TSTP Solution File: NUM376+1.015 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM376+1.015 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 08:43:46 EDT 2022
% Result : Unsatisfiable 8.68s 2.77s
% Output : Proof 23.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM376+1.015 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.33 % Computer : n026.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Thu Jul 7 05:56:39 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.55/0.58 ____ _
% 0.55/0.58 ___ / __ \_____(_)___ ________ __________
% 0.55/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.58
% 0.55/0.58 A Theorem Prover for First-Order Logic
% 0.55/0.58 (ePrincess v.1.0)
% 0.55/0.58
% 0.55/0.58 (c) Philipp Rümmer, 2009-2015
% 0.55/0.58 (c) Peter Backeman, 2014-2015
% 0.55/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.58 Bug reports to peter@backeman.se
% 0.55/0.58
% 0.55/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.58
% 0.55/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.14/1.08 Prover 0: Preprocessing ...
% 3.39/1.39 Prover 0: Constructing countermodel ...
% 8.68/2.77 Prover 0: proved (2134ms)
% 8.68/2.77
% 8.68/2.77 No countermodel exists, formula is valid
% 8.68/2.77 % SZS status Unsatisfiable for theBenchmark
% 8.68/2.77
% 8.68/2.77 Generating proof ... found it (size 4789)
% 20.47/5.67
% 20.47/5.67 % SZS output start Proof for theBenchmark
% 20.47/5.67 Assumed formulas after preprocessing and simplification:
% 20.47/5.67 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = v8) & ~ (n15 = n14) & ~ (n15 = n13) & ~ (n15 = n12) & ~ (n15 = n11) & ~ (n15 = n10) & ~ (n15 = n9) & ~ (n15 = n8) & ~ (n15 = n7) & ~ (n15 = n6) & ~ (n15 = n5) & ~ (n15 = n4) & ~ (n15 = n3) & ~ (n15 = n2) & ~ (n15 = n1) & ~ (n15 = n0) & ~ (n14 = n13) & ~ (n14 = n12) & ~ (n14 = n11) & ~ (n14 = n10) & ~ (n14 = n9) & ~ (n14 = n8) & ~ (n14 = n7) & ~ (n14 = n6) & ~ (n14 = n5) & ~ (n14 = n4) & ~ (n14 = n3) & ~ (n14 = n2) & ~ (n14 = n1) & ~ (n14 = n0) & ~ (n13 = n12) & ~ (n13 = n11) & ~ (n13 = n10) & ~ (n13 = n9) & ~ (n13 = n8) & ~ (n13 = n7) & ~ (n13 = n6) & ~ (n13 = n5) & ~ (n13 = n4) & ~ (n13 = n3) & ~ (n13 = n2) & ~ (n13 = n1) & ~ (n13 = n0) & ~ (n12 = n11) & ~ (n12 = n10) & ~ (n12 = n9) & ~ (n12 = n8) & ~ (n12 = n7) & ~ (n12 = n6) & ~ (n12 = n5) & ~ (n12 = n4) & ~ (n12 = n3) & ~ (n12 = n2) & ~ (n12 = n1) & ~ (n12 = n0) & ~ (n11 = n10) & ~ (n11 = n9) & ~ (n11 = n8) & ~ (n11 = n7) & ~ (n11 = n6) & ~ (n11 = n5) & ~ (n11 = n4) & ~ (n11 = n3) & ~ (n11 = n2) & ~ (n11 = n1) & ~ (n11 = n0) & ~ (n10 = n9) & ~ (n10 = n8) & ~ (n10 = n7) & ~ (n10 = n6) & ~ (n10 = n5) & ~ (n10 = n4) & ~ (n10 = n3) & ~ (n10 = n2) & ~ (n10 = n1) & ~ (n10 = n0) & ~ (n9 = n8) & ~ (n9 = n7) & ~ (n9 = n6) & ~ (n9 = n5) & ~ (n9 = n4) & ~ (n9 = n3) & ~ (n9 = n2) & ~ (n9 = n1) & ~ (n9 = n0) & ~ (n8 = n7) & ~ (n8 = n6) & ~ (n8 = n5) & ~ (n8 = n4) & ~ (n8 = n3) & ~ (n8 = n2) & ~ (n8 = n1) & ~ (n8 = n0) & ~ (n7 = n6) & ~ (n7 = n5) & ~ (n7 = n4) & ~ (n7 = n3) & ~ (n7 = n2) & ~ (n7 = n1) & ~ (n7 = n0) & ~ (n6 = n5) & ~ (n6 = n4) & ~ (n6 = n3) & ~ (n6 = n2) & ~ (n6 = n1) & ~ (n6 = n0) & ~ (n5 = n4) & ~ (n5 = n3) & ~ (n5 = n2) & ~ (n5 = n1) & ~ (n5 = n0) & ~ (n4 = n3) & ~ (n4 = n2) & ~ (n4 = n1) & ~ (n4 = n0) & ~ (n3 = n2) & ~ (n3 = n1) & ~ (n3 = n0) & ~ (n2 = n1) & ~ (n2 = n0) & ~ (n1 = n0) & pred(v1) = v5 & pred(v0) = v2 & pred(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 & succ(v1) = v3 & succ(v0) = v6 & 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 & sum(v9, v10) = v11 & sum(v5, v6) = v7 & sum(v5, v3) = v10 & sum(v4, v7) = v8 & sum(v2, v6) = v9 & sum(v2, v3) = v4 & sum(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 & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (sum(v15, v14) = v13) | ~ (sum(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (pred(v14) = v13) | ~ (pred(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (succ(v14) = v13) | ~ (succ(v14) = v12)) & (v1 = 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))
% 20.73/5.74 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11 yields:
% 20.73/5.74 | (1) ~ (all_0_0_0 = all_0_3_3) & ~ (n15 = n14) & ~ (n15 = n13) & ~ (n15 = n12) & ~ (n15 = n11) & ~ (n15 = n10) & ~ (n15 = n9) & ~ (n15 = n8) & ~ (n15 = n7) & ~ (n15 = n6) & ~ (n15 = n5) & ~ (n15 = n4) & ~ (n15 = n3) & ~ (n15 = n2) & ~ (n15 = n1) & ~ (n15 = n0) & ~ (n14 = n13) & ~ (n14 = n12) & ~ (n14 = n11) & ~ (n14 = n10) & ~ (n14 = n9) & ~ (n14 = n8) & ~ (n14 = n7) & ~ (n14 = n6) & ~ (n14 = n5) & ~ (n14 = n4) & ~ (n14 = n3) & ~ (n14 = n2) & ~ (n14 = n1) & ~ (n14 = n0) & ~ (n13 = n12) & ~ (n13 = n11) & ~ (n13 = n10) & ~ (n13 = n9) & ~ (n13 = n8) & ~ (n13 = n7) & ~ (n13 = n6) & ~ (n13 = n5) & ~ (n13 = n4) & ~ (n13 = n3) & ~ (n13 = n2) & ~ (n13 = n1) & ~ (n13 = n0) & ~ (n12 = n11) & ~ (n12 = n10) & ~ (n12 = n9) & ~ (n12 = n8) & ~ (n12 = n7) & ~ (n12 = n6) & ~ (n12 = n5) & ~ (n12 = n4) & ~ (n12 = n3) & ~ (n12 = n2) & ~ (n12 = n1) & ~ (n12 = n0) & ~ (n11 = n10) & ~ (n11 = n9) & ~ (n11 = n8) & ~ (n11 = n7) & ~ (n11 = n6) & ~ (n11 = n5) & ~ (n11 = n4) & ~ (n11 = n3) & ~ (n11 = n2) & ~ (n11 = n1) & ~ (n11 = n0) & ~ (n10 = n9) & ~ (n10 = n8) & ~ (n10 = n7) & ~ (n10 = n6) & ~ (n10 = n5) & ~ (n10 = n4) & ~ (n10 = n3) & ~ (n10 = n2) & ~ (n10 = n1) & ~ (n10 = n0) & ~ (n9 = n8) & ~ (n9 = n7) & ~ (n9 = n6) & ~ (n9 = n5) & ~ (n9 = n4) & ~ (n9 = n3) & ~ (n9 = n2) & ~ (n9 = n1) & ~ (n9 = n0) & ~ (n8 = n7) & ~ (n8 = n6) & ~ (n8 = n5) & ~ (n8 = n4) & ~ (n8 = n3) & ~ (n8 = n2) & ~ (n8 = n1) & ~ (n8 = n0) & ~ (n7 = n6) & ~ (n7 = n5) & ~ (n7 = n4) & ~ (n7 = n3) & ~ (n7 = n2) & ~ (n7 = n1) & ~ (n7 = n0) & ~ (n6 = n5) & ~ (n6 = n4) & ~ (n6 = n3) & ~ (n6 = n2) & ~ (n6 = n1) & ~ (n6 = n0) & ~ (n5 = n4) & ~ (n5 = n3) & ~ (n5 = n2) & ~ (n5 = n1) & ~ (n5 = n0) & ~ (n4 = n3) & ~ (n4 = n2) & ~ (n4 = n1) & ~ (n4 = n0) & ~ (n3 = n2) & ~ (n3 = n1) & ~ (n3 = n0) & ~ (n2 = n1) & ~ (n2 = n0) & ~ (n1 = n0) & pred(all_0_10_10) = all_0_6_6 & pred(all_0_11_11) = all_0_9_9 & pred(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 & succ(all_0_10_10) = all_0_8_8 & succ(all_0_11_11) = 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 & sum(all_0_2_2, all_0_1_1) = all_0_0_0 & sum(all_0_6_6, all_0_5_5) = all_0_4_4 & sum(all_0_6_6, all_0_8_8) = all_0_1_1 & sum(all_0_7_7, all_0_4_4) = all_0_3_3 & sum(all_0_9_9, all_0_5_5) = all_0_2_2 & sum(all_0_9_9, all_0_8_8) = all_0_7_7 & sum(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 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & (all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0) & (all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0)
% 20.87/5.76 |
% 20.87/5.76 | Applying alpha-rule on (1) yields:
% 20.87/5.76 | (2) sum(n11, n13) = n8
% 20.87/5.76 | (3) sum(n6, n11) = n1
% 20.87/5.76 | (4) sum(n7, n9) = n0
% 20.87/5.76 | (5) ~ (n4 = n0)
% 20.87/5.76 | (6) ~ (n15 = n3)
% 20.87/5.76 | (7) sum(n14, n0) = n14
% 20.87/5.76 | (8) sum(n11, n3) = n14
% 20.87/5.76 | (9) sum(n4, n3) = n7
% 20.87/5.76 | (10) sum(all_0_6_6, all_0_8_8) = all_0_1_1
% 20.87/5.76 | (11) sum(n12, n1) = n13
% 20.87/5.76 | (12) sum(n12, n3) = n15
% 20.87/5.76 | (13) sum(n12, n15) = n11
% 20.87/5.76 | (14) sum(n0, n7) = n7
% 20.87/5.76 | (15) sum(n1, n2) = n3
% 20.87/5.76 | (16) ~ (n10 = n6)
% 20.87/5.76 | (17) sum(n8, n8) = n0
% 20.87/5.76 | (18) sum(n13, n9) = n6
% 20.87/5.76 | (19) sum(n9, n11) = n4
% 20.87/5.76 | (20) ~ (n3 = n1)
% 20.87/5.76 | (21) sum(n10, n4) = n14
% 20.87/5.76 | (22) sum(n4, n2) = n6
% 20.87/5.76 | (23) ~ (n13 = n11)
% 20.87/5.76 | (24) sum(n2, n9) = n11
% 20.87/5.76 | (25) ~ (n14 = n9)
% 20.87/5.76 | (26) sum(n10, n13) = n7
% 20.87/5.76 | (27) sum(n5, n5) = n10
% 20.87/5.76 | (28) succ(n10) = n11
% 20.87/5.76 | (29) all_0_11_11 = n15 | all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 20.87/5.76 | (30) ~ (n13 = n5)
% 20.87/5.76 | (31) sum(n8, n13) = n5
% 20.87/5.76 | (32) sum(n9, n14) = n7
% 20.87/5.76 | (33) sum(n13, n15) = n12
% 20.87/5.76 | (34) ~ (n8 = n5)
% 20.87/5.76 | (35) sum(n13, n14) = n11
% 20.87/5.76 | (36) ~ (n15 = n11)
% 20.87/5.76 | (37) sum(n3, n1) = n4
% 20.87/5.76 | (38) ~ (n11 = n9)
% 20.87/5.76 | (39) sum(n12, n2) = n14
% 20.87/5.76 | (40) sum(n2, n2) = n4
% 20.87/5.76 | (41) sum(n6, n12) = n2
% 20.87/5.76 | (42) sum(n1, n1) = n2
% 20.87/5.76 | (43) sum(n15, n12) = n11
% 20.87/5.76 | (44) succ(n5) = n6
% 20.87/5.76 | (45) pred(n15) = n14
% 20.87/5.76 | (46) ~ (n10 = n5)
% 20.87/5.76 | (47) sum(n12, n7) = n3
% 20.87/5.76 | (48) sum(n8, n7) = n15
% 20.87/5.76 | (49) succ(n3) = n4
% 20.87/5.76 | (50) sum(n2, n10) = n12
% 20.87/5.76 | (51) sum(n7, n4) = n11
% 20.87/5.76 | (52) sum(n3, n3) = n6
% 20.87/5.76 | (53) sum(n3, n11) = n14
% 20.87/5.76 | (54) sum(n2, n11) = n13
% 20.87/5.76 | (55) sum(n13, n2) = n15
% 20.87/5.76 | (56) ~ (n11 = n2)
% 20.87/5.76 | (57) sum(n8, n3) = n11
% 20.87/5.76 | (58) sum(n7, n15) = n6
% 20.87/5.76 | (59) pred(n5) = n4
% 20.87/5.76 | (60) sum(n6, n5) = n11
% 20.87/5.76 | (61) sum(n13, n6) = n3
% 20.87/5.76 | (62) sum(n12, n0) = n12
% 20.87/5.76 | (63) all_0_10_10 = n15 | all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 20.87/5.76 | (64) sum(n5, n15) = n4
% 20.87/5.76 | (65) sum(n10, n10) = n4
% 20.87/5.76 | (66) ~ (n13 = n2)
% 20.87/5.76 | (67) sum(n0, n2) = n2
% 20.87/5.76 | (68) sum(n12, n11) = n7
% 20.87/5.76 | (69) ~ (n11 = n4)
% 20.87/5.76 | (70) sum(n15, n5) = n4
% 20.87/5.76 | (71) sum(n12, n4) = n0
% 20.87/5.76 | (72) ~ (n12 = n5)
% 20.87/5.76 | (73) sum(n11, n12) = n7
% 20.87/5.76 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0))
% 20.87/5.76 | (75) sum(n4, n4) = n8
% 20.87/5.77 | (76) sum(n2, n6) = n8
% 20.87/5.77 | (77) succ(n15) = n0
% 20.87/5.77 | (78) ~ (n9 = n0)
% 20.87/5.77 | (79) sum(n12, n9) = n5
% 20.87/5.77 | (80) sum(n15, n14) = n13
% 20.87/5.77 | (81) sum(n8, n0) = n8
% 20.87/5.77 | (82) sum(n2, n3) = n5
% 20.87/5.77 | (83) sum(n4, n1) = n5
% 20.87/5.77 | (84) sum(n6, n8) = n14
% 20.87/5.77 | (85) sum(n1, n13) = n14
% 20.87/5.77 | (86) sum(n7, n8) = n15
% 20.87/5.77 | (87) sum(n2, n1) = n3
% 20.87/5.77 | (88) sum(n9, n3) = n12
% 20.87/5.77 | (89) sum(n2, n8) = n10
% 20.87/5.77 | (90) ~ (n5 = n4)
% 20.87/5.77 | (91) pred(n2) = n1
% 20.87/5.77 | (92) sum(n7, n5) = n12
% 20.87/5.77 | (93) sum(n5, n10) = n15
% 20.87/5.77 | (94) sum(n1, n14) = n15
% 20.87/5.77 | (95) sum(n7, n2) = n9
% 20.87/5.77 | (96) sum(n10, n3) = n13
% 20.87/5.77 | (97) sum(n9, n12) = n5
% 20.87/5.77 | (98) sum(n10, n6) = n0
% 20.87/5.77 | (99) ~ (n6 = n4)
% 20.87/5.77 | (100) sum(n0, n11) = n11
% 20.87/5.77 | (101) sum(n15, n7) = n6
% 20.87/5.77 | (102) sum(n3, n12) = n15
% 20.87/5.77 | (103) ~ (n7 = n5)
% 20.87/5.77 | (104) sum(n8, n6) = n14
% 20.87/5.77 | (105) ~ (n6 = n5)
% 20.87/5.77 | (106) succ(n4) = n5
% 20.87/5.77 | (107) sum(n2, n12) = n14
% 20.87/5.77 | (108) ~ (n15 = n5)
% 20.87/5.77 | (109) sum(n3, n8) = n11
% 20.87/5.77 | (110) ~ (n9 = n6)
% 20.87/5.77 | (111) ~ (n13 = n0)
% 20.87/5.77 | (112) ~ (n15 = n1)
% 20.87/5.77 | (113) sum(n0, n0) = n0
% 20.87/5.77 | (114) ~ (n15 = n10)
% 20.87/5.77 | (115) ~ (n15 = n12)
% 20.87/5.77 | (116) sum(n14, n2) = n0
% 20.87/5.77 | (117) sum(n9, n13) = n6
% 20.87/5.77 | (118) sum(n1, n6) = n7
% 20.87/5.77 | (119) sum(n11, n11) = n6
% 20.87/5.77 | (120) ~ (n9 = n5)
% 20.87/5.77 | (121) ~ (n11 = n3)
% 20.87/5.77 | (122) ~ (n13 = n8)
% 20.87/5.77 | (123) sum(n0, n12) = n12
% 20.87/5.77 | (124) sum(n14, n10) = n8
% 20.87/5.77 | (125) pred(n11) = n10
% 20.87/5.77 | (126) sum(n12, n8) = n4
% 20.87/5.77 | (127) ~ (n13 = n4)
% 20.87/5.77 | (128) sum(n14, n8) = n6
% 20.87/5.77 | (129) sum(n6, n13) = n3
% 20.87/5.77 | (130) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 20.87/5.77 | (131) sum(n10, n11) = n5
% 20.87/5.77 | (132) sum(n0, n10) = n10
% 20.87/5.77 | (133) ~ (n14 = n7)
% 20.87/5.77 | (134) sum(n0, n8) = n8
% 20.87/5.77 | (135) sum(n6, n6) = n12
% 20.87/5.77 | (136) sum(n8, n9) = n1
% 20.87/5.77 | (137) ~ (n12 = n2)
% 20.87/5.77 | (138) sum(n10, n12) = n6
% 20.87/5.77 | (139) ~ (n9 = n3)
% 20.87/5.77 | (140) sum(n7, n12) = n3
% 20.87/5.77 | (141) sum(n2, n4) = n6
% 20.87/5.77 | (142) sum(n1, n4) = n5
% 20.87/5.78 | (143) succ(n14) = n15
% 20.87/5.78 | (144) sum(n12, n13) = n9
% 20.87/5.78 | (145) sum(n12, n5) = n1
% 20.87/5.78 | (146) succ(all_0_10_10) = all_0_8_8
% 20.87/5.78 | (147) sum(all_0_9_9, all_0_5_5) = all_0_2_2
% 20.87/5.78 | (148) sum(n11, n0) = n11
% 20.87/5.78 | (149) sum(n1, n12) = n13
% 20.87/5.78 | (150) succ(n2) = n3
% 20.87/5.78 | (151) sum(n14, n13) = n11
% 20.87/5.78 | (152) sum(n15, n11) = n10
% 20.87/5.78 | (153) sum(n1, n11) = n12
% 20.87/5.78 | (154) sum(n1, n15) = n0
% 20.87/5.78 | (155) sum(n5, n12) = n1
% 20.87/5.78 | (156) sum(n4, n12) = n0
% 20.87/5.78 | (157) ~ (n13 = n12)
% 20.87/5.78 | (158) sum(n7, n7) = n14
% 20.87/5.78 | (159) sum(n14, n14) = n12
% 20.87/5.78 | (160) sum(n4, n13) = n1
% 20.87/5.78 | (161) ~ (n8 = n7)
% 20.87/5.78 | (162) sum(n7, n11) = n2
% 20.87/5.78 | (163) ~ (n7 = n6)
% 20.87/5.78 | (164) sum(n5, n9) = n14
% 20.87/5.78 | (165) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0))
% 20.87/5.78 | (166) sum(n6, n2) = n8
% 20.87/5.78 | (167) sum(n4, n8) = n12
% 20.87/5.78 | (168) sum(n14, n9) = n7
% 20.87/5.78 | (169) sum(n14, n5) = n3
% 20.87/5.78 | (170) ~ (n1 = n0)
% 20.87/5.78 | (171) sum(n11, n5) = n0
% 20.87/5.78 | (172) sum(n9, n9) = n2
% 20.87/5.78 | (173) ~ (n10 = n9)
% 20.87/5.78 | (174) pred(n10) = n9
% 20.87/5.78 | (175) sum(n5, n3) = n8
% 20.87/5.78 | (176) sum(n8, n12) = n4
% 20.87/5.78 | (177) succ(n13) = n14
% 20.87/5.78 | (178) ~ (n13 = n3)
% 20.87/5.78 | (179) ~ (n5 = n3)
% 20.87/5.78 | (180) sum(n10, n8) = n2
% 20.87/5.78 | (181) ~ (n12 = n10)
% 20.87/5.78 | (182) succ(n1) = n2
% 20.87/5.78 | (183) sum(n14, n4) = n2
% 20.87/5.78 | (184) sum(n13, n12) = n9
% 20.87/5.78 | (185) ~ (n5 = n1)
% 20.87/5.78 | (186) sum(n8, n15) = n7
% 20.87/5.78 | (187) sum(n4, n15) = n3
% 20.87/5.78 | (188) sum(n3, n13) = n0
% 20.87/5.78 | (189) sum(n2, n7) = n9
% 20.87/5.78 | (190) sum(n13, n5) = n2
% 20.87/5.78 | (191) sum(n9, n5) = n14
% 20.87/5.78 | (192) succ(n6) = n7
% 20.87/5.78 | (193) sum(n6, n10) = n0
% 20.87/5.78 | (194) ~ (n14 = n2)
% 20.87/5.78 | (195) sum(n14, n15) = n13
% 20.87/5.78 | (196) sum(n11, n6) = n1
% 20.87/5.78 | (197) sum(n4, n11) = n15
% 20.87/5.78 | (198) sum(n2, n14) = n0
% 20.87/5.78 | (199) sum(n6, n4) = n10
% 20.87/5.79 | (200) sum(n15, n13) = n12
% 20.87/5.79 | (201) ~ (n8 = n3)
% 20.87/5.79 | (202) ~ (n15 = n8)
% 20.87/5.79 | (203) ~ (n14 = n12)
% 20.87/5.79 | (204) ~ (n15 = n6)
% 20.87/5.79 | (205) sum(n3, n0) = n3
% 20.87/5.79 | (206) ~ (n11 = n10)
% 20.87/5.79 | (207) ~ (n14 = n4)
% 20.87/5.79 | (208) sum(n10, n7) = n1
% 20.87/5.79 | (209) sum(n7, n1) = n8
% 20.87/5.79 | (210) sum(n4, n10) = n14
% 20.87/5.79 | (211) sum(n6, n3) = n9
% 20.87/5.79 | (212) sum(all_0_7_7, all_0_4_4) = all_0_3_3
% 20.87/5.79 | (213) sum(n5, n11) = n0
% 20.87/5.79 | (214) sum(n11, n14) = n9
% 20.87/5.79 | (215) ~ (n12 = n1)
% 20.87/5.79 | (216) sum(n6, n0) = n6
% 20.87/5.79 | (217) ~ (n11 = n8)
% 20.87/5.79 | (218) ~ (n14 = n1)
% 20.87/5.79 | (219) ~ (n14 = n13)
% 20.87/5.79 | (220) sum(n14, n6) = n4
% 20.87/5.79 | (221) ~ (n7 = n2)
% 20.87/5.79 | (222) sum(n0, n6) = n6
% 20.87/5.79 | (223) sum(n7, n0) = n7
% 20.87/5.79 | (224) sum(n0, n13) = n13
% 20.87/5.79 | (225) sum(n5, n1) = n6
% 20.87/5.79 | (226) pred(n14) = n13
% 20.87/5.79 | (227) sum(n4, n9) = n13
% 20.87/5.79 | (228) sum(n11, n10) = n5
% 20.87/5.79 | (229) sum(n15, n3) = n2
% 20.87/5.79 | (230) sum(n8, n1) = n9
% 20.87/5.79 | (231) sum(n7, n14) = n5
% 20.87/5.79 | (232) ~ (n3 = n2)
% 20.87/5.79 | (233) sum(n4, n6) = n10
% 20.87/5.79 | (234) sum(n10, n9) = n3
% 20.87/5.79 | (235) ~ (n8 = n1)
% 20.87/5.79 | (236) ~ (n15 = n2)
% 20.87/5.79 | (237) sum(n0, n1) = n1
% 20.87/5.79 | (238) sum(n15, n4) = n3
% 20.87/5.79 | (239) sum(n3, n7) = n10
% 20.87/5.79 | (240) pred(n8) = n7
% 20.87/5.79 | (241) sum(n0, n4) = n4
% 20.87/5.79 | (242) ~ (n10 = n2)
% 20.87/5.79 | (243) ~ (n8 = n6)
% 20.87/5.79 | (244) sum(n14, n3) = n1
% 20.87/5.79 | (245) pred(n0) = n15
% 20.87/5.79 | (246) sum(n13, n13) = n10
% 20.87/5.79 | (247) ~ (n7 = n1)
% 20.87/5.79 | (248) sum(n5, n0) = n5
% 20.87/5.79 | (249) sum(n11, n8) = n3
% 20.87/5.79 | (250) sum(n5, n14) = n3
% 20.87/5.80 | (251) sum(n9, n2) = n11
% 20.87/5.80 | (252) ~ (n15 = n0)
% 20.87/5.80 | (253) sum(n4, n5) = n9
% 20.87/5.80 | (254) ~ (n11 = n6)
% 20.87/5.80 | (255) sum(n13, n11) = n8
% 20.87/5.80 | (256) sum(all_0_2_2, all_0_1_1) = all_0_0_0
% 20.87/5.80 | (257) ~ (n15 = n9)
% 20.87/5.80 | (258) ~ (n11 = n1)
% 20.87/5.80 | (259) sum(n4, n7) = n11
% 20.87/5.80 | (260) sum(n10, n5) = n15
% 20.87/5.80 | (261) sum(n5, n8) = n13
% 20.87/5.80 | (262) succ(all_0_11_11) = all_0_5_5
% 20.87/5.80 | (263) sum(n13, n7) = n4
% 20.87/5.80 | (264) succ(n12) = n13
% 20.87/5.80 | (265) sum(n11, n4) = n15
% 20.87/5.80 | (266) pred(n12) = n11
% 20.87/5.80 | (267) sum(n15, n8) = n7
% 20.87/5.80 | (268) sum(n6, n9) = n15
% 20.87/5.80 | (269) sum(n9, n1) = n10
% 20.87/5.80 | (270) sum(n8, n10) = n2
% 20.87/5.80 | (271) sum(n15, n10) = n9
% 20.87/5.80 | (272) ~ (n5 = n0)
% 20.87/5.80 | (273) ~ (n11 = n0)
% 20.87/5.80 | (274) ~ (n6 = n0)
% 20.87/5.80 | (275) ~ (n9 = n1)
% 20.87/5.80 | (276) sum(all_0_6_6, all_0_5_5) = all_0_4_4
% 20.87/5.80 | (277) sum(n9, n7) = n0
% 20.87/5.80 | (278) sum(n11, n1) = n12
% 20.87/5.80 | (279) ~ (n11 = n7)
% 20.87/5.80 | (280) sum(n8, n14) = n6
% 20.87/5.80 | (281) sum(n9, n10) = n3
% 20.87/5.80 | (282) sum(n13, n1) = n14
% 20.87/5.80 | (283) sum(n8, n5) = n13
% 20.87/5.80 | (284) sum(n6, n7) = n13
% 20.87/5.80 | (285) sum(n0, n15) = n15
% 20.87/5.80 | (286) sum(n14, n11) = n9
% 20.87/5.80 | (287) sum(n9, n15) = n8
% 20.87/5.80 | (288) sum(n13, n4) = n1
% 20.87/5.80 | (289) ~ (n4 = n1)
% 20.87/5.80 | (290) sum(n15, n6) = n5
% 20.87/5.80 | (291) ~ (n14 = n5)
% 20.87/5.80 | (292) sum(n7, n10) = n1
% 20.87/5.80 | (293) sum(n2, n5) = n7
% 20.87/5.80 | (294) sum(n11, n7) = n2
% 20.87/5.80 | (295) ~ (n9 = n4)
% 20.87/5.81 | (296) ~ (n10 = n3)
% 20.87/5.81 | (297) sum(n0, n14) = n14
% 20.87/5.81 | (298) succ(n8) = n9
% 20.87/5.81 | (299) succ(n11) = n12
% 20.87/5.81 | (300) sum(n6, n15) = n5
% 20.87/5.81 | (301) sum(n13, n3) = n0
% 20.87/5.81 | (302) ~ (n8 = n0)
% 20.87/5.81 | (303) ~ (n14 = n0)
% 20.87/5.82 | (304) ~ (n5 = n2)
% 20.87/5.82 | (305) sum(n3, n4) = n7
% 20.87/5.82 | (306) pred(n1) = n0
% 20.87/5.82 | (307) sum(n5, n7) = n12
% 20.87/5.82 | (308) sum(n1, n7) = n8
% 20.87/5.83 | (309) sum(n15, n2) = n1
% 21.26/5.83 | (310) ~ (n12 = n7)
% 21.26/5.83 | (311) sum(n7, n13) = n4
% 21.26/5.83 | (312) sum(n5, n2) = n7
% 21.26/5.83 | (313) ~ (n14 = n6)
% 21.26/5.83 | (314) ~ (n13 = n9)
% 21.26/5.83 | (315) ~ (n8 = n2)
% 21.26/5.83 | (316) ~ (n3 = n0)
% 21.26/5.83 | (317) pred(all_0_10_10) = all_0_6_6
% 21.26/5.83 | (318) sum(n11, n15) = n10
% 21.26/5.83 | (319) sum(n3, n6) = n9
% 21.26/5.83 | (320) sum(n4, n0) = n4
% 21.26/5.83 | (321) sum(n12, n14) = n10
% 21.26/5.83 | (322) ~ (n10 = n1)
% 21.26/5.83 | (323) ~ (n14 = n8)
% 21.26/5.83 | (324) ~ (n14 = n3)
% 21.26/5.83 | (325) ~ (n2 = n1)
% 21.26/5.83 | (326) sum(n11, n9) = n4
% 21.26/5.83 | (327) ~ (n12 = n11)
% 21.26/5.83 | (328) ~ (n13 = n7)
% 21.26/5.83 | (329) sum(n2, n15) = n1
% 21.26/5.83 | (330) sum(n12, n10) = n6
% 21.26/5.83 | (331) sum(n3, n10) = n13
% 21.26/5.83 | (332) ~ (n12 = n6)
% 21.26/5.83 | (333) sum(n9, n8) = n1
% 21.26/5.83 | (334) ~ (n2 = n0)
% 21.26/5.83 | (335) ~ (n12 = n8)
% 21.26/5.83 | (336) ~ (n11 = n5)
% 21.26/5.83 | (337) ~ (n12 = n9)
% 21.26/5.83 | (338) sum(n0, n5) = n5
% 21.26/5.83 | (339) ~ (n9 = n7)
% 21.26/5.83 | (340) ~ (n9 = n8)
% 21.26/5.83 | (341) sum(n10, n2) = n12
% 21.26/5.83 | (342) sum(n2, n0) = n2
% 21.26/5.83 | (343) ~ (n12 = n0)
% 21.26/5.83 | (344) ~ (n14 = n10)
% 21.26/5.84 | (345) pred(n4) = n3
% 21.26/5.84 | (346) ~ (n6 = n3)
% 21.26/5.84 | (347) ~ (n12 = n4)
% 21.26/5.84 | (348) sum(n10, n0) = n10
% 21.26/5.84 | (349) sum(n6, n14) = n4
% 21.26/5.84 | (350) sum(all_0_9_9, all_0_8_8) = all_0_7_7
% 21.26/5.84 | (351) ~ (n8 = n4)
% 21.26/5.84 | (352) ~ (n9 = n2)
% 21.26/5.84 | (353) sum(n5, n4) = n9
% 21.26/5.84 | (354) ~ (n7 = n0)
% 21.26/5.84 | (355) pred(n6) = n5
% 21.26/5.84 | (356) succ(n7) = n8
% 21.26/5.84 | (357) ~ (n13 = n10)
% 21.26/5.84 | (358) succ(n9) = n10
% 21.26/5.84 | (359) sum(n14, n12) = n10
% 21.26/5.84 | (360) sum(n4, n14) = n2
% 21.26/5.84 | (361) sum(n8, n4) = n12
% 21.26/5.84 | (362) sum(n15, n9) = n8
% 21.26/5.84 | (363) ~ (all_0_0_0 = all_0_3_3)
% 21.26/5.84 | (364) ~ (n15 = n4)
% 21.26/5.84 | (365) sum(n15, n0) = n15
% 21.26/5.84 | (366) sum(n13, n8) = n5
% 21.26/5.84 | (367) sum(n11, n2) = n13
% 21.26/5.84 | (368) ~ (n12 = n3)
% 21.26/5.84 | (369) sum(n9, n4) = n13
% 21.26/5.84 | (370) sum(n13, n10) = n7
% 21.26/5.84 | (371) sum(n1, n10) = n11
% 21.26/5.84 | (372) sum(n10, n15) = n9
% 21.26/5.84 | (373) sum(n3, n14) = n1
% 21.26/5.84 | (374) ~ (n15 = n7)
% 21.26/5.84 | (375) ~ (n10 = n8)
% 21.26/5.84 | (376) sum(n1, n8) = n9
% 21.26/5.84 | (377) sum(n9, n6) = n15
% 21.26/5.84 | (378) ~ (n6 = n2)
% 21.26/5.84 | (379) sum(n3, n9) = n12
% 21.26/5.84 | (380) ~ (n10 = n7)
% 21.26/5.84 | (381) sum(n3, n15) = n2
% 21.26/5.84 | (382) pred(n13) = n12
% 21.26/5.84 | (383) sum(n13, n0) = n13
% 21.26/5.84 | (384) sum(n5, n6) = n11
% 21.26/5.84 | (385) ~ (n15 = n13)
% 21.26/5.84 | (386) sum(n10, n1) = n11
% 21.26/5.84 | (387) sum(n1, n5) = n6
% 21.26/5.84 | (388) sum(n9, n0) = n9
% 21.26/5.84 | (389) ~ (n15 = n14)
% 21.26/5.84 | (390) sum(n5, n13) = n2
% 21.26/5.84 | (391) sum(n1, n0) = n1
% 21.26/5.84 | (392) ~ (n4 = n3)
% 21.26/5.84 | (393) ~ (n13 = n1)
% 21.26/5.84 | (394) sum(n8, n2) = n10
% 21.26/5.84 | (395) sum(n7, n6) = n13
% 21.26/5.84 | (396) sum(n8, n11) = n3
% 21.26/5.84 | (397) ~ (n10 = n4)
% 21.26/5.85 | (398) sum(n15, n1) = n0
% 21.26/5.85 | (399) sum(n12, n6) = n2
% 21.26/5.85 | (400) sum(n0, n9) = n9
% 21.26/5.85 | (401) ~ (n14 = n11)
% 21.26/5.85 | (402) sum(n12, n12) = n8
% 21.26/5.85 | (403) ~ (n4 = n2)
% 21.26/5.85 | (404) ~ (n7 = n3)
% 21.26/5.85 | (405) sum(n14, n1) = n15
% 21.26/5.85 | (406) sum(n2, n13) = n15
% 21.26/5.85 | (407) ~ (n10 = n0)
% 21.26/5.85 | (408) sum(n3, n2) = n5
% 21.26/5.85 | (409) ~ (n7 = n4)
% 21.26/5.85 | (410) pred(n3) = n2
% 21.26/5.85 | (411) pred(n7) = n6
% 21.26/5.85 | (412) sum(n3, n5) = n8
% 21.26/5.85 | (413) sum(n6, n1) = n7
% 21.26/5.85 | (414) ~ (n6 = n1)
% 21.26/5.85 | (415) sum(n1, n9) = n10
% 21.26/5.85 | (416) sum(n15, n15) = n14
% 21.26/5.85 | (417) ~ (n13 = n6)
% 21.26/5.85 | (418) succ(n0) = n1
% 21.26/5.85 | (419) sum(n1, n3) = n4
% 21.26/5.85 | (420) sum(n0, n3) = n3
% 21.26/5.85 | (421) pred(n9) = n8
% 21.26/5.85 | (422) sum(n7, n3) = n10
% 21.26/5.85 | (423) pred(all_0_11_11) = all_0_9_9
% 21.26/5.85 | (424) sum(n10, n14) = n8
% 21.26/5.85 | (425) sum(n14, n7) = n5
% 21.26/5.85 |
% 21.26/5.85 +-Applying beta-rule and splitting (63), into two cases.
% 21.26/5.85 |-Branch one:
% 21.26/5.85 | (426) all_0_10_10 = n15
% 21.26/5.85 |
% 21.26/5.85 | From (426) and (317) follows:
% 21.26/5.85 | (427) pred(n15) = all_0_6_6
% 21.26/5.85 |
% 21.26/5.85 | From (426) and (146) follows:
% 21.26/5.85 | (428) succ(n15) = all_0_8_8
% 21.26/5.85 |
% 21.26/5.85 | Instantiating formula (130) with n15, all_0_6_6, n14 and discharging atoms pred(n15) = all_0_6_6, pred(n15) = n14, yields:
% 21.26/5.85 | (429) all_0_6_6 = n14
% 21.26/5.85 |
% 21.26/5.85 | Instantiating formula (165) with n15, all_0_8_8, n0 and discharging atoms succ(n15) = all_0_8_8, succ(n15) = n0, yields:
% 21.26/5.85 | (430) all_0_8_8 = n0
% 21.26/5.85 |
% 21.26/5.85 | From (429) and (427) follows:
% 21.26/5.85 | (45) pred(n15) = n14
% 21.26/5.85 |
% 21.26/5.85 | From (430) and (428) follows:
% 21.26/5.85 | (77) succ(n15) = n0
% 21.26/5.85 |
% 21.26/5.85 | From (429) and (276) follows:
% 21.26/5.85 | (433) sum(n14, all_0_5_5) = all_0_4_4
% 21.26/5.85 |
% 21.26/5.85 | From (429)(430) and (10) follows:
% 21.26/5.85 | (434) sum(n14, n0) = all_0_1_1
% 21.26/5.85 |
% 21.26/5.85 | From (430) and (350) follows:
% 21.26/5.85 | (435) sum(all_0_9_9, n0) = all_0_7_7
% 21.26/5.85 |
% 21.26/5.85 | Instantiating formula (74) with n14, n0, all_0_1_1, n14 and discharging atoms sum(n14, n0) = all_0_1_1, sum(n14, n0) = n14, yields:
% 21.26/5.85 | (436) all_0_1_1 = n14
% 21.26/5.85 |
% 21.26/5.85 | From (436) and (256) follows:
% 21.26/5.85 | (437) sum(all_0_2_2, n14) = all_0_0_0
% 21.26/5.85 |
% 21.26/5.85 | From (436) and (434) follows:
% 21.26/5.86 | (7) sum(n14, n0) = n14
% 21.26/5.86 |
% 21.26/5.86 +-Applying beta-rule and splitting (29), into two cases.
% 21.26/5.86 |-Branch one:
% 21.26/5.86 | (439) all_0_11_11 = n15
% 21.26/5.86 |
% 21.26/5.86 | From (439) and (423) follows:
% 21.26/5.86 | (440) pred(n15) = all_0_9_9
% 21.26/5.86 |
% 21.26/5.86 | From (439) and (262) follows:
% 21.26/5.86 | (441) succ(n15) = all_0_5_5
% 21.26/5.86 |
% 21.26/5.86 | Instantiating formula (130) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 21.26/5.86 | (442) all_0_9_9 = n14
% 21.26/5.86 |
% 21.26/5.86 | Instantiating formula (165) with n15, all_0_5_5, n0 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n0, yields:
% 21.26/5.86 | (443) all_0_5_5 = n0
% 21.26/5.86 |
% 21.26/5.86 | From (442)(443) and (147) follows:
% 21.26/5.86 | (444) sum(n14, n0) = all_0_2_2
% 21.26/5.86 |
% 21.26/5.86 | From (442) and (435) follows:
% 21.26/5.86 | (445) sum(n14, n0) = all_0_7_7
% 21.26/5.86 |
% 21.26/5.86 | From (443) and (433) follows:
% 21.26/5.86 | (446) sum(n14, n0) = all_0_4_4
% 21.26/5.86 |
% 21.26/5.86 | Instantiating formula (74) with n14, n0, all_0_2_2, n14 and discharging atoms sum(n14, n0) = all_0_2_2, sum(n14, n0) = n14, yields:
% 21.26/5.86 | (447) all_0_2_2 = n14
% 21.26/5.86 |
% 21.26/5.86 | Instantiating formula (74) with n14, n0, all_0_4_4, all_0_2_2 and discharging atoms sum(n14, n0) = all_0_2_2, sum(n14, n0) = all_0_4_4, yields:
% 21.26/5.86 | (448) all_0_2_2 = all_0_4_4
% 21.26/5.86 |
% 21.26/5.86 | Instantiating formula (74) with n14, n0, all_0_7_7, all_0_2_2 and discharging atoms sum(n14, n0) = all_0_2_2, sum(n14, n0) = all_0_7_7, yields:
% 21.26/5.86 | (449) all_0_2_2 = all_0_7_7
% 21.26/5.86 |
% 21.26/5.86 | Combining equations (449,448) yields a new equation:
% 21.26/5.86 | (450) all_0_4_4 = all_0_7_7
% 21.26/5.86 |
% 21.26/5.86 | Combining equations (447,448) yields a new equation:
% 21.26/5.86 | (451) all_0_4_4 = n14
% 21.26/5.86 |
% 21.26/5.86 | Combining equations (451,450) yields a new equation:
% 21.26/5.86 | (452) all_0_7_7 = n14
% 21.26/5.86 |
% 21.26/5.86 | Combining equations (452,450) yields a new equation:
% 21.26/5.86 | (451) all_0_4_4 = n14
% 21.26/5.86 |
% 21.26/5.86 | Combining equations (451,448) yields a new equation:
% 21.26/5.86 | (447) all_0_2_2 = n14
% 21.26/5.86 |
% 21.26/5.86 | From (447) and (437) follows:
% 21.26/5.86 | (455) sum(n14, n14) = all_0_0_0
% 21.26/5.86 |
% 21.26/5.86 | From (452)(451) and (212) follows:
% 21.26/5.86 | (456) sum(n14, n14) = all_0_3_3
% 21.26/5.86 |
% 21.26/5.86 | Instantiating formula (74) with n14, n14, all_0_0_0, n12 and discharging atoms sum(n14, n14) = all_0_0_0, sum(n14, n14) = n12, yields:
% 21.26/5.86 | (457) all_0_0_0 = n12
% 21.26/5.86 |
% 21.26/5.86 | Instantiating formula (74) with n14, n14, all_0_3_3, all_0_0_0 and discharging atoms sum(n14, n14) = all_0_0_0, sum(n14, n14) = all_0_3_3, yields:
% 21.26/5.86 | (458) all_0_0_0 = all_0_3_3
% 21.26/5.86 |
% 21.26/5.86 | Combining equations (457,458) yields a new equation:
% 21.26/5.86 | (459) all_0_3_3 = n12
% 21.26/5.86 |
% 21.26/5.86 | Combining equations (459,458) yields a new equation:
% 21.26/5.86 | (457) all_0_0_0 = n12
% 21.26/5.86 |
% 21.26/5.86 | Equations (457,459) can reduce 363 to:
% 21.26/5.86 | (461) $false
% 21.26/5.86 |
% 21.26/5.86 |-The branch is then unsatisfiable
% 21.26/5.86 |-Branch two:
% 21.26/5.86 | (462) ~ (all_0_11_11 = n15)
% 21.26/5.86 | (463) all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.26/5.87 |
% 21.26/5.87 +-Applying beta-rule and splitting (463), into two cases.
% 21.26/5.87 |-Branch one:
% 21.26/5.87 | (464) all_0_11_11 = n14
% 21.26/5.87 |
% 21.26/5.87 | From (464) and (423) follows:
% 21.26/5.87 | (465) pred(n14) = all_0_9_9
% 21.26/5.87 |
% 21.26/5.87 | From (464) and (262) follows:
% 21.26/5.87 | (466) succ(n14) = all_0_5_5
% 21.26/5.87 |
% 21.26/5.87 | Instantiating formula (130) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 21.26/5.87 | (467) all_0_9_9 = n13
% 21.26/5.87 |
% 21.26/5.87 | Instantiating formula (165) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 21.26/5.87 | (468) all_0_5_5 = n15
% 21.26/5.87 |
% 21.26/5.87 | From (467)(468) and (147) follows:
% 21.26/5.87 | (469) sum(n13, n15) = all_0_2_2
% 21.26/5.87 |
% 21.26/5.87 | From (467) and (435) follows:
% 21.26/5.87 | (470) sum(n13, n0) = all_0_7_7
% 21.26/5.87 |
% 21.26/5.87 | From (468) and (433) follows:
% 21.26/5.87 | (471) sum(n14, n15) = all_0_4_4
% 21.26/5.87 |
% 21.26/5.87 | Instantiating formula (74) with n14, n15, all_0_4_4, n13 and discharging atoms sum(n14, n15) = all_0_4_4, sum(n14, n15) = n13, yields:
% 21.26/5.87 | (472) all_0_4_4 = n13
% 21.26/5.87 |
% 21.26/5.87 | Instantiating formula (74) with n13, n15, all_0_2_2, n12 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n12, yields:
% 21.26/5.87 | (473) all_0_2_2 = n12
% 21.26/5.87 |
% 21.26/5.87 | Instantiating formula (74) with n13, n0, all_0_7_7, n13 and discharging atoms sum(n13, n0) = all_0_7_7, sum(n13, n0) = n13, yields:
% 21.26/5.87 | (474) all_0_7_7 = n13
% 21.26/5.87 |
% 21.26/5.87 | From (473) and (437) follows:
% 21.26/5.87 | (475) sum(n12, n14) = all_0_0_0
% 21.26/5.87 |
% 21.26/5.87 | From (474)(472) and (212) follows:
% 21.26/5.87 | (476) sum(n13, n13) = all_0_3_3
% 21.26/5.87 |
% 21.26/5.87 | Instantiating formula (74) with n13, n13, all_0_3_3, n10 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n10, yields:
% 21.26/5.87 | (477) all_0_3_3 = n10
% 21.26/5.87 |
% 21.26/5.87 | Instantiating formula (74) with n12, n14, all_0_0_0, n10 and discharging atoms sum(n12, n14) = all_0_0_0, sum(n12, n14) = n10, yields:
% 21.26/5.87 | (478) all_0_0_0 = n10
% 21.26/5.87 |
% 21.26/5.87 | Equations (478,477) can reduce 363 to:
% 21.26/5.87 | (461) $false
% 21.26/5.87 |
% 21.26/5.87 |-The branch is then unsatisfiable
% 21.26/5.87 |-Branch two:
% 21.26/5.87 | (480) ~ (all_0_11_11 = n14)
% 21.26/5.87 | (481) all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.26/5.87 |
% 21.26/5.87 +-Applying beta-rule and splitting (481), into two cases.
% 21.26/5.87 |-Branch one:
% 21.26/5.87 | (482) all_0_11_11 = n13
% 21.26/5.87 |
% 21.26/5.87 | From (482) and (423) follows:
% 21.26/5.87 | (483) pred(n13) = all_0_9_9
% 21.26/5.87 |
% 21.26/5.87 | From (482) and (262) follows:
% 21.26/5.87 | (484) succ(n13) = all_0_5_5
% 21.26/5.87 |
% 21.26/5.87 | Instantiating formula (130) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 21.26/5.87 | (485) all_0_9_9 = n12
% 21.26/5.87 |
% 21.26/5.87 | Instantiating formula (165) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 21.26/5.87 | (486) all_0_5_5 = n14
% 21.26/5.87 |
% 21.26/5.87 | From (485)(486) and (147) follows:
% 21.26/5.87 | (487) sum(n12, n14) = all_0_2_2
% 21.26/5.87 |
% 21.26/5.87 | From (485) and (435) follows:
% 21.26/5.87 | (488) sum(n12, n0) = all_0_7_7
% 21.26/5.87 |
% 21.26/5.87 | From (486) and (433) follows:
% 21.26/5.87 | (489) sum(n14, n14) = all_0_4_4
% 21.26/5.87 |
% 21.26/5.87 | Instantiating formula (74) with n14, n14, all_0_4_4, n12 and discharging atoms sum(n14, n14) = all_0_4_4, sum(n14, n14) = n12, yields:
% 21.26/5.87 | (490) all_0_4_4 = n12
% 21.26/5.87 |
% 21.26/5.87 | Instantiating formula (74) with n12, n14, all_0_2_2, n10 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n10, yields:
% 21.26/5.87 | (491) all_0_2_2 = n10
% 21.26/5.88 |
% 21.26/5.88 | Instantiating formula (74) with n12, n0, all_0_7_7, n12 and discharging atoms sum(n12, n0) = all_0_7_7, sum(n12, n0) = n12, yields:
% 21.26/5.88 | (492) all_0_7_7 = n12
% 21.26/5.88 |
% 21.26/5.88 | From (491) and (437) follows:
% 21.26/5.88 | (493) sum(n10, n14) = all_0_0_0
% 21.26/5.88 |
% 21.26/5.88 | From (492)(490) and (212) follows:
% 21.26/5.88 | (494) sum(n12, n12) = all_0_3_3
% 21.26/5.88 |
% 21.26/5.88 | Instantiating formula (74) with n12, n12, all_0_3_3, n8 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n8, yields:
% 21.26/5.88 | (495) all_0_3_3 = n8
% 21.26/5.88 |
% 21.26/5.88 | Instantiating formula (74) with n10, n14, all_0_0_0, n8 and discharging atoms sum(n10, n14) = all_0_0_0, sum(n10, n14) = n8, yields:
% 21.26/5.88 | (496) all_0_0_0 = n8
% 21.26/5.88 |
% 21.52/5.88 | Equations (496,495) can reduce 363 to:
% 21.52/5.88 | (461) $false
% 21.52/5.88 |
% 21.52/5.88 |-The branch is then unsatisfiable
% 21.52/5.88 |-Branch two:
% 21.52/5.88 | (498) ~ (all_0_11_11 = n13)
% 21.52/5.88 | (499) all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.52/5.88 |
% 21.52/5.88 +-Applying beta-rule and splitting (499), into two cases.
% 21.52/5.88 |-Branch one:
% 21.52/5.88 | (500) all_0_11_11 = n12
% 21.52/5.88 |
% 21.52/5.88 | From (500) and (423) follows:
% 21.52/5.88 | (501) pred(n12) = all_0_9_9
% 21.52/5.88 |
% 21.52/5.88 | From (500) and (262) follows:
% 21.52/5.88 | (502) succ(n12) = all_0_5_5
% 21.52/5.88 |
% 21.52/5.88 | Instantiating formula (130) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 21.52/5.88 | (503) all_0_9_9 = n11
% 21.52/5.88 |
% 21.52/5.88 | Instantiating formula (165) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 21.52/5.88 | (504) all_0_5_5 = n13
% 21.52/5.88 |
% 21.52/5.88 | From (503)(504) and (147) follows:
% 21.52/5.88 | (505) sum(n11, n13) = all_0_2_2
% 21.52/5.88 |
% 21.52/5.88 | From (503) and (435) follows:
% 21.52/5.88 | (506) sum(n11, n0) = all_0_7_7
% 21.52/5.88 |
% 21.52/5.88 | From (504) and (433) follows:
% 21.52/5.88 | (507) sum(n14, n13) = all_0_4_4
% 21.52/5.88 |
% 21.52/5.88 | Instantiating formula (74) with n14, n13, all_0_4_4, n11 and discharging atoms sum(n14, n13) = all_0_4_4, sum(n14, n13) = n11, yields:
% 21.52/5.88 | (508) all_0_4_4 = n11
% 21.52/5.88 |
% 21.52/5.88 | Instantiating formula (74) with n11, n13, all_0_2_2, n8 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n8, yields:
% 21.52/5.88 | (509) all_0_2_2 = n8
% 21.52/5.88 |
% 21.52/5.88 | Instantiating formula (74) with n11, n0, all_0_7_7, n11 and discharging atoms sum(n11, n0) = all_0_7_7, sum(n11, n0) = n11, yields:
% 21.52/5.88 | (510) all_0_7_7 = n11
% 21.52/5.88 |
% 21.52/5.88 | From (509) and (437) follows:
% 21.52/5.88 | (511) sum(n8, n14) = all_0_0_0
% 21.52/5.88 |
% 21.52/5.88 | From (510)(508) and (212) follows:
% 21.52/5.88 | (512) sum(n11, n11) = all_0_3_3
% 21.52/5.88 |
% 21.52/5.88 | Instantiating formula (74) with n11, n11, all_0_3_3, n6 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n6, yields:
% 21.52/5.88 | (513) all_0_3_3 = n6
% 21.52/5.88 |
% 21.52/5.88 | Instantiating formula (74) with n8, n14, all_0_0_0, n6 and discharging atoms sum(n8, n14) = all_0_0_0, sum(n8, n14) = n6, yields:
% 21.52/5.88 | (514) all_0_0_0 = n6
% 21.52/5.88 |
% 21.52/5.88 | Equations (514,513) can reduce 363 to:
% 21.52/5.88 | (461) $false
% 21.52/5.88 |
% 21.52/5.88 |-The branch is then unsatisfiable
% 21.52/5.88 |-Branch two:
% 21.52/5.88 | (516) ~ (all_0_11_11 = n12)
% 21.52/5.88 | (517) all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.52/5.88 |
% 21.52/5.88 +-Applying beta-rule and splitting (517), into two cases.
% 21.52/5.88 |-Branch one:
% 21.52/5.88 | (518) all_0_11_11 = n11
% 21.52/5.88 |
% 21.52/5.88 | From (518) and (423) follows:
% 21.52/5.88 | (519) pred(n11) = all_0_9_9
% 21.52/5.88 |
% 21.52/5.88 | From (518) and (262) follows:
% 21.52/5.88 | (520) succ(n11) = all_0_5_5
% 21.52/5.88 |
% 21.52/5.88 | Instantiating formula (130) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 21.52/5.88 | (521) all_0_9_9 = n10
% 21.52/5.88 |
% 21.52/5.88 | Instantiating formula (165) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 21.52/5.88 | (522) all_0_5_5 = n12
% 21.52/5.88 |
% 21.52/5.88 | From (521)(522) and (147) follows:
% 21.52/5.88 | (523) sum(n10, n12) = all_0_2_2
% 21.52/5.88 |
% 21.52/5.88 | From (521) and (435) follows:
% 21.52/5.88 | (524) sum(n10, n0) = all_0_7_7
% 21.52/5.88 |
% 21.52/5.88 | From (522) and (433) follows:
% 21.52/5.88 | (525) sum(n14, n12) = all_0_4_4
% 21.52/5.88 |
% 21.52/5.88 | Instantiating formula (74) with n14, n12, all_0_4_4, n10 and discharging atoms sum(n14, n12) = all_0_4_4, sum(n14, n12) = n10, yields:
% 21.52/5.88 | (526) all_0_4_4 = n10
% 21.52/5.88 |
% 21.52/5.88 | Instantiating formula (74) with n10, n12, all_0_2_2, n6 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n6, yields:
% 21.52/5.89 | (527) all_0_2_2 = n6
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n10, n0, all_0_7_7, n10 and discharging atoms sum(n10, n0) = all_0_7_7, sum(n10, n0) = n10, yields:
% 21.52/5.89 | (528) all_0_7_7 = n10
% 21.52/5.89 |
% 21.52/5.89 | From (527) and (437) follows:
% 21.52/5.89 | (529) sum(n6, n14) = all_0_0_0
% 21.52/5.89 |
% 21.52/5.89 | From (528)(526) and (212) follows:
% 21.52/5.89 | (530) sum(n10, n10) = all_0_3_3
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n10, n10, all_0_3_3, n4 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n4, yields:
% 21.52/5.89 | (531) all_0_3_3 = n4
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n6, n14, all_0_0_0, n4 and discharging atoms sum(n6, n14) = all_0_0_0, sum(n6, n14) = n4, yields:
% 21.52/5.89 | (532) all_0_0_0 = n4
% 21.52/5.89 |
% 21.52/5.89 | Equations (532,531) can reduce 363 to:
% 21.52/5.89 | (461) $false
% 21.52/5.89 |
% 21.52/5.89 |-The branch is then unsatisfiable
% 21.52/5.89 |-Branch two:
% 21.52/5.89 | (534) ~ (all_0_11_11 = n11)
% 21.52/5.89 | (535) all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.52/5.89 |
% 21.52/5.89 +-Applying beta-rule and splitting (535), into two cases.
% 21.52/5.89 |-Branch one:
% 21.52/5.89 | (536) all_0_11_11 = n10
% 21.52/5.89 |
% 21.52/5.89 | From (536) and (423) follows:
% 21.52/5.89 | (537) pred(n10) = all_0_9_9
% 21.52/5.89 |
% 21.52/5.89 | From (536) and (262) follows:
% 21.52/5.89 | (538) succ(n10) = all_0_5_5
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (130) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 21.52/5.89 | (539) all_0_9_9 = n9
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (165) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 21.52/5.89 | (540) all_0_5_5 = n11
% 21.52/5.89 |
% 21.52/5.89 | From (539)(540) and (147) follows:
% 21.52/5.89 | (541) sum(n9, n11) = all_0_2_2
% 21.52/5.89 |
% 21.52/5.89 | From (539) and (435) follows:
% 21.52/5.89 | (542) sum(n9, n0) = all_0_7_7
% 21.52/5.89 |
% 21.52/5.89 | From (540) and (433) follows:
% 21.52/5.89 | (543) sum(n14, n11) = all_0_4_4
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n14, n11, all_0_4_4, n9 and discharging atoms sum(n14, n11) = all_0_4_4, sum(n14, n11) = n9, yields:
% 21.52/5.89 | (544) all_0_4_4 = n9
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n9, n11, all_0_2_2, n4 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n4, yields:
% 21.52/5.89 | (545) all_0_2_2 = n4
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n9, n0, all_0_7_7, n9 and discharging atoms sum(n9, n0) = all_0_7_7, sum(n9, n0) = n9, yields:
% 21.52/5.89 | (546) all_0_7_7 = n9
% 21.52/5.89 |
% 21.52/5.89 | From (545) and (437) follows:
% 21.52/5.89 | (547) sum(n4, n14) = all_0_0_0
% 21.52/5.89 |
% 21.52/5.89 | From (546)(544) and (212) follows:
% 21.52/5.89 | (548) sum(n9, n9) = all_0_3_3
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n9, n9, all_0_3_3, n2 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n2, yields:
% 21.52/5.89 | (549) all_0_3_3 = n2
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n4, n14, all_0_0_0, n2 and discharging atoms sum(n4, n14) = all_0_0_0, sum(n4, n14) = n2, yields:
% 21.52/5.89 | (550) all_0_0_0 = n2
% 21.52/5.89 |
% 21.52/5.89 | Equations (550,549) can reduce 363 to:
% 21.52/5.89 | (461) $false
% 21.52/5.89 |
% 21.52/5.89 |-The branch is then unsatisfiable
% 21.52/5.89 |-Branch two:
% 21.52/5.89 | (552) ~ (all_0_11_11 = n10)
% 21.52/5.89 | (553) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.52/5.89 |
% 21.52/5.89 +-Applying beta-rule and splitting (553), into two cases.
% 21.52/5.89 |-Branch one:
% 21.52/5.89 | (554) all_0_11_11 = n9
% 21.52/5.89 |
% 21.52/5.89 | From (554) and (423) follows:
% 21.52/5.89 | (555) pred(n9) = all_0_9_9
% 21.52/5.89 |
% 21.52/5.89 | From (554) and (262) follows:
% 21.52/5.89 | (556) succ(n9) = all_0_5_5
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (130) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 21.52/5.89 | (557) all_0_9_9 = n8
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (165) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 21.52/5.89 | (558) all_0_5_5 = n10
% 21.52/5.89 |
% 21.52/5.89 | From (557)(558) and (147) follows:
% 21.52/5.89 | (559) sum(n8, n10) = all_0_2_2
% 21.52/5.89 |
% 21.52/5.89 | From (557) and (435) follows:
% 21.52/5.89 | (560) sum(n8, n0) = all_0_7_7
% 21.52/5.89 |
% 21.52/5.89 | From (558) and (433) follows:
% 21.52/5.89 | (561) sum(n14, n10) = all_0_4_4
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n14, n10, all_0_4_4, n8 and discharging atoms sum(n14, n10) = all_0_4_4, sum(n14, n10) = n8, yields:
% 21.52/5.89 | (562) all_0_4_4 = n8
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n8, n10, all_0_2_2, n2 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n2, yields:
% 21.52/5.89 | (563) all_0_2_2 = n2
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n8, n0, all_0_7_7, n8 and discharging atoms sum(n8, n0) = all_0_7_7, sum(n8, n0) = n8, yields:
% 21.52/5.89 | (564) all_0_7_7 = n8
% 21.52/5.89 |
% 21.52/5.89 | From (563) and (437) follows:
% 21.52/5.89 | (565) sum(n2, n14) = all_0_0_0
% 21.52/5.89 |
% 21.52/5.89 | From (564)(562) and (212) follows:
% 21.52/5.89 | (566) sum(n8, n8) = all_0_3_3
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n8, n8, all_0_3_3, n0 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n0, yields:
% 21.52/5.89 | (567) all_0_3_3 = n0
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n2, n14, all_0_0_0, n0 and discharging atoms sum(n2, n14) = all_0_0_0, sum(n2, n14) = n0, yields:
% 21.52/5.89 | (568) all_0_0_0 = n0
% 21.52/5.89 |
% 21.52/5.89 | Equations (568,567) can reduce 363 to:
% 21.52/5.89 | (461) $false
% 21.52/5.89 |
% 21.52/5.89 |-The branch is then unsatisfiable
% 21.52/5.89 |-Branch two:
% 21.52/5.89 | (570) ~ (all_0_11_11 = n9)
% 21.52/5.89 | (571) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.52/5.89 |
% 21.52/5.89 +-Applying beta-rule and splitting (571), into two cases.
% 21.52/5.89 |-Branch one:
% 21.52/5.89 | (572) all_0_11_11 = n8
% 21.52/5.89 |
% 21.52/5.89 | From (572) and (423) follows:
% 21.52/5.89 | (573) pred(n8) = all_0_9_9
% 21.52/5.89 |
% 21.52/5.89 | From (572) and (262) follows:
% 21.52/5.89 | (574) succ(n8) = all_0_5_5
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (130) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 21.52/5.89 | (575) all_0_9_9 = n7
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (165) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 21.52/5.89 | (576) all_0_5_5 = n9
% 21.52/5.89 |
% 21.52/5.89 | From (575)(576) and (147) follows:
% 21.52/5.89 | (577) sum(n7, n9) = all_0_2_2
% 21.52/5.89 |
% 21.52/5.89 | From (575) and (435) follows:
% 21.52/5.89 | (578) sum(n7, n0) = all_0_7_7
% 21.52/5.89 |
% 21.52/5.89 | From (576) and (433) follows:
% 21.52/5.89 | (579) sum(n14, n9) = all_0_4_4
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n14, n9, all_0_4_4, n7 and discharging atoms sum(n14, n9) = all_0_4_4, sum(n14, n9) = n7, yields:
% 21.52/5.89 | (580) all_0_4_4 = n7
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n7, n9, all_0_2_2, n0 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n0, yields:
% 21.52/5.89 | (581) all_0_2_2 = n0
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n7, n0, all_0_7_7, n7 and discharging atoms sum(n7, n0) = all_0_7_7, sum(n7, n0) = n7, yields:
% 21.52/5.89 | (582) all_0_7_7 = n7
% 21.52/5.89 |
% 21.52/5.89 | From (581) and (437) follows:
% 21.52/5.89 | (583) sum(n0, n14) = all_0_0_0
% 21.52/5.89 |
% 21.52/5.89 | From (582)(580) and (212) follows:
% 21.52/5.89 | (584) sum(n7, n7) = all_0_3_3
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 21.52/5.89 | (585) all_0_3_3 = n14
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n0, n14, all_0_0_0, n14 and discharging atoms sum(n0, n14) = all_0_0_0, sum(n0, n14) = n14, yields:
% 21.52/5.89 | (586) all_0_0_0 = n14
% 21.52/5.89 |
% 21.52/5.89 | Equations (586,585) can reduce 363 to:
% 21.52/5.89 | (461) $false
% 21.52/5.89 |
% 21.52/5.89 |-The branch is then unsatisfiable
% 21.52/5.89 |-Branch two:
% 21.52/5.89 | (588) ~ (all_0_11_11 = n8)
% 21.52/5.89 | (589) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.52/5.89 |
% 21.52/5.89 +-Applying beta-rule and splitting (589), into two cases.
% 21.52/5.89 |-Branch one:
% 21.52/5.89 | (590) all_0_11_11 = n7
% 21.52/5.89 |
% 21.52/5.89 | From (590) and (423) follows:
% 21.52/5.89 | (591) pred(n7) = all_0_9_9
% 21.52/5.89 |
% 21.52/5.89 | From (590) and (262) follows:
% 21.52/5.89 | (592) succ(n7) = all_0_5_5
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (130) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 21.52/5.89 | (593) all_0_9_9 = n6
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (165) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 21.52/5.89 | (594) all_0_5_5 = n8
% 21.52/5.89 |
% 21.52/5.89 | From (593)(594) and (147) follows:
% 21.52/5.89 | (595) sum(n6, n8) = all_0_2_2
% 21.52/5.89 |
% 21.52/5.89 | From (593) and (435) follows:
% 21.52/5.89 | (596) sum(n6, n0) = all_0_7_7
% 21.52/5.89 |
% 21.52/5.89 | From (594) and (433) follows:
% 21.52/5.89 | (597) sum(n14, n8) = all_0_4_4
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n14, n8, all_0_4_4, n6 and discharging atoms sum(n14, n8) = all_0_4_4, sum(n14, n8) = n6, yields:
% 21.52/5.89 | (598) all_0_4_4 = n6
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 21.52/5.89 | (447) all_0_2_2 = n14
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n6, n0, all_0_7_7, n6 and discharging atoms sum(n6, n0) = all_0_7_7, sum(n6, n0) = n6, yields:
% 21.52/5.89 | (600) all_0_7_7 = n6
% 21.52/5.89 |
% 21.52/5.89 | From (447) and (437) follows:
% 21.52/5.89 | (455) sum(n14, n14) = all_0_0_0
% 21.52/5.89 |
% 21.52/5.89 | From (600)(598) and (212) follows:
% 21.52/5.89 | (602) sum(n6, n6) = all_0_3_3
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n14, n14, all_0_0_0, n12 and discharging atoms sum(n14, n14) = all_0_0_0, sum(n14, n14) = n12, yields:
% 21.52/5.89 | (457) all_0_0_0 = n12
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (74) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 21.52/5.89 | (459) all_0_3_3 = n12
% 21.52/5.89 |
% 21.52/5.89 | Equations (457,459) can reduce 363 to:
% 21.52/5.89 | (461) $false
% 21.52/5.89 |
% 21.52/5.89 |-The branch is then unsatisfiable
% 21.52/5.89 |-Branch two:
% 21.52/5.89 | (606) ~ (all_0_11_11 = n7)
% 21.52/5.89 | (607) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.52/5.89 |
% 21.52/5.89 +-Applying beta-rule and splitting (607), into two cases.
% 21.52/5.89 |-Branch one:
% 21.52/5.89 | (608) all_0_11_11 = n6
% 21.52/5.89 |
% 21.52/5.89 | From (608) and (423) follows:
% 21.52/5.89 | (609) pred(n6) = all_0_9_9
% 21.52/5.89 |
% 21.52/5.89 | From (608) and (262) follows:
% 21.52/5.89 | (610) succ(n6) = all_0_5_5
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (130) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 21.52/5.89 | (611) all_0_9_9 = n5
% 21.52/5.89 |
% 21.52/5.89 | Instantiating formula (165) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 21.52/5.89 | (612) all_0_5_5 = n7
% 21.52/5.89 |
% 21.52/5.89 | From (611)(612) and (147) follows:
% 21.52/5.90 | (613) sum(n5, n7) = all_0_2_2
% 21.52/5.90 |
% 21.52/5.90 | From (611) and (435) follows:
% 21.52/5.90 | (614) sum(n5, n0) = all_0_7_7
% 21.52/5.90 |
% 21.52/5.90 | From (612) and (433) follows:
% 21.52/5.90 | (615) sum(n14, n7) = all_0_4_4
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n14, n7, all_0_4_4, n5 and discharging atoms sum(n14, n7) = all_0_4_4, sum(n14, n7) = n5, yields:
% 21.52/5.90 | (616) all_0_4_4 = n5
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 21.52/5.90 | (473) all_0_2_2 = n12
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n5, n0, all_0_7_7, n5 and discharging atoms sum(n5, n0) = all_0_7_7, sum(n5, n0) = n5, yields:
% 21.52/5.90 | (618) all_0_7_7 = n5
% 21.52/5.90 |
% 21.52/5.90 | From (473) and (437) follows:
% 21.52/5.90 | (475) sum(n12, n14) = all_0_0_0
% 21.52/5.90 |
% 21.52/5.90 | From (618)(616) and (212) follows:
% 21.52/5.90 | (620) sum(n5, n5) = all_0_3_3
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n12, n14, all_0_0_0, n10 and discharging atoms sum(n12, n14) = all_0_0_0, sum(n12, n14) = n10, yields:
% 21.52/5.90 | (478) all_0_0_0 = n10
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 21.52/5.90 | (477) all_0_3_3 = n10
% 21.52/5.90 |
% 21.52/5.90 | Equations (478,477) can reduce 363 to:
% 21.52/5.90 | (461) $false
% 21.52/5.90 |
% 21.52/5.90 |-The branch is then unsatisfiable
% 21.52/5.90 |-Branch two:
% 21.52/5.90 | (624) ~ (all_0_11_11 = n6)
% 21.52/5.90 | (625) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.52/5.90 |
% 21.52/5.90 +-Applying beta-rule and splitting (625), into two cases.
% 21.52/5.90 |-Branch one:
% 21.52/5.90 | (626) all_0_11_11 = n5
% 21.52/5.90 |
% 21.52/5.90 | From (626) and (423) follows:
% 21.52/5.90 | (627) pred(n5) = all_0_9_9
% 21.52/5.90 |
% 21.52/5.90 | From (626) and (262) follows:
% 21.52/5.90 | (628) succ(n5) = all_0_5_5
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (130) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 21.52/5.90 | (629) all_0_9_9 = n4
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (165) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 21.52/5.90 | (630) all_0_5_5 = n6
% 21.52/5.90 |
% 21.52/5.90 | From (629)(630) and (147) follows:
% 21.52/5.90 | (631) sum(n4, n6) = all_0_2_2
% 21.52/5.90 |
% 21.52/5.90 | From (629) and (435) follows:
% 21.52/5.90 | (632) sum(n4, n0) = all_0_7_7
% 21.52/5.90 |
% 21.52/5.90 | From (630) and (433) follows:
% 21.52/5.90 | (633) sum(n14, n6) = all_0_4_4
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n14, n6, all_0_4_4, n4 and discharging atoms sum(n14, n6) = all_0_4_4, sum(n14, n6) = n4, yields:
% 21.52/5.90 | (634) all_0_4_4 = n4
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 21.52/5.90 | (491) all_0_2_2 = n10
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n4, n0, all_0_7_7, n4 and discharging atoms sum(n4, n0) = all_0_7_7, sum(n4, n0) = n4, yields:
% 21.52/5.90 | (636) all_0_7_7 = n4
% 21.52/5.90 |
% 21.52/5.90 | From (491) and (437) follows:
% 21.52/5.90 | (493) sum(n10, n14) = all_0_0_0
% 21.52/5.90 |
% 21.52/5.90 | From (636)(634) and (212) follows:
% 21.52/5.90 | (638) sum(n4, n4) = all_0_3_3
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n10, n14, all_0_0_0, n8 and discharging atoms sum(n10, n14) = all_0_0_0, sum(n10, n14) = n8, yields:
% 21.52/5.90 | (496) all_0_0_0 = n8
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 21.52/5.90 | (495) all_0_3_3 = n8
% 21.52/5.90 |
% 21.52/5.90 | Equations (496,495) can reduce 363 to:
% 21.52/5.90 | (461) $false
% 21.52/5.90 |
% 21.52/5.90 |-The branch is then unsatisfiable
% 21.52/5.90 |-Branch two:
% 21.52/5.90 | (642) ~ (all_0_11_11 = n5)
% 21.52/5.90 | (643) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.52/5.90 |
% 21.52/5.90 +-Applying beta-rule and splitting (643), into two cases.
% 21.52/5.90 |-Branch one:
% 21.52/5.90 | (644) all_0_11_11 = n4
% 21.52/5.90 |
% 21.52/5.90 | From (644) and (423) follows:
% 21.52/5.90 | (645) pred(n4) = all_0_9_9
% 21.52/5.90 |
% 21.52/5.90 | From (644) and (262) follows:
% 21.52/5.90 | (646) succ(n4) = all_0_5_5
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (130) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 21.52/5.90 | (647) all_0_9_9 = n3
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (165) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 21.52/5.90 | (648) all_0_5_5 = n5
% 21.52/5.90 |
% 21.52/5.90 | From (647)(648) and (147) follows:
% 21.52/5.90 | (649) sum(n3, n5) = all_0_2_2
% 21.52/5.90 |
% 21.52/5.90 | From (647) and (435) follows:
% 21.52/5.90 | (650) sum(n3, n0) = all_0_7_7
% 21.52/5.90 |
% 21.52/5.90 | From (648) and (433) follows:
% 21.52/5.90 | (651) sum(n14, n5) = all_0_4_4
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n14, n5, all_0_4_4, n3 and discharging atoms sum(n14, n5) = all_0_4_4, sum(n14, n5) = n3, yields:
% 21.52/5.90 | (652) all_0_4_4 = n3
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 21.52/5.90 | (509) all_0_2_2 = n8
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n3, n0, all_0_7_7, n3 and discharging atoms sum(n3, n0) = all_0_7_7, sum(n3, n0) = n3, yields:
% 21.52/5.90 | (654) all_0_7_7 = n3
% 21.52/5.90 |
% 21.52/5.90 | From (509) and (437) follows:
% 21.52/5.90 | (511) sum(n8, n14) = all_0_0_0
% 21.52/5.90 |
% 21.52/5.90 | From (654)(652) and (212) follows:
% 21.52/5.90 | (656) sum(n3, n3) = all_0_3_3
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n8, n14, all_0_0_0, n6 and discharging atoms sum(n8, n14) = all_0_0_0, sum(n8, n14) = n6, yields:
% 21.52/5.90 | (514) all_0_0_0 = n6
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 21.52/5.90 | (513) all_0_3_3 = n6
% 21.52/5.90 |
% 21.52/5.90 | Equations (514,513) can reduce 363 to:
% 21.52/5.90 | (461) $false
% 21.52/5.90 |
% 21.52/5.90 |-The branch is then unsatisfiable
% 21.52/5.90 |-Branch two:
% 21.52/5.90 | (660) ~ (all_0_11_11 = n4)
% 21.52/5.90 | (661) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.52/5.90 |
% 21.52/5.90 +-Applying beta-rule and splitting (661), into two cases.
% 21.52/5.90 |-Branch one:
% 21.52/5.90 | (662) all_0_11_11 = n3
% 21.52/5.90 |
% 21.52/5.90 | From (662) and (423) follows:
% 21.52/5.90 | (663) pred(n3) = all_0_9_9
% 21.52/5.90 |
% 21.52/5.90 | From (662) and (262) follows:
% 21.52/5.90 | (664) succ(n3) = all_0_5_5
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (130) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 21.52/5.90 | (665) all_0_9_9 = n2
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (165) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 21.52/5.90 | (666) all_0_5_5 = n4
% 21.52/5.90 |
% 21.52/5.90 | From (665)(666) and (147) follows:
% 21.52/5.90 | (667) sum(n2, n4) = all_0_2_2
% 21.52/5.90 |
% 21.52/5.90 | From (665) and (435) follows:
% 21.52/5.90 | (668) sum(n2, n0) = all_0_7_7
% 21.52/5.90 |
% 21.52/5.90 | From (666) and (433) follows:
% 21.52/5.90 | (669) sum(n14, n4) = all_0_4_4
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n14, n4, all_0_4_4, n2 and discharging atoms sum(n14, n4) = all_0_4_4, sum(n14, n4) = n2, yields:
% 21.52/5.90 | (670) all_0_4_4 = n2
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 21.52/5.90 | (527) all_0_2_2 = n6
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n2, n0, all_0_7_7, n2 and discharging atoms sum(n2, n0) = all_0_7_7, sum(n2, n0) = n2, yields:
% 21.52/5.90 | (672) all_0_7_7 = n2
% 21.52/5.90 |
% 21.52/5.90 | From (527) and (437) follows:
% 21.52/5.90 | (529) sum(n6, n14) = all_0_0_0
% 21.52/5.90 |
% 21.52/5.90 | From (672)(670) and (212) follows:
% 21.52/5.90 | (674) sum(n2, n2) = all_0_3_3
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n6, n14, all_0_0_0, n4 and discharging atoms sum(n6, n14) = all_0_0_0, sum(n6, n14) = n4, yields:
% 21.52/5.90 | (532) all_0_0_0 = n4
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 21.52/5.90 | (531) all_0_3_3 = n4
% 21.52/5.90 |
% 21.52/5.90 | Equations (532,531) can reduce 363 to:
% 21.52/5.90 | (461) $false
% 21.52/5.90 |
% 21.52/5.90 |-The branch is then unsatisfiable
% 21.52/5.90 |-Branch two:
% 21.52/5.90 | (678) ~ (all_0_11_11 = n3)
% 21.52/5.90 | (679) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.52/5.90 |
% 21.52/5.90 +-Applying beta-rule and splitting (679), into two cases.
% 21.52/5.90 |-Branch one:
% 21.52/5.90 | (680) all_0_11_11 = n2
% 21.52/5.90 |
% 21.52/5.90 | From (680) and (423) follows:
% 21.52/5.90 | (681) pred(n2) = all_0_9_9
% 21.52/5.90 |
% 21.52/5.90 | From (680) and (262) follows:
% 21.52/5.90 | (682) succ(n2) = all_0_5_5
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (130) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 21.52/5.90 | (683) all_0_9_9 = n1
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (165) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 21.52/5.90 | (684) all_0_5_5 = n3
% 21.52/5.90 |
% 21.52/5.90 | From (683)(684) and (147) follows:
% 21.52/5.90 | (685) sum(n1, n3) = all_0_2_2
% 21.52/5.90 |
% 21.52/5.90 | From (683) and (435) follows:
% 21.52/5.90 | (686) sum(n1, n0) = all_0_7_7
% 21.52/5.90 |
% 21.52/5.90 | From (684) and (433) follows:
% 21.52/5.90 | (687) sum(n14, n3) = all_0_4_4
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n14, n3, all_0_4_4, n1 and discharging atoms sum(n14, n3) = all_0_4_4, sum(n14, n3) = n1, yields:
% 21.52/5.90 | (688) all_0_4_4 = n1
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 21.52/5.90 | (545) all_0_2_2 = n4
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n1, n0, all_0_7_7, n1 and discharging atoms sum(n1, n0) = all_0_7_7, sum(n1, n0) = n1, yields:
% 21.52/5.90 | (690) all_0_7_7 = n1
% 21.52/5.90 |
% 21.52/5.90 | From (545) and (437) follows:
% 21.52/5.90 | (547) sum(n4, n14) = all_0_0_0
% 21.52/5.90 |
% 21.52/5.90 | From (690)(688) and (212) follows:
% 21.52/5.90 | (692) sum(n1, n1) = all_0_3_3
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n4, n14, all_0_0_0, n2 and discharging atoms sum(n4, n14) = all_0_0_0, sum(n4, n14) = n2, yields:
% 21.52/5.90 | (550) all_0_0_0 = n2
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (74) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 21.52/5.90 | (549) all_0_3_3 = n2
% 21.52/5.90 |
% 21.52/5.90 | Equations (550,549) can reduce 363 to:
% 21.52/5.90 | (461) $false
% 21.52/5.90 |
% 21.52/5.90 |-The branch is then unsatisfiable
% 21.52/5.90 |-Branch two:
% 21.52/5.90 | (696) ~ (all_0_11_11 = n2)
% 21.52/5.90 | (697) all_0_11_11 = n1 | all_0_11_11 = n0
% 21.52/5.90 |
% 21.52/5.90 +-Applying beta-rule and splitting (697), into two cases.
% 21.52/5.90 |-Branch one:
% 21.52/5.90 | (698) all_0_11_11 = n1
% 21.52/5.90 |
% 21.52/5.90 | From (698) and (423) follows:
% 21.52/5.90 | (699) pred(n1) = all_0_9_9
% 21.52/5.90 |
% 21.52/5.90 | From (698) and (262) follows:
% 21.52/5.90 | (700) succ(n1) = all_0_5_5
% 21.52/5.90 |
% 21.52/5.90 | Instantiating formula (130) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 21.52/5.90 | (701) all_0_9_9 = n0
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (165) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 21.52/5.91 | (702) all_0_5_5 = n2
% 21.52/5.91 |
% 21.52/5.91 | From (701)(702) and (147) follows:
% 21.52/5.91 | (703) sum(n0, n2) = all_0_2_2
% 21.52/5.91 |
% 21.52/5.91 | From (701) and (435) follows:
% 21.52/5.91 | (704) sum(n0, n0) = all_0_7_7
% 21.52/5.91 |
% 21.52/5.91 | From (702) and (433) follows:
% 21.52/5.91 | (705) sum(n14, n2) = all_0_4_4
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n14, n2, all_0_4_4, n0 and discharging atoms sum(n14, n2) = all_0_4_4, sum(n14, n2) = n0, yields:
% 21.52/5.91 | (706) all_0_4_4 = n0
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 21.52/5.91 | (563) all_0_2_2 = n2
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n0, n0, all_0_7_7, n0 and discharging atoms sum(n0, n0) = all_0_7_7, sum(n0, n0) = n0, yields:
% 21.52/5.91 | (708) all_0_7_7 = n0
% 21.52/5.91 |
% 21.52/5.91 | From (563) and (437) follows:
% 21.52/5.91 | (565) sum(n2, n14) = all_0_0_0
% 21.52/5.91 |
% 21.52/5.91 | From (708)(706) and (212) follows:
% 21.52/5.91 | (710) sum(n0, n0) = all_0_3_3
% 21.52/5.91 |
% 21.52/5.91 | From (708) and (704) follows:
% 21.52/5.91 | (113) sum(n0, n0) = n0
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n2, n14, all_0_0_0, n0 and discharging atoms sum(n2, n14) = all_0_0_0, sum(n2, n14) = n0, yields:
% 21.52/5.91 | (568) all_0_0_0 = n0
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 21.52/5.91 | (567) all_0_3_3 = n0
% 21.52/5.91 |
% 21.52/5.91 | Equations (568,567) can reduce 363 to:
% 21.52/5.91 | (461) $false
% 21.52/5.91 |
% 21.52/5.91 |-The branch is then unsatisfiable
% 21.52/5.91 |-Branch two:
% 21.52/5.91 | (715) ~ (all_0_11_11 = n1)
% 21.52/5.91 | (716) all_0_11_11 = n0
% 21.52/5.91 |
% 21.52/5.91 | From (716) and (423) follows:
% 21.52/5.91 | (717) pred(n0) = all_0_9_9
% 21.52/5.91 |
% 21.52/5.91 | From (716) and (262) follows:
% 21.52/5.91 | (718) succ(n0) = all_0_5_5
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (130) with n0, all_0_9_9, n15 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n15, yields:
% 21.52/5.91 | (719) all_0_9_9 = n15
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (165) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 21.52/5.91 | (720) all_0_5_5 = n1
% 21.52/5.91 |
% 21.52/5.91 | From (719)(720) and (147) follows:
% 21.52/5.91 | (721) sum(n15, n1) = all_0_2_2
% 21.52/5.91 |
% 21.52/5.91 | From (719) and (435) follows:
% 21.52/5.91 | (722) sum(n15, n0) = all_0_7_7
% 21.52/5.91 |
% 21.52/5.91 | From (720) and (433) follows:
% 21.52/5.91 | (723) sum(n14, n1) = all_0_4_4
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n15, n1, all_0_2_2, n0 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n0, yields:
% 21.52/5.91 | (581) all_0_2_2 = n0
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n15, n0, all_0_7_7, n15 and discharging atoms sum(n15, n0) = all_0_7_7, sum(n15, n0) = n15, yields:
% 21.52/5.91 | (725) all_0_7_7 = n15
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n14, n1, all_0_4_4, n15 and discharging atoms sum(n14, n1) = all_0_4_4, sum(n14, n1) = n15, yields:
% 21.52/5.91 | (726) all_0_4_4 = n15
% 21.52/5.91 |
% 21.52/5.91 | From (581) and (437) follows:
% 21.52/5.91 | (583) sum(n0, n14) = all_0_0_0
% 21.52/5.91 |
% 21.52/5.91 | From (725)(726) and (212) follows:
% 21.52/5.91 | (728) sum(n15, n15) = all_0_3_3
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n15, n15, all_0_3_3, n14 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n14, yields:
% 21.52/5.91 | (585) all_0_3_3 = n14
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n0, n14, all_0_0_0, n14 and discharging atoms sum(n0, n14) = all_0_0_0, sum(n0, n14) = n14, yields:
% 21.52/5.91 | (586) all_0_0_0 = n14
% 21.52/5.91 |
% 21.52/5.91 | Equations (586,585) can reduce 363 to:
% 21.52/5.91 | (461) $false
% 21.52/5.91 |
% 21.52/5.91 |-The branch is then unsatisfiable
% 21.52/5.91 |-Branch two:
% 21.52/5.91 | (732) ~ (all_0_10_10 = n15)
% 21.52/5.91 | (733) all_0_10_10 = n14 | all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.52/5.91 |
% 21.52/5.91 +-Applying beta-rule and splitting (29), into two cases.
% 21.52/5.91 |-Branch one:
% 21.52/5.91 | (439) all_0_11_11 = n15
% 21.52/5.91 |
% 21.52/5.91 | From (439) and (423) follows:
% 21.52/5.91 | (440) pred(n15) = all_0_9_9
% 21.52/5.91 |
% 21.52/5.91 | From (439) and (262) follows:
% 21.52/5.91 | (441) succ(n15) = all_0_5_5
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (130) with n15, all_0_9_9, n14 and discharging atoms pred(n15) = all_0_9_9, pred(n15) = n14, yields:
% 21.52/5.91 | (442) all_0_9_9 = n14
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (165) with n15, all_0_5_5, n0 and discharging atoms succ(n15) = all_0_5_5, succ(n15) = n0, yields:
% 21.52/5.91 | (443) all_0_5_5 = n0
% 21.52/5.91 |
% 21.52/5.91 | From (443) and (276) follows:
% 21.52/5.91 | (739) sum(all_0_6_6, n0) = all_0_4_4
% 21.52/5.91 |
% 21.52/5.91 | From (442)(443) and (147) follows:
% 21.52/5.91 | (444) sum(n14, n0) = all_0_2_2
% 21.52/5.91 |
% 21.52/5.91 | From (442) and (350) follows:
% 21.52/5.91 | (741) sum(n14, all_0_8_8) = all_0_7_7
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n14, n0, all_0_2_2, n14 and discharging atoms sum(n14, n0) = all_0_2_2, sum(n14, n0) = n14, yields:
% 21.52/5.91 | (447) all_0_2_2 = n14
% 21.52/5.91 |
% 21.52/5.91 | From (447) and (256) follows:
% 21.52/5.91 | (743) sum(n14, all_0_1_1) = all_0_0_0
% 21.52/5.91 |
% 21.52/5.91 | From (447) and (444) follows:
% 21.52/5.91 | (7) sum(n14, n0) = n14
% 21.52/5.91 |
% 21.52/5.91 +-Applying beta-rule and splitting (733), into two cases.
% 21.52/5.91 |-Branch one:
% 21.52/5.91 | (745) all_0_10_10 = n14
% 21.52/5.91 |
% 21.52/5.91 | From (745) and (317) follows:
% 21.52/5.91 | (746) pred(n14) = all_0_6_6
% 21.52/5.91 |
% 21.52/5.91 | From (745) and (146) follows:
% 21.52/5.91 | (747) succ(n14) = all_0_8_8
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (130) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 21.52/5.91 | (748) all_0_6_6 = n13
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (165) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 21.52/5.91 | (749) all_0_8_8 = n15
% 21.52/5.91 |
% 21.52/5.91 | From (748)(749) and (10) follows:
% 21.52/5.91 | (750) sum(n13, n15) = all_0_1_1
% 21.52/5.91 |
% 21.52/5.91 | From (748) and (739) follows:
% 21.52/5.91 | (751) sum(n13, n0) = all_0_4_4
% 21.52/5.91 |
% 21.52/5.91 | From (749) and (741) follows:
% 21.52/5.91 | (752) sum(n14, n15) = all_0_7_7
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n14, n15, all_0_7_7, n13 and discharging atoms sum(n14, n15) = all_0_7_7, sum(n14, n15) = n13, yields:
% 21.52/5.91 | (474) all_0_7_7 = n13
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n13, n15, all_0_1_1, n12 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n12, yields:
% 21.52/5.91 | (754) all_0_1_1 = n12
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n13, n0, all_0_4_4, n13 and discharging atoms sum(n13, n0) = all_0_4_4, sum(n13, n0) = n13, yields:
% 21.52/5.91 | (472) all_0_4_4 = n13
% 21.52/5.91 |
% 21.52/5.91 | From (474)(472) and (212) follows:
% 21.52/5.91 | (476) sum(n13, n13) = all_0_3_3
% 21.52/5.91 |
% 21.52/5.91 | From (754) and (743) follows:
% 21.52/5.91 | (757) sum(n14, n12) = all_0_0_0
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n14, n12, all_0_0_0, n10 and discharging atoms sum(n14, n12) = all_0_0_0, sum(n14, n12) = n10, yields:
% 21.52/5.91 | (478) all_0_0_0 = n10
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n13, n13, all_0_3_3, n10 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n10, yields:
% 21.52/5.91 | (477) all_0_3_3 = n10
% 21.52/5.91 |
% 21.52/5.91 | Equations (478,477) can reduce 363 to:
% 21.52/5.91 | (461) $false
% 21.52/5.91 |
% 21.52/5.91 |-The branch is then unsatisfiable
% 21.52/5.91 |-Branch two:
% 21.52/5.91 | (761) ~ (all_0_10_10 = n14)
% 21.52/5.91 | (762) all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.52/5.91 |
% 21.52/5.91 +-Applying beta-rule and splitting (762), into two cases.
% 21.52/5.91 |-Branch one:
% 21.52/5.91 | (763) all_0_10_10 = n13
% 21.52/5.91 |
% 21.52/5.91 | From (763) and (317) follows:
% 21.52/5.91 | (764) pred(n13) = all_0_6_6
% 21.52/5.91 |
% 21.52/5.91 | From (763) and (146) follows:
% 21.52/5.91 | (765) succ(n13) = all_0_8_8
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (130) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 21.52/5.91 | (766) all_0_6_6 = n12
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (165) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 21.52/5.91 | (767) all_0_8_8 = n14
% 21.52/5.91 |
% 21.52/5.91 | From (766)(767) and (10) follows:
% 21.52/5.91 | (768) sum(n12, n14) = all_0_1_1
% 21.52/5.91 |
% 21.52/5.91 | From (766) and (739) follows:
% 21.52/5.91 | (769) sum(n12, n0) = all_0_4_4
% 21.52/5.91 |
% 21.52/5.91 | From (767) and (741) follows:
% 21.52/5.91 | (770) sum(n14, n14) = all_0_7_7
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n14, n14, all_0_7_7, n12 and discharging atoms sum(n14, n14) = all_0_7_7, sum(n14, n14) = n12, yields:
% 21.52/5.91 | (492) all_0_7_7 = n12
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n12, n14, all_0_1_1, n10 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n10, yields:
% 21.52/5.91 | (772) all_0_1_1 = n10
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n12, n0, all_0_4_4, n12 and discharging atoms sum(n12, n0) = all_0_4_4, sum(n12, n0) = n12, yields:
% 21.52/5.91 | (490) all_0_4_4 = n12
% 21.52/5.91 |
% 21.52/5.91 | From (492)(490) and (212) follows:
% 21.52/5.91 | (494) sum(n12, n12) = all_0_3_3
% 21.52/5.91 |
% 21.52/5.91 | From (772) and (743) follows:
% 21.52/5.91 | (775) sum(n14, n10) = all_0_0_0
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n14, n10, all_0_0_0, n8 and discharging atoms sum(n14, n10) = all_0_0_0, sum(n14, n10) = n8, yields:
% 21.52/5.91 | (496) all_0_0_0 = n8
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n12, n12, all_0_3_3, n8 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n8, yields:
% 21.52/5.91 | (495) all_0_3_3 = n8
% 21.52/5.91 |
% 21.52/5.91 | Equations (496,495) can reduce 363 to:
% 21.52/5.91 | (461) $false
% 21.52/5.91 |
% 21.52/5.91 |-The branch is then unsatisfiable
% 21.52/5.91 |-Branch two:
% 21.52/5.91 | (779) ~ (all_0_10_10 = n13)
% 21.52/5.91 | (780) all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.52/5.91 |
% 21.52/5.91 +-Applying beta-rule and splitting (780), into two cases.
% 21.52/5.91 |-Branch one:
% 21.52/5.91 | (781) all_0_10_10 = n12
% 21.52/5.91 |
% 21.52/5.91 | From (781) and (317) follows:
% 21.52/5.91 | (782) pred(n12) = all_0_6_6
% 21.52/5.91 |
% 21.52/5.91 | From (781) and (146) follows:
% 21.52/5.91 | (783) succ(n12) = all_0_8_8
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (130) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 21.52/5.91 | (784) all_0_6_6 = n11
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (165) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 21.52/5.91 | (785) all_0_8_8 = n13
% 21.52/5.91 |
% 21.52/5.91 | From (784)(785) and (10) follows:
% 21.52/5.91 | (786) sum(n11, n13) = all_0_1_1
% 21.52/5.91 |
% 21.52/5.91 | From (784) and (739) follows:
% 21.52/5.91 | (787) sum(n11, n0) = all_0_4_4
% 21.52/5.91 |
% 21.52/5.91 | From (785) and (741) follows:
% 21.52/5.91 | (788) sum(n14, n13) = all_0_7_7
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n14, n13, all_0_7_7, n11 and discharging atoms sum(n14, n13) = all_0_7_7, sum(n14, n13) = n11, yields:
% 21.52/5.91 | (510) all_0_7_7 = n11
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n11, n13, all_0_1_1, n8 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n8, yields:
% 21.52/5.91 | (790) all_0_1_1 = n8
% 21.52/5.91 |
% 21.52/5.91 | Instantiating formula (74) with n11, n0, all_0_4_4, n11 and discharging atoms sum(n11, n0) = all_0_4_4, sum(n11, n0) = n11, yields:
% 21.52/5.92 | (508) all_0_4_4 = n11
% 21.52/5.92 |
% 21.52/5.92 | From (510)(508) and (212) follows:
% 21.52/5.92 | (512) sum(n11, n11) = all_0_3_3
% 21.52/5.92 |
% 21.52/5.92 | From (790) and (743) follows:
% 21.52/5.92 | (793) sum(n14, n8) = all_0_0_0
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n14, n8, all_0_0_0, n6 and discharging atoms sum(n14, n8) = all_0_0_0, sum(n14, n8) = n6, yields:
% 21.52/5.92 | (514) all_0_0_0 = n6
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n11, n11, all_0_3_3, n6 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n6, yields:
% 21.52/5.92 | (513) all_0_3_3 = n6
% 21.52/5.92 |
% 21.52/5.92 | Equations (514,513) can reduce 363 to:
% 21.52/5.92 | (461) $false
% 21.52/5.92 |
% 21.52/5.92 |-The branch is then unsatisfiable
% 21.52/5.92 |-Branch two:
% 21.52/5.92 | (797) ~ (all_0_10_10 = n12)
% 21.52/5.92 | (798) all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.52/5.92 |
% 21.52/5.92 +-Applying beta-rule and splitting (798), into two cases.
% 21.52/5.92 |-Branch one:
% 21.52/5.92 | (799) all_0_10_10 = n11
% 21.52/5.92 |
% 21.52/5.92 | From (799) and (317) follows:
% 21.52/5.92 | (800) pred(n11) = all_0_6_6
% 21.52/5.92 |
% 21.52/5.92 | From (799) and (146) follows:
% 21.52/5.92 | (801) succ(n11) = all_0_8_8
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (130) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 21.52/5.92 | (802) all_0_6_6 = n10
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (165) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 21.52/5.92 | (803) all_0_8_8 = n12
% 21.52/5.92 |
% 21.52/5.92 | From (802)(803) and (10) follows:
% 21.52/5.92 | (804) sum(n10, n12) = all_0_1_1
% 21.52/5.92 |
% 21.52/5.92 | From (802) and (739) follows:
% 21.52/5.92 | (805) sum(n10, n0) = all_0_4_4
% 21.52/5.92 |
% 21.52/5.92 | From (803) and (741) follows:
% 21.52/5.92 | (806) sum(n14, n12) = all_0_7_7
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n14, n12, all_0_7_7, n10 and discharging atoms sum(n14, n12) = all_0_7_7, sum(n14, n12) = n10, yields:
% 21.52/5.92 | (528) all_0_7_7 = n10
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n10, n12, all_0_1_1, n6 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n6, yields:
% 21.52/5.92 | (808) all_0_1_1 = n6
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n10, n0, all_0_4_4, n10 and discharging atoms sum(n10, n0) = all_0_4_4, sum(n10, n0) = n10, yields:
% 21.52/5.92 | (526) all_0_4_4 = n10
% 21.52/5.92 |
% 21.52/5.92 | From (528)(526) and (212) follows:
% 21.52/5.92 | (530) sum(n10, n10) = all_0_3_3
% 21.52/5.92 |
% 21.52/5.92 | From (808) and (743) follows:
% 21.52/5.92 | (811) sum(n14, n6) = all_0_0_0
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n14, n6, all_0_0_0, n4 and discharging atoms sum(n14, n6) = all_0_0_0, sum(n14, n6) = n4, yields:
% 21.52/5.92 | (532) all_0_0_0 = n4
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n10, n10, all_0_3_3, n4 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n4, yields:
% 21.52/5.92 | (531) all_0_3_3 = n4
% 21.52/5.92 |
% 21.52/5.92 | Equations (532,531) can reduce 363 to:
% 21.52/5.92 | (461) $false
% 21.52/5.92 |
% 21.52/5.92 |-The branch is then unsatisfiable
% 21.52/5.92 |-Branch two:
% 21.52/5.92 | (815) ~ (all_0_10_10 = n11)
% 21.52/5.92 | (816) all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.52/5.92 |
% 21.52/5.92 +-Applying beta-rule and splitting (816), into two cases.
% 21.52/5.92 |-Branch one:
% 21.52/5.92 | (817) all_0_10_10 = n10
% 21.52/5.92 |
% 21.52/5.92 | From (817) and (317) follows:
% 21.52/5.92 | (818) pred(n10) = all_0_6_6
% 21.52/5.92 |
% 21.52/5.92 | From (817) and (146) follows:
% 21.52/5.92 | (819) succ(n10) = all_0_8_8
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (130) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 21.52/5.92 | (820) all_0_6_6 = n9
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (165) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 21.52/5.92 | (821) all_0_8_8 = n11
% 21.52/5.92 |
% 21.52/5.92 | From (820)(821) and (10) follows:
% 21.52/5.92 | (822) sum(n9, n11) = all_0_1_1
% 21.52/5.92 |
% 21.52/5.92 | From (820) and (739) follows:
% 21.52/5.92 | (823) sum(n9, n0) = all_0_4_4
% 21.52/5.92 |
% 21.52/5.92 | From (821) and (741) follows:
% 21.52/5.92 | (824) sum(n14, n11) = all_0_7_7
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n14, n11, all_0_7_7, n9 and discharging atoms sum(n14, n11) = all_0_7_7, sum(n14, n11) = n9, yields:
% 21.52/5.92 | (546) all_0_7_7 = n9
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n9, n11, all_0_1_1, n4 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n4, yields:
% 21.52/5.92 | (826) all_0_1_1 = n4
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n9, n0, all_0_4_4, n9 and discharging atoms sum(n9, n0) = all_0_4_4, sum(n9, n0) = n9, yields:
% 21.52/5.92 | (544) all_0_4_4 = n9
% 21.52/5.92 |
% 21.52/5.92 | From (546)(544) and (212) follows:
% 21.52/5.92 | (548) sum(n9, n9) = all_0_3_3
% 21.52/5.92 |
% 21.52/5.92 | From (826) and (743) follows:
% 21.52/5.92 | (829) sum(n14, n4) = all_0_0_0
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n14, n4, all_0_0_0, n2 and discharging atoms sum(n14, n4) = all_0_0_0, sum(n14, n4) = n2, yields:
% 21.52/5.92 | (550) all_0_0_0 = n2
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n9, n9, all_0_3_3, n2 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n2, yields:
% 21.52/5.92 | (549) all_0_3_3 = n2
% 21.52/5.92 |
% 21.52/5.92 | Equations (550,549) can reduce 363 to:
% 21.52/5.92 | (461) $false
% 21.52/5.92 |
% 21.52/5.92 |-The branch is then unsatisfiable
% 21.52/5.92 |-Branch two:
% 21.52/5.92 | (833) ~ (all_0_10_10 = n10)
% 21.52/5.92 | (834) all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.52/5.92 |
% 21.52/5.92 +-Applying beta-rule and splitting (834), into two cases.
