TSTP Solution File: NUM375+1.015 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM375+1.015 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 08:43:44 EDT 2022
% Result : Unsatisfiable 9.10s 2.95s
% Output : Proof 23.69s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM375+1.015 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jul 7 07:21:04 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.68/0.66 ____ _
% 0.68/0.66 ___ / __ \_____(_)___ ________ __________
% 0.68/0.66 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.68/0.66 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.68/0.66 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.68/0.66
% 0.68/0.66 A Theorem Prover for First-Order Logic
% 0.68/0.67 (ePrincess v.1.0)
% 0.68/0.67
% 0.68/0.67 (c) Philipp Rümmer, 2009-2015
% 0.68/0.67 (c) Peter Backeman, 2014-2015
% 0.68/0.67 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.68/0.67 Free software under GNU Lesser General Public License (LGPL).
% 0.68/0.67 Bug reports to peter@backeman.se
% 0.68/0.67
% 0.68/0.67 For more information, visit http://user.uu.se/~petba168/breu/
% 0.68/0.67
% 0.68/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.72 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.32/1.18 Prover 0: Preprocessing ...
% 3.67/1.50 Prover 0: Constructing countermodel ...
% 9.10/2.95 Prover 0: proved (2230ms)
% 9.10/2.95
% 9.10/2.95 No countermodel exists, formula is valid
% 9.10/2.95 % SZS status Unsatisfiable for theBenchmark
% 9.10/2.95
% 9.10/2.95 Generating proof ... found it (size 4448)
% 20.45/5.85
% 20.45/5.85 % SZS output start Proof for theBenchmark
% 20.45/5.85 Assumed formulas after preprocessing and simplification:
% 20.45/5.85 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v2 = n15) & ~ (v2 = n14) & ~ (v2 = n13) & ~ (v2 = n12) & ~ (v2 = n11) & ~ (v2 = n10) & ~ (v2 = n9) & ~ (v2 = n8) & ~ (v2 = n7) & ~ (v2 = n6) & ~ (v2 = n5) & ~ (v2 = n4) & ~ (v2 = n3) & ~ (v2 = n2) & ~ (v2 = n1) & ~ (v2 = n0) & ~ (n15 = n14) & ~ (n15 = n13) & ~ (n15 = n12) & ~ (n15 = n11) & ~ (n15 = n10) & ~ (n15 = n9) & ~ (n15 = n8) & ~ (n15 = n7) & ~ (n15 = n6) & ~ (n15 = n5) & ~ (n15 = n4) & ~ (n15 = n3) & ~ (n15 = n2) & ~ (n15 = n1) & ~ (n15 = n0) & ~ (n14 = n13) & ~ (n14 = n12) & ~ (n14 = n11) & ~ (n14 = n10) & ~ (n14 = n9) & ~ (n14 = n8) & ~ (n14 = n7) & ~ (n14 = n6) & ~ (n14 = n5) & ~ (n14 = n4) & ~ (n14 = n3) & ~ (n14 = n2) & ~ (n14 = n1) & ~ (n14 = n0) & ~ (n13 = n12) & ~ (n13 = n11) & ~ (n13 = n10) & ~ (n13 = n9) & ~ (n13 = n8) & ~ (n13 = n7) & ~ (n13 = n6) & ~ (n13 = n5) & ~ (n13 = n4) & ~ (n13 = n3) & ~ (n13 = n2) & ~ (n13 = n1) & ~ (n13 = n0) & ~ (n12 = n11) & ~ (n12 = n10) & ~ (n12 = n9) & ~ (n12 = n8) & ~ (n12 = n7) & ~ (n12 = n6) & ~ (n12 = n5) & ~ (n12 = n4) & ~ (n12 = n3) & ~ (n12 = n2) & ~ (n12 = n1) & ~ (n12 = n0) & ~ (n11 = n10) & ~ (n11 = n9) & ~ (n11 = n8) & ~ (n11 = n7) & ~ (n11 = n6) & ~ (n11 = n5) & ~ (n11 = n4) & ~ (n11 = n3) & ~ (n11 = n2) & ~ (n11 = n1) & ~ (n11 = n0) & ~ (n10 = n9) & ~ (n10 = n8) & ~ (n10 = n7) & ~ (n10 = n6) & ~ (n10 = n5) & ~ (n10 = n4) & ~ (n10 = n3) & ~ (n10 = n2) & ~ (n10 = n1) & ~ (n10 = n0) & ~ (n9 = n8) & ~ (n9 = n7) & ~ (n9 = n6) & ~ (n9 = n5) & ~ (n9 = n4) & ~ (n9 = n3) & ~ (n9 = n2) & ~ (n9 = n1) & ~ (n9 = n0) & ~ (n8 = n7) & ~ (n8 = n6) & ~ (n8 = n5) & ~ (n8 = n4) & ~ (n8 = n3) & ~ (n8 = n2) & ~ (n8 = n1) & ~ (n8 = n0) & ~ (n7 = n6) & ~ (n7 = n5) & ~ (n7 = n4) & ~ (n7 = n3) & ~ (n7 = n2) & ~ (n7 = n1) & ~ (n7 = n0) & ~ (n6 = n5) & ~ (n6 = n4) & ~ (n6 = n3) & ~ (n6 = n2) & ~ (n6 = n1) & ~ (n6 = n0) & ~ (n5 = n4) & ~ (n5 = n3) & ~ (n5 = n2) & ~ (n5 = n1) & ~ (n5 = n0) & ~ (n4 = n3) & ~ (n4 = n2) & ~ (n4 = n1) & ~ (n4 = n0) & ~ (n3 = n2) & ~ (n3 = n1) & ~ (n3 = n0) & ~ (n2 = n1) & ~ (n2 = n0) & ~ (n1 = n0) & succ(v1) = v3 & succ(n15) = n0 & succ(n14) = n15 & succ(n13) = n14 & succ(n12) = n13 & succ(n11) = n12 & succ(n10) = n11 & succ(n9) = n10 & succ(n8) = n9 & succ(n7) = n8 & succ(n6) = n7 & succ(n5) = n6 & succ(n4) = n5 & succ(n3) = n4 & succ(n2) = n3 & succ(n1) = n2 & succ(n0) = n1 & pred(v6) = v7 & pred(v4) = v5 & pred(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) = n15 & sum(v5, v8) = v2 & sum(v1, v7) = v8 & sum(v0, v3) = v4 & sum(v0, v1) = v6 & sum(n15, n15) = n14 & sum(n15, n14) = n13 & sum(n15, n13) = n12 & sum(n15, n12) = n11 & sum(n15, n11) = n10 & sum(n15, n10) = n9 & sum(n15, n9) = n8 & sum(n15, n8) = n7 & sum(n15, n7) = n6 & sum(n15, n6) = n5 & sum(n15, n5) = n4 & sum(n15, n4) = n3 & sum(n15, n3) = n2 & sum(n15, n2) = n1 & sum(n15, n1) = n0 & sum(n15, n0) = n15 & sum(n14, n15) = n13 & sum(n14, n14) = n12 & sum(n14, n13) = n11 & sum(n14, n12) = n10 & sum(n14, n11) = n9 & sum(n14, n10) = n8 & sum(n14, n9) = n7 & sum(n14, n8) = n6 & sum(n14, n7) = n5 & sum(n14, n6) = n4 & sum(n14, n5) = n3 & sum(n14, n4) = n2 & sum(n14, n3) = n1 & sum(n14, n2) = n0 & sum(n14, n1) = n15 & sum(n14, n0) = n14 & sum(n13, n15) = n12 & sum(n13, n14) = n11 & sum(n13, n13) = n10 & sum(n13, n12) = n9 & sum(n13, n11) = n8 & sum(n13, n10) = n7 & sum(n13, n9) = n6 & sum(n13, n8) = n5 & sum(n13, n7) = n4 & sum(n13, n6) = n3 & sum(n13, n5) = n2 & sum(n13, n4) = n1 & sum(n13, n3) = n0 & sum(n13, n2) = n15 & sum(n13, n1) = n14 & sum(n13, n0) = n13 & sum(n12, n15) = n11 & sum(n12, n14) = n10 & sum(n12, n13) = n9 & sum(n12, n12) = n8 & sum(n12, n11) = n7 & sum(n12, n10) = n6 & sum(n12, n9) = n5 & sum(n12, n8) = n4 & sum(n12, n7) = n3 & sum(n12, n6) = n2 & sum(n12, n5) = n1 & sum(n12, n4) = n0 & sum(n12, n3) = n15 & sum(n12, n2) = n14 & sum(n12, n1) = n13 & sum(n12, n0) = n12 & sum(n11, n15) = n10 & sum(n11, n14) = n9 & sum(n11, n13) = n8 & sum(n11, n12) = n7 & sum(n11, n11) = n6 & sum(n11, n10) = n5 & sum(n11, n9) = n4 & sum(n11, n8) = n3 & sum(n11, n7) = n2 & sum(n11, n6) = n1 & sum(n11, n5) = n0 & sum(n11, n4) = n15 & sum(n11, n3) = n14 & sum(n11, n2) = n13 & sum(n11, n1) = n12 & sum(n11, n0) = n11 & sum(n10, n15) = n9 & sum(n10, n14) = n8 & sum(n10, n13) = n7 & sum(n10, n12) = n6 & sum(n10, n11) = n5 & sum(n10, n10) = n4 & sum(n10, n9) = n3 & sum(n10, n8) = n2 & sum(n10, n7) = n1 & sum(n10, n6) = n0 & 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, n15) = n8 & sum(n9, n14) = n7 & sum(n9, n13) = n6 & sum(n9, n12) = n5 & sum(n9, n11) = n4 & sum(n9, n10) = n3 & sum(n9, n9) = n2 & sum(n9, n8) = n1 & sum(n9, n7) = n0 & 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, n15) = n7 & sum(n8, n14) = n6 & sum(n8, n13) = n5 & sum(n8, n12) = n4 & sum(n8, n11) = n3 & sum(n8, n10) = n2 & sum(n8, n9) = n1 & sum(n8, n8) = n0 & 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, n15) = n6 & sum(n7, n14) = n5 & sum(n7, n13) = n4 & sum(n7, n12) = n3 & sum(n7, n11) = n2 & sum(n7, n10) = n1 & sum(n7, n9) = n0 & 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, n15) = n5 & sum(n6, n14) = n4 & sum(n6, n13) = n3 & sum(n6, n12) = n2 & sum(n6, n11) = n1 & sum(n6, n10) = n0 & 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, n15) = n4 & sum(n5, n14) = n3 & sum(n5, n13) = n2 & sum(n5, n12) = n1 & sum(n5, n11) = n0 & 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, n15) = n3 & sum(n4, n14) = n2 & sum(n4, n13) = n1 & sum(n4, n12) = n0 & 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, n15) = n2 & sum(n3, n14) = n1 & sum(n3, n13) = n0 & 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, n15) = n1 & sum(n2, n14) = n0 & 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, n15) = n0 & 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, n15) = n15 & sum(n0, n14) = n14 & sum(n0, n13) = n13 & sum(n0, n12) = n12 & sum(n0, n11) = n11 & sum(n0, n10) = n10 & sum(n0, n9) = n9 & sum(n0, n8) = n8 & sum(n0, n7) = n7 & sum(n0, n6) = n6 & sum(n0, n5) = n5 & sum(n0, n4) = n4 & sum(n0, n3) = n3 & sum(n0, n2) = n2 & sum(n0, n1) = n1 & sum(n0, n0) = n0 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sum(v12, v11) = v10) | ~ (sum(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (succ(v11) = v10) | ~ (succ(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (pred(v11) = v10) | ~ (pred(v11) = v9)) & (v1 = 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 = 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))
% 20.92/5.93 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 yields:
% 20.92/5.93 | (1) ~ (all_0_6_6 = n15) & ~ (all_0_6_6 = n14) & ~ (all_0_6_6 = n13) & ~ (all_0_6_6 = n12) & ~ (all_0_6_6 = n11) & ~ (all_0_6_6 = n10) & ~ (all_0_6_6 = n9) & ~ (all_0_6_6 = n8) & ~ (all_0_6_6 = n7) & ~ (all_0_6_6 = n6) & ~ (all_0_6_6 = n5) & ~ (all_0_6_6 = n4) & ~ (all_0_6_6 = n3) & ~ (all_0_6_6 = n2) & ~ (all_0_6_6 = n1) & ~ (all_0_6_6 = n0) & ~ (n15 = n14) & ~ (n15 = n13) & ~ (n15 = n12) & ~ (n15 = n11) & ~ (n15 = n10) & ~ (n15 = n9) & ~ (n15 = n8) & ~ (n15 = n7) & ~ (n15 = n6) & ~ (n15 = n5) & ~ (n15 = n4) & ~ (n15 = n3) & ~ (n15 = n2) & ~ (n15 = n1) & ~ (n15 = n0) & ~ (n14 = n13) & ~ (n14 = n12) & ~ (n14 = n11) & ~ (n14 = n10) & ~ (n14 = n9) & ~ (n14 = n8) & ~ (n14 = n7) & ~ (n14 = n6) & ~ (n14 = n5) & ~ (n14 = n4) & ~ (n14 = n3) & ~ (n14 = n2) & ~ (n14 = n1) & ~ (n14 = n0) & ~ (n13 = n12) & ~ (n13 = n11) & ~ (n13 = n10) & ~ (n13 = n9) & ~ (n13 = n8) & ~ (n13 = n7) & ~ (n13 = n6) & ~ (n13 = n5) & ~ (n13 = n4) & ~ (n13 = n3) & ~ (n13 = n2) & ~ (n13 = n1) & ~ (n13 = n0) & ~ (n12 = n11) & ~ (n12 = n10) & ~ (n12 = n9) & ~ (n12 = n8) & ~ (n12 = n7) & ~ (n12 = n6) & ~ (n12 = n5) & ~ (n12 = n4) & ~ (n12 = n3) & ~ (n12 = n2) & ~ (n12 = n1) & ~ (n12 = n0) & ~ (n11 = n10) & ~ (n11 = n9) & ~ (n11 = n8) & ~ (n11 = n7) & ~ (n11 = n6) & ~ (n11 = n5) & ~ (n11 = n4) & ~ (n11 = n3) & ~ (n11 = n2) & ~ (n11 = n1) & ~ (n11 = n0) & ~ (n10 = n9) & ~ (n10 = n8) & ~ (n10 = n7) & ~ (n10 = n6) & ~ (n10 = n5) & ~ (n10 = n4) & ~ (n10 = n3) & ~ (n10 = n2) & ~ (n10 = n1) & ~ (n10 = n0) & ~ (n9 = n8) & ~ (n9 = n7) & ~ (n9 = n6) & ~ (n9 = n5) & ~ (n9 = n4) & ~ (n9 = n3) & ~ (n9 = n2) & ~ (n9 = n1) & ~ (n9 = n0) & ~ (n8 = n7) & ~ (n8 = n6) & ~ (n8 = n5) & ~ (n8 = n4) & ~ (n8 = n3) & ~ (n8 = n2) & ~ (n8 = n1) & ~ (n8 = n0) & ~ (n7 = n6) & ~ (n7 = n5) & ~ (n7 = n4) & ~ (n7 = n3) & ~ (n7 = n2) & ~ (n7 = n1) & ~ (n7 = n0) & ~ (n6 = n5) & ~ (n6 = n4) & ~ (n6 = n3) & ~ (n6 = n2) & ~ (n6 = n1) & ~ (n6 = n0) & ~ (n5 = n4) & ~ (n5 = n3) & ~ (n5 = n2) & ~ (n5 = n1) & ~ (n5 = n0) & ~ (n4 = n3) & ~ (n4 = n2) & ~ (n4 = n1) & ~ (n4 = n0) & ~ (n3 = n2) & ~ (n3 = n1) & ~ (n3 = n0) & ~ (n2 = n1) & ~ (n2 = n0) & ~ (n1 = n0) & succ(all_0_7_7) = all_0_5_5 & succ(n15) = n0 & succ(n14) = n15 & succ(n13) = n14 & succ(n12) = n13 & succ(n11) = n12 & succ(n10) = n11 & succ(n9) = n10 & succ(n8) = n9 & succ(n7) = n8 & succ(n6) = n7 & succ(n5) = n6 & succ(n4) = n5 & succ(n3) = n4 & succ(n2) = n3 & succ(n1) = n2 & succ(n0) = n1 & pred(all_0_2_2) = all_0_1_1 & pred(all_0_4_4) = all_0_3_3 & pred(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) = n15 & sum(all_0_3_3, all_0_0_0) = all_0_6_6 & sum(all_0_7_7, all_0_1_1) = all_0_0_0 & sum(all_0_8_8, all_0_5_5) = all_0_4_4 & sum(all_0_8_8, all_0_7_7) = all_0_2_2 & sum(n15, n15) = n14 & sum(n15, n14) = n13 & sum(n15, n13) = n12 & sum(n15, n12) = n11 & sum(n15, n11) = n10 & sum(n15, n10) = n9 & sum(n15, n9) = n8 & sum(n15, n8) = n7 & sum(n15, n7) = n6 & sum(n15, n6) = n5 & sum(n15, n5) = n4 & sum(n15, n4) = n3 & sum(n15, n3) = n2 & sum(n15, n2) = n1 & sum(n15, n1) = n0 & sum(n15, n0) = n15 & sum(n14, n15) = n13 & sum(n14, n14) = n12 & sum(n14, n13) = n11 & sum(n14, n12) = n10 & sum(n14, n11) = n9 & sum(n14, n10) = n8 & sum(n14, n9) = n7 & sum(n14, n8) = n6 & sum(n14, n7) = n5 & sum(n14, n6) = n4 & sum(n14, n5) = n3 & sum(n14, n4) = n2 & sum(n14, n3) = n1 & sum(n14, n2) = n0 & sum(n14, n1) = n15 & sum(n14, n0) = n14 & sum(n13, n15) = n12 & sum(n13, n14) = n11 & sum(n13, n13) = n10 & sum(n13, n12) = n9 & sum(n13, n11) = n8 & sum(n13, n10) = n7 & sum(n13, n9) = n6 & sum(n13, n8) = n5 & sum(n13, n7) = n4 & sum(n13, n6) = n3 & sum(n13, n5) = n2 & sum(n13, n4) = n1 & sum(n13, n3) = n0 & sum(n13, n2) = n15 & sum(n13, n1) = n14 & sum(n13, n0) = n13 & sum(n12, n15) = n11 & sum(n12, n14) = n10 & sum(n12, n13) = n9 & sum(n12, n12) = n8 & sum(n12, n11) = n7 & sum(n12, n10) = n6 & sum(n12, n9) = n5 & sum(n12, n8) = n4 & sum(n12, n7) = n3 & sum(n12, n6) = n2 & sum(n12, n5) = n1 & sum(n12, n4) = n0 & sum(n12, n3) = n15 & sum(n12, n2) = n14 & sum(n12, n1) = n13 & sum(n12, n0) = n12 & sum(n11, n15) = n10 & sum(n11, n14) = n9 & sum(n11, n13) = n8 & sum(n11, n12) = n7 & sum(n11, n11) = n6 & sum(n11, n10) = n5 & sum(n11, n9) = n4 & sum(n11, n8) = n3 & sum(n11, n7) = n2 & sum(n11, n6) = n1 & sum(n11, n5) = n0 & sum(n11, n4) = n15 & sum(n11, n3) = n14 & sum(n11, n2) = n13 & sum(n11, n1) = n12 & sum(n11, n0) = n11 & sum(n10, n15) = n9 & sum(n10, n14) = n8 & sum(n10, n13) = n7 & sum(n10, n12) = n6 & sum(n10, n11) = n5 & sum(n10, n10) = n4 & sum(n10, n9) = n3 & sum(n10, n8) = n2 & sum(n10, n7) = n1 & sum(n10, n6) = n0 & 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, n15) = n8 & sum(n9, n14) = n7 & sum(n9, n13) = n6 & sum(n9, n12) = n5 & sum(n9, n11) = n4 & sum(n9, n10) = n3 & sum(n9, n9) = n2 & sum(n9, n8) = n1 & sum(n9, n7) = n0 & 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, n15) = n7 & sum(n8, n14) = n6 & sum(n8, n13) = n5 & sum(n8, n12) = n4 & sum(n8, n11) = n3 & sum(n8, n10) = n2 & sum(n8, n9) = n1 & sum(n8, n8) = n0 & 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, n15) = n6 & sum(n7, n14) = n5 & sum(n7, n13) = n4 & sum(n7, n12) = n3 & sum(n7, n11) = n2 & sum(n7, n10) = n1 & sum(n7, n9) = n0 & 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, n15) = n5 & sum(n6, n14) = n4 & sum(n6, n13) = n3 & sum(n6, n12) = n2 & sum(n6, n11) = n1 & sum(n6, n10) = n0 & 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, n15) = n4 & sum(n5, n14) = n3 & sum(n5, n13) = n2 & sum(n5, n12) = n1 & sum(n5, n11) = n0 & 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, n15) = n3 & sum(n4, n14) = n2 & sum(n4, n13) = n1 & sum(n4, n12) = n0 & 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, n15) = n2 & sum(n3, n14) = n1 & sum(n3, n13) = n0 & 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, n15) = n1 & sum(n2, n14) = n0 & 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, n15) = n0 & 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, n15) = n15 & sum(n0, n14) = n14 & sum(n0, n13) = n13 & sum(n0, n12) = n12 & sum(n0, n11) = n11 & sum(n0, n10) = n10 & sum(n0, n9) = n9 & sum(n0, n8) = n8 & sum(n0, n7) = n7 & sum(n0, n6) = n6 & sum(n0, n5) = n5 & sum(n0, n4) = n4 & sum(n0, n3) = n3 & sum(n0, n2) = n2 & sum(n0, n1) = n1 & sum(n0, n0) = n0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) & (all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0) & (all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0)
% 20.97/5.97 |
% 20.97/5.97 | Applying alpha-rule on (1) yields:
% 20.97/5.97 | (2) sum(n2, n3) = n5
% 20.97/5.97 | (3) succ(n1) = n2
% 20.97/5.97 | (4) ~ (n14 = n6)
% 20.97/5.97 | (5) sum(n9, n8) = n1
% 20.97/5.97 | (6) sum(n11, n5) = n0
% 20.97/5.97 | (7) ~ (n13 = n11)
% 20.97/5.97 | (8) ~ (n12 = n8)
% 20.97/5.97 | (9) sum(n15, n1) = n0
% 20.97/5.97 | (10) ~ (n5 = n4)
% 20.97/5.97 | (11) ~ (n12 = n1)
% 20.97/5.97 | (12) ~ (all_0_6_6 = n4)
% 20.97/5.97 | (13) ~ (n14 = n2)
% 20.97/5.97 | (14) sum(n0, n14) = n14
% 20.97/5.97 | (15) sum(n1, n1) = n2
% 20.97/5.97 | (16) ~ (n6 = n1)
% 20.97/5.97 | (17) sum(n3, n11) = n14
% 20.97/5.97 | (18) sum(n2, n10) = n12
% 20.97/5.97 | (19) sum(n10, n14) = n8
% 20.97/5.97 | (20) sum(n9, n11) = n4
% 20.97/5.97 | (21) sum(n12, n8) = n4
% 20.97/5.97 | (22) sum(n8, n1) = n9
% 20.97/5.97 | (23) ~ (n15 = n10)
% 20.97/5.97 | (24) ~ (n11 = n9)
% 20.97/5.97 | (25) sum(n6, n11) = n1
% 20.97/5.97 | (26) ~ (n11 = n4)
% 20.97/5.97 | (27) ~ (n13 = n4)
% 20.97/5.97 | (28) ~ (n9 = n4)
% 20.97/5.97 | (29) sum(n4, n8) = n12
% 20.97/5.97 | (30) sum(n12, n10) = n6
% 20.97/5.97 | (31) sum(n3, n14) = n1
% 20.97/5.97 | (32) pred(n0) = n15
% 20.97/5.97 | (33) ~ (n11 = n3)
% 20.97/5.97 | (34) sum(n0, n15) = n15
% 20.97/5.97 | (35) sum(n14, n11) = n9
% 20.97/5.97 | (36) ~ (n12 = n3)
% 20.97/5.97 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 20.97/5.97 | (38) ~ (all_0_6_6 = n1)
% 20.97/5.97 | (39) sum(n0, n6) = n6
% 20.97/5.97 | (40) sum(n7, n14) = n5
% 20.97/5.97 | (41) sum(n4, n11) = n15
% 20.97/5.98 | (42) ~ (all_0_6_6 = n12)
% 20.97/5.98 | (43) sum(n1, n15) = n0
% 20.97/5.98 | (44) sum(n4, n7) = n11
% 20.97/5.98 | (45) sum(n12, n6) = n2
% 20.97/5.98 | (46) sum(n7, n8) = n15
% 20.97/5.98 | (47) pred(n15) = n14
% 20.97/5.98 | (48) sum(n15, n5) = n4
% 20.97/5.98 | (49) sum(n10, n15) = n9
% 20.97/5.98 | (50) ~ (n15 = n9)
% 20.97/5.98 | (51) ~ (n9 = n0)
% 20.97/5.98 | (52) ~ (n15 = n12)
% 20.97/5.98 | (53) sum(n5, n10) = n15
% 20.97/5.98 | (54) ~ (n6 = n3)
% 20.97/5.98 | (55) ~ (n14 = n12)
% 20.97/5.98 | (56) sum(n4, n10) = n14
% 20.97/5.98 | (57) ~ (n7 = n5)
% 20.97/5.98 | (58) sum(n2, n11) = n13
% 20.97/5.98 | (59) sum(all_0_7_7, all_0_1_1) = all_0_0_0
% 20.97/5.98 | (60) ~ (n11 = n7)
% 20.97/5.98 | (61) sum(n12, n13) = n9
% 20.97/5.98 | (62) sum(n2, n1) = n3
% 20.97/5.98 | (63) sum(n10, n12) = n6
% 20.97/5.98 | (64) sum(all_0_8_8, all_0_5_5) = all_0_4_4
% 20.97/5.98 | (65) sum(n8, n2) = n10
% 20.97/5.98 | (66) sum(n11, n15) = n10
% 20.97/5.98 | (67) ~ (n13 = n12)
% 20.97/5.98 | (68) sum(n8, n9) = n1
% 20.97/5.98 | (69) ~ (n14 = n4)
% 20.97/5.98 | (70) ~ (all_0_6_6 = n11)
% 20.97/5.98 | (71) sum(n13, n1) = n14
% 20.97/5.98 | (72) sum(n13, n6) = n3
% 20.97/5.98 | (73) sum(n6, n3) = n9
% 20.97/5.98 | (74) sum(n4, n6) = n10
% 20.97/5.98 | (75) sum(n13, n10) = n7
% 20.97/5.98 | (76) sum(n7, n2) = n9
% 20.97/5.98 | (77) sum(n4, n1) = n5
% 20.97/5.98 | (78) pred(n3) = n2
% 20.97/5.98 | (79) ~ (n10 = n3)
% 20.97/5.98 | (80) sum(n5, n11) = n0
% 20.97/5.98 | (81) ~ (n14 = n3)
% 20.97/5.98 | (82) succ(n9) = n10
% 20.97/5.98 | (83) sum(n6, n10) = n0
% 20.97/5.98 | (84) sum(n14, n3) = n1
% 20.97/5.98 | (85) ~ (n4 = n2)
% 20.97/5.98 | (86) ~ (all_0_6_6 = n8)
% 20.97/5.98 | (87) ~ (n4 = n0)
% 20.97/5.98 | (88) ~ (n9 = n1)
% 20.97/5.99 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0))
% 20.97/5.99 | (90) sum(n2, n5) = n7
% 20.97/5.99 | (91) sum(n8, n5) = n13
% 20.97/5.99 | (92) sum(n13, n2) = n15
% 20.97/5.99 | (93) pred(n13) = n12
% 20.97/5.99 | (94) sum(n6, n4) = n10
% 20.97/5.99 | (95) ~ (n14 = n5)
% 20.97/5.99 | (96) sum(n0, n11) = n11
% 20.97/5.99 | (97) sum(n0, n0) = n0
% 20.97/5.99 | (98) ~ (n6 = n0)
% 20.97/5.99 | (99) sum(n6, n6) = n12
% 20.97/5.99 | (100) sum(n6, n13) = n3
% 20.97/5.99 | (101) succ(n6) = n7
% 20.97/5.99 | (102) sum(n12, n0) = n12
% 20.97/5.99 | (103) ~ (n9 = n3)
% 20.97/5.99 | (104) ~ (n8 = n6)
% 20.97/5.99 | (105) sum(n14, n0) = n14
% 20.97/5.99 | (106) ~ (n10 = n0)
% 20.97/5.99 | (107) sum(n3, n13) = n0
% 20.97/5.99 | (108) ~ (n13 = n8)
% 20.97/5.99 | (109) ~ (n15 = n0)
% 20.97/5.99 | (110) ~ (n14 = n11)
% 20.97/5.99 | (111) ~ (n12 = n10)
% 20.97/5.99 | (112) ~ (n10 = n4)
% 20.97/5.99 | (113) all_0_8_8 = n15 | all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 20.97/5.99 | (114) ~ (n5 = n1)
% 20.97/5.99 | (115) sum(n3, n15) = n2
% 20.97/5.99 | (116) sum(n8, n10) = n2
% 20.97/5.99 | (117) sum(n9, n5) = n14
% 20.97/5.99 | (118) sum(n8, n3) = n11
% 20.97/5.99 | (119) ~ (n5 = n2)
% 20.97/5.99 | (120) ~ (n8 = n0)
% 20.97/5.99 | (121) sum(n10, n8) = n2
% 20.97/5.99 | (122) sum(n13, n5) = n2
% 20.97/5.99 | (123) sum(n2, n4) = n6
% 20.97/5.99 | (124) ~ (n15 = n6)
% 20.97/5.99 | (125) ~ (n15 = n7)
% 20.97/5.99 | (126) sum(n12, n12) = n8
% 20.97/5.99 | (127) sum(n11, n4) = n15
% 20.97/5.99 | (128) sum(n11, n1) = n12
% 20.97/5.99 | (129) sum(n5, n13) = n2
% 20.97/5.99 | (130) ~ (all_0_6_6 = n13)
% 20.97/6.00 | (131) sum(n11, n13) = n8
% 20.97/6.00 | (132) ~ (n13 = n0)
% 20.97/6.00 | (133) ~ (n10 = n7)
% 20.97/6.00 | (134) sum(n10, n10) = n4
% 20.97/6.00 | (135) sum(n7, n15) = n6
% 20.97/6.00 | (136) sum(n8, n4) = n12
% 20.97/6.00 | (137) ~ (n12 = n2)
% 20.97/6.00 | (138) ~ (n15 = n3)
% 20.97/6.00 | (139) sum(n10, n4) = n14
% 20.97/6.00 | (140) sum(n10, n1) = n11
% 20.97/6.00 | (141) sum(n10, n5) = n15
% 20.97/6.00 | (142) sum(n5, n14) = n3
% 20.97/6.00 | (143) ~ (n7 = n6)
% 20.97/6.00 | (144) ~ (n3 = n0)
% 20.97/6.00 | (145) ~ (n5 = n0)
% 20.97/6.00 | (146) sum(n10, n13) = n7
% 20.97/6.00 | (147) ~ (n13 = n2)
% 20.97/6.00 | (148) sum(n3, n12) = n15
% 20.97/6.00 | (149) sum(n3, n2) = n5
% 20.97/6.00 | (150) ~ (n10 = n2)
% 20.97/6.00 | (151) sum(n15, n0) = n15
% 20.97/6.00 | (152) sum(n14, n5) = n3
% 20.97/6.00 | (153) sum(n9, n3) = n12
% 20.97/6.00 | (154) pred(n12) = n11
% 20.97/6.00 | (155) sum(n9, n7) = n0
% 20.97/6.00 | (156) sum(n1, n8) = n9
% 20.97/6.00 | (157) sum(n14, n14) = n12
% 20.97/6.00 | (158) sum(n8, n8) = n0
% 20.97/6.00 | (159) ~ (n8 = n7)
% 20.97/6.00 | (160) sum(all_0_8_8, all_0_7_7) = all_0_2_2
% 20.97/6.00 | (161) sum(n4, n12) = n0
% 20.97/6.00 | (162) sum(n9, n0) = n9
% 20.97/6.00 | (163) ~ (n8 = n1)
% 20.97/6.00 | (164) sum(n10, n0) = n10
% 20.97/6.00 | (165) ~ (n10 = n5)
% 20.97/6.00 | (166) sum(n9, n4) = n13
% 20.97/6.00 | (167) sum(n5, n0) = n5
% 20.97/6.00 | (168) sum(n15, n4) = n3
% 20.97/6.00 | (169) ~ (all_0_6_6 = n10)
% 20.97/6.00 | (170) ~ (n15 = n2)
% 20.97/6.00 | (171) sum(n1, n9) = n10
% 20.97/6.00 | (172) sum(n1, n4) = n5
% 20.97/6.00 | (173) sum(n0, n3) = n3
% 20.97/6.00 | (174) ~ (n11 = n1)
% 20.97/6.00 | (175) pred(n4) = n3
% 20.97/6.00 | (176) succ(all_0_7_7) = all_0_5_5
% 20.97/6.00 | (177) ~ (n8 = n2)
% 20.97/6.00 | (178) pred(n11) = n10
% 20.97/6.00 | (179) ~ (n12 = n0)
% 20.97/6.00 | (180) ~ (n7 = n4)
% 20.97/6.00 | (181) sum(n0, n5) = n5
% 20.97/6.00 | (182) sum(n4, n9) = n13
% 20.97/6.00 | (183) ~ (n10 = n8)
% 20.97/6.00 | (184) sum(n7, n6) = n13
% 20.97/6.00 | (185) sum(n15, n2) = n1
% 20.97/6.00 | (186) ~ (n14 = n7)
% 20.97/6.00 | (187) pred(all_0_2_2) = all_0_1_1
% 20.97/6.01 | (188) ~ (n12 = n9)
% 20.97/6.01 | (189) ~ (n15 = n14)
% 20.97/6.01 | (190) sum(n8, n7) = n15
% 20.97/6.01 | (191) sum(n7, n3) = n10
% 20.97/6.01 | (192) ~ (n8 = n3)
% 20.97/6.01 | (193) sum(n0, n12) = n12
% 20.97/6.01 | (194) sum(n5, n15) = n4
% 20.97/6.01 | (195) ~ (n11 = n2)
% 20.97/6.01 | (196) succ(n11) = n12
% 20.97/6.01 | (197) sum(n1, n2) = n3
% 20.97/6.01 | (198) ~ (n4 = n1)
% 20.97/6.01 | (199) pred(n7) = n6
% 20.97/6.01 | (200) sum(n4, n3) = n7
% 20.97/6.01 | (201) succ(n7) = n8
% 21.35/6.01 | (202) sum(n13, n9) = n6
% 21.35/6.01 | (203) sum(n11, n9) = n4
% 21.35/6.01 | (204) sum(n3, n5) = n8
% 21.35/6.01 | (205) ~ (n12 = n11)
% 21.35/6.01 | (206) ~ (n7 = n0)
% 21.35/6.01 | (207) sum(n13, n15) = n12
% 21.35/6.01 | (208) sum(n4, n4) = n8
% 21.35/6.01 | (209) sum(n3, n3) = n6
% 21.35/6.01 | (210) sum(n4, n5) = n9
% 21.35/6.01 | (211) sum(n1, n11) = n12
% 21.35/6.01 | (212) sum(n11, n12) = n7
% 21.35/6.01 | (213) sum(n14, n2) = n0
% 21.35/6.01 | (214) sum(n13, n7) = n4
% 21.35/6.01 | (215) sum(n7, n0) = n7
% 21.35/6.01 | (216) sum(n15, n9) = n8
% 21.35/6.01 | (217) ~ (n15 = n13)
% 21.35/6.01 | (218) ~ (n10 = n9)
% 21.35/6.01 | (219) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0))
% 21.35/6.01 | (220) ~ (n2 = n1)
% 21.35/6.01 | (221) sum(n14, n8) = n6
% 21.35/6.01 | (222) sum(n2, n0) = n2
% 21.35/6.01 | (223) sum(n9, n6) = n15
% 21.35/6.01 | (224) sum(n15, n13) = n12
% 21.35/6.01 | (225) ~ (all_0_6_6 = n15)
% 21.35/6.01 | (226) sum(n15, n11) = n10
% 21.35/6.01 | (227) sum(n1, n12) = n13
% 21.35/6.01 | (228) sum(n1, n0) = n1
% 21.35/6.01 | (229) sum(n9, n15) = n8
% 21.35/6.01 | (230) ~ (n11 = n6)
% 21.35/6.01 | (231) ~ (all_0_6_6 = n2)
% 21.35/6.01 | (232) sum(n11, n10) = n5
% 21.35/6.01 | (233) sum(n14, n10) = n8
% 21.35/6.01 | (234) pred(n6) = n5
% 21.35/6.01 | (235) ~ (n2 = n0)
% 21.35/6.01 | (236) sum(n9, n12) = n5
% 21.35/6.01 | (237) sum(n13, n14) = n11
% 21.35/6.01 | (238) sum(n0, n1) = n1
% 21.35/6.01 | (239) sum(n12, n7) = n3
% 21.35/6.01 | (240) sum(n3, n1) = n4
% 21.35/6.01 | (241) ~ (n12 = n4)
% 21.35/6.01 | (242) sum(n13, n12) = n9
% 21.35/6.01 | (243) pred(n1) = n0
% 21.35/6.01 | (244) sum(n10, n3) = n13
% 21.35/6.01 | (245) ~ (all_0_6_6 = n3)
% 21.35/6.01 | (246) ~ (n13 = n6)
% 21.35/6.01 | (247) succ(n0) = n1
% 21.35/6.01 | (248) sum(n8, n6) = n14
% 21.35/6.01 | (249) sum(n11, n11) = n6
% 21.35/6.01 | (250) sum(n5, n12) = n1
% 21.35/6.01 | (251) succ(n8) = n9
% 21.35/6.01 | (252) sum(n2, n13) = n15
% 21.35/6.01 | (253) pred(n8) = n7
% 21.35/6.01 | (254) sum(n14, n6) = n4
% 21.35/6.02 | (255) succ(n3) = n4
% 21.35/6.02 | (256) sum(n15, n12) = n11
% 21.35/6.02 | (257) succ(n4) = n5
% 21.35/6.02 | (258) sum(n14, n13) = n11
% 21.35/6.02 | (259) succ(n2) = n3
% 21.35/6.02 | (260) sum(n12, n3) = n15
% 21.35/6.02 | (261) sum(all_0_3_3, all_0_0_0) = all_0_6_6
% 21.35/6.02 | (262) ~ (n15 = n4)
% 21.35/6.02 | (263) sum(n2, n6) = n8
% 21.35/6.02 | (264) sum(n4, n13) = n1
% 21.35/6.02 | (265) ~ (n12 = n5)
% 21.35/6.02 | (266) sum(n6, n14) = n4
% 21.35/6.02 | (267) ~ (n15 = n1)
% 21.35/6.02 | (268) pred(n9) = n8
% 21.35/6.02 | (269) sum(n6, n8) = n14
% 21.35/6.02 | (270) sum(n5, n5) = n10
% 21.35/6.02 | (271) ~ (n13 = n7)
% 21.35/6.02 | (272) sum(n15, n3) = n2
% 21.35/6.02 | (273) sum(n5, n8) = n13
% 21.35/6.02 | (274) ~ (all_0_6_6 = n7)
% 21.35/6.02 | (275) sum(n12, n1) = n13
% 21.35/6.02 | (276) ~ (n5 = n3)
% 21.35/6.02 | (277) ~ (n9 = n2)
% 21.35/6.02 | (278) sum(n5, n7) = n12
% 21.35/6.02 | (279) ~ (n9 = n6)
% 21.35/6.02 | (280) sum(n15, n8) = n7
% 21.35/6.02 | (281) sum(n5, n4) = n9
% 21.35/6.02 | (282) ~ (n13 = n5)
% 21.35/6.02 | (283) ~ (n14 = n1)
% 21.35/6.02 | (284) sum(n1, n3) = n4
% 21.35/6.02 | (285) sum(n12, n5) = n1
% 21.35/6.02 | (286) sum(n2, n8) = n10
% 21.35/6.02 | (287) sum(n3, n10) = n13
% 21.35/6.02 | (288) ~ (n9 = n8)
% 21.35/6.02 | (289) ~ (n14 = n10)
% 21.35/6.02 | (290) ~ (n8 = n5)
% 21.35/6.02 | (291) ~ (n7 = n1)
% 21.35/6.02 | (292) sum(n10, n9) = n3
% 21.35/6.02 | (293) sum(n3, n4) = n7
% 21.35/6.02 | (294) sum(n12, n14) = n10
% 21.35/6.02 | (295) sum(n6, n12) = n2
% 21.35/6.02 | (296) ~ (n15 = n11)
% 21.35/6.02 | (297) ~ (n12 = n7)
% 21.35/6.02 | (298) sum(n14, n12) = n10
% 21.35/6.02 | (299) sum(n6, n0) = n6
% 21.35/6.02 | (300) ~ (n13 = n1)
% 21.35/6.02 | (301) sum(n2, n14) = n0
% 21.35/6.02 | (302) sum(n12, n11) = n7
% 21.35/6.02 | (303) sum(n8, n14) = n6
% 21.35/6.02 | (304) ~ (n13 = n3)
% 21.35/6.02 | (305) sum(n0, n10) = n10
% 21.35/6.02 | (306) sum(n7, n12) = n3
% 21.35/6.02 | (307) sum(n13, n11) = n8
% 21.35/6.02 | (308) ~ (n6 = n5)
% 21.35/6.02 | (309) ~ (n8 = n4)
% 21.35/6.02 | (310) sum(n7, n11) = n2
% 21.35/6.02 | (311) sum(n0, n9) = n9
% 21.35/6.02 | (312) sum(n7, n7) = n14
% 21.35/6.02 | (313) sum(n0, n7) = n7
% 21.35/6.02 | (314) ~ (all_0_6_6 = n14)
% 21.35/6.02 | (315) succ(n15) = n0
% 21.35/6.02 | (316) sum(n12, n9) = n5
% 21.35/6.02 | (317) sum(n7, n4) = n11
% 21.35/6.02 | (318) sum(n1, n14) = n15
% 21.35/6.02 | (319) sum(n11, n6) = n1
% 21.35/6.02 | (320) ~ (n10 = n1)
% 21.35/6.02 | (321) sum(n3, n6) = n9
% 21.35/6.02 | (322) sum(n14, n4) = n2
% 21.35/6.02 | (323) sum(n12, n15) = n11
% 21.35/6.02 | (324) pred(n14) = n13
% 21.35/6.02 | (325) sum(n6, n5) = n11
% 21.35/6.02 | (326) sum(n7, n9) = n0
% 21.35/6.02 | (327) sum(n11, n2) = n13
% 21.35/6.02 | (328) sum(n7, n10) = n1
% 21.35/6.02 | (329) sum(n11, n8) = n3
% 21.35/6.02 | (330) succ(n5) = n6
% 21.35/6.02 | (331) ~ (n6 = n2)
% 21.35/6.02 | (332) succ(n10) = n11
% 21.35/6.02 | (333) sum(n12, n4) = n0
% 21.35/6.02 | (334) sum(n10, n7) = n1
% 21.35/6.02 | (335) ~ (n14 = n13)
% 21.35/6.02 | (336) ~ (n11 = n10)
% 21.35/6.02 | (337) sum(n15, n15) = n14
% 21.35/6.02 | (338) ~ (n11 = n8)
% 21.35/6.02 | (339) sum(n2, n9) = n11
% 21.35/6.02 | (340) ~ (n4 = n3)
% 21.35/6.02 | (341) sum(n7, n1) = n8
% 21.35/6.02 | (342) sum(n5, n9) = n14
% 21.35/6.02 | (343) sum(n13, n8) = n5
% 21.35/6.02 | (344) sum(n3, n9) = n12
% 21.35/6.02 | (345) sum(n6, n15) = n5
% 21.35/6.02 | (346) sum(n11, n7) = n2
% 21.35/6.02 | (347) sum(n1, n5) = n6
% 21.35/6.02 | (348) sum(n8, n11) = n3
% 21.35/6.02 | (349) sum(n15, n6) = n5
% 21.35/6.02 | (350) sum(n15, n10) = n9
% 21.35/6.02 | (351) sum(n8, n12) = n4
% 21.35/6.02 | (352) sum(n11, n0) = n11
% 21.35/6.02 | (353) sum(n10, n2) = n12
% 21.35/6.02 | (354) sum(n14, n1) = n15
% 21.35/6.02 | (355) sum(n9, n9) = n2
% 21.35/6.02 | (356) sum(n4, n15) = n3
% 21.35/6.03 | (357) sum(n11, n14) = n9
% 21.35/6.03 | (358) sum(n0, n8) = n8
% 21.35/6.03 | (359) ~ (n15 = n5)
% 21.35/6.03 | (360) sum(n0, n4) = n4
% 21.35/6.03 | (361) ~ (n7 = n2)
% 21.35/6.03 | (362) sum(n8, n0) = n8
% 21.35/6.03 | (363) ~ (n13 = n10)
% 21.35/6.03 | (364) sum(n15, n7) = n6
% 21.35/6.03 | (365) sum(n11, n3) = n14
% 21.35/6.03 | (366) sum(n4, n2) = n6
% 21.35/6.03 | (367) ~ (n13 = n9)
% 21.35/6.03 | (368) sum(n1, n6) = n7
% 21.35/6.03 | (369) sum(n0, n2) = n2
% 21.35/6.03 | (370) sum(n3, n7) = n10
% 21.35/6.03 | (371) ~ (n11 = n5)
% 21.35/6.03 | (372) sum(n8, n13) = n5
% 21.35/6.03 | (373) sum(n7, n5) = n12
% 21.35/6.03 | (374) sum(n9, n13) = n6
% 21.35/6.03 | (375) ~ (n9 = n5)
% 21.35/6.03 | (376) ~ (n15 = n8)
% 21.35/6.03 | (377) sum(n13, n0) = n13
% 21.35/6.03 | (378) ~ (n3 = n2)
% 21.35/6.03 | (379) sum(n2, n7) = n9
% 21.35/6.03 | (380) ~ (n3 = n1)
% 21.35/6.03 | (381) sum(n9, n2) = n11
% 21.35/6.03 | (382) sum(n4, n14) = n2
% 21.35/6.03 | (383) sum(n2, n15) = n1
% 21.35/6.03 | (384) sum(n1, n13) = n14
% 21.35/6.03 | (385) ~ (n9 = n7)
% 21.35/6.03 | (386) ~ (n10 = n6)
% 21.35/6.03 | (387) sum(n5, n2) = n7
% 21.35/6.03 | (388) sum(n8, n15) = n7
% 21.35/6.03 | (389) ~ (n12 = n6)
% 21.35/6.03 | (390) sum(n3, n8) = n11
% 21.35/6.03 | (391) sum(n6, n1) = n7
% 21.35/6.03 | (392) sum(n6, n9) = n15
% 21.35/6.03 | (393) sum(n12, n2) = n14
% 21.35/6.03 | (394) sum(n9, n1) = n10
% 21.35/6.03 | (395) ~ (n14 = n8)
% 21.35/6.03 | (396) pred(all_0_4_4) = all_0_3_3
% 21.35/6.03 | (397) all_0_7_7 = n15 | all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 21.35/6.03 | (398) sum(n13, n13) = n10
% 21.35/6.03 | (399) sum(n9, n14) = n7
% 21.35/6.03 | (400) ~ (all_0_6_6 = n0)
% 21.35/6.03 | (401) sum(n14, n15) = n13
% 21.35/6.03 | (402) pred(n2) = n1
% 21.35/6.03 | (403) pred(n5) = n4
% 21.35/6.03 | (404) ~ (all_0_6_6 = n9)
% 21.35/6.03 | (405) sum(n9, n10) = n3
% 21.35/6.03 | (406) ~ (n14 = n9)
% 21.35/6.03 | (407) ~ (n14 = n0)
% 21.35/6.03 | (408) sum(n6, n2) = n8
% 21.35/6.03 | (409) ~ (all_0_6_6 = n5)
% 21.35/6.03 | (410) sum(n3, n0) = n3
% 21.35/6.03 | (411) succ(n13) = n14
% 21.35/6.03 | (412) ~ (n1 = n0)
% 21.35/6.03 | (413) sum(n14, n7) = n5
% 21.35/6.03 | (414) sum(n5, n1) = n6
% 21.35/6.03 | (415) sum(n1, n7) = n8
% 21.35/6.03 | (416) pred(n10) = n9
% 21.35/6.03 | (417) sum(n2, n12) = n14
% 21.35/6.03 | (418) ~ (all_0_6_6 = n6)
% 21.35/6.03 | (419) sum(n0, n13) = n13
% 21.35/6.03 | (420) succ(n14) = n15
% 21.35/6.03 | (421) sum(n5, n6) = n11
% 21.35/6.03 | (422) sum(n10, n11) = n5
% 21.35/6.03 | (423) sum(n7, n13) = n4
% 21.35/6.03 | (424) sum(n10, n6) = n0
% 21.35/6.03 | (425) sum(n2, n2) = n4
% 21.35/6.03 | (426) sum(n4, n0) = n4
% 21.35/6.03 | (427) sum(n14, n9) = n7
% 21.35/6.03 | (428) sum(n1, n10) = n11
% 21.35/6.03 | (429) sum(n6, n7) = n13
% 21.35/6.03 | (430) ~ (n6 = n4)
% 21.35/6.03 | (431) succ(n12) = n13
% 21.35/6.03 | (432) sum(n13, n4) = n1
% 21.35/6.03 | (433) sum(n5, n3) = n8
% 21.35/6.03 | (434) sum(n13, n3) = n0
% 21.35/6.03 | (435) sum(n15, n14) = n13
% 21.35/6.03 | (436) ~ (n11 = n0)
% 21.35/6.03 | (437) ~ (n7 = n3)
% 21.35/6.03 |
% 21.35/6.03 +-Applying beta-rule and splitting (397), into two cases.
% 21.35/6.03 |-Branch one:
% 21.35/6.03 | (438) all_0_7_7 = n15
% 21.35/6.03 |
% 21.35/6.04 | From (438) and (176) follows:
% 21.35/6.04 | (439) succ(n15) = all_0_5_5
% 21.35/6.04 |
% 21.35/6.04 | From (438) and (59) follows:
% 21.35/6.04 | (440) sum(n15, all_0_1_1) = all_0_0_0
% 21.35/6.04 |
% 21.35/6.04 | From (438) and (160) follows:
% 21.35/6.04 | (441) sum(all_0_8_8, n15) = all_0_2_2
% 21.35/6.04 |
% 21.35/6.04 | Instantiating formula (219) with n15, all_0_5_5, n0 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n0, yields:
% 21.35/6.04 | (442) all_0_5_5 = n0
% 21.35/6.04 |
% 21.35/6.04 | From (442) and (64) follows:
% 21.35/6.04 | (443) sum(all_0_8_8, n0) = all_0_4_4
% 21.35/6.04 |
% 21.35/6.04 +-Applying beta-rule and splitting (113), into two cases.
% 21.35/6.04 |-Branch one:
% 21.35/6.04 | (444) all_0_8_8 = n15
% 21.35/6.04 |
% 21.35/6.04 | From (444) and (441) follows:
% 21.35/6.04 | (445) sum(n15, n15) = all_0_2_2
% 21.35/6.04 |
% 21.35/6.04 | From (444) and (443) follows:
% 21.35/6.04 | (446) sum(n15, n0) = all_0_4_4
% 21.35/6.04 |
% 21.35/6.04 | Instantiating formula (89) with n15, n15, all_0_2_2, n14 and discharging atoms sum(n15, n15) = all_0_2_2, sum(n15, n15) = n14, yields:
% 21.35/6.04 | (447) all_0_2_2 = n14
% 21.35/6.04 |
% 21.35/6.04 | Instantiating formula (89) with n15, n0, all_0_4_4, n15 and discharging atoms sum(n15, n0) = all_0_4_4, sum(n15, n0) = n15, yields:
% 21.35/6.04 | (448) all_0_4_4 = n15
% 21.35/6.04 |
% 21.35/6.04 | From (447) and (187) follows:
% 21.35/6.04 | (449) pred(n14) = all_0_1_1
% 21.35/6.04 |
% 21.35/6.04 | From (448) and (396) follows:
% 21.35/6.04 | (450) pred(n15) = all_0_3_3
% 21.35/6.04 |
% 21.35/6.04 | Instantiating formula (37) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 21.35/6.04 | (451) all_0_3_3 = n14
% 21.35/6.04 |
% 21.35/6.04 | Instantiating formula (37) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 21.35/6.04 | (452) all_0_1_1 = n13
% 21.35/6.04 |
% 21.35/6.04 | From (451) and (261) follows:
% 21.35/6.04 | (453) sum(n14, all_0_0_0) = all_0_6_6
% 21.35/6.04 |
% 21.35/6.04 | From (452) and (440) follows:
% 21.35/6.04 | (454) sum(n15, n13) = all_0_0_0
% 21.35/6.04 |
% 21.35/6.04 | Instantiating formula (89) with n15, n13, all_0_0_0, n12 and discharging atoms sum(n15, n13) = all_0_0_0, sum(n15, n13) = n12, yields:
% 21.35/6.04 | (455) all_0_0_0 = n12
% 21.35/6.04 |
% 21.35/6.04 | From (455) and (453) follows:
% 21.35/6.04 | (456) sum(n14, n12) = all_0_6_6
% 21.35/6.04 |
% 21.35/6.04 | Instantiating formula (89) with n14, n12, all_0_6_6, n10 and discharging atoms sum(n14, n12) = all_0_6_6, sum(n14, n12) = n10, yields:
% 21.35/6.04 | (457) all_0_6_6 = n10
% 21.35/6.04 |
% 21.35/6.04 | Equations (457) can reduce 169 to:
% 21.35/6.04 | (458) $false
% 21.35/6.04 |
% 21.35/6.04 |-The branch is then unsatisfiable
% 21.35/6.04 |-Branch two:
% 21.35/6.04 | (459) ~ (all_0_8_8 = n15)
% 21.35/6.04 | (460) all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.35/6.04 |
% 21.35/6.04 +-Applying beta-rule and splitting (460), into two cases.
% 21.35/6.04 |-Branch one:
% 21.35/6.04 | (461) all_0_8_8 = n14
% 21.35/6.04 |
% 21.35/6.04 | From (461) and (441) follows:
% 21.35/6.04 | (462) sum(n14, n15) = all_0_2_2
% 21.35/6.04 |
% 21.35/6.04 | From (461) and (443) follows:
% 21.35/6.04 | (463) sum(n14, n0) = all_0_4_4
% 21.35/6.04 |
% 21.35/6.04 | Instantiating formula (89) with n14, n15, all_0_2_2, n13 and discharging atoms sum(n14, n15) = all_0_2_2, sum(n14, n15) = n13, yields:
% 21.35/6.04 | (464) all_0_2_2 = n13
% 21.35/6.04 |
% 21.35/6.04 | Instantiating formula (89) with n14, n0, all_0_4_4, n14 and discharging atoms sum(n14, n0) = all_0_4_4, sum(n14, n0) = n14, yields:
% 21.35/6.04 | (465) all_0_4_4 = n14
% 21.35/6.04 |
% 21.35/6.04 | From (464) and (187) follows:
% 21.35/6.04 | (466) pred(n13) = all_0_1_1
% 21.35/6.04 |
% 21.35/6.04 | From (465) and (396) follows:
% 21.35/6.04 | (467) pred(n14) = all_0_3_3
% 21.35/6.04 |
% 21.35/6.04 | Instantiating formula (37) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 21.35/6.04 | (468) all_0_3_3 = n13
% 21.35/6.04 |
% 21.35/6.04 | Instantiating formula (37) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 21.35/6.04 | (469) all_0_1_1 = n12
% 21.35/6.04 |
% 21.35/6.04 | From (468) and (261) follows:
% 21.35/6.04 | (470) sum(n13, all_0_0_0) = all_0_6_6
% 21.35/6.04 |
% 21.35/6.04 | From (469) and (440) follows:
% 21.35/6.04 | (471) sum(n15, n12) = all_0_0_0
% 21.35/6.04 |
% 21.35/6.04 | Instantiating formula (89) with n15, n12, all_0_0_0, n11 and discharging atoms sum(n15, n12) = all_0_0_0, sum(n15, n12) = n11, yields:
% 21.35/6.04 | (472) all_0_0_0 = n11
% 21.35/6.04 |
% 21.35/6.04 | From (472) and (470) follows:
% 21.35/6.04 | (473) sum(n13, n11) = all_0_6_6
% 21.35/6.04 |
% 21.35/6.04 | Instantiating formula (89) with n13, n11, all_0_6_6, n8 and discharging atoms sum(n13, n11) = all_0_6_6, sum(n13, n11) = n8, yields:
% 21.35/6.04 | (474) all_0_6_6 = n8
% 21.35/6.04 |
% 21.35/6.04 | Equations (474) can reduce 86 to:
% 21.35/6.04 | (458) $false
% 21.35/6.04 |
% 21.35/6.04 |-The branch is then unsatisfiable
% 21.35/6.04 |-Branch two:
% 21.35/6.04 | (476) ~ (all_0_8_8 = n14)
% 21.35/6.04 | (477) all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.35/6.04 |
% 21.35/6.04 +-Applying beta-rule and splitting (477), into two cases.
% 21.35/6.04 |-Branch one:
% 21.35/6.04 | (478) all_0_8_8 = n13
% 21.35/6.04 |
% 21.35/6.04 | From (478) and (441) follows:
% 21.35/6.04 | (479) sum(n13, n15) = all_0_2_2
% 21.35/6.04 |
% 21.35/6.04 | From (478) and (443) follows:
% 21.35/6.04 | (480) sum(n13, n0) = all_0_4_4
% 21.35/6.04 |
% 21.35/6.04 | Instantiating formula (89) with n13, n15, all_0_2_2, n12 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n12, yields:
% 21.35/6.05 | (481) all_0_2_2 = n12
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (89) with n13, n0, all_0_4_4, n13 and discharging atoms sum(n13, n0) = all_0_4_4, sum(n13, n0) = n13, yields:
% 21.35/6.05 | (482) all_0_4_4 = n13
% 21.35/6.05 |
% 21.35/6.05 | From (481) and (187) follows:
% 21.35/6.05 | (483) pred(n12) = all_0_1_1
% 21.35/6.05 |
% 21.35/6.05 | From (482) and (396) follows:
% 21.35/6.05 | (484) pred(n13) = all_0_3_3
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (37) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 21.35/6.05 | (485) all_0_3_3 = n12
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (37) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 21.35/6.05 | (486) all_0_1_1 = n11
% 21.35/6.05 |
% 21.35/6.05 | From (485) and (261) follows:
% 21.35/6.05 | (487) sum(n12, all_0_0_0) = all_0_6_6
% 21.35/6.05 |
% 21.35/6.05 | From (486) and (440) follows:
% 21.35/6.05 | (488) sum(n15, n11) = all_0_0_0
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (89) with n15, n11, all_0_0_0, n10 and discharging atoms sum(n15, n11) = all_0_0_0, sum(n15, n11) = n10, yields:
% 21.35/6.05 | (489) all_0_0_0 = n10
% 21.35/6.05 |
% 21.35/6.05 | From (489) and (487) follows:
% 21.35/6.05 | (490) sum(n12, n10) = all_0_6_6
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (89) with n12, n10, all_0_6_6, n6 and discharging atoms sum(n12, n10) = all_0_6_6, sum(n12, n10) = n6, yields:
% 21.35/6.05 | (491) all_0_6_6 = n6
% 21.35/6.05 |
% 21.35/6.05 | Equations (491) can reduce 418 to:
% 21.35/6.05 | (458) $false
% 21.35/6.05 |
% 21.35/6.05 |-The branch is then unsatisfiable
% 21.35/6.05 |-Branch two:
% 21.35/6.05 | (493) ~ (all_0_8_8 = n13)
% 21.35/6.05 | (494) all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.35/6.05 |
% 21.35/6.05 +-Applying beta-rule and splitting (494), into two cases.
% 21.35/6.05 |-Branch one:
% 21.35/6.05 | (495) all_0_8_8 = n12
% 21.35/6.05 |
% 21.35/6.05 | From (495) and (441) follows:
% 21.35/6.05 | (496) sum(n12, n15) = all_0_2_2
% 21.35/6.05 |
% 21.35/6.05 | From (495) and (443) follows:
% 21.35/6.05 | (497) sum(n12, n0) = all_0_4_4
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (89) with n12, n15, all_0_2_2, n11 and discharging atoms sum(n12, n15) = all_0_2_2, sum(n12, n15) = n11, yields:
% 21.35/6.05 | (498) all_0_2_2 = n11
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (89) with n12, n0, all_0_4_4, n12 and discharging atoms sum(n12, n0) = all_0_4_4, sum(n12, n0) = n12, yields:
% 21.35/6.05 | (499) all_0_4_4 = n12
% 21.35/6.05 |
% 21.35/6.05 | From (498) and (187) follows:
% 21.35/6.05 | (500) pred(n11) = all_0_1_1
% 21.35/6.05 |
% 21.35/6.05 | From (499) and (396) follows:
% 21.35/6.05 | (501) pred(n12) = all_0_3_3
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (37) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 21.35/6.05 | (502) all_0_3_3 = n11
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (37) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 21.35/6.05 | (503) all_0_1_1 = n10
% 21.35/6.05 |
% 21.35/6.05 | From (502) and (261) follows:
% 21.35/6.05 | (504) sum(n11, all_0_0_0) = all_0_6_6
% 21.35/6.05 |
% 21.35/6.05 | From (503) and (440) follows:
% 21.35/6.05 | (505) sum(n15, n10) = all_0_0_0
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (89) with n15, n10, all_0_0_0, n9 and discharging atoms sum(n15, n10) = all_0_0_0, sum(n15, n10) = n9, yields:
% 21.35/6.05 | (506) all_0_0_0 = n9
% 21.35/6.05 |
% 21.35/6.05 | From (506) and (504) follows:
% 21.35/6.05 | (507) sum(n11, n9) = all_0_6_6
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (89) with n11, n9, all_0_6_6, n4 and discharging atoms sum(n11, n9) = all_0_6_6, sum(n11, n9) = n4, yields:
% 21.35/6.05 | (508) all_0_6_6 = n4
% 21.35/6.05 |
% 21.35/6.05 | Equations (508) can reduce 12 to:
% 21.35/6.05 | (458) $false
% 21.35/6.05 |
% 21.35/6.05 |-The branch is then unsatisfiable
% 21.35/6.05 |-Branch two:
% 21.35/6.05 | (510) ~ (all_0_8_8 = n12)
% 21.35/6.05 | (511) all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.35/6.05 |
% 21.35/6.05 +-Applying beta-rule and splitting (511), into two cases.
% 21.35/6.05 |-Branch one:
% 21.35/6.05 | (512) all_0_8_8 = n11
% 21.35/6.05 |
% 21.35/6.05 | From (512) and (441) follows:
% 21.35/6.05 | (513) sum(n11, n15) = all_0_2_2
% 21.35/6.05 |
% 21.35/6.05 | From (512) and (443) follows:
% 21.35/6.05 | (514) sum(n11, n0) = all_0_4_4
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (89) with n11, n15, all_0_2_2, n10 and discharging atoms sum(n11, n15) = all_0_2_2, sum(n11, n15) = n10, yields:
% 21.35/6.05 | (515) all_0_2_2 = n10
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (89) with n11, n0, all_0_4_4, n11 and discharging atoms sum(n11, n0) = all_0_4_4, sum(n11, n0) = n11, yields:
% 21.35/6.05 | (516) all_0_4_4 = n11
% 21.35/6.05 |
% 21.35/6.05 | From (515) and (187) follows:
% 21.35/6.05 | (517) pred(n10) = all_0_1_1
% 21.35/6.05 |
% 21.35/6.05 | From (516) and (396) follows:
% 21.35/6.05 | (518) pred(n11) = all_0_3_3
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (37) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 21.35/6.05 | (519) all_0_3_3 = n10
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (37) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 21.35/6.05 | (520) all_0_1_1 = n9
% 21.35/6.05 |
% 21.35/6.05 | From (519) and (261) follows:
% 21.35/6.05 | (521) sum(n10, all_0_0_0) = all_0_6_6
% 21.35/6.05 |
% 21.35/6.05 | From (520) and (440) follows:
% 21.35/6.05 | (522) sum(n15, n9) = all_0_0_0
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (89) with n15, n9, all_0_0_0, n8 and discharging atoms sum(n15, n9) = all_0_0_0, sum(n15, n9) = n8, yields:
% 21.35/6.05 | (523) all_0_0_0 = n8
% 21.35/6.05 |
% 21.35/6.05 | From (523) and (521) follows:
% 21.35/6.05 | (524) sum(n10, n8) = all_0_6_6
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (89) with n10, n8, all_0_6_6, n2 and discharging atoms sum(n10, n8) = all_0_6_6, sum(n10, n8) = n2, yields:
% 21.35/6.05 | (525) all_0_6_6 = n2
% 21.35/6.05 |
% 21.35/6.05 | Equations (525) can reduce 231 to:
% 21.35/6.05 | (458) $false
% 21.35/6.05 |
% 21.35/6.05 |-The branch is then unsatisfiable
% 21.35/6.05 |-Branch two:
% 21.35/6.05 | (527) ~ (all_0_8_8 = n11)
% 21.35/6.05 | (528) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.35/6.05 |
% 21.35/6.05 +-Applying beta-rule and splitting (528), into two cases.
% 21.35/6.05 |-Branch one:
% 21.35/6.05 | (529) all_0_8_8 = n10
% 21.35/6.05 |
% 21.35/6.05 | From (529) and (441) follows:
% 21.35/6.05 | (530) sum(n10, n15) = all_0_2_2
% 21.35/6.05 |
% 21.35/6.05 | From (529) and (443) follows:
% 21.35/6.05 | (531) sum(n10, n0) = all_0_4_4
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (89) with n10, n15, all_0_2_2, n9 and discharging atoms sum(n10, n15) = all_0_2_2, sum(n10, n15) = n9, yields:
% 21.35/6.05 | (532) all_0_2_2 = n9
% 21.35/6.05 |
% 21.35/6.05 | Instantiating formula (89) with n10, n0, all_0_4_4, n10 and discharging atoms sum(n10, n0) = all_0_4_4, sum(n10, n0) = n10, yields:
% 21.35/6.05 | (533) all_0_4_4 = n10
% 21.35/6.05 |
% 21.35/6.05 | From (532) and (187) follows:
% 21.35/6.05 | (534) pred(n9) = all_0_1_1
% 21.35/6.05 |
% 21.35/6.05 | From (533) and (396) follows:
% 21.35/6.06 | (535) pred(n10) = all_0_3_3
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (37) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 21.35/6.06 | (536) all_0_3_3 = n9
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (37) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 21.35/6.06 | (537) all_0_1_1 = n8
% 21.35/6.06 |
% 21.35/6.06 | From (536) and (261) follows:
% 21.35/6.06 | (538) sum(n9, all_0_0_0) = all_0_6_6
% 21.35/6.06 |
% 21.35/6.06 | From (537) and (440) follows:
% 21.35/6.06 | (539) sum(n15, n8) = all_0_0_0
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (89) with n15, n8, all_0_0_0, n7 and discharging atoms sum(n15, n8) = all_0_0_0, sum(n15, n8) = n7, yields:
% 21.35/6.06 | (540) all_0_0_0 = n7
% 21.35/6.06 |
% 21.35/6.06 | From (540) and (538) follows:
% 21.35/6.06 | (541) sum(n9, n7) = all_0_6_6
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (89) with n9, n7, all_0_6_6, n0 and discharging atoms sum(n9, n7) = all_0_6_6, sum(n9, n7) = n0, yields:
% 21.35/6.06 | (542) all_0_6_6 = n0
% 21.35/6.06 |
% 21.35/6.06 | Equations (542) can reduce 400 to:
% 21.35/6.06 | (458) $false
% 21.35/6.06 |
% 21.35/6.06 |-The branch is then unsatisfiable
% 21.35/6.06 |-Branch two:
% 21.35/6.06 | (544) ~ (all_0_8_8 = n10)
% 21.35/6.06 | (545) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.35/6.06 |
% 21.35/6.06 +-Applying beta-rule and splitting (545), into two cases.
% 21.35/6.06 |-Branch one:
% 21.35/6.06 | (546) all_0_8_8 = n9
% 21.35/6.06 |
% 21.35/6.06 | From (546) and (441) follows:
% 21.35/6.06 | (547) sum(n9, n15) = all_0_2_2
% 21.35/6.06 |
% 21.35/6.06 | From (546) and (443) follows:
% 21.35/6.06 | (548) sum(n9, n0) = all_0_4_4
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (89) with n9, n15, all_0_2_2, n8 and discharging atoms sum(n9, n15) = all_0_2_2, sum(n9, n15) = n8, yields:
% 21.35/6.06 | (549) all_0_2_2 = n8
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (89) with n9, n0, all_0_4_4, n9 and discharging atoms sum(n9, n0) = all_0_4_4, sum(n9, n0) = n9, yields:
% 21.35/6.06 | (550) all_0_4_4 = n9
% 21.35/6.06 |
% 21.35/6.06 | From (549) and (187) follows:
% 21.35/6.06 | (551) pred(n8) = all_0_1_1
% 21.35/6.06 |
% 21.35/6.06 | From (550) and (396) follows:
% 21.35/6.06 | (552) pred(n9) = all_0_3_3
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (37) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 21.35/6.06 | (553) all_0_3_3 = n8
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (37) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 21.35/6.06 | (554) all_0_1_1 = n7
% 21.35/6.06 |
% 21.35/6.06 | From (553) and (261) follows:
% 21.35/6.06 | (555) sum(n8, all_0_0_0) = all_0_6_6
% 21.35/6.06 |
% 21.35/6.06 | From (554) and (440) follows:
% 21.35/6.06 | (556) sum(n15, n7) = all_0_0_0
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (89) with n15, n7, all_0_0_0, n6 and discharging atoms sum(n15, n7) = all_0_0_0, sum(n15, n7) = n6, yields:
% 21.35/6.06 | (557) all_0_0_0 = n6
% 21.35/6.06 |
% 21.35/6.06 | From (557) and (555) follows:
% 21.35/6.06 | (558) sum(n8, n6) = all_0_6_6
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (89) with n8, n6, all_0_6_6, n14 and discharging atoms sum(n8, n6) = all_0_6_6, sum(n8, n6) = n14, yields:
% 21.35/6.06 | (559) all_0_6_6 = n14
% 21.35/6.06 |
% 21.35/6.06 | Equations (559) can reduce 314 to:
% 21.35/6.06 | (458) $false
% 21.35/6.06 |
% 21.35/6.06 |-The branch is then unsatisfiable
% 21.35/6.06 |-Branch two:
% 21.35/6.06 | (561) ~ (all_0_8_8 = n9)
% 21.35/6.06 | (562) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.35/6.06 |
% 21.35/6.06 +-Applying beta-rule and splitting (562), into two cases.
% 21.35/6.06 |-Branch one:
% 21.35/6.06 | (563) all_0_8_8 = n8
% 21.35/6.06 |
% 21.35/6.06 | From (563) and (441) follows:
% 21.35/6.06 | (564) sum(n8, n15) = all_0_2_2
% 21.35/6.06 |
% 21.35/6.06 | From (563) and (443) follows:
% 21.35/6.06 | (565) sum(n8, n0) = all_0_4_4
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (89) with n8, n15, all_0_2_2, n7 and discharging atoms sum(n8, n15) = all_0_2_2, sum(n8, n15) = n7, yields:
% 21.35/6.06 | (566) all_0_2_2 = n7
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (89) with n8, n0, all_0_4_4, n8 and discharging atoms sum(n8, n0) = all_0_4_4, sum(n8, n0) = n8, yields:
% 21.35/6.06 | (567) all_0_4_4 = n8
% 21.35/6.06 |
% 21.35/6.06 | From (566) and (187) follows:
% 21.35/6.06 | (568) pred(n7) = all_0_1_1
% 21.35/6.06 |
% 21.35/6.06 | From (567) and (396) follows:
% 21.35/6.06 | (569) pred(n8) = all_0_3_3
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (37) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 21.35/6.06 | (570) all_0_3_3 = n7
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (37) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 21.35/6.06 | (571) all_0_1_1 = n6
% 21.35/6.06 |
% 21.35/6.06 | From (570) and (261) follows:
% 21.35/6.06 | (572) sum(n7, all_0_0_0) = all_0_6_6
% 21.35/6.06 |
% 21.35/6.06 | From (571) and (440) follows:
% 21.35/6.06 | (573) sum(n15, n6) = all_0_0_0
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (89) with n15, n6, all_0_0_0, n5 and discharging atoms sum(n15, n6) = all_0_0_0, sum(n15, n6) = n5, yields:
% 21.35/6.06 | (574) all_0_0_0 = n5
% 21.35/6.06 |
% 21.35/6.06 | From (574) and (572) follows:
% 21.35/6.06 | (575) sum(n7, n5) = all_0_6_6
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (89) with n7, n5, all_0_6_6, n12 and discharging atoms sum(n7, n5) = all_0_6_6, sum(n7, n5) = n12, yields:
% 21.35/6.06 | (576) all_0_6_6 = n12
% 21.35/6.06 |
% 21.35/6.06 | Equations (576) can reduce 42 to:
% 21.35/6.06 | (458) $false
% 21.35/6.06 |
% 21.35/6.06 |-The branch is then unsatisfiable
% 21.35/6.06 |-Branch two:
% 21.35/6.06 | (578) ~ (all_0_8_8 = n8)
% 21.35/6.06 | (579) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.35/6.06 |
% 21.35/6.06 +-Applying beta-rule and splitting (579), into two cases.
% 21.35/6.06 |-Branch one:
% 21.35/6.06 | (580) all_0_8_8 = n7
% 21.35/6.06 |
% 21.35/6.06 | From (580) and (441) follows:
% 21.35/6.06 | (581) sum(n7, n15) = all_0_2_2
% 21.35/6.06 |
% 21.35/6.06 | From (580) and (443) follows:
% 21.35/6.06 | (582) sum(n7, n0) = all_0_4_4
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (89) with n7, n15, all_0_2_2, n6 and discharging atoms sum(n7, n15) = all_0_2_2, sum(n7, n15) = n6, yields:
% 21.35/6.06 | (583) all_0_2_2 = n6
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (89) with n7, n0, all_0_4_4, n7 and discharging atoms sum(n7, n0) = all_0_4_4, sum(n7, n0) = n7, yields:
% 21.35/6.06 | (584) all_0_4_4 = n7
% 21.35/6.06 |
% 21.35/6.06 | From (583) and (187) follows:
% 21.35/6.06 | (585) pred(n6) = all_0_1_1
% 21.35/6.06 |
% 21.35/6.06 | From (584) and (396) follows:
% 21.35/6.06 | (586) pred(n7) = all_0_3_3
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (37) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 21.35/6.06 | (587) all_0_3_3 = n6
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (37) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 21.35/6.06 | (588) all_0_1_1 = n5
% 21.35/6.06 |
% 21.35/6.06 | From (587) and (261) follows:
% 21.35/6.06 | (589) sum(n6, all_0_0_0) = all_0_6_6
% 21.35/6.06 |
% 21.35/6.06 | From (588) and (440) follows:
% 21.35/6.06 | (590) sum(n15, n5) = all_0_0_0
% 21.35/6.06 |
% 21.35/6.06 | Instantiating formula (89) with n15, n5, all_0_0_0, n4 and discharging atoms sum(n15, n5) = all_0_0_0, sum(n15, n5) = n4, yields:
% 21.35/6.06 | (591) all_0_0_0 = n4
% 21.35/6.06 |
% 21.35/6.06 | From (591) and (589) follows:
% 21.35/6.06 | (592) sum(n6, n4) = all_0_6_6
% 21.35/6.06 |
% 21.35/6.07 | Instantiating formula (89) with n6, n4, all_0_6_6, n10 and discharging atoms sum(n6, n4) = all_0_6_6, sum(n6, n4) = n10, yields:
% 21.35/6.07 | (457) all_0_6_6 = n10
% 21.35/6.07 |
% 21.35/6.07 | Equations (457) can reduce 169 to:
% 21.35/6.07 | (458) $false
% 21.35/6.07 |
% 21.35/6.07 |-The branch is then unsatisfiable
% 21.35/6.07 |-Branch two:
% 21.35/6.07 | (595) ~ (all_0_8_8 = n7)
% 21.35/6.07 | (596) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.35/6.07 |
% 21.35/6.07 +-Applying beta-rule and splitting (596), into two cases.
% 21.35/6.07 |-Branch one:
% 21.35/6.07 | (597) all_0_8_8 = n6
% 21.35/6.07 |
% 21.35/6.07 | From (597) and (441) follows:
% 21.35/6.07 | (598) sum(n6, n15) = all_0_2_2
% 21.35/6.07 |
% 21.35/6.07 | From (597) and (443) follows:
% 21.35/6.07 | (599) sum(n6, n0) = all_0_4_4
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (89) with n6, n15, all_0_2_2, n5 and discharging atoms sum(n6, n15) = all_0_2_2, sum(n6, n15) = n5, yields:
% 21.35/6.07 | (600) all_0_2_2 = n5
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (89) with n6, n0, all_0_4_4, n6 and discharging atoms sum(n6, n0) = all_0_4_4, sum(n6, n0) = n6, yields:
% 21.35/6.07 | (601) all_0_4_4 = n6
% 21.35/6.07 |
% 21.35/6.07 | From (600) and (187) follows:
% 21.35/6.07 | (602) pred(n5) = all_0_1_1
% 21.35/6.07 |
% 21.35/6.07 | From (601) and (396) follows:
% 21.35/6.07 | (603) pred(n6) = all_0_3_3
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (37) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 21.35/6.07 | (604) all_0_3_3 = n5
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (37) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 21.35/6.07 | (605) all_0_1_1 = n4
% 21.35/6.07 |
% 21.35/6.07 | From (604) and (261) follows:
% 21.35/6.07 | (606) sum(n5, all_0_0_0) = all_0_6_6
% 21.35/6.07 |
% 21.35/6.07 | From (605) and (440) follows:
% 21.35/6.07 | (607) sum(n15, n4) = all_0_0_0
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (89) with n15, n4, all_0_0_0, n3 and discharging atoms sum(n15, n4) = all_0_0_0, sum(n15, n4) = n3, yields:
% 21.35/6.07 | (608) all_0_0_0 = n3
% 21.35/6.07 |
% 21.35/6.07 | From (608) and (606) follows:
% 21.35/6.07 | (609) sum(n5, n3) = all_0_6_6
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (89) with n5, n3, all_0_6_6, n8 and discharging atoms sum(n5, n3) = all_0_6_6, sum(n5, n3) = n8, yields:
% 21.35/6.07 | (474) all_0_6_6 = n8
% 21.35/6.07 |
% 21.35/6.07 | Equations (474) can reduce 86 to:
% 21.35/6.07 | (458) $false
% 21.35/6.07 |
% 21.35/6.07 |-The branch is then unsatisfiable
% 21.35/6.07 |-Branch two:
% 21.35/6.07 | (612) ~ (all_0_8_8 = n6)
% 21.35/6.07 | (613) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.35/6.07 |
% 21.35/6.07 +-Applying beta-rule and splitting (613), into two cases.
% 21.35/6.07 |-Branch one:
% 21.35/6.07 | (614) all_0_8_8 = n5
% 21.35/6.07 |
% 21.35/6.07 | From (614) and (441) follows:
% 21.35/6.07 | (615) sum(n5, n15) = all_0_2_2
% 21.35/6.07 |
% 21.35/6.07 | From (614) and (443) follows:
% 21.35/6.07 | (616) sum(n5, n0) = all_0_4_4
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (89) with n5, n15, all_0_2_2, n4 and discharging atoms sum(n5, n15) = all_0_2_2, sum(n5, n15) = n4, yields:
% 21.35/6.07 | (617) all_0_2_2 = n4
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (89) with n5, n0, all_0_4_4, n5 and discharging atoms sum(n5, n0) = all_0_4_4, sum(n5, n0) = n5, yields:
% 21.35/6.07 | (618) all_0_4_4 = n5
% 21.35/6.07 |
% 21.35/6.07 | From (617) and (187) follows:
% 21.35/6.07 | (619) pred(n4) = all_0_1_1
% 21.35/6.07 |
% 21.35/6.07 | From (618) and (396) follows:
% 21.35/6.07 | (620) pred(n5) = all_0_3_3
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (37) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 21.35/6.07 | (621) all_0_3_3 = n4
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (37) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 21.35/6.07 | (622) all_0_1_1 = n3
% 21.35/6.07 |
% 21.35/6.07 | From (621) and (261) follows:
% 21.35/6.07 | (623) sum(n4, all_0_0_0) = all_0_6_6
% 21.35/6.07 |
% 21.35/6.07 | From (622) and (440) follows:
% 21.35/6.07 | (624) sum(n15, n3) = all_0_0_0
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (89) with n15, n3, all_0_0_0, n2 and discharging atoms sum(n15, n3) = all_0_0_0, sum(n15, n3) = n2, yields:
% 21.35/6.07 | (625) all_0_0_0 = n2
% 21.35/6.07 |
% 21.35/6.07 | From (625) and (623) follows:
% 21.35/6.07 | (626) sum(n4, n2) = all_0_6_6
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (89) with n4, n2, all_0_6_6, n6 and discharging atoms sum(n4, n2) = all_0_6_6, sum(n4, n2) = n6, yields:
% 21.35/6.07 | (491) all_0_6_6 = n6
% 21.35/6.07 |
% 21.35/6.07 | Equations (491) can reduce 418 to:
% 21.35/6.07 | (458) $false
% 21.35/6.07 |
% 21.35/6.07 |-The branch is then unsatisfiable
% 21.35/6.07 |-Branch two:
% 21.35/6.07 | (629) ~ (all_0_8_8 = n5)
% 21.35/6.07 | (630) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.35/6.07 |
% 21.35/6.07 +-Applying beta-rule and splitting (630), into two cases.
% 21.35/6.07 |-Branch one:
% 21.35/6.07 | (631) all_0_8_8 = n4
% 21.35/6.07 |
% 21.35/6.07 | From (631) and (441) follows:
% 21.35/6.07 | (632) sum(n4, n15) = all_0_2_2
% 21.35/6.07 |
% 21.35/6.07 | From (631) and (443) follows:
% 21.35/6.07 | (633) sum(n4, n0) = all_0_4_4
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (89) with n4, n15, all_0_2_2, n3 and discharging atoms sum(n4, n15) = all_0_2_2, sum(n4, n15) = n3, yields:
% 21.35/6.07 | (634) all_0_2_2 = n3
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (89) with n4, n0, all_0_4_4, n4 and discharging atoms sum(n4, n0) = all_0_4_4, sum(n4, n0) = n4, yields:
% 21.35/6.07 | (635) all_0_4_4 = n4
% 21.35/6.07 |
% 21.35/6.07 | From (634) and (187) follows:
% 21.35/6.07 | (636) pred(n3) = all_0_1_1
% 21.35/6.07 |
% 21.35/6.07 | From (635) and (396) follows:
% 21.35/6.07 | (637) pred(n4) = all_0_3_3
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (37) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 21.35/6.07 | (638) all_0_3_3 = n3
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (37) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 21.35/6.07 | (639) all_0_1_1 = n2
% 21.35/6.07 |
% 21.35/6.07 | From (638) and (261) follows:
% 21.35/6.07 | (640) sum(n3, all_0_0_0) = all_0_6_6
% 21.35/6.07 |
% 21.35/6.07 | From (639) and (440) follows:
% 21.35/6.07 | (641) sum(n15, n2) = all_0_0_0
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (89) with n15, n2, all_0_0_0, n1 and discharging atoms sum(n15, n2) = all_0_0_0, sum(n15, n2) = n1, yields:
% 21.35/6.07 | (642) all_0_0_0 = n1
% 21.35/6.07 |
% 21.35/6.07 | From (642) and (640) follows:
% 21.35/6.07 | (643) sum(n3, n1) = all_0_6_6
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (89) with n3, n1, all_0_6_6, n4 and discharging atoms sum(n3, n1) = all_0_6_6, sum(n3, n1) = n4, yields:
% 21.35/6.07 | (508) all_0_6_6 = n4
% 21.35/6.07 |
% 21.35/6.07 | Equations (508) can reduce 12 to:
% 21.35/6.07 | (458) $false
% 21.35/6.07 |
% 21.35/6.07 |-The branch is then unsatisfiable
% 21.35/6.07 |-Branch two:
% 21.35/6.07 | (646) ~ (all_0_8_8 = n4)
% 21.35/6.07 | (647) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.35/6.07 |
% 21.35/6.07 +-Applying beta-rule and splitting (647), into two cases.
% 21.35/6.07 |-Branch one:
% 21.35/6.07 | (648) all_0_8_8 = n3
% 21.35/6.07 |
% 21.35/6.07 | From (648) and (441) follows:
% 21.35/6.07 | (649) sum(n3, n15) = all_0_2_2
% 21.35/6.07 |
% 21.35/6.07 | From (648) and (443) follows:
% 21.35/6.07 | (650) sum(n3, n0) = all_0_4_4
% 21.35/6.07 |
% 21.35/6.07 | Instantiating formula (89) with n3, n15, all_0_2_2, n2 and discharging atoms sum(n3, n15) = all_0_2_2, sum(n3, n15) = n2, yields:
% 21.67/6.08 | (651) all_0_2_2 = n2
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (89) with n3, n0, all_0_4_4, n3 and discharging atoms sum(n3, n0) = all_0_4_4, sum(n3, n0) = n3, yields:
% 21.67/6.08 | (652) all_0_4_4 = n3
% 21.67/6.08 |
% 21.67/6.08 | From (651) and (187) follows:
% 21.67/6.08 | (653) pred(n2) = all_0_1_1
% 21.67/6.08 |
% 21.67/6.08 | From (652) and (396) follows:
% 21.67/6.08 | (654) pred(n3) = all_0_3_3
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (37) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 21.67/6.08 | (655) all_0_3_3 = n2
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (37) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 21.67/6.08 | (656) all_0_1_1 = n1
% 21.67/6.08 |
% 21.67/6.08 | From (655) and (261) follows:
% 21.67/6.08 | (657) sum(n2, all_0_0_0) = all_0_6_6
% 21.67/6.08 |
% 21.67/6.08 | From (656) and (440) follows:
% 21.67/6.08 | (658) sum(n15, n1) = all_0_0_0
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (89) with n15, n1, all_0_0_0, n0 and discharging atoms sum(n15, n1) = all_0_0_0, sum(n15, n1) = n0, yields:
% 21.67/6.08 | (659) all_0_0_0 = n0
% 21.67/6.08 |
% 21.67/6.08 | From (659) and (657) follows:
% 21.67/6.08 | (660) sum(n2, n0) = all_0_6_6
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (89) with n2, n0, all_0_6_6, n2 and discharging atoms sum(n2, n0) = all_0_6_6, sum(n2, n0) = n2, yields:
% 21.67/6.08 | (525) all_0_6_6 = n2
% 21.67/6.08 |
% 21.67/6.08 | Equations (525) can reduce 231 to:
% 21.67/6.08 | (458) $false
% 21.67/6.08 |
% 21.67/6.08 |-The branch is then unsatisfiable
% 21.67/6.08 |-Branch two:
% 21.67/6.08 | (663) ~ (all_0_8_8 = n3)
% 21.67/6.08 | (664) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.67/6.08 |
% 21.67/6.08 +-Applying beta-rule and splitting (664), into two cases.
% 21.67/6.08 |-Branch one:
% 21.67/6.08 | (665) all_0_8_8 = n2
% 21.67/6.08 |
% 21.67/6.08 | From (665) and (441) follows:
% 21.67/6.08 | (666) sum(n2, n15) = all_0_2_2
% 21.67/6.08 |
% 21.67/6.08 | From (665) and (443) follows:
% 21.67/6.08 | (667) sum(n2, n0) = all_0_4_4
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (89) with n2, n15, all_0_2_2, n1 and discharging atoms sum(n2, n15) = all_0_2_2, sum(n2, n15) = n1, yields:
% 21.67/6.08 | (668) all_0_2_2 = n1
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (89) with n2, n0, all_0_4_4, n2 and discharging atoms sum(n2, n0) = all_0_4_4, sum(n2, n0) = n2, yields:
% 21.67/6.08 | (669) all_0_4_4 = n2
% 21.67/6.08 |
% 21.67/6.08 | From (668) and (187) follows:
% 21.67/6.08 | (670) pred(n1) = all_0_1_1
% 21.67/6.08 |
% 21.67/6.08 | From (669) and (396) follows:
% 21.67/6.08 | (671) pred(n2) = all_0_3_3
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (37) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 21.67/6.08 | (672) all_0_3_3 = n1
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (37) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 21.67/6.08 | (673) all_0_1_1 = n0
% 21.67/6.08 |
% 21.67/6.08 | From (672) and (261) follows:
% 21.67/6.08 | (674) sum(n1, all_0_0_0) = all_0_6_6
% 21.67/6.08 |
% 21.67/6.08 | From (673) and (440) follows:
% 21.67/6.08 | (675) sum(n15, n0) = all_0_0_0
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (89) with n15, n0, all_0_0_0, n15 and discharging atoms sum(n15, n0) = all_0_0_0, sum(n15, n0) = n15, yields:
% 21.67/6.08 | (676) all_0_0_0 = n15
% 21.67/6.08 |
% 21.67/6.08 | From (676) and (674) follows:
% 21.67/6.08 | (677) sum(n1, n15) = all_0_6_6
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (89) with n1, n15, all_0_6_6, n0 and discharging atoms sum(n1, n15) = all_0_6_6, sum(n1, n15) = n0, yields:
% 21.67/6.08 | (542) all_0_6_6 = n0
% 21.67/6.08 |
% 21.67/6.08 | Equations (542) can reduce 400 to:
% 21.67/6.08 | (458) $false
% 21.67/6.08 |
% 21.67/6.08 |-The branch is then unsatisfiable
% 21.67/6.08 |-Branch two:
% 21.67/6.08 | (680) ~ (all_0_8_8 = n2)
% 21.67/6.08 | (681) all_0_8_8 = n1 | all_0_8_8 = n0
% 21.67/6.08 |
% 21.67/6.08 +-Applying beta-rule and splitting (681), into two cases.
% 21.67/6.08 |-Branch one:
% 21.67/6.08 | (682) all_0_8_8 = n1
% 21.67/6.08 |
% 21.67/6.08 | From (682) and (441) follows:
% 21.67/6.08 | (683) sum(n1, n15) = all_0_2_2
% 21.67/6.08 |
% 21.67/6.08 | From (682) and (443) follows:
% 21.67/6.08 | (684) sum(n1, n0) = all_0_4_4
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (89) with n1, n15, all_0_2_2, n0 and discharging atoms sum(n1, n15) = all_0_2_2, sum(n1, n15) = n0, yields:
% 21.67/6.08 | (685) all_0_2_2 = n0
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (89) with n1, n0, all_0_4_4, n1 and discharging atoms sum(n1, n0) = all_0_4_4, sum(n1, n0) = n1, yields:
% 21.67/6.08 | (686) all_0_4_4 = n1
% 21.67/6.08 |
% 21.67/6.08 | From (685) and (187) follows:
% 21.67/6.08 | (687) pred(n0) = all_0_1_1
% 21.67/6.08 |
% 21.67/6.08 | From (686) and (396) follows:
% 21.67/6.08 | (688) pred(n1) = all_0_3_3
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (37) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 21.67/6.08 | (689) all_0_3_3 = n0
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (37) with n0, all_0_1_1, n15 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n15, yields:
% 21.67/6.08 | (690) all_0_1_1 = n15
% 21.67/6.08 |
% 21.67/6.08 | From (689) and (261) follows:
% 21.67/6.08 | (691) sum(n0, all_0_0_0) = all_0_6_6
% 21.67/6.08 |
% 21.67/6.08 | From (690) and (440) follows:
% 21.67/6.08 | (692) sum(n15, n15) = all_0_0_0
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (89) with n15, n15, all_0_0_0, n14 and discharging atoms sum(n15, n15) = all_0_0_0, sum(n15, n15) = n14, yields:
% 21.67/6.08 | (693) all_0_0_0 = n14
% 21.67/6.08 |
% 21.67/6.08 | From (693) and (691) follows:
% 21.67/6.08 | (694) sum(n0, n14) = all_0_6_6
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (89) with n0, n14, all_0_6_6, n14 and discharging atoms sum(n0, n14) = all_0_6_6, sum(n0, n14) = n14, yields:
% 21.67/6.08 | (559) all_0_6_6 = n14
% 21.67/6.08 |
% 21.67/6.08 | Equations (559) can reduce 314 to:
% 21.67/6.08 | (458) $false
% 21.67/6.08 |
% 21.67/6.08 |-The branch is then unsatisfiable
% 21.67/6.08 |-Branch two:
% 21.67/6.08 | (697) ~ (all_0_8_8 = n1)
% 21.67/6.08 | (698) all_0_8_8 = n0
% 21.67/6.08 |
% 21.67/6.08 | From (698) and (441) follows:
% 21.67/6.08 | (699) sum(n0, n15) = all_0_2_2
% 21.67/6.08 |
% 21.67/6.08 | From (698) and (443) follows:
% 21.67/6.08 | (700) sum(n0, n0) = all_0_4_4
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (89) with n0, n15, all_0_2_2, n15 and discharging atoms sum(n0, n15) = all_0_2_2, sum(n0, n15) = n15, yields:
% 21.67/6.08 | (701) all_0_2_2 = n15
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (89) with n0, n0, all_0_4_4, n0 and discharging atoms sum(n0, n0) = all_0_4_4, sum(n0, n0) = n0, yields:
% 21.67/6.08 | (702) all_0_4_4 = n0
% 21.67/6.08 |
% 21.67/6.08 | From (701) and (187) follows:
% 21.67/6.08 | (703) pred(n15) = all_0_1_1
% 21.67/6.08 |
% 21.67/6.08 | From (702) and (396) follows:
% 21.67/6.08 | (704) pred(n0) = all_0_3_3
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (37) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 21.67/6.08 | (705) all_0_1_1 = n14
% 21.67/6.08 |
% 21.67/6.08 | Instantiating formula (37) with n0, all_0_3_3, n15 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n15, yields:
% 21.67/6.09 | (706) all_0_3_3 = n15
% 21.67/6.09 |
% 21.67/6.09 | From (706) and (261) follows:
% 21.67/6.09 | (707) sum(n15, all_0_0_0) = all_0_6_6
% 21.67/6.09 |
% 21.67/6.09 | From (705) and (440) follows:
% 21.67/6.09 | (708) sum(n15, n14) = all_0_0_0
% 21.67/6.09 |
% 21.67/6.09 | Instantiating formula (89) with n15, n14, all_0_0_0, n13 and discharging atoms sum(n15, n14) = all_0_0_0, sum(n15, n14) = n13, yields:
% 21.67/6.09 | (709) all_0_0_0 = n13
% 21.67/6.09 |
% 21.67/6.09 | From (709) and (707) follows:
% 21.67/6.09 | (710) sum(n15, n13) = all_0_6_6
% 21.67/6.09 |
% 21.67/6.09 | Instantiating formula (89) with n15, n13, all_0_6_6, n12 and discharging atoms sum(n15, n13) = all_0_6_6, sum(n15, n13) = n12, yields:
% 21.67/6.09 | (576) all_0_6_6 = n12
% 21.67/6.09 |
% 21.67/6.09 | Equations (576) can reduce 42 to:
% 21.67/6.09 | (458) $false
% 21.67/6.09 |
% 21.67/6.09 |-The branch is then unsatisfiable
% 21.67/6.09 |-Branch two:
% 21.67/6.09 | (713) ~ (all_0_7_7 = n15)
% 21.67/6.09 | (714) all_0_7_7 = n14 | all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 21.67/6.09 |
% 21.67/6.09 +-Applying beta-rule and splitting (113), into two cases.
% 21.67/6.09 |-Branch one:
% 21.67/6.09 | (444) all_0_8_8 = n15
% 21.67/6.09 |
% 21.67/6.09 | From (444) and (64) follows:
% 21.67/6.09 | (716) sum(n15, all_0_5_5) = all_0_4_4
% 21.67/6.09 |
% 21.67/6.09 | From (444) and (160) follows:
% 21.67/6.09 | (717) sum(n15, all_0_7_7) = all_0_2_2
% 21.67/6.09 |
% 21.67/6.09 +-Applying beta-rule and splitting (714), into two cases.
% 21.67/6.09 |-Branch one:
% 21.67/6.09 | (718) all_0_7_7 = n14
% 21.67/6.09 |
% 21.67/6.09 | From (718) and (176) follows:
% 21.67/6.09 | (719) succ(n14) = all_0_5_5
% 21.67/6.09 |
% 21.67/6.09 | From (718) and (59) follows:
% 21.67/6.09 | (720) sum(n14, all_0_1_1) = all_0_0_0
% 21.67/6.09 |
% 21.67/6.09 | From (718) and (717) follows:
% 21.67/6.09 | (721) sum(n15, n14) = all_0_2_2
% 21.67/6.09 |
% 21.67/6.09 | Instantiating formula (219) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 21.67/6.09 | (722) all_0_5_5 = n15
% 21.67/6.09 |
% 21.67/6.09 | Instantiating formula (89) with n15, n14, all_0_2_2, n13 and discharging atoms sum(n15, n14) = all_0_2_2, sum(n15, n14) = n13, yields:
% 21.67/6.09 | (464) all_0_2_2 = n13
% 21.67/6.09 |
% 21.67/6.09 | From (464) and (187) follows:
% 21.67/6.09 | (466) pred(n13) = all_0_1_1
% 21.67/6.09 |
% 21.67/6.09 | From (722) and (716) follows:
% 21.67/6.09 | (725) sum(n15, n15) = all_0_4_4
% 21.67/6.09 |
% 21.67/6.09 | Instantiating formula (37) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 21.67/6.09 | (469) all_0_1_1 = n12
% 21.67/6.09 |
% 21.67/6.09 | Instantiating formula (89) with n15, n15, all_0_4_4, n14 and discharging atoms sum(n15, n15) = all_0_4_4, sum(n15, n15) = n14, yields:
% 21.67/6.09 | (465) all_0_4_4 = n14
% 21.67/6.09 |
% 21.67/6.09 | From (465) and (396) follows:
% 21.67/6.09 | (467) pred(n14) = all_0_3_3
% 21.67/6.09 |
% 21.67/6.09 | From (469) and (720) follows:
% 21.67/6.09 | (729) sum(n14, n12) = all_0_0_0
% 21.67/6.09 |
% 21.67/6.09 | Instantiating formula (37) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 21.67/6.09 | (468) all_0_3_3 = n13
% 21.67/6.09 |
% 21.67/6.09 | Instantiating formula (89) with n14, n12, all_0_0_0, n10 and discharging atoms sum(n14, n12) = all_0_0_0, sum(n14, n12) = n10, yields:
% 21.67/6.09 | (489) all_0_0_0 = n10
% 21.67/6.09 |
% 21.67/6.09 | From (468)(489) and (261) follows:
% 21.67/6.09 | (732) sum(n13, n10) = all_0_6_6
% 21.67/6.09 |
% 21.67/6.09 | Instantiating formula (89) with n13, n10, all_0_6_6, n7 and discharging atoms sum(n13, n10) = all_0_6_6, sum(n13, n10) = n7, yields:
% 21.67/6.09 | (733) all_0_6_6 = n7
% 21.67/6.09 |
% 21.67/6.09 | Equations (733) can reduce 274 to:
% 21.67/6.09 | (458) $false
% 21.67/6.09 |
% 21.67/6.09 |-The branch is then unsatisfiable
% 21.67/6.09 |-Branch two:
% 21.67/6.09 | (735) ~ (all_0_7_7 = n14)
% 21.67/6.09 | (736) all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 21.67/6.09 |
% 21.67/6.09 +-Applying beta-rule and splitting (736), into two cases.
