.13/20.92 |
% 55.13/20.92 | From (1256)(1257) and (538) follows:
% 55.13/20.92 | (1258) sum(n15, n17) = all_0_2_2
% 55.13/20.92 |
% 55.13/20.92 | From (1256) and (6950) follows:
% 55.13/20.93 | (7003) sum(n15, n19) = all_0_7_7
% 55.13/20.93 |
% 55.13/20.93 | From (1257) and (6948) follows:
% 55.13/20.93 | (7004) sum(n17, n17) = all_0_4_4
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n17, n17, all_0_4_4, n8 and discharging atoms sum(n17, n17) = all_0_4_4, sum(n17, n17) = n8, yields:
% 55.13/20.93 | (1387) all_0_4_4 = n8
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n15, n19, all_0_7_7, n8 and discharging atoms sum(n15, n19) = all_0_7_7, sum(n15, n19) = n8, yields:
% 55.13/20.93 | (1389) all_0_7_7 = n8
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n15, n17, all_0_2_2, n6 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n6, yields:
% 55.13/20.93 | (1262) all_0_2_2 = n6
% 55.13/20.93 |
% 55.13/20.93 | From (1262) and (6952) follows:
% 55.13/20.93 | (7008) sum(n6, n10) = all_0_0_0
% 55.13/20.93 |
% 55.13/20.93 | From (1389)(1387) and (590) follows:
% 55.13/20.93 | (1391) sum(n8, n8) = all_0_3_3
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 55.13/20.93 | (1158) all_0_3_3 = n16
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n6, n10, all_0_0_0, n16 and discharging atoms sum(n6, n10) = all_0_0_0, sum(n6, n10) = n16, yields:
% 55.13/20.93 | (1159) all_0_0_0 = n16
% 55.13/20.93 |
% 55.13/20.93 | Equations (1159,1158) can reduce 679 to:
% 55.13/20.93 | (1106) $false
% 55.13/20.93 |
% 55.13/20.93 |-The branch is then unsatisfiable
% 55.13/20.93 |-Branch two:
% 55.13/20.93 | (1269) ~ (all_0_11_11 = n16)
% 55.13/20.93 | (1270) 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
% 55.13/20.93 |
% 55.13/20.93 +-Applying beta-rule and splitting (1270), into two cases.
% 55.13/20.93 |-Branch one:
% 55.13/20.93 | (1271) all_0_11_11 = n15
% 55.13/20.93 |
% 55.13/20.93 | From (1271) and (559) follows:
% 55.13/20.93 | (1272) pred(n15) = all_0_9_9
% 55.13/20.93 |
% 55.13/20.93 | From (1271) and (992) follows:
% 55.13/20.93 | (1273) succ(n15) = all_0_5_5
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (500) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 55.13/20.93 | (1274) all_0_9_9 = n14
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (617) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 55.13/20.93 | (1275) all_0_5_5 = n16
% 55.13/20.93 |
% 55.13/20.93 | From (1274)(1275) and (538) follows:
% 55.13/20.93 | (1276) sum(n14, n16) = all_0_2_2
% 55.13/20.93 |
% 55.13/20.93 | From (1274) and (6950) follows:
% 55.13/20.93 | (7021) sum(n14, n19) = all_0_7_7
% 55.13/20.93 |
% 55.13/20.93 | From (1275) and (6948) follows:
% 55.13/20.93 | (7022) sum(n17, n16) = all_0_4_4
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n17, n16, all_0_4_4, n7 and discharging atoms sum(n17, n16) = all_0_4_4, sum(n17, n16) = n7, yields:
% 55.13/20.93 | (1405) all_0_4_4 = n7
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n14, n19, all_0_7_7, n7 and discharging atoms sum(n14, n19) = all_0_7_7, sum(n14, n19) = n7, yields:
% 55.13/20.93 | (1407) all_0_7_7 = n7
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n14, n16, all_0_2_2, n4 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n4, yields:
% 55.13/20.93 | (1280) all_0_2_2 = n4
% 55.13/20.93 |
% 55.13/20.93 | From (1280) and (6952) follows:
% 55.13/20.93 | (7026) sum(n4, n10) = all_0_0_0
% 55.13/20.93 |
% 55.13/20.93 | From (1407)(1405) and (590) follows:
% 55.13/20.93 | (1409) sum(n7, n7) = all_0_3_3
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 55.13/20.93 | (1176) all_0_3_3 = n14
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n4, n10, all_0_0_0, n14 and discharging atoms sum(n4, n10) = all_0_0_0, sum(n4, n10) = n14, yields:
% 55.13/20.93 | (1177) all_0_0_0 = n14
% 55.13/20.93 |
% 55.13/20.93 | Equations (1177,1176) can reduce 679 to:
% 55.13/20.93 | (1106) $false
% 55.13/20.93 |
% 55.13/20.93 |-The branch is then unsatisfiable
% 55.13/20.93 |-Branch two:
% 55.13/20.93 | (1287) ~ (all_0_11_11 = n15)
% 55.13/20.93 | (1288) 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
% 55.13/20.93 |
% 55.13/20.93 +-Applying beta-rule and splitting (1288), into two cases.
% 55.13/20.93 |-Branch one:
% 55.13/20.93 | (1289) all_0_11_11 = n14
% 55.13/20.93 |
% 55.13/20.93 | From (1289) and (559) follows:
% 55.13/20.93 | (1290) pred(n14) = all_0_9_9
% 55.13/20.93 |
% 55.13/20.93 | From (1289) and (992) follows:
% 55.13/20.93 | (1291) succ(n14) = all_0_5_5
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (500) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 55.13/20.93 | (1292) all_0_9_9 = n13
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (617) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 55.13/20.93 | (1293) all_0_5_5 = n15
% 55.13/20.93 |
% 55.13/20.93 | From (1292)(1293) and (538) follows:
% 55.13/20.93 | (1294) sum(n13, n15) = all_0_2_2
% 55.13/20.93 |
% 55.13/20.93 | From (1292) and (6950) follows:
% 55.13/20.93 | (7039) sum(n13, n19) = all_0_7_7
% 55.13/20.93 |
% 55.13/20.93 | From (1293) and (6948) follows:
% 55.13/20.93 | (7040) sum(n17, n15) = all_0_4_4
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n17, n15, all_0_4_4, n6 and discharging atoms sum(n17, n15) = all_0_4_4, sum(n17, n15) = n6, yields:
% 55.13/20.93 | (1423) all_0_4_4 = n6
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n13, n19, all_0_7_7, n6 and discharging atoms sum(n13, n19) = all_0_7_7, sum(n13, n19) = n6, yields:
% 55.13/20.93 | (1425) all_0_7_7 = n6
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n13, n15, all_0_2_2, n2 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n2, yields:
% 55.13/20.93 | (1298) all_0_2_2 = n2
% 55.13/20.93 |
% 55.13/20.93 | From (1298) and (6952) follows:
% 55.13/20.93 | (7044) sum(n2, n10) = all_0_0_0
% 55.13/20.93 |
% 55.13/20.93 | From (1425)(1423) and (590) follows:
% 55.13/20.93 | (1427) sum(n6, n6) = all_0_3_3
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 55.13/20.93 | (1194) all_0_3_3 = n12
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n2, n10, all_0_0_0, n12 and discharging atoms sum(n2, n10) = all_0_0_0, sum(n2, n10) = n12, yields:
% 55.13/20.93 | (1195) all_0_0_0 = n12
% 55.13/20.93 |
% 55.13/20.93 | Equations (1195,1194) can reduce 679 to:
% 55.13/20.93 | (1106) $false
% 55.13/20.93 |
% 55.13/20.93 |-The branch is then unsatisfiable
% 55.13/20.93 |-Branch two:
% 55.13/20.93 | (1305) ~ (all_0_11_11 = n14)
% 55.13/20.93 | (1306) 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
% 55.13/20.93 |
% 55.13/20.93 +-Applying beta-rule and splitting (1306), into two cases.
% 55.13/20.93 |-Branch one:
% 55.13/20.93 | (1307) all_0_11_11 = n13
% 55.13/20.93 |
% 55.13/20.93 | From (1307) and (559) follows:
% 55.13/20.93 | (1308) pred(n13) = all_0_9_9
% 55.13/20.93 |
% 55.13/20.93 | From (1307) and (992) follows:
% 55.13/20.93 | (1309) succ(n13) = all_0_5_5
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (500) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 55.13/20.93 | (1310) all_0_9_9 = n12
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (617) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 55.13/20.93 | (1311) all_0_5_5 = n14
% 55.13/20.93 |
% 55.13/20.93 | From (1310)(1311) and (538) follows:
% 55.13/20.93 | (1312) sum(n12, n14) = all_0_2_2
% 55.13/20.93 |
% 55.13/20.93 | From (1310) and (6950) follows:
% 55.13/20.93 | (7057) sum(n12, n19) = all_0_7_7
% 55.13/20.93 |
% 55.13/20.93 | From (1311) and (6948) follows:
% 55.13/20.93 | (7058) sum(n17, n14) = all_0_4_4
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n17, n14, all_0_4_4, n5 and discharging atoms sum(n17, n14) = all_0_4_4, sum(n17, n14) = n5, yields:
% 55.13/20.93 | (1441) all_0_4_4 = n5
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n12, n19, all_0_7_7, n5 and discharging atoms sum(n12, n19) = all_0_7_7, sum(n12, n19) = n5, yields:
% 55.13/20.93 | (1443) all_0_7_7 = n5
% 55.13/20.93 |
% 55.13/20.93 | Instantiating formula (690) with n12, n14, all_0_2_2, n0 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n0, yields:
% 55.13/20.93 | (1316) all_0_2_2 = n0
% 55.13/20.93 |
% 55.13/20.93 | From (1316) and (6952) follows:
% 55.13/20.94 | (7062) sum(n0, n10) = all_0_0_0
% 55.13/20.94 |
% 55.13/20.94 | From (1443)(1441) and (590) follows:
% 55.13/20.94 | (1445) sum(n5, n5) = all_0_3_3
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 55.13/20.94 | (1212) all_0_3_3 = n10
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n0, n10, all_0_0_0, n10 and discharging atoms sum(n0, n10) = all_0_0_0, sum(n0, n10) = n10, yields:
% 55.13/20.94 | (1213) all_0_0_0 = n10
% 55.13/20.94 |
% 55.13/20.94 | Equations (1213,1212) can reduce 679 to:
% 55.13/20.94 | (1106) $false
% 55.13/20.94 |
% 55.13/20.94 |-The branch is then unsatisfiable
% 55.13/20.94 |-Branch two:
% 55.13/20.94 | (1323) ~ (all_0_11_11 = n13)
% 55.13/20.94 | (1324) 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
% 55.13/20.94 |
% 55.13/20.94 +-Applying beta-rule and splitting (1324), into two cases.
% 55.13/20.94 |-Branch one:
% 55.13/20.94 | (1325) all_0_11_11 = n12
% 55.13/20.94 |
% 55.13/20.94 | From (1325) and (559) follows:
% 55.13/20.94 | (1326) pred(n12) = all_0_9_9
% 55.13/20.94 |
% 55.13/20.94 | From (1325) and (992) follows:
% 55.13/20.94 | (1327) succ(n12) = all_0_5_5
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (500) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 55.13/20.94 | (1328) all_0_9_9 = n11
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (617) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 55.13/20.94 | (1329) all_0_5_5 = n13
% 55.13/20.94 |
% 55.13/20.94 | From (1328)(1329) and (538) follows:
% 55.13/20.94 | (1330) sum(n11, n13) = all_0_2_2
% 55.13/20.94 |
% 55.13/20.94 | From (1328) and (6950) follows:
% 55.13/20.94 | (7075) sum(n11, n19) = all_0_7_7
% 55.13/20.94 |
% 55.13/20.94 | From (1329) and (6948) follows:
% 55.13/20.94 | (7076) sum(n17, n13) = all_0_4_4
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n17, n13, all_0_4_4, n4 and discharging atoms sum(n17, n13) = all_0_4_4, sum(n17, n13) = n4, yields:
% 55.13/20.94 | (1459) all_0_4_4 = n4
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n11, n19, all_0_7_7, n4 and discharging atoms sum(n11, n19) = all_0_7_7, sum(n11, n19) = n4, yields:
% 55.13/20.94 | (1461) all_0_7_7 = n4
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n11, n13, all_0_2_2, n24 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n24, yields:
% 55.13/20.94 | (1092) all_0_2_2 = n24
% 55.13/20.94 |
% 55.13/20.94 | From (1092) and (6952) follows:
% 55.13/20.94 | (1690) sum(n24, n10) = all_0_0_0
% 55.13/20.94 |
% 55.13/20.94 | From (1461)(1459) and (590) follows:
% 55.13/20.94 | (1463) sum(n4, n4) = all_0_3_3
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n24, n10, all_0_0_0, n8 and discharging atoms sum(n24, n10) = all_0_0_0, sum(n24, n10) = n8, yields:
% 55.13/20.94 | (1231) all_0_0_0 = n8
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 55.13/20.94 | (1230) all_0_3_3 = n8
% 55.13/20.94 |
% 55.13/20.94 | Equations (1231,1230) can reduce 679 to:
% 55.13/20.94 | (1106) $false
% 55.13/20.94 |
% 55.13/20.94 |-The branch is then unsatisfiable
% 55.13/20.94 |-Branch two:
% 55.13/20.94 | (1341) ~ (all_0_11_11 = n12)
% 55.13/20.94 | (1342) 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
% 55.13/20.94 |
% 55.13/20.94 +-Applying beta-rule and splitting (1342), into two cases.
% 55.13/20.94 |-Branch one:
% 55.13/20.94 | (1343) all_0_11_11 = n11
% 55.13/20.94 |
% 55.13/20.94 | From (1343) and (559) follows:
% 55.13/20.94 | (1344) pred(n11) = all_0_9_9
% 55.13/20.94 |
% 55.13/20.94 | From (1343) and (992) follows:
% 55.13/20.94 | (1345) succ(n11) = all_0_5_5
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (500) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 55.13/20.94 | (1346) all_0_9_9 = n10
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (617) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 55.13/20.94 | (1347) all_0_5_5 = n12
% 55.13/20.94 |
% 55.13/20.94 | From (1346)(1347) and (538) follows:
% 55.13/20.94 | (1348) sum(n10, n12) = all_0_2_2
% 55.13/20.94 |
% 55.13/20.94 | From (1346) and (6950) follows:
% 55.13/20.94 | (7093) sum(n10, n19) = all_0_7_7
% 55.13/20.94 |
% 55.13/20.94 | From (1347) and (6948) follows:
% 55.13/20.94 | (7094) sum(n17, n12) = all_0_4_4
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n17, n12, all_0_4_4, n3 and discharging atoms sum(n17, n12) = all_0_4_4, sum(n17, n12) = n3, yields:
% 55.13/20.94 | (1477) all_0_4_4 = n3
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n10, n19, all_0_7_7, n3 and discharging atoms sum(n10, n19) = all_0_7_7, sum(n10, n19) = n3, yields:
% 55.13/20.94 | (1479) all_0_7_7 = n3
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n10, n12, all_0_2_2, n22 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n22, yields:
% 55.13/20.94 | (1118) all_0_2_2 = n22
% 55.13/20.94 |
% 55.13/20.94 | From (1118) and (6952) follows:
% 55.13/20.94 | (2602) sum(n22, n10) = all_0_0_0
% 55.13/20.94 |
% 55.13/20.94 | From (1479)(1477) and (590) follows:
% 55.13/20.94 | (1481) sum(n3, n3) = all_0_3_3
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n22, n10, all_0_0_0, n6 and discharging atoms sum(n22, n10) = all_0_0_0, sum(n22, n10) = n6, yields:
% 55.13/20.94 | (1249) all_0_0_0 = n6
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 55.13/20.94 | (1248) all_0_3_3 = n6
% 55.13/20.94 |
% 55.13/20.94 | Equations (1249,1248) can reduce 679 to:
% 55.13/20.94 | (1106) $false
% 55.13/20.94 |
% 55.13/20.94 |-The branch is then unsatisfiable
% 55.13/20.94 |-Branch two:
% 55.13/20.94 | (1359) ~ (all_0_11_11 = n11)
% 55.13/20.94 | (1360) 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
% 55.13/20.94 |
% 55.13/20.94 +-Applying beta-rule and splitting (1360), into two cases.
% 55.13/20.94 |-Branch one:
% 55.13/20.94 | (1361) all_0_11_11 = n10
% 55.13/20.94 |
% 55.13/20.94 | From (1361) and (559) follows:
% 55.13/20.94 | (1362) pred(n10) = all_0_9_9
% 55.13/20.94 |
% 55.13/20.94 | From (1361) and (992) follows:
% 55.13/20.94 | (1363) succ(n10) = all_0_5_5
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (500) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 55.13/20.94 | (1364) all_0_9_9 = n9
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (617) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 55.13/20.94 | (1365) all_0_5_5 = n11
% 55.13/20.94 |
% 55.13/20.94 | From (1364)(1365) and (538) follows:
% 55.13/20.94 | (1366) sum(n9, n11) = all_0_2_2
% 55.13/20.94 |
% 55.13/20.94 | From (1364) and (6950) follows:
% 55.13/20.94 | (7111) sum(n9, n19) = all_0_7_7
% 55.13/20.94 |
% 55.13/20.94 | From (1365) and (6948) follows:
% 55.13/20.94 | (7112) sum(n17, n11) = all_0_4_4
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n17, n11, all_0_4_4, n2 and discharging atoms sum(n17, n11) = all_0_4_4, sum(n17, n11) = n2, yields:
% 55.13/20.94 | (1495) all_0_4_4 = n2
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n9, n19, all_0_7_7, n2 and discharging atoms sum(n9, n19) = all_0_7_7, sum(n9, n19) = n2, yields:
% 55.13/20.94 | (1497) all_0_7_7 = n2
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 55.13/20.94 | (1136) all_0_2_2 = n20
% 55.13/20.94 |
% 55.13/20.94 | From (1136) and (6952) follows:
% 55.13/20.94 | (3476) sum(n20, n10) = all_0_0_0
% 55.13/20.94 |
% 55.13/20.94 | From (1497)(1495) and (590) follows:
% 55.13/20.94 | (1499) sum(n2, n2) = all_0_3_3
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n20, n10, all_0_0_0, n4 and discharging atoms sum(n20, n10) = all_0_0_0, sum(n20, n10) = n4, yields:
% 55.13/20.94 | (1267) all_0_0_0 = n4
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 55.13/20.94 | (1266) all_0_3_3 = n4
% 55.13/20.94 |
% 55.13/20.94 | Equations (1267,1266) can reduce 679 to:
% 55.13/20.94 | (1106) $false
% 55.13/20.94 |
% 55.13/20.94 |-The branch is then unsatisfiable
% 55.13/20.94 |-Branch two:
% 55.13/20.94 | (1377) ~ (all_0_11_11 = n10)
% 55.13/20.94 | (1378) 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
% 55.13/20.94 |
% 55.13/20.94 +-Applying beta-rule and splitting (1378), into two cases.
% 55.13/20.94 |-Branch one:
% 55.13/20.94 | (1379) all_0_11_11 = n9
% 55.13/20.94 |
% 55.13/20.94 | From (1379) and (559) follows:
% 55.13/20.94 | (1380) pred(n9) = all_0_9_9
% 55.13/20.94 |
% 55.13/20.94 | From (1379) and (992) follows:
% 55.13/20.94 | (1381) succ(n9) = all_0_5_5
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 55.13/20.94 | (1382) all_0_9_9 = n8
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 55.13/20.94 | (1383) all_0_5_5 = n10
% 55.13/20.94 |
% 55.13/20.94 | From (1382)(1383) and (538) follows:
% 55.13/20.94 | (1384) sum(n8, n10) = all_0_2_2
% 55.13/20.94 |
% 55.13/20.94 | From (1382) and (6950) follows:
% 55.13/20.94 | (7129) sum(n8, n19) = all_0_7_7
% 55.13/20.94 |
% 55.13/20.94 | From (1383) and (6948) follows:
% 55.13/20.94 | (7130) sum(n17, n10) = all_0_4_4
% 55.13/20.94 |
% 55.13/20.94 | Instantiating formula (690) with n17, n10, all_0_4_4, n1 and discharging atoms sum(n17, n10) = all_0_4_4, sum(n17, n10) = n1, yields:
% 55.13/20.94 | (1513) all_0_4_4 = n1
% 55.13/20.94 |
% 55.13/20.95 | Instantiating formula (690) with n8, n19, all_0_7_7, n1 and discharging atoms sum(n8, n19) = all_0_7_7, sum(n8, n19) = n1, yields:
% 55.13/20.95 | (1515) all_0_7_7 = n1
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 55.13/20.95 | (1154) all_0_2_2 = n18
% 55.13/20.95 |
% 55.13/20.95 | From (1154) and (6952) follows:
% 55.13/20.95 | (4314) sum(n18, n10) = all_0_0_0
% 55.13/20.95 |
% 55.13/20.95 | From (1515)(1513) and (590) follows:
% 55.13/20.95 | (1517) sum(n1, n1) = all_0_3_3
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n18, n10, all_0_0_0, n2 and discharging atoms sum(n18, n10) = all_0_0_0, sum(n18, n10) = n2, yields:
% 55.13/20.95 | (1285) all_0_0_0 = n2
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 55.13/20.95 | (1284) all_0_3_3 = n2
% 55.13/20.95 |
% 55.13/20.95 | Equations (1285,1284) can reduce 679 to:
% 55.13/20.95 | (1106) $false
% 55.13/20.95 |
% 55.13/20.95 |-The branch is then unsatisfiable
% 55.13/20.95 |-Branch two:
% 55.13/20.95 | (1395) ~ (all_0_11_11 = n9)
% 55.13/20.95 | (1396) 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
% 55.13/20.95 |
% 55.13/20.95 +-Applying beta-rule and splitting (1396), into two cases.
% 55.13/20.95 |-Branch one:
% 55.13/20.95 | (1397) all_0_11_11 = n8
% 55.13/20.95 |
% 55.13/20.95 | From (1397) and (559) follows:
% 55.13/20.95 | (1398) pred(n8) = all_0_9_9
% 55.13/20.95 |
% 55.13/20.95 | From (1397) and (992) follows:
% 55.13/20.95 | (1399) succ(n8) = all_0_5_5
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 55.13/20.95 | (1400) all_0_9_9 = n7
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 55.13/20.95 | (1401) all_0_5_5 = n9
% 55.13/20.95 |
% 55.13/20.95 | From (1400)(1401) and (538) follows:
% 55.13/20.95 | (1402) sum(n7, n9) = all_0_2_2
% 55.13/20.95 |
% 55.13/20.95 | From (1400) and (6950) follows:
% 55.13/20.95 | (7147) sum(n7, n19) = all_0_7_7
% 55.13/20.95 |
% 55.13/20.95 | From (1401) and (6948) follows:
% 55.13/20.95 | (7148) sum(n17, n9) = all_0_4_4
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n17, n9, all_0_4_4, n0 and discharging atoms sum(n17, n9) = all_0_4_4, sum(n17, n9) = n0, yields:
% 55.13/20.95 | (1531) all_0_4_4 = n0
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n7, n19, all_0_7_7, n0 and discharging atoms sum(n7, n19) = all_0_7_7, sum(n7, n19) = n0, yields:
% 55.13/20.95 | (1533) all_0_7_7 = n0
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 55.13/20.95 | (1172) all_0_2_2 = n16
% 55.13/20.95 |
% 55.13/20.95 | From (1172) and (6952) follows:
% 55.13/20.95 | (5116) sum(n16, n10) = all_0_0_0
% 55.13/20.95 |
% 55.13/20.95 | From (1533)(1531) and (590) follows:
% 55.13/20.95 | (1535) sum(n0, n0) = all_0_3_3
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n16, n10, all_0_0_0, n0 and discharging atoms sum(n16, n10) = all_0_0_0, sum(n16, n10) = n0, yields:
% 55.13/20.95 | (1303) all_0_0_0 = n0
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 55.13/20.95 | (1302) all_0_3_3 = n0
% 55.13/20.95 |
% 55.13/20.95 | Equations (1303,1302) can reduce 679 to:
% 55.13/20.95 | (1106) $false
% 55.13/20.95 |
% 55.13/20.95 |-The branch is then unsatisfiable
% 55.13/20.95 |-Branch two:
% 55.13/20.95 | (1413) ~ (all_0_11_11 = n8)
% 55.13/20.95 | (1414) 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
% 55.13/20.95 |
% 55.13/20.95 +-Applying beta-rule and splitting (1414), into two cases.
% 55.13/20.95 |-Branch one:
% 55.13/20.95 | (1415) all_0_11_11 = n7
% 55.13/20.95 |
% 55.13/20.95 | From (1415) and (559) follows:
% 55.13/20.95 | (1416) pred(n7) = all_0_9_9
% 55.13/20.95 |
% 55.13/20.95 | From (1415) and (992) follows:
% 55.13/20.95 | (1417) succ(n7) = all_0_5_5
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 55.13/20.95 | (1418) all_0_9_9 = n6
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 55.13/20.95 | (1419) all_0_5_5 = n8
% 55.13/20.95 |
% 55.13/20.95 | From (1418)(1419) and (538) follows:
% 55.13/20.95 | (1420) sum(n6, n8) = all_0_2_2
% 55.13/20.95 |
% 55.13/20.95 | From (1418) and (6950) follows:
% 55.13/20.95 | (7165) sum(n6, n19) = all_0_7_7
% 55.13/20.95 |
% 55.13/20.95 | From (1419) and (6948) follows:
% 55.13/20.95 | (7166) sum(n17, n8) = all_0_4_4
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n17, n8, all_0_4_4, n25 and discharging atoms sum(n17, n8) = all_0_4_4, sum(n17, n8) = n25, yields:
% 55.13/20.95 | (1551) all_0_4_4 = n25
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n6, n19, all_0_7_7, n25 and discharging atoms sum(n6, n19) = all_0_7_7, sum(n6, n19) = n25, yields:
% 55.13/20.95 | (1550) all_0_7_7 = n25
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 55.13/20.95 | (1190) all_0_2_2 = n14
% 55.13/20.95 |
% 55.13/20.95 | From (1190) and (6952) follows:
% 55.13/20.95 | (5882) sum(n14, n10) = all_0_0_0
% 55.13/20.95 |
% 55.13/20.95 | From (1550)(1551) and (590) follows:
% 55.13/20.95 | (1553) sum(n25, n25) = all_0_3_3
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 55.13/20.95 | (1320) all_0_3_3 = n24
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n14, n10, all_0_0_0, n24 and discharging atoms sum(n14, n10) = all_0_0_0, sum(n14, n10) = n24, yields:
% 55.13/20.95 | (1321) all_0_0_0 = n24
% 55.13/20.95 |
% 55.13/20.95 | Equations (1321,1320) can reduce 679 to:
% 55.13/20.95 | (1106) $false
% 55.13/20.95 |
% 55.13/20.95 |-The branch is then unsatisfiable
% 55.13/20.95 |-Branch two:
% 55.13/20.95 | (1431) ~ (all_0_11_11 = n7)
% 55.13/20.95 | (1432) 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
% 55.13/20.95 |
% 55.13/20.95 +-Applying beta-rule and splitting (1432), into two cases.
% 55.13/20.95 |-Branch one:
% 55.13/20.95 | (1433) all_0_11_11 = n6
% 55.13/20.95 |
% 55.13/20.95 | From (1433) and (559) follows:
% 55.13/20.95 | (1434) pred(n6) = all_0_9_9
% 55.13/20.95 |
% 55.13/20.95 | From (1433) and (992) follows:
% 55.13/20.95 | (1435) succ(n6) = all_0_5_5
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 55.13/20.95 | (1436) all_0_9_9 = n5
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 55.13/20.95 | (1437) all_0_5_5 = n7
% 55.13/20.95 |
% 55.13/20.95 | From (1436)(1437) and (538) follows:
% 55.13/20.95 | (1438) sum(n5, n7) = all_0_2_2
% 55.13/20.95 |
% 55.13/20.95 | From (1436) and (6950) follows:
% 55.13/20.95 | (7183) sum(n5, n19) = all_0_7_7
% 55.13/20.95 |
% 55.13/20.95 | From (1437) and (6948) follows:
% 55.13/20.95 | (7184) sum(n17, n7) = all_0_4_4
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n17, n7, all_0_4_4, n24 and discharging atoms sum(n17, n7) = all_0_4_4, sum(n17, n7) = n24, yields:
% 55.13/20.95 | (1096) all_0_4_4 = n24
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n5, n19, all_0_7_7, n24 and discharging atoms sum(n5, n19) = all_0_7_7, sum(n5, n19) = n24, yields:
% 55.13/20.95 | (1097) all_0_7_7 = n24
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 55.13/20.95 | (1208) all_0_2_2 = n12
% 55.13/20.95 |
% 55.13/20.95 | From (1208) and (6952) follows:
% 55.13/20.95 | (6612) sum(n12, n10) = all_0_0_0
% 55.13/20.95 |
% 55.13/20.95 | From (1097)(1096) and (590) follows:
% 55.13/20.95 | (1101) sum(n24, n24) = all_0_3_3
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 55.13/20.95 | (1104) all_0_3_3 = n22
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (690) with n12, n10, all_0_0_0, n22 and discharging atoms sum(n12, n10) = all_0_0_0, sum(n12, n10) = n22, yields:
% 55.13/20.95 | (1102) all_0_0_0 = n22
% 55.13/20.95 |
% 55.13/20.95 | Equations (1102,1104) can reduce 679 to:
% 55.13/20.95 | (1106) $false
% 55.13/20.95 |
% 55.13/20.95 |-The branch is then unsatisfiable
% 55.13/20.95 |-Branch two:
% 55.13/20.95 | (1449) ~ (all_0_11_11 = n6)
% 55.13/20.95 | (1450) 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
% 55.13/20.95 |
% 55.13/20.95 +-Applying beta-rule and splitting (1450), into two cases.
% 55.13/20.95 |-Branch one:
% 55.13/20.95 | (1451) all_0_11_11 = n5
% 55.13/20.95 |
% 55.13/20.95 | From (1451) and (559) follows:
% 55.13/20.95 | (1452) pred(n5) = all_0_9_9
% 55.13/20.95 |
% 55.13/20.95 | From (1451) and (992) follows:
% 55.13/20.95 | (1453) succ(n5) = all_0_5_5
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 55.13/20.95 | (1454) all_0_9_9 = n4
% 55.13/20.95 |
% 55.13/20.95 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 55.13/20.95 | (1455) all_0_5_5 = n6
% 55.13/20.96 |
% 55.13/20.96 | From (1454)(1455) and (538) follows:
% 55.13/20.96 | (1456) sum(n4, n6) = all_0_2_2
% 55.13/20.96 |
% 55.13/20.96 | From (1454) and (6950) follows:
% 55.13/20.96 | (7201) sum(n4, n19) = all_0_7_7
% 55.13/20.96 |
% 55.13/20.96 | From (1455) and (6948) follows:
% 55.13/20.96 | (7202) sum(n17, n6) = all_0_4_4
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n17, n6, all_0_4_4, n23 and discharging atoms sum(n17, n6) = all_0_4_4, sum(n17, n6) = n23, yields:
% 55.13/20.96 | (1117) all_0_4_4 = n23
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n4, n19, all_0_7_7, n23 and discharging atoms sum(n4, n19) = all_0_7_7, sum(n4, n19) = n23, yields:
% 55.13/20.96 | (1119) all_0_7_7 = n23
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 55.13/20.96 | (1226) all_0_2_2 = n10
% 55.13/20.96 |
% 55.13/20.96 | From (1226) and (6952) follows:
% 55.13/20.96 | (6970) sum(n10, n10) = all_0_0_0
% 55.13/20.96 |
% 55.13/20.96 | From (1119)(1117) and (590) follows:
% 55.13/20.96 | (1121) sum(n23, n23) = all_0_3_3
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 55.13/20.96 | (1122) all_0_3_3 = n20
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n10, n10, all_0_0_0, n20 and discharging atoms sum(n10, n10) = all_0_0_0, sum(n10, n10) = n20, yields:
% 55.13/20.96 | (1123) all_0_0_0 = n20
% 55.13/20.96 |
% 55.13/20.96 | Equations (1123,1122) can reduce 679 to:
% 55.13/20.96 | (1106) $false
% 55.13/20.96 |
% 55.13/20.96 |-The branch is then unsatisfiable
% 55.13/20.96 |-Branch two:
% 55.13/20.96 | (1467) ~ (all_0_11_11 = n5)
% 55.13/20.96 | (1468) 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
% 55.13/20.96 |
% 55.13/20.96 +-Applying beta-rule and splitting (1468), into two cases.
% 55.13/20.96 |-Branch one:
% 55.13/20.96 | (1469) all_0_11_11 = n4
% 55.13/20.96 |
% 55.13/20.96 | From (1469) and (559) follows:
% 55.13/20.96 | (1470) pred(n4) = all_0_9_9
% 55.13/20.96 |
% 55.13/20.96 | From (1469) and (992) follows:
% 55.13/20.96 | (1471) succ(n4) = all_0_5_5
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 55.13/20.96 | (1472) all_0_9_9 = n3
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 55.13/20.96 | (1473) all_0_5_5 = n5
% 55.13/20.96 |
% 55.13/20.96 | From (1472)(1473) and (538) follows:
% 55.13/20.96 | (1474) sum(n3, n5) = all_0_2_2
% 55.13/20.96 |
% 55.13/20.96 | From (1472) and (6950) follows:
% 55.13/20.96 | (7219) sum(n3, n19) = all_0_7_7
% 55.13/20.96 |
% 55.13/20.96 | From (1473) and (6948) follows:
% 55.13/20.96 | (7220) sum(n17, n5) = all_0_4_4
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n17, n5, all_0_4_4, n22 and discharging atoms sum(n17, n5) = all_0_4_4, sum(n17, n5) = n22, yields:
% 55.13/20.96 | (1135) all_0_4_4 = n22
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n3, n19, all_0_7_7, n22 and discharging atoms sum(n3, n19) = all_0_7_7, sum(n3, n19) = n22, yields:
% 55.13/20.96 | (1137) all_0_7_7 = n22
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 55.13/20.96 | (1244) all_0_2_2 = n8
% 55.13/20.96 |
% 55.13/20.96 | From (1244) and (6952) follows:
% 55.13/20.96 | (6990) sum(n8, n10) = all_0_0_0
% 55.13/20.96 |
% 55.13/20.96 | From (1137)(1135) and (590) follows:
% 55.13/20.96 | (1139) sum(n22, n22) = all_0_3_3
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 55.13/20.96 | (1140) all_0_3_3 = n18
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n8, n10, all_0_0_0, n18 and discharging atoms sum(n8, n10) = all_0_0_0, sum(n8, n10) = n18, yields:
% 55.13/20.96 | (1141) all_0_0_0 = n18
% 55.13/20.96 |
% 55.13/20.96 | Equations (1141,1140) can reduce 679 to:
% 55.13/20.96 | (1106) $false
% 55.13/20.96 |
% 55.13/20.96 |-The branch is then unsatisfiable
% 55.13/20.96 |-Branch two:
% 55.13/20.96 | (1485) ~ (all_0_11_11 = n4)
% 55.13/20.96 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 55.13/20.96 |
% 55.13/20.96 +-Applying beta-rule and splitting (1486), into two cases.
% 55.13/20.96 |-Branch one:
% 55.13/20.96 | (1487) all_0_11_11 = n3
% 55.13/20.96 |
% 55.13/20.96 | From (1487) and (559) follows:
% 55.13/20.96 | (1488) pred(n3) = all_0_9_9
% 55.13/20.96 |
% 55.13/20.96 | From (1487) and (992) follows:
% 55.13/20.96 | (1489) succ(n3) = all_0_5_5
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 55.13/20.96 | (1490) all_0_9_9 = n2
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 55.13/20.96 | (1491) all_0_5_5 = n4
% 55.13/20.96 |
% 55.13/20.96 | From (1490)(1491) and (538) follows:
% 55.13/20.96 | (1492) sum(n2, n4) = all_0_2_2
% 55.13/20.96 |
% 55.13/20.96 | From (1490) and (6950) follows:
% 55.13/20.96 | (7237) sum(n2, n19) = all_0_7_7
% 55.13/20.96 |
% 55.13/20.96 | From (1491) and (6948) follows:
% 55.13/20.96 | (7238) sum(n17, n4) = all_0_4_4
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n17, n4, all_0_4_4, n21 and discharging atoms sum(n17, n4) = all_0_4_4, sum(n17, n4) = n21, yields:
% 55.13/20.96 | (1153) all_0_4_4 = n21
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n2, n19, all_0_7_7, n21 and discharging atoms sum(n2, n19) = all_0_7_7, sum(n2, n19) = n21, yields:
% 55.13/20.96 | (1155) all_0_7_7 = n21
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 55.13/20.96 | (1262) all_0_2_2 = n6
% 55.13/20.96 |
% 55.13/20.96 | From (1262) and (6952) follows:
% 55.13/20.96 | (7008) sum(n6, n10) = all_0_0_0
% 55.13/20.96 |
% 55.13/20.96 | From (1155)(1153) and (590) follows:
% 55.13/20.96 | (1157) sum(n21, n21) = all_0_3_3
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 55.13/20.96 | (1158) all_0_3_3 = n16
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n6, n10, all_0_0_0, n16 and discharging atoms sum(n6, n10) = all_0_0_0, sum(n6, n10) = n16, yields:
% 55.13/20.96 | (1159) all_0_0_0 = n16
% 55.13/20.96 |
% 55.13/20.96 | Equations (1159,1158) can reduce 679 to:
% 55.13/20.96 | (1106) $false
% 55.13/20.96 |
% 55.13/20.96 |-The branch is then unsatisfiable
% 55.13/20.96 |-Branch two:
% 55.13/20.96 | (1503) ~ (all_0_11_11 = n3)
% 55.13/20.96 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 55.13/20.96 |
% 55.13/20.96 +-Applying beta-rule and splitting (1504), into two cases.
% 55.13/20.96 |-Branch one:
% 55.13/20.96 | (1505) all_0_11_11 = n2
% 55.13/20.96 |
% 55.13/20.96 | From (1505) and (559) follows:
% 55.13/20.96 | (1506) pred(n2) = all_0_9_9
% 55.13/20.96 |
% 55.13/20.96 | From (1505) and (992) follows:
% 55.13/20.96 | (1507) succ(n2) = all_0_5_5
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 55.13/20.96 | (1508) all_0_9_9 = n1
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 55.13/20.96 | (1509) all_0_5_5 = n3
% 55.13/20.96 |
% 55.13/20.96 | From (1508)(1509) and (538) follows:
% 55.13/20.96 | (1510) sum(n1, n3) = all_0_2_2
% 55.13/20.96 |
% 55.13/20.96 | From (1508) and (6950) follows:
% 55.13/20.96 | (7255) sum(n1, n19) = all_0_7_7
% 55.13/20.96 |
% 55.13/20.96 | From (1509) and (6948) follows:
% 55.13/20.96 | (7256) sum(n17, n3) = all_0_4_4
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n17, n3, all_0_4_4, n20 and discharging atoms sum(n17, n3) = all_0_4_4, sum(n17, n3) = n20, yields:
% 55.13/20.96 | (1171) all_0_4_4 = n20
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n1, n19, all_0_7_7, n20 and discharging atoms sum(n1, n19) = all_0_7_7, sum(n1, n19) = n20, yields:
% 55.13/20.96 | (1173) all_0_7_7 = n20
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 55.13/20.96 | (1280) all_0_2_2 = n4
% 55.13/20.96 |
% 55.13/20.96 | From (1280) and (6952) follows:
% 55.13/20.96 | (7026) sum(n4, n10) = all_0_0_0
% 55.13/20.96 |
% 55.13/20.96 | From (1173)(1171) and (590) follows:
% 55.13/20.96 | (1175) sum(n20, n20) = all_0_3_3
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 55.13/20.96 | (1176) all_0_3_3 = n14
% 55.13/20.96 |
% 55.13/20.96 | Instantiating formula (690) with n4, n10, all_0_0_0, n14 and discharging atoms sum(n4, n10) = all_0_0_0, sum(n4, n10) = n14, yields:
% 55.13/20.97 | (1177) all_0_0_0 = n14
% 55.13/20.97 |
% 55.13/20.97 | Equations (1177,1176) can reduce 679 to:
% 55.13/20.97 | (1106) $false
% 55.13/20.97 |
% 55.13/20.97 |-The branch is then unsatisfiable
% 55.13/20.97 |-Branch two:
% 55.13/20.97 | (1521) ~ (all_0_11_11 = n2)
% 55.13/20.97 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 55.13/20.97 |
% 55.13/20.97 +-Applying beta-rule and splitting (1522), into two cases.
% 55.13/20.97 |-Branch one:
% 55.13/20.97 | (1523) all_0_11_11 = n1
% 55.13/20.97 |
% 55.13/20.97 | From (1523) and (559) follows:
% 55.13/20.97 | (1524) pred(n1) = all_0_9_9
% 55.13/20.97 |
% 55.13/20.97 | From (1523) and (992) follows:
% 55.13/20.97 | (1525) succ(n1) = all_0_5_5
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 55.13/20.97 | (1526) all_0_9_9 = n0
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 55.13/20.97 | (1527) all_0_5_5 = n2
% 55.13/20.97 |
% 55.13/20.97 | From (1526)(1527) and (538) follows:
% 55.13/20.97 | (1528) sum(n0, n2) = all_0_2_2
% 55.13/20.97 |
% 55.13/20.97 | From (1526) and (6950) follows:
% 55.13/20.97 | (7273) sum(n0, n19) = all_0_7_7
% 55.13/20.97 |
% 55.13/20.97 | From (1527) and (6948) follows:
% 55.13/20.97 | (7274) sum(n17, n2) = all_0_4_4
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (690) with n17, n2, all_0_4_4, n19 and discharging atoms sum(n17, n2) = all_0_4_4, sum(n17, n2) = n19, yields:
% 55.13/20.97 | (1189) all_0_4_4 = n19
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (690) with n0, n19, all_0_7_7, n19 and discharging atoms sum(n0, n19) = all_0_7_7, sum(n0, n19) = n19, yields:
% 55.13/20.97 | (1191) all_0_7_7 = n19
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 55.13/20.97 | (1298) all_0_2_2 = n2
% 55.13/20.97 |
% 55.13/20.97 | From (1298) and (6952) follows:
% 55.13/20.97 | (7044) sum(n2, n10) = all_0_0_0
% 55.13/20.97 |
% 55.13/20.97 | From (1191)(1189) and (590) follows:
% 55.13/20.97 | (1193) sum(n19, n19) = all_0_3_3
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 55.13/20.97 | (1194) all_0_3_3 = n12
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (690) with n2, n10, all_0_0_0, n12 and discharging atoms sum(n2, n10) = all_0_0_0, sum(n2, n10) = n12, yields:
% 55.13/20.97 | (1195) all_0_0_0 = n12
% 55.13/20.97 |
% 55.13/20.97 | Equations (1195,1194) can reduce 679 to:
% 55.13/20.97 | (1106) $false
% 55.13/20.97 |
% 55.13/20.97 |-The branch is then unsatisfiable
% 55.13/20.97 |-Branch two:
% 55.13/20.97 | (1540) ~ (all_0_11_11 = n1)
% 55.13/20.97 | (1541) all_0_11_11 = n0
% 55.13/20.97 |
% 55.13/20.97 | From (1541) and (559) follows:
% 55.13/20.97 | (1542) pred(n0) = all_0_9_9
% 55.13/20.97 |
% 55.13/20.97 | From (1541) and (992) follows:
% 55.13/20.97 | (1543) succ(n0) = all_0_5_5
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 55.13/20.97 | (1544) all_0_9_9 = n25
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 55.13/20.97 | (1545) all_0_5_5 = n1
% 55.13/20.97 |
% 55.13/20.97 | From (1544)(1545) and (538) follows:
% 55.13/20.97 | (1546) sum(n25, n1) = all_0_2_2
% 55.13/20.97 |
% 55.13/20.97 | From (1544) and (6950) follows:
% 55.13/20.97 | (7290) sum(n25, n19) = all_0_7_7
% 55.13/20.97 |
% 55.13/20.97 | From (1545) and (6948) follows:
% 55.13/20.97 | (7291) sum(n17, n1) = all_0_4_4
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (690) with n25, n19, all_0_7_7, n18 and discharging atoms sum(n25, n19) = all_0_7_7, sum(n25, n19) = n18, yields:
% 55.13/20.97 | (1209) all_0_7_7 = n18
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 55.13/20.97 | (1316) all_0_2_2 = n0
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (690) with n17, n1, all_0_4_4, n18 and discharging atoms sum(n17, n1) = all_0_4_4, sum(n17, n1) = n18, yields:
% 55.13/20.97 | (1207) all_0_4_4 = n18
% 55.13/20.97 |
% 55.13/20.97 | From (1316) and (6952) follows:
% 55.13/20.97 | (7062) sum(n0, n10) = all_0_0_0
% 55.13/20.97 |
% 55.13/20.97 | From (1209)(1207) and (590) follows:
% 55.13/20.97 | (1211) sum(n18, n18) = all_0_3_3
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 55.13/20.97 | (1212) all_0_3_3 = n10
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (690) with n0, n10, all_0_0_0, n10 and discharging atoms sum(n0, n10) = all_0_0_0, sum(n0, n10) = n10, yields:
% 55.13/20.97 | (1213) all_0_0_0 = n10
% 55.13/20.97 |
% 55.13/20.97 | Equations (1213,1212) can reduce 679 to:
% 55.13/20.97 | (1106) $false
% 55.13/20.97 |
% 55.13/20.97 |-The branch is then unsatisfiable
% 55.13/20.97 |-Branch two:
% 55.13/20.97 | (1694) ~ (all_0_10_10 = n18)
% 55.13/20.97 | (1695) 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
% 55.13/20.97 |
% 55.13/20.97 +-Applying beta-rule and splitting (1216), into two cases.
% 55.13/20.97 |-Branch one:
% 55.13/20.97 | (1217) all_0_11_11 = n18
% 55.13/20.97 |
% 55.13/20.97 | From (1217) and (559) follows:
% 55.13/20.97 | (1218) pred(n18) = all_0_9_9
% 55.13/20.97 |
% 55.13/20.97 | From (1217) and (992) follows:
% 55.13/20.97 | (1219) succ(n18) = all_0_5_5
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (500) with n18, all_0_9_9, n17 and discharging atoms pred(n18) = all_0_9_9, pred(n18) = n17, yields:
% 55.13/20.97 | (1220) all_0_9_9 = n17
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (617) with n18, all_0_5_5, n19 and discharging atoms succ(n18) = all_0_5_5, succ(n18) = n19, yields:
% 55.13/20.97 | (1221) all_0_5_5 = n19
% 55.13/20.97 |
% 55.13/20.97 | From (1221) and (541) follows:
% 55.13/20.97 | (7307) sum(all_0_6_6, n19) = all_0_4_4
% 55.13/20.97 |
% 55.13/20.97 | From (1220)(1221) and (538) follows:
% 55.13/20.97 | (1222) sum(n17, n19) = all_0_2_2
% 55.13/20.97 |
% 55.13/20.97 | From (1220) and (427) follows:
% 55.13/20.97 | (7309) sum(n17, all_0_8_8) = all_0_7_7
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (690) with n17, n19, all_0_2_2, n10 and discharging atoms sum(n17, n19) = all_0_2_2, sum(n17, n19) = n10, yields:
% 55.13/20.97 | (1226) all_0_2_2 = n10
% 55.13/20.97 |
% 55.13/20.97 | From (1226) and (630) follows:
% 55.13/20.97 | (7311) sum(n10, all_0_1_1) = all_0_0_0
% 55.13/20.97 |
% 55.13/20.97 +-Applying beta-rule and splitting (1695), into two cases.
% 55.13/20.97 |-Branch one:
% 55.13/20.97 | (1696) all_0_10_10 = n17
% 55.13/20.97 |
% 55.13/20.97 | From (1696) and (292) follows:
% 55.13/20.97 | (1697) pred(n17) = all_0_6_6
% 55.13/20.97 |
% 55.13/20.97 | From (1696) and (760) follows:
% 55.13/20.97 | (1698) succ(n17) = all_0_8_8
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (500) with n17, all_0_6_6, n16 and discharging atoms pred(n17) = all_0_6_6, pred(n17) = n16, yields:
% 55.13/20.97 | (1699) all_0_6_6 = n16
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (617) with n17, all_0_8_8, n18 and discharging atoms succ(n17) = all_0_8_8, succ(n17) = n18, yields:
% 55.13/20.97 | (1700) all_0_8_8 = n18
% 55.13/20.97 |
% 55.13/20.97 | From (1699)(1700) and (411) follows:
% 55.13/20.97 | (1701) sum(n16, n18) = all_0_1_1
% 55.13/20.97 |
% 55.13/20.97 | From (1699) and (7307) follows:
% 55.13/20.97 | (7318) sum(n16, n19) = all_0_4_4
% 55.13/20.97 |
% 55.13/20.97 | From (1700) and (7309) follows:
% 55.13/20.97 | (7319) sum(n17, n18) = all_0_7_7
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (690) with n17, n18, all_0_7_7, n9 and discharging atoms sum(n17, n18) = all_0_7_7, sum(n17, n18) = n9, yields:
% 55.13/20.97 | (1371) all_0_7_7 = n9
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (690) with n16, n19, all_0_4_4, n9 and discharging atoms sum(n16, n19) = all_0_4_4, sum(n16, n19) = n9, yields:
% 55.13/20.97 | (1369) all_0_4_4 = n9
% 55.13/20.97 |
% 55.13/20.97 | Instantiating formula (690) with n16, n18, all_0_1_1, n8 and discharging atoms sum(n16, n18) = all_0_1_1, sum(n16, n18) = n8, yields:
% 55.13/20.97 | (1705) all_0_1_1 = n8
% 55.13/20.97 |
% 55.13/20.97 | From (1371)(1369) and (590) follows:
% 55.13/20.97 | (1373) sum(n9, n9) = all_0_3_3
% 55.13/20.97 |
% 55.13/20.97 | From (1705) and (7311) follows:
% 55.13/20.97 | (7324) sum(n10, n8) = all_0_0_0
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (690) with n10, n8, all_0_0_0, n18 and discharging atoms sum(n10, n8) = all_0_0_0, sum(n10, n8) = n18, yields:
% 55.13/20.98 | (1141) all_0_0_0 = n18
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 55.13/20.98 | (1140) all_0_3_3 = n18
% 55.13/20.98 |
% 55.13/20.98 | Equations (1141,1140) can reduce 679 to:
% 55.13/20.98 | (1106) $false
% 55.13/20.98 |
% 55.13/20.98 |-The branch is then unsatisfiable
% 55.13/20.98 |-Branch two:
% 55.13/20.98 | (1712) ~ (all_0_10_10 = n17)
% 55.13/20.98 | (1713) 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
% 55.13/20.98 |
% 55.13/20.98 +-Applying beta-rule and splitting (1713), into two cases.
% 55.13/20.98 |-Branch one:
% 55.13/20.98 | (1714) all_0_10_10 = n16
% 55.13/20.98 |
% 55.13/20.98 | From (1714) and (292) follows:
% 55.13/20.98 | (1715) pred(n16) = all_0_6_6
% 55.13/20.98 |
% 55.13/20.98 | From (1714) and (760) follows:
% 55.13/20.98 | (1716) succ(n16) = all_0_8_8
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (500) with n16, all_0_6_6, n15 and discharging atoms pred(n16) = all_0_6_6, pred(n16) = n15, yields:
% 55.13/20.98 | (1717) all_0_6_6 = n15
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (617) with n16, all_0_8_8, n17 and discharging atoms succ(n16) = all_0_8_8, succ(n16) = n17, yields:
% 55.13/20.98 | (1718) all_0_8_8 = n17
% 55.13/20.98 |
% 55.13/20.98 | From (1717)(1718) and (411) follows:
% 55.13/20.98 | (1719) sum(n15, n17) = all_0_1_1
% 55.13/20.98 |
% 55.13/20.98 | From (1717) and (7307) follows:
% 55.13/20.98 | (7336) sum(n15, n19) = all_0_4_4
% 55.13/20.98 |
% 55.13/20.98 | From (1718) and (7309) follows:
% 55.13/20.98 | (7337) sum(n17, n17) = all_0_7_7
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (690) with n17, n17, all_0_7_7, n8 and discharging atoms sum(n17, n17) = all_0_7_7, sum(n17, n17) = n8, yields:
% 55.13/20.98 | (1389) all_0_7_7 = n8
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (690) with n15, n19, all_0_4_4, n8 and discharging atoms sum(n15, n19) = all_0_4_4, sum(n15, n19) = n8, yields:
% 55.13/20.98 | (1387) all_0_4_4 = n8
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (690) with n15, n17, all_0_1_1, n6 and discharging atoms sum(n15, n17) = all_0_1_1, sum(n15, n17) = n6, yields:
% 55.13/20.98 | (1723) all_0_1_1 = n6
% 55.13/20.98 |
% 55.13/20.98 | From (1389)(1387) and (590) follows:
% 55.13/20.98 | (1391) sum(n8, n8) = all_0_3_3
% 55.13/20.98 |
% 55.13/20.98 | From (1723) and (7311) follows:
% 55.13/20.98 | (7342) sum(n10, n6) = all_0_0_0
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (690) with n10, n6, all_0_0_0, n16 and discharging atoms sum(n10, n6) = all_0_0_0, sum(n10, n6) = n16, yields:
% 55.13/20.98 | (1159) all_0_0_0 = n16
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 55.13/20.98 | (1158) all_0_3_3 = n16
% 55.13/20.98 |
% 55.13/20.98 | Equations (1159,1158) can reduce 679 to:
% 55.13/20.98 | (1106) $false
% 55.13/20.98 |
% 55.13/20.98 |-The branch is then unsatisfiable
% 55.13/20.98 |-Branch two:
% 55.13/20.98 | (1730) ~ (all_0_10_10 = n16)
% 55.13/20.98 | (1731) 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
% 55.13/20.98 |
% 55.13/20.98 +-Applying beta-rule and splitting (1731), into two cases.
% 55.13/20.98 |-Branch one:
% 55.13/20.98 | (1732) all_0_10_10 = n15
% 55.13/20.98 |
% 55.13/20.98 | From (1732) and (292) follows:
% 55.13/20.98 | (1733) pred(n15) = all_0_6_6
% 55.13/20.98 |
% 55.13/20.98 | From (1732) and (760) follows:
% 55.13/20.98 | (1734) succ(n15) = all_0_8_8
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (500) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 55.13/20.98 | (1735) all_0_6_6 = n14
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (617) with n15, all_0_8_8, n16 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n16, yields:
% 55.13/20.98 | (1736) all_0_8_8 = n16
% 55.13/20.98 |
% 55.13/20.98 | From (1735)(1736) and (411) follows:
% 55.13/20.98 | (1737) sum(n14, n16) = all_0_1_1
% 55.13/20.98 |
% 55.13/20.98 | From (1735) and (7307) follows:
% 55.13/20.98 | (7354) sum(n14, n19) = all_0_4_4
% 55.13/20.98 |
% 55.13/20.98 | From (1736) and (7309) follows:
% 55.13/20.98 | (7355) sum(n17, n16) = all_0_7_7
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (690) with n17, n16, all_0_7_7, n7 and discharging atoms sum(n17, n16) = all_0_7_7, sum(n17, n16) = n7, yields:
% 55.13/20.98 | (1407) all_0_7_7 = n7
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (690) with n14, n19, all_0_4_4, n7 and discharging atoms sum(n14, n19) = all_0_4_4, sum(n14, n19) = n7, yields:
% 55.13/20.98 | (1405) all_0_4_4 = n7
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (690) with n14, n16, all_0_1_1, n4 and discharging atoms sum(n14, n16) = all_0_1_1, sum(n14, n16) = n4, yields:
% 55.13/20.98 | (1741) all_0_1_1 = n4
% 55.13/20.98 |
% 55.13/20.98 | From (1407)(1405) and (590) follows:
% 55.13/20.98 | (1409) sum(n7, n7) = all_0_3_3
% 55.13/20.98 |
% 55.13/20.98 | From (1741) and (7311) follows:
% 55.13/20.98 | (7360) sum(n10, n4) = all_0_0_0
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (690) with n10, n4, all_0_0_0, n14 and discharging atoms sum(n10, n4) = all_0_0_0, sum(n10, n4) = n14, yields:
% 55.13/20.98 | (1177) all_0_0_0 = n14
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 55.13/20.98 | (1176) all_0_3_3 = n14
% 55.13/20.98 |
% 55.13/20.98 | Equations (1177,1176) can reduce 679 to:
% 55.13/20.98 | (1106) $false
% 55.13/20.98 |
% 55.13/20.98 |-The branch is then unsatisfiable
% 55.13/20.98 |-Branch two:
% 55.13/20.98 | (1748) ~ (all_0_10_10 = n15)
% 55.13/20.98 | (1749) 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
% 55.13/20.98 |
% 55.13/20.98 +-Applying beta-rule and splitting (1749), into two cases.
% 55.13/20.98 |-Branch one:
% 55.13/20.98 | (1750) all_0_10_10 = n14
% 55.13/20.98 |
% 55.13/20.98 | From (1750) and (292) follows:
% 55.13/20.98 | (1751) pred(n14) = all_0_6_6
% 55.13/20.98 |
% 55.13/20.98 | From (1750) and (760) follows:
% 55.13/20.98 | (1752) succ(n14) = all_0_8_8
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (500) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 55.13/20.98 | (1753) all_0_6_6 = n13
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (617) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 55.13/20.98 | (1754) all_0_8_8 = n15
% 55.13/20.98 |
% 55.13/20.98 | From (1753)(1754) and (411) follows:
% 55.13/20.98 | (1755) sum(n13, n15) = all_0_1_1
% 55.13/20.98 |
% 55.13/20.98 | From (1753) and (7307) follows:
% 55.13/20.98 | (7372) sum(n13, n19) = all_0_4_4
% 55.13/20.98 |
% 55.13/20.98 | From (1754) and (7309) follows:
% 55.13/20.98 | (7373) sum(n17, n15) = all_0_7_7
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (690) with n17, n15, all_0_7_7, n6 and discharging atoms sum(n17, n15) = all_0_7_7, sum(n17, n15) = n6, yields:
% 55.13/20.98 | (1425) all_0_7_7 = n6
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (690) with n13, n19, all_0_4_4, n6 and discharging atoms sum(n13, n19) = all_0_4_4, sum(n13, n19) = n6, yields:
% 55.13/20.98 | (1423) all_0_4_4 = n6
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (690) with n13, n15, all_0_1_1, n2 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n2, yields:
% 55.13/20.98 | (1759) all_0_1_1 = n2
% 55.13/20.98 |
% 55.13/20.98 | From (1425)(1423) and (590) follows:
% 55.13/20.98 | (1427) sum(n6, n6) = all_0_3_3
% 55.13/20.98 |
% 55.13/20.98 | From (1759) and (7311) follows:
% 55.13/20.98 | (7378) sum(n10, n2) = all_0_0_0
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (690) with n10, n2, all_0_0_0, n12 and discharging atoms sum(n10, n2) = all_0_0_0, sum(n10, n2) = n12, yields:
% 55.13/20.98 | (1195) all_0_0_0 = n12
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 55.13/20.98 | (1194) all_0_3_3 = n12
% 55.13/20.98 |
% 55.13/20.98 | Equations (1195,1194) can reduce 679 to:
% 55.13/20.98 | (1106) $false
% 55.13/20.98 |
% 55.13/20.98 |-The branch is then unsatisfiable
% 55.13/20.98 |-Branch two:
% 55.13/20.98 | (1766) ~ (all_0_10_10 = n14)
% 55.13/20.98 | (1767) 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
% 55.13/20.98 |
% 55.13/20.98 +-Applying beta-rule and splitting (1767), into two cases.
% 55.13/20.98 |-Branch one:
% 55.13/20.98 | (1768) all_0_10_10 = n13
% 55.13/20.98 |
% 55.13/20.98 | From (1768) and (292) follows:
% 55.13/20.98 | (1769) pred(n13) = all_0_6_6
% 55.13/20.98 |
% 55.13/20.98 | From (1768) and (760) follows:
% 55.13/20.98 | (1770) succ(n13) = all_0_8_8
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (500) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 55.13/20.98 | (1771) all_0_6_6 = n12
% 55.13/20.98 |
% 55.13/20.98 | Instantiating formula (617) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 55.13/20.98 | (1772) all_0_8_8 = n14
% 55.13/20.98 |
% 55.13/20.98 | From (1771)(1772) and (411) follows:
% 55.13/20.98 | (1773) sum(n12, n14) = all_0_1_1
% 55.13/20.98 |
% 55.13/20.98 | From (1771) and (7307) follows:
% 55.13/20.98 | (7390) sum(n12, n19) = all_0_4_4
% 55.13/20.98 |
% 55.13/20.98 | From (1772) and (7309) follows:
% 55.13/20.99 | (7391) sum(n17, n14) = all_0_7_7
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n17, n14, all_0_7_7, n5 and discharging atoms sum(n17, n14) = all_0_7_7, sum(n17, n14) = n5, yields:
% 55.13/20.99 | (1443) all_0_7_7 = n5
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n12, n19, all_0_4_4, n5 and discharging atoms sum(n12, n19) = all_0_4_4, sum(n12, n19) = n5, yields:
% 55.13/20.99 | (1441) all_0_4_4 = n5
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n12, n14, all_0_1_1, n0 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n0, yields:
% 55.13/20.99 | (1777) all_0_1_1 = n0
% 55.13/20.99 |
% 55.13/20.99 | From (1443)(1441) and (590) follows:
% 55.13/20.99 | (1445) sum(n5, n5) = all_0_3_3
% 55.13/20.99 |
% 55.13/20.99 | From (1777) and (7311) follows:
% 55.13/20.99 | (7396) sum(n10, n0) = all_0_0_0
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n10, n0, all_0_0_0, n10 and discharging atoms sum(n10, n0) = all_0_0_0, sum(n10, n0) = n10, yields:
% 55.13/20.99 | (1213) all_0_0_0 = n10
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 55.13/20.99 | (1212) all_0_3_3 = n10
% 55.13/20.99 |
% 55.13/20.99 | Equations (1213,1212) can reduce 679 to:
% 55.13/20.99 | (1106) $false
% 55.13/20.99 |
% 55.13/20.99 |-The branch is then unsatisfiable
% 55.13/20.99 |-Branch two:
% 55.13/20.99 | (1784) ~ (all_0_10_10 = n13)
% 55.13/20.99 | (1785) 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
% 55.13/20.99 |
% 55.13/20.99 +-Applying beta-rule and splitting (1785), into two cases.
% 55.13/20.99 |-Branch one:
% 55.13/20.99 | (1786) all_0_10_10 = n12
% 55.13/20.99 |
% 55.13/20.99 | From (1786) and (292) follows:
% 55.13/20.99 | (1787) pred(n12) = all_0_6_6
% 55.13/20.99 |
% 55.13/20.99 | From (1786) and (760) follows:
% 55.13/20.99 | (1788) succ(n12) = all_0_8_8
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (500) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 55.13/20.99 | (1789) all_0_6_6 = n11
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (617) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 55.13/20.99 | (1790) all_0_8_8 = n13
% 55.13/20.99 |
% 55.13/20.99 | From (1789)(1790) and (411) follows:
% 55.13/20.99 | (1791) sum(n11, n13) = all_0_1_1
% 55.13/20.99 |
% 55.13/20.99 | From (1789) and (7307) follows:
% 55.13/20.99 | (7408) sum(n11, n19) = all_0_4_4
% 55.13/20.99 |
% 55.13/20.99 | From (1790) and (7309) follows:
% 55.13/20.99 | (7409) sum(n17, n13) = all_0_7_7
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n17, n13, all_0_7_7, n4 and discharging atoms sum(n17, n13) = all_0_7_7, sum(n17, n13) = n4, yields:
% 55.13/20.99 | (1461) all_0_7_7 = n4
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n11, n19, all_0_4_4, n4 and discharging atoms sum(n11, n19) = all_0_4_4, sum(n11, n19) = n4, yields:
% 55.13/20.99 | (1459) all_0_4_4 = n4
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n11, n13, all_0_1_1, n24 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n24, yields:
% 55.13/20.99 | (1081) all_0_1_1 = n24
% 55.13/20.99 |
% 55.13/20.99 | From (1461)(1459) and (590) follows:
% 55.13/20.99 | (1463) sum(n4, n4) = all_0_3_3
% 55.13/20.99 |
% 55.13/20.99 | From (1081) and (7311) follows:
% 55.13/20.99 | (1228) sum(n10, n24) = all_0_0_0
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n10, n24, all_0_0_0, n8 and discharging atoms sum(n10, n24) = all_0_0_0, sum(n10, n24) = n8, yields:
% 55.13/20.99 | (1231) all_0_0_0 = n8
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 55.13/20.99 | (1230) all_0_3_3 = n8
% 55.13/20.99 |
% 55.13/20.99 | Equations (1231,1230) can reduce 679 to:
% 55.13/20.99 | (1106) $false
% 55.13/20.99 |
% 55.13/20.99 |-The branch is then unsatisfiable
% 55.13/20.99 |-Branch two:
% 55.13/20.99 | (1802) ~ (all_0_10_10 = n12)
% 55.13/20.99 | (1803) 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
% 55.13/20.99 |
% 55.13/20.99 +-Applying beta-rule and splitting (1803), into two cases.
% 55.13/20.99 |-Branch one:
% 55.13/20.99 | (1804) all_0_10_10 = n11
% 55.13/20.99 |
% 55.13/20.99 | From (1804) and (292) follows:
% 55.13/20.99 | (1805) pred(n11) = all_0_6_6
% 55.13/20.99 |
% 55.13/20.99 | From (1804) and (760) follows:
% 55.13/20.99 | (1806) succ(n11) = all_0_8_8
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (500) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 55.13/20.99 | (1807) all_0_6_6 = n10
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (617) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 55.13/20.99 | (1808) all_0_8_8 = n12
% 55.13/20.99 |
% 55.13/20.99 | From (1807)(1808) and (411) follows:
% 55.13/20.99 | (1809) sum(n10, n12) = all_0_1_1
% 55.13/20.99 |
% 55.13/20.99 | From (1807) and (7307) follows:
% 55.13/20.99 | (7426) sum(n10, n19) = all_0_4_4
% 55.13/20.99 |
% 55.13/20.99 | From (1808) and (7309) follows:
% 55.13/20.99 | (7427) sum(n17, n12) = all_0_7_7
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n17, n12, all_0_7_7, n3 and discharging atoms sum(n17, n12) = all_0_7_7, sum(n17, n12) = n3, yields:
% 55.13/20.99 | (1479) all_0_7_7 = n3
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n10, n19, all_0_4_4, n3 and discharging atoms sum(n10, n19) = all_0_4_4, sum(n10, n19) = n3, yields:
% 55.13/20.99 | (1477) all_0_4_4 = n3
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n10, n12, all_0_1_1, n22 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n22, yields:
% 55.13/20.99 | (1579) all_0_1_1 = n22
% 55.13/20.99 |
% 55.13/20.99 | From (1479)(1477) and (590) follows:
% 55.13/20.99 | (1481) sum(n3, n3) = all_0_3_3
% 55.13/20.99 |
% 55.13/20.99 | From (1579) and (7311) follows:
% 55.13/20.99 | (2160) sum(n10, n22) = all_0_0_0
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n10, n22, all_0_0_0, n6 and discharging atoms sum(n10, n22) = all_0_0_0, sum(n10, n22) = n6, yields:
% 55.13/20.99 | (1249) all_0_0_0 = n6
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 55.13/20.99 | (1248) all_0_3_3 = n6
% 55.13/20.99 |
% 55.13/20.99 | Equations (1249,1248) can reduce 679 to:
% 55.13/20.99 | (1106) $false
% 55.13/20.99 |
% 55.13/20.99 |-The branch is then unsatisfiable
% 55.13/20.99 |-Branch two:
% 55.13/20.99 | (1820) ~ (all_0_10_10 = n11)
% 55.13/20.99 | (1821) 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
% 55.13/20.99 |
% 55.13/20.99 +-Applying beta-rule and splitting (1821), into two cases.
% 55.13/20.99 |-Branch one:
% 55.13/20.99 | (1822) all_0_10_10 = n10
% 55.13/20.99 |
% 55.13/20.99 | From (1822) and (292) follows:
% 55.13/20.99 | (1823) pred(n10) = all_0_6_6
% 55.13/20.99 |
% 55.13/20.99 | From (1822) and (760) follows:
% 55.13/20.99 | (1824) succ(n10) = all_0_8_8
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (500) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 55.13/20.99 | (1825) all_0_6_6 = n9
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (617) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 55.13/20.99 | (1826) all_0_8_8 = n11
% 55.13/20.99 |
% 55.13/20.99 | From (1825)(1826) and (411) follows:
% 55.13/20.99 | (1827) sum(n9, n11) = all_0_1_1
% 55.13/20.99 |
% 55.13/20.99 | From (1825) and (7307) follows:
% 55.13/20.99 | (7444) sum(n9, n19) = all_0_4_4
% 55.13/20.99 |
% 55.13/20.99 | From (1826) and (7309) follows:
% 55.13/20.99 | (7445) sum(n17, n11) = all_0_7_7
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n17, n11, all_0_7_7, n2 and discharging atoms sum(n17, n11) = all_0_7_7, sum(n17, n11) = n2, yields:
% 55.13/20.99 | (1497) all_0_7_7 = n2
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n9, n19, all_0_4_4, n2 and discharging atoms sum(n9, n19) = all_0_4_4, sum(n9, n19) = n2, yields:
% 55.13/20.99 | (1495) all_0_4_4 = n2
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 55.13/20.99 | (1597) all_0_1_1 = n20
% 55.13/20.99 |
% 55.13/20.99 | From (1497)(1495) and (590) follows:
% 55.13/20.99 | (1499) sum(n2, n2) = all_0_3_3
% 55.13/20.99 |
% 55.13/20.99 | From (1597) and (7311) follows:
% 55.13/20.99 | (3052) sum(n10, n20) = all_0_0_0
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n10, n20, all_0_0_0, n4 and discharging atoms sum(n10, n20) = all_0_0_0, sum(n10, n20) = n4, yields:
% 55.13/20.99 | (1267) all_0_0_0 = n4
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 55.13/20.99 | (1266) all_0_3_3 = n4
% 55.13/20.99 |
% 55.13/20.99 | Equations (1267,1266) can reduce 679 to:
% 55.13/20.99 | (1106) $false
% 55.13/20.99 |
% 55.13/20.99 |-The branch is then unsatisfiable
% 55.13/20.99 |-Branch two:
% 55.13/20.99 | (1838) ~ (all_0_10_10 = n10)
% 55.13/20.99 | (1839) 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
% 55.13/20.99 |
% 55.13/20.99 +-Applying beta-rule and splitting (1839), into two cases.
% 55.13/20.99 |-Branch one:
% 55.13/20.99 | (1840) all_0_10_10 = n9
% 55.13/20.99 |
% 55.13/20.99 | From (1840) and (292) follows:
% 55.13/20.99 | (1841) pred(n9) = all_0_6_6
% 55.13/20.99 |
% 55.13/20.99 | From (1840) and (760) follows:
% 55.13/20.99 | (1842) succ(n9) = all_0_8_8
% 55.13/20.99 |
% 55.13/20.99 | Instantiating formula (500) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 55.13/20.99 | (1843) all_0_6_6 = n8
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (617) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 55.13/21.00 | (1844) all_0_8_8 = n10
% 55.13/21.00 |
% 55.13/21.00 | From (1843)(1844) and (411) follows:
% 55.13/21.00 | (1845) sum(n8, n10) = all_0_1_1
% 55.13/21.00 |
% 55.13/21.00 | From (1843) and (7307) follows:
% 55.13/21.00 | (7462) sum(n8, n19) = all_0_4_4
% 55.13/21.00 |
% 55.13/21.00 | From (1844) and (7309) follows:
% 55.13/21.00 | (7463) sum(n17, n10) = all_0_7_7
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (690) with n17, n10, all_0_7_7, n1 and discharging atoms sum(n17, n10) = all_0_7_7, sum(n17, n10) = n1, yields:
% 55.13/21.00 | (1515) all_0_7_7 = n1
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (690) with n8, n19, all_0_4_4, n1 and discharging atoms sum(n8, n19) = all_0_4_4, sum(n8, n19) = n1, yields:
% 55.13/21.00 | (1513) all_0_4_4 = n1
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (690) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 55.13/21.00 | (1615) all_0_1_1 = n18
% 55.13/21.00 |
% 55.13/21.00 | From (1515)(1513) and (590) follows:
% 55.13/21.00 | (1517) sum(n1, n1) = all_0_3_3
% 55.13/21.00 |
% 55.13/21.00 | From (1615) and (7311) follows:
% 55.13/21.00 | (3908) sum(n10, n18) = all_0_0_0
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (690) with n10, n18, all_0_0_0, n2 and discharging atoms sum(n10, n18) = all_0_0_0, sum(n10, n18) = n2, yields:
% 55.13/21.00 | (1285) all_0_0_0 = n2
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 55.13/21.00 | (1284) all_0_3_3 = n2
% 55.13/21.00 |
% 55.13/21.00 | Equations (1285,1284) can reduce 679 to:
% 55.13/21.00 | (1106) $false
% 55.13/21.00 |
% 55.13/21.00 |-The branch is then unsatisfiable
% 55.13/21.00 |-Branch two:
% 55.13/21.00 | (1856) ~ (all_0_10_10 = n9)
% 55.13/21.00 | (1857) 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
% 55.13/21.00 |
% 55.13/21.00 +-Applying beta-rule and splitting (1857), into two cases.
% 55.13/21.00 |-Branch one:
% 55.13/21.00 | (1858) all_0_10_10 = n8
% 55.13/21.00 |
% 55.13/21.00 | From (1858) and (292) follows:
% 55.13/21.00 | (1859) pred(n8) = all_0_6_6
% 55.13/21.00 |
% 55.13/21.00 | From (1858) and (760) follows:
% 55.13/21.00 | (1860) succ(n8) = all_0_8_8
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 55.13/21.00 | (1861) all_0_6_6 = n7
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 55.13/21.00 | (1862) all_0_8_8 = n9
% 55.13/21.00 |
% 55.13/21.00 | From (1861)(1862) and (411) follows:
% 55.13/21.00 | (1863) sum(n7, n9) = all_0_1_1
% 55.13/21.00 |
% 55.13/21.00 | From (1861) and (7307) follows:
% 55.13/21.00 | (7480) sum(n7, n19) = all_0_4_4
% 55.13/21.00 |
% 55.13/21.00 | From (1862) and (7309) follows:
% 55.13/21.00 | (7481) sum(n17, n9) = all_0_7_7
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (690) with n17, n9, all_0_7_7, n0 and discharging atoms sum(n17, n9) = all_0_7_7, sum(n17, n9) = n0, yields:
% 55.13/21.00 | (1533) all_0_7_7 = n0
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (690) with n7, n19, all_0_4_4, n0 and discharging atoms sum(n7, n19) = all_0_4_4, sum(n7, n19) = n0, yields:
% 55.13/21.00 | (1531) all_0_4_4 = n0
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 55.13/21.00 | (1633) all_0_1_1 = n16
% 55.13/21.00 |
% 55.13/21.00 | From (1533)(1531) and (590) follows:
% 55.13/21.00 | (1535) sum(n0, n0) = all_0_3_3
% 55.13/21.00 |
% 55.13/21.00 | From (1633) and (7311) follows:
% 55.13/21.00 | (4728) sum(n10, n16) = all_0_0_0
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (690) with n10, n16, all_0_0_0, n0 and discharging atoms sum(n10, n16) = all_0_0_0, sum(n10, n16) = n0, yields:
% 55.13/21.00 | (1303) all_0_0_0 = n0
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 55.13/21.00 | (1302) all_0_3_3 = n0
% 55.13/21.00 |
% 55.13/21.00 | Equations (1303,1302) can reduce 679 to:
% 55.13/21.00 | (1106) $false
% 55.13/21.00 |
% 55.13/21.00 |-The branch is then unsatisfiable
% 55.13/21.00 |-Branch two:
% 55.13/21.00 | (1874) ~ (all_0_10_10 = n8)
% 55.13/21.00 | (1875) 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
% 55.13/21.00 |
% 55.13/21.00 +-Applying beta-rule and splitting (1875), into two cases.
% 55.13/21.00 |-Branch one:
% 55.13/21.00 | (1876) all_0_10_10 = n7
% 55.13/21.00 |
% 55.13/21.00 | From (1876) and (292) follows:
% 55.13/21.00 | (1877) pred(n7) = all_0_6_6
% 55.13/21.00 |
% 55.13/21.00 | From (1876) and (760) follows:
% 55.13/21.00 | (1878) succ(n7) = all_0_8_8
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 55.13/21.00 | (1879) all_0_6_6 = n6
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 55.13/21.00 | (1880) all_0_8_8 = n8
% 55.13/21.00 |
% 55.13/21.00 | From (1879)(1880) and (411) follows:
% 55.13/21.00 | (1881) sum(n6, n8) = all_0_1_1
% 55.13/21.00 |
% 55.13/21.00 | From (1879) and (7307) follows:
% 55.13/21.00 | (7498) sum(n6, n19) = all_0_4_4
% 55.13/21.00 |
% 55.13/21.00 | From (1880) and (7309) follows:
% 55.13/21.00 | (7499) sum(n17, n8) = all_0_7_7
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (690) with n17, n8, all_0_7_7, n25 and discharging atoms sum(n17, n8) = all_0_7_7, sum(n17, n8) = n25, yields:
% 55.13/21.00 | (1550) all_0_7_7 = n25
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (690) with n6, n19, all_0_4_4, n25 and discharging atoms sum(n6, n19) = all_0_4_4, sum(n6, n19) = n25, yields:
% 55.13/21.00 | (1551) all_0_4_4 = n25
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 55.13/21.00 | (1651) all_0_1_1 = n14
% 55.13/21.00 |
% 55.13/21.00 | From (1550)(1551) and (590) follows:
% 55.13/21.00 | (1553) sum(n25, n25) = all_0_3_3
% 55.13/21.00 |
% 55.13/21.00 | From (1651) and (7311) follows:
% 55.13/21.00 | (5512) sum(n10, n14) = all_0_0_0
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 55.13/21.00 | (1320) all_0_3_3 = n24
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (690) with n10, n14, all_0_0_0, n24 and discharging atoms sum(n10, n14) = all_0_0_0, sum(n10, n14) = n24, yields:
% 55.13/21.00 | (1321) all_0_0_0 = n24
% 55.13/21.00 |
% 55.13/21.00 | Equations (1321,1320) can reduce 679 to:
% 55.13/21.00 | (1106) $false
% 55.13/21.00 |
% 55.13/21.00 |-The branch is then unsatisfiable
% 55.13/21.00 |-Branch two:
% 55.13/21.00 | (1892) ~ (all_0_10_10 = n7)
% 55.13/21.00 | (1893) 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
% 55.13/21.00 |
% 55.13/21.00 +-Applying beta-rule and splitting (1893), into two cases.
% 55.13/21.00 |-Branch one:
% 55.13/21.00 | (1894) all_0_10_10 = n6
% 55.13/21.00 |
% 55.13/21.00 | From (1894) and (292) follows:
% 55.13/21.00 | (1895) pred(n6) = all_0_6_6
% 55.13/21.00 |
% 55.13/21.00 | From (1894) and (760) follows:
% 55.13/21.00 | (1896) succ(n6) = all_0_8_8
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 55.13/21.00 | (1897) all_0_6_6 = n5
% 55.13/21.00 |
% 55.13/21.00 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 55.13/21.00 | (1898) all_0_8_8 = n7
% 55.13/21.00 |
% 55.13/21.00 | From (1897)(1898) and (411) follows:
% 55.13/21.00 | (1899) sum(n5, n7) = all_0_1_1
% 55.13/21.00 |
% 55.13/21.00 | From (1897) and (7307) follows:
% 55.13/21.00 | (7516) sum(n5, n19) = all_0_4_4
% 55.13/21.00 |
% 55.13/21.00 | From (1898) and (7309) follows:
% 55.13/21.01 | (7517) sum(n17, n7) = all_0_7_7
% 55.13/21.01 |
% 55.13/21.01 | Instantiating formula (690) with n17, n7, all_0_7_7, n24 and discharging atoms sum(n17, n7) = all_0_7_7, sum(n17, n7) = n24, yields:
% 55.13/21.01 | (1097) all_0_7_7 = n24
% 55.13/21.01 |
% 55.13/21.01 | Instantiating formula (690) with n5, n19, all_0_4_4, n24 and discharging atoms sum(n5, n19) = all_0_4_4, sum(n5, n19) = n24, yields:
% 55.13/21.01 | (1096) all_0_4_4 = n24
% 55.13/21.01 |
% 55.13/21.01 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 55.13/21.01 | (1669) all_0_1_1 = n12
% 55.13/21.01 |
% 55.13/21.01 | From (1097)(1096) and (590) follows:
% 55.13/21.01 | (1101) sum(n24, n24) = all_0_3_3
% 55.13/21.01 |
% 55.13/21.01 | From (1669) and (7311) follows:
% 55.13/21.01 | (6260) sum(n10, n12) = all_0_0_0
% 55.13/21.01 |
% 55.13/21.01 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 55.25/21.01 | (1104) all_0_3_3 = n22
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (690) with n10, n12, all_0_0_0, n22 and discharging atoms sum(n10, n12) = all_0_0_0, sum(n10, n12) = n22, yields:
% 55.25/21.01 | (1102) all_0_0_0 = n22
% 55.25/21.01 |
% 55.25/21.01 | Equations (1102,1104) can reduce 679 to:
% 55.25/21.01 | (1106) $false
% 55.25/21.01 |
% 55.25/21.01 |-The branch is then unsatisfiable
% 55.25/21.01 |-Branch two:
% 55.25/21.01 | (1910) ~ (all_0_10_10 = n6)
% 55.25/21.01 | (1911) 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
% 55.25/21.01 |
% 55.25/21.01 +-Applying beta-rule and splitting (1911), into two cases.
% 55.25/21.01 |-Branch one:
% 55.25/21.01 | (1912) all_0_10_10 = n5
% 55.25/21.01 |
% 55.25/21.01 | From (1912) and (292) follows:
% 55.25/21.01 | (1913) pred(n5) = all_0_6_6
% 55.25/21.01 |
% 55.25/21.01 | From (1912) and (760) follows:
% 55.25/21.01 | (1914) succ(n5) = all_0_8_8
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 55.25/21.01 | (1915) all_0_6_6 = n4
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 55.25/21.01 | (1916) all_0_8_8 = n6
% 55.25/21.01 |
% 55.25/21.01 | From (1915)(1916) and (411) follows:
% 55.25/21.01 | (1917) sum(n4, n6) = all_0_1_1
% 55.25/21.01 |
% 55.25/21.01 | From (1915) and (7307) follows:
% 55.25/21.01 | (7534) sum(n4, n19) = all_0_4_4
% 55.25/21.01 |
% 55.25/21.01 | From (1916) and (7309) follows:
% 55.25/21.01 | (7535) sum(n17, n6) = all_0_7_7
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (690) with n17, n6, all_0_7_7, n23 and discharging atoms sum(n17, n6) = all_0_7_7, sum(n17, n6) = n23, yields:
% 55.25/21.01 | (1119) all_0_7_7 = n23
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (690) with n4, n19, all_0_4_4, n23 and discharging atoms sum(n4, n19) = all_0_4_4, sum(n4, n19) = n23, yields:
% 55.25/21.01 | (1117) all_0_4_4 = n23
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 55.25/21.01 | (1687) all_0_1_1 = n10
% 55.25/21.01 |
% 55.25/21.01 | From (1119)(1117) and (590) follows:
% 55.25/21.01 | (1121) sum(n23, n23) = all_0_3_3
% 55.25/21.01 |
% 55.25/21.01 | From (1687) and (7311) follows:
% 55.25/21.01 | (6970) sum(n10, n10) = all_0_0_0
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 55.25/21.01 | (1122) all_0_3_3 = n20
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (690) with n10, n10, all_0_0_0, n20 and discharging atoms sum(n10, n10) = all_0_0_0, sum(n10, n10) = n20, yields:
% 55.25/21.01 | (1123) all_0_0_0 = n20
% 55.25/21.01 |
% 55.25/21.01 | Equations (1123,1122) can reduce 679 to:
% 55.25/21.01 | (1106) $false
% 55.25/21.01 |
% 55.25/21.01 |-The branch is then unsatisfiable
% 55.25/21.01 |-Branch two:
% 55.25/21.01 | (1928) ~ (all_0_10_10 = n5)
% 55.25/21.01 | (1929) 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
% 55.25/21.01 |
% 55.25/21.01 +-Applying beta-rule and splitting (1929), into two cases.
% 55.25/21.01 |-Branch one:
% 55.25/21.01 | (1930) all_0_10_10 = n4
% 55.25/21.01 |
% 55.25/21.01 | From (1930) and (292) follows:
% 55.25/21.01 | (1931) pred(n4) = all_0_6_6
% 55.25/21.01 |
% 55.25/21.01 | From (1930) and (760) follows:
% 55.25/21.01 | (1932) succ(n4) = all_0_8_8
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 55.25/21.01 | (1933) all_0_6_6 = n3
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 55.25/21.01 | (1934) all_0_8_8 = n5
% 55.25/21.01 |
% 55.25/21.01 | From (1933)(1934) and (411) follows:
% 55.25/21.01 | (1935) sum(n3, n5) = all_0_1_1
% 55.25/21.01 |
% 55.25/21.01 | From (1933) and (7307) follows:
% 55.25/21.01 | (7552) sum(n3, n19) = all_0_4_4
% 55.25/21.01 |
% 55.25/21.01 | From (1934) and (7309) follows:
% 55.25/21.01 | (7553) sum(n17, n5) = all_0_7_7
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (690) with n17, n5, all_0_7_7, n22 and discharging atoms sum(n17, n5) = all_0_7_7, sum(n17, n5) = n22, yields:
% 55.25/21.01 | (1137) all_0_7_7 = n22
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (690) with n3, n19, all_0_4_4, n22 and discharging atoms sum(n3, n19) = all_0_4_4, sum(n3, n19) = n22, yields:
% 55.25/21.01 | (1135) all_0_4_4 = n22
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 55.25/21.01 | (1705) all_0_1_1 = n8
% 55.25/21.01 |
% 55.25/21.01 | From (1137)(1135) and (590) follows:
% 55.25/21.01 | (1139) sum(n22, n22) = all_0_3_3
% 55.25/21.01 |
% 55.25/21.01 | From (1705) and (7311) follows:
% 55.25/21.01 | (7324) sum(n10, n8) = all_0_0_0
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 55.25/21.01 | (1140) all_0_3_3 = n18
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (690) with n10, n8, all_0_0_0, n18 and discharging atoms sum(n10, n8) = all_0_0_0, sum(n10, n8) = n18, yields:
% 55.25/21.01 | (1141) all_0_0_0 = n18
% 55.25/21.01 |
% 55.25/21.01 | Equations (1141,1140) can reduce 679 to:
% 55.25/21.01 | (1106) $false
% 55.25/21.01 |
% 55.25/21.01 |-The branch is then unsatisfiable
% 55.25/21.01 |-Branch two:
% 55.25/21.01 | (1946) ~ (all_0_10_10 = n4)
% 55.25/21.01 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 55.25/21.01 |
% 55.25/21.01 +-Applying beta-rule and splitting (1947), into two cases.
% 55.25/21.01 |-Branch one:
% 55.25/21.01 | (1948) all_0_10_10 = n3
% 55.25/21.01 |
% 55.25/21.01 | From (1948) and (292) follows:
% 55.25/21.01 | (1949) pred(n3) = all_0_6_6
% 55.25/21.01 |
% 55.25/21.01 | From (1948) and (760) follows:
% 55.25/21.01 | (1950) succ(n3) = all_0_8_8
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 55.25/21.01 | (1951) all_0_6_6 = n2
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 55.25/21.01 | (1952) all_0_8_8 = n4
% 55.25/21.01 |
% 55.25/21.01 | From (1951)(1952) and (411) follows:
% 55.25/21.01 | (1953) sum(n2, n4) = all_0_1_1
% 55.25/21.01 |
% 55.25/21.01 | From (1951) and (7307) follows:
% 55.25/21.01 | (7570) sum(n2, n19) = all_0_4_4
% 55.25/21.01 |
% 55.25/21.01 | From (1952) and (7309) follows:
% 55.25/21.01 | (7571) sum(n17, n4) = all_0_7_7
% 55.25/21.01 |
% 55.25/21.01 | Instantiating formula (690) with n17, n4, all_0_7_7, n21 and discharging atoms sum(n17, n4) = all_0_7_7, sum(n17, n4) = n21, yields:
% 55.25/21.02 | (1155) all_0_7_7 = n21
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (690) with n2, n19, all_0_4_4, n21 and discharging atoms sum(n2, n19) = all_0_4_4, sum(n2, n19) = n21, yields:
% 55.25/21.02 | (1153) all_0_4_4 = n21
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 55.25/21.02 | (1723) all_0_1_1 = n6
% 55.25/21.02 |
% 55.25/21.02 | From (1155)(1153) and (590) follows:
% 55.25/21.02 | (1157) sum(n21, n21) = all_0_3_3
% 55.25/21.02 |
% 55.25/21.02 | From (1723) and (7311) follows:
% 55.25/21.02 | (7342) sum(n10, n6) = all_0_0_0
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 55.25/21.02 | (1158) all_0_3_3 = n16
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (690) with n10, n6, all_0_0_0, n16 and discharging atoms sum(n10, n6) = all_0_0_0, sum(n10, n6) = n16, yields:
% 55.25/21.02 | (1159) all_0_0_0 = n16
% 55.25/21.02 |
% 55.25/21.02 | Equations (1159,1158) can reduce 679 to:
% 55.25/21.02 | (1106) $false
% 55.25/21.02 |
% 55.25/21.02 |-The branch is then unsatisfiable
% 55.25/21.02 |-Branch two:
% 55.25/21.02 | (1964) ~ (all_0_10_10 = n3)
% 55.25/21.02 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 55.25/21.02 |
% 55.25/21.02 +-Applying beta-rule and splitting (1965), into two cases.
% 55.25/21.02 |-Branch one:
% 55.25/21.02 | (1966) all_0_10_10 = n2
% 55.25/21.02 |
% 55.25/21.02 | From (1966) and (292) follows:
% 55.25/21.02 | (1967) pred(n2) = all_0_6_6
% 55.25/21.02 |
% 55.25/21.02 | From (1966) and (760) follows:
% 55.25/21.02 | (1968) succ(n2) = all_0_8_8
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 55.25/21.02 | (1969) all_0_6_6 = n1
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 55.25/21.02 | (1970) all_0_8_8 = n3
% 55.25/21.02 |
% 55.25/21.02 | From (1969)(1970) and (411) follows:
% 55.25/21.02 | (1971) sum(n1, n3) = all_0_1_1
% 55.25/21.02 |
% 55.25/21.02 | From (1969) and (7307) follows:
% 55.25/21.02 | (7588) sum(n1, n19) = all_0_4_4
% 55.25/21.02 |
% 55.25/21.02 | From (1970) and (7309) follows:
% 55.25/21.02 | (7589) sum(n17, n3) = all_0_7_7
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (690) with n17, n3, all_0_7_7, n20 and discharging atoms sum(n17, n3) = all_0_7_7, sum(n17, n3) = n20, yields:
% 55.25/21.02 | (1173) all_0_7_7 = n20
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (690) with n1, n19, all_0_4_4, n20 and discharging atoms sum(n1, n19) = all_0_4_4, sum(n1, n19) = n20, yields:
% 55.25/21.02 | (1171) all_0_4_4 = n20
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 55.25/21.02 | (1741) all_0_1_1 = n4
% 55.25/21.02 |
% 55.25/21.02 | From (1173)(1171) and (590) follows:
% 55.25/21.02 | (1175) sum(n20, n20) = all_0_3_3
% 55.25/21.02 |
% 55.25/21.02 | From (1741) and (7311) follows:
% 55.25/21.02 | (7360) sum(n10, n4) = all_0_0_0
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 55.25/21.02 | (1176) all_0_3_3 = n14
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (690) with n10, n4, all_0_0_0, n14 and discharging atoms sum(n10, n4) = all_0_0_0, sum(n10, n4) = n14, yields:
% 55.25/21.02 | (1177) all_0_0_0 = n14
% 55.25/21.02 |
% 55.25/21.02 | Equations (1177,1176) can reduce 679 to:
% 55.25/21.02 | (1106) $false
% 55.25/21.02 |
% 55.25/21.02 |-The branch is then unsatisfiable
% 55.25/21.02 |-Branch two:
% 55.25/21.02 | (1982) ~ (all_0_10_10 = n2)
% 55.25/21.02 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 55.25/21.02 |
% 55.25/21.02 +-Applying beta-rule and splitting (1983), into two cases.
% 55.25/21.02 |-Branch one:
% 55.25/21.02 | (1984) all_0_10_10 = n1
% 55.25/21.02 |
% 55.25/21.02 | From (1984) and (292) follows:
% 55.25/21.02 | (1985) pred(n1) = all_0_6_6
% 55.25/21.02 |
% 55.25/21.02 | From (1984) and (760) follows:
% 55.25/21.02 | (1986) succ(n1) = all_0_8_8
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 55.25/21.02 | (1987) all_0_6_6 = n0
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 55.25/21.02 | (1988) all_0_8_8 = n2
% 55.25/21.02 |
% 55.25/21.02 | From (1987)(1988) and (411) follows:
% 55.25/21.02 | (1989) sum(n0, n2) = all_0_1_1
% 55.25/21.02 |
% 55.25/21.02 | From (1987) and (7307) follows:
% 55.25/21.02 | (7606) sum(n0, n19) = all_0_4_4
% 55.25/21.02 |
% 55.25/21.02 | From (1988) and (7309) follows:
% 55.25/21.02 | (7607) sum(n17, n2) = all_0_7_7
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (690) with n17, n2, all_0_7_7, n19 and discharging atoms sum(n17, n2) = all_0_7_7, sum(n17, n2) = n19, yields:
% 55.25/21.02 | (1191) all_0_7_7 = n19
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (690) with n0, n19, all_0_4_4, n19 and discharging atoms sum(n0, n19) = all_0_4_4, sum(n0, n19) = n19, yields:
% 55.25/21.02 | (1189) all_0_4_4 = n19
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 55.25/21.02 | (1759) all_0_1_1 = n2
% 55.25/21.02 |
% 55.25/21.02 | From (1191)(1189) and (590) follows:
% 55.25/21.02 | (1193) sum(n19, n19) = all_0_3_3
% 55.25/21.02 |
% 55.25/21.02 | From (1759) and (7311) follows:
% 55.25/21.02 | (7378) sum(n10, n2) = all_0_0_0
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 55.25/21.02 | (1194) all_0_3_3 = n12
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (690) with n10, n2, all_0_0_0, n12 and discharging atoms sum(n10, n2) = all_0_0_0, sum(n10, n2) = n12, yields:
% 55.25/21.02 | (1195) all_0_0_0 = n12
% 55.25/21.02 |
% 55.25/21.02 | Equations (1195,1194) can reduce 679 to:
% 55.25/21.02 | (1106) $false
% 55.25/21.02 |
% 55.25/21.02 |-The branch is then unsatisfiable
% 55.25/21.02 |-Branch two:
% 55.25/21.02 | (2002) ~ (all_0_10_10 = n1)
% 55.25/21.02 | (2003) all_0_10_10 = n0
% 55.25/21.02 |
% 55.25/21.02 | From (2003) and (292) follows:
% 55.25/21.02 | (2004) pred(n0) = all_0_6_6
% 55.25/21.02 |
% 55.25/21.02 | From (2003) and (760) follows:
% 55.25/21.02 | (2005) succ(n0) = all_0_8_8
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 55.25/21.02 | (2006) all_0_6_6 = n25
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 55.25/21.02 | (2007) all_0_8_8 = n1
% 55.25/21.02 |
% 55.25/21.02 | From (2006)(2007) and (411) follows:
% 55.25/21.02 | (2008) sum(n25, n1) = all_0_1_1
% 55.25/21.02 |
% 55.25/21.02 | From (2006) and (7307) follows:
% 55.25/21.02 | (7623) sum(n25, n19) = all_0_4_4
% 55.25/21.02 |
% 55.25/21.02 | From (2007) and (7309) follows:
% 55.25/21.02 | (7624) sum(n17, n1) = all_0_7_7
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (690) with n25, n19, all_0_4_4, n18 and discharging atoms sum(n25, n19) = all_0_4_4, sum(n25, n19) = n18, yields:
% 55.25/21.02 | (1207) all_0_4_4 = n18
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 55.25/21.02 | (1777) all_0_1_1 = n0
% 55.25/21.02 |
% 55.25/21.02 | Instantiating formula (690) with n17, n1, all_0_7_7, n18 and discharging atoms sum(n17, n1) = all_0_7_7, sum(n17, n1) = n18, yields:
% 55.25/21.02 | (1209) all_0_7_7 = n18
% 55.25/21.02 |
% 55.25/21.02 | From (1209)(1207) and (590) follows:
% 55.25/21.02 | (1211) sum(n18, n18) = all_0_3_3
% 55.25/21.02 |
% 55.25/21.02 | From (1777) and (7311) follows:
% 55.25/21.03 | (7396) sum(n10, n0) = all_0_0_0
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 55.25/21.03 | (1212) all_0_3_3 = n10
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (690) with n10, n0, all_0_0_0, n10 and discharging atoms sum(n10, n0) = all_0_0_0, sum(n10, n0) = n10, yields:
% 55.25/21.03 | (1213) all_0_0_0 = n10
% 55.25/21.03 |
% 55.25/21.03 | Equations (1213,1212) can reduce 679 to:
% 55.25/21.03 | (1106) $false
% 55.25/21.03 |
% 55.25/21.03 |-The branch is then unsatisfiable
% 55.25/21.03 |-Branch two:
% 55.25/21.03 | (1233) ~ (all_0_11_11 = n18)
% 55.25/21.03 | (1234) 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
% 55.25/21.03 |
% 55.25/21.03 +-Applying beta-rule and splitting (1695), into two cases.
% 55.25/21.03 |-Branch one:
% 55.25/21.03 | (1696) all_0_10_10 = n17
% 55.25/21.03 |
% 55.25/21.03 | From (1696) and (292) follows:
% 55.25/21.03 | (1697) pred(n17) = all_0_6_6
% 55.25/21.03 |
% 55.25/21.03 | From (1696) and (760) follows:
% 55.25/21.03 | (1698) succ(n17) = all_0_8_8
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (500) with n17, all_0_6_6, n16 and discharging atoms pred(n17) = all_0_6_6, pred(n17) = n16, yields:
% 55.25/21.03 | (1699) all_0_6_6 = n16
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (617) with n17, all_0_8_8, n18 and discharging atoms succ(n17) = all_0_8_8, succ(n17) = n18, yields:
% 55.25/21.03 | (1700) all_0_8_8 = n18
% 55.25/21.03 |
% 55.25/21.03 | From (1699) and (1697) follows:
% 55.25/21.03 | (998) pred(n17) = n16
% 55.25/21.03 |
% 55.25/21.03 | From (1700) and (1698) follows:
% 55.25/21.03 | (914) succ(n17) = n18
% 55.25/21.03 |
% 55.25/21.03 | From (1699) and (541) follows:
% 55.25/21.03 | (7642) sum(n16, all_0_5_5) = all_0_4_4
% 55.25/21.03 |
% 55.25/21.03 | From (1699)(1700) and (411) follows:
% 55.25/21.03 | (1701) sum(n16, n18) = all_0_1_1
% 55.25/21.03 |
% 55.25/21.03 | From (1700) and (427) follows:
% 55.25/21.03 | (7644) sum(all_0_9_9, n18) = all_0_7_7
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (690) with n16, n18, all_0_1_1, n8 and discharging atoms sum(n16, n18) = all_0_1_1, sum(n16, n18) = n8, yields:
% 55.25/21.03 | (1705) all_0_1_1 = n8
% 55.25/21.03 |
% 55.25/21.03 | From (1705) and (630) follows:
% 55.25/21.03 | (7646) sum(all_0_2_2, n8) = all_0_0_0
% 55.25/21.03 |
% 55.25/21.03 | From (1705) and (1701) follows:
% 55.25/21.03 | (251) sum(n16, n18) = n8
% 55.25/21.03 |
% 55.25/21.03 +-Applying beta-rule and splitting (1234), into two cases.
% 55.25/21.03 |-Branch one:
% 55.25/21.03 | (1235) all_0_11_11 = n17
% 55.25/21.03 |
% 55.25/21.03 | From (1235) and (559) follows:
% 55.25/21.03 | (1236) pred(n17) = all_0_9_9
% 55.25/21.03 |
% 55.25/21.03 | From (1235) and (992) follows:
% 55.25/21.03 | (1237) succ(n17) = all_0_5_5
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (500) with n17, all_0_9_9, n16 and discharging atoms pred(n17) = all_0_9_9, pred(n17) = n16, yields:
% 55.25/21.03 | (1238) all_0_9_9 = n16
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (617) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 55.25/21.03 | (1239) all_0_5_5 = n18
% 55.25/21.03 |
% 55.25/21.03 | From (1238)(1239) and (538) follows:
% 55.25/21.03 | (1240) sum(n16, n18) = all_0_2_2
% 55.25/21.03 |
% 55.25/21.03 | From (1238) and (7644) follows:
% 55.25/21.03 | (7654) sum(n16, n18) = all_0_7_7
% 55.25/21.03 |
% 55.25/21.03 | From (1239) and (7642) follows:
% 55.25/21.03 | (7655) sum(n16, n18) = all_0_4_4
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (690) with n16, n18, all_0_2_2, n8 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = n8, yields:
% 55.25/21.03 | (1244) all_0_2_2 = n8
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (690) 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:
% 55.25/21.03 | (1093) all_0_2_2 = all_0_4_4
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (690) 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:
% 55.25/21.03 | (1094) all_0_2_2 = all_0_7_7
% 55.25/21.03 |
% 55.25/21.03 | Combining equations (1094,1093) yields a new equation:
% 55.25/21.03 | (1095) all_0_4_4 = all_0_7_7
% 55.25/21.03 |
% 55.25/21.03 | Combining equations (1244,1093) yields a new equation:
% 55.25/21.03 | (1387) all_0_4_4 = n8
% 55.25/21.03 |
% 55.25/21.03 | Combining equations (1387,1095) yields a new equation:
% 55.25/21.03 | (1389) all_0_7_7 = n8
% 55.25/21.03 |
% 55.25/21.03 | Combining equations (1389,1095) yields a new equation:
% 55.25/21.03 | (1387) all_0_4_4 = n8
% 55.25/21.03 |
% 55.25/21.03 | Combining equations (1387,1093) yields a new equation:
% 55.25/21.03 | (1244) all_0_2_2 = n8
% 55.25/21.03 |
% 55.25/21.03 | From (1244) and (7646) follows:
% 55.25/21.03 | (7664) sum(n8, n8) = all_0_0_0
% 55.25/21.03 |
% 55.25/21.03 | From (1389)(1387) and (590) follows:
% 55.25/21.03 | (1391) sum(n8, n8) = all_0_3_3
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (690) with n8, n8, all_0_0_0, n16 and discharging atoms sum(n8, n8) = all_0_0_0, sum(n8, n8) = n16, yields:
% 55.25/21.03 | (1159) all_0_0_0 = n16
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (690) 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:
% 55.25/21.03 | (1103) all_0_0_0 = all_0_3_3
% 55.25/21.03 |
% 55.25/21.03 | Combining equations (1159,1103) yields a new equation:
% 55.25/21.03 | (1158) all_0_3_3 = n16
% 55.25/21.03 |
% 55.25/21.03 | Combining equations (1158,1103) yields a new equation:
% 55.25/21.03 | (1159) all_0_0_0 = n16
% 55.25/21.03 |
% 55.25/21.03 | Equations (1159,1158) can reduce 679 to:
% 55.25/21.03 | (1106) $false
% 55.25/21.03 |
% 55.25/21.03 |-The branch is then unsatisfiable
% 55.25/21.03 |-Branch two:
% 55.25/21.03 | (1251) ~ (all_0_11_11 = n17)
% 55.25/21.03 | (1252) 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
% 55.25/21.03 |
% 55.25/21.03 +-Applying beta-rule and splitting (1252), into two cases.
% 55.25/21.03 |-Branch one:
% 55.25/21.03 | (1253) all_0_11_11 = n16
% 55.25/21.03 |
% 55.25/21.03 | From (1253) and (559) follows:
% 55.25/21.03 | (1254) pred(n16) = all_0_9_9
% 55.25/21.03 |
% 55.25/21.03 | From (1253) and (992) follows:
% 55.25/21.03 | (1255) succ(n16) = all_0_5_5
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (500) with n16, all_0_9_9, n15 and discharging atoms pred(n16) = all_0_9_9, pred(n16) = n15, yields:
% 55.25/21.03 | (1256) all_0_9_9 = n15
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (617) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 55.25/21.03 | (1257) all_0_5_5 = n17
% 55.25/21.03 |
% 55.25/21.03 | From (1256)(1257) and (538) follows:
% 55.25/21.03 | (1258) sum(n15, n17) = all_0_2_2
% 55.25/21.03 |
% 55.25/21.03 | From (1256) and (7644) follows:
% 55.25/21.03 | (7679) sum(n15, n18) = all_0_7_7
% 55.25/21.03 |
% 55.25/21.03 | From (1257) and (7642) follows:
% 55.25/21.03 | (7680) sum(n16, n17) = all_0_4_4
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (690) with n16, n17, all_0_4_4, n7 and discharging atoms sum(n16, n17) = all_0_4_4, sum(n16, n17) = n7, yields:
% 55.25/21.03 | (1405) all_0_4_4 = n7
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (690) with n15, n18, all_0_7_7, n7 and discharging atoms sum(n15, n18) = all_0_7_7, sum(n15, n18) = n7, yields:
% 55.25/21.03 | (1407) all_0_7_7 = n7
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (690) with n15, n17, all_0_2_2, n6 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n6, yields:
% 55.25/21.03 | (1262) all_0_2_2 = n6
% 55.25/21.03 |
% 55.25/21.03 | From (1262) and (7646) follows:
% 55.25/21.03 | (7684) sum(n6, n8) = all_0_0_0
% 55.25/21.03 |
% 55.25/21.03 | From (1407)(1405) and (590) follows:
% 55.25/21.03 | (1409) sum(n7, n7) = all_0_3_3
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 55.25/21.03 | (1176) all_0_3_3 = n14
% 55.25/21.03 |
% 55.25/21.03 | Instantiating formula (690) with n6, n8, all_0_0_0, n14 and discharging atoms sum(n6, n8) = all_0_0_0, sum(n6, n8) = n14, yields:
% 55.25/21.03 | (1177) all_0_0_0 = n14
% 55.25/21.03 |
% 55.25/21.03 | Equations (1177,1176) can reduce 679 to:
% 55.25/21.03 | (1106) $false
% 55.25/21.03 |
% 55.25/21.03 |-The branch is then unsatisfiable
% 55.25/21.03 |-Branch two:
% 55.25/21.03 | (1269) ~ (all_0_11_11 = n16)
% 55.25/21.03 | (1270) 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
% 55.25/21.03 |
% 55.25/21.03 +-Applying beta-rule and splitting (1270), into two cases.
% 55.25/21.03 |-Branch one:
% 55.25/21.03 | (1271) all_0_11_11 = n15
% 55.25/21.03 |
% 55.25/21.03 | From (1271) and (559) follows:
% 55.25/21.03 | (1272) pred(n15) = all_0_9_9
% 55.25/21.03 |
% 55.25/21.03 | From (1271) and (992) follows:
% 55.25/21.04 | (1273) succ(n15) = all_0_5_5
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (500) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 55.25/21.04 | (1274) all_0_9_9 = n14
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (617) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 55.25/21.04 | (1275) all_0_5_5 = n16
% 55.25/21.04 |
% 55.25/21.04 | From (1274)(1275) and (538) follows:
% 55.25/21.04 | (1276) sum(n14, n16) = all_0_2_2
% 55.25/21.04 |
% 55.25/21.04 | From (1274) and (7644) follows:
% 55.25/21.04 | (7697) sum(n14, n18) = all_0_7_7
% 55.25/21.04 |
% 55.25/21.04 | From (1275) and (7642) follows:
% 55.25/21.04 | (7698) sum(n16, n16) = all_0_4_4
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (690) with n16, n16, all_0_4_4, n6 and discharging atoms sum(n16, n16) = all_0_4_4, sum(n16, n16) = n6, yields:
% 55.25/21.04 | (1423) all_0_4_4 = n6
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (690) with n14, n18, all_0_7_7, n6 and discharging atoms sum(n14, n18) = all_0_7_7, sum(n14, n18) = n6, yields:
% 55.25/21.04 | (1425) all_0_7_7 = n6
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (690) with n14, n16, all_0_2_2, n4 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n4, yields:
% 55.25/21.04 | (1280) all_0_2_2 = n4
% 55.25/21.04 |
% 55.25/21.04 | From (1280) and (7646) follows:
% 55.25/21.04 | (7702) sum(n4, n8) = all_0_0_0
% 55.25/21.04 |
% 55.25/21.04 | From (1425)(1423) and (590) follows:
% 55.25/21.04 | (1427) sum(n6, n6) = all_0_3_3
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 55.25/21.04 | (1194) all_0_3_3 = n12
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (690) with n4, n8, all_0_0_0, n12 and discharging atoms sum(n4, n8) = all_0_0_0, sum(n4, n8) = n12, yields:
% 55.25/21.04 | (1195) all_0_0_0 = n12
% 55.25/21.04 |
% 55.25/21.04 | Equations (1195,1194) can reduce 679 to:
% 55.25/21.04 | (1106) $false
% 55.25/21.04 |
% 55.25/21.04 |-The branch is then unsatisfiable
% 55.25/21.04 |-Branch two:
% 55.25/21.04 | (1287) ~ (all_0_11_11 = n15)
% 55.25/21.04 | (1288) 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
% 55.25/21.04 |
% 55.25/21.04 +-Applying beta-rule and splitting (1288), into two cases.
% 55.25/21.04 |-Branch one:
% 55.25/21.04 | (1289) all_0_11_11 = n14
% 55.25/21.04 |
% 55.25/21.04 | From (1289) and (559) follows:
% 55.25/21.04 | (1290) pred(n14) = all_0_9_9
% 55.25/21.04 |
% 55.25/21.04 | From (1289) and (992) follows:
% 55.25/21.04 | (1291) succ(n14) = all_0_5_5
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (500) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 55.25/21.04 | (1292) all_0_9_9 = n13
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (617) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 55.25/21.04 | (1293) all_0_5_5 = n15
% 55.25/21.04 |
% 55.25/21.04 | From (1292)(1293) and (538) follows:
% 55.25/21.04 | (1294) sum(n13, n15) = all_0_2_2
% 55.25/21.04 |
% 55.25/21.04 | From (1292) and (7644) follows:
% 55.25/21.04 | (7715) sum(n13, n18) = all_0_7_7
% 55.25/21.04 |
% 55.25/21.04 | From (1293) and (7642) follows:
% 55.25/21.04 | (7716) sum(n16, n15) = all_0_4_4
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (690) with n16, n15, all_0_4_4, n5 and discharging atoms sum(n16, n15) = all_0_4_4, sum(n16, n15) = n5, yields:
% 55.25/21.04 | (1441) all_0_4_4 = n5
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (690) with n13, n18, all_0_7_7, n5 and discharging atoms sum(n13, n18) = all_0_7_7, sum(n13, n18) = n5, yields:
% 55.25/21.04 | (1443) all_0_7_7 = n5
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (690) with n13, n15, all_0_2_2, n2 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n2, yields:
% 55.25/21.04 | (1298) all_0_2_2 = n2
% 55.25/21.04 |
% 55.25/21.04 | From (1298) and (7646) follows:
% 55.25/21.04 | (7720) sum(n2, n8) = all_0_0_0
% 55.25/21.04 |
% 55.25/21.04 | From (1443)(1441) and (590) follows:
% 55.25/21.04 | (1445) sum(n5, n5) = all_0_3_3
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 55.25/21.04 | (1212) all_0_3_3 = n10
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (690) with n2, n8, all_0_0_0, n10 and discharging atoms sum(n2, n8) = all_0_0_0, sum(n2, n8) = n10, yields:
% 55.25/21.04 | (1213) all_0_0_0 = n10
% 55.25/21.04 |
% 55.25/21.04 | Equations (1213,1212) can reduce 679 to:
% 55.25/21.04 | (1106) $false
% 55.25/21.04 |
% 55.25/21.04 |-The branch is then unsatisfiable
% 55.25/21.04 |-Branch two:
% 55.25/21.04 | (1305) ~ (all_0_11_11 = n14)
% 55.25/21.04 | (1306) 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
% 55.25/21.04 |
% 55.25/21.04 +-Applying beta-rule and splitting (1306), into two cases.
% 55.25/21.04 |-Branch one:
% 55.25/21.04 | (1307) all_0_11_11 = n13
% 55.25/21.04 |
% 55.25/21.04 | From (1307) and (559) follows:
% 55.25/21.04 | (1308) pred(n13) = all_0_9_9
% 55.25/21.04 |
% 55.25/21.04 | From (1307) and (992) follows:
% 55.25/21.04 | (1309) succ(n13) = all_0_5_5
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (500) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 55.25/21.04 | (1310) all_0_9_9 = n12
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (617) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 55.25/21.04 | (1311) all_0_5_5 = n14
% 55.25/21.04 |
% 55.25/21.04 | From (1310)(1311) and (538) follows:
% 55.25/21.04 | (1312) sum(n12, n14) = all_0_2_2
% 55.25/21.04 |
% 55.25/21.04 | From (1310) and (7644) follows:
% 55.25/21.04 | (7733) sum(n12, n18) = all_0_7_7
% 55.25/21.04 |
% 55.25/21.04 | From (1311) and (7642) follows:
% 55.25/21.04 | (7734) sum(n16, n14) = all_0_4_4
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (690) with n16, n14, all_0_4_4, n4 and discharging atoms sum(n16, n14) = all_0_4_4, sum(n16, n14) = n4, yields:
% 55.25/21.04 | (1459) all_0_4_4 = n4
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (690) with n12, n18, all_0_7_7, n4 and discharging atoms sum(n12, n18) = all_0_7_7, sum(n12, n18) = n4, yields:
% 55.25/21.04 | (1461) all_0_7_7 = n4
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (690) with n12, n14, all_0_2_2, n0 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n0, yields:
% 55.25/21.04 | (1316) all_0_2_2 = n0
% 55.25/21.04 |
% 55.25/21.04 | From (1316) and (7646) follows:
% 55.25/21.04 | (7738) sum(n0, n8) = all_0_0_0
% 55.25/21.04 |
% 55.25/21.04 | From (1461)(1459) and (590) follows:
% 55.25/21.04 | (1463) sum(n4, n4) = all_0_3_3
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 55.25/21.04 | (1230) all_0_3_3 = n8
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (690) with n0, n8, all_0_0_0, n8 and discharging atoms sum(n0, n8) = all_0_0_0, sum(n0, n8) = n8, yields:
% 55.25/21.04 | (1231) all_0_0_0 = n8
% 55.25/21.04 |
% 55.25/21.04 | Equations (1231,1230) can reduce 679 to:
% 55.25/21.04 | (1106) $false
% 55.25/21.04 |
% 55.25/21.04 |-The branch is then unsatisfiable
% 55.25/21.04 |-Branch two:
% 55.25/21.04 | (1323) ~ (all_0_11_11 = n13)
% 55.25/21.04 | (1324) 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
% 55.25/21.04 |
% 55.25/21.04 +-Applying beta-rule and splitting (1324), into two cases.
% 55.25/21.04 |-Branch one:
% 55.25/21.04 | (1325) all_0_11_11 = n12
% 55.25/21.04 |
% 55.25/21.04 | From (1325) and (559) follows:
% 55.25/21.04 | (1326) pred(n12) = all_0_9_9
% 55.25/21.04 |
% 55.25/21.04 | From (1325) and (992) follows:
% 55.25/21.04 | (1327) succ(n12) = all_0_5_5
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (500) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 55.25/21.04 | (1328) all_0_9_9 = n11
% 55.25/21.04 |
% 55.25/21.04 | Instantiating formula (617) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 55.25/21.04 | (1329) all_0_5_5 = n13
% 55.25/21.04 |
% 55.25/21.04 | From (1328)(1329) and (538) follows:
% 55.25/21.04 | (1330) sum(n11, n13) = all_0_2_2
% 55.25/21.04 |
% 55.25/21.04 | From (1328) and (7644) follows:
% 55.25/21.05 | (7751) sum(n11, n18) = all_0_7_7
% 55.25/21.05 |
% 55.25/21.05 | From (1329) and (7642) follows:
% 55.25/21.05 | (7752) sum(n16, n13) = all_0_4_4
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n16, n13, all_0_4_4, n3 and discharging atoms sum(n16, n13) = all_0_4_4, sum(n16, n13) = n3, yields:
% 55.25/21.05 | (1477) all_0_4_4 = n3
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n11, n18, all_0_7_7, n3 and discharging atoms sum(n11, n18) = all_0_7_7, sum(n11, n18) = n3, yields:
% 55.25/21.05 | (1479) all_0_7_7 = n3
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n11, n13, all_0_2_2, n24 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n24, yields:
% 55.25/21.05 | (1092) all_0_2_2 = n24
% 55.25/21.05 |
% 55.25/21.05 | From (1092) and (7646) follows:
% 55.25/21.05 | (1708) sum(n24, n8) = all_0_0_0
% 55.25/21.05 |
% 55.25/21.05 | From (1479)(1477) and (590) follows:
% 55.25/21.05 | (1481) sum(n3, n3) = all_0_3_3
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n24, n8, all_0_0_0, n6 and discharging atoms sum(n24, n8) = all_0_0_0, sum(n24, n8) = n6, yields:
% 55.25/21.05 | (1249) all_0_0_0 = n6
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 55.25/21.05 | (1248) all_0_3_3 = n6
% 55.25/21.05 |
% 55.25/21.05 | Equations (1249,1248) can reduce 679 to:
% 55.25/21.05 | (1106) $false
% 55.25/21.05 |
% 55.25/21.05 |-The branch is then unsatisfiable
% 55.25/21.05 |-Branch two:
% 55.25/21.05 | (1341) ~ (all_0_11_11 = n12)
% 55.25/21.05 | (1342) 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
% 55.25/21.05 |
% 55.25/21.05 +-Applying beta-rule and splitting (1342), into two cases.
% 55.25/21.05 |-Branch one:
% 55.25/21.05 | (1343) all_0_11_11 = n11
% 55.25/21.05 |
% 55.25/21.05 | From (1343) and (559) follows:
% 55.25/21.05 | (1344) pred(n11) = all_0_9_9
% 55.25/21.05 |
% 55.25/21.05 | From (1343) and (992) follows:
% 55.25/21.05 | (1345) succ(n11) = all_0_5_5
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (500) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 55.25/21.05 | (1346) all_0_9_9 = n10
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (617) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 55.25/21.05 | (1347) all_0_5_5 = n12
% 55.25/21.05 |
% 55.25/21.05 | From (1346)(1347) and (538) follows:
% 55.25/21.05 | (1348) sum(n10, n12) = all_0_2_2
% 55.25/21.05 |
% 55.25/21.05 | From (1346) and (7644) follows:
% 55.25/21.05 | (7769) sum(n10, n18) = all_0_7_7
% 55.25/21.05 |
% 55.25/21.05 | From (1347) and (7642) follows:
% 55.25/21.05 | (7770) sum(n16, n12) = all_0_4_4
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n16, n12, all_0_4_4, n2 and discharging atoms sum(n16, n12) = all_0_4_4, sum(n16, n12) = n2, yields:
% 55.25/21.05 | (1495) all_0_4_4 = n2
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n10, n18, all_0_7_7, n2 and discharging atoms sum(n10, n18) = all_0_7_7, sum(n10, n18) = n2, yields:
% 55.25/21.05 | (1497) all_0_7_7 = n2
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n10, n12, all_0_2_2, n22 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n22, yields:
% 55.25/21.05 | (1118) all_0_2_2 = n22
% 55.25/21.05 |
% 55.25/21.05 | From (1118) and (7646) follows:
% 55.25/21.05 | (2620) sum(n22, n8) = all_0_0_0
% 55.25/21.05 |
% 55.25/21.05 | From (1497)(1495) and (590) follows:
% 55.25/21.05 | (1499) sum(n2, n2) = all_0_3_3
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n22, n8, all_0_0_0, n4 and discharging atoms sum(n22, n8) = all_0_0_0, sum(n22, n8) = n4, yields:
% 55.25/21.05 | (1267) all_0_0_0 = n4
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 55.25/21.05 | (1266) all_0_3_3 = n4
% 55.25/21.05 |
% 55.25/21.05 | Equations (1267,1266) can reduce 679 to:
% 55.25/21.05 | (1106) $false
% 55.25/21.05 |
% 55.25/21.05 |-The branch is then unsatisfiable
% 55.25/21.05 |-Branch two:
% 55.25/21.05 | (1359) ~ (all_0_11_11 = n11)
% 55.25/21.05 | (1360) 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
% 55.25/21.05 |
% 55.25/21.05 +-Applying beta-rule and splitting (1360), into two cases.
% 55.25/21.05 |-Branch one:
% 55.25/21.05 | (1361) all_0_11_11 = n10
% 55.25/21.05 |
% 55.25/21.05 | From (1361) and (559) follows:
% 55.25/21.05 | (1362) pred(n10) = all_0_9_9
% 55.25/21.05 |
% 55.25/21.05 | From (1361) and (992) follows:
% 55.25/21.05 | (1363) succ(n10) = all_0_5_5
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (500) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 55.25/21.05 | (1364) all_0_9_9 = n9
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (617) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 55.25/21.05 | (1365) all_0_5_5 = n11
% 55.25/21.05 |
% 55.25/21.05 | From (1364)(1365) and (538) follows:
% 55.25/21.05 | (1366) sum(n9, n11) = all_0_2_2
% 55.25/21.05 |
% 55.25/21.05 | From (1364) and (7644) follows:
% 55.25/21.05 | (7787) sum(n9, n18) = all_0_7_7
% 55.25/21.05 |
% 55.25/21.05 | From (1365) and (7642) follows:
% 55.25/21.05 | (7788) sum(n16, n11) = all_0_4_4
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n16, n11, all_0_4_4, n1 and discharging atoms sum(n16, n11) = all_0_4_4, sum(n16, n11) = n1, yields:
% 55.25/21.05 | (1513) all_0_4_4 = n1
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n9, n18, all_0_7_7, n1 and discharging atoms sum(n9, n18) = all_0_7_7, sum(n9, n18) = n1, yields:
% 55.25/21.05 | (1515) all_0_7_7 = n1
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 55.25/21.05 | (1136) all_0_2_2 = n20
% 55.25/21.05 |
% 55.25/21.05 | From (1136) and (7646) follows:
% 55.25/21.05 | (3494) sum(n20, n8) = all_0_0_0
% 55.25/21.05 |
% 55.25/21.05 | From (1515)(1513) and (590) follows:
% 55.25/21.05 | (1517) sum(n1, n1) = all_0_3_3
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n20, n8, all_0_0_0, n2 and discharging atoms sum(n20, n8) = all_0_0_0, sum(n20, n8) = n2, yields:
% 55.25/21.05 | (1285) all_0_0_0 = n2
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 55.25/21.05 | (1284) all_0_3_3 = n2
% 55.25/21.05 |
% 55.25/21.05 | Equations (1285,1284) can reduce 679 to:
% 55.25/21.05 | (1106) $false
% 55.25/21.05 |
% 55.25/21.05 |-The branch is then unsatisfiable
% 55.25/21.05 |-Branch two:
% 55.25/21.05 | (1377) ~ (all_0_11_11 = n10)
% 55.25/21.05 | (1378) 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
% 55.25/21.05 |
% 55.25/21.05 +-Applying beta-rule and splitting (1378), into two cases.
% 55.25/21.05 |-Branch one:
% 55.25/21.05 | (1379) all_0_11_11 = n9
% 55.25/21.05 |
% 55.25/21.05 | From (1379) and (559) follows:
% 55.25/21.05 | (1380) pred(n9) = all_0_9_9
% 55.25/21.05 |
% 55.25/21.05 | From (1379) and (992) follows:
% 55.25/21.05 | (1381) succ(n9) = all_0_5_5
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 55.25/21.05 | (1382) all_0_9_9 = n8
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 55.25/21.05 | (1383) all_0_5_5 = n10
% 55.25/21.05 |
% 55.25/21.05 | From (1382)(1383) and (538) follows:
% 55.25/21.05 | (1384) sum(n8, n10) = all_0_2_2
% 55.25/21.05 |
% 55.25/21.05 | From (1382) and (7644) follows:
% 55.25/21.05 | (7805) sum(n8, n18) = all_0_7_7
% 55.25/21.05 |
% 55.25/21.05 | From (1383) and (7642) follows:
% 55.25/21.05 | (7806) sum(n16, n10) = all_0_4_4
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n16, n10, all_0_4_4, n0 and discharging atoms sum(n16, n10) = all_0_4_4, sum(n16, n10) = n0, yields:
% 55.25/21.05 | (1531) all_0_4_4 = n0
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n8, n18, all_0_7_7, n0 and discharging atoms sum(n8, n18) = all_0_7_7, sum(n8, n18) = n0, yields:
% 55.25/21.05 | (1533) all_0_7_7 = n0
% 55.25/21.05 |
% 55.25/21.05 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 55.25/21.05 | (1154) all_0_2_2 = n18
% 55.25/21.05 |
% 55.25/21.05 | From (1154) and (7646) follows:
% 55.25/21.05 | (4332) sum(n18, n8) = all_0_0_0
% 55.25/21.05 |
% 55.25/21.05 | From (1533)(1531) and (590) follows:
% 55.25/21.06 | (1535) sum(n0, n0) = all_0_3_3
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (690) with n18, n8, all_0_0_0, n0 and discharging atoms sum(n18, n8) = all_0_0_0, sum(n18, n8) = n0, yields:
% 55.25/21.06 | (1303) all_0_0_0 = n0
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 55.25/21.06 | (1302) all_0_3_3 = n0
% 55.25/21.06 |
% 55.25/21.06 | Equations (1303,1302) can reduce 679 to:
% 55.25/21.06 | (1106) $false
% 55.25/21.06 |
% 55.25/21.06 |-The branch is then unsatisfiable
% 55.25/21.06 |-Branch two:
% 55.25/21.06 | (1395) ~ (all_0_11_11 = n9)
% 55.25/21.06 | (1396) 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
% 55.25/21.06 |
% 55.25/21.06 +-Applying beta-rule and splitting (1396), into two cases.
% 55.25/21.06 |-Branch one:
% 55.25/21.06 | (1397) all_0_11_11 = n8
% 55.25/21.06 |
% 55.25/21.06 | From (1397) and (559) follows:
% 55.25/21.06 | (1398) pred(n8) = all_0_9_9
% 55.25/21.06 |
% 55.25/21.06 | From (1397) and (992) follows:
% 55.25/21.06 | (1399) succ(n8) = all_0_5_5
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 55.25/21.06 | (1400) all_0_9_9 = n7
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 55.25/21.06 | (1401) all_0_5_5 = n9
% 55.25/21.06 |
% 55.25/21.06 | From (1400)(1401) and (538) follows:
% 55.25/21.06 | (1402) sum(n7, n9) = all_0_2_2
% 55.25/21.06 |
% 55.25/21.06 | From (1400) and (7644) follows:
% 55.25/21.06 | (7823) sum(n7, n18) = all_0_7_7
% 55.25/21.06 |
% 55.25/21.06 | From (1401) and (7642) follows:
% 55.25/21.06 | (7824) sum(n16, n9) = all_0_4_4
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (690) with n16, n9, all_0_4_4, n25 and discharging atoms sum(n16, n9) = all_0_4_4, sum(n16, n9) = n25, yields:
% 55.25/21.06 | (1551) all_0_4_4 = n25
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (690) with n7, n18, all_0_7_7, n25 and discharging atoms sum(n7, n18) = all_0_7_7, sum(n7, n18) = n25, yields:
% 55.25/21.06 | (1550) all_0_7_7 = n25
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 55.25/21.06 | (1172) all_0_2_2 = n16
% 55.25/21.06 |
% 55.25/21.06 | From (1172) and (7646) follows:
% 55.25/21.06 | (5134) sum(n16, n8) = all_0_0_0
% 55.25/21.06 |
% 55.25/21.06 | From (1550)(1551) and (590) follows:
% 55.25/21.06 | (1553) sum(n25, n25) = all_0_3_3
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 55.25/21.06 | (1320) all_0_3_3 = n24
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (690) with n16, n8, all_0_0_0, n24 and discharging atoms sum(n16, n8) = all_0_0_0, sum(n16, n8) = n24, yields:
% 55.25/21.06 | (1321) all_0_0_0 = n24
% 55.25/21.06 |
% 55.25/21.06 | Equations (1321,1320) can reduce 679 to:
% 55.25/21.06 | (1106) $false
% 55.25/21.06 |
% 55.25/21.06 |-The branch is then unsatisfiable
% 55.25/21.06 |-Branch two:
% 55.25/21.06 | (1413) ~ (all_0_11_11 = n8)
% 55.25/21.06 | (1414) 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
% 55.25/21.06 |
% 55.25/21.06 +-Applying beta-rule and splitting (1414), into two cases.
% 55.25/21.06 |-Branch one:
% 55.25/21.06 | (1415) all_0_11_11 = n7
% 55.25/21.06 |
% 55.25/21.06 | From (1415) and (559) follows:
% 55.25/21.06 | (1416) pred(n7) = all_0_9_9
% 55.25/21.06 |
% 55.25/21.06 | From (1415) and (992) follows:
% 55.25/21.06 | (1417) succ(n7) = all_0_5_5
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 55.25/21.06 | (1418) all_0_9_9 = n6
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 55.25/21.06 | (1419) all_0_5_5 = n8
% 55.25/21.06 |
% 55.25/21.06 | From (1418)(1419) and (538) follows:
% 55.25/21.06 | (1420) sum(n6, n8) = all_0_2_2
% 55.25/21.06 |
% 55.25/21.06 | From (1418) and (7644) follows:
% 55.25/21.06 | (7841) sum(n6, n18) = all_0_7_7
% 55.25/21.06 |
% 55.25/21.06 | From (1419) and (7642) follows:
% 55.25/21.06 | (7842) sum(n16, n8) = all_0_4_4
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (690) with n16, n8, all_0_4_4, n24 and discharging atoms sum(n16, n8) = all_0_4_4, sum(n16, n8) = n24, yields:
% 55.25/21.06 | (1096) all_0_4_4 = n24
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (690) with n6, n18, all_0_7_7, n24 and discharging atoms sum(n6, n18) = all_0_7_7, sum(n6, n18) = n24, yields:
% 55.25/21.06 | (1097) all_0_7_7 = n24
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 55.25/21.06 | (1190) all_0_2_2 = n14
% 55.25/21.06 |
% 55.25/21.06 | From (1190) and (7646) follows:
% 55.25/21.06 | (5900) sum(n14, n8) = all_0_0_0
% 55.25/21.06 |
% 55.25/21.06 | From (1097)(1096) and (590) follows:
% 55.25/21.06 | (1101) sum(n24, n24) = all_0_3_3
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 55.25/21.06 | (1104) all_0_3_3 = n22
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (690) with n14, n8, all_0_0_0, n22 and discharging atoms sum(n14, n8) = all_0_0_0, sum(n14, n8) = n22, yields:
% 55.25/21.06 | (1102) all_0_0_0 = n22
% 55.25/21.06 |
% 55.25/21.06 | Equations (1102,1104) can reduce 679 to:
% 55.25/21.06 | (1106) $false
% 55.25/21.06 |
% 55.25/21.06 |-The branch is then unsatisfiable
% 55.25/21.06 |-Branch two:
% 55.25/21.06 | (1431) ~ (all_0_11_11 = n7)
% 55.25/21.06 | (1432) 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
% 55.25/21.06 |
% 55.25/21.06 +-Applying beta-rule and splitting (1432), into two cases.
% 55.25/21.06 |-Branch one:
% 55.25/21.06 | (1433) all_0_11_11 = n6
% 55.25/21.06 |
% 55.25/21.06 | From (1433) and (559) follows:
% 55.25/21.06 | (1434) pred(n6) = all_0_9_9
% 55.25/21.06 |
% 55.25/21.06 | From (1433) and (992) follows:
% 55.25/21.06 | (1435) succ(n6) = all_0_5_5
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 55.25/21.06 | (1436) all_0_9_9 = n5
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 55.25/21.06 | (1437) all_0_5_5 = n7
% 55.25/21.06 |
% 55.25/21.06 | From (1436)(1437) and (538) follows:
% 55.25/21.06 | (1438) sum(n5, n7) = all_0_2_2
% 55.25/21.06 |
% 55.25/21.06 | From (1436) and (7644) follows:
% 55.25/21.06 | (7859) sum(n5, n18) = all_0_7_7
% 55.25/21.06 |
% 55.25/21.06 | From (1437) and (7642) follows:
% 55.25/21.06 | (7860) sum(n16, n7) = all_0_4_4
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (690) with n16, n7, all_0_4_4, n23 and discharging atoms sum(n16, n7) = all_0_4_4, sum(n16, n7) = n23, yields:
% 55.25/21.06 | (1117) all_0_4_4 = n23
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (690) with n5, n18, all_0_7_7, n23 and discharging atoms sum(n5, n18) = all_0_7_7, sum(n5, n18) = n23, yields:
% 55.25/21.06 | (1119) all_0_7_7 = n23
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 55.25/21.06 | (1208) all_0_2_2 = n12
% 55.25/21.06 |
% 55.25/21.06 | From (1208) and (7646) follows:
% 55.25/21.06 | (6630) sum(n12, n8) = all_0_0_0
% 55.25/21.06 |
% 55.25/21.06 | From (1119)(1117) and (590) follows:
% 55.25/21.06 | (1121) sum(n23, n23) = all_0_3_3
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 55.25/21.06 | (1122) all_0_3_3 = n20
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (690) with n12, n8, all_0_0_0, n20 and discharging atoms sum(n12, n8) = all_0_0_0, sum(n12, n8) = n20, yields:
% 55.25/21.06 | (1123) all_0_0_0 = n20
% 55.25/21.06 |
% 55.25/21.06 | Equations (1123,1122) can reduce 679 to:
% 55.25/21.06 | (1106) $false
% 55.25/21.06 |
% 55.25/21.06 |-The branch is then unsatisfiable
% 55.25/21.06 |-Branch two:
% 55.25/21.06 | (1449) ~ (all_0_11_11 = n6)
% 55.25/21.06 | (1450) 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
% 55.25/21.06 |
% 55.25/21.06 +-Applying beta-rule and splitting (1450), into two cases.
% 55.25/21.06 |-Branch one:
% 55.25/21.06 | (1451) all_0_11_11 = n5
% 55.25/21.06 |
% 55.25/21.06 | From (1451) and (559) follows:
% 55.25/21.06 | (1452) pred(n5) = all_0_9_9
% 55.25/21.06 |
% 55.25/21.06 | From (1451) and (992) follows:
% 55.25/21.06 | (1453) succ(n5) = all_0_5_5
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 55.25/21.06 | (1454) all_0_9_9 = n4
% 55.25/21.06 |
% 55.25/21.06 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 55.25/21.06 | (1455) all_0_5_5 = n6
% 55.25/21.06 |
% 55.25/21.06 | From (1454)(1455) and (538) follows:
% 55.25/21.06 | (1456) sum(n4, n6) = all_0_2_2
% 55.25/21.06 |
% 55.25/21.06 | From (1454) and (7644) follows:
% 55.25/21.07 | (7877) sum(n4, n18) = all_0_7_7
% 55.25/21.07 |
% 55.25/21.07 | From (1455) and (7642) follows:
% 55.25/21.07 | (7878) sum(n16, n6) = all_0_4_4
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (690) with n16, n6, all_0_4_4, n22 and discharging atoms sum(n16, n6) = all_0_4_4, sum(n16, n6) = n22, yields:
% 55.25/21.07 | (1135) all_0_4_4 = n22
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (690) with n4, n18, all_0_7_7, n22 and discharging atoms sum(n4, n18) = all_0_7_7, sum(n4, n18) = n22, yields:
% 55.25/21.07 | (1137) all_0_7_7 = n22
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 55.25/21.07 | (1226) all_0_2_2 = n10
% 55.25/21.07 |
% 55.25/21.07 | From (1226) and (7646) follows:
% 55.25/21.07 | (7324) sum(n10, n8) = all_0_0_0
% 55.25/21.07 |
% 55.25/21.07 | From (1137)(1135) and (590) follows:
% 55.25/21.07 | (1139) sum(n22, n22) = all_0_3_3
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 55.25/21.07 | (1140) all_0_3_3 = n18
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (690) with n10, n8, all_0_0_0, n18 and discharging atoms sum(n10, n8) = all_0_0_0, sum(n10, n8) = n18, yields:
% 55.25/21.07 | (1141) all_0_0_0 = n18
% 55.25/21.07 |
% 55.25/21.07 | Equations (1141,1140) can reduce 679 to:
% 55.25/21.07 | (1106) $false
% 55.25/21.07 |
% 55.25/21.07 |-The branch is then unsatisfiable
% 55.25/21.07 |-Branch two:
% 55.25/21.07 | (1467) ~ (all_0_11_11 = n5)
% 55.25/21.07 | (1468) 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
% 55.25/21.07 |
% 55.25/21.07 +-Applying beta-rule and splitting (1468), into two cases.
