TSTP Solution File: NUM376+1.010 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM376+1.010 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n008.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 5.36s 1.89s
% Output : Proof 14.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM376+1.010 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jul 6 07:38:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.57 ____ _
% 0.18/0.57 ___ / __ \_____(_)___ ________ __________
% 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.57
% 0.18/0.57 A Theorem Prover for First-Order Logic
% 0.18/0.57 (ePrincess v.1.0)
% 0.18/0.57
% 0.18/0.57 (c) Philipp Rümmer, 2009-2015
% 0.18/0.57 (c) Peter Backeman, 2014-2015
% 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.57 Bug reports to peter@backeman.se
% 0.18/0.57
% 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.57
% 0.18/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.64/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.66/0.95 Prover 0: Preprocessing ...
% 2.50/1.21 Prover 0: Constructing countermodel ...
% 5.36/1.89 Prover 0: proved (1268ms)
% 5.36/1.89
% 5.36/1.89 No countermodel exists, formula is valid
% 5.36/1.89 % SZS status Unsatisfiable for theBenchmark
% 5.36/1.89
% 5.36/1.89 Generating proof ... found it (size 2353)
% 12.36/3.42
% 12.36/3.42 % SZS output start Proof for theBenchmark
% 12.36/3.42 Assumed formulas after preprocessing and simplification:
% 12.36/3.42 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = v8) & ~ (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(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) = n10 & succ(v1) = v3 & succ(v0) = v6 & succ(n10) = n0 & 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(n10, n10) = n9 & sum(n10, n9) = n8 & sum(n10, n8) = n7 & sum(n10, n7) = n6 & sum(n10, n6) = n5 & sum(n10, n5) = n4 & sum(n10, n4) = n3 & sum(n10, n3) = n2 & sum(n10, n2) = n1 & sum(n10, n1) = n0 & sum(n10, n0) = n10 & sum(n9, n10) = n8 & sum(n9, n9) = n7 & sum(n9, n8) = n6 & sum(n9, n7) = n5 & sum(n9, n6) = n4 & sum(n9, n5) = n3 & sum(n9, n4) = n2 & sum(n9, n3) = n1 & sum(n9, n2) = n0 & sum(n9, n1) = n10 & sum(n9, n0) = n9 & sum(n8, n10) = n7 & sum(n8, n9) = n6 & sum(n8, n8) = n5 & sum(n8, n7) = n4 & sum(n8, n6) = n3 & sum(n8, n5) = n2 & sum(n8, n4) = n1 & sum(n8, n3) = n0 & sum(n8, n2) = n10 & sum(n8, n1) = n9 & sum(n8, n0) = n8 & sum(n7, n10) = n6 & sum(n7, n9) = n5 & sum(n7, n8) = n4 & sum(n7, n7) = n3 & sum(n7, n6) = n2 & sum(n7, n5) = n1 & sum(n7, n4) = n0 & sum(n7, n3) = n10 & sum(n7, n2) = n9 & sum(n7, n1) = n8 & sum(n7, n0) = n7 & sum(n6, n10) = n5 & sum(n6, n9) = n4 & sum(n6, n8) = n3 & sum(n6, n7) = n2 & sum(n6, n6) = n1 & sum(n6, n5) = n0 & sum(n6, n4) = n10 & sum(n6, n3) = n9 & sum(n6, n2) = n8 & sum(n6, n1) = n7 & sum(n6, n0) = n6 & sum(n5, n10) = n4 & sum(n5, n9) = n3 & sum(n5, n8) = n2 & sum(n5, n7) = n1 & sum(n5, n6) = n0 & 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, n10) = n3 & sum(n4, n9) = n2 & sum(n4, n8) = n1 & sum(n4, n7) = n0 & 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, n10) = n2 & sum(n3, n9) = n1 & sum(n3, n8) = n0 & 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, n10) = n1 & sum(n2, n9) = n0 & 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, n10) = n0 & 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, 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 = n10 | v1 = n9 | v1 = n8 | v1 = n7 | v1 = n6 | v1 = n5 | v1 = n4 | v1 = n3 | v1 = n2 | v1 = n1 | v1 = n0) & (v0 = n10 | v0 = n9 | v0 = n8 | v0 = n7 | v0 = n6 | v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0))
% 12.36/3.46 | 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:
% 12.36/3.46 | (1) ~ (all_0_0_0 = all_0_3_3) & ~ (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(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) = n10 & succ(all_0_10_10) = all_0_8_8 & succ(all_0_11_11) = all_0_5_5 & succ(n10) = n0 & 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(n10, n10) = n9 & sum(n10, n9) = n8 & sum(n10, n8) = n7 & sum(n10, n7) = n6 & sum(n10, n6) = n5 & sum(n10, n5) = n4 & sum(n10, n4) = n3 & sum(n10, n3) = n2 & sum(n10, n2) = n1 & sum(n10, n1) = n0 & sum(n10, n0) = n10 & sum(n9, n10) = n8 & sum(n9, n9) = n7 & sum(n9, n8) = n6 & sum(n9, n7) = n5 & sum(n9, n6) = n4 & sum(n9, n5) = n3 & sum(n9, n4) = n2 & sum(n9, n3) = n1 & sum(n9, n2) = n0 & sum(n9, n1) = n10 & sum(n9, n0) = n9 & sum(n8, n10) = n7 & sum(n8, n9) = n6 & sum(n8, n8) = n5 & sum(n8, n7) = n4 & sum(n8, n6) = n3 & sum(n8, n5) = n2 & sum(n8, n4) = n1 & sum(n8, n3) = n0 & sum(n8, n2) = n10 & sum(n8, n1) = n9 & sum(n8, n0) = n8 & sum(n7, n10) = n6 & sum(n7, n9) = n5 & sum(n7, n8) = n4 & sum(n7, n7) = n3 & sum(n7, n6) = n2 & sum(n7, n5) = n1 & sum(n7, n4) = n0 & sum(n7, n3) = n10 & sum(n7, n2) = n9 & sum(n7, n1) = n8 & sum(n7, n0) = n7 & sum(n6, n10) = n5 & sum(n6, n9) = n4 & sum(n6, n8) = n3 & sum(n6, n7) = n2 & sum(n6, n6) = n1 & sum(n6, n5) = n0 & sum(n6, n4) = n10 & sum(n6, n3) = n9 & sum(n6, n2) = n8 & sum(n6, n1) = n7 & sum(n6, n0) = n6 & sum(n5, n10) = n4 & sum(n5, n9) = n3 & sum(n5, n8) = n2 & sum(n5, n7) = n1 & sum(n5, n6) = n0 & 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, n10) = n3 & sum(n4, n9) = n2 & sum(n4, n8) = n1 & sum(n4, n7) = n0 & 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, n10) = n2 & sum(n3, n9) = n1 & sum(n3, n8) = n0 & 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, n10) = n1 & sum(n2, n9) = n0 & 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, n10) = n0 & 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, 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 = 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 = 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)
% 12.36/3.47 |
% 12.36/3.47 | Applying alpha-rule on (1) yields:
% 12.36/3.47 | (2) sum(n10, n5) = n4
% 12.36/3.47 | (3) sum(n5, n2) = n7
% 12.36/3.47 | (4) sum(all_0_2_2, all_0_1_1) = all_0_0_0
% 12.36/3.47 | (5) ~ (n9 = n6)
% 12.36/3.47 | (6) ~ (n6 = n0)
% 12.36/3.47 | (7) sum(n7, n4) = n0
% 12.36/3.47 | (8) ~ (n10 = n5)
% 12.36/3.47 | (9) sum(n1, n8) = n9
% 12.36/3.47 | (10) ~ (n10 = n8)
% 12.36/3.47 | (11) sum(n0, n8) = n8
% 12.36/3.47 | (12) ~ (n10 = n2)
% 12.36/3.47 | (13) succ(n6) = n7
% 12.36/3.47 | (14) ~ (n10 = n1)
% 12.36/3.48 | (15) sum(n1, n7) = n8
% 12.36/3.48 | (16) sum(n0, n1) = n1
% 12.36/3.48 | (17) sum(n3, n10) = n2
% 12.36/3.48 | (18) sum(n1, n1) = n2
% 12.36/3.48 | (19) ~ (n4 = n0)
% 12.36/3.48 | (20) ~ (n8 = n2)
% 12.36/3.48 | (21) pred(n6) = n5
% 12.36/3.48 | (22) sum(n10, n4) = n3
% 12.36/3.48 | (23) ~ (n8 = n0)
% 12.36/3.48 | (24) sum(n6, n5) = n0
% 12.36/3.48 | (25) sum(n4, n4) = n8
% 12.36/3.48 | (26) sum(n3, n6) = n9
% 12.36/3.48 | (27) pred(n2) = n1
% 12.36/3.48 | (28) sum(n1, n0) = n1
% 12.36/3.48 | (29) sum(n10, n0) = n10
% 12.36/3.48 | (30) sum(n5, n7) = n1
% 12.36/3.48 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0))
% 12.36/3.48 | (32) sum(n7, n9) = n5
% 12.36/3.48 | (33) sum(all_0_6_6, all_0_5_5) = all_0_4_4
% 12.36/3.48 | (34) sum(n6, n1) = n7
% 12.36/3.48 | (35) sum(n2, n3) = n5
% 12.36/3.48 | (36) pred(n5) = n4
% 12.36/3.48 | (37) succ(n4) = n5
% 12.36/3.48 | (38) sum(n6, n10) = n5
% 12.36/3.48 | (39) succ(n10) = n0
% 12.36/3.48 | (40) ~ (n8 = n1)
% 12.36/3.48 | (41) succ(all_0_10_10) = all_0_8_8
% 12.36/3.48 | (42) sum(n2, n6) = n8
% 12.36/3.48 | (43) sum(n5, n9) = n3
% 12.36/3.48 | (44) ~ (n7 = n2)
% 12.36/3.48 | (45) sum(n3, n1) = n4
% 12.36/3.48 | (46) sum(n3, n0) = n3
% 12.36/3.48 | (47) sum(n4, n1) = n5
% 12.36/3.48 | (48) sum(all_0_9_9, all_0_5_5) = all_0_2_2
% 12.36/3.48 | (49) ~ (n3 = n0)
% 12.36/3.48 | (50) sum(n0, n6) = n6
% 12.36/3.48 | (51) pred(n7) = n6
% 12.36/3.48 | (52) ~ (n7 = n6)
% 12.36/3.48 | (53) sum(n9, n2) = n0
% 12.36/3.48 | (54) pred(n0) = n10
% 12.36/3.48 | (55) sum(n6, n6) = n1