% 21.67/6.09 |-Branch one:
% 21.67/6.09 | (737) all_0_7_7 = n13
% 21.67/6.09 |
% 21.67/6.09 | From (737) and (176) follows:
% 21.67/6.09 | (738) succ(n13) = all_0_5_5
% 21.67/6.09 |
% 21.67/6.09 | From (737) and (59) follows:
% 21.67/6.09 | (739) sum(n13, all_0_1_1) = all_0_0_0
% 21.67/6.09 |
% 21.67/6.09 | From (737) and (717) follows:
% 21.67/6.09 | (740) sum(n15, n13) = all_0_2_2
% 21.67/6.09 |
% 21.67/6.09 | Instantiating formula (219) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 21.67/6.09 | (741) all_0_5_5 = n14
% 21.67/6.09 |
% 21.67/6.09 | Instantiating formula (89) with n15, n13, all_0_2_2, n12 and discharging atoms sum(n15, n13) = all_0_2_2, sum(n15, n13) = n12, yields:
% 21.67/6.09 | (481) all_0_2_2 = n12
% 21.67/6.09 |
% 21.67/6.09 | From (481) and (187) follows:
% 21.67/6.09 | (483) pred(n12) = all_0_1_1
% 21.67/6.09 |
% 21.67/6.09 | From (741) and (716) follows:
% 21.67/6.09 | (744) sum(n15, n14) = all_0_4_4
% 21.67/6.09 |
% 21.67/6.09 | Instantiating formula (37) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 21.67/6.09 | (486) all_0_1_1 = n11
% 21.67/6.09 |
% 21.67/6.09 | Instantiating formula (89) with n15, n14, all_0_4_4, n13 and discharging atoms sum(n15, n14) = all_0_4_4, sum(n15, n14) = n13, yields:
% 21.67/6.09 | (482) all_0_4_4 = n13
% 21.67/6.09 |
% 21.67/6.09 | From (482) and (396) follows:
% 21.67/6.09 | (484) pred(n13) = all_0_3_3
% 21.67/6.09 |
% 21.67/6.09 | From (486) and (739) follows:
% 21.67/6.09 | (748) sum(n13, n11) = all_0_0_0
% 21.67/6.09 |
% 21.67/6.09 | Instantiating formula (37) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 21.67/6.09 | (485) all_0_3_3 = n12
% 21.67/6.09 |
% 21.67/6.09 | Instantiating formula (89) with n13, n11, all_0_0_0, n8 and discharging atoms sum(n13, n11) = all_0_0_0, sum(n13, n11) = n8, yields:
% 21.67/6.09 | (523) all_0_0_0 = n8
% 21.67/6.09 |
% 21.67/6.09 | From (485)(523) and (261) follows:
% 21.67/6.09 | (751) sum(n12, n8) = all_0_6_6
% 21.67/6.09 |
% 21.67/6.09 | Instantiating formula (89) with n12, n8, all_0_6_6, n4 and discharging atoms sum(n12, n8) = all_0_6_6, sum(n12, n8) = n4, yields:
% 21.67/6.09 | (508) all_0_6_6 = n4
% 21.67/6.09 |
% 21.67/6.09 | Equations (508) can reduce 12 to:
% 21.67/6.09 | (458) $false
% 21.67/6.09 |
% 21.67/6.09 |-The branch is then unsatisfiable
% 21.67/6.09 |-Branch two:
% 21.67/6.09 | (754) ~ (all_0_7_7 = n13)
% 21.67/6.09 | (755) all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 21.67/6.09 |
% 21.67/6.09 +-Applying beta-rule and splitting (755), into two cases.
% 21.67/6.09 |-Branch one:
% 21.67/6.10 | (756) all_0_7_7 = n12
% 21.67/6.10 |
% 21.67/6.10 | From (756) and (176) follows:
% 21.67/6.10 | (757) succ(n12) = all_0_5_5
% 21.67/6.10 |
% 21.67/6.10 | From (756) and (59) follows:
% 21.67/6.10 | (758) sum(n12, all_0_1_1) = all_0_0_0
% 21.67/6.10 |
% 21.67/6.10 | From (756) and (717) follows:
% 21.67/6.10 | (759) sum(n15, n12) = all_0_2_2
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (219) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 21.67/6.10 | (760) all_0_5_5 = n13
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (89) with n15, n12, all_0_2_2, n11 and discharging atoms sum(n15, n12) = all_0_2_2, sum(n15, n12) = n11, yields:
% 21.67/6.10 | (498) all_0_2_2 = n11
% 21.67/6.10 |
% 21.67/6.10 | From (498) and (187) follows:
% 21.67/6.10 | (500) pred(n11) = all_0_1_1
% 21.67/6.10 |
% 21.67/6.10 | From (760) and (716) follows:
% 21.67/6.10 | (763) sum(n15, n13) = all_0_4_4
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (37) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 21.67/6.10 | (503) all_0_1_1 = n10
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (89) with n15, n13, all_0_4_4, n12 and discharging atoms sum(n15, n13) = all_0_4_4, sum(n15, n13) = n12, yields:
% 21.67/6.10 | (499) all_0_4_4 = n12
% 21.67/6.10 |
% 21.67/6.10 | From (499) and (396) follows:
% 21.67/6.10 | (501) pred(n12) = all_0_3_3
% 21.67/6.10 |
% 21.67/6.10 | From (503) and (758) follows:
% 21.67/6.10 | (767) sum(n12, n10) = all_0_0_0
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (37) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 21.67/6.10 | (502) all_0_3_3 = n11
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (89) with n12, n10, all_0_0_0, n6 and discharging atoms sum(n12, n10) = all_0_0_0, sum(n12, n10) = n6, yields:
% 21.67/6.10 | (557) all_0_0_0 = n6
% 21.67/6.10 |
% 21.67/6.10 | From (502)(557) and (261) follows:
% 21.67/6.10 | (770) sum(n11, n6) = all_0_6_6
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (89) with n11, n6, all_0_6_6, n1 and discharging atoms sum(n11, n6) = all_0_6_6, sum(n11, n6) = n1, yields:
% 21.67/6.10 | (771) all_0_6_6 = n1
% 21.67/6.10 |
% 21.67/6.10 | Equations (771) can reduce 38 to:
% 21.67/6.10 | (458) $false
% 21.67/6.10 |
% 21.67/6.10 |-The branch is then unsatisfiable
% 21.67/6.10 |-Branch two:
% 21.67/6.10 | (773) ~ (all_0_7_7 = n12)
% 21.67/6.10 | (774) all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 21.67/6.10 |
% 21.67/6.10 +-Applying beta-rule and splitting (774), into two cases.
% 21.67/6.10 |-Branch one:
% 21.67/6.10 | (775) all_0_7_7 = n11
% 21.67/6.10 |
% 21.67/6.10 | From (775) and (176) follows:
% 21.67/6.10 | (776) succ(n11) = all_0_5_5
% 21.67/6.10 |
% 21.67/6.10 | From (775) and (59) follows:
% 21.67/6.10 | (777) sum(n11, all_0_1_1) = all_0_0_0
% 21.67/6.10 |
% 21.67/6.10 | From (775) and (717) follows:
% 21.67/6.10 | (778) sum(n15, n11) = all_0_2_2
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (219) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 21.67/6.10 | (779) all_0_5_5 = n12
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (89) with n15, n11, all_0_2_2, n10 and discharging atoms sum(n15, n11) = all_0_2_2, sum(n15, n11) = n10, yields:
% 21.67/6.10 | (515) all_0_2_2 = n10
% 21.67/6.10 |
% 21.67/6.10 | From (515) and (187) follows:
% 21.67/6.10 | (517) pred(n10) = all_0_1_1
% 21.67/6.10 |
% 21.67/6.10 | From (779) and (716) follows:
% 21.67/6.10 | (782) sum(n15, n12) = all_0_4_4
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (37) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 21.67/6.10 | (520) all_0_1_1 = n9
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (89) with n15, n12, all_0_4_4, n11 and discharging atoms sum(n15, n12) = all_0_4_4, sum(n15, n12) = n11, yields:
% 21.67/6.10 | (516) all_0_4_4 = n11
% 21.67/6.10 |
% 21.67/6.10 | From (516) and (396) follows:
% 21.67/6.10 | (518) pred(n11) = all_0_3_3
% 21.67/6.10 |
% 21.67/6.10 | From (520) and (777) follows:
% 21.67/6.10 | (786) sum(n11, n9) = all_0_0_0
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (37) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 21.67/6.10 | (519) all_0_3_3 = n10
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (89) with n11, n9, all_0_0_0, n4 and discharging atoms sum(n11, n9) = all_0_0_0, sum(n11, n9) = n4, yields:
% 21.67/6.10 | (591) all_0_0_0 = n4
% 21.67/6.10 |
% 21.67/6.10 | From (519)(591) and (261) follows:
% 21.67/6.10 | (789) sum(n10, n4) = all_0_6_6
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (89) with n10, n4, all_0_6_6, n14 and discharging atoms sum(n10, n4) = all_0_6_6, sum(n10, n4) = n14, yields:
% 21.67/6.10 | (559) all_0_6_6 = n14
% 21.67/6.10 |
% 21.67/6.10 | Equations (559) can reduce 314 to:
% 21.67/6.10 | (458) $false
% 21.67/6.10 |
% 21.67/6.10 |-The branch is then unsatisfiable
% 21.67/6.10 |-Branch two:
% 21.67/6.10 | (792) ~ (all_0_7_7 = n11)
% 21.67/6.10 | (793) all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 21.67/6.10 |
% 21.67/6.10 +-Applying beta-rule and splitting (793), into two cases.
% 21.67/6.10 |-Branch one:
% 21.67/6.10 | (794) all_0_7_7 = n10
% 21.67/6.10 |
% 21.67/6.10 | From (794) and (176) follows:
% 21.67/6.10 | (795) succ(n10) = all_0_5_5
% 21.67/6.10 |
% 21.67/6.10 | From (794) and (59) follows:
% 21.67/6.10 | (796) sum(n10, all_0_1_1) = all_0_0_0
% 21.67/6.10 |
% 21.67/6.10 | From (794) and (717) follows:
% 21.67/6.10 | (797) sum(n15, n10) = all_0_2_2
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (219) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 21.67/6.10 | (798) all_0_5_5 = n11
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (89) with n15, n10, all_0_2_2, n9 and discharging atoms sum(n15, n10) = all_0_2_2, sum(n15, n10) = n9, yields:
% 21.67/6.10 | (532) all_0_2_2 = n9
% 21.67/6.10 |
% 21.67/6.10 | From (532) and (187) follows:
% 21.67/6.10 | (534) pred(n9) = all_0_1_1
% 21.67/6.10 |
% 21.67/6.10 | From (798) and (716) follows:
% 21.67/6.10 | (801) sum(n15, n11) = all_0_4_4
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (37) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 21.67/6.10 | (537) all_0_1_1 = n8
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (89) with n15, n11, all_0_4_4, n10 and discharging atoms sum(n15, n11) = all_0_4_4, sum(n15, n11) = n10, yields:
% 21.67/6.10 | (533) all_0_4_4 = n10
% 21.67/6.10 |
% 21.67/6.10 | From (533) and (396) follows:
% 21.67/6.10 | (535) pred(n10) = all_0_3_3
% 21.67/6.10 |
% 21.67/6.10 | From (537) and (796) follows:
% 21.67/6.10 | (805) sum(n10, n8) = all_0_0_0
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (37) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 21.67/6.10 | (536) all_0_3_3 = n9
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (89) with n10, n8, all_0_0_0, n2 and discharging atoms sum(n10, n8) = all_0_0_0, sum(n10, n8) = n2, yields:
% 21.67/6.10 | (625) all_0_0_0 = n2
% 21.67/6.10 |
% 21.67/6.10 | From (536)(625) and (261) follows:
% 21.67/6.10 | (808) sum(n9, n2) = all_0_6_6
% 21.67/6.10 |
% 21.67/6.10 | Instantiating formula (89) with n9, n2, all_0_6_6, n11 and discharging atoms sum(n9, n2) = all_0_6_6, sum(n9, n2) = n11, yields:
% 21.67/6.10 | (809) all_0_6_6 = n11
% 21.67/6.10 |
% 21.67/6.11 | Equations (809) can reduce 70 to:
% 21.67/6.11 | (458) $false
% 21.67/6.11 |
% 21.67/6.11 |-The branch is then unsatisfiable
% 21.67/6.11 |-Branch two:
% 21.67/6.11 | (811) ~ (all_0_7_7 = n10)
% 21.67/6.11 | (812) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 21.67/6.11 |
% 21.67/6.11 +-Applying beta-rule and splitting (812), into two cases.
% 21.67/6.11 |-Branch one:
% 21.67/6.11 | (813) all_0_7_7 = n9
% 21.67/6.11 |
% 21.67/6.11 | From (813) and (176) follows:
% 21.67/6.11 | (814) succ(n9) = all_0_5_5
% 21.67/6.11 |
% 21.67/6.11 | From (813) and (59) follows:
% 21.67/6.11 | (815) sum(n9, all_0_1_1) = all_0_0_0
% 21.67/6.11 |
% 21.67/6.11 | From (813) and (717) follows:
% 21.67/6.11 | (816) sum(n15, n9) = all_0_2_2
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (219) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 21.67/6.11 | (817) all_0_5_5 = n10
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (89) with n15, n9, all_0_2_2, n8 and discharging atoms sum(n15, n9) = all_0_2_2, sum(n15, n9) = n8, yields:
% 21.67/6.11 | (549) all_0_2_2 = n8
% 21.67/6.11 |
% 21.67/6.11 | From (549) and (187) follows:
% 21.67/6.11 | (551) pred(n8) = all_0_1_1
% 21.67/6.11 |
% 21.67/6.11 | From (817) and (716) follows:
% 21.67/6.11 | (820) sum(n15, n10) = all_0_4_4
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (37) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 21.67/6.11 | (554) all_0_1_1 = n7
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (89) with n15, n10, all_0_4_4, n9 and discharging atoms sum(n15, n10) = all_0_4_4, sum(n15, n10) = n9, yields:
% 21.67/6.11 | (550) all_0_4_4 = n9
% 21.67/6.11 |
% 21.67/6.11 | From (550) and (396) follows:
% 21.67/6.11 | (552) pred(n9) = all_0_3_3
% 21.67/6.11 |
% 21.67/6.11 | From (554) and (815) follows:
% 21.67/6.11 | (824) sum(n9, n7) = all_0_0_0
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (37) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 21.67/6.11 | (553) all_0_3_3 = n8
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (89) with n9, n7, all_0_0_0, n0 and discharging atoms sum(n9, n7) = all_0_0_0, sum(n9, n7) = n0, yields:
% 21.67/6.11 | (659) all_0_0_0 = n0
% 21.67/6.11 |
% 21.67/6.11 | From (553)(659) and (261) follows:
% 21.67/6.11 | (827) sum(n8, n0) = all_0_6_6
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (89) with n8, n0, all_0_6_6, n8 and discharging atoms sum(n8, n0) = all_0_6_6, sum(n8, n0) = n8, yields:
% 21.67/6.11 | (474) all_0_6_6 = n8
% 21.67/6.11 |
% 21.67/6.11 | Equations (474) can reduce 86 to:
% 21.67/6.11 | (458) $false
% 21.67/6.11 |
% 21.67/6.11 |-The branch is then unsatisfiable
% 21.67/6.11 |-Branch two:
% 21.67/6.11 | (830) ~ (all_0_7_7 = n9)
% 21.67/6.11 | (831) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 21.67/6.11 |
% 21.67/6.11 +-Applying beta-rule and splitting (831), into two cases.
% 21.67/6.11 |-Branch one:
% 21.67/6.11 | (832) all_0_7_7 = n8
% 21.67/6.11 |
% 21.67/6.11 | From (832) and (176) follows:
% 21.67/6.11 | (833) succ(n8) = all_0_5_5
% 21.67/6.11 |
% 21.67/6.11 | From (832) and (59) follows:
% 21.67/6.11 | (834) sum(n8, all_0_1_1) = all_0_0_0
% 21.67/6.11 |
% 21.67/6.11 | From (832) and (717) follows:
% 21.67/6.11 | (835) sum(n15, n8) = all_0_2_2
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (219) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 21.67/6.11 | (836) all_0_5_5 = n9
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (89) with n15, n8, all_0_2_2, n7 and discharging atoms sum(n15, n8) = all_0_2_2, sum(n15, n8) = n7, yields:
% 21.67/6.11 | (566) all_0_2_2 = n7
% 21.67/6.11 |
% 21.67/6.11 | From (566) and (187) follows:
% 21.67/6.11 | (568) pred(n7) = all_0_1_1
% 21.67/6.11 |
% 21.67/6.11 | From (836) and (716) follows:
% 21.67/6.11 | (839) sum(n15, n9) = all_0_4_4
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (37) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 21.67/6.11 | (571) all_0_1_1 = n6
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (89) with n15, n9, all_0_4_4, n8 and discharging atoms sum(n15, n9) = all_0_4_4, sum(n15, n9) = n8, yields:
% 21.67/6.11 | (567) all_0_4_4 = n8
% 21.67/6.11 |
% 21.67/6.11 | From (567) and (396) follows:
% 21.67/6.11 | (569) pred(n8) = all_0_3_3
% 21.67/6.11 |
% 21.67/6.11 | From (571) and (834) follows:
% 21.67/6.11 | (843) sum(n8, n6) = all_0_0_0
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (37) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 21.67/6.11 | (570) all_0_3_3 = n7
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (89) with n8, n6, all_0_0_0, n14 and discharging atoms sum(n8, n6) = all_0_0_0, sum(n8, n6) = n14, yields:
% 21.67/6.11 | (693) all_0_0_0 = n14
% 21.67/6.11 |
% 21.67/6.11 | From (570)(693) and (261) follows:
% 21.67/6.11 | (846) sum(n7, n14) = all_0_6_6
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (89) with n7, n14, all_0_6_6, n5 and discharging atoms sum(n7, n14) = all_0_6_6, sum(n7, n14) = n5, yields:
% 21.67/6.11 | (847) all_0_6_6 = n5
% 21.67/6.11 |
% 21.67/6.11 | Equations (847) can reduce 409 to:
% 21.67/6.11 | (458) $false
% 21.67/6.11 |
% 21.67/6.11 |-The branch is then unsatisfiable
% 21.67/6.11 |-Branch two:
% 21.67/6.11 | (849) ~ (all_0_7_7 = n8)
% 21.67/6.11 | (850) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 21.67/6.11 |
% 21.67/6.11 +-Applying beta-rule and splitting (850), into two cases.
% 21.67/6.11 |-Branch one:
% 21.67/6.11 | (851) all_0_7_7 = n7
% 21.67/6.11 |
% 21.67/6.11 | From (851) and (176) follows:
% 21.67/6.11 | (852) succ(n7) = all_0_5_5
% 21.67/6.11 |
% 21.67/6.11 | From (851) and (59) follows:
% 21.67/6.11 | (853) sum(n7, all_0_1_1) = all_0_0_0
% 21.67/6.11 |
% 21.67/6.11 | From (851) and (717) follows:
% 21.67/6.11 | (854) sum(n15, n7) = all_0_2_2
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (219) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 21.67/6.11 | (855) all_0_5_5 = n8
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (89) with n15, n7, all_0_2_2, n6 and discharging atoms sum(n15, n7) = all_0_2_2, sum(n15, n7) = n6, yields:
% 21.67/6.11 | (583) all_0_2_2 = n6
% 21.67/6.11 |
% 21.67/6.11 | From (583) and (187) follows:
% 21.67/6.11 | (585) pred(n6) = all_0_1_1
% 21.67/6.11 |
% 21.67/6.11 | From (855) and (716) follows:
% 21.67/6.11 | (858) sum(n15, n8) = all_0_4_4
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (37) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 21.67/6.11 | (588) all_0_1_1 = n5
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (89) with n15, n8, all_0_4_4, n7 and discharging atoms sum(n15, n8) = all_0_4_4, sum(n15, n8) = n7, yields:
% 21.67/6.11 | (584) all_0_4_4 = n7
% 21.67/6.11 |
% 21.67/6.11 | From (584) and (396) follows:
% 21.67/6.11 | (586) pred(n7) = all_0_3_3
% 21.67/6.11 |
% 21.67/6.11 | From (588) and (853) follows:
% 21.67/6.11 | (862) sum(n7, n5) = all_0_0_0
% 21.67/6.11 |
% 21.67/6.11 | Instantiating formula (37) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 21.67/6.12 | (587) all_0_3_3 = n6
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (89) with n7, n5, all_0_0_0, n12 and discharging atoms sum(n7, n5) = all_0_0_0, sum(n7, n5) = n12, yields:
% 21.67/6.12 | (455) all_0_0_0 = n12
% 21.67/6.12 |
% 21.67/6.12 | From (587)(455) and (261) follows:
% 21.67/6.12 | (865) sum(n6, n12) = all_0_6_6
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (89) with n6, n12, all_0_6_6, n2 and discharging atoms sum(n6, n12) = all_0_6_6, sum(n6, n12) = n2, yields:
% 21.67/6.12 | (525) all_0_6_6 = n2
% 21.67/6.12 |
% 21.67/6.12 | Equations (525) can reduce 231 to:
% 21.67/6.12 | (458) $false
% 21.67/6.12 |
% 21.67/6.12 |-The branch is then unsatisfiable
% 21.67/6.12 |-Branch two:
% 21.67/6.12 | (868) ~ (all_0_7_7 = n7)
% 21.67/6.12 | (869) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 21.67/6.12 |
% 21.67/6.12 +-Applying beta-rule and splitting (869), into two cases.
% 21.67/6.12 |-Branch one:
% 21.67/6.12 | (870) all_0_7_7 = n6
% 21.67/6.12 |
% 21.67/6.12 | From (870) and (176) follows:
% 21.67/6.12 | (871) succ(n6) = all_0_5_5
% 21.67/6.12 |
% 21.67/6.12 | From (870) and (59) follows:
% 21.67/6.12 | (872) sum(n6, all_0_1_1) = all_0_0_0
% 21.67/6.12 |
% 21.67/6.12 | From (870) and (717) follows:
% 21.67/6.12 | (873) sum(n15, n6) = all_0_2_2
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (219) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 21.67/6.12 | (874) all_0_5_5 = n7
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (89) with n15, n6, all_0_2_2, n5 and discharging atoms sum(n15, n6) = all_0_2_2, sum(n15, n6) = n5, yields:
% 21.67/6.12 | (600) all_0_2_2 = n5
% 21.67/6.12 |
% 21.67/6.12 | From (600) and (187) follows:
% 21.67/6.12 | (602) pred(n5) = all_0_1_1
% 21.67/6.12 |
% 21.67/6.12 | From (874) and (716) follows:
% 21.67/6.12 | (877) sum(n15, n7) = all_0_4_4
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (37) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 21.67/6.12 | (605) all_0_1_1 = n4
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (89) with n15, n7, all_0_4_4, n6 and discharging atoms sum(n15, n7) = all_0_4_4, sum(n15, n7) = n6, yields:
% 21.67/6.12 | (601) all_0_4_4 = n6
% 21.67/6.12 |
% 21.67/6.12 | From (601) and (396) follows:
% 21.67/6.12 | (603) pred(n6) = all_0_3_3
% 21.67/6.12 |
% 21.67/6.12 | From (605) and (872) follows:
% 21.67/6.12 | (881) sum(n6, n4) = all_0_0_0
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (37) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 21.67/6.12 | (604) all_0_3_3 = n5
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (89) with n6, n4, all_0_0_0, n10 and discharging atoms sum(n6, n4) = all_0_0_0, sum(n6, n4) = n10, yields:
% 21.67/6.12 | (489) all_0_0_0 = n10
% 21.67/6.12 |
% 21.67/6.12 | From (604)(489) and (261) follows:
% 21.67/6.12 | (884) sum(n5, n10) = all_0_6_6
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (89) with n5, n10, all_0_6_6, n15 and discharging atoms sum(n5, n10) = all_0_6_6, sum(n5, n10) = n15, yields:
% 21.67/6.12 | (885) all_0_6_6 = n15
% 21.67/6.12 |
% 21.67/6.12 | Equations (885) can reduce 225 to:
% 21.67/6.12 | (458) $false
% 21.67/6.12 |
% 21.67/6.12 |-The branch is then unsatisfiable
% 21.67/6.12 |-Branch two:
% 21.67/6.12 | (887) ~ (all_0_7_7 = n6)
% 21.67/6.12 | (888) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 21.67/6.12 |
% 21.67/6.12 +-Applying beta-rule and splitting (888), into two cases.
% 21.67/6.12 |-Branch one:
% 21.67/6.12 | (889) all_0_7_7 = n5
% 21.67/6.12 |
% 21.67/6.12 | From (889) and (176) follows:
% 21.67/6.12 | (890) succ(n5) = all_0_5_5
% 21.67/6.12 |
% 21.67/6.12 | From (889) and (59) follows:
% 21.67/6.12 | (891) sum(n5, all_0_1_1) = all_0_0_0
% 21.67/6.12 |
% 21.67/6.12 | From (889) and (717) follows:
% 21.67/6.12 | (892) sum(n15, n5) = all_0_2_2
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (219) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 21.67/6.12 | (893) all_0_5_5 = n6
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (89) with n15, n5, all_0_2_2, n4 and discharging atoms sum(n15, n5) = all_0_2_2, sum(n15, n5) = n4, yields:
% 21.67/6.12 | (617) all_0_2_2 = n4
% 21.67/6.12 |
% 21.67/6.12 | From (617) and (187) follows:
% 21.67/6.12 | (619) pred(n4) = all_0_1_1
% 21.67/6.12 |
% 21.67/6.12 | From (893) and (716) follows:
% 21.67/6.12 | (896) sum(n15, n6) = all_0_4_4
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (37) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 21.67/6.12 | (622) all_0_1_1 = n3
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (89) with n15, n6, all_0_4_4, n5 and discharging atoms sum(n15, n6) = all_0_4_4, sum(n15, n6) = n5, yields:
% 21.67/6.12 | (618) all_0_4_4 = n5
% 21.67/6.12 |
% 21.67/6.12 | From (618) and (396) follows:
% 21.67/6.12 | (620) pred(n5) = all_0_3_3
% 21.67/6.12 |
% 21.67/6.12 | From (622) and (891) follows:
% 21.67/6.12 | (900) sum(n5, n3) = all_0_0_0
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (37) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 21.67/6.12 | (621) all_0_3_3 = n4
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (89) with n5, n3, all_0_0_0, n8 and discharging atoms sum(n5, n3) = all_0_0_0, sum(n5, n3) = n8, yields:
% 21.67/6.12 | (523) all_0_0_0 = n8
% 21.67/6.12 |
% 21.67/6.12 | From (621)(523) and (261) follows:
% 21.67/6.12 | (903) sum(n4, n8) = all_0_6_6
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (89) with n4, n8, all_0_6_6, n12 and discharging atoms sum(n4, n8) = all_0_6_6, sum(n4, n8) = n12, yields:
% 21.67/6.12 | (576) all_0_6_6 = n12
% 21.67/6.12 |
% 21.67/6.12 | Equations (576) can reduce 42 to:
% 21.67/6.12 | (458) $false
% 21.67/6.12 |
% 21.67/6.12 |-The branch is then unsatisfiable
% 21.67/6.12 |-Branch two:
% 21.67/6.12 | (906) ~ (all_0_7_7 = n5)
% 21.67/6.12 | (907) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 21.67/6.12 |
% 21.67/6.12 +-Applying beta-rule and splitting (907), into two cases.
% 21.67/6.12 |-Branch one:
% 21.67/6.12 | (908) all_0_7_7 = n4
% 21.67/6.12 |
% 21.67/6.12 | From (908) and (176) follows:
% 21.67/6.12 | (909) succ(n4) = all_0_5_5
% 21.67/6.12 |
% 21.67/6.12 | From (908) and (59) follows:
% 21.67/6.12 | (910) sum(n4, all_0_1_1) = all_0_0_0
% 21.67/6.12 |
% 21.67/6.12 | From (908) and (717) follows:
% 21.67/6.12 | (911) sum(n15, n4) = all_0_2_2
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (219) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 21.67/6.12 | (912) all_0_5_5 = n5
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (89) with n15, n4, all_0_2_2, n3 and discharging atoms sum(n15, n4) = all_0_2_2, sum(n15, n4) = n3, yields:
% 21.67/6.12 | (634) all_0_2_2 = n3
% 21.67/6.12 |
% 21.67/6.12 | From (634) and (187) follows:
% 21.67/6.12 | (636) pred(n3) = all_0_1_1
% 21.67/6.12 |
% 21.67/6.12 | From (912) and (716) follows:
% 21.67/6.12 | (915) sum(n15, n5) = all_0_4_4
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (37) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 21.67/6.12 | (639) all_0_1_1 = n2
% 21.67/6.12 |
% 21.67/6.12 | Instantiating formula (89) with n15, n5, all_0_4_4, n4 and discharging atoms sum(n15, n5) = all_0_4_4, sum(n15, n5) = n4, yields:
% 21.67/6.12 | (635) all_0_4_4 = n4
% 21.67/6.13 |
% 21.67/6.13 | From (635) and (396) follows:
% 21.67/6.13 | (637) pred(n4) = all_0_3_3
% 21.67/6.13 |
% 21.67/6.13 | From (639) and (910) follows:
% 21.67/6.13 | (919) sum(n4, n2) = all_0_0_0
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (37) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 21.67/6.13 | (638) all_0_3_3 = n3
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (89) with n4, n2, all_0_0_0, n6 and discharging atoms sum(n4, n2) = all_0_0_0, sum(n4, n2) = n6, yields:
% 21.67/6.13 | (557) all_0_0_0 = n6
% 21.67/6.13 |
% 21.67/6.13 | From (638)(557) and (261) follows:
% 21.67/6.13 | (922) sum(n3, n6) = all_0_6_6
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (89) with n3, n6, all_0_6_6, n9 and discharging atoms sum(n3, n6) = all_0_6_6, sum(n3, n6) = n9, yields:
% 21.67/6.13 | (923) all_0_6_6 = n9
% 21.67/6.13 |
% 21.67/6.13 | Equations (923) can reduce 404 to:
% 21.67/6.13 | (458) $false
% 21.67/6.13 |
% 21.67/6.13 |-The branch is then unsatisfiable
% 21.67/6.13 |-Branch two:
% 21.67/6.13 | (925) ~ (all_0_7_7 = n4)
% 21.67/6.13 | (926) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 21.67/6.13 |
% 21.67/6.13 +-Applying beta-rule and splitting (926), into two cases.
% 21.67/6.13 |-Branch one:
% 21.67/6.13 | (927) all_0_7_7 = n3
% 21.67/6.13 |
% 21.67/6.13 | From (927) and (176) follows:
% 21.67/6.13 | (928) succ(n3) = all_0_5_5
% 21.67/6.13 |
% 21.67/6.13 | From (927) and (59) follows:
% 21.67/6.13 | (929) sum(n3, all_0_1_1) = all_0_0_0
% 21.67/6.13 |
% 21.67/6.13 | From (927) and (717) follows:
% 21.67/6.13 | (930) sum(n15, n3) = all_0_2_2
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (219) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 21.67/6.13 | (931) all_0_5_5 = n4
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (89) with n15, n3, all_0_2_2, n2 and discharging atoms sum(n15, n3) = all_0_2_2, sum(n15, n3) = n2, yields:
% 21.67/6.13 | (651) all_0_2_2 = n2
% 21.67/6.13 |
% 21.67/6.13 | From (651) and (187) follows:
% 21.67/6.13 | (653) pred(n2) = all_0_1_1
% 21.67/6.13 |
% 21.67/6.13 | From (931) and (716) follows:
% 21.67/6.13 | (934) sum(n15, n4) = all_0_4_4
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (37) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 21.67/6.13 | (656) all_0_1_1 = n1
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (89) with n15, n4, all_0_4_4, n3 and discharging atoms sum(n15, n4) = all_0_4_4, sum(n15, n4) = n3, yields:
% 21.67/6.13 | (652) all_0_4_4 = n3
% 21.67/6.13 |
% 21.67/6.13 | From (652) and (396) follows:
% 21.67/6.13 | (654) pred(n3) = all_0_3_3
% 21.67/6.13 |
% 21.67/6.13 | From (656) and (929) follows:
% 21.67/6.13 | (938) sum(n3, n1) = all_0_0_0
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (37) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 21.67/6.13 | (655) all_0_3_3 = n2
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (89) with n3, n1, all_0_0_0, n4 and discharging atoms sum(n3, n1) = all_0_0_0, sum(n3, n1) = n4, yields:
% 21.67/6.13 | (591) all_0_0_0 = n4
% 21.67/6.13 |
% 21.67/6.13 | From (655)(591) and (261) follows:
% 21.67/6.13 | (941) sum(n2, n4) = all_0_6_6
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (89) with n2, n4, all_0_6_6, n6 and discharging atoms sum(n2, n4) = all_0_6_6, sum(n2, n4) = n6, yields:
% 21.67/6.13 | (491) all_0_6_6 = n6
% 21.67/6.13 |
% 21.67/6.13 | Equations (491) can reduce 418 to:
% 21.67/6.13 | (458) $false
% 21.67/6.13 |
% 21.67/6.13 |-The branch is then unsatisfiable
% 21.67/6.13 |-Branch two:
% 21.67/6.13 | (944) ~ (all_0_7_7 = n3)
% 21.67/6.13 | (945) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 21.67/6.13 |
% 21.67/6.13 +-Applying beta-rule and splitting (945), into two cases.
% 21.67/6.13 |-Branch one:
% 21.67/6.13 | (946) all_0_7_7 = n2
% 21.67/6.13 |
% 21.67/6.13 | From (946) and (176) follows:
% 21.67/6.13 | (947) succ(n2) = all_0_5_5
% 21.67/6.13 |
% 21.67/6.13 | From (946) and (59) follows:
% 21.67/6.13 | (948) sum(n2, all_0_1_1) = all_0_0_0
% 21.67/6.13 |
% 21.67/6.13 | From (946) and (717) follows:
% 21.67/6.13 | (949) sum(n15, n2) = all_0_2_2
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (219) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 21.67/6.13 | (950) all_0_5_5 = n3
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (89) with n15, n2, all_0_2_2, n1 and discharging atoms sum(n15, n2) = all_0_2_2, sum(n15, n2) = n1, yields:
% 21.67/6.13 | (668) all_0_2_2 = n1
% 21.67/6.13 |
% 21.67/6.13 | From (668) and (187) follows:
% 21.67/6.13 | (670) pred(n1) = all_0_1_1
% 21.67/6.13 |
% 21.67/6.13 | From (950) and (716) follows:
% 21.67/6.13 | (953) sum(n15, n3) = all_0_4_4
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (37) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 21.67/6.13 | (673) all_0_1_1 = n0
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (89) with n15, n3, all_0_4_4, n2 and discharging atoms sum(n15, n3) = all_0_4_4, sum(n15, n3) = n2, yields:
% 21.67/6.13 | (669) all_0_4_4 = n2
% 21.67/6.13 |
% 21.67/6.13 | From (669) and (396) follows:
% 21.67/6.13 | (671) pred(n2) = all_0_3_3
% 21.67/6.13 |
% 21.67/6.13 | From (673) and (948) follows:
% 21.67/6.13 | (957) sum(n2, n0) = all_0_0_0
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (37) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 21.67/6.13 | (672) all_0_3_3 = n1
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (89) with n2, n0, all_0_0_0, n2 and discharging atoms sum(n2, n0) = all_0_0_0, sum(n2, n0) = n2, yields:
% 21.67/6.13 | (625) all_0_0_0 = n2
% 21.67/6.13 |
% 21.67/6.13 | From (672)(625) and (261) follows:
% 21.67/6.13 | (960) sum(n1, n2) = all_0_6_6
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (89) with n1, n2, all_0_6_6, n3 and discharging atoms sum(n1, n2) = all_0_6_6, sum(n1, n2) = n3, yields:
% 21.67/6.13 | (961) all_0_6_6 = n3
% 21.67/6.13 |
% 21.67/6.13 | Equations (961) can reduce 245 to:
% 21.67/6.13 | (458) $false
% 21.67/6.13 |
% 21.67/6.13 |-The branch is then unsatisfiable
% 21.67/6.13 |-Branch two:
% 21.67/6.13 | (963) ~ (all_0_7_7 = n2)
% 21.67/6.13 | (964) all_0_7_7 = n1 | all_0_7_7 = n0
% 21.67/6.13 |
% 21.67/6.13 +-Applying beta-rule and splitting (964), into two cases.
% 21.67/6.13 |-Branch one:
% 21.67/6.13 | (965) all_0_7_7 = n1
% 21.67/6.13 |
% 21.67/6.13 | From (965) and (176) follows:
% 21.67/6.13 | (966) succ(n1) = all_0_5_5
% 21.67/6.13 |
% 21.67/6.13 | From (965) and (59) follows:
% 21.67/6.13 | (967) sum(n1, all_0_1_1) = all_0_0_0
% 21.67/6.13 |
% 21.67/6.13 | From (965) and (717) follows:
% 21.67/6.13 | (968) sum(n15, n1) = all_0_2_2
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (219) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 21.67/6.13 | (969) all_0_5_5 = n2
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (89) with n15, n1, all_0_2_2, n0 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n0, yields:
% 21.67/6.13 | (685) all_0_2_2 = n0
% 21.67/6.13 |
% 21.67/6.13 | From (685) and (187) follows:
% 21.67/6.13 | (687) pred(n0) = all_0_1_1
% 21.67/6.13 |
% 21.67/6.13 | From (969) and (716) follows:
% 21.67/6.13 | (972) sum(n15, n2) = all_0_4_4
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (37) with n0, all_0_1_1, n15 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n15, yields:
% 21.67/6.13 | (690) all_0_1_1 = n15
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (89) with n15, n2, all_0_4_4, n1 and discharging atoms sum(n15, n2) = all_0_4_4, sum(n15, n2) = n1, yields:
% 21.67/6.13 | (686) all_0_4_4 = n1
% 21.67/6.13 |
% 21.67/6.13 | From (686) and (396) follows:
% 21.67/6.13 | (688) pred(n1) = all_0_3_3
% 21.67/6.13 |
% 21.67/6.13 | From (690) and (967) follows:
% 21.67/6.13 | (976) sum(n1, n15) = all_0_0_0
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (37) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 21.67/6.13 | (689) all_0_3_3 = n0
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (89) with n1, n15, all_0_0_0, n0 and discharging atoms sum(n1, n15) = all_0_0_0, sum(n1, n15) = n0, yields:
% 21.67/6.13 | (659) all_0_0_0 = n0
% 21.67/6.13 |
% 21.67/6.13 | From (689)(659) and (261) follows:
% 21.67/6.13 | (979) sum(n0, n0) = all_0_6_6
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (89) with n0, n0, all_0_6_6, n0 and discharging atoms sum(n0, n0) = all_0_6_6, sum(n0, n0) = n0, yields:
% 21.67/6.13 | (542) all_0_6_6 = n0
% 21.67/6.13 |
% 21.67/6.13 | Equations (542) can reduce 400 to:
% 21.67/6.13 | (458) $false
% 21.67/6.13 |
% 21.67/6.13 |-The branch is then unsatisfiable
% 21.67/6.13 |-Branch two:
% 21.67/6.13 | (982) ~ (all_0_7_7 = n1)
% 21.67/6.13 | (983) all_0_7_7 = n0
% 21.67/6.13 |
% 21.67/6.13 | From (983) and (176) follows:
% 21.67/6.13 | (984) succ(n0) = all_0_5_5
% 21.67/6.13 |
% 21.67/6.13 | From (983) and (59) follows:
% 21.67/6.13 | (985) sum(n0, all_0_1_1) = all_0_0_0
% 21.67/6.13 |
% 21.67/6.13 | From (983) and (717) follows:
% 21.67/6.13 | (986) sum(n15, n0) = all_0_2_2
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (219) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 21.67/6.13 | (987) all_0_5_5 = n1
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (89) with n15, n0, all_0_2_2, n15 and discharging atoms sum(n15, n0) = all_0_2_2, sum(n15, n0) = n15, yields:
% 21.67/6.13 | (701) all_0_2_2 = n15
% 21.67/6.13 |
% 21.67/6.13 | From (701) and (187) follows:
% 21.67/6.13 | (703) pred(n15) = all_0_1_1
% 21.67/6.13 |
% 21.67/6.13 | From (987) and (716) follows:
% 21.67/6.13 | (990) sum(n15, n1) = all_0_4_4
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (37) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 21.67/6.13 | (705) all_0_1_1 = n14
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (89) with n15, n1, all_0_4_4, n0 and discharging atoms sum(n15, n1) = all_0_4_4, sum(n15, n1) = n0, yields:
% 21.67/6.13 | (702) all_0_4_4 = n0
% 21.67/6.13 |
% 21.67/6.13 | From (702) and (396) follows:
% 21.67/6.13 | (704) pred(n0) = all_0_3_3
% 21.67/6.13 |
% 21.67/6.13 | From (705) and (985) follows:
% 21.67/6.13 | (994) sum(n0, n14) = all_0_0_0
% 21.67/6.13 |
% 21.67/6.13 | Instantiating formula (37) with n0, all_0_3_3, n15 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n15, yields:
% 21.67/6.14 | (706) all_0_3_3 = n15
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (89) with n0, n14, all_0_0_0, n14 and discharging atoms sum(n0, n14) = all_0_0_0, sum(n0, n14) = n14, yields:
% 21.67/6.14 | (693) all_0_0_0 = n14
% 21.67/6.14 |
% 21.67/6.14 | From (706)(693) and (261) follows:
% 21.67/6.14 | (997) sum(n15, n14) = all_0_6_6
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (89) with n15, n14, all_0_6_6, n13 and discharging atoms sum(n15, n14) = all_0_6_6, sum(n15, n14) = n13, yields:
% 21.67/6.14 | (998) all_0_6_6 = n13
% 21.67/6.14 |
% 21.67/6.14 | Equations (998) can reduce 130 to:
% 21.67/6.14 | (458) $false
% 21.67/6.14 |
% 21.67/6.14 |-The branch is then unsatisfiable
% 21.67/6.14 |-Branch two:
% 21.67/6.14 | (459) ~ (all_0_8_8 = n15)
% 21.67/6.14 | (460) all_0_8_8 = n14 | all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.67/6.14 |
% 21.67/6.14 +-Applying beta-rule and splitting (714), into two cases.
% 21.67/6.14 |-Branch one:
% 21.67/6.14 | (718) all_0_7_7 = n14
% 21.67/6.14 |
% 21.67/6.14 | From (718) and (176) follows:
% 21.67/6.14 | (719) succ(n14) = all_0_5_5
% 21.67/6.14 |
% 21.67/6.14 | From (718) and (59) follows:
% 21.67/6.14 | (720) sum(n14, all_0_1_1) = all_0_0_0
% 21.67/6.14 |
% 21.67/6.14 | From (718) and (160) follows:
% 21.67/6.14 | (1005) sum(all_0_8_8, n14) = all_0_2_2
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (219) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 21.67/6.14 | (722) all_0_5_5 = n15
% 21.67/6.14 |
% 21.67/6.14 | From (722) and (64) follows:
% 21.67/6.14 | (1007) sum(all_0_8_8, n15) = all_0_4_4
% 21.67/6.14 |
% 21.67/6.14 +-Applying beta-rule and splitting (460), into two cases.
% 21.67/6.14 |-Branch one:
% 21.67/6.14 | (461) all_0_8_8 = n14
% 21.67/6.14 |
% 21.67/6.14 | From (461) and (1007) follows:
% 21.67/6.14 | (1009) sum(n14, n15) = all_0_4_4
% 21.67/6.14 |
% 21.67/6.14 | From (461) and (1005) follows:
% 21.67/6.14 | (1010) sum(n14, n14) = all_0_2_2
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (89) with n14, n15, all_0_4_4, n13 and discharging atoms sum(n14, n15) = all_0_4_4, sum(n14, n15) = n13, yields:
% 21.67/6.14 | (482) all_0_4_4 = n13
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (89) with n14, n14, all_0_2_2, n12 and discharging atoms sum(n14, n14) = all_0_2_2, sum(n14, n14) = n12, yields:
% 21.67/6.14 | (481) all_0_2_2 = n12
% 21.67/6.14 |
% 21.67/6.14 | From (481) and (187) follows:
% 21.67/6.14 | (483) pred(n12) = all_0_1_1
% 21.67/6.14 |
% 21.67/6.14 | From (482) and (396) follows:
% 21.67/6.14 | (484) pred(n13) = all_0_3_3
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (37) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 21.67/6.14 | (485) all_0_3_3 = n12
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (37) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 21.67/6.14 | (486) all_0_1_1 = n11
% 21.67/6.14 |
% 21.67/6.14 | From (485) and (261) follows:
% 21.67/6.14 | (487) sum(n12, all_0_0_0) = all_0_6_6
% 21.67/6.14 |
% 21.67/6.14 | From (486) and (720) follows:
% 21.67/6.14 | (1018) sum(n14, n11) = all_0_0_0
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (89) with n14, n11, all_0_0_0, n9 and discharging atoms sum(n14, n11) = all_0_0_0, sum(n14, n11) = n9, yields:
% 21.67/6.14 | (506) all_0_0_0 = n9
% 21.67/6.14 |
% 21.67/6.14 | From (506) and (487) follows:
% 21.67/6.14 | (1020) sum(n12, n9) = all_0_6_6
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (89) with n12, n9, all_0_6_6, n5 and discharging atoms sum(n12, n9) = all_0_6_6, sum(n12, n9) = n5, yields:
% 21.67/6.14 | (847) all_0_6_6 = n5
% 21.67/6.14 |
% 21.67/6.14 | Equations (847) can reduce 409 to:
% 21.67/6.14 | (458) $false
% 21.67/6.14 |
% 21.67/6.14 |-The branch is then unsatisfiable
% 21.67/6.14 |-Branch two:
% 21.67/6.14 | (476) ~ (all_0_8_8 = n14)
% 21.67/6.14 | (477) all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.67/6.14 |
% 21.67/6.14 +-Applying beta-rule and splitting (477), into two cases.
% 21.67/6.14 |-Branch one:
% 21.67/6.14 | (478) all_0_8_8 = n13
% 21.67/6.14 |
% 21.67/6.14 | From (478) and (1007) follows:
% 21.67/6.14 | (1026) sum(n13, n15) = all_0_4_4
% 21.67/6.14 |
% 21.67/6.14 | From (478) and (1005) follows:
% 21.67/6.14 | (1027) sum(n13, n14) = all_0_2_2
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (89) with n13, n15, all_0_4_4, n12 and discharging atoms sum(n13, n15) = all_0_4_4, sum(n13, n15) = n12, yields:
% 21.67/6.14 | (499) all_0_4_4 = n12
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (89) with n13, n14, all_0_2_2, n11 and discharging atoms sum(n13, n14) = all_0_2_2, sum(n13, n14) = n11, yields:
% 21.67/6.14 | (498) all_0_2_2 = n11
% 21.67/6.14 |
% 21.67/6.14 | From (498) and (187) follows:
% 21.67/6.14 | (500) pred(n11) = all_0_1_1
% 21.67/6.14 |
% 21.67/6.14 | From (499) and (396) follows:
% 21.67/6.14 | (501) pred(n12) = all_0_3_3
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (37) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 21.67/6.14 | (502) all_0_3_3 = n11
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (37) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 21.67/6.14 | (503) all_0_1_1 = n10
% 21.67/6.14 |
% 21.67/6.14 | From (502) and (261) follows:
% 21.67/6.14 | (504) sum(n11, all_0_0_0) = all_0_6_6
% 21.67/6.14 |
% 21.67/6.14 | From (503) and (720) follows:
% 21.67/6.14 | (1035) sum(n14, n10) = all_0_0_0
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (89) with n14, n10, all_0_0_0, n8 and discharging atoms sum(n14, n10) = all_0_0_0, sum(n14, n10) = n8, yields:
% 21.67/6.14 | (523) all_0_0_0 = n8
% 21.67/6.14 |
% 21.67/6.14 | From (523) and (504) follows:
% 21.67/6.14 | (1037) sum(n11, n8) = all_0_6_6
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (89) with n11, n8, all_0_6_6, n3 and discharging atoms sum(n11, n8) = all_0_6_6, sum(n11, n8) = n3, yields:
% 21.67/6.14 | (961) all_0_6_6 = n3
% 21.67/6.14 |
% 21.67/6.14 | Equations (961) can reduce 245 to:
% 21.67/6.14 | (458) $false
% 21.67/6.14 |
% 21.67/6.14 |-The branch is then unsatisfiable
% 21.67/6.14 |-Branch two:
% 21.67/6.14 | (493) ~ (all_0_8_8 = n13)
% 21.67/6.14 | (494) all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.67/6.14 |
% 21.67/6.14 +-Applying beta-rule and splitting (494), into two cases.
% 21.67/6.14 |-Branch one:
% 21.67/6.14 | (495) all_0_8_8 = n12
% 21.67/6.14 |
% 21.67/6.14 | From (495) and (1007) follows:
% 21.67/6.14 | (1043) sum(n12, n15) = all_0_4_4
% 21.67/6.14 |
% 21.67/6.14 | From (495) and (1005) follows:
% 21.67/6.14 | (1044) sum(n12, n14) = all_0_2_2
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (89) with n12, n15, all_0_4_4, n11 and discharging atoms sum(n12, n15) = all_0_4_4, sum(n12, n15) = n11, yields:
% 21.67/6.14 | (516) all_0_4_4 = n11
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (89) with n12, n14, all_0_2_2, n10 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n10, yields:
% 21.67/6.14 | (515) all_0_2_2 = n10
% 21.67/6.14 |
% 21.67/6.14 | From (515) and (187) follows:
% 21.67/6.14 | (517) pred(n10) = all_0_1_1
% 21.67/6.14 |
% 21.67/6.14 | From (516) and (396) follows:
% 21.67/6.14 | (518) pred(n11) = all_0_3_3
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (37) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 21.67/6.14 | (519) all_0_3_3 = n10
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (37) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 21.67/6.14 | (520) all_0_1_1 = n9
% 21.67/6.14 |
% 21.67/6.14 | From (519) and (261) follows:
% 21.67/6.14 | (521) sum(n10, all_0_0_0) = all_0_6_6
% 21.67/6.14 |
% 21.67/6.14 | From (520) and (720) follows:
% 21.67/6.14 | (1052) sum(n14, n9) = all_0_0_0
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (89) with n14, n9, all_0_0_0, n7 and discharging atoms sum(n14, n9) = all_0_0_0, sum(n14, n9) = n7, yields:
% 21.67/6.14 | (540) all_0_0_0 = n7
% 21.67/6.14 |
% 21.67/6.14 | From (540) and (521) follows:
% 21.67/6.14 | (1054) sum(n10, n7) = all_0_6_6
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (89) with n10, n7, all_0_6_6, n1 and discharging atoms sum(n10, n7) = all_0_6_6, sum(n10, n7) = n1, yields:
% 21.67/6.14 | (771) all_0_6_6 = n1
% 21.67/6.14 |
% 21.67/6.14 | Equations (771) can reduce 38 to:
% 21.67/6.14 | (458) $false
% 21.67/6.14 |
% 21.67/6.14 |-The branch is then unsatisfiable
% 21.67/6.14 |-Branch two:
% 21.67/6.14 | (510) ~ (all_0_8_8 = n12)
% 21.67/6.14 | (511) all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.67/6.14 |
% 21.67/6.14 +-Applying beta-rule and splitting (511), into two cases.
% 21.67/6.14 |-Branch one:
% 21.67/6.14 | (512) all_0_8_8 = n11
% 21.67/6.14 |
% 21.67/6.14 | From (512) and (1007) follows:
% 21.67/6.14 | (1060) sum(n11, n15) = all_0_4_4
% 21.67/6.14 |
% 21.67/6.14 | From (512) and (1005) follows:
% 21.67/6.14 | (1061) sum(n11, n14) = all_0_2_2
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (89) with n11, n15, all_0_4_4, n10 and discharging atoms sum(n11, n15) = all_0_4_4, sum(n11, n15) = n10, yields:
% 21.67/6.14 | (533) all_0_4_4 = n10
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (89) with n11, n14, all_0_2_2, n9 and discharging atoms sum(n11, n14) = all_0_2_2, sum(n11, n14) = n9, yields:
% 21.67/6.14 | (532) all_0_2_2 = n9
% 21.67/6.14 |
% 21.67/6.14 | From (532) and (187) follows:
% 21.67/6.14 | (534) pred(n9) = all_0_1_1
% 21.67/6.14 |
% 21.67/6.14 | From (533) and (396) follows:
% 21.67/6.14 | (535) pred(n10) = all_0_3_3
% 21.67/6.14 |
% 21.67/6.14 | Instantiating formula (37) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 21.67/6.14 | (536) all_0_3_3 = n9
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (37) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 21.67/6.15 | (537) all_0_1_1 = n8
% 21.67/6.15 |
% 21.67/6.15 | From (536) and (261) follows:
% 21.67/6.15 | (538) sum(n9, all_0_0_0) = all_0_6_6
% 21.67/6.15 |
% 21.67/6.15 | From (537) and (720) follows:
% 21.67/6.15 | (1069) sum(n14, n8) = all_0_0_0
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n14, n8, all_0_0_0, n6 and discharging atoms sum(n14, n8) = all_0_0_0, sum(n14, n8) = n6, yields:
% 21.67/6.15 | (557) all_0_0_0 = n6
% 21.67/6.15 |
% 21.67/6.15 | From (557) and (538) follows:
% 21.67/6.15 | (1071) sum(n9, n6) = all_0_6_6
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n9, n6, all_0_6_6, n15 and discharging atoms sum(n9, n6) = all_0_6_6, sum(n9, n6) = n15, yields:
% 21.67/6.15 | (885) all_0_6_6 = n15
% 21.67/6.15 |
% 21.67/6.15 | Equations (885) can reduce 225 to:
% 21.67/6.15 | (458) $false
% 21.67/6.15 |
% 21.67/6.15 |-The branch is then unsatisfiable
% 21.67/6.15 |-Branch two:
% 21.67/6.15 | (527) ~ (all_0_8_8 = n11)
% 21.67/6.15 | (528) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.67/6.15 |
% 21.67/6.15 +-Applying beta-rule and splitting (528), into two cases.
% 21.67/6.15 |-Branch one:
% 21.67/6.15 | (529) all_0_8_8 = n10
% 21.67/6.15 |
% 21.67/6.15 | From (529) and (1007) follows:
% 21.67/6.15 | (1077) sum(n10, n15) = all_0_4_4
% 21.67/6.15 |
% 21.67/6.15 | From (529) and (1005) follows:
% 21.67/6.15 | (1078) sum(n10, n14) = all_0_2_2
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n10, n15, all_0_4_4, n9 and discharging atoms sum(n10, n15) = all_0_4_4, sum(n10, n15) = n9, yields:
% 21.67/6.15 | (550) all_0_4_4 = n9
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n10, n14, all_0_2_2, n8 and discharging atoms sum(n10, n14) = all_0_2_2, sum(n10, n14) = n8, yields:
% 21.67/6.15 | (549) all_0_2_2 = n8
% 21.67/6.15 |
% 21.67/6.15 | From (549) and (187) follows:
% 21.67/6.15 | (551) pred(n8) = all_0_1_1
% 21.67/6.15 |
% 21.67/6.15 | From (550) and (396) follows:
% 21.67/6.15 | (552) pred(n9) = all_0_3_3
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (37) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 21.67/6.15 | (553) all_0_3_3 = n8
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (37) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 21.67/6.15 | (554) all_0_1_1 = n7
% 21.67/6.15 |
% 21.67/6.15 | From (553) and (261) follows:
% 21.67/6.15 | (555) sum(n8, all_0_0_0) = all_0_6_6
% 21.67/6.15 |
% 21.67/6.15 | From (554) and (720) follows:
% 21.67/6.15 | (1086) sum(n14, n7) = all_0_0_0
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n14, n7, all_0_0_0, n5 and discharging atoms sum(n14, n7) = all_0_0_0, sum(n14, n7) = n5, yields:
% 21.67/6.15 | (574) all_0_0_0 = n5
% 21.67/6.15 |
% 21.67/6.15 | From (574) and (555) follows:
% 21.67/6.15 | (1088) sum(n8, n5) = all_0_6_6
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n8, n5, all_0_6_6, n13 and discharging atoms sum(n8, n5) = all_0_6_6, sum(n8, n5) = n13, yields:
% 21.67/6.15 | (998) all_0_6_6 = n13
% 21.67/6.15 |
% 21.67/6.15 | Equations (998) can reduce 130 to:
% 21.67/6.15 | (458) $false
% 21.67/6.15 |
% 21.67/6.15 |-The branch is then unsatisfiable
% 21.67/6.15 |-Branch two:
% 21.67/6.15 | (544) ~ (all_0_8_8 = n10)
% 21.67/6.15 | (545) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.67/6.15 |
% 21.67/6.15 +-Applying beta-rule and splitting (545), into two cases.
% 21.67/6.15 |-Branch one:
% 21.67/6.15 | (546) all_0_8_8 = n9
% 21.67/6.15 |
% 21.67/6.15 | From (546) and (1007) follows:
% 21.67/6.15 | (1094) sum(n9, n15) = all_0_4_4
% 21.67/6.15 |
% 21.67/6.15 | From (546) and (1005) follows:
% 21.67/6.15 | (1095) sum(n9, n14) = all_0_2_2
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n9, n15, all_0_4_4, n8 and discharging atoms sum(n9, n15) = all_0_4_4, sum(n9, n15) = n8, yields:
% 21.67/6.15 | (567) all_0_4_4 = n8
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n9, n14, all_0_2_2, n7 and discharging atoms sum(n9, n14) = all_0_2_2, sum(n9, n14) = n7, yields:
% 21.67/6.15 | (566) all_0_2_2 = n7
% 21.67/6.15 |
% 21.67/6.15 | From (566) and (187) follows:
% 21.67/6.15 | (568) pred(n7) = all_0_1_1
% 21.67/6.15 |
% 21.67/6.15 | From (567) and (396) follows:
% 21.67/6.15 | (569) pred(n8) = all_0_3_3
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (37) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 21.67/6.15 | (570) all_0_3_3 = n7
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (37) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 21.67/6.15 | (571) all_0_1_1 = n6
% 21.67/6.15 |
% 21.67/6.15 | From (570) and (261) follows:
% 21.67/6.15 | (572) sum(n7, all_0_0_0) = all_0_6_6
% 21.67/6.15 |
% 21.67/6.15 | From (571) and (720) follows:
% 21.67/6.15 | (1103) sum(n14, n6) = all_0_0_0
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n14, n6, all_0_0_0, n4 and discharging atoms sum(n14, n6) = all_0_0_0, sum(n14, n6) = n4, yields:
% 21.67/6.15 | (591) all_0_0_0 = n4
% 21.67/6.15 |
% 21.67/6.15 | From (591) and (572) follows:
% 21.67/6.15 | (1105) sum(n7, n4) = all_0_6_6
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n7, n4, all_0_6_6, n11 and discharging atoms sum(n7, n4) = all_0_6_6, sum(n7, n4) = n11, yields:
% 21.67/6.15 | (809) all_0_6_6 = n11
% 21.67/6.15 |
% 21.67/6.15 | Equations (809) can reduce 70 to:
% 21.67/6.15 | (458) $false
% 21.67/6.15 |
% 21.67/6.15 |-The branch is then unsatisfiable
% 21.67/6.15 |-Branch two:
% 21.67/6.15 | (561) ~ (all_0_8_8 = n9)
% 21.67/6.15 | (562) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.67/6.15 |
% 21.67/6.15 +-Applying beta-rule and splitting (562), into two cases.
% 21.67/6.15 |-Branch one:
% 21.67/6.15 | (563) all_0_8_8 = n8
% 21.67/6.15 |
% 21.67/6.15 | From (563) and (1007) follows:
% 21.67/6.15 | (1111) sum(n8, n15) = all_0_4_4
% 21.67/6.15 |
% 21.67/6.15 | From (563) and (1005) follows:
% 21.67/6.15 | (1112) sum(n8, n14) = all_0_2_2
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n8, n15, all_0_4_4, n7 and discharging atoms sum(n8, n15) = all_0_4_4, sum(n8, n15) = n7, yields:
% 21.67/6.15 | (584) all_0_4_4 = n7
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n8, n14, all_0_2_2, n6 and discharging atoms sum(n8, n14) = all_0_2_2, sum(n8, n14) = n6, yields:
% 21.67/6.15 | (583) all_0_2_2 = n6
% 21.67/6.15 |
% 21.67/6.15 | From (583) and (187) follows:
% 21.67/6.15 | (585) pred(n6) = all_0_1_1
% 21.67/6.15 |
% 21.67/6.15 | From (584) and (396) follows:
% 21.67/6.15 | (586) pred(n7) = all_0_3_3
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (37) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 21.67/6.15 | (587) all_0_3_3 = n6
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (37) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 21.67/6.15 | (588) all_0_1_1 = n5
% 21.67/6.15 |
% 21.67/6.15 | From (587) and (261) follows:
% 21.67/6.15 | (589) sum(n6, all_0_0_0) = all_0_6_6
% 21.67/6.15 |
% 21.67/6.15 | From (588) and (720) follows:
% 21.67/6.15 | (1120) sum(n14, n5) = all_0_0_0
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n14, n5, all_0_0_0, n3 and discharging atoms sum(n14, n5) = all_0_0_0, sum(n14, n5) = n3, yields:
% 21.67/6.15 | (608) all_0_0_0 = n3
% 21.67/6.15 |
% 21.67/6.15 | From (608) and (589) follows:
% 21.67/6.15 | (1122) sum(n6, n3) = all_0_6_6
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n6, n3, all_0_6_6, n9 and discharging atoms sum(n6, n3) = all_0_6_6, sum(n6, n3) = n9, yields:
% 21.67/6.15 | (923) all_0_6_6 = n9
% 21.67/6.15 |
% 21.67/6.15 | Equations (923) can reduce 404 to:
% 21.67/6.15 | (458) $false
% 21.67/6.15 |
% 21.67/6.15 |-The branch is then unsatisfiable
% 21.67/6.15 |-Branch two:
% 21.67/6.15 | (578) ~ (all_0_8_8 = n8)
% 21.67/6.15 | (579) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.67/6.15 |
% 21.67/6.15 +-Applying beta-rule and splitting (579), into two cases.
% 21.67/6.15 |-Branch one:
% 21.67/6.15 | (580) all_0_8_8 = n7
% 21.67/6.15 |
% 21.67/6.15 | From (580) and (1007) follows:
% 21.67/6.15 | (1128) sum(n7, n15) = all_0_4_4
% 21.67/6.15 |
% 21.67/6.15 | From (580) and (1005) follows:
% 21.67/6.15 | (1129) sum(n7, n14) = all_0_2_2
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n7, n15, all_0_4_4, n6 and discharging atoms sum(n7, n15) = all_0_4_4, sum(n7, n15) = n6, yields:
% 21.67/6.15 | (601) all_0_4_4 = n6
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n7, n14, all_0_2_2, n5 and discharging atoms sum(n7, n14) = all_0_2_2, sum(n7, n14) = n5, yields:
% 21.67/6.15 | (600) all_0_2_2 = n5
% 21.67/6.15 |
% 21.67/6.15 | From (600) and (187) follows:
% 21.67/6.15 | (602) pred(n5) = all_0_1_1
% 21.67/6.15 |
% 21.67/6.15 | From (601) and (396) follows:
% 21.67/6.15 | (603) pred(n6) = all_0_3_3
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (37) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 21.67/6.15 | (604) all_0_3_3 = n5
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (37) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 21.67/6.15 | (605) all_0_1_1 = n4
% 21.67/6.15 |
% 21.67/6.15 | From (604) and (261) follows:
% 21.67/6.15 | (606) sum(n5, all_0_0_0) = all_0_6_6
% 21.67/6.15 |
% 21.67/6.15 | From (605) and (720) follows:
% 21.67/6.15 | (1137) sum(n14, n4) = all_0_0_0
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n14, n4, all_0_0_0, n2 and discharging atoms sum(n14, n4) = all_0_0_0, sum(n14, n4) = n2, yields:
% 21.67/6.15 | (625) all_0_0_0 = n2
% 21.67/6.15 |
% 21.67/6.15 | From (625) and (606) follows:
% 21.67/6.15 | (1139) sum(n5, n2) = all_0_6_6
% 21.67/6.15 |
% 21.67/6.15 | Instantiating formula (89) with n5, n2, all_0_6_6, n7 and discharging atoms sum(n5, n2) = all_0_6_6, sum(n5, n2) = n7, yields:
% 21.67/6.15 | (733) all_0_6_6 = n7
% 21.67/6.15 |
% 21.67/6.15 | Equations (733) can reduce 274 to:
% 21.67/6.15 | (458) $false
% 21.67/6.15 |
% 21.67/6.15 |-The branch is then unsatisfiable
% 21.67/6.15 |-Branch two:
% 21.67/6.15 | (595) ~ (all_0_8_8 = n7)
% 21.67/6.16 | (596) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.67/6.16 |
% 21.67/6.16 +-Applying beta-rule and splitting (596), into two cases.
% 21.67/6.16 |-Branch one:
% 21.67/6.16 | (597) all_0_8_8 = n6
% 21.67/6.16 |
% 21.67/6.16 | From (597) and (1007) follows:
% 21.67/6.16 | (1145) sum(n6, n15) = all_0_4_4
% 21.67/6.16 |
% 21.67/6.16 | From (597) and (1005) follows:
% 21.67/6.16 | (1146) sum(n6, n14) = all_0_2_2
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n6, n15, all_0_4_4, n5 and discharging atoms sum(n6, n15) = all_0_4_4, sum(n6, n15) = n5, yields:
% 21.67/6.16 | (618) all_0_4_4 = n5
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n6, n14, all_0_2_2, n4 and discharging atoms sum(n6, n14) = all_0_2_2, sum(n6, n14) = n4, yields:
% 21.67/6.16 | (617) all_0_2_2 = n4
% 21.67/6.16 |
% 21.67/6.16 | From (617) and (187) follows:
% 21.67/6.16 | (619) pred(n4) = all_0_1_1
% 21.67/6.16 |
% 21.67/6.16 | From (618) and (396) follows:
% 21.67/6.16 | (620) pred(n5) = all_0_3_3
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (37) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 21.67/6.16 | (621) all_0_3_3 = n4
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (37) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 21.67/6.16 | (622) all_0_1_1 = n3
% 21.67/6.16 |
% 21.67/6.16 | From (621) and (261) follows:
% 21.67/6.16 | (623) sum(n4, all_0_0_0) = all_0_6_6
% 21.67/6.16 |
% 21.67/6.16 | From (622) and (720) follows:
% 21.67/6.16 | (1154) sum(n14, n3) = all_0_0_0
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n14, n3, all_0_0_0, n1 and discharging atoms sum(n14, n3) = all_0_0_0, sum(n14, n3) = n1, yields:
% 21.67/6.16 | (642) all_0_0_0 = n1
% 21.67/6.16 |
% 21.67/6.16 | From (642) and (623) follows:
% 21.67/6.16 | (1156) sum(n4, n1) = all_0_6_6
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n4, n1, all_0_6_6, n5 and discharging atoms sum(n4, n1) = all_0_6_6, sum(n4, n1) = n5, yields:
% 21.67/6.16 | (847) all_0_6_6 = n5
% 21.67/6.16 |
% 21.67/6.16 | Equations (847) can reduce 409 to:
% 21.67/6.16 | (458) $false
% 21.67/6.16 |
% 21.67/6.16 |-The branch is then unsatisfiable
% 21.67/6.16 |-Branch two:
% 21.67/6.16 | (612) ~ (all_0_8_8 = n6)
% 21.67/6.16 | (613) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.67/6.16 |
% 21.67/6.16 +-Applying beta-rule and splitting (613), into two cases.
% 21.67/6.16 |-Branch one:
% 21.67/6.16 | (614) all_0_8_8 = n5
% 21.67/6.16 |
% 21.67/6.16 | From (614) and (1007) follows:
% 21.67/6.16 | (1162) sum(n5, n15) = all_0_4_4
% 21.67/6.16 |
% 21.67/6.16 | From (614) and (1005) follows:
% 21.67/6.16 | (1163) sum(n5, n14) = all_0_2_2
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n5, n15, all_0_4_4, n4 and discharging atoms sum(n5, n15) = all_0_4_4, sum(n5, n15) = n4, yields:
% 21.67/6.16 | (635) all_0_4_4 = n4
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n5, n14, all_0_2_2, n3 and discharging atoms sum(n5, n14) = all_0_2_2, sum(n5, n14) = n3, yields:
% 21.67/6.16 | (634) all_0_2_2 = n3
% 21.67/6.16 |
% 21.67/6.16 | From (634) and (187) follows:
% 21.67/6.16 | (636) pred(n3) = all_0_1_1
% 21.67/6.16 |
% 21.67/6.16 | From (635) and (396) follows:
% 21.67/6.16 | (637) pred(n4) = all_0_3_3
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (37) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 21.67/6.16 | (638) all_0_3_3 = n3
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (37) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 21.67/6.16 | (639) all_0_1_1 = n2
% 21.67/6.16 |
% 21.67/6.16 | From (638) and (261) follows:
% 21.67/6.16 | (640) sum(n3, all_0_0_0) = all_0_6_6
% 21.67/6.16 |
% 21.67/6.16 | From (639) and (720) follows:
% 21.67/6.16 | (1171) sum(n14, n2) = all_0_0_0
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n14, n2, all_0_0_0, n0 and discharging atoms sum(n14, n2) = all_0_0_0, sum(n14, n2) = n0, yields:
% 21.67/6.16 | (659) all_0_0_0 = n0
% 21.67/6.16 |
% 21.67/6.16 | From (659) and (640) follows:
% 21.67/6.16 | (1173) sum(n3, n0) = all_0_6_6
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n3, n0, all_0_6_6, n3 and discharging atoms sum(n3, n0) = all_0_6_6, sum(n3, n0) = n3, yields:
% 21.67/6.16 | (961) all_0_6_6 = n3
% 21.67/6.16 |
% 21.67/6.16 | Equations (961) can reduce 245 to:
% 21.67/6.16 | (458) $false
% 21.67/6.16 |
% 21.67/6.16 |-The branch is then unsatisfiable
% 21.67/6.16 |-Branch two:
% 21.67/6.16 | (629) ~ (all_0_8_8 = n5)
% 21.67/6.16 | (630) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.67/6.16 |
% 21.67/6.16 +-Applying beta-rule and splitting (630), into two cases.
% 21.67/6.16 |-Branch one:
% 21.67/6.16 | (631) all_0_8_8 = n4
% 21.67/6.16 |
% 21.67/6.16 | From (631) and (1007) follows:
% 21.67/6.16 | (1179) sum(n4, n15) = all_0_4_4
% 21.67/6.16 |
% 21.67/6.16 | From (631) and (1005) follows:
% 21.67/6.16 | (1180) sum(n4, n14) = all_0_2_2
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n4, n15, all_0_4_4, n3 and discharging atoms sum(n4, n15) = all_0_4_4, sum(n4, n15) = n3, yields:
% 21.67/6.16 | (652) all_0_4_4 = n3
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n4, n14, all_0_2_2, n2 and discharging atoms sum(n4, n14) = all_0_2_2, sum(n4, n14) = n2, yields:
% 21.67/6.16 | (651) all_0_2_2 = n2
% 21.67/6.16 |
% 21.67/6.16 | From (651) and (187) follows:
% 21.67/6.16 | (653) pred(n2) = all_0_1_1
% 21.67/6.16 |
% 21.67/6.16 | From (652) and (396) follows:
% 21.67/6.16 | (654) pred(n3) = all_0_3_3
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (37) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 21.67/6.16 | (655) all_0_3_3 = n2
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (37) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 21.67/6.16 | (656) all_0_1_1 = n1
% 21.67/6.16 |
% 21.67/6.16 | From (655) and (261) follows:
% 21.67/6.16 | (657) sum(n2, all_0_0_0) = all_0_6_6
% 21.67/6.16 |
% 21.67/6.16 | From (656) and (720) follows:
% 21.67/6.16 | (1188) sum(n14, n1) = all_0_0_0
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n14, n1, all_0_0_0, n15 and discharging atoms sum(n14, n1) = all_0_0_0, sum(n14, n1) = n15, yields:
% 21.67/6.16 | (676) all_0_0_0 = n15
% 21.67/6.16 |
% 21.67/6.16 | From (676) and (657) follows:
% 21.67/6.16 | (1190) sum(n2, n15) = all_0_6_6
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n2, n15, all_0_6_6, n1 and discharging atoms sum(n2, n15) = all_0_6_6, sum(n2, n15) = n1, yields:
% 21.67/6.16 | (771) all_0_6_6 = n1
% 21.67/6.16 |
% 21.67/6.16 | Equations (771) can reduce 38 to:
% 21.67/6.16 | (458) $false
% 21.67/6.16 |
% 21.67/6.16 |-The branch is then unsatisfiable
% 21.67/6.16 |-Branch two:
% 21.67/6.16 | (646) ~ (all_0_8_8 = n4)
% 21.67/6.16 | (647) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.67/6.16 |
% 21.67/6.16 +-Applying beta-rule and splitting (647), into two cases.
% 21.67/6.16 |-Branch one:
% 21.67/6.16 | (648) all_0_8_8 = n3
% 21.67/6.16 |
% 21.67/6.16 | From (648) and (1007) follows:
% 21.67/6.16 | (1196) sum(n3, n15) = all_0_4_4
% 21.67/6.16 |
% 21.67/6.16 | From (648) and (1005) follows:
% 21.67/6.16 | (1197) sum(n3, n14) = all_0_2_2
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n3, n15, all_0_4_4, n2 and discharging atoms sum(n3, n15) = all_0_4_4, sum(n3, n15) = n2, yields:
% 21.67/6.16 | (669) all_0_4_4 = n2
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n3, n14, all_0_2_2, n1 and discharging atoms sum(n3, n14) = all_0_2_2, sum(n3, n14) = n1, yields:
% 21.67/6.16 | (668) all_0_2_2 = n1
% 21.67/6.16 |
% 21.67/6.16 | From (668) and (187) follows:
% 21.67/6.16 | (670) pred(n1) = all_0_1_1
% 21.67/6.16 |
% 21.67/6.16 | From (669) and (396) follows:
% 21.67/6.16 | (671) pred(n2) = all_0_3_3
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (37) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 21.67/6.16 | (672) all_0_3_3 = n1
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (37) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 21.67/6.16 | (673) all_0_1_1 = n0
% 21.67/6.16 |
% 21.67/6.16 | From (672) and (261) follows:
% 21.67/6.16 | (674) sum(n1, all_0_0_0) = all_0_6_6
% 21.67/6.16 |
% 21.67/6.16 | From (673) and (720) follows:
% 21.67/6.16 | (1205) sum(n14, n0) = all_0_0_0
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n14, n0, all_0_0_0, n14 and discharging atoms sum(n14, n0) = all_0_0_0, sum(n14, n0) = n14, yields:
% 21.67/6.16 | (693) all_0_0_0 = n14
% 21.67/6.16 |
% 21.67/6.16 | From (693) and (674) follows:
% 21.67/6.16 | (1207) sum(n1, n14) = all_0_6_6
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n1, n14, all_0_6_6, n15 and discharging atoms sum(n1, n14) = all_0_6_6, sum(n1, n14) = n15, yields:
% 21.67/6.16 | (885) all_0_6_6 = n15
% 21.67/6.16 |
% 21.67/6.16 | Equations (885) can reduce 225 to:
% 21.67/6.16 | (458) $false
% 21.67/6.16 |
% 21.67/6.16 |-The branch is then unsatisfiable
% 21.67/6.16 |-Branch two:
% 21.67/6.16 | (663) ~ (all_0_8_8 = n3)
% 21.67/6.16 | (664) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 21.67/6.16 |
% 21.67/6.16 +-Applying beta-rule and splitting (664), into two cases.
% 21.67/6.16 |-Branch one:
% 21.67/6.16 | (665) all_0_8_8 = n2
% 21.67/6.16 |
% 21.67/6.16 | From (665) and (1007) follows:
% 21.67/6.16 | (1213) sum(n2, n15) = all_0_4_4
% 21.67/6.16 |
% 21.67/6.16 | From (665) and (1005) follows:
% 21.67/6.16 | (1214) sum(n2, n14) = all_0_2_2
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n2, n15, all_0_4_4, n1 and discharging atoms sum(n2, n15) = all_0_4_4, sum(n2, n15) = n1, yields:
% 21.67/6.16 | (686) all_0_4_4 = n1
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n2, n14, all_0_2_2, n0 and discharging atoms sum(n2, n14) = all_0_2_2, sum(n2, n14) = n0, yields:
% 21.67/6.16 | (685) all_0_2_2 = n0
% 21.67/6.16 |
% 21.67/6.16 | From (685) and (187) follows:
% 21.67/6.16 | (687) pred(n0) = all_0_1_1
% 21.67/6.16 |
% 21.67/6.16 | From (686) and (396) follows:
% 21.67/6.16 | (688) pred(n1) = all_0_3_3
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (37) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 21.67/6.16 | (689) all_0_3_3 = n0
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (37) with n0, all_0_1_1, n15 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n15, yields:
% 21.67/6.16 | (690) all_0_1_1 = n15
% 21.67/6.16 |
% 21.67/6.16 | From (689) and (261) follows:
% 21.67/6.16 | (691) sum(n0, all_0_0_0) = all_0_6_6
% 21.67/6.16 |
% 21.67/6.16 | From (690) and (720) follows:
% 21.67/6.16 | (1222) sum(n14, n15) = all_0_0_0
% 21.67/6.16 |
% 21.67/6.16 | Instantiating formula (89) with n14, n15, all_0_0_0, n13 and discharging atoms sum(n14, n15) = all_0_0_0, sum(n14, n15) = n13, yields:
% 21.67/6.16 | (709) all_0_0_0 = n13
% 21.67/6.17 |
% 21.67/6.17 | From (709) and (691) follows:
% 22.05/6.17 | (1224) sum(n0, n13) = all_0_6_6
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (89) with n0, n13, all_0_6_6, n13 and discharging atoms sum(n0, n13) = all_0_6_6, sum(n0, n13) = n13, yields:
% 22.05/6.17 | (998) all_0_6_6 = n13
% 22.05/6.17 |
% 22.05/6.17 | Equations (998) can reduce 130 to:
% 22.05/6.17 | (458) $false
% 22.05/6.17 |
% 22.05/6.17 |-The branch is then unsatisfiable
% 22.05/6.17 |-Branch two:
% 22.05/6.17 | (680) ~ (all_0_8_8 = n2)
% 22.05/6.17 | (681) all_0_8_8 = n1 | all_0_8_8 = n0
% 22.05/6.17 |
% 22.05/6.17 +-Applying beta-rule and splitting (681), into two cases.
% 22.05/6.17 |-Branch one:
% 22.05/6.17 | (682) all_0_8_8 = n1
% 22.05/6.17 |
% 22.05/6.17 | From (682) and (1007) follows:
% 22.05/6.17 | (1230) sum(n1, n15) = all_0_4_4
% 22.05/6.17 |
% 22.05/6.17 | From (682) and (1005) follows:
% 22.05/6.17 | (1231) sum(n1, n14) = all_0_2_2
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (89) with n1, n15, all_0_4_4, n0 and discharging atoms sum(n1, n15) = all_0_4_4, sum(n1, n15) = n0, yields:
% 22.05/6.17 | (702) all_0_4_4 = n0
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (89) with n1, n14, all_0_2_2, n15 and discharging atoms sum(n1, n14) = all_0_2_2, sum(n1, n14) = n15, yields:
% 22.05/6.17 | (701) all_0_2_2 = n15
% 22.05/6.17 |
% 22.05/6.17 | From (701) and (187) follows:
% 22.05/6.17 | (703) pred(n15) = all_0_1_1
% 22.05/6.17 |
% 22.05/6.17 | From (702) and (396) follows:
% 22.05/6.17 | (704) pred(n0) = all_0_3_3
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (37) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 22.05/6.17 | (705) all_0_1_1 = n14
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (37) with n0, all_0_3_3, n15 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n15, yields:
% 22.05/6.17 | (706) all_0_3_3 = n15
% 22.05/6.17 |
% 22.05/6.17 | From (706) and (261) follows:
% 22.05/6.17 | (707) sum(n15, all_0_0_0) = all_0_6_6
% 22.05/6.17 |
% 22.05/6.17 | From (705) and (720) follows:
% 22.05/6.17 | (1239) sum(n14, n14) = all_0_0_0
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (89) with n14, n14, all_0_0_0, n12 and discharging atoms sum(n14, n14) = all_0_0_0, sum(n14, n14) = n12, yields:
% 22.05/6.17 | (455) all_0_0_0 = n12
% 22.05/6.17 |
% 22.05/6.17 | From (455) and (707) follows:
% 22.05/6.17 | (1241) sum(n15, n12) = all_0_6_6
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (89) with n15, n12, all_0_6_6, n11 and discharging atoms sum(n15, n12) = all_0_6_6, sum(n15, n12) = n11, yields:
% 22.05/6.17 | (809) all_0_6_6 = n11
% 22.05/6.17 |
% 22.05/6.17 | Equations (809) can reduce 70 to:
% 22.05/6.17 | (458) $false
% 22.05/6.17 |
% 22.05/6.17 |-The branch is then unsatisfiable
% 22.05/6.17 |-Branch two:
% 22.05/6.17 | (697) ~ (all_0_8_8 = n1)
% 22.05/6.17 | (698) all_0_8_8 = n0
% 22.05/6.17 |
% 22.05/6.17 | From (698) and (1007) follows:
% 22.05/6.17 | (1246) sum(n0, n15) = all_0_4_4
% 22.05/6.17 |
% 22.05/6.17 | From (698) and (1005) follows:
% 22.05/6.17 | (1247) sum(n0, n14) = all_0_2_2
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (89) with n0, n15, all_0_4_4, n15 and discharging atoms sum(n0, n15) = all_0_4_4, sum(n0, n15) = n15, yields:
% 22.05/6.17 | (448) all_0_4_4 = n15
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (89) with n0, n14, all_0_2_2, n14 and discharging atoms sum(n0, n14) = all_0_2_2, sum(n0, n14) = n14, yields:
% 22.05/6.17 | (447) all_0_2_2 = n14
% 22.05/6.17 |
% 22.05/6.17 | From (447) and (187) follows:
% 22.05/6.17 | (449) pred(n14) = all_0_1_1
% 22.05/6.17 |
% 22.05/6.17 | From (448) and (396) follows:
% 22.05/6.17 | (450) pred(n15) = all_0_3_3
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (37) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 22.05/6.17 | (451) all_0_3_3 = n14
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (37) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 22.05/6.17 | (452) all_0_1_1 = n13
% 22.05/6.17 |
% 22.05/6.17 | From (451) and (261) follows:
% 22.05/6.17 | (453) sum(n14, all_0_0_0) = all_0_6_6
% 22.05/6.17 |
% 22.05/6.17 | From (452) and (720) follows:
% 22.05/6.17 | (1255) sum(n14, n13) = all_0_0_0
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (89) with n14, n13, all_0_0_0, n11 and discharging atoms sum(n14, n13) = all_0_0_0, sum(n14, n13) = n11, yields:
% 22.05/6.17 | (472) all_0_0_0 = n11
% 22.05/6.17 |
% 22.05/6.17 | From (472) and (453) follows:
% 22.05/6.17 | (1257) sum(n14, n11) = all_0_6_6
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (89) with n14, n11, all_0_6_6, n9 and discharging atoms sum(n14, n11) = all_0_6_6, sum(n14, n11) = n9, yields:
% 22.05/6.17 | (923) all_0_6_6 = n9
% 22.05/6.17 |
% 22.05/6.17 | Equations (923) can reduce 404 to:
% 22.05/6.17 | (458) $false
% 22.05/6.17 |
% 22.05/6.17 |-The branch is then unsatisfiable
% 22.05/6.17 |-Branch two:
% 22.05/6.17 | (735) ~ (all_0_7_7 = n14)
% 22.05/6.17 | (736) all_0_7_7 = n13 | all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.05/6.17 |
% 22.05/6.17 +-Applying beta-rule and splitting (460), into two cases.
% 22.05/6.17 |-Branch one:
% 22.05/6.17 | (461) all_0_8_8 = n14
% 22.05/6.17 |
% 22.05/6.17 | From (461) and (64) follows:
% 22.05/6.17 | (1263) sum(n14, all_0_5_5) = all_0_4_4
% 22.05/6.17 |
% 22.05/6.17 | From (461) and (160) follows:
% 22.05/6.17 | (1264) sum(n14, all_0_7_7) = all_0_2_2
% 22.05/6.17 |
% 22.05/6.17 +-Applying beta-rule and splitting (736), into two cases.
% 22.05/6.17 |-Branch one:
% 22.05/6.17 | (737) all_0_7_7 = n13
% 22.05/6.17 |
% 22.05/6.17 | From (737) and (176) follows:
% 22.05/6.17 | (738) succ(n13) = all_0_5_5
% 22.05/6.17 |
% 22.05/6.17 | From (737) and (59) follows:
% 22.05/6.17 | (739) sum(n13, all_0_1_1) = all_0_0_0
% 22.05/6.17 |
% 22.05/6.17 | From (737) and (1264) follows:
% 22.05/6.17 | (1268) sum(n14, n13) = all_0_2_2
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (219) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 22.05/6.17 | (741) all_0_5_5 = n14
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (89) with n14, n13, all_0_2_2, n11 and discharging atoms sum(n14, n13) = all_0_2_2, sum(n14, n13) = n11, yields:
% 22.05/6.17 | (498) all_0_2_2 = n11
% 22.05/6.17 |
% 22.05/6.17 | From (498) and (187) follows:
% 22.05/6.17 | (500) pred(n11) = all_0_1_1
% 22.05/6.17 |
% 22.05/6.17 | From (741) and (1263) follows:
% 22.05/6.17 | (1272) sum(n14, n14) = all_0_4_4
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (37) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 22.05/6.17 | (503) all_0_1_1 = n10
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (89) with n14, n14, all_0_4_4, n12 and discharging atoms sum(n14, n14) = all_0_4_4, sum(n14, n14) = n12, yields:
% 22.05/6.17 | (499) all_0_4_4 = n12
% 22.05/6.17 |
% 22.05/6.17 | From (499) and (396) follows:
% 22.05/6.17 | (501) pred(n12) = all_0_3_3
% 22.05/6.17 |
% 22.05/6.17 | From (503) and (739) follows:
% 22.05/6.17 | (1276) sum(n13, n10) = all_0_0_0
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (37) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 22.05/6.17 | (502) all_0_3_3 = n11
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (89) with n13, n10, all_0_0_0, n7 and discharging atoms sum(n13, n10) = all_0_0_0, sum(n13, n10) = n7, yields:
% 22.05/6.17 | (540) all_0_0_0 = n7
% 22.05/6.17 |
% 22.05/6.17 | From (502)(540) and (261) follows:
% 22.05/6.17 | (1279) sum(n11, n7) = all_0_6_6
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (89) with n11, n7, all_0_6_6, n2 and discharging atoms sum(n11, n7) = all_0_6_6, sum(n11, n7) = n2, yields:
% 22.05/6.17 | (525) all_0_6_6 = n2
% 22.05/6.17 |
% 22.05/6.17 | Equations (525) can reduce 231 to:
% 22.05/6.17 | (458) $false
% 22.05/6.17 |
% 22.05/6.17 |-The branch is then unsatisfiable
% 22.05/6.17 |-Branch two:
% 22.05/6.17 | (754) ~ (all_0_7_7 = n13)
% 22.05/6.17 | (755) all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.05/6.17 |
% 22.05/6.17 +-Applying beta-rule and splitting (755), into two cases.
% 22.05/6.17 |-Branch one:
% 22.05/6.17 | (756) all_0_7_7 = n12
% 22.05/6.17 |
% 22.05/6.17 | From (756) and (176) follows:
% 22.05/6.17 | (757) succ(n12) = all_0_5_5
% 22.05/6.17 |
% 22.05/6.17 | From (756) and (59) follows:
% 22.05/6.17 | (758) sum(n12, all_0_1_1) = all_0_0_0
% 22.05/6.17 |
% 22.05/6.17 | From (756) and (1264) follows:
% 22.05/6.17 | (1287) sum(n14, n12) = all_0_2_2
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (219) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 22.05/6.17 | (760) all_0_5_5 = n13
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (89) with n14, n12, all_0_2_2, n10 and discharging atoms sum(n14, n12) = all_0_2_2, sum(n14, n12) = n10, yields:
% 22.05/6.17 | (515) all_0_2_2 = n10
% 22.05/6.17 |
% 22.05/6.17 | From (515) and (187) follows:
% 22.05/6.17 | (517) pred(n10) = all_0_1_1
% 22.05/6.17 |
% 22.05/6.17 | From (760) and (1263) follows:
% 22.05/6.17 | (1291) sum(n14, n13) = all_0_4_4
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (37) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 22.05/6.17 | (520) all_0_1_1 = n9
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (89) with n14, n13, all_0_4_4, n11 and discharging atoms sum(n14, n13) = all_0_4_4, sum(n14, n13) = n11, yields:
% 22.05/6.17 | (516) all_0_4_4 = n11
% 22.05/6.17 |
% 22.05/6.17 | From (516) and (396) follows:
% 22.05/6.17 | (518) pred(n11) = all_0_3_3
% 22.05/6.17 |
% 22.05/6.17 | From (520) and (758) follows:
% 22.05/6.17 | (1295) sum(n12, n9) = all_0_0_0
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (37) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 22.05/6.17 | (519) all_0_3_3 = n10
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (89) with n12, n9, all_0_0_0, n5 and discharging atoms sum(n12, n9) = all_0_0_0, sum(n12, n9) = n5, yields:
% 22.05/6.17 | (574) all_0_0_0 = n5
% 22.05/6.17 |
% 22.05/6.17 | From (519)(574) and (261) follows:
% 22.05/6.17 | (1298) sum(n10, n5) = all_0_6_6
% 22.05/6.17 |
% 22.05/6.17 | Instantiating formula (89) with n10, n5, all_0_6_6, n15 and discharging atoms sum(n10, n5) = all_0_6_6, sum(n10, n5) = n15, yields:
% 22.05/6.17 | (885) all_0_6_6 = n15
% 22.05/6.17 |
% 22.05/6.17 | Equations (885) can reduce 225 to:
% 22.05/6.17 | (458) $false
% 22.05/6.17 |
% 22.05/6.17 |-The branch is then unsatisfiable
% 22.05/6.17 |-Branch two:
% 22.05/6.17 | (773) ~ (all_0_7_7 = n12)
% 22.05/6.17 | (774) all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.05/6.18 |
% 22.05/6.18 +-Applying beta-rule and splitting (774), into two cases.
% 22.05/6.18 |-Branch one:
% 22.05/6.18 | (775) all_0_7_7 = n11
% 22.05/6.18 |
% 22.05/6.18 | From (775) and (176) follows:
% 22.05/6.18 | (776) succ(n11) = all_0_5_5
% 22.05/6.18 |
% 22.05/6.18 | From (775) and (59) follows:
% 22.05/6.18 | (777) sum(n11, all_0_1_1) = all_0_0_0
% 22.05/6.18 |
% 22.05/6.18 | From (775) and (1264) follows:
% 22.05/6.18 | (1306) sum(n14, n11) = all_0_2_2
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (219) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 22.05/6.18 | (779) all_0_5_5 = n12
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (89) with n14, n11, all_0_2_2, n9 and discharging atoms sum(n14, n11) = all_0_2_2, sum(n14, n11) = n9, yields:
% 22.05/6.18 | (532) all_0_2_2 = n9
% 22.05/6.18 |
% 22.05/6.18 | From (532) and (187) follows:
% 22.05/6.18 | (534) pred(n9) = all_0_1_1
% 22.05/6.18 |
% 22.05/6.18 | From (779) and (1263) follows:
% 22.05/6.18 | (1310) sum(n14, n12) = all_0_4_4
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (37) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 22.05/6.18 | (537) all_0_1_1 = n8
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (89) with n14, n12, all_0_4_4, n10 and discharging atoms sum(n14, n12) = all_0_4_4, sum(n14, n12) = n10, yields:
% 22.05/6.18 | (533) all_0_4_4 = n10
% 22.05/6.18 |
% 22.05/6.18 | From (533) and (396) follows:
% 22.05/6.18 | (535) pred(n10) = all_0_3_3
% 22.05/6.18 |
% 22.05/6.18 | From (537) and (777) follows:
% 22.05/6.18 | (1314) sum(n11, n8) = all_0_0_0
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (37) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 22.05/6.18 | (536) all_0_3_3 = n9
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (89) with n11, n8, all_0_0_0, n3 and discharging atoms sum(n11, n8) = all_0_0_0, sum(n11, n8) = n3, yields:
% 22.05/6.18 | (608) all_0_0_0 = n3
% 22.05/6.18 |
% 22.05/6.18 | From (536)(608) and (261) follows:
% 22.05/6.18 | (1317) sum(n9, n3) = all_0_6_6
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (89) with n9, n3, all_0_6_6, n12 and discharging atoms sum(n9, n3) = all_0_6_6, sum(n9, n3) = n12, yields:
% 22.05/6.18 | (576) all_0_6_6 = n12
% 22.05/6.18 |
% 22.05/6.18 | Equations (576) can reduce 42 to:
% 22.05/6.18 | (458) $false
% 22.05/6.18 |
% 22.05/6.18 |-The branch is then unsatisfiable
% 22.05/6.18 |-Branch two:
% 22.05/6.18 | (792) ~ (all_0_7_7 = n11)
% 22.05/6.18 | (793) all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.05/6.18 |
% 22.05/6.18 +-Applying beta-rule and splitting (793), into two cases.
% 22.05/6.18 |-Branch one:
% 22.05/6.18 | (794) all_0_7_7 = n10
% 22.05/6.18 |
% 22.05/6.18 | From (794) and (176) follows:
% 22.05/6.18 | (795) succ(n10) = all_0_5_5
% 22.05/6.18 |
% 22.05/6.18 | From (794) and (59) follows:
% 22.05/6.18 | (796) sum(n10, all_0_1_1) = all_0_0_0
% 22.05/6.18 |
% 22.05/6.18 | From (794) and (1264) follows:
% 22.05/6.18 | (1325) sum(n14, n10) = all_0_2_2
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (219) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 22.05/6.18 | (798) all_0_5_5 = n11
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (89) with n14, n10, all_0_2_2, n8 and discharging atoms sum(n14, n10) = all_0_2_2, sum(n14, n10) = n8, yields:
% 22.05/6.18 | (549) all_0_2_2 = n8
% 22.05/6.18 |
% 22.05/6.18 | From (549) and (187) follows:
% 22.05/6.18 | (551) pred(n8) = all_0_1_1
% 22.05/6.18 |
% 22.05/6.18 | From (798) and (1263) follows:
% 22.05/6.18 | (1329) sum(n14, n11) = all_0_4_4
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (37) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 22.05/6.18 | (554) all_0_1_1 = n7
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (89) with n14, n11, all_0_4_4, n9 and discharging atoms sum(n14, n11) = all_0_4_4, sum(n14, n11) = n9, yields:
% 22.05/6.18 | (550) all_0_4_4 = n9
% 22.05/6.18 |
% 22.05/6.18 | From (550) and (396) follows:
% 22.05/6.18 | (552) pred(n9) = all_0_3_3
% 22.05/6.18 |
% 22.05/6.18 | From (554) and (796) follows:
% 22.05/6.18 | (1333) sum(n10, n7) = all_0_0_0
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (37) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 22.05/6.18 | (553) all_0_3_3 = n8
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (89) with n10, n7, all_0_0_0, n1 and discharging atoms sum(n10, n7) = all_0_0_0, sum(n10, n7) = n1, yields:
% 22.05/6.18 | (642) all_0_0_0 = n1
% 22.05/6.18 |
% 22.05/6.18 | From (553)(642) and (261) follows:
% 22.05/6.18 | (1336) sum(n8, n1) = all_0_6_6
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (89) with n8, n1, all_0_6_6, n9 and discharging atoms sum(n8, n1) = all_0_6_6, sum(n8, n1) = n9, yields:
% 22.05/6.18 | (923) all_0_6_6 = n9
% 22.05/6.18 |
% 22.05/6.18 | Equations (923) can reduce 404 to:
% 22.05/6.18 | (458) $false
% 22.05/6.18 |
% 22.05/6.18 |-The branch is then unsatisfiable
% 22.05/6.18 |-Branch two:
% 22.05/6.18 | (811) ~ (all_0_7_7 = n10)
% 22.05/6.18 | (812) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.05/6.18 |
% 22.05/6.18 +-Applying beta-rule and splitting (812), into two cases.
% 22.05/6.18 |-Branch one:
% 22.05/6.18 | (813) all_0_7_7 = n9
% 22.05/6.18 |
% 22.05/6.18 | From (813) and (176) follows:
% 22.05/6.18 | (814) succ(n9) = all_0_5_5
% 22.05/6.18 |
% 22.05/6.18 | From (813) and (59) follows:
% 22.05/6.18 | (815) sum(n9, all_0_1_1) = all_0_0_0
% 22.05/6.18 |
% 22.05/6.18 | From (813) and (1264) follows:
% 22.05/6.18 | (1344) sum(n14, n9) = all_0_2_2
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (219) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 22.05/6.18 | (817) all_0_5_5 = n10
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (89) with n14, n9, all_0_2_2, n7 and discharging atoms sum(n14, n9) = all_0_2_2, sum(n14, n9) = n7, yields:
% 22.05/6.18 | (566) all_0_2_2 = n7
% 22.05/6.18 |
% 22.05/6.18 | From (566) and (187) follows:
% 22.05/6.18 | (568) pred(n7) = all_0_1_1
% 22.05/6.18 |
% 22.05/6.18 | From (817) and (1263) follows:
% 22.05/6.18 | (1348) sum(n14, n10) = all_0_4_4
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (37) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 22.05/6.18 | (571) all_0_1_1 = n6
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (89) with n14, n10, all_0_4_4, n8 and discharging atoms sum(n14, n10) = all_0_4_4, sum(n14, n10) = n8, yields:
% 22.05/6.18 | (567) all_0_4_4 = n8
% 22.05/6.18 |
% 22.05/6.18 | From (567) and (396) follows:
% 22.05/6.18 | (569) pred(n8) = all_0_3_3
% 22.05/6.18 |
% 22.05/6.18 | From (571) and (815) follows:
% 22.05/6.18 | (1352) sum(n9, n6) = all_0_0_0
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (37) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 22.05/6.18 | (570) all_0_3_3 = n7
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (89) with n9, n6, all_0_0_0, n15 and discharging atoms sum(n9, n6) = all_0_0_0, sum(n9, n6) = n15, yields:
% 22.05/6.18 | (676) all_0_0_0 = n15
% 22.05/6.18 |
% 22.05/6.18 | From (570)(676) and (261) follows:
% 22.05/6.18 | (1355) sum(n7, n15) = all_0_6_6
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (89) with n7, n15, all_0_6_6, n6 and discharging atoms sum(n7, n15) = all_0_6_6, sum(n7, n15) = n6, yields:
% 22.05/6.18 | (491) all_0_6_6 = n6
% 22.05/6.18 |
% 22.05/6.18 | Equations (491) can reduce 418 to:
% 22.05/6.18 | (458) $false
% 22.05/6.18 |
% 22.05/6.18 |-The branch is then unsatisfiable
% 22.05/6.18 |-Branch two:
% 22.05/6.18 | (830) ~ (all_0_7_7 = n9)
% 22.05/6.18 | (831) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.05/6.18 |
% 22.05/6.18 +-Applying beta-rule and splitting (831), into two cases.
% 22.05/6.18 |-Branch one:
% 22.05/6.18 | (832) all_0_7_7 = n8
% 22.05/6.18 |
% 22.05/6.18 | From (832) and (176) follows:
% 22.05/6.18 | (833) succ(n8) = all_0_5_5
% 22.05/6.18 |
% 22.05/6.18 | From (832) and (59) follows:
% 22.05/6.18 | (834) sum(n8, all_0_1_1) = all_0_0_0
% 22.05/6.18 |
% 22.05/6.18 | From (832) and (1264) follows:
% 22.05/6.18 | (1363) sum(n14, n8) = all_0_2_2
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (219) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 22.05/6.18 | (836) all_0_5_5 = n9
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (89) with n14, n8, all_0_2_2, n6 and discharging atoms sum(n14, n8) = all_0_2_2, sum(n14, n8) = n6, yields:
% 22.05/6.18 | (583) all_0_2_2 = n6
% 22.05/6.18 |
% 22.05/6.18 | From (583) and (187) follows:
% 22.05/6.18 | (585) pred(n6) = all_0_1_1
% 22.05/6.18 |
% 22.05/6.18 | From (836) and (1263) follows:
% 22.05/6.18 | (1367) sum(n14, n9) = all_0_4_4
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (37) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 22.05/6.18 | (588) all_0_1_1 = n5
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (89) with n14, n9, all_0_4_4, n7 and discharging atoms sum(n14, n9) = all_0_4_4, sum(n14, n9) = n7, yields:
% 22.05/6.18 | (584) all_0_4_4 = n7
% 22.05/6.18 |
% 22.05/6.18 | From (584) and (396) follows:
% 22.05/6.18 | (586) pred(n7) = all_0_3_3
% 22.05/6.18 |
% 22.05/6.18 | From (588) and (834) follows:
% 22.05/6.18 | (1371) sum(n8, n5) = all_0_0_0
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (37) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 22.05/6.18 | (587) all_0_3_3 = n6
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (89) with n8, n5, all_0_0_0, n13 and discharging atoms sum(n8, n5) = all_0_0_0, sum(n8, n5) = n13, yields:
% 22.05/6.18 | (709) all_0_0_0 = n13
% 22.05/6.18 |
% 22.05/6.18 | From (587)(709) and (261) follows:
% 22.05/6.18 | (1374) sum(n6, n13) = all_0_6_6
% 22.05/6.18 |
% 22.05/6.18 | Instantiating formula (89) with n6, n13, all_0_6_6, n3 and discharging atoms sum(n6, n13) = all_0_6_6, sum(n6, n13) = n3, yields:
% 22.05/6.18 | (961) all_0_6_6 = n3
% 22.05/6.18 |
% 22.05/6.18 | Equations (961) can reduce 245 to:
% 22.05/6.18 | (458) $false
% 22.05/6.18 |
% 22.05/6.18 |-The branch is then unsatisfiable
% 22.05/6.18 |-Branch two:
% 22.05/6.18 | (849) ~ (all_0_7_7 = n8)
% 22.05/6.18 | (850) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.05/6.18 |
% 22.05/6.18 +-Applying beta-rule and splitting (850), into two cases.