% 55.25/21.07 |-Branch one:
% 55.25/21.07 | (1469) all_0_11_11 = n4
% 55.25/21.07 |
% 55.25/21.07 | From (1469) and (559) follows:
% 55.25/21.07 | (1470) pred(n4) = all_0_9_9
% 55.25/21.07 |
% 55.25/21.07 | From (1469) and (992) follows:
% 55.25/21.07 | (1471) succ(n4) = all_0_5_5
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 55.25/21.07 | (1472) all_0_9_9 = n3
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 55.25/21.07 | (1473) all_0_5_5 = n5
% 55.25/21.07 |
% 55.25/21.07 | From (1472)(1473) and (538) follows:
% 55.25/21.07 | (1474) sum(n3, n5) = all_0_2_2
% 55.25/21.07 |
% 55.25/21.07 | From (1472) and (7644) follows:
% 55.25/21.07 | (7895) sum(n3, n18) = all_0_7_7
% 55.25/21.07 |
% 55.25/21.07 | From (1473) and (7642) follows:
% 55.25/21.07 | (7896) sum(n16, n5) = all_0_4_4
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (690) with n16, n5, all_0_4_4, n21 and discharging atoms sum(n16, n5) = all_0_4_4, sum(n16, n5) = n21, yields:
% 55.25/21.07 | (1153) all_0_4_4 = n21
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (690) with n3, n18, all_0_7_7, n21 and discharging atoms sum(n3, n18) = all_0_7_7, sum(n3, n18) = n21, yields:
% 55.25/21.07 | (1155) all_0_7_7 = n21
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 55.25/21.07 | (1244) all_0_2_2 = n8
% 55.25/21.07 |
% 55.25/21.07 | From (1244) and (7646) follows:
% 55.25/21.07 | (7664) sum(n8, n8) = all_0_0_0
% 55.25/21.07 |
% 55.25/21.07 | From (1155)(1153) and (590) follows:
% 55.25/21.07 | (1157) sum(n21, n21) = all_0_3_3
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 55.25/21.07 | (1158) all_0_3_3 = n16
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (690) with n8, n8, all_0_0_0, n16 and discharging atoms sum(n8, n8) = all_0_0_0, sum(n8, n8) = n16, yields:
% 55.25/21.07 | (1159) all_0_0_0 = n16
% 55.25/21.07 |
% 55.25/21.07 | Equations (1159,1158) can reduce 679 to:
% 55.25/21.07 | (1106) $false
% 55.25/21.07 |
% 55.25/21.07 |-The branch is then unsatisfiable
% 55.25/21.07 |-Branch two:
% 55.25/21.07 | (1485) ~ (all_0_11_11 = n4)
% 55.25/21.07 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 55.25/21.07 |
% 55.25/21.07 +-Applying beta-rule and splitting (1486), into two cases.
% 55.25/21.07 |-Branch one:
% 55.25/21.07 | (1487) all_0_11_11 = n3
% 55.25/21.07 |
% 55.25/21.07 | From (1487) and (559) follows:
% 55.25/21.07 | (1488) pred(n3) = all_0_9_9
% 55.25/21.07 |
% 55.25/21.07 | From (1487) and (992) follows:
% 55.25/21.07 | (1489) succ(n3) = all_0_5_5
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 55.25/21.07 | (1490) all_0_9_9 = n2
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 55.25/21.07 | (1491) all_0_5_5 = n4
% 55.25/21.07 |
% 55.25/21.07 | From (1490)(1491) and (538) follows:
% 55.25/21.07 | (1492) sum(n2, n4) = all_0_2_2
% 55.25/21.07 |
% 55.25/21.07 | From (1490) and (7644) follows:
% 55.25/21.07 | (7913) sum(n2, n18) = all_0_7_7
% 55.25/21.07 |
% 55.25/21.07 | From (1491) and (7642) follows:
% 55.25/21.07 | (7914) sum(n16, n4) = all_0_4_4
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (690) with n16, n4, all_0_4_4, n20 and discharging atoms sum(n16, n4) = all_0_4_4, sum(n16, n4) = n20, yields:
% 55.25/21.07 | (1171) all_0_4_4 = n20
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (690) with n2, n18, all_0_7_7, n20 and discharging atoms sum(n2, n18) = all_0_7_7, sum(n2, n18) = n20, yields:
% 55.25/21.07 | (1173) all_0_7_7 = n20
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 55.25/21.07 | (1262) all_0_2_2 = n6
% 55.25/21.07 |
% 55.25/21.07 | From (1262) and (7646) follows:
% 55.25/21.07 | (7684) sum(n6, n8) = all_0_0_0
% 55.25/21.07 |
% 55.25/21.07 | From (1173)(1171) and (590) follows:
% 55.25/21.07 | (1175) sum(n20, n20) = all_0_3_3
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 55.25/21.07 | (1176) all_0_3_3 = n14
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (690) with n6, n8, all_0_0_0, n14 and discharging atoms sum(n6, n8) = all_0_0_0, sum(n6, n8) = n14, yields:
% 55.25/21.07 | (1177) all_0_0_0 = n14
% 55.25/21.07 |
% 55.25/21.07 | Equations (1177,1176) can reduce 679 to:
% 55.25/21.07 | (1106) $false
% 55.25/21.07 |
% 55.25/21.07 |-The branch is then unsatisfiable
% 55.25/21.07 |-Branch two:
% 55.25/21.07 | (1503) ~ (all_0_11_11 = n3)
% 55.25/21.07 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 55.25/21.07 |
% 55.25/21.07 +-Applying beta-rule and splitting (1504), into two cases.
% 55.25/21.07 |-Branch one:
% 55.25/21.07 | (1505) all_0_11_11 = n2
% 55.25/21.07 |
% 55.25/21.07 | From (1505) and (559) follows:
% 55.25/21.07 | (1506) pred(n2) = all_0_9_9
% 55.25/21.07 |
% 55.25/21.07 | From (1505) and (992) follows:
% 55.25/21.07 | (1507) succ(n2) = all_0_5_5
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 55.25/21.07 | (1508) all_0_9_9 = n1
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 55.25/21.07 | (1509) all_0_5_5 = n3
% 55.25/21.07 |
% 55.25/21.07 | From (1508)(1509) and (538) follows:
% 55.25/21.07 | (1510) sum(n1, n3) = all_0_2_2
% 55.25/21.07 |
% 55.25/21.07 | From (1508) and (7644) follows:
% 55.25/21.07 | (7931) sum(n1, n18) = all_0_7_7
% 55.25/21.07 |
% 55.25/21.07 | From (1509) and (7642) follows:
% 55.25/21.07 | (7932) sum(n16, n3) = all_0_4_4
% 55.25/21.07 |
% 55.25/21.07 | Instantiating formula (690) with n16, n3, all_0_4_4, n19 and discharging atoms sum(n16, n3) = all_0_4_4, sum(n16, n3) = n19, yields:
% 55.25/21.08 | (1189) all_0_4_4 = n19
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (690) with n1, n18, all_0_7_7, n19 and discharging atoms sum(n1, n18) = all_0_7_7, sum(n1, n18) = n19, yields:
% 55.25/21.08 | (1191) all_0_7_7 = n19
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 55.25/21.08 | (1280) all_0_2_2 = n4
% 55.25/21.08 |
% 55.25/21.08 | From (1280) and (7646) follows:
% 55.25/21.08 | (7702) sum(n4, n8) = all_0_0_0
% 55.25/21.08 |
% 55.25/21.08 | From (1191)(1189) and (590) follows:
% 55.25/21.08 | (1193) sum(n19, n19) = all_0_3_3
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 55.25/21.08 | (1194) all_0_3_3 = n12
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (690) with n4, n8, all_0_0_0, n12 and discharging atoms sum(n4, n8) = all_0_0_0, sum(n4, n8) = n12, yields:
% 55.25/21.08 | (1195) all_0_0_0 = n12
% 55.25/21.08 |
% 55.25/21.08 | Equations (1195,1194) can reduce 679 to:
% 55.25/21.08 | (1106) $false
% 55.25/21.08 |
% 55.25/21.08 |-The branch is then unsatisfiable
% 55.25/21.08 |-Branch two:
% 55.25/21.08 | (1521) ~ (all_0_11_11 = n2)
% 55.25/21.08 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 55.25/21.08 |
% 55.25/21.08 +-Applying beta-rule and splitting (1522), into two cases.
% 55.25/21.08 |-Branch one:
% 55.25/21.08 | (1523) all_0_11_11 = n1
% 55.25/21.08 |
% 55.25/21.08 | From (1523) and (559) follows:
% 55.25/21.08 | (1524) pred(n1) = all_0_9_9
% 55.25/21.08 |
% 55.25/21.08 | From (1523) and (992) follows:
% 55.25/21.08 | (1525) succ(n1) = all_0_5_5
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 55.25/21.08 | (1526) all_0_9_9 = n0
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 55.25/21.08 | (1527) all_0_5_5 = n2
% 55.25/21.08 |
% 55.25/21.08 | From (1526)(1527) and (538) follows:
% 55.25/21.08 | (1528) sum(n0, n2) = all_0_2_2
% 55.25/21.08 |
% 55.25/21.08 | From (1526) and (7644) follows:
% 55.25/21.08 | (7949) sum(n0, n18) = all_0_7_7
% 55.25/21.08 |
% 55.25/21.08 | From (1527) and (7642) follows:
% 55.25/21.08 | (7950) sum(n16, n2) = all_0_4_4
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (690) with n16, n2, all_0_4_4, n18 and discharging atoms sum(n16, n2) = all_0_4_4, sum(n16, n2) = n18, yields:
% 55.25/21.08 | (1207) all_0_4_4 = n18
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (690) with n0, n18, all_0_7_7, n18 and discharging atoms sum(n0, n18) = all_0_7_7, sum(n0, n18) = n18, yields:
% 55.25/21.08 | (1209) all_0_7_7 = n18
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 55.25/21.08 | (1298) all_0_2_2 = n2
% 55.25/21.08 |
% 55.25/21.08 | From (1298) and (7646) follows:
% 55.25/21.08 | (7720) sum(n2, n8) = all_0_0_0
% 55.25/21.08 |
% 55.25/21.08 | From (1209)(1207) and (590) follows:
% 55.25/21.08 | (1211) sum(n18, n18) = all_0_3_3
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 55.25/21.08 | (1212) all_0_3_3 = n10
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (690) with n2, n8, all_0_0_0, n10 and discharging atoms sum(n2, n8) = all_0_0_0, sum(n2, n8) = n10, yields:
% 55.25/21.08 | (1213) all_0_0_0 = n10
% 55.25/21.08 |
% 55.25/21.08 | Equations (1213,1212) can reduce 679 to:
% 55.25/21.08 | (1106) $false
% 55.25/21.08 |
% 55.25/21.08 |-The branch is then unsatisfiable
% 55.25/21.08 |-Branch two:
% 55.25/21.08 | (1540) ~ (all_0_11_11 = n1)
% 55.25/21.08 | (1541) all_0_11_11 = n0
% 55.25/21.08 |
% 55.25/21.08 | From (1541) and (559) follows:
% 55.25/21.08 | (1542) pred(n0) = all_0_9_9
% 55.25/21.08 |
% 55.25/21.08 | From (1541) and (992) follows:
% 55.25/21.08 | (1543) succ(n0) = all_0_5_5
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 55.25/21.08 | (1544) all_0_9_9 = n25
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 55.25/21.08 | (1545) all_0_5_5 = n1
% 55.25/21.08 |
% 55.25/21.08 | From (1544)(1545) and (538) follows:
% 55.25/21.08 | (1546) sum(n25, n1) = all_0_2_2
% 55.25/21.08 |
% 55.25/21.08 | From (1544) and (7644) follows:
% 55.25/21.08 | (7966) sum(n25, n18) = all_0_7_7
% 55.25/21.08 |
% 55.25/21.08 | From (1545) and (7642) follows:
% 55.25/21.08 | (7967) sum(n16, n1) = all_0_4_4
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (690) with n25, n18, all_0_7_7, n17 and discharging atoms sum(n25, n18) = all_0_7_7, sum(n25, n18) = n17, yields:
% 55.25/21.08 | (1227) all_0_7_7 = n17
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 55.25/21.08 | (1316) all_0_2_2 = n0
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (690) with n16, n1, all_0_4_4, n17 and discharging atoms sum(n16, n1) = all_0_4_4, sum(n16, n1) = n17, yields:
% 55.25/21.08 | (1225) all_0_4_4 = n17
% 55.25/21.08 |
% 55.25/21.08 | From (1316) and (7646) follows:
% 55.25/21.08 | (7738) sum(n0, n8) = all_0_0_0
% 55.25/21.08 |
% 55.25/21.08 | From (1227)(1225) and (590) follows:
% 55.25/21.08 | (1229) sum(n17, n17) = all_0_3_3
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 55.25/21.08 | (1230) all_0_3_3 = n8
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (690) with n0, n8, all_0_0_0, n8 and discharging atoms sum(n0, n8) = all_0_0_0, sum(n0, n8) = n8, yields:
% 55.25/21.08 | (1231) all_0_0_0 = n8
% 55.25/21.08 |
% 55.25/21.08 | Equations (1231,1230) can reduce 679 to:
% 55.25/21.08 | (1106) $false
% 55.25/21.08 |
% 55.25/21.08 |-The branch is then unsatisfiable
% 55.25/21.08 |-Branch two:
% 55.25/21.08 | (1712) ~ (all_0_10_10 = n17)
% 55.25/21.08 | (1713) 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
% 55.25/21.08 |
% 55.25/21.08 +-Applying beta-rule and splitting (1234), into two cases.
% 55.25/21.08 |-Branch one:
% 55.25/21.08 | (1235) all_0_11_11 = n17
% 55.25/21.08 |
% 55.25/21.08 | From (1235) and (559) follows:
% 55.25/21.08 | (1236) pred(n17) = all_0_9_9
% 55.25/21.08 |
% 55.25/21.08 | From (1235) and (992) follows:
% 55.25/21.08 | (1237) succ(n17) = all_0_5_5
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (500) with n17, all_0_9_9, n16 and discharging atoms pred(n17) = all_0_9_9, pred(n17) = n16, yields:
% 55.25/21.08 | (1238) all_0_9_9 = n16
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (617) with n17, all_0_5_5, n18 and discharging atoms succ(n17) = all_0_5_5, succ(n17) = n18, yields:
% 55.25/21.08 | (1239) all_0_5_5 = n18
% 55.25/21.08 |
% 55.25/21.08 | From (1239) and (541) follows:
% 55.25/21.08 | (7983) sum(all_0_6_6, n18) = all_0_4_4
% 55.25/21.08 |
% 55.25/21.08 | From (1238)(1239) and (538) follows:
% 55.25/21.08 | (1240) sum(n16, n18) = all_0_2_2
% 55.25/21.08 |
% 55.25/21.08 | From (1238) and (427) follows:
% 55.25/21.08 | (7985) sum(n16, all_0_8_8) = all_0_7_7
% 55.25/21.08 |
% 55.25/21.08 | Instantiating formula (690) with n16, n18, all_0_2_2, n8 and discharging atoms sum(n16, n18) = all_0_2_2, sum(n16, n18) = n8, yields:
% 55.25/21.08 | (1244) all_0_2_2 = n8
% 55.25/21.08 |
% 55.25/21.08 | From (1244) and (630) follows:
% 55.25/21.08 | (7987) sum(n8, all_0_1_1) = all_0_0_0
% 55.25/21.08 |
% 55.25/21.08 +-Applying beta-rule and splitting (1713), into two cases.
% 55.25/21.08 |-Branch one:
% 55.25/21.08 | (1714) all_0_10_10 = n16
% 55.25/21.08 |
% 55.25/21.08 | From (1714) and (292) follows:
% 55.25/21.08 | (1715) pred(n16) = all_0_6_6
% 55.25/21.08 |
% 55.25/21.08 | From (1714) and (760) follows:
% 55.25/21.09 | (1716) succ(n16) = all_0_8_8
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (500) with n16, all_0_6_6, n15 and discharging atoms pred(n16) = all_0_6_6, pred(n16) = n15, yields:
% 55.25/21.09 | (1717) all_0_6_6 = n15
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (617) with n16, all_0_8_8, n17 and discharging atoms succ(n16) = all_0_8_8, succ(n16) = n17, yields:
% 55.25/21.09 | (1718) all_0_8_8 = n17
% 55.25/21.09 |
% 55.25/21.09 | From (1717)(1718) and (411) follows:
% 55.25/21.09 | (1719) sum(n15, n17) = all_0_1_1
% 55.25/21.09 |
% 55.25/21.09 | From (1717) and (7983) follows:
% 55.25/21.09 | (7994) sum(n15, n18) = all_0_4_4
% 55.25/21.09 |
% 55.25/21.09 | From (1718) and (7985) follows:
% 55.25/21.09 | (7995) sum(n16, n17) = all_0_7_7
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (690) with n16, n17, all_0_7_7, n7 and discharging atoms sum(n16, n17) = all_0_7_7, sum(n16, n17) = n7, yields:
% 55.25/21.09 | (1407) all_0_7_7 = n7
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (690) with n15, n18, all_0_4_4, n7 and discharging atoms sum(n15, n18) = all_0_4_4, sum(n15, n18) = n7, yields:
% 55.25/21.09 | (1405) all_0_4_4 = n7
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (690) with n15, n17, all_0_1_1, n6 and discharging atoms sum(n15, n17) = all_0_1_1, sum(n15, n17) = n6, yields:
% 55.25/21.09 | (1723) all_0_1_1 = n6
% 55.25/21.09 |
% 55.25/21.09 | From (1407)(1405) and (590) follows:
% 55.25/21.09 | (1409) sum(n7, n7) = all_0_3_3
% 55.25/21.09 |
% 55.25/21.09 | From (1723) and (7987) follows:
% 55.25/21.09 | (8000) sum(n8, n6) = all_0_0_0
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (690) with n8, n6, all_0_0_0, n14 and discharging atoms sum(n8, n6) = all_0_0_0, sum(n8, n6) = n14, yields:
% 55.25/21.09 | (1177) all_0_0_0 = n14
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 55.25/21.09 | (1176) all_0_3_3 = n14
% 55.25/21.09 |
% 55.25/21.09 | Equations (1177,1176) can reduce 679 to:
% 55.25/21.09 | (1106) $false
% 55.25/21.09 |
% 55.25/21.09 |-The branch is then unsatisfiable
% 55.25/21.09 |-Branch two:
% 55.25/21.09 | (1730) ~ (all_0_10_10 = n16)
% 55.25/21.09 | (1731) 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
% 55.25/21.09 |
% 55.25/21.09 +-Applying beta-rule and splitting (1731), into two cases.
% 55.25/21.09 |-Branch one:
% 55.25/21.09 | (1732) all_0_10_10 = n15
% 55.25/21.09 |
% 55.25/21.09 | From (1732) and (292) follows:
% 55.25/21.09 | (1733) pred(n15) = all_0_6_6
% 55.25/21.09 |
% 55.25/21.09 | From (1732) and (760) follows:
% 55.25/21.09 | (1734) succ(n15) = all_0_8_8
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (500) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 55.25/21.09 | (1735) all_0_6_6 = n14
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (617) with n15, all_0_8_8, n16 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n16, yields:
% 55.25/21.09 | (1736) all_0_8_8 = n16
% 55.25/21.09 |
% 55.25/21.09 | From (1735)(1736) and (411) follows:
% 55.25/21.09 | (1737) sum(n14, n16) = all_0_1_1
% 55.25/21.09 |
% 55.25/21.09 | From (1735) and (7983) follows:
% 55.25/21.09 | (8012) sum(n14, n18) = all_0_4_4
% 55.25/21.09 |
% 55.25/21.09 | From (1736) and (7985) follows:
% 55.25/21.09 | (8013) sum(n16, n16) = all_0_7_7
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (690) with n16, n16, all_0_7_7, n6 and discharging atoms sum(n16, n16) = all_0_7_7, sum(n16, n16) = n6, yields:
% 55.25/21.09 | (1425) all_0_7_7 = n6
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (690) with n14, n18, all_0_4_4, n6 and discharging atoms sum(n14, n18) = all_0_4_4, sum(n14, n18) = n6, yields:
% 55.25/21.09 | (1423) all_0_4_4 = n6
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (690) with n14, n16, all_0_1_1, n4 and discharging atoms sum(n14, n16) = all_0_1_1, sum(n14, n16) = n4, yields:
% 55.25/21.09 | (1741) all_0_1_1 = n4
% 55.25/21.09 |
% 55.25/21.09 | From (1425)(1423) and (590) follows:
% 55.25/21.09 | (1427) sum(n6, n6) = all_0_3_3
% 55.25/21.09 |
% 55.25/21.09 | From (1741) and (7987) follows:
% 55.25/21.09 | (8018) sum(n8, n4) = all_0_0_0
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (690) with n8, n4, all_0_0_0, n12 and discharging atoms sum(n8, n4) = all_0_0_0, sum(n8, n4) = n12, yields:
% 55.25/21.09 | (1195) all_0_0_0 = n12
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 55.25/21.09 | (1194) all_0_3_3 = n12
% 55.25/21.09 |
% 55.25/21.09 | Equations (1195,1194) can reduce 679 to:
% 55.25/21.09 | (1106) $false
% 55.25/21.09 |
% 55.25/21.09 |-The branch is then unsatisfiable
% 55.25/21.09 |-Branch two:
% 55.25/21.09 | (1748) ~ (all_0_10_10 = n15)
% 55.25/21.09 | (1749) 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
% 55.25/21.09 |
% 55.25/21.09 +-Applying beta-rule and splitting (1749), into two cases.
% 55.25/21.09 |-Branch one:
% 55.25/21.09 | (1750) all_0_10_10 = n14
% 55.25/21.09 |
% 55.25/21.09 | From (1750) and (292) follows:
% 55.25/21.09 | (1751) pred(n14) = all_0_6_6
% 55.25/21.09 |
% 55.25/21.09 | From (1750) and (760) follows:
% 55.25/21.09 | (1752) succ(n14) = all_0_8_8
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (500) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 55.25/21.09 | (1753) all_0_6_6 = n13
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (617) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 55.25/21.09 | (1754) all_0_8_8 = n15
% 55.25/21.09 |
% 55.25/21.09 | From (1753)(1754) and (411) follows:
% 55.25/21.09 | (1755) sum(n13, n15) = all_0_1_1
% 55.25/21.09 |
% 55.25/21.09 | From (1753) and (7983) follows:
% 55.25/21.09 | (8030) sum(n13, n18) = all_0_4_4
% 55.25/21.09 |
% 55.25/21.09 | From (1754) and (7985) follows:
% 55.25/21.09 | (8031) sum(n16, n15) = all_0_7_7
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (690) with n16, n15, all_0_7_7, n5 and discharging atoms sum(n16, n15) = all_0_7_7, sum(n16, n15) = n5, yields:
% 55.25/21.09 | (1443) all_0_7_7 = n5
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (690) with n13, n18, all_0_4_4, n5 and discharging atoms sum(n13, n18) = all_0_4_4, sum(n13, n18) = n5, yields:
% 55.25/21.09 | (1441) all_0_4_4 = n5
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (690) with n13, n15, all_0_1_1, n2 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n2, yields:
% 55.25/21.09 | (1759) all_0_1_1 = n2
% 55.25/21.09 |
% 55.25/21.09 | From (1443)(1441) and (590) follows:
% 55.25/21.09 | (1445) sum(n5, n5) = all_0_3_3
% 55.25/21.09 |
% 55.25/21.09 | From (1759) and (7987) follows:
% 55.25/21.09 | (8036) sum(n8, n2) = all_0_0_0
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (690) with n8, n2, all_0_0_0, n10 and discharging atoms sum(n8, n2) = all_0_0_0, sum(n8, n2) = n10, yields:
% 55.25/21.09 | (1213) all_0_0_0 = n10
% 55.25/21.09 |
% 55.25/21.09 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 55.25/21.09 | (1212) all_0_3_3 = n10
% 55.25/21.09 |
% 55.25/21.09 | Equations (1213,1212) can reduce 679 to:
% 55.25/21.09 | (1106) $false
% 55.25/21.09 |
% 55.25/21.09 |-The branch is then unsatisfiable
% 55.25/21.09 |-Branch two:
% 55.25/21.09 | (1766) ~ (all_0_10_10 = n14)
% 55.25/21.09 | (1767) 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
% 55.25/21.09 |
% 55.25/21.09 +-Applying beta-rule and splitting (1767), into two cases.
% 55.25/21.09 |-Branch one:
% 55.25/21.09 | (1768) all_0_10_10 = n13
% 55.25/21.09 |
% 55.25/21.09 | From (1768) and (292) follows:
% 55.25/21.10 | (1769) pred(n13) = all_0_6_6
% 55.25/21.10 |
% 55.25/21.10 | From (1768) and (760) follows:
% 55.25/21.10 | (1770) succ(n13) = all_0_8_8
% 55.25/21.10 |
% 55.25/21.10 | Instantiating formula (500) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 55.25/21.10 | (1771) all_0_6_6 = n12
% 55.25/21.10 |
% 55.25/21.10 | Instantiating formula (617) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 55.25/21.10 | (1772) all_0_8_8 = n14
% 55.25/21.10 |
% 55.25/21.10 | From (1771)(1772) and (411) follows:
% 55.43/21.10 | (1773) sum(n12, n14) = all_0_1_1
% 55.43/21.10 |
% 55.43/21.10 | From (1771) and (7983) follows:
% 55.43/21.10 | (8048) sum(n12, n18) = all_0_4_4
% 55.43/21.10 |
% 55.43/21.10 | From (1772) and (7985) follows:
% 55.43/21.10 | (8049) sum(n16, n14) = all_0_7_7
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (690) with n16, n14, all_0_7_7, n4 and discharging atoms sum(n16, n14) = all_0_7_7, sum(n16, n14) = n4, yields:
% 55.43/21.10 | (1461) all_0_7_7 = n4
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (690) with n12, n18, all_0_4_4, n4 and discharging atoms sum(n12, n18) = all_0_4_4, sum(n12, n18) = n4, yields:
% 55.43/21.10 | (1459) all_0_4_4 = n4
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (690) with n12, n14, all_0_1_1, n0 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n0, yields:
% 55.43/21.10 | (1777) all_0_1_1 = n0
% 55.43/21.10 |
% 55.43/21.10 | From (1461)(1459) and (590) follows:
% 55.43/21.10 | (1463) sum(n4, n4) = all_0_3_3
% 55.43/21.10 |
% 55.43/21.10 | From (1777) and (7987) follows:
% 55.43/21.10 | (8054) sum(n8, n0) = all_0_0_0
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (690) with n8, n0, all_0_0_0, n8 and discharging atoms sum(n8, n0) = all_0_0_0, sum(n8, n0) = n8, yields:
% 55.43/21.10 | (1231) all_0_0_0 = n8
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 55.43/21.10 | (1230) all_0_3_3 = n8
% 55.43/21.10 |
% 55.43/21.10 | Equations (1231,1230) can reduce 679 to:
% 55.43/21.10 | (1106) $false
% 55.43/21.10 |
% 55.43/21.10 |-The branch is then unsatisfiable
% 55.43/21.10 |-Branch two:
% 55.43/21.10 | (1784) ~ (all_0_10_10 = n13)
% 55.43/21.10 | (1785) 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
% 55.43/21.10 |
% 55.43/21.10 +-Applying beta-rule and splitting (1785), into two cases.
% 55.43/21.10 |-Branch one:
% 55.43/21.10 | (1786) all_0_10_10 = n12
% 55.43/21.10 |
% 55.43/21.10 | From (1786) and (292) follows:
% 55.43/21.10 | (1787) pred(n12) = all_0_6_6
% 55.43/21.10 |
% 55.43/21.10 | From (1786) and (760) follows:
% 55.43/21.10 | (1788) succ(n12) = all_0_8_8
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (500) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 55.43/21.10 | (1789) all_0_6_6 = n11
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (617) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 55.43/21.10 | (1790) all_0_8_8 = n13
% 55.43/21.10 |
% 55.43/21.10 | From (1789)(1790) and (411) follows:
% 55.43/21.10 | (1791) sum(n11, n13) = all_0_1_1
% 55.43/21.10 |
% 55.43/21.10 | From (1789) and (7983) follows:
% 55.43/21.10 | (8066) sum(n11, n18) = all_0_4_4
% 55.43/21.10 |
% 55.43/21.10 | From (1790) and (7985) follows:
% 55.43/21.10 | (8067) sum(n16, n13) = all_0_7_7
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (690) with n16, n13, all_0_7_7, n3 and discharging atoms sum(n16, n13) = all_0_7_7, sum(n16, n13) = n3, yields:
% 55.43/21.10 | (1479) all_0_7_7 = n3
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (690) with n11, n18, all_0_4_4, n3 and discharging atoms sum(n11, n18) = all_0_4_4, sum(n11, n18) = n3, yields:
% 55.43/21.10 | (1477) all_0_4_4 = n3
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (690) with n11, n13, all_0_1_1, n24 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n24, yields:
% 55.43/21.10 | (1081) all_0_1_1 = n24
% 55.43/21.10 |
% 55.43/21.10 | From (1479)(1477) and (590) follows:
% 55.43/21.10 | (1481) sum(n3, n3) = all_0_3_3
% 55.43/21.10 |
% 55.43/21.10 | From (1081) and (7987) follows:
% 55.43/21.10 | (1246) sum(n8, n24) = all_0_0_0
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (690) with n8, n24, all_0_0_0, n6 and discharging atoms sum(n8, n24) = all_0_0_0, sum(n8, n24) = n6, yields:
% 55.43/21.10 | (1249) all_0_0_0 = n6
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 55.43/21.10 | (1248) all_0_3_3 = n6
% 55.43/21.10 |
% 55.43/21.10 | Equations (1249,1248) can reduce 679 to:
% 55.43/21.10 | (1106) $false
% 55.43/21.10 |
% 55.43/21.10 |-The branch is then unsatisfiable
% 55.43/21.10 |-Branch two:
% 55.43/21.10 | (1802) ~ (all_0_10_10 = n12)
% 55.43/21.10 | (1803) 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
% 55.43/21.10 |
% 55.43/21.10 +-Applying beta-rule and splitting (1803), into two cases.
% 55.43/21.10 |-Branch one:
% 55.43/21.10 | (1804) all_0_10_10 = n11
% 55.43/21.10 |
% 55.43/21.10 | From (1804) and (292) follows:
% 55.43/21.10 | (1805) pred(n11) = all_0_6_6
% 55.43/21.10 |
% 55.43/21.10 | From (1804) and (760) follows:
% 55.43/21.10 | (1806) succ(n11) = all_0_8_8
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (500) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 55.43/21.10 | (1807) all_0_6_6 = n10
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (617) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 55.43/21.10 | (1808) all_0_8_8 = n12
% 55.43/21.10 |
% 55.43/21.10 | From (1807)(1808) and (411) follows:
% 55.43/21.10 | (1809) sum(n10, n12) = all_0_1_1
% 55.43/21.10 |
% 55.43/21.10 | From (1807) and (7983) follows:
% 55.43/21.10 | (8084) sum(n10, n18) = all_0_4_4
% 55.43/21.10 |
% 55.43/21.10 | From (1808) and (7985) follows:
% 55.43/21.10 | (8085) sum(n16, n12) = all_0_7_7
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (690) with n16, n12, all_0_7_7, n2 and discharging atoms sum(n16, n12) = all_0_7_7, sum(n16, n12) = n2, yields:
% 55.43/21.10 | (1497) all_0_7_7 = n2
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (690) with n10, n18, all_0_4_4, n2 and discharging atoms sum(n10, n18) = all_0_4_4, sum(n10, n18) = n2, yields:
% 55.43/21.10 | (1495) all_0_4_4 = n2
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (690) with n10, n12, all_0_1_1, n22 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n22, yields:
% 55.43/21.10 | (1579) all_0_1_1 = n22
% 55.43/21.10 |
% 55.43/21.10 | From (1497)(1495) and (590) follows:
% 55.43/21.10 | (1499) sum(n2, n2) = all_0_3_3
% 55.43/21.10 |
% 55.43/21.10 | From (1579) and (7987) follows:
% 55.43/21.10 | (2178) sum(n8, n22) = all_0_0_0
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (690) with n8, n22, all_0_0_0, n4 and discharging atoms sum(n8, n22) = all_0_0_0, sum(n8, n22) = n4, yields:
% 55.43/21.10 | (1267) all_0_0_0 = n4
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 55.43/21.10 | (1266) all_0_3_3 = n4
% 55.43/21.10 |
% 55.43/21.10 | Equations (1267,1266) can reduce 679 to:
% 55.43/21.10 | (1106) $false
% 55.43/21.10 |
% 55.43/21.10 |-The branch is then unsatisfiable
% 55.43/21.10 |-Branch two:
% 55.43/21.10 | (1820) ~ (all_0_10_10 = n11)
% 55.43/21.10 | (1821) 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
% 55.43/21.10 |
% 55.43/21.10 +-Applying beta-rule and splitting (1821), into two cases.
% 55.43/21.10 |-Branch one:
% 55.43/21.10 | (1822) all_0_10_10 = n10
% 55.43/21.10 |
% 55.43/21.10 | From (1822) and (292) follows:
% 55.43/21.10 | (1823) pred(n10) = all_0_6_6
% 55.43/21.10 |
% 55.43/21.10 | From (1822) and (760) follows:
% 55.43/21.10 | (1824) succ(n10) = all_0_8_8
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (500) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 55.43/21.10 | (1825) all_0_6_6 = n9
% 55.43/21.10 |
% 55.43/21.10 | Instantiating formula (617) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 55.43/21.10 | (1826) all_0_8_8 = n11
% 55.43/21.10 |
% 55.43/21.10 | From (1825)(1826) and (411) follows:
% 55.43/21.11 | (1827) sum(n9, n11) = all_0_1_1
% 55.43/21.11 |
% 55.43/21.11 | From (1825) and (7983) follows:
% 55.43/21.11 | (8102) sum(n9, n18) = all_0_4_4
% 55.43/21.11 |
% 55.43/21.11 | From (1826) and (7985) follows:
% 55.43/21.11 | (8103) sum(n16, n11) = all_0_7_7
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (690) with n16, n11, all_0_7_7, n1 and discharging atoms sum(n16, n11) = all_0_7_7, sum(n16, n11) = n1, yields:
% 55.43/21.11 | (1515) all_0_7_7 = n1
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (690) with n9, n18, all_0_4_4, n1 and discharging atoms sum(n9, n18) = all_0_4_4, sum(n9, n18) = n1, yields:
% 55.43/21.11 | (1513) all_0_4_4 = n1
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (690) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 55.43/21.11 | (1597) all_0_1_1 = n20
% 55.43/21.11 |
% 55.43/21.11 | From (1515)(1513) and (590) follows:
% 55.43/21.11 | (1517) sum(n1, n1) = all_0_3_3
% 55.43/21.11 |
% 55.43/21.11 | From (1597) and (7987) follows:
% 55.43/21.11 | (3070) sum(n8, n20) = all_0_0_0
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (690) with n8, n20, all_0_0_0, n2 and discharging atoms sum(n8, n20) = all_0_0_0, sum(n8, n20) = n2, yields:
% 55.43/21.11 | (1285) all_0_0_0 = n2
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 55.43/21.11 | (1284) all_0_3_3 = n2
% 55.43/21.11 |
% 55.43/21.11 | Equations (1285,1284) can reduce 679 to:
% 55.43/21.11 | (1106) $false
% 55.43/21.11 |
% 55.43/21.11 |-The branch is then unsatisfiable
% 55.43/21.11 |-Branch two:
% 55.43/21.11 | (1838) ~ (all_0_10_10 = n10)
% 55.43/21.11 | (1839) 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
% 55.43/21.11 |
% 55.43/21.11 +-Applying beta-rule and splitting (1839), into two cases.
% 55.43/21.11 |-Branch one:
% 55.43/21.11 | (1840) all_0_10_10 = n9
% 55.43/21.11 |
% 55.43/21.11 | From (1840) and (292) follows:
% 55.43/21.11 | (1841) pred(n9) = all_0_6_6
% 55.43/21.11 |
% 55.43/21.11 | From (1840) and (760) follows:
% 55.43/21.11 | (1842) succ(n9) = all_0_8_8
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (500) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 55.43/21.11 | (1843) all_0_6_6 = n8
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (617) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 55.43/21.11 | (1844) all_0_8_8 = n10
% 55.43/21.11 |
% 55.43/21.11 | From (1843)(1844) and (411) follows:
% 55.43/21.11 | (1845) sum(n8, n10) = all_0_1_1
% 55.43/21.11 |
% 55.43/21.11 | From (1843) and (7983) follows:
% 55.43/21.11 | (8120) sum(n8, n18) = all_0_4_4
% 55.43/21.11 |
% 55.43/21.11 | From (1844) and (7985) follows:
% 55.43/21.11 | (8121) sum(n16, n10) = all_0_7_7
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (690) with n16, n10, all_0_7_7, n0 and discharging atoms sum(n16, n10) = all_0_7_7, sum(n16, n10) = n0, yields:
% 55.43/21.11 | (1533) all_0_7_7 = n0
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (690) with n8, n18, all_0_4_4, n0 and discharging atoms sum(n8, n18) = all_0_4_4, sum(n8, n18) = n0, yields:
% 55.43/21.11 | (1531) all_0_4_4 = n0
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (690) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 55.43/21.11 | (1615) all_0_1_1 = n18
% 55.43/21.11 |
% 55.43/21.11 | From (1533)(1531) and (590) follows:
% 55.43/21.11 | (1535) sum(n0, n0) = all_0_3_3
% 55.43/21.11 |
% 55.43/21.11 | From (1615) and (7987) follows:
% 55.43/21.11 | (3926) sum(n8, n18) = all_0_0_0
% 55.43/21.11 |
% 55.43/21.11 | From (1531) and (8120) follows:
% 55.43/21.11 | (281) sum(n8, n18) = n0
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (690) with n8, n18, all_0_0_0, n0 and discharging atoms sum(n8, n18) = all_0_0_0, sum(n8, n18) = n0, yields:
% 55.43/21.11 | (1303) all_0_0_0 = n0
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 55.43/21.11 | (1302) all_0_3_3 = n0
% 55.43/21.11 |
% 55.43/21.11 | Equations (1303,1302) can reduce 679 to:
% 55.43/21.11 | (1106) $false
% 55.43/21.11 |
% 55.43/21.11 |-The branch is then unsatisfiable
% 55.43/21.11 |-Branch two:
% 55.43/21.11 | (1856) ~ (all_0_10_10 = n9)
% 55.43/21.11 | (1857) 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
% 55.43/21.11 |
% 55.43/21.11 +-Applying beta-rule and splitting (1857), into two cases.
% 55.43/21.11 |-Branch one:
% 55.43/21.11 | (1858) all_0_10_10 = n8
% 55.43/21.11 |
% 55.43/21.11 | From (1858) and (292) follows:
% 55.43/21.11 | (1859) pred(n8) = all_0_6_6
% 55.43/21.11 |
% 55.43/21.11 | From (1858) and (760) follows:
% 55.43/21.11 | (1860) succ(n8) = all_0_8_8
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 55.43/21.11 | (1861) all_0_6_6 = n7
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 55.43/21.11 | (1862) all_0_8_8 = n9
% 55.43/21.11 |
% 55.43/21.11 | From (1861)(1862) and (411) follows:
% 55.43/21.11 | (1863) sum(n7, n9) = all_0_1_1
% 55.43/21.11 |
% 55.43/21.11 | From (1861) and (7983) follows:
% 55.43/21.11 | (8139) sum(n7, n18) = all_0_4_4
% 55.43/21.11 |
% 55.43/21.11 | From (1862) and (7985) follows:
% 55.43/21.11 | (8140) sum(n16, n9) = all_0_7_7
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (690) with n16, n9, all_0_7_7, n25 and discharging atoms sum(n16, n9) = all_0_7_7, sum(n16, n9) = n25, yields:
% 55.43/21.11 | (1550) all_0_7_7 = n25
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (690) with n7, n18, all_0_4_4, n25 and discharging atoms sum(n7, n18) = all_0_4_4, sum(n7, n18) = n25, yields:
% 55.43/21.11 | (1551) all_0_4_4 = n25
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 55.43/21.11 | (1633) all_0_1_1 = n16
% 55.43/21.11 |
% 55.43/21.11 | From (1550)(1551) and (590) follows:
% 55.43/21.11 | (1553) sum(n25, n25) = all_0_3_3
% 55.43/21.11 |
% 55.43/21.11 | From (1633) and (7987) follows:
% 55.43/21.11 | (4746) sum(n8, n16) = all_0_0_0
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 55.43/21.11 | (1320) all_0_3_3 = n24
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (690) with n8, n16, all_0_0_0, n24 and discharging atoms sum(n8, n16) = all_0_0_0, sum(n8, n16) = n24, yields:
% 55.43/21.11 | (1321) all_0_0_0 = n24
% 55.43/21.11 |
% 55.43/21.11 | Equations (1321,1320) can reduce 679 to:
% 55.43/21.11 | (1106) $false
% 55.43/21.11 |
% 55.43/21.11 |-The branch is then unsatisfiable
% 55.43/21.11 |-Branch two:
% 55.43/21.11 | (1874) ~ (all_0_10_10 = n8)
% 55.43/21.11 | (1875) 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
% 55.43/21.11 |
% 55.43/21.11 +-Applying beta-rule and splitting (1875), into two cases.
% 55.43/21.11 |-Branch one:
% 55.43/21.11 | (1876) all_0_10_10 = n7
% 55.43/21.11 |
% 55.43/21.11 | From (1876) and (292) follows:
% 55.43/21.11 | (1877) pred(n7) = all_0_6_6
% 55.43/21.11 |
% 55.43/21.11 | From (1876) and (760) follows:
% 55.43/21.11 | (1878) succ(n7) = all_0_8_8
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 55.43/21.11 | (1879) all_0_6_6 = n6
% 55.43/21.11 |
% 55.43/21.11 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 55.43/21.11 | (1880) all_0_8_8 = n8
% 55.43/21.12 |
% 55.43/21.12 | From (1879)(1880) and (411) follows:
% 55.43/21.12 | (1881) sum(n6, n8) = all_0_1_1
% 55.43/21.12 |
% 55.43/21.12 | From (1879) and (7983) follows:
% 55.43/21.12 | (8157) sum(n6, n18) = all_0_4_4
% 55.43/21.12 |
% 55.43/21.12 | From (1880) and (7985) follows:
% 55.43/21.12 | (8158) sum(n16, n8) = all_0_7_7
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (690) with n16, n8, all_0_7_7, n24 and discharging atoms sum(n16, n8) = all_0_7_7, sum(n16, n8) = n24, yields:
% 55.43/21.12 | (1097) all_0_7_7 = n24
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (690) with n6, n18, all_0_4_4, n24 and discharging atoms sum(n6, n18) = all_0_4_4, sum(n6, n18) = n24, yields:
% 55.43/21.12 | (1096) all_0_4_4 = n24
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 55.43/21.12 | (1651) all_0_1_1 = n14
% 55.43/21.12 |
% 55.43/21.12 | From (1097)(1096) and (590) follows:
% 55.43/21.12 | (1101) sum(n24, n24) = all_0_3_3
% 55.43/21.12 |
% 55.43/21.12 | From (1651) and (7987) follows:
% 55.43/21.12 | (5530) sum(n8, n14) = all_0_0_0
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 55.43/21.12 | (1104) all_0_3_3 = n22
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (690) with n8, n14, all_0_0_0, n22 and discharging atoms sum(n8, n14) = all_0_0_0, sum(n8, n14) = n22, yields:
% 55.43/21.12 | (1102) all_0_0_0 = n22
% 55.43/21.12 |
% 55.43/21.12 | Equations (1102,1104) can reduce 679 to:
% 55.43/21.12 | (1106) $false
% 55.43/21.12 |
% 55.43/21.12 |-The branch is then unsatisfiable
% 55.43/21.12 |-Branch two:
% 55.43/21.12 | (1892) ~ (all_0_10_10 = n7)
% 55.43/21.12 | (1893) 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
% 55.43/21.12 |
% 55.43/21.12 +-Applying beta-rule and splitting (1893), into two cases.
% 55.43/21.12 |-Branch one:
% 55.43/21.12 | (1894) all_0_10_10 = n6
% 55.43/21.12 |
% 55.43/21.12 | From (1894) and (292) follows:
% 55.43/21.12 | (1895) pred(n6) = all_0_6_6
% 55.43/21.12 |
% 55.43/21.12 | From (1894) and (760) follows:
% 55.43/21.12 | (1896) succ(n6) = all_0_8_8
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 55.43/21.12 | (1897) all_0_6_6 = n5
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 55.43/21.12 | (1898) all_0_8_8 = n7
% 55.43/21.12 |
% 55.43/21.12 | From (1897)(1898) and (411) follows:
% 55.43/21.12 | (1899) sum(n5, n7) = all_0_1_1
% 55.43/21.12 |
% 55.43/21.12 | From (1897) and (7983) follows:
% 55.43/21.12 | (8175) sum(n5, n18) = all_0_4_4
% 55.43/21.12 |
% 55.43/21.12 | From (1898) and (7985) follows:
% 55.43/21.12 | (8176) sum(n16, n7) = all_0_7_7
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (690) with n16, n7, all_0_7_7, n23 and discharging atoms sum(n16, n7) = all_0_7_7, sum(n16, n7) = n23, yields:
% 55.43/21.12 | (1119) all_0_7_7 = n23
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (690) with n5, n18, all_0_4_4, n23 and discharging atoms sum(n5, n18) = all_0_4_4, sum(n5, n18) = n23, yields:
% 55.43/21.12 | (1117) all_0_4_4 = n23
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 55.43/21.12 | (1669) all_0_1_1 = n12
% 55.43/21.12 |
% 55.43/21.12 | From (1119)(1117) and (590) follows:
% 55.43/21.12 | (1121) sum(n23, n23) = all_0_3_3
% 55.43/21.12 |
% 55.43/21.12 | From (1669) and (7987) follows:
% 55.43/21.12 | (6278) sum(n8, n12) = all_0_0_0
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 55.43/21.12 | (1122) all_0_3_3 = n20
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (690) with n8, n12, all_0_0_0, n20 and discharging atoms sum(n8, n12) = all_0_0_0, sum(n8, n12) = n20, yields:
% 55.43/21.12 | (1123) all_0_0_0 = n20
% 55.43/21.12 |
% 55.43/21.12 | Equations (1123,1122) can reduce 679 to:
% 55.43/21.12 | (1106) $false
% 55.43/21.12 |
% 55.43/21.12 |-The branch is then unsatisfiable
% 55.43/21.12 |-Branch two:
% 55.43/21.12 | (1910) ~ (all_0_10_10 = n6)
% 55.43/21.12 | (1911) 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
% 55.43/21.12 |
% 55.43/21.12 +-Applying beta-rule and splitting (1911), into two cases.
% 55.43/21.12 |-Branch one:
% 55.43/21.12 | (1912) all_0_10_10 = n5
% 55.43/21.12 |
% 55.43/21.12 | From (1912) and (292) follows:
% 55.43/21.12 | (1913) pred(n5) = all_0_6_6
% 55.43/21.12 |
% 55.43/21.12 | From (1912) and (760) follows:
% 55.43/21.12 | (1914) succ(n5) = all_0_8_8
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 55.43/21.12 | (1915) all_0_6_6 = n4
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 55.43/21.12 | (1916) all_0_8_8 = n6
% 55.43/21.12 |
% 55.43/21.12 | From (1915)(1916) and (411) follows:
% 55.43/21.12 | (1917) sum(n4, n6) = all_0_1_1
% 55.43/21.12 |
% 55.43/21.12 | From (1915) and (7983) follows:
% 55.43/21.12 | (8193) sum(n4, n18) = all_0_4_4
% 55.43/21.12 |
% 55.43/21.12 | From (1916) and (7985) follows:
% 55.43/21.12 | (8194) sum(n16, n6) = all_0_7_7
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (690) with n16, n6, all_0_7_7, n22 and discharging atoms sum(n16, n6) = all_0_7_7, sum(n16, n6) = n22, yields:
% 55.43/21.12 | (1137) all_0_7_7 = n22
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (690) with n4, n18, all_0_4_4, n22 and discharging atoms sum(n4, n18) = all_0_4_4, sum(n4, n18) = n22, yields:
% 55.43/21.12 | (1135) all_0_4_4 = n22
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 55.43/21.12 | (1687) all_0_1_1 = n10
% 55.43/21.12 |
% 55.43/21.12 | From (1137)(1135) and (590) follows:
% 55.43/21.12 | (1139) sum(n22, n22) = all_0_3_3
% 55.43/21.12 |
% 55.43/21.12 | From (1687) and (7987) follows:
% 55.43/21.12 | (6990) sum(n8, n10) = all_0_0_0
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 55.43/21.12 | (1140) all_0_3_3 = n18
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (690) with n8, n10, all_0_0_0, n18 and discharging atoms sum(n8, n10) = all_0_0_0, sum(n8, n10) = n18, yields:
% 55.43/21.12 | (1141) all_0_0_0 = n18
% 55.43/21.12 |
% 55.43/21.12 | Equations (1141,1140) can reduce 679 to:
% 55.43/21.12 | (1106) $false
% 55.43/21.12 |
% 55.43/21.12 |-The branch is then unsatisfiable
% 55.43/21.12 |-Branch two:
% 55.43/21.12 | (1928) ~ (all_0_10_10 = n5)
% 55.43/21.12 | (1929) 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
% 55.43/21.12 |
% 55.43/21.12 +-Applying beta-rule and splitting (1929), into two cases.
% 55.43/21.12 |-Branch one:
% 55.43/21.12 | (1930) all_0_10_10 = n4
% 55.43/21.12 |
% 55.43/21.12 | From (1930) and (292) follows:
% 55.43/21.12 | (1931) pred(n4) = all_0_6_6
% 55.43/21.12 |
% 55.43/21.12 | From (1930) and (760) follows:
% 55.43/21.12 | (1932) succ(n4) = all_0_8_8
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 55.43/21.12 | (1933) all_0_6_6 = n3
% 55.43/21.12 |
% 55.43/21.12 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 55.43/21.12 | (1934) all_0_8_8 = n5
% 55.43/21.12 |
% 55.43/21.12 | From (1933)(1934) and (411) follows:
% 55.43/21.12 | (1935) sum(n3, n5) = all_0_1_1
% 55.43/21.12 |
% 55.43/21.12 | From (1933) and (7983) follows:
% 55.43/21.13 | (8211) sum(n3, n18) = all_0_4_4
% 55.43/21.13 |
% 55.43/21.13 | From (1934) and (7985) follows:
% 55.43/21.13 | (8212) sum(n16, n5) = all_0_7_7
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (690) with n16, n5, all_0_7_7, n21 and discharging atoms sum(n16, n5) = all_0_7_7, sum(n16, n5) = n21, yields:
% 55.43/21.13 | (1155) all_0_7_7 = n21
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (690) with n3, n18, all_0_4_4, n21 and discharging atoms sum(n3, n18) = all_0_4_4, sum(n3, n18) = n21, yields:
% 55.43/21.13 | (1153) all_0_4_4 = n21
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 55.43/21.13 | (1705) all_0_1_1 = n8
% 55.43/21.13 |
% 55.43/21.13 | From (1155)(1153) and (590) follows:
% 55.43/21.13 | (1157) sum(n21, n21) = all_0_3_3
% 55.43/21.13 |
% 55.43/21.13 | From (1705) and (7987) follows:
% 55.43/21.13 | (7664) sum(n8, n8) = all_0_0_0
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 55.43/21.13 | (1158) all_0_3_3 = n16
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (690) with n8, n8, all_0_0_0, n16 and discharging atoms sum(n8, n8) = all_0_0_0, sum(n8, n8) = n16, yields:
% 55.43/21.13 | (1159) all_0_0_0 = n16
% 55.43/21.13 |
% 55.43/21.13 | Equations (1159,1158) can reduce 679 to:
% 55.43/21.13 | (1106) $false
% 55.43/21.13 |
% 55.43/21.13 |-The branch is then unsatisfiable
% 55.43/21.13 |-Branch two:
% 55.43/21.13 | (1946) ~ (all_0_10_10 = n4)
% 55.43/21.13 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 55.43/21.13 |
% 55.43/21.13 +-Applying beta-rule and splitting (1947), into two cases.
% 55.43/21.13 |-Branch one:
% 55.43/21.13 | (1948) all_0_10_10 = n3
% 55.43/21.13 |
% 55.43/21.13 | From (1948) and (292) follows:
% 55.43/21.13 | (1949) pred(n3) = all_0_6_6
% 55.43/21.13 |
% 55.43/21.13 | From (1948) and (760) follows:
% 55.43/21.13 | (1950) succ(n3) = all_0_8_8
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 55.43/21.13 | (1951) all_0_6_6 = n2
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 55.43/21.13 | (1952) all_0_8_8 = n4
% 55.43/21.13 |
% 55.43/21.13 | From (1951)(1952) and (411) follows:
% 55.43/21.13 | (1953) sum(n2, n4) = all_0_1_1
% 55.43/21.13 |
% 55.43/21.13 | From (1951) and (7983) follows:
% 55.43/21.13 | (8229) sum(n2, n18) = all_0_4_4
% 55.43/21.13 |
% 55.43/21.13 | From (1952) and (7985) follows:
% 55.43/21.13 | (8230) sum(n16, n4) = all_0_7_7
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (690) with n16, n4, all_0_7_7, n20 and discharging atoms sum(n16, n4) = all_0_7_7, sum(n16, n4) = n20, yields:
% 55.43/21.13 | (1173) all_0_7_7 = n20
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (690) with n2, n18, all_0_4_4, n20 and discharging atoms sum(n2, n18) = all_0_4_4, sum(n2, n18) = n20, yields:
% 55.43/21.13 | (1171) all_0_4_4 = n20
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 55.43/21.13 | (1723) all_0_1_1 = n6
% 55.43/21.13 |
% 55.43/21.13 | From (1173)(1171) and (590) follows:
% 55.43/21.13 | (1175) sum(n20, n20) = all_0_3_3
% 55.43/21.13 |
% 55.43/21.13 | From (1723) and (7987) follows:
% 55.43/21.13 | (8000) sum(n8, n6) = all_0_0_0
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 55.43/21.13 | (1176) all_0_3_3 = n14
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (690) with n8, n6, all_0_0_0, n14 and discharging atoms sum(n8, n6) = all_0_0_0, sum(n8, n6) = n14, yields:
% 55.43/21.13 | (1177) all_0_0_0 = n14
% 55.43/21.13 |
% 55.43/21.13 | Equations (1177,1176) can reduce 679 to:
% 55.43/21.13 | (1106) $false
% 55.43/21.13 |
% 55.43/21.13 |-The branch is then unsatisfiable
% 55.43/21.13 |-Branch two:
% 55.43/21.13 | (1964) ~ (all_0_10_10 = n3)
% 55.43/21.13 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 55.43/21.13 |
% 55.43/21.13 +-Applying beta-rule and splitting (1965), into two cases.
% 55.43/21.13 |-Branch one:
% 55.43/21.13 | (1966) all_0_10_10 = n2
% 55.43/21.13 |
% 55.43/21.13 | From (1966) and (292) follows:
% 55.43/21.13 | (1967) pred(n2) = all_0_6_6
% 55.43/21.13 |
% 55.43/21.13 | From (1966) and (760) follows:
% 55.43/21.13 | (1968) succ(n2) = all_0_8_8
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 55.43/21.13 | (1969) all_0_6_6 = n1
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 55.43/21.13 | (1970) all_0_8_8 = n3
% 55.43/21.13 |
% 55.43/21.13 | From (1969)(1970) and (411) follows:
% 55.43/21.13 | (1971) sum(n1, n3) = all_0_1_1
% 55.43/21.13 |
% 55.43/21.13 | From (1969) and (7983) follows:
% 55.43/21.13 | (8247) sum(n1, n18) = all_0_4_4
% 55.43/21.13 |
% 55.43/21.13 | From (1970) and (7985) follows:
% 55.43/21.13 | (8248) sum(n16, n3) = all_0_7_7
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (690) with n16, n3, all_0_7_7, n19 and discharging atoms sum(n16, n3) = all_0_7_7, sum(n16, n3) = n19, yields:
% 55.43/21.13 | (1191) all_0_7_7 = n19
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (690) with n1, n18, all_0_4_4, n19 and discharging atoms sum(n1, n18) = all_0_4_4, sum(n1, n18) = n19, yields:
% 55.43/21.13 | (1189) all_0_4_4 = n19
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 55.43/21.13 | (1741) all_0_1_1 = n4
% 55.43/21.13 |
% 55.43/21.13 | From (1191)(1189) and (590) follows:
% 55.43/21.13 | (1193) sum(n19, n19) = all_0_3_3
% 55.43/21.13 |
% 55.43/21.13 | From (1741) and (7987) follows:
% 55.43/21.13 | (8018) sum(n8, n4) = all_0_0_0
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 55.43/21.13 | (1194) all_0_3_3 = n12
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (690) with n8, n4, all_0_0_0, n12 and discharging atoms sum(n8, n4) = all_0_0_0, sum(n8, n4) = n12, yields:
% 55.43/21.13 | (1195) all_0_0_0 = n12
% 55.43/21.13 |
% 55.43/21.13 | Equations (1195,1194) can reduce 679 to:
% 55.43/21.13 | (1106) $false
% 55.43/21.13 |
% 55.43/21.13 |-The branch is then unsatisfiable
% 55.43/21.13 |-Branch two:
% 55.43/21.13 | (1982) ~ (all_0_10_10 = n2)
% 55.43/21.13 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 55.43/21.13 |
% 55.43/21.13 +-Applying beta-rule and splitting (1983), into two cases.
% 55.43/21.13 |-Branch one:
% 55.43/21.13 | (1984) all_0_10_10 = n1
% 55.43/21.13 |
% 55.43/21.13 | From (1984) and (292) follows:
% 55.43/21.13 | (1985) pred(n1) = all_0_6_6
% 55.43/21.13 |
% 55.43/21.13 | From (1984) and (760) follows:
% 55.43/21.13 | (1986) succ(n1) = all_0_8_8
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 55.43/21.13 | (1987) all_0_6_6 = n0
% 55.43/21.13 |
% 55.43/21.13 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 55.43/21.13 | (1988) all_0_8_8 = n2
% 55.43/21.13 |
% 55.43/21.13 | From (1987)(1988) and (411) follows:
% 55.43/21.13 | (1989) sum(n0, n2) = all_0_1_1
% 55.43/21.13 |
% 55.43/21.13 | From (1987) and (7983) follows:
% 55.43/21.14 | (8265) sum(n0, n18) = all_0_4_4
% 55.43/21.14 |
% 55.43/21.14 | From (1988) and (7985) follows:
% 55.43/21.14 | (8266) sum(n16, n2) = all_0_7_7
% 55.43/21.14 |
% 55.43/21.14 | Instantiating formula (690) with n16, n2, all_0_7_7, n18 and discharging atoms sum(n16, n2) = all_0_7_7, sum(n16, n2) = n18, yields:
% 55.43/21.14 | (1209) all_0_7_7 = n18
% 55.43/21.14 |
% 55.43/21.14 | Instantiating formula (690) with n0, n18, all_0_4_4, n18 and discharging atoms sum(n0, n18) = all_0_4_4, sum(n0, n18) = n18, yields:
% 55.43/21.14 | (1207) all_0_4_4 = n18
% 55.43/21.14 |
% 55.43/21.14 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 55.43/21.14 | (1759) all_0_1_1 = n2
% 55.43/21.14 |
% 55.43/21.14 | From (1209)(1207) and (590) follows:
% 55.43/21.14 | (1211) sum(n18, n18) = all_0_3_3
% 55.43/21.14 |
% 55.43/21.14 | From (1759) and (7987) follows:
% 55.43/21.14 | (8036) sum(n8, n2) = all_0_0_0
% 55.43/21.14 |
% 55.43/21.14 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 55.43/21.14 | (1212) all_0_3_3 = n10
% 55.43/21.14 |
% 55.43/21.14 | Instantiating formula (690) with n8, n2, all_0_0_0, n10 and discharging atoms sum(n8, n2) = all_0_0_0, sum(n8, n2) = n10, yields:
% 55.43/21.14 | (1213) all_0_0_0 = n10
% 55.43/21.14 |
% 55.43/21.14 | Equations (1213,1212) can reduce 679 to:
% 55.43/21.14 | (1106) $false
% 55.43/21.14 |
% 55.43/21.14 |-The branch is then unsatisfiable
% 55.43/21.14 |-Branch two:
% 55.43/21.14 | (2002) ~ (all_0_10_10 = n1)
% 55.43/21.14 | (2003) all_0_10_10 = n0
% 55.43/21.14 |
% 55.43/21.14 | From (2003) and (292) follows:
% 55.43/21.14 | (2004) pred(n0) = all_0_6_6
% 55.43/21.14 |
% 55.43/21.14 | From (2003) and (760) follows:
% 55.43/21.14 | (2005) succ(n0) = all_0_8_8
% 55.43/21.14 |
% 55.43/21.14 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 55.43/21.14 | (2006) all_0_6_6 = n25
% 55.43/21.14 |
% 55.43/21.14 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 55.43/21.14 | (2007) all_0_8_8 = n1
% 55.43/21.14 |
% 55.43/21.14 | From (2006)(2007) and (411) follows:
% 55.43/21.14 | (2008) sum(n25, n1) = all_0_1_1
% 55.43/21.14 |
% 55.43/21.14 | From (2006) and (7983) follows:
% 55.43/21.14 | (8282) sum(n25, n18) = all_0_4_4
% 55.43/21.14 |
% 55.43/21.14 | From (2007) and (7985) follows:
% 55.43/21.14 | (8283) sum(n16, n1) = all_0_7_7
% 55.43/21.14 |
% 55.43/21.14 | Instantiating formula (690) with n25, n18, all_0_4_4, n17 and discharging atoms sum(n25, n18) = all_0_4_4, sum(n25, n18) = n17, yields:
% 55.43/21.14 | (1225) all_0_4_4 = n17
% 55.43/21.14 |
% 55.43/21.14 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 55.43/21.14 | (1777) all_0_1_1 = n0
% 55.43/21.14 |
% 55.43/21.14 | Instantiating formula (690) with n16, n1, all_0_7_7, n17 and discharging atoms sum(n16, n1) = all_0_7_7, sum(n16, n1) = n17, yields:
% 55.43/21.14 | (1227) all_0_7_7 = n17
% 55.43/21.14 |
% 55.43/21.14 | From (1227)(1225) and (590) follows:
% 55.43/21.14 | (1229) sum(n17, n17) = all_0_3_3
% 55.43/21.14 |
% 55.43/21.14 | From (1777) and (7987) follows:
% 55.43/21.14 | (8054) sum(n8, n0) = all_0_0_0
% 55.43/21.14 |
% 55.43/21.14 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 55.43/21.14 | (1230) all_0_3_3 = n8
% 55.43/21.14 |
% 55.43/21.14 | Instantiating formula (690) with n8, n0, all_0_0_0, n8 and discharging atoms sum(n8, n0) = all_0_0_0, sum(n8, n0) = n8, yields:
% 55.43/21.14 | (1231) all_0_0_0 = n8
% 55.43/21.14 |
% 55.43/21.14 | Equations (1231,1230) can reduce 679 to:
% 55.43/21.14 | (1106) $false
% 55.43/21.14 |
% 55.43/21.14 |-The branch is then unsatisfiable
% 55.43/21.14 |-Branch two:
% 55.43/21.14 | (1251) ~ (all_0_11_11 = n17)
% 55.43/21.14 | (1252) 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
% 55.43/21.14 |
% 55.43/21.14 +-Applying beta-rule and splitting (1713), into two cases.
% 55.43/21.14 |-Branch one:
% 55.43/21.14 | (1714) all_0_10_10 = n16
% 55.43/21.14 |
% 55.43/21.14 | From (1714) and (292) follows:
% 55.43/21.14 | (1715) pred(n16) = all_0_6_6
% 55.43/21.14 |
% 55.43/21.14 | From (1714) and (760) follows:
% 55.43/21.14 | (1716) succ(n16) = all_0_8_8
% 55.43/21.14 |
% 55.43/21.14 | Instantiating formula (500) with n16, all_0_6_6, n15 and discharging atoms pred(n16) = all_0_6_6, pred(n16) = n15, yields:
% 55.43/21.14 | (1717) all_0_6_6 = n15
% 55.43/21.14 |
% 55.43/21.14 | Instantiating formula (617) with n16, all_0_8_8, n17 and discharging atoms succ(n16) = all_0_8_8, succ(n16) = n17, yields:
% 55.43/21.14 | (1718) all_0_8_8 = n17
% 55.43/21.14 |
% 55.43/21.14 | From (1717) and (1715) follows:
% 55.43/21.14 | (275) pred(n16) = n15
% 55.43/21.14 |
% 55.43/21.14 | From (1718) and (1716) follows:
% 55.43/21.14 | (576) succ(n16) = n17
% 55.43/21.14 |
% 55.43/21.14 | From (1717) and (541) follows:
% 55.43/21.14 | (8301) sum(n15, all_0_5_5) = all_0_4_4
% 55.43/21.14 |
% 55.43/21.14 | From (1717)(1718) and (411) follows:
% 55.43/21.14 | (1719) sum(n15, n17) = all_0_1_1
% 55.43/21.14 |
% 55.43/21.14 | From (1718) and (427) follows:
% 55.43/21.14 | (8303) sum(all_0_9_9, n17) = all_0_7_7
% 55.43/21.14 |
% 55.43/21.14 | Instantiating formula (690) with n15, n17, all_0_1_1, n6 and discharging atoms sum(n15, n17) = all_0_1_1, sum(n15, n17) = n6, yields:
% 55.43/21.14 | (1723) all_0_1_1 = n6
% 55.43/21.14 |
% 55.43/21.14 | From (1723) and (630) follows:
% 55.43/21.14 | (8305) sum(all_0_2_2, n6) = all_0_0_0
% 55.43/21.14 |
% 55.43/21.14 | From (1723) and (1719) follows:
% 55.43/21.14 | (1024) sum(n15, n17) = n6
% 55.43/21.14 |
% 55.43/21.14 +-Applying beta-rule and splitting (1252), into two cases.
% 55.43/21.14 |-Branch one:
% 55.43/21.14 | (1253) all_0_11_11 = n16
% 55.43/21.14 |
% 55.43/21.14 | From (1253) and (559) follows:
% 55.43/21.14 | (1254) pred(n16) = all_0_9_9
% 55.43/21.14 |
% 55.43/21.14 | From (1253) and (992) follows:
% 55.43/21.14 | (1255) succ(n16) = all_0_5_5
% 55.43/21.14 |
% 55.43/21.14 | Instantiating formula (500) with n16, all_0_9_9, n15 and discharging atoms pred(n16) = all_0_9_9, pred(n16) = n15, yields:
% 55.43/21.14 | (1256) all_0_9_9 = n15
% 55.43/21.14 |
% 55.43/21.14 | Instantiating formula (617) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 55.43/21.14 | (1257) all_0_5_5 = n17
% 55.43/21.14 |
% 55.43/21.14 | From (1256)(1257) and (538) follows:
% 55.43/21.14 | (1258) sum(n15, n17) = all_0_2_2
% 55.43/21.14 |
% 55.43/21.14 | From (1256) and (8303) follows:
% 55.43/21.14 | (8313) sum(n15, n17) = all_0_7_7
% 55.43/21.14 |
% 55.43/21.14 | From (1257) and (8301) follows:
% 55.43/21.15 | (8314) sum(n15, n17) = all_0_4_4
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (690) with n15, n17, all_0_2_2, n6 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n6, yields:
% 55.43/21.15 | (1262) all_0_2_2 = n6
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (690) 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:
% 55.43/21.15 | (1093) all_0_2_2 = all_0_4_4
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (690) 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:
% 55.43/21.15 | (1094) all_0_2_2 = all_0_7_7
% 55.43/21.15 |
% 55.43/21.15 | Combining equations (1094,1093) yields a new equation:
% 55.43/21.15 | (1095) all_0_4_4 = all_0_7_7
% 55.43/21.15 |
% 55.43/21.15 | Combining equations (1262,1093) yields a new equation:
% 55.43/21.15 | (1423) all_0_4_4 = n6
% 55.43/21.15 |
% 55.43/21.15 | Combining equations (1423,1095) yields a new equation:
% 55.43/21.15 | (1425) all_0_7_7 = n6
% 55.43/21.15 |
% 55.43/21.15 | Combining equations (1425,1095) yields a new equation:
% 55.43/21.15 | (1423) all_0_4_4 = n6
% 55.43/21.15 |
% 55.43/21.15 | Combining equations (1423,1093) yields a new equation:
% 55.43/21.15 | (1262) all_0_2_2 = n6
% 55.43/21.15 |
% 55.43/21.15 | From (1262) and (8305) follows:
% 55.43/21.15 | (8323) sum(n6, n6) = all_0_0_0
% 55.43/21.15 |
% 55.43/21.15 | From (1425)(1423) and (590) follows:
% 55.43/21.15 | (1427) sum(n6, n6) = all_0_3_3
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (690) with n6, n6, all_0_0_0, n12 and discharging atoms sum(n6, n6) = all_0_0_0, sum(n6, n6) = n12, yields:
% 55.43/21.15 | (1195) all_0_0_0 = n12
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (690) 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:
% 55.43/21.15 | (1103) all_0_0_0 = all_0_3_3
% 55.43/21.15 |
% 55.43/21.15 | Combining equations (1195,1103) yields a new equation:
% 55.43/21.15 | (1194) all_0_3_3 = n12
% 55.43/21.15 |
% 55.43/21.15 | Combining equations (1194,1103) yields a new equation:
% 55.43/21.15 | (1195) all_0_0_0 = n12
% 55.43/21.15 |
% 55.43/21.15 | Equations (1195,1194) can reduce 679 to:
% 55.43/21.15 | (1106) $false
% 55.43/21.15 |
% 55.43/21.15 |-The branch is then unsatisfiable
% 55.43/21.15 |-Branch two:
% 55.43/21.15 | (1269) ~ (all_0_11_11 = n16)
% 55.43/21.15 | (1270) 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
% 55.43/21.15 |
% 55.43/21.15 +-Applying beta-rule and splitting (1270), into two cases.
% 55.43/21.15 |-Branch one:
% 55.43/21.15 | (1271) all_0_11_11 = n15
% 55.43/21.15 |
% 55.43/21.15 | From (1271) and (559) follows:
% 55.43/21.15 | (1272) pred(n15) = all_0_9_9
% 55.43/21.15 |
% 55.43/21.15 | From (1271) and (992) follows:
% 55.43/21.15 | (1273) succ(n15) = all_0_5_5
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (500) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 55.43/21.15 | (1274) all_0_9_9 = n14
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (617) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 55.43/21.15 | (1275) all_0_5_5 = n16
% 55.43/21.15 |
% 55.43/21.15 | From (1274)(1275) and (538) follows:
% 55.43/21.15 | (1276) sum(n14, n16) = all_0_2_2
% 55.43/21.15 |
% 55.43/21.15 | From (1274) and (8303) follows:
% 55.43/21.15 | (8338) sum(n14, n17) = all_0_7_7
% 55.43/21.15 |
% 55.43/21.15 | From (1275) and (8301) follows:
% 55.43/21.15 | (8339) sum(n15, n16) = all_0_4_4
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (690) with n15, n16, all_0_4_4, n5 and discharging atoms sum(n15, n16) = all_0_4_4, sum(n15, n16) = n5, yields:
% 55.43/21.15 | (1441) all_0_4_4 = n5
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (690) with n14, n17, all_0_7_7, n5 and discharging atoms sum(n14, n17) = all_0_7_7, sum(n14, n17) = n5, yields:
% 55.43/21.15 | (1443) all_0_7_7 = n5
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (690) with n14, n16, all_0_2_2, n4 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n4, yields:
% 55.43/21.15 | (1280) all_0_2_2 = n4
% 55.43/21.15 |
% 55.43/21.15 | From (1280) and (8305) follows:
% 55.43/21.15 | (8343) sum(n4, n6) = all_0_0_0
% 55.43/21.15 |
% 55.43/21.15 | From (1443)(1441) and (590) follows:
% 55.43/21.15 | (1445) sum(n5, n5) = all_0_3_3
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 55.43/21.15 | (1212) all_0_3_3 = n10
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (690) with n4, n6, all_0_0_0, n10 and discharging atoms sum(n4, n6) = all_0_0_0, sum(n4, n6) = n10, yields:
% 55.43/21.15 | (1213) all_0_0_0 = n10
% 55.43/21.15 |
% 55.43/21.15 | Equations (1213,1212) can reduce 679 to:
% 55.43/21.15 | (1106) $false
% 55.43/21.15 |
% 55.43/21.15 |-The branch is then unsatisfiable
% 55.43/21.15 |-Branch two:
% 55.43/21.15 | (1287) ~ (all_0_11_11 = n15)
% 55.43/21.15 | (1288) 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
% 55.43/21.15 |
% 55.43/21.15 +-Applying beta-rule and splitting (1288), into two cases.
% 55.43/21.15 |-Branch one:
% 55.43/21.15 | (1289) all_0_11_11 = n14
% 55.43/21.15 |
% 55.43/21.15 | From (1289) and (559) follows:
% 55.43/21.15 | (1290) pred(n14) = all_0_9_9
% 55.43/21.15 |
% 55.43/21.15 | From (1289) and (992) follows:
% 55.43/21.15 | (1291) succ(n14) = all_0_5_5
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (500) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 55.43/21.15 | (1292) all_0_9_9 = n13
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (617) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 55.43/21.15 | (1293) all_0_5_5 = n15
% 55.43/21.15 |
% 55.43/21.15 | From (1292)(1293) and (538) follows:
% 55.43/21.15 | (1294) sum(n13, n15) = all_0_2_2
% 55.43/21.15 |
% 55.43/21.15 | From (1292) and (8303) follows:
% 55.43/21.15 | (8356) sum(n13, n17) = all_0_7_7
% 55.43/21.15 |
% 55.43/21.15 | From (1293) and (8301) follows:
% 55.43/21.15 | (8357) sum(n15, n15) = all_0_4_4
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (690) with n15, n15, all_0_4_4, n4 and discharging atoms sum(n15, n15) = all_0_4_4, sum(n15, n15) = n4, yields:
% 55.43/21.15 | (1459) all_0_4_4 = n4
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (690) with n13, n17, all_0_7_7, n4 and discharging atoms sum(n13, n17) = all_0_7_7, sum(n13, n17) = n4, yields:
% 55.43/21.15 | (1461) all_0_7_7 = n4
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (690) with n13, n15, all_0_2_2, n2 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n2, yields:
% 55.43/21.15 | (1298) all_0_2_2 = n2
% 55.43/21.15 |
% 55.43/21.15 | From (1298) and (8305) follows:
% 55.43/21.15 | (8361) sum(n2, n6) = all_0_0_0
% 55.43/21.15 |
% 55.43/21.15 | From (1461)(1459) and (590) follows:
% 55.43/21.15 | (1463) sum(n4, n4) = all_0_3_3
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 55.43/21.15 | (1230) all_0_3_3 = n8
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (690) with n2, n6, all_0_0_0, n8 and discharging atoms sum(n2, n6) = all_0_0_0, sum(n2, n6) = n8, yields:
% 55.43/21.15 | (1231) all_0_0_0 = n8
% 55.43/21.15 |
% 55.43/21.15 | Equations (1231,1230) can reduce 679 to:
% 55.43/21.15 | (1106) $false
% 55.43/21.15 |
% 55.43/21.15 |-The branch is then unsatisfiable
% 55.43/21.15 |-Branch two:
% 55.43/21.15 | (1305) ~ (all_0_11_11 = n14)
% 55.43/21.15 | (1306) 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
% 55.43/21.15 |
% 55.43/21.15 +-Applying beta-rule and splitting (1306), into two cases.
% 55.43/21.15 |-Branch one:
% 55.43/21.15 | (1307) all_0_11_11 = n13
% 55.43/21.15 |
% 55.43/21.15 | From (1307) and (559) follows:
% 55.43/21.15 | (1308) pred(n13) = all_0_9_9
% 55.43/21.15 |
% 55.43/21.15 | From (1307) and (992) follows:
% 55.43/21.15 | (1309) succ(n13) = all_0_5_5
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (500) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 55.43/21.15 | (1310) all_0_9_9 = n12
% 55.43/21.15 |
% 55.43/21.15 | Instantiating formula (617) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 55.43/21.15 | (1311) all_0_5_5 = n14
% 55.43/21.15 |
% 55.43/21.15 | From (1310)(1311) and (538) follows:
% 55.43/21.15 | (1312) sum(n12, n14) = all_0_2_2
% 55.43/21.15 |
% 55.43/21.15 | From (1310) and (8303) follows:
% 55.43/21.15 | (8374) sum(n12, n17) = all_0_7_7
% 55.43/21.15 |
% 55.43/21.15 | From (1311) and (8301) follows:
% 55.43/21.16 | (8375) sum(n15, n14) = all_0_4_4
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n15, n14, all_0_4_4, n3 and discharging atoms sum(n15, n14) = all_0_4_4, sum(n15, n14) = n3, yields:
% 55.43/21.16 | (1477) all_0_4_4 = n3
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n12, n17, all_0_7_7, n3 and discharging atoms sum(n12, n17) = all_0_7_7, sum(n12, n17) = n3, yields:
% 55.43/21.16 | (1479) all_0_7_7 = n3
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n12, n14, all_0_2_2, n0 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n0, yields:
% 55.43/21.16 | (1316) all_0_2_2 = n0
% 55.43/21.16 |
% 55.43/21.16 | From (1316) and (8305) follows:
% 55.43/21.16 | (8379) sum(n0, n6) = all_0_0_0
% 55.43/21.16 |
% 55.43/21.16 | From (1479)(1477) and (590) follows:
% 55.43/21.16 | (1481) sum(n3, n3) = all_0_3_3
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 55.43/21.16 | (1248) all_0_3_3 = n6
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n0, n6, all_0_0_0, n6 and discharging atoms sum(n0, n6) = all_0_0_0, sum(n0, n6) = n6, yields:
% 55.43/21.16 | (1249) all_0_0_0 = n6
% 55.43/21.16 |
% 55.43/21.16 | Equations (1249,1248) can reduce 679 to:
% 55.43/21.16 | (1106) $false
% 55.43/21.16 |
% 55.43/21.16 |-The branch is then unsatisfiable
% 55.43/21.16 |-Branch two:
% 55.43/21.16 | (1323) ~ (all_0_11_11 = n13)
% 55.43/21.16 | (1324) 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
% 55.43/21.16 |
% 55.43/21.16 +-Applying beta-rule and splitting (1324), into two cases.
% 55.43/21.16 |-Branch one:
% 55.43/21.16 | (1325) all_0_11_11 = n12
% 55.43/21.16 |
% 55.43/21.16 | From (1325) and (559) follows:
% 55.43/21.16 | (1326) pred(n12) = all_0_9_9
% 55.43/21.16 |
% 55.43/21.16 | From (1325) and (992) follows:
% 55.43/21.16 | (1327) succ(n12) = all_0_5_5
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (500) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 55.43/21.16 | (1328) all_0_9_9 = n11
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (617) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 55.43/21.16 | (1329) all_0_5_5 = n13
% 55.43/21.16 |
% 55.43/21.16 | From (1328)(1329) and (538) follows:
% 55.43/21.16 | (1330) sum(n11, n13) = all_0_2_2
% 55.43/21.16 |
% 55.43/21.16 | From (1328) and (8303) follows:
% 55.43/21.16 | (8392) sum(n11, n17) = all_0_7_7
% 55.43/21.16 |
% 55.43/21.16 | From (1329) and (8301) follows:
% 55.43/21.16 | (8393) sum(n15, n13) = all_0_4_4
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n15, n13, all_0_4_4, n2 and discharging atoms sum(n15, n13) = all_0_4_4, sum(n15, n13) = n2, yields:
% 55.43/21.16 | (1495) all_0_4_4 = n2
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n11, n17, all_0_7_7, n2 and discharging atoms sum(n11, n17) = all_0_7_7, sum(n11, n17) = n2, yields:
% 55.43/21.16 | (1497) all_0_7_7 = n2
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n11, n13, all_0_2_2, n24 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n24, yields:
% 55.43/21.16 | (1092) all_0_2_2 = n24
% 55.43/21.16 |
% 55.43/21.16 | From (1092) and (8305) follows:
% 55.43/21.16 | (1726) sum(n24, n6) = all_0_0_0
% 55.43/21.16 |
% 55.43/21.16 | From (1497)(1495) and (590) follows:
% 55.43/21.16 | (1499) sum(n2, n2) = all_0_3_3
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n24, n6, all_0_0_0, n4 and discharging atoms sum(n24, n6) = all_0_0_0, sum(n24, n6) = n4, yields:
% 55.43/21.16 | (1267) all_0_0_0 = n4
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 55.43/21.16 | (1266) all_0_3_3 = n4
% 55.43/21.16 |
% 55.43/21.16 | Equations (1267,1266) can reduce 679 to:
% 55.43/21.16 | (1106) $false
% 55.43/21.16 |
% 55.43/21.16 |-The branch is then unsatisfiable
% 55.43/21.16 |-Branch two:
% 55.43/21.16 | (1341) ~ (all_0_11_11 = n12)
% 55.43/21.16 | (1342) 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
% 55.43/21.16 |
% 55.43/21.16 +-Applying beta-rule and splitting (1342), into two cases.
% 55.43/21.16 |-Branch one:
% 55.43/21.16 | (1343) all_0_11_11 = n11
% 55.43/21.16 |
% 55.43/21.16 | From (1343) and (559) follows:
% 55.43/21.16 | (1344) pred(n11) = all_0_9_9
% 55.43/21.16 |
% 55.43/21.16 | From (1343) and (992) follows:
% 55.43/21.16 | (1345) succ(n11) = all_0_5_5
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (500) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 55.43/21.16 | (1346) all_0_9_9 = n10
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (617) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 55.43/21.16 | (1347) all_0_5_5 = n12
% 55.43/21.16 |
% 55.43/21.16 | From (1346)(1347) and (538) follows:
% 55.43/21.16 | (1348) sum(n10, n12) = all_0_2_2
% 55.43/21.16 |
% 55.43/21.16 | From (1346) and (8303) follows:
% 55.43/21.16 | (8410) sum(n10, n17) = all_0_7_7
% 55.43/21.16 |
% 55.43/21.16 | From (1347) and (8301) follows:
% 55.43/21.16 | (8411) sum(n15, n12) = all_0_4_4
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n15, n12, all_0_4_4, n1 and discharging atoms sum(n15, n12) = all_0_4_4, sum(n15, n12) = n1, yields:
% 55.43/21.16 | (1513) all_0_4_4 = n1
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n10, n17, all_0_7_7, n1 and discharging atoms sum(n10, n17) = all_0_7_7, sum(n10, n17) = n1, yields:
% 55.43/21.16 | (1515) all_0_7_7 = n1
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n10, n12, all_0_2_2, n22 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n22, yields:
% 55.43/21.16 | (1118) all_0_2_2 = n22
% 55.43/21.16 |
% 55.43/21.16 | From (1118) and (8305) follows:
% 55.43/21.16 | (2638) sum(n22, n6) = all_0_0_0
% 55.43/21.16 |
% 55.43/21.16 | From (1515)(1513) and (590) follows:
% 55.43/21.16 | (1517) sum(n1, n1) = all_0_3_3
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n22, n6, all_0_0_0, n2 and discharging atoms sum(n22, n6) = all_0_0_0, sum(n22, n6) = n2, yields:
% 55.43/21.16 | (1285) all_0_0_0 = n2
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 55.43/21.16 | (1284) all_0_3_3 = n2
% 55.43/21.16 |
% 55.43/21.16 | Equations (1285,1284) can reduce 679 to:
% 55.43/21.16 | (1106) $false
% 55.43/21.16 |
% 55.43/21.16 |-The branch is then unsatisfiable
% 55.43/21.16 |-Branch two:
% 55.43/21.16 | (1359) ~ (all_0_11_11 = n11)
% 55.43/21.16 | (1360) 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
% 55.43/21.16 |
% 55.43/21.16 +-Applying beta-rule and splitting (1360), into two cases.
% 55.43/21.16 |-Branch one:
% 55.43/21.16 | (1361) all_0_11_11 = n10
% 55.43/21.16 |
% 55.43/21.16 | From (1361) and (559) follows:
% 55.43/21.16 | (1362) pred(n10) = all_0_9_9
% 55.43/21.16 |
% 55.43/21.16 | From (1361) and (992) follows:
% 55.43/21.16 | (1363) succ(n10) = all_0_5_5
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (500) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 55.43/21.16 | (1364) all_0_9_9 = n9
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (617) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 55.43/21.16 | (1365) all_0_5_5 = n11
% 55.43/21.16 |
% 55.43/21.16 | From (1364)(1365) and (538) follows:
% 55.43/21.16 | (1366) sum(n9, n11) = all_0_2_2
% 55.43/21.16 |
% 55.43/21.16 | From (1364) and (8303) follows:
% 55.43/21.16 | (8428) sum(n9, n17) = all_0_7_7
% 55.43/21.16 |
% 55.43/21.16 | From (1365) and (8301) follows:
% 55.43/21.16 | (8429) sum(n15, n11) = all_0_4_4
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n15, n11, all_0_4_4, n0 and discharging atoms sum(n15, n11) = all_0_4_4, sum(n15, n11) = n0, yields:
% 55.43/21.16 | (1531) all_0_4_4 = n0
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n9, n17, all_0_7_7, n0 and discharging atoms sum(n9, n17) = all_0_7_7, sum(n9, n17) = n0, yields:
% 55.43/21.16 | (1533) all_0_7_7 = n0
% 55.43/21.16 |
% 55.43/21.16 | Instantiating formula (690) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 55.43/21.16 | (1136) all_0_2_2 = n20
% 55.43/21.16 |
% 55.43/21.16 | From (1136) and (8305) follows:
% 55.43/21.17 | (3512) sum(n20, n6) = all_0_0_0
% 55.43/21.17 |
% 55.43/21.17 | From (1533)(1531) and (590) follows:
% 55.43/21.17 | (1535) sum(n0, n0) = all_0_3_3
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (690) with n20, n6, all_0_0_0, n0 and discharging atoms sum(n20, n6) = all_0_0_0, sum(n20, n6) = n0, yields:
% 55.43/21.17 | (1303) all_0_0_0 = n0
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 55.43/21.17 | (1302) all_0_3_3 = n0
% 55.43/21.17 |
% 55.43/21.17 | Equations (1303,1302) can reduce 679 to:
% 55.43/21.17 | (1106) $false
% 55.43/21.17 |
% 55.43/21.17 |-The branch is then unsatisfiable
% 55.43/21.17 |-Branch two:
% 55.43/21.17 | (1377) ~ (all_0_11_11 = n10)
% 55.43/21.17 | (1378) 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
% 55.43/21.17 |
% 55.43/21.17 +-Applying beta-rule and splitting (1378), into two cases.
% 55.43/21.17 |-Branch one:
% 55.43/21.17 | (1379) all_0_11_11 = n9
% 55.43/21.17 |
% 55.43/21.17 | From (1379) and (559) follows:
% 55.43/21.17 | (1380) pred(n9) = all_0_9_9
% 55.43/21.17 |
% 55.43/21.17 | From (1379) and (992) follows:
% 55.43/21.17 | (1381) succ(n9) = all_0_5_5
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 55.43/21.17 | (1382) all_0_9_9 = n8
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 55.43/21.17 | (1383) all_0_5_5 = n10
% 55.43/21.17 |
% 55.43/21.17 | From (1382)(1383) and (538) follows:
% 55.43/21.17 | (1384) sum(n8, n10) = all_0_2_2
% 55.43/21.17 |
% 55.43/21.17 | From (1382) and (8303) follows:
% 55.43/21.17 | (8446) sum(n8, n17) = all_0_7_7
% 55.43/21.17 |
% 55.43/21.17 | From (1383) and (8301) follows:
% 55.43/21.17 | (8447) sum(n15, n10) = all_0_4_4
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (690) with n15, n10, all_0_4_4, n25 and discharging atoms sum(n15, n10) = all_0_4_4, sum(n15, n10) = n25, yields:
% 55.43/21.17 | (1551) all_0_4_4 = n25
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (690) with n8, n17, all_0_7_7, n25 and discharging atoms sum(n8, n17) = all_0_7_7, sum(n8, n17) = n25, yields:
% 55.43/21.17 | (1550) all_0_7_7 = n25
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 55.43/21.17 | (1154) all_0_2_2 = n18
% 55.43/21.17 |
% 55.43/21.17 | From (1154) and (8305) follows:
% 55.43/21.17 | (4350) sum(n18, n6) = all_0_0_0
% 55.43/21.17 |
% 55.43/21.17 | From (1550)(1551) and (590) follows:
% 55.43/21.17 | (1553) sum(n25, n25) = all_0_3_3
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 55.43/21.17 | (1320) all_0_3_3 = n24
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (690) with n18, n6, all_0_0_0, n24 and discharging atoms sum(n18, n6) = all_0_0_0, sum(n18, n6) = n24, yields:
% 55.43/21.17 | (1321) all_0_0_0 = n24
% 55.43/21.17 |
% 55.43/21.17 | Equations (1321,1320) can reduce 679 to:
% 55.43/21.17 | (1106) $false
% 55.43/21.17 |
% 55.43/21.17 |-The branch is then unsatisfiable
% 55.43/21.17 |-Branch two:
% 55.43/21.17 | (1395) ~ (all_0_11_11 = n9)
% 55.43/21.17 | (1396) 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
% 55.43/21.17 |
% 55.43/21.17 +-Applying beta-rule and splitting (1396), into two cases.
% 55.43/21.17 |-Branch one:
% 55.43/21.17 | (1397) all_0_11_11 = n8
% 55.43/21.17 |
% 55.43/21.17 | From (1397) and (559) follows:
% 55.43/21.17 | (1398) pred(n8) = all_0_9_9
% 55.43/21.17 |
% 55.43/21.17 | From (1397) and (992) follows:
% 55.43/21.17 | (1399) succ(n8) = all_0_5_5
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 55.43/21.17 | (1400) all_0_9_9 = n7
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 55.43/21.17 | (1401) all_0_5_5 = n9
% 55.43/21.17 |
% 55.43/21.17 | From (1400)(1401) and (538) follows:
% 55.43/21.17 | (1402) sum(n7, n9) = all_0_2_2
% 55.43/21.17 |
% 55.43/21.17 | From (1400) and (8303) follows:
% 55.43/21.17 | (8464) sum(n7, n17) = all_0_7_7
% 55.43/21.17 |
% 55.43/21.17 | From (1401) and (8301) follows:
% 55.43/21.17 | (8465) sum(n15, n9) = all_0_4_4
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (690) with n15, n9, all_0_4_4, n24 and discharging atoms sum(n15, n9) = all_0_4_4, sum(n15, n9) = n24, yields:
% 55.43/21.17 | (1096) all_0_4_4 = n24
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (690) with n7, n17, all_0_7_7, n24 and discharging atoms sum(n7, n17) = all_0_7_7, sum(n7, n17) = n24, yields:
% 55.43/21.17 | (1097) all_0_7_7 = n24
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 55.43/21.17 | (1172) all_0_2_2 = n16
% 55.43/21.17 |
% 55.43/21.17 | From (1172) and (8305) follows:
% 55.43/21.17 | (5152) sum(n16, n6) = all_0_0_0
% 55.43/21.17 |
% 55.43/21.17 | From (1097)(1096) and (590) follows:
% 55.43/21.17 | (1101) sum(n24, n24) = all_0_3_3
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 55.43/21.17 | (1104) all_0_3_3 = n22
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (690) with n16, n6, all_0_0_0, n22 and discharging atoms sum(n16, n6) = all_0_0_0, sum(n16, n6) = n22, yields:
% 55.43/21.17 | (1102) all_0_0_0 = n22
% 55.43/21.17 |
% 55.43/21.17 | Equations (1102,1104) can reduce 679 to:
% 55.43/21.17 | (1106) $false
% 55.43/21.17 |
% 55.43/21.17 |-The branch is then unsatisfiable
% 55.43/21.17 |-Branch two:
% 55.43/21.17 | (1413) ~ (all_0_11_11 = n8)
% 55.43/21.17 | (1414) 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
% 55.43/21.17 |
% 55.43/21.17 +-Applying beta-rule and splitting (1414), into two cases.
% 55.43/21.17 |-Branch one:
% 55.43/21.17 | (1415) all_0_11_11 = n7
% 55.43/21.17 |
% 55.43/21.17 | From (1415) and (559) follows:
% 55.43/21.17 | (1416) pred(n7) = all_0_9_9
% 55.43/21.17 |
% 55.43/21.17 | From (1415) and (992) follows:
% 55.43/21.17 | (1417) succ(n7) = all_0_5_5
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 55.43/21.17 | (1418) all_0_9_9 = n6
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 55.43/21.17 | (1419) all_0_5_5 = n8
% 55.43/21.17 |
% 55.43/21.17 | From (1418)(1419) and (538) follows:
% 55.43/21.17 | (1420) sum(n6, n8) = all_0_2_2
% 55.43/21.17 |
% 55.43/21.17 | From (1418) and (8303) follows:
% 55.43/21.17 | (8482) sum(n6, n17) = all_0_7_7
% 55.43/21.17 |
% 55.43/21.17 | From (1419) and (8301) follows:
% 55.43/21.17 | (8483) sum(n15, n8) = all_0_4_4
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (690) with n15, n8, all_0_4_4, n23 and discharging atoms sum(n15, n8) = all_0_4_4, sum(n15, n8) = n23, yields:
% 55.43/21.17 | (1117) all_0_4_4 = n23
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (690) with n6, n17, all_0_7_7, n23 and discharging atoms sum(n6, n17) = all_0_7_7, sum(n6, n17) = n23, yields:
% 55.43/21.17 | (1119) all_0_7_7 = n23
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 55.43/21.17 | (1190) all_0_2_2 = n14
% 55.43/21.17 |
% 55.43/21.17 | From (1190) and (8305) follows:
% 55.43/21.17 | (5918) sum(n14, n6) = all_0_0_0
% 55.43/21.17 |
% 55.43/21.17 | From (1119)(1117) and (590) follows:
% 55.43/21.17 | (1121) sum(n23, n23) = all_0_3_3
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 55.43/21.17 | (1122) all_0_3_3 = n20
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (690) with n14, n6, all_0_0_0, n20 and discharging atoms sum(n14, n6) = all_0_0_0, sum(n14, n6) = n20, yields:
% 55.43/21.17 | (1123) all_0_0_0 = n20
% 55.43/21.17 |
% 55.43/21.17 | Equations (1123,1122) can reduce 679 to:
% 55.43/21.17 | (1106) $false
% 55.43/21.17 |
% 55.43/21.17 |-The branch is then unsatisfiable
% 55.43/21.17 |-Branch two:
% 55.43/21.17 | (1431) ~ (all_0_11_11 = n7)
% 55.43/21.17 | (1432) 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
% 55.43/21.17 |
% 55.43/21.17 +-Applying beta-rule and splitting (1432), into two cases.
% 55.43/21.17 |-Branch one:
% 55.43/21.17 | (1433) all_0_11_11 = n6
% 55.43/21.17 |
% 55.43/21.17 | From (1433) and (559) follows:
% 55.43/21.17 | (1434) pred(n6) = all_0_9_9
% 55.43/21.17 |
% 55.43/21.17 | From (1433) and (992) follows:
% 55.43/21.17 | (1435) succ(n6) = all_0_5_5
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 55.43/21.17 | (1436) all_0_9_9 = n5
% 55.43/21.17 |
% 55.43/21.17 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 55.43/21.17 | (1437) all_0_5_5 = n7
% 55.43/21.17 |
% 55.43/21.17 | From (1436)(1437) and (538) follows:
% 55.43/21.17 | (1438) sum(n5, n7) = all_0_2_2
% 55.43/21.17 |
% 55.43/21.17 | From (1436) and (8303) follows:
% 55.43/21.18 | (8500) sum(n5, n17) = all_0_7_7
% 55.43/21.18 |
% 55.43/21.18 | From (1437) and (8301) follows:
% 55.43/21.18 | (8501) sum(n15, n7) = all_0_4_4
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (690) with n15, n7, all_0_4_4, n22 and discharging atoms sum(n15, n7) = all_0_4_4, sum(n15, n7) = n22, yields:
% 55.43/21.18 | (1135) all_0_4_4 = n22
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (690) with n5, n17, all_0_7_7, n22 and discharging atoms sum(n5, n17) = all_0_7_7, sum(n5, n17) = n22, yields:
% 55.43/21.18 | (1137) all_0_7_7 = n22
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 55.43/21.18 | (1208) all_0_2_2 = n12
% 55.43/21.18 |
% 55.43/21.18 | From (1208) and (8305) follows:
% 55.43/21.18 | (6648) sum(n12, n6) = all_0_0_0
% 55.43/21.18 |
% 55.43/21.18 | From (1137)(1135) and (590) follows:
% 55.43/21.18 | (1139) sum(n22, n22) = all_0_3_3
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 55.43/21.18 | (1140) all_0_3_3 = n18
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (690) with n12, n6, all_0_0_0, n18 and discharging atoms sum(n12, n6) = all_0_0_0, sum(n12, n6) = n18, yields:
% 55.43/21.18 | (1141) all_0_0_0 = n18
% 55.43/21.18 |
% 55.43/21.18 | Equations (1141,1140) can reduce 679 to:
% 55.43/21.18 | (1106) $false
% 55.43/21.18 |
% 55.43/21.18 |-The branch is then unsatisfiable
% 55.43/21.18 |-Branch two:
% 55.43/21.18 | (1449) ~ (all_0_11_11 = n6)
% 55.43/21.18 | (1450) 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
% 55.43/21.18 |
% 55.43/21.18 +-Applying beta-rule and splitting (1450), into two cases.
% 55.43/21.18 |-Branch one:
% 55.43/21.18 | (1451) all_0_11_11 = n5
% 55.43/21.18 |
% 55.43/21.18 | From (1451) and (559) follows:
% 55.43/21.18 | (1452) pred(n5) = all_0_9_9
% 55.43/21.18 |
% 55.43/21.18 | From (1451) and (992) follows:
% 55.43/21.18 | (1453) succ(n5) = all_0_5_5
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 55.43/21.18 | (1454) all_0_9_9 = n4
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 55.43/21.18 | (1455) all_0_5_5 = n6
% 55.43/21.18 |
% 55.43/21.18 | From (1454)(1455) and (538) follows:
% 55.43/21.18 | (1456) sum(n4, n6) = all_0_2_2
% 55.43/21.18 |
% 55.43/21.18 | From (1454) and (8303) follows:
% 55.43/21.18 | (8518) sum(n4, n17) = all_0_7_7
% 55.43/21.18 |
% 55.43/21.18 | From (1455) and (8301) follows:
% 55.43/21.18 | (8519) sum(n15, n6) = all_0_4_4
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (690) with n15, n6, all_0_4_4, n21 and discharging atoms sum(n15, n6) = all_0_4_4, sum(n15, n6) = n21, yields:
% 55.43/21.18 | (1153) all_0_4_4 = n21
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (690) with n4, n17, all_0_7_7, n21 and discharging atoms sum(n4, n17) = all_0_7_7, sum(n4, n17) = n21, yields:
% 55.43/21.18 | (1155) all_0_7_7 = n21
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 55.43/21.18 | (1226) all_0_2_2 = n10
% 55.43/21.18 |
% 55.43/21.18 | From (1226) and (8305) follows:
% 55.43/21.18 | (7342) sum(n10, n6) = all_0_0_0
% 55.43/21.18 |
% 55.43/21.18 | From (1155)(1153) and (590) follows:
% 55.43/21.18 | (1157) sum(n21, n21) = all_0_3_3
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 55.43/21.18 | (1158) all_0_3_3 = n16
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (690) with n10, n6, all_0_0_0, n16 and discharging atoms sum(n10, n6) = all_0_0_0, sum(n10, n6) = n16, yields:
% 55.43/21.18 | (1159) all_0_0_0 = n16
% 55.43/21.18 |
% 55.43/21.18 | Equations (1159,1158) can reduce 679 to:
% 55.43/21.18 | (1106) $false
% 55.43/21.18 |
% 55.43/21.18 |-The branch is then unsatisfiable
% 55.43/21.18 |-Branch two:
% 55.43/21.18 | (1467) ~ (all_0_11_11 = n5)
% 55.43/21.18 | (1468) 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
% 55.43/21.18 |
% 55.43/21.18 +-Applying beta-rule and splitting (1468), into two cases.
% 55.43/21.18 |-Branch one:
% 55.43/21.18 | (1469) all_0_11_11 = n4
% 55.43/21.18 |
% 55.43/21.18 | From (1469) and (559) follows:
% 55.43/21.18 | (1470) pred(n4) = all_0_9_9
% 55.43/21.18 |
% 55.43/21.18 | From (1469) and (992) follows:
% 55.43/21.18 | (1471) succ(n4) = all_0_5_5
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 55.43/21.18 | (1472) all_0_9_9 = n3
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 55.43/21.18 | (1473) all_0_5_5 = n5
% 55.43/21.18 |
% 55.43/21.18 | From (1472)(1473) and (538) follows:
% 55.43/21.18 | (1474) sum(n3, n5) = all_0_2_2
% 55.43/21.18 |
% 55.43/21.18 | From (1472) and (8303) follows:
% 55.43/21.18 | (8536) sum(n3, n17) = all_0_7_7
% 55.43/21.18 |
% 55.43/21.18 | From (1473) and (8301) follows:
% 55.43/21.18 | (8537) sum(n15, n5) = all_0_4_4
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (690) with n15, n5, all_0_4_4, n20 and discharging atoms sum(n15, n5) = all_0_4_4, sum(n15, n5) = n20, yields:
% 55.43/21.18 | (1171) all_0_4_4 = n20
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (690) with n3, n17, all_0_7_7, n20 and discharging atoms sum(n3, n17) = all_0_7_7, sum(n3, n17) = n20, yields:
% 55.43/21.18 | (1173) all_0_7_7 = n20
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 55.43/21.18 | (1244) all_0_2_2 = n8
% 55.43/21.18 |
% 55.43/21.18 | From (1244) and (8305) follows:
% 55.43/21.18 | (8000) sum(n8, n6) = all_0_0_0
% 55.43/21.18 |
% 55.43/21.18 | From (1173)(1171) and (590) follows:
% 55.43/21.18 | (1175) sum(n20, n20) = all_0_3_3
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 55.43/21.18 | (1176) all_0_3_3 = n14
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (690) with n8, n6, all_0_0_0, n14 and discharging atoms sum(n8, n6) = all_0_0_0, sum(n8, n6) = n14, yields:
% 55.43/21.18 | (1177) all_0_0_0 = n14
% 55.43/21.18 |
% 55.43/21.18 | Equations (1177,1176) can reduce 679 to:
% 55.43/21.18 | (1106) $false
% 55.43/21.18 |
% 55.43/21.18 |-The branch is then unsatisfiable
% 55.43/21.18 |-Branch two:
% 55.43/21.18 | (1485) ~ (all_0_11_11 = n4)
% 55.43/21.18 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 55.43/21.18 |
% 55.43/21.18 +-Applying beta-rule and splitting (1486), into two cases.
% 55.43/21.18 |-Branch one:
% 55.43/21.18 | (1487) all_0_11_11 = n3
% 55.43/21.18 |
% 55.43/21.18 | From (1487) and (559) follows:
% 55.43/21.18 | (1488) pred(n3) = all_0_9_9
% 55.43/21.18 |
% 55.43/21.18 | From (1487) and (992) follows:
% 55.43/21.18 | (1489) succ(n3) = all_0_5_5
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 55.43/21.18 | (1490) all_0_9_9 = n2
% 55.43/21.18 |
% 55.43/21.18 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 55.43/21.18 | (1491) all_0_5_5 = n4
% 55.43/21.18 |
% 55.43/21.18 | From (1490)(1491) and (538) follows:
% 55.43/21.18 | (1492) sum(n2, n4) = all_0_2_2
% 55.43/21.18 |
% 55.43/21.18 | From (1490) and (8303) follows:
% 55.43/21.18 | (8554) sum(n2, n17) = all_0_7_7
% 55.43/21.18 |
% 55.43/21.18 | From (1491) and (8301) follows:
% 55.43/21.19 | (8555) sum(n15, n4) = all_0_4_4
% 55.43/21.19 |
% 55.43/21.19 | Instantiating formula (690) with n15, n4, all_0_4_4, n19 and discharging atoms sum(n15, n4) = all_0_4_4, sum(n15, n4) = n19, yields:
% 55.43/21.19 | (1189) all_0_4_4 = n19
% 55.43/21.19 |
% 55.43/21.19 | Instantiating formula (690) with n2, n17, all_0_7_7, n19 and discharging atoms sum(n2, n17) = all_0_7_7, sum(n2, n17) = n19, yields:
% 55.43/21.19 | (1191) all_0_7_7 = n19
% 55.43/21.19 |
% 55.43/21.19 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 55.43/21.19 | (1262) all_0_2_2 = n6
% 55.43/21.19 |
% 55.43/21.19 | From (1262) and (8305) follows:
% 55.62/21.19 | (8323) sum(n6, n6) = all_0_0_0
% 55.62/21.19 |
% 55.62/21.19 | From (1191)(1189) and (590) follows:
% 55.62/21.19 | (1193) sum(n19, n19) = all_0_3_3
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 55.62/21.19 | (1194) all_0_3_3 = n12
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (690) with n6, n6, all_0_0_0, n12 and discharging atoms sum(n6, n6) = all_0_0_0, sum(n6, n6) = n12, yields:
% 55.62/21.19 | (1195) all_0_0_0 = n12
% 55.62/21.19 |
% 55.62/21.19 | Equations (1195,1194) can reduce 679 to:
% 55.62/21.19 | (1106) $false
% 55.62/21.19 |
% 55.62/21.19 |-The branch is then unsatisfiable
% 55.62/21.19 |-Branch two:
% 55.62/21.19 | (1503) ~ (all_0_11_11 = n3)
% 55.62/21.19 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 55.62/21.19 |
% 55.62/21.19 +-Applying beta-rule and splitting (1504), into two cases.
% 55.62/21.19 |-Branch one:
% 55.62/21.19 | (1505) all_0_11_11 = n2
% 55.62/21.19 |
% 55.62/21.19 | From (1505) and (559) follows:
% 55.62/21.19 | (1506) pred(n2) = all_0_9_9
% 55.62/21.19 |
% 55.62/21.19 | From (1505) and (992) follows:
% 55.62/21.19 | (1507) succ(n2) = all_0_5_5
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 55.62/21.19 | (1508) all_0_9_9 = n1
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 55.62/21.19 | (1509) all_0_5_5 = n3
% 55.62/21.19 |
% 55.62/21.19 | From (1508)(1509) and (538) follows:
% 55.62/21.19 | (1510) sum(n1, n3) = all_0_2_2
% 55.62/21.19 |
% 55.62/21.19 | From (1508) and (8303) follows:
% 55.62/21.19 | (8572) sum(n1, n17) = all_0_7_7
% 55.62/21.19 |
% 55.62/21.19 | From (1509) and (8301) follows:
% 55.62/21.19 | (8573) sum(n15, n3) = all_0_4_4
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (690) with n15, n3, all_0_4_4, n18 and discharging atoms sum(n15, n3) = all_0_4_4, sum(n15, n3) = n18, yields:
% 55.62/21.19 | (1207) all_0_4_4 = n18
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (690) with n1, n17, all_0_7_7, n18 and discharging atoms sum(n1, n17) = all_0_7_7, sum(n1, n17) = n18, yields:
% 55.62/21.19 | (1209) all_0_7_7 = n18
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 55.62/21.19 | (1280) all_0_2_2 = n4
% 55.62/21.19 |
% 55.62/21.19 | From (1280) and (8305) follows:
% 55.62/21.19 | (8343) sum(n4, n6) = all_0_0_0
% 55.62/21.19 |
% 55.62/21.19 | From (1209)(1207) and (590) follows:
% 55.62/21.19 | (1211) sum(n18, n18) = all_0_3_3
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 55.62/21.19 | (1212) all_0_3_3 = n10
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (690) with n4, n6, all_0_0_0, n10 and discharging atoms sum(n4, n6) = all_0_0_0, sum(n4, n6) = n10, yields:
% 55.62/21.19 | (1213) all_0_0_0 = n10
% 55.62/21.19 |
% 55.62/21.19 | Equations (1213,1212) can reduce 679 to:
% 55.62/21.19 | (1106) $false
% 55.62/21.19 |
% 55.62/21.19 |-The branch is then unsatisfiable
% 55.62/21.19 |-Branch two:
% 55.62/21.19 | (1521) ~ (all_0_11_11 = n2)
% 55.62/21.19 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 55.62/21.19 |
% 55.62/21.19 +-Applying beta-rule and splitting (1522), into two cases.
% 55.62/21.19 |-Branch one:
% 55.62/21.19 | (1523) all_0_11_11 = n1
% 55.62/21.19 |
% 55.62/21.19 | From (1523) and (559) follows:
% 55.62/21.19 | (1524) pred(n1) = all_0_9_9
% 55.62/21.19 |
% 55.62/21.19 | From (1523) and (992) follows:
% 55.62/21.19 | (1525) succ(n1) = all_0_5_5
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 55.62/21.19 | (1526) all_0_9_9 = n0
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 55.62/21.19 | (1527) all_0_5_5 = n2
% 55.62/21.19 |
% 55.62/21.19 | From (1526)(1527) and (538) follows:
% 55.62/21.19 | (1528) sum(n0, n2) = all_0_2_2
% 55.62/21.19 |
% 55.62/21.19 | From (1526) and (8303) follows:
% 55.62/21.19 | (8590) sum(n0, n17) = all_0_7_7
% 55.62/21.19 |
% 55.62/21.19 | From (1527) and (8301) follows:
% 55.62/21.19 | (8591) sum(n15, n2) = all_0_4_4
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (690) with n15, n2, all_0_4_4, n17 and discharging atoms sum(n15, n2) = all_0_4_4, sum(n15, n2) = n17, yields:
% 55.62/21.19 | (1225) all_0_4_4 = n17
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (690) with n0, n17, all_0_7_7, n17 and discharging atoms sum(n0, n17) = all_0_7_7, sum(n0, n17) = n17, yields:
% 55.62/21.19 | (1227) all_0_7_7 = n17
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 55.62/21.19 | (1298) all_0_2_2 = n2
% 55.62/21.19 |
% 55.62/21.19 | From (1298) and (8305) follows:
% 55.62/21.19 | (8361) sum(n2, n6) = all_0_0_0
% 55.62/21.19 |
% 55.62/21.19 | From (1227)(1225) and (590) follows:
% 55.62/21.19 | (1229) sum(n17, n17) = all_0_3_3
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 55.62/21.19 | (1230) all_0_3_3 = n8
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (690) with n2, n6, all_0_0_0, n8 and discharging atoms sum(n2, n6) = all_0_0_0, sum(n2, n6) = n8, yields:
% 55.62/21.19 | (1231) all_0_0_0 = n8
% 55.62/21.19 |
% 55.62/21.19 | Equations (1231,1230) can reduce 679 to:
% 55.62/21.19 | (1106) $false
% 55.62/21.19 |
% 55.62/21.19 |-The branch is then unsatisfiable
% 55.62/21.19 |-Branch two:
% 55.62/21.19 | (1540) ~ (all_0_11_11 = n1)
% 55.62/21.19 | (1541) all_0_11_11 = n0
% 55.62/21.19 |
% 55.62/21.19 | From (1541) and (559) follows:
% 55.62/21.19 | (1542) pred(n0) = all_0_9_9
% 55.62/21.19 |
% 55.62/21.19 | From (1541) and (992) follows:
% 55.62/21.19 | (1543) succ(n0) = all_0_5_5
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 55.62/21.19 | (1544) all_0_9_9 = n25
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 55.62/21.19 | (1545) all_0_5_5 = n1
% 55.62/21.19 |
% 55.62/21.19 | From (1544)(1545) and (538) follows:
% 55.62/21.19 | (1546) sum(n25, n1) = all_0_2_2
% 55.62/21.19 |
% 55.62/21.19 | From (1544) and (8303) follows:
% 55.62/21.19 | (8607) sum(n25, n17) = all_0_7_7
% 55.62/21.19 |
% 55.62/21.19 | From (1545) and (8301) follows:
% 55.62/21.19 | (8608) sum(n15, n1) = all_0_4_4
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (690) with n25, n17, all_0_7_7, n16 and discharging atoms sum(n25, n17) = all_0_7_7, sum(n25, n17) = n16, yields:
% 55.62/21.19 | (1245) all_0_7_7 = n16
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 55.62/21.19 | (1316) all_0_2_2 = n0
% 55.62/21.19 |
% 55.62/21.19 | Instantiating formula (690) with n15, n1, all_0_4_4, n16 and discharging atoms sum(n15, n1) = all_0_4_4, sum(n15, n1) = n16, yields:
% 55.62/21.19 | (1243) all_0_4_4 = n16
% 55.62/21.19 |
% 55.62/21.19 | From (1316) and (8305) follows:
% 55.62/21.20 | (8379) sum(n0, n6) = all_0_0_0
% 55.62/21.20 |
% 55.62/21.20 | From (1245)(1243) and (590) follows:
% 55.62/21.20 | (1247) sum(n16, n16) = all_0_3_3
% 55.62/21.20 |
% 55.62/21.20 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 55.62/21.20 | (1248) all_0_3_3 = n6
% 55.62/21.20 |
% 55.62/21.20 | Instantiating formula (690) with n0, n6, all_0_0_0, n6 and discharging atoms sum(n0, n6) = all_0_0_0, sum(n0, n6) = n6, yields:
% 55.62/21.20 | (1249) all_0_0_0 = n6
% 55.62/21.20 |
% 55.62/21.20 | Equations (1249,1248) can reduce 679 to:
% 55.62/21.20 | (1106) $false
% 55.62/21.20 |
% 55.62/21.20 |-The branch is then unsatisfiable
% 55.62/21.20 |-Branch two:
% 55.62/21.20 | (1730) ~ (all_0_10_10 = n16)
% 55.62/21.20 | (1731) 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
% 55.62/21.20 |
% 55.62/21.20 +-Applying beta-rule and splitting (1252), into two cases.
% 55.62/21.20 |-Branch one:
% 55.62/21.20 | (1253) all_0_11_11 = n16
% 55.62/21.20 |
% 55.62/21.20 | From (1253) and (559) follows:
% 55.62/21.20 | (1254) pred(n16) = all_0_9_9
% 55.62/21.20 |
% 55.62/21.20 | From (1253) and (992) follows:
% 55.62/21.20 | (1255) succ(n16) = all_0_5_5
% 55.62/21.20 |
% 55.62/21.20 | Instantiating formula (500) with n16, all_0_9_9, n15 and discharging atoms pred(n16) = all_0_9_9, pred(n16) = n15, yields:
% 55.62/21.20 | (1256) all_0_9_9 = n15
% 55.62/21.20 |
% 55.62/21.20 | Instantiating formula (617) with n16, all_0_5_5, n17 and discharging atoms succ(n16) = all_0_5_5, succ(n16) = n17, yields:
% 55.62/21.20 | (1257) all_0_5_5 = n17
% 55.62/21.20 |
% 55.62/21.20 | From (1257) and (541) follows:
% 55.62/21.20 | (8624) sum(all_0_6_6, n17) = all_0_4_4
% 55.62/21.20 |
% 55.62/21.20 | From (1256)(1257) and (538) follows:
% 55.62/21.20 | (1258) sum(n15, n17) = all_0_2_2
% 55.62/21.20 |
% 55.62/21.20 | From (1256) and (427) follows:
% 55.62/21.20 | (8626) sum(n15, all_0_8_8) = all_0_7_7
% 55.62/21.20 |
% 55.62/21.20 | Instantiating formula (690) with n15, n17, all_0_2_2, n6 and discharging atoms sum(n15, n17) = all_0_2_2, sum(n15, n17) = n6, yields:
% 55.62/21.20 | (1262) all_0_2_2 = n6
% 55.62/21.20 |
% 55.62/21.20 | From (1262) and (630) follows:
% 55.62/21.20 | (8628) sum(n6, all_0_1_1) = all_0_0_0
% 55.62/21.20 |
% 55.62/21.20 +-Applying beta-rule and splitting (1731), into two cases.
% 55.62/21.20 |-Branch one:
% 55.62/21.20 | (1732) all_0_10_10 = n15
% 55.62/21.20 |
% 55.62/21.20 | From (1732) and (292) follows:
% 55.62/21.20 | (1733) pred(n15) = all_0_6_6
% 55.62/21.20 |
% 55.62/21.20 | From (1732) and (760) follows:
% 55.62/21.20 | (1734) succ(n15) = all_0_8_8
% 55.62/21.20 |
% 55.62/21.20 | Instantiating formula (500) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 55.62/21.20 | (1735) all_0_6_6 = n14
% 55.62/21.20 |
% 55.62/21.20 | Instantiating formula (617) with n15, all_0_8_8, n16 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n16, yields:
% 55.62/21.20 | (1736) all_0_8_8 = n16
% 55.62/21.20 |
% 55.62/21.20 | From (1735)(1736) and (411) follows:
% 55.62/21.20 | (1737) sum(n14, n16) = all_0_1_1
% 55.62/21.20 |
% 55.62/21.20 | From (1735) and (8624) follows:
% 55.62/21.20 | (8635) sum(n14, n17) = all_0_4_4
% 55.62/21.20 |
% 55.62/21.20 | From (1736) and (8626) follows:
% 55.62/21.20 | (8636) sum(n15, n16) = all_0_7_7
% 55.62/21.20 |
% 55.62/21.20 | Instantiating formula (690) with n15, n16, all_0_7_7, n5 and discharging atoms sum(n15, n16) = all_0_7_7, sum(n15, n16) = n5, yields:
% 55.62/21.20 | (1443) all_0_7_7 = n5
% 55.62/21.20 |
% 55.62/21.20 | Instantiating formula (690) with n14, n17, all_0_4_4, n5 and discharging atoms sum(n14, n17) = all_0_4_4, sum(n14, n17) = n5, yields:
% 55.62/21.20 | (1441) all_0_4_4 = n5
% 55.62/21.20 |
% 55.62/21.20 | Instantiating formula (690) with n14, n16, all_0_1_1, n4 and discharging atoms sum(n14, n16) = all_0_1_1, sum(n14, n16) = n4, yields:
% 55.62/21.20 | (1741) all_0_1_1 = n4
% 55.62/21.20 |
% 55.62/21.20 | From (1443)(1441) and (590) follows:
% 55.62/21.20 | (1445) sum(n5, n5) = all_0_3_3
% 55.62/21.20 |
% 55.62/21.20 | From (1741) and (8628) follows:
% 55.62/21.20 | (8641) sum(n6, n4) = all_0_0_0
% 55.62/21.20 |
% 55.62/21.20 | Instantiating formula (690) with n6, n4, all_0_0_0, n10 and discharging atoms sum(n6, n4) = all_0_0_0, sum(n6, n4) = n10, yields:
% 55.62/21.20 | (1213) all_0_0_0 = n10
% 55.62/21.20 |
% 55.62/21.20 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 55.62/21.20 | (1212) all_0_3_3 = n10
% 55.62/21.20 |
% 55.62/21.20 | Equations (1213,1212) can reduce 679 to:
% 55.62/21.20 | (1106) $false
% 55.62/21.20 |
% 55.62/21.20 |-The branch is then unsatisfiable
% 55.62/21.20 |-Branch two:
% 55.62/21.20 | (1748) ~ (all_0_10_10 = n15)
% 55.62/21.20 | (1749) 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
% 55.62/21.20 |
% 55.62/21.20 +-Applying beta-rule and splitting (1749), into two cases.
% 55.62/21.20 |-Branch one:
% 55.62/21.20 | (1750) all_0_10_10 = n14
% 55.62/21.20 |
% 55.62/21.20 | From (1750) and (292) follows:
% 55.62/21.20 | (1751) pred(n14) = all_0_6_6
% 55.62/21.20 |
% 55.62/21.20 | From (1750) and (760) follows:
% 55.62/21.20 | (1752) succ(n14) = all_0_8_8
% 55.62/21.20 |
% 55.62/21.20 | Instantiating formula (500) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 55.62/21.20 | (1753) all_0_6_6 = n13
% 55.62/21.20 |
% 55.62/21.20 | Instantiating formula (617) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 55.62/21.20 | (1754) all_0_8_8 = n15
% 55.62/21.20 |
% 55.62/21.20 | From (1753)(1754) and (411) follows:
% 55.62/21.20 | (1755) sum(n13, n15) = all_0_1_1
% 55.62/21.20 |
% 55.62/21.20 | From (1753) and (8624) follows:
% 55.62/21.20 | (8653) sum(n13, n17) = all_0_4_4
% 55.62/21.20 |
% 55.62/21.20 | From (1754) and (8626) follows:
% 55.62/21.20 | (8654) sum(n15, n15) = all_0_7_7
% 55.62/21.20 |
% 55.62/21.20 | Instantiating formula (690) with n15, n15, all_0_7_7, n4 and discharging atoms sum(n15, n15) = all_0_7_7, sum(n15, n15) = n4, yields:
% 55.62/21.20 | (1461) all_0_7_7 = n4
% 55.62/21.20 |
% 55.62/21.20 | Instantiating formula (690) with n13, n17, all_0_4_4, n4 and discharging atoms sum(n13, n17) = all_0_4_4, sum(n13, n17) = n4, yields:
% 55.62/21.20 | (1459) all_0_4_4 = n4
% 55.62/21.20 |
% 55.62/21.20 | Instantiating formula (690) with n13, n15, all_0_1_1, n2 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n2, yields:
% 55.62/21.20 | (1759) all_0_1_1 = n2
% 55.62/21.20 |
% 55.62/21.20 | From (1461)(1459) and (590) follows:
% 55.62/21.20 | (1463) sum(n4, n4) = all_0_3_3
% 55.62/21.20 |
% 55.62/21.20 | From (1759) and (8628) follows:
% 55.64/21.20 | (8659) sum(n6, n2) = all_0_0_0
% 55.64/21.20 |
% 55.64/21.20 | Instantiating formula (690) with n6, n2, all_0_0_0, n8 and discharging atoms sum(n6, n2) = all_0_0_0, sum(n6, n2) = n8, yields:
% 55.64/21.20 | (1231) all_0_0_0 = n8
% 55.64/21.20 |
% 55.64/21.20 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 55.64/21.20 | (1230) all_0_3_3 = n8
% 55.64/21.20 |
% 55.64/21.20 | Equations (1231,1230) can reduce 679 to:
% 55.64/21.20 | (1106) $false
% 55.64/21.20 |
% 55.64/21.20 |-The branch is then unsatisfiable
% 55.64/21.20 |-Branch two:
% 55.64/21.20 | (1766) ~ (all_0_10_10 = n14)
% 55.64/21.20 | (1767) 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
% 55.64/21.20 |
% 55.64/21.20 +-Applying beta-rule and splitting (1767), into two cases.
% 55.64/21.20 |-Branch one:
% 55.64/21.20 | (1768) all_0_10_10 = n13
% 55.64/21.20 |
% 55.64/21.20 | From (1768) and (292) follows:
% 55.64/21.20 | (1769) pred(n13) = all_0_6_6
% 55.64/21.20 |
% 55.64/21.20 | From (1768) and (760) follows:
% 55.64/21.20 | (1770) succ(n13) = all_0_8_8
% 55.64/21.20 |
% 55.64/21.20 | Instantiating formula (500) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 55.64/21.20 | (1771) all_0_6_6 = n12
% 55.64/21.20 |
% 55.64/21.20 | Instantiating formula (617) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 55.64/21.20 | (1772) all_0_8_8 = n14
% 55.64/21.20 |
% 55.64/21.20 | From (1771)(1772) and (411) follows:
% 55.64/21.20 | (1773) sum(n12, n14) = all_0_1_1
% 55.64/21.20 |
% 55.64/21.20 | From (1771) and (8624) follows:
% 55.64/21.21 | (8671) sum(n12, n17) = all_0_4_4
% 55.64/21.21 |
% 55.64/21.21 | From (1772) and (8626) follows:
% 55.64/21.21 | (8672) sum(n15, n14) = all_0_7_7
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (690) with n15, n14, all_0_7_7, n3 and discharging atoms sum(n15, n14) = all_0_7_7, sum(n15, n14) = n3, yields:
% 55.64/21.21 | (1479) all_0_7_7 = n3
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (690) with n12, n17, all_0_4_4, n3 and discharging atoms sum(n12, n17) = all_0_4_4, sum(n12, n17) = n3, yields:
% 55.64/21.21 | (1477) all_0_4_4 = n3
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (690) with n12, n14, all_0_1_1, n0 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n0, yields:
% 55.64/21.21 | (1777) all_0_1_1 = n0
% 55.64/21.21 |
% 55.64/21.21 | From (1479)(1477) and (590) follows:
% 55.64/21.21 | (1481) sum(n3, n3) = all_0_3_3
% 55.64/21.21 |
% 55.64/21.21 | From (1777) and (8628) follows:
% 55.64/21.21 | (8677) sum(n6, n0) = all_0_0_0
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (690) with n6, n0, all_0_0_0, n6 and discharging atoms sum(n6, n0) = all_0_0_0, sum(n6, n0) = n6, yields:
% 55.64/21.21 | (1249) all_0_0_0 = n6
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 55.64/21.21 | (1248) all_0_3_3 = n6
% 55.64/21.21 |
% 55.64/21.21 | Equations (1249,1248) can reduce 679 to:
% 55.64/21.21 | (1106) $false
% 55.64/21.21 |
% 55.64/21.21 |-The branch is then unsatisfiable
% 55.64/21.21 |-Branch two:
% 55.64/21.21 | (1784) ~ (all_0_10_10 = n13)
% 55.64/21.21 | (1785) 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
% 55.64/21.21 |
% 55.64/21.21 +-Applying beta-rule and splitting (1785), into two cases.
% 55.64/21.21 |-Branch one:
% 55.64/21.21 | (1786) all_0_10_10 = n12
% 55.64/21.21 |
% 55.64/21.21 | From (1786) and (292) follows:
% 55.64/21.21 | (1787) pred(n12) = all_0_6_6
% 55.64/21.21 |
% 55.64/21.21 | From (1786) and (760) follows:
% 55.64/21.21 | (1788) succ(n12) = all_0_8_8
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (500) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 55.64/21.21 | (1789) all_0_6_6 = n11
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (617) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 55.64/21.21 | (1790) all_0_8_8 = n13
% 55.64/21.21 |
% 55.64/21.21 | From (1789)(1790) and (411) follows:
% 55.64/21.21 | (1791) sum(n11, n13) = all_0_1_1
% 55.64/21.21 |
% 55.64/21.21 | From (1789) and (8624) follows:
% 55.64/21.21 | (8689) sum(n11, n17) = all_0_4_4
% 55.64/21.21 |
% 55.64/21.21 | From (1790) and (8626) follows:
% 55.64/21.21 | (8690) sum(n15, n13) = all_0_7_7
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (690) with n15, n13, all_0_7_7, n2 and discharging atoms sum(n15, n13) = all_0_7_7, sum(n15, n13) = n2, yields:
% 55.64/21.21 | (1497) all_0_7_7 = n2
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (690) with n11, n17, all_0_4_4, n2 and discharging atoms sum(n11, n17) = all_0_4_4, sum(n11, n17) = n2, yields:
% 55.64/21.21 | (1495) all_0_4_4 = n2
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (690) with n11, n13, all_0_1_1, n24 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n24, yields:
% 55.64/21.21 | (1081) all_0_1_1 = n24
% 55.64/21.21 |
% 55.64/21.21 | From (1497)(1495) and (590) follows:
% 55.64/21.21 | (1499) sum(n2, n2) = all_0_3_3
% 55.64/21.21 |
% 55.64/21.21 | From (1081) and (8628) follows:
% 55.64/21.21 | (1264) sum(n6, n24) = all_0_0_0
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (690) with n6, n24, all_0_0_0, n4 and discharging atoms sum(n6, n24) = all_0_0_0, sum(n6, n24) = n4, yields:
% 55.64/21.21 | (1267) all_0_0_0 = n4
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 55.64/21.21 | (1266) all_0_3_3 = n4
% 55.64/21.21 |
% 55.64/21.21 | Equations (1267,1266) can reduce 679 to:
% 55.64/21.21 | (1106) $false
% 55.64/21.21 |
% 55.64/21.21 |-The branch is then unsatisfiable
% 55.64/21.21 |-Branch two:
% 55.64/21.21 | (1802) ~ (all_0_10_10 = n12)
% 55.64/21.21 | (1803) 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
% 55.64/21.21 |
% 55.64/21.21 +-Applying beta-rule and splitting (1803), into two cases.
% 55.64/21.21 |-Branch one:
% 55.64/21.21 | (1804) all_0_10_10 = n11
% 55.64/21.21 |
% 55.64/21.21 | From (1804) and (292) follows:
% 55.64/21.21 | (1805) pred(n11) = all_0_6_6
% 55.64/21.21 |
% 55.64/21.21 | From (1804) and (760) follows:
% 55.64/21.21 | (1806) succ(n11) = all_0_8_8
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (500) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 55.64/21.21 | (1807) all_0_6_6 = n10
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (617) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 55.64/21.21 | (1808) all_0_8_8 = n12
% 55.64/21.21 |
% 55.64/21.21 | From (1807)(1808) and (411) follows:
% 55.64/21.21 | (1809) sum(n10, n12) = all_0_1_1
% 55.64/21.21 |
% 55.64/21.21 | From (1807) and (8624) follows:
% 55.64/21.21 | (8707) sum(n10, n17) = all_0_4_4
% 55.64/21.21 |
% 55.64/21.21 | From (1808) and (8626) follows:
% 55.64/21.21 | (8708) sum(n15, n12) = all_0_7_7
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (690) with n15, n12, all_0_7_7, n1 and discharging atoms sum(n15, n12) = all_0_7_7, sum(n15, n12) = n1, yields:
% 55.64/21.21 | (1515) all_0_7_7 = n1
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (690) with n10, n17, all_0_4_4, n1 and discharging atoms sum(n10, n17) = all_0_4_4, sum(n10, n17) = n1, yields:
% 55.64/21.21 | (1513) all_0_4_4 = n1
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (690) with n10, n12, all_0_1_1, n22 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n22, yields:
% 55.64/21.21 | (1579) all_0_1_1 = n22
% 55.64/21.21 |
% 55.64/21.21 | From (1515)(1513) and (590) follows:
% 55.64/21.21 | (1517) sum(n1, n1) = all_0_3_3
% 55.64/21.21 |
% 55.64/21.21 | From (1579) and (8628) follows:
% 55.64/21.21 | (2196) sum(n6, n22) = all_0_0_0
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (690) with n6, n22, all_0_0_0, n2 and discharging atoms sum(n6, n22) = all_0_0_0, sum(n6, n22) = n2, yields:
% 55.64/21.21 | (1285) all_0_0_0 = n2
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 55.64/21.21 | (1284) all_0_3_3 = n2
% 55.64/21.21 |
% 55.64/21.21 | Equations (1285,1284) can reduce 679 to:
% 55.64/21.21 | (1106) $false
% 55.64/21.21 |
% 55.64/21.21 |-The branch is then unsatisfiable
% 55.64/21.21 |-Branch two:
% 55.64/21.21 | (1820) ~ (all_0_10_10 = n11)
% 55.64/21.21 | (1821) 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
% 55.64/21.21 |
% 55.64/21.21 +-Applying beta-rule and splitting (1821), into two cases.
% 55.64/21.21 |-Branch one:
% 55.64/21.21 | (1822) all_0_10_10 = n10
% 55.64/21.21 |
% 55.64/21.21 | From (1822) and (292) follows:
% 55.64/21.21 | (1823) pred(n10) = all_0_6_6
% 55.64/21.21 |
% 55.64/21.21 | From (1822) and (760) follows:
% 55.64/21.21 | (1824) succ(n10) = all_0_8_8
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (500) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 55.64/21.21 | (1825) all_0_6_6 = n9
% 55.64/21.21 |
% 55.64/21.21 | Instantiating formula (617) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 55.64/21.21 | (1826) all_0_8_8 = n11
% 55.64/21.21 |
% 55.64/21.21 | From (1825)(1826) and (411) follows:
% 55.64/21.21 | (1827) sum(n9, n11) = all_0_1_1
% 55.64/21.21 |
% 55.64/21.21 | From (1825) and (8624) follows:
% 55.65/21.22 | (8725) sum(n9, n17) = all_0_4_4
% 55.65/21.22 |
% 55.65/21.22 | From (1826) and (8626) follows:
% 55.65/21.22 | (8726) sum(n15, n11) = all_0_7_7
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (690) with n15, n11, all_0_7_7, n0 and discharging atoms sum(n15, n11) = all_0_7_7, sum(n15, n11) = n0, yields:
% 55.65/21.22 | (1533) all_0_7_7 = n0
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (690) with n9, n17, all_0_4_4, n0 and discharging atoms sum(n9, n17) = all_0_4_4, sum(n9, n17) = n0, yields:
% 55.65/21.22 | (1531) all_0_4_4 = n0
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (690) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 55.65/21.22 | (1597) all_0_1_1 = n20
% 55.65/21.22 |
% 55.65/21.22 | From (1533)(1531) and (590) follows:
% 55.65/21.22 | (1535) sum(n0, n0) = all_0_3_3
% 55.65/21.22 |
% 55.65/21.22 | From (1597) and (8628) follows:
% 55.65/21.22 | (3088) sum(n6, n20) = all_0_0_0
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (690) with n6, n20, all_0_0_0, n0 and discharging atoms sum(n6, n20) = all_0_0_0, sum(n6, n20) = n0, yields:
% 55.65/21.22 | (1303) all_0_0_0 = n0
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 55.65/21.22 | (1302) all_0_3_3 = n0
% 55.65/21.22 |
% 55.65/21.22 | Equations (1303,1302) can reduce 679 to:
% 55.65/21.22 | (1106) $false
% 55.65/21.22 |
% 55.65/21.22 |-The branch is then unsatisfiable
% 55.65/21.22 |-Branch two:
% 55.65/21.22 | (1838) ~ (all_0_10_10 = n10)
% 55.65/21.22 | (1839) 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
% 55.65/21.22 |
% 55.65/21.22 +-Applying beta-rule and splitting (1839), into two cases.