% 12.36/3.48 | (56) sum(n2, n1) = n3
% 12.36/3.48 | (57) sum(n0, n9) = n9
% 12.36/3.48 | (58) sum(n5, n0) = n5
% 12.36/3.48 | (59) sum(n9, n9) = n7
% 12.36/3.48 | (60) ~ (n10 = n4)
% 12.36/3.48 | (61) sum(n9, n7) = n5
% 12.36/3.48 | (62) sum(n0, n7) = n7
% 12.36/3.48 | (63) sum(n10, n10) = n9
% 12.36/3.48 | (64) ~ (n4 = n1)
% 12.36/3.48 | (65) sum(n8, n2) = n10
% 12.36/3.48 | (66) sum(n3, n8) = n0
% 12.36/3.48 | (67) sum(n0, n5) = n5
% 12.36/3.48 | (68) sum(n2, n0) = n2
% 12.36/3.48 | (69) ~ (n6 = n4)
% 12.36/3.48 | (70) sum(n8, n9) = n6
% 12.36/3.48 | (71) ~ (n8 = n6)
% 12.36/3.48 | (72) ~ (n5 = n4)
% 12.36/3.48 | (73) sum(n6, n2) = n8
% 12.36/3.48 | (74) succ(n8) = n9
% 12.36/3.48 | (75) sum(n8, n10) = n7
% 12.36/3.48 | (76) ~ (n7 = n1)
% 12.36/3.48 | (77) ~ (n7 = n5)
% 12.36/3.48 | (78) ~ (n9 = n0)
% 12.36/3.48 | (79) succ(n2) = n3
% 12.36/3.48 | (80) sum(n10, n8) = n7
% 12.36/3.48 | (81) sum(n1, n6) = n7
% 12.36/3.48 | (82) sum(n10, n3) = n2
% 12.36/3.48 | (83) succ(n0) = n1
% 12.36/3.48 | (84) pred(all_0_11_11) = all_0_9_9
% 12.36/3.48 | (85) ~ (n9 = n3)
% 12.36/3.48 | (86) sum(n7, n6) = n2
% 12.36/3.48 | (87) pred(n8) = n7
% 12.36/3.48 | (88) sum(n4, n9) = n2
% 12.36/3.48 | (89) sum(n9, n1) = n10
% 12.36/3.48 | (90) ~ (n5 = n2)
% 12.36/3.48 | (91) sum(n0, n0) = n0
% 12.36/3.48 | (92) sum(n7, n10) = n6
% 12.36/3.48 | (93) sum(n10, n2) = n1
% 12.36/3.48 | (94) sum(n3, n9) = n1
% 12.36/3.48 | (95) sum(n6, n4) = n10
% 12.36/3.48 | (96) ~ (n10 = n6)
% 12.36/3.48 | (97) sum(n8, n8) = n5
% 12.36/3.48 | (98) ~ (n3 = n2)
% 12.36/3.49 | (99) succ(n1) = n2
% 12.36/3.49 | (100) sum(n4, n10) = n3
% 12.36/3.49 | (101) ~ (n9 = n2)
% 12.36/3.49 | (102) ~ (n5 = n1)
% 12.36/3.49 | (103) sum(n5, n10) = n4
% 12.36/3.49 | (104) ~ (all_0_0_0 = all_0_3_3)
% 12.36/3.49 | (105) ~ (n1 = n0)
% 12.36/3.49 | (106) ~ (n3 = n1)
% 12.36/3.49 | (107) sum(n4, n6) = n10
% 12.36/3.49 | (108) sum(n4, n5) = n9
% 12.36/3.49 | (109) sum(n7, n2) = n9
% 12.36/3.49 | (110) sum(n6, n9) = n4
% 12.36/3.49 | (111) sum(n7, n0) = n7
% 12.36/3.49 | (112) ~ (n8 = n5)
% 12.36/3.49 | (113) sum(n10, n9) = n8
% 12.36/3.49 | (114) succ(n7) = n8
% 12.36/3.49 | (115) ~ (n10 = n3)
% 12.36/3.49 | (116) sum(n9, n8) = n6
% 12.36/3.49 | (117) sum(n3, n5) = n8
% 12.36/3.49 | (118) pred(n10) = n9
% 12.36/3.49 | (119) sum(all_0_7_7, all_0_4_4) = all_0_3_3
% 12.36/3.49 | (120) sum(n5, n8) = n2
% 12.36/3.49 | (121) sum(n1, n3) = n4
% 12.36/3.49 | (122) sum(n8, n7) = n4
% 12.36/3.49 | (123) 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
% 12.36/3.49 | (124) sum(n9, n6) = n4
% 12.36/3.49 | (125) sum(n1, n10) = n0
% 12.36/3.49 | (126) sum(n7, n8) = n4
% 12.36/3.49 | (127) sum(n9, n10) = n8
% 12.36/3.49 | (128) sum(n1, n5) = n6
% 12.36/3.49 | (129) ~ (n9 = n5)
% 12.36/3.49 | (130) sum(n7, n3) = n10
% 12.36/3.49 | (131) pred(n3) = n2
% 12.36/3.49 | (132) sum(n2, n8) = n10
% 12.36/3.49 | (133) sum(n0, n3) = n3
% 12.36/3.49 | (134) ~ (n9 = n7)
% 12.36/3.49 | (135) sum(n5, n1) = n6
% 12.36/3.49 | (136) ~ (n6 = n2)
% 12.36/3.49 | (137) sum(all_0_9_9, all_0_8_8) = all_0_7_7
% 12.36/3.49 | (138) sum(n4, n7) = n0
% 12.36/3.49 | (139) ~ (n5 = n0)
% 12.36/3.49 | (140) sum(n10, n1) = n0
% 12.36/3.49 | (141) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0))
% 12.36/3.49 | (142) sum(n6, n0) = n6
% 12.36/3.49 | (143) sum(n5, n5) = n10
% 12.36/3.49 | (144) sum(n8, n0) = n8
% 12.36/3.49 | (145) ~ (n10 = n7)
% 12.36/3.49 | (146) sum(n1, n4) = n5
% 12.75/3.49 | (147) ~ (n7 = n0)
% 12.75/3.49 | (148) sum(n7, n7) = n3
% 12.75/3.49 | (149) ~ (n5 = n3)
% 12.75/3.49 | (150) ~ (n6 = n3)
% 12.75/3.49 | (151) ~ (n9 = n8)
% 12.75/3.49 | (152) ~ (n7 = n3)
% 12.75/3.49 | (153) ~ (n8 = n3)
% 12.75/3.49 | (154) sum(n4, n3) = n7
% 12.75/3.49 | (155) sum(n2, n9) = n0
% 12.75/3.49 | (156) sum(n0, n2) = n2
% 12.75/3.49 | (157) pred(n4) = n3
% 12.75/3.49 | (158) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 12.75/3.49 | (159) sum(n5, n6) = n0
% 12.75/3.49 | (160) sum(n7, n5) = n1
% 12.75/3.50 | (161) ~ (n10 = n9)
% 12.75/3.50 | (162) sum(n5, n4) = n9
% 12.75/3.50 | (163) sum(n3, n4) = n7
% 12.75/3.50 | (164) sum(n8, n6) = n3
% 12.75/3.50 | (165) sum(n3, n2) = n5
% 12.75/3.50 | (166) sum(n2, n7) = n9
% 12.75/3.50 | (167) sum(n1, n9) = n10
% 12.75/3.50 | (168) ~ (n7 = n4)
% 12.75/3.50 | (169) sum(n10, n7) = n6
% 12.75/3.50 | (170) 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
% 12.75/3.50 | (171) sum(n8, n5) = n2
% 12.75/3.50 | (172) sum(n9, n3) = n1
% 12.75/3.50 | (173) ~ (n4 = n3)
% 12.75/3.50 | (174) ~ (n8 = n4)
% 12.75/3.50 | (175) sum(n2, n5) = n7
% 12.75/3.50 | (176) ~ (n4 = n2)
% 12.75/3.50 | (177) succ(n5) = n6
% 12.75/3.50 | (178) sum(all_0_6_6, all_0_8_8) = all_0_1_1
% 12.75/3.50 | (179) sum(n4, n0) = n4
% 12.75/3.50 | (180) sum(n3, n3) = n6
% 12.75/3.50 | (181) sum(n8, n4) = n1
% 12.75/3.50 | (182) sum(n6, n7) = n2
% 12.75/3.50 | (183) ~ (n6 = n5)
% 12.75/3.50 | (184) succ(n9) = n10
% 12.75/3.50 | (185) sum(n3, n7) = n10
% 12.75/3.50 | (186) sum(n8, n3) = n0
% 12.75/3.50 | (187) sum(n9, n5) = n3
% 12.75/3.50 | (188) sum(n2, n2) = n4
% 12.75/3.50 | (189) ~ (n9 = n4)
% 12.75/3.50 | (190) sum(n10, n6) = n5
% 12.75/3.50 | (191) sum(n8, n1) = n9
% 12.75/3.50 | (192) ~ (n9 = n1)
% 12.75/3.50 | (193) sum(n5, n3) = n8
% 12.75/3.50 | (194) sum(n4, n8) = n1
% 12.75/3.50 | (195) ~ (n2 = n1)
% 12.75/3.50 | (196) succ(n3) = n4
% 12.75/3.50 | (197) sum(n9, n0) = n9
% 12.75/3.50 | (198) sum(n6, n8) = n3
% 12.75/3.50 | (199) ~ (n10 = n0)
% 12.75/3.50 | (200) sum(n2, n10) = n1
% 12.75/3.50 | (201) sum(n9, n4) = n2
% 12.75/3.50 | (202) ~ (n8 = n7)
% 12.75/3.50 | (203) sum(n1, n2) = n3
% 12.75/3.50 | (204) ~ (n2 = n0)
% 12.75/3.50 | (205) ~ (n6 = n1)
% 12.75/3.50 | (206) sum(n2, n4) = n6
% 12.75/3.50 | (207) sum(n6, n3) = n9
% 12.75/3.50 | (208) sum(n0, n10) = n10
% 12.75/3.50 | (209) sum(n4, n2) = n6
% 12.75/3.50 | (210) succ(all_0_11_11) = all_0_5_5
% 12.75/3.50 | (211) pred(all_0_10_10) = all_0_6_6
% 12.75/3.50 | (212) pred(n1) = n0
% 12.75/3.50 | (213) sum(n0, n4) = n4
% 12.75/3.51 | (214) pred(n9) = n8
% 12.75/3.51 | (215) sum(n7, n1) = n8
% 12.75/3.51 |
% 12.75/3.51 +-Applying beta-rule and splitting (170), into two cases.
% 12.75/3.51 |-Branch one:
% 12.75/3.51 | (216) all_0_10_10 = n10
% 12.75/3.51 |
% 12.75/3.51 | From (216) and (211) follows:
% 12.75/3.51 | (217) pred(n10) = all_0_6_6
% 12.75/3.51 |
% 12.75/3.51 | From (216) and (41) follows:
% 12.75/3.51 | (218) succ(n10) = all_0_8_8
% 12.75/3.51 |
% 12.75/3.51 | Instantiating formula (158) with n10, all_0_6_6, n9 and discharging atoms pred(n10) = all_0_6_6, pred(n10) = n9, yields:
% 12.75/3.51 | (219) all_0_6_6 = n9
% 12.75/3.51 |
% 12.75/3.51 | Instantiating formula (141) with n10, all_0_8_8, n0 and discharging atoms succ(n10) = all_0_8_8, succ(n10) = n0, yields:
% 12.75/3.51 | (220) all_0_8_8 = n0
% 12.75/3.51 |
% 12.75/3.51 | From (219) and (217) follows:
% 12.75/3.51 | (118) pred(n10) = n9
% 12.75/3.51 |
% 12.75/3.51 | From (220) and (218) follows:
% 12.75/3.51 | (39) succ(n10) = n0
% 12.75/3.51 |
% 12.75/3.51 | From (219) and (33) follows:
% 12.75/3.51 | (223) sum(n9, all_0_5_5) = all_0_4_4
% 12.75/3.51 |
% 12.75/3.51 | From (219)(220) and (178) follows:
% 12.75/3.51 | (224) sum(n9, n0) = all_0_1_1
% 12.75/3.51 |
% 12.75/3.51 | From (220) and (137) follows:
% 12.75/3.51 | (225) sum(all_0_9_9, n0) = all_0_7_7
% 12.75/3.51 |
% 12.75/3.51 | Instantiating formula (31) with n9, n0, all_0_1_1, n9 and discharging atoms sum(n9, n0) = all_0_1_1, sum(n9, n0) = n9, yields:
% 12.75/3.51 | (226) all_0_1_1 = n9
% 12.75/3.51 |
% 12.75/3.51 | From (226) and (4) follows:
% 12.75/3.51 | (227) sum(all_0_2_2, n9) = all_0_0_0
% 12.75/3.51 |
% 12.75/3.51 | From (226) and (224) follows:
% 12.75/3.51 | (197) sum(n9, n0) = n9
% 12.75/3.51 |
% 12.75/3.51 +-Applying beta-rule and splitting (123), into two cases.