% 22.05/6.18 |-Branch one:
% 22.05/6.18 | (851) all_0_7_7 = n7
% 22.05/6.18 |
% 22.05/6.18 | From (851) and (176) follows:
% 22.05/6.18 | (852) succ(n7) = all_0_5_5
% 22.05/6.18 |
% 22.05/6.18 | From (851) and (59) follows:
% 22.05/6.19 | (853) sum(n7, all_0_1_1) = all_0_0_0
% 22.05/6.19 |
% 22.05/6.19 | From (851) and (1264) follows:
% 22.05/6.19 | (1382) sum(n14, n7) = all_0_2_2
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (219) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 22.05/6.19 | (855) all_0_5_5 = n8
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (89) with n14, n7, all_0_2_2, n5 and discharging atoms sum(n14, n7) = all_0_2_2, sum(n14, n7) = n5, yields:
% 22.05/6.19 | (600) all_0_2_2 = n5
% 22.05/6.19 |
% 22.05/6.19 | From (600) and (187) follows:
% 22.05/6.19 | (602) pred(n5) = all_0_1_1
% 22.05/6.19 |
% 22.05/6.19 | From (855) and (1263) follows:
% 22.05/6.19 | (1386) sum(n14, n8) = all_0_4_4
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (37) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 22.05/6.19 | (605) all_0_1_1 = n4
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (89) with n14, n8, all_0_4_4, n6 and discharging atoms sum(n14, n8) = all_0_4_4, sum(n14, n8) = n6, yields:
% 22.05/6.19 | (601) all_0_4_4 = n6
% 22.05/6.19 |
% 22.05/6.19 | From (601) and (396) follows:
% 22.05/6.19 | (603) pred(n6) = all_0_3_3
% 22.05/6.19 |
% 22.05/6.19 | From (605) and (853) follows:
% 22.05/6.19 | (1390) sum(n7, n4) = all_0_0_0
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (37) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 22.05/6.19 | (604) all_0_3_3 = n5
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (89) with n7, n4, all_0_0_0, n11 and discharging atoms sum(n7, n4) = all_0_0_0, sum(n7, n4) = n11, yields:
% 22.05/6.19 | (472) all_0_0_0 = n11
% 22.05/6.19 |
% 22.05/6.19 | From (604)(472) and (261) follows:
% 22.05/6.19 | (1393) sum(n5, n11) = all_0_6_6
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (89) with n5, n11, all_0_6_6, n0 and discharging atoms sum(n5, n11) = all_0_6_6, sum(n5, n11) = n0, yields:
% 22.05/6.19 | (542) all_0_6_6 = n0
% 22.05/6.19 |
% 22.05/6.19 | Equations (542) can reduce 400 to:
% 22.05/6.19 | (458) $false
% 22.05/6.19 |
% 22.05/6.19 |-The branch is then unsatisfiable
% 22.05/6.19 |-Branch two:
% 22.05/6.19 | (868) ~ (all_0_7_7 = n7)
% 22.05/6.19 | (869) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.05/6.19 |
% 22.05/6.19 +-Applying beta-rule and splitting (869), into two cases.
% 22.05/6.19 |-Branch one:
% 22.05/6.19 | (870) all_0_7_7 = n6
% 22.05/6.19 |
% 22.05/6.19 | From (870) and (176) follows:
% 22.05/6.19 | (871) succ(n6) = all_0_5_5
% 22.05/6.19 |
% 22.05/6.19 | From (870) and (59) follows:
% 22.05/6.19 | (872) sum(n6, all_0_1_1) = all_0_0_0
% 22.05/6.19 |
% 22.05/6.19 | From (870) and (1264) follows:
% 22.05/6.19 | (1401) sum(n14, n6) = all_0_2_2
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (219) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 22.05/6.19 | (874) all_0_5_5 = n7
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (89) with n14, n6, all_0_2_2, n4 and discharging atoms sum(n14, n6) = all_0_2_2, sum(n14, n6) = n4, yields:
% 22.05/6.19 | (617) all_0_2_2 = n4
% 22.05/6.19 |
% 22.05/6.19 | From (617) and (187) follows:
% 22.05/6.19 | (619) pred(n4) = all_0_1_1
% 22.05/6.19 |
% 22.05/6.19 | From (874) and (1263) follows:
% 22.05/6.19 | (1405) sum(n14, n7) = all_0_4_4
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (37) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 22.05/6.19 | (622) all_0_1_1 = n3
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (89) with n14, n7, all_0_4_4, n5 and discharging atoms sum(n14, n7) = all_0_4_4, sum(n14, n7) = n5, yields:
% 22.05/6.19 | (618) all_0_4_4 = n5
% 22.05/6.19 |
% 22.05/6.19 | From (618) and (396) follows:
% 22.05/6.19 | (620) pred(n5) = all_0_3_3
% 22.05/6.19 |
% 22.05/6.19 | From (622) and (872) follows:
% 22.05/6.19 | (1409) sum(n6, n3) = all_0_0_0
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (37) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 22.05/6.19 | (621) all_0_3_3 = n4
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (89) with n6, n3, all_0_0_0, n9 and discharging atoms sum(n6, n3) = all_0_0_0, sum(n6, n3) = n9, yields:
% 22.05/6.19 | (506) all_0_0_0 = n9
% 22.05/6.19 |
% 22.05/6.19 | From (621)(506) and (261) follows:
% 22.05/6.19 | (1412) sum(n4, n9) = all_0_6_6
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (89) with n4, n9, all_0_6_6, n13 and discharging atoms sum(n4, n9) = all_0_6_6, sum(n4, n9) = n13, yields:
% 22.05/6.19 | (998) all_0_6_6 = n13
% 22.05/6.19 |
% 22.05/6.19 | Equations (998) can reduce 130 to:
% 22.05/6.19 | (458) $false
% 22.05/6.19 |
% 22.05/6.19 |-The branch is then unsatisfiable
% 22.05/6.19 |-Branch two:
% 22.05/6.19 | (887) ~ (all_0_7_7 = n6)
% 22.05/6.19 | (888) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.05/6.19 |
% 22.05/6.19 +-Applying beta-rule and splitting (888), into two cases.
% 22.05/6.19 |-Branch one:
% 22.05/6.19 | (889) all_0_7_7 = n5
% 22.05/6.19 |
% 22.05/6.19 | From (889) and (176) follows:
% 22.05/6.19 | (890) succ(n5) = all_0_5_5
% 22.05/6.19 |
% 22.05/6.19 | From (889) and (59) follows:
% 22.05/6.19 | (891) sum(n5, all_0_1_1) = all_0_0_0
% 22.05/6.19 |
% 22.05/6.19 | From (889) and (1264) follows:
% 22.05/6.19 | (1420) sum(n14, n5) = all_0_2_2
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (219) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 22.05/6.19 | (893) all_0_5_5 = n6
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (89) with n14, n5, all_0_2_2, n3 and discharging atoms sum(n14, n5) = all_0_2_2, sum(n14, n5) = n3, yields:
% 22.05/6.19 | (634) all_0_2_2 = n3
% 22.05/6.19 |
% 22.05/6.19 | From (634) and (187) follows:
% 22.05/6.19 | (636) pred(n3) = all_0_1_1
% 22.05/6.19 |
% 22.05/6.19 | From (893) and (1263) follows:
% 22.05/6.19 | (1424) sum(n14, n6) = all_0_4_4
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (37) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 22.05/6.19 | (639) all_0_1_1 = n2
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (89) with n14, n6, all_0_4_4, n4 and discharging atoms sum(n14, n6) = all_0_4_4, sum(n14, n6) = n4, yields:
% 22.05/6.19 | (635) all_0_4_4 = n4
% 22.05/6.19 |
% 22.05/6.19 | From (635) and (396) follows:
% 22.05/6.19 | (637) pred(n4) = all_0_3_3
% 22.05/6.19 |
% 22.05/6.19 | From (639) and (891) follows:
% 22.05/6.19 | (1428) sum(n5, n2) = all_0_0_0
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (37) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 22.05/6.19 | (638) all_0_3_3 = n3
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (89) with n5, n2, all_0_0_0, n7 and discharging atoms sum(n5, n2) = all_0_0_0, sum(n5, n2) = n7, yields:
% 22.05/6.19 | (540) all_0_0_0 = n7
% 22.05/6.19 |
% 22.05/6.19 | From (638)(540) and (261) follows:
% 22.05/6.19 | (1431) sum(n3, n7) = all_0_6_6
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (89) with n3, n7, all_0_6_6, n10 and discharging atoms sum(n3, n7) = all_0_6_6, sum(n3, n7) = n10, yields:
% 22.05/6.19 | (457) all_0_6_6 = n10
% 22.05/6.19 |
% 22.05/6.19 | Equations (457) can reduce 169 to:
% 22.05/6.19 | (458) $false
% 22.05/6.19 |
% 22.05/6.19 |-The branch is then unsatisfiable
% 22.05/6.19 |-Branch two:
% 22.05/6.19 | (906) ~ (all_0_7_7 = n5)
% 22.05/6.19 | (907) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.05/6.19 |
% 22.05/6.19 +-Applying beta-rule and splitting (907), into two cases.
% 22.05/6.19 |-Branch one:
% 22.05/6.19 | (908) all_0_7_7 = n4
% 22.05/6.19 |
% 22.05/6.19 | From (908) and (176) follows:
% 22.05/6.19 | (909) succ(n4) = all_0_5_5
% 22.05/6.19 |
% 22.05/6.19 | From (908) and (59) follows:
% 22.05/6.19 | (910) sum(n4, all_0_1_1) = all_0_0_0
% 22.05/6.19 |
% 22.05/6.19 | From (908) and (1264) follows:
% 22.05/6.19 | (1439) sum(n14, n4) = all_0_2_2
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (219) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 22.05/6.19 | (912) all_0_5_5 = n5
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (89) with n14, n4, all_0_2_2, n2 and discharging atoms sum(n14, n4) = all_0_2_2, sum(n14, n4) = n2, yields:
% 22.05/6.19 | (651) all_0_2_2 = n2
% 22.05/6.19 |
% 22.05/6.19 | From (651) and (187) follows:
% 22.05/6.19 | (653) pred(n2) = all_0_1_1
% 22.05/6.19 |
% 22.05/6.19 | From (912) and (1263) follows:
% 22.05/6.19 | (1443) sum(n14, n5) = all_0_4_4
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (37) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 22.05/6.19 | (656) all_0_1_1 = n1
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (89) with n14, n5, all_0_4_4, n3 and discharging atoms sum(n14, n5) = all_0_4_4, sum(n14, n5) = n3, yields:
% 22.05/6.19 | (652) all_0_4_4 = n3
% 22.05/6.19 |
% 22.05/6.19 | From (652) and (396) follows:
% 22.05/6.19 | (654) pred(n3) = all_0_3_3
% 22.05/6.19 |
% 22.05/6.19 | From (656) and (910) follows:
% 22.05/6.19 | (1447) sum(n4, n1) = all_0_0_0
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (37) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 22.05/6.19 | (655) all_0_3_3 = n2
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (89) with n4, n1, all_0_0_0, n5 and discharging atoms sum(n4, n1) = all_0_0_0, sum(n4, n1) = n5, yields:
% 22.05/6.19 | (574) all_0_0_0 = n5
% 22.05/6.19 |
% 22.05/6.19 | From (655)(574) and (261) follows:
% 22.05/6.19 | (1450) sum(n2, n5) = all_0_6_6
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (89) with n2, n5, all_0_6_6, n7 and discharging atoms sum(n2, n5) = all_0_6_6, sum(n2, n5) = n7, yields:
% 22.05/6.19 | (733) all_0_6_6 = n7
% 22.05/6.19 |
% 22.05/6.19 | Equations (733) can reduce 274 to:
% 22.05/6.19 | (458) $false
% 22.05/6.19 |
% 22.05/6.19 |-The branch is then unsatisfiable
% 22.05/6.19 |-Branch two:
% 22.05/6.19 | (925) ~ (all_0_7_7 = n4)
% 22.05/6.19 | (926) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.05/6.19 |
% 22.05/6.19 +-Applying beta-rule and splitting (926), into two cases.
% 22.05/6.19 |-Branch one:
% 22.05/6.19 | (927) all_0_7_7 = n3
% 22.05/6.19 |
% 22.05/6.19 | From (927) and (176) follows:
% 22.05/6.19 | (928) succ(n3) = all_0_5_5
% 22.05/6.19 |
% 22.05/6.19 | From (927) and (59) follows:
% 22.05/6.19 | (929) sum(n3, all_0_1_1) = all_0_0_0
% 22.05/6.19 |
% 22.05/6.19 | From (927) and (1264) follows:
% 22.05/6.19 | (1458) sum(n14, n3) = all_0_2_2
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (219) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 22.05/6.19 | (931) all_0_5_5 = n4
% 22.05/6.19 |
% 22.05/6.19 | Instantiating formula (89) with n14, n3, all_0_2_2, n1 and discharging atoms sum(n14, n3) = all_0_2_2, sum(n14, n3) = n1, yields:
% 22.05/6.20 | (668) all_0_2_2 = n1
% 22.05/6.20 |
% 22.05/6.20 | From (668) and (187) follows:
% 22.05/6.20 | (670) pred(n1) = all_0_1_1
% 22.05/6.20 |
% 22.05/6.20 | From (931) and (1263) follows:
% 22.05/6.20 | (1462) sum(n14, n4) = all_0_4_4
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (37) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 22.05/6.20 | (673) all_0_1_1 = n0
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (89) with n14, n4, all_0_4_4, n2 and discharging atoms sum(n14, n4) = all_0_4_4, sum(n14, n4) = n2, yields:
% 22.05/6.20 | (669) all_0_4_4 = n2
% 22.05/6.20 |
% 22.05/6.20 | From (669) and (396) follows:
% 22.05/6.20 | (671) pred(n2) = all_0_3_3
% 22.05/6.20 |
% 22.05/6.20 | From (673) and (929) follows:
% 22.05/6.20 | (1466) sum(n3, n0) = all_0_0_0
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (37) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 22.05/6.20 | (672) all_0_3_3 = n1
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (89) with n3, n0, all_0_0_0, n3 and discharging atoms sum(n3, n0) = all_0_0_0, sum(n3, n0) = n3, yields:
% 22.05/6.20 | (608) all_0_0_0 = n3
% 22.05/6.20 |
% 22.05/6.20 | From (672)(608) and (261) follows:
% 22.05/6.20 | (1469) sum(n1, n3) = all_0_6_6
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (89) with n1, n3, all_0_6_6, n4 and discharging atoms sum(n1, n3) = all_0_6_6, sum(n1, n3) = n4, yields:
% 22.05/6.20 | (508) all_0_6_6 = n4
% 22.05/6.20 |
% 22.05/6.20 | Equations (508) can reduce 12 to:
% 22.05/6.20 | (458) $false
% 22.05/6.20 |
% 22.05/6.20 |-The branch is then unsatisfiable
% 22.05/6.20 |-Branch two:
% 22.05/6.20 | (944) ~ (all_0_7_7 = n3)
% 22.05/6.20 | (945) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.05/6.20 |
% 22.05/6.20 +-Applying beta-rule and splitting (945), into two cases.
% 22.05/6.20 |-Branch one:
% 22.05/6.20 | (946) all_0_7_7 = n2
% 22.05/6.20 |
% 22.05/6.20 | From (946) and (176) follows:
% 22.05/6.20 | (947) succ(n2) = all_0_5_5
% 22.05/6.20 |
% 22.05/6.20 | From (946) and (59) follows:
% 22.05/6.20 | (948) sum(n2, all_0_1_1) = all_0_0_0
% 22.05/6.20 |
% 22.05/6.20 | From (946) and (1264) follows:
% 22.05/6.20 | (1477) sum(n14, n2) = all_0_2_2
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (219) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 22.05/6.20 | (950) all_0_5_5 = n3
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (89) with n14, n2, all_0_2_2, n0 and discharging atoms sum(n14, n2) = all_0_2_2, sum(n14, n2) = n0, yields:
% 22.05/6.20 | (685) all_0_2_2 = n0
% 22.05/6.20 |
% 22.05/6.20 | From (685) and (187) follows:
% 22.05/6.20 | (687) pred(n0) = all_0_1_1
% 22.05/6.20 |
% 22.05/6.20 | From (950) and (1263) follows:
% 22.05/6.20 | (1481) sum(n14, n3) = all_0_4_4
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (37) with n0, all_0_1_1, n15 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n15, yields:
% 22.05/6.20 | (690) all_0_1_1 = n15
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (89) with n14, n3, all_0_4_4, n1 and discharging atoms sum(n14, n3) = all_0_4_4, sum(n14, n3) = n1, yields:
% 22.05/6.20 | (686) all_0_4_4 = n1
% 22.05/6.20 |
% 22.05/6.20 | From (686) and (396) follows:
% 22.05/6.20 | (688) pred(n1) = all_0_3_3
% 22.05/6.20 |
% 22.05/6.20 | From (690) and (948) follows:
% 22.05/6.20 | (1485) sum(n2, n15) = all_0_0_0
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (37) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 22.05/6.20 | (689) all_0_3_3 = n0
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (89) with n2, n15, all_0_0_0, n1 and discharging atoms sum(n2, n15) = all_0_0_0, sum(n2, n15) = n1, yields:
% 22.05/6.20 | (642) all_0_0_0 = n1
% 22.05/6.20 |
% 22.05/6.20 | From (689)(642) and (261) follows:
% 22.05/6.20 | (1488) sum(n0, n1) = all_0_6_6
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (89) with n0, n1, all_0_6_6, n1 and discharging atoms sum(n0, n1) = all_0_6_6, sum(n0, n1) = n1, yields:
% 22.05/6.20 | (771) all_0_6_6 = n1
% 22.05/6.20 |
% 22.05/6.20 | Equations (771) can reduce 38 to:
% 22.05/6.20 | (458) $false
% 22.05/6.20 |
% 22.05/6.20 |-The branch is then unsatisfiable
% 22.05/6.20 |-Branch two:
% 22.05/6.20 | (963) ~ (all_0_7_7 = n2)
% 22.05/6.20 | (964) all_0_7_7 = n1 | all_0_7_7 = n0
% 22.05/6.20 |
% 22.05/6.20 +-Applying beta-rule and splitting (964), into two cases.
% 22.05/6.20 |-Branch one:
% 22.05/6.20 | (965) all_0_7_7 = n1
% 22.05/6.20 |
% 22.05/6.20 | From (965) and (176) follows:
% 22.05/6.20 | (966) succ(n1) = all_0_5_5
% 22.05/6.20 |
% 22.05/6.20 | From (965) and (59) follows:
% 22.05/6.20 | (967) sum(n1, all_0_1_1) = all_0_0_0
% 22.05/6.20 |
% 22.05/6.20 | From (965) and (1264) follows:
% 22.05/6.20 | (1496) sum(n14, n1) = all_0_2_2
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (219) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 22.05/6.20 | (969) all_0_5_5 = n2
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (89) with n14, n1, all_0_2_2, n15 and discharging atoms sum(n14, n1) = all_0_2_2, sum(n14, n1) = n15, yields:
% 22.05/6.20 | (701) all_0_2_2 = n15
% 22.05/6.20 |
% 22.05/6.20 | From (701) and (187) follows:
% 22.05/6.20 | (703) pred(n15) = all_0_1_1
% 22.05/6.20 |
% 22.05/6.20 | From (969) and (1263) follows:
% 22.05/6.20 | (1500) sum(n14, n2) = all_0_4_4
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (37) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 22.05/6.20 | (705) all_0_1_1 = n14
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (89) with n14, n2, all_0_4_4, n0 and discharging atoms sum(n14, n2) = all_0_4_4, sum(n14, n2) = n0, yields:
% 22.05/6.20 | (702) all_0_4_4 = n0
% 22.05/6.20 |
% 22.05/6.20 | From (702) and (396) follows:
% 22.05/6.20 | (704) pred(n0) = all_0_3_3
% 22.05/6.20 |
% 22.05/6.20 | From (705) and (967) follows:
% 22.05/6.20 | (1504) sum(n1, n14) = all_0_0_0
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (37) with n0, all_0_3_3, n15 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n15, yields:
% 22.05/6.20 | (706) all_0_3_3 = n15
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (89) with n1, n14, all_0_0_0, n15 and discharging atoms sum(n1, n14) = all_0_0_0, sum(n1, n14) = n15, yields:
% 22.05/6.20 | (676) all_0_0_0 = n15
% 22.05/6.20 |
% 22.05/6.20 | From (706)(676) and (261) follows:
% 22.05/6.20 | (1507) sum(n15, n15) = all_0_6_6
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (89) with n15, n15, all_0_6_6, n14 and discharging atoms sum(n15, n15) = all_0_6_6, sum(n15, n15) = n14, yields:
% 22.05/6.20 | (559) all_0_6_6 = n14
% 22.05/6.20 |
% 22.05/6.20 | Equations (559) can reduce 314 to:
% 22.05/6.20 | (458) $false
% 22.05/6.20 |
% 22.05/6.20 |-The branch is then unsatisfiable
% 22.05/6.20 |-Branch two:
% 22.05/6.20 | (982) ~ (all_0_7_7 = n1)
% 22.05/6.20 | (983) all_0_7_7 = n0
% 22.05/6.20 |
% 22.05/6.20 | From (983) and (176) follows:
% 22.05/6.20 | (984) succ(n0) = all_0_5_5
% 22.05/6.20 |
% 22.05/6.20 | From (983) and (59) follows:
% 22.05/6.20 | (985) sum(n0, all_0_1_1) = all_0_0_0
% 22.05/6.20 |
% 22.05/6.20 | From (983) and (1264) follows:
% 22.05/6.20 | (1514) sum(n14, n0) = all_0_2_2
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (219) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 22.05/6.20 | (987) all_0_5_5 = n1
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (89) with n14, n0, all_0_2_2, n14 and discharging atoms sum(n14, n0) = all_0_2_2, sum(n14, n0) = n14, yields:
% 22.05/6.20 | (447) all_0_2_2 = n14
% 22.05/6.20 |
% 22.05/6.20 | From (447) and (187) follows:
% 22.05/6.20 | (449) pred(n14) = all_0_1_1
% 22.05/6.20 |
% 22.05/6.20 | From (987) and (1263) follows:
% 22.05/6.20 | (1518) sum(n14, n1) = all_0_4_4
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (37) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 22.05/6.20 | (452) all_0_1_1 = n13
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (89) with n14, n1, all_0_4_4, n15 and discharging atoms sum(n14, n1) = all_0_4_4, sum(n14, n1) = n15, yields:
% 22.05/6.20 | (448) all_0_4_4 = n15
% 22.05/6.20 |
% 22.05/6.20 | From (448) and (396) follows:
% 22.05/6.20 | (450) pred(n15) = all_0_3_3
% 22.05/6.20 |
% 22.05/6.20 | From (452) and (985) follows:
% 22.05/6.20 | (1522) sum(n0, n13) = all_0_0_0
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (37) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 22.05/6.20 | (451) all_0_3_3 = n14
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (89) with n0, n13, all_0_0_0, n13 and discharging atoms sum(n0, n13) = all_0_0_0, sum(n0, n13) = n13, yields:
% 22.05/6.20 | (709) all_0_0_0 = n13
% 22.05/6.20 |
% 22.05/6.20 | From (451)(709) and (261) follows:
% 22.05/6.20 | (1525) sum(n14, n13) = all_0_6_6
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (89) with n14, n13, all_0_6_6, n11 and discharging atoms sum(n14, n13) = all_0_6_6, sum(n14, n13) = n11, yields:
% 22.05/6.20 | (809) all_0_6_6 = n11
% 22.05/6.20 |
% 22.05/6.20 | Equations (809) can reduce 70 to:
% 22.05/6.20 | (458) $false
% 22.05/6.20 |
% 22.05/6.20 |-The branch is then unsatisfiable
% 22.05/6.20 |-Branch two:
% 22.05/6.20 | (476) ~ (all_0_8_8 = n14)
% 22.05/6.20 | (477) all_0_8_8 = n13 | all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.05/6.20 |
% 22.05/6.20 +-Applying beta-rule and splitting (736), into two cases.
% 22.05/6.20 |-Branch one:
% 22.05/6.20 | (737) all_0_7_7 = n13
% 22.05/6.20 |
% 22.05/6.20 | From (737) and (176) follows:
% 22.05/6.20 | (738) succ(n13) = all_0_5_5
% 22.05/6.20 |
% 22.05/6.20 | From (737) and (59) follows:
% 22.05/6.20 | (739) sum(n13, all_0_1_1) = all_0_0_0
% 22.05/6.20 |
% 22.05/6.20 | From (737) and (160) follows:
% 22.05/6.20 | (1533) sum(all_0_8_8, n13) = all_0_2_2
% 22.05/6.20 |
% 22.05/6.20 | Instantiating formula (219) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 22.05/6.20 | (741) all_0_5_5 = n14
% 22.05/6.20 |
% 22.05/6.20 | From (741) and (64) follows:
% 22.05/6.20 | (1535) sum(all_0_8_8, n14) = all_0_4_4
% 22.05/6.20 |
% 22.05/6.20 +-Applying beta-rule and splitting (477), into two cases.
% 22.05/6.20 |-Branch one:
% 22.05/6.20 | (478) all_0_8_8 = n13
% 22.05/6.20 |
% 22.05/6.20 | From (478) and (1535) follows:
% 22.05/6.20 | (1537) sum(n13, n14) = all_0_4_4
% 22.05/6.20 |
% 22.05/6.20 | From (478) and (1533) follows:
% 22.05/6.21 | (1538) sum(n13, n13) = all_0_2_2
% 22.05/6.21 |
% 22.05/6.21 | Instantiating formula (89) with n13, n14, all_0_4_4, n11 and discharging atoms sum(n13, n14) = all_0_4_4, sum(n13, n14) = n11, yields:
% 22.05/6.21 | (516) all_0_4_4 = n11
% 22.05/6.21 |
% 22.05/6.21 | Instantiating formula (89) with n13, n13, all_0_2_2, n10 and discharging atoms sum(n13, n13) = all_0_2_2, sum(n13, n13) = n10, yields:
% 22.05/6.21 | (515) all_0_2_2 = n10
% 22.05/6.21 |
% 22.05/6.21 | From (515) and (187) follows:
% 22.05/6.21 | (517) pred(n10) = all_0_1_1
% 22.05/6.21 |
% 22.05/6.21 | From (516) and (396) follows:
% 22.05/6.21 | (518) pred(n11) = all_0_3_3
% 22.05/6.21 |
% 22.05/6.21 | Instantiating formula (37) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 22.05/6.21 | (519) all_0_3_3 = n10
% 22.05/6.21 |
% 22.05/6.21 | Instantiating formula (37) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 22.05/6.21 | (520) all_0_1_1 = n9
% 22.05/6.21 |
% 22.05/6.21 | From (519) and (261) follows:
% 22.05/6.21 | (521) sum(n10, all_0_0_0) = all_0_6_6
% 22.05/6.21 |
% 22.05/6.21 | From (520) and (739) follows:
% 22.21/6.21 | (1546) sum(n13, n9) = all_0_0_0
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (89) with n13, n9, all_0_0_0, n6 and discharging atoms sum(n13, n9) = all_0_0_0, sum(n13, n9) = n6, yields:
% 22.21/6.21 | (557) all_0_0_0 = n6
% 22.21/6.21 |
% 22.21/6.21 | From (557) and (521) follows:
% 22.21/6.21 | (1548) sum(n10, n6) = all_0_6_6
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (89) with n10, n6, all_0_6_6, n0 and discharging atoms sum(n10, n6) = all_0_6_6, sum(n10, n6) = n0, yields:
% 22.21/6.21 | (542) all_0_6_6 = n0
% 22.21/6.21 |
% 22.21/6.21 | Equations (542) can reduce 400 to:
% 22.21/6.21 | (458) $false
% 22.21/6.21 |
% 22.21/6.21 |-The branch is then unsatisfiable
% 22.21/6.21 |-Branch two:
% 22.21/6.21 | (493) ~ (all_0_8_8 = n13)
% 22.21/6.21 | (494) all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.21/6.21 |
% 22.21/6.21 +-Applying beta-rule and splitting (494), into two cases.
% 22.21/6.21 |-Branch one:
% 22.21/6.21 | (495) all_0_8_8 = n12
% 22.21/6.21 |
% 22.21/6.21 | From (495) and (1535) follows:
% 22.21/6.21 | (1554) sum(n12, n14) = all_0_4_4
% 22.21/6.21 |
% 22.21/6.21 | From (495) and (1533) follows:
% 22.21/6.21 | (1555) sum(n12, n13) = all_0_2_2
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (89) with n12, n14, all_0_4_4, n10 and discharging atoms sum(n12, n14) = all_0_4_4, sum(n12, n14) = n10, yields:
% 22.21/6.21 | (533) all_0_4_4 = n10
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (89) with n12, n13, all_0_2_2, n9 and discharging atoms sum(n12, n13) = all_0_2_2, sum(n12, n13) = n9, yields:
% 22.21/6.21 | (532) all_0_2_2 = n9
% 22.21/6.21 |
% 22.21/6.21 | From (532) and (187) follows:
% 22.21/6.21 | (534) pred(n9) = all_0_1_1
% 22.21/6.21 |
% 22.21/6.21 | From (533) and (396) follows:
% 22.21/6.21 | (535) pred(n10) = all_0_3_3
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (37) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 22.21/6.21 | (536) all_0_3_3 = n9
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (37) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 22.21/6.21 | (537) all_0_1_1 = n8
% 22.21/6.21 |
% 22.21/6.21 | From (536) and (261) follows:
% 22.21/6.21 | (538) sum(n9, all_0_0_0) = all_0_6_6
% 22.21/6.21 |
% 22.21/6.21 | From (537) and (739) follows:
% 22.21/6.21 | (1563) sum(n13, n8) = all_0_0_0
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (89) with n13, n8, all_0_0_0, n5 and discharging atoms sum(n13, n8) = all_0_0_0, sum(n13, n8) = n5, yields:
% 22.21/6.21 | (574) all_0_0_0 = n5
% 22.21/6.21 |
% 22.21/6.21 | From (574) and (538) follows:
% 22.21/6.21 | (1565) sum(n9, n5) = all_0_6_6
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (89) with n9, n5, all_0_6_6, n14 and discharging atoms sum(n9, n5) = all_0_6_6, sum(n9, n5) = n14, yields:
% 22.21/6.21 | (559) all_0_6_6 = n14
% 22.21/6.21 |
% 22.21/6.21 | Equations (559) can reduce 314 to:
% 22.21/6.21 | (458) $false
% 22.21/6.21 |
% 22.21/6.21 |-The branch is then unsatisfiable
% 22.21/6.21 |-Branch two:
% 22.21/6.21 | (510) ~ (all_0_8_8 = n12)
% 22.21/6.21 | (511) all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.21/6.21 |
% 22.21/6.21 +-Applying beta-rule and splitting (511), into two cases.
% 22.21/6.21 |-Branch one:
% 22.21/6.21 | (512) all_0_8_8 = n11
% 22.21/6.21 |
% 22.21/6.21 | From (512) and (1535) follows:
% 22.21/6.21 | (1571) sum(n11, n14) = all_0_4_4
% 22.21/6.21 |
% 22.21/6.21 | From (512) and (1533) follows:
% 22.21/6.21 | (1572) sum(n11, n13) = all_0_2_2
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (89) with n11, n14, all_0_4_4, n9 and discharging atoms sum(n11, n14) = all_0_4_4, sum(n11, n14) = n9, yields:
% 22.21/6.21 | (550) all_0_4_4 = n9
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (89) with n11, n13, all_0_2_2, n8 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n8, yields:
% 22.21/6.21 | (549) all_0_2_2 = n8
% 22.21/6.21 |
% 22.21/6.21 | From (549) and (187) follows:
% 22.21/6.21 | (551) pred(n8) = all_0_1_1
% 22.21/6.21 |
% 22.21/6.21 | From (550) and (396) follows:
% 22.21/6.21 | (552) pred(n9) = all_0_3_3
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (37) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 22.21/6.21 | (553) all_0_3_3 = n8
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (37) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 22.21/6.21 | (554) all_0_1_1 = n7
% 22.21/6.21 |
% 22.21/6.21 | From (553) and (261) follows:
% 22.21/6.21 | (555) sum(n8, all_0_0_0) = all_0_6_6
% 22.21/6.21 |
% 22.21/6.21 | From (554) and (739) follows:
% 22.21/6.21 | (1580) sum(n13, n7) = all_0_0_0
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (89) with n13, n7, all_0_0_0, n4 and discharging atoms sum(n13, n7) = all_0_0_0, sum(n13, n7) = n4, yields:
% 22.21/6.21 | (591) all_0_0_0 = n4
% 22.21/6.21 |
% 22.21/6.21 | From (591) and (555) follows:
% 22.21/6.21 | (1582) sum(n8, n4) = all_0_6_6
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (89) with n8, n4, all_0_6_6, n12 and discharging atoms sum(n8, n4) = all_0_6_6, sum(n8, n4) = n12, yields:
% 22.21/6.21 | (576) all_0_6_6 = n12
% 22.21/6.21 |
% 22.21/6.21 | Equations (576) can reduce 42 to:
% 22.21/6.21 | (458) $false
% 22.21/6.21 |
% 22.21/6.21 |-The branch is then unsatisfiable
% 22.21/6.21 |-Branch two:
% 22.21/6.21 | (527) ~ (all_0_8_8 = n11)
% 22.21/6.21 | (528) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.21/6.21 |
% 22.21/6.21 +-Applying beta-rule and splitting (528), into two cases.
% 22.21/6.21 |-Branch one:
% 22.21/6.21 | (529) all_0_8_8 = n10
% 22.21/6.21 |
% 22.21/6.21 | From (529) and (1535) follows:
% 22.21/6.21 | (1588) sum(n10, n14) = all_0_4_4
% 22.21/6.21 |
% 22.21/6.21 | From (529) and (1533) follows:
% 22.21/6.21 | (1589) sum(n10, n13) = all_0_2_2
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (89) with n10, n14, all_0_4_4, n8 and discharging atoms sum(n10, n14) = all_0_4_4, sum(n10, n14) = n8, yields:
% 22.21/6.21 | (567) all_0_4_4 = n8
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (89) with n10, n13, all_0_2_2, n7 and discharging atoms sum(n10, n13) = all_0_2_2, sum(n10, n13) = n7, yields:
% 22.21/6.21 | (566) all_0_2_2 = n7
% 22.21/6.21 |
% 22.21/6.21 | From (566) and (187) follows:
% 22.21/6.21 | (568) pred(n7) = all_0_1_1
% 22.21/6.21 |
% 22.21/6.21 | From (567) and (396) follows:
% 22.21/6.21 | (569) pred(n8) = all_0_3_3
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (37) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 22.21/6.21 | (570) all_0_3_3 = n7
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (37) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 22.21/6.21 | (571) all_0_1_1 = n6
% 22.21/6.21 |
% 22.21/6.21 | From (570) and (261) follows:
% 22.21/6.21 | (572) sum(n7, all_0_0_0) = all_0_6_6
% 22.21/6.21 |
% 22.21/6.21 | From (571) and (739) follows:
% 22.21/6.21 | (1597) sum(n13, n6) = all_0_0_0
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (89) with n13, n6, all_0_0_0, n3 and discharging atoms sum(n13, n6) = all_0_0_0, sum(n13, n6) = n3, yields:
% 22.21/6.21 | (608) all_0_0_0 = n3
% 22.21/6.21 |
% 22.21/6.21 | From (608) and (572) follows:
% 22.21/6.21 | (1599) sum(n7, n3) = all_0_6_6
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (89) with n7, n3, all_0_6_6, n10 and discharging atoms sum(n7, n3) = all_0_6_6, sum(n7, n3) = n10, yields:
% 22.21/6.21 | (457) all_0_6_6 = n10
% 22.21/6.21 |
% 22.21/6.21 | Equations (457) can reduce 169 to:
% 22.21/6.21 | (458) $false
% 22.21/6.21 |
% 22.21/6.21 |-The branch is then unsatisfiable
% 22.21/6.21 |-Branch two:
% 22.21/6.21 | (544) ~ (all_0_8_8 = n10)
% 22.21/6.21 | (545) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.21/6.21 |
% 22.21/6.21 +-Applying beta-rule and splitting (545), into two cases.
% 22.21/6.21 |-Branch one:
% 22.21/6.21 | (546) all_0_8_8 = n9
% 22.21/6.21 |
% 22.21/6.21 | From (546) and (1535) follows:
% 22.21/6.21 | (1605) sum(n9, n14) = all_0_4_4
% 22.21/6.21 |
% 22.21/6.21 | From (546) and (1533) follows:
% 22.21/6.21 | (1606) sum(n9, n13) = all_0_2_2
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (89) with n9, n14, all_0_4_4, n7 and discharging atoms sum(n9, n14) = all_0_4_4, sum(n9, n14) = n7, yields:
% 22.21/6.21 | (584) all_0_4_4 = n7
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (89) with n9, n13, all_0_2_2, n6 and discharging atoms sum(n9, n13) = all_0_2_2, sum(n9, n13) = n6, yields:
% 22.21/6.21 | (583) all_0_2_2 = n6
% 22.21/6.21 |
% 22.21/6.21 | From (583) and (187) follows:
% 22.21/6.21 | (585) pred(n6) = all_0_1_1
% 22.21/6.21 |
% 22.21/6.21 | From (584) and (396) follows:
% 22.21/6.21 | (586) pred(n7) = all_0_3_3
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (37) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 22.21/6.21 | (587) all_0_3_3 = n6
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (37) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 22.21/6.21 | (588) all_0_1_1 = n5
% 22.21/6.21 |
% 22.21/6.21 | From (587) and (261) follows:
% 22.21/6.21 | (589) sum(n6, all_0_0_0) = all_0_6_6
% 22.21/6.21 |
% 22.21/6.21 | From (588) and (739) follows:
% 22.21/6.21 | (1614) sum(n13, n5) = all_0_0_0
% 22.21/6.21 |
% 22.21/6.21 | Instantiating formula (89) with n13, n5, all_0_0_0, n2 and discharging atoms sum(n13, n5) = all_0_0_0, sum(n13, n5) = n2, yields:
% 22.21/6.22 | (625) all_0_0_0 = n2
% 22.21/6.22 |
% 22.21/6.22 | From (625) and (589) follows:
% 22.21/6.22 | (1616) sum(n6, n2) = all_0_6_6
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n6, n2, all_0_6_6, n8 and discharging atoms sum(n6, n2) = all_0_6_6, sum(n6, n2) = n8, yields:
% 22.21/6.22 | (474) all_0_6_6 = n8
% 22.21/6.22 |
% 22.21/6.22 | Equations (474) can reduce 86 to:
% 22.21/6.22 | (458) $false
% 22.21/6.22 |
% 22.21/6.22 |-The branch is then unsatisfiable
% 22.21/6.22 |-Branch two:
% 22.21/6.22 | (561) ~ (all_0_8_8 = n9)
% 22.21/6.22 | (562) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.21/6.22 |
% 22.21/6.22 +-Applying beta-rule and splitting (562), into two cases.
% 22.21/6.22 |-Branch one:
% 22.21/6.22 | (563) all_0_8_8 = n8
% 22.21/6.22 |
% 22.21/6.22 | From (563) and (1535) follows:
% 22.21/6.22 | (1622) sum(n8, n14) = all_0_4_4
% 22.21/6.22 |
% 22.21/6.22 | From (563) and (1533) follows:
% 22.21/6.22 | (1623) sum(n8, n13) = all_0_2_2
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n8, n14, all_0_4_4, n6 and discharging atoms sum(n8, n14) = all_0_4_4, sum(n8, n14) = n6, yields:
% 22.21/6.22 | (601) all_0_4_4 = n6
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n8, n13, all_0_2_2, n5 and discharging atoms sum(n8, n13) = all_0_2_2, sum(n8, n13) = n5, yields:
% 22.21/6.22 | (600) all_0_2_2 = n5
% 22.21/6.22 |
% 22.21/6.22 | From (600) and (187) follows:
% 22.21/6.22 | (602) pred(n5) = all_0_1_1
% 22.21/6.22 |
% 22.21/6.22 | From (601) and (396) follows:
% 22.21/6.22 | (603) pred(n6) = all_0_3_3
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (37) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 22.21/6.22 | (604) all_0_3_3 = n5
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (37) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 22.21/6.22 | (605) all_0_1_1 = n4
% 22.21/6.22 |
% 22.21/6.22 | From (604) and (261) follows:
% 22.21/6.22 | (606) sum(n5, all_0_0_0) = all_0_6_6
% 22.21/6.22 |
% 22.21/6.22 | From (605) and (739) follows:
% 22.21/6.22 | (1631) sum(n13, n4) = all_0_0_0
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n13, n4, all_0_0_0, n1 and discharging atoms sum(n13, n4) = all_0_0_0, sum(n13, n4) = n1, yields:
% 22.21/6.22 | (642) all_0_0_0 = n1
% 22.21/6.22 |
% 22.21/6.22 | From (642) and (606) follows:
% 22.21/6.22 | (1633) sum(n5, n1) = all_0_6_6
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n5, n1, all_0_6_6, n6 and discharging atoms sum(n5, n1) = all_0_6_6, sum(n5, n1) = n6, yields:
% 22.21/6.22 | (491) all_0_6_6 = n6
% 22.21/6.22 |
% 22.21/6.22 | Equations (491) can reduce 418 to:
% 22.21/6.22 | (458) $false
% 22.21/6.22 |
% 22.21/6.22 |-The branch is then unsatisfiable
% 22.21/6.22 |-Branch two:
% 22.21/6.22 | (578) ~ (all_0_8_8 = n8)
% 22.21/6.22 | (579) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.21/6.22 |
% 22.21/6.22 +-Applying beta-rule and splitting (579), into two cases.
% 22.21/6.22 |-Branch one:
% 22.21/6.22 | (580) all_0_8_8 = n7
% 22.21/6.22 |
% 22.21/6.22 | From (580) and (1535) follows:
% 22.21/6.22 | (1639) sum(n7, n14) = all_0_4_4
% 22.21/6.22 |
% 22.21/6.22 | From (580) and (1533) follows:
% 22.21/6.22 | (1640) sum(n7, n13) = all_0_2_2
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n7, n14, all_0_4_4, n5 and discharging atoms sum(n7, n14) = all_0_4_4, sum(n7, n14) = n5, yields:
% 22.21/6.22 | (618) all_0_4_4 = n5
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n7, n13, all_0_2_2, n4 and discharging atoms sum(n7, n13) = all_0_2_2, sum(n7, n13) = n4, yields:
% 22.21/6.22 | (617) all_0_2_2 = n4
% 22.21/6.22 |
% 22.21/6.22 | From (617) and (187) follows:
% 22.21/6.22 | (619) pred(n4) = all_0_1_1
% 22.21/6.22 |
% 22.21/6.22 | From (618) and (396) follows:
% 22.21/6.22 | (620) pred(n5) = all_0_3_3
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (37) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 22.21/6.22 | (621) all_0_3_3 = n4
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (37) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 22.21/6.22 | (622) all_0_1_1 = n3
% 22.21/6.22 |
% 22.21/6.22 | From (621) and (261) follows:
% 22.21/6.22 | (623) sum(n4, all_0_0_0) = all_0_6_6
% 22.21/6.22 |
% 22.21/6.22 | From (622) and (739) follows:
% 22.21/6.22 | (1648) sum(n13, n3) = all_0_0_0
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n13, n3, all_0_0_0, n0 and discharging atoms sum(n13, n3) = all_0_0_0, sum(n13, n3) = n0, yields:
% 22.21/6.22 | (659) all_0_0_0 = n0
% 22.21/6.22 |
% 22.21/6.22 | From (659) and (623) follows:
% 22.21/6.22 | (1650) sum(n4, n0) = all_0_6_6
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n4, n0, all_0_6_6, n4 and discharging atoms sum(n4, n0) = all_0_6_6, sum(n4, n0) = n4, yields:
% 22.21/6.22 | (508) all_0_6_6 = n4
% 22.21/6.22 |
% 22.21/6.22 | Equations (508) can reduce 12 to:
% 22.21/6.22 | (458) $false
% 22.21/6.22 |
% 22.21/6.22 |-The branch is then unsatisfiable
% 22.21/6.22 |-Branch two:
% 22.21/6.22 | (595) ~ (all_0_8_8 = n7)
% 22.21/6.22 | (596) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.21/6.22 |
% 22.21/6.22 +-Applying beta-rule and splitting (596), into two cases.
% 22.21/6.22 |-Branch one:
% 22.21/6.22 | (597) all_0_8_8 = n6
% 22.21/6.22 |
% 22.21/6.22 | From (597) and (1535) follows:
% 22.21/6.22 | (1656) sum(n6, n14) = all_0_4_4
% 22.21/6.22 |
% 22.21/6.22 | From (597) and (1533) follows:
% 22.21/6.22 | (1657) sum(n6, n13) = all_0_2_2
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n6, n14, all_0_4_4, n4 and discharging atoms sum(n6, n14) = all_0_4_4, sum(n6, n14) = n4, yields:
% 22.21/6.22 | (635) all_0_4_4 = n4
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n6, n13, all_0_2_2, n3 and discharging atoms sum(n6, n13) = all_0_2_2, sum(n6, n13) = n3, yields:
% 22.21/6.22 | (634) all_0_2_2 = n3
% 22.21/6.22 |
% 22.21/6.22 | From (634) and (187) follows:
% 22.21/6.22 | (636) pred(n3) = all_0_1_1
% 22.21/6.22 |
% 22.21/6.22 | From (635) and (396) follows:
% 22.21/6.22 | (637) pred(n4) = all_0_3_3
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (37) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 22.21/6.22 | (638) all_0_3_3 = n3
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (37) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 22.21/6.22 | (639) all_0_1_1 = n2
% 22.21/6.22 |
% 22.21/6.22 | From (638) and (261) follows:
% 22.21/6.22 | (640) sum(n3, all_0_0_0) = all_0_6_6
% 22.21/6.22 |
% 22.21/6.22 | From (639) and (739) follows:
% 22.21/6.22 | (1665) sum(n13, n2) = all_0_0_0
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n13, n2, all_0_0_0, n15 and discharging atoms sum(n13, n2) = all_0_0_0, sum(n13, n2) = n15, yields:
% 22.21/6.22 | (676) all_0_0_0 = n15
% 22.21/6.22 |
% 22.21/6.22 | From (676) and (640) follows:
% 22.21/6.22 | (1667) sum(n3, n15) = all_0_6_6
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n3, n15, all_0_6_6, n2 and discharging atoms sum(n3, n15) = all_0_6_6, sum(n3, n15) = n2, yields:
% 22.21/6.22 | (525) all_0_6_6 = n2
% 22.21/6.22 |
% 22.21/6.22 | Equations (525) can reduce 231 to:
% 22.21/6.22 | (458) $false
% 22.21/6.22 |
% 22.21/6.22 |-The branch is then unsatisfiable
% 22.21/6.22 |-Branch two:
% 22.21/6.22 | (612) ~ (all_0_8_8 = n6)
% 22.21/6.22 | (613) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.21/6.22 |
% 22.21/6.22 +-Applying beta-rule and splitting (613), into two cases.
% 22.21/6.22 |-Branch one:
% 22.21/6.22 | (614) all_0_8_8 = n5
% 22.21/6.22 |
% 22.21/6.22 | From (614) and (1535) follows:
% 22.21/6.22 | (1673) sum(n5, n14) = all_0_4_4
% 22.21/6.22 |
% 22.21/6.22 | From (614) and (1533) follows:
% 22.21/6.22 | (1674) sum(n5, n13) = all_0_2_2
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n5, n14, all_0_4_4, n3 and discharging atoms sum(n5, n14) = all_0_4_4, sum(n5, n14) = n3, yields:
% 22.21/6.22 | (652) all_0_4_4 = n3
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n5, n13, all_0_2_2, n2 and discharging atoms sum(n5, n13) = all_0_2_2, sum(n5, n13) = n2, yields:
% 22.21/6.22 | (651) all_0_2_2 = n2
% 22.21/6.22 |
% 22.21/6.22 | From (651) and (187) follows:
% 22.21/6.22 | (653) pred(n2) = all_0_1_1
% 22.21/6.22 |
% 22.21/6.22 | From (652) and (396) follows:
% 22.21/6.22 | (654) pred(n3) = all_0_3_3
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (37) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 22.21/6.22 | (655) all_0_3_3 = n2
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (37) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 22.21/6.22 | (656) all_0_1_1 = n1
% 22.21/6.22 |
% 22.21/6.22 | From (655) and (261) follows:
% 22.21/6.22 | (657) sum(n2, all_0_0_0) = all_0_6_6
% 22.21/6.22 |
% 22.21/6.22 | From (656) and (739) follows:
% 22.21/6.22 | (1682) sum(n13, n1) = all_0_0_0
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n13, n1, all_0_0_0, n14 and discharging atoms sum(n13, n1) = all_0_0_0, sum(n13, n1) = n14, yields:
% 22.21/6.22 | (693) all_0_0_0 = n14
% 22.21/6.22 |
% 22.21/6.22 | From (693) and (657) follows:
% 22.21/6.22 | (1684) sum(n2, n14) = all_0_6_6
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n2, n14, all_0_6_6, n0 and discharging atoms sum(n2, n14) = all_0_6_6, sum(n2, n14) = n0, yields:
% 22.21/6.22 | (542) all_0_6_6 = n0
% 22.21/6.22 |
% 22.21/6.22 | Equations (542) can reduce 400 to:
% 22.21/6.22 | (458) $false
% 22.21/6.22 |
% 22.21/6.22 |-The branch is then unsatisfiable
% 22.21/6.22 |-Branch two:
% 22.21/6.22 | (629) ~ (all_0_8_8 = n5)
% 22.21/6.22 | (630) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.21/6.22 |
% 22.21/6.22 +-Applying beta-rule and splitting (630), into two cases.
% 22.21/6.22 |-Branch one:
% 22.21/6.22 | (631) all_0_8_8 = n4
% 22.21/6.22 |
% 22.21/6.22 | From (631) and (1535) follows:
% 22.21/6.22 | (1690) sum(n4, n14) = all_0_4_4
% 22.21/6.22 |
% 22.21/6.22 | From (631) and (1533) follows:
% 22.21/6.22 | (1691) sum(n4, n13) = all_0_2_2
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n4, n14, all_0_4_4, n2 and discharging atoms sum(n4, n14) = all_0_4_4, sum(n4, n14) = n2, yields:
% 22.21/6.22 | (669) all_0_4_4 = n2
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (89) with n4, n13, all_0_2_2, n1 and discharging atoms sum(n4, n13) = all_0_2_2, sum(n4, n13) = n1, yields:
% 22.21/6.22 | (668) all_0_2_2 = n1
% 22.21/6.22 |
% 22.21/6.22 | From (668) and (187) follows:
% 22.21/6.22 | (670) pred(n1) = all_0_1_1
% 22.21/6.22 |
% 22.21/6.22 | From (669) and (396) follows:
% 22.21/6.22 | (671) pred(n2) = all_0_3_3
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (37) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 22.21/6.22 | (672) all_0_3_3 = n1
% 22.21/6.22 |
% 22.21/6.22 | Instantiating formula (37) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 22.21/6.23 | (673) all_0_1_1 = n0
% 22.21/6.23 |
% 22.21/6.23 | From (672) and (261) follows:
% 22.21/6.23 | (674) sum(n1, all_0_0_0) = all_0_6_6
% 22.21/6.23 |
% 22.21/6.23 | From (673) and (739) follows:
% 22.21/6.23 | (1699) sum(n13, n0) = all_0_0_0
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n13, n0, all_0_0_0, n13 and discharging atoms sum(n13, n0) = all_0_0_0, sum(n13, n0) = n13, yields:
% 22.21/6.23 | (709) all_0_0_0 = n13
% 22.21/6.23 |
% 22.21/6.23 | From (709) and (674) follows:
% 22.21/6.23 | (1701) sum(n1, n13) = all_0_6_6
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n1, n13, all_0_6_6, n14 and discharging atoms sum(n1, n13) = all_0_6_6, sum(n1, n13) = n14, yields:
% 22.21/6.23 | (559) all_0_6_6 = n14
% 22.21/6.23 |
% 22.21/6.23 | Equations (559) can reduce 314 to:
% 22.21/6.23 | (458) $false
% 22.21/6.23 |
% 22.21/6.23 |-The branch is then unsatisfiable
% 22.21/6.23 |-Branch two:
% 22.21/6.23 | (646) ~ (all_0_8_8 = n4)
% 22.21/6.23 | (647) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.21/6.23 |
% 22.21/6.23 +-Applying beta-rule and splitting (647), into two cases.
% 22.21/6.23 |-Branch one:
% 22.21/6.23 | (648) all_0_8_8 = n3
% 22.21/6.23 |
% 22.21/6.23 | From (648) and (1535) follows:
% 22.21/6.23 | (1707) sum(n3, n14) = all_0_4_4
% 22.21/6.23 |
% 22.21/6.23 | From (648) and (1533) follows:
% 22.21/6.23 | (1708) sum(n3, n13) = all_0_2_2
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n3, n14, all_0_4_4, n1 and discharging atoms sum(n3, n14) = all_0_4_4, sum(n3, n14) = n1, yields:
% 22.21/6.23 | (686) all_0_4_4 = n1
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n3, n13, all_0_2_2, n0 and discharging atoms sum(n3, n13) = all_0_2_2, sum(n3, n13) = n0, yields:
% 22.21/6.23 | (685) all_0_2_2 = n0
% 22.21/6.23 |
% 22.21/6.23 | From (685) and (187) follows:
% 22.21/6.23 | (687) pred(n0) = all_0_1_1
% 22.21/6.23 |
% 22.21/6.23 | From (686) and (396) follows:
% 22.21/6.23 | (688) pred(n1) = all_0_3_3
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (37) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 22.21/6.23 | (689) all_0_3_3 = n0
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (37) with n0, all_0_1_1, n15 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n15, yields:
% 22.21/6.23 | (690) all_0_1_1 = n15
% 22.21/6.23 |
% 22.21/6.23 | From (689) and (261) follows:
% 22.21/6.23 | (691) sum(n0, all_0_0_0) = all_0_6_6
% 22.21/6.23 |
% 22.21/6.23 | From (690) and (739) follows:
% 22.21/6.23 | (1716) sum(n13, n15) = all_0_0_0
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n13, n15, all_0_0_0, n12 and discharging atoms sum(n13, n15) = all_0_0_0, sum(n13, n15) = n12, yields:
% 22.21/6.23 | (455) all_0_0_0 = n12
% 22.21/6.23 |
% 22.21/6.23 | From (455) and (691) follows:
% 22.21/6.23 | (1718) sum(n0, n12) = all_0_6_6
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n0, n12, all_0_6_6, n12 and discharging atoms sum(n0, n12) = all_0_6_6, sum(n0, n12) = n12, yields:
% 22.21/6.23 | (576) all_0_6_6 = n12
% 22.21/6.23 |
% 22.21/6.23 | Equations (576) can reduce 42 to:
% 22.21/6.23 | (458) $false
% 22.21/6.23 |
% 22.21/6.23 |-The branch is then unsatisfiable
% 22.21/6.23 |-Branch two:
% 22.21/6.23 | (663) ~ (all_0_8_8 = n3)
% 22.21/6.23 | (664) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.21/6.23 |
% 22.21/6.23 +-Applying beta-rule and splitting (664), into two cases.
% 22.21/6.23 |-Branch one:
% 22.21/6.23 | (665) all_0_8_8 = n2
% 22.21/6.23 |
% 22.21/6.23 | From (665) and (1535) follows:
% 22.21/6.23 | (1724) sum(n2, n14) = all_0_4_4
% 22.21/6.23 |
% 22.21/6.23 | From (665) and (1533) follows:
% 22.21/6.23 | (1725) sum(n2, n13) = all_0_2_2
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n2, n14, all_0_4_4, n0 and discharging atoms sum(n2, n14) = all_0_4_4, sum(n2, n14) = n0, yields:
% 22.21/6.23 | (702) all_0_4_4 = n0
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n2, n13, all_0_2_2, n15 and discharging atoms sum(n2, n13) = all_0_2_2, sum(n2, n13) = n15, yields:
% 22.21/6.23 | (701) all_0_2_2 = n15
% 22.21/6.23 |
% 22.21/6.23 | From (701) and (187) follows:
% 22.21/6.23 | (703) pred(n15) = all_0_1_1
% 22.21/6.23 |
% 22.21/6.23 | From (702) and (396) follows:
% 22.21/6.23 | (704) pred(n0) = all_0_3_3
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (37) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 22.21/6.23 | (705) all_0_1_1 = n14
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (37) with n0, all_0_3_3, n15 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n15, yields:
% 22.21/6.23 | (706) all_0_3_3 = n15
% 22.21/6.23 |
% 22.21/6.23 | From (706) and (261) follows:
% 22.21/6.23 | (707) sum(n15, all_0_0_0) = all_0_6_6
% 22.21/6.23 |
% 22.21/6.23 | From (705) and (739) follows:
% 22.21/6.23 | (1733) sum(n13, n14) = all_0_0_0
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n13, n14, all_0_0_0, n11 and discharging atoms sum(n13, n14) = all_0_0_0, sum(n13, n14) = n11, yields:
% 22.21/6.23 | (472) all_0_0_0 = n11
% 22.21/6.23 |
% 22.21/6.23 | From (472) and (707) follows:
% 22.21/6.23 | (1735) sum(n15, n11) = all_0_6_6
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n15, n11, all_0_6_6, n10 and discharging atoms sum(n15, n11) = all_0_6_6, sum(n15, n11) = n10, yields:
% 22.21/6.23 | (457) all_0_6_6 = n10
% 22.21/6.23 |
% 22.21/6.23 | Equations (457) can reduce 169 to:
% 22.21/6.23 | (458) $false
% 22.21/6.23 |
% 22.21/6.23 |-The branch is then unsatisfiable
% 22.21/6.23 |-Branch two:
% 22.21/6.23 | (680) ~ (all_0_8_8 = n2)
% 22.21/6.23 | (681) all_0_8_8 = n1 | all_0_8_8 = n0
% 22.21/6.23 |
% 22.21/6.23 +-Applying beta-rule and splitting (681), into two cases.
% 22.21/6.23 |-Branch one:
% 22.21/6.23 | (682) all_0_8_8 = n1
% 22.21/6.23 |
% 22.21/6.23 | From (682) and (1535) follows:
% 22.21/6.23 | (1741) sum(n1, n14) = all_0_4_4
% 22.21/6.23 |
% 22.21/6.23 | From (682) and (1533) follows:
% 22.21/6.23 | (1742) sum(n1, n13) = all_0_2_2
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n1, n14, all_0_4_4, n15 and discharging atoms sum(n1, n14) = all_0_4_4, sum(n1, n14) = n15, yields:
% 22.21/6.23 | (448) all_0_4_4 = n15
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n1, n13, all_0_2_2, n14 and discharging atoms sum(n1, n13) = all_0_2_2, sum(n1, n13) = n14, yields:
% 22.21/6.23 | (447) all_0_2_2 = n14
% 22.21/6.23 |
% 22.21/6.23 | From (447) and (187) follows:
% 22.21/6.23 | (449) pred(n14) = all_0_1_1
% 22.21/6.23 |
% 22.21/6.23 | From (448) and (396) follows:
% 22.21/6.23 | (450) pred(n15) = all_0_3_3
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (37) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 22.21/6.23 | (451) all_0_3_3 = n14
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (37) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 22.21/6.23 | (452) all_0_1_1 = n13
% 22.21/6.23 |
% 22.21/6.23 | From (451) and (261) follows:
% 22.21/6.23 | (453) sum(n14, all_0_0_0) = all_0_6_6
% 22.21/6.23 |
% 22.21/6.23 | From (452) and (739) follows:
% 22.21/6.23 | (1750) sum(n13, n13) = all_0_0_0
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n13, n13, all_0_0_0, n10 and discharging atoms sum(n13, n13) = all_0_0_0, sum(n13, n13) = n10, yields:
% 22.21/6.23 | (489) all_0_0_0 = n10
% 22.21/6.23 |
% 22.21/6.23 | From (489) and (453) follows:
% 22.21/6.23 | (1752) sum(n14, n10) = all_0_6_6
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n14, n10, all_0_6_6, n8 and discharging atoms sum(n14, n10) = all_0_6_6, sum(n14, n10) = n8, yields:
% 22.21/6.23 | (474) all_0_6_6 = n8
% 22.21/6.23 |
% 22.21/6.23 | Equations (474) can reduce 86 to:
% 22.21/6.23 | (458) $false
% 22.21/6.23 |
% 22.21/6.23 |-The branch is then unsatisfiable
% 22.21/6.23 |-Branch two:
% 22.21/6.23 | (697) ~ (all_0_8_8 = n1)
% 22.21/6.23 | (698) all_0_8_8 = n0
% 22.21/6.23 |
% 22.21/6.23 | From (698) and (1535) follows:
% 22.21/6.23 | (1757) sum(n0, n14) = all_0_4_4
% 22.21/6.23 |
% 22.21/6.23 | From (698) and (1533) follows:
% 22.21/6.23 | (1758) sum(n0, n13) = all_0_2_2
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n0, n14, all_0_4_4, n14 and discharging atoms sum(n0, n14) = all_0_4_4, sum(n0, n14) = n14, yields:
% 22.21/6.23 | (465) all_0_4_4 = n14
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n0, n13, all_0_2_2, n13 and discharging atoms sum(n0, n13) = all_0_2_2, sum(n0, n13) = n13, yields:
% 22.21/6.23 | (464) all_0_2_2 = n13
% 22.21/6.23 |
% 22.21/6.23 | From (464) and (187) follows:
% 22.21/6.23 | (466) pred(n13) = all_0_1_1
% 22.21/6.23 |
% 22.21/6.23 | From (465) and (396) follows:
% 22.21/6.23 | (467) pred(n14) = all_0_3_3
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (37) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 22.21/6.23 | (468) all_0_3_3 = n13
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (37) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 22.21/6.23 | (469) all_0_1_1 = n12
% 22.21/6.23 |
% 22.21/6.23 | From (468) and (261) follows:
% 22.21/6.23 | (470) sum(n13, all_0_0_0) = all_0_6_6
% 22.21/6.23 |
% 22.21/6.23 | From (469) and (739) follows:
% 22.21/6.23 | (1766) sum(n13, n12) = all_0_0_0
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n13, n12, all_0_0_0, n9 and discharging atoms sum(n13, n12) = all_0_0_0, sum(n13, n12) = n9, yields:
% 22.21/6.23 | (506) all_0_0_0 = n9
% 22.21/6.23 |
% 22.21/6.23 | From (506) and (470) follows:
% 22.21/6.23 | (1768) sum(n13, n9) = all_0_6_6
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n13, n9, all_0_6_6, n6 and discharging atoms sum(n13, n9) = all_0_6_6, sum(n13, n9) = n6, yields:
% 22.21/6.23 | (491) all_0_6_6 = n6
% 22.21/6.23 |
% 22.21/6.23 | Equations (491) can reduce 418 to:
% 22.21/6.23 | (458) $false
% 22.21/6.23 |
% 22.21/6.23 |-The branch is then unsatisfiable
% 22.21/6.23 |-Branch two:
% 22.21/6.23 | (754) ~ (all_0_7_7 = n13)
% 22.21/6.23 | (755) all_0_7_7 = n12 | all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.21/6.23 |
% 22.21/6.23 +-Applying beta-rule and splitting (477), into two cases.
% 22.21/6.23 |-Branch one:
% 22.21/6.23 | (478) all_0_8_8 = n13
% 22.21/6.23 |
% 22.21/6.23 | From (478) and (64) follows:
% 22.21/6.23 | (1774) sum(n13, all_0_5_5) = all_0_4_4
% 22.21/6.23 |
% 22.21/6.23 | From (478) and (160) follows:
% 22.21/6.23 | (1775) sum(n13, all_0_7_7) = all_0_2_2
% 22.21/6.23 |
% 22.21/6.23 +-Applying beta-rule and splitting (755), into two cases.
% 22.21/6.23 |-Branch one:
% 22.21/6.23 | (756) all_0_7_7 = n12
% 22.21/6.23 |
% 22.21/6.23 | From (756) and (176) follows:
% 22.21/6.23 | (757) succ(n12) = all_0_5_5
% 22.21/6.23 |
% 22.21/6.23 | From (756) and (59) follows:
% 22.21/6.23 | (758) sum(n12, all_0_1_1) = all_0_0_0
% 22.21/6.23 |
% 22.21/6.23 | From (756) and (1775) follows:
% 22.21/6.23 | (1779) sum(n13, n12) = all_0_2_2
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (219) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 22.21/6.23 | (760) all_0_5_5 = n13
% 22.21/6.23 |
% 22.21/6.23 | Instantiating formula (89) with n13, n12, all_0_2_2, n9 and discharging atoms sum(n13, n12) = all_0_2_2, sum(n13, n12) = n9, yields:
% 22.21/6.24 | (532) all_0_2_2 = n9
% 22.21/6.24 |
% 22.21/6.24 | From (532) and (187) follows:
% 22.21/6.24 | (534) pred(n9) = all_0_1_1
% 22.21/6.24 |
% 22.21/6.24 | From (760) and (1774) follows:
% 22.21/6.24 | (1783) sum(n13, n13) = all_0_4_4
% 22.21/6.24 |
% 22.21/6.24 | Instantiating formula (37) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 22.21/6.24 | (537) all_0_1_1 = n8
% 22.21/6.24 |
% 22.21/6.24 | Instantiating formula (89) with n13, n13, all_0_4_4, n10 and discharging atoms sum(n13, n13) = all_0_4_4, sum(n13, n13) = n10, yields:
% 22.21/6.24 | (533) all_0_4_4 = n10
% 22.21/6.24 |
% 22.21/6.24 | From (533) and (396) follows:
% 22.21/6.24 | (535) pred(n10) = all_0_3_3
% 22.21/6.24 |
% 22.21/6.24 | From (537) and (758) follows:
% 22.21/6.24 | (1787) sum(n12, n8) = all_0_0_0
% 22.21/6.24 |
% 22.21/6.24 | Instantiating formula (37) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 22.21/6.24 | (536) all_0_3_3 = n9
% 22.21/6.24 |
% 22.21/6.24 | Instantiating formula (89) with n12, n8, all_0_0_0, n4 and discharging atoms sum(n12, n8) = all_0_0_0, sum(n12, n8) = n4, yields:
% 22.21/6.24 | (591) all_0_0_0 = n4
% 22.21/6.24 |
% 22.21/6.24 | From (536)(591) and (261) follows:
% 22.21/6.24 | (1790) sum(n9, n4) = all_0_6_6
% 22.21/6.24 |
% 22.21/6.24 | Instantiating formula (89) with n9, n4, all_0_6_6, n13 and discharging atoms sum(n9, n4) = all_0_6_6, sum(n9, n4) = n13, yields:
% 22.21/6.24 | (998) all_0_6_6 = n13
% 22.21/6.24 |
% 22.21/6.24 | Equations (998) can reduce 130 to:
% 22.21/6.24 | (458) $false
% 22.21/6.24 |
% 22.21/6.24 |-The branch is then unsatisfiable
% 22.21/6.24 |-Branch two:
% 22.21/6.24 | (773) ~ (all_0_7_7 = n12)
% 22.21/6.24 | (774) all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.21/6.24 |
% 22.21/6.24 +-Applying beta-rule and splitting (774), into two cases.
% 22.21/6.24 |-Branch one:
% 22.21/6.24 | (775) all_0_7_7 = n11
% 22.21/6.24 |
% 22.21/6.24 | From (775) and (176) follows:
% 22.21/6.24 | (776) succ(n11) = all_0_5_5
% 22.21/6.24 |
% 22.21/6.24 | From (775) and (59) follows:
% 22.21/6.24 | (777) sum(n11, all_0_1_1) = all_0_0_0
% 22.21/6.24 |
% 22.21/6.24 | From (775) and (1775) follows:
% 22.21/6.24 | (1798) sum(n13, n11) = all_0_2_2
% 22.21/6.24 |
% 22.21/6.24 | Instantiating formula (219) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 22.21/6.24 | (779) all_0_5_5 = n12
% 22.21/6.24 |
% 22.21/6.24 | Instantiating formula (89) with n13, n11, all_0_2_2, n8 and discharging atoms sum(n13, n11) = all_0_2_2, sum(n13, n11) = n8, yields:
% 22.21/6.24 | (549) all_0_2_2 = n8
% 22.21/6.24 |
% 22.21/6.24 | From (549) and (187) follows:
% 22.21/6.24 | (551) pred(n8) = all_0_1_1
% 22.21/6.24 |
% 22.21/6.24 | From (779) and (1774) follows:
% 22.21/6.24 | (1802) sum(n13, n12) = all_0_4_4
% 22.21/6.24 |
% 22.21/6.24 | Instantiating formula (37) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 22.21/6.24 | (554) all_0_1_1 = n7
% 22.21/6.24 |
% 22.21/6.24 | Instantiating formula (89) with n13, n12, all_0_4_4, n9 and discharging atoms sum(n13, n12) = all_0_4_4, sum(n13, n12) = n9, yields:
% 22.21/6.24 | (550) all_0_4_4 = n9
% 22.21/6.24 |
% 22.21/6.24 | From (550) and (396) follows:
% 22.21/6.24 | (552) pred(n9) = all_0_3_3
% 22.21/6.24 |
% 22.21/6.24 | From (554) and (777) follows:
% 22.35/6.24 | (1806) sum(n11, n7) = all_0_0_0
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (37) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 22.35/6.24 | (553) all_0_3_3 = n8
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (89) with n11, n7, all_0_0_0, n2 and discharging atoms sum(n11, n7) = all_0_0_0, sum(n11, n7) = n2, yields:
% 22.35/6.24 | (625) all_0_0_0 = n2
% 22.35/6.24 |
% 22.35/6.24 | From (553)(625) and (261) follows:
% 22.35/6.24 | (1809) sum(n8, n2) = all_0_6_6
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (89) with n8, n2, all_0_6_6, n10 and discharging atoms sum(n8, n2) = all_0_6_6, sum(n8, n2) = n10, yields:
% 22.35/6.24 | (457) all_0_6_6 = n10
% 22.35/6.24 |
% 22.35/6.24 | Equations (457) can reduce 169 to:
% 22.35/6.24 | (458) $false
% 22.35/6.24 |
% 22.35/6.24 |-The branch is then unsatisfiable
% 22.35/6.24 |-Branch two:
% 22.35/6.24 | (792) ~ (all_0_7_7 = n11)
% 22.35/6.24 | (793) all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.35/6.24 |
% 22.35/6.24 +-Applying beta-rule and splitting (793), into two cases.
% 22.35/6.24 |-Branch one:
% 22.35/6.24 | (794) all_0_7_7 = n10
% 22.35/6.24 |
% 22.35/6.24 | From (794) and (176) follows:
% 22.35/6.24 | (795) succ(n10) = all_0_5_5
% 22.35/6.24 |
% 22.35/6.24 | From (794) and (59) follows:
% 22.35/6.24 | (796) sum(n10, all_0_1_1) = all_0_0_0
% 22.35/6.24 |
% 22.35/6.24 | From (794) and (1775) follows:
% 22.35/6.24 | (1817) sum(n13, n10) = all_0_2_2
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (219) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 22.35/6.24 | (798) all_0_5_5 = n11
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (89) with n13, n10, all_0_2_2, n7 and discharging atoms sum(n13, n10) = all_0_2_2, sum(n13, n10) = n7, yields:
% 22.35/6.24 | (566) all_0_2_2 = n7
% 22.35/6.24 |
% 22.35/6.24 | From (566) and (187) follows:
% 22.35/6.24 | (568) pred(n7) = all_0_1_1
% 22.35/6.24 |
% 22.35/6.24 | From (798) and (1774) follows:
% 22.35/6.24 | (1821) sum(n13, n11) = all_0_4_4
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (37) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 22.35/6.24 | (571) all_0_1_1 = n6
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (89) with n13, n11, all_0_4_4, n8 and discharging atoms sum(n13, n11) = all_0_4_4, sum(n13, n11) = n8, yields:
% 22.35/6.24 | (567) all_0_4_4 = n8
% 22.35/6.24 |
% 22.35/6.24 | From (567) and (396) follows:
% 22.35/6.24 | (569) pred(n8) = all_0_3_3
% 22.35/6.24 |
% 22.35/6.24 | From (571) and (796) follows:
% 22.35/6.24 | (1825) sum(n10, n6) = all_0_0_0
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (37) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 22.35/6.24 | (570) all_0_3_3 = n7
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (89) with n10, n6, all_0_0_0, n0 and discharging atoms sum(n10, n6) = all_0_0_0, sum(n10, n6) = n0, yields:
% 22.35/6.24 | (659) all_0_0_0 = n0
% 22.35/6.24 |
% 22.35/6.24 | From (570)(659) and (261) follows:
% 22.35/6.24 | (1828) sum(n7, n0) = all_0_6_6
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (89) with n7, n0, all_0_6_6, n7 and discharging atoms sum(n7, n0) = all_0_6_6, sum(n7, n0) = n7, yields:
% 22.35/6.24 | (733) all_0_6_6 = n7
% 22.35/6.24 |
% 22.35/6.24 | Equations (733) can reduce 274 to:
% 22.35/6.24 | (458) $false
% 22.35/6.24 |
% 22.35/6.24 |-The branch is then unsatisfiable
% 22.35/6.24 |-Branch two:
% 22.35/6.24 | (811) ~ (all_0_7_7 = n10)
% 22.35/6.24 | (812) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.35/6.24 |
% 22.35/6.24 +-Applying beta-rule and splitting (812), into two cases.
% 22.35/6.24 |-Branch one:
% 22.35/6.24 | (813) all_0_7_7 = n9
% 22.35/6.24 |
% 22.35/6.24 | From (813) and (176) follows:
% 22.35/6.24 | (814) succ(n9) = all_0_5_5
% 22.35/6.24 |
% 22.35/6.24 | From (813) and (59) follows:
% 22.35/6.24 | (815) sum(n9, all_0_1_1) = all_0_0_0
% 22.35/6.24 |
% 22.35/6.24 | From (813) and (1775) follows:
% 22.35/6.24 | (1836) sum(n13, n9) = all_0_2_2
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (219) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 22.35/6.24 | (817) all_0_5_5 = n10
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (89) with n13, n9, all_0_2_2, n6 and discharging atoms sum(n13, n9) = all_0_2_2, sum(n13, n9) = n6, yields:
% 22.35/6.24 | (583) all_0_2_2 = n6
% 22.35/6.24 |
% 22.35/6.24 | From (583) and (187) follows:
% 22.35/6.24 | (585) pred(n6) = all_0_1_1
% 22.35/6.24 |
% 22.35/6.24 | From (817) and (1774) follows:
% 22.35/6.24 | (1840) sum(n13, n10) = all_0_4_4
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (37) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 22.35/6.24 | (588) all_0_1_1 = n5
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (89) with n13, n10, all_0_4_4, n7 and discharging atoms sum(n13, n10) = all_0_4_4, sum(n13, n10) = n7, yields:
% 22.35/6.24 | (584) all_0_4_4 = n7
% 22.35/6.24 |
% 22.35/6.24 | From (584) and (396) follows:
% 22.35/6.24 | (586) pred(n7) = all_0_3_3
% 22.35/6.24 |
% 22.35/6.24 | From (588) and (815) follows:
% 22.35/6.24 | (1844) sum(n9, n5) = all_0_0_0
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (37) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 22.35/6.24 | (587) all_0_3_3 = n6
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (89) with n9, n5, all_0_0_0, n14 and discharging atoms sum(n9, n5) = all_0_0_0, sum(n9, n5) = n14, yields:
% 22.35/6.24 | (693) all_0_0_0 = n14
% 22.35/6.24 |
% 22.35/6.24 | From (587)(693) and (261) follows:
% 22.35/6.24 | (1847) sum(n6, n14) = all_0_6_6
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (89) with n6, n14, all_0_6_6, n4 and discharging atoms sum(n6, n14) = all_0_6_6, sum(n6, n14) = n4, yields:
% 22.35/6.24 | (508) all_0_6_6 = n4
% 22.35/6.24 |
% 22.35/6.24 | Equations (508) can reduce 12 to:
% 22.35/6.24 | (458) $false
% 22.35/6.24 |
% 22.35/6.24 |-The branch is then unsatisfiable
% 22.35/6.24 |-Branch two:
% 22.35/6.24 | (830) ~ (all_0_7_7 = n9)
% 22.35/6.24 | (831) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.35/6.24 |
% 22.35/6.24 +-Applying beta-rule and splitting (831), into two cases.
% 22.35/6.24 |-Branch one:
% 22.35/6.24 | (832) all_0_7_7 = n8
% 22.35/6.24 |
% 22.35/6.24 | From (832) and (176) follows:
% 22.35/6.24 | (833) succ(n8) = all_0_5_5
% 22.35/6.24 |
% 22.35/6.24 | From (832) and (59) follows:
% 22.35/6.24 | (834) sum(n8, all_0_1_1) = all_0_0_0
% 22.35/6.24 |
% 22.35/6.24 | From (832) and (1775) follows:
% 22.35/6.24 | (1855) sum(n13, n8) = all_0_2_2
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (219) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 22.35/6.24 | (836) all_0_5_5 = n9
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (89) with n13, n8, all_0_2_2, n5 and discharging atoms sum(n13, n8) = all_0_2_2, sum(n13, n8) = n5, yields:
% 22.35/6.24 | (600) all_0_2_2 = n5
% 22.35/6.24 |
% 22.35/6.24 | From (600) and (187) follows:
% 22.35/6.24 | (602) pred(n5) = all_0_1_1
% 22.35/6.24 |
% 22.35/6.24 | From (836) and (1774) follows:
% 22.35/6.24 | (1859) sum(n13, n9) = all_0_4_4
% 22.35/6.24 |
% 22.35/6.24 | Instantiating formula (37) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 22.35/6.25 | (605) all_0_1_1 = n4
% 22.35/6.25 |
% 22.35/6.25 | Instantiating formula (89) with n13, n9, all_0_4_4, n6 and discharging atoms sum(n13, n9) = all_0_4_4, sum(n13, n9) = n6, yields:
% 22.35/6.25 | (601) all_0_4_4 = n6
% 22.35/6.25 |
% 22.35/6.25 | From (601) and (396) follows:
% 22.35/6.25 | (603) pred(n6) = all_0_3_3
% 22.35/6.25 |
% 22.35/6.25 | From (605) and (834) follows:
% 22.35/6.25 | (1863) sum(n8, n4) = all_0_0_0
% 22.35/6.25 |
% 22.35/6.25 | Instantiating formula (37) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 22.35/6.25 | (604) all_0_3_3 = n5
% 22.35/6.25 |
% 22.35/6.25 | Instantiating formula (89) with n8, n4, all_0_0_0, n12 and discharging atoms sum(n8, n4) = all_0_0_0, sum(n8, n4) = n12, yields:
% 22.35/6.25 | (455) all_0_0_0 = n12
% 22.35/6.25 |
% 22.35/6.25 | From (604)(455) and (261) follows:
% 22.35/6.25 | (1866) sum(n5, n12) = all_0_6_6
% 22.35/6.25 |
% 22.35/6.25 | Instantiating formula (89) with n5, n12, all_0_6_6, n1 and discharging atoms sum(n5, n12) = all_0_6_6, sum(n5, n12) = n1, yields:
% 22.35/6.25 | (771) all_0_6_6 = n1
% 22.35/6.25 |
% 22.35/6.25 | Equations (771) can reduce 38 to:
% 22.35/6.25 | (458) $false
% 22.35/6.25 |
% 22.35/6.25 |-The branch is then unsatisfiable
% 22.35/6.25 |-Branch two:
% 22.35/6.25 | (849) ~ (all_0_7_7 = n8)
% 22.35/6.25 | (850) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.35/6.25 |
% 22.35/6.25 +-Applying beta-rule and splitting (850), into two cases.
% 22.35/6.25 |-Branch one:
% 22.35/6.25 | (851) all_0_7_7 = n7
% 22.35/6.25 |
% 22.35/6.25 | From (851) and (176) follows:
% 22.35/6.25 | (852) succ(n7) = all_0_5_5
% 22.35/6.25 |
% 22.35/6.25 | From (851) and (59) follows:
% 22.35/6.25 | (853) sum(n7, all_0_1_1) = all_0_0_0
% 22.35/6.25 |
% 22.35/6.25 | From (851) and (1775) follows:
% 22.35/6.25 | (1874) sum(n13, n7) = all_0_2_2
% 22.35/6.25 |
% 22.35/6.25 | Instantiating formula (219) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 22.35/6.25 | (855) all_0_5_5 = n8
% 22.35/6.25 |
% 22.35/6.25 | Instantiating formula (89) with n13, n7, all_0_2_2, n4 and discharging atoms sum(n13, n7) = all_0_2_2, sum(n13, n7) = n4, yields:
% 22.35/6.25 | (617) all_0_2_2 = n4
% 22.35/6.25 |
% 22.35/6.25 | From (617) and (187) follows:
% 22.35/6.25 | (619) pred(n4) = all_0_1_1
% 22.35/6.25 |
% 22.35/6.25 | From (855) and (1774) follows:
% 22.35/6.25 | (1878) sum(n13, n8) = all_0_4_4
% 22.35/6.25 |
% 22.35/6.25 | Instantiating formula (37) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 22.35/6.25 | (622) all_0_1_1 = n3
% 22.35/6.25 |
% 22.35/6.25 | Instantiating formula (89) with n13, n8, all_0_4_4, n5 and discharging atoms sum(n13, n8) = all_0_4_4, sum(n13, n8) = n5, yields:
% 22.35/6.25 | (618) all_0_4_4 = n5
% 22.35/6.25 |
% 22.35/6.25 | From (618) and (396) follows:
% 22.35/6.25 | (620) pred(n5) = all_0_3_3
% 22.35/6.25 |
% 22.35/6.25 | From (622) and (853) follows:
% 22.35/6.25 | (1882) sum(n7, n3) = all_0_0_0
% 22.35/6.25 |
% 22.35/6.25 | Instantiating formula (37) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 22.35/6.25 | (621) all_0_3_3 = n4
% 22.35/6.25 |
% 22.35/6.25 | Instantiating formula (89) with n7, n3, all_0_0_0, n10 and discharging atoms sum(n7, n3) = all_0_0_0, sum(n7, n3) = n10, yields:
% 22.35/6.25 | (489) all_0_0_0 = n10
% 22.35/6.25 |
% 22.35/6.25 | From (621)(489) and (261) follows:
% 22.39/6.25 | (1885) sum(n4, n10) = all_0_6_6
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (89) with n4, n10, all_0_6_6, n14 and discharging atoms sum(n4, n10) = all_0_6_6, sum(n4, n10) = n14, yields:
% 22.39/6.25 | (559) all_0_6_6 = n14
% 22.39/6.25 |
% 22.39/6.25 | Equations (559) can reduce 314 to:
% 22.39/6.25 | (458) $false
% 22.39/6.25 |
% 22.39/6.25 |-The branch is then unsatisfiable
% 22.39/6.25 |-Branch two:
% 22.39/6.25 | (868) ~ (all_0_7_7 = n7)
% 22.39/6.25 | (869) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.39/6.25 |
% 22.39/6.25 +-Applying beta-rule and splitting (869), into two cases.
% 22.39/6.25 |-Branch one:
% 22.39/6.25 | (870) all_0_7_7 = n6
% 22.39/6.25 |
% 22.39/6.25 | From (870) and (176) follows:
% 22.39/6.25 | (871) succ(n6) = all_0_5_5
% 22.39/6.25 |
% 22.39/6.25 | From (870) and (59) follows:
% 22.39/6.25 | (872) sum(n6, all_0_1_1) = all_0_0_0
% 22.39/6.25 |
% 22.39/6.25 | From (870) and (1775) follows:
% 22.39/6.25 | (1893) sum(n13, n6) = all_0_2_2
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (219) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 22.39/6.25 | (874) all_0_5_5 = n7
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (89) with n13, n6, all_0_2_2, n3 and discharging atoms sum(n13, n6) = all_0_2_2, sum(n13, n6) = n3, yields:
% 22.39/6.25 | (634) all_0_2_2 = n3
% 22.39/6.25 |
% 22.39/6.25 | From (634) and (187) follows:
% 22.39/6.25 | (636) pred(n3) = all_0_1_1
% 22.39/6.25 |
% 22.39/6.25 | From (874) and (1774) follows:
% 22.39/6.25 | (1897) sum(n13, n7) = all_0_4_4
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (37) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 22.39/6.25 | (639) all_0_1_1 = n2
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (89) with n13, n7, all_0_4_4, n4 and discharging atoms sum(n13, n7) = all_0_4_4, sum(n13, n7) = n4, yields:
% 22.39/6.25 | (635) all_0_4_4 = n4
% 22.39/6.25 |
% 22.39/6.25 | From (635) and (396) follows:
% 22.39/6.25 | (637) pred(n4) = all_0_3_3
% 22.39/6.25 |
% 22.39/6.25 | From (639) and (872) follows:
% 22.39/6.25 | (1901) sum(n6, n2) = all_0_0_0
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (37) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 22.39/6.25 | (638) all_0_3_3 = n3
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (89) with n6, n2, all_0_0_0, n8 and discharging atoms sum(n6, n2) = all_0_0_0, sum(n6, n2) = n8, yields:
% 22.39/6.25 | (523) all_0_0_0 = n8
% 22.39/6.25 |
% 22.39/6.25 | From (638)(523) and (261) follows:
% 22.39/6.25 | (1904) sum(n3, n8) = all_0_6_6
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (89) with n3, n8, all_0_6_6, n11 and discharging atoms sum(n3, n8) = all_0_6_6, sum(n3, n8) = n11, yields:
% 22.39/6.25 | (809) all_0_6_6 = n11
% 22.39/6.25 |
% 22.39/6.25 | Equations (809) can reduce 70 to:
% 22.39/6.25 | (458) $false
% 22.39/6.25 |
% 22.39/6.25 |-The branch is then unsatisfiable
% 22.39/6.25 |-Branch two:
% 22.39/6.25 | (887) ~ (all_0_7_7 = n6)
% 22.39/6.25 | (888) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.39/6.25 |
% 22.39/6.25 +-Applying beta-rule and splitting (888), into two cases.
% 22.39/6.25 |-Branch one:
% 22.39/6.25 | (889) all_0_7_7 = n5
% 22.39/6.25 |
% 22.39/6.25 | From (889) and (176) follows:
% 22.39/6.25 | (890) succ(n5) = all_0_5_5
% 22.39/6.25 |
% 22.39/6.25 | From (889) and (59) follows:
% 22.39/6.25 | (891) sum(n5, all_0_1_1) = all_0_0_0
% 22.39/6.25 |
% 22.39/6.25 | From (889) and (1775) follows:
% 22.39/6.25 | (1912) sum(n13, n5) = all_0_2_2
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (219) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 22.39/6.25 | (893) all_0_5_5 = n6
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (89) with n13, n5, all_0_2_2, n2 and discharging atoms sum(n13, n5) = all_0_2_2, sum(n13, n5) = n2, yields:
% 22.39/6.25 | (651) all_0_2_2 = n2
% 22.39/6.25 |
% 22.39/6.25 | From (651) and (187) follows:
% 22.39/6.25 | (653) pred(n2) = all_0_1_1
% 22.39/6.25 |
% 22.39/6.25 | From (893) and (1774) follows:
% 22.39/6.25 | (1916) sum(n13, n6) = all_0_4_4
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (37) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 22.39/6.25 | (656) all_0_1_1 = n1
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (89) with n13, n6, all_0_4_4, n3 and discharging atoms sum(n13, n6) = all_0_4_4, sum(n13, n6) = n3, yields:
% 22.39/6.25 | (652) all_0_4_4 = n3
% 22.39/6.25 |
% 22.39/6.25 | From (652) and (396) follows:
% 22.39/6.25 | (654) pred(n3) = all_0_3_3
% 22.39/6.25 |
% 22.39/6.25 | From (656) and (891) follows:
% 22.39/6.25 | (1920) sum(n5, n1) = all_0_0_0
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (37) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 22.39/6.25 | (655) all_0_3_3 = n2
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (89) with n5, n1, all_0_0_0, n6 and discharging atoms sum(n5, n1) = all_0_0_0, sum(n5, n1) = n6, yields:
% 22.39/6.25 | (557) all_0_0_0 = n6
% 22.39/6.25 |
% 22.39/6.25 | From (655)(557) and (261) follows:
% 22.39/6.25 | (1923) sum(n2, n6) = all_0_6_6
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (89) with n2, n6, all_0_6_6, n8 and discharging atoms sum(n2, n6) = all_0_6_6, sum(n2, n6) = n8, yields:
% 22.39/6.25 | (474) all_0_6_6 = n8
% 22.39/6.25 |
% 22.39/6.25 | Equations (474) can reduce 86 to:
% 22.39/6.25 | (458) $false
% 22.39/6.25 |
% 22.39/6.25 |-The branch is then unsatisfiable
% 22.39/6.25 |-Branch two:
% 22.39/6.25 | (906) ~ (all_0_7_7 = n5)
% 22.39/6.25 | (907) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.39/6.25 |
% 22.39/6.25 +-Applying beta-rule and splitting (907), into two cases.
% 22.39/6.25 |-Branch one:
% 22.39/6.25 | (908) all_0_7_7 = n4
% 22.39/6.25 |
% 22.39/6.25 | From (908) and (176) follows:
% 22.39/6.25 | (909) succ(n4) = all_0_5_5
% 22.39/6.25 |
% 22.39/6.25 | From (908) and (59) follows:
% 22.39/6.25 | (910) sum(n4, all_0_1_1) = all_0_0_0
% 22.39/6.25 |
% 22.39/6.25 | From (908) and (1775) follows:
% 22.39/6.25 | (1931) sum(n13, n4) = all_0_2_2
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (219) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 22.39/6.25 | (912) all_0_5_5 = n5
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (89) with n13, n4, all_0_2_2, n1 and discharging atoms sum(n13, n4) = all_0_2_2, sum(n13, n4) = n1, yields:
% 22.39/6.25 | (668) all_0_2_2 = n1
% 22.39/6.25 |
% 22.39/6.25 | From (668) and (187) follows:
% 22.39/6.25 | (670) pred(n1) = all_0_1_1
% 22.39/6.25 |
% 22.39/6.25 | From (912) and (1774) follows:
% 22.39/6.25 | (1935) sum(n13, n5) = all_0_4_4
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (37) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 22.39/6.25 | (673) all_0_1_1 = n0
% 22.39/6.25 |
% 22.39/6.25 | Instantiating formula (89) with n13, n5, all_0_4_4, n2 and discharging atoms sum(n13, n5) = all_0_4_4, sum(n13, n5) = n2, yields:
% 22.39/6.25 | (669) all_0_4_4 = n2
% 22.39/6.25 |
% 22.39/6.25 | From (669) and (396) follows:
% 22.39/6.25 | (671) pred(n2) = all_0_3_3
% 22.39/6.25 |
% 22.39/6.25 | From (673) and (910) follows:
% 22.39/6.26 | (1939) sum(n4, n0) = all_0_0_0
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (37) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 22.39/6.26 | (672) all_0_3_3 = n1
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n4, n0, all_0_0_0, n4 and discharging atoms sum(n4, n0) = all_0_0_0, sum(n4, n0) = n4, yields:
% 22.39/6.26 | (591) all_0_0_0 = n4
% 22.39/6.26 |
% 22.39/6.26 | From (672)(591) and (261) follows:
% 22.39/6.26 | (1942) sum(n1, n4) = all_0_6_6
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n1, n4, all_0_6_6, n5 and discharging atoms sum(n1, n4) = all_0_6_6, sum(n1, n4) = n5, yields:
% 22.39/6.26 | (847) all_0_6_6 = n5
% 22.39/6.26 |
% 22.39/6.26 | Equations (847) can reduce 409 to:
% 22.39/6.26 | (458) $false
% 22.39/6.26 |
% 22.39/6.26 |-The branch is then unsatisfiable
% 22.39/6.26 |-Branch two:
% 22.39/6.26 | (925) ~ (all_0_7_7 = n4)
% 22.39/6.26 | (926) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.39/6.26 |
% 22.39/6.26 +-Applying beta-rule and splitting (926), into two cases.
% 22.39/6.26 |-Branch one:
% 22.39/6.26 | (927) all_0_7_7 = n3
% 22.39/6.26 |
% 22.39/6.26 | From (927) and (176) follows:
% 22.39/6.26 | (928) succ(n3) = all_0_5_5
% 22.39/6.26 |
% 22.39/6.26 | From (927) and (59) follows:
% 22.39/6.26 | (929) sum(n3, all_0_1_1) = all_0_0_0
% 22.39/6.26 |
% 22.39/6.26 | From (927) and (1775) follows:
% 22.39/6.26 | (1950) sum(n13, n3) = all_0_2_2
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (219) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 22.39/6.26 | (931) all_0_5_5 = n4
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n13, n3, all_0_2_2, n0 and discharging atoms sum(n13, n3) = all_0_2_2, sum(n13, n3) = n0, yields:
% 22.39/6.26 | (685) all_0_2_2 = n0
% 22.39/6.26 |
% 22.39/6.26 | From (685) and (187) follows:
% 22.39/6.26 | (687) pred(n0) = all_0_1_1
% 22.39/6.26 |
% 22.39/6.26 | From (931) and (1774) follows:
% 22.39/6.26 | (1954) sum(n13, n4) = all_0_4_4
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (37) with n0, all_0_1_1, n15 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n15, yields:
% 22.39/6.26 | (690) all_0_1_1 = n15
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n13, n4, all_0_4_4, n1 and discharging atoms sum(n13, n4) = all_0_4_4, sum(n13, n4) = n1, yields:
% 22.39/6.26 | (686) all_0_4_4 = n1
% 22.39/6.26 |
% 22.39/6.26 | From (686) and (396) follows:
% 22.39/6.26 | (688) pred(n1) = all_0_3_3
% 22.39/6.26 |
% 22.39/6.26 | From (690) and (929) follows:
% 22.39/6.26 | (1958) sum(n3, n15) = all_0_0_0
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (37) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 22.39/6.26 | (689) all_0_3_3 = n0
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n3, n15, all_0_0_0, n2 and discharging atoms sum(n3, n15) = all_0_0_0, sum(n3, n15) = n2, yields:
% 22.39/6.26 | (625) all_0_0_0 = n2
% 22.39/6.26 |
% 22.39/6.26 | From (689)(625) and (261) follows:
% 22.39/6.26 | (1961) sum(n0, n2) = all_0_6_6
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n0, n2, all_0_6_6, n2 and discharging atoms sum(n0, n2) = all_0_6_6, sum(n0, n2) = n2, yields:
% 22.39/6.26 | (525) all_0_6_6 = n2
% 22.39/6.26 |
% 22.39/6.26 | Equations (525) can reduce 231 to:
% 22.39/6.26 | (458) $false
% 22.39/6.26 |
% 22.39/6.26 |-The branch is then unsatisfiable
% 22.39/6.26 |-Branch two:
% 22.39/6.26 | (944) ~ (all_0_7_7 = n3)
% 22.39/6.26 | (945) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.39/6.26 |
% 22.39/6.26 +-Applying beta-rule and splitting (945), into two cases.
% 22.39/6.26 |-Branch one:
% 22.39/6.26 | (946) all_0_7_7 = n2
% 22.39/6.26 |
% 22.39/6.26 | From (946) and (176) follows:
% 22.39/6.26 | (947) succ(n2) = all_0_5_5
% 22.39/6.26 |
% 22.39/6.26 | From (946) and (59) follows:
% 22.39/6.26 | (948) sum(n2, all_0_1_1) = all_0_0_0
% 22.39/6.26 |
% 22.39/6.26 | From (946) and (1775) follows:
% 22.39/6.26 | (1969) sum(n13, n2) = all_0_2_2
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (219) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 22.39/6.26 | (950) all_0_5_5 = n3
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n13, n2, all_0_2_2, n15 and discharging atoms sum(n13, n2) = all_0_2_2, sum(n13, n2) = n15, yields:
% 22.39/6.26 | (701) all_0_2_2 = n15
% 22.39/6.26 |
% 22.39/6.26 | From (701) and (187) follows:
% 22.39/6.26 | (703) pred(n15) = all_0_1_1
% 22.39/6.26 |
% 22.39/6.26 | From (950) and (1774) follows:
% 22.39/6.26 | (1973) sum(n13, n3) = all_0_4_4
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (37) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 22.39/6.26 | (705) all_0_1_1 = n14
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n13, n3, all_0_4_4, n0 and discharging atoms sum(n13, n3) = all_0_4_4, sum(n13, n3) = n0, yields:
% 22.39/6.26 | (702) all_0_4_4 = n0
% 22.39/6.26 |
% 22.39/6.26 | From (702) and (396) follows:
% 22.39/6.26 | (704) pred(n0) = all_0_3_3
% 22.39/6.26 |
% 22.39/6.26 | From (705) and (948) follows:
% 22.39/6.26 | (1977) sum(n2, n14) = all_0_0_0
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (37) with n0, all_0_3_3, n15 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n15, yields:
% 22.39/6.26 | (706) all_0_3_3 = n15
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n2, n14, all_0_0_0, n0 and discharging atoms sum(n2, n14) = all_0_0_0, sum(n2, n14) = n0, yields:
% 22.39/6.26 | (659) all_0_0_0 = n0
% 22.39/6.26 |
% 22.39/6.26 | From (706)(659) and (261) follows:
% 22.39/6.26 | (1980) sum(n15, n0) = all_0_6_6
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n15, n0, all_0_6_6, n15 and discharging atoms sum(n15, n0) = all_0_6_6, sum(n15, n0) = n15, yields:
% 22.39/6.26 | (885) all_0_6_6 = n15
% 22.39/6.26 |
% 22.39/6.26 | Equations (885) can reduce 225 to:
% 22.39/6.26 | (458) $false
% 22.39/6.26 |
% 22.39/6.26 |-The branch is then unsatisfiable
% 22.39/6.26 |-Branch two:
% 22.39/6.26 | (963) ~ (all_0_7_7 = n2)
% 22.39/6.26 | (964) all_0_7_7 = n1 | all_0_7_7 = n0
% 22.39/6.26 |
% 22.39/6.26 +-Applying beta-rule and splitting (964), into two cases.