% 55.65/21.22 |-Branch one:
% 55.65/21.22 | (1840) all_0_10_10 = n9
% 55.65/21.22 |
% 55.65/21.22 | From (1840) and (292) follows:
% 55.65/21.22 | (1841) pred(n9) = all_0_6_6
% 55.65/21.22 |
% 55.65/21.22 | From (1840) and (760) follows:
% 55.65/21.22 | (1842) succ(n9) = all_0_8_8
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (500) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 55.65/21.22 | (1843) all_0_6_6 = n8
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (617) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 55.65/21.22 | (1844) all_0_8_8 = n10
% 55.65/21.22 |
% 55.65/21.22 | From (1843)(1844) and (411) follows:
% 55.65/21.22 | (1845) sum(n8, n10) = all_0_1_1
% 55.65/21.22 |
% 55.65/21.22 | From (1843) and (8624) follows:
% 55.65/21.22 | (8743) sum(n8, n17) = all_0_4_4
% 55.65/21.22 |
% 55.65/21.22 | From (1844) and (8626) follows:
% 55.65/21.22 | (8744) sum(n15, n10) = all_0_7_7
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (690) with n15, n10, all_0_7_7, n25 and discharging atoms sum(n15, n10) = all_0_7_7, sum(n15, n10) = n25, yields:
% 55.65/21.22 | (1550) all_0_7_7 = n25
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (690) with n8, n17, all_0_4_4, n25 and discharging atoms sum(n8, n17) = all_0_4_4, sum(n8, n17) = n25, yields:
% 55.65/21.22 | (1551) all_0_4_4 = n25
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (690) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 55.65/21.22 | (1615) all_0_1_1 = n18
% 55.65/21.22 |
% 55.65/21.22 | From (1550)(1551) and (590) follows:
% 55.65/21.22 | (1553) sum(n25, n25) = all_0_3_3
% 55.65/21.22 |
% 55.65/21.22 | From (1615) and (8628) follows:
% 55.65/21.22 | (3944) sum(n6, n18) = all_0_0_0
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 55.65/21.22 | (1320) all_0_3_3 = n24
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (690) with n6, n18, all_0_0_0, n24 and discharging atoms sum(n6, n18) = all_0_0_0, sum(n6, n18) = n24, yields:
% 55.65/21.22 | (1321) all_0_0_0 = n24
% 55.65/21.22 |
% 55.65/21.22 | Equations (1321,1320) can reduce 679 to:
% 55.65/21.22 | (1106) $false
% 55.65/21.22 |
% 55.65/21.22 |-The branch is then unsatisfiable
% 55.65/21.22 |-Branch two:
% 55.65/21.22 | (1856) ~ (all_0_10_10 = n9)
% 55.65/21.22 | (1857) 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
% 55.65/21.22 |
% 55.65/21.22 +-Applying beta-rule and splitting (1857), into two cases.
% 55.65/21.22 |-Branch one:
% 55.65/21.22 | (1858) all_0_10_10 = n8
% 55.65/21.22 |
% 55.65/21.22 | From (1858) and (292) follows:
% 55.65/21.22 | (1859) pred(n8) = all_0_6_6
% 55.65/21.22 |
% 55.65/21.22 | From (1858) and (760) follows:
% 55.65/21.22 | (1860) succ(n8) = all_0_8_8
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 55.65/21.22 | (1861) all_0_6_6 = n7
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 55.65/21.22 | (1862) all_0_8_8 = n9
% 55.65/21.22 |
% 55.65/21.22 | From (1861)(1862) and (411) follows:
% 55.65/21.22 | (1863) sum(n7, n9) = all_0_1_1
% 55.65/21.22 |
% 55.65/21.22 | From (1861) and (8624) follows:
% 55.65/21.22 | (8761) sum(n7, n17) = all_0_4_4
% 55.65/21.22 |
% 55.65/21.22 | From (1862) and (8626) follows:
% 55.65/21.22 | (8762) sum(n15, n9) = all_0_7_7
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (690) with n15, n9, all_0_7_7, n24 and discharging atoms sum(n15, n9) = all_0_7_7, sum(n15, n9) = n24, yields:
% 55.65/21.22 | (1097) all_0_7_7 = n24
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (690) with n7, n17, all_0_4_4, n24 and discharging atoms sum(n7, n17) = all_0_4_4, sum(n7, n17) = n24, yields:
% 55.65/21.22 | (1096) all_0_4_4 = n24
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 55.65/21.22 | (1633) all_0_1_1 = n16
% 55.65/21.22 |
% 55.65/21.22 | From (1097)(1096) and (590) follows:
% 55.65/21.22 | (1101) sum(n24, n24) = all_0_3_3
% 55.65/21.22 |
% 55.65/21.22 | From (1633) and (8628) follows:
% 55.65/21.22 | (4764) sum(n6, n16) = all_0_0_0
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 55.65/21.22 | (1104) all_0_3_3 = n22
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (690) with n6, n16, all_0_0_0, n22 and discharging atoms sum(n6, n16) = all_0_0_0, sum(n6, n16) = n22, yields:
% 55.65/21.22 | (1102) all_0_0_0 = n22
% 55.65/21.22 |
% 55.65/21.22 | Equations (1102,1104) can reduce 679 to:
% 55.65/21.22 | (1106) $false
% 55.65/21.22 |
% 55.65/21.22 |-The branch is then unsatisfiable
% 55.65/21.22 |-Branch two:
% 55.65/21.22 | (1874) ~ (all_0_10_10 = n8)
% 55.65/21.22 | (1875) 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
% 55.65/21.22 |
% 55.65/21.22 +-Applying beta-rule and splitting (1875), into two cases.
% 55.65/21.22 |-Branch one:
% 55.65/21.22 | (1876) all_0_10_10 = n7
% 55.65/21.22 |
% 55.65/21.22 | From (1876) and (292) follows:
% 55.65/21.22 | (1877) pred(n7) = all_0_6_6
% 55.65/21.22 |
% 55.65/21.22 | From (1876) and (760) follows:
% 55.65/21.22 | (1878) succ(n7) = all_0_8_8
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 55.65/21.22 | (1879) all_0_6_6 = n6
% 55.65/21.22 |
% 55.65/21.22 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 55.65/21.22 | (1880) all_0_8_8 = n8
% 55.65/21.22 |
% 55.65/21.22 | From (1879)(1880) and (411) follows:
% 55.65/21.22 | (1881) sum(n6, n8) = all_0_1_1
% 55.65/21.22 |
% 55.65/21.22 | From (1879) and (8624) follows:
% 55.65/21.22 | (8779) sum(n6, n17) = all_0_4_4
% 55.65/21.22 |
% 55.65/21.22 | From (1880) and (8626) follows:
% 55.65/21.23 | (8780) sum(n15, n8) = all_0_7_7
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n15, n8, all_0_7_7, n23 and discharging atoms sum(n15, n8) = all_0_7_7, sum(n15, n8) = n23, yields:
% 55.65/21.23 | (1119) all_0_7_7 = n23
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n6, n17, all_0_4_4, n23 and discharging atoms sum(n6, n17) = all_0_4_4, sum(n6, n17) = n23, yields:
% 55.65/21.23 | (1117) all_0_4_4 = n23
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 55.65/21.23 | (1651) all_0_1_1 = n14
% 55.65/21.23 |
% 55.65/21.23 | From (1119)(1117) and (590) follows:
% 55.65/21.23 | (1121) sum(n23, n23) = all_0_3_3
% 55.65/21.23 |
% 55.65/21.23 | From (1651) and (8628) follows:
% 55.65/21.23 | (5548) sum(n6, n14) = all_0_0_0
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 55.65/21.23 | (1122) all_0_3_3 = n20
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n6, n14, all_0_0_0, n20 and discharging atoms sum(n6, n14) = all_0_0_0, sum(n6, n14) = n20, yields:
% 55.65/21.23 | (1123) all_0_0_0 = n20
% 55.65/21.23 |
% 55.65/21.23 | Equations (1123,1122) can reduce 679 to:
% 55.65/21.23 | (1106) $false
% 55.65/21.23 |
% 55.65/21.23 |-The branch is then unsatisfiable
% 55.65/21.23 |-Branch two:
% 55.65/21.23 | (1892) ~ (all_0_10_10 = n7)
% 55.65/21.23 | (1893) 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
% 55.65/21.23 |
% 55.65/21.23 +-Applying beta-rule and splitting (1893), into two cases.
% 55.65/21.23 |-Branch one:
% 55.65/21.23 | (1894) all_0_10_10 = n6
% 55.65/21.23 |
% 55.65/21.23 | From (1894) and (292) follows:
% 55.65/21.23 | (1895) pred(n6) = all_0_6_6
% 55.65/21.23 |
% 55.65/21.23 | From (1894) and (760) follows:
% 55.65/21.23 | (1896) succ(n6) = all_0_8_8
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 55.65/21.23 | (1897) all_0_6_6 = n5
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 55.65/21.23 | (1898) all_0_8_8 = n7
% 55.65/21.23 |
% 55.65/21.23 | From (1897)(1898) and (411) follows:
% 55.65/21.23 | (1899) sum(n5, n7) = all_0_1_1
% 55.65/21.23 |
% 55.65/21.23 | From (1897) and (8624) follows:
% 55.65/21.23 | (8797) sum(n5, n17) = all_0_4_4
% 55.65/21.23 |
% 55.65/21.23 | From (1898) and (8626) follows:
% 55.65/21.23 | (8798) sum(n15, n7) = all_0_7_7
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n15, n7, all_0_7_7, n22 and discharging atoms sum(n15, n7) = all_0_7_7, sum(n15, n7) = n22, yields:
% 55.65/21.23 | (1137) all_0_7_7 = n22
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n5, n17, all_0_4_4, n22 and discharging atoms sum(n5, n17) = all_0_4_4, sum(n5, n17) = n22, yields:
% 55.65/21.23 | (1135) all_0_4_4 = n22
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 55.65/21.23 | (1669) all_0_1_1 = n12
% 55.65/21.23 |
% 55.65/21.23 | From (1137)(1135) and (590) follows:
% 55.65/21.23 | (1139) sum(n22, n22) = all_0_3_3
% 55.65/21.23 |
% 55.65/21.23 | From (1669) and (8628) follows:
% 55.65/21.23 | (6296) sum(n6, n12) = all_0_0_0
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 55.65/21.23 | (1140) all_0_3_3 = n18
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n6, n12, all_0_0_0, n18 and discharging atoms sum(n6, n12) = all_0_0_0, sum(n6, n12) = n18, yields:
% 55.65/21.23 | (1141) all_0_0_0 = n18
% 55.65/21.23 |
% 55.65/21.23 | Equations (1141,1140) can reduce 679 to:
% 55.65/21.23 | (1106) $false
% 55.65/21.23 |
% 55.65/21.23 |-The branch is then unsatisfiable
% 55.65/21.23 |-Branch two:
% 55.65/21.23 | (1910) ~ (all_0_10_10 = n6)
% 55.65/21.23 | (1911) 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
% 55.65/21.23 |
% 55.65/21.23 +-Applying beta-rule and splitting (1911), into two cases.
% 55.65/21.23 |-Branch one:
% 55.65/21.23 | (1912) all_0_10_10 = n5
% 55.65/21.23 |
% 55.65/21.23 | From (1912) and (292) follows:
% 55.65/21.23 | (1913) pred(n5) = all_0_6_6
% 55.65/21.23 |
% 55.65/21.23 | From (1912) and (760) follows:
% 55.65/21.23 | (1914) succ(n5) = all_0_8_8
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 55.65/21.23 | (1915) all_0_6_6 = n4
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 55.65/21.23 | (1916) all_0_8_8 = n6
% 55.65/21.23 |
% 55.65/21.23 | From (1915)(1916) and (411) follows:
% 55.65/21.23 | (1917) sum(n4, n6) = all_0_1_1
% 55.65/21.23 |
% 55.65/21.23 | From (1915) and (8624) follows:
% 55.65/21.23 | (8815) sum(n4, n17) = all_0_4_4
% 55.65/21.23 |
% 55.65/21.23 | From (1916) and (8626) follows:
% 55.65/21.23 | (8816) sum(n15, n6) = all_0_7_7
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n15, n6, all_0_7_7, n21 and discharging atoms sum(n15, n6) = all_0_7_7, sum(n15, n6) = n21, yields:
% 55.65/21.23 | (1155) all_0_7_7 = n21
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n4, n17, all_0_4_4, n21 and discharging atoms sum(n4, n17) = all_0_4_4, sum(n4, n17) = n21, yields:
% 55.65/21.23 | (1153) all_0_4_4 = n21
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 55.65/21.23 | (1687) all_0_1_1 = n10
% 55.65/21.23 |
% 55.65/21.23 | From (1155)(1153) and (590) follows:
% 55.65/21.23 | (1157) sum(n21, n21) = all_0_3_3
% 55.65/21.23 |
% 55.65/21.23 | From (1687) and (8628) follows:
% 55.65/21.23 | (7008) sum(n6, n10) = all_0_0_0
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 55.65/21.23 | (1158) all_0_3_3 = n16
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n6, n10, all_0_0_0, n16 and discharging atoms sum(n6, n10) = all_0_0_0, sum(n6, n10) = n16, yields:
% 55.65/21.23 | (1159) all_0_0_0 = n16
% 55.65/21.23 |
% 55.65/21.23 | Equations (1159,1158) can reduce 679 to:
% 55.65/21.23 | (1106) $false
% 55.65/21.23 |
% 55.65/21.23 |-The branch is then unsatisfiable
% 55.65/21.23 |-Branch two:
% 55.65/21.23 | (1928) ~ (all_0_10_10 = n5)
% 55.65/21.23 | (1929) 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
% 55.65/21.23 |
% 55.65/21.23 +-Applying beta-rule and splitting (1929), into two cases.
% 55.65/21.23 |-Branch one:
% 55.65/21.23 | (1930) all_0_10_10 = n4
% 55.65/21.23 |
% 55.65/21.23 | From (1930) and (292) follows:
% 55.65/21.23 | (1931) pred(n4) = all_0_6_6
% 55.65/21.23 |
% 55.65/21.23 | From (1930) and (760) follows:
% 55.65/21.23 | (1932) succ(n4) = all_0_8_8
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 55.65/21.23 | (1933) all_0_6_6 = n3
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 55.65/21.23 | (1934) all_0_8_8 = n5
% 55.65/21.23 |
% 55.65/21.23 | From (1933)(1934) and (411) follows:
% 55.65/21.23 | (1935) sum(n3, n5) = all_0_1_1
% 55.65/21.23 |
% 55.65/21.23 | From (1933) and (8624) follows:
% 55.65/21.23 | (8833) sum(n3, n17) = all_0_4_4
% 55.65/21.23 |
% 55.65/21.23 | From (1934) and (8626) follows:
% 55.65/21.23 | (8834) sum(n15, n5) = all_0_7_7
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n15, n5, all_0_7_7, n20 and discharging atoms sum(n15, n5) = all_0_7_7, sum(n15, n5) = n20, yields:
% 55.65/21.23 | (1173) all_0_7_7 = n20
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n3, n17, all_0_4_4, n20 and discharging atoms sum(n3, n17) = all_0_4_4, sum(n3, n17) = n20, yields:
% 55.65/21.23 | (1171) all_0_4_4 = n20
% 55.65/21.23 |
% 55.65/21.23 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 55.65/21.23 | (1705) all_0_1_1 = n8
% 55.65/21.23 |
% 55.65/21.23 | From (1173)(1171) and (590) follows:
% 55.65/21.24 | (1175) sum(n20, n20) = all_0_3_3
% 55.65/21.24 |
% 55.65/21.24 | From (1705) and (8628) follows:
% 55.65/21.24 | (7684) sum(n6, n8) = all_0_0_0
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 55.65/21.24 | (1176) all_0_3_3 = n14
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (690) with n6, n8, all_0_0_0, n14 and discharging atoms sum(n6, n8) = all_0_0_0, sum(n6, n8) = n14, yields:
% 55.65/21.24 | (1177) all_0_0_0 = n14
% 55.65/21.24 |
% 55.65/21.24 | Equations (1177,1176) can reduce 679 to:
% 55.65/21.24 | (1106) $false
% 55.65/21.24 |
% 55.65/21.24 |-The branch is then unsatisfiable
% 55.65/21.24 |-Branch two:
% 55.65/21.24 | (1946) ~ (all_0_10_10 = n4)
% 55.65/21.24 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 55.65/21.24 |
% 55.65/21.24 +-Applying beta-rule and splitting (1947), into two cases.
% 55.65/21.24 |-Branch one:
% 55.65/21.24 | (1948) all_0_10_10 = n3
% 55.65/21.24 |
% 55.65/21.24 | From (1948) and (292) follows:
% 55.65/21.24 | (1949) pred(n3) = all_0_6_6
% 55.65/21.24 |
% 55.65/21.24 | From (1948) and (760) follows:
% 55.65/21.24 | (1950) succ(n3) = all_0_8_8
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 55.65/21.24 | (1951) all_0_6_6 = n2
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 55.65/21.24 | (1952) all_0_8_8 = n4
% 55.65/21.24 |
% 55.65/21.24 | From (1951)(1952) and (411) follows:
% 55.65/21.24 | (1953) sum(n2, n4) = all_0_1_1
% 55.65/21.24 |
% 55.65/21.24 | From (1951) and (8624) follows:
% 55.65/21.24 | (8851) sum(n2, n17) = all_0_4_4
% 55.65/21.24 |
% 55.65/21.24 | From (1952) and (8626) follows:
% 55.65/21.24 | (8852) sum(n15, n4) = all_0_7_7
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (690) with n15, n4, all_0_7_7, n19 and discharging atoms sum(n15, n4) = all_0_7_7, sum(n15, n4) = n19, yields:
% 55.65/21.24 | (1191) all_0_7_7 = n19
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (690) with n2, n17, all_0_4_4, n19 and discharging atoms sum(n2, n17) = all_0_4_4, sum(n2, n17) = n19, yields:
% 55.65/21.24 | (1189) all_0_4_4 = n19
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 55.65/21.24 | (1723) all_0_1_1 = n6
% 55.65/21.24 |
% 55.65/21.24 | From (1191)(1189) and (590) follows:
% 55.65/21.24 | (1193) sum(n19, n19) = all_0_3_3
% 55.65/21.24 |
% 55.65/21.24 | From (1723) and (8628) follows:
% 55.65/21.24 | (8323) sum(n6, n6) = all_0_0_0
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 55.65/21.24 | (1194) all_0_3_3 = n12
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (690) with n6, n6, all_0_0_0, n12 and discharging atoms sum(n6, n6) = all_0_0_0, sum(n6, n6) = n12, yields:
% 55.65/21.24 | (1195) all_0_0_0 = n12
% 55.65/21.24 |
% 55.65/21.24 | Equations (1195,1194) can reduce 679 to:
% 55.65/21.24 | (1106) $false
% 55.65/21.24 |
% 55.65/21.24 |-The branch is then unsatisfiable
% 55.65/21.24 |-Branch two:
% 55.65/21.24 | (1964) ~ (all_0_10_10 = n3)
% 55.65/21.24 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 55.65/21.24 |
% 55.65/21.24 +-Applying beta-rule and splitting (1965), into two cases.
% 55.65/21.24 |-Branch one:
% 55.65/21.24 | (1966) all_0_10_10 = n2
% 55.65/21.24 |
% 55.65/21.24 | From (1966) and (292) follows:
% 55.65/21.24 | (1967) pred(n2) = all_0_6_6
% 55.65/21.24 |
% 55.65/21.24 | From (1966) and (760) follows:
% 55.65/21.24 | (1968) succ(n2) = all_0_8_8
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 55.65/21.24 | (1969) all_0_6_6 = n1
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 55.65/21.24 | (1970) all_0_8_8 = n3
% 55.65/21.24 |
% 55.65/21.24 | From (1969)(1970) and (411) follows:
% 55.65/21.24 | (1971) sum(n1, n3) = all_0_1_1
% 55.65/21.24 |
% 55.65/21.24 | From (1969) and (8624) follows:
% 55.65/21.24 | (8869) sum(n1, n17) = all_0_4_4
% 55.65/21.24 |
% 55.65/21.24 | From (1970) and (8626) follows:
% 55.65/21.24 | (8870) sum(n15, n3) = all_0_7_7
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (690) with n15, n3, all_0_7_7, n18 and discharging atoms sum(n15, n3) = all_0_7_7, sum(n15, n3) = n18, yields:
% 55.65/21.24 | (1209) all_0_7_7 = n18
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (690) with n1, n17, all_0_4_4, n18 and discharging atoms sum(n1, n17) = all_0_4_4, sum(n1, n17) = n18, yields:
% 55.65/21.24 | (1207) all_0_4_4 = n18
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 55.65/21.24 | (1741) all_0_1_1 = n4
% 55.65/21.24 |
% 55.65/21.24 | From (1209)(1207) and (590) follows:
% 55.65/21.24 | (1211) sum(n18, n18) = all_0_3_3
% 55.65/21.24 |
% 55.65/21.24 | From (1741) and (8628) follows:
% 55.65/21.24 | (8641) sum(n6, n4) = all_0_0_0
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 55.65/21.24 | (1212) all_0_3_3 = n10
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (690) with n6, n4, all_0_0_0, n10 and discharging atoms sum(n6, n4) = all_0_0_0, sum(n6, n4) = n10, yields:
% 55.65/21.24 | (1213) all_0_0_0 = n10
% 55.65/21.24 |
% 55.65/21.24 | Equations (1213,1212) can reduce 679 to:
% 55.65/21.24 | (1106) $false
% 55.65/21.24 |
% 55.65/21.24 |-The branch is then unsatisfiable
% 55.65/21.24 |-Branch two:
% 55.65/21.24 | (1982) ~ (all_0_10_10 = n2)
% 55.65/21.24 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 55.65/21.24 |
% 55.65/21.24 +-Applying beta-rule and splitting (1983), into two cases.
% 55.65/21.24 |-Branch one:
% 55.65/21.24 | (1984) all_0_10_10 = n1
% 55.65/21.24 |
% 55.65/21.24 | From (1984) and (292) follows:
% 55.65/21.24 | (1985) pred(n1) = all_0_6_6
% 55.65/21.24 |
% 55.65/21.24 | From (1984) and (760) follows:
% 55.65/21.24 | (1986) succ(n1) = all_0_8_8
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 55.65/21.24 | (1987) all_0_6_6 = n0
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 55.65/21.24 | (1988) all_0_8_8 = n2
% 55.65/21.24 |
% 55.65/21.24 | From (1987)(1988) and (411) follows:
% 55.65/21.24 | (1989) sum(n0, n2) = all_0_1_1
% 55.65/21.24 |
% 55.65/21.24 | From (1987) and (8624) follows:
% 55.65/21.24 | (8887) sum(n0, n17) = all_0_4_4
% 55.65/21.24 |
% 55.65/21.24 | From (1988) and (8626) follows:
% 55.65/21.24 | (8888) sum(n15, n2) = all_0_7_7
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (690) with n15, n2, all_0_7_7, n17 and discharging atoms sum(n15, n2) = all_0_7_7, sum(n15, n2) = n17, yields:
% 55.65/21.24 | (1227) all_0_7_7 = n17
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (690) with n0, n17, all_0_4_4, n17 and discharging atoms sum(n0, n17) = all_0_4_4, sum(n0, n17) = n17, yields:
% 55.65/21.24 | (1225) all_0_4_4 = n17
% 55.65/21.24 |
% 55.65/21.24 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 55.65/21.24 | (1759) all_0_1_1 = n2
% 55.65/21.24 |
% 55.65/21.24 | From (1227)(1225) and (590) follows:
% 55.65/21.24 | (1229) sum(n17, n17) = all_0_3_3
% 55.65/21.24 |
% 55.65/21.24 | From (1759) and (8628) follows:
% 55.65/21.25 | (8659) sum(n6, n2) = all_0_0_0
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 55.65/21.25 | (1230) all_0_3_3 = n8
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (690) with n6, n2, all_0_0_0, n8 and discharging atoms sum(n6, n2) = all_0_0_0, sum(n6, n2) = n8, yields:
% 55.65/21.25 | (1231) all_0_0_0 = n8
% 55.65/21.25 |
% 55.65/21.25 | Equations (1231,1230) can reduce 679 to:
% 55.65/21.25 | (1106) $false
% 55.65/21.25 |
% 55.65/21.25 |-The branch is then unsatisfiable
% 55.65/21.25 |-Branch two:
% 55.65/21.25 | (2002) ~ (all_0_10_10 = n1)
% 55.65/21.25 | (2003) all_0_10_10 = n0
% 55.65/21.25 |
% 55.65/21.25 | From (2003) and (292) follows:
% 55.65/21.25 | (2004) pred(n0) = all_0_6_6
% 55.65/21.25 |
% 55.65/21.25 | From (2003) and (760) follows:
% 55.65/21.25 | (2005) succ(n0) = all_0_8_8
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 55.65/21.25 | (2006) all_0_6_6 = n25
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 55.65/21.25 | (2007) all_0_8_8 = n1
% 55.65/21.25 |
% 55.65/21.25 | From (2006)(2007) and (411) follows:
% 55.65/21.25 | (2008) sum(n25, n1) = all_0_1_1
% 55.65/21.25 |
% 55.65/21.25 | From (2006) and (8624) follows:
% 55.65/21.25 | (8904) sum(n25, n17) = all_0_4_4
% 55.65/21.25 |
% 55.65/21.25 | From (2007) and (8626) follows:
% 55.65/21.25 | (8905) sum(n15, n1) = all_0_7_7
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (690) with n25, n17, all_0_4_4, n16 and discharging atoms sum(n25, n17) = all_0_4_4, sum(n25, n17) = n16, yields:
% 55.65/21.25 | (1243) all_0_4_4 = n16
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 55.65/21.25 | (1777) all_0_1_1 = n0
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (690) with n15, n1, all_0_7_7, n16 and discharging atoms sum(n15, n1) = all_0_7_7, sum(n15, n1) = n16, yields:
% 55.65/21.25 | (1245) all_0_7_7 = n16
% 55.65/21.25 |
% 55.65/21.25 | From (1245)(1243) and (590) follows:
% 55.65/21.25 | (1247) sum(n16, n16) = all_0_3_3
% 55.65/21.25 |
% 55.65/21.25 | From (1777) and (8628) follows:
% 55.65/21.25 | (8677) sum(n6, n0) = all_0_0_0
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 55.65/21.25 | (1248) all_0_3_3 = n6
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (690) with n6, n0, all_0_0_0, n6 and discharging atoms sum(n6, n0) = all_0_0_0, sum(n6, n0) = n6, yields:
% 55.65/21.25 | (1249) all_0_0_0 = n6
% 55.65/21.25 |
% 55.65/21.25 | Equations (1249,1248) can reduce 679 to:
% 55.65/21.25 | (1106) $false
% 55.65/21.25 |
% 55.65/21.25 |-The branch is then unsatisfiable
% 55.65/21.25 |-Branch two:
% 55.65/21.25 | (1269) ~ (all_0_11_11 = n16)
% 55.65/21.25 | (1270) 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
% 55.65/21.25 |
% 55.65/21.25 +-Applying beta-rule and splitting (1731), into two cases.
% 55.65/21.25 |-Branch one:
% 55.65/21.25 | (1732) all_0_10_10 = n15
% 55.65/21.25 |
% 55.65/21.25 | From (1732) and (292) follows:
% 55.65/21.25 | (1733) pred(n15) = all_0_6_6
% 55.65/21.25 |
% 55.65/21.25 | From (1732) and (760) follows:
% 55.65/21.25 | (1734) succ(n15) = all_0_8_8
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (500) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 55.65/21.25 | (1735) all_0_6_6 = n14
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (617) with n15, all_0_8_8, n16 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n16, yields:
% 55.65/21.25 | (1736) all_0_8_8 = n16
% 55.65/21.25 |
% 55.65/21.25 | From (1735) and (1733) follows:
% 55.65/21.25 | (609) pred(n15) = n14
% 55.65/21.25 |
% 55.65/21.25 | From (1736) and (1734) follows:
% 55.65/21.25 | (337) succ(n15) = n16
% 55.65/21.25 |
% 55.65/21.25 | From (1735) and (541) follows:
% 55.65/21.25 | (8923) sum(n14, all_0_5_5) = all_0_4_4
% 55.65/21.25 |
% 55.65/21.25 | From (1735)(1736) and (411) follows:
% 55.65/21.25 | (1737) sum(n14, n16) = all_0_1_1
% 55.65/21.25 |
% 55.65/21.25 | From (1736) and (427) follows:
% 55.65/21.25 | (8925) sum(all_0_9_9, n16) = all_0_7_7
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (690) with n14, n16, all_0_1_1, n4 and discharging atoms sum(n14, n16) = all_0_1_1, sum(n14, n16) = n4, yields:
% 55.65/21.25 | (1741) all_0_1_1 = n4
% 55.65/21.25 |
% 55.65/21.25 | From (1741) and (630) follows:
% 55.65/21.25 | (8927) sum(all_0_2_2, n4) = all_0_0_0
% 55.65/21.25 |
% 55.65/21.25 | From (1741) and (1737) follows:
% 55.65/21.25 | (433) sum(n14, n16) = n4
% 55.65/21.25 |
% 55.65/21.25 +-Applying beta-rule and splitting (1270), into two cases.
% 55.65/21.25 |-Branch one:
% 55.65/21.25 | (1271) all_0_11_11 = n15
% 55.65/21.25 |
% 55.65/21.25 | From (1271) and (559) follows:
% 55.65/21.25 | (1272) pred(n15) = all_0_9_9
% 55.65/21.25 |
% 55.65/21.25 | From (1271) and (992) follows:
% 55.65/21.25 | (1273) succ(n15) = all_0_5_5
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (500) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 55.65/21.25 | (1274) all_0_9_9 = n14
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (617) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 55.65/21.25 | (1275) all_0_5_5 = n16
% 55.65/21.25 |
% 55.65/21.25 | From (1274)(1275) and (538) follows:
% 55.65/21.25 | (1276) sum(n14, n16) = all_0_2_2
% 55.65/21.25 |
% 55.65/21.25 | From (1274) and (8925) follows:
% 55.65/21.25 | (8935) sum(n14, n16) = all_0_7_7
% 55.65/21.25 |
% 55.65/21.25 | From (1275) and (8923) follows:
% 55.65/21.25 | (8936) sum(n14, n16) = all_0_4_4
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (690) with n14, n16, all_0_2_2, n4 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n4, yields:
% 55.65/21.25 | (1280) all_0_2_2 = n4
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (690) 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:
% 55.65/21.25 | (1093) all_0_2_2 = all_0_4_4
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (690) 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:
% 55.65/21.25 | (1094) all_0_2_2 = all_0_7_7
% 55.65/21.25 |
% 55.65/21.25 | Combining equations (1094,1093) yields a new equation:
% 55.65/21.25 | (1095) all_0_4_4 = all_0_7_7
% 55.65/21.25 |
% 55.65/21.25 | Combining equations (1280,1093) yields a new equation:
% 55.65/21.25 | (1459) all_0_4_4 = n4
% 55.65/21.25 |
% 55.65/21.25 | Combining equations (1459,1095) yields a new equation:
% 55.65/21.25 | (1461) all_0_7_7 = n4
% 55.65/21.25 |
% 55.65/21.25 | Combining equations (1461,1095) yields a new equation:
% 55.65/21.25 | (1459) all_0_4_4 = n4
% 55.65/21.25 |
% 55.65/21.25 | Combining equations (1459,1093) yields a new equation:
% 55.65/21.25 | (1280) all_0_2_2 = n4
% 55.65/21.25 |
% 55.65/21.25 | From (1280) and (8927) follows:
% 55.65/21.25 | (8945) sum(n4, n4) = all_0_0_0
% 55.65/21.25 |
% 55.65/21.25 | From (1461)(1459) and (590) follows:
% 55.65/21.25 | (1463) sum(n4, n4) = all_0_3_3
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (690) with n4, n4, all_0_0_0, n8 and discharging atoms sum(n4, n4) = all_0_0_0, sum(n4, n4) = n8, yields:
% 55.65/21.25 | (1231) all_0_0_0 = n8
% 55.65/21.25 |
% 55.65/21.25 | Instantiating formula (690) 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:
% 55.65/21.25 | (1103) all_0_0_0 = all_0_3_3
% 55.65/21.25 |
% 55.65/21.25 | Combining equations (1231,1103) yields a new equation:
% 55.65/21.25 | (1230) all_0_3_3 = n8
% 55.65/21.25 |
% 55.65/21.25 | Combining equations (1230,1103) yields a new equation:
% 55.65/21.25 | (1231) all_0_0_0 = n8
% 55.65/21.25 |
% 55.65/21.25 | Equations (1231,1230) can reduce 679 to:
% 55.65/21.25 | (1106) $false
% 55.65/21.25 |
% 55.65/21.25 |-The branch is then unsatisfiable
% 55.65/21.25 |-Branch two:
% 55.65/21.26 | (1287) ~ (all_0_11_11 = n15)
% 55.65/21.26 | (1288) 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
% 55.65/21.26 |
% 55.65/21.26 +-Applying beta-rule and splitting (1288), into two cases.
% 55.65/21.26 |-Branch one:
% 55.65/21.26 | (1289) all_0_11_11 = n14
% 55.65/21.26 |
% 55.65/21.26 | From (1289) and (559) follows:
% 55.65/21.26 | (1290) pred(n14) = all_0_9_9
% 55.65/21.26 |
% 55.65/21.26 | From (1289) and (992) follows:
% 55.65/21.26 | (1291) succ(n14) = all_0_5_5
% 55.65/21.26 |
% 55.65/21.26 | Instantiating formula (500) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 55.65/21.26 | (1292) all_0_9_9 = n13
% 55.65/21.26 |
% 55.65/21.26 | Instantiating formula (617) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 55.65/21.26 | (1293) all_0_5_5 = n15
% 55.65/21.26 |
% 55.65/21.26 | From (1292)(1293) and (538) follows:
% 55.65/21.26 | (1294) sum(n13, n15) = all_0_2_2
% 55.65/21.26 |
% 55.65/21.26 | From (1292) and (8925) follows:
% 55.65/21.26 | (8960) sum(n13, n16) = all_0_7_7
% 55.65/21.26 |
% 55.65/21.26 | From (1293) and (8923) follows:
% 55.65/21.26 | (8961) sum(n14, n15) = all_0_4_4
% 55.65/21.26 |
% 55.65/21.26 | Instantiating formula (690) with n14, n15, all_0_4_4, n3 and discharging atoms sum(n14, n15) = all_0_4_4, sum(n14, n15) = n3, yields:
% 55.65/21.26 | (1477) all_0_4_4 = n3
% 55.65/21.26 |
% 55.65/21.26 | Instantiating formula (690) with n13, n16, all_0_7_7, n3 and discharging atoms sum(n13, n16) = all_0_7_7, sum(n13, n16) = n3, yields:
% 55.65/21.26 | (1479) all_0_7_7 = n3
% 55.65/21.26 |
% 55.65/21.26 | Instantiating formula (690) with n13, n15, all_0_2_2, n2 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n2, yields:
% 55.65/21.26 | (1298) all_0_2_2 = n2
% 55.65/21.26 |
% 55.65/21.26 | From (1298) and (8927) follows:
% 55.65/21.26 | (8965) sum(n2, n4) = all_0_0_0
% 55.65/21.26 |
% 55.65/21.26 | From (1479)(1477) and (590) follows:
% 55.65/21.26 | (1481) sum(n3, n3) = all_0_3_3
% 55.65/21.26 |
% 55.65/21.26 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 55.65/21.26 | (1248) all_0_3_3 = n6
% 55.65/21.26 |
% 55.65/21.26 | Instantiating formula (690) with n2, n4, all_0_0_0, n6 and discharging atoms sum(n2, n4) = all_0_0_0, sum(n2, n4) = n6, yields:
% 55.65/21.26 | (1249) all_0_0_0 = n6
% 55.65/21.26 |
% 55.65/21.26 | Equations (1249,1248) can reduce 679 to:
% 55.65/21.26 | (1106) $false
% 55.65/21.26 |
% 55.65/21.26 |-The branch is then unsatisfiable
% 55.65/21.26 |-Branch two:
% 55.65/21.26 | (1305) ~ (all_0_11_11 = n14)
% 55.65/21.26 | (1306) 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
% 55.65/21.26 |
% 55.65/21.26 +-Applying beta-rule and splitting (1306), into two cases.
% 55.65/21.26 |-Branch one:
% 55.65/21.26 | (1307) all_0_11_11 = n13
% 55.65/21.26 |
% 55.65/21.26 | From (1307) and (559) follows:
% 55.65/21.26 | (1308) pred(n13) = all_0_9_9
% 55.65/21.26 |
% 55.65/21.26 | From (1307) and (992) follows:
% 55.65/21.26 | (1309) succ(n13) = all_0_5_5
% 55.65/21.26 |
% 55.65/21.26 | Instantiating formula (500) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 55.65/21.26 | (1310) all_0_9_9 = n12
% 55.65/21.26 |
% 55.65/21.26 | Instantiating formula (617) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 55.65/21.26 | (1311) all_0_5_5 = n14
% 55.65/21.26 |
% 55.65/21.26 | From (1310)(1311) and (538) follows:
% 55.65/21.26 | (1312) sum(n12, n14) = all_0_2_2
% 55.65/21.26 |
% 55.65/21.26 | From (1310) and (8925) follows:
% 55.65/21.26 | (8978) sum(n12, n16) = all_0_7_7
% 55.65/21.26 |
% 55.65/21.26 | From (1311) and (8923) follows:
% 55.65/21.26 | (8979) sum(n14, n14) = all_0_4_4
% 55.65/21.26 |
% 55.65/21.26 | Instantiating formula (690) with n14, n14, all_0_4_4, n2 and discharging atoms sum(n14, n14) = all_0_4_4, sum(n14, n14) = n2, yields:
% 55.65/21.26 | (1495) all_0_4_4 = n2
% 55.65/21.26 |
% 55.65/21.26 | Instantiating formula (690) with n12, n16, all_0_7_7, n2 and discharging atoms sum(n12, n16) = all_0_7_7, sum(n12, n16) = n2, yields:
% 55.65/21.26 | (1497) all_0_7_7 = n2
% 55.65/21.26 |
% 55.65/21.26 | Instantiating formula (690) with n12, n14, all_0_2_2, n0 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n0, yields:
% 55.65/21.26 | (1316) all_0_2_2 = n0
% 55.65/21.26 |
% 55.65/21.26 | From (1316) and (8927) follows:
% 55.65/21.26 | (8983) sum(n0, n4) = all_0_0_0
% 55.65/21.26 |
% 55.65/21.26 | From (1497)(1495) and (590) follows:
% 55.65/21.26 | (1499) sum(n2, n2) = all_0_3_3
% 55.65/21.26 |
% 55.65/21.26 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 55.65/21.26 | (1266) all_0_3_3 = n4
% 55.65/21.26 |
% 55.65/21.26 | Instantiating formula (690) with n0, n4, all_0_0_0, n4 and discharging atoms sum(n0, n4) = all_0_0_0, sum(n0, n4) = n4, yields:
% 55.65/21.26 | (1267) all_0_0_0 = n4
% 55.65/21.26 |
% 55.65/21.26 | Equations (1267,1266) can reduce 679 to:
% 55.65/21.26 | (1106) $false
% 55.65/21.26 |
% 55.65/21.26 |-The branch is then unsatisfiable
% 55.65/21.26 |-Branch two:
% 55.65/21.26 | (1323) ~ (all_0_11_11 = n13)
% 55.65/21.26 | (1324) 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
% 55.65/21.26 |
% 55.65/21.26 +-Applying beta-rule and splitting (1324), into two cases.
% 55.65/21.26 |-Branch one:
% 55.65/21.26 | (1325) all_0_11_11 = n12
% 55.65/21.26 |
% 55.65/21.26 | From (1325) and (559) follows:
% 55.65/21.26 | (1326) pred(n12) = all_0_9_9
% 55.65/21.26 |
% 55.65/21.26 | From (1325) and (992) follows:
% 55.65/21.26 | (1327) succ(n12) = all_0_5_5
% 55.65/21.26 |
% 55.65/21.26 | Instantiating formula (500) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 55.65/21.26 | (1328) all_0_9_9 = n11
% 55.65/21.26 |
% 55.65/21.26 | Instantiating formula (617) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 55.65/21.26 | (1329) all_0_5_5 = n13
% 55.65/21.26 |
% 55.65/21.26 | From (1328)(1329) and (538) follows:
% 55.65/21.27 | (1330) sum(n11, n13) = all_0_2_2
% 55.65/21.27 |
% 55.65/21.27 | From (1328) and (8925) follows:
% 55.65/21.27 | (8996) sum(n11, n16) = all_0_7_7
% 55.65/21.27 |
% 55.65/21.27 | From (1329) and (8923) follows:
% 55.65/21.27 | (8997) sum(n14, n13) = all_0_4_4
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (690) with n14, n13, all_0_4_4, n1 and discharging atoms sum(n14, n13) = all_0_4_4, sum(n14, n13) = n1, yields:
% 55.65/21.27 | (1513) all_0_4_4 = n1
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (690) with n11, n16, all_0_7_7, n1 and discharging atoms sum(n11, n16) = all_0_7_7, sum(n11, n16) = n1, yields:
% 55.65/21.27 | (1515) all_0_7_7 = n1
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (690) with n11, n13, all_0_2_2, n24 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n24, yields:
% 55.65/21.27 | (1092) all_0_2_2 = n24
% 55.65/21.27 |
% 55.65/21.27 | From (1092) and (8927) follows:
% 55.65/21.27 | (1744) sum(n24, n4) = all_0_0_0
% 55.65/21.27 |
% 55.65/21.27 | From (1515)(1513) and (590) follows:
% 55.65/21.27 | (1517) sum(n1, n1) = all_0_3_3
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (690) with n24, n4, all_0_0_0, n2 and discharging atoms sum(n24, n4) = all_0_0_0, sum(n24, n4) = n2, yields:
% 55.65/21.27 | (1285) all_0_0_0 = n2
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 55.65/21.27 | (1284) all_0_3_3 = n2
% 55.65/21.27 |
% 55.65/21.27 | Equations (1285,1284) can reduce 679 to:
% 55.65/21.27 | (1106) $false
% 55.65/21.27 |
% 55.65/21.27 |-The branch is then unsatisfiable
% 55.65/21.27 |-Branch two:
% 55.65/21.27 | (1341) ~ (all_0_11_11 = n12)
% 55.65/21.27 | (1342) 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
% 55.65/21.27 |
% 55.65/21.27 +-Applying beta-rule and splitting (1342), into two cases.
% 55.65/21.27 |-Branch one:
% 55.65/21.27 | (1343) all_0_11_11 = n11
% 55.65/21.27 |
% 55.65/21.27 | From (1343) and (559) follows:
% 55.65/21.27 | (1344) pred(n11) = all_0_9_9
% 55.65/21.27 |
% 55.65/21.27 | From (1343) and (992) follows:
% 55.65/21.27 | (1345) succ(n11) = all_0_5_5
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (500) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 55.65/21.27 | (1346) all_0_9_9 = n10
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (617) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 55.65/21.27 | (1347) all_0_5_5 = n12
% 55.65/21.27 |
% 55.65/21.27 | From (1346)(1347) and (538) follows:
% 55.65/21.27 | (1348) sum(n10, n12) = all_0_2_2
% 55.65/21.27 |
% 55.65/21.27 | From (1346) and (8925) follows:
% 55.65/21.27 | (9014) sum(n10, n16) = all_0_7_7
% 55.65/21.27 |
% 55.65/21.27 | From (1347) and (8923) follows:
% 55.65/21.27 | (9015) sum(n14, n12) = all_0_4_4
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (690) with n14, n12, all_0_4_4, n0 and discharging atoms sum(n14, n12) = all_0_4_4, sum(n14, n12) = n0, yields:
% 55.65/21.27 | (1531) all_0_4_4 = n0
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (690) with n10, n16, all_0_7_7, n0 and discharging atoms sum(n10, n16) = all_0_7_7, sum(n10, n16) = n0, yields:
% 55.65/21.27 | (1533) all_0_7_7 = n0
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (690) with n10, n12, all_0_2_2, n22 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n22, yields:
% 55.65/21.27 | (1118) all_0_2_2 = n22
% 55.65/21.27 |
% 55.65/21.27 | From (1118) and (8927) follows:
% 55.65/21.27 | (2656) sum(n22, n4) = all_0_0_0
% 55.65/21.27 |
% 55.65/21.27 | From (1533)(1531) and (590) follows:
% 55.65/21.27 | (1535) sum(n0, n0) = all_0_3_3
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (690) with n22, n4, all_0_0_0, n0 and discharging atoms sum(n22, n4) = all_0_0_0, sum(n22, n4) = n0, yields:
% 55.65/21.27 | (1303) all_0_0_0 = n0
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 55.65/21.27 | (1302) all_0_3_3 = n0
% 55.65/21.27 |
% 55.65/21.27 | Equations (1303,1302) can reduce 679 to:
% 55.65/21.27 | (1106) $false
% 55.65/21.27 |
% 55.65/21.27 |-The branch is then unsatisfiable
% 55.65/21.27 |-Branch two:
% 55.65/21.27 | (1359) ~ (all_0_11_11 = n11)
% 55.65/21.27 | (1360) 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
% 55.65/21.27 |
% 55.65/21.27 +-Applying beta-rule and splitting (1360), into two cases.
% 55.65/21.27 |-Branch one:
% 55.65/21.27 | (1361) all_0_11_11 = n10
% 55.65/21.27 |
% 55.65/21.27 | From (1361) and (559) follows:
% 55.65/21.27 | (1362) pred(n10) = all_0_9_9
% 55.65/21.27 |
% 55.65/21.27 | From (1361) and (992) follows:
% 55.65/21.27 | (1363) succ(n10) = all_0_5_5
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (500) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 55.65/21.27 | (1364) all_0_9_9 = n9
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (617) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 55.65/21.27 | (1365) all_0_5_5 = n11
% 55.65/21.27 |
% 55.65/21.27 | From (1364)(1365) and (538) follows:
% 55.65/21.27 | (1366) sum(n9, n11) = all_0_2_2
% 55.65/21.27 |
% 55.65/21.27 | From (1364) and (8925) follows:
% 55.65/21.27 | (9032) sum(n9, n16) = all_0_7_7
% 55.65/21.27 |
% 55.65/21.27 | From (1365) and (8923) follows:
% 55.65/21.27 | (9033) sum(n14, n11) = all_0_4_4
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (690) with n14, n11, all_0_4_4, n25 and discharging atoms sum(n14, n11) = all_0_4_4, sum(n14, n11) = n25, yields:
% 55.65/21.27 | (1551) all_0_4_4 = n25
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (690) with n9, n16, all_0_7_7, n25 and discharging atoms sum(n9, n16) = all_0_7_7, sum(n9, n16) = n25, yields:
% 55.65/21.27 | (1550) all_0_7_7 = n25
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (690) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 55.65/21.27 | (1136) all_0_2_2 = n20
% 55.65/21.27 |
% 55.65/21.27 | From (1136) and (8927) follows:
% 55.65/21.27 | (3530) sum(n20, n4) = all_0_0_0
% 55.65/21.27 |
% 55.65/21.27 | From (1550)(1551) and (590) follows:
% 55.65/21.27 | (1553) sum(n25, n25) = all_0_3_3
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 55.65/21.27 | (1320) all_0_3_3 = n24
% 55.65/21.27 |
% 55.65/21.27 | Instantiating formula (690) with n20, n4, all_0_0_0, n24 and discharging atoms sum(n20, n4) = all_0_0_0, sum(n20, n4) = n24, yields:
% 55.65/21.28 | (1321) all_0_0_0 = n24
% 55.65/21.28 |
% 55.65/21.28 | Equations (1321,1320) can reduce 679 to:
% 55.65/21.28 | (1106) $false
% 55.65/21.28 |
% 55.65/21.28 |-The branch is then unsatisfiable
% 55.65/21.28 |-Branch two:
% 55.65/21.28 | (1377) ~ (all_0_11_11 = n10)
% 55.65/21.28 | (1378) 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
% 55.65/21.28 |
% 55.65/21.28 +-Applying beta-rule and splitting (1378), into two cases.
% 55.65/21.28 |-Branch one:
% 55.65/21.28 | (1379) all_0_11_11 = n9
% 55.65/21.28 |
% 55.65/21.28 | From (1379) and (559) follows:
% 55.65/21.28 | (1380) pred(n9) = all_0_9_9
% 55.65/21.28 |
% 55.65/21.28 | From (1379) and (992) follows:
% 55.65/21.28 | (1381) succ(n9) = all_0_5_5
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 55.65/21.28 | (1382) all_0_9_9 = n8
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 55.65/21.28 | (1383) all_0_5_5 = n10
% 55.65/21.28 |
% 55.65/21.28 | From (1382)(1383) and (538) follows:
% 55.65/21.28 | (1384) sum(n8, n10) = all_0_2_2
% 55.65/21.28 |
% 55.65/21.28 | From (1382) and (8925) follows:
% 55.65/21.28 | (9050) sum(n8, n16) = all_0_7_7
% 55.65/21.28 |
% 55.65/21.28 | From (1383) and (8923) follows:
% 55.65/21.28 | (9051) sum(n14, n10) = all_0_4_4
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (690) with n14, n10, all_0_4_4, n24 and discharging atoms sum(n14, n10) = all_0_4_4, sum(n14, n10) = n24, yields:
% 55.65/21.28 | (1096) all_0_4_4 = n24
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (690) with n8, n16, all_0_7_7, n24 and discharging atoms sum(n8, n16) = all_0_7_7, sum(n8, n16) = n24, yields:
% 55.65/21.28 | (1097) all_0_7_7 = n24
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 55.65/21.28 | (1154) all_0_2_2 = n18
% 55.65/21.28 |
% 55.65/21.28 | From (1154) and (8927) follows:
% 55.65/21.28 | (4368) sum(n18, n4) = all_0_0_0
% 55.65/21.28 |
% 55.65/21.28 | From (1097)(1096) and (590) follows:
% 55.65/21.28 | (1101) sum(n24, n24) = all_0_3_3
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 55.65/21.28 | (1104) all_0_3_3 = n22
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (690) with n18, n4, all_0_0_0, n22 and discharging atoms sum(n18, n4) = all_0_0_0, sum(n18, n4) = n22, yields:
% 55.65/21.28 | (1102) all_0_0_0 = n22
% 55.65/21.28 |
% 55.65/21.28 | Equations (1102,1104) can reduce 679 to:
% 55.65/21.28 | (1106) $false
% 55.65/21.28 |
% 55.65/21.28 |-The branch is then unsatisfiable
% 55.65/21.28 |-Branch two:
% 55.65/21.28 | (1395) ~ (all_0_11_11 = n9)
% 55.65/21.28 | (1396) 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
% 55.65/21.28 |
% 55.65/21.28 +-Applying beta-rule and splitting (1396), into two cases.
% 55.65/21.28 |-Branch one:
% 55.65/21.28 | (1397) all_0_11_11 = n8
% 55.65/21.28 |
% 55.65/21.28 | From (1397) and (559) follows:
% 55.65/21.28 | (1398) pred(n8) = all_0_9_9
% 55.65/21.28 |
% 55.65/21.28 | From (1397) and (992) follows:
% 55.65/21.28 | (1399) succ(n8) = all_0_5_5
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 55.65/21.28 | (1400) all_0_9_9 = n7
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 55.65/21.28 | (1401) all_0_5_5 = n9
% 55.65/21.28 |
% 55.65/21.28 | From (1400)(1401) and (538) follows:
% 55.65/21.28 | (1402) sum(n7, n9) = all_0_2_2
% 55.65/21.28 |
% 55.65/21.28 | From (1400) and (8925) follows:
% 55.65/21.28 | (9068) sum(n7, n16) = all_0_7_7
% 55.65/21.28 |
% 55.65/21.28 | From (1401) and (8923) follows:
% 55.65/21.28 | (9069) sum(n14, n9) = all_0_4_4
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (690) with n14, n9, all_0_4_4, n23 and discharging atoms sum(n14, n9) = all_0_4_4, sum(n14, n9) = n23, yields:
% 55.65/21.28 | (1117) all_0_4_4 = n23
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (690) with n7, n16, all_0_7_7, n23 and discharging atoms sum(n7, n16) = all_0_7_7, sum(n7, n16) = n23, yields:
% 55.65/21.28 | (1119) all_0_7_7 = n23
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 55.65/21.28 | (1172) all_0_2_2 = n16
% 55.65/21.28 |
% 55.65/21.28 | From (1172) and (8927) follows:
% 55.65/21.28 | (5170) sum(n16, n4) = all_0_0_0
% 55.65/21.28 |
% 55.65/21.28 | From (1119)(1117) and (590) follows:
% 55.65/21.28 | (1121) sum(n23, n23) = all_0_3_3
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 55.65/21.28 | (1122) all_0_3_3 = n20
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (690) with n16, n4, all_0_0_0, n20 and discharging atoms sum(n16, n4) = all_0_0_0, sum(n16, n4) = n20, yields:
% 55.65/21.28 | (1123) all_0_0_0 = n20
% 55.65/21.28 |
% 55.65/21.28 | Equations (1123,1122) can reduce 679 to:
% 55.65/21.28 | (1106) $false
% 55.65/21.28 |
% 55.65/21.28 |-The branch is then unsatisfiable
% 55.65/21.28 |-Branch two:
% 55.65/21.28 | (1413) ~ (all_0_11_11 = n8)
% 55.65/21.28 | (1414) 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
% 55.65/21.28 |
% 55.65/21.28 +-Applying beta-rule and splitting (1414), into two cases.
% 55.65/21.28 |-Branch one:
% 55.65/21.28 | (1415) all_0_11_11 = n7
% 55.65/21.28 |
% 55.65/21.28 | From (1415) and (559) follows:
% 55.65/21.28 | (1416) pred(n7) = all_0_9_9
% 55.65/21.28 |
% 55.65/21.28 | From (1415) and (992) follows:
% 55.65/21.28 | (1417) succ(n7) = all_0_5_5
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 55.65/21.28 | (1418) all_0_9_9 = n6
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 55.65/21.28 | (1419) all_0_5_5 = n8
% 55.65/21.28 |
% 55.65/21.28 | From (1418)(1419) and (538) follows:
% 55.65/21.28 | (1420) sum(n6, n8) = all_0_2_2
% 55.65/21.28 |
% 55.65/21.28 | From (1418) and (8925) follows:
% 55.65/21.28 | (9086) sum(n6, n16) = all_0_7_7
% 55.65/21.28 |
% 55.65/21.28 | From (1419) and (8923) follows:
% 55.65/21.28 | (9087) sum(n14, n8) = all_0_4_4
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (690) with n14, n8, all_0_4_4, n22 and discharging atoms sum(n14, n8) = all_0_4_4, sum(n14, n8) = n22, yields:
% 55.65/21.28 | (1135) all_0_4_4 = n22
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (690) with n6, n16, all_0_7_7, n22 and discharging atoms sum(n6, n16) = all_0_7_7, sum(n6, n16) = n22, yields:
% 55.65/21.28 | (1137) all_0_7_7 = n22
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 55.65/21.28 | (1190) all_0_2_2 = n14
% 55.65/21.28 |
% 55.65/21.28 | From (1190) and (8927) follows:
% 55.65/21.28 | (5936) sum(n14, n4) = all_0_0_0
% 55.65/21.28 |
% 55.65/21.28 | From (1137)(1135) and (590) follows:
% 55.65/21.28 | (1139) sum(n22, n22) = all_0_3_3
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 55.65/21.28 | (1140) all_0_3_3 = n18
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (690) with n14, n4, all_0_0_0, n18 and discharging atoms sum(n14, n4) = all_0_0_0, sum(n14, n4) = n18, yields:
% 55.65/21.28 | (1141) all_0_0_0 = n18
% 55.65/21.28 |
% 55.65/21.28 | Equations (1141,1140) can reduce 679 to:
% 55.65/21.28 | (1106) $false
% 55.65/21.28 |
% 55.65/21.28 |-The branch is then unsatisfiable
% 55.65/21.28 |-Branch two:
% 55.65/21.28 | (1431) ~ (all_0_11_11 = n7)
% 55.65/21.28 | (1432) 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
% 55.65/21.28 |
% 55.65/21.28 +-Applying beta-rule and splitting (1432), into two cases.
% 55.65/21.28 |-Branch one:
% 55.65/21.28 | (1433) all_0_11_11 = n6
% 55.65/21.28 |
% 55.65/21.28 | From (1433) and (559) follows:
% 55.65/21.28 | (1434) pred(n6) = all_0_9_9
% 55.65/21.28 |
% 55.65/21.28 | From (1433) and (992) follows:
% 55.65/21.28 | (1435) succ(n6) = all_0_5_5
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 55.65/21.28 | (1436) all_0_9_9 = n5
% 55.65/21.28 |
% 55.65/21.28 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 55.65/21.28 | (1437) all_0_5_5 = n7
% 55.65/21.28 |
% 55.65/21.28 | From (1436)(1437) and (538) follows:
% 55.65/21.28 | (1438) sum(n5, n7) = all_0_2_2
% 55.65/21.28 |
% 55.65/21.28 | From (1436) and (8925) follows:
% 55.65/21.29 | (9104) sum(n5, n16) = all_0_7_7
% 55.65/21.29 |
% 55.65/21.29 | From (1437) and (8923) follows:
% 55.65/21.29 | (9105) sum(n14, n7) = all_0_4_4
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (690) with n14, n7, all_0_4_4, n21 and discharging atoms sum(n14, n7) = all_0_4_4, sum(n14, n7) = n21, yields:
% 55.65/21.29 | (1153) all_0_4_4 = n21
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (690) with n5, n16, all_0_7_7, n21 and discharging atoms sum(n5, n16) = all_0_7_7, sum(n5, n16) = n21, yields:
% 55.65/21.29 | (1155) all_0_7_7 = n21
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 55.65/21.29 | (1208) all_0_2_2 = n12
% 55.65/21.29 |
% 55.65/21.29 | From (1208) and (8927) follows:
% 55.65/21.29 | (6666) sum(n12, n4) = all_0_0_0
% 55.65/21.29 |
% 55.65/21.29 | From (1155)(1153) and (590) follows:
% 55.65/21.29 | (1157) sum(n21, n21) = all_0_3_3
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 55.65/21.29 | (1158) all_0_3_3 = n16
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (690) with n12, n4, all_0_0_0, n16 and discharging atoms sum(n12, n4) = all_0_0_0, sum(n12, n4) = n16, yields:
% 55.65/21.29 | (1159) all_0_0_0 = n16
% 55.65/21.29 |
% 55.65/21.29 | Equations (1159,1158) can reduce 679 to:
% 55.65/21.29 | (1106) $false
% 55.65/21.29 |
% 55.65/21.29 |-The branch is then unsatisfiable
% 55.65/21.29 |-Branch two:
% 55.65/21.29 | (1449) ~ (all_0_11_11 = n6)
% 55.65/21.29 | (1450) 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
% 55.65/21.29 |
% 55.65/21.29 +-Applying beta-rule and splitting (1450), into two cases.
% 55.65/21.29 |-Branch one:
% 55.65/21.29 | (1451) all_0_11_11 = n5
% 55.65/21.29 |
% 55.65/21.29 | From (1451) and (559) follows:
% 55.65/21.29 | (1452) pred(n5) = all_0_9_9
% 55.65/21.29 |
% 55.65/21.29 | From (1451) and (992) follows:
% 55.65/21.29 | (1453) succ(n5) = all_0_5_5
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 55.65/21.29 | (1454) all_0_9_9 = n4
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 55.65/21.29 | (1455) all_0_5_5 = n6
% 55.65/21.29 |
% 55.65/21.29 | From (1454)(1455) and (538) follows:
% 55.65/21.29 | (1456) sum(n4, n6) = all_0_2_2
% 55.65/21.29 |
% 55.65/21.29 | From (1454) and (8925) follows:
% 55.65/21.29 | (9122) sum(n4, n16) = all_0_7_7
% 55.65/21.29 |
% 55.65/21.29 | From (1455) and (8923) follows:
% 55.65/21.29 | (9123) sum(n14, n6) = all_0_4_4
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (690) with n14, n6, all_0_4_4, n20 and discharging atoms sum(n14, n6) = all_0_4_4, sum(n14, n6) = n20, yields:
% 55.65/21.29 | (1171) all_0_4_4 = n20
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (690) with n4, n16, all_0_7_7, n20 and discharging atoms sum(n4, n16) = all_0_7_7, sum(n4, n16) = n20, yields:
% 55.65/21.29 | (1173) all_0_7_7 = n20
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 55.65/21.29 | (1226) all_0_2_2 = n10
% 55.65/21.29 |
% 55.65/21.29 | From (1226) and (8927) follows:
% 55.65/21.29 | (7360) sum(n10, n4) = all_0_0_0
% 55.65/21.29 |
% 55.65/21.29 | From (1173)(1171) and (590) follows:
% 55.65/21.29 | (1175) sum(n20, n20) = all_0_3_3
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 55.65/21.29 | (1176) all_0_3_3 = n14
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (690) with n10, n4, all_0_0_0, n14 and discharging atoms sum(n10, n4) = all_0_0_0, sum(n10, n4) = n14, yields:
% 55.65/21.29 | (1177) all_0_0_0 = n14
% 55.65/21.29 |
% 55.65/21.29 | Equations (1177,1176) can reduce 679 to:
% 55.65/21.29 | (1106) $false
% 55.65/21.29 |
% 55.65/21.29 |-The branch is then unsatisfiable
% 55.65/21.29 |-Branch two:
% 55.65/21.29 | (1467) ~ (all_0_11_11 = n5)
% 55.65/21.29 | (1468) 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
% 55.65/21.29 |
% 55.65/21.29 +-Applying beta-rule and splitting (1468), into two cases.
% 55.65/21.29 |-Branch one:
% 55.65/21.29 | (1469) all_0_11_11 = n4
% 55.65/21.29 |
% 55.65/21.29 | From (1469) and (559) follows:
% 55.65/21.29 | (1470) pred(n4) = all_0_9_9
% 55.65/21.29 |
% 55.65/21.29 | From (1469) and (992) follows:
% 55.65/21.29 | (1471) succ(n4) = all_0_5_5
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 55.65/21.29 | (1472) all_0_9_9 = n3
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 55.65/21.29 | (1473) all_0_5_5 = n5
% 55.65/21.29 |
% 55.65/21.29 | From (1472)(1473) and (538) follows:
% 55.65/21.29 | (1474) sum(n3, n5) = all_0_2_2
% 55.65/21.29 |
% 55.65/21.29 | From (1472) and (8925) follows:
% 55.65/21.29 | (9140) sum(n3, n16) = all_0_7_7
% 55.65/21.29 |
% 55.65/21.29 | From (1473) and (8923) follows:
% 55.65/21.29 | (9141) sum(n14, n5) = all_0_4_4
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (690) with n14, n5, all_0_4_4, n19 and discharging atoms sum(n14, n5) = all_0_4_4, sum(n14, n5) = n19, yields:
% 55.65/21.29 | (1189) all_0_4_4 = n19
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (690) with n3, n16, all_0_7_7, n19 and discharging atoms sum(n3, n16) = all_0_7_7, sum(n3, n16) = n19, yields:
% 55.65/21.29 | (1191) all_0_7_7 = n19
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 55.65/21.29 | (1244) all_0_2_2 = n8
% 55.65/21.29 |
% 55.65/21.29 | From (1244) and (8927) follows:
% 55.65/21.29 | (8018) sum(n8, n4) = all_0_0_0
% 55.65/21.29 |
% 55.65/21.29 | From (1191)(1189) and (590) follows:
% 55.65/21.29 | (1193) sum(n19, n19) = all_0_3_3
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 55.65/21.29 | (1194) all_0_3_3 = n12
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (690) with n8, n4, all_0_0_0, n12 and discharging atoms sum(n8, n4) = all_0_0_0, sum(n8, n4) = n12, yields:
% 55.65/21.29 | (1195) all_0_0_0 = n12
% 55.65/21.29 |
% 55.65/21.29 | Equations (1195,1194) can reduce 679 to:
% 55.65/21.29 | (1106) $false
% 55.65/21.29 |
% 55.65/21.29 |-The branch is then unsatisfiable
% 55.65/21.29 |-Branch two:
% 55.65/21.29 | (1485) ~ (all_0_11_11 = n4)
% 55.65/21.29 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 55.65/21.29 |
% 55.65/21.29 +-Applying beta-rule and splitting (1486), into two cases.
% 55.65/21.29 |-Branch one:
% 55.65/21.29 | (1487) all_0_11_11 = n3
% 55.65/21.29 |
% 55.65/21.29 | From (1487) and (559) follows:
% 55.65/21.29 | (1488) pred(n3) = all_0_9_9
% 55.65/21.29 |
% 55.65/21.29 | From (1487) and (992) follows:
% 55.65/21.29 | (1489) succ(n3) = all_0_5_5
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 55.65/21.29 | (1490) all_0_9_9 = n2
% 55.65/21.29 |
% 55.65/21.29 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 55.65/21.29 | (1491) all_0_5_5 = n4
% 55.65/21.29 |
% 55.65/21.29 | From (1490)(1491) and (538) follows:
% 55.65/21.29 | (1492) sum(n2, n4) = all_0_2_2
% 55.65/21.29 |
% 55.65/21.29 | From (1490) and (8925) follows:
% 55.65/21.29 | (9158) sum(n2, n16) = all_0_7_7
% 55.65/21.29 |
% 55.65/21.29 | From (1491) and (8923) follows:
% 55.65/21.30 | (9159) sum(n14, n4) = all_0_4_4
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n14, n4, all_0_4_4, n18 and discharging atoms sum(n14, n4) = all_0_4_4, sum(n14, n4) = n18, yields:
% 55.65/21.30 | (1207) all_0_4_4 = n18
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n2, n16, all_0_7_7, n18 and discharging atoms sum(n2, n16) = all_0_7_7, sum(n2, n16) = n18, yields:
% 55.65/21.30 | (1209) all_0_7_7 = n18
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 55.65/21.30 | (1262) all_0_2_2 = n6
% 55.65/21.30 |
% 55.65/21.30 | From (1262) and (8927) follows:
% 55.65/21.30 | (8641) sum(n6, n4) = all_0_0_0
% 55.65/21.30 |
% 55.65/21.30 | From (1209)(1207) and (590) follows:
% 55.65/21.30 | (1211) sum(n18, n18) = all_0_3_3
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 55.65/21.30 | (1212) all_0_3_3 = n10
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n6, n4, all_0_0_0, n10 and discharging atoms sum(n6, n4) = all_0_0_0, sum(n6, n4) = n10, yields:
% 55.65/21.30 | (1213) all_0_0_0 = n10
% 55.65/21.30 |
% 55.65/21.30 | Equations (1213,1212) can reduce 679 to:
% 55.65/21.30 | (1106) $false
% 55.65/21.30 |
% 55.65/21.30 |-The branch is then unsatisfiable
% 55.65/21.30 |-Branch two:
% 55.65/21.30 | (1503) ~ (all_0_11_11 = n3)
% 55.65/21.30 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 55.65/21.30 |
% 55.65/21.30 +-Applying beta-rule and splitting (1504), into two cases.
% 55.65/21.30 |-Branch one:
% 55.65/21.30 | (1505) all_0_11_11 = n2
% 55.65/21.30 |
% 55.65/21.30 | From (1505) and (559) follows:
% 55.65/21.30 | (1506) pred(n2) = all_0_9_9
% 55.65/21.30 |
% 55.65/21.30 | From (1505) and (992) follows:
% 55.65/21.30 | (1507) succ(n2) = all_0_5_5
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 55.65/21.30 | (1508) all_0_9_9 = n1
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 55.65/21.30 | (1509) all_0_5_5 = n3
% 55.65/21.30 |
% 55.65/21.30 | From (1508)(1509) and (538) follows:
% 55.65/21.30 | (1510) sum(n1, n3) = all_0_2_2
% 55.65/21.30 |
% 55.65/21.30 | From (1508) and (8925) follows:
% 55.65/21.30 | (9176) sum(n1, n16) = all_0_7_7
% 55.65/21.30 |
% 55.65/21.30 | From (1509) and (8923) follows:
% 55.65/21.30 | (9177) sum(n14, n3) = all_0_4_4
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n14, n3, all_0_4_4, n17 and discharging atoms sum(n14, n3) = all_0_4_4, sum(n14, n3) = n17, yields:
% 55.65/21.30 | (1225) all_0_4_4 = n17
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n1, n16, all_0_7_7, n17 and discharging atoms sum(n1, n16) = all_0_7_7, sum(n1, n16) = n17, yields:
% 55.65/21.30 | (1227) all_0_7_7 = n17
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 55.65/21.30 | (1280) all_0_2_2 = n4
% 55.65/21.30 |
% 55.65/21.30 | From (1280) and (8927) follows:
% 55.65/21.30 | (8945) sum(n4, n4) = all_0_0_0
% 55.65/21.30 |
% 55.65/21.30 | From (1227)(1225) and (590) follows:
% 55.65/21.30 | (1229) sum(n17, n17) = all_0_3_3
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 55.65/21.30 | (1230) all_0_3_3 = n8
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n4, n4, all_0_0_0, n8 and discharging atoms sum(n4, n4) = all_0_0_0, sum(n4, n4) = n8, yields:
% 55.65/21.30 | (1231) all_0_0_0 = n8
% 55.65/21.30 |
% 55.65/21.30 | Equations (1231,1230) can reduce 679 to:
% 55.65/21.30 | (1106) $false
% 55.65/21.30 |
% 55.65/21.30 |-The branch is then unsatisfiable
% 55.65/21.30 |-Branch two:
% 55.65/21.30 | (1521) ~ (all_0_11_11 = n2)
% 55.65/21.30 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 55.65/21.30 |
% 55.65/21.30 +-Applying beta-rule and splitting (1522), into two cases.
% 55.65/21.30 |-Branch one:
% 55.65/21.30 | (1523) all_0_11_11 = n1
% 55.65/21.30 |
% 55.65/21.30 | From (1523) and (559) follows:
% 55.65/21.30 | (1524) pred(n1) = all_0_9_9
% 55.65/21.30 |
% 55.65/21.30 | From (1523) and (992) follows:
% 55.65/21.30 | (1525) succ(n1) = all_0_5_5
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 55.65/21.30 | (1526) all_0_9_9 = n0
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 55.65/21.30 | (1527) all_0_5_5 = n2
% 55.65/21.30 |
% 55.65/21.30 | From (1526)(1527) and (538) follows:
% 55.65/21.30 | (1528) sum(n0, n2) = all_0_2_2
% 55.65/21.30 |
% 55.65/21.30 | From (1526) and (8925) follows:
% 55.65/21.30 | (9194) sum(n0, n16) = all_0_7_7
% 55.65/21.30 |
% 55.65/21.30 | From (1527) and (8923) follows:
% 55.65/21.30 | (9195) sum(n14, n2) = all_0_4_4
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n14, n2, all_0_4_4, n16 and discharging atoms sum(n14, n2) = all_0_4_4, sum(n14, n2) = n16, yields:
% 55.65/21.30 | (1243) all_0_4_4 = n16
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n0, n16, all_0_7_7, n16 and discharging atoms sum(n0, n16) = all_0_7_7, sum(n0, n16) = n16, yields:
% 55.65/21.30 | (1245) all_0_7_7 = n16
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 55.65/21.30 | (1298) all_0_2_2 = n2
% 55.65/21.30 |
% 55.65/21.30 | From (1298) and (8927) follows:
% 55.65/21.30 | (8965) sum(n2, n4) = all_0_0_0
% 55.65/21.30 |
% 55.65/21.30 | From (1245)(1243) and (590) follows:
% 55.65/21.30 | (1247) sum(n16, n16) = all_0_3_3
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 55.65/21.30 | (1248) all_0_3_3 = n6
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n2, n4, all_0_0_0, n6 and discharging atoms sum(n2, n4) = all_0_0_0, sum(n2, n4) = n6, yields:
% 55.65/21.30 | (1249) all_0_0_0 = n6
% 55.65/21.30 |
% 55.65/21.30 | Equations (1249,1248) can reduce 679 to:
% 55.65/21.30 | (1106) $false
% 55.65/21.30 |
% 55.65/21.30 |-The branch is then unsatisfiable
% 55.65/21.30 |-Branch two:
% 55.65/21.30 | (1540) ~ (all_0_11_11 = n1)
% 55.65/21.30 | (1541) all_0_11_11 = n0
% 55.65/21.30 |
% 55.65/21.30 | From (1541) and (559) follows:
% 55.65/21.30 | (1542) pred(n0) = all_0_9_9
% 55.65/21.30 |
% 55.65/21.30 | From (1541) and (992) follows:
% 55.65/21.30 | (1543) succ(n0) = all_0_5_5
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 55.65/21.30 | (1544) all_0_9_9 = n25
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 55.65/21.30 | (1545) all_0_5_5 = n1
% 55.65/21.30 |
% 55.65/21.30 | From (1544)(1545) and (538) follows:
% 55.65/21.30 | (1546) sum(n25, n1) = all_0_2_2
% 55.65/21.30 |
% 55.65/21.30 | From (1544) and (8925) follows:
% 55.65/21.30 | (9211) sum(n25, n16) = all_0_7_7
% 55.65/21.30 |
% 55.65/21.30 | From (1545) and (8923) follows:
% 55.65/21.30 | (9212) sum(n14, n1) = all_0_4_4
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n25, n16, all_0_7_7, n15 and discharging atoms sum(n25, n16) = all_0_7_7, sum(n25, n16) = n15, yields:
% 55.65/21.30 | (1263) all_0_7_7 = n15
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 55.65/21.30 | (1316) all_0_2_2 = n0
% 55.65/21.30 |
% 55.65/21.30 | Instantiating formula (690) with n14, n1, all_0_4_4, n15 and discharging atoms sum(n14, n1) = all_0_4_4, sum(n14, n1) = n15, yields:
% 55.65/21.30 | (1261) all_0_4_4 = n15
% 55.65/21.30 |
% 55.65/21.30 | From (1316) and (8927) follows:
% 55.65/21.31 | (8983) sum(n0, n4) = all_0_0_0
% 55.65/21.31 |
% 55.65/21.31 | From (1263)(1261) and (590) follows:
% 55.65/21.31 | (1265) sum(n15, n15) = all_0_3_3
% 55.65/21.31 |
% 55.65/21.31 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 55.65/21.31 | (1266) all_0_3_3 = n4
% 55.65/21.31 |
% 55.65/21.31 | Instantiating formula (690) with n0, n4, all_0_0_0, n4 and discharging atoms sum(n0, n4) = all_0_0_0, sum(n0, n4) = n4, yields:
% 55.65/21.31 | (1267) all_0_0_0 = n4
% 55.65/21.31 |
% 55.65/21.31 | Equations (1267,1266) can reduce 679 to:
% 55.65/21.31 | (1106) $false
% 55.65/21.31 |
% 55.65/21.31 |-The branch is then unsatisfiable
% 55.65/21.31 |-Branch two:
% 55.65/21.31 | (1748) ~ (all_0_10_10 = n15)
% 55.65/21.31 | (1749) 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
% 55.65/21.31 |
% 55.65/21.31 +-Applying beta-rule and splitting (1270), into two cases.
% 55.65/21.31 |-Branch one:
% 55.65/21.31 | (1271) all_0_11_11 = n15
% 55.65/21.31 |
% 55.65/21.31 | From (1271) and (559) follows:
% 55.65/21.31 | (1272) pred(n15) = all_0_9_9
% 55.65/21.31 |
% 55.65/21.31 | From (1271) and (992) follows:
% 55.65/21.31 | (1273) succ(n15) = all_0_5_5
% 55.65/21.31 |
% 55.65/21.31 | Instantiating formula (500) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 55.76/21.31 | (1274) all_0_9_9 = n14
% 55.76/21.31 |
% 55.76/21.31 | Instantiating formula (617) with n15, all_0_5_5, n16 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n16, yields:
% 55.76/21.31 | (1275) all_0_5_5 = n16
% 55.76/21.31 |
% 55.76/21.31 | From (1275) and (541) follows:
% 55.76/21.31 | (9228) sum(all_0_6_6, n16) = all_0_4_4
% 55.76/21.31 |
% 55.76/21.31 | From (1274)(1275) and (538) follows:
% 55.76/21.31 | (1276) sum(n14, n16) = all_0_2_2
% 55.76/21.31 |
% 55.76/21.31 | From (1274) and (427) follows:
% 55.76/21.31 | (9230) sum(n14, all_0_8_8) = all_0_7_7
% 55.76/21.31 |
% 55.76/21.31 | Instantiating formula (690) with n14, n16, all_0_2_2, n4 and discharging atoms sum(n14, n16) = all_0_2_2, sum(n14, n16) = n4, yields:
% 55.76/21.31 | (1280) all_0_2_2 = n4
% 55.76/21.31 |
% 55.76/21.31 | From (1280) and (630) follows:
% 55.76/21.31 | (9232) sum(n4, all_0_1_1) = all_0_0_0
% 55.76/21.31 |
% 55.76/21.31 +-Applying beta-rule and splitting (1749), into two cases.
% 55.76/21.31 |-Branch one:
% 55.76/21.31 | (1750) all_0_10_10 = n14
% 55.76/21.31 |
% 55.76/21.31 | From (1750) and (292) follows:
% 55.76/21.31 | (1751) pred(n14) = all_0_6_6
% 55.76/21.31 |
% 55.76/21.31 | From (1750) and (760) follows:
% 55.76/21.31 | (1752) succ(n14) = all_0_8_8
% 55.76/21.31 |
% 55.76/21.31 | Instantiating formula (500) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 55.76/21.31 | (1753) all_0_6_6 = n13
% 55.76/21.31 |
% 55.76/21.31 | Instantiating formula (617) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 55.76/21.31 | (1754) all_0_8_8 = n15
% 55.76/21.31 |
% 55.76/21.31 | From (1753)(1754) and (411) follows:
% 55.76/21.31 | (1755) sum(n13, n15) = all_0_1_1
% 55.76/21.31 |
% 55.76/21.31 | From (1753) and (9228) follows:
% 55.76/21.31 | (9239) sum(n13, n16) = all_0_4_4
% 55.76/21.31 |
% 55.76/21.31 | From (1754) and (9230) follows:
% 55.76/21.31 | (9240) sum(n14, n15) = all_0_7_7
% 55.76/21.31 |
% 55.76/21.31 | Instantiating formula (690) with n14, n15, all_0_7_7, n3 and discharging atoms sum(n14, n15) = all_0_7_7, sum(n14, n15) = n3, yields:
% 55.76/21.31 | (1479) all_0_7_7 = n3
% 55.76/21.31 |
% 55.76/21.31 | Instantiating formula (690) with n13, n16, all_0_4_4, n3 and discharging atoms sum(n13, n16) = all_0_4_4, sum(n13, n16) = n3, yields:
% 55.76/21.31 | (1477) all_0_4_4 = n3
% 55.76/21.31 |
% 55.76/21.31 | Instantiating formula (690) with n13, n15, all_0_1_1, n2 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n2, yields:
% 55.76/21.31 | (1759) all_0_1_1 = n2
% 55.76/21.31 |
% 55.76/21.31 | From (1479)(1477) and (590) follows:
% 55.76/21.31 | (1481) sum(n3, n3) = all_0_3_3
% 55.76/21.31 |
% 55.76/21.31 | From (1759) and (9232) follows:
% 55.76/21.31 | (9245) sum(n4, n2) = all_0_0_0
% 55.76/21.31 |
% 55.76/21.31 | Instantiating formula (690) with n4, n2, all_0_0_0, n6 and discharging atoms sum(n4, n2) = all_0_0_0, sum(n4, n2) = n6, yields:
% 55.76/21.31 | (1249) all_0_0_0 = n6
% 55.76/21.31 |
% 55.76/21.31 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 55.76/21.31 | (1248) all_0_3_3 = n6
% 55.76/21.31 |
% 55.76/21.31 | Equations (1249,1248) can reduce 679 to:
% 55.76/21.31 | (1106) $false
% 55.76/21.31 |
% 55.76/21.31 |-The branch is then unsatisfiable
% 55.76/21.31 |-Branch two:
% 55.76/21.31 | (1766) ~ (all_0_10_10 = n14)
% 55.76/21.31 | (1767) 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
% 55.76/21.31 |
% 55.76/21.31 +-Applying beta-rule and splitting (1767), into two cases.
% 55.76/21.31 |-Branch one:
% 55.76/21.31 | (1768) all_0_10_10 = n13
% 55.76/21.31 |
% 55.76/21.31 | From (1768) and (292) follows:
% 55.76/21.31 | (1769) pred(n13) = all_0_6_6
% 55.76/21.31 |
% 55.76/21.31 | From (1768) and (760) follows:
% 55.76/21.31 | (1770) succ(n13) = all_0_8_8
% 55.76/21.31 |
% 55.76/21.31 | Instantiating formula (500) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 55.76/21.31 | (1771) all_0_6_6 = n12
% 55.76/21.31 |
% 55.76/21.31 | Instantiating formula (617) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 55.76/21.31 | (1772) all_0_8_8 = n14
% 55.76/21.31 |
% 55.76/21.31 | From (1771)(1772) and (411) follows:
% 55.76/21.31 | (1773) sum(n12, n14) = all_0_1_1
% 55.76/21.31 |
% 55.76/21.31 | From (1771) and (9228) follows:
% 55.76/21.31 | (9257) sum(n12, n16) = all_0_4_4
% 55.76/21.31 |
% 55.76/21.31 | From (1772) and (9230) follows:
% 55.76/21.31 | (9258) sum(n14, n14) = all_0_7_7
% 55.76/21.31 |
% 55.76/21.31 | Instantiating formula (690) with n14, n14, all_0_7_7, n2 and discharging atoms sum(n14, n14) = all_0_7_7, sum(n14, n14) = n2, yields:
% 55.76/21.31 | (1497) all_0_7_7 = n2
% 55.76/21.31 |
% 55.76/21.31 | Instantiating formula (690) with n12, n16, all_0_4_4, n2 and discharging atoms sum(n12, n16) = all_0_4_4, sum(n12, n16) = n2, yields:
% 55.76/21.31 | (1495) all_0_4_4 = n2
% 55.76/21.31 |
% 55.76/21.31 | Instantiating formula (690) with n12, n14, all_0_1_1, n0 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n0, yields:
% 55.76/21.31 | (1777) all_0_1_1 = n0
% 55.76/21.31 |
% 55.76/21.31 | From (1497)(1495) and (590) follows:
% 55.76/21.31 | (1499) sum(n2, n2) = all_0_3_3
% 55.76/21.31 |
% 55.76/21.31 | From (1777) and (9232) follows:
% 55.76/21.31 | (9263) sum(n4, n0) = all_0_0_0
% 55.76/21.31 |
% 55.76/21.31 | Instantiating formula (690) with n4, n0, all_0_0_0, n4 and discharging atoms sum(n4, n0) = all_0_0_0, sum(n4, n0) = n4, yields:
% 55.76/21.31 | (1267) all_0_0_0 = n4
% 55.76/21.31 |
% 55.76/21.31 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 55.76/21.31 | (1266) all_0_3_3 = n4
% 55.76/21.31 |
% 55.76/21.31 | Equations (1267,1266) can reduce 679 to:
% 55.76/21.31 | (1106) $false
% 55.76/21.31 |
% 55.76/21.31 |-The branch is then unsatisfiable
% 55.76/21.31 |-Branch two:
% 55.76/21.31 | (1784) ~ (all_0_10_10 = n13)
% 55.76/21.32 | (1785) 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
% 55.76/21.32 |
% 55.76/21.32 +-Applying beta-rule and splitting (1785), into two cases.
% 55.76/21.32 |-Branch one:
% 55.76/21.32 | (1786) all_0_10_10 = n12
% 55.76/21.32 |
% 55.76/21.32 | From (1786) and (292) follows:
% 55.76/21.32 | (1787) pred(n12) = all_0_6_6
% 55.76/21.32 |
% 55.76/21.32 | From (1786) and (760) follows:
% 55.76/21.32 | (1788) succ(n12) = all_0_8_8
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (500) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 55.76/21.32 | (1789) all_0_6_6 = n11
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (617) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 55.76/21.32 | (1790) all_0_8_8 = n13
% 55.76/21.32 |
% 55.76/21.32 | From (1789)(1790) and (411) follows:
% 55.76/21.32 | (1791) sum(n11, n13) = all_0_1_1
% 55.76/21.32 |
% 55.76/21.32 | From (1789) and (9228) follows:
% 55.76/21.32 | (9275) sum(n11, n16) = all_0_4_4
% 55.76/21.32 |
% 55.76/21.32 | From (1790) and (9230) follows:
% 55.76/21.32 | (9276) sum(n14, n13) = all_0_7_7
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (690) with n14, n13, all_0_7_7, n1 and discharging atoms sum(n14, n13) = all_0_7_7, sum(n14, n13) = n1, yields:
% 55.76/21.32 | (1515) all_0_7_7 = n1
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (690) with n11, n16, all_0_4_4, n1 and discharging atoms sum(n11, n16) = all_0_4_4, sum(n11, n16) = n1, yields:
% 55.76/21.32 | (1513) all_0_4_4 = n1
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (690) with n11, n13, all_0_1_1, n24 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n24, yields:
% 55.76/21.32 | (1081) all_0_1_1 = n24
% 55.76/21.32 |
% 55.76/21.32 | From (1515)(1513) and (590) follows:
% 55.76/21.32 | (1517) sum(n1, n1) = all_0_3_3
% 55.76/21.32 |
% 55.76/21.32 | From (1081) and (9232) follows:
% 55.76/21.32 | (1282) sum(n4, n24) = all_0_0_0
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (690) with n4, n24, all_0_0_0, n2 and discharging atoms sum(n4, n24) = all_0_0_0, sum(n4, n24) = n2, yields:
% 55.76/21.32 | (1285) all_0_0_0 = n2
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 55.76/21.32 | (1284) all_0_3_3 = n2
% 55.76/21.32 |
% 55.76/21.32 | Equations (1285,1284) can reduce 679 to:
% 55.76/21.32 | (1106) $false
% 55.76/21.32 |
% 55.76/21.32 |-The branch is then unsatisfiable
% 55.76/21.32 |-Branch two:
% 55.76/21.32 | (1802) ~ (all_0_10_10 = n12)
% 55.76/21.32 | (1803) 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
% 55.76/21.32 |
% 55.76/21.32 +-Applying beta-rule and splitting (1803), into two cases.
% 55.76/21.32 |-Branch one:
% 55.76/21.32 | (1804) all_0_10_10 = n11
% 55.76/21.32 |
% 55.76/21.32 | From (1804) and (292) follows:
% 55.76/21.32 | (1805) pred(n11) = all_0_6_6
% 55.76/21.32 |
% 55.76/21.32 | From (1804) and (760) follows:
% 55.76/21.32 | (1806) succ(n11) = all_0_8_8
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (500) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 55.76/21.32 | (1807) all_0_6_6 = n10
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (617) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 55.76/21.32 | (1808) all_0_8_8 = n12
% 55.76/21.32 |
% 55.76/21.32 | From (1807)(1808) and (411) follows:
% 55.76/21.32 | (1809) sum(n10, n12) = all_0_1_1
% 55.76/21.32 |
% 55.76/21.32 | From (1807) and (9228) follows:
% 55.76/21.32 | (9293) sum(n10, n16) = all_0_4_4
% 55.76/21.32 |
% 55.76/21.32 | From (1808) and (9230) follows:
% 55.76/21.32 | (9294) sum(n14, n12) = all_0_7_7
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (690) with n14, n12, all_0_7_7, n0 and discharging atoms sum(n14, n12) = all_0_7_7, sum(n14, n12) = n0, yields:
% 55.76/21.32 | (1533) all_0_7_7 = n0
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (690) with n10, n16, all_0_4_4, n0 and discharging atoms sum(n10, n16) = all_0_4_4, sum(n10, n16) = n0, yields:
% 55.76/21.32 | (1531) all_0_4_4 = n0
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (690) with n10, n12, all_0_1_1, n22 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n22, yields:
% 55.76/21.32 | (1579) all_0_1_1 = n22
% 55.76/21.32 |
% 55.76/21.32 | From (1533)(1531) and (590) follows:
% 55.76/21.32 | (1535) sum(n0, n0) = all_0_3_3
% 55.76/21.32 |
% 55.76/21.32 | From (1579) and (9232) follows:
% 55.76/21.32 | (2214) sum(n4, n22) = all_0_0_0
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (690) with n4, n22, all_0_0_0, n0 and discharging atoms sum(n4, n22) = all_0_0_0, sum(n4, n22) = n0, yields:
% 55.76/21.32 | (1303) all_0_0_0 = n0
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 55.76/21.32 | (1302) all_0_3_3 = n0
% 55.76/21.32 |
% 55.76/21.32 | Equations (1303,1302) can reduce 679 to:
% 55.76/21.32 | (1106) $false
% 55.76/21.32 |
% 55.76/21.32 |-The branch is then unsatisfiable
% 55.76/21.32 |-Branch two:
% 55.76/21.32 | (1820) ~ (all_0_10_10 = n11)
% 55.76/21.32 | (1821) 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
% 55.76/21.32 |
% 55.76/21.32 +-Applying beta-rule and splitting (1821), into two cases.
% 55.76/21.32 |-Branch one:
% 55.76/21.32 | (1822) all_0_10_10 = n10
% 55.76/21.32 |
% 55.76/21.32 | From (1822) and (292) follows:
% 55.76/21.32 | (1823) pred(n10) = all_0_6_6
% 55.76/21.32 |
% 55.76/21.32 | From (1822) and (760) follows:
% 55.76/21.32 | (1824) succ(n10) = all_0_8_8
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (500) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 55.76/21.32 | (1825) all_0_6_6 = n9
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (617) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 55.76/21.32 | (1826) all_0_8_8 = n11
% 55.76/21.32 |
% 55.76/21.32 | From (1825)(1826) and (411) follows:
% 55.76/21.32 | (1827) sum(n9, n11) = all_0_1_1
% 55.76/21.32 |
% 55.76/21.32 | From (1825) and (9228) follows:
% 55.76/21.32 | (9311) sum(n9, n16) = all_0_4_4
% 55.76/21.32 |
% 55.76/21.32 | From (1826) and (9230) follows:
% 55.76/21.32 | (9312) sum(n14, n11) = all_0_7_7
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (690) with n14, n11, all_0_7_7, n25 and discharging atoms sum(n14, n11) = all_0_7_7, sum(n14, n11) = n25, yields:
% 55.76/21.32 | (1550) all_0_7_7 = n25
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (690) with n9, n16, all_0_4_4, n25 and discharging atoms sum(n9, n16) = all_0_4_4, sum(n9, n16) = n25, yields:
% 55.76/21.32 | (1551) all_0_4_4 = n25
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (690) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 55.76/21.32 | (1597) all_0_1_1 = n20
% 55.76/21.32 |
% 55.76/21.32 | From (1550)(1551) and (590) follows:
% 55.76/21.32 | (1553) sum(n25, n25) = all_0_3_3
% 55.76/21.32 |
% 55.76/21.32 | From (1597) and (9232) follows:
% 55.76/21.32 | (3106) sum(n4, n20) = all_0_0_0
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 55.76/21.32 | (1320) all_0_3_3 = n24
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (690) with n4, n20, all_0_0_0, n24 and discharging atoms sum(n4, n20) = all_0_0_0, sum(n4, n20) = n24, yields:
% 55.76/21.32 | (1321) all_0_0_0 = n24
% 55.76/21.32 |
% 55.76/21.32 | Equations (1321,1320) can reduce 679 to:
% 55.76/21.32 | (1106) $false
% 55.76/21.32 |
% 55.76/21.32 |-The branch is then unsatisfiable
% 55.76/21.32 |-Branch two:
% 55.76/21.32 | (1838) ~ (all_0_10_10 = n10)
% 55.76/21.32 | (1839) 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
% 55.76/21.32 |
% 55.76/21.32 +-Applying beta-rule and splitting (1839), into two cases.
% 55.76/21.32 |-Branch one:
% 55.76/21.32 | (1840) all_0_10_10 = n9
% 55.76/21.32 |
% 55.76/21.32 | From (1840) and (292) follows:
% 55.76/21.32 | (1841) pred(n9) = all_0_6_6
% 55.76/21.32 |
% 55.76/21.32 | From (1840) and (760) follows:
% 55.76/21.32 | (1842) succ(n9) = all_0_8_8
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (500) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 55.76/21.32 | (1843) all_0_6_6 = n8
% 55.76/21.32 |
% 55.76/21.32 | Instantiating formula (617) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 55.76/21.32 | (1844) all_0_8_8 = n10
% 55.76/21.32 |
% 55.76/21.32 | From (1843)(1844) and (411) follows:
% 55.76/21.32 | (1845) sum(n8, n10) = all_0_1_1
% 55.76/21.32 |
% 55.76/21.32 | From (1843) and (9228) follows:
% 55.76/21.33 | (9329) sum(n8, n16) = all_0_4_4
% 55.76/21.33 |
% 55.76/21.33 | From (1844) and (9230) follows:
% 55.76/21.33 | (9330) sum(n14, n10) = all_0_7_7
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (690) with n14, n10, all_0_7_7, n24 and discharging atoms sum(n14, n10) = all_0_7_7, sum(n14, n10) = n24, yields:
% 55.76/21.33 | (1097) all_0_7_7 = n24
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (690) with n8, n16, all_0_4_4, n24 and discharging atoms sum(n8, n16) = all_0_4_4, sum(n8, n16) = n24, yields:
% 55.76/21.33 | (1096) all_0_4_4 = n24
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (690) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 55.76/21.33 | (1615) all_0_1_1 = n18
% 55.76/21.33 |
% 55.76/21.33 | From (1097)(1096) and (590) follows:
% 55.76/21.33 | (1101) sum(n24, n24) = all_0_3_3
% 55.76/21.33 |
% 55.76/21.33 | From (1615) and (9232) follows:
% 55.76/21.33 | (3962) sum(n4, n18) = all_0_0_0
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 55.76/21.33 | (1104) all_0_3_3 = n22
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (690) with n4, n18, all_0_0_0, n22 and discharging atoms sum(n4, n18) = all_0_0_0, sum(n4, n18) = n22, yields:
% 55.76/21.33 | (1102) all_0_0_0 = n22
% 55.76/21.33 |
% 55.76/21.33 | Equations (1102,1104) can reduce 679 to:
% 55.76/21.33 | (1106) $false
% 55.76/21.33 |
% 55.76/21.33 |-The branch is then unsatisfiable
% 55.76/21.33 |-Branch two:
% 55.76/21.33 | (1856) ~ (all_0_10_10 = n9)
% 55.76/21.33 | (1857) 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
% 55.76/21.33 |
% 55.76/21.33 +-Applying beta-rule and splitting (1857), into two cases.
% 55.76/21.33 |-Branch one:
% 55.76/21.33 | (1858) all_0_10_10 = n8
% 55.76/21.33 |
% 55.76/21.33 | From (1858) and (292) follows:
% 55.76/21.33 | (1859) pred(n8) = all_0_6_6
% 55.76/21.33 |
% 55.76/21.33 | From (1858) and (760) follows:
% 55.76/21.33 | (1860) succ(n8) = all_0_8_8
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 55.76/21.33 | (1861) all_0_6_6 = n7
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 55.76/21.33 | (1862) all_0_8_8 = n9
% 55.76/21.33 |
% 55.76/21.33 | From (1861)(1862) and (411) follows:
% 55.76/21.33 | (1863) sum(n7, n9) = all_0_1_1
% 55.76/21.33 |
% 55.76/21.33 | From (1861) and (9228) follows:
% 55.76/21.33 | (9347) sum(n7, n16) = all_0_4_4
% 55.76/21.33 |
% 55.76/21.33 | From (1862) and (9230) follows:
% 55.76/21.33 | (9348) sum(n14, n9) = all_0_7_7
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (690) with n14, n9, all_0_7_7, n23 and discharging atoms sum(n14, n9) = all_0_7_7, sum(n14, n9) = n23, yields:
% 55.76/21.33 | (1119) all_0_7_7 = n23
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (690) with n7, n16, all_0_4_4, n23 and discharging atoms sum(n7, n16) = all_0_4_4, sum(n7, n16) = n23, yields:
% 55.76/21.33 | (1117) all_0_4_4 = n23
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 55.76/21.33 | (1633) all_0_1_1 = n16
% 55.76/21.33 |
% 55.76/21.33 | From (1119)(1117) and (590) follows:
% 55.76/21.33 | (1121) sum(n23, n23) = all_0_3_3
% 55.76/21.33 |
% 55.76/21.33 | From (1633) and (9232) follows:
% 55.76/21.33 | (4782) sum(n4, n16) = all_0_0_0
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 55.76/21.33 | (1122) all_0_3_3 = n20
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (690) with n4, n16, all_0_0_0, n20 and discharging atoms sum(n4, n16) = all_0_0_0, sum(n4, n16) = n20, yields:
% 55.76/21.33 | (1123) all_0_0_0 = n20
% 55.76/21.33 |
% 55.76/21.33 | Equations (1123,1122) can reduce 679 to:
% 55.76/21.33 | (1106) $false
% 55.76/21.33 |
% 55.76/21.33 |-The branch is then unsatisfiable
% 55.76/21.33 |-Branch two:
% 55.76/21.33 | (1874) ~ (all_0_10_10 = n8)
% 55.76/21.33 | (1875) 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
% 55.76/21.33 |
% 55.76/21.33 +-Applying beta-rule and splitting (1875), into two cases.
% 55.76/21.33 |-Branch one:
% 55.76/21.33 | (1876) all_0_10_10 = n7
% 55.76/21.33 |
% 55.76/21.33 | From (1876) and (292) follows:
% 55.76/21.33 | (1877) pred(n7) = all_0_6_6
% 55.76/21.33 |
% 55.76/21.33 | From (1876) and (760) follows:
% 55.76/21.33 | (1878) succ(n7) = all_0_8_8
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 55.76/21.33 | (1879) all_0_6_6 = n6
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 55.76/21.33 | (1880) all_0_8_8 = n8
% 55.76/21.33 |
% 55.76/21.33 | From (1879)(1880) and (411) follows:
% 55.76/21.33 | (1881) sum(n6, n8) = all_0_1_1
% 55.76/21.33 |
% 55.76/21.33 | From (1879) and (9228) follows:
% 55.76/21.33 | (9365) sum(n6, n16) = all_0_4_4
% 55.76/21.33 |
% 55.76/21.33 | From (1880) and (9230) follows:
% 55.76/21.33 | (9366) sum(n14, n8) = all_0_7_7
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (690) with n14, n8, all_0_7_7, n22 and discharging atoms sum(n14, n8) = all_0_7_7, sum(n14, n8) = n22, yields:
% 55.76/21.33 | (1137) all_0_7_7 = n22
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (690) with n6, n16, all_0_4_4, n22 and discharging atoms sum(n6, n16) = all_0_4_4, sum(n6, n16) = n22, yields:
% 55.76/21.33 | (1135) all_0_4_4 = n22
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 55.76/21.33 | (1651) all_0_1_1 = n14
% 55.76/21.33 |
% 55.76/21.33 | From (1137)(1135) and (590) follows:
% 55.76/21.33 | (1139) sum(n22, n22) = all_0_3_3
% 55.76/21.33 |
% 55.76/21.33 | From (1651) and (9232) follows:
% 55.76/21.33 | (5566) sum(n4, n14) = all_0_0_0
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 55.76/21.33 | (1140) all_0_3_3 = n18
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (690) with n4, n14, all_0_0_0, n18 and discharging atoms sum(n4, n14) = all_0_0_0, sum(n4, n14) = n18, yields:
% 55.76/21.33 | (1141) all_0_0_0 = n18
% 55.76/21.33 |
% 55.76/21.33 | Equations (1141,1140) can reduce 679 to:
% 55.76/21.33 | (1106) $false
% 55.76/21.33 |
% 55.76/21.33 |-The branch is then unsatisfiable
% 55.76/21.33 |-Branch two:
% 55.76/21.33 | (1892) ~ (all_0_10_10 = n7)
% 55.76/21.33 | (1893) 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
% 55.76/21.33 |
% 55.76/21.33 +-Applying beta-rule and splitting (1893), into two cases.
% 55.76/21.33 |-Branch one:
% 55.76/21.33 | (1894) all_0_10_10 = n6
% 55.76/21.33 |
% 55.76/21.33 | From (1894) and (292) follows:
% 55.76/21.33 | (1895) pred(n6) = all_0_6_6
% 55.76/21.33 |
% 55.76/21.33 | From (1894) and (760) follows:
% 55.76/21.33 | (1896) succ(n6) = all_0_8_8
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 55.76/21.33 | (1897) all_0_6_6 = n5
% 55.76/21.33 |
% 55.76/21.33 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 55.76/21.33 | (1898) all_0_8_8 = n7
% 55.76/21.33 |
% 55.76/21.33 | From (1897)(1898) and (411) follows:
% 55.76/21.33 | (1899) sum(n5, n7) = all_0_1_1
% 55.76/21.33 |
% 55.76/21.33 | From (1897) and (9228) follows:
% 55.76/21.33 | (9383) sum(n5, n16) = all_0_4_4
% 55.76/21.33 |
% 55.76/21.33 | From (1898) and (9230) follows:
% 55.76/21.34 | (9384) sum(n14, n7) = all_0_7_7
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (690) with n14, n7, all_0_7_7, n21 and discharging atoms sum(n14, n7) = all_0_7_7, sum(n14, n7) = n21, yields:
% 55.76/21.34 | (1155) all_0_7_7 = n21
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (690) with n5, n16, all_0_4_4, n21 and discharging atoms sum(n5, n16) = all_0_4_4, sum(n5, n16) = n21, yields:
% 55.76/21.34 | (1153) all_0_4_4 = n21
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 55.76/21.34 | (1669) all_0_1_1 = n12
% 55.76/21.34 |
% 55.76/21.34 | From (1155)(1153) and (590) follows:
% 55.76/21.34 | (1157) sum(n21, n21) = all_0_3_3
% 55.76/21.34 |
% 55.76/21.34 | From (1669) and (9232) follows:
% 55.76/21.34 | (6314) sum(n4, n12) = all_0_0_0
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 55.76/21.34 | (1158) all_0_3_3 = n16
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (690) with n4, n12, all_0_0_0, n16 and discharging atoms sum(n4, n12) = all_0_0_0, sum(n4, n12) = n16, yields:
% 55.76/21.34 | (1159) all_0_0_0 = n16
% 55.76/21.34 |
% 55.76/21.34 | Equations (1159,1158) can reduce 679 to:
% 55.76/21.34 | (1106) $false
% 55.76/21.34 |
% 55.76/21.34 |-The branch is then unsatisfiable
% 55.76/21.34 |-Branch two:
% 55.76/21.34 | (1910) ~ (all_0_10_10 = n6)
% 55.76/21.34 | (1911) 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
% 55.76/21.34 |
% 55.76/21.34 +-Applying beta-rule and splitting (1911), into two cases.
% 55.76/21.34 |-Branch one:
% 55.76/21.34 | (1912) all_0_10_10 = n5
% 55.76/21.34 |
% 55.76/21.34 | From (1912) and (292) follows:
% 55.76/21.34 | (1913) pred(n5) = all_0_6_6
% 55.76/21.34 |
% 55.76/21.34 | From (1912) and (760) follows:
% 55.76/21.34 | (1914) succ(n5) = all_0_8_8
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 55.76/21.34 | (1915) all_0_6_6 = n4
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 55.76/21.34 | (1916) all_0_8_8 = n6
% 55.76/21.34 |
% 55.76/21.34 | From (1915)(1916) and (411) follows:
% 55.76/21.34 | (1917) sum(n4, n6) = all_0_1_1
% 55.76/21.34 |
% 55.76/21.34 | From (1915) and (9228) follows:
% 55.76/21.34 | (9401) sum(n4, n16) = all_0_4_4
% 55.76/21.34 |
% 55.76/21.34 | From (1916) and (9230) follows:
% 55.76/21.34 | (9402) sum(n14, n6) = all_0_7_7
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (690) with n14, n6, all_0_7_7, n20 and discharging atoms sum(n14, n6) = all_0_7_7, sum(n14, n6) = n20, yields:
% 55.76/21.34 | (1173) all_0_7_7 = n20
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (690) with n4, n16, all_0_4_4, n20 and discharging atoms sum(n4, n16) = all_0_4_4, sum(n4, n16) = n20, yields:
% 55.76/21.34 | (1171) all_0_4_4 = n20
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 55.76/21.34 | (1687) all_0_1_1 = n10
% 55.76/21.34 |
% 55.76/21.34 | From (1173)(1171) and (590) follows:
% 55.76/21.34 | (1175) sum(n20, n20) = all_0_3_3
% 55.76/21.34 |
% 55.76/21.34 | From (1687) and (9232) follows:
% 55.76/21.34 | (7026) sum(n4, n10) = all_0_0_0
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 55.76/21.34 | (1176) all_0_3_3 = n14
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (690) with n4, n10, all_0_0_0, n14 and discharging atoms sum(n4, n10) = all_0_0_0, sum(n4, n10) = n14, yields:
% 55.76/21.34 | (1177) all_0_0_0 = n14
% 55.76/21.34 |
% 55.76/21.34 | Equations (1177,1176) can reduce 679 to:
% 55.76/21.34 | (1106) $false
% 55.76/21.34 |
% 55.76/21.34 |-The branch is then unsatisfiable
% 55.76/21.34 |-Branch two:
% 55.76/21.34 | (1928) ~ (all_0_10_10 = n5)
% 55.76/21.34 | (1929) 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
% 55.76/21.34 |
% 55.76/21.34 +-Applying beta-rule and splitting (1929), into two cases.
% 55.76/21.34 |-Branch one:
% 55.76/21.34 | (1930) all_0_10_10 = n4
% 55.76/21.34 |
% 55.76/21.34 | From (1930) and (292) follows:
% 55.76/21.34 | (1931) pred(n4) = all_0_6_6
% 55.76/21.34 |
% 55.76/21.34 | From (1930) and (760) follows:
% 55.76/21.34 | (1932) succ(n4) = all_0_8_8
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 55.76/21.34 | (1933) all_0_6_6 = n3
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 55.76/21.34 | (1934) all_0_8_8 = n5
% 55.76/21.34 |
% 55.76/21.34 | From (1933)(1934) and (411) follows:
% 55.76/21.34 | (1935) sum(n3, n5) = all_0_1_1
% 55.76/21.34 |
% 55.76/21.34 | From (1933) and (9228) follows:
% 55.76/21.34 | (9419) sum(n3, n16) = all_0_4_4
% 55.76/21.34 |
% 55.76/21.34 | From (1934) and (9230) follows:
% 55.76/21.34 | (9420) sum(n14, n5) = all_0_7_7
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (690) with n14, n5, all_0_7_7, n19 and discharging atoms sum(n14, n5) = all_0_7_7, sum(n14, n5) = n19, yields:
% 55.76/21.34 | (1191) all_0_7_7 = n19
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (690) with n3, n16, all_0_4_4, n19 and discharging atoms sum(n3, n16) = all_0_4_4, sum(n3, n16) = n19, yields:
% 55.76/21.34 | (1189) all_0_4_4 = n19
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 55.76/21.34 | (1705) all_0_1_1 = n8
% 55.76/21.34 |
% 55.76/21.34 | From (1191)(1189) and (590) follows:
% 55.76/21.34 | (1193) sum(n19, n19) = all_0_3_3
% 55.76/21.34 |
% 55.76/21.34 | From (1705) and (9232) follows:
% 55.76/21.34 | (7702) sum(n4, n8) = all_0_0_0
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 55.76/21.34 | (1194) all_0_3_3 = n12
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (690) with n4, n8, all_0_0_0, n12 and discharging atoms sum(n4, n8) = all_0_0_0, sum(n4, n8) = n12, yields:
% 55.76/21.34 | (1195) all_0_0_0 = n12
% 55.76/21.34 |
% 55.76/21.34 | Equations (1195,1194) can reduce 679 to:
% 55.76/21.34 | (1106) $false
% 55.76/21.34 |
% 55.76/21.34 |-The branch is then unsatisfiable
% 55.76/21.34 |-Branch two:
% 55.76/21.34 | (1946) ~ (all_0_10_10 = n4)
% 55.76/21.34 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 55.76/21.34 |
% 55.76/21.34 +-Applying beta-rule and splitting (1947), into two cases.
% 55.76/21.34 |-Branch one:
% 55.76/21.34 | (1948) all_0_10_10 = n3
% 55.76/21.34 |
% 55.76/21.34 | From (1948) and (292) follows:
% 55.76/21.34 | (1949) pred(n3) = all_0_6_6
% 55.76/21.34 |
% 55.76/21.34 | From (1948) and (760) follows:
% 55.76/21.34 | (1950) succ(n3) = all_0_8_8
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 55.76/21.34 | (1951) all_0_6_6 = n2
% 55.76/21.34 |
% 55.76/21.34 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 55.76/21.34 | (1952) all_0_8_8 = n4
% 55.76/21.34 |
% 55.76/21.34 | From (1951)(1952) and (411) follows:
% 55.76/21.34 | (1953) sum(n2, n4) = all_0_1_1
% 55.76/21.34 |
% 55.76/21.34 | From (1951) and (9228) follows:
% 55.76/21.34 | (9437) sum(n2, n16) = all_0_4_4
% 55.76/21.34 |
% 55.76/21.34 | From (1952) and (9230) follows:
% 55.76/21.35 | (9438) sum(n14, n4) = all_0_7_7
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (690) with n14, n4, all_0_7_7, n18 and discharging atoms sum(n14, n4) = all_0_7_7, sum(n14, n4) = n18, yields:
% 55.76/21.35 | (1209) all_0_7_7 = n18
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (690) with n2, n16, all_0_4_4, n18 and discharging atoms sum(n2, n16) = all_0_4_4, sum(n2, n16) = n18, yields:
% 55.76/21.35 | (1207) all_0_4_4 = n18
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 55.76/21.35 | (1723) all_0_1_1 = n6
% 55.76/21.35 |
% 55.76/21.35 | From (1209)(1207) and (590) follows:
% 55.76/21.35 | (1211) sum(n18, n18) = all_0_3_3
% 55.76/21.35 |
% 55.76/21.35 | From (1723) and (9232) follows:
% 55.76/21.35 | (8343) sum(n4, n6) = all_0_0_0
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 55.76/21.35 | (1212) all_0_3_3 = n10
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (690) with n4, n6, all_0_0_0, n10 and discharging atoms sum(n4, n6) = all_0_0_0, sum(n4, n6) = n10, yields:
% 55.76/21.35 | (1213) all_0_0_0 = n10
% 55.76/21.35 |
% 55.76/21.35 | Equations (1213,1212) can reduce 679 to:
% 55.76/21.35 | (1106) $false
% 55.76/21.35 |
% 55.76/21.35 |-The branch is then unsatisfiable
% 55.76/21.35 |-Branch two:
% 55.76/21.35 | (1964) ~ (all_0_10_10 = n3)
% 55.76/21.35 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 55.76/21.35 |
% 55.76/21.35 +-Applying beta-rule and splitting (1965), into two cases.
% 55.76/21.35 |-Branch one:
% 55.76/21.35 | (1966) all_0_10_10 = n2
% 55.76/21.35 |
% 55.76/21.35 | From (1966) and (292) follows:
% 55.76/21.35 | (1967) pred(n2) = all_0_6_6
% 55.76/21.35 |
% 55.76/21.35 | From (1966) and (760) follows:
% 55.76/21.35 | (1968) succ(n2) = all_0_8_8
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 55.76/21.35 | (1969) all_0_6_6 = n1
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 55.76/21.35 | (1970) all_0_8_8 = n3
% 55.76/21.35 |
% 55.76/21.35 | From (1969)(1970) and (411) follows:
% 55.76/21.35 | (1971) sum(n1, n3) = all_0_1_1
% 55.76/21.35 |
% 55.76/21.35 | From (1969) and (9228) follows:
% 55.76/21.35 | (9455) sum(n1, n16) = all_0_4_4
% 55.76/21.35 |
% 55.76/21.35 | From (1970) and (9230) follows:
% 55.76/21.35 | (9456) sum(n14, n3) = all_0_7_7
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (690) with n14, n3, all_0_7_7, n17 and discharging atoms sum(n14, n3) = all_0_7_7, sum(n14, n3) = n17, yields:
% 55.76/21.35 | (1227) all_0_7_7 = n17
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (690) with n1, n16, all_0_4_4, n17 and discharging atoms sum(n1, n16) = all_0_4_4, sum(n1, n16) = n17, yields:
% 55.76/21.35 | (1225) all_0_4_4 = n17
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 55.76/21.35 | (1741) all_0_1_1 = n4
% 55.76/21.35 |
% 55.76/21.35 | From (1227)(1225) and (590) follows:
% 55.76/21.35 | (1229) sum(n17, n17) = all_0_3_3
% 55.76/21.35 |
% 55.76/21.35 | From (1741) and (9232) follows:
% 55.76/21.35 | (8945) sum(n4, n4) = all_0_0_0
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 55.76/21.35 | (1230) all_0_3_3 = n8
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (690) with n4, n4, all_0_0_0, n8 and discharging atoms sum(n4, n4) = all_0_0_0, sum(n4, n4) = n8, yields:
% 55.76/21.35 | (1231) all_0_0_0 = n8
% 55.76/21.35 |
% 55.76/21.35 | Equations (1231,1230) can reduce 679 to:
% 55.76/21.35 | (1106) $false
% 55.76/21.35 |
% 55.76/21.35 |-The branch is then unsatisfiable
% 55.76/21.35 |-Branch two:
% 55.76/21.35 | (1982) ~ (all_0_10_10 = n2)
% 55.76/21.35 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 55.76/21.35 |
% 55.76/21.35 +-Applying beta-rule and splitting (1983), into two cases.
% 55.76/21.35 |-Branch one:
% 55.76/21.35 | (1984) all_0_10_10 = n1
% 55.76/21.35 |
% 55.76/21.35 | From (1984) and (292) follows:
% 55.76/21.35 | (1985) pred(n1) = all_0_6_6
% 55.76/21.35 |
% 55.76/21.35 | From (1984) and (760) follows:
% 55.76/21.35 | (1986) succ(n1) = all_0_8_8
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 55.76/21.35 | (1987) all_0_6_6 = n0
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 55.76/21.35 | (1988) all_0_8_8 = n2
% 55.76/21.35 |
% 55.76/21.35 | From (1987)(1988) and (411) follows:
% 55.76/21.35 | (1989) sum(n0, n2) = all_0_1_1
% 55.76/21.35 |
% 55.76/21.35 | From (1987) and (9228) follows:
% 55.76/21.35 | (9473) sum(n0, n16) = all_0_4_4
% 55.76/21.35 |
% 55.76/21.35 | From (1988) and (9230) follows:
% 55.76/21.35 | (9474) sum(n14, n2) = all_0_7_7
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (690) with n14, n2, all_0_7_7, n16 and discharging atoms sum(n14, n2) = all_0_7_7, sum(n14, n2) = n16, yields:
% 55.76/21.35 | (1245) all_0_7_7 = n16
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (690) with n0, n16, all_0_4_4, n16 and discharging atoms sum(n0, n16) = all_0_4_4, sum(n0, n16) = n16, yields:
% 55.76/21.35 | (1243) all_0_4_4 = n16
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 55.76/21.35 | (1759) all_0_1_1 = n2
% 55.76/21.35 |
% 55.76/21.35 | From (1245)(1243) and (590) follows:
% 55.76/21.35 | (1247) sum(n16, n16) = all_0_3_3
% 55.76/21.35 |
% 55.76/21.35 | From (1759) and (9232) follows:
% 55.76/21.35 | (9245) sum(n4, n2) = all_0_0_0
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 55.76/21.35 | (1248) all_0_3_3 = n6
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (690) with n4, n2, all_0_0_0, n6 and discharging atoms sum(n4, n2) = all_0_0_0, sum(n4, n2) = n6, yields:
% 55.76/21.35 | (1249) all_0_0_0 = n6
% 55.76/21.35 |
% 55.76/21.35 | Equations (1249,1248) can reduce 679 to:
% 55.76/21.35 | (1106) $false
% 55.76/21.35 |
% 55.76/21.35 |-The branch is then unsatisfiable
% 55.76/21.35 |-Branch two:
% 55.76/21.35 | (2002) ~ (all_0_10_10 = n1)
% 55.76/21.35 | (2003) all_0_10_10 = n0
% 55.76/21.35 |
% 55.76/21.35 | From (2003) and (292) follows:
% 55.76/21.35 | (2004) pred(n0) = all_0_6_6
% 55.76/21.35 |
% 55.76/21.35 | From (2003) and (760) follows:
% 55.76/21.35 | (2005) succ(n0) = all_0_8_8
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 55.76/21.35 | (2006) all_0_6_6 = n25
% 55.76/21.35 |
% 55.76/21.35 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 55.76/21.35 | (2007) all_0_8_8 = n1
% 55.76/21.35 |
% 55.76/21.35 | From (2006)(2007) and (411) follows:
% 55.76/21.35 | (2008) sum(n25, n1) = all_0_1_1
% 55.76/21.35 |
% 55.76/21.35 | From (2006) and (9228) follows:
% 55.76/21.35 | (9490) sum(n25, n16) = all_0_4_4
% 55.76/21.35 |
% 55.76/21.35 | From (2007) and (9230) follows:
% 55.76/21.36 | (9491) sum(n14, n1) = all_0_7_7
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (690) with n25, n16, all_0_4_4, n15 and discharging atoms sum(n25, n16) = all_0_4_4, sum(n25, n16) = n15, yields:
% 55.76/21.36 | (1261) all_0_4_4 = n15
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 55.76/21.36 | (1777) all_0_1_1 = n0
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (690) with n14, n1, all_0_7_7, n15 and discharging atoms sum(n14, n1) = all_0_7_7, sum(n14, n1) = n15, yields:
% 55.76/21.36 | (1263) all_0_7_7 = n15
% 55.76/21.36 |
% 55.76/21.36 | From (1263)(1261) and (590) follows:
% 55.76/21.36 | (1265) sum(n15, n15) = all_0_3_3
% 55.76/21.36 |
% 55.76/21.36 | From (1777) and (9232) follows:
% 55.76/21.36 | (9263) sum(n4, n0) = all_0_0_0
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 55.76/21.36 | (1266) all_0_3_3 = n4
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (690) with n4, n0, all_0_0_0, n4 and discharging atoms sum(n4, n0) = all_0_0_0, sum(n4, n0) = n4, yields:
% 55.76/21.36 | (1267) all_0_0_0 = n4
% 55.76/21.36 |
% 55.76/21.36 | Equations (1267,1266) can reduce 679 to:
% 55.76/21.36 | (1106) $false
% 55.76/21.36 |
% 55.76/21.36 |-The branch is then unsatisfiable
% 55.76/21.36 |-Branch two:
% 55.76/21.36 | (1287) ~ (all_0_11_11 = n15)
% 55.76/21.36 | (1288) 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
% 55.76/21.36 |
% 55.76/21.36 +-Applying beta-rule and splitting (1749), into two cases.
% 55.76/21.36 |-Branch one:
% 55.76/21.36 | (1750) all_0_10_10 = n14
% 55.76/21.36 |
% 55.76/21.36 | From (1750) and (292) follows:
% 55.76/21.36 | (1751) pred(n14) = all_0_6_6
% 55.76/21.36 |
% 55.76/21.36 | From (1750) and (760) follows:
% 55.76/21.36 | (1752) succ(n14) = all_0_8_8
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (500) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 55.76/21.36 | (1753) all_0_6_6 = n13
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (617) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 55.76/21.36 | (1754) all_0_8_8 = n15
% 55.76/21.36 |
% 55.76/21.36 | From (1753) and (1751) follows:
% 55.76/21.36 | (26) pred(n14) = n13
% 55.76/21.36 |
% 55.76/21.36 | From (1754) and (1752) follows:
% 55.76/21.36 | (924) succ(n14) = n15
% 55.76/21.36 |
% 55.76/21.36 | From (1753) and (541) follows:
% 55.76/21.36 | (9509) sum(n13, all_0_5_5) = all_0_4_4
% 55.76/21.36 |
% 55.76/21.36 | From (1753)(1754) and (411) follows:
% 55.76/21.36 | (1755) sum(n13, n15) = all_0_1_1
% 55.76/21.36 |
% 55.76/21.36 | From (1754) and (427) follows:
% 55.76/21.36 | (9511) sum(all_0_9_9, n15) = all_0_7_7
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (690) with n13, n15, all_0_1_1, n2 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n2, yields:
% 55.76/21.36 | (1759) all_0_1_1 = n2
% 55.76/21.36 |
% 55.76/21.36 | From (1759) and (630) follows:
% 55.76/21.36 | (9513) sum(all_0_2_2, n2) = all_0_0_0
% 55.76/21.36 |
% 55.76/21.36 | From (1759) and (1755) follows:
% 55.76/21.36 | (841) sum(n13, n15) = n2
% 55.76/21.36 |
% 55.76/21.36 +-Applying beta-rule and splitting (1288), into two cases.
% 55.76/21.36 |-Branch one:
% 55.76/21.36 | (1289) all_0_11_11 = n14
% 55.76/21.36 |
% 55.76/21.36 | From (1289) and (559) follows:
% 55.76/21.36 | (1290) pred(n14) = all_0_9_9
% 55.76/21.36 |
% 55.76/21.36 | From (1289) and (992) follows:
% 55.76/21.36 | (1291) succ(n14) = all_0_5_5
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (500) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 55.76/21.36 | (1292) all_0_9_9 = n13
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (617) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 55.76/21.36 | (1293) all_0_5_5 = n15
% 55.76/21.36 |
% 55.76/21.36 | From (1292)(1293) and (538) follows:
% 55.76/21.36 | (1294) sum(n13, n15) = all_0_2_2
% 55.76/21.36 |
% 55.76/21.36 | From (1292) and (9511) follows:
% 55.76/21.36 | (9521) sum(n13, n15) = all_0_7_7
% 55.76/21.36 |
% 55.76/21.36 | From (1293) and (9509) follows:
% 55.76/21.36 | (9522) sum(n13, n15) = all_0_4_4
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (690) with n13, n15, all_0_2_2, n2 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n2, yields:
% 55.76/21.36 | (1298) all_0_2_2 = n2
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (690) 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:
% 55.76/21.36 | (1093) all_0_2_2 = all_0_4_4
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (690) 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:
% 55.76/21.36 | (1094) all_0_2_2 = all_0_7_7
% 55.76/21.36 |
% 55.76/21.36 | Combining equations (1094,1093) yields a new equation:
% 55.76/21.36 | (1095) all_0_4_4 = all_0_7_7
% 55.76/21.36 |
% 55.76/21.36 | Combining equations (1298,1093) yields a new equation:
% 55.76/21.36 | (1495) all_0_4_4 = n2
% 55.76/21.36 |
% 55.76/21.36 | Combining equations (1495,1095) yields a new equation:
% 55.76/21.36 | (1497) all_0_7_7 = n2
% 55.76/21.36 |
% 55.76/21.36 | Combining equations (1497,1095) yields a new equation:
% 55.76/21.36 | (1495) all_0_4_4 = n2
% 55.76/21.36 |
% 55.76/21.36 | Combining equations (1495,1093) yields a new equation:
% 55.76/21.36 | (1298) all_0_2_2 = n2
% 55.76/21.36 |
% 55.76/21.36 | From (1298) and (9513) follows:
% 55.76/21.36 | (9531) sum(n2, n2) = all_0_0_0
% 55.76/21.36 |
% 55.76/21.36 | From (1497)(1495) and (590) follows:
% 55.76/21.36 | (1499) sum(n2, n2) = all_0_3_3
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (690) with n2, n2, all_0_0_0, n4 and discharging atoms sum(n2, n2) = all_0_0_0, sum(n2, n2) = n4, yields:
% 55.76/21.36 | (1267) all_0_0_0 = n4
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (690) 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:
% 55.76/21.36 | (1103) all_0_0_0 = all_0_3_3
% 55.76/21.36 |
% 55.76/21.36 | Combining equations (1267,1103) yields a new equation:
% 55.76/21.36 | (1266) all_0_3_3 = n4
% 55.76/21.36 |
% 55.76/21.36 | Combining equations (1266,1103) yields a new equation:
% 55.76/21.36 | (1267) all_0_0_0 = n4
% 55.76/21.36 |
% 55.76/21.36 | Equations (1267,1266) can reduce 679 to:
% 55.76/21.36 | (1106) $false
% 55.76/21.36 |
% 55.76/21.36 |-The branch is then unsatisfiable
% 55.76/21.36 |-Branch two:
% 55.76/21.36 | (1305) ~ (all_0_11_11 = n14)
% 55.76/21.36 | (1306) 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
% 55.76/21.36 |
% 55.76/21.36 +-Applying beta-rule and splitting (1306), into two cases.
% 55.76/21.36 |-Branch one:
% 55.76/21.36 | (1307) all_0_11_11 = n13
% 55.76/21.36 |
% 55.76/21.36 | From (1307) and (559) follows:
% 55.76/21.36 | (1308) pred(n13) = all_0_9_9
% 55.76/21.36 |
% 55.76/21.36 | From (1307) and (992) follows:
% 55.76/21.36 | (1309) succ(n13) = all_0_5_5
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (500) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 55.76/21.36 | (1310) all_0_9_9 = n12
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (617) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 55.76/21.36 | (1311) all_0_5_5 = n14
% 55.76/21.36 |
% 55.76/21.36 | From (1310)(1311) and (538) follows:
% 55.76/21.36 | (1312) sum(n12, n14) = all_0_2_2
% 55.76/21.36 |
% 55.76/21.36 | From (1310) and (9511) follows:
% 55.76/21.36 | (9546) sum(n12, n15) = all_0_7_7
% 55.76/21.36 |
% 55.76/21.36 | From (1311) and (9509) follows:
% 55.76/21.36 | (9547) sum(n13, n14) = all_0_4_4
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (690) with n13, n14, all_0_4_4, n1 and discharging atoms sum(n13, n14) = all_0_4_4, sum(n13, n14) = n1, yields:
% 55.76/21.36 | (1513) all_0_4_4 = n1
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (690) with n12, n15, all_0_7_7, n1 and discharging atoms sum(n12, n15) = all_0_7_7, sum(n12, n15) = n1, yields:
% 55.76/21.36 | (1515) all_0_7_7 = n1
% 55.76/21.36 |
% 55.76/21.36 | Instantiating formula (690) with n12, n14, all_0_2_2, n0 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n0, yields:
% 55.76/21.36 | (1316) all_0_2_2 = n0
% 55.76/21.36 |
% 55.76/21.36 | From (1316) and (9513) follows:
% 55.76/21.37 | (9551) sum(n0, n2) = all_0_0_0
% 55.76/21.37 |
% 55.76/21.37 | From (1515)(1513) and (590) follows:
% 55.76/21.37 | (1517) sum(n1, n1) = all_0_3_3
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 55.76/21.37 | (1284) all_0_3_3 = n2
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (690) with n0, n2, all_0_0_0, n2 and discharging atoms sum(n0, n2) = all_0_0_0, sum(n0, n2) = n2, yields:
% 55.76/21.37 | (1285) all_0_0_0 = n2
% 55.76/21.37 |
% 55.76/21.37 | Equations (1285,1284) can reduce 679 to:
% 55.76/21.37 | (1106) $false
% 55.76/21.37 |
% 55.76/21.37 |-The branch is then unsatisfiable
% 55.76/21.37 |-Branch two:
% 55.76/21.37 | (1323) ~ (all_0_11_11 = n13)
% 55.76/21.37 | (1324) 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
% 55.76/21.37 |
% 55.76/21.37 +-Applying beta-rule and splitting (1324), into two cases.
% 55.76/21.37 |-Branch one:
% 55.76/21.37 | (1325) all_0_11_11 = n12
% 55.76/21.37 |
% 55.76/21.37 | From (1325) and (559) follows:
% 55.76/21.37 | (1326) pred(n12) = all_0_9_9
% 55.76/21.37 |
% 55.76/21.37 | From (1325) and (992) follows:
% 55.76/21.37 | (1327) succ(n12) = all_0_5_5
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (500) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 55.76/21.37 | (1328) all_0_9_9 = n11
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (617) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 55.76/21.37 | (1329) all_0_5_5 = n13
% 55.76/21.37 |
% 55.76/21.37 | From (1328)(1329) and (538) follows:
% 55.76/21.37 | (1330) sum(n11, n13) = all_0_2_2
% 55.76/21.37 |
% 55.76/21.37 | From (1328) and (9511) follows:
% 55.76/21.37 | (9564) sum(n11, n15) = all_0_7_7
% 55.76/21.37 |
% 55.76/21.37 | From (1329) and (9509) follows:
% 55.76/21.37 | (9565) sum(n13, n13) = all_0_4_4
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (690) with n13, n13, all_0_4_4, n0 and discharging atoms sum(n13, n13) = all_0_4_4, sum(n13, n13) = n0, yields:
% 55.76/21.37 | (1531) all_0_4_4 = n0
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (690) with n11, n15, all_0_7_7, n0 and discharging atoms sum(n11, n15) = all_0_7_7, sum(n11, n15) = n0, yields:
% 55.76/21.37 | (1533) all_0_7_7 = n0
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (690) with n11, n13, all_0_2_2, n24 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n24, yields:
% 55.76/21.37 | (1092) all_0_2_2 = n24
% 55.76/21.37 |
% 55.76/21.37 | From (1092) and (9513) follows:
% 55.76/21.37 | (1762) sum(n24, n2) = all_0_0_0
% 55.76/21.37 |
% 55.76/21.37 | From (1533)(1531) and (590) follows:
% 55.76/21.37 | (1535) sum(n0, n0) = all_0_3_3
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (690) with n24, n2, all_0_0_0, n0 and discharging atoms sum(n24, n2) = all_0_0_0, sum(n24, n2) = n0, yields:
% 55.76/21.37 | (1303) all_0_0_0 = n0
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 55.76/21.37 | (1302) all_0_3_3 = n0
% 55.76/21.37 |
% 55.76/21.37 | Equations (1303,1302) can reduce 679 to:
% 55.76/21.37 | (1106) $false
% 55.76/21.37 |
% 55.76/21.37 |-The branch is then unsatisfiable
% 55.76/21.37 |-Branch two:
% 55.76/21.37 | (1341) ~ (all_0_11_11 = n12)
% 55.76/21.37 | (1342) 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
% 55.76/21.37 |
% 55.76/21.37 +-Applying beta-rule and splitting (1342), into two cases.
% 55.76/21.37 |-Branch one:
% 55.76/21.37 | (1343) all_0_11_11 = n11
% 55.76/21.37 |
% 55.76/21.37 | From (1343) and (559) follows:
% 55.76/21.37 | (1344) pred(n11) = all_0_9_9
% 55.76/21.37 |
% 55.76/21.37 | From (1343) and (992) follows:
% 55.76/21.37 | (1345) succ(n11) = all_0_5_5
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (500) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 55.76/21.37 | (1346) all_0_9_9 = n10
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (617) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 55.76/21.37 | (1347) all_0_5_5 = n12
% 55.76/21.37 |
% 55.76/21.37 | From (1346)(1347) and (538) follows:
% 55.76/21.37 | (1348) sum(n10, n12) = all_0_2_2
% 55.76/21.37 |
% 55.76/21.37 | From (1346) and (9511) follows:
% 55.76/21.37 | (9582) sum(n10, n15) = all_0_7_7
% 55.76/21.37 |
% 55.76/21.37 | From (1347) and (9509) follows:
% 55.76/21.37 | (9583) sum(n13, n12) = all_0_4_4
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (690) with n13, n12, all_0_4_4, n25 and discharging atoms sum(n13, n12) = all_0_4_4, sum(n13, n12) = n25, yields:
% 55.76/21.37 | (1551) all_0_4_4 = n25
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (690) with n10, n15, all_0_7_7, n25 and discharging atoms sum(n10, n15) = all_0_7_7, sum(n10, n15) = n25, yields:
% 55.76/21.37 | (1550) all_0_7_7 = n25
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (690) with n10, n12, all_0_2_2, n22 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n22, yields:
% 55.76/21.37 | (1118) all_0_2_2 = n22
% 55.76/21.37 |
% 55.76/21.37 | From (1118) and (9513) follows:
% 55.76/21.37 | (2674) sum(n22, n2) = all_0_0_0
% 55.76/21.37 |
% 55.76/21.37 | From (1550)(1551) and (590) follows:
% 55.76/21.37 | (1553) sum(n25, n25) = all_0_3_3
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 55.76/21.37 | (1320) all_0_3_3 = n24
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (690) with n22, n2, all_0_0_0, n24 and discharging atoms sum(n22, n2) = all_0_0_0, sum(n22, n2) = n24, yields:
% 55.76/21.37 | (1321) all_0_0_0 = n24
% 55.76/21.37 |
% 55.76/21.37 | Equations (1321,1320) can reduce 679 to:
% 55.76/21.37 | (1106) $false
% 55.76/21.37 |
% 55.76/21.37 |-The branch is then unsatisfiable
% 55.76/21.37 |-Branch two:
% 55.76/21.37 | (1359) ~ (all_0_11_11 = n11)
% 55.76/21.37 | (1360) 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
% 55.76/21.37 |
% 55.76/21.37 +-Applying beta-rule and splitting (1360), into two cases.
% 55.76/21.37 |-Branch one:
% 55.76/21.37 | (1361) all_0_11_11 = n10
% 55.76/21.37 |
% 55.76/21.37 | From (1361) and (559) follows:
% 55.76/21.37 | (1362) pred(n10) = all_0_9_9
% 55.76/21.37 |
% 55.76/21.37 | From (1361) and (992) follows:
% 55.76/21.37 | (1363) succ(n10) = all_0_5_5
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (500) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 55.76/21.37 | (1364) all_0_9_9 = n9
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (617) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 55.76/21.37 | (1365) all_0_5_5 = n11
% 55.76/21.37 |
% 55.76/21.37 | From (1364)(1365) and (538) follows:
% 55.76/21.37 | (1366) sum(n9, n11) = all_0_2_2
% 55.76/21.37 |
% 55.76/21.37 | From (1364) and (9511) follows:
% 55.76/21.37 | (9600) sum(n9, n15) = all_0_7_7
% 55.76/21.37 |
% 55.76/21.37 | From (1365) and (9509) follows:
% 55.76/21.37 | (9601) sum(n13, n11) = all_0_4_4
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (690) with n13, n11, all_0_4_4, n24 and discharging atoms sum(n13, n11) = all_0_4_4, sum(n13, n11) = n24, yields:
% 55.76/21.37 | (1096) all_0_4_4 = n24
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (690) with n9, n15, all_0_7_7, n24 and discharging atoms sum(n9, n15) = all_0_7_7, sum(n9, n15) = n24, yields:
% 55.76/21.37 | (1097) all_0_7_7 = n24
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (690) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 55.76/21.37 | (1136) all_0_2_2 = n20
% 55.76/21.37 |
% 55.76/21.37 | From (1136) and (9513) follows:
% 55.76/21.37 | (3548) sum(n20, n2) = all_0_0_0
% 55.76/21.37 |
% 55.76/21.37 | From (1097)(1096) and (590) follows:
% 55.76/21.37 | (1101) sum(n24, n24) = all_0_3_3
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 55.76/21.37 | (1104) all_0_3_3 = n22
% 55.76/21.37 |
% 55.76/21.37 | Instantiating formula (690) with n20, n2, all_0_0_0, n22 and discharging atoms sum(n20, n2) = all_0_0_0, sum(n20, n2) = n22, yields:
% 55.76/21.37 | (1102) all_0_0_0 = n22
% 55.76/21.37 |
% 55.76/21.37 | Equations (1102,1104) can reduce 679 to:
% 55.76/21.37 | (1106) $false
% 55.76/21.37 |
% 55.76/21.37 |-The branch is then unsatisfiable
% 55.76/21.37 |-Branch two:
% 55.76/21.37 | (1377) ~ (all_0_11_11 = n10)
% 55.76/21.37 | (1378) 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
% 55.76/21.37 |
% 55.76/21.38 +-Applying beta-rule and splitting (1378), into two cases.