% 21.52/5.92 |-Branch one:
% 21.52/5.92 | (835) all_0_10_10 = n9
% 21.52/5.92 |
% 21.52/5.92 | From (835) and (317) follows:
% 21.52/5.92 | (836) pred(n9) = all_0_6_6
% 21.52/5.92 |
% 21.52/5.92 | From (835) and (146) follows:
% 21.52/5.92 | (837) succ(n9) = all_0_8_8
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (130) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 21.52/5.92 | (838) all_0_6_6 = n8
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (165) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 21.52/5.92 | (839) all_0_8_8 = n10
% 21.52/5.92 |
% 21.52/5.92 | From (838)(839) and (10) follows:
% 21.52/5.92 | (840) sum(n8, n10) = all_0_1_1
% 21.52/5.92 |
% 21.52/5.92 | From (838) and (739) follows:
% 21.52/5.92 | (841) sum(n8, n0) = all_0_4_4
% 21.52/5.92 |
% 21.52/5.92 | From (839) and (741) follows:
% 21.52/5.92 | (842) sum(n14, n10) = all_0_7_7
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n14, n10, all_0_7_7, n8 and discharging atoms sum(n14, n10) = all_0_7_7, sum(n14, n10) = n8, yields:
% 21.52/5.92 | (564) all_0_7_7 = n8
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n8, n10, all_0_1_1, n2 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n2, yields:
% 21.52/5.92 | (844) all_0_1_1 = n2
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n8, n0, all_0_4_4, n8 and discharging atoms sum(n8, n0) = all_0_4_4, sum(n8, n0) = n8, yields:
% 21.52/5.92 | (562) all_0_4_4 = n8
% 21.52/5.92 |
% 21.52/5.92 | From (564)(562) and (212) follows:
% 21.52/5.92 | (566) sum(n8, n8) = all_0_3_3
% 21.52/5.92 |
% 21.52/5.92 | From (844) and (743) follows:
% 21.52/5.92 | (847) sum(n14, n2) = all_0_0_0
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n14, n2, all_0_0_0, n0 and discharging atoms sum(n14, n2) = all_0_0_0, sum(n14, n2) = n0, yields:
% 21.52/5.92 | (568) all_0_0_0 = n0
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n8, n8, all_0_3_3, n0 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n0, yields:
% 21.52/5.92 | (567) all_0_3_3 = n0
% 21.52/5.92 |
% 21.52/5.92 | Equations (568,567) can reduce 363 to:
% 21.52/5.92 | (461) $false
% 21.52/5.92 |
% 21.52/5.92 |-The branch is then unsatisfiable
% 21.52/5.92 |-Branch two:
% 21.52/5.92 | (851) ~ (all_0_10_10 = n9)
% 21.52/5.92 | (852) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.52/5.92 |
% 21.52/5.92 +-Applying beta-rule and splitting (852), into two cases.
% 21.52/5.92 |-Branch one:
% 21.52/5.92 | (853) all_0_10_10 = n8
% 21.52/5.92 |
% 21.52/5.92 | From (853) and (317) follows:
% 21.52/5.92 | (854) pred(n8) = all_0_6_6
% 21.52/5.92 |
% 21.52/5.92 | From (853) and (146) follows:
% 21.52/5.92 | (855) succ(n8) = all_0_8_8
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (130) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 21.52/5.92 | (856) all_0_6_6 = n7
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (165) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 21.52/5.92 | (857) all_0_8_8 = n9
% 21.52/5.92 |
% 21.52/5.92 | From (856)(857) and (10) follows:
% 21.52/5.92 | (858) sum(n7, n9) = all_0_1_1
% 21.52/5.92 |
% 21.52/5.92 | From (856) and (739) follows:
% 21.52/5.92 | (859) sum(n7, n0) = all_0_4_4
% 21.52/5.92 |
% 21.52/5.92 | From (857) and (741) follows:
% 21.52/5.92 | (860) sum(n14, n9) = all_0_7_7
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n14, n9, all_0_7_7, n7 and discharging atoms sum(n14, n9) = all_0_7_7, sum(n14, n9) = n7, yields:
% 21.52/5.92 | (582) all_0_7_7 = n7
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n7, n9, all_0_1_1, n0 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n0, yields:
% 21.52/5.92 | (862) all_0_1_1 = n0
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n7, n0, all_0_4_4, n7 and discharging atoms sum(n7, n0) = all_0_4_4, sum(n7, n0) = n7, yields:
% 21.52/5.92 | (580) all_0_4_4 = n7
% 21.52/5.92 |
% 21.52/5.92 | From (582)(580) and (212) follows:
% 21.52/5.92 | (584) sum(n7, n7) = all_0_3_3
% 21.52/5.92 |
% 21.52/5.92 | From (862) and (743) follows:
% 21.52/5.92 | (865) sum(n14, n0) = all_0_0_0
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n14, n0, all_0_0_0, n14 and discharging atoms sum(n14, n0) = all_0_0_0, sum(n14, n0) = n14, yields:
% 21.52/5.92 | (586) all_0_0_0 = n14
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 21.52/5.92 | (585) all_0_3_3 = n14
% 21.52/5.92 |
% 21.52/5.92 | Equations (586,585) can reduce 363 to:
% 21.52/5.92 | (461) $false
% 21.52/5.92 |
% 21.52/5.92 |-The branch is then unsatisfiable
% 21.52/5.92 |-Branch two:
% 21.52/5.92 | (869) ~ (all_0_10_10 = n8)
% 21.52/5.92 | (870) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.52/5.92 |
% 21.52/5.92 +-Applying beta-rule and splitting (870), into two cases.
% 21.52/5.92 |-Branch one:
% 21.52/5.92 | (871) all_0_10_10 = n7
% 21.52/5.92 |
% 21.52/5.92 | From (871) and (317) follows:
% 21.52/5.92 | (872) pred(n7) = all_0_6_6
% 21.52/5.92 |
% 21.52/5.92 | From (871) and (146) follows:
% 21.52/5.92 | (873) succ(n7) = all_0_8_8
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (130) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 21.52/5.92 | (874) all_0_6_6 = n6
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (165) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 21.52/5.92 | (875) all_0_8_8 = n8
% 21.52/5.92 |
% 21.52/5.92 | From (874)(875) and (10) follows:
% 21.52/5.92 | (876) sum(n6, n8) = all_0_1_1
% 21.52/5.92 |
% 21.52/5.92 | From (874) and (739) follows:
% 21.52/5.92 | (877) sum(n6, n0) = all_0_4_4
% 21.52/5.92 |
% 21.52/5.92 | From (875) and (741) follows:
% 21.52/5.92 | (878) sum(n14, n8) = all_0_7_7
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n14, n8, all_0_7_7, n6 and discharging atoms sum(n14, n8) = all_0_7_7, sum(n14, n8) = n6, yields:
% 21.52/5.92 | (600) all_0_7_7 = n6
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 21.52/5.92 | (436) all_0_1_1 = n14
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n6, n0, all_0_4_4, n6 and discharging atoms sum(n6, n0) = all_0_4_4, sum(n6, n0) = n6, yields:
% 21.52/5.92 | (598) all_0_4_4 = n6
% 21.52/5.92 |
% 21.52/5.92 | From (600)(598) and (212) follows:
% 21.52/5.92 | (602) sum(n6, n6) = all_0_3_3
% 21.52/5.92 |
% 21.52/5.92 | From (436) and (743) follows:
% 21.52/5.92 | (455) sum(n14, n14) = all_0_0_0
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n14, n14, all_0_0_0, n12 and discharging atoms sum(n14, n14) = all_0_0_0, sum(n14, n14) = n12, yields:
% 21.52/5.92 | (457) all_0_0_0 = n12
% 21.52/5.92 |
% 21.52/5.92 | Instantiating formula (74) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 21.52/5.92 | (459) all_0_3_3 = n12
% 21.52/5.93 |
% 21.52/5.93 | Equations (457,459) can reduce 363 to:
% 21.52/5.93 | (461) $false
% 21.52/5.93 |
% 21.52/5.93 |-The branch is then unsatisfiable
% 21.52/5.93 |-Branch two:
% 21.52/5.93 | (887) ~ (all_0_10_10 = n7)
% 21.52/5.93 | (888) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.52/5.93 |
% 21.52/5.93 +-Applying beta-rule and splitting (888), into two cases.
% 21.52/5.93 |-Branch one:
% 21.52/5.93 | (889) all_0_10_10 = n6
% 21.52/5.93 |
% 21.52/5.93 | From (889) and (317) follows:
% 21.52/5.93 | (890) pred(n6) = all_0_6_6
% 21.52/5.93 |
% 21.52/5.93 | From (889) and (146) follows:
% 21.52/5.93 | (891) succ(n6) = all_0_8_8
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (130) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 21.52/5.93 | (892) all_0_6_6 = n5
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (165) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 21.52/5.93 | (893) all_0_8_8 = n7
% 21.52/5.93 |
% 21.52/5.93 | From (892)(893) and (10) follows:
% 21.52/5.93 | (894) sum(n5, n7) = all_0_1_1
% 21.52/5.93 |
% 21.52/5.93 | From (892) and (739) follows:
% 21.52/5.93 | (895) sum(n5, n0) = all_0_4_4
% 21.52/5.93 |
% 21.52/5.93 | From (893) and (741) follows:
% 21.52/5.93 | (896) sum(n14, n7) = all_0_7_7
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n14, n7, all_0_7_7, n5 and discharging atoms sum(n14, n7) = all_0_7_7, sum(n14, n7) = n5, yields:
% 21.52/5.93 | (618) all_0_7_7 = n5
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 21.52/5.93 | (754) all_0_1_1 = n12
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n5, n0, all_0_4_4, n5 and discharging atoms sum(n5, n0) = all_0_4_4, sum(n5, n0) = n5, yields:
% 21.52/5.93 | (616) all_0_4_4 = n5
% 21.52/5.93 |
% 21.52/5.93 | From (618)(616) and (212) follows:
% 21.52/5.93 | (620) sum(n5, n5) = all_0_3_3
% 21.52/5.93 |
% 21.52/5.93 | From (754) and (743) follows:
% 21.52/5.93 | (757) sum(n14, n12) = all_0_0_0
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n14, n12, all_0_0_0, n10 and discharging atoms sum(n14, n12) = all_0_0_0, sum(n14, n12) = n10, yields:
% 21.52/5.93 | (478) all_0_0_0 = n10
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 21.52/5.93 | (477) all_0_3_3 = n10
% 21.52/5.93 |
% 21.52/5.93 | Equations (478,477) can reduce 363 to:
% 21.52/5.93 | (461) $false
% 21.52/5.93 |
% 21.52/5.93 |-The branch is then unsatisfiable
% 21.52/5.93 |-Branch two:
% 21.52/5.93 | (905) ~ (all_0_10_10 = n6)
% 21.52/5.93 | (906) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.52/5.93 |
% 21.52/5.93 +-Applying beta-rule and splitting (906), into two cases.
% 21.52/5.93 |-Branch one:
% 21.52/5.93 | (907) all_0_10_10 = n5
% 21.52/5.93 |
% 21.52/5.93 | From (907) and (317) follows:
% 21.52/5.93 | (908) pred(n5) = all_0_6_6
% 21.52/5.93 |
% 21.52/5.93 | From (907) and (146) follows:
% 21.52/5.93 | (909) succ(n5) = all_0_8_8
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (130) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 21.52/5.93 | (910) all_0_6_6 = n4
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (165) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 21.52/5.93 | (911) all_0_8_8 = n6
% 21.52/5.93 |
% 21.52/5.93 | From (910)(911) and (10) follows:
% 21.52/5.93 | (912) sum(n4, n6) = all_0_1_1
% 21.52/5.93 |
% 21.52/5.93 | From (910) and (739) follows:
% 21.52/5.93 | (913) sum(n4, n0) = all_0_4_4
% 21.52/5.93 |
% 21.52/5.93 | From (911) and (741) follows:
% 21.52/5.93 | (914) sum(n14, n6) = all_0_7_7
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n14, n6, all_0_7_7, n4 and discharging atoms sum(n14, n6) = all_0_7_7, sum(n14, n6) = n4, yields:
% 21.52/5.93 | (636) all_0_7_7 = n4
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 21.52/5.93 | (772) all_0_1_1 = n10
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n4, n0, all_0_4_4, n4 and discharging atoms sum(n4, n0) = all_0_4_4, sum(n4, n0) = n4, yields:
% 21.52/5.93 | (634) all_0_4_4 = n4
% 21.52/5.93 |
% 21.52/5.93 | From (636)(634) and (212) follows:
% 21.52/5.93 | (638) sum(n4, n4) = all_0_3_3
% 21.52/5.93 |
% 21.52/5.93 | From (772) and (743) follows:
% 21.52/5.93 | (775) sum(n14, n10) = all_0_0_0
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n14, n10, all_0_0_0, n8 and discharging atoms sum(n14, n10) = all_0_0_0, sum(n14, n10) = n8, yields:
% 21.52/5.93 | (496) all_0_0_0 = n8
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 21.52/5.93 | (495) all_0_3_3 = n8
% 21.52/5.93 |
% 21.52/5.93 | Equations (496,495) can reduce 363 to:
% 21.52/5.93 | (461) $false
% 21.52/5.93 |
% 21.52/5.93 |-The branch is then unsatisfiable
% 21.52/5.93 |-Branch two:
% 21.52/5.93 | (923) ~ (all_0_10_10 = n5)
% 21.52/5.93 | (924) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.52/5.93 |
% 21.52/5.93 +-Applying beta-rule and splitting (924), into two cases.
% 21.52/5.93 |-Branch one:
% 21.52/5.93 | (925) all_0_10_10 = n4
% 21.52/5.93 |
% 21.52/5.93 | From (925) and (317) follows:
% 21.52/5.93 | (926) pred(n4) = all_0_6_6
% 21.52/5.93 |
% 21.52/5.93 | From (925) and (146) follows:
% 21.52/5.93 | (927) succ(n4) = all_0_8_8
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (130) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 21.52/5.93 | (928) all_0_6_6 = n3
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (165) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 21.52/5.93 | (929) all_0_8_8 = n5
% 21.52/5.93 |
% 21.52/5.93 | From (928)(929) and (10) follows:
% 21.52/5.93 | (930) sum(n3, n5) = all_0_1_1
% 21.52/5.93 |
% 21.52/5.93 | From (928) and (739) follows:
% 21.52/5.93 | (931) sum(n3, n0) = all_0_4_4
% 21.52/5.93 |
% 21.52/5.93 | From (929) and (741) follows:
% 21.52/5.93 | (932) sum(n14, n5) = all_0_7_7
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n14, n5, all_0_7_7, n3 and discharging atoms sum(n14, n5) = all_0_7_7, sum(n14, n5) = n3, yields:
% 21.52/5.93 | (654) all_0_7_7 = n3
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 21.52/5.93 | (790) all_0_1_1 = n8
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n3, n0, all_0_4_4, n3 and discharging atoms sum(n3, n0) = all_0_4_4, sum(n3, n0) = n3, yields:
% 21.52/5.93 | (652) all_0_4_4 = n3
% 21.52/5.93 |
% 21.52/5.93 | From (654)(652) and (212) follows:
% 21.52/5.93 | (656) sum(n3, n3) = all_0_3_3
% 21.52/5.93 |
% 21.52/5.93 | From (790) and (743) follows:
% 21.52/5.93 | (793) sum(n14, n8) = all_0_0_0
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n14, n8, all_0_0_0, n6 and discharging atoms sum(n14, n8) = all_0_0_0, sum(n14, n8) = n6, yields:
% 21.52/5.93 | (514) all_0_0_0 = n6
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 21.52/5.93 | (513) all_0_3_3 = n6
% 21.52/5.93 |
% 21.52/5.93 | Equations (514,513) can reduce 363 to:
% 21.52/5.93 | (461) $false
% 21.52/5.93 |
% 21.52/5.93 |-The branch is then unsatisfiable
% 21.52/5.93 |-Branch two:
% 21.52/5.93 | (941) ~ (all_0_10_10 = n4)
% 21.52/5.93 | (942) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.52/5.93 |
% 21.52/5.93 +-Applying beta-rule and splitting (942), into two cases.
% 21.52/5.93 |-Branch one:
% 21.52/5.93 | (943) all_0_10_10 = n3
% 21.52/5.93 |
% 21.52/5.93 | From (943) and (317) follows:
% 21.52/5.93 | (944) pred(n3) = all_0_6_6
% 21.52/5.93 |
% 21.52/5.93 | From (943) and (146) follows:
% 21.52/5.93 | (945) succ(n3) = all_0_8_8
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (130) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 21.52/5.93 | (946) all_0_6_6 = n2
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (165) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 21.52/5.93 | (947) all_0_8_8 = n4
% 21.52/5.93 |
% 21.52/5.93 | From (946)(947) and (10) follows:
% 21.52/5.93 | (948) sum(n2, n4) = all_0_1_1
% 21.52/5.93 |
% 21.52/5.93 | From (946) and (739) follows:
% 21.52/5.93 | (949) sum(n2, n0) = all_0_4_4
% 21.52/5.93 |
% 21.52/5.93 | From (947) and (741) follows:
% 21.52/5.93 | (950) sum(n14, n4) = all_0_7_7
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n14, n4, all_0_7_7, n2 and discharging atoms sum(n14, n4) = all_0_7_7, sum(n14, n4) = n2, yields:
% 21.52/5.93 | (672) all_0_7_7 = n2
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 21.52/5.93 | (808) all_0_1_1 = n6
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n2, n0, all_0_4_4, n2 and discharging atoms sum(n2, n0) = all_0_4_4, sum(n2, n0) = n2, yields:
% 21.52/5.93 | (670) all_0_4_4 = n2
% 21.52/5.93 |
% 21.52/5.93 | From (672)(670) and (212) follows:
% 21.52/5.93 | (674) sum(n2, n2) = all_0_3_3
% 21.52/5.93 |
% 21.52/5.93 | From (808) and (743) follows:
% 21.52/5.93 | (811) sum(n14, n6) = all_0_0_0
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n14, n6, all_0_0_0, n4 and discharging atoms sum(n14, n6) = all_0_0_0, sum(n14, n6) = n4, yields:
% 21.52/5.93 | (532) all_0_0_0 = n4
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 21.52/5.93 | (531) all_0_3_3 = n4
% 21.52/5.93 |
% 21.52/5.93 | Equations (532,531) can reduce 363 to:
% 21.52/5.93 | (461) $false
% 21.52/5.93 |
% 21.52/5.93 |-The branch is then unsatisfiable
% 21.52/5.93 |-Branch two:
% 21.52/5.93 | (959) ~ (all_0_10_10 = n3)
% 21.52/5.93 | (960) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.52/5.93 |
% 21.52/5.93 +-Applying beta-rule and splitting (960), into two cases.
% 21.52/5.93 |-Branch one:
% 21.52/5.93 | (961) all_0_10_10 = n2
% 21.52/5.93 |
% 21.52/5.93 | From (961) and (317) follows:
% 21.52/5.93 | (962) pred(n2) = all_0_6_6
% 21.52/5.93 |
% 21.52/5.93 | From (961) and (146) follows:
% 21.52/5.93 | (963) succ(n2) = all_0_8_8
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (130) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 21.52/5.93 | (964) all_0_6_6 = n1
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (165) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 21.52/5.93 | (965) all_0_8_8 = n3
% 21.52/5.93 |
% 21.52/5.93 | From (964)(965) and (10) follows:
% 21.52/5.93 | (966) sum(n1, n3) = all_0_1_1
% 21.52/5.93 |
% 21.52/5.93 | From (964) and (739) follows:
% 21.52/5.93 | (967) sum(n1, n0) = all_0_4_4
% 21.52/5.93 |
% 21.52/5.93 | From (965) and (741) follows:
% 21.52/5.93 | (968) sum(n14, n3) = all_0_7_7
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n14, n3, all_0_7_7, n1 and discharging atoms sum(n14, n3) = all_0_7_7, sum(n14, n3) = n1, yields:
% 21.52/5.93 | (690) all_0_7_7 = n1
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 21.52/5.93 | (826) all_0_1_1 = n4
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n1, n0, all_0_4_4, n1 and discharging atoms sum(n1, n0) = all_0_4_4, sum(n1, n0) = n1, yields:
% 21.52/5.93 | (688) all_0_4_4 = n1
% 21.52/5.93 |
% 21.52/5.93 | From (690)(688) and (212) follows:
% 21.52/5.93 | (692) sum(n1, n1) = all_0_3_3
% 21.52/5.93 |
% 21.52/5.93 | From (826) and (743) follows:
% 21.52/5.93 | (829) sum(n14, n4) = all_0_0_0
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n14, n4, all_0_0_0, n2 and discharging atoms sum(n14, n4) = all_0_0_0, sum(n14, n4) = n2, yields:
% 21.52/5.93 | (550) all_0_0_0 = n2
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (74) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 21.52/5.93 | (549) all_0_3_3 = n2
% 21.52/5.93 |
% 21.52/5.93 | Equations (550,549) can reduce 363 to:
% 21.52/5.93 | (461) $false
% 21.52/5.93 |
% 21.52/5.93 |-The branch is then unsatisfiable
% 21.52/5.93 |-Branch two:
% 21.52/5.93 | (977) ~ (all_0_10_10 = n2)
% 21.52/5.93 | (978) all_0_10_10 = n1 | all_0_10_10 = n0
% 21.52/5.93 |
% 21.52/5.93 +-Applying beta-rule and splitting (978), into two cases.
% 21.52/5.93 |-Branch one:
% 21.52/5.93 | (979) all_0_10_10 = n1
% 21.52/5.93 |
% 21.52/5.93 | From (979) and (317) follows:
% 21.52/5.93 | (980) pred(n1) = all_0_6_6
% 21.52/5.93 |
% 21.52/5.93 | From (979) and (146) follows:
% 21.52/5.93 | (981) succ(n1) = all_0_8_8
% 21.52/5.93 |
% 21.52/5.93 | Instantiating formula (130) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 21.52/5.93 | (982) all_0_6_6 = n0
% 21.52/5.93 |
% 21.52/5.94 | Instantiating formula (165) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 21.52/5.94 | (983) all_0_8_8 = n2
% 21.52/5.94 |
% 21.52/5.94 | From (982)(983) and (10) follows:
% 21.52/5.94 | (984) sum(n0, n2) = all_0_1_1
% 21.52/5.94 |
% 21.52/5.94 | From (982) and (739) follows:
% 21.52/5.94 | (985) sum(n0, n0) = all_0_4_4
% 21.52/5.94 |
% 21.52/5.94 | From (983) and (741) follows:
% 21.52/5.94 | (986) sum(n14, n2) = all_0_7_7
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n14, n2, all_0_7_7, n0 and discharging atoms sum(n14, n2) = all_0_7_7, sum(n14, n2) = n0, yields:
% 21.52/5.94 | (708) all_0_7_7 = n0
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 21.52/5.94 | (844) all_0_1_1 = n2
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n0, n0, all_0_4_4, n0 and discharging atoms sum(n0, n0) = all_0_4_4, sum(n0, n0) = n0, yields:
% 21.52/5.94 | (706) all_0_4_4 = n0
% 21.52/5.94 |
% 21.52/5.94 | From (708)(706) and (212) follows:
% 21.52/5.94 | (710) sum(n0, n0) = all_0_3_3
% 21.52/5.94 |
% 21.52/5.94 | From (844) and (743) follows:
% 21.52/5.94 | (847) sum(n14, n2) = all_0_0_0
% 21.52/5.94 |
% 21.52/5.94 | From (708) and (986) follows:
% 21.52/5.94 | (116) sum(n14, n2) = n0
% 21.52/5.94 |
% 21.52/5.94 | From (706) and (985) follows:
% 21.52/5.94 | (113) sum(n0, n0) = n0
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n14, n2, all_0_0_0, n0 and discharging atoms sum(n14, n2) = all_0_0_0, sum(n14, n2) = n0, yields:
% 21.52/5.94 | (568) all_0_0_0 = n0
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 21.52/5.94 | (567) all_0_3_3 = n0
% 21.52/5.94 |
% 21.52/5.94 | Equations (568,567) can reduce 363 to:
% 21.52/5.94 | (461) $false
% 21.52/5.94 |
% 21.52/5.94 |-The branch is then unsatisfiable
% 21.52/5.94 |-Branch two:
% 21.52/5.94 | (997) ~ (all_0_10_10 = n1)
% 21.52/5.94 | (998) all_0_10_10 = n0
% 21.52/5.94 |
% 21.52/5.94 | From (998) and (317) follows:
% 21.52/5.94 | (999) pred(n0) = all_0_6_6
% 21.52/5.94 |
% 21.52/5.94 | From (998) and (146) follows:
% 21.52/5.94 | (1000) succ(n0) = all_0_8_8
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (130) with n0, all_0_6_6, n15 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n15, yields:
% 21.52/5.94 | (1001) all_0_6_6 = n15
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (165) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 21.52/5.94 | (1002) all_0_8_8 = n1
% 21.52/5.94 |
% 21.52/5.94 | From (1001)(1002) and (10) follows:
% 21.52/5.94 | (1003) sum(n15, n1) = all_0_1_1
% 21.52/5.94 |
% 21.52/5.94 | From (1001) and (739) follows:
% 21.52/5.94 | (1004) sum(n15, n0) = all_0_4_4
% 21.52/5.94 |
% 21.52/5.94 | From (1002) and (741) follows:
% 21.52/5.94 | (1005) sum(n14, n1) = all_0_7_7
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n15, n1, all_0_1_1, n0 and discharging atoms sum(n15, n1) = all_0_1_1, sum(n15, n1) = n0, yields:
% 21.52/5.94 | (862) all_0_1_1 = n0
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n15, n0, all_0_4_4, n15 and discharging atoms sum(n15, n0) = all_0_4_4, sum(n15, n0) = n15, yields:
% 21.52/5.94 | (726) all_0_4_4 = n15
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n14, n1, all_0_7_7, n15 and discharging atoms sum(n14, n1) = all_0_7_7, sum(n14, n1) = n15, yields:
% 21.52/5.94 | (725) all_0_7_7 = n15
% 21.52/5.94 |
% 21.52/5.94 | From (725)(726) and (212) follows:
% 21.52/5.94 | (728) sum(n15, n15) = all_0_3_3
% 21.52/5.94 |
% 21.52/5.94 | From (862) and (743) follows:
% 21.52/5.94 | (865) sum(n14, n0) = all_0_0_0
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n15, n15, all_0_3_3, n14 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n14, yields:
% 21.52/5.94 | (585) all_0_3_3 = n14
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n14, n0, all_0_0_0, n14 and discharging atoms sum(n14, n0) = all_0_0_0, sum(n14, n0) = n14, yields:
% 21.52/5.94 | (586) all_0_0_0 = n14
% 21.52/5.94 |
% 21.52/5.94 | Equations (586,585) can reduce 363 to:
% 21.52/5.94 | (461) $false
% 21.52/5.94 |
% 21.52/5.94 |-The branch is then unsatisfiable
% 21.52/5.94 |-Branch two:
% 21.52/5.94 | (462) ~ (all_0_11_11 = n15)
% 21.52/5.94 | (463) all_0_11_11 = n14 | all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.52/5.94 |
% 21.52/5.94 +-Applying beta-rule and splitting (733), into two cases.
% 21.52/5.94 |-Branch one:
% 21.52/5.94 | (745) all_0_10_10 = n14
% 21.52/5.94 |
% 21.52/5.94 | From (745) and (317) follows:
% 21.52/5.94 | (746) pred(n14) = all_0_6_6
% 21.52/5.94 |
% 21.52/5.94 | From (745) and (146) follows:
% 21.52/5.94 | (747) succ(n14) = all_0_8_8
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (130) with n14, all_0_6_6, n13 and discharging atoms pred(n14) = all_0_6_6, pred(n14) = n13, yields:
% 21.52/5.94 | (748) all_0_6_6 = n13
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (165) with n14, all_0_8_8, n15 and discharging atoms succ(n14) = all_0_8_8, succ(n14) = n15, yields:
% 21.52/5.94 | (749) all_0_8_8 = n15
% 21.52/5.94 |
% 21.52/5.94 | From (748) and (746) follows:
% 21.52/5.94 | (226) pred(n14) = n13
% 21.52/5.94 |
% 21.52/5.94 | From (749) and (747) follows:
% 21.52/5.94 | (143) succ(n14) = n15
% 21.52/5.94 |
% 21.52/5.94 | From (748) and (276) follows:
% 21.52/5.94 | (1023) sum(n13, all_0_5_5) = all_0_4_4
% 21.52/5.94 |
% 21.52/5.94 | From (748)(749) and (10) follows:
% 21.52/5.94 | (750) sum(n13, n15) = all_0_1_1
% 21.52/5.94 |
% 21.52/5.94 | From (749) and (350) follows:
% 21.52/5.94 | (1025) sum(all_0_9_9, n15) = all_0_7_7
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n13, n15, all_0_1_1, n12 and discharging atoms sum(n13, n15) = all_0_1_1, sum(n13, n15) = n12, yields:
% 21.52/5.94 | (754) all_0_1_1 = n12
% 21.52/5.94 |
% 21.52/5.94 | From (754) and (256) follows:
% 21.52/5.94 | (1027) sum(all_0_2_2, n12) = all_0_0_0
% 21.52/5.94 |
% 21.52/5.94 | From (754) and (750) follows:
% 21.52/5.94 | (33) sum(n13, n15) = n12
% 21.52/5.94 |
% 21.52/5.94 +-Applying beta-rule and splitting (463), into two cases.
% 21.52/5.94 |-Branch one:
% 21.52/5.94 | (464) all_0_11_11 = n14
% 21.52/5.94 |
% 21.52/5.94 | From (464) and (423) follows:
% 21.52/5.94 | (465) pred(n14) = all_0_9_9
% 21.52/5.94 |
% 21.52/5.94 | From (464) and (262) follows:
% 21.52/5.94 | (466) succ(n14) = all_0_5_5
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (130) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 21.52/5.94 | (467) all_0_9_9 = n13
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (165) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 21.52/5.94 | (468) all_0_5_5 = n15
% 21.52/5.94 |
% 21.52/5.94 | From (467)(468) and (147) follows:
% 21.52/5.94 | (469) sum(n13, n15) = all_0_2_2
% 21.52/5.94 |
% 21.52/5.94 | From (467) and (1025) follows:
% 21.52/5.94 | (1035) sum(n13, n15) = all_0_7_7
% 21.52/5.94 |
% 21.52/5.94 | From (468) and (1023) follows:
% 21.52/5.94 | (1036) sum(n13, n15) = all_0_4_4
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n13, n15, all_0_2_2, n12 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n12, yields:
% 21.52/5.94 | (473) all_0_2_2 = n12
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n13, n15, all_0_4_4, all_0_2_2 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = all_0_4_4, yields:
% 21.52/5.94 | (448) all_0_2_2 = all_0_4_4
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n13, n15, all_0_7_7, all_0_2_2 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = all_0_7_7, yields:
% 21.52/5.94 | (449) all_0_2_2 = all_0_7_7
% 21.52/5.94 |
% 21.52/5.94 | Combining equations (449,448) yields a new equation:
% 21.52/5.94 | (450) all_0_4_4 = all_0_7_7
% 21.52/5.94 |
% 21.52/5.94 | Combining equations (473,448) yields a new equation:
% 21.52/5.94 | (490) all_0_4_4 = n12
% 21.52/5.94 |
% 21.52/5.94 | Combining equations (490,450) yields a new equation:
% 21.52/5.94 | (492) all_0_7_7 = n12
% 21.52/5.94 |
% 21.52/5.94 | Combining equations (492,450) yields a new equation:
% 21.52/5.94 | (490) all_0_4_4 = n12
% 21.52/5.94 |
% 21.52/5.94 | Combining equations (490,448) yields a new equation:
% 21.52/5.94 | (473) all_0_2_2 = n12
% 21.52/5.94 |
% 21.52/5.94 | From (473) and (1027) follows:
% 21.52/5.94 | (1045) sum(n12, n12) = all_0_0_0
% 21.52/5.94 |
% 21.52/5.94 | From (492)(490) and (212) follows:
% 21.52/5.94 | (494) sum(n12, n12) = all_0_3_3
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n12, n12, all_0_0_0, n8 and discharging atoms sum(n12, n12) = all_0_0_0, sum(n12, n12) = n8, yields:
% 21.52/5.94 | (496) all_0_0_0 = n8
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n12, n12, all_0_3_3, all_0_0_0 and discharging atoms sum(n12, n12) = all_0_0_0, sum(n12, n12) = all_0_3_3, yields:
% 21.52/5.94 | (458) all_0_0_0 = all_0_3_3
% 21.52/5.94 |
% 21.52/5.94 | Combining equations (496,458) yields a new equation:
% 21.52/5.94 | (495) all_0_3_3 = n8
% 21.52/5.94 |
% 21.52/5.94 | Combining equations (495,458) yields a new equation:
% 21.52/5.94 | (496) all_0_0_0 = n8
% 21.52/5.94 |
% 21.52/5.94 | Equations (496,495) can reduce 363 to:
% 21.52/5.94 | (461) $false
% 21.52/5.94 |
% 21.52/5.94 |-The branch is then unsatisfiable
% 21.52/5.94 |-Branch two:
% 21.52/5.94 | (480) ~ (all_0_11_11 = n14)
% 21.52/5.94 | (481) all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.52/5.94 |
% 21.52/5.94 +-Applying beta-rule and splitting (481), into two cases.
% 21.52/5.94 |-Branch one:
% 21.52/5.94 | (482) all_0_11_11 = n13
% 21.52/5.94 |
% 21.52/5.94 | From (482) and (423) follows:
% 21.52/5.94 | (483) pred(n13) = all_0_9_9
% 21.52/5.94 |
% 21.52/5.94 | From (482) and (262) follows:
% 21.52/5.94 | (484) succ(n13) = all_0_5_5
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (130) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 21.52/5.94 | (485) all_0_9_9 = n12
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (165) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 21.52/5.94 | (486) all_0_5_5 = n14
% 21.52/5.94 |
% 21.52/5.94 | From (485)(486) and (147) follows:
% 21.52/5.94 | (487) sum(n12, n14) = all_0_2_2
% 21.52/5.94 |
% 21.52/5.94 | From (485) and (1025) follows:
% 21.52/5.94 | (1060) sum(n12, n15) = all_0_7_7
% 21.52/5.94 |
% 21.52/5.94 | From (486) and (1023) follows:
% 21.52/5.94 | (1061) sum(n13, n14) = all_0_4_4
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n13, n14, all_0_4_4, n11 and discharging atoms sum(n13, n14) = all_0_4_4, sum(n13, n14) = n11, yields:
% 21.52/5.94 | (508) all_0_4_4 = n11
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n12, n15, all_0_7_7, n11 and discharging atoms sum(n12, n15) = all_0_7_7, sum(n12, n15) = n11, yields:
% 21.52/5.94 | (510) all_0_7_7 = n11
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n12, n14, all_0_2_2, n10 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n10, yields:
% 21.52/5.94 | (491) all_0_2_2 = n10
% 21.52/5.94 |
% 21.52/5.94 | From (491) and (1027) follows:
% 21.52/5.94 | (1065) sum(n10, n12) = all_0_0_0
% 21.52/5.94 |
% 21.52/5.94 | From (510)(508) and (212) follows:
% 21.52/5.94 | (512) sum(n11, n11) = all_0_3_3
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n11, n11, all_0_3_3, n6 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n6, yields:
% 21.52/5.94 | (513) all_0_3_3 = n6
% 21.52/5.94 |
% 21.52/5.94 | Instantiating formula (74) with n10, n12, all_0_0_0, n6 and discharging atoms sum(n10, n12) = all_0_0_0, sum(n10, n12) = n6, yields:
% 21.52/5.94 | (514) all_0_0_0 = n6
% 21.52/5.94 |
% 21.52/5.94 | Equations (514,513) can reduce 363 to:
% 21.52/5.94 | (461) $false
% 21.52/5.94 |
% 21.52/5.94 |-The branch is then unsatisfiable
% 21.52/5.94 |-Branch two:
% 21.52/5.94 | (498) ~ (all_0_11_11 = n13)
% 21.52/5.94 | (499) all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.52/5.94 |
% 21.52/5.94 +-Applying beta-rule and splitting (499), into two cases.
% 21.52/5.94 |-Branch one:
% 21.52/5.94 | (500) all_0_11_11 = n12
% 21.52/5.94 |
% 21.52/5.94 | From (500) and (423) follows:
% 21.52/5.94 | (501) pred(n12) = all_0_9_9
% 21.52/5.94 |
% 21.52/5.95 | From (500) and (262) follows:
% 21.52/5.95 | (502) succ(n12) = all_0_5_5
% 21.52/5.95 |
% 21.52/5.95 | Instantiating formula (130) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 21.52/5.95 | (503) all_0_9_9 = n11
% 21.52/5.95 |
% 21.52/5.95 | Instantiating formula (165) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 21.52/5.95 | (504) all_0_5_5 = n13
% 21.52/5.95 |
% 21.52/5.95 | From (503)(504) and (147) follows:
% 21.52/5.95 | (505) sum(n11, n13) = all_0_2_2
% 21.52/5.95 |
% 21.52/5.95 | From (503) and (1025) follows:
% 21.52/5.95 | (1078) sum(n11, n15) = all_0_7_7
% 21.52/5.95 |
% 21.52/5.95 | From (504) and (1023) follows:
% 21.52/5.95 | (1079) sum(n13, n13) = all_0_4_4
% 21.52/5.95 |
% 21.52/5.95 | Instantiating formula (74) with n13, n13, all_0_4_4, n10 and discharging atoms sum(n13, n13) = all_0_4_4, sum(n13, n13) = n10, yields:
% 21.52/5.95 | (526) all_0_4_4 = n10
% 21.52/5.95 |
% 21.52/5.95 | Instantiating formula (74) with n11, n15, all_0_7_7, n10 and discharging atoms sum(n11, n15) = all_0_7_7, sum(n11, n15) = n10, yields:
% 21.52/5.95 | (528) all_0_7_7 = n10
% 21.52/5.95 |
% 21.52/5.95 | Instantiating formula (74) with n11, n13, all_0_2_2, n8 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n8, yields:
% 21.52/5.95 | (509) all_0_2_2 = n8
% 21.52/5.95 |
% 21.52/5.95 | From (509) and (1027) follows:
% 21.52/5.95 | (1083) sum(n8, n12) = all_0_0_0
% 21.52/5.95 |
% 21.52/5.95 | From (528)(526) and (212) follows:
% 21.52/5.95 | (530) sum(n10, n10) = all_0_3_3
% 21.52/5.95 |
% 21.52/5.95 | Instantiating formula (74) with n10, n10, all_0_3_3, n4 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n4, yields:
% 21.52/5.95 | (531) all_0_3_3 = n4
% 21.52/5.95 |
% 21.52/5.95 | Instantiating formula (74) with n8, n12, all_0_0_0, n4 and discharging atoms sum(n8, n12) = all_0_0_0, sum(n8, n12) = n4, yields:
% 21.52/5.95 | (532) all_0_0_0 = n4
% 21.52/5.95 |
% 21.52/5.95 | Equations (532,531) can reduce 363 to:
% 21.52/5.95 | (461) $false
% 21.52/5.95 |
% 21.52/5.95 |-The branch is then unsatisfiable
% 21.52/5.95 |-Branch two:
% 21.52/5.95 | (516) ~ (all_0_11_11 = n12)
% 21.52/5.95 | (517) all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.52/5.95 |
% 21.52/5.95 +-Applying beta-rule and splitting (517), into two cases.
% 21.52/5.95 |-Branch one:
% 21.52/5.95 | (518) all_0_11_11 = n11
% 21.52/5.95 |
% 21.52/5.95 | From (518) and (423) follows:
% 21.52/5.95 | (519) pred(n11) = all_0_9_9
% 21.52/5.95 |
% 21.52/5.95 | From (518) and (262) follows:
% 21.52/5.95 | (520) succ(n11) = all_0_5_5
% 21.52/5.95 |
% 21.52/5.95 | Instantiating formula (130) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 21.52/5.95 | (521) all_0_9_9 = n10
% 21.52/5.95 |
% 21.52/5.95 | Instantiating formula (165) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 21.52/5.95 | (522) all_0_5_5 = n12
% 21.52/5.95 |
% 21.52/5.95 | From (521)(522) and (147) follows:
% 21.52/5.95 | (523) sum(n10, n12) = all_0_2_2
% 21.52/5.95 |
% 21.52/5.95 | From (521) and (1025) follows:
% 21.52/5.95 | (1096) sum(n10, n15) = all_0_7_7
% 21.52/5.95 |
% 21.52/5.95 | From (522) and (1023) follows:
% 21.52/5.95 | (1097) sum(n13, n12) = all_0_4_4
% 21.52/5.95 |
% 21.52/5.95 | Instantiating formula (74) with n13, n12, all_0_4_4, n9 and discharging atoms sum(n13, n12) = all_0_4_4, sum(n13, n12) = n9, yields:
% 21.52/5.95 | (544) all_0_4_4 = n9
% 21.52/5.95 |
% 21.52/5.95 | Instantiating formula (74) with n10, n15, all_0_7_7, n9 and discharging atoms sum(n10, n15) = all_0_7_7, sum(n10, n15) = n9, yields:
% 21.52/5.95 | (546) all_0_7_7 = n9
% 21.52/5.95 |
% 21.52/5.95 | Instantiating formula (74) with n10, n12, all_0_2_2, n6 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n6, yields:
% 21.52/5.95 | (527) all_0_2_2 = n6
% 21.52/5.95 |
% 21.52/5.95 | From (527) and (1027) follows:
% 21.52/5.95 | (1101) sum(n6, n12) = all_0_0_0
% 21.52/5.95 |
% 21.52/5.95 | From (546)(544) and (212) follows:
% 21.52/5.95 | (548) sum(n9, n9) = all_0_3_3
% 21.52/5.95 |
% 21.52/5.95 | Instantiating formula (74) with n9, n9, all_0_3_3, n2 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n2, yields:
% 21.52/5.95 | (549) all_0_3_3 = n2
% 21.52/5.95 |
% 21.52/5.95 | Instantiating formula (74) with n6, n12, all_0_0_0, n2 and discharging atoms sum(n6, n12) = all_0_0_0, sum(n6, n12) = n2, yields:
% 21.52/5.95 | (550) all_0_0_0 = n2
% 21.52/5.95 |
% 21.84/5.95 | Equations (550,549) can reduce 363 to:
% 21.84/5.95 | (461) $false
% 21.84/5.95 |
% 21.84/5.95 |-The branch is then unsatisfiable
% 21.84/5.95 |-Branch two:
% 21.84/5.95 | (534) ~ (all_0_11_11 = n11)
% 21.84/5.95 | (535) all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.84/5.95 |
% 21.84/5.95 +-Applying beta-rule and splitting (535), into two cases.
% 21.84/5.95 |-Branch one:
% 21.84/5.95 | (536) all_0_11_11 = n10
% 21.84/5.95 |
% 21.84/5.95 | From (536) and (423) follows:
% 21.84/5.95 | (537) pred(n10) = all_0_9_9
% 21.84/5.95 |
% 21.84/5.95 | From (536) and (262) follows:
% 21.84/5.95 | (538) succ(n10) = all_0_5_5
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (130) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 21.84/5.95 | (539) all_0_9_9 = n9
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (165) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 21.84/5.95 | (540) all_0_5_5 = n11
% 21.84/5.95 |
% 21.84/5.95 | From (539)(540) and (147) follows:
% 21.84/5.95 | (541) sum(n9, n11) = all_0_2_2
% 21.84/5.95 |
% 21.84/5.95 | From (539) and (1025) follows:
% 21.84/5.95 | (1114) sum(n9, n15) = all_0_7_7
% 21.84/5.95 |
% 21.84/5.95 | From (540) and (1023) follows:
% 21.84/5.95 | (1115) sum(n13, n11) = all_0_4_4
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (74) with n13, n11, all_0_4_4, n8 and discharging atoms sum(n13, n11) = all_0_4_4, sum(n13, n11) = n8, yields:
% 21.84/5.95 | (562) all_0_4_4 = n8
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (74) with n9, n15, all_0_7_7, n8 and discharging atoms sum(n9, n15) = all_0_7_7, sum(n9, n15) = n8, yields:
% 21.84/5.95 | (564) all_0_7_7 = n8
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (74) with n9, n11, all_0_2_2, n4 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n4, yields:
% 21.84/5.95 | (545) all_0_2_2 = n4
% 21.84/5.95 |
% 21.84/5.95 | From (545) and (1027) follows:
% 21.84/5.95 | (1119) sum(n4, n12) = all_0_0_0
% 21.84/5.95 |
% 21.84/5.95 | From (564)(562) and (212) follows:
% 21.84/5.95 | (566) sum(n8, n8) = all_0_3_3
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (74) with n8, n8, all_0_3_3, n0 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n0, yields:
% 21.84/5.95 | (567) all_0_3_3 = n0
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (74) with n4, n12, all_0_0_0, n0 and discharging atoms sum(n4, n12) = all_0_0_0, sum(n4, n12) = n0, yields:
% 21.84/5.95 | (568) all_0_0_0 = n0
% 21.84/5.95 |
% 21.84/5.95 | Equations (568,567) can reduce 363 to:
% 21.84/5.95 | (461) $false
% 21.84/5.95 |
% 21.84/5.95 |-The branch is then unsatisfiable
% 21.84/5.95 |-Branch two:
% 21.84/5.95 | (552) ~ (all_0_11_11 = n10)
% 21.84/5.95 | (553) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.84/5.95 |
% 21.84/5.95 +-Applying beta-rule and splitting (553), into two cases.
% 21.84/5.95 |-Branch one:
% 21.84/5.95 | (554) all_0_11_11 = n9
% 21.84/5.95 |
% 21.84/5.95 | From (554) and (423) follows:
% 21.84/5.95 | (555) pred(n9) = all_0_9_9
% 21.84/5.95 |
% 21.84/5.95 | From (554) and (262) follows:
% 21.84/5.95 | (556) succ(n9) = all_0_5_5
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (130) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 21.84/5.95 | (557) all_0_9_9 = n8
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (165) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 21.84/5.95 | (558) all_0_5_5 = n10
% 21.84/5.95 |
% 21.84/5.95 | From (557)(558) and (147) follows:
% 21.84/5.95 | (559) sum(n8, n10) = all_0_2_2
% 21.84/5.95 |
% 21.84/5.95 | From (557) and (1025) follows:
% 21.84/5.95 | (1132) sum(n8, n15) = all_0_7_7
% 21.84/5.95 |
% 21.84/5.95 | From (558) and (1023) follows:
% 21.84/5.95 | (1133) sum(n13, n10) = all_0_4_4
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (74) with n13, n10, all_0_4_4, n7 and discharging atoms sum(n13, n10) = all_0_4_4, sum(n13, n10) = n7, yields:
% 21.84/5.95 | (580) all_0_4_4 = n7
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (74) with n8, n15, all_0_7_7, n7 and discharging atoms sum(n8, n15) = all_0_7_7, sum(n8, n15) = n7, yields:
% 21.84/5.95 | (582) all_0_7_7 = n7
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (74) with n8, n10, all_0_2_2, n2 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n2, yields:
% 21.84/5.95 | (563) all_0_2_2 = n2
% 21.84/5.95 |
% 21.84/5.95 | From (563) and (1027) follows:
% 21.84/5.95 | (1137) sum(n2, n12) = all_0_0_0
% 21.84/5.95 |
% 21.84/5.95 | From (582)(580) and (212) follows:
% 21.84/5.95 | (584) sum(n7, n7) = all_0_3_3
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (74) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 21.84/5.95 | (585) all_0_3_3 = n14
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (74) with n2, n12, all_0_0_0, n14 and discharging atoms sum(n2, n12) = all_0_0_0, sum(n2, n12) = n14, yields:
% 21.84/5.95 | (586) all_0_0_0 = n14
% 21.84/5.95 |
% 21.84/5.95 | Equations (586,585) can reduce 363 to:
% 21.84/5.95 | (461) $false
% 21.84/5.95 |
% 21.84/5.95 |-The branch is then unsatisfiable
% 21.84/5.95 |-Branch two:
% 21.84/5.95 | (570) ~ (all_0_11_11 = n9)
% 21.84/5.95 | (571) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.84/5.95 |
% 21.84/5.95 +-Applying beta-rule and splitting (571), into two cases.
% 21.84/5.95 |-Branch one:
% 21.84/5.95 | (572) all_0_11_11 = n8
% 21.84/5.95 |
% 21.84/5.95 | From (572) and (423) follows:
% 21.84/5.95 | (573) pred(n8) = all_0_9_9
% 21.84/5.95 |
% 21.84/5.95 | From (572) and (262) follows:
% 21.84/5.95 | (574) succ(n8) = all_0_5_5
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (130) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 21.84/5.95 | (575) all_0_9_9 = n7
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (165) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 21.84/5.95 | (576) all_0_5_5 = n9
% 21.84/5.95 |
% 21.84/5.95 | From (575)(576) and (147) follows:
% 21.84/5.95 | (577) sum(n7, n9) = all_0_2_2
% 21.84/5.95 |
% 21.84/5.95 | From (575) and (1025) follows:
% 21.84/5.95 | (1150) sum(n7, n15) = all_0_7_7
% 21.84/5.95 |
% 21.84/5.95 | From (576) and (1023) follows:
% 21.84/5.95 | (1151) sum(n13, n9) = all_0_4_4
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (74) with n13, n9, all_0_4_4, n6 and discharging atoms sum(n13, n9) = all_0_4_4, sum(n13, n9) = n6, yields:
% 21.84/5.95 | (598) all_0_4_4 = n6
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (74) with n7, n15, all_0_7_7, n6 and discharging atoms sum(n7, n15) = all_0_7_7, sum(n7, n15) = n6, yields:
% 21.84/5.95 | (600) all_0_7_7 = n6
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (74) with n7, n9, all_0_2_2, n0 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n0, yields:
% 21.84/5.95 | (581) all_0_2_2 = n0
% 21.84/5.95 |
% 21.84/5.95 | From (581) and (1027) follows:
% 21.84/5.95 | (1155) sum(n0, n12) = all_0_0_0
% 21.84/5.95 |
% 21.84/5.95 | From (600)(598) and (212) follows:
% 21.84/5.95 | (602) sum(n6, n6) = all_0_3_3
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (74) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 21.84/5.95 | (459) all_0_3_3 = n12
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (74) with n0, n12, all_0_0_0, n12 and discharging atoms sum(n0, n12) = all_0_0_0, sum(n0, n12) = n12, yields:
% 21.84/5.95 | (457) all_0_0_0 = n12
% 21.84/5.95 |
% 21.84/5.95 | Equations (457,459) can reduce 363 to:
% 21.84/5.95 | (461) $false
% 21.84/5.95 |
% 21.84/5.95 |-The branch is then unsatisfiable
% 21.84/5.95 |-Branch two:
% 21.84/5.95 | (588) ~ (all_0_11_11 = n8)
% 21.84/5.95 | (589) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.84/5.95 |
% 21.84/5.95 +-Applying beta-rule and splitting (589), into two cases.
% 21.84/5.95 |-Branch one:
% 21.84/5.95 | (590) all_0_11_11 = n7
% 21.84/5.95 |
% 21.84/5.95 | From (590) and (423) follows:
% 21.84/5.95 | (591) pred(n7) = all_0_9_9
% 21.84/5.95 |
% 21.84/5.95 | From (590) and (262) follows:
% 21.84/5.95 | (592) succ(n7) = all_0_5_5
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (130) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 21.84/5.95 | (593) all_0_9_9 = n6
% 21.84/5.95 |
% 21.84/5.95 | Instantiating formula (165) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 21.84/5.95 | (594) all_0_5_5 = n8
% 21.84/5.95 |
% 21.84/5.95 | From (593)(594) and (147) follows:
% 21.84/5.96 | (595) sum(n6, n8) = all_0_2_2
% 21.84/5.96 |
% 21.84/5.96 | From (593) and (1025) follows:
% 21.84/5.96 | (1168) sum(n6, n15) = all_0_7_7
% 21.84/5.96 |
% 21.84/5.96 | From (594) and (1023) follows:
% 21.84/5.96 | (1169) sum(n13, n8) = all_0_4_4
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n13, n8, all_0_4_4, n5 and discharging atoms sum(n13, n8) = all_0_4_4, sum(n13, n8) = n5, yields:
% 21.84/5.96 | (616) all_0_4_4 = n5
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n6, n15, all_0_7_7, n5 and discharging atoms sum(n6, n15) = all_0_7_7, sum(n6, n15) = n5, yields:
% 21.84/5.96 | (618) all_0_7_7 = n5
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 21.84/5.96 | (447) all_0_2_2 = n14
% 21.84/5.96 |
% 21.84/5.96 | From (447) and (1027) follows:
% 21.84/5.96 | (757) sum(n14, n12) = all_0_0_0
% 21.84/5.96 |
% 21.84/5.96 | From (618)(616) and (212) follows:
% 21.84/5.96 | (620) sum(n5, n5) = all_0_3_3
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n14, n12, all_0_0_0, n10 and discharging atoms sum(n14, n12) = all_0_0_0, sum(n14, n12) = n10, yields:
% 21.84/5.96 | (478) all_0_0_0 = n10
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 21.84/5.96 | (477) all_0_3_3 = n10
% 21.84/5.96 |
% 21.84/5.96 | Equations (478,477) can reduce 363 to:
% 21.84/5.96 | (461) $false
% 21.84/5.96 |
% 21.84/5.96 |-The branch is then unsatisfiable
% 21.84/5.96 |-Branch two:
% 21.84/5.96 | (606) ~ (all_0_11_11 = n7)
% 21.84/5.96 | (607) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.84/5.96 |
% 21.84/5.96 +-Applying beta-rule and splitting (607), into two cases.
% 21.84/5.96 |-Branch one:
% 21.84/5.96 | (608) all_0_11_11 = n6
% 21.84/5.96 |
% 21.84/5.96 | From (608) and (423) follows:
% 21.84/5.96 | (609) pred(n6) = all_0_9_9
% 21.84/5.96 |
% 21.84/5.96 | From (608) and (262) follows:
% 21.84/5.96 | (610) succ(n6) = all_0_5_5
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (130) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 21.84/5.96 | (611) all_0_9_9 = n5
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (165) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 21.84/5.96 | (612) all_0_5_5 = n7
% 21.84/5.96 |
% 21.84/5.96 | From (611)(612) and (147) follows:
% 21.84/5.96 | (613) sum(n5, n7) = all_0_2_2
% 21.84/5.96 |
% 21.84/5.96 | From (611) and (1025) follows:
% 21.84/5.96 | (1186) sum(n5, n15) = all_0_7_7
% 21.84/5.96 |
% 21.84/5.96 | From (612) and (1023) follows:
% 21.84/5.96 | (1187) sum(n13, n7) = all_0_4_4
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n13, n7, all_0_4_4, n4 and discharging atoms sum(n13, n7) = all_0_4_4, sum(n13, n7) = n4, yields:
% 21.84/5.96 | (634) all_0_4_4 = n4
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n5, n15, all_0_7_7, n4 and discharging atoms sum(n5, n15) = all_0_7_7, sum(n5, n15) = n4, yields:
% 21.84/5.96 | (636) all_0_7_7 = n4
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 21.84/5.96 | (473) all_0_2_2 = n12
% 21.84/5.96 |
% 21.84/5.96 | From (473) and (1027) follows:
% 21.84/5.96 | (1045) sum(n12, n12) = all_0_0_0
% 21.84/5.96 |
% 21.84/5.96 | From (636)(634) and (212) follows:
% 21.84/5.96 | (638) sum(n4, n4) = all_0_3_3
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n12, n12, all_0_0_0, n8 and discharging atoms sum(n12, n12) = all_0_0_0, sum(n12, n12) = n8, yields:
% 21.84/5.96 | (496) all_0_0_0 = n8
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 21.84/5.96 | (495) all_0_3_3 = n8
% 21.84/5.96 |
% 21.84/5.96 | Equations (496,495) can reduce 363 to:
% 21.84/5.96 | (461) $false
% 21.84/5.96 |
% 21.84/5.96 |-The branch is then unsatisfiable
% 21.84/5.96 |-Branch two:
% 21.84/5.96 | (624) ~ (all_0_11_11 = n6)
% 21.84/5.96 | (625) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.84/5.96 |
% 21.84/5.96 +-Applying beta-rule and splitting (625), into two cases.
% 21.84/5.96 |-Branch one:
% 21.84/5.96 | (626) all_0_11_11 = n5
% 21.84/5.96 |
% 21.84/5.96 | From (626) and (423) follows:
% 21.84/5.96 | (627) pred(n5) = all_0_9_9
% 21.84/5.96 |
% 21.84/5.96 | From (626) and (262) follows:
% 21.84/5.96 | (628) succ(n5) = all_0_5_5
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (130) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 21.84/5.96 | (629) all_0_9_9 = n4
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (165) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 21.84/5.96 | (630) all_0_5_5 = n6
% 21.84/5.96 |
% 21.84/5.96 | From (629)(630) and (147) follows:
% 21.84/5.96 | (631) sum(n4, n6) = all_0_2_2
% 21.84/5.96 |
% 21.84/5.96 | From (629) and (1025) follows:
% 21.84/5.96 | (1204) sum(n4, n15) = all_0_7_7
% 21.84/5.96 |
% 21.84/5.96 | From (630) and (1023) follows:
% 21.84/5.96 | (1205) sum(n13, n6) = all_0_4_4
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n13, n6, all_0_4_4, n3 and discharging atoms sum(n13, n6) = all_0_4_4, sum(n13, n6) = n3, yields:
% 21.84/5.96 | (652) all_0_4_4 = n3
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n4, n15, all_0_7_7, n3 and discharging atoms sum(n4, n15) = all_0_7_7, sum(n4, n15) = n3, yields:
% 21.84/5.96 | (654) all_0_7_7 = n3
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 21.84/5.96 | (491) all_0_2_2 = n10
% 21.84/5.96 |
% 21.84/5.96 | From (491) and (1027) follows:
% 21.84/5.96 | (1065) sum(n10, n12) = all_0_0_0
% 21.84/5.96 |
% 21.84/5.96 | From (654)(652) and (212) follows:
% 21.84/5.96 | (656) sum(n3, n3) = all_0_3_3
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n10, n12, all_0_0_0, n6 and discharging atoms sum(n10, n12) = all_0_0_0, sum(n10, n12) = n6, yields:
% 21.84/5.96 | (514) all_0_0_0 = n6
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 21.84/5.96 | (513) all_0_3_3 = n6
% 21.84/5.96 |
% 21.84/5.96 | Equations (514,513) can reduce 363 to:
% 21.84/5.96 | (461) $false
% 21.84/5.96 |
% 21.84/5.96 |-The branch is then unsatisfiable
% 21.84/5.96 |-Branch two:
% 21.84/5.96 | (642) ~ (all_0_11_11 = n5)
% 21.84/5.96 | (643) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.84/5.96 |
% 21.84/5.96 +-Applying beta-rule and splitting (643), into two cases.
% 21.84/5.96 |-Branch one:
% 21.84/5.96 | (644) all_0_11_11 = n4
% 21.84/5.96 |
% 21.84/5.96 | From (644) and (423) follows:
% 21.84/5.96 | (645) pred(n4) = all_0_9_9
% 21.84/5.96 |
% 21.84/5.96 | From (644) and (262) follows:
% 21.84/5.96 | (646) succ(n4) = all_0_5_5
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (130) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 21.84/5.96 | (647) all_0_9_9 = n3
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (165) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 21.84/5.96 | (648) all_0_5_5 = n5
% 21.84/5.96 |
% 21.84/5.96 | From (647)(648) and (147) follows:
% 21.84/5.96 | (649) sum(n3, n5) = all_0_2_2
% 21.84/5.96 |
% 21.84/5.96 | From (647) and (1025) follows:
% 21.84/5.96 | (1222) sum(n3, n15) = all_0_7_7
% 21.84/5.96 |
% 21.84/5.96 | From (648) and (1023) follows:
% 21.84/5.96 | (1223) sum(n13, n5) = all_0_4_4
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n13, n5, all_0_4_4, n2 and discharging atoms sum(n13, n5) = all_0_4_4, sum(n13, n5) = n2, yields:
% 21.84/5.96 | (670) all_0_4_4 = n2
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n3, n15, all_0_7_7, n2 and discharging atoms sum(n3, n15) = all_0_7_7, sum(n3, n15) = n2, yields:
% 21.84/5.96 | (672) all_0_7_7 = n2
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 21.84/5.96 | (509) all_0_2_2 = n8
% 21.84/5.96 |
% 21.84/5.96 | From (509) and (1027) follows:
% 21.84/5.96 | (1083) sum(n8, n12) = all_0_0_0
% 21.84/5.96 |
% 21.84/5.96 | From (672)(670) and (212) follows:
% 21.84/5.96 | (674) sum(n2, n2) = all_0_3_3
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n8, n12, all_0_0_0, n4 and discharging atoms sum(n8, n12) = all_0_0_0, sum(n8, n12) = n4, yields:
% 21.84/5.96 | (532) all_0_0_0 = n4
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 21.84/5.96 | (531) all_0_3_3 = n4
% 21.84/5.96 |
% 21.84/5.96 | Equations (532,531) can reduce 363 to:
% 21.84/5.96 | (461) $false
% 21.84/5.96 |
% 21.84/5.96 |-The branch is then unsatisfiable
% 21.84/5.96 |-Branch two:
% 21.84/5.96 | (660) ~ (all_0_11_11 = n4)
% 21.84/5.96 | (661) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.84/5.96 |
% 21.84/5.96 +-Applying beta-rule and splitting (661), into two cases.
% 21.84/5.96 |-Branch one:
% 21.84/5.96 | (662) all_0_11_11 = n3
% 21.84/5.96 |
% 21.84/5.96 | From (662) and (423) follows:
% 21.84/5.96 | (663) pred(n3) = all_0_9_9
% 21.84/5.96 |
% 21.84/5.96 | From (662) and (262) follows:
% 21.84/5.96 | (664) succ(n3) = all_0_5_5
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (130) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 21.84/5.96 | (665) all_0_9_9 = n2
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (165) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 21.84/5.96 | (666) all_0_5_5 = n4
% 21.84/5.96 |
% 21.84/5.96 | From (665)(666) and (147) follows:
% 21.84/5.96 | (667) sum(n2, n4) = all_0_2_2
% 21.84/5.96 |
% 21.84/5.96 | From (665) and (1025) follows:
% 21.84/5.96 | (1240) sum(n2, n15) = all_0_7_7
% 21.84/5.96 |
% 21.84/5.96 | From (666) and (1023) follows:
% 21.84/5.96 | (1241) sum(n13, n4) = all_0_4_4
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n13, n4, all_0_4_4, n1 and discharging atoms sum(n13, n4) = all_0_4_4, sum(n13, n4) = n1, yields:
% 21.84/5.96 | (688) all_0_4_4 = n1
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n2, n15, all_0_7_7, n1 and discharging atoms sum(n2, n15) = all_0_7_7, sum(n2, n15) = n1, yields:
% 21.84/5.96 | (690) all_0_7_7 = n1
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 21.84/5.96 | (527) all_0_2_2 = n6
% 21.84/5.96 |
% 21.84/5.96 | From (527) and (1027) follows:
% 21.84/5.96 | (1101) sum(n6, n12) = all_0_0_0
% 21.84/5.96 |
% 21.84/5.96 | From (690)(688) and (212) follows:
% 21.84/5.96 | (692) sum(n1, n1) = all_0_3_3
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n6, n12, all_0_0_0, n2 and discharging atoms sum(n6, n12) = all_0_0_0, sum(n6, n12) = n2, yields:
% 21.84/5.96 | (550) all_0_0_0 = n2
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 21.84/5.96 | (549) all_0_3_3 = n2
% 21.84/5.96 |
% 21.84/5.96 | Equations (550,549) can reduce 363 to:
% 21.84/5.96 | (461) $false
% 21.84/5.96 |
% 21.84/5.96 |-The branch is then unsatisfiable
% 21.84/5.96 |-Branch two:
% 21.84/5.96 | (678) ~ (all_0_11_11 = n3)
% 21.84/5.96 | (679) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.84/5.96 |
% 21.84/5.96 +-Applying beta-rule and splitting (679), into two cases.
% 21.84/5.96 |-Branch one:
% 21.84/5.96 | (680) all_0_11_11 = n2
% 21.84/5.96 |
% 21.84/5.96 | From (680) and (423) follows:
% 21.84/5.96 | (681) pred(n2) = all_0_9_9
% 21.84/5.96 |
% 21.84/5.96 | From (680) and (262) follows:
% 21.84/5.96 | (682) succ(n2) = all_0_5_5
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (130) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 21.84/5.96 | (683) all_0_9_9 = n1
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (165) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 21.84/5.96 | (684) all_0_5_5 = n3
% 21.84/5.96 |
% 21.84/5.96 | From (683)(684) and (147) follows:
% 21.84/5.96 | (685) sum(n1, n3) = all_0_2_2
% 21.84/5.96 |
% 21.84/5.96 | From (683) and (1025) follows:
% 21.84/5.96 | (1258) sum(n1, n15) = all_0_7_7
% 21.84/5.96 |
% 21.84/5.96 | From (684) and (1023) follows:
% 21.84/5.96 | (1259) sum(n13, n3) = all_0_4_4
% 21.84/5.96 |
% 21.84/5.96 | Instantiating formula (74) with n13, n3, all_0_4_4, n0 and discharging atoms sum(n13, n3) = all_0_4_4, sum(n13, n3) = n0, yields:
% 21.84/5.96 | (706) all_0_4_4 = n0
% 21.84/5.97 |
% 21.84/5.97 | Instantiating formula (74) with n1, n15, all_0_7_7, n0 and discharging atoms sum(n1, n15) = all_0_7_7, sum(n1, n15) = n0, yields:
% 21.84/5.97 | (708) all_0_7_7 = n0
% 21.84/5.97 |
% 21.84/5.97 | Instantiating formula (74) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 21.84/5.97 | (545) all_0_2_2 = n4
% 21.84/5.97 |
% 21.84/5.97 | From (545) and (1027) follows:
% 21.84/5.97 | (1119) sum(n4, n12) = all_0_0_0
% 21.84/5.97 |
% 21.84/5.97 | From (708)(706) and (212) follows:
% 21.84/5.97 | (710) sum(n0, n0) = all_0_3_3
% 21.84/5.97 |
% 21.84/5.97 | Instantiating formula (74) with n4, n12, all_0_0_0, n0 and discharging atoms sum(n4, n12) = all_0_0_0, sum(n4, n12) = n0, yields:
% 21.84/5.97 | (568) all_0_0_0 = n0
% 21.84/5.97 |
% 21.84/5.97 | Instantiating formula (74) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 21.84/5.97 | (567) all_0_3_3 = n0
% 21.84/5.97 |
% 21.84/5.97 | Equations (568,567) can reduce 363 to:
% 21.84/5.97 | (461) $false
% 21.84/5.97 |
% 21.84/5.97 |-The branch is then unsatisfiable
% 21.84/5.97 |-Branch two:
% 21.84/5.97 | (696) ~ (all_0_11_11 = n2)
% 21.84/5.97 | (697) all_0_11_11 = n1 | all_0_11_11 = n0
% 21.84/5.97 |
% 21.84/5.97 +-Applying beta-rule and splitting (697), into two cases.
% 21.84/5.97 |-Branch one:
% 21.84/5.97 | (698) all_0_11_11 = n1
% 21.84/5.97 |
% 21.84/5.97 | From (698) and (423) follows:
% 21.84/5.97 | (699) pred(n1) = all_0_9_9
% 21.84/5.97 |
% 21.84/5.97 | From (698) and (262) follows:
% 21.84/5.97 | (700) succ(n1) = all_0_5_5
% 21.84/5.97 |
% 21.84/5.97 | Instantiating formula (130) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 21.84/5.97 | (701) all_0_9_9 = n0
% 21.84/5.97 |
% 21.84/5.97 | Instantiating formula (165) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 21.84/5.97 | (702) all_0_5_5 = n2
% 21.84/5.97 |
% 21.84/5.97 | From (701)(702) and (147) follows:
% 21.84/5.97 | (703) sum(n0, n2) = all_0_2_2
% 21.84/5.97 |
% 21.84/5.97 | From (701) and (1025) follows:
% 21.84/5.97 | (1276) sum(n0, n15) = all_0_7_7
% 21.84/5.97 |
% 21.84/5.97 | From (702) and (1023) follows:
% 21.84/5.97 | (1277) sum(n13, n2) = all_0_4_4
% 21.84/5.97 |
% 21.84/5.97 | Instantiating formula (74) with n13, n2, all_0_4_4, n15 and discharging atoms sum(n13, n2) = all_0_4_4, sum(n13, n2) = n15, yields:
% 21.84/5.97 | (726) all_0_4_4 = n15
% 21.84/5.97 |
% 21.84/5.97 | Instantiating formula (74) with n0, n15, all_0_7_7, n15 and discharging atoms sum(n0, n15) = all_0_7_7, sum(n0, n15) = n15, yields:
% 21.84/5.97 | (725) all_0_7_7 = n15
% 21.84/5.97 |
% 21.84/5.97 | Instantiating formula (74) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 21.84/5.97 | (563) all_0_2_2 = n2
% 21.84/5.97 |
% 21.84/5.97 | From (563) and (1027) follows:
% 21.84/5.97 | (1137) sum(n2, n12) = all_0_0_0
% 21.84/5.97 |
% 21.84/5.97 | From (725)(726) and (212) follows:
% 21.84/5.97 | (728) sum(n15, n15) = all_0_3_3
% 21.84/5.97 |
% 21.84/5.97 | Instantiating formula (74) with n15, n15, all_0_3_3, n14 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n14, yields:
% 21.84/5.97 | (585) all_0_3_3 = n14
% 21.84/5.97 |
% 21.84/5.97 | Instantiating formula (74) with n2, n12, all_0_0_0, n14 and discharging atoms sum(n2, n12) = all_0_0_0, sum(n2, n12) = n14, yields:
% 21.84/5.97 | (586) all_0_0_0 = n14
% 21.84/5.97 |
% 21.84/5.97 | Equations (586,585) can reduce 363 to:
% 21.84/5.97 | (461) $false
% 21.84/5.97 |
% 21.84/5.97 |-The branch is then unsatisfiable
% 21.84/5.97 |-Branch two:
% 21.84/5.97 | (715) ~ (all_0_11_11 = n1)
% 21.84/5.97 | (716) all_0_11_11 = n0
% 21.84/5.97 |
% 21.84/5.97 | From (716) and (423) follows:
% 21.84/5.97 | (717) pred(n0) = all_0_9_9
% 21.84/5.97 |
% 21.84/5.97 | From (716) and (262) follows:
% 21.84/5.97 | (718) succ(n0) = all_0_5_5
% 21.84/5.97 |
% 21.84/5.97 | Instantiating formula (130) with n0, all_0_9_9, n15 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n15, yields:
% 21.84/5.97 | (719) all_0_9_9 = n15
% 21.84/5.97 |
% 21.84/5.97 | Instantiating formula (165) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 21.84/5.97 | (720) all_0_5_5 = n1
% 21.84/5.97 |
% 21.84/5.97 | From (719)(720) and (147) follows:
% 21.92/5.97 | (721) sum(n15, n1) = all_0_2_2
% 21.92/5.97 |
% 21.92/5.97 | From (719) and (1025) follows:
% 21.92/5.97 | (1293) sum(n15, n15) = all_0_7_7
% 21.92/5.97 |
% 21.92/5.97 | From (720) and (1023) follows:
% 21.92/5.97 | (1294) sum(n13, n1) = all_0_4_4
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (74) with n15, n15, all_0_7_7, n14 and discharging atoms sum(n15, n15) = all_0_7_7, sum(n15, n15) = n14, yields:
% 21.92/5.97 | (452) all_0_7_7 = n14
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (74) with n15, n1, all_0_2_2, n0 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n0, yields:
% 21.92/5.97 | (581) all_0_2_2 = n0
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (74) with n13, n1, all_0_4_4, n14 and discharging atoms sum(n13, n1) = all_0_4_4, sum(n13, n1) = n14, yields:
% 21.92/5.97 | (451) all_0_4_4 = n14
% 21.92/5.97 |
% 21.92/5.97 | From (581) and (1027) follows:
% 21.92/5.97 | (1155) sum(n0, n12) = all_0_0_0
% 21.92/5.97 |
% 21.92/5.97 | From (452)(451) and (212) follows:
% 21.92/5.97 | (456) sum(n14, n14) = all_0_3_3
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (74) with n14, n14, all_0_3_3, n12 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n12, yields:
% 21.92/5.97 | (459) all_0_3_3 = n12
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (74) with n0, n12, all_0_0_0, n12 and discharging atoms sum(n0, n12) = all_0_0_0, sum(n0, n12) = n12, yields:
% 21.92/5.97 | (457) all_0_0_0 = n12
% 21.92/5.97 |
% 21.92/5.97 | Equations (457,459) can reduce 363 to:
% 21.92/5.97 | (461) $false
% 21.92/5.97 |
% 21.92/5.97 |-The branch is then unsatisfiable
% 21.92/5.97 |-Branch two:
% 21.92/5.97 | (761) ~ (all_0_10_10 = n14)
% 21.92/5.97 | (762) all_0_10_10 = n13 | all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/5.97 |
% 21.92/5.97 +-Applying beta-rule and splitting (463), into two cases.
% 21.92/5.97 |-Branch one:
% 21.92/5.97 | (464) all_0_11_11 = n14
% 21.92/5.97 |
% 21.92/5.97 | From (464) and (423) follows:
% 21.92/5.97 | (465) pred(n14) = all_0_9_9
% 21.92/5.97 |
% 21.92/5.97 | From (464) and (262) follows:
% 21.92/5.97 | (466) succ(n14) = all_0_5_5
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (130) with n14, all_0_9_9, n13 and discharging atoms pred(n14) = all_0_9_9, pred(n14) = n13, yields:
% 21.92/5.97 | (467) all_0_9_9 = n13
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (165) with n14, all_0_5_5, n15 and discharging atoms succ(n14) = all_0_5_5, succ(n14) = n15, yields:
% 21.92/5.97 | (468) all_0_5_5 = n15
% 21.92/5.97 |
% 21.92/5.97 | From (468) and (276) follows:
% 21.92/5.97 | (1310) sum(all_0_6_6, n15) = all_0_4_4
% 21.92/5.97 |
% 21.92/5.97 | From (467)(468) and (147) follows:
% 21.92/5.97 | (469) sum(n13, n15) = all_0_2_2
% 21.92/5.97 |
% 21.92/5.97 | From (467) and (350) follows:
% 21.92/5.97 | (1312) sum(n13, all_0_8_8) = all_0_7_7
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (74) with n13, n15, all_0_2_2, n12 and discharging atoms sum(n13, n15) = all_0_2_2, sum(n13, n15) = n12, yields:
% 21.92/5.97 | (473) all_0_2_2 = n12
% 21.92/5.97 |
% 21.92/5.97 | From (473) and (256) follows:
% 21.92/5.97 | (1314) sum(n12, all_0_1_1) = all_0_0_0
% 21.92/5.97 |
% 21.92/5.97 +-Applying beta-rule and splitting (762), into two cases.
% 21.92/5.97 |-Branch one:
% 21.92/5.97 | (763) all_0_10_10 = n13
% 21.92/5.97 |
% 21.92/5.97 | From (763) and (317) follows:
% 21.92/5.97 | (764) pred(n13) = all_0_6_6
% 21.92/5.97 |
% 21.92/5.97 | From (763) and (146) follows:
% 21.92/5.97 | (765) succ(n13) = all_0_8_8
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (130) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 21.92/5.97 | (766) all_0_6_6 = n12
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (165) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 21.92/5.97 | (767) all_0_8_8 = n14
% 21.92/5.97 |
% 21.92/5.97 | From (766)(767) and (10) follows:
% 21.92/5.97 | (768) sum(n12, n14) = all_0_1_1
% 21.92/5.97 |
% 21.92/5.97 | From (766) and (1310) follows:
% 21.92/5.97 | (1321) sum(n12, n15) = all_0_4_4
% 21.92/5.97 |
% 21.92/5.97 | From (767) and (1312) follows:
% 21.92/5.97 | (1322) sum(n13, n14) = all_0_7_7
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (74) with n13, n14, all_0_7_7, n11 and discharging atoms sum(n13, n14) = all_0_7_7, sum(n13, n14) = n11, yields:
% 21.92/5.97 | (510) all_0_7_7 = n11
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (74) with n12, n15, all_0_4_4, n11 and discharging atoms sum(n12, n15) = all_0_4_4, sum(n12, n15) = n11, yields:
% 21.92/5.97 | (508) all_0_4_4 = n11
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (74) with n12, n14, all_0_1_1, n10 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n10, yields:
% 21.92/5.97 | (772) all_0_1_1 = n10
% 21.92/5.97 |
% 21.92/5.97 | From (510)(508) and (212) follows:
% 21.92/5.97 | (512) sum(n11, n11) = all_0_3_3
% 21.92/5.97 |
% 21.92/5.97 | From (772) and (1314) follows:
% 21.92/5.97 | (1327) sum(n12, n10) = all_0_0_0
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (74) with n12, n10, all_0_0_0, n6 and discharging atoms sum(n12, n10) = all_0_0_0, sum(n12, n10) = n6, yields:
% 21.92/5.97 | (514) all_0_0_0 = n6
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (74) with n11, n11, all_0_3_3, n6 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n6, yields:
% 21.92/5.97 | (513) all_0_3_3 = n6
% 21.92/5.97 |
% 21.92/5.97 | Equations (514,513) can reduce 363 to:
% 21.92/5.97 | (461) $false
% 21.92/5.97 |
% 21.92/5.97 |-The branch is then unsatisfiable
% 21.92/5.97 |-Branch two:
% 21.92/5.97 | (779) ~ (all_0_10_10 = n13)
% 21.92/5.97 | (780) all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/5.97 |
% 21.92/5.97 +-Applying beta-rule and splitting (780), into two cases.
% 21.92/5.97 |-Branch one:
% 21.92/5.97 | (781) all_0_10_10 = n12
% 21.92/5.97 |
% 21.92/5.97 | From (781) and (317) follows:
% 21.92/5.97 | (782) pred(n12) = all_0_6_6
% 21.92/5.97 |
% 21.92/5.97 | From (781) and (146) follows:
% 21.92/5.97 | (783) succ(n12) = all_0_8_8
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (130) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 21.92/5.97 | (784) all_0_6_6 = n11
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (165) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 21.92/5.97 | (785) all_0_8_8 = n13
% 21.92/5.97 |
% 21.92/5.97 | From (784)(785) and (10) follows:
% 21.92/5.97 | (786) sum(n11, n13) = all_0_1_1
% 21.92/5.97 |
% 21.92/5.97 | From (784) and (1310) follows:
% 21.92/5.97 | (1339) sum(n11, n15) = all_0_4_4
% 21.92/5.97 |
% 21.92/5.97 | From (785) and (1312) follows:
% 21.92/5.97 | (1340) sum(n13, n13) = all_0_7_7
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (74) with n13, n13, all_0_7_7, n10 and discharging atoms sum(n13, n13) = all_0_7_7, sum(n13, n13) = n10, yields:
% 21.92/5.97 | (528) all_0_7_7 = n10
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (74) with n11, n15, all_0_4_4, n10 and discharging atoms sum(n11, n15) = all_0_4_4, sum(n11, n15) = n10, yields:
% 21.92/5.97 | (526) all_0_4_4 = n10
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (74) with n11, n13, all_0_1_1, n8 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n8, yields:
% 21.92/5.97 | (790) all_0_1_1 = n8
% 21.92/5.97 |
% 21.92/5.97 | From (528)(526) and (212) follows:
% 21.92/5.97 | (530) sum(n10, n10) = all_0_3_3
% 21.92/5.97 |
% 21.92/5.97 | From (790) and (1314) follows:
% 21.92/5.97 | (1345) sum(n12, n8) = all_0_0_0
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (74) with n12, n8, all_0_0_0, n4 and discharging atoms sum(n12, n8) = all_0_0_0, sum(n12, n8) = n4, yields:
% 21.92/5.97 | (532) all_0_0_0 = n4
% 21.92/5.97 |
% 21.92/5.97 | Instantiating formula (74) with n10, n10, all_0_3_3, n4 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n4, yields:
% 21.92/5.97 | (531) all_0_3_3 = n4
% 21.92/5.97 |
% 21.92/5.98 | Equations (532,531) can reduce 363 to:
% 21.92/5.98 | (461) $false
% 21.92/5.98 |
% 21.92/5.98 |-The branch is then unsatisfiable
% 21.92/5.98 |-Branch two:
% 21.92/5.98 | (797) ~ (all_0_10_10 = n12)
% 21.92/5.98 | (798) all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/5.98 |
% 21.92/5.98 +-Applying beta-rule and splitting (798), into two cases.
% 21.92/5.98 |-Branch one:
% 21.92/5.98 | (799) all_0_10_10 = n11
% 21.92/5.98 |
% 21.92/5.98 | From (799) and (317) follows:
% 21.92/5.98 | (800) pred(n11) = all_0_6_6
% 21.92/5.98 |
% 21.92/5.98 | From (799) and (146) follows:
% 21.92/5.98 | (801) succ(n11) = all_0_8_8
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (130) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 21.92/5.98 | (802) all_0_6_6 = n10
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (165) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 21.92/5.98 | (803) all_0_8_8 = n12
% 21.92/5.98 |
% 21.92/5.98 | From (802)(803) and (10) follows:
% 21.92/5.98 | (804) sum(n10, n12) = all_0_1_1
% 21.92/5.98 |
% 21.92/5.98 | From (802) and (1310) follows:
% 21.92/5.98 | (1357) sum(n10, n15) = all_0_4_4
% 21.92/5.98 |
% 21.92/5.98 | From (803) and (1312) follows:
% 21.92/5.98 | (1358) sum(n13, n12) = all_0_7_7
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n13, n12, all_0_7_7, n9 and discharging atoms sum(n13, n12) = all_0_7_7, sum(n13, n12) = n9, yields:
% 21.92/5.98 | (546) all_0_7_7 = n9
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n10, n15, all_0_4_4, n9 and discharging atoms sum(n10, n15) = all_0_4_4, sum(n10, n15) = n9, yields:
% 21.92/5.98 | (544) all_0_4_4 = n9
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n10, n12, all_0_1_1, n6 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n6, yields:
% 21.92/5.98 | (808) all_0_1_1 = n6
% 21.92/5.98 |
% 21.92/5.98 | From (546)(544) and (212) follows:
% 21.92/5.98 | (548) sum(n9, n9) = all_0_3_3
% 21.92/5.98 |
% 21.92/5.98 | From (808) and (1314) follows:
% 21.92/5.98 | (1363) sum(n12, n6) = all_0_0_0
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n12, n6, all_0_0_0, n2 and discharging atoms sum(n12, n6) = all_0_0_0, sum(n12, n6) = n2, yields:
% 21.92/5.98 | (550) all_0_0_0 = n2
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n9, n9, all_0_3_3, n2 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n2, yields:
% 21.92/5.98 | (549) all_0_3_3 = n2
% 21.92/5.98 |
% 21.92/5.98 | Equations (550,549) can reduce 363 to:
% 21.92/5.98 | (461) $false
% 21.92/5.98 |
% 21.92/5.98 |-The branch is then unsatisfiable
% 21.92/5.98 |-Branch two:
% 21.92/5.98 | (815) ~ (all_0_10_10 = n11)
% 21.92/5.98 | (816) all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/5.98 |
% 21.92/5.98 +-Applying beta-rule and splitting (816), into two cases.
% 21.92/5.98 |-Branch one:
% 21.92/5.98 | (817) all_0_10_10 = n10
% 21.92/5.98 |
% 21.92/5.98 | From (817) and (317) follows:
% 21.92/5.98 | (818) pred(n10) = all_0_6_6
% 21.92/5.98 |
% 21.92/5.98 | From (817) and (146) follows:
% 21.92/5.98 | (819) succ(n10) = all_0_8_8
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (130) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 21.92/5.98 | (820) all_0_6_6 = n9
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (165) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 21.92/5.98 | (821) all_0_8_8 = n11
% 21.92/5.98 |
% 21.92/5.98 | From (820)(821) and (10) follows:
% 21.92/5.98 | (822) sum(n9, n11) = all_0_1_1
% 21.92/5.98 |
% 21.92/5.98 | From (820) and (1310) follows:
% 21.92/5.98 | (1375) sum(n9, n15) = all_0_4_4
% 21.92/5.98 |
% 21.92/5.98 | From (821) and (1312) follows:
% 21.92/5.98 | (1376) sum(n13, n11) = all_0_7_7
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n13, n11, all_0_7_7, n8 and discharging atoms sum(n13, n11) = all_0_7_7, sum(n13, n11) = n8, yields:
% 21.92/5.98 | (564) all_0_7_7 = n8
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n9, n15, all_0_4_4, n8 and discharging atoms sum(n9, n15) = all_0_4_4, sum(n9, n15) = n8, yields:
% 21.92/5.98 | (562) all_0_4_4 = n8
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n9, n11, all_0_1_1, n4 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n4, yields:
% 21.92/5.98 | (826) all_0_1_1 = n4
% 21.92/5.98 |
% 21.92/5.98 | From (564)(562) and (212) follows:
% 21.92/5.98 | (566) sum(n8, n8) = all_0_3_3
% 21.92/5.98 |
% 21.92/5.98 | From (826) and (1314) follows:
% 21.92/5.98 | (1381) sum(n12, n4) = all_0_0_0
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n12, n4, all_0_0_0, n0 and discharging atoms sum(n12, n4) = all_0_0_0, sum(n12, n4) = n0, yields:
% 21.92/5.98 | (568) all_0_0_0 = n0
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n8, n8, all_0_3_3, n0 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n0, yields:
% 21.92/5.98 | (567) all_0_3_3 = n0
% 21.92/5.98 |
% 21.92/5.98 | Equations (568,567) can reduce 363 to:
% 21.92/5.98 | (461) $false
% 21.92/5.98 |
% 21.92/5.98 |-The branch is then unsatisfiable
% 21.92/5.98 |-Branch two:
% 21.92/5.98 | (833) ~ (all_0_10_10 = n10)
% 21.92/5.98 | (834) all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/5.98 |
% 21.92/5.98 +-Applying beta-rule and splitting (834), into two cases.
% 21.92/5.98 |-Branch one:
% 21.92/5.98 | (835) all_0_10_10 = n9
% 21.92/5.98 |
% 21.92/5.98 | From (835) and (317) follows:
% 21.92/5.98 | (836) pred(n9) = all_0_6_6
% 21.92/5.98 |
% 21.92/5.98 | From (835) and (146) follows:
% 21.92/5.98 | (837) succ(n9) = all_0_8_8
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (130) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 21.92/5.98 | (838) all_0_6_6 = n8
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (165) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 21.92/5.98 | (839) all_0_8_8 = n10
% 21.92/5.98 |
% 21.92/5.98 | From (838)(839) and (10) follows:
% 21.92/5.98 | (840) sum(n8, n10) = all_0_1_1
% 21.92/5.98 |
% 21.92/5.98 | From (838) and (1310) follows:
% 21.92/5.98 | (1393) sum(n8, n15) = all_0_4_4
% 21.92/5.98 |
% 21.92/5.98 | From (839) and (1312) follows:
% 21.92/5.98 | (1394) sum(n13, n10) = all_0_7_7
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n13, n10, all_0_7_7, n7 and discharging atoms sum(n13, n10) = all_0_7_7, sum(n13, n10) = n7, yields:
% 21.92/5.98 | (582) all_0_7_7 = n7
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n8, n15, all_0_4_4, n7 and discharging atoms sum(n8, n15) = all_0_4_4, sum(n8, n15) = n7, yields:
% 21.92/5.98 | (580) all_0_4_4 = n7
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n8, n10, all_0_1_1, n2 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n2, yields:
% 21.92/5.98 | (844) all_0_1_1 = n2
% 21.92/5.98 |
% 21.92/5.98 | From (582)(580) and (212) follows:
% 21.92/5.98 | (584) sum(n7, n7) = all_0_3_3
% 21.92/5.98 |
% 21.92/5.98 | From (844) and (1314) follows:
% 21.92/5.98 | (1399) sum(n12, n2) = all_0_0_0
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n12, n2, all_0_0_0, n14 and discharging atoms sum(n12, n2) = all_0_0_0, sum(n12, n2) = n14, yields:
% 21.92/5.98 | (586) all_0_0_0 = n14
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 21.92/5.98 | (585) all_0_3_3 = n14
% 21.92/5.98 |
% 21.92/5.98 | Equations (586,585) can reduce 363 to:
% 21.92/5.98 | (461) $false
% 21.92/5.98 |
% 21.92/5.98 |-The branch is then unsatisfiable
% 21.92/5.98 |-Branch two:
% 21.92/5.98 | (851) ~ (all_0_10_10 = n9)
% 21.92/5.98 | (852) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/5.98 |
% 21.92/5.98 +-Applying beta-rule and splitting (852), into two cases.
% 21.92/5.98 |-Branch one:
% 21.92/5.98 | (853) all_0_10_10 = n8
% 21.92/5.98 |
% 21.92/5.98 | From (853) and (317) follows:
% 21.92/5.98 | (854) pred(n8) = all_0_6_6
% 21.92/5.98 |
% 21.92/5.98 | From (853) and (146) follows:
% 21.92/5.98 | (855) succ(n8) = all_0_8_8
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (130) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 21.92/5.98 | (856) all_0_6_6 = n7
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (165) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 21.92/5.98 | (857) all_0_8_8 = n9
% 21.92/5.98 |
% 21.92/5.98 | From (856)(857) and (10) follows:
% 21.92/5.98 | (858) sum(n7, n9) = all_0_1_1
% 21.92/5.98 |
% 21.92/5.98 | From (856) and (1310) follows:
% 21.92/5.98 | (1411) sum(n7, n15) = all_0_4_4
% 21.92/5.98 |
% 21.92/5.98 | From (857) and (1312) follows:
% 21.92/5.98 | (1412) sum(n13, n9) = all_0_7_7
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n13, n9, all_0_7_7, n6 and discharging atoms sum(n13, n9) = all_0_7_7, sum(n13, n9) = n6, yields:
% 21.92/5.98 | (600) all_0_7_7 = n6
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n7, n15, all_0_4_4, n6 and discharging atoms sum(n7, n15) = all_0_4_4, sum(n7, n15) = n6, yields:
% 21.92/5.98 | (598) all_0_4_4 = n6
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n7, n9, all_0_1_1, n0 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n0, yields:
% 21.92/5.98 | (862) all_0_1_1 = n0
% 21.92/5.98 |
% 21.92/5.98 | From (600)(598) and (212) follows:
% 21.92/5.98 | (602) sum(n6, n6) = all_0_3_3
% 21.92/5.98 |
% 21.92/5.98 | From (862) and (1314) follows:
% 21.92/5.98 | (1417) sum(n12, n0) = all_0_0_0
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n12, n0, all_0_0_0, n12 and discharging atoms sum(n12, n0) = all_0_0_0, sum(n12, n0) = n12, yields:
% 21.92/5.98 | (457) all_0_0_0 = n12
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 21.92/5.98 | (459) all_0_3_3 = n12
% 21.92/5.98 |
% 21.92/5.98 | Equations (457,459) can reduce 363 to:
% 21.92/5.98 | (461) $false
% 21.92/5.98 |
% 21.92/5.98 |-The branch is then unsatisfiable
% 21.92/5.98 |-Branch two:
% 21.92/5.98 | (869) ~ (all_0_10_10 = n8)
% 21.92/5.98 | (870) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/5.98 |
% 21.92/5.98 +-Applying beta-rule and splitting (870), into two cases.
% 21.92/5.98 |-Branch one:
% 21.92/5.98 | (871) all_0_10_10 = n7
% 21.92/5.98 |
% 21.92/5.98 | From (871) and (317) follows:
% 21.92/5.98 | (872) pred(n7) = all_0_6_6
% 21.92/5.98 |
% 21.92/5.98 | From (871) and (146) follows:
% 21.92/5.98 | (873) succ(n7) = all_0_8_8
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (130) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 21.92/5.98 | (874) all_0_6_6 = n6
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (165) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 21.92/5.98 | (875) all_0_8_8 = n8
% 21.92/5.98 |
% 21.92/5.98 | From (874)(875) and (10) follows:
% 21.92/5.98 | (876) sum(n6, n8) = all_0_1_1
% 21.92/5.98 |
% 21.92/5.98 | From (874) and (1310) follows:
% 21.92/5.98 | (1429) sum(n6, n15) = all_0_4_4
% 21.92/5.98 |
% 21.92/5.98 | From (875) and (1312) follows:
% 21.92/5.98 | (1430) sum(n13, n8) = all_0_7_7
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n13, n8, all_0_7_7, n5 and discharging atoms sum(n13, n8) = all_0_7_7, sum(n13, n8) = n5, yields:
% 21.92/5.98 | (618) all_0_7_7 = n5
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n6, n15, all_0_4_4, n5 and discharging atoms sum(n6, n15) = all_0_4_4, sum(n6, n15) = n5, yields:
% 21.92/5.98 | (616) all_0_4_4 = n5
% 21.92/5.98 |
% 21.92/5.98 | Instantiating formula (74) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 21.92/5.98 | (436) all_0_1_1 = n14
% 21.92/5.98 |
% 21.92/5.98 | From (618)(616) and (212) follows:
% 21.92/5.98 | (620) sum(n5, n5) = all_0_3_3
% 21.92/5.98 |
% 21.92/5.98 | From (436) and (1314) follows:
% 21.92/5.99 | (475) sum(n12, n14) = all_0_0_0
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n12, n14, all_0_0_0, n10 and discharging atoms sum(n12, n14) = all_0_0_0, sum(n12, n14) = n10, yields:
% 21.92/5.99 | (478) all_0_0_0 = n10
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 21.92/5.99 | (477) all_0_3_3 = n10
% 21.92/5.99 |
% 21.92/5.99 | Equations (478,477) can reduce 363 to:
% 21.92/5.99 | (461) $false
% 21.92/5.99 |
% 21.92/5.99 |-The branch is then unsatisfiable
% 21.92/5.99 |-Branch two:
% 21.92/5.99 | (887) ~ (all_0_10_10 = n7)
% 21.92/5.99 | (888) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/5.99 |
% 21.92/5.99 +-Applying beta-rule and splitting (888), into two cases.
% 21.92/5.99 |-Branch one:
% 21.92/5.99 | (889) all_0_10_10 = n6
% 21.92/5.99 |
% 21.92/5.99 | From (889) and (317) follows:
% 21.92/5.99 | (890) pred(n6) = all_0_6_6
% 21.92/5.99 |
% 21.92/5.99 | From (889) and (146) follows:
% 21.92/5.99 | (891) succ(n6) = all_0_8_8
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (130) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 21.92/5.99 | (892) all_0_6_6 = n5
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (165) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 21.92/5.99 | (893) all_0_8_8 = n7
% 21.92/5.99 |
% 21.92/5.99 | From (892)(893) and (10) follows:
% 21.92/5.99 | (894) sum(n5, n7) = all_0_1_1
% 21.92/5.99 |
% 21.92/5.99 | From (892) and (1310) follows:
% 21.92/5.99 | (1447) sum(n5, n15) = all_0_4_4
% 21.92/5.99 |
% 21.92/5.99 | From (893) and (1312) follows:
% 21.92/5.99 | (1448) sum(n13, n7) = all_0_7_7
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n13, n7, all_0_7_7, n4 and discharging atoms sum(n13, n7) = all_0_7_7, sum(n13, n7) = n4, yields:
% 21.92/5.99 | (636) all_0_7_7 = n4
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n5, n15, all_0_4_4, n4 and discharging atoms sum(n5, n15) = all_0_4_4, sum(n5, n15) = n4, yields:
% 21.92/5.99 | (634) all_0_4_4 = n4
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 21.92/5.99 | (754) all_0_1_1 = n12
% 21.92/5.99 |
% 21.92/5.99 | From (636)(634) and (212) follows:
% 21.92/5.99 | (638) sum(n4, n4) = all_0_3_3
% 21.92/5.99 |
% 21.92/5.99 | From (754) and (1314) follows:
% 21.92/5.99 | (1045) sum(n12, n12) = all_0_0_0
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n12, n12, all_0_0_0, n8 and discharging atoms sum(n12, n12) = all_0_0_0, sum(n12, n12) = n8, yields:
% 21.92/5.99 | (496) all_0_0_0 = n8
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 21.92/5.99 | (495) all_0_3_3 = n8
% 21.92/5.99 |
% 21.92/5.99 | Equations (496,495) can reduce 363 to:
% 21.92/5.99 | (461) $false
% 21.92/5.99 |
% 21.92/5.99 |-The branch is then unsatisfiable
% 21.92/5.99 |-Branch two:
% 21.92/5.99 | (905) ~ (all_0_10_10 = n6)
% 21.92/5.99 | (906) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/5.99 |
% 21.92/5.99 +-Applying beta-rule and splitting (906), into two cases.
% 21.92/5.99 |-Branch one:
% 21.92/5.99 | (907) all_0_10_10 = n5
% 21.92/5.99 |
% 21.92/5.99 | From (907) and (317) follows:
% 21.92/5.99 | (908) pred(n5) = all_0_6_6
% 21.92/5.99 |
% 21.92/5.99 | From (907) and (146) follows:
% 21.92/5.99 | (909) succ(n5) = all_0_8_8
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (130) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 21.92/5.99 | (910) all_0_6_6 = n4
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (165) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 21.92/5.99 | (911) all_0_8_8 = n6
% 21.92/5.99 |
% 21.92/5.99 | From (910)(911) and (10) follows:
% 21.92/5.99 | (912) sum(n4, n6) = all_0_1_1
% 21.92/5.99 |
% 21.92/5.99 | From (910) and (1310) follows:
% 21.92/5.99 | (1465) sum(n4, n15) = all_0_4_4
% 21.92/5.99 |
% 21.92/5.99 | From (911) and (1312) follows:
% 21.92/5.99 | (1466) sum(n13, n6) = all_0_7_7
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n13, n6, all_0_7_7, n3 and discharging atoms sum(n13, n6) = all_0_7_7, sum(n13, n6) = n3, yields:
% 21.92/5.99 | (654) all_0_7_7 = n3
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n4, n15, all_0_4_4, n3 and discharging atoms sum(n4, n15) = all_0_4_4, sum(n4, n15) = n3, yields:
% 21.92/5.99 | (652) all_0_4_4 = n3
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 21.92/5.99 | (772) all_0_1_1 = n10
% 21.92/5.99 |
% 21.92/5.99 | From (654)(652) and (212) follows:
% 21.92/5.99 | (656) sum(n3, n3) = all_0_3_3
% 21.92/5.99 |
% 21.92/5.99 | From (772) and (1314) follows:
% 21.92/5.99 | (1327) sum(n12, n10) = all_0_0_0
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n12, n10, all_0_0_0, n6 and discharging atoms sum(n12, n10) = all_0_0_0, sum(n12, n10) = n6, yields:
% 21.92/5.99 | (514) all_0_0_0 = n6
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 21.92/5.99 | (513) all_0_3_3 = n6
% 21.92/5.99 |
% 21.92/5.99 | Equations (514,513) can reduce 363 to:
% 21.92/5.99 | (461) $false
% 21.92/5.99 |
% 21.92/5.99 |-The branch is then unsatisfiable
% 21.92/5.99 |-Branch two:
% 21.92/5.99 | (923) ~ (all_0_10_10 = n5)
% 21.92/5.99 | (924) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/5.99 |
% 21.92/5.99 +-Applying beta-rule and splitting (924), into two cases.
% 21.92/5.99 |-Branch one:
% 21.92/5.99 | (925) all_0_10_10 = n4
% 21.92/5.99 |
% 21.92/5.99 | From (925) and (317) follows:
% 21.92/5.99 | (926) pred(n4) = all_0_6_6
% 21.92/5.99 |
% 21.92/5.99 | From (925) and (146) follows:
% 21.92/5.99 | (927) succ(n4) = all_0_8_8
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (130) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 21.92/5.99 | (928) all_0_6_6 = n3
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (165) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 21.92/5.99 | (929) all_0_8_8 = n5
% 21.92/5.99 |
% 21.92/5.99 | From (928)(929) and (10) follows:
% 21.92/5.99 | (930) sum(n3, n5) = all_0_1_1
% 21.92/5.99 |
% 21.92/5.99 | From (928) and (1310) follows:
% 21.92/5.99 | (1483) sum(n3, n15) = all_0_4_4
% 21.92/5.99 |
% 21.92/5.99 | From (929) and (1312) follows:
% 21.92/5.99 | (1484) sum(n13, n5) = all_0_7_7
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n13, n5, all_0_7_7, n2 and discharging atoms sum(n13, n5) = all_0_7_7, sum(n13, n5) = n2, yields:
% 21.92/5.99 | (672) all_0_7_7 = n2
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n3, n15, all_0_4_4, n2 and discharging atoms sum(n3, n15) = all_0_4_4, sum(n3, n15) = n2, yields:
% 21.92/5.99 | (670) all_0_4_4 = n2
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 21.92/5.99 | (790) all_0_1_1 = n8
% 21.92/5.99 |
% 21.92/5.99 | From (672)(670) and (212) follows:
% 21.92/5.99 | (674) sum(n2, n2) = all_0_3_3
% 21.92/5.99 |
% 21.92/5.99 | From (790) and (1314) follows:
% 21.92/5.99 | (1345) sum(n12, n8) = all_0_0_0
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n12, n8, all_0_0_0, n4 and discharging atoms sum(n12, n8) = all_0_0_0, sum(n12, n8) = n4, yields:
% 21.92/5.99 | (532) all_0_0_0 = n4
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 21.92/5.99 | (531) all_0_3_3 = n4
% 21.92/5.99 |
% 21.92/5.99 | Equations (532,531) can reduce 363 to:
% 21.92/5.99 | (461) $false
% 21.92/5.99 |
% 21.92/5.99 |-The branch is then unsatisfiable
% 21.92/5.99 |-Branch two:
% 21.92/5.99 | (941) ~ (all_0_10_10 = n4)
% 21.92/5.99 | (942) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/5.99 |
% 21.92/5.99 +-Applying beta-rule and splitting (942), into two cases.