% 22.39/6.26 |-Branch one:
% 22.39/6.26 | (965) all_0_7_7 = n1
% 22.39/6.26 |
% 22.39/6.26 | From (965) and (176) follows:
% 22.39/6.26 | (966) succ(n1) = all_0_5_5
% 22.39/6.26 |
% 22.39/6.26 | From (965) and (59) follows:
% 22.39/6.26 | (967) sum(n1, all_0_1_1) = all_0_0_0
% 22.39/6.26 |
% 22.39/6.26 | From (965) and (1775) follows:
% 22.39/6.26 | (1988) sum(n13, n1) = all_0_2_2
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (219) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 22.39/6.26 | (969) all_0_5_5 = n2
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n13, n1, all_0_2_2, n14 and discharging atoms sum(n13, n1) = all_0_2_2, sum(n13, n1) = n14, yields:
% 22.39/6.26 | (447) all_0_2_2 = n14
% 22.39/6.26 |
% 22.39/6.26 | From (447) and (187) follows:
% 22.39/6.26 | (449) pred(n14) = all_0_1_1
% 22.39/6.26 |
% 22.39/6.26 | From (969) and (1774) follows:
% 22.39/6.26 | (1992) sum(n13, n2) = all_0_4_4
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (37) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 22.39/6.26 | (452) all_0_1_1 = n13
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n13, n2, all_0_4_4, n15 and discharging atoms sum(n13, n2) = all_0_4_4, sum(n13, n2) = n15, yields:
% 22.39/6.26 | (448) all_0_4_4 = n15
% 22.39/6.26 |
% 22.39/6.26 | From (448) and (396) follows:
% 22.39/6.26 | (450) pred(n15) = all_0_3_3
% 22.39/6.26 |
% 22.39/6.26 | From (452) and (967) follows:
% 22.39/6.26 | (1996) sum(n1, n13) = all_0_0_0
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (37) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 22.39/6.26 | (451) all_0_3_3 = n14
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n1, n13, all_0_0_0, n14 and discharging atoms sum(n1, n13) = all_0_0_0, sum(n1, n13) = n14, yields:
% 22.39/6.26 | (693) all_0_0_0 = n14
% 22.39/6.26 |
% 22.39/6.26 | From (451)(693) and (261) follows:
% 22.39/6.26 | (1999) sum(n14, n14) = all_0_6_6
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n14, n14, all_0_6_6, n12 and discharging atoms sum(n14, n14) = all_0_6_6, sum(n14, n14) = n12, yields:
% 22.39/6.26 | (576) all_0_6_6 = n12
% 22.39/6.26 |
% 22.39/6.26 | Equations (576) can reduce 42 to:
% 22.39/6.26 | (458) $false
% 22.39/6.26 |
% 22.39/6.26 |-The branch is then unsatisfiable
% 22.39/6.26 |-Branch two:
% 22.39/6.26 | (982) ~ (all_0_7_7 = n1)
% 22.39/6.26 | (983) all_0_7_7 = n0
% 22.39/6.26 |
% 22.39/6.26 | From (983) and (176) follows:
% 22.39/6.26 | (984) succ(n0) = all_0_5_5
% 22.39/6.26 |
% 22.39/6.26 | From (983) and (59) follows:
% 22.39/6.26 | (985) sum(n0, all_0_1_1) = all_0_0_0
% 22.39/6.26 |
% 22.39/6.26 | From (983) and (1775) follows:
% 22.39/6.26 | (2006) sum(n13, n0) = all_0_2_2
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (219) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 22.39/6.26 | (987) all_0_5_5 = n1
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n13, n0, all_0_2_2, n13 and discharging atoms sum(n13, n0) = all_0_2_2, sum(n13, n0) = n13, yields:
% 22.39/6.26 | (464) all_0_2_2 = n13
% 22.39/6.26 |
% 22.39/6.26 | From (464) and (187) follows:
% 22.39/6.26 | (466) pred(n13) = all_0_1_1
% 22.39/6.26 |
% 22.39/6.26 | From (987) and (1774) follows:
% 22.39/6.26 | (2010) sum(n13, n1) = all_0_4_4
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (37) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 22.39/6.26 | (469) all_0_1_1 = n12
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n13, n1, all_0_4_4, n14 and discharging atoms sum(n13, n1) = all_0_4_4, sum(n13, n1) = n14, yields:
% 22.39/6.26 | (465) all_0_4_4 = n14
% 22.39/6.26 |
% 22.39/6.26 | From (465) and (396) follows:
% 22.39/6.26 | (467) pred(n14) = all_0_3_3
% 22.39/6.26 |
% 22.39/6.26 | From (469) and (985) follows:
% 22.39/6.26 | (2014) sum(n0, n12) = all_0_0_0
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (37) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 22.39/6.26 | (468) all_0_3_3 = n13
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n0, n12, all_0_0_0, n12 and discharging atoms sum(n0, n12) = all_0_0_0, sum(n0, n12) = n12, yields:
% 22.39/6.26 | (455) all_0_0_0 = n12
% 22.39/6.26 |
% 22.39/6.26 | From (468)(455) and (261) follows:
% 22.39/6.26 | (2017) sum(n13, n12) = all_0_6_6
% 22.39/6.26 |
% 22.39/6.26 | Instantiating formula (89) with n13, n12, all_0_6_6, n9 and discharging atoms sum(n13, n12) = all_0_6_6, sum(n13, n12) = n9, yields:
% 22.39/6.27 | (923) all_0_6_6 = n9
% 22.39/6.27 |
% 22.39/6.27 | Equations (923) can reduce 404 to:
% 22.39/6.27 | (458) $false
% 22.39/6.27 |
% 22.39/6.27 |-The branch is then unsatisfiable
% 22.39/6.27 |-Branch two:
% 22.39/6.27 | (493) ~ (all_0_8_8 = n13)
% 22.39/6.27 | (494) all_0_8_8 = n12 | all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.39/6.27 |
% 22.39/6.27 +-Applying beta-rule and splitting (755), into two cases.
% 22.39/6.27 |-Branch one:
% 22.39/6.27 | (756) all_0_7_7 = n12
% 22.39/6.27 |
% 22.39/6.27 | From (756) and (176) follows:
% 22.39/6.27 | (757) succ(n12) = all_0_5_5
% 22.39/6.27 |
% 22.39/6.27 | From (756) and (59) follows:
% 22.39/6.27 | (758) sum(n12, all_0_1_1) = all_0_0_0
% 22.39/6.27 |
% 22.39/6.27 | From (756) and (160) follows:
% 22.39/6.27 | (2025) sum(all_0_8_8, n12) = all_0_2_2
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (219) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 22.39/6.27 | (760) all_0_5_5 = n13
% 22.39/6.27 |
% 22.39/6.27 | From (760) and (64) follows:
% 22.39/6.27 | (2027) sum(all_0_8_8, n13) = all_0_4_4
% 22.39/6.27 |
% 22.39/6.27 +-Applying beta-rule and splitting (494), into two cases.
% 22.39/6.27 |-Branch one:
% 22.39/6.27 | (495) all_0_8_8 = n12
% 22.39/6.27 |
% 22.39/6.27 | From (495) and (2027) follows:
% 22.39/6.27 | (2029) sum(n12, n13) = all_0_4_4
% 22.39/6.27 |
% 22.39/6.27 | From (495) and (2025) follows:
% 22.39/6.27 | (2030) sum(n12, n12) = all_0_2_2
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n12, n13, all_0_4_4, n9 and discharging atoms sum(n12, n13) = all_0_4_4, sum(n12, n13) = n9, yields:
% 22.39/6.27 | (550) all_0_4_4 = n9
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n12, n12, all_0_2_2, n8 and discharging atoms sum(n12, n12) = all_0_2_2, sum(n12, n12) = n8, yields:
% 22.39/6.27 | (549) all_0_2_2 = n8
% 22.39/6.27 |
% 22.39/6.27 | From (549) and (187) follows:
% 22.39/6.27 | (551) pred(n8) = all_0_1_1
% 22.39/6.27 |
% 22.39/6.27 | From (550) and (396) follows:
% 22.39/6.27 | (552) pred(n9) = all_0_3_3
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (37) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 22.39/6.27 | (553) all_0_3_3 = n8
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (37) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 22.39/6.27 | (554) all_0_1_1 = n7
% 22.39/6.27 |
% 22.39/6.27 | From (553) and (261) follows:
% 22.39/6.27 | (555) sum(n8, all_0_0_0) = all_0_6_6
% 22.39/6.27 |
% 22.39/6.27 | From (554) and (758) follows:
% 22.39/6.27 | (2038) sum(n12, n7) = all_0_0_0
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n12, n7, all_0_0_0, n3 and discharging atoms sum(n12, n7) = all_0_0_0, sum(n12, n7) = n3, yields:
% 22.39/6.27 | (608) all_0_0_0 = n3
% 22.39/6.27 |
% 22.39/6.27 | From (608) and (555) follows:
% 22.39/6.27 | (2040) sum(n8, n3) = all_0_6_6
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n8, n3, all_0_6_6, n11 and discharging atoms sum(n8, n3) = all_0_6_6, sum(n8, n3) = n11, yields:
% 22.39/6.27 | (809) all_0_6_6 = n11
% 22.39/6.27 |
% 22.39/6.27 | Equations (809) can reduce 70 to:
% 22.39/6.27 | (458) $false
% 22.39/6.27 |
% 22.39/6.27 |-The branch is then unsatisfiable
% 22.39/6.27 |-Branch two:
% 22.39/6.27 | (510) ~ (all_0_8_8 = n12)
% 22.39/6.27 | (511) all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.39/6.27 |
% 22.39/6.27 +-Applying beta-rule and splitting (511), into two cases.
% 22.39/6.27 |-Branch one:
% 22.39/6.27 | (512) all_0_8_8 = n11
% 22.39/6.27 |
% 22.39/6.27 | From (512) and (2027) follows:
% 22.39/6.27 | (2046) sum(n11, n13) = all_0_4_4
% 22.39/6.27 |
% 22.39/6.27 | From (512) and (2025) follows:
% 22.39/6.27 | (2047) sum(n11, n12) = all_0_2_2
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n11, n13, all_0_4_4, n8 and discharging atoms sum(n11, n13) = all_0_4_4, sum(n11, n13) = n8, yields:
% 22.39/6.27 | (567) all_0_4_4 = n8
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n11, n12, all_0_2_2, n7 and discharging atoms sum(n11, n12) = all_0_2_2, sum(n11, n12) = n7, yields:
% 22.39/6.27 | (566) all_0_2_2 = n7
% 22.39/6.27 |
% 22.39/6.27 | From (566) and (187) follows:
% 22.39/6.27 | (568) pred(n7) = all_0_1_1
% 22.39/6.27 |
% 22.39/6.27 | From (567) and (396) follows:
% 22.39/6.27 | (569) pred(n8) = all_0_3_3
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (37) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 22.39/6.27 | (570) all_0_3_3 = n7
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (37) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 22.39/6.27 | (571) all_0_1_1 = n6
% 22.39/6.27 |
% 22.39/6.27 | From (570) and (261) follows:
% 22.39/6.27 | (572) sum(n7, all_0_0_0) = all_0_6_6
% 22.39/6.27 |
% 22.39/6.27 | From (571) and (758) follows:
% 22.39/6.27 | (2055) sum(n12, n6) = all_0_0_0
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n12, n6, all_0_0_0, n2 and discharging atoms sum(n12, n6) = all_0_0_0, sum(n12, n6) = n2, yields:
% 22.39/6.27 | (625) all_0_0_0 = n2
% 22.39/6.27 |
% 22.39/6.27 | From (625) and (572) follows:
% 22.39/6.27 | (2057) sum(n7, n2) = all_0_6_6
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n7, n2, all_0_6_6, n9 and discharging atoms sum(n7, n2) = all_0_6_6, sum(n7, n2) = n9, yields:
% 22.39/6.27 | (923) all_0_6_6 = n9
% 22.39/6.27 |
% 22.39/6.27 | Equations (923) can reduce 404 to:
% 22.39/6.27 | (458) $false
% 22.39/6.27 |
% 22.39/6.27 |-The branch is then unsatisfiable
% 22.39/6.27 |-Branch two:
% 22.39/6.27 | (527) ~ (all_0_8_8 = n11)
% 22.39/6.27 | (528) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.39/6.27 |
% 22.39/6.27 +-Applying beta-rule and splitting (528), into two cases.
% 22.39/6.27 |-Branch one:
% 22.39/6.27 | (529) all_0_8_8 = n10
% 22.39/6.27 |
% 22.39/6.27 | From (529) and (2027) follows:
% 22.39/6.27 | (2063) sum(n10, n13) = all_0_4_4
% 22.39/6.27 |
% 22.39/6.27 | From (529) and (2025) follows:
% 22.39/6.27 | (2064) sum(n10, n12) = all_0_2_2
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n10, n13, all_0_4_4, n7 and discharging atoms sum(n10, n13) = all_0_4_4, sum(n10, n13) = n7, yields:
% 22.39/6.27 | (584) all_0_4_4 = n7
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n10, n12, all_0_2_2, n6 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n6, yields:
% 22.39/6.27 | (583) all_0_2_2 = n6
% 22.39/6.27 |
% 22.39/6.27 | From (583) and (187) follows:
% 22.39/6.27 | (585) pred(n6) = all_0_1_1
% 22.39/6.27 |
% 22.39/6.27 | From (584) and (396) follows:
% 22.39/6.27 | (586) pred(n7) = all_0_3_3
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (37) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 22.39/6.27 | (587) all_0_3_3 = n6
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (37) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 22.39/6.27 | (588) all_0_1_1 = n5
% 22.39/6.27 |
% 22.39/6.27 | From (587) and (261) follows:
% 22.39/6.27 | (589) sum(n6, all_0_0_0) = all_0_6_6
% 22.39/6.27 |
% 22.39/6.27 | From (588) and (758) follows:
% 22.39/6.27 | (2072) sum(n12, n5) = all_0_0_0
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n12, n5, all_0_0_0, n1 and discharging atoms sum(n12, n5) = all_0_0_0, sum(n12, n5) = n1, yields:
% 22.39/6.27 | (642) all_0_0_0 = n1
% 22.39/6.27 |
% 22.39/6.27 | From (642) and (589) follows:
% 22.39/6.27 | (2074) sum(n6, n1) = all_0_6_6
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n6, n1, all_0_6_6, n7 and discharging atoms sum(n6, n1) = all_0_6_6, sum(n6, n1) = n7, yields:
% 22.39/6.27 | (733) all_0_6_6 = n7
% 22.39/6.27 |
% 22.39/6.27 | Equations (733) can reduce 274 to:
% 22.39/6.27 | (458) $false
% 22.39/6.27 |
% 22.39/6.27 |-The branch is then unsatisfiable
% 22.39/6.27 |-Branch two:
% 22.39/6.27 | (544) ~ (all_0_8_8 = n10)
% 22.39/6.27 | (545) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.39/6.27 |
% 22.39/6.27 +-Applying beta-rule and splitting (545), into two cases.
% 22.39/6.27 |-Branch one:
% 22.39/6.27 | (546) all_0_8_8 = n9
% 22.39/6.27 |
% 22.39/6.27 | From (546) and (2027) follows:
% 22.39/6.27 | (2080) sum(n9, n13) = all_0_4_4
% 22.39/6.27 |
% 22.39/6.27 | From (546) and (2025) follows:
% 22.39/6.27 | (2081) sum(n9, n12) = all_0_2_2
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n9, n13, all_0_4_4, n6 and discharging atoms sum(n9, n13) = all_0_4_4, sum(n9, n13) = n6, yields:
% 22.39/6.27 | (601) all_0_4_4 = n6
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n9, n12, all_0_2_2, n5 and discharging atoms sum(n9, n12) = all_0_2_2, sum(n9, n12) = n5, yields:
% 22.39/6.27 | (600) all_0_2_2 = n5
% 22.39/6.27 |
% 22.39/6.27 | From (600) and (187) follows:
% 22.39/6.27 | (602) pred(n5) = all_0_1_1
% 22.39/6.27 |
% 22.39/6.27 | From (601) and (396) follows:
% 22.39/6.27 | (603) pred(n6) = all_0_3_3
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (37) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 22.39/6.27 | (604) all_0_3_3 = n5
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (37) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 22.39/6.27 | (605) all_0_1_1 = n4
% 22.39/6.27 |
% 22.39/6.27 | From (604) and (261) follows:
% 22.39/6.27 | (606) sum(n5, all_0_0_0) = all_0_6_6
% 22.39/6.27 |
% 22.39/6.27 | From (605) and (758) follows:
% 22.39/6.27 | (2089) sum(n12, n4) = all_0_0_0
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n12, n4, all_0_0_0, n0 and discharging atoms sum(n12, n4) = all_0_0_0, sum(n12, n4) = n0, yields:
% 22.39/6.27 | (659) all_0_0_0 = n0
% 22.39/6.27 |
% 22.39/6.27 | From (659) and (606) follows:
% 22.39/6.27 | (2091) sum(n5, n0) = all_0_6_6
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n5, n0, all_0_6_6, n5 and discharging atoms sum(n5, n0) = all_0_6_6, sum(n5, n0) = n5, yields:
% 22.39/6.27 | (847) all_0_6_6 = n5
% 22.39/6.27 |
% 22.39/6.27 | Equations (847) can reduce 409 to:
% 22.39/6.27 | (458) $false
% 22.39/6.27 |
% 22.39/6.27 |-The branch is then unsatisfiable
% 22.39/6.27 |-Branch two:
% 22.39/6.27 | (561) ~ (all_0_8_8 = n9)
% 22.39/6.27 | (562) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.39/6.27 |
% 22.39/6.27 +-Applying beta-rule and splitting (562), into two cases.
% 22.39/6.27 |-Branch one:
% 22.39/6.27 | (563) all_0_8_8 = n8
% 22.39/6.27 |
% 22.39/6.27 | From (563) and (2027) follows:
% 22.39/6.27 | (2097) sum(n8, n13) = all_0_4_4
% 22.39/6.27 |
% 22.39/6.27 | From (563) and (2025) follows:
% 22.39/6.27 | (2098) sum(n8, n12) = all_0_2_2
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n8, n13, all_0_4_4, n5 and discharging atoms sum(n8, n13) = all_0_4_4, sum(n8, n13) = n5, yields:
% 22.39/6.27 | (618) all_0_4_4 = n5
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (89) with n8, n12, all_0_2_2, n4 and discharging atoms sum(n8, n12) = all_0_2_2, sum(n8, n12) = n4, yields:
% 22.39/6.27 | (617) all_0_2_2 = n4
% 22.39/6.27 |
% 22.39/6.27 | From (617) and (187) follows:
% 22.39/6.27 | (619) pred(n4) = all_0_1_1
% 22.39/6.27 |
% 22.39/6.27 | From (618) and (396) follows:
% 22.39/6.27 | (620) pred(n5) = all_0_3_3
% 22.39/6.27 |
% 22.39/6.27 | Instantiating formula (37) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 22.39/6.28 | (621) all_0_3_3 = n4
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (37) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 22.39/6.28 | (622) all_0_1_1 = n3
% 22.39/6.28 |
% 22.39/6.28 | From (621) and (261) follows:
% 22.39/6.28 | (623) sum(n4, all_0_0_0) = all_0_6_6
% 22.39/6.28 |
% 22.39/6.28 | From (622) and (758) follows:
% 22.39/6.28 | (2106) sum(n12, n3) = all_0_0_0
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n12, n3, all_0_0_0, n15 and discharging atoms sum(n12, n3) = all_0_0_0, sum(n12, n3) = n15, yields:
% 22.39/6.28 | (676) all_0_0_0 = n15
% 22.39/6.28 |
% 22.39/6.28 | From (676) and (623) follows:
% 22.39/6.28 | (2108) sum(n4, n15) = all_0_6_6
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n4, n15, all_0_6_6, n3 and discharging atoms sum(n4, n15) = all_0_6_6, sum(n4, n15) = n3, yields:
% 22.39/6.28 | (961) all_0_6_6 = n3
% 22.39/6.28 |
% 22.39/6.28 | Equations (961) can reduce 245 to:
% 22.39/6.28 | (458) $false
% 22.39/6.28 |
% 22.39/6.28 |-The branch is then unsatisfiable
% 22.39/6.28 |-Branch two:
% 22.39/6.28 | (578) ~ (all_0_8_8 = n8)
% 22.39/6.28 | (579) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.39/6.28 |
% 22.39/6.28 +-Applying beta-rule and splitting (579), into two cases.
% 22.39/6.28 |-Branch one:
% 22.39/6.28 | (580) all_0_8_8 = n7
% 22.39/6.28 |
% 22.39/6.28 | From (580) and (2027) follows:
% 22.39/6.28 | (2114) sum(n7, n13) = all_0_4_4
% 22.39/6.28 |
% 22.39/6.28 | From (580) and (2025) follows:
% 22.39/6.28 | (2115) sum(n7, n12) = all_0_2_2
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n7, n13, all_0_4_4, n4 and discharging atoms sum(n7, n13) = all_0_4_4, sum(n7, n13) = n4, yields:
% 22.39/6.28 | (635) all_0_4_4 = n4
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n7, n12, all_0_2_2, n3 and discharging atoms sum(n7, n12) = all_0_2_2, sum(n7, n12) = n3, yields:
% 22.39/6.28 | (634) all_0_2_2 = n3
% 22.39/6.28 |
% 22.39/6.28 | From (634) and (187) follows:
% 22.39/6.28 | (636) pred(n3) = all_0_1_1
% 22.39/6.28 |
% 22.39/6.28 | From (635) and (396) follows:
% 22.39/6.28 | (637) pred(n4) = all_0_3_3
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (37) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 22.39/6.28 | (638) all_0_3_3 = n3
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (37) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 22.39/6.28 | (639) all_0_1_1 = n2
% 22.39/6.28 |
% 22.39/6.28 | From (638) and (261) follows:
% 22.39/6.28 | (640) sum(n3, all_0_0_0) = all_0_6_6
% 22.39/6.28 |
% 22.39/6.28 | From (639) and (758) follows:
% 22.39/6.28 | (2123) sum(n12, n2) = all_0_0_0
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n12, n2, all_0_0_0, n14 and discharging atoms sum(n12, n2) = all_0_0_0, sum(n12, n2) = n14, yields:
% 22.39/6.28 | (693) all_0_0_0 = n14
% 22.39/6.28 |
% 22.39/6.28 | From (693) and (640) follows:
% 22.39/6.28 | (2125) sum(n3, n14) = all_0_6_6
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n3, n14, all_0_6_6, n1 and discharging atoms sum(n3, n14) = all_0_6_6, sum(n3, n14) = n1, yields:
% 22.39/6.28 | (771) all_0_6_6 = n1
% 22.39/6.28 |
% 22.39/6.28 | Equations (771) can reduce 38 to:
% 22.39/6.28 | (458) $false
% 22.39/6.28 |
% 22.39/6.28 |-The branch is then unsatisfiable
% 22.39/6.28 |-Branch two:
% 22.39/6.28 | (595) ~ (all_0_8_8 = n7)
% 22.39/6.28 | (596) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.39/6.28 |
% 22.39/6.28 +-Applying beta-rule and splitting (596), into two cases.
% 22.39/6.28 |-Branch one:
% 22.39/6.28 | (597) all_0_8_8 = n6
% 22.39/6.28 |
% 22.39/6.28 | From (597) and (2027) follows:
% 22.39/6.28 | (2131) sum(n6, n13) = all_0_4_4
% 22.39/6.28 |
% 22.39/6.28 | From (597) and (2025) follows:
% 22.39/6.28 | (2132) sum(n6, n12) = all_0_2_2
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n6, n13, all_0_4_4, n3 and discharging atoms sum(n6, n13) = all_0_4_4, sum(n6, n13) = n3, yields:
% 22.39/6.28 | (652) all_0_4_4 = n3
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n6, n12, all_0_2_2, n2 and discharging atoms sum(n6, n12) = all_0_2_2, sum(n6, n12) = n2, yields:
% 22.39/6.28 | (651) all_0_2_2 = n2
% 22.39/6.28 |
% 22.39/6.28 | From (651) and (187) follows:
% 22.39/6.28 | (653) pred(n2) = all_0_1_1
% 22.39/6.28 |
% 22.39/6.28 | From (652) and (396) follows:
% 22.39/6.28 | (654) pred(n3) = all_0_3_3
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (37) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 22.39/6.28 | (655) all_0_3_3 = n2
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (37) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 22.39/6.28 | (656) all_0_1_1 = n1
% 22.39/6.28 |
% 22.39/6.28 | From (655) and (261) follows:
% 22.39/6.28 | (657) sum(n2, all_0_0_0) = all_0_6_6
% 22.39/6.28 |
% 22.39/6.28 | From (656) and (758) follows:
% 22.39/6.28 | (2140) sum(n12, n1) = all_0_0_0
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n12, n1, all_0_0_0, n13 and discharging atoms sum(n12, n1) = all_0_0_0, sum(n12, n1) = n13, yields:
% 22.39/6.28 | (709) all_0_0_0 = n13
% 22.39/6.28 |
% 22.39/6.28 | From (709) and (657) follows:
% 22.39/6.28 | (2142) sum(n2, n13) = all_0_6_6
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n2, n13, all_0_6_6, n15 and discharging atoms sum(n2, n13) = all_0_6_6, sum(n2, n13) = n15, yields:
% 22.39/6.28 | (885) all_0_6_6 = n15
% 22.39/6.28 |
% 22.39/6.28 | Equations (885) can reduce 225 to:
% 22.39/6.28 | (458) $false
% 22.39/6.28 |
% 22.39/6.28 |-The branch is then unsatisfiable
% 22.39/6.28 |-Branch two:
% 22.39/6.28 | (612) ~ (all_0_8_8 = n6)
% 22.39/6.28 | (613) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.39/6.28 |
% 22.39/6.28 +-Applying beta-rule and splitting (613), into two cases.
% 22.39/6.28 |-Branch one:
% 22.39/6.28 | (614) all_0_8_8 = n5
% 22.39/6.28 |
% 22.39/6.28 | From (614) and (2027) follows:
% 22.39/6.28 | (2148) sum(n5, n13) = all_0_4_4
% 22.39/6.28 |
% 22.39/6.28 | From (614) and (2025) follows:
% 22.39/6.28 | (2149) sum(n5, n12) = all_0_2_2
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n5, n13, all_0_4_4, n2 and discharging atoms sum(n5, n13) = all_0_4_4, sum(n5, n13) = n2, yields:
% 22.39/6.28 | (669) all_0_4_4 = n2
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n5, n12, all_0_2_2, n1 and discharging atoms sum(n5, n12) = all_0_2_2, sum(n5, n12) = n1, yields:
% 22.39/6.28 | (668) all_0_2_2 = n1
% 22.39/6.28 |
% 22.39/6.28 | From (668) and (187) follows:
% 22.39/6.28 | (670) pred(n1) = all_0_1_1
% 22.39/6.28 |
% 22.39/6.28 | From (669) and (396) follows:
% 22.39/6.28 | (671) pred(n2) = all_0_3_3
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (37) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 22.39/6.28 | (672) all_0_3_3 = n1
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (37) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 22.39/6.28 | (673) all_0_1_1 = n0
% 22.39/6.28 |
% 22.39/6.28 | From (672) and (261) follows:
% 22.39/6.28 | (674) sum(n1, all_0_0_0) = all_0_6_6
% 22.39/6.28 |
% 22.39/6.28 | From (673) and (758) follows:
% 22.39/6.28 | (2157) sum(n12, n0) = all_0_0_0
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n12, n0, all_0_0_0, n12 and discharging atoms sum(n12, n0) = all_0_0_0, sum(n12, n0) = n12, yields:
% 22.39/6.28 | (455) all_0_0_0 = n12
% 22.39/6.28 |
% 22.39/6.28 | From (455) and (674) follows:
% 22.39/6.28 | (2159) sum(n1, n12) = all_0_6_6
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n1, n12, all_0_6_6, n13 and discharging atoms sum(n1, n12) = all_0_6_6, sum(n1, n12) = n13, yields:
% 22.39/6.28 | (998) all_0_6_6 = n13
% 22.39/6.28 |
% 22.39/6.28 | Equations (998) can reduce 130 to:
% 22.39/6.28 | (458) $false
% 22.39/6.28 |
% 22.39/6.28 |-The branch is then unsatisfiable
% 22.39/6.28 |-Branch two:
% 22.39/6.28 | (629) ~ (all_0_8_8 = n5)
% 22.39/6.28 | (630) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.39/6.28 |
% 22.39/6.28 +-Applying beta-rule and splitting (630), into two cases.
% 22.39/6.28 |-Branch one:
% 22.39/6.28 | (631) all_0_8_8 = n4
% 22.39/6.28 |
% 22.39/6.28 | From (631) and (2027) follows:
% 22.39/6.28 | (2165) sum(n4, n13) = all_0_4_4
% 22.39/6.28 |
% 22.39/6.28 | From (631) and (2025) follows:
% 22.39/6.28 | (2166) sum(n4, n12) = all_0_2_2
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n4, n13, all_0_4_4, n1 and discharging atoms sum(n4, n13) = all_0_4_4, sum(n4, n13) = n1, yields:
% 22.39/6.28 | (686) all_0_4_4 = n1
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n4, n12, all_0_2_2, n0 and discharging atoms sum(n4, n12) = all_0_2_2, sum(n4, n12) = n0, yields:
% 22.39/6.28 | (685) all_0_2_2 = n0
% 22.39/6.28 |
% 22.39/6.28 | From (685) and (187) follows:
% 22.39/6.28 | (687) pred(n0) = all_0_1_1
% 22.39/6.28 |
% 22.39/6.28 | From (686) and (396) follows:
% 22.39/6.28 | (688) pred(n1) = all_0_3_3
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (37) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 22.39/6.28 | (689) all_0_3_3 = n0
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (37) with n0, all_0_1_1, n15 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n15, yields:
% 22.39/6.28 | (690) all_0_1_1 = n15
% 22.39/6.28 |
% 22.39/6.28 | From (689) and (261) follows:
% 22.39/6.28 | (691) sum(n0, all_0_0_0) = all_0_6_6
% 22.39/6.28 |
% 22.39/6.28 | From (690) and (758) follows:
% 22.39/6.28 | (2174) sum(n12, n15) = all_0_0_0
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n12, n15, all_0_0_0, n11 and discharging atoms sum(n12, n15) = all_0_0_0, sum(n12, n15) = n11, yields:
% 22.39/6.28 | (472) all_0_0_0 = n11
% 22.39/6.28 |
% 22.39/6.28 | From (472) and (691) follows:
% 22.39/6.28 | (2176) sum(n0, n11) = all_0_6_6
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n0, n11, all_0_6_6, n11 and discharging atoms sum(n0, n11) = all_0_6_6, sum(n0, n11) = n11, yields:
% 22.39/6.28 | (809) all_0_6_6 = n11
% 22.39/6.28 |
% 22.39/6.28 | Equations (809) can reduce 70 to:
% 22.39/6.28 | (458) $false
% 22.39/6.28 |
% 22.39/6.28 |-The branch is then unsatisfiable
% 22.39/6.28 |-Branch two:
% 22.39/6.28 | (646) ~ (all_0_8_8 = n4)
% 22.39/6.28 | (647) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.39/6.28 |
% 22.39/6.28 +-Applying beta-rule and splitting (647), into two cases.
% 22.39/6.28 |-Branch one:
% 22.39/6.28 | (648) all_0_8_8 = n3
% 22.39/6.28 |
% 22.39/6.28 | From (648) and (2027) follows:
% 22.39/6.28 | (2182) sum(n3, n13) = all_0_4_4
% 22.39/6.28 |
% 22.39/6.28 | From (648) and (2025) follows:
% 22.39/6.28 | (2183) sum(n3, n12) = all_0_2_2
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n3, n13, all_0_4_4, n0 and discharging atoms sum(n3, n13) = all_0_4_4, sum(n3, n13) = n0, yields:
% 22.39/6.28 | (702) all_0_4_4 = n0
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n3, n12, all_0_2_2, n15 and discharging atoms sum(n3, n12) = all_0_2_2, sum(n3, n12) = n15, yields:
% 22.39/6.28 | (701) all_0_2_2 = n15
% 22.39/6.28 |
% 22.39/6.28 | From (701) and (187) follows:
% 22.39/6.28 | (703) pred(n15) = all_0_1_1
% 22.39/6.28 |
% 22.39/6.28 | From (702) and (396) follows:
% 22.39/6.28 | (704) pred(n0) = all_0_3_3
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (37) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 22.39/6.28 | (705) all_0_1_1 = n14
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (37) with n0, all_0_3_3, n15 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n15, yields:
% 22.39/6.28 | (706) all_0_3_3 = n15
% 22.39/6.28 |
% 22.39/6.28 | From (706) and (261) follows:
% 22.39/6.28 | (707) sum(n15, all_0_0_0) = all_0_6_6
% 22.39/6.28 |
% 22.39/6.28 | From (705) and (758) follows:
% 22.39/6.28 | (2191) sum(n12, n14) = all_0_0_0
% 22.39/6.28 |
% 22.39/6.28 | Instantiating formula (89) with n12, n14, all_0_0_0, n10 and discharging atoms sum(n12, n14) = all_0_0_0, sum(n12, n14) = n10, yields:
% 22.39/6.28 | (489) all_0_0_0 = n10
% 22.39/6.28 |
% 22.39/6.28 | From (489) and (707) follows:
% 22.39/6.29 | (2193) sum(n15, n10) = all_0_6_6
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n15, n10, all_0_6_6, n9 and discharging atoms sum(n15, n10) = all_0_6_6, sum(n15, n10) = n9, yields:
% 22.39/6.29 | (923) all_0_6_6 = n9
% 22.39/6.29 |
% 22.39/6.29 | Equations (923) can reduce 404 to:
% 22.39/6.29 | (458) $false
% 22.39/6.29 |
% 22.39/6.29 |-The branch is then unsatisfiable
% 22.39/6.29 |-Branch two:
% 22.39/6.29 | (663) ~ (all_0_8_8 = n3)
% 22.39/6.29 | (664) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.39/6.29 |
% 22.39/6.29 +-Applying beta-rule and splitting (664), into two cases.
% 22.39/6.29 |-Branch one:
% 22.39/6.29 | (665) all_0_8_8 = n2
% 22.39/6.29 |
% 22.39/6.29 | From (665) and (2027) follows:
% 22.39/6.29 | (2199) sum(n2, n13) = all_0_4_4
% 22.39/6.29 |
% 22.39/6.29 | From (665) and (2025) follows:
% 22.39/6.29 | (2200) sum(n2, n12) = all_0_2_2
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n2, n13, all_0_4_4, n15 and discharging atoms sum(n2, n13) = all_0_4_4, sum(n2, n13) = n15, yields:
% 22.39/6.29 | (448) all_0_4_4 = n15
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n2, n12, all_0_2_2, n14 and discharging atoms sum(n2, n12) = all_0_2_2, sum(n2, n12) = n14, yields:
% 22.39/6.29 | (447) all_0_2_2 = n14
% 22.39/6.29 |
% 22.39/6.29 | From (447) and (187) follows:
% 22.39/6.29 | (449) pred(n14) = all_0_1_1
% 22.39/6.29 |
% 22.39/6.29 | From (448) and (396) follows:
% 22.39/6.29 | (450) pred(n15) = all_0_3_3
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (37) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 22.39/6.29 | (451) all_0_3_3 = n14
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (37) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 22.39/6.29 | (452) all_0_1_1 = n13
% 22.39/6.29 |
% 22.39/6.29 | From (451) and (261) follows:
% 22.39/6.29 | (453) sum(n14, all_0_0_0) = all_0_6_6
% 22.39/6.29 |
% 22.39/6.29 | From (452) and (758) follows:
% 22.39/6.29 | (2208) sum(n12, n13) = all_0_0_0
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n12, n13, all_0_0_0, n9 and discharging atoms sum(n12, n13) = all_0_0_0, sum(n12, n13) = n9, yields:
% 22.39/6.29 | (506) all_0_0_0 = n9
% 22.39/6.29 |
% 22.39/6.29 | From (506) and (453) follows:
% 22.39/6.29 | (2210) sum(n14, n9) = all_0_6_6
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n14, n9, all_0_6_6, n7 and discharging atoms sum(n14, n9) = all_0_6_6, sum(n14, n9) = n7, yields:
% 22.39/6.29 | (733) all_0_6_6 = n7
% 22.39/6.29 |
% 22.39/6.29 | Equations (733) can reduce 274 to:
% 22.39/6.29 | (458) $false
% 22.39/6.29 |
% 22.39/6.29 |-The branch is then unsatisfiable
% 22.39/6.29 |-Branch two:
% 22.39/6.29 | (680) ~ (all_0_8_8 = n2)
% 22.39/6.29 | (681) all_0_8_8 = n1 | all_0_8_8 = n0
% 22.39/6.29 |
% 22.39/6.29 +-Applying beta-rule and splitting (681), into two cases.
% 22.39/6.29 |-Branch one:
% 22.39/6.29 | (682) all_0_8_8 = n1
% 22.39/6.29 |
% 22.39/6.29 | From (682) and (2027) follows:
% 22.39/6.29 | (2216) sum(n1, n13) = all_0_4_4
% 22.39/6.29 |
% 22.39/6.29 | From (682) and (2025) follows:
% 22.39/6.29 | (2217) sum(n1, n12) = all_0_2_2
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n1, n13, all_0_4_4, n14 and discharging atoms sum(n1, n13) = all_0_4_4, sum(n1, n13) = n14, yields:
% 22.39/6.29 | (465) all_0_4_4 = n14
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n1, n12, all_0_2_2, n13 and discharging atoms sum(n1, n12) = all_0_2_2, sum(n1, n12) = n13, yields:
% 22.39/6.29 | (464) all_0_2_2 = n13
% 22.39/6.29 |
% 22.39/6.29 | From (464) and (187) follows:
% 22.39/6.29 | (466) pred(n13) = all_0_1_1
% 22.39/6.29 |
% 22.39/6.29 | From (465) and (396) follows:
% 22.39/6.29 | (467) pred(n14) = all_0_3_3
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (37) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 22.39/6.29 | (468) all_0_3_3 = n13
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (37) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 22.39/6.29 | (469) all_0_1_1 = n12
% 22.39/6.29 |
% 22.39/6.29 | From (468) and (261) follows:
% 22.39/6.29 | (470) sum(n13, all_0_0_0) = all_0_6_6
% 22.39/6.29 |
% 22.39/6.29 | From (469) and (758) follows:
% 22.39/6.29 | (2225) sum(n12, n12) = all_0_0_0
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n12, n12, all_0_0_0, n8 and discharging atoms sum(n12, n12) = all_0_0_0, sum(n12, n12) = n8, yields:
% 22.39/6.29 | (523) all_0_0_0 = n8
% 22.39/6.29 |
% 22.39/6.29 | From (523) and (470) follows:
% 22.39/6.29 | (2227) sum(n13, n8) = all_0_6_6
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n13, n8, all_0_6_6, n5 and discharging atoms sum(n13, n8) = all_0_6_6, sum(n13, n8) = n5, yields:
% 22.39/6.29 | (847) all_0_6_6 = n5
% 22.39/6.29 |
% 22.39/6.29 | Equations (847) can reduce 409 to:
% 22.39/6.29 | (458) $false
% 22.39/6.29 |
% 22.39/6.29 |-The branch is then unsatisfiable
% 22.39/6.29 |-Branch two:
% 22.39/6.29 | (697) ~ (all_0_8_8 = n1)
% 22.39/6.29 | (698) all_0_8_8 = n0
% 22.39/6.29 |
% 22.39/6.29 | From (698) and (2027) follows:
% 22.39/6.29 | (2232) sum(n0, n13) = all_0_4_4
% 22.39/6.29 |
% 22.39/6.29 | From (698) and (2025) follows:
% 22.39/6.29 | (2233) sum(n0, n12) = all_0_2_2
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n0, n13, all_0_4_4, n13 and discharging atoms sum(n0, n13) = all_0_4_4, sum(n0, n13) = n13, yields:
% 22.39/6.29 | (482) all_0_4_4 = n13
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n0, n12, all_0_2_2, n12 and discharging atoms sum(n0, n12) = all_0_2_2, sum(n0, n12) = n12, yields:
% 22.39/6.29 | (481) all_0_2_2 = n12
% 22.39/6.29 |
% 22.39/6.29 | From (481) and (187) follows:
% 22.39/6.29 | (483) pred(n12) = all_0_1_1
% 22.39/6.29 |
% 22.39/6.29 | From (482) and (396) follows:
% 22.39/6.29 | (484) pred(n13) = all_0_3_3
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (37) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 22.39/6.29 | (485) all_0_3_3 = n12
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (37) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 22.39/6.29 | (486) all_0_1_1 = n11
% 22.39/6.29 |
% 22.39/6.29 | From (485) and (261) follows:
% 22.39/6.29 | (487) sum(n12, all_0_0_0) = all_0_6_6
% 22.39/6.29 |
% 22.39/6.29 | From (486) and (758) follows:
% 22.39/6.29 | (2241) sum(n12, n11) = all_0_0_0
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n12, n11, all_0_0_0, n7 and discharging atoms sum(n12, n11) = all_0_0_0, sum(n12, n11) = n7, yields:
% 22.39/6.29 | (540) all_0_0_0 = n7
% 22.39/6.29 |
% 22.39/6.29 | From (540) and (487) follows:
% 22.39/6.29 | (2243) sum(n12, n7) = all_0_6_6
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n12, n7, all_0_6_6, n3 and discharging atoms sum(n12, n7) = all_0_6_6, sum(n12, n7) = n3, yields:
% 22.39/6.29 | (961) all_0_6_6 = n3
% 22.39/6.29 |
% 22.39/6.29 | Equations (961) can reduce 245 to:
% 22.39/6.29 | (458) $false
% 22.39/6.29 |
% 22.39/6.29 |-The branch is then unsatisfiable
% 22.39/6.29 |-Branch two:
% 22.39/6.29 | (773) ~ (all_0_7_7 = n12)
% 22.39/6.29 | (774) all_0_7_7 = n11 | all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.39/6.29 |
% 22.39/6.29 +-Applying beta-rule and splitting (494), into two cases.
% 22.39/6.29 |-Branch one:
% 22.39/6.29 | (495) all_0_8_8 = n12
% 22.39/6.29 |
% 22.39/6.29 | From (495) and (64) follows:
% 22.39/6.29 | (2249) sum(n12, all_0_5_5) = all_0_4_4
% 22.39/6.29 |
% 22.39/6.29 | From (495) and (160) follows:
% 22.39/6.29 | (2250) sum(n12, all_0_7_7) = all_0_2_2
% 22.39/6.29 |
% 22.39/6.29 +-Applying beta-rule and splitting (774), into two cases.
% 22.39/6.29 |-Branch one:
% 22.39/6.29 | (775) all_0_7_7 = n11
% 22.39/6.29 |
% 22.39/6.29 | From (775) and (176) follows:
% 22.39/6.29 | (776) succ(n11) = all_0_5_5
% 22.39/6.29 |
% 22.39/6.29 | From (775) and (59) follows:
% 22.39/6.29 | (777) sum(n11, all_0_1_1) = all_0_0_0
% 22.39/6.29 |
% 22.39/6.29 | From (775) and (2250) follows:
% 22.39/6.29 | (2254) sum(n12, n11) = all_0_2_2
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (219) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 22.39/6.29 | (779) all_0_5_5 = n12
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n12, n11, all_0_2_2, n7 and discharging atoms sum(n12, n11) = all_0_2_2, sum(n12, n11) = n7, yields:
% 22.39/6.29 | (566) all_0_2_2 = n7
% 22.39/6.29 |
% 22.39/6.29 | From (566) and (187) follows:
% 22.39/6.29 | (568) pred(n7) = all_0_1_1
% 22.39/6.29 |
% 22.39/6.29 | From (779) and (2249) follows:
% 22.39/6.29 | (2258) sum(n12, n12) = all_0_4_4
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (37) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 22.39/6.29 | (571) all_0_1_1 = n6
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n12, n12, all_0_4_4, n8 and discharging atoms sum(n12, n12) = all_0_4_4, sum(n12, n12) = n8, yields:
% 22.39/6.29 | (567) all_0_4_4 = n8
% 22.39/6.29 |
% 22.39/6.29 | From (567) and (396) follows:
% 22.39/6.29 | (569) pred(n8) = all_0_3_3
% 22.39/6.29 |
% 22.39/6.29 | From (571) and (777) follows:
% 22.39/6.29 | (2262) sum(n11, n6) = all_0_0_0
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (37) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 22.39/6.29 | (570) all_0_3_3 = n7
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n11, n6, all_0_0_0, n1 and discharging atoms sum(n11, n6) = all_0_0_0, sum(n11, n6) = n1, yields:
% 22.39/6.29 | (642) all_0_0_0 = n1
% 22.39/6.29 |
% 22.39/6.29 | From (570)(642) and (261) follows:
% 22.39/6.29 | (2265) sum(n7, n1) = all_0_6_6
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n7, n1, all_0_6_6, n8 and discharging atoms sum(n7, n1) = all_0_6_6, sum(n7, n1) = n8, yields:
% 22.39/6.29 | (474) all_0_6_6 = n8
% 22.39/6.29 |
% 22.39/6.29 | Equations (474) can reduce 86 to:
% 22.39/6.29 | (458) $false
% 22.39/6.29 |
% 22.39/6.29 |-The branch is then unsatisfiable
% 22.39/6.29 |-Branch two:
% 22.39/6.29 | (792) ~ (all_0_7_7 = n11)
% 22.39/6.29 | (793) all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.39/6.29 |
% 22.39/6.29 +-Applying beta-rule and splitting (793), into two cases.
% 22.39/6.29 |-Branch one:
% 22.39/6.29 | (794) all_0_7_7 = n10
% 22.39/6.29 |
% 22.39/6.29 | From (794) and (176) follows:
% 22.39/6.29 | (795) succ(n10) = all_0_5_5
% 22.39/6.29 |
% 22.39/6.29 | From (794) and (59) follows:
% 22.39/6.29 | (796) sum(n10, all_0_1_1) = all_0_0_0
% 22.39/6.29 |
% 22.39/6.29 | From (794) and (2250) follows:
% 22.39/6.29 | (2273) sum(n12, n10) = all_0_2_2
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (219) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 22.39/6.29 | (798) all_0_5_5 = n11
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n12, n10, all_0_2_2, n6 and discharging atoms sum(n12, n10) = all_0_2_2, sum(n12, n10) = n6, yields:
% 22.39/6.29 | (583) all_0_2_2 = n6
% 22.39/6.29 |
% 22.39/6.29 | From (583) and (187) follows:
% 22.39/6.29 | (585) pred(n6) = all_0_1_1
% 22.39/6.29 |
% 22.39/6.29 | From (798) and (2249) follows:
% 22.39/6.29 | (2277) sum(n12, n11) = all_0_4_4
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (37) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 22.39/6.29 | (588) all_0_1_1 = n5
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n12, n11, all_0_4_4, n7 and discharging atoms sum(n12, n11) = all_0_4_4, sum(n12, n11) = n7, yields:
% 22.39/6.29 | (584) all_0_4_4 = n7
% 22.39/6.29 |
% 22.39/6.29 | From (584) and (396) follows:
% 22.39/6.29 | (586) pred(n7) = all_0_3_3
% 22.39/6.29 |
% 22.39/6.29 | From (588) and (796) follows:
% 22.39/6.29 | (2281) sum(n10, n5) = all_0_0_0
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (37) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 22.39/6.29 | (587) all_0_3_3 = n6
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n10, n5, all_0_0_0, n15 and discharging atoms sum(n10, n5) = all_0_0_0, sum(n10, n5) = n15, yields:
% 22.39/6.29 | (676) all_0_0_0 = n15
% 22.39/6.29 |
% 22.39/6.29 | From (587)(676) and (261) follows:
% 22.39/6.29 | (2284) sum(n6, n15) = all_0_6_6
% 22.39/6.29 |
% 22.39/6.29 | Instantiating formula (89) with n6, n15, all_0_6_6, n5 and discharging atoms sum(n6, n15) = all_0_6_6, sum(n6, n15) = n5, yields:
% 22.39/6.29 | (847) all_0_6_6 = n5
% 22.39/6.29 |
% 22.39/6.29 | Equations (847) can reduce 409 to:
% 22.39/6.29 | (458) $false
% 22.39/6.29 |
% 22.39/6.29 |-The branch is then unsatisfiable
% 22.39/6.29 |-Branch two:
% 22.39/6.29 | (811) ~ (all_0_7_7 = n10)
% 22.39/6.30 | (812) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.39/6.30 |
% 22.39/6.30 +-Applying beta-rule and splitting (812), into two cases.
% 22.39/6.30 |-Branch one:
% 22.39/6.30 | (813) all_0_7_7 = n9
% 22.39/6.30 |
% 22.39/6.30 | From (813) and (176) follows:
% 22.39/6.30 | (814) succ(n9) = all_0_5_5
% 22.39/6.30 |
% 22.39/6.30 | From (813) and (59) follows:
% 22.39/6.30 | (815) sum(n9, all_0_1_1) = all_0_0_0
% 22.39/6.30 |
% 22.39/6.30 | From (813) and (2250) follows:
% 22.39/6.30 | (2292) sum(n12, n9) = all_0_2_2
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (219) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 22.39/6.30 | (817) all_0_5_5 = n10
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n12, n9, all_0_2_2, n5 and discharging atoms sum(n12, n9) = all_0_2_2, sum(n12, n9) = n5, yields:
% 22.39/6.30 | (600) all_0_2_2 = n5
% 22.39/6.30 |
% 22.39/6.30 | From (600) and (187) follows:
% 22.39/6.30 | (602) pred(n5) = all_0_1_1
% 22.39/6.30 |
% 22.39/6.30 | From (817) and (2249) follows:
% 22.39/6.30 | (2296) sum(n12, n10) = all_0_4_4
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (37) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 22.39/6.30 | (605) all_0_1_1 = n4
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n12, n10, all_0_4_4, n6 and discharging atoms sum(n12, n10) = all_0_4_4, sum(n12, n10) = n6, yields:
% 22.39/6.30 | (601) all_0_4_4 = n6
% 22.39/6.30 |
% 22.39/6.30 | From (601) and (396) follows:
% 22.39/6.30 | (603) pred(n6) = all_0_3_3
% 22.39/6.30 |
% 22.39/6.30 | From (605) and (815) follows:
% 22.39/6.30 | (2300) sum(n9, n4) = all_0_0_0
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (37) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 22.39/6.30 | (604) all_0_3_3 = n5
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n9, n4, all_0_0_0, n13 and discharging atoms sum(n9, n4) = all_0_0_0, sum(n9, n4) = n13, yields:
% 22.39/6.30 | (709) all_0_0_0 = n13
% 22.39/6.30 |
% 22.39/6.30 | From (604)(709) and (261) follows:
% 22.39/6.30 | (2303) sum(n5, n13) = all_0_6_6
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n5, n13, all_0_6_6, n2 and discharging atoms sum(n5, n13) = all_0_6_6, sum(n5, n13) = n2, yields:
% 22.39/6.30 | (525) all_0_6_6 = n2
% 22.39/6.30 |
% 22.39/6.30 | Equations (525) can reduce 231 to:
% 22.39/6.30 | (458) $false
% 22.39/6.30 |
% 22.39/6.30 |-The branch is then unsatisfiable
% 22.39/6.30 |-Branch two:
% 22.39/6.30 | (830) ~ (all_0_7_7 = n9)
% 22.39/6.30 | (831) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.39/6.30 |
% 22.39/6.30 +-Applying beta-rule and splitting (831), into two cases.
% 22.39/6.30 |-Branch one:
% 22.39/6.30 | (832) all_0_7_7 = n8
% 22.39/6.30 |
% 22.39/6.30 | From (832) and (176) follows:
% 22.39/6.30 | (833) succ(n8) = all_0_5_5
% 22.39/6.30 |
% 22.39/6.30 | From (832) and (59) follows:
% 22.39/6.30 | (834) sum(n8, all_0_1_1) = all_0_0_0
% 22.39/6.30 |
% 22.39/6.30 | From (832) and (2250) follows:
% 22.39/6.30 | (2311) sum(n12, n8) = all_0_2_2
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (219) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 22.39/6.30 | (836) all_0_5_5 = n9
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n12, n8, all_0_2_2, n4 and discharging atoms sum(n12, n8) = all_0_2_2, sum(n12, n8) = n4, yields:
% 22.39/6.30 | (617) all_0_2_2 = n4
% 22.39/6.30 |
% 22.39/6.30 | From (617) and (187) follows:
% 22.39/6.30 | (619) pred(n4) = all_0_1_1
% 22.39/6.30 |
% 22.39/6.30 | From (836) and (2249) follows:
% 22.39/6.30 | (2315) sum(n12, n9) = all_0_4_4
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (37) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 22.39/6.30 | (622) all_0_1_1 = n3
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n12, n9, all_0_4_4, n5 and discharging atoms sum(n12, n9) = all_0_4_4, sum(n12, n9) = n5, yields:
% 22.39/6.30 | (618) all_0_4_4 = n5
% 22.39/6.30 |
% 22.39/6.30 | From (618) and (396) follows:
% 22.39/6.30 | (620) pred(n5) = all_0_3_3
% 22.39/6.30 |
% 22.39/6.30 | From (622) and (834) follows:
% 22.39/6.30 | (2319) sum(n8, n3) = all_0_0_0
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (37) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 22.39/6.30 | (621) all_0_3_3 = n4
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n8, n3, all_0_0_0, n11 and discharging atoms sum(n8, n3) = all_0_0_0, sum(n8, n3) = n11, yields:
% 22.39/6.30 | (472) all_0_0_0 = n11
% 22.39/6.30 |
% 22.39/6.30 | From (621)(472) and (261) follows:
% 22.39/6.30 | (2322) sum(n4, n11) = all_0_6_6
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n4, n11, all_0_6_6, n15 and discharging atoms sum(n4, n11) = all_0_6_6, sum(n4, n11) = n15, yields:
% 22.39/6.30 | (885) all_0_6_6 = n15
% 22.39/6.30 |
% 22.39/6.30 | Equations (885) can reduce 225 to:
% 22.39/6.30 | (458) $false
% 22.39/6.30 |
% 22.39/6.30 |-The branch is then unsatisfiable
% 22.39/6.30 |-Branch two:
% 22.39/6.30 | (849) ~ (all_0_7_7 = n8)
% 22.39/6.30 | (850) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.39/6.30 |
% 22.39/6.30 +-Applying beta-rule and splitting (850), into two cases.
% 22.39/6.30 |-Branch one:
% 22.39/6.30 | (851) all_0_7_7 = n7
% 22.39/6.30 |
% 22.39/6.30 | From (851) and (176) follows:
% 22.39/6.30 | (852) succ(n7) = all_0_5_5
% 22.39/6.30 |
% 22.39/6.30 | From (851) and (59) follows:
% 22.39/6.30 | (853) sum(n7, all_0_1_1) = all_0_0_0
% 22.39/6.30 |
% 22.39/6.30 | From (851) and (2250) follows:
% 22.39/6.30 | (2330) sum(n12, n7) = all_0_2_2
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (219) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 22.39/6.30 | (855) all_0_5_5 = n8
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n12, n7, all_0_2_2, n3 and discharging atoms sum(n12, n7) = all_0_2_2, sum(n12, n7) = n3, yields:
% 22.39/6.30 | (634) all_0_2_2 = n3
% 22.39/6.30 |
% 22.39/6.30 | From (634) and (187) follows:
% 22.39/6.30 | (636) pred(n3) = all_0_1_1
% 22.39/6.30 |
% 22.39/6.30 | From (855) and (2249) follows:
% 22.39/6.30 | (2334) sum(n12, n8) = all_0_4_4
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (37) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 22.39/6.30 | (639) all_0_1_1 = n2
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n12, n8, all_0_4_4, n4 and discharging atoms sum(n12, n8) = all_0_4_4, sum(n12, n8) = n4, yields:
% 22.39/6.30 | (635) all_0_4_4 = n4
% 22.39/6.30 |
% 22.39/6.30 | From (635) and (396) follows:
% 22.39/6.30 | (637) pred(n4) = all_0_3_3
% 22.39/6.30 |
% 22.39/6.30 | From (639) and (853) follows:
% 22.39/6.30 | (2338) sum(n7, n2) = all_0_0_0
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (37) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 22.39/6.30 | (638) all_0_3_3 = n3
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n7, n2, all_0_0_0, n9 and discharging atoms sum(n7, n2) = all_0_0_0, sum(n7, n2) = n9, yields:
% 22.39/6.30 | (506) all_0_0_0 = n9
% 22.39/6.30 |
% 22.39/6.30 | From (638)(506) and (261) follows:
% 22.39/6.30 | (2341) sum(n3, n9) = all_0_6_6
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n3, n9, all_0_6_6, n12 and discharging atoms sum(n3, n9) = all_0_6_6, sum(n3, n9) = n12, yields:
% 22.39/6.30 | (576) all_0_6_6 = n12
% 22.39/6.30 |
% 22.39/6.30 | Equations (576) can reduce 42 to:
% 22.39/6.30 | (458) $false
% 22.39/6.30 |
% 22.39/6.30 |-The branch is then unsatisfiable
% 22.39/6.30 |-Branch two:
% 22.39/6.30 | (868) ~ (all_0_7_7 = n7)
% 22.39/6.30 | (869) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.39/6.30 |
% 22.39/6.30 +-Applying beta-rule and splitting (869), into two cases.
% 22.39/6.30 |-Branch one:
% 22.39/6.30 | (870) all_0_7_7 = n6
% 22.39/6.30 |
% 22.39/6.30 | From (870) and (176) follows:
% 22.39/6.30 | (871) succ(n6) = all_0_5_5
% 22.39/6.30 |
% 22.39/6.30 | From (870) and (59) follows:
% 22.39/6.30 | (872) sum(n6, all_0_1_1) = all_0_0_0
% 22.39/6.30 |
% 22.39/6.30 | From (870) and (2250) follows:
% 22.39/6.30 | (2349) sum(n12, n6) = all_0_2_2
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (219) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 22.39/6.30 | (874) all_0_5_5 = n7
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n12, n6, all_0_2_2, n2 and discharging atoms sum(n12, n6) = all_0_2_2, sum(n12, n6) = n2, yields:
% 22.39/6.30 | (651) all_0_2_2 = n2
% 22.39/6.30 |
% 22.39/6.30 | From (651) and (187) follows:
% 22.39/6.30 | (653) pred(n2) = all_0_1_1
% 22.39/6.30 |
% 22.39/6.30 | From (874) and (2249) follows:
% 22.39/6.30 | (2353) sum(n12, n7) = all_0_4_4
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (37) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 22.39/6.30 | (656) all_0_1_1 = n1
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n12, n7, all_0_4_4, n3 and discharging atoms sum(n12, n7) = all_0_4_4, sum(n12, n7) = n3, yields:
% 22.39/6.30 | (652) all_0_4_4 = n3
% 22.39/6.30 |
% 22.39/6.30 | From (652) and (396) follows:
% 22.39/6.30 | (654) pred(n3) = all_0_3_3
% 22.39/6.30 |
% 22.39/6.30 | From (656) and (872) follows:
% 22.39/6.30 | (2357) sum(n6, n1) = all_0_0_0
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (37) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 22.39/6.30 | (655) all_0_3_3 = n2
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n6, n1, all_0_0_0, n7 and discharging atoms sum(n6, n1) = all_0_0_0, sum(n6, n1) = n7, yields:
% 22.39/6.30 | (540) all_0_0_0 = n7
% 22.39/6.30 |
% 22.39/6.30 | From (655)(540) and (261) follows:
% 22.39/6.30 | (2360) sum(n2, n7) = all_0_6_6
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n2, n7, all_0_6_6, n9 and discharging atoms sum(n2, n7) = all_0_6_6, sum(n2, n7) = n9, yields:
% 22.39/6.30 | (923) all_0_6_6 = n9
% 22.39/6.30 |
% 22.39/6.30 | Equations (923) can reduce 404 to:
% 22.39/6.30 | (458) $false
% 22.39/6.30 |
% 22.39/6.30 |-The branch is then unsatisfiable
% 22.39/6.30 |-Branch two:
% 22.39/6.30 | (887) ~ (all_0_7_7 = n6)
% 22.39/6.30 | (888) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.39/6.30 |
% 22.39/6.30 +-Applying beta-rule and splitting (888), into two cases.
% 22.39/6.30 |-Branch one:
% 22.39/6.30 | (889) all_0_7_7 = n5
% 22.39/6.30 |
% 22.39/6.30 | From (889) and (176) follows:
% 22.39/6.30 | (890) succ(n5) = all_0_5_5
% 22.39/6.30 |
% 22.39/6.30 | From (889) and (59) follows:
% 22.39/6.30 | (891) sum(n5, all_0_1_1) = all_0_0_0
% 22.39/6.30 |
% 22.39/6.30 | From (889) and (2250) follows:
% 22.39/6.30 | (2368) sum(n12, n5) = all_0_2_2
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (219) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 22.39/6.30 | (893) all_0_5_5 = n6
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n12, n5, all_0_2_2, n1 and discharging atoms sum(n12, n5) = all_0_2_2, sum(n12, n5) = n1, yields:
% 22.39/6.30 | (668) all_0_2_2 = n1
% 22.39/6.30 |
% 22.39/6.30 | From (668) and (187) follows:
% 22.39/6.30 | (670) pred(n1) = all_0_1_1
% 22.39/6.30 |
% 22.39/6.30 | From (893) and (2249) follows:
% 22.39/6.30 | (2372) sum(n12, n6) = all_0_4_4
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (37) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 22.39/6.30 | (673) all_0_1_1 = n0
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (89) with n12, n6, all_0_4_4, n2 and discharging atoms sum(n12, n6) = all_0_4_4, sum(n12, n6) = n2, yields:
% 22.39/6.30 | (669) all_0_4_4 = n2
% 22.39/6.30 |
% 22.39/6.30 | From (669) and (396) follows:
% 22.39/6.30 | (671) pred(n2) = all_0_3_3
% 22.39/6.30 |
% 22.39/6.30 | From (673) and (891) follows:
% 22.39/6.30 | (2376) sum(n5, n0) = all_0_0_0
% 22.39/6.30 |
% 22.39/6.30 | Instantiating formula (37) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 22.39/6.30 | (672) all_0_3_3 = n1
% 22.39/6.31 |
% 22.39/6.31 | Instantiating formula (89) with n5, n0, all_0_0_0, n5 and discharging atoms sum(n5, n0) = all_0_0_0, sum(n5, n0) = n5, yields:
% 22.39/6.31 | (574) all_0_0_0 = n5
% 22.39/6.31 |
% 22.39/6.31 | From (672)(574) and (261) follows:
% 22.39/6.31 | (2379) sum(n1, n5) = all_0_6_6
% 22.39/6.31 |
% 22.39/6.31 | Instantiating formula (89) with n1, n5, all_0_6_6, n6 and discharging atoms sum(n1, n5) = all_0_6_6, sum(n1, n5) = n6, yields:
% 22.39/6.31 | (491) all_0_6_6 = n6
% 22.39/6.31 |
% 22.39/6.31 | Equations (491) can reduce 418 to:
% 22.39/6.31 | (458) $false
% 22.39/6.31 |
% 22.39/6.31 |-The branch is then unsatisfiable
% 22.39/6.31 |-Branch two:
% 22.39/6.31 | (906) ~ (all_0_7_7 = n5)
% 22.39/6.31 | (907) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.39/6.31 |
% 22.39/6.31 +-Applying beta-rule and splitting (907), into two cases.
% 22.39/6.31 |-Branch one:
% 22.39/6.31 | (908) all_0_7_7 = n4
% 22.39/6.31 |
% 22.39/6.31 | From (908) and (176) follows:
% 22.39/6.31 | (909) succ(n4) = all_0_5_5
% 22.39/6.31 |
% 22.39/6.31 | From (908) and (59) follows:
% 22.39/6.31 | (910) sum(n4, all_0_1_1) = all_0_0_0
% 22.39/6.31 |
% 22.39/6.31 | From (908) and (2250) follows:
% 22.39/6.31 | (2387) sum(n12, n4) = all_0_2_2
% 22.39/6.31 |
% 22.39/6.31 | Instantiating formula (219) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 22.39/6.31 | (912) all_0_5_5 = n5
% 22.39/6.31 |
% 22.39/6.31 | Instantiating formula (89) with n12, n4, all_0_2_2, n0 and discharging atoms sum(n12, n4) = all_0_2_2, sum(n12, n4) = n0, yields:
% 22.39/6.31 | (685) all_0_2_2 = n0
% 22.39/6.31 |
% 22.39/6.31 | From (685) and (187) follows:
% 22.39/6.31 | (687) pred(n0) = all_0_1_1
% 22.39/6.31 |
% 22.39/6.31 | From (912) and (2249) follows:
% 22.39/6.31 | (2391) sum(n12, n5) = all_0_4_4
% 22.39/6.31 |
% 22.39/6.31 | Instantiating formula (37) with n0, all_0_1_1, n15 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n15, yields:
% 22.39/6.31 | (690) all_0_1_1 = n15
% 22.39/6.31 |
% 22.39/6.31 | Instantiating formula (89) with n12, n5, all_0_4_4, n1 and discharging atoms sum(n12, n5) = all_0_4_4, sum(n12, n5) = n1, yields:
% 22.39/6.31 | (686) all_0_4_4 = n1
% 22.39/6.31 |
% 22.39/6.31 | From (686) and (396) follows:
% 22.39/6.31 | (688) pred(n1) = all_0_3_3
% 22.39/6.31 |
% 22.39/6.31 | From (690) and (910) follows:
% 22.39/6.31 | (2395) sum(n4, n15) = all_0_0_0
% 22.39/6.31 |
% 22.39/6.31 | Instantiating formula (37) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 22.39/6.31 | (689) all_0_3_3 = n0
% 22.39/6.31 |
% 22.39/6.31 | Instantiating formula (89) with n4, n15, all_0_0_0, n3 and discharging atoms sum(n4, n15) = all_0_0_0, sum(n4, n15) = n3, yields:
% 22.63/6.31 | (608) all_0_0_0 = n3
% 22.63/6.31 |
% 22.63/6.31 | From (689)(608) and (261) follows:
% 22.63/6.31 | (2398) sum(n0, n3) = all_0_6_6
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (89) with n0, n3, all_0_6_6, n3 and discharging atoms sum(n0, n3) = all_0_6_6, sum(n0, n3) = n3, yields:
% 22.63/6.31 | (961) all_0_6_6 = n3
% 22.63/6.31 |
% 22.63/6.31 | Equations (961) can reduce 245 to:
% 22.63/6.31 | (458) $false
% 22.63/6.31 |
% 22.63/6.31 |-The branch is then unsatisfiable
% 22.63/6.31 |-Branch two:
% 22.63/6.31 | (925) ~ (all_0_7_7 = n4)
% 22.63/6.31 | (926) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.63/6.31 |
% 22.63/6.31 +-Applying beta-rule and splitting (926), into two cases.
% 22.63/6.31 |-Branch one:
% 22.63/6.31 | (927) all_0_7_7 = n3
% 22.63/6.31 |
% 22.63/6.31 | From (927) and (176) follows:
% 22.63/6.31 | (928) succ(n3) = all_0_5_5
% 22.63/6.31 |
% 22.63/6.31 | From (927) and (59) follows:
% 22.63/6.31 | (929) sum(n3, all_0_1_1) = all_0_0_0
% 22.63/6.31 |
% 22.63/6.31 | From (927) and (2250) follows:
% 22.63/6.31 | (2406) sum(n12, n3) = all_0_2_2
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (219) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 22.63/6.31 | (931) all_0_5_5 = n4
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (89) with n12, n3, all_0_2_2, n15 and discharging atoms sum(n12, n3) = all_0_2_2, sum(n12, n3) = n15, yields:
% 22.63/6.31 | (701) all_0_2_2 = n15
% 22.63/6.31 |
% 22.63/6.31 | From (701) and (187) follows:
% 22.63/6.31 | (703) pred(n15) = all_0_1_1
% 22.63/6.31 |
% 22.63/6.31 | From (931) and (2249) follows:
% 22.63/6.31 | (2410) sum(n12, n4) = all_0_4_4
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (37) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 22.63/6.31 | (705) all_0_1_1 = n14
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (89) with n12, n4, all_0_4_4, n0 and discharging atoms sum(n12, n4) = all_0_4_4, sum(n12, n4) = n0, yields:
% 22.63/6.31 | (702) all_0_4_4 = n0
% 22.63/6.31 |
% 22.63/6.31 | From (702) and (396) follows:
% 22.63/6.31 | (704) pred(n0) = all_0_3_3
% 22.63/6.31 |
% 22.63/6.31 | From (705) and (929) follows:
% 22.63/6.31 | (2414) sum(n3, n14) = all_0_0_0
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (37) with n0, all_0_3_3, n15 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n15, yields:
% 22.63/6.31 | (706) all_0_3_3 = n15
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (89) with n3, n14, all_0_0_0, n1 and discharging atoms sum(n3, n14) = all_0_0_0, sum(n3, n14) = n1, yields:
% 22.63/6.31 | (642) all_0_0_0 = n1
% 22.63/6.31 |
% 22.63/6.31 | From (706)(642) and (261) follows:
% 22.63/6.31 | (2417) sum(n15, n1) = all_0_6_6
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (89) with n15, n1, all_0_6_6, n0 and discharging atoms sum(n15, n1) = all_0_6_6, sum(n15, n1) = n0, yields:
% 22.63/6.31 | (542) all_0_6_6 = n0
% 22.63/6.31 |
% 22.63/6.31 | Equations (542) can reduce 400 to:
% 22.63/6.31 | (458) $false
% 22.63/6.31 |
% 22.63/6.31 |-The branch is then unsatisfiable
% 22.63/6.31 |-Branch two:
% 22.63/6.31 | (944) ~ (all_0_7_7 = n3)
% 22.63/6.31 | (945) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.63/6.31 |
% 22.63/6.31 +-Applying beta-rule and splitting (945), into two cases.
% 22.63/6.31 |-Branch one:
% 22.63/6.31 | (946) all_0_7_7 = n2
% 22.63/6.31 |
% 22.63/6.31 | From (946) and (176) follows:
% 22.63/6.31 | (947) succ(n2) = all_0_5_5
% 22.63/6.31 |
% 22.63/6.31 | From (946) and (59) follows:
% 22.63/6.31 | (948) sum(n2, all_0_1_1) = all_0_0_0
% 22.63/6.31 |
% 22.63/6.31 | From (946) and (2250) follows:
% 22.63/6.31 | (2425) sum(n12, n2) = all_0_2_2
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (219) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 22.63/6.31 | (950) all_0_5_5 = n3
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (89) with n12, n2, all_0_2_2, n14 and discharging atoms sum(n12, n2) = all_0_2_2, sum(n12, n2) = n14, yields:
% 22.63/6.31 | (447) all_0_2_2 = n14
% 22.63/6.31 |
% 22.63/6.31 | From (447) and (187) follows:
% 22.63/6.31 | (449) pred(n14) = all_0_1_1
% 22.63/6.31 |
% 22.63/6.31 | From (950) and (2249) follows:
% 22.63/6.31 | (2429) sum(n12, n3) = all_0_4_4
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (37) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 22.63/6.31 | (452) all_0_1_1 = n13
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (89) with n12, n3, all_0_4_4, n15 and discharging atoms sum(n12, n3) = all_0_4_4, sum(n12, n3) = n15, yields:
% 22.63/6.31 | (448) all_0_4_4 = n15
% 22.63/6.31 |
% 22.63/6.31 | From (448) and (396) follows:
% 22.63/6.31 | (450) pred(n15) = all_0_3_3
% 22.63/6.31 |
% 22.63/6.31 | From (452) and (948) follows:
% 22.63/6.31 | (2433) sum(n2, n13) = all_0_0_0
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (37) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 22.63/6.31 | (451) all_0_3_3 = n14
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (89) with n2, n13, all_0_0_0, n15 and discharging atoms sum(n2, n13) = all_0_0_0, sum(n2, n13) = n15, yields:
% 22.63/6.31 | (676) all_0_0_0 = n15
% 22.63/6.31 |
% 22.63/6.31 | From (451)(676) and (261) follows:
% 22.63/6.31 | (2436) sum(n14, n15) = all_0_6_6
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (89) with n14, n15, all_0_6_6, n13 and discharging atoms sum(n14, n15) = all_0_6_6, sum(n14, n15) = n13, yields:
% 22.63/6.31 | (998) all_0_6_6 = n13
% 22.63/6.31 |
% 22.63/6.31 | Equations (998) can reduce 130 to:
% 22.63/6.31 | (458) $false
% 22.63/6.31 |
% 22.63/6.31 |-The branch is then unsatisfiable
% 22.63/6.31 |-Branch two:
% 22.63/6.31 | (963) ~ (all_0_7_7 = n2)
% 22.63/6.31 | (964) all_0_7_7 = n1 | all_0_7_7 = n0
% 22.63/6.31 |
% 22.63/6.31 +-Applying beta-rule and splitting (964), into two cases.
% 22.63/6.31 |-Branch one:
% 22.63/6.31 | (965) all_0_7_7 = n1
% 22.63/6.31 |
% 22.63/6.31 | From (965) and (176) follows:
% 22.63/6.31 | (966) succ(n1) = all_0_5_5
% 22.63/6.31 |
% 22.63/6.31 | From (965) and (59) follows:
% 22.63/6.31 | (967) sum(n1, all_0_1_1) = all_0_0_0
% 22.63/6.31 |
% 22.63/6.31 | From (965) and (2250) follows:
% 22.63/6.31 | (2444) sum(n12, n1) = all_0_2_2
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (219) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 22.63/6.31 | (969) all_0_5_5 = n2
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (89) with n12, n1, all_0_2_2, n13 and discharging atoms sum(n12, n1) = all_0_2_2, sum(n12, n1) = n13, yields:
% 22.63/6.31 | (464) all_0_2_2 = n13
% 22.63/6.31 |
% 22.63/6.31 | From (464) and (187) follows:
% 22.63/6.31 | (466) pred(n13) = all_0_1_1
% 22.63/6.31 |
% 22.63/6.31 | From (969) and (2249) follows:
% 22.63/6.31 | (2448) sum(n12, n2) = all_0_4_4
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (37) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 22.63/6.31 | (469) all_0_1_1 = n12
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (89) with n12, n2, all_0_4_4, n14 and discharging atoms sum(n12, n2) = all_0_4_4, sum(n12, n2) = n14, yields:
% 22.63/6.31 | (465) all_0_4_4 = n14
% 22.63/6.31 |
% 22.63/6.31 | From (465) and (396) follows:
% 22.63/6.31 | (467) pred(n14) = all_0_3_3
% 22.63/6.31 |
% 22.63/6.31 | From (469) and (967) follows:
% 22.63/6.31 | (2452) sum(n1, n12) = all_0_0_0
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (37) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 22.63/6.31 | (468) all_0_3_3 = n13
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (89) with n1, n12, all_0_0_0, n13 and discharging atoms sum(n1, n12) = all_0_0_0, sum(n1, n12) = n13, yields:
% 22.63/6.31 | (709) all_0_0_0 = n13
% 22.63/6.31 |
% 22.63/6.31 | From (468)(709) and (261) follows:
% 22.63/6.31 | (2455) sum(n13, n13) = all_0_6_6
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (89) with n13, n13, all_0_6_6, n10 and discharging atoms sum(n13, n13) = all_0_6_6, sum(n13, n13) = n10, yields:
% 22.63/6.31 | (457) all_0_6_6 = n10
% 22.63/6.31 |
% 22.63/6.31 | Equations (457) can reduce 169 to:
% 22.63/6.31 | (458) $false
% 22.63/6.31 |
% 22.63/6.31 |-The branch is then unsatisfiable
% 22.63/6.31 |-Branch two:
% 22.63/6.31 | (982) ~ (all_0_7_7 = n1)
% 22.63/6.31 | (983) all_0_7_7 = n0
% 22.63/6.31 |
% 22.63/6.31 | From (983) and (176) follows:
% 22.63/6.31 | (984) succ(n0) = all_0_5_5
% 22.63/6.31 |
% 22.63/6.31 | From (983) and (59) follows:
% 22.63/6.31 | (985) sum(n0, all_0_1_1) = all_0_0_0
% 22.63/6.31 |
% 22.63/6.31 | From (983) and (2250) follows:
% 22.63/6.31 | (2462) sum(n12, n0) = all_0_2_2
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (219) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 22.63/6.31 | (987) all_0_5_5 = n1
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (89) with n12, n0, all_0_2_2, n12 and discharging atoms sum(n12, n0) = all_0_2_2, sum(n12, n0) = n12, yields:
% 22.63/6.31 | (481) all_0_2_2 = n12
% 22.63/6.31 |
% 22.63/6.31 | From (481) and (187) follows:
% 22.63/6.31 | (483) pred(n12) = all_0_1_1
% 22.63/6.31 |
% 22.63/6.31 | From (987) and (2249) follows:
% 22.63/6.31 | (2466) sum(n12, n1) = all_0_4_4
% 22.63/6.31 |
% 22.63/6.31 | Instantiating formula (37) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 22.63/6.32 | (486) all_0_1_1 = n11
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n12, n1, all_0_4_4, n13 and discharging atoms sum(n12, n1) = all_0_4_4, sum(n12, n1) = n13, yields:
% 22.63/6.32 | (482) all_0_4_4 = n13
% 22.63/6.32 |
% 22.63/6.32 | From (482) and (396) follows:
% 22.63/6.32 | (484) pred(n13) = all_0_3_3
% 22.63/6.32 |
% 22.63/6.32 | From (486) and (985) follows:
% 22.63/6.32 | (2470) sum(n0, n11) = all_0_0_0
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (37) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 22.63/6.32 | (485) all_0_3_3 = n12
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n0, n11, all_0_0_0, n11 and discharging atoms sum(n0, n11) = all_0_0_0, sum(n0, n11) = n11, yields:
% 22.63/6.32 | (472) all_0_0_0 = n11
% 22.63/6.32 |
% 22.63/6.32 | From (485)(472) and (261) follows:
% 22.63/6.32 | (2473) sum(n12, n11) = all_0_6_6
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n12, n11, all_0_6_6, n7 and discharging atoms sum(n12, n11) = all_0_6_6, sum(n12, n11) = n7, yields:
% 22.63/6.32 | (733) all_0_6_6 = n7
% 22.63/6.32 |
% 22.63/6.32 | Equations (733) can reduce 274 to:
% 22.63/6.32 | (458) $false
% 22.63/6.32 |
% 22.63/6.32 |-The branch is then unsatisfiable
% 22.63/6.32 |-Branch two:
% 22.63/6.32 | (510) ~ (all_0_8_8 = n12)
% 22.63/6.32 | (511) all_0_8_8 = n11 | all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.63/6.32 |
% 22.63/6.32 +-Applying beta-rule and splitting (774), into two cases.
% 22.63/6.32 |-Branch one:
% 22.63/6.32 | (775) all_0_7_7 = n11
% 22.63/6.32 |
% 22.63/6.32 | From (775) and (176) follows:
% 22.63/6.32 | (776) succ(n11) = all_0_5_5
% 22.63/6.32 |
% 22.63/6.32 | From (775) and (59) follows:
% 22.63/6.32 | (777) sum(n11, all_0_1_1) = all_0_0_0
% 22.63/6.32 |
% 22.63/6.32 | From (775) and (160) follows:
% 22.63/6.32 | (2481) sum(all_0_8_8, n11) = all_0_2_2
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (219) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 22.63/6.32 | (779) all_0_5_5 = n12
% 22.63/6.32 |
% 22.63/6.32 | From (779) and (64) follows:
% 22.63/6.32 | (2483) sum(all_0_8_8, n12) = all_0_4_4
% 22.63/6.32 |
% 22.63/6.32 +-Applying beta-rule and splitting (511), into two cases.
% 22.63/6.32 |-Branch one:
% 22.63/6.32 | (512) all_0_8_8 = n11
% 22.63/6.32 |
% 22.63/6.32 | From (512) and (2483) follows:
% 22.63/6.32 | (2485) sum(n11, n12) = all_0_4_4
% 22.63/6.32 |
% 22.63/6.32 | From (512) and (2481) follows:
% 22.63/6.32 | (2486) sum(n11, n11) = all_0_2_2
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n11, n12, all_0_4_4, n7 and discharging atoms sum(n11, n12) = all_0_4_4, sum(n11, n12) = n7, yields:
% 22.63/6.32 | (584) all_0_4_4 = n7
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n11, n11, all_0_2_2, n6 and discharging atoms sum(n11, n11) = all_0_2_2, sum(n11, n11) = n6, yields:
% 22.63/6.32 | (583) all_0_2_2 = n6
% 22.63/6.32 |
% 22.63/6.32 | From (583) and (187) follows:
% 22.63/6.32 | (585) pred(n6) = all_0_1_1
% 22.63/6.32 |
% 22.63/6.32 | From (584) and (396) follows:
% 22.63/6.32 | (586) pred(n7) = all_0_3_3
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (37) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 22.63/6.32 | (587) all_0_3_3 = n6
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (37) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 22.63/6.32 | (588) all_0_1_1 = n5
% 22.63/6.32 |
% 22.63/6.32 | From (587) and (261) follows:
% 22.63/6.32 | (589) sum(n6, all_0_0_0) = all_0_6_6
% 22.63/6.32 |
% 22.63/6.32 | From (588) and (777) follows:
% 22.63/6.32 | (2494) sum(n11, n5) = all_0_0_0
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n11, n5, all_0_0_0, n0 and discharging atoms sum(n11, n5) = all_0_0_0, sum(n11, n5) = n0, yields:
% 22.63/6.32 | (659) all_0_0_0 = n0
% 22.63/6.32 |
% 22.63/6.32 | From (659) and (589) follows:
% 22.63/6.32 | (2496) sum(n6, n0) = all_0_6_6
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n6, n0, all_0_6_6, n6 and discharging atoms sum(n6, n0) = all_0_6_6, sum(n6, n0) = n6, yields:
% 22.63/6.32 | (491) all_0_6_6 = n6
% 22.63/6.32 |
% 22.63/6.32 | Equations (491) can reduce 418 to:
% 22.63/6.32 | (458) $false
% 22.63/6.32 |
% 22.63/6.32 |-The branch is then unsatisfiable
% 22.63/6.32 |-Branch two:
% 22.63/6.32 | (527) ~ (all_0_8_8 = n11)
% 22.63/6.32 | (528) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.63/6.32 |
% 22.63/6.32 +-Applying beta-rule and splitting (528), into two cases.
% 22.63/6.32 |-Branch one:
% 22.63/6.32 | (529) all_0_8_8 = n10
% 22.63/6.32 |
% 22.63/6.32 | From (529) and (2483) follows:
% 22.63/6.32 | (2502) sum(n10, n12) = all_0_4_4
% 22.63/6.32 |
% 22.63/6.32 | From (529) and (2481) follows:
% 22.63/6.32 | (2503) sum(n10, n11) = all_0_2_2
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n10, n12, all_0_4_4, n6 and discharging atoms sum(n10, n12) = all_0_4_4, sum(n10, n12) = n6, yields:
% 22.63/6.32 | (601) all_0_4_4 = n6
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n10, n11, all_0_2_2, n5 and discharging atoms sum(n10, n11) = all_0_2_2, sum(n10, n11) = n5, yields:
% 22.63/6.32 | (600) all_0_2_2 = n5
% 22.63/6.32 |
% 22.63/6.32 | From (600) and (187) follows:
% 22.63/6.32 | (602) pred(n5) = all_0_1_1
% 22.63/6.32 |
% 22.63/6.32 | From (601) and (396) follows:
% 22.63/6.32 | (603) pred(n6) = all_0_3_3
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (37) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 22.63/6.32 | (604) all_0_3_3 = n5
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (37) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 22.63/6.32 | (605) all_0_1_1 = n4
% 22.63/6.32 |
% 22.63/6.32 | From (604) and (261) follows:
% 22.63/6.32 | (606) sum(n5, all_0_0_0) = all_0_6_6
% 22.63/6.32 |
% 22.63/6.32 | From (605) and (777) follows:
% 22.63/6.32 | (2511) sum(n11, n4) = all_0_0_0
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n11, n4, all_0_0_0, n15 and discharging atoms sum(n11, n4) = all_0_0_0, sum(n11, n4) = n15, yields:
% 22.63/6.32 | (676) all_0_0_0 = n15
% 22.63/6.32 |
% 22.63/6.32 | From (676) and (606) follows:
% 22.63/6.32 | (2513) sum(n5, n15) = all_0_6_6
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n5, n15, all_0_6_6, n4 and discharging atoms sum(n5, n15) = all_0_6_6, sum(n5, n15) = n4, yields:
% 22.63/6.32 | (508) all_0_6_6 = n4
% 22.63/6.32 |
% 22.63/6.32 | Equations (508) can reduce 12 to:
% 22.63/6.32 | (458) $false
% 22.63/6.32 |
% 22.63/6.32 |-The branch is then unsatisfiable
% 22.63/6.32 |-Branch two:
% 22.63/6.32 | (544) ~ (all_0_8_8 = n10)
% 22.63/6.32 | (545) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.63/6.32 |
% 22.63/6.32 +-Applying beta-rule and splitting (545), into two cases.
% 22.63/6.32 |-Branch one:
% 22.63/6.32 | (546) all_0_8_8 = n9
% 22.63/6.32 |
% 22.63/6.32 | From (546) and (2483) follows:
% 22.63/6.32 | (2519) sum(n9, n12) = all_0_4_4
% 22.63/6.32 |
% 22.63/6.32 | From (546) and (2481) follows:
% 22.63/6.32 | (2520) sum(n9, n11) = all_0_2_2
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n9, n12, all_0_4_4, n5 and discharging atoms sum(n9, n12) = all_0_4_4, sum(n9, n12) = n5, yields:
% 22.63/6.32 | (618) all_0_4_4 = n5
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n9, n11, all_0_2_2, n4 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n4, yields:
% 22.63/6.32 | (617) all_0_2_2 = n4
% 22.63/6.32 |
% 22.63/6.32 | From (617) and (187) follows:
% 22.63/6.32 | (619) pred(n4) = all_0_1_1
% 22.63/6.32 |
% 22.63/6.32 | From (618) and (396) follows:
% 22.63/6.32 | (620) pred(n5) = all_0_3_3
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (37) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 22.63/6.32 | (621) all_0_3_3 = n4
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (37) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 22.63/6.32 | (622) all_0_1_1 = n3
% 22.63/6.32 |
% 22.63/6.32 | From (621) and (261) follows:
% 22.63/6.32 | (623) sum(n4, all_0_0_0) = all_0_6_6
% 22.63/6.32 |
% 22.63/6.32 | From (622) and (777) follows:
% 22.63/6.32 | (2528) sum(n11, n3) = all_0_0_0
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n11, n3, all_0_0_0, n14 and discharging atoms sum(n11, n3) = all_0_0_0, sum(n11, n3) = n14, yields:
% 22.63/6.32 | (693) all_0_0_0 = n14
% 22.63/6.32 |
% 22.63/6.32 | From (693) and (623) follows:
% 22.63/6.32 | (2530) sum(n4, n14) = all_0_6_6
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n4, n14, all_0_6_6, n2 and discharging atoms sum(n4, n14) = all_0_6_6, sum(n4, n14) = n2, yields:
% 22.63/6.32 | (525) all_0_6_6 = n2
% 22.63/6.32 |
% 22.63/6.32 | Equations (525) can reduce 231 to:
% 22.63/6.32 | (458) $false
% 22.63/6.32 |
% 22.63/6.32 |-The branch is then unsatisfiable
% 22.63/6.32 |-Branch two:
% 22.63/6.32 | (561) ~ (all_0_8_8 = n9)
% 22.63/6.32 | (562) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.63/6.32 |
% 22.63/6.32 +-Applying beta-rule and splitting (562), into two cases.
% 22.63/6.32 |-Branch one:
% 22.63/6.32 | (563) all_0_8_8 = n8
% 22.63/6.32 |
% 22.63/6.32 | From (563) and (2483) follows:
% 22.63/6.32 | (2536) sum(n8, n12) = all_0_4_4
% 22.63/6.32 |
% 22.63/6.32 | From (563) and (2481) follows:
% 22.63/6.32 | (2537) sum(n8, n11) = all_0_2_2
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n8, n12, all_0_4_4, n4 and discharging atoms sum(n8, n12) = all_0_4_4, sum(n8, n12) = n4, yields:
% 22.63/6.32 | (635) all_0_4_4 = n4
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n8, n11, all_0_2_2, n3 and discharging atoms sum(n8, n11) = all_0_2_2, sum(n8, n11) = n3, yields:
% 22.63/6.32 | (634) all_0_2_2 = n3
% 22.63/6.32 |
% 22.63/6.32 | From (634) and (187) follows:
% 22.63/6.32 | (636) pred(n3) = all_0_1_1
% 22.63/6.32 |
% 22.63/6.32 | From (635) and (396) follows:
% 22.63/6.32 | (637) pred(n4) = all_0_3_3
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (37) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 22.63/6.32 | (638) all_0_3_3 = n3
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (37) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 22.63/6.32 | (639) all_0_1_1 = n2
% 22.63/6.32 |
% 22.63/6.32 | From (638) and (261) follows:
% 22.63/6.32 | (640) sum(n3, all_0_0_0) = all_0_6_6
% 22.63/6.32 |
% 22.63/6.32 | From (639) and (777) follows:
% 22.63/6.32 | (2545) sum(n11, n2) = all_0_0_0
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n11, n2, all_0_0_0, n13 and discharging atoms sum(n11, n2) = all_0_0_0, sum(n11, n2) = n13, yields:
% 22.63/6.32 | (709) all_0_0_0 = n13
% 22.63/6.32 |
% 22.63/6.32 | From (709) and (640) follows:
% 22.63/6.32 | (2547) sum(n3, n13) = all_0_6_6
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n3, n13, all_0_6_6, n0 and discharging atoms sum(n3, n13) = all_0_6_6, sum(n3, n13) = n0, yields:
% 22.63/6.32 | (542) all_0_6_6 = n0
% 22.63/6.32 |
% 22.63/6.32 | Equations (542) can reduce 400 to:
% 22.63/6.32 | (458) $false
% 22.63/6.32 |
% 22.63/6.32 |-The branch is then unsatisfiable
% 22.63/6.32 |-Branch two:
% 22.63/6.32 | (578) ~ (all_0_8_8 = n8)
% 22.63/6.32 | (579) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.63/6.32 |
% 22.63/6.32 +-Applying beta-rule and splitting (579), into two cases.
% 22.63/6.32 |-Branch one:
% 22.63/6.32 | (580) all_0_8_8 = n7
% 22.63/6.32 |
% 22.63/6.32 | From (580) and (2483) follows:
% 22.63/6.32 | (2553) sum(n7, n12) = all_0_4_4
% 22.63/6.32 |
% 22.63/6.32 | From (580) and (2481) follows:
% 22.63/6.32 | (2554) sum(n7, n11) = all_0_2_2
% 22.63/6.32 |
% 22.63/6.32 | Instantiating formula (89) with n7, n12, all_0_4_4, n3 and discharging atoms sum(n7, n12) = all_0_4_4, sum(n7, n12) = n3, yields:
% 22.63/6.33 | (652) all_0_4_4 = n3
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n7, n11, all_0_2_2, n2 and discharging atoms sum(n7, n11) = all_0_2_2, sum(n7, n11) = n2, yields:
% 22.63/6.33 | (651) all_0_2_2 = n2
% 22.63/6.33 |
% 22.63/6.33 | From (651) and (187) follows:
% 22.63/6.33 | (653) pred(n2) = all_0_1_1
% 22.63/6.33 |
% 22.63/6.33 | From (652) and (396) follows:
% 22.63/6.33 | (654) pred(n3) = all_0_3_3
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (37) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 22.63/6.33 | (655) all_0_3_3 = n2
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (37) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 22.63/6.33 | (656) all_0_1_1 = n1
% 22.63/6.33 |
% 22.63/6.33 | From (655) and (261) follows:
% 22.63/6.33 | (657) sum(n2, all_0_0_0) = all_0_6_6
% 22.63/6.33 |
% 22.63/6.33 | From (656) and (777) follows:
% 22.63/6.33 | (2562) sum(n11, n1) = all_0_0_0
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n11, n1, all_0_0_0, n12 and discharging atoms sum(n11, n1) = all_0_0_0, sum(n11, n1) = n12, yields:
% 22.63/6.33 | (455) all_0_0_0 = n12
% 22.63/6.33 |
% 22.63/6.33 | From (455) and (657) follows:
% 22.63/6.33 | (2564) sum(n2, n12) = all_0_6_6
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n2, n12, all_0_6_6, n14 and discharging atoms sum(n2, n12) = all_0_6_6, sum(n2, n12) = n14, yields:
% 22.63/6.33 | (559) all_0_6_6 = n14
% 22.63/6.33 |
% 22.63/6.33 | Equations (559) can reduce 314 to:
% 22.63/6.33 | (458) $false
% 22.63/6.33 |
% 22.63/6.33 |-The branch is then unsatisfiable
% 22.63/6.33 |-Branch two:
% 22.63/6.33 | (595) ~ (all_0_8_8 = n7)
% 22.63/6.33 | (596) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.63/6.33 |
% 22.63/6.33 +-Applying beta-rule and splitting (596), into two cases.
% 22.63/6.33 |-Branch one:
% 22.63/6.33 | (597) all_0_8_8 = n6
% 22.63/6.33 |
% 22.63/6.33 | From (597) and (2483) follows:
% 22.63/6.33 | (2570) sum(n6, n12) = all_0_4_4
% 22.63/6.33 |
% 22.63/6.33 | From (597) and (2481) follows:
% 22.63/6.33 | (2571) sum(n6, n11) = all_0_2_2
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n6, n12, all_0_4_4, n2 and discharging atoms sum(n6, n12) = all_0_4_4, sum(n6, n12) = n2, yields:
% 22.63/6.33 | (669) all_0_4_4 = n2
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n6, n11, all_0_2_2, n1 and discharging atoms sum(n6, n11) = all_0_2_2, sum(n6, n11) = n1, yields:
% 22.63/6.33 | (668) all_0_2_2 = n1
% 22.63/6.33 |
% 22.63/6.33 | From (668) and (187) follows:
% 22.63/6.33 | (670) pred(n1) = all_0_1_1
% 22.63/6.33 |
% 22.63/6.33 | From (669) and (396) follows:
% 22.63/6.33 | (671) pred(n2) = all_0_3_3
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (37) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 22.63/6.33 | (672) all_0_3_3 = n1
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (37) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 22.63/6.33 | (673) all_0_1_1 = n0
% 22.63/6.33 |
% 22.63/6.33 | From (672) and (261) follows:
% 22.63/6.33 | (674) sum(n1, all_0_0_0) = all_0_6_6
% 22.63/6.33 |
% 22.63/6.33 | From (673) and (777) follows:
% 22.63/6.33 | (2579) sum(n11, n0) = all_0_0_0
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n11, n0, all_0_0_0, n11 and discharging atoms sum(n11, n0) = all_0_0_0, sum(n11, n0) = n11, yields:
% 22.63/6.33 | (472) all_0_0_0 = n11
% 22.63/6.33 |
% 22.63/6.33 | From (472) and (674) follows:
% 22.63/6.33 | (2581) sum(n1, n11) = all_0_6_6
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n1, n11, all_0_6_6, n12 and discharging atoms sum(n1, n11) = all_0_6_6, sum(n1, n11) = n12, yields:
% 22.63/6.33 | (576) all_0_6_6 = n12
% 22.63/6.33 |
% 22.63/6.33 | Equations (576) can reduce 42 to:
% 22.63/6.33 | (458) $false
% 22.63/6.33 |
% 22.63/6.33 |-The branch is then unsatisfiable
% 22.63/6.33 |-Branch two:
% 22.63/6.33 | (612) ~ (all_0_8_8 = n6)
% 22.63/6.33 | (613) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.63/6.33 |
% 22.63/6.33 +-Applying beta-rule and splitting (613), into two cases.
% 22.63/6.33 |-Branch one:
% 22.63/6.33 | (614) all_0_8_8 = n5
% 22.63/6.33 |
% 22.63/6.33 | From (614) and (2483) follows:
% 22.63/6.33 | (2587) sum(n5, n12) = all_0_4_4
% 22.63/6.33 |
% 22.63/6.33 | From (614) and (2481) follows:
% 22.63/6.33 | (2588) sum(n5, n11) = all_0_2_2
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n5, n12, all_0_4_4, n1 and discharging atoms sum(n5, n12) = all_0_4_4, sum(n5, n12) = n1, yields:
% 22.63/6.33 | (686) all_0_4_4 = n1
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n5, n11, all_0_2_2, n0 and discharging atoms sum(n5, n11) = all_0_2_2, sum(n5, n11) = n0, yields:
% 22.63/6.33 | (685) all_0_2_2 = n0
% 22.63/6.33 |
% 22.63/6.33 | From (685) and (187) follows:
% 22.63/6.33 | (687) pred(n0) = all_0_1_1
% 22.63/6.33 |
% 22.63/6.33 | From (686) and (396) follows:
% 22.63/6.33 | (688) pred(n1) = all_0_3_3
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (37) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 22.63/6.33 | (689) all_0_3_3 = n0
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (37) with n0, all_0_1_1, n15 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n15, yields:
% 22.63/6.33 | (690) all_0_1_1 = n15
% 22.63/6.33 |
% 22.63/6.33 | From (689) and (261) follows:
% 22.63/6.33 | (691) sum(n0, all_0_0_0) = all_0_6_6
% 22.63/6.33 |
% 22.63/6.33 | From (690) and (777) follows:
% 22.63/6.33 | (2596) sum(n11, n15) = all_0_0_0
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n11, n15, all_0_0_0, n10 and discharging atoms sum(n11, n15) = all_0_0_0, sum(n11, n15) = n10, yields:
% 22.63/6.33 | (489) all_0_0_0 = n10
% 22.63/6.33 |
% 22.63/6.33 | From (489) and (691) follows:
% 22.63/6.33 | (2598) sum(n0, n10) = all_0_6_6
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n0, n10, all_0_6_6, n10 and discharging atoms sum(n0, n10) = all_0_6_6, sum(n0, n10) = n10, yields:
% 22.63/6.33 | (457) all_0_6_6 = n10
% 22.63/6.33 |
% 22.63/6.33 | Equations (457) can reduce 169 to:
% 22.63/6.33 | (458) $false
% 22.63/6.33 |
% 22.63/6.33 |-The branch is then unsatisfiable
% 22.63/6.33 |-Branch two:
% 22.63/6.33 | (629) ~ (all_0_8_8 = n5)
% 22.63/6.33 | (630) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.63/6.33 |
% 22.63/6.33 +-Applying beta-rule and splitting (630), into two cases.
% 22.63/6.33 |-Branch one:
% 22.63/6.33 | (631) all_0_8_8 = n4
% 22.63/6.33 |
% 22.63/6.33 | From (631) and (2483) follows:
% 22.63/6.33 | (2604) sum(n4, n12) = all_0_4_4
% 22.63/6.33 |
% 22.63/6.33 | From (631) and (2481) follows:
% 22.63/6.33 | (2605) sum(n4, n11) = all_0_2_2
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n4, n12, all_0_4_4, n0 and discharging atoms sum(n4, n12) = all_0_4_4, sum(n4, n12) = n0, yields:
% 22.63/6.33 | (702) all_0_4_4 = n0
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n4, n11, all_0_2_2, n15 and discharging atoms sum(n4, n11) = all_0_2_2, sum(n4, n11) = n15, yields:
% 22.63/6.33 | (701) all_0_2_2 = n15
% 22.63/6.33 |
% 22.63/6.33 | From (701) and (187) follows:
% 22.63/6.33 | (703) pred(n15) = all_0_1_1
% 22.63/6.33 |
% 22.63/6.33 | From (702) and (396) follows:
% 22.63/6.33 | (704) pred(n0) = all_0_3_3
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (37) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 22.63/6.33 | (705) all_0_1_1 = n14
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (37) with n0, all_0_3_3, n15 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n15, yields:
% 22.63/6.33 | (706) all_0_3_3 = n15
% 22.63/6.33 |
% 22.63/6.33 | From (706) and (261) follows:
% 22.63/6.33 | (707) sum(n15, all_0_0_0) = all_0_6_6
% 22.63/6.33 |
% 22.63/6.33 | From (705) and (777) follows:
% 22.63/6.33 | (2613) sum(n11, n14) = all_0_0_0
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n11, n14, all_0_0_0, n9 and discharging atoms sum(n11, n14) = all_0_0_0, sum(n11, n14) = n9, yields:
% 22.63/6.33 | (506) all_0_0_0 = n9
% 22.63/6.33 |
% 22.63/6.33 | From (506) and (707) follows:
% 22.63/6.33 | (2615) sum(n15, n9) = all_0_6_6
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n15, n9, all_0_6_6, n8 and discharging atoms sum(n15, n9) = all_0_6_6, sum(n15, n9) = n8, yields:
% 22.63/6.33 | (474) all_0_6_6 = n8
% 22.63/6.33 |
% 22.63/6.33 | Equations (474) can reduce 86 to:
% 22.63/6.33 | (458) $false
% 22.63/6.33 |
% 22.63/6.33 |-The branch is then unsatisfiable
% 22.63/6.33 |-Branch two:
% 22.63/6.33 | (646) ~ (all_0_8_8 = n4)
% 22.63/6.33 | (647) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.63/6.33 |
% 22.63/6.33 +-Applying beta-rule and splitting (647), into two cases.