% 55.76/21.38 |-Branch one:
% 55.76/21.38 | (1379) all_0_11_11 = n9
% 55.76/21.38 |
% 55.76/21.38 | From (1379) and (559) follows:
% 55.76/21.38 | (1380) pred(n9) = all_0_9_9
% 55.76/21.38 |
% 55.76/21.38 | From (1379) and (992) follows:
% 55.76/21.38 | (1381) succ(n9) = all_0_5_5
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 55.76/21.38 | (1382) all_0_9_9 = n8
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 55.76/21.38 | (1383) all_0_5_5 = n10
% 55.76/21.38 |
% 55.76/21.38 | From (1382)(1383) and (538) follows:
% 55.76/21.38 | (1384) sum(n8, n10) = all_0_2_2
% 55.76/21.38 |
% 55.76/21.38 | From (1382) and (9511) follows:
% 55.76/21.38 | (9618) sum(n8, n15) = all_0_7_7
% 55.76/21.38 |
% 55.76/21.38 | From (1383) and (9509) follows:
% 55.76/21.38 | (9619) sum(n13, n10) = all_0_4_4
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (690) with n13, n10, all_0_4_4, n23 and discharging atoms sum(n13, n10) = all_0_4_4, sum(n13, n10) = n23, yields:
% 55.76/21.38 | (1117) all_0_4_4 = n23
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (690) with n8, n15, all_0_7_7, n23 and discharging atoms sum(n8, n15) = all_0_7_7, sum(n8, n15) = n23, yields:
% 55.76/21.38 | (1119) all_0_7_7 = n23
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 55.76/21.38 | (1154) all_0_2_2 = n18
% 55.76/21.38 |
% 55.76/21.38 | From (1154) and (9513) follows:
% 55.76/21.38 | (4386) sum(n18, n2) = all_0_0_0
% 55.76/21.38 |
% 55.76/21.38 | From (1119)(1117) and (590) follows:
% 55.76/21.38 | (1121) sum(n23, n23) = all_0_3_3
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 55.76/21.38 | (1122) all_0_3_3 = n20
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (690) with n18, n2, all_0_0_0, n20 and discharging atoms sum(n18, n2) = all_0_0_0, sum(n18, n2) = n20, yields:
% 55.76/21.38 | (1123) all_0_0_0 = n20
% 55.76/21.38 |
% 55.76/21.38 | Equations (1123,1122) can reduce 679 to:
% 55.76/21.38 | (1106) $false
% 55.76/21.38 |
% 55.76/21.38 |-The branch is then unsatisfiable
% 55.76/21.38 |-Branch two:
% 55.76/21.38 | (1395) ~ (all_0_11_11 = n9)
% 55.76/21.38 | (1396) 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
% 55.76/21.38 |
% 55.76/21.38 +-Applying beta-rule and splitting (1396), into two cases.
% 55.76/21.38 |-Branch one:
% 55.76/21.38 | (1397) all_0_11_11 = n8
% 55.76/21.38 |
% 55.76/21.38 | From (1397) and (559) follows:
% 55.76/21.38 | (1398) pred(n8) = all_0_9_9
% 55.76/21.38 |
% 55.76/21.38 | From (1397) and (992) follows:
% 55.76/21.38 | (1399) succ(n8) = all_0_5_5
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 55.76/21.38 | (1400) all_0_9_9 = n7
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 55.76/21.38 | (1401) all_0_5_5 = n9
% 55.76/21.38 |
% 55.76/21.38 | From (1400)(1401) and (538) follows:
% 55.76/21.38 | (1402) sum(n7, n9) = all_0_2_2
% 55.76/21.38 |
% 55.76/21.38 | From (1400) and (9511) follows:
% 55.76/21.38 | (9636) sum(n7, n15) = all_0_7_7
% 55.76/21.38 |
% 55.76/21.38 | From (1401) and (9509) follows:
% 55.76/21.38 | (9637) sum(n13, n9) = all_0_4_4
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (690) with n13, n9, all_0_4_4, n22 and discharging atoms sum(n13, n9) = all_0_4_4, sum(n13, n9) = n22, yields:
% 55.76/21.38 | (1135) all_0_4_4 = n22
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (690) with n7, n15, all_0_7_7, n22 and discharging atoms sum(n7, n15) = all_0_7_7, sum(n7, n15) = n22, yields:
% 55.76/21.38 | (1137) all_0_7_7 = n22
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 55.76/21.38 | (1172) all_0_2_2 = n16
% 55.76/21.38 |
% 55.76/21.38 | From (1172) and (9513) follows:
% 55.76/21.38 | (5188) sum(n16, n2) = all_0_0_0
% 55.76/21.38 |
% 55.76/21.38 | From (1137)(1135) and (590) follows:
% 55.76/21.38 | (1139) sum(n22, n22) = all_0_3_3
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 55.76/21.38 | (1140) all_0_3_3 = n18
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (690) with n16, n2, all_0_0_0, n18 and discharging atoms sum(n16, n2) = all_0_0_0, sum(n16, n2) = n18, yields:
% 55.76/21.38 | (1141) all_0_0_0 = n18
% 55.76/21.38 |
% 55.76/21.38 | Equations (1141,1140) can reduce 679 to:
% 55.76/21.38 | (1106) $false
% 55.76/21.38 |
% 55.76/21.38 |-The branch is then unsatisfiable
% 55.76/21.38 |-Branch two:
% 55.76/21.38 | (1413) ~ (all_0_11_11 = n8)
% 55.76/21.38 | (1414) 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
% 55.76/21.38 |
% 55.76/21.38 +-Applying beta-rule and splitting (1414), into two cases.
% 55.76/21.38 |-Branch one:
% 55.76/21.38 | (1415) all_0_11_11 = n7
% 55.76/21.38 |
% 55.76/21.38 | From (1415) and (559) follows:
% 55.76/21.38 | (1416) pred(n7) = all_0_9_9
% 55.76/21.38 |
% 55.76/21.38 | From (1415) and (992) follows:
% 55.76/21.38 | (1417) succ(n7) = all_0_5_5
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 55.76/21.38 | (1418) all_0_9_9 = n6
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 55.76/21.38 | (1419) all_0_5_5 = n8
% 55.76/21.38 |
% 55.76/21.38 | From (1418)(1419) and (538) follows:
% 55.76/21.38 | (1420) sum(n6, n8) = all_0_2_2
% 55.76/21.38 |
% 55.76/21.38 | From (1418) and (9511) follows:
% 55.76/21.38 | (9654) sum(n6, n15) = all_0_7_7
% 55.76/21.38 |
% 55.76/21.38 | From (1419) and (9509) follows:
% 55.76/21.38 | (9655) sum(n13, n8) = all_0_4_4
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (690) with n13, n8, all_0_4_4, n21 and discharging atoms sum(n13, n8) = all_0_4_4, sum(n13, n8) = n21, yields:
% 55.76/21.38 | (1153) all_0_4_4 = n21
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (690) with n6, n15, all_0_7_7, n21 and discharging atoms sum(n6, n15) = all_0_7_7, sum(n6, n15) = n21, yields:
% 55.76/21.38 | (1155) all_0_7_7 = n21
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 55.76/21.38 | (1190) all_0_2_2 = n14
% 55.76/21.38 |
% 55.76/21.38 | From (1190) and (9513) follows:
% 55.76/21.38 | (5954) sum(n14, n2) = all_0_0_0
% 55.76/21.38 |
% 55.76/21.38 | From (1155)(1153) and (590) follows:
% 55.76/21.38 | (1157) sum(n21, n21) = all_0_3_3
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 55.76/21.38 | (1158) all_0_3_3 = n16
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (690) with n14, n2, all_0_0_0, n16 and discharging atoms sum(n14, n2) = all_0_0_0, sum(n14, n2) = n16, yields:
% 55.76/21.38 | (1159) all_0_0_0 = n16
% 55.76/21.38 |
% 55.76/21.38 | Equations (1159,1158) can reduce 679 to:
% 55.76/21.38 | (1106) $false
% 55.76/21.38 |
% 55.76/21.38 |-The branch is then unsatisfiable
% 55.76/21.38 |-Branch two:
% 55.76/21.38 | (1431) ~ (all_0_11_11 = n7)
% 55.76/21.38 | (1432) 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
% 55.76/21.38 |
% 55.76/21.38 +-Applying beta-rule and splitting (1432), into two cases.
% 55.76/21.38 |-Branch one:
% 55.76/21.38 | (1433) all_0_11_11 = n6
% 55.76/21.38 |
% 55.76/21.38 | From (1433) and (559) follows:
% 55.76/21.38 | (1434) pred(n6) = all_0_9_9
% 55.76/21.38 |
% 55.76/21.38 | From (1433) and (992) follows:
% 55.76/21.38 | (1435) succ(n6) = all_0_5_5
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 55.76/21.38 | (1436) all_0_9_9 = n5
% 55.76/21.38 |
% 55.76/21.38 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 55.76/21.38 | (1437) all_0_5_5 = n7
% 55.76/21.38 |
% 55.76/21.38 | From (1436)(1437) and (538) follows:
% 55.76/21.38 | (1438) sum(n5, n7) = all_0_2_2
% 55.76/21.38 |
% 55.76/21.38 | From (1436) and (9511) follows:
% 55.76/21.39 | (9672) sum(n5, n15) = all_0_7_7
% 55.76/21.39 |
% 55.76/21.39 | From (1437) and (9509) follows:
% 55.76/21.39 | (9673) sum(n13, n7) = all_0_4_4
% 55.76/21.39 |
% 55.76/21.39 | Instantiating formula (690) with n13, n7, all_0_4_4, n20 and discharging atoms sum(n13, n7) = all_0_4_4, sum(n13, n7) = n20, yields:
% 55.76/21.39 | (1171) all_0_4_4 = n20
% 55.76/21.39 |
% 55.76/21.39 | Instantiating formula (690) with n5, n15, all_0_7_7, n20 and discharging atoms sum(n5, n15) = all_0_7_7, sum(n5, n15) = n20, yields:
% 55.76/21.39 | (1173) all_0_7_7 = n20
% 55.76/21.39 |
% 55.76/21.39 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 55.76/21.39 | (1208) all_0_2_2 = n12
% 55.76/21.39 |
% 55.76/21.39 | From (1208) and (9513) follows:
% 55.76/21.39 | (6684) sum(n12, n2) = all_0_0_0
% 55.76/21.39 |
% 55.76/21.39 | From (1173)(1171) and (590) follows:
% 55.76/21.39 | (1175) sum(n20, n20) = all_0_3_3
% 55.76/21.39 |
% 55.76/21.39 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 55.76/21.39 | (1176) all_0_3_3 = n14
% 55.76/21.39 |
% 55.76/21.39 | Instantiating formula (690) with n12, n2, all_0_0_0, n14 and discharging atoms sum(n12, n2) = all_0_0_0, sum(n12, n2) = n14, yields:
% 55.76/21.39 | (1177) all_0_0_0 = n14
% 55.76/21.39 |
% 55.76/21.39 | Equations (1177,1176) can reduce 679 to:
% 55.76/21.39 | (1106) $false
% 55.76/21.39 |
% 55.76/21.39 |-The branch is then unsatisfiable
% 55.76/21.39 |-Branch two:
% 55.76/21.39 | (1449) ~ (all_0_11_11 = n6)
% 55.76/21.39 | (1450) 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
% 55.76/21.39 |
% 55.76/21.39 +-Applying beta-rule and splitting (1450), into two cases.
% 55.76/21.39 |-Branch one:
% 55.76/21.39 | (1451) all_0_11_11 = n5
% 55.76/21.39 |
% 55.76/21.39 | From (1451) and (559) follows:
% 55.76/21.39 | (1452) pred(n5) = all_0_9_9
% 55.76/21.39 |
% 55.76/21.39 | From (1451) and (992) follows:
% 55.76/21.39 | (1453) succ(n5) = all_0_5_5
% 55.76/21.39 |
% 55.76/21.39 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 55.76/21.39 | (1454) all_0_9_9 = n4
% 55.76/21.39 |
% 55.76/21.39 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 55.76/21.39 | (1455) all_0_5_5 = n6
% 55.76/21.39 |
% 55.76/21.39 | From (1454)(1455) and (538) follows:
% 55.76/21.39 | (1456) sum(n4, n6) = all_0_2_2
% 55.76/21.39 |
% 55.76/21.39 | From (1454) and (9511) follows:
% 55.76/21.39 | (9690) sum(n4, n15) = all_0_7_7
% 55.76/21.39 |
% 55.76/21.39 | From (1455) and (9509) follows:
% 55.76/21.39 | (9691) sum(n13, n6) = all_0_4_4
% 55.76/21.39 |
% 55.76/21.39 | Instantiating formula (690) with n13, n6, all_0_4_4, n19 and discharging atoms sum(n13, n6) = all_0_4_4, sum(n13, n6) = n19, yields:
% 55.76/21.39 | (1189) all_0_4_4 = n19
% 55.76/21.39 |
% 55.76/21.39 | Instantiating formula (690) with n4, n15, all_0_7_7, n19 and discharging atoms sum(n4, n15) = all_0_7_7, sum(n4, n15) = n19, yields:
% 55.76/21.39 | (1191) all_0_7_7 = n19
% 55.76/21.39 |
% 55.76/21.39 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 55.76/21.39 | (1226) all_0_2_2 = n10
% 55.76/21.39 |
% 55.76/21.39 | From (1226) and (9513) follows:
% 55.85/21.39 | (7378) sum(n10, n2) = all_0_0_0
% 55.85/21.39 |
% 55.85/21.39 | From (1191)(1189) and (590) follows:
% 55.85/21.39 | (1193) sum(n19, n19) = all_0_3_3
% 55.85/21.39 |
% 55.85/21.39 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 55.85/21.39 | (1194) all_0_3_3 = n12
% 55.85/21.39 |
% 55.85/21.39 | Instantiating formula (690) with n10, n2, all_0_0_0, n12 and discharging atoms sum(n10, n2) = all_0_0_0, sum(n10, n2) = n12, yields:
% 55.85/21.39 | (1195) all_0_0_0 = n12
% 55.85/21.39 |
% 55.85/21.39 | Equations (1195,1194) can reduce 679 to:
% 55.85/21.39 | (1106) $false
% 55.85/21.39 |
% 55.85/21.39 |-The branch is then unsatisfiable
% 55.85/21.39 |-Branch two:
% 55.85/21.39 | (1467) ~ (all_0_11_11 = n5)
% 55.85/21.39 | (1468) 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
% 55.85/21.39 |
% 55.85/21.39 +-Applying beta-rule and splitting (1468), into two cases.
% 55.85/21.39 |-Branch one:
% 55.85/21.39 | (1469) all_0_11_11 = n4
% 55.85/21.39 |
% 55.85/21.39 | From (1469) and (559) follows:
% 55.85/21.39 | (1470) pred(n4) = all_0_9_9
% 55.85/21.39 |
% 55.85/21.39 | From (1469) and (992) follows:
% 55.85/21.39 | (1471) succ(n4) = all_0_5_5
% 55.85/21.39 |
% 55.85/21.39 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 55.85/21.39 | (1472) all_0_9_9 = n3
% 55.85/21.39 |
% 55.85/21.39 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 55.85/21.39 | (1473) all_0_5_5 = n5
% 55.85/21.39 |
% 55.85/21.39 | From (1472)(1473) and (538) follows:
% 55.85/21.39 | (1474) sum(n3, n5) = all_0_2_2
% 55.85/21.39 |
% 55.85/21.39 | From (1472) and (9511) follows:
% 55.85/21.39 | (9708) sum(n3, n15) = all_0_7_7
% 55.85/21.39 |
% 55.85/21.39 | From (1473) and (9509) follows:
% 55.85/21.39 | (9709) sum(n13, n5) = all_0_4_4
% 55.85/21.39 |
% 55.85/21.39 | Instantiating formula (690) with n13, n5, all_0_4_4, n18 and discharging atoms sum(n13, n5) = all_0_4_4, sum(n13, n5) = n18, yields:
% 55.85/21.39 | (1207) all_0_4_4 = n18
% 55.85/21.39 |
% 55.85/21.39 | Instantiating formula (690) with n3, n15, all_0_7_7, n18 and discharging atoms sum(n3, n15) = all_0_7_7, sum(n3, n15) = n18, yields:
% 55.85/21.39 | (1209) all_0_7_7 = n18
% 55.85/21.39 |
% 55.85/21.39 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 55.85/21.39 | (1244) all_0_2_2 = n8
% 55.85/21.39 |
% 55.85/21.39 | From (1244) and (9513) follows:
% 55.85/21.39 | (8036) sum(n8, n2) = all_0_0_0
% 55.85/21.39 |
% 55.85/21.39 | From (1209)(1207) and (590) follows:
% 55.85/21.39 | (1211) sum(n18, n18) = all_0_3_3
% 55.85/21.39 |
% 55.85/21.39 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 55.85/21.39 | (1212) all_0_3_3 = n10
% 55.85/21.39 |
% 55.85/21.39 | Instantiating formula (690) with n8, n2, all_0_0_0, n10 and discharging atoms sum(n8, n2) = all_0_0_0, sum(n8, n2) = n10, yields:
% 55.85/21.39 | (1213) all_0_0_0 = n10
% 55.85/21.39 |
% 55.85/21.39 | Equations (1213,1212) can reduce 679 to:
% 55.85/21.39 | (1106) $false
% 55.85/21.39 |
% 55.85/21.39 |-The branch is then unsatisfiable
% 55.85/21.39 |-Branch two:
% 55.85/21.39 | (1485) ~ (all_0_11_11 = n4)
% 55.85/21.39 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 55.85/21.39 |
% 55.85/21.39 +-Applying beta-rule and splitting (1486), into two cases.
% 55.85/21.39 |-Branch one:
% 55.85/21.39 | (1487) all_0_11_11 = n3
% 55.85/21.39 |
% 55.85/21.39 | From (1487) and (559) follows:
% 55.85/21.39 | (1488) pred(n3) = all_0_9_9
% 55.85/21.39 |
% 55.85/21.39 | From (1487) and (992) follows:
% 55.85/21.39 | (1489) succ(n3) = all_0_5_5
% 55.85/21.39 |
% 55.85/21.39 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 55.85/21.39 | (1490) all_0_9_9 = n2
% 55.85/21.39 |
% 55.85/21.39 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 55.85/21.39 | (1491) all_0_5_5 = n4
% 55.85/21.39 |
% 55.85/21.39 | From (1490)(1491) and (538) follows:
% 55.85/21.39 | (1492) sum(n2, n4) = all_0_2_2
% 55.85/21.39 |
% 55.85/21.39 | From (1490) and (9511) follows:
% 55.85/21.40 | (9726) sum(n2, n15) = all_0_7_7
% 55.85/21.40 |
% 55.85/21.40 | From (1491) and (9509) follows:
% 55.85/21.40 | (9727) sum(n13, n4) = all_0_4_4
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (690) with n13, n4, all_0_4_4, n17 and discharging atoms sum(n13, n4) = all_0_4_4, sum(n13, n4) = n17, yields:
% 55.85/21.40 | (1225) all_0_4_4 = n17
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (690) with n2, n15, all_0_7_7, n17 and discharging atoms sum(n2, n15) = all_0_7_7, sum(n2, n15) = n17, yields:
% 55.85/21.40 | (1227) all_0_7_7 = n17
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 55.85/21.40 | (1262) all_0_2_2 = n6
% 55.85/21.40 |
% 55.85/21.40 | From (1262) and (9513) follows:
% 55.85/21.40 | (8659) sum(n6, n2) = all_0_0_0
% 55.85/21.40 |
% 55.85/21.40 | From (1227)(1225) and (590) follows:
% 55.85/21.40 | (1229) sum(n17, n17) = all_0_3_3
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 55.85/21.40 | (1230) all_0_3_3 = n8
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (690) with n6, n2, all_0_0_0, n8 and discharging atoms sum(n6, n2) = all_0_0_0, sum(n6, n2) = n8, yields:
% 55.85/21.40 | (1231) all_0_0_0 = n8
% 55.85/21.40 |
% 55.85/21.40 | Equations (1231,1230) can reduce 679 to:
% 55.85/21.40 | (1106) $false
% 55.85/21.40 |
% 55.85/21.40 |-The branch is then unsatisfiable
% 55.85/21.40 |-Branch two:
% 55.85/21.40 | (1503) ~ (all_0_11_11 = n3)
% 55.85/21.40 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 55.85/21.40 |
% 55.85/21.40 +-Applying beta-rule and splitting (1504), into two cases.
% 55.85/21.40 |-Branch one:
% 55.85/21.40 | (1505) all_0_11_11 = n2
% 55.85/21.40 |
% 55.85/21.40 | From (1505) and (559) follows:
% 55.85/21.40 | (1506) pred(n2) = all_0_9_9
% 55.85/21.40 |
% 55.85/21.40 | From (1505) and (992) follows:
% 55.85/21.40 | (1507) succ(n2) = all_0_5_5
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 55.85/21.40 | (1508) all_0_9_9 = n1
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 55.85/21.40 | (1509) all_0_5_5 = n3
% 55.85/21.40 |
% 55.85/21.40 | From (1508)(1509) and (538) follows:
% 55.85/21.40 | (1510) sum(n1, n3) = all_0_2_2
% 55.85/21.40 |
% 55.85/21.40 | From (1508) and (9511) follows:
% 55.85/21.40 | (9744) sum(n1, n15) = all_0_7_7
% 55.85/21.40 |
% 55.85/21.40 | From (1509) and (9509) follows:
% 55.85/21.40 | (9745) sum(n13, n3) = all_0_4_4
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (690) with n13, n3, all_0_4_4, n16 and discharging atoms sum(n13, n3) = all_0_4_4, sum(n13, n3) = n16, yields:
% 55.85/21.40 | (1243) all_0_4_4 = n16
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (690) with n1, n15, all_0_7_7, n16 and discharging atoms sum(n1, n15) = all_0_7_7, sum(n1, n15) = n16, yields:
% 55.85/21.40 | (1245) all_0_7_7 = n16
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 55.85/21.40 | (1280) all_0_2_2 = n4
% 55.85/21.40 |
% 55.85/21.40 | From (1280) and (9513) follows:
% 55.85/21.40 | (9245) sum(n4, n2) = all_0_0_0
% 55.85/21.40 |
% 55.85/21.40 | From (1245)(1243) and (590) follows:
% 55.85/21.40 | (1247) sum(n16, n16) = all_0_3_3
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 55.85/21.40 | (1248) all_0_3_3 = n6
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (690) with n4, n2, all_0_0_0, n6 and discharging atoms sum(n4, n2) = all_0_0_0, sum(n4, n2) = n6, yields:
% 55.85/21.40 | (1249) all_0_0_0 = n6
% 55.85/21.40 |
% 55.85/21.40 | Equations (1249,1248) can reduce 679 to:
% 55.85/21.40 | (1106) $false
% 55.85/21.40 |
% 55.85/21.40 |-The branch is then unsatisfiable
% 55.85/21.40 |-Branch two:
% 55.85/21.40 | (1521) ~ (all_0_11_11 = n2)
% 55.85/21.40 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 55.85/21.40 |
% 55.85/21.40 +-Applying beta-rule and splitting (1522), into two cases.
% 55.85/21.40 |-Branch one:
% 55.85/21.40 | (1523) all_0_11_11 = n1
% 55.85/21.40 |
% 55.85/21.40 | From (1523) and (559) follows:
% 55.85/21.40 | (1524) pred(n1) = all_0_9_9
% 55.85/21.40 |
% 55.85/21.40 | From (1523) and (992) follows:
% 55.85/21.40 | (1525) succ(n1) = all_0_5_5
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 55.85/21.40 | (1526) all_0_9_9 = n0
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 55.85/21.40 | (1527) all_0_5_5 = n2
% 55.85/21.40 |
% 55.85/21.40 | From (1526)(1527) and (538) follows:
% 55.85/21.40 | (1528) sum(n0, n2) = all_0_2_2
% 55.85/21.40 |
% 55.85/21.40 | From (1526) and (9511) follows:
% 55.85/21.40 | (9762) sum(n0, n15) = all_0_7_7
% 55.85/21.40 |
% 55.85/21.40 | From (1527) and (9509) follows:
% 55.85/21.40 | (9763) sum(n13, n2) = all_0_4_4
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (690) with n13, n2, all_0_4_4, n15 and discharging atoms sum(n13, n2) = all_0_4_4, sum(n13, n2) = n15, yields:
% 55.85/21.40 | (1261) all_0_4_4 = n15
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (690) with n0, n15, all_0_7_7, n15 and discharging atoms sum(n0, n15) = all_0_7_7, sum(n0, n15) = n15, yields:
% 55.85/21.40 | (1263) all_0_7_7 = n15
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 55.85/21.40 | (1298) all_0_2_2 = n2
% 55.85/21.40 |
% 55.85/21.40 | From (1298) and (9513) follows:
% 55.85/21.40 | (9531) sum(n2, n2) = all_0_0_0
% 55.85/21.40 |
% 55.85/21.40 | From (1263)(1261) and (590) follows:
% 55.85/21.40 | (1265) sum(n15, n15) = all_0_3_3
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 55.85/21.40 | (1266) all_0_3_3 = n4
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (690) with n2, n2, all_0_0_0, n4 and discharging atoms sum(n2, n2) = all_0_0_0, sum(n2, n2) = n4, yields:
% 55.85/21.40 | (1267) all_0_0_0 = n4
% 55.85/21.40 |
% 55.85/21.40 | Equations (1267,1266) can reduce 679 to:
% 55.85/21.40 | (1106) $false
% 55.85/21.40 |
% 55.85/21.40 |-The branch is then unsatisfiable
% 55.85/21.40 |-Branch two:
% 55.85/21.40 | (1540) ~ (all_0_11_11 = n1)
% 55.85/21.40 | (1541) all_0_11_11 = n0
% 55.85/21.40 |
% 55.85/21.40 | From (1541) and (559) follows:
% 55.85/21.40 | (1542) pred(n0) = all_0_9_9
% 55.85/21.40 |
% 55.85/21.40 | From (1541) and (992) follows:
% 55.85/21.40 | (1543) succ(n0) = all_0_5_5
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 55.85/21.40 | (1544) all_0_9_9 = n25
% 55.85/21.40 |
% 55.85/21.40 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 55.85/21.40 | (1545) all_0_5_5 = n1
% 55.85/21.40 |
% 55.85/21.40 | From (1544)(1545) and (538) follows:
% 55.85/21.40 | (1546) sum(n25, n1) = all_0_2_2
% 55.85/21.40 |
% 55.85/21.40 | From (1544) and (9511) follows:
% 55.85/21.41 | (9779) sum(n25, n15) = all_0_7_7
% 55.85/21.41 |
% 55.85/21.41 | From (1545) and (9509) follows:
% 55.85/21.41 | (9780) sum(n13, n1) = all_0_4_4
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (690) with n25, n15, all_0_7_7, n14 and discharging atoms sum(n25, n15) = all_0_7_7, sum(n25, n15) = n14, yields:
% 55.85/21.41 | (1281) all_0_7_7 = n14
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 55.85/21.41 | (1316) all_0_2_2 = n0
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (690) with n13, n1, all_0_4_4, n14 and discharging atoms sum(n13, n1) = all_0_4_4, sum(n13, n1) = n14, yields:
% 55.85/21.41 | (1279) all_0_4_4 = n14
% 55.85/21.41 |
% 55.85/21.41 | From (1316) and (9513) follows:
% 55.85/21.41 | (9551) sum(n0, n2) = all_0_0_0
% 55.85/21.41 |
% 55.85/21.41 | From (1281)(1279) and (590) follows:
% 55.85/21.41 | (1283) sum(n14, n14) = all_0_3_3
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 55.85/21.41 | (1284) all_0_3_3 = n2
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (690) with n0, n2, all_0_0_0, n2 and discharging atoms sum(n0, n2) = all_0_0_0, sum(n0, n2) = n2, yields:
% 55.85/21.41 | (1285) all_0_0_0 = n2
% 55.85/21.41 |
% 55.85/21.41 | Equations (1285,1284) can reduce 679 to:
% 55.85/21.41 | (1106) $false
% 55.85/21.41 |
% 55.85/21.41 |-The branch is then unsatisfiable
% 55.85/21.41 |-Branch two:
% 55.85/21.41 | (1766) ~ (all_0_10_10 = n14)
% 55.85/21.41 | (1767) 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
% 55.85/21.41 |
% 55.85/21.41 +-Applying beta-rule and splitting (1288), into two cases.
% 55.85/21.41 |-Branch one:
% 55.85/21.41 | (1289) all_0_11_11 = n14
% 55.85/21.41 |
% 55.85/21.41 | From (1289) and (559) follows:
% 55.85/21.41 | (1290) pred(n14) = all_0_9_9
% 55.85/21.41 |
% 55.85/21.41 | From (1289) and (992) follows:
% 55.85/21.41 | (1291) succ(n14) = all_0_5_5
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (500) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 55.85/21.41 | (1292) all_0_9_9 = n13
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (617) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 55.85/21.41 | (1293) all_0_5_5 = n15
% 55.85/21.41 |
% 55.85/21.41 | From (1293) and (541) follows:
% 55.85/21.41 | (9796) sum(all_0_6_6, n15) = all_0_4_4
% 55.85/21.41 |
% 55.85/21.41 | From (1292)(1293) and (538) follows:
% 55.85/21.41 | (1294) sum(n13, n15) = all_0_2_2
% 55.85/21.41 |
% 55.85/21.41 | From (1292) and (427) follows:
% 55.85/21.41 | (9798) sum(n13, all_0_8_8) = all_0_7_7
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (690) with n13, n15, all_0_2_2, n2 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n2, yields:
% 55.85/21.41 | (1298) all_0_2_2 = n2
% 55.85/21.41 |
% 55.85/21.41 | From (1298) and (630) follows:
% 55.85/21.41 | (9800) sum(n2, all_0_1_1) = all_0_0_0
% 55.85/21.41 |
% 55.85/21.41 +-Applying beta-rule and splitting (1767), into two cases.
% 55.85/21.41 |-Branch one:
% 55.85/21.41 | (1768) all_0_10_10 = n13
% 55.85/21.41 |
% 55.85/21.41 | From (1768) and (292) follows:
% 55.85/21.41 | (1769) pred(n13) = all_0_6_6
% 55.85/21.41 |
% 55.85/21.41 | From (1768) and (760) follows:
% 55.85/21.41 | (1770) succ(n13) = all_0_8_8
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (500) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 55.85/21.41 | (1771) all_0_6_6 = n12
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (617) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 55.85/21.41 | (1772) all_0_8_8 = n14
% 55.85/21.41 |
% 55.85/21.41 | From (1771)(1772) and (411) follows:
% 55.85/21.41 | (1773) sum(n12, n14) = all_0_1_1
% 55.85/21.41 |
% 55.85/21.41 | From (1771) and (9796) follows:
% 55.85/21.41 | (9807) sum(n12, n15) = all_0_4_4
% 55.85/21.41 |
% 55.85/21.41 | From (1772) and (9798) follows:
% 55.85/21.41 | (9808) sum(n13, n14) = all_0_7_7
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (690) with n13, n14, all_0_7_7, n1 and discharging atoms sum(n13, n14) = all_0_7_7, sum(n13, n14) = n1, yields:
% 55.85/21.41 | (1515) all_0_7_7 = n1
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (690) with n12, n15, all_0_4_4, n1 and discharging atoms sum(n12, n15) = all_0_4_4, sum(n12, n15) = n1, yields:
% 55.85/21.41 | (1513) all_0_4_4 = n1
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (690) with n12, n14, all_0_1_1, n0 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n0, yields:
% 55.85/21.41 | (1777) all_0_1_1 = n0
% 55.85/21.41 |
% 55.85/21.41 | From (1515)(1513) and (590) follows:
% 55.85/21.41 | (1517) sum(n1, n1) = all_0_3_3
% 55.85/21.41 |
% 55.85/21.41 | From (1777) and (9800) follows:
% 55.85/21.41 | (9813) sum(n2, n0) = all_0_0_0
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (690) with n2, n0, all_0_0_0, n2 and discharging atoms sum(n2, n0) = all_0_0_0, sum(n2, n0) = n2, yields:
% 55.85/21.41 | (1285) all_0_0_0 = n2
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 55.85/21.41 | (1284) all_0_3_3 = n2
% 55.85/21.41 |
% 55.85/21.41 | Equations (1285,1284) can reduce 679 to:
% 55.85/21.41 | (1106) $false
% 55.85/21.41 |
% 55.85/21.41 |-The branch is then unsatisfiable
% 55.85/21.41 |-Branch two:
% 55.85/21.41 | (1784) ~ (all_0_10_10 = n13)
% 55.85/21.41 | (1785) 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
% 55.85/21.41 |
% 55.85/21.41 +-Applying beta-rule and splitting (1785), into two cases.
% 55.85/21.41 |-Branch one:
% 55.85/21.41 | (1786) all_0_10_10 = n12
% 55.85/21.41 |
% 55.85/21.41 | From (1786) and (292) follows:
% 55.85/21.41 | (1787) pred(n12) = all_0_6_6
% 55.85/21.41 |
% 55.85/21.41 | From (1786) and (760) follows:
% 55.85/21.41 | (1788) succ(n12) = all_0_8_8
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (500) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 55.85/21.41 | (1789) all_0_6_6 = n11
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (617) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 55.85/21.41 | (1790) all_0_8_8 = n13
% 55.85/21.41 |
% 55.85/21.41 | From (1789)(1790) and (411) follows:
% 55.85/21.41 | (1791) sum(n11, n13) = all_0_1_1
% 55.85/21.41 |
% 55.85/21.41 | From (1789) and (9796) follows:
% 55.85/21.41 | (9825) sum(n11, n15) = all_0_4_4
% 55.85/21.41 |
% 55.85/21.41 | From (1790) and (9798) follows:
% 55.85/21.41 | (9826) sum(n13, n13) = all_0_7_7
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (690) with n13, n13, all_0_7_7, n0 and discharging atoms sum(n13, n13) = all_0_7_7, sum(n13, n13) = n0, yields:
% 55.85/21.41 | (1533) all_0_7_7 = n0
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (690) with n11, n15, all_0_4_4, n0 and discharging atoms sum(n11, n15) = all_0_4_4, sum(n11, n15) = n0, yields:
% 55.85/21.41 | (1531) all_0_4_4 = n0
% 55.85/21.41 |
% 55.85/21.41 | Instantiating formula (690) with n11, n13, all_0_1_1, n24 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n24, yields:
% 55.85/21.41 | (1081) all_0_1_1 = n24
% 55.85/21.41 |
% 55.85/21.41 | From (1533)(1531) and (590) follows:
% 55.85/21.41 | (1535) sum(n0, n0) = all_0_3_3
% 55.85/21.41 |
% 55.85/21.41 | From (1081) and (9800) follows:
% 55.85/21.42 | (1300) sum(n2, n24) = all_0_0_0
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (690) with n2, n24, all_0_0_0, n0 and discharging atoms sum(n2, n24) = all_0_0_0, sum(n2, n24) = n0, yields:
% 55.85/21.42 | (1303) all_0_0_0 = n0
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (690) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 55.85/21.42 | (1302) all_0_3_3 = n0
% 55.85/21.42 |
% 55.85/21.42 | Equations (1303,1302) can reduce 679 to:
% 55.85/21.42 | (1106) $false
% 55.85/21.42 |
% 55.85/21.42 |-The branch is then unsatisfiable
% 55.85/21.42 |-Branch two:
% 55.85/21.42 | (1802) ~ (all_0_10_10 = n12)
% 55.85/21.42 | (1803) 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
% 55.85/21.42 |
% 55.85/21.42 +-Applying beta-rule and splitting (1803), into two cases.
% 55.85/21.42 |-Branch one:
% 55.85/21.42 | (1804) all_0_10_10 = n11
% 55.85/21.42 |
% 55.85/21.42 | From (1804) and (292) follows:
% 55.85/21.42 | (1805) pred(n11) = all_0_6_6
% 55.85/21.42 |
% 55.85/21.42 | From (1804) and (760) follows:
% 55.85/21.42 | (1806) succ(n11) = all_0_8_8
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (500) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 55.85/21.42 | (1807) all_0_6_6 = n10
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (617) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 55.85/21.42 | (1808) all_0_8_8 = n12
% 55.85/21.42 |
% 55.85/21.42 | From (1807)(1808) and (411) follows:
% 55.85/21.42 | (1809) sum(n10, n12) = all_0_1_1
% 55.85/21.42 |
% 55.85/21.42 | From (1807) and (9796) follows:
% 55.85/21.42 | (9843) sum(n10, n15) = all_0_4_4
% 55.85/21.42 |
% 55.85/21.42 | From (1808) and (9798) follows:
% 55.85/21.42 | (9844) sum(n13, n12) = all_0_7_7
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (690) with n13, n12, all_0_7_7, n25 and discharging atoms sum(n13, n12) = all_0_7_7, sum(n13, n12) = n25, yields:
% 55.85/21.42 | (1550) all_0_7_7 = n25
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (690) with n10, n15, all_0_4_4, n25 and discharging atoms sum(n10, n15) = all_0_4_4, sum(n10, n15) = n25, yields:
% 55.85/21.42 | (1551) all_0_4_4 = n25
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (690) with n10, n12, all_0_1_1, n22 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n22, yields:
% 55.85/21.42 | (1579) all_0_1_1 = n22
% 55.85/21.42 |
% 55.85/21.42 | From (1550)(1551) and (590) follows:
% 55.85/21.42 | (1553) sum(n25, n25) = all_0_3_3
% 55.85/21.42 |
% 55.85/21.42 | From (1579) and (9800) follows:
% 55.85/21.42 | (2232) sum(n2, n22) = all_0_0_0
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 55.85/21.42 | (1320) all_0_3_3 = n24
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (690) with n2, n22, all_0_0_0, n24 and discharging atoms sum(n2, n22) = all_0_0_0, sum(n2, n22) = n24, yields:
% 55.85/21.42 | (1321) all_0_0_0 = n24
% 55.85/21.42 |
% 55.85/21.42 | Equations (1321,1320) can reduce 679 to:
% 55.85/21.42 | (1106) $false
% 55.85/21.42 |
% 55.85/21.42 |-The branch is then unsatisfiable
% 55.85/21.42 |-Branch two:
% 55.85/21.42 | (1820) ~ (all_0_10_10 = n11)
% 55.85/21.42 | (1821) 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
% 55.85/21.42 |
% 55.85/21.42 +-Applying beta-rule and splitting (1821), into two cases.
% 55.85/21.42 |-Branch one:
% 55.85/21.42 | (1822) all_0_10_10 = n10
% 55.85/21.42 |
% 55.85/21.42 | From (1822) and (292) follows:
% 55.85/21.42 | (1823) pred(n10) = all_0_6_6
% 55.85/21.42 |
% 55.85/21.42 | From (1822) and (760) follows:
% 55.85/21.42 | (1824) succ(n10) = all_0_8_8
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (500) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 55.85/21.42 | (1825) all_0_6_6 = n9
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (617) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 55.85/21.42 | (1826) all_0_8_8 = n11
% 55.85/21.42 |
% 55.85/21.42 | From (1825)(1826) and (411) follows:
% 55.85/21.42 | (1827) sum(n9, n11) = all_0_1_1
% 55.85/21.42 |
% 55.85/21.42 | From (1825) and (9796) follows:
% 55.85/21.42 | (9861) sum(n9, n15) = all_0_4_4
% 55.85/21.42 |
% 55.85/21.42 | From (1826) and (9798) follows:
% 55.85/21.42 | (9862) sum(n13, n11) = all_0_7_7
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (690) with n13, n11, all_0_7_7, n24 and discharging atoms sum(n13, n11) = all_0_7_7, sum(n13, n11) = n24, yields:
% 55.85/21.42 | (1097) all_0_7_7 = n24
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (690) with n9, n15, all_0_4_4, n24 and discharging atoms sum(n9, n15) = all_0_4_4, sum(n9, n15) = n24, yields:
% 55.85/21.42 | (1096) all_0_4_4 = n24
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (690) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 55.85/21.42 | (1597) all_0_1_1 = n20
% 55.85/21.42 |
% 55.85/21.42 | From (1097)(1096) and (590) follows:
% 55.85/21.42 | (1101) sum(n24, n24) = all_0_3_3
% 55.85/21.42 |
% 55.85/21.42 | From (1597) and (9800) follows:
% 55.85/21.42 | (3124) sum(n2, n20) = all_0_0_0
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 55.85/21.42 | (1104) all_0_3_3 = n22
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (690) with n2, n20, all_0_0_0, n22 and discharging atoms sum(n2, n20) = all_0_0_0, sum(n2, n20) = n22, yields:
% 55.85/21.42 | (1102) all_0_0_0 = n22
% 55.85/21.42 |
% 55.85/21.42 | Equations (1102,1104) can reduce 679 to:
% 55.85/21.42 | (1106) $false
% 55.85/21.42 |
% 55.85/21.42 |-The branch is then unsatisfiable
% 55.85/21.42 |-Branch two:
% 55.85/21.42 | (1838) ~ (all_0_10_10 = n10)
% 55.85/21.42 | (1839) 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
% 55.85/21.42 |
% 55.85/21.42 +-Applying beta-rule and splitting (1839), into two cases.
% 55.85/21.42 |-Branch one:
% 55.85/21.42 | (1840) all_0_10_10 = n9
% 55.85/21.42 |
% 55.85/21.42 | From (1840) and (292) follows:
% 55.85/21.42 | (1841) pred(n9) = all_0_6_6
% 55.85/21.42 |
% 55.85/21.42 | From (1840) and (760) follows:
% 55.85/21.42 | (1842) succ(n9) = all_0_8_8
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (500) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 55.85/21.42 | (1843) all_0_6_6 = n8
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (617) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 55.85/21.42 | (1844) all_0_8_8 = n10
% 55.85/21.42 |
% 55.85/21.42 | From (1843)(1844) and (411) follows:
% 55.85/21.42 | (1845) sum(n8, n10) = all_0_1_1
% 55.85/21.42 |
% 55.85/21.42 | From (1843) and (9796) follows:
% 55.85/21.42 | (9879) sum(n8, n15) = all_0_4_4
% 55.85/21.42 |
% 55.85/21.42 | From (1844) and (9798) follows:
% 55.85/21.42 | (9880) sum(n13, n10) = all_0_7_7
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (690) with n13, n10, all_0_7_7, n23 and discharging atoms sum(n13, n10) = all_0_7_7, sum(n13, n10) = n23, yields:
% 55.85/21.42 | (1119) all_0_7_7 = n23
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (690) with n8, n15, all_0_4_4, n23 and discharging atoms sum(n8, n15) = all_0_4_4, sum(n8, n15) = n23, yields:
% 55.85/21.42 | (1117) all_0_4_4 = n23
% 55.85/21.42 |
% 55.85/21.42 | Instantiating formula (690) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 55.85/21.42 | (1615) all_0_1_1 = n18
% 55.85/21.42 |
% 55.85/21.42 | From (1119)(1117) and (590) follows:
% 55.85/21.42 | (1121) sum(n23, n23) = all_0_3_3
% 55.85/21.42 |
% 55.85/21.42 | From (1615) and (9800) follows:
% 55.85/21.42 | (3980) sum(n2, n18) = all_0_0_0
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 55.85/21.43 | (1122) all_0_3_3 = n20
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (690) with n2, n18, all_0_0_0, n20 and discharging atoms sum(n2, n18) = all_0_0_0, sum(n2, n18) = n20, yields:
% 55.85/21.43 | (1123) all_0_0_0 = n20
% 55.85/21.43 |
% 55.85/21.43 | Equations (1123,1122) can reduce 679 to:
% 55.85/21.43 | (1106) $false
% 55.85/21.43 |
% 55.85/21.43 |-The branch is then unsatisfiable
% 55.85/21.43 |-Branch two:
% 55.85/21.43 | (1856) ~ (all_0_10_10 = n9)
% 55.85/21.43 | (1857) 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
% 55.85/21.43 |
% 55.85/21.43 +-Applying beta-rule and splitting (1857), into two cases.
% 55.85/21.43 |-Branch one:
% 55.85/21.43 | (1858) all_0_10_10 = n8
% 55.85/21.43 |
% 55.85/21.43 | From (1858) and (292) follows:
% 55.85/21.43 | (1859) pred(n8) = all_0_6_6
% 55.85/21.43 |
% 55.85/21.43 | From (1858) and (760) follows:
% 55.85/21.43 | (1860) succ(n8) = all_0_8_8
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 55.85/21.43 | (1861) all_0_6_6 = n7
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 55.85/21.43 | (1862) all_0_8_8 = n9
% 55.85/21.43 |
% 55.85/21.43 | From (1861)(1862) and (411) follows:
% 55.85/21.43 | (1863) sum(n7, n9) = all_0_1_1
% 55.85/21.43 |
% 55.85/21.43 | From (1861) and (9796) follows:
% 55.85/21.43 | (9897) sum(n7, n15) = all_0_4_4
% 55.85/21.43 |
% 55.85/21.43 | From (1862) and (9798) follows:
% 55.85/21.43 | (9898) sum(n13, n9) = all_0_7_7
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (690) with n13, n9, all_0_7_7, n22 and discharging atoms sum(n13, n9) = all_0_7_7, sum(n13, n9) = n22, yields:
% 55.85/21.43 | (1137) all_0_7_7 = n22
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (690) with n7, n15, all_0_4_4, n22 and discharging atoms sum(n7, n15) = all_0_4_4, sum(n7, n15) = n22, yields:
% 55.85/21.43 | (1135) all_0_4_4 = n22
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 55.85/21.43 | (1633) all_0_1_1 = n16
% 55.85/21.43 |
% 55.85/21.43 | From (1137)(1135) and (590) follows:
% 55.85/21.43 | (1139) sum(n22, n22) = all_0_3_3
% 55.85/21.43 |
% 55.85/21.43 | From (1633) and (9800) follows:
% 55.85/21.43 | (4800) sum(n2, n16) = all_0_0_0
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 55.85/21.43 | (1140) all_0_3_3 = n18
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (690) with n2, n16, all_0_0_0, n18 and discharging atoms sum(n2, n16) = all_0_0_0, sum(n2, n16) = n18, yields:
% 55.85/21.43 | (1141) all_0_0_0 = n18
% 55.85/21.43 |
% 55.85/21.43 | Equations (1141,1140) can reduce 679 to:
% 55.85/21.43 | (1106) $false
% 55.85/21.43 |
% 55.85/21.43 |-The branch is then unsatisfiable
% 55.85/21.43 |-Branch two:
% 55.85/21.43 | (1874) ~ (all_0_10_10 = n8)
% 55.85/21.43 | (1875) 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
% 55.85/21.43 |
% 55.85/21.43 +-Applying beta-rule and splitting (1875), into two cases.
% 55.85/21.43 |-Branch one:
% 55.85/21.43 | (1876) all_0_10_10 = n7
% 55.85/21.43 |
% 55.85/21.43 | From (1876) and (292) follows:
% 55.85/21.43 | (1877) pred(n7) = all_0_6_6
% 55.85/21.43 |
% 55.85/21.43 | From (1876) and (760) follows:
% 55.85/21.43 | (1878) succ(n7) = all_0_8_8
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 55.85/21.43 | (1879) all_0_6_6 = n6
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 55.85/21.43 | (1880) all_0_8_8 = n8
% 55.85/21.43 |
% 55.85/21.43 | From (1879)(1880) and (411) follows:
% 55.85/21.43 | (1881) sum(n6, n8) = all_0_1_1
% 55.85/21.43 |
% 55.85/21.43 | From (1879) and (9796) follows:
% 55.85/21.43 | (9915) sum(n6, n15) = all_0_4_4
% 55.85/21.43 |
% 55.85/21.43 | From (1880) and (9798) follows:
% 55.85/21.43 | (9916) sum(n13, n8) = all_0_7_7
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (690) with n13, n8, all_0_7_7, n21 and discharging atoms sum(n13, n8) = all_0_7_7, sum(n13, n8) = n21, yields:
% 55.85/21.43 | (1155) all_0_7_7 = n21
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (690) with n6, n15, all_0_4_4, n21 and discharging atoms sum(n6, n15) = all_0_4_4, sum(n6, n15) = n21, yields:
% 55.85/21.43 | (1153) all_0_4_4 = n21
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 55.85/21.43 | (1651) all_0_1_1 = n14
% 55.85/21.43 |
% 55.85/21.43 | From (1155)(1153) and (590) follows:
% 55.85/21.43 | (1157) sum(n21, n21) = all_0_3_3
% 55.85/21.43 |
% 55.85/21.43 | From (1651) and (9800) follows:
% 55.85/21.43 | (5584) sum(n2, n14) = all_0_0_0
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 55.85/21.43 | (1158) all_0_3_3 = n16
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (690) with n2, n14, all_0_0_0, n16 and discharging atoms sum(n2, n14) = all_0_0_0, sum(n2, n14) = n16, yields:
% 55.85/21.43 | (1159) all_0_0_0 = n16
% 55.85/21.43 |
% 55.85/21.43 | Equations (1159,1158) can reduce 679 to:
% 55.85/21.43 | (1106) $false
% 55.85/21.43 |
% 55.85/21.43 |-The branch is then unsatisfiable
% 55.85/21.43 |-Branch two:
% 55.85/21.43 | (1892) ~ (all_0_10_10 = n7)
% 55.85/21.43 | (1893) 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
% 55.85/21.43 |
% 55.85/21.43 +-Applying beta-rule and splitting (1893), into two cases.
% 55.85/21.43 |-Branch one:
% 55.85/21.43 | (1894) all_0_10_10 = n6
% 55.85/21.43 |
% 55.85/21.43 | From (1894) and (292) follows:
% 55.85/21.43 | (1895) pred(n6) = all_0_6_6
% 55.85/21.43 |
% 55.85/21.43 | From (1894) and (760) follows:
% 55.85/21.43 | (1896) succ(n6) = all_0_8_8
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 55.85/21.43 | (1897) all_0_6_6 = n5
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 55.85/21.43 | (1898) all_0_8_8 = n7
% 55.85/21.43 |
% 55.85/21.43 | From (1897)(1898) and (411) follows:
% 55.85/21.43 | (1899) sum(n5, n7) = all_0_1_1
% 55.85/21.43 |
% 55.85/21.43 | From (1897) and (9796) follows:
% 55.85/21.43 | (9933) sum(n5, n15) = all_0_4_4
% 55.85/21.43 |
% 55.85/21.43 | From (1898) and (9798) follows:
% 55.85/21.43 | (9934) sum(n13, n7) = all_0_7_7
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (690) with n13, n7, all_0_7_7, n20 and discharging atoms sum(n13, n7) = all_0_7_7, sum(n13, n7) = n20, yields:
% 55.85/21.43 | (1173) all_0_7_7 = n20
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (690) with n5, n15, all_0_4_4, n20 and discharging atoms sum(n5, n15) = all_0_4_4, sum(n5, n15) = n20, yields:
% 55.85/21.43 | (1171) all_0_4_4 = n20
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 55.85/21.43 | (1669) all_0_1_1 = n12
% 55.85/21.43 |
% 55.85/21.43 | From (1173)(1171) and (590) follows:
% 55.85/21.43 | (1175) sum(n20, n20) = all_0_3_3
% 55.85/21.43 |
% 55.85/21.43 | From (1669) and (9800) follows:
% 55.85/21.43 | (6332) sum(n2, n12) = all_0_0_0
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 55.85/21.43 | (1176) all_0_3_3 = n14
% 55.85/21.43 |
% 55.85/21.43 | Instantiating formula (690) with n2, n12, all_0_0_0, n14 and discharging atoms sum(n2, n12) = all_0_0_0, sum(n2, n12) = n14, yields:
% 55.85/21.43 | (1177) all_0_0_0 = n14
% 55.85/21.43 |
% 55.85/21.43 | Equations (1177,1176) can reduce 679 to:
% 55.85/21.43 | (1106) $false
% 55.85/21.43 |
% 55.85/21.43 |-The branch is then unsatisfiable
% 55.85/21.43 |-Branch two:
% 55.85/21.43 | (1910) ~ (all_0_10_10 = n6)
% 55.85/21.43 | (1911) 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
% 55.85/21.44 |
% 55.85/21.44 +-Applying beta-rule and splitting (1911), into two cases.
% 55.85/21.44 |-Branch one:
% 55.85/21.44 | (1912) all_0_10_10 = n5
% 55.85/21.44 |
% 55.85/21.44 | From (1912) and (292) follows:
% 55.85/21.44 | (1913) pred(n5) = all_0_6_6
% 55.85/21.44 |
% 55.85/21.44 | From (1912) and (760) follows:
% 55.85/21.44 | (1914) succ(n5) = all_0_8_8
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 55.85/21.44 | (1915) all_0_6_6 = n4
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 55.85/21.44 | (1916) all_0_8_8 = n6
% 55.85/21.44 |
% 55.85/21.44 | From (1915)(1916) and (411) follows:
% 55.85/21.44 | (1917) sum(n4, n6) = all_0_1_1
% 55.85/21.44 |
% 55.85/21.44 | From (1915) and (9796) follows:
% 55.85/21.44 | (9951) sum(n4, n15) = all_0_4_4
% 55.85/21.44 |
% 55.85/21.44 | From (1916) and (9798) follows:
% 55.85/21.44 | (9952) sum(n13, n6) = all_0_7_7
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (690) with n13, n6, all_0_7_7, n19 and discharging atoms sum(n13, n6) = all_0_7_7, sum(n13, n6) = n19, yields:
% 55.85/21.44 | (1191) all_0_7_7 = n19
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (690) with n4, n15, all_0_4_4, n19 and discharging atoms sum(n4, n15) = all_0_4_4, sum(n4, n15) = n19, yields:
% 55.85/21.44 | (1189) all_0_4_4 = n19
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 55.85/21.44 | (1687) all_0_1_1 = n10
% 55.85/21.44 |
% 55.85/21.44 | From (1191)(1189) and (590) follows:
% 55.85/21.44 | (1193) sum(n19, n19) = all_0_3_3
% 55.85/21.44 |
% 55.85/21.44 | From (1687) and (9800) follows:
% 55.85/21.44 | (7044) sum(n2, n10) = all_0_0_0
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 55.85/21.44 | (1194) all_0_3_3 = n12
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (690) with n2, n10, all_0_0_0, n12 and discharging atoms sum(n2, n10) = all_0_0_0, sum(n2, n10) = n12, yields:
% 55.85/21.44 | (1195) all_0_0_0 = n12
% 55.85/21.44 |
% 55.85/21.44 | Equations (1195,1194) can reduce 679 to:
% 55.85/21.44 | (1106) $false
% 55.85/21.44 |
% 55.85/21.44 |-The branch is then unsatisfiable
% 55.85/21.44 |-Branch two:
% 55.85/21.44 | (1928) ~ (all_0_10_10 = n5)
% 55.85/21.44 | (1929) 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
% 55.85/21.44 |
% 55.85/21.44 +-Applying beta-rule and splitting (1929), into two cases.
% 55.85/21.44 |-Branch one:
% 55.85/21.44 | (1930) all_0_10_10 = n4
% 55.85/21.44 |
% 55.85/21.44 | From (1930) and (292) follows:
% 55.85/21.44 | (1931) pred(n4) = all_0_6_6
% 55.85/21.44 |
% 55.85/21.44 | From (1930) and (760) follows:
% 55.85/21.44 | (1932) succ(n4) = all_0_8_8
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 55.85/21.44 | (1933) all_0_6_6 = n3
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 55.85/21.44 | (1934) all_0_8_8 = n5
% 55.85/21.44 |
% 55.85/21.44 | From (1933)(1934) and (411) follows:
% 55.85/21.44 | (1935) sum(n3, n5) = all_0_1_1
% 55.85/21.44 |
% 55.85/21.44 | From (1933) and (9796) follows:
% 55.85/21.44 | (9969) sum(n3, n15) = all_0_4_4
% 55.85/21.44 |
% 55.85/21.44 | From (1934) and (9798) follows:
% 55.85/21.44 | (9970) sum(n13, n5) = all_0_7_7
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (690) with n13, n5, all_0_7_7, n18 and discharging atoms sum(n13, n5) = all_0_7_7, sum(n13, n5) = n18, yields:
% 55.85/21.44 | (1209) all_0_7_7 = n18
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (690) with n3, n15, all_0_4_4, n18 and discharging atoms sum(n3, n15) = all_0_4_4, sum(n3, n15) = n18, yields:
% 55.85/21.44 | (1207) all_0_4_4 = n18
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 55.85/21.44 | (1705) all_0_1_1 = n8
% 55.85/21.44 |
% 55.85/21.44 | From (1209)(1207) and (590) follows:
% 55.85/21.44 | (1211) sum(n18, n18) = all_0_3_3
% 55.85/21.44 |
% 55.85/21.44 | From (1705) and (9800) follows:
% 55.85/21.44 | (7720) sum(n2, n8) = all_0_0_0
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 55.85/21.44 | (1212) all_0_3_3 = n10
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (690) with n2, n8, all_0_0_0, n10 and discharging atoms sum(n2, n8) = all_0_0_0, sum(n2, n8) = n10, yields:
% 55.85/21.44 | (1213) all_0_0_0 = n10
% 55.85/21.44 |
% 55.85/21.44 | Equations (1213,1212) can reduce 679 to:
% 55.85/21.44 | (1106) $false
% 55.85/21.44 |
% 55.85/21.44 |-The branch is then unsatisfiable
% 55.85/21.44 |-Branch two:
% 55.85/21.44 | (1946) ~ (all_0_10_10 = n4)
% 55.85/21.44 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 55.85/21.44 |
% 55.85/21.44 +-Applying beta-rule and splitting (1947), into two cases.
% 55.85/21.44 |-Branch one:
% 55.85/21.44 | (1948) all_0_10_10 = n3
% 55.85/21.44 |
% 55.85/21.44 | From (1948) and (292) follows:
% 55.85/21.44 | (1949) pred(n3) = all_0_6_6
% 55.85/21.44 |
% 55.85/21.44 | From (1948) and (760) follows:
% 55.85/21.44 | (1950) succ(n3) = all_0_8_8
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 55.85/21.44 | (1951) all_0_6_6 = n2
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 55.85/21.44 | (1952) all_0_8_8 = n4
% 55.85/21.44 |
% 55.85/21.44 | From (1951)(1952) and (411) follows:
% 55.85/21.44 | (1953) sum(n2, n4) = all_0_1_1
% 55.85/21.44 |
% 55.85/21.44 | From (1951) and (9796) follows:
% 55.85/21.44 | (9987) sum(n2, n15) = all_0_4_4
% 55.85/21.44 |
% 55.85/21.44 | From (1952) and (9798) follows:
% 55.85/21.44 | (9988) sum(n13, n4) = all_0_7_7
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (690) with n13, n4, all_0_7_7, n17 and discharging atoms sum(n13, n4) = all_0_7_7, sum(n13, n4) = n17, yields:
% 55.85/21.44 | (1227) all_0_7_7 = n17
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (690) with n2, n15, all_0_4_4, n17 and discharging atoms sum(n2, n15) = all_0_4_4, sum(n2, n15) = n17, yields:
% 55.85/21.44 | (1225) all_0_4_4 = n17
% 55.85/21.44 |
% 55.85/21.44 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 55.85/21.44 | (1723) all_0_1_1 = n6
% 55.85/21.44 |
% 55.85/21.44 | From (1227)(1225) and (590) follows:
% 55.85/21.44 | (1229) sum(n17, n17) = all_0_3_3
% 55.85/21.44 |
% 55.85/21.44 | From (1723) and (9800) follows:
% 55.85/21.45 | (8361) sum(n2, n6) = all_0_0_0
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 55.85/21.45 | (1230) all_0_3_3 = n8
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (690) with n2, n6, all_0_0_0, n8 and discharging atoms sum(n2, n6) = all_0_0_0, sum(n2, n6) = n8, yields:
% 55.85/21.45 | (1231) all_0_0_0 = n8
% 55.85/21.45 |
% 55.85/21.45 | Equations (1231,1230) can reduce 679 to:
% 55.85/21.45 | (1106) $false
% 55.85/21.45 |
% 55.85/21.45 |-The branch is then unsatisfiable
% 55.85/21.45 |-Branch two:
% 55.85/21.45 | (1964) ~ (all_0_10_10 = n3)
% 55.85/21.45 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 55.85/21.45 |
% 55.85/21.45 +-Applying beta-rule and splitting (1965), into two cases.
% 55.85/21.45 |-Branch one:
% 55.85/21.45 | (1966) all_0_10_10 = n2
% 55.85/21.45 |
% 55.85/21.45 | From (1966) and (292) follows:
% 55.85/21.45 | (1967) pred(n2) = all_0_6_6
% 55.85/21.45 |
% 55.85/21.45 | From (1966) and (760) follows:
% 55.85/21.45 | (1968) succ(n2) = all_0_8_8
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 55.85/21.45 | (1969) all_0_6_6 = n1
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 55.85/21.45 | (1970) all_0_8_8 = n3
% 55.85/21.45 |
% 55.85/21.45 | From (1969)(1970) and (411) follows:
% 55.85/21.45 | (1971) sum(n1, n3) = all_0_1_1
% 55.85/21.45 |
% 55.85/21.45 | From (1969) and (9796) follows:
% 55.85/21.45 | (10005) sum(n1, n15) = all_0_4_4
% 55.85/21.45 |
% 55.85/21.45 | From (1970) and (9798) follows:
% 55.85/21.45 | (10006) sum(n13, n3) = all_0_7_7
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (690) with n13, n3, all_0_7_7, n16 and discharging atoms sum(n13, n3) = all_0_7_7, sum(n13, n3) = n16, yields:
% 55.85/21.45 | (1245) all_0_7_7 = n16
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (690) with n1, n15, all_0_4_4, n16 and discharging atoms sum(n1, n15) = all_0_4_4, sum(n1, n15) = n16, yields:
% 55.85/21.45 | (1243) all_0_4_4 = n16
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 55.85/21.45 | (1741) all_0_1_1 = n4
% 55.85/21.45 |
% 55.85/21.45 | From (1245)(1243) and (590) follows:
% 55.85/21.45 | (1247) sum(n16, n16) = all_0_3_3
% 55.85/21.45 |
% 55.85/21.45 | From (1741) and (9800) follows:
% 55.85/21.45 | (8965) sum(n2, n4) = all_0_0_0
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 55.85/21.45 | (1248) all_0_3_3 = n6
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (690) with n2, n4, all_0_0_0, n6 and discharging atoms sum(n2, n4) = all_0_0_0, sum(n2, n4) = n6, yields:
% 55.85/21.45 | (1249) all_0_0_0 = n6
% 55.85/21.45 |
% 55.85/21.45 | Equations (1249,1248) can reduce 679 to:
% 55.85/21.45 | (1106) $false
% 55.85/21.45 |
% 55.85/21.45 |-The branch is then unsatisfiable
% 55.85/21.45 |-Branch two:
% 55.85/21.45 | (1982) ~ (all_0_10_10 = n2)
% 55.85/21.45 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 55.85/21.45 |
% 55.85/21.45 +-Applying beta-rule and splitting (1983), into two cases.
% 55.85/21.45 |-Branch one:
% 55.85/21.45 | (1984) all_0_10_10 = n1
% 55.85/21.45 |
% 55.85/21.45 | From (1984) and (292) follows:
% 55.85/21.45 | (1985) pred(n1) = all_0_6_6
% 55.85/21.45 |
% 55.85/21.45 | From (1984) and (760) follows:
% 55.85/21.45 | (1986) succ(n1) = all_0_8_8
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 55.85/21.45 | (1987) all_0_6_6 = n0
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 55.85/21.45 | (1988) all_0_8_8 = n2
% 55.85/21.45 |
% 55.85/21.45 | From (1987)(1988) and (411) follows:
% 55.85/21.45 | (1989) sum(n0, n2) = all_0_1_1
% 55.85/21.45 |
% 55.85/21.45 | From (1987) and (9796) follows:
% 55.85/21.45 | (10023) sum(n0, n15) = all_0_4_4
% 55.85/21.45 |
% 55.85/21.45 | From (1988) and (9798) follows:
% 55.85/21.45 | (10024) sum(n13, n2) = all_0_7_7
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (690) with n13, n2, all_0_7_7, n15 and discharging atoms sum(n13, n2) = all_0_7_7, sum(n13, n2) = n15, yields:
% 55.85/21.45 | (1263) all_0_7_7 = n15
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (690) with n0, n15, all_0_4_4, n15 and discharging atoms sum(n0, n15) = all_0_4_4, sum(n0, n15) = n15, yields:
% 55.85/21.45 | (1261) all_0_4_4 = n15
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 55.85/21.45 | (1759) all_0_1_1 = n2
% 55.85/21.45 |
% 55.85/21.45 | From (1263)(1261) and (590) follows:
% 55.85/21.45 | (1265) sum(n15, n15) = all_0_3_3
% 55.85/21.45 |
% 55.85/21.45 | From (1759) and (9800) follows:
% 55.85/21.45 | (9531) sum(n2, n2) = all_0_0_0
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 55.85/21.45 | (1266) all_0_3_3 = n4
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (690) with n2, n2, all_0_0_0, n4 and discharging atoms sum(n2, n2) = all_0_0_0, sum(n2, n2) = n4, yields:
% 55.85/21.45 | (1267) all_0_0_0 = n4
% 55.85/21.45 |
% 55.85/21.45 | Equations (1267,1266) can reduce 679 to:
% 55.85/21.45 | (1106) $false
% 55.85/21.45 |
% 55.85/21.45 |-The branch is then unsatisfiable
% 55.85/21.45 |-Branch two:
% 55.85/21.45 | (2002) ~ (all_0_10_10 = n1)
% 55.85/21.45 | (2003) all_0_10_10 = n0
% 55.85/21.45 |
% 55.85/21.45 | From (2003) and (292) follows:
% 55.85/21.45 | (2004) pred(n0) = all_0_6_6
% 55.85/21.45 |
% 55.85/21.45 | From (2003) and (760) follows:
% 55.85/21.45 | (2005) succ(n0) = all_0_8_8
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 55.85/21.45 | (2006) all_0_6_6 = n25
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 55.85/21.45 | (2007) all_0_8_8 = n1
% 55.85/21.45 |
% 55.85/21.45 | From (2006)(2007) and (411) follows:
% 55.85/21.45 | (2008) sum(n25, n1) = all_0_1_1
% 55.85/21.45 |
% 55.85/21.45 | From (2006) and (9796) follows:
% 55.85/21.45 | (10040) sum(n25, n15) = all_0_4_4
% 55.85/21.45 |
% 55.85/21.45 | From (2007) and (9798) follows:
% 55.85/21.45 | (10041) sum(n13, n1) = all_0_7_7
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (690) with n25, n15, all_0_4_4, n14 and discharging atoms sum(n25, n15) = all_0_4_4, sum(n25, n15) = n14, yields:
% 55.85/21.45 | (1279) all_0_4_4 = n14
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 55.85/21.45 | (1777) all_0_1_1 = n0
% 55.85/21.45 |
% 55.85/21.45 | Instantiating formula (690) with n13, n1, all_0_7_7, n14 and discharging atoms sum(n13, n1) = all_0_7_7, sum(n13, n1) = n14, yields:
% 55.85/21.45 | (1281) all_0_7_7 = n14
% 55.85/21.45 |
% 55.85/21.45 | From (1281)(1279) and (590) follows:
% 55.85/21.45 | (1283) sum(n14, n14) = all_0_3_3
% 55.85/21.45 |
% 55.85/21.45 | From (1777) and (9800) follows:
% 55.85/21.46 | (9813) sum(n2, n0) = all_0_0_0
% 55.85/21.46 |
% 55.85/21.46 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 55.85/21.46 | (1284) all_0_3_3 = n2
% 55.85/21.46 |
% 55.85/21.46 | Instantiating formula (690) with n2, n0, all_0_0_0, n2 and discharging atoms sum(n2, n0) = all_0_0_0, sum(n2, n0) = n2, yields:
% 55.85/21.46 | (1285) all_0_0_0 = n2
% 55.85/21.46 |
% 55.85/21.46 | Equations (1285,1284) can reduce 679 to:
% 55.85/21.46 | (1106) $false
% 55.85/21.46 |
% 55.85/21.46 |-The branch is then unsatisfiable
% 55.85/21.46 |-Branch two:
% 55.85/21.46 | (1305) ~ (all_0_11_11 = n14)
% 55.85/21.46 | (1306) 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
% 55.85/21.46 |
% 55.85/21.46 +-Applying beta-rule and splitting (1767), into two cases.
% 55.85/21.46 |-Branch one:
% 55.85/21.46 | (1768) all_0_10_10 = n13
% 55.85/21.46 |
% 55.85/21.46 | From (1768) and (292) follows:
% 55.85/21.46 | (1769) pred(n13) = all_0_6_6
% 55.85/21.46 |
% 55.85/21.46 | From (1768) and (760) follows:
% 55.85/21.46 | (1770) succ(n13) = all_0_8_8
% 55.85/21.46 |
% 55.85/21.46 | Instantiating formula (500) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 55.85/21.46 | (1771) all_0_6_6 = n12
% 55.85/21.46 |
% 55.85/21.46 | Instantiating formula (617) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 55.85/21.46 | (1772) all_0_8_8 = n14
% 55.85/21.46 |
% 55.85/21.46 | From (1771) and (1769) follows:
% 55.85/21.46 | (517) pred(n13) = n12
% 55.85/21.46 |
% 55.85/21.46 | From (1772) and (1770) follows:
% 55.85/21.46 | (389) succ(n13) = n14
% 55.85/21.46 |
% 55.85/21.46 | From (1771) and (541) follows:
% 55.85/21.46 | (10059) sum(n12, all_0_5_5) = all_0_4_4
% 55.85/21.46 |
% 55.85/21.46 | From (1771)(1772) and (411) follows:
% 55.85/21.46 | (1773) sum(n12, n14) = all_0_1_1
% 55.85/21.46 |
% 55.85/21.46 | From (1772) and (427) follows:
% 55.85/21.46 | (10061) sum(all_0_9_9, n14) = all_0_7_7
% 55.85/21.46 |
% 55.85/21.46 | Instantiating formula (690) with n12, n14, all_0_1_1, n0 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n0, yields:
% 55.85/21.46 | (1777) all_0_1_1 = n0
% 55.85/21.46 |
% 55.85/21.46 | From (1777) and (630) follows:
% 55.85/21.46 | (10063) sum(all_0_2_2, n0) = all_0_0_0
% 55.85/21.46 |
% 55.85/21.46 | From (1777) and (1773) follows:
% 55.85/21.46 | (756) sum(n12, n14) = n0
% 55.85/21.46 |
% 55.85/21.46 +-Applying beta-rule and splitting (1306), into two cases.
% 55.85/21.46 |-Branch one:
% 55.85/21.46 | (1307) all_0_11_11 = n13
% 55.85/21.46 |
% 55.85/21.46 | From (1307) and (559) follows:
% 55.85/21.46 | (1308) pred(n13) = all_0_9_9
% 55.85/21.46 |
% 55.85/21.46 | From (1307) and (992) follows:
% 55.85/21.46 | (1309) succ(n13) = all_0_5_5
% 55.85/21.46 |
% 55.85/21.46 | Instantiating formula (500) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 55.85/21.46 | (1310) all_0_9_9 = n12
% 55.85/21.46 |
% 55.85/21.46 | Instantiating formula (617) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 55.85/21.46 | (1311) all_0_5_5 = n14
% 55.85/21.46 |
% 55.85/21.46 | From (1310)(1311) and (538) follows:
% 55.85/21.46 | (1312) sum(n12, n14) = all_0_2_2
% 55.85/21.46 |
% 55.85/21.46 | From (1310) and (10061) follows:
% 55.85/21.46 | (10071) sum(n12, n14) = all_0_7_7
% 55.85/21.46 |
% 55.85/21.46 | From (1311) and (10059) follows:
% 55.85/21.46 | (10072) sum(n12, n14) = all_0_4_4
% 55.85/21.46 |
% 55.85/21.46 | Instantiating formula (690) with n12, n14, all_0_2_2, n0 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n0, yields:
% 55.85/21.46 | (1316) all_0_2_2 = n0
% 55.85/21.46 |
% 55.85/21.46 | Instantiating formula (690) 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:
% 55.85/21.46 | (1093) all_0_2_2 = all_0_4_4
% 55.85/21.46 |
% 55.85/21.46 | Instantiating formula (690) 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:
% 55.85/21.46 | (1094) all_0_2_2 = all_0_7_7
% 55.85/21.46 |
% 55.85/21.46 | Combining equations (1094,1093) yields a new equation:
% 55.85/21.46 | (1095) all_0_4_4 = all_0_7_7
% 55.85/21.46 |
% 55.85/21.46 | Combining equations (1316,1093) yields a new equation:
% 55.85/21.46 | (1531) all_0_4_4 = n0
% 55.85/21.46 |
% 55.85/21.46 | Combining equations (1531,1095) yields a new equation:
% 55.85/21.46 | (1533) all_0_7_7 = n0
% 55.85/21.46 |
% 55.85/21.46 | Combining equations (1533,1095) yields a new equation:
% 55.85/21.46 | (1531) all_0_4_4 = n0
% 55.85/21.46 |
% 55.85/21.46 | Combining equations (1531,1093) yields a new equation:
% 55.85/21.46 | (1316) all_0_2_2 = n0
% 55.85/21.46 |
% 55.85/21.46 | From (1316) and (10063) follows:
% 55.85/21.46 | (10081) sum(n0, n0) = all_0_0_0
% 55.85/21.46 |
% 55.85/21.46 | From (1533)(1531) and (590) follows:
% 55.85/21.46 | (1535) sum(n0, n0) = all_0_3_3
% 55.85/21.46 |
% 55.85/21.46 | Instantiating formula (690) with n0, n0, all_0_0_0, n0 and discharging atoms sum(n0, n0) = all_0_0_0, sum(n0, n0) = n0, yields:
% 55.85/21.46 | (1303) all_0_0_0 = n0
% 55.85/21.46 |
% 55.85/21.46 | Instantiating formula (690) 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:
% 55.85/21.46 | (1103) all_0_0_0 = all_0_3_3
% 55.85/21.46 |
% 55.85/21.46 | Combining equations (1303,1103) yields a new equation:
% 55.85/21.46 | (1302) all_0_3_3 = n0
% 55.85/21.46 |
% 55.85/21.46 | Combining equations (1302,1103) yields a new equation:
% 55.85/21.46 | (1303) all_0_0_0 = n0
% 55.85/21.46 |
% 55.85/21.46 | Equations (1303,1302) can reduce 679 to:
% 55.85/21.46 | (1106) $false
% 55.85/21.46 |
% 55.85/21.46 |-The branch is then unsatisfiable
% 55.85/21.46 |-Branch two:
% 55.85/21.46 | (1323) ~ (all_0_11_11 = n13)
% 55.85/21.46 | (1324) 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
% 55.85/21.46 |
% 55.85/21.46 +-Applying beta-rule and splitting (1324), into two cases.
% 55.85/21.46 |-Branch one:
% 55.85/21.46 | (1325) all_0_11_11 = n12
% 55.85/21.46 |
% 55.85/21.46 | From (1325) and (559) follows:
% 55.85/21.46 | (1326) pred(n12) = all_0_9_9
% 55.85/21.46 |
% 55.85/21.46 | From (1325) and (992) follows:
% 55.85/21.46 | (1327) succ(n12) = all_0_5_5
% 55.85/21.46 |
% 55.85/21.46 | Instantiating formula (500) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 55.85/21.46 | (1328) all_0_9_9 = n11
% 55.85/21.46 |
% 55.85/21.46 | Instantiating formula (617) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 55.85/21.46 | (1329) all_0_5_5 = n13
% 55.85/21.46 |
% 55.85/21.46 | From (1328)(1329) and (538) follows:
% 55.85/21.46 | (1330) sum(n11, n13) = all_0_2_2
% 55.85/21.46 |
% 55.85/21.46 | From (1328) and (10061) follows:
% 55.85/21.46 | (10096) sum(n11, n14) = all_0_7_7
% 55.85/21.46 |
% 55.85/21.46 | From (1329) and (10059) follows:
% 55.85/21.46 | (10097) sum(n12, n13) = all_0_4_4
% 55.85/21.46 |
% 55.85/21.46 | Instantiating formula (690) with n12, n13, all_0_4_4, n25 and discharging atoms sum(n12, n13) = all_0_4_4, sum(n12, n13) = n25, yields:
% 55.85/21.46 | (1551) all_0_4_4 = n25
% 55.85/21.46 |
% 55.85/21.46 | Instantiating formula (690) with n11, n14, all_0_7_7, n25 and discharging atoms sum(n11, n14) = all_0_7_7, sum(n11, n14) = n25, yields:
% 55.85/21.46 | (1550) all_0_7_7 = n25
% 55.85/21.46 |
% 55.85/21.46 | Instantiating formula (690) with n11, n13, all_0_2_2, n24 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n24, yields:
% 55.85/21.46 | (1092) all_0_2_2 = n24
% 55.85/21.46 |
% 55.85/21.46 | From (1092) and (10063) follows:
% 55.85/21.46 | (1780) sum(n24, n0) = all_0_0_0
% 55.85/21.46 |
% 55.85/21.46 | From (1550)(1551) and (590) follows:
% 55.85/21.47 | (1553) sum(n25, n25) = all_0_3_3
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 55.85/21.47 | (1320) all_0_3_3 = n24
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (690) with n24, n0, all_0_0_0, n24 and discharging atoms sum(n24, n0) = all_0_0_0, sum(n24, n0) = n24, yields:
% 55.85/21.47 | (1321) all_0_0_0 = n24
% 55.85/21.47 |
% 55.85/21.47 | Equations (1321,1320) can reduce 679 to:
% 55.85/21.47 | (1106) $false
% 55.85/21.47 |
% 55.85/21.47 |-The branch is then unsatisfiable
% 55.85/21.47 |-Branch two:
% 55.85/21.47 | (1341) ~ (all_0_11_11 = n12)
% 55.85/21.47 | (1342) 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
% 55.85/21.47 |
% 55.85/21.47 +-Applying beta-rule and splitting (1342), into two cases.
% 55.85/21.47 |-Branch one:
% 55.85/21.47 | (1343) all_0_11_11 = n11
% 55.85/21.47 |
% 55.85/21.47 | From (1343) and (559) follows:
% 55.85/21.47 | (1344) pred(n11) = all_0_9_9
% 55.85/21.47 |
% 55.85/21.47 | From (1343) and (992) follows:
% 55.85/21.47 | (1345) succ(n11) = all_0_5_5
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (500) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 55.85/21.47 | (1346) all_0_9_9 = n10
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (617) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 55.85/21.47 | (1347) all_0_5_5 = n12
% 55.85/21.47 |
% 55.85/21.47 | From (1346)(1347) and (538) follows:
% 55.85/21.47 | (1348) sum(n10, n12) = all_0_2_2
% 55.85/21.47 |
% 55.85/21.47 | From (1346) and (10061) follows:
% 55.85/21.47 | (10114) sum(n10, n14) = all_0_7_7
% 55.85/21.47 |
% 55.85/21.47 | From (1347) and (10059) follows:
% 55.85/21.47 | (10115) sum(n12, n12) = all_0_4_4
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (690) with n12, n12, all_0_4_4, n24 and discharging atoms sum(n12, n12) = all_0_4_4, sum(n12, n12) = n24, yields:
% 55.85/21.47 | (1096) all_0_4_4 = n24
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (690) with n10, n14, all_0_7_7, n24 and discharging atoms sum(n10, n14) = all_0_7_7, sum(n10, n14) = n24, yields:
% 55.85/21.47 | (1097) all_0_7_7 = n24
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (690) with n10, n12, all_0_2_2, n22 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n22, yields:
% 55.85/21.47 | (1118) all_0_2_2 = n22
% 55.85/21.47 |
% 55.85/21.47 | From (1118) and (10063) follows:
% 55.85/21.47 | (2692) sum(n22, n0) = all_0_0_0
% 55.85/21.47 |
% 55.85/21.47 | From (1097)(1096) and (590) follows:
% 55.85/21.47 | (1101) sum(n24, n24) = all_0_3_3
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 55.85/21.47 | (1104) all_0_3_3 = n22
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (690) with n22, n0, all_0_0_0, n22 and discharging atoms sum(n22, n0) = all_0_0_0, sum(n22, n0) = n22, yields:
% 55.85/21.47 | (1102) all_0_0_0 = n22
% 55.85/21.47 |
% 55.85/21.47 | Equations (1102,1104) can reduce 679 to:
% 55.85/21.47 | (1106) $false
% 55.85/21.47 |
% 55.85/21.47 |-The branch is then unsatisfiable
% 55.85/21.47 |-Branch two:
% 55.85/21.47 | (1359) ~ (all_0_11_11 = n11)
% 55.85/21.47 | (1360) 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
% 55.85/21.47 |
% 55.85/21.47 +-Applying beta-rule and splitting (1360), into two cases.
% 55.85/21.47 |-Branch one:
% 55.85/21.47 | (1361) all_0_11_11 = n10
% 55.85/21.47 |
% 55.85/21.47 | From (1361) and (559) follows:
% 55.85/21.47 | (1362) pred(n10) = all_0_9_9
% 55.85/21.47 |
% 55.85/21.47 | From (1361) and (992) follows:
% 55.85/21.47 | (1363) succ(n10) = all_0_5_5
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (500) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 55.85/21.47 | (1364) all_0_9_9 = n9
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (617) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 55.85/21.47 | (1365) all_0_5_5 = n11
% 55.85/21.47 |
% 55.85/21.47 | From (1364)(1365) and (538) follows:
% 55.85/21.47 | (1366) sum(n9, n11) = all_0_2_2
% 55.85/21.47 |
% 55.85/21.47 | From (1364) and (10061) follows:
% 55.85/21.47 | (10132) sum(n9, n14) = all_0_7_7
% 55.85/21.47 |
% 55.85/21.47 | From (1365) and (10059) follows:
% 55.85/21.47 | (10133) sum(n12, n11) = all_0_4_4
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (690) with n12, n11, all_0_4_4, n23 and discharging atoms sum(n12, n11) = all_0_4_4, sum(n12, n11) = n23, yields:
% 55.85/21.47 | (1117) all_0_4_4 = n23
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (690) with n9, n14, all_0_7_7, n23 and discharging atoms sum(n9, n14) = all_0_7_7, sum(n9, n14) = n23, yields:
% 55.85/21.47 | (1119) all_0_7_7 = n23
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (690) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 55.85/21.47 | (1136) all_0_2_2 = n20
% 55.85/21.47 |
% 55.85/21.47 | From (1136) and (10063) follows:
% 55.85/21.47 | (3566) sum(n20, n0) = all_0_0_0
% 55.85/21.47 |
% 55.85/21.47 | From (1119)(1117) and (590) follows:
% 55.85/21.47 | (1121) sum(n23, n23) = all_0_3_3
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 55.85/21.47 | (1122) all_0_3_3 = n20
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (690) with n20, n0, all_0_0_0, n20 and discharging atoms sum(n20, n0) = all_0_0_0, sum(n20, n0) = n20, yields:
% 55.85/21.47 | (1123) all_0_0_0 = n20
% 55.85/21.47 |
% 55.85/21.47 | Equations (1123,1122) can reduce 679 to:
% 55.85/21.47 | (1106) $false
% 55.85/21.47 |
% 55.85/21.47 |-The branch is then unsatisfiable
% 55.85/21.47 |-Branch two:
% 55.85/21.47 | (1377) ~ (all_0_11_11 = n10)
% 55.85/21.47 | (1378) 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
% 55.85/21.47 |
% 55.85/21.47 +-Applying beta-rule and splitting (1378), into two cases.
% 55.85/21.47 |-Branch one:
% 55.85/21.47 | (1379) all_0_11_11 = n9
% 55.85/21.47 |
% 55.85/21.47 | From (1379) and (559) follows:
% 55.85/21.47 | (1380) pred(n9) = all_0_9_9
% 55.85/21.47 |
% 55.85/21.47 | From (1379) and (992) follows:
% 55.85/21.47 | (1381) succ(n9) = all_0_5_5
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 55.85/21.47 | (1382) all_0_9_9 = n8
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 55.85/21.47 | (1383) all_0_5_5 = n10
% 55.85/21.47 |
% 55.85/21.47 | From (1382)(1383) and (538) follows:
% 55.85/21.47 | (1384) sum(n8, n10) = all_0_2_2
% 55.85/21.47 |
% 55.85/21.47 | From (1382) and (10061) follows:
% 55.85/21.47 | (10150) sum(n8, n14) = all_0_7_7
% 55.85/21.47 |
% 55.85/21.47 | From (1383) and (10059) follows:
% 55.85/21.47 | (10151) sum(n12, n10) = all_0_4_4
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (690) with n12, n10, all_0_4_4, n22 and discharging atoms sum(n12, n10) = all_0_4_4, sum(n12, n10) = n22, yields:
% 55.85/21.47 | (1135) all_0_4_4 = n22
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (690) with n8, n14, all_0_7_7, n22 and discharging atoms sum(n8, n14) = all_0_7_7, sum(n8, n14) = n22, yields:
% 55.85/21.47 | (1137) all_0_7_7 = n22
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 55.85/21.47 | (1154) all_0_2_2 = n18
% 55.85/21.47 |
% 55.85/21.47 | From (1154) and (10063) follows:
% 55.85/21.47 | (4404) sum(n18, n0) = all_0_0_0
% 55.85/21.47 |
% 55.85/21.47 | From (1137)(1135) and (590) follows:
% 55.85/21.47 | (1139) sum(n22, n22) = all_0_3_3
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 55.85/21.47 | (1140) all_0_3_3 = n18
% 55.85/21.47 |
% 55.85/21.47 | Instantiating formula (690) with n18, n0, all_0_0_0, n18 and discharging atoms sum(n18, n0) = all_0_0_0, sum(n18, n0) = n18, yields:
% 55.85/21.47 | (1141) all_0_0_0 = n18
% 55.85/21.47 |
% 55.85/21.47 | Equations (1141,1140) can reduce 679 to:
% 55.85/21.48 | (1106) $false
% 55.85/21.48 |
% 55.85/21.48 |-The branch is then unsatisfiable
% 55.85/21.48 |-Branch two:
% 55.85/21.48 | (1395) ~ (all_0_11_11 = n9)
% 55.85/21.48 | (1396) 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
% 55.85/21.48 |
% 55.85/21.48 +-Applying beta-rule and splitting (1396), into two cases.
% 55.85/21.48 |-Branch one:
% 55.85/21.48 | (1397) all_0_11_11 = n8
% 55.85/21.48 |
% 55.85/21.48 | From (1397) and (559) follows:
% 55.85/21.48 | (1398) pred(n8) = all_0_9_9
% 55.85/21.48 |
% 55.85/21.48 | From (1397) and (992) follows:
% 55.85/21.48 | (1399) succ(n8) = all_0_5_5
% 55.85/21.48 |
% 55.85/21.48 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 55.85/21.48 | (1400) all_0_9_9 = n7
% 55.85/21.48 |
% 55.85/21.48 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 55.85/21.48 | (1401) all_0_5_5 = n9
% 55.85/21.48 |
% 55.85/21.48 | From (1400)(1401) and (538) follows:
% 55.85/21.48 | (1402) sum(n7, n9) = all_0_2_2
% 55.85/21.48 |
% 55.85/21.48 | From (1400) and (10061) follows:
% 55.85/21.48 | (10168) sum(n7, n14) = all_0_7_7
% 55.85/21.48 |
% 55.85/21.48 | From (1401) and (10059) follows:
% 55.85/21.48 | (10169) sum(n12, n9) = all_0_4_4
% 55.85/21.48 |
% 55.85/21.48 | Instantiating formula (690) with n12, n9, all_0_4_4, n21 and discharging atoms sum(n12, n9) = all_0_4_4, sum(n12, n9) = n21, yields:
% 55.85/21.48 | (1153) all_0_4_4 = n21
% 55.85/21.48 |
% 55.85/21.48 | Instantiating formula (690) with n7, n14, all_0_7_7, n21 and discharging atoms sum(n7, n14) = all_0_7_7, sum(n7, n14) = n21, yields:
% 55.85/21.48 | (1155) all_0_7_7 = n21
% 55.85/21.48 |
% 55.85/21.48 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 55.85/21.48 | (1172) all_0_2_2 = n16
% 55.85/21.48 |
% 55.85/21.48 | From (1172) and (10063) follows:
% 55.85/21.48 | (5206) sum(n16, n0) = all_0_0_0
% 55.85/21.48 |
% 55.85/21.48 | From (1155)(1153) and (590) follows:
% 55.85/21.48 | (1157) sum(n21, n21) = all_0_3_3
% 55.85/21.48 |
% 55.85/21.48 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 55.85/21.48 | (1158) all_0_3_3 = n16
% 55.85/21.48 |
% 55.85/21.48 | Instantiating formula (690) with n16, n0, all_0_0_0, n16 and discharging atoms sum(n16, n0) = all_0_0_0, sum(n16, n0) = n16, yields:
% 55.85/21.48 | (1159) all_0_0_0 = n16
% 55.85/21.48 |
% 55.85/21.48 | Equations (1159,1158) can reduce 679 to:
% 55.85/21.48 | (1106) $false
% 55.85/21.48 |
% 55.85/21.48 |-The branch is then unsatisfiable
% 55.85/21.48 |-Branch two:
% 55.85/21.48 | (1413) ~ (all_0_11_11 = n8)
% 55.85/21.48 | (1414) 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
% 55.85/21.48 |
% 55.85/21.48 +-Applying beta-rule and splitting (1414), into two cases.
% 55.85/21.48 |-Branch one:
% 55.85/21.48 | (1415) all_0_11_11 = n7
% 55.85/21.48 |
% 55.85/21.48 | From (1415) and (559) follows:
% 55.85/21.48 | (1416) pred(n7) = all_0_9_9
% 55.85/21.48 |
% 55.85/21.48 | From (1415) and (992) follows:
% 55.85/21.48 | (1417) succ(n7) = all_0_5_5
% 55.85/21.48 |
% 55.85/21.48 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 55.85/21.48 | (1418) all_0_9_9 = n6
% 55.85/21.48 |
% 55.85/21.48 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 55.85/21.48 | (1419) all_0_5_5 = n8
% 55.85/21.48 |
% 55.85/21.48 | From (1418)(1419) and (538) follows:
% 55.85/21.48 | (1420) sum(n6, n8) = all_0_2_2
% 55.85/21.48 |
% 55.85/21.48 | From (1418) and (10061) follows:
% 55.94/21.48 | (10186) sum(n6, n14) = all_0_7_7
% 55.94/21.48 |
% 55.94/21.48 | From (1419) and (10059) follows:
% 55.94/21.48 | (10187) sum(n12, n8) = all_0_4_4
% 55.94/21.48 |
% 55.94/21.48 | Instantiating formula (690) with n12, n8, all_0_4_4, n20 and discharging atoms sum(n12, n8) = all_0_4_4, sum(n12, n8) = n20, yields:
% 55.94/21.48 | (1171) all_0_4_4 = n20
% 55.94/21.48 |
% 55.94/21.48 | Instantiating formula (690) with n6, n14, all_0_7_7, n20 and discharging atoms sum(n6, n14) = all_0_7_7, sum(n6, n14) = n20, yields:
% 55.94/21.48 | (1173) all_0_7_7 = n20
% 55.94/21.48 |
% 55.94/21.48 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 55.94/21.48 | (1190) all_0_2_2 = n14
% 55.94/21.48 |
% 55.94/21.48 | From (1190) and (10063) follows:
% 55.94/21.48 | (5972) sum(n14, n0) = all_0_0_0
% 55.94/21.48 |
% 55.94/21.48 | From (1173)(1171) and (590) follows:
% 55.94/21.48 | (1175) sum(n20, n20) = all_0_3_3
% 55.94/21.48 |
% 55.94/21.48 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 55.94/21.48 | (1176) all_0_3_3 = n14
% 55.94/21.48 |
% 55.94/21.48 | Instantiating formula (690) with n14, n0, all_0_0_0, n14 and discharging atoms sum(n14, n0) = all_0_0_0, sum(n14, n0) = n14, yields:
% 55.94/21.48 | (1177) all_0_0_0 = n14
% 55.94/21.48 |
% 55.94/21.48 | Equations (1177,1176) can reduce 679 to:
% 55.94/21.48 | (1106) $false
% 55.94/21.48 |
% 55.94/21.48 |-The branch is then unsatisfiable
% 55.94/21.48 |-Branch two:
% 55.94/21.48 | (1431) ~ (all_0_11_11 = n7)
% 55.94/21.48 | (1432) 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
% 55.94/21.48 |
% 55.94/21.48 +-Applying beta-rule and splitting (1432), into two cases.
% 55.94/21.48 |-Branch one:
% 55.94/21.48 | (1433) all_0_11_11 = n6
% 55.94/21.48 |
% 55.94/21.48 | From (1433) and (559) follows:
% 55.94/21.48 | (1434) pred(n6) = all_0_9_9
% 55.94/21.48 |
% 55.94/21.48 | From (1433) and (992) follows:
% 55.94/21.48 | (1435) succ(n6) = all_0_5_5
% 55.94/21.48 |
% 55.94/21.48 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 55.94/21.48 | (1436) all_0_9_9 = n5
% 55.94/21.48 |
% 55.94/21.48 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 55.94/21.48 | (1437) all_0_5_5 = n7
% 55.94/21.48 |
% 55.94/21.48 | From (1436)(1437) and (538) follows:
% 55.94/21.48 | (1438) sum(n5, n7) = all_0_2_2
% 55.94/21.48 |
% 55.94/21.48 | From (1436) and (10061) follows:
% 55.94/21.48 | (10204) sum(n5, n14) = all_0_7_7
% 55.94/21.48 |
% 55.94/21.48 | From (1437) and (10059) follows:
% 55.94/21.48 | (10205) sum(n12, n7) = all_0_4_4
% 55.94/21.48 |
% 55.94/21.48 | Instantiating formula (690) with n12, n7, all_0_4_4, n19 and discharging atoms sum(n12, n7) = all_0_4_4, sum(n12, n7) = n19, yields:
% 55.94/21.48 | (1189) all_0_4_4 = n19
% 55.94/21.48 |
% 55.94/21.48 | Instantiating formula (690) with n5, n14, all_0_7_7, n19 and discharging atoms sum(n5, n14) = all_0_7_7, sum(n5, n14) = n19, yields:
% 55.94/21.48 | (1191) all_0_7_7 = n19
% 55.94/21.48 |
% 55.94/21.48 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 55.94/21.48 | (1208) all_0_2_2 = n12
% 55.94/21.48 |
% 55.94/21.48 | From (1208) and (10063) follows:
% 55.94/21.48 | (6702) sum(n12, n0) = all_0_0_0
% 55.94/21.48 |
% 55.94/21.48 | From (1191)(1189) and (590) follows:
% 55.94/21.48 | (1193) sum(n19, n19) = all_0_3_3
% 55.94/21.48 |
% 55.94/21.48 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 55.94/21.48 | (1194) all_0_3_3 = n12
% 55.94/21.48 |
% 55.94/21.48 | Instantiating formula (690) with n12, n0, all_0_0_0, n12 and discharging atoms sum(n12, n0) = all_0_0_0, sum(n12, n0) = n12, yields:
% 55.94/21.48 | (1195) all_0_0_0 = n12
% 55.94/21.49 |
% 55.94/21.49 | Equations (1195,1194) can reduce 679 to:
% 55.94/21.49 | (1106) $false
% 55.94/21.49 |
% 55.94/21.49 |-The branch is then unsatisfiable
% 55.94/21.49 |-Branch two:
% 55.94/21.49 | (1449) ~ (all_0_11_11 = n6)
% 55.94/21.49 | (1450) 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
% 55.94/21.49 |
% 55.94/21.49 +-Applying beta-rule and splitting (1450), into two cases.
% 55.94/21.49 |-Branch one:
% 55.94/21.49 | (1451) all_0_11_11 = n5
% 55.94/21.49 |
% 55.94/21.49 | From (1451) and (559) follows:
% 55.94/21.49 | (1452) pred(n5) = all_0_9_9
% 55.94/21.49 |
% 55.94/21.49 | From (1451) and (992) follows:
% 55.94/21.49 | (1453) succ(n5) = all_0_5_5
% 55.94/21.49 |
% 55.94/21.49 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 55.94/21.49 | (1454) all_0_9_9 = n4
% 55.94/21.49 |
% 55.94/21.49 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 55.94/21.49 | (1455) all_0_5_5 = n6
% 55.94/21.49 |
% 55.94/21.49 | From (1454)(1455) and (538) follows:
% 55.94/21.49 | (1456) sum(n4, n6) = all_0_2_2
% 55.94/21.49 |
% 55.94/21.49 | From (1454) and (10061) follows:
% 55.94/21.49 | (10222) sum(n4, n14) = all_0_7_7
% 55.94/21.49 |
% 55.94/21.49 | From (1455) and (10059) follows:
% 55.94/21.49 | (10223) sum(n12, n6) = all_0_4_4
% 55.94/21.49 |
% 55.94/21.49 | Instantiating formula (690) with n12, n6, all_0_4_4, n18 and discharging atoms sum(n12, n6) = all_0_4_4, sum(n12, n6) = n18, yields:
% 55.94/21.49 | (1207) all_0_4_4 = n18
% 55.94/21.49 |
% 55.94/21.49 | Instantiating formula (690) with n4, n14, all_0_7_7, n18 and discharging atoms sum(n4, n14) = all_0_7_7, sum(n4, n14) = n18, yields:
% 55.94/21.49 | (1209) all_0_7_7 = n18
% 55.94/21.49 |
% 55.94/21.49 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 55.94/21.49 | (1226) all_0_2_2 = n10
% 55.94/21.49 |
% 55.94/21.49 | From (1226) and (10063) follows:
% 55.94/21.49 | (7396) sum(n10, n0) = all_0_0_0
% 55.94/21.49 |
% 55.94/21.49 | From (1209)(1207) and (590) follows:
% 55.94/21.49 | (1211) sum(n18, n18) = all_0_3_3
% 55.94/21.49 |
% 55.94/21.49 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 55.94/21.49 | (1212) all_0_3_3 = n10
% 55.94/21.49 |
% 55.94/21.49 | Instantiating formula (690) with n10, n0, all_0_0_0, n10 and discharging atoms sum(n10, n0) = all_0_0_0, sum(n10, n0) = n10, yields:
% 55.94/21.49 | (1213) all_0_0_0 = n10
% 55.94/21.49 |
% 55.94/21.49 | Equations (1213,1212) can reduce 679 to:
% 55.94/21.49 | (1106) $false
% 55.94/21.49 |
% 55.94/21.49 |-The branch is then unsatisfiable
% 55.94/21.49 |-Branch two:
% 55.94/21.49 | (1467) ~ (all_0_11_11 = n5)
% 55.94/21.49 | (1468) 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
% 55.94/21.49 |
% 55.94/21.49 +-Applying beta-rule and splitting (1468), into two cases.
% 55.94/21.49 |-Branch one:
% 55.94/21.49 | (1469) all_0_11_11 = n4
% 55.94/21.49 |
% 55.94/21.49 | From (1469) and (559) follows:
% 55.94/21.49 | (1470) pred(n4) = all_0_9_9
% 55.94/21.49 |
% 55.94/21.49 | From (1469) and (992) follows:
% 55.94/21.49 | (1471) succ(n4) = all_0_5_5
% 55.94/21.49 |
% 55.94/21.49 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 55.94/21.49 | (1472) all_0_9_9 = n3
% 55.94/21.49 |
% 55.94/21.49 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 55.94/21.49 | (1473) all_0_5_5 = n5
% 55.94/21.49 |
% 55.94/21.49 | From (1472)(1473) and (538) follows:
% 55.94/21.49 | (1474) sum(n3, n5) = all_0_2_2
% 55.94/21.49 |
% 55.94/21.49 | From (1472) and (10061) follows:
% 55.94/21.49 | (10240) sum(n3, n14) = all_0_7_7
% 55.94/21.49 |
% 55.94/21.49 | From (1473) and (10059) follows:
% 55.94/21.49 | (10241) sum(n12, n5) = all_0_4_4
% 55.94/21.49 |
% 55.94/21.49 | Instantiating formula (690) with n12, n5, all_0_4_4, n17 and discharging atoms sum(n12, n5) = all_0_4_4, sum(n12, n5) = n17, yields:
% 55.94/21.49 | (1225) all_0_4_4 = n17
% 55.94/21.49 |
% 55.94/21.49 | Instantiating formula (690) with n3, n14, all_0_7_7, n17 and discharging atoms sum(n3, n14) = all_0_7_7, sum(n3, n14) = n17, yields:
% 55.94/21.49 | (1227) all_0_7_7 = n17
% 55.94/21.49 |
% 55.94/21.49 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 55.94/21.49 | (1244) all_0_2_2 = n8
% 55.94/21.49 |
% 55.94/21.49 | From (1244) and (10063) follows:
% 55.94/21.49 | (8054) sum(n8, n0) = all_0_0_0
% 55.94/21.49 |
% 55.94/21.49 | From (1227)(1225) and (590) follows:
% 55.94/21.49 | (1229) sum(n17, n17) = all_0_3_3
% 55.94/21.49 |
% 55.94/21.49 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 55.94/21.49 | (1230) all_0_3_3 = n8
% 55.94/21.49 |
% 55.94/21.49 | Instantiating formula (690) with n8, n0, all_0_0_0, n8 and discharging atoms sum(n8, n0) = all_0_0_0, sum(n8, n0) = n8, yields:
% 55.94/21.49 | (1231) all_0_0_0 = n8
% 55.94/21.49 |
% 55.94/21.49 | Equations (1231,1230) can reduce 679 to:
% 55.94/21.49 | (1106) $false
% 55.94/21.49 |
% 55.94/21.49 |-The branch is then unsatisfiable
% 55.94/21.49 |-Branch two:
% 55.94/21.49 | (1485) ~ (all_0_11_11 = n4)
% 55.94/21.49 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 55.94/21.49 |
% 55.94/21.49 +-Applying beta-rule and splitting (1486), into two cases.
% 55.94/21.49 |-Branch one:
% 55.94/21.49 | (1487) all_0_11_11 = n3
% 55.94/21.49 |
% 55.94/21.49 | From (1487) and (559) follows:
% 55.94/21.49 | (1488) pred(n3) = all_0_9_9
% 55.94/21.49 |
% 55.94/21.49 | From (1487) and (992) follows:
% 55.94/21.49 | (1489) succ(n3) = all_0_5_5
% 55.94/21.49 |
% 55.94/21.49 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 55.94/21.49 | (1490) all_0_9_9 = n2
% 55.94/21.49 |
% 55.94/21.49 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 55.94/21.49 | (1491) all_0_5_5 = n4
% 55.94/21.49 |
% 55.94/21.49 | From (1490)(1491) and (538) follows:
% 55.94/21.49 | (1492) sum(n2, n4) = all_0_2_2
% 55.94/21.49 |
% 55.94/21.49 | From (1490) and (10061) follows:
% 55.94/21.49 | (10258) sum(n2, n14) = all_0_7_7
% 55.94/21.49 |
% 55.94/21.49 | From (1491) and (10059) follows:
% 55.94/21.50 | (10259) sum(n12, n4) = all_0_4_4
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (690) with n12, n4, all_0_4_4, n16 and discharging atoms sum(n12, n4) = all_0_4_4, sum(n12, n4) = n16, yields:
% 55.94/21.50 | (1243) all_0_4_4 = n16
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (690) with n2, n14, all_0_7_7, n16 and discharging atoms sum(n2, n14) = all_0_7_7, sum(n2, n14) = n16, yields:
% 55.94/21.50 | (1245) all_0_7_7 = n16
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 55.94/21.50 | (1262) all_0_2_2 = n6
% 55.94/21.50 |
% 55.94/21.50 | From (1262) and (10063) follows:
% 55.94/21.50 | (8677) sum(n6, n0) = all_0_0_0
% 55.94/21.50 |
% 55.94/21.50 | From (1245)(1243) and (590) follows:
% 55.94/21.50 | (1247) sum(n16, n16) = all_0_3_3
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 55.94/21.50 | (1248) all_0_3_3 = n6
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (690) with n6, n0, all_0_0_0, n6 and discharging atoms sum(n6, n0) = all_0_0_0, sum(n6, n0) = n6, yields:
% 55.94/21.50 | (1249) all_0_0_0 = n6
% 55.94/21.50 |
% 55.94/21.50 | Equations (1249,1248) can reduce 679 to:
% 55.94/21.50 | (1106) $false
% 55.94/21.50 |
% 55.94/21.50 |-The branch is then unsatisfiable
% 55.94/21.50 |-Branch two:
% 55.94/21.50 | (1503) ~ (all_0_11_11 = n3)
% 55.94/21.50 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 55.94/21.50 |
% 55.94/21.50 +-Applying beta-rule and splitting (1504), into two cases.
% 55.94/21.50 |-Branch one:
% 55.94/21.50 | (1505) all_0_11_11 = n2
% 55.94/21.50 |
% 55.94/21.50 | From (1505) and (559) follows:
% 55.94/21.50 | (1506) pred(n2) = all_0_9_9
% 55.94/21.50 |
% 55.94/21.50 | From (1505) and (992) follows:
% 55.94/21.50 | (1507) succ(n2) = all_0_5_5
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 55.94/21.50 | (1508) all_0_9_9 = n1
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 55.94/21.50 | (1509) all_0_5_5 = n3
% 55.94/21.50 |
% 55.94/21.50 | From (1508)(1509) and (538) follows:
% 55.94/21.50 | (1510) sum(n1, n3) = all_0_2_2
% 55.94/21.50 |
% 55.94/21.50 | From (1508) and (10061) follows:
% 55.94/21.50 | (10276) sum(n1, n14) = all_0_7_7
% 55.94/21.50 |
% 55.94/21.50 | From (1509) and (10059) follows:
% 55.94/21.50 | (10277) sum(n12, n3) = all_0_4_4
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (690) with n12, n3, all_0_4_4, n15 and discharging atoms sum(n12, n3) = all_0_4_4, sum(n12, n3) = n15, yields:
% 55.94/21.50 | (1261) all_0_4_4 = n15
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (690) with n1, n14, all_0_7_7, n15 and discharging atoms sum(n1, n14) = all_0_7_7, sum(n1, n14) = n15, yields:
% 55.94/21.50 | (1263) all_0_7_7 = n15
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 55.94/21.50 | (1280) all_0_2_2 = n4
% 55.94/21.50 |
% 55.94/21.50 | From (1280) and (10063) follows:
% 55.94/21.50 | (9263) sum(n4, n0) = all_0_0_0
% 55.94/21.50 |
% 55.94/21.50 | From (1263)(1261) and (590) follows:
% 55.94/21.50 | (1265) sum(n15, n15) = all_0_3_3
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 55.94/21.50 | (1266) all_0_3_3 = n4
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (690) with n4, n0, all_0_0_0, n4 and discharging atoms sum(n4, n0) = all_0_0_0, sum(n4, n0) = n4, yields:
% 55.94/21.50 | (1267) all_0_0_0 = n4
% 55.94/21.50 |
% 55.94/21.50 | Equations (1267,1266) can reduce 679 to:
% 55.94/21.50 | (1106) $false
% 55.94/21.50 |
% 55.94/21.50 |-The branch is then unsatisfiable
% 55.94/21.50 |-Branch two:
% 55.94/21.50 | (1521) ~ (all_0_11_11 = n2)
% 55.94/21.50 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 55.94/21.50 |
% 55.94/21.50 +-Applying beta-rule and splitting (1522), into two cases.
% 55.94/21.50 |-Branch one:
% 55.94/21.50 | (1523) all_0_11_11 = n1
% 55.94/21.50 |
% 55.94/21.50 | From (1523) and (559) follows:
% 55.94/21.50 | (1524) pred(n1) = all_0_9_9
% 55.94/21.50 |
% 55.94/21.50 | From (1523) and (992) follows:
% 55.94/21.50 | (1525) succ(n1) = all_0_5_5
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 55.94/21.50 | (1526) all_0_9_9 = n0
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 55.94/21.50 | (1527) all_0_5_5 = n2
% 55.94/21.50 |
% 55.94/21.50 | From (1526)(1527) and (538) follows:
% 55.94/21.50 | (1528) sum(n0, n2) = all_0_2_2
% 55.94/21.50 |
% 55.94/21.50 | From (1526) and (10061) follows:
% 55.94/21.50 | (10294) sum(n0, n14) = all_0_7_7
% 55.94/21.50 |
% 55.94/21.50 | From (1527) and (10059) follows:
% 55.94/21.50 | (10295) sum(n12, n2) = all_0_4_4
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (690) with n12, n2, all_0_4_4, n14 and discharging atoms sum(n12, n2) = all_0_4_4, sum(n12, n2) = n14, yields:
% 55.94/21.50 | (1279) all_0_4_4 = n14
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (690) with n0, n14, all_0_7_7, n14 and discharging atoms sum(n0, n14) = all_0_7_7, sum(n0, n14) = n14, yields:
% 55.94/21.50 | (1281) all_0_7_7 = n14
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 55.94/21.50 | (1298) all_0_2_2 = n2
% 55.94/21.50 |
% 55.94/21.50 | From (1298) and (10063) follows:
% 55.94/21.50 | (9813) sum(n2, n0) = all_0_0_0
% 55.94/21.50 |
% 55.94/21.50 | From (1281)(1279) and (590) follows:
% 55.94/21.50 | (1283) sum(n14, n14) = all_0_3_3
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 55.94/21.50 | (1284) all_0_3_3 = n2
% 55.94/21.50 |
% 55.94/21.50 | Instantiating formula (690) with n2, n0, all_0_0_0, n2 and discharging atoms sum(n2, n0) = all_0_0_0, sum(n2, n0) = n2, yields:
% 55.94/21.50 | (1285) all_0_0_0 = n2
% 55.94/21.50 |
% 55.94/21.50 | Equations (1285,1284) can reduce 679 to:
% 55.94/21.50 | (1106) $false
% 55.94/21.50 |
% 55.94/21.50 |-The branch is then unsatisfiable
% 55.94/21.50 |-Branch two:
% 55.94/21.50 | (1540) ~ (all_0_11_11 = n1)
% 55.94/21.50 | (1541) all_0_11_11 = n0
% 55.94/21.50 |
% 55.94/21.50 | From (1541) and (559) follows:
% 55.94/21.50 | (1542) pred(n0) = all_0_9_9
% 55.94/21.50 |
% 55.94/21.50 | From (1541) and (992) follows:
% 55.96/21.50 | (1543) succ(n0) = all_0_5_5
% 55.96/21.50 |
% 55.96/21.50 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 55.96/21.50 | (1544) all_0_9_9 = n25
% 55.96/21.50 |
% 55.96/21.50 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 55.96/21.50 | (1545) all_0_5_5 = n1
% 55.96/21.50 |
% 55.96/21.50 | From (1544)(1545) and (538) follows:
% 55.96/21.50 | (1546) sum(n25, n1) = all_0_2_2
% 55.96/21.50 |
% 55.96/21.50 | From (1544) and (10061) follows:
% 55.96/21.50 | (10311) sum(n25, n14) = all_0_7_7
% 55.96/21.50 |
% 55.96/21.50 | From (1545) and (10059) follows:
% 55.96/21.51 | (10312) sum(n12, n1) = all_0_4_4
% 55.96/21.51 |
% 55.96/21.51 | Instantiating formula (690) with n25, n14, all_0_7_7, n13 and discharging atoms sum(n25, n14) = all_0_7_7, sum(n25, n14) = n13, yields:
% 55.96/21.51 | (1299) all_0_7_7 = n13
% 55.96/21.51 |
% 55.96/21.51 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 55.96/21.51 | (1316) all_0_2_2 = n0
% 55.96/21.51 |
% 55.96/21.51 | Instantiating formula (690) with n12, n1, all_0_4_4, n13 and discharging atoms sum(n12, n1) = all_0_4_4, sum(n12, n1) = n13, yields:
% 55.96/21.51 | (1297) all_0_4_4 = n13
% 55.96/21.51 |
% 55.96/21.51 | From (1316) and (10063) follows:
% 55.96/21.51 | (10081) sum(n0, n0) = all_0_0_0
% 55.96/21.51 |
% 55.96/21.51 | From (1299)(1297) and (590) follows:
% 55.96/21.51 | (1301) sum(n13, n13) = all_0_3_3
% 55.96/21.51 |
% 55.96/21.51 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 55.96/21.51 | (1302) all_0_3_3 = n0
% 55.96/21.51 |
% 55.96/21.51 | Instantiating formula (690) with n0, n0, all_0_0_0, n0 and discharging atoms sum(n0, n0) = all_0_0_0, sum(n0, n0) = n0, yields:
% 55.96/21.51 | (1303) all_0_0_0 = n0
% 55.96/21.51 |
% 55.96/21.51 | Equations (1303,1302) can reduce 679 to:
% 55.96/21.51 | (1106) $false
% 55.96/21.51 |
% 55.96/21.51 |-The branch is then unsatisfiable
% 55.96/21.51 |-Branch two:
% 55.96/21.51 | (1784) ~ (all_0_10_10 = n13)
% 55.96/21.51 | (1785) 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
% 55.96/21.51 |
% 55.96/21.51 +-Applying beta-rule and splitting (1306), into two cases.
% 55.96/21.51 |-Branch one:
% 55.96/21.51 | (1307) all_0_11_11 = n13
% 55.96/21.51 |
% 55.96/21.51 | From (1307) and (559) follows:
% 55.96/21.51 | (1308) pred(n13) = all_0_9_9
% 55.96/21.51 |
% 55.96/21.51 | From (1307) and (992) follows:
% 55.96/21.51 | (1309) succ(n13) = all_0_5_5
% 55.96/21.51 |
% 55.96/21.51 | Instantiating formula (500) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 55.96/21.51 | (1310) all_0_9_9 = n12
% 55.96/21.51 |
% 55.96/21.51 | Instantiating formula (617) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 55.96/21.51 | (1311) all_0_5_5 = n14
% 55.96/21.51 |
% 55.96/21.51 | From (1311) and (541) follows:
% 55.96/21.51 | (10328) sum(all_0_6_6, n14) = all_0_4_4
% 55.96/21.51 |
% 55.96/21.51 | From (1310)(1311) and (538) follows:
% 55.96/21.51 | (1312) sum(n12, n14) = all_0_2_2
% 55.96/21.51 |
% 55.96/21.51 | From (1310) and (427) follows:
% 55.96/21.51 | (10330) sum(n12, all_0_8_8) = all_0_7_7
% 55.96/21.51 |
% 55.96/21.51 | Instantiating formula (690) with n12, n14, all_0_2_2, n0 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n0, yields:
% 55.96/21.51 | (1316) all_0_2_2 = n0
% 55.96/21.51 |
% 55.96/21.51 | From (1316) and (630) follows:
% 55.96/21.51 | (10332) sum(n0, all_0_1_1) = all_0_0_0
% 55.96/21.51 |
% 55.96/21.51 +-Applying beta-rule and splitting (1785), into two cases.
% 55.96/21.51 |-Branch one:
% 55.96/21.51 | (1786) all_0_10_10 = n12
% 55.96/21.51 |
% 55.96/21.51 | From (1786) and (292) follows:
% 55.96/21.51 | (1787) pred(n12) = all_0_6_6
% 55.96/21.51 |
% 55.96/21.51 | From (1786) and (760) follows:
% 55.96/21.51 | (1788) succ(n12) = all_0_8_8
% 55.96/21.51 |
% 55.96/21.51 | Instantiating formula (500) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 55.96/21.51 | (1789) all_0_6_6 = n11
% 55.96/21.51 |
% 55.96/21.51 | Instantiating formula (617) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 55.96/21.51 | (1790) all_0_8_8 = n13
% 55.96/21.51 |
% 55.96/21.51 | From (1789)(1790) and (411) follows:
% 55.96/21.51 | (1791) sum(n11, n13) = all_0_1_1
% 55.96/21.51 |
% 55.96/21.51 | From (1789) and (10328) follows:
% 55.96/21.51 | (10339) sum(n11, n14) = all_0_4_4
% 55.96/21.51 |
% 55.96/21.51 | From (1790) and (10330) follows:
% 55.96/21.51 | (10340) sum(n12, n13) = all_0_7_7
% 55.96/21.51 |
% 55.96/21.51 | Instantiating formula (690) with n12, n13, all_0_7_7, n25 and discharging atoms sum(n12, n13) = all_0_7_7, sum(n12, n13) = n25, yields:
% 55.96/21.51 | (1550) all_0_7_7 = n25
% 55.96/21.51 |
% 55.96/21.51 | Instantiating formula (690) with n11, n14, all_0_4_4, n25 and discharging atoms sum(n11, n14) = all_0_4_4, sum(n11, n14) = n25, yields:
% 55.96/21.51 | (1551) all_0_4_4 = n25
% 55.96/21.51 |
% 55.96/21.51 | Instantiating formula (690) with n11, n13, all_0_1_1, n24 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n24, yields:
% 55.96/21.51 | (1081) all_0_1_1 = n24
% 55.96/21.51 |
% 55.96/21.51 | From (1550)(1551) and (590) follows:
% 55.96/21.51 | (1553) sum(n25, n25) = all_0_3_3
% 55.96/21.51 |
% 55.96/21.51 | From (1081) and (10332) follows:
% 55.96/21.51 | (1318) sum(n0, n24) = all_0_0_0
% 55.96/21.51 |
% 55.96/21.51 | Instantiating formula (690) with n25, n25, all_0_3_3, n24 and discharging atoms sum(n25, n25) = all_0_3_3, sum(n25, n25) = n24, yields:
% 55.96/21.51 | (1320) all_0_3_3 = n24
% 55.96/21.51 |
% 55.96/21.51 | Instantiating formula (690) with n0, n24, all_0_0_0, n24 and discharging atoms sum(n0, n24) = all_0_0_0, sum(n0, n24) = n24, yields:
% 55.96/21.51 | (1321) all_0_0_0 = n24
% 55.96/21.51 |
% 55.96/21.51 | Equations (1321,1320) can reduce 679 to:
% 55.96/21.51 | (1106) $false
% 55.96/21.51 |
% 55.96/21.51 |-The branch is then unsatisfiable
% 55.96/21.51 |-Branch two:
% 55.96/21.51 | (1802) ~ (all_0_10_10 = n12)
% 55.96/21.51 | (1803) 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
% 55.96/21.51 |
% 55.96/21.51 +-Applying beta-rule and splitting (1803), into two cases.
% 55.96/21.51 |-Branch one:
% 55.96/21.51 | (1804) all_0_10_10 = n11
% 55.96/21.51 |
% 55.96/21.51 | From (1804) and (292) follows:
% 55.96/21.51 | (1805) pred(n11) = all_0_6_6
% 55.96/21.51 |
% 55.96/21.51 | From (1804) and (760) follows:
% 55.96/21.51 | (1806) succ(n11) = all_0_8_8
% 55.96/21.51 |
% 55.96/21.51 | Instantiating formula (500) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 55.96/21.51 | (1807) all_0_6_6 = n10
% 55.96/21.51 |
% 55.96/21.51 | Instantiating formula (617) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 55.96/21.51 | (1808) all_0_8_8 = n12
% 55.96/21.51 |
% 55.96/21.51 | From (1807)(1808) and (411) follows:
% 55.96/21.51 | (1809) sum(n10, n12) = all_0_1_1
% 55.96/21.51 |
% 55.96/21.51 | From (1807) and (10328) follows:
% 55.96/21.51 | (10357) sum(n10, n14) = all_0_4_4
% 55.96/21.51 |
% 55.96/21.51 | From (1808) and (10330) follows:
% 55.97/21.51 | (10358) sum(n12, n12) = all_0_7_7
% 55.97/21.51 |
% 55.97/21.51 | Instantiating formula (690) with n12, n12, all_0_7_7, n24 and discharging atoms sum(n12, n12) = all_0_7_7, sum(n12, n12) = n24, yields:
% 55.97/21.51 | (1097) all_0_7_7 = n24
% 55.97/21.51 |
% 55.97/21.51 | Instantiating formula (690) with n10, n14, all_0_4_4, n24 and discharging atoms sum(n10, n14) = all_0_4_4, sum(n10, n14) = n24, yields:
% 55.97/21.51 | (1096) all_0_4_4 = n24
% 55.97/21.51 |
% 55.97/21.51 | Instantiating formula (690) with n10, n12, all_0_1_1, n22 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n22, yields:
% 55.97/21.51 | (1579) all_0_1_1 = n22
% 55.97/21.51 |
% 55.97/21.51 | From (1097)(1096) and (590) follows:
% 55.97/21.52 | (1101) sum(n24, n24) = all_0_3_3
% 55.97/21.52 |
% 55.97/21.52 | From (1579) and (10332) follows:
% 55.97/21.52 | (2250) sum(n0, n22) = all_0_0_0
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (690) with n24, n24, all_0_3_3, n22 and discharging atoms sum(n24, n24) = all_0_3_3, sum(n24, n24) = n22, yields:
% 55.97/21.52 | (1104) all_0_3_3 = n22
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (690) with n0, n22, all_0_0_0, n22 and discharging atoms sum(n0, n22) = all_0_0_0, sum(n0, n22) = n22, yields:
% 55.97/21.52 | (1102) all_0_0_0 = n22
% 55.97/21.52 |
% 55.97/21.52 | Equations (1102,1104) can reduce 679 to:
% 55.97/21.52 | (1106) $false
% 55.97/21.52 |
% 55.97/21.52 |-The branch is then unsatisfiable
% 55.97/21.52 |-Branch two:
% 55.97/21.52 | (1820) ~ (all_0_10_10 = n11)
% 55.97/21.52 | (1821) 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
% 55.97/21.52 |
% 55.97/21.52 +-Applying beta-rule and splitting (1821), into two cases.
% 55.97/21.52 |-Branch one:
% 55.97/21.52 | (1822) all_0_10_10 = n10
% 55.97/21.52 |
% 55.97/21.52 | From (1822) and (292) follows:
% 55.97/21.52 | (1823) pred(n10) = all_0_6_6
% 55.97/21.52 |
% 55.97/21.52 | From (1822) and (760) follows:
% 55.97/21.52 | (1824) succ(n10) = all_0_8_8
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (500) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 55.97/21.52 | (1825) all_0_6_6 = n9
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (617) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 55.97/21.52 | (1826) all_0_8_8 = n11
% 55.97/21.52 |
% 55.97/21.52 | From (1825)(1826) and (411) follows:
% 55.97/21.52 | (1827) sum(n9, n11) = all_0_1_1
% 55.97/21.52 |
% 55.97/21.52 | From (1825) and (10328) follows:
% 55.97/21.52 | (10375) sum(n9, n14) = all_0_4_4
% 55.97/21.52 |
% 55.97/21.52 | From (1826) and (10330) follows:
% 55.97/21.52 | (10376) sum(n12, n11) = all_0_7_7
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (690) with n12, n11, all_0_7_7, n23 and discharging atoms sum(n12, n11) = all_0_7_7, sum(n12, n11) = n23, yields:
% 55.97/21.52 | (1119) all_0_7_7 = n23
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (690) with n9, n14, all_0_4_4, n23 and discharging atoms sum(n9, n14) = all_0_4_4, sum(n9, n14) = n23, yields:
% 55.97/21.52 | (1117) all_0_4_4 = n23
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (690) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 55.97/21.52 | (1597) all_0_1_1 = n20
% 55.97/21.52 |
% 55.97/21.52 | From (1119)(1117) and (590) follows:
% 55.97/21.52 | (1121) sum(n23, n23) = all_0_3_3
% 55.97/21.52 |
% 55.97/21.52 | From (1597) and (10332) follows:
% 55.97/21.52 | (3142) sum(n0, n20) = all_0_0_0
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 55.97/21.52 | (1122) all_0_3_3 = n20
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (690) with n0, n20, all_0_0_0, n20 and discharging atoms sum(n0, n20) = all_0_0_0, sum(n0, n20) = n20, yields:
% 55.97/21.52 | (1123) all_0_0_0 = n20
% 55.97/21.52 |
% 55.97/21.52 | Equations (1123,1122) can reduce 679 to:
% 55.97/21.52 | (1106) $false
% 55.97/21.52 |
% 55.97/21.52 |-The branch is then unsatisfiable
% 55.97/21.52 |-Branch two:
% 55.97/21.52 | (1838) ~ (all_0_10_10 = n10)
% 55.97/21.52 | (1839) 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
% 55.97/21.52 |
% 55.97/21.52 +-Applying beta-rule and splitting (1839), into two cases.
% 55.97/21.52 |-Branch one:
% 55.97/21.52 | (1840) all_0_10_10 = n9
% 55.97/21.52 |
% 55.97/21.52 | From (1840) and (292) follows:
% 55.97/21.52 | (1841) pred(n9) = all_0_6_6
% 55.97/21.52 |
% 55.97/21.52 | From (1840) and (760) follows:
% 55.97/21.52 | (1842) succ(n9) = all_0_8_8
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (500) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 55.97/21.52 | (1843) all_0_6_6 = n8
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (617) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 55.97/21.52 | (1844) all_0_8_8 = n10
% 55.97/21.52 |
% 55.97/21.52 | From (1843)(1844) and (411) follows:
% 55.97/21.52 | (1845) sum(n8, n10) = all_0_1_1
% 55.97/21.52 |
% 55.97/21.52 | From (1843) and (10328) follows:
% 55.97/21.52 | (10393) sum(n8, n14) = all_0_4_4
% 55.97/21.52 |
% 55.97/21.52 | From (1844) and (10330) follows:
% 55.97/21.52 | (10394) sum(n12, n10) = all_0_7_7
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (690) with n12, n10, all_0_7_7, n22 and discharging atoms sum(n12, n10) = all_0_7_7, sum(n12, n10) = n22, yields:
% 55.97/21.52 | (1137) all_0_7_7 = n22
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (690) with n8, n14, all_0_4_4, n22 and discharging atoms sum(n8, n14) = all_0_4_4, sum(n8, n14) = n22, yields:
% 55.97/21.52 | (1135) all_0_4_4 = n22
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (690) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 55.97/21.52 | (1615) all_0_1_1 = n18
% 55.97/21.52 |
% 55.97/21.52 | From (1137)(1135) and (590) follows:
% 55.97/21.52 | (1139) sum(n22, n22) = all_0_3_3
% 55.97/21.52 |
% 55.97/21.52 | From (1615) and (10332) follows:
% 55.97/21.52 | (3998) sum(n0, n18) = all_0_0_0
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 55.97/21.52 | (1140) all_0_3_3 = n18
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (690) with n0, n18, all_0_0_0, n18 and discharging atoms sum(n0, n18) = all_0_0_0, sum(n0, n18) = n18, yields:
% 55.97/21.52 | (1141) all_0_0_0 = n18
% 55.97/21.52 |
% 55.97/21.52 | Equations (1141,1140) can reduce 679 to:
% 55.97/21.52 | (1106) $false
% 55.97/21.52 |
% 55.97/21.52 |-The branch is then unsatisfiable
% 55.97/21.52 |-Branch two:
% 55.97/21.52 | (1856) ~ (all_0_10_10 = n9)
% 55.97/21.52 | (1857) 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
% 55.97/21.52 |
% 55.97/21.52 +-Applying beta-rule and splitting (1857), into two cases.
% 55.97/21.52 |-Branch one:
% 55.97/21.52 | (1858) all_0_10_10 = n8
% 55.97/21.52 |
% 55.97/21.52 | From (1858) and (292) follows:
% 55.97/21.52 | (1859) pred(n8) = all_0_6_6
% 55.97/21.52 |
% 55.97/21.52 | From (1858) and (760) follows:
% 55.97/21.52 | (1860) succ(n8) = all_0_8_8
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 55.97/21.52 | (1861) all_0_6_6 = n7
% 55.97/21.52 |
% 55.97/21.52 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 55.97/21.52 | (1862) all_0_8_8 = n9
% 55.97/21.52 |
% 55.97/21.52 | From (1861)(1862) and (411) follows:
% 55.97/21.52 | (1863) sum(n7, n9) = all_0_1_1
% 55.97/21.52 |
% 55.97/21.52 | From (1861) and (10328) follows:
% 55.97/21.52 | (10411) sum(n7, n14) = all_0_4_4
% 55.97/21.52 |
% 55.97/21.52 | From (1862) and (10330) follows:
% 55.97/21.53 | (10412) sum(n12, n9) = all_0_7_7
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (690) with n12, n9, all_0_7_7, n21 and discharging atoms sum(n12, n9) = all_0_7_7, sum(n12, n9) = n21, yields:
% 55.97/21.53 | (1155) all_0_7_7 = n21
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (690) with n7, n14, all_0_4_4, n21 and discharging atoms sum(n7, n14) = all_0_4_4, sum(n7, n14) = n21, yields:
% 55.97/21.53 | (1153) all_0_4_4 = n21
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 55.97/21.53 | (1633) all_0_1_1 = n16
% 55.97/21.53 |
% 55.97/21.53 | From (1155)(1153) and (590) follows:
% 55.97/21.53 | (1157) sum(n21, n21) = all_0_3_3
% 55.97/21.53 |
% 55.97/21.53 | From (1633) and (10332) follows:
% 55.97/21.53 | (4818) sum(n0, n16) = all_0_0_0
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 55.97/21.53 | (1158) all_0_3_3 = n16
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (690) with n0, n16, all_0_0_0, n16 and discharging atoms sum(n0, n16) = all_0_0_0, sum(n0, n16) = n16, yields:
% 55.97/21.53 | (1159) all_0_0_0 = n16
% 55.97/21.53 |
% 55.97/21.53 | Equations (1159,1158) can reduce 679 to:
% 55.97/21.53 | (1106) $false
% 55.97/21.53 |
% 55.97/21.53 |-The branch is then unsatisfiable
% 55.97/21.53 |-Branch two:
% 55.97/21.53 | (1874) ~ (all_0_10_10 = n8)
% 55.97/21.53 | (1875) 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
% 55.97/21.53 |
% 55.97/21.53 +-Applying beta-rule and splitting (1875), into two cases.
% 55.97/21.53 |-Branch one:
% 55.97/21.53 | (1876) all_0_10_10 = n7
% 55.97/21.53 |
% 55.97/21.53 | From (1876) and (292) follows:
% 55.97/21.53 | (1877) pred(n7) = all_0_6_6
% 55.97/21.53 |
% 55.97/21.53 | From (1876) and (760) follows:
% 55.97/21.53 | (1878) succ(n7) = all_0_8_8
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 55.97/21.53 | (1879) all_0_6_6 = n6
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 55.97/21.53 | (1880) all_0_8_8 = n8
% 55.97/21.53 |
% 55.97/21.53 | From (1879)(1880) and (411) follows:
% 55.97/21.53 | (1881) sum(n6, n8) = all_0_1_1
% 55.97/21.53 |
% 55.97/21.53 | From (1879) and (10328) follows:
% 55.97/21.53 | (10429) sum(n6, n14) = all_0_4_4
% 55.97/21.53 |
% 55.97/21.53 | From (1880) and (10330) follows:
% 55.97/21.53 | (10430) sum(n12, n8) = all_0_7_7
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (690) with n12, n8, all_0_7_7, n20 and discharging atoms sum(n12, n8) = all_0_7_7, sum(n12, n8) = n20, yields:
% 55.97/21.53 | (1173) all_0_7_7 = n20
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (690) with n6, n14, all_0_4_4, n20 and discharging atoms sum(n6, n14) = all_0_4_4, sum(n6, n14) = n20, yields:
% 55.97/21.53 | (1171) all_0_4_4 = n20
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 55.97/21.53 | (1651) all_0_1_1 = n14
% 55.97/21.53 |
% 55.97/21.53 | From (1173)(1171) and (590) follows:
% 55.97/21.53 | (1175) sum(n20, n20) = all_0_3_3
% 55.97/21.53 |
% 55.97/21.53 | From (1651) and (10332) follows:
% 55.97/21.53 | (5602) sum(n0, n14) = all_0_0_0
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 55.97/21.53 | (1176) all_0_3_3 = n14
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (690) with n0, n14, all_0_0_0, n14 and discharging atoms sum(n0, n14) = all_0_0_0, sum(n0, n14) = n14, yields:
% 55.97/21.53 | (1177) all_0_0_0 = n14
% 55.97/21.53 |
% 55.97/21.53 | Equations (1177,1176) can reduce 679 to:
% 55.97/21.53 | (1106) $false
% 55.97/21.53 |
% 55.97/21.53 |-The branch is then unsatisfiable
% 55.97/21.53 |-Branch two:
% 55.97/21.53 | (1892) ~ (all_0_10_10 = n7)
% 55.97/21.53 | (1893) 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
% 55.97/21.53 |
% 55.97/21.53 +-Applying beta-rule and splitting (1893), into two cases.
% 55.97/21.53 |-Branch one:
% 55.97/21.53 | (1894) all_0_10_10 = n6
% 55.97/21.53 |
% 55.97/21.53 | From (1894) and (292) follows:
% 55.97/21.53 | (1895) pred(n6) = all_0_6_6
% 55.97/21.53 |
% 55.97/21.53 | From (1894) and (760) follows:
% 55.97/21.53 | (1896) succ(n6) = all_0_8_8
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 55.97/21.53 | (1897) all_0_6_6 = n5
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 55.97/21.53 | (1898) all_0_8_8 = n7
% 55.97/21.53 |
% 55.97/21.53 | From (1897)(1898) and (411) follows:
% 55.97/21.53 | (1899) sum(n5, n7) = all_0_1_1
% 55.97/21.53 |
% 55.97/21.53 | From (1897) and (10328) follows:
% 55.97/21.53 | (10447) sum(n5, n14) = all_0_4_4
% 55.97/21.53 |
% 55.97/21.53 | From (1898) and (10330) follows:
% 55.97/21.53 | (10448) sum(n12, n7) = all_0_7_7
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (690) with n12, n7, all_0_7_7, n19 and discharging atoms sum(n12, n7) = all_0_7_7, sum(n12, n7) = n19, yields:
% 55.97/21.53 | (1191) all_0_7_7 = n19
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (690) with n5, n14, all_0_4_4, n19 and discharging atoms sum(n5, n14) = all_0_4_4, sum(n5, n14) = n19, yields:
% 55.97/21.53 | (1189) all_0_4_4 = n19
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 55.97/21.53 | (1669) all_0_1_1 = n12
% 55.97/21.53 |
% 55.97/21.53 | From (1191)(1189) and (590) follows:
% 55.97/21.53 | (1193) sum(n19, n19) = all_0_3_3
% 55.97/21.53 |
% 55.97/21.53 | From (1669) and (10332) follows:
% 55.97/21.53 | (6350) sum(n0, n12) = all_0_0_0
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 55.97/21.53 | (1194) all_0_3_3 = n12
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (690) with n0, n12, all_0_0_0, n12 and discharging atoms sum(n0, n12) = all_0_0_0, sum(n0, n12) = n12, yields:
% 55.97/21.53 | (1195) all_0_0_0 = n12
% 55.97/21.53 |
% 55.97/21.53 | Equations (1195,1194) can reduce 679 to:
% 55.97/21.53 | (1106) $false
% 55.97/21.53 |
% 55.97/21.53 |-The branch is then unsatisfiable
% 55.97/21.53 |-Branch two:
% 55.97/21.53 | (1910) ~ (all_0_10_10 = n6)
% 55.97/21.53 | (1911) 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
% 55.97/21.53 |
% 55.97/21.53 +-Applying beta-rule and splitting (1911), into two cases.
% 55.97/21.53 |-Branch one:
% 55.97/21.53 | (1912) all_0_10_10 = n5
% 55.97/21.53 |
% 55.97/21.53 | From (1912) and (292) follows:
% 55.97/21.53 | (1913) pred(n5) = all_0_6_6
% 55.97/21.53 |
% 55.97/21.53 | From (1912) and (760) follows:
% 55.97/21.53 | (1914) succ(n5) = all_0_8_8
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 55.97/21.53 | (1915) all_0_6_6 = n4
% 55.97/21.53 |
% 55.97/21.53 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 55.97/21.53 | (1916) all_0_8_8 = n6
% 55.97/21.53 |
% 55.97/21.53 | From (1915)(1916) and (411) follows:
% 55.97/21.53 | (1917) sum(n4, n6) = all_0_1_1
% 55.97/21.53 |
% 55.97/21.53 | From (1915) and (10328) follows:
% 55.97/21.53 | (10465) sum(n4, n14) = all_0_4_4
% 55.97/21.53 |
% 55.97/21.53 | From (1916) and (10330) follows:
% 55.97/21.54 | (10466) sum(n12, n6) = all_0_7_7
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (690) with n12, n6, all_0_7_7, n18 and discharging atoms sum(n12, n6) = all_0_7_7, sum(n12, n6) = n18, yields:
% 55.97/21.54 | (1209) all_0_7_7 = n18
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (690) with n4, n14, all_0_4_4, n18 and discharging atoms sum(n4, n14) = all_0_4_4, sum(n4, n14) = n18, yields:
% 55.97/21.54 | (1207) all_0_4_4 = n18
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 55.97/21.54 | (1687) all_0_1_1 = n10
% 55.97/21.54 |
% 55.97/21.54 | From (1209)(1207) and (590) follows:
% 55.97/21.54 | (1211) sum(n18, n18) = all_0_3_3
% 55.97/21.54 |
% 55.97/21.54 | From (1687) and (10332) follows:
% 55.97/21.54 | (7062) sum(n0, n10) = all_0_0_0
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 55.97/21.54 | (1212) all_0_3_3 = n10
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (690) with n0, n10, all_0_0_0, n10 and discharging atoms sum(n0, n10) = all_0_0_0, sum(n0, n10) = n10, yields:
% 55.97/21.54 | (1213) all_0_0_0 = n10
% 55.97/21.54 |
% 55.97/21.54 | Equations (1213,1212) can reduce 679 to:
% 55.97/21.54 | (1106) $false
% 55.97/21.54 |
% 55.97/21.54 |-The branch is then unsatisfiable
% 55.97/21.54 |-Branch two:
% 55.97/21.54 | (1928) ~ (all_0_10_10 = n5)
% 55.97/21.54 | (1929) 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
% 55.97/21.54 |
% 55.97/21.54 +-Applying beta-rule and splitting (1929), into two cases.