% 12.75/3.51 |-Branch one:
% 12.75/3.51 | (229) all_0_11_11 = n10
% 12.75/3.51 |
% 12.75/3.51 | From (229) and (84) follows:
% 12.75/3.51 | (230) pred(n10) = all_0_9_9
% 12.75/3.51 |
% 12.75/3.51 | From (229) and (210) follows:
% 12.75/3.51 | (231) succ(n10) = all_0_5_5
% 12.75/3.51 |
% 12.75/3.51 | Instantiating formula (158) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 12.75/3.51 | (232) all_0_9_9 = n9
% 12.75/3.51 |
% 12.75/3.51 | Instantiating formula (141) with n10, all_0_5_5, n0 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n0, yields:
% 12.75/3.51 | (233) all_0_5_5 = n0
% 12.75/3.51 |
% 12.75/3.51 | From (232)(233) and (48) follows:
% 12.75/3.51 | (234) sum(n9, n0) = all_0_2_2
% 12.75/3.51 |
% 12.75/3.51 | From (232) and (225) follows:
% 12.75/3.51 | (235) sum(n9, n0) = all_0_7_7
% 12.75/3.51 |
% 12.75/3.51 | From (233) and (223) follows:
% 12.75/3.52 | (236) sum(n9, n0) = all_0_4_4
% 12.75/3.52 |
% 12.75/3.52 | Instantiating formula (31) with n9, n0, all_0_2_2, n9 and discharging atoms sum(n9, n0) = all_0_2_2, sum(n9, n0) = n9, yields:
% 12.75/3.52 | (237) all_0_2_2 = n9
% 12.75/3.52 |
% 12.75/3.52 | Instantiating formula (31) with n9, n0, all_0_4_4, all_0_2_2 and discharging atoms sum(n9, n0) = all_0_2_2, sum(n9, n0) = all_0_4_4, yields:
% 12.75/3.52 | (238) all_0_2_2 = all_0_4_4
% 12.75/3.52 |
% 12.75/3.52 | Instantiating formula (31) with n9, n0, all_0_7_7, all_0_2_2 and discharging atoms sum(n9, n0) = all_0_2_2, sum(n9, n0) = all_0_7_7, yields:
% 12.75/3.52 | (239) all_0_2_2 = all_0_7_7
% 12.75/3.52 |
% 12.75/3.52 | Combining equations (239,238) yields a new equation:
% 12.75/3.52 | (240) all_0_4_4 = all_0_7_7
% 12.75/3.52 |
% 12.75/3.52 | Combining equations (237,238) yields a new equation:
% 12.75/3.52 | (241) all_0_4_4 = n9
% 12.75/3.52 |
% 12.75/3.52 | Combining equations (241,240) yields a new equation:
% 12.75/3.52 | (242) all_0_7_7 = n9
% 12.75/3.52 |
% 12.75/3.52 | Combining equations (242,240) yields a new equation:
% 12.75/3.52 | (241) all_0_4_4 = n9
% 12.75/3.52 |
% 12.75/3.52 | Combining equations (241,238) yields a new equation:
% 12.75/3.52 | (237) all_0_2_2 = n9
% 12.75/3.52 |
% 12.75/3.52 | From (237) and (227) follows:
% 12.75/3.52 | (245) sum(n9, n9) = all_0_0_0
% 12.75/3.52 |
% 12.75/3.52 | From (242)(241) and (119) follows:
% 12.75/3.52 | (246) sum(n9, n9) = all_0_3_3
% 12.75/3.52 |
% 12.75/3.52 | Instantiating formula (31) with n9, n9, all_0_0_0, n7 and discharging atoms sum(n9, n9) = all_0_0_0, sum(n9, n9) = n7, yields:
% 12.75/3.52 | (247) all_0_0_0 = n7
% 12.75/3.52 |
% 12.75/3.52 | Instantiating formula (31) with n9, n9, all_0_3_3, all_0_0_0 and discharging atoms sum(n9, n9) = all_0_0_0, sum(n9, n9) = all_0_3_3, yields:
% 12.75/3.52 | (248) all_0_0_0 = all_0_3_3
% 12.75/3.52 |
% 12.75/3.52 | Combining equations (247,248) yields a new equation:
% 12.75/3.52 | (249) all_0_3_3 = n7
% 12.75/3.52 |
% 12.75/3.52 | Combining equations (249,248) yields a new equation:
% 12.75/3.52 | (247) all_0_0_0 = n7
% 12.75/3.52 |
% 12.75/3.52 | Equations (247,249) can reduce 104 to:
% 12.75/3.52 | (251) $false
% 12.75/3.52 |
% 12.75/3.52 |-The branch is then unsatisfiable
% 12.75/3.52 |-Branch two:
% 12.75/3.52 | (252) ~ (all_0_11_11 = n10)
% 12.75/3.52 | (253) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 12.75/3.52 |
% 12.75/3.52 +-Applying beta-rule and splitting (253), into two cases.
% 12.75/3.52 |-Branch one:
% 12.75/3.52 | (254) all_0_11_11 = n9
% 12.75/3.52 |
% 12.75/3.52 | From (254) and (84) follows:
% 12.75/3.52 | (255) pred(n9) = all_0_9_9
% 12.75/3.52 |
% 12.75/3.52 | From (254) and (210) follows:
% 12.75/3.53 | (256) succ(n9) = all_0_5_5
% 12.75/3.53 |
% 12.75/3.53 | Instantiating formula (158) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 12.75/3.53 | (257) all_0_9_9 = n8
% 12.75/3.53 |
% 12.75/3.53 | Instantiating formula (141) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 12.75/3.53 | (258) all_0_5_5 = n10
% 12.75/3.53 |
% 12.75/3.53 | From (257)(258) and (48) follows:
% 12.75/3.53 | (259) sum(n8, n10) = all_0_2_2
% 12.75/3.53 |
% 12.75/3.53 | From (257) and (225) follows:
% 12.75/3.53 | (260) sum(n8, n0) = all_0_7_7
% 12.75/3.53 |
% 12.75/3.53 | From (258) and (223) follows:
% 12.75/3.53 | (261) sum(n9, n10) = all_0_4_4
% 12.75/3.53 |
% 12.75/3.53 | Instantiating formula (31) with n9, n10, all_0_4_4, n8 and discharging atoms sum(n9, n10) = all_0_4_4, sum(n9, n10) = n8, yields:
% 12.75/3.53 | (262) all_0_4_4 = n8
% 12.75/3.53 |
% 12.75/3.53 | Instantiating formula (31) with n8, n10, all_0_2_2, n7 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n7, yields:
% 12.75/3.53 | (263) all_0_2_2 = n7
% 12.75/3.53 |
% 12.75/3.53 | Instantiating formula (31) with n8, n0, all_0_7_7, n8 and discharging atoms sum(n8, n0) = all_0_7_7, sum(n8, n0) = n8, yields:
% 12.75/3.53 | (264) all_0_7_7 = n8
% 12.75/3.53 |
% 12.75/3.53 | From (263) and (227) follows:
% 12.75/3.53 | (265) sum(n7, n9) = all_0_0_0
% 12.75/3.53 |
% 12.75/3.53 | From (264)(262) and (119) follows:
% 12.75/3.53 | (266) sum(n8, n8) = all_0_3_3
% 12.75/3.53 |
% 12.75/3.53 | Instantiating formula (31) with n8, n8, all_0_3_3, n5 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n5, yields:
% 12.75/3.53 | (267) all_0_3_3 = n5
% 12.75/3.53 |
% 12.75/3.53 | Instantiating formula (31) with n7, n9, all_0_0_0, n5 and discharging atoms sum(n7, n9) = all_0_0_0, sum(n7, n9) = n5, yields:
% 12.75/3.53 | (268) all_0_0_0 = n5
% 12.75/3.53 |
% 12.75/3.53 | Equations (268,267) can reduce 104 to:
% 12.75/3.53 | (251) $false
% 12.75/3.53 |
% 12.75/3.53 |-The branch is then unsatisfiable
% 12.75/3.53 |-Branch two:
% 12.75/3.53 | (270) ~ (all_0_11_11 = n9)
% 12.75/3.53 | (271) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 12.75/3.53 |
% 12.75/3.53 +-Applying beta-rule and splitting (271), into two cases.
% 12.75/3.53 |-Branch one:
% 12.75/3.53 | (272) all_0_11_11 = n8
% 12.75/3.53 |
% 12.75/3.53 | From (272) and (84) follows:
% 12.75/3.53 | (273) pred(n8) = all_0_9_9
% 12.75/3.53 |
% 12.75/3.53 | From (272) and (210) follows:
% 12.75/3.53 | (274) succ(n8) = all_0_5_5
% 12.75/3.53 |
% 12.75/3.53 | Instantiating formula (158) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 12.75/3.53 | (275) all_0_9_9 = n7
% 12.75/3.53 |
% 12.75/3.53 | Instantiating formula (141) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 12.75/3.53 | (276) all_0_5_5 = n9
% 12.75/3.53 |
% 12.75/3.53 | From (275)(276) and (48) follows:
% 12.75/3.53 | (277) sum(n7, n9) = all_0_2_2
% 12.75/3.53 |
% 12.75/3.53 | From (275) and (225) follows:
% 12.75/3.53 | (278) sum(n7, n0) = all_0_7_7
% 12.75/3.53 |
% 12.75/3.53 | From (276) and (223) follows:
% 12.75/3.53 | (279) sum(n9, n9) = all_0_4_4
% 12.75/3.53 |
% 12.75/3.53 | Instantiating formula (31) with n9, n9, all_0_4_4, n7 and discharging atoms sum(n9, n9) = all_0_4_4, sum(n9, n9) = n7, yields:
% 12.75/3.53 | (280) all_0_4_4 = n7
% 12.75/3.53 |
% 12.75/3.53 | Instantiating formula (31) with n7, n9, all_0_2_2, n5 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n5, yields:
% 12.75/3.53 | (281) all_0_2_2 = n5
% 12.75/3.53 |
% 12.75/3.53 | Instantiating formula (31) with n7, n0, all_0_7_7, n7 and discharging atoms sum(n7, n0) = all_0_7_7, sum(n7, n0) = n7, yields:
% 12.75/3.53 | (282) all_0_7_7 = n7
% 12.75/3.53 |
% 12.75/3.53 | From (281) and (227) follows:
% 12.75/3.53 | (283) sum(n5, n9) = all_0_0_0
% 12.75/3.53 |
% 12.75/3.53 | From (282)(280) and (119) follows:
% 12.75/3.53 | (284) sum(n7, n7) = all_0_3_3
% 12.75/3.53 |
% 12.75/3.54 | Instantiating formula (31) with n7, n7, all_0_3_3, n3 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n3, yields:
% 12.75/3.54 | (285) all_0_3_3 = n3
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (31) with n5, n9, all_0_0_0, n3 and discharging atoms sum(n5, n9) = all_0_0_0, sum(n5, n9) = n3, yields:
% 12.75/3.54 | (286) all_0_0_0 = n3
% 12.75/3.54 |
% 12.75/3.54 | Equations (286,285) can reduce 104 to:
% 12.75/3.54 | (251) $false
% 12.75/3.54 |
% 12.75/3.54 |-The branch is then unsatisfiable
% 12.75/3.54 |-Branch two:
% 12.75/3.54 | (288) ~ (all_0_11_11 = n8)
% 12.75/3.54 | (289) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 12.75/3.54 |
% 12.75/3.54 +-Applying beta-rule and splitting (289), into two cases.