% 22.63/6.33 |-Branch one:
% 22.63/6.33 | (648) all_0_8_8 = n3
% 22.63/6.33 |
% 22.63/6.33 | From (648) and (2483) follows:
% 22.63/6.33 | (2621) sum(n3, n12) = all_0_4_4
% 22.63/6.33 |
% 22.63/6.33 | From (648) and (2481) follows:
% 22.63/6.33 | (2622) sum(n3, n11) = all_0_2_2
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n3, n12, all_0_4_4, n15 and discharging atoms sum(n3, n12) = all_0_4_4, sum(n3, n12) = n15, yields:
% 22.63/6.33 | (448) all_0_4_4 = n15
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n3, n11, all_0_2_2, n14 and discharging atoms sum(n3, n11) = all_0_2_2, sum(n3, n11) = n14, yields:
% 22.63/6.33 | (447) all_0_2_2 = n14
% 22.63/6.33 |
% 22.63/6.33 | From (447) and (187) follows:
% 22.63/6.33 | (449) pred(n14) = all_0_1_1
% 22.63/6.33 |
% 22.63/6.33 | From (448) and (396) follows:
% 22.63/6.33 | (450) pred(n15) = all_0_3_3
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (37) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 22.63/6.33 | (451) all_0_3_3 = n14
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (37) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 22.63/6.33 | (452) all_0_1_1 = n13
% 22.63/6.33 |
% 22.63/6.33 | From (451) and (261) follows:
% 22.63/6.33 | (453) sum(n14, all_0_0_0) = all_0_6_6
% 22.63/6.33 |
% 22.63/6.33 | From (452) and (777) follows:
% 22.63/6.33 | (2630) sum(n11, n13) = all_0_0_0
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n11, n13, all_0_0_0, n8 and discharging atoms sum(n11, n13) = all_0_0_0, sum(n11, n13) = n8, yields:
% 22.63/6.33 | (523) all_0_0_0 = n8
% 22.63/6.33 |
% 22.63/6.33 | From (523) and (453) follows:
% 22.63/6.33 | (2632) sum(n14, n8) = all_0_6_6
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n14, n8, all_0_6_6, n6 and discharging atoms sum(n14, n8) = all_0_6_6, sum(n14, n8) = n6, yields:
% 22.63/6.33 | (491) all_0_6_6 = n6
% 22.63/6.33 |
% 22.63/6.33 | Equations (491) can reduce 418 to:
% 22.63/6.33 | (458) $false
% 22.63/6.33 |
% 22.63/6.33 |-The branch is then unsatisfiable
% 22.63/6.33 |-Branch two:
% 22.63/6.33 | (663) ~ (all_0_8_8 = n3)
% 22.63/6.33 | (664) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.63/6.33 |
% 22.63/6.33 +-Applying beta-rule and splitting (664), into two cases.
% 22.63/6.33 |-Branch one:
% 22.63/6.33 | (665) all_0_8_8 = n2
% 22.63/6.33 |
% 22.63/6.33 | From (665) and (2483) follows:
% 22.63/6.33 | (2638) sum(n2, n12) = all_0_4_4
% 22.63/6.33 |
% 22.63/6.33 | From (665) and (2481) follows:
% 22.63/6.33 | (2639) sum(n2, n11) = all_0_2_2
% 22.63/6.33 |
% 22.63/6.33 | Instantiating formula (89) with n2, n12, all_0_4_4, n14 and discharging atoms sum(n2, n12) = all_0_4_4, sum(n2, n12) = n14, yields:
% 22.63/6.34 | (465) all_0_4_4 = n14
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n2, n11, all_0_2_2, n13 and discharging atoms sum(n2, n11) = all_0_2_2, sum(n2, n11) = n13, yields:
% 22.63/6.34 | (464) all_0_2_2 = n13
% 22.63/6.34 |
% 22.63/6.34 | From (464) and (187) follows:
% 22.63/6.34 | (466) pred(n13) = all_0_1_1
% 22.63/6.34 |
% 22.63/6.34 | From (465) and (396) follows:
% 22.63/6.34 | (467) pred(n14) = all_0_3_3
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (37) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 22.63/6.34 | (468) all_0_3_3 = n13
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (37) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 22.63/6.34 | (469) all_0_1_1 = n12
% 22.63/6.34 |
% 22.63/6.34 | From (468) and (261) follows:
% 22.63/6.34 | (470) sum(n13, all_0_0_0) = all_0_6_6
% 22.63/6.34 |
% 22.63/6.34 | From (469) and (777) follows:
% 22.63/6.34 | (2647) sum(n11, n12) = all_0_0_0
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n11, n12, all_0_0_0, n7 and discharging atoms sum(n11, n12) = all_0_0_0, sum(n11, n12) = n7, yields:
% 22.63/6.34 | (540) all_0_0_0 = n7
% 22.63/6.34 |
% 22.63/6.34 | From (540) and (470) follows:
% 22.63/6.34 | (2649) sum(n13, n7) = all_0_6_6
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n13, n7, all_0_6_6, n4 and discharging atoms sum(n13, n7) = all_0_6_6, sum(n13, n7) = n4, yields:
% 22.63/6.34 | (508) all_0_6_6 = n4
% 22.63/6.34 |
% 22.63/6.34 | Equations (508) can reduce 12 to:
% 22.63/6.34 | (458) $false
% 22.63/6.34 |
% 22.63/6.34 |-The branch is then unsatisfiable
% 22.63/6.34 |-Branch two:
% 22.63/6.34 | (680) ~ (all_0_8_8 = n2)
% 22.63/6.34 | (681) all_0_8_8 = n1 | all_0_8_8 = n0
% 22.63/6.34 |
% 22.63/6.34 +-Applying beta-rule and splitting (681), into two cases.
% 22.63/6.34 |-Branch one:
% 22.63/6.34 | (682) all_0_8_8 = n1
% 22.63/6.34 |
% 22.63/6.34 | From (682) and (2483) follows:
% 22.63/6.34 | (2655) sum(n1, n12) = all_0_4_4
% 22.63/6.34 |
% 22.63/6.34 | From (682) and (2481) follows:
% 22.63/6.34 | (2656) sum(n1, n11) = all_0_2_2
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n1, n12, all_0_4_4, n13 and discharging atoms sum(n1, n12) = all_0_4_4, sum(n1, n12) = n13, yields:
% 22.63/6.34 | (482) all_0_4_4 = n13
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n1, n11, all_0_2_2, n12 and discharging atoms sum(n1, n11) = all_0_2_2, sum(n1, n11) = n12, yields:
% 22.63/6.34 | (481) all_0_2_2 = n12
% 22.63/6.34 |
% 22.63/6.34 | From (481) and (187) follows:
% 22.63/6.34 | (483) pred(n12) = all_0_1_1
% 22.63/6.34 |
% 22.63/6.34 | From (482) and (396) follows:
% 22.63/6.34 | (484) pred(n13) = all_0_3_3
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (37) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 22.63/6.34 | (485) all_0_3_3 = n12
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (37) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 22.63/6.34 | (486) all_0_1_1 = n11
% 22.63/6.34 |
% 22.63/6.34 | From (485) and (261) follows:
% 22.63/6.34 | (487) sum(n12, all_0_0_0) = all_0_6_6
% 22.63/6.34 |
% 22.63/6.34 | From (486) and (777) follows:
% 22.63/6.34 | (2664) sum(n11, n11) = all_0_0_0
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n11, n11, all_0_0_0, n6 and discharging atoms sum(n11, n11) = all_0_0_0, sum(n11, n11) = n6, yields:
% 22.63/6.34 | (557) all_0_0_0 = n6
% 22.63/6.34 |
% 22.63/6.34 | From (557) and (487) follows:
% 22.63/6.34 | (2666) sum(n12, n6) = all_0_6_6
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n12, n6, all_0_6_6, n2 and discharging atoms sum(n12, n6) = all_0_6_6, sum(n12, n6) = n2, yields:
% 22.63/6.34 | (525) all_0_6_6 = n2
% 22.63/6.34 |
% 22.63/6.34 | Equations (525) can reduce 231 to:
% 22.63/6.34 | (458) $false
% 22.63/6.34 |
% 22.63/6.34 |-The branch is then unsatisfiable
% 22.63/6.34 |-Branch two:
% 22.63/6.34 | (697) ~ (all_0_8_8 = n1)
% 22.63/6.34 | (698) all_0_8_8 = n0
% 22.63/6.34 |
% 22.63/6.34 | From (698) and (2483) follows:
% 22.63/6.34 | (2671) sum(n0, n12) = all_0_4_4
% 22.63/6.34 |
% 22.63/6.34 | From (698) and (2481) follows:
% 22.63/6.34 | (2672) sum(n0, n11) = all_0_2_2
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n0, n12, all_0_4_4, n12 and discharging atoms sum(n0, n12) = all_0_4_4, sum(n0, n12) = n12, yields:
% 22.63/6.34 | (499) all_0_4_4 = n12
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n0, n11, all_0_2_2, n11 and discharging atoms sum(n0, n11) = all_0_2_2, sum(n0, n11) = n11, yields:
% 22.63/6.34 | (498) all_0_2_2 = n11
% 22.63/6.34 |
% 22.63/6.34 | From (498) and (187) follows:
% 22.63/6.34 | (500) pred(n11) = all_0_1_1
% 22.63/6.34 |
% 22.63/6.34 | From (499) and (396) follows:
% 22.63/6.34 | (501) pred(n12) = all_0_3_3
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (37) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 22.63/6.34 | (502) all_0_3_3 = n11
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (37) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 22.63/6.34 | (503) all_0_1_1 = n10
% 22.63/6.34 |
% 22.63/6.34 | From (502) and (261) follows:
% 22.63/6.34 | (504) sum(n11, all_0_0_0) = all_0_6_6
% 22.63/6.34 |
% 22.63/6.34 | From (503) and (777) follows:
% 22.63/6.34 | (2680) sum(n11, n10) = all_0_0_0
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n11, n10, all_0_0_0, n5 and discharging atoms sum(n11, n10) = all_0_0_0, sum(n11, n10) = n5, yields:
% 22.63/6.34 | (574) all_0_0_0 = n5
% 22.63/6.34 |
% 22.63/6.34 | From (574) and (504) follows:
% 22.63/6.34 | (2682) sum(n11, n5) = all_0_6_6
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n11, n5, all_0_6_6, n0 and discharging atoms sum(n11, n5) = all_0_6_6, sum(n11, n5) = n0, yields:
% 22.63/6.34 | (542) all_0_6_6 = n0
% 22.63/6.34 |
% 22.63/6.34 | Equations (542) can reduce 400 to:
% 22.63/6.34 | (458) $false
% 22.63/6.34 |
% 22.63/6.34 |-The branch is then unsatisfiable
% 22.63/6.34 |-Branch two:
% 22.63/6.34 | (792) ~ (all_0_7_7 = n11)
% 22.63/6.34 | (793) all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.63/6.34 |
% 22.63/6.34 +-Applying beta-rule and splitting (511), into two cases.
% 22.63/6.34 |-Branch one:
% 22.63/6.34 | (512) all_0_8_8 = n11
% 22.63/6.34 |
% 22.63/6.34 | From (512) and (64) follows:
% 22.63/6.34 | (2688) sum(n11, all_0_5_5) = all_0_4_4
% 22.63/6.34 |
% 22.63/6.34 | From (512) and (160) follows:
% 22.63/6.34 | (2689) sum(n11, all_0_7_7) = all_0_2_2
% 22.63/6.34 |
% 22.63/6.34 +-Applying beta-rule and splitting (793), into two cases.
% 22.63/6.34 |-Branch one:
% 22.63/6.34 | (794) all_0_7_7 = n10
% 22.63/6.34 |
% 22.63/6.34 | From (794) and (176) follows:
% 22.63/6.34 | (795) succ(n10) = all_0_5_5
% 22.63/6.34 |
% 22.63/6.34 | From (794) and (59) follows:
% 22.63/6.34 | (796) sum(n10, all_0_1_1) = all_0_0_0
% 22.63/6.34 |
% 22.63/6.34 | From (794) and (2689) follows:
% 22.63/6.34 | (2693) sum(n11, n10) = all_0_2_2
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (219) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 22.63/6.34 | (798) all_0_5_5 = n11
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n11, n10, all_0_2_2, n5 and discharging atoms sum(n11, n10) = all_0_2_2, sum(n11, n10) = n5, yields:
% 22.63/6.34 | (600) all_0_2_2 = n5
% 22.63/6.34 |
% 22.63/6.34 | From (600) and (187) follows:
% 22.63/6.34 | (602) pred(n5) = all_0_1_1
% 22.63/6.34 |
% 22.63/6.34 | From (798) and (2688) follows:
% 22.63/6.34 | (2697) sum(n11, n11) = all_0_4_4
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (37) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 22.63/6.34 | (605) all_0_1_1 = n4
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n11, n11, all_0_4_4, n6 and discharging atoms sum(n11, n11) = all_0_4_4, sum(n11, n11) = n6, yields:
% 22.63/6.34 | (601) all_0_4_4 = n6
% 22.63/6.34 |
% 22.63/6.34 | From (601) and (396) follows:
% 22.63/6.34 | (603) pred(n6) = all_0_3_3
% 22.63/6.34 |
% 22.63/6.34 | From (605) and (796) follows:
% 22.63/6.34 | (2701) sum(n10, n4) = all_0_0_0
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (37) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 22.63/6.34 | (604) all_0_3_3 = n5
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n10, n4, all_0_0_0, n14 and discharging atoms sum(n10, n4) = all_0_0_0, sum(n10, n4) = n14, yields:
% 22.63/6.34 | (693) all_0_0_0 = n14
% 22.63/6.34 |
% 22.63/6.34 | From (604)(693) and (261) follows:
% 22.63/6.34 | (2704) sum(n5, n14) = all_0_6_6
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n5, n14, all_0_6_6, n3 and discharging atoms sum(n5, n14) = all_0_6_6, sum(n5, n14) = n3, yields:
% 22.63/6.34 | (961) all_0_6_6 = n3
% 22.63/6.34 |
% 22.63/6.34 | Equations (961) can reduce 245 to:
% 22.63/6.34 | (458) $false
% 22.63/6.34 |
% 22.63/6.34 |-The branch is then unsatisfiable
% 22.63/6.34 |-Branch two:
% 22.63/6.34 | (811) ~ (all_0_7_7 = n10)
% 22.63/6.34 | (812) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.63/6.34 |
% 22.63/6.34 +-Applying beta-rule and splitting (812), into two cases.
% 22.63/6.34 |-Branch one:
% 22.63/6.34 | (813) all_0_7_7 = n9
% 22.63/6.34 |
% 22.63/6.34 | From (813) and (176) follows:
% 22.63/6.34 | (814) succ(n9) = all_0_5_5
% 22.63/6.34 |
% 22.63/6.34 | From (813) and (59) follows:
% 22.63/6.34 | (815) sum(n9, all_0_1_1) = all_0_0_0
% 22.63/6.34 |
% 22.63/6.34 | From (813) and (2689) follows:
% 22.63/6.34 | (2712) sum(n11, n9) = all_0_2_2
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (219) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 22.63/6.34 | (817) all_0_5_5 = n10
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n11, n9, all_0_2_2, n4 and discharging atoms sum(n11, n9) = all_0_2_2, sum(n11, n9) = n4, yields:
% 22.63/6.34 | (617) all_0_2_2 = n4
% 22.63/6.34 |
% 22.63/6.34 | From (617) and (187) follows:
% 22.63/6.34 | (619) pred(n4) = all_0_1_1
% 22.63/6.34 |
% 22.63/6.34 | From (817) and (2688) follows:
% 22.63/6.34 | (2716) sum(n11, n10) = all_0_4_4
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (37) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 22.63/6.34 | (622) all_0_1_1 = n3
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n11, n10, all_0_4_4, n5 and discharging atoms sum(n11, n10) = all_0_4_4, sum(n11, n10) = n5, yields:
% 22.63/6.34 | (618) all_0_4_4 = n5
% 22.63/6.34 |
% 22.63/6.34 | From (618) and (396) follows:
% 22.63/6.34 | (620) pred(n5) = all_0_3_3
% 22.63/6.34 |
% 22.63/6.34 | From (622) and (815) follows:
% 22.63/6.34 | (2720) sum(n9, n3) = all_0_0_0
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (37) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 22.63/6.34 | (621) all_0_3_3 = n4
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n9, n3, all_0_0_0, n12 and discharging atoms sum(n9, n3) = all_0_0_0, sum(n9, n3) = n12, yields:
% 22.63/6.34 | (455) all_0_0_0 = n12
% 22.63/6.34 |
% 22.63/6.34 | From (621)(455) and (261) follows:
% 22.63/6.34 | (2723) sum(n4, n12) = all_0_6_6
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n4, n12, all_0_6_6, n0 and discharging atoms sum(n4, n12) = all_0_6_6, sum(n4, n12) = n0, yields:
% 22.63/6.34 | (542) all_0_6_6 = n0
% 22.63/6.34 |
% 22.63/6.34 | Equations (542) can reduce 400 to:
% 22.63/6.34 | (458) $false
% 22.63/6.34 |
% 22.63/6.34 |-The branch is then unsatisfiable
% 22.63/6.34 |-Branch two:
% 22.63/6.34 | (830) ~ (all_0_7_7 = n9)
% 22.63/6.34 | (831) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.63/6.34 |
% 22.63/6.34 +-Applying beta-rule and splitting (831), into two cases.
% 22.63/6.34 |-Branch one:
% 22.63/6.34 | (832) all_0_7_7 = n8
% 22.63/6.34 |
% 22.63/6.34 | From (832) and (176) follows:
% 22.63/6.34 | (833) succ(n8) = all_0_5_5
% 22.63/6.34 |
% 22.63/6.34 | From (832) and (59) follows:
% 22.63/6.34 | (834) sum(n8, all_0_1_1) = all_0_0_0
% 22.63/6.34 |
% 22.63/6.34 | From (832) and (2689) follows:
% 22.63/6.34 | (2731) sum(n11, n8) = all_0_2_2
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (219) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 22.63/6.34 | (836) all_0_5_5 = n9
% 22.63/6.34 |
% 22.63/6.34 | Instantiating formula (89) with n11, n8, all_0_2_2, n3 and discharging atoms sum(n11, n8) = all_0_2_2, sum(n11, n8) = n3, yields:
% 22.63/6.34 | (634) all_0_2_2 = n3
% 22.63/6.34 |
% 22.63/6.34 | From (634) and (187) follows:
% 22.63/6.34 | (636) pred(n3) = all_0_1_1
% 22.63/6.34 |
% 22.63/6.34 | From (836) and (2688) follows:
% 22.63/6.35 | (2735) sum(n11, n9) = all_0_4_4
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (37) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 22.63/6.35 | (639) all_0_1_1 = n2
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n11, n9, all_0_4_4, n4 and discharging atoms sum(n11, n9) = all_0_4_4, sum(n11, n9) = n4, yields:
% 22.63/6.35 | (635) all_0_4_4 = n4
% 22.63/6.35 |
% 22.63/6.35 | From (635) and (396) follows:
% 22.63/6.35 | (637) pred(n4) = all_0_3_3
% 22.63/6.35 |
% 22.63/6.35 | From (639) and (834) follows:
% 22.63/6.35 | (2739) sum(n8, n2) = all_0_0_0
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (37) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 22.63/6.35 | (638) all_0_3_3 = n3
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n8, n2, all_0_0_0, n10 and discharging atoms sum(n8, n2) = all_0_0_0, sum(n8, n2) = n10, yields:
% 22.63/6.35 | (489) all_0_0_0 = n10
% 22.63/6.35 |
% 22.63/6.35 | From (638)(489) and (261) follows:
% 22.63/6.35 | (2742) sum(n3, n10) = all_0_6_6
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n3, n10, all_0_6_6, n13 and discharging atoms sum(n3, n10) = all_0_6_6, sum(n3, n10) = n13, yields:
% 22.63/6.35 | (998) all_0_6_6 = n13
% 22.63/6.35 |
% 22.63/6.35 | Equations (998) can reduce 130 to:
% 22.63/6.35 | (458) $false
% 22.63/6.35 |
% 22.63/6.35 |-The branch is then unsatisfiable
% 22.63/6.35 |-Branch two:
% 22.63/6.35 | (849) ~ (all_0_7_7 = n8)
% 22.63/6.35 | (850) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.63/6.35 |
% 22.63/6.35 +-Applying beta-rule and splitting (850), into two cases.
% 22.63/6.35 |-Branch one:
% 22.63/6.35 | (851) all_0_7_7 = n7
% 22.63/6.35 |
% 22.63/6.35 | From (851) and (176) follows:
% 22.63/6.35 | (852) succ(n7) = all_0_5_5
% 22.63/6.35 |
% 22.63/6.35 | From (851) and (59) follows:
% 22.63/6.35 | (853) sum(n7, all_0_1_1) = all_0_0_0
% 22.63/6.35 |
% 22.63/6.35 | From (851) and (2689) follows:
% 22.63/6.35 | (2750) sum(n11, n7) = all_0_2_2
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (219) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 22.63/6.35 | (855) all_0_5_5 = n8
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n11, n7, all_0_2_2, n2 and discharging atoms sum(n11, n7) = all_0_2_2, sum(n11, n7) = n2, yields:
% 22.63/6.35 | (651) all_0_2_2 = n2
% 22.63/6.35 |
% 22.63/6.35 | From (651) and (187) follows:
% 22.63/6.35 | (653) pred(n2) = all_0_1_1
% 22.63/6.35 |
% 22.63/6.35 | From (855) and (2688) follows:
% 22.63/6.35 | (2754) sum(n11, n8) = all_0_4_4
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (37) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 22.63/6.35 | (656) all_0_1_1 = n1
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n11, n8, all_0_4_4, n3 and discharging atoms sum(n11, n8) = all_0_4_4, sum(n11, n8) = n3, yields:
% 22.63/6.35 | (652) all_0_4_4 = n3
% 22.63/6.35 |
% 22.63/6.35 | From (652) and (396) follows:
% 22.63/6.35 | (654) pred(n3) = all_0_3_3
% 22.63/6.35 |
% 22.63/6.35 | From (656) and (853) follows:
% 22.63/6.35 | (2758) sum(n7, n1) = all_0_0_0
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (37) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 22.63/6.35 | (655) all_0_3_3 = n2
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n7, n1, all_0_0_0, n8 and discharging atoms sum(n7, n1) = all_0_0_0, sum(n7, n1) = n8, yields:
% 22.63/6.35 | (523) all_0_0_0 = n8
% 22.63/6.35 |
% 22.63/6.35 | From (655)(523) and (261) follows:
% 22.63/6.35 | (2761) sum(n2, n8) = all_0_6_6
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n2, n8, all_0_6_6, n10 and discharging atoms sum(n2, n8) = all_0_6_6, sum(n2, n8) = n10, yields:
% 22.63/6.35 | (457) all_0_6_6 = n10
% 22.63/6.35 |
% 22.63/6.35 | Equations (457) can reduce 169 to:
% 22.63/6.35 | (458) $false
% 22.63/6.35 |
% 22.63/6.35 |-The branch is then unsatisfiable
% 22.63/6.35 |-Branch two:
% 22.63/6.35 | (868) ~ (all_0_7_7 = n7)
% 22.63/6.35 | (869) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.63/6.35 |
% 22.63/6.35 +-Applying beta-rule and splitting (869), into two cases.
% 22.63/6.35 |-Branch one:
% 22.63/6.35 | (870) all_0_7_7 = n6
% 22.63/6.35 |
% 22.63/6.35 | From (870) and (176) follows:
% 22.63/6.35 | (871) succ(n6) = all_0_5_5
% 22.63/6.35 |
% 22.63/6.35 | From (870) and (59) follows:
% 22.63/6.35 | (872) sum(n6, all_0_1_1) = all_0_0_0
% 22.63/6.35 |
% 22.63/6.35 | From (870) and (2689) follows:
% 22.63/6.35 | (2769) sum(n11, n6) = all_0_2_2
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (219) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 22.63/6.35 | (874) all_0_5_5 = n7
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n11, n6, all_0_2_2, n1 and discharging atoms sum(n11, n6) = all_0_2_2, sum(n11, n6) = n1, yields:
% 22.63/6.35 | (668) all_0_2_2 = n1
% 22.63/6.35 |
% 22.63/6.35 | From (668) and (187) follows:
% 22.63/6.35 | (670) pred(n1) = all_0_1_1
% 22.63/6.35 |
% 22.63/6.35 | From (874) and (2688) follows:
% 22.63/6.35 | (2773) sum(n11, n7) = all_0_4_4
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (37) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 22.63/6.35 | (673) all_0_1_1 = n0
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n11, n7, all_0_4_4, n2 and discharging atoms sum(n11, n7) = all_0_4_4, sum(n11, n7) = n2, yields:
% 22.63/6.35 | (669) all_0_4_4 = n2
% 22.63/6.35 |
% 22.63/6.35 | From (669) and (396) follows:
% 22.63/6.35 | (671) pred(n2) = all_0_3_3
% 22.63/6.35 |
% 22.63/6.35 | From (673) and (872) follows:
% 22.63/6.35 | (2777) sum(n6, n0) = all_0_0_0
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (37) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 22.63/6.35 | (672) all_0_3_3 = n1
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n6, n0, all_0_0_0, n6 and discharging atoms sum(n6, n0) = all_0_0_0, sum(n6, n0) = n6, yields:
% 22.63/6.35 | (557) all_0_0_0 = n6
% 22.63/6.35 |
% 22.63/6.35 | From (672)(557) and (261) follows:
% 22.63/6.35 | (2780) sum(n1, n6) = all_0_6_6
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n1, n6, all_0_6_6, n7 and discharging atoms sum(n1, n6) = all_0_6_6, sum(n1, n6) = n7, yields:
% 22.63/6.35 | (733) all_0_6_6 = n7
% 22.63/6.35 |
% 22.63/6.35 | Equations (733) can reduce 274 to:
% 22.63/6.35 | (458) $false
% 22.63/6.35 |
% 22.63/6.35 |-The branch is then unsatisfiable
% 22.63/6.35 |-Branch two:
% 22.63/6.35 | (887) ~ (all_0_7_7 = n6)
% 22.63/6.35 | (888) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.63/6.35 |
% 22.63/6.35 +-Applying beta-rule and splitting (888), into two cases.
% 22.63/6.35 |-Branch one:
% 22.63/6.35 | (889) all_0_7_7 = n5
% 22.63/6.35 |
% 22.63/6.35 | From (889) and (176) follows:
% 22.63/6.35 | (890) succ(n5) = all_0_5_5
% 22.63/6.35 |
% 22.63/6.35 | From (889) and (59) follows:
% 22.63/6.35 | (891) sum(n5, all_0_1_1) = all_0_0_0
% 22.63/6.35 |
% 22.63/6.35 | From (889) and (2689) follows:
% 22.63/6.35 | (2788) sum(n11, n5) = all_0_2_2
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (219) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 22.63/6.35 | (893) all_0_5_5 = n6
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n11, n5, all_0_2_2, n0 and discharging atoms sum(n11, n5) = all_0_2_2, sum(n11, n5) = n0, yields:
% 22.63/6.35 | (685) all_0_2_2 = n0
% 22.63/6.35 |
% 22.63/6.35 | From (685) and (187) follows:
% 22.63/6.35 | (687) pred(n0) = all_0_1_1
% 22.63/6.35 |
% 22.63/6.35 | From (893) and (2688) follows:
% 22.63/6.35 | (2792) sum(n11, n6) = all_0_4_4
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (37) with n0, all_0_1_1, n15 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n15, yields:
% 22.63/6.35 | (690) all_0_1_1 = n15
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n11, n6, all_0_4_4, n1 and discharging atoms sum(n11, n6) = all_0_4_4, sum(n11, n6) = n1, yields:
% 22.63/6.35 | (686) all_0_4_4 = n1
% 22.63/6.35 |
% 22.63/6.35 | From (686) and (396) follows:
% 22.63/6.35 | (688) pred(n1) = all_0_3_3
% 22.63/6.35 |
% 22.63/6.35 | From (690) and (891) follows:
% 22.63/6.35 | (2796) sum(n5, n15) = all_0_0_0
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (37) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 22.63/6.35 | (689) all_0_3_3 = n0
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n5, n15, all_0_0_0, n4 and discharging atoms sum(n5, n15) = all_0_0_0, sum(n5, n15) = n4, yields:
% 22.63/6.35 | (591) all_0_0_0 = n4
% 22.63/6.35 |
% 22.63/6.35 | From (689)(591) and (261) follows:
% 22.63/6.35 | (2799) sum(n0, n4) = all_0_6_6
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n0, n4, all_0_6_6, n4 and discharging atoms sum(n0, n4) = all_0_6_6, sum(n0, n4) = n4, yields:
% 22.63/6.35 | (508) all_0_6_6 = n4
% 22.63/6.35 |
% 22.63/6.35 | Equations (508) can reduce 12 to:
% 22.63/6.35 | (458) $false
% 22.63/6.35 |
% 22.63/6.35 |-The branch is then unsatisfiable
% 22.63/6.35 |-Branch two:
% 22.63/6.35 | (906) ~ (all_0_7_7 = n5)
% 22.63/6.35 | (907) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.63/6.35 |
% 22.63/6.35 +-Applying beta-rule and splitting (907), into two cases.
% 22.63/6.35 |-Branch one:
% 22.63/6.35 | (908) all_0_7_7 = n4
% 22.63/6.35 |
% 22.63/6.35 | From (908) and (176) follows:
% 22.63/6.35 | (909) succ(n4) = all_0_5_5
% 22.63/6.35 |
% 22.63/6.35 | From (908) and (59) follows:
% 22.63/6.35 | (910) sum(n4, all_0_1_1) = all_0_0_0
% 22.63/6.35 |
% 22.63/6.35 | From (908) and (2689) follows:
% 22.63/6.35 | (2807) sum(n11, n4) = all_0_2_2
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (219) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 22.63/6.35 | (912) all_0_5_5 = n5
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n11, n4, all_0_2_2, n15 and discharging atoms sum(n11, n4) = all_0_2_2, sum(n11, n4) = n15, yields:
% 22.63/6.35 | (701) all_0_2_2 = n15
% 22.63/6.35 |
% 22.63/6.35 | From (701) and (187) follows:
% 22.63/6.35 | (703) pred(n15) = all_0_1_1
% 22.63/6.35 |
% 22.63/6.35 | From (912) and (2688) follows:
% 22.63/6.35 | (2811) sum(n11, n5) = all_0_4_4
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (37) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 22.63/6.35 | (705) all_0_1_1 = n14
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n11, n5, all_0_4_4, n0 and discharging atoms sum(n11, n5) = all_0_4_4, sum(n11, n5) = n0, yields:
% 22.63/6.35 | (702) all_0_4_4 = n0
% 22.63/6.35 |
% 22.63/6.35 | From (702) and (396) follows:
% 22.63/6.35 | (704) pred(n0) = all_0_3_3
% 22.63/6.35 |
% 22.63/6.35 | From (705) and (910) follows:
% 22.63/6.35 | (2815) sum(n4, n14) = all_0_0_0
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (37) with n0, all_0_3_3, n15 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n15, yields:
% 22.63/6.35 | (706) all_0_3_3 = n15
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n4, n14, all_0_0_0, n2 and discharging atoms sum(n4, n14) = all_0_0_0, sum(n4, n14) = n2, yields:
% 22.63/6.35 | (625) all_0_0_0 = n2
% 22.63/6.35 |
% 22.63/6.35 | From (706)(625) and (261) follows:
% 22.63/6.35 | (2818) sum(n15, n2) = all_0_6_6
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (89) with n15, n2, all_0_6_6, n1 and discharging atoms sum(n15, n2) = all_0_6_6, sum(n15, n2) = n1, yields:
% 22.63/6.35 | (771) all_0_6_6 = n1
% 22.63/6.35 |
% 22.63/6.35 | Equations (771) can reduce 38 to:
% 22.63/6.35 | (458) $false
% 22.63/6.35 |
% 22.63/6.35 |-The branch is then unsatisfiable
% 22.63/6.35 |-Branch two:
% 22.63/6.35 | (925) ~ (all_0_7_7 = n4)
% 22.63/6.35 | (926) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.63/6.35 |
% 22.63/6.35 +-Applying beta-rule and splitting (926), into two cases.
% 22.63/6.35 |-Branch one:
% 22.63/6.35 | (927) all_0_7_7 = n3
% 22.63/6.35 |
% 22.63/6.35 | From (927) and (176) follows:
% 22.63/6.35 | (928) succ(n3) = all_0_5_5
% 22.63/6.35 |
% 22.63/6.35 | From (927) and (59) follows:
% 22.63/6.35 | (929) sum(n3, all_0_1_1) = all_0_0_0
% 22.63/6.35 |
% 22.63/6.35 | From (927) and (2689) follows:
% 22.63/6.35 | (2826) sum(n11, n3) = all_0_2_2
% 22.63/6.35 |
% 22.63/6.35 | Instantiating formula (219) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 22.63/6.35 | (931) all_0_5_5 = n4
% 22.63/6.36 |
% 22.63/6.36 | Instantiating formula (89) with n11, n3, all_0_2_2, n14 and discharging atoms sum(n11, n3) = all_0_2_2, sum(n11, n3) = n14, yields:
% 22.63/6.36 | (447) all_0_2_2 = n14
% 22.63/6.36 |
% 22.63/6.36 | From (447) and (187) follows:
% 22.63/6.36 | (449) pred(n14) = all_0_1_1
% 22.63/6.36 |
% 22.63/6.36 | From (931) and (2688) follows:
% 22.63/6.36 | (2830) sum(n11, n4) = all_0_4_4
% 22.63/6.36 |
% 22.63/6.36 | Instantiating formula (37) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 22.63/6.36 | (452) all_0_1_1 = n13
% 22.63/6.36 |
% 22.63/6.36 | Instantiating formula (89) with n11, n4, all_0_4_4, n15 and discharging atoms sum(n11, n4) = all_0_4_4, sum(n11, n4) = n15, yields:
% 22.63/6.36 | (448) all_0_4_4 = n15
% 22.63/6.36 |
% 22.63/6.36 | From (448) and (396) follows:
% 22.63/6.36 | (450) pred(n15) = all_0_3_3
% 22.63/6.36 |
% 22.63/6.36 | From (452) and (929) follows:
% 22.63/6.36 | (2834) sum(n3, n13) = all_0_0_0
% 22.63/6.36 |
% 22.63/6.36 | Instantiating formula (37) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 22.63/6.36 | (451) all_0_3_3 = n14
% 22.63/6.36 |
% 22.63/6.36 | Instantiating formula (89) with n3, n13, all_0_0_0, n0 and discharging atoms sum(n3, n13) = all_0_0_0, sum(n3, n13) = n0, yields:
% 22.63/6.36 | (659) all_0_0_0 = n0
% 22.63/6.36 |
% 22.63/6.36 | From (451)(659) and (261) follows:
% 22.63/6.36 | (2837) sum(n14, n0) = all_0_6_6
% 22.63/6.36 |
% 22.63/6.36 | Instantiating formula (89) with n14, n0, all_0_6_6, n14 and discharging atoms sum(n14, n0) = all_0_6_6, sum(n14, n0) = n14, yields:
% 22.63/6.36 | (559) all_0_6_6 = n14
% 22.63/6.36 |
% 22.63/6.36 | Equations (559) can reduce 314 to:
% 22.63/6.36 | (458) $false
% 22.63/6.36 |
% 22.79/6.36 |-The branch is then unsatisfiable
% 22.79/6.36 |-Branch two:
% 22.79/6.36 | (944) ~ (all_0_7_7 = n3)
% 22.79/6.36 | (945) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.36 |
% 22.79/6.36 +-Applying beta-rule and splitting (945), into two cases.
% 22.79/6.36 |-Branch one:
% 22.79/6.36 | (946) all_0_7_7 = n2
% 22.79/6.36 |
% 22.79/6.36 | From (946) and (176) follows:
% 22.79/6.36 | (947) succ(n2) = all_0_5_5
% 22.79/6.36 |
% 22.79/6.36 | From (946) and (59) follows:
% 22.79/6.36 | (948) sum(n2, all_0_1_1) = all_0_0_0
% 22.79/6.36 |
% 22.79/6.36 | From (946) and (2689) follows:
% 22.79/6.36 | (2845) sum(n11, n2) = all_0_2_2
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (219) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 22.79/6.36 | (950) all_0_5_5 = n3
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (89) with n11, n2, all_0_2_2, n13 and discharging atoms sum(n11, n2) = all_0_2_2, sum(n11, n2) = n13, yields:
% 22.79/6.36 | (464) all_0_2_2 = n13
% 22.79/6.36 |
% 22.79/6.36 | From (464) and (187) follows:
% 22.79/6.36 | (466) pred(n13) = all_0_1_1
% 22.79/6.36 |
% 22.79/6.36 | From (950) and (2688) follows:
% 22.79/6.36 | (2849) sum(n11, n3) = all_0_4_4
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (37) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 22.79/6.36 | (469) all_0_1_1 = n12
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (89) with n11, n3, all_0_4_4, n14 and discharging atoms sum(n11, n3) = all_0_4_4, sum(n11, n3) = n14, yields:
% 22.79/6.36 | (465) all_0_4_4 = n14
% 22.79/6.36 |
% 22.79/6.36 | From (465) and (396) follows:
% 22.79/6.36 | (467) pred(n14) = all_0_3_3
% 22.79/6.36 |
% 22.79/6.36 | From (469) and (948) follows:
% 22.79/6.36 | (2853) sum(n2, n12) = all_0_0_0
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (37) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 22.79/6.36 | (468) all_0_3_3 = n13
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (89) with n2, n12, all_0_0_0, n14 and discharging atoms sum(n2, n12) = all_0_0_0, sum(n2, n12) = n14, yields:
% 22.79/6.36 | (693) all_0_0_0 = n14
% 22.79/6.36 |
% 22.79/6.36 | From (468)(693) and (261) follows:
% 22.79/6.36 | (2856) sum(n13, n14) = all_0_6_6
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (89) with n13, n14, all_0_6_6, n11 and discharging atoms sum(n13, n14) = all_0_6_6, sum(n13, n14) = n11, yields:
% 22.79/6.36 | (809) all_0_6_6 = n11
% 22.79/6.36 |
% 22.79/6.36 | Equations (809) can reduce 70 to:
% 22.79/6.36 | (458) $false
% 22.79/6.36 |
% 22.79/6.36 |-The branch is then unsatisfiable
% 22.79/6.36 |-Branch two:
% 22.79/6.36 | (963) ~ (all_0_7_7 = n2)
% 22.79/6.36 | (964) all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.36 |
% 22.79/6.36 +-Applying beta-rule and splitting (964), into two cases.
% 22.79/6.36 |-Branch one:
% 22.79/6.36 | (965) all_0_7_7 = n1
% 22.79/6.36 |
% 22.79/6.36 | From (965) and (176) follows:
% 22.79/6.36 | (966) succ(n1) = all_0_5_5
% 22.79/6.36 |
% 22.79/6.36 | From (965) and (59) follows:
% 22.79/6.36 | (967) sum(n1, all_0_1_1) = all_0_0_0
% 22.79/6.36 |
% 22.79/6.36 | From (965) and (2689) follows:
% 22.79/6.36 | (2864) sum(n11, n1) = all_0_2_2
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (219) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 22.79/6.36 | (969) all_0_5_5 = n2
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (89) with n11, n1, all_0_2_2, n12 and discharging atoms sum(n11, n1) = all_0_2_2, sum(n11, n1) = n12, yields:
% 22.79/6.36 | (481) all_0_2_2 = n12
% 22.79/6.36 |
% 22.79/6.36 | From (481) and (187) follows:
% 22.79/6.36 | (483) pred(n12) = all_0_1_1
% 22.79/6.36 |
% 22.79/6.36 | From (969) and (2688) follows:
% 22.79/6.36 | (2868) sum(n11, n2) = all_0_4_4
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (37) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 22.79/6.36 | (486) all_0_1_1 = n11
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (89) with n11, n2, all_0_4_4, n13 and discharging atoms sum(n11, n2) = all_0_4_4, sum(n11, n2) = n13, yields:
% 22.79/6.36 | (482) all_0_4_4 = n13
% 22.79/6.36 |
% 22.79/6.36 | From (482) and (396) follows:
% 22.79/6.36 | (484) pred(n13) = all_0_3_3
% 22.79/6.36 |
% 22.79/6.36 | From (486) and (967) follows:
% 22.79/6.36 | (2872) sum(n1, n11) = all_0_0_0
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (37) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 22.79/6.36 | (485) all_0_3_3 = n12
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (89) with n1, n11, all_0_0_0, n12 and discharging atoms sum(n1, n11) = all_0_0_0, sum(n1, n11) = n12, yields:
% 22.79/6.36 | (455) all_0_0_0 = n12
% 22.79/6.36 |
% 22.79/6.36 | From (485)(455) and (261) follows:
% 22.79/6.36 | (2875) sum(n12, n12) = all_0_6_6
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (89) with n12, n12, all_0_6_6, n8 and discharging atoms sum(n12, n12) = all_0_6_6, sum(n12, n12) = n8, yields:
% 22.79/6.36 | (474) all_0_6_6 = n8
% 22.79/6.36 |
% 22.79/6.36 | Equations (474) can reduce 86 to:
% 22.79/6.36 | (458) $false
% 22.79/6.36 |
% 22.79/6.36 |-The branch is then unsatisfiable
% 22.79/6.36 |-Branch two:
% 22.79/6.36 | (982) ~ (all_0_7_7 = n1)
% 22.79/6.36 | (983) all_0_7_7 = n0
% 22.79/6.36 |
% 22.79/6.36 | From (983) and (176) follows:
% 22.79/6.36 | (984) succ(n0) = all_0_5_5
% 22.79/6.36 |
% 22.79/6.36 | From (983) and (59) follows:
% 22.79/6.36 | (985) sum(n0, all_0_1_1) = all_0_0_0
% 22.79/6.36 |
% 22.79/6.36 | From (983) and (2689) follows:
% 22.79/6.36 | (2882) sum(n11, n0) = all_0_2_2
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (219) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 22.79/6.36 | (987) all_0_5_5 = n1
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (89) with n11, n0, all_0_2_2, n11 and discharging atoms sum(n11, n0) = all_0_2_2, sum(n11, n0) = n11, yields:
% 22.79/6.36 | (498) all_0_2_2 = n11
% 22.79/6.36 |
% 22.79/6.36 | From (498) and (187) follows:
% 22.79/6.36 | (500) pred(n11) = all_0_1_1
% 22.79/6.36 |
% 22.79/6.36 | From (987) and (2688) follows:
% 22.79/6.36 | (2886) sum(n11, n1) = all_0_4_4
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (37) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 22.79/6.36 | (503) all_0_1_1 = n10
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (89) with n11, n1, all_0_4_4, n12 and discharging atoms sum(n11, n1) = all_0_4_4, sum(n11, n1) = n12, yields:
% 22.79/6.36 | (499) all_0_4_4 = n12
% 22.79/6.36 |
% 22.79/6.36 | From (499) and (396) follows:
% 22.79/6.36 | (501) pred(n12) = all_0_3_3
% 22.79/6.36 |
% 22.79/6.36 | From (503) and (985) follows:
% 22.79/6.36 | (2890) sum(n0, n10) = all_0_0_0
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (37) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 22.79/6.36 | (502) all_0_3_3 = n11
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (89) with n0, n10, all_0_0_0, n10 and discharging atoms sum(n0, n10) = all_0_0_0, sum(n0, n10) = n10, yields:
% 22.79/6.36 | (489) all_0_0_0 = n10
% 22.79/6.36 |
% 22.79/6.36 | From (502)(489) and (261) follows:
% 22.79/6.36 | (2893) sum(n11, n10) = all_0_6_6
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (89) with n11, n10, all_0_6_6, n5 and discharging atoms sum(n11, n10) = all_0_6_6, sum(n11, n10) = n5, yields:
% 22.79/6.36 | (847) all_0_6_6 = n5
% 22.79/6.36 |
% 22.79/6.36 | Equations (847) can reduce 409 to:
% 22.79/6.36 | (458) $false
% 22.79/6.36 |
% 22.79/6.36 |-The branch is then unsatisfiable
% 22.79/6.36 |-Branch two:
% 22.79/6.36 | (527) ~ (all_0_8_8 = n11)
% 22.79/6.36 | (528) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.36 |
% 22.79/6.36 +-Applying beta-rule and splitting (793), into two cases.
% 22.79/6.36 |-Branch one:
% 22.79/6.36 | (794) all_0_7_7 = n10
% 22.79/6.36 |
% 22.79/6.36 | From (794) and (176) follows:
% 22.79/6.36 | (795) succ(n10) = all_0_5_5
% 22.79/6.36 |
% 22.79/6.36 | From (794) and (59) follows:
% 22.79/6.36 | (796) sum(n10, all_0_1_1) = all_0_0_0
% 22.79/6.36 |
% 22.79/6.36 | From (794) and (160) follows:
% 22.79/6.36 | (2901) sum(all_0_8_8, n10) = all_0_2_2
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (219) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 22.79/6.36 | (798) all_0_5_5 = n11
% 22.79/6.36 |
% 22.79/6.36 | From (798) and (64) follows:
% 22.79/6.36 | (2903) sum(all_0_8_8, n11) = all_0_4_4
% 22.79/6.36 |
% 22.79/6.36 +-Applying beta-rule and splitting (528), into two cases.
% 22.79/6.36 |-Branch one:
% 22.79/6.36 | (529) all_0_8_8 = n10
% 22.79/6.36 |
% 22.79/6.36 | From (529) and (2903) follows:
% 22.79/6.36 | (2905) sum(n10, n11) = all_0_4_4
% 22.79/6.36 |
% 22.79/6.36 | From (529) and (2901) follows:
% 22.79/6.36 | (2906) sum(n10, n10) = all_0_2_2
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (89) with n10, n11, all_0_4_4, n5 and discharging atoms sum(n10, n11) = all_0_4_4, sum(n10, n11) = n5, yields:
% 22.79/6.36 | (618) all_0_4_4 = n5
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (89) with n10, n10, all_0_2_2, n4 and discharging atoms sum(n10, n10) = all_0_2_2, sum(n10, n10) = n4, yields:
% 22.79/6.36 | (617) all_0_2_2 = n4
% 22.79/6.36 |
% 22.79/6.36 | From (617) and (187) follows:
% 22.79/6.36 | (619) pred(n4) = all_0_1_1
% 22.79/6.36 |
% 22.79/6.36 | From (618) and (396) follows:
% 22.79/6.36 | (620) pred(n5) = all_0_3_3
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (37) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 22.79/6.36 | (621) all_0_3_3 = n4
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (37) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 22.79/6.36 | (622) all_0_1_1 = n3
% 22.79/6.36 |
% 22.79/6.36 | From (621) and (261) follows:
% 22.79/6.36 | (623) sum(n4, all_0_0_0) = all_0_6_6
% 22.79/6.36 |
% 22.79/6.36 | From (622) and (796) follows:
% 22.79/6.36 | (2914) sum(n10, n3) = all_0_0_0
% 22.79/6.36 |
% 22.79/6.36 | Instantiating formula (89) with n10, n3, all_0_0_0, n13 and discharging atoms sum(n10, n3) = all_0_0_0, sum(n10, n3) = n13, yields:
% 22.79/6.36 | (709) all_0_0_0 = n13
% 22.79/6.36 |
% 22.79/6.36 | From (709) and (623) follows:
% 22.79/6.37 | (2916) sum(n4, n13) = all_0_6_6
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n4, n13, all_0_6_6, n1 and discharging atoms sum(n4, n13) = all_0_6_6, sum(n4, n13) = n1, yields:
% 22.79/6.37 | (771) all_0_6_6 = n1
% 22.79/6.37 |
% 22.79/6.37 | Equations (771) can reduce 38 to:
% 22.79/6.37 | (458) $false
% 22.79/6.37 |
% 22.79/6.37 |-The branch is then unsatisfiable
% 22.79/6.37 |-Branch two:
% 22.79/6.37 | (544) ~ (all_0_8_8 = n10)
% 22.79/6.37 | (545) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.37 |
% 22.79/6.37 +-Applying beta-rule and splitting (545), into two cases.
% 22.79/6.37 |-Branch one:
% 22.79/6.37 | (546) all_0_8_8 = n9
% 22.79/6.37 |
% 22.79/6.37 | From (546) and (2903) follows:
% 22.79/6.37 | (2922) sum(n9, n11) = all_0_4_4
% 22.79/6.37 |
% 22.79/6.37 | From (546) and (2901) follows:
% 22.79/6.37 | (2923) sum(n9, n10) = all_0_2_2
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n9, n11, all_0_4_4, n4 and discharging atoms sum(n9, n11) = all_0_4_4, sum(n9, n11) = n4, yields:
% 22.79/6.37 | (635) all_0_4_4 = n4
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n9, n10, all_0_2_2, n3 and discharging atoms sum(n9, n10) = all_0_2_2, sum(n9, n10) = n3, yields:
% 22.79/6.37 | (634) all_0_2_2 = n3
% 22.79/6.37 |
% 22.79/6.37 | From (634) and (187) follows:
% 22.79/6.37 | (636) pred(n3) = all_0_1_1
% 22.79/6.37 |
% 22.79/6.37 | From (635) and (396) follows:
% 22.79/6.37 | (637) pred(n4) = all_0_3_3
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (37) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 22.79/6.37 | (638) all_0_3_3 = n3
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (37) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 22.79/6.37 | (639) all_0_1_1 = n2
% 22.79/6.37 |
% 22.79/6.37 | From (638) and (261) follows:
% 22.79/6.37 | (640) sum(n3, all_0_0_0) = all_0_6_6
% 22.79/6.37 |
% 22.79/6.37 | From (639) and (796) follows:
% 22.79/6.37 | (2931) sum(n10, n2) = all_0_0_0
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n10, n2, all_0_0_0, n12 and discharging atoms sum(n10, n2) = all_0_0_0, sum(n10, n2) = n12, yields:
% 22.79/6.37 | (455) all_0_0_0 = n12
% 22.79/6.37 |
% 22.79/6.37 | From (455) and (640) follows:
% 22.79/6.37 | (2933) sum(n3, n12) = all_0_6_6
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n3, n12, all_0_6_6, n15 and discharging atoms sum(n3, n12) = all_0_6_6, sum(n3, n12) = n15, yields:
% 22.79/6.37 | (885) all_0_6_6 = n15
% 22.79/6.37 |
% 22.79/6.37 | Equations (885) can reduce 225 to:
% 22.79/6.37 | (458) $false
% 22.79/6.37 |
% 22.79/6.37 |-The branch is then unsatisfiable
% 22.79/6.37 |-Branch two:
% 22.79/6.37 | (561) ~ (all_0_8_8 = n9)
% 22.79/6.37 | (562) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.37 |
% 22.79/6.37 +-Applying beta-rule and splitting (562), into two cases.
% 22.79/6.37 |-Branch one:
% 22.79/6.37 | (563) all_0_8_8 = n8
% 22.79/6.37 |
% 22.79/6.37 | From (563) and (2903) follows:
% 22.79/6.37 | (2939) sum(n8, n11) = all_0_4_4
% 22.79/6.37 |
% 22.79/6.37 | From (563) and (2901) follows:
% 22.79/6.37 | (2940) sum(n8, n10) = all_0_2_2
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n8, n11, all_0_4_4, n3 and discharging atoms sum(n8, n11) = all_0_4_4, sum(n8, n11) = n3, yields:
% 22.79/6.37 | (652) all_0_4_4 = n3
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n8, n10, all_0_2_2, n2 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n2, yields:
% 22.79/6.37 | (651) all_0_2_2 = n2
% 22.79/6.37 |
% 22.79/6.37 | From (651) and (187) follows:
% 22.79/6.37 | (653) pred(n2) = all_0_1_1
% 22.79/6.37 |
% 22.79/6.37 | From (652) and (396) follows:
% 22.79/6.37 | (654) pred(n3) = all_0_3_3
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (37) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 22.79/6.37 | (655) all_0_3_3 = n2
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (37) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 22.79/6.37 | (656) all_0_1_1 = n1
% 22.79/6.37 |
% 22.79/6.37 | From (655) and (261) follows:
% 22.79/6.37 | (657) sum(n2, all_0_0_0) = all_0_6_6
% 22.79/6.37 |
% 22.79/6.37 | From (656) and (796) follows:
% 22.79/6.37 | (2948) sum(n10, n1) = all_0_0_0
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n10, n1, all_0_0_0, n11 and discharging atoms sum(n10, n1) = all_0_0_0, sum(n10, n1) = n11, yields:
% 22.79/6.37 | (472) all_0_0_0 = n11
% 22.79/6.37 |
% 22.79/6.37 | From (472) and (657) follows:
% 22.79/6.37 | (2950) sum(n2, n11) = all_0_6_6
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n2, n11, all_0_6_6, n13 and discharging atoms sum(n2, n11) = all_0_6_6, sum(n2, n11) = n13, yields:
% 22.79/6.37 | (998) all_0_6_6 = n13
% 22.79/6.37 |
% 22.79/6.37 | Equations (998) can reduce 130 to:
% 22.79/6.37 | (458) $false
% 22.79/6.37 |
% 22.79/6.37 |-The branch is then unsatisfiable
% 22.79/6.37 |-Branch two:
% 22.79/6.37 | (578) ~ (all_0_8_8 = n8)
% 22.79/6.37 | (579) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.37 |
% 22.79/6.37 +-Applying beta-rule and splitting (579), into two cases.
% 22.79/6.37 |-Branch one:
% 22.79/6.37 | (580) all_0_8_8 = n7
% 22.79/6.37 |
% 22.79/6.37 | From (580) and (2903) follows:
% 22.79/6.37 | (2956) sum(n7, n11) = all_0_4_4
% 22.79/6.37 |
% 22.79/6.37 | From (580) and (2901) follows:
% 22.79/6.37 | (2957) sum(n7, n10) = all_0_2_2
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n7, n11, all_0_4_4, n2 and discharging atoms sum(n7, n11) = all_0_4_4, sum(n7, n11) = n2, yields:
% 22.79/6.37 | (669) all_0_4_4 = n2
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n7, n10, all_0_2_2, n1 and discharging atoms sum(n7, n10) = all_0_2_2, sum(n7, n10) = n1, yields:
% 22.79/6.37 | (668) all_0_2_2 = n1
% 22.79/6.37 |
% 22.79/6.37 | From (668) and (187) follows:
% 22.79/6.37 | (670) pred(n1) = all_0_1_1
% 22.79/6.37 |
% 22.79/6.37 | From (669) and (396) follows:
% 22.79/6.37 | (671) pred(n2) = all_0_3_3
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (37) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 22.79/6.37 | (672) all_0_3_3 = n1
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (37) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 22.79/6.37 | (673) all_0_1_1 = n0
% 22.79/6.37 |
% 22.79/6.37 | From (672) and (261) follows:
% 22.79/6.37 | (674) sum(n1, all_0_0_0) = all_0_6_6
% 22.79/6.37 |
% 22.79/6.37 | From (673) and (796) follows:
% 22.79/6.37 | (2965) sum(n10, n0) = all_0_0_0
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n10, n0, all_0_0_0, n10 and discharging atoms sum(n10, n0) = all_0_0_0, sum(n10, n0) = n10, yields:
% 22.79/6.37 | (489) all_0_0_0 = n10
% 22.79/6.37 |
% 22.79/6.37 | From (489) and (674) follows:
% 22.79/6.37 | (2967) sum(n1, n10) = all_0_6_6
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n1, n10, all_0_6_6, n11 and discharging atoms sum(n1, n10) = all_0_6_6, sum(n1, n10) = n11, yields:
% 22.79/6.37 | (809) all_0_6_6 = n11
% 22.79/6.37 |
% 22.79/6.37 | Equations (809) can reduce 70 to:
% 22.79/6.37 | (458) $false
% 22.79/6.37 |
% 22.79/6.37 |-The branch is then unsatisfiable
% 22.79/6.37 |-Branch two:
% 22.79/6.37 | (595) ~ (all_0_8_8 = n7)
% 22.79/6.37 | (596) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.37 |
% 22.79/6.37 +-Applying beta-rule and splitting (596), into two cases.
% 22.79/6.37 |-Branch one:
% 22.79/6.37 | (597) all_0_8_8 = n6
% 22.79/6.37 |
% 22.79/6.37 | From (597) and (2903) follows:
% 22.79/6.37 | (2973) sum(n6, n11) = all_0_4_4
% 22.79/6.37 |
% 22.79/6.37 | From (597) and (2901) follows:
% 22.79/6.37 | (2974) sum(n6, n10) = all_0_2_2
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n6, n11, all_0_4_4, n1 and discharging atoms sum(n6, n11) = all_0_4_4, sum(n6, n11) = n1, yields:
% 22.79/6.37 | (686) all_0_4_4 = n1
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n6, n10, all_0_2_2, n0 and discharging atoms sum(n6, n10) = all_0_2_2, sum(n6, n10) = n0, yields:
% 22.79/6.37 | (685) all_0_2_2 = n0
% 22.79/6.37 |
% 22.79/6.37 | From (685) and (187) follows:
% 22.79/6.37 | (687) pred(n0) = all_0_1_1
% 22.79/6.37 |
% 22.79/6.37 | From (686) and (396) follows:
% 22.79/6.37 | (688) pred(n1) = all_0_3_3
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (37) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 22.79/6.37 | (689) all_0_3_3 = n0
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (37) with n0, all_0_1_1, n15 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n15, yields:
% 22.79/6.37 | (690) all_0_1_1 = n15
% 22.79/6.37 |
% 22.79/6.37 | From (689) and (261) follows:
% 22.79/6.37 | (691) sum(n0, all_0_0_0) = all_0_6_6
% 22.79/6.37 |
% 22.79/6.37 | From (690) and (796) follows:
% 22.79/6.37 | (2982) sum(n10, n15) = all_0_0_0
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n10, n15, all_0_0_0, n9 and discharging atoms sum(n10, n15) = all_0_0_0, sum(n10, n15) = n9, yields:
% 22.79/6.37 | (506) all_0_0_0 = n9
% 22.79/6.37 |
% 22.79/6.37 | From (506) and (691) follows:
% 22.79/6.37 | (2984) sum(n0, n9) = all_0_6_6
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n0, n9, all_0_6_6, n9 and discharging atoms sum(n0, n9) = all_0_6_6, sum(n0, n9) = n9, yields:
% 22.79/6.37 | (923) all_0_6_6 = n9
% 22.79/6.37 |
% 22.79/6.37 | Equations (923) can reduce 404 to:
% 22.79/6.37 | (458) $false
% 22.79/6.37 |
% 22.79/6.37 |-The branch is then unsatisfiable
% 22.79/6.37 |-Branch two:
% 22.79/6.37 | (612) ~ (all_0_8_8 = n6)
% 22.79/6.37 | (613) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.37 |
% 22.79/6.37 +-Applying beta-rule and splitting (613), into two cases.
% 22.79/6.37 |-Branch one:
% 22.79/6.37 | (614) all_0_8_8 = n5
% 22.79/6.37 |
% 22.79/6.37 | From (614) and (2903) follows:
% 22.79/6.37 | (2990) sum(n5, n11) = all_0_4_4
% 22.79/6.37 |
% 22.79/6.37 | From (614) and (2901) follows:
% 22.79/6.37 | (2991) sum(n5, n10) = all_0_2_2
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n5, n11, all_0_4_4, n0 and discharging atoms sum(n5, n11) = all_0_4_4, sum(n5, n11) = n0, yields:
% 22.79/6.37 | (702) all_0_4_4 = n0
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n5, n10, all_0_2_2, n15 and discharging atoms sum(n5, n10) = all_0_2_2, sum(n5, n10) = n15, yields:
% 22.79/6.37 | (701) all_0_2_2 = n15
% 22.79/6.37 |
% 22.79/6.37 | From (701) and (187) follows:
% 22.79/6.37 | (703) pred(n15) = all_0_1_1
% 22.79/6.37 |
% 22.79/6.37 | From (702) and (396) follows:
% 22.79/6.37 | (704) pred(n0) = all_0_3_3
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (37) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 22.79/6.37 | (705) all_0_1_1 = n14
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (37) with n0, all_0_3_3, n15 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n15, yields:
% 22.79/6.37 | (706) all_0_3_3 = n15
% 22.79/6.37 |
% 22.79/6.37 | From (706) and (261) follows:
% 22.79/6.37 | (707) sum(n15, all_0_0_0) = all_0_6_6
% 22.79/6.37 |
% 22.79/6.37 | From (705) and (796) follows:
% 22.79/6.37 | (2999) sum(n10, n14) = all_0_0_0
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n10, n14, all_0_0_0, n8 and discharging atoms sum(n10, n14) = all_0_0_0, sum(n10, n14) = n8, yields:
% 22.79/6.37 | (523) all_0_0_0 = n8
% 22.79/6.37 |
% 22.79/6.37 | From (523) and (707) follows:
% 22.79/6.37 | (3001) sum(n15, n8) = all_0_6_6
% 22.79/6.37 |
% 22.79/6.37 | Instantiating formula (89) with n15, n8, all_0_6_6, n7 and discharging atoms sum(n15, n8) = all_0_6_6, sum(n15, n8) = n7, yields:
% 22.79/6.37 | (733) all_0_6_6 = n7
% 22.79/6.37 |
% 22.79/6.38 | Equations (733) can reduce 274 to:
% 22.79/6.38 | (458) $false
% 22.79/6.38 |
% 22.79/6.38 |-The branch is then unsatisfiable
% 22.79/6.38 |-Branch two:
% 22.79/6.38 | (629) ~ (all_0_8_8 = n5)
% 22.79/6.38 | (630) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.38 |
% 22.79/6.38 +-Applying beta-rule and splitting (630), into two cases.
% 22.79/6.38 |-Branch one:
% 22.79/6.38 | (631) all_0_8_8 = n4
% 22.79/6.38 |
% 22.79/6.38 | From (631) and (2903) follows:
% 22.79/6.38 | (3007) sum(n4, n11) = all_0_4_4
% 22.79/6.38 |
% 22.79/6.38 | From (631) and (2901) follows:
% 22.79/6.38 | (3008) sum(n4, n10) = all_0_2_2
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n4, n11, all_0_4_4, n15 and discharging atoms sum(n4, n11) = all_0_4_4, sum(n4, n11) = n15, yields:
% 22.79/6.38 | (448) all_0_4_4 = n15
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n4, n10, all_0_2_2, n14 and discharging atoms sum(n4, n10) = all_0_2_2, sum(n4, n10) = n14, yields:
% 22.79/6.38 | (447) all_0_2_2 = n14
% 22.79/6.38 |
% 22.79/6.38 | From (447) and (187) follows:
% 22.79/6.38 | (449) pred(n14) = all_0_1_1
% 22.79/6.38 |
% 22.79/6.38 | From (448) and (396) follows:
% 22.79/6.38 | (450) pred(n15) = all_0_3_3
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (37) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 22.79/6.38 | (451) all_0_3_3 = n14
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (37) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 22.79/6.38 | (452) all_0_1_1 = n13
% 22.79/6.38 |
% 22.79/6.38 | From (451) and (261) follows:
% 22.79/6.38 | (453) sum(n14, all_0_0_0) = all_0_6_6
% 22.79/6.38 |
% 22.79/6.38 | From (452) and (796) follows:
% 22.79/6.38 | (3016) sum(n10, n13) = all_0_0_0
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n10, n13, all_0_0_0, n7 and discharging atoms sum(n10, n13) = all_0_0_0, sum(n10, n13) = n7, yields:
% 22.79/6.38 | (540) all_0_0_0 = n7
% 22.79/6.38 |
% 22.79/6.38 | From (540) and (453) follows:
% 22.79/6.38 | (3018) sum(n14, n7) = all_0_6_6
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n14, n7, all_0_6_6, n5 and discharging atoms sum(n14, n7) = all_0_6_6, sum(n14, n7) = n5, yields:
% 22.79/6.38 | (847) all_0_6_6 = n5
% 22.79/6.38 |
% 22.79/6.38 | Equations (847) can reduce 409 to:
% 22.79/6.38 | (458) $false
% 22.79/6.38 |
% 22.79/6.38 |-The branch is then unsatisfiable
% 22.79/6.38 |-Branch two:
% 22.79/6.38 | (646) ~ (all_0_8_8 = n4)
% 22.79/6.38 | (647) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.38 |
% 22.79/6.38 +-Applying beta-rule and splitting (647), into two cases.
% 22.79/6.38 |-Branch one:
% 22.79/6.38 | (648) all_0_8_8 = n3
% 22.79/6.38 |
% 22.79/6.38 | From (648) and (2903) follows:
% 22.79/6.38 | (3024) sum(n3, n11) = all_0_4_4
% 22.79/6.38 |
% 22.79/6.38 | From (648) and (2901) follows:
% 22.79/6.38 | (3025) sum(n3, n10) = all_0_2_2
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n3, n11, all_0_4_4, n14 and discharging atoms sum(n3, n11) = all_0_4_4, sum(n3, n11) = n14, yields:
% 22.79/6.38 | (465) all_0_4_4 = n14
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n3, n10, all_0_2_2, n13 and discharging atoms sum(n3, n10) = all_0_2_2, sum(n3, n10) = n13, yields:
% 22.79/6.38 | (464) all_0_2_2 = n13
% 22.79/6.38 |
% 22.79/6.38 | From (464) and (187) follows:
% 22.79/6.38 | (466) pred(n13) = all_0_1_1
% 22.79/6.38 |
% 22.79/6.38 | From (465) and (396) follows:
% 22.79/6.38 | (467) pred(n14) = all_0_3_3
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (37) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 22.79/6.38 | (468) all_0_3_3 = n13
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (37) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 22.79/6.38 | (469) all_0_1_1 = n12
% 22.79/6.38 |
% 22.79/6.38 | From (468) and (261) follows:
% 22.79/6.38 | (470) sum(n13, all_0_0_0) = all_0_6_6
% 22.79/6.38 |
% 22.79/6.38 | From (469) and (796) follows:
% 22.79/6.38 | (3033) sum(n10, n12) = all_0_0_0
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n10, n12, all_0_0_0, n6 and discharging atoms sum(n10, n12) = all_0_0_0, sum(n10, n12) = n6, yields:
% 22.79/6.38 | (557) all_0_0_0 = n6
% 22.79/6.38 |
% 22.79/6.38 | From (557) and (470) follows:
% 22.79/6.38 | (3035) sum(n13, n6) = all_0_6_6
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n13, n6, all_0_6_6, n3 and discharging atoms sum(n13, n6) = all_0_6_6, sum(n13, n6) = n3, yields:
% 22.79/6.38 | (961) all_0_6_6 = n3
% 22.79/6.38 |
% 22.79/6.38 | Equations (961) can reduce 245 to:
% 22.79/6.38 | (458) $false
% 22.79/6.38 |
% 22.79/6.38 |-The branch is then unsatisfiable
% 22.79/6.38 |-Branch two:
% 22.79/6.38 | (663) ~ (all_0_8_8 = n3)
% 22.79/6.38 | (664) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.38 |
% 22.79/6.38 +-Applying beta-rule and splitting (664), into two cases.
% 22.79/6.38 |-Branch one:
% 22.79/6.38 | (665) all_0_8_8 = n2
% 22.79/6.38 |
% 22.79/6.38 | From (665) and (2903) follows:
% 22.79/6.38 | (3041) sum(n2, n11) = all_0_4_4
% 22.79/6.38 |
% 22.79/6.38 | From (665) and (2901) follows:
% 22.79/6.38 | (3042) sum(n2, n10) = all_0_2_2
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n2, n11, all_0_4_4, n13 and discharging atoms sum(n2, n11) = all_0_4_4, sum(n2, n11) = n13, yields:
% 22.79/6.38 | (482) all_0_4_4 = n13
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n2, n10, all_0_2_2, n12 and discharging atoms sum(n2, n10) = all_0_2_2, sum(n2, n10) = n12, yields:
% 22.79/6.38 | (481) all_0_2_2 = n12
% 22.79/6.38 |
% 22.79/6.38 | From (481) and (187) follows:
% 22.79/6.38 | (483) pred(n12) = all_0_1_1
% 22.79/6.38 |
% 22.79/6.38 | From (482) and (396) follows:
% 22.79/6.38 | (484) pred(n13) = all_0_3_3
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (37) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 22.79/6.38 | (485) all_0_3_3 = n12
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (37) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 22.79/6.38 | (486) all_0_1_1 = n11
% 22.79/6.38 |
% 22.79/6.38 | From (485) and (261) follows:
% 22.79/6.38 | (487) sum(n12, all_0_0_0) = all_0_6_6
% 22.79/6.38 |
% 22.79/6.38 | From (486) and (796) follows:
% 22.79/6.38 | (3050) sum(n10, n11) = all_0_0_0
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n10, n11, all_0_0_0, n5 and discharging atoms sum(n10, n11) = all_0_0_0, sum(n10, n11) = n5, yields:
% 22.79/6.38 | (574) all_0_0_0 = n5
% 22.79/6.38 |
% 22.79/6.38 | From (574) and (487) follows:
% 22.79/6.38 | (3052) sum(n12, n5) = all_0_6_6
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n12, n5, all_0_6_6, n1 and discharging atoms sum(n12, n5) = all_0_6_6, sum(n12, n5) = n1, yields:
% 22.79/6.38 | (771) all_0_6_6 = n1
% 22.79/6.38 |
% 22.79/6.38 | Equations (771) can reduce 38 to:
% 22.79/6.38 | (458) $false
% 22.79/6.38 |
% 22.79/6.38 |-The branch is then unsatisfiable
% 22.79/6.38 |-Branch two:
% 22.79/6.38 | (680) ~ (all_0_8_8 = n2)
% 22.79/6.38 | (681) all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.38 |
% 22.79/6.38 +-Applying beta-rule and splitting (681), into two cases.
% 22.79/6.38 |-Branch one:
% 22.79/6.38 | (682) all_0_8_8 = n1
% 22.79/6.38 |
% 22.79/6.38 | From (682) and (2903) follows:
% 22.79/6.38 | (3058) sum(n1, n11) = all_0_4_4
% 22.79/6.38 |
% 22.79/6.38 | From (682) and (2901) follows:
% 22.79/6.38 | (3059) sum(n1, n10) = all_0_2_2
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n1, n11, all_0_4_4, n12 and discharging atoms sum(n1, n11) = all_0_4_4, sum(n1, n11) = n12, yields:
% 22.79/6.38 | (499) all_0_4_4 = n12
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n1, n10, all_0_2_2, n11 and discharging atoms sum(n1, n10) = all_0_2_2, sum(n1, n10) = n11, yields:
% 22.79/6.38 | (498) all_0_2_2 = n11
% 22.79/6.38 |
% 22.79/6.38 | From (498) and (187) follows:
% 22.79/6.38 | (500) pred(n11) = all_0_1_1
% 22.79/6.38 |
% 22.79/6.38 | From (499) and (396) follows:
% 22.79/6.38 | (501) pred(n12) = all_0_3_3
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (37) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 22.79/6.38 | (502) all_0_3_3 = n11
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (37) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 22.79/6.38 | (503) all_0_1_1 = n10
% 22.79/6.38 |
% 22.79/6.38 | From (502) and (261) follows:
% 22.79/6.38 | (504) sum(n11, all_0_0_0) = all_0_6_6
% 22.79/6.38 |
% 22.79/6.38 | From (503) and (796) follows:
% 22.79/6.38 | (3067) sum(n10, n10) = all_0_0_0
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n10, n10, all_0_0_0, n4 and discharging atoms sum(n10, n10) = all_0_0_0, sum(n10, n10) = n4, yields:
% 22.79/6.38 | (591) all_0_0_0 = n4
% 22.79/6.38 |
% 22.79/6.38 | From (591) and (504) follows:
% 22.79/6.38 | (3069) sum(n11, n4) = all_0_6_6
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n11, n4, all_0_6_6, n15 and discharging atoms sum(n11, n4) = all_0_6_6, sum(n11, n4) = n15, yields:
% 22.79/6.38 | (885) all_0_6_6 = n15
% 22.79/6.38 |
% 22.79/6.38 | Equations (885) can reduce 225 to:
% 22.79/6.38 | (458) $false
% 22.79/6.38 |
% 22.79/6.38 |-The branch is then unsatisfiable
% 22.79/6.38 |-Branch two:
% 22.79/6.38 | (697) ~ (all_0_8_8 = n1)
% 22.79/6.38 | (698) all_0_8_8 = n0
% 22.79/6.38 |
% 22.79/6.38 | From (698) and (2903) follows:
% 22.79/6.38 | (3074) sum(n0, n11) = all_0_4_4
% 22.79/6.38 |
% 22.79/6.38 | From (698) and (2901) follows:
% 22.79/6.38 | (3075) sum(n0, n10) = all_0_2_2
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n0, n11, all_0_4_4, n11 and discharging atoms sum(n0, n11) = all_0_4_4, sum(n0, n11) = n11, yields:
% 22.79/6.38 | (516) all_0_4_4 = n11
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n0, n10, all_0_2_2, n10 and discharging atoms sum(n0, n10) = all_0_2_2, sum(n0, n10) = n10, yields:
% 22.79/6.38 | (515) all_0_2_2 = n10
% 22.79/6.38 |
% 22.79/6.38 | From (515) and (187) follows:
% 22.79/6.38 | (517) pred(n10) = all_0_1_1
% 22.79/6.38 |
% 22.79/6.38 | From (516) and (396) follows:
% 22.79/6.38 | (518) pred(n11) = all_0_3_3
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (37) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 22.79/6.38 | (519) all_0_3_3 = n10
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (37) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 22.79/6.38 | (520) all_0_1_1 = n9
% 22.79/6.38 |
% 22.79/6.38 | From (519) and (261) follows:
% 22.79/6.38 | (521) sum(n10, all_0_0_0) = all_0_6_6
% 22.79/6.38 |
% 22.79/6.38 | From (520) and (796) follows:
% 22.79/6.38 | (3083) sum(n10, n9) = all_0_0_0
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n10, n9, all_0_0_0, n3 and discharging atoms sum(n10, n9) = all_0_0_0, sum(n10, n9) = n3, yields:
% 22.79/6.38 | (608) all_0_0_0 = n3
% 22.79/6.38 |
% 22.79/6.38 | From (608) and (521) follows:
% 22.79/6.38 | (3085) sum(n10, n3) = all_0_6_6
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n10, n3, all_0_6_6, n13 and discharging atoms sum(n10, n3) = all_0_6_6, sum(n10, n3) = n13, yields:
% 22.79/6.38 | (998) all_0_6_6 = n13
% 22.79/6.38 |
% 22.79/6.38 | Equations (998) can reduce 130 to:
% 22.79/6.38 | (458) $false
% 22.79/6.38 |
% 22.79/6.38 |-The branch is then unsatisfiable
% 22.79/6.38 |-Branch two:
% 22.79/6.38 | (811) ~ (all_0_7_7 = n10)
% 22.79/6.38 | (812) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.38 |
% 22.79/6.38 +-Applying beta-rule and splitting (528), into two cases.
% 22.79/6.38 |-Branch one:
% 22.79/6.38 | (529) all_0_8_8 = n10
% 22.79/6.38 |
% 22.79/6.38 | From (529) and (64) follows:
% 22.79/6.38 | (3091) sum(n10, all_0_5_5) = all_0_4_4
% 22.79/6.38 |
% 22.79/6.38 | From (529) and (160) follows:
% 22.79/6.38 | (3092) sum(n10, all_0_7_7) = all_0_2_2
% 22.79/6.38 |
% 22.79/6.38 +-Applying beta-rule and splitting (812), into two cases.
% 22.79/6.38 |-Branch one:
% 22.79/6.38 | (813) all_0_7_7 = n9
% 22.79/6.38 |
% 22.79/6.38 | From (813) and (176) follows:
% 22.79/6.38 | (814) succ(n9) = all_0_5_5
% 22.79/6.38 |
% 22.79/6.38 | From (813) and (59) follows:
% 22.79/6.38 | (815) sum(n9, all_0_1_1) = all_0_0_0
% 22.79/6.38 |
% 22.79/6.38 | From (813) and (3092) follows:
% 22.79/6.38 | (3096) sum(n10, n9) = all_0_2_2
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (219) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 22.79/6.38 | (817) all_0_5_5 = n10
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n10, n9, all_0_2_2, n3 and discharging atoms sum(n10, n9) = all_0_2_2, sum(n10, n9) = n3, yields:
% 22.79/6.38 | (634) all_0_2_2 = n3
% 22.79/6.38 |
% 22.79/6.38 | From (634) and (187) follows:
% 22.79/6.38 | (636) pred(n3) = all_0_1_1
% 22.79/6.38 |
% 22.79/6.38 | From (817) and (3091) follows:
% 22.79/6.38 | (3100) sum(n10, n10) = all_0_4_4
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (37) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 22.79/6.38 | (639) all_0_1_1 = n2
% 22.79/6.38 |
% 22.79/6.38 | Instantiating formula (89) with n10, n10, all_0_4_4, n4 and discharging atoms sum(n10, n10) = all_0_4_4, sum(n10, n10) = n4, yields:
% 22.79/6.39 | (635) all_0_4_4 = n4
% 22.79/6.39 |
% 22.79/6.39 | From (635) and (396) follows:
% 22.79/6.39 | (637) pred(n4) = all_0_3_3
% 22.79/6.39 |
% 22.79/6.39 | From (639) and (815) follows:
% 22.79/6.39 | (3104) sum(n9, n2) = all_0_0_0
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (37) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 22.79/6.39 | (638) all_0_3_3 = n3
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n9, n2, all_0_0_0, n11 and discharging atoms sum(n9, n2) = all_0_0_0, sum(n9, n2) = n11, yields:
% 22.79/6.39 | (472) all_0_0_0 = n11
% 22.79/6.39 |
% 22.79/6.39 | From (638)(472) and (261) follows:
% 22.79/6.39 | (3107) sum(n3, n11) = all_0_6_6
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n3, n11, all_0_6_6, n14 and discharging atoms sum(n3, n11) = all_0_6_6, sum(n3, n11) = n14, yields:
% 22.79/6.39 | (559) all_0_6_6 = n14
% 22.79/6.39 |
% 22.79/6.39 | Equations (559) can reduce 314 to:
% 22.79/6.39 | (458) $false
% 22.79/6.39 |
% 22.79/6.39 |-The branch is then unsatisfiable
% 22.79/6.39 |-Branch two:
% 22.79/6.39 | (830) ~ (all_0_7_7 = n9)
% 22.79/6.39 | (831) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.39 |
% 22.79/6.39 +-Applying beta-rule and splitting (831), into two cases.
% 22.79/6.39 |-Branch one:
% 22.79/6.39 | (832) all_0_7_7 = n8
% 22.79/6.39 |
% 22.79/6.39 | From (832) and (176) follows:
% 22.79/6.39 | (833) succ(n8) = all_0_5_5
% 22.79/6.39 |
% 22.79/6.39 | From (832) and (59) follows:
% 22.79/6.39 | (834) sum(n8, all_0_1_1) = all_0_0_0
% 22.79/6.39 |
% 22.79/6.39 | From (832) and (3092) follows:
% 22.79/6.39 | (3115) sum(n10, n8) = all_0_2_2
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (219) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 22.79/6.39 | (836) all_0_5_5 = n9
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n10, n8, all_0_2_2, n2 and discharging atoms sum(n10, n8) = all_0_2_2, sum(n10, n8) = n2, yields:
% 22.79/6.39 | (651) all_0_2_2 = n2
% 22.79/6.39 |
% 22.79/6.39 | From (651) and (187) follows:
% 22.79/6.39 | (653) pred(n2) = all_0_1_1
% 22.79/6.39 |
% 22.79/6.39 | From (836) and (3091) follows:
% 22.79/6.39 | (3119) sum(n10, n9) = all_0_4_4
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (37) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 22.79/6.39 | (656) all_0_1_1 = n1
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n10, n9, all_0_4_4, n3 and discharging atoms sum(n10, n9) = all_0_4_4, sum(n10, n9) = n3, yields:
% 22.79/6.39 | (652) all_0_4_4 = n3
% 22.79/6.39 |
% 22.79/6.39 | From (652) and (396) follows:
% 22.79/6.39 | (654) pred(n3) = all_0_3_3
% 22.79/6.39 |
% 22.79/6.39 | From (656) and (834) follows:
% 22.79/6.39 | (3123) sum(n8, n1) = all_0_0_0
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (37) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 22.79/6.39 | (655) all_0_3_3 = n2
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n8, n1, all_0_0_0, n9 and discharging atoms sum(n8, n1) = all_0_0_0, sum(n8, n1) = n9, yields:
% 22.79/6.39 | (506) all_0_0_0 = n9
% 22.79/6.39 |
% 22.79/6.39 | From (655)(506) and (261) follows:
% 22.79/6.39 | (3126) sum(n2, n9) = all_0_6_6
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n2, n9, all_0_6_6, n11 and discharging atoms sum(n2, n9) = all_0_6_6, sum(n2, n9) = n11, yields:
% 22.79/6.39 | (809) all_0_6_6 = n11
% 22.79/6.39 |
% 22.79/6.39 | Equations (809) can reduce 70 to:
% 22.79/6.39 | (458) $false
% 22.79/6.39 |
% 22.79/6.39 |-The branch is then unsatisfiable
% 22.79/6.39 |-Branch two:
% 22.79/6.39 | (849) ~ (all_0_7_7 = n8)
% 22.79/6.39 | (850) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.39 |
% 22.79/6.39 +-Applying beta-rule and splitting (850), into two cases.
% 22.79/6.39 |-Branch one:
% 22.79/6.39 | (851) all_0_7_7 = n7
% 22.79/6.39 |
% 22.79/6.39 | From (851) and (176) follows:
% 22.79/6.39 | (852) succ(n7) = all_0_5_5
% 22.79/6.39 |
% 22.79/6.39 | From (851) and (59) follows:
% 22.79/6.39 | (853) sum(n7, all_0_1_1) = all_0_0_0
% 22.79/6.39 |
% 22.79/6.39 | From (851) and (3092) follows:
% 22.79/6.39 | (3134) sum(n10, n7) = all_0_2_2
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (219) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 22.79/6.39 | (855) all_0_5_5 = n8
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n10, n7, all_0_2_2, n1 and discharging atoms sum(n10, n7) = all_0_2_2, sum(n10, n7) = n1, yields:
% 22.79/6.39 | (668) all_0_2_2 = n1
% 22.79/6.39 |
% 22.79/6.39 | From (668) and (187) follows:
% 22.79/6.39 | (670) pred(n1) = all_0_1_1
% 22.79/6.39 |
% 22.79/6.39 | From (855) and (3091) follows:
% 22.79/6.39 | (3138) sum(n10, n8) = all_0_4_4
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (37) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 22.79/6.39 | (673) all_0_1_1 = n0
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n10, n8, all_0_4_4, n2 and discharging atoms sum(n10, n8) = all_0_4_4, sum(n10, n8) = n2, yields:
% 22.79/6.39 | (669) all_0_4_4 = n2
% 22.79/6.39 |
% 22.79/6.39 | From (669) and (396) follows:
% 22.79/6.39 | (671) pred(n2) = all_0_3_3
% 22.79/6.39 |
% 22.79/6.39 | From (673) and (853) follows:
% 22.79/6.39 | (3142) sum(n7, n0) = all_0_0_0
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (37) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 22.79/6.39 | (672) all_0_3_3 = n1
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n7, n0, all_0_0_0, n7 and discharging atoms sum(n7, n0) = all_0_0_0, sum(n7, n0) = n7, yields:
% 22.79/6.39 | (540) all_0_0_0 = n7
% 22.79/6.39 |
% 22.79/6.39 | From (672)(540) and (261) follows:
% 22.79/6.39 | (3145) sum(n1, n7) = all_0_6_6
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n1, n7, all_0_6_6, n8 and discharging atoms sum(n1, n7) = all_0_6_6, sum(n1, n7) = n8, yields:
% 22.79/6.39 | (474) all_0_6_6 = n8
% 22.79/6.39 |
% 22.79/6.39 | Equations (474) can reduce 86 to:
% 22.79/6.39 | (458) $false
% 22.79/6.39 |
% 22.79/6.39 |-The branch is then unsatisfiable
% 22.79/6.39 |-Branch two:
% 22.79/6.39 | (868) ~ (all_0_7_7 = n7)
% 22.79/6.39 | (869) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.39 |
% 22.79/6.39 +-Applying beta-rule and splitting (869), into two cases.
% 22.79/6.39 |-Branch one:
% 22.79/6.39 | (870) all_0_7_7 = n6
% 22.79/6.39 |
% 22.79/6.39 | From (870) and (176) follows:
% 22.79/6.39 | (871) succ(n6) = all_0_5_5
% 22.79/6.39 |
% 22.79/6.39 | From (870) and (59) follows:
% 22.79/6.39 | (872) sum(n6, all_0_1_1) = all_0_0_0
% 22.79/6.39 |
% 22.79/6.39 | From (870) and (3092) follows:
% 22.79/6.39 | (3153) sum(n10, n6) = all_0_2_2
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (219) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 22.79/6.39 | (874) all_0_5_5 = n7
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n10, n6, all_0_2_2, n0 and discharging atoms sum(n10, n6) = all_0_2_2, sum(n10, n6) = n0, yields:
% 22.79/6.39 | (685) all_0_2_2 = n0
% 22.79/6.39 |
% 22.79/6.39 | From (685) and (187) follows:
% 22.79/6.39 | (687) pred(n0) = all_0_1_1
% 22.79/6.39 |
% 22.79/6.39 | From (874) and (3091) follows:
% 22.79/6.39 | (3157) sum(n10, n7) = all_0_4_4
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (37) with n0, all_0_1_1, n15 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n15, yields:
% 22.79/6.39 | (690) all_0_1_1 = n15
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n10, n7, all_0_4_4, n1 and discharging atoms sum(n10, n7) = all_0_4_4, sum(n10, n7) = n1, yields:
% 22.79/6.39 | (686) all_0_4_4 = n1
% 22.79/6.39 |
% 22.79/6.39 | From (686) and (396) follows:
% 22.79/6.39 | (688) pred(n1) = all_0_3_3
% 22.79/6.39 |
% 22.79/6.39 | From (690) and (872) follows:
% 22.79/6.39 | (3161) sum(n6, n15) = all_0_0_0
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (37) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 22.79/6.39 | (689) all_0_3_3 = n0
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n6, n15, all_0_0_0, n5 and discharging atoms sum(n6, n15) = all_0_0_0, sum(n6, n15) = n5, yields:
% 22.79/6.39 | (574) all_0_0_0 = n5
% 22.79/6.39 |
% 22.79/6.39 | From (689)(574) and (261) follows:
% 22.79/6.39 | (3164) sum(n0, n5) = all_0_6_6
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n0, n5, all_0_6_6, n5 and discharging atoms sum(n0, n5) = all_0_6_6, sum(n0, n5) = n5, yields:
% 22.79/6.39 | (847) all_0_6_6 = n5
% 22.79/6.39 |
% 22.79/6.39 | Equations (847) can reduce 409 to:
% 22.79/6.39 | (458) $false
% 22.79/6.39 |
% 22.79/6.39 |-The branch is then unsatisfiable
% 22.79/6.39 |-Branch two:
% 22.79/6.39 | (887) ~ (all_0_7_7 = n6)
% 22.79/6.39 | (888) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.39 |
% 22.79/6.39 +-Applying beta-rule and splitting (888), into two cases.
% 22.79/6.39 |-Branch one:
% 22.79/6.39 | (889) all_0_7_7 = n5
% 22.79/6.39 |
% 22.79/6.39 | From (889) and (176) follows:
% 22.79/6.39 | (890) succ(n5) = all_0_5_5
% 22.79/6.39 |
% 22.79/6.39 | From (889) and (59) follows:
% 22.79/6.39 | (891) sum(n5, all_0_1_1) = all_0_0_0
% 22.79/6.39 |
% 22.79/6.39 | From (889) and (3092) follows:
% 22.79/6.39 | (3172) sum(n10, n5) = all_0_2_2
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (219) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 22.79/6.39 | (893) all_0_5_5 = n6
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n10, n5, all_0_2_2, n15 and discharging atoms sum(n10, n5) = all_0_2_2, sum(n10, n5) = n15, yields:
% 22.79/6.39 | (701) all_0_2_2 = n15
% 22.79/6.39 |
% 22.79/6.39 | From (701) and (187) follows:
% 22.79/6.39 | (703) pred(n15) = all_0_1_1
% 22.79/6.39 |
% 22.79/6.39 | From (893) and (3091) follows:
% 22.79/6.39 | (3176) sum(n10, n6) = all_0_4_4
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (37) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 22.79/6.39 | (705) all_0_1_1 = n14
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n10, n6, all_0_4_4, n0 and discharging atoms sum(n10, n6) = all_0_4_4, sum(n10, n6) = n0, yields:
% 22.79/6.39 | (702) all_0_4_4 = n0
% 22.79/6.39 |
% 22.79/6.39 | From (702) and (396) follows:
% 22.79/6.39 | (704) pred(n0) = all_0_3_3
% 22.79/6.39 |
% 22.79/6.39 | From (705) and (891) follows:
% 22.79/6.39 | (3180) sum(n5, n14) = all_0_0_0
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (37) with n0, all_0_3_3, n15 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n15, yields:
% 22.79/6.39 | (706) all_0_3_3 = n15
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n5, n14, all_0_0_0, n3 and discharging atoms sum(n5, n14) = all_0_0_0, sum(n5, n14) = n3, yields:
% 22.79/6.39 | (608) all_0_0_0 = n3
% 22.79/6.39 |
% 22.79/6.39 | From (706)(608) and (261) follows:
% 22.79/6.39 | (3183) sum(n15, n3) = all_0_6_6
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n15, n3, all_0_6_6, n2 and discharging atoms sum(n15, n3) = all_0_6_6, sum(n15, n3) = n2, yields:
% 22.79/6.39 | (525) all_0_6_6 = n2
% 22.79/6.39 |
% 22.79/6.39 | Equations (525) can reduce 231 to:
% 22.79/6.39 | (458) $false
% 22.79/6.39 |
% 22.79/6.39 |-The branch is then unsatisfiable
% 22.79/6.39 |-Branch two:
% 22.79/6.39 | (906) ~ (all_0_7_7 = n5)
% 22.79/6.39 | (907) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.39 |
% 22.79/6.39 +-Applying beta-rule and splitting (907), into two cases.
% 22.79/6.39 |-Branch one:
% 22.79/6.39 | (908) all_0_7_7 = n4
% 22.79/6.39 |
% 22.79/6.39 | From (908) and (176) follows:
% 22.79/6.39 | (909) succ(n4) = all_0_5_5
% 22.79/6.39 |
% 22.79/6.39 | From (908) and (59) follows:
% 22.79/6.39 | (910) sum(n4, all_0_1_1) = all_0_0_0
% 22.79/6.39 |
% 22.79/6.39 | From (908) and (3092) follows:
% 22.79/6.39 | (3191) sum(n10, n4) = all_0_2_2
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (219) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 22.79/6.39 | (912) all_0_5_5 = n5
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n10, n4, all_0_2_2, n14 and discharging atoms sum(n10, n4) = all_0_2_2, sum(n10, n4) = n14, yields:
% 22.79/6.39 | (447) all_0_2_2 = n14
% 22.79/6.39 |
% 22.79/6.39 | From (447) and (187) follows:
% 22.79/6.39 | (449) pred(n14) = all_0_1_1
% 22.79/6.39 |
% 22.79/6.39 | From (912) and (3091) follows:
% 22.79/6.39 | (3195) sum(n10, n5) = all_0_4_4
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (37) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 22.79/6.39 | (452) all_0_1_1 = n13
% 22.79/6.39 |
% 22.79/6.39 | Instantiating formula (89) with n10, n5, all_0_4_4, n15 and discharging atoms sum(n10, n5) = all_0_4_4, sum(n10, n5) = n15, yields:
% 22.79/6.39 | (448) all_0_4_4 = n15
% 22.79/6.39 |
% 22.79/6.39 | From (448) and (396) follows:
% 22.79/6.39 | (450) pred(n15) = all_0_3_3
% 22.79/6.39 |
% 22.79/6.39 | From (452) and (910) follows:
% 22.79/6.40 | (3199) sum(n4, n13) = all_0_0_0
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (37) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 22.79/6.40 | (451) all_0_3_3 = n14
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n4, n13, all_0_0_0, n1 and discharging atoms sum(n4, n13) = all_0_0_0, sum(n4, n13) = n1, yields:
% 22.79/6.40 | (642) all_0_0_0 = n1
% 22.79/6.40 |
% 22.79/6.40 | From (451)(642) and (261) follows:
% 22.79/6.40 | (3202) sum(n14, n1) = all_0_6_6
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n14, n1, all_0_6_6, n15 and discharging atoms sum(n14, n1) = all_0_6_6, sum(n14, n1) = n15, yields:
% 22.79/6.40 | (885) all_0_6_6 = n15
% 22.79/6.40 |
% 22.79/6.40 | Equations (885) can reduce 225 to:
% 22.79/6.40 | (458) $false
% 22.79/6.40 |
% 22.79/6.40 |-The branch is then unsatisfiable
% 22.79/6.40 |-Branch two:
% 22.79/6.40 | (925) ~ (all_0_7_7 = n4)
% 22.79/6.40 | (926) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.40 |
% 22.79/6.40 +-Applying beta-rule and splitting (926), into two cases.
% 22.79/6.40 |-Branch one:
% 22.79/6.40 | (927) all_0_7_7 = n3
% 22.79/6.40 |
% 22.79/6.40 | From (927) and (176) follows:
% 22.79/6.40 | (928) succ(n3) = all_0_5_5
% 22.79/6.40 |
% 22.79/6.40 | From (927) and (59) follows:
% 22.79/6.40 | (929) sum(n3, all_0_1_1) = all_0_0_0
% 22.79/6.40 |
% 22.79/6.40 | From (927) and (3092) follows:
% 22.79/6.40 | (3210) sum(n10, n3) = all_0_2_2
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (219) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 22.79/6.40 | (931) all_0_5_5 = n4
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n10, n3, all_0_2_2, n13 and discharging atoms sum(n10, n3) = all_0_2_2, sum(n10, n3) = n13, yields:
% 22.79/6.40 | (464) all_0_2_2 = n13
% 22.79/6.40 |
% 22.79/6.40 | From (464) and (187) follows:
% 22.79/6.40 | (466) pred(n13) = all_0_1_1
% 22.79/6.40 |
% 22.79/6.40 | From (931) and (3091) follows:
% 22.79/6.40 | (3214) sum(n10, n4) = all_0_4_4
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (37) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 22.79/6.40 | (469) all_0_1_1 = n12
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n10, n4, all_0_4_4, n14 and discharging atoms sum(n10, n4) = all_0_4_4, sum(n10, n4) = n14, yields:
% 22.79/6.40 | (465) all_0_4_4 = n14
% 22.79/6.40 |
% 22.79/6.40 | From (465) and (396) follows:
% 22.79/6.40 | (467) pred(n14) = all_0_3_3
% 22.79/6.40 |
% 22.79/6.40 | From (469) and (929) follows:
% 22.79/6.40 | (3218) sum(n3, n12) = all_0_0_0
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (37) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 22.79/6.40 | (468) all_0_3_3 = n13
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n3, n12, all_0_0_0, n15 and discharging atoms sum(n3, n12) = all_0_0_0, sum(n3, n12) = n15, yields:
% 22.79/6.40 | (676) all_0_0_0 = n15
% 22.79/6.40 |
% 22.79/6.40 | From (468)(676) and (261) follows:
% 22.79/6.40 | (3221) sum(n13, n15) = all_0_6_6
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n13, n15, all_0_6_6, n12 and discharging atoms sum(n13, n15) = all_0_6_6, sum(n13, n15) = n12, yields:
% 22.79/6.40 | (576) all_0_6_6 = n12
% 22.79/6.40 |
% 22.79/6.40 | Equations (576) can reduce 42 to:
% 22.79/6.40 | (458) $false
% 22.79/6.40 |
% 22.79/6.40 |-The branch is then unsatisfiable
% 22.79/6.40 |-Branch two:
% 22.79/6.40 | (944) ~ (all_0_7_7 = n3)
% 22.79/6.40 | (945) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.40 |
% 22.79/6.40 +-Applying beta-rule and splitting (945), into two cases.
% 22.79/6.40 |-Branch one:
% 22.79/6.40 | (946) all_0_7_7 = n2
% 22.79/6.40 |
% 22.79/6.40 | From (946) and (176) follows:
% 22.79/6.40 | (947) succ(n2) = all_0_5_5
% 22.79/6.40 |
% 22.79/6.40 | From (946) and (59) follows:
% 22.79/6.40 | (948) sum(n2, all_0_1_1) = all_0_0_0
% 22.79/6.40 |
% 22.79/6.40 | From (946) and (3092) follows:
% 22.79/6.40 | (3229) sum(n10, n2) = all_0_2_2
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (219) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 22.79/6.40 | (950) all_0_5_5 = n3
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n10, n2, all_0_2_2, n12 and discharging atoms sum(n10, n2) = all_0_2_2, sum(n10, n2) = n12, yields:
% 22.79/6.40 | (481) all_0_2_2 = n12
% 22.79/6.40 |
% 22.79/6.40 | From (481) and (187) follows:
% 22.79/6.40 | (483) pred(n12) = all_0_1_1
% 22.79/6.40 |
% 22.79/6.40 | From (950) and (3091) follows:
% 22.79/6.40 | (3233) sum(n10, n3) = all_0_4_4
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (37) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 22.79/6.40 | (486) all_0_1_1 = n11
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n10, n3, all_0_4_4, n13 and discharging atoms sum(n10, n3) = all_0_4_4, sum(n10, n3) = n13, yields:
% 22.79/6.40 | (482) all_0_4_4 = n13
% 22.79/6.40 |
% 22.79/6.40 | From (482) and (396) follows:
% 22.79/6.40 | (484) pred(n13) = all_0_3_3
% 22.79/6.40 |
% 22.79/6.40 | From (486) and (948) follows:
% 22.79/6.40 | (3237) sum(n2, n11) = all_0_0_0
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (37) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 22.79/6.40 | (485) all_0_3_3 = n12
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n2, n11, all_0_0_0, n13 and discharging atoms sum(n2, n11) = all_0_0_0, sum(n2, n11) = n13, yields:
% 22.79/6.40 | (709) all_0_0_0 = n13
% 22.79/6.40 |
% 22.79/6.40 | From (485)(709) and (261) follows:
% 22.79/6.40 | (3240) sum(n12, n13) = all_0_6_6
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n12, n13, all_0_6_6, n9 and discharging atoms sum(n12, n13) = all_0_6_6, sum(n12, n13) = n9, yields:
% 22.79/6.40 | (923) all_0_6_6 = n9
% 22.79/6.40 |
% 22.79/6.40 | Equations (923) can reduce 404 to:
% 22.79/6.40 | (458) $false
% 22.79/6.40 |
% 22.79/6.40 |-The branch is then unsatisfiable
% 22.79/6.40 |-Branch two:
% 22.79/6.40 | (963) ~ (all_0_7_7 = n2)
% 22.79/6.40 | (964) all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.40 |
% 22.79/6.40 +-Applying beta-rule and splitting (964), into two cases.