% 55.97/21.54 |-Branch one:
% 55.97/21.54 | (1930) all_0_10_10 = n4
% 55.97/21.54 |
% 55.97/21.54 | From (1930) and (292) follows:
% 55.97/21.54 | (1931) pred(n4) = all_0_6_6
% 55.97/21.54 |
% 55.97/21.54 | From (1930) and (760) follows:
% 55.97/21.54 | (1932) succ(n4) = all_0_8_8
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 55.97/21.54 | (1933) all_0_6_6 = n3
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 55.97/21.54 | (1934) all_0_8_8 = n5
% 55.97/21.54 |
% 55.97/21.54 | From (1933)(1934) and (411) follows:
% 55.97/21.54 | (1935) sum(n3, n5) = all_0_1_1
% 55.97/21.54 |
% 55.97/21.54 | From (1933) and (10328) follows:
% 55.97/21.54 | (10483) sum(n3, n14) = all_0_4_4
% 55.97/21.54 |
% 55.97/21.54 | From (1934) and (10330) follows:
% 55.97/21.54 | (10484) sum(n12, n5) = all_0_7_7
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (690) with n12, n5, all_0_7_7, n17 and discharging atoms sum(n12, n5) = all_0_7_7, sum(n12, n5) = n17, yields:
% 55.97/21.54 | (1227) all_0_7_7 = n17
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (690) with n3, n14, all_0_4_4, n17 and discharging atoms sum(n3, n14) = all_0_4_4, sum(n3, n14) = n17, yields:
% 55.97/21.54 | (1225) all_0_4_4 = n17
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 55.97/21.54 | (1705) all_0_1_1 = n8
% 55.97/21.54 |
% 55.97/21.54 | From (1227)(1225) and (590) follows:
% 55.97/21.54 | (1229) sum(n17, n17) = all_0_3_3
% 55.97/21.54 |
% 55.97/21.54 | From (1705) and (10332) follows:
% 55.97/21.54 | (7738) sum(n0, n8) = all_0_0_0
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 55.97/21.54 | (1230) all_0_3_3 = n8
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (690) with n0, n8, all_0_0_0, n8 and discharging atoms sum(n0, n8) = all_0_0_0, sum(n0, n8) = n8, yields:
% 55.97/21.54 | (1231) all_0_0_0 = n8
% 55.97/21.54 |
% 55.97/21.54 | Equations (1231,1230) can reduce 679 to:
% 55.97/21.54 | (1106) $false
% 55.97/21.54 |
% 55.97/21.54 |-The branch is then unsatisfiable
% 55.97/21.54 |-Branch two:
% 55.97/21.54 | (1946) ~ (all_0_10_10 = n4)
% 55.97/21.54 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 55.97/21.54 |
% 55.97/21.54 +-Applying beta-rule and splitting (1947), into two cases.
% 55.97/21.54 |-Branch one:
% 55.97/21.54 | (1948) all_0_10_10 = n3
% 55.97/21.54 |
% 55.97/21.54 | From (1948) and (292) follows:
% 55.97/21.54 | (1949) pred(n3) = all_0_6_6
% 55.97/21.54 |
% 55.97/21.54 | From (1948) and (760) follows:
% 55.97/21.54 | (1950) succ(n3) = all_0_8_8
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 55.97/21.54 | (1951) all_0_6_6 = n2
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 55.97/21.54 | (1952) all_0_8_8 = n4
% 55.97/21.54 |
% 55.97/21.54 | From (1951)(1952) and (411) follows:
% 55.97/21.54 | (1953) sum(n2, n4) = all_0_1_1
% 55.97/21.54 |
% 55.97/21.54 | From (1951) and (10328) follows:
% 55.97/21.54 | (10501) sum(n2, n14) = all_0_4_4
% 55.97/21.54 |
% 55.97/21.54 | From (1952) and (10330) follows:
% 55.97/21.54 | (10502) sum(n12, n4) = all_0_7_7
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (690) with n12, n4, all_0_7_7, n16 and discharging atoms sum(n12, n4) = all_0_7_7, sum(n12, n4) = n16, yields:
% 55.97/21.54 | (1245) all_0_7_7 = n16
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (690) with n2, n14, all_0_4_4, n16 and discharging atoms sum(n2, n14) = all_0_4_4, sum(n2, n14) = n16, yields:
% 55.97/21.54 | (1243) all_0_4_4 = n16
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 55.97/21.54 | (1723) all_0_1_1 = n6
% 55.97/21.54 |
% 55.97/21.54 | From (1245)(1243) and (590) follows:
% 55.97/21.54 | (1247) sum(n16, n16) = all_0_3_3
% 55.97/21.54 |
% 55.97/21.54 | From (1723) and (10332) follows:
% 55.97/21.54 | (8379) sum(n0, n6) = all_0_0_0
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 55.97/21.54 | (1248) all_0_3_3 = n6
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (690) with n0, n6, all_0_0_0, n6 and discharging atoms sum(n0, n6) = all_0_0_0, sum(n0, n6) = n6, yields:
% 55.97/21.54 | (1249) all_0_0_0 = n6
% 55.97/21.54 |
% 55.97/21.54 | Equations (1249,1248) can reduce 679 to:
% 55.97/21.54 | (1106) $false
% 55.97/21.54 |
% 55.97/21.54 |-The branch is then unsatisfiable
% 55.97/21.54 |-Branch two:
% 55.97/21.54 | (1964) ~ (all_0_10_10 = n3)
% 55.97/21.54 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 55.97/21.54 |
% 55.97/21.54 +-Applying beta-rule and splitting (1965), into two cases.
% 55.97/21.54 |-Branch one:
% 55.97/21.54 | (1966) all_0_10_10 = n2
% 55.97/21.54 |
% 55.97/21.54 | From (1966) and (292) follows:
% 55.97/21.54 | (1967) pred(n2) = all_0_6_6
% 55.97/21.54 |
% 55.97/21.54 | From (1966) and (760) follows:
% 55.97/21.54 | (1968) succ(n2) = all_0_8_8
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 55.97/21.54 | (1969) all_0_6_6 = n1
% 55.97/21.54 |
% 55.97/21.54 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 55.97/21.54 | (1970) all_0_8_8 = n3
% 55.97/21.54 |
% 55.97/21.54 | From (1969)(1970) and (411) follows:
% 55.97/21.54 | (1971) sum(n1, n3) = all_0_1_1
% 55.97/21.54 |
% 55.97/21.54 | From (1969) and (10328) follows:
% 55.97/21.55 | (10519) sum(n1, n14) = all_0_4_4
% 55.97/21.55 |
% 55.97/21.55 | From (1970) and (10330) follows:
% 55.97/21.55 | (10520) sum(n12, n3) = all_0_7_7
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (690) with n12, n3, all_0_7_7, n15 and discharging atoms sum(n12, n3) = all_0_7_7, sum(n12, n3) = n15, yields:
% 55.97/21.55 | (1263) all_0_7_7 = n15
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (690) with n1, n14, all_0_4_4, n15 and discharging atoms sum(n1, n14) = all_0_4_4, sum(n1, n14) = n15, yields:
% 55.97/21.55 | (1261) all_0_4_4 = n15
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 55.97/21.55 | (1741) all_0_1_1 = n4
% 55.97/21.55 |
% 55.97/21.55 | From (1263)(1261) and (590) follows:
% 55.97/21.55 | (1265) sum(n15, n15) = all_0_3_3
% 55.97/21.55 |
% 55.97/21.55 | From (1741) and (10332) follows:
% 55.97/21.55 | (8983) sum(n0, n4) = all_0_0_0
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 55.97/21.55 | (1266) all_0_3_3 = n4
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (690) with n0, n4, all_0_0_0, n4 and discharging atoms sum(n0, n4) = all_0_0_0, sum(n0, n4) = n4, yields:
% 55.97/21.55 | (1267) all_0_0_0 = n4
% 55.97/21.55 |
% 55.97/21.55 | Equations (1267,1266) can reduce 679 to:
% 55.97/21.55 | (1106) $false
% 55.97/21.55 |
% 55.97/21.55 |-The branch is then unsatisfiable
% 55.97/21.55 |-Branch two:
% 55.97/21.55 | (1982) ~ (all_0_10_10 = n2)
% 55.97/21.55 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 55.97/21.55 |
% 55.97/21.55 +-Applying beta-rule and splitting (1983), into two cases.
% 55.97/21.55 |-Branch one:
% 55.97/21.55 | (1984) all_0_10_10 = n1
% 55.97/21.55 |
% 55.97/21.55 | From (1984) and (292) follows:
% 55.97/21.55 | (1985) pred(n1) = all_0_6_6
% 55.97/21.55 |
% 55.97/21.55 | From (1984) and (760) follows:
% 55.97/21.55 | (1986) succ(n1) = all_0_8_8
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 55.97/21.55 | (1987) all_0_6_6 = n0
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 55.97/21.55 | (1988) all_0_8_8 = n2
% 55.97/21.55 |
% 55.97/21.55 | From (1987)(1988) and (411) follows:
% 55.97/21.55 | (1989) sum(n0, n2) = all_0_1_1
% 55.97/21.55 |
% 55.97/21.55 | From (1987) and (10328) follows:
% 55.97/21.55 | (10537) sum(n0, n14) = all_0_4_4
% 55.97/21.55 |
% 55.97/21.55 | From (1988) and (10330) follows:
% 55.97/21.55 | (10538) sum(n12, n2) = all_0_7_7
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (690) with n12, n2, all_0_7_7, n14 and discharging atoms sum(n12, n2) = all_0_7_7, sum(n12, n2) = n14, yields:
% 55.97/21.55 | (1281) all_0_7_7 = n14
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (690) with n0, n14, all_0_4_4, n14 and discharging atoms sum(n0, n14) = all_0_4_4, sum(n0, n14) = n14, yields:
% 55.97/21.55 | (1279) all_0_4_4 = n14
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 55.97/21.55 | (1759) all_0_1_1 = n2
% 55.97/21.55 |
% 55.97/21.55 | From (1281)(1279) and (590) follows:
% 55.97/21.55 | (1283) sum(n14, n14) = all_0_3_3
% 55.97/21.55 |
% 55.97/21.55 | From (1759) and (10332) follows:
% 55.97/21.55 | (9551) sum(n0, n2) = all_0_0_0
% 55.97/21.55 |
% 55.97/21.55 | From (1759) and (1989) follows:
% 55.97/21.55 | (327) sum(n0, n2) = n2
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 55.97/21.55 | (1284) all_0_3_3 = n2
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (690) with n0, n2, all_0_0_0, n2 and discharging atoms sum(n0, n2) = all_0_0_0, sum(n0, n2) = n2, yields:
% 55.97/21.55 | (1285) all_0_0_0 = n2
% 55.97/21.55 |
% 55.97/21.55 | Equations (1285,1284) can reduce 679 to:
% 55.97/21.55 | (1106) $false
% 55.97/21.55 |
% 55.97/21.55 |-The branch is then unsatisfiable
% 55.97/21.55 |-Branch two:
% 55.97/21.55 | (2002) ~ (all_0_10_10 = n1)
% 55.97/21.55 | (2003) all_0_10_10 = n0
% 55.97/21.55 |
% 55.97/21.55 | From (2003) and (292) follows:
% 55.97/21.55 | (2004) pred(n0) = all_0_6_6
% 55.97/21.55 |
% 55.97/21.55 | From (2003) and (760) follows:
% 55.97/21.55 | (2005) succ(n0) = all_0_8_8
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 55.97/21.55 | (2006) all_0_6_6 = n25
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 55.97/21.55 | (2007) all_0_8_8 = n1
% 55.97/21.55 |
% 55.97/21.55 | From (2006)(2007) and (411) follows:
% 55.97/21.55 | (2008) sum(n25, n1) = all_0_1_1
% 55.97/21.55 |
% 55.97/21.55 | From (2006) and (10328) follows:
% 55.97/21.55 | (10555) sum(n25, n14) = all_0_4_4
% 55.97/21.55 |
% 55.97/21.55 | From (2007) and (10330) follows:
% 55.97/21.55 | (10556) sum(n12, n1) = all_0_7_7
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (690) with n25, n14, all_0_4_4, n13 and discharging atoms sum(n25, n14) = all_0_4_4, sum(n25, n14) = n13, yields:
% 55.97/21.55 | (1297) all_0_4_4 = n13
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 55.97/21.55 | (1777) all_0_1_1 = n0
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (690) with n12, n1, all_0_7_7, n13 and discharging atoms sum(n12, n1) = all_0_7_7, sum(n12, n1) = n13, yields:
% 55.97/21.55 | (1299) all_0_7_7 = n13
% 55.97/21.55 |
% 55.97/21.55 | From (1299)(1297) and (590) follows:
% 55.97/21.55 | (1301) sum(n13, n13) = all_0_3_3
% 55.97/21.55 |
% 55.97/21.55 | From (1777) and (10332) follows:
% 55.97/21.55 | (10081) sum(n0, n0) = all_0_0_0
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 55.97/21.55 | (1302) all_0_3_3 = n0
% 55.97/21.55 |
% 55.97/21.55 | Instantiating formula (690) with n0, n0, all_0_0_0, n0 and discharging atoms sum(n0, n0) = all_0_0_0, sum(n0, n0) = n0, yields:
% 55.97/21.55 | (1303) all_0_0_0 = n0
% 55.97/21.55 |
% 55.97/21.55 | Equations (1303,1302) can reduce 679 to:
% 55.97/21.55 | (1106) $false
% 55.97/21.55 |
% 55.97/21.55 |-The branch is then unsatisfiable
% 55.97/21.56 |-Branch two:
% 55.97/21.56 | (1323) ~ (all_0_11_11 = n13)
% 55.97/21.56 | (1324) 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
% 55.97/21.56 |
% 55.97/21.56 +-Applying beta-rule and splitting (1785), into two cases.
% 55.97/21.56 |-Branch one:
% 55.97/21.56 | (1786) all_0_10_10 = n12
% 55.97/21.56 |
% 55.97/21.56 | From (1786) and (292) follows:
% 55.97/21.56 | (1787) pred(n12) = all_0_6_6
% 55.97/21.56 |
% 55.97/21.56 | From (1786) and (760) follows:
% 55.97/21.56 | (1788) succ(n12) = all_0_8_8
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (500) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 55.97/21.56 | (1789) all_0_6_6 = n11
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (617) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 55.97/21.56 | (1790) all_0_8_8 = n13
% 55.97/21.56 |
% 55.97/21.56 | From (1789) and (1787) follows:
% 55.97/21.56 | (135) pred(n12) = n11
% 55.97/21.56 |
% 55.97/21.56 | From (1790) and (1788) follows:
% 55.97/21.56 | (308) succ(n12) = n13
% 55.97/21.56 |
% 55.97/21.56 | From (1789) and (541) follows:
% 55.97/21.56 | (10574) sum(n11, all_0_5_5) = all_0_4_4
% 55.97/21.56 |
% 55.97/21.56 | From (1789)(1790) and (411) follows:
% 55.97/21.56 | (1791) sum(n11, n13) = all_0_1_1
% 55.97/21.56 |
% 55.97/21.56 | From (1790) and (427) follows:
% 55.97/21.56 | (10576) sum(all_0_9_9, n13) = all_0_7_7
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (690) with n11, n13, all_0_1_1, n24 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n24, yields:
% 55.97/21.56 | (1081) all_0_1_1 = n24
% 55.97/21.56 |
% 55.97/21.56 | From (1081) and (630) follows:
% 55.97/21.56 | (1082) sum(all_0_2_2, n24) = all_0_0_0
% 55.97/21.56 |
% 55.97/21.56 | From (1081) and (1791) follows:
% 55.97/21.56 | (38) sum(n11, n13) = n24
% 55.97/21.56 |
% 55.97/21.56 +-Applying beta-rule and splitting (1324), into two cases.
% 55.97/21.56 |-Branch one:
% 55.97/21.56 | (1325) all_0_11_11 = n12
% 55.97/21.56 |
% 55.97/21.56 | From (1325) and (559) follows:
% 55.97/21.56 | (1326) pred(n12) = all_0_9_9
% 55.97/21.56 |
% 55.97/21.56 | From (1325) and (992) follows:
% 55.97/21.56 | (1327) succ(n12) = all_0_5_5
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (500) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 55.97/21.56 | (1328) all_0_9_9 = n11
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (617) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 55.97/21.56 | (1329) all_0_5_5 = n13
% 55.97/21.56 |
% 55.97/21.56 | From (1328)(1329) and (538) follows:
% 55.97/21.56 | (1330) sum(n11, n13) = all_0_2_2
% 55.97/21.56 |
% 55.97/21.56 | From (1328) and (10576) follows:
% 55.97/21.56 | (10586) sum(n11, n13) = all_0_7_7
% 55.97/21.56 |
% 55.97/21.56 | From (1329) and (10574) follows:
% 55.97/21.56 | (10587) sum(n11, n13) = all_0_4_4
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (690) with n11, n13, all_0_2_2, n24 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n24, yields:
% 55.97/21.56 | (1092) all_0_2_2 = n24
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (690) 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:
% 55.97/21.56 | (1093) all_0_2_2 = all_0_4_4
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (690) 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:
% 55.97/21.56 | (1094) all_0_2_2 = all_0_7_7
% 55.97/21.56 |
% 55.97/21.56 | Combining equations (1094,1093) yields a new equation:
% 55.97/21.56 | (1095) all_0_4_4 = all_0_7_7
% 55.97/21.56 |
% 55.97/21.56 | Combining equations (1092,1093) yields a new equation:
% 55.97/21.56 | (1096) all_0_4_4 = n24
% 55.97/21.56 |
% 55.97/21.56 | Combining equations (1096,1095) yields a new equation:
% 55.97/21.56 | (1097) all_0_7_7 = n24
% 55.97/21.56 |
% 55.97/21.56 | Combining equations (1097,1095) yields a new equation:
% 55.97/21.56 | (1096) all_0_4_4 = n24
% 55.97/21.56 |
% 55.97/21.56 | Combining equations (1096,1093) yields a new equation:
% 55.97/21.56 | (1092) all_0_2_2 = n24
% 55.97/21.56 |
% 55.97/21.56 | From (1092) and (1082) follows:
% 55.97/21.56 | (1100) sum(n24, n24) = all_0_0_0
% 55.97/21.56 |
% 55.97/21.56 | From (1097)(1096) and (590) follows:
% 55.97/21.56 | (1101) sum(n24, n24) = all_0_3_3
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (690) with n24, n24, all_0_0_0, n22 and discharging atoms sum(n24, n24) = all_0_0_0, sum(n24, n24) = n22, yields:
% 55.97/21.56 | (1102) all_0_0_0 = n22
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (690) with n24, n24, all_0_3_3, all_0_0_0 and discharging atoms sum(n24, n24) = all_0_0_0, sum(n24, n24) = all_0_3_3, yields:
% 55.97/21.56 | (1103) all_0_0_0 = all_0_3_3
% 55.97/21.56 |
% 55.97/21.56 | Combining equations (1102,1103) yields a new equation:
% 55.97/21.56 | (1104) all_0_3_3 = n22
% 55.97/21.56 |
% 55.97/21.56 | Combining equations (1104,1103) yields a new equation:
% 55.97/21.56 | (1102) all_0_0_0 = n22
% 55.97/21.56 |
% 55.97/21.56 | Equations (1102,1104) can reduce 679 to:
% 55.97/21.56 | (1106) $false
% 55.97/21.56 |
% 55.97/21.56 |-The branch is then unsatisfiable
% 55.97/21.56 |-Branch two:
% 55.97/21.56 | (1341) ~ (all_0_11_11 = n12)
% 55.97/21.56 | (1342) 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
% 55.97/21.56 |
% 55.97/21.56 +-Applying beta-rule and splitting (1342), into two cases.
% 55.97/21.56 |-Branch one:
% 55.97/21.56 | (1343) all_0_11_11 = n11
% 55.97/21.56 |
% 55.97/21.56 | From (1343) and (559) follows:
% 55.97/21.56 | (1344) pred(n11) = all_0_9_9
% 55.97/21.56 |
% 55.97/21.56 | From (1343) and (992) follows:
% 55.97/21.56 | (1345) succ(n11) = all_0_5_5
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (500) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 55.97/21.56 | (1346) all_0_9_9 = n10
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (617) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 55.97/21.56 | (1347) all_0_5_5 = n12
% 55.97/21.56 |
% 55.97/21.56 | From (1346)(1347) and (538) follows:
% 55.97/21.56 | (1348) sum(n10, n12) = all_0_2_2
% 55.97/21.56 |
% 55.97/21.56 | From (1346) and (10576) follows:
% 55.97/21.56 | (10611) sum(n10, n13) = all_0_7_7
% 55.97/21.56 |
% 55.97/21.56 | From (1347) and (10574) follows:
% 55.97/21.56 | (10612) sum(n11, n12) = all_0_4_4
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (690) with n11, n12, all_0_4_4, n23 and discharging atoms sum(n11, n12) = all_0_4_4, sum(n11, n12) = n23, yields:
% 55.97/21.56 | (1117) all_0_4_4 = n23
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (690) with n10, n13, all_0_7_7, n23 and discharging atoms sum(n10, n13) = all_0_7_7, sum(n10, n13) = n23, yields:
% 55.97/21.56 | (1119) all_0_7_7 = n23
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (690) with n10, n12, all_0_2_2, n22 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n22, yields:
% 55.97/21.56 | (1118) all_0_2_2 = n22
% 55.97/21.56 |
% 55.97/21.56 | From (1118) and (1082) follows:
% 55.97/21.56 | (1120) sum(n22, n24) = all_0_0_0
% 55.97/21.56 |
% 55.97/21.56 | From (1119)(1117) and (590) follows:
% 55.97/21.56 | (1121) sum(n23, n23) = all_0_3_3
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 55.97/21.56 | (1122) all_0_3_3 = n20
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (690) with n22, n24, all_0_0_0, n20 and discharging atoms sum(n22, n24) = all_0_0_0, sum(n22, n24) = n20, yields:
% 55.97/21.56 | (1123) all_0_0_0 = n20
% 55.97/21.56 |
% 55.97/21.56 | Equations (1123,1122) can reduce 679 to:
% 55.97/21.56 | (1106) $false
% 55.97/21.56 |
% 55.97/21.56 |-The branch is then unsatisfiable
% 55.97/21.56 |-Branch two:
% 55.97/21.56 | (1359) ~ (all_0_11_11 = n11)
% 55.97/21.56 | (1360) 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
% 55.97/21.56 |
% 55.97/21.56 +-Applying beta-rule and splitting (1360), into two cases.
% 55.97/21.56 |-Branch one:
% 55.97/21.56 | (1361) all_0_11_11 = n10
% 55.97/21.56 |
% 55.97/21.56 | From (1361) and (559) follows:
% 55.97/21.56 | (1362) pred(n10) = all_0_9_9
% 55.97/21.56 |
% 55.97/21.56 | From (1361) and (992) follows:
% 55.97/21.56 | (1363) succ(n10) = all_0_5_5
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (500) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 55.97/21.56 | (1364) all_0_9_9 = n9
% 55.97/21.56 |
% 55.97/21.56 | Instantiating formula (617) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 55.97/21.56 | (1365) all_0_5_5 = n11
% 55.97/21.56 |
% 55.97/21.56 | From (1364)(1365) and (538) follows:
% 55.97/21.56 | (1366) sum(n9, n11) = all_0_2_2
% 55.97/21.56 |
% 55.97/21.56 | From (1364) and (10576) follows:
% 55.97/21.57 | (10629) sum(n9, n13) = all_0_7_7
% 55.97/21.57 |
% 55.97/21.57 | From (1365) and (10574) follows:
% 55.97/21.57 | (10630) sum(n11, n11) = all_0_4_4
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (690) with n11, n11, all_0_4_4, n22 and discharging atoms sum(n11, n11) = all_0_4_4, sum(n11, n11) = n22, yields:
% 55.97/21.57 | (1135) all_0_4_4 = n22
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (690) with n9, n13, all_0_7_7, n22 and discharging atoms sum(n9, n13) = all_0_7_7, sum(n9, n13) = n22, yields:
% 55.97/21.57 | (1137) all_0_7_7 = n22
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (690) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 55.97/21.57 | (1136) all_0_2_2 = n20
% 55.97/21.57 |
% 55.97/21.57 | From (1136) and (1082) follows:
% 55.97/21.57 | (1138) sum(n20, n24) = all_0_0_0
% 55.97/21.57 |
% 55.97/21.57 | From (1137)(1135) and (590) follows:
% 55.97/21.57 | (1139) sum(n22, n22) = all_0_3_3
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 55.97/21.57 | (1140) all_0_3_3 = n18
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (690) with n20, n24, all_0_0_0, n18 and discharging atoms sum(n20, n24) = all_0_0_0, sum(n20, n24) = n18, yields:
% 55.97/21.57 | (1141) all_0_0_0 = n18
% 55.97/21.57 |
% 55.97/21.57 | Equations (1141,1140) can reduce 679 to:
% 55.97/21.57 | (1106) $false
% 55.97/21.57 |
% 55.97/21.57 |-The branch is then unsatisfiable
% 55.97/21.57 |-Branch two:
% 55.97/21.57 | (1377) ~ (all_0_11_11 = n10)
% 55.97/21.57 | (1378) 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
% 55.97/21.57 |
% 55.97/21.57 +-Applying beta-rule and splitting (1378), into two cases.
% 55.97/21.57 |-Branch one:
% 55.97/21.57 | (1379) all_0_11_11 = n9
% 55.97/21.57 |
% 55.97/21.57 | From (1379) and (559) follows:
% 55.97/21.57 | (1380) pred(n9) = all_0_9_9
% 55.97/21.57 |
% 55.97/21.57 | From (1379) and (992) follows:
% 55.97/21.57 | (1381) succ(n9) = all_0_5_5
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 55.97/21.57 | (1382) all_0_9_9 = n8
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 55.97/21.57 | (1383) all_0_5_5 = n10
% 55.97/21.57 |
% 55.97/21.57 | From (1382)(1383) and (538) follows:
% 55.97/21.57 | (1384) sum(n8, n10) = all_0_2_2
% 55.97/21.57 |
% 55.97/21.57 | From (1382) and (10576) follows:
% 55.97/21.57 | (10647) sum(n8, n13) = all_0_7_7
% 55.97/21.57 |
% 55.97/21.57 | From (1383) and (10574) follows:
% 55.97/21.57 | (10648) sum(n11, n10) = all_0_4_4
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (690) with n11, n10, all_0_4_4, n21 and discharging atoms sum(n11, n10) = all_0_4_4, sum(n11, n10) = n21, yields:
% 55.97/21.57 | (1153) all_0_4_4 = n21
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (690) with n8, n13, all_0_7_7, n21 and discharging atoms sum(n8, n13) = all_0_7_7, sum(n8, n13) = n21, yields:
% 55.97/21.57 | (1155) all_0_7_7 = n21
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 55.97/21.57 | (1154) all_0_2_2 = n18
% 55.97/21.57 |
% 55.97/21.57 | From (1154) and (1082) follows:
% 55.97/21.57 | (1156) sum(n18, n24) = all_0_0_0
% 55.97/21.57 |
% 55.97/21.57 | From (1155)(1153) and (590) follows:
% 55.97/21.57 | (1157) sum(n21, n21) = all_0_3_3
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 55.97/21.57 | (1158) all_0_3_3 = n16
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (690) with n18, n24, all_0_0_0, n16 and discharging atoms sum(n18, n24) = all_0_0_0, sum(n18, n24) = n16, yields:
% 55.97/21.57 | (1159) all_0_0_0 = n16
% 55.97/21.57 |
% 55.97/21.57 | Equations (1159,1158) can reduce 679 to:
% 55.97/21.57 | (1106) $false
% 55.97/21.57 |
% 55.97/21.57 |-The branch is then unsatisfiable
% 55.97/21.57 |-Branch two:
% 55.97/21.57 | (1395) ~ (all_0_11_11 = n9)
% 55.97/21.57 | (1396) 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
% 55.97/21.57 |
% 55.97/21.57 +-Applying beta-rule and splitting (1396), into two cases.
% 55.97/21.57 |-Branch one:
% 55.97/21.57 | (1397) all_0_11_11 = n8
% 55.97/21.57 |
% 55.97/21.57 | From (1397) and (559) follows:
% 55.97/21.57 | (1398) pred(n8) = all_0_9_9
% 55.97/21.57 |
% 55.97/21.57 | From (1397) and (992) follows:
% 55.97/21.57 | (1399) succ(n8) = all_0_5_5
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 55.97/21.57 | (1400) all_0_9_9 = n7
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 55.97/21.57 | (1401) all_0_5_5 = n9
% 55.97/21.57 |
% 55.97/21.57 | From (1400)(1401) and (538) follows:
% 55.97/21.57 | (1402) sum(n7, n9) = all_0_2_2
% 55.97/21.57 |
% 55.97/21.57 | From (1400) and (10576) follows:
% 55.97/21.57 | (10665) sum(n7, n13) = all_0_7_7
% 55.97/21.57 |
% 55.97/21.57 | From (1401) and (10574) follows:
% 55.97/21.57 | (10666) sum(n11, n9) = all_0_4_4
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (690) with n11, n9, all_0_4_4, n20 and discharging atoms sum(n11, n9) = all_0_4_4, sum(n11, n9) = n20, yields:
% 55.97/21.57 | (1171) all_0_4_4 = n20
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (690) with n7, n13, all_0_7_7, n20 and discharging atoms sum(n7, n13) = all_0_7_7, sum(n7, n13) = n20, yields:
% 55.97/21.57 | (1173) all_0_7_7 = n20
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 55.97/21.57 | (1172) all_0_2_2 = n16
% 55.97/21.57 |
% 55.97/21.57 | From (1172) and (1082) follows:
% 55.97/21.57 | (1174) sum(n16, n24) = all_0_0_0
% 55.97/21.57 |
% 55.97/21.57 | From (1173)(1171) and (590) follows:
% 55.97/21.57 | (1175) sum(n20, n20) = all_0_3_3
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 55.97/21.57 | (1176) all_0_3_3 = n14
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (690) with n16, n24, all_0_0_0, n14 and discharging atoms sum(n16, n24) = all_0_0_0, sum(n16, n24) = n14, yields:
% 55.97/21.57 | (1177) all_0_0_0 = n14
% 55.97/21.57 |
% 55.97/21.57 | Equations (1177,1176) can reduce 679 to:
% 55.97/21.57 | (1106) $false
% 55.97/21.57 |
% 55.97/21.57 |-The branch is then unsatisfiable
% 55.97/21.57 |-Branch two:
% 55.97/21.57 | (1413) ~ (all_0_11_11 = n8)
% 55.97/21.57 | (1414) 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
% 55.97/21.57 |
% 55.97/21.57 +-Applying beta-rule and splitting (1414), into two cases.
% 55.97/21.57 |-Branch one:
% 55.97/21.57 | (1415) all_0_11_11 = n7
% 55.97/21.57 |
% 55.97/21.57 | From (1415) and (559) follows:
% 55.97/21.57 | (1416) pred(n7) = all_0_9_9
% 55.97/21.57 |
% 55.97/21.57 | From (1415) and (992) follows:
% 55.97/21.57 | (1417) succ(n7) = all_0_5_5
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 55.97/21.57 | (1418) all_0_9_9 = n6
% 55.97/21.57 |
% 55.97/21.57 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 55.97/21.57 | (1419) all_0_5_5 = n8
% 55.97/21.57 |
% 55.97/21.57 | From (1418)(1419) and (538) follows:
% 55.97/21.57 | (1420) sum(n6, n8) = all_0_2_2
% 55.97/21.57 |
% 55.97/21.57 | From (1418) and (10576) follows:
% 55.97/21.57 | (10683) sum(n6, n13) = all_0_7_7
% 55.97/21.57 |
% 55.97/21.57 | From (1419) and (10574) follows:
% 55.97/21.58 | (10684) sum(n11, n8) = all_0_4_4
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n11, n8, all_0_4_4, n19 and discharging atoms sum(n11, n8) = all_0_4_4, sum(n11, n8) = n19, yields:
% 55.97/21.58 | (1189) all_0_4_4 = n19
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n6, n13, all_0_7_7, n19 and discharging atoms sum(n6, n13) = all_0_7_7, sum(n6, n13) = n19, yields:
% 55.97/21.58 | (1191) all_0_7_7 = n19
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 55.97/21.58 | (1190) all_0_2_2 = n14
% 55.97/21.58 |
% 55.97/21.58 | From (1190) and (1082) follows:
% 55.97/21.58 | (1192) sum(n14, n24) = all_0_0_0
% 55.97/21.58 |
% 55.97/21.58 | From (1191)(1189) and (590) follows:
% 55.97/21.58 | (1193) sum(n19, n19) = all_0_3_3
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 55.97/21.58 | (1194) all_0_3_3 = n12
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n14, n24, all_0_0_0, n12 and discharging atoms sum(n14, n24) = all_0_0_0, sum(n14, n24) = n12, yields:
% 55.97/21.58 | (1195) all_0_0_0 = n12
% 55.97/21.58 |
% 55.97/21.58 | Equations (1195,1194) can reduce 679 to:
% 55.97/21.58 | (1106) $false
% 55.97/21.58 |
% 55.97/21.58 |-The branch is then unsatisfiable
% 55.97/21.58 |-Branch two:
% 55.97/21.58 | (1431) ~ (all_0_11_11 = n7)
% 55.97/21.58 | (1432) 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
% 55.97/21.58 |
% 55.97/21.58 +-Applying beta-rule and splitting (1432), into two cases.
% 55.97/21.58 |-Branch one:
% 55.97/21.58 | (1433) all_0_11_11 = n6
% 55.97/21.58 |
% 55.97/21.58 | From (1433) and (559) follows:
% 55.97/21.58 | (1434) pred(n6) = all_0_9_9
% 55.97/21.58 |
% 55.97/21.58 | From (1433) and (992) follows:
% 55.97/21.58 | (1435) succ(n6) = all_0_5_5
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 55.97/21.58 | (1436) all_0_9_9 = n5
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 55.97/21.58 | (1437) all_0_5_5 = n7
% 55.97/21.58 |
% 55.97/21.58 | From (1436)(1437) and (538) follows:
% 55.97/21.58 | (1438) sum(n5, n7) = all_0_2_2
% 55.97/21.58 |
% 55.97/21.58 | From (1436) and (10576) follows:
% 55.97/21.58 | (10701) sum(n5, n13) = all_0_7_7
% 55.97/21.58 |
% 55.97/21.58 | From (1437) and (10574) follows:
% 55.97/21.58 | (10702) sum(n11, n7) = all_0_4_4
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n11, n7, all_0_4_4, n18 and discharging atoms sum(n11, n7) = all_0_4_4, sum(n11, n7) = n18, yields:
% 55.97/21.58 | (1207) all_0_4_4 = n18
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n5, n13, all_0_7_7, n18 and discharging atoms sum(n5, n13) = all_0_7_7, sum(n5, n13) = n18, yields:
% 55.97/21.58 | (1209) all_0_7_7 = n18
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 55.97/21.58 | (1208) all_0_2_2 = n12
% 55.97/21.58 |
% 55.97/21.58 | From (1208) and (1082) follows:
% 55.97/21.58 | (1210) sum(n12, n24) = all_0_0_0
% 55.97/21.58 |
% 55.97/21.58 | From (1209)(1207) and (590) follows:
% 55.97/21.58 | (1211) sum(n18, n18) = all_0_3_3
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 55.97/21.58 | (1212) all_0_3_3 = n10
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n12, n24, all_0_0_0, n10 and discharging atoms sum(n12, n24) = all_0_0_0, sum(n12, n24) = n10, yields:
% 55.97/21.58 | (1213) all_0_0_0 = n10
% 55.97/21.58 |
% 55.97/21.58 | Equations (1213,1212) can reduce 679 to:
% 55.97/21.58 | (1106) $false
% 55.97/21.58 |
% 55.97/21.58 |-The branch is then unsatisfiable
% 55.97/21.58 |-Branch two:
% 55.97/21.58 | (1449) ~ (all_0_11_11 = n6)
% 55.97/21.58 | (1450) 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
% 55.97/21.58 |
% 55.97/21.58 +-Applying beta-rule and splitting (1450), into two cases.
% 55.97/21.58 |-Branch one:
% 55.97/21.58 | (1451) all_0_11_11 = n5
% 55.97/21.58 |
% 55.97/21.58 | From (1451) and (559) follows:
% 55.97/21.58 | (1452) pred(n5) = all_0_9_9
% 55.97/21.58 |
% 55.97/21.58 | From (1451) and (992) follows:
% 55.97/21.58 | (1453) succ(n5) = all_0_5_5
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 55.97/21.58 | (1454) all_0_9_9 = n4
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 55.97/21.58 | (1455) all_0_5_5 = n6
% 55.97/21.58 |
% 55.97/21.58 | From (1454)(1455) and (538) follows:
% 55.97/21.58 | (1456) sum(n4, n6) = all_0_2_2
% 55.97/21.58 |
% 55.97/21.58 | From (1454) and (10576) follows:
% 55.97/21.58 | (10719) sum(n4, n13) = all_0_7_7
% 55.97/21.58 |
% 55.97/21.58 | From (1455) and (10574) follows:
% 55.97/21.58 | (10720) sum(n11, n6) = all_0_4_4
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n11, n6, all_0_4_4, n17 and discharging atoms sum(n11, n6) = all_0_4_4, sum(n11, n6) = n17, yields:
% 55.97/21.58 | (1225) all_0_4_4 = n17
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n4, n13, all_0_7_7, n17 and discharging atoms sum(n4, n13) = all_0_7_7, sum(n4, n13) = n17, yields:
% 55.97/21.58 | (1227) all_0_7_7 = n17
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 55.97/21.58 | (1226) all_0_2_2 = n10
% 55.97/21.58 |
% 55.97/21.58 | From (1226) and (1082) follows:
% 55.97/21.58 | (1228) sum(n10, n24) = all_0_0_0
% 55.97/21.58 |
% 55.97/21.58 | From (1227)(1225) and (590) follows:
% 55.97/21.58 | (1229) sum(n17, n17) = all_0_3_3
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 55.97/21.58 | (1230) all_0_3_3 = n8
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n10, n24, all_0_0_0, n8 and discharging atoms sum(n10, n24) = all_0_0_0, sum(n10, n24) = n8, yields:
% 55.97/21.58 | (1231) all_0_0_0 = n8
% 55.97/21.58 |
% 55.97/21.58 | Equations (1231,1230) can reduce 679 to:
% 55.97/21.58 | (1106) $false
% 55.97/21.58 |
% 55.97/21.58 |-The branch is then unsatisfiable
% 55.97/21.58 |-Branch two:
% 55.97/21.58 | (1467) ~ (all_0_11_11 = n5)
% 55.97/21.58 | (1468) 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
% 55.97/21.58 |
% 55.97/21.58 +-Applying beta-rule and splitting (1468), into two cases.
% 55.97/21.58 |-Branch one:
% 55.97/21.58 | (1469) all_0_11_11 = n4
% 55.97/21.58 |
% 55.97/21.58 | From (1469) and (559) follows:
% 55.97/21.58 | (1470) pred(n4) = all_0_9_9
% 55.97/21.58 |
% 55.97/21.58 | From (1469) and (992) follows:
% 55.97/21.58 | (1471) succ(n4) = all_0_5_5
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 55.97/21.58 | (1472) all_0_9_9 = n3
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 55.97/21.58 | (1473) all_0_5_5 = n5
% 55.97/21.58 |
% 55.97/21.58 | From (1472)(1473) and (538) follows:
% 55.97/21.58 | (1474) sum(n3, n5) = all_0_2_2
% 55.97/21.58 |
% 55.97/21.58 | From (1472) and (10576) follows:
% 55.97/21.58 | (10737) sum(n3, n13) = all_0_7_7
% 55.97/21.58 |
% 55.97/21.58 | From (1473) and (10574) follows:
% 55.97/21.58 | (10738) sum(n11, n5) = all_0_4_4
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n11, n5, all_0_4_4, n16 and discharging atoms sum(n11, n5) = all_0_4_4, sum(n11, n5) = n16, yields:
% 55.97/21.58 | (1243) all_0_4_4 = n16
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n3, n13, all_0_7_7, n16 and discharging atoms sum(n3, n13) = all_0_7_7, sum(n3, n13) = n16, yields:
% 55.97/21.58 | (1245) all_0_7_7 = n16
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 55.97/21.58 | (1244) all_0_2_2 = n8
% 55.97/21.58 |
% 55.97/21.58 | From (1244) and (1082) follows:
% 55.97/21.58 | (1246) sum(n8, n24) = all_0_0_0
% 55.97/21.58 |
% 55.97/21.58 | From (1245)(1243) and (590) follows:
% 55.97/21.58 | (1247) sum(n16, n16) = all_0_3_3
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 55.97/21.58 | (1248) all_0_3_3 = n6
% 55.97/21.58 |
% 55.97/21.58 | Instantiating formula (690) with n8, n24, all_0_0_0, n6 and discharging atoms sum(n8, n24) = all_0_0_0, sum(n8, n24) = n6, yields:
% 55.97/21.58 | (1249) all_0_0_0 = n6
% 55.97/21.58 |
% 55.97/21.58 | Equations (1249,1248) can reduce 679 to:
% 55.97/21.58 | (1106) $false
% 55.97/21.58 |
% 55.97/21.58 |-The branch is then unsatisfiable
% 55.97/21.58 |-Branch two:
% 55.97/21.58 | (1485) ~ (all_0_11_11 = n4)
% 55.97/21.59 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 55.97/21.59 |
% 55.97/21.59 +-Applying beta-rule and splitting (1486), into two cases.
% 55.97/21.59 |-Branch one:
% 55.97/21.59 | (1487) all_0_11_11 = n3
% 55.97/21.59 |
% 55.97/21.59 | From (1487) and (559) follows:
% 55.97/21.59 | (1488) pred(n3) = all_0_9_9
% 55.97/21.59 |
% 55.97/21.59 | From (1487) and (992) follows:
% 55.97/21.59 | (1489) succ(n3) = all_0_5_5
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 55.97/21.59 | (1490) all_0_9_9 = n2
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 55.97/21.59 | (1491) all_0_5_5 = n4
% 55.97/21.59 |
% 55.97/21.59 | From (1490)(1491) and (538) follows:
% 55.97/21.59 | (1492) sum(n2, n4) = all_0_2_2
% 55.97/21.59 |
% 55.97/21.59 | From (1490) and (10576) follows:
% 55.97/21.59 | (10755) sum(n2, n13) = all_0_7_7
% 55.97/21.59 |
% 55.97/21.59 | From (1491) and (10574) follows:
% 55.97/21.59 | (10756) sum(n11, n4) = all_0_4_4
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (690) with n11, n4, all_0_4_4, n15 and discharging atoms sum(n11, n4) = all_0_4_4, sum(n11, n4) = n15, yields:
% 55.97/21.59 | (1261) all_0_4_4 = n15
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (690) with n2, n13, all_0_7_7, n15 and discharging atoms sum(n2, n13) = all_0_7_7, sum(n2, n13) = n15, yields:
% 55.97/21.59 | (1263) all_0_7_7 = n15
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 55.97/21.59 | (1262) all_0_2_2 = n6
% 55.97/21.59 |
% 55.97/21.59 | From (1262) and (1082) follows:
% 55.97/21.59 | (1264) sum(n6, n24) = all_0_0_0
% 55.97/21.59 |
% 55.97/21.59 | From (1263)(1261) and (590) follows:
% 55.97/21.59 | (1265) sum(n15, n15) = all_0_3_3
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 55.97/21.59 | (1266) all_0_3_3 = n4
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (690) with n6, n24, all_0_0_0, n4 and discharging atoms sum(n6, n24) = all_0_0_0, sum(n6, n24) = n4, yields:
% 55.97/21.59 | (1267) all_0_0_0 = n4
% 55.97/21.59 |
% 55.97/21.59 | Equations (1267,1266) can reduce 679 to:
% 55.97/21.59 | (1106) $false
% 55.97/21.59 |
% 55.97/21.59 |-The branch is then unsatisfiable
% 55.97/21.59 |-Branch two:
% 55.97/21.59 | (1503) ~ (all_0_11_11 = n3)
% 55.97/21.59 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 55.97/21.59 |
% 55.97/21.59 +-Applying beta-rule and splitting (1504), into two cases.
% 55.97/21.59 |-Branch one:
% 55.97/21.59 | (1505) all_0_11_11 = n2
% 55.97/21.59 |
% 55.97/21.59 | From (1505) and (559) follows:
% 55.97/21.59 | (1506) pred(n2) = all_0_9_9
% 55.97/21.59 |
% 55.97/21.59 | From (1505) and (992) follows:
% 55.97/21.59 | (1507) succ(n2) = all_0_5_5
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 55.97/21.59 | (1508) all_0_9_9 = n1
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 55.97/21.59 | (1509) all_0_5_5 = n3
% 55.97/21.59 |
% 55.97/21.59 | From (1508)(1509) and (538) follows:
% 55.97/21.59 | (1510) sum(n1, n3) = all_0_2_2
% 55.97/21.59 |
% 55.97/21.59 | From (1508) and (10576) follows:
% 55.97/21.59 | (10773) sum(n1, n13) = all_0_7_7
% 55.97/21.59 |
% 55.97/21.59 | From (1509) and (10574) follows:
% 55.97/21.59 | (10774) sum(n11, n3) = all_0_4_4
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (690) with n11, n3, all_0_4_4, n14 and discharging atoms sum(n11, n3) = all_0_4_4, sum(n11, n3) = n14, yields:
% 55.97/21.59 | (1279) all_0_4_4 = n14
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (690) with n1, n13, all_0_7_7, n14 and discharging atoms sum(n1, n13) = all_0_7_7, sum(n1, n13) = n14, yields:
% 55.97/21.59 | (1281) all_0_7_7 = n14
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 55.97/21.59 | (1280) all_0_2_2 = n4
% 55.97/21.59 |
% 55.97/21.59 | From (1280) and (1082) follows:
% 55.97/21.59 | (1282) sum(n4, n24) = all_0_0_0
% 55.97/21.59 |
% 55.97/21.59 | From (1281)(1279) and (590) follows:
% 55.97/21.59 | (1283) sum(n14, n14) = all_0_3_3
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 55.97/21.59 | (1284) all_0_3_3 = n2
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (690) with n4, n24, all_0_0_0, n2 and discharging atoms sum(n4, n24) = all_0_0_0, sum(n4, n24) = n2, yields:
% 55.97/21.59 | (1285) all_0_0_0 = n2
% 55.97/21.59 |
% 55.97/21.59 | Equations (1285,1284) can reduce 679 to:
% 55.97/21.59 | (1106) $false
% 55.97/21.59 |
% 55.97/21.59 |-The branch is then unsatisfiable
% 55.97/21.59 |-Branch two:
% 55.97/21.59 | (1521) ~ (all_0_11_11 = n2)
% 55.97/21.59 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 55.97/21.59 |
% 55.97/21.59 +-Applying beta-rule and splitting (1522), into two cases.
% 55.97/21.59 |-Branch one:
% 55.97/21.59 | (1523) all_0_11_11 = n1
% 55.97/21.59 |
% 55.97/21.59 | From (1523) and (559) follows:
% 55.97/21.59 | (1524) pred(n1) = all_0_9_9
% 55.97/21.59 |
% 55.97/21.59 | From (1523) and (992) follows:
% 55.97/21.59 | (1525) succ(n1) = all_0_5_5
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 55.97/21.59 | (1526) all_0_9_9 = n0
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 55.97/21.59 | (1527) all_0_5_5 = n2
% 55.97/21.59 |
% 55.97/21.59 | From (1526)(1527) and (538) follows:
% 55.97/21.59 | (1528) sum(n0, n2) = all_0_2_2
% 55.97/21.59 |
% 55.97/21.59 | From (1526) and (10576) follows:
% 55.97/21.59 | (10791) sum(n0, n13) = all_0_7_7
% 55.97/21.59 |
% 55.97/21.59 | From (1527) and (10574) follows:
% 55.97/21.59 | (10792) sum(n11, n2) = all_0_4_4
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (690) with n11, n2, all_0_4_4, n13 and discharging atoms sum(n11, n2) = all_0_4_4, sum(n11, n2) = n13, yields:
% 55.97/21.59 | (1297) all_0_4_4 = n13
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (690) with n0, n13, all_0_7_7, n13 and discharging atoms sum(n0, n13) = all_0_7_7, sum(n0, n13) = n13, yields:
% 55.97/21.59 | (1299) all_0_7_7 = n13
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 55.97/21.59 | (1298) all_0_2_2 = n2
% 55.97/21.59 |
% 55.97/21.59 | From (1298) and (1082) follows:
% 55.97/21.59 | (1300) sum(n2, n24) = all_0_0_0
% 55.97/21.59 |
% 55.97/21.59 | From (1299)(1297) and (590) follows:
% 55.97/21.59 | (1301) sum(n13, n13) = all_0_3_3
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 55.97/21.59 | (1302) all_0_3_3 = n0
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (690) with n2, n24, all_0_0_0, n0 and discharging atoms sum(n2, n24) = all_0_0_0, sum(n2, n24) = n0, yields:
% 55.97/21.59 | (1303) all_0_0_0 = n0
% 55.97/21.59 |
% 55.97/21.59 | Equations (1303,1302) can reduce 679 to:
% 55.97/21.59 | (1106) $false
% 55.97/21.59 |
% 55.97/21.59 |-The branch is then unsatisfiable
% 55.97/21.59 |-Branch two:
% 55.97/21.59 | (1540) ~ (all_0_11_11 = n1)
% 55.97/21.59 | (1541) all_0_11_11 = n0
% 55.97/21.59 |
% 55.97/21.59 | From (1541) and (559) follows:
% 55.97/21.59 | (1542) pred(n0) = all_0_9_9
% 55.97/21.59 |
% 55.97/21.59 | From (1541) and (992) follows:
% 55.97/21.59 | (1543) succ(n0) = all_0_5_5
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 55.97/21.59 | (1544) all_0_9_9 = n25
% 55.97/21.59 |
% 55.97/21.59 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 55.97/21.59 | (1545) all_0_5_5 = n1
% 55.97/21.59 |
% 55.97/21.59 | From (1544)(1545) and (538) follows:
% 55.97/21.59 | (1546) sum(n25, n1) = all_0_2_2
% 55.97/21.59 |
% 55.97/21.59 | From (1544) and (10576) follows:
% 55.97/21.60 | (10808) sum(n25, n13) = all_0_7_7
% 55.97/21.60 |
% 55.97/21.60 | From (1545) and (10574) follows:
% 55.97/21.60 | (10809) sum(n11, n1) = all_0_4_4
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (690) with n25, n13, all_0_7_7, n12 and discharging atoms sum(n25, n13) = all_0_7_7, sum(n25, n13) = n12, yields:
% 55.97/21.60 | (1317) all_0_7_7 = n12
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 55.97/21.60 | (1316) all_0_2_2 = n0
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (690) with n11, n1, all_0_4_4, n12 and discharging atoms sum(n11, n1) = all_0_4_4, sum(n11, n1) = n12, yields:
% 55.97/21.60 | (1315) all_0_4_4 = n12
% 55.97/21.60 |
% 55.97/21.60 | From (1316) and (1082) follows:
% 55.97/21.60 | (1318) sum(n0, n24) = all_0_0_0
% 55.97/21.60 |
% 55.97/21.60 | From (1317)(1315) and (590) follows:
% 55.97/21.60 | (1319) sum(n12, n12) = all_0_3_3
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 55.97/21.60 | (1320) all_0_3_3 = n24
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (690) with n0, n24, all_0_0_0, n24 and discharging atoms sum(n0, n24) = all_0_0_0, sum(n0, n24) = n24, yields:
% 55.97/21.60 | (1321) all_0_0_0 = n24
% 55.97/21.60 |
% 55.97/21.60 | Equations (1321,1320) can reduce 679 to:
% 55.97/21.60 | (1106) $false
% 55.97/21.60 |
% 55.97/21.60 |-The branch is then unsatisfiable
% 55.97/21.60 |-Branch two:
% 55.97/21.60 | (1802) ~ (all_0_10_10 = n12)
% 55.97/21.60 | (1803) 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
% 55.97/21.60 |
% 55.97/21.60 +-Applying beta-rule and splitting (1324), into two cases.
% 55.97/21.60 |-Branch one:
% 55.97/21.60 | (1325) all_0_11_11 = n12
% 55.97/21.60 |
% 55.97/21.60 | From (1325) and (559) follows:
% 55.97/21.60 | (1326) pred(n12) = all_0_9_9
% 55.97/21.60 |
% 55.97/21.60 | From (1325) and (992) follows:
% 55.97/21.60 | (1327) succ(n12) = all_0_5_5
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (500) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 55.97/21.60 | (1328) all_0_9_9 = n11
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (617) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 55.97/21.60 | (1329) all_0_5_5 = n13
% 55.97/21.60 |
% 55.97/21.60 | From (1329) and (541) follows:
% 55.97/21.60 | (10825) sum(all_0_6_6, n13) = all_0_4_4
% 55.97/21.60 |
% 55.97/21.60 | From (1328)(1329) and (538) follows:
% 55.97/21.60 | (1330) sum(n11, n13) = all_0_2_2
% 55.97/21.60 |
% 55.97/21.60 | From (1328) and (427) follows:
% 55.97/21.60 | (10827) sum(n11, all_0_8_8) = all_0_7_7
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (690) with n11, n13, all_0_2_2, n24 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n24, yields:
% 55.97/21.60 | (1092) all_0_2_2 = n24
% 55.97/21.60 |
% 55.97/21.60 | From (1092) and (630) follows:
% 55.97/21.60 | (1568) sum(n24, all_0_1_1) = all_0_0_0
% 55.97/21.60 |
% 55.97/21.60 +-Applying beta-rule and splitting (1803), into two cases.
% 55.97/21.60 |-Branch one:
% 55.97/21.60 | (1804) all_0_10_10 = n11
% 55.97/21.60 |
% 55.97/21.60 | From (1804) and (292) follows:
% 55.97/21.60 | (1805) pred(n11) = all_0_6_6
% 55.97/21.60 |
% 55.97/21.60 | From (1804) and (760) follows:
% 55.97/21.60 | (1806) succ(n11) = all_0_8_8
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (500) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 55.97/21.60 | (1807) all_0_6_6 = n10
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (617) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 55.97/21.60 | (1808) all_0_8_8 = n12
% 55.97/21.60 |
% 55.97/21.60 | From (1807)(1808) and (411) follows:
% 55.97/21.60 | (1809) sum(n10, n12) = all_0_1_1
% 55.97/21.60 |
% 55.97/21.60 | From (1807) and (10825) follows:
% 55.97/21.60 | (10836) sum(n10, n13) = all_0_4_4
% 55.97/21.60 |
% 55.97/21.60 | From (1808) and (10827) follows:
% 55.97/21.60 | (10837) sum(n11, n12) = all_0_7_7
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (690) with n11, n12, all_0_7_7, n23 and discharging atoms sum(n11, n12) = all_0_7_7, sum(n11, n12) = n23, yields:
% 55.97/21.60 | (1119) all_0_7_7 = n23
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (690) with n10, n13, all_0_4_4, n23 and discharging atoms sum(n10, n13) = all_0_4_4, sum(n10, n13) = n23, yields:
% 55.97/21.60 | (1117) all_0_4_4 = n23
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (690) with n10, n12, all_0_1_1, n22 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n22, yields:
% 55.97/21.60 | (1579) all_0_1_1 = n22
% 55.97/21.60 |
% 55.97/21.60 | From (1119)(1117) and (590) follows:
% 55.97/21.60 | (1121) sum(n23, n23) = all_0_3_3
% 55.97/21.60 |
% 55.97/21.60 | From (1579) and (1568) follows:
% 55.97/21.60 | (1582) sum(n24, n22) = all_0_0_0
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (690) with n24, n22, all_0_0_0, n20 and discharging atoms sum(n24, n22) = all_0_0_0, sum(n24, n22) = n20, yields:
% 55.97/21.60 | (1123) all_0_0_0 = n20
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (690) with n23, n23, all_0_3_3, n20 and discharging atoms sum(n23, n23) = all_0_3_3, sum(n23, n23) = n20, yields:
% 55.97/21.60 | (1122) all_0_3_3 = n20
% 55.97/21.60 |
% 55.97/21.60 | Equations (1123,1122) can reduce 679 to:
% 55.97/21.60 | (1106) $false
% 55.97/21.60 |
% 55.97/21.60 |-The branch is then unsatisfiable
% 55.97/21.60 |-Branch two:
% 55.97/21.60 | (1820) ~ (all_0_10_10 = n11)
% 55.97/21.60 | (1821) 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
% 55.97/21.60 |
% 55.97/21.60 +-Applying beta-rule and splitting (1821), into two cases.
% 55.97/21.60 |-Branch one:
% 55.97/21.60 | (1822) all_0_10_10 = n10
% 55.97/21.60 |
% 55.97/21.60 | From (1822) and (292) follows:
% 55.97/21.60 | (1823) pred(n10) = all_0_6_6
% 55.97/21.60 |
% 55.97/21.60 | From (1822) and (760) follows:
% 55.97/21.60 | (1824) succ(n10) = all_0_8_8
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (500) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 55.97/21.60 | (1825) all_0_6_6 = n9
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (617) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 55.97/21.60 | (1826) all_0_8_8 = n11
% 55.97/21.60 |
% 55.97/21.60 | From (1825)(1826) and (411) follows:
% 55.97/21.60 | (1827) sum(n9, n11) = all_0_1_1
% 55.97/21.60 |
% 55.97/21.60 | From (1825) and (10825) follows:
% 55.97/21.60 | (10854) sum(n9, n13) = all_0_4_4
% 55.97/21.60 |
% 55.97/21.60 | From (1826) and (10827) follows:
% 55.97/21.60 | (10855) sum(n11, n11) = all_0_7_7
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (690) with n11, n11, all_0_7_7, n22 and discharging atoms sum(n11, n11) = all_0_7_7, sum(n11, n11) = n22, yields:
% 55.97/21.60 | (1137) all_0_7_7 = n22
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (690) with n9, n13, all_0_4_4, n22 and discharging atoms sum(n9, n13) = all_0_4_4, sum(n9, n13) = n22, yields:
% 55.97/21.60 | (1135) all_0_4_4 = n22
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (690) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 55.97/21.60 | (1597) all_0_1_1 = n20
% 55.97/21.60 |
% 55.97/21.60 | From (1137)(1135) and (590) follows:
% 55.97/21.60 | (1139) sum(n22, n22) = all_0_3_3
% 55.97/21.60 |
% 55.97/21.60 | From (1597) and (1568) follows:
% 55.97/21.60 | (1600) sum(n24, n20) = all_0_0_0
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (690) with n24, n20, all_0_0_0, n18 and discharging atoms sum(n24, n20) = all_0_0_0, sum(n24, n20) = n18, yields:
% 55.97/21.60 | (1141) all_0_0_0 = n18
% 55.97/21.60 |
% 55.97/21.60 | Instantiating formula (690) with n22, n22, all_0_3_3, n18 and discharging atoms sum(n22, n22) = all_0_3_3, sum(n22, n22) = n18, yields:
% 55.97/21.60 | (1140) all_0_3_3 = n18
% 55.97/21.60 |
% 55.97/21.60 | Equations (1141,1140) can reduce 679 to:
% 55.97/21.60 | (1106) $false
% 55.97/21.60 |
% 55.97/21.60 |-The branch is then unsatisfiable
% 55.97/21.60 |-Branch two:
% 55.97/21.60 | (1838) ~ (all_0_10_10 = n10)
% 55.97/21.60 | (1839) 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
% 55.97/21.60 |
% 55.97/21.60 +-Applying beta-rule and splitting (1839), into two cases.
% 55.97/21.60 |-Branch one:
% 55.97/21.60 | (1840) all_0_10_10 = n9
% 55.97/21.60 |
% 55.97/21.60 | From (1840) and (292) follows:
% 55.97/21.61 | (1841) pred(n9) = all_0_6_6
% 55.97/21.61 |
% 55.97/21.61 | From (1840) and (760) follows:
% 55.97/21.61 | (1842) succ(n9) = all_0_8_8
% 55.97/21.61 |
% 55.97/21.61 | Instantiating formula (500) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 55.97/21.61 | (1843) all_0_6_6 = n8
% 55.97/21.61 |
% 55.97/21.61 | Instantiating formula (617) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 55.97/21.61 | (1844) all_0_8_8 = n10
% 55.97/21.61 |
% 55.97/21.61 | From (1843)(1844) and (411) follows:
% 55.97/21.61 | (1845) sum(n8, n10) = all_0_1_1
% 55.97/21.61 |
% 55.97/21.61 | From (1843) and (10825) follows:
% 55.97/21.61 | (10872) sum(n8, n13) = all_0_4_4
% 55.97/21.61 |
% 55.97/21.61 | From (1844) and (10827) follows:
% 55.97/21.61 | (10873) sum(n11, n10) = all_0_7_7
% 55.97/21.61 |
% 55.97/21.61 | Instantiating formula (690) with n11, n10, all_0_7_7, n21 and discharging atoms sum(n11, n10) = all_0_7_7, sum(n11, n10) = n21, yields:
% 55.97/21.61 | (1155) all_0_7_7 = n21
% 55.97/21.61 |
% 55.97/21.61 | Instantiating formula (690) with n8, n13, all_0_4_4, n21 and discharging atoms sum(n8, n13) = all_0_4_4, sum(n8, n13) = n21, yields:
% 55.97/21.61 | (1153) all_0_4_4 = n21
% 55.97/21.61 |
% 55.97/21.61 | Instantiating formula (690) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 55.97/21.61 | (1615) all_0_1_1 = n18
% 55.97/21.61 |
% 55.97/21.61 | From (1155)(1153) and (590) follows:
% 56.11/21.61 | (1157) sum(n21, n21) = all_0_3_3
% 56.11/21.61 |
% 56.11/21.61 | From (1615) and (1568) follows:
% 56.11/21.61 | (1618) sum(n24, n18) = all_0_0_0
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (690) with n24, n18, all_0_0_0, n16 and discharging atoms sum(n24, n18) = all_0_0_0, sum(n24, n18) = n16, yields:
% 56.11/21.61 | (1159) all_0_0_0 = n16
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 56.11/21.61 | (1158) all_0_3_3 = n16
% 56.11/21.61 |
% 56.11/21.61 | Equations (1159,1158) can reduce 679 to:
% 56.11/21.61 | (1106) $false
% 56.11/21.61 |
% 56.11/21.61 |-The branch is then unsatisfiable
% 56.11/21.61 |-Branch two:
% 56.11/21.61 | (1856) ~ (all_0_10_10 = n9)
% 56.11/21.61 | (1857) 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
% 56.11/21.61 |
% 56.11/21.61 +-Applying beta-rule and splitting (1857), into two cases.
% 56.11/21.61 |-Branch one:
% 56.11/21.61 | (1858) all_0_10_10 = n8
% 56.11/21.61 |
% 56.11/21.61 | From (1858) and (292) follows:
% 56.11/21.61 | (1859) pred(n8) = all_0_6_6
% 56.11/21.61 |
% 56.11/21.61 | From (1858) and (760) follows:
% 56.11/21.61 | (1860) succ(n8) = all_0_8_8
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 56.11/21.61 | (1861) all_0_6_6 = n7
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 56.11/21.61 | (1862) all_0_8_8 = n9
% 56.11/21.61 |
% 56.11/21.61 | From (1861)(1862) and (411) follows:
% 56.11/21.61 | (1863) sum(n7, n9) = all_0_1_1
% 56.11/21.61 |
% 56.11/21.61 | From (1861) and (10825) follows:
% 56.11/21.61 | (10890) sum(n7, n13) = all_0_4_4
% 56.11/21.61 |
% 56.11/21.61 | From (1862) and (10827) follows:
% 56.11/21.61 | (10891) sum(n11, n9) = all_0_7_7
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (690) with n11, n9, all_0_7_7, n20 and discharging atoms sum(n11, n9) = all_0_7_7, sum(n11, n9) = n20, yields:
% 56.11/21.61 | (1173) all_0_7_7 = n20
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (690) with n7, n13, all_0_4_4, n20 and discharging atoms sum(n7, n13) = all_0_4_4, sum(n7, n13) = n20, yields:
% 56.11/21.61 | (1171) all_0_4_4 = n20
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 56.11/21.61 | (1633) all_0_1_1 = n16
% 56.11/21.61 |
% 56.11/21.61 | From (1173)(1171) and (590) follows:
% 56.11/21.61 | (1175) sum(n20, n20) = all_0_3_3
% 56.11/21.61 |
% 56.11/21.61 | From (1633) and (1568) follows:
% 56.11/21.61 | (1636) sum(n24, n16) = all_0_0_0
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (690) with n24, n16, all_0_0_0, n14 and discharging atoms sum(n24, n16) = all_0_0_0, sum(n24, n16) = n14, yields:
% 56.11/21.61 | (1177) all_0_0_0 = n14
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 56.11/21.61 | (1176) all_0_3_3 = n14
% 56.11/21.61 |
% 56.11/21.61 | Equations (1177,1176) can reduce 679 to:
% 56.11/21.61 | (1106) $false
% 56.11/21.61 |
% 56.11/21.61 |-The branch is then unsatisfiable
% 56.11/21.61 |-Branch two:
% 56.11/21.61 | (1874) ~ (all_0_10_10 = n8)
% 56.11/21.61 | (1875) 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
% 56.11/21.61 |
% 56.11/21.61 +-Applying beta-rule and splitting (1875), into two cases.
% 56.11/21.61 |-Branch one:
% 56.11/21.61 | (1876) all_0_10_10 = n7
% 56.11/21.61 |
% 56.11/21.61 | From (1876) and (292) follows:
% 56.11/21.61 | (1877) pred(n7) = all_0_6_6
% 56.11/21.61 |
% 56.11/21.61 | From (1876) and (760) follows:
% 56.11/21.61 | (1878) succ(n7) = all_0_8_8
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 56.11/21.61 | (1879) all_0_6_6 = n6
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 56.11/21.61 | (1880) all_0_8_8 = n8
% 56.11/21.61 |
% 56.11/21.61 | From (1879)(1880) and (411) follows:
% 56.11/21.61 | (1881) sum(n6, n8) = all_0_1_1
% 56.11/21.61 |
% 56.11/21.61 | From (1879) and (10825) follows:
% 56.11/21.61 | (10908) sum(n6, n13) = all_0_4_4
% 56.11/21.61 |
% 56.11/21.61 | From (1880) and (10827) follows:
% 56.11/21.61 | (10909) sum(n11, n8) = all_0_7_7
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (690) with n11, n8, all_0_7_7, n19 and discharging atoms sum(n11, n8) = all_0_7_7, sum(n11, n8) = n19, yields:
% 56.11/21.61 | (1191) all_0_7_7 = n19
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (690) with n6, n13, all_0_4_4, n19 and discharging atoms sum(n6, n13) = all_0_4_4, sum(n6, n13) = n19, yields:
% 56.11/21.61 | (1189) all_0_4_4 = n19
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 56.11/21.61 | (1651) all_0_1_1 = n14
% 56.11/21.61 |
% 56.11/21.61 | From (1191)(1189) and (590) follows:
% 56.11/21.61 | (1193) sum(n19, n19) = all_0_3_3
% 56.11/21.61 |
% 56.11/21.61 | From (1651) and (1568) follows:
% 56.11/21.61 | (1654) sum(n24, n14) = all_0_0_0
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (690) with n24, n14, all_0_0_0, n12 and discharging atoms sum(n24, n14) = all_0_0_0, sum(n24, n14) = n12, yields:
% 56.11/21.61 | (1195) all_0_0_0 = n12
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 56.11/21.61 | (1194) all_0_3_3 = n12
% 56.11/21.61 |
% 56.11/21.61 | Equations (1195,1194) can reduce 679 to:
% 56.11/21.61 | (1106) $false
% 56.11/21.61 |
% 56.11/21.61 |-The branch is then unsatisfiable
% 56.11/21.61 |-Branch two:
% 56.11/21.61 | (1892) ~ (all_0_10_10 = n7)
% 56.11/21.61 | (1893) 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
% 56.11/21.61 |
% 56.11/21.61 +-Applying beta-rule and splitting (1893), into two cases.
% 56.11/21.61 |-Branch one:
% 56.11/21.61 | (1894) all_0_10_10 = n6
% 56.11/21.61 |
% 56.11/21.61 | From (1894) and (292) follows:
% 56.11/21.61 | (1895) pred(n6) = all_0_6_6
% 56.11/21.61 |
% 56.11/21.61 | From (1894) and (760) follows:
% 56.11/21.61 | (1896) succ(n6) = all_0_8_8
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 56.11/21.61 | (1897) all_0_6_6 = n5
% 56.11/21.61 |
% 56.11/21.61 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 56.11/21.61 | (1898) all_0_8_8 = n7
% 56.11/21.61 |
% 56.11/21.61 | From (1897)(1898) and (411) follows:
% 56.11/21.61 | (1899) sum(n5, n7) = all_0_1_1
% 56.11/21.61 |
% 56.11/21.61 | From (1897) and (10825) follows:
% 56.11/21.62 | (10926) sum(n5, n13) = all_0_4_4
% 56.11/21.62 |
% 56.11/21.62 | From (1898) and (10827) follows:
% 56.11/21.62 | (10927) sum(n11, n7) = all_0_7_7
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (690) with n11, n7, all_0_7_7, n18 and discharging atoms sum(n11, n7) = all_0_7_7, sum(n11, n7) = n18, yields:
% 56.11/21.62 | (1209) all_0_7_7 = n18
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (690) with n5, n13, all_0_4_4, n18 and discharging atoms sum(n5, n13) = all_0_4_4, sum(n5, n13) = n18, yields:
% 56.11/21.62 | (1207) all_0_4_4 = n18
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 56.11/21.62 | (1669) all_0_1_1 = n12
% 56.11/21.62 |
% 56.11/21.62 | From (1209)(1207) and (590) follows:
% 56.11/21.62 | (1211) sum(n18, n18) = all_0_3_3
% 56.11/21.62 |
% 56.11/21.62 | From (1669) and (1568) follows:
% 56.11/21.62 | (1672) sum(n24, n12) = all_0_0_0
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (690) with n24, n12, all_0_0_0, n10 and discharging atoms sum(n24, n12) = all_0_0_0, sum(n24, n12) = n10, yields:
% 56.11/21.62 | (1213) all_0_0_0 = n10
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 56.11/21.62 | (1212) all_0_3_3 = n10
% 56.11/21.62 |
% 56.11/21.62 | Equations (1213,1212) can reduce 679 to:
% 56.11/21.62 | (1106) $false
% 56.11/21.62 |
% 56.11/21.62 |-The branch is then unsatisfiable
% 56.11/21.62 |-Branch two:
% 56.11/21.62 | (1910) ~ (all_0_10_10 = n6)
% 56.11/21.62 | (1911) 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
% 56.11/21.62 |
% 56.11/21.62 +-Applying beta-rule and splitting (1911), into two cases.
% 56.11/21.62 |-Branch one:
% 56.11/21.62 | (1912) all_0_10_10 = n5
% 56.11/21.62 |
% 56.11/21.62 | From (1912) and (292) follows:
% 56.11/21.62 | (1913) pred(n5) = all_0_6_6
% 56.11/21.62 |
% 56.11/21.62 | From (1912) and (760) follows:
% 56.11/21.62 | (1914) succ(n5) = all_0_8_8
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 56.11/21.62 | (1915) all_0_6_6 = n4
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 56.11/21.62 | (1916) all_0_8_8 = n6
% 56.11/21.62 |
% 56.11/21.62 | From (1915)(1916) and (411) follows:
% 56.11/21.62 | (1917) sum(n4, n6) = all_0_1_1
% 56.11/21.62 |
% 56.11/21.62 | From (1915) and (10825) follows:
% 56.11/21.62 | (10944) sum(n4, n13) = all_0_4_4
% 56.11/21.62 |
% 56.11/21.62 | From (1916) and (10827) follows:
% 56.11/21.62 | (10945) sum(n11, n6) = all_0_7_7
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (690) with n11, n6, all_0_7_7, n17 and discharging atoms sum(n11, n6) = all_0_7_7, sum(n11, n6) = n17, yields:
% 56.11/21.62 | (1227) all_0_7_7 = n17
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (690) with n4, n13, all_0_4_4, n17 and discharging atoms sum(n4, n13) = all_0_4_4, sum(n4, n13) = n17, yields:
% 56.11/21.62 | (1225) all_0_4_4 = n17
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 56.11/21.62 | (1687) all_0_1_1 = n10
% 56.11/21.62 |
% 56.11/21.62 | From (1227)(1225) and (590) follows:
% 56.11/21.62 | (1229) sum(n17, n17) = all_0_3_3
% 56.11/21.62 |
% 56.11/21.62 | From (1687) and (1568) follows:
% 56.11/21.62 | (1690) sum(n24, n10) = all_0_0_0
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (690) with n24, n10, all_0_0_0, n8 and discharging atoms sum(n24, n10) = all_0_0_0, sum(n24, n10) = n8, yields:
% 56.11/21.62 | (1231) all_0_0_0 = n8
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 56.11/21.62 | (1230) all_0_3_3 = n8
% 56.11/21.62 |
% 56.11/21.62 | Equations (1231,1230) can reduce 679 to:
% 56.11/21.62 | (1106) $false
% 56.11/21.62 |
% 56.11/21.62 |-The branch is then unsatisfiable
% 56.11/21.62 |-Branch two:
% 56.11/21.62 | (1928) ~ (all_0_10_10 = n5)
% 56.11/21.62 | (1929) 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
% 56.11/21.62 |
% 56.11/21.62 +-Applying beta-rule and splitting (1929), into two cases.
% 56.11/21.62 |-Branch one:
% 56.11/21.62 | (1930) all_0_10_10 = n4
% 56.11/21.62 |
% 56.11/21.62 | From (1930) and (292) follows:
% 56.11/21.62 | (1931) pred(n4) = all_0_6_6
% 56.11/21.62 |
% 56.11/21.62 | From (1930) and (760) follows:
% 56.11/21.62 | (1932) succ(n4) = all_0_8_8
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 56.11/21.62 | (1933) all_0_6_6 = n3
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 56.11/21.62 | (1934) all_0_8_8 = n5
% 56.11/21.62 |
% 56.11/21.62 | From (1933)(1934) and (411) follows:
% 56.11/21.62 | (1935) sum(n3, n5) = all_0_1_1
% 56.11/21.62 |
% 56.11/21.62 | From (1933) and (10825) follows:
% 56.11/21.62 | (10962) sum(n3, n13) = all_0_4_4
% 56.11/21.62 |
% 56.11/21.62 | From (1934) and (10827) follows:
% 56.11/21.62 | (10963) sum(n11, n5) = all_0_7_7
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (690) with n11, n5, all_0_7_7, n16 and discharging atoms sum(n11, n5) = all_0_7_7, sum(n11, n5) = n16, yields:
% 56.11/21.62 | (1245) all_0_7_7 = n16
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (690) with n3, n13, all_0_4_4, n16 and discharging atoms sum(n3, n13) = all_0_4_4, sum(n3, n13) = n16, yields:
% 56.11/21.62 | (1243) all_0_4_4 = n16
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 56.11/21.62 | (1705) all_0_1_1 = n8
% 56.11/21.62 |
% 56.11/21.62 | From (1245)(1243) and (590) follows:
% 56.11/21.62 | (1247) sum(n16, n16) = all_0_3_3
% 56.11/21.62 |
% 56.11/21.62 | From (1705) and (1568) follows:
% 56.11/21.62 | (1708) sum(n24, n8) = all_0_0_0
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (690) with n24, n8, all_0_0_0, n6 and discharging atoms sum(n24, n8) = all_0_0_0, sum(n24, n8) = n6, yields:
% 56.11/21.62 | (1249) all_0_0_0 = n6
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 56.11/21.62 | (1248) all_0_3_3 = n6
% 56.11/21.62 |
% 56.11/21.62 | Equations (1249,1248) can reduce 679 to:
% 56.11/21.62 | (1106) $false
% 56.11/21.62 |
% 56.11/21.62 |-The branch is then unsatisfiable
% 56.11/21.62 |-Branch two:
% 56.11/21.62 | (1946) ~ (all_0_10_10 = n4)
% 56.11/21.62 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.11/21.62 |
% 56.11/21.62 +-Applying beta-rule and splitting (1947), into two cases.
% 56.11/21.62 |-Branch one:
% 56.11/21.62 | (1948) all_0_10_10 = n3
% 56.11/21.62 |
% 56.11/21.62 | From (1948) and (292) follows:
% 56.11/21.62 | (1949) pred(n3) = all_0_6_6
% 56.11/21.62 |
% 56.11/21.62 | From (1948) and (760) follows:
% 56.11/21.62 | (1950) succ(n3) = all_0_8_8
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 56.11/21.62 | (1951) all_0_6_6 = n2
% 56.11/21.62 |
% 56.11/21.62 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 56.11/21.62 | (1952) all_0_8_8 = n4
% 56.11/21.62 |
% 56.11/21.62 | From (1951)(1952) and (411) follows:
% 56.11/21.62 | (1953) sum(n2, n4) = all_0_1_1
% 56.11/21.62 |
% 56.11/21.62 | From (1951) and (10825) follows:
% 56.11/21.62 | (10980) sum(n2, n13) = all_0_4_4
% 56.11/21.62 |
% 56.11/21.62 | From (1952) and (10827) follows:
% 56.11/21.63 | (10981) sum(n11, n4) = all_0_7_7
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n11, n4, all_0_7_7, n15 and discharging atoms sum(n11, n4) = all_0_7_7, sum(n11, n4) = n15, yields:
% 56.11/21.63 | (1263) all_0_7_7 = n15
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n2, n13, all_0_4_4, n15 and discharging atoms sum(n2, n13) = all_0_4_4, sum(n2, n13) = n15, yields:
% 56.11/21.63 | (1261) all_0_4_4 = n15
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 56.11/21.63 | (1723) all_0_1_1 = n6
% 56.11/21.63 |
% 56.11/21.63 | From (1263)(1261) and (590) follows:
% 56.11/21.63 | (1265) sum(n15, n15) = all_0_3_3
% 56.11/21.63 |
% 56.11/21.63 | From (1723) and (1568) follows:
% 56.11/21.63 | (1726) sum(n24, n6) = all_0_0_0
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n24, n6, all_0_0_0, n4 and discharging atoms sum(n24, n6) = all_0_0_0, sum(n24, n6) = n4, yields:
% 56.11/21.63 | (1267) all_0_0_0 = n4
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 56.11/21.63 | (1266) all_0_3_3 = n4
% 56.11/21.63 |
% 56.11/21.63 | Equations (1267,1266) can reduce 679 to:
% 56.11/21.63 | (1106) $false
% 56.11/21.63 |
% 56.11/21.63 |-The branch is then unsatisfiable
% 56.11/21.63 |-Branch two:
% 56.11/21.63 | (1964) ~ (all_0_10_10 = n3)
% 56.11/21.63 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.11/21.63 |
% 56.11/21.63 +-Applying beta-rule and splitting (1965), into two cases.
% 56.11/21.63 |-Branch one:
% 56.11/21.63 | (1966) all_0_10_10 = n2
% 56.11/21.63 |
% 56.11/21.63 | From (1966) and (292) follows:
% 56.11/21.63 | (1967) pred(n2) = all_0_6_6
% 56.11/21.63 |
% 56.11/21.63 | From (1966) and (760) follows:
% 56.11/21.63 | (1968) succ(n2) = all_0_8_8
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 56.11/21.63 | (1969) all_0_6_6 = n1
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 56.11/21.63 | (1970) all_0_8_8 = n3
% 56.11/21.63 |
% 56.11/21.63 | From (1969)(1970) and (411) follows:
% 56.11/21.63 | (1971) sum(n1, n3) = all_0_1_1
% 56.11/21.63 |
% 56.11/21.63 | From (1969) and (10825) follows:
% 56.11/21.63 | (10998) sum(n1, n13) = all_0_4_4
% 56.11/21.63 |
% 56.11/21.63 | From (1970) and (10827) follows:
% 56.11/21.63 | (10999) sum(n11, n3) = all_0_7_7
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n11, n3, all_0_7_7, n14 and discharging atoms sum(n11, n3) = all_0_7_7, sum(n11, n3) = n14, yields:
% 56.11/21.63 | (1281) all_0_7_7 = n14
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n1, n13, all_0_4_4, n14 and discharging atoms sum(n1, n13) = all_0_4_4, sum(n1, n13) = n14, yields:
% 56.11/21.63 | (1279) all_0_4_4 = n14
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 56.11/21.63 | (1741) all_0_1_1 = n4
% 56.11/21.63 |
% 56.11/21.63 | From (1281)(1279) and (590) follows:
% 56.11/21.63 | (1283) sum(n14, n14) = all_0_3_3
% 56.11/21.63 |
% 56.11/21.63 | From (1741) and (1568) follows:
% 56.11/21.63 | (1744) sum(n24, n4) = all_0_0_0
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n24, n4, all_0_0_0, n2 and discharging atoms sum(n24, n4) = all_0_0_0, sum(n24, n4) = n2, yields:
% 56.11/21.63 | (1285) all_0_0_0 = n2
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 56.11/21.63 | (1284) all_0_3_3 = n2
% 56.11/21.63 |
% 56.11/21.63 | Equations (1285,1284) can reduce 679 to:
% 56.11/21.63 | (1106) $false
% 56.11/21.63 |
% 56.11/21.63 |-The branch is then unsatisfiable
% 56.11/21.63 |-Branch two:
% 56.11/21.63 | (1982) ~ (all_0_10_10 = n2)
% 56.11/21.63 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 56.11/21.63 |
% 56.11/21.63 +-Applying beta-rule and splitting (1983), into two cases.
% 56.11/21.63 |-Branch one:
% 56.11/21.63 | (1984) all_0_10_10 = n1
% 56.11/21.63 |
% 56.11/21.63 | From (1984) and (292) follows:
% 56.11/21.63 | (1985) pred(n1) = all_0_6_6
% 56.11/21.63 |
% 56.11/21.63 | From (1984) and (760) follows:
% 56.11/21.63 | (1986) succ(n1) = all_0_8_8
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 56.11/21.63 | (1987) all_0_6_6 = n0
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 56.11/21.63 | (1988) all_0_8_8 = n2
% 56.11/21.63 |
% 56.11/21.63 | From (1987)(1988) and (411) follows:
% 56.11/21.63 | (1989) sum(n0, n2) = all_0_1_1
% 56.11/21.63 |
% 56.11/21.63 | From (1987) and (10825) follows:
% 56.11/21.63 | (11016) sum(n0, n13) = all_0_4_4
% 56.11/21.63 |
% 56.11/21.63 | From (1988) and (10827) follows:
% 56.11/21.63 | (11017) sum(n11, n2) = all_0_7_7
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n11, n2, all_0_7_7, n13 and discharging atoms sum(n11, n2) = all_0_7_7, sum(n11, n2) = n13, yields:
% 56.11/21.63 | (1299) all_0_7_7 = n13
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n0, n13, all_0_4_4, n13 and discharging atoms sum(n0, n13) = all_0_4_4, sum(n0, n13) = n13, yields:
% 56.11/21.63 | (1297) all_0_4_4 = n13
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 56.11/21.63 | (1759) all_0_1_1 = n2
% 56.11/21.63 |
% 56.11/21.63 | From (1299)(1297) and (590) follows:
% 56.11/21.63 | (1301) sum(n13, n13) = all_0_3_3
% 56.11/21.63 |
% 56.11/21.63 | From (1759) and (1568) follows:
% 56.11/21.63 | (1762) sum(n24, n2) = all_0_0_0
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n24, n2, all_0_0_0, n0 and discharging atoms sum(n24, n2) = all_0_0_0, sum(n24, n2) = n0, yields:
% 56.11/21.63 | (1303) all_0_0_0 = n0
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 56.11/21.63 | (1302) all_0_3_3 = n0
% 56.11/21.63 |
% 56.11/21.63 | Equations (1303,1302) can reduce 679 to:
% 56.11/21.63 | (1106) $false
% 56.11/21.63 |
% 56.11/21.63 |-The branch is then unsatisfiable
% 56.11/21.63 |-Branch two:
% 56.11/21.63 | (2002) ~ (all_0_10_10 = n1)
% 56.11/21.63 | (2003) all_0_10_10 = n0
% 56.11/21.63 |
% 56.11/21.63 | From (2003) and (292) follows:
% 56.11/21.63 | (2004) pred(n0) = all_0_6_6
% 56.11/21.63 |
% 56.11/21.63 | From (2003) and (760) follows:
% 56.11/21.63 | (2005) succ(n0) = all_0_8_8
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 56.11/21.63 | (2006) all_0_6_6 = n25
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 56.11/21.63 | (2007) all_0_8_8 = n1
% 56.11/21.63 |
% 56.11/21.63 | From (2006)(2007) and (411) follows:
% 56.11/21.63 | (2008) sum(n25, n1) = all_0_1_1
% 56.11/21.63 |
% 56.11/21.63 | From (2006) and (10825) follows:
% 56.11/21.63 | (11033) sum(n25, n13) = all_0_4_4
% 56.11/21.63 |
% 56.11/21.63 | From (2007) and (10827) follows:
% 56.11/21.63 | (11034) sum(n11, n1) = all_0_7_7
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n25, n13, all_0_4_4, n12 and discharging atoms sum(n25, n13) = all_0_4_4, sum(n25, n13) = n12, yields:
% 56.11/21.63 | (1315) all_0_4_4 = n12
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 56.11/21.63 | (1777) all_0_1_1 = n0
% 56.11/21.63 |
% 56.11/21.63 | Instantiating formula (690) with n11, n1, all_0_7_7, n12 and discharging atoms sum(n11, n1) = all_0_7_7, sum(n11, n1) = n12, yields:
% 56.11/21.63 | (1317) all_0_7_7 = n12
% 56.11/21.63 |
% 56.11/21.63 | From (1317)(1315) and (590) follows:
% 56.11/21.64 | (1319) sum(n12, n12) = all_0_3_3
% 56.11/21.64 |
% 56.11/21.64 | From (1777) and (1568) follows:
% 56.11/21.64 | (1780) sum(n24, n0) = all_0_0_0
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (690) with n24, n0, all_0_0_0, n24 and discharging atoms sum(n24, n0) = all_0_0_0, sum(n24, n0) = n24, yields:
% 56.11/21.64 | (1321) all_0_0_0 = n24
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 56.11/21.64 | (1320) all_0_3_3 = n24
% 56.11/21.64 |
% 56.11/21.64 | Equations (1321,1320) can reduce 679 to:
% 56.11/21.64 | (1106) $false
% 56.11/21.64 |
% 56.11/21.64 |-The branch is then unsatisfiable
% 56.11/21.64 |-Branch two:
% 56.11/21.64 | (1341) ~ (all_0_11_11 = n12)
% 56.11/21.64 | (1342) 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
% 56.11/21.64 |
% 56.11/21.64 +-Applying beta-rule and splitting (1803), into two cases.
% 56.11/21.64 |-Branch one:
% 56.11/21.64 | (1804) all_0_10_10 = n11
% 56.11/21.64 |
% 56.11/21.64 | From (1804) and (292) follows:
% 56.11/21.64 | (1805) pred(n11) = all_0_6_6
% 56.11/21.64 |
% 56.11/21.64 | From (1804) and (760) follows:
% 56.11/21.64 | (1806) succ(n11) = all_0_8_8
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (500) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 56.11/21.64 | (1807) all_0_6_6 = n10
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (617) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 56.11/21.64 | (1808) all_0_8_8 = n12
% 56.11/21.64 |
% 56.11/21.64 | From (1807) and (1805) follows:
% 56.11/21.64 | (589) pred(n11) = n10
% 56.11/21.64 |
% 56.11/21.64 | From (1808) and (1806) follows:
% 56.11/21.64 | (252) succ(n11) = n12
% 56.11/21.64 |
% 56.11/21.64 | From (1807) and (541) follows:
% 56.11/21.64 | (11052) sum(n10, all_0_5_5) = all_0_4_4
% 56.11/21.64 |
% 56.11/21.64 | From (1807)(1808) and (411) follows:
% 56.11/21.64 | (1809) sum(n10, n12) = all_0_1_1
% 56.11/21.64 |
% 56.11/21.64 | From (1808) and (427) follows:
% 56.11/21.64 | (11054) sum(all_0_9_9, n12) = all_0_7_7
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (690) with n10, n12, all_0_1_1, n22 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n22, yields:
% 56.11/21.64 | (1579) all_0_1_1 = n22
% 56.11/21.64 |
% 56.11/21.64 | From (1579) and (630) follows:
% 56.11/21.64 | (2032) sum(all_0_2_2, n22) = all_0_0_0
% 56.11/21.64 |
% 56.11/21.64 | From (1579) and (1809) follows:
% 56.11/21.64 | (601) sum(n10, n12) = n22
% 56.11/21.64 |
% 56.11/21.64 +-Applying beta-rule and splitting (1342), into two cases.
% 56.11/21.64 |-Branch one:
% 56.11/21.64 | (1343) all_0_11_11 = n11
% 56.11/21.64 |
% 56.11/21.64 | From (1343) and (559) follows:
% 56.11/21.64 | (1344) pred(n11) = all_0_9_9
% 56.11/21.64 |
% 56.11/21.64 | From (1343) and (992) follows:
% 56.11/21.64 | (1345) succ(n11) = all_0_5_5
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (500) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 56.11/21.64 | (1346) all_0_9_9 = n10
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (617) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 56.11/21.64 | (1347) all_0_5_5 = n12
% 56.11/21.64 |
% 56.11/21.64 | From (1346)(1347) and (538) follows:
% 56.11/21.64 | (1348) sum(n10, n12) = all_0_2_2
% 56.11/21.64 |
% 56.11/21.64 | From (1346) and (11054) follows:
% 56.11/21.64 | (11064) sum(n10, n12) = all_0_7_7
% 56.11/21.64 |
% 56.11/21.64 | From (1347) and (11052) follows:
% 56.11/21.64 | (11065) sum(n10, n12) = all_0_4_4
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (690) with n10, n12, all_0_2_2, n22 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n22, yields:
% 56.11/21.64 | (1118) all_0_2_2 = n22
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (690) 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:
% 56.11/21.64 | (1093) all_0_2_2 = all_0_4_4
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (690) 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:
% 56.11/21.64 | (1094) all_0_2_2 = all_0_7_7
% 56.11/21.64 |
% 56.11/21.64 | Combining equations (1094,1093) yields a new equation:
% 56.11/21.64 | (1095) all_0_4_4 = all_0_7_7
% 56.11/21.64 |
% 56.11/21.64 | Combining equations (1118,1093) yields a new equation:
% 56.11/21.64 | (1135) all_0_4_4 = n22
% 56.11/21.64 |
% 56.11/21.64 | Combining equations (1135,1095) yields a new equation:
% 56.11/21.64 | (1137) all_0_7_7 = n22
% 56.11/21.64 |
% 56.11/21.64 | Combining equations (1137,1095) yields a new equation:
% 56.11/21.64 | (1135) all_0_4_4 = n22
% 56.11/21.64 |
% 56.11/21.64 | Combining equations (1135,1093) yields a new equation:
% 56.11/21.64 | (1118) all_0_2_2 = n22
% 56.11/21.64 |
% 56.11/21.64 | From (1118) and (2032) follows:
% 56.11/21.64 | (2050) sum(n22, n22) = all_0_0_0
% 56.11/21.64 |
% 56.11/21.64 | From (1137)(1135) and (590) follows:
% 56.11/21.64 | (1139) sum(n22, n22) = all_0_3_3
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (690) with n22, n22, all_0_0_0, n18 and discharging atoms sum(n22, n22) = all_0_0_0, sum(n22, n22) = n18, yields:
% 56.11/21.64 | (1141) all_0_0_0 = n18
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (690) with n22, n22, all_0_3_3, all_0_0_0 and discharging atoms sum(n22, n22) = all_0_0_0, sum(n22, n22) = all_0_3_3, yields:
% 56.11/21.64 | (1103) all_0_0_0 = all_0_3_3
% 56.11/21.64 |
% 56.11/21.64 | Combining equations (1141,1103) yields a new equation:
% 56.11/21.64 | (1140) all_0_3_3 = n18
% 56.11/21.64 |
% 56.11/21.64 | Combining equations (1140,1103) yields a new equation:
% 56.11/21.64 | (1141) all_0_0_0 = n18
% 56.11/21.64 |
% 56.11/21.64 | Equations (1141,1140) can reduce 679 to:
% 56.11/21.64 | (1106) $false
% 56.11/21.64 |
% 56.11/21.64 |-The branch is then unsatisfiable
% 56.11/21.64 |-Branch two:
% 56.11/21.64 | (1359) ~ (all_0_11_11 = n11)
% 56.11/21.64 | (1360) 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
% 56.11/21.64 |
% 56.11/21.64 +-Applying beta-rule and splitting (1360), into two cases.
% 56.11/21.64 |-Branch one:
% 56.11/21.64 | (1361) all_0_11_11 = n10
% 56.11/21.64 |
% 56.11/21.64 | From (1361) and (559) follows:
% 56.11/21.64 | (1362) pred(n10) = all_0_9_9
% 56.11/21.64 |
% 56.11/21.64 | From (1361) and (992) follows:
% 56.11/21.64 | (1363) succ(n10) = all_0_5_5
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (500) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 56.11/21.64 | (1364) all_0_9_9 = n9
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (617) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 56.11/21.64 | (1365) all_0_5_5 = n11
% 56.11/21.64 |
% 56.11/21.64 | From (1364)(1365) and (538) follows:
% 56.11/21.64 | (1366) sum(n9, n11) = all_0_2_2
% 56.11/21.64 |
% 56.11/21.64 | From (1364) and (11054) follows:
% 56.11/21.64 | (11089) sum(n9, n12) = all_0_7_7
% 56.11/21.64 |
% 56.11/21.64 | From (1365) and (11052) follows:
% 56.11/21.64 | (11090) sum(n10, n11) = all_0_4_4
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (690) with n10, n11, all_0_4_4, n21 and discharging atoms sum(n10, n11) = all_0_4_4, sum(n10, n11) = n21, yields:
% 56.11/21.64 | (1153) all_0_4_4 = n21
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (690) with n9, n12, all_0_7_7, n21 and discharging atoms sum(n9, n12) = all_0_7_7, sum(n9, n12) = n21, yields:
% 56.11/21.64 | (1155) all_0_7_7 = n21
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (690) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 56.11/21.64 | (1136) all_0_2_2 = n20
% 56.11/21.64 |
% 56.11/21.64 | From (1136) and (2032) follows:
% 56.11/21.64 | (2070) sum(n20, n22) = all_0_0_0
% 56.11/21.64 |
% 56.11/21.64 | From (1155)(1153) and (590) follows:
% 56.11/21.64 | (1157) sum(n21, n21) = all_0_3_3
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 56.11/21.64 | (1158) all_0_3_3 = n16
% 56.11/21.64 |
% 56.11/21.64 | Instantiating formula (690) with n20, n22, all_0_0_0, n16 and discharging atoms sum(n20, n22) = all_0_0_0, sum(n20, n22) = n16, yields:
% 56.11/21.64 | (1159) all_0_0_0 = n16
% 56.11/21.64 |
% 56.11/21.64 | Equations (1159,1158) can reduce 679 to:
% 56.11/21.64 | (1106) $false
% 56.11/21.64 |
% 56.11/21.64 |-The branch is then unsatisfiable
% 56.11/21.64 |-Branch two:
% 56.11/21.64 | (1377) ~ (all_0_11_11 = n10)
% 56.11/21.64 | (1378) 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
% 56.11/21.65 |
% 56.11/21.65 +-Applying beta-rule and splitting (1378), into two cases.
% 56.11/21.65 |-Branch one:
% 56.11/21.65 | (1379) all_0_11_11 = n9
% 56.11/21.65 |
% 56.11/21.65 | From (1379) and (559) follows:
% 56.11/21.65 | (1380) pred(n9) = all_0_9_9
% 56.11/21.65 |
% 56.11/21.65 | From (1379) and (992) follows:
% 56.11/21.65 | (1381) succ(n9) = all_0_5_5
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 56.11/21.65 | (1382) all_0_9_9 = n8
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 56.11/21.65 | (1383) all_0_5_5 = n10
% 56.11/21.65 |
% 56.11/21.65 | From (1382)(1383) and (538) follows:
% 56.11/21.65 | (1384) sum(n8, n10) = all_0_2_2
% 56.11/21.65 |
% 56.11/21.65 | From (1382) and (11054) follows:
% 56.11/21.65 | (11107) sum(n8, n12) = all_0_7_7
% 56.11/21.65 |
% 56.11/21.65 | From (1383) and (11052) follows:
% 56.11/21.65 | (11108) sum(n10, n10) = all_0_4_4
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (690) with n10, n10, all_0_4_4, n20 and discharging atoms sum(n10, n10) = all_0_4_4, sum(n10, n10) = n20, yields:
% 56.11/21.65 | (1171) all_0_4_4 = n20
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (690) with n8, n12, all_0_7_7, n20 and discharging atoms sum(n8, n12) = all_0_7_7, sum(n8, n12) = n20, yields:
% 56.11/21.65 | (1173) all_0_7_7 = n20
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 56.11/21.65 | (1154) all_0_2_2 = n18
% 56.11/21.65 |
% 56.11/21.65 | From (1154) and (2032) follows:
% 56.11/21.65 | (2088) sum(n18, n22) = all_0_0_0
% 56.11/21.65 |
% 56.11/21.65 | From (1173)(1171) and (590) follows:
% 56.11/21.65 | (1175) sum(n20, n20) = all_0_3_3
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 56.11/21.65 | (1176) all_0_3_3 = n14
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (690) with n18, n22, all_0_0_0, n14 and discharging atoms sum(n18, n22) = all_0_0_0, sum(n18, n22) = n14, yields:
% 56.11/21.65 | (1177) all_0_0_0 = n14
% 56.11/21.65 |
% 56.11/21.65 | Equations (1177,1176) can reduce 679 to:
% 56.11/21.65 | (1106) $false
% 56.11/21.65 |
% 56.11/21.65 |-The branch is then unsatisfiable
% 56.11/21.65 |-Branch two:
% 56.11/21.65 | (1395) ~ (all_0_11_11 = n9)
% 56.11/21.65 | (1396) 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
% 56.11/21.65 |
% 56.11/21.65 +-Applying beta-rule and splitting (1396), into two cases.
% 56.11/21.65 |-Branch one:
% 56.11/21.65 | (1397) all_0_11_11 = n8
% 56.11/21.65 |
% 56.11/21.65 | From (1397) and (559) follows:
% 56.11/21.65 | (1398) pred(n8) = all_0_9_9
% 56.11/21.65 |
% 56.11/21.65 | From (1397) and (992) follows:
% 56.11/21.65 | (1399) succ(n8) = all_0_5_5
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 56.11/21.65 | (1400) all_0_9_9 = n7
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 56.11/21.65 | (1401) all_0_5_5 = n9
% 56.11/21.65 |
% 56.11/21.65 | From (1400)(1401) and (538) follows:
% 56.11/21.65 | (1402) sum(n7, n9) = all_0_2_2
% 56.11/21.65 |
% 56.11/21.65 | From (1400) and (11054) follows:
% 56.11/21.65 | (11125) sum(n7, n12) = all_0_7_7
% 56.11/21.65 |
% 56.11/21.65 | From (1401) and (11052) follows:
% 56.11/21.65 | (11126) sum(n10, n9) = all_0_4_4
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (690) with n10, n9, all_0_4_4, n19 and discharging atoms sum(n10, n9) = all_0_4_4, sum(n10, n9) = n19, yields:
% 56.11/21.65 | (1189) all_0_4_4 = n19
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (690) with n7, n12, all_0_7_7, n19 and discharging atoms sum(n7, n12) = all_0_7_7, sum(n7, n12) = n19, yields:
% 56.11/21.65 | (1191) all_0_7_7 = n19
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 56.11/21.65 | (1172) all_0_2_2 = n16
% 56.11/21.65 |
% 56.11/21.65 | From (1172) and (2032) follows:
% 56.11/21.65 | (2106) sum(n16, n22) = all_0_0_0
% 56.11/21.65 |
% 56.11/21.65 | From (1191)(1189) and (590) follows:
% 56.11/21.65 | (1193) sum(n19, n19) = all_0_3_3
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 56.11/21.65 | (1194) all_0_3_3 = n12
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (690) with n16, n22, all_0_0_0, n12 and discharging atoms sum(n16, n22) = all_0_0_0, sum(n16, n22) = n12, yields:
% 56.11/21.65 | (1195) all_0_0_0 = n12
% 56.11/21.65 |
% 56.11/21.65 | Equations (1195,1194) can reduce 679 to:
% 56.11/21.65 | (1106) $false
% 56.11/21.65 |
% 56.11/21.65 |-The branch is then unsatisfiable
% 56.11/21.65 |-Branch two:
% 56.11/21.65 | (1413) ~ (all_0_11_11 = n8)
% 56.11/21.65 | (1414) 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
% 56.11/21.65 |
% 56.11/21.65 +-Applying beta-rule and splitting (1414), into two cases.
% 56.11/21.65 |-Branch one:
% 56.11/21.65 | (1415) all_0_11_11 = n7
% 56.11/21.65 |
% 56.11/21.65 | From (1415) and (559) follows:
% 56.11/21.65 | (1416) pred(n7) = all_0_9_9
% 56.11/21.65 |
% 56.11/21.65 | From (1415) and (992) follows:
% 56.11/21.65 | (1417) succ(n7) = all_0_5_5
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 56.11/21.65 | (1418) all_0_9_9 = n6
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 56.11/21.65 | (1419) all_0_5_5 = n8
% 56.11/21.65 |
% 56.11/21.65 | From (1418)(1419) and (538) follows:
% 56.11/21.65 | (1420) sum(n6, n8) = all_0_2_2
% 56.11/21.65 |
% 56.11/21.65 | From (1418) and (11054) follows:
% 56.11/21.65 | (11143) sum(n6, n12) = all_0_7_7
% 56.11/21.65 |
% 56.11/21.65 | From (1419) and (11052) follows:
% 56.11/21.65 | (11144) sum(n10, n8) = all_0_4_4
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (690) with n10, n8, all_0_4_4, n18 and discharging atoms sum(n10, n8) = all_0_4_4, sum(n10, n8) = n18, yields:
% 56.11/21.65 | (1207) all_0_4_4 = n18
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (690) with n6, n12, all_0_7_7, n18 and discharging atoms sum(n6, n12) = all_0_7_7, sum(n6, n12) = n18, yields:
% 56.11/21.65 | (1209) all_0_7_7 = n18
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 56.11/21.65 | (1190) all_0_2_2 = n14
% 56.11/21.65 |
% 56.11/21.65 | From (1190) and (2032) follows:
% 56.11/21.65 | (2124) sum(n14, n22) = all_0_0_0
% 56.11/21.65 |
% 56.11/21.65 | From (1209)(1207) and (590) follows:
% 56.11/21.65 | (1211) sum(n18, n18) = all_0_3_3
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 56.11/21.65 | (1212) all_0_3_3 = n10
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (690) with n14, n22, all_0_0_0, n10 and discharging atoms sum(n14, n22) = all_0_0_0, sum(n14, n22) = n10, yields:
% 56.11/21.65 | (1213) all_0_0_0 = n10
% 56.11/21.65 |
% 56.11/21.65 | Equations (1213,1212) can reduce 679 to:
% 56.11/21.65 | (1106) $false
% 56.11/21.65 |
% 56.11/21.65 |-The branch is then unsatisfiable
% 56.11/21.65 |-Branch two:
% 56.11/21.65 | (1431) ~ (all_0_11_11 = n7)
% 56.11/21.65 | (1432) 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
% 56.11/21.65 |
% 56.11/21.65 +-Applying beta-rule and splitting (1432), into two cases.
% 56.11/21.65 |-Branch one:
% 56.11/21.65 | (1433) all_0_11_11 = n6
% 56.11/21.65 |
% 56.11/21.65 | From (1433) and (559) follows:
% 56.11/21.65 | (1434) pred(n6) = all_0_9_9
% 56.11/21.65 |
% 56.11/21.65 | From (1433) and (992) follows:
% 56.11/21.65 | (1435) succ(n6) = all_0_5_5
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 56.11/21.65 | (1436) all_0_9_9 = n5
% 56.11/21.65 |
% 56.11/21.65 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 56.11/21.65 | (1437) all_0_5_5 = n7
% 56.11/21.65 |
% 56.11/21.65 | From (1436)(1437) and (538) follows:
% 56.11/21.65 | (1438) sum(n5, n7) = all_0_2_2
% 56.11/21.65 |
% 56.11/21.65 | From (1436) and (11054) follows:
% 56.11/21.66 | (11161) sum(n5, n12) = all_0_7_7
% 56.11/21.66 |
% 56.11/21.66 | From (1437) and (11052) follows:
% 56.11/21.66 | (11162) sum(n10, n7) = all_0_4_4
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (690) with n10, n7, all_0_4_4, n17 and discharging atoms sum(n10, n7) = all_0_4_4, sum(n10, n7) = n17, yields:
% 56.11/21.66 | (1225) all_0_4_4 = n17
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (690) with n5, n12, all_0_7_7, n17 and discharging atoms sum(n5, n12) = all_0_7_7, sum(n5, n12) = n17, yields:
% 56.11/21.66 | (1227) all_0_7_7 = n17
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 56.11/21.66 | (1208) all_0_2_2 = n12
% 56.11/21.66 |
% 56.11/21.66 | From (1208) and (2032) follows:
% 56.11/21.66 | (2142) sum(n12, n22) = all_0_0_0
% 56.11/21.66 |
% 56.11/21.66 | From (1227)(1225) and (590) follows:
% 56.11/21.66 | (1229) sum(n17, n17) = all_0_3_3
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 56.11/21.66 | (1230) all_0_3_3 = n8
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (690) with n12, n22, all_0_0_0, n8 and discharging atoms sum(n12, n22) = all_0_0_0, sum(n12, n22) = n8, yields:
% 56.11/21.66 | (1231) all_0_0_0 = n8
% 56.11/21.66 |
% 56.11/21.66 | Equations (1231,1230) can reduce 679 to:
% 56.11/21.66 | (1106) $false
% 56.11/21.66 |
% 56.11/21.66 |-The branch is then unsatisfiable
% 56.11/21.66 |-Branch two:
% 56.11/21.66 | (1449) ~ (all_0_11_11 = n6)
% 56.11/21.66 | (1450) 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
% 56.11/21.66 |
% 56.11/21.66 +-Applying beta-rule and splitting (1450), into two cases.
% 56.11/21.66 |-Branch one:
% 56.11/21.66 | (1451) all_0_11_11 = n5
% 56.11/21.66 |
% 56.11/21.66 | From (1451) and (559) follows:
% 56.11/21.66 | (1452) pred(n5) = all_0_9_9
% 56.11/21.66 |
% 56.11/21.66 | From (1451) and (992) follows:
% 56.11/21.66 | (1453) succ(n5) = all_0_5_5
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 56.11/21.66 | (1454) all_0_9_9 = n4
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 56.11/21.66 | (1455) all_0_5_5 = n6
% 56.11/21.66 |
% 56.11/21.66 | From (1454)(1455) and (538) follows:
% 56.11/21.66 | (1456) sum(n4, n6) = all_0_2_2
% 56.11/21.66 |
% 56.11/21.66 | From (1454) and (11054) follows:
% 56.11/21.66 | (11179) sum(n4, n12) = all_0_7_7
% 56.11/21.66 |
% 56.11/21.66 | From (1455) and (11052) follows:
% 56.11/21.66 | (11180) sum(n10, n6) = all_0_4_4
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (690) with n10, n6, all_0_4_4, n16 and discharging atoms sum(n10, n6) = all_0_4_4, sum(n10, n6) = n16, yields:
% 56.11/21.66 | (1243) all_0_4_4 = n16
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (690) with n4, n12, all_0_7_7, n16 and discharging atoms sum(n4, n12) = all_0_7_7, sum(n4, n12) = n16, yields:
% 56.11/21.66 | (1245) all_0_7_7 = n16
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 56.11/21.66 | (1226) all_0_2_2 = n10
% 56.11/21.66 |
% 56.11/21.66 | From (1226) and (2032) follows:
% 56.11/21.66 | (2160) sum(n10, n22) = all_0_0_0
% 56.11/21.66 |
% 56.11/21.66 | From (1245)(1243) and (590) follows:
% 56.11/21.66 | (1247) sum(n16, n16) = all_0_3_3
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 56.11/21.66 | (1248) all_0_3_3 = n6
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (690) with n10, n22, all_0_0_0, n6 and discharging atoms sum(n10, n22) = all_0_0_0, sum(n10, n22) = n6, yields:
% 56.11/21.66 | (1249) all_0_0_0 = n6
% 56.11/21.66 |
% 56.11/21.66 | Equations (1249,1248) can reduce 679 to:
% 56.11/21.66 | (1106) $false
% 56.11/21.66 |
% 56.11/21.66 |-The branch is then unsatisfiable
% 56.11/21.66 |-Branch two:
% 56.11/21.66 | (1467) ~ (all_0_11_11 = n5)
% 56.11/21.66 | (1468) 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
% 56.11/21.66 |
% 56.11/21.66 +-Applying beta-rule and splitting (1468), into two cases.
% 56.11/21.66 |-Branch one:
% 56.11/21.66 | (1469) all_0_11_11 = n4
% 56.11/21.66 |
% 56.11/21.66 | From (1469) and (559) follows:
% 56.11/21.66 | (1470) pred(n4) = all_0_9_9
% 56.11/21.66 |
% 56.11/21.66 | From (1469) and (992) follows:
% 56.11/21.66 | (1471) succ(n4) = all_0_5_5
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 56.11/21.66 | (1472) all_0_9_9 = n3
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 56.11/21.66 | (1473) all_0_5_5 = n5
% 56.11/21.66 |
% 56.11/21.66 | From (1472)(1473) and (538) follows:
% 56.11/21.66 | (1474) sum(n3, n5) = all_0_2_2
% 56.11/21.66 |
% 56.11/21.66 | From (1472) and (11054) follows:
% 56.11/21.66 | (11197) sum(n3, n12) = all_0_7_7
% 56.11/21.66 |
% 56.11/21.66 | From (1473) and (11052) follows:
% 56.11/21.66 | (11198) sum(n10, n5) = all_0_4_4
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (690) with n10, n5, all_0_4_4, n15 and discharging atoms sum(n10, n5) = all_0_4_4, sum(n10, n5) = n15, yields:
% 56.11/21.66 | (1261) all_0_4_4 = n15
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (690) with n3, n12, all_0_7_7, n15 and discharging atoms sum(n3, n12) = all_0_7_7, sum(n3, n12) = n15, yields:
% 56.11/21.66 | (1263) all_0_7_7 = n15
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 56.11/21.66 | (1244) all_0_2_2 = n8
% 56.11/21.66 |
% 56.11/21.66 | From (1244) and (2032) follows:
% 56.11/21.66 | (2178) sum(n8, n22) = all_0_0_0
% 56.11/21.66 |
% 56.11/21.66 | From (1263)(1261) and (590) follows:
% 56.11/21.66 | (1265) sum(n15, n15) = all_0_3_3
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 56.11/21.66 | (1266) all_0_3_3 = n4
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (690) with n8, n22, all_0_0_0, n4 and discharging atoms sum(n8, n22) = all_0_0_0, sum(n8, n22) = n4, yields:
% 56.11/21.66 | (1267) all_0_0_0 = n4
% 56.11/21.66 |
% 56.11/21.66 | Equations (1267,1266) can reduce 679 to:
% 56.11/21.66 | (1106) $false
% 56.11/21.66 |
% 56.11/21.66 |-The branch is then unsatisfiable
% 56.11/21.66 |-Branch two:
% 56.11/21.66 | (1485) ~ (all_0_11_11 = n4)
% 56.11/21.66 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.11/21.66 |
% 56.11/21.66 +-Applying beta-rule and splitting (1486), into two cases.
% 56.11/21.66 |-Branch one:
% 56.11/21.66 | (1487) all_0_11_11 = n3
% 56.11/21.66 |
% 56.11/21.66 | From (1487) and (559) follows:
% 56.11/21.66 | (1488) pred(n3) = all_0_9_9
% 56.11/21.66 |
% 56.11/21.66 | From (1487) and (992) follows:
% 56.11/21.66 | (1489) succ(n3) = all_0_5_5
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 56.11/21.66 | (1490) all_0_9_9 = n2
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 56.11/21.66 | (1491) all_0_5_5 = n4
% 56.11/21.66 |
% 56.11/21.66 | From (1490)(1491) and (538) follows:
% 56.11/21.66 | (1492) sum(n2, n4) = all_0_2_2
% 56.11/21.66 |
% 56.11/21.66 | From (1490) and (11054) follows:
% 56.11/21.66 | (11215) sum(n2, n12) = all_0_7_7
% 56.11/21.66 |
% 56.11/21.66 | From (1491) and (11052) follows:
% 56.11/21.66 | (11216) sum(n10, n4) = all_0_4_4
% 56.11/21.66 |
% 56.11/21.66 | Instantiating formula (690) with n10, n4, all_0_4_4, n14 and discharging atoms sum(n10, n4) = all_0_4_4, sum(n10, n4) = n14, yields:
% 56.11/21.67 | (1279) all_0_4_4 = n14
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n2, n12, all_0_7_7, n14 and discharging atoms sum(n2, n12) = all_0_7_7, sum(n2, n12) = n14, yields:
% 56.11/21.67 | (1281) all_0_7_7 = n14
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 56.11/21.67 | (1262) all_0_2_2 = n6
% 56.11/21.67 |
% 56.11/21.67 | From (1262) and (2032) follows:
% 56.11/21.67 | (2196) sum(n6, n22) = all_0_0_0
% 56.11/21.67 |
% 56.11/21.67 | From (1281)(1279) and (590) follows:
% 56.11/21.67 | (1283) sum(n14, n14) = all_0_3_3
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 56.11/21.67 | (1284) all_0_3_3 = n2
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n6, n22, all_0_0_0, n2 and discharging atoms sum(n6, n22) = all_0_0_0, sum(n6, n22) = n2, yields:
% 56.11/21.67 | (1285) all_0_0_0 = n2
% 56.11/21.67 |
% 56.11/21.67 | Equations (1285,1284) can reduce 679 to:
% 56.11/21.67 | (1106) $false
% 56.11/21.67 |
% 56.11/21.67 |-The branch is then unsatisfiable
% 56.11/21.67 |-Branch two:
% 56.11/21.67 | (1503) ~ (all_0_11_11 = n3)
% 56.11/21.67 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.11/21.67 |
% 56.11/21.67 +-Applying beta-rule and splitting (1504), into two cases.
% 56.11/21.67 |-Branch one:
% 56.11/21.67 | (1505) all_0_11_11 = n2
% 56.11/21.67 |
% 56.11/21.67 | From (1505) and (559) follows:
% 56.11/21.67 | (1506) pred(n2) = all_0_9_9
% 56.11/21.67 |
% 56.11/21.67 | From (1505) and (992) follows:
% 56.11/21.67 | (1507) succ(n2) = all_0_5_5
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 56.11/21.67 | (1508) all_0_9_9 = n1
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 56.11/21.67 | (1509) all_0_5_5 = n3
% 56.11/21.67 |
% 56.11/21.67 | From (1508)(1509) and (538) follows:
% 56.11/21.67 | (1510) sum(n1, n3) = all_0_2_2
% 56.11/21.67 |
% 56.11/21.67 | From (1508) and (11054) follows:
% 56.11/21.67 | (11233) sum(n1, n12) = all_0_7_7
% 56.11/21.67 |
% 56.11/21.67 | From (1509) and (11052) follows:
% 56.11/21.67 | (11234) sum(n10, n3) = all_0_4_4
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n10, n3, all_0_4_4, n13 and discharging atoms sum(n10, n3) = all_0_4_4, sum(n10, n3) = n13, yields:
% 56.11/21.67 | (1297) all_0_4_4 = n13
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n1, n12, all_0_7_7, n13 and discharging atoms sum(n1, n12) = all_0_7_7, sum(n1, n12) = n13, yields:
% 56.11/21.67 | (1299) all_0_7_7 = n13
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 56.11/21.67 | (1280) all_0_2_2 = n4
% 56.11/21.67 |
% 56.11/21.67 | From (1280) and (2032) follows:
% 56.11/21.67 | (2214) sum(n4, n22) = all_0_0_0
% 56.11/21.67 |
% 56.11/21.67 | From (1299)(1297) and (590) follows:
% 56.11/21.67 | (1301) sum(n13, n13) = all_0_3_3
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 56.11/21.67 | (1302) all_0_3_3 = n0
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n4, n22, all_0_0_0, n0 and discharging atoms sum(n4, n22) = all_0_0_0, sum(n4, n22) = n0, yields:
% 56.11/21.67 | (1303) all_0_0_0 = n0
% 56.11/21.67 |
% 56.11/21.67 | Equations (1303,1302) can reduce 679 to:
% 56.11/21.67 | (1106) $false
% 56.11/21.67 |
% 56.11/21.67 |-The branch is then unsatisfiable
% 56.11/21.67 |-Branch two:
% 56.11/21.67 | (1521) ~ (all_0_11_11 = n2)
% 56.11/21.67 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 56.11/21.67 |
% 56.11/21.67 +-Applying beta-rule and splitting (1522), into two cases.
% 56.11/21.67 |-Branch one:
% 56.11/21.67 | (1523) all_0_11_11 = n1
% 56.11/21.67 |
% 56.11/21.67 | From (1523) and (559) follows:
% 56.11/21.67 | (1524) pred(n1) = all_0_9_9
% 56.11/21.67 |
% 56.11/21.67 | From (1523) and (992) follows:
% 56.11/21.67 | (1525) succ(n1) = all_0_5_5
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 56.11/21.67 | (1526) all_0_9_9 = n0
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 56.11/21.67 | (1527) all_0_5_5 = n2
% 56.11/21.67 |
% 56.11/21.67 | From (1526)(1527) and (538) follows:
% 56.11/21.67 | (1528) sum(n0, n2) = all_0_2_2
% 56.11/21.67 |
% 56.11/21.67 | From (1526) and (11054) follows:
% 56.11/21.67 | (11251) sum(n0, n12) = all_0_7_7
% 56.11/21.67 |
% 56.11/21.67 | From (1527) and (11052) follows:
% 56.11/21.67 | (11252) sum(n10, n2) = all_0_4_4
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n10, n2, all_0_4_4, n12 and discharging atoms sum(n10, n2) = all_0_4_4, sum(n10, n2) = n12, yields:
% 56.11/21.67 | (1315) all_0_4_4 = n12
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n0, n12, all_0_7_7, n12 and discharging atoms sum(n0, n12) = all_0_7_7, sum(n0, n12) = n12, yields:
% 56.11/21.67 | (1317) all_0_7_7 = n12
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 56.11/21.67 | (1298) all_0_2_2 = n2
% 56.11/21.67 |
% 56.11/21.67 | From (1298) and (2032) follows:
% 56.11/21.67 | (2232) sum(n2, n22) = all_0_0_0
% 56.11/21.67 |
% 56.11/21.67 | From (1317)(1315) and (590) follows:
% 56.11/21.67 | (1319) sum(n12, n12) = all_0_3_3
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 56.11/21.67 | (1320) all_0_3_3 = n24
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n2, n22, all_0_0_0, n24 and discharging atoms sum(n2, n22) = all_0_0_0, sum(n2, n22) = n24, yields:
% 56.11/21.67 | (1321) all_0_0_0 = n24
% 56.11/21.67 |
% 56.11/21.67 | Equations (1321,1320) can reduce 679 to:
% 56.11/21.67 | (1106) $false
% 56.11/21.67 |
% 56.11/21.67 |-The branch is then unsatisfiable
% 56.11/21.67 |-Branch two:
% 56.11/21.67 | (1540) ~ (all_0_11_11 = n1)
% 56.11/21.67 | (1541) all_0_11_11 = n0
% 56.11/21.67 |
% 56.11/21.67 | From (1541) and (559) follows:
% 56.11/21.67 | (1542) pred(n0) = all_0_9_9
% 56.11/21.67 |
% 56.11/21.67 | From (1541) and (992) follows:
% 56.11/21.67 | (1543) succ(n0) = all_0_5_5
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 56.11/21.67 | (1544) all_0_9_9 = n25
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 56.11/21.67 | (1545) all_0_5_5 = n1
% 56.11/21.67 |
% 56.11/21.67 | From (1544)(1545) and (538) follows:
% 56.11/21.67 | (1546) sum(n25, n1) = all_0_2_2
% 56.11/21.67 |
% 56.11/21.67 | From (1544) and (11054) follows:
% 56.11/21.67 | (11268) sum(n25, n12) = all_0_7_7
% 56.11/21.67 |
% 56.11/21.67 | From (1545) and (11052) follows:
% 56.11/21.67 | (11269) sum(n10, n1) = all_0_4_4
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n25, n12, all_0_7_7, n11 and discharging atoms sum(n25, n12) = all_0_7_7, sum(n25, n12) = n11, yields:
% 56.11/21.67 | (1335) all_0_7_7 = n11
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 56.11/21.67 | (1316) all_0_2_2 = n0
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n10, n1, all_0_4_4, n11 and discharging atoms sum(n10, n1) = all_0_4_4, sum(n10, n1) = n11, yields:
% 56.11/21.67 | (1333) all_0_4_4 = n11
% 56.11/21.67 |
% 56.11/21.67 | From (1316) and (2032) follows:
% 56.11/21.67 | (2250) sum(n0, n22) = all_0_0_0
% 56.11/21.67 |
% 56.11/21.67 | From (1335)(1333) and (590) follows:
% 56.11/21.67 | (1337) sum(n11, n11) = all_0_3_3
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 56.11/21.67 | (1104) all_0_3_3 = n22
% 56.11/21.67 |
% 56.11/21.67 | Instantiating formula (690) with n0, n22, all_0_0_0, n22 and discharging atoms sum(n0, n22) = all_0_0_0, sum(n0, n22) = n22, yields:
% 56.11/21.67 | (1102) all_0_0_0 = n22
% 56.11/21.67 |
% 56.11/21.67 | Equations (1102,1104) can reduce 679 to:
% 56.11/21.67 | (1106) $false
% 56.11/21.67 |
% 56.11/21.67 |-The branch is then unsatisfiable
% 56.11/21.68 |-Branch two:
% 56.11/21.68 | (1820) ~ (all_0_10_10 = n11)
% 56.11/21.68 | (1821) 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
% 56.11/21.68 |
% 56.11/21.68 +-Applying beta-rule and splitting (1342), into two cases.
% 56.11/21.68 |-Branch one:
% 56.11/21.68 | (1343) all_0_11_11 = n11
% 56.11/21.68 |
% 56.11/21.68 | From (1343) and (559) follows:
% 56.11/21.68 | (1344) pred(n11) = all_0_9_9
% 56.11/21.68 |
% 56.11/21.68 | From (1343) and (992) follows:
% 56.11/21.68 | (1345) succ(n11) = all_0_5_5
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (500) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 56.11/21.68 | (1346) all_0_9_9 = n10
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (617) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 56.11/21.68 | (1347) all_0_5_5 = n12
% 56.11/21.68 |
% 56.11/21.68 | From (1347) and (541) follows:
% 56.11/21.68 | (11285) sum(all_0_6_6, n12) = all_0_4_4
% 56.11/21.68 |
% 56.11/21.68 | From (1346)(1347) and (538) follows:
% 56.11/21.68 | (1348) sum(n10, n12) = all_0_2_2
% 56.11/21.68 |
% 56.11/21.68 | From (1346) and (427) follows:
% 56.11/21.68 | (11287) sum(n10, all_0_8_8) = all_0_7_7
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (690) with n10, n12, all_0_2_2, n22 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n22, yields:
% 56.11/21.68 | (1118) all_0_2_2 = n22
% 56.11/21.68 |
% 56.11/21.68 | From (1118) and (630) follows:
% 56.11/21.68 | (2499) sum(n22, all_0_1_1) = all_0_0_0
% 56.11/21.68 |
% 56.11/21.68 +-Applying beta-rule and splitting (1821), into two cases.
% 56.11/21.68 |-Branch one:
% 56.11/21.68 | (1822) all_0_10_10 = n10
% 56.11/21.68 |
% 56.11/21.68 | From (1822) and (292) follows:
% 56.11/21.68 | (1823) pred(n10) = all_0_6_6
% 56.11/21.68 |
% 56.11/21.68 | From (1822) and (760) follows:
% 56.11/21.68 | (1824) succ(n10) = all_0_8_8
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (500) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 56.11/21.68 | (1825) all_0_6_6 = n9
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (617) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 56.11/21.68 | (1826) all_0_8_8 = n11
% 56.11/21.68 |
% 56.11/21.68 | From (1825)(1826) and (411) follows:
% 56.11/21.68 | (1827) sum(n9, n11) = all_0_1_1
% 56.11/21.68 |
% 56.11/21.68 | From (1825) and (11285) follows:
% 56.11/21.68 | (11296) sum(n9, n12) = all_0_4_4
% 56.11/21.68 |
% 56.11/21.68 | From (1826) and (11287) follows:
% 56.11/21.68 | (11297) sum(n10, n11) = all_0_7_7
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (690) with n10, n11, all_0_7_7, n21 and discharging atoms sum(n10, n11) = all_0_7_7, sum(n10, n11) = n21, yields:
% 56.11/21.68 | (1155) all_0_7_7 = n21
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (690) with n9, n12, all_0_4_4, n21 and discharging atoms sum(n9, n12) = all_0_4_4, sum(n9, n12) = n21, yields:
% 56.11/21.68 | (1153) all_0_4_4 = n21
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (690) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 56.11/21.68 | (1597) all_0_1_1 = n20
% 56.11/21.68 |
% 56.11/21.68 | From (1155)(1153) and (590) follows:
% 56.11/21.68 | (1157) sum(n21, n21) = all_0_3_3
% 56.11/21.68 |
% 56.11/21.68 | From (1597) and (2499) follows:
% 56.11/21.68 | (2512) sum(n22, n20) = all_0_0_0
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (690) with n22, n20, all_0_0_0, n16 and discharging atoms sum(n22, n20) = all_0_0_0, sum(n22, n20) = n16, yields:
% 56.11/21.68 | (1159) all_0_0_0 = n16
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (690) with n21, n21, all_0_3_3, n16 and discharging atoms sum(n21, n21) = all_0_3_3, sum(n21, n21) = n16, yields:
% 56.11/21.68 | (1158) all_0_3_3 = n16
% 56.11/21.68 |
% 56.11/21.68 | Equations (1159,1158) can reduce 679 to:
% 56.11/21.68 | (1106) $false
% 56.11/21.68 |
% 56.11/21.68 |-The branch is then unsatisfiable
% 56.11/21.68 |-Branch two:
% 56.11/21.68 | (1838) ~ (all_0_10_10 = n10)
% 56.11/21.68 | (1839) 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
% 56.11/21.68 |
% 56.11/21.68 +-Applying beta-rule and splitting (1839), into two cases.
% 56.11/21.68 |-Branch one:
% 56.11/21.68 | (1840) all_0_10_10 = n9
% 56.11/21.68 |
% 56.11/21.68 | From (1840) and (292) follows:
% 56.11/21.68 | (1841) pred(n9) = all_0_6_6
% 56.11/21.68 |
% 56.11/21.68 | From (1840) and (760) follows:
% 56.11/21.68 | (1842) succ(n9) = all_0_8_8
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (500) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 56.11/21.68 | (1843) all_0_6_6 = n8
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (617) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 56.11/21.68 | (1844) all_0_8_8 = n10
% 56.11/21.68 |
% 56.11/21.68 | From (1843)(1844) and (411) follows:
% 56.11/21.68 | (1845) sum(n8, n10) = all_0_1_1
% 56.11/21.68 |
% 56.11/21.68 | From (1843) and (11285) follows:
% 56.11/21.68 | (11314) sum(n8, n12) = all_0_4_4
% 56.11/21.68 |
% 56.11/21.68 | From (1844) and (11287) follows:
% 56.11/21.68 | (11315) sum(n10, n10) = all_0_7_7
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (690) with n10, n10, all_0_7_7, n20 and discharging atoms sum(n10, n10) = all_0_7_7, sum(n10, n10) = n20, yields:
% 56.11/21.68 | (1173) all_0_7_7 = n20
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (690) with n8, n12, all_0_4_4, n20 and discharging atoms sum(n8, n12) = all_0_4_4, sum(n8, n12) = n20, yields:
% 56.11/21.68 | (1171) all_0_4_4 = n20
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (690) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 56.11/21.68 | (1615) all_0_1_1 = n18
% 56.11/21.68 |
% 56.11/21.68 | From (1173)(1171) and (590) follows:
% 56.11/21.68 | (1175) sum(n20, n20) = all_0_3_3
% 56.11/21.68 |
% 56.11/21.68 | From (1615) and (2499) follows:
% 56.11/21.68 | (2530) sum(n22, n18) = all_0_0_0
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (690) with n22, n18, all_0_0_0, n14 and discharging atoms sum(n22, n18) = all_0_0_0, sum(n22, n18) = n14, yields:
% 56.11/21.68 | (1177) all_0_0_0 = n14
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (690) with n20, n20, all_0_3_3, n14 and discharging atoms sum(n20, n20) = all_0_3_3, sum(n20, n20) = n14, yields:
% 56.11/21.68 | (1176) all_0_3_3 = n14
% 56.11/21.68 |
% 56.11/21.68 | Equations (1177,1176) can reduce 679 to:
% 56.11/21.68 | (1106) $false
% 56.11/21.68 |
% 56.11/21.68 |-The branch is then unsatisfiable
% 56.11/21.68 |-Branch two:
% 56.11/21.68 | (1856) ~ (all_0_10_10 = n9)
% 56.11/21.68 | (1857) 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
% 56.11/21.68 |
% 56.11/21.68 +-Applying beta-rule and splitting (1857), into two cases.
% 56.11/21.68 |-Branch one:
% 56.11/21.68 | (1858) all_0_10_10 = n8
% 56.11/21.68 |
% 56.11/21.68 | From (1858) and (292) follows:
% 56.11/21.68 | (1859) pred(n8) = all_0_6_6
% 56.11/21.68 |
% 56.11/21.68 | From (1858) and (760) follows:
% 56.11/21.68 | (1860) succ(n8) = all_0_8_8
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 56.11/21.68 | (1861) all_0_6_6 = n7
% 56.11/21.68 |
% 56.11/21.68 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 56.11/21.68 | (1862) all_0_8_8 = n9
% 56.11/21.68 |
% 56.11/21.68 | From (1861)(1862) and (411) follows:
% 56.11/21.68 | (1863) sum(n7, n9) = all_0_1_1
% 56.11/21.68 |
% 56.11/21.68 | From (1861) and (11285) follows:
% 56.11/21.68 | (11332) sum(n7, n12) = all_0_4_4
% 56.11/21.68 |
% 56.11/21.68 | From (1862) and (11287) follows:
% 56.11/21.69 | (11333) sum(n10, n9) = all_0_7_7
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (690) with n10, n9, all_0_7_7, n19 and discharging atoms sum(n10, n9) = all_0_7_7, sum(n10, n9) = n19, yields:
% 56.11/21.69 | (1191) all_0_7_7 = n19
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (690) with n7, n12, all_0_4_4, n19 and discharging atoms sum(n7, n12) = all_0_4_4, sum(n7, n12) = n19, yields:
% 56.11/21.69 | (1189) all_0_4_4 = n19
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 56.11/21.69 | (1633) all_0_1_1 = n16
% 56.11/21.69 |
% 56.11/21.69 | From (1191)(1189) and (590) follows:
% 56.11/21.69 | (1193) sum(n19, n19) = all_0_3_3
% 56.11/21.69 |
% 56.11/21.69 | From (1633) and (2499) follows:
% 56.11/21.69 | (2548) sum(n22, n16) = all_0_0_0
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (690) with n22, n16, all_0_0_0, n12 and discharging atoms sum(n22, n16) = all_0_0_0, sum(n22, n16) = n12, yields:
% 56.11/21.69 | (1195) all_0_0_0 = n12
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 56.11/21.69 | (1194) all_0_3_3 = n12
% 56.11/21.69 |
% 56.11/21.69 | Equations (1195,1194) can reduce 679 to:
% 56.11/21.69 | (1106) $false
% 56.11/21.69 |
% 56.11/21.69 |-The branch is then unsatisfiable
% 56.11/21.69 |-Branch two:
% 56.11/21.69 | (1874) ~ (all_0_10_10 = n8)
% 56.11/21.69 | (1875) 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
% 56.11/21.69 |
% 56.11/21.69 +-Applying beta-rule and splitting (1875), into two cases.
% 56.11/21.69 |-Branch one:
% 56.11/21.69 | (1876) all_0_10_10 = n7
% 56.11/21.69 |
% 56.11/21.69 | From (1876) and (292) follows:
% 56.11/21.69 | (1877) pred(n7) = all_0_6_6
% 56.11/21.69 |
% 56.11/21.69 | From (1876) and (760) follows:
% 56.11/21.69 | (1878) succ(n7) = all_0_8_8
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 56.11/21.69 | (1879) all_0_6_6 = n6
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 56.11/21.69 | (1880) all_0_8_8 = n8
% 56.11/21.69 |
% 56.11/21.69 | From (1879)(1880) and (411) follows:
% 56.11/21.69 | (1881) sum(n6, n8) = all_0_1_1
% 56.11/21.69 |
% 56.11/21.69 | From (1879) and (11285) follows:
% 56.11/21.69 | (11350) sum(n6, n12) = all_0_4_4
% 56.11/21.69 |
% 56.11/21.69 | From (1880) and (11287) follows:
% 56.11/21.69 | (11351) sum(n10, n8) = all_0_7_7
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (690) with n10, n8, all_0_7_7, n18 and discharging atoms sum(n10, n8) = all_0_7_7, sum(n10, n8) = n18, yields:
% 56.11/21.69 | (1209) all_0_7_7 = n18
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (690) with n6, n12, all_0_4_4, n18 and discharging atoms sum(n6, n12) = all_0_4_4, sum(n6, n12) = n18, yields:
% 56.11/21.69 | (1207) all_0_4_4 = n18
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 56.11/21.69 | (1651) all_0_1_1 = n14
% 56.11/21.69 |
% 56.11/21.69 | From (1209)(1207) and (590) follows:
% 56.11/21.69 | (1211) sum(n18, n18) = all_0_3_3
% 56.11/21.69 |
% 56.11/21.69 | From (1651) and (2499) follows:
% 56.11/21.69 | (2566) sum(n22, n14) = all_0_0_0
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (690) with n22, n14, all_0_0_0, n10 and discharging atoms sum(n22, n14) = all_0_0_0, sum(n22, n14) = n10, yields:
% 56.11/21.69 | (1213) all_0_0_0 = n10
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 56.11/21.69 | (1212) all_0_3_3 = n10
% 56.11/21.69 |
% 56.11/21.69 | Equations (1213,1212) can reduce 679 to:
% 56.11/21.69 | (1106) $false
% 56.11/21.69 |
% 56.11/21.69 |-The branch is then unsatisfiable
% 56.11/21.69 |-Branch two:
% 56.11/21.69 | (1892) ~ (all_0_10_10 = n7)
% 56.11/21.69 | (1893) 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
% 56.11/21.69 |
% 56.11/21.69 +-Applying beta-rule and splitting (1893), into two cases.