% 21.92/5.99 |-Branch one:
% 21.92/5.99 | (943) all_0_10_10 = n3
% 21.92/5.99 |
% 21.92/5.99 | From (943) and (317) follows:
% 21.92/5.99 | (944) pred(n3) = all_0_6_6
% 21.92/5.99 |
% 21.92/5.99 | From (943) and (146) follows:
% 21.92/5.99 | (945) succ(n3) = all_0_8_8
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (130) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 21.92/5.99 | (946) all_0_6_6 = n2
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (165) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 21.92/5.99 | (947) all_0_8_8 = n4
% 21.92/5.99 |
% 21.92/5.99 | From (946)(947) and (10) follows:
% 21.92/5.99 | (948) sum(n2, n4) = all_0_1_1
% 21.92/5.99 |
% 21.92/5.99 | From (946) and (1310) follows:
% 21.92/5.99 | (1501) sum(n2, n15) = all_0_4_4
% 21.92/5.99 |
% 21.92/5.99 | From (947) and (1312) follows:
% 21.92/5.99 | (1502) sum(n13, n4) = all_0_7_7
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n13, n4, all_0_7_7, n1 and discharging atoms sum(n13, n4) = all_0_7_7, sum(n13, n4) = n1, yields:
% 21.92/5.99 | (690) all_0_7_7 = n1
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n2, n15, all_0_4_4, n1 and discharging atoms sum(n2, n15) = all_0_4_4, sum(n2, n15) = n1, yields:
% 21.92/5.99 | (688) all_0_4_4 = n1
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 21.92/5.99 | (808) all_0_1_1 = n6
% 21.92/5.99 |
% 21.92/5.99 | From (690)(688) and (212) follows:
% 21.92/5.99 | (692) sum(n1, n1) = all_0_3_3
% 21.92/5.99 |
% 21.92/5.99 | From (808) and (1314) follows:
% 21.92/5.99 | (1363) sum(n12, n6) = all_0_0_0
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n12, n6, all_0_0_0, n2 and discharging atoms sum(n12, n6) = all_0_0_0, sum(n12, n6) = n2, yields:
% 21.92/5.99 | (550) all_0_0_0 = n2
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 21.92/5.99 | (549) all_0_3_3 = n2
% 21.92/5.99 |
% 21.92/5.99 | Equations (550,549) can reduce 363 to:
% 21.92/5.99 | (461) $false
% 21.92/5.99 |
% 21.92/5.99 |-The branch is then unsatisfiable
% 21.92/5.99 |-Branch two:
% 21.92/5.99 | (959) ~ (all_0_10_10 = n3)
% 21.92/5.99 | (960) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/5.99 |
% 21.92/5.99 +-Applying beta-rule and splitting (960), into two cases.
% 21.92/5.99 |-Branch one:
% 21.92/5.99 | (961) all_0_10_10 = n2
% 21.92/5.99 |
% 21.92/5.99 | From (961) and (317) follows:
% 21.92/5.99 | (962) pred(n2) = all_0_6_6
% 21.92/5.99 |
% 21.92/5.99 | From (961) and (146) follows:
% 21.92/5.99 | (963) succ(n2) = all_0_8_8
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (130) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 21.92/5.99 | (964) all_0_6_6 = n1
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (165) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 21.92/5.99 | (965) all_0_8_8 = n3
% 21.92/5.99 |
% 21.92/5.99 | From (964)(965) and (10) follows:
% 21.92/5.99 | (966) sum(n1, n3) = all_0_1_1
% 21.92/5.99 |
% 21.92/5.99 | From (964) and (1310) follows:
% 21.92/5.99 | (1519) sum(n1, n15) = all_0_4_4
% 21.92/5.99 |
% 21.92/5.99 | From (965) and (1312) follows:
% 21.92/5.99 | (1520) sum(n13, n3) = all_0_7_7
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n13, n3, all_0_7_7, n0 and discharging atoms sum(n13, n3) = all_0_7_7, sum(n13, n3) = n0, yields:
% 21.92/5.99 | (708) all_0_7_7 = n0
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n1, n15, all_0_4_4, n0 and discharging atoms sum(n1, n15) = all_0_4_4, sum(n1, n15) = n0, yields:
% 21.92/5.99 | (706) all_0_4_4 = n0
% 21.92/5.99 |
% 21.92/5.99 | Instantiating formula (74) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 21.92/5.99 | (826) all_0_1_1 = n4
% 21.92/5.99 |
% 21.92/5.99 | From (708)(706) and (212) follows:
% 21.92/5.99 | (710) sum(n0, n0) = all_0_3_3
% 21.92/5.99 |
% 21.92/5.99 | From (826) and (1314) follows:
% 21.92/6.00 | (1381) sum(n12, n4) = all_0_0_0
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n12, n4, all_0_0_0, n0 and discharging atoms sum(n12, n4) = all_0_0_0, sum(n12, n4) = n0, yields:
% 21.92/6.00 | (568) all_0_0_0 = n0
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 21.92/6.00 | (567) all_0_3_3 = n0
% 21.92/6.00 |
% 21.92/6.00 | Equations (568,567) can reduce 363 to:
% 21.92/6.00 | (461) $false
% 21.92/6.00 |
% 21.92/6.00 |-The branch is then unsatisfiable
% 21.92/6.00 |-Branch two:
% 21.92/6.00 | (977) ~ (all_0_10_10 = n2)
% 21.92/6.00 | (978) all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/6.00 |
% 21.92/6.00 +-Applying beta-rule and splitting (978), into two cases.
% 21.92/6.00 |-Branch one:
% 21.92/6.00 | (979) all_0_10_10 = n1
% 21.92/6.00 |
% 21.92/6.00 | From (979) and (317) follows:
% 21.92/6.00 | (980) pred(n1) = all_0_6_6
% 21.92/6.00 |
% 21.92/6.00 | From (979) and (146) follows:
% 21.92/6.00 | (981) succ(n1) = all_0_8_8
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (130) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 21.92/6.00 | (982) all_0_6_6 = n0
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (165) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 21.92/6.00 | (983) all_0_8_8 = n2
% 21.92/6.00 |
% 21.92/6.00 | From (982)(983) and (10) follows:
% 21.92/6.00 | (984) sum(n0, n2) = all_0_1_1
% 21.92/6.00 |
% 21.92/6.00 | From (982) and (1310) follows:
% 21.92/6.00 | (1537) sum(n0, n15) = all_0_4_4
% 21.92/6.00 |
% 21.92/6.00 | From (983) and (1312) follows:
% 21.92/6.00 | (1538) sum(n13, n2) = all_0_7_7
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n13, n2, all_0_7_7, n15 and discharging atoms sum(n13, n2) = all_0_7_7, sum(n13, n2) = n15, yields:
% 21.92/6.00 | (725) all_0_7_7 = n15
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n0, n15, all_0_4_4, n15 and discharging atoms sum(n0, n15) = all_0_4_4, sum(n0, n15) = n15, yields:
% 21.92/6.00 | (726) all_0_4_4 = n15
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 21.92/6.00 | (844) all_0_1_1 = n2
% 21.92/6.00 |
% 21.92/6.00 | From (725)(726) and (212) follows:
% 21.92/6.00 | (728) sum(n15, n15) = all_0_3_3
% 21.92/6.00 |
% 21.92/6.00 | From (844) and (1314) follows:
% 21.92/6.00 | (1399) sum(n12, n2) = all_0_0_0
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n15, n15, all_0_3_3, n14 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n14, yields:
% 21.92/6.00 | (585) all_0_3_3 = n14
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n12, n2, all_0_0_0, n14 and discharging atoms sum(n12, n2) = all_0_0_0, sum(n12, n2) = n14, yields:
% 21.92/6.00 | (586) all_0_0_0 = n14
% 21.92/6.00 |
% 21.92/6.00 | Equations (586,585) can reduce 363 to:
% 21.92/6.00 | (461) $false
% 21.92/6.00 |
% 21.92/6.00 |-The branch is then unsatisfiable
% 21.92/6.00 |-Branch two:
% 21.92/6.00 | (997) ~ (all_0_10_10 = n1)
% 21.92/6.00 | (998) all_0_10_10 = n0
% 21.92/6.00 |
% 21.92/6.00 | From (998) and (317) follows:
% 21.92/6.00 | (999) pred(n0) = all_0_6_6
% 21.92/6.00 |
% 21.92/6.00 | From (998) and (146) follows:
% 21.92/6.00 | (1000) succ(n0) = all_0_8_8
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (130) with n0, all_0_6_6, n15 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n15, yields:
% 21.92/6.00 | (1001) all_0_6_6 = n15
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (165) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 21.92/6.00 | (1002) all_0_8_8 = n1
% 21.92/6.00 |
% 21.92/6.00 | From (1001)(1002) and (10) follows:
% 21.92/6.00 | (1003) sum(n15, n1) = all_0_1_1
% 21.92/6.00 |
% 21.92/6.00 | From (1001) and (1310) follows:
% 21.92/6.00 | (1554) sum(n15, n15) = all_0_4_4
% 21.92/6.00 |
% 21.92/6.00 | From (1002) and (1312) follows:
% 21.92/6.00 | (1555) sum(n13, n1) = all_0_7_7
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n15, n15, all_0_4_4, n14 and discharging atoms sum(n15, n15) = all_0_4_4, sum(n15, n15) = n14, yields:
% 21.92/6.00 | (451) all_0_4_4 = n14
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n15, n1, all_0_1_1, n0 and discharging atoms sum(n15, n1) = all_0_1_1, sum(n15, n1) = n0, yields:
% 21.92/6.00 | (862) all_0_1_1 = n0
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n13, n1, all_0_7_7, n14 and discharging atoms sum(n13, n1) = all_0_7_7, sum(n13, n1) = n14, yields:
% 21.92/6.00 | (452) all_0_7_7 = n14
% 21.92/6.00 |
% 21.92/6.00 | From (452)(451) and (212) follows:
% 21.92/6.00 | (456) sum(n14, n14) = all_0_3_3
% 21.92/6.00 |
% 21.92/6.00 | From (862) and (1314) follows:
% 21.92/6.00 | (1417) sum(n12, n0) = all_0_0_0
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n14, n14, all_0_3_3, n12 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n12, yields:
% 21.92/6.00 | (459) all_0_3_3 = n12
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n12, n0, all_0_0_0, n12 and discharging atoms sum(n12, n0) = all_0_0_0, sum(n12, n0) = n12, yields:
% 21.92/6.00 | (457) all_0_0_0 = n12
% 21.92/6.00 |
% 21.92/6.00 | Equations (457,459) can reduce 363 to:
% 21.92/6.00 | (461) $false
% 21.92/6.00 |
% 21.92/6.00 |-The branch is then unsatisfiable
% 21.92/6.00 |-Branch two:
% 21.92/6.00 | (480) ~ (all_0_11_11 = n14)
% 21.92/6.00 | (481) all_0_11_11 = n13 | all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.92/6.00 |
% 21.92/6.00 +-Applying beta-rule and splitting (762), into two cases.
% 21.92/6.00 |-Branch one:
% 21.92/6.00 | (763) all_0_10_10 = n13
% 21.92/6.00 |
% 21.92/6.00 | From (763) and (317) follows:
% 21.92/6.00 | (764) pred(n13) = all_0_6_6
% 21.92/6.00 |
% 21.92/6.00 | From (763) and (146) follows:
% 21.92/6.00 | (765) succ(n13) = all_0_8_8
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (130) with n13, all_0_6_6, n12 and discharging atoms pred(n13) = all_0_6_6, pred(n13) = n12, yields:
% 21.92/6.00 | (766) all_0_6_6 = n12
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (165) with n13, all_0_8_8, n14 and discharging atoms succ(n13) = all_0_8_8, succ(n13) = n14, yields:
% 21.92/6.00 | (767) all_0_8_8 = n14
% 21.92/6.00 |
% 21.92/6.00 | From (766) and (764) follows:
% 21.92/6.00 | (382) pred(n13) = n12
% 21.92/6.00 |
% 21.92/6.00 | From (767) and (765) follows:
% 21.92/6.00 | (177) succ(n13) = n14
% 21.92/6.00 |
% 21.92/6.00 | From (766) and (276) follows:
% 21.92/6.00 | (1573) sum(n12, all_0_5_5) = all_0_4_4
% 21.92/6.00 |
% 21.92/6.00 | From (766)(767) and (10) follows:
% 21.92/6.00 | (768) sum(n12, n14) = all_0_1_1
% 21.92/6.00 |
% 21.92/6.00 | From (767) and (350) follows:
% 21.92/6.00 | (1575) sum(all_0_9_9, n14) = all_0_7_7
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n12, n14, all_0_1_1, n10 and discharging atoms sum(n12, n14) = all_0_1_1, sum(n12, n14) = n10, yields:
% 21.92/6.00 | (772) all_0_1_1 = n10
% 21.92/6.00 |
% 21.92/6.00 | From (772) and (256) follows:
% 21.92/6.00 | (1577) sum(all_0_2_2, n10) = all_0_0_0
% 21.92/6.00 |
% 21.92/6.00 | From (772) and (768) follows:
% 21.92/6.00 | (321) sum(n12, n14) = n10
% 21.92/6.00 |
% 21.92/6.00 +-Applying beta-rule and splitting (481), into two cases.
% 21.92/6.00 |-Branch one:
% 21.92/6.00 | (482) all_0_11_11 = n13
% 21.92/6.00 |
% 21.92/6.00 | From (482) and (423) follows:
% 21.92/6.00 | (483) pred(n13) = all_0_9_9
% 21.92/6.00 |
% 21.92/6.00 | From (482) and (262) follows:
% 21.92/6.00 | (484) succ(n13) = all_0_5_5
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (130) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 21.92/6.00 | (485) all_0_9_9 = n12
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (165) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 21.92/6.00 | (486) all_0_5_5 = n14
% 21.92/6.00 |
% 21.92/6.00 | From (485)(486) and (147) follows:
% 21.92/6.00 | (487) sum(n12, n14) = all_0_2_2
% 21.92/6.00 |
% 21.92/6.00 | From (485) and (1575) follows:
% 21.92/6.00 | (1585) sum(n12, n14) = all_0_7_7
% 21.92/6.00 |
% 21.92/6.00 | From (486) and (1573) follows:
% 21.92/6.00 | (1586) sum(n12, n14) = all_0_4_4
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n12, n14, all_0_2_2, n10 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n10, yields:
% 21.92/6.00 | (491) all_0_2_2 = n10
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n12, n14, all_0_4_4, all_0_2_2 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = all_0_4_4, yields:
% 21.92/6.00 | (448) all_0_2_2 = all_0_4_4
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n12, n14, all_0_7_7, all_0_2_2 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = all_0_7_7, yields:
% 21.92/6.00 | (449) all_0_2_2 = all_0_7_7
% 21.92/6.00 |
% 21.92/6.00 | Combining equations (449,448) yields a new equation:
% 21.92/6.00 | (450) all_0_4_4 = all_0_7_7
% 21.92/6.00 |
% 21.92/6.00 | Combining equations (491,448) yields a new equation:
% 21.92/6.00 | (526) all_0_4_4 = n10
% 21.92/6.00 |
% 21.92/6.00 | Combining equations (526,450) yields a new equation:
% 21.92/6.00 | (528) all_0_7_7 = n10
% 21.92/6.00 |
% 21.92/6.00 | Combining equations (528,450) yields a new equation:
% 21.92/6.00 | (526) all_0_4_4 = n10
% 21.92/6.00 |
% 21.92/6.00 | Combining equations (526,448) yields a new equation:
% 21.92/6.00 | (491) all_0_2_2 = n10
% 21.92/6.00 |
% 21.92/6.00 | From (491) and (1577) follows:
% 21.92/6.00 | (1595) sum(n10, n10) = all_0_0_0
% 21.92/6.00 |
% 21.92/6.00 | From (528)(526) and (212) follows:
% 21.92/6.00 | (530) sum(n10, n10) = all_0_3_3
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n10, n10, all_0_0_0, n4 and discharging atoms sum(n10, n10) = all_0_0_0, sum(n10, n10) = n4, yields:
% 21.92/6.00 | (532) all_0_0_0 = n4
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n10, n10, all_0_3_3, all_0_0_0 and discharging atoms sum(n10, n10) = all_0_0_0, sum(n10, n10) = all_0_3_3, yields:
% 21.92/6.00 | (458) all_0_0_0 = all_0_3_3
% 21.92/6.00 |
% 21.92/6.00 | Combining equations (532,458) yields a new equation:
% 21.92/6.00 | (531) all_0_3_3 = n4
% 21.92/6.00 |
% 21.92/6.00 | Combining equations (531,458) yields a new equation:
% 21.92/6.00 | (532) all_0_0_0 = n4
% 21.92/6.00 |
% 21.92/6.00 | Equations (532,531) can reduce 363 to:
% 21.92/6.00 | (461) $false
% 21.92/6.00 |
% 21.92/6.00 |-The branch is then unsatisfiable
% 21.92/6.00 |-Branch two:
% 21.92/6.00 | (498) ~ (all_0_11_11 = n13)
% 21.92/6.00 | (499) all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.92/6.00 |
% 21.92/6.00 +-Applying beta-rule and splitting (499), into two cases.
% 21.92/6.00 |-Branch one:
% 21.92/6.00 | (500) all_0_11_11 = n12
% 21.92/6.00 |
% 21.92/6.00 | From (500) and (423) follows:
% 21.92/6.00 | (501) pred(n12) = all_0_9_9
% 21.92/6.00 |
% 21.92/6.00 | From (500) and (262) follows:
% 21.92/6.00 | (502) succ(n12) = all_0_5_5
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (130) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 21.92/6.00 | (503) all_0_9_9 = n11
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (165) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 21.92/6.00 | (504) all_0_5_5 = n13
% 21.92/6.00 |
% 21.92/6.00 | From (503)(504) and (147) follows:
% 21.92/6.00 | (505) sum(n11, n13) = all_0_2_2
% 21.92/6.00 |
% 21.92/6.00 | From (503) and (1575) follows:
% 21.92/6.00 | (1610) sum(n11, n14) = all_0_7_7
% 21.92/6.00 |
% 21.92/6.00 | From (504) and (1573) follows:
% 21.92/6.00 | (1611) sum(n12, n13) = all_0_4_4
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n12, n13, all_0_4_4, n9 and discharging atoms sum(n12, n13) = all_0_4_4, sum(n12, n13) = n9, yields:
% 21.92/6.00 | (544) all_0_4_4 = n9
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n11, n14, all_0_7_7, n9 and discharging atoms sum(n11, n14) = all_0_7_7, sum(n11, n14) = n9, yields:
% 21.92/6.00 | (546) all_0_7_7 = n9
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n11, n13, all_0_2_2, n8 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n8, yields:
% 21.92/6.00 | (509) all_0_2_2 = n8
% 21.92/6.00 |
% 21.92/6.00 | From (509) and (1577) follows:
% 21.92/6.00 | (1615) sum(n8, n10) = all_0_0_0
% 21.92/6.00 |
% 21.92/6.00 | From (546)(544) and (212) follows:
% 21.92/6.00 | (548) sum(n9, n9) = all_0_3_3
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n9, n9, all_0_3_3, n2 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n2, yields:
% 21.92/6.00 | (549) all_0_3_3 = n2
% 21.92/6.00 |
% 21.92/6.00 | Instantiating formula (74) with n8, n10, all_0_0_0, n2 and discharging atoms sum(n8, n10) = all_0_0_0, sum(n8, n10) = n2, yields:
% 21.92/6.00 | (550) all_0_0_0 = n2
% 21.92/6.00 |
% 21.92/6.00 | Equations (550,549) can reduce 363 to:
% 21.92/6.00 | (461) $false
% 21.92/6.01 |
% 21.92/6.01 |-The branch is then unsatisfiable
% 21.92/6.01 |-Branch two:
% 21.92/6.01 | (516) ~ (all_0_11_11 = n12)
% 21.92/6.01 | (517) all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.92/6.01 |
% 21.92/6.01 +-Applying beta-rule and splitting (517), into two cases.
% 21.92/6.01 |-Branch one:
% 21.92/6.01 | (518) all_0_11_11 = n11
% 21.92/6.01 |
% 21.92/6.01 | From (518) and (423) follows:
% 21.92/6.01 | (519) pred(n11) = all_0_9_9
% 21.92/6.01 |
% 21.92/6.01 | From (518) and (262) follows:
% 21.92/6.01 | (520) succ(n11) = all_0_5_5
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (130) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 21.92/6.01 | (521) all_0_9_9 = n10
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (165) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 21.92/6.01 | (522) all_0_5_5 = n12
% 21.92/6.01 |
% 21.92/6.01 | From (521)(522) and (147) follows:
% 21.92/6.01 | (523) sum(n10, n12) = all_0_2_2
% 21.92/6.01 |
% 21.92/6.01 | From (521) and (1575) follows:
% 21.92/6.01 | (1628) sum(n10, n14) = all_0_7_7
% 21.92/6.01 |
% 21.92/6.01 | From (522) and (1573) follows:
% 21.92/6.01 | (1629) sum(n12, n12) = all_0_4_4
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n12, n12, all_0_4_4, n8 and discharging atoms sum(n12, n12) = all_0_4_4, sum(n12, n12) = n8, yields:
% 21.92/6.01 | (562) all_0_4_4 = n8
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n10, n14, all_0_7_7, n8 and discharging atoms sum(n10, n14) = all_0_7_7, sum(n10, n14) = n8, yields:
% 21.92/6.01 | (564) all_0_7_7 = n8
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n10, n12, all_0_2_2, n6 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n6, yields:
% 21.92/6.01 | (527) all_0_2_2 = n6
% 21.92/6.01 |
% 21.92/6.01 | From (527) and (1577) follows:
% 21.92/6.01 | (1633) sum(n6, n10) = all_0_0_0
% 21.92/6.01 |
% 21.92/6.01 | From (564)(562) and (212) follows:
% 21.92/6.01 | (566) sum(n8, n8) = all_0_3_3
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n8, n8, all_0_3_3, n0 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n0, yields:
% 21.92/6.01 | (567) all_0_3_3 = n0
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n6, n10, all_0_0_0, n0 and discharging atoms sum(n6, n10) = all_0_0_0, sum(n6, n10) = n0, yields:
% 21.92/6.01 | (568) all_0_0_0 = n0
% 21.92/6.01 |
% 21.92/6.01 | Equations (568,567) can reduce 363 to:
% 21.92/6.01 | (461) $false
% 21.92/6.01 |
% 21.92/6.01 |-The branch is then unsatisfiable
% 21.92/6.01 |-Branch two:
% 21.92/6.01 | (534) ~ (all_0_11_11 = n11)
% 21.92/6.01 | (535) all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.92/6.01 |
% 21.92/6.01 +-Applying beta-rule and splitting (535), into two cases.
% 21.92/6.01 |-Branch one:
% 21.92/6.01 | (536) all_0_11_11 = n10
% 21.92/6.01 |
% 21.92/6.01 | From (536) and (423) follows:
% 21.92/6.01 | (537) pred(n10) = all_0_9_9
% 21.92/6.01 |
% 21.92/6.01 | From (536) and (262) follows:
% 21.92/6.01 | (538) succ(n10) = all_0_5_5
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (130) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 21.92/6.01 | (539) all_0_9_9 = n9
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (165) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 21.92/6.01 | (540) all_0_5_5 = n11
% 21.92/6.01 |
% 21.92/6.01 | From (539)(540) and (147) follows:
% 21.92/6.01 | (541) sum(n9, n11) = all_0_2_2
% 21.92/6.01 |
% 21.92/6.01 | From (539) and (1575) follows:
% 21.92/6.01 | (1646) sum(n9, n14) = all_0_7_7
% 21.92/6.01 |
% 21.92/6.01 | From (540) and (1573) follows:
% 21.92/6.01 | (1647) sum(n12, n11) = all_0_4_4
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n12, n11, all_0_4_4, n7 and discharging atoms sum(n12, n11) = all_0_4_4, sum(n12, n11) = n7, yields:
% 21.92/6.01 | (580) all_0_4_4 = n7
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n9, n14, all_0_7_7, n7 and discharging atoms sum(n9, n14) = all_0_7_7, sum(n9, n14) = n7, yields:
% 21.92/6.01 | (582) all_0_7_7 = n7
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n9, n11, all_0_2_2, n4 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n4, yields:
% 21.92/6.01 | (545) all_0_2_2 = n4
% 21.92/6.01 |
% 21.92/6.01 | From (545) and (1577) follows:
% 21.92/6.01 | (1651) sum(n4, n10) = all_0_0_0
% 21.92/6.01 |
% 21.92/6.01 | From (582)(580) and (212) follows:
% 21.92/6.01 | (584) sum(n7, n7) = all_0_3_3
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 21.92/6.01 | (585) all_0_3_3 = n14
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n4, n10, all_0_0_0, n14 and discharging atoms sum(n4, n10) = all_0_0_0, sum(n4, n10) = n14, yields:
% 21.92/6.01 | (586) all_0_0_0 = n14
% 21.92/6.01 |
% 21.92/6.01 | Equations (586,585) can reduce 363 to:
% 21.92/6.01 | (461) $false
% 21.92/6.01 |
% 21.92/6.01 |-The branch is then unsatisfiable
% 21.92/6.01 |-Branch two:
% 21.92/6.01 | (552) ~ (all_0_11_11 = n10)
% 21.92/6.01 | (553) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.92/6.01 |
% 21.92/6.01 +-Applying beta-rule and splitting (553), into two cases.
% 21.92/6.01 |-Branch one:
% 21.92/6.01 | (554) all_0_11_11 = n9
% 21.92/6.01 |
% 21.92/6.01 | From (554) and (423) follows:
% 21.92/6.01 | (555) pred(n9) = all_0_9_9
% 21.92/6.01 |
% 21.92/6.01 | From (554) and (262) follows:
% 21.92/6.01 | (556) succ(n9) = all_0_5_5
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (130) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 21.92/6.01 | (557) all_0_9_9 = n8
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (165) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 21.92/6.01 | (558) all_0_5_5 = n10
% 21.92/6.01 |
% 21.92/6.01 | From (557)(558) and (147) follows:
% 21.92/6.01 | (559) sum(n8, n10) = all_0_2_2
% 21.92/6.01 |
% 21.92/6.01 | From (557) and (1575) follows:
% 21.92/6.01 | (1664) sum(n8, n14) = all_0_7_7
% 21.92/6.01 |
% 21.92/6.01 | From (558) and (1573) follows:
% 21.92/6.01 | (1665) sum(n12, n10) = all_0_4_4
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n12, n10, all_0_4_4, n6 and discharging atoms sum(n12, n10) = all_0_4_4, sum(n12, n10) = n6, yields:
% 21.92/6.01 | (598) all_0_4_4 = n6
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n8, n14, all_0_7_7, n6 and discharging atoms sum(n8, n14) = all_0_7_7, sum(n8, n14) = n6, yields:
% 21.92/6.01 | (600) all_0_7_7 = n6
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n8, n10, all_0_2_2, n2 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n2, yields:
% 21.92/6.01 | (563) all_0_2_2 = n2
% 21.92/6.01 |
% 21.92/6.01 | From (563) and (1577) follows:
% 21.92/6.01 | (1669) sum(n2, n10) = all_0_0_0
% 21.92/6.01 |
% 21.92/6.01 | From (600)(598) and (212) follows:
% 21.92/6.01 | (602) sum(n6, n6) = all_0_3_3
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 21.92/6.01 | (459) all_0_3_3 = n12
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n2, n10, all_0_0_0, n12 and discharging atoms sum(n2, n10) = all_0_0_0, sum(n2, n10) = n12, yields:
% 21.92/6.01 | (457) all_0_0_0 = n12
% 21.92/6.01 |
% 21.92/6.01 | Equations (457,459) can reduce 363 to:
% 21.92/6.01 | (461) $false
% 21.92/6.01 |
% 21.92/6.01 |-The branch is then unsatisfiable
% 21.92/6.01 |-Branch two:
% 21.92/6.01 | (570) ~ (all_0_11_11 = n9)
% 21.92/6.01 | (571) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.92/6.01 |
% 21.92/6.01 +-Applying beta-rule and splitting (571), into two cases.
% 21.92/6.01 |-Branch one:
% 21.92/6.01 | (572) all_0_11_11 = n8
% 21.92/6.01 |
% 21.92/6.01 | From (572) and (423) follows:
% 21.92/6.01 | (573) pred(n8) = all_0_9_9
% 21.92/6.01 |
% 21.92/6.01 | From (572) and (262) follows:
% 21.92/6.01 | (574) succ(n8) = all_0_5_5
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (130) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 21.92/6.01 | (575) all_0_9_9 = n7
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (165) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 21.92/6.01 | (576) all_0_5_5 = n9
% 21.92/6.01 |
% 21.92/6.01 | From (575)(576) and (147) follows:
% 21.92/6.01 | (577) sum(n7, n9) = all_0_2_2
% 21.92/6.01 |
% 21.92/6.01 | From (575) and (1575) follows:
% 21.92/6.01 | (1682) sum(n7, n14) = all_0_7_7
% 21.92/6.01 |
% 21.92/6.01 | From (576) and (1573) follows:
% 21.92/6.01 | (1683) sum(n12, n9) = all_0_4_4
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n12, n9, all_0_4_4, n5 and discharging atoms sum(n12, n9) = all_0_4_4, sum(n12, n9) = n5, yields:
% 21.92/6.01 | (616) all_0_4_4 = n5
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n7, n14, all_0_7_7, n5 and discharging atoms sum(n7, n14) = all_0_7_7, sum(n7, n14) = n5, yields:
% 21.92/6.01 | (618) all_0_7_7 = n5
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n7, n9, all_0_2_2, n0 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n0, yields:
% 21.92/6.01 | (581) all_0_2_2 = n0
% 21.92/6.01 |
% 21.92/6.01 | From (581) and (1577) follows:
% 21.92/6.01 | (1687) sum(n0, n10) = all_0_0_0
% 21.92/6.01 |
% 21.92/6.01 | From (618)(616) and (212) follows:
% 21.92/6.01 | (620) sum(n5, n5) = all_0_3_3
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 21.92/6.01 | (477) all_0_3_3 = n10
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n0, n10, all_0_0_0, n10 and discharging atoms sum(n0, n10) = all_0_0_0, sum(n0, n10) = n10, yields:
% 21.92/6.01 | (478) all_0_0_0 = n10
% 21.92/6.01 |
% 21.92/6.01 | Equations (478,477) can reduce 363 to:
% 21.92/6.01 | (461) $false
% 21.92/6.01 |
% 21.92/6.01 |-The branch is then unsatisfiable
% 21.92/6.01 |-Branch two:
% 21.92/6.01 | (588) ~ (all_0_11_11 = n8)
% 21.92/6.01 | (589) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.92/6.01 |
% 21.92/6.01 +-Applying beta-rule and splitting (589), into two cases.
% 21.92/6.01 |-Branch one:
% 21.92/6.01 | (590) all_0_11_11 = n7
% 21.92/6.01 |
% 21.92/6.01 | From (590) and (423) follows:
% 21.92/6.01 | (591) pred(n7) = all_0_9_9
% 21.92/6.01 |
% 21.92/6.01 | From (590) and (262) follows:
% 21.92/6.01 | (592) succ(n7) = all_0_5_5
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (130) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 21.92/6.01 | (593) all_0_9_9 = n6
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (165) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 21.92/6.01 | (594) all_0_5_5 = n8
% 21.92/6.01 |
% 21.92/6.01 | From (593)(594) and (147) follows:
% 21.92/6.01 | (595) sum(n6, n8) = all_0_2_2
% 21.92/6.01 |
% 21.92/6.01 | From (593) and (1575) follows:
% 21.92/6.01 | (1700) sum(n6, n14) = all_0_7_7
% 21.92/6.01 |
% 21.92/6.01 | From (594) and (1573) follows:
% 21.92/6.01 | (1701) sum(n12, n8) = all_0_4_4
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n12, n8, all_0_4_4, n4 and discharging atoms sum(n12, n8) = all_0_4_4, sum(n12, n8) = n4, yields:
% 21.92/6.01 | (634) all_0_4_4 = n4
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n6, n14, all_0_7_7, n4 and discharging atoms sum(n6, n14) = all_0_7_7, sum(n6, n14) = n4, yields:
% 21.92/6.01 | (636) all_0_7_7 = n4
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 21.92/6.01 | (447) all_0_2_2 = n14
% 21.92/6.01 |
% 21.92/6.01 | From (447) and (1577) follows:
% 21.92/6.01 | (775) sum(n14, n10) = all_0_0_0
% 21.92/6.01 |
% 21.92/6.01 | From (636)(634) and (212) follows:
% 21.92/6.01 | (638) sum(n4, n4) = all_0_3_3
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n14, n10, all_0_0_0, n8 and discharging atoms sum(n14, n10) = all_0_0_0, sum(n14, n10) = n8, yields:
% 21.92/6.01 | (496) all_0_0_0 = n8
% 21.92/6.01 |
% 21.92/6.01 | Instantiating formula (74) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 21.92/6.01 | (495) all_0_3_3 = n8
% 21.92/6.01 |
% 21.92/6.01 | Equations (496,495) can reduce 363 to:
% 21.92/6.01 | (461) $false
% 21.92/6.01 |
% 21.92/6.01 |-The branch is then unsatisfiable
% 21.92/6.01 |-Branch two:
% 21.92/6.01 | (606) ~ (all_0_11_11 = n7)
% 21.92/6.01 | (607) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.92/6.01 |
% 21.92/6.01 +-Applying beta-rule and splitting (607), into two cases.
% 21.92/6.01 |-Branch one:
% 21.92/6.01 | (608) all_0_11_11 = n6
% 21.92/6.01 |
% 21.92/6.01 | From (608) and (423) follows:
% 21.92/6.02 | (609) pred(n6) = all_0_9_9
% 21.92/6.02 |
% 21.92/6.02 | From (608) and (262) follows:
% 21.92/6.02 | (610) succ(n6) = all_0_5_5
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (130) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 21.92/6.02 | (611) all_0_9_9 = n5
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (165) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 21.92/6.02 | (612) all_0_5_5 = n7
% 21.92/6.02 |
% 21.92/6.02 | From (611)(612) and (147) follows:
% 21.92/6.02 | (613) sum(n5, n7) = all_0_2_2
% 21.92/6.02 |
% 21.92/6.02 | From (611) and (1575) follows:
% 21.92/6.02 | (1718) sum(n5, n14) = all_0_7_7
% 21.92/6.02 |
% 21.92/6.02 | From (612) and (1573) follows:
% 21.92/6.02 | (1719) sum(n12, n7) = all_0_4_4
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n12, n7, all_0_4_4, n3 and discharging atoms sum(n12, n7) = all_0_4_4, sum(n12, n7) = n3, yields:
% 21.92/6.02 | (652) all_0_4_4 = n3
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n5, n14, all_0_7_7, n3 and discharging atoms sum(n5, n14) = all_0_7_7, sum(n5, n14) = n3, yields:
% 21.92/6.02 | (654) all_0_7_7 = n3
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 21.92/6.02 | (473) all_0_2_2 = n12
% 21.92/6.02 |
% 21.92/6.02 | From (473) and (1577) follows:
% 21.92/6.02 | (1327) sum(n12, n10) = all_0_0_0
% 21.92/6.02 |
% 21.92/6.02 | From (654)(652) and (212) follows:
% 21.92/6.02 | (656) sum(n3, n3) = all_0_3_3
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n12, n10, all_0_0_0, n6 and discharging atoms sum(n12, n10) = all_0_0_0, sum(n12, n10) = n6, yields:
% 21.92/6.02 | (514) all_0_0_0 = n6
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 21.92/6.02 | (513) all_0_3_3 = n6
% 21.92/6.02 |
% 21.92/6.02 | Equations (514,513) can reduce 363 to:
% 21.92/6.02 | (461) $false
% 21.92/6.02 |
% 21.92/6.02 |-The branch is then unsatisfiable
% 21.92/6.02 |-Branch two:
% 21.92/6.02 | (624) ~ (all_0_11_11 = n6)
% 21.92/6.02 | (625) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.92/6.02 |
% 21.92/6.02 +-Applying beta-rule and splitting (625), into two cases.
% 21.92/6.02 |-Branch one:
% 21.92/6.02 | (626) all_0_11_11 = n5
% 21.92/6.02 |
% 21.92/6.02 | From (626) and (423) follows:
% 21.92/6.02 | (627) pred(n5) = all_0_9_9
% 21.92/6.02 |
% 21.92/6.02 | From (626) and (262) follows:
% 21.92/6.02 | (628) succ(n5) = all_0_5_5
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (130) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 21.92/6.02 | (629) all_0_9_9 = n4
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (165) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 21.92/6.02 | (630) all_0_5_5 = n6
% 21.92/6.02 |
% 21.92/6.02 | From (629)(630) and (147) follows:
% 21.92/6.02 | (631) sum(n4, n6) = all_0_2_2
% 21.92/6.02 |
% 21.92/6.02 | From (629) and (1575) follows:
% 21.92/6.02 | (1736) sum(n4, n14) = all_0_7_7
% 21.92/6.02 |
% 21.92/6.02 | From (630) and (1573) follows:
% 21.92/6.02 | (1737) sum(n12, n6) = all_0_4_4
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n12, n6, all_0_4_4, n2 and discharging atoms sum(n12, n6) = all_0_4_4, sum(n12, n6) = n2, yields:
% 21.92/6.02 | (670) all_0_4_4 = n2
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n4, n14, all_0_7_7, n2 and discharging atoms sum(n4, n14) = all_0_7_7, sum(n4, n14) = n2, yields:
% 21.92/6.02 | (672) all_0_7_7 = n2
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 21.92/6.02 | (491) all_0_2_2 = n10
% 21.92/6.02 |
% 21.92/6.02 | From (491) and (1577) follows:
% 21.92/6.02 | (1595) sum(n10, n10) = all_0_0_0
% 21.92/6.02 |
% 21.92/6.02 | From (672)(670) and (212) follows:
% 21.92/6.02 | (674) sum(n2, n2) = all_0_3_3
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n10, n10, all_0_0_0, n4 and discharging atoms sum(n10, n10) = all_0_0_0, sum(n10, n10) = n4, yields:
% 21.92/6.02 | (532) all_0_0_0 = n4
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 21.92/6.02 | (531) all_0_3_3 = n4
% 21.92/6.02 |
% 21.92/6.02 | Equations (532,531) can reduce 363 to:
% 21.92/6.02 | (461) $false
% 21.92/6.02 |
% 21.92/6.02 |-The branch is then unsatisfiable
% 21.92/6.02 |-Branch two:
% 21.92/6.02 | (642) ~ (all_0_11_11 = n5)
% 21.92/6.02 | (643) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.92/6.02 |
% 21.92/6.02 +-Applying beta-rule and splitting (643), into two cases.
% 21.92/6.02 |-Branch one:
% 21.92/6.02 | (644) all_0_11_11 = n4
% 21.92/6.02 |
% 21.92/6.02 | From (644) and (423) follows:
% 21.92/6.02 | (645) pred(n4) = all_0_9_9
% 21.92/6.02 |
% 21.92/6.02 | From (644) and (262) follows:
% 21.92/6.02 | (646) succ(n4) = all_0_5_5
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (130) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 21.92/6.02 | (647) all_0_9_9 = n3
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (165) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 21.92/6.02 | (648) all_0_5_5 = n5
% 21.92/6.02 |
% 21.92/6.02 | From (647)(648) and (147) follows:
% 21.92/6.02 | (649) sum(n3, n5) = all_0_2_2
% 21.92/6.02 |
% 21.92/6.02 | From (647) and (1575) follows:
% 21.92/6.02 | (1754) sum(n3, n14) = all_0_7_7
% 21.92/6.02 |
% 21.92/6.02 | From (648) and (1573) follows:
% 21.92/6.02 | (1755) sum(n12, n5) = all_0_4_4
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n12, n5, all_0_4_4, n1 and discharging atoms sum(n12, n5) = all_0_4_4, sum(n12, n5) = n1, yields:
% 21.92/6.02 | (688) all_0_4_4 = n1
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n3, n14, all_0_7_7, n1 and discharging atoms sum(n3, n14) = all_0_7_7, sum(n3, n14) = n1, yields:
% 21.92/6.02 | (690) all_0_7_7 = n1
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 21.92/6.02 | (509) all_0_2_2 = n8
% 21.92/6.02 |
% 21.92/6.02 | From (509) and (1577) follows:
% 21.92/6.02 | (1615) sum(n8, n10) = all_0_0_0
% 21.92/6.02 |
% 21.92/6.02 | From (690)(688) and (212) follows:
% 21.92/6.02 | (692) sum(n1, n1) = all_0_3_3
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n8, n10, all_0_0_0, n2 and discharging atoms sum(n8, n10) = all_0_0_0, sum(n8, n10) = n2, yields:
% 21.92/6.02 | (550) all_0_0_0 = n2
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 21.92/6.02 | (549) all_0_3_3 = n2
% 21.92/6.02 |
% 21.92/6.02 | Equations (550,549) can reduce 363 to:
% 21.92/6.02 | (461) $false
% 21.92/6.02 |
% 21.92/6.02 |-The branch is then unsatisfiable
% 21.92/6.02 |-Branch two:
% 21.92/6.02 | (660) ~ (all_0_11_11 = n4)
% 21.92/6.02 | (661) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.92/6.02 |
% 21.92/6.02 +-Applying beta-rule and splitting (661), into two cases.
% 21.92/6.02 |-Branch one:
% 21.92/6.02 | (662) all_0_11_11 = n3
% 21.92/6.02 |
% 21.92/6.02 | From (662) and (423) follows:
% 21.92/6.02 | (663) pred(n3) = all_0_9_9
% 21.92/6.02 |
% 21.92/6.02 | From (662) and (262) follows:
% 21.92/6.02 | (664) succ(n3) = all_0_5_5
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (130) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 21.92/6.02 | (665) all_0_9_9 = n2
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (165) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 21.92/6.02 | (666) all_0_5_5 = n4
% 21.92/6.02 |
% 21.92/6.02 | From (665)(666) and (147) follows:
% 21.92/6.02 | (667) sum(n2, n4) = all_0_2_2
% 21.92/6.02 |
% 21.92/6.02 | From (665) and (1575) follows:
% 21.92/6.02 | (1772) sum(n2, n14) = all_0_7_7
% 21.92/6.02 |
% 21.92/6.02 | From (666) and (1573) follows:
% 21.92/6.02 | (1773) sum(n12, n4) = all_0_4_4
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n12, n4, all_0_4_4, n0 and discharging atoms sum(n12, n4) = all_0_4_4, sum(n12, n4) = n0, yields:
% 21.92/6.02 | (706) all_0_4_4 = n0
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n2, n14, all_0_7_7, n0 and discharging atoms sum(n2, n14) = all_0_7_7, sum(n2, n14) = n0, yields:
% 21.92/6.02 | (708) all_0_7_7 = n0
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 21.92/6.02 | (527) all_0_2_2 = n6
% 21.92/6.02 |
% 21.92/6.02 | From (527) and (1577) follows:
% 21.92/6.02 | (1633) sum(n6, n10) = all_0_0_0
% 21.92/6.02 |
% 21.92/6.02 | From (708)(706) and (212) follows:
% 21.92/6.02 | (710) sum(n0, n0) = all_0_3_3
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n6, n10, all_0_0_0, n0 and discharging atoms sum(n6, n10) = all_0_0_0, sum(n6, n10) = n0, yields:
% 21.92/6.02 | (568) all_0_0_0 = n0
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 21.92/6.02 | (567) all_0_3_3 = n0
% 21.92/6.02 |
% 21.92/6.02 | Equations (568,567) can reduce 363 to:
% 21.92/6.02 | (461) $false
% 21.92/6.02 |
% 21.92/6.02 |-The branch is then unsatisfiable
% 21.92/6.02 |-Branch two:
% 21.92/6.02 | (678) ~ (all_0_11_11 = n3)
% 21.92/6.02 | (679) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 21.92/6.02 |
% 21.92/6.02 +-Applying beta-rule and splitting (679), into two cases.
% 21.92/6.02 |-Branch one:
% 21.92/6.02 | (680) all_0_11_11 = n2
% 21.92/6.02 |
% 21.92/6.02 | From (680) and (423) follows:
% 21.92/6.02 | (681) pred(n2) = all_0_9_9
% 21.92/6.02 |
% 21.92/6.02 | From (680) and (262) follows:
% 21.92/6.02 | (682) succ(n2) = all_0_5_5
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (130) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 21.92/6.02 | (683) all_0_9_9 = n1
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (165) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 21.92/6.02 | (684) all_0_5_5 = n3
% 21.92/6.02 |
% 21.92/6.02 | From (683)(684) and (147) follows:
% 21.92/6.02 | (685) sum(n1, n3) = all_0_2_2
% 21.92/6.02 |
% 21.92/6.02 | From (683) and (1575) follows:
% 21.92/6.02 | (1790) sum(n1, n14) = all_0_7_7
% 21.92/6.02 |
% 21.92/6.02 | From (684) and (1573) follows:
% 21.92/6.02 | (1791) sum(n12, n3) = all_0_4_4
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n12, n3, all_0_4_4, n15 and discharging atoms sum(n12, n3) = all_0_4_4, sum(n12, n3) = n15, yields:
% 21.92/6.02 | (726) all_0_4_4 = n15
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n1, n14, all_0_7_7, n15 and discharging atoms sum(n1, n14) = all_0_7_7, sum(n1, n14) = n15, yields:
% 21.92/6.02 | (725) all_0_7_7 = n15
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 21.92/6.02 | (545) all_0_2_2 = n4
% 21.92/6.02 |
% 21.92/6.02 | From (545) and (1577) follows:
% 21.92/6.02 | (1651) sum(n4, n10) = all_0_0_0
% 21.92/6.02 |
% 21.92/6.02 | From (725)(726) and (212) follows:
% 21.92/6.02 | (728) sum(n15, n15) = all_0_3_3
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n15, n15, all_0_3_3, n14 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n14, yields:
% 21.92/6.02 | (585) all_0_3_3 = n14
% 21.92/6.02 |
% 21.92/6.02 | Instantiating formula (74) with n4, n10, all_0_0_0, n14 and discharging atoms sum(n4, n10) = all_0_0_0, sum(n4, n10) = n14, yields:
% 21.92/6.02 | (586) all_0_0_0 = n14
% 21.92/6.02 |
% 21.92/6.03 | Equations (586,585) can reduce 363 to:
% 21.92/6.03 | (461) $false
% 21.92/6.03 |
% 21.92/6.03 |-The branch is then unsatisfiable
% 21.92/6.03 |-Branch two:
% 21.92/6.03 | (696) ~ (all_0_11_11 = n2)
% 21.92/6.03 | (697) all_0_11_11 = n1 | all_0_11_11 = n0
% 21.92/6.03 |
% 21.92/6.03 +-Applying beta-rule and splitting (697), into two cases.
% 21.92/6.03 |-Branch one:
% 21.92/6.03 | (698) all_0_11_11 = n1
% 21.92/6.03 |
% 21.92/6.03 | From (698) and (423) follows:
% 21.92/6.03 | (699) pred(n1) = all_0_9_9
% 21.92/6.03 |
% 21.92/6.03 | From (698) and (262) follows:
% 21.92/6.03 | (700) succ(n1) = all_0_5_5
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (130) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 21.92/6.03 | (701) all_0_9_9 = n0
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (165) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 21.92/6.03 | (702) all_0_5_5 = n2
% 21.92/6.03 |
% 21.92/6.03 | From (701)(702) and (147) follows:
% 21.92/6.03 | (703) sum(n0, n2) = all_0_2_2
% 21.92/6.03 |
% 21.92/6.03 | From (701) and (1575) follows:
% 21.92/6.03 | (1808) sum(n0, n14) = all_0_7_7
% 21.92/6.03 |
% 21.92/6.03 | From (702) and (1573) follows:
% 21.92/6.03 | (1809) sum(n12, n2) = all_0_4_4
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n12, n2, all_0_4_4, n14 and discharging atoms sum(n12, n2) = all_0_4_4, sum(n12, n2) = n14, yields:
% 21.92/6.03 | (451) all_0_4_4 = n14
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n0, n14, all_0_7_7, n14 and discharging atoms sum(n0, n14) = all_0_7_7, sum(n0, n14) = n14, yields:
% 21.92/6.03 | (452) all_0_7_7 = n14
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 21.92/6.03 | (563) all_0_2_2 = n2
% 21.92/6.03 |
% 21.92/6.03 | From (563) and (1577) follows:
% 21.92/6.03 | (1669) sum(n2, n10) = all_0_0_0
% 21.92/6.03 |
% 21.92/6.03 | From (452)(451) and (212) follows:
% 21.92/6.03 | (456) sum(n14, n14) = all_0_3_3
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n14, n14, all_0_3_3, n12 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n12, yields:
% 21.92/6.03 | (459) all_0_3_3 = n12
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n2, n10, all_0_0_0, n12 and discharging atoms sum(n2, n10) = all_0_0_0, sum(n2, n10) = n12, yields:
% 21.92/6.03 | (457) all_0_0_0 = n12
% 21.92/6.03 |
% 21.92/6.03 | Equations (457,459) can reduce 363 to:
% 21.92/6.03 | (461) $false
% 21.92/6.03 |
% 21.92/6.03 |-The branch is then unsatisfiable
% 21.92/6.03 |-Branch two:
% 21.92/6.03 | (715) ~ (all_0_11_11 = n1)
% 21.92/6.03 | (716) all_0_11_11 = n0
% 21.92/6.03 |
% 21.92/6.03 | From (716) and (423) follows:
% 21.92/6.03 | (717) pred(n0) = all_0_9_9
% 21.92/6.03 |
% 21.92/6.03 | From (716) and (262) follows:
% 21.92/6.03 | (718) succ(n0) = all_0_5_5
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (130) with n0, all_0_9_9, n15 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n15, yields:
% 21.92/6.03 | (719) all_0_9_9 = n15
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (165) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 21.92/6.03 | (720) all_0_5_5 = n1
% 21.92/6.03 |
% 21.92/6.03 | From (719)(720) and (147) follows:
% 21.92/6.03 | (721) sum(n15, n1) = all_0_2_2
% 21.92/6.03 |
% 21.92/6.03 | From (719) and (1575) follows:
% 21.92/6.03 | (1825) sum(n15, n14) = all_0_7_7
% 21.92/6.03 |
% 21.92/6.03 | From (720) and (1573) follows:
% 21.92/6.03 | (1826) sum(n12, n1) = all_0_4_4
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n15, n14, all_0_7_7, n13 and discharging atoms sum(n15, n14) = all_0_7_7, sum(n15, n14) = n13, yields:
% 21.92/6.03 | (474) all_0_7_7 = n13
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n15, n1, all_0_2_2, n0 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n0, yields:
% 21.92/6.03 | (581) all_0_2_2 = n0
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n12, n1, all_0_4_4, n13 and discharging atoms sum(n12, n1) = all_0_4_4, sum(n12, n1) = n13, yields:
% 21.92/6.03 | (472) all_0_4_4 = n13
% 21.92/6.03 |
% 21.92/6.03 | From (581) and (1577) follows:
% 21.92/6.03 | (1687) sum(n0, n10) = all_0_0_0
% 21.92/6.03 |
% 21.92/6.03 | From (474)(472) and (212) follows:
% 21.92/6.03 | (476) sum(n13, n13) = all_0_3_3
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n13, n13, all_0_3_3, n10 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n10, yields:
% 21.92/6.03 | (477) all_0_3_3 = n10
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n0, n10, all_0_0_0, n10 and discharging atoms sum(n0, n10) = all_0_0_0, sum(n0, n10) = n10, yields:
% 21.92/6.03 | (478) all_0_0_0 = n10
% 21.92/6.03 |
% 21.92/6.03 | Equations (478,477) can reduce 363 to:
% 21.92/6.03 | (461) $false
% 21.92/6.03 |
% 21.92/6.03 |-The branch is then unsatisfiable
% 21.92/6.03 |-Branch two:
% 21.92/6.03 | (779) ~ (all_0_10_10 = n13)
% 21.92/6.03 | (780) all_0_10_10 = n12 | all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/6.03 |
% 21.92/6.03 +-Applying beta-rule and splitting (481), into two cases.
% 21.92/6.03 |-Branch one:
% 21.92/6.03 | (482) all_0_11_11 = n13
% 21.92/6.03 |
% 21.92/6.03 | From (482) and (423) follows:
% 21.92/6.03 | (483) pred(n13) = all_0_9_9
% 21.92/6.03 |
% 21.92/6.03 | From (482) and (262) follows:
% 21.92/6.03 | (484) succ(n13) = all_0_5_5
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (130) with n13, all_0_9_9, n12 and discharging atoms pred(n13) = all_0_9_9, pred(n13) = n12, yields:
% 21.92/6.03 | (485) all_0_9_9 = n12
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (165) with n13, all_0_5_5, n14 and discharging atoms succ(n13) = all_0_5_5, succ(n13) = n14, yields:
% 21.92/6.03 | (486) all_0_5_5 = n14
% 21.92/6.03 |
% 21.92/6.03 | From (486) and (276) follows:
% 21.92/6.03 | (1842) sum(all_0_6_6, n14) = all_0_4_4
% 21.92/6.03 |
% 21.92/6.03 | From (485)(486) and (147) follows:
% 21.92/6.03 | (487) sum(n12, n14) = all_0_2_2
% 21.92/6.03 |
% 21.92/6.03 | From (485) and (350) follows:
% 21.92/6.03 | (1844) sum(n12, all_0_8_8) = all_0_7_7
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n12, n14, all_0_2_2, n10 and discharging atoms sum(n12, n14) = all_0_2_2, sum(n12, n14) = n10, yields:
% 21.92/6.03 | (491) all_0_2_2 = n10
% 21.92/6.03 |
% 21.92/6.03 | From (491) and (256) follows:
% 21.92/6.03 | (1846) sum(n10, all_0_1_1) = all_0_0_0
% 21.92/6.03 |
% 21.92/6.03 +-Applying beta-rule and splitting (780), into two cases.
% 21.92/6.03 |-Branch one:
% 21.92/6.03 | (781) all_0_10_10 = n12
% 21.92/6.03 |
% 21.92/6.03 | From (781) and (317) follows:
% 21.92/6.03 | (782) pred(n12) = all_0_6_6
% 21.92/6.03 |
% 21.92/6.03 | From (781) and (146) follows:
% 21.92/6.03 | (783) succ(n12) = all_0_8_8
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (130) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 21.92/6.03 | (784) all_0_6_6 = n11
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (165) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 21.92/6.03 | (785) all_0_8_8 = n13
% 21.92/6.03 |
% 21.92/6.03 | From (784)(785) and (10) follows:
% 21.92/6.03 | (786) sum(n11, n13) = all_0_1_1
% 21.92/6.03 |
% 21.92/6.03 | From (784) and (1842) follows:
% 21.92/6.03 | (1853) sum(n11, n14) = all_0_4_4
% 21.92/6.03 |
% 21.92/6.03 | From (785) and (1844) follows:
% 21.92/6.03 | (1854) sum(n12, n13) = all_0_7_7
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n12, n13, all_0_7_7, n9 and discharging atoms sum(n12, n13) = all_0_7_7, sum(n12, n13) = n9, yields:
% 21.92/6.03 | (546) all_0_7_7 = n9
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n11, n14, all_0_4_4, n9 and discharging atoms sum(n11, n14) = all_0_4_4, sum(n11, n14) = n9, yields:
% 21.92/6.03 | (544) all_0_4_4 = n9
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n11, n13, all_0_1_1, n8 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n8, yields:
% 21.92/6.03 | (790) all_0_1_1 = n8
% 21.92/6.03 |
% 21.92/6.03 | From (546)(544) and (212) follows:
% 21.92/6.03 | (548) sum(n9, n9) = all_0_3_3
% 21.92/6.03 |
% 21.92/6.03 | From (790) and (1846) follows:
% 21.92/6.03 | (1859) sum(n10, n8) = all_0_0_0
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n10, n8, all_0_0_0, n2 and discharging atoms sum(n10, n8) = all_0_0_0, sum(n10, n8) = n2, yields:
% 21.92/6.03 | (550) all_0_0_0 = n2
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n9, n9, all_0_3_3, n2 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n2, yields:
% 21.92/6.03 | (549) all_0_3_3 = n2
% 21.92/6.03 |
% 21.92/6.03 | Equations (550,549) can reduce 363 to:
% 21.92/6.03 | (461) $false
% 21.92/6.03 |
% 21.92/6.03 |-The branch is then unsatisfiable
% 21.92/6.03 |-Branch two:
% 21.92/6.03 | (797) ~ (all_0_10_10 = n12)
% 21.92/6.03 | (798) all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/6.03 |
% 21.92/6.03 +-Applying beta-rule and splitting (798), into two cases.
% 21.92/6.03 |-Branch one:
% 21.92/6.03 | (799) all_0_10_10 = n11
% 21.92/6.03 |
% 21.92/6.03 | From (799) and (317) follows:
% 21.92/6.03 | (800) pred(n11) = all_0_6_6
% 21.92/6.03 |
% 21.92/6.03 | From (799) and (146) follows:
% 21.92/6.03 | (801) succ(n11) = all_0_8_8
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (130) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 21.92/6.03 | (802) all_0_6_6 = n10
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (165) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 21.92/6.03 | (803) all_0_8_8 = n12
% 21.92/6.03 |
% 21.92/6.03 | From (802)(803) and (10) follows:
% 21.92/6.03 | (804) sum(n10, n12) = all_0_1_1
% 21.92/6.03 |
% 21.92/6.03 | From (802) and (1842) follows:
% 21.92/6.03 | (1871) sum(n10, n14) = all_0_4_4
% 21.92/6.03 |
% 21.92/6.03 | From (803) and (1844) follows:
% 21.92/6.03 | (1872) sum(n12, n12) = all_0_7_7
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n12, n12, all_0_7_7, n8 and discharging atoms sum(n12, n12) = all_0_7_7, sum(n12, n12) = n8, yields:
% 21.92/6.03 | (564) all_0_7_7 = n8
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n10, n14, all_0_4_4, n8 and discharging atoms sum(n10, n14) = all_0_4_4, sum(n10, n14) = n8, yields:
% 21.92/6.03 | (562) all_0_4_4 = n8
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n10, n12, all_0_1_1, n6 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n6, yields:
% 21.92/6.03 | (808) all_0_1_1 = n6
% 21.92/6.03 |
% 21.92/6.03 | From (564)(562) and (212) follows:
% 21.92/6.03 | (566) sum(n8, n8) = all_0_3_3
% 21.92/6.03 |
% 21.92/6.03 | From (808) and (1846) follows:
% 21.92/6.03 | (1877) sum(n10, n6) = all_0_0_0
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n10, n6, all_0_0_0, n0 and discharging atoms sum(n10, n6) = all_0_0_0, sum(n10, n6) = n0, yields:
% 21.92/6.03 | (568) all_0_0_0 = n0
% 21.92/6.03 |
% 21.92/6.03 | Instantiating formula (74) with n8, n8, all_0_3_3, n0 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n0, yields:
% 21.92/6.03 | (567) all_0_3_3 = n0
% 21.92/6.03 |
% 21.92/6.03 | Equations (568,567) can reduce 363 to:
% 21.92/6.03 | (461) $false
% 21.92/6.03 |
% 21.92/6.03 |-The branch is then unsatisfiable
% 21.92/6.03 |-Branch two:
% 21.92/6.03 | (815) ~ (all_0_10_10 = n11)
% 21.92/6.03 | (816) all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/6.03 |
% 21.92/6.03 +-Applying beta-rule and splitting (816), into two cases.
% 21.92/6.03 |-Branch one:
% 21.92/6.03 | (817) all_0_10_10 = n10
% 21.92/6.03 |
% 21.92/6.03 | From (817) and (317) follows:
% 21.92/6.04 | (818) pred(n10) = all_0_6_6
% 21.92/6.04 |
% 21.92/6.04 | From (817) and (146) follows:
% 21.92/6.04 | (819) succ(n10) = all_0_8_8
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (130) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 21.92/6.04 | (820) all_0_6_6 = n9
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (165) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 21.92/6.04 | (821) all_0_8_8 = n11
% 21.92/6.04 |
% 21.92/6.04 | From (820)(821) and (10) follows:
% 21.92/6.04 | (822) sum(n9, n11) = all_0_1_1
% 21.92/6.04 |
% 21.92/6.04 | From (820) and (1842) follows:
% 21.92/6.04 | (1889) sum(n9, n14) = all_0_4_4
% 21.92/6.04 |
% 21.92/6.04 | From (821) and (1844) follows:
% 21.92/6.04 | (1890) sum(n12, n11) = all_0_7_7
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (74) with n12, n11, all_0_7_7, n7 and discharging atoms sum(n12, n11) = all_0_7_7, sum(n12, n11) = n7, yields:
% 21.92/6.04 | (582) all_0_7_7 = n7
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (74) with n9, n14, all_0_4_4, n7 and discharging atoms sum(n9, n14) = all_0_4_4, sum(n9, n14) = n7, yields:
% 21.92/6.04 | (580) all_0_4_4 = n7
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (74) with n9, n11, all_0_1_1, n4 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n4, yields:
% 21.92/6.04 | (826) all_0_1_1 = n4
% 21.92/6.04 |
% 21.92/6.04 | From (582)(580) and (212) follows:
% 21.92/6.04 | (584) sum(n7, n7) = all_0_3_3
% 21.92/6.04 |
% 21.92/6.04 | From (826) and (1846) follows:
% 21.92/6.04 | (1895) sum(n10, n4) = all_0_0_0
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (74) with n10, n4, all_0_0_0, n14 and discharging atoms sum(n10, n4) = all_0_0_0, sum(n10, n4) = n14, yields:
% 21.92/6.04 | (586) all_0_0_0 = n14
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (74) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 21.92/6.04 | (585) all_0_3_3 = n14
% 21.92/6.04 |
% 21.92/6.04 | Equations (586,585) can reduce 363 to:
% 21.92/6.04 | (461) $false
% 21.92/6.04 |
% 21.92/6.04 |-The branch is then unsatisfiable
% 21.92/6.04 |-Branch two:
% 21.92/6.04 | (833) ~ (all_0_10_10 = n10)
% 21.92/6.04 | (834) all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/6.04 |
% 21.92/6.04 +-Applying beta-rule and splitting (834), into two cases.
% 21.92/6.04 |-Branch one:
% 21.92/6.04 | (835) all_0_10_10 = n9
% 21.92/6.04 |
% 21.92/6.04 | From (835) and (317) follows:
% 21.92/6.04 | (836) pred(n9) = all_0_6_6
% 21.92/6.04 |
% 21.92/6.04 | From (835) and (146) follows:
% 21.92/6.04 | (837) succ(n9) = all_0_8_8
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (130) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 21.92/6.04 | (838) all_0_6_6 = n8
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (165) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 21.92/6.04 | (839) all_0_8_8 = n10
% 21.92/6.04 |
% 21.92/6.04 | From (838)(839) and (10) follows:
% 21.92/6.04 | (840) sum(n8, n10) = all_0_1_1
% 21.92/6.04 |
% 21.92/6.04 | From (838) and (1842) follows:
% 21.92/6.04 | (1907) sum(n8, n14) = all_0_4_4
% 21.92/6.04 |
% 21.92/6.04 | From (839) and (1844) follows:
% 21.92/6.04 | (1908) sum(n12, n10) = all_0_7_7
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (74) with n12, n10, all_0_7_7, n6 and discharging atoms sum(n12, n10) = all_0_7_7, sum(n12, n10) = n6, yields:
% 21.92/6.04 | (600) all_0_7_7 = n6
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (74) with n8, n14, all_0_4_4, n6 and discharging atoms sum(n8, n14) = all_0_4_4, sum(n8, n14) = n6, yields:
% 21.92/6.04 | (598) all_0_4_4 = n6
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (74) with n8, n10, all_0_1_1, n2 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n2, yields:
% 21.92/6.04 | (844) all_0_1_1 = n2
% 21.92/6.04 |
% 21.92/6.04 | From (600)(598) and (212) follows:
% 21.92/6.04 | (602) sum(n6, n6) = all_0_3_3
% 21.92/6.04 |
% 21.92/6.04 | From (844) and (1846) follows:
% 21.92/6.04 | (1913) sum(n10, n2) = all_0_0_0
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (74) with n10, n2, all_0_0_0, n12 and discharging atoms sum(n10, n2) = all_0_0_0, sum(n10, n2) = n12, yields:
% 21.92/6.04 | (457) all_0_0_0 = n12
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (74) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 21.92/6.04 | (459) all_0_3_3 = n12
% 21.92/6.04 |
% 21.92/6.04 | Equations (457,459) can reduce 363 to:
% 21.92/6.04 | (461) $false
% 21.92/6.04 |
% 21.92/6.04 |-The branch is then unsatisfiable
% 21.92/6.04 |-Branch two:
% 21.92/6.04 | (851) ~ (all_0_10_10 = n9)
% 21.92/6.04 | (852) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 21.92/6.04 |
% 21.92/6.04 +-Applying beta-rule and splitting (852), into two cases.
% 21.92/6.04 |-Branch one:
% 21.92/6.04 | (853) all_0_10_10 = n8
% 21.92/6.04 |
% 21.92/6.04 | From (853) and (317) follows:
% 21.92/6.04 | (854) pred(n8) = all_0_6_6
% 21.92/6.04 |
% 21.92/6.04 | From (853) and (146) follows:
% 21.92/6.04 | (855) succ(n8) = all_0_8_8
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (130) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 21.92/6.04 | (856) all_0_6_6 = n7
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (165) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 21.92/6.04 | (857) all_0_8_8 = n9
% 21.92/6.04 |
% 21.92/6.04 | From (856)(857) and (10) follows:
% 21.92/6.04 | (858) sum(n7, n9) = all_0_1_1
% 21.92/6.04 |
% 21.92/6.04 | From (856) and (1842) follows:
% 21.92/6.04 | (1925) sum(n7, n14) = all_0_4_4
% 21.92/6.04 |
% 21.92/6.04 | From (857) and (1844) follows:
% 21.92/6.04 | (1926) sum(n12, n9) = all_0_7_7
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (74) with n12, n9, all_0_7_7, n5 and discharging atoms sum(n12, n9) = all_0_7_7, sum(n12, n9) = n5, yields:
% 21.92/6.04 | (618) all_0_7_7 = n5
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (74) with n7, n14, all_0_4_4, n5 and discharging atoms sum(n7, n14) = all_0_4_4, sum(n7, n14) = n5, yields:
% 21.92/6.04 | (616) all_0_4_4 = n5
% 21.92/6.04 |
% 21.92/6.04 | Instantiating formula (74) with n7, n9, all_0_1_1, n0 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n0, yields:
% 21.92/6.04 | (862) all_0_1_1 = n0
% 21.92/6.04 |
% 21.92/6.04 | From (618)(616) and (212) follows:
% 21.92/6.04 | (620) sum(n5, n5) = all_0_3_3
% 21.92/6.04 |
% 21.92/6.04 | From (862) and (1846) follows:
% 22.20/6.04 | (1931) sum(n10, n0) = all_0_0_0
% 22.20/6.04 |
% 22.20/6.04 | Instantiating formula (74) with n10, n0, all_0_0_0, n10 and discharging atoms sum(n10, n0) = all_0_0_0, sum(n10, n0) = n10, yields:
% 22.20/6.04 | (478) all_0_0_0 = n10
% 22.20/6.04 |
% 22.20/6.04 | Instantiating formula (74) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 22.20/6.04 | (477) all_0_3_3 = n10
% 22.20/6.04 |
% 22.20/6.04 | Equations (478,477) can reduce 363 to:
% 22.20/6.04 | (461) $false
% 22.20/6.04 |
% 22.20/6.04 |-The branch is then unsatisfiable
% 22.20/6.04 |-Branch two:
% 22.20/6.04 | (869) ~ (all_0_10_10 = n8)
% 22.20/6.04 | (870) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.20/6.04 |
% 22.20/6.04 +-Applying beta-rule and splitting (870), into two cases.
% 22.20/6.04 |-Branch one:
% 22.20/6.04 | (871) all_0_10_10 = n7
% 22.20/6.04 |
% 22.20/6.04 | From (871) and (317) follows:
% 22.20/6.04 | (872) pred(n7) = all_0_6_6
% 22.20/6.04 |
% 22.20/6.04 | From (871) and (146) follows:
% 22.20/6.04 | (873) succ(n7) = all_0_8_8
% 22.20/6.04 |
% 22.20/6.04 | Instantiating formula (130) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 22.20/6.04 | (874) all_0_6_6 = n6
% 22.20/6.04 |
% 22.20/6.04 | Instantiating formula (165) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 22.20/6.04 | (875) all_0_8_8 = n8
% 22.20/6.04 |
% 22.20/6.04 | From (874)(875) and (10) follows:
% 22.20/6.04 | (876) sum(n6, n8) = all_0_1_1
% 22.20/6.04 |
% 22.20/6.04 | From (874) and (1842) follows:
% 22.20/6.04 | (1943) sum(n6, n14) = all_0_4_4
% 22.20/6.04 |
% 22.20/6.04 | From (875) and (1844) follows:
% 22.20/6.04 | (1944) sum(n12, n8) = all_0_7_7
% 22.20/6.04 |
% 22.20/6.04 | Instantiating formula (74) with n12, n8, all_0_7_7, n4 and discharging atoms sum(n12, n8) = all_0_7_7, sum(n12, n8) = n4, yields:
% 22.20/6.04 | (636) all_0_7_7 = n4
% 22.20/6.04 |
% 22.20/6.04 | Instantiating formula (74) with n6, n14, all_0_4_4, n4 and discharging atoms sum(n6, n14) = all_0_4_4, sum(n6, n14) = n4, yields:
% 22.20/6.04 | (634) all_0_4_4 = n4
% 22.20/6.04 |
% 22.20/6.04 | Instantiating formula (74) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 22.20/6.04 | (436) all_0_1_1 = n14
% 22.20/6.04 |
% 22.20/6.04 | From (636)(634) and (212) follows:
% 22.20/6.04 | (638) sum(n4, n4) = all_0_3_3
% 22.20/6.04 |
% 22.20/6.04 | From (436) and (1846) follows:
% 22.20/6.04 | (493) sum(n10, n14) = all_0_0_0
% 22.20/6.04 |
% 22.20/6.04 | Instantiating formula (74) with n10, n14, all_0_0_0, n8 and discharging atoms sum(n10, n14) = all_0_0_0, sum(n10, n14) = n8, yields:
% 22.20/6.04 | (496) all_0_0_0 = n8
% 22.20/6.04 |
% 22.20/6.04 | Instantiating formula (74) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 22.20/6.04 | (495) all_0_3_3 = n8
% 22.20/6.04 |
% 22.20/6.04 | Equations (496,495) can reduce 363 to:
% 22.20/6.04 | (461) $false
% 22.20/6.04 |
% 22.20/6.04 |-The branch is then unsatisfiable
% 22.20/6.04 |-Branch two:
% 22.20/6.04 | (887) ~ (all_0_10_10 = n7)
% 22.20/6.04 | (888) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.20/6.04 |
% 22.20/6.04 +-Applying beta-rule and splitting (888), into two cases.
% 22.20/6.04 |-Branch one:
% 22.20/6.04 | (889) all_0_10_10 = n6
% 22.20/6.04 |
% 22.20/6.04 | From (889) and (317) follows:
% 22.20/6.04 | (890) pred(n6) = all_0_6_6
% 22.20/6.04 |
% 22.20/6.04 | From (889) and (146) follows:
% 22.20/6.04 | (891) succ(n6) = all_0_8_8
% 22.20/6.04 |
% 22.20/6.04 | Instantiating formula (130) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 22.20/6.04 | (892) all_0_6_6 = n5
% 22.20/6.04 |
% 22.20/6.04 | Instantiating formula (165) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 22.20/6.04 | (893) all_0_8_8 = n7
% 22.20/6.04 |
% 22.20/6.04 | From (892)(893) and (10) follows:
% 22.20/6.04 | (894) sum(n5, n7) = all_0_1_1
% 22.20/6.04 |
% 22.20/6.04 | From (892) and (1842) follows:
% 22.20/6.04 | (1961) sum(n5, n14) = all_0_4_4
% 22.20/6.04 |
% 22.20/6.04 | From (893) and (1844) follows:
% 22.20/6.04 | (1962) sum(n12, n7) = all_0_7_7
% 22.20/6.04 |
% 22.20/6.04 | Instantiating formula (74) with n12, n7, all_0_7_7, n3 and discharging atoms sum(n12, n7) = all_0_7_7, sum(n12, n7) = n3, yields:
% 22.20/6.04 | (654) all_0_7_7 = n3
% 22.20/6.04 |
% 22.20/6.04 | Instantiating formula (74) with n5, n14, all_0_4_4, n3 and discharging atoms sum(n5, n14) = all_0_4_4, sum(n5, n14) = n3, yields:
% 22.20/6.04 | (652) all_0_4_4 = n3
% 22.20/6.04 |
% 22.20/6.04 | Instantiating formula (74) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 22.20/6.04 | (754) all_0_1_1 = n12
% 22.20/6.04 |
% 22.20/6.04 | From (654)(652) and (212) follows:
% 22.20/6.04 | (656) sum(n3, n3) = all_0_3_3
% 22.20/6.04 |
% 22.20/6.04 | From (754) and (1846) follows:
% 22.20/6.05 | (1065) sum(n10, n12) = all_0_0_0
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n10, n12, all_0_0_0, n6 and discharging atoms sum(n10, n12) = all_0_0_0, sum(n10, n12) = n6, yields:
% 22.20/6.05 | (514) all_0_0_0 = n6
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 22.20/6.05 | (513) all_0_3_3 = n6
% 22.20/6.05 |
% 22.20/6.05 | Equations (514,513) can reduce 363 to:
% 22.20/6.05 | (461) $false
% 22.20/6.05 |
% 22.20/6.05 |-The branch is then unsatisfiable
% 22.20/6.05 |-Branch two:
% 22.20/6.05 | (905) ~ (all_0_10_10 = n6)
% 22.20/6.05 | (906) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.20/6.05 |
% 22.20/6.05 +-Applying beta-rule and splitting (906), into two cases.
% 22.20/6.05 |-Branch one:
% 22.20/6.05 | (907) all_0_10_10 = n5
% 22.20/6.05 |
% 22.20/6.05 | From (907) and (317) follows:
% 22.20/6.05 | (908) pred(n5) = all_0_6_6
% 22.20/6.05 |
% 22.20/6.05 | From (907) and (146) follows:
% 22.20/6.05 | (909) succ(n5) = all_0_8_8
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (130) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 22.20/6.05 | (910) all_0_6_6 = n4
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (165) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 22.20/6.05 | (911) all_0_8_8 = n6
% 22.20/6.05 |
% 22.20/6.05 | From (910)(911) and (10) follows:
% 22.20/6.05 | (912) sum(n4, n6) = all_0_1_1
% 22.20/6.05 |
% 22.20/6.05 | From (910) and (1842) follows:
% 22.20/6.05 | (1979) sum(n4, n14) = all_0_4_4
% 22.20/6.05 |
% 22.20/6.05 | From (911) and (1844) follows:
% 22.20/6.05 | (1980) sum(n12, n6) = all_0_7_7
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n12, n6, all_0_7_7, n2 and discharging atoms sum(n12, n6) = all_0_7_7, sum(n12, n6) = n2, yields:
% 22.20/6.05 | (672) all_0_7_7 = n2
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n4, n14, all_0_4_4, n2 and discharging atoms sum(n4, n14) = all_0_4_4, sum(n4, n14) = n2, yields:
% 22.20/6.05 | (670) all_0_4_4 = n2
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 22.20/6.05 | (772) all_0_1_1 = n10
% 22.20/6.05 |
% 22.20/6.05 | From (672)(670) and (212) follows:
% 22.20/6.05 | (674) sum(n2, n2) = all_0_3_3
% 22.20/6.05 |
% 22.20/6.05 | From (772) and (1846) follows:
% 22.20/6.05 | (1595) sum(n10, n10) = all_0_0_0
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n10, n10, all_0_0_0, n4 and discharging atoms sum(n10, n10) = all_0_0_0, sum(n10, n10) = n4, yields:
% 22.20/6.05 | (532) all_0_0_0 = n4
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 22.20/6.05 | (531) all_0_3_3 = n4
% 22.20/6.05 |
% 22.20/6.05 | Equations (532,531) can reduce 363 to:
% 22.20/6.05 | (461) $false
% 22.20/6.05 |
% 22.20/6.05 |-The branch is then unsatisfiable
% 22.20/6.05 |-Branch two:
% 22.20/6.05 | (923) ~ (all_0_10_10 = n5)
% 22.20/6.05 | (924) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.20/6.05 |
% 22.20/6.05 +-Applying beta-rule and splitting (924), into two cases.
% 22.20/6.05 |-Branch one:
% 22.20/6.05 | (925) all_0_10_10 = n4
% 22.20/6.05 |
% 22.20/6.05 | From (925) and (317) follows:
% 22.20/6.05 | (926) pred(n4) = all_0_6_6
% 22.20/6.05 |
% 22.20/6.05 | From (925) and (146) follows:
% 22.20/6.05 | (927) succ(n4) = all_0_8_8
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (130) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 22.20/6.05 | (928) all_0_6_6 = n3
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (165) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 22.20/6.05 | (929) all_0_8_8 = n5
% 22.20/6.05 |
% 22.20/6.05 | From (928)(929) and (10) follows:
% 22.20/6.05 | (930) sum(n3, n5) = all_0_1_1
% 22.20/6.05 |
% 22.20/6.05 | From (928) and (1842) follows:
% 22.20/6.05 | (1997) sum(n3, n14) = all_0_4_4
% 22.20/6.05 |
% 22.20/6.05 | From (929) and (1844) follows:
% 22.20/6.05 | (1998) sum(n12, n5) = all_0_7_7
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n12, n5, all_0_7_7, n1 and discharging atoms sum(n12, n5) = all_0_7_7, sum(n12, n5) = n1, yields:
% 22.20/6.05 | (690) all_0_7_7 = n1
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n3, n14, all_0_4_4, n1 and discharging atoms sum(n3, n14) = all_0_4_4, sum(n3, n14) = n1, yields:
% 22.20/6.05 | (688) all_0_4_4 = n1
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 22.20/6.05 | (790) all_0_1_1 = n8
% 22.20/6.05 |
% 22.20/6.05 | From (690)(688) and (212) follows:
% 22.20/6.05 | (692) sum(n1, n1) = all_0_3_3
% 22.20/6.05 |
% 22.20/6.05 | From (790) and (1846) follows:
% 22.20/6.05 | (1859) sum(n10, n8) = all_0_0_0
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n10, n8, all_0_0_0, n2 and discharging atoms sum(n10, n8) = all_0_0_0, sum(n10, n8) = n2, yields:
% 22.20/6.05 | (550) all_0_0_0 = n2
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 22.20/6.05 | (549) all_0_3_3 = n2
% 22.20/6.05 |
% 22.20/6.05 | Equations (550,549) can reduce 363 to:
% 22.20/6.05 | (461) $false
% 22.20/6.05 |
% 22.20/6.05 |-The branch is then unsatisfiable
% 22.20/6.05 |-Branch two:
% 22.20/6.05 | (941) ~ (all_0_10_10 = n4)
% 22.20/6.05 | (942) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.20/6.05 |
% 22.20/6.05 +-Applying beta-rule and splitting (942), into two cases.
% 22.20/6.05 |-Branch one:
% 22.20/6.05 | (943) all_0_10_10 = n3
% 22.20/6.05 |
% 22.20/6.05 | From (943) and (317) follows:
% 22.20/6.05 | (944) pred(n3) = all_0_6_6
% 22.20/6.05 |
% 22.20/6.05 | From (943) and (146) follows:
% 22.20/6.05 | (945) succ(n3) = all_0_8_8
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (130) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 22.20/6.05 | (946) all_0_6_6 = n2
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (165) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 22.20/6.05 | (947) all_0_8_8 = n4
% 22.20/6.05 |
% 22.20/6.05 | From (946)(947) and (10) follows:
% 22.20/6.05 | (948) sum(n2, n4) = all_0_1_1
% 22.20/6.05 |
% 22.20/6.05 | From (946) and (1842) follows:
% 22.20/6.05 | (2015) sum(n2, n14) = all_0_4_4
% 22.20/6.05 |
% 22.20/6.05 | From (947) and (1844) follows:
% 22.20/6.05 | (2016) sum(n12, n4) = all_0_7_7
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n12, n4, all_0_7_7, n0 and discharging atoms sum(n12, n4) = all_0_7_7, sum(n12, n4) = n0, yields:
% 22.20/6.05 | (708) all_0_7_7 = n0
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n2, n14, all_0_4_4, n0 and discharging atoms sum(n2, n14) = all_0_4_4, sum(n2, n14) = n0, yields:
% 22.20/6.05 | (706) all_0_4_4 = n0
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 22.20/6.05 | (808) all_0_1_1 = n6
% 22.20/6.05 |
% 22.20/6.05 | From (708)(706) and (212) follows:
% 22.20/6.05 | (710) sum(n0, n0) = all_0_3_3
% 22.20/6.05 |
% 22.20/6.05 | From (808) and (1846) follows:
% 22.20/6.05 | (1877) sum(n10, n6) = all_0_0_0
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n10, n6, all_0_0_0, n0 and discharging atoms sum(n10, n6) = all_0_0_0, sum(n10, n6) = n0, yields:
% 22.20/6.05 | (568) all_0_0_0 = n0
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 22.20/6.05 | (567) all_0_3_3 = n0
% 22.20/6.05 |
% 22.20/6.05 | Equations (568,567) can reduce 363 to:
% 22.20/6.05 | (461) $false
% 22.20/6.05 |
% 22.20/6.05 |-The branch is then unsatisfiable
% 22.20/6.05 |-Branch two:
% 22.20/6.05 | (959) ~ (all_0_10_10 = n3)
% 22.20/6.05 | (960) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.20/6.05 |
% 22.20/6.05 +-Applying beta-rule and splitting (960), into two cases.
% 22.20/6.05 |-Branch one:
% 22.20/6.05 | (961) all_0_10_10 = n2
% 22.20/6.05 |
% 22.20/6.05 | From (961) and (317) follows:
% 22.20/6.05 | (962) pred(n2) = all_0_6_6
% 22.20/6.05 |
% 22.20/6.05 | From (961) and (146) follows:
% 22.20/6.05 | (963) succ(n2) = all_0_8_8
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (130) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 22.20/6.05 | (964) all_0_6_6 = n1
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (165) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 22.20/6.05 | (965) all_0_8_8 = n3
% 22.20/6.05 |
% 22.20/6.05 | From (964)(965) and (10) follows:
% 22.20/6.05 | (966) sum(n1, n3) = all_0_1_1
% 22.20/6.05 |
% 22.20/6.05 | From (964) and (1842) follows:
% 22.20/6.05 | (2033) sum(n1, n14) = all_0_4_4
% 22.20/6.05 |
% 22.20/6.05 | From (965) and (1844) follows:
% 22.20/6.05 | (2034) sum(n12, n3) = all_0_7_7
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n12, n3, all_0_7_7, n15 and discharging atoms sum(n12, n3) = all_0_7_7, sum(n12, n3) = n15, yields:
% 22.20/6.05 | (725) all_0_7_7 = n15
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n1, n14, all_0_4_4, n15 and discharging atoms sum(n1, n14) = all_0_4_4, sum(n1, n14) = n15, yields:
% 22.20/6.05 | (726) all_0_4_4 = n15
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 22.20/6.05 | (826) all_0_1_1 = n4
% 22.20/6.05 |
% 22.20/6.05 | From (725)(726) and (212) follows:
% 22.20/6.05 | (728) sum(n15, n15) = all_0_3_3
% 22.20/6.05 |
% 22.20/6.05 | From (826) and (1846) follows:
% 22.20/6.05 | (1895) sum(n10, n4) = all_0_0_0
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n15, n15, all_0_3_3, n14 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n14, yields:
% 22.20/6.05 | (585) all_0_3_3 = n14
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (74) with n10, n4, all_0_0_0, n14 and discharging atoms sum(n10, n4) = all_0_0_0, sum(n10, n4) = n14, yields:
% 22.20/6.05 | (586) all_0_0_0 = n14
% 22.20/6.05 |
% 22.20/6.05 | Equations (586,585) can reduce 363 to:
% 22.20/6.05 | (461) $false
% 22.20/6.05 |
% 22.20/6.05 |-The branch is then unsatisfiable
% 22.20/6.05 |-Branch two:
% 22.20/6.05 | (977) ~ (all_0_10_10 = n2)
% 22.20/6.05 | (978) all_0_10_10 = n1 | all_0_10_10 = n0
% 22.20/6.05 |
% 22.20/6.05 +-Applying beta-rule and splitting (978), into two cases.
% 22.20/6.05 |-Branch one:
% 22.20/6.05 | (979) all_0_10_10 = n1
% 22.20/6.05 |
% 22.20/6.05 | From (979) and (317) follows:
% 22.20/6.05 | (980) pred(n1) = all_0_6_6
% 22.20/6.05 |
% 22.20/6.05 | From (979) and (146) follows:
% 22.20/6.05 | (981) succ(n1) = all_0_8_8
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (130) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 22.20/6.05 | (982) all_0_6_6 = n0
% 22.20/6.05 |
% 22.20/6.05 | Instantiating formula (165) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 22.20/6.05 | (983) all_0_8_8 = n2
% 22.20/6.05 |
% 22.20/6.05 | From (982)(983) and (10) follows:
% 22.20/6.05 | (984) sum(n0, n2) = all_0_1_1
% 22.20/6.05 |
% 22.20/6.05 | From (982) and (1842) follows:
% 22.20/6.06 | (2051) sum(n0, n14) = all_0_4_4
% 22.20/6.06 |
% 22.20/6.06 | From (983) and (1844) follows:
% 22.20/6.06 | (2052) sum(n12, n2) = all_0_7_7
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n12, n2, all_0_7_7, n14 and discharging atoms sum(n12, n2) = all_0_7_7, sum(n12, n2) = n14, yields:
% 22.20/6.06 | (452) all_0_7_7 = n14
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n0, n14, all_0_4_4, n14 and discharging atoms sum(n0, n14) = all_0_4_4, sum(n0, n14) = n14, yields:
% 22.20/6.06 | (451) all_0_4_4 = n14
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 22.20/6.06 | (844) all_0_1_1 = n2
% 22.20/6.06 |
% 22.20/6.06 | From (452)(451) and (212) follows:
% 22.20/6.06 | (456) sum(n14, n14) = all_0_3_3
% 22.20/6.06 |
% 22.20/6.06 | From (844) and (1846) follows:
% 22.20/6.06 | (1913) sum(n10, n2) = all_0_0_0
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n14, n14, all_0_3_3, n12 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n12, yields:
% 22.20/6.06 | (459) all_0_3_3 = n12
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n10, n2, all_0_0_0, n12 and discharging atoms sum(n10, n2) = all_0_0_0, sum(n10, n2) = n12, yields:
% 22.20/6.06 | (457) all_0_0_0 = n12
% 22.20/6.06 |
% 22.20/6.06 | Equations (457,459) can reduce 363 to:
% 22.20/6.06 | (461) $false
% 22.20/6.06 |
% 22.20/6.06 |-The branch is then unsatisfiable
% 22.20/6.06 |-Branch two:
% 22.20/6.06 | (997) ~ (all_0_10_10 = n1)
% 22.20/6.06 | (998) all_0_10_10 = n0
% 22.20/6.06 |
% 22.20/6.06 | From (998) and (317) follows:
% 22.20/6.06 | (999) pred(n0) = all_0_6_6
% 22.20/6.06 |
% 22.20/6.06 | From (998) and (146) follows:
% 22.20/6.06 | (1000) succ(n0) = all_0_8_8
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (130) with n0, all_0_6_6, n15 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n15, yields:
% 22.20/6.06 | (1001) all_0_6_6 = n15
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (165) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 22.20/6.06 | (1002) all_0_8_8 = n1
% 22.20/6.06 |
% 22.20/6.06 | From (1001)(1002) and (10) follows:
% 22.20/6.06 | (1003) sum(n15, n1) = all_0_1_1
% 22.20/6.06 |
% 22.20/6.06 | From (1001) and (1842) follows:
% 22.20/6.06 | (2068) sum(n15, n14) = all_0_4_4
% 22.20/6.06 |
% 22.20/6.06 | From (1002) and (1844) follows:
% 22.20/6.06 | (2069) sum(n12, n1) = all_0_7_7
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n15, n14, all_0_4_4, n13 and discharging atoms sum(n15, n14) = all_0_4_4, sum(n15, n14) = n13, yields:
% 22.20/6.06 | (472) all_0_4_4 = n13
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n15, n1, all_0_1_1, n0 and discharging atoms sum(n15, n1) = all_0_1_1, sum(n15, n1) = n0, yields:
% 22.20/6.06 | (862) all_0_1_1 = n0
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n12, n1, all_0_7_7, n13 and discharging atoms sum(n12, n1) = all_0_7_7, sum(n12, n1) = n13, yields:
% 22.20/6.06 | (474) all_0_7_7 = n13
% 22.20/6.06 |
% 22.20/6.06 | From (474)(472) and (212) follows:
% 22.20/6.06 | (476) sum(n13, n13) = all_0_3_3
% 22.20/6.06 |
% 22.20/6.06 | From (862) and (1846) follows:
% 22.20/6.06 | (1931) sum(n10, n0) = all_0_0_0
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n13, n13, all_0_3_3, n10 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n10, yields:
% 22.20/6.06 | (477) all_0_3_3 = n10
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n10, n0, all_0_0_0, n10 and discharging atoms sum(n10, n0) = all_0_0_0, sum(n10, n0) = n10, yields:
% 22.20/6.06 | (478) all_0_0_0 = n10
% 22.20/6.06 |
% 22.20/6.06 | Equations (478,477) can reduce 363 to:
% 22.20/6.06 | (461) $false
% 22.20/6.06 |
% 22.20/6.06 |-The branch is then unsatisfiable
% 22.20/6.06 |-Branch two:
% 22.20/6.06 | (498) ~ (all_0_11_11 = n13)
% 22.20/6.06 | (499) all_0_11_11 = n12 | all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.20/6.06 |
% 22.20/6.06 +-Applying beta-rule and splitting (780), into two cases.
% 22.20/6.06 |-Branch one:
% 22.20/6.06 | (781) all_0_10_10 = n12
% 22.20/6.06 |
% 22.20/6.06 | From (781) and (317) follows:
% 22.20/6.06 | (782) pred(n12) = all_0_6_6
% 22.20/6.06 |
% 22.20/6.06 | From (781) and (146) follows:
% 22.20/6.06 | (783) succ(n12) = all_0_8_8
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (130) with n12, all_0_6_6, n11 and discharging atoms pred(n12) = all_0_6_6, pred(n12) = n11, yields:
% 22.20/6.06 | (784) all_0_6_6 = n11
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (165) with n12, all_0_8_8, n13 and discharging atoms succ(n12) = all_0_8_8, succ(n12) = n13, yields:
% 22.20/6.06 | (785) all_0_8_8 = n13
% 22.20/6.06 |
% 22.20/6.06 | From (784) and (782) follows:
% 22.20/6.06 | (266) pred(n12) = n11
% 22.20/6.06 |
% 22.20/6.06 | From (785) and (783) follows:
% 22.20/6.06 | (264) succ(n12) = n13
% 22.20/6.06 |
% 22.20/6.06 | From (784) and (276) follows:
% 22.20/6.06 | (2087) sum(n11, all_0_5_5) = all_0_4_4
% 22.20/6.06 |
% 22.20/6.06 | From (784)(785) and (10) follows:
% 22.20/6.06 | (786) sum(n11, n13) = all_0_1_1
% 22.20/6.06 |
% 22.20/6.06 | From (785) and (350) follows:
% 22.20/6.06 | (2089) sum(all_0_9_9, n13) = all_0_7_7
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n11, n13, all_0_1_1, n8 and discharging atoms sum(n11, n13) = all_0_1_1, sum(n11, n13) = n8, yields:
% 22.20/6.06 | (790) all_0_1_1 = n8
% 22.20/6.06 |
% 22.20/6.06 | From (790) and (256) follows:
% 22.20/6.06 | (2091) sum(all_0_2_2, n8) = all_0_0_0
% 22.20/6.06 |
% 22.20/6.06 | From (790) and (786) follows:
% 22.20/6.06 | (2) sum(n11, n13) = n8
% 22.20/6.06 |
% 22.20/6.06 +-Applying beta-rule and splitting (499), into two cases.
% 22.20/6.06 |-Branch one:
% 22.20/6.06 | (500) all_0_11_11 = n12
% 22.20/6.06 |
% 22.20/6.06 | From (500) and (423) follows:
% 22.20/6.06 | (501) pred(n12) = all_0_9_9
% 22.20/6.06 |
% 22.20/6.06 | From (500) and (262) follows:
% 22.20/6.06 | (502) succ(n12) = all_0_5_5
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (130) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 22.20/6.06 | (503) all_0_9_9 = n11
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (165) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 22.20/6.06 | (504) all_0_5_5 = n13
% 22.20/6.06 |
% 22.20/6.06 | From (503)(504) and (147) follows:
% 22.20/6.06 | (505) sum(n11, n13) = all_0_2_2
% 22.20/6.06 |
% 22.20/6.06 | From (503) and (2089) follows:
% 22.20/6.06 | (2099) sum(n11, n13) = all_0_7_7
% 22.20/6.06 |
% 22.20/6.06 | From (504) and (2087) follows:
% 22.20/6.06 | (2100) sum(n11, n13) = all_0_4_4
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n11, n13, all_0_2_2, n8 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n8, yields:
% 22.20/6.06 | (509) all_0_2_2 = n8
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n11, n13, all_0_4_4, all_0_2_2 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = all_0_4_4, yields:
% 22.20/6.06 | (448) all_0_2_2 = all_0_4_4
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n11, n13, all_0_7_7, all_0_2_2 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = all_0_7_7, yields:
% 22.20/6.06 | (449) all_0_2_2 = all_0_7_7
% 22.20/6.06 |
% 22.20/6.06 | Combining equations (449,448) yields a new equation:
% 22.20/6.06 | (450) all_0_4_4 = all_0_7_7
% 22.20/6.06 |
% 22.20/6.06 | Combining equations (509,448) yields a new equation:
% 22.20/6.06 | (562) all_0_4_4 = n8
% 22.20/6.06 |
% 22.20/6.06 | Combining equations (562,450) yields a new equation:
% 22.20/6.06 | (564) all_0_7_7 = n8
% 22.20/6.06 |
% 22.20/6.06 | Combining equations (564,450) yields a new equation:
% 22.20/6.06 | (562) all_0_4_4 = n8
% 22.20/6.06 |
% 22.20/6.06 | Combining equations (562,448) yields a new equation:
% 22.20/6.06 | (509) all_0_2_2 = n8
% 22.20/6.06 |
% 22.20/6.06 | From (509) and (2091) follows:
% 22.20/6.06 | (2109) sum(n8, n8) = all_0_0_0
% 22.20/6.06 |
% 22.20/6.06 | From (564)(562) and (212) follows:
% 22.20/6.06 | (566) sum(n8, n8) = all_0_3_3
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n8, n8, all_0_0_0, n0 and discharging atoms sum(n8, n8) = all_0_0_0, sum(n8, n8) = n0, yields:
% 22.20/6.06 | (568) all_0_0_0 = n0
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n8, n8, all_0_3_3, all_0_0_0 and discharging atoms sum(n8, n8) = all_0_0_0, sum(n8, n8) = all_0_3_3, yields:
% 22.20/6.06 | (458) all_0_0_0 = all_0_3_3
% 22.20/6.06 |
% 22.20/6.06 | Combining equations (568,458) yields a new equation:
% 22.20/6.06 | (567) all_0_3_3 = n0
% 22.20/6.06 |
% 22.20/6.06 | Combining equations (567,458) yields a new equation:
% 22.20/6.06 | (568) all_0_0_0 = n0
% 22.20/6.06 |
% 22.20/6.06 | Equations (568,567) can reduce 363 to:
% 22.20/6.06 | (461) $false
% 22.20/6.06 |
% 22.20/6.06 |-The branch is then unsatisfiable
% 22.20/6.06 |-Branch two:
% 22.20/6.06 | (516) ~ (all_0_11_11 = n12)
% 22.20/6.06 | (517) all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.20/6.06 |
% 22.20/6.06 +-Applying beta-rule and splitting (517), into two cases.
% 22.20/6.06 |-Branch one:
% 22.20/6.06 | (518) all_0_11_11 = n11
% 22.20/6.06 |
% 22.20/6.06 | From (518) and (423) follows:
% 22.20/6.06 | (519) pred(n11) = all_0_9_9
% 22.20/6.06 |
% 22.20/6.06 | From (518) and (262) follows:
% 22.20/6.06 | (520) succ(n11) = all_0_5_5
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (130) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 22.20/6.06 | (521) all_0_9_9 = n10
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (165) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 22.20/6.06 | (522) all_0_5_5 = n12
% 22.20/6.06 |
% 22.20/6.06 | From (521)(522) and (147) follows:
% 22.20/6.06 | (523) sum(n10, n12) = all_0_2_2
% 22.20/6.06 |
% 22.20/6.06 | From (521) and (2089) follows:
% 22.20/6.06 | (2124) sum(n10, n13) = all_0_7_7
% 22.20/6.06 |
% 22.20/6.06 | From (522) and (2087) follows:
% 22.20/6.06 | (2125) sum(n11, n12) = all_0_4_4
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n11, n12, all_0_4_4, n7 and discharging atoms sum(n11, n12) = all_0_4_4, sum(n11, n12) = n7, yields:
% 22.20/6.06 | (580) all_0_4_4 = n7
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n10, n13, all_0_7_7, n7 and discharging atoms sum(n10, n13) = all_0_7_7, sum(n10, n13) = n7, yields:
% 22.20/6.06 | (582) all_0_7_7 = n7
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n10, n12, all_0_2_2, n6 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n6, yields:
% 22.20/6.06 | (527) all_0_2_2 = n6
% 22.20/6.06 |
% 22.20/6.06 | From (527) and (2091) follows:
% 22.20/6.06 | (2129) sum(n6, n8) = all_0_0_0
% 22.20/6.06 |
% 22.20/6.06 | From (582)(580) and (212) follows:
% 22.20/6.06 | (584) sum(n7, n7) = all_0_3_3
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 22.20/6.06 | (585) all_0_3_3 = n14
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (74) with n6, n8, all_0_0_0, n14 and discharging atoms sum(n6, n8) = all_0_0_0, sum(n6, n8) = n14, yields:
% 22.20/6.06 | (586) all_0_0_0 = n14
% 22.20/6.06 |
% 22.20/6.06 | Equations (586,585) can reduce 363 to:
% 22.20/6.06 | (461) $false
% 22.20/6.06 |
% 22.20/6.06 |-The branch is then unsatisfiable
% 22.20/6.06 |-Branch two:
% 22.20/6.06 | (534) ~ (all_0_11_11 = n11)
% 22.20/6.06 | (535) all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.20/6.06 |
% 22.20/6.06 +-Applying beta-rule and splitting (535), into two cases.
% 22.20/6.06 |-Branch one:
% 22.20/6.06 | (536) all_0_11_11 = n10
% 22.20/6.06 |
% 22.20/6.06 | From (536) and (423) follows:
% 22.20/6.06 | (537) pred(n10) = all_0_9_9
% 22.20/6.06 |
% 22.20/6.06 | From (536) and (262) follows:
% 22.20/6.06 | (538) succ(n10) = all_0_5_5
% 22.20/6.06 |
% 22.20/6.06 | Instantiating formula (130) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 22.20/6.07 | (539) all_0_9_9 = n9
% 22.20/6.07 |
% 22.20/6.07 | Instantiating formula (165) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 22.20/6.07 | (540) all_0_5_5 = n11
% 22.20/6.07 |
% 22.20/6.07 | From (539)(540) and (147) follows:
% 22.20/6.07 | (541) sum(n9, n11) = all_0_2_2
% 22.20/6.07 |
% 22.20/6.07 | From (539) and (2089) follows:
% 22.20/6.07 | (2142) sum(n9, n13) = all_0_7_7
% 22.20/6.07 |
% 22.20/6.07 | From (540) and (2087) follows:
% 22.20/6.07 | (2143) sum(n11, n11) = all_0_4_4
% 22.20/6.07 |
% 22.20/6.07 | Instantiating formula (74) with n11, n11, all_0_4_4, n6 and discharging atoms sum(n11, n11) = all_0_4_4, sum(n11, n11) = n6, yields:
% 22.20/6.07 | (598) all_0_4_4 = n6
% 22.20/6.07 |
% 22.20/6.07 | Instantiating formula (74) with n9, n13, all_0_7_7, n6 and discharging atoms sum(n9, n13) = all_0_7_7, sum(n9, n13) = n6, yields:
% 22.20/6.07 | (600) all_0_7_7 = n6
% 22.20/6.07 |
% 22.20/6.07 | Instantiating formula (74) with n9, n11, all_0_2_2, n4 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n4, yields:
% 22.20/6.07 | (545) all_0_2_2 = n4
% 22.20/6.07 |
% 22.20/6.07 | From (545) and (2091) follows:
% 22.20/6.07 | (2147) sum(n4, n8) = all_0_0_0
% 22.20/6.07 |
% 22.20/6.07 | From (600)(598) and (212) follows:
% 22.20/6.07 | (602) sum(n6, n6) = all_0_3_3
% 22.20/6.07 |
% 22.20/6.07 | Instantiating formula (74) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 22.20/6.07 | (459) all_0_3_3 = n12
% 22.20/6.07 |
% 22.20/6.07 | Instantiating formula (74) with n4, n8, all_0_0_0, n12 and discharging atoms sum(n4, n8) = all_0_0_0, sum(n4, n8) = n12, yields:
% 22.20/6.07 | (457) all_0_0_0 = n12
% 22.20/6.07 |
% 22.20/6.07 | Equations (457,459) can reduce 363 to:
% 22.20/6.07 | (461) $false
% 22.20/6.07 |
% 22.20/6.07 |-The branch is then unsatisfiable
% 22.20/6.07 |-Branch two:
% 22.20/6.07 | (552) ~ (all_0_11_11 = n10)
% 22.20/6.07 | (553) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.20/6.07 |
% 22.20/6.07 +-Applying beta-rule and splitting (553), into two cases.