% 22.79/6.40 |-Branch one:
% 22.79/6.40 | (965) all_0_7_7 = n1
% 22.79/6.40 |
% 22.79/6.40 | From (965) and (176) follows:
% 22.79/6.40 | (966) succ(n1) = all_0_5_5
% 22.79/6.40 |
% 22.79/6.40 | From (965) and (59) follows:
% 22.79/6.40 | (967) sum(n1, all_0_1_1) = all_0_0_0
% 22.79/6.40 |
% 22.79/6.40 | From (965) and (3092) follows:
% 22.79/6.40 | (3248) sum(n10, n1) = all_0_2_2
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (219) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 22.79/6.40 | (969) all_0_5_5 = n2
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n10, n1, all_0_2_2, n11 and discharging atoms sum(n10, n1) = all_0_2_2, sum(n10, n1) = n11, yields:
% 22.79/6.40 | (498) all_0_2_2 = n11
% 22.79/6.40 |
% 22.79/6.40 | From (498) and (187) follows:
% 22.79/6.40 | (500) pred(n11) = all_0_1_1
% 22.79/6.40 |
% 22.79/6.40 | From (969) and (3091) follows:
% 22.79/6.40 | (3252) sum(n10, n2) = all_0_4_4
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (37) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 22.79/6.40 | (503) all_0_1_1 = n10
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n10, n2, all_0_4_4, n12 and discharging atoms sum(n10, n2) = all_0_4_4, sum(n10, n2) = n12, yields:
% 22.79/6.40 | (499) all_0_4_4 = n12
% 22.79/6.40 |
% 22.79/6.40 | From (499) and (396) follows:
% 22.79/6.40 | (501) pred(n12) = all_0_3_3
% 22.79/6.40 |
% 22.79/6.40 | From (503) and (967) follows:
% 22.79/6.40 | (3256) sum(n1, n10) = all_0_0_0
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (37) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 22.79/6.40 | (502) all_0_3_3 = n11
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n1, n10, all_0_0_0, n11 and discharging atoms sum(n1, n10) = all_0_0_0, sum(n1, n10) = n11, yields:
% 22.79/6.40 | (472) all_0_0_0 = n11
% 22.79/6.40 |
% 22.79/6.40 | From (502)(472) and (261) follows:
% 22.79/6.40 | (3259) sum(n11, n11) = all_0_6_6
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n11, n11, all_0_6_6, n6 and discharging atoms sum(n11, n11) = all_0_6_6, sum(n11, n11) = n6, yields:
% 22.79/6.40 | (491) all_0_6_6 = n6
% 22.79/6.40 |
% 22.79/6.40 | Equations (491) can reduce 418 to:
% 22.79/6.40 | (458) $false
% 22.79/6.40 |
% 22.79/6.40 |-The branch is then unsatisfiable
% 22.79/6.40 |-Branch two:
% 22.79/6.40 | (982) ~ (all_0_7_7 = n1)
% 22.79/6.40 | (983) all_0_7_7 = n0
% 22.79/6.40 |
% 22.79/6.40 | From (983) and (176) follows:
% 22.79/6.40 | (984) succ(n0) = all_0_5_5
% 22.79/6.40 |
% 22.79/6.40 | From (983) and (59) follows:
% 22.79/6.40 | (985) sum(n0, all_0_1_1) = all_0_0_0
% 22.79/6.40 |
% 22.79/6.40 | From (983) and (3092) follows:
% 22.79/6.40 | (3266) sum(n10, n0) = all_0_2_2
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (219) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 22.79/6.40 | (987) all_0_5_5 = n1
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n10, n0, all_0_2_2, n10 and discharging atoms sum(n10, n0) = all_0_2_2, sum(n10, n0) = n10, yields:
% 22.79/6.40 | (515) all_0_2_2 = n10
% 22.79/6.40 |
% 22.79/6.40 | From (515) and (187) follows:
% 22.79/6.40 | (517) pred(n10) = all_0_1_1
% 22.79/6.40 |
% 22.79/6.40 | From (987) and (3091) follows:
% 22.79/6.40 | (3270) sum(n10, n1) = all_0_4_4
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (37) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 22.79/6.40 | (520) all_0_1_1 = n9
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n10, n1, all_0_4_4, n11 and discharging atoms sum(n10, n1) = all_0_4_4, sum(n10, n1) = n11, yields:
% 22.79/6.40 | (516) all_0_4_4 = n11
% 22.79/6.40 |
% 22.79/6.40 | From (516) and (396) follows:
% 22.79/6.40 | (518) pred(n11) = all_0_3_3
% 22.79/6.40 |
% 22.79/6.40 | From (520) and (985) follows:
% 22.79/6.40 | (3274) sum(n0, n9) = all_0_0_0
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (37) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 22.79/6.40 | (519) all_0_3_3 = n10
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n0, n9, all_0_0_0, n9 and discharging atoms sum(n0, n9) = all_0_0_0, sum(n0, n9) = n9, yields:
% 22.79/6.40 | (506) all_0_0_0 = n9
% 22.79/6.40 |
% 22.79/6.40 | From (519)(506) and (261) follows:
% 22.79/6.40 | (3277) sum(n10, n9) = all_0_6_6
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (89) with n10, n9, all_0_6_6, n3 and discharging atoms sum(n10, n9) = all_0_6_6, sum(n10, n9) = n3, yields:
% 22.79/6.40 | (961) all_0_6_6 = n3
% 22.79/6.40 |
% 22.79/6.40 | Equations (961) can reduce 245 to:
% 22.79/6.40 | (458) $false
% 22.79/6.40 |
% 22.79/6.40 |-The branch is then unsatisfiable
% 22.79/6.40 |-Branch two:
% 22.79/6.40 | (544) ~ (all_0_8_8 = n10)
% 22.79/6.40 | (545) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.40 |
% 22.79/6.40 +-Applying beta-rule and splitting (812), into two cases.
% 22.79/6.40 |-Branch one:
% 22.79/6.40 | (813) all_0_7_7 = n9
% 22.79/6.40 |
% 22.79/6.40 | From (813) and (176) follows:
% 22.79/6.40 | (814) succ(n9) = all_0_5_5
% 22.79/6.40 |
% 22.79/6.40 | From (813) and (59) follows:
% 22.79/6.40 | (815) sum(n9, all_0_1_1) = all_0_0_0
% 22.79/6.40 |
% 22.79/6.40 | From (813) and (160) follows:
% 22.79/6.40 | (3285) sum(all_0_8_8, n9) = all_0_2_2
% 22.79/6.40 |
% 22.79/6.40 | Instantiating formula (219) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 22.79/6.40 | (817) all_0_5_5 = n10
% 22.79/6.40 |
% 22.79/6.40 | From (817) and (64) follows:
% 22.79/6.40 | (3287) sum(all_0_8_8, n10) = all_0_4_4
% 22.79/6.40 |
% 22.79/6.40 +-Applying beta-rule and splitting (545), into two cases.
% 22.79/6.40 |-Branch one:
% 22.79/6.40 | (546) all_0_8_8 = n9
% 22.79/6.40 |
% 22.79/6.40 | From (546) and (3287) follows:
% 22.79/6.40 | (3289) sum(n9, n10) = all_0_4_4
% 22.79/6.40 |
% 22.79/6.40 | From (546) and (3285) follows:
% 22.79/6.41 | (3290) sum(n9, n9) = all_0_2_2
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n9, n10, all_0_4_4, n3 and discharging atoms sum(n9, n10) = all_0_4_4, sum(n9, n10) = n3, yields:
% 22.79/6.41 | (652) all_0_4_4 = n3
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n9, n9, all_0_2_2, n2 and discharging atoms sum(n9, n9) = all_0_2_2, sum(n9, n9) = n2, yields:
% 22.79/6.41 | (651) all_0_2_2 = n2
% 22.79/6.41 |
% 22.79/6.41 | From (651) and (187) follows:
% 22.79/6.41 | (653) pred(n2) = all_0_1_1
% 22.79/6.41 |
% 22.79/6.41 | From (652) and (396) follows:
% 22.79/6.41 | (654) pred(n3) = all_0_3_3
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (37) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 22.79/6.41 | (655) all_0_3_3 = n2
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (37) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 22.79/6.41 | (656) all_0_1_1 = n1
% 22.79/6.41 |
% 22.79/6.41 | From (655) and (261) follows:
% 22.79/6.41 | (657) sum(n2, all_0_0_0) = all_0_6_6
% 22.79/6.41 |
% 22.79/6.41 | From (656) and (815) follows:
% 22.79/6.41 | (3298) sum(n9, n1) = all_0_0_0
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n9, n1, all_0_0_0, n10 and discharging atoms sum(n9, n1) = all_0_0_0, sum(n9, n1) = n10, yields:
% 22.79/6.41 | (489) all_0_0_0 = n10
% 22.79/6.41 |
% 22.79/6.41 | From (489) and (657) follows:
% 22.79/6.41 | (3300) sum(n2, n10) = all_0_6_6
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n2, n10, all_0_6_6, n12 and discharging atoms sum(n2, n10) = all_0_6_6, sum(n2, n10) = n12, yields:
% 22.79/6.41 | (576) all_0_6_6 = n12
% 22.79/6.41 |
% 22.79/6.41 | Equations (576) can reduce 42 to:
% 22.79/6.41 | (458) $false
% 22.79/6.41 |
% 22.79/6.41 |-The branch is then unsatisfiable
% 22.79/6.41 |-Branch two:
% 22.79/6.41 | (561) ~ (all_0_8_8 = n9)
% 22.79/6.41 | (562) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.41 |
% 22.79/6.41 +-Applying beta-rule and splitting (562), into two cases.
% 22.79/6.41 |-Branch one:
% 22.79/6.41 | (563) all_0_8_8 = n8
% 22.79/6.41 |
% 22.79/6.41 | From (563) and (3287) follows:
% 22.79/6.41 | (3306) sum(n8, n10) = all_0_4_4
% 22.79/6.41 |
% 22.79/6.41 | From (563) and (3285) follows:
% 22.79/6.41 | (3307) sum(n8, n9) = all_0_2_2
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n8, n10, all_0_4_4, n2 and discharging atoms sum(n8, n10) = all_0_4_4, sum(n8, n10) = n2, yields:
% 22.79/6.41 | (669) all_0_4_4 = n2
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n8, n9, all_0_2_2, n1 and discharging atoms sum(n8, n9) = all_0_2_2, sum(n8, n9) = n1, yields:
% 22.79/6.41 | (668) all_0_2_2 = n1
% 22.79/6.41 |
% 22.79/6.41 | From (668) and (187) follows:
% 22.79/6.41 | (670) pred(n1) = all_0_1_1
% 22.79/6.41 |
% 22.79/6.41 | From (669) and (396) follows:
% 22.79/6.41 | (671) pred(n2) = all_0_3_3
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (37) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 22.79/6.41 | (672) all_0_3_3 = n1
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (37) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 22.79/6.41 | (673) all_0_1_1 = n0
% 22.79/6.41 |
% 22.79/6.41 | From (672) and (261) follows:
% 22.79/6.41 | (674) sum(n1, all_0_0_0) = all_0_6_6
% 22.79/6.41 |
% 22.79/6.41 | From (673) and (815) follows:
% 22.79/6.41 | (3315) sum(n9, n0) = all_0_0_0
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n9, n0, all_0_0_0, n9 and discharging atoms sum(n9, n0) = all_0_0_0, sum(n9, n0) = n9, yields:
% 22.79/6.41 | (506) all_0_0_0 = n9
% 22.79/6.41 |
% 22.79/6.41 | From (506) and (674) follows:
% 22.79/6.41 | (3317) sum(n1, n9) = all_0_6_6
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n1, n9, all_0_6_6, n10 and discharging atoms sum(n1, n9) = all_0_6_6, sum(n1, n9) = n10, yields:
% 22.79/6.41 | (457) all_0_6_6 = n10
% 22.79/6.41 |
% 22.79/6.41 | Equations (457) can reduce 169 to:
% 22.79/6.41 | (458) $false
% 22.79/6.41 |
% 22.79/6.41 |-The branch is then unsatisfiable
% 22.79/6.41 |-Branch two:
% 22.79/6.41 | (578) ~ (all_0_8_8 = n8)
% 22.79/6.41 | (579) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.41 |
% 22.79/6.41 +-Applying beta-rule and splitting (579), into two cases.
% 22.79/6.41 |-Branch one:
% 22.79/6.41 | (580) all_0_8_8 = n7
% 22.79/6.41 |
% 22.79/6.41 | From (580) and (3287) follows:
% 22.79/6.41 | (3323) sum(n7, n10) = all_0_4_4
% 22.79/6.41 |
% 22.79/6.41 | From (580) and (3285) follows:
% 22.79/6.41 | (3324) sum(n7, n9) = all_0_2_2
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n7, n10, all_0_4_4, n1 and discharging atoms sum(n7, n10) = all_0_4_4, sum(n7, n10) = n1, yields:
% 22.79/6.41 | (686) all_0_4_4 = n1
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n7, n9, all_0_2_2, n0 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n0, yields:
% 22.79/6.41 | (685) all_0_2_2 = n0
% 22.79/6.41 |
% 22.79/6.41 | From (685) and (187) follows:
% 22.79/6.41 | (687) pred(n0) = all_0_1_1
% 22.79/6.41 |
% 22.79/6.41 | From (686) and (396) follows:
% 22.79/6.41 | (688) pred(n1) = all_0_3_3
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (37) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 22.79/6.41 | (689) all_0_3_3 = n0
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (37) with n0, all_0_1_1, n15 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n15, yields:
% 22.79/6.41 | (690) all_0_1_1 = n15
% 22.79/6.41 |
% 22.79/6.41 | From (689) and (261) follows:
% 22.79/6.41 | (691) sum(n0, all_0_0_0) = all_0_6_6
% 22.79/6.41 |
% 22.79/6.41 | From (690) and (815) follows:
% 22.79/6.41 | (3332) sum(n9, n15) = all_0_0_0
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n9, n15, all_0_0_0, n8 and discharging atoms sum(n9, n15) = all_0_0_0, sum(n9, n15) = n8, yields:
% 22.79/6.41 | (523) all_0_0_0 = n8
% 22.79/6.41 |
% 22.79/6.41 | From (523) and (691) follows:
% 22.79/6.41 | (3334) sum(n0, n8) = all_0_6_6
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n0, n8, all_0_6_6, n8 and discharging atoms sum(n0, n8) = all_0_6_6, sum(n0, n8) = n8, yields:
% 22.79/6.41 | (474) all_0_6_6 = n8
% 22.79/6.41 |
% 22.79/6.41 | Equations (474) can reduce 86 to:
% 22.79/6.41 | (458) $false
% 22.79/6.41 |
% 22.79/6.41 |-The branch is then unsatisfiable
% 22.79/6.41 |-Branch two:
% 22.79/6.41 | (595) ~ (all_0_8_8 = n7)
% 22.79/6.41 | (596) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.41 |
% 22.79/6.41 +-Applying beta-rule and splitting (596), into two cases.
% 22.79/6.41 |-Branch one:
% 22.79/6.41 | (597) all_0_8_8 = n6
% 22.79/6.41 |
% 22.79/6.41 | From (597) and (3287) follows:
% 22.79/6.41 | (3340) sum(n6, n10) = all_0_4_4
% 22.79/6.41 |
% 22.79/6.41 | From (597) and (3285) follows:
% 22.79/6.41 | (3341) sum(n6, n9) = all_0_2_2
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n6, n10, all_0_4_4, n0 and discharging atoms sum(n6, n10) = all_0_4_4, sum(n6, n10) = n0, yields:
% 22.79/6.41 | (702) all_0_4_4 = n0
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n6, n9, all_0_2_2, n15 and discharging atoms sum(n6, n9) = all_0_2_2, sum(n6, n9) = n15, yields:
% 22.79/6.41 | (701) all_0_2_2 = n15
% 22.79/6.41 |
% 22.79/6.41 | From (701) and (187) follows:
% 22.79/6.41 | (703) pred(n15) = all_0_1_1
% 22.79/6.41 |
% 22.79/6.41 | From (702) and (396) follows:
% 22.79/6.41 | (704) pred(n0) = all_0_3_3
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (37) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 22.79/6.41 | (705) all_0_1_1 = n14
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (37) with n0, all_0_3_3, n15 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n15, yields:
% 22.79/6.41 | (706) all_0_3_3 = n15
% 22.79/6.41 |
% 22.79/6.41 | From (706) and (261) follows:
% 22.79/6.41 | (707) sum(n15, all_0_0_0) = all_0_6_6
% 22.79/6.41 |
% 22.79/6.41 | From (705) and (815) follows:
% 22.79/6.41 | (3349) sum(n9, n14) = all_0_0_0
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n9, n14, all_0_0_0, n7 and discharging atoms sum(n9, n14) = all_0_0_0, sum(n9, n14) = n7, yields:
% 22.79/6.41 | (540) all_0_0_0 = n7
% 22.79/6.41 |
% 22.79/6.41 | From (540) and (707) follows:
% 22.79/6.41 | (3351) sum(n15, n7) = all_0_6_6
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n15, n7, all_0_6_6, n6 and discharging atoms sum(n15, n7) = all_0_6_6, sum(n15, n7) = n6, yields:
% 22.79/6.41 | (491) all_0_6_6 = n6
% 22.79/6.41 |
% 22.79/6.41 | Equations (491) can reduce 418 to:
% 22.79/6.41 | (458) $false
% 22.79/6.41 |
% 22.79/6.41 |-The branch is then unsatisfiable
% 22.79/6.41 |-Branch two:
% 22.79/6.41 | (612) ~ (all_0_8_8 = n6)
% 22.79/6.41 | (613) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.41 |
% 22.79/6.41 +-Applying beta-rule and splitting (613), into two cases.
% 22.79/6.41 |-Branch one:
% 22.79/6.41 | (614) all_0_8_8 = n5
% 22.79/6.41 |
% 22.79/6.41 | From (614) and (3287) follows:
% 22.79/6.41 | (3357) sum(n5, n10) = all_0_4_4
% 22.79/6.41 |
% 22.79/6.41 | From (614) and (3285) follows:
% 22.79/6.41 | (3358) sum(n5, n9) = all_0_2_2
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n5, n10, all_0_4_4, n15 and discharging atoms sum(n5, n10) = all_0_4_4, sum(n5, n10) = n15, yields:
% 22.79/6.41 | (448) all_0_4_4 = n15
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n5, n9, all_0_2_2, n14 and discharging atoms sum(n5, n9) = all_0_2_2, sum(n5, n9) = n14, yields:
% 22.79/6.41 | (447) all_0_2_2 = n14
% 22.79/6.41 |
% 22.79/6.41 | From (447) and (187) follows:
% 22.79/6.41 | (449) pred(n14) = all_0_1_1
% 22.79/6.41 |
% 22.79/6.41 | From (448) and (396) follows:
% 22.79/6.41 | (450) pred(n15) = all_0_3_3
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (37) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 22.79/6.41 | (451) all_0_3_3 = n14
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (37) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 22.79/6.41 | (452) all_0_1_1 = n13
% 22.79/6.41 |
% 22.79/6.41 | From (451) and (261) follows:
% 22.79/6.41 | (453) sum(n14, all_0_0_0) = all_0_6_6
% 22.79/6.41 |
% 22.79/6.41 | From (452) and (815) follows:
% 22.79/6.41 | (3366) sum(n9, n13) = all_0_0_0
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n9, n13, all_0_0_0, n6 and discharging atoms sum(n9, n13) = all_0_0_0, sum(n9, n13) = n6, yields:
% 22.79/6.41 | (557) all_0_0_0 = n6
% 22.79/6.41 |
% 22.79/6.41 | From (557) and (453) follows:
% 22.79/6.41 | (3368) sum(n14, n6) = all_0_6_6
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n14, n6, all_0_6_6, n4 and discharging atoms sum(n14, n6) = all_0_6_6, sum(n14, n6) = n4, yields:
% 22.79/6.41 | (508) all_0_6_6 = n4
% 22.79/6.41 |
% 22.79/6.41 | Equations (508) can reduce 12 to:
% 22.79/6.41 | (458) $false
% 22.79/6.41 |
% 22.79/6.41 |-The branch is then unsatisfiable
% 22.79/6.41 |-Branch two:
% 22.79/6.41 | (629) ~ (all_0_8_8 = n5)
% 22.79/6.41 | (630) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.41 |
% 22.79/6.41 +-Applying beta-rule and splitting (630), into two cases.
% 22.79/6.41 |-Branch one:
% 22.79/6.41 | (631) all_0_8_8 = n4
% 22.79/6.41 |
% 22.79/6.41 | From (631) and (3287) follows:
% 22.79/6.41 | (3374) sum(n4, n10) = all_0_4_4
% 22.79/6.41 |
% 22.79/6.41 | From (631) and (3285) follows:
% 22.79/6.41 | (3375) sum(n4, n9) = all_0_2_2
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n4, n10, all_0_4_4, n14 and discharging atoms sum(n4, n10) = all_0_4_4, sum(n4, n10) = n14, yields:
% 22.79/6.41 | (465) all_0_4_4 = n14
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (89) with n4, n9, all_0_2_2, n13 and discharging atoms sum(n4, n9) = all_0_2_2, sum(n4, n9) = n13, yields:
% 22.79/6.41 | (464) all_0_2_2 = n13
% 22.79/6.41 |
% 22.79/6.41 | From (464) and (187) follows:
% 22.79/6.41 | (466) pred(n13) = all_0_1_1
% 22.79/6.41 |
% 22.79/6.41 | From (465) and (396) follows:
% 22.79/6.41 | (467) pred(n14) = all_0_3_3
% 22.79/6.41 |
% 22.79/6.41 | Instantiating formula (37) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 22.79/6.41 | (468) all_0_3_3 = n13
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (37) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 22.79/6.42 | (469) all_0_1_1 = n12
% 22.79/6.42 |
% 22.79/6.42 | From (468) and (261) follows:
% 22.79/6.42 | (470) sum(n13, all_0_0_0) = all_0_6_6
% 22.79/6.42 |
% 22.79/6.42 | From (469) and (815) follows:
% 22.79/6.42 | (3383) sum(n9, n12) = all_0_0_0
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n9, n12, all_0_0_0, n5 and discharging atoms sum(n9, n12) = all_0_0_0, sum(n9, n12) = n5, yields:
% 22.79/6.42 | (574) all_0_0_0 = n5
% 22.79/6.42 |
% 22.79/6.42 | From (574) and (470) follows:
% 22.79/6.42 | (3385) sum(n13, n5) = all_0_6_6
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n13, n5, all_0_6_6, n2 and discharging atoms sum(n13, n5) = all_0_6_6, sum(n13, n5) = n2, yields:
% 22.79/6.42 | (525) all_0_6_6 = n2
% 22.79/6.42 |
% 22.79/6.42 | Equations (525) can reduce 231 to:
% 22.79/6.42 | (458) $false
% 22.79/6.42 |
% 22.79/6.42 |-The branch is then unsatisfiable
% 22.79/6.42 |-Branch two:
% 22.79/6.42 | (646) ~ (all_0_8_8 = n4)
% 22.79/6.42 | (647) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.42 |
% 22.79/6.42 +-Applying beta-rule and splitting (647), into two cases.
% 22.79/6.42 |-Branch one:
% 22.79/6.42 | (648) all_0_8_8 = n3
% 22.79/6.42 |
% 22.79/6.42 | From (648) and (3287) follows:
% 22.79/6.42 | (3391) sum(n3, n10) = all_0_4_4
% 22.79/6.42 |
% 22.79/6.42 | From (648) and (3285) follows:
% 22.79/6.42 | (3392) sum(n3, n9) = all_0_2_2
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n3, n10, all_0_4_4, n13 and discharging atoms sum(n3, n10) = all_0_4_4, sum(n3, n10) = n13, yields:
% 22.79/6.42 | (482) all_0_4_4 = n13
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n3, n9, all_0_2_2, n12 and discharging atoms sum(n3, n9) = all_0_2_2, sum(n3, n9) = n12, yields:
% 22.79/6.42 | (481) all_0_2_2 = n12
% 22.79/6.42 |
% 22.79/6.42 | From (481) and (187) follows:
% 22.79/6.42 | (483) pred(n12) = all_0_1_1
% 22.79/6.42 |
% 22.79/6.42 | From (482) and (396) follows:
% 22.79/6.42 | (484) pred(n13) = all_0_3_3
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (37) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 22.79/6.42 | (485) all_0_3_3 = n12
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (37) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 22.79/6.42 | (486) all_0_1_1 = n11
% 22.79/6.42 |
% 22.79/6.42 | From (485) and (261) follows:
% 22.79/6.42 | (487) sum(n12, all_0_0_0) = all_0_6_6
% 22.79/6.42 |
% 22.79/6.42 | From (486) and (815) follows:
% 22.79/6.42 | (3400) sum(n9, n11) = all_0_0_0
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n9, n11, all_0_0_0, n4 and discharging atoms sum(n9, n11) = all_0_0_0, sum(n9, n11) = n4, yields:
% 22.79/6.42 | (591) all_0_0_0 = n4
% 22.79/6.42 |
% 22.79/6.42 | From (591) and (487) follows:
% 22.79/6.42 | (3402) sum(n12, n4) = all_0_6_6
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n12, n4, all_0_6_6, n0 and discharging atoms sum(n12, n4) = all_0_6_6, sum(n12, n4) = n0, yields:
% 22.79/6.42 | (542) all_0_6_6 = n0
% 22.79/6.42 |
% 22.79/6.42 | Equations (542) can reduce 400 to:
% 22.79/6.42 | (458) $false
% 22.79/6.42 |
% 22.79/6.42 |-The branch is then unsatisfiable
% 22.79/6.42 |-Branch two:
% 22.79/6.42 | (663) ~ (all_0_8_8 = n3)
% 22.79/6.42 | (664) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.42 |
% 22.79/6.42 +-Applying beta-rule and splitting (664), into two cases.
% 22.79/6.42 |-Branch one:
% 22.79/6.42 | (665) all_0_8_8 = n2
% 22.79/6.42 |
% 22.79/6.42 | From (665) and (3287) follows:
% 22.79/6.42 | (3408) sum(n2, n10) = all_0_4_4
% 22.79/6.42 |
% 22.79/6.42 | From (665) and (3285) follows:
% 22.79/6.42 | (3409) sum(n2, n9) = all_0_2_2
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n2, n10, all_0_4_4, n12 and discharging atoms sum(n2, n10) = all_0_4_4, sum(n2, n10) = n12, yields:
% 22.79/6.42 | (499) all_0_4_4 = n12
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n2, n9, all_0_2_2, n11 and discharging atoms sum(n2, n9) = all_0_2_2, sum(n2, n9) = n11, yields:
% 22.79/6.42 | (498) all_0_2_2 = n11
% 22.79/6.42 |
% 22.79/6.42 | From (498) and (187) follows:
% 22.79/6.42 | (500) pred(n11) = all_0_1_1
% 22.79/6.42 |
% 22.79/6.42 | From (499) and (396) follows:
% 22.79/6.42 | (501) pred(n12) = all_0_3_3
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (37) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 22.79/6.42 | (502) all_0_3_3 = n11
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (37) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 22.79/6.42 | (503) all_0_1_1 = n10
% 22.79/6.42 |
% 22.79/6.42 | From (502) and (261) follows:
% 22.79/6.42 | (504) sum(n11, all_0_0_0) = all_0_6_6
% 22.79/6.42 |
% 22.79/6.42 | From (503) and (815) follows:
% 22.79/6.42 | (3417) sum(n9, n10) = all_0_0_0
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n9, n10, all_0_0_0, n3 and discharging atoms sum(n9, n10) = all_0_0_0, sum(n9, n10) = n3, yields:
% 22.79/6.42 | (608) all_0_0_0 = n3
% 22.79/6.42 |
% 22.79/6.42 | From (608) and (504) follows:
% 22.79/6.42 | (3419) sum(n11, n3) = all_0_6_6
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n11, n3, all_0_6_6, n14 and discharging atoms sum(n11, n3) = all_0_6_6, sum(n11, n3) = n14, yields:
% 22.79/6.42 | (559) all_0_6_6 = n14
% 22.79/6.42 |
% 22.79/6.42 | Equations (559) can reduce 314 to:
% 22.79/6.42 | (458) $false
% 22.79/6.42 |
% 22.79/6.42 |-The branch is then unsatisfiable
% 22.79/6.42 |-Branch two:
% 22.79/6.42 | (680) ~ (all_0_8_8 = n2)
% 22.79/6.42 | (681) all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.42 |
% 22.79/6.42 +-Applying beta-rule and splitting (681), into two cases.
% 22.79/6.42 |-Branch one:
% 22.79/6.42 | (682) all_0_8_8 = n1
% 22.79/6.42 |
% 22.79/6.42 | From (682) and (3287) follows:
% 22.79/6.42 | (3425) sum(n1, n10) = all_0_4_4
% 22.79/6.42 |
% 22.79/6.42 | From (682) and (3285) follows:
% 22.79/6.42 | (3426) sum(n1, n9) = all_0_2_2
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n1, n10, all_0_4_4, n11 and discharging atoms sum(n1, n10) = all_0_4_4, sum(n1, n10) = n11, yields:
% 22.79/6.42 | (516) all_0_4_4 = n11
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n1, n9, all_0_2_2, n10 and discharging atoms sum(n1, n9) = all_0_2_2, sum(n1, n9) = n10, yields:
% 22.79/6.42 | (515) all_0_2_2 = n10
% 22.79/6.42 |
% 22.79/6.42 | From (515) and (187) follows:
% 22.79/6.42 | (517) pred(n10) = all_0_1_1
% 22.79/6.42 |
% 22.79/6.42 | From (516) and (396) follows:
% 22.79/6.42 | (518) pred(n11) = all_0_3_3
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (37) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 22.79/6.42 | (519) all_0_3_3 = n10
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (37) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 22.79/6.42 | (520) all_0_1_1 = n9
% 22.79/6.42 |
% 22.79/6.42 | From (519) and (261) follows:
% 22.79/6.42 | (521) sum(n10, all_0_0_0) = all_0_6_6
% 22.79/6.42 |
% 22.79/6.42 | From (520) and (815) follows:
% 22.79/6.42 | (3434) sum(n9, n9) = all_0_0_0
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n9, n9, all_0_0_0, n2 and discharging atoms sum(n9, n9) = all_0_0_0, sum(n9, n9) = n2, yields:
% 22.79/6.42 | (625) all_0_0_0 = n2
% 22.79/6.42 |
% 22.79/6.42 | From (625) and (521) follows:
% 22.79/6.42 | (3436) sum(n10, n2) = all_0_6_6
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n10, n2, all_0_6_6, n12 and discharging atoms sum(n10, n2) = all_0_6_6, sum(n10, n2) = n12, yields:
% 22.79/6.42 | (576) all_0_6_6 = n12
% 22.79/6.42 |
% 22.79/6.42 | Equations (576) can reduce 42 to:
% 22.79/6.42 | (458) $false
% 22.79/6.42 |
% 22.79/6.42 |-The branch is then unsatisfiable
% 22.79/6.42 |-Branch two:
% 22.79/6.42 | (697) ~ (all_0_8_8 = n1)
% 22.79/6.42 | (698) all_0_8_8 = n0
% 22.79/6.42 |
% 22.79/6.42 | From (698) and (3287) follows:
% 22.79/6.42 | (3441) sum(n0, n10) = all_0_4_4
% 22.79/6.42 |
% 22.79/6.42 | From (698) and (3285) follows:
% 22.79/6.42 | (3442) sum(n0, n9) = all_0_2_2
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n0, n10, all_0_4_4, n10 and discharging atoms sum(n0, n10) = all_0_4_4, sum(n0, n10) = n10, yields:
% 22.79/6.42 | (533) all_0_4_4 = n10
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n0, n9, all_0_2_2, n9 and discharging atoms sum(n0, n9) = all_0_2_2, sum(n0, n9) = n9, yields:
% 22.79/6.42 | (532) all_0_2_2 = n9
% 22.79/6.42 |
% 22.79/6.42 | From (532) and (187) follows:
% 22.79/6.42 | (534) pred(n9) = all_0_1_1
% 22.79/6.42 |
% 22.79/6.42 | From (533) and (396) follows:
% 22.79/6.42 | (535) pred(n10) = all_0_3_3
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (37) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 22.79/6.42 | (536) all_0_3_3 = n9
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (37) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 22.79/6.42 | (537) all_0_1_1 = n8
% 22.79/6.42 |
% 22.79/6.42 | From (536) and (261) follows:
% 22.79/6.42 | (538) sum(n9, all_0_0_0) = all_0_6_6
% 22.79/6.42 |
% 22.79/6.42 | From (537) and (815) follows:
% 22.79/6.42 | (3450) sum(n9, n8) = all_0_0_0
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n9, n8, all_0_0_0, n1 and discharging atoms sum(n9, n8) = all_0_0_0, sum(n9, n8) = n1, yields:
% 22.79/6.42 | (642) all_0_0_0 = n1
% 22.79/6.42 |
% 22.79/6.42 | From (642) and (538) follows:
% 22.79/6.42 | (3452) sum(n9, n1) = all_0_6_6
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n9, n1, all_0_6_6, n10 and discharging atoms sum(n9, n1) = all_0_6_6, sum(n9, n1) = n10, yields:
% 22.79/6.42 | (457) all_0_6_6 = n10
% 22.79/6.42 |
% 22.79/6.42 | Equations (457) can reduce 169 to:
% 22.79/6.42 | (458) $false
% 22.79/6.42 |
% 22.79/6.42 |-The branch is then unsatisfiable
% 22.79/6.42 |-Branch two:
% 22.79/6.42 | (830) ~ (all_0_7_7 = n9)
% 22.79/6.42 | (831) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.42 |
% 22.79/6.42 +-Applying beta-rule and splitting (545), into two cases.
% 22.79/6.42 |-Branch one:
% 22.79/6.42 | (546) all_0_8_8 = n9
% 22.79/6.42 |
% 22.79/6.42 | From (546) and (64) follows:
% 22.79/6.42 | (3458) sum(n9, all_0_5_5) = all_0_4_4
% 22.79/6.42 |
% 22.79/6.42 | From (546) and (160) follows:
% 22.79/6.42 | (3459) sum(n9, all_0_7_7) = all_0_2_2
% 22.79/6.42 |
% 22.79/6.42 +-Applying beta-rule and splitting (831), into two cases.
% 22.79/6.42 |-Branch one:
% 22.79/6.42 | (832) all_0_7_7 = n8
% 22.79/6.42 |
% 22.79/6.42 | From (832) and (176) follows:
% 22.79/6.42 | (833) succ(n8) = all_0_5_5
% 22.79/6.42 |
% 22.79/6.42 | From (832) and (59) follows:
% 22.79/6.42 | (834) sum(n8, all_0_1_1) = all_0_0_0
% 22.79/6.42 |
% 22.79/6.42 | From (832) and (3459) follows:
% 22.79/6.42 | (3463) sum(n9, n8) = all_0_2_2
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (219) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 22.79/6.42 | (836) all_0_5_5 = n9
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n9, n8, all_0_2_2, n1 and discharging atoms sum(n9, n8) = all_0_2_2, sum(n9, n8) = n1, yields:
% 22.79/6.42 | (668) all_0_2_2 = n1
% 22.79/6.42 |
% 22.79/6.42 | From (668) and (187) follows:
% 22.79/6.42 | (670) pred(n1) = all_0_1_1
% 22.79/6.42 |
% 22.79/6.42 | From (836) and (3458) follows:
% 22.79/6.42 | (3467) sum(n9, n9) = all_0_4_4
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (37) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 22.79/6.42 | (673) all_0_1_1 = n0
% 22.79/6.42 |
% 22.79/6.42 | Instantiating formula (89) with n9, n9, all_0_4_4, n2 and discharging atoms sum(n9, n9) = all_0_4_4, sum(n9, n9) = n2, yields:
% 22.79/6.43 | (669) all_0_4_4 = n2
% 22.79/6.43 |
% 22.79/6.43 | From (669) and (396) follows:
% 22.79/6.43 | (671) pred(n2) = all_0_3_3
% 22.79/6.43 |
% 22.79/6.43 | From (673) and (834) follows:
% 22.79/6.43 | (3471) sum(n8, n0) = all_0_0_0
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (37) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 22.79/6.43 | (672) all_0_3_3 = n1
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n8, n0, all_0_0_0, n8 and discharging atoms sum(n8, n0) = all_0_0_0, sum(n8, n0) = n8, yields:
% 22.79/6.43 | (523) all_0_0_0 = n8
% 22.79/6.43 |
% 22.79/6.43 | From (672)(523) and (261) follows:
% 22.79/6.43 | (3474) sum(n1, n8) = all_0_6_6
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n1, n8, all_0_6_6, n9 and discharging atoms sum(n1, n8) = all_0_6_6, sum(n1, n8) = n9, yields:
% 22.79/6.43 | (923) all_0_6_6 = n9
% 22.79/6.43 |
% 22.79/6.43 | Equations (923) can reduce 404 to:
% 22.79/6.43 | (458) $false
% 22.79/6.43 |
% 22.79/6.43 |-The branch is then unsatisfiable
% 22.79/6.43 |-Branch two:
% 22.79/6.43 | (849) ~ (all_0_7_7 = n8)
% 22.79/6.43 | (850) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.43 |
% 22.79/6.43 +-Applying beta-rule and splitting (850), into two cases.
% 22.79/6.43 |-Branch one:
% 22.79/6.43 | (851) all_0_7_7 = n7
% 22.79/6.43 |
% 22.79/6.43 | From (851) and (176) follows:
% 22.79/6.43 | (852) succ(n7) = all_0_5_5
% 22.79/6.43 |
% 22.79/6.43 | From (851) and (59) follows:
% 22.79/6.43 | (853) sum(n7, all_0_1_1) = all_0_0_0
% 22.79/6.43 |
% 22.79/6.43 | From (851) and (3459) follows:
% 22.79/6.43 | (3482) sum(n9, n7) = all_0_2_2
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (219) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 22.79/6.43 | (855) all_0_5_5 = n8
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n9, n7, all_0_2_2, n0 and discharging atoms sum(n9, n7) = all_0_2_2, sum(n9, n7) = n0, yields:
% 22.79/6.43 | (685) all_0_2_2 = n0
% 22.79/6.43 |
% 22.79/6.43 | From (685) and (187) follows:
% 22.79/6.43 | (687) pred(n0) = all_0_1_1
% 22.79/6.43 |
% 22.79/6.43 | From (855) and (3458) follows:
% 22.79/6.43 | (3486) sum(n9, n8) = all_0_4_4
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (37) with n0, all_0_1_1, n15 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n15, yields:
% 22.79/6.43 | (690) all_0_1_1 = n15
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n9, n8, all_0_4_4, n1 and discharging atoms sum(n9, n8) = all_0_4_4, sum(n9, n8) = n1, yields:
% 22.79/6.43 | (686) all_0_4_4 = n1
% 22.79/6.43 |
% 22.79/6.43 | From (686) and (396) follows:
% 22.79/6.43 | (688) pred(n1) = all_0_3_3
% 22.79/6.43 |
% 22.79/6.43 | From (690) and (853) follows:
% 22.79/6.43 | (3490) sum(n7, n15) = all_0_0_0
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (37) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 22.79/6.43 | (689) all_0_3_3 = n0
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n7, n15, all_0_0_0, n6 and discharging atoms sum(n7, n15) = all_0_0_0, sum(n7, n15) = n6, yields:
% 22.79/6.43 | (557) all_0_0_0 = n6
% 22.79/6.43 |
% 22.79/6.43 | From (689)(557) and (261) follows:
% 22.79/6.43 | (3493) sum(n0, n6) = all_0_6_6
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n0, n6, all_0_6_6, n6 and discharging atoms sum(n0, n6) = all_0_6_6, sum(n0, n6) = n6, yields:
% 22.79/6.43 | (491) all_0_6_6 = n6
% 22.79/6.43 |
% 22.79/6.43 | Equations (491) can reduce 418 to:
% 22.79/6.43 | (458) $false
% 22.79/6.43 |
% 22.79/6.43 |-The branch is then unsatisfiable
% 22.79/6.43 |-Branch two:
% 22.79/6.43 | (868) ~ (all_0_7_7 = n7)
% 22.79/6.43 | (869) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.43 |
% 22.79/6.43 +-Applying beta-rule and splitting (869), into two cases.
% 22.79/6.43 |-Branch one:
% 22.79/6.43 | (870) all_0_7_7 = n6
% 22.79/6.43 |
% 22.79/6.43 | From (870) and (176) follows:
% 22.79/6.43 | (871) succ(n6) = all_0_5_5
% 22.79/6.43 |
% 22.79/6.43 | From (870) and (59) follows:
% 22.79/6.43 | (872) sum(n6, all_0_1_1) = all_0_0_0
% 22.79/6.43 |
% 22.79/6.43 | From (870) and (3459) follows:
% 22.79/6.43 | (3501) sum(n9, n6) = all_0_2_2
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (219) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 22.79/6.43 | (874) all_0_5_5 = n7
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n9, n6, all_0_2_2, n15 and discharging atoms sum(n9, n6) = all_0_2_2, sum(n9, n6) = n15, yields:
% 22.79/6.43 | (701) all_0_2_2 = n15
% 22.79/6.43 |
% 22.79/6.43 | From (701) and (187) follows:
% 22.79/6.43 | (703) pred(n15) = all_0_1_1
% 22.79/6.43 |
% 22.79/6.43 | From (874) and (3458) follows:
% 22.79/6.43 | (3505) sum(n9, n7) = all_0_4_4
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (37) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 22.79/6.43 | (705) all_0_1_1 = n14
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n9, n7, all_0_4_4, n0 and discharging atoms sum(n9, n7) = all_0_4_4, sum(n9, n7) = n0, yields:
% 22.79/6.43 | (702) all_0_4_4 = n0
% 22.79/6.43 |
% 22.79/6.43 | From (702) and (396) follows:
% 22.79/6.43 | (704) pred(n0) = all_0_3_3
% 22.79/6.43 |
% 22.79/6.43 | From (705) and (872) follows:
% 22.79/6.43 | (3509) sum(n6, n14) = all_0_0_0
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (37) with n0, all_0_3_3, n15 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n15, yields:
% 22.79/6.43 | (706) all_0_3_3 = n15
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n6, n14, all_0_0_0, n4 and discharging atoms sum(n6, n14) = all_0_0_0, sum(n6, n14) = n4, yields:
% 22.79/6.43 | (591) all_0_0_0 = n4
% 22.79/6.43 |
% 22.79/6.43 | From (706)(591) and (261) follows:
% 22.79/6.43 | (3512) sum(n15, n4) = all_0_6_6
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n15, n4, all_0_6_6, n3 and discharging atoms sum(n15, n4) = all_0_6_6, sum(n15, n4) = n3, yields:
% 22.79/6.43 | (961) all_0_6_6 = n3
% 22.79/6.43 |
% 22.79/6.43 | Equations (961) can reduce 245 to:
% 22.79/6.43 | (458) $false
% 22.79/6.43 |
% 22.79/6.43 |-The branch is then unsatisfiable
% 22.79/6.43 |-Branch two:
% 22.79/6.43 | (887) ~ (all_0_7_7 = n6)
% 22.79/6.43 | (888) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.43 |
% 22.79/6.43 +-Applying beta-rule and splitting (888), into two cases.
% 22.79/6.43 |-Branch one:
% 22.79/6.43 | (889) all_0_7_7 = n5
% 22.79/6.43 |
% 22.79/6.43 | From (889) and (176) follows:
% 22.79/6.43 | (890) succ(n5) = all_0_5_5
% 22.79/6.43 |
% 22.79/6.43 | From (889) and (59) follows:
% 22.79/6.43 | (891) sum(n5, all_0_1_1) = all_0_0_0
% 22.79/6.43 |
% 22.79/6.43 | From (889) and (3459) follows:
% 22.79/6.43 | (3520) sum(n9, n5) = all_0_2_2
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (219) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 22.79/6.43 | (893) all_0_5_5 = n6
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n9, n5, all_0_2_2, n14 and discharging atoms sum(n9, n5) = all_0_2_2, sum(n9, n5) = n14, yields:
% 22.79/6.43 | (447) all_0_2_2 = n14
% 22.79/6.43 |
% 22.79/6.43 | From (447) and (187) follows:
% 22.79/6.43 | (449) pred(n14) = all_0_1_1
% 22.79/6.43 |
% 22.79/6.43 | From (893) and (3458) follows:
% 22.79/6.43 | (3524) sum(n9, n6) = all_0_4_4
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (37) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 22.79/6.43 | (452) all_0_1_1 = n13
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n9, n6, all_0_4_4, n15 and discharging atoms sum(n9, n6) = all_0_4_4, sum(n9, n6) = n15, yields:
% 22.79/6.43 | (448) all_0_4_4 = n15
% 22.79/6.43 |
% 22.79/6.43 | From (448) and (396) follows:
% 22.79/6.43 | (450) pred(n15) = all_0_3_3
% 22.79/6.43 |
% 22.79/6.43 | From (452) and (891) follows:
% 22.79/6.43 | (3528) sum(n5, n13) = all_0_0_0
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (37) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 22.79/6.43 | (451) all_0_3_3 = n14
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n5, n13, all_0_0_0, n2 and discharging atoms sum(n5, n13) = all_0_0_0, sum(n5, n13) = n2, yields:
% 22.79/6.43 | (625) all_0_0_0 = n2
% 22.79/6.43 |
% 22.79/6.43 | From (451)(625) and (261) follows:
% 22.79/6.43 | (3531) sum(n14, n2) = all_0_6_6
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n14, n2, all_0_6_6, n0 and discharging atoms sum(n14, n2) = all_0_6_6, sum(n14, n2) = n0, yields:
% 22.79/6.43 | (542) all_0_6_6 = n0
% 22.79/6.43 |
% 22.79/6.43 | Equations (542) can reduce 400 to:
% 22.79/6.43 | (458) $false
% 22.79/6.43 |
% 22.79/6.43 |-The branch is then unsatisfiable
% 22.79/6.43 |-Branch two:
% 22.79/6.43 | (906) ~ (all_0_7_7 = n5)
% 22.79/6.43 | (907) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.43 |
% 22.79/6.43 +-Applying beta-rule and splitting (907), into two cases.
% 22.79/6.43 |-Branch one:
% 22.79/6.43 | (908) all_0_7_7 = n4
% 22.79/6.43 |
% 22.79/6.43 | From (908) and (176) follows:
% 22.79/6.43 | (909) succ(n4) = all_0_5_5
% 22.79/6.43 |
% 22.79/6.43 | From (908) and (59) follows:
% 22.79/6.43 | (910) sum(n4, all_0_1_1) = all_0_0_0
% 22.79/6.43 |
% 22.79/6.43 | From (908) and (3459) follows:
% 22.79/6.43 | (3539) sum(n9, n4) = all_0_2_2
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (219) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 22.79/6.43 | (912) all_0_5_5 = n5
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n9, n4, all_0_2_2, n13 and discharging atoms sum(n9, n4) = all_0_2_2, sum(n9, n4) = n13, yields:
% 22.79/6.43 | (464) all_0_2_2 = n13
% 22.79/6.43 |
% 22.79/6.43 | From (464) and (187) follows:
% 22.79/6.43 | (466) pred(n13) = all_0_1_1
% 22.79/6.43 |
% 22.79/6.43 | From (912) and (3458) follows:
% 22.79/6.43 | (3543) sum(n9, n5) = all_0_4_4
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (37) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 22.79/6.43 | (469) all_0_1_1 = n12
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n9, n5, all_0_4_4, n14 and discharging atoms sum(n9, n5) = all_0_4_4, sum(n9, n5) = n14, yields:
% 22.79/6.43 | (465) all_0_4_4 = n14
% 22.79/6.43 |
% 22.79/6.43 | From (465) and (396) follows:
% 22.79/6.43 | (467) pred(n14) = all_0_3_3
% 22.79/6.43 |
% 22.79/6.43 | From (469) and (910) follows:
% 22.79/6.43 | (3547) sum(n4, n12) = all_0_0_0
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (37) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 22.79/6.43 | (468) all_0_3_3 = n13
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n4, n12, all_0_0_0, n0 and discharging atoms sum(n4, n12) = all_0_0_0, sum(n4, n12) = n0, yields:
% 22.79/6.43 | (659) all_0_0_0 = n0
% 22.79/6.43 |
% 22.79/6.43 | From (468)(659) and (261) follows:
% 22.79/6.43 | (3550) sum(n13, n0) = all_0_6_6
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n13, n0, all_0_6_6, n13 and discharging atoms sum(n13, n0) = all_0_6_6, sum(n13, n0) = n13, yields:
% 22.79/6.43 | (998) all_0_6_6 = n13
% 22.79/6.43 |
% 22.79/6.43 | Equations (998) can reduce 130 to:
% 22.79/6.43 | (458) $false
% 22.79/6.43 |
% 22.79/6.43 |-The branch is then unsatisfiable
% 22.79/6.43 |-Branch two:
% 22.79/6.43 | (925) ~ (all_0_7_7 = n4)
% 22.79/6.43 | (926) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.43 |
% 22.79/6.43 +-Applying beta-rule and splitting (926), into two cases.
% 22.79/6.43 |-Branch one:
% 22.79/6.43 | (927) all_0_7_7 = n3
% 22.79/6.43 |
% 22.79/6.43 | From (927) and (176) follows:
% 22.79/6.43 | (928) succ(n3) = all_0_5_5
% 22.79/6.43 |
% 22.79/6.43 | From (927) and (59) follows:
% 22.79/6.43 | (929) sum(n3, all_0_1_1) = all_0_0_0
% 22.79/6.43 |
% 22.79/6.43 | From (927) and (3459) follows:
% 22.79/6.43 | (3558) sum(n9, n3) = all_0_2_2
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (219) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 22.79/6.43 | (931) all_0_5_5 = n4
% 22.79/6.43 |
% 22.79/6.43 | Instantiating formula (89) with n9, n3, all_0_2_2, n12 and discharging atoms sum(n9, n3) = all_0_2_2, sum(n9, n3) = n12, yields:
% 22.79/6.43 | (481) all_0_2_2 = n12
% 22.79/6.43 |
% 22.79/6.43 | From (481) and (187) follows:
% 22.79/6.44 | (483) pred(n12) = all_0_1_1
% 22.79/6.44 |
% 22.79/6.44 | From (931) and (3458) follows:
% 22.79/6.44 | (3562) sum(n9, n4) = all_0_4_4
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (37) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 22.79/6.44 | (486) all_0_1_1 = n11
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n9, n4, all_0_4_4, n13 and discharging atoms sum(n9, n4) = all_0_4_4, sum(n9, n4) = n13, yields:
% 22.79/6.44 | (482) all_0_4_4 = n13
% 22.79/6.44 |
% 22.79/6.44 | From (482) and (396) follows:
% 22.79/6.44 | (484) pred(n13) = all_0_3_3
% 22.79/6.44 |
% 22.79/6.44 | From (486) and (929) follows:
% 22.79/6.44 | (3566) sum(n3, n11) = all_0_0_0
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (37) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 22.79/6.44 | (485) all_0_3_3 = n12
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n3, n11, all_0_0_0, n14 and discharging atoms sum(n3, n11) = all_0_0_0, sum(n3, n11) = n14, yields:
% 22.79/6.44 | (693) all_0_0_0 = n14
% 22.79/6.44 |
% 22.79/6.44 | From (485)(693) and (261) follows:
% 22.79/6.44 | (3569) sum(n12, n14) = all_0_6_6
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n12, n14, all_0_6_6, n10 and discharging atoms sum(n12, n14) = all_0_6_6, sum(n12, n14) = n10, yields:
% 22.79/6.44 | (457) all_0_6_6 = n10
% 22.79/6.44 |
% 22.79/6.44 | Equations (457) can reduce 169 to:
% 22.79/6.44 | (458) $false
% 22.79/6.44 |
% 22.79/6.44 |-The branch is then unsatisfiable
% 22.79/6.44 |-Branch two:
% 22.79/6.44 | (944) ~ (all_0_7_7 = n3)
% 22.79/6.44 | (945) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.44 |
% 22.79/6.44 +-Applying beta-rule and splitting (945), into two cases.
% 22.79/6.44 |-Branch one:
% 22.79/6.44 | (946) all_0_7_7 = n2
% 22.79/6.44 |
% 22.79/6.44 | From (946) and (176) follows:
% 22.79/6.44 | (947) succ(n2) = all_0_5_5
% 22.79/6.44 |
% 22.79/6.44 | From (946) and (59) follows:
% 22.79/6.44 | (948) sum(n2, all_0_1_1) = all_0_0_0
% 22.79/6.44 |
% 22.79/6.44 | From (946) and (3459) follows:
% 22.79/6.44 | (3577) sum(n9, n2) = all_0_2_2
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (219) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 22.79/6.44 | (950) all_0_5_5 = n3
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n9, n2, all_0_2_2, n11 and discharging atoms sum(n9, n2) = all_0_2_2, sum(n9, n2) = n11, yields:
% 22.79/6.44 | (498) all_0_2_2 = n11
% 22.79/6.44 |
% 22.79/6.44 | From (498) and (187) follows:
% 22.79/6.44 | (500) pred(n11) = all_0_1_1
% 22.79/6.44 |
% 22.79/6.44 | From (950) and (3458) follows:
% 22.79/6.44 | (3581) sum(n9, n3) = all_0_4_4
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (37) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 22.79/6.44 | (503) all_0_1_1 = n10
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n9, n3, all_0_4_4, n12 and discharging atoms sum(n9, n3) = all_0_4_4, sum(n9, n3) = n12, yields:
% 22.79/6.44 | (499) all_0_4_4 = n12
% 22.79/6.44 |
% 22.79/6.44 | From (499) and (396) follows:
% 22.79/6.44 | (501) pred(n12) = all_0_3_3
% 22.79/6.44 |
% 22.79/6.44 | From (503) and (948) follows:
% 22.79/6.44 | (3585) sum(n2, n10) = all_0_0_0
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (37) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 22.79/6.44 | (502) all_0_3_3 = n11
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n2, n10, all_0_0_0, n12 and discharging atoms sum(n2, n10) = all_0_0_0, sum(n2, n10) = n12, yields:
% 22.79/6.44 | (455) all_0_0_0 = n12
% 22.79/6.44 |
% 22.79/6.44 | From (502)(455) and (261) follows:
% 22.79/6.44 | (3588) sum(n11, n12) = all_0_6_6
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n11, n12, all_0_6_6, n7 and discharging atoms sum(n11, n12) = all_0_6_6, sum(n11, n12) = n7, yields:
% 22.79/6.44 | (733) all_0_6_6 = n7
% 22.79/6.44 |
% 22.79/6.44 | Equations (733) can reduce 274 to:
% 22.79/6.44 | (458) $false
% 22.79/6.44 |
% 22.79/6.44 |-The branch is then unsatisfiable
% 22.79/6.44 |-Branch two:
% 22.79/6.44 | (963) ~ (all_0_7_7 = n2)
% 22.79/6.44 | (964) all_0_7_7 = n1 | all_0_7_7 = n0
% 22.79/6.44 |
% 22.79/6.44 +-Applying beta-rule and splitting (964), into two cases.
% 22.79/6.44 |-Branch one:
% 22.79/6.44 | (965) all_0_7_7 = n1
% 22.79/6.44 |
% 22.79/6.44 | From (965) and (176) follows:
% 22.79/6.44 | (966) succ(n1) = all_0_5_5
% 22.79/6.44 |
% 22.79/6.44 | From (965) and (59) follows:
% 22.79/6.44 | (967) sum(n1, all_0_1_1) = all_0_0_0
% 22.79/6.44 |
% 22.79/6.44 | From (965) and (3459) follows:
% 22.79/6.44 | (3596) sum(n9, n1) = all_0_2_2
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (219) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 22.79/6.44 | (969) all_0_5_5 = n2
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n9, n1, all_0_2_2, n10 and discharging atoms sum(n9, n1) = all_0_2_2, sum(n9, n1) = n10, yields:
% 22.79/6.44 | (515) all_0_2_2 = n10
% 22.79/6.44 |
% 22.79/6.44 | From (515) and (187) follows:
% 22.79/6.44 | (517) pred(n10) = all_0_1_1
% 22.79/6.44 |
% 22.79/6.44 | From (969) and (3458) follows:
% 22.79/6.44 | (3600) sum(n9, n2) = all_0_4_4
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (37) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 22.79/6.44 | (520) all_0_1_1 = n9
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n9, n2, all_0_4_4, n11 and discharging atoms sum(n9, n2) = all_0_4_4, sum(n9, n2) = n11, yields:
% 22.79/6.44 | (516) all_0_4_4 = n11
% 22.79/6.44 |
% 22.79/6.44 | From (516) and (396) follows:
% 22.79/6.44 | (518) pred(n11) = all_0_3_3
% 22.79/6.44 |
% 22.79/6.44 | From (520) and (967) follows:
% 22.79/6.44 | (3604) sum(n1, n9) = all_0_0_0
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (37) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 22.79/6.44 | (519) all_0_3_3 = n10
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n1, n9, all_0_0_0, n10 and discharging atoms sum(n1, n9) = all_0_0_0, sum(n1, n9) = n10, yields:
% 22.79/6.44 | (489) all_0_0_0 = n10
% 22.79/6.44 |
% 22.79/6.44 | From (519)(489) and (261) follows:
% 22.79/6.44 | (3607) sum(n10, n10) = all_0_6_6
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n10, n10, all_0_6_6, n4 and discharging atoms sum(n10, n10) = all_0_6_6, sum(n10, n10) = n4, yields:
% 22.79/6.44 | (508) all_0_6_6 = n4
% 22.79/6.44 |
% 22.79/6.44 | Equations (508) can reduce 12 to:
% 22.79/6.44 | (458) $false
% 22.79/6.44 |
% 22.79/6.44 |-The branch is then unsatisfiable
% 22.79/6.44 |-Branch two:
% 22.79/6.44 | (982) ~ (all_0_7_7 = n1)
% 22.79/6.44 | (983) all_0_7_7 = n0
% 22.79/6.44 |
% 22.79/6.44 | From (983) and (176) follows:
% 22.79/6.44 | (984) succ(n0) = all_0_5_5
% 22.79/6.44 |
% 22.79/6.44 | From (983) and (59) follows:
% 22.79/6.44 | (985) sum(n0, all_0_1_1) = all_0_0_0
% 22.79/6.44 |
% 22.79/6.44 | From (983) and (3459) follows:
% 22.79/6.44 | (3614) sum(n9, n0) = all_0_2_2
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (219) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 22.79/6.44 | (987) all_0_5_5 = n1
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n9, n0, all_0_2_2, n9 and discharging atoms sum(n9, n0) = all_0_2_2, sum(n9, n0) = n9, yields:
% 22.79/6.44 | (532) all_0_2_2 = n9
% 22.79/6.44 |
% 22.79/6.44 | From (532) and (187) follows:
% 22.79/6.44 | (534) pred(n9) = all_0_1_1
% 22.79/6.44 |
% 22.79/6.44 | From (987) and (3458) follows:
% 22.79/6.44 | (3618) sum(n9, n1) = all_0_4_4
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (37) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 22.79/6.44 | (537) all_0_1_1 = n8
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n9, n1, all_0_4_4, n10 and discharging atoms sum(n9, n1) = all_0_4_4, sum(n9, n1) = n10, yields:
% 22.79/6.44 | (533) all_0_4_4 = n10
% 22.79/6.44 |
% 22.79/6.44 | From (533) and (396) follows:
% 22.79/6.44 | (535) pred(n10) = all_0_3_3
% 22.79/6.44 |
% 22.79/6.44 | From (537) and (985) follows:
% 22.79/6.44 | (3622) sum(n0, n8) = all_0_0_0
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (37) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 22.79/6.44 | (536) all_0_3_3 = n9
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n0, n8, all_0_0_0, n8 and discharging atoms sum(n0, n8) = all_0_0_0, sum(n0, n8) = n8, yields:
% 22.79/6.44 | (523) all_0_0_0 = n8
% 22.79/6.44 |
% 22.79/6.44 | From (536)(523) and (261) follows:
% 22.79/6.44 | (3625) sum(n9, n8) = all_0_6_6
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n9, n8, all_0_6_6, n1 and discharging atoms sum(n9, n8) = all_0_6_6, sum(n9, n8) = n1, yields:
% 22.79/6.44 | (771) all_0_6_6 = n1
% 22.79/6.44 |
% 22.79/6.44 | Equations (771) can reduce 38 to:
% 22.79/6.44 | (458) $false
% 22.79/6.44 |
% 22.79/6.44 |-The branch is then unsatisfiable
% 22.79/6.44 |-Branch two:
% 22.79/6.44 | (561) ~ (all_0_8_8 = n9)
% 22.79/6.44 | (562) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.44 |
% 22.79/6.44 +-Applying beta-rule and splitting (831), into two cases.
% 22.79/6.44 |-Branch one:
% 22.79/6.44 | (832) all_0_7_7 = n8
% 22.79/6.44 |
% 22.79/6.44 | From (832) and (176) follows:
% 22.79/6.44 | (833) succ(n8) = all_0_5_5
% 22.79/6.44 |
% 22.79/6.44 | From (832) and (59) follows:
% 22.79/6.44 | (834) sum(n8, all_0_1_1) = all_0_0_0
% 22.79/6.44 |
% 22.79/6.44 | From (832) and (160) follows:
% 22.79/6.44 | (3633) sum(all_0_8_8, n8) = all_0_2_2
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (219) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 22.79/6.44 | (836) all_0_5_5 = n9
% 22.79/6.44 |
% 22.79/6.44 | From (836) and (64) follows:
% 22.79/6.44 | (3635) sum(all_0_8_8, n9) = all_0_4_4
% 22.79/6.44 |
% 22.79/6.44 +-Applying beta-rule and splitting (562), into two cases.
% 22.79/6.44 |-Branch one:
% 22.79/6.44 | (563) all_0_8_8 = n8
% 22.79/6.44 |
% 22.79/6.44 | From (563) and (3635) follows:
% 22.79/6.44 | (3637) sum(n8, n9) = all_0_4_4
% 22.79/6.44 |
% 22.79/6.44 | From (563) and (3633) follows:
% 22.79/6.44 | (3638) sum(n8, n8) = all_0_2_2
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n8, n9, all_0_4_4, n1 and discharging atoms sum(n8, n9) = all_0_4_4, sum(n8, n9) = n1, yields:
% 22.79/6.44 | (686) all_0_4_4 = n1
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n8, n8, all_0_2_2, n0 and discharging atoms sum(n8, n8) = all_0_2_2, sum(n8, n8) = n0, yields:
% 22.79/6.44 | (685) all_0_2_2 = n0
% 22.79/6.44 |
% 22.79/6.44 | From (685) and (187) follows:
% 22.79/6.44 | (687) pred(n0) = all_0_1_1
% 22.79/6.44 |
% 22.79/6.44 | From (686) and (396) follows:
% 22.79/6.44 | (688) pred(n1) = all_0_3_3
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (37) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 22.79/6.44 | (689) all_0_3_3 = n0
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (37) with n0, all_0_1_1, n15 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n15, yields:
% 22.79/6.44 | (690) all_0_1_1 = n15
% 22.79/6.44 |
% 22.79/6.44 | From (689) and (261) follows:
% 22.79/6.44 | (691) sum(n0, all_0_0_0) = all_0_6_6
% 22.79/6.44 |
% 22.79/6.44 | From (690) and (834) follows:
% 22.79/6.44 | (3646) sum(n8, n15) = all_0_0_0
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n8, n15, all_0_0_0, n7 and discharging atoms sum(n8, n15) = all_0_0_0, sum(n8, n15) = n7, yields:
% 22.79/6.44 | (540) all_0_0_0 = n7
% 22.79/6.44 |
% 22.79/6.44 | From (540) and (691) follows:
% 22.79/6.44 | (3648) sum(n0, n7) = all_0_6_6
% 22.79/6.44 |
% 22.79/6.44 | Instantiating formula (89) with n0, n7, all_0_6_6, n7 and discharging atoms sum(n0, n7) = all_0_6_6, sum(n0, n7) = n7, yields:
% 22.79/6.45 | (733) all_0_6_6 = n7
% 22.79/6.45 |
% 22.79/6.45 | Equations (733) can reduce 274 to:
% 22.79/6.45 | (458) $false
% 22.79/6.45 |
% 22.79/6.45 |-The branch is then unsatisfiable
% 22.79/6.45 |-Branch two:
% 22.79/6.45 | (578) ~ (all_0_8_8 = n8)
% 22.79/6.45 | (579) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 22.79/6.45 |
% 22.79/6.45 +-Applying beta-rule and splitting (579), into two cases.
% 22.79/6.45 |-Branch one:
% 22.79/6.45 | (580) all_0_8_8 = n7
% 22.79/6.45 |
% 22.79/6.45 | From (580) and (3635) follows:
% 22.79/6.45 | (3654) sum(n7, n9) = all_0_4_4
% 22.79/6.45 |
% 22.79/6.45 | From (580) and (3633) follows:
% 22.79/6.45 | (3655) sum(n7, n8) = all_0_2_2
% 22.79/6.45 |
% 22.79/6.45 | Instantiating formula (89) with n7, n9, all_0_4_4, n0 and discharging atoms sum(n7, n9) = all_0_4_4, sum(n7, n9) = n0, yields:
% 22.79/6.45 | (702) all_0_4_4 = n0
% 22.79/6.45 |
% 22.79/6.45 | Instantiating formula (89) with n7, n8, all_0_2_2, n15 and discharging atoms sum(n7, n8) = all_0_2_2, sum(n7, n8) = n15, yields:
% 22.79/6.45 | (701) all_0_2_2 = n15
% 22.79/6.45 |
% 22.79/6.45 | From (701) and (187) follows:
% 22.79/6.45 | (703) pred(n15) = all_0_1_1
% 22.79/6.45 |
% 22.79/6.45 | From (702) and (396) follows:
% 22.79/6.45 | (704) pred(n0) = all_0_3_3
% 22.79/6.45 |
% 22.79/6.45 | Instantiating formula (37) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 23.05/6.45 | (705) all_0_1_1 = n14
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (37) with n0, all_0_3_3, n15 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n15, yields:
% 23.05/6.45 | (706) all_0_3_3 = n15
% 23.05/6.45 |
% 23.05/6.45 | From (706) and (261) follows:
% 23.05/6.45 | (707) sum(n15, all_0_0_0) = all_0_6_6
% 23.05/6.45 |
% 23.05/6.45 | From (705) and (834) follows:
% 23.05/6.45 | (3663) sum(n8, n14) = all_0_0_0
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n8, n14, all_0_0_0, n6 and discharging atoms sum(n8, n14) = all_0_0_0, sum(n8, n14) = n6, yields:
% 23.05/6.45 | (557) all_0_0_0 = n6
% 23.05/6.45 |
% 23.05/6.45 | From (557) and (707) follows:
% 23.05/6.45 | (3665) sum(n15, n6) = all_0_6_6
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n15, n6, all_0_6_6, n5 and discharging atoms sum(n15, n6) = all_0_6_6, sum(n15, n6) = n5, yields:
% 23.05/6.45 | (847) all_0_6_6 = n5
% 23.05/6.45 |
% 23.05/6.45 | Equations (847) can reduce 409 to:
% 23.05/6.45 | (458) $false
% 23.05/6.45 |
% 23.05/6.45 |-The branch is then unsatisfiable
% 23.05/6.45 |-Branch two:
% 23.05/6.45 | (595) ~ (all_0_8_8 = n7)
% 23.05/6.45 | (596) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.05/6.45 |
% 23.05/6.45 +-Applying beta-rule and splitting (596), into two cases.
% 23.05/6.45 |-Branch one:
% 23.05/6.45 | (597) all_0_8_8 = n6
% 23.05/6.45 |
% 23.05/6.45 | From (597) and (3635) follows:
% 23.05/6.45 | (3671) sum(n6, n9) = all_0_4_4
% 23.05/6.45 |
% 23.05/6.45 | From (597) and (3633) follows:
% 23.05/6.45 | (3672) sum(n6, n8) = all_0_2_2
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n6, n9, all_0_4_4, n15 and discharging atoms sum(n6, n9) = all_0_4_4, sum(n6, n9) = n15, yields:
% 23.05/6.45 | (448) all_0_4_4 = n15
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 23.05/6.45 | (447) all_0_2_2 = n14
% 23.05/6.45 |
% 23.05/6.45 | From (447) and (187) follows:
% 23.05/6.45 | (449) pred(n14) = all_0_1_1
% 23.05/6.45 |
% 23.05/6.45 | From (448) and (396) follows:
% 23.05/6.45 | (450) pred(n15) = all_0_3_3
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (37) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 23.05/6.45 | (451) all_0_3_3 = n14
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (37) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 23.05/6.45 | (452) all_0_1_1 = n13
% 23.05/6.45 |
% 23.05/6.45 | From (451) and (261) follows:
% 23.05/6.45 | (453) sum(n14, all_0_0_0) = all_0_6_6
% 23.05/6.45 |
% 23.05/6.45 | From (452) and (834) follows:
% 23.05/6.45 | (3680) sum(n8, n13) = all_0_0_0
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n8, n13, all_0_0_0, n5 and discharging atoms sum(n8, n13) = all_0_0_0, sum(n8, n13) = n5, yields:
% 23.05/6.45 | (574) all_0_0_0 = n5
% 23.05/6.45 |
% 23.05/6.45 | From (574) and (453) follows:
% 23.05/6.45 | (3682) sum(n14, n5) = all_0_6_6
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n14, n5, all_0_6_6, n3 and discharging atoms sum(n14, n5) = all_0_6_6, sum(n14, n5) = n3, yields:
% 23.05/6.45 | (961) all_0_6_6 = n3
% 23.05/6.45 |
% 23.05/6.45 | Equations (961) can reduce 245 to:
% 23.05/6.45 | (458) $false
% 23.05/6.45 |
% 23.05/6.45 |-The branch is then unsatisfiable
% 23.05/6.45 |-Branch two:
% 23.05/6.45 | (612) ~ (all_0_8_8 = n6)
% 23.05/6.45 | (613) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.05/6.45 |
% 23.05/6.45 +-Applying beta-rule and splitting (613), into two cases.
% 23.05/6.45 |-Branch one:
% 23.05/6.45 | (614) all_0_8_8 = n5
% 23.05/6.45 |
% 23.05/6.45 | From (614) and (3635) follows:
% 23.05/6.45 | (3688) sum(n5, n9) = all_0_4_4
% 23.05/6.45 |
% 23.05/6.45 | From (614) and (3633) follows:
% 23.05/6.45 | (3689) sum(n5, n8) = all_0_2_2
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n5, n9, all_0_4_4, n14 and discharging atoms sum(n5, n9) = all_0_4_4, sum(n5, n9) = n14, yields:
% 23.05/6.45 | (465) all_0_4_4 = n14
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n5, n8, all_0_2_2, n13 and discharging atoms sum(n5, n8) = all_0_2_2, sum(n5, n8) = n13, yields:
% 23.05/6.45 | (464) all_0_2_2 = n13
% 23.05/6.45 |
% 23.05/6.45 | From (464) and (187) follows:
% 23.05/6.45 | (466) pred(n13) = all_0_1_1
% 23.05/6.45 |
% 23.05/6.45 | From (465) and (396) follows:
% 23.05/6.45 | (467) pred(n14) = all_0_3_3
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (37) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 23.05/6.45 | (468) all_0_3_3 = n13
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (37) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 23.05/6.45 | (469) all_0_1_1 = n12
% 23.05/6.45 |
% 23.05/6.45 | From (468) and (261) follows:
% 23.05/6.45 | (470) sum(n13, all_0_0_0) = all_0_6_6
% 23.05/6.45 |
% 23.05/6.45 | From (469) and (834) follows:
% 23.05/6.45 | (3697) sum(n8, n12) = all_0_0_0
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n8, n12, all_0_0_0, n4 and discharging atoms sum(n8, n12) = all_0_0_0, sum(n8, n12) = n4, yields:
% 23.05/6.45 | (591) all_0_0_0 = n4
% 23.05/6.45 |
% 23.05/6.45 | From (591) and (470) follows:
% 23.05/6.45 | (3699) sum(n13, n4) = all_0_6_6
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n13, n4, all_0_6_6, n1 and discharging atoms sum(n13, n4) = all_0_6_6, sum(n13, n4) = n1, yields:
% 23.05/6.45 | (771) all_0_6_6 = n1
% 23.05/6.45 |
% 23.05/6.45 | Equations (771) can reduce 38 to:
% 23.05/6.45 | (458) $false
% 23.05/6.45 |
% 23.05/6.45 |-The branch is then unsatisfiable
% 23.05/6.45 |-Branch two:
% 23.05/6.45 | (629) ~ (all_0_8_8 = n5)
% 23.05/6.45 | (630) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.05/6.45 |
% 23.05/6.45 +-Applying beta-rule and splitting (630), into two cases.
% 23.05/6.45 |-Branch one:
% 23.05/6.45 | (631) all_0_8_8 = n4
% 23.05/6.45 |
% 23.05/6.45 | From (631) and (3635) follows:
% 23.05/6.45 | (3705) sum(n4, n9) = all_0_4_4
% 23.05/6.45 |
% 23.05/6.45 | From (631) and (3633) follows:
% 23.05/6.45 | (3706) sum(n4, n8) = all_0_2_2
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n4, n9, all_0_4_4, n13 and discharging atoms sum(n4, n9) = all_0_4_4, sum(n4, n9) = n13, yields:
% 23.05/6.45 | (482) all_0_4_4 = n13
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n4, n8, all_0_2_2, n12 and discharging atoms sum(n4, n8) = all_0_2_2, sum(n4, n8) = n12, yields:
% 23.05/6.45 | (481) all_0_2_2 = n12
% 23.05/6.45 |
% 23.05/6.45 | From (481) and (187) follows:
% 23.05/6.45 | (483) pred(n12) = all_0_1_1
% 23.05/6.45 |
% 23.05/6.45 | From (482) and (396) follows:
% 23.05/6.45 | (484) pred(n13) = all_0_3_3
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (37) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 23.05/6.45 | (485) all_0_3_3 = n12
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (37) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 23.05/6.45 | (486) all_0_1_1 = n11
% 23.05/6.45 |
% 23.05/6.45 | From (485) and (261) follows:
% 23.05/6.45 | (487) sum(n12, all_0_0_0) = all_0_6_6
% 23.05/6.45 |
% 23.05/6.45 | From (486) and (834) follows:
% 23.05/6.45 | (3714) sum(n8, n11) = all_0_0_0
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n8, n11, all_0_0_0, n3 and discharging atoms sum(n8, n11) = all_0_0_0, sum(n8, n11) = n3, yields:
% 23.05/6.45 | (608) all_0_0_0 = n3
% 23.05/6.45 |
% 23.05/6.45 | From (608) and (487) follows:
% 23.05/6.45 | (3716) sum(n12, n3) = all_0_6_6
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n12, n3, all_0_6_6, n15 and discharging atoms sum(n12, n3) = all_0_6_6, sum(n12, n3) = n15, yields:
% 23.05/6.45 | (885) all_0_6_6 = n15
% 23.05/6.45 |
% 23.05/6.45 | Equations (885) can reduce 225 to:
% 23.05/6.45 | (458) $false
% 23.05/6.45 |
% 23.05/6.45 |-The branch is then unsatisfiable
% 23.05/6.45 |-Branch two:
% 23.05/6.45 | (646) ~ (all_0_8_8 = n4)
% 23.05/6.45 | (647) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.05/6.45 |
% 23.05/6.45 +-Applying beta-rule and splitting (647), into two cases.
% 23.05/6.45 |-Branch one:
% 23.05/6.45 | (648) all_0_8_8 = n3
% 23.05/6.45 |
% 23.05/6.45 | From (648) and (3635) follows:
% 23.05/6.45 | (3722) sum(n3, n9) = all_0_4_4
% 23.05/6.45 |
% 23.05/6.45 | From (648) and (3633) follows:
% 23.05/6.45 | (3723) sum(n3, n8) = all_0_2_2
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n3, n9, all_0_4_4, n12 and discharging atoms sum(n3, n9) = all_0_4_4, sum(n3, n9) = n12, yields:
% 23.05/6.45 | (499) all_0_4_4 = n12
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n3, n8, all_0_2_2, n11 and discharging atoms sum(n3, n8) = all_0_2_2, sum(n3, n8) = n11, yields:
% 23.05/6.45 | (498) all_0_2_2 = n11
% 23.05/6.45 |
% 23.05/6.45 | From (498) and (187) follows:
% 23.05/6.45 | (500) pred(n11) = all_0_1_1
% 23.05/6.45 |
% 23.05/6.45 | From (499) and (396) follows:
% 23.05/6.45 | (501) pred(n12) = all_0_3_3
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (37) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 23.05/6.45 | (502) all_0_3_3 = n11
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (37) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 23.05/6.45 | (503) all_0_1_1 = n10
% 23.05/6.45 |
% 23.05/6.45 | From (502) and (261) follows:
% 23.05/6.45 | (504) sum(n11, all_0_0_0) = all_0_6_6
% 23.05/6.45 |
% 23.05/6.45 | From (503) and (834) follows:
% 23.05/6.45 | (3731) sum(n8, n10) = all_0_0_0
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n8, n10, all_0_0_0, n2 and discharging atoms sum(n8, n10) = all_0_0_0, sum(n8, n10) = n2, yields:
% 23.05/6.45 | (625) all_0_0_0 = n2
% 23.05/6.45 |
% 23.05/6.45 | From (625) and (504) follows:
% 23.05/6.45 | (3733) sum(n11, n2) = all_0_6_6
% 23.05/6.45 |
% 23.05/6.45 | Instantiating formula (89) with n11, n2, all_0_6_6, n13 and discharging atoms sum(n11, n2) = all_0_6_6, sum(n11, n2) = n13, yields:
% 23.05/6.45 | (998) all_0_6_6 = n13
% 23.05/6.45 |
% 23.05/6.45 | Equations (998) can reduce 130 to:
% 23.05/6.45 | (458) $false
% 23.05/6.45 |
% 23.05/6.45 |-The branch is then unsatisfiable
% 23.05/6.45 |-Branch two:
% 23.05/6.45 | (663) ~ (all_0_8_8 = n3)
% 23.05/6.45 | (664) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.05/6.45 |
% 23.05/6.45 +-Applying beta-rule and splitting (664), into two cases.
% 23.05/6.45 |-Branch one:
% 23.05/6.45 | (665) all_0_8_8 = n2
% 23.05/6.45 |
% 23.05/6.45 | From (665) and (3635) follows:
% 23.05/6.46 | (3739) sum(n2, n9) = all_0_4_4
% 23.05/6.46 |
% 23.05/6.46 | From (665) and (3633) follows:
% 23.05/6.46 | (3740) sum(n2, n8) = all_0_2_2
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n2, n9, all_0_4_4, n11 and discharging atoms sum(n2, n9) = all_0_4_4, sum(n2, n9) = n11, yields:
% 23.05/6.46 | (516) all_0_4_4 = n11
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n2, n8, all_0_2_2, n10 and discharging atoms sum(n2, n8) = all_0_2_2, sum(n2, n8) = n10, yields:
% 23.05/6.46 | (515) all_0_2_2 = n10
% 23.05/6.46 |
% 23.05/6.46 | From (515) and (187) follows:
% 23.05/6.46 | (517) pred(n10) = all_0_1_1
% 23.05/6.46 |
% 23.05/6.46 | From (516) and (396) follows:
% 23.05/6.46 | (518) pred(n11) = all_0_3_3
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (37) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 23.05/6.46 | (519) all_0_3_3 = n10
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (37) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 23.05/6.46 | (520) all_0_1_1 = n9
% 23.05/6.46 |
% 23.05/6.46 | From (519) and (261) follows:
% 23.05/6.46 | (521) sum(n10, all_0_0_0) = all_0_6_6
% 23.05/6.46 |
% 23.05/6.46 | From (520) and (834) follows:
% 23.05/6.46 | (3748) sum(n8, n9) = all_0_0_0
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n8, n9, all_0_0_0, n1 and discharging atoms sum(n8, n9) = all_0_0_0, sum(n8, n9) = n1, yields:
% 23.05/6.46 | (642) all_0_0_0 = n1
% 23.05/6.46 |
% 23.05/6.46 | From (642) and (521) follows:
% 23.05/6.46 | (3750) sum(n10, n1) = all_0_6_6
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n10, n1, all_0_6_6, n11 and discharging atoms sum(n10, n1) = all_0_6_6, sum(n10, n1) = n11, yields:
% 23.05/6.46 | (809) all_0_6_6 = n11
% 23.05/6.46 |
% 23.05/6.46 | Equations (809) can reduce 70 to:
% 23.05/6.46 | (458) $false
% 23.05/6.46 |
% 23.05/6.46 |-The branch is then unsatisfiable
% 23.05/6.46 |-Branch two:
% 23.05/6.46 | (680) ~ (all_0_8_8 = n2)
% 23.05/6.46 | (681) all_0_8_8 = n1 | all_0_8_8 = n0
% 23.05/6.46 |
% 23.05/6.46 +-Applying beta-rule and splitting (681), into two cases.
% 23.05/6.46 |-Branch one:
% 23.05/6.46 | (682) all_0_8_8 = n1
% 23.05/6.46 |
% 23.05/6.46 | From (682) and (3635) follows:
% 23.05/6.46 | (3756) sum(n1, n9) = all_0_4_4
% 23.05/6.46 |
% 23.05/6.46 | From (682) and (3633) follows:
% 23.05/6.46 | (3757) sum(n1, n8) = all_0_2_2
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n1, n9, all_0_4_4, n10 and discharging atoms sum(n1, n9) = all_0_4_4, sum(n1, n9) = n10, yields:
% 23.05/6.46 | (533) all_0_4_4 = n10
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n1, n8, all_0_2_2, n9 and discharging atoms sum(n1, n8) = all_0_2_2, sum(n1, n8) = n9, yields:
% 23.05/6.46 | (532) all_0_2_2 = n9
% 23.05/6.46 |
% 23.05/6.46 | From (532) and (187) follows:
% 23.05/6.46 | (534) pred(n9) = all_0_1_1
% 23.05/6.46 |
% 23.05/6.46 | From (533) and (396) follows:
% 23.05/6.46 | (535) pred(n10) = all_0_3_3
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (37) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 23.05/6.46 | (536) all_0_3_3 = n9
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (37) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 23.05/6.46 | (537) all_0_1_1 = n8
% 23.05/6.46 |
% 23.05/6.46 | From (536) and (261) follows:
% 23.05/6.46 | (538) sum(n9, all_0_0_0) = all_0_6_6
% 23.05/6.46 |
% 23.05/6.46 | From (537) and (834) follows:
% 23.05/6.46 | (3765) sum(n8, n8) = all_0_0_0
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n8, n8, all_0_0_0, n0 and discharging atoms sum(n8, n8) = all_0_0_0, sum(n8, n8) = n0, yields:
% 23.05/6.46 | (659) all_0_0_0 = n0
% 23.05/6.46 |
% 23.05/6.46 | From (659) and (538) follows:
% 23.05/6.46 | (3767) sum(n9, n0) = all_0_6_6
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n9, n0, all_0_6_6, n9 and discharging atoms sum(n9, n0) = all_0_6_6, sum(n9, n0) = n9, yields:
% 23.05/6.46 | (923) all_0_6_6 = n9
% 23.05/6.46 |
% 23.05/6.46 | Equations (923) can reduce 404 to:
% 23.05/6.46 | (458) $false
% 23.05/6.46 |
% 23.05/6.46 |-The branch is then unsatisfiable
% 23.05/6.46 |-Branch two:
% 23.05/6.46 | (697) ~ (all_0_8_8 = n1)
% 23.05/6.46 | (698) all_0_8_8 = n0
% 23.05/6.46 |
% 23.05/6.46 | From (698) and (3635) follows:
% 23.05/6.46 | (3772) sum(n0, n9) = all_0_4_4
% 23.05/6.46 |
% 23.05/6.46 | From (698) and (3633) follows:
% 23.05/6.46 | (3773) sum(n0, n8) = all_0_2_2
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n0, n9, all_0_4_4, n9 and discharging atoms sum(n0, n9) = all_0_4_4, sum(n0, n9) = n9, yields:
% 23.05/6.46 | (550) all_0_4_4 = n9
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n0, n8, all_0_2_2, n8 and discharging atoms sum(n0, n8) = all_0_2_2, sum(n0, n8) = n8, yields:
% 23.05/6.46 | (549) all_0_2_2 = n8
% 23.05/6.46 |
% 23.05/6.46 | From (549) and (187) follows:
% 23.05/6.46 | (551) pred(n8) = all_0_1_1
% 23.05/6.46 |
% 23.05/6.46 | From (550) and (396) follows:
% 23.05/6.46 | (552) pred(n9) = all_0_3_3
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (37) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 23.05/6.46 | (553) all_0_3_3 = n8
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (37) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 23.05/6.46 | (554) all_0_1_1 = n7
% 23.05/6.46 |
% 23.05/6.46 | From (553) and (261) follows:
% 23.05/6.46 | (555) sum(n8, all_0_0_0) = all_0_6_6
% 23.05/6.46 |
% 23.05/6.46 | From (554) and (834) follows:
% 23.05/6.46 | (3781) sum(n8, n7) = all_0_0_0
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n8, n7, all_0_0_0, n15 and discharging atoms sum(n8, n7) = all_0_0_0, sum(n8, n7) = n15, yields:
% 23.05/6.46 | (676) all_0_0_0 = n15
% 23.05/6.46 |
% 23.05/6.46 | From (676) and (555) follows:
% 23.05/6.46 | (3783) sum(n8, n15) = all_0_6_6
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n8, n15, all_0_6_6, n7 and discharging atoms sum(n8, n15) = all_0_6_6, sum(n8, n15) = n7, yields:
% 23.05/6.46 | (733) all_0_6_6 = n7
% 23.05/6.46 |
% 23.05/6.46 | Equations (733) can reduce 274 to:
% 23.05/6.46 | (458) $false
% 23.05/6.46 |
% 23.05/6.46 |-The branch is then unsatisfiable
% 23.05/6.46 |-Branch two:
% 23.05/6.46 | (849) ~ (all_0_7_7 = n8)
% 23.05/6.46 | (850) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.05/6.46 |
% 23.05/6.46 +-Applying beta-rule and splitting (562), into two cases.
% 23.05/6.46 |-Branch one:
% 23.05/6.46 | (563) all_0_8_8 = n8
% 23.05/6.46 |
% 23.05/6.46 | From (563) and (64) follows:
% 23.05/6.46 | (3789) sum(n8, all_0_5_5) = all_0_4_4
% 23.05/6.46 |
% 23.05/6.46 | From (563) and (160) follows:
% 23.05/6.46 | (3790) sum(n8, all_0_7_7) = all_0_2_2
% 23.05/6.46 |
% 23.05/6.46 +-Applying beta-rule and splitting (850), into two cases.
% 23.05/6.46 |-Branch one:
% 23.05/6.46 | (851) all_0_7_7 = n7
% 23.05/6.46 |
% 23.05/6.46 | From (851) and (176) follows:
% 23.05/6.46 | (852) succ(n7) = all_0_5_5
% 23.05/6.46 |
% 23.05/6.46 | From (851) and (59) follows:
% 23.05/6.46 | (853) sum(n7, all_0_1_1) = all_0_0_0
% 23.05/6.46 |
% 23.05/6.46 | From (851) and (3790) follows:
% 23.05/6.46 | (3794) sum(n8, n7) = all_0_2_2
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (219) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 23.05/6.46 | (855) all_0_5_5 = n8
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n8, n7, all_0_2_2, n15 and discharging atoms sum(n8, n7) = all_0_2_2, sum(n8, n7) = n15, yields:
% 23.05/6.46 | (701) all_0_2_2 = n15
% 23.05/6.46 |
% 23.05/6.46 | From (701) and (187) follows:
% 23.05/6.46 | (703) pred(n15) = all_0_1_1
% 23.05/6.46 |
% 23.05/6.46 | From (855) and (3789) follows:
% 23.05/6.46 | (3798) sum(n8, n8) = all_0_4_4
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (37) with n15, all_0_1_1, n14 and discharging atoms pred(n15) = all_0_1_1, pred(n15) = n14, yields:
% 23.05/6.46 | (705) all_0_1_1 = n14
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n8, n8, all_0_4_4, n0 and discharging atoms sum(n8, n8) = all_0_4_4, sum(n8, n8) = n0, yields:
% 23.05/6.46 | (702) all_0_4_4 = n0
% 23.05/6.46 |
% 23.05/6.46 | From (702) and (396) follows:
% 23.05/6.46 | (704) pred(n0) = all_0_3_3
% 23.05/6.46 |
% 23.05/6.46 | From (705) and (853) follows:
% 23.05/6.46 | (3802) sum(n7, n14) = all_0_0_0
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (37) with n0, all_0_3_3, n15 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n15, yields:
% 23.05/6.46 | (706) all_0_3_3 = n15
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n7, n14, all_0_0_0, n5 and discharging atoms sum(n7, n14) = all_0_0_0, sum(n7, n14) = n5, yields:
% 23.05/6.46 | (574) all_0_0_0 = n5
% 23.05/6.46 |
% 23.05/6.46 | From (706)(574) and (261) follows:
% 23.05/6.46 | (3805) sum(n15, n5) = all_0_6_6
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n15, n5, all_0_6_6, n4 and discharging atoms sum(n15, n5) = all_0_6_6, sum(n15, n5) = n4, yields:
% 23.05/6.46 | (508) all_0_6_6 = n4
% 23.05/6.46 |
% 23.05/6.46 | Equations (508) can reduce 12 to:
% 23.05/6.46 | (458) $false
% 23.05/6.46 |
% 23.05/6.46 |-The branch is then unsatisfiable
% 23.05/6.46 |-Branch two:
% 23.05/6.46 | (868) ~ (all_0_7_7 = n7)
% 23.05/6.46 | (869) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.05/6.46 |
% 23.05/6.46 +-Applying beta-rule and splitting (869), into two cases.
% 23.05/6.46 |-Branch one:
% 23.05/6.46 | (870) all_0_7_7 = n6
% 23.05/6.46 |
% 23.05/6.46 | From (870) and (176) follows:
% 23.05/6.46 | (871) succ(n6) = all_0_5_5
% 23.05/6.46 |
% 23.05/6.46 | From (870) and (59) follows:
% 23.05/6.46 | (872) sum(n6, all_0_1_1) = all_0_0_0
% 23.05/6.46 |
% 23.05/6.46 | From (870) and (3790) follows:
% 23.05/6.46 | (3813) sum(n8, n6) = all_0_2_2
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (219) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 23.05/6.46 | (874) all_0_5_5 = n7
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n8, n6, all_0_2_2, n14 and discharging atoms sum(n8, n6) = all_0_2_2, sum(n8, n6) = n14, yields:
% 23.05/6.46 | (447) all_0_2_2 = n14
% 23.05/6.46 |
% 23.05/6.46 | From (447) and (187) follows:
% 23.05/6.46 | (449) pred(n14) = all_0_1_1
% 23.05/6.46 |
% 23.05/6.46 | From (874) and (3789) follows:
% 23.05/6.46 | (3817) sum(n8, n7) = all_0_4_4
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (37) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 23.05/6.46 | (452) all_0_1_1 = n13
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n8, n7, all_0_4_4, n15 and discharging atoms sum(n8, n7) = all_0_4_4, sum(n8, n7) = n15, yields:
% 23.05/6.46 | (448) all_0_4_4 = n15
% 23.05/6.46 |
% 23.05/6.46 | From (448) and (396) follows:
% 23.05/6.46 | (450) pred(n15) = all_0_3_3
% 23.05/6.46 |
% 23.05/6.46 | From (452) and (872) follows:
% 23.05/6.46 | (3821) sum(n6, n13) = all_0_0_0
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (37) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 23.05/6.46 | (451) all_0_3_3 = n14
% 23.05/6.46 |
% 23.05/6.46 | Instantiating formula (89) with n6, n13, all_0_0_0, n3 and discharging atoms sum(n6, n13) = all_0_0_0, sum(n6, n13) = n3, yields:
% 23.05/6.47 | (608) all_0_0_0 = n3
% 23.05/6.47 |
% 23.05/6.47 | From (451)(608) and (261) follows:
% 23.05/6.47 | (3824) sum(n14, n3) = all_0_6_6
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n14, n3, all_0_6_6, n1 and discharging atoms sum(n14, n3) = all_0_6_6, sum(n14, n3) = n1, yields:
% 23.05/6.47 | (771) all_0_6_6 = n1
% 23.05/6.47 |
% 23.05/6.47 | Equations (771) can reduce 38 to:
% 23.05/6.47 | (458) $false
% 23.05/6.47 |
% 23.05/6.47 |-The branch is then unsatisfiable
% 23.05/6.47 |-Branch two:
% 23.05/6.47 | (887) ~ (all_0_7_7 = n6)
% 23.05/6.47 | (888) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.05/6.47 |
% 23.05/6.47 +-Applying beta-rule and splitting (888), into two cases.
% 23.05/6.47 |-Branch one:
% 23.05/6.47 | (889) all_0_7_7 = n5
% 23.05/6.47 |
% 23.05/6.47 | From (889) and (176) follows:
% 23.05/6.47 | (890) succ(n5) = all_0_5_5
% 23.05/6.47 |
% 23.05/6.47 | From (889) and (59) follows:
% 23.05/6.47 | (891) sum(n5, all_0_1_1) = all_0_0_0
% 23.05/6.47 |
% 23.05/6.47 | From (889) and (3790) follows:
% 23.05/6.47 | (3832) sum(n8, n5) = all_0_2_2
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (219) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 23.05/6.47 | (893) all_0_5_5 = n6
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n8, n5, all_0_2_2, n13 and discharging atoms sum(n8, n5) = all_0_2_2, sum(n8, n5) = n13, yields:
% 23.05/6.47 | (464) all_0_2_2 = n13
% 23.05/6.47 |
% 23.05/6.47 | From (464) and (187) follows:
% 23.05/6.47 | (466) pred(n13) = all_0_1_1
% 23.05/6.47 |
% 23.05/6.47 | From (893) and (3789) follows:
% 23.05/6.47 | (3836) sum(n8, n6) = all_0_4_4
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (37) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 23.05/6.47 | (469) all_0_1_1 = n12
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n8, n6, all_0_4_4, n14 and discharging atoms sum(n8, n6) = all_0_4_4, sum(n8, n6) = n14, yields:
% 23.05/6.47 | (465) all_0_4_4 = n14
% 23.05/6.47 |
% 23.05/6.47 | From (465) and (396) follows:
% 23.05/6.47 | (467) pred(n14) = all_0_3_3
% 23.05/6.47 |
% 23.05/6.47 | From (469) and (891) follows:
% 23.05/6.47 | (3840) sum(n5, n12) = all_0_0_0
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (37) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 23.05/6.47 | (468) all_0_3_3 = n13
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n5, n12, all_0_0_0, n1 and discharging atoms sum(n5, n12) = all_0_0_0, sum(n5, n12) = n1, yields:
% 23.05/6.47 | (642) all_0_0_0 = n1
% 23.05/6.47 |
% 23.05/6.47 | From (468)(642) and (261) follows:
% 23.05/6.47 | (3843) sum(n13, n1) = all_0_6_6
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n13, n1, all_0_6_6, n14 and discharging atoms sum(n13, n1) = all_0_6_6, sum(n13, n1) = n14, yields:
% 23.05/6.47 | (559) all_0_6_6 = n14
% 23.05/6.47 |
% 23.05/6.47 | Equations (559) can reduce 314 to:
% 23.05/6.47 | (458) $false
% 23.05/6.47 |
% 23.05/6.47 |-The branch is then unsatisfiable
% 23.05/6.47 |-Branch two:
% 23.05/6.47 | (906) ~ (all_0_7_7 = n5)
% 23.05/6.47 | (907) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.05/6.47 |
% 23.05/6.47 +-Applying beta-rule and splitting (907), into two cases.
% 23.05/6.47 |-Branch one:
% 23.05/6.47 | (908) all_0_7_7 = n4
% 23.05/6.47 |
% 23.05/6.47 | From (908) and (176) follows:
% 23.05/6.47 | (909) succ(n4) = all_0_5_5
% 23.05/6.47 |
% 23.05/6.47 | From (908) and (59) follows:
% 23.05/6.47 | (910) sum(n4, all_0_1_1) = all_0_0_0
% 23.05/6.47 |
% 23.05/6.47 | From (908) and (3790) follows:
% 23.05/6.47 | (3851) sum(n8, n4) = all_0_2_2
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (219) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 23.05/6.47 | (912) all_0_5_5 = n5
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n8, n4, all_0_2_2, n12 and discharging atoms sum(n8, n4) = all_0_2_2, sum(n8, n4) = n12, yields:
% 23.05/6.47 | (481) all_0_2_2 = n12
% 23.05/6.47 |
% 23.05/6.47 | From (481) and (187) follows:
% 23.05/6.47 | (483) pred(n12) = all_0_1_1
% 23.05/6.47 |
% 23.05/6.47 | From (912) and (3789) follows:
% 23.05/6.47 | (3855) sum(n8, n5) = all_0_4_4
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (37) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 23.05/6.47 | (486) all_0_1_1 = n11
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n8, n5, all_0_4_4, n13 and discharging atoms sum(n8, n5) = all_0_4_4, sum(n8, n5) = n13, yields:
% 23.05/6.47 | (482) all_0_4_4 = n13
% 23.05/6.47 |
% 23.05/6.47 | From (482) and (396) follows:
% 23.05/6.47 | (484) pred(n13) = all_0_3_3
% 23.05/6.47 |
% 23.05/6.47 | From (486) and (910) follows:
% 23.05/6.47 | (3859) sum(n4, n11) = all_0_0_0
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (37) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 23.05/6.47 | (485) all_0_3_3 = n12
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n4, n11, all_0_0_0, n15 and discharging atoms sum(n4, n11) = all_0_0_0, sum(n4, n11) = n15, yields:
% 23.05/6.47 | (676) all_0_0_0 = n15
% 23.05/6.47 |
% 23.05/6.47 | From (485)(676) and (261) follows:
% 23.05/6.47 | (3862) sum(n12, n15) = all_0_6_6
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n12, n15, all_0_6_6, n11 and discharging atoms sum(n12, n15) = all_0_6_6, sum(n12, n15) = n11, yields:
% 23.05/6.47 | (809) all_0_6_6 = n11
% 23.05/6.47 |
% 23.05/6.47 | Equations (809) can reduce 70 to:
% 23.05/6.47 | (458) $false
% 23.05/6.47 |
% 23.05/6.47 |-The branch is then unsatisfiable
% 23.05/6.47 |-Branch two:
% 23.05/6.47 | (925) ~ (all_0_7_7 = n4)
% 23.05/6.47 | (926) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.05/6.47 |
% 23.05/6.47 +-Applying beta-rule and splitting (926), into two cases.
% 23.05/6.47 |-Branch one:
% 23.05/6.47 | (927) all_0_7_7 = n3
% 23.05/6.47 |
% 23.05/6.47 | From (927) and (176) follows:
% 23.05/6.47 | (928) succ(n3) = all_0_5_5
% 23.05/6.47 |
% 23.05/6.47 | From (927) and (59) follows:
% 23.05/6.47 | (929) sum(n3, all_0_1_1) = all_0_0_0
% 23.05/6.47 |
% 23.05/6.47 | From (927) and (3790) follows:
% 23.05/6.47 | (3870) sum(n8, n3) = all_0_2_2
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (219) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 23.05/6.47 | (931) all_0_5_5 = n4
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n8, n3, all_0_2_2, n11 and discharging atoms sum(n8, n3) = all_0_2_2, sum(n8, n3) = n11, yields:
% 23.05/6.47 | (498) all_0_2_2 = n11
% 23.05/6.47 |
% 23.05/6.47 | From (498) and (187) follows:
% 23.05/6.47 | (500) pred(n11) = all_0_1_1
% 23.05/6.47 |
% 23.05/6.47 | From (931) and (3789) follows:
% 23.05/6.47 | (3874) sum(n8, n4) = all_0_4_4
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (37) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 23.05/6.47 | (503) all_0_1_1 = n10
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n8, n4, all_0_4_4, n12 and discharging atoms sum(n8, n4) = all_0_4_4, sum(n8, n4) = n12, yields:
% 23.05/6.47 | (499) all_0_4_4 = n12
% 23.05/6.47 |
% 23.05/6.47 | From (499) and (396) follows:
% 23.05/6.47 | (501) pred(n12) = all_0_3_3
% 23.05/6.47 |
% 23.05/6.47 | From (503) and (929) follows:
% 23.05/6.47 | (3878) sum(n3, n10) = all_0_0_0
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (37) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 23.05/6.47 | (502) all_0_3_3 = n11
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n3, n10, all_0_0_0, n13 and discharging atoms sum(n3, n10) = all_0_0_0, sum(n3, n10) = n13, yields:
% 23.05/6.47 | (709) all_0_0_0 = n13
% 23.05/6.47 |
% 23.05/6.47 | From (502)(709) and (261) follows:
% 23.05/6.47 | (3881) sum(n11, n13) = all_0_6_6
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n11, n13, all_0_6_6, n8 and discharging atoms sum(n11, n13) = all_0_6_6, sum(n11, n13) = n8, yields:
% 23.05/6.47 | (474) all_0_6_6 = n8
% 23.05/6.47 |
% 23.05/6.47 | Equations (474) can reduce 86 to:
% 23.05/6.47 | (458) $false
% 23.05/6.47 |
% 23.05/6.47 |-The branch is then unsatisfiable
% 23.05/6.47 |-Branch two:
% 23.05/6.47 | (944) ~ (all_0_7_7 = n3)
% 23.05/6.47 | (945) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.05/6.47 |
% 23.05/6.47 +-Applying beta-rule and splitting (945), into two cases.
% 23.05/6.47 |-Branch one:
% 23.05/6.47 | (946) all_0_7_7 = n2
% 23.05/6.47 |
% 23.05/6.47 | From (946) and (176) follows:
% 23.05/6.47 | (947) succ(n2) = all_0_5_5
% 23.05/6.47 |
% 23.05/6.47 | From (946) and (59) follows:
% 23.05/6.47 | (948) sum(n2, all_0_1_1) = all_0_0_0
% 23.05/6.47 |
% 23.05/6.47 | From (946) and (3790) follows:
% 23.05/6.47 | (3889) sum(n8, n2) = all_0_2_2
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (219) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 23.05/6.47 | (950) all_0_5_5 = n3
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n8, n2, all_0_2_2, n10 and discharging atoms sum(n8, n2) = all_0_2_2, sum(n8, n2) = n10, yields:
% 23.05/6.47 | (515) all_0_2_2 = n10
% 23.05/6.47 |
% 23.05/6.47 | From (515) and (187) follows:
% 23.05/6.47 | (517) pred(n10) = all_0_1_1
% 23.05/6.47 |
% 23.05/6.47 | From (950) and (3789) follows:
% 23.05/6.47 | (3893) sum(n8, n3) = all_0_4_4
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (37) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 23.05/6.47 | (520) all_0_1_1 = n9
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n8, n3, all_0_4_4, n11 and discharging atoms sum(n8, n3) = all_0_4_4, sum(n8, n3) = n11, yields:
% 23.05/6.47 | (516) all_0_4_4 = n11
% 23.05/6.47 |
% 23.05/6.47 | From (516) and (396) follows:
% 23.05/6.47 | (518) pred(n11) = all_0_3_3
% 23.05/6.47 |
% 23.05/6.47 | From (520) and (948) follows:
% 23.05/6.47 | (3897) sum(n2, n9) = all_0_0_0
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (37) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 23.05/6.47 | (519) all_0_3_3 = n10
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n2, n9, all_0_0_0, n11 and discharging atoms sum(n2, n9) = all_0_0_0, sum(n2, n9) = n11, yields:
% 23.05/6.47 | (472) all_0_0_0 = n11
% 23.05/6.47 |
% 23.05/6.47 | From (519)(472) and (261) follows:
% 23.05/6.47 | (3900) sum(n10, n11) = all_0_6_6
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n10, n11, all_0_6_6, n5 and discharging atoms sum(n10, n11) = all_0_6_6, sum(n10, n11) = n5, yields:
% 23.05/6.47 | (847) all_0_6_6 = n5
% 23.05/6.47 |
% 23.05/6.47 | Equations (847) can reduce 409 to:
% 23.05/6.47 | (458) $false
% 23.05/6.47 |
% 23.05/6.47 |-The branch is then unsatisfiable
% 23.05/6.47 |-Branch two:
% 23.05/6.47 | (963) ~ (all_0_7_7 = n2)
% 23.05/6.47 | (964) all_0_7_7 = n1 | all_0_7_7 = n0
% 23.05/6.47 |
% 23.05/6.47 +-Applying beta-rule and splitting (964), into two cases.