% 56.11/21.69 |-Branch one:
% 56.11/21.69 | (1894) all_0_10_10 = n6
% 56.11/21.69 |
% 56.11/21.69 | From (1894) and (292) follows:
% 56.11/21.69 | (1895) pred(n6) = all_0_6_6
% 56.11/21.69 |
% 56.11/21.69 | From (1894) and (760) follows:
% 56.11/21.69 | (1896) succ(n6) = all_0_8_8
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 56.11/21.69 | (1897) all_0_6_6 = n5
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 56.11/21.69 | (1898) all_0_8_8 = n7
% 56.11/21.69 |
% 56.11/21.69 | From (1897)(1898) and (411) follows:
% 56.11/21.69 | (1899) sum(n5, n7) = all_0_1_1
% 56.11/21.69 |
% 56.11/21.69 | From (1897) and (11285) follows:
% 56.11/21.69 | (11368) sum(n5, n12) = all_0_4_4
% 56.11/21.69 |
% 56.11/21.69 | From (1898) and (11287) follows:
% 56.11/21.69 | (11369) sum(n10, n7) = all_0_7_7
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (690) with n10, n7, all_0_7_7, n17 and discharging atoms sum(n10, n7) = all_0_7_7, sum(n10, n7) = n17, yields:
% 56.11/21.69 | (1227) all_0_7_7 = n17
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (690) with n5, n12, all_0_4_4, n17 and discharging atoms sum(n5, n12) = all_0_4_4, sum(n5, n12) = n17, yields:
% 56.11/21.69 | (1225) all_0_4_4 = n17
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 56.11/21.69 | (1669) all_0_1_1 = n12
% 56.11/21.69 |
% 56.11/21.69 | From (1227)(1225) and (590) follows:
% 56.11/21.69 | (1229) sum(n17, n17) = all_0_3_3
% 56.11/21.69 |
% 56.11/21.69 | From (1669) and (2499) follows:
% 56.11/21.69 | (2584) sum(n22, n12) = all_0_0_0
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (690) with n22, n12, all_0_0_0, n8 and discharging atoms sum(n22, n12) = all_0_0_0, sum(n22, n12) = n8, yields:
% 56.11/21.69 | (1231) all_0_0_0 = n8
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 56.11/21.69 | (1230) all_0_3_3 = n8
% 56.11/21.69 |
% 56.11/21.69 | Equations (1231,1230) can reduce 679 to:
% 56.11/21.69 | (1106) $false
% 56.11/21.69 |
% 56.11/21.69 |-The branch is then unsatisfiable
% 56.11/21.69 |-Branch two:
% 56.11/21.69 | (1910) ~ (all_0_10_10 = n6)
% 56.11/21.69 | (1911) 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
% 56.11/21.69 |
% 56.11/21.69 +-Applying beta-rule and splitting (1911), into two cases.
% 56.11/21.69 |-Branch one:
% 56.11/21.69 | (1912) all_0_10_10 = n5
% 56.11/21.69 |
% 56.11/21.69 | From (1912) and (292) follows:
% 56.11/21.69 | (1913) pred(n5) = all_0_6_6
% 56.11/21.69 |
% 56.11/21.69 | From (1912) and (760) follows:
% 56.11/21.69 | (1914) succ(n5) = all_0_8_8
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 56.11/21.69 | (1915) all_0_6_6 = n4
% 56.11/21.69 |
% 56.11/21.69 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 56.11/21.69 | (1916) all_0_8_8 = n6
% 56.11/21.69 |
% 56.11/21.69 | From (1915)(1916) and (411) follows:
% 56.11/21.69 | (1917) sum(n4, n6) = all_0_1_1
% 56.11/21.69 |
% 56.11/21.69 | From (1915) and (11285) follows:
% 56.11/21.69 | (11386) sum(n4, n12) = all_0_4_4
% 56.11/21.69 |
% 56.11/21.69 | From (1916) and (11287) follows:
% 56.11/21.70 | (11387) sum(n10, n6) = all_0_7_7
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (690) with n10, n6, all_0_7_7, n16 and discharging atoms sum(n10, n6) = all_0_7_7, sum(n10, n6) = n16, yields:
% 56.11/21.70 | (1245) all_0_7_7 = n16
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (690) with n4, n12, all_0_4_4, n16 and discharging atoms sum(n4, n12) = all_0_4_4, sum(n4, n12) = n16, yields:
% 56.11/21.70 | (1243) all_0_4_4 = n16
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 56.11/21.70 | (1687) all_0_1_1 = n10
% 56.11/21.70 |
% 56.11/21.70 | From (1245)(1243) and (590) follows:
% 56.11/21.70 | (1247) sum(n16, n16) = all_0_3_3
% 56.11/21.70 |
% 56.11/21.70 | From (1687) and (2499) follows:
% 56.11/21.70 | (2602) sum(n22, n10) = all_0_0_0
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (690) with n22, n10, all_0_0_0, n6 and discharging atoms sum(n22, n10) = all_0_0_0, sum(n22, n10) = n6, yields:
% 56.11/21.70 | (1249) all_0_0_0 = n6
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 56.11/21.70 | (1248) all_0_3_3 = n6
% 56.11/21.70 |
% 56.11/21.70 | Equations (1249,1248) can reduce 679 to:
% 56.11/21.70 | (1106) $false
% 56.11/21.70 |
% 56.11/21.70 |-The branch is then unsatisfiable
% 56.11/21.70 |-Branch two:
% 56.11/21.70 | (1928) ~ (all_0_10_10 = n5)
% 56.11/21.70 | (1929) 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
% 56.11/21.70 |
% 56.11/21.70 +-Applying beta-rule and splitting (1929), into two cases.
% 56.11/21.70 |-Branch one:
% 56.11/21.70 | (1930) all_0_10_10 = n4
% 56.11/21.70 |
% 56.11/21.70 | From (1930) and (292) follows:
% 56.11/21.70 | (1931) pred(n4) = all_0_6_6
% 56.11/21.70 |
% 56.11/21.70 | From (1930) and (760) follows:
% 56.11/21.70 | (1932) succ(n4) = all_0_8_8
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 56.11/21.70 | (1933) all_0_6_6 = n3
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 56.11/21.70 | (1934) all_0_8_8 = n5
% 56.11/21.70 |
% 56.11/21.70 | From (1933)(1934) and (411) follows:
% 56.11/21.70 | (1935) sum(n3, n5) = all_0_1_1
% 56.11/21.70 |
% 56.11/21.70 | From (1933) and (11285) follows:
% 56.11/21.70 | (11404) sum(n3, n12) = all_0_4_4
% 56.11/21.70 |
% 56.11/21.70 | From (1934) and (11287) follows:
% 56.11/21.70 | (11405) sum(n10, n5) = all_0_7_7
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (690) with n10, n5, all_0_7_7, n15 and discharging atoms sum(n10, n5) = all_0_7_7, sum(n10, n5) = n15, yields:
% 56.11/21.70 | (1263) all_0_7_7 = n15
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (690) with n3, n12, all_0_4_4, n15 and discharging atoms sum(n3, n12) = all_0_4_4, sum(n3, n12) = n15, yields:
% 56.11/21.70 | (1261) all_0_4_4 = n15
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 56.11/21.70 | (1705) all_0_1_1 = n8
% 56.11/21.70 |
% 56.11/21.70 | From (1263)(1261) and (590) follows:
% 56.11/21.70 | (1265) sum(n15, n15) = all_0_3_3
% 56.11/21.70 |
% 56.11/21.70 | From (1705) and (2499) follows:
% 56.11/21.70 | (2620) sum(n22, n8) = all_0_0_0
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (690) with n22, n8, all_0_0_0, n4 and discharging atoms sum(n22, n8) = all_0_0_0, sum(n22, n8) = n4, yields:
% 56.11/21.70 | (1267) all_0_0_0 = n4
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 56.11/21.70 | (1266) all_0_3_3 = n4
% 56.11/21.70 |
% 56.11/21.70 | Equations (1267,1266) can reduce 679 to:
% 56.11/21.70 | (1106) $false
% 56.11/21.70 |
% 56.11/21.70 |-The branch is then unsatisfiable
% 56.11/21.70 |-Branch two:
% 56.11/21.70 | (1946) ~ (all_0_10_10 = n4)
% 56.11/21.70 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.11/21.70 |
% 56.11/21.70 +-Applying beta-rule and splitting (1947), into two cases.
% 56.11/21.70 |-Branch one:
% 56.11/21.70 | (1948) all_0_10_10 = n3
% 56.11/21.70 |
% 56.11/21.70 | From (1948) and (292) follows:
% 56.11/21.70 | (1949) pred(n3) = all_0_6_6
% 56.11/21.70 |
% 56.11/21.70 | From (1948) and (760) follows:
% 56.11/21.70 | (1950) succ(n3) = all_0_8_8
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 56.11/21.70 | (1951) all_0_6_6 = n2
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 56.11/21.70 | (1952) all_0_8_8 = n4
% 56.11/21.70 |
% 56.11/21.70 | From (1951)(1952) and (411) follows:
% 56.11/21.70 | (1953) sum(n2, n4) = all_0_1_1
% 56.11/21.70 |
% 56.11/21.70 | From (1951) and (11285) follows:
% 56.11/21.70 | (11422) sum(n2, n12) = all_0_4_4
% 56.11/21.70 |
% 56.11/21.70 | From (1952) and (11287) follows:
% 56.11/21.70 | (11423) sum(n10, n4) = all_0_7_7
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (690) with n10, n4, all_0_7_7, n14 and discharging atoms sum(n10, n4) = all_0_7_7, sum(n10, n4) = n14, yields:
% 56.11/21.70 | (1281) all_0_7_7 = n14
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (690) with n2, n12, all_0_4_4, n14 and discharging atoms sum(n2, n12) = all_0_4_4, sum(n2, n12) = n14, yields:
% 56.11/21.70 | (1279) all_0_4_4 = n14
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 56.11/21.70 | (1723) all_0_1_1 = n6
% 56.11/21.70 |
% 56.11/21.70 | From (1281)(1279) and (590) follows:
% 56.11/21.70 | (1283) sum(n14, n14) = all_0_3_3
% 56.11/21.70 |
% 56.11/21.70 | From (1723) and (2499) follows:
% 56.11/21.70 | (2638) sum(n22, n6) = all_0_0_0
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (690) with n22, n6, all_0_0_0, n2 and discharging atoms sum(n22, n6) = all_0_0_0, sum(n22, n6) = n2, yields:
% 56.11/21.70 | (1285) all_0_0_0 = n2
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 56.11/21.70 | (1284) all_0_3_3 = n2
% 56.11/21.70 |
% 56.11/21.70 | Equations (1285,1284) can reduce 679 to:
% 56.11/21.70 | (1106) $false
% 56.11/21.70 |
% 56.11/21.70 |-The branch is then unsatisfiable
% 56.11/21.70 |-Branch two:
% 56.11/21.70 | (1964) ~ (all_0_10_10 = n3)
% 56.11/21.70 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.11/21.70 |
% 56.11/21.70 +-Applying beta-rule and splitting (1965), into two cases.
% 56.11/21.70 |-Branch one:
% 56.11/21.70 | (1966) all_0_10_10 = n2
% 56.11/21.70 |
% 56.11/21.70 | From (1966) and (292) follows:
% 56.11/21.70 | (1967) pred(n2) = all_0_6_6
% 56.11/21.70 |
% 56.11/21.70 | From (1966) and (760) follows:
% 56.11/21.70 | (1968) succ(n2) = all_0_8_8
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 56.11/21.70 | (1969) all_0_6_6 = n1
% 56.11/21.70 |
% 56.11/21.70 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 56.11/21.70 | (1970) all_0_8_8 = n3
% 56.11/21.70 |
% 56.11/21.70 | From (1969)(1970) and (411) follows:
% 56.11/21.70 | (1971) sum(n1, n3) = all_0_1_1
% 56.11/21.70 |
% 56.11/21.70 | From (1969) and (11285) follows:
% 56.11/21.70 | (11440) sum(n1, n12) = all_0_4_4
% 56.11/21.70 |
% 56.11/21.70 | From (1970) and (11287) follows:
% 56.11/21.71 | (11441) sum(n10, n3) = all_0_7_7
% 56.11/21.71 |
% 56.11/21.71 | Instantiating formula (690) with n10, n3, all_0_7_7, n13 and discharging atoms sum(n10, n3) = all_0_7_7, sum(n10, n3) = n13, yields:
% 56.11/21.71 | (1299) all_0_7_7 = n13
% 56.11/21.71 |
% 56.11/21.71 | Instantiating formula (690) with n1, n12, all_0_4_4, n13 and discharging atoms sum(n1, n12) = all_0_4_4, sum(n1, n12) = n13, yields:
% 56.11/21.71 | (1297) all_0_4_4 = n13
% 56.11/21.71 |
% 56.11/21.71 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 56.11/21.71 | (1741) all_0_1_1 = n4
% 56.11/21.71 |
% 56.11/21.71 | From (1299)(1297) and (590) follows:
% 56.21/21.71 | (1301) sum(n13, n13) = all_0_3_3
% 56.21/21.71 |
% 56.21/21.71 | From (1741) and (2499) follows:
% 56.21/21.71 | (2656) sum(n22, n4) = all_0_0_0
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (690) with n22, n4, all_0_0_0, n0 and discharging atoms sum(n22, n4) = all_0_0_0, sum(n22, n4) = n0, yields:
% 56.21/21.71 | (1303) all_0_0_0 = n0
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 56.21/21.71 | (1302) all_0_3_3 = n0
% 56.21/21.71 |
% 56.21/21.71 | Equations (1303,1302) can reduce 679 to:
% 56.21/21.71 | (1106) $false
% 56.21/21.71 |
% 56.21/21.71 |-The branch is then unsatisfiable
% 56.21/21.71 |-Branch two:
% 56.21/21.71 | (1982) ~ (all_0_10_10 = n2)
% 56.21/21.71 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 56.21/21.71 |
% 56.21/21.71 +-Applying beta-rule and splitting (1983), into two cases.
% 56.21/21.71 |-Branch one:
% 56.21/21.71 | (1984) all_0_10_10 = n1
% 56.21/21.71 |
% 56.21/21.71 | From (1984) and (292) follows:
% 56.21/21.71 | (1985) pred(n1) = all_0_6_6
% 56.21/21.71 |
% 56.21/21.71 | From (1984) and (760) follows:
% 56.21/21.71 | (1986) succ(n1) = all_0_8_8
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 56.21/21.71 | (1987) all_0_6_6 = n0
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 56.21/21.71 | (1988) all_0_8_8 = n2
% 56.21/21.71 |
% 56.21/21.71 | From (1987)(1988) and (411) follows:
% 56.21/21.71 | (1989) sum(n0, n2) = all_0_1_1
% 56.21/21.71 |
% 56.21/21.71 | From (1987) and (11285) follows:
% 56.21/21.71 | (11458) sum(n0, n12) = all_0_4_4
% 56.21/21.71 |
% 56.21/21.71 | From (1988) and (11287) follows:
% 56.21/21.71 | (11459) sum(n10, n2) = all_0_7_7
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (690) with n10, n2, all_0_7_7, n12 and discharging atoms sum(n10, n2) = all_0_7_7, sum(n10, n2) = n12, yields:
% 56.21/21.71 | (1317) all_0_7_7 = n12
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (690) with n0, n12, all_0_4_4, n12 and discharging atoms sum(n0, n12) = all_0_4_4, sum(n0, n12) = n12, yields:
% 56.21/21.71 | (1315) all_0_4_4 = n12
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 56.21/21.71 | (1759) all_0_1_1 = n2
% 56.21/21.71 |
% 56.21/21.71 | From (1317)(1315) and (590) follows:
% 56.21/21.71 | (1319) sum(n12, n12) = all_0_3_3
% 56.21/21.71 |
% 56.21/21.71 | From (1759) and (2499) follows:
% 56.21/21.71 | (2674) sum(n22, n2) = all_0_0_0
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (690) with n22, n2, all_0_0_0, n24 and discharging atoms sum(n22, n2) = all_0_0_0, sum(n22, n2) = n24, yields:
% 56.21/21.71 | (1321) all_0_0_0 = n24
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 56.21/21.71 | (1320) all_0_3_3 = n24
% 56.21/21.71 |
% 56.21/21.71 | Equations (1321,1320) can reduce 679 to:
% 56.21/21.71 | (1106) $false
% 56.21/21.71 |
% 56.21/21.71 |-The branch is then unsatisfiable
% 56.21/21.71 |-Branch two:
% 56.21/21.71 | (2002) ~ (all_0_10_10 = n1)
% 56.21/21.71 | (2003) all_0_10_10 = n0
% 56.21/21.71 |
% 56.21/21.71 | From (2003) and (292) follows:
% 56.21/21.71 | (2004) pred(n0) = all_0_6_6
% 56.21/21.71 |
% 56.21/21.71 | From (2003) and (760) follows:
% 56.21/21.71 | (2005) succ(n0) = all_0_8_8
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 56.21/21.71 | (2006) all_0_6_6 = n25
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 56.21/21.71 | (2007) all_0_8_8 = n1
% 56.21/21.71 |
% 56.21/21.71 | From (2006)(2007) and (411) follows:
% 56.21/21.71 | (2008) sum(n25, n1) = all_0_1_1
% 56.21/21.71 |
% 56.21/21.71 | From (2006) and (11285) follows:
% 56.21/21.71 | (11475) sum(n25, n12) = all_0_4_4
% 56.21/21.71 |
% 56.21/21.71 | From (2007) and (11287) follows:
% 56.21/21.71 | (11476) sum(n10, n1) = all_0_7_7
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (690) with n25, n12, all_0_4_4, n11 and discharging atoms sum(n25, n12) = all_0_4_4, sum(n25, n12) = n11, yields:
% 56.21/21.71 | (1333) all_0_4_4 = n11
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 56.21/21.71 | (1777) all_0_1_1 = n0
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (690) with n10, n1, all_0_7_7, n11 and discharging atoms sum(n10, n1) = all_0_7_7, sum(n10, n1) = n11, yields:
% 56.21/21.71 | (1335) all_0_7_7 = n11
% 56.21/21.71 |
% 56.21/21.71 | From (1335)(1333) and (590) follows:
% 56.21/21.71 | (1337) sum(n11, n11) = all_0_3_3
% 56.21/21.71 |
% 56.21/21.71 | From (1777) and (2499) follows:
% 56.21/21.71 | (2692) sum(n22, n0) = all_0_0_0
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (690) with n22, n0, all_0_0_0, n22 and discharging atoms sum(n22, n0) = all_0_0_0, sum(n22, n0) = n22, yields:
% 56.21/21.71 | (1102) all_0_0_0 = n22
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 56.21/21.71 | (1104) all_0_3_3 = n22
% 56.21/21.71 |
% 56.21/21.71 | Equations (1102,1104) can reduce 679 to:
% 56.21/21.71 | (1106) $false
% 56.21/21.71 |
% 56.21/21.71 |-The branch is then unsatisfiable
% 56.21/21.71 |-Branch two:
% 56.21/21.71 | (1359) ~ (all_0_11_11 = n11)
% 56.21/21.71 | (1360) 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
% 56.21/21.71 |
% 56.21/21.71 +-Applying beta-rule and splitting (1821), into two cases.
% 56.21/21.71 |-Branch one:
% 56.21/21.71 | (1822) all_0_10_10 = n10
% 56.21/21.71 |
% 56.21/21.71 | From (1822) and (292) follows:
% 56.21/21.71 | (1823) pred(n10) = all_0_6_6
% 56.21/21.71 |
% 56.21/21.71 | From (1822) and (760) follows:
% 56.21/21.71 | (1824) succ(n10) = all_0_8_8
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (500) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 56.21/21.71 | (1825) all_0_6_6 = n9
% 56.21/21.71 |
% 56.21/21.71 | Instantiating formula (617) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 56.21/21.71 | (1826) all_0_8_8 = n11
% 56.21/21.71 |
% 56.21/21.71 | From (1825) and (1823) follows:
% 56.21/21.71 | (405) pred(n10) = n9
% 56.21/21.71 |
% 56.21/21.71 | From (1826) and (1824) follows:
% 56.21/21.71 | (134) succ(n10) = n11
% 56.21/21.71 |
% 56.21/21.71 | From (1825) and (541) follows:
% 56.21/21.72 | (11494) sum(n9, all_0_5_5) = all_0_4_4
% 56.21/21.72 |
% 56.21/21.72 | From (1825)(1826) and (411) follows:
% 56.21/21.72 | (1827) sum(n9, n11) = all_0_1_1
% 56.21/21.72 |
% 56.21/21.72 | From (1826) and (427) follows:
% 56.21/21.72 | (11496) sum(all_0_9_9, n11) = all_0_7_7
% 56.21/21.72 |
% 56.21/21.72 | Instantiating formula (690) with n9, n11, all_0_1_1, n20 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n20, yields:
% 56.21/21.72 | (1597) all_0_1_1 = n20
% 56.21/21.72 |
% 56.21/21.72 | From (1597) and (630) follows:
% 56.21/21.72 | (2942) sum(all_0_2_2, n20) = all_0_0_0
% 56.21/21.72 |
% 56.21/21.72 | From (1597) and (1827) follows:
% 56.21/21.72 | (926) sum(n9, n11) = n20
% 56.21/21.72 |
% 56.21/21.72 +-Applying beta-rule and splitting (1360), into two cases.
% 56.21/21.72 |-Branch one:
% 56.21/21.72 | (1361) all_0_11_11 = n10
% 56.21/21.72 |
% 56.21/21.72 | From (1361) and (559) follows:
% 56.21/21.72 | (1362) pred(n10) = all_0_9_9
% 56.21/21.72 |
% 56.21/21.72 | From (1361) and (992) follows:
% 56.21/21.72 | (1363) succ(n10) = all_0_5_5
% 56.21/21.72 |
% 56.21/21.72 | Instantiating formula (500) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 56.21/21.72 | (1364) all_0_9_9 = n9
% 56.21/21.72 |
% 56.21/21.72 | Instantiating formula (617) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 56.21/21.72 | (1365) all_0_5_5 = n11
% 56.21/21.72 |
% 56.21/21.72 | From (1364)(1365) and (538) follows:
% 56.21/21.72 | (1366) sum(n9, n11) = all_0_2_2
% 56.21/21.72 |
% 56.21/21.72 | From (1364) and (11496) follows:
% 56.21/21.72 | (11506) sum(n9, n11) = all_0_7_7
% 56.21/21.72 |
% 56.21/21.72 | From (1365) and (11494) follows:
% 56.21/21.72 | (11507) sum(n9, n11) = all_0_4_4
% 56.21/21.72 |
% 56.21/21.72 | Instantiating formula (690) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 56.21/21.72 | (1136) all_0_2_2 = n20
% 56.21/21.72 |
% 56.21/21.72 | Instantiating formula (690) 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:
% 56.21/21.72 | (1093) all_0_2_2 = all_0_4_4
% 56.21/21.72 |
% 56.21/21.72 | Instantiating formula (690) 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:
% 56.21/21.72 | (1094) all_0_2_2 = all_0_7_7
% 56.21/21.72 |
% 56.21/21.72 | Combining equations (1094,1093) yields a new equation:
% 56.21/21.72 | (1095) all_0_4_4 = all_0_7_7
% 56.21/21.72 |
% 56.21/21.72 | Combining equations (1136,1093) yields a new equation:
% 56.21/21.72 | (1171) all_0_4_4 = n20
% 56.21/21.72 |
% 56.21/21.72 | Combining equations (1171,1095) yields a new equation:
% 56.21/21.72 | (1173) all_0_7_7 = n20
% 56.21/21.72 |
% 56.21/21.72 | Combining equations (1173,1095) yields a new equation:
% 56.21/21.72 | (1171) all_0_4_4 = n20
% 56.21/21.72 |
% 56.21/21.72 | Combining equations (1171,1093) yields a new equation:
% 56.21/21.72 | (1136) all_0_2_2 = n20
% 56.21/21.72 |
% 56.21/21.72 | From (1136) and (2942) follows:
% 56.21/21.72 | (2960) sum(n20, n20) = all_0_0_0
% 56.21/21.72 |
% 56.21/21.72 | From (1173)(1171) and (590) follows:
% 56.21/21.72 | (1175) sum(n20, n20) = all_0_3_3
% 56.21/21.72 |
% 56.21/21.72 | Instantiating formula (690) with n20, n20, all_0_0_0, n14 and discharging atoms sum(n20, n20) = all_0_0_0, sum(n20, n20) = n14, yields:
% 56.21/21.72 | (1177) all_0_0_0 = n14
% 56.21/21.72 |
% 56.21/21.72 | Instantiating formula (690) 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:
% 56.21/21.72 | (1103) all_0_0_0 = all_0_3_3
% 56.21/21.72 |
% 56.21/21.72 | Combining equations (1177,1103) yields a new equation:
% 56.21/21.72 | (1176) all_0_3_3 = n14
% 56.21/21.72 |
% 56.21/21.72 | Combining equations (1176,1103) yields a new equation:
% 56.21/21.72 | (1177) all_0_0_0 = n14
% 56.21/21.72 |
% 56.21/21.72 | Equations (1177,1176) can reduce 679 to:
% 56.21/21.72 | (1106) $false
% 56.21/21.72 |
% 56.21/21.72 |-The branch is then unsatisfiable
% 56.21/21.72 |-Branch two:
% 56.21/21.72 | (1377) ~ (all_0_11_11 = n10)
% 56.21/21.72 | (1378) 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
% 56.21/21.72 |
% 56.21/21.72 +-Applying beta-rule and splitting (1378), into two cases.
% 56.21/21.72 |-Branch one:
% 56.21/21.72 | (1379) all_0_11_11 = n9
% 56.21/21.72 |
% 56.21/21.72 | From (1379) and (559) follows:
% 56.21/21.72 | (1380) pred(n9) = all_0_9_9
% 56.21/21.72 |
% 56.21/21.72 | From (1379) and (992) follows:
% 56.21/21.72 | (1381) succ(n9) = all_0_5_5
% 56.21/21.72 |
% 56.21/21.72 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 56.21/21.72 | (1382) all_0_9_9 = n8
% 56.21/21.72 |
% 56.21/21.72 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 56.21/21.72 | (1383) all_0_5_5 = n10
% 56.21/21.72 |
% 56.21/21.72 | From (1382)(1383) and (538) follows:
% 56.21/21.72 | (1384) sum(n8, n10) = all_0_2_2
% 56.21/21.72 |
% 56.21/21.72 | From (1382) and (11496) follows:
% 56.21/21.72 | (11531) sum(n8, n11) = all_0_7_7
% 56.21/21.72 |
% 56.21/21.72 | From (1383) and (11494) follows:
% 56.21/21.72 | (11532) sum(n9, n10) = all_0_4_4
% 56.21/21.72 |
% 56.21/21.72 | Instantiating formula (690) with n9, n10, all_0_4_4, n19 and discharging atoms sum(n9, n10) = all_0_4_4, sum(n9, n10) = n19, yields:
% 56.21/21.72 | (1189) all_0_4_4 = n19
% 56.21/21.72 |
% 56.21/21.72 | Instantiating formula (690) with n8, n11, all_0_7_7, n19 and discharging atoms sum(n8, n11) = all_0_7_7, sum(n8, n11) = n19, yields:
% 56.21/21.72 | (1191) all_0_7_7 = n19
% 56.21/21.72 |
% 56.21/21.72 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 56.21/21.72 | (1154) all_0_2_2 = n18
% 56.21/21.72 |
% 56.21/21.72 | From (1154) and (2942) follows:
% 56.21/21.72 | (2980) sum(n18, n20) = all_0_0_0
% 56.21/21.72 |
% 56.21/21.72 | From (1191)(1189) and (590) follows:
% 56.21/21.72 | (1193) sum(n19, n19) = all_0_3_3
% 56.21/21.72 |
% 56.21/21.72 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 56.21/21.72 | (1194) all_0_3_3 = n12
% 56.21/21.72 |
% 56.21/21.72 | Instantiating formula (690) with n18, n20, all_0_0_0, n12 and discharging atoms sum(n18, n20) = all_0_0_0, sum(n18, n20) = n12, yields:
% 56.21/21.72 | (1195) all_0_0_0 = n12
% 56.21/21.72 |
% 56.21/21.72 | Equations (1195,1194) can reduce 679 to:
% 56.21/21.72 | (1106) $false
% 56.21/21.72 |
% 56.21/21.72 |-The branch is then unsatisfiable
% 56.21/21.72 |-Branch two:
% 56.21/21.72 | (1395) ~ (all_0_11_11 = n9)
% 56.21/21.72 | (1396) 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
% 56.21/21.72 |
% 56.21/21.72 +-Applying beta-rule and splitting (1396), into two cases.
% 56.21/21.72 |-Branch one:
% 56.21/21.72 | (1397) all_0_11_11 = n8
% 56.21/21.72 |
% 56.21/21.72 | From (1397) and (559) follows:
% 56.21/21.72 | (1398) pred(n8) = all_0_9_9
% 56.21/21.72 |
% 56.21/21.72 | From (1397) and (992) follows:
% 56.21/21.72 | (1399) succ(n8) = all_0_5_5
% 56.21/21.72 |
% 56.21/21.72 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 56.21/21.72 | (1400) all_0_9_9 = n7
% 56.21/21.72 |
% 56.21/21.72 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 56.21/21.72 | (1401) all_0_5_5 = n9
% 56.21/21.72 |
% 56.21/21.72 | From (1400)(1401) and (538) follows:
% 56.21/21.72 | (1402) sum(n7, n9) = all_0_2_2
% 56.21/21.72 |
% 56.21/21.72 | From (1400) and (11496) follows:
% 56.21/21.73 | (11549) sum(n7, n11) = all_0_7_7
% 56.21/21.73 |
% 56.21/21.73 | From (1401) and (11494) follows:
% 56.21/21.73 | (11550) sum(n9, n9) = all_0_4_4
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (690) with n9, n9, all_0_4_4, n18 and discharging atoms sum(n9, n9) = all_0_4_4, sum(n9, n9) = n18, yields:
% 56.21/21.73 | (1207) all_0_4_4 = n18
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (690) with n7, n11, all_0_7_7, n18 and discharging atoms sum(n7, n11) = all_0_7_7, sum(n7, n11) = n18, yields:
% 56.21/21.73 | (1209) all_0_7_7 = n18
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 56.21/21.73 | (1172) all_0_2_2 = n16
% 56.21/21.73 |
% 56.21/21.73 | From (1172) and (2942) follows:
% 56.21/21.73 | (2998) sum(n16, n20) = all_0_0_0
% 56.21/21.73 |
% 56.21/21.73 | From (1209)(1207) and (590) follows:
% 56.21/21.73 | (1211) sum(n18, n18) = all_0_3_3
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 56.21/21.73 | (1212) all_0_3_3 = n10
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (690) with n16, n20, all_0_0_0, n10 and discharging atoms sum(n16, n20) = all_0_0_0, sum(n16, n20) = n10, yields:
% 56.21/21.73 | (1213) all_0_0_0 = n10
% 56.21/21.73 |
% 56.21/21.73 | Equations (1213,1212) can reduce 679 to:
% 56.21/21.73 | (1106) $false
% 56.21/21.73 |
% 56.21/21.73 |-The branch is then unsatisfiable
% 56.21/21.73 |-Branch two:
% 56.21/21.73 | (1413) ~ (all_0_11_11 = n8)
% 56.21/21.73 | (1414) 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
% 56.21/21.73 |
% 56.21/21.73 +-Applying beta-rule and splitting (1414), into two cases.
% 56.21/21.73 |-Branch one:
% 56.21/21.73 | (1415) all_0_11_11 = n7
% 56.21/21.73 |
% 56.21/21.73 | From (1415) and (559) follows:
% 56.21/21.73 | (1416) pred(n7) = all_0_9_9
% 56.21/21.73 |
% 56.21/21.73 | From (1415) and (992) follows:
% 56.21/21.73 | (1417) succ(n7) = all_0_5_5
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 56.21/21.73 | (1418) all_0_9_9 = n6
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 56.21/21.73 | (1419) all_0_5_5 = n8
% 56.21/21.73 |
% 56.21/21.73 | From (1418)(1419) and (538) follows:
% 56.21/21.73 | (1420) sum(n6, n8) = all_0_2_2
% 56.21/21.73 |
% 56.21/21.73 | From (1418) and (11496) follows:
% 56.21/21.73 | (11567) sum(n6, n11) = all_0_7_7
% 56.21/21.73 |
% 56.21/21.73 | From (1419) and (11494) follows:
% 56.21/21.73 | (11568) sum(n9, n8) = all_0_4_4
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (690) with n9, n8, all_0_4_4, n17 and discharging atoms sum(n9, n8) = all_0_4_4, sum(n9, n8) = n17, yields:
% 56.21/21.73 | (1225) all_0_4_4 = n17
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (690) with n6, n11, all_0_7_7, n17 and discharging atoms sum(n6, n11) = all_0_7_7, sum(n6, n11) = n17, yields:
% 56.21/21.73 | (1227) all_0_7_7 = n17
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 56.21/21.73 | (1190) all_0_2_2 = n14
% 56.21/21.73 |
% 56.21/21.73 | From (1190) and (2942) follows:
% 56.21/21.73 | (3016) sum(n14, n20) = all_0_0_0
% 56.21/21.73 |
% 56.21/21.73 | From (1227)(1225) and (590) follows:
% 56.21/21.73 | (1229) sum(n17, n17) = all_0_3_3
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 56.21/21.73 | (1230) all_0_3_3 = n8
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (690) with n14, n20, all_0_0_0, n8 and discharging atoms sum(n14, n20) = all_0_0_0, sum(n14, n20) = n8, yields:
% 56.21/21.73 | (1231) all_0_0_0 = n8
% 56.21/21.73 |
% 56.21/21.73 | Equations (1231,1230) can reduce 679 to:
% 56.21/21.73 | (1106) $false
% 56.21/21.73 |
% 56.21/21.73 |-The branch is then unsatisfiable
% 56.21/21.73 |-Branch two:
% 56.21/21.73 | (1431) ~ (all_0_11_11 = n7)
% 56.21/21.73 | (1432) 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
% 56.21/21.73 |
% 56.21/21.73 +-Applying beta-rule and splitting (1432), into two cases.
% 56.21/21.73 |-Branch one:
% 56.21/21.73 | (1433) all_0_11_11 = n6
% 56.21/21.73 |
% 56.21/21.73 | From (1433) and (559) follows:
% 56.21/21.73 | (1434) pred(n6) = all_0_9_9
% 56.21/21.73 |
% 56.21/21.73 | From (1433) and (992) follows:
% 56.21/21.73 | (1435) succ(n6) = all_0_5_5
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 56.21/21.73 | (1436) all_0_9_9 = n5
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 56.21/21.73 | (1437) all_0_5_5 = n7
% 56.21/21.73 |
% 56.21/21.73 | From (1436)(1437) and (538) follows:
% 56.21/21.73 | (1438) sum(n5, n7) = all_0_2_2
% 56.21/21.73 |
% 56.21/21.73 | From (1436) and (11496) follows:
% 56.21/21.73 | (11585) sum(n5, n11) = all_0_7_7
% 56.21/21.73 |
% 56.21/21.73 | From (1437) and (11494) follows:
% 56.21/21.73 | (11586) sum(n9, n7) = all_0_4_4
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (690) with n9, n7, all_0_4_4, n16 and discharging atoms sum(n9, n7) = all_0_4_4, sum(n9, n7) = n16, yields:
% 56.21/21.73 | (1243) all_0_4_4 = n16
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (690) with n5, n11, all_0_7_7, n16 and discharging atoms sum(n5, n11) = all_0_7_7, sum(n5, n11) = n16, yields:
% 56.21/21.73 | (1245) all_0_7_7 = n16
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 56.21/21.73 | (1208) all_0_2_2 = n12
% 56.21/21.73 |
% 56.21/21.73 | From (1208) and (2942) follows:
% 56.21/21.73 | (3034) sum(n12, n20) = all_0_0_0
% 56.21/21.73 |
% 56.21/21.73 | From (1245)(1243) and (590) follows:
% 56.21/21.73 | (1247) sum(n16, n16) = all_0_3_3
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 56.21/21.73 | (1248) all_0_3_3 = n6
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (690) with n12, n20, all_0_0_0, n6 and discharging atoms sum(n12, n20) = all_0_0_0, sum(n12, n20) = n6, yields:
% 56.21/21.73 | (1249) all_0_0_0 = n6
% 56.21/21.73 |
% 56.21/21.73 | Equations (1249,1248) can reduce 679 to:
% 56.21/21.73 | (1106) $false
% 56.21/21.73 |
% 56.21/21.73 |-The branch is then unsatisfiable
% 56.21/21.73 |-Branch two:
% 56.21/21.73 | (1449) ~ (all_0_11_11 = n6)
% 56.21/21.73 | (1450) 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
% 56.21/21.73 |
% 56.21/21.73 +-Applying beta-rule and splitting (1450), into two cases.
% 56.21/21.73 |-Branch one:
% 56.21/21.73 | (1451) all_0_11_11 = n5
% 56.21/21.73 |
% 56.21/21.73 | From (1451) and (559) follows:
% 56.21/21.73 | (1452) pred(n5) = all_0_9_9
% 56.21/21.73 |
% 56.21/21.73 | From (1451) and (992) follows:
% 56.21/21.73 | (1453) succ(n5) = all_0_5_5
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 56.21/21.73 | (1454) all_0_9_9 = n4
% 56.21/21.73 |
% 56.21/21.73 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 56.21/21.73 | (1455) all_0_5_5 = n6
% 56.21/21.73 |
% 56.21/21.73 | From (1454)(1455) and (538) follows:
% 56.21/21.73 | (1456) sum(n4, n6) = all_0_2_2
% 56.21/21.73 |
% 56.21/21.73 | From (1454) and (11496) follows:
% 56.21/21.73 | (11603) sum(n4, n11) = all_0_7_7
% 56.21/21.73 |
% 56.21/21.73 | From (1455) and (11494) follows:
% 56.21/21.74 | (11604) sum(n9, n6) = all_0_4_4
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (690) with n9, n6, all_0_4_4, n15 and discharging atoms sum(n9, n6) = all_0_4_4, sum(n9, n6) = n15, yields:
% 56.21/21.74 | (1261) all_0_4_4 = n15
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (690) with n4, n11, all_0_7_7, n15 and discharging atoms sum(n4, n11) = all_0_7_7, sum(n4, n11) = n15, yields:
% 56.21/21.74 | (1263) all_0_7_7 = n15
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 56.21/21.74 | (1226) all_0_2_2 = n10
% 56.21/21.74 |
% 56.21/21.74 | From (1226) and (2942) follows:
% 56.21/21.74 | (3052) sum(n10, n20) = all_0_0_0
% 56.21/21.74 |
% 56.21/21.74 | From (1263)(1261) and (590) follows:
% 56.21/21.74 | (1265) sum(n15, n15) = all_0_3_3
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 56.21/21.74 | (1266) all_0_3_3 = n4
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (690) with n10, n20, all_0_0_0, n4 and discharging atoms sum(n10, n20) = all_0_0_0, sum(n10, n20) = n4, yields:
% 56.21/21.74 | (1267) all_0_0_0 = n4
% 56.21/21.74 |
% 56.21/21.74 | Equations (1267,1266) can reduce 679 to:
% 56.21/21.74 | (1106) $false
% 56.21/21.74 |
% 56.21/21.74 |-The branch is then unsatisfiable
% 56.21/21.74 |-Branch two:
% 56.21/21.74 | (1467) ~ (all_0_11_11 = n5)
% 56.21/21.74 | (1468) 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
% 56.21/21.74 |
% 56.21/21.74 +-Applying beta-rule and splitting (1468), into two cases.
% 56.21/21.74 |-Branch one:
% 56.21/21.74 | (1469) all_0_11_11 = n4
% 56.21/21.74 |
% 56.21/21.74 | From (1469) and (559) follows:
% 56.21/21.74 | (1470) pred(n4) = all_0_9_9
% 56.21/21.74 |
% 56.21/21.74 | From (1469) and (992) follows:
% 56.21/21.74 | (1471) succ(n4) = all_0_5_5
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 56.21/21.74 | (1472) all_0_9_9 = n3
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 56.21/21.74 | (1473) all_0_5_5 = n5
% 56.21/21.74 |
% 56.21/21.74 | From (1472)(1473) and (538) follows:
% 56.21/21.74 | (1474) sum(n3, n5) = all_0_2_2
% 56.21/21.74 |
% 56.21/21.74 | From (1472) and (11496) follows:
% 56.21/21.74 | (11621) sum(n3, n11) = all_0_7_7
% 56.21/21.74 |
% 56.21/21.74 | From (1473) and (11494) follows:
% 56.21/21.74 | (11622) sum(n9, n5) = all_0_4_4
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (690) with n9, n5, all_0_4_4, n14 and discharging atoms sum(n9, n5) = all_0_4_4, sum(n9, n5) = n14, yields:
% 56.21/21.74 | (1279) all_0_4_4 = n14
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (690) with n3, n11, all_0_7_7, n14 and discharging atoms sum(n3, n11) = all_0_7_7, sum(n3, n11) = n14, yields:
% 56.21/21.74 | (1281) all_0_7_7 = n14
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 56.21/21.74 | (1244) all_0_2_2 = n8
% 56.21/21.74 |
% 56.21/21.74 | From (1244) and (2942) follows:
% 56.21/21.74 | (3070) sum(n8, n20) = all_0_0_0
% 56.21/21.74 |
% 56.21/21.74 | From (1281)(1279) and (590) follows:
% 56.21/21.74 | (1283) sum(n14, n14) = all_0_3_3
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 56.21/21.74 | (1284) all_0_3_3 = n2
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (690) with n8, n20, all_0_0_0, n2 and discharging atoms sum(n8, n20) = all_0_0_0, sum(n8, n20) = n2, yields:
% 56.21/21.74 | (1285) all_0_0_0 = n2
% 56.21/21.74 |
% 56.21/21.74 | Equations (1285,1284) can reduce 679 to:
% 56.21/21.74 | (1106) $false
% 56.21/21.74 |
% 56.21/21.74 |-The branch is then unsatisfiable
% 56.21/21.74 |-Branch two:
% 56.21/21.74 | (1485) ~ (all_0_11_11 = n4)
% 56.21/21.74 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.21/21.74 |
% 56.21/21.74 +-Applying beta-rule and splitting (1486), into two cases.
% 56.21/21.74 |-Branch one:
% 56.21/21.74 | (1487) all_0_11_11 = n3
% 56.21/21.74 |
% 56.21/21.74 | From (1487) and (559) follows:
% 56.21/21.74 | (1488) pred(n3) = all_0_9_9
% 56.21/21.74 |
% 56.21/21.74 | From (1487) and (992) follows:
% 56.21/21.74 | (1489) succ(n3) = all_0_5_5
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 56.21/21.74 | (1490) all_0_9_9 = n2
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 56.21/21.74 | (1491) all_0_5_5 = n4
% 56.21/21.74 |
% 56.21/21.74 | From (1490)(1491) and (538) follows:
% 56.21/21.74 | (1492) sum(n2, n4) = all_0_2_2
% 56.21/21.74 |
% 56.21/21.74 | From (1490) and (11496) follows:
% 56.21/21.74 | (11639) sum(n2, n11) = all_0_7_7
% 56.21/21.74 |
% 56.21/21.74 | From (1491) and (11494) follows:
% 56.21/21.74 | (11640) sum(n9, n4) = all_0_4_4
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (690) with n9, n4, all_0_4_4, n13 and discharging atoms sum(n9, n4) = all_0_4_4, sum(n9, n4) = n13, yields:
% 56.21/21.74 | (1297) all_0_4_4 = n13
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (690) with n2, n11, all_0_7_7, n13 and discharging atoms sum(n2, n11) = all_0_7_7, sum(n2, n11) = n13, yields:
% 56.21/21.74 | (1299) all_0_7_7 = n13
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 56.21/21.74 | (1262) all_0_2_2 = n6
% 56.21/21.74 |
% 56.21/21.74 | From (1262) and (2942) follows:
% 56.21/21.74 | (3088) sum(n6, n20) = all_0_0_0
% 56.21/21.74 |
% 56.21/21.74 | From (1299)(1297) and (590) follows:
% 56.21/21.74 | (1301) sum(n13, n13) = all_0_3_3
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 56.21/21.74 | (1302) all_0_3_3 = n0
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (690) with n6, n20, all_0_0_0, n0 and discharging atoms sum(n6, n20) = all_0_0_0, sum(n6, n20) = n0, yields:
% 56.21/21.74 | (1303) all_0_0_0 = n0
% 56.21/21.74 |
% 56.21/21.74 | Equations (1303,1302) can reduce 679 to:
% 56.21/21.74 | (1106) $false
% 56.21/21.74 |
% 56.21/21.74 |-The branch is then unsatisfiable
% 56.21/21.74 |-Branch two:
% 56.21/21.74 | (1503) ~ (all_0_11_11 = n3)
% 56.21/21.74 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.21/21.74 |
% 56.21/21.74 +-Applying beta-rule and splitting (1504), into two cases.
% 56.21/21.74 |-Branch one:
% 56.21/21.74 | (1505) all_0_11_11 = n2
% 56.21/21.74 |
% 56.21/21.74 | From (1505) and (559) follows:
% 56.21/21.74 | (1506) pred(n2) = all_0_9_9
% 56.21/21.74 |
% 56.21/21.74 | From (1505) and (992) follows:
% 56.21/21.74 | (1507) succ(n2) = all_0_5_5
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 56.21/21.74 | (1508) all_0_9_9 = n1
% 56.21/21.74 |
% 56.21/21.74 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 56.21/21.74 | (1509) all_0_5_5 = n3
% 56.21/21.74 |
% 56.21/21.74 | From (1508)(1509) and (538) follows:
% 56.21/21.74 | (1510) sum(n1, n3) = all_0_2_2
% 56.21/21.74 |
% 56.21/21.74 | From (1508) and (11496) follows:
% 56.21/21.74 | (11657) sum(n1, n11) = all_0_7_7
% 56.21/21.74 |
% 56.21/21.74 | From (1509) and (11494) follows:
% 56.21/21.75 | (11658) sum(n9, n3) = all_0_4_4
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (690) with n9, n3, all_0_4_4, n12 and discharging atoms sum(n9, n3) = all_0_4_4, sum(n9, n3) = n12, yields:
% 56.21/21.75 | (1315) all_0_4_4 = n12
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (690) with n1, n11, all_0_7_7, n12 and discharging atoms sum(n1, n11) = all_0_7_7, sum(n1, n11) = n12, yields:
% 56.21/21.75 | (1317) all_0_7_7 = n12
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 56.21/21.75 | (1280) all_0_2_2 = n4
% 56.21/21.75 |
% 56.21/21.75 | From (1280) and (2942) follows:
% 56.21/21.75 | (3106) sum(n4, n20) = all_0_0_0
% 56.21/21.75 |
% 56.21/21.75 | From (1317)(1315) and (590) follows:
% 56.21/21.75 | (1319) sum(n12, n12) = all_0_3_3
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 56.21/21.75 | (1320) all_0_3_3 = n24
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (690) with n4, n20, all_0_0_0, n24 and discharging atoms sum(n4, n20) = all_0_0_0, sum(n4, n20) = n24, yields:
% 56.21/21.75 | (1321) all_0_0_0 = n24
% 56.21/21.75 |
% 56.21/21.75 | Equations (1321,1320) can reduce 679 to:
% 56.21/21.75 | (1106) $false
% 56.21/21.75 |
% 56.21/21.75 |-The branch is then unsatisfiable
% 56.21/21.75 |-Branch two:
% 56.21/21.75 | (1521) ~ (all_0_11_11 = n2)
% 56.21/21.75 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 56.21/21.75 |
% 56.21/21.75 +-Applying beta-rule and splitting (1522), into two cases.
% 56.21/21.75 |-Branch one:
% 56.21/21.75 | (1523) all_0_11_11 = n1
% 56.21/21.75 |
% 56.21/21.75 | From (1523) and (559) follows:
% 56.21/21.75 | (1524) pred(n1) = all_0_9_9
% 56.21/21.75 |
% 56.21/21.75 | From (1523) and (992) follows:
% 56.21/21.75 | (1525) succ(n1) = all_0_5_5
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 56.21/21.75 | (1526) all_0_9_9 = n0
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 56.21/21.75 | (1527) all_0_5_5 = n2
% 56.21/21.75 |
% 56.21/21.75 | From (1526)(1527) and (538) follows:
% 56.21/21.75 | (1528) sum(n0, n2) = all_0_2_2
% 56.21/21.75 |
% 56.21/21.75 | From (1526) and (11496) follows:
% 56.21/21.75 | (11675) sum(n0, n11) = all_0_7_7
% 56.21/21.75 |
% 56.21/21.75 | From (1527) and (11494) follows:
% 56.21/21.75 | (11676) sum(n9, n2) = all_0_4_4
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (690) with n9, n2, all_0_4_4, n11 and discharging atoms sum(n9, n2) = all_0_4_4, sum(n9, n2) = n11, yields:
% 56.21/21.75 | (1333) all_0_4_4 = n11
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (690) with n0, n11, all_0_7_7, n11 and discharging atoms sum(n0, n11) = all_0_7_7, sum(n0, n11) = n11, yields:
% 56.21/21.75 | (1335) all_0_7_7 = n11
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 56.21/21.75 | (1298) all_0_2_2 = n2
% 56.21/21.75 |
% 56.21/21.75 | From (1298) and (2942) follows:
% 56.21/21.75 | (3124) sum(n2, n20) = all_0_0_0
% 56.21/21.75 |
% 56.21/21.75 | From (1335)(1333) and (590) follows:
% 56.21/21.75 | (1337) sum(n11, n11) = all_0_3_3
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 56.21/21.75 | (1104) all_0_3_3 = n22
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (690) with n2, n20, all_0_0_0, n22 and discharging atoms sum(n2, n20) = all_0_0_0, sum(n2, n20) = n22, yields:
% 56.21/21.75 | (1102) all_0_0_0 = n22
% 56.21/21.75 |
% 56.21/21.75 | Equations (1102,1104) can reduce 679 to:
% 56.21/21.75 | (1106) $false
% 56.21/21.75 |
% 56.21/21.75 |-The branch is then unsatisfiable
% 56.21/21.75 |-Branch two:
% 56.21/21.75 | (1540) ~ (all_0_11_11 = n1)
% 56.21/21.75 | (1541) all_0_11_11 = n0
% 56.21/21.75 |
% 56.21/21.75 | From (1541) and (559) follows:
% 56.21/21.75 | (1542) pred(n0) = all_0_9_9
% 56.21/21.75 |
% 56.21/21.75 | From (1541) and (992) follows:
% 56.21/21.75 | (1543) succ(n0) = all_0_5_5
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 56.21/21.75 | (1544) all_0_9_9 = n25
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 56.21/21.75 | (1545) all_0_5_5 = n1
% 56.21/21.75 |
% 56.21/21.75 | From (1544)(1545) and (538) follows:
% 56.21/21.75 | (1546) sum(n25, n1) = all_0_2_2
% 56.21/21.75 |
% 56.21/21.75 | From (1544) and (11496) follows:
% 56.21/21.75 | (11692) sum(n25, n11) = all_0_7_7
% 56.21/21.75 |
% 56.21/21.75 | From (1545) and (11494) follows:
% 56.21/21.75 | (11693) sum(n9, n1) = all_0_4_4
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (690) with n25, n11, all_0_7_7, n10 and discharging atoms sum(n25, n11) = all_0_7_7, sum(n25, n11) = n10, yields:
% 56.21/21.75 | (1353) all_0_7_7 = n10
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 56.21/21.75 | (1316) all_0_2_2 = n0
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (690) with n9, n1, all_0_4_4, n10 and discharging atoms sum(n9, n1) = all_0_4_4, sum(n9, n1) = n10, yields:
% 56.21/21.75 | (1351) all_0_4_4 = n10
% 56.21/21.75 |
% 56.21/21.75 | From (1316) and (2942) follows:
% 56.21/21.75 | (3142) sum(n0, n20) = all_0_0_0
% 56.21/21.75 |
% 56.21/21.75 | From (1353)(1351) and (590) follows:
% 56.21/21.75 | (1355) sum(n10, n10) = all_0_3_3
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 56.21/21.75 | (1122) all_0_3_3 = n20
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (690) with n0, n20, all_0_0_0, n20 and discharging atoms sum(n0, n20) = all_0_0_0, sum(n0, n20) = n20, yields:
% 56.21/21.75 | (1123) all_0_0_0 = n20
% 56.21/21.75 |
% 56.21/21.75 | Equations (1123,1122) can reduce 679 to:
% 56.21/21.75 | (1106) $false
% 56.21/21.75 |
% 56.21/21.75 |-The branch is then unsatisfiable
% 56.21/21.75 |-Branch two:
% 56.21/21.75 | (1838) ~ (all_0_10_10 = n10)
% 56.21/21.75 | (1839) 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
% 56.21/21.75 |
% 56.21/21.75 +-Applying beta-rule and splitting (1360), into two cases.
% 56.21/21.75 |-Branch one:
% 56.21/21.75 | (1361) all_0_11_11 = n10
% 56.21/21.75 |
% 56.21/21.75 | From (1361) and (559) follows:
% 56.21/21.75 | (1362) pred(n10) = all_0_9_9
% 56.21/21.75 |
% 56.21/21.75 | From (1361) and (992) follows:
% 56.21/21.75 | (1363) succ(n10) = all_0_5_5
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (500) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 56.21/21.75 | (1364) all_0_9_9 = n9
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (617) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 56.21/21.75 | (1365) all_0_5_5 = n11
% 56.21/21.75 |
% 56.21/21.75 | From (1365) and (541) follows:
% 56.21/21.75 | (11709) sum(all_0_6_6, n11) = all_0_4_4
% 56.21/21.75 |
% 56.21/21.75 | From (1364)(1365) and (538) follows:
% 56.21/21.75 | (1366) sum(n9, n11) = all_0_2_2
% 56.21/21.75 |
% 56.21/21.75 | From (1364) and (427) follows:
% 56.21/21.75 | (11711) sum(n9, all_0_8_8) = all_0_7_7
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (690) with n9, n11, all_0_2_2, n20 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n20, yields:
% 56.21/21.75 | (1136) all_0_2_2 = n20
% 56.21/21.75 |
% 56.21/21.75 | From (1136) and (630) follows:
% 56.21/21.75 | (3391) sum(n20, all_0_1_1) = all_0_0_0
% 56.21/21.75 |
% 56.21/21.75 +-Applying beta-rule and splitting (1839), into two cases.
% 56.21/21.75 |-Branch one:
% 56.21/21.75 | (1840) all_0_10_10 = n9
% 56.21/21.75 |
% 56.21/21.75 | From (1840) and (292) follows:
% 56.21/21.75 | (1841) pred(n9) = all_0_6_6
% 56.21/21.75 |
% 56.21/21.75 | From (1840) and (760) follows:
% 56.21/21.75 | (1842) succ(n9) = all_0_8_8
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (500) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 56.21/21.75 | (1843) all_0_6_6 = n8
% 56.21/21.75 |
% 56.21/21.75 | Instantiating formula (617) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 56.21/21.75 | (1844) all_0_8_8 = n10
% 56.21/21.75 |
% 56.21/21.75 | From (1843)(1844) and (411) follows:
% 56.21/21.75 | (1845) sum(n8, n10) = all_0_1_1
% 56.21/21.75 |
% 56.21/21.75 | From (1843) and (11709) follows:
% 56.21/21.76 | (11720) sum(n8, n11) = all_0_4_4
% 56.21/21.76 |
% 56.21/21.76 | From (1844) and (11711) follows:
% 56.21/21.76 | (11721) sum(n9, n10) = all_0_7_7
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (690) with n9, n10, all_0_7_7, n19 and discharging atoms sum(n9, n10) = all_0_7_7, sum(n9, n10) = n19, yields:
% 56.21/21.76 | (1191) all_0_7_7 = n19
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (690) with n8, n11, all_0_4_4, n19 and discharging atoms sum(n8, n11) = all_0_4_4, sum(n8, n11) = n19, yields:
% 56.21/21.76 | (1189) all_0_4_4 = n19
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (690) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 56.21/21.76 | (1615) all_0_1_1 = n18
% 56.21/21.76 |
% 56.21/21.76 | From (1191)(1189) and (590) follows:
% 56.21/21.76 | (1193) sum(n19, n19) = all_0_3_3
% 56.21/21.76 |
% 56.21/21.76 | From (1615) and (3391) follows:
% 56.21/21.76 | (3404) sum(n20, n18) = all_0_0_0
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (690) with n20, n18, all_0_0_0, n12 and discharging atoms sum(n20, n18) = all_0_0_0, sum(n20, n18) = n12, yields:
% 56.21/21.76 | (1195) all_0_0_0 = n12
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (690) with n19, n19, all_0_3_3, n12 and discharging atoms sum(n19, n19) = all_0_3_3, sum(n19, n19) = n12, yields:
% 56.21/21.76 | (1194) all_0_3_3 = n12
% 56.21/21.76 |
% 56.21/21.76 | Equations (1195,1194) can reduce 679 to:
% 56.21/21.76 | (1106) $false
% 56.21/21.76 |
% 56.21/21.76 |-The branch is then unsatisfiable
% 56.21/21.76 |-Branch two:
% 56.21/21.76 | (1856) ~ (all_0_10_10 = n9)
% 56.21/21.76 | (1857) 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
% 56.21/21.76 |
% 56.21/21.76 +-Applying beta-rule and splitting (1857), into two cases.
% 56.21/21.76 |-Branch one:
% 56.21/21.76 | (1858) all_0_10_10 = n8
% 56.21/21.76 |
% 56.21/21.76 | From (1858) and (292) follows:
% 56.21/21.76 | (1859) pred(n8) = all_0_6_6
% 56.21/21.76 |
% 56.21/21.76 | From (1858) and (760) follows:
% 56.21/21.76 | (1860) succ(n8) = all_0_8_8
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 56.21/21.76 | (1861) all_0_6_6 = n7
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 56.21/21.76 | (1862) all_0_8_8 = n9
% 56.21/21.76 |
% 56.21/21.76 | From (1861)(1862) and (411) follows:
% 56.21/21.76 | (1863) sum(n7, n9) = all_0_1_1
% 56.21/21.76 |
% 56.21/21.76 | From (1861) and (11709) follows:
% 56.21/21.76 | (11738) sum(n7, n11) = all_0_4_4
% 56.21/21.76 |
% 56.21/21.76 | From (1862) and (11711) follows:
% 56.21/21.76 | (11739) sum(n9, n9) = all_0_7_7
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (690) with n9, n9, all_0_7_7, n18 and discharging atoms sum(n9, n9) = all_0_7_7, sum(n9, n9) = n18, yields:
% 56.21/21.76 | (1209) all_0_7_7 = n18
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (690) with n7, n11, all_0_4_4, n18 and discharging atoms sum(n7, n11) = all_0_4_4, sum(n7, n11) = n18, yields:
% 56.21/21.76 | (1207) all_0_4_4 = n18
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 56.21/21.76 | (1633) all_0_1_1 = n16
% 56.21/21.76 |
% 56.21/21.76 | From (1209)(1207) and (590) follows:
% 56.21/21.76 | (1211) sum(n18, n18) = all_0_3_3
% 56.21/21.76 |
% 56.21/21.76 | From (1633) and (3391) follows:
% 56.21/21.76 | (3422) sum(n20, n16) = all_0_0_0
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (690) with n20, n16, all_0_0_0, n10 and discharging atoms sum(n20, n16) = all_0_0_0, sum(n20, n16) = n10, yields:
% 56.21/21.76 | (1213) all_0_0_0 = n10
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (690) with n18, n18, all_0_3_3, n10 and discharging atoms sum(n18, n18) = all_0_3_3, sum(n18, n18) = n10, yields:
% 56.21/21.76 | (1212) all_0_3_3 = n10
% 56.21/21.76 |
% 56.21/21.76 | Equations (1213,1212) can reduce 679 to:
% 56.21/21.76 | (1106) $false
% 56.21/21.76 |
% 56.21/21.76 |-The branch is then unsatisfiable
% 56.21/21.76 |-Branch two:
% 56.21/21.76 | (1874) ~ (all_0_10_10 = n8)
% 56.21/21.76 | (1875) 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
% 56.21/21.76 |
% 56.21/21.76 +-Applying beta-rule and splitting (1875), into two cases.
% 56.21/21.76 |-Branch one:
% 56.21/21.76 | (1876) all_0_10_10 = n7
% 56.21/21.76 |
% 56.21/21.76 | From (1876) and (292) follows:
% 56.21/21.76 | (1877) pred(n7) = all_0_6_6
% 56.21/21.76 |
% 56.21/21.76 | From (1876) and (760) follows:
% 56.21/21.76 | (1878) succ(n7) = all_0_8_8
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 56.21/21.76 | (1879) all_0_6_6 = n6
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 56.21/21.76 | (1880) all_0_8_8 = n8
% 56.21/21.76 |
% 56.21/21.76 | From (1879)(1880) and (411) follows:
% 56.21/21.76 | (1881) sum(n6, n8) = all_0_1_1
% 56.21/21.76 |
% 56.21/21.76 | From (1879) and (11709) follows:
% 56.21/21.76 | (11756) sum(n6, n11) = all_0_4_4
% 56.21/21.76 |
% 56.21/21.76 | From (1880) and (11711) follows:
% 56.21/21.76 | (11757) sum(n9, n8) = all_0_7_7
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (690) with n9, n8, all_0_7_7, n17 and discharging atoms sum(n9, n8) = all_0_7_7, sum(n9, n8) = n17, yields:
% 56.21/21.76 | (1227) all_0_7_7 = n17
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (690) with n6, n11, all_0_4_4, n17 and discharging atoms sum(n6, n11) = all_0_4_4, sum(n6, n11) = n17, yields:
% 56.21/21.76 | (1225) all_0_4_4 = n17
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 56.21/21.76 | (1651) all_0_1_1 = n14
% 56.21/21.76 |
% 56.21/21.76 | From (1227)(1225) and (590) follows:
% 56.21/21.76 | (1229) sum(n17, n17) = all_0_3_3
% 56.21/21.76 |
% 56.21/21.76 | From (1651) and (3391) follows:
% 56.21/21.76 | (3440) sum(n20, n14) = all_0_0_0
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (690) with n20, n14, all_0_0_0, n8 and discharging atoms sum(n20, n14) = all_0_0_0, sum(n20, n14) = n8, yields:
% 56.21/21.76 | (1231) all_0_0_0 = n8
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 56.21/21.76 | (1230) all_0_3_3 = n8
% 56.21/21.76 |
% 56.21/21.76 | Equations (1231,1230) can reduce 679 to:
% 56.21/21.76 | (1106) $false
% 56.21/21.76 |
% 56.21/21.76 |-The branch is then unsatisfiable
% 56.21/21.76 |-Branch two:
% 56.21/21.76 | (1892) ~ (all_0_10_10 = n7)
% 56.21/21.76 | (1893) 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
% 56.21/21.76 |
% 56.21/21.76 +-Applying beta-rule and splitting (1893), into two cases.
% 56.21/21.76 |-Branch one:
% 56.21/21.76 | (1894) all_0_10_10 = n6
% 56.21/21.76 |
% 56.21/21.76 | From (1894) and (292) follows:
% 56.21/21.76 | (1895) pred(n6) = all_0_6_6
% 56.21/21.76 |
% 56.21/21.76 | From (1894) and (760) follows:
% 56.21/21.76 | (1896) succ(n6) = all_0_8_8
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 56.21/21.76 | (1897) all_0_6_6 = n5
% 56.21/21.76 |
% 56.21/21.76 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 56.21/21.76 | (1898) all_0_8_8 = n7
% 56.21/21.76 |
% 56.21/21.76 | From (1897)(1898) and (411) follows:
% 56.21/21.76 | (1899) sum(n5, n7) = all_0_1_1
% 56.21/21.76 |
% 56.21/21.76 | From (1897) and (11709) follows:
% 56.21/21.77 | (11774) sum(n5, n11) = all_0_4_4
% 56.21/21.77 |
% 56.21/21.77 | From (1898) and (11711) follows:
% 56.21/21.77 | (11775) sum(n9, n7) = all_0_7_7
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (690) with n9, n7, all_0_7_7, n16 and discharging atoms sum(n9, n7) = all_0_7_7, sum(n9, n7) = n16, yields:
% 56.21/21.77 | (1245) all_0_7_7 = n16
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (690) with n5, n11, all_0_4_4, n16 and discharging atoms sum(n5, n11) = all_0_4_4, sum(n5, n11) = n16, yields:
% 56.21/21.77 | (1243) all_0_4_4 = n16
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 56.21/21.77 | (1669) all_0_1_1 = n12
% 56.21/21.77 |
% 56.21/21.77 | From (1245)(1243) and (590) follows:
% 56.21/21.77 | (1247) sum(n16, n16) = all_0_3_3
% 56.21/21.77 |
% 56.21/21.77 | From (1669) and (3391) follows:
% 56.21/21.77 | (3458) sum(n20, n12) = all_0_0_0
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (690) with n20, n12, all_0_0_0, n6 and discharging atoms sum(n20, n12) = all_0_0_0, sum(n20, n12) = n6, yields:
% 56.21/21.77 | (1249) all_0_0_0 = n6
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 56.21/21.77 | (1248) all_0_3_3 = n6
% 56.21/21.77 |
% 56.21/21.77 | Equations (1249,1248) can reduce 679 to:
% 56.21/21.77 | (1106) $false
% 56.21/21.77 |
% 56.21/21.77 |-The branch is then unsatisfiable
% 56.21/21.77 |-Branch two:
% 56.21/21.77 | (1910) ~ (all_0_10_10 = n6)
% 56.21/21.77 | (1911) 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
% 56.21/21.77 |
% 56.21/21.77 +-Applying beta-rule and splitting (1911), into two cases.
% 56.21/21.77 |-Branch one:
% 56.21/21.77 | (1912) all_0_10_10 = n5
% 56.21/21.77 |
% 56.21/21.77 | From (1912) and (292) follows:
% 56.21/21.77 | (1913) pred(n5) = all_0_6_6
% 56.21/21.77 |
% 56.21/21.77 | From (1912) and (760) follows:
% 56.21/21.77 | (1914) succ(n5) = all_0_8_8
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 56.21/21.77 | (1915) all_0_6_6 = n4
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 56.21/21.77 | (1916) all_0_8_8 = n6
% 56.21/21.77 |
% 56.21/21.77 | From (1915)(1916) and (411) follows:
% 56.21/21.77 | (1917) sum(n4, n6) = all_0_1_1
% 56.21/21.77 |
% 56.21/21.77 | From (1915) and (11709) follows:
% 56.21/21.77 | (11792) sum(n4, n11) = all_0_4_4
% 56.21/21.77 |
% 56.21/21.77 | From (1916) and (11711) follows:
% 56.21/21.77 | (11793) sum(n9, n6) = all_0_7_7
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (690) with n9, n6, all_0_7_7, n15 and discharging atoms sum(n9, n6) = all_0_7_7, sum(n9, n6) = n15, yields:
% 56.21/21.77 | (1263) all_0_7_7 = n15
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (690) with n4, n11, all_0_4_4, n15 and discharging atoms sum(n4, n11) = all_0_4_4, sum(n4, n11) = n15, yields:
% 56.21/21.77 | (1261) all_0_4_4 = n15
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 56.21/21.77 | (1687) all_0_1_1 = n10
% 56.21/21.77 |
% 56.21/21.77 | From (1263)(1261) and (590) follows:
% 56.21/21.77 | (1265) sum(n15, n15) = all_0_3_3
% 56.21/21.77 |
% 56.21/21.77 | From (1687) and (3391) follows:
% 56.21/21.77 | (3476) sum(n20, n10) = all_0_0_0
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (690) with n20, n10, all_0_0_0, n4 and discharging atoms sum(n20, n10) = all_0_0_0, sum(n20, n10) = n4, yields:
% 56.21/21.77 | (1267) all_0_0_0 = n4
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 56.21/21.77 | (1266) all_0_3_3 = n4
% 56.21/21.77 |
% 56.21/21.77 | Equations (1267,1266) can reduce 679 to:
% 56.21/21.77 | (1106) $false
% 56.21/21.77 |
% 56.21/21.77 |-The branch is then unsatisfiable
% 56.21/21.77 |-Branch two:
% 56.21/21.77 | (1928) ~ (all_0_10_10 = n5)
% 56.21/21.77 | (1929) 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
% 56.21/21.77 |
% 56.21/21.77 +-Applying beta-rule and splitting (1929), into two cases.
% 56.21/21.77 |-Branch one:
% 56.21/21.77 | (1930) all_0_10_10 = n4
% 56.21/21.77 |
% 56.21/21.77 | From (1930) and (292) follows:
% 56.21/21.77 | (1931) pred(n4) = all_0_6_6
% 56.21/21.77 |
% 56.21/21.77 | From (1930) and (760) follows:
% 56.21/21.77 | (1932) succ(n4) = all_0_8_8
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 56.21/21.77 | (1933) all_0_6_6 = n3
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 56.21/21.77 | (1934) all_0_8_8 = n5
% 56.21/21.77 |
% 56.21/21.77 | From (1933)(1934) and (411) follows:
% 56.21/21.77 | (1935) sum(n3, n5) = all_0_1_1
% 56.21/21.77 |
% 56.21/21.77 | From (1933) and (11709) follows:
% 56.21/21.77 | (11810) sum(n3, n11) = all_0_4_4
% 56.21/21.77 |
% 56.21/21.77 | From (1934) and (11711) follows:
% 56.21/21.77 | (11811) sum(n9, n5) = all_0_7_7
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (690) with n9, n5, all_0_7_7, n14 and discharging atoms sum(n9, n5) = all_0_7_7, sum(n9, n5) = n14, yields:
% 56.21/21.77 | (1281) all_0_7_7 = n14
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (690) with n3, n11, all_0_4_4, n14 and discharging atoms sum(n3, n11) = all_0_4_4, sum(n3, n11) = n14, yields:
% 56.21/21.77 | (1279) all_0_4_4 = n14
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 56.21/21.77 | (1705) all_0_1_1 = n8
% 56.21/21.77 |
% 56.21/21.77 | From (1281)(1279) and (590) follows:
% 56.21/21.77 | (1283) sum(n14, n14) = all_0_3_3
% 56.21/21.77 |
% 56.21/21.77 | From (1705) and (3391) follows:
% 56.21/21.77 | (3494) sum(n20, n8) = all_0_0_0
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (690) with n20, n8, all_0_0_0, n2 and discharging atoms sum(n20, n8) = all_0_0_0, sum(n20, n8) = n2, yields:
% 56.21/21.77 | (1285) all_0_0_0 = n2
% 56.21/21.77 |
% 56.21/21.77 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 56.21/21.77 | (1284) all_0_3_3 = n2
% 56.21/21.77 |
% 56.21/21.78 | Equations (1285,1284) can reduce 679 to:
% 56.21/21.78 | (1106) $false
% 56.21/21.78 |
% 56.21/21.78 |-The branch is then unsatisfiable
% 56.21/21.78 |-Branch two:
% 56.21/21.78 | (1946) ~ (all_0_10_10 = n4)
% 56.21/21.78 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.21/21.78 |
% 56.21/21.78 +-Applying beta-rule and splitting (1947), into two cases.
% 56.21/21.78 |-Branch one:
% 56.21/21.78 | (1948) all_0_10_10 = n3
% 56.21/21.78 |
% 56.21/21.78 | From (1948) and (292) follows:
% 56.21/21.78 | (1949) pred(n3) = all_0_6_6
% 56.21/21.78 |
% 56.21/21.78 | From (1948) and (760) follows:
% 56.21/21.78 | (1950) succ(n3) = all_0_8_8
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 56.21/21.78 | (1951) all_0_6_6 = n2
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 56.21/21.78 | (1952) all_0_8_8 = n4
% 56.21/21.78 |
% 56.21/21.78 | From (1951)(1952) and (411) follows:
% 56.21/21.78 | (1953) sum(n2, n4) = all_0_1_1
% 56.21/21.78 |
% 56.21/21.78 | From (1951) and (11709) follows:
% 56.21/21.78 | (11828) sum(n2, n11) = all_0_4_4
% 56.21/21.78 |
% 56.21/21.78 | From (1952) and (11711) follows:
% 56.21/21.78 | (11829) sum(n9, n4) = all_0_7_7
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (690) with n9, n4, all_0_7_7, n13 and discharging atoms sum(n9, n4) = all_0_7_7, sum(n9, n4) = n13, yields:
% 56.21/21.78 | (1299) all_0_7_7 = n13
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (690) with n2, n11, all_0_4_4, n13 and discharging atoms sum(n2, n11) = all_0_4_4, sum(n2, n11) = n13, yields:
% 56.21/21.78 | (1297) all_0_4_4 = n13
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 56.21/21.78 | (1723) all_0_1_1 = n6
% 56.21/21.78 |
% 56.21/21.78 | From (1299)(1297) and (590) follows:
% 56.21/21.78 | (1301) sum(n13, n13) = all_0_3_3
% 56.21/21.78 |
% 56.21/21.78 | From (1723) and (3391) follows:
% 56.21/21.78 | (3512) sum(n20, n6) = all_0_0_0
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (690) with n20, n6, all_0_0_0, n0 and discharging atoms sum(n20, n6) = all_0_0_0, sum(n20, n6) = n0, yields:
% 56.21/21.78 | (1303) all_0_0_0 = n0
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 56.21/21.78 | (1302) all_0_3_3 = n0
% 56.21/21.78 |
% 56.21/21.78 | Equations (1303,1302) can reduce 679 to:
% 56.21/21.78 | (1106) $false
% 56.21/21.78 |
% 56.21/21.78 |-The branch is then unsatisfiable
% 56.21/21.78 |-Branch two:
% 56.21/21.78 | (1964) ~ (all_0_10_10 = n3)
% 56.21/21.78 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.21/21.78 |
% 56.21/21.78 +-Applying beta-rule and splitting (1965), into two cases.
% 56.21/21.78 |-Branch one:
% 56.21/21.78 | (1966) all_0_10_10 = n2
% 56.21/21.78 |
% 56.21/21.78 | From (1966) and (292) follows:
% 56.21/21.78 | (1967) pred(n2) = all_0_6_6
% 56.21/21.78 |
% 56.21/21.78 | From (1966) and (760) follows:
% 56.21/21.78 | (1968) succ(n2) = all_0_8_8
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 56.21/21.78 | (1969) all_0_6_6 = n1
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 56.21/21.78 | (1970) all_0_8_8 = n3
% 56.21/21.78 |
% 56.21/21.78 | From (1969)(1970) and (411) follows:
% 56.21/21.78 | (1971) sum(n1, n3) = all_0_1_1
% 56.21/21.78 |
% 56.21/21.78 | From (1969) and (11709) follows:
% 56.21/21.78 | (11846) sum(n1, n11) = all_0_4_4
% 56.21/21.78 |
% 56.21/21.78 | From (1970) and (11711) follows:
% 56.21/21.78 | (11847) sum(n9, n3) = all_0_7_7
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (690) with n9, n3, all_0_7_7, n12 and discharging atoms sum(n9, n3) = all_0_7_7, sum(n9, n3) = n12, yields:
% 56.21/21.78 | (1317) all_0_7_7 = n12
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (690) with n1, n11, all_0_4_4, n12 and discharging atoms sum(n1, n11) = all_0_4_4, sum(n1, n11) = n12, yields:
% 56.21/21.78 | (1315) all_0_4_4 = n12
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 56.21/21.78 | (1741) all_0_1_1 = n4
% 56.21/21.78 |
% 56.21/21.78 | From (1317)(1315) and (590) follows:
% 56.21/21.78 | (1319) sum(n12, n12) = all_0_3_3
% 56.21/21.78 |
% 56.21/21.78 | From (1741) and (3391) follows:
% 56.21/21.78 | (3530) sum(n20, n4) = all_0_0_0
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (690) with n20, n4, all_0_0_0, n24 and discharging atoms sum(n20, n4) = all_0_0_0, sum(n20, n4) = n24, yields:
% 56.21/21.78 | (1321) all_0_0_0 = n24
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 56.21/21.78 | (1320) all_0_3_3 = n24
% 56.21/21.78 |
% 56.21/21.78 | Equations (1321,1320) can reduce 679 to:
% 56.21/21.78 | (1106) $false
% 56.21/21.78 |
% 56.21/21.78 |-The branch is then unsatisfiable
% 56.21/21.78 |-Branch two:
% 56.21/21.78 | (1982) ~ (all_0_10_10 = n2)
% 56.21/21.78 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 56.21/21.78 |
% 56.21/21.78 +-Applying beta-rule and splitting (1983), into two cases.
% 56.21/21.78 |-Branch one:
% 56.21/21.78 | (1984) all_0_10_10 = n1
% 56.21/21.78 |
% 56.21/21.78 | From (1984) and (292) follows:
% 56.21/21.78 | (1985) pred(n1) = all_0_6_6
% 56.21/21.78 |
% 56.21/21.78 | From (1984) and (760) follows:
% 56.21/21.78 | (1986) succ(n1) = all_0_8_8
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 56.21/21.78 | (1987) all_0_6_6 = n0
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 56.21/21.78 | (1988) all_0_8_8 = n2
% 56.21/21.78 |
% 56.21/21.78 | From (1987)(1988) and (411) follows:
% 56.21/21.78 | (1989) sum(n0, n2) = all_0_1_1
% 56.21/21.78 |
% 56.21/21.78 | From (1987) and (11709) follows:
% 56.21/21.78 | (11864) sum(n0, n11) = all_0_4_4
% 56.21/21.78 |
% 56.21/21.78 | From (1988) and (11711) follows:
% 56.21/21.78 | (11865) sum(n9, n2) = all_0_7_7
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (690) with n9, n2, all_0_7_7, n11 and discharging atoms sum(n9, n2) = all_0_7_7, sum(n9, n2) = n11, yields:
% 56.21/21.78 | (1335) all_0_7_7 = n11
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (690) with n0, n11, all_0_4_4, n11 and discharging atoms sum(n0, n11) = all_0_4_4, sum(n0, n11) = n11, yields:
% 56.21/21.78 | (1333) all_0_4_4 = n11
% 56.21/21.78 |
% 56.21/21.78 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 56.21/21.79 | (1759) all_0_1_1 = n2
% 56.21/21.79 |
% 56.21/21.79 | From (1335)(1333) and (590) follows:
% 56.21/21.79 | (1337) sum(n11, n11) = all_0_3_3
% 56.21/21.79 |
% 56.21/21.79 | From (1759) and (3391) follows:
% 56.21/21.79 | (3548) sum(n20, n2) = all_0_0_0
% 56.21/21.79 |
% 56.21/21.79 | Instantiating formula (690) with n20, n2, all_0_0_0, n22 and discharging atoms sum(n20, n2) = all_0_0_0, sum(n20, n2) = n22, yields:
% 56.21/21.79 | (1102) all_0_0_0 = n22
% 56.21/21.79 |
% 56.21/21.79 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 56.21/21.79 | (1104) all_0_3_3 = n22
% 56.21/21.79 |
% 56.21/21.79 | Equations (1102,1104) can reduce 679 to:
% 56.21/21.79 | (1106) $false
% 56.21/21.79 |
% 56.21/21.79 |-The branch is then unsatisfiable
% 56.21/21.79 |-Branch two:
% 56.21/21.79 | (2002) ~ (all_0_10_10 = n1)
% 56.21/21.79 | (2003) all_0_10_10 = n0
% 56.21/21.79 |
% 56.21/21.79 | From (2003) and (292) follows:
% 56.21/21.79 | (2004) pred(n0) = all_0_6_6
% 56.21/21.79 |
% 56.21/21.79 | From (2003) and (760) follows:
% 56.21/21.79 | (2005) succ(n0) = all_0_8_8
% 56.21/21.79 |
% 56.21/21.79 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 56.21/21.79 | (2006) all_0_6_6 = n25
% 56.21/21.79 |
% 56.21/21.79 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 56.21/21.79 | (2007) all_0_8_8 = n1
% 56.21/21.79 |
% 56.21/21.79 | From (2006)(2007) and (411) follows:
% 56.21/21.79 | (2008) sum(n25, n1) = all_0_1_1
% 56.21/21.79 |
% 56.21/21.79 | From (2006) and (11709) follows:
% 56.21/21.79 | (11881) sum(n25, n11) = all_0_4_4
% 56.21/21.79 |
% 56.21/21.79 | From (2007) and (11711) follows:
% 56.21/21.79 | (11882) sum(n9, n1) = all_0_7_7
% 56.21/21.79 |
% 56.21/21.79 | Instantiating formula (690) with n25, n11, all_0_4_4, n10 and discharging atoms sum(n25, n11) = all_0_4_4, sum(n25, n11) = n10, yields:
% 56.21/21.79 | (1351) all_0_4_4 = n10
% 56.21/21.79 |
% 56.21/21.79 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 56.21/21.79 | (1777) all_0_1_1 = n0
% 56.21/21.79 |
% 56.21/21.79 | Instantiating formula (690) with n9, n1, all_0_7_7, n10 and discharging atoms sum(n9, n1) = all_0_7_7, sum(n9, n1) = n10, yields:
% 56.21/21.79 | (1353) all_0_7_7 = n10
% 56.21/21.79 |
% 56.21/21.79 | From (1353)(1351) and (590) follows:
% 56.21/21.79 | (1355) sum(n10, n10) = all_0_3_3
% 56.21/21.79 |
% 56.21/21.79 | From (1777) and (3391) follows:
% 56.21/21.79 | (3566) sum(n20, n0) = all_0_0_0
% 56.21/21.79 |
% 56.21/21.79 | Instantiating formula (690) with n20, n0, all_0_0_0, n20 and discharging atoms sum(n20, n0) = all_0_0_0, sum(n20, n0) = n20, yields:
% 56.21/21.79 | (1123) all_0_0_0 = n20
% 56.21/21.79 |
% 56.21/21.79 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 56.21/21.79 | (1122) all_0_3_3 = n20
% 56.21/21.79 |
% 56.21/21.79 | Equations (1123,1122) can reduce 679 to:
% 56.21/21.79 | (1106) $false
% 56.21/21.79 |
% 56.21/21.79 |-The branch is then unsatisfiable
% 56.21/21.79 |-Branch two:
% 56.21/21.79 | (1377) ~ (all_0_11_11 = n10)
% 56.21/21.79 | (1378) 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
% 56.21/21.79 |
% 56.21/21.79 +-Applying beta-rule and splitting (1839), into two cases.
% 56.21/21.79 |-Branch one:
% 56.21/21.79 | (1840) all_0_10_10 = n9
% 56.21/21.79 |
% 56.21/21.79 | From (1840) and (292) follows:
% 56.21/21.79 | (1841) pred(n9) = all_0_6_6
% 56.21/21.79 |
% 56.21/21.79 | From (1840) and (760) follows:
% 56.21/21.79 | (1842) succ(n9) = all_0_8_8
% 56.21/21.79 |
% 56.21/21.79 | Instantiating formula (500) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 56.21/21.79 | (1843) all_0_6_6 = n8
% 56.21/21.79 |
% 56.21/21.79 | Instantiating formula (617) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 56.21/21.79 | (1844) all_0_8_8 = n10
% 56.21/21.79 |
% 56.21/21.79 | From (1843) and (1841) follows:
% 56.21/21.79 | (610) pred(n9) = n8
% 56.21/21.79 |
% 56.21/21.79 | From (1844) and (1842) follows:
% 56.21/21.79 | (824) succ(n9) = n10
% 56.21/21.79 |
% 56.21/21.79 | From (1843) and (541) follows:
% 56.21/21.79 | (11900) sum(n8, all_0_5_5) = all_0_4_4
% 56.21/21.79 |
% 56.21/21.79 | From (1843)(1844) and (411) follows:
% 56.21/21.79 | (1845) sum(n8, n10) = all_0_1_1
% 56.21/21.79 |
% 56.21/21.79 | From (1844) and (427) follows:
% 56.21/21.79 | (11902) sum(all_0_9_9, n10) = all_0_7_7
% 56.21/21.79 |
% 56.21/21.79 | Instantiating formula (690) with n8, n10, all_0_1_1, n18 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n18, yields:
% 56.21/21.79 | (1615) all_0_1_1 = n18
% 56.21/21.79 |
% 56.21/21.79 | From (1615) and (630) follows:
% 56.21/21.79 | (3816) sum(all_0_2_2, n18) = all_0_0_0
% 56.21/21.79 |
% 56.21/21.79 | From (1615) and (1845) follows:
% 56.21/21.79 | (498) sum(n8, n10) = n18
% 56.21/21.79 |
% 56.21/21.79 +-Applying beta-rule and splitting (1378), into two cases.
% 56.21/21.79 |-Branch one:
% 56.21/21.79 | (1379) all_0_11_11 = n9
% 56.21/21.79 |
% 56.21/21.79 | From (1379) and (559) follows:
% 56.21/21.79 | (1380) pred(n9) = all_0_9_9
% 56.21/21.79 |
% 56.21/21.79 | From (1379) and (992) follows:
% 56.21/21.79 | (1381) succ(n9) = all_0_5_5
% 56.21/21.79 |
% 56.21/21.79 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 56.21/21.79 | (1382) all_0_9_9 = n8
% 56.21/21.79 |
% 56.21/21.79 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 56.21/21.79 | (1383) all_0_5_5 = n10
% 56.21/21.79 |
% 56.21/21.79 | From (1382)(1383) and (538) follows:
% 56.21/21.79 | (1384) sum(n8, n10) = all_0_2_2
% 56.21/21.79 |
% 56.21/21.79 | From (1382) and (11902) follows:
% 56.21/21.79 | (11912) sum(n8, n10) = all_0_7_7
% 56.21/21.79 |
% 56.21/21.79 | From (1383) and (11900) follows:
% 56.21/21.79 | (11913) sum(n8, n10) = all_0_4_4
% 56.21/21.79 |
% 56.21/21.79 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 56.21/21.79 | (1154) all_0_2_2 = n18
% 56.21/21.79 |
% 56.21/21.79 | Instantiating formula (690) 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:
% 56.21/21.79 | (1093) all_0_2_2 = all_0_4_4
% 56.21/21.79 |
% 56.21/21.79 | Instantiating formula (690) 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:
% 56.21/21.79 | (1094) all_0_2_2 = all_0_7_7
% 56.21/21.79 |
% 56.21/21.79 | Combining equations (1094,1093) yields a new equation:
% 56.21/21.79 | (1095) all_0_4_4 = all_0_7_7
% 56.21/21.79 |
% 56.21/21.79 | Combining equations (1154,1093) yields a new equation:
% 56.21/21.79 | (1207) all_0_4_4 = n18
% 56.21/21.79 |
% 56.21/21.79 | Combining equations (1207,1095) yields a new equation:
% 56.21/21.79 | (1209) all_0_7_7 = n18
% 56.21/21.79 |
% 56.21/21.79 | Combining equations (1209,1095) yields a new equation:
% 56.21/21.79 | (1207) all_0_4_4 = n18
% 56.21/21.79 |
% 56.21/21.79 | Combining equations (1207,1093) yields a new equation:
% 56.21/21.79 | (1154) all_0_2_2 = n18
% 56.21/21.79 |
% 56.21/21.79 | From (1154) and (3816) follows:
% 56.21/21.79 | (3834) sum(n18, n18) = all_0_0_0
% 56.21/21.79 |
% 56.21/21.79 | From (1209)(1207) and (590) follows:
% 56.21/21.80 | (1211) sum(n18, n18) = all_0_3_3
% 56.21/21.80 |
% 56.21/21.80 | Instantiating formula (690) with n18, n18, all_0_0_0, n10 and discharging atoms sum(n18, n18) = all_0_0_0, sum(n18, n18) = n10, yields:
% 56.21/21.80 | (1213) all_0_0_0 = n10
% 56.21/21.80 |
% 56.21/21.80 | Instantiating formula (690) 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:
% 56.21/21.80 | (1103) all_0_0_0 = all_0_3_3
% 56.21/21.80 |
% 56.21/21.80 | Combining equations (1213,1103) yields a new equation:
% 56.21/21.80 | (1212) all_0_3_3 = n10
% 56.21/21.80 |
% 56.21/21.80 | Combining equations (1212,1103) yields a new equation:
% 56.21/21.80 | (1213) all_0_0_0 = n10
% 56.21/21.80 |
% 56.21/21.80 | Equations (1213,1212) can reduce 679 to:
% 56.21/21.80 | (1106) $false
% 56.21/21.80 |
% 56.21/21.80 |-The branch is then unsatisfiable
% 56.21/21.80 |-Branch two:
% 56.21/21.80 | (1395) ~ (all_0_11_11 = n9)
% 56.35/21.80 | (1396) 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
% 56.35/21.80 |
% 56.35/21.80 +-Applying beta-rule and splitting (1396), into two cases.
% 56.35/21.80 |-Branch one:
% 56.35/21.80 | (1397) all_0_11_11 = n8
% 56.35/21.80 |
% 56.35/21.80 | From (1397) and (559) follows:
% 56.35/21.80 | (1398) pred(n8) = all_0_9_9
% 56.35/21.80 |
% 56.35/21.80 | From (1397) and (992) follows:
% 56.35/21.80 | (1399) succ(n8) = all_0_5_5
% 56.35/21.80 |
% 56.35/21.80 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 56.35/21.80 | (1400) all_0_9_9 = n7
% 56.35/21.80 |
% 56.35/21.80 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 56.35/21.80 | (1401) all_0_5_5 = n9
% 56.35/21.80 |
% 56.35/21.80 | From (1400)(1401) and (538) follows:
% 56.35/21.80 | (1402) sum(n7, n9) = all_0_2_2
% 56.35/21.80 |
% 56.35/21.80 | From (1400) and (11902) follows:
% 56.35/21.80 | (11937) sum(n7, n10) = all_0_7_7
% 56.35/21.80 |
% 56.35/21.80 | From (1401) and (11900) follows:
% 56.35/21.80 | (11938) sum(n8, n9) = all_0_4_4
% 56.35/21.80 |
% 56.35/21.80 | Instantiating formula (690) with n8, n9, all_0_4_4, n17 and discharging atoms sum(n8, n9) = all_0_4_4, sum(n8, n9) = n17, yields:
% 56.35/21.80 | (1225) all_0_4_4 = n17
% 56.35/21.80 |
% 56.35/21.80 | Instantiating formula (690) with n7, n10, all_0_7_7, n17 and discharging atoms sum(n7, n10) = all_0_7_7, sum(n7, n10) = n17, yields:
% 56.35/21.80 | (1227) all_0_7_7 = n17
% 56.35/21.80 |
% 56.35/21.80 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 56.35/21.80 | (1172) all_0_2_2 = n16
% 56.35/21.80 |
% 56.35/21.80 | From (1172) and (3816) follows:
% 56.35/21.80 | (3854) sum(n16, n18) = all_0_0_0
% 56.35/21.80 |
% 56.35/21.80 | From (1227)(1225) and (590) follows:
% 56.35/21.80 | (1229) sum(n17, n17) = all_0_3_3
% 56.35/21.80 |
% 56.35/21.80 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 56.35/21.80 | (1230) all_0_3_3 = n8
% 56.35/21.80 |
% 56.35/21.80 | Instantiating formula (690) with n16, n18, all_0_0_0, n8 and discharging atoms sum(n16, n18) = all_0_0_0, sum(n16, n18) = n8, yields:
% 56.35/21.80 | (1231) all_0_0_0 = n8
% 56.35/21.80 |
% 56.35/21.80 | Equations (1231,1230) can reduce 679 to:
% 56.35/21.80 | (1106) $false
% 56.35/21.80 |
% 56.35/21.80 |-The branch is then unsatisfiable
% 56.35/21.80 |-Branch two:
% 56.35/21.80 | (1413) ~ (all_0_11_11 = n8)
% 56.35/21.80 | (1414) 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
% 56.35/21.80 |
% 56.35/21.80 +-Applying beta-rule and splitting (1414), into two cases.
% 56.35/21.80 |-Branch one:
% 56.35/21.80 | (1415) all_0_11_11 = n7
% 56.35/21.80 |
% 56.35/21.80 | From (1415) and (559) follows:
% 56.35/21.80 | (1416) pred(n7) = all_0_9_9
% 56.35/21.80 |
% 56.35/21.80 | From (1415) and (992) follows:
% 56.35/21.80 | (1417) succ(n7) = all_0_5_5
% 56.35/21.80 |
% 56.35/21.80 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 56.35/21.80 | (1418) all_0_9_9 = n6
% 56.35/21.80 |
% 56.35/21.80 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 56.35/21.80 | (1419) all_0_5_5 = n8
% 56.35/21.80 |
% 56.35/21.80 | From (1418)(1419) and (538) follows:
% 56.35/21.80 | (1420) sum(n6, n8) = all_0_2_2
% 56.35/21.80 |
% 56.35/21.80 | From (1418) and (11902) follows:
% 56.35/21.80 | (11955) sum(n6, n10) = all_0_7_7
% 56.35/21.80 |
% 56.35/21.80 | From (1419) and (11900) follows:
% 56.35/21.80 | (11956) sum(n8, n8) = all_0_4_4
% 56.35/21.80 |
% 56.35/21.80 | Instantiating formula (690) with n8, n8, all_0_4_4, n16 and discharging atoms sum(n8, n8) = all_0_4_4, sum(n8, n8) = n16, yields:
% 56.35/21.80 | (1243) all_0_4_4 = n16
% 56.35/21.80 |
% 56.35/21.80 | Instantiating formula (690) with n6, n10, all_0_7_7, n16 and discharging atoms sum(n6, n10) = all_0_7_7, sum(n6, n10) = n16, yields:
% 56.35/21.80 | (1245) all_0_7_7 = n16
% 56.35/21.80 |
% 56.35/21.80 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 56.35/21.80 | (1190) all_0_2_2 = n14
% 56.35/21.80 |
% 56.35/21.80 | From (1190) and (3816) follows:
% 56.35/21.80 | (3872) sum(n14, n18) = all_0_0_0
% 56.35/21.80 |
% 56.35/21.80 | From (1245)(1243) and (590) follows:
% 56.35/21.80 | (1247) sum(n16, n16) = all_0_3_3
% 56.35/21.80 |
% 56.35/21.80 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 56.35/21.80 | (1248) all_0_3_3 = n6
% 56.35/21.80 |
% 56.35/21.80 | Instantiating formula (690) with n14, n18, all_0_0_0, n6 and discharging atoms sum(n14, n18) = all_0_0_0, sum(n14, n18) = n6, yields:
% 56.35/21.80 | (1249) all_0_0_0 = n6
% 56.35/21.80 |
% 56.35/21.80 | Equations (1249,1248) can reduce 679 to:
% 56.35/21.80 | (1106) $false
% 56.35/21.80 |
% 56.35/21.80 |-The branch is then unsatisfiable
% 56.35/21.80 |-Branch two:
% 56.35/21.80 | (1431) ~ (all_0_11_11 = n7)
% 56.35/21.80 | (1432) 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
% 56.35/21.80 |
% 56.36/21.80 +-Applying beta-rule and splitting (1432), into two cases.
% 56.36/21.80 |-Branch one:
% 56.36/21.80 | (1433) all_0_11_11 = n6
% 56.36/21.80 |
% 56.36/21.80 | From (1433) and (559) follows:
% 56.36/21.80 | (1434) pred(n6) = all_0_9_9
% 56.36/21.80 |
% 56.36/21.80 | From (1433) and (992) follows:
% 56.36/21.80 | (1435) succ(n6) = all_0_5_5
% 56.36/21.80 |
% 56.36/21.80 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 56.36/21.80 | (1436) all_0_9_9 = n5
% 56.36/21.80 |
% 56.36/21.80 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 56.36/21.80 | (1437) all_0_5_5 = n7
% 56.36/21.80 |
% 56.36/21.80 | From (1436)(1437) and (538) follows:
% 56.36/21.80 | (1438) sum(n5, n7) = all_0_2_2
% 56.36/21.80 |
% 56.36/21.80 | From (1436) and (11902) follows:
% 56.36/21.80 | (11973) sum(n5, n10) = all_0_7_7
% 56.36/21.80 |
% 56.36/21.80 | From (1437) and (11900) follows:
% 56.36/21.80 | (11974) sum(n8, n7) = all_0_4_4
% 56.36/21.80 |
% 56.36/21.80 | Instantiating formula (690) with n8, n7, all_0_4_4, n15 and discharging atoms sum(n8, n7) = all_0_4_4, sum(n8, n7) = n15, yields:
% 56.36/21.80 | (1261) all_0_4_4 = n15
% 56.36/21.80 |
% 56.36/21.80 | Instantiating formula (690) with n5, n10, all_0_7_7, n15 and discharging atoms sum(n5, n10) = all_0_7_7, sum(n5, n10) = n15, yields:
% 56.36/21.81 | (1263) all_0_7_7 = n15
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 56.36/21.81 | (1208) all_0_2_2 = n12
% 56.36/21.81 |
% 56.36/21.81 | From (1208) and (3816) follows:
% 56.36/21.81 | (3890) sum(n12, n18) = all_0_0_0
% 56.36/21.81 |
% 56.36/21.81 | From (1263)(1261) and (590) follows:
% 56.36/21.81 | (1265) sum(n15, n15) = all_0_3_3
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 56.36/21.81 | (1266) all_0_3_3 = n4
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (690) with n12, n18, all_0_0_0, n4 and discharging atoms sum(n12, n18) = all_0_0_0, sum(n12, n18) = n4, yields:
% 56.36/21.81 | (1267) all_0_0_0 = n4
% 56.36/21.81 |
% 56.36/21.81 | Equations (1267,1266) can reduce 679 to:
% 56.36/21.81 | (1106) $false
% 56.36/21.81 |
% 56.36/21.81 |-The branch is then unsatisfiable
% 56.36/21.81 |-Branch two:
% 56.36/21.81 | (1449) ~ (all_0_11_11 = n6)
% 56.36/21.81 | (1450) 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
% 56.36/21.81 |
% 56.36/21.81 +-Applying beta-rule and splitting (1450), into two cases.
% 56.36/21.81 |-Branch one:
% 56.36/21.81 | (1451) all_0_11_11 = n5
% 56.36/21.81 |
% 56.36/21.81 | From (1451) and (559) follows:
% 56.36/21.81 | (1452) pred(n5) = all_0_9_9
% 56.36/21.81 |
% 56.36/21.81 | From (1451) and (992) follows:
% 56.36/21.81 | (1453) succ(n5) = all_0_5_5
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 56.36/21.81 | (1454) all_0_9_9 = n4
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 56.36/21.81 | (1455) all_0_5_5 = n6
% 56.36/21.81 |
% 56.36/21.81 | From (1454)(1455) and (538) follows:
% 56.36/21.81 | (1456) sum(n4, n6) = all_0_2_2
% 56.36/21.81 |
% 56.36/21.81 | From (1454) and (11902) follows:
% 56.36/21.81 | (11991) sum(n4, n10) = all_0_7_7
% 56.36/21.81 |
% 56.36/21.81 | From (1455) and (11900) follows:
% 56.36/21.81 | (11992) sum(n8, n6) = all_0_4_4
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (690) with n8, n6, all_0_4_4, n14 and discharging atoms sum(n8, n6) = all_0_4_4, sum(n8, n6) = n14, yields:
% 56.36/21.81 | (1279) all_0_4_4 = n14
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (690) with n4, n10, all_0_7_7, n14 and discharging atoms sum(n4, n10) = all_0_7_7, sum(n4, n10) = n14, yields:
% 56.36/21.81 | (1281) all_0_7_7 = n14
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 56.36/21.81 | (1226) all_0_2_2 = n10
% 56.36/21.81 |
% 56.36/21.81 | From (1226) and (3816) follows:
% 56.36/21.81 | (3908) sum(n10, n18) = all_0_0_0
% 56.36/21.81 |
% 56.36/21.81 | From (1281)(1279) and (590) follows:
% 56.36/21.81 | (1283) sum(n14, n14) = all_0_3_3
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 56.36/21.81 | (1284) all_0_3_3 = n2
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (690) with n10, n18, all_0_0_0, n2 and discharging atoms sum(n10, n18) = all_0_0_0, sum(n10, n18) = n2, yields:
% 56.36/21.81 | (1285) all_0_0_0 = n2
% 56.36/21.81 |
% 56.36/21.81 | Equations (1285,1284) can reduce 679 to:
% 56.36/21.81 | (1106) $false
% 56.36/21.81 |
% 56.36/21.81 |-The branch is then unsatisfiable
% 56.36/21.81 |-Branch two:
% 56.36/21.81 | (1467) ~ (all_0_11_11 = n5)
% 56.36/21.81 | (1468) 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
% 56.36/21.81 |
% 56.36/21.81 +-Applying beta-rule and splitting (1468), into two cases.
% 56.36/21.81 |-Branch one:
% 56.36/21.81 | (1469) all_0_11_11 = n4
% 56.36/21.81 |
% 56.36/21.81 | From (1469) and (559) follows:
% 56.36/21.81 | (1470) pred(n4) = all_0_9_9
% 56.36/21.81 |
% 56.36/21.81 | From (1469) and (992) follows:
% 56.36/21.81 | (1471) succ(n4) = all_0_5_5
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 56.36/21.81 | (1472) all_0_9_9 = n3
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 56.36/21.81 | (1473) all_0_5_5 = n5
% 56.36/21.81 |
% 56.36/21.81 | From (1472)(1473) and (538) follows:
% 56.36/21.81 | (1474) sum(n3, n5) = all_0_2_2
% 56.36/21.81 |
% 56.36/21.81 | From (1472) and (11902) follows:
% 56.36/21.81 | (12009) sum(n3, n10) = all_0_7_7
% 56.36/21.81 |
% 56.36/21.81 | From (1473) and (11900) follows:
% 56.36/21.81 | (12010) sum(n8, n5) = all_0_4_4
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (690) with n8, n5, all_0_4_4, n13 and discharging atoms sum(n8, n5) = all_0_4_4, sum(n8, n5) = n13, yields:
% 56.36/21.81 | (1297) all_0_4_4 = n13
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (690) with n3, n10, all_0_7_7, n13 and discharging atoms sum(n3, n10) = all_0_7_7, sum(n3, n10) = n13, yields:
% 56.36/21.81 | (1299) all_0_7_7 = n13
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 56.36/21.81 | (1244) all_0_2_2 = n8
% 56.36/21.81 |
% 56.36/21.81 | From (1244) and (3816) follows:
% 56.36/21.81 | (3926) sum(n8, n18) = all_0_0_0
% 56.36/21.81 |
% 56.36/21.81 | From (1299)(1297) and (590) follows:
% 56.36/21.81 | (1301) sum(n13, n13) = all_0_3_3
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 56.36/21.81 | (1302) all_0_3_3 = n0
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (690) with n8, n18, all_0_0_0, n0 and discharging atoms sum(n8, n18) = all_0_0_0, sum(n8, n18) = n0, yields:
% 56.36/21.81 | (1303) all_0_0_0 = n0
% 56.36/21.81 |
% 56.36/21.81 | Equations (1303,1302) can reduce 679 to:
% 56.36/21.81 | (1106) $false
% 56.36/21.81 |
% 56.36/21.81 |-The branch is then unsatisfiable
% 56.36/21.81 |-Branch two:
% 56.36/21.81 | (1485) ~ (all_0_11_11 = n4)
% 56.36/21.81 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.36/21.81 |
% 56.36/21.81 +-Applying beta-rule and splitting (1486), into two cases.
% 56.36/21.81 |-Branch one:
% 56.36/21.81 | (1487) all_0_11_11 = n3
% 56.36/21.81 |
% 56.36/21.81 | From (1487) and (559) follows:
% 56.36/21.81 | (1488) pred(n3) = all_0_9_9
% 56.36/21.81 |
% 56.36/21.81 | From (1487) and (992) follows:
% 56.36/21.81 | (1489) succ(n3) = all_0_5_5
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 56.36/21.81 | (1490) all_0_9_9 = n2
% 56.36/21.81 |
% 56.36/21.81 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 56.36/21.81 | (1491) all_0_5_5 = n4
% 56.36/21.81 |
% 56.36/21.81 | From (1490)(1491) and (538) follows:
% 56.36/21.81 | (1492) sum(n2, n4) = all_0_2_2
% 56.36/21.81 |
% 56.36/21.81 | From (1490) and (11902) follows:
% 56.36/21.81 | (12027) sum(n2, n10) = all_0_7_7
% 56.36/21.81 |
% 56.36/21.81 | From (1491) and (11900) follows:
% 56.36/21.82 | (12028) sum(n8, n4) = all_0_4_4
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (690) with n8, n4, all_0_4_4, n12 and discharging atoms sum(n8, n4) = all_0_4_4, sum(n8, n4) = n12, yields:
% 56.36/21.82 | (1315) all_0_4_4 = n12
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (690) with n2, n10, all_0_7_7, n12 and discharging atoms sum(n2, n10) = all_0_7_7, sum(n2, n10) = n12, yields:
% 56.36/21.82 | (1317) all_0_7_7 = n12
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 56.36/21.82 | (1262) all_0_2_2 = n6
% 56.36/21.82 |
% 56.36/21.82 | From (1262) and (3816) follows:
% 56.36/21.82 | (3944) sum(n6, n18) = all_0_0_0
% 56.36/21.82 |
% 56.36/21.82 | From (1317)(1315) and (590) follows:
% 56.36/21.82 | (1319) sum(n12, n12) = all_0_3_3
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 56.36/21.82 | (1320) all_0_3_3 = n24
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (690) with n6, n18, all_0_0_0, n24 and discharging atoms sum(n6, n18) = all_0_0_0, sum(n6, n18) = n24, yields:
% 56.36/21.82 | (1321) all_0_0_0 = n24
% 56.36/21.82 |
% 56.36/21.82 | Equations (1321,1320) can reduce 679 to:
% 56.36/21.82 | (1106) $false
% 56.36/21.82 |
% 56.36/21.82 |-The branch is then unsatisfiable
% 56.36/21.82 |-Branch two:
% 56.36/21.82 | (1503) ~ (all_0_11_11 = n3)
% 56.36/21.82 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.36/21.82 |
% 56.36/21.82 +-Applying beta-rule and splitting (1504), into two cases.
% 56.36/21.82 |-Branch one:
% 56.36/21.82 | (1505) all_0_11_11 = n2
% 56.36/21.82 |
% 56.36/21.82 | From (1505) and (559) follows:
% 56.36/21.82 | (1506) pred(n2) = all_0_9_9
% 56.36/21.82 |
% 56.36/21.82 | From (1505) and (992) follows:
% 56.36/21.82 | (1507) succ(n2) = all_0_5_5
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 56.36/21.82 | (1508) all_0_9_9 = n1
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 56.36/21.82 | (1509) all_0_5_5 = n3
% 56.36/21.82 |
% 56.36/21.82 | From (1508)(1509) and (538) follows:
% 56.36/21.82 | (1510) sum(n1, n3) = all_0_2_2
% 56.36/21.82 |
% 56.36/21.82 | From (1508) and (11902) follows:
% 56.36/21.82 | (12045) sum(n1, n10) = all_0_7_7
% 56.36/21.82 |
% 56.36/21.82 | From (1509) and (11900) follows:
% 56.36/21.82 | (12046) sum(n8, n3) = all_0_4_4
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (690) with n8, n3, all_0_4_4, n11 and discharging atoms sum(n8, n3) = all_0_4_4, sum(n8, n3) = n11, yields:
% 56.36/21.82 | (1333) all_0_4_4 = n11
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (690) with n1, n10, all_0_7_7, n11 and discharging atoms sum(n1, n10) = all_0_7_7, sum(n1, n10) = n11, yields:
% 56.36/21.82 | (1335) all_0_7_7 = n11
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 56.36/21.82 | (1280) all_0_2_2 = n4
% 56.36/21.82 |
% 56.36/21.82 | From (1280) and (3816) follows:
% 56.36/21.82 | (3962) sum(n4, n18) = all_0_0_0
% 56.36/21.82 |
% 56.36/21.82 | From (1335)(1333) and (590) follows:
% 56.36/21.82 | (1337) sum(n11, n11) = all_0_3_3
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 56.36/21.82 | (1104) all_0_3_3 = n22
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (690) with n4, n18, all_0_0_0, n22 and discharging atoms sum(n4, n18) = all_0_0_0, sum(n4, n18) = n22, yields:
% 56.36/21.82 | (1102) all_0_0_0 = n22
% 56.36/21.82 |
% 56.36/21.82 | Equations (1102,1104) can reduce 679 to:
% 56.36/21.82 | (1106) $false
% 56.36/21.82 |
% 56.36/21.82 |-The branch is then unsatisfiable
% 56.36/21.82 |-Branch two:
% 56.36/21.82 | (1521) ~ (all_0_11_11 = n2)
% 56.36/21.82 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 56.36/21.82 |
% 56.36/21.82 +-Applying beta-rule and splitting (1522), into two cases.
% 56.36/21.82 |-Branch one:
% 56.36/21.82 | (1523) all_0_11_11 = n1
% 56.36/21.82 |
% 56.36/21.82 | From (1523) and (559) follows:
% 56.36/21.82 | (1524) pred(n1) = all_0_9_9
% 56.36/21.82 |
% 56.36/21.82 | From (1523) and (992) follows:
% 56.36/21.82 | (1525) succ(n1) = all_0_5_5
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 56.36/21.82 | (1526) all_0_9_9 = n0
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 56.36/21.82 | (1527) all_0_5_5 = n2
% 56.36/21.82 |
% 56.36/21.82 | From (1526)(1527) and (538) follows:
% 56.36/21.82 | (1528) sum(n0, n2) = all_0_2_2
% 56.36/21.82 |
% 56.36/21.82 | From (1526) and (11902) follows:
% 56.36/21.82 | (12063) sum(n0, n10) = all_0_7_7
% 56.36/21.82 |
% 56.36/21.82 | From (1527) and (11900) follows:
% 56.36/21.82 | (12064) sum(n8, n2) = all_0_4_4
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (690) with n8, n2, all_0_4_4, n10 and discharging atoms sum(n8, n2) = all_0_4_4, sum(n8, n2) = n10, yields:
% 56.36/21.82 | (1351) all_0_4_4 = n10
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (690) with n0, n10, all_0_7_7, n10 and discharging atoms sum(n0, n10) = all_0_7_7, sum(n0, n10) = n10, yields:
% 56.36/21.82 | (1353) all_0_7_7 = n10
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 56.36/21.82 | (1298) all_0_2_2 = n2
% 56.36/21.82 |
% 56.36/21.82 | From (1298) and (3816) follows:
% 56.36/21.82 | (3980) sum(n2, n18) = all_0_0_0
% 56.36/21.82 |
% 56.36/21.82 | From (1353)(1351) and (590) follows:
% 56.36/21.82 | (1355) sum(n10, n10) = all_0_3_3
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 56.36/21.82 | (1122) all_0_3_3 = n20
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (690) with n2, n18, all_0_0_0, n20 and discharging atoms sum(n2, n18) = all_0_0_0, sum(n2, n18) = n20, yields:
% 56.36/21.82 | (1123) all_0_0_0 = n20
% 56.36/21.82 |
% 56.36/21.82 | Equations (1123,1122) can reduce 679 to:
% 56.36/21.82 | (1106) $false
% 56.36/21.82 |
% 56.36/21.82 |-The branch is then unsatisfiable
% 56.36/21.82 |-Branch two:
% 56.36/21.82 | (1540) ~ (all_0_11_11 = n1)
% 56.36/21.82 | (1541) all_0_11_11 = n0
% 56.36/21.82 |
% 56.36/21.82 | From (1541) and (559) follows:
% 56.36/21.82 | (1542) pred(n0) = all_0_9_9
% 56.36/21.82 |
% 56.36/21.82 | From (1541) and (992) follows:
% 56.36/21.82 | (1543) succ(n0) = all_0_5_5
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 56.36/21.82 | (1544) all_0_9_9 = n25
% 56.36/21.82 |
% 56.36/21.82 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 56.36/21.82 | (1545) all_0_5_5 = n1
% 56.36/21.82 |
% 56.36/21.82 | From (1544)(1545) and (538) follows:
% 56.36/21.82 | (1546) sum(n25, n1) = all_0_2_2
% 56.36/21.82 |
% 56.36/21.82 | From (1544) and (11902) follows:
% 56.36/21.82 | (12080) sum(n25, n10) = all_0_7_7
% 56.36/21.82 |
% 56.36/21.82 | From (1545) and (11900) follows:
% 56.36/21.83 | (12081) sum(n8, n1) = all_0_4_4
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (690) with n25, n10, all_0_7_7, n9 and discharging atoms sum(n25, n10) = all_0_7_7, sum(n25, n10) = n9, yields:
% 56.36/21.83 | (1371) all_0_7_7 = n9
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 56.36/21.83 | (1316) all_0_2_2 = n0
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (690) with n8, n1, all_0_4_4, n9 and discharging atoms sum(n8, n1) = all_0_4_4, sum(n8, n1) = n9, yields:
% 56.36/21.83 | (1369) all_0_4_4 = n9
% 56.36/21.83 |
% 56.36/21.83 | From (1316) and (3816) follows:
% 56.36/21.83 | (3998) sum(n0, n18) = all_0_0_0
% 56.36/21.83 |
% 56.36/21.83 | From (1371)(1369) and (590) follows:
% 56.36/21.83 | (1373) sum(n9, n9) = all_0_3_3
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 56.36/21.83 | (1140) all_0_3_3 = n18
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (690) with n0, n18, all_0_0_0, n18 and discharging atoms sum(n0, n18) = all_0_0_0, sum(n0, n18) = n18, yields:
% 56.36/21.83 | (1141) all_0_0_0 = n18
% 56.36/21.83 |
% 56.36/21.83 | Equations (1141,1140) can reduce 679 to:
% 56.36/21.83 | (1106) $false
% 56.36/21.83 |
% 56.36/21.83 |-The branch is then unsatisfiable
% 56.36/21.83 |-Branch two:
% 56.36/21.83 | (1856) ~ (all_0_10_10 = n9)
% 56.36/21.83 | (1857) 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
% 56.36/21.83 |
% 56.36/21.83 +-Applying beta-rule and splitting (1378), into two cases.
% 56.36/21.83 |-Branch one:
% 56.36/21.83 | (1379) all_0_11_11 = n9
% 56.36/21.83 |
% 56.36/21.83 | From (1379) and (559) follows:
% 56.36/21.83 | (1380) pred(n9) = all_0_9_9
% 56.36/21.83 |
% 56.36/21.83 | From (1379) and (992) follows:
% 56.36/21.83 | (1381) succ(n9) = all_0_5_5
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (500) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 56.36/21.83 | (1382) all_0_9_9 = n8
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (617) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 56.36/21.83 | (1383) all_0_5_5 = n10
% 56.36/21.83 |
% 56.36/21.83 | From (1383) and (541) follows:
% 56.36/21.83 | (12097) sum(all_0_6_6, n10) = all_0_4_4
% 56.36/21.83 |
% 56.36/21.83 | From (1382)(1383) and (538) follows:
% 56.36/21.83 | (1384) sum(n8, n10) = all_0_2_2
% 56.36/21.83 |
% 56.36/21.83 | From (1382) and (427) follows:
% 56.36/21.83 | (12099) sum(n8, all_0_8_8) = all_0_7_7
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (690) with n8, n10, all_0_2_2, n18 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n18, yields:
% 56.36/21.83 | (1154) all_0_2_2 = n18
% 56.36/21.83 |
% 56.36/21.83 | From (1154) and (630) follows:
% 56.36/21.83 | (4247) sum(n18, all_0_1_1) = all_0_0_0
% 56.36/21.83 |
% 56.36/21.83 +-Applying beta-rule and splitting (1857), into two cases.
% 56.36/21.83 |-Branch one:
% 56.36/21.83 | (1858) all_0_10_10 = n8
% 56.36/21.83 |
% 56.36/21.83 | From (1858) and (292) follows:
% 56.36/21.83 | (1859) pred(n8) = all_0_6_6
% 56.36/21.83 |
% 56.36/21.83 | From (1858) and (760) follows:
% 56.36/21.83 | (1860) succ(n8) = all_0_8_8
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 56.36/21.83 | (1861) all_0_6_6 = n7
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 56.36/21.83 | (1862) all_0_8_8 = n9
% 56.36/21.83 |
% 56.36/21.83 | From (1861)(1862) and (411) follows:
% 56.36/21.83 | (1863) sum(n7, n9) = all_0_1_1
% 56.36/21.83 |
% 56.36/21.83 | From (1861) and (12097) follows:
% 56.36/21.83 | (12108) sum(n7, n10) = all_0_4_4
% 56.36/21.83 |
% 56.36/21.83 | From (1862) and (12099) follows:
% 56.36/21.83 | (12109) sum(n8, n9) = all_0_7_7
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (690) with n8, n9, all_0_7_7, n17 and discharging atoms sum(n8, n9) = all_0_7_7, sum(n8, n9) = n17, yields:
% 56.36/21.83 | (1227) all_0_7_7 = n17
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (690) with n7, n10, all_0_4_4, n17 and discharging atoms sum(n7, n10) = all_0_4_4, sum(n7, n10) = n17, yields:
% 56.36/21.83 | (1225) all_0_4_4 = n17
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 56.36/21.83 | (1633) all_0_1_1 = n16
% 56.36/21.83 |
% 56.36/21.83 | From (1227)(1225) and (590) follows:
% 56.36/21.83 | (1229) sum(n17, n17) = all_0_3_3
% 56.36/21.83 |
% 56.36/21.83 | From (1633) and (4247) follows:
% 56.36/21.83 | (4260) sum(n18, n16) = all_0_0_0
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (690) with n18, n16, all_0_0_0, n8 and discharging atoms sum(n18, n16) = all_0_0_0, sum(n18, n16) = n8, yields:
% 56.36/21.83 | (1231) all_0_0_0 = n8
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (690) with n17, n17, all_0_3_3, n8 and discharging atoms sum(n17, n17) = all_0_3_3, sum(n17, n17) = n8, yields:
% 56.36/21.83 | (1230) all_0_3_3 = n8
% 56.36/21.83 |
% 56.36/21.83 | Equations (1231,1230) can reduce 679 to:
% 56.36/21.83 | (1106) $false
% 56.36/21.83 |
% 56.36/21.83 |-The branch is then unsatisfiable
% 56.36/21.83 |-Branch two:
% 56.36/21.83 | (1874) ~ (all_0_10_10 = n8)
% 56.36/21.83 | (1875) 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
% 56.36/21.83 |
% 56.36/21.83 +-Applying beta-rule and splitting (1875), into two cases.
% 56.36/21.83 |-Branch one:
% 56.36/21.83 | (1876) all_0_10_10 = n7
% 56.36/21.83 |
% 56.36/21.83 | From (1876) and (292) follows:
% 56.36/21.83 | (1877) pred(n7) = all_0_6_6
% 56.36/21.83 |
% 56.36/21.83 | From (1876) and (760) follows:
% 56.36/21.83 | (1878) succ(n7) = all_0_8_8
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 56.36/21.83 | (1879) all_0_6_6 = n6
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 56.36/21.83 | (1880) all_0_8_8 = n8
% 56.36/21.83 |
% 56.36/21.83 | From (1879)(1880) and (411) follows:
% 56.36/21.83 | (1881) sum(n6, n8) = all_0_1_1
% 56.36/21.83 |
% 56.36/21.83 | From (1879) and (12097) follows:
% 56.36/21.83 | (12126) sum(n6, n10) = all_0_4_4
% 56.36/21.83 |
% 56.36/21.83 | From (1880) and (12099) follows:
% 56.36/21.83 | (12127) sum(n8, n8) = all_0_7_7
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (690) with n8, n8, all_0_7_7, n16 and discharging atoms sum(n8, n8) = all_0_7_7, sum(n8, n8) = n16, yields:
% 56.36/21.83 | (1245) all_0_7_7 = n16
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (690) with n6, n10, all_0_4_4, n16 and discharging atoms sum(n6, n10) = all_0_4_4, sum(n6, n10) = n16, yields:
% 56.36/21.83 | (1243) all_0_4_4 = n16
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 56.36/21.83 | (1651) all_0_1_1 = n14
% 56.36/21.83 |
% 56.36/21.83 | From (1245)(1243) and (590) follows:
% 56.36/21.83 | (1247) sum(n16, n16) = all_0_3_3
% 56.36/21.83 |
% 56.36/21.83 | From (1651) and (4247) follows:
% 56.36/21.83 | (4278) sum(n18, n14) = all_0_0_0
% 56.36/21.83 |
% 56.36/21.83 | Instantiating formula (690) with n18, n14, all_0_0_0, n6 and discharging atoms sum(n18, n14) = all_0_0_0, sum(n18, n14) = n6, yields:
% 56.36/21.84 | (1249) all_0_0_0 = n6
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (690) with n16, n16, all_0_3_3, n6 and discharging atoms sum(n16, n16) = all_0_3_3, sum(n16, n16) = n6, yields:
% 56.36/21.84 | (1248) all_0_3_3 = n6
% 56.36/21.84 |
% 56.36/21.84 | Equations (1249,1248) can reduce 679 to:
% 56.36/21.84 | (1106) $false
% 56.36/21.84 |
% 56.36/21.84 |-The branch is then unsatisfiable
% 56.36/21.84 |-Branch two:
% 56.36/21.84 | (1892) ~ (all_0_10_10 = n7)
% 56.36/21.84 | (1893) 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
% 56.36/21.84 |
% 56.36/21.84 +-Applying beta-rule and splitting (1893), into two cases.
% 56.36/21.84 |-Branch one:
% 56.36/21.84 | (1894) all_0_10_10 = n6
% 56.36/21.84 |
% 56.36/21.84 | From (1894) and (292) follows:
% 56.36/21.84 | (1895) pred(n6) = all_0_6_6
% 56.36/21.84 |
% 56.36/21.84 | From (1894) and (760) follows:
% 56.36/21.84 | (1896) succ(n6) = all_0_8_8
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 56.36/21.84 | (1897) all_0_6_6 = n5
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 56.36/21.84 | (1898) all_0_8_8 = n7
% 56.36/21.84 |
% 56.36/21.84 | From (1897)(1898) and (411) follows:
% 56.36/21.84 | (1899) sum(n5, n7) = all_0_1_1
% 56.36/21.84 |
% 56.36/21.84 | From (1897) and (12097) follows:
% 56.36/21.84 | (12144) sum(n5, n10) = all_0_4_4
% 56.36/21.84 |
% 56.36/21.84 | From (1898) and (12099) follows:
% 56.36/21.84 | (12145) sum(n8, n7) = all_0_7_7
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (690) with n8, n7, all_0_7_7, n15 and discharging atoms sum(n8, n7) = all_0_7_7, sum(n8, n7) = n15, yields:
% 56.36/21.84 | (1263) all_0_7_7 = n15
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (690) with n5, n10, all_0_4_4, n15 and discharging atoms sum(n5, n10) = all_0_4_4, sum(n5, n10) = n15, yields:
% 56.36/21.84 | (1261) all_0_4_4 = n15
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 56.36/21.84 | (1669) all_0_1_1 = n12
% 56.36/21.84 |
% 56.36/21.84 | From (1263)(1261) and (590) follows:
% 56.36/21.84 | (1265) sum(n15, n15) = all_0_3_3
% 56.36/21.84 |
% 56.36/21.84 | From (1669) and (4247) follows:
% 56.36/21.84 | (4296) sum(n18, n12) = all_0_0_0
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (690) with n18, n12, all_0_0_0, n4 and discharging atoms sum(n18, n12) = all_0_0_0, sum(n18, n12) = n4, yields:
% 56.36/21.84 | (1267) all_0_0_0 = n4
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 56.36/21.84 | (1266) all_0_3_3 = n4
% 56.36/21.84 |
% 56.36/21.84 | Equations (1267,1266) can reduce 679 to:
% 56.36/21.84 | (1106) $false
% 56.36/21.84 |
% 56.36/21.84 |-The branch is then unsatisfiable
% 56.36/21.84 |-Branch two:
% 56.36/21.84 | (1910) ~ (all_0_10_10 = n6)
% 56.36/21.84 | (1911) 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
% 56.36/21.84 |
% 56.36/21.84 +-Applying beta-rule and splitting (1911), into two cases.
% 56.36/21.84 |-Branch one:
% 56.36/21.84 | (1912) all_0_10_10 = n5
% 56.36/21.84 |
% 56.36/21.84 | From (1912) and (292) follows:
% 56.36/21.84 | (1913) pred(n5) = all_0_6_6
% 56.36/21.84 |
% 56.36/21.84 | From (1912) and (760) follows:
% 56.36/21.84 | (1914) succ(n5) = all_0_8_8
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 56.36/21.84 | (1915) all_0_6_6 = n4
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 56.36/21.84 | (1916) all_0_8_8 = n6
% 56.36/21.84 |
% 56.36/21.84 | From (1915)(1916) and (411) follows:
% 56.36/21.84 | (1917) sum(n4, n6) = all_0_1_1
% 56.36/21.84 |
% 56.36/21.84 | From (1915) and (12097) follows:
% 56.36/21.84 | (12162) sum(n4, n10) = all_0_4_4
% 56.36/21.84 |
% 56.36/21.84 | From (1916) and (12099) follows:
% 56.36/21.84 | (12163) sum(n8, n6) = all_0_7_7
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (690) with n8, n6, all_0_7_7, n14 and discharging atoms sum(n8, n6) = all_0_7_7, sum(n8, n6) = n14, yields:
% 56.36/21.84 | (1281) all_0_7_7 = n14
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (690) with n4, n10, all_0_4_4, n14 and discharging atoms sum(n4, n10) = all_0_4_4, sum(n4, n10) = n14, yields:
% 56.36/21.84 | (1279) all_0_4_4 = n14
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 56.36/21.84 | (1687) all_0_1_1 = n10
% 56.36/21.84 |
% 56.36/21.84 | From (1281)(1279) and (590) follows:
% 56.36/21.84 | (1283) sum(n14, n14) = all_0_3_3
% 56.36/21.84 |
% 56.36/21.84 | From (1687) and (4247) follows:
% 56.36/21.84 | (4314) sum(n18, n10) = all_0_0_0
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (690) with n18, n10, all_0_0_0, n2 and discharging atoms sum(n18, n10) = all_0_0_0, sum(n18, n10) = n2, yields:
% 56.36/21.84 | (1285) all_0_0_0 = n2
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 56.36/21.84 | (1284) all_0_3_3 = n2
% 56.36/21.84 |
% 56.36/21.84 | Equations (1285,1284) can reduce 679 to:
% 56.36/21.84 | (1106) $false
% 56.36/21.84 |
% 56.36/21.84 |-The branch is then unsatisfiable
% 56.36/21.84 |-Branch two:
% 56.36/21.84 | (1928) ~ (all_0_10_10 = n5)
% 56.36/21.84 | (1929) 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
% 56.36/21.84 |
% 56.36/21.84 +-Applying beta-rule and splitting (1929), into two cases.
% 56.36/21.84 |-Branch one:
% 56.36/21.84 | (1930) all_0_10_10 = n4
% 56.36/21.84 |
% 56.36/21.84 | From (1930) and (292) follows:
% 56.36/21.84 | (1931) pred(n4) = all_0_6_6
% 56.36/21.84 |
% 56.36/21.84 | From (1930) and (760) follows:
% 56.36/21.84 | (1932) succ(n4) = all_0_8_8
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 56.36/21.84 | (1933) all_0_6_6 = n3
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 56.36/21.84 | (1934) all_0_8_8 = n5
% 56.36/21.84 |
% 56.36/21.84 | From (1933)(1934) and (411) follows:
% 56.36/21.84 | (1935) sum(n3, n5) = all_0_1_1
% 56.36/21.84 |
% 56.36/21.84 | From (1933) and (12097) follows:
% 56.36/21.84 | (12180) sum(n3, n10) = all_0_4_4
% 56.36/21.84 |
% 56.36/21.84 | From (1934) and (12099) follows:
% 56.36/21.84 | (12181) sum(n8, n5) = all_0_7_7
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (690) with n8, n5, all_0_7_7, n13 and discharging atoms sum(n8, n5) = all_0_7_7, sum(n8, n5) = n13, yields:
% 56.36/21.84 | (1299) all_0_7_7 = n13
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (690) with n3, n10, all_0_4_4, n13 and discharging atoms sum(n3, n10) = all_0_4_4, sum(n3, n10) = n13, yields:
% 56.36/21.84 | (1297) all_0_4_4 = n13
% 56.36/21.84 |
% 56.36/21.84 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 56.36/21.84 | (1705) all_0_1_1 = n8
% 56.36/21.84 |
% 56.36/21.84 | From (1299)(1297) and (590) follows:
% 56.36/21.84 | (1301) sum(n13, n13) = all_0_3_3
% 56.36/21.84 |
% 56.36/21.84 | From (1705) and (4247) follows:
% 56.36/21.85 | (4332) sum(n18, n8) = all_0_0_0
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (690) with n18, n8, all_0_0_0, n0 and discharging atoms sum(n18, n8) = all_0_0_0, sum(n18, n8) = n0, yields:
% 56.36/21.85 | (1303) all_0_0_0 = n0
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 56.36/21.85 | (1302) all_0_3_3 = n0
% 56.36/21.85 |
% 56.36/21.85 | Equations (1303,1302) can reduce 679 to:
% 56.36/21.85 | (1106) $false
% 56.36/21.85 |
% 56.36/21.85 |-The branch is then unsatisfiable
% 56.36/21.85 |-Branch two:
% 56.36/21.85 | (1946) ~ (all_0_10_10 = n4)
% 56.36/21.85 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.36/21.85 |
% 56.36/21.85 +-Applying beta-rule and splitting (1947), into two cases.
% 56.36/21.85 |-Branch one:
% 56.36/21.85 | (1948) all_0_10_10 = n3
% 56.36/21.85 |
% 56.36/21.85 | From (1948) and (292) follows:
% 56.36/21.85 | (1949) pred(n3) = all_0_6_6
% 56.36/21.85 |
% 56.36/21.85 | From (1948) and (760) follows:
% 56.36/21.85 | (1950) succ(n3) = all_0_8_8
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 56.36/21.85 | (1951) all_0_6_6 = n2
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 56.36/21.85 | (1952) all_0_8_8 = n4
% 56.36/21.85 |
% 56.36/21.85 | From (1951)(1952) and (411) follows:
% 56.36/21.85 | (1953) sum(n2, n4) = all_0_1_1
% 56.36/21.85 |
% 56.36/21.85 | From (1951) and (12097) follows:
% 56.36/21.85 | (12198) sum(n2, n10) = all_0_4_4
% 56.36/21.85 |
% 56.36/21.85 | From (1952) and (12099) follows:
% 56.36/21.85 | (12199) sum(n8, n4) = all_0_7_7
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (690) with n8, n4, all_0_7_7, n12 and discharging atoms sum(n8, n4) = all_0_7_7, sum(n8, n4) = n12, yields:
% 56.36/21.85 | (1317) all_0_7_7 = n12
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (690) with n2, n10, all_0_4_4, n12 and discharging atoms sum(n2, n10) = all_0_4_4, sum(n2, n10) = n12, yields:
% 56.36/21.85 | (1315) all_0_4_4 = n12
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 56.36/21.85 | (1723) all_0_1_1 = n6
% 56.36/21.85 |
% 56.36/21.85 | From (1317)(1315) and (590) follows:
% 56.36/21.85 | (1319) sum(n12, n12) = all_0_3_3
% 56.36/21.85 |
% 56.36/21.85 | From (1723) and (4247) follows:
% 56.36/21.85 | (4350) sum(n18, n6) = all_0_0_0
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (690) with n18, n6, all_0_0_0, n24 and discharging atoms sum(n18, n6) = all_0_0_0, sum(n18, n6) = n24, yields:
% 56.36/21.85 | (1321) all_0_0_0 = n24
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 56.36/21.85 | (1320) all_0_3_3 = n24
% 56.36/21.85 |
% 56.36/21.85 | Equations (1321,1320) can reduce 679 to:
% 56.36/21.85 | (1106) $false
% 56.36/21.85 |
% 56.36/21.85 |-The branch is then unsatisfiable
% 56.36/21.85 |-Branch two:
% 56.36/21.85 | (1964) ~ (all_0_10_10 = n3)
% 56.36/21.85 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.36/21.85 |
% 56.36/21.85 +-Applying beta-rule and splitting (1965), into two cases.
% 56.36/21.85 |-Branch one:
% 56.36/21.85 | (1966) all_0_10_10 = n2
% 56.36/21.85 |
% 56.36/21.85 | From (1966) and (292) follows:
% 56.36/21.85 | (1967) pred(n2) = all_0_6_6
% 56.36/21.85 |
% 56.36/21.85 | From (1966) and (760) follows:
% 56.36/21.85 | (1968) succ(n2) = all_0_8_8
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 56.36/21.85 | (1969) all_0_6_6 = n1
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 56.36/21.85 | (1970) all_0_8_8 = n3
% 56.36/21.85 |
% 56.36/21.85 | From (1969)(1970) and (411) follows:
% 56.36/21.85 | (1971) sum(n1, n3) = all_0_1_1
% 56.36/21.85 |
% 56.36/21.85 | From (1969) and (12097) follows:
% 56.36/21.85 | (12216) sum(n1, n10) = all_0_4_4
% 56.36/21.85 |
% 56.36/21.85 | From (1970) and (12099) follows:
% 56.36/21.85 | (12217) sum(n8, n3) = all_0_7_7
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (690) with n8, n3, all_0_7_7, n11 and discharging atoms sum(n8, n3) = all_0_7_7, sum(n8, n3) = n11, yields:
% 56.36/21.85 | (1335) all_0_7_7 = n11
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (690) with n1, n10, all_0_4_4, n11 and discharging atoms sum(n1, n10) = all_0_4_4, sum(n1, n10) = n11, yields:
% 56.36/21.85 | (1333) all_0_4_4 = n11
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 56.36/21.85 | (1741) all_0_1_1 = n4
% 56.36/21.85 |
% 56.36/21.85 | From (1335)(1333) and (590) follows:
% 56.36/21.85 | (1337) sum(n11, n11) = all_0_3_3
% 56.36/21.85 |
% 56.36/21.85 | From (1741) and (4247) follows:
% 56.36/21.85 | (4368) sum(n18, n4) = all_0_0_0
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (690) with n18, n4, all_0_0_0, n22 and discharging atoms sum(n18, n4) = all_0_0_0, sum(n18, n4) = n22, yields:
% 56.36/21.85 | (1102) all_0_0_0 = n22
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 56.36/21.85 | (1104) all_0_3_3 = n22
% 56.36/21.85 |
% 56.36/21.85 | Equations (1102,1104) can reduce 679 to:
% 56.36/21.85 | (1106) $false
% 56.36/21.85 |
% 56.36/21.85 |-The branch is then unsatisfiable
% 56.36/21.85 |-Branch two:
% 56.36/21.85 | (1982) ~ (all_0_10_10 = n2)
% 56.36/21.85 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 56.36/21.85 |
% 56.36/21.85 +-Applying beta-rule and splitting (1983), into two cases.