% 12.75/3.54 |-Branch one:
% 12.75/3.54 | (290) all_0_11_11 = n7
% 12.75/3.54 |
% 12.75/3.54 | From (290) and (84) follows:
% 12.75/3.54 | (291) pred(n7) = all_0_9_9
% 12.75/3.54 |
% 12.75/3.54 | From (290) and (210) follows:
% 12.75/3.54 | (292) succ(n7) = all_0_5_5
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (158) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 12.75/3.54 | (293) all_0_9_9 = n6
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (141) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 12.75/3.54 | (294) all_0_5_5 = n8
% 12.75/3.54 |
% 12.75/3.54 | From (293)(294) and (48) follows:
% 12.75/3.54 | (295) sum(n6, n8) = all_0_2_2
% 12.75/3.54 |
% 12.75/3.54 | From (293) and (225) follows:
% 12.75/3.54 | (296) sum(n6, n0) = all_0_7_7
% 12.75/3.54 |
% 12.75/3.54 | From (294) and (223) follows:
% 12.75/3.54 | (297) sum(n9, n8) = all_0_4_4
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (31) with n9, n8, all_0_4_4, n6 and discharging atoms sum(n9, n8) = all_0_4_4, sum(n9, n8) = n6, yields:
% 12.75/3.54 | (298) all_0_4_4 = n6
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (31) with n6, n8, all_0_2_2, n3 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n3, yields:
% 12.75/3.54 | (299) all_0_2_2 = n3
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (31) with n6, n0, all_0_7_7, n6 and discharging atoms sum(n6, n0) = all_0_7_7, sum(n6, n0) = n6, yields:
% 12.75/3.54 | (300) all_0_7_7 = n6
% 12.75/3.54 |
% 12.75/3.54 | From (299) and (227) follows:
% 12.75/3.54 | (301) sum(n3, n9) = all_0_0_0
% 12.75/3.54 |
% 12.75/3.54 | From (300)(298) and (119) follows:
% 12.75/3.54 | (302) sum(n6, n6) = all_0_3_3
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (31) with n6, n6, all_0_3_3, n1 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n1, yields:
% 12.75/3.54 | (303) all_0_3_3 = n1
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (31) with n3, n9, all_0_0_0, n1 and discharging atoms sum(n3, n9) = all_0_0_0, sum(n3, n9) = n1, yields:
% 12.75/3.54 | (304) all_0_0_0 = n1
% 12.75/3.54 |
% 12.75/3.54 | Equations (304,303) can reduce 104 to:
% 12.75/3.54 | (251) $false
% 12.75/3.54 |
% 12.75/3.54 |-The branch is then unsatisfiable
% 12.75/3.54 |-Branch two:
% 12.75/3.54 | (306) ~ (all_0_11_11 = n7)
% 12.75/3.54 | (307) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 12.75/3.54 |
% 12.75/3.54 +-Applying beta-rule and splitting (307), into two cases.
% 12.75/3.54 |-Branch one:
% 12.75/3.54 | (308) all_0_11_11 = n6
% 12.75/3.54 |
% 12.75/3.54 | From (308) and (84) follows:
% 12.75/3.54 | (309) pred(n6) = all_0_9_9
% 12.75/3.54 |
% 12.75/3.54 | From (308) and (210) follows:
% 12.75/3.54 | (310) succ(n6) = all_0_5_5
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (158) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 12.75/3.54 | (311) all_0_9_9 = n5
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (141) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 12.75/3.54 | (312) all_0_5_5 = n7
% 12.75/3.54 |
% 12.75/3.54 | From (311)(312) and (48) follows:
% 12.75/3.54 | (313) sum(n5, n7) = all_0_2_2
% 12.75/3.54 |
% 12.75/3.54 | From (311) and (225) follows:
% 12.75/3.54 | (314) sum(n5, n0) = all_0_7_7
% 12.75/3.54 |
% 12.75/3.54 | From (312) and (223) follows:
% 12.75/3.54 | (315) sum(n9, n7) = all_0_4_4
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (31) with n9, n7, all_0_4_4, n5 and discharging atoms sum(n9, n7) = all_0_4_4, sum(n9, n7) = n5, yields:
% 12.75/3.54 | (316) all_0_4_4 = n5
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (31) with n5, n7, all_0_2_2, n1 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n1, yields:
% 12.75/3.54 | (317) all_0_2_2 = n1
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (31) with n5, n0, all_0_7_7, n5 and discharging atoms sum(n5, n0) = all_0_7_7, sum(n5, n0) = n5, yields:
% 12.75/3.54 | (318) all_0_7_7 = n5
% 12.75/3.54 |
% 12.75/3.54 | From (317) and (227) follows:
% 12.75/3.54 | (319) sum(n1, n9) = all_0_0_0
% 12.75/3.54 |
% 12.75/3.54 | From (318)(316) and (119) follows:
% 12.75/3.54 | (320) sum(n5, n5) = all_0_3_3
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (31) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 12.75/3.54 | (321) all_0_3_3 = n10
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (31) with n1, n9, all_0_0_0, n10 and discharging atoms sum(n1, n9) = all_0_0_0, sum(n1, n9) = n10, yields:
% 12.75/3.54 | (322) all_0_0_0 = n10
% 12.75/3.54 |
% 12.75/3.54 | Equations (322,321) can reduce 104 to:
% 12.75/3.54 | (251) $false
% 12.75/3.54 |
% 12.75/3.54 |-The branch is then unsatisfiable
% 12.75/3.54 |-Branch two:
% 12.75/3.54 | (324) ~ (all_0_11_11 = n6)
% 12.75/3.54 | (325) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 12.75/3.54 |
% 12.75/3.54 +-Applying beta-rule and splitting (325), into two cases.
% 12.75/3.54 |-Branch one:
% 12.75/3.54 | (326) all_0_11_11 = n5
% 12.75/3.54 |
% 12.75/3.54 | From (326) and (84) follows:
% 12.75/3.54 | (327) pred(n5) = all_0_9_9
% 12.75/3.54 |
% 12.75/3.54 | From (326) and (210) follows:
% 12.75/3.54 | (328) succ(n5) = all_0_5_5
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (158) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 12.75/3.54 | (329) all_0_9_9 = n4
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (141) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 12.75/3.54 | (330) all_0_5_5 = n6
% 12.75/3.54 |
% 12.75/3.54 | From (329)(330) and (48) follows:
% 12.75/3.54 | (331) sum(n4, n6) = all_0_2_2
% 12.75/3.54 |
% 12.75/3.54 | From (329) and (225) follows:
% 12.75/3.54 | (332) sum(n4, n0) = all_0_7_7
% 12.75/3.54 |
% 12.75/3.54 | From (330) and (223) follows:
% 12.75/3.54 | (333) sum(n9, n6) = all_0_4_4
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (31) with n9, n6, all_0_4_4, n4 and discharging atoms sum(n9, n6) = all_0_4_4, sum(n9, n6) = n4, yields:
% 12.75/3.54 | (334) all_0_4_4 = n4
% 12.75/3.54 |
% 12.75/3.54 | Instantiating formula (31) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 12.75/3.55 | (335) all_0_2_2 = n10
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (31) with n4, n0, all_0_7_7, n4 and discharging atoms sum(n4, n0) = all_0_7_7, sum(n4, n0) = n4, yields:
% 12.75/3.55 | (336) all_0_7_7 = n4
% 12.75/3.55 |
% 12.75/3.55 | From (335) and (227) follows:
% 12.75/3.55 | (337) sum(n10, n9) = all_0_0_0
% 12.75/3.55 |
% 12.75/3.55 | From (336)(334) and (119) follows:
% 12.75/3.55 | (338) sum(n4, n4) = all_0_3_3
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (31) with n10, n9, all_0_0_0, n8 and discharging atoms sum(n10, n9) = all_0_0_0, sum(n10, n9) = n8, yields:
% 12.75/3.55 | (339) all_0_0_0 = n8
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (31) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 12.75/3.55 | (340) all_0_3_3 = n8
% 12.75/3.55 |
% 12.75/3.55 | Equations (339,340) can reduce 104 to:
% 12.75/3.55 | (251) $false
% 12.75/3.55 |
% 12.75/3.55 |-The branch is then unsatisfiable
% 12.75/3.55 |-Branch two:
% 12.75/3.55 | (342) ~ (all_0_11_11 = n5)
% 12.75/3.55 | (343) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 12.75/3.55 |
% 12.75/3.55 +-Applying beta-rule and splitting (343), into two cases.
% 12.75/3.55 |-Branch one:
% 12.75/3.55 | (344) all_0_11_11 = n4
% 12.75/3.55 |
% 12.75/3.55 | From (344) and (84) follows:
% 12.75/3.55 | (345) pred(n4) = all_0_9_9
% 12.75/3.55 |
% 12.75/3.55 | From (344) and (210) follows:
% 12.75/3.55 | (346) succ(n4) = all_0_5_5
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (158) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 12.75/3.55 | (347) all_0_9_9 = n3
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (141) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 12.75/3.55 | (348) all_0_5_5 = n5
% 12.75/3.55 |
% 12.75/3.55 | From (347)(348) and (48) follows:
% 12.75/3.55 | (349) sum(n3, n5) = all_0_2_2
% 12.75/3.55 |
% 12.75/3.55 | From (347) and (225) follows:
% 12.75/3.55 | (350) sum(n3, n0) = all_0_7_7
% 12.75/3.55 |
% 12.75/3.55 | From (348) and (223) follows:
% 12.75/3.55 | (351) sum(n9, n5) = all_0_4_4
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (31) with n9, n5, all_0_4_4, n3 and discharging atoms sum(n9, n5) = all_0_4_4, sum(n9, n5) = n3, yields:
% 12.75/3.55 | (352) all_0_4_4 = n3
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (31) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 12.75/3.55 | (353) all_0_2_2 = n8
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (31) with n3, n0, all_0_7_7, n3 and discharging atoms sum(n3, n0) = all_0_7_7, sum(n3, n0) = n3, yields:
% 12.75/3.55 | (354) all_0_7_7 = n3
% 12.75/3.55 |
% 12.75/3.55 | From (353) and (227) follows:
% 12.75/3.55 | (355) sum(n8, n9) = all_0_0_0
% 12.75/3.55 |
% 12.75/3.55 | From (354)(352) and (119) follows:
% 12.75/3.55 | (356) sum(n3, n3) = all_0_3_3
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (31) with n8, n9, all_0_0_0, n6 and discharging atoms sum(n8, n9) = all_0_0_0, sum(n8, n9) = n6, yields:
% 12.75/3.55 | (357) all_0_0_0 = n6
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (31) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 12.75/3.55 | (358) all_0_3_3 = n6
% 12.75/3.55 |
% 12.75/3.55 | Equations (357,358) can reduce 104 to:
% 12.75/3.55 | (251) $false
% 12.75/3.55 |
% 12.75/3.55 |-The branch is then unsatisfiable
% 12.75/3.55 |-Branch two:
% 12.75/3.55 | (360) ~ (all_0_11_11 = n4)
% 12.75/3.55 | (361) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 12.75/3.55 |
% 12.75/3.55 +-Applying beta-rule and splitting (361), into two cases.