% 22.20/6.07 |-Branch one:
% 22.20/6.07 | (554) all_0_11_11 = n9
% 22.20/6.07 |
% 22.20/6.07 | From (554) and (423) follows:
% 22.20/6.07 | (555) pred(n9) = all_0_9_9
% 22.20/6.07 |
% 22.20/6.07 | From (554) and (262) follows:
% 22.20/6.07 | (556) succ(n9) = all_0_5_5
% 22.20/6.07 |
% 22.20/6.07 | Instantiating formula (130) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 22.20/6.07 | (557) all_0_9_9 = n8
% 22.20/6.07 |
% 22.20/6.07 | Instantiating formula (165) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 22.20/6.07 | (558) all_0_5_5 = n10
% 22.20/6.07 |
% 22.20/6.07 | From (557)(558) and (147) follows:
% 22.20/6.07 | (559) sum(n8, n10) = all_0_2_2
% 22.20/6.07 |
% 22.20/6.07 | From (557) and (2089) follows:
% 22.20/6.07 | (2160) sum(n8, n13) = all_0_7_7
% 22.20/6.07 |
% 22.20/6.07 | From (558) and (2087) follows:
% 22.20/6.07 | (2161) sum(n11, n10) = all_0_4_4
% 22.20/6.07 |
% 22.20/6.07 | Instantiating formula (74) with n11, n10, all_0_4_4, n5 and discharging atoms sum(n11, n10) = all_0_4_4, sum(n11, n10) = n5, yields:
% 22.20/6.07 | (616) all_0_4_4 = n5
% 22.20/6.07 |
% 22.20/6.07 | Instantiating formula (74) with n8, n13, all_0_7_7, n5 and discharging atoms sum(n8, n13) = all_0_7_7, sum(n8, n13) = n5, yields:
% 22.20/6.07 | (618) all_0_7_7 = n5
% 22.20/6.07 |
% 22.20/6.07 | Instantiating formula (74) with n8, n10, all_0_2_2, n2 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n2, yields:
% 22.20/6.07 | (563) all_0_2_2 = n2
% 22.20/6.07 |
% 22.20/6.07 | From (563) and (2091) follows:
% 22.20/6.07 | (2165) sum(n2, n8) = all_0_0_0
% 22.20/6.07 |
% 22.20/6.07 | From (618)(616) and (212) follows:
% 22.20/6.07 | (620) sum(n5, n5) = all_0_3_3
% 22.20/6.07 |
% 22.20/6.07 | Instantiating formula (74) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 22.20/6.07 | (477) all_0_3_3 = n10
% 22.20/6.07 |
% 22.20/6.07 | Instantiating formula (74) with n2, n8, all_0_0_0, n10 and discharging atoms sum(n2, n8) = all_0_0_0, sum(n2, n8) = n10, yields:
% 22.20/6.07 | (478) all_0_0_0 = n10
% 22.20/6.07 |
% 22.20/6.07 | Equations (478,477) can reduce 363 to:
% 22.20/6.07 | (461) $false
% 22.20/6.07 |
% 22.20/6.07 |-The branch is then unsatisfiable
% 22.20/6.07 |-Branch two:
% 22.20/6.07 | (570) ~ (all_0_11_11 = n9)
% 22.20/6.07 | (571) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.20/6.07 |
% 22.20/6.07 +-Applying beta-rule and splitting (571), into two cases.
% 22.20/6.07 |-Branch one:
% 22.20/6.07 | (572) all_0_11_11 = n8
% 22.20/6.07 |
% 22.20/6.07 | From (572) and (423) follows:
% 22.20/6.07 | (573) pred(n8) = all_0_9_9
% 22.20/6.07 |
% 22.20/6.07 | From (572) and (262) follows:
% 22.20/6.07 | (574) succ(n8) = all_0_5_5
% 22.20/6.07 |
% 22.20/6.07 | Instantiating formula (130) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 22.20/6.07 | (575) all_0_9_9 = n7
% 22.20/6.07 |
% 22.20/6.07 | Instantiating formula (165) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 22.20/6.07 | (576) all_0_5_5 = n9
% 22.20/6.07 |
% 22.20/6.07 | From (575)(576) and (147) follows:
% 22.20/6.07 | (577) sum(n7, n9) = all_0_2_2
% 22.20/6.07 |
% 22.20/6.07 | From (575) and (2089) follows:
% 22.20/6.07 | (2178) sum(n7, n13) = all_0_7_7
% 22.20/6.07 |
% 22.32/6.07 | From (576) and (2087) follows:
% 22.32/6.07 | (2179) sum(n11, n9) = all_0_4_4
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (74) with n11, n9, all_0_4_4, n4 and discharging atoms sum(n11, n9) = all_0_4_4, sum(n11, n9) = n4, yields:
% 22.32/6.07 | (634) all_0_4_4 = n4
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (74) with n7, n13, all_0_7_7, n4 and discharging atoms sum(n7, n13) = all_0_7_7, sum(n7, n13) = n4, yields:
% 22.32/6.07 | (636) all_0_7_7 = n4
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (74) with n7, n9, all_0_2_2, n0 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n0, yields:
% 22.32/6.07 | (581) all_0_2_2 = n0
% 22.32/6.07 |
% 22.32/6.07 | From (581) and (2091) follows:
% 22.32/6.07 | (2183) sum(n0, n8) = all_0_0_0
% 22.32/6.07 |
% 22.32/6.07 | From (636)(634) and (212) follows:
% 22.32/6.07 | (638) sum(n4, n4) = all_0_3_3
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (74) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 22.32/6.07 | (495) all_0_3_3 = n8
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (74) with n0, n8, all_0_0_0, n8 and discharging atoms sum(n0, n8) = all_0_0_0, sum(n0, n8) = n8, yields:
% 22.32/6.07 | (496) all_0_0_0 = n8
% 22.32/6.07 |
% 22.32/6.07 | Equations (496,495) can reduce 363 to:
% 22.32/6.07 | (461) $false
% 22.32/6.07 |
% 22.32/6.07 |-The branch is then unsatisfiable
% 22.32/6.07 |-Branch two:
% 22.32/6.07 | (588) ~ (all_0_11_11 = n8)
% 22.32/6.07 | (589) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.07 |
% 22.32/6.07 +-Applying beta-rule and splitting (589), into two cases.
% 22.32/6.07 |-Branch one:
% 22.32/6.07 | (590) all_0_11_11 = n7
% 22.32/6.07 |
% 22.32/6.07 | From (590) and (423) follows:
% 22.32/6.07 | (591) pred(n7) = all_0_9_9
% 22.32/6.07 |
% 22.32/6.07 | From (590) and (262) follows:
% 22.32/6.07 | (592) succ(n7) = all_0_5_5
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (130) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 22.32/6.07 | (593) all_0_9_9 = n6
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (165) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 22.32/6.07 | (594) all_0_5_5 = n8
% 22.32/6.07 |
% 22.32/6.07 | From (593)(594) and (147) follows:
% 22.32/6.07 | (595) sum(n6, n8) = all_0_2_2
% 22.32/6.07 |
% 22.32/6.07 | From (593) and (2089) follows:
% 22.32/6.07 | (2196) sum(n6, n13) = all_0_7_7
% 22.32/6.07 |
% 22.32/6.07 | From (594) and (2087) follows:
% 22.32/6.07 | (2197) sum(n11, n8) = all_0_4_4
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (74) with n11, n8, all_0_4_4, n3 and discharging atoms sum(n11, n8) = all_0_4_4, sum(n11, n8) = n3, yields:
% 22.32/6.07 | (652) all_0_4_4 = n3
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (74) with n6, n13, all_0_7_7, n3 and discharging atoms sum(n6, n13) = all_0_7_7, sum(n6, n13) = n3, yields:
% 22.32/6.07 | (654) all_0_7_7 = n3
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (74) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 22.32/6.07 | (447) all_0_2_2 = n14
% 22.32/6.07 |
% 22.32/6.07 | From (447) and (2091) follows:
% 22.32/6.07 | (793) sum(n14, n8) = all_0_0_0
% 22.32/6.07 |
% 22.32/6.07 | From (654)(652) and (212) follows:
% 22.32/6.07 | (656) sum(n3, n3) = all_0_3_3
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (74) with n14, n8, all_0_0_0, n6 and discharging atoms sum(n14, n8) = all_0_0_0, sum(n14, n8) = n6, yields:
% 22.32/6.07 | (514) all_0_0_0 = n6
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (74) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 22.32/6.07 | (513) all_0_3_3 = n6
% 22.32/6.07 |
% 22.32/6.07 | Equations (514,513) can reduce 363 to:
% 22.32/6.07 | (461) $false
% 22.32/6.07 |
% 22.32/6.07 |-The branch is then unsatisfiable
% 22.32/6.07 |-Branch two:
% 22.32/6.07 | (606) ~ (all_0_11_11 = n7)
% 22.32/6.07 | (607) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.07 |
% 22.32/6.07 +-Applying beta-rule and splitting (607), into two cases.
% 22.32/6.07 |-Branch one:
% 22.32/6.07 | (608) all_0_11_11 = n6
% 22.32/6.07 |
% 22.32/6.07 | From (608) and (423) follows:
% 22.32/6.07 | (609) pred(n6) = all_0_9_9
% 22.32/6.07 |
% 22.32/6.07 | From (608) and (262) follows:
% 22.32/6.07 | (610) succ(n6) = all_0_5_5
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (130) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 22.32/6.07 | (611) all_0_9_9 = n5
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (165) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 22.32/6.07 | (612) all_0_5_5 = n7
% 22.32/6.07 |
% 22.32/6.07 | From (611)(612) and (147) follows:
% 22.32/6.07 | (613) sum(n5, n7) = all_0_2_2
% 22.32/6.07 |
% 22.32/6.07 | From (611) and (2089) follows:
% 22.32/6.07 | (2214) sum(n5, n13) = all_0_7_7
% 22.32/6.07 |
% 22.32/6.07 | From (612) and (2087) follows:
% 22.32/6.07 | (2215) sum(n11, n7) = all_0_4_4
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (74) with n11, n7, all_0_4_4, n2 and discharging atoms sum(n11, n7) = all_0_4_4, sum(n11, n7) = n2, yields:
% 22.32/6.07 | (670) all_0_4_4 = n2
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (74) with n5, n13, all_0_7_7, n2 and discharging atoms sum(n5, n13) = all_0_7_7, sum(n5, n13) = n2, yields:
% 22.32/6.07 | (672) all_0_7_7 = n2
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (74) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 22.32/6.07 | (473) all_0_2_2 = n12
% 22.32/6.07 |
% 22.32/6.07 | From (473) and (2091) follows:
% 22.32/6.07 | (1345) sum(n12, n8) = all_0_0_0
% 22.32/6.07 |
% 22.32/6.07 | From (672)(670) and (212) follows:
% 22.32/6.07 | (674) sum(n2, n2) = all_0_3_3
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (74) with n12, n8, all_0_0_0, n4 and discharging atoms sum(n12, n8) = all_0_0_0, sum(n12, n8) = n4, yields:
% 22.32/6.07 | (532) all_0_0_0 = n4
% 22.32/6.07 |
% 22.32/6.07 | Instantiating formula (74) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 22.32/6.07 | (531) all_0_3_3 = n4
% 22.32/6.07 |
% 22.32/6.07 | Equations (532,531) can reduce 363 to:
% 22.32/6.07 | (461) $false
% 22.32/6.07 |
% 22.32/6.07 |-The branch is then unsatisfiable
% 22.32/6.07 |-Branch two:
% 22.32/6.07 | (624) ~ (all_0_11_11 = n6)
% 22.32/6.07 | (625) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.07 |
% 22.32/6.07 +-Applying beta-rule and splitting (625), into two cases.
% 22.32/6.07 |-Branch one:
% 22.32/6.07 | (626) all_0_11_11 = n5
% 22.32/6.07 |
% 22.32/6.07 | From (626) and (423) follows:
% 22.32/6.07 | (627) pred(n5) = all_0_9_9
% 22.32/6.07 |
% 22.32/6.07 | From (626) and (262) follows:
% 22.32/6.08 | (628) succ(n5) = all_0_5_5
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (130) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 22.32/6.08 | (629) all_0_9_9 = n4
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (165) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 22.32/6.08 | (630) all_0_5_5 = n6
% 22.32/6.08 |
% 22.32/6.08 | From (629)(630) and (147) follows:
% 22.32/6.08 | (631) sum(n4, n6) = all_0_2_2
% 22.32/6.08 |
% 22.32/6.08 | From (629) and (2089) follows:
% 22.32/6.08 | (2232) sum(n4, n13) = all_0_7_7
% 22.32/6.08 |
% 22.32/6.08 | From (630) and (2087) follows:
% 22.32/6.08 | (2233) sum(n11, n6) = all_0_4_4
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n11, n6, all_0_4_4, n1 and discharging atoms sum(n11, n6) = all_0_4_4, sum(n11, n6) = n1, yields:
% 22.32/6.08 | (688) all_0_4_4 = n1
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n4, n13, all_0_7_7, n1 and discharging atoms sum(n4, n13) = all_0_7_7, sum(n4, n13) = n1, yields:
% 22.32/6.08 | (690) all_0_7_7 = n1
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 22.32/6.08 | (491) all_0_2_2 = n10
% 22.32/6.08 |
% 22.32/6.08 | From (491) and (2091) follows:
% 22.32/6.08 | (1859) sum(n10, n8) = all_0_0_0
% 22.32/6.08 |
% 22.32/6.08 | From (690)(688) and (212) follows:
% 22.32/6.08 | (692) sum(n1, n1) = all_0_3_3
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n10, n8, all_0_0_0, n2 and discharging atoms sum(n10, n8) = all_0_0_0, sum(n10, n8) = n2, yields:
% 22.32/6.08 | (550) all_0_0_0 = n2
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 22.32/6.08 | (549) all_0_3_3 = n2
% 22.32/6.08 |
% 22.32/6.08 | Equations (550,549) can reduce 363 to:
% 22.32/6.08 | (461) $false
% 22.32/6.08 |
% 22.32/6.08 |-The branch is then unsatisfiable
% 22.32/6.08 |-Branch two:
% 22.32/6.08 | (642) ~ (all_0_11_11 = n5)
% 22.32/6.08 | (643) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.08 |
% 22.32/6.08 +-Applying beta-rule and splitting (643), into two cases.
% 22.32/6.08 |-Branch one:
% 22.32/6.08 | (644) all_0_11_11 = n4
% 22.32/6.08 |
% 22.32/6.08 | From (644) and (423) follows:
% 22.32/6.08 | (645) pred(n4) = all_0_9_9
% 22.32/6.08 |
% 22.32/6.08 | From (644) and (262) follows:
% 22.32/6.08 | (646) succ(n4) = all_0_5_5
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (130) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 22.32/6.08 | (647) all_0_9_9 = n3
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (165) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 22.32/6.08 | (648) all_0_5_5 = n5
% 22.32/6.08 |
% 22.32/6.08 | From (647)(648) and (147) follows:
% 22.32/6.08 | (649) sum(n3, n5) = all_0_2_2
% 22.32/6.08 |
% 22.32/6.08 | From (647) and (2089) follows:
% 22.32/6.08 | (2250) sum(n3, n13) = all_0_7_7
% 22.32/6.08 |
% 22.32/6.08 | From (648) and (2087) follows:
% 22.32/6.08 | (2251) sum(n11, n5) = all_0_4_4
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n11, n5, all_0_4_4, n0 and discharging atoms sum(n11, n5) = all_0_4_4, sum(n11, n5) = n0, yields:
% 22.32/6.08 | (706) all_0_4_4 = n0
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n3, n13, all_0_7_7, n0 and discharging atoms sum(n3, n13) = all_0_7_7, sum(n3, n13) = n0, yields:
% 22.32/6.08 | (708) all_0_7_7 = n0
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 22.32/6.08 | (509) all_0_2_2 = n8
% 22.32/6.08 |
% 22.32/6.08 | From (509) and (2091) follows:
% 22.32/6.08 | (2109) sum(n8, n8) = all_0_0_0
% 22.32/6.08 |
% 22.32/6.08 | From (708)(706) and (212) follows:
% 22.32/6.08 | (710) sum(n0, n0) = all_0_3_3
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n8, n8, all_0_0_0, n0 and discharging atoms sum(n8, n8) = all_0_0_0, sum(n8, n8) = n0, yields:
% 22.32/6.08 | (568) all_0_0_0 = n0
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 22.32/6.08 | (567) all_0_3_3 = n0
% 22.32/6.08 |
% 22.32/6.08 | Equations (568,567) can reduce 363 to:
% 22.32/6.08 | (461) $false
% 22.32/6.08 |
% 22.32/6.08 |-The branch is then unsatisfiable
% 22.32/6.08 |-Branch two:
% 22.32/6.08 | (660) ~ (all_0_11_11 = n4)
% 22.32/6.08 | (661) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.08 |
% 22.32/6.08 +-Applying beta-rule and splitting (661), into two cases.
% 22.32/6.08 |-Branch one:
% 22.32/6.08 | (662) all_0_11_11 = n3
% 22.32/6.08 |
% 22.32/6.08 | From (662) and (423) follows:
% 22.32/6.08 | (663) pred(n3) = all_0_9_9
% 22.32/6.08 |
% 22.32/6.08 | From (662) and (262) follows:
% 22.32/6.08 | (664) succ(n3) = all_0_5_5
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (130) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 22.32/6.08 | (665) all_0_9_9 = n2
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (165) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 22.32/6.08 | (666) all_0_5_5 = n4
% 22.32/6.08 |
% 22.32/6.08 | From (665)(666) and (147) follows:
% 22.32/6.08 | (667) sum(n2, n4) = all_0_2_2
% 22.32/6.08 |
% 22.32/6.08 | From (665) and (2089) follows:
% 22.32/6.08 | (2268) sum(n2, n13) = all_0_7_7
% 22.32/6.08 |
% 22.32/6.08 | From (666) and (2087) follows:
% 22.32/6.08 | (2269) sum(n11, n4) = all_0_4_4
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n11, n4, all_0_4_4, n15 and discharging atoms sum(n11, n4) = all_0_4_4, sum(n11, n4) = n15, yields:
% 22.32/6.08 | (726) all_0_4_4 = n15
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n2, n13, all_0_7_7, n15 and discharging atoms sum(n2, n13) = all_0_7_7, sum(n2, n13) = n15, yields:
% 22.32/6.08 | (725) all_0_7_7 = n15
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 22.32/6.08 | (527) all_0_2_2 = n6
% 22.32/6.08 |
% 22.32/6.08 | From (527) and (2091) follows:
% 22.32/6.08 | (2129) sum(n6, n8) = all_0_0_0
% 22.32/6.08 |
% 22.32/6.08 | From (725)(726) and (212) follows:
% 22.32/6.08 | (728) sum(n15, n15) = all_0_3_3
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n15, n15, all_0_3_3, n14 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n14, yields:
% 22.32/6.08 | (585) all_0_3_3 = n14
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n6, n8, all_0_0_0, n14 and discharging atoms sum(n6, n8) = all_0_0_0, sum(n6, n8) = n14, yields:
% 22.32/6.08 | (586) all_0_0_0 = n14
% 22.32/6.08 |
% 22.32/6.08 | Equations (586,585) can reduce 363 to:
% 22.32/6.08 | (461) $false
% 22.32/6.08 |
% 22.32/6.08 |-The branch is then unsatisfiable
% 22.32/6.08 |-Branch two:
% 22.32/6.08 | (678) ~ (all_0_11_11 = n3)
% 22.32/6.08 | (679) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.08 |
% 22.32/6.08 +-Applying beta-rule and splitting (679), into two cases.
% 22.32/6.08 |-Branch one:
% 22.32/6.08 | (680) all_0_11_11 = n2
% 22.32/6.08 |
% 22.32/6.08 | From (680) and (423) follows:
% 22.32/6.08 | (681) pred(n2) = all_0_9_9
% 22.32/6.08 |
% 22.32/6.08 | From (680) and (262) follows:
% 22.32/6.08 | (682) succ(n2) = all_0_5_5
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (130) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 22.32/6.08 | (683) all_0_9_9 = n1
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (165) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 22.32/6.08 | (684) all_0_5_5 = n3
% 22.32/6.08 |
% 22.32/6.08 | From (683)(684) and (147) follows:
% 22.32/6.08 | (685) sum(n1, n3) = all_0_2_2
% 22.32/6.08 |
% 22.32/6.08 | From (683) and (2089) follows:
% 22.32/6.08 | (2286) sum(n1, n13) = all_0_7_7
% 22.32/6.08 |
% 22.32/6.08 | From (684) and (2087) follows:
% 22.32/6.08 | (2287) sum(n11, n3) = all_0_4_4
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n11, n3, all_0_4_4, n14 and discharging atoms sum(n11, n3) = all_0_4_4, sum(n11, n3) = n14, yields:
% 22.32/6.08 | (451) all_0_4_4 = n14
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n1, n13, all_0_7_7, n14 and discharging atoms sum(n1, n13) = all_0_7_7, sum(n1, n13) = n14, yields:
% 22.32/6.08 | (452) all_0_7_7 = n14
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 22.32/6.08 | (545) all_0_2_2 = n4
% 22.32/6.08 |
% 22.32/6.08 | From (545) and (2091) follows:
% 22.32/6.08 | (2147) sum(n4, n8) = all_0_0_0
% 22.32/6.08 |
% 22.32/6.08 | From (452)(451) and (212) follows:
% 22.32/6.08 | (456) sum(n14, n14) = all_0_3_3
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n14, n14, all_0_3_3, n12 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n12, yields:
% 22.32/6.08 | (459) all_0_3_3 = n12
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n4, n8, all_0_0_0, n12 and discharging atoms sum(n4, n8) = all_0_0_0, sum(n4, n8) = n12, yields:
% 22.32/6.08 | (457) all_0_0_0 = n12
% 22.32/6.08 |
% 22.32/6.08 | Equations (457,459) can reduce 363 to:
% 22.32/6.08 | (461) $false
% 22.32/6.08 |
% 22.32/6.08 |-The branch is then unsatisfiable
% 22.32/6.08 |-Branch two:
% 22.32/6.08 | (696) ~ (all_0_11_11 = n2)
% 22.32/6.08 | (697) all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.08 |
% 22.32/6.08 +-Applying beta-rule and splitting (697), into two cases.
% 22.32/6.08 |-Branch one:
% 22.32/6.08 | (698) all_0_11_11 = n1
% 22.32/6.08 |
% 22.32/6.08 | From (698) and (423) follows:
% 22.32/6.08 | (699) pred(n1) = all_0_9_9
% 22.32/6.08 |
% 22.32/6.08 | From (698) and (262) follows:
% 22.32/6.08 | (700) succ(n1) = all_0_5_5
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (130) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 22.32/6.08 | (701) all_0_9_9 = n0
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (165) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 22.32/6.08 | (702) all_0_5_5 = n2
% 22.32/6.08 |
% 22.32/6.08 | From (701)(702) and (147) follows:
% 22.32/6.08 | (703) sum(n0, n2) = all_0_2_2
% 22.32/6.08 |
% 22.32/6.08 | From (701) and (2089) follows:
% 22.32/6.08 | (2304) sum(n0, n13) = all_0_7_7
% 22.32/6.08 |
% 22.32/6.08 | From (702) and (2087) follows:
% 22.32/6.08 | (2305) sum(n11, n2) = all_0_4_4
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n11, n2, all_0_4_4, n13 and discharging atoms sum(n11, n2) = all_0_4_4, sum(n11, n2) = n13, yields:
% 22.32/6.08 | (472) all_0_4_4 = n13
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n0, n13, all_0_7_7, n13 and discharging atoms sum(n0, n13) = all_0_7_7, sum(n0, n13) = n13, yields:
% 22.32/6.08 | (474) all_0_7_7 = n13
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 22.32/6.08 | (563) all_0_2_2 = n2
% 22.32/6.08 |
% 22.32/6.08 | From (563) and (2091) follows:
% 22.32/6.08 | (2165) sum(n2, n8) = all_0_0_0
% 22.32/6.08 |
% 22.32/6.08 | From (474)(472) and (212) follows:
% 22.32/6.08 | (476) sum(n13, n13) = all_0_3_3
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n13, n13, all_0_3_3, n10 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n10, yields:
% 22.32/6.08 | (477) all_0_3_3 = n10
% 22.32/6.08 |
% 22.32/6.08 | Instantiating formula (74) with n2, n8, all_0_0_0, n10 and discharging atoms sum(n2, n8) = all_0_0_0, sum(n2, n8) = n10, yields:
% 22.32/6.08 | (478) all_0_0_0 = n10
% 22.32/6.08 |
% 22.32/6.08 | Equations (478,477) can reduce 363 to:
% 22.32/6.08 | (461) $false
% 22.32/6.08 |
% 22.32/6.08 |-The branch is then unsatisfiable
% 22.32/6.08 |-Branch two:
% 22.32/6.08 | (715) ~ (all_0_11_11 = n1)
% 22.32/6.08 | (716) all_0_11_11 = n0
% 22.32/6.09 |
% 22.32/6.09 | From (716) and (423) follows:
% 22.32/6.09 | (717) pred(n0) = all_0_9_9
% 22.32/6.09 |
% 22.32/6.09 | From (716) and (262) follows:
% 22.32/6.09 | (718) succ(n0) = all_0_5_5
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (130) with n0, all_0_9_9, n15 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n15, yields:
% 22.32/6.09 | (719) all_0_9_9 = n15
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (165) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 22.32/6.09 | (720) all_0_5_5 = n1
% 22.32/6.09 |
% 22.32/6.09 | From (719)(720) and (147) follows:
% 22.32/6.09 | (721) sum(n15, n1) = all_0_2_2
% 22.32/6.09 |
% 22.32/6.09 | From (719) and (2089) follows:
% 22.32/6.09 | (2321) sum(n15, n13) = all_0_7_7
% 22.32/6.09 |
% 22.32/6.09 | From (720) and (2087) follows:
% 22.32/6.09 | (2322) sum(n11, n1) = all_0_4_4
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n15, n13, all_0_7_7, n12 and discharging atoms sum(n15, n13) = all_0_7_7, sum(n15, n13) = n12, yields:
% 22.32/6.09 | (492) all_0_7_7 = n12
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n15, n1, all_0_2_2, n0 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n0, yields:
% 22.32/6.09 | (581) all_0_2_2 = n0
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n11, n1, all_0_4_4, n12 and discharging atoms sum(n11, n1) = all_0_4_4, sum(n11, n1) = n12, yields:
% 22.32/6.09 | (490) all_0_4_4 = n12
% 22.32/6.09 |
% 22.32/6.09 | From (581) and (2091) follows:
% 22.32/6.09 | (2183) sum(n0, n8) = all_0_0_0
% 22.32/6.09 |
% 22.32/6.09 | From (492)(490) and (212) follows:
% 22.32/6.09 | (494) sum(n12, n12) = all_0_3_3
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n12, n12, all_0_3_3, n8 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n8, yields:
% 22.32/6.09 | (495) all_0_3_3 = n8
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n0, n8, all_0_0_0, n8 and discharging atoms sum(n0, n8) = all_0_0_0, sum(n0, n8) = n8, yields:
% 22.32/6.09 | (496) all_0_0_0 = n8
% 22.32/6.09 |
% 22.32/6.09 | Equations (496,495) can reduce 363 to:
% 22.32/6.09 | (461) $false
% 22.32/6.09 |
% 22.32/6.09 |-The branch is then unsatisfiable
% 22.32/6.09 |-Branch two:
% 22.32/6.09 | (797) ~ (all_0_10_10 = n12)
% 22.32/6.09 | (798) all_0_10_10 = n11 | all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.32/6.09 |
% 22.32/6.09 +-Applying beta-rule and splitting (499), into two cases.
% 22.32/6.09 |-Branch one:
% 22.32/6.09 | (500) all_0_11_11 = n12
% 22.32/6.09 |
% 22.32/6.09 | From (500) and (423) follows:
% 22.32/6.09 | (501) pred(n12) = all_0_9_9
% 22.32/6.09 |
% 22.32/6.09 | From (500) and (262) follows:
% 22.32/6.09 | (502) succ(n12) = all_0_5_5
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (130) with n12, all_0_9_9, n11 and discharging atoms pred(n12) = all_0_9_9, pred(n12) = n11, yields:
% 22.32/6.09 | (503) all_0_9_9 = n11
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (165) with n12, all_0_5_5, n13 and discharging atoms succ(n12) = all_0_5_5, succ(n12) = n13, yields:
% 22.32/6.09 | (504) all_0_5_5 = n13
% 22.32/6.09 |
% 22.32/6.09 | From (504) and (276) follows:
% 22.32/6.09 | (2338) sum(all_0_6_6, n13) = all_0_4_4
% 22.32/6.09 |
% 22.32/6.09 | From (503)(504) and (147) follows:
% 22.32/6.09 | (505) sum(n11, n13) = all_0_2_2
% 22.32/6.09 |
% 22.32/6.09 | From (503) and (350) follows:
% 22.32/6.09 | (2340) sum(n11, all_0_8_8) = all_0_7_7
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n11, n13, all_0_2_2, n8 and discharging atoms sum(n11, n13) = all_0_2_2, sum(n11, n13) = n8, yields:
% 22.32/6.09 | (509) all_0_2_2 = n8
% 22.32/6.09 |
% 22.32/6.09 | From (509) and (256) follows:
% 22.32/6.09 | (2342) sum(n8, all_0_1_1) = all_0_0_0
% 22.32/6.09 |
% 22.32/6.09 +-Applying beta-rule and splitting (798), into two cases.
% 22.32/6.09 |-Branch one:
% 22.32/6.09 | (799) all_0_10_10 = n11
% 22.32/6.09 |
% 22.32/6.09 | From (799) and (317) follows:
% 22.32/6.09 | (800) pred(n11) = all_0_6_6
% 22.32/6.09 |
% 22.32/6.09 | From (799) and (146) follows:
% 22.32/6.09 | (801) succ(n11) = all_0_8_8
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (130) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 22.32/6.09 | (802) all_0_6_6 = n10
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (165) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 22.32/6.09 | (803) all_0_8_8 = n12
% 22.32/6.09 |
% 22.32/6.09 | From (802)(803) and (10) follows:
% 22.32/6.09 | (804) sum(n10, n12) = all_0_1_1
% 22.32/6.09 |
% 22.32/6.09 | From (802) and (2338) follows:
% 22.32/6.09 | (2349) sum(n10, n13) = all_0_4_4
% 22.32/6.09 |
% 22.32/6.09 | From (803) and (2340) follows:
% 22.32/6.09 | (2350) sum(n11, n12) = all_0_7_7
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n11, n12, all_0_7_7, n7 and discharging atoms sum(n11, n12) = all_0_7_7, sum(n11, n12) = n7, yields:
% 22.32/6.09 | (582) all_0_7_7 = n7
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n10, n13, all_0_4_4, n7 and discharging atoms sum(n10, n13) = all_0_4_4, sum(n10, n13) = n7, yields:
% 22.32/6.09 | (580) all_0_4_4 = n7
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n10, n12, all_0_1_1, n6 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n6, yields:
% 22.32/6.09 | (808) all_0_1_1 = n6
% 22.32/6.09 |
% 22.32/6.09 | From (582)(580) and (212) follows:
% 22.32/6.09 | (584) sum(n7, n7) = all_0_3_3
% 22.32/6.09 |
% 22.32/6.09 | From (808) and (2342) follows:
% 22.32/6.09 | (2355) sum(n8, n6) = all_0_0_0
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n8, n6, all_0_0_0, n14 and discharging atoms sum(n8, n6) = all_0_0_0, sum(n8, n6) = n14, yields:
% 22.32/6.09 | (586) all_0_0_0 = n14
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 22.32/6.09 | (585) all_0_3_3 = n14
% 22.32/6.09 |
% 22.32/6.09 | Equations (586,585) can reduce 363 to:
% 22.32/6.09 | (461) $false
% 22.32/6.09 |
% 22.32/6.09 |-The branch is then unsatisfiable
% 22.32/6.09 |-Branch two:
% 22.32/6.09 | (815) ~ (all_0_10_10 = n11)
% 22.32/6.09 | (816) all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.32/6.09 |
% 22.32/6.09 +-Applying beta-rule and splitting (816), into two cases.
% 22.32/6.09 |-Branch one:
% 22.32/6.09 | (817) all_0_10_10 = n10
% 22.32/6.09 |
% 22.32/6.09 | From (817) and (317) follows:
% 22.32/6.09 | (818) pred(n10) = all_0_6_6
% 22.32/6.09 |
% 22.32/6.09 | From (817) and (146) follows:
% 22.32/6.09 | (819) succ(n10) = all_0_8_8
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (130) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 22.32/6.09 | (820) all_0_6_6 = n9
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (165) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 22.32/6.09 | (821) all_0_8_8 = n11
% 22.32/6.09 |
% 22.32/6.09 | From (820)(821) and (10) follows:
% 22.32/6.09 | (822) sum(n9, n11) = all_0_1_1
% 22.32/6.09 |
% 22.32/6.09 | From (820) and (2338) follows:
% 22.32/6.09 | (2367) sum(n9, n13) = all_0_4_4
% 22.32/6.09 |
% 22.32/6.09 | From (821) and (2340) follows:
% 22.32/6.09 | (2368) sum(n11, n11) = all_0_7_7
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n11, n11, all_0_7_7, n6 and discharging atoms sum(n11, n11) = all_0_7_7, sum(n11, n11) = n6, yields:
% 22.32/6.09 | (600) all_0_7_7 = n6
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n9, n13, all_0_4_4, n6 and discharging atoms sum(n9, n13) = all_0_4_4, sum(n9, n13) = n6, yields:
% 22.32/6.09 | (598) all_0_4_4 = n6
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n9, n11, all_0_1_1, n4 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n4, yields:
% 22.32/6.09 | (826) all_0_1_1 = n4
% 22.32/6.09 |
% 22.32/6.09 | From (600)(598) and (212) follows:
% 22.32/6.09 | (602) sum(n6, n6) = all_0_3_3
% 22.32/6.09 |
% 22.32/6.09 | From (826) and (2342) follows:
% 22.32/6.09 | (2373) sum(n8, n4) = all_0_0_0
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n8, n4, all_0_0_0, n12 and discharging atoms sum(n8, n4) = all_0_0_0, sum(n8, n4) = n12, yields:
% 22.32/6.09 | (457) all_0_0_0 = n12
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 22.32/6.09 | (459) all_0_3_3 = n12
% 22.32/6.09 |
% 22.32/6.09 | Equations (457,459) can reduce 363 to:
% 22.32/6.09 | (461) $false
% 22.32/6.09 |
% 22.32/6.09 |-The branch is then unsatisfiable
% 22.32/6.09 |-Branch two:
% 22.32/6.09 | (833) ~ (all_0_10_10 = n10)
% 22.32/6.09 | (834) all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.32/6.09 |
% 22.32/6.09 +-Applying beta-rule and splitting (834), into two cases.
% 22.32/6.09 |-Branch one:
% 22.32/6.09 | (835) all_0_10_10 = n9
% 22.32/6.09 |
% 22.32/6.09 | From (835) and (317) follows:
% 22.32/6.09 | (836) pred(n9) = all_0_6_6
% 22.32/6.09 |
% 22.32/6.09 | From (835) and (146) follows:
% 22.32/6.09 | (837) succ(n9) = all_0_8_8
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (130) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 22.32/6.09 | (838) all_0_6_6 = n8
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (165) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 22.32/6.09 | (839) all_0_8_8 = n10
% 22.32/6.09 |
% 22.32/6.09 | From (838)(839) and (10) follows:
% 22.32/6.09 | (840) sum(n8, n10) = all_0_1_1
% 22.32/6.09 |
% 22.32/6.09 | From (838) and (2338) follows:
% 22.32/6.09 | (2385) sum(n8, n13) = all_0_4_4
% 22.32/6.09 |
% 22.32/6.09 | From (839) and (2340) follows:
% 22.32/6.09 | (2386) sum(n11, n10) = all_0_7_7
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n11, n10, all_0_7_7, n5 and discharging atoms sum(n11, n10) = all_0_7_7, sum(n11, n10) = n5, yields:
% 22.32/6.09 | (618) all_0_7_7 = n5
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n8, n13, all_0_4_4, n5 and discharging atoms sum(n8, n13) = all_0_4_4, sum(n8, n13) = n5, yields:
% 22.32/6.09 | (616) all_0_4_4 = n5
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n8, n10, all_0_1_1, n2 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n2, yields:
% 22.32/6.09 | (844) all_0_1_1 = n2
% 22.32/6.09 |
% 22.32/6.09 | From (618)(616) and (212) follows:
% 22.32/6.09 | (620) sum(n5, n5) = all_0_3_3
% 22.32/6.09 |
% 22.32/6.09 | From (844) and (2342) follows:
% 22.32/6.09 | (2391) sum(n8, n2) = all_0_0_0
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n8, n2, all_0_0_0, n10 and discharging atoms sum(n8, n2) = all_0_0_0, sum(n8, n2) = n10, yields:
% 22.32/6.09 | (478) all_0_0_0 = n10
% 22.32/6.09 |
% 22.32/6.09 | Instantiating formula (74) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 22.32/6.09 | (477) all_0_3_3 = n10
% 22.32/6.09 |
% 22.32/6.09 | Equations (478,477) can reduce 363 to:
% 22.32/6.09 | (461) $false
% 22.32/6.09 |
% 22.32/6.09 |-The branch is then unsatisfiable
% 22.32/6.09 |-Branch two:
% 22.32/6.09 | (851) ~ (all_0_10_10 = n9)
% 22.32/6.09 | (852) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.32/6.09 |
% 22.32/6.09 +-Applying beta-rule and splitting (852), into two cases.
% 22.32/6.10 |-Branch one:
% 22.32/6.10 | (853) all_0_10_10 = n8
% 22.32/6.10 |
% 22.32/6.10 | From (853) and (317) follows:
% 22.32/6.10 | (854) pred(n8) = all_0_6_6
% 22.32/6.10 |
% 22.32/6.10 | From (853) and (146) follows:
% 22.32/6.10 | (855) succ(n8) = all_0_8_8
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (130) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 22.32/6.10 | (856) all_0_6_6 = n7
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (165) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 22.32/6.10 | (857) all_0_8_8 = n9
% 22.32/6.10 |
% 22.32/6.10 | From (856)(857) and (10) follows:
% 22.32/6.10 | (858) sum(n7, n9) = all_0_1_1
% 22.32/6.10 |
% 22.32/6.10 | From (856) and (2338) follows:
% 22.32/6.10 | (2403) sum(n7, n13) = all_0_4_4
% 22.32/6.10 |
% 22.32/6.10 | From (857) and (2340) follows:
% 22.32/6.10 | (2404) sum(n11, n9) = all_0_7_7
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n11, n9, all_0_7_7, n4 and discharging atoms sum(n11, n9) = all_0_7_7, sum(n11, n9) = n4, yields:
% 22.32/6.10 | (636) all_0_7_7 = n4
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n7, n13, all_0_4_4, n4 and discharging atoms sum(n7, n13) = all_0_4_4, sum(n7, n13) = n4, yields:
% 22.32/6.10 | (634) all_0_4_4 = n4
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n7, n9, all_0_1_1, n0 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n0, yields:
% 22.32/6.10 | (862) all_0_1_1 = n0
% 22.32/6.10 |
% 22.32/6.10 | From (636)(634) and (212) follows:
% 22.32/6.10 | (638) sum(n4, n4) = all_0_3_3
% 22.32/6.10 |
% 22.32/6.10 | From (862) and (2342) follows:
% 22.32/6.10 | (2409) sum(n8, n0) = all_0_0_0
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n8, n0, all_0_0_0, n8 and discharging atoms sum(n8, n0) = all_0_0_0, sum(n8, n0) = n8, yields:
% 22.32/6.10 | (496) all_0_0_0 = n8
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 22.32/6.10 | (495) all_0_3_3 = n8
% 22.32/6.10 |
% 22.32/6.10 | Equations (496,495) can reduce 363 to:
% 22.32/6.10 | (461) $false
% 22.32/6.10 |
% 22.32/6.10 |-The branch is then unsatisfiable
% 22.32/6.10 |-Branch two:
% 22.32/6.10 | (869) ~ (all_0_10_10 = n8)
% 22.32/6.10 | (870) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.32/6.10 |
% 22.32/6.10 +-Applying beta-rule and splitting (870), into two cases.
% 22.32/6.10 |-Branch one:
% 22.32/6.10 | (871) all_0_10_10 = n7
% 22.32/6.10 |
% 22.32/6.10 | From (871) and (317) follows:
% 22.32/6.10 | (872) pred(n7) = all_0_6_6
% 22.32/6.10 |
% 22.32/6.10 | From (871) and (146) follows:
% 22.32/6.10 | (873) succ(n7) = all_0_8_8
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (130) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 22.32/6.10 | (874) all_0_6_6 = n6
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (165) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 22.32/6.10 | (875) all_0_8_8 = n8
% 22.32/6.10 |
% 22.32/6.10 | From (874)(875) and (10) follows:
% 22.32/6.10 | (876) sum(n6, n8) = all_0_1_1
% 22.32/6.10 |
% 22.32/6.10 | From (874) and (2338) follows:
% 22.32/6.10 | (2421) sum(n6, n13) = all_0_4_4
% 22.32/6.10 |
% 22.32/6.10 | From (875) and (2340) follows:
% 22.32/6.10 | (2422) sum(n11, n8) = all_0_7_7
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n11, n8, all_0_7_7, n3 and discharging atoms sum(n11, n8) = all_0_7_7, sum(n11, n8) = n3, yields:
% 22.32/6.10 | (654) all_0_7_7 = n3
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n6, n13, all_0_4_4, n3 and discharging atoms sum(n6, n13) = all_0_4_4, sum(n6, n13) = n3, yields:
% 22.32/6.10 | (652) all_0_4_4 = n3
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 22.32/6.10 | (436) all_0_1_1 = n14
% 22.32/6.10 |
% 22.32/6.10 | From (654)(652) and (212) follows:
% 22.32/6.10 | (656) sum(n3, n3) = all_0_3_3
% 22.32/6.10 |
% 22.32/6.10 | From (436) and (2342) follows:
% 22.32/6.10 | (511) sum(n8, n14) = all_0_0_0
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n8, n14, all_0_0_0, n6 and discharging atoms sum(n8, n14) = all_0_0_0, sum(n8, n14) = n6, yields:
% 22.32/6.10 | (514) all_0_0_0 = n6
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 22.32/6.10 | (513) all_0_3_3 = n6
% 22.32/6.10 |
% 22.32/6.10 | Equations (514,513) can reduce 363 to:
% 22.32/6.10 | (461) $false
% 22.32/6.10 |
% 22.32/6.10 |-The branch is then unsatisfiable
% 22.32/6.10 |-Branch two:
% 22.32/6.10 | (887) ~ (all_0_10_10 = n7)
% 22.32/6.10 | (888) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.32/6.10 |
% 22.32/6.10 +-Applying beta-rule and splitting (888), into two cases.
% 22.32/6.10 |-Branch one:
% 22.32/6.10 | (889) all_0_10_10 = n6
% 22.32/6.10 |
% 22.32/6.10 | From (889) and (317) follows:
% 22.32/6.10 | (890) pred(n6) = all_0_6_6
% 22.32/6.10 |
% 22.32/6.10 | From (889) and (146) follows:
% 22.32/6.10 | (891) succ(n6) = all_0_8_8
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (130) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 22.32/6.10 | (892) all_0_6_6 = n5
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (165) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 22.32/6.10 | (893) all_0_8_8 = n7
% 22.32/6.10 |
% 22.32/6.10 | From (892)(893) and (10) follows:
% 22.32/6.10 | (894) sum(n5, n7) = all_0_1_1
% 22.32/6.10 |
% 22.32/6.10 | From (892) and (2338) follows:
% 22.32/6.10 | (2439) sum(n5, n13) = all_0_4_4
% 22.32/6.10 |
% 22.32/6.10 | From (893) and (2340) follows:
% 22.32/6.10 | (2440) sum(n11, n7) = all_0_7_7
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n11, n7, all_0_7_7, n2 and discharging atoms sum(n11, n7) = all_0_7_7, sum(n11, n7) = n2, yields:
% 22.32/6.10 | (672) all_0_7_7 = n2
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n5, n13, all_0_4_4, n2 and discharging atoms sum(n5, n13) = all_0_4_4, sum(n5, n13) = n2, yields:
% 22.32/6.10 | (670) all_0_4_4 = n2
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 22.32/6.10 | (754) all_0_1_1 = n12
% 22.32/6.10 |
% 22.32/6.10 | From (672)(670) and (212) follows:
% 22.32/6.10 | (674) sum(n2, n2) = all_0_3_3
% 22.32/6.10 |
% 22.32/6.10 | From (754) and (2342) follows:
% 22.32/6.10 | (1083) sum(n8, n12) = all_0_0_0
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n8, n12, all_0_0_0, n4 and discharging atoms sum(n8, n12) = all_0_0_0, sum(n8, n12) = n4, yields:
% 22.32/6.10 | (532) all_0_0_0 = n4
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 22.32/6.10 | (531) all_0_3_3 = n4
% 22.32/6.10 |
% 22.32/6.10 | Equations (532,531) can reduce 363 to:
% 22.32/6.10 | (461) $false
% 22.32/6.10 |
% 22.32/6.10 |-The branch is then unsatisfiable
% 22.32/6.10 |-Branch two:
% 22.32/6.10 | (905) ~ (all_0_10_10 = n6)
% 22.32/6.10 | (906) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.32/6.10 |
% 22.32/6.10 +-Applying beta-rule and splitting (906), into two cases.
% 22.32/6.10 |-Branch one:
% 22.32/6.10 | (907) all_0_10_10 = n5
% 22.32/6.10 |
% 22.32/6.10 | From (907) and (317) follows:
% 22.32/6.10 | (908) pred(n5) = all_0_6_6
% 22.32/6.10 |
% 22.32/6.10 | From (907) and (146) follows:
% 22.32/6.10 | (909) succ(n5) = all_0_8_8
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (130) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 22.32/6.10 | (910) all_0_6_6 = n4
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (165) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 22.32/6.10 | (911) all_0_8_8 = n6
% 22.32/6.10 |
% 22.32/6.10 | From (910)(911) and (10) follows:
% 22.32/6.10 | (912) sum(n4, n6) = all_0_1_1
% 22.32/6.10 |
% 22.32/6.10 | From (910) and (2338) follows:
% 22.32/6.10 | (2457) sum(n4, n13) = all_0_4_4
% 22.32/6.10 |
% 22.32/6.10 | From (911) and (2340) follows:
% 22.32/6.10 | (2458) sum(n11, n6) = all_0_7_7
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n11, n6, all_0_7_7, n1 and discharging atoms sum(n11, n6) = all_0_7_7, sum(n11, n6) = n1, yields:
% 22.32/6.10 | (690) all_0_7_7 = n1
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n4, n13, all_0_4_4, n1 and discharging atoms sum(n4, n13) = all_0_4_4, sum(n4, n13) = n1, yields:
% 22.32/6.10 | (688) all_0_4_4 = n1
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 22.32/6.10 | (772) all_0_1_1 = n10
% 22.32/6.10 |
% 22.32/6.10 | From (690)(688) and (212) follows:
% 22.32/6.10 | (692) sum(n1, n1) = all_0_3_3
% 22.32/6.10 |
% 22.32/6.10 | From (772) and (2342) follows:
% 22.32/6.10 | (1615) sum(n8, n10) = all_0_0_0
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n8, n10, all_0_0_0, n2 and discharging atoms sum(n8, n10) = all_0_0_0, sum(n8, n10) = n2, yields:
% 22.32/6.10 | (550) all_0_0_0 = n2
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (74) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 22.32/6.10 | (549) all_0_3_3 = n2
% 22.32/6.10 |
% 22.32/6.10 | Equations (550,549) can reduce 363 to:
% 22.32/6.10 | (461) $false
% 22.32/6.10 |
% 22.32/6.10 |-The branch is then unsatisfiable
% 22.32/6.10 |-Branch two:
% 22.32/6.10 | (923) ~ (all_0_10_10 = n5)
% 22.32/6.10 | (924) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.32/6.10 |
% 22.32/6.10 +-Applying beta-rule and splitting (924), into two cases.
% 22.32/6.10 |-Branch one:
% 22.32/6.10 | (925) all_0_10_10 = n4
% 22.32/6.10 |
% 22.32/6.10 | From (925) and (317) follows:
% 22.32/6.10 | (926) pred(n4) = all_0_6_6
% 22.32/6.10 |
% 22.32/6.10 | From (925) and (146) follows:
% 22.32/6.10 | (927) succ(n4) = all_0_8_8
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (130) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 22.32/6.10 | (928) all_0_6_6 = n3
% 22.32/6.10 |
% 22.32/6.10 | Instantiating formula (165) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 22.32/6.10 | (929) all_0_8_8 = n5
% 22.32/6.10 |
% 22.32/6.10 | From (928)(929) and (10) follows:
% 22.32/6.10 | (930) sum(n3, n5) = all_0_1_1
% 22.32/6.10 |
% 22.32/6.10 | From (928) and (2338) follows:
% 22.32/6.11 | (2475) sum(n3, n13) = all_0_4_4
% 22.32/6.11 |
% 22.32/6.11 | From (929) and (2340) follows:
% 22.32/6.11 | (2476) sum(n11, n5) = all_0_7_7
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n11, n5, all_0_7_7, n0 and discharging atoms sum(n11, n5) = all_0_7_7, sum(n11, n5) = n0, yields:
% 22.32/6.11 | (708) all_0_7_7 = n0
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n3, n13, all_0_4_4, n0 and discharging atoms sum(n3, n13) = all_0_4_4, sum(n3, n13) = n0, yields:
% 22.32/6.11 | (706) all_0_4_4 = n0
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 22.32/6.11 | (790) all_0_1_1 = n8
% 22.32/6.11 |
% 22.32/6.11 | From (708)(706) and (212) follows:
% 22.32/6.11 | (710) sum(n0, n0) = all_0_3_3
% 22.32/6.11 |
% 22.32/6.11 | From (790) and (2342) follows:
% 22.32/6.11 | (2109) sum(n8, n8) = all_0_0_0
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n8, n8, all_0_0_0, n0 and discharging atoms sum(n8, n8) = all_0_0_0, sum(n8, n8) = n0, yields:
% 22.32/6.11 | (568) all_0_0_0 = n0
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 22.32/6.11 | (567) all_0_3_3 = n0
% 22.32/6.11 |
% 22.32/6.11 | Equations (568,567) can reduce 363 to:
% 22.32/6.11 | (461) $false
% 22.32/6.11 |
% 22.32/6.11 |-The branch is then unsatisfiable
% 22.32/6.11 |-Branch two:
% 22.32/6.11 | (941) ~ (all_0_10_10 = n4)
% 22.32/6.11 | (942) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.32/6.11 |
% 22.32/6.11 +-Applying beta-rule and splitting (942), into two cases.
% 22.32/6.11 |-Branch one:
% 22.32/6.11 | (943) all_0_10_10 = n3
% 22.32/6.11 |
% 22.32/6.11 | From (943) and (317) follows:
% 22.32/6.11 | (944) pred(n3) = all_0_6_6
% 22.32/6.11 |
% 22.32/6.11 | From (943) and (146) follows:
% 22.32/6.11 | (945) succ(n3) = all_0_8_8
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (130) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 22.32/6.11 | (946) all_0_6_6 = n2
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (165) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 22.32/6.11 | (947) all_0_8_8 = n4
% 22.32/6.11 |
% 22.32/6.11 | From (946)(947) and (10) follows:
% 22.32/6.11 | (948) sum(n2, n4) = all_0_1_1
% 22.32/6.11 |
% 22.32/6.11 | From (946) and (2338) follows:
% 22.32/6.11 | (2493) sum(n2, n13) = all_0_4_4
% 22.32/6.11 |
% 22.32/6.11 | From (947) and (2340) follows:
% 22.32/6.11 | (2494) sum(n11, n4) = all_0_7_7
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n11, n4, all_0_7_7, n15 and discharging atoms sum(n11, n4) = all_0_7_7, sum(n11, n4) = n15, yields:
% 22.32/6.11 | (725) all_0_7_7 = n15
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n2, n13, all_0_4_4, n15 and discharging atoms sum(n2, n13) = all_0_4_4, sum(n2, n13) = n15, yields:
% 22.32/6.11 | (726) all_0_4_4 = n15
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 22.32/6.11 | (808) all_0_1_1 = n6
% 22.32/6.11 |
% 22.32/6.11 | From (725)(726) and (212) follows:
% 22.32/6.11 | (728) sum(n15, n15) = all_0_3_3
% 22.32/6.11 |
% 22.32/6.11 | From (808) and (2342) follows:
% 22.32/6.11 | (2355) sum(n8, n6) = all_0_0_0
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n15, n15, all_0_3_3, n14 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n14, yields:
% 22.32/6.11 | (585) all_0_3_3 = n14
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n8, n6, all_0_0_0, n14 and discharging atoms sum(n8, n6) = all_0_0_0, sum(n8, n6) = n14, yields:
% 22.32/6.11 | (586) all_0_0_0 = n14
% 22.32/6.11 |
% 22.32/6.11 | Equations (586,585) can reduce 363 to:
% 22.32/6.11 | (461) $false
% 22.32/6.11 |
% 22.32/6.11 |-The branch is then unsatisfiable
% 22.32/6.11 |-Branch two:
% 22.32/6.11 | (959) ~ (all_0_10_10 = n3)
% 22.32/6.11 | (960) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.32/6.11 |
% 22.32/6.11 +-Applying beta-rule and splitting (960), into two cases.
% 22.32/6.11 |-Branch one:
% 22.32/6.11 | (961) all_0_10_10 = n2
% 22.32/6.11 |
% 22.32/6.11 | From (961) and (317) follows:
% 22.32/6.11 | (962) pred(n2) = all_0_6_6
% 22.32/6.11 |
% 22.32/6.11 | From (961) and (146) follows:
% 22.32/6.11 | (963) succ(n2) = all_0_8_8
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (130) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 22.32/6.11 | (964) all_0_6_6 = n1
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (165) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 22.32/6.11 | (965) all_0_8_8 = n3
% 22.32/6.11 |
% 22.32/6.11 | From (964)(965) and (10) follows:
% 22.32/6.11 | (966) sum(n1, n3) = all_0_1_1
% 22.32/6.11 |
% 22.32/6.11 | From (964) and (2338) follows:
% 22.32/6.11 | (2511) sum(n1, n13) = all_0_4_4
% 22.32/6.11 |
% 22.32/6.11 | From (965) and (2340) follows:
% 22.32/6.11 | (2512) sum(n11, n3) = all_0_7_7
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n11, n3, all_0_7_7, n14 and discharging atoms sum(n11, n3) = all_0_7_7, sum(n11, n3) = n14, yields:
% 22.32/6.11 | (452) all_0_7_7 = n14
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n1, n13, all_0_4_4, n14 and discharging atoms sum(n1, n13) = all_0_4_4, sum(n1, n13) = n14, yields:
% 22.32/6.11 | (451) all_0_4_4 = n14
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 22.32/6.11 | (826) all_0_1_1 = n4
% 22.32/6.11 |
% 22.32/6.11 | From (452)(451) and (212) follows:
% 22.32/6.11 | (456) sum(n14, n14) = all_0_3_3
% 22.32/6.11 |
% 22.32/6.11 | From (826) and (2342) follows:
% 22.32/6.11 | (2373) sum(n8, n4) = all_0_0_0
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n14, n14, all_0_3_3, n12 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n12, yields:
% 22.32/6.11 | (459) all_0_3_3 = n12
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n8, n4, all_0_0_0, n12 and discharging atoms sum(n8, n4) = all_0_0_0, sum(n8, n4) = n12, yields:
% 22.32/6.11 | (457) all_0_0_0 = n12
% 22.32/6.11 |
% 22.32/6.11 | Equations (457,459) can reduce 363 to:
% 22.32/6.11 | (461) $false
% 22.32/6.11 |
% 22.32/6.11 |-The branch is then unsatisfiable
% 22.32/6.11 |-Branch two:
% 22.32/6.11 | (977) ~ (all_0_10_10 = n2)
% 22.32/6.11 | (978) all_0_10_10 = n1 | all_0_10_10 = n0
% 22.32/6.11 |
% 22.32/6.11 +-Applying beta-rule and splitting (978), into two cases.
% 22.32/6.11 |-Branch one:
% 22.32/6.11 | (979) all_0_10_10 = n1
% 22.32/6.11 |
% 22.32/6.11 | From (979) and (317) follows:
% 22.32/6.11 | (980) pred(n1) = all_0_6_6
% 22.32/6.11 |
% 22.32/6.11 | From (979) and (146) follows:
% 22.32/6.11 | (981) succ(n1) = all_0_8_8
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (130) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 22.32/6.11 | (982) all_0_6_6 = n0
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (165) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 22.32/6.11 | (983) all_0_8_8 = n2
% 22.32/6.11 |
% 22.32/6.11 | From (982)(983) and (10) follows:
% 22.32/6.11 | (984) sum(n0, n2) = all_0_1_1
% 22.32/6.11 |
% 22.32/6.11 | From (982) and (2338) follows:
% 22.32/6.11 | (2529) sum(n0, n13) = all_0_4_4
% 22.32/6.11 |
% 22.32/6.11 | From (983) and (2340) follows:
% 22.32/6.11 | (2530) sum(n11, n2) = all_0_7_7
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n11, n2, all_0_7_7, n13 and discharging atoms sum(n11, n2) = all_0_7_7, sum(n11, n2) = n13, yields:
% 22.32/6.11 | (474) all_0_7_7 = n13
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n0, n13, all_0_4_4, n13 and discharging atoms sum(n0, n13) = all_0_4_4, sum(n0, n13) = n13, yields:
% 22.32/6.11 | (472) all_0_4_4 = n13
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 22.32/6.11 | (844) all_0_1_1 = n2
% 22.32/6.11 |
% 22.32/6.11 | From (474)(472) and (212) follows:
% 22.32/6.11 | (476) sum(n13, n13) = all_0_3_3
% 22.32/6.11 |
% 22.32/6.11 | From (844) and (2342) follows:
% 22.32/6.11 | (2391) sum(n8, n2) = all_0_0_0
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n13, n13, all_0_3_3, n10 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n10, yields:
% 22.32/6.11 | (477) all_0_3_3 = n10
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (74) with n8, n2, all_0_0_0, n10 and discharging atoms sum(n8, n2) = all_0_0_0, sum(n8, n2) = n10, yields:
% 22.32/6.11 | (478) all_0_0_0 = n10
% 22.32/6.11 |
% 22.32/6.11 | Equations (478,477) can reduce 363 to:
% 22.32/6.11 | (461) $false
% 22.32/6.11 |
% 22.32/6.11 |-The branch is then unsatisfiable
% 22.32/6.11 |-Branch two:
% 22.32/6.11 | (997) ~ (all_0_10_10 = n1)
% 22.32/6.11 | (998) all_0_10_10 = n0
% 22.32/6.11 |
% 22.32/6.11 | From (998) and (317) follows:
% 22.32/6.11 | (999) pred(n0) = all_0_6_6
% 22.32/6.11 |
% 22.32/6.11 | From (998) and (146) follows:
% 22.32/6.11 | (1000) succ(n0) = all_0_8_8
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (130) with n0, all_0_6_6, n15 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n15, yields:
% 22.32/6.11 | (1001) all_0_6_6 = n15
% 22.32/6.11 |
% 22.32/6.11 | Instantiating formula (165) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 22.32/6.11 | (1002) all_0_8_8 = n1
% 22.32/6.11 |
% 22.32/6.11 | From (1001)(1002) and (10) follows:
% 22.32/6.12 | (1003) sum(n15, n1) = all_0_1_1
% 22.32/6.12 |
% 22.32/6.12 | From (1001) and (2338) follows:
% 22.32/6.12 | (2546) sum(n15, n13) = all_0_4_4
% 22.32/6.12 |
% 22.32/6.12 | From (1002) and (2340) follows:
% 22.32/6.12 | (2547) sum(n11, n1) = all_0_7_7
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (74) with n15, n13, all_0_4_4, n12 and discharging atoms sum(n15, n13) = all_0_4_4, sum(n15, n13) = n12, yields:
% 22.32/6.12 | (490) all_0_4_4 = n12
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (74) with n15, n1, all_0_1_1, n0 and discharging atoms sum(n15, n1) = all_0_1_1, sum(n15, n1) = n0, yields:
% 22.32/6.12 | (862) all_0_1_1 = n0
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (74) with n11, n1, all_0_7_7, n12 and discharging atoms sum(n11, n1) = all_0_7_7, sum(n11, n1) = n12, yields:
% 22.32/6.12 | (492) all_0_7_7 = n12
% 22.32/6.12 |
% 22.32/6.12 | From (492)(490) and (212) follows:
% 22.32/6.12 | (494) sum(n12, n12) = all_0_3_3
% 22.32/6.12 |
% 22.32/6.12 | From (862) and (2342) follows:
% 22.32/6.12 | (2409) sum(n8, n0) = all_0_0_0
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (74) with n12, n12, all_0_3_3, n8 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n8, yields:
% 22.32/6.12 | (495) all_0_3_3 = n8
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (74) with n8, n0, all_0_0_0, n8 and discharging atoms sum(n8, n0) = all_0_0_0, sum(n8, n0) = n8, yields:
% 22.32/6.12 | (496) all_0_0_0 = n8
% 22.32/6.12 |
% 22.32/6.12 | Equations (496,495) can reduce 363 to:
% 22.32/6.12 | (461) $false
% 22.32/6.12 |
% 22.32/6.12 |-The branch is then unsatisfiable
% 22.32/6.12 |-Branch two:
% 22.32/6.12 | (516) ~ (all_0_11_11 = n12)
% 22.32/6.12 | (517) all_0_11_11 = n11 | all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.12 |
% 22.32/6.12 +-Applying beta-rule and splitting (798), into two cases.
% 22.32/6.12 |-Branch one:
% 22.32/6.12 | (799) all_0_10_10 = n11
% 22.32/6.12 |
% 22.32/6.12 | From (799) and (317) follows:
% 22.32/6.12 | (800) pred(n11) = all_0_6_6
% 22.32/6.12 |
% 22.32/6.12 | From (799) and (146) follows:
% 22.32/6.12 | (801) succ(n11) = all_0_8_8
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (130) with n11, all_0_6_6, n10 and discharging atoms pred(n11) = all_0_6_6, pred(n11) = n10, yields:
% 22.32/6.12 | (802) all_0_6_6 = n10
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (165) with n11, all_0_8_8, n12 and discharging atoms succ(n11) = all_0_8_8, succ(n11) = n12, yields:
% 22.32/6.12 | (803) all_0_8_8 = n12
% 22.32/6.12 |
% 22.32/6.12 | From (802) and (800) follows:
% 22.32/6.12 | (125) pred(n11) = n10
% 22.32/6.12 |
% 22.32/6.12 | From (803) and (801) follows:
% 22.32/6.12 | (299) succ(n11) = n12
% 22.32/6.12 |
% 22.32/6.12 | From (802) and (276) follows:
% 22.32/6.12 | (2565) sum(n10, all_0_5_5) = all_0_4_4
% 22.32/6.12 |
% 22.32/6.12 | From (802)(803) and (10) follows:
% 22.32/6.12 | (804) sum(n10, n12) = all_0_1_1
% 22.32/6.12 |
% 22.32/6.12 | From (803) and (350) follows:
% 22.32/6.12 | (2567) sum(all_0_9_9, n12) = all_0_7_7
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (74) with n10, n12, all_0_1_1, n6 and discharging atoms sum(n10, n12) = all_0_1_1, sum(n10, n12) = n6, yields:
% 22.32/6.12 | (808) all_0_1_1 = n6
% 22.32/6.12 |
% 22.32/6.12 | From (808) and (256) follows:
% 22.32/6.12 | (2569) sum(all_0_2_2, n6) = all_0_0_0
% 22.32/6.12 |
% 22.32/6.12 | From (808) and (804) follows:
% 22.32/6.12 | (138) sum(n10, n12) = n6
% 22.32/6.12 |
% 22.32/6.12 +-Applying beta-rule and splitting (517), into two cases.
% 22.32/6.12 |-Branch one:
% 22.32/6.12 | (518) all_0_11_11 = n11
% 22.32/6.12 |
% 22.32/6.12 | From (518) and (423) follows:
% 22.32/6.12 | (519) pred(n11) = all_0_9_9
% 22.32/6.12 |
% 22.32/6.12 | From (518) and (262) follows:
% 22.32/6.12 | (520) succ(n11) = all_0_5_5
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (130) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 22.32/6.12 | (521) all_0_9_9 = n10
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (165) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 22.32/6.12 | (522) all_0_5_5 = n12
% 22.32/6.12 |
% 22.32/6.12 | From (521)(522) and (147) follows:
% 22.32/6.12 | (523) sum(n10, n12) = all_0_2_2
% 22.32/6.12 |
% 22.32/6.12 | From (521) and (2567) follows:
% 22.32/6.12 | (2577) sum(n10, n12) = all_0_7_7
% 22.32/6.12 |
% 22.32/6.12 | From (522) and (2565) follows:
% 22.32/6.12 | (2578) sum(n10, n12) = all_0_4_4
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (74) with n10, n12, all_0_2_2, n6 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n6, yields:
% 22.32/6.12 | (527) all_0_2_2 = n6
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (74) with n10, n12, all_0_4_4, all_0_2_2 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = all_0_4_4, yields:
% 22.32/6.12 | (448) all_0_2_2 = all_0_4_4
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (74) with n10, n12, all_0_7_7, all_0_2_2 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = all_0_7_7, yields:
% 22.32/6.12 | (449) all_0_2_2 = all_0_7_7
% 22.32/6.12 |
% 22.32/6.12 | Combining equations (449,448) yields a new equation:
% 22.32/6.12 | (450) all_0_4_4 = all_0_7_7
% 22.32/6.12 |
% 22.32/6.12 | Combining equations (527,448) yields a new equation:
% 22.32/6.12 | (598) all_0_4_4 = n6
% 22.32/6.12 |
% 22.32/6.12 | Combining equations (598,450) yields a new equation:
% 22.32/6.12 | (600) all_0_7_7 = n6
% 22.32/6.12 |
% 22.32/6.12 | Combining equations (600,450) yields a new equation:
% 22.32/6.12 | (598) all_0_4_4 = n6
% 22.32/6.12 |
% 22.32/6.12 | Combining equations (598,448) yields a new equation:
% 22.32/6.12 | (527) all_0_2_2 = n6
% 22.32/6.12 |
% 22.32/6.12 | From (527) and (2569) follows:
% 22.32/6.12 | (2587) sum(n6, n6) = all_0_0_0
% 22.32/6.12 |
% 22.32/6.12 | From (600)(598) and (212) follows:
% 22.32/6.12 | (602) sum(n6, n6) = all_0_3_3
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (74) with n6, n6, all_0_0_0, n12 and discharging atoms sum(n6, n6) = all_0_0_0, sum(n6, n6) = n12, yields:
% 22.32/6.12 | (457) all_0_0_0 = n12
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (74) with n6, n6, all_0_3_3, all_0_0_0 and discharging atoms sum(n6, n6) = all_0_0_0, sum(n6, n6) = all_0_3_3, yields:
% 22.32/6.12 | (458) all_0_0_0 = all_0_3_3
% 22.32/6.12 |
% 22.32/6.12 | Combining equations (457,458) yields a new equation:
% 22.32/6.12 | (459) all_0_3_3 = n12
% 22.32/6.12 |
% 22.32/6.12 | Combining equations (459,458) yields a new equation:
% 22.32/6.12 | (457) all_0_0_0 = n12
% 22.32/6.12 |
% 22.32/6.12 | Equations (457,459) can reduce 363 to:
% 22.32/6.12 | (461) $false
% 22.32/6.12 |
% 22.32/6.12 |-The branch is then unsatisfiable
% 22.32/6.12 |-Branch two:
% 22.32/6.12 | (534) ~ (all_0_11_11 = n11)
% 22.32/6.12 | (535) all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.12 |
% 22.32/6.12 +-Applying beta-rule and splitting (535), into two cases.
% 22.32/6.12 |-Branch one:
% 22.32/6.12 | (536) all_0_11_11 = n10
% 22.32/6.12 |
% 22.32/6.12 | From (536) and (423) follows:
% 22.32/6.12 | (537) pred(n10) = all_0_9_9
% 22.32/6.12 |
% 22.32/6.12 | From (536) and (262) follows:
% 22.32/6.12 | (538) succ(n10) = all_0_5_5
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (130) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 22.32/6.12 | (539) all_0_9_9 = n9
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (165) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 22.32/6.12 | (540) all_0_5_5 = n11
% 22.32/6.12 |
% 22.32/6.12 | From (539)(540) and (147) follows:
% 22.32/6.12 | (541) sum(n9, n11) = all_0_2_2
% 22.32/6.12 |
% 22.32/6.12 | From (539) and (2567) follows:
% 22.32/6.12 | (2602) sum(n9, n12) = all_0_7_7
% 22.32/6.12 |
% 22.32/6.12 | From (540) and (2565) follows:
% 22.32/6.12 | (2603) sum(n10, n11) = all_0_4_4
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (74) with n10, n11, all_0_4_4, n5 and discharging atoms sum(n10, n11) = all_0_4_4, sum(n10, n11) = n5, yields:
% 22.32/6.12 | (616) all_0_4_4 = n5
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (74) with n9, n12, all_0_7_7, n5 and discharging atoms sum(n9, n12) = all_0_7_7, sum(n9, n12) = n5, yields:
% 22.32/6.12 | (618) all_0_7_7 = n5
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (74) with n9, n11, all_0_2_2, n4 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n4, yields:
% 22.32/6.12 | (545) all_0_2_2 = n4
% 22.32/6.12 |
% 22.32/6.12 | From (545) and (2569) follows:
% 22.32/6.12 | (2607) sum(n4, n6) = all_0_0_0
% 22.32/6.12 |
% 22.32/6.12 | From (618)(616) and (212) follows:
% 22.32/6.12 | (620) sum(n5, n5) = all_0_3_3
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (74) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 22.32/6.12 | (477) all_0_3_3 = n10
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (74) with n4, n6, all_0_0_0, n10 and discharging atoms sum(n4, n6) = all_0_0_0, sum(n4, n6) = n10, yields:
% 22.32/6.12 | (478) all_0_0_0 = n10
% 22.32/6.12 |
% 22.32/6.12 | Equations (478,477) can reduce 363 to:
% 22.32/6.12 | (461) $false
% 22.32/6.12 |
% 22.32/6.12 |-The branch is then unsatisfiable
% 22.32/6.12 |-Branch two:
% 22.32/6.12 | (552) ~ (all_0_11_11 = n10)
% 22.32/6.12 | (553) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.12 |
% 22.32/6.12 +-Applying beta-rule and splitting (553), into two cases.
% 22.32/6.12 |-Branch one:
% 22.32/6.12 | (554) all_0_11_11 = n9
% 22.32/6.12 |
% 22.32/6.12 | From (554) and (423) follows:
% 22.32/6.12 | (555) pred(n9) = all_0_9_9
% 22.32/6.12 |
% 22.32/6.12 | From (554) and (262) follows:
% 22.32/6.12 | (556) succ(n9) = all_0_5_5
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (130) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 22.32/6.12 | (557) all_0_9_9 = n8
% 22.32/6.12 |
% 22.32/6.12 | Instantiating formula (165) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 22.32/6.12 | (558) all_0_5_5 = n10
% 22.32/6.12 |
% 22.32/6.12 | From (557)(558) and (147) follows:
% 22.32/6.12 | (559) sum(n8, n10) = all_0_2_2
% 22.32/6.12 |
% 22.32/6.12 | From (557) and (2567) follows:
% 22.32/6.13 | (2620) sum(n8, n12) = all_0_7_7
% 22.32/6.13 |
% 22.32/6.13 | From (558) and (2565) follows:
% 22.32/6.13 | (2621) sum(n10, n10) = all_0_4_4
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n10, n10, all_0_4_4, n4 and discharging atoms sum(n10, n10) = all_0_4_4, sum(n10, n10) = n4, yields:
% 22.32/6.13 | (634) all_0_4_4 = n4
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n8, n12, all_0_7_7, n4 and discharging atoms sum(n8, n12) = all_0_7_7, sum(n8, n12) = n4, yields:
% 22.32/6.13 | (636) all_0_7_7 = n4
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n8, n10, all_0_2_2, n2 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n2, yields:
% 22.32/6.13 | (563) all_0_2_2 = n2
% 22.32/6.13 |
% 22.32/6.13 | From (563) and (2569) follows:
% 22.32/6.13 | (2625) sum(n2, n6) = all_0_0_0
% 22.32/6.13 |
% 22.32/6.13 | From (636)(634) and (212) follows:
% 22.32/6.13 | (638) sum(n4, n4) = all_0_3_3
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 22.32/6.13 | (495) all_0_3_3 = n8
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n2, n6, all_0_0_0, n8 and discharging atoms sum(n2, n6) = all_0_0_0, sum(n2, n6) = n8, yields:
% 22.32/6.13 | (496) all_0_0_0 = n8
% 22.32/6.13 |
% 22.32/6.13 | Equations (496,495) can reduce 363 to:
% 22.32/6.13 | (461) $false
% 22.32/6.13 |
% 22.32/6.13 |-The branch is then unsatisfiable
% 22.32/6.13 |-Branch two:
% 22.32/6.13 | (570) ~ (all_0_11_11 = n9)
% 22.32/6.13 | (571) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.13 |
% 22.32/6.13 +-Applying beta-rule and splitting (571), into two cases.
% 22.32/6.13 |-Branch one:
% 22.32/6.13 | (572) all_0_11_11 = n8
% 22.32/6.13 |
% 22.32/6.13 | From (572) and (423) follows:
% 22.32/6.13 | (573) pred(n8) = all_0_9_9
% 22.32/6.13 |
% 22.32/6.13 | From (572) and (262) follows:
% 22.32/6.13 | (574) succ(n8) = all_0_5_5
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (130) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 22.32/6.13 | (575) all_0_9_9 = n7
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (165) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 22.32/6.13 | (576) all_0_5_5 = n9
% 22.32/6.13 |
% 22.32/6.13 | From (575)(576) and (147) follows:
% 22.32/6.13 | (577) sum(n7, n9) = all_0_2_2
% 22.32/6.13 |
% 22.32/6.13 | From (575) and (2567) follows:
% 22.32/6.13 | (2638) sum(n7, n12) = all_0_7_7
% 22.32/6.13 |
% 22.32/6.13 | From (576) and (2565) follows:
% 22.32/6.13 | (2639) sum(n10, n9) = all_0_4_4
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n10, n9, all_0_4_4, n3 and discharging atoms sum(n10, n9) = all_0_4_4, sum(n10, n9) = n3, yields:
% 22.32/6.13 | (652) all_0_4_4 = n3
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n7, n12, all_0_7_7, n3 and discharging atoms sum(n7, n12) = all_0_7_7, sum(n7, n12) = n3, yields:
% 22.32/6.13 | (654) all_0_7_7 = n3
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n7, n9, all_0_2_2, n0 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n0, yields:
% 22.32/6.13 | (581) all_0_2_2 = n0
% 22.32/6.13 |
% 22.32/6.13 | From (581) and (2569) follows:
% 22.32/6.13 | (2643) sum(n0, n6) = all_0_0_0
% 22.32/6.13 |
% 22.32/6.13 | From (654)(652) and (212) follows:
% 22.32/6.13 | (656) sum(n3, n3) = all_0_3_3
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 22.32/6.13 | (513) all_0_3_3 = n6
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n0, n6, all_0_0_0, n6 and discharging atoms sum(n0, n6) = all_0_0_0, sum(n0, n6) = n6, yields:
% 22.32/6.13 | (514) all_0_0_0 = n6
% 22.32/6.13 |
% 22.32/6.13 | Equations (514,513) can reduce 363 to:
% 22.32/6.13 | (461) $false
% 22.32/6.13 |
% 22.32/6.13 |-The branch is then unsatisfiable
% 22.32/6.13 |-Branch two:
% 22.32/6.13 | (588) ~ (all_0_11_11 = n8)
% 22.32/6.13 | (589) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.13 |
% 22.32/6.13 +-Applying beta-rule and splitting (589), into two cases.
% 22.32/6.13 |-Branch one:
% 22.32/6.13 | (590) all_0_11_11 = n7
% 22.32/6.13 |
% 22.32/6.13 | From (590) and (423) follows:
% 22.32/6.13 | (591) pred(n7) = all_0_9_9
% 22.32/6.13 |
% 22.32/6.13 | From (590) and (262) follows:
% 22.32/6.13 | (592) succ(n7) = all_0_5_5
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (130) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 22.32/6.13 | (593) all_0_9_9 = n6
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (165) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 22.32/6.13 | (594) all_0_5_5 = n8
% 22.32/6.13 |
% 22.32/6.13 | From (593)(594) and (147) follows:
% 22.32/6.13 | (595) sum(n6, n8) = all_0_2_2
% 22.32/6.13 |
% 22.32/6.13 | From (593) and (2567) follows:
% 22.32/6.13 | (2656) sum(n6, n12) = all_0_7_7
% 22.32/6.13 |
% 22.32/6.13 | From (594) and (2565) follows:
% 22.32/6.13 | (2657) sum(n10, n8) = all_0_4_4
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n10, n8, all_0_4_4, n2 and discharging atoms sum(n10, n8) = all_0_4_4, sum(n10, n8) = n2, yields:
% 22.32/6.13 | (670) all_0_4_4 = n2
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n6, n12, all_0_7_7, n2 and discharging atoms sum(n6, n12) = all_0_7_7, sum(n6, n12) = n2, yields:
% 22.32/6.13 | (672) all_0_7_7 = n2
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 22.32/6.13 | (447) all_0_2_2 = n14
% 22.32/6.13 |
% 22.32/6.13 | From (447) and (2569) follows:
% 22.32/6.13 | (811) sum(n14, n6) = all_0_0_0
% 22.32/6.13 |
% 22.32/6.13 | From (672)(670) and (212) follows:
% 22.32/6.13 | (674) sum(n2, n2) = all_0_3_3
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n14, n6, all_0_0_0, n4 and discharging atoms sum(n14, n6) = all_0_0_0, sum(n14, n6) = n4, yields:
% 22.32/6.13 | (532) all_0_0_0 = n4
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 22.32/6.13 | (531) all_0_3_3 = n4
% 22.32/6.13 |
% 22.32/6.13 | Equations (532,531) can reduce 363 to:
% 22.32/6.13 | (461) $false
% 22.32/6.13 |
% 22.32/6.13 |-The branch is then unsatisfiable
% 22.32/6.13 |-Branch two:
% 22.32/6.13 | (606) ~ (all_0_11_11 = n7)
% 22.32/6.13 | (607) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.13 |
% 22.32/6.13 +-Applying beta-rule and splitting (607), into two cases.
% 22.32/6.13 |-Branch one:
% 22.32/6.13 | (608) all_0_11_11 = n6
% 22.32/6.13 |
% 22.32/6.13 | From (608) and (423) follows:
% 22.32/6.13 | (609) pred(n6) = all_0_9_9
% 22.32/6.13 |
% 22.32/6.13 | From (608) and (262) follows:
% 22.32/6.13 | (610) succ(n6) = all_0_5_5
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (130) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 22.32/6.13 | (611) all_0_9_9 = n5
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (165) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 22.32/6.13 | (612) all_0_5_5 = n7
% 22.32/6.13 |
% 22.32/6.13 | From (611)(612) and (147) follows:
% 22.32/6.13 | (613) sum(n5, n7) = all_0_2_2
% 22.32/6.13 |
% 22.32/6.13 | From (611) and (2567) follows:
% 22.32/6.13 | (2674) sum(n5, n12) = all_0_7_7
% 22.32/6.13 |
% 22.32/6.13 | From (612) and (2565) follows:
% 22.32/6.13 | (2675) sum(n10, n7) = all_0_4_4
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n10, n7, all_0_4_4, n1 and discharging atoms sum(n10, n7) = all_0_4_4, sum(n10, n7) = n1, yields:
% 22.32/6.13 | (688) all_0_4_4 = n1
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n5, n12, all_0_7_7, n1 and discharging atoms sum(n5, n12) = all_0_7_7, sum(n5, n12) = n1, yields:
% 22.32/6.13 | (690) all_0_7_7 = n1
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 22.32/6.13 | (473) all_0_2_2 = n12
% 22.32/6.13 |
% 22.32/6.13 | From (473) and (2569) follows:
% 22.32/6.13 | (1363) sum(n12, n6) = all_0_0_0
% 22.32/6.13 |
% 22.32/6.13 | From (690)(688) and (212) follows:
% 22.32/6.13 | (692) sum(n1, n1) = all_0_3_3
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n12, n6, all_0_0_0, n2 and discharging atoms sum(n12, n6) = all_0_0_0, sum(n12, n6) = n2, yields:
% 22.32/6.13 | (550) all_0_0_0 = n2
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 22.32/6.13 | (549) all_0_3_3 = n2
% 22.32/6.13 |
% 22.32/6.13 | Equations (550,549) can reduce 363 to:
% 22.32/6.13 | (461) $false
% 22.32/6.13 |
% 22.32/6.13 |-The branch is then unsatisfiable
% 22.32/6.13 |-Branch two:
% 22.32/6.13 | (624) ~ (all_0_11_11 = n6)
% 22.32/6.13 | (625) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.13 |
% 22.32/6.13 +-Applying beta-rule and splitting (625), into two cases.
% 22.32/6.13 |-Branch one:
% 22.32/6.13 | (626) all_0_11_11 = n5
% 22.32/6.13 |
% 22.32/6.13 | From (626) and (423) follows:
% 22.32/6.13 | (627) pred(n5) = all_0_9_9
% 22.32/6.13 |
% 22.32/6.13 | From (626) and (262) follows:
% 22.32/6.13 | (628) succ(n5) = all_0_5_5
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (130) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 22.32/6.13 | (629) all_0_9_9 = n4
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (165) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 22.32/6.13 | (630) all_0_5_5 = n6
% 22.32/6.13 |
% 22.32/6.13 | From (629)(630) and (147) follows:
% 22.32/6.13 | (631) sum(n4, n6) = all_0_2_2
% 22.32/6.13 |
% 22.32/6.13 | From (629) and (2567) follows:
% 22.32/6.13 | (2692) sum(n4, n12) = all_0_7_7
% 22.32/6.13 |
% 22.32/6.13 | From (630) and (2565) follows:
% 22.32/6.13 | (2693) sum(n10, n6) = all_0_4_4
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n10, n6, all_0_4_4, n0 and discharging atoms sum(n10, n6) = all_0_4_4, sum(n10, n6) = n0, yields:
% 22.32/6.13 | (706) all_0_4_4 = n0
% 22.32/6.13 |
% 22.32/6.13 | Instantiating formula (74) with n4, n12, all_0_7_7, n0 and discharging atoms sum(n4, n12) = all_0_7_7, sum(n4, n12) = n0, yields:
% 22.32/6.14 | (708) all_0_7_7 = n0
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 22.32/6.14 | (491) all_0_2_2 = n10
% 22.32/6.14 |
% 22.32/6.14 | From (491) and (2569) follows:
% 22.32/6.14 | (1877) sum(n10, n6) = all_0_0_0
% 22.32/6.14 |
% 22.32/6.14 | From (708)(706) and (212) follows:
% 22.32/6.14 | (710) sum(n0, n0) = all_0_3_3
% 22.32/6.14 |
% 22.32/6.14 | From (706) and (2693) follows:
% 22.32/6.14 | (98) sum(n10, n6) = n0
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n10, n6, all_0_0_0, n0 and discharging atoms sum(n10, n6) = all_0_0_0, sum(n10, n6) = n0, yields:
% 22.32/6.14 | (568) all_0_0_0 = n0
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 22.32/6.14 | (567) all_0_3_3 = n0
% 22.32/6.14 |
% 22.32/6.14 | Equations (568,567) can reduce 363 to:
% 22.32/6.14 | (461) $false
% 22.32/6.14 |
% 22.32/6.14 |-The branch is then unsatisfiable
% 22.32/6.14 |-Branch two:
% 22.32/6.14 | (642) ~ (all_0_11_11 = n5)
% 22.32/6.14 | (643) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.14 |
% 22.32/6.14 +-Applying beta-rule and splitting (643), into two cases.
% 22.32/6.14 |-Branch one:
% 22.32/6.14 | (644) all_0_11_11 = n4
% 22.32/6.14 |
% 22.32/6.14 | From (644) and (423) follows:
% 22.32/6.14 | (645) pred(n4) = all_0_9_9
% 22.32/6.14 |
% 22.32/6.14 | From (644) and (262) follows:
% 22.32/6.14 | (646) succ(n4) = all_0_5_5
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (130) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 22.32/6.14 | (647) all_0_9_9 = n3
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (165) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 22.32/6.14 | (648) all_0_5_5 = n5
% 22.32/6.14 |
% 22.32/6.14 | From (647)(648) and (147) follows:
% 22.32/6.14 | (649) sum(n3, n5) = all_0_2_2
% 22.32/6.14 |
% 22.32/6.14 | From (647) and (2567) follows:
% 22.32/6.14 | (2711) sum(n3, n12) = all_0_7_7
% 22.32/6.14 |
% 22.32/6.14 | From (648) and (2565) follows:
% 22.32/6.14 | (2712) sum(n10, n5) = all_0_4_4
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n10, n5, all_0_4_4, n15 and discharging atoms sum(n10, n5) = all_0_4_4, sum(n10, n5) = n15, yields:
% 22.32/6.14 | (726) all_0_4_4 = n15
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n3, n12, all_0_7_7, n15 and discharging atoms sum(n3, n12) = all_0_7_7, sum(n3, n12) = n15, yields:
% 22.32/6.14 | (725) all_0_7_7 = n15
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 22.32/6.14 | (509) all_0_2_2 = n8
% 22.32/6.14 |
% 22.32/6.14 | From (509) and (2569) follows:
% 22.32/6.14 | (2355) sum(n8, n6) = all_0_0_0
% 22.32/6.14 |
% 22.32/6.14 | From (725)(726) and (212) follows:
% 22.32/6.14 | (728) sum(n15, n15) = all_0_3_3
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n15, n15, all_0_3_3, n14 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n14, yields:
% 22.32/6.14 | (585) all_0_3_3 = n14
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n8, n6, all_0_0_0, n14 and discharging atoms sum(n8, n6) = all_0_0_0, sum(n8, n6) = n14, yields:
% 22.32/6.14 | (586) all_0_0_0 = n14
% 22.32/6.14 |
% 22.32/6.14 | Equations (586,585) can reduce 363 to:
% 22.32/6.14 | (461) $false
% 22.32/6.14 |
% 22.32/6.14 |-The branch is then unsatisfiable
% 22.32/6.14 |-Branch two:
% 22.32/6.14 | (660) ~ (all_0_11_11 = n4)
% 22.32/6.14 | (661) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.14 |
% 22.32/6.14 +-Applying beta-rule and splitting (661), into two cases.
% 22.32/6.14 |-Branch one:
% 22.32/6.14 | (662) all_0_11_11 = n3
% 22.32/6.14 |
% 22.32/6.14 | From (662) and (423) follows:
% 22.32/6.14 | (663) pred(n3) = all_0_9_9
% 22.32/6.14 |
% 22.32/6.14 | From (662) and (262) follows:
% 22.32/6.14 | (664) succ(n3) = all_0_5_5
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (130) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 22.32/6.14 | (665) all_0_9_9 = n2
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (165) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 22.32/6.14 | (666) all_0_5_5 = n4
% 22.32/6.14 |
% 22.32/6.14 | From (665)(666) and (147) follows:
% 22.32/6.14 | (667) sum(n2, n4) = all_0_2_2
% 22.32/6.14 |
% 22.32/6.14 | From (665) and (2567) follows:
% 22.32/6.14 | (2729) sum(n2, n12) = all_0_7_7
% 22.32/6.14 |
% 22.32/6.14 | From (666) and (2565) follows:
% 22.32/6.14 | (2730) sum(n10, n4) = all_0_4_4
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n10, n4, all_0_4_4, n14 and discharging atoms sum(n10, n4) = all_0_4_4, sum(n10, n4) = n14, yields:
% 22.32/6.14 | (451) all_0_4_4 = n14
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n2, n12, all_0_7_7, n14 and discharging atoms sum(n2, n12) = all_0_7_7, sum(n2, n12) = n14, yields:
% 22.32/6.14 | (452) all_0_7_7 = n14
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 22.32/6.14 | (527) all_0_2_2 = n6
% 22.32/6.14 |
% 22.32/6.14 | From (527) and (2569) follows:
% 22.32/6.14 | (2587) sum(n6, n6) = all_0_0_0
% 22.32/6.14 |
% 22.32/6.14 | From (452)(451) and (212) follows:
% 22.32/6.14 | (456) sum(n14, n14) = all_0_3_3
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n14, n14, all_0_3_3, n12 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n12, yields:
% 22.32/6.14 | (459) all_0_3_3 = n12
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n6, n6, all_0_0_0, n12 and discharging atoms sum(n6, n6) = all_0_0_0, sum(n6, n6) = n12, yields:
% 22.32/6.14 | (457) all_0_0_0 = n12
% 22.32/6.14 |
% 22.32/6.14 | Equations (457,459) can reduce 363 to:
% 22.32/6.14 | (461) $false
% 22.32/6.14 |
% 22.32/6.14 |-The branch is then unsatisfiable
% 22.32/6.14 |-Branch two:
% 22.32/6.14 | (678) ~ (all_0_11_11 = n3)
% 22.32/6.14 | (679) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.14 |
% 22.32/6.14 +-Applying beta-rule and splitting (679), into two cases.
% 22.32/6.14 |-Branch one:
% 22.32/6.14 | (680) all_0_11_11 = n2
% 22.32/6.14 |
% 22.32/6.14 | From (680) and (423) follows:
% 22.32/6.14 | (681) pred(n2) = all_0_9_9
% 22.32/6.14 |
% 22.32/6.14 | From (680) and (262) follows:
% 22.32/6.14 | (682) succ(n2) = all_0_5_5
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (130) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 22.32/6.14 | (683) all_0_9_9 = n1
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (165) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 22.32/6.14 | (684) all_0_5_5 = n3
% 22.32/6.14 |
% 22.32/6.14 | From (683)(684) and (147) follows:
% 22.32/6.14 | (685) sum(n1, n3) = all_0_2_2
% 22.32/6.14 |
% 22.32/6.14 | From (683) and (2567) follows:
% 22.32/6.14 | (2747) sum(n1, n12) = all_0_7_7
% 22.32/6.14 |
% 22.32/6.14 | From (684) and (2565) follows:
% 22.32/6.14 | (2748) sum(n10, n3) = all_0_4_4
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n10, n3, all_0_4_4, n13 and discharging atoms sum(n10, n3) = all_0_4_4, sum(n10, n3) = n13, yields:
% 22.32/6.14 | (472) all_0_4_4 = n13
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n1, n12, all_0_7_7, n13 and discharging atoms sum(n1, n12) = all_0_7_7, sum(n1, n12) = n13, yields:
% 22.32/6.14 | (474) all_0_7_7 = n13
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 22.32/6.14 | (545) all_0_2_2 = n4
% 22.32/6.14 |
% 22.32/6.14 | From (545) and (2569) follows:
% 22.32/6.14 | (2607) sum(n4, n6) = all_0_0_0
% 22.32/6.14 |
% 22.32/6.14 | From (474)(472) and (212) follows:
% 22.32/6.14 | (476) sum(n13, n13) = all_0_3_3
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n13, n13, all_0_3_3, n10 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n10, yields:
% 22.32/6.14 | (477) all_0_3_3 = n10
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n4, n6, all_0_0_0, n10 and discharging atoms sum(n4, n6) = all_0_0_0, sum(n4, n6) = n10, yields:
% 22.32/6.14 | (478) all_0_0_0 = n10
% 22.32/6.14 |
% 22.32/6.14 | Equations (478,477) can reduce 363 to:
% 22.32/6.14 | (461) $false
% 22.32/6.14 |
% 22.32/6.14 |-The branch is then unsatisfiable
% 22.32/6.14 |-Branch two:
% 22.32/6.14 | (696) ~ (all_0_11_11 = n2)
% 22.32/6.14 | (697) all_0_11_11 = n1 | all_0_11_11 = n0
% 22.32/6.14 |
% 22.32/6.14 +-Applying beta-rule and splitting (697), into two cases.
% 22.32/6.14 |-Branch one:
% 22.32/6.14 | (698) all_0_11_11 = n1
% 22.32/6.14 |
% 22.32/6.14 | From (698) and (423) follows:
% 22.32/6.14 | (699) pred(n1) = all_0_9_9
% 22.32/6.14 |
% 22.32/6.14 | From (698) and (262) follows:
% 22.32/6.14 | (700) succ(n1) = all_0_5_5
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (130) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 22.32/6.14 | (701) all_0_9_9 = n0
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (165) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 22.32/6.14 | (702) all_0_5_5 = n2
% 22.32/6.14 |
% 22.32/6.14 | From (701)(702) and (147) follows:
% 22.32/6.14 | (703) sum(n0, n2) = all_0_2_2
% 22.32/6.14 |
% 22.32/6.14 | From (701) and (2567) follows:
% 22.32/6.14 | (2765) sum(n0, n12) = all_0_7_7
% 22.32/6.14 |
% 22.32/6.14 | From (702) and (2565) follows:
% 22.32/6.14 | (2766) sum(n10, n2) = all_0_4_4
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n10, n2, all_0_4_4, n12 and discharging atoms sum(n10, n2) = all_0_4_4, sum(n10, n2) = n12, yields:
% 22.32/6.14 | (490) all_0_4_4 = n12
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n0, n12, all_0_7_7, n12 and discharging atoms sum(n0, n12) = all_0_7_7, sum(n0, n12) = n12, yields:
% 22.32/6.14 | (492) all_0_7_7 = n12
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 22.32/6.14 | (563) all_0_2_2 = n2
% 22.32/6.14 |
% 22.32/6.14 | From (563) and (2569) follows:
% 22.32/6.14 | (2625) sum(n2, n6) = all_0_0_0
% 22.32/6.14 |
% 22.32/6.14 | From (492)(490) and (212) follows:
% 22.32/6.14 | (494) sum(n12, n12) = all_0_3_3
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n12, n12, all_0_3_3, n8 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n8, yields:
% 22.32/6.14 | (495) all_0_3_3 = n8
% 22.32/6.14 |
% 22.32/6.14 | Instantiating formula (74) with n2, n6, all_0_0_0, n8 and discharging atoms sum(n2, n6) = all_0_0_0, sum(n2, n6) = n8, yields:
% 22.32/6.15 | (496) all_0_0_0 = n8
% 22.32/6.15 |
% 22.32/6.15 | Equations (496,495) can reduce 363 to:
% 22.32/6.15 | (461) $false
% 22.32/6.15 |
% 22.32/6.15 |-The branch is then unsatisfiable
% 22.32/6.15 |-Branch two:
% 22.32/6.15 | (715) ~ (all_0_11_11 = n1)
% 22.32/6.15 | (716) all_0_11_11 = n0
% 22.32/6.15 |
% 22.32/6.15 | From (716) and (423) follows:
% 22.32/6.15 | (717) pred(n0) = all_0_9_9
% 22.32/6.15 |
% 22.32/6.15 | From (716) and (262) follows:
% 22.32/6.15 | (718) succ(n0) = all_0_5_5
% 22.32/6.15 |
% 22.32/6.15 | Instantiating formula (130) with n0, all_0_9_9, n15 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n15, yields:
% 22.32/6.15 | (719) all_0_9_9 = n15
% 22.32/6.15 |
% 22.32/6.15 | Instantiating formula (165) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 22.32/6.15 | (720) all_0_5_5 = n1
% 22.32/6.15 |
% 22.32/6.15 | From (719)(720) and (147) follows:
% 22.32/6.15 | (721) sum(n15, n1) = all_0_2_2
% 22.32/6.15 |
% 22.32/6.15 | From (719) and (2567) follows:
% 22.32/6.15 | (2782) sum(n15, n12) = all_0_7_7
% 22.32/6.15 |
% 22.32/6.15 | From (720) and (2565) follows:
% 22.32/6.15 | (2783) sum(n10, n1) = all_0_4_4
% 22.32/6.15 |
% 22.32/6.15 | Instantiating formula (74) with n15, n12, all_0_7_7, n11 and discharging atoms sum(n15, n12) = all_0_7_7, sum(n15, n12) = n11, yields:
% 22.32/6.15 | (510) all_0_7_7 = n11
% 22.32/6.15 |
% 22.32/6.15 | Instantiating formula (74) with n15, n1, all_0_2_2, n0 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n0, yields:
% 22.32/6.15 | (581) all_0_2_2 = n0
% 22.32/6.15 |
% 22.32/6.15 | Instantiating formula (74) with n10, n1, all_0_4_4, n11 and discharging atoms sum(n10, n1) = all_0_4_4, sum(n10, n1) = n11, yields:
% 22.32/6.15 | (508) all_0_4_4 = n11
% 22.32/6.15 |
% 22.32/6.15 | From (581) and (2569) follows:
% 22.32/6.15 | (2643) sum(n0, n6) = all_0_0_0
% 22.32/6.15 |
% 22.32/6.15 | From (510)(508) and (212) follows:
% 22.32/6.15 | (512) sum(n11, n11) = all_0_3_3
% 22.32/6.15 |
% 22.32/6.15 | Instantiating formula (74) with n11, n11, all_0_3_3, n6 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n6, yields:
% 22.32/6.15 | (513) all_0_3_3 = n6
% 22.32/6.15 |
% 22.32/6.15 | Instantiating formula (74) with n0, n6, all_0_0_0, n6 and discharging atoms sum(n0, n6) = all_0_0_0, sum(n0, n6) = n6, yields:
% 22.32/6.15 | (514) all_0_0_0 = n6
% 22.32/6.15 |
% 22.32/6.15 | Equations (514,513) can reduce 363 to:
% 22.32/6.15 | (461) $false
% 22.32/6.15 |
% 22.32/6.15 |-The branch is then unsatisfiable
% 22.32/6.15 |-Branch two:
% 22.32/6.15 | (815) ~ (all_0_10_10 = n11)
% 22.32/6.15 | (816) all_0_10_10 = n10 | all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.32/6.15 |
% 22.32/6.15 +-Applying beta-rule and splitting (517), into two cases.
% 22.32/6.15 |-Branch one:
% 22.32/6.15 | (518) all_0_11_11 = n11
% 22.32/6.15 |
% 22.32/6.15 | From (518) and (423) follows:
% 22.32/6.15 | (519) pred(n11) = all_0_9_9
% 22.32/6.15 |
% 22.32/6.15 | From (518) and (262) follows:
% 22.32/6.15 | (520) succ(n11) = all_0_5_5
% 22.32/6.15 |
% 22.32/6.15 | Instantiating formula (130) with n11, all_0_9_9, n10 and discharging atoms pred(n11) = all_0_9_9, pred(n11) = n10, yields:
% 22.32/6.15 | (521) all_0_9_9 = n10
% 22.32/6.15 |
% 22.32/6.15 | Instantiating formula (165) with n11, all_0_5_5, n12 and discharging atoms succ(n11) = all_0_5_5, succ(n11) = n12, yields:
% 22.32/6.15 | (522) all_0_5_5 = n12
% 22.32/6.15 |
% 22.32/6.15 | From (522) and (276) follows:
% 22.32/6.15 | (2799) sum(all_0_6_6, n12) = all_0_4_4
% 22.32/6.15 |
% 22.32/6.15 | From (521)(522) and (147) follows:
% 22.32/6.15 | (523) sum(n10, n12) = all_0_2_2
% 22.32/6.15 |
% 22.32/6.15 | From (521) and (350) follows:
% 22.32/6.15 | (2801) sum(n10, all_0_8_8) = all_0_7_7
% 22.32/6.15 |
% 22.32/6.15 | Instantiating formula (74) with n10, n12, all_0_2_2, n6 and discharging atoms sum(n10, n12) = all_0_2_2, sum(n10, n12) = n6, yields:
% 22.32/6.15 | (527) all_0_2_2 = n6
% 22.32/6.15 |
% 22.32/6.15 | From (527) and (256) follows:
% 22.32/6.15 | (2803) sum(n6, all_0_1_1) = all_0_0_0
% 22.32/6.15 |
% 22.32/6.15 +-Applying beta-rule and splitting (816), into two cases.
% 22.32/6.15 |-Branch one:
% 22.32/6.15 | (817) all_0_10_10 = n10
% 22.32/6.15 |
% 22.32/6.15 | From (817) and (317) follows:
% 22.32/6.15 | (818) pred(n10) = all_0_6_6
% 22.32/6.15 |
% 22.32/6.15 | From (817) and (146) follows:
% 22.32/6.15 | (819) succ(n10) = all_0_8_8
% 22.32/6.15 |
% 22.32/6.15 | Instantiating formula (130) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 22.32/6.15 | (820) all_0_6_6 = n9
% 22.32/6.15 |
% 22.32/6.15 | Instantiating formula (165) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 22.32/6.15 | (821) all_0_8_8 = n11
% 22.32/6.15 |
% 22.32/6.15 | From (820)(821) and (10) follows:
% 22.32/6.15 | (822) sum(n9, n11) = all_0_1_1
% 22.32/6.15 |
% 22.32/6.15 | From (820) and (2799) follows:
% 22.60/6.15 | (2810) sum(n9, n12) = all_0_4_4
% 22.60/6.15 |
% 22.60/6.15 | From (821) and (2801) follows:
% 22.60/6.15 | (2811) sum(n10, n11) = all_0_7_7
% 22.60/6.15 |
% 22.60/6.15 | Instantiating formula (74) with n10, n11, all_0_7_7, n5 and discharging atoms sum(n10, n11) = all_0_7_7, sum(n10, n11) = n5, yields:
% 22.60/6.15 | (618) all_0_7_7 = n5
% 22.60/6.15 |
% 22.60/6.15 | Instantiating formula (74) with n9, n12, all_0_4_4, n5 and discharging atoms sum(n9, n12) = all_0_4_4, sum(n9, n12) = n5, yields:
% 22.60/6.15 | (616) all_0_4_4 = n5
% 22.60/6.15 |
% 22.60/6.15 | Instantiating formula (74) with n9, n11, all_0_1_1, n4 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n4, yields:
% 22.60/6.15 | (826) all_0_1_1 = n4
% 22.60/6.15 |
% 22.60/6.15 | From (618)(616) and (212) follows:
% 22.60/6.15 | (620) sum(n5, n5) = all_0_3_3
% 22.60/6.15 |
% 22.60/6.15 | From (826) and (2803) follows:
% 22.60/6.15 | (2816) sum(n6, n4) = all_0_0_0
% 22.60/6.15 |
% 22.60/6.15 | Instantiating formula (74) with n6, n4, all_0_0_0, n10 and discharging atoms sum(n6, n4) = all_0_0_0, sum(n6, n4) = n10, yields:
% 22.60/6.15 | (478) all_0_0_0 = n10
% 22.60/6.15 |
% 22.60/6.15 | Instantiating formula (74) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 22.60/6.15 | (477) all_0_3_3 = n10
% 22.60/6.15 |
% 22.60/6.15 | Equations (478,477) can reduce 363 to:
% 22.60/6.15 | (461) $false
% 22.60/6.15 |
% 22.60/6.15 |-The branch is then unsatisfiable
% 22.60/6.15 |-Branch two:
% 22.60/6.15 | (833) ~ (all_0_10_10 = n10)
% 22.60/6.15 | (834) all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.60/6.15 |
% 22.60/6.15 +-Applying beta-rule and splitting (834), into two cases.