% 56.36/21.85 |-Branch one:
% 56.36/21.85 | (1984) all_0_10_10 = n1
% 56.36/21.85 |
% 56.36/21.85 | From (1984) and (292) follows:
% 56.36/21.85 | (1985) pred(n1) = all_0_6_6
% 56.36/21.85 |
% 56.36/21.85 | From (1984) and (760) follows:
% 56.36/21.85 | (1986) succ(n1) = all_0_8_8
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 56.36/21.85 | (1987) all_0_6_6 = n0
% 56.36/21.85 |
% 56.36/21.85 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 56.36/21.85 | (1988) all_0_8_8 = n2
% 56.36/21.85 |
% 56.36/21.85 | From (1987)(1988) and (411) follows:
% 56.36/21.85 | (1989) sum(n0, n2) = all_0_1_1
% 56.36/21.85 |
% 56.36/21.85 | From (1987) and (12097) follows:
% 56.36/21.85 | (12234) sum(n0, n10) = all_0_4_4
% 56.36/21.85 |
% 56.36/21.85 | From (1988) and (12099) follows:
% 56.36/21.86 | (12235) sum(n8, n2) = all_0_7_7
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (690) with n8, n2, all_0_7_7, n10 and discharging atoms sum(n8, n2) = all_0_7_7, sum(n8, n2) = n10, yields:
% 56.36/21.86 | (1353) all_0_7_7 = n10
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (690) with n0, n10, all_0_4_4, n10 and discharging atoms sum(n0, n10) = all_0_4_4, sum(n0, n10) = n10, yields:
% 56.36/21.86 | (1351) all_0_4_4 = n10
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 56.36/21.86 | (1759) all_0_1_1 = n2
% 56.36/21.86 |
% 56.36/21.86 | From (1353)(1351) and (590) follows:
% 56.36/21.86 | (1355) sum(n10, n10) = all_0_3_3
% 56.36/21.86 |
% 56.36/21.86 | From (1759) and (4247) follows:
% 56.36/21.86 | (4386) sum(n18, n2) = all_0_0_0
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (690) with n18, n2, all_0_0_0, n20 and discharging atoms sum(n18, n2) = all_0_0_0, sum(n18, n2) = n20, yields:
% 56.36/21.86 | (1123) all_0_0_0 = n20
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 56.36/21.86 | (1122) all_0_3_3 = n20
% 56.36/21.86 |
% 56.36/21.86 | Equations (1123,1122) can reduce 679 to:
% 56.36/21.86 | (1106) $false
% 56.36/21.86 |
% 56.36/21.86 |-The branch is then unsatisfiable
% 56.36/21.86 |-Branch two:
% 56.36/21.86 | (2002) ~ (all_0_10_10 = n1)
% 56.36/21.86 | (2003) all_0_10_10 = n0
% 56.36/21.86 |
% 56.36/21.86 | From (2003) and (292) follows:
% 56.36/21.86 | (2004) pred(n0) = all_0_6_6
% 56.36/21.86 |
% 56.36/21.86 | From (2003) and (760) follows:
% 56.36/21.86 | (2005) succ(n0) = all_0_8_8
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 56.36/21.86 | (2006) all_0_6_6 = n25
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 56.36/21.86 | (2007) all_0_8_8 = n1
% 56.36/21.86 |
% 56.36/21.86 | From (2006)(2007) and (411) follows:
% 56.36/21.86 | (2008) sum(n25, n1) = all_0_1_1
% 56.36/21.86 |
% 56.36/21.86 | From (2006) and (12097) follows:
% 56.36/21.86 | (12251) sum(n25, n10) = all_0_4_4
% 56.36/21.86 |
% 56.36/21.86 | From (2007) and (12099) follows:
% 56.36/21.86 | (12252) sum(n8, n1) = all_0_7_7
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (690) with n25, n10, all_0_4_4, n9 and discharging atoms sum(n25, n10) = all_0_4_4, sum(n25, n10) = n9, yields:
% 56.36/21.86 | (1369) all_0_4_4 = n9
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 56.36/21.86 | (1777) all_0_1_1 = n0
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (690) with n8, n1, all_0_7_7, n9 and discharging atoms sum(n8, n1) = all_0_7_7, sum(n8, n1) = n9, yields:
% 56.36/21.86 | (1371) all_0_7_7 = n9
% 56.36/21.86 |
% 56.36/21.86 | From (1371)(1369) and (590) follows:
% 56.36/21.86 | (1373) sum(n9, n9) = all_0_3_3
% 56.36/21.86 |
% 56.36/21.86 | From (1777) and (4247) follows:
% 56.36/21.86 | (4404) sum(n18, n0) = all_0_0_0
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (690) with n18, n0, all_0_0_0, n18 and discharging atoms sum(n18, n0) = all_0_0_0, sum(n18, n0) = n18, yields:
% 56.36/21.86 | (1141) all_0_0_0 = n18
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 56.36/21.86 | (1140) all_0_3_3 = n18
% 56.36/21.86 |
% 56.36/21.86 | Equations (1141,1140) can reduce 679 to:
% 56.36/21.86 | (1106) $false
% 56.36/21.86 |
% 56.36/21.86 |-The branch is then unsatisfiable
% 56.36/21.86 |-Branch two:
% 56.36/21.86 | (1395) ~ (all_0_11_11 = n9)
% 56.36/21.86 | (1396) 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
% 56.36/21.86 |
% 56.36/21.86 +-Applying beta-rule and splitting (1857), into two cases.
% 56.36/21.86 |-Branch one:
% 56.36/21.86 | (1858) all_0_10_10 = n8
% 56.36/21.86 |
% 56.36/21.86 | From (1858) and (292) follows:
% 56.36/21.86 | (1859) pred(n8) = all_0_6_6
% 56.36/21.86 |
% 56.36/21.86 | From (1858) and (760) follows:
% 56.36/21.86 | (1860) succ(n8) = all_0_8_8
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (500) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 56.36/21.86 | (1861) all_0_6_6 = n7
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (617) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 56.36/21.86 | (1862) all_0_8_8 = n9
% 56.36/21.86 |
% 56.36/21.86 | From (1861) and (1859) follows:
% 56.36/21.86 | (92) pred(n8) = n7
% 56.36/21.86 |
% 56.36/21.86 | From (1862) and (1860) follows:
% 56.36/21.86 | (475) succ(n8) = n9
% 56.36/21.86 |
% 56.36/21.86 | From (1861) and (541) follows:
% 56.36/21.86 | (12270) sum(n7, all_0_5_5) = all_0_4_4
% 56.36/21.86 |
% 56.36/21.86 | From (1861)(1862) and (411) follows:
% 56.36/21.86 | (1863) sum(n7, n9) = all_0_1_1
% 56.36/21.86 |
% 56.36/21.86 | From (1862) and (427) follows:
% 56.36/21.86 | (12272) sum(all_0_9_9, n9) = all_0_7_7
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (690) with n7, n9, all_0_1_1, n16 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n16, yields:
% 56.36/21.86 | (1633) all_0_1_1 = n16
% 56.36/21.86 |
% 56.36/21.86 | From (1633) and (630) follows:
% 56.36/21.86 | (4654) sum(all_0_2_2, n16) = all_0_0_0
% 56.36/21.86 |
% 56.36/21.86 | From (1633) and (1863) follows:
% 56.36/21.86 | (754) sum(n7, n9) = n16
% 56.36/21.86 |
% 56.36/21.86 +-Applying beta-rule and splitting (1396), into two cases.
% 56.36/21.86 |-Branch one:
% 56.36/21.86 | (1397) all_0_11_11 = n8
% 56.36/21.86 |
% 56.36/21.86 | From (1397) and (559) follows:
% 56.36/21.86 | (1398) pred(n8) = all_0_9_9
% 56.36/21.86 |
% 56.36/21.86 | From (1397) and (992) follows:
% 56.36/21.86 | (1399) succ(n8) = all_0_5_5
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 56.36/21.86 | (1400) all_0_9_9 = n7
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 56.36/21.86 | (1401) all_0_5_5 = n9
% 56.36/21.86 |
% 56.36/21.86 | From (1400)(1401) and (538) follows:
% 56.36/21.86 | (1402) sum(n7, n9) = all_0_2_2
% 56.36/21.86 |
% 56.36/21.86 | From (1400) and (12272) follows:
% 56.36/21.86 | (12282) sum(n7, n9) = all_0_7_7
% 56.36/21.86 |
% 56.36/21.86 | From (1401) and (12270) follows:
% 56.36/21.86 | (12283) sum(n7, n9) = all_0_4_4
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 56.36/21.86 | (1172) all_0_2_2 = n16
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (690) 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:
% 56.36/21.86 | (1093) all_0_2_2 = all_0_4_4
% 56.36/21.86 |
% 56.36/21.86 | Instantiating formula (690) 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:
% 56.36/21.86 | (1094) all_0_2_2 = all_0_7_7
% 56.36/21.86 |
% 56.36/21.86 | Combining equations (1094,1093) yields a new equation:
% 56.36/21.86 | (1095) all_0_4_4 = all_0_7_7
% 56.36/21.86 |
% 56.36/21.86 | Combining equations (1172,1093) yields a new equation:
% 56.36/21.86 | (1243) all_0_4_4 = n16
% 56.36/21.86 |
% 56.36/21.86 | Combining equations (1243,1095) yields a new equation:
% 56.36/21.86 | (1245) all_0_7_7 = n16
% 56.36/21.86 |
% 56.36/21.86 | Combining equations (1245,1095) yields a new equation:
% 56.36/21.86 | (1243) all_0_4_4 = n16
% 56.36/21.86 |
% 56.36/21.86 | Combining equations (1243,1093) yields a new equation:
% 56.36/21.86 | (1172) all_0_2_2 = n16
% 56.36/21.86 |
% 56.36/21.86 | From (1172) and (4654) follows:
% 56.36/21.87 | (4672) sum(n16, n16) = all_0_0_0
% 56.36/21.87 |
% 56.36/21.87 | From (1245)(1243) and (590) follows:
% 56.36/21.87 | (1247) sum(n16, n16) = all_0_3_3
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (690) with n16, n16, all_0_0_0, n6 and discharging atoms sum(n16, n16) = all_0_0_0, sum(n16, n16) = n6, yields:
% 56.36/21.87 | (1249) all_0_0_0 = n6
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (690) 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:
% 56.36/21.87 | (1103) all_0_0_0 = all_0_3_3
% 56.36/21.87 |
% 56.36/21.87 | Combining equations (1249,1103) yields a new equation:
% 56.36/21.87 | (1248) all_0_3_3 = n6
% 56.36/21.87 |
% 56.36/21.87 | Combining equations (1248,1103) yields a new equation:
% 56.36/21.87 | (1249) all_0_0_0 = n6
% 56.36/21.87 |
% 56.36/21.87 | Equations (1249,1248) can reduce 679 to:
% 56.36/21.87 | (1106) $false
% 56.36/21.87 |
% 56.36/21.87 |-The branch is then unsatisfiable
% 56.36/21.87 |-Branch two:
% 56.36/21.87 | (1413) ~ (all_0_11_11 = n8)
% 56.36/21.87 | (1414) 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
% 56.36/21.87 |
% 56.36/21.87 +-Applying beta-rule and splitting (1414), into two cases.
% 56.36/21.87 |-Branch one:
% 56.36/21.87 | (1415) all_0_11_11 = n7
% 56.36/21.87 |
% 56.36/21.87 | From (1415) and (559) follows:
% 56.36/21.87 | (1416) pred(n7) = all_0_9_9
% 56.36/21.87 |
% 56.36/21.87 | From (1415) and (992) follows:
% 56.36/21.87 | (1417) succ(n7) = all_0_5_5
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 56.36/21.87 | (1418) all_0_9_9 = n6
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 56.36/21.87 | (1419) all_0_5_5 = n8
% 56.36/21.87 |
% 56.36/21.87 | From (1418)(1419) and (538) follows:
% 56.36/21.87 | (1420) sum(n6, n8) = all_0_2_2
% 56.36/21.87 |
% 56.36/21.87 | From (1418) and (12272) follows:
% 56.36/21.87 | (12307) sum(n6, n9) = all_0_7_7
% 56.36/21.87 |
% 56.36/21.87 | From (1419) and (12270) follows:
% 56.36/21.87 | (12308) sum(n7, n8) = all_0_4_4
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (690) with n7, n8, all_0_4_4, n15 and discharging atoms sum(n7, n8) = all_0_4_4, sum(n7, n8) = n15, yields:
% 56.36/21.87 | (1261) all_0_4_4 = n15
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (690) with n6, n9, all_0_7_7, n15 and discharging atoms sum(n6, n9) = all_0_7_7, sum(n6, n9) = n15, yields:
% 56.36/21.87 | (1263) all_0_7_7 = n15
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 56.36/21.87 | (1190) all_0_2_2 = n14
% 56.36/21.87 |
% 56.36/21.87 | From (1190) and (4654) follows:
% 56.36/21.87 | (4692) sum(n14, n16) = all_0_0_0
% 56.36/21.87 |
% 56.36/21.87 | From (1263)(1261) and (590) follows:
% 56.36/21.87 | (1265) sum(n15, n15) = all_0_3_3
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 56.36/21.87 | (1266) all_0_3_3 = n4
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (690) with n14, n16, all_0_0_0, n4 and discharging atoms sum(n14, n16) = all_0_0_0, sum(n14, n16) = n4, yields:
% 56.36/21.87 | (1267) all_0_0_0 = n4
% 56.36/21.87 |
% 56.36/21.87 | Equations (1267,1266) can reduce 679 to:
% 56.36/21.87 | (1106) $false
% 56.36/21.87 |
% 56.36/21.87 |-The branch is then unsatisfiable
% 56.36/21.87 |-Branch two:
% 56.36/21.87 | (1431) ~ (all_0_11_11 = n7)
% 56.36/21.87 | (1432) 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
% 56.36/21.87 |
% 56.36/21.87 +-Applying beta-rule and splitting (1432), into two cases.
% 56.36/21.87 |-Branch one:
% 56.36/21.87 | (1433) all_0_11_11 = n6
% 56.36/21.87 |
% 56.36/21.87 | From (1433) and (559) follows:
% 56.36/21.87 | (1434) pred(n6) = all_0_9_9
% 56.36/21.87 |
% 56.36/21.87 | From (1433) and (992) follows:
% 56.36/21.87 | (1435) succ(n6) = all_0_5_5
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 56.36/21.87 | (1436) all_0_9_9 = n5
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 56.36/21.87 | (1437) all_0_5_5 = n7
% 56.36/21.87 |
% 56.36/21.87 | From (1436)(1437) and (538) follows:
% 56.36/21.87 | (1438) sum(n5, n7) = all_0_2_2
% 56.36/21.87 |
% 56.36/21.87 | From (1436) and (12272) follows:
% 56.36/21.87 | (12325) sum(n5, n9) = all_0_7_7
% 56.36/21.87 |
% 56.36/21.87 | From (1437) and (12270) follows:
% 56.36/21.87 | (12326) sum(n7, n7) = all_0_4_4
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (690) with n7, n7, all_0_4_4, n14 and discharging atoms sum(n7, n7) = all_0_4_4, sum(n7, n7) = n14, yields:
% 56.36/21.87 | (1279) all_0_4_4 = n14
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (690) with n5, n9, all_0_7_7, n14 and discharging atoms sum(n5, n9) = all_0_7_7, sum(n5, n9) = n14, yields:
% 56.36/21.87 | (1281) all_0_7_7 = n14
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 56.36/21.87 | (1208) all_0_2_2 = n12
% 56.36/21.87 |
% 56.36/21.87 | From (1208) and (4654) follows:
% 56.36/21.87 | (4710) sum(n12, n16) = all_0_0_0
% 56.36/21.87 |
% 56.36/21.87 | From (1281)(1279) and (590) follows:
% 56.36/21.87 | (1283) sum(n14, n14) = all_0_3_3
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 56.36/21.87 | (1284) all_0_3_3 = n2
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (690) with n12, n16, all_0_0_0, n2 and discharging atoms sum(n12, n16) = all_0_0_0, sum(n12, n16) = n2, yields:
% 56.36/21.87 | (1285) all_0_0_0 = n2
% 56.36/21.87 |
% 56.36/21.87 | Equations (1285,1284) can reduce 679 to:
% 56.36/21.87 | (1106) $false
% 56.36/21.87 |
% 56.36/21.87 |-The branch is then unsatisfiable
% 56.36/21.87 |-Branch two:
% 56.36/21.87 | (1449) ~ (all_0_11_11 = n6)
% 56.36/21.87 | (1450) 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
% 56.36/21.87 |
% 56.36/21.87 +-Applying beta-rule and splitting (1450), into two cases.
% 56.36/21.87 |-Branch one:
% 56.36/21.87 | (1451) all_0_11_11 = n5
% 56.36/21.87 |
% 56.36/21.87 | From (1451) and (559) follows:
% 56.36/21.87 | (1452) pred(n5) = all_0_9_9
% 56.36/21.87 |
% 56.36/21.87 | From (1451) and (992) follows:
% 56.36/21.87 | (1453) succ(n5) = all_0_5_5
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 56.36/21.87 | (1454) all_0_9_9 = n4
% 56.36/21.87 |
% 56.36/21.87 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 56.36/21.87 | (1455) all_0_5_5 = n6
% 56.36/21.87 |
% 56.36/21.87 | From (1454)(1455) and (538) follows:
% 56.36/21.87 | (1456) sum(n4, n6) = all_0_2_2
% 56.36/21.87 |
% 56.36/21.87 | From (1454) and (12272) follows:
% 56.36/21.87 | (12343) sum(n4, n9) = all_0_7_7
% 56.36/21.87 |
% 56.36/21.87 | From (1455) and (12270) follows:
% 56.36/21.88 | (12344) sum(n7, n6) = all_0_4_4
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (690) with n7, n6, all_0_4_4, n13 and discharging atoms sum(n7, n6) = all_0_4_4, sum(n7, n6) = n13, yields:
% 56.36/21.88 | (1297) all_0_4_4 = n13
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (690) with n4, n9, all_0_7_7, n13 and discharging atoms sum(n4, n9) = all_0_7_7, sum(n4, n9) = n13, yields:
% 56.36/21.88 | (1299) all_0_7_7 = n13
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 56.36/21.88 | (1226) all_0_2_2 = n10
% 56.36/21.88 |
% 56.36/21.88 | From (1226) and (4654) follows:
% 56.36/21.88 | (4728) sum(n10, n16) = all_0_0_0
% 56.36/21.88 |
% 56.36/21.88 | From (1299)(1297) and (590) follows:
% 56.36/21.88 | (1301) sum(n13, n13) = all_0_3_3
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 56.36/21.88 | (1302) all_0_3_3 = n0
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (690) with n10, n16, all_0_0_0, n0 and discharging atoms sum(n10, n16) = all_0_0_0, sum(n10, n16) = n0, yields:
% 56.36/21.88 | (1303) all_0_0_0 = n0
% 56.36/21.88 |
% 56.36/21.88 | Equations (1303,1302) can reduce 679 to:
% 56.36/21.88 | (1106) $false
% 56.36/21.88 |
% 56.36/21.88 |-The branch is then unsatisfiable
% 56.36/21.88 |-Branch two:
% 56.36/21.88 | (1467) ~ (all_0_11_11 = n5)
% 56.36/21.88 | (1468) 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
% 56.36/21.88 |
% 56.36/21.88 +-Applying beta-rule and splitting (1468), into two cases.
% 56.36/21.88 |-Branch one:
% 56.36/21.88 | (1469) all_0_11_11 = n4
% 56.36/21.88 |
% 56.36/21.88 | From (1469) and (559) follows:
% 56.36/21.88 | (1470) pred(n4) = all_0_9_9
% 56.36/21.88 |
% 56.36/21.88 | From (1469) and (992) follows:
% 56.36/21.88 | (1471) succ(n4) = all_0_5_5
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 56.36/21.88 | (1472) all_0_9_9 = n3
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 56.36/21.88 | (1473) all_0_5_5 = n5
% 56.36/21.88 |
% 56.36/21.88 | From (1472)(1473) and (538) follows:
% 56.36/21.88 | (1474) sum(n3, n5) = all_0_2_2
% 56.36/21.88 |
% 56.36/21.88 | From (1472) and (12272) follows:
% 56.36/21.88 | (12361) sum(n3, n9) = all_0_7_7
% 56.36/21.88 |
% 56.36/21.88 | From (1473) and (12270) follows:
% 56.36/21.88 | (12362) sum(n7, n5) = all_0_4_4
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (690) with n7, n5, all_0_4_4, n12 and discharging atoms sum(n7, n5) = all_0_4_4, sum(n7, n5) = n12, yields:
% 56.36/21.88 | (1315) all_0_4_4 = n12
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (690) with n3, n9, all_0_7_7, n12 and discharging atoms sum(n3, n9) = all_0_7_7, sum(n3, n9) = n12, yields:
% 56.36/21.88 | (1317) all_0_7_7 = n12
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 56.36/21.88 | (1244) all_0_2_2 = n8
% 56.36/21.88 |
% 56.36/21.88 | From (1244) and (4654) follows:
% 56.36/21.88 | (4746) sum(n8, n16) = all_0_0_0
% 56.36/21.88 |
% 56.36/21.88 | From (1317)(1315) and (590) follows:
% 56.36/21.88 | (1319) sum(n12, n12) = all_0_3_3
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 56.36/21.88 | (1320) all_0_3_3 = n24
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (690) with n8, n16, all_0_0_0, n24 and discharging atoms sum(n8, n16) = all_0_0_0, sum(n8, n16) = n24, yields:
% 56.36/21.88 | (1321) all_0_0_0 = n24
% 56.36/21.88 |
% 56.36/21.88 | Equations (1321,1320) can reduce 679 to:
% 56.36/21.88 | (1106) $false
% 56.36/21.88 |
% 56.36/21.88 |-The branch is then unsatisfiable
% 56.36/21.88 |-Branch two:
% 56.36/21.88 | (1485) ~ (all_0_11_11 = n4)
% 56.36/21.88 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.36/21.88 |
% 56.36/21.88 +-Applying beta-rule and splitting (1486), into two cases.
% 56.36/21.88 |-Branch one:
% 56.36/21.88 | (1487) all_0_11_11 = n3
% 56.36/21.88 |
% 56.36/21.88 | From (1487) and (559) follows:
% 56.36/21.88 | (1488) pred(n3) = all_0_9_9
% 56.36/21.88 |
% 56.36/21.88 | From (1487) and (992) follows:
% 56.36/21.88 | (1489) succ(n3) = all_0_5_5
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 56.36/21.88 | (1490) all_0_9_9 = n2
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 56.36/21.88 | (1491) all_0_5_5 = n4
% 56.36/21.88 |
% 56.36/21.88 | From (1490)(1491) and (538) follows:
% 56.36/21.88 | (1492) sum(n2, n4) = all_0_2_2
% 56.36/21.88 |
% 56.36/21.88 | From (1490) and (12272) follows:
% 56.36/21.88 | (12379) sum(n2, n9) = all_0_7_7
% 56.36/21.88 |
% 56.36/21.88 | From (1491) and (12270) follows:
% 56.36/21.88 | (12380) sum(n7, n4) = all_0_4_4
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (690) with n7, n4, all_0_4_4, n11 and discharging atoms sum(n7, n4) = all_0_4_4, sum(n7, n4) = n11, yields:
% 56.36/21.88 | (1333) all_0_4_4 = n11
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (690) with n2, n9, all_0_7_7, n11 and discharging atoms sum(n2, n9) = all_0_7_7, sum(n2, n9) = n11, yields:
% 56.36/21.88 | (1335) all_0_7_7 = n11
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 56.36/21.88 | (1262) all_0_2_2 = n6
% 56.36/21.88 |
% 56.36/21.88 | From (1262) and (4654) follows:
% 56.36/21.88 | (4764) sum(n6, n16) = all_0_0_0
% 56.36/21.88 |
% 56.36/21.88 | From (1335)(1333) and (590) follows:
% 56.36/21.88 | (1337) sum(n11, n11) = all_0_3_3
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 56.36/21.88 | (1104) all_0_3_3 = n22
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (690) with n6, n16, all_0_0_0, n22 and discharging atoms sum(n6, n16) = all_0_0_0, sum(n6, n16) = n22, yields:
% 56.36/21.88 | (1102) all_0_0_0 = n22
% 56.36/21.88 |
% 56.36/21.88 | Equations (1102,1104) can reduce 679 to:
% 56.36/21.88 | (1106) $false
% 56.36/21.88 |
% 56.36/21.88 |-The branch is then unsatisfiable
% 56.36/21.88 |-Branch two:
% 56.36/21.88 | (1503) ~ (all_0_11_11 = n3)
% 56.36/21.88 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.36/21.88 |
% 56.36/21.88 +-Applying beta-rule and splitting (1504), into two cases.
% 56.36/21.88 |-Branch one:
% 56.36/21.88 | (1505) all_0_11_11 = n2
% 56.36/21.88 |
% 56.36/21.88 | From (1505) and (559) follows:
% 56.36/21.88 | (1506) pred(n2) = all_0_9_9
% 56.36/21.88 |
% 56.36/21.88 | From (1505) and (992) follows:
% 56.36/21.88 | (1507) succ(n2) = all_0_5_5
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 56.36/21.88 | (1508) all_0_9_9 = n1
% 56.36/21.88 |
% 56.36/21.88 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 56.36/21.88 | (1509) all_0_5_5 = n3
% 56.36/21.88 |
% 56.36/21.88 | From (1508)(1509) and (538) follows:
% 56.36/21.88 | (1510) sum(n1, n3) = all_0_2_2
% 56.36/21.88 |
% 56.36/21.88 | From (1508) and (12272) follows:
% 56.36/21.88 | (12397) sum(n1, n9) = all_0_7_7
% 56.36/21.88 |
% 56.36/21.88 | From (1509) and (12270) follows:
% 56.36/21.89 | (12398) sum(n7, n3) = all_0_4_4
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (690) with n7, n3, all_0_4_4, n10 and discharging atoms sum(n7, n3) = all_0_4_4, sum(n7, n3) = n10, yields:
% 56.36/21.89 | (1351) all_0_4_4 = n10
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (690) with n1, n9, all_0_7_7, n10 and discharging atoms sum(n1, n9) = all_0_7_7, sum(n1, n9) = n10, yields:
% 56.36/21.89 | (1353) all_0_7_7 = n10
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 56.36/21.89 | (1280) all_0_2_2 = n4
% 56.36/21.89 |
% 56.36/21.89 | From (1280) and (4654) follows:
% 56.36/21.89 | (4782) sum(n4, n16) = all_0_0_0
% 56.36/21.89 |
% 56.36/21.89 | From (1353)(1351) and (590) follows:
% 56.36/21.89 | (1355) sum(n10, n10) = all_0_3_3
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 56.36/21.89 | (1122) all_0_3_3 = n20
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (690) with n4, n16, all_0_0_0, n20 and discharging atoms sum(n4, n16) = all_0_0_0, sum(n4, n16) = n20, yields:
% 56.36/21.89 | (1123) all_0_0_0 = n20
% 56.36/21.89 |
% 56.36/21.89 | Equations (1123,1122) can reduce 679 to:
% 56.36/21.89 | (1106) $false
% 56.36/21.89 |
% 56.36/21.89 |-The branch is then unsatisfiable
% 56.36/21.89 |-Branch two:
% 56.36/21.89 | (1521) ~ (all_0_11_11 = n2)
% 56.36/21.89 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 56.36/21.89 |
% 56.36/21.89 +-Applying beta-rule and splitting (1522), into two cases.
% 56.36/21.89 |-Branch one:
% 56.36/21.89 | (1523) all_0_11_11 = n1
% 56.36/21.89 |
% 56.36/21.89 | From (1523) and (559) follows:
% 56.36/21.89 | (1524) pred(n1) = all_0_9_9
% 56.36/21.89 |
% 56.36/21.89 | From (1523) and (992) follows:
% 56.36/21.89 | (1525) succ(n1) = all_0_5_5
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 56.36/21.89 | (1526) all_0_9_9 = n0
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 56.36/21.89 | (1527) all_0_5_5 = n2
% 56.36/21.89 |
% 56.36/21.89 | From (1526)(1527) and (538) follows:
% 56.36/21.89 | (1528) sum(n0, n2) = all_0_2_2
% 56.36/21.89 |
% 56.36/21.89 | From (1526) and (12272) follows:
% 56.36/21.89 | (12415) sum(n0, n9) = all_0_7_7
% 56.36/21.89 |
% 56.36/21.89 | From (1527) and (12270) follows:
% 56.36/21.89 | (12416) sum(n7, n2) = all_0_4_4
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (690) with n7, n2, all_0_4_4, n9 and discharging atoms sum(n7, n2) = all_0_4_4, sum(n7, n2) = n9, yields:
% 56.36/21.89 | (1369) all_0_4_4 = n9
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (690) with n0, n9, all_0_7_7, n9 and discharging atoms sum(n0, n9) = all_0_7_7, sum(n0, n9) = n9, yields:
% 56.36/21.89 | (1371) all_0_7_7 = n9
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 56.36/21.89 | (1298) all_0_2_2 = n2
% 56.36/21.89 |
% 56.36/21.89 | From (1298) and (4654) follows:
% 56.36/21.89 | (4800) sum(n2, n16) = all_0_0_0
% 56.36/21.89 |
% 56.36/21.89 | From (1371)(1369) and (590) follows:
% 56.36/21.89 | (1373) sum(n9, n9) = all_0_3_3
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 56.36/21.89 | (1140) all_0_3_3 = n18
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (690) with n2, n16, all_0_0_0, n18 and discharging atoms sum(n2, n16) = all_0_0_0, sum(n2, n16) = n18, yields:
% 56.36/21.89 | (1141) all_0_0_0 = n18
% 56.36/21.89 |
% 56.36/21.89 | Equations (1141,1140) can reduce 679 to:
% 56.36/21.89 | (1106) $false
% 56.36/21.89 |
% 56.36/21.89 |-The branch is then unsatisfiable
% 56.36/21.89 |-Branch two:
% 56.36/21.89 | (1540) ~ (all_0_11_11 = n1)
% 56.36/21.89 | (1541) all_0_11_11 = n0
% 56.36/21.89 |
% 56.36/21.89 | From (1541) and (559) follows:
% 56.36/21.89 | (1542) pred(n0) = all_0_9_9
% 56.36/21.89 |
% 56.36/21.89 | From (1541) and (992) follows:
% 56.36/21.89 | (1543) succ(n0) = all_0_5_5
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 56.36/21.89 | (1544) all_0_9_9 = n25
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 56.36/21.89 | (1545) all_0_5_5 = n1
% 56.36/21.89 |
% 56.36/21.89 | From (1544)(1545) and (538) follows:
% 56.36/21.89 | (1546) sum(n25, n1) = all_0_2_2
% 56.36/21.89 |
% 56.36/21.89 | From (1544) and (12272) follows:
% 56.36/21.89 | (12432) sum(n25, n9) = all_0_7_7
% 56.36/21.89 |
% 56.36/21.89 | From (1545) and (12270) follows:
% 56.36/21.89 | (12433) sum(n7, n1) = all_0_4_4
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (690) with n25, n9, all_0_7_7, n8 and discharging atoms sum(n25, n9) = all_0_7_7, sum(n25, n9) = n8, yields:
% 56.36/21.89 | (1389) all_0_7_7 = n8
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 56.36/21.89 | (1316) all_0_2_2 = n0
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (690) with n7, n1, all_0_4_4, n8 and discharging atoms sum(n7, n1) = all_0_4_4, sum(n7, n1) = n8, yields:
% 56.36/21.89 | (1387) all_0_4_4 = n8
% 56.36/21.89 |
% 56.36/21.89 | From (1316) and (4654) follows:
% 56.36/21.89 | (4818) sum(n0, n16) = all_0_0_0
% 56.36/21.89 |
% 56.36/21.89 | From (1389)(1387) and (590) follows:
% 56.36/21.89 | (1391) sum(n8, n8) = all_0_3_3
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 56.36/21.89 | (1158) all_0_3_3 = n16
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (690) with n0, n16, all_0_0_0, n16 and discharging atoms sum(n0, n16) = all_0_0_0, sum(n0, n16) = n16, yields:
% 56.36/21.89 | (1159) all_0_0_0 = n16
% 56.36/21.89 |
% 56.36/21.89 | Equations (1159,1158) can reduce 679 to:
% 56.36/21.89 | (1106) $false
% 56.36/21.89 |
% 56.36/21.89 |-The branch is then unsatisfiable
% 56.36/21.89 |-Branch two:
% 56.36/21.89 | (1874) ~ (all_0_10_10 = n8)
% 56.36/21.89 | (1875) 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
% 56.36/21.89 |
% 56.36/21.89 +-Applying beta-rule and splitting (1396), into two cases.
% 56.36/21.89 |-Branch one:
% 56.36/21.89 | (1397) all_0_11_11 = n8
% 56.36/21.89 |
% 56.36/21.89 | From (1397) and (559) follows:
% 56.36/21.89 | (1398) pred(n8) = all_0_9_9
% 56.36/21.89 |
% 56.36/21.89 | From (1397) and (992) follows:
% 56.36/21.89 | (1399) succ(n8) = all_0_5_5
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (500) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 56.36/21.89 | (1400) all_0_9_9 = n7
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (617) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 56.36/21.89 | (1401) all_0_5_5 = n9
% 56.36/21.89 |
% 56.36/21.89 | From (1401) and (541) follows:
% 56.36/21.89 | (12449) sum(all_0_6_6, n9) = all_0_4_4
% 56.36/21.89 |
% 56.36/21.89 | From (1400)(1401) and (538) follows:
% 56.36/21.89 | (1402) sum(n7, n9) = all_0_2_2
% 56.36/21.89 |
% 56.36/21.89 | From (1400) and (427) follows:
% 56.36/21.89 | (12451) sum(n7, all_0_8_8) = all_0_7_7
% 56.36/21.89 |
% 56.36/21.89 | Instantiating formula (690) with n7, n9, all_0_2_2, n16 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n16, yields:
% 56.36/21.89 | (1172) all_0_2_2 = n16
% 56.36/21.89 |
% 56.36/21.89 | From (1172) and (630) follows:
% 56.36/21.89 | (5067) sum(n16, all_0_1_1) = all_0_0_0
% 56.36/21.89 |
% 56.36/21.89 +-Applying beta-rule and splitting (1875), into two cases.
% 56.36/21.89 |-Branch one:
% 56.36/21.90 | (1876) all_0_10_10 = n7
% 56.36/21.90 |
% 56.36/21.90 | From (1876) and (292) follows:
% 56.36/21.90 | (1877) pred(n7) = all_0_6_6
% 56.36/21.90 |
% 56.36/21.90 | From (1876) and (760) follows:
% 56.36/21.90 | (1878) succ(n7) = all_0_8_8
% 56.36/21.90 |
% 56.36/21.90 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 56.36/21.90 | (1879) all_0_6_6 = n6
% 56.36/21.90 |
% 56.36/21.90 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 56.36/21.90 | (1880) all_0_8_8 = n8
% 56.36/21.90 |
% 56.36/21.90 | From (1879)(1880) and (411) follows:
% 56.36/21.90 | (1881) sum(n6, n8) = all_0_1_1
% 56.36/21.90 |
% 56.36/21.90 | From (1879) and (12449) follows:
% 56.36/21.90 | (12460) sum(n6, n9) = all_0_4_4
% 56.36/21.90 |
% 56.36/21.90 | From (1880) and (12451) follows:
% 56.36/21.90 | (12461) sum(n7, n8) = all_0_7_7
% 56.36/21.90 |
% 56.36/21.90 | Instantiating formula (690) with n7, n8, all_0_7_7, n15 and discharging atoms sum(n7, n8) = all_0_7_7, sum(n7, n8) = n15, yields:
% 56.36/21.90 | (1263) all_0_7_7 = n15
% 56.36/21.90 |
% 56.36/21.90 | Instantiating formula (690) with n6, n9, all_0_4_4, n15 and discharging atoms sum(n6, n9) = all_0_4_4, sum(n6, n9) = n15, yields:
% 56.36/21.90 | (1261) all_0_4_4 = n15
% 56.36/21.90 |
% 56.36/21.90 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 56.36/21.90 | (1651) all_0_1_1 = n14
% 56.36/21.90 |
% 56.36/21.90 | From (1263)(1261) and (590) follows:
% 56.36/21.90 | (1265) sum(n15, n15) = all_0_3_3
% 56.36/21.90 |
% 56.36/21.90 | From (1651) and (5067) follows:
% 56.44/21.90 | (5080) sum(n16, n14) = all_0_0_0
% 56.44/21.90 |
% 56.44/21.90 | Instantiating formula (690) with n16, n14, all_0_0_0, n4 and discharging atoms sum(n16, n14) = all_0_0_0, sum(n16, n14) = n4, yields:
% 56.44/21.90 | (1267) all_0_0_0 = n4
% 56.44/21.90 |
% 56.44/21.90 | Instantiating formula (690) with n15, n15, all_0_3_3, n4 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n4, yields:
% 56.44/21.90 | (1266) all_0_3_3 = n4
% 56.44/21.90 |
% 56.44/21.90 | Equations (1267,1266) can reduce 679 to:
% 56.44/21.90 | (1106) $false
% 56.44/21.90 |
% 56.44/21.90 |-The branch is then unsatisfiable
% 56.44/21.90 |-Branch two:
% 56.44/21.90 | (1892) ~ (all_0_10_10 = n7)
% 56.44/21.90 | (1893) 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
% 56.44/21.90 |
% 56.44/21.90 +-Applying beta-rule and splitting (1893), into two cases.
% 56.44/21.90 |-Branch one:
% 56.44/21.90 | (1894) all_0_10_10 = n6
% 56.44/21.90 |
% 56.44/21.90 | From (1894) and (292) follows:
% 56.44/21.90 | (1895) pred(n6) = all_0_6_6
% 56.44/21.90 |
% 56.44/21.90 | From (1894) and (760) follows:
% 56.44/21.90 | (1896) succ(n6) = all_0_8_8
% 56.44/21.90 |
% 56.44/21.90 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 56.44/21.90 | (1897) all_0_6_6 = n5
% 56.44/21.90 |
% 56.44/21.90 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 56.44/21.90 | (1898) all_0_8_8 = n7
% 56.44/21.90 |
% 56.44/21.90 | From (1897)(1898) and (411) follows:
% 56.44/21.90 | (1899) sum(n5, n7) = all_0_1_1
% 56.44/21.90 |
% 56.44/21.90 | From (1897) and (12449) follows:
% 56.44/21.90 | (12478) sum(n5, n9) = all_0_4_4
% 56.44/21.90 |
% 56.44/21.90 | From (1898) and (12451) follows:
% 56.44/21.90 | (12479) sum(n7, n7) = all_0_7_7
% 56.44/21.90 |
% 56.44/21.90 | Instantiating formula (690) with n7, n7, all_0_7_7, n14 and discharging atoms sum(n7, n7) = all_0_7_7, sum(n7, n7) = n14, yields:
% 56.44/21.90 | (1281) all_0_7_7 = n14
% 56.44/21.90 |
% 56.44/21.90 | Instantiating formula (690) with n5, n9, all_0_4_4, n14 and discharging atoms sum(n5, n9) = all_0_4_4, sum(n5, n9) = n14, yields:
% 56.44/21.90 | (1279) all_0_4_4 = n14
% 56.44/21.90 |
% 56.44/21.90 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 56.44/21.90 | (1669) all_0_1_1 = n12
% 56.44/21.90 |
% 56.44/21.90 | From (1281)(1279) and (590) follows:
% 56.44/21.90 | (1283) sum(n14, n14) = all_0_3_3
% 56.44/21.90 |
% 56.44/21.90 | From (1669) and (5067) follows:
% 56.44/21.90 | (5098) sum(n16, n12) = all_0_0_0
% 56.44/21.90 |
% 56.44/21.90 | Instantiating formula (690) with n16, n12, all_0_0_0, n2 and discharging atoms sum(n16, n12) = all_0_0_0, sum(n16, n12) = n2, yields:
% 56.44/21.90 | (1285) all_0_0_0 = n2
% 56.44/21.90 |
% 56.44/21.90 | Instantiating formula (690) with n14, n14, all_0_3_3, n2 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n2, yields:
% 56.44/21.90 | (1284) all_0_3_3 = n2
% 56.44/21.90 |
% 56.44/21.90 | Equations (1285,1284) can reduce 679 to:
% 56.44/21.90 | (1106) $false
% 56.44/21.90 |
% 56.44/21.90 |-The branch is then unsatisfiable
% 56.44/21.90 |-Branch two:
% 56.44/21.90 | (1910) ~ (all_0_10_10 = n6)
% 56.44/21.90 | (1911) 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
% 56.44/21.90 |
% 56.44/21.90 +-Applying beta-rule and splitting (1911), into two cases.
% 56.44/21.90 |-Branch one:
% 56.44/21.90 | (1912) all_0_10_10 = n5
% 56.44/21.90 |
% 56.44/21.90 | From (1912) and (292) follows:
% 56.44/21.90 | (1913) pred(n5) = all_0_6_6
% 56.44/21.90 |
% 56.44/21.90 | From (1912) and (760) follows:
% 56.44/21.90 | (1914) succ(n5) = all_0_8_8
% 56.44/21.90 |
% 56.44/21.90 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 56.44/21.90 | (1915) all_0_6_6 = n4
% 56.44/21.90 |
% 56.44/21.90 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 56.44/21.90 | (1916) all_0_8_8 = n6
% 56.44/21.90 |
% 56.44/21.90 | From (1915)(1916) and (411) follows:
% 56.44/21.90 | (1917) sum(n4, n6) = all_0_1_1
% 56.44/21.90 |
% 56.44/21.90 | From (1915) and (12449) follows:
% 56.44/21.90 | (12496) sum(n4, n9) = all_0_4_4
% 56.44/21.90 |
% 56.44/21.90 | From (1916) and (12451) follows:
% 56.44/21.91 | (12497) sum(n7, n6) = all_0_7_7
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (690) with n7, n6, all_0_7_7, n13 and discharging atoms sum(n7, n6) = all_0_7_7, sum(n7, n6) = n13, yields:
% 56.44/21.91 | (1299) all_0_7_7 = n13
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (690) with n4, n9, all_0_4_4, n13 and discharging atoms sum(n4, n9) = all_0_4_4, sum(n4, n9) = n13, yields:
% 56.44/21.91 | (1297) all_0_4_4 = n13
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 56.44/21.91 | (1687) all_0_1_1 = n10
% 56.44/21.91 |
% 56.44/21.91 | From (1299)(1297) and (590) follows:
% 56.44/21.91 | (1301) sum(n13, n13) = all_0_3_3
% 56.44/21.91 |
% 56.44/21.91 | From (1687) and (5067) follows:
% 56.44/21.91 | (5116) sum(n16, n10) = all_0_0_0
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (690) with n16, n10, all_0_0_0, n0 and discharging atoms sum(n16, n10) = all_0_0_0, sum(n16, n10) = n0, yields:
% 56.44/21.91 | (1303) all_0_0_0 = n0
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 56.44/21.91 | (1302) all_0_3_3 = n0
% 56.44/21.91 |
% 56.44/21.91 | Equations (1303,1302) can reduce 679 to:
% 56.44/21.91 | (1106) $false
% 56.44/21.91 |
% 56.44/21.91 |-The branch is then unsatisfiable
% 56.44/21.91 |-Branch two:
% 56.44/21.91 | (1928) ~ (all_0_10_10 = n5)
% 56.44/21.91 | (1929) 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
% 56.44/21.91 |
% 56.44/21.91 +-Applying beta-rule and splitting (1929), into two cases.
% 56.44/21.91 |-Branch one:
% 56.44/21.91 | (1930) all_0_10_10 = n4
% 56.44/21.91 |
% 56.44/21.91 | From (1930) and (292) follows:
% 56.44/21.91 | (1931) pred(n4) = all_0_6_6
% 56.44/21.91 |
% 56.44/21.91 | From (1930) and (760) follows:
% 56.44/21.91 | (1932) succ(n4) = all_0_8_8
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 56.44/21.91 | (1933) all_0_6_6 = n3
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 56.44/21.91 | (1934) all_0_8_8 = n5
% 56.44/21.91 |
% 56.44/21.91 | From (1933)(1934) and (411) follows:
% 56.44/21.91 | (1935) sum(n3, n5) = all_0_1_1
% 56.44/21.91 |
% 56.44/21.91 | From (1933) and (12449) follows:
% 56.44/21.91 | (12514) sum(n3, n9) = all_0_4_4
% 56.44/21.91 |
% 56.44/21.91 | From (1934) and (12451) follows:
% 56.44/21.91 | (12515) sum(n7, n5) = all_0_7_7
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (690) with n7, n5, all_0_7_7, n12 and discharging atoms sum(n7, n5) = all_0_7_7, sum(n7, n5) = n12, yields:
% 56.44/21.91 | (1317) all_0_7_7 = n12
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (690) with n3, n9, all_0_4_4, n12 and discharging atoms sum(n3, n9) = all_0_4_4, sum(n3, n9) = n12, yields:
% 56.44/21.91 | (1315) all_0_4_4 = n12
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 56.44/21.91 | (1705) all_0_1_1 = n8
% 56.44/21.91 |
% 56.44/21.91 | From (1317)(1315) and (590) follows:
% 56.44/21.91 | (1319) sum(n12, n12) = all_0_3_3
% 56.44/21.91 |
% 56.44/21.91 | From (1705) and (5067) follows:
% 56.44/21.91 | (5134) sum(n16, n8) = all_0_0_0
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (690) with n16, n8, all_0_0_0, n24 and discharging atoms sum(n16, n8) = all_0_0_0, sum(n16, n8) = n24, yields:
% 56.44/21.91 | (1321) all_0_0_0 = n24
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 56.44/21.91 | (1320) all_0_3_3 = n24
% 56.44/21.91 |
% 56.44/21.91 | Equations (1321,1320) can reduce 679 to:
% 56.44/21.91 | (1106) $false
% 56.44/21.91 |
% 56.44/21.91 |-The branch is then unsatisfiable
% 56.44/21.91 |-Branch two:
% 56.44/21.91 | (1946) ~ (all_0_10_10 = n4)
% 56.44/21.91 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.44/21.91 |
% 56.44/21.91 +-Applying beta-rule and splitting (1947), into two cases.
% 56.44/21.91 |-Branch one:
% 56.44/21.91 | (1948) all_0_10_10 = n3
% 56.44/21.91 |
% 56.44/21.91 | From (1948) and (292) follows:
% 56.44/21.91 | (1949) pred(n3) = all_0_6_6
% 56.44/21.91 |
% 56.44/21.91 | From (1948) and (760) follows:
% 56.44/21.91 | (1950) succ(n3) = all_0_8_8
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 56.44/21.91 | (1951) all_0_6_6 = n2
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 56.44/21.91 | (1952) all_0_8_8 = n4
% 56.44/21.91 |
% 56.44/21.91 | From (1951)(1952) and (411) follows:
% 56.44/21.91 | (1953) sum(n2, n4) = all_0_1_1
% 56.44/21.91 |
% 56.44/21.91 | From (1951) and (12449) follows:
% 56.44/21.91 | (12532) sum(n2, n9) = all_0_4_4
% 56.44/21.91 |
% 56.44/21.91 | From (1952) and (12451) follows:
% 56.44/21.91 | (12533) sum(n7, n4) = all_0_7_7
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (690) with n7, n4, all_0_7_7, n11 and discharging atoms sum(n7, n4) = all_0_7_7, sum(n7, n4) = n11, yields:
% 56.44/21.91 | (1335) all_0_7_7 = n11
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (690) with n2, n9, all_0_4_4, n11 and discharging atoms sum(n2, n9) = all_0_4_4, sum(n2, n9) = n11, yields:
% 56.44/21.91 | (1333) all_0_4_4 = n11
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 56.44/21.91 | (1723) all_0_1_1 = n6
% 56.44/21.91 |
% 56.44/21.91 | From (1335)(1333) and (590) follows:
% 56.44/21.91 | (1337) sum(n11, n11) = all_0_3_3
% 56.44/21.91 |
% 56.44/21.91 | From (1723) and (5067) follows:
% 56.44/21.91 | (5152) sum(n16, n6) = all_0_0_0
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (690) with n16, n6, all_0_0_0, n22 and discharging atoms sum(n16, n6) = all_0_0_0, sum(n16, n6) = n22, yields:
% 56.44/21.91 | (1102) all_0_0_0 = n22
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 56.44/21.91 | (1104) all_0_3_3 = n22
% 56.44/21.91 |
% 56.44/21.91 | Equations (1102,1104) can reduce 679 to:
% 56.44/21.91 | (1106) $false
% 56.44/21.91 |
% 56.44/21.91 |-The branch is then unsatisfiable
% 56.44/21.91 |-Branch two:
% 56.44/21.91 | (1964) ~ (all_0_10_10 = n3)
% 56.44/21.91 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.44/21.91 |
% 56.44/21.91 +-Applying beta-rule and splitting (1965), into two cases.
% 56.44/21.91 |-Branch one:
% 56.44/21.91 | (1966) all_0_10_10 = n2
% 56.44/21.91 |
% 56.44/21.91 | From (1966) and (292) follows:
% 56.44/21.91 | (1967) pred(n2) = all_0_6_6
% 56.44/21.91 |
% 56.44/21.91 | From (1966) and (760) follows:
% 56.44/21.91 | (1968) succ(n2) = all_0_8_8
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 56.44/21.91 | (1969) all_0_6_6 = n1
% 56.44/21.91 |
% 56.44/21.91 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 56.44/21.91 | (1970) all_0_8_8 = n3
% 56.44/21.91 |
% 56.44/21.91 | From (1969)(1970) and (411) follows:
% 56.44/21.91 | (1971) sum(n1, n3) = all_0_1_1
% 56.44/21.91 |
% 56.44/21.91 | From (1969) and (12449) follows:
% 56.44/21.92 | (12550) sum(n1, n9) = all_0_4_4
% 56.44/21.92 |
% 56.44/21.92 | From (1970) and (12451) follows:
% 56.44/21.92 | (12551) sum(n7, n3) = all_0_7_7
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (690) with n7, n3, all_0_7_7, n10 and discharging atoms sum(n7, n3) = all_0_7_7, sum(n7, n3) = n10, yields:
% 56.44/21.92 | (1353) all_0_7_7 = n10
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (690) with n1, n9, all_0_4_4, n10 and discharging atoms sum(n1, n9) = all_0_4_4, sum(n1, n9) = n10, yields:
% 56.44/21.92 | (1351) all_0_4_4 = n10
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 56.44/21.92 | (1741) all_0_1_1 = n4
% 56.44/21.92 |
% 56.44/21.92 | From (1353)(1351) and (590) follows:
% 56.44/21.92 | (1355) sum(n10, n10) = all_0_3_3
% 56.44/21.92 |
% 56.44/21.92 | From (1741) and (5067) follows:
% 56.44/21.92 | (5170) sum(n16, n4) = all_0_0_0
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (690) with n16, n4, all_0_0_0, n20 and discharging atoms sum(n16, n4) = all_0_0_0, sum(n16, n4) = n20, yields:
% 56.44/21.92 | (1123) all_0_0_0 = n20
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 56.44/21.92 | (1122) all_0_3_3 = n20
% 56.44/21.92 |
% 56.44/21.92 | Equations (1123,1122) can reduce 679 to:
% 56.44/21.92 | (1106) $false
% 56.44/21.92 |
% 56.44/21.92 |-The branch is then unsatisfiable
% 56.44/21.92 |-Branch two:
% 56.44/21.92 | (1982) ~ (all_0_10_10 = n2)
% 56.44/21.92 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 56.44/21.92 |
% 56.44/21.92 +-Applying beta-rule and splitting (1983), into two cases.
% 56.44/21.92 |-Branch one:
% 56.44/21.92 | (1984) all_0_10_10 = n1
% 56.44/21.92 |
% 56.44/21.92 | From (1984) and (292) follows:
% 56.44/21.92 | (1985) pred(n1) = all_0_6_6
% 56.44/21.92 |
% 56.44/21.92 | From (1984) and (760) follows:
% 56.44/21.92 | (1986) succ(n1) = all_0_8_8
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 56.44/21.92 | (1987) all_0_6_6 = n0
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 56.44/21.92 | (1988) all_0_8_8 = n2
% 56.44/21.92 |
% 56.44/21.92 | From (1987)(1988) and (411) follows:
% 56.44/21.92 | (1989) sum(n0, n2) = all_0_1_1
% 56.44/21.92 |
% 56.44/21.92 | From (1987) and (12449) follows:
% 56.44/21.92 | (12568) sum(n0, n9) = all_0_4_4
% 56.44/21.92 |
% 56.44/21.92 | From (1988) and (12451) follows:
% 56.44/21.92 | (12569) sum(n7, n2) = all_0_7_7
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (690) with n7, n2, all_0_7_7, n9 and discharging atoms sum(n7, n2) = all_0_7_7, sum(n7, n2) = n9, yields:
% 56.44/21.92 | (1371) all_0_7_7 = n9
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (690) with n0, n9, all_0_4_4, n9 and discharging atoms sum(n0, n9) = all_0_4_4, sum(n0, n9) = n9, yields:
% 56.44/21.92 | (1369) all_0_4_4 = n9
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 56.44/21.92 | (1759) all_0_1_1 = n2
% 56.44/21.92 |
% 56.44/21.92 | From (1371)(1369) and (590) follows:
% 56.44/21.92 | (1373) sum(n9, n9) = all_0_3_3
% 56.44/21.92 |
% 56.44/21.92 | From (1759) and (5067) follows:
% 56.44/21.92 | (5188) sum(n16, n2) = all_0_0_0
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (690) with n16, n2, all_0_0_0, n18 and discharging atoms sum(n16, n2) = all_0_0_0, sum(n16, n2) = n18, yields:
% 56.44/21.92 | (1141) all_0_0_0 = n18
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 56.44/21.92 | (1140) all_0_3_3 = n18
% 56.44/21.92 |
% 56.44/21.92 | Equations (1141,1140) can reduce 679 to:
% 56.44/21.92 | (1106) $false
% 56.44/21.92 |
% 56.44/21.92 |-The branch is then unsatisfiable
% 56.44/21.92 |-Branch two:
% 56.44/21.92 | (2002) ~ (all_0_10_10 = n1)
% 56.44/21.92 | (2003) all_0_10_10 = n0
% 56.44/21.92 |
% 56.44/21.92 | From (2003) and (292) follows:
% 56.44/21.92 | (2004) pred(n0) = all_0_6_6
% 56.44/21.92 |
% 56.44/21.92 | From (2003) and (760) follows:
% 56.44/21.92 | (2005) succ(n0) = all_0_8_8
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 56.44/21.92 | (2006) all_0_6_6 = n25
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 56.44/21.92 | (2007) all_0_8_8 = n1
% 56.44/21.92 |
% 56.44/21.92 | From (2006)(2007) and (411) follows:
% 56.44/21.92 | (2008) sum(n25, n1) = all_0_1_1
% 56.44/21.92 |
% 56.44/21.92 | From (2006) and (12449) follows:
% 56.44/21.92 | (12585) sum(n25, n9) = all_0_4_4
% 56.44/21.92 |
% 56.44/21.92 | From (2007) and (12451) follows:
% 56.44/21.92 | (12586) sum(n7, n1) = all_0_7_7
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (690) with n25, n9, all_0_4_4, n8 and discharging atoms sum(n25, n9) = all_0_4_4, sum(n25, n9) = n8, yields:
% 56.44/21.92 | (1387) all_0_4_4 = n8
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 56.44/21.92 | (1777) all_0_1_1 = n0
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (690) with n7, n1, all_0_7_7, n8 and discharging atoms sum(n7, n1) = all_0_7_7, sum(n7, n1) = n8, yields:
% 56.44/21.92 | (1389) all_0_7_7 = n8
% 56.44/21.92 |
% 56.44/21.92 | From (1389)(1387) and (590) follows:
% 56.44/21.92 | (1391) sum(n8, n8) = all_0_3_3
% 56.44/21.92 |
% 56.44/21.92 | From (1777) and (5067) follows:
% 56.44/21.92 | (5206) sum(n16, n0) = all_0_0_0
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (690) with n16, n0, all_0_0_0, n16 and discharging atoms sum(n16, n0) = all_0_0_0, sum(n16, n0) = n16, yields:
% 56.44/21.92 | (1159) all_0_0_0 = n16
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 56.44/21.92 | (1158) all_0_3_3 = n16
% 56.44/21.92 |
% 56.44/21.92 | Equations (1159,1158) can reduce 679 to:
% 56.44/21.92 | (1106) $false
% 56.44/21.92 |
% 56.44/21.92 |-The branch is then unsatisfiable
% 56.44/21.92 |-Branch two:
% 56.44/21.92 | (1413) ~ (all_0_11_11 = n8)
% 56.44/21.92 | (1414) 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
% 56.44/21.92 |
% 56.44/21.92 +-Applying beta-rule and splitting (1875), into two cases.
% 56.44/21.92 |-Branch one:
% 56.44/21.92 | (1876) all_0_10_10 = n7
% 56.44/21.92 |
% 56.44/21.92 | From (1876) and (292) follows:
% 56.44/21.92 | (1877) pred(n7) = all_0_6_6
% 56.44/21.92 |
% 56.44/21.92 | From (1876) and (760) follows:
% 56.44/21.92 | (1878) succ(n7) = all_0_8_8
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (500) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 56.44/21.92 | (1879) all_0_6_6 = n6
% 56.44/21.92 |
% 56.44/21.92 | Instantiating formula (617) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 56.44/21.92 | (1880) all_0_8_8 = n8
% 56.44/21.92 |
% 56.44/21.92 | From (1879) and (1877) follows:
% 56.44/21.93 | (890) pred(n7) = n6
% 56.44/21.93 |
% 56.44/21.93 | From (1880) and (1878) follows:
% 56.44/21.93 | (1002) succ(n7) = n8
% 56.44/21.93 |
% 56.44/21.93 | From (1879) and (541) follows:
% 56.44/21.93 | (12604) sum(n6, all_0_5_5) = all_0_4_4
% 56.44/21.93 |
% 56.44/21.93 | From (1879)(1880) and (411) follows:
% 56.44/21.93 | (1881) sum(n6, n8) = all_0_1_1
% 56.44/21.93 |
% 56.44/21.93 | From (1880) and (427) follows:
% 56.44/21.93 | (12606) sum(all_0_9_9, n8) = all_0_7_7
% 56.44/21.93 |
% 56.44/21.93 | Instantiating formula (690) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 56.44/21.93 | (1651) all_0_1_1 = n14
% 56.44/21.93 |
% 56.44/21.93 | From (1651) and (630) follows:
% 56.44/21.93 | (5456) sum(all_0_2_2, n14) = all_0_0_0
% 56.44/21.93 |
% 56.44/21.93 | From (1651) and (1881) follows:
% 56.44/21.93 | (828) sum(n6, n8) = n14
% 56.44/21.93 |
% 56.44/21.93 +-Applying beta-rule and splitting (1414), into two cases.
% 56.44/21.93 |-Branch one:
% 56.44/21.93 | (1415) all_0_11_11 = n7
% 56.44/21.93 |
% 56.44/21.93 | From (1415) and (559) follows:
% 56.44/21.93 | (1416) pred(n7) = all_0_9_9
% 56.44/21.93 |
% 56.44/21.93 | From (1415) and (992) follows:
% 56.44/21.93 | (1417) succ(n7) = all_0_5_5
% 56.44/21.93 |
% 56.44/21.93 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 56.44/21.93 | (1418) all_0_9_9 = n6
% 56.44/21.93 |
% 56.44/21.93 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 56.44/21.93 | (1419) all_0_5_5 = n8
% 56.44/21.93 |
% 56.44/21.93 | From (1418)(1419) and (538) follows:
% 56.44/21.93 | (1420) sum(n6, n8) = all_0_2_2
% 56.44/21.93 |
% 56.44/21.93 | From (1418) and (12606) follows:
% 56.44/21.93 | (12616) sum(n6, n8) = all_0_7_7
% 56.44/21.93 |
% 56.44/21.93 | From (1419) and (12604) follows:
% 56.44/21.93 | (12617) sum(n6, n8) = all_0_4_4
% 56.44/21.93 |
% 56.44/21.93 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 56.44/21.93 | (1190) all_0_2_2 = n14
% 56.44/21.93 |
% 56.44/21.93 | Instantiating formula (690) 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:
% 56.44/21.93 | (1093) all_0_2_2 = all_0_4_4
% 56.44/21.93 |
% 56.44/21.93 | Instantiating formula (690) 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:
% 56.44/21.93 | (1094) all_0_2_2 = all_0_7_7
% 56.44/21.93 |
% 56.44/21.93 | Combining equations (1094,1093) yields a new equation:
% 56.44/21.93 | (1095) all_0_4_4 = all_0_7_7
% 56.44/21.93 |
% 56.44/21.93 | Combining equations (1190,1093) yields a new equation:
% 56.44/21.93 | (1279) all_0_4_4 = n14
% 56.44/21.93 |
% 56.44/21.93 | Combining equations (1279,1095) yields a new equation:
% 56.44/21.93 | (1281) all_0_7_7 = n14
% 56.44/21.93 |
% 56.44/21.93 | Combining equations (1281,1095) yields a new equation:
% 56.44/21.93 | (1279) all_0_4_4 = n14
% 56.44/21.93 |
% 56.44/21.93 | Combining equations (1279,1093) yields a new equation:
% 56.44/21.93 | (1190) all_0_2_2 = n14
% 56.44/21.93 |
% 56.44/21.93 | From (1190) and (5456) follows:
% 56.44/21.93 | (5474) sum(n14, n14) = all_0_0_0
% 56.44/21.93 |
% 56.44/21.93 | From (1281)(1279) and (590) follows:
% 56.44/21.93 | (1283) sum(n14, n14) = all_0_3_3
% 56.44/21.93 |
% 56.44/21.93 | Instantiating formula (690) with n14, n14, all_0_0_0, n2 and discharging atoms sum(n14, n14) = all_0_0_0, sum(n14, n14) = n2, yields:
% 56.44/21.93 | (1285) all_0_0_0 = n2
% 56.44/21.93 |
% 56.44/21.93 | Instantiating formula (690) 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:
% 56.44/21.93 | (1103) all_0_0_0 = all_0_3_3
% 56.44/21.93 |
% 56.44/21.93 | Combining equations (1285,1103) yields a new equation:
% 56.44/21.93 | (1284) all_0_3_3 = n2
% 56.44/21.93 |
% 56.44/21.93 | Combining equations (1284,1103) yields a new equation:
% 56.44/21.93 | (1285) all_0_0_0 = n2
% 56.44/21.93 |
% 56.44/21.93 | Equations (1285,1284) can reduce 679 to:
% 56.44/21.93 | (1106) $false
% 56.44/21.93 |
% 56.44/21.93 |-The branch is then unsatisfiable
% 56.44/21.93 |-Branch two:
% 56.44/21.93 | (1431) ~ (all_0_11_11 = n7)
% 56.44/21.93 | (1432) 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
% 56.44/21.93 |
% 56.44/21.93 +-Applying beta-rule and splitting (1432), into two cases.
% 56.44/21.93 |-Branch one:
% 56.44/21.93 | (1433) all_0_11_11 = n6
% 56.44/21.93 |
% 56.44/21.93 | From (1433) and (559) follows:
% 56.44/21.93 | (1434) pred(n6) = all_0_9_9
% 56.44/21.93 |
% 56.44/21.93 | From (1433) and (992) follows:
% 56.44/21.93 | (1435) succ(n6) = all_0_5_5
% 56.44/21.93 |
% 56.44/21.93 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 56.44/21.93 | (1436) all_0_9_9 = n5
% 56.44/21.93 |
% 56.44/21.93 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 56.44/21.93 | (1437) all_0_5_5 = n7
% 56.44/21.93 |
% 56.44/21.93 | From (1436)(1437) and (538) follows:
% 56.44/21.93 | (1438) sum(n5, n7) = all_0_2_2
% 56.44/21.93 |
% 56.44/21.93 | From (1436) and (12606) follows:
% 56.44/21.93 | (12641) sum(n5, n8) = all_0_7_7
% 56.44/21.93 |
% 56.44/21.93 | From (1437) and (12604) follows:
% 56.44/21.93 | (12642) sum(n6, n7) = all_0_4_4
% 56.44/21.93 |
% 56.44/21.93 | Instantiating formula (690) with n6, n7, all_0_4_4, n13 and discharging atoms sum(n6, n7) = all_0_4_4, sum(n6, n7) = n13, yields:
% 56.44/21.93 | (1297) all_0_4_4 = n13
% 56.44/21.93 |
% 56.44/21.93 | Instantiating formula (690) with n5, n8, all_0_7_7, n13 and discharging atoms sum(n5, n8) = all_0_7_7, sum(n5, n8) = n13, yields:
% 56.44/21.93 | (1299) all_0_7_7 = n13
% 56.44/21.93 |
% 56.44/21.93 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 56.44/21.93 | (1208) all_0_2_2 = n12
% 56.44/21.93 |
% 56.44/21.93 | From (1208) and (5456) follows:
% 56.44/21.93 | (5494) sum(n12, n14) = all_0_0_0
% 56.44/21.93 |
% 56.44/21.93 | From (1299)(1297) and (590) follows:
% 56.44/21.93 | (1301) sum(n13, n13) = all_0_3_3
% 56.44/21.93 |
% 56.44/21.93 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 56.44/21.93 | (1302) all_0_3_3 = n0
% 56.44/21.93 |
% 56.44/21.93 | Instantiating formula (690) with n12, n14, all_0_0_0, n0 and discharging atoms sum(n12, n14) = all_0_0_0, sum(n12, n14) = n0, yields:
% 56.44/21.93 | (1303) all_0_0_0 = n0
% 56.44/21.93 |
% 56.44/21.93 | Equations (1303,1302) can reduce 679 to:
% 56.44/21.93 | (1106) $false
% 56.44/21.93 |
% 56.44/21.93 |-The branch is then unsatisfiable
% 56.44/21.93 |-Branch two:
% 56.44/21.93 | (1449) ~ (all_0_11_11 = n6)
% 56.44/21.93 | (1450) 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
% 56.44/21.93 |
% 56.44/21.93 +-Applying beta-rule and splitting (1450), into two cases.
% 56.44/21.93 |-Branch one:
% 56.44/21.93 | (1451) all_0_11_11 = n5
% 56.44/21.93 |
% 56.44/21.93 | From (1451) and (559) follows:
% 56.44/21.93 | (1452) pred(n5) = all_0_9_9
% 56.44/21.93 |
% 56.44/21.93 | From (1451) and (992) follows:
% 56.44/21.94 | (1453) succ(n5) = all_0_5_5
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 56.44/21.94 | (1454) all_0_9_9 = n4
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 56.44/21.94 | (1455) all_0_5_5 = n6
% 56.44/21.94 |
% 56.44/21.94 | From (1454)(1455) and (538) follows:
% 56.44/21.94 | (1456) sum(n4, n6) = all_0_2_2
% 56.44/21.94 |
% 56.44/21.94 | From (1454) and (12606) follows:
% 56.44/21.94 | (12659) sum(n4, n8) = all_0_7_7
% 56.44/21.94 |
% 56.44/21.94 | From (1455) and (12604) follows:
% 56.44/21.94 | (12660) sum(n6, n6) = all_0_4_4
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (690) with n6, n6, all_0_4_4, n12 and discharging atoms sum(n6, n6) = all_0_4_4, sum(n6, n6) = n12, yields:
% 56.44/21.94 | (1315) all_0_4_4 = n12
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (690) with n4, n8, all_0_7_7, n12 and discharging atoms sum(n4, n8) = all_0_7_7, sum(n4, n8) = n12, yields:
% 56.44/21.94 | (1317) all_0_7_7 = n12
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 56.44/21.94 | (1226) all_0_2_2 = n10
% 56.44/21.94 |
% 56.44/21.94 | From (1226) and (5456) follows:
% 56.44/21.94 | (5512) sum(n10, n14) = all_0_0_0
% 56.44/21.94 |
% 56.44/21.94 | From (1317)(1315) and (590) follows:
% 56.44/21.94 | (1319) sum(n12, n12) = all_0_3_3
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 56.44/21.94 | (1320) all_0_3_3 = n24
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (690) with n10, n14, all_0_0_0, n24 and discharging atoms sum(n10, n14) = all_0_0_0, sum(n10, n14) = n24, yields:
% 56.44/21.94 | (1321) all_0_0_0 = n24
% 56.44/21.94 |
% 56.44/21.94 | Equations (1321,1320) can reduce 679 to:
% 56.44/21.94 | (1106) $false
% 56.44/21.94 |
% 56.44/21.94 |-The branch is then unsatisfiable
% 56.44/21.94 |-Branch two:
% 56.44/21.94 | (1467) ~ (all_0_11_11 = n5)
% 56.44/21.94 | (1468) 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
% 56.44/21.94 |
% 56.44/21.94 +-Applying beta-rule and splitting (1468), into two cases.
% 56.44/21.94 |-Branch one:
% 56.44/21.94 | (1469) all_0_11_11 = n4
% 56.44/21.94 |
% 56.44/21.94 | From (1469) and (559) follows:
% 56.44/21.94 | (1470) pred(n4) = all_0_9_9
% 56.44/21.94 |
% 56.44/21.94 | From (1469) and (992) follows:
% 56.44/21.94 | (1471) succ(n4) = all_0_5_5
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 56.44/21.94 | (1472) all_0_9_9 = n3
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 56.44/21.94 | (1473) all_0_5_5 = n5
% 56.44/21.94 |
% 56.44/21.94 | From (1472)(1473) and (538) follows:
% 56.44/21.94 | (1474) sum(n3, n5) = all_0_2_2
% 56.44/21.94 |
% 56.44/21.94 | From (1472) and (12606) follows:
% 56.44/21.94 | (12677) sum(n3, n8) = all_0_7_7
% 56.44/21.94 |
% 56.44/21.94 | From (1473) and (12604) follows:
% 56.44/21.94 | (12678) sum(n6, n5) = all_0_4_4
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (690) with n6, n5, all_0_4_4, n11 and discharging atoms sum(n6, n5) = all_0_4_4, sum(n6, n5) = n11, yields:
% 56.44/21.94 | (1333) all_0_4_4 = n11
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (690) with n3, n8, all_0_7_7, n11 and discharging atoms sum(n3, n8) = all_0_7_7, sum(n3, n8) = n11, yields:
% 56.44/21.94 | (1335) all_0_7_7 = n11
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 56.44/21.94 | (1244) all_0_2_2 = n8
% 56.44/21.94 |
% 56.44/21.94 | From (1244) and (5456) follows:
% 56.44/21.94 | (5530) sum(n8, n14) = all_0_0_0
% 56.44/21.94 |
% 56.44/21.94 | From (1335)(1333) and (590) follows:
% 56.44/21.94 | (1337) sum(n11, n11) = all_0_3_3
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 56.44/21.94 | (1104) all_0_3_3 = n22
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (690) with n8, n14, all_0_0_0, n22 and discharging atoms sum(n8, n14) = all_0_0_0, sum(n8, n14) = n22, yields:
% 56.44/21.94 | (1102) all_0_0_0 = n22
% 56.44/21.94 |
% 56.44/21.94 | Equations (1102,1104) can reduce 679 to:
% 56.44/21.94 | (1106) $false
% 56.44/21.94 |
% 56.44/21.94 |-The branch is then unsatisfiable
% 56.44/21.94 |-Branch two:
% 56.44/21.94 | (1485) ~ (all_0_11_11 = n4)
% 56.44/21.94 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.44/21.94 |
% 56.44/21.94 +-Applying beta-rule and splitting (1486), into two cases.
% 56.44/21.94 |-Branch one:
% 56.44/21.94 | (1487) all_0_11_11 = n3
% 56.44/21.94 |
% 56.44/21.94 | From (1487) and (559) follows:
% 56.44/21.94 | (1488) pred(n3) = all_0_9_9
% 56.44/21.94 |
% 56.44/21.94 | From (1487) and (992) follows:
% 56.44/21.94 | (1489) succ(n3) = all_0_5_5
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 56.44/21.94 | (1490) all_0_9_9 = n2
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 56.44/21.94 | (1491) all_0_5_5 = n4
% 56.44/21.94 |
% 56.44/21.94 | From (1490)(1491) and (538) follows:
% 56.44/21.94 | (1492) sum(n2, n4) = all_0_2_2
% 56.44/21.94 |
% 56.44/21.94 | From (1490) and (12606) follows:
% 56.44/21.94 | (12695) sum(n2, n8) = all_0_7_7
% 56.44/21.94 |
% 56.44/21.94 | From (1491) and (12604) follows:
% 56.44/21.94 | (12696) sum(n6, n4) = all_0_4_4
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (690) with n6, n4, all_0_4_4, n10 and discharging atoms sum(n6, n4) = all_0_4_4, sum(n6, n4) = n10, yields:
% 56.44/21.94 | (1351) all_0_4_4 = n10
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (690) with n2, n8, all_0_7_7, n10 and discharging atoms sum(n2, n8) = all_0_7_7, sum(n2, n8) = n10, yields:
% 56.44/21.94 | (1353) all_0_7_7 = n10
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 56.44/21.94 | (1262) all_0_2_2 = n6
% 56.44/21.94 |
% 56.44/21.94 | From (1262) and (5456) follows:
% 56.44/21.94 | (5548) sum(n6, n14) = all_0_0_0
% 56.44/21.94 |
% 56.44/21.94 | From (1353)(1351) and (590) follows:
% 56.44/21.94 | (1355) sum(n10, n10) = all_0_3_3
% 56.44/21.94 |
% 56.44/21.94 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 56.44/21.95 | (1122) all_0_3_3 = n20
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (690) with n6, n14, all_0_0_0, n20 and discharging atoms sum(n6, n14) = all_0_0_0, sum(n6, n14) = n20, yields:
% 56.44/21.95 | (1123) all_0_0_0 = n20
% 56.44/21.95 |
% 56.44/21.95 | Equations (1123,1122) can reduce 679 to:
% 56.44/21.95 | (1106) $false
% 56.44/21.95 |
% 56.44/21.95 |-The branch is then unsatisfiable
% 56.44/21.95 |-Branch two:
% 56.44/21.95 | (1503) ~ (all_0_11_11 = n3)
% 56.44/21.95 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.44/21.95 |
% 56.44/21.95 +-Applying beta-rule and splitting (1504), into two cases.
% 56.44/21.95 |-Branch one:
% 56.44/21.95 | (1505) all_0_11_11 = n2
% 56.44/21.95 |
% 56.44/21.95 | From (1505) and (559) follows:
% 56.44/21.95 | (1506) pred(n2) = all_0_9_9
% 56.44/21.95 |
% 56.44/21.95 | From (1505) and (992) follows:
% 56.44/21.95 | (1507) succ(n2) = all_0_5_5
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 56.44/21.95 | (1508) all_0_9_9 = n1
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 56.44/21.95 | (1509) all_0_5_5 = n3
% 56.44/21.95 |
% 56.44/21.95 | From (1508)(1509) and (538) follows:
% 56.44/21.95 | (1510) sum(n1, n3) = all_0_2_2
% 56.44/21.95 |
% 56.44/21.95 | From (1508) and (12606) follows:
% 56.44/21.95 | (12713) sum(n1, n8) = all_0_7_7
% 56.44/21.95 |
% 56.44/21.95 | From (1509) and (12604) follows:
% 56.44/21.95 | (12714) sum(n6, n3) = all_0_4_4
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (690) with n6, n3, all_0_4_4, n9 and discharging atoms sum(n6, n3) = all_0_4_4, sum(n6, n3) = n9, yields:
% 56.44/21.95 | (1369) all_0_4_4 = n9
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (690) with n1, n8, all_0_7_7, n9 and discharging atoms sum(n1, n8) = all_0_7_7, sum(n1, n8) = n9, yields:
% 56.44/21.95 | (1371) all_0_7_7 = n9
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 56.44/21.95 | (1280) all_0_2_2 = n4
% 56.44/21.95 |
% 56.44/21.95 | From (1280) and (5456) follows:
% 56.44/21.95 | (5566) sum(n4, n14) = all_0_0_0
% 56.44/21.95 |
% 56.44/21.95 | From (1371)(1369) and (590) follows:
% 56.44/21.95 | (1373) sum(n9, n9) = all_0_3_3
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 56.44/21.95 | (1140) all_0_3_3 = n18
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (690) with n4, n14, all_0_0_0, n18 and discharging atoms sum(n4, n14) = all_0_0_0, sum(n4, n14) = n18, yields:
% 56.44/21.95 | (1141) all_0_0_0 = n18
% 56.44/21.95 |
% 56.44/21.95 | Equations (1141,1140) can reduce 679 to:
% 56.44/21.95 | (1106) $false
% 56.44/21.95 |
% 56.44/21.95 |-The branch is then unsatisfiable
% 56.44/21.95 |-Branch two:
% 56.44/21.95 | (1521) ~ (all_0_11_11 = n2)
% 56.44/21.95 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 56.44/21.95 |
% 56.44/21.95 +-Applying beta-rule and splitting (1522), into two cases.
% 56.44/21.95 |-Branch one:
% 56.44/21.95 | (1523) all_0_11_11 = n1
% 56.44/21.95 |
% 56.44/21.95 | From (1523) and (559) follows:
% 56.44/21.95 | (1524) pred(n1) = all_0_9_9
% 56.44/21.95 |
% 56.44/21.95 | From (1523) and (992) follows:
% 56.44/21.95 | (1525) succ(n1) = all_0_5_5
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 56.44/21.95 | (1526) all_0_9_9 = n0
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 56.44/21.95 | (1527) all_0_5_5 = n2
% 56.44/21.95 |
% 56.44/21.95 | From (1526)(1527) and (538) follows:
% 56.44/21.95 | (1528) sum(n0, n2) = all_0_2_2
% 56.44/21.95 |
% 56.44/21.95 | From (1526) and (12606) follows:
% 56.44/21.95 | (12731) sum(n0, n8) = all_0_7_7
% 56.44/21.95 |
% 56.44/21.95 | From (1527) and (12604) follows:
% 56.44/21.95 | (12732) sum(n6, n2) = all_0_4_4
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (690) with n6, n2, all_0_4_4, n8 and discharging atoms sum(n6, n2) = all_0_4_4, sum(n6, n2) = n8, yields:
% 56.44/21.95 | (1387) all_0_4_4 = n8
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (690) with n0, n8, all_0_7_7, n8 and discharging atoms sum(n0, n8) = all_0_7_7, sum(n0, n8) = n8, yields:
% 56.44/21.95 | (1389) all_0_7_7 = n8
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 56.44/21.95 | (1298) all_0_2_2 = n2
% 56.44/21.95 |
% 56.44/21.95 | From (1298) and (5456) follows:
% 56.44/21.95 | (5584) sum(n2, n14) = all_0_0_0
% 56.44/21.95 |
% 56.44/21.95 | From (1389)(1387) and (590) follows:
% 56.44/21.95 | (1391) sum(n8, n8) = all_0_3_3
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 56.44/21.95 | (1158) all_0_3_3 = n16
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (690) with n2, n14, all_0_0_0, n16 and discharging atoms sum(n2, n14) = all_0_0_0, sum(n2, n14) = n16, yields:
% 56.44/21.95 | (1159) all_0_0_0 = n16
% 56.44/21.95 |
% 56.44/21.95 | Equations (1159,1158) can reduce 679 to:
% 56.44/21.95 | (1106) $false
% 56.44/21.95 |
% 56.44/21.95 |-The branch is then unsatisfiable
% 56.44/21.95 |-Branch two:
% 56.44/21.95 | (1540) ~ (all_0_11_11 = n1)
% 56.44/21.95 | (1541) all_0_11_11 = n0
% 56.44/21.95 |
% 56.44/21.95 | From (1541) and (559) follows:
% 56.44/21.95 | (1542) pred(n0) = all_0_9_9
% 56.44/21.95 |
% 56.44/21.95 | From (1541) and (992) follows:
% 56.44/21.95 | (1543) succ(n0) = all_0_5_5
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 56.44/21.95 | (1544) all_0_9_9 = n25
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 56.44/21.95 | (1545) all_0_5_5 = n1
% 56.44/21.95 |
% 56.44/21.95 | From (1544)(1545) and (538) follows:
% 56.44/21.95 | (1546) sum(n25, n1) = all_0_2_2
% 56.44/21.95 |
% 56.44/21.95 | From (1544) and (12606) follows:
% 56.44/21.95 | (12748) sum(n25, n8) = all_0_7_7
% 56.44/21.95 |
% 56.44/21.95 | From (1545) and (12604) follows:
% 56.44/21.95 | (12749) sum(n6, n1) = all_0_4_4
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (690) with n25, n8, all_0_7_7, n7 and discharging atoms sum(n25, n8) = all_0_7_7, sum(n25, n8) = n7, yields:
% 56.44/21.95 | (1407) all_0_7_7 = n7
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 56.44/21.95 | (1316) all_0_2_2 = n0
% 56.44/21.95 |
% 56.44/21.95 | Instantiating formula (690) with n6, n1, all_0_4_4, n7 and discharging atoms sum(n6, n1) = all_0_4_4, sum(n6, n1) = n7, yields:
% 56.44/21.95 | (1405) all_0_4_4 = n7
% 56.44/21.95 |
% 56.44/21.95 | From (1316) and (5456) follows:
% 56.44/21.96 | (5602) sum(n0, n14) = all_0_0_0
% 56.44/21.96 |
% 56.44/21.96 | From (1407)(1405) and (590) follows:
% 56.44/21.96 | (1409) sum(n7, n7) = all_0_3_3
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 56.44/21.96 | (1176) all_0_3_3 = n14
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (690) with n0, n14, all_0_0_0, n14 and discharging atoms sum(n0, n14) = all_0_0_0, sum(n0, n14) = n14, yields:
% 56.44/21.96 | (1177) all_0_0_0 = n14
% 56.44/21.96 |
% 56.44/21.96 | Equations (1177,1176) can reduce 679 to:
% 56.44/21.96 | (1106) $false
% 56.44/21.96 |
% 56.44/21.96 |-The branch is then unsatisfiable
% 56.44/21.96 |-Branch two:
% 56.44/21.96 | (1892) ~ (all_0_10_10 = n7)
% 56.44/21.96 | (1893) 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
% 56.44/21.96 |
% 56.44/21.96 +-Applying beta-rule and splitting (1414), into two cases.
% 56.44/21.96 |-Branch one:
% 56.44/21.96 | (1415) all_0_11_11 = n7
% 56.44/21.96 |
% 56.44/21.96 | From (1415) and (559) follows:
% 56.44/21.96 | (1416) pred(n7) = all_0_9_9
% 56.44/21.96 |
% 56.44/21.96 | From (1415) and (992) follows:
% 56.44/21.96 | (1417) succ(n7) = all_0_5_5
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (500) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 56.44/21.96 | (1418) all_0_9_9 = n6
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (617) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 56.44/21.96 | (1419) all_0_5_5 = n8
% 56.44/21.96 |
% 56.44/21.96 | From (1419) and (541) follows:
% 56.44/21.96 | (12765) sum(all_0_6_6, n8) = all_0_4_4
% 56.44/21.96 |
% 56.44/21.96 | From (1418)(1419) and (538) follows:
% 56.44/21.96 | (1420) sum(n6, n8) = all_0_2_2
% 56.44/21.96 |
% 56.44/21.96 | From (1418) and (427) follows:
% 56.44/21.96 | (12767) sum(n6, all_0_8_8) = all_0_7_7
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (690) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 56.44/21.96 | (1190) all_0_2_2 = n14
% 56.44/21.96 |
% 56.44/21.96 | From (1190) and (630) follows:
% 56.44/21.96 | (5851) sum(n14, all_0_1_1) = all_0_0_0
% 56.44/21.96 |
% 56.44/21.96 +-Applying beta-rule and splitting (1893), into two cases.
% 56.44/21.96 |-Branch one:
% 56.44/21.96 | (1894) all_0_10_10 = n6
% 56.44/21.96 |
% 56.44/21.96 | From (1894) and (292) follows:
% 56.44/21.96 | (1895) pred(n6) = all_0_6_6
% 56.44/21.96 |
% 56.44/21.96 | From (1894) and (760) follows:
% 56.44/21.96 | (1896) succ(n6) = all_0_8_8
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 56.44/21.96 | (1897) all_0_6_6 = n5
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 56.44/21.96 | (1898) all_0_8_8 = n7
% 56.44/21.96 |
% 56.44/21.96 | From (1897)(1898) and (411) follows:
% 56.44/21.96 | (1899) sum(n5, n7) = all_0_1_1
% 56.44/21.96 |
% 56.44/21.96 | From (1897) and (12765) follows:
% 56.44/21.96 | (12776) sum(n5, n8) = all_0_4_4
% 56.44/21.96 |
% 56.44/21.96 | From (1898) and (12767) follows:
% 56.44/21.96 | (12777) sum(n6, n7) = all_0_7_7
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (690) with n6, n7, all_0_7_7, n13 and discharging atoms sum(n6, n7) = all_0_7_7, sum(n6, n7) = n13, yields:
% 56.44/21.96 | (1299) all_0_7_7 = n13
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (690) with n5, n8, all_0_4_4, n13 and discharging atoms sum(n5, n8) = all_0_4_4, sum(n5, n8) = n13, yields:
% 56.44/21.96 | (1297) all_0_4_4 = n13
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 56.44/21.96 | (1669) all_0_1_1 = n12
% 56.44/21.96 |
% 56.44/21.96 | From (1299)(1297) and (590) follows:
% 56.44/21.96 | (1301) sum(n13, n13) = all_0_3_3
% 56.44/21.96 |
% 56.44/21.96 | From (1669) and (5851) follows:
% 56.44/21.96 | (5864) sum(n14, n12) = all_0_0_0
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (690) with n14, n12, all_0_0_0, n0 and discharging atoms sum(n14, n12) = all_0_0_0, sum(n14, n12) = n0, yields:
% 56.44/21.96 | (1303) all_0_0_0 = n0
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (690) with n13, n13, all_0_3_3, n0 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n0, yields:
% 56.44/21.96 | (1302) all_0_3_3 = n0
% 56.44/21.96 |
% 56.44/21.96 | Equations (1303,1302) can reduce 679 to:
% 56.44/21.96 | (1106) $false
% 56.44/21.96 |
% 56.44/21.96 |-The branch is then unsatisfiable
% 56.44/21.96 |-Branch two:
% 56.44/21.96 | (1910) ~ (all_0_10_10 = n6)
% 56.44/21.96 | (1911) 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
% 56.44/21.96 |
% 56.44/21.96 +-Applying beta-rule and splitting (1911), into two cases.
% 56.44/21.96 |-Branch one:
% 56.44/21.96 | (1912) all_0_10_10 = n5
% 56.44/21.96 |
% 56.44/21.96 | From (1912) and (292) follows:
% 56.44/21.96 | (1913) pred(n5) = all_0_6_6
% 56.44/21.96 |
% 56.44/21.96 | From (1912) and (760) follows:
% 56.44/21.96 | (1914) succ(n5) = all_0_8_8
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 56.44/21.96 | (1915) all_0_6_6 = n4
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 56.44/21.96 | (1916) all_0_8_8 = n6
% 56.44/21.96 |
% 56.44/21.96 | From (1915)(1916) and (411) follows:
% 56.44/21.96 | (1917) sum(n4, n6) = all_0_1_1
% 56.44/21.96 |
% 56.44/21.96 | From (1915) and (12765) follows:
% 56.44/21.96 | (12794) sum(n4, n8) = all_0_4_4
% 56.44/21.96 |
% 56.44/21.96 | From (1916) and (12767) follows:
% 56.44/21.96 | (12795) sum(n6, n6) = all_0_7_7
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (690) with n6, n6, all_0_7_7, n12 and discharging atoms sum(n6, n6) = all_0_7_7, sum(n6, n6) = n12, yields:
% 56.44/21.96 | (1317) all_0_7_7 = n12
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (690) with n4, n8, all_0_4_4, n12 and discharging atoms sum(n4, n8) = all_0_4_4, sum(n4, n8) = n12, yields:
% 56.44/21.96 | (1315) all_0_4_4 = n12
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 56.44/21.96 | (1687) all_0_1_1 = n10
% 56.44/21.96 |
% 56.44/21.96 | From (1317)(1315) and (590) follows:
% 56.44/21.96 | (1319) sum(n12, n12) = all_0_3_3
% 56.44/21.96 |
% 56.44/21.96 | From (1687) and (5851) follows:
% 56.44/21.96 | (5882) sum(n14, n10) = all_0_0_0
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (690) with n14, n10, all_0_0_0, n24 and discharging atoms sum(n14, n10) = all_0_0_0, sum(n14, n10) = n24, yields:
% 56.44/21.96 | (1321) all_0_0_0 = n24
% 56.44/21.96 |
% 56.44/21.96 | Instantiating formula (690) with n12, n12, all_0_3_3, n24 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n24, yields:
% 56.44/21.96 | (1320) all_0_3_3 = n24
% 56.44/21.96 |
% 56.44/21.97 | Equations (1321,1320) can reduce 679 to:
% 56.44/21.97 | (1106) $false
% 56.44/21.97 |
% 56.44/21.97 |-The branch is then unsatisfiable
% 56.44/21.97 |-Branch two:
% 56.44/21.97 | (1928) ~ (all_0_10_10 = n5)
% 56.44/21.97 | (1929) 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
% 56.44/21.97 |
% 56.44/21.97 +-Applying beta-rule and splitting (1929), into two cases.
% 56.44/21.97 |-Branch one:
% 56.44/21.97 | (1930) all_0_10_10 = n4
% 56.44/21.97 |
% 56.44/21.97 | From (1930) and (292) follows:
% 56.44/21.97 | (1931) pred(n4) = all_0_6_6
% 56.44/21.97 |
% 56.44/21.97 | From (1930) and (760) follows:
% 56.44/21.97 | (1932) succ(n4) = all_0_8_8
% 56.44/21.97 |
% 56.44/21.97 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 56.44/21.97 | (1933) all_0_6_6 = n3
% 56.44/21.97 |
% 56.44/21.97 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 56.44/21.97 | (1934) all_0_8_8 = n5
% 56.44/21.97 |
% 56.44/21.97 | From (1933)(1934) and (411) follows:
% 56.44/21.97 | (1935) sum(n3, n5) = all_0_1_1
% 56.44/21.97 |
% 56.44/21.97 | From (1933) and (12765) follows:
% 56.44/21.97 | (12812) sum(n3, n8) = all_0_4_4
% 56.44/21.97 |
% 56.44/21.97 | From (1934) and (12767) follows:
% 56.44/21.97 | (12813) sum(n6, n5) = all_0_7_7
% 56.44/21.97 |
% 56.44/21.97 | Instantiating formula (690) with n6, n5, all_0_7_7, n11 and discharging atoms sum(n6, n5) = all_0_7_7, sum(n6, n5) = n11, yields:
% 56.44/21.97 | (1335) all_0_7_7 = n11
% 56.44/21.97 |
% 56.44/21.97 | Instantiating formula (690) with n3, n8, all_0_4_4, n11 and discharging atoms sum(n3, n8) = all_0_4_4, sum(n3, n8) = n11, yields:
% 56.44/21.97 | (1333) all_0_4_4 = n11
% 56.44/21.97 |
% 56.44/21.97 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 56.44/21.97 | (1705) all_0_1_1 = n8
% 56.44/21.97 |
% 56.44/21.97 | From (1335)(1333) and (590) follows:
% 56.44/21.97 | (1337) sum(n11, n11) = all_0_3_3
% 56.44/21.97 |
% 56.44/21.97 | From (1705) and (5851) follows:
% 56.44/21.97 | (5900) sum(n14, n8) = all_0_0_0
% 56.44/21.97 |
% 56.44/21.97 | Instantiating formula (690) with n14, n8, all_0_0_0, n22 and discharging atoms sum(n14, n8) = all_0_0_0, sum(n14, n8) = n22, yields:
% 56.44/21.97 | (1102) all_0_0_0 = n22
% 56.44/21.97 |
% 56.44/21.97 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 56.44/21.97 | (1104) all_0_3_3 = n22
% 56.44/21.97 |
% 56.44/21.97 | Equations (1102,1104) can reduce 679 to:
% 56.44/21.97 | (1106) $false
% 56.44/21.97 |
% 56.44/21.97 |-The branch is then unsatisfiable
% 56.44/21.97 |-Branch two:
% 56.44/21.97 | (1946) ~ (all_0_10_10 = n4)
% 56.44/21.97 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.44/21.97 |
% 56.44/21.97 +-Applying beta-rule and splitting (1947), into two cases.
% 56.44/21.97 |-Branch one:
% 56.44/21.97 | (1948) all_0_10_10 = n3
% 56.44/21.97 |
% 56.44/21.97 | From (1948) and (292) follows:
% 56.44/21.97 | (1949) pred(n3) = all_0_6_6
% 56.44/21.97 |
% 56.44/21.97 | From (1948) and (760) follows:
% 56.44/21.97 | (1950) succ(n3) = all_0_8_8
% 56.44/21.97 |
% 56.44/21.97 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 56.44/21.97 | (1951) all_0_6_6 = n2
% 56.44/21.97 |
% 56.44/21.97 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 56.44/21.97 | (1952) all_0_8_8 = n4
% 56.44/21.97 |
% 56.44/21.97 | From (1951)(1952) and (411) follows:
% 56.44/21.97 | (1953) sum(n2, n4) = all_0_1_1
% 56.44/21.97 |
% 56.44/21.97 | From (1951) and (12765) follows:
% 56.44/21.97 | (12830) sum(n2, n8) = all_0_4_4
% 56.44/21.97 |
% 56.44/21.97 | From (1952) and (12767) follows:
% 56.44/21.97 | (12831) sum(n6, n4) = all_0_7_7
% 56.44/21.97 |
% 56.44/21.97 | Instantiating formula (690) with n6, n4, all_0_7_7, n10 and discharging atoms sum(n6, n4) = all_0_7_7, sum(n6, n4) = n10, yields:
% 56.44/21.97 | (1353) all_0_7_7 = n10
% 56.44/21.97 |
% 56.44/21.97 | Instantiating formula (690) with n2, n8, all_0_4_4, n10 and discharging atoms sum(n2, n8) = all_0_4_4, sum(n2, n8) = n10, yields:
% 56.44/21.97 | (1351) all_0_4_4 = n10
% 56.44/21.97 |
% 56.44/21.97 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 56.44/21.97 | (1723) all_0_1_1 = n6
% 56.44/21.97 |
% 56.44/21.97 | From (1353)(1351) and (590) follows:
% 56.44/21.97 | (1355) sum(n10, n10) = all_0_3_3
% 56.44/21.97 |
% 56.44/21.97 | From (1723) and (5851) follows:
% 56.44/21.97 | (5918) sum(n14, n6) = all_0_0_0
% 56.44/21.97 |
% 56.44/21.97 | Instantiating formula (690) with n14, n6, all_0_0_0, n20 and discharging atoms sum(n14, n6) = all_0_0_0, sum(n14, n6) = n20, yields:
% 56.44/21.97 | (1123) all_0_0_0 = n20
% 56.44/21.97 |
% 56.44/21.97 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 56.44/21.97 | (1122) all_0_3_3 = n20
% 56.44/21.97 |
% 56.44/21.97 | Equations (1123,1122) can reduce 679 to:
% 56.44/21.97 | (1106) $false
% 56.44/21.97 |
% 56.44/21.97 |-The branch is then unsatisfiable
% 56.44/21.97 |-Branch two:
% 56.44/21.97 | (1964) ~ (all_0_10_10 = n3)
% 56.44/21.97 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.44/21.97 |
% 56.44/21.97 +-Applying beta-rule and splitting (1965), into two cases.
% 56.44/21.97 |-Branch one:
% 56.44/21.97 | (1966) all_0_10_10 = n2
% 56.44/21.97 |
% 56.44/21.97 | From (1966) and (292) follows:
% 56.44/21.97 | (1967) pred(n2) = all_0_6_6
% 56.44/21.97 |
% 56.44/21.97 | From (1966) and (760) follows:
% 56.44/21.97 | (1968) succ(n2) = all_0_8_8
% 56.44/21.97 |
% 56.44/21.97 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 56.44/21.97 | (1969) all_0_6_6 = n1
% 56.44/21.97 |
% 56.44/21.97 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 56.44/21.97 | (1970) all_0_8_8 = n3
% 56.44/21.97 |
% 56.44/21.97 | From (1969)(1970) and (411) follows:
% 56.44/21.97 | (1971) sum(n1, n3) = all_0_1_1
% 56.44/21.97 |
% 56.44/21.97 | From (1969) and (12765) follows:
% 56.44/21.97 | (12848) sum(n1, n8) = all_0_4_4
% 56.44/21.97 |
% 56.44/21.97 | From (1970) and (12767) follows:
% 56.44/21.98 | (12849) sum(n6, n3) = all_0_7_7
% 56.44/21.98 |
% 56.44/21.98 | Instantiating formula (690) with n6, n3, all_0_7_7, n9 and discharging atoms sum(n6, n3) = all_0_7_7, sum(n6, n3) = n9, yields:
% 56.44/21.98 | (1371) all_0_7_7 = n9
% 56.44/21.98 |
% 56.44/21.98 | Instantiating formula (690) with n1, n8, all_0_4_4, n9 and discharging atoms sum(n1, n8) = all_0_4_4, sum(n1, n8) = n9, yields:
% 56.44/21.98 | (1369) all_0_4_4 = n9
% 56.44/21.98 |
% 56.44/21.98 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 56.44/21.98 | (1741) all_0_1_1 = n4
% 56.44/21.98 |
% 56.44/21.98 | From (1371)(1369) and (590) follows:
% 56.44/21.98 | (1373) sum(n9, n9) = all_0_3_3
% 56.44/21.98 |
% 56.44/21.98 | From (1741) and (5851) follows:
% 56.44/21.98 | (5936) sum(n14, n4) = all_0_0_0
% 56.44/21.98 |
% 56.44/21.98 | Instantiating formula (690) with n14, n4, all_0_0_0, n18 and discharging atoms sum(n14, n4) = all_0_0_0, sum(n14, n4) = n18, yields:
% 56.44/21.98 | (1141) all_0_0_0 = n18
% 56.44/21.98 |
% 56.44/21.98 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 56.44/21.98 | (1140) all_0_3_3 = n18
% 56.44/21.98 |
% 56.44/21.98 | Equations (1141,1140) can reduce 679 to:
% 56.44/21.98 | (1106) $false
% 56.44/21.98 |
% 56.44/21.98 |-The branch is then unsatisfiable
% 56.44/21.98 |-Branch two:
% 56.44/21.98 | (1982) ~ (all_0_10_10 = n2)
% 56.44/21.98 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 56.44/21.98 |
% 56.44/21.98 +-Applying beta-rule and splitting (1983), into two cases.
% 56.44/21.98 |-Branch one:
% 56.44/21.98 | (1984) all_0_10_10 = n1
% 56.44/21.98 |
% 56.44/21.98 | From (1984) and (292) follows:
% 56.44/21.98 | (1985) pred(n1) = all_0_6_6
% 56.44/21.98 |
% 56.44/21.98 | From (1984) and (760) follows:
% 56.44/21.98 | (1986) succ(n1) = all_0_8_8
% 56.44/21.98 |
% 56.44/21.98 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 56.44/21.98 | (1987) all_0_6_6 = n0
% 56.44/21.98 |
% 56.44/21.98 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 56.44/21.98 | (1988) all_0_8_8 = n2
% 56.44/21.98 |
% 56.44/21.98 | From (1987)(1988) and (411) follows:
% 56.44/21.98 | (1989) sum(n0, n2) = all_0_1_1
% 56.44/21.98 |
% 56.44/21.98 | From (1987) and (12765) follows:
% 56.44/21.98 | (12866) sum(n0, n8) = all_0_4_4
% 56.44/21.98 |
% 56.44/21.98 | From (1988) and (12767) follows:
% 56.44/21.98 | (12867) sum(n6, n2) = all_0_7_7
% 56.44/21.98 |
% 56.44/21.98 | Instantiating formula (690) with n6, n2, all_0_7_7, n8 and discharging atoms sum(n6, n2) = all_0_7_7, sum(n6, n2) = n8, yields:
% 56.44/21.98 | (1389) all_0_7_7 = n8
% 56.44/21.98 |
% 56.44/21.98 | Instantiating formula (690) with n0, n8, all_0_4_4, n8 and discharging atoms sum(n0, n8) = all_0_4_4, sum(n0, n8) = n8, yields:
% 56.44/21.98 | (1387) all_0_4_4 = n8
% 56.44/21.98 |
% 56.44/21.98 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 56.44/21.98 | (1759) all_0_1_1 = n2
% 56.44/21.98 |
% 56.44/21.98 | From (1389)(1387) and (590) follows:
% 56.44/21.98 | (1391) sum(n8, n8) = all_0_3_3
% 56.44/21.98 |
% 56.44/21.98 | From (1759) and (5851) follows:
% 56.44/21.98 | (5954) sum(n14, n2) = all_0_0_0
% 56.44/21.98 |
% 56.44/21.98 | Instantiating formula (690) with n14, n2, all_0_0_0, n16 and discharging atoms sum(n14, n2) = all_0_0_0, sum(n14, n2) = n16, yields:
% 56.44/21.98 | (1159) all_0_0_0 = n16
% 56.44/21.98 |
% 56.44/21.98 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 56.44/21.98 | (1158) all_0_3_3 = n16
% 56.44/21.98 |
% 56.44/21.98 | Equations (1159,1158) can reduce 679 to:
% 56.44/21.98 | (1106) $false
% 56.44/21.98 |
% 56.44/21.98 |-The branch is then unsatisfiable
% 56.44/21.98 |-Branch two:
% 56.44/21.98 | (2002) ~ (all_0_10_10 = n1)
% 56.44/21.98 | (2003) all_0_10_10 = n0
% 56.44/21.98 |
% 56.44/21.98 | From (2003) and (292) follows:
% 56.44/21.98 | (2004) pred(n0) = all_0_6_6
% 56.44/21.98 |
% 56.44/21.98 | From (2003) and (760) follows:
% 56.44/21.98 | (2005) succ(n0) = all_0_8_8
% 56.44/21.98 |
% 56.44/21.98 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 56.44/21.99 | (2006) all_0_6_6 = n25
% 56.44/21.99 |
% 56.44/21.99 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 56.44/21.99 | (2007) all_0_8_8 = n1
% 56.44/21.99 |
% 56.44/21.99 | From (2006)(2007) and (411) follows:
% 56.44/21.99 | (2008) sum(n25, n1) = all_0_1_1
% 56.44/21.99 |
% 56.44/21.99 | From (2006) and (12765) follows:
% 56.44/21.99 | (12883) sum(n25, n8) = all_0_4_4
% 56.44/21.99 |
% 56.44/21.99 | From (2007) and (12767) follows:
% 56.44/21.99 | (12884) sum(n6, n1) = all_0_7_7
% 56.44/21.99 |
% 56.44/21.99 | Instantiating formula (690) with n25, n8, all_0_4_4, n7 and discharging atoms sum(n25, n8) = all_0_4_4, sum(n25, n8) = n7, yields:
% 56.44/21.99 | (1405) all_0_4_4 = n7
% 56.44/21.99 |
% 56.44/21.99 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 56.44/21.99 | (1777) all_0_1_1 = n0
% 56.44/21.99 |
% 56.44/21.99 | Instantiating formula (690) with n6, n1, all_0_7_7, n7 and discharging atoms sum(n6, n1) = all_0_7_7, sum(n6, n1) = n7, yields:
% 56.44/21.99 | (1407) all_0_7_7 = n7
% 56.44/21.99 |
% 56.44/21.99 | From (1407)(1405) and (590) follows:
% 56.44/21.99 | (1409) sum(n7, n7) = all_0_3_3
% 56.44/21.99 |
% 56.44/21.99 | From (1777) and (5851) follows:
% 56.44/21.99 | (5972) sum(n14, n0) = all_0_0_0
% 56.44/21.99 |
% 56.44/21.99 | Instantiating formula (690) with n14, n0, all_0_0_0, n14 and discharging atoms sum(n14, n0) = all_0_0_0, sum(n14, n0) = n14, yields:
% 56.44/21.99 | (1177) all_0_0_0 = n14
% 56.44/21.99 |
% 56.44/21.99 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 56.44/21.99 | (1176) all_0_3_3 = n14
% 56.44/21.99 |
% 56.44/21.99 | Equations (1177,1176) can reduce 679 to:
% 56.44/21.99 | (1106) $false
% 56.44/21.99 |
% 56.44/21.99 |-The branch is then unsatisfiable
% 56.44/21.99 |-Branch two:
% 56.44/21.99 | (1431) ~ (all_0_11_11 = n7)
% 56.44/21.99 | (1432) 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
% 56.44/21.99 |
% 56.44/21.99 +-Applying beta-rule and splitting (1893), into two cases.
% 56.44/21.99 |-Branch one:
% 56.44/21.99 | (1894) all_0_10_10 = n6
% 56.44/21.99 |
% 56.44/21.99 | From (1894) and (292) follows:
% 56.44/21.99 | (1895) pred(n6) = all_0_6_6
% 56.44/21.99 |
% 56.44/21.99 | From (1894) and (760) follows:
% 56.44/21.99 | (1896) succ(n6) = all_0_8_8
% 56.44/21.99 |
% 56.44/21.99 | Instantiating formula (500) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 56.44/21.99 | (1897) all_0_6_6 = n5
% 56.44/21.99 |
% 56.44/21.99 | Instantiating formula (617) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 56.44/21.99 | (1898) all_0_8_8 = n7
% 56.44/21.99 |
% 56.44/21.99 | From (1897) and (1895) follows:
% 56.44/21.99 | (866) pred(n6) = n5
% 56.44/21.99 |
% 56.44/21.99 | From (1898) and (1896) follows:
% 56.44/21.99 | (825) succ(n6) = n7
% 56.44/21.99 |
% 56.44/21.99 | From (1897) and (541) follows:
% 56.44/21.99 | (12902) sum(n5, all_0_5_5) = all_0_4_4
% 56.44/21.99 |
% 56.44/21.99 | From (1897)(1898) and (411) follows:
% 56.44/21.99 | (1899) sum(n5, n7) = all_0_1_1
% 56.44/21.99 |
% 56.44/21.99 | From (1898) and (427) follows:
% 56.44/21.99 | (12904) sum(all_0_9_9, n7) = all_0_7_7
% 56.44/21.99 |
% 56.44/21.99 | Instantiating formula (690) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 56.44/21.99 | (1669) all_0_1_1 = n12
% 56.44/21.99 |
% 56.44/21.99 | From (1669) and (630) follows:
% 56.44/21.99 | (6222) sum(all_0_2_2, n12) = all_0_0_0
% 56.44/21.99 |
% 56.44/21.99 | From (1669) and (1899) follows:
% 56.58/21.99 | (344) sum(n5, n7) = n12
% 56.58/21.99 |
% 56.58/21.99 +-Applying beta-rule and splitting (1432), into two cases.
% 56.58/21.99 |-Branch one:
% 56.58/21.99 | (1433) all_0_11_11 = n6
% 56.58/21.99 |
% 56.58/21.99 | From (1433) and (559) follows:
% 56.58/21.99 | (1434) pred(n6) = all_0_9_9
% 56.58/21.99 |
% 56.58/21.99 | From (1433) and (992) follows:
% 56.58/21.99 | (1435) succ(n6) = all_0_5_5
% 56.58/21.99 |
% 56.58/21.99 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 56.58/21.99 | (1436) all_0_9_9 = n5
% 56.58/21.99 |
% 56.58/21.99 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 56.58/21.99 | (1437) all_0_5_5 = n7
% 56.58/21.99 |
% 56.58/21.99 | From (1436)(1437) and (538) follows:
% 56.58/21.99 | (1438) sum(n5, n7) = all_0_2_2
% 56.58/21.99 |
% 56.58/21.99 | From (1436) and (12904) follows:
% 56.58/21.99 | (12914) sum(n5, n7) = all_0_7_7
% 56.58/21.99 |
% 56.58/21.99 | From (1437) and (12902) follows:
% 56.58/21.99 | (12915) sum(n5, n7) = all_0_4_4
% 56.58/21.99 |
% 56.58/21.99 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 56.58/21.99 | (1208) all_0_2_2 = n12
% 56.58/21.99 |
% 56.58/21.99 | Instantiating formula (690) 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:
% 56.58/21.99 | (1093) all_0_2_2 = all_0_4_4
% 56.58/21.99 |
% 56.58/21.99 | Instantiating formula (690) 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:
% 56.58/21.99 | (1094) all_0_2_2 = all_0_7_7
% 56.58/21.99 |
% 56.58/21.99 | Combining equations (1094,1093) yields a new equation:
% 56.58/21.99 | (1095) all_0_4_4 = all_0_7_7
% 56.58/21.99 |
% 56.58/21.99 | Combining equations (1208,1093) yields a new equation:
% 56.58/21.99 | (1315) all_0_4_4 = n12
% 56.58/21.99 |
% 56.58/21.99 | Combining equations (1315,1095) yields a new equation:
% 56.58/21.99 | (1317) all_0_7_7 = n12
% 56.58/21.99 |
% 56.58/21.99 | Combining equations (1317,1095) yields a new equation:
% 56.58/21.99 | (1315) all_0_4_4 = n12
% 56.58/21.99 |
% 56.58/21.99 | Combining equations (1315,1093) yields a new equation:
% 56.58/21.99 | (1208) all_0_2_2 = n12
% 56.58/21.99 |
% 56.58/21.99 | From (1208) and (6222) follows:
% 56.58/21.99 | (6240) sum(n12, n12) = all_0_0_0
% 56.58/21.99 |
% 56.58/21.99 | From (1317)(1315) and (590) follows:
% 56.58/21.99 | (1319) sum(n12, n12) = all_0_3_3
% 56.58/21.99 |
% 56.58/21.99 | Instantiating formula (690) with n12, n12, all_0_0_0, n24 and discharging atoms sum(n12, n12) = all_0_0_0, sum(n12, n12) = n24, yields:
% 56.58/21.99 | (1321) all_0_0_0 = n24
% 56.58/21.99 |
% 56.58/21.99 | Instantiating formula (690) 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:
% 56.58/21.99 | (1103) all_0_0_0 = all_0_3_3
% 56.58/21.99 |
% 56.58/21.99 | Combining equations (1321,1103) yields a new equation:
% 56.58/21.99 | (1320) all_0_3_3 = n24
% 56.58/21.99 |
% 56.58/21.99 | Combining equations (1320,1103) yields a new equation:
% 56.58/21.99 | (1321) all_0_0_0 = n24
% 56.58/21.99 |
% 56.58/21.99 | Equations (1321,1320) can reduce 679 to:
% 56.58/21.99 | (1106) $false
% 56.58/21.99 |
% 56.58/21.99 |-The branch is then unsatisfiable
% 56.58/21.99 |-Branch two:
% 56.58/21.99 | (1449) ~ (all_0_11_11 = n6)
% 56.58/21.99 | (1450) 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
% 56.58/21.99 |
% 56.58/21.99 +-Applying beta-rule and splitting (1450), into two cases.
% 56.58/21.99 |-Branch one:
% 56.58/21.99 | (1451) all_0_11_11 = n5
% 56.58/21.99 |
% 56.58/21.99 | From (1451) and (559) follows:
% 56.58/22.00 | (1452) pred(n5) = all_0_9_9
% 56.58/22.00 |
% 56.58/22.00 | From (1451) and (992) follows:
% 56.58/22.00 | (1453) succ(n5) = all_0_5_5
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 56.58/22.00 | (1454) all_0_9_9 = n4
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 56.58/22.00 | (1455) all_0_5_5 = n6
% 56.58/22.00 |
% 56.58/22.00 | From (1454)(1455) and (538) follows:
% 56.58/22.00 | (1456) sum(n4, n6) = all_0_2_2
% 56.58/22.00 |
% 56.58/22.00 | From (1454) and (12904) follows:
% 56.58/22.00 | (12939) sum(n4, n7) = all_0_7_7
% 56.58/22.00 |
% 56.58/22.00 | From (1455) and (12902) follows:
% 56.58/22.00 | (12940) sum(n5, n6) = all_0_4_4
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (690) with n5, n6, all_0_4_4, n11 and discharging atoms sum(n5, n6) = all_0_4_4, sum(n5, n6) = n11, yields:
% 56.58/22.00 | (1333) all_0_4_4 = n11
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (690) with n4, n7, all_0_7_7, n11 and discharging atoms sum(n4, n7) = all_0_7_7, sum(n4, n7) = n11, yields:
% 56.58/22.00 | (1335) all_0_7_7 = n11
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 56.58/22.00 | (1226) all_0_2_2 = n10
% 56.58/22.00 |
% 56.58/22.00 | From (1226) and (6222) follows:
% 56.58/22.00 | (6260) sum(n10, n12) = all_0_0_0
% 56.58/22.00 |
% 56.58/22.00 | From (1335)(1333) and (590) follows:
% 56.58/22.00 | (1337) sum(n11, n11) = all_0_3_3
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 56.58/22.00 | (1104) all_0_3_3 = n22
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (690) with n10, n12, all_0_0_0, n22 and discharging atoms sum(n10, n12) = all_0_0_0, sum(n10, n12) = n22, yields:
% 56.58/22.00 | (1102) all_0_0_0 = n22
% 56.58/22.00 |
% 56.58/22.00 | Equations (1102,1104) can reduce 679 to:
% 56.58/22.00 | (1106) $false
% 56.58/22.00 |
% 56.58/22.00 |-The branch is then unsatisfiable
% 56.58/22.00 |-Branch two:
% 56.58/22.00 | (1467) ~ (all_0_11_11 = n5)
% 56.58/22.00 | (1468) 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
% 56.58/22.00 |
% 56.58/22.00 +-Applying beta-rule and splitting (1468), into two cases.
% 56.58/22.00 |-Branch one:
% 56.58/22.00 | (1469) all_0_11_11 = n4
% 56.58/22.00 |
% 56.58/22.00 | From (1469) and (559) follows:
% 56.58/22.00 | (1470) pred(n4) = all_0_9_9
% 56.58/22.00 |
% 56.58/22.00 | From (1469) and (992) follows:
% 56.58/22.00 | (1471) succ(n4) = all_0_5_5
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 56.58/22.00 | (1472) all_0_9_9 = n3
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 56.58/22.00 | (1473) all_0_5_5 = n5
% 56.58/22.00 |
% 56.58/22.00 | From (1472)(1473) and (538) follows:
% 56.58/22.00 | (1474) sum(n3, n5) = all_0_2_2
% 56.58/22.00 |
% 56.58/22.00 | From (1472) and (12904) follows:
% 56.58/22.00 | (12957) sum(n3, n7) = all_0_7_7
% 56.58/22.00 |
% 56.58/22.00 | From (1473) and (12902) follows:
% 56.58/22.00 | (12958) sum(n5, n5) = all_0_4_4
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (690) with n5, n5, all_0_4_4, n10 and discharging atoms sum(n5, n5) = all_0_4_4, sum(n5, n5) = n10, yields:
% 56.58/22.00 | (1351) all_0_4_4 = n10
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (690) with n3, n7, all_0_7_7, n10 and discharging atoms sum(n3, n7) = all_0_7_7, sum(n3, n7) = n10, yields:
% 56.58/22.00 | (1353) all_0_7_7 = n10
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 56.58/22.00 | (1244) all_0_2_2 = n8
% 56.58/22.00 |
% 56.58/22.00 | From (1244) and (6222) follows:
% 56.58/22.00 | (6278) sum(n8, n12) = all_0_0_0
% 56.58/22.00 |
% 56.58/22.00 | From (1353)(1351) and (590) follows:
% 56.58/22.00 | (1355) sum(n10, n10) = all_0_3_3
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 56.58/22.00 | (1122) all_0_3_3 = n20
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (690) with n8, n12, all_0_0_0, n20 and discharging atoms sum(n8, n12) = all_0_0_0, sum(n8, n12) = n20, yields:
% 56.58/22.00 | (1123) all_0_0_0 = n20
% 56.58/22.00 |
% 56.58/22.00 | Equations (1123,1122) can reduce 679 to:
% 56.58/22.00 | (1106) $false
% 56.58/22.00 |
% 56.58/22.00 |-The branch is then unsatisfiable
% 56.58/22.00 |-Branch two:
% 56.58/22.00 | (1485) ~ (all_0_11_11 = n4)
% 56.58/22.00 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.58/22.00 |
% 56.58/22.00 +-Applying beta-rule and splitting (1486), into two cases.
% 56.58/22.00 |-Branch one:
% 56.58/22.00 | (1487) all_0_11_11 = n3
% 56.58/22.00 |
% 56.58/22.00 | From (1487) and (559) follows:
% 56.58/22.00 | (1488) pred(n3) = all_0_9_9
% 56.58/22.00 |
% 56.58/22.00 | From (1487) and (992) follows:
% 56.58/22.00 | (1489) succ(n3) = all_0_5_5
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 56.58/22.00 | (1490) all_0_9_9 = n2
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 56.58/22.00 | (1491) all_0_5_5 = n4
% 56.58/22.00 |
% 56.58/22.00 | From (1490)(1491) and (538) follows:
% 56.58/22.00 | (1492) sum(n2, n4) = all_0_2_2
% 56.58/22.00 |
% 56.58/22.00 | From (1490) and (12904) follows:
% 56.58/22.00 | (12975) sum(n2, n7) = all_0_7_7
% 56.58/22.00 |
% 56.58/22.00 | From (1491) and (12902) follows:
% 56.58/22.00 | (12976) sum(n5, n4) = all_0_4_4
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (690) with n5, n4, all_0_4_4, n9 and discharging atoms sum(n5, n4) = all_0_4_4, sum(n5, n4) = n9, yields:
% 56.58/22.00 | (1369) all_0_4_4 = n9
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (690) with n2, n7, all_0_7_7, n9 and discharging atoms sum(n2, n7) = all_0_7_7, sum(n2, n7) = n9, yields:
% 56.58/22.00 | (1371) all_0_7_7 = n9
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 56.58/22.00 | (1262) all_0_2_2 = n6
% 56.58/22.00 |
% 56.58/22.00 | From (1262) and (6222) follows:
% 56.58/22.00 | (6296) sum(n6, n12) = all_0_0_0
% 56.58/22.00 |
% 56.58/22.00 | From (1371)(1369) and (590) follows:
% 56.58/22.00 | (1373) sum(n9, n9) = all_0_3_3
% 56.58/22.00 |
% 56.58/22.00 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 56.58/22.01 | (1140) all_0_3_3 = n18
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (690) with n6, n12, all_0_0_0, n18 and discharging atoms sum(n6, n12) = all_0_0_0, sum(n6, n12) = n18, yields:
% 56.58/22.01 | (1141) all_0_0_0 = n18
% 56.58/22.01 |
% 56.58/22.01 | Equations (1141,1140) can reduce 679 to:
% 56.58/22.01 | (1106) $false
% 56.58/22.01 |
% 56.58/22.01 |-The branch is then unsatisfiable
% 56.58/22.01 |-Branch two:
% 56.58/22.01 | (1503) ~ (all_0_11_11 = n3)
% 56.58/22.01 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.58/22.01 |
% 56.58/22.01 +-Applying beta-rule and splitting (1504), into two cases.
% 56.58/22.01 |-Branch one:
% 56.58/22.01 | (1505) all_0_11_11 = n2
% 56.58/22.01 |
% 56.58/22.01 | From (1505) and (559) follows:
% 56.58/22.01 | (1506) pred(n2) = all_0_9_9
% 56.58/22.01 |
% 56.58/22.01 | From (1505) and (992) follows:
% 56.58/22.01 | (1507) succ(n2) = all_0_5_5
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 56.58/22.01 | (1508) all_0_9_9 = n1
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 56.58/22.01 | (1509) all_0_5_5 = n3
% 56.58/22.01 |
% 56.58/22.01 | From (1508)(1509) and (538) follows:
% 56.58/22.01 | (1510) sum(n1, n3) = all_0_2_2
% 56.58/22.01 |
% 56.58/22.01 | From (1508) and (12904) follows:
% 56.58/22.01 | (12993) sum(n1, n7) = all_0_7_7
% 56.58/22.01 |
% 56.58/22.01 | From (1509) and (12902) follows:
% 56.58/22.01 | (12994) sum(n5, n3) = all_0_4_4
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (690) with n5, n3, all_0_4_4, n8 and discharging atoms sum(n5, n3) = all_0_4_4, sum(n5, n3) = n8, yields:
% 56.58/22.01 | (1387) all_0_4_4 = n8
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (690) with n1, n7, all_0_7_7, n8 and discharging atoms sum(n1, n7) = all_0_7_7, sum(n1, n7) = n8, yields:
% 56.58/22.01 | (1389) all_0_7_7 = n8
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 56.58/22.01 | (1280) all_0_2_2 = n4
% 56.58/22.01 |
% 56.58/22.01 | From (1280) and (6222) follows:
% 56.58/22.01 | (6314) sum(n4, n12) = all_0_0_0
% 56.58/22.01 |
% 56.58/22.01 | From (1389)(1387) and (590) follows:
% 56.58/22.01 | (1391) sum(n8, n8) = all_0_3_3
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 56.58/22.01 | (1158) all_0_3_3 = n16
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (690) with n4, n12, all_0_0_0, n16 and discharging atoms sum(n4, n12) = all_0_0_0, sum(n4, n12) = n16, yields:
% 56.58/22.01 | (1159) all_0_0_0 = n16
% 56.58/22.01 |
% 56.58/22.01 | Equations (1159,1158) can reduce 679 to:
% 56.58/22.01 | (1106) $false
% 56.58/22.01 |
% 56.58/22.01 |-The branch is then unsatisfiable
% 56.58/22.01 |-Branch two:
% 56.58/22.01 | (1521) ~ (all_0_11_11 = n2)
% 56.58/22.01 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 56.58/22.01 |
% 56.58/22.01 +-Applying beta-rule and splitting (1522), into two cases.
% 56.58/22.01 |-Branch one:
% 56.58/22.01 | (1523) all_0_11_11 = n1
% 56.58/22.01 |
% 56.58/22.01 | From (1523) and (559) follows:
% 56.58/22.01 | (1524) pred(n1) = all_0_9_9
% 56.58/22.01 |
% 56.58/22.01 | From (1523) and (992) follows:
% 56.58/22.01 | (1525) succ(n1) = all_0_5_5
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 56.58/22.01 | (1526) all_0_9_9 = n0
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 56.58/22.01 | (1527) all_0_5_5 = n2
% 56.58/22.01 |
% 56.58/22.01 | From (1526)(1527) and (538) follows:
% 56.58/22.01 | (1528) sum(n0, n2) = all_0_2_2
% 56.58/22.01 |
% 56.58/22.01 | From (1526) and (12904) follows:
% 56.58/22.01 | (13011) sum(n0, n7) = all_0_7_7
% 56.58/22.01 |
% 56.58/22.01 | From (1527) and (12902) follows:
% 56.58/22.01 | (13012) sum(n5, n2) = all_0_4_4
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (690) with n5, n2, all_0_4_4, n7 and discharging atoms sum(n5, n2) = all_0_4_4, sum(n5, n2) = n7, yields:
% 56.58/22.01 | (1405) all_0_4_4 = n7
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (690) with n0, n7, all_0_7_7, n7 and discharging atoms sum(n0, n7) = all_0_7_7, sum(n0, n7) = n7, yields:
% 56.58/22.01 | (1407) all_0_7_7 = n7
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 56.58/22.01 | (1298) all_0_2_2 = n2
% 56.58/22.01 |
% 56.58/22.01 | From (1298) and (6222) follows:
% 56.58/22.01 | (6332) sum(n2, n12) = all_0_0_0
% 56.58/22.01 |
% 56.58/22.01 | From (1407)(1405) and (590) follows:
% 56.58/22.01 | (1409) sum(n7, n7) = all_0_3_3
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 56.58/22.01 | (1176) all_0_3_3 = n14
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (690) with n2, n12, all_0_0_0, n14 and discharging atoms sum(n2, n12) = all_0_0_0, sum(n2, n12) = n14, yields:
% 56.58/22.01 | (1177) all_0_0_0 = n14
% 56.58/22.01 |
% 56.58/22.01 | Equations (1177,1176) can reduce 679 to:
% 56.58/22.01 | (1106) $false
% 56.58/22.01 |
% 56.58/22.01 |-The branch is then unsatisfiable
% 56.58/22.01 |-Branch two:
% 56.58/22.01 | (1540) ~ (all_0_11_11 = n1)
% 56.58/22.01 | (1541) all_0_11_11 = n0
% 56.58/22.01 |
% 56.58/22.01 | From (1541) and (559) follows:
% 56.58/22.01 | (1542) pred(n0) = all_0_9_9
% 56.58/22.01 |
% 56.58/22.01 | From (1541) and (992) follows:
% 56.58/22.01 | (1543) succ(n0) = all_0_5_5
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 56.58/22.01 | (1544) all_0_9_9 = n25
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 56.58/22.01 | (1545) all_0_5_5 = n1
% 56.58/22.01 |
% 56.58/22.01 | From (1544)(1545) and (538) follows:
% 56.58/22.01 | (1546) sum(n25, n1) = all_0_2_2
% 56.58/22.01 |
% 56.58/22.01 | From (1544) and (12904) follows:
% 56.58/22.01 | (13028) sum(n25, n7) = all_0_7_7
% 56.58/22.01 |
% 56.58/22.01 | From (1545) and (12902) follows:
% 56.58/22.01 | (13029) sum(n5, n1) = all_0_4_4
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (690) with n25, n7, all_0_7_7, n6 and discharging atoms sum(n25, n7) = all_0_7_7, sum(n25, n7) = n6, yields:
% 56.58/22.01 | (1425) all_0_7_7 = n6
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 56.58/22.01 | (1316) all_0_2_2 = n0
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (690) with n5, n1, all_0_4_4, n6 and discharging atoms sum(n5, n1) = all_0_4_4, sum(n5, n1) = n6, yields:
% 56.58/22.01 | (1423) all_0_4_4 = n6
% 56.58/22.01 |
% 56.58/22.01 | From (1316) and (6222) follows:
% 56.58/22.01 | (6350) sum(n0, n12) = all_0_0_0
% 56.58/22.01 |
% 56.58/22.01 | From (1425)(1423) and (590) follows:
% 56.58/22.01 | (1427) sum(n6, n6) = all_0_3_3
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 56.58/22.01 | (1194) all_0_3_3 = n12
% 56.58/22.01 |
% 56.58/22.01 | Instantiating formula (690) with n0, n12, all_0_0_0, n12 and discharging atoms sum(n0, n12) = all_0_0_0, sum(n0, n12) = n12, yields:
% 56.58/22.01 | (1195) all_0_0_0 = n12
% 56.58/22.01 |
% 56.58/22.01 | Equations (1195,1194) can reduce 679 to:
% 56.58/22.01 | (1106) $false
% 56.58/22.01 |
% 56.58/22.01 |-The branch is then unsatisfiable
% 56.58/22.02 |-Branch two:
% 56.58/22.02 | (1910) ~ (all_0_10_10 = n6)
% 56.58/22.02 | (1911) 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
% 56.58/22.02 |
% 56.58/22.02 +-Applying beta-rule and splitting (1432), into two cases.
% 56.58/22.02 |-Branch one:
% 56.58/22.02 | (1433) all_0_11_11 = n6
% 56.58/22.02 |
% 56.58/22.02 | From (1433) and (559) follows:
% 56.58/22.02 | (1434) pred(n6) = all_0_9_9
% 56.58/22.02 |
% 56.58/22.02 | From (1433) and (992) follows:
% 56.58/22.02 | (1435) succ(n6) = all_0_5_5
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (500) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 56.58/22.02 | (1436) all_0_9_9 = n5
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (617) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 56.58/22.02 | (1437) all_0_5_5 = n7
% 56.58/22.02 |
% 56.58/22.02 | From (1437) and (541) follows:
% 56.58/22.02 | (13045) sum(all_0_6_6, n7) = all_0_4_4
% 56.58/22.02 |
% 56.58/22.02 | From (1436)(1437) and (538) follows:
% 56.58/22.02 | (1438) sum(n5, n7) = all_0_2_2
% 56.58/22.02 |
% 56.58/22.02 | From (1436) and (427) follows:
% 56.58/22.02 | (13047) sum(n5, all_0_8_8) = all_0_7_7
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (690) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 56.58/22.02 | (1208) all_0_2_2 = n12
% 56.58/22.02 |
% 56.58/22.02 | From (1208) and (630) follows:
% 56.58/22.02 | (6599) sum(n12, all_0_1_1) = all_0_0_0
% 56.58/22.02 |
% 56.58/22.02 +-Applying beta-rule and splitting (1911), into two cases.
% 56.58/22.02 |-Branch one:
% 56.58/22.02 | (1912) all_0_10_10 = n5
% 56.58/22.02 |
% 56.58/22.02 | From (1912) and (292) follows:
% 56.58/22.02 | (1913) pred(n5) = all_0_6_6
% 56.58/22.02 |
% 56.58/22.02 | From (1912) and (760) follows:
% 56.58/22.02 | (1914) succ(n5) = all_0_8_8
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 56.58/22.02 | (1915) all_0_6_6 = n4
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 56.58/22.02 | (1916) all_0_8_8 = n6
% 56.58/22.02 |
% 56.58/22.02 | From (1915)(1916) and (411) follows:
% 56.58/22.02 | (1917) sum(n4, n6) = all_0_1_1
% 56.58/22.02 |
% 56.58/22.02 | From (1915) and (13045) follows:
% 56.58/22.02 | (13056) sum(n4, n7) = all_0_4_4
% 56.58/22.02 |
% 56.58/22.02 | From (1916) and (13047) follows:
% 56.58/22.02 | (13057) sum(n5, n6) = all_0_7_7
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (690) with n5, n6, all_0_7_7, n11 and discharging atoms sum(n5, n6) = all_0_7_7, sum(n5, n6) = n11, yields:
% 56.58/22.02 | (1335) all_0_7_7 = n11
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (690) with n4, n7, all_0_4_4, n11 and discharging atoms sum(n4, n7) = all_0_4_4, sum(n4, n7) = n11, yields:
% 56.58/22.02 | (1333) all_0_4_4 = n11
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 56.58/22.02 | (1687) all_0_1_1 = n10
% 56.58/22.02 |
% 56.58/22.02 | From (1335)(1333) and (590) follows:
% 56.58/22.02 | (1337) sum(n11, n11) = all_0_3_3
% 56.58/22.02 |
% 56.58/22.02 | From (1687) and (6599) follows:
% 56.58/22.02 | (6612) sum(n12, n10) = all_0_0_0
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (690) with n12, n10, all_0_0_0, n22 and discharging atoms sum(n12, n10) = all_0_0_0, sum(n12, n10) = n22, yields:
% 56.58/22.02 | (1102) all_0_0_0 = n22
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (690) with n11, n11, all_0_3_3, n22 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n22, yields:
% 56.58/22.02 | (1104) all_0_3_3 = n22
% 56.58/22.02 |
% 56.58/22.02 | Equations (1102,1104) can reduce 679 to:
% 56.58/22.02 | (1106) $false
% 56.58/22.02 |
% 56.58/22.02 |-The branch is then unsatisfiable
% 56.58/22.02 |-Branch two:
% 56.58/22.02 | (1928) ~ (all_0_10_10 = n5)
% 56.58/22.02 | (1929) 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
% 56.58/22.02 |
% 56.58/22.02 +-Applying beta-rule and splitting (1929), into two cases.
% 56.58/22.02 |-Branch one:
% 56.58/22.02 | (1930) all_0_10_10 = n4
% 56.58/22.02 |
% 56.58/22.02 | From (1930) and (292) follows:
% 56.58/22.02 | (1931) pred(n4) = all_0_6_6
% 56.58/22.02 |
% 56.58/22.02 | From (1930) and (760) follows:
% 56.58/22.02 | (1932) succ(n4) = all_0_8_8
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 56.58/22.02 | (1933) all_0_6_6 = n3
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 56.58/22.02 | (1934) all_0_8_8 = n5
% 56.58/22.02 |
% 56.58/22.02 | From (1933)(1934) and (411) follows:
% 56.58/22.02 | (1935) sum(n3, n5) = all_0_1_1
% 56.58/22.02 |
% 56.58/22.02 | From (1933) and (13045) follows:
% 56.58/22.02 | (13074) sum(n3, n7) = all_0_4_4
% 56.58/22.02 |
% 56.58/22.02 | From (1934) and (13047) follows:
% 56.58/22.02 | (13075) sum(n5, n5) = all_0_7_7
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (690) with n5, n5, all_0_7_7, n10 and discharging atoms sum(n5, n5) = all_0_7_7, sum(n5, n5) = n10, yields:
% 56.58/22.02 | (1353) all_0_7_7 = n10
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (690) with n3, n7, all_0_4_4, n10 and discharging atoms sum(n3, n7) = all_0_4_4, sum(n3, n7) = n10, yields:
% 56.58/22.02 | (1351) all_0_4_4 = n10
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 56.58/22.02 | (1705) all_0_1_1 = n8
% 56.58/22.02 |
% 56.58/22.02 | From (1353)(1351) and (590) follows:
% 56.58/22.02 | (1355) sum(n10, n10) = all_0_3_3
% 56.58/22.02 |
% 56.58/22.02 | From (1705) and (6599) follows:
% 56.58/22.02 | (6630) sum(n12, n8) = all_0_0_0
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (690) with n12, n8, all_0_0_0, n20 and discharging atoms sum(n12, n8) = all_0_0_0, sum(n12, n8) = n20, yields:
% 56.58/22.02 | (1123) all_0_0_0 = n20
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (690) with n10, n10, all_0_3_3, n20 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n20, yields:
% 56.58/22.02 | (1122) all_0_3_3 = n20
% 56.58/22.02 |
% 56.58/22.02 | Equations (1123,1122) can reduce 679 to:
% 56.58/22.02 | (1106) $false
% 56.58/22.02 |
% 56.58/22.02 |-The branch is then unsatisfiable
% 56.58/22.02 |-Branch two:
% 56.58/22.02 | (1946) ~ (all_0_10_10 = n4)
% 56.58/22.02 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.58/22.02 |
% 56.58/22.02 +-Applying beta-rule and splitting (1947), into two cases.
% 56.58/22.02 |-Branch one:
% 56.58/22.02 | (1948) all_0_10_10 = n3
% 56.58/22.02 |
% 56.58/22.02 | From (1948) and (292) follows:
% 56.58/22.02 | (1949) pred(n3) = all_0_6_6
% 56.58/22.02 |
% 56.58/22.02 | From (1948) and (760) follows:
% 56.58/22.02 | (1950) succ(n3) = all_0_8_8
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 56.58/22.02 | (1951) all_0_6_6 = n2
% 56.58/22.02 |
% 56.58/22.02 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 56.58/22.02 | (1952) all_0_8_8 = n4
% 56.58/22.02 |
% 56.58/22.02 | From (1951)(1952) and (411) follows:
% 56.58/22.03 | (1953) sum(n2, n4) = all_0_1_1
% 56.58/22.03 |
% 56.58/22.03 | From (1951) and (13045) follows:
% 56.58/22.03 | (13092) sum(n2, n7) = all_0_4_4
% 56.58/22.03 |
% 56.58/22.03 | From (1952) and (13047) follows:
% 56.58/22.03 | (13093) sum(n5, n4) = all_0_7_7
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (690) with n5, n4, all_0_7_7, n9 and discharging atoms sum(n5, n4) = all_0_7_7, sum(n5, n4) = n9, yields:
% 56.58/22.03 | (1371) all_0_7_7 = n9
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (690) with n2, n7, all_0_4_4, n9 and discharging atoms sum(n2, n7) = all_0_4_4, sum(n2, n7) = n9, yields:
% 56.58/22.03 | (1369) all_0_4_4 = n9
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 56.58/22.03 | (1723) all_0_1_1 = n6
% 56.58/22.03 |
% 56.58/22.03 | From (1371)(1369) and (590) follows:
% 56.58/22.03 | (1373) sum(n9, n9) = all_0_3_3
% 56.58/22.03 |
% 56.58/22.03 | From (1723) and (6599) follows:
% 56.58/22.03 | (6648) sum(n12, n6) = all_0_0_0
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (690) with n12, n6, all_0_0_0, n18 and discharging atoms sum(n12, n6) = all_0_0_0, sum(n12, n6) = n18, yields:
% 56.58/22.03 | (1141) all_0_0_0 = n18
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 56.58/22.03 | (1140) all_0_3_3 = n18
% 56.58/22.03 |
% 56.58/22.03 | Equations (1141,1140) can reduce 679 to:
% 56.58/22.03 | (1106) $false
% 56.58/22.03 |
% 56.58/22.03 |-The branch is then unsatisfiable
% 56.58/22.03 |-Branch two:
% 56.58/22.03 | (1964) ~ (all_0_10_10 = n3)
% 56.58/22.03 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.58/22.03 |
% 56.58/22.03 +-Applying beta-rule and splitting (1965), into two cases.
% 56.58/22.03 |-Branch one:
% 56.58/22.03 | (1966) all_0_10_10 = n2
% 56.58/22.03 |
% 56.58/22.03 | From (1966) and (292) follows:
% 56.58/22.03 | (1967) pred(n2) = all_0_6_6
% 56.58/22.03 |
% 56.58/22.03 | From (1966) and (760) follows:
% 56.58/22.03 | (1968) succ(n2) = all_0_8_8
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 56.58/22.03 | (1969) all_0_6_6 = n1
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 56.58/22.03 | (1970) all_0_8_8 = n3
% 56.58/22.03 |
% 56.58/22.03 | From (1969)(1970) and (411) follows:
% 56.58/22.03 | (1971) sum(n1, n3) = all_0_1_1
% 56.58/22.03 |
% 56.58/22.03 | From (1969) and (13045) follows:
% 56.58/22.03 | (13110) sum(n1, n7) = all_0_4_4
% 56.58/22.03 |
% 56.58/22.03 | From (1970) and (13047) follows:
% 56.58/22.03 | (13111) sum(n5, n3) = all_0_7_7
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (690) with n5, n3, all_0_7_7, n8 and discharging atoms sum(n5, n3) = all_0_7_7, sum(n5, n3) = n8, yields:
% 56.58/22.03 | (1389) all_0_7_7 = n8
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (690) with n1, n7, all_0_4_4, n8 and discharging atoms sum(n1, n7) = all_0_4_4, sum(n1, n7) = n8, yields:
% 56.58/22.03 | (1387) all_0_4_4 = n8
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 56.58/22.03 | (1741) all_0_1_1 = n4
% 56.58/22.03 |
% 56.58/22.03 | From (1389)(1387) and (590) follows:
% 56.58/22.03 | (1391) sum(n8, n8) = all_0_3_3
% 56.58/22.03 |
% 56.58/22.03 | From (1741) and (6599) follows:
% 56.58/22.03 | (6666) sum(n12, n4) = all_0_0_0
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (690) with n12, n4, all_0_0_0, n16 and discharging atoms sum(n12, n4) = all_0_0_0, sum(n12, n4) = n16, yields:
% 56.58/22.03 | (1159) all_0_0_0 = n16
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 56.58/22.03 | (1158) all_0_3_3 = n16
% 56.58/22.03 |
% 56.58/22.03 | Equations (1159,1158) can reduce 679 to:
% 56.58/22.03 | (1106) $false
% 56.58/22.03 |
% 56.58/22.03 |-The branch is then unsatisfiable
% 56.58/22.03 |-Branch two:
% 56.58/22.03 | (1982) ~ (all_0_10_10 = n2)
% 56.58/22.03 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 56.58/22.03 |
% 56.58/22.03 +-Applying beta-rule and splitting (1983), into two cases.