% 12.75/3.55 |-Branch one:
% 12.75/3.55 | (362) all_0_11_11 = n3
% 12.75/3.55 |
% 12.75/3.55 | From (362) and (84) follows:
% 12.75/3.55 | (363) pred(n3) = all_0_9_9
% 12.75/3.55 |
% 12.75/3.55 | From (362) and (210) follows:
% 12.75/3.55 | (364) succ(n3) = all_0_5_5
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (158) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 12.75/3.55 | (365) all_0_9_9 = n2
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (141) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 12.75/3.55 | (366) all_0_5_5 = n4
% 12.75/3.55 |
% 12.75/3.55 | From (365)(366) and (48) follows:
% 12.75/3.55 | (367) sum(n2, n4) = all_0_2_2
% 12.75/3.55 |
% 12.75/3.55 | From (365) and (225) follows:
% 12.75/3.55 | (368) sum(n2, n0) = all_0_7_7
% 12.75/3.55 |
% 12.75/3.55 | From (366) and (223) follows:
% 12.75/3.55 | (369) sum(n9, n4) = all_0_4_4
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (31) with n9, n4, all_0_4_4, n2 and discharging atoms sum(n9, n4) = all_0_4_4, sum(n9, n4) = n2, yields:
% 12.75/3.55 | (370) all_0_4_4 = n2
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (31) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 12.75/3.55 | (371) all_0_2_2 = n6
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (31) with n2, n0, all_0_7_7, n2 and discharging atoms sum(n2, n0) = all_0_7_7, sum(n2, n0) = n2, yields:
% 12.75/3.55 | (372) all_0_7_7 = n2
% 12.75/3.55 |
% 12.75/3.55 | From (371) and (227) follows:
% 12.75/3.55 | (373) sum(n6, n9) = all_0_0_0
% 12.75/3.55 |
% 12.75/3.55 | From (372)(370) and (119) follows:
% 12.75/3.55 | (374) sum(n2, n2) = all_0_3_3
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (31) with n6, n9, all_0_0_0, n4 and discharging atoms sum(n6, n9) = all_0_0_0, sum(n6, n9) = n4, yields:
% 12.75/3.55 | (375) all_0_0_0 = n4
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (31) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 12.75/3.55 | (376) all_0_3_3 = n4
% 12.75/3.55 |
% 12.75/3.55 | Equations (375,376) can reduce 104 to:
% 12.75/3.55 | (251) $false
% 12.75/3.55 |
% 12.75/3.55 |-The branch is then unsatisfiable
% 12.75/3.55 |-Branch two:
% 12.75/3.55 | (378) ~ (all_0_11_11 = n3)
% 12.75/3.55 | (379) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 12.75/3.55 |
% 12.75/3.55 +-Applying beta-rule and splitting (379), into two cases.
% 12.75/3.55 |-Branch one:
% 12.75/3.55 | (380) all_0_11_11 = n2
% 12.75/3.55 |
% 12.75/3.55 | From (380) and (84) follows:
% 12.75/3.55 | (381) pred(n2) = all_0_9_9
% 12.75/3.55 |
% 12.75/3.55 | From (380) and (210) follows:
% 12.75/3.55 | (382) succ(n2) = all_0_5_5
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (158) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 12.75/3.55 | (383) all_0_9_9 = n1
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (141) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 12.75/3.55 | (384) all_0_5_5 = n3
% 12.75/3.55 |
% 12.75/3.55 | From (383)(384) and (48) follows:
% 12.75/3.55 | (385) sum(n1, n3) = all_0_2_2
% 12.75/3.55 |
% 12.75/3.55 | From (383) and (225) follows:
% 12.75/3.55 | (386) sum(n1, n0) = all_0_7_7
% 12.75/3.55 |
% 12.75/3.55 | From (384) and (223) follows:
% 12.75/3.55 | (387) sum(n9, n3) = all_0_4_4
% 12.75/3.55 |
% 12.75/3.55 | Instantiating formula (31) with n9, n3, all_0_4_4, n1 and discharging atoms sum(n9, n3) = all_0_4_4, sum(n9, n3) = n1, yields:
% 12.75/3.56 | (388) all_0_4_4 = n1
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (31) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 12.75/3.56 | (389) all_0_2_2 = n4
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (31) with n1, n0, all_0_7_7, n1 and discharging atoms sum(n1, n0) = all_0_7_7, sum(n1, n0) = n1, yields:
% 12.75/3.56 | (390) all_0_7_7 = n1
% 12.75/3.56 |
% 12.75/3.56 | From (389) and (227) follows:
% 12.75/3.56 | (391) sum(n4, n9) = all_0_0_0
% 12.75/3.56 |
% 12.75/3.56 | From (390)(388) and (119) follows:
% 12.75/3.56 | (392) sum(n1, n1) = all_0_3_3
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (31) with n4, n9, all_0_0_0, n2 and discharging atoms sum(n4, n9) = all_0_0_0, sum(n4, n9) = n2, yields:
% 12.75/3.56 | (393) all_0_0_0 = n2
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (31) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 12.75/3.56 | (394) all_0_3_3 = n2
% 12.75/3.56 |
% 12.75/3.56 | Equations (393,394) can reduce 104 to:
% 12.75/3.56 | (251) $false
% 12.75/3.56 |
% 12.75/3.56 |-The branch is then unsatisfiable
% 12.75/3.56 |-Branch two:
% 12.75/3.56 | (396) ~ (all_0_11_11 = n2)
% 12.75/3.56 | (397) all_0_11_11 = n1 | all_0_11_11 = n0
% 12.75/3.56 |
% 12.75/3.56 +-Applying beta-rule and splitting (397), into two cases.
% 12.75/3.56 |-Branch one:
% 12.75/3.56 | (398) all_0_11_11 = n1
% 12.75/3.56 |
% 12.75/3.56 | From (398) and (84) follows:
% 12.75/3.56 | (399) pred(n1) = all_0_9_9
% 12.75/3.56 |
% 12.75/3.56 | From (398) and (210) follows:
% 12.75/3.56 | (400) succ(n1) = all_0_5_5
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (158) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 12.75/3.56 | (401) all_0_9_9 = n0
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (141) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 12.75/3.56 | (402) all_0_5_5 = n2
% 12.75/3.56 |
% 12.75/3.56 | From (401)(402) and (48) follows:
% 12.75/3.56 | (403) sum(n0, n2) = all_0_2_2
% 12.75/3.56 |
% 12.75/3.56 | From (401) and (225) follows:
% 12.75/3.56 | (404) sum(n0, n0) = all_0_7_7
% 12.75/3.56 |
% 12.75/3.56 | From (402) and (223) follows:
% 12.75/3.56 | (405) sum(n9, n2) = all_0_4_4
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (31) with n9, n2, all_0_4_4, n0 and discharging atoms sum(n9, n2) = all_0_4_4, sum(n9, n2) = n0, yields:
% 12.75/3.56 | (406) all_0_4_4 = n0
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (31) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 12.75/3.56 | (407) all_0_2_2 = n2
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (31) with n0, n0, all_0_7_7, n0 and discharging atoms sum(n0, n0) = all_0_7_7, sum(n0, n0) = n0, yields:
% 12.75/3.56 | (408) all_0_7_7 = n0
% 12.75/3.56 |
% 12.75/3.56 | From (407) and (227) follows:
% 12.75/3.56 | (409) sum(n2, n9) = all_0_0_0
% 12.75/3.56 |
% 12.75/3.56 | From (408)(406) and (119) follows:
% 12.75/3.56 | (410) sum(n0, n0) = all_0_3_3
% 12.75/3.56 |
% 12.75/3.56 | From (408) and (404) follows:
% 12.75/3.56 | (91) sum(n0, n0) = n0
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (31) with n2, n9, all_0_0_0, n0 and discharging atoms sum(n2, n9) = all_0_0_0, sum(n2, n9) = n0, yields:
% 12.75/3.56 | (412) all_0_0_0 = n0
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (31) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 12.75/3.56 | (413) all_0_3_3 = n0
% 12.75/3.56 |
% 12.75/3.56 | Equations (412,413) can reduce 104 to:
% 12.75/3.56 | (251) $false
% 12.75/3.56 |
% 12.75/3.56 |-The branch is then unsatisfiable
% 12.75/3.56 |-Branch two:
% 12.75/3.56 | (415) ~ (all_0_11_11 = n1)
% 12.75/3.56 | (416) all_0_11_11 = n0
% 12.75/3.56 |
% 12.75/3.56 | From (416) and (84) follows:
% 12.75/3.56 | (417) pred(n0) = all_0_9_9
% 12.75/3.56 |
% 12.75/3.56 | From (416) and (210) follows:
% 12.75/3.56 | (418) succ(n0) = all_0_5_5
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (158) with n0, all_0_9_9, n10 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n10, yields:
% 12.75/3.56 | (419) all_0_9_9 = n10
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (141) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 12.75/3.56 | (420) all_0_5_5 = n1
% 12.75/3.56 |
% 12.75/3.56 | From (419)(420) and (48) follows:
% 12.75/3.56 | (421) sum(n10, n1) = all_0_2_2
% 12.75/3.56 |
% 12.75/3.56 | From (419) and (225) follows:
% 12.75/3.56 | (422) sum(n10, n0) = all_0_7_7
% 12.75/3.56 |
% 12.75/3.56 | From (420) and (223) follows:
% 12.75/3.56 | (423) sum(n9, n1) = all_0_4_4
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (31) with n10, n1, all_0_2_2, n0 and discharging atoms sum(n10, n1) = all_0_2_2, sum(n10, n1) = n0, yields:
% 12.75/3.56 | (424) all_0_2_2 = n0
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (31) with n10, n0, all_0_7_7, n10 and discharging atoms sum(n10, n0) = all_0_7_7, sum(n10, n0) = n10, yields:
% 12.75/3.56 | (425) all_0_7_7 = n10
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (31) with n9, n1, all_0_4_4, n10 and discharging atoms sum(n9, n1) = all_0_4_4, sum(n9, n1) = n10, yields:
% 12.75/3.56 | (426) all_0_4_4 = n10
% 12.75/3.56 |
% 12.75/3.56 | From (424) and (227) follows:
% 12.75/3.56 | (427) sum(n0, n9) = all_0_0_0
% 12.75/3.56 |
% 12.75/3.56 | From (425)(426) and (119) follows:
% 12.75/3.56 | (428) sum(n10, n10) = all_0_3_3
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (31) with n10, n10, all_0_3_3, n9 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n9, yields:
% 12.75/3.56 | (429) all_0_3_3 = n9
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (31) with n0, n9, all_0_0_0, n9 and discharging atoms sum(n0, n9) = all_0_0_0, sum(n0, n9) = n9, yields:
% 12.75/3.56 | (430) all_0_0_0 = n9
% 12.75/3.56 |
% 12.75/3.56 | Equations (430,429) can reduce 104 to:
% 12.75/3.56 | (251) $false
% 12.75/3.56 |
% 12.75/3.56 |-The branch is then unsatisfiable
% 12.75/3.56 |-Branch two:
% 12.75/3.56 | (432) ~ (all_0_10_10 = n10)
% 12.75/3.56 | (433) 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
% 12.75/3.56 |
% 12.75/3.56 +-Applying beta-rule and splitting (123), into two cases.