% 22.60/6.15 |-Branch one:
% 22.60/6.15 | (835) all_0_10_10 = n9
% 22.60/6.15 |
% 22.60/6.15 | From (835) and (317) follows:
% 22.60/6.15 | (836) pred(n9) = all_0_6_6
% 22.60/6.15 |
% 22.60/6.15 | From (835) and (146) follows:
% 22.60/6.15 | (837) succ(n9) = all_0_8_8
% 22.60/6.15 |
% 22.60/6.15 | Instantiating formula (130) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 22.60/6.15 | (838) all_0_6_6 = n8
% 22.60/6.15 |
% 22.60/6.15 | Instantiating formula (165) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 22.60/6.15 | (839) all_0_8_8 = n10
% 22.60/6.15 |
% 22.60/6.15 | From (838)(839) and (10) follows:
% 22.60/6.15 | (840) sum(n8, n10) = all_0_1_1
% 22.60/6.15 |
% 22.60/6.15 | From (838) and (2799) follows:
% 22.60/6.15 | (2828) sum(n8, n12) = all_0_4_4
% 22.60/6.15 |
% 22.60/6.15 | From (839) and (2801) follows:
% 22.60/6.15 | (2829) sum(n10, n10) = all_0_7_7
% 22.60/6.15 |
% 22.60/6.15 | Instantiating formula (74) with n10, n10, all_0_7_7, n4 and discharging atoms sum(n10, n10) = all_0_7_7, sum(n10, n10) = n4, yields:
% 22.60/6.15 | (636) all_0_7_7 = n4
% 22.60/6.15 |
% 22.60/6.15 | Instantiating formula (74) with n8, n12, all_0_4_4, n4 and discharging atoms sum(n8, n12) = all_0_4_4, sum(n8, n12) = n4, yields:
% 22.60/6.15 | (634) all_0_4_4 = n4
% 22.60/6.15 |
% 22.60/6.15 | Instantiating formula (74) with n8, n10, all_0_1_1, n2 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n2, yields:
% 22.60/6.15 | (844) all_0_1_1 = n2
% 22.60/6.15 |
% 22.60/6.15 | From (636)(634) and (212) follows:
% 22.60/6.15 | (638) sum(n4, n4) = all_0_3_3
% 22.60/6.15 |
% 22.60/6.15 | From (844) and (2803) follows:
% 22.60/6.15 | (2834) sum(n6, n2) = all_0_0_0
% 22.60/6.15 |
% 22.60/6.15 | Instantiating formula (74) with n6, n2, all_0_0_0, n8 and discharging atoms sum(n6, n2) = all_0_0_0, sum(n6, n2) = n8, yields:
% 22.60/6.15 | (496) all_0_0_0 = n8
% 22.60/6.15 |
% 22.60/6.15 | Instantiating formula (74) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 22.60/6.15 | (495) all_0_3_3 = n8
% 22.60/6.15 |
% 22.60/6.15 | Equations (496,495) can reduce 363 to:
% 22.60/6.15 | (461) $false
% 22.60/6.15 |
% 22.60/6.15 |-The branch is then unsatisfiable
% 22.60/6.15 |-Branch two:
% 22.60/6.15 | (851) ~ (all_0_10_10 = n9)
% 22.60/6.15 | (852) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.60/6.15 |
% 22.60/6.15 +-Applying beta-rule and splitting (852), into two cases.
% 22.60/6.15 |-Branch one:
% 22.60/6.15 | (853) all_0_10_10 = n8
% 22.60/6.15 |
% 22.60/6.15 | From (853) and (317) follows:
% 22.60/6.15 | (854) pred(n8) = all_0_6_6
% 22.60/6.15 |
% 22.60/6.15 | From (853) and (146) follows:
% 22.60/6.15 | (855) succ(n8) = all_0_8_8
% 22.60/6.15 |
% 22.60/6.15 | Instantiating formula (130) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 22.60/6.15 | (856) all_0_6_6 = n7
% 22.60/6.15 |
% 22.60/6.15 | Instantiating formula (165) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 22.60/6.15 | (857) all_0_8_8 = n9
% 22.60/6.15 |
% 22.60/6.15 | From (856)(857) and (10) follows:
% 22.60/6.15 | (858) sum(n7, n9) = all_0_1_1
% 22.60/6.15 |
% 22.60/6.15 | From (856) and (2799) follows:
% 22.60/6.16 | (2846) sum(n7, n12) = all_0_4_4
% 22.60/6.16 |
% 22.60/6.16 | From (857) and (2801) follows:
% 22.60/6.16 | (2847) sum(n10, n9) = all_0_7_7
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n10, n9, all_0_7_7, n3 and discharging atoms sum(n10, n9) = all_0_7_7, sum(n10, n9) = n3, yields:
% 22.60/6.16 | (654) all_0_7_7 = n3
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n7, n12, all_0_4_4, n3 and discharging atoms sum(n7, n12) = all_0_4_4, sum(n7, n12) = n3, yields:
% 22.60/6.16 | (652) all_0_4_4 = n3
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n7, n9, all_0_1_1, n0 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n0, yields:
% 22.60/6.16 | (862) all_0_1_1 = n0
% 22.60/6.16 |
% 22.60/6.16 | From (654)(652) and (212) follows:
% 22.60/6.16 | (656) sum(n3, n3) = all_0_3_3
% 22.60/6.16 |
% 22.60/6.16 | From (862) and (2803) follows:
% 22.60/6.16 | (2852) sum(n6, n0) = all_0_0_0
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n6, n0, all_0_0_0, n6 and discharging atoms sum(n6, n0) = all_0_0_0, sum(n6, n0) = n6, yields:
% 22.60/6.16 | (514) all_0_0_0 = n6
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 22.60/6.16 | (513) all_0_3_3 = n6
% 22.60/6.16 |
% 22.60/6.16 | Equations (514,513) can reduce 363 to:
% 22.60/6.16 | (461) $false
% 22.60/6.16 |
% 22.60/6.16 |-The branch is then unsatisfiable
% 22.60/6.16 |-Branch two:
% 22.60/6.16 | (869) ~ (all_0_10_10 = n8)
% 22.60/6.16 | (870) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.60/6.16 |
% 22.60/6.16 +-Applying beta-rule and splitting (870), into two cases.
% 22.60/6.16 |-Branch one:
% 22.60/6.16 | (871) all_0_10_10 = n7
% 22.60/6.16 |
% 22.60/6.16 | From (871) and (317) follows:
% 22.60/6.16 | (872) pred(n7) = all_0_6_6
% 22.60/6.16 |
% 22.60/6.16 | From (871) and (146) follows:
% 22.60/6.16 | (873) succ(n7) = all_0_8_8
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (130) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 22.60/6.16 | (874) all_0_6_6 = n6
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (165) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 22.60/6.16 | (875) all_0_8_8 = n8
% 22.60/6.16 |
% 22.60/6.16 | From (874)(875) and (10) follows:
% 22.60/6.16 | (876) sum(n6, n8) = all_0_1_1
% 22.60/6.16 |
% 22.60/6.16 | From (874) and (2799) follows:
% 22.60/6.16 | (2864) sum(n6, n12) = all_0_4_4
% 22.60/6.16 |
% 22.60/6.16 | From (875) and (2801) follows:
% 22.60/6.16 | (2865) sum(n10, n8) = all_0_7_7
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n10, n8, all_0_7_7, n2 and discharging atoms sum(n10, n8) = all_0_7_7, sum(n10, n8) = n2, yields:
% 22.60/6.16 | (672) all_0_7_7 = n2
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n6, n12, all_0_4_4, n2 and discharging atoms sum(n6, n12) = all_0_4_4, sum(n6, n12) = n2, yields:
% 22.60/6.16 | (670) all_0_4_4 = n2
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 22.60/6.16 | (436) all_0_1_1 = n14
% 22.60/6.16 |
% 22.60/6.16 | From (672)(670) and (212) follows:
% 22.60/6.16 | (674) sum(n2, n2) = all_0_3_3
% 22.60/6.16 |
% 22.60/6.16 | From (436) and (2803) follows:
% 22.60/6.16 | (529) sum(n6, n14) = all_0_0_0
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n6, n14, all_0_0_0, n4 and discharging atoms sum(n6, n14) = all_0_0_0, sum(n6, n14) = n4, yields:
% 22.60/6.16 | (532) all_0_0_0 = n4
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 22.60/6.16 | (531) all_0_3_3 = n4
% 22.60/6.16 |
% 22.60/6.16 | Equations (532,531) can reduce 363 to:
% 22.60/6.16 | (461) $false
% 22.60/6.16 |
% 22.60/6.16 |-The branch is then unsatisfiable
% 22.60/6.16 |-Branch two:
% 22.60/6.16 | (887) ~ (all_0_10_10 = n7)
% 22.60/6.16 | (888) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.60/6.16 |
% 22.60/6.16 +-Applying beta-rule and splitting (888), into two cases.
% 22.60/6.16 |-Branch one:
% 22.60/6.16 | (889) all_0_10_10 = n6
% 22.60/6.16 |
% 22.60/6.16 | From (889) and (317) follows:
% 22.60/6.16 | (890) pred(n6) = all_0_6_6
% 22.60/6.16 |
% 22.60/6.16 | From (889) and (146) follows:
% 22.60/6.16 | (891) succ(n6) = all_0_8_8
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (130) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 22.60/6.16 | (892) all_0_6_6 = n5
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (165) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 22.60/6.16 | (893) all_0_8_8 = n7
% 22.60/6.16 |
% 22.60/6.16 | From (892)(893) and (10) follows:
% 22.60/6.16 | (894) sum(n5, n7) = all_0_1_1
% 22.60/6.16 |
% 22.60/6.16 | From (892) and (2799) follows:
% 22.60/6.16 | (2882) sum(n5, n12) = all_0_4_4
% 22.60/6.16 |
% 22.60/6.16 | From (893) and (2801) follows:
% 22.60/6.16 | (2883) sum(n10, n7) = all_0_7_7
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n10, n7, all_0_7_7, n1 and discharging atoms sum(n10, n7) = all_0_7_7, sum(n10, n7) = n1, yields:
% 22.60/6.16 | (690) all_0_7_7 = n1
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n5, n12, all_0_4_4, n1 and discharging atoms sum(n5, n12) = all_0_4_4, sum(n5, n12) = n1, yields:
% 22.60/6.16 | (688) all_0_4_4 = n1
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 22.60/6.16 | (754) all_0_1_1 = n12
% 22.60/6.16 |
% 22.60/6.16 | From (690)(688) and (212) follows:
% 22.60/6.16 | (692) sum(n1, n1) = all_0_3_3
% 22.60/6.16 |
% 22.60/6.16 | From (754) and (2803) follows:
% 22.60/6.16 | (1101) sum(n6, n12) = all_0_0_0
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n6, n12, all_0_0_0, n2 and discharging atoms sum(n6, n12) = all_0_0_0, sum(n6, n12) = n2, yields:
% 22.60/6.16 | (550) all_0_0_0 = n2
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 22.60/6.16 | (549) all_0_3_3 = n2
% 22.60/6.16 |
% 22.60/6.16 | Equations (550,549) can reduce 363 to:
% 22.60/6.16 | (461) $false
% 22.60/6.16 |
% 22.60/6.16 |-The branch is then unsatisfiable
% 22.60/6.16 |-Branch two:
% 22.60/6.16 | (905) ~ (all_0_10_10 = n6)
% 22.60/6.16 | (906) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.60/6.16 |
% 22.60/6.16 +-Applying beta-rule and splitting (906), into two cases.
% 22.60/6.16 |-Branch one:
% 22.60/6.16 | (907) all_0_10_10 = n5
% 22.60/6.16 |
% 22.60/6.16 | From (907) and (317) follows:
% 22.60/6.16 | (908) pred(n5) = all_0_6_6
% 22.60/6.16 |
% 22.60/6.16 | From (907) and (146) follows:
% 22.60/6.16 | (909) succ(n5) = all_0_8_8
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (130) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 22.60/6.16 | (910) all_0_6_6 = n4
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (165) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 22.60/6.16 | (911) all_0_8_8 = n6
% 22.60/6.16 |
% 22.60/6.16 | From (910)(911) and (10) follows:
% 22.60/6.16 | (912) sum(n4, n6) = all_0_1_1
% 22.60/6.16 |
% 22.60/6.16 | From (910) and (2799) follows:
% 22.60/6.16 | (2900) sum(n4, n12) = all_0_4_4
% 22.60/6.16 |
% 22.60/6.16 | From (911) and (2801) follows:
% 22.60/6.16 | (2901) sum(n10, n6) = all_0_7_7
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n10, n6, all_0_7_7, n0 and discharging atoms sum(n10, n6) = all_0_7_7, sum(n10, n6) = n0, yields:
% 22.60/6.16 | (708) all_0_7_7 = n0
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n4, n12, all_0_4_4, n0 and discharging atoms sum(n4, n12) = all_0_4_4, sum(n4, n12) = n0, yields:
% 22.60/6.16 | (706) all_0_4_4 = n0
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 22.60/6.16 | (772) all_0_1_1 = n10
% 22.60/6.16 |
% 22.60/6.16 | From (708)(706) and (212) follows:
% 22.60/6.16 | (710) sum(n0, n0) = all_0_3_3
% 22.60/6.16 |
% 22.60/6.16 | From (772) and (2803) follows:
% 22.60/6.16 | (1633) sum(n6, n10) = all_0_0_0
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n6, n10, all_0_0_0, n0 and discharging atoms sum(n6, n10) = all_0_0_0, sum(n6, n10) = n0, yields:
% 22.60/6.16 | (568) all_0_0_0 = n0
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (74) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 22.60/6.16 | (567) all_0_3_3 = n0
% 22.60/6.16 |
% 22.60/6.16 | Equations (568,567) can reduce 363 to:
% 22.60/6.16 | (461) $false
% 22.60/6.16 |
% 22.60/6.16 |-The branch is then unsatisfiable
% 22.60/6.16 |-Branch two:
% 22.60/6.16 | (923) ~ (all_0_10_10 = n5)
% 22.60/6.16 | (924) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.60/6.16 |
% 22.60/6.16 +-Applying beta-rule and splitting (924), into two cases.
% 22.60/6.16 |-Branch one:
% 22.60/6.16 | (925) all_0_10_10 = n4
% 22.60/6.16 |
% 22.60/6.16 | From (925) and (317) follows:
% 22.60/6.16 | (926) pred(n4) = all_0_6_6
% 22.60/6.16 |
% 22.60/6.16 | From (925) and (146) follows:
% 22.60/6.16 | (927) succ(n4) = all_0_8_8
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (130) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 22.60/6.16 | (928) all_0_6_6 = n3
% 22.60/6.16 |
% 22.60/6.16 | Instantiating formula (165) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 22.60/6.17 | (929) all_0_8_8 = n5
% 22.60/6.17 |
% 22.60/6.17 | From (928)(929) and (10) follows:
% 22.60/6.17 | (930) sum(n3, n5) = all_0_1_1
% 22.60/6.17 |
% 22.60/6.17 | From (928) and (2799) follows:
% 22.60/6.17 | (2918) sum(n3, n12) = all_0_4_4
% 22.60/6.17 |
% 22.60/6.17 | From (929) and (2801) follows:
% 22.60/6.17 | (2919) sum(n10, n5) = all_0_7_7
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n10, n5, all_0_7_7, n15 and discharging atoms sum(n10, n5) = all_0_7_7, sum(n10, n5) = n15, yields:
% 22.60/6.17 | (725) all_0_7_7 = n15
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n3, n12, all_0_4_4, n15 and discharging atoms sum(n3, n12) = all_0_4_4, sum(n3, n12) = n15, yields:
% 22.60/6.17 | (726) all_0_4_4 = n15
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 22.60/6.17 | (790) all_0_1_1 = n8
% 22.60/6.17 |
% 22.60/6.17 | From (725)(726) and (212) follows:
% 22.60/6.17 | (728) sum(n15, n15) = all_0_3_3
% 22.60/6.17 |
% 22.60/6.17 | From (790) and (2803) follows:
% 22.60/6.17 | (2129) sum(n6, n8) = all_0_0_0
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n15, n15, all_0_3_3, n14 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n14, yields:
% 22.60/6.17 | (585) all_0_3_3 = n14
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n6, n8, all_0_0_0, n14 and discharging atoms sum(n6, n8) = all_0_0_0, sum(n6, n8) = n14, yields:
% 22.60/6.17 | (586) all_0_0_0 = n14
% 22.60/6.17 |
% 22.60/6.17 | Equations (586,585) can reduce 363 to:
% 22.60/6.17 | (461) $false
% 22.60/6.17 |
% 22.60/6.17 |-The branch is then unsatisfiable
% 22.60/6.17 |-Branch two:
% 22.60/6.17 | (941) ~ (all_0_10_10 = n4)
% 22.60/6.17 | (942) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.60/6.17 |
% 22.60/6.17 +-Applying beta-rule and splitting (942), into two cases.
% 22.60/6.17 |-Branch one:
% 22.60/6.17 | (943) all_0_10_10 = n3
% 22.60/6.17 |
% 22.60/6.17 | From (943) and (317) follows:
% 22.60/6.17 | (944) pred(n3) = all_0_6_6
% 22.60/6.17 |
% 22.60/6.17 | From (943) and (146) follows:
% 22.60/6.17 | (945) succ(n3) = all_0_8_8
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (130) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 22.60/6.17 | (946) all_0_6_6 = n2
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (165) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 22.60/6.17 | (947) all_0_8_8 = n4
% 22.60/6.17 |
% 22.60/6.17 | From (946)(947) and (10) follows:
% 22.60/6.17 | (948) sum(n2, n4) = all_0_1_1
% 22.60/6.17 |
% 22.60/6.17 | From (946) and (2799) follows:
% 22.60/6.17 | (2936) sum(n2, n12) = all_0_4_4
% 22.60/6.17 |
% 22.60/6.17 | From (947) and (2801) follows:
% 22.60/6.17 | (2937) sum(n10, n4) = all_0_7_7
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n10, n4, all_0_7_7, n14 and discharging atoms sum(n10, n4) = all_0_7_7, sum(n10, n4) = n14, yields:
% 22.60/6.17 | (452) all_0_7_7 = n14
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n2, n12, all_0_4_4, n14 and discharging atoms sum(n2, n12) = all_0_4_4, sum(n2, n12) = n14, yields:
% 22.60/6.17 | (451) all_0_4_4 = n14
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 22.60/6.17 | (808) all_0_1_1 = n6
% 22.60/6.17 |
% 22.60/6.17 | From (452)(451) and (212) follows:
% 22.60/6.17 | (456) sum(n14, n14) = all_0_3_3
% 22.60/6.17 |
% 22.60/6.17 | From (808) and (2803) follows:
% 22.60/6.17 | (2587) sum(n6, n6) = all_0_0_0
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n14, n14, all_0_3_3, n12 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n12, yields:
% 22.60/6.17 | (459) all_0_3_3 = n12
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n6, n6, all_0_0_0, n12 and discharging atoms sum(n6, n6) = all_0_0_0, sum(n6, n6) = n12, yields:
% 22.60/6.17 | (457) all_0_0_0 = n12
% 22.60/6.17 |
% 22.60/6.17 | Equations (457,459) can reduce 363 to:
% 22.60/6.17 | (461) $false
% 22.60/6.17 |
% 22.60/6.17 |-The branch is then unsatisfiable
% 22.60/6.17 |-Branch two:
% 22.60/6.17 | (959) ~ (all_0_10_10 = n3)
% 22.60/6.17 | (960) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.60/6.17 |
% 22.60/6.17 +-Applying beta-rule and splitting (960), into two cases.
% 22.60/6.17 |-Branch one:
% 22.60/6.17 | (961) all_0_10_10 = n2
% 22.60/6.17 |
% 22.60/6.17 | From (961) and (317) follows:
% 22.60/6.17 | (962) pred(n2) = all_0_6_6
% 22.60/6.17 |
% 22.60/6.17 | From (961) and (146) follows:
% 22.60/6.17 | (963) succ(n2) = all_0_8_8
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (130) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 22.60/6.17 | (964) all_0_6_6 = n1
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (165) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 22.60/6.17 | (965) all_0_8_8 = n3
% 22.60/6.17 |
% 22.60/6.17 | From (964)(965) and (10) follows:
% 22.60/6.17 | (966) sum(n1, n3) = all_0_1_1
% 22.60/6.17 |
% 22.60/6.17 | From (964) and (2799) follows:
% 22.60/6.17 | (2954) sum(n1, n12) = all_0_4_4
% 22.60/6.17 |
% 22.60/6.17 | From (965) and (2801) follows:
% 22.60/6.17 | (2955) sum(n10, n3) = all_0_7_7
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n10, n3, all_0_7_7, n13 and discharging atoms sum(n10, n3) = all_0_7_7, sum(n10, n3) = n13, yields:
% 22.60/6.17 | (474) all_0_7_7 = n13
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n1, n12, all_0_4_4, n13 and discharging atoms sum(n1, n12) = all_0_4_4, sum(n1, n12) = n13, yields:
% 22.60/6.17 | (472) all_0_4_4 = n13
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 22.60/6.17 | (826) all_0_1_1 = n4
% 22.60/6.17 |
% 22.60/6.17 | From (474)(472) and (212) follows:
% 22.60/6.17 | (476) sum(n13, n13) = all_0_3_3
% 22.60/6.17 |
% 22.60/6.17 | From (826) and (2803) follows:
% 22.60/6.17 | (2816) sum(n6, n4) = all_0_0_0
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n13, n13, all_0_3_3, n10 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n10, yields:
% 22.60/6.17 | (477) all_0_3_3 = n10
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n6, n4, all_0_0_0, n10 and discharging atoms sum(n6, n4) = all_0_0_0, sum(n6, n4) = n10, yields:
% 22.60/6.17 | (478) all_0_0_0 = n10
% 22.60/6.17 |
% 22.60/6.17 | Equations (478,477) can reduce 363 to:
% 22.60/6.17 | (461) $false
% 22.60/6.17 |
% 22.60/6.17 |-The branch is then unsatisfiable
% 22.60/6.17 |-Branch two:
% 22.60/6.17 | (977) ~ (all_0_10_10 = n2)
% 22.60/6.17 | (978) all_0_10_10 = n1 | all_0_10_10 = n0
% 22.60/6.17 |
% 22.60/6.17 +-Applying beta-rule and splitting (978), into two cases.
% 22.60/6.17 |-Branch one:
% 22.60/6.17 | (979) all_0_10_10 = n1
% 22.60/6.17 |
% 22.60/6.17 | From (979) and (317) follows:
% 22.60/6.17 | (980) pred(n1) = all_0_6_6
% 22.60/6.17 |
% 22.60/6.17 | From (979) and (146) follows:
% 22.60/6.17 | (981) succ(n1) = all_0_8_8
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (130) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 22.60/6.17 | (982) all_0_6_6 = n0
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (165) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 22.60/6.17 | (983) all_0_8_8 = n2
% 22.60/6.17 |
% 22.60/6.17 | From (982)(983) and (10) follows:
% 22.60/6.17 | (984) sum(n0, n2) = all_0_1_1
% 22.60/6.17 |
% 22.60/6.17 | From (982) and (2799) follows:
% 22.60/6.17 | (2972) sum(n0, n12) = all_0_4_4
% 22.60/6.17 |
% 22.60/6.17 | From (983) and (2801) follows:
% 22.60/6.17 | (2973) sum(n10, n2) = all_0_7_7
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n10, n2, all_0_7_7, n12 and discharging atoms sum(n10, n2) = all_0_7_7, sum(n10, n2) = n12, yields:
% 22.60/6.17 | (492) all_0_7_7 = n12
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n0, n12, all_0_4_4, n12 and discharging atoms sum(n0, n12) = all_0_4_4, sum(n0, n12) = n12, yields:
% 22.60/6.17 | (490) all_0_4_4 = n12
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 22.60/6.17 | (844) all_0_1_1 = n2
% 22.60/6.17 |
% 22.60/6.17 | From (492)(490) and (212) follows:
% 22.60/6.17 | (494) sum(n12, n12) = all_0_3_3
% 22.60/6.17 |
% 22.60/6.17 | From (844) and (2803) follows:
% 22.60/6.17 | (2834) sum(n6, n2) = all_0_0_0
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n12, n12, all_0_3_3, n8 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n8, yields:
% 22.60/6.17 | (495) all_0_3_3 = n8
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (74) with n6, n2, all_0_0_0, n8 and discharging atoms sum(n6, n2) = all_0_0_0, sum(n6, n2) = n8, yields:
% 22.60/6.17 | (496) all_0_0_0 = n8
% 22.60/6.17 |
% 22.60/6.17 | Equations (496,495) can reduce 363 to:
% 22.60/6.17 | (461) $false
% 22.60/6.17 |
% 22.60/6.17 |-The branch is then unsatisfiable
% 22.60/6.17 |-Branch two:
% 22.60/6.17 | (997) ~ (all_0_10_10 = n1)
% 22.60/6.17 | (998) all_0_10_10 = n0
% 22.60/6.17 |
% 22.60/6.17 | From (998) and (317) follows:
% 22.60/6.17 | (999) pred(n0) = all_0_6_6
% 22.60/6.17 |
% 22.60/6.17 | From (998) and (146) follows:
% 22.60/6.17 | (1000) succ(n0) = all_0_8_8
% 22.60/6.17 |
% 22.60/6.17 | Instantiating formula (130) with n0, all_0_6_6, n15 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n15, yields:
% 22.60/6.18 | (1001) all_0_6_6 = n15
% 22.60/6.18 |
% 22.60/6.18 | Instantiating formula (165) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 22.60/6.18 | (1002) all_0_8_8 = n1
% 22.60/6.18 |
% 22.60/6.18 | From (1001)(1002) and (10) follows:
% 22.60/6.18 | (1003) sum(n15, n1) = all_0_1_1
% 22.60/6.18 |
% 22.60/6.18 | From (1001) and (2799) follows:
% 22.60/6.18 | (2989) sum(n15, n12) = all_0_4_4
% 22.60/6.18 |
% 22.60/6.18 | From (1002) and (2801) follows:
% 22.60/6.18 | (2990) sum(n10, n1) = all_0_7_7
% 22.60/6.18 |
% 22.60/6.18 | Instantiating formula (74) with n15, n12, all_0_4_4, n11 and discharging atoms sum(n15, n12) = all_0_4_4, sum(n15, n12) = n11, yields:
% 22.60/6.18 | (508) all_0_4_4 = n11
% 22.60/6.18 |
% 22.60/6.18 | Instantiating formula (74) with n15, n1, all_0_1_1, n0 and discharging atoms sum(n15, n1) = all_0_1_1, sum(n15, n1) = n0, yields:
% 22.60/6.18 | (862) all_0_1_1 = n0
% 22.60/6.18 |
% 22.60/6.18 | Instantiating formula (74) with n10, n1, all_0_7_7, n11 and discharging atoms sum(n10, n1) = all_0_7_7, sum(n10, n1) = n11, yields:
% 22.60/6.18 | (510) all_0_7_7 = n11
% 22.60/6.18 |
% 22.60/6.18 | From (510)(508) and (212) follows:
% 22.60/6.18 | (512) sum(n11, n11) = all_0_3_3
% 22.60/6.18 |
% 22.60/6.18 | From (862) and (2803) follows:
% 22.60/6.18 | (2852) sum(n6, n0) = all_0_0_0
% 22.60/6.18 |
% 22.60/6.18 | Instantiating formula (74) with n11, n11, all_0_3_3, n6 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n6, yields:
% 22.60/6.18 | (513) all_0_3_3 = n6
% 22.60/6.18 |
% 22.60/6.18 | Instantiating formula (74) with n6, n0, all_0_0_0, n6 and discharging atoms sum(n6, n0) = all_0_0_0, sum(n6, n0) = n6, yields:
% 22.60/6.18 | (514) all_0_0_0 = n6
% 22.60/6.18 |
% 22.60/6.18 | Equations (514,513) can reduce 363 to:
% 22.60/6.18 | (461) $false
% 22.60/6.18 |
% 22.60/6.18 |-The branch is then unsatisfiable
% 22.60/6.18 |-Branch two:
% 22.69/6.18 | (534) ~ (all_0_11_11 = n11)
% 22.69/6.18 | (535) all_0_11_11 = n10 | all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.69/6.18 |
% 22.69/6.18 +-Applying beta-rule and splitting (816), into two cases.
% 22.69/6.18 |-Branch one:
% 22.69/6.18 | (817) all_0_10_10 = n10
% 22.69/6.18 |
% 22.69/6.18 | From (817) and (317) follows:
% 22.69/6.18 | (818) pred(n10) = all_0_6_6
% 22.69/6.18 |
% 22.69/6.18 | From (817) and (146) follows:
% 22.69/6.18 | (819) succ(n10) = all_0_8_8
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (130) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 22.69/6.18 | (820) all_0_6_6 = n9
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (165) with n10, all_0_8_8, n11 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n11, yields:
% 22.69/6.18 | (821) all_0_8_8 = n11
% 22.69/6.18 |
% 22.69/6.18 | From (820) and (818) follows:
% 22.69/6.18 | (174) pred(n10) = n9
% 22.69/6.18 |
% 22.69/6.18 | From (821) and (819) follows:
% 22.69/6.18 | (28) succ(n10) = n11
% 22.69/6.18 |
% 22.69/6.18 | From (820) and (276) follows:
% 22.69/6.18 | (3008) sum(n9, all_0_5_5) = all_0_4_4
% 22.69/6.18 |
% 22.69/6.18 | From (820)(821) and (10) follows:
% 22.69/6.18 | (822) sum(n9, n11) = all_0_1_1
% 22.69/6.18 |
% 22.69/6.18 | From (821) and (350) follows:
% 22.69/6.18 | (3010) sum(all_0_9_9, n11) = all_0_7_7
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (74) with n9, n11, all_0_1_1, n4 and discharging atoms sum(n9, n11) = all_0_1_1, sum(n9, n11) = n4, yields:
% 22.69/6.18 | (826) all_0_1_1 = n4
% 22.69/6.18 |
% 22.69/6.18 | From (826) and (256) follows:
% 22.69/6.18 | (3012) sum(all_0_2_2, n4) = all_0_0_0
% 22.69/6.18 |
% 22.69/6.18 | From (826) and (822) follows:
% 22.69/6.18 | (19) sum(n9, n11) = n4
% 22.69/6.18 |
% 22.69/6.18 +-Applying beta-rule and splitting (535), into two cases.
% 22.69/6.18 |-Branch one:
% 22.69/6.18 | (536) all_0_11_11 = n10
% 22.69/6.18 |
% 22.69/6.18 | From (536) and (423) follows:
% 22.69/6.18 | (537) pred(n10) = all_0_9_9
% 22.69/6.18 |
% 22.69/6.18 | From (536) and (262) follows:
% 22.69/6.18 | (538) succ(n10) = all_0_5_5
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (130) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 22.69/6.18 | (539) all_0_9_9 = n9
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (165) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 22.69/6.18 | (540) all_0_5_5 = n11
% 22.69/6.18 |
% 22.69/6.18 | From (539)(540) and (147) follows:
% 22.69/6.18 | (541) sum(n9, n11) = all_0_2_2
% 22.69/6.18 |
% 22.69/6.18 | From (539) and (3010) follows:
% 22.69/6.18 | (3020) sum(n9, n11) = all_0_7_7
% 22.69/6.18 |
% 22.69/6.18 | From (540) and (3008) follows:
% 22.69/6.18 | (3021) sum(n9, n11) = all_0_4_4
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (74) with n9, n11, all_0_2_2, n4 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n4, yields:
% 22.69/6.18 | (545) all_0_2_2 = n4
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (74) with n9, n11, all_0_4_4, all_0_2_2 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = all_0_4_4, yields:
% 22.69/6.18 | (448) all_0_2_2 = all_0_4_4
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (74) with n9, n11, all_0_7_7, all_0_2_2 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = all_0_7_7, yields:
% 22.69/6.18 | (449) all_0_2_2 = all_0_7_7
% 22.69/6.18 |
% 22.69/6.18 | Combining equations (449,448) yields a new equation:
% 22.69/6.18 | (450) all_0_4_4 = all_0_7_7
% 22.69/6.18 |
% 22.69/6.18 | Combining equations (545,448) yields a new equation:
% 22.69/6.18 | (634) all_0_4_4 = n4
% 22.69/6.18 |
% 22.69/6.18 | Combining equations (634,450) yields a new equation:
% 22.69/6.18 | (636) all_0_7_7 = n4
% 22.69/6.18 |
% 22.69/6.18 | Combining equations (636,450) yields a new equation:
% 22.69/6.18 | (634) all_0_4_4 = n4
% 22.69/6.18 |
% 22.69/6.18 | Combining equations (634,448) yields a new equation:
% 22.69/6.18 | (545) all_0_2_2 = n4
% 22.69/6.18 |
% 22.69/6.18 | From (545) and (3012) follows:
% 22.69/6.18 | (3030) sum(n4, n4) = all_0_0_0
% 22.69/6.18 |
% 22.69/6.18 | From (636)(634) and (212) follows:
% 22.69/6.18 | (638) sum(n4, n4) = all_0_3_3
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (74) with n4, n4, all_0_0_0, n8 and discharging atoms sum(n4, n4) = all_0_0_0, sum(n4, n4) = n8, yields:
% 22.69/6.18 | (496) all_0_0_0 = n8
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (74) with n4, n4, all_0_3_3, all_0_0_0 and discharging atoms sum(n4, n4) = all_0_0_0, sum(n4, n4) = all_0_3_3, yields:
% 22.69/6.18 | (458) all_0_0_0 = all_0_3_3
% 22.69/6.18 |
% 22.69/6.18 | Combining equations (496,458) yields a new equation:
% 22.69/6.18 | (495) all_0_3_3 = n8
% 22.69/6.18 |
% 22.69/6.18 | Combining equations (495,458) yields a new equation:
% 22.69/6.18 | (496) all_0_0_0 = n8
% 22.69/6.18 |
% 22.69/6.18 | Equations (496,495) can reduce 363 to:
% 22.69/6.18 | (461) $false
% 22.69/6.18 |
% 22.69/6.18 |-The branch is then unsatisfiable
% 22.69/6.18 |-Branch two:
% 22.69/6.18 | (552) ~ (all_0_11_11 = n10)
% 22.69/6.18 | (553) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.69/6.18 |
% 22.69/6.18 +-Applying beta-rule and splitting (553), into two cases.
% 22.69/6.18 |-Branch one:
% 22.69/6.18 | (554) all_0_11_11 = n9
% 22.69/6.18 |
% 22.69/6.18 | From (554) and (423) follows:
% 22.69/6.18 | (555) pred(n9) = all_0_9_9
% 22.69/6.18 |
% 22.69/6.18 | From (554) and (262) follows:
% 22.69/6.18 | (556) succ(n9) = all_0_5_5
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (130) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 22.69/6.18 | (557) all_0_9_9 = n8
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (165) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 22.69/6.18 | (558) all_0_5_5 = n10
% 22.69/6.18 |
% 22.69/6.18 | From (557)(558) and (147) follows:
% 22.69/6.18 | (559) sum(n8, n10) = all_0_2_2
% 22.69/6.18 |
% 22.69/6.18 | From (557) and (3010) follows:
% 22.69/6.18 | (3045) sum(n8, n11) = all_0_7_7
% 22.69/6.18 |
% 22.69/6.18 | From (558) and (3008) follows:
% 22.69/6.18 | (3046) sum(n9, n10) = all_0_4_4
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (74) with n9, n10, all_0_4_4, n3 and discharging atoms sum(n9, n10) = all_0_4_4, sum(n9, n10) = n3, yields:
% 22.69/6.18 | (652) all_0_4_4 = n3
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (74) with n8, n11, all_0_7_7, n3 and discharging atoms sum(n8, n11) = all_0_7_7, sum(n8, n11) = n3, yields:
% 22.69/6.18 | (654) all_0_7_7 = n3
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (74) with n8, n10, all_0_2_2, n2 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n2, yields:
% 22.69/6.18 | (563) all_0_2_2 = n2
% 22.69/6.18 |
% 22.69/6.18 | From (563) and (3012) follows:
% 22.69/6.18 | (3050) sum(n2, n4) = all_0_0_0
% 22.69/6.18 |
% 22.69/6.18 | From (654)(652) and (212) follows:
% 22.69/6.18 | (656) sum(n3, n3) = all_0_3_3
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (74) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 22.69/6.18 | (513) all_0_3_3 = n6
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (74) with n2, n4, all_0_0_0, n6 and discharging atoms sum(n2, n4) = all_0_0_0, sum(n2, n4) = n6, yields:
% 22.69/6.18 | (514) all_0_0_0 = n6
% 22.69/6.18 |
% 22.69/6.18 | Equations (514,513) can reduce 363 to:
% 22.69/6.18 | (461) $false
% 22.69/6.18 |
% 22.69/6.18 |-The branch is then unsatisfiable
% 22.69/6.18 |-Branch two:
% 22.69/6.18 | (570) ~ (all_0_11_11 = n9)
% 22.69/6.18 | (571) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.69/6.18 |
% 22.69/6.18 +-Applying beta-rule and splitting (571), into two cases.
% 22.69/6.18 |-Branch one:
% 22.69/6.18 | (572) all_0_11_11 = n8
% 22.69/6.18 |
% 22.69/6.18 | From (572) and (423) follows:
% 22.69/6.18 | (573) pred(n8) = all_0_9_9
% 22.69/6.18 |
% 22.69/6.18 | From (572) and (262) follows:
% 22.69/6.18 | (574) succ(n8) = all_0_5_5
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (130) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 22.69/6.18 | (575) all_0_9_9 = n7
% 22.69/6.18 |
% 22.69/6.18 | Instantiating formula (165) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 22.69/6.18 | (576) all_0_5_5 = n9
% 22.69/6.18 |
% 22.69/6.18 | From (575)(576) and (147) follows:
% 22.69/6.18 | (577) sum(n7, n9) = all_0_2_2
% 22.69/6.18 |
% 22.69/6.18 | From (575) and (3010) follows:
% 22.69/6.19 | (3063) sum(n7, n11) = all_0_7_7
% 22.69/6.19 |
% 22.69/6.19 | From (576) and (3008) follows:
% 22.69/6.19 | (3064) sum(n9, n9) = all_0_4_4
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n9, n9, all_0_4_4, n2 and discharging atoms sum(n9, n9) = all_0_4_4, sum(n9, n9) = n2, yields:
% 22.69/6.19 | (670) all_0_4_4 = n2
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n7, n11, all_0_7_7, n2 and discharging atoms sum(n7, n11) = all_0_7_7, sum(n7, n11) = n2, yields:
% 22.69/6.19 | (672) all_0_7_7 = n2
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n7, n9, all_0_2_2, n0 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n0, yields:
% 22.69/6.19 | (581) all_0_2_2 = n0
% 22.69/6.19 |
% 22.69/6.19 | From (581) and (3012) follows:
% 22.69/6.19 | (3068) sum(n0, n4) = all_0_0_0
% 22.69/6.19 |
% 22.69/6.19 | From (672)(670) and (212) follows:
% 22.69/6.19 | (674) sum(n2, n2) = all_0_3_3
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 22.69/6.19 | (531) all_0_3_3 = n4
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n0, n4, all_0_0_0, n4 and discharging atoms sum(n0, n4) = all_0_0_0, sum(n0, n4) = n4, yields:
% 22.69/6.19 | (532) all_0_0_0 = n4
% 22.69/6.19 |
% 22.69/6.19 | Equations (532,531) can reduce 363 to:
% 22.69/6.19 | (461) $false
% 22.69/6.19 |
% 22.69/6.19 |-The branch is then unsatisfiable
% 22.69/6.19 |-Branch two:
% 22.69/6.19 | (588) ~ (all_0_11_11 = n8)
% 22.69/6.19 | (589) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.69/6.19 |
% 22.69/6.19 +-Applying beta-rule and splitting (589), into two cases.
% 22.69/6.19 |-Branch one:
% 22.69/6.19 | (590) all_0_11_11 = n7
% 22.69/6.19 |
% 22.69/6.19 | From (590) and (423) follows:
% 22.69/6.19 | (591) pred(n7) = all_0_9_9
% 22.69/6.19 |
% 22.69/6.19 | From (590) and (262) follows:
% 22.69/6.19 | (592) succ(n7) = all_0_5_5
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (130) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 22.69/6.19 | (593) all_0_9_9 = n6
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (165) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 22.69/6.19 | (594) all_0_5_5 = n8
% 22.69/6.19 |
% 22.69/6.19 | From (593)(594) and (147) follows:
% 22.69/6.19 | (595) sum(n6, n8) = all_0_2_2
% 22.69/6.19 |
% 22.69/6.19 | From (593) and (3010) follows:
% 22.69/6.19 | (3081) sum(n6, n11) = all_0_7_7
% 22.69/6.19 |
% 22.69/6.19 | From (594) and (3008) follows:
% 22.69/6.19 | (3082) sum(n9, n8) = all_0_4_4
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n9, n8, all_0_4_4, n1 and discharging atoms sum(n9, n8) = all_0_4_4, sum(n9, n8) = n1, yields:
% 22.69/6.19 | (688) all_0_4_4 = n1
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n6, n11, all_0_7_7, n1 and discharging atoms sum(n6, n11) = all_0_7_7, sum(n6, n11) = n1, yields:
% 22.69/6.19 | (690) all_0_7_7 = n1
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 22.69/6.19 | (447) all_0_2_2 = n14
% 22.69/6.19 |
% 22.69/6.19 | From (447) and (3012) follows:
% 22.69/6.19 | (829) sum(n14, n4) = all_0_0_0
% 22.69/6.19 |
% 22.69/6.19 | From (690)(688) and (212) follows:
% 22.69/6.19 | (692) sum(n1, n1) = all_0_3_3
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n14, n4, all_0_0_0, n2 and discharging atoms sum(n14, n4) = all_0_0_0, sum(n14, n4) = n2, yields:
% 22.69/6.19 | (550) all_0_0_0 = n2
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 22.69/6.19 | (549) all_0_3_3 = n2
% 22.69/6.19 |
% 22.69/6.19 | Equations (550,549) can reduce 363 to:
% 22.69/6.19 | (461) $false
% 22.69/6.19 |
% 22.69/6.19 |-The branch is then unsatisfiable
% 22.69/6.19 |-Branch two:
% 22.69/6.19 | (606) ~ (all_0_11_11 = n7)
% 22.69/6.19 | (607) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.69/6.19 |
% 22.69/6.19 +-Applying beta-rule and splitting (607), into two cases.
% 22.69/6.19 |-Branch one:
% 22.69/6.19 | (608) all_0_11_11 = n6
% 22.69/6.19 |
% 22.69/6.19 | From (608) and (423) follows:
% 22.69/6.19 | (609) pred(n6) = all_0_9_9
% 22.69/6.19 |
% 22.69/6.19 | From (608) and (262) follows:
% 22.69/6.19 | (610) succ(n6) = all_0_5_5
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (130) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 22.69/6.19 | (611) all_0_9_9 = n5
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (165) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 22.69/6.19 | (612) all_0_5_5 = n7
% 22.69/6.19 |
% 22.69/6.19 | From (611)(612) and (147) follows:
% 22.69/6.19 | (613) sum(n5, n7) = all_0_2_2
% 22.69/6.19 |
% 22.69/6.19 | From (611) and (3010) follows:
% 22.69/6.19 | (3099) sum(n5, n11) = all_0_7_7
% 22.69/6.19 |
% 22.69/6.19 | From (612) and (3008) follows:
% 22.69/6.19 | (3100) sum(n9, n7) = all_0_4_4
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n9, n7, all_0_4_4, n0 and discharging atoms sum(n9, n7) = all_0_4_4, sum(n9, n7) = n0, yields:
% 22.69/6.19 | (706) all_0_4_4 = n0
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n5, n11, all_0_7_7, n0 and discharging atoms sum(n5, n11) = all_0_7_7, sum(n5, n11) = n0, yields:
% 22.69/6.19 | (708) all_0_7_7 = n0
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 22.69/6.19 | (473) all_0_2_2 = n12
% 22.69/6.19 |
% 22.69/6.19 | From (473) and (3012) follows:
% 22.69/6.19 | (1381) sum(n12, n4) = all_0_0_0
% 22.69/6.19 |
% 22.69/6.19 | From (708)(706) and (212) follows:
% 22.69/6.19 | (710) sum(n0, n0) = all_0_3_3
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n12, n4, all_0_0_0, n0 and discharging atoms sum(n12, n4) = all_0_0_0, sum(n12, n4) = n0, yields:
% 22.69/6.19 | (568) all_0_0_0 = n0
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 22.69/6.19 | (567) all_0_3_3 = n0
% 22.69/6.19 |
% 22.69/6.19 | Equations (568,567) can reduce 363 to:
% 22.69/6.19 | (461) $false
% 22.69/6.19 |
% 22.69/6.19 |-The branch is then unsatisfiable
% 22.69/6.19 |-Branch two:
% 22.69/6.19 | (624) ~ (all_0_11_11 = n6)
% 22.69/6.19 | (625) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.69/6.19 |
% 22.69/6.19 +-Applying beta-rule and splitting (625), into two cases.
% 22.69/6.19 |-Branch one:
% 22.69/6.19 | (626) all_0_11_11 = n5
% 22.69/6.19 |
% 22.69/6.19 | From (626) and (423) follows:
% 22.69/6.19 | (627) pred(n5) = all_0_9_9
% 22.69/6.19 |
% 22.69/6.19 | From (626) and (262) follows:
% 22.69/6.19 | (628) succ(n5) = all_0_5_5
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (130) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 22.69/6.19 | (629) all_0_9_9 = n4
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (165) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 22.69/6.19 | (630) all_0_5_5 = n6
% 22.69/6.19 |
% 22.69/6.19 | From (629)(630) and (147) follows:
% 22.69/6.19 | (631) sum(n4, n6) = all_0_2_2
% 22.69/6.19 |
% 22.69/6.19 | From (629) and (3010) follows:
% 22.69/6.19 | (3117) sum(n4, n11) = all_0_7_7
% 22.69/6.19 |
% 22.69/6.19 | From (630) and (3008) follows:
% 22.69/6.19 | (3118) sum(n9, n6) = all_0_4_4
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n9, n6, all_0_4_4, n15 and discharging atoms sum(n9, n6) = all_0_4_4, sum(n9, n6) = n15, yields:
% 22.69/6.19 | (726) all_0_4_4 = n15
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n4, n11, all_0_7_7, n15 and discharging atoms sum(n4, n11) = all_0_7_7, sum(n4, n11) = n15, yields:
% 22.69/6.19 | (725) all_0_7_7 = n15
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 22.69/6.19 | (491) all_0_2_2 = n10
% 22.69/6.19 |
% 22.69/6.19 | From (491) and (3012) follows:
% 22.69/6.19 | (1895) sum(n10, n4) = all_0_0_0
% 22.69/6.19 |
% 22.69/6.19 | From (725)(726) and (212) follows:
% 22.69/6.19 | (728) sum(n15, n15) = all_0_3_3
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n15, n15, all_0_3_3, n14 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n14, yields:
% 22.69/6.19 | (585) all_0_3_3 = n14
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (74) with n10, n4, all_0_0_0, n14 and discharging atoms sum(n10, n4) = all_0_0_0, sum(n10, n4) = n14, yields:
% 22.69/6.19 | (586) all_0_0_0 = n14
% 22.69/6.19 |
% 22.69/6.19 | Equations (586,585) can reduce 363 to:
% 22.69/6.19 | (461) $false
% 22.69/6.19 |
% 22.69/6.19 |-The branch is then unsatisfiable
% 22.69/6.19 |-Branch two:
% 22.69/6.19 | (642) ~ (all_0_11_11 = n5)
% 22.69/6.19 | (643) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.69/6.19 |
% 22.69/6.19 +-Applying beta-rule and splitting (643), into two cases.
% 22.69/6.19 |-Branch one:
% 22.69/6.19 | (644) all_0_11_11 = n4
% 22.69/6.19 |
% 22.69/6.19 | From (644) and (423) follows:
% 22.69/6.19 | (645) pred(n4) = all_0_9_9
% 22.69/6.19 |
% 22.69/6.19 | From (644) and (262) follows:
% 22.69/6.19 | (646) succ(n4) = all_0_5_5
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (130) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 22.69/6.19 | (647) all_0_9_9 = n3
% 22.69/6.19 |
% 22.69/6.19 | Instantiating formula (165) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 22.69/6.19 | (648) all_0_5_5 = n5
% 22.69/6.19 |
% 22.69/6.19 | From (647)(648) and (147) follows:
% 22.69/6.19 | (649) sum(n3, n5) = all_0_2_2
% 22.69/6.19 |
% 22.69/6.19 | From (647) and (3010) follows:
% 22.69/6.19 | (3135) sum(n3, n11) = all_0_7_7
% 22.69/6.19 |
% 22.69/6.19 | From (648) and (3008) follows:
% 22.69/6.20 | (3136) sum(n9, n5) = all_0_4_4
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n9, n5, all_0_4_4, n14 and discharging atoms sum(n9, n5) = all_0_4_4, sum(n9, n5) = n14, yields:
% 22.69/6.20 | (451) all_0_4_4 = n14
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n3, n11, all_0_7_7, n14 and discharging atoms sum(n3, n11) = all_0_7_7, sum(n3, n11) = n14, yields:
% 22.69/6.20 | (452) all_0_7_7 = n14
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 22.69/6.20 | (509) all_0_2_2 = n8
% 22.69/6.20 |
% 22.69/6.20 | From (509) and (3012) follows:
% 22.69/6.20 | (2373) sum(n8, n4) = all_0_0_0
% 22.69/6.20 |
% 22.69/6.20 | From (452)(451) and (212) follows:
% 22.69/6.20 | (456) sum(n14, n14) = all_0_3_3
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n14, n14, all_0_3_3, n12 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n12, yields:
% 22.69/6.20 | (459) all_0_3_3 = n12
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n8, n4, all_0_0_0, n12 and discharging atoms sum(n8, n4) = all_0_0_0, sum(n8, n4) = n12, yields:
% 22.69/6.20 | (457) all_0_0_0 = n12
% 22.69/6.20 |
% 22.69/6.20 | Equations (457,459) can reduce 363 to:
% 22.69/6.20 | (461) $false
% 22.69/6.20 |
% 22.69/6.20 |-The branch is then unsatisfiable
% 22.69/6.20 |-Branch two:
% 22.69/6.20 | (660) ~ (all_0_11_11 = n4)
% 22.69/6.20 | (661) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.69/6.20 |
% 22.69/6.20 +-Applying beta-rule and splitting (661), into two cases.
% 22.69/6.20 |-Branch one:
% 22.69/6.20 | (662) all_0_11_11 = n3
% 22.69/6.20 |
% 22.69/6.20 | From (662) and (423) follows:
% 22.69/6.20 | (663) pred(n3) = all_0_9_9
% 22.69/6.20 |
% 22.69/6.20 | From (662) and (262) follows:
% 22.69/6.20 | (664) succ(n3) = all_0_5_5
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (130) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 22.69/6.20 | (665) all_0_9_9 = n2
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (165) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 22.69/6.20 | (666) all_0_5_5 = n4
% 22.69/6.20 |
% 22.69/6.20 | From (665)(666) and (147) follows:
% 22.69/6.20 | (667) sum(n2, n4) = all_0_2_2
% 22.69/6.20 |
% 22.69/6.20 | From (665) and (3010) follows:
% 22.69/6.20 | (3153) sum(n2, n11) = all_0_7_7
% 22.69/6.20 |
% 22.69/6.20 | From (666) and (3008) follows:
% 22.69/6.20 | (3154) sum(n9, n4) = all_0_4_4
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n9, n4, all_0_4_4, n13 and discharging atoms sum(n9, n4) = all_0_4_4, sum(n9, n4) = n13, yields:
% 22.69/6.20 | (472) all_0_4_4 = n13
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n2, n11, all_0_7_7, n13 and discharging atoms sum(n2, n11) = all_0_7_7, sum(n2, n11) = n13, yields:
% 22.69/6.20 | (474) all_0_7_7 = n13
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 22.69/6.20 | (527) all_0_2_2 = n6
% 22.69/6.20 |
% 22.69/6.20 | From (527) and (3012) follows:
% 22.69/6.20 | (2816) sum(n6, n4) = all_0_0_0
% 22.69/6.20 |
% 22.69/6.20 | From (474)(472) and (212) follows:
% 22.69/6.20 | (476) sum(n13, n13) = all_0_3_3
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n13, n13, all_0_3_3, n10 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n10, yields:
% 22.69/6.20 | (477) all_0_3_3 = n10
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n6, n4, all_0_0_0, n10 and discharging atoms sum(n6, n4) = all_0_0_0, sum(n6, n4) = n10, yields:
% 22.69/6.20 | (478) all_0_0_0 = n10
% 22.69/6.20 |
% 22.69/6.20 | Equations (478,477) can reduce 363 to:
% 22.69/6.20 | (461) $false
% 22.69/6.20 |
% 22.69/6.20 |-The branch is then unsatisfiable
% 22.69/6.20 |-Branch two:
% 22.69/6.20 | (678) ~ (all_0_11_11 = n3)
% 22.69/6.20 | (679) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.69/6.20 |
% 22.69/6.20 +-Applying beta-rule and splitting (679), into two cases.
% 22.69/6.20 |-Branch one:
% 22.69/6.20 | (680) all_0_11_11 = n2
% 22.69/6.20 |
% 22.69/6.20 | From (680) and (423) follows:
% 22.69/6.20 | (681) pred(n2) = all_0_9_9
% 22.69/6.20 |
% 22.69/6.20 | From (680) and (262) follows:
% 22.69/6.20 | (682) succ(n2) = all_0_5_5
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (130) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 22.69/6.20 | (683) all_0_9_9 = n1
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (165) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 22.69/6.20 | (684) all_0_5_5 = n3
% 22.69/6.20 |
% 22.69/6.20 | From (683)(684) and (147) follows:
% 22.69/6.20 | (685) sum(n1, n3) = all_0_2_2
% 22.69/6.20 |
% 22.69/6.20 | From (683) and (3010) follows:
% 22.69/6.20 | (3171) sum(n1, n11) = all_0_7_7
% 22.69/6.20 |
% 22.69/6.20 | From (684) and (3008) follows:
% 22.69/6.20 | (3172) sum(n9, n3) = all_0_4_4
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n9, n3, all_0_4_4, n12 and discharging atoms sum(n9, n3) = all_0_4_4, sum(n9, n3) = n12, yields:
% 22.69/6.20 | (490) all_0_4_4 = n12
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n1, n11, all_0_7_7, n12 and discharging atoms sum(n1, n11) = all_0_7_7, sum(n1, n11) = n12, yields:
% 22.69/6.20 | (492) all_0_7_7 = n12
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 22.69/6.20 | (545) all_0_2_2 = n4
% 22.69/6.20 |
% 22.69/6.20 | From (545) and (3012) follows:
% 22.69/6.20 | (3030) sum(n4, n4) = all_0_0_0
% 22.69/6.20 |
% 22.69/6.20 | From (492)(490) and (212) follows:
% 22.69/6.20 | (494) sum(n12, n12) = all_0_3_3
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n12, n12, all_0_3_3, n8 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n8, yields:
% 22.69/6.20 | (495) all_0_3_3 = n8
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n4, n4, all_0_0_0, n8 and discharging atoms sum(n4, n4) = all_0_0_0, sum(n4, n4) = n8, yields:
% 22.69/6.20 | (496) all_0_0_0 = n8
% 22.69/6.20 |
% 22.69/6.20 | Equations (496,495) can reduce 363 to:
% 22.69/6.20 | (461) $false
% 22.69/6.20 |
% 22.69/6.20 |-The branch is then unsatisfiable
% 22.69/6.20 |-Branch two:
% 22.69/6.20 | (696) ~ (all_0_11_11 = n2)
% 22.69/6.20 | (697) all_0_11_11 = n1 | all_0_11_11 = n0
% 22.69/6.20 |
% 22.69/6.20 +-Applying beta-rule and splitting (697), into two cases.
% 22.69/6.20 |-Branch one:
% 22.69/6.20 | (698) all_0_11_11 = n1
% 22.69/6.20 |
% 22.69/6.20 | From (698) and (423) follows:
% 22.69/6.20 | (699) pred(n1) = all_0_9_9
% 22.69/6.20 |
% 22.69/6.20 | From (698) and (262) follows:
% 22.69/6.20 | (700) succ(n1) = all_0_5_5
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (130) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 22.69/6.20 | (701) all_0_9_9 = n0
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (165) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 22.69/6.20 | (702) all_0_5_5 = n2
% 22.69/6.20 |
% 22.69/6.20 | From (701)(702) and (147) follows:
% 22.69/6.20 | (703) sum(n0, n2) = all_0_2_2
% 22.69/6.20 |
% 22.69/6.20 | From (701) and (3010) follows:
% 22.69/6.20 | (3189) sum(n0, n11) = all_0_7_7
% 22.69/6.20 |
% 22.69/6.20 | From (702) and (3008) follows:
% 22.69/6.20 | (3190) sum(n9, n2) = all_0_4_4
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n9, n2, all_0_4_4, n11 and discharging atoms sum(n9, n2) = all_0_4_4, sum(n9, n2) = n11, yields:
% 22.69/6.20 | (508) all_0_4_4 = n11
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n0, n11, all_0_7_7, n11 and discharging atoms sum(n0, n11) = all_0_7_7, sum(n0, n11) = n11, yields:
% 22.69/6.20 | (510) all_0_7_7 = n11
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 22.69/6.20 | (563) all_0_2_2 = n2
% 22.69/6.20 |
% 22.69/6.20 | From (563) and (3012) follows:
% 22.69/6.20 | (3050) sum(n2, n4) = all_0_0_0
% 22.69/6.20 |
% 22.69/6.20 | From (510)(508) and (212) follows:
% 22.69/6.20 | (512) sum(n11, n11) = all_0_3_3
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n11, n11, all_0_3_3, n6 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n6, yields:
% 22.69/6.20 | (513) all_0_3_3 = n6
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n2, n4, all_0_0_0, n6 and discharging atoms sum(n2, n4) = all_0_0_0, sum(n2, n4) = n6, yields:
% 22.69/6.20 | (514) all_0_0_0 = n6
% 22.69/6.20 |
% 22.69/6.20 | Equations (514,513) can reduce 363 to:
% 22.69/6.20 | (461) $false
% 22.69/6.20 |
% 22.69/6.20 |-The branch is then unsatisfiable
% 22.69/6.20 |-Branch two:
% 22.69/6.20 | (715) ~ (all_0_11_11 = n1)
% 22.69/6.20 | (716) all_0_11_11 = n0
% 22.69/6.20 |
% 22.69/6.20 | From (716) and (423) follows:
% 22.69/6.20 | (717) pred(n0) = all_0_9_9
% 22.69/6.20 |
% 22.69/6.20 | From (716) and (262) follows:
% 22.69/6.20 | (718) succ(n0) = all_0_5_5
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (130) with n0, all_0_9_9, n15 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n15, yields:
% 22.69/6.20 | (719) all_0_9_9 = n15
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (165) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 22.69/6.20 | (720) all_0_5_5 = n1
% 22.69/6.20 |
% 22.69/6.20 | From (719)(720) and (147) follows:
% 22.69/6.20 | (721) sum(n15, n1) = all_0_2_2
% 22.69/6.20 |
% 22.69/6.20 | From (719) and (3010) follows:
% 22.69/6.20 | (3206) sum(n15, n11) = all_0_7_7
% 22.69/6.20 |
% 22.69/6.20 | From (720) and (3008) follows:
% 22.69/6.20 | (3207) sum(n9, n1) = all_0_4_4
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n15, n11, all_0_7_7, n10 and discharging atoms sum(n15, n11) = all_0_7_7, sum(n15, n11) = n10, yields:
% 22.69/6.20 | (528) all_0_7_7 = n10
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n15, n1, all_0_2_2, n0 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n0, yields:
% 22.69/6.20 | (581) all_0_2_2 = n0
% 22.69/6.20 |
% 22.69/6.20 | Instantiating formula (74) with n9, n1, all_0_4_4, n10 and discharging atoms sum(n9, n1) = all_0_4_4, sum(n9, n1) = n10, yields:
% 22.69/6.20 | (526) all_0_4_4 = n10
% 22.69/6.20 |
% 22.69/6.20 | From (581) and (3012) follows:
% 22.69/6.21 | (3068) sum(n0, n4) = all_0_0_0
% 22.69/6.21 |
% 22.69/6.21 | From (528)(526) and (212) follows:
% 22.69/6.21 | (530) sum(n10, n10) = all_0_3_3
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n10, n10, all_0_3_3, n4 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n4, yields:
% 22.69/6.21 | (531) all_0_3_3 = n4
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n0, n4, all_0_0_0, n4 and discharging atoms sum(n0, n4) = all_0_0_0, sum(n0, n4) = n4, yields:
% 22.69/6.21 | (532) all_0_0_0 = n4
% 22.69/6.21 |
% 22.69/6.21 | Equations (532,531) can reduce 363 to:
% 22.69/6.21 | (461) $false
% 22.69/6.21 |
% 22.69/6.21 |-The branch is then unsatisfiable
% 22.69/6.21 |-Branch two:
% 22.69/6.21 | (833) ~ (all_0_10_10 = n10)
% 22.69/6.21 | (834) all_0_10_10 = n9 | all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.69/6.21 |
% 22.69/6.21 +-Applying beta-rule and splitting (535), into two cases.
% 22.69/6.21 |-Branch one:
% 22.69/6.21 | (536) all_0_11_11 = n10
% 22.69/6.21 |
% 22.69/6.21 | From (536) and (423) follows:
% 22.69/6.21 | (537) pred(n10) = all_0_9_9
% 22.69/6.21 |
% 22.69/6.21 | From (536) and (262) follows:
% 22.69/6.21 | (538) succ(n10) = all_0_5_5
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (130) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 22.69/6.21 | (539) all_0_9_9 = n9
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (165) with n10, all_0_5_5, n11 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n11, yields:
% 22.69/6.21 | (540) all_0_5_5 = n11
% 22.69/6.21 |
% 22.69/6.21 | From (540) and (276) follows:
% 22.69/6.21 | (3223) sum(all_0_6_6, n11) = all_0_4_4
% 22.69/6.21 |
% 22.69/6.21 | From (539)(540) and (147) follows:
% 22.69/6.21 | (541) sum(n9, n11) = all_0_2_2
% 22.69/6.21 |
% 22.69/6.21 | From (539) and (350) follows:
% 22.69/6.21 | (3225) sum(n9, all_0_8_8) = all_0_7_7
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n9, n11, all_0_2_2, n4 and discharging atoms sum(n9, n11) = all_0_2_2, sum(n9, n11) = n4, yields:
% 22.69/6.21 | (545) all_0_2_2 = n4
% 22.69/6.21 |
% 22.69/6.21 | From (545) and (256) follows:
% 22.69/6.21 | (3227) sum(n4, all_0_1_1) = all_0_0_0
% 22.69/6.21 |
% 22.69/6.21 +-Applying beta-rule and splitting (834), into two cases.
% 22.69/6.21 |-Branch one:
% 22.69/6.21 | (835) all_0_10_10 = n9
% 22.69/6.21 |
% 22.69/6.21 | From (835) and (317) follows:
% 22.69/6.21 | (836) pred(n9) = all_0_6_6
% 22.69/6.21 |
% 22.69/6.21 | From (835) and (146) follows:
% 22.69/6.21 | (837) succ(n9) = all_0_8_8
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (130) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 22.69/6.21 | (838) all_0_6_6 = n8
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (165) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 22.69/6.21 | (839) all_0_8_8 = n10
% 22.69/6.21 |
% 22.69/6.21 | From (838)(839) and (10) follows:
% 22.69/6.21 | (840) sum(n8, n10) = all_0_1_1
% 22.69/6.21 |
% 22.69/6.21 | From (838) and (3223) follows:
% 22.69/6.21 | (3234) sum(n8, n11) = all_0_4_4
% 22.69/6.21 |
% 22.69/6.21 | From (839) and (3225) follows:
% 22.69/6.21 | (3235) sum(n9, n10) = all_0_7_7
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n9, n10, all_0_7_7, n3 and discharging atoms sum(n9, n10) = all_0_7_7, sum(n9, n10) = n3, yields:
% 22.69/6.21 | (654) all_0_7_7 = n3
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n8, n11, all_0_4_4, n3 and discharging atoms sum(n8, n11) = all_0_4_4, sum(n8, n11) = n3, yields:
% 22.69/6.21 | (652) all_0_4_4 = n3
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n8, n10, all_0_1_1, n2 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n2, yields:
% 22.69/6.21 | (844) all_0_1_1 = n2
% 22.69/6.21 |
% 22.69/6.21 | From (654)(652) and (212) follows:
% 22.69/6.21 | (656) sum(n3, n3) = all_0_3_3
% 22.69/6.21 |
% 22.69/6.21 | From (844) and (3227) follows:
% 22.69/6.21 | (3240) sum(n4, n2) = all_0_0_0
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n4, n2, all_0_0_0, n6 and discharging atoms sum(n4, n2) = all_0_0_0, sum(n4, n2) = n6, yields:
% 22.69/6.21 | (514) all_0_0_0 = n6
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 22.69/6.21 | (513) all_0_3_3 = n6
% 22.69/6.21 |
% 22.69/6.21 | Equations (514,513) can reduce 363 to:
% 22.69/6.21 | (461) $false
% 22.69/6.21 |
% 22.69/6.21 |-The branch is then unsatisfiable
% 22.69/6.21 |-Branch two:
% 22.69/6.21 | (851) ~ (all_0_10_10 = n9)
% 22.69/6.21 | (852) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.69/6.21 |
% 22.69/6.21 +-Applying beta-rule and splitting (852), into two cases.
% 22.69/6.21 |-Branch one:
% 22.69/6.21 | (853) all_0_10_10 = n8
% 22.69/6.21 |
% 22.69/6.21 | From (853) and (317) follows:
% 22.69/6.21 | (854) pred(n8) = all_0_6_6
% 22.69/6.21 |
% 22.69/6.21 | From (853) and (146) follows:
% 22.69/6.21 | (855) succ(n8) = all_0_8_8
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (130) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 22.69/6.21 | (856) all_0_6_6 = n7
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (165) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 22.69/6.21 | (857) all_0_8_8 = n9
% 22.69/6.21 |
% 22.69/6.21 | From (856)(857) and (10) follows:
% 22.69/6.21 | (858) sum(n7, n9) = all_0_1_1
% 22.69/6.21 |
% 22.69/6.21 | From (856) and (3223) follows:
% 22.69/6.21 | (3252) sum(n7, n11) = all_0_4_4
% 22.69/6.21 |
% 22.69/6.21 | From (857) and (3225) follows:
% 22.69/6.21 | (3253) sum(n9, n9) = all_0_7_7
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n9, n9, all_0_7_7, n2 and discharging atoms sum(n9, n9) = all_0_7_7, sum(n9, n9) = n2, yields:
% 22.69/6.21 | (672) all_0_7_7 = n2
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n7, n11, all_0_4_4, n2 and discharging atoms sum(n7, n11) = all_0_4_4, sum(n7, n11) = n2, yields:
% 22.69/6.21 | (670) all_0_4_4 = n2
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n7, n9, all_0_1_1, n0 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n0, yields:
% 22.69/6.21 | (862) all_0_1_1 = n0
% 22.69/6.21 |
% 22.69/6.21 | From (672)(670) and (212) follows:
% 22.69/6.21 | (674) sum(n2, n2) = all_0_3_3
% 22.69/6.21 |
% 22.69/6.21 | From (862) and (3227) follows:
% 22.69/6.21 | (3258) sum(n4, n0) = all_0_0_0
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n4, n0, all_0_0_0, n4 and discharging atoms sum(n4, n0) = all_0_0_0, sum(n4, n0) = n4, yields:
% 22.69/6.21 | (532) all_0_0_0 = n4
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 22.69/6.21 | (531) all_0_3_3 = n4
% 22.69/6.21 |
% 22.69/6.21 | Equations (532,531) can reduce 363 to:
% 22.69/6.21 | (461) $false
% 22.69/6.21 |
% 22.69/6.21 |-The branch is then unsatisfiable
% 22.69/6.21 |-Branch two:
% 22.69/6.21 | (869) ~ (all_0_10_10 = n8)
% 22.69/6.21 | (870) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.69/6.21 |
% 22.69/6.21 +-Applying beta-rule and splitting (870), into two cases.
% 22.69/6.21 |-Branch one:
% 22.69/6.21 | (871) all_0_10_10 = n7
% 22.69/6.21 |
% 22.69/6.21 | From (871) and (317) follows:
% 22.69/6.21 | (872) pred(n7) = all_0_6_6
% 22.69/6.21 |
% 22.69/6.21 | From (871) and (146) follows:
% 22.69/6.21 | (873) succ(n7) = all_0_8_8
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (130) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 22.69/6.21 | (874) all_0_6_6 = n6
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (165) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 22.69/6.21 | (875) all_0_8_8 = n8
% 22.69/6.21 |
% 22.69/6.21 | From (874)(875) and (10) follows:
% 22.69/6.21 | (876) sum(n6, n8) = all_0_1_1
% 22.69/6.21 |
% 22.69/6.21 | From (874) and (3223) follows:
% 22.69/6.21 | (3270) sum(n6, n11) = all_0_4_4
% 22.69/6.21 |
% 22.69/6.21 | From (875) and (3225) follows:
% 22.69/6.21 | (3271) sum(n9, n8) = all_0_7_7
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n9, n8, all_0_7_7, n1 and discharging atoms sum(n9, n8) = all_0_7_7, sum(n9, n8) = n1, yields:
% 22.69/6.21 | (690) all_0_7_7 = n1
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n6, n11, all_0_4_4, n1 and discharging atoms sum(n6, n11) = all_0_4_4, sum(n6, n11) = n1, yields:
% 22.69/6.21 | (688) all_0_4_4 = n1
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 22.69/6.21 | (436) all_0_1_1 = n14
% 22.69/6.21 |
% 22.69/6.21 | From (690)(688) and (212) follows:
% 22.69/6.21 | (692) sum(n1, n1) = all_0_3_3
% 22.69/6.21 |
% 22.69/6.21 | From (436) and (3227) follows:
% 22.69/6.21 | (547) sum(n4, n14) = all_0_0_0
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n4, n14, all_0_0_0, n2 and discharging atoms sum(n4, n14) = all_0_0_0, sum(n4, n14) = n2, yields:
% 22.69/6.21 | (550) all_0_0_0 = n2
% 22.69/6.21 |
% 22.69/6.21 | Instantiating formula (74) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 22.69/6.21 | (549) all_0_3_3 = n2
% 22.69/6.21 |
% 22.69/6.21 | Equations (550,549) can reduce 363 to:
% 22.69/6.21 | (461) $false
% 22.69/6.21 |
% 22.69/6.21 |-The branch is then unsatisfiable
% 22.69/6.21 |-Branch two:
% 22.69/6.21 | (887) ~ (all_0_10_10 = n7)
% 22.69/6.21 | (888) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.69/6.21 |
% 22.69/6.21 +-Applying beta-rule and splitting (888), into two cases.
% 22.69/6.21 |-Branch one:
% 22.69/6.21 | (889) all_0_10_10 = n6
% 22.69/6.21 |
% 22.69/6.21 | From (889) and (317) follows:
% 22.69/6.21 | (890) pred(n6) = all_0_6_6
% 22.69/6.22 |
% 22.69/6.22 | From (889) and (146) follows:
% 22.69/6.22 | (891) succ(n6) = all_0_8_8
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (130) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 22.69/6.22 | (892) all_0_6_6 = n5
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (165) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 22.69/6.22 | (893) all_0_8_8 = n7
% 22.69/6.22 |
% 22.69/6.22 | From (892)(893) and (10) follows:
% 22.69/6.22 | (894) sum(n5, n7) = all_0_1_1
% 22.69/6.22 |
% 22.69/6.22 | From (892) and (3223) follows:
% 22.69/6.22 | (3288) sum(n5, n11) = all_0_4_4
% 22.69/6.22 |
% 22.69/6.22 | From (893) and (3225) follows:
% 22.69/6.22 | (3289) sum(n9, n7) = all_0_7_7
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n9, n7, all_0_7_7, n0 and discharging atoms sum(n9, n7) = all_0_7_7, sum(n9, n7) = n0, yields:
% 22.69/6.22 | (708) all_0_7_7 = n0
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n5, n11, all_0_4_4, n0 and discharging atoms sum(n5, n11) = all_0_4_4, sum(n5, n11) = n0, yields:
% 22.69/6.22 | (706) all_0_4_4 = n0
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 22.69/6.22 | (754) all_0_1_1 = n12
% 22.69/6.22 |
% 22.69/6.22 | From (708)(706) and (212) follows:
% 22.69/6.22 | (710) sum(n0, n0) = all_0_3_3
% 22.69/6.22 |
% 22.69/6.22 | From (754) and (3227) follows:
% 22.69/6.22 | (1119) sum(n4, n12) = all_0_0_0
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n4, n12, all_0_0_0, n0 and discharging atoms sum(n4, n12) = all_0_0_0, sum(n4, n12) = n0, yields:
% 22.69/6.22 | (568) all_0_0_0 = n0
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 22.69/6.22 | (567) all_0_3_3 = n0
% 22.69/6.22 |
% 22.69/6.22 | Equations (568,567) can reduce 363 to:
% 22.69/6.22 | (461) $false
% 22.69/6.22 |
% 22.69/6.22 |-The branch is then unsatisfiable
% 22.69/6.22 |-Branch two:
% 22.69/6.22 | (905) ~ (all_0_10_10 = n6)
% 22.69/6.22 | (906) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.69/6.22 |
% 22.69/6.22 +-Applying beta-rule and splitting (906), into two cases.
% 22.69/6.22 |-Branch one:
% 22.69/6.22 | (907) all_0_10_10 = n5
% 22.69/6.22 |
% 22.69/6.22 | From (907) and (317) follows:
% 22.69/6.22 | (908) pred(n5) = all_0_6_6
% 22.69/6.22 |
% 22.69/6.22 | From (907) and (146) follows:
% 22.69/6.22 | (909) succ(n5) = all_0_8_8
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (130) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 22.69/6.22 | (910) all_0_6_6 = n4
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (165) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 22.69/6.22 | (911) all_0_8_8 = n6
% 22.69/6.22 |
% 22.69/6.22 | From (910)(911) and (10) follows:
% 22.69/6.22 | (912) sum(n4, n6) = all_0_1_1
% 22.69/6.22 |
% 22.69/6.22 | From (910) and (3223) follows:
% 22.69/6.22 | (3306) sum(n4, n11) = all_0_4_4
% 22.69/6.22 |
% 22.69/6.22 | From (911) and (3225) follows:
% 22.69/6.22 | (3307) sum(n9, n6) = all_0_7_7
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n9, n6, all_0_7_7, n15 and discharging atoms sum(n9, n6) = all_0_7_7, sum(n9, n6) = n15, yields:
% 22.69/6.22 | (725) all_0_7_7 = n15
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n4, n11, all_0_4_4, n15 and discharging atoms sum(n4, n11) = all_0_4_4, sum(n4, n11) = n15, yields:
% 22.69/6.22 | (726) all_0_4_4 = n15
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 22.69/6.22 | (772) all_0_1_1 = n10
% 22.69/6.22 |
% 22.69/6.22 | From (725)(726) and (212) follows:
% 22.69/6.22 | (728) sum(n15, n15) = all_0_3_3
% 22.69/6.22 |
% 22.69/6.22 | From (772) and (3227) follows:
% 22.69/6.22 | (1651) sum(n4, n10) = all_0_0_0
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n15, n15, all_0_3_3, n14 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n14, yields:
% 22.69/6.22 | (585) all_0_3_3 = n14
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n4, n10, all_0_0_0, n14 and discharging atoms sum(n4, n10) = all_0_0_0, sum(n4, n10) = n14, yields:
% 22.69/6.22 | (586) all_0_0_0 = n14
% 22.69/6.22 |
% 22.69/6.22 | Equations (586,585) can reduce 363 to:
% 22.69/6.22 | (461) $false
% 22.69/6.22 |
% 22.69/6.22 |-The branch is then unsatisfiable
% 22.69/6.22 |-Branch two:
% 22.69/6.22 | (923) ~ (all_0_10_10 = n5)
% 22.69/6.22 | (924) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.69/6.22 |
% 22.69/6.22 +-Applying beta-rule and splitting (924), into two cases.
% 22.69/6.22 |-Branch one:
% 22.69/6.22 | (925) all_0_10_10 = n4
% 22.69/6.22 |
% 22.69/6.22 | From (925) and (317) follows:
% 22.69/6.22 | (926) pred(n4) = all_0_6_6
% 22.69/6.22 |
% 22.69/6.22 | From (925) and (146) follows:
% 22.69/6.22 | (927) succ(n4) = all_0_8_8
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (130) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 22.69/6.22 | (928) all_0_6_6 = n3
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (165) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 22.69/6.22 | (929) all_0_8_8 = n5
% 22.69/6.22 |
% 22.69/6.22 | From (928)(929) and (10) follows:
% 22.69/6.22 | (930) sum(n3, n5) = all_0_1_1
% 22.69/6.22 |
% 22.69/6.22 | From (928) and (3223) follows:
% 22.69/6.22 | (3324) sum(n3, n11) = all_0_4_4
% 22.69/6.22 |
% 22.69/6.22 | From (929) and (3225) follows:
% 22.69/6.22 | (3325) sum(n9, n5) = all_0_7_7
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n9, n5, all_0_7_7, n14 and discharging atoms sum(n9, n5) = all_0_7_7, sum(n9, n5) = n14, yields:
% 22.69/6.22 | (452) all_0_7_7 = n14
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n3, n11, all_0_4_4, n14 and discharging atoms sum(n3, n11) = all_0_4_4, sum(n3, n11) = n14, yields:
% 22.69/6.22 | (451) all_0_4_4 = n14
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 22.69/6.22 | (790) all_0_1_1 = n8
% 22.69/6.22 |
% 22.69/6.22 | From (452)(451) and (212) follows:
% 22.69/6.22 | (456) sum(n14, n14) = all_0_3_3
% 22.69/6.22 |
% 22.69/6.22 | From (790) and (3227) follows:
% 22.69/6.22 | (2147) sum(n4, n8) = all_0_0_0
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n14, n14, all_0_3_3, n12 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n12, yields:
% 22.69/6.22 | (459) all_0_3_3 = n12
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n4, n8, all_0_0_0, n12 and discharging atoms sum(n4, n8) = all_0_0_0, sum(n4, n8) = n12, yields:
% 22.69/6.22 | (457) all_0_0_0 = n12
% 22.69/6.22 |
% 22.69/6.22 | Equations (457,459) can reduce 363 to:
% 22.69/6.22 | (461) $false
% 22.69/6.22 |
% 22.69/6.22 |-The branch is then unsatisfiable
% 22.69/6.22 |-Branch two:
% 22.69/6.22 | (941) ~ (all_0_10_10 = n4)
% 22.69/6.22 | (942) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.69/6.22 |
% 22.69/6.22 +-Applying beta-rule and splitting (942), into two cases.
% 22.69/6.22 |-Branch one:
% 22.69/6.22 | (943) all_0_10_10 = n3
% 22.69/6.22 |
% 22.69/6.22 | From (943) and (317) follows:
% 22.69/6.22 | (944) pred(n3) = all_0_6_6
% 22.69/6.22 |
% 22.69/6.22 | From (943) and (146) follows:
% 22.69/6.22 | (945) succ(n3) = all_0_8_8
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (130) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 22.69/6.22 | (946) all_0_6_6 = n2
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (165) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 22.69/6.22 | (947) all_0_8_8 = n4
% 22.69/6.22 |
% 22.69/6.22 | From (946)(947) and (10) follows:
% 22.69/6.22 | (948) sum(n2, n4) = all_0_1_1
% 22.69/6.22 |
% 22.69/6.22 | From (946) and (3223) follows:
% 22.69/6.22 | (3342) sum(n2, n11) = all_0_4_4
% 22.69/6.22 |
% 22.69/6.22 | From (947) and (3225) follows:
% 22.69/6.22 | (3343) sum(n9, n4) = all_0_7_7
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n9, n4, all_0_7_7, n13 and discharging atoms sum(n9, n4) = all_0_7_7, sum(n9, n4) = n13, yields:
% 22.69/6.22 | (474) all_0_7_7 = n13
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n2, n11, all_0_4_4, n13 and discharging atoms sum(n2, n11) = all_0_4_4, sum(n2, n11) = n13, yields:
% 22.69/6.22 | (472) all_0_4_4 = n13
% 22.69/6.22 |
% 22.69/6.22 | Instantiating formula (74) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 22.69/6.22 | (808) all_0_1_1 = n6
% 22.69/6.22 |
% 22.69/6.22 | From (474)(472) and (212) follows:
% 22.69/6.22 | (476) sum(n13, n13) = all_0_3_3
% 22.69/6.22 |
% 22.69/6.22 | From (808) and (3227) follows:
% 22.83/6.22 | (2607) sum(n4, n6) = all_0_0_0
% 22.83/6.22 |
% 22.83/6.22 | Instantiating formula (74) with n13, n13, all_0_3_3, n10 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n10, yields:
% 22.83/6.22 | (477) all_0_3_3 = n10
% 22.83/6.22 |
% 22.83/6.22 | Instantiating formula (74) with n4, n6, all_0_0_0, n10 and discharging atoms sum(n4, n6) = all_0_0_0, sum(n4, n6) = n10, yields:
% 22.83/6.22 | (478) all_0_0_0 = n10
% 22.83/6.22 |
% 22.83/6.22 | Equations (478,477) can reduce 363 to:
% 22.83/6.22 | (461) $false
% 22.83/6.22 |
% 22.83/6.22 |-The branch is then unsatisfiable
% 22.83/6.23 |-Branch two:
% 22.83/6.23 | (959) ~ (all_0_10_10 = n3)
% 22.83/6.23 | (960) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.83/6.23 |
% 22.83/6.23 +-Applying beta-rule and splitting (960), into two cases.
% 22.83/6.23 |-Branch one:
% 22.83/6.23 | (961) all_0_10_10 = n2
% 22.83/6.23 |
% 22.83/6.23 | From (961) and (317) follows:
% 22.83/6.23 | (962) pred(n2) = all_0_6_6
% 22.83/6.23 |
% 22.83/6.23 | From (961) and (146) follows:
% 22.83/6.23 | (963) succ(n2) = all_0_8_8
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (130) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 22.83/6.23 | (964) all_0_6_6 = n1
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (165) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 22.83/6.23 | (965) all_0_8_8 = n3
% 22.83/6.23 |
% 22.83/6.23 | From (964)(965) and (10) follows:
% 22.83/6.23 | (966) sum(n1, n3) = all_0_1_1
% 22.83/6.23 |
% 22.83/6.23 | From (964) and (3223) follows:
% 22.83/6.23 | (3360) sum(n1, n11) = all_0_4_4
% 22.83/6.23 |
% 22.83/6.23 | From (965) and (3225) follows:
% 22.83/6.23 | (3361) sum(n9, n3) = all_0_7_7
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (74) with n9, n3, all_0_7_7, n12 and discharging atoms sum(n9, n3) = all_0_7_7, sum(n9, n3) = n12, yields:
% 22.83/6.23 | (492) all_0_7_7 = n12
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (74) with n1, n11, all_0_4_4, n12 and discharging atoms sum(n1, n11) = all_0_4_4, sum(n1, n11) = n12, yields:
% 22.83/6.23 | (490) all_0_4_4 = n12
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (74) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 22.83/6.23 | (826) all_0_1_1 = n4
% 22.83/6.23 |
% 22.83/6.23 | From (492)(490) and (212) follows:
% 22.83/6.23 | (494) sum(n12, n12) = all_0_3_3
% 22.83/6.23 |
% 22.83/6.23 | From (826) and (3227) follows:
% 22.83/6.23 | (3030) sum(n4, n4) = all_0_0_0
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (74) with n12, n12, all_0_3_3, n8 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n8, yields:
% 22.83/6.23 | (495) all_0_3_3 = n8
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (74) with n4, n4, all_0_0_0, n8 and discharging atoms sum(n4, n4) = all_0_0_0, sum(n4, n4) = n8, yields:
% 22.83/6.23 | (496) all_0_0_0 = n8
% 22.83/6.23 |
% 22.83/6.23 | Equations (496,495) can reduce 363 to:
% 22.83/6.23 | (461) $false
% 22.83/6.23 |
% 22.83/6.23 |-The branch is then unsatisfiable
% 22.83/6.23 |-Branch two:
% 22.83/6.23 | (977) ~ (all_0_10_10 = n2)
% 22.83/6.23 | (978) all_0_10_10 = n1 | all_0_10_10 = n0
% 22.83/6.23 |
% 22.83/6.23 +-Applying beta-rule and splitting (978), into two cases.
% 22.83/6.23 |-Branch one:
% 22.83/6.23 | (979) all_0_10_10 = n1
% 22.83/6.23 |
% 22.83/6.23 | From (979) and (317) follows:
% 22.83/6.23 | (980) pred(n1) = all_0_6_6
% 22.83/6.23 |
% 22.83/6.23 | From (979) and (146) follows:
% 22.83/6.23 | (981) succ(n1) = all_0_8_8
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (130) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 22.83/6.23 | (982) all_0_6_6 = n0
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (165) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 22.83/6.23 | (983) all_0_8_8 = n2
% 22.83/6.23 |
% 22.83/6.23 | From (982)(983) and (10) follows:
% 22.83/6.23 | (984) sum(n0, n2) = all_0_1_1
% 22.83/6.23 |
% 22.83/6.23 | From (982) and (3223) follows:
% 22.83/6.23 | (3378) sum(n0, n11) = all_0_4_4
% 22.83/6.23 |
% 22.83/6.23 | From (983) and (3225) follows:
% 22.83/6.23 | (3379) sum(n9, n2) = all_0_7_7
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (74) with n9, n2, all_0_7_7, n11 and discharging atoms sum(n9, n2) = all_0_7_7, sum(n9, n2) = n11, yields:
% 22.83/6.23 | (510) all_0_7_7 = n11
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (74) with n0, n11, all_0_4_4, n11 and discharging atoms sum(n0, n11) = all_0_4_4, sum(n0, n11) = n11, yields:
% 22.83/6.23 | (508) all_0_4_4 = n11
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (74) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 22.83/6.23 | (844) all_0_1_1 = n2
% 22.83/6.23 |
% 22.83/6.23 | From (510)(508) and (212) follows:
% 22.83/6.23 | (512) sum(n11, n11) = all_0_3_3
% 22.83/6.23 |
% 22.83/6.23 | From (844) and (3227) follows:
% 22.83/6.23 | (3240) sum(n4, n2) = all_0_0_0
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (74) with n11, n11, all_0_3_3, n6 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n6, yields:
% 22.83/6.23 | (513) all_0_3_3 = n6
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (74) with n4, n2, all_0_0_0, n6 and discharging atoms sum(n4, n2) = all_0_0_0, sum(n4, n2) = n6, yields:
% 22.83/6.23 | (514) all_0_0_0 = n6
% 22.83/6.23 |
% 22.83/6.23 | Equations (514,513) can reduce 363 to:
% 22.83/6.23 | (461) $false
% 22.83/6.23 |
% 22.83/6.23 |-The branch is then unsatisfiable
% 22.83/6.23 |-Branch two:
% 22.83/6.23 | (997) ~ (all_0_10_10 = n1)
% 22.83/6.23 | (998) all_0_10_10 = n0
% 22.83/6.23 |
% 22.83/6.23 | From (998) and (317) follows:
% 22.83/6.23 | (999) pred(n0) = all_0_6_6
% 22.83/6.23 |
% 22.83/6.23 | From (998) and (146) follows:
% 22.83/6.23 | (1000) succ(n0) = all_0_8_8
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (130) with n0, all_0_6_6, n15 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n15, yields:
% 22.83/6.23 | (1001) all_0_6_6 = n15
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (165) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 22.83/6.23 | (1002) all_0_8_8 = n1
% 22.83/6.23 |
% 22.83/6.23 | From (1001)(1002) and (10) follows:
% 22.83/6.23 | (1003) sum(n15, n1) = all_0_1_1
% 22.83/6.23 |
% 22.83/6.23 | From (1001) and (3223) follows:
% 22.83/6.23 | (3395) sum(n15, n11) = all_0_4_4
% 22.83/6.23 |
% 22.83/6.23 | From (1002) and (3225) follows:
% 22.83/6.23 | (3396) sum(n9, n1) = all_0_7_7
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (74) with n15, n11, all_0_4_4, n10 and discharging atoms sum(n15, n11) = all_0_4_4, sum(n15, n11) = n10, yields:
% 22.83/6.23 | (526) all_0_4_4 = n10
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (74) with n15, n1, all_0_1_1, n0 and discharging atoms sum(n15, n1) = all_0_1_1, sum(n15, n1) = n0, yields:
% 22.83/6.23 | (862) all_0_1_1 = n0
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (74) with n9, n1, all_0_7_7, n10 and discharging atoms sum(n9, n1) = all_0_7_7, sum(n9, n1) = n10, yields:
% 22.83/6.23 | (528) all_0_7_7 = n10
% 22.83/6.23 |
% 22.83/6.23 | From (528)(526) and (212) follows:
% 22.83/6.23 | (530) sum(n10, n10) = all_0_3_3
% 22.83/6.23 |
% 22.83/6.23 | From (862) and (3227) follows:
% 22.83/6.23 | (3258) sum(n4, n0) = all_0_0_0
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (74) with n10, n10, all_0_3_3, n4 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n4, yields:
% 22.83/6.23 | (531) all_0_3_3 = n4
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (74) with n4, n0, all_0_0_0, n4 and discharging atoms sum(n4, n0) = all_0_0_0, sum(n4, n0) = n4, yields:
% 22.83/6.23 | (532) all_0_0_0 = n4
% 22.83/6.23 |
% 22.83/6.23 | Equations (532,531) can reduce 363 to:
% 22.83/6.23 | (461) $false
% 22.83/6.23 |
% 22.83/6.23 |-The branch is then unsatisfiable
% 22.83/6.23 |-Branch two:
% 22.83/6.23 | (552) ~ (all_0_11_11 = n10)
% 22.83/6.23 | (553) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.83/6.23 |
% 22.83/6.23 +-Applying beta-rule and splitting (834), into two cases.
% 22.83/6.23 |-Branch one:
% 22.83/6.23 | (835) all_0_10_10 = n9
% 22.83/6.23 |
% 22.83/6.23 | From (835) and (317) follows:
% 22.83/6.23 | (836) pred(n9) = all_0_6_6
% 22.83/6.23 |
% 22.83/6.23 | From (835) and (146) follows:
% 22.83/6.23 | (837) succ(n9) = all_0_8_8
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (130) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 22.83/6.23 | (838) all_0_6_6 = n8
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (165) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 22.83/6.23 | (839) all_0_8_8 = n10
% 22.83/6.23 |
% 22.83/6.23 | From (838) and (836) follows:
% 22.83/6.23 | (421) pred(n9) = n8
% 22.83/6.23 |
% 22.83/6.23 | From (839) and (837) follows:
% 22.83/6.23 | (358) succ(n9) = n10
% 22.83/6.23 |
% 22.83/6.23 | From (838) and (276) follows:
% 22.83/6.23 | (3414) sum(n8, all_0_5_5) = all_0_4_4
% 22.83/6.23 |
% 22.83/6.23 | From (838)(839) and (10) follows:
% 22.83/6.23 | (840) sum(n8, n10) = all_0_1_1
% 22.83/6.23 |
% 22.83/6.23 | From (839) and (350) follows:
% 22.83/6.23 | (3416) sum(all_0_9_9, n10) = all_0_7_7
% 22.83/6.23 |
% 22.83/6.23 | Instantiating formula (74) with n8, n10, all_0_1_1, n2 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n2, yields:
% 22.83/6.23 | (844) all_0_1_1 = n2
% 22.83/6.23 |
% 22.83/6.23 | From (844) and (256) follows:
% 22.83/6.23 | (3418) sum(all_0_2_2, n2) = all_0_0_0
% 22.83/6.24 |
% 22.83/6.24 | From (844) and (840) follows:
% 22.83/6.24 | (270) sum(n8, n10) = n2
% 22.83/6.24 |
% 22.83/6.24 +-Applying beta-rule and splitting (553), into two cases.
% 22.83/6.24 |-Branch one:
% 22.83/6.24 | (554) all_0_11_11 = n9
% 22.83/6.24 |
% 22.83/6.24 | From (554) and (423) follows:
% 22.83/6.24 | (555) pred(n9) = all_0_9_9
% 22.83/6.24 |
% 22.83/6.24 | From (554) and (262) follows:
% 22.83/6.24 | (556) succ(n9) = all_0_5_5
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (130) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 22.83/6.24 | (557) all_0_9_9 = n8
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (165) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 22.83/6.24 | (558) all_0_5_5 = n10
% 22.83/6.24 |
% 22.83/6.24 | From (557)(558) and (147) follows:
% 22.83/6.24 | (559) sum(n8, n10) = all_0_2_2
% 22.83/6.24 |
% 22.83/6.24 | From (557) and (3416) follows:
% 22.83/6.24 | (3426) sum(n8, n10) = all_0_7_7
% 22.83/6.24 |
% 22.83/6.24 | From (558) and (3414) follows:
% 22.83/6.24 | (3427) sum(n8, n10) = all_0_4_4
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (74) with n8, n10, all_0_2_2, n2 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n2, yields:
% 22.83/6.24 | (563) all_0_2_2 = n2
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (74) with n8, n10, all_0_4_4, all_0_2_2 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = all_0_4_4, yields:
% 22.83/6.24 | (448) all_0_2_2 = all_0_4_4
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (74) with n8, n10, all_0_7_7, all_0_2_2 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = all_0_7_7, yields:
% 22.83/6.24 | (449) all_0_2_2 = all_0_7_7
% 22.83/6.24 |
% 22.83/6.24 | Combining equations (449,448) yields a new equation:
% 22.83/6.24 | (450) all_0_4_4 = all_0_7_7
% 22.83/6.24 |
% 22.83/6.24 | Combining equations (563,448) yields a new equation:
% 22.83/6.24 | (670) all_0_4_4 = n2
% 22.83/6.24 |
% 22.83/6.24 | Combining equations (670,450) yields a new equation:
% 22.83/6.24 | (672) all_0_7_7 = n2
% 22.83/6.24 |
% 22.83/6.24 | Combining equations (672,450) yields a new equation:
% 22.83/6.24 | (670) all_0_4_4 = n2
% 22.83/6.24 |
% 22.83/6.24 | Combining equations (670,448) yields a new equation:
% 22.83/6.24 | (563) all_0_2_2 = n2
% 22.83/6.24 |
% 22.83/6.24 | From (563) and (3418) follows:
% 22.83/6.24 | (3436) sum(n2, n2) = all_0_0_0
% 22.83/6.24 |
% 22.83/6.24 | From (672)(670) and (212) follows:
% 22.83/6.24 | (674) sum(n2, n2) = all_0_3_3
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (74) with n2, n2, all_0_0_0, n4 and discharging atoms sum(n2, n2) = all_0_0_0, sum(n2, n2) = n4, yields:
% 22.83/6.24 | (532) all_0_0_0 = n4
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (74) with n2, n2, all_0_3_3, all_0_0_0 and discharging atoms sum(n2, n2) = all_0_0_0, sum(n2, n2) = all_0_3_3, yields:
% 22.83/6.24 | (458) all_0_0_0 = all_0_3_3
% 22.83/6.24 |
% 22.83/6.24 | Combining equations (532,458) yields a new equation:
% 22.83/6.24 | (531) all_0_3_3 = n4
% 22.83/6.24 |
% 22.83/6.24 | Combining equations (531,458) yields a new equation:
% 22.83/6.24 | (532) all_0_0_0 = n4
% 22.83/6.24 |
% 22.83/6.24 | Equations (532,531) can reduce 363 to:
% 22.83/6.24 | (461) $false
% 22.83/6.24 |
% 22.83/6.24 |-The branch is then unsatisfiable
% 22.83/6.24 |-Branch two:
% 22.83/6.24 | (570) ~ (all_0_11_11 = n9)
% 22.83/6.24 | (571) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.83/6.24 |
% 22.83/6.24 +-Applying beta-rule and splitting (571), into two cases.
% 22.83/6.24 |-Branch one:
% 22.83/6.24 | (572) all_0_11_11 = n8
% 22.83/6.24 |
% 22.83/6.24 | From (572) and (423) follows:
% 22.83/6.24 | (573) pred(n8) = all_0_9_9
% 22.83/6.24 |
% 22.83/6.24 | From (572) and (262) follows:
% 22.83/6.24 | (574) succ(n8) = all_0_5_5
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (130) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 22.83/6.24 | (575) all_0_9_9 = n7
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (165) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 22.83/6.24 | (576) all_0_5_5 = n9
% 22.83/6.24 |
% 22.83/6.24 | From (575)(576) and (147) follows:
% 22.83/6.24 | (577) sum(n7, n9) = all_0_2_2
% 22.83/6.24 |
% 22.83/6.24 | From (575) and (3416) follows:
% 22.83/6.24 | (3451) sum(n7, n10) = all_0_7_7
% 22.83/6.24 |
% 22.83/6.24 | From (576) and (3414) follows:
% 22.83/6.24 | (3452) sum(n8, n9) = all_0_4_4
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (74) with n8, n9, all_0_4_4, n1 and discharging atoms sum(n8, n9) = all_0_4_4, sum(n8, n9) = n1, yields:
% 22.83/6.24 | (688) all_0_4_4 = n1
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (74) with n7, n10, all_0_7_7, n1 and discharging atoms sum(n7, n10) = all_0_7_7, sum(n7, n10) = n1, yields:
% 22.83/6.24 | (690) all_0_7_7 = n1
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (74) with n7, n9, all_0_2_2, n0 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n0, yields:
% 22.83/6.24 | (581) all_0_2_2 = n0
% 22.83/6.24 |
% 22.83/6.24 | From (581) and (3418) follows:
% 22.83/6.24 | (3456) sum(n0, n2) = all_0_0_0
% 22.83/6.24 |
% 22.83/6.24 | From (690)(688) and (212) follows:
% 22.83/6.24 | (692) sum(n1, n1) = all_0_3_3
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (74) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 22.83/6.24 | (549) all_0_3_3 = n2
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (74) with n0, n2, all_0_0_0, n2 and discharging atoms sum(n0, n2) = all_0_0_0, sum(n0, n2) = n2, yields:
% 22.83/6.24 | (550) all_0_0_0 = n2
% 22.83/6.24 |
% 22.83/6.24 | Equations (550,549) can reduce 363 to:
% 22.83/6.24 | (461) $false
% 22.83/6.24 |
% 22.83/6.24 |-The branch is then unsatisfiable
% 22.83/6.24 |-Branch two:
% 22.83/6.24 | (588) ~ (all_0_11_11 = n8)
% 22.83/6.24 | (589) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.83/6.24 |
% 22.83/6.24 +-Applying beta-rule and splitting (589), into two cases.
% 22.83/6.24 |-Branch one:
% 22.83/6.24 | (590) all_0_11_11 = n7
% 22.83/6.24 |
% 22.83/6.24 | From (590) and (423) follows:
% 22.83/6.24 | (591) pred(n7) = all_0_9_9
% 22.83/6.24 |
% 22.83/6.24 | From (590) and (262) follows:
% 22.83/6.24 | (592) succ(n7) = all_0_5_5
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (130) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 22.83/6.24 | (593) all_0_9_9 = n6
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (165) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 22.83/6.24 | (594) all_0_5_5 = n8
% 22.83/6.24 |
% 22.83/6.24 | From (593)(594) and (147) follows:
% 22.83/6.24 | (595) sum(n6, n8) = all_0_2_2
% 22.83/6.24 |
% 22.83/6.24 | From (593) and (3416) follows:
% 22.83/6.24 | (3469) sum(n6, n10) = all_0_7_7
% 22.83/6.24 |
% 22.83/6.24 | From (594) and (3414) follows:
% 22.83/6.24 | (3470) sum(n8, n8) = all_0_4_4
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (74) with n8, n8, all_0_4_4, n0 and discharging atoms sum(n8, n8) = all_0_4_4, sum(n8, n8) = n0, yields:
% 22.83/6.24 | (706) all_0_4_4 = n0
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (74) with n6, n10, all_0_7_7, n0 and discharging atoms sum(n6, n10) = all_0_7_7, sum(n6, n10) = n0, yields:
% 22.83/6.24 | (708) all_0_7_7 = n0
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (74) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 22.83/6.24 | (447) all_0_2_2 = n14
% 22.83/6.24 |
% 22.83/6.24 | From (447) and (3418) follows:
% 22.83/6.24 | (847) sum(n14, n2) = all_0_0_0
% 22.83/6.24 |
% 22.83/6.24 | From (708)(706) and (212) follows:
% 22.83/6.24 | (710) sum(n0, n0) = all_0_3_3
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (74) with n14, n2, all_0_0_0, n0 and discharging atoms sum(n14, n2) = all_0_0_0, sum(n14, n2) = n0, yields:
% 22.83/6.24 | (568) all_0_0_0 = n0
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (74) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 22.83/6.24 | (567) all_0_3_3 = n0
% 22.83/6.24 |
% 22.83/6.24 | Equations (568,567) can reduce 363 to:
% 22.83/6.24 | (461) $false
% 22.83/6.24 |
% 22.83/6.24 |-The branch is then unsatisfiable
% 22.83/6.24 |-Branch two:
% 22.83/6.24 | (606) ~ (all_0_11_11 = n7)
% 22.83/6.24 | (607) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.83/6.24 |
% 22.83/6.24 +-Applying beta-rule and splitting (607), into two cases.