% 56.58/22.03 |-Branch one:
% 56.58/22.03 | (1984) all_0_10_10 = n1
% 56.58/22.03 |
% 56.58/22.03 | From (1984) and (292) follows:
% 56.58/22.03 | (1985) pred(n1) = all_0_6_6
% 56.58/22.03 |
% 56.58/22.03 | From (1984) and (760) follows:
% 56.58/22.03 | (1986) succ(n1) = all_0_8_8
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 56.58/22.03 | (1987) all_0_6_6 = n0
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 56.58/22.03 | (1988) all_0_8_8 = n2
% 56.58/22.03 |
% 56.58/22.03 | From (1987)(1988) and (411) follows:
% 56.58/22.03 | (1989) sum(n0, n2) = all_0_1_1
% 56.58/22.03 |
% 56.58/22.03 | From (1987) and (13045) follows:
% 56.58/22.03 | (13128) sum(n0, n7) = all_0_4_4
% 56.58/22.03 |
% 56.58/22.03 | From (1988) and (13047) follows:
% 56.58/22.03 | (13129) sum(n5, n2) = all_0_7_7
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (690) with n5, n2, all_0_7_7, n7 and discharging atoms sum(n5, n2) = all_0_7_7, sum(n5, n2) = n7, yields:
% 56.58/22.03 | (1407) all_0_7_7 = n7
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (690) with n0, n7, all_0_4_4, n7 and discharging atoms sum(n0, n7) = all_0_4_4, sum(n0, n7) = n7, yields:
% 56.58/22.03 | (1405) all_0_4_4 = n7
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 56.58/22.03 | (1759) all_0_1_1 = n2
% 56.58/22.03 |
% 56.58/22.03 | From (1407)(1405) and (590) follows:
% 56.58/22.03 | (1409) sum(n7, n7) = all_0_3_3
% 56.58/22.03 |
% 56.58/22.03 | From (1759) and (6599) follows:
% 56.58/22.03 | (6684) sum(n12, n2) = all_0_0_0
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (690) with n12, n2, all_0_0_0, n14 and discharging atoms sum(n12, n2) = all_0_0_0, sum(n12, n2) = n14, yields:
% 56.58/22.03 | (1177) all_0_0_0 = n14
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 56.58/22.03 | (1176) all_0_3_3 = n14
% 56.58/22.03 |
% 56.58/22.03 | Equations (1177,1176) can reduce 679 to:
% 56.58/22.03 | (1106) $false
% 56.58/22.03 |
% 56.58/22.03 |-The branch is then unsatisfiable
% 56.58/22.03 |-Branch two:
% 56.58/22.03 | (2002) ~ (all_0_10_10 = n1)
% 56.58/22.03 | (2003) all_0_10_10 = n0
% 56.58/22.03 |
% 56.58/22.03 | From (2003) and (292) follows:
% 56.58/22.03 | (2004) pred(n0) = all_0_6_6
% 56.58/22.03 |
% 56.58/22.03 | From (2003) and (760) follows:
% 56.58/22.03 | (2005) succ(n0) = all_0_8_8
% 56.58/22.03 |
% 56.58/22.03 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 56.58/22.04 | (2006) all_0_6_6 = n25
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 56.58/22.04 | (2007) all_0_8_8 = n1
% 56.58/22.04 |
% 56.58/22.04 | From (2006)(2007) and (411) follows:
% 56.58/22.04 | (2008) sum(n25, n1) = all_0_1_1
% 56.58/22.04 |
% 56.58/22.04 | From (2006) and (13045) follows:
% 56.58/22.04 | (13145) sum(n25, n7) = all_0_4_4
% 56.58/22.04 |
% 56.58/22.04 | From (2007) and (13047) follows:
% 56.58/22.04 | (13146) sum(n5, n1) = all_0_7_7
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (690) with n25, n7, all_0_4_4, n6 and discharging atoms sum(n25, n7) = all_0_4_4, sum(n25, n7) = n6, yields:
% 56.58/22.04 | (1423) all_0_4_4 = n6
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 56.58/22.04 | (1777) all_0_1_1 = n0
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (690) with n5, n1, all_0_7_7, n6 and discharging atoms sum(n5, n1) = all_0_7_7, sum(n5, n1) = n6, yields:
% 56.58/22.04 | (1425) all_0_7_7 = n6
% 56.58/22.04 |
% 56.58/22.04 | From (1425)(1423) and (590) follows:
% 56.58/22.04 | (1427) sum(n6, n6) = all_0_3_3
% 56.58/22.04 |
% 56.58/22.04 | From (1777) and (6599) follows:
% 56.58/22.04 | (6702) sum(n12, n0) = all_0_0_0
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (690) with n12, n0, all_0_0_0, n12 and discharging atoms sum(n12, n0) = all_0_0_0, sum(n12, n0) = n12, yields:
% 56.58/22.04 | (1195) all_0_0_0 = n12
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 56.58/22.04 | (1194) all_0_3_3 = n12
% 56.58/22.04 |
% 56.58/22.04 | Equations (1195,1194) can reduce 679 to:
% 56.58/22.04 | (1106) $false
% 56.58/22.04 |
% 56.58/22.04 |-The branch is then unsatisfiable
% 56.58/22.04 |-Branch two:
% 56.58/22.04 | (1449) ~ (all_0_11_11 = n6)
% 56.58/22.04 | (1450) 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
% 56.58/22.04 |
% 56.58/22.04 +-Applying beta-rule and splitting (1911), into two cases.
% 56.58/22.04 |-Branch one:
% 56.58/22.04 | (1912) all_0_10_10 = n5
% 56.58/22.04 |
% 56.58/22.04 | From (1912) and (292) follows:
% 56.58/22.04 | (1913) pred(n5) = all_0_6_6
% 56.58/22.04 |
% 56.58/22.04 | From (1912) and (760) follows:
% 56.58/22.04 | (1914) succ(n5) = all_0_8_8
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (500) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 56.58/22.04 | (1915) all_0_6_6 = n4
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (617) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 56.58/22.04 | (1916) all_0_8_8 = n6
% 56.58/22.04 |
% 56.58/22.04 | From (1915) and (1913) follows:
% 56.58/22.04 | (970) pred(n5) = n4
% 56.58/22.04 |
% 56.58/22.04 | From (1916) and (1914) follows:
% 56.58/22.04 | (759) succ(n5) = n6
% 56.58/22.04 |
% 56.58/22.04 | From (1915) and (541) follows:
% 56.58/22.04 | (13164) sum(n4, all_0_5_5) = all_0_4_4
% 56.58/22.04 |
% 56.58/22.04 | From (1915)(1916) and (411) follows:
% 56.58/22.04 | (1917) sum(n4, n6) = all_0_1_1
% 56.58/22.04 |
% 56.58/22.04 | From (1916) and (427) follows:
% 56.58/22.04 | (13166) sum(all_0_9_9, n6) = all_0_7_7
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (690) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 56.58/22.04 | (1687) all_0_1_1 = n10
% 56.58/22.04 |
% 56.58/22.04 | From (1687) and (630) follows:
% 56.58/22.04 | (6952) sum(all_0_2_2, n10) = all_0_0_0
% 56.58/22.04 |
% 56.58/22.04 | From (1687) and (1917) follows:
% 56.58/22.04 | (603) sum(n4, n6) = n10
% 56.58/22.04 |
% 56.58/22.04 +-Applying beta-rule and splitting (1450), into two cases.
% 56.58/22.04 |-Branch one:
% 56.58/22.04 | (1451) all_0_11_11 = n5
% 56.58/22.04 |
% 56.58/22.04 | From (1451) and (559) follows:
% 56.58/22.04 | (1452) pred(n5) = all_0_9_9
% 56.58/22.04 |
% 56.58/22.04 | From (1451) and (992) follows:
% 56.58/22.04 | (1453) succ(n5) = all_0_5_5
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 56.58/22.04 | (1454) all_0_9_9 = n4
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 56.58/22.04 | (1455) all_0_5_5 = n6
% 56.58/22.04 |
% 56.58/22.04 | From (1454)(1455) and (538) follows:
% 56.58/22.04 | (1456) sum(n4, n6) = all_0_2_2
% 56.58/22.04 |
% 56.58/22.04 | From (1454) and (13166) follows:
% 56.58/22.04 | (13176) sum(n4, n6) = all_0_7_7
% 56.58/22.04 |
% 56.58/22.04 | From (1455) and (13164) follows:
% 56.58/22.04 | (13177) sum(n4, n6) = all_0_4_4
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 56.58/22.04 | (1226) all_0_2_2 = n10
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (690) 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:
% 56.58/22.04 | (1093) all_0_2_2 = all_0_4_4
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (690) 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:
% 56.58/22.04 | (1094) all_0_2_2 = all_0_7_7
% 56.58/22.04 |
% 56.58/22.04 | Combining equations (1094,1093) yields a new equation:
% 56.58/22.04 | (1095) all_0_4_4 = all_0_7_7
% 56.58/22.04 |
% 56.58/22.04 | Combining equations (1226,1093) yields a new equation:
% 56.58/22.04 | (1351) all_0_4_4 = n10
% 56.58/22.04 |
% 56.58/22.04 | Combining equations (1351,1095) yields a new equation:
% 56.58/22.04 | (1353) all_0_7_7 = n10
% 56.58/22.04 |
% 56.58/22.04 | Combining equations (1353,1095) yields a new equation:
% 56.58/22.04 | (1351) all_0_4_4 = n10
% 56.58/22.04 |
% 56.58/22.04 | Combining equations (1351,1093) yields a new equation:
% 56.58/22.04 | (1226) all_0_2_2 = n10
% 56.58/22.04 |
% 56.58/22.04 | From (1226) and (6952) follows:
% 56.58/22.04 | (6970) sum(n10, n10) = all_0_0_0
% 56.58/22.04 |
% 56.58/22.04 | From (1353)(1351) and (590) follows:
% 56.58/22.04 | (1355) sum(n10, n10) = all_0_3_3
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (690) with n10, n10, all_0_0_0, n20 and discharging atoms sum(n10, n10) = all_0_0_0, sum(n10, n10) = n20, yields:
% 56.58/22.04 | (1123) all_0_0_0 = n20
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (690) 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:
% 56.58/22.04 | (1103) all_0_0_0 = all_0_3_3
% 56.58/22.04 |
% 56.58/22.04 | Combining equations (1123,1103) yields a new equation:
% 56.58/22.04 | (1122) all_0_3_3 = n20
% 56.58/22.04 |
% 56.58/22.04 | Combining equations (1122,1103) yields a new equation:
% 56.58/22.04 | (1123) all_0_0_0 = n20
% 56.58/22.04 |
% 56.58/22.04 | Equations (1123,1122) can reduce 679 to:
% 56.58/22.04 | (1106) $false
% 56.58/22.04 |
% 56.58/22.04 |-The branch is then unsatisfiable
% 56.58/22.04 |-Branch two:
% 56.58/22.04 | (1467) ~ (all_0_11_11 = n5)
% 56.58/22.04 | (1468) 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
% 56.58/22.04 |
% 56.58/22.04 +-Applying beta-rule and splitting (1468), into two cases.
% 56.58/22.04 |-Branch one:
% 56.58/22.04 | (1469) all_0_11_11 = n4
% 56.58/22.04 |
% 56.58/22.04 | From (1469) and (559) follows:
% 56.58/22.04 | (1470) pred(n4) = all_0_9_9
% 56.58/22.04 |
% 56.58/22.04 | From (1469) and (992) follows:
% 56.58/22.04 | (1471) succ(n4) = all_0_5_5
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 56.58/22.04 | (1472) all_0_9_9 = n3
% 56.58/22.04 |
% 56.58/22.04 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 56.58/22.04 | (1473) all_0_5_5 = n5
% 56.58/22.04 |
% 56.58/22.04 | From (1472)(1473) and (538) follows:
% 56.58/22.04 | (1474) sum(n3, n5) = all_0_2_2
% 56.58/22.04 |
% 56.58/22.04 | From (1472) and (13166) follows:
% 56.58/22.05 | (13201) sum(n3, n6) = all_0_7_7
% 56.58/22.05 |
% 56.58/22.05 | From (1473) and (13164) follows:
% 56.58/22.05 | (13202) sum(n4, n5) = all_0_4_4
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (690) with n4, n5, all_0_4_4, n9 and discharging atoms sum(n4, n5) = all_0_4_4, sum(n4, n5) = n9, yields:
% 56.58/22.05 | (1369) all_0_4_4 = n9
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (690) with n3, n6, all_0_7_7, n9 and discharging atoms sum(n3, n6) = all_0_7_7, sum(n3, n6) = n9, yields:
% 56.58/22.05 | (1371) all_0_7_7 = n9
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 56.58/22.05 | (1244) all_0_2_2 = n8
% 56.58/22.05 |
% 56.58/22.05 | From (1244) and (6952) follows:
% 56.58/22.05 | (6990) sum(n8, n10) = all_0_0_0
% 56.58/22.05 |
% 56.58/22.05 | From (1371)(1369) and (590) follows:
% 56.58/22.05 | (1373) sum(n9, n9) = all_0_3_3
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 56.58/22.05 | (1140) all_0_3_3 = n18
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (690) with n8, n10, all_0_0_0, n18 and discharging atoms sum(n8, n10) = all_0_0_0, sum(n8, n10) = n18, yields:
% 56.58/22.05 | (1141) all_0_0_0 = n18
% 56.58/22.05 |
% 56.58/22.05 | Equations (1141,1140) can reduce 679 to:
% 56.58/22.05 | (1106) $false
% 56.58/22.05 |
% 56.58/22.05 |-The branch is then unsatisfiable
% 56.58/22.05 |-Branch two:
% 56.58/22.05 | (1485) ~ (all_0_11_11 = n4)
% 56.58/22.05 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.58/22.05 |
% 56.58/22.05 +-Applying beta-rule and splitting (1486), into two cases.
% 56.58/22.05 |-Branch one:
% 56.58/22.05 | (1487) all_0_11_11 = n3
% 56.58/22.05 |
% 56.58/22.05 | From (1487) and (559) follows:
% 56.58/22.05 | (1488) pred(n3) = all_0_9_9
% 56.58/22.05 |
% 56.58/22.05 | From (1487) and (992) follows:
% 56.58/22.05 | (1489) succ(n3) = all_0_5_5
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 56.58/22.05 | (1490) all_0_9_9 = n2
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 56.58/22.05 | (1491) all_0_5_5 = n4
% 56.58/22.05 |
% 56.58/22.05 | From (1490)(1491) and (538) follows:
% 56.58/22.05 | (1492) sum(n2, n4) = all_0_2_2
% 56.58/22.05 |
% 56.58/22.05 | From (1490) and (13166) follows:
% 56.58/22.05 | (13219) sum(n2, n6) = all_0_7_7
% 56.58/22.05 |
% 56.58/22.05 | From (1491) and (13164) follows:
% 56.58/22.05 | (13220) sum(n4, n4) = all_0_4_4
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (690) with n4, n4, all_0_4_4, n8 and discharging atoms sum(n4, n4) = all_0_4_4, sum(n4, n4) = n8, yields:
% 56.58/22.05 | (1387) all_0_4_4 = n8
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (690) with n2, n6, all_0_7_7, n8 and discharging atoms sum(n2, n6) = all_0_7_7, sum(n2, n6) = n8, yields:
% 56.58/22.05 | (1389) all_0_7_7 = n8
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 56.58/22.05 | (1262) all_0_2_2 = n6
% 56.58/22.05 |
% 56.58/22.05 | From (1262) and (6952) follows:
% 56.58/22.05 | (7008) sum(n6, n10) = all_0_0_0
% 56.58/22.05 |
% 56.58/22.05 | From (1389)(1387) and (590) follows:
% 56.58/22.05 | (1391) sum(n8, n8) = all_0_3_3
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 56.58/22.05 | (1158) all_0_3_3 = n16
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (690) with n6, n10, all_0_0_0, n16 and discharging atoms sum(n6, n10) = all_0_0_0, sum(n6, n10) = n16, yields:
% 56.58/22.05 | (1159) all_0_0_0 = n16
% 56.58/22.05 |
% 56.58/22.05 | Equations (1159,1158) can reduce 679 to:
% 56.58/22.05 | (1106) $false
% 56.58/22.05 |
% 56.58/22.05 |-The branch is then unsatisfiable
% 56.58/22.05 |-Branch two:
% 56.58/22.05 | (1503) ~ (all_0_11_11 = n3)
% 56.58/22.05 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.58/22.05 |
% 56.58/22.05 +-Applying beta-rule and splitting (1504), into two cases.
% 56.58/22.05 |-Branch one:
% 56.58/22.05 | (1505) all_0_11_11 = n2
% 56.58/22.05 |
% 56.58/22.05 | From (1505) and (559) follows:
% 56.58/22.05 | (1506) pred(n2) = all_0_9_9
% 56.58/22.05 |
% 56.58/22.05 | From (1505) and (992) follows:
% 56.58/22.05 | (1507) succ(n2) = all_0_5_5
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 56.58/22.05 | (1508) all_0_9_9 = n1
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 56.58/22.05 | (1509) all_0_5_5 = n3
% 56.58/22.05 |
% 56.58/22.05 | From (1508)(1509) and (538) follows:
% 56.58/22.05 | (1510) sum(n1, n3) = all_0_2_2
% 56.58/22.05 |
% 56.58/22.05 | From (1508) and (13166) follows:
% 56.58/22.05 | (13237) sum(n1, n6) = all_0_7_7
% 56.58/22.05 |
% 56.58/22.05 | From (1509) and (13164) follows:
% 56.58/22.05 | (13238) sum(n4, n3) = all_0_4_4
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (690) with n4, n3, all_0_4_4, n7 and discharging atoms sum(n4, n3) = all_0_4_4, sum(n4, n3) = n7, yields:
% 56.58/22.05 | (1405) all_0_4_4 = n7
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (690) with n1, n6, all_0_7_7, n7 and discharging atoms sum(n1, n6) = all_0_7_7, sum(n1, n6) = n7, yields:
% 56.58/22.05 | (1407) all_0_7_7 = n7
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 56.58/22.05 | (1280) all_0_2_2 = n4
% 56.58/22.05 |
% 56.58/22.05 | From (1280) and (6952) follows:
% 56.58/22.05 | (7026) sum(n4, n10) = all_0_0_0
% 56.58/22.05 |
% 56.58/22.05 | From (1407)(1405) and (590) follows:
% 56.58/22.05 | (1409) sum(n7, n7) = all_0_3_3
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 56.58/22.05 | (1176) all_0_3_3 = n14
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (690) with n4, n10, all_0_0_0, n14 and discharging atoms sum(n4, n10) = all_0_0_0, sum(n4, n10) = n14, yields:
% 56.58/22.05 | (1177) all_0_0_0 = n14
% 56.58/22.05 |
% 56.58/22.05 | Equations (1177,1176) can reduce 679 to:
% 56.58/22.05 | (1106) $false
% 56.58/22.05 |
% 56.58/22.05 |-The branch is then unsatisfiable
% 56.58/22.05 |-Branch two:
% 56.58/22.05 | (1521) ~ (all_0_11_11 = n2)
% 56.58/22.05 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 56.58/22.05 |
% 56.58/22.05 +-Applying beta-rule and splitting (1522), into two cases.
% 56.58/22.05 |-Branch one:
% 56.58/22.05 | (1523) all_0_11_11 = n1
% 56.58/22.05 |
% 56.58/22.05 | From (1523) and (559) follows:
% 56.58/22.05 | (1524) pred(n1) = all_0_9_9
% 56.58/22.05 |
% 56.58/22.05 | From (1523) and (992) follows:
% 56.58/22.05 | (1525) succ(n1) = all_0_5_5
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 56.58/22.05 | (1526) all_0_9_9 = n0
% 56.58/22.05 |
% 56.58/22.05 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 56.58/22.05 | (1527) all_0_5_5 = n2
% 56.58/22.05 |
% 56.58/22.05 | From (1526)(1527) and (538) follows:
% 56.58/22.05 | (1528) sum(n0, n2) = all_0_2_2
% 56.58/22.05 |
% 56.58/22.05 | From (1526) and (13166) follows:
% 56.58/22.06 | (13255) sum(n0, n6) = all_0_7_7
% 56.58/22.06 |
% 56.58/22.06 | From (1527) and (13164) follows:
% 56.58/22.06 | (13256) sum(n4, n2) = all_0_4_4
% 56.58/22.06 |
% 56.58/22.06 | Instantiating formula (690) with n4, n2, all_0_4_4, n6 and discharging atoms sum(n4, n2) = all_0_4_4, sum(n4, n2) = n6, yields:
% 56.58/22.06 | (1423) all_0_4_4 = n6
% 56.58/22.06 |
% 56.58/22.06 | Instantiating formula (690) with n0, n6, all_0_7_7, n6 and discharging atoms sum(n0, n6) = all_0_7_7, sum(n0, n6) = n6, yields:
% 56.58/22.06 | (1425) all_0_7_7 = n6
% 56.58/22.06 |
% 56.58/22.06 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 56.58/22.06 | (1298) all_0_2_2 = n2
% 56.58/22.06 |
% 56.58/22.06 | From (1298) and (6952) follows:
% 56.58/22.06 | (7044) sum(n2, n10) = all_0_0_0
% 56.58/22.06 |
% 56.58/22.06 | From (1425)(1423) and (590) follows:
% 56.58/22.06 | (1427) sum(n6, n6) = all_0_3_3
% 56.58/22.06 |
% 56.58/22.06 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 56.58/22.06 | (1194) all_0_3_3 = n12
% 56.58/22.06 |
% 56.58/22.06 | Instantiating formula (690) with n2, n10, all_0_0_0, n12 and discharging atoms sum(n2, n10) = all_0_0_0, sum(n2, n10) = n12, yields:
% 56.58/22.06 | (1195) all_0_0_0 = n12
% 56.58/22.06 |
% 56.58/22.06 | Equations (1195,1194) can reduce 679 to:
% 56.58/22.06 | (1106) $false
% 56.58/22.06 |
% 56.58/22.06 |-The branch is then unsatisfiable
% 56.58/22.06 |-Branch two:
% 56.58/22.06 | (1540) ~ (all_0_11_11 = n1)
% 56.58/22.06 | (1541) all_0_11_11 = n0
% 56.58/22.06 |
% 56.58/22.06 | From (1541) and (559) follows:
% 56.58/22.06 | (1542) pred(n0) = all_0_9_9
% 56.58/22.06 |
% 56.58/22.06 | From (1541) and (992) follows:
% 56.58/22.06 | (1543) succ(n0) = all_0_5_5
% 56.58/22.06 |
% 56.58/22.06 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 56.58/22.06 | (1544) all_0_9_9 = n25
% 56.58/22.06 |
% 56.58/22.06 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 56.58/22.06 | (1545) all_0_5_5 = n1
% 56.58/22.06 |
% 56.58/22.06 | From (1544)(1545) and (538) follows:
% 56.58/22.06 | (1546) sum(n25, n1) = all_0_2_2
% 56.58/22.06 |
% 56.58/22.06 | From (1544) and (13166) follows:
% 56.58/22.06 | (13272) sum(n25, n6) = all_0_7_7
% 56.58/22.06 |
% 56.58/22.06 | From (1545) and (13164) follows:
% 56.58/22.06 | (13273) sum(n4, n1) = all_0_4_4
% 56.58/22.06 |
% 56.58/22.06 | Instantiating formula (690) with n25, n6, all_0_7_7, n5 and discharging atoms sum(n25, n6) = all_0_7_7, sum(n25, n6) = n5, yields:
% 56.58/22.06 | (1443) all_0_7_7 = n5
% 56.58/22.06 |
% 56.58/22.06 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 56.58/22.06 | (1316) all_0_2_2 = n0
% 56.58/22.06 |
% 56.58/22.06 | Instantiating formula (690) with n4, n1, all_0_4_4, n5 and discharging atoms sum(n4, n1) = all_0_4_4, sum(n4, n1) = n5, yields:
% 56.58/22.06 | (1441) all_0_4_4 = n5
% 56.58/22.06 |
% 56.58/22.06 | From (1316) and (6952) follows:
% 56.58/22.06 | (7062) sum(n0, n10) = all_0_0_0
% 56.58/22.06 |
% 56.58/22.06 | From (1443)(1441) and (590) follows:
% 56.58/22.06 | (1445) sum(n5, n5) = all_0_3_3
% 56.58/22.06 |
% 56.58/22.06 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 56.58/22.06 | (1212) all_0_3_3 = n10
% 56.58/22.06 |
% 56.58/22.06 | Instantiating formula (690) with n0, n10, all_0_0_0, n10 and discharging atoms sum(n0, n10) = all_0_0_0, sum(n0, n10) = n10, yields:
% 56.58/22.06 | (1213) all_0_0_0 = n10
% 56.58/22.06 |
% 56.58/22.06 | Equations (1213,1212) can reduce 679 to:
% 56.58/22.06 | (1106) $false
% 56.58/22.06 |
% 56.58/22.06 |-The branch is then unsatisfiable
% 56.58/22.06 |-Branch two:
% 56.58/22.06 | (1928) ~ (all_0_10_10 = n5)
% 56.58/22.06 | (1929) 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
% 56.58/22.06 |
% 56.58/22.06 +-Applying beta-rule and splitting (1450), into two cases.
% 56.58/22.06 |-Branch one:
% 56.58/22.06 | (1451) all_0_11_11 = n5
% 56.58/22.06 |
% 56.58/22.06 | From (1451) and (559) follows:
% 56.58/22.06 | (1452) pred(n5) = all_0_9_9
% 56.58/22.06 |
% 56.58/22.06 | From (1451) and (992) follows:
% 56.58/22.06 | (1453) succ(n5) = all_0_5_5
% 56.58/22.06 |
% 56.58/22.06 | Instantiating formula (500) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 56.58/22.06 | (1454) all_0_9_9 = n4
% 56.58/22.06 |
% 56.58/22.06 | Instantiating formula (617) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 56.58/22.06 | (1455) all_0_5_5 = n6
% 56.58/22.06 |
% 56.58/22.06 | From (1455) and (541) follows:
% 56.58/22.06 | (13289) sum(all_0_6_6, n6) = all_0_4_4
% 56.58/22.06 |
% 56.58/22.06 | From (1454)(1455) and (538) follows:
% 56.58/22.06 | (1456) sum(n4, n6) = all_0_2_2
% 56.58/22.06 |
% 56.58/22.06 | From (1454) and (427) follows:
% 56.58/22.06 | (13291) sum(n4, all_0_8_8) = all_0_7_7
% 56.58/22.06 |
% 56.58/22.06 | Instantiating formula (690) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 56.58/22.06 | (1226) all_0_2_2 = n10
% 56.58/22.06 |
% 56.58/22.06 | From (1226) and (630) follows:
% 56.58/22.06 | (7311) sum(n10, all_0_1_1) = all_0_0_0
% 56.58/22.06 |
% 56.58/22.06 +-Applying beta-rule and splitting (1929), into two cases.
% 56.58/22.06 |-Branch one:
% 56.58/22.06 | (1930) all_0_10_10 = n4
% 56.58/22.06 |
% 56.58/22.06 | From (1930) and (292) follows:
% 56.58/22.06 | (1931) pred(n4) = all_0_6_6
% 56.58/22.06 |
% 56.58/22.06 | From (1930) and (760) follows:
% 56.58/22.06 | (1932) succ(n4) = all_0_8_8
% 56.58/22.06 |
% 56.58/22.06 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 56.58/22.06 | (1933) all_0_6_6 = n3
% 56.58/22.06 |
% 56.58/22.06 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 56.58/22.06 | (1934) all_0_8_8 = n5
% 56.58/22.06 |
% 56.58/22.06 | From (1933)(1934) and (411) follows:
% 56.58/22.06 | (1935) sum(n3, n5) = all_0_1_1
% 56.58/22.06 |
% 56.58/22.06 | From (1933) and (13289) follows:
% 56.58/22.06 | (13300) sum(n3, n6) = all_0_4_4
% 56.58/22.06 |
% 56.58/22.06 | From (1934) and (13291) follows:
% 56.58/22.07 | (13301) sum(n4, n5) = all_0_7_7
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (690) with n4, n5, all_0_7_7, n9 and discharging atoms sum(n4, n5) = all_0_7_7, sum(n4, n5) = n9, yields:
% 56.58/22.07 | (1371) all_0_7_7 = n9
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (690) with n3, n6, all_0_4_4, n9 and discharging atoms sum(n3, n6) = all_0_4_4, sum(n3, n6) = n9, yields:
% 56.58/22.07 | (1369) all_0_4_4 = n9
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 56.58/22.07 | (1705) all_0_1_1 = n8
% 56.58/22.07 |
% 56.58/22.07 | From (1371)(1369) and (590) follows:
% 56.58/22.07 | (1373) sum(n9, n9) = all_0_3_3
% 56.58/22.07 |
% 56.58/22.07 | From (1705) and (7311) follows:
% 56.58/22.07 | (7324) sum(n10, n8) = all_0_0_0
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (690) with n10, n8, all_0_0_0, n18 and discharging atoms sum(n10, n8) = all_0_0_0, sum(n10, n8) = n18, yields:
% 56.58/22.07 | (1141) all_0_0_0 = n18
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (690) with n9, n9, all_0_3_3, n18 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n18, yields:
% 56.58/22.07 | (1140) all_0_3_3 = n18
% 56.58/22.07 |
% 56.58/22.07 | Equations (1141,1140) can reduce 679 to:
% 56.58/22.07 | (1106) $false
% 56.58/22.07 |
% 56.58/22.07 |-The branch is then unsatisfiable
% 56.58/22.07 |-Branch two:
% 56.58/22.07 | (1946) ~ (all_0_10_10 = n4)
% 56.58/22.07 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.58/22.07 |
% 56.58/22.07 +-Applying beta-rule and splitting (1947), into two cases.
% 56.58/22.07 |-Branch one:
% 56.58/22.07 | (1948) all_0_10_10 = n3
% 56.58/22.07 |
% 56.58/22.07 | From (1948) and (292) follows:
% 56.58/22.07 | (1949) pred(n3) = all_0_6_6
% 56.58/22.07 |
% 56.58/22.07 | From (1948) and (760) follows:
% 56.58/22.07 | (1950) succ(n3) = all_0_8_8
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 56.58/22.07 | (1951) all_0_6_6 = n2
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 56.58/22.07 | (1952) all_0_8_8 = n4
% 56.58/22.07 |
% 56.58/22.07 | From (1951)(1952) and (411) follows:
% 56.58/22.07 | (1953) sum(n2, n4) = all_0_1_1
% 56.58/22.07 |
% 56.58/22.07 | From (1951) and (13289) follows:
% 56.58/22.07 | (13318) sum(n2, n6) = all_0_4_4
% 56.58/22.07 |
% 56.58/22.07 | From (1952) and (13291) follows:
% 56.58/22.07 | (13319) sum(n4, n4) = all_0_7_7
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (690) with n4, n4, all_0_7_7, n8 and discharging atoms sum(n4, n4) = all_0_7_7, sum(n4, n4) = n8, yields:
% 56.58/22.07 | (1389) all_0_7_7 = n8
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (690) with n2, n6, all_0_4_4, n8 and discharging atoms sum(n2, n6) = all_0_4_4, sum(n2, n6) = n8, yields:
% 56.58/22.07 | (1387) all_0_4_4 = n8
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 56.58/22.07 | (1723) all_0_1_1 = n6
% 56.58/22.07 |
% 56.58/22.07 | From (1389)(1387) and (590) follows:
% 56.58/22.07 | (1391) sum(n8, n8) = all_0_3_3
% 56.58/22.07 |
% 56.58/22.07 | From (1723) and (7311) follows:
% 56.58/22.07 | (7342) sum(n10, n6) = all_0_0_0
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (690) with n10, n6, all_0_0_0, n16 and discharging atoms sum(n10, n6) = all_0_0_0, sum(n10, n6) = n16, yields:
% 56.58/22.07 | (1159) all_0_0_0 = n16
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (690) with n8, n8, all_0_3_3, n16 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n16, yields:
% 56.58/22.07 | (1158) all_0_3_3 = n16
% 56.58/22.07 |
% 56.58/22.07 | Equations (1159,1158) can reduce 679 to:
% 56.58/22.07 | (1106) $false
% 56.58/22.07 |
% 56.58/22.07 |-The branch is then unsatisfiable
% 56.58/22.07 |-Branch two:
% 56.58/22.07 | (1964) ~ (all_0_10_10 = n3)
% 56.58/22.07 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.58/22.07 |
% 56.58/22.07 +-Applying beta-rule and splitting (1965), into two cases.
% 56.58/22.07 |-Branch one:
% 56.58/22.07 | (1966) all_0_10_10 = n2
% 56.58/22.07 |
% 56.58/22.07 | From (1966) and (292) follows:
% 56.58/22.07 | (1967) pred(n2) = all_0_6_6
% 56.58/22.07 |
% 56.58/22.07 | From (1966) and (760) follows:
% 56.58/22.07 | (1968) succ(n2) = all_0_8_8
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 56.58/22.07 | (1969) all_0_6_6 = n1
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 56.58/22.07 | (1970) all_0_8_8 = n3
% 56.58/22.07 |
% 56.58/22.07 | From (1969)(1970) and (411) follows:
% 56.58/22.07 | (1971) sum(n1, n3) = all_0_1_1
% 56.58/22.07 |
% 56.58/22.07 | From (1969) and (13289) follows:
% 56.58/22.07 | (13336) sum(n1, n6) = all_0_4_4
% 56.58/22.07 |
% 56.58/22.07 | From (1970) and (13291) follows:
% 56.58/22.07 | (13337) sum(n4, n3) = all_0_7_7
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (690) with n4, n3, all_0_7_7, n7 and discharging atoms sum(n4, n3) = all_0_7_7, sum(n4, n3) = n7, yields:
% 56.58/22.07 | (1407) all_0_7_7 = n7
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (690) with n1, n6, all_0_4_4, n7 and discharging atoms sum(n1, n6) = all_0_4_4, sum(n1, n6) = n7, yields:
% 56.58/22.07 | (1405) all_0_4_4 = n7
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 56.58/22.07 | (1741) all_0_1_1 = n4
% 56.58/22.07 |
% 56.58/22.07 | From (1407)(1405) and (590) follows:
% 56.58/22.07 | (1409) sum(n7, n7) = all_0_3_3
% 56.58/22.07 |
% 56.58/22.07 | From (1741) and (7311) follows:
% 56.58/22.07 | (7360) sum(n10, n4) = all_0_0_0
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (690) with n10, n4, all_0_0_0, n14 and discharging atoms sum(n10, n4) = all_0_0_0, sum(n10, n4) = n14, yields:
% 56.58/22.07 | (1177) all_0_0_0 = n14
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 56.58/22.07 | (1176) all_0_3_3 = n14
% 56.58/22.07 |
% 56.58/22.07 | Equations (1177,1176) can reduce 679 to:
% 56.58/22.07 | (1106) $false
% 56.58/22.07 |
% 56.58/22.07 |-The branch is then unsatisfiable
% 56.58/22.07 |-Branch two:
% 56.58/22.07 | (1982) ~ (all_0_10_10 = n2)
% 56.58/22.07 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 56.58/22.07 |
% 56.58/22.07 +-Applying beta-rule and splitting (1983), into two cases.
% 56.58/22.07 |-Branch one:
% 56.58/22.07 | (1984) all_0_10_10 = n1
% 56.58/22.07 |
% 56.58/22.07 | From (1984) and (292) follows:
% 56.58/22.07 | (1985) pred(n1) = all_0_6_6
% 56.58/22.07 |
% 56.58/22.07 | From (1984) and (760) follows:
% 56.58/22.07 | (1986) succ(n1) = all_0_8_8
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 56.58/22.07 | (1987) all_0_6_6 = n0
% 56.58/22.07 |
% 56.58/22.07 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 56.58/22.07 | (1988) all_0_8_8 = n2
% 56.58/22.07 |
% 56.58/22.07 | From (1987)(1988) and (411) follows:
% 56.58/22.07 | (1989) sum(n0, n2) = all_0_1_1
% 56.58/22.07 |
% 56.58/22.07 | From (1987) and (13289) follows:
% 56.58/22.08 | (13354) sum(n0, n6) = all_0_4_4
% 56.58/22.08 |
% 56.58/22.08 | From (1988) and (13291) follows:
% 56.58/22.08 | (13355) sum(n4, n2) = all_0_7_7
% 56.58/22.08 |
% 56.58/22.08 | Instantiating formula (690) with n4, n2, all_0_7_7, n6 and discharging atoms sum(n4, n2) = all_0_7_7, sum(n4, n2) = n6, yields:
% 56.58/22.08 | (1425) all_0_7_7 = n6
% 56.58/22.08 |
% 56.58/22.08 | Instantiating formula (690) with n0, n6, all_0_4_4, n6 and discharging atoms sum(n0, n6) = all_0_4_4, sum(n0, n6) = n6, yields:
% 56.58/22.08 | (1423) all_0_4_4 = n6
% 56.58/22.08 |
% 56.58/22.08 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 56.58/22.08 | (1759) all_0_1_1 = n2
% 56.58/22.08 |
% 56.58/22.08 | From (1425)(1423) and (590) follows:
% 56.58/22.08 | (1427) sum(n6, n6) = all_0_3_3
% 56.58/22.08 |
% 56.58/22.08 | From (1759) and (7311) follows:
% 56.58/22.08 | (7378) sum(n10, n2) = all_0_0_0
% 56.58/22.08 |
% 56.58/22.08 | Instantiating formula (690) with n10, n2, all_0_0_0, n12 and discharging atoms sum(n10, n2) = all_0_0_0, sum(n10, n2) = n12, yields:
% 56.58/22.08 | (1195) all_0_0_0 = n12
% 56.58/22.08 |
% 56.58/22.08 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 56.58/22.08 | (1194) all_0_3_3 = n12
% 56.58/22.08 |
% 56.58/22.08 | Equations (1195,1194) can reduce 679 to:
% 56.58/22.08 | (1106) $false
% 56.58/22.08 |
% 56.58/22.08 |-The branch is then unsatisfiable
% 56.58/22.08 |-Branch two:
% 56.58/22.08 | (2002) ~ (all_0_10_10 = n1)
% 56.58/22.08 | (2003) all_0_10_10 = n0
% 56.58/22.08 |
% 56.58/22.08 | From (2003) and (292) follows:
% 56.58/22.08 | (2004) pred(n0) = all_0_6_6
% 56.58/22.08 |
% 56.58/22.08 | From (2003) and (760) follows:
% 56.58/22.08 | (2005) succ(n0) = all_0_8_8
% 56.58/22.08 |
% 56.58/22.08 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 56.58/22.08 | (2006) all_0_6_6 = n25
% 56.58/22.08 |
% 56.58/22.08 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 56.58/22.08 | (2007) all_0_8_8 = n1
% 56.58/22.08 |
% 56.58/22.08 | From (2006)(2007) and (411) follows:
% 56.58/22.08 | (2008) sum(n25, n1) = all_0_1_1
% 56.58/22.08 |
% 56.58/22.08 | From (2006) and (13289) follows:
% 56.58/22.08 | (13371) sum(n25, n6) = all_0_4_4
% 56.58/22.08 |
% 56.58/22.08 | From (2007) and (13291) follows:
% 56.58/22.08 | (13372) sum(n4, n1) = all_0_7_7
% 56.58/22.08 |
% 56.58/22.08 | Instantiating formula (690) with n25, n6, all_0_4_4, n5 and discharging atoms sum(n25, n6) = all_0_4_4, sum(n25, n6) = n5, yields:
% 56.58/22.08 | (1441) all_0_4_4 = n5
% 56.58/22.08 |
% 56.58/22.08 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 56.58/22.08 | (1777) all_0_1_1 = n0
% 56.58/22.08 |
% 56.58/22.08 | Instantiating formula (690) with n4, n1, all_0_7_7, n5 and discharging atoms sum(n4, n1) = all_0_7_7, sum(n4, n1) = n5, yields:
% 56.58/22.08 | (1443) all_0_7_7 = n5
% 56.58/22.08 |
% 56.58/22.08 | From (1443)(1441) and (590) follows:
% 56.58/22.08 | (1445) sum(n5, n5) = all_0_3_3
% 56.58/22.08 |
% 56.58/22.08 | From (1777) and (7311) follows:
% 56.58/22.08 | (7396) sum(n10, n0) = all_0_0_0
% 56.58/22.08 |
% 56.58/22.08 | Instantiating formula (690) with n10, n0, all_0_0_0, n10 and discharging atoms sum(n10, n0) = all_0_0_0, sum(n10, n0) = n10, yields:
% 56.58/22.08 | (1213) all_0_0_0 = n10
% 56.58/22.08 |
% 56.58/22.08 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 56.58/22.08 | (1212) all_0_3_3 = n10
% 56.58/22.08 |
% 56.58/22.08 | Equations (1213,1212) can reduce 679 to:
% 56.58/22.08 | (1106) $false
% 56.58/22.08 |
% 56.58/22.08 |-The branch is then unsatisfiable
% 56.58/22.08 |-Branch two:
% 56.58/22.08 | (1467) ~ (all_0_11_11 = n5)
% 56.58/22.08 | (1468) 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
% 56.58/22.08 |
% 56.58/22.08 +-Applying beta-rule and splitting (1929), into two cases.
% 56.58/22.08 |-Branch one:
% 56.58/22.08 | (1930) all_0_10_10 = n4
% 56.58/22.08 |
% 56.58/22.08 | From (1930) and (292) follows:
% 56.58/22.08 | (1931) pred(n4) = all_0_6_6
% 56.58/22.08 |
% 56.58/22.08 | From (1930) and (760) follows:
% 56.58/22.08 | (1932) succ(n4) = all_0_8_8
% 56.58/22.08 |
% 56.58/22.08 | Instantiating formula (500) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 56.58/22.08 | (1933) all_0_6_6 = n3
% 56.58/22.08 |
% 56.58/22.08 | Instantiating formula (617) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 56.58/22.08 | (1934) all_0_8_8 = n5
% 56.58/22.08 |
% 56.58/22.08 | From (1933) and (1931) follows:
% 56.58/22.08 | (423) pred(n4) = n3
% 56.58/22.08 |
% 56.58/22.08 | From (1934) and (1932) follows:
% 56.58/22.08 | (796) succ(n4) = n5
% 56.58/22.08 |
% 56.58/22.08 | From (1933) and (541) follows:
% 56.58/22.08 | (13390) sum(n3, all_0_5_5) = all_0_4_4
% 56.58/22.08 |
% 56.58/22.08 | From (1933)(1934) and (411) follows:
% 56.58/22.08 | (1935) sum(n3, n5) = all_0_1_1
% 56.58/22.08 |
% 56.58/22.08 | From (1934) and (427) follows:
% 56.58/22.08 | (13392) sum(all_0_9_9, n5) = all_0_7_7
% 56.58/22.08 |
% 56.58/22.08 | Instantiating formula (690) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 56.58/22.08 | (1705) all_0_1_1 = n8
% 56.58/22.08 |
% 56.58/22.08 | From (1705) and (630) follows:
% 56.58/22.08 | (7646) sum(all_0_2_2, n8) = all_0_0_0
% 56.58/22.08 |
% 56.58/22.08 | From (1705) and (1935) follows:
% 56.58/22.08 | (32) sum(n3, n5) = n8
% 56.58/22.08 |
% 56.58/22.08 +-Applying beta-rule and splitting (1468), into two cases.
% 56.58/22.08 |-Branch one:
% 56.58/22.08 | (1469) all_0_11_11 = n4
% 56.58/22.08 |
% 56.58/22.08 | From (1469) and (559) follows:
% 56.58/22.08 | (1470) pred(n4) = all_0_9_9
% 56.58/22.08 |
% 56.58/22.08 | From (1469) and (992) follows:
% 56.58/22.08 | (1471) succ(n4) = all_0_5_5
% 56.58/22.08 |
% 56.58/22.08 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 56.58/22.08 | (1472) all_0_9_9 = n3
% 56.58/22.08 |
% 56.58/22.08 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 56.58/22.08 | (1473) all_0_5_5 = n5
% 56.58/22.08 |
% 56.58/22.08 | From (1472)(1473) and (538) follows:
% 56.58/22.08 | (1474) sum(n3, n5) = all_0_2_2
% 56.58/22.08 |
% 56.58/22.08 | From (1472) and (13392) follows:
% 56.58/22.08 | (13402) sum(n3, n5) = all_0_7_7
% 56.58/22.08 |
% 56.58/22.08 | From (1473) and (13390) follows:
% 56.58/22.09 | (13403) sum(n3, n5) = all_0_4_4
% 56.58/22.09 |
% 56.58/22.09 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 56.58/22.09 | (1244) all_0_2_2 = n8
% 56.58/22.09 |
% 56.58/22.09 | Instantiating formula (690) 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:
% 56.58/22.09 | (1093) all_0_2_2 = all_0_4_4
% 56.58/22.09 |
% 56.58/22.09 | Instantiating formula (690) 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:
% 56.58/22.09 | (1094) all_0_2_2 = all_0_7_7
% 56.58/22.09 |
% 56.58/22.09 | Combining equations (1094,1093) yields a new equation:
% 56.58/22.09 | (1095) all_0_4_4 = all_0_7_7
% 56.58/22.09 |
% 56.58/22.09 | Combining equations (1244,1093) yields a new equation:
% 56.58/22.09 | (1387) all_0_4_4 = n8
% 56.58/22.09 |
% 56.58/22.09 | Combining equations (1387,1095) yields a new equation:
% 56.58/22.09 | (1389) all_0_7_7 = n8
% 56.58/22.09 |
% 56.58/22.09 | Combining equations (1389,1095) yields a new equation:
% 56.58/22.09 | (1387) all_0_4_4 = n8
% 56.58/22.09 |
% 56.58/22.09 | Combining equations (1387,1093) yields a new equation:
% 56.58/22.09 | (1244) all_0_2_2 = n8
% 56.58/22.09 |
% 56.58/22.09 | From (1244) and (7646) follows:
% 56.58/22.09 | (7664) sum(n8, n8) = all_0_0_0
% 56.58/22.09 |
% 56.58/22.09 | From (1389)(1387) and (590) follows:
% 56.58/22.09 | (1391) sum(n8, n8) = all_0_3_3
% 56.58/22.09 |
% 56.58/22.09 | Instantiating formula (690) with n8, n8, all_0_0_0, n16 and discharging atoms sum(n8, n8) = all_0_0_0, sum(n8, n8) = n16, yields:
% 56.58/22.09 | (1159) all_0_0_0 = n16
% 56.58/22.09 |
% 56.58/22.09 | Instantiating formula (690) 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:
% 56.58/22.09 | (1103) all_0_0_0 = all_0_3_3
% 56.58/22.09 |
% 56.58/22.09 | Combining equations (1159,1103) yields a new equation:
% 56.58/22.09 | (1158) all_0_3_3 = n16
% 56.58/22.09 |
% 56.58/22.09 | Combining equations (1158,1103) yields a new equation:
% 56.58/22.09 | (1159) all_0_0_0 = n16
% 56.58/22.09 |
% 56.58/22.09 | Equations (1159,1158) can reduce 679 to:
% 56.58/22.09 | (1106) $false
% 56.58/22.09 |
% 56.58/22.09 |-The branch is then unsatisfiable
% 56.58/22.09 |-Branch two:
% 56.58/22.09 | (1485) ~ (all_0_11_11 = n4)
% 56.58/22.09 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.58/22.09 |
% 56.58/22.09 +-Applying beta-rule and splitting (1486), into two cases.
% 56.58/22.09 |-Branch one:
% 56.58/22.09 | (1487) all_0_11_11 = n3
% 56.58/22.09 |
% 56.58/22.09 | From (1487) and (559) follows:
% 56.58/22.09 | (1488) pred(n3) = all_0_9_9
% 56.58/22.09 |
% 56.58/22.09 | From (1487) and (992) follows:
% 56.58/22.09 | (1489) succ(n3) = all_0_5_5
% 56.58/22.09 |
% 56.58/22.09 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 56.58/22.09 | (1490) all_0_9_9 = n2
% 56.58/22.09 |
% 56.58/22.09 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 56.58/22.09 | (1491) all_0_5_5 = n4
% 56.58/22.09 |
% 56.58/22.09 | From (1490)(1491) and (538) follows:
% 56.58/22.09 | (1492) sum(n2, n4) = all_0_2_2
% 56.58/22.09 |
% 56.58/22.09 | From (1490) and (13392) follows:
% 56.58/22.09 | (13427) sum(n2, n5) = all_0_7_7
% 56.58/22.09 |
% 56.58/22.09 | From (1491) and (13390) follows:
% 56.58/22.09 | (13428) sum(n3, n4) = all_0_4_4
% 56.58/22.09 |
% 56.58/22.09 | Instantiating formula (690) with n3, n4, all_0_4_4, n7 and discharging atoms sum(n3, n4) = all_0_4_4, sum(n3, n4) = n7, yields:
% 56.58/22.09 | (1405) all_0_4_4 = n7
% 56.58/22.09 |
% 56.58/22.09 | Instantiating formula (690) with n2, n5, all_0_7_7, n7 and discharging atoms sum(n2, n5) = all_0_7_7, sum(n2, n5) = n7, yields:
% 56.58/22.09 | (1407) all_0_7_7 = n7
% 56.58/22.09 |
% 56.58/22.09 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 56.58/22.09 | (1262) all_0_2_2 = n6
% 56.58/22.09 |
% 56.58/22.09 | From (1262) and (7646) follows:
% 56.68/22.09 | (7684) sum(n6, n8) = all_0_0_0
% 56.68/22.09 |
% 56.68/22.09 | From (1407)(1405) and (590) follows:
% 56.68/22.09 | (1409) sum(n7, n7) = all_0_3_3
% 56.68/22.09 |
% 56.68/22.09 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 56.68/22.09 | (1176) all_0_3_3 = n14
% 56.68/22.09 |
% 56.68/22.09 | Instantiating formula (690) with n6, n8, all_0_0_0, n14 and discharging atoms sum(n6, n8) = all_0_0_0, sum(n6, n8) = n14, yields:
% 56.68/22.09 | (1177) all_0_0_0 = n14
% 56.68/22.09 |
% 56.68/22.09 | Equations (1177,1176) can reduce 679 to:
% 56.68/22.09 | (1106) $false
% 56.68/22.09 |
% 56.68/22.09 |-The branch is then unsatisfiable
% 56.68/22.09 |-Branch two:
% 56.68/22.09 | (1503) ~ (all_0_11_11 = n3)
% 56.68/22.09 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.68/22.09 |
% 56.68/22.09 +-Applying beta-rule and splitting (1504), into two cases.
% 56.68/22.09 |-Branch one:
% 56.68/22.09 | (1505) all_0_11_11 = n2
% 56.68/22.09 |
% 56.68/22.09 | From (1505) and (559) follows:
% 56.68/22.09 | (1506) pred(n2) = all_0_9_9
% 56.68/22.09 |
% 56.68/22.09 | From (1505) and (992) follows:
% 56.68/22.09 | (1507) succ(n2) = all_0_5_5
% 56.68/22.09 |
% 56.68/22.09 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 56.68/22.09 | (1508) all_0_9_9 = n1
% 56.68/22.09 |
% 56.68/22.09 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 56.68/22.09 | (1509) all_0_5_5 = n3
% 56.68/22.09 |
% 56.68/22.09 | From (1508)(1509) and (538) follows:
% 56.68/22.09 | (1510) sum(n1, n3) = all_0_2_2
% 56.68/22.09 |
% 56.68/22.09 | From (1508) and (13392) follows:
% 56.68/22.09 | (13445) sum(n1, n5) = all_0_7_7
% 56.68/22.09 |
% 56.68/22.09 | From (1509) and (13390) follows:
% 56.68/22.09 | (13446) sum(n3, n3) = all_0_4_4
% 56.68/22.09 |
% 56.68/22.09 | Instantiating formula (690) with n3, n3, all_0_4_4, n6 and discharging atoms sum(n3, n3) = all_0_4_4, sum(n3, n3) = n6, yields:
% 56.68/22.09 | (1423) all_0_4_4 = n6
% 56.68/22.09 |
% 56.68/22.09 | Instantiating formula (690) with n1, n5, all_0_7_7, n6 and discharging atoms sum(n1, n5) = all_0_7_7, sum(n1, n5) = n6, yields:
% 56.68/22.09 | (1425) all_0_7_7 = n6
% 56.68/22.09 |
% 56.68/22.09 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 56.68/22.09 | (1280) all_0_2_2 = n4
% 56.68/22.09 |
% 56.68/22.09 | From (1280) and (7646) follows:
% 56.68/22.09 | (7702) sum(n4, n8) = all_0_0_0
% 56.68/22.09 |
% 56.68/22.09 | From (1425)(1423) and (590) follows:
% 56.68/22.09 | (1427) sum(n6, n6) = all_0_3_3
% 56.68/22.09 |
% 56.68/22.09 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 56.68/22.09 | (1194) all_0_3_3 = n12
% 56.68/22.09 |
% 56.68/22.09 | Instantiating formula (690) with n4, n8, all_0_0_0, n12 and discharging atoms sum(n4, n8) = all_0_0_0, sum(n4, n8) = n12, yields:
% 56.68/22.09 | (1195) all_0_0_0 = n12
% 56.68/22.09 |
% 56.68/22.09 | Equations (1195,1194) can reduce 679 to:
% 56.68/22.09 | (1106) $false
% 56.68/22.09 |
% 56.68/22.09 |-The branch is then unsatisfiable
% 56.68/22.09 |-Branch two:
% 56.68/22.09 | (1521) ~ (all_0_11_11 = n2)
% 56.68/22.09 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 56.68/22.09 |
% 56.68/22.09 +-Applying beta-rule and splitting (1522), into two cases.
% 56.68/22.09 |-Branch one:
% 56.68/22.09 | (1523) all_0_11_11 = n1
% 56.68/22.09 |
% 56.68/22.09 | From (1523) and (559) follows:
% 56.68/22.09 | (1524) pred(n1) = all_0_9_9
% 56.68/22.09 |
% 56.68/22.09 | From (1523) and (992) follows:
% 56.68/22.09 | (1525) succ(n1) = all_0_5_5
% 56.68/22.09 |
% 56.68/22.09 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 56.68/22.09 | (1526) all_0_9_9 = n0
% 56.68/22.09 |
% 56.68/22.09 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 56.68/22.09 | (1527) all_0_5_5 = n2
% 56.68/22.09 |
% 56.68/22.09 | From (1526)(1527) and (538) follows:
% 56.68/22.09 | (1528) sum(n0, n2) = all_0_2_2
% 56.68/22.09 |
% 56.68/22.09 | From (1526) and (13392) follows:
% 56.68/22.10 | (13463) sum(n0, n5) = all_0_7_7
% 56.68/22.10 |
% 56.68/22.10 | From (1527) and (13390) follows:
% 56.68/22.10 | (13464) sum(n3, n2) = all_0_4_4
% 56.68/22.10 |
% 56.68/22.10 | Instantiating formula (690) with n3, n2, all_0_4_4, n5 and discharging atoms sum(n3, n2) = all_0_4_4, sum(n3, n2) = n5, yields:
% 56.68/22.10 | (1441) all_0_4_4 = n5
% 56.68/22.10 |
% 56.68/22.10 | Instantiating formula (690) with n0, n5, all_0_7_7, n5 and discharging atoms sum(n0, n5) = all_0_7_7, sum(n0, n5) = n5, yields:
% 56.68/22.10 | (1443) all_0_7_7 = n5
% 56.68/22.10 |
% 56.68/22.10 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 56.68/22.10 | (1298) all_0_2_2 = n2
% 56.68/22.10 |
% 56.68/22.10 | From (1298) and (7646) follows:
% 56.68/22.10 | (7720) sum(n2, n8) = all_0_0_0
% 56.68/22.10 |
% 56.68/22.10 | From (1443)(1441) and (590) follows:
% 56.68/22.10 | (1445) sum(n5, n5) = all_0_3_3
% 56.68/22.10 |
% 56.68/22.10 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 56.68/22.10 | (1212) all_0_3_3 = n10
% 56.68/22.10 |
% 56.68/22.10 | Instantiating formula (690) with n2, n8, all_0_0_0, n10 and discharging atoms sum(n2, n8) = all_0_0_0, sum(n2, n8) = n10, yields:
% 56.68/22.10 | (1213) all_0_0_0 = n10
% 56.68/22.10 |
% 56.68/22.10 | Equations (1213,1212) can reduce 679 to:
% 56.68/22.10 | (1106) $false
% 56.68/22.10 |
% 56.68/22.10 |-The branch is then unsatisfiable
% 56.68/22.10 |-Branch two:
% 56.68/22.10 | (1540) ~ (all_0_11_11 = n1)
% 56.68/22.10 | (1541) all_0_11_11 = n0
% 56.68/22.10 |
% 56.68/22.10 | From (1541) and (559) follows:
% 56.68/22.10 | (1542) pred(n0) = all_0_9_9
% 56.68/22.10 |
% 56.68/22.10 | From (1541) and (992) follows:
% 56.68/22.10 | (1543) succ(n0) = all_0_5_5
% 56.68/22.10 |
% 56.68/22.10 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 56.68/22.10 | (1544) all_0_9_9 = n25
% 56.68/22.10 |
% 56.68/22.10 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 56.68/22.10 | (1545) all_0_5_5 = n1
% 56.68/22.10 |
% 56.68/22.10 | From (1544)(1545) and (538) follows:
% 56.68/22.10 | (1546) sum(n25, n1) = all_0_2_2
% 56.68/22.10 |
% 56.68/22.10 | From (1544) and (13392) follows:
% 56.68/22.10 | (13480) sum(n25, n5) = all_0_7_7
% 56.68/22.10 |
% 56.68/22.10 | From (1545) and (13390) follows:
% 56.68/22.10 | (13481) sum(n3, n1) = all_0_4_4
% 56.68/22.10 |
% 56.68/22.10 | Instantiating formula (690) with n25, n5, all_0_7_7, n4 and discharging atoms sum(n25, n5) = all_0_7_7, sum(n25, n5) = n4, yields:
% 56.68/22.10 | (1461) all_0_7_7 = n4
% 56.68/22.10 |
% 56.68/22.10 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 56.68/22.10 | (1316) all_0_2_2 = n0
% 56.68/22.10 |
% 56.68/22.10 | Instantiating formula (690) with n3, n1, all_0_4_4, n4 and discharging atoms sum(n3, n1) = all_0_4_4, sum(n3, n1) = n4, yields:
% 56.68/22.10 | (1459) all_0_4_4 = n4
% 56.68/22.10 |
% 56.68/22.10 | From (1316) and (7646) follows:
% 56.68/22.10 | (7738) sum(n0, n8) = all_0_0_0
% 56.68/22.10 |
% 56.68/22.10 | From (1461)(1459) and (590) follows:
% 56.68/22.10 | (1463) sum(n4, n4) = all_0_3_3
% 56.68/22.10 |
% 56.68/22.10 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 56.68/22.10 | (1230) all_0_3_3 = n8
% 56.68/22.10 |
% 56.68/22.10 | Instantiating formula (690) with n0, n8, all_0_0_0, n8 and discharging atoms sum(n0, n8) = all_0_0_0, sum(n0, n8) = n8, yields:
% 56.68/22.10 | (1231) all_0_0_0 = n8
% 56.68/22.10 |
% 56.68/22.10 | Equations (1231,1230) can reduce 679 to:
% 56.68/22.10 | (1106) $false
% 56.68/22.10 |
% 56.68/22.10 |-The branch is then unsatisfiable
% 56.68/22.10 |-Branch two:
% 56.68/22.10 | (1946) ~ (all_0_10_10 = n4)
% 56.68/22.10 | (1947) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.68/22.10 |
% 56.68/22.10 +-Applying beta-rule and splitting (1468), into two cases.
% 56.68/22.10 |-Branch one:
% 56.68/22.10 | (1469) all_0_11_11 = n4
% 56.68/22.10 |
% 56.68/22.10 | From (1469) and (559) follows:
% 56.68/22.10 | (1470) pred(n4) = all_0_9_9
% 56.68/22.10 |
% 56.68/22.10 | From (1469) and (992) follows:
% 56.68/22.10 | (1471) succ(n4) = all_0_5_5
% 56.68/22.10 |
% 56.68/22.10 | Instantiating formula (500) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 56.68/22.10 | (1472) all_0_9_9 = n3
% 56.68/22.10 |
% 56.68/22.10 | Instantiating formula (617) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 56.68/22.10 | (1473) all_0_5_5 = n5
% 56.68/22.10 |
% 56.68/22.10 | From (1473) and (541) follows:
% 56.68/22.10 | (13497) sum(all_0_6_6, n5) = all_0_4_4
% 56.68/22.10 |
% 56.68/22.10 | From (1472)(1473) and (538) follows:
% 56.68/22.10 | (1474) sum(n3, n5) = all_0_2_2
% 56.69/22.10 |
% 56.69/22.10 | From (1472) and (427) follows:
% 56.69/22.10 | (13499) sum(n3, all_0_8_8) = all_0_7_7
% 56.69/22.10 |
% 56.69/22.10 | Instantiating formula (690) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 56.69/22.10 | (1244) all_0_2_2 = n8
% 56.69/22.10 |
% 56.69/22.10 | From (1244) and (630) follows:
% 56.69/22.10 | (7987) sum(n8, all_0_1_1) = all_0_0_0
% 56.69/22.10 |
% 56.69/22.10 +-Applying beta-rule and splitting (1947), into two cases.
% 56.69/22.10 |-Branch one:
% 56.69/22.10 | (1948) all_0_10_10 = n3
% 56.69/22.10 |
% 56.69/22.10 | From (1948) and (292) follows:
% 56.69/22.10 | (1949) pred(n3) = all_0_6_6
% 56.69/22.10 |
% 56.69/22.10 | From (1948) and (760) follows:
% 56.69/22.10 | (1950) succ(n3) = all_0_8_8
% 56.69/22.10 |
% 56.69/22.10 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 56.69/22.10 | (1951) all_0_6_6 = n2
% 56.69/22.10 |
% 56.69/22.10 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 56.69/22.10 | (1952) all_0_8_8 = n4
% 56.69/22.10 |
% 56.69/22.10 | From (1951)(1952) and (411) follows:
% 56.69/22.10 | (1953) sum(n2, n4) = all_0_1_1
% 56.69/22.10 |
% 56.69/22.10 | From (1951) and (13497) follows:
% 56.69/22.10 | (13508) sum(n2, n5) = all_0_4_4
% 56.69/22.10 |
% 56.69/22.10 | From (1952) and (13499) follows:
% 56.69/22.11 | (13509) sum(n3, n4) = all_0_7_7
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (690) with n3, n4, all_0_7_7, n7 and discharging atoms sum(n3, n4) = all_0_7_7, sum(n3, n4) = n7, yields:
% 56.69/22.11 | (1407) all_0_7_7 = n7
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (690) with n2, n5, all_0_4_4, n7 and discharging atoms sum(n2, n5) = all_0_4_4, sum(n2, n5) = n7, yields:
% 56.69/22.11 | (1405) all_0_4_4 = n7
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 56.69/22.11 | (1723) all_0_1_1 = n6
% 56.69/22.11 |
% 56.69/22.11 | From (1407)(1405) and (590) follows:
% 56.69/22.11 | (1409) sum(n7, n7) = all_0_3_3
% 56.69/22.11 |
% 56.69/22.11 | From (1723) and (7987) follows:
% 56.69/22.11 | (8000) sum(n8, n6) = all_0_0_0
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (690) with n8, n6, all_0_0_0, n14 and discharging atoms sum(n8, n6) = all_0_0_0, sum(n8, n6) = n14, yields:
% 56.69/22.11 | (1177) all_0_0_0 = n14
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (690) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 56.69/22.11 | (1176) all_0_3_3 = n14
% 56.69/22.11 |
% 56.69/22.11 | Equations (1177,1176) can reduce 679 to:
% 56.69/22.11 | (1106) $false
% 56.69/22.11 |
% 56.69/22.11 |-The branch is then unsatisfiable
% 56.69/22.11 |-Branch two:
% 56.69/22.11 | (1964) ~ (all_0_10_10 = n3)
% 56.69/22.11 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.69/22.11 |
% 56.69/22.11 +-Applying beta-rule and splitting (1965), into two cases.
% 56.69/22.11 |-Branch one:
% 56.69/22.11 | (1966) all_0_10_10 = n2
% 56.69/22.11 |
% 56.69/22.11 | From (1966) and (292) follows:
% 56.69/22.11 | (1967) pred(n2) = all_0_6_6
% 56.69/22.11 |
% 56.69/22.11 | From (1966) and (760) follows:
% 56.69/22.11 | (1968) succ(n2) = all_0_8_8
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 56.69/22.11 | (1969) all_0_6_6 = n1
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 56.69/22.11 | (1970) all_0_8_8 = n3
% 56.69/22.11 |
% 56.69/22.11 | From (1969)(1970) and (411) follows:
% 56.69/22.11 | (1971) sum(n1, n3) = all_0_1_1
% 56.69/22.11 |
% 56.69/22.11 | From (1969) and (13497) follows:
% 56.69/22.11 | (13526) sum(n1, n5) = all_0_4_4
% 56.69/22.11 |
% 56.69/22.11 | From (1970) and (13499) follows:
% 56.69/22.11 | (13527) sum(n3, n3) = all_0_7_7
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (690) with n3, n3, all_0_7_7, n6 and discharging atoms sum(n3, n3) = all_0_7_7, sum(n3, n3) = n6, yields:
% 56.69/22.11 | (1425) all_0_7_7 = n6
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (690) with n1, n5, all_0_4_4, n6 and discharging atoms sum(n1, n5) = all_0_4_4, sum(n1, n5) = n6, yields:
% 56.69/22.11 | (1423) all_0_4_4 = n6
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 56.69/22.11 | (1741) all_0_1_1 = n4
% 56.69/22.11 |
% 56.69/22.11 | From (1425)(1423) and (590) follows:
% 56.69/22.11 | (1427) sum(n6, n6) = all_0_3_3
% 56.69/22.11 |
% 56.69/22.11 | From (1741) and (7987) follows:
% 56.69/22.11 | (8018) sum(n8, n4) = all_0_0_0
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (690) with n8, n4, all_0_0_0, n12 and discharging atoms sum(n8, n4) = all_0_0_0, sum(n8, n4) = n12, yields:
% 56.69/22.11 | (1195) all_0_0_0 = n12
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (690) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 56.69/22.11 | (1194) all_0_3_3 = n12
% 56.69/22.11 |
% 56.69/22.11 | Equations (1195,1194) can reduce 679 to:
% 56.69/22.11 | (1106) $false
% 56.69/22.11 |
% 56.69/22.11 |-The branch is then unsatisfiable
% 56.69/22.11 |-Branch two:
% 56.69/22.11 | (1982) ~ (all_0_10_10 = n2)
% 56.69/22.11 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 56.69/22.11 |
% 56.69/22.11 +-Applying beta-rule and splitting (1983), into two cases.
% 56.69/22.11 |-Branch one:
% 56.69/22.11 | (1984) all_0_10_10 = n1
% 56.69/22.11 |
% 56.69/22.11 | From (1984) and (292) follows:
% 56.69/22.11 | (1985) pred(n1) = all_0_6_6
% 56.69/22.11 |
% 56.69/22.11 | From (1984) and (760) follows:
% 56.69/22.11 | (1986) succ(n1) = all_0_8_8
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 56.69/22.11 | (1987) all_0_6_6 = n0
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 56.69/22.11 | (1988) all_0_8_8 = n2
% 56.69/22.11 |
% 56.69/22.11 | From (1987)(1988) and (411) follows:
% 56.69/22.11 | (1989) sum(n0, n2) = all_0_1_1
% 56.69/22.11 |
% 56.69/22.11 | From (1987) and (13497) follows:
% 56.69/22.11 | (13544) sum(n0, n5) = all_0_4_4
% 56.69/22.11 |
% 56.69/22.11 | From (1988) and (13499) follows:
% 56.69/22.11 | (13545) sum(n3, n2) = all_0_7_7
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (690) with n3, n2, all_0_7_7, n5 and discharging atoms sum(n3, n2) = all_0_7_7, sum(n3, n2) = n5, yields:
% 56.69/22.11 | (1443) all_0_7_7 = n5
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (690) with n0, n5, all_0_4_4, n5 and discharging atoms sum(n0, n5) = all_0_4_4, sum(n0, n5) = n5, yields:
% 56.69/22.11 | (1441) all_0_4_4 = n5
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 56.69/22.11 | (1759) all_0_1_1 = n2
% 56.69/22.11 |
% 56.69/22.11 | From (1443)(1441) and (590) follows:
% 56.69/22.11 | (1445) sum(n5, n5) = all_0_3_3
% 56.69/22.11 |
% 56.69/22.11 | From (1759) and (7987) follows:
% 56.69/22.11 | (8036) sum(n8, n2) = all_0_0_0
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (690) with n8, n2, all_0_0_0, n10 and discharging atoms sum(n8, n2) = all_0_0_0, sum(n8, n2) = n10, yields:
% 56.69/22.11 | (1213) all_0_0_0 = n10
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 56.69/22.11 | (1212) all_0_3_3 = n10
% 56.69/22.11 |
% 56.69/22.11 | Equations (1213,1212) can reduce 679 to:
% 56.69/22.11 | (1106) $false
% 56.69/22.11 |
% 56.69/22.11 |-The branch is then unsatisfiable
% 56.69/22.11 |-Branch two:
% 56.69/22.11 | (2002) ~ (all_0_10_10 = n1)
% 56.69/22.11 | (2003) all_0_10_10 = n0
% 56.69/22.11 |
% 56.69/22.11 | From (2003) and (292) follows:
% 56.69/22.11 | (2004) pred(n0) = all_0_6_6
% 56.69/22.11 |
% 56.69/22.11 | From (2003) and (760) follows:
% 56.69/22.11 | (2005) succ(n0) = all_0_8_8
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 56.69/22.11 | (2006) all_0_6_6 = n25
% 56.69/22.11 |
% 56.69/22.11 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 56.69/22.11 | (2007) all_0_8_8 = n1
% 56.69/22.11 |
% 56.69/22.11 | From (2006)(2007) and (411) follows:
% 56.69/22.12 | (2008) sum(n25, n1) = all_0_1_1
% 56.69/22.12 |
% 56.69/22.12 | From (2006) and (13497) follows:
% 56.69/22.12 | (13561) sum(n25, n5) = all_0_4_4
% 56.69/22.12 |
% 56.69/22.12 | From (2007) and (13499) follows:
% 56.69/22.12 | (13562) sum(n3, n1) = all_0_7_7
% 56.69/22.12 |
% 56.69/22.12 | Instantiating formula (690) with n25, n5, all_0_4_4, n4 and discharging atoms sum(n25, n5) = all_0_4_4, sum(n25, n5) = n4, yields:
% 56.69/22.12 | (1459) all_0_4_4 = n4
% 56.69/22.12 |
% 56.69/22.12 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 56.69/22.12 | (1777) all_0_1_1 = n0
% 56.69/22.12 |
% 56.69/22.12 | Instantiating formula (690) with n3, n1, all_0_7_7, n4 and discharging atoms sum(n3, n1) = all_0_7_7, sum(n3, n1) = n4, yields:
% 56.69/22.12 | (1461) all_0_7_7 = n4
% 56.69/22.12 |
% 56.69/22.12 | From (1461)(1459) and (590) follows:
% 56.69/22.12 | (1463) sum(n4, n4) = all_0_3_3
% 56.69/22.12 |
% 56.69/22.12 | From (1777) and (7987) follows:
% 56.69/22.12 | (8054) sum(n8, n0) = all_0_0_0
% 56.69/22.12 |
% 56.69/22.12 | Instantiating formula (690) with n8, n0, all_0_0_0, n8 and discharging atoms sum(n8, n0) = all_0_0_0, sum(n8, n0) = n8, yields:
% 56.69/22.12 | (1231) all_0_0_0 = n8
% 56.69/22.12 |
% 56.69/22.12 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 56.69/22.12 | (1230) all_0_3_3 = n8
% 56.69/22.12 |
% 56.69/22.12 | Equations (1231,1230) can reduce 679 to:
% 56.69/22.12 | (1106) $false
% 56.69/22.12 |
% 56.69/22.12 |-The branch is then unsatisfiable
% 56.69/22.12 |-Branch two:
% 56.69/22.12 | (1485) ~ (all_0_11_11 = n4)
% 56.69/22.12 | (1486) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.69/22.12 |
% 56.69/22.12 +-Applying beta-rule and splitting (1947), into two cases.
% 56.69/22.12 |-Branch one:
% 56.69/22.12 | (1948) all_0_10_10 = n3
% 56.69/22.12 |
% 56.69/22.12 | From (1948) and (292) follows:
% 56.69/22.12 | (1949) pred(n3) = all_0_6_6
% 56.69/22.12 |
% 56.69/22.12 | From (1948) and (760) follows:
% 56.69/22.12 | (1950) succ(n3) = all_0_8_8
% 56.69/22.12 |
% 56.69/22.12 | Instantiating formula (500) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 56.69/22.12 | (1951) all_0_6_6 = n2
% 56.69/22.12 |
% 56.69/22.12 | Instantiating formula (617) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 56.69/22.12 | (1952) all_0_8_8 = n4
% 56.69/22.12 |
% 56.69/22.12 | From (1951) and (1949) follows:
% 56.69/22.12 | (953) pred(n3) = n2
% 56.69/22.12 |
% 56.69/22.12 | From (1952) and (1950) follows:
% 56.69/22.12 | (280) succ(n3) = n4
% 56.69/22.12 |
% 56.69/22.12 | From (1951) and (541) follows:
% 56.69/22.12 | (13580) sum(n2, all_0_5_5) = all_0_4_4
% 56.69/22.12 |
% 56.69/22.12 | From (1951)(1952) and (411) follows:
% 56.69/22.12 | (1953) sum(n2, n4) = all_0_1_1
% 56.69/22.12 |
% 56.69/22.12 | From (1952) and (427) follows:
% 56.69/22.12 | (13582) sum(all_0_9_9, n4) = all_0_7_7
% 56.69/22.12 |
% 56.69/22.12 | Instantiating formula (690) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 56.69/22.12 | (1723) all_0_1_1 = n6
% 56.69/22.12 |
% 56.69/22.12 | From (1723) and (630) follows:
% 56.69/22.12 | (8305) sum(all_0_2_2, n6) = all_0_0_0
% 56.69/22.12 |
% 56.69/22.12 | From (1723) and (1953) follows:
% 56.69/22.12 | (332) sum(n2, n4) = n6
% 56.69/22.12 |
% 56.69/22.12 +-Applying beta-rule and splitting (1486), into two cases.
% 56.69/22.12 |-Branch one:
% 56.69/22.12 | (1487) all_0_11_11 = n3
% 56.69/22.12 |
% 56.69/22.12 | From (1487) and (559) follows:
% 56.69/22.12 | (1488) pred(n3) = all_0_9_9
% 56.69/22.12 |
% 56.69/22.12 | From (1487) and (992) follows:
% 56.69/22.12 | (1489) succ(n3) = all_0_5_5
% 56.69/22.12 |
% 56.69/22.12 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 56.69/22.12 | (1490) all_0_9_9 = n2
% 56.69/22.12 |
% 56.69/22.12 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 56.69/22.12 | (1491) all_0_5_5 = n4
% 56.69/22.12 |
% 56.69/22.12 | From (1490)(1491) and (538) follows:
% 56.69/22.12 | (1492) sum(n2, n4) = all_0_2_2
% 56.69/22.12 |
% 56.69/22.12 | From (1490) and (13582) follows:
% 56.69/22.12 | (13592) sum(n2, n4) = all_0_7_7
% 56.69/22.12 |
% 56.69/22.12 | From (1491) and (13580) follows:
% 56.69/22.12 | (13593) sum(n2, n4) = all_0_4_4
% 56.69/22.12 |
% 56.69/22.12 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 56.69/22.12 | (1262) all_0_2_2 = n6
% 56.69/22.12 |
% 56.69/22.12 | Instantiating formula (690) 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:
% 56.69/22.12 | (1093) all_0_2_2 = all_0_4_4
% 56.69/22.12 |
% 56.69/22.12 | Instantiating formula (690) 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:
% 56.69/22.12 | (1094) all_0_2_2 = all_0_7_7
% 56.69/22.12 |
% 56.69/22.12 | Combining equations (1094,1093) yields a new equation:
% 56.69/22.12 | (1095) all_0_4_4 = all_0_7_7
% 56.69/22.12 |
% 56.69/22.12 | Combining equations (1262,1093) yields a new equation:
% 56.69/22.12 | (1423) all_0_4_4 = n6
% 56.69/22.12 |
% 56.69/22.12 | Combining equations (1423,1095) yields a new equation:
% 56.69/22.12 | (1425) all_0_7_7 = n6
% 56.69/22.12 |
% 56.69/22.12 | Combining equations (1425,1095) yields a new equation:
% 56.69/22.12 | (1423) all_0_4_4 = n6
% 56.69/22.12 |
% 56.69/22.12 | Combining equations (1423,1093) yields a new equation:
% 56.69/22.12 | (1262) all_0_2_2 = n6
% 56.69/22.12 |
% 56.69/22.12 | From (1262) and (8305) follows:
% 56.69/22.12 | (8323) sum(n6, n6) = all_0_0_0
% 56.69/22.12 |
% 56.69/22.12 | From (1425)(1423) and (590) follows:
% 56.69/22.12 | (1427) sum(n6, n6) = all_0_3_3
% 56.69/22.12 |
% 56.69/22.12 | Instantiating formula (690) with n6, n6, all_0_0_0, n12 and discharging atoms sum(n6, n6) = all_0_0_0, sum(n6, n6) = n12, yields:
% 56.69/22.12 | (1195) all_0_0_0 = n12
% 56.69/22.12 |
% 56.69/22.12 | Instantiating formula (690) 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:
% 56.69/22.12 | (1103) all_0_0_0 = all_0_3_3
% 56.69/22.12 |
% 56.69/22.12 | Combining equations (1195,1103) yields a new equation:
% 56.69/22.12 | (1194) all_0_3_3 = n12
% 56.69/22.12 |
% 56.69/22.12 | Combining equations (1194,1103) yields a new equation:
% 56.69/22.12 | (1195) all_0_0_0 = n12
% 56.69/22.12 |
% 56.69/22.12 | Equations (1195,1194) can reduce 679 to:
% 56.69/22.12 | (1106) $false
% 56.69/22.12 |
% 56.69/22.12 |-The branch is then unsatisfiable
% 56.69/22.12 |-Branch two:
% 56.69/22.12 | (1503) ~ (all_0_11_11 = n3)
% 56.69/22.12 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.69/22.12 |
% 56.69/22.12 +-Applying beta-rule and splitting (1504), into two cases.
% 56.69/22.12 |-Branch one:
% 56.69/22.12 | (1505) all_0_11_11 = n2
% 56.69/22.12 |
% 56.69/22.12 | From (1505) and (559) follows:
% 56.69/22.12 | (1506) pred(n2) = all_0_9_9
% 56.69/22.12 |
% 56.69/22.12 | From (1505) and (992) follows:
% 56.69/22.13 | (1507) succ(n2) = all_0_5_5
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 56.69/22.13 | (1508) all_0_9_9 = n1
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 56.69/22.13 | (1509) all_0_5_5 = n3
% 56.69/22.13 |
% 56.69/22.13 | From (1508)(1509) and (538) follows:
% 56.69/22.13 | (1510) sum(n1, n3) = all_0_2_2
% 56.69/22.13 |
% 56.69/22.13 | From (1508) and (13582) follows:
% 56.69/22.13 | (13617) sum(n1, n4) = all_0_7_7
% 56.69/22.13 |
% 56.69/22.13 | From (1509) and (13580) follows:
% 56.69/22.13 | (13618) sum(n2, n3) = all_0_4_4
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (690) with n2, n3, all_0_4_4, n5 and discharging atoms sum(n2, n3) = all_0_4_4, sum(n2, n3) = n5, yields:
% 56.69/22.13 | (1441) all_0_4_4 = n5
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (690) with n1, n4, all_0_7_7, n5 and discharging atoms sum(n1, n4) = all_0_7_7, sum(n1, n4) = n5, yields:
% 56.69/22.13 | (1443) all_0_7_7 = n5
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 56.69/22.13 | (1280) all_0_2_2 = n4
% 56.69/22.13 |
% 56.69/22.13 | From (1280) and (8305) follows:
% 56.69/22.13 | (8343) sum(n4, n6) = all_0_0_0
% 56.69/22.13 |
% 56.69/22.13 | From (1443)(1441) and (590) follows:
% 56.69/22.13 | (1445) sum(n5, n5) = all_0_3_3
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 56.69/22.13 | (1212) all_0_3_3 = n10
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (690) with n4, n6, all_0_0_0, n10 and discharging atoms sum(n4, n6) = all_0_0_0, sum(n4, n6) = n10, yields:
% 56.69/22.13 | (1213) all_0_0_0 = n10
% 56.69/22.13 |
% 56.69/22.13 | Equations (1213,1212) can reduce 679 to:
% 56.69/22.13 | (1106) $false
% 56.69/22.13 |
% 56.69/22.13 |-The branch is then unsatisfiable
% 56.69/22.13 |-Branch two:
% 56.69/22.13 | (1521) ~ (all_0_11_11 = n2)
% 56.69/22.13 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 56.69/22.13 |
% 56.69/22.13 +-Applying beta-rule and splitting (1522), into two cases.
% 56.69/22.13 |-Branch one:
% 56.69/22.13 | (1523) all_0_11_11 = n1
% 56.69/22.13 |
% 56.69/22.13 | From (1523) and (559) follows:
% 56.69/22.13 | (1524) pred(n1) = all_0_9_9
% 56.69/22.13 |
% 56.69/22.13 | From (1523) and (992) follows:
% 56.69/22.13 | (1525) succ(n1) = all_0_5_5
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 56.69/22.13 | (1526) all_0_9_9 = n0
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 56.69/22.13 | (1527) all_0_5_5 = n2
% 56.69/22.13 |
% 56.69/22.13 | From (1526)(1527) and (538) follows:
% 56.69/22.13 | (1528) sum(n0, n2) = all_0_2_2
% 56.69/22.13 |
% 56.69/22.13 | From (1526) and (13582) follows:
% 56.69/22.13 | (13635) sum(n0, n4) = all_0_7_7
% 56.69/22.13 |
% 56.69/22.13 | From (1527) and (13580) follows:
% 56.69/22.13 | (13636) sum(n2, n2) = all_0_4_4
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (690) with n2, n2, all_0_4_4, n4 and discharging atoms sum(n2, n2) = all_0_4_4, sum(n2, n2) = n4, yields:
% 56.69/22.13 | (1459) all_0_4_4 = n4
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (690) with n0, n4, all_0_7_7, n4 and discharging atoms sum(n0, n4) = all_0_7_7, sum(n0, n4) = n4, yields:
% 56.69/22.13 | (1461) all_0_7_7 = n4
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 56.69/22.13 | (1298) all_0_2_2 = n2
% 56.69/22.13 |
% 56.69/22.13 | From (1298) and (8305) follows:
% 56.69/22.13 | (8361) sum(n2, n6) = all_0_0_0
% 56.69/22.13 |
% 56.69/22.13 | From (1461)(1459) and (590) follows:
% 56.69/22.13 | (1463) sum(n4, n4) = all_0_3_3
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 56.69/22.13 | (1230) all_0_3_3 = n8
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (690) with n2, n6, all_0_0_0, n8 and discharging atoms sum(n2, n6) = all_0_0_0, sum(n2, n6) = n8, yields:
% 56.69/22.13 | (1231) all_0_0_0 = n8
% 56.69/22.13 |
% 56.69/22.13 | Equations (1231,1230) can reduce 679 to:
% 56.69/22.13 | (1106) $false
% 56.69/22.13 |
% 56.69/22.13 |-The branch is then unsatisfiable
% 56.69/22.13 |-Branch two:
% 56.69/22.13 | (1540) ~ (all_0_11_11 = n1)
% 56.69/22.13 | (1541) all_0_11_11 = n0
% 56.69/22.13 |
% 56.69/22.13 | From (1541) and (559) follows:
% 56.69/22.13 | (1542) pred(n0) = all_0_9_9
% 56.69/22.13 |
% 56.69/22.13 | From (1541) and (992) follows:
% 56.69/22.13 | (1543) succ(n0) = all_0_5_5
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 56.69/22.13 | (1544) all_0_9_9 = n25
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 56.69/22.13 | (1545) all_0_5_5 = n1
% 56.69/22.13 |
% 56.69/22.13 | From (1544)(1545) and (538) follows:
% 56.69/22.13 | (1546) sum(n25, n1) = all_0_2_2
% 56.69/22.13 |
% 56.69/22.13 | From (1544) and (13582) follows:
% 56.69/22.13 | (13652) sum(n25, n4) = all_0_7_7
% 56.69/22.13 |
% 56.69/22.13 | From (1545) and (13580) follows:
% 56.69/22.13 | (13653) sum(n2, n1) = all_0_4_4
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (690) with n25, n4, all_0_7_7, n3 and discharging atoms sum(n25, n4) = all_0_7_7, sum(n25, n4) = n3, yields:
% 56.69/22.13 | (1479) all_0_7_7 = n3
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 56.69/22.13 | (1316) all_0_2_2 = n0
% 56.69/22.13 |
% 56.69/22.13 | Instantiating formula (690) with n2, n1, all_0_4_4, n3 and discharging atoms sum(n2, n1) = all_0_4_4, sum(n2, n1) = n3, yields:
% 56.69/22.13 | (1477) all_0_4_4 = n3
% 56.69/22.13 |
% 56.69/22.13 | From (1316) and (8305) follows:
% 56.69/22.13 | (8379) sum(n0, n6) = all_0_0_0
% 56.69/22.13 |
% 56.69/22.13 | From (1479)(1477) and (590) follows:
% 56.69/22.14 | (1481) sum(n3, n3) = all_0_3_3
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 56.69/22.14 | (1248) all_0_3_3 = n6
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (690) with n0, n6, all_0_0_0, n6 and discharging atoms sum(n0, n6) = all_0_0_0, sum(n0, n6) = n6, yields:
% 56.69/22.14 | (1249) all_0_0_0 = n6
% 56.69/22.14 |
% 56.69/22.14 | Equations (1249,1248) can reduce 679 to:
% 56.69/22.14 | (1106) $false
% 56.69/22.14 |
% 56.69/22.14 |-The branch is then unsatisfiable
% 56.69/22.14 |-Branch two:
% 56.69/22.14 | (1964) ~ (all_0_10_10 = n3)
% 56.69/22.14 | (1965) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 56.69/22.14 |
% 56.69/22.14 +-Applying beta-rule and splitting (1486), into two cases.
% 56.69/22.14 |-Branch one:
% 56.69/22.14 | (1487) all_0_11_11 = n3
% 56.69/22.14 |
% 56.69/22.14 | From (1487) and (559) follows:
% 56.69/22.14 | (1488) pred(n3) = all_0_9_9
% 56.69/22.14 |
% 56.69/22.14 | From (1487) and (992) follows:
% 56.69/22.14 | (1489) succ(n3) = all_0_5_5
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (500) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 56.69/22.14 | (1490) all_0_9_9 = n2
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (617) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 56.69/22.14 | (1491) all_0_5_5 = n4
% 56.69/22.14 |
% 56.69/22.14 | From (1491) and (541) follows:
% 56.69/22.14 | (13669) sum(all_0_6_6, n4) = all_0_4_4
% 56.69/22.14 |
% 56.69/22.14 | From (1490)(1491) and (538) follows:
% 56.69/22.14 | (1492) sum(n2, n4) = all_0_2_2
% 56.69/22.14 |
% 56.69/22.14 | From (1490) and (427) follows:
% 56.69/22.14 | (13671) sum(n2, all_0_8_8) = all_0_7_7
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (690) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 56.69/22.14 | (1262) all_0_2_2 = n6
% 56.69/22.14 |
% 56.69/22.14 | From (1262) and (630) follows:
% 56.69/22.14 | (8628) sum(n6, all_0_1_1) = all_0_0_0
% 56.69/22.14 |
% 56.69/22.14 +-Applying beta-rule and splitting (1965), into two cases.
% 56.69/22.14 |-Branch one:
% 56.69/22.14 | (1966) all_0_10_10 = n2
% 56.69/22.14 |
% 56.69/22.14 | From (1966) and (292) follows:
% 56.69/22.14 | (1967) pred(n2) = all_0_6_6
% 56.69/22.14 |
% 56.69/22.14 | From (1966) and (760) follows:
% 56.69/22.14 | (1968) succ(n2) = all_0_8_8
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 56.69/22.14 | (1969) all_0_6_6 = n1
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 56.69/22.14 | (1970) all_0_8_8 = n3
% 56.69/22.14 |
% 56.69/22.14 | From (1969)(1970) and (411) follows:
% 56.69/22.14 | (1971) sum(n1, n3) = all_0_1_1
% 56.69/22.14 |
% 56.69/22.14 | From (1969) and (13669) follows:
% 56.69/22.14 | (13680) sum(n1, n4) = all_0_4_4
% 56.69/22.14 |
% 56.69/22.14 | From (1970) and (13671) follows:
% 56.69/22.14 | (13681) sum(n2, n3) = all_0_7_7
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (690) with n2, n3, all_0_7_7, n5 and discharging atoms sum(n2, n3) = all_0_7_7, sum(n2, n3) = n5, yields:
% 56.69/22.14 | (1443) all_0_7_7 = n5
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (690) with n1, n4, all_0_4_4, n5 and discharging atoms sum(n1, n4) = all_0_4_4, sum(n1, n4) = n5, yields:
% 56.69/22.14 | (1441) all_0_4_4 = n5
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 56.69/22.14 | (1741) all_0_1_1 = n4
% 56.69/22.14 |
% 56.69/22.14 | From (1443)(1441) and (590) follows:
% 56.69/22.14 | (1445) sum(n5, n5) = all_0_3_3
% 56.69/22.14 |
% 56.69/22.14 | From (1741) and (8628) follows:
% 56.69/22.14 | (8641) sum(n6, n4) = all_0_0_0
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (690) with n6, n4, all_0_0_0, n10 and discharging atoms sum(n6, n4) = all_0_0_0, sum(n6, n4) = n10, yields:
% 56.69/22.14 | (1213) all_0_0_0 = n10
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (690) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 56.69/22.14 | (1212) all_0_3_3 = n10
% 56.69/22.14 |
% 56.69/22.14 | Equations (1213,1212) can reduce 679 to:
% 56.69/22.14 | (1106) $false
% 56.69/22.14 |
% 56.69/22.14 |-The branch is then unsatisfiable
% 56.69/22.14 |-Branch two:
% 56.69/22.14 | (1982) ~ (all_0_10_10 = n2)
% 56.69/22.14 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 56.69/22.14 |
% 56.69/22.14 +-Applying beta-rule and splitting (1983), into two cases.
% 56.69/22.14 |-Branch one:
% 56.69/22.14 | (1984) all_0_10_10 = n1
% 56.69/22.14 |
% 56.69/22.14 | From (1984) and (292) follows:
% 56.69/22.14 | (1985) pred(n1) = all_0_6_6
% 56.69/22.14 |
% 56.69/22.14 | From (1984) and (760) follows:
% 56.69/22.14 | (1986) succ(n1) = all_0_8_8
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 56.69/22.14 | (1987) all_0_6_6 = n0
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 56.69/22.14 | (1988) all_0_8_8 = n2
% 56.69/22.14 |
% 56.69/22.14 | From (1987)(1988) and (411) follows:
% 56.69/22.14 | (1989) sum(n0, n2) = all_0_1_1
% 56.69/22.14 |
% 56.69/22.14 | From (1987) and (13669) follows:
% 56.69/22.14 | (13698) sum(n0, n4) = all_0_4_4
% 56.69/22.14 |
% 56.69/22.14 | From (1988) and (13671) follows:
% 56.69/22.14 | (13699) sum(n2, n2) = all_0_7_7
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (690) with n2, n2, all_0_7_7, n4 and discharging atoms sum(n2, n2) = all_0_7_7, sum(n2, n2) = n4, yields:
% 56.69/22.14 | (1461) all_0_7_7 = n4
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (690) with n0, n4, all_0_4_4, n4 and discharging atoms sum(n0, n4) = all_0_4_4, sum(n0, n4) = n4, yields:
% 56.69/22.14 | (1459) all_0_4_4 = n4
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 56.69/22.14 | (1759) all_0_1_1 = n2
% 56.69/22.14 |
% 56.69/22.14 | From (1461)(1459) and (590) follows:
% 56.69/22.14 | (1463) sum(n4, n4) = all_0_3_3
% 56.69/22.14 |
% 56.69/22.14 | From (1759) and (8628) follows:
% 56.69/22.14 | (8659) sum(n6, n2) = all_0_0_0
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (690) with n6, n2, all_0_0_0, n8 and discharging atoms sum(n6, n2) = all_0_0_0, sum(n6, n2) = n8, yields:
% 56.69/22.14 | (1231) all_0_0_0 = n8
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (690) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 56.69/22.14 | (1230) all_0_3_3 = n8
% 56.69/22.14 |
% 56.69/22.14 | Equations (1231,1230) can reduce 679 to:
% 56.69/22.14 | (1106) $false
% 56.69/22.14 |
% 56.69/22.14 |-The branch is then unsatisfiable
% 56.69/22.14 |-Branch two:
% 56.69/22.14 | (2002) ~ (all_0_10_10 = n1)
% 56.69/22.14 | (2003) all_0_10_10 = n0
% 56.69/22.14 |
% 56.69/22.14 | From (2003) and (292) follows:
% 56.69/22.14 | (2004) pred(n0) = all_0_6_6
% 56.69/22.14 |
% 56.69/22.14 | From (2003) and (760) follows:
% 56.69/22.14 | (2005) succ(n0) = all_0_8_8
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 56.69/22.14 | (2006) all_0_6_6 = n25
% 56.69/22.14 |
% 56.69/22.14 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 56.69/22.14 | (2007) all_0_8_8 = n1
% 56.69/22.14 |
% 56.69/22.14 | From (2006)(2007) and (411) follows:
% 56.69/22.15 | (2008) sum(n25, n1) = all_0_1_1
% 56.69/22.15 |
% 56.69/22.15 | From (2006) and (13669) follows:
% 56.69/22.15 | (13715) sum(n25, n4) = all_0_4_4
% 56.69/22.15 |
% 56.69/22.15 | From (2007) and (13671) follows:
% 56.69/22.15 | (13716) sum(n2, n1) = all_0_7_7
% 56.69/22.15 |
% 56.69/22.15 | Instantiating formula (690) with n25, n4, all_0_4_4, n3 and discharging atoms sum(n25, n4) = all_0_4_4, sum(n25, n4) = n3, yields:
% 56.69/22.15 | (1477) all_0_4_4 = n3
% 56.69/22.15 |
% 56.69/22.15 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 56.69/22.15 | (1777) all_0_1_1 = n0
% 56.69/22.15 |
% 56.69/22.15 | Instantiating formula (690) with n2, n1, all_0_7_7, n3 and discharging atoms sum(n2, n1) = all_0_7_7, sum(n2, n1) = n3, yields:
% 56.69/22.15 | (1479) all_0_7_7 = n3
% 56.69/22.15 |
% 56.69/22.15 | From (1479)(1477) and (590) follows:
% 56.69/22.15 | (1481) sum(n3, n3) = all_0_3_3
% 56.69/22.15 |
% 56.69/22.15 | From (1777) and (8628) follows:
% 56.69/22.15 | (8677) sum(n6, n0) = all_0_0_0
% 56.69/22.15 |
% 56.69/22.15 | Instantiating formula (690) with n6, n0, all_0_0_0, n6 and discharging atoms sum(n6, n0) = all_0_0_0, sum(n6, n0) = n6, yields:
% 56.69/22.15 | (1249) all_0_0_0 = n6
% 56.69/22.15 |
% 56.69/22.15 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 56.69/22.15 | (1248) all_0_3_3 = n6
% 56.69/22.15 |
% 56.69/22.15 | Equations (1249,1248) can reduce 679 to:
% 56.69/22.15 | (1106) $false
% 56.69/22.15 |
% 56.69/22.15 |-The branch is then unsatisfiable
% 56.69/22.15 |-Branch two:
% 56.69/22.15 | (1503) ~ (all_0_11_11 = n3)
% 56.69/22.15 | (1504) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 56.69/22.15 |
% 56.69/22.15 +-Applying beta-rule and splitting (1965), into two cases.
% 56.69/22.15 |-Branch one:
% 56.69/22.15 | (1966) all_0_10_10 = n2
% 56.69/22.15 |
% 56.69/22.15 | From (1966) and (292) follows:
% 56.69/22.15 | (1967) pred(n2) = all_0_6_6
% 56.69/22.15 |
% 56.69/22.15 | From (1966) and (760) follows:
% 56.69/22.15 | (1968) succ(n2) = all_0_8_8
% 56.69/22.15 |
% 56.69/22.15 | Instantiating formula (500) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 56.69/22.15 | (1969) all_0_6_6 = n1
% 56.69/22.15 |
% 56.69/22.15 | Instantiating formula (617) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 56.69/22.15 | (1970) all_0_8_8 = n3
% 56.69/22.15 |
% 56.69/22.15 | From (1969) and (1967) follows:
% 56.69/22.15 | (159) pred(n2) = n1
% 56.69/22.15 |
% 56.69/22.15 | From (1970) and (1968) follows:
% 56.69/22.15 | (74) succ(n2) = n3
% 56.69/22.15 |
% 56.69/22.15 | From (1969) and (541) follows:
% 56.69/22.15 | (13734) sum(n1, all_0_5_5) = all_0_4_4
% 56.69/22.15 |
% 56.69/22.15 | From (1969)(1970) and (411) follows:
% 56.69/22.15 | (1971) sum(n1, n3) = all_0_1_1
% 56.69/22.15 |
% 56.69/22.15 | From (1970) and (427) follows:
% 56.69/22.15 | (13736) sum(all_0_9_9, n3) = all_0_7_7
% 56.69/22.15 |
% 56.69/22.15 | Instantiating formula (690) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 56.69/22.15 | (1741) all_0_1_1 = n4
% 56.69/22.15 |
% 56.69/22.15 | From (1741) and (630) follows:
% 56.69/22.15 | (8927) sum(all_0_2_2, n4) = all_0_0_0
% 56.69/22.15 |
% 56.69/22.15 | From (1741) and (1971) follows:
% 56.69/22.15 | (111) sum(n1, n3) = n4
% 56.69/22.15 |
% 56.69/22.15 +-Applying beta-rule and splitting (1504), into two cases.
% 56.69/22.15 |-Branch one:
% 56.69/22.15 | (1505) all_0_11_11 = n2
% 56.69/22.15 |
% 56.69/22.15 | From (1505) and (559) follows:
% 56.69/22.15 | (1506) pred(n2) = all_0_9_9
% 56.69/22.15 |
% 56.69/22.15 | From (1505) and (992) follows:
% 56.69/22.15 | (1507) succ(n2) = all_0_5_5
% 56.69/22.15 |
% 56.69/22.15 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 56.69/22.15 | (1508) all_0_9_9 = n1
% 56.69/22.15 |
% 56.69/22.15 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 56.69/22.15 | (1509) all_0_5_5 = n3
% 56.69/22.15 |
% 56.69/22.15 | From (1508)(1509) and (538) follows:
% 56.69/22.15 | (1510) sum(n1, n3) = all_0_2_2
% 56.69/22.15 |
% 56.69/22.15 | From (1508) and (13736) follows:
% 56.69/22.15 | (13746) sum(n1, n3) = all_0_7_7
% 56.69/22.15 |
% 56.69/22.15 | From (1509) and (13734) follows:
% 56.69/22.15 | (13747) sum(n1, n3) = all_0_4_4
% 56.69/22.15 |
% 56.69/22.15 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 56.69/22.15 | (1280) all_0_2_2 = n4
% 56.69/22.15 |
% 56.69/22.15 | Instantiating formula (690) 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:
% 56.69/22.15 | (1093) all_0_2_2 = all_0_4_4
% 56.69/22.15 |
% 56.69/22.15 | Instantiating formula (690) 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:
% 56.69/22.15 | (1094) all_0_2_2 = all_0_7_7
% 56.69/22.15 |
% 56.69/22.15 | Combining equations (1094,1093) yields a new equation:
% 56.69/22.15 | (1095) all_0_4_4 = all_0_7_7
% 56.69/22.15 |
% 56.69/22.15 | Combining equations (1280,1093) yields a new equation:
% 56.69/22.15 | (1459) all_0_4_4 = n4
% 56.69/22.15 |
% 56.69/22.15 | Combining equations (1459,1095) yields a new equation:
% 56.69/22.15 | (1461) all_0_7_7 = n4
% 56.69/22.15 |
% 56.69/22.15 | Combining equations (1461,1095) yields a new equation:
% 56.69/22.15 | (1459) all_0_4_4 = n4
% 56.69/22.15 |
% 56.69/22.15 | Combining equations (1459,1093) yields a new equation:
% 56.69/22.15 | (1280) all_0_2_2 = n4
% 56.69/22.15 |
% 56.69/22.15 | From (1280) and (8927) follows:
% 56.69/22.15 | (8945) sum(n4, n4) = all_0_0_0
% 56.69/22.15 |
% 56.69/22.15 | From (1461)(1459) and (590) follows:
% 56.69/22.15 | (1463) sum(n4, n4) = all_0_3_3
% 56.69/22.15 |
% 56.69/22.15 | Instantiating formula (690) with n4, n4, all_0_0_0, n8 and discharging atoms sum(n4, n4) = all_0_0_0, sum(n4, n4) = n8, yields:
% 56.69/22.15 | (1231) all_0_0_0 = n8
% 56.69/22.15 |
% 56.69/22.15 | Instantiating formula (690) 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:
% 56.69/22.15 | (1103) all_0_0_0 = all_0_3_3
% 56.69/22.15 |
% 56.69/22.15 | Combining equations (1231,1103) yields a new equation:
% 56.69/22.15 | (1230) all_0_3_3 = n8
% 56.69/22.15 |
% 56.69/22.15 | Combining equations (1230,1103) yields a new equation:
% 56.69/22.15 | (1231) all_0_0_0 = n8
% 56.69/22.15 |
% 56.69/22.15 | Equations (1231,1230) can reduce 679 to:
% 56.69/22.15 | (1106) $false
% 56.69/22.15 |
% 56.69/22.15 |-The branch is then unsatisfiable
% 56.69/22.15 |-Branch two:
% 56.69/22.15 | (1521) ~ (all_0_11_11 = n2)
% 56.69/22.15 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 56.69/22.15 |
% 56.69/22.15 +-Applying beta-rule and splitting (1522), into two cases.
% 56.69/22.15 |-Branch one:
% 56.69/22.15 | (1523) all_0_11_11 = n1
% 56.69/22.15 |
% 56.69/22.15 | From (1523) and (559) follows:
% 56.69/22.15 | (1524) pred(n1) = all_0_9_9
% 56.69/22.15 |
% 56.69/22.15 | From (1523) and (992) follows:
% 56.69/22.15 | (1525) succ(n1) = all_0_5_5
% 56.69/22.15 |
% 56.69/22.15 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 56.69/22.15 | (1526) all_0_9_9 = n0
% 56.69/22.15 |
% 56.69/22.15 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 56.69/22.15 | (1527) all_0_5_5 = n2
% 56.69/22.15 |
% 56.69/22.15 | From (1526)(1527) and (538) follows:
% 56.69/22.16 | (1528) sum(n0, n2) = all_0_2_2
% 56.69/22.16 |
% 56.69/22.16 | From (1526) and (13736) follows:
% 56.69/22.16 | (13771) sum(n0, n3) = all_0_7_7
% 56.69/22.16 |
% 56.69/22.16 | From (1527) and (13734) follows:
% 56.69/22.16 | (13772) sum(n1, n2) = all_0_4_4
% 56.69/22.16 |
% 56.69/22.16 | Instantiating formula (690) with n1, n2, all_0_4_4, n3 and discharging atoms sum(n1, n2) = all_0_4_4, sum(n1, n2) = n3, yields:
% 56.69/22.16 | (1477) all_0_4_4 = n3
% 56.69/22.16 |
% 56.69/22.16 | Instantiating formula (690) with n0, n3, all_0_7_7, n3 and discharging atoms sum(n0, n3) = all_0_7_7, sum(n0, n3) = n3, yields:
% 56.69/22.16 | (1479) all_0_7_7 = n3
% 56.69/22.16 |
% 56.69/22.16 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 56.69/22.16 | (1298) all_0_2_2 = n2
% 56.69/22.16 |
% 56.69/22.16 | From (1298) and (8927) follows:
% 56.69/22.16 | (8965) sum(n2, n4) = all_0_0_0
% 56.69/22.16 |
% 56.69/22.16 | From (1479)(1477) and (590) follows:
% 56.69/22.16 | (1481) sum(n3, n3) = all_0_3_3
% 56.69/22.16 |
% 56.69/22.16 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 56.69/22.16 | (1248) all_0_3_3 = n6
% 56.69/22.16 |
% 56.69/22.16 | Instantiating formula (690) with n2, n4, all_0_0_0, n6 and discharging atoms sum(n2, n4) = all_0_0_0, sum(n2, n4) = n6, yields:
% 56.69/22.16 | (1249) all_0_0_0 = n6
% 56.69/22.16 |
% 56.69/22.16 | Equations (1249,1248) can reduce 679 to:
% 56.69/22.16 | (1106) $false
% 56.69/22.16 |
% 56.69/22.16 |-The branch is then unsatisfiable
% 56.69/22.16 |-Branch two:
% 56.69/22.16 | (1540) ~ (all_0_11_11 = n1)
% 56.69/22.16 | (1541) all_0_11_11 = n0
% 56.69/22.16 |
% 56.69/22.16 | From (1541) and (559) follows:
% 56.69/22.16 | (1542) pred(n0) = all_0_9_9
% 56.69/22.16 |
% 56.69/22.16 | From (1541) and (992) follows:
% 56.69/22.16 | (1543) succ(n0) = all_0_5_5
% 56.69/22.16 |
% 56.69/22.16 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 56.69/22.16 | (1544) all_0_9_9 = n25
% 56.69/22.16 |
% 56.69/22.16 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 56.69/22.16 | (1545) all_0_5_5 = n1
% 56.69/22.16 |
% 56.69/22.16 | From (1544)(1545) and (538) follows:
% 56.69/22.16 | (1546) sum(n25, n1) = all_0_2_2
% 56.69/22.16 |
% 56.69/22.16 | From (1544) and (13736) follows:
% 56.69/22.16 | (13788) sum(n25, n3) = all_0_7_7
% 56.69/22.16 |
% 56.69/22.16 | From (1545) and (13734) follows:
% 56.69/22.16 | (13789) sum(n1, n1) = all_0_4_4
% 56.69/22.16 |
% 56.69/22.16 | Instantiating formula (690) with n25, n3, all_0_7_7, n2 and discharging atoms sum(n25, n3) = all_0_7_7, sum(n25, n3) = n2, yields:
% 56.69/22.16 | (1497) all_0_7_7 = n2
% 56.69/22.16 |
% 56.69/22.16 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 56.69/22.16 | (1316) all_0_2_2 = n0
% 56.69/22.16 |
% 56.69/22.16 | Instantiating formula (690) with n1, n1, all_0_4_4, n2 and discharging atoms sum(n1, n1) = all_0_4_4, sum(n1, n1) = n2, yields:
% 56.69/22.16 | (1495) all_0_4_4 = n2
% 56.69/22.16 |
% 56.69/22.16 | From (1316) and (8927) follows:
% 56.69/22.16 | (8983) sum(n0, n4) = all_0_0_0
% 56.69/22.16 |
% 56.69/22.16 | From (1497)(1495) and (590) follows:
% 56.69/22.16 | (1499) sum(n2, n2) = all_0_3_3
% 56.69/22.16 |
% 56.69/22.16 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 56.69/22.16 | (1266) all_0_3_3 = n4
% 56.69/22.16 |
% 56.69/22.16 | Instantiating formula (690) with n0, n4, all_0_0_0, n4 and discharging atoms sum(n0, n4) = all_0_0_0, sum(n0, n4) = n4, yields:
% 56.69/22.16 | (1267) all_0_0_0 = n4
% 56.69/22.16 |
% 56.69/22.16 | Equations (1267,1266) can reduce 679 to:
% 56.69/22.16 | (1106) $false
% 56.69/22.16 |
% 56.69/22.16 |-The branch is then unsatisfiable
% 56.69/22.16 |-Branch two:
% 56.69/22.16 | (1982) ~ (all_0_10_10 = n2)
% 56.69/22.16 | (1983) all_0_10_10 = n1 | all_0_10_10 = n0
% 56.69/22.16 |
% 56.69/22.16 +-Applying beta-rule and splitting (1504), into two cases.
% 56.69/22.16 |-Branch one:
% 56.69/22.16 | (1505) all_0_11_11 = n2
% 56.69/22.16 |
% 56.69/22.16 | From (1505) and (559) follows:
% 56.69/22.16 | (1506) pred(n2) = all_0_9_9
% 56.69/22.16 |
% 56.69/22.16 | From (1505) and (992) follows:
% 56.69/22.16 | (1507) succ(n2) = all_0_5_5
% 56.69/22.16 |
% 56.69/22.16 | Instantiating formula (500) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 56.69/22.16 | (1508) all_0_9_9 = n1
% 56.69/22.16 |
% 56.69/22.16 | Instantiating formula (617) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 56.69/22.16 | (1509) all_0_5_5 = n3
% 56.69/22.16 |
% 56.69/22.16 | From (1509) and (541) follows:
% 56.69/22.16 | (13805) sum(all_0_6_6, n3) = all_0_4_4
% 56.69/22.16 |
% 56.69/22.16 | From (1508)(1509) and (538) follows:
% 56.69/22.16 | (1510) sum(n1, n3) = all_0_2_2
% 56.69/22.16 |
% 56.69/22.16 | From (1508) and (427) follows:
% 56.69/22.16 | (13807) sum(n1, all_0_8_8) = all_0_7_7
% 56.69/22.16 |
% 56.69/22.16 | Instantiating formula (690) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 56.69/22.16 | (1280) all_0_2_2 = n4
% 56.69/22.16 |
% 56.69/22.16 | From (1280) and (630) follows:
% 56.69/22.16 | (9232) sum(n4, all_0_1_1) = all_0_0_0
% 56.69/22.16 |
% 56.69/22.16 +-Applying beta-rule and splitting (1983), into two cases.
% 56.69/22.16 |-Branch one:
% 56.69/22.16 | (1984) all_0_10_10 = n1
% 56.69/22.16 |
% 56.69/22.16 | From (1984) and (292) follows:
% 56.69/22.16 | (1985) pred(n1) = all_0_6_6
% 56.69/22.16 |
% 56.69/22.16 | From (1984) and (760) follows:
% 56.69/22.16 | (1986) succ(n1) = all_0_8_8
% 56.69/22.16 |
% 56.69/22.16 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 56.69/22.16 | (1987) all_0_6_6 = n0
% 56.69/22.16 |
% 56.69/22.16 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 56.69/22.16 | (1988) all_0_8_8 = n2
% 56.69/22.16 |
% 56.69/22.16 | From (1987)(1988) and (411) follows:
% 56.69/22.16 | (1989) sum(n0, n2) = all_0_1_1
% 56.69/22.16 |
% 56.69/22.16 | From (1987) and (13805) follows:
% 56.69/22.17 | (13816) sum(n0, n3) = all_0_4_4
% 56.69/22.17 |
% 56.69/22.17 | From (1988) and (13807) follows:
% 56.69/22.17 | (13817) sum(n1, n2) = all_0_7_7
% 56.69/22.17 |
% 56.69/22.17 | Instantiating formula (690) with n1, n2, all_0_7_7, n3 and discharging atoms sum(n1, n2) = all_0_7_7, sum(n1, n2) = n3, yields:
% 56.69/22.17 | (1479) all_0_7_7 = n3
% 56.69/22.17 |
% 56.69/22.17 | Instantiating formula (690) with n0, n3, all_0_4_4, n3 and discharging atoms sum(n0, n3) = all_0_4_4, sum(n0, n3) = n3, yields:
% 56.69/22.17 | (1477) all_0_4_4 = n3
% 56.69/22.17 |
% 56.69/22.17 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 56.69/22.17 | (1759) all_0_1_1 = n2
% 56.69/22.17 |
% 56.69/22.17 | From (1479)(1477) and (590) follows:
% 56.69/22.17 | (1481) sum(n3, n3) = all_0_3_3
% 56.69/22.17 |
% 56.69/22.17 | From (1759) and (9232) follows:
% 56.69/22.17 | (9245) sum(n4, n2) = all_0_0_0
% 56.69/22.17 |
% 56.69/22.17 | Instantiating formula (690) with n4, n2, all_0_0_0, n6 and discharging atoms sum(n4, n2) = all_0_0_0, sum(n4, n2) = n6, yields:
% 56.69/22.17 | (1249) all_0_0_0 = n6
% 56.69/22.17 |
% 56.69/22.17 | Instantiating formula (690) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 56.69/22.17 | (1248) all_0_3_3 = n6
% 56.69/22.17 |
% 56.69/22.17 | Equations (1249,1248) can reduce 679 to:
% 56.69/22.17 | (1106) $false
% 56.69/22.17 |
% 56.69/22.17 |-The branch is then unsatisfiable
% 56.69/22.17 |-Branch two:
% 56.69/22.17 | (2002) ~ (all_0_10_10 = n1)
% 56.69/22.17 | (2003) all_0_10_10 = n0
% 56.69/22.17 |
% 56.69/22.17 | From (2003) and (292) follows:
% 56.69/22.17 | (2004) pred(n0) = all_0_6_6
% 56.69/22.17 |
% 56.69/22.17 | From (2003) and (760) follows:
% 56.69/22.17 | (2005) succ(n0) = all_0_8_8
% 56.69/22.17 |
% 56.69/22.17 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 56.69/22.17 | (2006) all_0_6_6 = n25
% 56.69/22.17 |
% 56.69/22.17 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 56.69/22.17 | (2007) all_0_8_8 = n1
% 56.69/22.17 |
% 56.69/22.17 | From (2006)(2007) and (411) follows:
% 56.69/22.17 | (2008) sum(n25, n1) = all_0_1_1
% 56.69/22.17 |
% 56.69/22.17 | From (2006) and (13805) follows:
% 56.69/22.17 | (13833) sum(n25, n3) = all_0_4_4
% 56.69/22.17 |
% 56.69/22.17 | From (2007) and (13807) follows:
% 56.69/22.17 | (13834) sum(n1, n1) = all_0_7_7
% 56.69/22.17 |
% 56.69/22.17 | Instantiating formula (690) with n25, n3, all_0_4_4, n2 and discharging atoms sum(n25, n3) = all_0_4_4, sum(n25, n3) = n2, yields:
% 56.69/22.17 | (1495) all_0_4_4 = n2
% 56.69/22.17 |
% 56.69/22.17 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 56.69/22.17 | (1777) all_0_1_1 = n0
% 56.69/22.17 |
% 56.69/22.17 | Instantiating formula (690) with n1, n1, all_0_7_7, n2 and discharging atoms sum(n1, n1) = all_0_7_7, sum(n1, n1) = n2, yields:
% 56.69/22.17 | (1497) all_0_7_7 = n2
% 56.69/22.17 |
% 56.69/22.17 | From (1497)(1495) and (590) follows:
% 56.69/22.17 | (1499) sum(n2, n2) = all_0_3_3
% 56.69/22.17 |
% 56.69/22.17 | From (1777) and (9232) follows:
% 56.69/22.17 | (9263) sum(n4, n0) = all_0_0_0
% 56.69/22.17 |
% 56.69/22.17 | Instantiating formula (690) with n4, n0, all_0_0_0, n4 and discharging atoms sum(n4, n0) = all_0_0_0, sum(n4, n0) = n4, yields:
% 56.69/22.17 | (1267) all_0_0_0 = n4
% 56.69/22.17 |
% 56.69/22.17 | Instantiating formula (690) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 56.69/22.17 | (1266) all_0_3_3 = n4
% 56.69/22.17 |
% 56.69/22.17 | Equations (1267,1266) can reduce 679 to:
% 56.69/22.17 | (1106) $false
% 56.69/22.17 |
% 56.69/22.17 |-The branch is then unsatisfiable
% 56.69/22.17 |-Branch two:
% 56.69/22.17 | (1521) ~ (all_0_11_11 = n2)
% 56.69/22.17 | (1522) all_0_11_11 = n1 | all_0_11_11 = n0
% 56.69/22.17 |
% 56.69/22.17 +-Applying beta-rule and splitting (1983), into two cases.
% 56.69/22.17 |-Branch one:
% 56.69/22.17 | (1984) all_0_10_10 = n1
% 56.69/22.17 |
% 56.69/22.17 | From (1984) and (292) follows:
% 56.69/22.17 | (1985) pred(n1) = all_0_6_6
% 56.69/22.17 |
% 56.69/22.17 | From (1984) and (760) follows:
% 56.69/22.17 | (1986) succ(n1) = all_0_8_8
% 56.69/22.17 |
% 56.69/22.17 | Instantiating formula (500) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 56.69/22.17 | (1987) all_0_6_6 = n0
% 56.69/22.17 |
% 56.69/22.17 | Instantiating formula (617) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 56.69/22.17 | (1988) all_0_8_8 = n2
% 56.69/22.17 |
% 56.69/22.17 | From (1987) and (1985) follows:
% 56.69/22.17 | (152) pred(n1) = n0
% 56.69/22.17 |
% 56.69/22.17 | From (1988) and (1986) follows:
% 56.69/22.17 | (10) succ(n1) = n2
% 56.69/22.17 |
% 56.69/22.17 | From (1987) and (541) follows:
% 56.69/22.17 | (13852) sum(n0, all_0_5_5) = all_0_4_4
% 56.69/22.17 |
% 56.69/22.17 | From (1987)(1988) and (411) follows:
% 56.69/22.17 | (1989) sum(n0, n2) = all_0_1_1
% 56.69/22.17 |
% 56.69/22.17 | From (1988) and (427) follows:
% 56.69/22.17 | (13854) sum(all_0_9_9, n2) = all_0_7_7
% 56.69/22.17 |
% 56.69/22.17 | Instantiating formula (690) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 56.69/22.17 | (1759) all_0_1_1 = n2
% 56.69/22.17 |
% 56.69/22.17 | From (1759) and (630) follows:
% 56.69/22.17 | (9513) sum(all_0_2_2, n2) = all_0_0_0
% 56.69/22.17 |
% 56.69/22.17 | From (1759) and (1989) follows:
% 56.69/22.17 | (327) sum(n0, n2) = n2
% 56.69/22.17 |
% 56.69/22.17 +-Applying beta-rule and splitting (1522), into two cases.
% 56.69/22.17 |-Branch one:
% 56.69/22.17 | (1523) all_0_11_11 = n1
% 56.69/22.17 |
% 56.69/22.17 | From (1523) and (559) follows:
% 56.69/22.17 | (1524) pred(n1) = all_0_9_9
% 56.69/22.17 |
% 56.69/22.17 | From (1523) and (992) follows:
% 56.69/22.17 | (1525) succ(n1) = all_0_5_5
% 56.69/22.17 |
% 56.69/22.17 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 56.69/22.17 | (1526) all_0_9_9 = n0
% 56.69/22.17 |
% 56.69/22.17 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 56.69/22.17 | (1527) all_0_5_5 = n2
% 56.69/22.17 |
% 56.69/22.17 | From (1526)(1527) and (538) follows:
% 56.69/22.17 | (1528) sum(n0, n2) = all_0_2_2
% 56.69/22.17 |
% 56.69/22.17 | From (1526) and (13854) follows:
% 56.69/22.17 | (13864) sum(n0, n2) = all_0_7_7
% 56.69/22.17 |
% 56.69/22.17 | From (1527) and (13852) follows:
% 56.69/22.18 | (13865) sum(n0, n2) = all_0_4_4
% 56.69/22.18 |
% 56.69/22.18 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 56.69/22.18 | (1298) all_0_2_2 = n2
% 56.69/22.18 |
% 56.69/22.18 | Instantiating formula (690) 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:
% 56.69/22.18 | (1093) all_0_2_2 = all_0_4_4
% 56.69/22.18 |
% 56.69/22.18 | Instantiating formula (690) 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:
% 56.69/22.18 | (1094) all_0_2_2 = all_0_7_7
% 56.69/22.18 |
% 56.69/22.18 | Combining equations (1094,1093) yields a new equation:
% 56.69/22.18 | (1095) all_0_4_4 = all_0_7_7
% 56.69/22.18 |
% 56.69/22.18 | Combining equations (1298,1093) yields a new equation:
% 56.69/22.18 | (1495) all_0_4_4 = n2
% 56.69/22.18 |
% 56.69/22.18 | Combining equations (1495,1095) yields a new equation:
% 56.69/22.18 | (1497) all_0_7_7 = n2
% 56.69/22.18 |
% 56.69/22.18 | Combining equations (1497,1095) yields a new equation:
% 56.69/22.18 | (1495) all_0_4_4 = n2
% 56.69/22.18 |
% 56.69/22.18 | Combining equations (1495,1093) yields a new equation:
% 56.69/22.18 | (1298) all_0_2_2 = n2
% 56.69/22.18 |
% 56.69/22.18 | From (1298) and (9513) follows:
% 56.69/22.18 | (9531) sum(n2, n2) = all_0_0_0
% 56.69/22.18 |
% 56.69/22.18 | From (1497)(1495) and (590) follows:
% 56.69/22.18 | (1499) sum(n2, n2) = all_0_3_3
% 56.69/22.18 |
% 56.69/22.18 | Instantiating formula (690) with n2, n2, all_0_0_0, n4 and discharging atoms sum(n2, n2) = all_0_0_0, sum(n2, n2) = n4, yields:
% 56.69/22.18 | (1267) all_0_0_0 = n4
% 56.69/22.18 |
% 56.69/22.18 | Instantiating formula (690) 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:
% 56.69/22.18 | (1103) all_0_0_0 = all_0_3_3
% 56.69/22.18 |
% 56.69/22.18 | Combining equations (1267,1103) yields a new equation:
% 56.69/22.18 | (1266) all_0_3_3 = n4
% 56.69/22.18 |
% 56.69/22.18 | Combining equations (1266,1103) yields a new equation:
% 56.69/22.18 | (1267) all_0_0_0 = n4
% 56.69/22.18 |
% 56.69/22.18 | Equations (1267,1266) can reduce 679 to:
% 56.69/22.18 | (1106) $false
% 56.69/22.18 |
% 56.69/22.18 |-The branch is then unsatisfiable
% 56.69/22.18 |-Branch two:
% 56.69/22.18 | (1540) ~ (all_0_11_11 = n1)
% 56.69/22.18 | (1541) all_0_11_11 = n0
% 56.69/22.18 |
% 56.69/22.18 | From (1541) and (559) follows:
% 56.69/22.18 | (1542) pred(n0) = all_0_9_9
% 56.69/22.18 |
% 56.69/22.18 | From (1541) and (992) follows:
% 56.69/22.18 | (1543) succ(n0) = all_0_5_5
% 56.69/22.18 |
% 56.69/22.18 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 56.69/22.18 | (1544) all_0_9_9 = n25
% 56.69/22.18 |
% 56.69/22.18 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 56.69/22.18 | (1545) all_0_5_5 = n1
% 56.69/22.18 |
% 56.69/22.18 | From (1544)(1545) and (538) follows:
% 56.69/22.18 | (1546) sum(n25, n1) = all_0_2_2
% 56.69/22.18 |
% 56.69/22.18 | From (1544) and (13854) follows:
% 56.69/22.18 | (13888) sum(n25, n2) = all_0_7_7
% 56.69/22.18 |
% 56.69/22.18 | From (1545) and (13852) follows:
% 56.69/22.18 | (13889) sum(n0, n1) = all_0_4_4
% 56.69/22.18 |
% 56.69/22.18 | Instantiating formula (690) with n25, n2, all_0_7_7, n1 and discharging atoms sum(n25, n2) = all_0_7_7, sum(n25, n2) = n1, yields:
% 56.69/22.18 | (1515) all_0_7_7 = n1
% 56.69/22.18 |
% 56.69/22.18 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 56.69/22.18 | (1316) all_0_2_2 = n0
% 56.69/22.18 |
% 56.69/22.18 | Instantiating formula (690) with n0, n1, all_0_4_4, n1 and discharging atoms sum(n0, n1) = all_0_4_4, sum(n0, n1) = n1, yields:
% 56.69/22.18 | (1513) all_0_4_4 = n1
% 56.69/22.18 |
% 56.69/22.18 | From (1316) and (9513) follows:
% 56.69/22.18 | (9551) sum(n0, n2) = all_0_0_0
% 56.69/22.18 |
% 56.69/22.18 | From (1515)(1513) and (590) follows:
% 56.69/22.18 | (1517) sum(n1, n1) = all_0_3_3
% 56.69/22.18 |
% 56.69/22.18 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 56.69/22.18 | (1284) all_0_3_3 = n2
% 56.69/22.18 |
% 56.69/22.18 | Instantiating formula (690) with n0, n2, all_0_0_0, n2 and discharging atoms sum(n0, n2) = all_0_0_0, sum(n0, n2) = n2, yields:
% 56.69/22.18 | (1285) all_0_0_0 = n2
% 56.69/22.18 |
% 56.69/22.18 | Equations (1285,1284) can reduce 679 to:
% 56.69/22.18 | (1106) $false
% 56.69/22.18 |
% 56.69/22.18 |-The branch is then unsatisfiable
% 56.69/22.18 |-Branch two:
% 56.69/22.18 | (2002) ~ (all_0_10_10 = n1)
% 56.69/22.18 | (2003) all_0_10_10 = n0
% 56.69/22.18 |
% 56.69/22.18 | From (2003) and (292) follows:
% 56.69/22.18 | (2004) pred(n0) = all_0_6_6
% 56.69/22.18 |
% 56.69/22.18 | From (2003) and (760) follows:
% 56.69/22.18 | (2005) succ(n0) = all_0_8_8
% 56.69/22.18 |
% 56.69/22.18 | Instantiating formula (500) with n0, all_0_6_6, n25 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n25, yields:
% 56.69/22.18 | (2006) all_0_6_6 = n25
% 56.69/22.18 |
% 56.69/22.18 | Instantiating formula (617) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 56.69/22.18 | (2007) all_0_8_8 = n1
% 56.69/22.18 |
% 56.69/22.18 | From (2006) and (2004) follows:
% 56.69/22.18 | (793) pred(n0) = n25
% 56.69/22.18 |
% 56.69/22.18 | From (2007) and (2005) follows:
% 56.69/22.18 | (835) succ(n0) = n1
% 56.69/22.18 |
% 56.69/22.18 | From (2006) and (541) follows:
% 56.69/22.18 | (13906) sum(n25, all_0_5_5) = all_0_4_4
% 56.69/22.18 |
% 56.69/22.18 | From (2006)(2007) and (411) follows:
% 56.69/22.18 | (2008) sum(n25, n1) = all_0_1_1
% 56.69/22.18 |
% 56.69/22.18 | From (2007) and (427) follows:
% 56.69/22.18 | (13908) sum(all_0_9_9, n1) = all_0_7_7
% 56.69/22.18 |
% 56.69/22.18 | Instantiating formula (690) with n25, n1, all_0_1_1, n0 and discharging atoms sum(n25, n1) = all_0_1_1, sum(n25, n1) = n0, yields:
% 56.69/22.18 | (1777) all_0_1_1 = n0
% 56.69/22.18 |
% 56.69/22.18 | From (1777) and (630) follows:
% 56.69/22.18 | (10063) sum(all_0_2_2, n0) = all_0_0_0
% 56.69/22.18 |
% 56.69/22.18 | From (1777) and (2008) follows:
% 56.69/22.18 | (777) sum(n25, n1) = n0
% 56.69/22.18 |
% 56.69/22.18 +-Applying beta-rule and splitting (1522), into two cases.
% 56.69/22.18 |-Branch one:
% 56.69/22.18 | (1523) all_0_11_11 = n1
% 56.69/22.18 |
% 56.69/22.18 | From (1523) and (559) follows:
% 56.69/22.18 | (1524) pred(n1) = all_0_9_9
% 56.69/22.18 |
% 56.69/22.18 | From (1523) and (992) follows:
% 56.69/22.18 | (1525) succ(n1) = all_0_5_5
% 56.69/22.18 |
% 56.69/22.18 | Instantiating formula (500) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 56.69/22.18 | (1526) all_0_9_9 = n0
% 56.69/22.18 |
% 56.69/22.18 | Instantiating formula (617) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 56.69/22.18 | (1527) all_0_5_5 = n2
% 56.69/22.18 |
% 56.69/22.18 | From (1526)(1527) and (538) follows:
% 56.69/22.18 | (1528) sum(n0, n2) = all_0_2_2
% 56.69/22.18 |
% 56.69/22.18 | From (1526) and (13908) follows:
% 56.69/22.18 | (13918) sum(n0, n1) = all_0_7_7
% 56.69/22.18 |
% 56.69/22.18 | From (1527) and (13906) follows:
% 56.69/22.19 | (13919) sum(n25, n2) = all_0_4_4
% 56.69/22.19 |
% 56.69/22.19 | Instantiating formula (690) with n25, n2, all_0_4_4, n1 and discharging atoms sum(n25, n2) = all_0_4_4, sum(n25, n2) = n1, yields:
% 56.69/22.19 | (1513) all_0_4_4 = n1
% 56.69/22.19 |
% 56.69/22.19 | Instantiating formula (690) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 56.69/22.19 | (1298) all_0_2_2 = n2
% 56.69/22.19 |
% 56.69/22.19 | Instantiating formula (690) with n0, n1, all_0_7_7, n1 and discharging atoms sum(n0, n1) = all_0_7_7, sum(n0, n1) = n1, yields:
% 56.69/22.19 | (1515) all_0_7_7 = n1
% 56.69/22.19 |
% 56.69/22.19 | From (1298) and (10063) follows:
% 56.69/22.19 | (9813) sum(n2, n0) = all_0_0_0
% 56.69/22.19 |
% 56.69/22.19 | From (1515)(1513) and (590) follows:
% 56.69/22.19 | (1517) sum(n1, n1) = all_0_3_3
% 56.69/22.19 |
% 56.69/22.19 | Instantiating formula (690) with n2, n0, all_0_0_0, n2 and discharging atoms sum(n2, n0) = all_0_0_0, sum(n2, n0) = n2, yields:
% 56.69/22.19 | (1285) all_0_0_0 = n2
% 56.69/22.19 |
% 56.69/22.19 | Instantiating formula (690) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 56.69/22.19 | (1284) all_0_3_3 = n2
% 56.69/22.19 |
% 56.69/22.19 | Equations (1285,1284) can reduce 679 to:
% 56.69/22.19 | (1106) $false
% 56.69/22.19 |
% 56.69/22.19 |-The branch is then unsatisfiable
% 56.69/22.19 |-Branch two:
% 56.69/22.19 | (1540) ~ (all_0_11_11 = n1)
% 56.69/22.19 | (1541) all_0_11_11 = n0
% 56.69/22.19 |
% 56.69/22.19 | From (1541) and (559) follows:
% 56.69/22.19 | (1542) pred(n0) = all_0_9_9
% 56.69/22.19 |
% 56.69/22.19 | From (1541) and (992) follows:
% 56.69/22.19 | (1543) succ(n0) = all_0_5_5
% 56.69/22.19 |
% 56.69/22.19 | Instantiating formula (500) with n0, all_0_9_9, n25 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n25, yields:
% 56.69/22.19 | (1544) all_0_9_9 = n25
% 56.69/22.19 |
% 56.69/22.19 | Instantiating formula (617) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 56.69/22.19 | (1545) all_0_5_5 = n1
% 56.69/22.19 |
% 56.69/22.19 | From (1544)(1545) and (538) follows:
% 56.69/22.19 | (1546) sum(n25, n1) = all_0_2_2
% 56.69/22.19 |
% 56.69/22.19 | From (1544) and (13908) follows:
% 56.69/22.19 | (13935) sum(n25, n1) = all_0_7_7
% 56.69/22.19 |
% 56.69/22.19 | From (1545) and (13906) follows:
% 56.69/22.19 | (13936) sum(n25, n1) = all_0_4_4
% 56.69/22.19 |
% 56.69/22.19 | Instantiating formula (690) with n25, n1, all_0_2_2, n0 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = n0, yields:
% 56.69/22.19 | (1316) all_0_2_2 = n0
% 56.69/22.19 |
% 56.69/22.19 | Instantiating formula (690) with n25, n1, all_0_4_4, all_0_2_2 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = all_0_4_4, yields:
% 56.69/22.19 | (1093) all_0_2_2 = all_0_4_4
% 56.69/22.19 |
% 56.69/22.19 | Instantiating formula (690) with n25, n1, all_0_7_7, all_0_2_2 and discharging atoms sum(n25, n1) = all_0_2_2, sum(n25, n1) = all_0_7_7, yields:
% 56.69/22.19 | (1094) all_0_2_2 = all_0_7_7
% 56.69/22.19 |
% 56.69/22.19 | Combining equations (1094,1093) yields a new equation:
% 56.69/22.19 | (1095) all_0_4_4 = all_0_7_7
% 56.69/22.19 |
% 56.69/22.19 | Combining equations (1316,1093) yields a new equation:
% 56.69/22.19 | (1531) all_0_4_4 = n0
% 56.69/22.19 |
% 56.69/22.19 | Combining equations (1531,1095) yields a new equation:
% 56.69/22.19 | (1533) all_0_7_7 = n0
% 56.69/22.19 |
% 56.69/22.19 | Combining equations (1533,1095) yields a new equation:
% 56.69/22.19 | (1531) all_0_4_4 = n0
% 56.69/22.19 |
% 56.69/22.19 | Combining equations (1531,1093) yields a new equation:
% 56.69/22.19 | (1316) all_0_2_2 = n0
% 56.69/22.19 |
% 56.69/22.19 | From (1316) and (10063) follows:
% 56.69/22.19 | (10081) sum(n0, n0) = all_0_0_0
% 56.69/22.19 |
% 56.69/22.19 | From (1533)(1531) and (590) follows:
% 56.69/22.19 | (1535) sum(n0, n0) = all_0_3_3
% 56.69/22.19 |
% 56.69/22.19 | Instantiating formula (690) with n0, n0, all_0_0_0, n0 and discharging atoms sum(n0, n0) = all_0_0_0, sum(n0, n0) = n0, yields:
% 56.69/22.19 | (1303) all_0_0_0 = n0
% 56.69/22.19 |
% 56.69/22.19 | Instantiating formula (690) 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:
% 56.69/22.19 | (1103) all_0_0_0 = all_0_3_3
% 56.69/22.19 |
% 56.69/22.19 | Combining equations (1303,1103) yields a new equation:
% 56.69/22.19 | (1302) all_0_3_3 = n0
% 56.69/22.19 |
% 56.69/22.19 | Combining equations (1302,1103) yields a new equation:
% 56.69/22.19 | (1303) all_0_0_0 = n0
% 56.69/22.19 |
% 56.69/22.19 | Equations (1303,1302) can reduce 679 to:
% 56.69/22.19 | (1106) $false
% 56.69/22.19 |
% 56.69/22.19 |-The branch is then unsatisfiable
% 56.69/22.19 % SZS output end Proof for theBenchmark
% 56.69/22.19
% 56.69/22.19 21599ms
%------------------------------------------------------------------------------