% 12.75/3.56 |-Branch one:
% 12.75/3.56 | (229) all_0_11_11 = n10
% 12.75/3.56 |
% 12.75/3.56 | From (229) and (84) follows:
% 12.75/3.56 | (230) pred(n10) = all_0_9_9
% 12.75/3.56 |
% 12.75/3.56 | From (229) and (210) follows:
% 12.75/3.56 | (231) succ(n10) = all_0_5_5
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (158) with n10, all_0_9_9, n9 and discharging atoms pred(n10) = all_0_9_9, pred(n10) = n9, yields:
% 12.75/3.56 | (232) all_0_9_9 = n9
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (141) with n10, all_0_5_5, n0 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n0, yields:
% 12.75/3.56 | (233) all_0_5_5 = n0
% 12.75/3.56 |
% 12.75/3.56 | From (233) and (33) follows:
% 12.75/3.56 | (439) sum(all_0_6_6, n0) = all_0_4_4
% 12.75/3.56 |
% 12.75/3.56 | From (232)(233) and (48) follows:
% 12.75/3.56 | (234) sum(n9, n0) = all_0_2_2
% 12.75/3.56 |
% 12.75/3.56 | From (232) and (137) follows:
% 12.75/3.56 | (441) sum(n9, all_0_8_8) = all_0_7_7
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (31) with n9, n0, all_0_2_2, n9 and discharging atoms sum(n9, n0) = all_0_2_2, sum(n9, n0) = n9, yields:
% 12.75/3.56 | (237) all_0_2_2 = n9
% 12.75/3.56 |
% 12.75/3.56 | From (237) and (4) follows:
% 12.75/3.56 | (443) sum(n9, all_0_1_1) = all_0_0_0
% 12.75/3.56 |
% 12.75/3.56 | From (237) and (234) follows:
% 12.75/3.56 | (197) sum(n9, n0) = n9
% 12.75/3.56 |
% 12.75/3.56 +-Applying beta-rule and splitting (433), into two cases.
% 12.75/3.56 |-Branch one:
% 12.75/3.56 | (445) all_0_10_10 = n9
% 12.75/3.56 |
% 12.75/3.56 | From (445) and (211) follows:
% 12.75/3.56 | (446) pred(n9) = all_0_6_6
% 12.75/3.56 |
% 12.75/3.56 | From (445) and (41) follows:
% 12.75/3.56 | (447) succ(n9) = all_0_8_8
% 12.75/3.56 |
% 12.75/3.56 | Instantiating formula (158) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 12.75/3.57 | (448) all_0_6_6 = n8
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (141) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 12.75/3.57 | (449) all_0_8_8 = n10
% 12.75/3.57 |
% 12.75/3.57 | From (448)(449) and (178) follows:
% 12.75/3.57 | (450) sum(n8, n10) = all_0_1_1
% 12.75/3.57 |
% 12.75/3.57 | From (448) and (439) follows:
% 12.75/3.57 | (451) sum(n8, n0) = all_0_4_4
% 12.75/3.57 |
% 12.75/3.57 | From (449) and (441) follows:
% 12.75/3.57 | (452) sum(n9, n10) = all_0_7_7
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n9, n10, all_0_7_7, n8 and discharging atoms sum(n9, n10) = all_0_7_7, sum(n9, n10) = n8, yields:
% 12.75/3.57 | (264) all_0_7_7 = n8
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n8, n10, all_0_1_1, n7 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n7, yields:
% 12.75/3.57 | (454) all_0_1_1 = n7
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n8, n0, all_0_4_4, n8 and discharging atoms sum(n8, n0) = all_0_4_4, sum(n8, n0) = n8, yields:
% 12.75/3.57 | (262) all_0_4_4 = n8
% 12.75/3.57 |
% 12.75/3.57 | From (264)(262) and (119) follows:
% 12.75/3.57 | (266) sum(n8, n8) = all_0_3_3
% 12.75/3.57 |
% 12.75/3.57 | From (454) and (443) follows:
% 12.75/3.57 | (457) sum(n9, n7) = all_0_0_0
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n9, n7, all_0_0_0, n5 and discharging atoms sum(n9, n7) = all_0_0_0, sum(n9, n7) = n5, yields:
% 12.75/3.57 | (268) all_0_0_0 = n5
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n8, n8, all_0_3_3, n5 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n5, yields:
% 12.75/3.57 | (267) all_0_3_3 = n5
% 12.75/3.57 |
% 12.75/3.57 | Equations (268,267) can reduce 104 to:
% 12.75/3.57 | (251) $false
% 12.75/3.57 |
% 12.75/3.57 |-The branch is then unsatisfiable
% 12.75/3.57 |-Branch two:
% 12.75/3.57 | (461) ~ (all_0_10_10 = n9)
% 12.75/3.57 | (462) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 12.75/3.57 |
% 12.75/3.57 +-Applying beta-rule and splitting (462), into two cases.
% 12.75/3.57 |-Branch one:
% 12.75/3.57 | (463) all_0_10_10 = n8
% 12.75/3.57 |
% 12.75/3.57 | From (463) and (211) follows:
% 12.75/3.57 | (464) pred(n8) = all_0_6_6
% 12.75/3.57 |
% 12.75/3.57 | From (463) and (41) follows:
% 12.75/3.57 | (465) succ(n8) = all_0_8_8
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (158) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 12.75/3.57 | (466) all_0_6_6 = n7
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (141) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 12.75/3.57 | (467) all_0_8_8 = n9
% 12.75/3.57 |
% 12.75/3.57 | From (466)(467) and (178) follows:
% 12.75/3.57 | (468) sum(n7, n9) = all_0_1_1
% 12.75/3.57 |
% 12.75/3.57 | From (466) and (439) follows:
% 12.75/3.57 | (469) sum(n7, n0) = all_0_4_4
% 12.75/3.57 |
% 12.75/3.57 | From (467) and (441) follows:
% 12.75/3.57 | (470) sum(n9, n9) = all_0_7_7
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n9, n9, all_0_7_7, n7 and discharging atoms sum(n9, n9) = all_0_7_7, sum(n9, n9) = n7, yields:
% 12.75/3.57 | (282) all_0_7_7 = n7
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n7, n9, all_0_1_1, n5 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n5, yields:
% 12.75/3.57 | (472) all_0_1_1 = n5
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n7, n0, all_0_4_4, n7 and discharging atoms sum(n7, n0) = all_0_4_4, sum(n7, n0) = n7, yields:
% 12.75/3.57 | (280) all_0_4_4 = n7
% 12.75/3.57 |
% 12.75/3.57 | From (282)(280) and (119) follows:
% 12.75/3.57 | (284) sum(n7, n7) = all_0_3_3
% 12.75/3.57 |
% 12.75/3.57 | From (472) and (443) follows:
% 12.75/3.57 | (475) sum(n9, n5) = all_0_0_0
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n9, n5, all_0_0_0, n3 and discharging atoms sum(n9, n5) = all_0_0_0, sum(n9, n5) = n3, yields:
% 12.75/3.57 | (286) all_0_0_0 = n3
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n7, n7, all_0_3_3, n3 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n3, yields:
% 12.75/3.57 | (285) all_0_3_3 = n3
% 12.75/3.57 |
% 12.75/3.57 | Equations (286,285) can reduce 104 to:
% 12.75/3.57 | (251) $false
% 12.75/3.57 |
% 12.75/3.57 |-The branch is then unsatisfiable
% 12.75/3.57 |-Branch two:
% 12.75/3.57 | (479) ~ (all_0_10_10 = n8)
% 12.75/3.57 | (480) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 12.75/3.57 |
% 12.75/3.57 +-Applying beta-rule and splitting (480), into two cases.
% 12.75/3.57 |-Branch one:
% 12.75/3.57 | (481) all_0_10_10 = n7
% 12.75/3.57 |
% 12.75/3.57 | From (481) and (211) follows:
% 12.75/3.57 | (482) pred(n7) = all_0_6_6
% 12.75/3.57 |
% 12.75/3.57 | From (481) and (41) follows:
% 12.75/3.57 | (483) succ(n7) = all_0_8_8
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (158) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 12.75/3.57 | (484) all_0_6_6 = n6
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (141) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 12.75/3.57 | (485) all_0_8_8 = n8
% 12.75/3.57 |
% 12.75/3.57 | From (484)(485) and (178) follows:
% 12.75/3.57 | (486) sum(n6, n8) = all_0_1_1
% 12.75/3.57 |
% 12.75/3.57 | From (484) and (439) follows:
% 12.75/3.57 | (487) sum(n6, n0) = all_0_4_4
% 12.75/3.57 |
% 12.75/3.57 | From (485) and (441) follows:
% 12.75/3.57 | (488) sum(n9, n8) = all_0_7_7
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n9, n8, all_0_7_7, n6 and discharging atoms sum(n9, n8) = all_0_7_7, sum(n9, n8) = n6, yields:
% 12.75/3.57 | (300) all_0_7_7 = n6
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n6, n8, all_0_1_1, n3 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n3, yields:
% 12.75/3.57 | (490) all_0_1_1 = n3
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n6, n0, all_0_4_4, n6 and discharging atoms sum(n6, n0) = all_0_4_4, sum(n6, n0) = n6, yields:
% 12.75/3.57 | (298) all_0_4_4 = n6
% 12.75/3.57 |
% 12.75/3.57 | From (300)(298) and (119) follows:
% 12.75/3.57 | (302) sum(n6, n6) = all_0_3_3
% 12.75/3.57 |
% 12.75/3.57 | From (490) and (443) follows:
% 12.75/3.57 | (493) sum(n9, n3) = all_0_0_0
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n9, n3, all_0_0_0, n1 and discharging atoms sum(n9, n3) = all_0_0_0, sum(n9, n3) = n1, yields:
% 12.75/3.57 | (304) all_0_0_0 = n1
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n6, n6, all_0_3_3, n1 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n1, yields:
% 12.75/3.57 | (303) all_0_3_3 = n1
% 12.75/3.57 |
% 12.75/3.57 | Equations (304,303) can reduce 104 to:
% 12.75/3.57 | (251) $false
% 12.75/3.57 |
% 12.75/3.57 |-The branch is then unsatisfiable
% 12.75/3.57 |-Branch two:
% 12.75/3.57 | (497) ~ (all_0_10_10 = n7)
% 12.75/3.57 | (498) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 12.75/3.57 |
% 12.75/3.57 +-Applying beta-rule and splitting (498), into two cases.