% 22.83/6.24 |-Branch one:
% 22.83/6.24 | (608) all_0_11_11 = n6
% 22.83/6.24 |
% 22.83/6.24 | From (608) and (423) follows:
% 22.83/6.24 | (609) pred(n6) = all_0_9_9
% 22.83/6.24 |
% 22.83/6.24 | From (608) and (262) follows:
% 22.83/6.24 | (610) succ(n6) = all_0_5_5
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (130) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 22.83/6.24 | (611) all_0_9_9 = n5
% 22.83/6.24 |
% 22.83/6.24 | Instantiating formula (165) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 22.83/6.24 | (612) all_0_5_5 = n7
% 22.83/6.24 |
% 22.83/6.24 | From (611)(612) and (147) follows:
% 22.83/6.24 | (613) sum(n5, n7) = all_0_2_2
% 22.83/6.24 |
% 22.83/6.24 | From (611) and (3416) follows:
% 22.91/6.24 | (3487) sum(n5, n10) = all_0_7_7
% 22.91/6.24 |
% 22.91/6.24 | From (612) and (3414) follows:
% 22.91/6.24 | (3488) sum(n8, n7) = all_0_4_4
% 22.91/6.24 |
% 22.91/6.24 | Instantiating formula (74) with n8, n7, all_0_4_4, n15 and discharging atoms sum(n8, n7) = all_0_4_4, sum(n8, n7) = n15, yields:
% 22.91/6.24 | (726) all_0_4_4 = n15
% 22.91/6.24 |
% 22.91/6.24 | Instantiating formula (74) with n5, n10, all_0_7_7, n15 and discharging atoms sum(n5, n10) = all_0_7_7, sum(n5, n10) = n15, yields:
% 22.91/6.25 | (725) all_0_7_7 = n15
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 22.91/6.25 | (473) all_0_2_2 = n12
% 22.91/6.25 |
% 22.91/6.25 | From (473) and (3418) follows:
% 22.91/6.25 | (1399) sum(n12, n2) = all_0_0_0
% 22.91/6.25 |
% 22.91/6.25 | From (725)(726) and (212) follows:
% 22.91/6.25 | (728) sum(n15, n15) = all_0_3_3
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n15, n15, all_0_3_3, n14 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n14, yields:
% 22.91/6.25 | (585) all_0_3_3 = n14
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n12, n2, all_0_0_0, n14 and discharging atoms sum(n12, n2) = all_0_0_0, sum(n12, n2) = n14, yields:
% 22.91/6.25 | (586) all_0_0_0 = n14
% 22.91/6.25 |
% 22.91/6.25 | Equations (586,585) can reduce 363 to:
% 22.91/6.25 | (461) $false
% 22.91/6.25 |
% 22.91/6.25 |-The branch is then unsatisfiable
% 22.91/6.25 |-Branch two:
% 22.91/6.25 | (624) ~ (all_0_11_11 = n6)
% 22.91/6.25 | (625) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.91/6.25 |
% 22.91/6.25 +-Applying beta-rule and splitting (625), into two cases.
% 22.91/6.25 |-Branch one:
% 22.91/6.25 | (626) all_0_11_11 = n5
% 22.91/6.25 |
% 22.91/6.25 | From (626) and (423) follows:
% 22.91/6.25 | (627) pred(n5) = all_0_9_9
% 22.91/6.25 |
% 22.91/6.25 | From (626) and (262) follows:
% 22.91/6.25 | (628) succ(n5) = all_0_5_5
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (130) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 22.91/6.25 | (629) all_0_9_9 = n4
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (165) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 22.91/6.25 | (630) all_0_5_5 = n6
% 22.91/6.25 |
% 22.91/6.25 | From (629)(630) and (147) follows:
% 22.91/6.25 | (631) sum(n4, n6) = all_0_2_2
% 22.91/6.25 |
% 22.91/6.25 | From (629) and (3416) follows:
% 22.91/6.25 | (3505) sum(n4, n10) = all_0_7_7
% 22.91/6.25 |
% 22.91/6.25 | From (630) and (3414) follows:
% 22.91/6.25 | (3506) sum(n8, n6) = all_0_4_4
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n8, n6, all_0_4_4, n14 and discharging atoms sum(n8, n6) = all_0_4_4, sum(n8, n6) = n14, yields:
% 22.91/6.25 | (451) all_0_4_4 = n14
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n4, n10, all_0_7_7, n14 and discharging atoms sum(n4, n10) = all_0_7_7, sum(n4, n10) = n14, yields:
% 22.91/6.25 | (452) all_0_7_7 = n14
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 22.91/6.25 | (491) all_0_2_2 = n10
% 22.91/6.25 |
% 22.91/6.25 | From (491) and (3418) follows:
% 22.91/6.25 | (1913) sum(n10, n2) = all_0_0_0
% 22.91/6.25 |
% 22.91/6.25 | From (452)(451) and (212) follows:
% 22.91/6.25 | (456) sum(n14, n14) = all_0_3_3
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n14, n14, all_0_3_3, n12 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n12, yields:
% 22.91/6.25 | (459) all_0_3_3 = n12
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n10, n2, all_0_0_0, n12 and discharging atoms sum(n10, n2) = all_0_0_0, sum(n10, n2) = n12, yields:
% 22.91/6.25 | (457) all_0_0_0 = n12
% 22.91/6.25 |
% 22.91/6.25 | Equations (457,459) can reduce 363 to:
% 22.91/6.25 | (461) $false
% 22.91/6.25 |
% 22.91/6.25 |-The branch is then unsatisfiable
% 22.91/6.25 |-Branch two:
% 22.91/6.25 | (642) ~ (all_0_11_11 = n5)
% 22.91/6.25 | (643) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.91/6.25 |
% 22.91/6.25 +-Applying beta-rule and splitting (643), into two cases.
% 22.91/6.25 |-Branch one:
% 22.91/6.25 | (644) all_0_11_11 = n4
% 22.91/6.25 |
% 22.91/6.25 | From (644) and (423) follows:
% 22.91/6.25 | (645) pred(n4) = all_0_9_9
% 22.91/6.25 |
% 22.91/6.25 | From (644) and (262) follows:
% 22.91/6.25 | (646) succ(n4) = all_0_5_5
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (130) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 22.91/6.25 | (647) all_0_9_9 = n3
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (165) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 22.91/6.25 | (648) all_0_5_5 = n5
% 22.91/6.25 |
% 22.91/6.25 | From (647)(648) and (147) follows:
% 22.91/6.25 | (649) sum(n3, n5) = all_0_2_2
% 22.91/6.25 |
% 22.91/6.25 | From (647) and (3416) follows:
% 22.91/6.25 | (3523) sum(n3, n10) = all_0_7_7
% 22.91/6.25 |
% 22.91/6.25 | From (648) and (3414) follows:
% 22.91/6.25 | (3524) sum(n8, n5) = all_0_4_4
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n8, n5, all_0_4_4, n13 and discharging atoms sum(n8, n5) = all_0_4_4, sum(n8, n5) = n13, yields:
% 22.91/6.25 | (472) all_0_4_4 = n13
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n3, n10, all_0_7_7, n13 and discharging atoms sum(n3, n10) = all_0_7_7, sum(n3, n10) = n13, yields:
% 22.91/6.25 | (474) all_0_7_7 = n13
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 22.91/6.25 | (509) all_0_2_2 = n8
% 22.91/6.25 |
% 22.91/6.25 | From (509) and (3418) follows:
% 22.91/6.25 | (2391) sum(n8, n2) = all_0_0_0
% 22.91/6.25 |
% 22.91/6.25 | From (474)(472) and (212) follows:
% 22.91/6.25 | (476) sum(n13, n13) = all_0_3_3
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n13, n13, all_0_3_3, n10 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n10, yields:
% 22.91/6.25 | (477) all_0_3_3 = n10
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n8, n2, all_0_0_0, n10 and discharging atoms sum(n8, n2) = all_0_0_0, sum(n8, n2) = n10, yields:
% 22.91/6.25 | (478) all_0_0_0 = n10
% 22.91/6.25 |
% 22.91/6.25 | Equations (478,477) can reduce 363 to:
% 22.91/6.25 | (461) $false
% 22.91/6.25 |
% 22.91/6.25 |-The branch is then unsatisfiable
% 22.91/6.25 |-Branch two:
% 22.91/6.25 | (660) ~ (all_0_11_11 = n4)
% 22.91/6.25 | (661) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.91/6.25 |
% 22.91/6.25 +-Applying beta-rule and splitting (661), into two cases.
% 22.91/6.25 |-Branch one:
% 22.91/6.25 | (662) all_0_11_11 = n3
% 22.91/6.25 |
% 22.91/6.25 | From (662) and (423) follows:
% 22.91/6.25 | (663) pred(n3) = all_0_9_9
% 22.91/6.25 |
% 22.91/6.25 | From (662) and (262) follows:
% 22.91/6.25 | (664) succ(n3) = all_0_5_5
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (130) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 22.91/6.25 | (665) all_0_9_9 = n2
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (165) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 22.91/6.25 | (666) all_0_5_5 = n4
% 22.91/6.25 |
% 22.91/6.25 | From (665)(666) and (147) follows:
% 22.91/6.25 | (667) sum(n2, n4) = all_0_2_2
% 22.91/6.25 |
% 22.91/6.25 | From (665) and (3416) follows:
% 22.91/6.25 | (3541) sum(n2, n10) = all_0_7_7
% 22.91/6.25 |
% 22.91/6.25 | From (666) and (3414) follows:
% 22.91/6.25 | (3542) sum(n8, n4) = all_0_4_4
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n8, n4, all_0_4_4, n12 and discharging atoms sum(n8, n4) = all_0_4_4, sum(n8, n4) = n12, yields:
% 22.91/6.25 | (490) all_0_4_4 = n12
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n2, n10, all_0_7_7, n12 and discharging atoms sum(n2, n10) = all_0_7_7, sum(n2, n10) = n12, yields:
% 22.91/6.25 | (492) all_0_7_7 = n12
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 22.91/6.25 | (527) all_0_2_2 = n6
% 22.91/6.25 |
% 22.91/6.25 | From (527) and (3418) follows:
% 22.91/6.25 | (2834) sum(n6, n2) = all_0_0_0
% 22.91/6.25 |
% 22.91/6.25 | From (492)(490) and (212) follows:
% 22.91/6.25 | (494) sum(n12, n12) = all_0_3_3
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n12, n12, all_0_3_3, n8 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n8, yields:
% 22.91/6.25 | (495) all_0_3_3 = n8
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (74) with n6, n2, all_0_0_0, n8 and discharging atoms sum(n6, n2) = all_0_0_0, sum(n6, n2) = n8, yields:
% 22.91/6.25 | (496) all_0_0_0 = n8
% 22.91/6.25 |
% 22.91/6.25 | Equations (496,495) can reduce 363 to:
% 22.91/6.25 | (461) $false
% 22.91/6.25 |
% 22.91/6.25 |-The branch is then unsatisfiable
% 22.91/6.25 |-Branch two:
% 22.91/6.25 | (678) ~ (all_0_11_11 = n3)
% 22.91/6.25 | (679) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.91/6.25 |
% 22.91/6.25 +-Applying beta-rule and splitting (679), into two cases.
% 22.91/6.25 |-Branch one:
% 22.91/6.25 | (680) all_0_11_11 = n2
% 22.91/6.25 |
% 22.91/6.25 | From (680) and (423) follows:
% 22.91/6.25 | (681) pred(n2) = all_0_9_9
% 22.91/6.25 |
% 22.91/6.25 | From (680) and (262) follows:
% 22.91/6.25 | (682) succ(n2) = all_0_5_5
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (130) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 22.91/6.25 | (683) all_0_9_9 = n1
% 22.91/6.25 |
% 22.91/6.25 | Instantiating formula (165) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 22.91/6.25 | (684) all_0_5_5 = n3
% 22.91/6.25 |
% 22.91/6.25 | From (683)(684) and (147) follows:
% 22.91/6.25 | (685) sum(n1, n3) = all_0_2_2
% 22.91/6.25 |
% 22.91/6.25 | From (683) and (3416) follows:
% 22.91/6.25 | (3559) sum(n1, n10) = all_0_7_7
% 22.91/6.25 |
% 22.91/6.25 | From (684) and (3414) follows:
% 22.91/6.25 | (3560) sum(n8, n3) = all_0_4_4
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n8, n3, all_0_4_4, n11 and discharging atoms sum(n8, n3) = all_0_4_4, sum(n8, n3) = n11, yields:
% 22.91/6.26 | (508) all_0_4_4 = n11
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n1, n10, all_0_7_7, n11 and discharging atoms sum(n1, n10) = all_0_7_7, sum(n1, n10) = n11, yields:
% 22.91/6.26 | (510) all_0_7_7 = n11
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 22.91/6.26 | (545) all_0_2_2 = n4
% 22.91/6.26 |
% 22.91/6.26 | From (545) and (3418) follows:
% 22.91/6.26 | (3240) sum(n4, n2) = all_0_0_0
% 22.91/6.26 |
% 22.91/6.26 | From (510)(508) and (212) follows:
% 22.91/6.26 | (512) sum(n11, n11) = all_0_3_3
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n11, n11, all_0_3_3, n6 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n6, yields:
% 22.91/6.26 | (513) all_0_3_3 = n6
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n4, n2, all_0_0_0, n6 and discharging atoms sum(n4, n2) = all_0_0_0, sum(n4, n2) = n6, yields:
% 22.91/6.26 | (514) all_0_0_0 = n6
% 22.91/6.26 |
% 22.91/6.26 | Equations (514,513) can reduce 363 to:
% 22.91/6.26 | (461) $false
% 22.91/6.26 |
% 22.91/6.26 |-The branch is then unsatisfiable
% 22.91/6.26 |-Branch two:
% 22.91/6.26 | (696) ~ (all_0_11_11 = n2)
% 22.91/6.26 | (697) all_0_11_11 = n1 | all_0_11_11 = n0
% 22.91/6.26 |
% 22.91/6.26 +-Applying beta-rule and splitting (697), into two cases.
% 22.91/6.26 |-Branch one:
% 22.91/6.26 | (698) all_0_11_11 = n1
% 22.91/6.26 |
% 22.91/6.26 | From (698) and (423) follows:
% 22.91/6.26 | (699) pred(n1) = all_0_9_9
% 22.91/6.26 |
% 22.91/6.26 | From (698) and (262) follows:
% 22.91/6.26 | (700) succ(n1) = all_0_5_5
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (130) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 22.91/6.26 | (701) all_0_9_9 = n0
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (165) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 22.91/6.26 | (702) all_0_5_5 = n2
% 22.91/6.26 |
% 22.91/6.26 | From (701)(702) and (147) follows:
% 22.91/6.26 | (703) sum(n0, n2) = all_0_2_2
% 22.91/6.26 |
% 22.91/6.26 | From (701) and (3416) follows:
% 22.91/6.26 | (3577) sum(n0, n10) = all_0_7_7
% 22.91/6.26 |
% 22.91/6.26 | From (702) and (3414) follows:
% 22.91/6.26 | (3578) sum(n8, n2) = all_0_4_4
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n8, n2, all_0_4_4, n10 and discharging atoms sum(n8, n2) = all_0_4_4, sum(n8, n2) = n10, yields:
% 22.91/6.26 | (526) all_0_4_4 = n10
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n0, n10, all_0_7_7, n10 and discharging atoms sum(n0, n10) = all_0_7_7, sum(n0, n10) = n10, yields:
% 22.91/6.26 | (528) all_0_7_7 = n10
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 22.91/6.26 | (563) all_0_2_2 = n2
% 22.91/6.26 |
% 22.91/6.26 | From (563) and (3418) follows:
% 22.91/6.26 | (3436) sum(n2, n2) = all_0_0_0
% 22.91/6.26 |
% 22.91/6.26 | From (528)(526) and (212) follows:
% 22.91/6.26 | (530) sum(n10, n10) = all_0_3_3
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n10, n10, all_0_3_3, n4 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n4, yields:
% 22.91/6.26 | (531) all_0_3_3 = n4
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n2, n2, all_0_0_0, n4 and discharging atoms sum(n2, n2) = all_0_0_0, sum(n2, n2) = n4, yields:
% 22.91/6.26 | (532) all_0_0_0 = n4
% 22.91/6.26 |
% 22.91/6.26 | Equations (532,531) can reduce 363 to:
% 22.91/6.26 | (461) $false
% 22.91/6.26 |
% 22.91/6.26 |-The branch is then unsatisfiable
% 22.91/6.26 |-Branch two:
% 22.91/6.26 | (715) ~ (all_0_11_11 = n1)
% 22.91/6.26 | (716) all_0_11_11 = n0
% 22.91/6.26 |
% 22.91/6.26 | From (716) and (423) follows:
% 22.91/6.26 | (717) pred(n0) = all_0_9_9
% 22.91/6.26 |
% 22.91/6.26 | From (716) and (262) follows:
% 22.91/6.26 | (718) succ(n0) = all_0_5_5
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (130) with n0, all_0_9_9, n15 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n15, yields:
% 22.91/6.26 | (719) all_0_9_9 = n15
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (165) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 22.91/6.26 | (720) all_0_5_5 = n1
% 22.91/6.26 |
% 22.91/6.26 | From (719)(720) and (147) follows:
% 22.91/6.26 | (721) sum(n15, n1) = all_0_2_2
% 22.91/6.26 |
% 22.91/6.26 | From (719) and (3416) follows:
% 22.91/6.26 | (3594) sum(n15, n10) = all_0_7_7
% 22.91/6.26 |
% 22.91/6.26 | From (720) and (3414) follows:
% 22.91/6.26 | (3595) sum(n8, n1) = all_0_4_4
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n15, n10, all_0_7_7, n9 and discharging atoms sum(n15, n10) = all_0_7_7, sum(n15, n10) = n9, yields:
% 22.91/6.26 | (546) all_0_7_7 = n9
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n15, n1, all_0_2_2, n0 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n0, yields:
% 22.91/6.26 | (581) all_0_2_2 = n0
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n8, n1, all_0_4_4, n9 and discharging atoms sum(n8, n1) = all_0_4_4, sum(n8, n1) = n9, yields:
% 22.91/6.26 | (544) all_0_4_4 = n9
% 22.91/6.26 |
% 22.91/6.26 | From (581) and (3418) follows:
% 22.91/6.26 | (3456) sum(n0, n2) = all_0_0_0
% 22.91/6.26 |
% 22.91/6.26 | From (546)(544) and (212) follows:
% 22.91/6.26 | (548) sum(n9, n9) = all_0_3_3
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n9, n9, all_0_3_3, n2 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n2, yields:
% 22.91/6.26 | (549) all_0_3_3 = n2
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n0, n2, all_0_0_0, n2 and discharging atoms sum(n0, n2) = all_0_0_0, sum(n0, n2) = n2, yields:
% 22.91/6.26 | (550) all_0_0_0 = n2
% 22.91/6.26 |
% 22.91/6.26 | Equations (550,549) can reduce 363 to:
% 22.91/6.26 | (461) $false
% 22.91/6.26 |
% 22.91/6.26 |-The branch is then unsatisfiable
% 22.91/6.26 |-Branch two:
% 22.91/6.26 | (851) ~ (all_0_10_10 = n9)
% 22.91/6.26 | (852) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.91/6.26 |
% 22.91/6.26 +-Applying beta-rule and splitting (553), into two cases.
% 22.91/6.26 |-Branch one:
% 22.91/6.26 | (554) all_0_11_11 = n9
% 22.91/6.26 |
% 22.91/6.26 | From (554) and (423) follows:
% 22.91/6.26 | (555) pred(n9) = all_0_9_9
% 22.91/6.26 |
% 22.91/6.26 | From (554) and (262) follows:
% 22.91/6.26 | (556) succ(n9) = all_0_5_5
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (130) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 22.91/6.26 | (557) all_0_9_9 = n8
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (165) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 22.91/6.26 | (558) all_0_5_5 = n10
% 22.91/6.26 |
% 22.91/6.26 | From (558) and (276) follows:
% 22.91/6.26 | (3611) sum(all_0_6_6, n10) = all_0_4_4
% 22.91/6.26 |
% 22.91/6.26 | From (557)(558) and (147) follows:
% 22.91/6.26 | (559) sum(n8, n10) = all_0_2_2
% 22.91/6.26 |
% 22.91/6.26 | From (557) and (350) follows:
% 22.91/6.26 | (3613) sum(n8, all_0_8_8) = all_0_7_7
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n8, n10, all_0_2_2, n2 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n2, yields:
% 22.91/6.26 | (563) all_0_2_2 = n2
% 22.91/6.26 |
% 22.91/6.26 | From (563) and (256) follows:
% 22.91/6.26 | (3615) sum(n2, all_0_1_1) = all_0_0_0
% 22.91/6.26 |
% 22.91/6.26 +-Applying beta-rule and splitting (852), into two cases.
% 22.91/6.26 |-Branch one:
% 22.91/6.26 | (853) all_0_10_10 = n8
% 22.91/6.26 |
% 22.91/6.26 | From (853) and (317) follows:
% 22.91/6.26 | (854) pred(n8) = all_0_6_6
% 22.91/6.26 |
% 22.91/6.26 | From (853) and (146) follows:
% 22.91/6.26 | (855) succ(n8) = all_0_8_8
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (130) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 22.91/6.26 | (856) all_0_6_6 = n7
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (165) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 22.91/6.26 | (857) all_0_8_8 = n9
% 22.91/6.26 |
% 22.91/6.26 | From (856)(857) and (10) follows:
% 22.91/6.26 | (858) sum(n7, n9) = all_0_1_1
% 22.91/6.26 |
% 22.91/6.26 | From (856) and (3611) follows:
% 22.91/6.26 | (3622) sum(n7, n10) = all_0_4_4
% 22.91/6.26 |
% 22.91/6.26 | From (857) and (3613) follows:
% 22.91/6.26 | (3623) sum(n8, n9) = all_0_7_7
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n8, n9, all_0_7_7, n1 and discharging atoms sum(n8, n9) = all_0_7_7, sum(n8, n9) = n1, yields:
% 22.91/6.26 | (690) all_0_7_7 = n1
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n7, n10, all_0_4_4, n1 and discharging atoms sum(n7, n10) = all_0_4_4, sum(n7, n10) = n1, yields:
% 22.91/6.26 | (688) all_0_4_4 = n1
% 22.91/6.26 |
% 22.91/6.26 | Instantiating formula (74) with n7, n9, all_0_1_1, n0 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n0, yields:
% 22.91/6.26 | (862) all_0_1_1 = n0
% 22.91/6.26 |
% 22.91/6.26 | From (690)(688) and (212) follows:
% 22.91/6.26 | (692) sum(n1, n1) = all_0_3_3
% 22.91/6.26 |
% 22.91/6.26 | From (862) and (3615) follows:
% 22.91/6.26 | (3628) sum(n2, n0) = all_0_0_0
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n2, n0, all_0_0_0, n2 and discharging atoms sum(n2, n0) = all_0_0_0, sum(n2, n0) = n2, yields:
% 22.91/6.27 | (550) all_0_0_0 = n2
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 22.91/6.27 | (549) all_0_3_3 = n2
% 22.91/6.27 |
% 22.91/6.27 | Equations (550,549) can reduce 363 to:
% 22.91/6.27 | (461) $false
% 22.91/6.27 |
% 22.91/6.27 |-The branch is then unsatisfiable
% 22.91/6.27 |-Branch two:
% 22.91/6.27 | (869) ~ (all_0_10_10 = n8)
% 22.91/6.27 | (870) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.91/6.27 |
% 22.91/6.27 +-Applying beta-rule and splitting (870), into two cases.
% 22.91/6.27 |-Branch one:
% 22.91/6.27 | (871) all_0_10_10 = n7
% 22.91/6.27 |
% 22.91/6.27 | From (871) and (317) follows:
% 22.91/6.27 | (872) pred(n7) = all_0_6_6
% 22.91/6.27 |
% 22.91/6.27 | From (871) and (146) follows:
% 22.91/6.27 | (873) succ(n7) = all_0_8_8
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (130) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 22.91/6.27 | (874) all_0_6_6 = n6
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (165) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 22.91/6.27 | (875) all_0_8_8 = n8
% 22.91/6.27 |
% 22.91/6.27 | From (874)(875) and (10) follows:
% 22.91/6.27 | (876) sum(n6, n8) = all_0_1_1
% 22.91/6.27 |
% 22.91/6.27 | From (874) and (3611) follows:
% 22.91/6.27 | (3640) sum(n6, n10) = all_0_4_4
% 22.91/6.27 |
% 22.91/6.27 | From (875) and (3613) follows:
% 22.91/6.27 | (3641) sum(n8, n8) = all_0_7_7
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n8, n8, all_0_7_7, n0 and discharging atoms sum(n8, n8) = all_0_7_7, sum(n8, n8) = n0, yields:
% 22.91/6.27 | (708) all_0_7_7 = n0
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n6, n10, all_0_4_4, n0 and discharging atoms sum(n6, n10) = all_0_4_4, sum(n6, n10) = n0, yields:
% 22.91/6.27 | (706) all_0_4_4 = n0
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 22.91/6.27 | (436) all_0_1_1 = n14
% 22.91/6.27 |
% 22.91/6.27 | From (708)(706) and (212) follows:
% 22.91/6.27 | (710) sum(n0, n0) = all_0_3_3
% 22.91/6.27 |
% 22.91/6.27 | From (436) and (3615) follows:
% 22.91/6.27 | (565) sum(n2, n14) = all_0_0_0
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n2, n14, all_0_0_0, n0 and discharging atoms sum(n2, n14) = all_0_0_0, sum(n2, n14) = n0, yields:
% 22.91/6.27 | (568) all_0_0_0 = n0
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 22.91/6.27 | (567) all_0_3_3 = n0
% 22.91/6.27 |
% 22.91/6.27 | Equations (568,567) can reduce 363 to:
% 22.91/6.27 | (461) $false
% 22.91/6.27 |
% 22.91/6.27 |-The branch is then unsatisfiable
% 22.91/6.27 |-Branch two:
% 22.91/6.27 | (887) ~ (all_0_10_10 = n7)
% 22.91/6.27 | (888) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.91/6.27 |
% 22.91/6.27 +-Applying beta-rule and splitting (888), into two cases.
% 22.91/6.27 |-Branch one:
% 22.91/6.27 | (889) all_0_10_10 = n6
% 22.91/6.27 |
% 22.91/6.27 | From (889) and (317) follows:
% 22.91/6.27 | (890) pred(n6) = all_0_6_6
% 22.91/6.27 |
% 22.91/6.27 | From (889) and (146) follows:
% 22.91/6.27 | (891) succ(n6) = all_0_8_8
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (130) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 22.91/6.27 | (892) all_0_6_6 = n5
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (165) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 22.91/6.27 | (893) all_0_8_8 = n7
% 22.91/6.27 |
% 22.91/6.27 | From (892)(893) and (10) follows:
% 22.91/6.27 | (894) sum(n5, n7) = all_0_1_1
% 22.91/6.27 |
% 22.91/6.27 | From (892) and (3611) follows:
% 22.91/6.27 | (3658) sum(n5, n10) = all_0_4_4
% 22.91/6.27 |
% 22.91/6.27 | From (893) and (3613) follows:
% 22.91/6.27 | (3659) sum(n8, n7) = all_0_7_7
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n8, n7, all_0_7_7, n15 and discharging atoms sum(n8, n7) = all_0_7_7, sum(n8, n7) = n15, yields:
% 22.91/6.27 | (725) all_0_7_7 = n15
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n5, n10, all_0_4_4, n15 and discharging atoms sum(n5, n10) = all_0_4_4, sum(n5, n10) = n15, yields:
% 22.91/6.27 | (726) all_0_4_4 = n15
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 22.91/6.27 | (754) all_0_1_1 = n12
% 22.91/6.27 |
% 22.91/6.27 | From (725)(726) and (212) follows:
% 22.91/6.27 | (728) sum(n15, n15) = all_0_3_3
% 22.91/6.27 |
% 22.91/6.27 | From (754) and (3615) follows:
% 22.91/6.27 | (1137) sum(n2, n12) = all_0_0_0
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n15, n15, all_0_3_3, n14 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n14, yields:
% 22.91/6.27 | (585) all_0_3_3 = n14
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n2, n12, all_0_0_0, n14 and discharging atoms sum(n2, n12) = all_0_0_0, sum(n2, n12) = n14, yields:
% 22.91/6.27 | (586) all_0_0_0 = n14
% 22.91/6.27 |
% 22.91/6.27 | Equations (586,585) can reduce 363 to:
% 22.91/6.27 | (461) $false
% 22.91/6.27 |
% 22.91/6.27 |-The branch is then unsatisfiable
% 22.91/6.27 |-Branch two:
% 22.91/6.27 | (905) ~ (all_0_10_10 = n6)
% 22.91/6.27 | (906) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.91/6.27 |
% 22.91/6.27 +-Applying beta-rule and splitting (906), into two cases.
% 22.91/6.27 |-Branch one:
% 22.91/6.27 | (907) all_0_10_10 = n5
% 22.91/6.27 |
% 22.91/6.27 | From (907) and (317) follows:
% 22.91/6.27 | (908) pred(n5) = all_0_6_6
% 22.91/6.27 |
% 22.91/6.27 | From (907) and (146) follows:
% 22.91/6.27 | (909) succ(n5) = all_0_8_8
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (130) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 22.91/6.27 | (910) all_0_6_6 = n4
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (165) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 22.91/6.27 | (911) all_0_8_8 = n6
% 22.91/6.27 |
% 22.91/6.27 | From (910)(911) and (10) follows:
% 22.91/6.27 | (912) sum(n4, n6) = all_0_1_1
% 22.91/6.27 |
% 22.91/6.27 | From (910) and (3611) follows:
% 22.91/6.27 | (3676) sum(n4, n10) = all_0_4_4
% 22.91/6.27 |
% 22.91/6.27 | From (911) and (3613) follows:
% 22.91/6.27 | (3677) sum(n8, n6) = all_0_7_7
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n8, n6, all_0_7_7, n14 and discharging atoms sum(n8, n6) = all_0_7_7, sum(n8, n6) = n14, yields:
% 22.91/6.27 | (452) all_0_7_7 = n14
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n4, n10, all_0_4_4, n14 and discharging atoms sum(n4, n10) = all_0_4_4, sum(n4, n10) = n14, yields:
% 22.91/6.27 | (451) all_0_4_4 = n14
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 22.91/6.27 | (772) all_0_1_1 = n10
% 22.91/6.27 |
% 22.91/6.27 | From (452)(451) and (212) follows:
% 22.91/6.27 | (456) sum(n14, n14) = all_0_3_3
% 22.91/6.27 |
% 22.91/6.27 | From (772) and (3615) follows:
% 22.91/6.27 | (1669) sum(n2, n10) = all_0_0_0
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n14, n14, all_0_3_3, n12 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n12, yields:
% 22.91/6.27 | (459) all_0_3_3 = n12
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n2, n10, all_0_0_0, n12 and discharging atoms sum(n2, n10) = all_0_0_0, sum(n2, n10) = n12, yields:
% 22.91/6.27 | (457) all_0_0_0 = n12
% 22.91/6.27 |
% 22.91/6.27 | Equations (457,459) can reduce 363 to:
% 22.91/6.27 | (461) $false
% 22.91/6.27 |
% 22.91/6.27 |-The branch is then unsatisfiable
% 22.91/6.27 |-Branch two:
% 22.91/6.27 | (923) ~ (all_0_10_10 = n5)
% 22.91/6.27 | (924) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.91/6.27 |
% 22.91/6.27 +-Applying beta-rule and splitting (924), into two cases.
% 22.91/6.27 |-Branch one:
% 22.91/6.27 | (925) all_0_10_10 = n4
% 22.91/6.27 |
% 22.91/6.27 | From (925) and (317) follows:
% 22.91/6.27 | (926) pred(n4) = all_0_6_6
% 22.91/6.27 |
% 22.91/6.27 | From (925) and (146) follows:
% 22.91/6.27 | (927) succ(n4) = all_0_8_8
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (130) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 22.91/6.27 | (928) all_0_6_6 = n3
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (165) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 22.91/6.27 | (929) all_0_8_8 = n5
% 22.91/6.27 |
% 22.91/6.27 | From (928)(929) and (10) follows:
% 22.91/6.27 | (930) sum(n3, n5) = all_0_1_1
% 22.91/6.27 |
% 22.91/6.27 | From (928) and (3611) follows:
% 22.91/6.27 | (3694) sum(n3, n10) = all_0_4_4
% 22.91/6.27 |
% 22.91/6.27 | From (929) and (3613) follows:
% 22.91/6.27 | (3695) sum(n8, n5) = all_0_7_7
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n8, n5, all_0_7_7, n13 and discharging atoms sum(n8, n5) = all_0_7_7, sum(n8, n5) = n13, yields:
% 22.91/6.27 | (474) all_0_7_7 = n13
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n3, n10, all_0_4_4, n13 and discharging atoms sum(n3, n10) = all_0_4_4, sum(n3, n10) = n13, yields:
% 22.91/6.27 | (472) all_0_4_4 = n13
% 22.91/6.27 |
% 22.91/6.27 | Instantiating formula (74) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 22.91/6.27 | (790) all_0_1_1 = n8
% 22.91/6.27 |
% 22.91/6.27 | From (474)(472) and (212) follows:
% 22.91/6.27 | (476) sum(n13, n13) = all_0_3_3
% 22.91/6.27 |
% 22.91/6.27 | From (790) and (3615) follows:
% 22.91/6.28 | (2165) sum(n2, n8) = all_0_0_0
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n13, n13, all_0_3_3, n10 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n10, yields:
% 22.91/6.28 | (477) all_0_3_3 = n10
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n2, n8, all_0_0_0, n10 and discharging atoms sum(n2, n8) = all_0_0_0, sum(n2, n8) = n10, yields:
% 22.91/6.28 | (478) all_0_0_0 = n10
% 22.91/6.28 |
% 22.91/6.28 | Equations (478,477) can reduce 363 to:
% 22.91/6.28 | (461) $false
% 22.91/6.28 |
% 22.91/6.28 |-The branch is then unsatisfiable
% 22.91/6.28 |-Branch two:
% 22.91/6.28 | (941) ~ (all_0_10_10 = n4)
% 22.91/6.28 | (942) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.91/6.28 |
% 22.91/6.28 +-Applying beta-rule and splitting (942), into two cases.
% 22.91/6.28 |-Branch one:
% 22.91/6.28 | (943) all_0_10_10 = n3
% 22.91/6.28 |
% 22.91/6.28 | From (943) and (317) follows:
% 22.91/6.28 | (944) pred(n3) = all_0_6_6
% 22.91/6.28 |
% 22.91/6.28 | From (943) and (146) follows:
% 22.91/6.28 | (945) succ(n3) = all_0_8_8
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (130) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 22.91/6.28 | (946) all_0_6_6 = n2
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (165) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 22.91/6.28 | (947) all_0_8_8 = n4
% 22.91/6.28 |
% 22.91/6.28 | From (946)(947) and (10) follows:
% 22.91/6.28 | (948) sum(n2, n4) = all_0_1_1
% 22.91/6.28 |
% 22.91/6.28 | From (946) and (3611) follows:
% 22.91/6.28 | (3712) sum(n2, n10) = all_0_4_4
% 22.91/6.28 |
% 22.91/6.28 | From (947) and (3613) follows:
% 22.91/6.28 | (3713) sum(n8, n4) = all_0_7_7
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n8, n4, all_0_7_7, n12 and discharging atoms sum(n8, n4) = all_0_7_7, sum(n8, n4) = n12, yields:
% 22.91/6.28 | (492) all_0_7_7 = n12
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n2, n10, all_0_4_4, n12 and discharging atoms sum(n2, n10) = all_0_4_4, sum(n2, n10) = n12, yields:
% 22.91/6.28 | (490) all_0_4_4 = n12
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 22.91/6.28 | (808) all_0_1_1 = n6
% 22.91/6.28 |
% 22.91/6.28 | From (492)(490) and (212) follows:
% 22.91/6.28 | (494) sum(n12, n12) = all_0_3_3
% 22.91/6.28 |
% 22.91/6.28 | From (808) and (3615) follows:
% 22.91/6.28 | (2625) sum(n2, n6) = all_0_0_0
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n12, n12, all_0_3_3, n8 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n8, yields:
% 22.91/6.28 | (495) all_0_3_3 = n8
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n2, n6, all_0_0_0, n8 and discharging atoms sum(n2, n6) = all_0_0_0, sum(n2, n6) = n8, yields:
% 22.91/6.28 | (496) all_0_0_0 = n8
% 22.91/6.28 |
% 22.91/6.28 | Equations (496,495) can reduce 363 to:
% 22.91/6.28 | (461) $false
% 22.91/6.28 |
% 22.91/6.28 |-The branch is then unsatisfiable
% 22.91/6.28 |-Branch two:
% 22.91/6.28 | (959) ~ (all_0_10_10 = n3)
% 22.91/6.28 | (960) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.91/6.28 |
% 22.91/6.28 +-Applying beta-rule and splitting (960), into two cases.
% 22.91/6.28 |-Branch one:
% 22.91/6.28 | (961) all_0_10_10 = n2
% 22.91/6.28 |
% 22.91/6.28 | From (961) and (317) follows:
% 22.91/6.28 | (962) pred(n2) = all_0_6_6
% 22.91/6.28 |
% 22.91/6.28 | From (961) and (146) follows:
% 22.91/6.28 | (963) succ(n2) = all_0_8_8
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (130) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 22.91/6.28 | (964) all_0_6_6 = n1
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (165) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 22.91/6.28 | (965) all_0_8_8 = n3
% 22.91/6.28 |
% 22.91/6.28 | From (964)(965) and (10) follows:
% 22.91/6.28 | (966) sum(n1, n3) = all_0_1_1
% 22.91/6.28 |
% 22.91/6.28 | From (964) and (3611) follows:
% 22.91/6.28 | (3730) sum(n1, n10) = all_0_4_4
% 22.91/6.28 |
% 22.91/6.28 | From (965) and (3613) follows:
% 22.91/6.28 | (3731) sum(n8, n3) = all_0_7_7
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n8, n3, all_0_7_7, n11 and discharging atoms sum(n8, n3) = all_0_7_7, sum(n8, n3) = n11, yields:
% 22.91/6.28 | (510) all_0_7_7 = n11
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n1, n10, all_0_4_4, n11 and discharging atoms sum(n1, n10) = all_0_4_4, sum(n1, n10) = n11, yields:
% 22.91/6.28 | (508) all_0_4_4 = n11
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 22.91/6.28 | (826) all_0_1_1 = n4
% 22.91/6.28 |
% 22.91/6.28 | From (510)(508) and (212) follows:
% 22.91/6.28 | (512) sum(n11, n11) = all_0_3_3
% 22.91/6.28 |
% 22.91/6.28 | From (826) and (3615) follows:
% 22.91/6.28 | (3050) sum(n2, n4) = all_0_0_0
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n11, n11, all_0_3_3, n6 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n6, yields:
% 22.91/6.28 | (513) all_0_3_3 = n6
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n2, n4, all_0_0_0, n6 and discharging atoms sum(n2, n4) = all_0_0_0, sum(n2, n4) = n6, yields:
% 22.91/6.28 | (514) all_0_0_0 = n6
% 22.91/6.28 |
% 22.91/6.28 | Equations (514,513) can reduce 363 to:
% 22.91/6.28 | (461) $false
% 22.91/6.28 |
% 22.91/6.28 |-The branch is then unsatisfiable
% 22.91/6.28 |-Branch two:
% 22.91/6.28 | (977) ~ (all_0_10_10 = n2)
% 22.91/6.28 | (978) all_0_10_10 = n1 | all_0_10_10 = n0
% 22.91/6.28 |
% 22.91/6.28 +-Applying beta-rule and splitting (978), into two cases.
% 22.91/6.28 |-Branch one:
% 22.91/6.28 | (979) all_0_10_10 = n1
% 22.91/6.28 |
% 22.91/6.28 | From (979) and (317) follows:
% 22.91/6.28 | (980) pred(n1) = all_0_6_6
% 22.91/6.28 |
% 22.91/6.28 | From (979) and (146) follows:
% 22.91/6.28 | (981) succ(n1) = all_0_8_8
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (130) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 22.91/6.28 | (982) all_0_6_6 = n0
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (165) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 22.91/6.28 | (983) all_0_8_8 = n2
% 22.91/6.28 |
% 22.91/6.28 | From (982)(983) and (10) follows:
% 22.91/6.28 | (984) sum(n0, n2) = all_0_1_1
% 22.91/6.28 |
% 22.91/6.28 | From (982) and (3611) follows:
% 22.91/6.28 | (3748) sum(n0, n10) = all_0_4_4
% 22.91/6.28 |
% 22.91/6.28 | From (983) and (3613) follows:
% 22.91/6.28 | (3749) sum(n8, n2) = all_0_7_7
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n8, n2, all_0_7_7, n10 and discharging atoms sum(n8, n2) = all_0_7_7, sum(n8, n2) = n10, yields:
% 22.91/6.28 | (528) all_0_7_7 = n10
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n0, n10, all_0_4_4, n10 and discharging atoms sum(n0, n10) = all_0_4_4, sum(n0, n10) = n10, yields:
% 22.91/6.28 | (526) all_0_4_4 = n10
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 22.91/6.28 | (844) all_0_1_1 = n2
% 22.91/6.28 |
% 22.91/6.28 | From (528)(526) and (212) follows:
% 22.91/6.28 | (530) sum(n10, n10) = all_0_3_3
% 22.91/6.28 |
% 22.91/6.28 | From (844) and (3615) follows:
% 22.91/6.28 | (3436) sum(n2, n2) = all_0_0_0
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n10, n10, all_0_3_3, n4 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n4, yields:
% 22.91/6.28 | (531) all_0_3_3 = n4
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n2, n2, all_0_0_0, n4 and discharging atoms sum(n2, n2) = all_0_0_0, sum(n2, n2) = n4, yields:
% 22.91/6.28 | (532) all_0_0_0 = n4
% 22.91/6.28 |
% 22.91/6.28 | Equations (532,531) can reduce 363 to:
% 22.91/6.28 | (461) $false
% 22.91/6.28 |
% 22.91/6.28 |-The branch is then unsatisfiable
% 22.91/6.28 |-Branch two:
% 22.91/6.28 | (997) ~ (all_0_10_10 = n1)
% 22.91/6.28 | (998) all_0_10_10 = n0
% 22.91/6.28 |
% 22.91/6.28 | From (998) and (317) follows:
% 22.91/6.28 | (999) pred(n0) = all_0_6_6
% 22.91/6.28 |
% 22.91/6.28 | From (998) and (146) follows:
% 22.91/6.28 | (1000) succ(n0) = all_0_8_8
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (130) with n0, all_0_6_6, n15 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n15, yields:
% 22.91/6.28 | (1001) all_0_6_6 = n15
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (165) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 22.91/6.28 | (1002) all_0_8_8 = n1
% 22.91/6.28 |
% 22.91/6.28 | From (1001)(1002) and (10) follows:
% 22.91/6.28 | (1003) sum(n15, n1) = all_0_1_1
% 22.91/6.28 |
% 22.91/6.28 | From (1001) and (3611) follows:
% 22.91/6.28 | (3765) sum(n15, n10) = all_0_4_4
% 22.91/6.28 |
% 22.91/6.28 | From (1002) and (3613) follows:
% 22.91/6.28 | (3766) sum(n8, n1) = all_0_7_7
% 22.91/6.28 |
% 22.91/6.28 | Instantiating formula (74) with n15, n10, all_0_4_4, n9 and discharging atoms sum(n15, n10) = all_0_4_4, sum(n15, n10) = n9, yields:
% 22.91/6.29 | (544) all_0_4_4 = n9
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (74) with n15, n1, all_0_1_1, n0 and discharging atoms sum(n15, n1) = all_0_1_1, sum(n15, n1) = n0, yields:
% 22.91/6.29 | (862) all_0_1_1 = n0
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (74) with n8, n1, all_0_7_7, n9 and discharging atoms sum(n8, n1) = all_0_7_7, sum(n8, n1) = n9, yields:
% 22.91/6.29 | (546) all_0_7_7 = n9
% 22.91/6.29 |
% 22.91/6.29 | From (546)(544) and (212) follows:
% 22.91/6.29 | (548) sum(n9, n9) = all_0_3_3
% 22.91/6.29 |
% 22.91/6.29 | From (862) and (3615) follows:
% 22.91/6.29 | (3628) sum(n2, n0) = all_0_0_0
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (74) with n9, n9, all_0_3_3, n2 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n2, yields:
% 22.91/6.29 | (549) all_0_3_3 = n2
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (74) with n2, n0, all_0_0_0, n2 and discharging atoms sum(n2, n0) = all_0_0_0, sum(n2, n0) = n2, yields:
% 22.91/6.29 | (550) all_0_0_0 = n2
% 22.91/6.29 |
% 22.91/6.29 | Equations (550,549) can reduce 363 to:
% 22.91/6.29 | (461) $false
% 22.91/6.29 |
% 22.91/6.29 |-The branch is then unsatisfiable
% 22.91/6.29 |-Branch two:
% 22.91/6.29 | (570) ~ (all_0_11_11 = n9)
% 22.91/6.29 | (571) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.91/6.29 |
% 22.91/6.29 +-Applying beta-rule and splitting (852), into two cases.
% 22.91/6.29 |-Branch one:
% 22.91/6.29 | (853) all_0_10_10 = n8
% 22.91/6.29 |
% 22.91/6.29 | From (853) and (317) follows:
% 22.91/6.29 | (854) pred(n8) = all_0_6_6
% 22.91/6.29 |
% 22.91/6.29 | From (853) and (146) follows:
% 22.91/6.29 | (855) succ(n8) = all_0_8_8
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (130) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 22.91/6.29 | (856) all_0_6_6 = n7
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (165) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 22.91/6.29 | (857) all_0_8_8 = n9
% 22.91/6.29 |
% 22.91/6.29 | From (856) and (854) follows:
% 22.91/6.29 | (240) pred(n8) = n7
% 22.91/6.29 |
% 22.91/6.29 | From (857) and (855) follows:
% 22.91/6.29 | (298) succ(n8) = n9
% 22.91/6.29 |
% 22.91/6.29 | From (856) and (276) follows:
% 22.91/6.29 | (3784) sum(n7, all_0_5_5) = all_0_4_4
% 22.91/6.29 |
% 22.91/6.29 | From (856)(857) and (10) follows:
% 22.91/6.29 | (858) sum(n7, n9) = all_0_1_1
% 22.91/6.29 |
% 22.91/6.29 | From (857) and (350) follows:
% 22.91/6.29 | (3786) sum(all_0_9_9, n9) = all_0_7_7
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (74) with n7, n9, all_0_1_1, n0 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n0, yields:
% 22.91/6.29 | (862) all_0_1_1 = n0
% 22.91/6.29 |
% 22.91/6.29 | From (862) and (256) follows:
% 22.91/6.29 | (3788) sum(all_0_2_2, n0) = all_0_0_0
% 22.91/6.29 |
% 22.91/6.29 | From (862) and (858) follows:
% 22.91/6.29 | (4) sum(n7, n9) = n0
% 22.91/6.29 |
% 22.91/6.29 +-Applying beta-rule and splitting (571), into two cases.
% 22.91/6.29 |-Branch one:
% 22.91/6.29 | (572) all_0_11_11 = n8
% 22.91/6.29 |
% 22.91/6.29 | From (572) and (423) follows:
% 22.91/6.29 | (573) pred(n8) = all_0_9_9
% 22.91/6.29 |
% 22.91/6.29 | From (572) and (262) follows:
% 22.91/6.29 | (574) succ(n8) = all_0_5_5
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (130) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 22.91/6.29 | (575) all_0_9_9 = n7
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (165) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 22.91/6.29 | (576) all_0_5_5 = n9
% 22.91/6.29 |
% 22.91/6.29 | From (575)(576) and (147) follows:
% 22.91/6.29 | (577) sum(n7, n9) = all_0_2_2
% 22.91/6.29 |
% 22.91/6.29 | From (575) and (3786) follows:
% 22.91/6.29 | (3796) sum(n7, n9) = all_0_7_7
% 22.91/6.29 |
% 22.91/6.29 | From (576) and (3784) follows:
% 22.91/6.29 | (3797) sum(n7, n9) = all_0_4_4
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (74) with n7, n9, all_0_2_2, n0 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n0, yields:
% 22.91/6.29 | (581) all_0_2_2 = n0
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (74) with n7, n9, all_0_4_4, all_0_2_2 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = all_0_4_4, yields:
% 22.91/6.29 | (448) all_0_2_2 = all_0_4_4
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (74) with n7, n9, all_0_7_7, all_0_2_2 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = all_0_7_7, yields:
% 22.91/6.29 | (449) all_0_2_2 = all_0_7_7
% 22.91/6.29 |
% 22.91/6.29 | Combining equations (449,448) yields a new equation:
% 22.91/6.29 | (450) all_0_4_4 = all_0_7_7
% 22.91/6.29 |
% 22.91/6.29 | Combining equations (581,448) yields a new equation:
% 22.91/6.29 | (706) all_0_4_4 = n0
% 22.91/6.29 |
% 22.91/6.29 | Combining equations (706,450) yields a new equation:
% 22.91/6.29 | (708) all_0_7_7 = n0
% 22.91/6.29 |
% 22.91/6.29 | Combining equations (708,450) yields a new equation:
% 22.91/6.29 | (706) all_0_4_4 = n0
% 22.91/6.29 |
% 22.91/6.29 | Combining equations (706,448) yields a new equation:
% 22.91/6.29 | (581) all_0_2_2 = n0
% 22.91/6.29 |
% 22.91/6.29 | From (581) and (3788) follows:
% 22.91/6.29 | (3806) sum(n0, n0) = all_0_0_0
% 22.91/6.29 |
% 22.91/6.29 | From (708)(706) and (212) follows:
% 22.91/6.29 | (710) sum(n0, n0) = all_0_3_3
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (74) with n0, n0, all_0_0_0, n0 and discharging atoms sum(n0, n0) = all_0_0_0, sum(n0, n0) = n0, yields:
% 22.91/6.29 | (568) all_0_0_0 = n0
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (74) with n0, n0, all_0_3_3, all_0_0_0 and discharging atoms sum(n0, n0) = all_0_0_0, sum(n0, n0) = all_0_3_3, yields:
% 22.91/6.29 | (458) all_0_0_0 = all_0_3_3
% 22.91/6.29 |
% 22.91/6.29 | Combining equations (568,458) yields a new equation:
% 22.91/6.29 | (567) all_0_3_3 = n0
% 22.91/6.29 |
% 22.91/6.29 | Combining equations (567,458) yields a new equation:
% 22.91/6.29 | (568) all_0_0_0 = n0
% 22.91/6.29 |
% 22.91/6.29 | Equations (568,567) can reduce 363 to:
% 22.91/6.29 | (461) $false
% 22.91/6.29 |
% 22.91/6.29 |-The branch is then unsatisfiable
% 22.91/6.29 |-Branch two:
% 22.91/6.29 | (588) ~ (all_0_11_11 = n8)
% 22.91/6.29 | (589) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.91/6.29 |
% 22.91/6.29 +-Applying beta-rule and splitting (589), into two cases.
% 22.91/6.29 |-Branch one:
% 22.91/6.29 | (590) all_0_11_11 = n7
% 22.91/6.29 |
% 22.91/6.29 | From (590) and (423) follows:
% 22.91/6.29 | (591) pred(n7) = all_0_9_9
% 22.91/6.29 |
% 22.91/6.29 | From (590) and (262) follows:
% 22.91/6.29 | (592) succ(n7) = all_0_5_5
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (130) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 22.91/6.29 | (593) all_0_9_9 = n6
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (165) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 22.91/6.29 | (594) all_0_5_5 = n8
% 22.91/6.29 |
% 22.91/6.29 | From (593)(594) and (147) follows:
% 22.91/6.29 | (595) sum(n6, n8) = all_0_2_2
% 22.91/6.29 |
% 22.91/6.29 | From (593) and (3786) follows:
% 22.91/6.29 | (3821) sum(n6, n9) = all_0_7_7
% 22.91/6.29 |
% 22.91/6.29 | From (594) and (3784) follows:
% 22.91/6.29 | (3822) sum(n7, n8) = all_0_4_4
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (74) with n7, n8, all_0_4_4, n15 and discharging atoms sum(n7, n8) = all_0_4_4, sum(n7, n8) = n15, yields:
% 22.91/6.29 | (726) all_0_4_4 = n15
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (74) with n6, n9, all_0_7_7, n15 and discharging atoms sum(n6, n9) = all_0_7_7, sum(n6, n9) = n15, yields:
% 22.91/6.29 | (725) all_0_7_7 = n15
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (74) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 22.91/6.29 | (447) all_0_2_2 = n14
% 22.91/6.29 |
% 22.91/6.29 | From (447) and (3788) follows:
% 22.91/6.29 | (865) sum(n14, n0) = all_0_0_0
% 22.91/6.29 |
% 22.91/6.29 | From (725)(726) and (212) follows:
% 22.91/6.29 | (728) sum(n15, n15) = all_0_3_3
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (74) with n15, n15, all_0_3_3, n14 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n14, yields:
% 22.91/6.29 | (585) all_0_3_3 = n14
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (74) with n14, n0, all_0_0_0, n14 and discharging atoms sum(n14, n0) = all_0_0_0, sum(n14, n0) = n14, yields:
% 22.91/6.29 | (586) all_0_0_0 = n14
% 22.91/6.29 |
% 22.91/6.29 | Equations (586,585) can reduce 363 to:
% 22.91/6.29 | (461) $false
% 22.91/6.29 |
% 22.91/6.29 |-The branch is then unsatisfiable
% 22.91/6.29 |-Branch two:
% 22.91/6.29 | (606) ~ (all_0_11_11 = n7)
% 22.91/6.29 | (607) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.91/6.29 |
% 22.91/6.29 +-Applying beta-rule and splitting (607), into two cases.
% 22.91/6.29 |-Branch one:
% 22.91/6.29 | (608) all_0_11_11 = n6
% 22.91/6.29 |
% 22.91/6.29 | From (608) and (423) follows:
% 22.91/6.29 | (609) pred(n6) = all_0_9_9
% 22.91/6.29 |
% 22.91/6.29 | From (608) and (262) follows:
% 22.91/6.29 | (610) succ(n6) = all_0_5_5
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (130) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 22.91/6.29 | (611) all_0_9_9 = n5
% 22.91/6.29 |
% 22.91/6.29 | Instantiating formula (165) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 22.91/6.29 | (612) all_0_5_5 = n7
% 22.91/6.29 |
% 22.91/6.29 | From (611)(612) and (147) follows:
% 22.91/6.29 | (613) sum(n5, n7) = all_0_2_2
% 22.91/6.29 |
% 22.91/6.29 | From (611) and (3786) follows:
% 22.91/6.29 | (3839) sum(n5, n9) = all_0_7_7
% 22.91/6.29 |
% 22.91/6.29 | From (612) and (3784) follows:
% 22.91/6.30 | (3840) sum(n7, n7) = all_0_4_4
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n7, n7, all_0_4_4, n14 and discharging atoms sum(n7, n7) = all_0_4_4, sum(n7, n7) = n14, yields:
% 22.91/6.30 | (451) all_0_4_4 = n14
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n5, n9, all_0_7_7, n14 and discharging atoms sum(n5, n9) = all_0_7_7, sum(n5, n9) = n14, yields:
% 22.91/6.30 | (452) all_0_7_7 = n14
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 22.91/6.30 | (473) all_0_2_2 = n12
% 22.91/6.30 |
% 22.91/6.30 | From (473) and (3788) follows:
% 22.91/6.30 | (1417) sum(n12, n0) = all_0_0_0
% 22.91/6.30 |
% 22.91/6.30 | From (452)(451) and (212) follows:
% 22.91/6.30 | (456) sum(n14, n14) = all_0_3_3
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n14, n14, all_0_3_3, n12 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n12, yields:
% 22.91/6.30 | (459) all_0_3_3 = n12
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n12, n0, all_0_0_0, n12 and discharging atoms sum(n12, n0) = all_0_0_0, sum(n12, n0) = n12, yields:
% 22.91/6.30 | (457) all_0_0_0 = n12
% 22.91/6.30 |
% 22.91/6.30 | Equations (457,459) can reduce 363 to:
% 22.91/6.30 | (461) $false
% 22.91/6.30 |
% 22.91/6.30 |-The branch is then unsatisfiable
% 22.91/6.30 |-Branch two:
% 22.91/6.30 | (624) ~ (all_0_11_11 = n6)
% 22.91/6.30 | (625) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.91/6.30 |
% 22.91/6.30 +-Applying beta-rule and splitting (625), into two cases.
% 22.91/6.30 |-Branch one:
% 22.91/6.30 | (626) all_0_11_11 = n5
% 22.91/6.30 |
% 22.91/6.30 | From (626) and (423) follows:
% 22.91/6.30 | (627) pred(n5) = all_0_9_9
% 22.91/6.30 |
% 22.91/6.30 | From (626) and (262) follows:
% 22.91/6.30 | (628) succ(n5) = all_0_5_5
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (130) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 22.91/6.30 | (629) all_0_9_9 = n4
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (165) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 22.91/6.30 | (630) all_0_5_5 = n6
% 22.91/6.30 |
% 22.91/6.30 | From (629)(630) and (147) follows:
% 22.91/6.30 | (631) sum(n4, n6) = all_0_2_2
% 22.91/6.30 |
% 22.91/6.30 | From (629) and (3786) follows:
% 22.91/6.30 | (3857) sum(n4, n9) = all_0_7_7
% 22.91/6.30 |
% 22.91/6.30 | From (630) and (3784) follows:
% 22.91/6.30 | (3858) sum(n7, n6) = all_0_4_4
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n7, n6, all_0_4_4, n13 and discharging atoms sum(n7, n6) = all_0_4_4, sum(n7, n6) = n13, yields:
% 22.91/6.30 | (472) all_0_4_4 = n13
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n4, n9, all_0_7_7, n13 and discharging atoms sum(n4, n9) = all_0_7_7, sum(n4, n9) = n13, yields:
% 22.91/6.30 | (474) all_0_7_7 = n13
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 22.91/6.30 | (491) all_0_2_2 = n10
% 22.91/6.30 |
% 22.91/6.30 | From (491) and (3788) follows:
% 22.91/6.30 | (1931) sum(n10, n0) = all_0_0_0
% 22.91/6.30 |
% 22.91/6.30 | From (474)(472) and (212) follows:
% 22.91/6.30 | (476) sum(n13, n13) = all_0_3_3
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n13, n13, all_0_3_3, n10 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n10, yields:
% 22.91/6.30 | (477) all_0_3_3 = n10
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n10, n0, all_0_0_0, n10 and discharging atoms sum(n10, n0) = all_0_0_0, sum(n10, n0) = n10, yields:
% 22.91/6.30 | (478) all_0_0_0 = n10
% 22.91/6.30 |
% 22.91/6.30 | Equations (478,477) can reduce 363 to:
% 22.91/6.30 | (461) $false
% 22.91/6.30 |
% 22.91/6.30 |-The branch is then unsatisfiable
% 22.91/6.30 |-Branch two:
% 22.91/6.30 | (642) ~ (all_0_11_11 = n5)
% 22.91/6.30 | (643) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.91/6.30 |
% 22.91/6.30 +-Applying beta-rule and splitting (643), into two cases.
% 22.91/6.30 |-Branch one:
% 22.91/6.30 | (644) all_0_11_11 = n4
% 22.91/6.30 |
% 22.91/6.30 | From (644) and (423) follows:
% 22.91/6.30 | (645) pred(n4) = all_0_9_9
% 22.91/6.30 |
% 22.91/6.30 | From (644) and (262) follows:
% 22.91/6.30 | (646) succ(n4) = all_0_5_5
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (130) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 22.91/6.30 | (647) all_0_9_9 = n3
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (165) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 22.91/6.30 | (648) all_0_5_5 = n5
% 22.91/6.30 |
% 22.91/6.30 | From (647)(648) and (147) follows:
% 22.91/6.30 | (649) sum(n3, n5) = all_0_2_2
% 22.91/6.30 |
% 22.91/6.30 | From (647) and (3786) follows:
% 22.91/6.30 | (3875) sum(n3, n9) = all_0_7_7
% 22.91/6.30 |
% 22.91/6.30 | From (648) and (3784) follows:
% 22.91/6.30 | (3876) sum(n7, n5) = all_0_4_4
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n7, n5, all_0_4_4, n12 and discharging atoms sum(n7, n5) = all_0_4_4, sum(n7, n5) = n12, yields:
% 22.91/6.30 | (490) all_0_4_4 = n12
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n3, n9, all_0_7_7, n12 and discharging atoms sum(n3, n9) = all_0_7_7, sum(n3, n9) = n12, yields:
% 22.91/6.30 | (492) all_0_7_7 = n12
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 22.91/6.30 | (509) all_0_2_2 = n8
% 22.91/6.30 |
% 22.91/6.30 | From (509) and (3788) follows:
% 22.91/6.30 | (2409) sum(n8, n0) = all_0_0_0
% 22.91/6.30 |
% 22.91/6.30 | From (492)(490) and (212) follows:
% 22.91/6.30 | (494) sum(n12, n12) = all_0_3_3
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n12, n12, all_0_3_3, n8 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n8, yields:
% 22.91/6.30 | (495) all_0_3_3 = n8
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n8, n0, all_0_0_0, n8 and discharging atoms sum(n8, n0) = all_0_0_0, sum(n8, n0) = n8, yields:
% 22.91/6.30 | (496) all_0_0_0 = n8
% 22.91/6.30 |
% 22.91/6.30 | Equations (496,495) can reduce 363 to:
% 22.91/6.30 | (461) $false
% 22.91/6.30 |
% 22.91/6.30 |-The branch is then unsatisfiable
% 22.91/6.30 |-Branch two:
% 22.91/6.30 | (660) ~ (all_0_11_11 = n4)
% 22.91/6.30 | (661) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.91/6.30 |
% 22.91/6.30 +-Applying beta-rule and splitting (661), into two cases.
% 22.91/6.30 |-Branch one:
% 22.91/6.30 | (662) all_0_11_11 = n3
% 22.91/6.30 |
% 22.91/6.30 | From (662) and (423) follows:
% 22.91/6.30 | (663) pred(n3) = all_0_9_9
% 22.91/6.30 |
% 22.91/6.30 | From (662) and (262) follows:
% 22.91/6.30 | (664) succ(n3) = all_0_5_5
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (130) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 22.91/6.30 | (665) all_0_9_9 = n2
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (165) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 22.91/6.30 | (666) all_0_5_5 = n4
% 22.91/6.30 |
% 22.91/6.30 | From (665)(666) and (147) follows:
% 22.91/6.30 | (667) sum(n2, n4) = all_0_2_2
% 22.91/6.30 |
% 22.91/6.30 | From (665) and (3786) follows:
% 22.91/6.30 | (3893) sum(n2, n9) = all_0_7_7
% 22.91/6.30 |
% 22.91/6.30 | From (666) and (3784) follows:
% 22.91/6.30 | (3894) sum(n7, n4) = all_0_4_4
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n7, n4, all_0_4_4, n11 and discharging atoms sum(n7, n4) = all_0_4_4, sum(n7, n4) = n11, yields:
% 22.91/6.30 | (508) all_0_4_4 = n11
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n2, n9, all_0_7_7, n11 and discharging atoms sum(n2, n9) = all_0_7_7, sum(n2, n9) = n11, yields:
% 22.91/6.30 | (510) all_0_7_7 = n11
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 22.91/6.30 | (527) all_0_2_2 = n6
% 22.91/6.30 |
% 22.91/6.30 | From (527) and (3788) follows:
% 22.91/6.30 | (2852) sum(n6, n0) = all_0_0_0
% 22.91/6.30 |
% 22.91/6.30 | From (510)(508) and (212) follows:
% 22.91/6.30 | (512) sum(n11, n11) = all_0_3_3
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n11, n11, all_0_3_3, n6 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n6, yields:
% 22.91/6.30 | (513) all_0_3_3 = n6
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (74) with n6, n0, all_0_0_0, n6 and discharging atoms sum(n6, n0) = all_0_0_0, sum(n6, n0) = n6, yields:
% 22.91/6.30 | (514) all_0_0_0 = n6
% 22.91/6.30 |
% 22.91/6.30 | Equations (514,513) can reduce 363 to:
% 22.91/6.30 | (461) $false
% 22.91/6.30 |
% 22.91/6.30 |-The branch is then unsatisfiable
% 22.91/6.30 |-Branch two:
% 22.91/6.30 | (678) ~ (all_0_11_11 = n3)
% 22.91/6.30 | (679) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 22.91/6.30 |
% 22.91/6.30 +-Applying beta-rule and splitting (679), into two cases.
% 22.91/6.30 |-Branch one:
% 22.91/6.30 | (680) all_0_11_11 = n2
% 22.91/6.30 |
% 22.91/6.30 | From (680) and (423) follows:
% 22.91/6.30 | (681) pred(n2) = all_0_9_9
% 22.91/6.30 |
% 22.91/6.30 | From (680) and (262) follows:
% 22.91/6.30 | (682) succ(n2) = all_0_5_5
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (130) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 22.91/6.30 | (683) all_0_9_9 = n1
% 22.91/6.30 |
% 22.91/6.30 | Instantiating formula (165) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 22.91/6.30 | (684) all_0_5_5 = n3
% 22.91/6.30 |
% 22.91/6.30 | From (683)(684) and (147) follows:
% 22.91/6.30 | (685) sum(n1, n3) = all_0_2_2
% 22.91/6.30 |
% 22.91/6.30 | From (683) and (3786) follows:
% 22.91/6.30 | (3911) sum(n1, n9) = all_0_7_7
% 22.91/6.30 |
% 22.91/6.30 | From (684) and (3784) follows:
% 22.91/6.31 | (3912) sum(n7, n3) = all_0_4_4
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n7, n3, all_0_4_4, n10 and discharging atoms sum(n7, n3) = all_0_4_4, sum(n7, n3) = n10, yields:
% 22.91/6.31 | (526) all_0_4_4 = n10
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n1, n9, all_0_7_7, n10 and discharging atoms sum(n1, n9) = all_0_7_7, sum(n1, n9) = n10, yields:
% 22.91/6.31 | (528) all_0_7_7 = n10
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 22.91/6.31 | (545) all_0_2_2 = n4
% 22.91/6.31 |
% 22.91/6.31 | From (545) and (3788) follows:
% 22.91/6.31 | (3258) sum(n4, n0) = all_0_0_0
% 22.91/6.31 |
% 22.91/6.31 | From (528)(526) and (212) follows:
% 22.91/6.31 | (530) sum(n10, n10) = all_0_3_3
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n10, n10, all_0_3_3, n4 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n4, yields:
% 22.91/6.31 | (531) all_0_3_3 = n4
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n4, n0, all_0_0_0, n4 and discharging atoms sum(n4, n0) = all_0_0_0, sum(n4, n0) = n4, yields:
% 22.91/6.31 | (532) all_0_0_0 = n4
% 22.91/6.31 |
% 22.91/6.31 | Equations (532,531) can reduce 363 to:
% 22.91/6.31 | (461) $false
% 22.91/6.31 |
% 22.91/6.31 |-The branch is then unsatisfiable
% 22.91/6.31 |-Branch two:
% 22.91/6.31 | (696) ~ (all_0_11_11 = n2)
% 22.91/6.31 | (697) all_0_11_11 = n1 | all_0_11_11 = n0
% 22.91/6.31 |
% 22.91/6.31 +-Applying beta-rule and splitting (697), into two cases.
% 22.91/6.31 |-Branch one:
% 22.91/6.31 | (698) all_0_11_11 = n1
% 22.91/6.31 |
% 22.91/6.31 | From (698) and (423) follows:
% 22.91/6.31 | (699) pred(n1) = all_0_9_9
% 22.91/6.31 |
% 22.91/6.31 | From (698) and (262) follows:
% 22.91/6.31 | (700) succ(n1) = all_0_5_5
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (130) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 22.91/6.31 | (701) all_0_9_9 = n0
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (165) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 22.91/6.31 | (702) all_0_5_5 = n2
% 22.91/6.31 |
% 22.91/6.31 | From (701)(702) and (147) follows:
% 22.91/6.31 | (703) sum(n0, n2) = all_0_2_2
% 22.91/6.31 |
% 22.91/6.31 | From (701) and (3786) follows:
% 22.91/6.31 | (3929) sum(n0, n9) = all_0_7_7
% 22.91/6.31 |
% 22.91/6.31 | From (702) and (3784) follows:
% 22.91/6.31 | (3930) sum(n7, n2) = all_0_4_4
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n7, n2, all_0_4_4, n9 and discharging atoms sum(n7, n2) = all_0_4_4, sum(n7, n2) = n9, yields:
% 22.91/6.31 | (544) all_0_4_4 = n9
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n0, n9, all_0_7_7, n9 and discharging atoms sum(n0, n9) = all_0_7_7, sum(n0, n9) = n9, yields:
% 22.91/6.31 | (546) all_0_7_7 = n9
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 22.91/6.31 | (563) all_0_2_2 = n2
% 22.91/6.31 |
% 22.91/6.31 | From (563) and (3788) follows:
% 22.91/6.31 | (3628) sum(n2, n0) = all_0_0_0
% 22.91/6.31 |
% 22.91/6.31 | From (546)(544) and (212) follows:
% 22.91/6.31 | (548) sum(n9, n9) = all_0_3_3
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n9, n9, all_0_3_3, n2 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n2, yields:
% 22.91/6.31 | (549) all_0_3_3 = n2
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n2, n0, all_0_0_0, n2 and discharging atoms sum(n2, n0) = all_0_0_0, sum(n2, n0) = n2, yields:
% 22.91/6.31 | (550) all_0_0_0 = n2
% 22.91/6.31 |
% 22.91/6.31 | Equations (550,549) can reduce 363 to:
% 22.91/6.31 | (461) $false
% 22.91/6.31 |
% 22.91/6.31 |-The branch is then unsatisfiable
% 22.91/6.31 |-Branch two:
% 22.91/6.31 | (715) ~ (all_0_11_11 = n1)
% 22.91/6.31 | (716) all_0_11_11 = n0
% 22.91/6.31 |
% 22.91/6.31 | From (716) and (423) follows:
% 22.91/6.31 | (717) pred(n0) = all_0_9_9
% 22.91/6.31 |
% 22.91/6.31 | From (716) and (262) follows:
% 22.91/6.31 | (718) succ(n0) = all_0_5_5
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (130) with n0, all_0_9_9, n15 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n15, yields:
% 22.91/6.31 | (719) all_0_9_9 = n15
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (165) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 22.91/6.31 | (720) all_0_5_5 = n1
% 22.91/6.31 |
% 22.91/6.31 | From (719)(720) and (147) follows:
% 22.91/6.31 | (721) sum(n15, n1) = all_0_2_2
% 22.91/6.31 |
% 22.91/6.31 | From (719) and (3786) follows:
% 22.91/6.31 | (3946) sum(n15, n9) = all_0_7_7
% 22.91/6.31 |
% 22.91/6.31 | From (720) and (3784) follows:
% 22.91/6.31 | (3947) sum(n7, n1) = all_0_4_4
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n15, n9, all_0_7_7, n8 and discharging atoms sum(n15, n9) = all_0_7_7, sum(n15, n9) = n8, yields:
% 22.91/6.31 | (564) all_0_7_7 = n8
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n15, n1, all_0_2_2, n0 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n0, yields:
% 22.91/6.31 | (581) all_0_2_2 = n0
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n7, n1, all_0_4_4, n8 and discharging atoms sum(n7, n1) = all_0_4_4, sum(n7, n1) = n8, yields:
% 22.91/6.31 | (562) all_0_4_4 = n8
% 22.91/6.31 |
% 22.91/6.31 | From (581) and (3788) follows:
% 22.91/6.31 | (3806) sum(n0, n0) = all_0_0_0
% 22.91/6.31 |
% 22.91/6.31 | From (564)(562) and (212) follows:
% 22.91/6.31 | (566) sum(n8, n8) = all_0_3_3
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n8, n8, all_0_3_3, n0 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n0, yields:
% 22.91/6.31 | (567) all_0_3_3 = n0
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n0, n0, all_0_0_0, n0 and discharging atoms sum(n0, n0) = all_0_0_0, sum(n0, n0) = n0, yields:
% 22.91/6.31 | (568) all_0_0_0 = n0
% 22.91/6.31 |
% 22.91/6.31 | Equations (568,567) can reduce 363 to:
% 22.91/6.31 | (461) $false
% 22.91/6.31 |
% 22.91/6.31 |-The branch is then unsatisfiable
% 22.91/6.31 |-Branch two:
% 22.91/6.31 | (869) ~ (all_0_10_10 = n8)
% 22.91/6.31 | (870) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.91/6.31 |
% 22.91/6.31 +-Applying beta-rule and splitting (571), into two cases.
% 22.91/6.31 |-Branch one:
% 22.91/6.31 | (572) all_0_11_11 = n8
% 22.91/6.31 |
% 22.91/6.31 | From (572) and (423) follows:
% 22.91/6.31 | (573) pred(n8) = all_0_9_9
% 22.91/6.31 |
% 22.91/6.31 | From (572) and (262) follows:
% 22.91/6.31 | (574) succ(n8) = all_0_5_5
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (130) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 22.91/6.31 | (575) all_0_9_9 = n7
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (165) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 22.91/6.31 | (576) all_0_5_5 = n9
% 22.91/6.31 |
% 22.91/6.31 | From (576) and (276) follows:
% 22.91/6.31 | (3963) sum(all_0_6_6, n9) = all_0_4_4
% 22.91/6.31 |
% 22.91/6.31 | From (575)(576) and (147) follows:
% 22.91/6.31 | (577) sum(n7, n9) = all_0_2_2
% 22.91/6.31 |
% 22.91/6.31 | From (575) and (350) follows:
% 22.91/6.31 | (3965) sum(n7, all_0_8_8) = all_0_7_7
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n7, n9, all_0_2_2, n0 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n0, yields:
% 22.91/6.31 | (581) all_0_2_2 = n0
% 22.91/6.31 |
% 22.91/6.31 | From (581) and (256) follows:
% 22.91/6.31 | (3967) sum(n0, all_0_1_1) = all_0_0_0
% 22.91/6.31 |
% 22.91/6.31 +-Applying beta-rule and splitting (870), into two cases.
% 22.91/6.31 |-Branch one:
% 22.91/6.31 | (871) all_0_10_10 = n7
% 22.91/6.31 |
% 22.91/6.31 | From (871) and (317) follows:
% 22.91/6.31 | (872) pred(n7) = all_0_6_6
% 22.91/6.31 |
% 22.91/6.31 | From (871) and (146) follows:
% 22.91/6.31 | (873) succ(n7) = all_0_8_8
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (130) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 22.91/6.31 | (874) all_0_6_6 = n6
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (165) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 22.91/6.31 | (875) all_0_8_8 = n8
% 22.91/6.31 |
% 22.91/6.31 | From (874)(875) and (10) follows:
% 22.91/6.31 | (876) sum(n6, n8) = all_0_1_1
% 22.91/6.31 |
% 22.91/6.31 | From (874) and (3963) follows:
% 22.91/6.31 | (3974) sum(n6, n9) = all_0_4_4
% 22.91/6.31 |
% 22.91/6.31 | From (875) and (3965) follows:
% 22.91/6.31 | (3975) sum(n7, n8) = all_0_7_7
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n7, n8, all_0_7_7, n15 and discharging atoms sum(n7, n8) = all_0_7_7, sum(n7, n8) = n15, yields:
% 22.91/6.31 | (725) all_0_7_7 = n15
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n6, n9, all_0_4_4, n15 and discharging atoms sum(n6, n9) = all_0_4_4, sum(n6, n9) = n15, yields:
% 22.91/6.31 | (726) all_0_4_4 = n15
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 22.91/6.31 | (436) all_0_1_1 = n14
% 22.91/6.31 |
% 22.91/6.31 | From (725)(726) and (212) follows:
% 22.91/6.31 | (728) sum(n15, n15) = all_0_3_3
% 22.91/6.31 |
% 22.91/6.31 | From (436) and (3967) follows:
% 22.91/6.31 | (583) sum(n0, n14) = all_0_0_0
% 22.91/6.31 |
% 22.91/6.31 | Instantiating formula (74) with n15, n15, all_0_3_3, n14 and discharging atoms sum(n15, n15) = all_0_3_3, sum(n15, n15) = n14, yields:
% 22.91/6.32 | (585) all_0_3_3 = n14
% 22.91/6.32 |
% 22.91/6.32 | Instantiating formula (74) with n0, n14, all_0_0_0, n14 and discharging atoms sum(n0, n14) = all_0_0_0, sum(n0, n14) = n14, yields:
% 22.91/6.32 | (586) all_0_0_0 = n14
% 22.91/6.32 |
% 22.91/6.32 | Equations (586,585) can reduce 363 to:
% 22.91/6.32 | (461) $false
% 22.91/6.32 |
% 22.91/6.32 |-The branch is then unsatisfiable
% 22.91/6.32 |-Branch two:
% 22.91/6.32 | (887) ~ (all_0_10_10 = n7)
% 22.91/6.32 | (888) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 22.91/6.32 |
% 22.91/6.32 +-Applying beta-rule and splitting (888), into two cases.
% 22.91/6.32 |-Branch one:
% 22.91/6.32 | (889) all_0_10_10 = n6
% 22.91/6.32 |
% 22.91/6.32 | From (889) and (317) follows:
% 22.91/6.32 | (890) pred(n6) = all_0_6_6
% 22.91/6.32 |
% 22.91/6.32 | From (889) and (146) follows:
% 22.91/6.32 | (891) succ(n6) = all_0_8_8
% 22.91/6.32 |
% 22.91/6.32 | Instantiating formula (130) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 22.91/6.32 | (892) all_0_6_6 = n5
% 22.91/6.32 |
% 22.91/6.32 | Instantiating formula (165) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 22.91/6.32 | (893) all_0_8_8 = n7
% 22.91/6.32 |
% 22.91/6.32 | From (892)(893) and (10) follows:
% 22.91/6.32 | (894) sum(n5, n7) = all_0_1_1
% 22.91/6.32 |
% 22.91/6.32 | From (892) and (3963) follows:
% 22.91/6.32 | (3992) sum(n5, n9) = all_0_4_4
% 22.91/6.32 |
% 22.91/6.32 | From (893) and (3965) follows:
% 23.20/6.32 | (3993) sum(n7, n7) = all_0_7_7
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n7, n7, all_0_7_7, n14 and discharging atoms sum(n7, n7) = all_0_7_7, sum(n7, n7) = n14, yields:
% 23.20/6.32 | (452) all_0_7_7 = n14
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n5, n9, all_0_4_4, n14 and discharging atoms sum(n5, n9) = all_0_4_4, sum(n5, n9) = n14, yields:
% 23.20/6.32 | (451) all_0_4_4 = n14
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 23.20/6.32 | (754) all_0_1_1 = n12
% 23.20/6.32 |
% 23.20/6.32 | From (452)(451) and (212) follows:
% 23.20/6.32 | (456) sum(n14, n14) = all_0_3_3
% 23.20/6.32 |
% 23.20/6.32 | From (754) and (3967) follows:
% 23.20/6.32 | (1155) sum(n0, n12) = all_0_0_0
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n14, n14, all_0_3_3, n12 and discharging atoms sum(n14, n14) = all_0_3_3, sum(n14, n14) = n12, yields:
% 23.20/6.32 | (459) all_0_3_3 = n12
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n0, n12, all_0_0_0, n12 and discharging atoms sum(n0, n12) = all_0_0_0, sum(n0, n12) = n12, yields:
% 23.20/6.32 | (457) all_0_0_0 = n12
% 23.20/6.32 |
% 23.20/6.32 | Equations (457,459) can reduce 363 to:
% 23.20/6.32 | (461) $false
% 23.20/6.32 |
% 23.20/6.32 |-The branch is then unsatisfiable
% 23.20/6.32 |-Branch two:
% 23.20/6.32 | (905) ~ (all_0_10_10 = n6)
% 23.20/6.32 | (906) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.20/6.32 |
% 23.20/6.32 +-Applying beta-rule and splitting (906), into two cases.
% 23.20/6.32 |-Branch one:
% 23.20/6.32 | (907) all_0_10_10 = n5
% 23.20/6.32 |
% 23.20/6.32 | From (907) and (317) follows:
% 23.20/6.32 | (908) pred(n5) = all_0_6_6
% 23.20/6.32 |
% 23.20/6.32 | From (907) and (146) follows:
% 23.20/6.32 | (909) succ(n5) = all_0_8_8
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (130) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 23.20/6.32 | (910) all_0_6_6 = n4
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (165) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 23.20/6.32 | (911) all_0_8_8 = n6
% 23.20/6.32 |
% 23.20/6.32 | From (910)(911) and (10) follows:
% 23.20/6.32 | (912) sum(n4, n6) = all_0_1_1
% 23.20/6.32 |
% 23.20/6.32 | From (910) and (3963) follows:
% 23.20/6.32 | (4010) sum(n4, n9) = all_0_4_4
% 23.20/6.32 |
% 23.20/6.32 | From (911) and (3965) follows:
% 23.20/6.32 | (4011) sum(n7, n6) = all_0_7_7
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n7, n6, all_0_7_7, n13 and discharging atoms sum(n7, n6) = all_0_7_7, sum(n7, n6) = n13, yields:
% 23.20/6.32 | (474) all_0_7_7 = n13
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n4, n9, all_0_4_4, n13 and discharging atoms sum(n4, n9) = all_0_4_4, sum(n4, n9) = n13, yields:
% 23.20/6.32 | (472) all_0_4_4 = n13
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 23.20/6.32 | (772) all_0_1_1 = n10
% 23.20/6.32 |
% 23.20/6.32 | From (474)(472) and (212) follows:
% 23.20/6.32 | (476) sum(n13, n13) = all_0_3_3
% 23.20/6.32 |
% 23.20/6.32 | From (772) and (3967) follows:
% 23.20/6.32 | (1687) sum(n0, n10) = all_0_0_0
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n13, n13, all_0_3_3, n10 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n10, yields:
% 23.20/6.32 | (477) all_0_3_3 = n10
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n0, n10, all_0_0_0, n10 and discharging atoms sum(n0, n10) = all_0_0_0, sum(n0, n10) = n10, yields:
% 23.20/6.32 | (478) all_0_0_0 = n10
% 23.20/6.32 |
% 23.20/6.32 | Equations (478,477) can reduce 363 to:
% 23.20/6.32 | (461) $false
% 23.20/6.32 |
% 23.20/6.32 |-The branch is then unsatisfiable
% 23.20/6.32 |-Branch two:
% 23.20/6.32 | (923) ~ (all_0_10_10 = n5)
% 23.20/6.32 | (924) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.20/6.32 |
% 23.20/6.32 +-Applying beta-rule and splitting (924), into two cases.
% 23.20/6.32 |-Branch one:
% 23.20/6.32 | (925) all_0_10_10 = n4
% 23.20/6.32 |
% 23.20/6.32 | From (925) and (317) follows:
% 23.20/6.32 | (926) pred(n4) = all_0_6_6
% 23.20/6.32 |
% 23.20/6.32 | From (925) and (146) follows:
% 23.20/6.32 | (927) succ(n4) = all_0_8_8
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (130) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 23.20/6.32 | (928) all_0_6_6 = n3
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (165) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 23.20/6.32 | (929) all_0_8_8 = n5
% 23.20/6.32 |
% 23.20/6.32 | From (928)(929) and (10) follows:
% 23.20/6.32 | (930) sum(n3, n5) = all_0_1_1
% 23.20/6.32 |
% 23.20/6.32 | From (928) and (3963) follows:
% 23.20/6.32 | (4028) sum(n3, n9) = all_0_4_4
% 23.20/6.32 |
% 23.20/6.32 | From (929) and (3965) follows:
% 23.20/6.32 | (4029) sum(n7, n5) = all_0_7_7
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n7, n5, all_0_7_7, n12 and discharging atoms sum(n7, n5) = all_0_7_7, sum(n7, n5) = n12, yields:
% 23.20/6.32 | (492) all_0_7_7 = n12
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n3, n9, all_0_4_4, n12 and discharging atoms sum(n3, n9) = all_0_4_4, sum(n3, n9) = n12, yields:
% 23.20/6.32 | (490) all_0_4_4 = n12
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 23.20/6.32 | (790) all_0_1_1 = n8
% 23.20/6.32 |
% 23.20/6.32 | From (492)(490) and (212) follows:
% 23.20/6.32 | (494) sum(n12, n12) = all_0_3_3
% 23.20/6.32 |
% 23.20/6.32 | From (790) and (3967) follows:
% 23.20/6.32 | (2183) sum(n0, n8) = all_0_0_0
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n12, n12, all_0_3_3, n8 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n8, yields:
% 23.20/6.32 | (495) all_0_3_3 = n8
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n0, n8, all_0_0_0, n8 and discharging atoms sum(n0, n8) = all_0_0_0, sum(n0, n8) = n8, yields:
% 23.20/6.32 | (496) all_0_0_0 = n8
% 23.20/6.32 |
% 23.20/6.32 | Equations (496,495) can reduce 363 to:
% 23.20/6.32 | (461) $false
% 23.20/6.32 |
% 23.20/6.32 |-The branch is then unsatisfiable
% 23.20/6.32 |-Branch two:
% 23.20/6.32 | (941) ~ (all_0_10_10 = n4)
% 23.20/6.32 | (942) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.20/6.32 |
% 23.20/6.32 +-Applying beta-rule and splitting (942), into two cases.
% 23.20/6.32 |-Branch one:
% 23.20/6.32 | (943) all_0_10_10 = n3
% 23.20/6.32 |
% 23.20/6.32 | From (943) and (317) follows:
% 23.20/6.32 | (944) pred(n3) = all_0_6_6
% 23.20/6.32 |
% 23.20/6.32 | From (943) and (146) follows:
% 23.20/6.32 | (945) succ(n3) = all_0_8_8
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (130) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 23.20/6.32 | (946) all_0_6_6 = n2
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (165) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 23.20/6.32 | (947) all_0_8_8 = n4
% 23.20/6.32 |
% 23.20/6.32 | From (946)(947) and (10) follows:
% 23.20/6.32 | (948) sum(n2, n4) = all_0_1_1
% 23.20/6.32 |
% 23.20/6.32 | From (946) and (3963) follows:
% 23.20/6.32 | (4046) sum(n2, n9) = all_0_4_4
% 23.20/6.32 |
% 23.20/6.32 | From (947) and (3965) follows:
% 23.20/6.32 | (4047) sum(n7, n4) = all_0_7_7
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n7, n4, all_0_7_7, n11 and discharging atoms sum(n7, n4) = all_0_7_7, sum(n7, n4) = n11, yields:
% 23.20/6.32 | (510) all_0_7_7 = n11
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n2, n9, all_0_4_4, n11 and discharging atoms sum(n2, n9) = all_0_4_4, sum(n2, n9) = n11, yields:
% 23.20/6.32 | (508) all_0_4_4 = n11
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 23.20/6.32 | (808) all_0_1_1 = n6
% 23.20/6.32 |
% 23.20/6.32 | From (510)(508) and (212) follows:
% 23.20/6.32 | (512) sum(n11, n11) = all_0_3_3
% 23.20/6.32 |
% 23.20/6.32 | From (808) and (3967) follows:
% 23.20/6.32 | (2643) sum(n0, n6) = all_0_0_0
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n11, n11, all_0_3_3, n6 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n6, yields:
% 23.20/6.32 | (513) all_0_3_3 = n6
% 23.20/6.32 |
% 23.20/6.32 | Instantiating formula (74) with n0, n6, all_0_0_0, n6 and discharging atoms sum(n0, n6) = all_0_0_0, sum(n0, n6) = n6, yields:
% 23.20/6.32 | (514) all_0_0_0 = n6
% 23.20/6.32 |
% 23.20/6.32 | Equations (514,513) can reduce 363 to:
% 23.20/6.33 | (461) $false
% 23.20/6.33 |
% 23.20/6.33 |-The branch is then unsatisfiable
% 23.20/6.33 |-Branch two:
% 23.20/6.33 | (959) ~ (all_0_10_10 = n3)
% 23.20/6.33 | (960) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.20/6.33 |
% 23.20/6.33 +-Applying beta-rule and splitting (960), into two cases.
% 23.20/6.33 |-Branch one:
% 23.20/6.33 | (961) all_0_10_10 = n2
% 23.20/6.33 |
% 23.20/6.33 | From (961) and (317) follows:
% 23.20/6.33 | (962) pred(n2) = all_0_6_6
% 23.20/6.33 |
% 23.20/6.33 | From (961) and (146) follows:
% 23.20/6.33 | (963) succ(n2) = all_0_8_8
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (130) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 23.20/6.33 | (964) all_0_6_6 = n1
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (165) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 23.20/6.33 | (965) all_0_8_8 = n3
% 23.20/6.33 |
% 23.20/6.33 | From (964)(965) and (10) follows:
% 23.20/6.33 | (966) sum(n1, n3) = all_0_1_1
% 23.20/6.33 |
% 23.20/6.33 | From (964) and (3963) follows:
% 23.20/6.33 | (4064) sum(n1, n9) = all_0_4_4
% 23.20/6.33 |
% 23.20/6.33 | From (965) and (3965) follows:
% 23.20/6.33 | (4065) sum(n7, n3) = all_0_7_7
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (74) with n7, n3, all_0_7_7, n10 and discharging atoms sum(n7, n3) = all_0_7_7, sum(n7, n3) = n10, yields:
% 23.20/6.33 | (528) all_0_7_7 = n10
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (74) with n1, n9, all_0_4_4, n10 and discharging atoms sum(n1, n9) = all_0_4_4, sum(n1, n9) = n10, yields:
% 23.20/6.33 | (526) all_0_4_4 = n10
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (74) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 23.20/6.33 | (826) all_0_1_1 = n4
% 23.20/6.33 |
% 23.20/6.33 | From (528)(526) and (212) follows:
% 23.20/6.33 | (530) sum(n10, n10) = all_0_3_3
% 23.20/6.33 |
% 23.20/6.33 | From (826) and (3967) follows:
% 23.20/6.33 | (3068) sum(n0, n4) = all_0_0_0
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (74) with n10, n10, all_0_3_3, n4 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n4, yields:
% 23.20/6.33 | (531) all_0_3_3 = n4
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (74) with n0, n4, all_0_0_0, n4 and discharging atoms sum(n0, n4) = all_0_0_0, sum(n0, n4) = n4, yields:
% 23.20/6.33 | (532) all_0_0_0 = n4
% 23.20/6.33 |
% 23.20/6.33 | Equations (532,531) can reduce 363 to:
% 23.20/6.33 | (461) $false
% 23.20/6.33 |
% 23.20/6.33 |-The branch is then unsatisfiable
% 23.20/6.33 |-Branch two:
% 23.20/6.33 | (977) ~ (all_0_10_10 = n2)
% 23.20/6.33 | (978) all_0_10_10 = n1 | all_0_10_10 = n0
% 23.20/6.33 |
% 23.20/6.33 +-Applying beta-rule and splitting (978), into two cases.
% 23.20/6.33 |-Branch one:
% 23.20/6.33 | (979) all_0_10_10 = n1
% 23.20/6.33 |
% 23.20/6.33 | From (979) and (317) follows:
% 23.20/6.33 | (980) pred(n1) = all_0_6_6
% 23.20/6.33 |
% 23.20/6.33 | From (979) and (146) follows:
% 23.20/6.33 | (981) succ(n1) = all_0_8_8
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (130) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 23.20/6.33 | (982) all_0_6_6 = n0
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (165) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 23.20/6.33 | (983) all_0_8_8 = n2
% 23.20/6.33 |
% 23.20/6.33 | From (982)(983) and (10) follows:
% 23.20/6.33 | (984) sum(n0, n2) = all_0_1_1
% 23.20/6.33 |
% 23.20/6.33 | From (982) and (3963) follows:
% 23.20/6.33 | (4082) sum(n0, n9) = all_0_4_4
% 23.20/6.33 |
% 23.20/6.33 | From (983) and (3965) follows:
% 23.20/6.33 | (4083) sum(n7, n2) = all_0_7_7
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (74) with n7, n2, all_0_7_7, n9 and discharging atoms sum(n7, n2) = all_0_7_7, sum(n7, n2) = n9, yields:
% 23.20/6.33 | (546) all_0_7_7 = n9
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (74) with n0, n9, all_0_4_4, n9 and discharging atoms sum(n0, n9) = all_0_4_4, sum(n0, n9) = n9, yields:
% 23.20/6.33 | (544) all_0_4_4 = n9
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (74) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 23.20/6.33 | (844) all_0_1_1 = n2
% 23.20/6.33 |
% 23.20/6.33 | From (546)(544) and (212) follows:
% 23.20/6.33 | (548) sum(n9, n9) = all_0_3_3
% 23.20/6.33 |
% 23.20/6.33 | From (844) and (3967) follows:
% 23.20/6.33 | (3456) sum(n0, n2) = all_0_0_0
% 23.20/6.33 |
% 23.20/6.33 | From (844) and (984) follows:
% 23.20/6.33 | (67) sum(n0, n2) = n2
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (74) with n9, n9, all_0_3_3, n2 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n2, yields:
% 23.20/6.33 | (549) all_0_3_3 = n2
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (74) with n0, n2, all_0_0_0, n2 and discharging atoms sum(n0, n2) = all_0_0_0, sum(n0, n2) = n2, yields:
% 23.20/6.33 | (550) all_0_0_0 = n2
% 23.20/6.33 |
% 23.20/6.33 | Equations (550,549) can reduce 363 to:
% 23.20/6.33 | (461) $false
% 23.20/6.33 |
% 23.20/6.33 |-The branch is then unsatisfiable
% 23.20/6.33 |-Branch two:
% 23.20/6.33 | (997) ~ (all_0_10_10 = n1)
% 23.20/6.33 | (998) all_0_10_10 = n0
% 23.20/6.33 |
% 23.20/6.33 | From (998) and (317) follows:
% 23.20/6.33 | (999) pred(n0) = all_0_6_6
% 23.20/6.33 |
% 23.20/6.33 | From (998) and (146) follows:
% 23.20/6.33 | (1000) succ(n0) = all_0_8_8
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (130) with n0, all_0_6_6, n15 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n15, yields:
% 23.20/6.33 | (1001) all_0_6_6 = n15
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (165) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 23.20/6.33 | (1002) all_0_8_8 = n1
% 23.20/6.33 |
% 23.20/6.33 | From (1001)(1002) and (10) follows:
% 23.20/6.33 | (1003) sum(n15, n1) = all_0_1_1
% 23.20/6.33 |
% 23.20/6.33 | From (1001) and (3963) follows:
% 23.20/6.33 | (4100) sum(n15, n9) = all_0_4_4
% 23.20/6.33 |
% 23.20/6.33 | From (1002) and (3965) follows:
% 23.20/6.33 | (4101) sum(n7, n1) = all_0_7_7
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (74) with n15, n9, all_0_4_4, n8 and discharging atoms sum(n15, n9) = all_0_4_4, sum(n15, n9) = n8, yields:
% 23.20/6.33 | (562) all_0_4_4 = n8
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (74) with n15, n1, all_0_1_1, n0 and discharging atoms sum(n15, n1) = all_0_1_1, sum(n15, n1) = n0, yields:
% 23.20/6.33 | (862) all_0_1_1 = n0
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (74) with n7, n1, all_0_7_7, n8 and discharging atoms sum(n7, n1) = all_0_7_7, sum(n7, n1) = n8, yields:
% 23.20/6.33 | (564) all_0_7_7 = n8
% 23.20/6.33 |
% 23.20/6.33 | From (564)(562) and (212) follows:
% 23.20/6.33 | (566) sum(n8, n8) = all_0_3_3
% 23.20/6.33 |
% 23.20/6.33 | From (862) and (3967) follows:
% 23.20/6.33 | (3806) sum(n0, n0) = all_0_0_0
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (74) with n8, n8, all_0_3_3, n0 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n0, yields:
% 23.20/6.33 | (567) all_0_3_3 = n0
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (74) with n0, n0, all_0_0_0, n0 and discharging atoms sum(n0, n0) = all_0_0_0, sum(n0, n0) = n0, yields:
% 23.20/6.33 | (568) all_0_0_0 = n0
% 23.20/6.33 |
% 23.20/6.33 | Equations (568,567) can reduce 363 to:
% 23.20/6.33 | (461) $false
% 23.20/6.33 |
% 23.20/6.33 |-The branch is then unsatisfiable
% 23.20/6.33 |-Branch two:
% 23.20/6.33 | (588) ~ (all_0_11_11 = n8)
% 23.20/6.33 | (589) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.20/6.33 |
% 23.20/6.33 +-Applying beta-rule and splitting (870), into two cases.
% 23.20/6.33 |-Branch one:
% 23.20/6.33 | (871) all_0_10_10 = n7
% 23.20/6.33 |
% 23.20/6.33 | From (871) and (317) follows:
% 23.20/6.33 | (872) pred(n7) = all_0_6_6
% 23.20/6.33 |
% 23.20/6.33 | From (871) and (146) follows:
% 23.20/6.33 | (873) succ(n7) = all_0_8_8
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (130) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 23.20/6.33 | (874) all_0_6_6 = n6
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (165) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 23.20/6.33 | (875) all_0_8_8 = n8
% 23.20/6.33 |
% 23.20/6.33 | From (874) and (872) follows:
% 23.20/6.33 | (411) pred(n7) = n6
% 23.20/6.33 |
% 23.20/6.33 | From (875) and (873) follows:
% 23.20/6.33 | (356) succ(n7) = n8
% 23.20/6.33 |
% 23.20/6.33 | From (874) and (276) follows:
% 23.20/6.33 | (4119) sum(n6, all_0_5_5) = all_0_4_4
% 23.20/6.33 |
% 23.20/6.33 | From (874)(875) and (10) follows:
% 23.20/6.33 | (876) sum(n6, n8) = all_0_1_1
% 23.20/6.33 |
% 23.20/6.33 | From (875) and (350) follows:
% 23.20/6.33 | (4121) sum(all_0_9_9, n8) = all_0_7_7
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (74) with n6, n8, all_0_1_1, n14 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n14, yields:
% 23.20/6.33 | (436) all_0_1_1 = n14
% 23.20/6.33 |
% 23.20/6.33 | From (436) and (256) follows:
% 23.20/6.33 | (437) sum(all_0_2_2, n14) = all_0_0_0
% 23.20/6.33 |
% 23.20/6.33 | From (436) and (876) follows:
% 23.20/6.33 | (84) sum(n6, n8) = n14
% 23.20/6.33 |
% 23.20/6.33 +-Applying beta-rule and splitting (589), into two cases.
% 23.20/6.33 |-Branch one:
% 23.20/6.33 | (590) all_0_11_11 = n7
% 23.20/6.33 |
% 23.20/6.33 | From (590) and (423) follows:
% 23.20/6.33 | (591) pred(n7) = all_0_9_9
% 23.20/6.33 |
% 23.20/6.33 | From (590) and (262) follows:
% 23.20/6.33 | (592) succ(n7) = all_0_5_5
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (130) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 23.20/6.33 | (593) all_0_9_9 = n6
% 23.20/6.33 |
% 23.20/6.33 | Instantiating formula (165) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 23.20/6.33 | (594) all_0_5_5 = n8
% 23.20/6.33 |
% 23.20/6.33 | From (593)(594) and (147) follows:
% 23.20/6.33 | (595) sum(n6, n8) = all_0_2_2
% 23.20/6.33 |
% 23.20/6.33 | From (593) and (4121) follows:
% 23.20/6.34 | (4131) sum(n6, n8) = all_0_7_7
% 23.20/6.34 |
% 23.20/6.34 | From (594) and (4119) follows:
% 23.20/6.34 | (4132) sum(n6, n8) = all_0_4_4
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 23.20/6.34 | (447) all_0_2_2 = n14
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n6, n8, all_0_4_4, all_0_2_2 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = all_0_4_4, yields:
% 23.20/6.34 | (448) all_0_2_2 = all_0_4_4
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n6, n8, all_0_7_7, all_0_2_2 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = all_0_7_7, yields:
% 23.20/6.34 | (449) all_0_2_2 = all_0_7_7
% 23.20/6.34 |
% 23.20/6.34 | Combining equations (449,448) yields a new equation:
% 23.20/6.34 | (450) all_0_4_4 = all_0_7_7
% 23.20/6.34 |
% 23.20/6.34 | Combining equations (447,448) yields a new equation:
% 23.20/6.34 | (451) all_0_4_4 = n14
% 23.20/6.34 |
% 23.20/6.34 | Combining equations (451,450) yields a new equation:
% 23.20/6.34 | (452) all_0_7_7 = n14
% 23.20/6.34 |
% 23.20/6.34 | Combining equations (452,450) yields a new equation:
% 23.20/6.34 | (451) all_0_4_4 = n14
% 23.20/6.34 |
% 23.20/6.34 | Combining equations (451,448) yields a new equation:
% 23.20/6.34 | (447) all_0_2_2 = n14
% 23.20/6.34 |
% 23.20/6.34 | From (447) and (437) follows:
% 23.20/6.34 | (455) sum(n14, n14) = all_0_0_0
% 23.20/6.34 |
% 23.20/6.34 | From (452)(451) and (212) follows:
% 23.20/6.34 | (456) sum(n14, n14) = all_0_3_3
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n14, n14, all_0_0_0, n12 and discharging atoms sum(n14, n14) = all_0_0_0, sum(n14, n14) = n12, yields:
% 23.20/6.34 | (457) all_0_0_0 = n12
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n14, n14, all_0_3_3, all_0_0_0 and discharging atoms sum(n14, n14) = all_0_0_0, sum(n14, n14) = all_0_3_3, yields:
% 23.20/6.34 | (458) all_0_0_0 = all_0_3_3
% 23.20/6.34 |
% 23.20/6.34 | Combining equations (457,458) yields a new equation:
% 23.20/6.34 | (459) all_0_3_3 = n12
% 23.20/6.34 |
% 23.20/6.34 | Combining equations (459,458) yields a new equation:
% 23.20/6.34 | (457) all_0_0_0 = n12
% 23.20/6.34 |
% 23.20/6.34 | Equations (457,459) can reduce 363 to:
% 23.20/6.34 | (461) $false
% 23.20/6.34 |
% 23.20/6.34 |-The branch is then unsatisfiable
% 23.20/6.34 |-Branch two:
% 23.20/6.34 | (606) ~ (all_0_11_11 = n7)
% 23.20/6.34 | (607) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.20/6.34 |
% 23.20/6.34 +-Applying beta-rule and splitting (607), into two cases.