% 23.05/6.47 |-Branch one:
% 23.05/6.47 | (965) all_0_7_7 = n1
% 23.05/6.47 |
% 23.05/6.47 | From (965) and (176) follows:
% 23.05/6.47 | (966) succ(n1) = all_0_5_5
% 23.05/6.47 |
% 23.05/6.47 | From (965) and (59) follows:
% 23.05/6.47 | (967) sum(n1, all_0_1_1) = all_0_0_0
% 23.05/6.47 |
% 23.05/6.47 | From (965) and (3790) follows:
% 23.05/6.47 | (3908) sum(n8, n1) = all_0_2_2
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (219) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 23.05/6.47 | (969) all_0_5_5 = n2
% 23.05/6.47 |
% 23.05/6.47 | Instantiating formula (89) with n8, n1, all_0_2_2, n9 and discharging atoms sum(n8, n1) = all_0_2_2, sum(n8, n1) = n9, yields:
% 23.05/6.47 | (532) all_0_2_2 = n9
% 23.05/6.47 |
% 23.05/6.47 | From (532) and (187) follows:
% 23.05/6.48 | (534) pred(n9) = all_0_1_1
% 23.05/6.48 |
% 23.05/6.48 | From (969) and (3789) follows:
% 23.05/6.48 | (3912) sum(n8, n2) = all_0_4_4
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (37) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 23.05/6.48 | (537) all_0_1_1 = n8
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n8, n2, all_0_4_4, n10 and discharging atoms sum(n8, n2) = all_0_4_4, sum(n8, n2) = n10, yields:
% 23.05/6.48 | (533) all_0_4_4 = n10
% 23.05/6.48 |
% 23.05/6.48 | From (533) and (396) follows:
% 23.05/6.48 | (535) pred(n10) = all_0_3_3
% 23.05/6.48 |
% 23.05/6.48 | From (537) and (967) follows:
% 23.05/6.48 | (3916) sum(n1, n8) = all_0_0_0
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (37) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 23.05/6.48 | (536) all_0_3_3 = n9
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n1, n8, all_0_0_0, n9 and discharging atoms sum(n1, n8) = all_0_0_0, sum(n1, n8) = n9, yields:
% 23.05/6.48 | (506) all_0_0_0 = n9
% 23.05/6.48 |
% 23.05/6.48 | From (536)(506) and (261) follows:
% 23.05/6.48 | (3919) sum(n9, n9) = all_0_6_6
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n9, n9, all_0_6_6, n2 and discharging atoms sum(n9, n9) = all_0_6_6, sum(n9, n9) = n2, yields:
% 23.05/6.48 | (525) all_0_6_6 = n2
% 23.05/6.48 |
% 23.05/6.48 | Equations (525) can reduce 231 to:
% 23.05/6.48 | (458) $false
% 23.05/6.48 |
% 23.05/6.48 |-The branch is then unsatisfiable
% 23.05/6.48 |-Branch two:
% 23.05/6.48 | (982) ~ (all_0_7_7 = n1)
% 23.05/6.48 | (983) all_0_7_7 = n0
% 23.05/6.48 |
% 23.05/6.48 | From (983) and (176) follows:
% 23.05/6.48 | (984) succ(n0) = all_0_5_5
% 23.05/6.48 |
% 23.05/6.48 | From (983) and (59) follows:
% 23.05/6.48 | (985) sum(n0, all_0_1_1) = all_0_0_0
% 23.05/6.48 |
% 23.05/6.48 | From (983) and (3790) follows:
% 23.05/6.48 | (3926) sum(n8, n0) = all_0_2_2
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (219) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 23.05/6.48 | (987) all_0_5_5 = n1
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n8, n0, all_0_2_2, n8 and discharging atoms sum(n8, n0) = all_0_2_2, sum(n8, n0) = n8, yields:
% 23.05/6.48 | (549) all_0_2_2 = n8
% 23.05/6.48 |
% 23.05/6.48 | From (549) and (187) follows:
% 23.05/6.48 | (551) pred(n8) = all_0_1_1
% 23.05/6.48 |
% 23.05/6.48 | From (987) and (3789) follows:
% 23.05/6.48 | (3930) sum(n8, n1) = all_0_4_4
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (37) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 23.05/6.48 | (554) all_0_1_1 = n7
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n8, n1, all_0_4_4, n9 and discharging atoms sum(n8, n1) = all_0_4_4, sum(n8, n1) = n9, yields:
% 23.05/6.48 | (550) all_0_4_4 = n9
% 23.05/6.48 |
% 23.05/6.48 | From (550) and (396) follows:
% 23.05/6.48 | (552) pred(n9) = all_0_3_3
% 23.05/6.48 |
% 23.05/6.48 | From (554) and (985) follows:
% 23.05/6.48 | (3934) sum(n0, n7) = all_0_0_0
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (37) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 23.05/6.48 | (553) all_0_3_3 = n8
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n0, n7, all_0_0_0, n7 and discharging atoms sum(n0, n7) = all_0_0_0, sum(n0, n7) = n7, yields:
% 23.05/6.48 | (540) all_0_0_0 = n7
% 23.05/6.48 |
% 23.05/6.48 | From (553)(540) and (261) follows:
% 23.05/6.48 | (3937) sum(n8, n7) = all_0_6_6
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n8, n7, all_0_6_6, n15 and discharging atoms sum(n8, n7) = all_0_6_6, sum(n8, n7) = n15, yields:
% 23.05/6.48 | (885) all_0_6_6 = n15
% 23.05/6.48 |
% 23.05/6.48 | Equations (885) can reduce 225 to:
% 23.05/6.48 | (458) $false
% 23.05/6.48 |
% 23.05/6.48 |-The branch is then unsatisfiable
% 23.05/6.48 |-Branch two:
% 23.05/6.48 | (578) ~ (all_0_8_8 = n8)
% 23.05/6.48 | (579) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.05/6.48 |
% 23.05/6.48 +-Applying beta-rule and splitting (850), into two cases.
% 23.05/6.48 |-Branch one:
% 23.05/6.48 | (851) all_0_7_7 = n7
% 23.05/6.48 |
% 23.05/6.48 | From (851) and (176) follows:
% 23.05/6.48 | (852) succ(n7) = all_0_5_5
% 23.05/6.48 |
% 23.05/6.48 | From (851) and (59) follows:
% 23.05/6.48 | (853) sum(n7, all_0_1_1) = all_0_0_0
% 23.05/6.48 |
% 23.05/6.48 | From (851) and (160) follows:
% 23.05/6.48 | (3945) sum(all_0_8_8, n7) = all_0_2_2
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (219) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 23.05/6.48 | (855) all_0_5_5 = n8
% 23.05/6.48 |
% 23.05/6.48 | From (855) and (64) follows:
% 23.05/6.48 | (3947) sum(all_0_8_8, n8) = all_0_4_4
% 23.05/6.48 |
% 23.05/6.48 +-Applying beta-rule and splitting (579), into two cases.
% 23.05/6.48 |-Branch one:
% 23.05/6.48 | (580) all_0_8_8 = n7
% 23.05/6.48 |
% 23.05/6.48 | From (580) and (3947) follows:
% 23.05/6.48 | (3949) sum(n7, n8) = all_0_4_4
% 23.05/6.48 |
% 23.05/6.48 | From (580) and (3945) follows:
% 23.05/6.48 | (3950) sum(n7, n7) = all_0_2_2
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n7, n8, all_0_4_4, n15 and discharging atoms sum(n7, n8) = all_0_4_4, sum(n7, n8) = n15, yields:
% 23.05/6.48 | (448) all_0_4_4 = n15
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n7, n7, all_0_2_2, n14 and discharging atoms sum(n7, n7) = all_0_2_2, sum(n7, n7) = n14, yields:
% 23.05/6.48 | (447) all_0_2_2 = n14
% 23.05/6.48 |
% 23.05/6.48 | From (447) and (187) follows:
% 23.05/6.48 | (449) pred(n14) = all_0_1_1
% 23.05/6.48 |
% 23.05/6.48 | From (448) and (396) follows:
% 23.05/6.48 | (450) pred(n15) = all_0_3_3
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (37) with n15, all_0_3_3, n14 and discharging atoms pred(n15) = all_0_3_3, pred(n15) = n14, yields:
% 23.05/6.48 | (451) all_0_3_3 = n14
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (37) with n14, all_0_1_1, n13 and discharging atoms pred(n14) = all_0_1_1, pred(n14) = n13, yields:
% 23.05/6.48 | (452) all_0_1_1 = n13
% 23.05/6.48 |
% 23.05/6.48 | From (451) and (261) follows:
% 23.05/6.48 | (453) sum(n14, all_0_0_0) = all_0_6_6
% 23.05/6.48 |
% 23.05/6.48 | From (452) and (853) follows:
% 23.05/6.48 | (3958) sum(n7, n13) = all_0_0_0
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n7, n13, all_0_0_0, n4 and discharging atoms sum(n7, n13) = all_0_0_0, sum(n7, n13) = n4, yields:
% 23.05/6.48 | (591) all_0_0_0 = n4
% 23.05/6.48 |
% 23.05/6.48 | From (591) and (453) follows:
% 23.05/6.48 | (3960) sum(n14, n4) = all_0_6_6
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n14, n4, all_0_6_6, n2 and discharging atoms sum(n14, n4) = all_0_6_6, sum(n14, n4) = n2, yields:
% 23.05/6.48 | (525) all_0_6_6 = n2
% 23.05/6.48 |
% 23.05/6.48 | Equations (525) can reduce 231 to:
% 23.05/6.48 | (458) $false
% 23.05/6.48 |
% 23.05/6.48 |-The branch is then unsatisfiable
% 23.05/6.48 |-Branch two:
% 23.05/6.48 | (595) ~ (all_0_8_8 = n7)
% 23.05/6.48 | (596) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.05/6.48 |
% 23.05/6.48 +-Applying beta-rule and splitting (596), into two cases.
% 23.05/6.48 |-Branch one:
% 23.05/6.48 | (597) all_0_8_8 = n6
% 23.05/6.48 |
% 23.05/6.48 | From (597) and (3947) follows:
% 23.05/6.48 | (3966) sum(n6, n8) = all_0_4_4
% 23.05/6.48 |
% 23.05/6.48 | From (597) and (3945) follows:
% 23.05/6.48 | (3967) sum(n6, n7) = all_0_2_2
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n6, n8, all_0_4_4, n14 and discharging atoms sum(n6, n8) = all_0_4_4, sum(n6, n8) = n14, yields:
% 23.05/6.48 | (465) all_0_4_4 = n14
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n6, n7, all_0_2_2, n13 and discharging atoms sum(n6, n7) = all_0_2_2, sum(n6, n7) = n13, yields:
% 23.05/6.48 | (464) all_0_2_2 = n13
% 23.05/6.48 |
% 23.05/6.48 | From (464) and (187) follows:
% 23.05/6.48 | (466) pred(n13) = all_0_1_1
% 23.05/6.48 |
% 23.05/6.48 | From (465) and (396) follows:
% 23.05/6.48 | (467) pred(n14) = all_0_3_3
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (37) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 23.05/6.48 | (468) all_0_3_3 = n13
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (37) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 23.05/6.48 | (469) all_0_1_1 = n12
% 23.05/6.48 |
% 23.05/6.48 | From (468) and (261) follows:
% 23.05/6.48 | (470) sum(n13, all_0_0_0) = all_0_6_6
% 23.05/6.48 |
% 23.05/6.48 | From (469) and (853) follows:
% 23.05/6.48 | (3975) sum(n7, n12) = all_0_0_0
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n7, n12, all_0_0_0, n3 and discharging atoms sum(n7, n12) = all_0_0_0, sum(n7, n12) = n3, yields:
% 23.05/6.48 | (608) all_0_0_0 = n3
% 23.05/6.48 |
% 23.05/6.48 | From (608) and (470) follows:
% 23.05/6.48 | (3977) sum(n13, n3) = all_0_6_6
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n13, n3, all_0_6_6, n0 and discharging atoms sum(n13, n3) = all_0_6_6, sum(n13, n3) = n0, yields:
% 23.05/6.48 | (542) all_0_6_6 = n0
% 23.05/6.48 |
% 23.05/6.48 | Equations (542) can reduce 400 to:
% 23.05/6.48 | (458) $false
% 23.05/6.48 |
% 23.05/6.48 |-The branch is then unsatisfiable
% 23.05/6.48 |-Branch two:
% 23.05/6.48 | (612) ~ (all_0_8_8 = n6)
% 23.05/6.48 | (613) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.05/6.48 |
% 23.05/6.48 +-Applying beta-rule and splitting (613), into two cases.
% 23.05/6.48 |-Branch one:
% 23.05/6.48 | (614) all_0_8_8 = n5
% 23.05/6.48 |
% 23.05/6.48 | From (614) and (3947) follows:
% 23.05/6.48 | (3983) sum(n5, n8) = all_0_4_4
% 23.05/6.48 |
% 23.05/6.48 | From (614) and (3945) follows:
% 23.05/6.48 | (3984) sum(n5, n7) = all_0_2_2
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n5, n8, all_0_4_4, n13 and discharging atoms sum(n5, n8) = all_0_4_4, sum(n5, n8) = n13, yields:
% 23.05/6.48 | (482) all_0_4_4 = n13
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 23.05/6.48 | (481) all_0_2_2 = n12
% 23.05/6.48 |
% 23.05/6.48 | From (481) and (187) follows:
% 23.05/6.48 | (483) pred(n12) = all_0_1_1
% 23.05/6.48 |
% 23.05/6.48 | From (482) and (396) follows:
% 23.05/6.48 | (484) pred(n13) = all_0_3_3
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (37) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 23.05/6.48 | (485) all_0_3_3 = n12
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (37) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 23.05/6.48 | (486) all_0_1_1 = n11
% 23.05/6.48 |
% 23.05/6.48 | From (485) and (261) follows:
% 23.05/6.48 | (487) sum(n12, all_0_0_0) = all_0_6_6
% 23.05/6.48 |
% 23.05/6.48 | From (486) and (853) follows:
% 23.05/6.48 | (3992) sum(n7, n11) = all_0_0_0
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n7, n11, all_0_0_0, n2 and discharging atoms sum(n7, n11) = all_0_0_0, sum(n7, n11) = n2, yields:
% 23.05/6.48 | (625) all_0_0_0 = n2
% 23.05/6.48 |
% 23.05/6.48 | From (625) and (487) follows:
% 23.05/6.48 | (3994) sum(n12, n2) = all_0_6_6
% 23.05/6.48 |
% 23.05/6.48 | Instantiating formula (89) with n12, n2, all_0_6_6, n14 and discharging atoms sum(n12, n2) = all_0_6_6, sum(n12, n2) = n14, yields:
% 23.05/6.48 | (559) all_0_6_6 = n14
% 23.05/6.48 |
% 23.05/6.48 | Equations (559) can reduce 314 to:
% 23.05/6.48 | (458) $false
% 23.05/6.48 |
% 23.05/6.48 |-The branch is then unsatisfiable
% 23.05/6.48 |-Branch two:
% 23.05/6.48 | (629) ~ (all_0_8_8 = n5)
% 23.05/6.48 | (630) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.05/6.48 |
% 23.05/6.48 +-Applying beta-rule and splitting (630), into two cases.
% 23.05/6.48 |-Branch one:
% 23.05/6.48 | (631) all_0_8_8 = n4
% 23.05/6.48 |
% 23.05/6.48 | From (631) and (3947) follows:
% 23.05/6.49 | (4000) sum(n4, n8) = all_0_4_4
% 23.05/6.49 |
% 23.05/6.49 | From (631) and (3945) follows:
% 23.05/6.49 | (4001) sum(n4, n7) = all_0_2_2
% 23.05/6.49 |
% 23.05/6.49 | Instantiating formula (89) with n4, n8, all_0_4_4, n12 and discharging atoms sum(n4, n8) = all_0_4_4, sum(n4, n8) = n12, yields:
% 23.05/6.49 | (499) all_0_4_4 = n12
% 23.05/6.49 |
% 23.05/6.49 | Instantiating formula (89) with n4, n7, all_0_2_2, n11 and discharging atoms sum(n4, n7) = all_0_2_2, sum(n4, n7) = n11, yields:
% 23.05/6.49 | (498) all_0_2_2 = n11
% 23.05/6.49 |
% 23.05/6.49 | From (498) and (187) follows:
% 23.05/6.49 | (500) pred(n11) = all_0_1_1
% 23.05/6.49 |
% 23.05/6.49 | From (499) and (396) follows:
% 23.05/6.49 | (501) pred(n12) = all_0_3_3
% 23.05/6.49 |
% 23.05/6.49 | Instantiating formula (37) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 23.05/6.49 | (502) all_0_3_3 = n11
% 23.05/6.49 |
% 23.05/6.49 | Instantiating formula (37) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 23.05/6.49 | (503) all_0_1_1 = n10
% 23.05/6.49 |
% 23.05/6.49 | From (502) and (261) follows:
% 23.05/6.49 | (504) sum(n11, all_0_0_0) = all_0_6_6
% 23.05/6.49 |
% 23.05/6.49 | From (503) and (853) follows:
% 23.05/6.49 | (4009) sum(n7, n10) = all_0_0_0
% 23.05/6.49 |
% 23.05/6.49 | Instantiating formula (89) with n7, n10, all_0_0_0, n1 and discharging atoms sum(n7, n10) = all_0_0_0, sum(n7, n10) = n1, yields:
% 23.05/6.49 | (642) all_0_0_0 = n1
% 23.05/6.49 |
% 23.05/6.49 | From (642) and (504) follows:
% 23.05/6.49 | (4011) sum(n11, n1) = all_0_6_6
% 23.05/6.49 |
% 23.05/6.49 | Instantiating formula (89) with n11, n1, all_0_6_6, n12 and discharging atoms sum(n11, n1) = all_0_6_6, sum(n11, n1) = n12, yields:
% 23.05/6.49 | (576) all_0_6_6 = n12
% 23.05/6.49 |
% 23.05/6.49 | Equations (576) can reduce 42 to:
% 23.05/6.49 | (458) $false
% 23.05/6.49 |
% 23.05/6.49 |-The branch is then unsatisfiable
% 23.20/6.49 |-Branch two:
% 23.20/6.49 | (646) ~ (all_0_8_8 = n4)
% 23.20/6.49 | (647) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.20/6.49 |
% 23.20/6.49 +-Applying beta-rule and splitting (647), into two cases.
% 23.20/6.49 |-Branch one:
% 23.20/6.49 | (648) all_0_8_8 = n3
% 23.20/6.49 |
% 23.20/6.49 | From (648) and (3947) follows:
% 23.20/6.49 | (4017) sum(n3, n8) = all_0_4_4
% 23.20/6.49 |
% 23.20/6.49 | From (648) and (3945) follows:
% 23.20/6.49 | (4018) sum(n3, n7) = all_0_2_2
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (89) with n3, n8, all_0_4_4, n11 and discharging atoms sum(n3, n8) = all_0_4_4, sum(n3, n8) = n11, yields:
% 23.20/6.49 | (516) all_0_4_4 = n11
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (89) with n3, n7, all_0_2_2, n10 and discharging atoms sum(n3, n7) = all_0_2_2, sum(n3, n7) = n10, yields:
% 23.20/6.49 | (515) all_0_2_2 = n10
% 23.20/6.49 |
% 23.20/6.49 | From (515) and (187) follows:
% 23.20/6.49 | (517) pred(n10) = all_0_1_1
% 23.20/6.49 |
% 23.20/6.49 | From (516) and (396) follows:
% 23.20/6.49 | (518) pred(n11) = all_0_3_3
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (37) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 23.20/6.49 | (519) all_0_3_3 = n10
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (37) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 23.20/6.49 | (520) all_0_1_1 = n9
% 23.20/6.49 |
% 23.20/6.49 | From (519) and (261) follows:
% 23.20/6.49 | (521) sum(n10, all_0_0_0) = all_0_6_6
% 23.20/6.49 |
% 23.20/6.49 | From (520) and (853) follows:
% 23.20/6.49 | (4026) sum(n7, n9) = all_0_0_0
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (89) with n7, n9, all_0_0_0, n0 and discharging atoms sum(n7, n9) = all_0_0_0, sum(n7, n9) = n0, yields:
% 23.20/6.49 | (659) all_0_0_0 = n0
% 23.20/6.49 |
% 23.20/6.49 | From (659) and (521) follows:
% 23.20/6.49 | (4028) sum(n10, n0) = all_0_6_6
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (89) with n10, n0, all_0_6_6, n10 and discharging atoms sum(n10, n0) = all_0_6_6, sum(n10, n0) = n10, yields:
% 23.20/6.49 | (457) all_0_6_6 = n10
% 23.20/6.49 |
% 23.20/6.49 | Equations (457) can reduce 169 to:
% 23.20/6.49 | (458) $false
% 23.20/6.49 |
% 23.20/6.49 |-The branch is then unsatisfiable
% 23.20/6.49 |-Branch two:
% 23.20/6.49 | (663) ~ (all_0_8_8 = n3)
% 23.20/6.49 | (664) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.20/6.49 |
% 23.20/6.49 +-Applying beta-rule and splitting (664), into two cases.
% 23.20/6.49 |-Branch one:
% 23.20/6.49 | (665) all_0_8_8 = n2
% 23.20/6.49 |
% 23.20/6.49 | From (665) and (3947) follows:
% 23.20/6.49 | (4034) sum(n2, n8) = all_0_4_4
% 23.20/6.49 |
% 23.20/6.49 | From (665) and (3945) follows:
% 23.20/6.49 | (4035) sum(n2, n7) = all_0_2_2
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (89) with n2, n8, all_0_4_4, n10 and discharging atoms sum(n2, n8) = all_0_4_4, sum(n2, n8) = n10, yields:
% 23.20/6.49 | (533) all_0_4_4 = n10
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (89) with n2, n7, all_0_2_2, n9 and discharging atoms sum(n2, n7) = all_0_2_2, sum(n2, n7) = n9, yields:
% 23.20/6.49 | (532) all_0_2_2 = n9
% 23.20/6.49 |
% 23.20/6.49 | From (532) and (187) follows:
% 23.20/6.49 | (534) pred(n9) = all_0_1_1
% 23.20/6.49 |
% 23.20/6.49 | From (533) and (396) follows:
% 23.20/6.49 | (535) pred(n10) = all_0_3_3
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (37) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 23.20/6.49 | (536) all_0_3_3 = n9
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (37) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 23.20/6.49 | (537) all_0_1_1 = n8
% 23.20/6.49 |
% 23.20/6.49 | From (536) and (261) follows:
% 23.20/6.49 | (538) sum(n9, all_0_0_0) = all_0_6_6
% 23.20/6.49 |
% 23.20/6.49 | From (537) and (853) follows:
% 23.20/6.49 | (4043) sum(n7, n8) = all_0_0_0
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (89) with n7, n8, all_0_0_0, n15 and discharging atoms sum(n7, n8) = all_0_0_0, sum(n7, n8) = n15, yields:
% 23.20/6.49 | (676) all_0_0_0 = n15
% 23.20/6.49 |
% 23.20/6.49 | From (676) and (538) follows:
% 23.20/6.49 | (4045) sum(n9, n15) = all_0_6_6
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (89) with n9, n15, all_0_6_6, n8 and discharging atoms sum(n9, n15) = all_0_6_6, sum(n9, n15) = n8, yields:
% 23.20/6.49 | (474) all_0_6_6 = n8
% 23.20/6.49 |
% 23.20/6.49 | Equations (474) can reduce 86 to:
% 23.20/6.49 | (458) $false
% 23.20/6.49 |
% 23.20/6.49 |-The branch is then unsatisfiable
% 23.20/6.49 |-Branch two:
% 23.20/6.49 | (680) ~ (all_0_8_8 = n2)
% 23.20/6.49 | (681) all_0_8_8 = n1 | all_0_8_8 = n0
% 23.20/6.49 |
% 23.20/6.49 +-Applying beta-rule and splitting (681), into two cases.
% 23.20/6.49 |-Branch one:
% 23.20/6.49 | (682) all_0_8_8 = n1
% 23.20/6.49 |
% 23.20/6.49 | From (682) and (3947) follows:
% 23.20/6.49 | (4051) sum(n1, n8) = all_0_4_4
% 23.20/6.49 |
% 23.20/6.49 | From (682) and (3945) follows:
% 23.20/6.49 | (4052) sum(n1, n7) = all_0_2_2
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (89) with n1, n8, all_0_4_4, n9 and discharging atoms sum(n1, n8) = all_0_4_4, sum(n1, n8) = n9, yields:
% 23.20/6.49 | (550) all_0_4_4 = n9
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (89) with n1, n7, all_0_2_2, n8 and discharging atoms sum(n1, n7) = all_0_2_2, sum(n1, n7) = n8, yields:
% 23.20/6.49 | (549) all_0_2_2 = n8
% 23.20/6.49 |
% 23.20/6.49 | From (549) and (187) follows:
% 23.20/6.49 | (551) pred(n8) = all_0_1_1
% 23.20/6.49 |
% 23.20/6.49 | From (550) and (396) follows:
% 23.20/6.49 | (552) pred(n9) = all_0_3_3
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (37) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 23.20/6.49 | (553) all_0_3_3 = n8
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (37) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 23.20/6.49 | (554) all_0_1_1 = n7
% 23.20/6.49 |
% 23.20/6.49 | From (553) and (261) follows:
% 23.20/6.49 | (555) sum(n8, all_0_0_0) = all_0_6_6
% 23.20/6.49 |
% 23.20/6.49 | From (554) and (853) follows:
% 23.20/6.49 | (4060) sum(n7, n7) = all_0_0_0
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (89) with n7, n7, all_0_0_0, n14 and discharging atoms sum(n7, n7) = all_0_0_0, sum(n7, n7) = n14, yields:
% 23.20/6.49 | (693) all_0_0_0 = n14
% 23.20/6.49 |
% 23.20/6.49 | From (693) and (555) follows:
% 23.20/6.49 | (4062) sum(n8, n14) = all_0_6_6
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (89) with n8, n14, all_0_6_6, n6 and discharging atoms sum(n8, n14) = all_0_6_6, sum(n8, n14) = n6, yields:
% 23.20/6.49 | (491) all_0_6_6 = n6
% 23.20/6.49 |
% 23.20/6.49 | Equations (491) can reduce 418 to:
% 23.20/6.49 | (458) $false
% 23.20/6.49 |
% 23.20/6.49 |-The branch is then unsatisfiable
% 23.20/6.49 |-Branch two:
% 23.20/6.49 | (697) ~ (all_0_8_8 = n1)
% 23.20/6.49 | (698) all_0_8_8 = n0
% 23.20/6.49 |
% 23.20/6.49 | From (698) and (3947) follows:
% 23.20/6.49 | (4067) sum(n0, n8) = all_0_4_4
% 23.20/6.49 |
% 23.20/6.49 | From (698) and (3945) follows:
% 23.20/6.49 | (4068) sum(n0, n7) = all_0_2_2
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (89) with n0, n8, all_0_4_4, n8 and discharging atoms sum(n0, n8) = all_0_4_4, sum(n0, n8) = n8, yields:
% 23.20/6.49 | (567) all_0_4_4 = n8
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (89) with n0, n7, all_0_2_2, n7 and discharging atoms sum(n0, n7) = all_0_2_2, sum(n0, n7) = n7, yields:
% 23.20/6.49 | (566) all_0_2_2 = n7
% 23.20/6.49 |
% 23.20/6.49 | From (566) and (187) follows:
% 23.20/6.49 | (568) pred(n7) = all_0_1_1
% 23.20/6.49 |
% 23.20/6.49 | From (567) and (396) follows:
% 23.20/6.49 | (569) pred(n8) = all_0_3_3
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (37) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 23.20/6.49 | (570) all_0_3_3 = n7
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (37) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 23.20/6.49 | (571) all_0_1_1 = n6
% 23.20/6.49 |
% 23.20/6.49 | From (570) and (261) follows:
% 23.20/6.49 | (572) sum(n7, all_0_0_0) = all_0_6_6
% 23.20/6.49 |
% 23.20/6.49 | From (571) and (853) follows:
% 23.20/6.49 | (4076) sum(n7, n6) = all_0_0_0
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (89) with n7, n6, all_0_0_0, n13 and discharging atoms sum(n7, n6) = all_0_0_0, sum(n7, n6) = n13, yields:
% 23.20/6.49 | (709) all_0_0_0 = n13
% 23.20/6.49 |
% 23.20/6.49 | From (709) and (572) follows:
% 23.20/6.49 | (4078) sum(n7, n13) = all_0_6_6
% 23.20/6.49 |
% 23.20/6.49 | Instantiating formula (89) with n7, n13, all_0_6_6, n4 and discharging atoms sum(n7, n13) = all_0_6_6, sum(n7, n13) = n4, yields:
% 23.20/6.49 | (508) all_0_6_6 = n4
% 23.20/6.49 |
% 23.20/6.49 | Equations (508) can reduce 12 to:
% 23.20/6.49 | (458) $false
% 23.20/6.49 |
% 23.20/6.49 |-The branch is then unsatisfiable
% 23.20/6.49 |-Branch two:
% 23.20/6.49 | (868) ~ (all_0_7_7 = n7)
% 23.20/6.49 | (869) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.20/6.49 |
% 23.20/6.49 +-Applying beta-rule and splitting (579), into two cases.
% 23.20/6.49 |-Branch one:
% 23.20/6.49 | (580) all_0_8_8 = n7
% 23.20/6.49 |
% 23.20/6.49 | From (580) and (64) follows:
% 23.20/6.50 | (4084) sum(n7, all_0_5_5) = all_0_4_4
% 23.20/6.50 |
% 23.20/6.50 | From (580) and (160) follows:
% 23.20/6.50 | (4085) sum(n7, all_0_7_7) = all_0_2_2
% 23.20/6.50 |
% 23.20/6.50 +-Applying beta-rule and splitting (869), into two cases.
% 23.20/6.50 |-Branch one:
% 23.20/6.50 | (870) all_0_7_7 = n6
% 23.20/6.50 |
% 23.20/6.50 | From (870) and (176) follows:
% 23.20/6.50 | (871) succ(n6) = all_0_5_5
% 23.20/6.50 |
% 23.20/6.50 | From (870) and (59) follows:
% 23.20/6.50 | (872) sum(n6, all_0_1_1) = all_0_0_0
% 23.20/6.50 |
% 23.20/6.50 | From (870) and (4085) follows:
% 23.20/6.50 | (4089) sum(n7, n6) = all_0_2_2
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (219) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 23.20/6.50 | (874) all_0_5_5 = n7
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (89) with n7, n6, all_0_2_2, n13 and discharging atoms sum(n7, n6) = all_0_2_2, sum(n7, n6) = n13, yields:
% 23.20/6.50 | (464) all_0_2_2 = n13
% 23.20/6.50 |
% 23.20/6.50 | From (464) and (187) follows:
% 23.20/6.50 | (466) pred(n13) = all_0_1_1
% 23.20/6.50 |
% 23.20/6.50 | From (874) and (4084) follows:
% 23.20/6.50 | (4093) sum(n7, n7) = all_0_4_4
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (37) with n13, all_0_1_1, n12 and discharging atoms pred(n13) = all_0_1_1, pred(n13) = n12, yields:
% 23.20/6.50 | (469) all_0_1_1 = n12
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (89) with n7, n7, all_0_4_4, n14 and discharging atoms sum(n7, n7) = all_0_4_4, sum(n7, n7) = n14, yields:
% 23.20/6.50 | (465) all_0_4_4 = n14
% 23.20/6.50 |
% 23.20/6.50 | From (465) and (396) follows:
% 23.20/6.50 | (467) pred(n14) = all_0_3_3
% 23.20/6.50 |
% 23.20/6.50 | From (469) and (872) follows:
% 23.20/6.50 | (4097) sum(n6, n12) = all_0_0_0
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (37) with n14, all_0_3_3, n13 and discharging atoms pred(n14) = all_0_3_3, pred(n14) = n13, yields:
% 23.20/6.50 | (468) all_0_3_3 = n13
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (89) with n6, n12, all_0_0_0, n2 and discharging atoms sum(n6, n12) = all_0_0_0, sum(n6, n12) = n2, yields:
% 23.20/6.50 | (625) all_0_0_0 = n2
% 23.20/6.50 |
% 23.20/6.50 | From (468)(625) and (261) follows:
% 23.20/6.50 | (4100) sum(n13, n2) = all_0_6_6
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (89) with n13, n2, all_0_6_6, n15 and discharging atoms sum(n13, n2) = all_0_6_6, sum(n13, n2) = n15, yields:
% 23.20/6.50 | (885) all_0_6_6 = n15
% 23.20/6.50 |
% 23.20/6.50 | Equations (885) can reduce 225 to:
% 23.20/6.50 | (458) $false
% 23.20/6.50 |
% 23.20/6.50 |-The branch is then unsatisfiable
% 23.20/6.50 |-Branch two:
% 23.20/6.50 | (887) ~ (all_0_7_7 = n6)
% 23.20/6.50 | (888) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.20/6.50 |
% 23.20/6.50 +-Applying beta-rule and splitting (888), into two cases.
% 23.20/6.50 |-Branch one:
% 23.20/6.50 | (889) all_0_7_7 = n5
% 23.20/6.50 |
% 23.20/6.50 | From (889) and (176) follows:
% 23.20/6.50 | (890) succ(n5) = all_0_5_5
% 23.20/6.50 |
% 23.20/6.50 | From (889) and (59) follows:
% 23.20/6.50 | (891) sum(n5, all_0_1_1) = all_0_0_0
% 23.20/6.50 |
% 23.20/6.50 | From (889) and (4085) follows:
% 23.20/6.50 | (4108) sum(n7, n5) = all_0_2_2
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (219) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 23.20/6.50 | (893) all_0_5_5 = n6
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (89) with n7, n5, all_0_2_2, n12 and discharging atoms sum(n7, n5) = all_0_2_2, sum(n7, n5) = n12, yields:
% 23.20/6.50 | (481) all_0_2_2 = n12
% 23.20/6.50 |
% 23.20/6.50 | From (481) and (187) follows:
% 23.20/6.50 | (483) pred(n12) = all_0_1_1
% 23.20/6.50 |
% 23.20/6.50 | From (893) and (4084) follows:
% 23.20/6.50 | (4112) sum(n7, n6) = all_0_4_4
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (37) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 23.20/6.50 | (486) all_0_1_1 = n11
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (89) with n7, n6, all_0_4_4, n13 and discharging atoms sum(n7, n6) = all_0_4_4, sum(n7, n6) = n13, yields:
% 23.20/6.50 | (482) all_0_4_4 = n13
% 23.20/6.50 |
% 23.20/6.50 | From (482) and (396) follows:
% 23.20/6.50 | (484) pred(n13) = all_0_3_3
% 23.20/6.50 |
% 23.20/6.50 | From (486) and (891) follows:
% 23.20/6.50 | (4116) sum(n5, n11) = all_0_0_0
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (37) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 23.20/6.50 | (485) all_0_3_3 = n12
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (89) with n5, n11, all_0_0_0, n0 and discharging atoms sum(n5, n11) = all_0_0_0, sum(n5, n11) = n0, yields:
% 23.20/6.50 | (659) all_0_0_0 = n0
% 23.20/6.50 |
% 23.20/6.50 | From (485)(659) and (261) follows:
% 23.20/6.50 | (4119) sum(n12, n0) = all_0_6_6
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (89) with n12, n0, all_0_6_6, n12 and discharging atoms sum(n12, n0) = all_0_6_6, sum(n12, n0) = n12, yields:
% 23.20/6.50 | (576) all_0_6_6 = n12
% 23.20/6.50 |
% 23.20/6.50 | Equations (576) can reduce 42 to:
% 23.20/6.50 | (458) $false
% 23.20/6.50 |
% 23.20/6.50 |-The branch is then unsatisfiable
% 23.20/6.50 |-Branch two:
% 23.20/6.50 | (906) ~ (all_0_7_7 = n5)
% 23.20/6.50 | (907) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.20/6.50 |
% 23.20/6.50 +-Applying beta-rule and splitting (907), into two cases.
% 23.20/6.50 |-Branch one:
% 23.20/6.50 | (908) all_0_7_7 = n4
% 23.20/6.50 |
% 23.20/6.50 | From (908) and (176) follows:
% 23.20/6.50 | (909) succ(n4) = all_0_5_5
% 23.20/6.50 |
% 23.20/6.50 | From (908) and (59) follows:
% 23.20/6.50 | (910) sum(n4, all_0_1_1) = all_0_0_0
% 23.20/6.50 |
% 23.20/6.50 | From (908) and (4085) follows:
% 23.20/6.50 | (4127) sum(n7, n4) = all_0_2_2
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (219) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 23.20/6.50 | (912) all_0_5_5 = n5
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (89) with n7, n4, all_0_2_2, n11 and discharging atoms sum(n7, n4) = all_0_2_2, sum(n7, n4) = n11, yields:
% 23.20/6.50 | (498) all_0_2_2 = n11
% 23.20/6.50 |
% 23.20/6.50 | From (498) and (187) follows:
% 23.20/6.50 | (500) pred(n11) = all_0_1_1
% 23.20/6.50 |
% 23.20/6.50 | From (912) and (4084) follows:
% 23.20/6.50 | (4131) sum(n7, n5) = all_0_4_4
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (37) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 23.20/6.50 | (503) all_0_1_1 = n10
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (89) with n7, n5, all_0_4_4, n12 and discharging atoms sum(n7, n5) = all_0_4_4, sum(n7, n5) = n12, yields:
% 23.20/6.50 | (499) all_0_4_4 = n12
% 23.20/6.50 |
% 23.20/6.50 | From (499) and (396) follows:
% 23.20/6.50 | (501) pred(n12) = all_0_3_3
% 23.20/6.50 |
% 23.20/6.50 | From (503) and (910) follows:
% 23.20/6.50 | (4135) sum(n4, n10) = all_0_0_0
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (37) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 23.20/6.50 | (502) all_0_3_3 = n11
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (89) with n4, n10, all_0_0_0, n14 and discharging atoms sum(n4, n10) = all_0_0_0, sum(n4, n10) = n14, yields:
% 23.20/6.50 | (693) all_0_0_0 = n14
% 23.20/6.50 |
% 23.20/6.50 | From (502)(693) and (261) follows:
% 23.20/6.50 | (4138) sum(n11, n14) = all_0_6_6
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (89) with n11, n14, all_0_6_6, n9 and discharging atoms sum(n11, n14) = all_0_6_6, sum(n11, n14) = n9, yields:
% 23.20/6.50 | (923) all_0_6_6 = n9
% 23.20/6.50 |
% 23.20/6.50 | Equations (923) can reduce 404 to:
% 23.20/6.50 | (458) $false
% 23.20/6.50 |
% 23.20/6.50 |-The branch is then unsatisfiable
% 23.20/6.50 |-Branch two:
% 23.20/6.50 | (925) ~ (all_0_7_7 = n4)
% 23.20/6.50 | (926) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.20/6.50 |
% 23.20/6.50 +-Applying beta-rule and splitting (926), into two cases.
% 23.20/6.50 |-Branch one:
% 23.20/6.50 | (927) all_0_7_7 = n3
% 23.20/6.50 |
% 23.20/6.50 | From (927) and (176) follows:
% 23.20/6.50 | (928) succ(n3) = all_0_5_5
% 23.20/6.50 |
% 23.20/6.50 | From (927) and (59) follows:
% 23.20/6.50 | (929) sum(n3, all_0_1_1) = all_0_0_0
% 23.20/6.50 |
% 23.20/6.50 | From (927) and (4085) follows:
% 23.20/6.50 | (4146) sum(n7, n3) = all_0_2_2
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (219) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 23.20/6.50 | (931) all_0_5_5 = n4
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (89) with n7, n3, all_0_2_2, n10 and discharging atoms sum(n7, n3) = all_0_2_2, sum(n7, n3) = n10, yields:
% 23.20/6.50 | (515) all_0_2_2 = n10
% 23.20/6.50 |
% 23.20/6.50 | From (515) and (187) follows:
% 23.20/6.50 | (517) pred(n10) = all_0_1_1
% 23.20/6.50 |
% 23.20/6.50 | From (931) and (4084) follows:
% 23.20/6.50 | (4150) sum(n7, n4) = all_0_4_4
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (37) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 23.20/6.50 | (520) all_0_1_1 = n9
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (89) with n7, n4, all_0_4_4, n11 and discharging atoms sum(n7, n4) = all_0_4_4, sum(n7, n4) = n11, yields:
% 23.20/6.50 | (516) all_0_4_4 = n11
% 23.20/6.50 |
% 23.20/6.50 | From (516) and (396) follows:
% 23.20/6.50 | (518) pred(n11) = all_0_3_3
% 23.20/6.50 |
% 23.20/6.50 | From (520) and (929) follows:
% 23.20/6.50 | (4154) sum(n3, n9) = all_0_0_0
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (37) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 23.20/6.50 | (519) all_0_3_3 = n10
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (89) with n3, n9, all_0_0_0, n12 and discharging atoms sum(n3, n9) = all_0_0_0, sum(n3, n9) = n12, yields:
% 23.20/6.50 | (455) all_0_0_0 = n12
% 23.20/6.50 |
% 23.20/6.50 | From (519)(455) and (261) follows:
% 23.20/6.50 | (4157) sum(n10, n12) = all_0_6_6
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (89) with n10, n12, all_0_6_6, n6 and discharging atoms sum(n10, n12) = all_0_6_6, sum(n10, n12) = n6, yields:
% 23.20/6.50 | (491) all_0_6_6 = n6
% 23.20/6.50 |
% 23.20/6.50 | Equations (491) can reduce 418 to:
% 23.20/6.50 | (458) $false
% 23.20/6.50 |
% 23.20/6.50 |-The branch is then unsatisfiable
% 23.20/6.50 |-Branch two:
% 23.20/6.50 | (944) ~ (all_0_7_7 = n3)
% 23.20/6.50 | (945) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.20/6.50 |
% 23.20/6.50 +-Applying beta-rule and splitting (945), into two cases.
% 23.20/6.50 |-Branch one:
% 23.20/6.50 | (946) all_0_7_7 = n2
% 23.20/6.50 |
% 23.20/6.50 | From (946) and (176) follows:
% 23.20/6.50 | (947) succ(n2) = all_0_5_5
% 23.20/6.50 |
% 23.20/6.50 | From (946) and (59) follows:
% 23.20/6.50 | (948) sum(n2, all_0_1_1) = all_0_0_0
% 23.20/6.50 |
% 23.20/6.50 | From (946) and (4085) follows:
% 23.20/6.50 | (4165) sum(n7, n2) = all_0_2_2
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (219) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 23.20/6.50 | (950) all_0_5_5 = n3
% 23.20/6.50 |
% 23.20/6.50 | Instantiating formula (89) with n7, n2, all_0_2_2, n9 and discharging atoms sum(n7, n2) = all_0_2_2, sum(n7, n2) = n9, yields:
% 23.20/6.50 | (532) all_0_2_2 = n9
% 23.20/6.50 |
% 23.20/6.50 | From (532) and (187) follows:
% 23.20/6.50 | (534) pred(n9) = all_0_1_1
% 23.20/6.50 |
% 23.20/6.50 | From (950) and (4084) follows:
% 23.20/6.51 | (4169) sum(n7, n3) = all_0_4_4
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (37) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 23.20/6.51 | (537) all_0_1_1 = n8
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n7, n3, all_0_4_4, n10 and discharging atoms sum(n7, n3) = all_0_4_4, sum(n7, n3) = n10, yields:
% 23.20/6.51 | (533) all_0_4_4 = n10
% 23.20/6.51 |
% 23.20/6.51 | From (533) and (396) follows:
% 23.20/6.51 | (535) pred(n10) = all_0_3_3
% 23.20/6.51 |
% 23.20/6.51 | From (537) and (948) follows:
% 23.20/6.51 | (4173) sum(n2, n8) = all_0_0_0
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (37) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 23.20/6.51 | (536) all_0_3_3 = n9
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n2, n8, all_0_0_0, n10 and discharging atoms sum(n2, n8) = all_0_0_0, sum(n2, n8) = n10, yields:
% 23.20/6.51 | (489) all_0_0_0 = n10
% 23.20/6.51 |
% 23.20/6.51 | From (536)(489) and (261) follows:
% 23.20/6.51 | (4176) sum(n9, n10) = all_0_6_6
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n9, n10, all_0_6_6, n3 and discharging atoms sum(n9, n10) = all_0_6_6, sum(n9, n10) = n3, yields:
% 23.20/6.51 | (961) all_0_6_6 = n3
% 23.20/6.51 |
% 23.20/6.51 | Equations (961) can reduce 245 to:
% 23.20/6.51 | (458) $false
% 23.20/6.51 |
% 23.20/6.51 |-The branch is then unsatisfiable
% 23.20/6.51 |-Branch two:
% 23.20/6.51 | (963) ~ (all_0_7_7 = n2)
% 23.20/6.51 | (964) all_0_7_7 = n1 | all_0_7_7 = n0
% 23.20/6.51 |
% 23.20/6.51 +-Applying beta-rule and splitting (964), into two cases.
% 23.20/6.51 |-Branch one:
% 23.20/6.51 | (965) all_0_7_7 = n1
% 23.20/6.51 |
% 23.20/6.51 | From (965) and (176) follows:
% 23.20/6.51 | (966) succ(n1) = all_0_5_5
% 23.20/6.51 |
% 23.20/6.51 | From (965) and (59) follows:
% 23.20/6.51 | (967) sum(n1, all_0_1_1) = all_0_0_0
% 23.20/6.51 |
% 23.20/6.51 | From (965) and (4085) follows:
% 23.20/6.51 | (4184) sum(n7, n1) = all_0_2_2
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (219) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 23.20/6.51 | (969) all_0_5_5 = n2
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n7, n1, all_0_2_2, n8 and discharging atoms sum(n7, n1) = all_0_2_2, sum(n7, n1) = n8, yields:
% 23.20/6.51 | (549) all_0_2_2 = n8
% 23.20/6.51 |
% 23.20/6.51 | From (549) and (187) follows:
% 23.20/6.51 | (551) pred(n8) = all_0_1_1
% 23.20/6.51 |
% 23.20/6.51 | From (969) and (4084) follows:
% 23.20/6.51 | (4188) sum(n7, n2) = all_0_4_4
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (37) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 23.20/6.51 | (554) all_0_1_1 = n7
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n7, n2, all_0_4_4, n9 and discharging atoms sum(n7, n2) = all_0_4_4, sum(n7, n2) = n9, yields:
% 23.20/6.51 | (550) all_0_4_4 = n9
% 23.20/6.51 |
% 23.20/6.51 | From (550) and (396) follows:
% 23.20/6.51 | (552) pred(n9) = all_0_3_3
% 23.20/6.51 |
% 23.20/6.51 | From (554) and (967) follows:
% 23.20/6.51 | (4192) sum(n1, n7) = all_0_0_0
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (37) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 23.20/6.51 | (553) all_0_3_3 = n8
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n1, n7, all_0_0_0, n8 and discharging atoms sum(n1, n7) = all_0_0_0, sum(n1, n7) = n8, yields:
% 23.20/6.51 | (523) all_0_0_0 = n8
% 23.20/6.51 |
% 23.20/6.51 | From (553)(523) and (261) follows:
% 23.20/6.51 | (4195) sum(n8, n8) = all_0_6_6
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n8, n8, all_0_6_6, n0 and discharging atoms sum(n8, n8) = all_0_6_6, sum(n8, n8) = n0, yields:
% 23.20/6.51 | (542) all_0_6_6 = n0
% 23.20/6.51 |
% 23.20/6.51 | Equations (542) can reduce 400 to:
% 23.20/6.51 | (458) $false
% 23.20/6.51 |
% 23.20/6.51 |-The branch is then unsatisfiable
% 23.20/6.51 |-Branch two:
% 23.20/6.51 | (982) ~ (all_0_7_7 = n1)
% 23.20/6.51 | (983) all_0_7_7 = n0
% 23.20/6.51 |
% 23.20/6.51 | From (983) and (176) follows:
% 23.20/6.51 | (984) succ(n0) = all_0_5_5
% 23.20/6.51 |
% 23.20/6.51 | From (983) and (59) follows:
% 23.20/6.51 | (985) sum(n0, all_0_1_1) = all_0_0_0
% 23.20/6.51 |
% 23.20/6.51 | From (983) and (4085) follows:
% 23.20/6.51 | (4202) sum(n7, n0) = all_0_2_2
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (219) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 23.20/6.51 | (987) all_0_5_5 = n1
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n7, n0, all_0_2_2, n7 and discharging atoms sum(n7, n0) = all_0_2_2, sum(n7, n0) = n7, yields:
% 23.20/6.51 | (566) all_0_2_2 = n7
% 23.20/6.51 |
% 23.20/6.51 | From (566) and (187) follows:
% 23.20/6.51 | (568) pred(n7) = all_0_1_1
% 23.20/6.51 |
% 23.20/6.51 | From (987) and (4084) follows:
% 23.20/6.51 | (4206) sum(n7, n1) = all_0_4_4
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (37) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 23.20/6.51 | (571) all_0_1_1 = n6
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n7, n1, all_0_4_4, n8 and discharging atoms sum(n7, n1) = all_0_4_4, sum(n7, n1) = n8, yields:
% 23.20/6.51 | (567) all_0_4_4 = n8
% 23.20/6.51 |
% 23.20/6.51 | From (567) and (396) follows:
% 23.20/6.51 | (569) pred(n8) = all_0_3_3
% 23.20/6.51 |
% 23.20/6.51 | From (571) and (985) follows:
% 23.20/6.51 | (4210) sum(n0, n6) = all_0_0_0
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (37) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 23.20/6.51 | (570) all_0_3_3 = n7
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n0, n6, all_0_0_0, n6 and discharging atoms sum(n0, n6) = all_0_0_0, sum(n0, n6) = n6, yields:
% 23.20/6.51 | (557) all_0_0_0 = n6
% 23.20/6.51 |
% 23.20/6.51 | From (570)(557) and (261) follows:
% 23.20/6.51 | (4213) sum(n7, n6) = all_0_6_6
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n7, n6, all_0_6_6, n13 and discharging atoms sum(n7, n6) = all_0_6_6, sum(n7, n6) = n13, yields:
% 23.20/6.51 | (998) all_0_6_6 = n13
% 23.20/6.51 |
% 23.20/6.51 | Equations (998) can reduce 130 to:
% 23.20/6.51 | (458) $false
% 23.20/6.51 |
% 23.20/6.51 |-The branch is then unsatisfiable
% 23.20/6.51 |-Branch two:
% 23.20/6.51 | (595) ~ (all_0_8_8 = n7)
% 23.20/6.51 | (596) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.20/6.51 |
% 23.20/6.51 +-Applying beta-rule and splitting (869), into two cases.
% 23.20/6.51 |-Branch one:
% 23.20/6.51 | (870) all_0_7_7 = n6
% 23.20/6.51 |
% 23.20/6.51 | From (870) and (176) follows:
% 23.20/6.51 | (871) succ(n6) = all_0_5_5
% 23.20/6.51 |
% 23.20/6.51 | From (870) and (59) follows:
% 23.20/6.51 | (872) sum(n6, all_0_1_1) = all_0_0_0
% 23.20/6.51 |
% 23.20/6.51 | From (870) and (160) follows:
% 23.20/6.51 | (4221) sum(all_0_8_8, n6) = all_0_2_2
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (219) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 23.20/6.51 | (874) all_0_5_5 = n7
% 23.20/6.51 |
% 23.20/6.51 | From (874) and (64) follows:
% 23.20/6.51 | (4223) sum(all_0_8_8, n7) = all_0_4_4
% 23.20/6.51 |
% 23.20/6.51 +-Applying beta-rule and splitting (596), into two cases.
% 23.20/6.51 |-Branch one:
% 23.20/6.51 | (597) all_0_8_8 = n6
% 23.20/6.51 |
% 23.20/6.51 | From (597) and (4223) follows:
% 23.20/6.51 | (4225) sum(n6, n7) = all_0_4_4
% 23.20/6.51 |
% 23.20/6.51 | From (597) and (4221) follows:
% 23.20/6.51 | (4226) sum(n6, n6) = all_0_2_2
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n6, n7, all_0_4_4, n13 and discharging atoms sum(n6, n7) = all_0_4_4, sum(n6, n7) = n13, yields:
% 23.20/6.51 | (482) all_0_4_4 = n13
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n6, n6, all_0_2_2, n12 and discharging atoms sum(n6, n6) = all_0_2_2, sum(n6, n6) = n12, yields:
% 23.20/6.51 | (481) all_0_2_2 = n12
% 23.20/6.51 |
% 23.20/6.51 | From (481) and (187) follows:
% 23.20/6.51 | (483) pred(n12) = all_0_1_1
% 23.20/6.51 |
% 23.20/6.51 | From (482) and (396) follows:
% 23.20/6.51 | (484) pred(n13) = all_0_3_3
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (37) with n13, all_0_3_3, n12 and discharging atoms pred(n13) = all_0_3_3, pred(n13) = n12, yields:
% 23.20/6.51 | (485) all_0_3_3 = n12
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (37) with n12, all_0_1_1, n11 and discharging atoms pred(n12) = all_0_1_1, pred(n12) = n11, yields:
% 23.20/6.51 | (486) all_0_1_1 = n11
% 23.20/6.51 |
% 23.20/6.51 | From (485) and (261) follows:
% 23.20/6.51 | (487) sum(n12, all_0_0_0) = all_0_6_6
% 23.20/6.51 |
% 23.20/6.51 | From (486) and (872) follows:
% 23.20/6.51 | (4234) sum(n6, n11) = all_0_0_0
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n6, n11, all_0_0_0, n1 and discharging atoms sum(n6, n11) = all_0_0_0, sum(n6, n11) = n1, yields:
% 23.20/6.51 | (642) all_0_0_0 = n1
% 23.20/6.51 |
% 23.20/6.51 | From (642) and (487) follows:
% 23.20/6.51 | (4236) sum(n12, n1) = all_0_6_6
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n12, n1, all_0_6_6, n13 and discharging atoms sum(n12, n1) = all_0_6_6, sum(n12, n1) = n13, yields:
% 23.20/6.51 | (998) all_0_6_6 = n13
% 23.20/6.51 |
% 23.20/6.51 | Equations (998) can reduce 130 to:
% 23.20/6.51 | (458) $false
% 23.20/6.51 |
% 23.20/6.51 |-The branch is then unsatisfiable
% 23.20/6.51 |-Branch two:
% 23.20/6.51 | (612) ~ (all_0_8_8 = n6)
% 23.20/6.51 | (613) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.20/6.51 |
% 23.20/6.51 +-Applying beta-rule and splitting (613), into two cases.
% 23.20/6.51 |-Branch one:
% 23.20/6.51 | (614) all_0_8_8 = n5
% 23.20/6.51 |
% 23.20/6.51 | From (614) and (4223) follows:
% 23.20/6.51 | (4242) sum(n5, n7) = all_0_4_4
% 23.20/6.51 |
% 23.20/6.51 | From (614) and (4221) follows:
% 23.20/6.51 | (4243) sum(n5, n6) = all_0_2_2
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n5, n7, all_0_4_4, n12 and discharging atoms sum(n5, n7) = all_0_4_4, sum(n5, n7) = n12, yields:
% 23.20/6.51 | (499) all_0_4_4 = n12
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n5, n6, all_0_2_2, n11 and discharging atoms sum(n5, n6) = all_0_2_2, sum(n5, n6) = n11, yields:
% 23.20/6.51 | (498) all_0_2_2 = n11
% 23.20/6.51 |
% 23.20/6.51 | From (498) and (187) follows:
% 23.20/6.51 | (500) pred(n11) = all_0_1_1
% 23.20/6.51 |
% 23.20/6.51 | From (499) and (396) follows:
% 23.20/6.51 | (501) pred(n12) = all_0_3_3
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (37) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 23.20/6.51 | (502) all_0_3_3 = n11
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (37) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 23.20/6.51 | (503) all_0_1_1 = n10
% 23.20/6.51 |
% 23.20/6.51 | From (502) and (261) follows:
% 23.20/6.51 | (504) sum(n11, all_0_0_0) = all_0_6_6
% 23.20/6.51 |
% 23.20/6.51 | From (503) and (872) follows:
% 23.20/6.51 | (4251) sum(n6, n10) = all_0_0_0
% 23.20/6.51 |
% 23.20/6.51 | Instantiating formula (89) with n6, n10, all_0_0_0, n0 and discharging atoms sum(n6, n10) = all_0_0_0, sum(n6, n10) = n0, yields:
% 23.20/6.51 | (659) all_0_0_0 = n0
% 23.20/6.51 |
% 23.20/6.51 | From (659) and (504) follows:
% 23.20/6.51 | (4253) sum(n11, n0) = all_0_6_6
% 23.20/6.51 |
% 23.20/6.52 | Instantiating formula (89) with n11, n0, all_0_6_6, n11 and discharging atoms sum(n11, n0) = all_0_6_6, sum(n11, n0) = n11, yields:
% 23.20/6.52 | (809) all_0_6_6 = n11
% 23.20/6.52 |
% 23.20/6.52 | Equations (809) can reduce 70 to:
% 23.20/6.52 | (458) $false
% 23.20/6.52 |
% 23.20/6.52 |-The branch is then unsatisfiable
% 23.20/6.52 |-Branch two:
% 23.20/6.52 | (629) ~ (all_0_8_8 = n5)
% 23.20/6.52 | (630) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.20/6.52 |
% 23.20/6.52 +-Applying beta-rule and splitting (630), into two cases.
% 23.20/6.52 |-Branch one:
% 23.20/6.52 | (631) all_0_8_8 = n4
% 23.20/6.52 |
% 23.20/6.52 | From (631) and (4223) follows:
% 23.20/6.52 | (4259) sum(n4, n7) = all_0_4_4
% 23.20/6.52 |
% 23.20/6.52 | From (631) and (4221) follows:
% 23.20/6.52 | (4260) sum(n4, n6) = all_0_2_2
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n4, n7, all_0_4_4, n11 and discharging atoms sum(n4, n7) = all_0_4_4, sum(n4, n7) = n11, yields:
% 23.20/6.52 | (516) all_0_4_4 = n11
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 23.20/6.52 | (515) all_0_2_2 = n10
% 23.20/6.52 |
% 23.20/6.52 | From (515) and (187) follows:
% 23.20/6.52 | (517) pred(n10) = all_0_1_1
% 23.20/6.52 |
% 23.20/6.52 | From (516) and (396) follows:
% 23.20/6.52 | (518) pred(n11) = all_0_3_3
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (37) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 23.20/6.52 | (519) all_0_3_3 = n10
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (37) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 23.20/6.52 | (520) all_0_1_1 = n9
% 23.20/6.52 |
% 23.20/6.52 | From (519) and (261) follows:
% 23.20/6.52 | (521) sum(n10, all_0_0_0) = all_0_6_6
% 23.20/6.52 |
% 23.20/6.52 | From (520) and (872) follows:
% 23.20/6.52 | (4268) sum(n6, n9) = all_0_0_0
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n6, n9, all_0_0_0, n15 and discharging atoms sum(n6, n9) = all_0_0_0, sum(n6, n9) = n15, yields:
% 23.20/6.52 | (676) all_0_0_0 = n15
% 23.20/6.52 |
% 23.20/6.52 | From (676) and (521) follows:
% 23.20/6.52 | (4270) sum(n10, n15) = all_0_6_6
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n10, n15, all_0_6_6, n9 and discharging atoms sum(n10, n15) = all_0_6_6, sum(n10, n15) = n9, yields:
% 23.20/6.52 | (923) all_0_6_6 = n9
% 23.20/6.52 |
% 23.20/6.52 | Equations (923) can reduce 404 to:
% 23.20/6.52 | (458) $false
% 23.20/6.52 |
% 23.20/6.52 |-The branch is then unsatisfiable
% 23.20/6.52 |-Branch two:
% 23.20/6.52 | (646) ~ (all_0_8_8 = n4)
% 23.20/6.52 | (647) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.20/6.52 |
% 23.20/6.52 +-Applying beta-rule and splitting (647), into two cases.
% 23.20/6.52 |-Branch one:
% 23.20/6.52 | (648) all_0_8_8 = n3
% 23.20/6.52 |
% 23.20/6.52 | From (648) and (4223) follows:
% 23.20/6.52 | (4276) sum(n3, n7) = all_0_4_4
% 23.20/6.52 |
% 23.20/6.52 | From (648) and (4221) follows:
% 23.20/6.52 | (4277) sum(n3, n6) = all_0_2_2
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n3, n7, all_0_4_4, n10 and discharging atoms sum(n3, n7) = all_0_4_4, sum(n3, n7) = n10, yields:
% 23.20/6.52 | (533) all_0_4_4 = n10
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n3, n6, all_0_2_2, n9 and discharging atoms sum(n3, n6) = all_0_2_2, sum(n3, n6) = n9, yields:
% 23.20/6.52 | (532) all_0_2_2 = n9
% 23.20/6.52 |
% 23.20/6.52 | From (532) and (187) follows:
% 23.20/6.52 | (534) pred(n9) = all_0_1_1
% 23.20/6.52 |
% 23.20/6.52 | From (533) and (396) follows:
% 23.20/6.52 | (535) pred(n10) = all_0_3_3
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (37) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 23.20/6.52 | (536) all_0_3_3 = n9
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (37) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 23.20/6.52 | (537) all_0_1_1 = n8
% 23.20/6.52 |
% 23.20/6.52 | From (536) and (261) follows:
% 23.20/6.52 | (538) sum(n9, all_0_0_0) = all_0_6_6
% 23.20/6.52 |
% 23.20/6.52 | From (537) and (872) follows:
% 23.20/6.52 | (4285) sum(n6, n8) = all_0_0_0
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n6, n8, all_0_0_0, n14 and discharging atoms sum(n6, n8) = all_0_0_0, sum(n6, n8) = n14, yields:
% 23.20/6.52 | (693) all_0_0_0 = n14
% 23.20/6.52 |
% 23.20/6.52 | From (693) and (538) follows:
% 23.20/6.52 | (4287) sum(n9, n14) = all_0_6_6
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n9, n14, all_0_6_6, n7 and discharging atoms sum(n9, n14) = all_0_6_6, sum(n9, n14) = n7, yields:
% 23.20/6.52 | (733) all_0_6_6 = n7
% 23.20/6.52 |
% 23.20/6.52 | Equations (733) can reduce 274 to:
% 23.20/6.52 | (458) $false
% 23.20/6.52 |
% 23.20/6.52 |-The branch is then unsatisfiable
% 23.20/6.52 |-Branch two:
% 23.20/6.52 | (663) ~ (all_0_8_8 = n3)
% 23.20/6.52 | (664) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.20/6.52 |
% 23.20/6.52 +-Applying beta-rule and splitting (664), into two cases.
% 23.20/6.52 |-Branch one:
% 23.20/6.52 | (665) all_0_8_8 = n2
% 23.20/6.52 |
% 23.20/6.52 | From (665) and (4223) follows:
% 23.20/6.52 | (4293) sum(n2, n7) = all_0_4_4
% 23.20/6.52 |
% 23.20/6.52 | From (665) and (4221) follows:
% 23.20/6.52 | (4294) sum(n2, n6) = all_0_2_2
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n2, n7, all_0_4_4, n9 and discharging atoms sum(n2, n7) = all_0_4_4, sum(n2, n7) = n9, yields:
% 23.20/6.52 | (550) all_0_4_4 = n9
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n2, n6, all_0_2_2, n8 and discharging atoms sum(n2, n6) = all_0_2_2, sum(n2, n6) = n8, yields:
% 23.20/6.52 | (549) all_0_2_2 = n8
% 23.20/6.52 |
% 23.20/6.52 | From (549) and (187) follows:
% 23.20/6.52 | (551) pred(n8) = all_0_1_1
% 23.20/6.52 |
% 23.20/6.52 | From (550) and (396) follows:
% 23.20/6.52 | (552) pred(n9) = all_0_3_3
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (37) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 23.20/6.52 | (553) all_0_3_3 = n8
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (37) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 23.20/6.52 | (554) all_0_1_1 = n7
% 23.20/6.52 |
% 23.20/6.52 | From (553) and (261) follows:
% 23.20/6.52 | (555) sum(n8, all_0_0_0) = all_0_6_6
% 23.20/6.52 |
% 23.20/6.52 | From (554) and (872) follows:
% 23.20/6.52 | (4302) sum(n6, n7) = all_0_0_0
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n6, n7, all_0_0_0, n13 and discharging atoms sum(n6, n7) = all_0_0_0, sum(n6, n7) = n13, yields:
% 23.20/6.52 | (709) all_0_0_0 = n13
% 23.20/6.52 |
% 23.20/6.52 | From (709) and (555) follows:
% 23.20/6.52 | (4304) sum(n8, n13) = all_0_6_6
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n8, n13, all_0_6_6, n5 and discharging atoms sum(n8, n13) = all_0_6_6, sum(n8, n13) = n5, yields:
% 23.20/6.52 | (847) all_0_6_6 = n5
% 23.20/6.52 |
% 23.20/6.52 | Equations (847) can reduce 409 to:
% 23.20/6.52 | (458) $false
% 23.20/6.52 |
% 23.20/6.52 |-The branch is then unsatisfiable
% 23.20/6.52 |-Branch two:
% 23.20/6.52 | (680) ~ (all_0_8_8 = n2)
% 23.20/6.52 | (681) all_0_8_8 = n1 | all_0_8_8 = n0
% 23.20/6.52 |
% 23.20/6.52 +-Applying beta-rule and splitting (681), into two cases.
% 23.20/6.52 |-Branch one:
% 23.20/6.52 | (682) all_0_8_8 = n1
% 23.20/6.52 |
% 23.20/6.52 | From (682) and (4223) follows:
% 23.20/6.52 | (4310) sum(n1, n7) = all_0_4_4
% 23.20/6.52 |
% 23.20/6.52 | From (682) and (4221) follows:
% 23.20/6.52 | (4311) sum(n1, n6) = all_0_2_2
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n1, n7, all_0_4_4, n8 and discharging atoms sum(n1, n7) = all_0_4_4, sum(n1, n7) = n8, yields:
% 23.20/6.52 | (567) all_0_4_4 = n8
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n1, n6, all_0_2_2, n7 and discharging atoms sum(n1, n6) = all_0_2_2, sum(n1, n6) = n7, yields:
% 23.20/6.52 | (566) all_0_2_2 = n7
% 23.20/6.52 |
% 23.20/6.52 | From (566) and (187) follows:
% 23.20/6.52 | (568) pred(n7) = all_0_1_1
% 23.20/6.52 |
% 23.20/6.52 | From (567) and (396) follows:
% 23.20/6.52 | (569) pred(n8) = all_0_3_3
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (37) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 23.20/6.52 | (570) all_0_3_3 = n7
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (37) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 23.20/6.52 | (571) all_0_1_1 = n6
% 23.20/6.52 |
% 23.20/6.52 | From (570) and (261) follows:
% 23.20/6.52 | (572) sum(n7, all_0_0_0) = all_0_6_6
% 23.20/6.52 |
% 23.20/6.52 | From (571) and (872) follows:
% 23.20/6.52 | (4319) sum(n6, n6) = all_0_0_0
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n6, n6, all_0_0_0, n12 and discharging atoms sum(n6, n6) = all_0_0_0, sum(n6, n6) = n12, yields:
% 23.20/6.52 | (455) all_0_0_0 = n12
% 23.20/6.52 |
% 23.20/6.52 | From (455) and (572) follows:
% 23.20/6.52 | (4321) sum(n7, n12) = all_0_6_6
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n7, n12, all_0_6_6, n3 and discharging atoms sum(n7, n12) = all_0_6_6, sum(n7, n12) = n3, yields:
% 23.20/6.52 | (961) all_0_6_6 = n3
% 23.20/6.52 |
% 23.20/6.52 | Equations (961) can reduce 245 to:
% 23.20/6.52 | (458) $false
% 23.20/6.52 |
% 23.20/6.52 |-The branch is then unsatisfiable
% 23.20/6.52 |-Branch two:
% 23.20/6.52 | (697) ~ (all_0_8_8 = n1)
% 23.20/6.52 | (698) all_0_8_8 = n0
% 23.20/6.52 |
% 23.20/6.52 | From (698) and (4223) follows:
% 23.20/6.52 | (4326) sum(n0, n7) = all_0_4_4
% 23.20/6.52 |
% 23.20/6.52 | From (698) and (4221) follows:
% 23.20/6.52 | (4327) sum(n0, n6) = all_0_2_2
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n0, n7, all_0_4_4, n7 and discharging atoms sum(n0, n7) = all_0_4_4, sum(n0, n7) = n7, yields:
% 23.20/6.52 | (584) all_0_4_4 = n7
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n0, n6, all_0_2_2, n6 and discharging atoms sum(n0, n6) = all_0_2_2, sum(n0, n6) = n6, yields:
% 23.20/6.52 | (583) all_0_2_2 = n6
% 23.20/6.52 |
% 23.20/6.52 | From (583) and (187) follows:
% 23.20/6.52 | (585) pred(n6) = all_0_1_1
% 23.20/6.52 |
% 23.20/6.52 | From (584) and (396) follows:
% 23.20/6.52 | (586) pred(n7) = all_0_3_3
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (37) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 23.20/6.52 | (587) all_0_3_3 = n6
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (37) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 23.20/6.52 | (588) all_0_1_1 = n5
% 23.20/6.52 |
% 23.20/6.52 | From (587) and (261) follows:
% 23.20/6.52 | (589) sum(n6, all_0_0_0) = all_0_6_6
% 23.20/6.52 |
% 23.20/6.52 | From (588) and (872) follows:
% 23.20/6.52 | (4335) sum(n6, n5) = all_0_0_0
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n6, n5, all_0_0_0, n11 and discharging atoms sum(n6, n5) = all_0_0_0, sum(n6, n5) = n11, yields:
% 23.20/6.52 | (472) all_0_0_0 = n11
% 23.20/6.52 |
% 23.20/6.52 | From (472) and (589) follows:
% 23.20/6.52 | (4337) sum(n6, n11) = all_0_6_6
% 23.20/6.52 |
% 23.20/6.52 | Instantiating formula (89) with n6, n11, all_0_6_6, n1 and discharging atoms sum(n6, n11) = all_0_6_6, sum(n6, n11) = n1, yields:
% 23.20/6.52 | (771) all_0_6_6 = n1
% 23.20/6.52 |
% 23.20/6.52 | Equations (771) can reduce 38 to:
% 23.20/6.52 | (458) $false
% 23.20/6.52 |
% 23.20/6.52 |-The branch is then unsatisfiable
% 23.20/6.52 |-Branch two:
% 23.20/6.52 | (887) ~ (all_0_7_7 = n6)
% 23.20/6.52 | (888) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.20/6.52 |
% 23.20/6.52 +-Applying beta-rule and splitting (596), into two cases.
% 23.20/6.52 |-Branch one:
% 23.20/6.52 | (597) all_0_8_8 = n6
% 23.20/6.52 |
% 23.20/6.52 | From (597) and (64) follows:
% 23.20/6.53 | (4343) sum(n6, all_0_5_5) = all_0_4_4
% 23.20/6.53 |
% 23.20/6.53 | From (597) and (160) follows:
% 23.20/6.53 | (4344) sum(n6, all_0_7_7) = all_0_2_2
% 23.20/6.53 |
% 23.20/6.53 +-Applying beta-rule and splitting (888), into two cases.
% 23.20/6.53 |-Branch one:
% 23.20/6.53 | (889) all_0_7_7 = n5
% 23.20/6.53 |
% 23.20/6.53 | From (889) and (176) follows:
% 23.20/6.53 | (890) succ(n5) = all_0_5_5
% 23.20/6.53 |
% 23.20/6.53 | From (889) and (59) follows:
% 23.20/6.53 | (891) sum(n5, all_0_1_1) = all_0_0_0
% 23.20/6.53 |
% 23.20/6.53 | From (889) and (4344) follows:
% 23.20/6.53 | (4348) sum(n6, n5) = all_0_2_2
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (219) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 23.20/6.53 | (893) all_0_5_5 = n6
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (89) with n6, n5, all_0_2_2, n11 and discharging atoms sum(n6, n5) = all_0_2_2, sum(n6, n5) = n11, yields:
% 23.20/6.53 | (498) all_0_2_2 = n11
% 23.20/6.53 |
% 23.20/6.53 | From (498) and (187) follows:
% 23.20/6.53 | (500) pred(n11) = all_0_1_1
% 23.20/6.53 |
% 23.20/6.53 | From (893) and (4343) follows:
% 23.20/6.53 | (4352) sum(n6, n6) = all_0_4_4
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (37) with n11, all_0_1_1, n10 and discharging atoms pred(n11) = all_0_1_1, pred(n11) = n10, yields:
% 23.20/6.53 | (503) all_0_1_1 = n10
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (89) with n6, n6, all_0_4_4, n12 and discharging atoms sum(n6, n6) = all_0_4_4, sum(n6, n6) = n12, yields:
% 23.20/6.53 | (499) all_0_4_4 = n12
% 23.20/6.53 |
% 23.20/6.53 | From (499) and (396) follows:
% 23.20/6.53 | (501) pred(n12) = all_0_3_3
% 23.20/6.53 |
% 23.20/6.53 | From (503) and (891) follows:
% 23.20/6.53 | (4356) sum(n5, n10) = all_0_0_0
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (37) with n12, all_0_3_3, n11 and discharging atoms pred(n12) = all_0_3_3, pred(n12) = n11, yields:
% 23.20/6.53 | (502) all_0_3_3 = n11
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (89) with n5, n10, all_0_0_0, n15 and discharging atoms sum(n5, n10) = all_0_0_0, sum(n5, n10) = n15, yields:
% 23.20/6.53 | (676) all_0_0_0 = n15
% 23.20/6.53 |
% 23.20/6.53 | From (502)(676) and (261) follows:
% 23.20/6.53 | (4359) sum(n11, n15) = all_0_6_6
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (89) with n11, n15, all_0_6_6, n10 and discharging atoms sum(n11, n15) = all_0_6_6, sum(n11, n15) = n10, yields:
% 23.20/6.53 | (457) all_0_6_6 = n10
% 23.20/6.53 |
% 23.20/6.53 | Equations (457) can reduce 169 to:
% 23.20/6.53 | (458) $false
% 23.20/6.53 |
% 23.20/6.53 |-The branch is then unsatisfiable
% 23.20/6.53 |-Branch two:
% 23.20/6.53 | (906) ~ (all_0_7_7 = n5)
% 23.20/6.53 | (907) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.20/6.53 |
% 23.20/6.53 +-Applying beta-rule and splitting (907), into two cases.
% 23.20/6.53 |-Branch one:
% 23.20/6.53 | (908) all_0_7_7 = n4
% 23.20/6.53 |
% 23.20/6.53 | From (908) and (176) follows:
% 23.20/6.53 | (909) succ(n4) = all_0_5_5
% 23.20/6.53 |
% 23.20/6.53 | From (908) and (59) follows:
% 23.20/6.53 | (910) sum(n4, all_0_1_1) = all_0_0_0
% 23.20/6.53 |
% 23.20/6.53 | From (908) and (4344) follows:
% 23.20/6.53 | (4367) sum(n6, n4) = all_0_2_2
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (219) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 23.20/6.53 | (912) all_0_5_5 = n5
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (89) with n6, n4, all_0_2_2, n10 and discharging atoms sum(n6, n4) = all_0_2_2, sum(n6, n4) = n10, yields:
% 23.20/6.53 | (515) all_0_2_2 = n10
% 23.20/6.53 |
% 23.20/6.53 | From (515) and (187) follows:
% 23.20/6.53 | (517) pred(n10) = all_0_1_1
% 23.20/6.53 |
% 23.20/6.53 | From (912) and (4343) follows:
% 23.20/6.53 | (4371) sum(n6, n5) = all_0_4_4
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (37) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 23.20/6.53 | (520) all_0_1_1 = n9
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (89) with n6, n5, all_0_4_4, n11 and discharging atoms sum(n6, n5) = all_0_4_4, sum(n6, n5) = n11, yields:
% 23.20/6.53 | (516) all_0_4_4 = n11
% 23.20/6.53 |
% 23.20/6.53 | From (516) and (396) follows:
% 23.20/6.53 | (518) pred(n11) = all_0_3_3
% 23.20/6.53 |
% 23.20/6.53 | From (520) and (910) follows:
% 23.20/6.53 | (4375) sum(n4, n9) = all_0_0_0
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (37) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 23.20/6.53 | (519) all_0_3_3 = n10
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (89) with n4, n9, all_0_0_0, n13 and discharging atoms sum(n4, n9) = all_0_0_0, sum(n4, n9) = n13, yields:
% 23.20/6.53 | (709) all_0_0_0 = n13
% 23.20/6.53 |
% 23.20/6.53 | From (519)(709) and (261) follows:
% 23.20/6.53 | (4378) sum(n10, n13) = all_0_6_6
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (89) with n10, n13, all_0_6_6, n7 and discharging atoms sum(n10, n13) = all_0_6_6, sum(n10, n13) = n7, yields:
% 23.20/6.53 | (733) all_0_6_6 = n7
% 23.20/6.53 |
% 23.20/6.53 | Equations (733) can reduce 274 to:
% 23.20/6.53 | (458) $false
% 23.20/6.53 |
% 23.20/6.53 |-The branch is then unsatisfiable
% 23.20/6.53 |-Branch two:
% 23.20/6.53 | (925) ~ (all_0_7_7 = n4)
% 23.20/6.53 | (926) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.20/6.53 |
% 23.20/6.53 +-Applying beta-rule and splitting (926), into two cases.
% 23.20/6.53 |-Branch one:
% 23.20/6.53 | (927) all_0_7_7 = n3
% 23.20/6.53 |
% 23.20/6.53 | From (927) and (176) follows:
% 23.20/6.53 | (928) succ(n3) = all_0_5_5
% 23.20/6.53 |
% 23.20/6.53 | From (927) and (59) follows:
% 23.20/6.53 | (929) sum(n3, all_0_1_1) = all_0_0_0
% 23.20/6.53 |
% 23.20/6.53 | From (927) and (4344) follows:
% 23.20/6.53 | (4386) sum(n6, n3) = all_0_2_2
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (219) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 23.20/6.53 | (931) all_0_5_5 = n4
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (89) with n6, n3, all_0_2_2, n9 and discharging atoms sum(n6, n3) = all_0_2_2, sum(n6, n3) = n9, yields:
% 23.20/6.53 | (532) all_0_2_2 = n9
% 23.20/6.53 |
% 23.20/6.53 | From (532) and (187) follows:
% 23.20/6.53 | (534) pred(n9) = all_0_1_1
% 23.20/6.53 |
% 23.20/6.53 | From (931) and (4343) follows:
% 23.20/6.53 | (4390) sum(n6, n4) = all_0_4_4
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (37) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 23.20/6.53 | (537) all_0_1_1 = n8
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (89) with n6, n4, all_0_4_4, n10 and discharging atoms sum(n6, n4) = all_0_4_4, sum(n6, n4) = n10, yields:
% 23.20/6.53 | (533) all_0_4_4 = n10
% 23.20/6.53 |
% 23.20/6.53 | From (533) and (396) follows:
% 23.20/6.53 | (535) pred(n10) = all_0_3_3
% 23.20/6.53 |
% 23.20/6.53 | From (537) and (929) follows:
% 23.20/6.53 | (4394) sum(n3, n8) = all_0_0_0
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (37) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 23.20/6.53 | (536) all_0_3_3 = n9
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (89) with n3, n8, all_0_0_0, n11 and discharging atoms sum(n3, n8) = all_0_0_0, sum(n3, n8) = n11, yields:
% 23.20/6.53 | (472) all_0_0_0 = n11
% 23.20/6.53 |
% 23.20/6.53 | From (536)(472) and (261) follows:
% 23.20/6.53 | (4397) sum(n9, n11) = all_0_6_6
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (89) with n9, n11, all_0_6_6, n4 and discharging atoms sum(n9, n11) = all_0_6_6, sum(n9, n11) = n4, yields:
% 23.20/6.53 | (508) all_0_6_6 = n4
% 23.20/6.53 |
% 23.20/6.53 | Equations (508) can reduce 12 to:
% 23.20/6.53 | (458) $false
% 23.20/6.53 |
% 23.20/6.53 |-The branch is then unsatisfiable
% 23.20/6.53 |-Branch two:
% 23.20/6.53 | (944) ~ (all_0_7_7 = n3)
% 23.20/6.53 | (945) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.20/6.53 |
% 23.20/6.53 +-Applying beta-rule and splitting (945), into two cases.
% 23.20/6.53 |-Branch one:
% 23.20/6.53 | (946) all_0_7_7 = n2
% 23.20/6.53 |
% 23.20/6.53 | From (946) and (176) follows:
% 23.20/6.53 | (947) succ(n2) = all_0_5_5
% 23.20/6.53 |
% 23.20/6.53 | From (946) and (59) follows:
% 23.20/6.53 | (948) sum(n2, all_0_1_1) = all_0_0_0
% 23.20/6.53 |
% 23.20/6.53 | From (946) and (4344) follows:
% 23.20/6.53 | (4405) sum(n6, n2) = all_0_2_2
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (219) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 23.20/6.53 | (950) all_0_5_5 = n3
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (89) with n6, n2, all_0_2_2, n8 and discharging atoms sum(n6, n2) = all_0_2_2, sum(n6, n2) = n8, yields:
% 23.20/6.53 | (549) all_0_2_2 = n8
% 23.20/6.53 |
% 23.20/6.53 | From (549) and (187) follows:
% 23.20/6.53 | (551) pred(n8) = all_0_1_1
% 23.20/6.53 |
% 23.20/6.53 | From (950) and (4343) follows:
% 23.20/6.53 | (4409) sum(n6, n3) = all_0_4_4
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (37) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 23.20/6.53 | (554) all_0_1_1 = n7
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (89) with n6, n3, all_0_4_4, n9 and discharging atoms sum(n6, n3) = all_0_4_4, sum(n6, n3) = n9, yields:
% 23.20/6.53 | (550) all_0_4_4 = n9
% 23.20/6.53 |
% 23.20/6.53 | From (550) and (396) follows:
% 23.20/6.53 | (552) pred(n9) = all_0_3_3
% 23.20/6.53 |
% 23.20/6.53 | From (554) and (948) follows:
% 23.20/6.53 | (4413) sum(n2, n7) = all_0_0_0
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (37) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 23.20/6.53 | (553) all_0_3_3 = n8
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (89) with n2, n7, all_0_0_0, n9 and discharging atoms sum(n2, n7) = all_0_0_0, sum(n2, n7) = n9, yields:
% 23.20/6.53 | (506) all_0_0_0 = n9
% 23.20/6.53 |
% 23.20/6.53 | From (553)(506) and (261) follows:
% 23.20/6.53 | (4416) sum(n8, n9) = all_0_6_6
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (89) with n8, n9, all_0_6_6, n1 and discharging atoms sum(n8, n9) = all_0_6_6, sum(n8, n9) = n1, yields:
% 23.20/6.53 | (771) all_0_6_6 = n1
% 23.20/6.53 |
% 23.20/6.53 | Equations (771) can reduce 38 to:
% 23.20/6.53 | (458) $false
% 23.20/6.53 |
% 23.20/6.53 |-The branch is then unsatisfiable
% 23.20/6.53 |-Branch two:
% 23.20/6.53 | (963) ~ (all_0_7_7 = n2)
% 23.20/6.53 | (964) all_0_7_7 = n1 | all_0_7_7 = n0
% 23.20/6.53 |
% 23.20/6.53 +-Applying beta-rule and splitting (964), into two cases.
% 23.20/6.53 |-Branch one:
% 23.20/6.53 | (965) all_0_7_7 = n1
% 23.20/6.53 |
% 23.20/6.53 | From (965) and (176) follows:
% 23.20/6.53 | (966) succ(n1) = all_0_5_5
% 23.20/6.53 |
% 23.20/6.53 | From (965) and (59) follows:
% 23.20/6.53 | (967) sum(n1, all_0_1_1) = all_0_0_0
% 23.20/6.53 |
% 23.20/6.53 | From (965) and (4344) follows:
% 23.20/6.53 | (4424) sum(n6, n1) = all_0_2_2
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (219) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 23.20/6.53 | (969) all_0_5_5 = n2
% 23.20/6.53 |
% 23.20/6.53 | Instantiating formula (89) with n6, n1, all_0_2_2, n7 and discharging atoms sum(n6, n1) = all_0_2_2, sum(n6, n1) = n7, yields:
% 23.20/6.53 | (566) all_0_2_2 = n7
% 23.20/6.53 |
% 23.20/6.53 | From (566) and (187) follows:
% 23.20/6.53 | (568) pred(n7) = all_0_1_1
% 23.20/6.53 |
% 23.20/6.53 | From (969) and (4343) follows:
% 23.20/6.54 | (4428) sum(n6, n2) = all_0_4_4
% 23.20/6.54 |
% 23.20/6.54 | Instantiating formula (37) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 23.20/6.54 | (571) all_0_1_1 = n6
% 23.20/6.54 |
% 23.20/6.54 | Instantiating formula (89) with n6, n2, all_0_4_4, n8 and discharging atoms sum(n6, n2) = all_0_4_4, sum(n6, n2) = n8, yields:
% 23.20/6.54 | (567) all_0_4_4 = n8
% 23.20/6.54 |
% 23.20/6.54 | From (567) and (396) follows:
% 23.20/6.54 | (569) pred(n8) = all_0_3_3
% 23.20/6.54 |
% 23.20/6.54 | From (571) and (967) follows:
% 23.20/6.54 | (4432) sum(n1, n6) = all_0_0_0
% 23.20/6.54 |
% 23.20/6.54 | Instantiating formula (37) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 23.20/6.54 | (570) all_0_3_3 = n7
% 23.20/6.54 |
% 23.20/6.54 | Instantiating formula (89) with n1, n6, all_0_0_0, n7 and discharging atoms sum(n1, n6) = all_0_0_0, sum(n1, n6) = n7, yields:
% 23.20/6.54 | (540) all_0_0_0 = n7
% 23.20/6.54 |
% 23.20/6.54 | From (570)(540) and (261) follows:
% 23.20/6.54 | (4435) sum(n7, n7) = all_0_6_6
% 23.20/6.54 |
% 23.20/6.54 | Instantiating formula (89) with n7, n7, all_0_6_6, n14 and discharging atoms sum(n7, n7) = all_0_6_6, sum(n7, n7) = n14, yields:
% 23.20/6.54 | (559) all_0_6_6 = n14
% 23.20/6.54 |
% 23.20/6.54 | Equations (559) can reduce 314 to:
% 23.20/6.54 | (458) $false
% 23.20/6.54 |
% 23.20/6.54 |-The branch is then unsatisfiable
% 23.20/6.54 |-Branch two:
% 23.20/6.54 | (982) ~ (all_0_7_7 = n1)
% 23.20/6.54 | (983) all_0_7_7 = n0
% 23.20/6.54 |
% 23.20/6.54 | From (983) and (176) follows:
% 23.20/6.54 | (984) succ(n0) = all_0_5_5
% 23.20/6.54 |
% 23.20/6.54 | From (983) and (59) follows:
% 23.20/6.54 | (985) sum(n0, all_0_1_1) = all_0_0_0
% 23.20/6.54 |
% 23.20/6.54 | From (983) and (4344) follows:
% 23.20/6.54 | (4442) sum(n6, n0) = all_0_2_2
% 23.20/6.54 |
% 23.20/6.54 | Instantiating formula (219) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 23.20/6.54 | (987) all_0_5_5 = n1
% 23.20/6.54 |
% 23.20/6.54 | Instantiating formula (89) with n6, n0, all_0_2_2, n6 and discharging atoms sum(n6, n0) = all_0_2_2, sum(n6, n0) = n6, yields:
% 23.20/6.54 | (583) all_0_2_2 = n6
% 23.20/6.54 |
% 23.20/6.54 | From (583) and (187) follows:
% 23.20/6.54 | (585) pred(n6) = all_0_1_1
% 23.20/6.54 |
% 23.20/6.54 | From (987) and (4343) follows:
% 23.20/6.54 | (4446) sum(n6, n1) = all_0_4_4
% 23.20/6.54 |
% 23.20/6.54 | Instantiating formula (37) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 23.20/6.54 | (588) all_0_1_1 = n5
% 23.20/6.54 |
% 23.20/6.54 | Instantiating formula (89) with n6, n1, all_0_4_4, n7 and discharging atoms sum(n6, n1) = all_0_4_4, sum(n6, n1) = n7, yields:
% 23.20/6.54 | (584) all_0_4_4 = n7
% 23.20/6.54 |
% 23.20/6.54 | From (584) and (396) follows:
% 23.20/6.54 | (586) pred(n7) = all_0_3_3
% 23.20/6.54 |
% 23.20/6.54 | From (588) and (985) follows:
% 23.41/6.54 | (4450) sum(n0, n5) = all_0_0_0
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (37) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 23.41/6.54 | (587) all_0_3_3 = n6
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (89) with n0, n5, all_0_0_0, n5 and discharging atoms sum(n0, n5) = all_0_0_0, sum(n0, n5) = n5, yields:
% 23.41/6.54 | (574) all_0_0_0 = n5
% 23.41/6.54 |
% 23.41/6.54 | From (587)(574) and (261) follows:
% 23.41/6.54 | (4453) sum(n6, n5) = all_0_6_6
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (89) with n6, n5, all_0_6_6, n11 and discharging atoms sum(n6, n5) = all_0_6_6, sum(n6, n5) = n11, yields:
% 23.41/6.54 | (809) all_0_6_6 = n11
% 23.41/6.54 |
% 23.41/6.54 | Equations (809) can reduce 70 to:
% 23.41/6.54 | (458) $false
% 23.41/6.54 |
% 23.41/6.54 |-The branch is then unsatisfiable
% 23.41/6.54 |-Branch two:
% 23.41/6.54 | (612) ~ (all_0_8_8 = n6)
% 23.41/6.54 | (613) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.41/6.54 |
% 23.41/6.54 +-Applying beta-rule and splitting (888), into two cases.
% 23.41/6.54 |-Branch one:
% 23.41/6.54 | (889) all_0_7_7 = n5
% 23.41/6.54 |
% 23.41/6.54 | From (889) and (176) follows:
% 23.41/6.54 | (890) succ(n5) = all_0_5_5
% 23.41/6.54 |
% 23.41/6.54 | From (889) and (59) follows:
% 23.41/6.54 | (891) sum(n5, all_0_1_1) = all_0_0_0
% 23.41/6.54 |
% 23.41/6.54 | From (889) and (160) follows:
% 23.41/6.54 | (4461) sum(all_0_8_8, n5) = all_0_2_2
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (219) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 23.41/6.54 | (893) all_0_5_5 = n6
% 23.41/6.54 |
% 23.41/6.54 | From (893) and (64) follows:
% 23.41/6.54 | (4463) sum(all_0_8_8, n6) = all_0_4_4
% 23.41/6.54 |
% 23.41/6.54 +-Applying beta-rule and splitting (613), into two cases.
% 23.41/6.54 |-Branch one:
% 23.41/6.54 | (614) all_0_8_8 = n5
% 23.41/6.54 |
% 23.41/6.54 | From (614) and (4463) follows:
% 23.41/6.54 | (4465) sum(n5, n6) = all_0_4_4
% 23.41/6.54 |
% 23.41/6.54 | From (614) and (4461) follows:
% 23.41/6.54 | (4466) sum(n5, n5) = all_0_2_2
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (89) with n5, n6, all_0_4_4, n11 and discharging atoms sum(n5, n6) = all_0_4_4, sum(n5, n6) = n11, yields:
% 23.41/6.54 | (516) all_0_4_4 = n11
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (89) with n5, n5, all_0_2_2, n10 and discharging atoms sum(n5, n5) = all_0_2_2, sum(n5, n5) = n10, yields:
% 23.41/6.54 | (515) all_0_2_2 = n10
% 23.41/6.54 |
% 23.41/6.54 | From (515) and (187) follows:
% 23.41/6.54 | (517) pred(n10) = all_0_1_1
% 23.41/6.54 |
% 23.41/6.54 | From (516) and (396) follows:
% 23.41/6.54 | (518) pred(n11) = all_0_3_3
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (37) with n11, all_0_3_3, n10 and discharging atoms pred(n11) = all_0_3_3, pred(n11) = n10, yields:
% 23.41/6.54 | (519) all_0_3_3 = n10
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (37) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 23.41/6.54 | (520) all_0_1_1 = n9
% 23.41/6.54 |
% 23.41/6.54 | From (519) and (261) follows:
% 23.41/6.54 | (521) sum(n10, all_0_0_0) = all_0_6_6
% 23.41/6.54 |
% 23.41/6.54 | From (520) and (891) follows:
% 23.41/6.54 | (4474) sum(n5, n9) = all_0_0_0
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (89) with n5, n9, all_0_0_0, n14 and discharging atoms sum(n5, n9) = all_0_0_0, sum(n5, n9) = n14, yields:
% 23.41/6.54 | (693) all_0_0_0 = n14
% 23.41/6.54 |
% 23.41/6.54 | From (693) and (521) follows:
% 23.41/6.54 | (4476) sum(n10, n14) = all_0_6_6
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (89) with n10, n14, all_0_6_6, n8 and discharging atoms sum(n10, n14) = all_0_6_6, sum(n10, n14) = n8, yields:
% 23.41/6.54 | (474) all_0_6_6 = n8
% 23.41/6.54 |
% 23.41/6.54 | Equations (474) can reduce 86 to:
% 23.41/6.54 | (458) $false
% 23.41/6.54 |
% 23.41/6.54 |-The branch is then unsatisfiable
% 23.41/6.54 |-Branch two:
% 23.41/6.54 | (629) ~ (all_0_8_8 = n5)
% 23.41/6.54 | (630) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.41/6.54 |
% 23.41/6.54 +-Applying beta-rule and splitting (630), into two cases.
% 23.41/6.54 |-Branch one:
% 23.41/6.54 | (631) all_0_8_8 = n4
% 23.41/6.54 |
% 23.41/6.54 | From (631) and (4463) follows:
% 23.41/6.54 | (4482) sum(n4, n6) = all_0_4_4
% 23.41/6.54 |
% 23.41/6.54 | From (631) and (4461) follows:
% 23.41/6.54 | (4483) sum(n4, n5) = all_0_2_2
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (89) with n4, n6, all_0_4_4, n10 and discharging atoms sum(n4, n6) = all_0_4_4, sum(n4, n6) = n10, yields:
% 23.41/6.54 | (533) all_0_4_4 = n10
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (89) with n4, n5, all_0_2_2, n9 and discharging atoms sum(n4, n5) = all_0_2_2, sum(n4, n5) = n9, yields:
% 23.41/6.54 | (532) all_0_2_2 = n9
% 23.41/6.54 |
% 23.41/6.54 | From (532) and (187) follows:
% 23.41/6.54 | (534) pred(n9) = all_0_1_1
% 23.41/6.54 |
% 23.41/6.54 | From (533) and (396) follows:
% 23.41/6.54 | (535) pred(n10) = all_0_3_3
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (37) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 23.41/6.54 | (536) all_0_3_3 = n9
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (37) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 23.41/6.54 | (537) all_0_1_1 = n8
% 23.41/6.54 |
% 23.41/6.54 | From (536) and (261) follows:
% 23.41/6.54 | (538) sum(n9, all_0_0_0) = all_0_6_6
% 23.41/6.54 |
% 23.41/6.54 | From (537) and (891) follows:
% 23.41/6.54 | (4491) sum(n5, n8) = all_0_0_0
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (89) with n5, n8, all_0_0_0, n13 and discharging atoms sum(n5, n8) = all_0_0_0, sum(n5, n8) = n13, yields:
% 23.41/6.54 | (709) all_0_0_0 = n13
% 23.41/6.54 |
% 23.41/6.54 | From (709) and (538) follows:
% 23.41/6.54 | (4493) sum(n9, n13) = all_0_6_6
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (89) with n9, n13, all_0_6_6, n6 and discharging atoms sum(n9, n13) = all_0_6_6, sum(n9, n13) = n6, yields:
% 23.41/6.54 | (491) all_0_6_6 = n6
% 23.41/6.54 |
% 23.41/6.54 | Equations (491) can reduce 418 to:
% 23.41/6.54 | (458) $false
% 23.41/6.54 |
% 23.41/6.54 |-The branch is then unsatisfiable
% 23.41/6.54 |-Branch two:
% 23.41/6.54 | (646) ~ (all_0_8_8 = n4)
% 23.41/6.54 | (647) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.41/6.54 |
% 23.41/6.54 +-Applying beta-rule and splitting (647), into two cases.
% 23.41/6.54 |-Branch one:
% 23.41/6.54 | (648) all_0_8_8 = n3
% 23.41/6.54 |
% 23.41/6.54 | From (648) and (4463) follows:
% 23.41/6.54 | (4499) sum(n3, n6) = all_0_4_4
% 23.41/6.54 |
% 23.41/6.54 | From (648) and (4461) follows:
% 23.41/6.54 | (4500) sum(n3, n5) = all_0_2_2
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (89) with n3, n6, all_0_4_4, n9 and discharging atoms sum(n3, n6) = all_0_4_4, sum(n3, n6) = n9, yields:
% 23.41/6.54 | (550) all_0_4_4 = n9
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (89) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 23.41/6.54 | (549) all_0_2_2 = n8
% 23.41/6.54 |
% 23.41/6.54 | From (549) and (187) follows:
% 23.41/6.54 | (551) pred(n8) = all_0_1_1
% 23.41/6.54 |
% 23.41/6.54 | From (550) and (396) follows:
% 23.41/6.54 | (552) pred(n9) = all_0_3_3
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (37) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 23.41/6.54 | (553) all_0_3_3 = n8
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (37) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 23.41/6.54 | (554) all_0_1_1 = n7
% 23.41/6.54 |
% 23.41/6.54 | From (553) and (261) follows:
% 23.41/6.54 | (555) sum(n8, all_0_0_0) = all_0_6_6
% 23.41/6.54 |
% 23.41/6.54 | From (554) and (891) follows:
% 23.41/6.54 | (4508) sum(n5, n7) = all_0_0_0
% 23.41/6.54 |
% 23.41/6.54 | Instantiating formula (89) with n5, n7, all_0_0_0, n12 and discharging atoms sum(n5, n7) = all_0_0_0, sum(n5, n7) = n12, yields:
% 23.41/6.54 | (455) all_0_0_0 = n12
% 23.41/6.54 |
% 23.41/6.54 | From (455) and (555) follows:
% 23.41/6.55 | (4510) sum(n8, n12) = all_0_6_6
% 23.41/6.55 |
% 23.41/6.55 | Instantiating formula (89) with n8, n12, all_0_6_6, n4 and discharging atoms sum(n8, n12) = all_0_6_6, sum(n8, n12) = n4, yields:
% 23.41/6.55 | (508) all_0_6_6 = n4
% 23.41/6.55 |
% 23.41/6.55 | Equations (508) can reduce 12 to:
% 23.41/6.55 | (458) $false
% 23.41/6.55 |
% 23.41/6.55 |-The branch is then unsatisfiable
% 23.41/6.55 |-Branch two:
% 23.41/6.55 | (663) ~ (all_0_8_8 = n3)
% 23.41/6.55 | (664) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.41/6.55 |
% 23.41/6.55 +-Applying beta-rule and splitting (664), into two cases.