% 12.75/3.57 |-Branch one:
% 12.75/3.57 | (499) all_0_10_10 = n6
% 12.75/3.57 |
% 12.75/3.57 | From (499) and (211) follows:
% 12.75/3.57 | (500) pred(n6) = all_0_6_6
% 12.75/3.57 |
% 12.75/3.57 | From (499) and (41) follows:
% 12.75/3.57 | (501) succ(n6) = all_0_8_8
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (158) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 12.75/3.57 | (502) all_0_6_6 = n5
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (141) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 12.75/3.57 | (503) all_0_8_8 = n7
% 12.75/3.57 |
% 12.75/3.57 | From (502)(503) and (178) follows:
% 12.75/3.57 | (504) sum(n5, n7) = all_0_1_1
% 12.75/3.57 |
% 12.75/3.57 | From (502) and (439) follows:
% 12.75/3.57 | (505) sum(n5, n0) = all_0_4_4
% 12.75/3.57 |
% 12.75/3.57 | From (503) and (441) follows:
% 12.75/3.57 | (506) sum(n9, n7) = all_0_7_7
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n9, n7, all_0_7_7, n5 and discharging atoms sum(n9, n7) = all_0_7_7, sum(n9, n7) = n5, yields:
% 12.75/3.57 | (318) all_0_7_7 = n5
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n5, n7, all_0_1_1, n1 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n1, yields:
% 12.75/3.57 | (508) all_0_1_1 = n1
% 12.75/3.57 |
% 12.75/3.57 | Instantiating formula (31) with n5, n0, all_0_4_4, n5 and discharging atoms sum(n5, n0) = all_0_4_4, sum(n5, n0) = n5, yields:
% 12.75/3.58 | (316) all_0_4_4 = n5
% 12.75/3.58 |
% 12.75/3.58 | From (318)(316) and (119) follows:
% 12.75/3.58 | (320) sum(n5, n5) = all_0_3_3
% 12.75/3.58 |
% 12.75/3.58 | From (508) and (443) follows:
% 12.75/3.58 | (511) sum(n9, n1) = all_0_0_0
% 12.75/3.58 |
% 12.75/3.58 | Instantiating formula (31) with n9, n1, all_0_0_0, n10 and discharging atoms sum(n9, n1) = all_0_0_0, sum(n9, n1) = n10, yields:
% 12.75/3.58 | (322) all_0_0_0 = n10
% 12.75/3.58 |
% 12.75/3.58 | Instantiating formula (31) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 12.75/3.58 | (321) all_0_3_3 = n10
% 12.75/3.58 |
% 12.75/3.58 | Equations (322,321) can reduce 104 to:
% 12.75/3.58 | (251) $false
% 12.75/3.58 |
% 12.75/3.58 |-The branch is then unsatisfiable
% 12.75/3.58 |-Branch two:
% 12.75/3.58 | (515) ~ (all_0_10_10 = n6)
% 12.75/3.58 | (516) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 12.75/3.58 |
% 12.75/3.58 +-Applying beta-rule and splitting (516), into two cases.
% 12.75/3.58 |-Branch one:
% 12.75/3.58 | (517) all_0_10_10 = n5
% 12.75/3.58 |
% 12.75/3.58 | From (517) and (211) follows:
% 12.75/3.58 | (518) pred(n5) = all_0_6_6
% 12.75/3.58 |
% 12.75/3.58 | From (517) and (41) follows:
% 12.75/3.58 | (519) succ(n5) = all_0_8_8
% 12.75/3.58 |
% 12.75/3.58 | Instantiating formula (158) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 12.75/3.58 | (520) all_0_6_6 = n4
% 12.75/3.58 |
% 12.75/3.58 | Instantiating formula (141) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 12.75/3.58 | (521) all_0_8_8 = n6
% 12.75/3.58 |
% 12.75/3.58 | From (520)(521) and (178) follows:
% 13.17/3.58 | (522) sum(n4, n6) = all_0_1_1
% 13.17/3.58 |
% 13.17/3.58 | From (520) and (439) follows:
% 13.17/3.58 | (523) sum(n4, n0) = all_0_4_4
% 13.17/3.58 |
% 13.17/3.58 | From (521) and (441) follows:
% 13.17/3.58 | (524) sum(n9, n6) = all_0_7_7
% 13.17/3.58 |
% 13.17/3.58 | Instantiating formula (31) with n9, n6, all_0_7_7, n4 and discharging atoms sum(n9, n6) = all_0_7_7, sum(n9, n6) = n4, yields:
% 13.17/3.58 | (336) all_0_7_7 = n4
% 13.17/3.58 |
% 13.17/3.58 | Instantiating formula (31) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 13.17/3.58 | (526) all_0_1_1 = n10
% 13.17/3.58 |
% 13.17/3.58 | Instantiating formula (31) with n4, n0, all_0_4_4, n4 and discharging atoms sum(n4, n0) = all_0_4_4, sum(n4, n0) = n4, yields:
% 13.17/3.58 | (334) all_0_4_4 = n4
% 13.17/3.58 |
% 13.17/3.58 | From (336)(334) and (119) follows:
% 13.17/3.58 | (338) sum(n4, n4) = all_0_3_3
% 13.17/3.58 |
% 13.17/3.58 | From (526) and (443) follows:
% 13.17/3.58 | (529) sum(n9, n10) = all_0_0_0
% 13.17/3.58 |
% 13.17/3.58 | Instantiating formula (31) with n9, n10, all_0_0_0, n8 and discharging atoms sum(n9, n10) = all_0_0_0, sum(n9, n10) = n8, yields:
% 13.17/3.58 | (339) all_0_0_0 = n8
% 13.17/3.58 |
% 13.17/3.58 | Instantiating formula (31) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 13.17/3.58 | (340) all_0_3_3 = n8
% 13.17/3.58 |
% 13.17/3.58 | Equations (339,340) can reduce 104 to:
% 13.17/3.58 | (251) $false
% 13.17/3.58 |
% 13.17/3.58 |-The branch is then unsatisfiable
% 13.17/3.58 |-Branch two:
% 13.17/3.58 | (533) ~ (all_0_10_10 = n5)
% 13.17/3.58 | (534) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.17/3.58 |
% 13.17/3.58 +-Applying beta-rule and splitting (534), into two cases.
% 13.17/3.58 |-Branch one:
% 13.17/3.58 | (535) all_0_10_10 = n4
% 13.17/3.58 |
% 13.17/3.58 | From (535) and (211) follows:
% 13.17/3.58 | (536) pred(n4) = all_0_6_6
% 13.17/3.58 |
% 13.17/3.58 | From (535) and (41) follows:
% 13.17/3.58 | (537) succ(n4) = all_0_8_8
% 13.17/3.58 |
% 13.17/3.58 | Instantiating formula (158) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 13.17/3.58 | (538) all_0_6_6 = n3
% 13.17/3.58 |
% 13.17/3.58 | Instantiating formula (141) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 13.17/3.58 | (539) all_0_8_8 = n5
% 13.17/3.58 |
% 13.17/3.58 | From (538)(539) and (178) follows:
% 13.17/3.58 | (540) sum(n3, n5) = all_0_1_1
% 13.17/3.58 |
% 13.17/3.58 | From (538) and (439) follows:
% 13.17/3.58 | (541) sum(n3, n0) = all_0_4_4
% 13.17/3.58 |
% 13.17/3.58 | From (539) and (441) follows:
% 13.17/3.58 | (542) sum(n9, n5) = all_0_7_7
% 13.17/3.58 |
% 13.17/3.58 | Instantiating formula (31) with n9, n5, all_0_7_7, n3 and discharging atoms sum(n9, n5) = all_0_7_7, sum(n9, n5) = n3, yields:
% 13.17/3.58 | (354) all_0_7_7 = n3
% 13.17/3.58 |
% 13.17/3.58 | Instantiating formula (31) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 13.17/3.58 | (544) all_0_1_1 = n8
% 13.17/3.58 |
% 13.17/3.58 | Instantiating formula (31) with n3, n0, all_0_4_4, n3 and discharging atoms sum(n3, n0) = all_0_4_4, sum(n3, n0) = n3, yields:
% 13.17/3.58 | (352) all_0_4_4 = n3
% 13.17/3.58 |
% 13.17/3.58 | From (354)(352) and (119) follows:
% 13.17/3.58 | (356) sum(n3, n3) = all_0_3_3
% 13.17/3.58 |
% 13.17/3.58 | From (544) and (443) follows:
% 13.17/3.58 | (547) sum(n9, n8) = all_0_0_0
% 13.17/3.58 |
% 13.17/3.58 | Instantiating formula (31) with n9, n8, all_0_0_0, n6 and discharging atoms sum(n9, n8) = all_0_0_0, sum(n9, n8) = n6, yields:
% 13.17/3.58 | (357) all_0_0_0 = n6
% 13.17/3.58 |
% 13.17/3.58 | Instantiating formula (31) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 13.17/3.58 | (358) all_0_3_3 = n6
% 13.17/3.58 |
% 13.17/3.58 | Equations (357,358) can reduce 104 to:
% 13.17/3.58 | (251) $false
% 13.17/3.58 |
% 13.17/3.58 |-The branch is then unsatisfiable
% 13.17/3.58 |-Branch two:
% 13.17/3.58 | (551) ~ (all_0_10_10 = n4)
% 13.17/3.58 | (552) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.17/3.58 |
% 13.17/3.58 +-Applying beta-rule and splitting (552), into two cases.
% 13.17/3.58 |-Branch one:
% 13.17/3.58 | (553) all_0_10_10 = n3
% 13.17/3.58 |
% 13.17/3.58 | From (553) and (211) follows:
% 13.17/3.58 | (554) pred(n3) = all_0_6_6
% 13.17/3.58 |
% 13.17/3.58 | From (553) and (41) follows:
% 13.17/3.58 | (555) succ(n3) = all_0_8_8
% 13.17/3.58 |
% 13.17/3.58 | Instantiating formula (158) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 13.17/3.58 | (556) all_0_6_6 = n2
% 13.17/3.58 |
% 13.17/3.58 | Instantiating formula (141) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 13.17/3.58 | (557) all_0_8_8 = n4
% 13.17/3.58 |
% 13.17/3.58 | From (556)(557) and (178) follows:
% 13.17/3.58 | (558) sum(n2, n4) = all_0_1_1
% 13.17/3.58 |
% 13.17/3.58 | From (556) and (439) follows:
% 13.17/3.58 | (559) sum(n2, n0) = all_0_4_4
% 13.17/3.58 |
% 13.17/3.58 | From (557) and (441) follows:
% 13.17/3.58 | (560) sum(n9, n4) = all_0_7_7
% 13.17/3.58 |
% 13.17/3.58 | Instantiating formula (31) with n9, n4, all_0_7_7, n2 and discharging atoms sum(n9, n4) = all_0_7_7, sum(n9, n4) = n2, yields:
% 13.17/3.58 | (372) all_0_7_7 = n2
% 13.17/3.58 |
% 13.17/3.58 | Instantiating formula (31) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 13.17/3.58 | (562) all_0_1_1 = n6
% 13.17/3.58 |
% 13.17/3.58 | Instantiating formula (31) with n2, n0, all_0_4_4, n2 and discharging atoms sum(n2, n0) = all_0_4_4, sum(n2, n0) = n2, yields:
% 13.17/3.58 | (370) all_0_4_4 = n2
% 13.17/3.58 |
% 13.17/3.58 | From (372)(370) and (119) follows:
% 13.17/3.59 | (374) sum(n2, n2) = all_0_3_3
% 13.17/3.59 |
% 13.17/3.59 | From (562) and (443) follows:
% 13.17/3.59 | (565) sum(n9, n6) = all_0_0_0
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (31) with n9, n6, all_0_0_0, n4 and discharging atoms sum(n9, n6) = all_0_0_0, sum(n9, n6) = n4, yields:
% 13.17/3.59 | (375) all_0_0_0 = n4
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (31) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 13.17/3.59 | (376) all_0_3_3 = n4
% 13.17/3.59 |
% 13.17/3.59 | Equations (375,376) can reduce 104 to:
% 13.17/3.59 | (251) $false
% 13.17/3.59 |
% 13.17/3.59 |-The branch is then unsatisfiable
% 13.17/3.59 |-Branch two:
% 13.17/3.59 | (569) ~ (all_0_10_10 = n3)
% 13.17/3.59 | (570) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.17/3.59 |
% 13.17/3.59 +-Applying beta-rule and splitting (570), into two cases.