% 23.20/6.34 |-Branch one:
% 23.20/6.34 | (608) all_0_11_11 = n6
% 23.20/6.34 |
% 23.20/6.34 | From (608) and (423) follows:
% 23.20/6.34 | (609) pred(n6) = all_0_9_9
% 23.20/6.34 |
% 23.20/6.34 | From (608) and (262) follows:
% 23.20/6.34 | (610) succ(n6) = all_0_5_5
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (130) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 23.20/6.34 | (611) all_0_9_9 = n5
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (165) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 23.20/6.34 | (612) all_0_5_5 = n7
% 23.20/6.34 |
% 23.20/6.34 | From (611)(612) and (147) follows:
% 23.20/6.34 | (613) sum(n5, n7) = all_0_2_2
% 23.20/6.34 |
% 23.20/6.34 | From (611) and (4121) follows:
% 23.20/6.34 | (4156) sum(n5, n8) = all_0_7_7
% 23.20/6.34 |
% 23.20/6.34 | From (612) and (4119) follows:
% 23.20/6.34 | (4157) sum(n6, n7) = all_0_4_4
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n6, n7, all_0_4_4, n13 and discharging atoms sum(n6, n7) = all_0_4_4, sum(n6, n7) = n13, yields:
% 23.20/6.34 | (472) all_0_4_4 = n13
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n5, n8, all_0_7_7, n13 and discharging atoms sum(n5, n8) = all_0_7_7, sum(n5, n8) = n13, yields:
% 23.20/6.34 | (474) all_0_7_7 = n13
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 23.20/6.34 | (473) all_0_2_2 = n12
% 23.20/6.34 |
% 23.20/6.34 | From (473) and (437) follows:
% 23.20/6.34 | (475) sum(n12, n14) = all_0_0_0
% 23.20/6.34 |
% 23.20/6.34 | From (474)(472) and (212) follows:
% 23.20/6.34 | (476) sum(n13, n13) = all_0_3_3
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n13, n13, all_0_3_3, n10 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n10, yields:
% 23.20/6.34 | (477) all_0_3_3 = n10
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n12, n14, all_0_0_0, n10 and discharging atoms sum(n12, n14) = all_0_0_0, sum(n12, n14) = n10, yields:
% 23.20/6.34 | (478) all_0_0_0 = n10
% 23.20/6.34 |
% 23.20/6.34 | Equations (478,477) can reduce 363 to:
% 23.20/6.34 | (461) $false
% 23.20/6.34 |
% 23.20/6.34 |-The branch is then unsatisfiable
% 23.20/6.34 |-Branch two:
% 23.20/6.34 | (624) ~ (all_0_11_11 = n6)
% 23.20/6.34 | (625) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.20/6.34 |
% 23.20/6.34 +-Applying beta-rule and splitting (625), into two cases.
% 23.20/6.34 |-Branch one:
% 23.20/6.34 | (626) all_0_11_11 = n5
% 23.20/6.34 |
% 23.20/6.34 | From (626) and (423) follows:
% 23.20/6.34 | (627) pred(n5) = all_0_9_9
% 23.20/6.34 |
% 23.20/6.34 | From (626) and (262) follows:
% 23.20/6.34 | (628) succ(n5) = all_0_5_5
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (130) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 23.20/6.34 | (629) all_0_9_9 = n4
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (165) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 23.20/6.34 | (630) all_0_5_5 = n6
% 23.20/6.34 |
% 23.20/6.34 | From (629)(630) and (147) follows:
% 23.20/6.34 | (631) sum(n4, n6) = all_0_2_2
% 23.20/6.34 |
% 23.20/6.34 | From (629) and (4121) follows:
% 23.20/6.34 | (4174) sum(n4, n8) = all_0_7_7
% 23.20/6.34 |
% 23.20/6.34 | From (630) and (4119) follows:
% 23.20/6.34 | (4175) sum(n6, n6) = all_0_4_4
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n6, n6, all_0_4_4, n12 and discharging atoms sum(n6, n6) = all_0_4_4, sum(n6, n6) = n12, yields:
% 23.20/6.34 | (490) all_0_4_4 = n12
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n4, n8, all_0_7_7, n12 and discharging atoms sum(n4, n8) = all_0_7_7, sum(n4, n8) = n12, yields:
% 23.20/6.34 | (492) all_0_7_7 = n12
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 23.20/6.34 | (491) all_0_2_2 = n10
% 23.20/6.34 |
% 23.20/6.34 | From (491) and (437) follows:
% 23.20/6.34 | (493) sum(n10, n14) = all_0_0_0
% 23.20/6.34 |
% 23.20/6.34 | From (492)(490) and (212) follows:
% 23.20/6.34 | (494) sum(n12, n12) = all_0_3_3
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n12, n12, all_0_3_3, n8 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n8, yields:
% 23.20/6.34 | (495) all_0_3_3 = n8
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n10, n14, all_0_0_0, n8 and discharging atoms sum(n10, n14) = all_0_0_0, sum(n10, n14) = n8, yields:
% 23.20/6.34 | (496) all_0_0_0 = n8
% 23.20/6.34 |
% 23.20/6.34 | Equations (496,495) can reduce 363 to:
% 23.20/6.34 | (461) $false
% 23.20/6.34 |
% 23.20/6.34 |-The branch is then unsatisfiable
% 23.20/6.34 |-Branch two:
% 23.20/6.34 | (642) ~ (all_0_11_11 = n5)
% 23.20/6.34 | (643) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.20/6.34 |
% 23.20/6.34 +-Applying beta-rule and splitting (643), into two cases.
% 23.20/6.34 |-Branch one:
% 23.20/6.34 | (644) all_0_11_11 = n4
% 23.20/6.34 |
% 23.20/6.34 | From (644) and (423) follows:
% 23.20/6.34 | (645) pred(n4) = all_0_9_9
% 23.20/6.34 |
% 23.20/6.34 | From (644) and (262) follows:
% 23.20/6.34 | (646) succ(n4) = all_0_5_5
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (130) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 23.20/6.34 | (647) all_0_9_9 = n3
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (165) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 23.20/6.34 | (648) all_0_5_5 = n5
% 23.20/6.34 |
% 23.20/6.34 | From (647)(648) and (147) follows:
% 23.20/6.34 | (649) sum(n3, n5) = all_0_2_2
% 23.20/6.34 |
% 23.20/6.34 | From (647) and (4121) follows:
% 23.20/6.34 | (4192) sum(n3, n8) = all_0_7_7
% 23.20/6.34 |
% 23.20/6.34 | From (648) and (4119) follows:
% 23.20/6.34 | (4193) sum(n6, n5) = all_0_4_4
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n6, n5, all_0_4_4, n11 and discharging atoms sum(n6, n5) = all_0_4_4, sum(n6, n5) = n11, yields:
% 23.20/6.34 | (508) all_0_4_4 = n11
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n3, n8, all_0_7_7, n11 and discharging atoms sum(n3, n8) = all_0_7_7, sum(n3, n8) = n11, yields:
% 23.20/6.34 | (510) all_0_7_7 = n11
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 23.20/6.34 | (509) all_0_2_2 = n8
% 23.20/6.34 |
% 23.20/6.34 | From (509) and (437) follows:
% 23.20/6.34 | (511) sum(n8, n14) = all_0_0_0
% 23.20/6.34 |
% 23.20/6.34 | From (510)(508) and (212) follows:
% 23.20/6.34 | (512) sum(n11, n11) = all_0_3_3
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n11, n11, all_0_3_3, n6 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n6, yields:
% 23.20/6.34 | (513) all_0_3_3 = n6
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n8, n14, all_0_0_0, n6 and discharging atoms sum(n8, n14) = all_0_0_0, sum(n8, n14) = n6, yields:
% 23.20/6.34 | (514) all_0_0_0 = n6
% 23.20/6.34 |
% 23.20/6.34 | Equations (514,513) can reduce 363 to:
% 23.20/6.34 | (461) $false
% 23.20/6.34 |
% 23.20/6.34 |-The branch is then unsatisfiable
% 23.20/6.34 |-Branch two:
% 23.20/6.34 | (660) ~ (all_0_11_11 = n4)
% 23.20/6.34 | (661) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.20/6.34 |
% 23.20/6.34 +-Applying beta-rule and splitting (661), into two cases.
% 23.20/6.34 |-Branch one:
% 23.20/6.34 | (662) all_0_11_11 = n3
% 23.20/6.34 |
% 23.20/6.34 | From (662) and (423) follows:
% 23.20/6.34 | (663) pred(n3) = all_0_9_9
% 23.20/6.34 |
% 23.20/6.34 | From (662) and (262) follows:
% 23.20/6.34 | (664) succ(n3) = all_0_5_5
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (130) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 23.20/6.34 | (665) all_0_9_9 = n2
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (165) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 23.20/6.34 | (666) all_0_5_5 = n4
% 23.20/6.34 |
% 23.20/6.34 | From (665)(666) and (147) follows:
% 23.20/6.34 | (667) sum(n2, n4) = all_0_2_2
% 23.20/6.34 |
% 23.20/6.34 | From (665) and (4121) follows:
% 23.20/6.34 | (4210) sum(n2, n8) = all_0_7_7
% 23.20/6.34 |
% 23.20/6.34 | From (666) and (4119) follows:
% 23.20/6.34 | (4211) sum(n6, n4) = all_0_4_4
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n6, n4, all_0_4_4, n10 and discharging atoms sum(n6, n4) = all_0_4_4, sum(n6, n4) = n10, yields:
% 23.20/6.34 | (526) all_0_4_4 = n10
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n2, n8, all_0_7_7, n10 and discharging atoms sum(n2, n8) = all_0_7_7, sum(n2, n8) = n10, yields:
% 23.20/6.34 | (528) all_0_7_7 = n10
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 23.20/6.34 | (527) all_0_2_2 = n6
% 23.20/6.34 |
% 23.20/6.34 | From (527) and (437) follows:
% 23.20/6.34 | (529) sum(n6, n14) = all_0_0_0
% 23.20/6.34 |
% 23.20/6.34 | From (528)(526) and (212) follows:
% 23.20/6.34 | (530) sum(n10, n10) = all_0_3_3
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n10, n10, all_0_3_3, n4 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n4, yields:
% 23.20/6.34 | (531) all_0_3_3 = n4
% 23.20/6.34 |
% 23.20/6.34 | Instantiating formula (74) with n6, n14, all_0_0_0, n4 and discharging atoms sum(n6, n14) = all_0_0_0, sum(n6, n14) = n4, yields:
% 23.20/6.34 | (532) all_0_0_0 = n4
% 23.20/6.34 |
% 23.20/6.34 | Equations (532,531) can reduce 363 to:
% 23.20/6.34 | (461) $false
% 23.20/6.34 |
% 23.20/6.34 |-The branch is then unsatisfiable
% 23.20/6.34 |-Branch two:
% 23.20/6.34 | (678) ~ (all_0_11_11 = n3)
% 23.20/6.34 | (679) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.20/6.34 |
% 23.20/6.34 +-Applying beta-rule and splitting (679), into two cases.
% 23.20/6.34 |-Branch one:
% 23.20/6.34 | (680) all_0_11_11 = n2
% 23.20/6.34 |
% 23.20/6.34 | From (680) and (423) follows:
% 23.20/6.34 | (681) pred(n2) = all_0_9_9
% 23.20/6.34 |
% 23.20/6.34 | From (680) and (262) follows:
% 23.20/6.34 | (682) succ(n2) = all_0_5_5
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (130) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 23.20/6.35 | (683) all_0_9_9 = n1
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (165) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 23.20/6.35 | (684) all_0_5_5 = n3
% 23.20/6.35 |
% 23.20/6.35 | From (683)(684) and (147) follows:
% 23.20/6.35 | (685) sum(n1, n3) = all_0_2_2
% 23.20/6.35 |
% 23.20/6.35 | From (683) and (4121) follows:
% 23.20/6.35 | (4228) sum(n1, n8) = all_0_7_7
% 23.20/6.35 |
% 23.20/6.35 | From (684) and (4119) follows:
% 23.20/6.35 | (4229) sum(n6, n3) = all_0_4_4
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n6, n3, all_0_4_4, n9 and discharging atoms sum(n6, n3) = all_0_4_4, sum(n6, n3) = n9, yields:
% 23.20/6.35 | (544) all_0_4_4 = n9
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n1, n8, all_0_7_7, n9 and discharging atoms sum(n1, n8) = all_0_7_7, sum(n1, n8) = n9, yields:
% 23.20/6.35 | (546) all_0_7_7 = n9
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 23.20/6.35 | (545) all_0_2_2 = n4
% 23.20/6.35 |
% 23.20/6.35 | From (545) and (437) follows:
% 23.20/6.35 | (547) sum(n4, n14) = all_0_0_0
% 23.20/6.35 |
% 23.20/6.35 | From (546)(544) and (212) follows:
% 23.20/6.35 | (548) sum(n9, n9) = all_0_3_3
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n9, n9, all_0_3_3, n2 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n2, yields:
% 23.20/6.35 | (549) all_0_3_3 = n2
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n4, n14, all_0_0_0, n2 and discharging atoms sum(n4, n14) = all_0_0_0, sum(n4, n14) = n2, yields:
% 23.20/6.35 | (550) all_0_0_0 = n2
% 23.20/6.35 |
% 23.20/6.35 | Equations (550,549) can reduce 363 to:
% 23.20/6.35 | (461) $false
% 23.20/6.35 |
% 23.20/6.35 |-The branch is then unsatisfiable
% 23.20/6.35 |-Branch two:
% 23.20/6.35 | (696) ~ (all_0_11_11 = n2)
% 23.20/6.35 | (697) all_0_11_11 = n1 | all_0_11_11 = n0
% 23.20/6.35 |
% 23.20/6.35 +-Applying beta-rule and splitting (697), into two cases.
% 23.20/6.35 |-Branch one:
% 23.20/6.35 | (698) all_0_11_11 = n1
% 23.20/6.35 |
% 23.20/6.35 | From (698) and (423) follows:
% 23.20/6.35 | (699) pred(n1) = all_0_9_9
% 23.20/6.35 |
% 23.20/6.35 | From (698) and (262) follows:
% 23.20/6.35 | (700) succ(n1) = all_0_5_5
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (130) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 23.20/6.35 | (701) all_0_9_9 = n0
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (165) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 23.20/6.35 | (702) all_0_5_5 = n2
% 23.20/6.35 |
% 23.20/6.35 | From (701)(702) and (147) follows:
% 23.20/6.35 | (703) sum(n0, n2) = all_0_2_2
% 23.20/6.35 |
% 23.20/6.35 | From (701) and (4121) follows:
% 23.20/6.35 | (4246) sum(n0, n8) = all_0_7_7
% 23.20/6.35 |
% 23.20/6.35 | From (702) and (4119) follows:
% 23.20/6.35 | (4247) sum(n6, n2) = all_0_4_4
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n6, n2, all_0_4_4, n8 and discharging atoms sum(n6, n2) = all_0_4_4, sum(n6, n2) = n8, yields:
% 23.20/6.35 | (562) all_0_4_4 = n8
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n0, n8, all_0_7_7, n8 and discharging atoms sum(n0, n8) = all_0_7_7, sum(n0, n8) = n8, yields:
% 23.20/6.35 | (564) all_0_7_7 = n8
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 23.20/6.35 | (563) all_0_2_2 = n2
% 23.20/6.35 |
% 23.20/6.35 | From (563) and (437) follows:
% 23.20/6.35 | (565) sum(n2, n14) = all_0_0_0
% 23.20/6.35 |
% 23.20/6.35 | From (564)(562) and (212) follows:
% 23.20/6.35 | (566) sum(n8, n8) = all_0_3_3
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n8, n8, all_0_3_3, n0 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n0, yields:
% 23.20/6.35 | (567) all_0_3_3 = n0
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n2, n14, all_0_0_0, n0 and discharging atoms sum(n2, n14) = all_0_0_0, sum(n2, n14) = n0, yields:
% 23.20/6.35 | (568) all_0_0_0 = n0
% 23.20/6.35 |
% 23.20/6.35 | Equations (568,567) can reduce 363 to:
% 23.20/6.35 | (461) $false
% 23.20/6.35 |
% 23.20/6.35 |-The branch is then unsatisfiable
% 23.20/6.35 |-Branch two:
% 23.20/6.35 | (715) ~ (all_0_11_11 = n1)
% 23.20/6.35 | (716) all_0_11_11 = n0
% 23.20/6.35 |
% 23.20/6.35 | From (716) and (423) follows:
% 23.20/6.35 | (717) pred(n0) = all_0_9_9
% 23.20/6.35 |
% 23.20/6.35 | From (716) and (262) follows:
% 23.20/6.35 | (718) succ(n0) = all_0_5_5
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (130) with n0, all_0_9_9, n15 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n15, yields:
% 23.20/6.35 | (719) all_0_9_9 = n15
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (165) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 23.20/6.35 | (720) all_0_5_5 = n1
% 23.20/6.35 |
% 23.20/6.35 | From (719)(720) and (147) follows:
% 23.20/6.35 | (721) sum(n15, n1) = all_0_2_2
% 23.20/6.35 |
% 23.20/6.35 | From (719) and (4121) follows:
% 23.20/6.35 | (4263) sum(n15, n8) = all_0_7_7
% 23.20/6.35 |
% 23.20/6.35 | From (720) and (4119) follows:
% 23.20/6.35 | (4264) sum(n6, n1) = all_0_4_4
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n15, n8, all_0_7_7, n7 and discharging atoms sum(n15, n8) = all_0_7_7, sum(n15, n8) = n7, yields:
% 23.20/6.35 | (582) all_0_7_7 = n7
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n15, n1, all_0_2_2, n0 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n0, yields:
% 23.20/6.35 | (581) all_0_2_2 = n0
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n6, n1, all_0_4_4, n7 and discharging atoms sum(n6, n1) = all_0_4_4, sum(n6, n1) = n7, yields:
% 23.20/6.35 | (580) all_0_4_4 = n7
% 23.20/6.35 |
% 23.20/6.35 | From (581) and (437) follows:
% 23.20/6.35 | (583) sum(n0, n14) = all_0_0_0
% 23.20/6.35 |
% 23.20/6.35 | From (582)(580) and (212) follows:
% 23.20/6.35 | (584) sum(n7, n7) = all_0_3_3
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 23.20/6.35 | (585) all_0_3_3 = n14
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n0, n14, all_0_0_0, n14 and discharging atoms sum(n0, n14) = all_0_0_0, sum(n0, n14) = n14, yields:
% 23.20/6.35 | (586) all_0_0_0 = n14
% 23.20/6.35 |
% 23.20/6.35 | Equations (586,585) can reduce 363 to:
% 23.20/6.35 | (461) $false
% 23.20/6.35 |
% 23.20/6.35 |-The branch is then unsatisfiable
% 23.20/6.35 |-Branch two:
% 23.20/6.35 | (887) ~ (all_0_10_10 = n7)
% 23.20/6.35 | (888) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.20/6.35 |
% 23.20/6.35 +-Applying beta-rule and splitting (589), into two cases.
% 23.20/6.35 |-Branch one:
% 23.20/6.35 | (590) all_0_11_11 = n7
% 23.20/6.35 |
% 23.20/6.35 | From (590) and (423) follows:
% 23.20/6.35 | (591) pred(n7) = all_0_9_9
% 23.20/6.35 |
% 23.20/6.35 | From (590) and (262) follows:
% 23.20/6.35 | (592) succ(n7) = all_0_5_5
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (130) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 23.20/6.35 | (593) all_0_9_9 = n6
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (165) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 23.20/6.35 | (594) all_0_5_5 = n8
% 23.20/6.35 |
% 23.20/6.35 | From (594) and (276) follows:
% 23.20/6.35 | (4280) sum(all_0_6_6, n8) = all_0_4_4
% 23.20/6.35 |
% 23.20/6.35 | From (593)(594) and (147) follows:
% 23.20/6.35 | (595) sum(n6, n8) = all_0_2_2
% 23.20/6.35 |
% 23.20/6.35 | From (593) and (350) follows:
% 23.20/6.35 | (4282) sum(n6, all_0_8_8) = all_0_7_7
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n6, n8, all_0_2_2, n14 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n14, yields:
% 23.20/6.35 | (447) all_0_2_2 = n14
% 23.20/6.35 |
% 23.20/6.35 | From (447) and (256) follows:
% 23.20/6.35 | (743) sum(n14, all_0_1_1) = all_0_0_0
% 23.20/6.35 |
% 23.20/6.35 +-Applying beta-rule and splitting (888), into two cases.
% 23.20/6.35 |-Branch one:
% 23.20/6.35 | (889) all_0_10_10 = n6
% 23.20/6.35 |
% 23.20/6.35 | From (889) and (317) follows:
% 23.20/6.35 | (890) pred(n6) = all_0_6_6
% 23.20/6.35 |
% 23.20/6.35 | From (889) and (146) follows:
% 23.20/6.35 | (891) succ(n6) = all_0_8_8
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (130) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 23.20/6.35 | (892) all_0_6_6 = n5
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (165) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 23.20/6.35 | (893) all_0_8_8 = n7
% 23.20/6.35 |
% 23.20/6.35 | From (892)(893) and (10) follows:
% 23.20/6.35 | (894) sum(n5, n7) = all_0_1_1
% 23.20/6.35 |
% 23.20/6.35 | From (892) and (4280) follows:
% 23.20/6.35 | (4291) sum(n5, n8) = all_0_4_4
% 23.20/6.35 |
% 23.20/6.35 | From (893) and (4282) follows:
% 23.20/6.35 | (4292) sum(n6, n7) = all_0_7_7
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n6, n7, all_0_7_7, n13 and discharging atoms sum(n6, n7) = all_0_7_7, sum(n6, n7) = n13, yields:
% 23.20/6.35 | (474) all_0_7_7 = n13
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n5, n8, all_0_4_4, n13 and discharging atoms sum(n5, n8) = all_0_4_4, sum(n5, n8) = n13, yields:
% 23.20/6.35 | (472) all_0_4_4 = n13
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 23.20/6.35 | (754) all_0_1_1 = n12
% 23.20/6.35 |
% 23.20/6.35 | From (474)(472) and (212) follows:
% 23.20/6.35 | (476) sum(n13, n13) = all_0_3_3
% 23.20/6.35 |
% 23.20/6.35 | From (754) and (743) follows:
% 23.20/6.35 | (757) sum(n14, n12) = all_0_0_0
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n14, n12, all_0_0_0, n10 and discharging atoms sum(n14, n12) = all_0_0_0, sum(n14, n12) = n10, yields:
% 23.20/6.35 | (478) all_0_0_0 = n10
% 23.20/6.35 |
% 23.20/6.35 | Instantiating formula (74) with n13, n13, all_0_3_3, n10 and discharging atoms sum(n13, n13) = all_0_3_3, sum(n13, n13) = n10, yields:
% 23.20/6.35 | (477) all_0_3_3 = n10
% 23.20/6.35 |
% 23.20/6.35 | Equations (478,477) can reduce 363 to:
% 23.20/6.35 | (461) $false
% 23.20/6.35 |
% 23.20/6.35 |-The branch is then unsatisfiable
% 23.20/6.35 |-Branch two:
% 23.20/6.35 | (905) ~ (all_0_10_10 = n6)
% 23.20/6.35 | (906) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.20/6.35 |
% 23.20/6.35 +-Applying beta-rule and splitting (906), into two cases.
% 23.20/6.35 |-Branch one:
% 23.20/6.35 | (907) all_0_10_10 = n5
% 23.20/6.35 |
% 23.20/6.35 | From (907) and (317) follows:
% 23.20/6.35 | (908) pred(n5) = all_0_6_6
% 23.20/6.35 |
% 23.20/6.35 | From (907) and (146) follows:
% 23.20/6.36 | (909) succ(n5) = all_0_8_8
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (130) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 23.20/6.36 | (910) all_0_6_6 = n4
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (165) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 23.20/6.36 | (911) all_0_8_8 = n6
% 23.20/6.36 |
% 23.20/6.36 | From (910)(911) and (10) follows:
% 23.20/6.36 | (912) sum(n4, n6) = all_0_1_1
% 23.20/6.36 |
% 23.20/6.36 | From (910) and (4280) follows:
% 23.20/6.36 | (4309) sum(n4, n8) = all_0_4_4
% 23.20/6.36 |
% 23.20/6.36 | From (911) and (4282) follows:
% 23.20/6.36 | (4310) sum(n6, n6) = all_0_7_7
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n6, n6, all_0_7_7, n12 and discharging atoms sum(n6, n6) = all_0_7_7, sum(n6, n6) = n12, yields:
% 23.20/6.36 | (492) all_0_7_7 = n12
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n4, n8, all_0_4_4, n12 and discharging atoms sum(n4, n8) = all_0_4_4, sum(n4, n8) = n12, yields:
% 23.20/6.36 | (490) all_0_4_4 = n12
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 23.20/6.36 | (772) all_0_1_1 = n10
% 23.20/6.36 |
% 23.20/6.36 | From (492)(490) and (212) follows:
% 23.20/6.36 | (494) sum(n12, n12) = all_0_3_3
% 23.20/6.36 |
% 23.20/6.36 | From (772) and (743) follows:
% 23.20/6.36 | (775) sum(n14, n10) = all_0_0_0
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n14, n10, all_0_0_0, n8 and discharging atoms sum(n14, n10) = all_0_0_0, sum(n14, n10) = n8, yields:
% 23.20/6.36 | (496) all_0_0_0 = n8
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n12, n12, all_0_3_3, n8 and discharging atoms sum(n12, n12) = all_0_3_3, sum(n12, n12) = n8, yields:
% 23.20/6.36 | (495) all_0_3_3 = n8
% 23.20/6.36 |
% 23.20/6.36 | Equations (496,495) can reduce 363 to:
% 23.20/6.36 | (461) $false
% 23.20/6.36 |
% 23.20/6.36 |-The branch is then unsatisfiable
% 23.20/6.36 |-Branch two:
% 23.20/6.36 | (923) ~ (all_0_10_10 = n5)
% 23.20/6.36 | (924) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.20/6.36 |
% 23.20/6.36 +-Applying beta-rule and splitting (924), into two cases.
% 23.20/6.36 |-Branch one:
% 23.20/6.36 | (925) all_0_10_10 = n4
% 23.20/6.36 |
% 23.20/6.36 | From (925) and (317) follows:
% 23.20/6.36 | (926) pred(n4) = all_0_6_6
% 23.20/6.36 |
% 23.20/6.36 | From (925) and (146) follows:
% 23.20/6.36 | (927) succ(n4) = all_0_8_8
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (130) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 23.20/6.36 | (928) all_0_6_6 = n3
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (165) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 23.20/6.36 | (929) all_0_8_8 = n5
% 23.20/6.36 |
% 23.20/6.36 | From (928)(929) and (10) follows:
% 23.20/6.36 | (930) sum(n3, n5) = all_0_1_1
% 23.20/6.36 |
% 23.20/6.36 | From (928) and (4280) follows:
% 23.20/6.36 | (4327) sum(n3, n8) = all_0_4_4
% 23.20/6.36 |
% 23.20/6.36 | From (929) and (4282) follows:
% 23.20/6.36 | (4328) sum(n6, n5) = all_0_7_7
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n6, n5, all_0_7_7, n11 and discharging atoms sum(n6, n5) = all_0_7_7, sum(n6, n5) = n11, yields:
% 23.20/6.36 | (510) all_0_7_7 = n11
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n3, n8, all_0_4_4, n11 and discharging atoms sum(n3, n8) = all_0_4_4, sum(n3, n8) = n11, yields:
% 23.20/6.36 | (508) all_0_4_4 = n11
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 23.20/6.36 | (790) all_0_1_1 = n8
% 23.20/6.36 |
% 23.20/6.36 | From (510)(508) and (212) follows:
% 23.20/6.36 | (512) sum(n11, n11) = all_0_3_3
% 23.20/6.36 |
% 23.20/6.36 | From (790) and (743) follows:
% 23.20/6.36 | (793) sum(n14, n8) = all_0_0_0
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n14, n8, all_0_0_0, n6 and discharging atoms sum(n14, n8) = all_0_0_0, sum(n14, n8) = n6, yields:
% 23.20/6.36 | (514) all_0_0_0 = n6
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n11, n11, all_0_3_3, n6 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n6, yields:
% 23.20/6.36 | (513) all_0_3_3 = n6
% 23.20/6.36 |
% 23.20/6.36 | Equations (514,513) can reduce 363 to:
% 23.20/6.36 | (461) $false
% 23.20/6.36 |
% 23.20/6.36 |-The branch is then unsatisfiable
% 23.20/6.36 |-Branch two:
% 23.20/6.36 | (941) ~ (all_0_10_10 = n4)
% 23.20/6.36 | (942) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.20/6.36 |
% 23.20/6.36 +-Applying beta-rule and splitting (942), into two cases.
% 23.20/6.36 |-Branch one:
% 23.20/6.36 | (943) all_0_10_10 = n3
% 23.20/6.36 |
% 23.20/6.36 | From (943) and (317) follows:
% 23.20/6.36 | (944) pred(n3) = all_0_6_6
% 23.20/6.36 |
% 23.20/6.36 | From (943) and (146) follows:
% 23.20/6.36 | (945) succ(n3) = all_0_8_8
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (130) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 23.20/6.36 | (946) all_0_6_6 = n2
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (165) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 23.20/6.36 | (947) all_0_8_8 = n4
% 23.20/6.36 |
% 23.20/6.36 | From (946)(947) and (10) follows:
% 23.20/6.36 | (948) sum(n2, n4) = all_0_1_1
% 23.20/6.36 |
% 23.20/6.36 | From (946) and (4280) follows:
% 23.20/6.36 | (4345) sum(n2, n8) = all_0_4_4
% 23.20/6.36 |
% 23.20/6.36 | From (947) and (4282) follows:
% 23.20/6.36 | (4346) sum(n6, n4) = all_0_7_7
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n6, n4, all_0_7_7, n10 and discharging atoms sum(n6, n4) = all_0_7_7, sum(n6, n4) = n10, yields:
% 23.20/6.36 | (528) all_0_7_7 = n10
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n2, n8, all_0_4_4, n10 and discharging atoms sum(n2, n8) = all_0_4_4, sum(n2, n8) = n10, yields:
% 23.20/6.36 | (526) all_0_4_4 = n10
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 23.20/6.36 | (808) all_0_1_1 = n6
% 23.20/6.36 |
% 23.20/6.36 | From (528)(526) and (212) follows:
% 23.20/6.36 | (530) sum(n10, n10) = all_0_3_3
% 23.20/6.36 |
% 23.20/6.36 | From (808) and (743) follows:
% 23.20/6.36 | (811) sum(n14, n6) = all_0_0_0
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n14, n6, all_0_0_0, n4 and discharging atoms sum(n14, n6) = all_0_0_0, sum(n14, n6) = n4, yields:
% 23.20/6.36 | (532) all_0_0_0 = n4
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n10, n10, all_0_3_3, n4 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n4, yields:
% 23.20/6.36 | (531) all_0_3_3 = n4
% 23.20/6.36 |
% 23.20/6.36 | Equations (532,531) can reduce 363 to:
% 23.20/6.36 | (461) $false
% 23.20/6.36 |
% 23.20/6.36 |-The branch is then unsatisfiable
% 23.20/6.36 |-Branch two:
% 23.20/6.36 | (959) ~ (all_0_10_10 = n3)
% 23.20/6.36 | (960) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.20/6.36 |
% 23.20/6.36 +-Applying beta-rule and splitting (960), into two cases.
% 23.20/6.36 |-Branch one:
% 23.20/6.36 | (961) all_0_10_10 = n2
% 23.20/6.36 |
% 23.20/6.36 | From (961) and (317) follows:
% 23.20/6.36 | (962) pred(n2) = all_0_6_6
% 23.20/6.36 |
% 23.20/6.36 | From (961) and (146) follows:
% 23.20/6.36 | (963) succ(n2) = all_0_8_8
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (130) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 23.20/6.36 | (964) all_0_6_6 = n1
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (165) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 23.20/6.36 | (965) all_0_8_8 = n3
% 23.20/6.36 |
% 23.20/6.36 | From (964)(965) and (10) follows:
% 23.20/6.36 | (966) sum(n1, n3) = all_0_1_1
% 23.20/6.36 |
% 23.20/6.36 | From (964) and (4280) follows:
% 23.20/6.36 | (4363) sum(n1, n8) = all_0_4_4
% 23.20/6.36 |
% 23.20/6.36 | From (965) and (4282) follows:
% 23.20/6.36 | (4364) sum(n6, n3) = all_0_7_7
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n6, n3, all_0_7_7, n9 and discharging atoms sum(n6, n3) = all_0_7_7, sum(n6, n3) = n9, yields:
% 23.20/6.36 | (546) all_0_7_7 = n9
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n1, n8, all_0_4_4, n9 and discharging atoms sum(n1, n8) = all_0_4_4, sum(n1, n8) = n9, yields:
% 23.20/6.36 | (544) all_0_4_4 = n9
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 23.20/6.36 | (826) all_0_1_1 = n4
% 23.20/6.36 |
% 23.20/6.36 | From (546)(544) and (212) follows:
% 23.20/6.36 | (548) sum(n9, n9) = all_0_3_3
% 23.20/6.36 |
% 23.20/6.36 | From (826) and (743) follows:
% 23.20/6.36 | (829) sum(n14, n4) = all_0_0_0
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n14, n4, all_0_0_0, n2 and discharging atoms sum(n14, n4) = all_0_0_0, sum(n14, n4) = n2, yields:
% 23.20/6.36 | (550) all_0_0_0 = n2
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (74) with n9, n9, all_0_3_3, n2 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n2, yields:
% 23.20/6.36 | (549) all_0_3_3 = n2
% 23.20/6.36 |
% 23.20/6.36 | Equations (550,549) can reduce 363 to:
% 23.20/6.36 | (461) $false
% 23.20/6.36 |
% 23.20/6.36 |-The branch is then unsatisfiable
% 23.20/6.36 |-Branch two:
% 23.20/6.36 | (977) ~ (all_0_10_10 = n2)
% 23.20/6.36 | (978) all_0_10_10 = n1 | all_0_10_10 = n0
% 23.20/6.36 |
% 23.20/6.36 +-Applying beta-rule and splitting (978), into two cases.
% 23.20/6.36 |-Branch one:
% 23.20/6.36 | (979) all_0_10_10 = n1
% 23.20/6.36 |
% 23.20/6.36 | From (979) and (317) follows:
% 23.20/6.36 | (980) pred(n1) = all_0_6_6
% 23.20/6.36 |
% 23.20/6.36 | From (979) and (146) follows:
% 23.20/6.36 | (981) succ(n1) = all_0_8_8
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (130) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 23.20/6.36 | (982) all_0_6_6 = n0
% 23.20/6.36 |
% 23.20/6.36 | Instantiating formula (165) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 23.20/6.36 | (983) all_0_8_8 = n2
% 23.20/6.36 |
% 23.20/6.36 | From (982)(983) and (10) follows:
% 23.20/6.36 | (984) sum(n0, n2) = all_0_1_1
% 23.20/6.36 |
% 23.20/6.36 | From (982) and (4280) follows:
% 23.20/6.36 | (4381) sum(n0, n8) = all_0_4_4
% 23.20/6.36 |
% 23.20/6.36 | From (983) and (4282) follows:
% 23.20/6.37 | (4382) sum(n6, n2) = all_0_7_7
% 23.20/6.37 |
% 23.20/6.37 | Instantiating formula (74) with n6, n2, all_0_7_7, n8 and discharging atoms sum(n6, n2) = all_0_7_7, sum(n6, n2) = n8, yields:
% 23.20/6.37 | (564) all_0_7_7 = n8
% 23.20/6.37 |
% 23.20/6.37 | Instantiating formula (74) with n0, n8, all_0_4_4, n8 and discharging atoms sum(n0, n8) = all_0_4_4, sum(n0, n8) = n8, yields:
% 23.20/6.37 | (562) all_0_4_4 = n8
% 23.20/6.37 |
% 23.20/6.37 | Instantiating formula (74) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 23.20/6.37 | (844) all_0_1_1 = n2
% 23.20/6.37 |
% 23.20/6.37 | From (564)(562) and (212) follows:
% 23.20/6.37 | (566) sum(n8, n8) = all_0_3_3
% 23.20/6.37 |
% 23.20/6.37 | From (844) and (743) follows:
% 23.20/6.37 | (847) sum(n14, n2) = all_0_0_0
% 23.20/6.37 |
% 23.20/6.37 | Instantiating formula (74) with n14, n2, all_0_0_0, n0 and discharging atoms sum(n14, n2) = all_0_0_0, sum(n14, n2) = n0, yields:
% 23.20/6.37 | (568) all_0_0_0 = n0
% 23.20/6.37 |
% 23.20/6.37 | Instantiating formula (74) with n8, n8, all_0_3_3, n0 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n0, yields:
% 23.20/6.37 | (567) all_0_3_3 = n0
% 23.20/6.37 |
% 23.20/6.37 | Equations (568,567) can reduce 363 to:
% 23.20/6.37 | (461) $false
% 23.20/6.37 |
% 23.20/6.37 |-The branch is then unsatisfiable
% 23.20/6.37 |-Branch two:
% 23.20/6.37 | (997) ~ (all_0_10_10 = n1)
% 23.20/6.37 | (998) all_0_10_10 = n0
% 23.20/6.37 |
% 23.20/6.37 | From (998) and (317) follows:
% 23.20/6.37 | (999) pred(n0) = all_0_6_6
% 23.20/6.37 |
% 23.20/6.37 | From (998) and (146) follows:
% 23.20/6.37 | (1000) succ(n0) = all_0_8_8
% 23.20/6.37 |
% 23.20/6.37 | Instantiating formula (130) with n0, all_0_6_6, n15 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n15, yields:
% 23.20/6.37 | (1001) all_0_6_6 = n15
% 23.20/6.37 |
% 23.20/6.37 | Instantiating formula (165) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 23.20/6.37 | (1002) all_0_8_8 = n1
% 23.20/6.37 |
% 23.20/6.37 | From (1001)(1002) and (10) follows:
% 23.20/6.37 | (1003) sum(n15, n1) = all_0_1_1
% 23.20/6.37 |
% 23.20/6.37 | From (1001) and (4280) follows:
% 23.20/6.37 | (4398) sum(n15, n8) = all_0_4_4
% 23.20/6.37 |
% 23.20/6.37 | From (1002) and (4282) follows:
% 23.20/6.37 | (4399) sum(n6, n1) = all_0_7_7
% 23.20/6.37 |
% 23.20/6.37 | Instantiating formula (74) with n15, n8, all_0_4_4, n7 and discharging atoms sum(n15, n8) = all_0_4_4, sum(n15, n8) = n7, yields:
% 23.20/6.37 | (580) all_0_4_4 = n7
% 23.20/6.37 |
% 23.20/6.37 | Instantiating formula (74) with n15, n1, all_0_1_1, n0 and discharging atoms sum(n15, n1) = all_0_1_1, sum(n15, n1) = n0, yields:
% 23.20/6.37 | (862) all_0_1_1 = n0
% 23.20/6.37 |
% 23.20/6.37 | Instantiating formula (74) with n6, n1, all_0_7_7, n7 and discharging atoms sum(n6, n1) = all_0_7_7, sum(n6, n1) = n7, yields:
% 23.20/6.37 | (582) all_0_7_7 = n7
% 23.20/6.37 |
% 23.20/6.37 | From (582)(580) and (212) follows:
% 23.20/6.37 | (584) sum(n7, n7) = all_0_3_3
% 23.20/6.37 |
% 23.20/6.37 | From (862) and (743) follows:
% 23.20/6.37 | (865) sum(n14, n0) = all_0_0_0
% 23.20/6.37 |
% 23.20/6.37 | Instantiating formula (74) with n14, n0, all_0_0_0, n14 and discharging atoms sum(n14, n0) = all_0_0_0, sum(n14, n0) = n14, yields:
% 23.20/6.37 | (586) all_0_0_0 = n14
% 23.20/6.37 |
% 23.20/6.37 | Instantiating formula (74) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 23.20/6.37 | (585) all_0_3_3 = n14
% 23.20/6.37 |
% 23.20/6.37 | Equations (586,585) can reduce 363 to:
% 23.20/6.37 | (461) $false
% 23.20/6.37 |
% 23.20/6.37 |-The branch is then unsatisfiable
% 23.20/6.37 |-Branch two:
% 23.20/6.37 | (606) ~ (all_0_11_11 = n7)
% 23.20/6.37 | (607) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.20/6.37 |
% 23.20/6.37 +-Applying beta-rule and splitting (888), into two cases.
% 23.20/6.37 |-Branch one:
% 23.20/6.37 | (889) all_0_10_10 = n6
% 23.20/6.37 |
% 23.20/6.37 | From (889) and (317) follows:
% 23.20/6.37 | (890) pred(n6) = all_0_6_6
% 23.20/6.37 |
% 23.20/6.37 | From (889) and (146) follows:
% 23.20/6.37 | (891) succ(n6) = all_0_8_8
% 23.20/6.37 |
% 23.20/6.37 | Instantiating formula (130) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 23.20/6.37 | (892) all_0_6_6 = n5
% 23.20/6.37 |
% 23.20/6.37 | Instantiating formula (165) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 23.20/6.37 | (893) all_0_8_8 = n7
% 23.20/6.37 |
% 23.20/6.37 | From (892) and (890) follows:
% 23.20/6.37 | (355) pred(n6) = n5
% 23.20/6.37 |
% 23.20/6.37 | From (893) and (891) follows:
% 23.20/6.37 | (192) succ(n6) = n7
% 23.20/6.37 |
% 23.20/6.37 | From (892) and (276) follows:
% 23.20/6.37 | (4417) sum(n5, all_0_5_5) = all_0_4_4
% 23.20/6.37 |
% 23.20/6.37 | From (892)(893) and (10) follows:
% 23.20/6.37 | (894) sum(n5, n7) = all_0_1_1
% 23.20/6.37 |
% 23.20/6.37 | From (893) and (350) follows:
% 23.41/6.37 | (4419) sum(all_0_9_9, n7) = all_0_7_7
% 23.41/6.37 |
% 23.41/6.37 | Instantiating formula (74) with n5, n7, all_0_1_1, n12 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n12, yields:
% 23.41/6.37 | (754) all_0_1_1 = n12
% 23.41/6.37 |
% 23.41/6.37 | From (754) and (256) follows:
% 23.41/6.37 | (1027) sum(all_0_2_2, n12) = all_0_0_0
% 23.41/6.37 |
% 23.41/6.37 | From (754) and (894) follows:
% 23.41/6.37 | (307) sum(n5, n7) = n12
% 23.41/6.37 |
% 23.41/6.37 +-Applying beta-rule and splitting (607), into two cases.
% 23.41/6.37 |-Branch one:
% 23.41/6.37 | (608) all_0_11_11 = n6
% 23.41/6.37 |
% 23.41/6.37 | From (608) and (423) follows:
% 23.41/6.37 | (609) pred(n6) = all_0_9_9
% 23.41/6.37 |
% 23.41/6.37 | From (608) and (262) follows:
% 23.41/6.37 | (610) succ(n6) = all_0_5_5
% 23.41/6.37 |
% 23.41/6.37 | Instantiating formula (130) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 23.41/6.37 | (611) all_0_9_9 = n5
% 23.41/6.37 |
% 23.41/6.37 | Instantiating formula (165) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 23.41/6.37 | (612) all_0_5_5 = n7
% 23.41/6.37 |
% 23.41/6.37 | From (611)(612) and (147) follows:
% 23.41/6.37 | (613) sum(n5, n7) = all_0_2_2
% 23.41/6.37 |
% 23.41/6.37 | From (611) and (4419) follows:
% 23.41/6.37 | (4429) sum(n5, n7) = all_0_7_7
% 23.41/6.37 |
% 23.41/6.37 | From (612) and (4417) follows:
% 23.41/6.37 | (4430) sum(n5, n7) = all_0_4_4
% 23.41/6.37 |
% 23.41/6.37 | Instantiating formula (74) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 23.41/6.37 | (473) all_0_2_2 = n12
% 23.41/6.37 |
% 23.41/6.37 | Instantiating formula (74) with n5, n7, all_0_4_4, all_0_2_2 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = all_0_4_4, yields:
% 23.41/6.37 | (448) all_0_2_2 = all_0_4_4
% 23.41/6.37 |
% 23.41/6.37 | Instantiating formula (74) with n5, n7, all_0_7_7, all_0_2_2 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = all_0_7_7, yields:
% 23.41/6.37 | (449) all_0_2_2 = all_0_7_7
% 23.41/6.37 |
% 23.41/6.37 | Combining equations (449,448) yields a new equation:
% 23.41/6.37 | (450) all_0_4_4 = all_0_7_7
% 23.41/6.37 |
% 23.41/6.37 | Combining equations (473,448) yields a new equation:
% 23.41/6.37 | (490) all_0_4_4 = n12
% 23.41/6.37 |
% 23.41/6.37 | Combining equations (490,450) yields a new equation:
% 23.41/6.37 | (492) all_0_7_7 = n12
% 23.41/6.37 |
% 23.41/6.37 | Combining equations (492,450) yields a new equation:
% 23.41/6.37 | (490) all_0_4_4 = n12
% 23.41/6.37 |
% 23.41/6.37 | Combining equations (490,448) yields a new equation:
% 23.41/6.37 | (473) all_0_2_2 = n12
% 23.41/6.37 |
% 23.41/6.37 | From (473) and (1027) follows:
% 23.41/6.37 | (1045) sum(n12, n12) = all_0_0_0
% 23.41/6.37 |
% 23.41/6.37 | From (492)(490) and (212) follows:
% 23.41/6.37 | (494) sum(n12, n12) = all_0_3_3
% 23.41/6.37 |
% 23.41/6.37 | Instantiating formula (74) with n12, n12, all_0_0_0, n8 and discharging atoms sum(n12, n12) = all_0_0_0, sum(n12, n12) = n8, yields:
% 23.41/6.37 | (496) all_0_0_0 = n8
% 23.41/6.37 |
% 23.41/6.37 | Instantiating formula (74) with n12, n12, all_0_3_3, all_0_0_0 and discharging atoms sum(n12, n12) = all_0_0_0, sum(n12, n12) = all_0_3_3, yields:
% 23.41/6.37 | (458) all_0_0_0 = all_0_3_3
% 23.41/6.37 |
% 23.41/6.37 | Combining equations (496,458) yields a new equation:
% 23.41/6.37 | (495) all_0_3_3 = n8
% 23.41/6.37 |
% 23.41/6.37 | Combining equations (495,458) yields a new equation:
% 23.41/6.37 | (496) all_0_0_0 = n8
% 23.41/6.37 |
% 23.41/6.37 | Equations (496,495) can reduce 363 to:
% 23.41/6.37 | (461) $false
% 23.41/6.37 |
% 23.41/6.37 |-The branch is then unsatisfiable
% 23.41/6.37 |-Branch two:
% 23.41/6.37 | (624) ~ (all_0_11_11 = n6)
% 23.41/6.37 | (625) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.41/6.37 |
% 23.41/6.37 +-Applying beta-rule and splitting (625), into two cases.
% 23.41/6.37 |-Branch one:
% 23.41/6.37 | (626) all_0_11_11 = n5
% 23.41/6.37 |
% 23.41/6.37 | From (626) and (423) follows:
% 23.41/6.37 | (627) pred(n5) = all_0_9_9
% 23.41/6.37 |
% 23.41/6.37 | From (626) and (262) follows:
% 23.41/6.37 | (628) succ(n5) = all_0_5_5
% 23.41/6.37 |
% 23.41/6.37 | Instantiating formula (130) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 23.41/6.37 | (629) all_0_9_9 = n4
% 23.41/6.37 |
% 23.41/6.37 | Instantiating formula (165) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 23.41/6.37 | (630) all_0_5_5 = n6
% 23.41/6.37 |
% 23.41/6.37 | From (629)(630) and (147) follows:
% 23.41/6.37 | (631) sum(n4, n6) = all_0_2_2
% 23.41/6.37 |
% 23.41/6.37 | From (629) and (4419) follows:
% 23.41/6.37 | (4454) sum(n4, n7) = all_0_7_7
% 23.41/6.37 |
% 23.41/6.37 | From (630) and (4417) follows:
% 23.41/6.37 | (4455) sum(n5, n6) = all_0_4_4
% 23.41/6.37 |
% 23.41/6.37 | Instantiating formula (74) with n5, n6, all_0_4_4, n11 and discharging atoms sum(n5, n6) = all_0_4_4, sum(n5, n6) = n11, yields:
% 23.41/6.37 | (508) all_0_4_4 = n11
% 23.41/6.37 |
% 23.41/6.37 | Instantiating formula (74) with n4, n7, all_0_7_7, n11 and discharging atoms sum(n4, n7) = all_0_7_7, sum(n4, n7) = n11, yields:
% 23.41/6.37 | (510) all_0_7_7 = n11
% 23.41/6.37 |
% 23.41/6.37 | Instantiating formula (74) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 23.41/6.37 | (491) all_0_2_2 = n10
% 23.41/6.37 |
% 23.41/6.37 | From (491) and (1027) follows:
% 23.41/6.37 | (1065) sum(n10, n12) = all_0_0_0
% 23.41/6.37 |
% 23.41/6.37 | From (510)(508) and (212) follows:
% 23.41/6.37 | (512) sum(n11, n11) = all_0_3_3
% 23.41/6.37 |
% 23.41/6.37 | Instantiating formula (74) with n11, n11, all_0_3_3, n6 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n6, yields:
% 23.41/6.37 | (513) all_0_3_3 = n6
% 23.41/6.37 |
% 23.41/6.37 | Instantiating formula (74) with n10, n12, all_0_0_0, n6 and discharging atoms sum(n10, n12) = all_0_0_0, sum(n10, n12) = n6, yields:
% 23.41/6.37 | (514) all_0_0_0 = n6
% 23.41/6.37 |
% 23.41/6.37 | Equations (514,513) can reduce 363 to:
% 23.41/6.37 | (461) $false
% 23.41/6.37 |
% 23.41/6.37 |-The branch is then unsatisfiable
% 23.41/6.37 |-Branch two:
% 23.41/6.37 | (642) ~ (all_0_11_11 = n5)
% 23.41/6.37 | (643) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.41/6.37 |
% 23.41/6.37 +-Applying beta-rule and splitting (643), into two cases.
% 23.41/6.37 |-Branch one:
% 23.41/6.37 | (644) all_0_11_11 = n4
% 23.41/6.37 |
% 23.41/6.37 | From (644) and (423) follows:
% 23.41/6.37 | (645) pred(n4) = all_0_9_9
% 23.41/6.37 |
% 23.41/6.37 | From (644) and (262) follows:
% 23.41/6.37 | (646) succ(n4) = all_0_5_5
% 23.41/6.37 |
% 23.41/6.37 | Instantiating formula (130) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 23.41/6.37 | (647) all_0_9_9 = n3
% 23.41/6.37 |
% 23.41/6.37 | Instantiating formula (165) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 23.41/6.37 | (648) all_0_5_5 = n5
% 23.41/6.37 |
% 23.41/6.37 | From (647)(648) and (147) follows:
% 23.41/6.38 | (649) sum(n3, n5) = all_0_2_2
% 23.41/6.38 |
% 23.41/6.38 | From (647) and (4419) follows:
% 23.41/6.38 | (4472) sum(n3, n7) = all_0_7_7
% 23.41/6.38 |
% 23.41/6.38 | From (648) and (4417) follows:
% 23.41/6.38 | (4473) sum(n5, n5) = all_0_4_4
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n5, n5, all_0_4_4, n10 and discharging atoms sum(n5, n5) = all_0_4_4, sum(n5, n5) = n10, yields:
% 23.41/6.38 | (526) all_0_4_4 = n10
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n3, n7, all_0_7_7, n10 and discharging atoms sum(n3, n7) = all_0_7_7, sum(n3, n7) = n10, yields:
% 23.41/6.38 | (528) all_0_7_7 = n10
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 23.41/6.38 | (509) all_0_2_2 = n8
% 23.41/6.38 |
% 23.41/6.38 | From (509) and (1027) follows:
% 23.41/6.38 | (1083) sum(n8, n12) = all_0_0_0
% 23.41/6.38 |
% 23.41/6.38 | From (528)(526) and (212) follows:
% 23.41/6.38 | (530) sum(n10, n10) = all_0_3_3
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n10, n10, all_0_3_3, n4 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n4, yields:
% 23.41/6.38 | (531) all_0_3_3 = n4
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n8, n12, all_0_0_0, n4 and discharging atoms sum(n8, n12) = all_0_0_0, sum(n8, n12) = n4, yields:
% 23.41/6.38 | (532) all_0_0_0 = n4
% 23.41/6.38 |
% 23.41/6.38 | Equations (532,531) can reduce 363 to:
% 23.41/6.38 | (461) $false
% 23.41/6.38 |
% 23.41/6.38 |-The branch is then unsatisfiable
% 23.41/6.38 |-Branch two:
% 23.41/6.38 | (660) ~ (all_0_11_11 = n4)
% 23.41/6.38 | (661) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.41/6.38 |
% 23.41/6.38 +-Applying beta-rule and splitting (661), into two cases.
% 23.41/6.38 |-Branch one:
% 23.41/6.38 | (662) all_0_11_11 = n3
% 23.41/6.38 |
% 23.41/6.38 | From (662) and (423) follows:
% 23.41/6.38 | (663) pred(n3) = all_0_9_9
% 23.41/6.38 |
% 23.41/6.38 | From (662) and (262) follows:
% 23.41/6.38 | (664) succ(n3) = all_0_5_5
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (130) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 23.41/6.38 | (665) all_0_9_9 = n2
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (165) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 23.41/6.38 | (666) all_0_5_5 = n4
% 23.41/6.38 |
% 23.41/6.38 | From (665)(666) and (147) follows:
% 23.41/6.38 | (667) sum(n2, n4) = all_0_2_2
% 23.41/6.38 |
% 23.41/6.38 | From (665) and (4419) follows:
% 23.41/6.38 | (4490) sum(n2, n7) = all_0_7_7
% 23.41/6.38 |
% 23.41/6.38 | From (666) and (4417) follows:
% 23.41/6.38 | (4491) sum(n5, n4) = all_0_4_4
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n5, n4, all_0_4_4, n9 and discharging atoms sum(n5, n4) = all_0_4_4, sum(n5, n4) = n9, yields:
% 23.41/6.38 | (544) all_0_4_4 = n9
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n2, n7, all_0_7_7, n9 and discharging atoms sum(n2, n7) = all_0_7_7, sum(n2, n7) = n9, yields:
% 23.41/6.38 | (546) all_0_7_7 = n9
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 23.41/6.38 | (527) all_0_2_2 = n6
% 23.41/6.38 |
% 23.41/6.38 | From (527) and (1027) follows:
% 23.41/6.38 | (1101) sum(n6, n12) = all_0_0_0
% 23.41/6.38 |
% 23.41/6.38 | From (546)(544) and (212) follows:
% 23.41/6.38 | (548) sum(n9, n9) = all_0_3_3
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n9, n9, all_0_3_3, n2 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n2, yields:
% 23.41/6.38 | (549) all_0_3_3 = n2
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n6, n12, all_0_0_0, n2 and discharging atoms sum(n6, n12) = all_0_0_0, sum(n6, n12) = n2, yields:
% 23.41/6.38 | (550) all_0_0_0 = n2
% 23.41/6.38 |
% 23.41/6.38 | Equations (550,549) can reduce 363 to:
% 23.41/6.38 | (461) $false
% 23.41/6.38 |
% 23.41/6.38 |-The branch is then unsatisfiable
% 23.41/6.38 |-Branch two:
% 23.41/6.38 | (678) ~ (all_0_11_11 = n3)
% 23.41/6.38 | (679) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.41/6.38 |
% 23.41/6.38 +-Applying beta-rule and splitting (679), into two cases.
% 23.41/6.38 |-Branch one:
% 23.41/6.38 | (680) all_0_11_11 = n2
% 23.41/6.38 |
% 23.41/6.38 | From (680) and (423) follows:
% 23.41/6.38 | (681) pred(n2) = all_0_9_9
% 23.41/6.38 |
% 23.41/6.38 | From (680) and (262) follows:
% 23.41/6.38 | (682) succ(n2) = all_0_5_5
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (130) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 23.41/6.38 | (683) all_0_9_9 = n1
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (165) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 23.41/6.38 | (684) all_0_5_5 = n3
% 23.41/6.38 |
% 23.41/6.38 | From (683)(684) and (147) follows:
% 23.41/6.38 | (685) sum(n1, n3) = all_0_2_2
% 23.41/6.38 |
% 23.41/6.38 | From (683) and (4419) follows:
% 23.41/6.38 | (4508) sum(n1, n7) = all_0_7_7
% 23.41/6.38 |
% 23.41/6.38 | From (684) and (4417) follows:
% 23.41/6.38 | (4509) sum(n5, n3) = all_0_4_4
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n5, n3, all_0_4_4, n8 and discharging atoms sum(n5, n3) = all_0_4_4, sum(n5, n3) = n8, yields:
% 23.41/6.38 | (562) all_0_4_4 = n8
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n1, n7, all_0_7_7, n8 and discharging atoms sum(n1, n7) = all_0_7_7, sum(n1, n7) = n8, yields:
% 23.41/6.38 | (564) all_0_7_7 = n8
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 23.41/6.38 | (545) all_0_2_2 = n4
% 23.41/6.38 |
% 23.41/6.38 | From (545) and (1027) follows:
% 23.41/6.38 | (1119) sum(n4, n12) = all_0_0_0
% 23.41/6.38 |
% 23.41/6.38 | From (564)(562) and (212) follows:
% 23.41/6.38 | (566) sum(n8, n8) = all_0_3_3
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n8, n8, all_0_3_3, n0 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n0, yields:
% 23.41/6.38 | (567) all_0_3_3 = n0
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n4, n12, all_0_0_0, n0 and discharging atoms sum(n4, n12) = all_0_0_0, sum(n4, n12) = n0, yields:
% 23.41/6.38 | (568) all_0_0_0 = n0
% 23.41/6.38 |
% 23.41/6.38 | Equations (568,567) can reduce 363 to:
% 23.41/6.38 | (461) $false
% 23.41/6.38 |
% 23.41/6.38 |-The branch is then unsatisfiable
% 23.41/6.38 |-Branch two:
% 23.41/6.38 | (696) ~ (all_0_11_11 = n2)
% 23.41/6.38 | (697) all_0_11_11 = n1 | all_0_11_11 = n0
% 23.41/6.38 |
% 23.41/6.38 +-Applying beta-rule and splitting (697), into two cases.
% 23.41/6.38 |-Branch one:
% 23.41/6.38 | (698) all_0_11_11 = n1
% 23.41/6.38 |
% 23.41/6.38 | From (698) and (423) follows:
% 23.41/6.38 | (699) pred(n1) = all_0_9_9
% 23.41/6.38 |
% 23.41/6.38 | From (698) and (262) follows:
% 23.41/6.38 | (700) succ(n1) = all_0_5_5
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (130) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 23.41/6.38 | (701) all_0_9_9 = n0
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (165) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 23.41/6.38 | (702) all_0_5_5 = n2
% 23.41/6.38 |
% 23.41/6.38 | From (701)(702) and (147) follows:
% 23.41/6.38 | (703) sum(n0, n2) = all_0_2_2
% 23.41/6.38 |
% 23.41/6.38 | From (701) and (4419) follows:
% 23.41/6.38 | (4526) sum(n0, n7) = all_0_7_7
% 23.41/6.38 |
% 23.41/6.38 | From (702) and (4417) follows:
% 23.41/6.38 | (4527) sum(n5, n2) = all_0_4_4
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n5, n2, all_0_4_4, n7 and discharging atoms sum(n5, n2) = all_0_4_4, sum(n5, n2) = n7, yields:
% 23.41/6.38 | (580) all_0_4_4 = n7
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n0, n7, all_0_7_7, n7 and discharging atoms sum(n0, n7) = all_0_7_7, sum(n0, n7) = n7, yields:
% 23.41/6.38 | (582) all_0_7_7 = n7
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 23.41/6.38 | (563) all_0_2_2 = n2
% 23.41/6.38 |
% 23.41/6.38 | From (563) and (1027) follows:
% 23.41/6.38 | (1137) sum(n2, n12) = all_0_0_0
% 23.41/6.38 |
% 23.41/6.38 | From (582)(580) and (212) follows:
% 23.41/6.38 | (584) sum(n7, n7) = all_0_3_3
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 23.41/6.38 | (585) all_0_3_3 = n14
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n2, n12, all_0_0_0, n14 and discharging atoms sum(n2, n12) = all_0_0_0, sum(n2, n12) = n14, yields:
% 23.41/6.38 | (586) all_0_0_0 = n14
% 23.41/6.38 |
% 23.41/6.38 | Equations (586,585) can reduce 363 to:
% 23.41/6.38 | (461) $false
% 23.41/6.38 |
% 23.41/6.38 |-The branch is then unsatisfiable
% 23.41/6.38 |-Branch two:
% 23.41/6.38 | (715) ~ (all_0_11_11 = n1)
% 23.41/6.38 | (716) all_0_11_11 = n0
% 23.41/6.38 |
% 23.41/6.38 | From (716) and (423) follows:
% 23.41/6.38 | (717) pred(n0) = all_0_9_9
% 23.41/6.38 |
% 23.41/6.38 | From (716) and (262) follows:
% 23.41/6.38 | (718) succ(n0) = all_0_5_5
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (130) with n0, all_0_9_9, n15 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n15, yields:
% 23.41/6.38 | (719) all_0_9_9 = n15
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (165) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 23.41/6.38 | (720) all_0_5_5 = n1
% 23.41/6.38 |
% 23.41/6.38 | From (719)(720) and (147) follows:
% 23.41/6.38 | (721) sum(n15, n1) = all_0_2_2
% 23.41/6.38 |
% 23.41/6.38 | From (719) and (4419) follows:
% 23.41/6.38 | (4543) sum(n15, n7) = all_0_7_7
% 23.41/6.38 |
% 23.41/6.38 | From (720) and (4417) follows:
% 23.41/6.38 | (4544) sum(n5, n1) = all_0_4_4
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n15, n7, all_0_7_7, n6 and discharging atoms sum(n15, n7) = all_0_7_7, sum(n15, n7) = n6, yields:
% 23.41/6.38 | (600) all_0_7_7 = n6
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n15, n1, all_0_2_2, n0 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n0, yields:
% 23.41/6.38 | (581) all_0_2_2 = n0
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n5, n1, all_0_4_4, n6 and discharging atoms sum(n5, n1) = all_0_4_4, sum(n5, n1) = n6, yields:
% 23.41/6.38 | (598) all_0_4_4 = n6
% 23.41/6.38 |
% 23.41/6.38 | From (581) and (1027) follows:
% 23.41/6.38 | (1155) sum(n0, n12) = all_0_0_0
% 23.41/6.38 |
% 23.41/6.38 | From (600)(598) and (212) follows:
% 23.41/6.38 | (602) sum(n6, n6) = all_0_3_3
% 23.41/6.38 |
% 23.41/6.38 | Instantiating formula (74) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 23.41/6.39 | (459) all_0_3_3 = n12
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (74) with n0, n12, all_0_0_0, n12 and discharging atoms sum(n0, n12) = all_0_0_0, sum(n0, n12) = n12, yields:
% 23.41/6.39 | (457) all_0_0_0 = n12
% 23.41/6.39 |
% 23.41/6.39 | Equations (457,459) can reduce 363 to:
% 23.41/6.39 | (461) $false
% 23.41/6.39 |
% 23.41/6.39 |-The branch is then unsatisfiable
% 23.41/6.39 |-Branch two:
% 23.41/6.39 | (905) ~ (all_0_10_10 = n6)
% 23.41/6.39 | (906) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.41/6.39 |
% 23.41/6.39 +-Applying beta-rule and splitting (607), into two cases.
% 23.41/6.39 |-Branch one:
% 23.41/6.39 | (608) all_0_11_11 = n6
% 23.41/6.39 |
% 23.41/6.39 | From (608) and (423) follows:
% 23.41/6.39 | (609) pred(n6) = all_0_9_9
% 23.41/6.39 |
% 23.41/6.39 | From (608) and (262) follows:
% 23.41/6.39 | (610) succ(n6) = all_0_5_5
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (130) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 23.41/6.39 | (611) all_0_9_9 = n5
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (165) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 23.41/6.39 | (612) all_0_5_5 = n7
% 23.41/6.39 |
% 23.41/6.39 | From (612) and (276) follows:
% 23.41/6.39 | (4560) sum(all_0_6_6, n7) = all_0_4_4
% 23.41/6.39 |
% 23.41/6.39 | From (611)(612) and (147) follows:
% 23.41/6.39 | (613) sum(n5, n7) = all_0_2_2
% 23.41/6.39 |
% 23.41/6.39 | From (611) and (350) follows:
% 23.41/6.39 | (4562) sum(n5, all_0_8_8) = all_0_7_7
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (74) with n5, n7, all_0_2_2, n12 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n12, yields:
% 23.41/6.39 | (473) all_0_2_2 = n12
% 23.41/6.39 |
% 23.41/6.39 | From (473) and (256) follows:
% 23.41/6.39 | (1314) sum(n12, all_0_1_1) = all_0_0_0
% 23.41/6.39 |
% 23.41/6.39 +-Applying beta-rule and splitting (906), into two cases.
% 23.41/6.39 |-Branch one:
% 23.41/6.39 | (907) all_0_10_10 = n5
% 23.41/6.39 |
% 23.41/6.39 | From (907) and (317) follows:
% 23.41/6.39 | (908) pred(n5) = all_0_6_6
% 23.41/6.39 |
% 23.41/6.39 | From (907) and (146) follows:
% 23.41/6.39 | (909) succ(n5) = all_0_8_8
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (130) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 23.41/6.39 | (910) all_0_6_6 = n4
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (165) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 23.41/6.39 | (911) all_0_8_8 = n6
% 23.41/6.39 |
% 23.41/6.39 | From (910)(911) and (10) follows:
% 23.41/6.39 | (912) sum(n4, n6) = all_0_1_1
% 23.41/6.39 |
% 23.41/6.39 | From (910) and (4560) follows:
% 23.41/6.39 | (4571) sum(n4, n7) = all_0_4_4
% 23.41/6.39 |
% 23.41/6.39 | From (911) and (4562) follows:
% 23.41/6.39 | (4572) sum(n5, n6) = all_0_7_7
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (74) with n5, n6, all_0_7_7, n11 and discharging atoms sum(n5, n6) = all_0_7_7, sum(n5, n6) = n11, yields:
% 23.41/6.39 | (510) all_0_7_7 = n11
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (74) with n4, n7, all_0_4_4, n11 and discharging atoms sum(n4, n7) = all_0_4_4, sum(n4, n7) = n11, yields:
% 23.41/6.39 | (508) all_0_4_4 = n11
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (74) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 23.41/6.39 | (772) all_0_1_1 = n10
% 23.41/6.39 |
% 23.41/6.39 | From (510)(508) and (212) follows:
% 23.41/6.39 | (512) sum(n11, n11) = all_0_3_3
% 23.41/6.39 |
% 23.41/6.39 | From (772) and (1314) follows:
% 23.41/6.39 | (1327) sum(n12, n10) = all_0_0_0
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (74) with n12, n10, all_0_0_0, n6 and discharging atoms sum(n12, n10) = all_0_0_0, sum(n12, n10) = n6, yields:
% 23.41/6.39 | (514) all_0_0_0 = n6
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (74) with n11, n11, all_0_3_3, n6 and discharging atoms sum(n11, n11) = all_0_3_3, sum(n11, n11) = n6, yields:
% 23.41/6.39 | (513) all_0_3_3 = n6
% 23.41/6.39 |
% 23.41/6.39 | Equations (514,513) can reduce 363 to:
% 23.41/6.39 | (461) $false
% 23.41/6.39 |
% 23.41/6.39 |-The branch is then unsatisfiable
% 23.41/6.39 |-Branch two:
% 23.41/6.39 | (923) ~ (all_0_10_10 = n5)
% 23.41/6.39 | (924) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.41/6.39 |
% 23.41/6.39 +-Applying beta-rule and splitting (924), into two cases.
% 23.41/6.39 |-Branch one:
% 23.41/6.39 | (925) all_0_10_10 = n4
% 23.41/6.39 |
% 23.41/6.39 | From (925) and (317) follows:
% 23.41/6.39 | (926) pred(n4) = all_0_6_6
% 23.41/6.39 |
% 23.41/6.39 | From (925) and (146) follows:
% 23.41/6.39 | (927) succ(n4) = all_0_8_8
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (130) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 23.41/6.39 | (928) all_0_6_6 = n3
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (165) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 23.41/6.39 | (929) all_0_8_8 = n5
% 23.41/6.39 |
% 23.41/6.39 | From (928)(929) and (10) follows:
% 23.41/6.39 | (930) sum(n3, n5) = all_0_1_1
% 23.41/6.39 |
% 23.41/6.39 | From (928) and (4560) follows:
% 23.41/6.39 | (4589) sum(n3, n7) = all_0_4_4
% 23.41/6.39 |
% 23.41/6.39 | From (929) and (4562) follows:
% 23.41/6.39 | (4590) sum(n5, n5) = all_0_7_7
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (74) with n5, n5, all_0_7_7, n10 and discharging atoms sum(n5, n5) = all_0_7_7, sum(n5, n5) = n10, yields:
% 23.41/6.39 | (528) all_0_7_7 = n10
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (74) with n3, n7, all_0_4_4, n10 and discharging atoms sum(n3, n7) = all_0_4_4, sum(n3, n7) = n10, yields:
% 23.41/6.39 | (526) all_0_4_4 = n10
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (74) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 23.41/6.39 | (790) all_0_1_1 = n8
% 23.41/6.39 |
% 23.41/6.39 | From (528)(526) and (212) follows:
% 23.41/6.39 | (530) sum(n10, n10) = all_0_3_3
% 23.41/6.39 |
% 23.41/6.39 | From (790) and (1314) follows:
% 23.41/6.39 | (1345) sum(n12, n8) = all_0_0_0
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (74) with n12, n8, all_0_0_0, n4 and discharging atoms sum(n12, n8) = all_0_0_0, sum(n12, n8) = n4, yields:
% 23.41/6.39 | (532) all_0_0_0 = n4
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (74) with n10, n10, all_0_3_3, n4 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n4, yields:
% 23.41/6.39 | (531) all_0_3_3 = n4
% 23.41/6.39 |
% 23.41/6.39 | Equations (532,531) can reduce 363 to:
% 23.41/6.39 | (461) $false
% 23.41/6.39 |
% 23.41/6.39 |-The branch is then unsatisfiable
% 23.41/6.39 |-Branch two:
% 23.41/6.39 | (941) ~ (all_0_10_10 = n4)
% 23.41/6.39 | (942) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.41/6.39 |
% 23.41/6.39 +-Applying beta-rule and splitting (942), into two cases.
% 23.41/6.39 |-Branch one:
% 23.41/6.39 | (943) all_0_10_10 = n3
% 23.41/6.39 |
% 23.41/6.39 | From (943) and (317) follows:
% 23.41/6.39 | (944) pred(n3) = all_0_6_6
% 23.41/6.39 |
% 23.41/6.39 | From (943) and (146) follows:
% 23.41/6.39 | (945) succ(n3) = all_0_8_8
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (130) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 23.41/6.39 | (946) all_0_6_6 = n2
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (165) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 23.41/6.39 | (947) all_0_8_8 = n4
% 23.41/6.39 |
% 23.41/6.39 | From (946)(947) and (10) follows:
% 23.41/6.39 | (948) sum(n2, n4) = all_0_1_1
% 23.41/6.39 |
% 23.41/6.39 | From (946) and (4560) follows:
% 23.41/6.39 | (4607) sum(n2, n7) = all_0_4_4
% 23.41/6.39 |
% 23.41/6.39 | From (947) and (4562) follows:
% 23.41/6.39 | (4608) sum(n5, n4) = all_0_7_7
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (74) with n5, n4, all_0_7_7, n9 and discharging atoms sum(n5, n4) = all_0_7_7, sum(n5, n4) = n9, yields:
% 23.41/6.39 | (546) all_0_7_7 = n9
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (74) with n2, n7, all_0_4_4, n9 and discharging atoms sum(n2, n7) = all_0_4_4, sum(n2, n7) = n9, yields:
% 23.41/6.39 | (544) all_0_4_4 = n9
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (74) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 23.41/6.39 | (808) all_0_1_1 = n6
% 23.41/6.39 |
% 23.41/6.39 | From (546)(544) and (212) follows:
% 23.41/6.39 | (548) sum(n9, n9) = all_0_3_3
% 23.41/6.39 |
% 23.41/6.39 | From (808) and (1314) follows:
% 23.41/6.39 | (1363) sum(n12, n6) = all_0_0_0
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (74) with n12, n6, all_0_0_0, n2 and discharging atoms sum(n12, n6) = all_0_0_0, sum(n12, n6) = n2, yields:
% 23.41/6.39 | (550) all_0_0_0 = n2
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (74) with n9, n9, all_0_3_3, n2 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n2, yields:
% 23.41/6.39 | (549) all_0_3_3 = n2
% 23.41/6.39 |
% 23.41/6.39 | Equations (550,549) can reduce 363 to:
% 23.41/6.39 | (461) $false
% 23.41/6.39 |
% 23.41/6.39 |-The branch is then unsatisfiable
% 23.41/6.39 |-Branch two:
% 23.41/6.39 | (959) ~ (all_0_10_10 = n3)
% 23.41/6.39 | (960) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.41/6.39 |
% 23.41/6.39 +-Applying beta-rule and splitting (960), into two cases.
% 23.41/6.39 |-Branch one:
% 23.41/6.39 | (961) all_0_10_10 = n2
% 23.41/6.39 |
% 23.41/6.39 | From (961) and (317) follows:
% 23.41/6.39 | (962) pred(n2) = all_0_6_6
% 23.41/6.39 |
% 23.41/6.39 | From (961) and (146) follows:
% 23.41/6.39 | (963) succ(n2) = all_0_8_8
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (130) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 23.41/6.39 | (964) all_0_6_6 = n1
% 23.41/6.39 |
% 23.41/6.39 | Instantiating formula (165) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 23.41/6.39 | (965) all_0_8_8 = n3
% 23.41/6.39 |
% 23.41/6.39 | From (964)(965) and (10) follows:
% 23.41/6.39 | (966) sum(n1, n3) = all_0_1_1
% 23.41/6.39 |
% 23.41/6.39 | From (964) and (4560) follows:
% 23.41/6.39 | (4625) sum(n1, n7) = all_0_4_4
% 23.41/6.39 |
% 23.41/6.39 | From (965) and (4562) follows:
% 23.41/6.40 | (4626) sum(n5, n3) = all_0_7_7
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n5, n3, all_0_7_7, n8 and discharging atoms sum(n5, n3) = all_0_7_7, sum(n5, n3) = n8, yields:
% 23.41/6.40 | (564) all_0_7_7 = n8
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n1, n7, all_0_4_4, n8 and discharging atoms sum(n1, n7) = all_0_4_4, sum(n1, n7) = n8, yields:
% 23.41/6.40 | (562) all_0_4_4 = n8
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 23.41/6.40 | (826) all_0_1_1 = n4
% 23.41/6.40 |
% 23.41/6.40 | From (564)(562) and (212) follows:
% 23.41/6.40 | (566) sum(n8, n8) = all_0_3_3
% 23.41/6.40 |
% 23.41/6.40 | From (826) and (1314) follows:
% 23.41/6.40 | (1381) sum(n12, n4) = all_0_0_0
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n12, n4, all_0_0_0, n0 and discharging atoms sum(n12, n4) = all_0_0_0, sum(n12, n4) = n0, yields:
% 23.41/6.40 | (568) all_0_0_0 = n0
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n8, n8, all_0_3_3, n0 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n0, yields:
% 23.41/6.40 | (567) all_0_3_3 = n0
% 23.41/6.40 |
% 23.41/6.40 | Equations (568,567) can reduce 363 to:
% 23.41/6.40 | (461) $false
% 23.41/6.40 |
% 23.41/6.40 |-The branch is then unsatisfiable
% 23.41/6.40 |-Branch two:
% 23.41/6.40 | (977) ~ (all_0_10_10 = n2)
% 23.41/6.40 | (978) all_0_10_10 = n1 | all_0_10_10 = n0
% 23.41/6.40 |
% 23.41/6.40 +-Applying beta-rule and splitting (978), into two cases.
% 23.41/6.40 |-Branch one:
% 23.41/6.40 | (979) all_0_10_10 = n1
% 23.41/6.40 |
% 23.41/6.40 | From (979) and (317) follows:
% 23.41/6.40 | (980) pred(n1) = all_0_6_6
% 23.41/6.40 |
% 23.41/6.40 | From (979) and (146) follows:
% 23.41/6.40 | (981) succ(n1) = all_0_8_8
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (130) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 23.41/6.40 | (982) all_0_6_6 = n0
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (165) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 23.41/6.40 | (983) all_0_8_8 = n2
% 23.41/6.40 |
% 23.41/6.40 | From (982)(983) and (10) follows:
% 23.41/6.40 | (984) sum(n0, n2) = all_0_1_1
% 23.41/6.40 |
% 23.41/6.40 | From (982) and (4560) follows:
% 23.41/6.40 | (4643) sum(n0, n7) = all_0_4_4
% 23.41/6.40 |
% 23.41/6.40 | From (983) and (4562) follows:
% 23.41/6.40 | (4644) sum(n5, n2) = all_0_7_7
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n5, n2, all_0_7_7, n7 and discharging atoms sum(n5, n2) = all_0_7_7, sum(n5, n2) = n7, yields:
% 23.41/6.40 | (582) all_0_7_7 = n7
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n0, n7, all_0_4_4, n7 and discharging atoms sum(n0, n7) = all_0_4_4, sum(n0, n7) = n7, yields:
% 23.41/6.40 | (580) all_0_4_4 = n7
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 23.41/6.40 | (844) all_0_1_1 = n2
% 23.41/6.40 |
% 23.41/6.40 | From (582)(580) and (212) follows:
% 23.41/6.40 | (584) sum(n7, n7) = all_0_3_3
% 23.41/6.40 |
% 23.41/6.40 | From (844) and (1314) follows:
% 23.41/6.40 | (1399) sum(n12, n2) = all_0_0_0
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n12, n2, all_0_0_0, n14 and discharging atoms sum(n12, n2) = all_0_0_0, sum(n12, n2) = n14, yields:
% 23.41/6.40 | (586) all_0_0_0 = n14
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 23.41/6.40 | (585) all_0_3_3 = n14
% 23.41/6.40 |
% 23.41/6.40 | Equations (586,585) can reduce 363 to:
% 23.41/6.40 | (461) $false
% 23.41/6.40 |
% 23.41/6.40 |-The branch is then unsatisfiable
% 23.41/6.40 |-Branch two:
% 23.41/6.40 | (997) ~ (all_0_10_10 = n1)
% 23.41/6.40 | (998) all_0_10_10 = n0
% 23.41/6.40 |
% 23.41/6.40 | From (998) and (317) follows:
% 23.41/6.40 | (999) pred(n0) = all_0_6_6
% 23.41/6.40 |
% 23.41/6.40 | From (998) and (146) follows:
% 23.41/6.40 | (1000) succ(n0) = all_0_8_8
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (130) with n0, all_0_6_6, n15 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n15, yields:
% 23.41/6.40 | (1001) all_0_6_6 = n15
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (165) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 23.41/6.40 | (1002) all_0_8_8 = n1
% 23.41/6.40 |
% 23.41/6.40 | From (1001)(1002) and (10) follows:
% 23.41/6.40 | (1003) sum(n15, n1) = all_0_1_1
% 23.41/6.40 |
% 23.41/6.40 | From (1001) and (4560) follows:
% 23.41/6.40 | (4660) sum(n15, n7) = all_0_4_4
% 23.41/6.40 |
% 23.41/6.40 | From (1002) and (4562) follows:
% 23.41/6.40 | (4661) sum(n5, n1) = all_0_7_7
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n15, n7, all_0_4_4, n6 and discharging atoms sum(n15, n7) = all_0_4_4, sum(n15, n7) = n6, yields:
% 23.41/6.40 | (598) all_0_4_4 = n6
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n15, n1, all_0_1_1, n0 and discharging atoms sum(n15, n1) = all_0_1_1, sum(n15, n1) = n0, yields:
% 23.41/6.40 | (862) all_0_1_1 = n0
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n5, n1, all_0_7_7, n6 and discharging atoms sum(n5, n1) = all_0_7_7, sum(n5, n1) = n6, yields:
% 23.41/6.40 | (600) all_0_7_7 = n6
% 23.41/6.40 |
% 23.41/6.40 | From (600)(598) and (212) follows:
% 23.41/6.40 | (602) sum(n6, n6) = all_0_3_3
% 23.41/6.40 |
% 23.41/6.40 | From (862) and (1314) follows:
% 23.41/6.40 | (1417) sum(n12, n0) = all_0_0_0
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n12, n0, all_0_0_0, n12 and discharging atoms sum(n12, n0) = all_0_0_0, sum(n12, n0) = n12, yields:
% 23.41/6.40 | (457) all_0_0_0 = n12
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 23.41/6.40 | (459) all_0_3_3 = n12
% 23.41/6.40 |
% 23.41/6.40 | Equations (457,459) can reduce 363 to:
% 23.41/6.40 | (461) $false
% 23.41/6.40 |
% 23.41/6.40 |-The branch is then unsatisfiable
% 23.41/6.40 |-Branch two:
% 23.41/6.40 | (624) ~ (all_0_11_11 = n6)
% 23.41/6.40 | (625) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.41/6.40 |
% 23.41/6.40 +-Applying beta-rule and splitting (906), into two cases.
% 23.41/6.40 |-Branch one:
% 23.41/6.40 | (907) all_0_10_10 = n5
% 23.41/6.40 |
% 23.41/6.40 | From (907) and (317) follows:
% 23.41/6.40 | (908) pred(n5) = all_0_6_6
% 23.41/6.40 |
% 23.41/6.40 | From (907) and (146) follows:
% 23.41/6.40 | (909) succ(n5) = all_0_8_8
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (130) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 23.41/6.40 | (910) all_0_6_6 = n4
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (165) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 23.41/6.40 | (911) all_0_8_8 = n6
% 23.41/6.40 |
% 23.41/6.40 | From (910) and (908) follows:
% 23.41/6.40 | (59) pred(n5) = n4
% 23.41/6.40 |
% 23.41/6.40 | From (911) and (909) follows:
% 23.41/6.40 | (44) succ(n5) = n6
% 23.41/6.40 |
% 23.41/6.40 | From (910) and (276) follows:
% 23.41/6.40 | (4679) sum(n4, all_0_5_5) = all_0_4_4
% 23.41/6.40 |
% 23.41/6.40 | From (910)(911) and (10) follows:
% 23.41/6.40 | (912) sum(n4, n6) = all_0_1_1
% 23.41/6.40 |
% 23.41/6.40 | From (911) and (350) follows:
% 23.41/6.40 | (4681) sum(all_0_9_9, n6) = all_0_7_7
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 23.41/6.40 | (772) all_0_1_1 = n10
% 23.41/6.40 |
% 23.41/6.40 | From (772) and (256) follows:
% 23.41/6.40 | (1577) sum(all_0_2_2, n10) = all_0_0_0
% 23.41/6.40 |
% 23.41/6.40 | From (772) and (912) follows:
% 23.41/6.40 | (233) sum(n4, n6) = n10
% 23.41/6.40 |
% 23.41/6.40 +-Applying beta-rule and splitting (625), into two cases.
% 23.41/6.40 |-Branch one:
% 23.41/6.40 | (626) all_0_11_11 = n5
% 23.41/6.40 |
% 23.41/6.40 | From (626) and (423) follows:
% 23.41/6.40 | (627) pred(n5) = all_0_9_9
% 23.41/6.40 |
% 23.41/6.40 | From (626) and (262) follows:
% 23.41/6.40 | (628) succ(n5) = all_0_5_5
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (130) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 23.41/6.40 | (629) all_0_9_9 = n4
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (165) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 23.41/6.40 | (630) all_0_5_5 = n6
% 23.41/6.40 |
% 23.41/6.40 | From (629)(630) and (147) follows:
% 23.41/6.40 | (631) sum(n4, n6) = all_0_2_2
% 23.41/6.40 |
% 23.41/6.40 | From (629) and (4681) follows:
% 23.41/6.40 | (4691) sum(n4, n6) = all_0_7_7
% 23.41/6.40 |
% 23.41/6.40 | From (630) and (4679) follows:
% 23.41/6.40 | (4692) sum(n4, n6) = all_0_4_4
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 23.41/6.40 | (491) all_0_2_2 = n10
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n4, n6, all_0_4_4, all_0_2_2 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = all_0_4_4, yields:
% 23.41/6.40 | (448) all_0_2_2 = all_0_4_4
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n4, n6, all_0_7_7, all_0_2_2 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = all_0_7_7, yields:
% 23.41/6.40 | (449) all_0_2_2 = all_0_7_7
% 23.41/6.40 |
% 23.41/6.40 | Combining equations (449,448) yields a new equation:
% 23.41/6.40 | (450) all_0_4_4 = all_0_7_7
% 23.41/6.40 |
% 23.41/6.40 | Combining equations (491,448) yields a new equation:
% 23.41/6.40 | (526) all_0_4_4 = n10
% 23.41/6.40 |
% 23.41/6.40 | Combining equations (526,450) yields a new equation:
% 23.41/6.40 | (528) all_0_7_7 = n10
% 23.41/6.40 |
% 23.41/6.40 | Combining equations (528,450) yields a new equation:
% 23.41/6.40 | (526) all_0_4_4 = n10
% 23.41/6.40 |
% 23.41/6.40 | Combining equations (526,448) yields a new equation:
% 23.41/6.40 | (491) all_0_2_2 = n10
% 23.41/6.40 |
% 23.41/6.40 | From (491) and (1577) follows:
% 23.41/6.40 | (1595) sum(n10, n10) = all_0_0_0
% 23.41/6.40 |
% 23.41/6.40 | From (528)(526) and (212) follows:
% 23.41/6.40 | (530) sum(n10, n10) = all_0_3_3
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n10, n10, all_0_0_0, n4 and discharging atoms sum(n10, n10) = all_0_0_0, sum(n10, n10) = n4, yields:
% 23.41/6.40 | (532) all_0_0_0 = n4
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (74) with n10, n10, all_0_3_3, all_0_0_0 and discharging atoms sum(n10, n10) = all_0_0_0, sum(n10, n10) = all_0_3_3, yields:
% 23.41/6.40 | (458) all_0_0_0 = all_0_3_3
% 23.41/6.40 |
% 23.41/6.40 | Combining equations (532,458) yields a new equation:
% 23.41/6.40 | (531) all_0_3_3 = n4
% 23.41/6.40 |
% 23.41/6.40 | Combining equations (531,458) yields a new equation:
% 23.41/6.40 | (532) all_0_0_0 = n4
% 23.41/6.40 |
% 23.41/6.40 | Equations (532,531) can reduce 363 to:
% 23.41/6.40 | (461) $false
% 23.41/6.40 |
% 23.41/6.40 |-The branch is then unsatisfiable
% 23.41/6.40 |-Branch two:
% 23.41/6.40 | (642) ~ (all_0_11_11 = n5)
% 23.41/6.40 | (643) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.41/6.40 |
% 23.41/6.40 +-Applying beta-rule and splitting (643), into two cases.
% 23.41/6.40 |-Branch one:
% 23.41/6.40 | (644) all_0_11_11 = n4
% 23.41/6.40 |
% 23.41/6.40 | From (644) and (423) follows:
% 23.41/6.40 | (645) pred(n4) = all_0_9_9
% 23.41/6.40 |
% 23.41/6.40 | From (644) and (262) follows:
% 23.41/6.40 | (646) succ(n4) = all_0_5_5
% 23.41/6.40 |
% 23.41/6.40 | Instantiating formula (130) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 23.41/6.40 | (647) all_0_9_9 = n3
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (165) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 23.41/6.41 | (648) all_0_5_5 = n5
% 23.41/6.41 |
% 23.41/6.41 | From (647)(648) and (147) follows:
% 23.41/6.41 | (649) sum(n3, n5) = all_0_2_2
% 23.41/6.41 |
% 23.41/6.41 | From (647) and (4681) follows:
% 23.41/6.41 | (4716) sum(n3, n6) = all_0_7_7
% 23.41/6.41 |
% 23.41/6.41 | From (648) and (4679) follows:
% 23.41/6.41 | (4717) sum(n4, n5) = all_0_4_4
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n4, n5, all_0_4_4, n9 and discharging atoms sum(n4, n5) = all_0_4_4, sum(n4, n5) = n9, yields:
% 23.41/6.41 | (544) all_0_4_4 = n9
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n3, n6, all_0_7_7, n9 and discharging atoms sum(n3, n6) = all_0_7_7, sum(n3, n6) = n9, yields:
% 23.41/6.41 | (546) all_0_7_7 = n9
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 23.41/6.41 | (509) all_0_2_2 = n8
% 23.41/6.41 |
% 23.41/6.41 | From (509) and (1577) follows:
% 23.41/6.41 | (1615) sum(n8, n10) = all_0_0_0
% 23.41/6.41 |
% 23.41/6.41 | From (546)(544) and (212) follows:
% 23.41/6.41 | (548) sum(n9, n9) = all_0_3_3
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n9, n9, all_0_3_3, n2 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n2, yields:
% 23.41/6.41 | (549) all_0_3_3 = n2
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n8, n10, all_0_0_0, n2 and discharging atoms sum(n8, n10) = all_0_0_0, sum(n8, n10) = n2, yields:
% 23.41/6.41 | (550) all_0_0_0 = n2
% 23.41/6.41 |
% 23.41/6.41 | Equations (550,549) can reduce 363 to:
% 23.41/6.41 | (461) $false
% 23.41/6.41 |
% 23.41/6.41 |-The branch is then unsatisfiable
% 23.41/6.41 |-Branch two:
% 23.41/6.41 | (660) ~ (all_0_11_11 = n4)
% 23.41/6.41 | (661) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.41/6.41 |
% 23.41/6.41 +-Applying beta-rule and splitting (661), into two cases.
% 23.41/6.41 |-Branch one:
% 23.41/6.41 | (662) all_0_11_11 = n3
% 23.41/6.41 |
% 23.41/6.41 | From (662) and (423) follows:
% 23.41/6.41 | (663) pred(n3) = all_0_9_9
% 23.41/6.41 |
% 23.41/6.41 | From (662) and (262) follows:
% 23.41/6.41 | (664) succ(n3) = all_0_5_5
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (130) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 23.41/6.41 | (665) all_0_9_9 = n2
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (165) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 23.41/6.41 | (666) all_0_5_5 = n4
% 23.41/6.41 |
% 23.41/6.41 | From (665)(666) and (147) follows:
% 23.41/6.41 | (667) sum(n2, n4) = all_0_2_2
% 23.41/6.41 |
% 23.41/6.41 | From (665) and (4681) follows:
% 23.41/6.41 | (4734) sum(n2, n6) = all_0_7_7
% 23.41/6.41 |
% 23.41/6.41 | From (666) and (4679) follows:
% 23.41/6.41 | (4735) sum(n4, n4) = all_0_4_4
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n4, n4, all_0_4_4, n8 and discharging atoms sum(n4, n4) = all_0_4_4, sum(n4, n4) = n8, yields:
% 23.41/6.41 | (562) all_0_4_4 = n8
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n2, n6, all_0_7_7, n8 and discharging atoms sum(n2, n6) = all_0_7_7, sum(n2, n6) = n8, yields:
% 23.41/6.41 | (564) all_0_7_7 = n8
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 23.41/6.41 | (527) all_0_2_2 = n6
% 23.41/6.41 |
% 23.41/6.41 | From (527) and (1577) follows:
% 23.41/6.41 | (1633) sum(n6, n10) = all_0_0_0
% 23.41/6.41 |
% 23.41/6.41 | From (564)(562) and (212) follows:
% 23.41/6.41 | (566) sum(n8, n8) = all_0_3_3
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n8, n8, all_0_3_3, n0 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n0, yields:
% 23.41/6.41 | (567) all_0_3_3 = n0
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n6, n10, all_0_0_0, n0 and discharging atoms sum(n6, n10) = all_0_0_0, sum(n6, n10) = n0, yields:
% 23.41/6.41 | (568) all_0_0_0 = n0
% 23.41/6.41 |
% 23.41/6.41 | Equations (568,567) can reduce 363 to:
% 23.41/6.41 | (461) $false
% 23.41/6.41 |
% 23.41/6.41 |-The branch is then unsatisfiable
% 23.41/6.41 |-Branch two:
% 23.41/6.41 | (678) ~ (all_0_11_11 = n3)
% 23.41/6.41 | (679) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.41/6.41 |
% 23.41/6.41 +-Applying beta-rule and splitting (679), into two cases.
% 23.41/6.41 |-Branch one:
% 23.41/6.41 | (680) all_0_11_11 = n2
% 23.41/6.41 |
% 23.41/6.41 | From (680) and (423) follows:
% 23.41/6.41 | (681) pred(n2) = all_0_9_9
% 23.41/6.41 |
% 23.41/6.41 | From (680) and (262) follows:
% 23.41/6.41 | (682) succ(n2) = all_0_5_5
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (130) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 23.41/6.41 | (683) all_0_9_9 = n1
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (165) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 23.41/6.41 | (684) all_0_5_5 = n3
% 23.41/6.41 |
% 23.41/6.41 | From (683)(684) and (147) follows:
% 23.41/6.41 | (685) sum(n1, n3) = all_0_2_2
% 23.41/6.41 |
% 23.41/6.41 | From (683) and (4681) follows:
% 23.41/6.41 | (4752) sum(n1, n6) = all_0_7_7
% 23.41/6.41 |
% 23.41/6.41 | From (684) and (4679) follows:
% 23.41/6.41 | (4753) sum(n4, n3) = all_0_4_4
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n4, n3, all_0_4_4, n7 and discharging atoms sum(n4, n3) = all_0_4_4, sum(n4, n3) = n7, yields:
% 23.41/6.41 | (580) all_0_4_4 = n7
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n1, n6, all_0_7_7, n7 and discharging atoms sum(n1, n6) = all_0_7_7, sum(n1, n6) = n7, yields:
% 23.41/6.41 | (582) all_0_7_7 = n7
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 23.41/6.41 | (545) all_0_2_2 = n4
% 23.41/6.41 |
% 23.41/6.41 | From (545) and (1577) follows:
% 23.41/6.41 | (1651) sum(n4, n10) = all_0_0_0
% 23.41/6.41 |
% 23.41/6.41 | From (582)(580) and (212) follows:
% 23.41/6.41 | (584) sum(n7, n7) = all_0_3_3
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 23.41/6.41 | (585) all_0_3_3 = n14
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n4, n10, all_0_0_0, n14 and discharging atoms sum(n4, n10) = all_0_0_0, sum(n4, n10) = n14, yields:
% 23.41/6.41 | (586) all_0_0_0 = n14
% 23.41/6.41 |
% 23.41/6.41 | Equations (586,585) can reduce 363 to:
% 23.41/6.41 | (461) $false
% 23.41/6.41 |
% 23.41/6.41 |-The branch is then unsatisfiable
% 23.41/6.41 |-Branch two:
% 23.41/6.41 | (696) ~ (all_0_11_11 = n2)
% 23.41/6.41 | (697) all_0_11_11 = n1 | all_0_11_11 = n0
% 23.41/6.41 |
% 23.41/6.41 +-Applying beta-rule and splitting (697), into two cases.
% 23.41/6.41 |-Branch one:
% 23.41/6.41 | (698) all_0_11_11 = n1
% 23.41/6.41 |
% 23.41/6.41 | From (698) and (423) follows:
% 23.41/6.41 | (699) pred(n1) = all_0_9_9
% 23.41/6.41 |
% 23.41/6.41 | From (698) and (262) follows:
% 23.41/6.41 | (700) succ(n1) = all_0_5_5
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (130) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 23.41/6.41 | (701) all_0_9_9 = n0
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (165) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 23.41/6.41 | (702) all_0_5_5 = n2
% 23.41/6.41 |
% 23.41/6.41 | From (701)(702) and (147) follows:
% 23.41/6.41 | (703) sum(n0, n2) = all_0_2_2
% 23.41/6.41 |
% 23.41/6.41 | From (701) and (4681) follows:
% 23.41/6.41 | (4770) sum(n0, n6) = all_0_7_7
% 23.41/6.41 |
% 23.41/6.41 | From (702) and (4679) follows:
% 23.41/6.41 | (4771) sum(n4, n2) = all_0_4_4
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n4, n2, all_0_4_4, n6 and discharging atoms sum(n4, n2) = all_0_4_4, sum(n4, n2) = n6, yields:
% 23.41/6.41 | (598) all_0_4_4 = n6
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n0, n6, all_0_7_7, n6 and discharging atoms sum(n0, n6) = all_0_7_7, sum(n0, n6) = n6, yields:
% 23.41/6.41 | (600) all_0_7_7 = n6
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 23.41/6.41 | (563) all_0_2_2 = n2
% 23.41/6.41 |
% 23.41/6.41 | From (563) and (1577) follows:
% 23.41/6.41 | (1669) sum(n2, n10) = all_0_0_0
% 23.41/6.41 |
% 23.41/6.41 | From (600)(598) and (212) follows:
% 23.41/6.41 | (602) sum(n6, n6) = all_0_3_3
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 23.41/6.41 | (459) all_0_3_3 = n12
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (74) with n2, n10, all_0_0_0, n12 and discharging atoms sum(n2, n10) = all_0_0_0, sum(n2, n10) = n12, yields:
% 23.41/6.41 | (457) all_0_0_0 = n12
% 23.41/6.41 |
% 23.41/6.41 | Equations (457,459) can reduce 363 to:
% 23.41/6.41 | (461) $false
% 23.41/6.41 |
% 23.41/6.41 |-The branch is then unsatisfiable
% 23.41/6.41 |-Branch two:
% 23.41/6.41 | (715) ~ (all_0_11_11 = n1)
% 23.41/6.41 | (716) all_0_11_11 = n0
% 23.41/6.41 |
% 23.41/6.41 | From (716) and (423) follows:
% 23.41/6.41 | (717) pred(n0) = all_0_9_9
% 23.41/6.41 |
% 23.41/6.41 | From (716) and (262) follows:
% 23.41/6.41 | (718) succ(n0) = all_0_5_5
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (130) with n0, all_0_9_9, n15 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n15, yields:
% 23.41/6.41 | (719) all_0_9_9 = n15
% 23.41/6.41 |
% 23.41/6.41 | Instantiating formula (165) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 23.41/6.41 | (720) all_0_5_5 = n1
% 23.41/6.41 |
% 23.41/6.41 | From (719)(720) and (147) follows:
% 23.41/6.41 | (721) sum(n15, n1) = all_0_2_2
% 23.41/6.41 |
% 23.41/6.41 | From (719) and (4681) follows:
% 23.41/6.41 | (4787) sum(n15, n6) = all_0_7_7
% 23.41/6.41 |
% 23.41/6.41 | From (720) and (4679) follows:
% 23.41/6.42 | (4788) sum(n4, n1) = all_0_4_4
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n15, n6, all_0_7_7, n5 and discharging atoms sum(n15, n6) = all_0_7_7, sum(n15, n6) = n5, yields:
% 23.41/6.42 | (618) all_0_7_7 = n5
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n15, n1, all_0_2_2, n0 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n0, yields:
% 23.41/6.42 | (581) all_0_2_2 = n0
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n4, n1, all_0_4_4, n5 and discharging atoms sum(n4, n1) = all_0_4_4, sum(n4, n1) = n5, yields:
% 23.41/6.42 | (616) all_0_4_4 = n5
% 23.41/6.42 |
% 23.41/6.42 | From (581) and (1577) follows:
% 23.41/6.42 | (1687) sum(n0, n10) = all_0_0_0
% 23.41/6.42 |
% 23.41/6.42 | From (618)(616) and (212) follows:
% 23.41/6.42 | (620) sum(n5, n5) = all_0_3_3
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 23.41/6.42 | (477) all_0_3_3 = n10
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n0, n10, all_0_0_0, n10 and discharging atoms sum(n0, n10) = all_0_0_0, sum(n0, n10) = n10, yields:
% 23.41/6.42 | (478) all_0_0_0 = n10
% 23.41/6.42 |
% 23.41/6.42 | Equations (478,477) can reduce 363 to:
% 23.41/6.42 | (461) $false
% 23.41/6.42 |
% 23.41/6.42 |-The branch is then unsatisfiable
% 23.41/6.42 |-Branch two:
% 23.41/6.42 | (923) ~ (all_0_10_10 = n5)
% 23.41/6.42 | (924) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.41/6.42 |
% 23.41/6.42 +-Applying beta-rule and splitting (625), into two cases.
% 23.41/6.42 |-Branch one:
% 23.41/6.42 | (626) all_0_11_11 = n5
% 23.41/6.42 |
% 23.41/6.42 | From (626) and (423) follows:
% 23.41/6.42 | (627) pred(n5) = all_0_9_9
% 23.41/6.42 |
% 23.41/6.42 | From (626) and (262) follows:
% 23.41/6.42 | (628) succ(n5) = all_0_5_5
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (130) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 23.41/6.42 | (629) all_0_9_9 = n4
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (165) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 23.41/6.42 | (630) all_0_5_5 = n6
% 23.41/6.42 |
% 23.41/6.42 | From (630) and (276) follows:
% 23.41/6.42 | (4804) sum(all_0_6_6, n6) = all_0_4_4
% 23.41/6.42 |
% 23.41/6.42 | From (629)(630) and (147) follows:
% 23.41/6.42 | (631) sum(n4, n6) = all_0_2_2
% 23.41/6.42 |
% 23.41/6.42 | From (629) and (350) follows:
% 23.41/6.42 | (4806) sum(n4, all_0_8_8) = all_0_7_7
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 23.41/6.42 | (491) all_0_2_2 = n10
% 23.41/6.42 |
% 23.41/6.42 | From (491) and (256) follows:
% 23.41/6.42 | (1846) sum(n10, all_0_1_1) = all_0_0_0
% 23.41/6.42 |
% 23.41/6.42 +-Applying beta-rule and splitting (924), into two cases.