% 23.41/6.55 |-Branch one:
% 23.41/6.55 | (665) all_0_8_8 = n2
% 23.41/6.55 |
% 23.41/6.55 | From (665) and (4463) follows:
% 23.41/6.55 | (4516) sum(n2, n6) = all_0_4_4
% 23.41/6.55 |
% 23.41/6.55 | From (665) and (4461) follows:
% 23.41/6.55 | (4517) sum(n2, n5) = all_0_2_2
% 23.41/6.55 |
% 23.41/6.55 | Instantiating formula (89) with n2, n6, all_0_4_4, n8 and discharging atoms sum(n2, n6) = all_0_4_4, sum(n2, n6) = n8, yields:
% 23.41/6.55 | (567) all_0_4_4 = n8
% 23.41/6.55 |
% 23.41/6.55 | Instantiating formula (89) with n2, n5, all_0_2_2, n7 and discharging atoms sum(n2, n5) = all_0_2_2, sum(n2, n5) = n7, yields:
% 23.41/6.55 | (566) all_0_2_2 = n7
% 23.41/6.55 |
% 23.41/6.55 | From (566) and (187) follows:
% 23.41/6.55 | (568) pred(n7) = all_0_1_1
% 23.41/6.55 |
% 23.41/6.55 | From (567) and (396) follows:
% 23.41/6.55 | (569) pred(n8) = all_0_3_3
% 23.41/6.55 |
% 23.41/6.55 | Instantiating formula (37) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 23.41/6.55 | (570) all_0_3_3 = n7
% 23.41/6.55 |
% 23.41/6.55 | Instantiating formula (37) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 23.41/6.55 | (571) all_0_1_1 = n6
% 23.41/6.55 |
% 23.41/6.55 | From (570) and (261) follows:
% 23.41/6.55 | (572) sum(n7, all_0_0_0) = all_0_6_6
% 23.41/6.55 |
% 23.41/6.55 | From (571) and (891) follows:
% 23.41/6.55 | (4525) sum(n5, n6) = all_0_0_0
% 23.41/6.55 |
% 23.41/6.55 | Instantiating formula (89) with n5, n6, all_0_0_0, n11 and discharging atoms sum(n5, n6) = all_0_0_0, sum(n5, n6) = n11, yields:
% 23.41/6.55 | (472) all_0_0_0 = n11
% 23.41/6.55 |
% 23.41/6.55 | From (472) and (572) follows:
% 23.41/6.55 | (4527) sum(n7, n11) = all_0_6_6
% 23.41/6.55 |
% 23.41/6.55 | Instantiating formula (89) with n7, n11, all_0_6_6, n2 and discharging atoms sum(n7, n11) = all_0_6_6, sum(n7, n11) = n2, yields:
% 23.41/6.55 | (525) all_0_6_6 = n2
% 23.41/6.55 |
% 23.41/6.55 | Equations (525) can reduce 231 to:
% 23.41/6.55 | (458) $false
% 23.41/6.55 |
% 23.41/6.55 |-The branch is then unsatisfiable
% 23.41/6.55 |-Branch two:
% 23.41/6.55 | (680) ~ (all_0_8_8 = n2)
% 23.41/6.55 | (681) all_0_8_8 = n1 | all_0_8_8 = n0
% 23.41/6.55 |
% 23.41/6.55 +-Applying beta-rule and splitting (681), into two cases.
% 23.41/6.55 |-Branch one:
% 23.41/6.55 | (682) all_0_8_8 = n1
% 23.41/6.55 |
% 23.41/6.55 | From (682) and (4463) follows:
% 23.45/6.55 | (4533) sum(n1, n6) = all_0_4_4
% 23.45/6.55 |
% 23.45/6.55 | From (682) and (4461) follows:
% 23.45/6.55 | (4534) sum(n1, n5) = all_0_2_2
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (89) with n1, n6, all_0_4_4, n7 and discharging atoms sum(n1, n6) = all_0_4_4, sum(n1, n6) = n7, yields:
% 23.45/6.55 | (584) all_0_4_4 = n7
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (89) with n1, n5, all_0_2_2, n6 and discharging atoms sum(n1, n5) = all_0_2_2, sum(n1, n5) = n6, yields:
% 23.45/6.55 | (583) all_0_2_2 = n6
% 23.45/6.55 |
% 23.45/6.55 | From (583) and (187) follows:
% 23.45/6.55 | (585) pred(n6) = all_0_1_1
% 23.45/6.55 |
% 23.45/6.55 | From (584) and (396) follows:
% 23.45/6.55 | (586) pred(n7) = all_0_3_3
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (37) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 23.45/6.55 | (587) all_0_3_3 = n6
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (37) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 23.45/6.55 | (588) all_0_1_1 = n5
% 23.45/6.55 |
% 23.45/6.55 | From (587) and (261) follows:
% 23.45/6.55 | (589) sum(n6, all_0_0_0) = all_0_6_6
% 23.45/6.55 |
% 23.45/6.55 | From (588) and (891) follows:
% 23.45/6.55 | (4542) sum(n5, n5) = all_0_0_0
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (89) with n5, n5, all_0_0_0, n10 and discharging atoms sum(n5, n5) = all_0_0_0, sum(n5, n5) = n10, yields:
% 23.45/6.55 | (489) all_0_0_0 = n10
% 23.45/6.55 |
% 23.45/6.55 | From (489) and (589) follows:
% 23.45/6.55 | (4544) sum(n6, n10) = all_0_6_6
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (89) with n6, n10, all_0_6_6, n0 and discharging atoms sum(n6, n10) = all_0_6_6, sum(n6, n10) = n0, yields:
% 23.45/6.55 | (542) all_0_6_6 = n0
% 23.45/6.55 |
% 23.45/6.55 | Equations (542) can reduce 400 to:
% 23.45/6.55 | (458) $false
% 23.45/6.55 |
% 23.45/6.55 |-The branch is then unsatisfiable
% 23.45/6.55 |-Branch two:
% 23.45/6.55 | (697) ~ (all_0_8_8 = n1)
% 23.45/6.55 | (698) all_0_8_8 = n0
% 23.45/6.55 |
% 23.45/6.55 | From (698) and (4463) follows:
% 23.45/6.55 | (4549) sum(n0, n6) = all_0_4_4
% 23.45/6.55 |
% 23.45/6.55 | From (698) and (4461) follows:
% 23.45/6.55 | (4550) sum(n0, n5) = all_0_2_2
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (89) with n0, n6, all_0_4_4, n6 and discharging atoms sum(n0, n6) = all_0_4_4, sum(n0, n6) = n6, yields:
% 23.45/6.55 | (601) all_0_4_4 = n6
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (89) with n0, n5, all_0_2_2, n5 and discharging atoms sum(n0, n5) = all_0_2_2, sum(n0, n5) = n5, yields:
% 23.45/6.55 | (600) all_0_2_2 = n5
% 23.45/6.55 |
% 23.45/6.55 | From (600) and (187) follows:
% 23.45/6.55 | (602) pred(n5) = all_0_1_1
% 23.45/6.55 |
% 23.45/6.55 | From (601) and (396) follows:
% 23.45/6.55 | (603) pred(n6) = all_0_3_3
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (37) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 23.45/6.55 | (604) all_0_3_3 = n5
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (37) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 23.45/6.55 | (605) all_0_1_1 = n4
% 23.45/6.55 |
% 23.45/6.55 | From (604) and (261) follows:
% 23.45/6.55 | (606) sum(n5, all_0_0_0) = all_0_6_6
% 23.45/6.55 |
% 23.45/6.55 | From (605) and (891) follows:
% 23.45/6.55 | (4558) sum(n5, n4) = all_0_0_0
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (89) with n5, n4, all_0_0_0, n9 and discharging atoms sum(n5, n4) = all_0_0_0, sum(n5, n4) = n9, yields:
% 23.45/6.55 | (506) all_0_0_0 = n9
% 23.45/6.55 |
% 23.45/6.55 | From (506) and (606) follows:
% 23.45/6.55 | (4560) sum(n5, n9) = all_0_6_6
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (89) with n5, n9, all_0_6_6, n14 and discharging atoms sum(n5, n9) = all_0_6_6, sum(n5, n9) = n14, yields:
% 23.45/6.55 | (559) all_0_6_6 = n14
% 23.45/6.55 |
% 23.45/6.55 | Equations (559) can reduce 314 to:
% 23.45/6.55 | (458) $false
% 23.45/6.55 |
% 23.45/6.55 |-The branch is then unsatisfiable
% 23.45/6.55 |-Branch two:
% 23.45/6.55 | (906) ~ (all_0_7_7 = n5)
% 23.45/6.55 | (907) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.45/6.55 |
% 23.45/6.55 +-Applying beta-rule and splitting (613), into two cases.
% 23.45/6.55 |-Branch one:
% 23.45/6.55 | (614) all_0_8_8 = n5
% 23.45/6.55 |
% 23.45/6.55 | From (614) and (64) follows:
% 23.45/6.55 | (4566) sum(n5, all_0_5_5) = all_0_4_4
% 23.45/6.55 |
% 23.45/6.55 | From (614) and (160) follows:
% 23.45/6.55 | (4567) sum(n5, all_0_7_7) = all_0_2_2
% 23.45/6.55 |
% 23.45/6.55 +-Applying beta-rule and splitting (907), into two cases.
% 23.45/6.55 |-Branch one:
% 23.45/6.55 | (908) all_0_7_7 = n4
% 23.45/6.55 |
% 23.45/6.55 | From (908) and (176) follows:
% 23.45/6.55 | (909) succ(n4) = all_0_5_5
% 23.45/6.55 |
% 23.45/6.55 | From (908) and (59) follows:
% 23.45/6.55 | (910) sum(n4, all_0_1_1) = all_0_0_0
% 23.45/6.55 |
% 23.45/6.55 | From (908) and (4567) follows:
% 23.45/6.55 | (4571) sum(n5, n4) = all_0_2_2
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (219) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 23.45/6.55 | (912) all_0_5_5 = n5
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (89) with n5, n4, all_0_2_2, n9 and discharging atoms sum(n5, n4) = all_0_2_2, sum(n5, n4) = n9, yields:
% 23.45/6.55 | (532) all_0_2_2 = n9
% 23.45/6.55 |
% 23.45/6.55 | From (532) and (187) follows:
% 23.45/6.55 | (534) pred(n9) = all_0_1_1
% 23.45/6.55 |
% 23.45/6.55 | From (912) and (4566) follows:
% 23.45/6.55 | (4575) sum(n5, n5) = all_0_4_4
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (37) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 23.45/6.55 | (537) all_0_1_1 = n8
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (89) with n5, n5, all_0_4_4, n10 and discharging atoms sum(n5, n5) = all_0_4_4, sum(n5, n5) = n10, yields:
% 23.45/6.55 | (533) all_0_4_4 = n10
% 23.45/6.55 |
% 23.45/6.55 | From (533) and (396) follows:
% 23.45/6.55 | (535) pred(n10) = all_0_3_3
% 23.45/6.55 |
% 23.45/6.55 | From (537) and (910) follows:
% 23.45/6.55 | (4579) sum(n4, n8) = all_0_0_0
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (37) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 23.45/6.55 | (536) all_0_3_3 = n9
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (89) with n4, n8, all_0_0_0, n12 and discharging atoms sum(n4, n8) = all_0_0_0, sum(n4, n8) = n12, yields:
% 23.45/6.55 | (455) all_0_0_0 = n12
% 23.45/6.55 |
% 23.45/6.55 | From (536)(455) and (261) follows:
% 23.45/6.55 | (4582) sum(n9, n12) = all_0_6_6
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (89) with n9, n12, all_0_6_6, n5 and discharging atoms sum(n9, n12) = all_0_6_6, sum(n9, n12) = n5, yields:
% 23.45/6.55 | (847) all_0_6_6 = n5
% 23.45/6.55 |
% 23.45/6.55 | Equations (847) can reduce 409 to:
% 23.45/6.55 | (458) $false
% 23.45/6.55 |
% 23.45/6.55 |-The branch is then unsatisfiable
% 23.45/6.55 |-Branch two:
% 23.45/6.55 | (925) ~ (all_0_7_7 = n4)
% 23.45/6.55 | (926) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.45/6.55 |
% 23.45/6.55 +-Applying beta-rule and splitting (926), into two cases.
% 23.45/6.55 |-Branch one:
% 23.45/6.55 | (927) all_0_7_7 = n3
% 23.45/6.55 |
% 23.45/6.55 | From (927) and (176) follows:
% 23.45/6.55 | (928) succ(n3) = all_0_5_5
% 23.45/6.55 |
% 23.45/6.55 | From (927) and (59) follows:
% 23.45/6.55 | (929) sum(n3, all_0_1_1) = all_0_0_0
% 23.45/6.55 |
% 23.45/6.55 | From (927) and (4567) follows:
% 23.45/6.55 | (4590) sum(n5, n3) = all_0_2_2
% 23.45/6.55 |
% 23.45/6.55 | Instantiating formula (219) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 23.45/6.56 | (931) all_0_5_5 = n4
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (89) with n5, n3, all_0_2_2, n8 and discharging atoms sum(n5, n3) = all_0_2_2, sum(n5, n3) = n8, yields:
% 23.45/6.56 | (549) all_0_2_2 = n8
% 23.45/6.56 |
% 23.45/6.56 | From (549) and (187) follows:
% 23.45/6.56 | (551) pred(n8) = all_0_1_1
% 23.45/6.56 |
% 23.45/6.56 | From (931) and (4566) follows:
% 23.45/6.56 | (4594) sum(n5, n4) = all_0_4_4
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (37) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 23.45/6.56 | (554) all_0_1_1 = n7
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (89) with n5, n4, all_0_4_4, n9 and discharging atoms sum(n5, n4) = all_0_4_4, sum(n5, n4) = n9, yields:
% 23.45/6.56 | (550) all_0_4_4 = n9
% 23.45/6.56 |
% 23.45/6.56 | From (550) and (396) follows:
% 23.45/6.56 | (552) pred(n9) = all_0_3_3
% 23.45/6.56 |
% 23.45/6.56 | From (554) and (929) follows:
% 23.45/6.56 | (4598) sum(n3, n7) = all_0_0_0
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (37) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 23.45/6.56 | (553) all_0_3_3 = n8
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (89) with n3, n7, all_0_0_0, n10 and discharging atoms sum(n3, n7) = all_0_0_0, sum(n3, n7) = n10, yields:
% 23.45/6.56 | (489) all_0_0_0 = n10
% 23.45/6.56 |
% 23.45/6.56 | From (553)(489) and (261) follows:
% 23.45/6.56 | (4601) sum(n8, n10) = all_0_6_6
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (89) with n8, n10, all_0_6_6, n2 and discharging atoms sum(n8, n10) = all_0_6_6, sum(n8, n10) = n2, yields:
% 23.45/6.56 | (525) all_0_6_6 = n2
% 23.45/6.56 |
% 23.45/6.56 | Equations (525) can reduce 231 to:
% 23.45/6.56 | (458) $false
% 23.45/6.56 |
% 23.45/6.56 |-The branch is then unsatisfiable
% 23.45/6.56 |-Branch two:
% 23.45/6.56 | (944) ~ (all_0_7_7 = n3)
% 23.45/6.56 | (945) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.45/6.56 |
% 23.45/6.56 +-Applying beta-rule and splitting (945), into two cases.
% 23.45/6.56 |-Branch one:
% 23.45/6.56 | (946) all_0_7_7 = n2
% 23.45/6.56 |
% 23.45/6.56 | From (946) and (176) follows:
% 23.45/6.56 | (947) succ(n2) = all_0_5_5
% 23.45/6.56 |
% 23.45/6.56 | From (946) and (59) follows:
% 23.45/6.56 | (948) sum(n2, all_0_1_1) = all_0_0_0
% 23.45/6.56 |
% 23.45/6.56 | From (946) and (4567) follows:
% 23.45/6.56 | (4609) sum(n5, n2) = all_0_2_2
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (219) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 23.45/6.56 | (950) all_0_5_5 = n3
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (89) with n5, n2, all_0_2_2, n7 and discharging atoms sum(n5, n2) = all_0_2_2, sum(n5, n2) = n7, yields:
% 23.45/6.56 | (566) all_0_2_2 = n7
% 23.45/6.56 |
% 23.45/6.56 | From (566) and (187) follows:
% 23.45/6.56 | (568) pred(n7) = all_0_1_1
% 23.45/6.56 |
% 23.45/6.56 | From (950) and (4566) follows:
% 23.45/6.56 | (4613) sum(n5, n3) = all_0_4_4
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (37) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 23.45/6.56 | (571) all_0_1_1 = n6
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (89) with n5, n3, all_0_4_4, n8 and discharging atoms sum(n5, n3) = all_0_4_4, sum(n5, n3) = n8, yields:
% 23.45/6.56 | (567) all_0_4_4 = n8
% 23.45/6.56 |
% 23.45/6.56 | From (567) and (396) follows:
% 23.45/6.56 | (569) pred(n8) = all_0_3_3
% 23.45/6.56 |
% 23.45/6.56 | From (571) and (948) follows:
% 23.45/6.56 | (4617) sum(n2, n6) = all_0_0_0
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (37) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 23.45/6.56 | (570) all_0_3_3 = n7
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (89) with n2, n6, all_0_0_0, n8 and discharging atoms sum(n2, n6) = all_0_0_0, sum(n2, n6) = n8, yields:
% 23.45/6.56 | (523) all_0_0_0 = n8
% 23.45/6.56 |
% 23.45/6.56 | From (570)(523) and (261) follows:
% 23.45/6.56 | (4620) sum(n7, n8) = all_0_6_6
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (89) with n7, n8, all_0_6_6, n15 and discharging atoms sum(n7, n8) = all_0_6_6, sum(n7, n8) = n15, yields:
% 23.45/6.56 | (885) all_0_6_6 = n15
% 23.45/6.56 |
% 23.45/6.56 | Equations (885) can reduce 225 to:
% 23.45/6.56 | (458) $false
% 23.45/6.56 |
% 23.45/6.56 |-The branch is then unsatisfiable
% 23.45/6.56 |-Branch two:
% 23.45/6.56 | (963) ~ (all_0_7_7 = n2)
% 23.45/6.56 | (964) all_0_7_7 = n1 | all_0_7_7 = n0
% 23.45/6.56 |
% 23.45/6.56 +-Applying beta-rule and splitting (964), into two cases.
% 23.45/6.56 |-Branch one:
% 23.45/6.56 | (965) all_0_7_7 = n1
% 23.45/6.56 |
% 23.45/6.56 | From (965) and (176) follows:
% 23.45/6.56 | (966) succ(n1) = all_0_5_5
% 23.45/6.56 |
% 23.45/6.56 | From (965) and (59) follows:
% 23.45/6.56 | (967) sum(n1, all_0_1_1) = all_0_0_0
% 23.45/6.56 |
% 23.45/6.56 | From (965) and (4567) follows:
% 23.45/6.56 | (4628) sum(n5, n1) = all_0_2_2
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (219) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 23.45/6.56 | (969) all_0_5_5 = n2
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (89) with n5, n1, all_0_2_2, n6 and discharging atoms sum(n5, n1) = all_0_2_2, sum(n5, n1) = n6, yields:
% 23.45/6.56 | (583) all_0_2_2 = n6
% 23.45/6.56 |
% 23.45/6.56 | From (583) and (187) follows:
% 23.45/6.56 | (585) pred(n6) = all_0_1_1
% 23.45/6.56 |
% 23.45/6.56 | From (969) and (4566) follows:
% 23.45/6.56 | (4632) sum(n5, n2) = all_0_4_4
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (37) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 23.45/6.56 | (588) all_0_1_1 = n5
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (89) with n5, n2, all_0_4_4, n7 and discharging atoms sum(n5, n2) = all_0_4_4, sum(n5, n2) = n7, yields:
% 23.45/6.56 | (584) all_0_4_4 = n7
% 23.45/6.56 |
% 23.45/6.56 | From (584) and (396) follows:
% 23.45/6.56 | (586) pred(n7) = all_0_3_3
% 23.45/6.56 |
% 23.45/6.56 | From (588) and (967) follows:
% 23.45/6.56 | (4636) sum(n1, n5) = all_0_0_0
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (37) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 23.45/6.56 | (587) all_0_3_3 = n6
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (89) with n1, n5, all_0_0_0, n6 and discharging atoms sum(n1, n5) = all_0_0_0, sum(n1, n5) = n6, yields:
% 23.45/6.56 | (557) all_0_0_0 = n6
% 23.45/6.56 |
% 23.45/6.56 | From (587)(557) and (261) follows:
% 23.45/6.56 | (4639) sum(n6, n6) = all_0_6_6
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (89) with n6, n6, all_0_6_6, n12 and discharging atoms sum(n6, n6) = all_0_6_6, sum(n6, n6) = n12, yields:
% 23.45/6.56 | (576) all_0_6_6 = n12
% 23.45/6.56 |
% 23.45/6.56 | Equations (576) can reduce 42 to:
% 23.45/6.56 | (458) $false
% 23.45/6.56 |
% 23.45/6.56 |-The branch is then unsatisfiable
% 23.45/6.56 |-Branch two:
% 23.45/6.56 | (982) ~ (all_0_7_7 = n1)
% 23.45/6.56 | (983) all_0_7_7 = n0
% 23.45/6.56 |
% 23.45/6.56 | From (983) and (176) follows:
% 23.45/6.56 | (984) succ(n0) = all_0_5_5
% 23.45/6.56 |
% 23.45/6.56 | From (983) and (59) follows:
% 23.45/6.56 | (985) sum(n0, all_0_1_1) = all_0_0_0
% 23.45/6.56 |
% 23.45/6.56 | From (983) and (4567) follows:
% 23.45/6.56 | (4646) sum(n5, n0) = all_0_2_2
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (219) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 23.45/6.56 | (987) all_0_5_5 = n1
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (89) with n5, n0, all_0_2_2, n5 and discharging atoms sum(n5, n0) = all_0_2_2, sum(n5, n0) = n5, yields:
% 23.45/6.56 | (600) all_0_2_2 = n5
% 23.45/6.56 |
% 23.45/6.56 | From (600) and (187) follows:
% 23.45/6.56 | (602) pred(n5) = all_0_1_1
% 23.45/6.56 |
% 23.45/6.56 | From (987) and (4566) follows:
% 23.45/6.56 | (4650) sum(n5, n1) = all_0_4_4
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (37) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 23.45/6.56 | (605) all_0_1_1 = n4
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (89) with n5, n1, all_0_4_4, n6 and discharging atoms sum(n5, n1) = all_0_4_4, sum(n5, n1) = n6, yields:
% 23.45/6.56 | (601) all_0_4_4 = n6
% 23.45/6.56 |
% 23.45/6.56 | From (601) and (396) follows:
% 23.45/6.56 | (603) pred(n6) = all_0_3_3
% 23.45/6.56 |
% 23.45/6.56 | From (605) and (985) follows:
% 23.45/6.56 | (4654) sum(n0, n4) = all_0_0_0
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (37) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 23.45/6.56 | (604) all_0_3_3 = n5
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (89) with n0, n4, all_0_0_0, n4 and discharging atoms sum(n0, n4) = all_0_0_0, sum(n0, n4) = n4, yields:
% 23.45/6.56 | (591) all_0_0_0 = n4
% 23.45/6.56 |
% 23.45/6.56 | From (604)(591) and (261) follows:
% 23.45/6.56 | (4657) sum(n5, n4) = all_0_6_6
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (89) with n5, n4, all_0_6_6, n9 and discharging atoms sum(n5, n4) = all_0_6_6, sum(n5, n4) = n9, yields:
% 23.45/6.56 | (923) all_0_6_6 = n9
% 23.45/6.56 |
% 23.45/6.56 | Equations (923) can reduce 404 to:
% 23.45/6.56 | (458) $false
% 23.45/6.56 |
% 23.45/6.56 |-The branch is then unsatisfiable
% 23.45/6.56 |-Branch two:
% 23.45/6.56 | (629) ~ (all_0_8_8 = n5)
% 23.45/6.56 | (630) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.45/6.56 |
% 23.45/6.56 +-Applying beta-rule and splitting (907), into two cases.
% 23.45/6.56 |-Branch one:
% 23.45/6.56 | (908) all_0_7_7 = n4
% 23.45/6.56 |
% 23.45/6.56 | From (908) and (176) follows:
% 23.45/6.56 | (909) succ(n4) = all_0_5_5
% 23.45/6.56 |
% 23.45/6.56 | From (908) and (59) follows:
% 23.45/6.56 | (910) sum(n4, all_0_1_1) = all_0_0_0
% 23.45/6.56 |
% 23.45/6.56 | From (908) and (160) follows:
% 23.45/6.56 | (4665) sum(all_0_8_8, n4) = all_0_2_2
% 23.45/6.56 |
% 23.45/6.56 | Instantiating formula (219) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 23.45/6.56 | (912) all_0_5_5 = n5
% 23.45/6.56 |
% 23.45/6.56 | From (912) and (64) follows:
% 23.45/6.56 | (4667) sum(all_0_8_8, n5) = all_0_4_4
% 23.45/6.56 |
% 23.45/6.56 +-Applying beta-rule and splitting (630), into two cases.
% 23.45/6.56 |-Branch one:
% 23.45/6.56 | (631) all_0_8_8 = n4
% 23.45/6.56 |
% 23.45/6.56 | From (631) and (4667) follows:
% 23.45/6.56 | (4669) sum(n4, n5) = all_0_4_4
% 23.45/6.56 |
% 23.45/6.56 | From (631) and (4665) follows:
% 23.45/6.57 | (4670) sum(n4, n4) = all_0_2_2
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n4, n5, all_0_4_4, n9 and discharging atoms sum(n4, n5) = all_0_4_4, sum(n4, n5) = n9, yields:
% 23.45/6.57 | (550) all_0_4_4 = n9
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n4, n4, all_0_2_2, n8 and discharging atoms sum(n4, n4) = all_0_2_2, sum(n4, n4) = n8, yields:
% 23.45/6.57 | (549) all_0_2_2 = n8
% 23.45/6.57 |
% 23.45/6.57 | From (549) and (187) follows:
% 23.45/6.57 | (551) pred(n8) = all_0_1_1
% 23.45/6.57 |
% 23.45/6.57 | From (550) and (396) follows:
% 23.45/6.57 | (552) pred(n9) = all_0_3_3
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (37) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 23.45/6.57 | (553) all_0_3_3 = n8
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (37) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 23.45/6.57 | (554) all_0_1_1 = n7
% 23.45/6.57 |
% 23.45/6.57 | From (553) and (261) follows:
% 23.45/6.57 | (555) sum(n8, all_0_0_0) = all_0_6_6
% 23.45/6.57 |
% 23.45/6.57 | From (554) and (910) follows:
% 23.45/6.57 | (4678) sum(n4, n7) = all_0_0_0
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n4, n7, all_0_0_0, n11 and discharging atoms sum(n4, n7) = all_0_0_0, sum(n4, n7) = n11, yields:
% 23.45/6.57 | (472) all_0_0_0 = n11
% 23.45/6.57 |
% 23.45/6.57 | From (472) and (555) follows:
% 23.45/6.57 | (4680) sum(n8, n11) = all_0_6_6
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n8, n11, all_0_6_6, n3 and discharging atoms sum(n8, n11) = all_0_6_6, sum(n8, n11) = n3, yields:
% 23.45/6.57 | (961) all_0_6_6 = n3
% 23.45/6.57 |
% 23.45/6.57 | Equations (961) can reduce 245 to:
% 23.45/6.57 | (458) $false
% 23.45/6.57 |
% 23.45/6.57 |-The branch is then unsatisfiable
% 23.45/6.57 |-Branch two:
% 23.45/6.57 | (646) ~ (all_0_8_8 = n4)
% 23.45/6.57 | (647) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.45/6.57 |
% 23.45/6.57 +-Applying beta-rule and splitting (647), into two cases.
% 23.45/6.57 |-Branch one:
% 23.45/6.57 | (648) all_0_8_8 = n3
% 23.45/6.57 |
% 23.45/6.57 | From (648) and (4667) follows:
% 23.45/6.57 | (4686) sum(n3, n5) = all_0_4_4
% 23.45/6.57 |
% 23.45/6.57 | From (648) and (4665) follows:
% 23.45/6.57 | (4687) sum(n3, n4) = all_0_2_2
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n3, n5, all_0_4_4, n8 and discharging atoms sum(n3, n5) = all_0_4_4, sum(n3, n5) = n8, yields:
% 23.45/6.57 | (567) all_0_4_4 = n8
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n3, n4, all_0_2_2, n7 and discharging atoms sum(n3, n4) = all_0_2_2, sum(n3, n4) = n7, yields:
% 23.45/6.57 | (566) all_0_2_2 = n7
% 23.45/6.57 |
% 23.45/6.57 | From (566) and (187) follows:
% 23.45/6.57 | (568) pred(n7) = all_0_1_1
% 23.45/6.57 |
% 23.45/6.57 | From (567) and (396) follows:
% 23.45/6.57 | (569) pred(n8) = all_0_3_3
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (37) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 23.45/6.57 | (570) all_0_3_3 = n7
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (37) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 23.45/6.57 | (571) all_0_1_1 = n6
% 23.45/6.57 |
% 23.45/6.57 | From (570) and (261) follows:
% 23.45/6.57 | (572) sum(n7, all_0_0_0) = all_0_6_6
% 23.45/6.57 |
% 23.45/6.57 | From (571) and (910) follows:
% 23.45/6.57 | (4695) sum(n4, n6) = all_0_0_0
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n4, n6, all_0_0_0, n10 and discharging atoms sum(n4, n6) = all_0_0_0, sum(n4, n6) = n10, yields:
% 23.45/6.57 | (489) all_0_0_0 = n10
% 23.45/6.57 |
% 23.45/6.57 | From (489) and (572) follows:
% 23.45/6.57 | (4697) sum(n7, n10) = all_0_6_6
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n7, n10, all_0_6_6, n1 and discharging atoms sum(n7, n10) = all_0_6_6, sum(n7, n10) = n1, yields:
% 23.45/6.57 | (771) all_0_6_6 = n1
% 23.45/6.57 |
% 23.45/6.57 | Equations (771) can reduce 38 to:
% 23.45/6.57 | (458) $false
% 23.45/6.57 |
% 23.45/6.57 |-The branch is then unsatisfiable
% 23.45/6.57 |-Branch two:
% 23.45/6.57 | (663) ~ (all_0_8_8 = n3)
% 23.45/6.57 | (664) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.45/6.57 |
% 23.45/6.57 +-Applying beta-rule and splitting (664), into two cases.
% 23.45/6.57 |-Branch one:
% 23.45/6.57 | (665) all_0_8_8 = n2
% 23.45/6.57 |
% 23.45/6.57 | From (665) and (4667) follows:
% 23.45/6.57 | (4703) sum(n2, n5) = all_0_4_4
% 23.45/6.57 |
% 23.45/6.57 | From (665) and (4665) follows:
% 23.45/6.57 | (4704) sum(n2, n4) = all_0_2_2
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n2, n5, all_0_4_4, n7 and discharging atoms sum(n2, n5) = all_0_4_4, sum(n2, n5) = n7, yields:
% 23.45/6.57 | (584) all_0_4_4 = n7
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 23.45/6.57 | (583) all_0_2_2 = n6
% 23.45/6.57 |
% 23.45/6.57 | From (583) and (187) follows:
% 23.45/6.57 | (585) pred(n6) = all_0_1_1
% 23.45/6.57 |
% 23.45/6.57 | From (584) and (396) follows:
% 23.45/6.57 | (586) pred(n7) = all_0_3_3
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (37) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 23.45/6.57 | (587) all_0_3_3 = n6
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (37) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 23.45/6.57 | (588) all_0_1_1 = n5
% 23.45/6.57 |
% 23.45/6.57 | From (587) and (261) follows:
% 23.45/6.57 | (589) sum(n6, all_0_0_0) = all_0_6_6
% 23.45/6.57 |
% 23.45/6.57 | From (588) and (910) follows:
% 23.45/6.57 | (4712) sum(n4, n5) = all_0_0_0
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n4, n5, all_0_0_0, n9 and discharging atoms sum(n4, n5) = all_0_0_0, sum(n4, n5) = n9, yields:
% 23.45/6.57 | (506) all_0_0_0 = n9
% 23.45/6.57 |
% 23.45/6.57 | From (506) and (589) follows:
% 23.45/6.57 | (4714) sum(n6, n9) = all_0_6_6
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n6, n9, all_0_6_6, n15 and discharging atoms sum(n6, n9) = all_0_6_6, sum(n6, n9) = n15, yields:
% 23.45/6.57 | (885) all_0_6_6 = n15
% 23.45/6.57 |
% 23.45/6.57 | Equations (885) can reduce 225 to:
% 23.45/6.57 | (458) $false
% 23.45/6.57 |
% 23.45/6.57 |-The branch is then unsatisfiable
% 23.45/6.57 |-Branch two:
% 23.45/6.57 | (680) ~ (all_0_8_8 = n2)
% 23.45/6.57 | (681) all_0_8_8 = n1 | all_0_8_8 = n0
% 23.45/6.57 |
% 23.45/6.57 +-Applying beta-rule and splitting (681), into two cases.
% 23.45/6.57 |-Branch one:
% 23.45/6.57 | (682) all_0_8_8 = n1
% 23.45/6.57 |
% 23.45/6.57 | From (682) and (4667) follows:
% 23.45/6.57 | (4720) sum(n1, n5) = all_0_4_4
% 23.45/6.57 |
% 23.45/6.57 | From (682) and (4665) follows:
% 23.45/6.57 | (4721) sum(n1, n4) = all_0_2_2
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n1, n5, all_0_4_4, n6 and discharging atoms sum(n1, n5) = all_0_4_4, sum(n1, n5) = n6, yields:
% 23.45/6.57 | (601) all_0_4_4 = n6
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n1, n4, all_0_2_2, n5 and discharging atoms sum(n1, n4) = all_0_2_2, sum(n1, n4) = n5, yields:
% 23.45/6.57 | (600) all_0_2_2 = n5
% 23.45/6.57 |
% 23.45/6.57 | From (600) and (187) follows:
% 23.45/6.57 | (602) pred(n5) = all_0_1_1
% 23.45/6.57 |
% 23.45/6.57 | From (601) and (396) follows:
% 23.45/6.57 | (603) pred(n6) = all_0_3_3
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (37) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 23.45/6.57 | (604) all_0_3_3 = n5
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (37) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 23.45/6.57 | (605) all_0_1_1 = n4
% 23.45/6.57 |
% 23.45/6.57 | From (604) and (261) follows:
% 23.45/6.57 | (606) sum(n5, all_0_0_0) = all_0_6_6
% 23.45/6.57 |
% 23.45/6.57 | From (605) and (910) follows:
% 23.45/6.57 | (4729) sum(n4, n4) = all_0_0_0
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n4, n4, all_0_0_0, n8 and discharging atoms sum(n4, n4) = all_0_0_0, sum(n4, n4) = n8, yields:
% 23.45/6.57 | (523) all_0_0_0 = n8
% 23.45/6.57 |
% 23.45/6.57 | From (523) and (606) follows:
% 23.45/6.57 | (4731) sum(n5, n8) = all_0_6_6
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n5, n8, all_0_6_6, n13 and discharging atoms sum(n5, n8) = all_0_6_6, sum(n5, n8) = n13, yields:
% 23.45/6.57 | (998) all_0_6_6 = n13
% 23.45/6.57 |
% 23.45/6.57 | Equations (998) can reduce 130 to:
% 23.45/6.57 | (458) $false
% 23.45/6.57 |
% 23.45/6.57 |-The branch is then unsatisfiable
% 23.45/6.57 |-Branch two:
% 23.45/6.57 | (697) ~ (all_0_8_8 = n1)
% 23.45/6.57 | (698) all_0_8_8 = n0
% 23.45/6.57 |
% 23.45/6.57 | From (698) and (4667) follows:
% 23.45/6.57 | (4736) sum(n0, n5) = all_0_4_4
% 23.45/6.57 |
% 23.45/6.57 | From (698) and (4665) follows:
% 23.45/6.57 | (4737) sum(n0, n4) = all_0_2_2
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n0, n5, all_0_4_4, n5 and discharging atoms sum(n0, n5) = all_0_4_4, sum(n0, n5) = n5, yields:
% 23.45/6.57 | (618) all_0_4_4 = n5
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n0, n4, all_0_2_2, n4 and discharging atoms sum(n0, n4) = all_0_2_2, sum(n0, n4) = n4, yields:
% 23.45/6.57 | (617) all_0_2_2 = n4
% 23.45/6.57 |
% 23.45/6.57 | From (617) and (187) follows:
% 23.45/6.57 | (619) pred(n4) = all_0_1_1
% 23.45/6.57 |
% 23.45/6.57 | From (618) and (396) follows:
% 23.45/6.57 | (620) pred(n5) = all_0_3_3
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (37) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 23.45/6.57 | (621) all_0_3_3 = n4
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (37) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 23.45/6.57 | (622) all_0_1_1 = n3
% 23.45/6.57 |
% 23.45/6.57 | From (621) and (261) follows:
% 23.45/6.57 | (623) sum(n4, all_0_0_0) = all_0_6_6
% 23.45/6.57 |
% 23.45/6.57 | From (622) and (910) follows:
% 23.45/6.57 | (4745) sum(n4, n3) = all_0_0_0
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n4, n3, all_0_0_0, n7 and discharging atoms sum(n4, n3) = all_0_0_0, sum(n4, n3) = n7, yields:
% 23.45/6.57 | (540) all_0_0_0 = n7
% 23.45/6.57 |
% 23.45/6.57 | From (540) and (623) follows:
% 23.45/6.57 | (4747) sum(n4, n7) = all_0_6_6
% 23.45/6.57 |
% 23.45/6.57 | Instantiating formula (89) with n4, n7, all_0_6_6, n11 and discharging atoms sum(n4, n7) = all_0_6_6, sum(n4, n7) = n11, yields:
% 23.45/6.57 | (809) all_0_6_6 = n11
% 23.45/6.57 |
% 23.45/6.57 | Equations (809) can reduce 70 to:
% 23.45/6.57 | (458) $false
% 23.45/6.57 |
% 23.45/6.57 |-The branch is then unsatisfiable
% 23.45/6.57 |-Branch two:
% 23.45/6.57 | (925) ~ (all_0_7_7 = n4)
% 23.45/6.57 | (926) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.45/6.57 |
% 23.45/6.57 +-Applying beta-rule and splitting (630), into two cases.
% 23.45/6.57 |-Branch one:
% 23.45/6.57 | (631) all_0_8_8 = n4
% 23.45/6.57 |
% 23.45/6.57 | From (631) and (64) follows:
% 23.45/6.58 | (4753) sum(n4, all_0_5_5) = all_0_4_4
% 23.45/6.58 |
% 23.45/6.58 | From (631) and (160) follows:
% 23.45/6.58 | (4754) sum(n4, all_0_7_7) = all_0_2_2
% 23.45/6.58 |
% 23.45/6.58 +-Applying beta-rule and splitting (926), into two cases.
% 23.45/6.58 |-Branch one:
% 23.45/6.58 | (927) all_0_7_7 = n3
% 23.45/6.58 |
% 23.45/6.58 | From (927) and (176) follows:
% 23.45/6.58 | (928) succ(n3) = all_0_5_5
% 23.45/6.58 |
% 23.45/6.58 | From (927) and (59) follows:
% 23.45/6.58 | (929) sum(n3, all_0_1_1) = all_0_0_0
% 23.45/6.58 |
% 23.45/6.58 | From (927) and (4754) follows:
% 23.45/6.58 | (4758) sum(n4, n3) = all_0_2_2
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (219) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 23.45/6.58 | (931) all_0_5_5 = n4
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (89) with n4, n3, all_0_2_2, n7 and discharging atoms sum(n4, n3) = all_0_2_2, sum(n4, n3) = n7, yields:
% 23.45/6.58 | (566) all_0_2_2 = n7
% 23.45/6.58 |
% 23.45/6.58 | From (566) and (187) follows:
% 23.45/6.58 | (568) pred(n7) = all_0_1_1
% 23.45/6.58 |
% 23.45/6.58 | From (931) and (4753) follows:
% 23.45/6.58 | (4762) sum(n4, n4) = all_0_4_4
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (37) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 23.45/6.58 | (571) all_0_1_1 = n6
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (89) with n4, n4, all_0_4_4, n8 and discharging atoms sum(n4, n4) = all_0_4_4, sum(n4, n4) = n8, yields:
% 23.45/6.58 | (567) all_0_4_4 = n8
% 23.45/6.58 |
% 23.45/6.58 | From (567) and (396) follows:
% 23.45/6.58 | (569) pred(n8) = all_0_3_3
% 23.45/6.58 |
% 23.45/6.58 | From (571) and (929) follows:
% 23.45/6.58 | (4766) sum(n3, n6) = all_0_0_0
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (37) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 23.45/6.58 | (570) all_0_3_3 = n7
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (89) with n3, n6, all_0_0_0, n9 and discharging atoms sum(n3, n6) = all_0_0_0, sum(n3, n6) = n9, yields:
% 23.45/6.58 | (506) all_0_0_0 = n9
% 23.45/6.58 |
% 23.45/6.58 | From (570)(506) and (261) follows:
% 23.45/6.58 | (4769) sum(n7, n9) = all_0_6_6
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (89) with n7, n9, all_0_6_6, n0 and discharging atoms sum(n7, n9) = all_0_6_6, sum(n7, n9) = n0, yields:
% 23.45/6.58 | (542) all_0_6_6 = n0
% 23.45/6.58 |
% 23.45/6.58 | Equations (542) can reduce 400 to:
% 23.45/6.58 | (458) $false
% 23.45/6.58 |
% 23.45/6.58 |-The branch is then unsatisfiable
% 23.45/6.58 |-Branch two:
% 23.45/6.58 | (944) ~ (all_0_7_7 = n3)
% 23.45/6.58 | (945) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.45/6.58 |
% 23.45/6.58 +-Applying beta-rule and splitting (945), into two cases.
% 23.45/6.58 |-Branch one:
% 23.45/6.58 | (946) all_0_7_7 = n2
% 23.45/6.58 |
% 23.45/6.58 | From (946) and (176) follows:
% 23.45/6.58 | (947) succ(n2) = all_0_5_5
% 23.45/6.58 |
% 23.45/6.58 | From (946) and (59) follows:
% 23.45/6.58 | (948) sum(n2, all_0_1_1) = all_0_0_0
% 23.45/6.58 |
% 23.45/6.58 | From (946) and (4754) follows:
% 23.45/6.58 | (4777) sum(n4, n2) = all_0_2_2
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (219) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 23.45/6.58 | (950) all_0_5_5 = n3
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (89) with n4, n2, all_0_2_2, n6 and discharging atoms sum(n4, n2) = all_0_2_2, sum(n4, n2) = n6, yields:
% 23.45/6.58 | (583) all_0_2_2 = n6
% 23.45/6.58 |
% 23.45/6.58 | From (583) and (187) follows:
% 23.45/6.58 | (585) pred(n6) = all_0_1_1
% 23.45/6.58 |
% 23.45/6.58 | From (950) and (4753) follows:
% 23.45/6.58 | (4781) sum(n4, n3) = all_0_4_4
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (37) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 23.45/6.58 | (588) all_0_1_1 = n5
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (89) with n4, n3, all_0_4_4, n7 and discharging atoms sum(n4, n3) = all_0_4_4, sum(n4, n3) = n7, yields:
% 23.45/6.58 | (584) all_0_4_4 = n7
% 23.45/6.58 |
% 23.45/6.58 | From (584) and (396) follows:
% 23.45/6.58 | (586) pred(n7) = all_0_3_3
% 23.45/6.58 |
% 23.45/6.58 | From (588) and (948) follows:
% 23.45/6.58 | (4785) sum(n2, n5) = all_0_0_0
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (37) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 23.45/6.58 | (587) all_0_3_3 = n6
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (89) with n2, n5, all_0_0_0, n7 and discharging atoms sum(n2, n5) = all_0_0_0, sum(n2, n5) = n7, yields:
% 23.45/6.58 | (540) all_0_0_0 = n7
% 23.45/6.58 |
% 23.45/6.58 | From (587)(540) and (261) follows:
% 23.45/6.58 | (4788) sum(n6, n7) = all_0_6_6
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (89) with n6, n7, all_0_6_6, n13 and discharging atoms sum(n6, n7) = all_0_6_6, sum(n6, n7) = n13, yields:
% 23.45/6.58 | (998) all_0_6_6 = n13
% 23.45/6.58 |
% 23.45/6.58 | Equations (998) can reduce 130 to:
% 23.45/6.58 | (458) $false
% 23.45/6.58 |
% 23.45/6.58 |-The branch is then unsatisfiable
% 23.45/6.58 |-Branch two:
% 23.45/6.58 | (963) ~ (all_0_7_7 = n2)
% 23.45/6.58 | (964) all_0_7_7 = n1 | all_0_7_7 = n0
% 23.45/6.58 |
% 23.45/6.58 +-Applying beta-rule and splitting (964), into two cases.
% 23.45/6.58 |-Branch one:
% 23.45/6.58 | (965) all_0_7_7 = n1
% 23.45/6.58 |
% 23.45/6.58 | From (965) and (176) follows:
% 23.45/6.58 | (966) succ(n1) = all_0_5_5
% 23.45/6.58 |
% 23.45/6.58 | From (965) and (59) follows:
% 23.45/6.58 | (967) sum(n1, all_0_1_1) = all_0_0_0
% 23.45/6.58 |
% 23.45/6.58 | From (965) and (4754) follows:
% 23.45/6.58 | (4796) sum(n4, n1) = all_0_2_2
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (219) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 23.45/6.58 | (969) all_0_5_5 = n2
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (89) with n4, n1, all_0_2_2, n5 and discharging atoms sum(n4, n1) = all_0_2_2, sum(n4, n1) = n5, yields:
% 23.45/6.58 | (600) all_0_2_2 = n5
% 23.45/6.58 |
% 23.45/6.58 | From (600) and (187) follows:
% 23.45/6.58 | (602) pred(n5) = all_0_1_1
% 23.45/6.58 |
% 23.45/6.58 | From (969) and (4753) follows:
% 23.45/6.58 | (4800) sum(n4, n2) = all_0_4_4
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (37) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 23.45/6.58 | (605) all_0_1_1 = n4
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (89) with n4, n2, all_0_4_4, n6 and discharging atoms sum(n4, n2) = all_0_4_4, sum(n4, n2) = n6, yields:
% 23.45/6.58 | (601) all_0_4_4 = n6
% 23.45/6.58 |
% 23.45/6.58 | From (601) and (396) follows:
% 23.45/6.58 | (603) pred(n6) = all_0_3_3
% 23.45/6.58 |
% 23.45/6.58 | From (605) and (967) follows:
% 23.45/6.58 | (4804) sum(n1, n4) = all_0_0_0
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (37) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 23.45/6.58 | (604) all_0_3_3 = n5
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (89) with n1, n4, all_0_0_0, n5 and discharging atoms sum(n1, n4) = all_0_0_0, sum(n1, n4) = n5, yields:
% 23.45/6.58 | (574) all_0_0_0 = n5
% 23.45/6.58 |
% 23.45/6.58 | From (604)(574) and (261) follows:
% 23.45/6.58 | (4807) sum(n5, n5) = all_0_6_6
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (89) with n5, n5, all_0_6_6, n10 and discharging atoms sum(n5, n5) = all_0_6_6, sum(n5, n5) = n10, yields:
% 23.45/6.58 | (457) all_0_6_6 = n10
% 23.45/6.58 |
% 23.45/6.58 | Equations (457) can reduce 169 to:
% 23.45/6.58 | (458) $false
% 23.45/6.58 |
% 23.45/6.58 |-The branch is then unsatisfiable
% 23.45/6.58 |-Branch two:
% 23.45/6.58 | (982) ~ (all_0_7_7 = n1)
% 23.45/6.58 | (983) all_0_7_7 = n0
% 23.45/6.58 |
% 23.45/6.58 | From (983) and (176) follows:
% 23.45/6.58 | (984) succ(n0) = all_0_5_5
% 23.45/6.58 |
% 23.45/6.58 | From (983) and (59) follows:
% 23.45/6.58 | (985) sum(n0, all_0_1_1) = all_0_0_0
% 23.45/6.58 |
% 23.45/6.58 | From (983) and (4754) follows:
% 23.45/6.58 | (4814) sum(n4, n0) = all_0_2_2
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (219) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 23.45/6.58 | (987) all_0_5_5 = n1
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (89) with n4, n0, all_0_2_2, n4 and discharging atoms sum(n4, n0) = all_0_2_2, sum(n4, n0) = n4, yields:
% 23.45/6.58 | (617) all_0_2_2 = n4
% 23.45/6.58 |
% 23.45/6.58 | From (617) and (187) follows:
% 23.45/6.58 | (619) pred(n4) = all_0_1_1
% 23.45/6.58 |
% 23.45/6.58 | From (987) and (4753) follows:
% 23.45/6.58 | (4818) sum(n4, n1) = all_0_4_4
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (37) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 23.45/6.58 | (622) all_0_1_1 = n3
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (89) with n4, n1, all_0_4_4, n5 and discharging atoms sum(n4, n1) = all_0_4_4, sum(n4, n1) = n5, yields:
% 23.45/6.58 | (618) all_0_4_4 = n5
% 23.45/6.58 |
% 23.45/6.58 | From (618) and (396) follows:
% 23.45/6.58 | (620) pred(n5) = all_0_3_3
% 23.45/6.58 |
% 23.45/6.58 | From (622) and (985) follows:
% 23.45/6.58 | (4822) sum(n0, n3) = all_0_0_0
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (37) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 23.45/6.58 | (621) all_0_3_3 = n4
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (89) with n0, n3, all_0_0_0, n3 and discharging atoms sum(n0, n3) = all_0_0_0, sum(n0, n3) = n3, yields:
% 23.45/6.58 | (608) all_0_0_0 = n3
% 23.45/6.58 |
% 23.45/6.58 | From (621)(608) and (261) follows:
% 23.45/6.58 | (4825) sum(n4, n3) = all_0_6_6
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (89) with n4, n3, all_0_6_6, n7 and discharging atoms sum(n4, n3) = all_0_6_6, sum(n4, n3) = n7, yields:
% 23.45/6.58 | (733) all_0_6_6 = n7
% 23.45/6.58 |
% 23.45/6.58 | Equations (733) can reduce 274 to:
% 23.45/6.58 | (458) $false
% 23.45/6.58 |
% 23.45/6.58 |-The branch is then unsatisfiable
% 23.45/6.58 |-Branch two:
% 23.45/6.58 | (646) ~ (all_0_8_8 = n4)
% 23.45/6.58 | (647) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.45/6.58 |
% 23.45/6.58 +-Applying beta-rule and splitting (926), into two cases.
% 23.45/6.58 |-Branch one:
% 23.45/6.58 | (927) all_0_7_7 = n3
% 23.45/6.58 |
% 23.45/6.58 | From (927) and (176) follows:
% 23.45/6.58 | (928) succ(n3) = all_0_5_5
% 23.45/6.58 |
% 23.45/6.58 | From (927) and (59) follows:
% 23.45/6.58 | (929) sum(n3, all_0_1_1) = all_0_0_0
% 23.45/6.58 |
% 23.45/6.58 | From (927) and (160) follows:
% 23.45/6.58 | (4833) sum(all_0_8_8, n3) = all_0_2_2
% 23.45/6.58 |
% 23.45/6.58 | Instantiating formula (219) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 23.45/6.59 | (931) all_0_5_5 = n4
% 23.45/6.59 |
% 23.45/6.59 | From (931) and (64) follows:
% 23.45/6.59 | (4835) sum(all_0_8_8, n4) = all_0_4_4
% 23.45/6.59 |
% 23.45/6.59 +-Applying beta-rule and splitting (647), into two cases.
% 23.45/6.59 |-Branch one:
% 23.45/6.59 | (648) all_0_8_8 = n3
% 23.45/6.59 |
% 23.45/6.59 | From (648) and (4835) follows:
% 23.45/6.59 | (4837) sum(n3, n4) = all_0_4_4
% 23.45/6.59 |
% 23.45/6.59 | From (648) and (4833) follows:
% 23.45/6.59 | (4838) sum(n3, n3) = all_0_2_2
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (89) with n3, n4, all_0_4_4, n7 and discharging atoms sum(n3, n4) = all_0_4_4, sum(n3, n4) = n7, yields:
% 23.45/6.59 | (584) all_0_4_4 = n7
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (89) with n3, n3, all_0_2_2, n6 and discharging atoms sum(n3, n3) = all_0_2_2, sum(n3, n3) = n6, yields:
% 23.45/6.59 | (583) all_0_2_2 = n6
% 23.45/6.59 |
% 23.45/6.59 | From (583) and (187) follows:
% 23.45/6.59 | (585) pred(n6) = all_0_1_1
% 23.45/6.59 |
% 23.45/6.59 | From (584) and (396) follows:
% 23.45/6.59 | (586) pred(n7) = all_0_3_3
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (37) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 23.45/6.59 | (587) all_0_3_3 = n6
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (37) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 23.45/6.59 | (588) all_0_1_1 = n5
% 23.45/6.59 |
% 23.45/6.59 | From (587) and (261) follows:
% 23.45/6.59 | (589) sum(n6, all_0_0_0) = all_0_6_6
% 23.45/6.59 |
% 23.45/6.59 | From (588) and (929) follows:
% 23.45/6.59 | (4846) sum(n3, n5) = all_0_0_0
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (89) with n3, n5, all_0_0_0, n8 and discharging atoms sum(n3, n5) = all_0_0_0, sum(n3, n5) = n8, yields:
% 23.45/6.59 | (523) all_0_0_0 = n8
% 23.45/6.59 |
% 23.45/6.59 | From (523) and (589) follows:
% 23.45/6.59 | (4848) sum(n6, n8) = all_0_6_6
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (89) with n6, n8, all_0_6_6, n14 and discharging atoms sum(n6, n8) = all_0_6_6, sum(n6, n8) = n14, yields:
% 23.45/6.59 | (559) all_0_6_6 = n14
% 23.45/6.59 |
% 23.45/6.59 | Equations (559) can reduce 314 to:
% 23.45/6.59 | (458) $false
% 23.45/6.59 |
% 23.45/6.59 |-The branch is then unsatisfiable
% 23.45/6.59 |-Branch two:
% 23.45/6.59 | (663) ~ (all_0_8_8 = n3)
% 23.45/6.59 | (664) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.45/6.59 |
% 23.45/6.59 +-Applying beta-rule and splitting (664), into two cases.
% 23.45/6.59 |-Branch one:
% 23.45/6.59 | (665) all_0_8_8 = n2
% 23.45/6.59 |
% 23.45/6.59 | From (665) and (4835) follows:
% 23.45/6.59 | (4854) sum(n2, n4) = all_0_4_4
% 23.45/6.59 |
% 23.45/6.59 | From (665) and (4833) follows:
% 23.45/6.59 | (4855) sum(n2, n3) = all_0_2_2
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (89) with n2, n4, all_0_4_4, n6 and discharging atoms sum(n2, n4) = all_0_4_4, sum(n2, n4) = n6, yields:
% 23.45/6.59 | (601) all_0_4_4 = n6
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (89) with n2, n3, all_0_2_2, n5 and discharging atoms sum(n2, n3) = all_0_2_2, sum(n2, n3) = n5, yields:
% 23.45/6.59 | (600) all_0_2_2 = n5
% 23.45/6.59 |
% 23.45/6.59 | From (600) and (187) follows:
% 23.45/6.59 | (602) pred(n5) = all_0_1_1
% 23.45/6.59 |
% 23.45/6.59 | From (601) and (396) follows:
% 23.45/6.59 | (603) pred(n6) = all_0_3_3
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (37) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 23.45/6.59 | (604) all_0_3_3 = n5
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (37) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 23.45/6.59 | (605) all_0_1_1 = n4
% 23.45/6.59 |
% 23.45/6.59 | From (604) and (261) follows:
% 23.45/6.59 | (606) sum(n5, all_0_0_0) = all_0_6_6
% 23.45/6.59 |
% 23.45/6.59 | From (605) and (929) follows:
% 23.45/6.59 | (4863) sum(n3, n4) = all_0_0_0
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (89) with n3, n4, all_0_0_0, n7 and discharging atoms sum(n3, n4) = all_0_0_0, sum(n3, n4) = n7, yields:
% 23.45/6.59 | (540) all_0_0_0 = n7
% 23.45/6.59 |
% 23.45/6.59 | From (540) and (606) follows:
% 23.45/6.59 | (4865) sum(n5, n7) = all_0_6_6
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (89) with n5, n7, all_0_6_6, n12 and discharging atoms sum(n5, n7) = all_0_6_6, sum(n5, n7) = n12, yields:
% 23.45/6.59 | (576) all_0_6_6 = n12
% 23.45/6.59 |
% 23.45/6.59 | Equations (576) can reduce 42 to:
% 23.45/6.59 | (458) $false
% 23.45/6.59 |
% 23.45/6.59 |-The branch is then unsatisfiable
% 23.45/6.59 |-Branch two:
% 23.45/6.59 | (680) ~ (all_0_8_8 = n2)
% 23.45/6.59 | (681) all_0_8_8 = n1 | all_0_8_8 = n0
% 23.45/6.59 |
% 23.45/6.59 +-Applying beta-rule and splitting (681), into two cases.
% 23.45/6.59 |-Branch one:
% 23.45/6.59 | (682) all_0_8_8 = n1
% 23.45/6.59 |
% 23.45/6.59 | From (682) and (4835) follows:
% 23.45/6.59 | (4871) sum(n1, n4) = all_0_4_4
% 23.45/6.59 |
% 23.45/6.59 | From (682) and (4833) follows:
% 23.45/6.59 | (4872) sum(n1, n3) = all_0_2_2
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (89) with n1, n4, all_0_4_4, n5 and discharging atoms sum(n1, n4) = all_0_4_4, sum(n1, n4) = n5, yields:
% 23.45/6.59 | (618) all_0_4_4 = n5
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (89) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 23.45/6.59 | (617) all_0_2_2 = n4
% 23.45/6.59 |
% 23.45/6.59 | From (617) and (187) follows:
% 23.45/6.59 | (619) pred(n4) = all_0_1_1
% 23.45/6.59 |
% 23.45/6.59 | From (618) and (396) follows:
% 23.45/6.59 | (620) pred(n5) = all_0_3_3
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (37) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 23.45/6.59 | (621) all_0_3_3 = n4
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (37) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 23.45/6.59 | (622) all_0_1_1 = n3
% 23.45/6.59 |
% 23.45/6.59 | From (621) and (261) follows:
% 23.45/6.59 | (623) sum(n4, all_0_0_0) = all_0_6_6
% 23.45/6.59 |
% 23.45/6.59 | From (622) and (929) follows:
% 23.45/6.59 | (4880) sum(n3, n3) = all_0_0_0
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (89) with n3, n3, all_0_0_0, n6 and discharging atoms sum(n3, n3) = all_0_0_0, sum(n3, n3) = n6, yields:
% 23.45/6.59 | (557) all_0_0_0 = n6
% 23.45/6.59 |
% 23.45/6.59 | From (557) and (623) follows:
% 23.45/6.59 | (4882) sum(n4, n6) = all_0_6_6
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (89) with n4, n6, all_0_6_6, n10 and discharging atoms sum(n4, n6) = all_0_6_6, sum(n4, n6) = n10, yields:
% 23.45/6.59 | (457) all_0_6_6 = n10
% 23.45/6.59 |
% 23.45/6.59 | Equations (457) can reduce 169 to:
% 23.45/6.59 | (458) $false
% 23.45/6.59 |
% 23.45/6.59 |-The branch is then unsatisfiable
% 23.45/6.59 |-Branch two:
% 23.45/6.59 | (697) ~ (all_0_8_8 = n1)
% 23.45/6.59 | (698) all_0_8_8 = n0
% 23.45/6.59 |
% 23.45/6.59 | From (698) and (4835) follows:
% 23.45/6.59 | (4887) sum(n0, n4) = all_0_4_4
% 23.45/6.59 |
% 23.45/6.59 | From (698) and (4833) follows:
% 23.45/6.59 | (4888) sum(n0, n3) = all_0_2_2
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (89) with n0, n4, all_0_4_4, n4 and discharging atoms sum(n0, n4) = all_0_4_4, sum(n0, n4) = n4, yields:
% 23.45/6.59 | (635) all_0_4_4 = n4
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (89) with n0, n3, all_0_2_2, n3 and discharging atoms sum(n0, n3) = all_0_2_2, sum(n0, n3) = n3, yields:
% 23.45/6.59 | (634) all_0_2_2 = n3
% 23.45/6.59 |
% 23.45/6.59 | From (634) and (187) follows:
% 23.45/6.59 | (636) pred(n3) = all_0_1_1
% 23.45/6.59 |
% 23.45/6.59 | From (635) and (396) follows:
% 23.45/6.59 | (637) pred(n4) = all_0_3_3
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (37) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 23.45/6.59 | (638) all_0_3_3 = n3
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (37) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 23.45/6.59 | (639) all_0_1_1 = n2
% 23.45/6.59 |
% 23.45/6.59 | From (638) and (261) follows:
% 23.45/6.59 | (640) sum(n3, all_0_0_0) = all_0_6_6
% 23.45/6.59 |
% 23.45/6.59 | From (639) and (929) follows:
% 23.45/6.59 | (4896) sum(n3, n2) = all_0_0_0
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (89) with n3, n2, all_0_0_0, n5 and discharging atoms sum(n3, n2) = all_0_0_0, sum(n3, n2) = n5, yields:
% 23.45/6.59 | (574) all_0_0_0 = n5
% 23.45/6.59 |
% 23.45/6.59 | From (574) and (640) follows:
% 23.45/6.59 | (4898) sum(n3, n5) = all_0_6_6
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (89) with n3, n5, all_0_6_6, n8 and discharging atoms sum(n3, n5) = all_0_6_6, sum(n3, n5) = n8, yields:
% 23.45/6.59 | (474) all_0_6_6 = n8
% 23.45/6.59 |
% 23.45/6.59 | Equations (474) can reduce 86 to:
% 23.45/6.59 | (458) $false
% 23.45/6.59 |
% 23.45/6.59 |-The branch is then unsatisfiable
% 23.45/6.59 |-Branch two:
% 23.45/6.59 | (944) ~ (all_0_7_7 = n3)
% 23.45/6.59 | (945) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 23.45/6.59 |
% 23.45/6.59 +-Applying beta-rule and splitting (647), into two cases.
% 23.45/6.59 |-Branch one:
% 23.45/6.59 | (648) all_0_8_8 = n3
% 23.45/6.59 |
% 23.45/6.59 | From (648) and (64) follows:
% 23.45/6.59 | (4904) sum(n3, all_0_5_5) = all_0_4_4
% 23.45/6.59 |
% 23.45/6.59 | From (648) and (160) follows:
% 23.45/6.59 | (4905) sum(n3, all_0_7_7) = all_0_2_2
% 23.45/6.59 |
% 23.45/6.59 +-Applying beta-rule and splitting (945), into two cases.
% 23.45/6.59 |-Branch one:
% 23.45/6.59 | (946) all_0_7_7 = n2
% 23.45/6.59 |
% 23.45/6.59 | From (946) and (176) follows:
% 23.45/6.59 | (947) succ(n2) = all_0_5_5
% 23.45/6.59 |
% 23.45/6.59 | From (946) and (59) follows:
% 23.45/6.59 | (948) sum(n2, all_0_1_1) = all_0_0_0
% 23.45/6.59 |
% 23.45/6.59 | From (946) and (4905) follows:
% 23.45/6.59 | (4909) sum(n3, n2) = all_0_2_2
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (219) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 23.45/6.59 | (950) all_0_5_5 = n3
% 23.45/6.59 |
% 23.45/6.59 | Instantiating formula (89) with n3, n2, all_0_2_2, n5 and discharging atoms sum(n3, n2) = all_0_2_2, sum(n3, n2) = n5, yields:
% 23.45/6.59 | (600) all_0_2_2 = n5
% 23.45/6.59 |
% 23.45/6.59 | From (600) and (187) follows:
% 23.45/6.60 | (602) pred(n5) = all_0_1_1
% 23.45/6.60 |
% 23.45/6.60 | From (950) and (4904) follows:
% 23.45/6.60 | (4913) sum(n3, n3) = all_0_4_4
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (37) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 23.45/6.60 | (605) all_0_1_1 = n4
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (89) with n3, n3, all_0_4_4, n6 and discharging atoms sum(n3, n3) = all_0_4_4, sum(n3, n3) = n6, yields:
% 23.45/6.60 | (601) all_0_4_4 = n6
% 23.45/6.60 |
% 23.45/6.60 | From (601) and (396) follows:
% 23.45/6.60 | (603) pred(n6) = all_0_3_3
% 23.45/6.60 |
% 23.45/6.60 | From (605) and (948) follows:
% 23.45/6.60 | (4917) sum(n2, n4) = all_0_0_0
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (37) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 23.45/6.60 | (604) all_0_3_3 = n5
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (89) with n2, n4, all_0_0_0, n6 and discharging atoms sum(n2, n4) = all_0_0_0, sum(n2, n4) = n6, yields:
% 23.45/6.60 | (557) all_0_0_0 = n6
% 23.45/6.60 |
% 23.45/6.60 | From (604)(557) and (261) follows:
% 23.45/6.60 | (4920) sum(n5, n6) = all_0_6_6
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (89) with n5, n6, all_0_6_6, n11 and discharging atoms sum(n5, n6) = all_0_6_6, sum(n5, n6) = n11, yields:
% 23.45/6.60 | (809) all_0_6_6 = n11
% 23.45/6.60 |
% 23.45/6.60 | Equations (809) can reduce 70 to:
% 23.45/6.60 | (458) $false
% 23.45/6.60 |
% 23.45/6.60 |-The branch is then unsatisfiable
% 23.45/6.60 |-Branch two:
% 23.45/6.60 | (963) ~ (all_0_7_7 = n2)
% 23.45/6.60 | (964) all_0_7_7 = n1 | all_0_7_7 = n0
% 23.45/6.60 |
% 23.45/6.60 +-Applying beta-rule and splitting (964), into two cases.
% 23.45/6.60 |-Branch one:
% 23.45/6.60 | (965) all_0_7_7 = n1
% 23.45/6.60 |
% 23.45/6.60 | From (965) and (176) follows:
% 23.45/6.60 | (966) succ(n1) = all_0_5_5
% 23.45/6.60 |
% 23.45/6.60 | From (965) and (59) follows:
% 23.45/6.60 | (967) sum(n1, all_0_1_1) = all_0_0_0
% 23.45/6.60 |
% 23.45/6.60 | From (965) and (4905) follows:
% 23.45/6.60 | (4928) sum(n3, n1) = all_0_2_2
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (219) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 23.45/6.60 | (969) all_0_5_5 = n2
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (89) with n3, n1, all_0_2_2, n4 and discharging atoms sum(n3, n1) = all_0_2_2, sum(n3, n1) = n4, yields:
% 23.45/6.60 | (617) all_0_2_2 = n4
% 23.45/6.60 |
% 23.45/6.60 | From (617) and (187) follows:
% 23.45/6.60 | (619) pred(n4) = all_0_1_1
% 23.45/6.60 |
% 23.45/6.60 | From (969) and (4904) follows:
% 23.45/6.60 | (4932) sum(n3, n2) = all_0_4_4
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (37) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 23.45/6.60 | (622) all_0_1_1 = n3
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (89) with n3, n2, all_0_4_4, n5 and discharging atoms sum(n3, n2) = all_0_4_4, sum(n3, n2) = n5, yields:
% 23.45/6.60 | (618) all_0_4_4 = n5
% 23.45/6.60 |
% 23.45/6.60 | From (618) and (396) follows:
% 23.45/6.60 | (620) pred(n5) = all_0_3_3
% 23.45/6.60 |
% 23.45/6.60 | From (622) and (967) follows:
% 23.45/6.60 | (4936) sum(n1, n3) = all_0_0_0
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (37) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 23.45/6.60 | (621) all_0_3_3 = n4
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (89) with n1, n3, all_0_0_0, n4 and discharging atoms sum(n1, n3) = all_0_0_0, sum(n1, n3) = n4, yields:
% 23.45/6.60 | (591) all_0_0_0 = n4
% 23.45/6.60 |
% 23.45/6.60 | From (621)(591) and (261) follows:
% 23.45/6.60 | (4939) sum(n4, n4) = all_0_6_6
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (89) with n4, n4, all_0_6_6, n8 and discharging atoms sum(n4, n4) = all_0_6_6, sum(n4, n4) = n8, yields:
% 23.45/6.60 | (474) all_0_6_6 = n8
% 23.45/6.60 |
% 23.45/6.60 | Equations (474) can reduce 86 to:
% 23.45/6.60 | (458) $false
% 23.45/6.60 |
% 23.45/6.60 |-The branch is then unsatisfiable
% 23.45/6.60 |-Branch two:
% 23.45/6.60 | (982) ~ (all_0_7_7 = n1)
% 23.45/6.60 | (983) all_0_7_7 = n0
% 23.45/6.60 |
% 23.45/6.60 | From (983) and (176) follows:
% 23.45/6.60 | (984) succ(n0) = all_0_5_5
% 23.45/6.60 |
% 23.45/6.60 | From (983) and (59) follows:
% 23.45/6.60 | (985) sum(n0, all_0_1_1) = all_0_0_0
% 23.45/6.60 |
% 23.45/6.60 | From (983) and (4905) follows:
% 23.45/6.60 | (4946) sum(n3, n0) = all_0_2_2
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (219) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 23.45/6.60 | (987) all_0_5_5 = n1
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (89) with n3, n0, all_0_2_2, n3 and discharging atoms sum(n3, n0) = all_0_2_2, sum(n3, n0) = n3, yields:
% 23.45/6.60 | (634) all_0_2_2 = n3
% 23.45/6.60 |
% 23.45/6.60 | From (634) and (187) follows:
% 23.45/6.60 | (636) pred(n3) = all_0_1_1
% 23.45/6.60 |
% 23.45/6.60 | From (987) and (4904) follows:
% 23.45/6.60 | (4950) sum(n3, n1) = all_0_4_4
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (37) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 23.45/6.60 | (639) all_0_1_1 = n2
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (89) with n3, n1, all_0_4_4, n4 and discharging atoms sum(n3, n1) = all_0_4_4, sum(n3, n1) = n4, yields:
% 23.45/6.60 | (635) all_0_4_4 = n4
% 23.45/6.60 |
% 23.45/6.60 | From (635) and (396) follows:
% 23.45/6.60 | (637) pred(n4) = all_0_3_3
% 23.45/6.60 |
% 23.45/6.60 | From (639) and (985) follows:
% 23.45/6.60 | (4954) sum(n0, n2) = all_0_0_0
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (37) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 23.45/6.60 | (638) all_0_3_3 = n3
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (89) with n0, n2, all_0_0_0, n2 and discharging atoms sum(n0, n2) = all_0_0_0, sum(n0, n2) = n2, yields:
% 23.45/6.60 | (625) all_0_0_0 = n2
% 23.45/6.60 |
% 23.45/6.60 | From (638)(625) and (261) follows:
% 23.45/6.60 | (4957) sum(n3, n2) = all_0_6_6
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (89) with n3, n2, all_0_6_6, n5 and discharging atoms sum(n3, n2) = all_0_6_6, sum(n3, n2) = n5, yields:
% 23.45/6.60 | (847) all_0_6_6 = n5
% 23.45/6.60 |
% 23.45/6.60 | Equations (847) can reduce 409 to:
% 23.45/6.60 | (458) $false
% 23.45/6.60 |
% 23.45/6.60 |-The branch is then unsatisfiable
% 23.45/6.60 |-Branch two:
% 23.45/6.60 | (663) ~ (all_0_8_8 = n3)
% 23.45/6.60 | (664) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 23.45/6.60 |
% 23.45/6.60 +-Applying beta-rule and splitting (945), into two cases.
% 23.45/6.60 |-Branch one:
% 23.45/6.60 | (946) all_0_7_7 = n2
% 23.45/6.60 |
% 23.45/6.60 | From (946) and (176) follows:
% 23.45/6.60 | (947) succ(n2) = all_0_5_5
% 23.45/6.60 |
% 23.45/6.60 | From (946) and (59) follows:
% 23.45/6.60 | (948) sum(n2, all_0_1_1) = all_0_0_0
% 23.45/6.60 |
% 23.45/6.60 | From (946) and (160) follows:
% 23.45/6.60 | (4965) sum(all_0_8_8, n2) = all_0_2_2
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (219) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 23.45/6.60 | (950) all_0_5_5 = n3
% 23.45/6.60 |
% 23.45/6.60 | From (950) and (64) follows:
% 23.45/6.60 | (4967) sum(all_0_8_8, n3) = all_0_4_4
% 23.45/6.60 |
% 23.45/6.60 +-Applying beta-rule and splitting (664), into two cases.
% 23.45/6.60 |-Branch one:
% 23.45/6.60 | (665) all_0_8_8 = n2
% 23.45/6.60 |
% 23.45/6.60 | From (665) and (4967) follows:
% 23.45/6.60 | (4969) sum(n2, n3) = all_0_4_4
% 23.45/6.60 |
% 23.45/6.60 | From (665) and (4965) follows:
% 23.45/6.60 | (4970) sum(n2, n2) = all_0_2_2
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (89) with n2, n3, all_0_4_4, n5 and discharging atoms sum(n2, n3) = all_0_4_4, sum(n2, n3) = n5, yields:
% 23.45/6.60 | (618) all_0_4_4 = n5
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (89) with n2, n2, all_0_2_2, n4 and discharging atoms sum(n2, n2) = all_0_2_2, sum(n2, n2) = n4, yields:
% 23.45/6.60 | (617) all_0_2_2 = n4
% 23.45/6.60 |
% 23.45/6.60 | From (617) and (187) follows:
% 23.45/6.60 | (619) pred(n4) = all_0_1_1
% 23.45/6.60 |
% 23.45/6.60 | From (618) and (396) follows:
% 23.45/6.60 | (620) pred(n5) = all_0_3_3
% 23.45/6.60 |
% 23.45/6.60 | From (618) and (4969) follows:
% 23.45/6.60 | (2) sum(n2, n3) = n5
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (37) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 23.45/6.60 | (621) all_0_3_3 = n4
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (37) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 23.45/6.60 | (622) all_0_1_1 = n3
% 23.45/6.60 |
% 23.45/6.60 | From (621) and (261) follows:
% 23.45/6.60 | (623) sum(n4, all_0_0_0) = all_0_6_6
% 23.45/6.60 |
% 23.45/6.60 | From (622) and (948) follows:
% 23.45/6.60 | (4979) sum(n2, n3) = all_0_0_0
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (89) with n2, n3, all_0_0_0, n5 and discharging atoms sum(n2, n3) = all_0_0_0, sum(n2, n3) = n5, yields:
% 23.45/6.60 | (574) all_0_0_0 = n5
% 23.45/6.60 |
% 23.45/6.60 | From (574) and (623) follows:
% 23.45/6.60 | (4981) sum(n4, n5) = all_0_6_6
% 23.45/6.60 |
% 23.45/6.60 | Instantiating formula (89) with n4, n5, all_0_6_6, n9 and discharging atoms sum(n4, n5) = all_0_6_6, sum(n4, n5) = n9, yields:
% 23.45/6.60 | (923) all_0_6_6 = n9
% 23.45/6.60 |
% 23.45/6.60 | Equations (923) can reduce 404 to:
% 23.45/6.60 | (458) $false
% 23.45/6.60 |
% 23.45/6.60 |-The branch is then unsatisfiable
% 23.45/6.60 |-Branch two:
% 23.45/6.60 | (680) ~ (all_0_8_8 = n2)
% 23.45/6.60 | (681) all_0_8_8 = n1 | all_0_8_8 = n0
% 23.45/6.60 |
% 23.45/6.60 +-Applying beta-rule and splitting (681), into two cases.
% 23.45/6.60 |-Branch one:
% 23.45/6.60 | (682) all_0_8_8 = n1
% 23.45/6.60 |
% 23.45/6.60 | From (682) and (4967) follows:
% 23.45/6.60 | (4987) sum(n1, n3) = all_0_4_4
% 23.45/6.60 |
% 23.45/6.60 | From (682) and (4965) follows:
% 23.45/6.61 | (4988) sum(n1, n2) = all_0_2_2
% 23.45/6.61 |
% 23.45/6.61 | Instantiating formula (89) with n1, n3, all_0_4_4, n4 and discharging atoms sum(n1, n3) = all_0_4_4, sum(n1, n3) = n4, yields:
% 23.45/6.61 | (635) all_0_4_4 = n4
% 23.45/6.61 |
% 23.45/6.61 | Instantiating formula (89) with n1, n2, all_0_2_2, n3 and discharging atoms sum(n1, n2) = all_0_2_2, sum(n1, n2) = n3, yields:
% 23.45/6.61 | (634) all_0_2_2 = n3
% 23.45/6.61 |
% 23.45/6.61 | From (634) and (187) follows:
% 23.45/6.61 | (636) pred(n3) = all_0_1_1
% 23.45/6.61 |
% 23.45/6.61 | From (635) and (396) follows:
% 23.45/6.61 | (637) pred(n4) = all_0_3_3
% 23.45/6.61 |
% 23.45/6.61 | Instantiating formula (37) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 23.45/6.61 | (638) all_0_3_3 = n3
% 23.45/6.61 |
% 23.45/6.61 | Instantiating formula (37) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 23.45/6.61 | (639) all_0_1_1 = n2
% 23.45/6.61 |
% 23.45/6.61 | From (638) and (261) follows:
% 23.45/6.61 | (640) sum(n3, all_0_0_0) = all_0_6_6
% 23.45/6.61 |
% 23.45/6.61 | From (639) and (948) follows:
% 23.45/6.61 | (4996) sum(n2, n2) = all_0_0_0
% 23.45/6.61 |
% 23.45/6.61 | Instantiating formula (89) with n2, n2, all_0_0_0, n4 and discharging atoms sum(n2, n2) = all_0_0_0, sum(n2, n2) = n4, yields:
% 23.45/6.61 | (591) all_0_0_0 = n4
% 23.45/6.61 |
% 23.45/6.61 | From (591) and (640) follows:
% 23.45/6.61 | (4998) sum(n3, n4) = all_0_6_6
% 23.45/6.61 |
% 23.45/6.61 | Instantiating formula (89) with n3, n4, all_0_6_6, n7 and discharging atoms sum(n3, n4) = all_0_6_6, sum(n3, n4) = n7, yields:
% 23.45/6.61 | (733) all_0_6_6 = n7
% 23.45/6.61 |
% 23.45/6.61 | Equations (733) can reduce 274 to:
% 23.45/6.61 | (458) $false
% 23.45/6.61 |
% 23.45/6.61 |-The branch is then unsatisfiable
% 23.45/6.61 |-Branch two:
% 23.45/6.61 | (697) ~ (all_0_8_8 = n1)
% 23.45/6.61 | (698) all_0_8_8 = n0
% 23.45/6.61 |
% 23.45/6.61 | From (698) and (4967) follows:
% 23.45/6.61 | (5003) sum(n0, n3) = all_0_4_4
% 23.45/6.61 |
% 23.45/6.61 | From (698) and (4965) follows:
% 23.69/6.61 | (5004) sum(n0, n2) = all_0_2_2
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (89) with n0, n3, all_0_4_4, n3 and discharging atoms sum(n0, n3) = all_0_4_4, sum(n0, n3) = n3, yields:
% 23.69/6.61 | (652) all_0_4_4 = n3
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (89) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 23.69/6.61 | (651) all_0_2_2 = n2
% 23.69/6.61 |
% 23.69/6.61 | From (651) and (187) follows:
% 23.69/6.61 | (653) pred(n2) = all_0_1_1
% 23.69/6.61 |
% 23.69/6.61 | From (652) and (396) follows:
% 23.69/6.61 | (654) pred(n3) = all_0_3_3
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (37) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 23.69/6.61 | (655) all_0_3_3 = n2
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (37) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 23.69/6.61 | (656) all_0_1_1 = n1
% 23.69/6.61 |
% 23.69/6.61 | From (655) and (261) follows:
% 23.69/6.61 | (657) sum(n2, all_0_0_0) = all_0_6_6
% 23.69/6.61 |
% 23.69/6.61 | From (656) and (948) follows:
% 23.69/6.61 | (5012) sum(n2, n1) = all_0_0_0
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (89) with n2, n1, all_0_0_0, n3 and discharging atoms sum(n2, n1) = all_0_0_0, sum(n2, n1) = n3, yields:
% 23.69/6.61 | (608) all_0_0_0 = n3
% 23.69/6.61 |
% 23.69/6.61 | From (608) and (657) follows:
% 23.69/6.61 | (5014) sum(n2, n3) = all_0_6_6
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (89) with n2, n3, all_0_6_6, n5 and discharging atoms sum(n2, n3) = all_0_6_6, sum(n2, n3) = n5, yields:
% 23.69/6.61 | (847) all_0_6_6 = n5
% 23.69/6.61 |
% 23.69/6.61 | Equations (847) can reduce 409 to:
% 23.69/6.61 | (458) $false
% 23.69/6.61 |
% 23.69/6.61 |-The branch is then unsatisfiable
% 23.69/6.61 |-Branch two:
% 23.69/6.61 | (963) ~ (all_0_7_7 = n2)
% 23.69/6.61 | (964) all_0_7_7 = n1 | all_0_7_7 = n0
% 23.69/6.61 |
% 23.69/6.61 +-Applying beta-rule and splitting (664), into two cases.
% 23.69/6.61 |-Branch one:
% 23.69/6.61 | (665) all_0_8_8 = n2
% 23.69/6.61 |
% 23.69/6.61 | From (665) and (64) follows:
% 23.69/6.61 | (5020) sum(n2, all_0_5_5) = all_0_4_4
% 23.69/6.61 |
% 23.69/6.61 | From (665) and (160) follows:
% 23.69/6.61 | (5021) sum(n2, all_0_7_7) = all_0_2_2
% 23.69/6.61 |
% 23.69/6.61 +-Applying beta-rule and splitting (964), into two cases.
% 23.69/6.61 |-Branch one:
% 23.69/6.61 | (965) all_0_7_7 = n1
% 23.69/6.61 |
% 23.69/6.61 | From (965) and (176) follows:
% 23.69/6.61 | (966) succ(n1) = all_0_5_5
% 23.69/6.61 |
% 23.69/6.61 | From (965) and (59) follows:
% 23.69/6.61 | (967) sum(n1, all_0_1_1) = all_0_0_0
% 23.69/6.61 |
% 23.69/6.61 | From (965) and (5021) follows:
% 23.69/6.61 | (5025) sum(n2, n1) = all_0_2_2
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (219) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 23.69/6.61 | (969) all_0_5_5 = n2
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (89) with n2, n1, all_0_2_2, n3 and discharging atoms sum(n2, n1) = all_0_2_2, sum(n2, n1) = n3, yields:
% 23.69/6.61 | (634) all_0_2_2 = n3
% 23.69/6.61 |
% 23.69/6.61 | From (634) and (187) follows:
% 23.69/6.61 | (636) pred(n3) = all_0_1_1
% 23.69/6.61 |
% 23.69/6.61 | From (969) and (5020) follows:
% 23.69/6.61 | (5029) sum(n2, n2) = all_0_4_4
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (37) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 23.69/6.61 | (639) all_0_1_1 = n2
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (89) with n2, n2, all_0_4_4, n4 and discharging atoms sum(n2, n2) = all_0_4_4, sum(n2, n2) = n4, yields:
% 23.69/6.61 | (635) all_0_4_4 = n4
% 23.69/6.61 |
% 23.69/6.61 | From (635) and (396) follows:
% 23.69/6.61 | (637) pred(n4) = all_0_3_3
% 23.69/6.61 |
% 23.69/6.61 | From (639) and (967) follows:
% 23.69/6.61 | (5033) sum(n1, n2) = all_0_0_0
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (37) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 23.69/6.61 | (638) all_0_3_3 = n3
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (89) with n1, n2, all_0_0_0, n3 and discharging atoms sum(n1, n2) = all_0_0_0, sum(n1, n2) = n3, yields:
% 23.69/6.61 | (608) all_0_0_0 = n3
% 23.69/6.61 |
% 23.69/6.61 | From (638)(608) and (261) follows:
% 23.69/6.61 | (5036) sum(n3, n3) = all_0_6_6
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (89) with n3, n3, all_0_6_6, n6 and discharging atoms sum(n3, n3) = all_0_6_6, sum(n3, n3) = n6, yields:
% 23.69/6.61 | (491) all_0_6_6 = n6
% 23.69/6.61 |
% 23.69/6.61 | Equations (491) can reduce 418 to:
% 23.69/6.61 | (458) $false
% 23.69/6.61 |
% 23.69/6.61 |-The branch is then unsatisfiable
% 23.69/6.61 |-Branch two:
% 23.69/6.61 | (982) ~ (all_0_7_7 = n1)
% 23.69/6.61 | (983) all_0_7_7 = n0
% 23.69/6.61 |
% 23.69/6.61 | From (983) and (176) follows:
% 23.69/6.61 | (984) succ(n0) = all_0_5_5
% 23.69/6.61 |
% 23.69/6.61 | From (983) and (59) follows:
% 23.69/6.61 | (985) sum(n0, all_0_1_1) = all_0_0_0
% 23.69/6.61 |
% 23.69/6.61 | From (983) and (5021) follows:
% 23.69/6.61 | (5043) sum(n2, n0) = all_0_2_2
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (219) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 23.69/6.61 | (987) all_0_5_5 = n1
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (89) with n2, n0, all_0_2_2, n2 and discharging atoms sum(n2, n0) = all_0_2_2, sum(n2, n0) = n2, yields:
% 23.69/6.61 | (651) all_0_2_2 = n2
% 23.69/6.61 |
% 23.69/6.61 | From (651) and (187) follows:
% 23.69/6.61 | (653) pred(n2) = all_0_1_1
% 23.69/6.61 |
% 23.69/6.61 | From (987) and (5020) follows:
% 23.69/6.61 | (5047) sum(n2, n1) = all_0_4_4
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (37) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 23.69/6.61 | (656) all_0_1_1 = n1
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (89) with n2, n1, all_0_4_4, n3 and discharging atoms sum(n2, n1) = all_0_4_4, sum(n2, n1) = n3, yields:
% 23.69/6.61 | (652) all_0_4_4 = n3
% 23.69/6.61 |
% 23.69/6.61 | From (652) and (396) follows:
% 23.69/6.61 | (654) pred(n3) = all_0_3_3
% 23.69/6.61 |
% 23.69/6.61 | From (652) and (5047) follows:
% 23.69/6.61 | (62) sum(n2, n1) = n3
% 23.69/6.61 |
% 23.69/6.61 | From (656) and (985) follows:
% 23.69/6.61 | (5052) sum(n0, n1) = all_0_0_0
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (37) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 23.69/6.61 | (655) all_0_3_3 = n2
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (89) with n0, n1, all_0_0_0, n1 and discharging atoms sum(n0, n1) = all_0_0_0, sum(n0, n1) = n1, yields:
% 23.69/6.61 | (642) all_0_0_0 = n1
% 23.69/6.61 |
% 23.69/6.61 | From (655)(642) and (261) follows:
% 23.69/6.61 | (5055) sum(n2, n1) = all_0_6_6
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (89) with n2, n1, all_0_6_6, n3 and discharging atoms sum(n2, n1) = all_0_6_6, sum(n2, n1) = n3, yields:
% 23.69/6.61 | (961) all_0_6_6 = n3
% 23.69/6.61 |
% 23.69/6.61 | Equations (961) can reduce 245 to:
% 23.69/6.61 | (458) $false
% 23.69/6.61 |
% 23.69/6.61 |-The branch is then unsatisfiable
% 23.69/6.61 |-Branch two:
% 23.69/6.61 | (680) ~ (all_0_8_8 = n2)
% 23.69/6.61 | (681) all_0_8_8 = n1 | all_0_8_8 = n0
% 23.69/6.61 |
% 23.69/6.61 +-Applying beta-rule and splitting (964), into two cases.
% 23.69/6.61 |-Branch one:
% 23.69/6.61 | (965) all_0_7_7 = n1
% 23.69/6.61 |
% 23.69/6.61 | From (965) and (176) follows:
% 23.69/6.61 | (966) succ(n1) = all_0_5_5
% 23.69/6.61 |
% 23.69/6.61 | From (965) and (59) follows:
% 23.69/6.61 | (967) sum(n1, all_0_1_1) = all_0_0_0
% 23.69/6.61 |
% 23.69/6.61 | From (965) and (160) follows:
% 23.69/6.61 | (5063) sum(all_0_8_8, n1) = all_0_2_2
% 23.69/6.61 |
% 23.69/6.61 | Instantiating formula (219) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 23.69/6.61 | (969) all_0_5_5 = n2
% 23.69/6.61 |
% 23.69/6.61 | From (969) and (64) follows:
% 23.69/6.62 | (5065) sum(all_0_8_8, n2) = all_0_4_4
% 23.69/6.62 |
% 23.69/6.62 +-Applying beta-rule and splitting (681), into two cases.
% 23.69/6.62 |-Branch one:
% 23.69/6.62 | (682) all_0_8_8 = n1
% 23.69/6.62 |
% 23.69/6.62 | From (682) and (5065) follows:
% 23.69/6.62 | (5067) sum(n1, n2) = all_0_4_4
% 23.69/6.62 |
% 23.69/6.62 | From (682) and (5063) follows:
% 23.69/6.62 | (5068) sum(n1, n1) = all_0_2_2
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (89) with n1, n2, all_0_4_4, n3 and discharging atoms sum(n1, n2) = all_0_4_4, sum(n1, n2) = n3, yields:
% 23.69/6.62 | (652) all_0_4_4 = n3
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (89) with n1, n1, all_0_2_2, n2 and discharging atoms sum(n1, n1) = all_0_2_2, sum(n1, n1) = n2, yields:
% 23.69/6.62 | (651) all_0_2_2 = n2
% 23.69/6.62 |
% 23.69/6.62 | From (651) and (187) follows:
% 23.69/6.62 | (653) pred(n2) = all_0_1_1
% 23.69/6.62 |
% 23.69/6.62 | From (652) and (396) follows:
% 23.69/6.62 | (654) pred(n3) = all_0_3_3
% 23.69/6.62 |
% 23.69/6.62 | From (651) and (5068) follows:
% 23.69/6.62 | (15) sum(n1, n1) = n2
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (37) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 23.69/6.62 | (655) all_0_3_3 = n2
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (37) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 23.69/6.62 | (656) all_0_1_1 = n1
% 23.69/6.62 |
% 23.69/6.62 | From (655) and (261) follows:
% 23.69/6.62 | (657) sum(n2, all_0_0_0) = all_0_6_6
% 23.69/6.62 |
% 23.69/6.62 | From (656) and (967) follows:
% 23.69/6.62 | (5077) sum(n1, n1) = all_0_0_0
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (89) with n1, n1, all_0_0_0, n2 and discharging atoms sum(n1, n1) = all_0_0_0, sum(n1, n1) = n2, yields:
% 23.69/6.62 | (625) all_0_0_0 = n2
% 23.69/6.62 |
% 23.69/6.62 | From (625) and (657) follows:
% 23.69/6.62 | (5079) sum(n2, n2) = all_0_6_6
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (89) with n2, n2, all_0_6_6, n4 and discharging atoms sum(n2, n2) = all_0_6_6, sum(n2, n2) = n4, yields:
% 23.69/6.62 | (508) all_0_6_6 = n4
% 23.69/6.62 |
% 23.69/6.62 | Equations (508) can reduce 12 to:
% 23.69/6.62 | (458) $false
% 23.69/6.62 |
% 23.69/6.62 |-The branch is then unsatisfiable
% 23.69/6.62 |-Branch two:
% 23.69/6.62 | (697) ~ (all_0_8_8 = n1)
% 23.69/6.62 | (698) all_0_8_8 = n0
% 23.69/6.62 |
% 23.69/6.62 | From (698) and (5065) follows:
% 23.69/6.62 | (5084) sum(n0, n2) = all_0_4_4
% 23.69/6.62 |
% 23.69/6.62 | From (698) and (5063) follows:
% 23.69/6.62 | (5085) sum(n0, n1) = all_0_2_2
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (89) with n0, n2, all_0_4_4, n2 and discharging atoms sum(n0, n2) = all_0_4_4, sum(n0, n2) = n2, yields:
% 23.69/6.62 | (669) all_0_4_4 = n2
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (89) with n0, n1, all_0_2_2, n1 and discharging atoms sum(n0, n1) = all_0_2_2, sum(n0, n1) = n1, yields:
% 23.69/6.62 | (668) all_0_2_2 = n1
% 23.69/6.62 |
% 23.69/6.62 | From (668) and (187) follows:
% 23.69/6.62 | (670) pred(n1) = all_0_1_1
% 23.69/6.62 |
% 23.69/6.62 | From (669) and (396) follows:
% 23.69/6.62 | (671) pred(n2) = all_0_3_3
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (37) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 23.69/6.62 | (672) all_0_3_3 = n1
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (37) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 23.69/6.62 | (673) all_0_1_1 = n0
% 23.69/6.62 |
% 23.69/6.62 | From (672) and (261) follows:
% 23.69/6.62 | (674) sum(n1, all_0_0_0) = all_0_6_6
% 23.69/6.62 |
% 23.69/6.62 | From (673) and (967) follows:
% 23.69/6.62 | (5093) sum(n1, n0) = all_0_0_0
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (89) with n1, n0, all_0_0_0, n1 and discharging atoms sum(n1, n0) = all_0_0_0, sum(n1, n0) = n1, yields:
% 23.69/6.62 | (642) all_0_0_0 = n1
% 23.69/6.62 |
% 23.69/6.62 | From (642) and (674) follows:
% 23.69/6.62 | (5095) sum(n1, n1) = all_0_6_6
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (89) with n1, n1, all_0_6_6, n2 and discharging atoms sum(n1, n1) = all_0_6_6, sum(n1, n1) = n2, yields:
% 23.69/6.62 | (525) all_0_6_6 = n2
% 23.69/6.62 |
% 23.69/6.62 | Equations (525) can reduce 231 to:
% 23.69/6.62 | (458) $false
% 23.69/6.62 |
% 23.69/6.62 |-The branch is then unsatisfiable
% 23.69/6.62 |-Branch two:
% 23.69/6.62 | (982) ~ (all_0_7_7 = n1)
% 23.69/6.62 | (983) all_0_7_7 = n0
% 23.69/6.62 |
% 23.69/6.62 | From (983) and (176) follows:
% 23.69/6.62 | (984) succ(n0) = all_0_5_5
% 23.69/6.62 |
% 23.69/6.62 | From (983) and (59) follows:
% 23.69/6.62 | (985) sum(n0, all_0_1_1) = all_0_0_0
% 23.69/6.62 |
% 23.69/6.62 | From (983) and (160) follows:
% 23.69/6.62 | (5102) sum(all_0_8_8, n0) = all_0_2_2
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (219) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 23.69/6.62 | (987) all_0_5_5 = n1
% 23.69/6.62 |
% 23.69/6.62 | From (987) and (64) follows:
% 23.69/6.62 | (5104) sum(all_0_8_8, n1) = all_0_4_4
% 23.69/6.62 |
% 23.69/6.62 +-Applying beta-rule and splitting (681), into two cases.
% 23.69/6.62 |-Branch one:
% 23.69/6.62 | (682) all_0_8_8 = n1
% 23.69/6.62 |
% 23.69/6.62 | From (682) and (5104) follows:
% 23.69/6.62 | (5106) sum(n1, n1) = all_0_4_4
% 23.69/6.62 |
% 23.69/6.62 | From (682) and (5102) follows:
% 23.69/6.62 | (5107) sum(n1, n0) = all_0_2_2
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (89) with n1, n1, all_0_4_4, n2 and discharging atoms sum(n1, n1) = all_0_4_4, sum(n1, n1) = n2, yields:
% 23.69/6.62 | (669) all_0_4_4 = n2
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (89) with n1, n0, all_0_2_2, n1 and discharging atoms sum(n1, n0) = all_0_2_2, sum(n1, n0) = n1, yields:
% 23.69/6.62 | (668) all_0_2_2 = n1
% 23.69/6.62 |
% 23.69/6.62 | From (668) and (187) follows:
% 23.69/6.62 | (670) pred(n1) = all_0_1_1
% 23.69/6.62 |
% 23.69/6.62 | From (669) and (396) follows:
% 23.69/6.62 | (671) pred(n2) = all_0_3_3
% 23.69/6.62 |
% 23.69/6.62 | From (668) and (5107) follows:
% 23.69/6.62 | (228) sum(n1, n0) = n1
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (37) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 23.69/6.62 | (672) all_0_3_3 = n1
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (37) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 23.69/6.62 | (673) all_0_1_1 = n0
% 23.69/6.62 |
% 23.69/6.62 | From (672) and (261) follows:
% 23.69/6.62 | (674) sum(n1, all_0_0_0) = all_0_6_6
% 23.69/6.62 |
% 23.69/6.62 | From (673) and (985) follows:
% 23.69/6.62 | (5116) sum(n0, n0) = all_0_0_0
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (89) with n0, n0, all_0_0_0, n0 and discharging atoms sum(n0, n0) = all_0_0_0, sum(n0, n0) = n0, yields:
% 23.69/6.62 | (659) all_0_0_0 = n0
% 23.69/6.62 |
% 23.69/6.62 | From (659) and (674) follows:
% 23.69/6.62 | (5118) sum(n1, n0) = all_0_6_6
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (89) with n1, n0, all_0_6_6, n1 and discharging atoms sum(n1, n0) = all_0_6_6, sum(n1, n0) = n1, yields:
% 23.69/6.62 | (771) all_0_6_6 = n1
% 23.69/6.62 |
% 23.69/6.62 | Equations (771) can reduce 38 to:
% 23.69/6.62 | (458) $false
% 23.69/6.62 |
% 23.69/6.62 |-The branch is then unsatisfiable
% 23.69/6.62 |-Branch two:
% 23.69/6.62 | (697) ~ (all_0_8_8 = n1)
% 23.69/6.62 | (698) all_0_8_8 = n0
% 23.69/6.62 |
% 23.69/6.62 | From (698) and (5104) follows:
% 23.69/6.62 | (5123) sum(n0, n1) = all_0_4_4
% 23.69/6.62 |
% 23.69/6.62 | From (698) and (5102) follows:
% 23.69/6.62 | (5124) sum(n0, n0) = all_0_2_2
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (89) with n0, n1, all_0_4_4, n1 and discharging atoms sum(n0, n1) = all_0_4_4, sum(n0, n1) = n1, yields:
% 23.69/6.62 | (686) all_0_4_4 = n1
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (89) with n0, n0, all_0_2_2, n0 and discharging atoms sum(n0, n0) = all_0_2_2, sum(n0, n0) = n0, yields:
% 23.69/6.62 | (685) all_0_2_2 = n0
% 23.69/6.62 |
% 23.69/6.62 | From (685) and (187) follows:
% 23.69/6.62 | (687) pred(n0) = all_0_1_1
% 23.69/6.62 |
% 23.69/6.62 | From (686) and (396) follows:
% 23.69/6.62 | (688) pred(n1) = all_0_3_3
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (37) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 23.69/6.62 | (689) all_0_3_3 = n0
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (37) with n0, all_0_1_1, n15 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n15, yields:
% 23.69/6.62 | (690) all_0_1_1 = n15
% 23.69/6.62 |
% 23.69/6.62 | From (689) and (261) follows:
% 23.69/6.62 | (691) sum(n0, all_0_0_0) = all_0_6_6
% 23.69/6.62 |
% 23.69/6.62 | From (690) and (985) follows:
% 23.69/6.62 | (5132) sum(n0, n15) = all_0_0_0
% 23.69/6.62 |
% 23.69/6.62 | Instantiating formula (89) with n0, n15, all_0_0_0, n15 and discharging atoms sum(n0, n15) = all_0_0_0, sum(n0, n15) = n15, yields:
% 23.69/6.62 | (676) all_0_0_0 = n15
% 23.69/6.62 |
% 23.69/6.62 | From (676) and (691) follows:
% 23.69/6.62 | (5134) sum(n0, n15) = all_0_6_6
% 23.69/6.62 |
% 23.69/6.62 | From (676) and (5132) follows:
% 23.69/6.63 | (34) sum(n0, n15) = n15
% 23.69/6.63 |
% 23.69/6.63 | Instantiating formula (89) with n0, n15, all_0_6_6, n15 and discharging atoms sum(n0, n15) = all_0_6_6, sum(n0, n15) = n15, yields:
% 23.69/6.63 | (885) all_0_6_6 = n15
% 23.69/6.63 |
% 23.69/6.63 | Equations (885) can reduce 225 to:
% 23.69/6.63 | (458) $false
% 23.69/6.63 |
% 23.69/6.63 |-The branch is then unsatisfiable
% 23.69/6.63 % SZS output end Proof for theBenchmark
% 23.69/6.63
% 23.69/6.63 5944ms
%------------------------------------------------------------------------------