% 23.41/6.42 |-Branch one:
% 23.41/6.42 | (925) all_0_10_10 = n4
% 23.41/6.42 |
% 23.41/6.42 | From (925) and (317) follows:
% 23.41/6.42 | (926) pred(n4) = all_0_6_6
% 23.41/6.42 |
% 23.41/6.42 | From (925) and (146) follows:
% 23.41/6.42 | (927) succ(n4) = all_0_8_8
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (130) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 23.41/6.42 | (928) all_0_6_6 = n3
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (165) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 23.41/6.42 | (929) all_0_8_8 = n5
% 23.41/6.42 |
% 23.41/6.42 | From (928)(929) and (10) follows:
% 23.41/6.42 | (930) sum(n3, n5) = all_0_1_1
% 23.41/6.42 |
% 23.41/6.42 | From (928) and (4804) follows:
% 23.41/6.42 | (4815) sum(n3, n6) = all_0_4_4
% 23.41/6.42 |
% 23.41/6.42 | From (929) and (4806) follows:
% 23.41/6.42 | (4816) sum(n4, n5) = all_0_7_7
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n4, n5, all_0_7_7, n9 and discharging atoms sum(n4, n5) = all_0_7_7, sum(n4, n5) = n9, yields:
% 23.41/6.42 | (546) all_0_7_7 = n9
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n3, n6, all_0_4_4, n9 and discharging atoms sum(n3, n6) = all_0_4_4, sum(n3, n6) = n9, yields:
% 23.41/6.42 | (544) all_0_4_4 = n9
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 23.41/6.42 | (790) all_0_1_1 = n8
% 23.41/6.42 |
% 23.41/6.42 | From (546)(544) and (212) follows:
% 23.41/6.42 | (548) sum(n9, n9) = all_0_3_3
% 23.41/6.42 |
% 23.41/6.42 | From (790) and (1846) follows:
% 23.41/6.42 | (1859) sum(n10, n8) = all_0_0_0
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n10, n8, all_0_0_0, n2 and discharging atoms sum(n10, n8) = all_0_0_0, sum(n10, n8) = n2, yields:
% 23.41/6.42 | (550) all_0_0_0 = n2
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n9, n9, all_0_3_3, n2 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n2, yields:
% 23.41/6.42 | (549) all_0_3_3 = n2
% 23.41/6.42 |
% 23.41/6.42 | Equations (550,549) can reduce 363 to:
% 23.41/6.42 | (461) $false
% 23.41/6.42 |
% 23.41/6.42 |-The branch is then unsatisfiable
% 23.41/6.42 |-Branch two:
% 23.41/6.42 | (941) ~ (all_0_10_10 = n4)
% 23.41/6.42 | (942) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.41/6.42 |
% 23.41/6.42 +-Applying beta-rule and splitting (942), into two cases.
% 23.41/6.42 |-Branch one:
% 23.41/6.42 | (943) all_0_10_10 = n3
% 23.41/6.42 |
% 23.41/6.42 | From (943) and (317) follows:
% 23.41/6.42 | (944) pred(n3) = all_0_6_6
% 23.41/6.42 |
% 23.41/6.42 | From (943) and (146) follows:
% 23.41/6.42 | (945) succ(n3) = all_0_8_8
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (130) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 23.41/6.42 | (946) all_0_6_6 = n2
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (165) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 23.41/6.42 | (947) all_0_8_8 = n4
% 23.41/6.42 |
% 23.41/6.42 | From (946)(947) and (10) follows:
% 23.41/6.42 | (948) sum(n2, n4) = all_0_1_1
% 23.41/6.42 |
% 23.41/6.42 | From (946) and (4804) follows:
% 23.41/6.42 | (4833) sum(n2, n6) = all_0_4_4
% 23.41/6.42 |
% 23.41/6.42 | From (947) and (4806) follows:
% 23.41/6.42 | (4834) sum(n4, n4) = all_0_7_7
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n4, n4, all_0_7_7, n8 and discharging atoms sum(n4, n4) = all_0_7_7, sum(n4, n4) = n8, yields:
% 23.41/6.42 | (564) all_0_7_7 = n8
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n2, n6, all_0_4_4, n8 and discharging atoms sum(n2, n6) = all_0_4_4, sum(n2, n6) = n8, yields:
% 23.41/6.42 | (562) all_0_4_4 = n8
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 23.41/6.42 | (808) all_0_1_1 = n6
% 23.41/6.42 |
% 23.41/6.42 | From (564)(562) and (212) follows:
% 23.41/6.42 | (566) sum(n8, n8) = all_0_3_3
% 23.41/6.42 |
% 23.41/6.42 | From (808) and (1846) follows:
% 23.41/6.42 | (1877) sum(n10, n6) = all_0_0_0
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n10, n6, all_0_0_0, n0 and discharging atoms sum(n10, n6) = all_0_0_0, sum(n10, n6) = n0, yields:
% 23.41/6.42 | (568) all_0_0_0 = n0
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n8, n8, all_0_3_3, n0 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n0, yields:
% 23.41/6.42 | (567) all_0_3_3 = n0
% 23.41/6.42 |
% 23.41/6.42 | Equations (568,567) can reduce 363 to:
% 23.41/6.42 | (461) $false
% 23.41/6.42 |
% 23.41/6.42 |-The branch is then unsatisfiable
% 23.41/6.42 |-Branch two:
% 23.41/6.42 | (959) ~ (all_0_10_10 = n3)
% 23.41/6.42 | (960) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.41/6.42 |
% 23.41/6.42 +-Applying beta-rule and splitting (960), into two cases.
% 23.41/6.42 |-Branch one:
% 23.41/6.42 | (961) all_0_10_10 = n2
% 23.41/6.42 |
% 23.41/6.42 | From (961) and (317) follows:
% 23.41/6.42 | (962) pred(n2) = all_0_6_6
% 23.41/6.42 |
% 23.41/6.42 | From (961) and (146) follows:
% 23.41/6.42 | (963) succ(n2) = all_0_8_8
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (130) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 23.41/6.42 | (964) all_0_6_6 = n1
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (165) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 23.41/6.42 | (965) all_0_8_8 = n3
% 23.41/6.42 |
% 23.41/6.42 | From (964)(965) and (10) follows:
% 23.41/6.42 | (966) sum(n1, n3) = all_0_1_1
% 23.41/6.42 |
% 23.41/6.42 | From (964) and (4804) follows:
% 23.41/6.42 | (4851) sum(n1, n6) = all_0_4_4
% 23.41/6.42 |
% 23.41/6.42 | From (965) and (4806) follows:
% 23.41/6.42 | (4852) sum(n4, n3) = all_0_7_7
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n4, n3, all_0_7_7, n7 and discharging atoms sum(n4, n3) = all_0_7_7, sum(n4, n3) = n7, yields:
% 23.41/6.42 | (582) all_0_7_7 = n7
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n1, n6, all_0_4_4, n7 and discharging atoms sum(n1, n6) = all_0_4_4, sum(n1, n6) = n7, yields:
% 23.41/6.42 | (580) all_0_4_4 = n7
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 23.41/6.42 | (826) all_0_1_1 = n4
% 23.41/6.42 |
% 23.41/6.42 | From (582)(580) and (212) follows:
% 23.41/6.42 | (584) sum(n7, n7) = all_0_3_3
% 23.41/6.42 |
% 23.41/6.42 | From (826) and (1846) follows:
% 23.41/6.42 | (1895) sum(n10, n4) = all_0_0_0
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n10, n4, all_0_0_0, n14 and discharging atoms sum(n10, n4) = all_0_0_0, sum(n10, n4) = n14, yields:
% 23.41/6.42 | (586) all_0_0_0 = n14
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (74) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 23.41/6.42 | (585) all_0_3_3 = n14
% 23.41/6.42 |
% 23.41/6.42 | Equations (586,585) can reduce 363 to:
% 23.41/6.42 | (461) $false
% 23.41/6.42 |
% 23.41/6.42 |-The branch is then unsatisfiable
% 23.41/6.42 |-Branch two:
% 23.41/6.42 | (977) ~ (all_0_10_10 = n2)
% 23.41/6.42 | (978) all_0_10_10 = n1 | all_0_10_10 = n0
% 23.41/6.42 |
% 23.41/6.42 +-Applying beta-rule and splitting (978), into two cases.
% 23.41/6.42 |-Branch one:
% 23.41/6.42 | (979) all_0_10_10 = n1
% 23.41/6.42 |
% 23.41/6.42 | From (979) and (317) follows:
% 23.41/6.42 | (980) pred(n1) = all_0_6_6
% 23.41/6.42 |
% 23.41/6.42 | From (979) and (146) follows:
% 23.41/6.42 | (981) succ(n1) = all_0_8_8
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (130) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 23.41/6.42 | (982) all_0_6_6 = n0
% 23.41/6.42 |
% 23.41/6.42 | Instantiating formula (165) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 23.41/6.43 | (983) all_0_8_8 = n2
% 23.41/6.43 |
% 23.41/6.43 | From (982)(983) and (10) follows:
% 23.41/6.43 | (984) sum(n0, n2) = all_0_1_1
% 23.41/6.43 |
% 23.41/6.43 | From (982) and (4804) follows:
% 23.41/6.43 | (4869) sum(n0, n6) = all_0_4_4
% 23.41/6.43 |
% 23.41/6.43 | From (983) and (4806) follows:
% 23.41/6.43 | (4870) sum(n4, n2) = all_0_7_7
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (74) with n4, n2, all_0_7_7, n6 and discharging atoms sum(n4, n2) = all_0_7_7, sum(n4, n2) = n6, yields:
% 23.41/6.43 | (600) all_0_7_7 = n6
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (74) with n0, n6, all_0_4_4, n6 and discharging atoms sum(n0, n6) = all_0_4_4, sum(n0, n6) = n6, yields:
% 23.41/6.43 | (598) all_0_4_4 = n6
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (74) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 23.41/6.43 | (844) all_0_1_1 = n2
% 23.41/6.43 |
% 23.41/6.43 | From (600)(598) and (212) follows:
% 23.41/6.43 | (602) sum(n6, n6) = all_0_3_3
% 23.41/6.43 |
% 23.41/6.43 | From (844) and (1846) follows:
% 23.41/6.43 | (1913) sum(n10, n2) = all_0_0_0
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (74) with n10, n2, all_0_0_0, n12 and discharging atoms sum(n10, n2) = all_0_0_0, sum(n10, n2) = n12, yields:
% 23.41/6.43 | (457) all_0_0_0 = n12
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (74) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 23.41/6.43 | (459) all_0_3_3 = n12
% 23.41/6.43 |
% 23.41/6.43 | Equations (457,459) can reduce 363 to:
% 23.41/6.43 | (461) $false
% 23.41/6.43 |
% 23.41/6.43 |-The branch is then unsatisfiable
% 23.41/6.43 |-Branch two:
% 23.41/6.43 | (997) ~ (all_0_10_10 = n1)
% 23.41/6.43 | (998) all_0_10_10 = n0
% 23.41/6.43 |
% 23.41/6.43 | From (998) and (317) follows:
% 23.41/6.43 | (999) pred(n0) = all_0_6_6
% 23.41/6.43 |
% 23.41/6.43 | From (998) and (146) follows:
% 23.41/6.43 | (1000) succ(n0) = all_0_8_8
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (130) with n0, all_0_6_6, n15 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n15, yields:
% 23.41/6.43 | (1001) all_0_6_6 = n15
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (165) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 23.41/6.43 | (1002) all_0_8_8 = n1
% 23.41/6.43 |
% 23.41/6.43 | From (1001)(1002) and (10) follows:
% 23.41/6.43 | (1003) sum(n15, n1) = all_0_1_1
% 23.41/6.43 |
% 23.41/6.43 | From (1001) and (4804) follows:
% 23.41/6.43 | (4886) sum(n15, n6) = all_0_4_4
% 23.41/6.43 |
% 23.41/6.43 | From (1002) and (4806) follows:
% 23.41/6.43 | (4887) sum(n4, n1) = all_0_7_7
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (74) with n15, n6, all_0_4_4, n5 and discharging atoms sum(n15, n6) = all_0_4_4, sum(n15, n6) = n5, yields:
% 23.41/6.43 | (616) all_0_4_4 = n5
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (74) with n15, n1, all_0_1_1, n0 and discharging atoms sum(n15, n1) = all_0_1_1, sum(n15, n1) = n0, yields:
% 23.41/6.43 | (862) all_0_1_1 = n0
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (74) with n4, n1, all_0_7_7, n5 and discharging atoms sum(n4, n1) = all_0_7_7, sum(n4, n1) = n5, yields:
% 23.41/6.43 | (618) all_0_7_7 = n5
% 23.41/6.43 |
% 23.41/6.43 | From (618)(616) and (212) follows:
% 23.41/6.43 | (620) sum(n5, n5) = all_0_3_3
% 23.41/6.43 |
% 23.41/6.43 | From (862) and (1846) follows:
% 23.41/6.43 | (1931) sum(n10, n0) = all_0_0_0
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (74) with n10, n0, all_0_0_0, n10 and discharging atoms sum(n10, n0) = all_0_0_0, sum(n10, n0) = n10, yields:
% 23.41/6.43 | (478) all_0_0_0 = n10
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (74) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 23.41/6.43 | (477) all_0_3_3 = n10
% 23.41/6.43 |
% 23.41/6.43 | Equations (478,477) can reduce 363 to:
% 23.41/6.43 | (461) $false
% 23.41/6.43 |
% 23.41/6.43 |-The branch is then unsatisfiable
% 23.41/6.43 |-Branch two:
% 23.41/6.43 | (642) ~ (all_0_11_11 = n5)
% 23.41/6.43 | (643) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.41/6.43 |
% 23.41/6.43 +-Applying beta-rule and splitting (924), into two cases.
% 23.41/6.43 |-Branch one:
% 23.41/6.43 | (925) all_0_10_10 = n4
% 23.41/6.43 |
% 23.41/6.43 | From (925) and (317) follows:
% 23.41/6.43 | (926) pred(n4) = all_0_6_6
% 23.41/6.43 |
% 23.41/6.43 | From (925) and (146) follows:
% 23.41/6.43 | (927) succ(n4) = all_0_8_8
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (130) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 23.41/6.43 | (928) all_0_6_6 = n3
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (165) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 23.41/6.43 | (929) all_0_8_8 = n5
% 23.41/6.43 |
% 23.41/6.43 | From (928) and (926) follows:
% 23.41/6.43 | (345) pred(n4) = n3
% 23.41/6.43 |
% 23.41/6.43 | From (929) and (927) follows:
% 23.41/6.43 | (106) succ(n4) = n5
% 23.41/6.43 |
% 23.41/6.43 | From (928) and (276) follows:
% 23.41/6.43 | (4905) sum(n3, all_0_5_5) = all_0_4_4
% 23.41/6.43 |
% 23.41/6.43 | From (928)(929) and (10) follows:
% 23.41/6.43 | (930) sum(n3, n5) = all_0_1_1
% 23.41/6.43 |
% 23.41/6.43 | From (929) and (350) follows:
% 23.41/6.43 | (4907) sum(all_0_9_9, n5) = all_0_7_7
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (74) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 23.41/6.43 | (790) all_0_1_1 = n8
% 23.41/6.43 |
% 23.41/6.43 | From (790) and (256) follows:
% 23.41/6.43 | (2091) sum(all_0_2_2, n8) = all_0_0_0
% 23.41/6.43 |
% 23.41/6.43 | From (790) and (930) follows:
% 23.41/6.43 | (412) sum(n3, n5) = n8
% 23.41/6.43 |
% 23.41/6.43 +-Applying beta-rule and splitting (643), into two cases.
% 23.41/6.43 |-Branch one:
% 23.41/6.43 | (644) all_0_11_11 = n4
% 23.41/6.43 |
% 23.41/6.43 | From (644) and (423) follows:
% 23.41/6.43 | (645) pred(n4) = all_0_9_9
% 23.41/6.43 |
% 23.41/6.43 | From (644) and (262) follows:
% 23.41/6.43 | (646) succ(n4) = all_0_5_5
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (130) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 23.41/6.43 | (647) all_0_9_9 = n3
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (165) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 23.41/6.43 | (648) all_0_5_5 = n5
% 23.41/6.43 |
% 23.41/6.43 | From (647)(648) and (147) follows:
% 23.41/6.43 | (649) sum(n3, n5) = all_0_2_2
% 23.41/6.43 |
% 23.41/6.43 | From (647) and (4907) follows:
% 23.41/6.43 | (4917) sum(n3, n5) = all_0_7_7
% 23.41/6.43 |
% 23.41/6.43 | From (648) and (4905) follows:
% 23.41/6.43 | (4918) sum(n3, n5) = all_0_4_4
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (74) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 23.41/6.43 | (509) all_0_2_2 = n8
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (74) with n3, n5, all_0_4_4, all_0_2_2 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = all_0_4_4, yields:
% 23.41/6.43 | (448) all_0_2_2 = all_0_4_4
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (74) with n3, n5, all_0_7_7, all_0_2_2 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = all_0_7_7, yields:
% 23.41/6.43 | (449) all_0_2_2 = all_0_7_7
% 23.41/6.43 |
% 23.41/6.43 | Combining equations (449,448) yields a new equation:
% 23.41/6.43 | (450) all_0_4_4 = all_0_7_7
% 23.41/6.43 |
% 23.41/6.43 | Combining equations (509,448) yields a new equation:
% 23.41/6.43 | (562) all_0_4_4 = n8
% 23.41/6.43 |
% 23.41/6.43 | Combining equations (562,450) yields a new equation:
% 23.41/6.43 | (564) all_0_7_7 = n8
% 23.41/6.43 |
% 23.41/6.43 | Combining equations (564,450) yields a new equation:
% 23.41/6.43 | (562) all_0_4_4 = n8
% 23.41/6.43 |
% 23.41/6.43 | Combining equations (562,448) yields a new equation:
% 23.41/6.43 | (509) all_0_2_2 = n8
% 23.41/6.43 |
% 23.41/6.43 | From (509) and (2091) follows:
% 23.41/6.43 | (2109) sum(n8, n8) = all_0_0_0
% 23.41/6.43 |
% 23.41/6.43 | From (564)(562) and (212) follows:
% 23.41/6.43 | (566) sum(n8, n8) = all_0_3_3
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (74) with n8, n8, all_0_0_0, n0 and discharging atoms sum(n8, n8) = all_0_0_0, sum(n8, n8) = n0, yields:
% 23.41/6.43 | (568) all_0_0_0 = n0
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (74) with n8, n8, all_0_3_3, all_0_0_0 and discharging atoms sum(n8, n8) = all_0_0_0, sum(n8, n8) = all_0_3_3, yields:
% 23.41/6.43 | (458) all_0_0_0 = all_0_3_3
% 23.41/6.43 |
% 23.41/6.43 | Combining equations (568,458) yields a new equation:
% 23.41/6.43 | (567) all_0_3_3 = n0
% 23.41/6.43 |
% 23.41/6.43 | Combining equations (567,458) yields a new equation:
% 23.41/6.43 | (568) all_0_0_0 = n0
% 23.41/6.43 |
% 23.41/6.43 | Equations (568,567) can reduce 363 to:
% 23.41/6.43 | (461) $false
% 23.41/6.43 |
% 23.41/6.43 |-The branch is then unsatisfiable
% 23.41/6.43 |-Branch two:
% 23.41/6.43 | (660) ~ (all_0_11_11 = n4)
% 23.41/6.43 | (661) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.41/6.43 |
% 23.41/6.43 +-Applying beta-rule and splitting (661), into two cases.
% 23.41/6.43 |-Branch one:
% 23.41/6.43 | (662) all_0_11_11 = n3
% 23.41/6.43 |
% 23.41/6.43 | From (662) and (423) follows:
% 23.41/6.43 | (663) pred(n3) = all_0_9_9
% 23.41/6.43 |
% 23.41/6.43 | From (662) and (262) follows:
% 23.41/6.43 | (664) succ(n3) = all_0_5_5
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (130) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 23.41/6.43 | (665) all_0_9_9 = n2
% 23.41/6.43 |
% 23.41/6.43 | Instantiating formula (165) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 23.41/6.43 | (666) all_0_5_5 = n4
% 23.41/6.43 |
% 23.41/6.43 | From (665)(666) and (147) follows:
% 23.41/6.43 | (667) sum(n2, n4) = all_0_2_2
% 23.41/6.43 |
% 23.41/6.43 | From (665) and (4907) follows:
% 23.41/6.43 | (4942) sum(n2, n5) = all_0_7_7
% 23.41/6.43 |
% 23.41/6.43 | From (666) and (4905) follows:
% 23.41/6.44 | (4943) sum(n3, n4) = all_0_4_4
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n3, n4, all_0_4_4, n7 and discharging atoms sum(n3, n4) = all_0_4_4, sum(n3, n4) = n7, yields:
% 23.41/6.44 | (580) all_0_4_4 = n7
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n2, n5, all_0_7_7, n7 and discharging atoms sum(n2, n5) = all_0_7_7, sum(n2, n5) = n7, yields:
% 23.41/6.44 | (582) all_0_7_7 = n7
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 23.41/6.44 | (527) all_0_2_2 = n6
% 23.41/6.44 |
% 23.41/6.44 | From (527) and (2091) follows:
% 23.41/6.44 | (2129) sum(n6, n8) = all_0_0_0
% 23.41/6.44 |
% 23.41/6.44 | From (582)(580) and (212) follows:
% 23.41/6.44 | (584) sum(n7, n7) = all_0_3_3
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 23.41/6.44 | (585) all_0_3_3 = n14
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n6, n8, all_0_0_0, n14 and discharging atoms sum(n6, n8) = all_0_0_0, sum(n6, n8) = n14, yields:
% 23.41/6.44 | (586) all_0_0_0 = n14
% 23.41/6.44 |
% 23.41/6.44 | Equations (586,585) can reduce 363 to:
% 23.41/6.44 | (461) $false
% 23.41/6.44 |
% 23.41/6.44 |-The branch is then unsatisfiable
% 23.41/6.44 |-Branch two:
% 23.41/6.44 | (678) ~ (all_0_11_11 = n3)
% 23.41/6.44 | (679) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.41/6.44 |
% 23.41/6.44 +-Applying beta-rule and splitting (679), into two cases.
% 23.41/6.44 |-Branch one:
% 23.41/6.44 | (680) all_0_11_11 = n2
% 23.41/6.44 |
% 23.41/6.44 | From (680) and (423) follows:
% 23.41/6.44 | (681) pred(n2) = all_0_9_9
% 23.41/6.44 |
% 23.41/6.44 | From (680) and (262) follows:
% 23.41/6.44 | (682) succ(n2) = all_0_5_5
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (130) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 23.41/6.44 | (683) all_0_9_9 = n1
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (165) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 23.41/6.44 | (684) all_0_5_5 = n3
% 23.41/6.44 |
% 23.41/6.44 | From (683)(684) and (147) follows:
% 23.41/6.44 | (685) sum(n1, n3) = all_0_2_2
% 23.41/6.44 |
% 23.41/6.44 | From (683) and (4907) follows:
% 23.41/6.44 | (4960) sum(n1, n5) = all_0_7_7
% 23.41/6.44 |
% 23.41/6.44 | From (684) and (4905) follows:
% 23.41/6.44 | (4961) sum(n3, n3) = all_0_4_4
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n3, n3, all_0_4_4, n6 and discharging atoms sum(n3, n3) = all_0_4_4, sum(n3, n3) = n6, yields:
% 23.41/6.44 | (598) all_0_4_4 = n6
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n1, n5, all_0_7_7, n6 and discharging atoms sum(n1, n5) = all_0_7_7, sum(n1, n5) = n6, yields:
% 23.41/6.44 | (600) all_0_7_7 = n6
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 23.41/6.44 | (545) all_0_2_2 = n4
% 23.41/6.44 |
% 23.41/6.44 | From (545) and (2091) follows:
% 23.41/6.44 | (2147) sum(n4, n8) = all_0_0_0
% 23.41/6.44 |
% 23.41/6.44 | From (600)(598) and (212) follows:
% 23.41/6.44 | (602) sum(n6, n6) = all_0_3_3
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 23.41/6.44 | (459) all_0_3_3 = n12
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n4, n8, all_0_0_0, n12 and discharging atoms sum(n4, n8) = all_0_0_0, sum(n4, n8) = n12, yields:
% 23.41/6.44 | (457) all_0_0_0 = n12
% 23.41/6.44 |
% 23.41/6.44 | Equations (457,459) can reduce 363 to:
% 23.41/6.44 | (461) $false
% 23.41/6.44 |
% 23.41/6.44 |-The branch is then unsatisfiable
% 23.41/6.44 |-Branch two:
% 23.41/6.44 | (696) ~ (all_0_11_11 = n2)
% 23.41/6.44 | (697) all_0_11_11 = n1 | all_0_11_11 = n0
% 23.41/6.44 |
% 23.41/6.44 +-Applying beta-rule and splitting (697), into two cases.
% 23.41/6.44 |-Branch one:
% 23.41/6.44 | (698) all_0_11_11 = n1
% 23.41/6.44 |
% 23.41/6.44 | From (698) and (423) follows:
% 23.41/6.44 | (699) pred(n1) = all_0_9_9
% 23.41/6.44 |
% 23.41/6.44 | From (698) and (262) follows:
% 23.41/6.44 | (700) succ(n1) = all_0_5_5
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (130) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 23.41/6.44 | (701) all_0_9_9 = n0
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (165) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 23.41/6.44 | (702) all_0_5_5 = n2
% 23.41/6.44 |
% 23.41/6.44 | From (701)(702) and (147) follows:
% 23.41/6.44 | (703) sum(n0, n2) = all_0_2_2
% 23.41/6.44 |
% 23.41/6.44 | From (701) and (4907) follows:
% 23.41/6.44 | (4978) sum(n0, n5) = all_0_7_7
% 23.41/6.44 |
% 23.41/6.44 | From (702) and (4905) follows:
% 23.41/6.44 | (4979) sum(n3, n2) = all_0_4_4
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n3, n2, all_0_4_4, n5 and discharging atoms sum(n3, n2) = all_0_4_4, sum(n3, n2) = n5, yields:
% 23.41/6.44 | (616) all_0_4_4 = n5
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n0, n5, all_0_7_7, n5 and discharging atoms sum(n0, n5) = all_0_7_7, sum(n0, n5) = n5, yields:
% 23.41/6.44 | (618) all_0_7_7 = n5
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 23.41/6.44 | (563) all_0_2_2 = n2
% 23.41/6.44 |
% 23.41/6.44 | From (563) and (2091) follows:
% 23.41/6.44 | (2165) sum(n2, n8) = all_0_0_0
% 23.41/6.44 |
% 23.41/6.44 | From (618)(616) and (212) follows:
% 23.41/6.44 | (620) sum(n5, n5) = all_0_3_3
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 23.41/6.44 | (477) all_0_3_3 = n10
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n2, n8, all_0_0_0, n10 and discharging atoms sum(n2, n8) = all_0_0_0, sum(n2, n8) = n10, yields:
% 23.41/6.44 | (478) all_0_0_0 = n10
% 23.41/6.44 |
% 23.41/6.44 | Equations (478,477) can reduce 363 to:
% 23.41/6.44 | (461) $false
% 23.41/6.44 |
% 23.41/6.44 |-The branch is then unsatisfiable
% 23.41/6.44 |-Branch two:
% 23.41/6.44 | (715) ~ (all_0_11_11 = n1)
% 23.41/6.44 | (716) all_0_11_11 = n0
% 23.41/6.44 |
% 23.41/6.44 | From (716) and (423) follows:
% 23.41/6.44 | (717) pred(n0) = all_0_9_9
% 23.41/6.44 |
% 23.41/6.44 | From (716) and (262) follows:
% 23.41/6.44 | (718) succ(n0) = all_0_5_5
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (130) with n0, all_0_9_9, n15 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n15, yields:
% 23.41/6.44 | (719) all_0_9_9 = n15
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (165) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 23.41/6.44 | (720) all_0_5_5 = n1
% 23.41/6.44 |
% 23.41/6.44 | From (719)(720) and (147) follows:
% 23.41/6.44 | (721) sum(n15, n1) = all_0_2_2
% 23.41/6.44 |
% 23.41/6.44 | From (719) and (4907) follows:
% 23.41/6.44 | (4995) sum(n15, n5) = all_0_7_7
% 23.41/6.44 |
% 23.41/6.44 | From (720) and (4905) follows:
% 23.41/6.44 | (4996) sum(n3, n1) = all_0_4_4
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n15, n5, all_0_7_7, n4 and discharging atoms sum(n15, n5) = all_0_7_7, sum(n15, n5) = n4, yields:
% 23.41/6.44 | (636) all_0_7_7 = n4
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n15, n1, all_0_2_2, n0 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n0, yields:
% 23.41/6.44 | (581) all_0_2_2 = n0
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n3, n1, all_0_4_4, n4 and discharging atoms sum(n3, n1) = all_0_4_4, sum(n3, n1) = n4, yields:
% 23.41/6.44 | (634) all_0_4_4 = n4
% 23.41/6.44 |
% 23.41/6.44 | From (581) and (2091) follows:
% 23.41/6.44 | (2183) sum(n0, n8) = all_0_0_0
% 23.41/6.44 |
% 23.41/6.44 | From (636)(634) and (212) follows:
% 23.41/6.44 | (638) sum(n4, n4) = all_0_3_3
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 23.41/6.44 | (495) all_0_3_3 = n8
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n0, n8, all_0_0_0, n8 and discharging atoms sum(n0, n8) = all_0_0_0, sum(n0, n8) = n8, yields:
% 23.41/6.44 | (496) all_0_0_0 = n8
% 23.41/6.44 |
% 23.41/6.44 | Equations (496,495) can reduce 363 to:
% 23.41/6.44 | (461) $false
% 23.41/6.44 |
% 23.41/6.44 |-The branch is then unsatisfiable
% 23.41/6.44 |-Branch two:
% 23.41/6.44 | (941) ~ (all_0_10_10 = n4)
% 23.41/6.44 | (942) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.41/6.44 |
% 23.41/6.44 +-Applying beta-rule and splitting (643), into two cases.
% 23.41/6.44 |-Branch one:
% 23.41/6.44 | (644) all_0_11_11 = n4
% 23.41/6.44 |
% 23.41/6.44 | From (644) and (423) follows:
% 23.41/6.44 | (645) pred(n4) = all_0_9_9
% 23.41/6.44 |
% 23.41/6.44 | From (644) and (262) follows:
% 23.41/6.44 | (646) succ(n4) = all_0_5_5
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (130) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 23.41/6.44 | (647) all_0_9_9 = n3
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (165) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 23.41/6.44 | (648) all_0_5_5 = n5
% 23.41/6.44 |
% 23.41/6.44 | From (648) and (276) follows:
% 23.41/6.44 | (5012) sum(all_0_6_6, n5) = all_0_4_4
% 23.41/6.44 |
% 23.41/6.44 | From (647)(648) and (147) follows:
% 23.41/6.44 | (649) sum(n3, n5) = all_0_2_2
% 23.41/6.44 |
% 23.41/6.44 | From (647) and (350) follows:
% 23.41/6.44 | (5014) sum(n3, all_0_8_8) = all_0_7_7
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (74) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 23.41/6.44 | (509) all_0_2_2 = n8
% 23.41/6.44 |
% 23.41/6.44 | From (509) and (256) follows:
% 23.41/6.44 | (2342) sum(n8, all_0_1_1) = all_0_0_0
% 23.41/6.44 |
% 23.41/6.44 +-Applying beta-rule and splitting (942), into two cases.
% 23.41/6.44 |-Branch one:
% 23.41/6.44 | (943) all_0_10_10 = n3
% 23.41/6.44 |
% 23.41/6.44 | From (943) and (317) follows:
% 23.41/6.44 | (944) pred(n3) = all_0_6_6
% 23.41/6.44 |
% 23.41/6.44 | From (943) and (146) follows:
% 23.41/6.44 | (945) succ(n3) = all_0_8_8
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (130) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 23.41/6.44 | (946) all_0_6_6 = n2
% 23.41/6.44 |
% 23.41/6.44 | Instantiating formula (165) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 23.41/6.44 | (947) all_0_8_8 = n4
% 23.41/6.44 |
% 23.41/6.44 | From (946)(947) and (10) follows:
% 23.41/6.44 | (948) sum(n2, n4) = all_0_1_1
% 23.41/6.44 |
% 23.41/6.44 | From (946) and (5012) follows:
% 23.41/6.45 | (5023) sum(n2, n5) = all_0_4_4
% 23.41/6.45 |
% 23.41/6.45 | From (947) and (5014) follows:
% 23.41/6.45 | (5024) sum(n3, n4) = all_0_7_7
% 23.41/6.45 |
% 23.41/6.45 | Instantiating formula (74) with n3, n4, all_0_7_7, n7 and discharging atoms sum(n3, n4) = all_0_7_7, sum(n3, n4) = n7, yields:
% 23.41/6.45 | (582) all_0_7_7 = n7
% 23.41/6.45 |
% 23.41/6.45 | Instantiating formula (74) with n2, n5, all_0_4_4, n7 and discharging atoms sum(n2, n5) = all_0_4_4, sum(n2, n5) = n7, yields:
% 23.41/6.45 | (580) all_0_4_4 = n7
% 23.41/6.45 |
% 23.41/6.45 | Instantiating formula (74) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 23.41/6.45 | (808) all_0_1_1 = n6
% 23.41/6.45 |
% 23.41/6.45 | From (582)(580) and (212) follows:
% 23.41/6.45 | (584) sum(n7, n7) = all_0_3_3
% 23.41/6.45 |
% 23.41/6.45 | From (808) and (2342) follows:
% 23.41/6.45 | (2355) sum(n8, n6) = all_0_0_0
% 23.41/6.45 |
% 23.41/6.45 | Instantiating formula (74) with n8, n6, all_0_0_0, n14 and discharging atoms sum(n8, n6) = all_0_0_0, sum(n8, n6) = n14, yields:
% 23.41/6.45 | (586) all_0_0_0 = n14
% 23.41/6.45 |
% 23.41/6.45 | Instantiating formula (74) with n7, n7, all_0_3_3, n14 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n14, yields:
% 23.41/6.45 | (585) all_0_3_3 = n14
% 23.41/6.45 |
% 23.41/6.45 | Equations (586,585) can reduce 363 to:
% 23.41/6.45 | (461) $false
% 23.41/6.45 |
% 23.41/6.45 |-The branch is then unsatisfiable
% 23.41/6.45 |-Branch two:
% 23.41/6.45 | (959) ~ (all_0_10_10 = n3)
% 23.41/6.45 | (960) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.41/6.45 |
% 23.41/6.45 +-Applying beta-rule and splitting (960), into two cases.
% 23.41/6.45 |-Branch one:
% 23.41/6.45 | (961) all_0_10_10 = n2
% 23.41/6.45 |
% 23.41/6.45 | From (961) and (317) follows:
% 23.41/6.45 | (962) pred(n2) = all_0_6_6
% 23.41/6.45 |
% 23.41/6.45 | From (961) and (146) follows:
% 23.41/6.45 | (963) succ(n2) = all_0_8_8
% 23.41/6.45 |
% 23.41/6.45 | Instantiating formula (130) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 23.41/6.45 | (964) all_0_6_6 = n1
% 23.41/6.45 |
% 23.41/6.45 | Instantiating formula (165) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 23.41/6.45 | (965) all_0_8_8 = n3
% 23.41/6.45 |
% 23.41/6.45 | From (964)(965) and (10) follows:
% 23.41/6.45 | (966) sum(n1, n3) = all_0_1_1
% 23.41/6.45 |
% 23.41/6.45 | From (964) and (5012) follows:
% 23.41/6.45 | (5041) sum(n1, n5) = all_0_4_4
% 23.41/6.45 |
% 23.41/6.45 | From (965) and (5014) follows:
% 23.41/6.45 | (5042) sum(n3, n3) = all_0_7_7
% 23.41/6.45 |
% 23.41/6.45 | Instantiating formula (74) with n3, n3, all_0_7_7, n6 and discharging atoms sum(n3, n3) = all_0_7_7, sum(n3, n3) = n6, yields:
% 23.41/6.45 | (600) all_0_7_7 = n6
% 23.41/6.45 |
% 23.41/6.45 | Instantiating formula (74) with n1, n5, all_0_4_4, n6 and discharging atoms sum(n1, n5) = all_0_4_4, sum(n1, n5) = n6, yields:
% 23.41/6.45 | (598) all_0_4_4 = n6
% 23.41/6.45 |
% 23.41/6.45 | Instantiating formula (74) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 23.41/6.45 | (826) all_0_1_1 = n4
% 23.41/6.45 |
% 23.41/6.45 | From (600)(598) and (212) follows:
% 23.41/6.45 | (602) sum(n6, n6) = all_0_3_3
% 23.41/6.45 |
% 23.41/6.45 | From (826) and (2342) follows:
% 23.41/6.45 | (2373) sum(n8, n4) = all_0_0_0
% 23.41/6.45 |
% 23.41/6.45 | Instantiating formula (74) with n8, n4, all_0_0_0, n12 and discharging atoms sum(n8, n4) = all_0_0_0, sum(n8, n4) = n12, yields:
% 23.41/6.45 | (457) all_0_0_0 = n12
% 23.41/6.45 |
% 23.41/6.45 | Instantiating formula (74) with n6, n6, all_0_3_3, n12 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n12, yields:
% 23.41/6.45 | (459) all_0_3_3 = n12
% 23.41/6.45 |
% 23.41/6.45 | Equations (457,459) can reduce 363 to:
% 23.41/6.45 | (461) $false
% 23.41/6.45 |
% 23.41/6.45 |-The branch is then unsatisfiable
% 23.41/6.45 |-Branch two:
% 23.41/6.45 | (977) ~ (all_0_10_10 = n2)
% 23.41/6.45 | (978) all_0_10_10 = n1 | all_0_10_10 = n0
% 23.41/6.45 |
% 23.41/6.45 +-Applying beta-rule and splitting (978), into two cases.
% 23.41/6.45 |-Branch one:
% 23.41/6.45 | (979) all_0_10_10 = n1
% 23.41/6.45 |
% 23.41/6.45 | From (979) and (317) follows:
% 23.41/6.45 | (980) pred(n1) = all_0_6_6
% 23.41/6.45 |
% 23.41/6.45 | From (979) and (146) follows:
% 23.41/6.45 | (981) succ(n1) = all_0_8_8
% 23.41/6.45 |
% 23.41/6.45 | Instantiating formula (130) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 23.41/6.45 | (982) all_0_6_6 = n0
% 23.41/6.45 |
% 23.41/6.45 | Instantiating formula (165) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 23.41/6.45 | (983) all_0_8_8 = n2
% 23.41/6.45 |
% 23.41/6.45 | From (982)(983) and (10) follows:
% 23.41/6.45 | (984) sum(n0, n2) = all_0_1_1
% 23.41/6.45 |
% 23.41/6.45 | From (982) and (5012) follows:
% 23.73/6.45 | (5059) sum(n0, n5) = all_0_4_4
% 23.73/6.45 |
% 23.73/6.45 | From (983) and (5014) follows:
% 23.73/6.45 | (5060) sum(n3, n2) = all_0_7_7
% 23.73/6.45 |
% 23.73/6.45 | Instantiating formula (74) with n3, n2, all_0_7_7, n5 and discharging atoms sum(n3, n2) = all_0_7_7, sum(n3, n2) = n5, yields:
% 23.73/6.45 | (618) all_0_7_7 = n5
% 23.73/6.45 |
% 23.73/6.45 | Instantiating formula (74) with n0, n5, all_0_4_4, n5 and discharging atoms sum(n0, n5) = all_0_4_4, sum(n0, n5) = n5, yields:
% 23.73/6.45 | (616) all_0_4_4 = n5
% 23.73/6.45 |
% 23.73/6.45 | Instantiating formula (74) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 23.73/6.45 | (844) all_0_1_1 = n2
% 23.73/6.45 |
% 23.73/6.45 | From (618)(616) and (212) follows:
% 23.73/6.45 | (620) sum(n5, n5) = all_0_3_3
% 23.73/6.45 |
% 23.73/6.45 | From (844) and (2342) follows:
% 23.73/6.45 | (2391) sum(n8, n2) = all_0_0_0
% 23.73/6.45 |
% 23.73/6.45 | Instantiating formula (74) with n8, n2, all_0_0_0, n10 and discharging atoms sum(n8, n2) = all_0_0_0, sum(n8, n2) = n10, yields:
% 23.73/6.45 | (478) all_0_0_0 = n10
% 23.73/6.45 |
% 23.73/6.45 | Instantiating formula (74) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 23.73/6.45 | (477) all_0_3_3 = n10
% 23.73/6.45 |
% 23.73/6.45 | Equations (478,477) can reduce 363 to:
% 23.73/6.45 | (461) $false
% 23.73/6.45 |
% 23.73/6.45 |-The branch is then unsatisfiable
% 23.73/6.45 |-Branch two:
% 23.73/6.45 | (997) ~ (all_0_10_10 = n1)
% 23.73/6.45 | (998) all_0_10_10 = n0
% 23.73/6.45 |
% 23.73/6.45 | From (998) and (317) follows:
% 23.73/6.45 | (999) pred(n0) = all_0_6_6
% 23.73/6.45 |
% 23.73/6.45 | From (998) and (146) follows:
% 23.73/6.45 | (1000) succ(n0) = all_0_8_8
% 23.73/6.45 |
% 23.73/6.45 | Instantiating formula (130) with n0, all_0_6_6, n15 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n15, yields:
% 23.73/6.45 | (1001) all_0_6_6 = n15
% 23.73/6.45 |
% 23.73/6.45 | Instantiating formula (165) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 23.73/6.45 | (1002) all_0_8_8 = n1
% 23.73/6.45 |
% 23.73/6.45 | From (1001)(1002) and (10) follows:
% 23.73/6.45 | (1003) sum(n15, n1) = all_0_1_1
% 23.73/6.45 |
% 23.73/6.45 | From (1001) and (5012) follows:
% 23.73/6.45 | (5076) sum(n15, n5) = all_0_4_4
% 23.73/6.45 |
% 23.73/6.45 | From (1002) and (5014) follows:
% 23.73/6.45 | (5077) sum(n3, n1) = all_0_7_7
% 23.73/6.45 |
% 23.73/6.45 | Instantiating formula (74) with n15, n5, all_0_4_4, n4 and discharging atoms sum(n15, n5) = all_0_4_4, sum(n15, n5) = n4, yields:
% 23.73/6.45 | (634) all_0_4_4 = n4
% 23.73/6.45 |
% 23.73/6.45 | Instantiating formula (74) with n15, n1, all_0_1_1, n0 and discharging atoms sum(n15, n1) = all_0_1_1, sum(n15, n1) = n0, yields:
% 23.73/6.45 | (862) all_0_1_1 = n0
% 23.73/6.45 |
% 23.73/6.45 | Instantiating formula (74) with n3, n1, all_0_7_7, n4 and discharging atoms sum(n3, n1) = all_0_7_7, sum(n3, n1) = n4, yields:
% 23.73/6.45 | (636) all_0_7_7 = n4
% 23.73/6.45 |
% 23.73/6.45 | From (636)(634) and (212) follows:
% 23.73/6.45 | (638) sum(n4, n4) = all_0_3_3
% 23.73/6.45 |
% 23.73/6.45 | From (862) and (2342) follows:
% 23.73/6.45 | (2409) sum(n8, n0) = all_0_0_0
% 23.73/6.45 |
% 23.73/6.45 | Instantiating formula (74) with n8, n0, all_0_0_0, n8 and discharging atoms sum(n8, n0) = all_0_0_0, sum(n8, n0) = n8, yields:
% 23.73/6.45 | (496) all_0_0_0 = n8
% 23.73/6.45 |
% 23.73/6.45 | Instantiating formula (74) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 23.73/6.45 | (495) all_0_3_3 = n8
% 23.73/6.45 |
% 23.73/6.45 | Equations (496,495) can reduce 363 to:
% 23.73/6.45 | (461) $false
% 23.73/6.45 |
% 23.73/6.45 |-The branch is then unsatisfiable
% 23.73/6.45 |-Branch two:
% 23.73/6.45 | (660) ~ (all_0_11_11 = n4)
% 23.73/6.45 | (661) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.73/6.45 |
% 23.73/6.45 +-Applying beta-rule and splitting (942), into two cases.
% 23.73/6.45 |-Branch one:
% 23.73/6.45 | (943) all_0_10_10 = n3
% 23.73/6.45 |
% 23.73/6.45 | From (943) and (317) follows:
% 23.73/6.45 | (944) pred(n3) = all_0_6_6
% 23.73/6.45 |
% 23.73/6.45 | From (943) and (146) follows:
% 23.73/6.45 | (945) succ(n3) = all_0_8_8
% 23.73/6.45 |
% 23.73/6.45 | Instantiating formula (130) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 23.73/6.45 | (946) all_0_6_6 = n2
% 23.73/6.45 |
% 23.73/6.45 | Instantiating formula (165) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 23.73/6.45 | (947) all_0_8_8 = n4
% 23.73/6.45 |
% 23.73/6.45 | From (946) and (944) follows:
% 23.73/6.45 | (410) pred(n3) = n2
% 23.73/6.45 |
% 23.73/6.45 | From (947) and (945) follows:
% 23.73/6.45 | (49) succ(n3) = n4
% 23.73/6.45 |
% 23.73/6.45 | From (946) and (276) follows:
% 23.73/6.46 | (5095) sum(n2, all_0_5_5) = all_0_4_4
% 23.73/6.46 |
% 23.73/6.46 | From (946)(947) and (10) follows:
% 23.73/6.46 | (948) sum(n2, n4) = all_0_1_1
% 23.73/6.46 |
% 23.73/6.46 | From (947) and (350) follows:
% 23.73/6.46 | (5097) sum(all_0_9_9, n4) = all_0_7_7
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (74) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 23.73/6.46 | (808) all_0_1_1 = n6
% 23.73/6.46 |
% 23.73/6.46 | From (808) and (256) follows:
% 23.73/6.46 | (2569) sum(all_0_2_2, n6) = all_0_0_0
% 23.73/6.46 |
% 23.73/6.46 | From (808) and (948) follows:
% 23.73/6.46 | (141) sum(n2, n4) = n6
% 23.73/6.46 |
% 23.73/6.46 +-Applying beta-rule and splitting (661), into two cases.
% 23.73/6.46 |-Branch one:
% 23.73/6.46 | (662) all_0_11_11 = n3
% 23.73/6.46 |
% 23.73/6.46 | From (662) and (423) follows:
% 23.73/6.46 | (663) pred(n3) = all_0_9_9
% 23.73/6.46 |
% 23.73/6.46 | From (662) and (262) follows:
% 23.73/6.46 | (664) succ(n3) = all_0_5_5
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (130) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 23.73/6.46 | (665) all_0_9_9 = n2
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (165) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 23.73/6.46 | (666) all_0_5_5 = n4
% 23.73/6.46 |
% 23.73/6.46 | From (665)(666) and (147) follows:
% 23.73/6.46 | (667) sum(n2, n4) = all_0_2_2
% 23.73/6.46 |
% 23.73/6.46 | From (665) and (5097) follows:
% 23.73/6.46 | (5107) sum(n2, n4) = all_0_7_7
% 23.73/6.46 |
% 23.73/6.46 | From (666) and (5095) follows:
% 23.73/6.46 | (5108) sum(n2, n4) = all_0_4_4
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (74) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 23.73/6.46 | (527) all_0_2_2 = n6
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (74) with n2, n4, all_0_4_4, all_0_2_2 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = all_0_4_4, yields:
% 23.73/6.46 | (448) all_0_2_2 = all_0_4_4
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (74) with n2, n4, all_0_7_7, all_0_2_2 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = all_0_7_7, yields:
% 23.73/6.46 | (449) all_0_2_2 = all_0_7_7
% 23.73/6.46 |
% 23.73/6.46 | Combining equations (449,448) yields a new equation:
% 23.73/6.46 | (450) all_0_4_4 = all_0_7_7
% 23.73/6.46 |
% 23.73/6.46 | Combining equations (527,448) yields a new equation:
% 23.73/6.46 | (598) all_0_4_4 = n6
% 23.73/6.46 |
% 23.73/6.46 | Combining equations (598,450) yields a new equation:
% 23.73/6.46 | (600) all_0_7_7 = n6
% 23.73/6.46 |
% 23.73/6.46 | Combining equations (600,450) yields a new equation:
% 23.73/6.46 | (598) all_0_4_4 = n6
% 23.73/6.46 |
% 23.73/6.46 | Combining equations (598,448) yields a new equation:
% 23.73/6.46 | (527) all_0_2_2 = n6
% 23.73/6.46 |
% 23.73/6.46 | From (527) and (2569) follows:
% 23.73/6.46 | (2587) sum(n6, n6) = all_0_0_0
% 23.73/6.46 |
% 23.73/6.46 | From (600)(598) and (212) follows:
% 23.73/6.46 | (602) sum(n6, n6) = all_0_3_3
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (74) with n6, n6, all_0_0_0, n12 and discharging atoms sum(n6, n6) = all_0_0_0, sum(n6, n6) = n12, yields:
% 23.73/6.46 | (457) all_0_0_0 = n12
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (74) with n6, n6, all_0_3_3, all_0_0_0 and discharging atoms sum(n6, n6) = all_0_0_0, sum(n6, n6) = all_0_3_3, yields:
% 23.73/6.46 | (458) all_0_0_0 = all_0_3_3
% 23.73/6.46 |
% 23.73/6.46 | Combining equations (457,458) yields a new equation:
% 23.73/6.46 | (459) all_0_3_3 = n12
% 23.73/6.46 |
% 23.73/6.46 | Combining equations (459,458) yields a new equation:
% 23.73/6.46 | (457) all_0_0_0 = n12
% 23.73/6.46 |
% 23.73/6.46 | Equations (457,459) can reduce 363 to:
% 23.73/6.46 | (461) $false
% 23.73/6.46 |
% 23.73/6.46 |-The branch is then unsatisfiable
% 23.73/6.46 |-Branch two:
% 23.73/6.46 | (678) ~ (all_0_11_11 = n3)
% 23.73/6.46 | (679) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.73/6.46 |
% 23.73/6.46 +-Applying beta-rule and splitting (679), into two cases.
% 23.73/6.46 |-Branch one:
% 23.73/6.46 | (680) all_0_11_11 = n2
% 23.73/6.46 |
% 23.73/6.46 | From (680) and (423) follows:
% 23.73/6.46 | (681) pred(n2) = all_0_9_9
% 23.73/6.46 |
% 23.73/6.46 | From (680) and (262) follows:
% 23.73/6.46 | (682) succ(n2) = all_0_5_5
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (130) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 23.73/6.46 | (683) all_0_9_9 = n1
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (165) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 23.73/6.46 | (684) all_0_5_5 = n3
% 23.73/6.46 |
% 23.73/6.46 | From (683)(684) and (147) follows:
% 23.73/6.46 | (685) sum(n1, n3) = all_0_2_2
% 23.73/6.46 |
% 23.73/6.46 | From (683) and (5097) follows:
% 23.73/6.46 | (5132) sum(n1, n4) = all_0_7_7
% 23.73/6.46 |
% 23.73/6.46 | From (684) and (5095) follows:
% 23.73/6.46 | (5133) sum(n2, n3) = all_0_4_4
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (74) with n2, n3, all_0_4_4, n5 and discharging atoms sum(n2, n3) = all_0_4_4, sum(n2, n3) = n5, yields:
% 23.73/6.46 | (616) all_0_4_4 = n5
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (74) with n1, n4, all_0_7_7, n5 and discharging atoms sum(n1, n4) = all_0_7_7, sum(n1, n4) = n5, yields:
% 23.73/6.46 | (618) all_0_7_7 = n5
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (74) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 23.73/6.46 | (545) all_0_2_2 = n4
% 23.73/6.46 |
% 23.73/6.46 | From (545) and (2569) follows:
% 23.73/6.46 | (2607) sum(n4, n6) = all_0_0_0
% 23.73/6.46 |
% 23.73/6.46 | From (618)(616) and (212) follows:
% 23.73/6.46 | (620) sum(n5, n5) = all_0_3_3
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (74) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 23.73/6.46 | (477) all_0_3_3 = n10
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (74) with n4, n6, all_0_0_0, n10 and discharging atoms sum(n4, n6) = all_0_0_0, sum(n4, n6) = n10, yields:
% 23.73/6.46 | (478) all_0_0_0 = n10
% 23.73/6.46 |
% 23.73/6.46 | Equations (478,477) can reduce 363 to:
% 23.73/6.46 | (461) $false
% 23.73/6.46 |
% 23.73/6.46 |-The branch is then unsatisfiable
% 23.73/6.46 |-Branch two:
% 23.73/6.46 | (696) ~ (all_0_11_11 = n2)
% 23.73/6.46 | (697) all_0_11_11 = n1 | all_0_11_11 = n0
% 23.73/6.46 |
% 23.73/6.46 +-Applying beta-rule and splitting (697), into two cases.
% 23.73/6.46 |-Branch one:
% 23.73/6.46 | (698) all_0_11_11 = n1
% 23.73/6.46 |
% 23.73/6.46 | From (698) and (423) follows:
% 23.73/6.46 | (699) pred(n1) = all_0_9_9
% 23.73/6.46 |
% 23.73/6.46 | From (698) and (262) follows:
% 23.73/6.46 | (700) succ(n1) = all_0_5_5
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (130) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 23.73/6.46 | (701) all_0_9_9 = n0
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (165) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 23.73/6.46 | (702) all_0_5_5 = n2
% 23.73/6.46 |
% 23.73/6.46 | From (701)(702) and (147) follows:
% 23.73/6.46 | (703) sum(n0, n2) = all_0_2_2
% 23.73/6.46 |
% 23.73/6.46 | From (701) and (5097) follows:
% 23.73/6.46 | (5150) sum(n0, n4) = all_0_7_7
% 23.73/6.46 |
% 23.73/6.46 | From (702) and (5095) follows:
% 23.73/6.46 | (5151) sum(n2, n2) = all_0_4_4
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (74) with n2, n2, all_0_4_4, n4 and discharging atoms sum(n2, n2) = all_0_4_4, sum(n2, n2) = n4, yields:
% 23.73/6.46 | (634) all_0_4_4 = n4
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (74) with n0, n4, all_0_7_7, n4 and discharging atoms sum(n0, n4) = all_0_7_7, sum(n0, n4) = n4, yields:
% 23.73/6.46 | (636) all_0_7_7 = n4
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (74) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 23.73/6.46 | (563) all_0_2_2 = n2
% 23.73/6.46 |
% 23.73/6.46 | From (563) and (2569) follows:
% 23.73/6.46 | (2625) sum(n2, n6) = all_0_0_0
% 23.73/6.46 |
% 23.73/6.46 | From (636)(634) and (212) follows:
% 23.73/6.46 | (638) sum(n4, n4) = all_0_3_3
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (74) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 23.73/6.46 | (495) all_0_3_3 = n8
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (74) with n2, n6, all_0_0_0, n8 and discharging atoms sum(n2, n6) = all_0_0_0, sum(n2, n6) = n8, yields:
% 23.73/6.46 | (496) all_0_0_0 = n8
% 23.73/6.46 |
% 23.73/6.46 | Equations (496,495) can reduce 363 to:
% 23.73/6.46 | (461) $false
% 23.73/6.46 |
% 23.73/6.46 |-The branch is then unsatisfiable
% 23.73/6.46 |-Branch two:
% 23.73/6.46 | (715) ~ (all_0_11_11 = n1)
% 23.73/6.46 | (716) all_0_11_11 = n0
% 23.73/6.46 |
% 23.73/6.46 | From (716) and (423) follows:
% 23.73/6.46 | (717) pred(n0) = all_0_9_9
% 23.73/6.46 |
% 23.73/6.46 | From (716) and (262) follows:
% 23.73/6.46 | (718) succ(n0) = all_0_5_5
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (130) with n0, all_0_9_9, n15 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n15, yields:
% 23.73/6.46 | (719) all_0_9_9 = n15
% 23.73/6.46 |
% 23.73/6.46 | Instantiating formula (165) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 23.73/6.46 | (720) all_0_5_5 = n1
% 23.73/6.46 |
% 23.73/6.46 | From (719)(720) and (147) follows:
% 23.73/6.46 | (721) sum(n15, n1) = all_0_2_2
% 23.73/6.46 |
% 23.73/6.46 | From (719) and (5097) follows:
% 23.73/6.46 | (5167) sum(n15, n4) = all_0_7_7
% 23.73/6.46 |
% 23.73/6.46 | From (720) and (5095) follows:
% 23.73/6.47 | (5168) sum(n2, n1) = all_0_4_4
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n15, n4, all_0_7_7, n3 and discharging atoms sum(n15, n4) = all_0_7_7, sum(n15, n4) = n3, yields:
% 23.73/6.47 | (654) all_0_7_7 = n3
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n15, n1, all_0_2_2, n0 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n0, yields:
% 23.73/6.47 | (581) all_0_2_2 = n0
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n2, n1, all_0_4_4, n3 and discharging atoms sum(n2, n1) = all_0_4_4, sum(n2, n1) = n3, yields:
% 23.73/6.47 | (652) all_0_4_4 = n3
% 23.73/6.47 |
% 23.73/6.47 | From (581) and (2569) follows:
% 23.73/6.47 | (2643) sum(n0, n6) = all_0_0_0
% 23.73/6.47 |
% 23.73/6.47 | From (654)(652) and (212) follows:
% 23.73/6.47 | (656) sum(n3, n3) = all_0_3_3
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 23.73/6.47 | (513) all_0_3_3 = n6
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n0, n6, all_0_0_0, n6 and discharging atoms sum(n0, n6) = all_0_0_0, sum(n0, n6) = n6, yields:
% 23.73/6.47 | (514) all_0_0_0 = n6
% 23.73/6.47 |
% 23.73/6.47 | Equations (514,513) can reduce 363 to:
% 23.73/6.47 | (461) $false
% 23.73/6.47 |
% 23.73/6.47 |-The branch is then unsatisfiable
% 23.73/6.47 |-Branch two:
% 23.73/6.47 | (959) ~ (all_0_10_10 = n3)
% 23.73/6.47 | (960) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 23.73/6.47 |
% 23.73/6.47 +-Applying beta-rule and splitting (661), into two cases.
% 23.73/6.47 |-Branch one:
% 23.73/6.47 | (662) all_0_11_11 = n3
% 23.73/6.47 |
% 23.73/6.47 | From (662) and (423) follows:
% 23.73/6.47 | (663) pred(n3) = all_0_9_9
% 23.73/6.47 |
% 23.73/6.47 | From (662) and (262) follows:
% 23.73/6.47 | (664) succ(n3) = all_0_5_5
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (130) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 23.73/6.47 | (665) all_0_9_9 = n2
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (165) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 23.73/6.47 | (666) all_0_5_5 = n4
% 23.73/6.47 |
% 23.73/6.47 | From (666) and (276) follows:
% 23.73/6.47 | (5184) sum(all_0_6_6, n4) = all_0_4_4
% 23.73/6.47 |
% 23.73/6.47 | From (665)(666) and (147) follows:
% 23.73/6.47 | (667) sum(n2, n4) = all_0_2_2
% 23.73/6.47 |
% 23.73/6.47 | From (665) and (350) follows:
% 23.73/6.47 | (5186) sum(n2, all_0_8_8) = all_0_7_7
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 23.73/6.47 | (527) all_0_2_2 = n6
% 23.73/6.47 |
% 23.73/6.47 | From (527) and (256) follows:
% 23.73/6.47 | (2803) sum(n6, all_0_1_1) = all_0_0_0
% 23.73/6.47 |
% 23.73/6.47 +-Applying beta-rule and splitting (960), into two cases.
% 23.73/6.47 |-Branch one:
% 23.73/6.47 | (961) all_0_10_10 = n2
% 23.73/6.47 |
% 23.73/6.47 | From (961) and (317) follows:
% 23.73/6.47 | (962) pred(n2) = all_0_6_6
% 23.73/6.47 |
% 23.73/6.47 | From (961) and (146) follows:
% 23.73/6.47 | (963) succ(n2) = all_0_8_8
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (130) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 23.73/6.47 | (964) all_0_6_6 = n1
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (165) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 23.73/6.47 | (965) all_0_8_8 = n3
% 23.73/6.47 |
% 23.73/6.47 | From (964)(965) and (10) follows:
% 23.73/6.47 | (966) sum(n1, n3) = all_0_1_1
% 23.73/6.47 |
% 23.73/6.47 | From (964) and (5184) follows:
% 23.73/6.47 | (5195) sum(n1, n4) = all_0_4_4
% 23.73/6.47 |
% 23.73/6.47 | From (965) and (5186) follows:
% 23.73/6.47 | (5196) sum(n2, n3) = all_0_7_7
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n2, n3, all_0_7_7, n5 and discharging atoms sum(n2, n3) = all_0_7_7, sum(n2, n3) = n5, yields:
% 23.73/6.47 | (618) all_0_7_7 = n5
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n1, n4, all_0_4_4, n5 and discharging atoms sum(n1, n4) = all_0_4_4, sum(n1, n4) = n5, yields:
% 23.73/6.47 | (616) all_0_4_4 = n5
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 23.73/6.47 | (826) all_0_1_1 = n4
% 23.73/6.47 |
% 23.73/6.47 | From (618)(616) and (212) follows:
% 23.73/6.47 | (620) sum(n5, n5) = all_0_3_3
% 23.73/6.47 |
% 23.73/6.47 | From (826) and (2803) follows:
% 23.73/6.47 | (2816) sum(n6, n4) = all_0_0_0
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n6, n4, all_0_0_0, n10 and discharging atoms sum(n6, n4) = all_0_0_0, sum(n6, n4) = n10, yields:
% 23.73/6.47 | (478) all_0_0_0 = n10
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 23.73/6.47 | (477) all_0_3_3 = n10
% 23.73/6.47 |
% 23.73/6.47 | Equations (478,477) can reduce 363 to:
% 23.73/6.47 | (461) $false
% 23.73/6.47 |
% 23.73/6.47 |-The branch is then unsatisfiable
% 23.73/6.47 |-Branch two:
% 23.73/6.47 | (977) ~ (all_0_10_10 = n2)
% 23.73/6.47 | (978) all_0_10_10 = n1 | all_0_10_10 = n0
% 23.73/6.47 |
% 23.73/6.47 +-Applying beta-rule and splitting (978), into two cases.
% 23.73/6.47 |-Branch one:
% 23.73/6.47 | (979) all_0_10_10 = n1
% 23.73/6.47 |
% 23.73/6.47 | From (979) and (317) follows:
% 23.73/6.47 | (980) pred(n1) = all_0_6_6
% 23.73/6.47 |
% 23.73/6.47 | From (979) and (146) follows:
% 23.73/6.47 | (981) succ(n1) = all_0_8_8
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (130) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 23.73/6.47 | (982) all_0_6_6 = n0
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (165) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 23.73/6.47 | (983) all_0_8_8 = n2
% 23.73/6.47 |
% 23.73/6.47 | From (982)(983) and (10) follows:
% 23.73/6.47 | (984) sum(n0, n2) = all_0_1_1
% 23.73/6.47 |
% 23.73/6.47 | From (982) and (5184) follows:
% 23.73/6.47 | (5213) sum(n0, n4) = all_0_4_4
% 23.73/6.47 |
% 23.73/6.47 | From (983) and (5186) follows:
% 23.73/6.47 | (5214) sum(n2, n2) = all_0_7_7
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n2, n2, all_0_7_7, n4 and discharging atoms sum(n2, n2) = all_0_7_7, sum(n2, n2) = n4, yields:
% 23.73/6.47 | (636) all_0_7_7 = n4
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n0, n4, all_0_4_4, n4 and discharging atoms sum(n0, n4) = all_0_4_4, sum(n0, n4) = n4, yields:
% 23.73/6.47 | (634) all_0_4_4 = n4
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 23.73/6.47 | (844) all_0_1_1 = n2
% 23.73/6.47 |
% 23.73/6.47 | From (636)(634) and (212) follows:
% 23.73/6.47 | (638) sum(n4, n4) = all_0_3_3
% 23.73/6.47 |
% 23.73/6.47 | From (844) and (2803) follows:
% 23.73/6.47 | (2834) sum(n6, n2) = all_0_0_0
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n6, n2, all_0_0_0, n8 and discharging atoms sum(n6, n2) = all_0_0_0, sum(n6, n2) = n8, yields:
% 23.73/6.47 | (496) all_0_0_0 = n8
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 23.73/6.47 | (495) all_0_3_3 = n8
% 23.73/6.47 |
% 23.73/6.47 | Equations (496,495) can reduce 363 to:
% 23.73/6.47 | (461) $false
% 23.73/6.47 |
% 23.73/6.47 |-The branch is then unsatisfiable
% 23.73/6.47 |-Branch two:
% 23.73/6.47 | (997) ~ (all_0_10_10 = n1)
% 23.73/6.47 | (998) all_0_10_10 = n0
% 23.73/6.47 |
% 23.73/6.47 | From (998) and (317) follows:
% 23.73/6.47 | (999) pred(n0) = all_0_6_6
% 23.73/6.47 |
% 23.73/6.47 | From (998) and (146) follows:
% 23.73/6.47 | (1000) succ(n0) = all_0_8_8
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (130) with n0, all_0_6_6, n15 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n15, yields:
% 23.73/6.47 | (1001) all_0_6_6 = n15
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (165) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 23.73/6.47 | (1002) all_0_8_8 = n1
% 23.73/6.47 |
% 23.73/6.47 | From (1001)(1002) and (10) follows:
% 23.73/6.47 | (1003) sum(n15, n1) = all_0_1_1
% 23.73/6.47 |
% 23.73/6.47 | From (1001) and (5184) follows:
% 23.73/6.47 | (5230) sum(n15, n4) = all_0_4_4
% 23.73/6.47 |
% 23.73/6.47 | From (1002) and (5186) follows:
% 23.73/6.47 | (5231) sum(n2, n1) = all_0_7_7
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n15, n4, all_0_4_4, n3 and discharging atoms sum(n15, n4) = all_0_4_4, sum(n15, n4) = n3, yields:
% 23.73/6.47 | (652) all_0_4_4 = n3
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n15, n1, all_0_1_1, n0 and discharging atoms sum(n15, n1) = all_0_1_1, sum(n15, n1) = n0, yields:
% 23.73/6.47 | (862) all_0_1_1 = n0
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n2, n1, all_0_7_7, n3 and discharging atoms sum(n2, n1) = all_0_7_7, sum(n2, n1) = n3, yields:
% 23.73/6.47 | (654) all_0_7_7 = n3
% 23.73/6.47 |
% 23.73/6.47 | From (654)(652) and (212) follows:
% 23.73/6.47 | (656) sum(n3, n3) = all_0_3_3
% 23.73/6.47 |
% 23.73/6.47 | From (862) and (2803) follows:
% 23.73/6.47 | (2852) sum(n6, n0) = all_0_0_0
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n6, n0, all_0_0_0, n6 and discharging atoms sum(n6, n0) = all_0_0_0, sum(n6, n0) = n6, yields:
% 23.73/6.47 | (514) all_0_0_0 = n6
% 23.73/6.47 |
% 23.73/6.47 | Instantiating formula (74) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 23.73/6.47 | (513) all_0_3_3 = n6
% 23.73/6.47 |
% 23.73/6.47 | Equations (514,513) can reduce 363 to:
% 23.73/6.47 | (461) $false
% 23.73/6.48 |
% 23.73/6.48 |-The branch is then unsatisfiable
% 23.73/6.48 |-Branch two:
% 23.73/6.48 | (678) ~ (all_0_11_11 = n3)
% 23.73/6.48 | (679) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 23.73/6.48 |
% 23.73/6.48 +-Applying beta-rule and splitting (960), into two cases.
% 23.73/6.48 |-Branch one:
% 23.73/6.48 | (961) all_0_10_10 = n2
% 23.73/6.48 |
% 23.73/6.48 | From (961) and (317) follows:
% 23.73/6.48 | (962) pred(n2) = all_0_6_6
% 23.73/6.48 |
% 23.73/6.48 | From (961) and (146) follows:
% 23.73/6.48 | (963) succ(n2) = all_0_8_8
% 23.73/6.48 |
% 23.73/6.48 | Instantiating formula (130) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 23.73/6.48 | (964) all_0_6_6 = n1
% 23.73/6.48 |
% 23.73/6.48 | Instantiating formula (165) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 23.73/6.48 | (965) all_0_8_8 = n3
% 23.73/6.48 |
% 23.73/6.48 | From (964) and (962) follows:
% 23.73/6.48 | (91) pred(n2) = n1
% 23.73/6.48 |
% 23.73/6.48 | From (965) and (963) follows:
% 23.73/6.48 | (150) succ(n2) = n3
% 23.73/6.48 |
% 23.73/6.48 | From (964) and (276) follows:
% 23.73/6.48 | (5249) sum(n1, all_0_5_5) = all_0_4_4
% 23.73/6.48 |
% 23.73/6.48 | From (964)(965) and (10) follows:
% 23.73/6.48 | (966) sum(n1, n3) = all_0_1_1
% 23.73/6.48 |
% 23.73/6.48 | From (965) and (350) follows:
% 23.73/6.48 | (5251) sum(all_0_9_9, n3) = all_0_7_7
% 23.73/6.48 |
% 23.73/6.48 | Instantiating formula (74) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 23.73/6.48 | (826) all_0_1_1 = n4
% 23.73/6.48 |
% 23.73/6.48 | From (826) and (256) follows:
% 23.73/6.48 | (3012) sum(all_0_2_2, n4) = all_0_0_0
% 23.73/6.48 |
% 23.73/6.48 | From (826) and (966) follows:
% 23.73/6.48 | (419) sum(n1, n3) = n4
% 23.73/6.48 |
% 23.73/6.48 +-Applying beta-rule and splitting (679), into two cases.
% 23.73/6.48 |-Branch one:
% 23.73/6.48 | (680) all_0_11_11 = n2
% 23.73/6.48 |
% 23.73/6.48 | From (680) and (423) follows:
% 23.73/6.48 | (681) pred(n2) = all_0_9_9
% 23.73/6.48 |
% 23.73/6.48 | From (680) and (262) follows:
% 23.73/6.48 | (682) succ(n2) = all_0_5_5
% 23.73/6.48 |
% 23.73/6.48 | Instantiating formula (130) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 23.73/6.48 | (683) all_0_9_9 = n1
% 23.73/6.48 |
% 23.73/6.48 | Instantiating formula (165) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 23.73/6.48 | (684) all_0_5_5 = n3
% 23.84/6.48 |
% 23.84/6.48 | From (683)(684) and (147) follows:
% 23.84/6.48 | (685) sum(n1, n3) = all_0_2_2
% 23.84/6.48 |
% 23.84/6.48 | From (683) and (5251) follows:
% 23.84/6.48 | (5261) sum(n1, n3) = all_0_7_7
% 23.84/6.48 |
% 23.84/6.48 | From (684) and (5249) follows:
% 23.84/6.48 | (5262) sum(n1, n3) = all_0_4_4
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (74) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 23.84/6.48 | (545) all_0_2_2 = n4
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (74) with n1, n3, all_0_4_4, all_0_2_2 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = all_0_4_4, yields:
% 23.84/6.48 | (448) all_0_2_2 = all_0_4_4
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (74) with n1, n3, all_0_7_7, all_0_2_2 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = all_0_7_7, yields:
% 23.84/6.48 | (449) all_0_2_2 = all_0_7_7
% 23.84/6.48 |
% 23.84/6.48 | Combining equations (449,448) yields a new equation:
% 23.84/6.48 | (450) all_0_4_4 = all_0_7_7
% 23.84/6.48 |
% 23.84/6.48 | Combining equations (545,448) yields a new equation:
% 23.84/6.48 | (634) all_0_4_4 = n4
% 23.84/6.48 |
% 23.84/6.48 | Combining equations (634,450) yields a new equation:
% 23.84/6.48 | (636) all_0_7_7 = n4
% 23.84/6.48 |
% 23.84/6.48 | Combining equations (636,450) yields a new equation:
% 23.84/6.48 | (634) all_0_4_4 = n4
% 23.84/6.48 |
% 23.84/6.48 | Combining equations (634,448) yields a new equation:
% 23.84/6.48 | (545) all_0_2_2 = n4
% 23.84/6.48 |
% 23.84/6.48 | From (545) and (3012) follows:
% 23.84/6.48 | (3030) sum(n4, n4) = all_0_0_0
% 23.84/6.48 |
% 23.84/6.48 | From (636)(634) and (212) follows:
% 23.84/6.48 | (638) sum(n4, n4) = all_0_3_3
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (74) with n4, n4, all_0_0_0, n8 and discharging atoms sum(n4, n4) = all_0_0_0, sum(n4, n4) = n8, yields:
% 23.84/6.48 | (496) all_0_0_0 = n8
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (74) with n4, n4, all_0_3_3, all_0_0_0 and discharging atoms sum(n4, n4) = all_0_0_0, sum(n4, n4) = all_0_3_3, yields:
% 23.84/6.48 | (458) all_0_0_0 = all_0_3_3
% 23.84/6.48 |
% 23.84/6.48 | Combining equations (496,458) yields a new equation:
% 23.84/6.48 | (495) all_0_3_3 = n8
% 23.84/6.48 |
% 23.84/6.48 | Combining equations (495,458) yields a new equation:
% 23.84/6.48 | (496) all_0_0_0 = n8
% 23.84/6.48 |
% 23.84/6.48 | Equations (496,495) can reduce 363 to:
% 23.84/6.48 | (461) $false
% 23.84/6.48 |
% 23.84/6.48 |-The branch is then unsatisfiable
% 23.84/6.48 |-Branch two:
% 23.84/6.48 | (696) ~ (all_0_11_11 = n2)
% 23.84/6.48 | (697) all_0_11_11 = n1 | all_0_11_11 = n0
% 23.84/6.48 |
% 23.84/6.48 +-Applying beta-rule and splitting (697), into two cases.
% 23.84/6.48 |-Branch one:
% 23.84/6.48 | (698) all_0_11_11 = n1
% 23.84/6.48 |
% 23.84/6.48 | From (698) and (423) follows:
% 23.84/6.48 | (699) pred(n1) = all_0_9_9
% 23.84/6.48 |
% 23.84/6.48 | From (698) and (262) follows:
% 23.84/6.48 | (700) succ(n1) = all_0_5_5
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (130) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 23.84/6.48 | (701) all_0_9_9 = n0
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (165) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 23.84/6.48 | (702) all_0_5_5 = n2
% 23.84/6.48 |
% 23.84/6.48 | From (701)(702) and (147) follows:
% 23.84/6.48 | (703) sum(n0, n2) = all_0_2_2
% 23.84/6.48 |
% 23.84/6.48 | From (701) and (5251) follows:
% 23.84/6.48 | (5286) sum(n0, n3) = all_0_7_7
% 23.84/6.48 |
% 23.84/6.48 | From (702) and (5249) follows:
% 23.84/6.48 | (5287) sum(n1, n2) = all_0_4_4
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (74) with n1, n2, all_0_4_4, n3 and discharging atoms sum(n1, n2) = all_0_4_4, sum(n1, n2) = n3, yields:
% 23.84/6.48 | (652) all_0_4_4 = n3
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (74) with n0, n3, all_0_7_7, n3 and discharging atoms sum(n0, n3) = all_0_7_7, sum(n0, n3) = n3, yields:
% 23.84/6.48 | (654) all_0_7_7 = n3
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (74) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 23.84/6.48 | (563) all_0_2_2 = n2
% 23.84/6.48 |
% 23.84/6.48 | From (563) and (3012) follows:
% 23.84/6.48 | (3050) sum(n2, n4) = all_0_0_0
% 23.84/6.48 |
% 23.84/6.48 | From (654)(652) and (212) follows:
% 23.84/6.48 | (656) sum(n3, n3) = all_0_3_3
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (74) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 23.84/6.48 | (513) all_0_3_3 = n6
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (74) with n2, n4, all_0_0_0, n6 and discharging atoms sum(n2, n4) = all_0_0_0, sum(n2, n4) = n6, yields:
% 23.84/6.48 | (514) all_0_0_0 = n6
% 23.84/6.48 |
% 23.84/6.48 | Equations (514,513) can reduce 363 to:
% 23.84/6.48 | (461) $false
% 23.84/6.48 |
% 23.84/6.48 |-The branch is then unsatisfiable
% 23.84/6.48 |-Branch two:
% 23.84/6.48 | (715) ~ (all_0_11_11 = n1)
% 23.84/6.48 | (716) all_0_11_11 = n0
% 23.84/6.48 |
% 23.84/6.48 | From (716) and (423) follows:
% 23.84/6.48 | (717) pred(n0) = all_0_9_9
% 23.84/6.48 |
% 23.84/6.48 | From (716) and (262) follows:
% 23.84/6.48 | (718) succ(n0) = all_0_5_5
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (130) with n0, all_0_9_9, n15 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n15, yields:
% 23.84/6.48 | (719) all_0_9_9 = n15
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (165) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 23.84/6.48 | (720) all_0_5_5 = n1
% 23.84/6.48 |
% 23.84/6.48 | From (719)(720) and (147) follows:
% 23.84/6.48 | (721) sum(n15, n1) = all_0_2_2
% 23.84/6.48 |
% 23.84/6.48 | From (719) and (5251) follows:
% 23.84/6.48 | (5303) sum(n15, n3) = all_0_7_7
% 23.84/6.48 |
% 23.84/6.48 | From (720) and (5249) follows:
% 23.84/6.48 | (5304) sum(n1, n1) = all_0_4_4
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (74) with n15, n3, all_0_7_7, n2 and discharging atoms sum(n15, n3) = all_0_7_7, sum(n15, n3) = n2, yields:
% 23.84/6.48 | (672) all_0_7_7 = n2
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (74) with n15, n1, all_0_2_2, n0 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n0, yields:
% 23.84/6.48 | (581) all_0_2_2 = n0
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (74) with n1, n1, all_0_4_4, n2 and discharging atoms sum(n1, n1) = all_0_4_4, sum(n1, n1) = n2, yields:
% 23.84/6.48 | (670) all_0_4_4 = n2
% 23.84/6.48 |
% 23.84/6.48 | From (581) and (3012) follows:
% 23.84/6.48 | (3068) sum(n0, n4) = all_0_0_0
% 23.84/6.48 |
% 23.84/6.48 | From (672)(670) and (212) follows:
% 23.84/6.48 | (674) sum(n2, n2) = all_0_3_3
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (74) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 23.84/6.48 | (531) all_0_3_3 = n4
% 23.84/6.48 |
% 23.84/6.48 | Instantiating formula (74) with n0, n4, all_0_0_0, n4 and discharging atoms sum(n0, n4) = all_0_0_0, sum(n0, n4) = n4, yields:
% 23.84/6.48 | (532) all_0_0_0 = n4
% 23.84/6.48 |
% 23.84/6.48 | Equations (532,531) can reduce 363 to:
% 23.84/6.48 | (461) $false
% 23.84/6.48 |
% 23.84/6.48 |-The branch is then unsatisfiable
% 23.84/6.48 |-Branch two:
% 23.84/6.48 | (977) ~ (all_0_10_10 = n2)
% 23.84/6.48 | (978) all_0_10_10 = n1 | all_0_10_10 = n0
% 23.84/6.48 |
% 23.84/6.48 +-Applying beta-rule and splitting (679), into two cases.
% 23.84/6.48 |-Branch one:
% 23.84/6.48 | (680) all_0_11_11 = n2
% 23.84/6.48 |
% 23.84/6.48 | From (680) and (423) follows:
% 23.84/6.48 | (681) pred(n2) = all_0_9_9
% 23.84/6.49 |
% 23.84/6.49 | From (680) and (262) follows:
% 23.84/6.49 | (682) succ(n2) = all_0_5_5
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (130) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 23.84/6.49 | (683) all_0_9_9 = n1
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (165) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 23.84/6.49 | (684) all_0_5_5 = n3
% 23.84/6.49 |
% 23.84/6.49 | From (684) and (276) follows:
% 23.84/6.49 | (5320) sum(all_0_6_6, n3) = all_0_4_4
% 23.84/6.49 |
% 23.84/6.49 | From (683)(684) and (147) follows:
% 23.84/6.49 | (685) sum(n1, n3) = all_0_2_2
% 23.84/6.49 |
% 23.84/6.49 | From (683) and (350) follows:
% 23.84/6.49 | (5322) sum(n1, all_0_8_8) = all_0_7_7
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (74) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 23.84/6.49 | (545) all_0_2_2 = n4
% 23.84/6.49 |
% 23.84/6.49 | From (545) and (256) follows:
% 23.84/6.49 | (3227) sum(n4, all_0_1_1) = all_0_0_0
% 23.84/6.49 |
% 23.84/6.49 +-Applying beta-rule and splitting (978), into two cases.
% 23.84/6.49 |-Branch one:
% 23.84/6.49 | (979) all_0_10_10 = n1
% 23.84/6.49 |
% 23.84/6.49 | From (979) and (317) follows:
% 23.84/6.49 | (980) pred(n1) = all_0_6_6
% 23.84/6.49 |
% 23.84/6.49 | From (979) and (146) follows:
% 23.84/6.49 | (981) succ(n1) = all_0_8_8
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (130) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 23.84/6.49 | (982) all_0_6_6 = n0
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (165) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 23.84/6.49 | (983) all_0_8_8 = n2
% 23.84/6.49 |
% 23.84/6.49 | From (982)(983) and (10) follows:
% 23.84/6.49 | (984) sum(n0, n2) = all_0_1_1
% 23.84/6.49 |
% 23.84/6.49 | From (982) and (5320) follows:
% 23.84/6.49 | (5331) sum(n0, n3) = all_0_4_4
% 23.84/6.49 |
% 23.84/6.49 | From (983) and (5322) follows:
% 23.84/6.49 | (5332) sum(n1, n2) = all_0_7_7
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (74) with n1, n2, all_0_7_7, n3 and discharging atoms sum(n1, n2) = all_0_7_7, sum(n1, n2) = n3, yields:
% 23.84/6.49 | (654) all_0_7_7 = n3
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (74) with n0, n3, all_0_4_4, n3 and discharging atoms sum(n0, n3) = all_0_4_4, sum(n0, n3) = n3, yields:
% 23.84/6.49 | (652) all_0_4_4 = n3
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (74) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 23.84/6.49 | (844) all_0_1_1 = n2
% 23.84/6.49 |
% 23.84/6.49 | From (654)(652) and (212) follows:
% 23.84/6.49 | (656) sum(n3, n3) = all_0_3_3
% 23.84/6.49 |
% 23.84/6.49 | From (844) and (3227) follows:
% 23.84/6.49 | (3240) sum(n4, n2) = all_0_0_0
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (74) with n4, n2, all_0_0_0, n6 and discharging atoms sum(n4, n2) = all_0_0_0, sum(n4, n2) = n6, yields:
% 23.84/6.49 | (514) all_0_0_0 = n6
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (74) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 23.84/6.49 | (513) all_0_3_3 = n6
% 23.84/6.49 |
% 23.84/6.49 | Equations (514,513) can reduce 363 to:
% 23.84/6.49 | (461) $false
% 23.84/6.49 |
% 23.84/6.49 |-The branch is then unsatisfiable
% 23.84/6.49 |-Branch two:
% 23.84/6.49 | (997) ~ (all_0_10_10 = n1)
% 23.84/6.49 | (998) all_0_10_10 = n0
% 23.84/6.49 |
% 23.84/6.49 | From (998) and (317) follows:
% 23.84/6.49 | (999) pred(n0) = all_0_6_6
% 23.84/6.49 |
% 23.84/6.49 | From (998) and (146) follows:
% 23.84/6.49 | (1000) succ(n0) = all_0_8_8
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (130) with n0, all_0_6_6, n15 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n15, yields:
% 23.84/6.49 | (1001) all_0_6_6 = n15
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (165) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 23.84/6.49 | (1002) all_0_8_8 = n1
% 23.84/6.49 |
% 23.84/6.49 | From (1001)(1002) and (10) follows:
% 23.84/6.49 | (1003) sum(n15, n1) = all_0_1_1
% 23.84/6.49 |
% 23.84/6.49 | From (1001) and (5320) follows:
% 23.84/6.49 | (5348) sum(n15, n3) = all_0_4_4
% 23.84/6.49 |
% 23.84/6.49 | From (1002) and (5322) follows:
% 23.84/6.49 | (5349) sum(n1, n1) = all_0_7_7
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (74) with n15, n3, all_0_4_4, n2 and discharging atoms sum(n15, n3) = all_0_4_4, sum(n15, n3) = n2, yields:
% 23.84/6.49 | (670) all_0_4_4 = n2
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (74) with n15, n1, all_0_1_1, n0 and discharging atoms sum(n15, n1) = all_0_1_1, sum(n15, n1) = n0, yields:
% 23.84/6.49 | (862) all_0_1_1 = n0
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (74) with n1, n1, all_0_7_7, n2 and discharging atoms sum(n1, n1) = all_0_7_7, sum(n1, n1) = n2, yields:
% 23.84/6.49 | (672) all_0_7_7 = n2
% 23.84/6.49 |
% 23.84/6.49 | From (672)(670) and (212) follows:
% 23.84/6.49 | (674) sum(n2, n2) = all_0_3_3
% 23.84/6.49 |
% 23.84/6.49 | From (862) and (3227) follows:
% 23.84/6.49 | (3258) sum(n4, n0) = all_0_0_0
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (74) with n4, n0, all_0_0_0, n4 and discharging atoms sum(n4, n0) = all_0_0_0, sum(n4, n0) = n4, yields:
% 23.84/6.49 | (532) all_0_0_0 = n4
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (74) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 23.84/6.49 | (531) all_0_3_3 = n4
% 23.84/6.49 |
% 23.84/6.49 | Equations (532,531) can reduce 363 to:
% 23.84/6.49 | (461) $false
% 23.84/6.49 |
% 23.84/6.49 |-The branch is then unsatisfiable
% 23.84/6.49 |-Branch two:
% 23.84/6.49 | (696) ~ (all_0_11_11 = n2)
% 23.84/6.49 | (697) all_0_11_11 = n1 | all_0_11_11 = n0
% 23.84/6.49 |
% 23.84/6.49 +-Applying beta-rule and splitting (978), into two cases.
% 23.84/6.49 |-Branch one:
% 23.84/6.49 | (979) all_0_10_10 = n1
% 23.84/6.49 |
% 23.84/6.49 | From (979) and (317) follows:
% 23.84/6.49 | (980) pred(n1) = all_0_6_6
% 23.84/6.49 |
% 23.84/6.49 | From (979) and (146) follows:
% 23.84/6.49 | (981) succ(n1) = all_0_8_8
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (130) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 23.84/6.49 | (982) all_0_6_6 = n0
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (165) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 23.84/6.49 | (983) all_0_8_8 = n2
% 23.84/6.49 |
% 23.84/6.49 | From (982) and (980) follows:
% 23.84/6.49 | (306) pred(n1) = n0
% 23.84/6.49 |
% 23.84/6.49 | From (983) and (981) follows:
% 23.84/6.49 | (182) succ(n1) = n2
% 23.84/6.49 |
% 23.84/6.49 | From (982) and (276) follows:
% 23.84/6.49 | (5367) sum(n0, all_0_5_5) = all_0_4_4
% 23.84/6.49 |
% 23.84/6.49 | From (982)(983) and (10) follows:
% 23.84/6.49 | (984) sum(n0, n2) = all_0_1_1
% 23.84/6.49 |
% 23.84/6.49 | From (983) and (350) follows:
% 23.84/6.49 | (5369) sum(all_0_9_9, n2) = all_0_7_7
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (74) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 23.84/6.49 | (844) all_0_1_1 = n2
% 23.84/6.49 |
% 23.84/6.49 | From (844) and (256) follows:
% 23.84/6.49 | (3418) sum(all_0_2_2, n2) = all_0_0_0
% 23.84/6.49 |
% 23.84/6.49 | From (844) and (984) follows:
% 23.84/6.49 | (67) sum(n0, n2) = n2
% 23.84/6.49 |
% 23.84/6.49 +-Applying beta-rule and splitting (697), into two cases.
% 23.84/6.49 |-Branch one:
% 23.84/6.49 | (698) all_0_11_11 = n1
% 23.84/6.49 |
% 23.84/6.49 | From (698) and (423) follows:
% 23.84/6.49 | (699) pred(n1) = all_0_9_9
% 23.84/6.49 |
% 23.84/6.49 | From (698) and (262) follows:
% 23.84/6.49 | (700) succ(n1) = all_0_5_5
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (130) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 23.84/6.49 | (701) all_0_9_9 = n0
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (165) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 23.84/6.49 | (702) all_0_5_5 = n2
% 23.84/6.49 |
% 23.84/6.49 | From (701)(702) and (147) follows:
% 23.84/6.49 | (703) sum(n0, n2) = all_0_2_2
% 23.84/6.49 |
% 23.84/6.49 | From (701) and (5369) follows:
% 23.84/6.49 | (5379) sum(n0, n2) = all_0_7_7
% 23.84/6.49 |
% 23.84/6.49 | From (702) and (5367) follows:
% 23.84/6.49 | (5380) sum(n0, n2) = all_0_4_4
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (74) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 23.84/6.49 | (563) all_0_2_2 = n2
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (74) with n0, n2, all_0_4_4, all_0_2_2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = all_0_4_4, yields:
% 23.84/6.49 | (448) all_0_2_2 = all_0_4_4
% 23.84/6.49 |
% 23.84/6.49 | Instantiating formula (74) with n0, n2, all_0_7_7, all_0_2_2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = all_0_7_7, yields:
% 23.84/6.50 | (449) all_0_2_2 = all_0_7_7
% 23.84/6.50 |
% 23.84/6.50 | Combining equations (449,448) yields a new equation:
% 23.84/6.50 | (450) all_0_4_4 = all_0_7_7
% 23.84/6.50 |
% 23.84/6.50 | Combining equations (563,448) yields a new equation:
% 23.84/6.50 | (670) all_0_4_4 = n2
% 23.84/6.50 |
% 23.84/6.50 | Combining equations (670,450) yields a new equation:
% 23.84/6.50 | (672) all_0_7_7 = n2
% 23.84/6.50 |
% 23.84/6.50 | Combining equations (672,450) yields a new equation:
% 23.84/6.50 | (670) all_0_4_4 = n2
% 23.84/6.50 |
% 23.84/6.50 | Combining equations (670,448) yields a new equation:
% 23.84/6.50 | (563) all_0_2_2 = n2
% 23.84/6.50 |
% 23.84/6.50 | From (563) and (3418) follows:
% 23.84/6.50 | (3436) sum(n2, n2) = all_0_0_0
% 23.84/6.50 |
% 23.84/6.50 | From (672)(670) and (212) follows:
% 23.84/6.50 | (674) sum(n2, n2) = all_0_3_3
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (74) with n2, n2, all_0_0_0, n4 and discharging atoms sum(n2, n2) = all_0_0_0, sum(n2, n2) = n4, yields:
% 23.84/6.50 | (532) all_0_0_0 = n4
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (74) with n2, n2, all_0_3_3, all_0_0_0 and discharging atoms sum(n2, n2) = all_0_0_0, sum(n2, n2) = all_0_3_3, yields:
% 23.84/6.50 | (458) all_0_0_0 = all_0_3_3
% 23.84/6.50 |
% 23.84/6.50 | Combining equations (532,458) yields a new equation:
% 23.84/6.50 | (531) all_0_3_3 = n4
% 23.84/6.50 |
% 23.84/6.50 | Combining equations (531,458) yields a new equation:
% 23.84/6.50 | (532) all_0_0_0 = n4
% 23.84/6.50 |
% 23.84/6.50 | Equations (532,531) can reduce 363 to:
% 23.84/6.50 | (461) $false
% 23.84/6.50 |
% 23.84/6.50 |-The branch is then unsatisfiable
% 23.84/6.50 |-Branch two:
% 23.84/6.50 | (715) ~ (all_0_11_11 = n1)
% 23.84/6.50 | (716) all_0_11_11 = n0
% 23.84/6.50 |
% 23.84/6.50 | From (716) and (423) follows:
% 23.84/6.50 | (717) pred(n0) = all_0_9_9
% 23.84/6.50 |
% 23.84/6.50 | From (716) and (262) follows:
% 23.84/6.50 | (718) succ(n0) = all_0_5_5
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (130) with n0, all_0_9_9, n15 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n15, yields:
% 23.84/6.50 | (719) all_0_9_9 = n15
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (165) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 23.84/6.50 | (720) all_0_5_5 = n1
% 23.84/6.50 |
% 23.84/6.50 | From (719)(720) and (147) follows:
% 23.84/6.50 | (721) sum(n15, n1) = all_0_2_2
% 23.84/6.50 |
% 23.84/6.50 | From (719) and (5369) follows:
% 23.84/6.50 | (5403) sum(n15, n2) = all_0_7_7
% 23.84/6.50 |
% 23.84/6.50 | From (720) and (5367) follows:
% 23.84/6.50 | (5404) sum(n0, n1) = all_0_4_4
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (74) with n15, n2, all_0_7_7, n1 and discharging atoms sum(n15, n2) = all_0_7_7, sum(n15, n2) = n1, yields:
% 23.84/6.50 | (690) all_0_7_7 = n1
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (74) with n15, n1, all_0_2_2, n0 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n0, yields:
% 23.84/6.50 | (581) all_0_2_2 = n0
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (74) with n0, n1, all_0_4_4, n1 and discharging atoms sum(n0, n1) = all_0_4_4, sum(n0, n1) = n1, yields:
% 23.84/6.50 | (688) all_0_4_4 = n1
% 23.84/6.50 |
% 23.84/6.50 | From (581) and (3418) follows:
% 23.84/6.50 | (3456) sum(n0, n2) = all_0_0_0
% 23.84/6.50 |
% 23.84/6.50 | From (690)(688) and (212) follows:
% 23.84/6.50 | (692) sum(n1, n1) = all_0_3_3
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (74) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 23.84/6.50 | (549) all_0_3_3 = n2
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (74) with n0, n2, all_0_0_0, n2 and discharging atoms sum(n0, n2) = all_0_0_0, sum(n0, n2) = n2, yields:
% 23.84/6.50 | (550) all_0_0_0 = n2
% 23.84/6.50 |
% 23.84/6.50 | Equations (550,549) can reduce 363 to:
% 23.84/6.50 | (461) $false
% 23.84/6.50 |
% 23.84/6.50 |-The branch is then unsatisfiable
% 23.84/6.50 |-Branch two:
% 23.84/6.50 | (997) ~ (all_0_10_10 = n1)
% 23.84/6.50 | (998) all_0_10_10 = n0
% 23.84/6.50 |
% 23.84/6.50 | From (998) and (317) follows:
% 23.84/6.50 | (999) pred(n0) = all_0_6_6
% 23.84/6.50 |
% 23.84/6.50 | From (998) and (146) follows:
% 23.84/6.50 | (1000) succ(n0) = all_0_8_8
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (130) with n0, all_0_6_6, n15 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n15, yields:
% 23.84/6.50 | (1001) all_0_6_6 = n15
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (165) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 23.84/6.50 | (1002) all_0_8_8 = n1
% 23.84/6.50 |
% 23.84/6.50 | From (1001) and (999) follows:
% 23.84/6.50 | (245) pred(n0) = n15
% 23.84/6.50 |
% 23.84/6.50 | From (1002) and (1000) follows:
% 23.84/6.50 | (418) succ(n0) = n1
% 23.84/6.50 |
% 23.84/6.50 | From (1001) and (276) follows:
% 23.84/6.50 | (5421) sum(n15, all_0_5_5) = all_0_4_4
% 23.84/6.50 |
% 23.84/6.50 | From (1001)(1002) and (10) follows:
% 23.84/6.50 | (1003) sum(n15, n1) = all_0_1_1
% 23.84/6.50 |
% 23.84/6.50 | From (1002) and (350) follows:
% 23.84/6.50 | (5423) sum(all_0_9_9, n1) = all_0_7_7
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (74) with n15, n1, all_0_1_1, n0 and discharging atoms sum(n15, n1) = all_0_1_1, sum(n15, n1) = n0, yields:
% 23.84/6.50 | (862) all_0_1_1 = n0
% 23.84/6.50 |
% 23.84/6.50 | From (862) and (256) follows:
% 23.84/6.50 | (3788) sum(all_0_2_2, n0) = all_0_0_0
% 23.84/6.50 |
% 23.84/6.50 | From (862) and (1003) follows:
% 23.84/6.50 | (398) sum(n15, n1) = n0
% 23.84/6.50 |
% 23.84/6.50 +-Applying beta-rule and splitting (697), into two cases.
% 23.84/6.50 |-Branch one:
% 23.84/6.50 | (698) all_0_11_11 = n1
% 23.84/6.50 |
% 23.84/6.50 | From (698) and (423) follows:
% 23.84/6.50 | (699) pred(n1) = all_0_9_9
% 23.84/6.50 |
% 23.84/6.50 | From (698) and (262) follows:
% 23.84/6.50 | (700) succ(n1) = all_0_5_5
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (130) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 23.84/6.50 | (701) all_0_9_9 = n0
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (165) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 23.84/6.50 | (702) all_0_5_5 = n2
% 23.84/6.50 |
% 23.84/6.50 | From (701)(702) and (147) follows:
% 23.84/6.50 | (703) sum(n0, n2) = all_0_2_2
% 23.84/6.50 |
% 23.84/6.50 | From (701) and (5423) follows:
% 23.84/6.50 | (5433) sum(n0, n1) = all_0_7_7
% 23.84/6.50 |
% 23.84/6.50 | From (702) and (5421) follows:
% 23.84/6.50 | (5434) sum(n15, n2) = all_0_4_4
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (74) with n15, n2, all_0_4_4, n1 and discharging atoms sum(n15, n2) = all_0_4_4, sum(n15, n2) = n1, yields:
% 23.84/6.50 | (688) all_0_4_4 = n1
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (74) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 23.84/6.50 | (563) all_0_2_2 = n2
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (74) with n0, n1, all_0_7_7, n1 and discharging atoms sum(n0, n1) = all_0_7_7, sum(n0, n1) = n1, yields:
% 23.84/6.50 | (690) all_0_7_7 = n1
% 23.84/6.50 |
% 23.84/6.50 | From (563) and (3788) follows:
% 23.84/6.50 | (3628) sum(n2, n0) = all_0_0_0
% 23.84/6.50 |
% 23.84/6.50 | From (690)(688) and (212) follows:
% 23.84/6.50 | (692) sum(n1, n1) = all_0_3_3
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (74) with n2, n0, all_0_0_0, n2 and discharging atoms sum(n2, n0) = all_0_0_0, sum(n2, n0) = n2, yields:
% 23.84/6.50 | (550) all_0_0_0 = n2
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (74) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 23.84/6.50 | (549) all_0_3_3 = n2
% 23.84/6.50 |
% 23.84/6.50 | Equations (550,549) can reduce 363 to:
% 23.84/6.50 | (461) $false
% 23.84/6.50 |
% 23.84/6.50 |-The branch is then unsatisfiable
% 23.84/6.50 |-Branch two:
% 23.84/6.50 | (715) ~ (all_0_11_11 = n1)
% 23.84/6.50 | (716) all_0_11_11 = n0
% 23.84/6.50 |
% 23.84/6.50 | From (716) and (423) follows:
% 23.84/6.50 | (717) pred(n0) = all_0_9_9
% 23.84/6.50 |
% 23.84/6.50 | From (716) and (262) follows:
% 23.84/6.50 | (718) succ(n0) = all_0_5_5
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (130) with n0, all_0_9_9, n15 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n15, yields:
% 23.84/6.50 | (719) all_0_9_9 = n15
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (165) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 23.84/6.50 | (720) all_0_5_5 = n1
% 23.84/6.50 |
% 23.84/6.50 | From (719)(720) and (147) follows:
% 23.84/6.50 | (721) sum(n15, n1) = all_0_2_2
% 23.84/6.50 |
% 23.84/6.50 | From (719) and (5423) follows:
% 23.84/6.50 | (5450) sum(n15, n1) = all_0_7_7
% 23.84/6.50 |
% 23.84/6.50 | From (720) and (5421) follows:
% 23.84/6.50 | (5451) sum(n15, n1) = all_0_4_4
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (74) with n15, n1, all_0_2_2, n0 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = n0, yields:
% 23.84/6.50 | (581) all_0_2_2 = n0
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (74) with n15, n1, all_0_4_4, all_0_2_2 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = all_0_4_4, yields:
% 23.84/6.50 | (448) all_0_2_2 = all_0_4_4
% 23.84/6.50 |
% 23.84/6.50 | Instantiating formula (74) with n15, n1, all_0_7_7, all_0_2_2 and discharging atoms sum(n15, n1) = all_0_2_2, sum(n15, n1) = all_0_7_7, yields:
% 23.84/6.50 | (449) all_0_2_2 = all_0_7_7
% 23.84/6.50 |
% 23.84/6.50 | Combining equations (449,448) yields a new equation:
% 23.84/6.50 | (450) all_0_4_4 = all_0_7_7
% 23.84/6.50 |
% 23.84/6.50 | Combining equations (581,448) yields a new equation:
% 23.84/6.50 | (706) all_0_4_4 = n0
% 23.84/6.50 |
% 23.84/6.50 | Combining equations (706,450) yields a new equation:
% 23.84/6.50 | (708) all_0_7_7 = n0
% 23.84/6.50 |
% 23.84/6.50 | Combining equations (708,450) yields a new equation:
% 23.84/6.50 | (706) all_0_4_4 = n0
% 23.84/6.50 |
% 23.84/6.50 | Combining equations (706,448) yields a new equation:
% 23.84/6.50 | (581) all_0_2_2 = n0
% 23.84/6.50 |
% 23.84/6.50 | From (581) and (3788) follows:
% 23.84/6.51 | (3806) sum(n0, n0) = all_0_0_0
% 23.84/6.51 |
% 23.84/6.51 | From (708)(706) and (212) follows:
% 23.84/6.51 | (710) sum(n0, n0) = all_0_3_3
% 23.84/6.51 |
% 23.84/6.51 | Instantiating formula (74) with n0, n0, all_0_0_0, n0 and discharging atoms sum(n0, n0) = all_0_0_0, sum(n0, n0) = n0, yields:
% 23.84/6.51 | (568) all_0_0_0 = n0
% 23.84/6.51 |
% 23.84/6.51 | Instantiating formula (74) with n0, n0, all_0_3_3, all_0_0_0 and discharging atoms sum(n0, n0) = all_0_0_0, sum(n0, n0) = all_0_3_3, yields:
% 23.84/6.51 | (458) all_0_0_0 = all_0_3_3
% 23.84/6.51 |
% 23.84/6.51 | Combining equations (568,458) yields a new equation:
% 23.84/6.51 | (567) all_0_3_3 = n0
% 23.84/6.51 |
% 23.84/6.51 | Combining equations (567,458) yields a new equation:
% 23.84/6.51 | (568) all_0_0_0 = n0
% 23.84/6.51 |
% 23.84/6.51 | Equations (568,567) can reduce 363 to:
% 23.84/6.51 | (461) $false
% 23.84/6.51 |
% 23.84/6.51 |-The branch is then unsatisfiable
% 23.84/6.51 % SZS output end Proof for theBenchmark
% 23.84/6.51
% 23.84/6.51 5914ms
%------------------------------------------------------------------------------