% 13.17/3.59 |-Branch one:
% 13.17/3.59 | (571) all_0_10_10 = n2
% 13.17/3.59 |
% 13.17/3.59 | From (571) and (211) follows:
% 13.17/3.59 | (572) pred(n2) = all_0_6_6
% 13.17/3.59 |
% 13.17/3.59 | From (571) and (41) follows:
% 13.17/3.59 | (573) succ(n2) = all_0_8_8
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (158) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 13.17/3.59 | (574) all_0_6_6 = n1
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (141) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 13.17/3.59 | (575) all_0_8_8 = n3
% 13.17/3.59 |
% 13.17/3.59 | From (574)(575) and (178) follows:
% 13.17/3.59 | (576) sum(n1, n3) = all_0_1_1
% 13.17/3.59 |
% 13.17/3.59 | From (574) and (439) follows:
% 13.17/3.59 | (577) sum(n1, n0) = all_0_4_4
% 13.17/3.59 |
% 13.17/3.59 | From (575) and (441) follows:
% 13.17/3.59 | (578) sum(n9, n3) = all_0_7_7
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (31) with n9, n3, all_0_7_7, n1 and discharging atoms sum(n9, n3) = all_0_7_7, sum(n9, n3) = n1, yields:
% 13.17/3.59 | (390) all_0_7_7 = n1
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (31) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 13.17/3.59 | (580) all_0_1_1 = n4
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (31) with n1, n0, all_0_4_4, n1 and discharging atoms sum(n1, n0) = all_0_4_4, sum(n1, n0) = n1, yields:
% 13.17/3.59 | (388) all_0_4_4 = n1
% 13.17/3.59 |
% 13.17/3.59 | From (390)(388) and (119) follows:
% 13.17/3.59 | (392) sum(n1, n1) = all_0_3_3
% 13.17/3.59 |
% 13.17/3.59 | From (580) and (443) follows:
% 13.17/3.59 | (583) sum(n9, n4) = all_0_0_0
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (31) with n9, n4, all_0_0_0, n2 and discharging atoms sum(n9, n4) = all_0_0_0, sum(n9, n4) = n2, yields:
% 13.17/3.59 | (393) all_0_0_0 = n2
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (31) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 13.17/3.59 | (394) all_0_3_3 = n2
% 13.17/3.59 |
% 13.17/3.59 | Equations (393,394) can reduce 104 to:
% 13.17/3.59 | (251) $false
% 13.17/3.59 |
% 13.17/3.59 |-The branch is then unsatisfiable
% 13.17/3.59 |-Branch two:
% 13.17/3.59 | (587) ~ (all_0_10_10 = n2)
% 13.17/3.59 | (588) all_0_10_10 = n1 | all_0_10_10 = n0
% 13.17/3.59 |
% 13.17/3.59 +-Applying beta-rule and splitting (588), into two cases.
% 13.17/3.59 |-Branch one:
% 13.17/3.59 | (589) all_0_10_10 = n1
% 13.17/3.59 |
% 13.17/3.59 | From (589) and (211) follows:
% 13.17/3.59 | (590) pred(n1) = all_0_6_6
% 13.17/3.59 |
% 13.17/3.59 | From (589) and (41) follows:
% 13.17/3.59 | (591) succ(n1) = all_0_8_8
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (158) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 13.17/3.59 | (592) all_0_6_6 = n0
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (141) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 13.17/3.59 | (593) all_0_8_8 = n2
% 13.17/3.59 |
% 13.17/3.59 | From (592)(593) and (178) follows:
% 13.17/3.59 | (594) sum(n0, n2) = all_0_1_1
% 13.17/3.59 |
% 13.17/3.59 | From (592) and (439) follows:
% 13.17/3.59 | (595) sum(n0, n0) = all_0_4_4
% 13.17/3.59 |
% 13.17/3.59 | From (593) and (441) follows:
% 13.17/3.59 | (596) sum(n9, n2) = all_0_7_7
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (31) with n9, n2, all_0_7_7, n0 and discharging atoms sum(n9, n2) = all_0_7_7, sum(n9, n2) = n0, yields:
% 13.17/3.59 | (408) all_0_7_7 = n0
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (31) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 13.17/3.59 | (598) all_0_1_1 = n2
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (31) with n0, n0, all_0_4_4, n0 and discharging atoms sum(n0, n0) = all_0_4_4, sum(n0, n0) = n0, yields:
% 13.17/3.59 | (406) all_0_4_4 = n0
% 13.17/3.59 |
% 13.17/3.59 | From (408)(406) and (119) follows:
% 13.17/3.59 | (410) sum(n0, n0) = all_0_3_3
% 13.17/3.59 |
% 13.17/3.59 | From (598) and (443) follows:
% 13.17/3.59 | (601) sum(n9, n2) = all_0_0_0
% 13.17/3.59 |
% 13.17/3.59 | From (408) and (596) follows:
% 13.17/3.59 | (53) sum(n9, n2) = n0
% 13.17/3.59 |
% 13.17/3.59 | From (406) and (595) follows:
% 13.17/3.59 | (91) sum(n0, n0) = n0
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (31) with n9, n2, all_0_0_0, n0 and discharging atoms sum(n9, n2) = all_0_0_0, sum(n9, n2) = n0, yields:
% 13.17/3.59 | (412) all_0_0_0 = n0
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (31) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 13.17/3.59 | (413) all_0_3_3 = n0
% 13.17/3.59 |
% 13.17/3.59 | Equations (412,413) can reduce 104 to:
% 13.17/3.59 | (251) $false
% 13.17/3.59 |
% 13.17/3.59 |-The branch is then unsatisfiable
% 13.17/3.59 |-Branch two:
% 13.17/3.59 | (607) ~ (all_0_10_10 = n1)
% 13.17/3.59 | (608) all_0_10_10 = n0
% 13.17/3.59 |
% 13.17/3.59 | From (608) and (211) follows:
% 13.17/3.59 | (609) pred(n0) = all_0_6_6
% 13.17/3.59 |
% 13.17/3.59 | From (608) and (41) follows:
% 13.17/3.59 | (610) succ(n0) = all_0_8_8
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (158) with n0, all_0_6_6, n10 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n10, yields:
% 13.17/3.59 | (611) all_0_6_6 = n10
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (141) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 13.17/3.59 | (612) all_0_8_8 = n1
% 13.17/3.59 |
% 13.17/3.59 | From (611)(612) and (178) follows:
% 13.17/3.59 | (613) sum(n10, n1) = all_0_1_1
% 13.17/3.59 |
% 13.17/3.59 | From (611) and (439) follows:
% 13.17/3.59 | (614) sum(n10, n0) = all_0_4_4
% 13.17/3.59 |
% 13.17/3.59 | From (612) and (441) follows:
% 13.17/3.59 | (615) sum(n9, n1) = all_0_7_7
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (31) with n10, n1, all_0_1_1, n0 and discharging atoms sum(n10, n1) = all_0_1_1, sum(n10, n1) = n0, yields:
% 13.17/3.59 | (616) all_0_1_1 = n0
% 13.17/3.59 |
% 13.17/3.59 | Instantiating formula (31) with n10, n0, all_0_4_4, n10 and discharging atoms sum(n10, n0) = all_0_4_4, sum(n10, n0) = n10, yields:
% 13.17/3.59 | (426) all_0_4_4 = n10
% 13.17/3.59 |
% 13.17/3.60 | Instantiating formula (31) with n9, n1, all_0_7_7, n10 and discharging atoms sum(n9, n1) = all_0_7_7, sum(n9, n1) = n10, yields:
% 13.17/3.60 | (425) all_0_7_7 = n10
% 13.17/3.60 |
% 13.17/3.60 | From (425)(426) and (119) follows:
% 13.17/3.60 | (428) sum(n10, n10) = all_0_3_3
% 13.17/3.60 |
% 13.17/3.60 | From (616) and (443) follows:
% 13.17/3.60 | (620) sum(n9, n0) = all_0_0_0
% 13.17/3.60 |
% 13.17/3.60 | Instantiating formula (31) with n10, n10, all_0_3_3, n9 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n9, yields:
% 13.17/3.60 | (429) all_0_3_3 = n9
% 13.17/3.60 |
% 13.17/3.60 | Instantiating formula (31) with n9, n0, all_0_0_0, n9 and discharging atoms sum(n9, n0) = all_0_0_0, sum(n9, n0) = n9, yields:
% 13.17/3.60 | (430) all_0_0_0 = n9
% 13.17/3.60 |
% 13.17/3.60 | Equations (430,429) can reduce 104 to:
% 13.17/3.60 | (251) $false
% 13.17/3.60 |
% 13.17/3.60 |-The branch is then unsatisfiable
% 13.17/3.60 |-Branch two:
% 13.17/3.60 | (252) ~ (all_0_11_11 = n10)
% 13.17/3.60 | (253) all_0_11_11 = n9 | all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.17/3.60 |
% 13.17/3.60 +-Applying beta-rule and splitting (433), into two cases.
% 13.17/3.60 |-Branch one:
% 13.17/3.60 | (445) all_0_10_10 = n9
% 13.17/3.60 |
% 13.17/3.60 | From (445) and (211) follows:
% 13.17/3.60 | (446) pred(n9) = all_0_6_6
% 13.17/3.60 |
% 13.17/3.60 | From (445) and (41) follows:
% 13.17/3.60 | (447) succ(n9) = all_0_8_8
% 13.17/3.60 |
% 13.17/3.60 | Instantiating formula (158) with n9, all_0_6_6, n8 and discharging atoms pred(n9) = all_0_6_6, pred(n9) = n8, yields:
% 13.17/3.60 | (448) all_0_6_6 = n8
% 13.17/3.60 |
% 13.17/3.60 | Instantiating formula (141) with n9, all_0_8_8, n10 and discharging atoms succ(n9) = all_0_8_8, succ(n9) = n10, yields:
% 13.17/3.60 | (449) all_0_8_8 = n10
% 13.17/3.60 |
% 13.17/3.60 | From (448) and (446) follows:
% 13.17/3.60 | (214) pred(n9) = n8
% 13.17/3.60 |
% 13.17/3.60 | From (449) and (447) follows:
% 13.17/3.60 | (184) succ(n9) = n10
% 13.17/3.60 |
% 13.17/3.60 | From (448) and (33) follows:
% 13.17/3.60 | (633) sum(n8, all_0_5_5) = all_0_4_4
% 13.17/3.60 |
% 13.17/3.60 | From (448)(449) and (178) follows:
% 13.17/3.60 | (450) sum(n8, n10) = all_0_1_1
% 13.17/3.60 |
% 13.17/3.60 | From (449) and (137) follows:
% 13.26/3.60 | (635) sum(all_0_9_9, n10) = all_0_7_7
% 13.26/3.60 |
% 13.26/3.60 | Instantiating formula (31) with n8, n10, all_0_1_1, n7 and discharging atoms sum(n8, n10) = all_0_1_1, sum(n8, n10) = n7, yields:
% 13.26/3.60 | (454) all_0_1_1 = n7
% 13.26/3.60 |
% 13.26/3.60 | From (454) and (4) follows:
% 13.26/3.60 | (637) sum(all_0_2_2, n7) = all_0_0_0
% 13.26/3.60 |
% 13.26/3.60 | From (454) and (450) follows:
% 13.26/3.60 | (75) sum(n8, n10) = n7
% 13.26/3.60 |
% 13.26/3.60 +-Applying beta-rule and splitting (253), into two cases.
% 13.26/3.60 |-Branch one:
% 13.26/3.60 | (254) all_0_11_11 = n9
% 13.26/3.60 |
% 13.26/3.60 | From (254) and (84) follows:
% 13.26/3.60 | (255) pred(n9) = all_0_9_9
% 13.26/3.60 |
% 13.26/3.60 | From (254) and (210) follows:
% 13.26/3.60 | (256) succ(n9) = all_0_5_5
% 13.26/3.60 |
% 13.26/3.60 | Instantiating formula (158) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 13.26/3.60 | (257) all_0_9_9 = n8
% 13.26/3.60 |
% 13.26/3.60 | Instantiating formula (141) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 13.26/3.60 | (258) all_0_5_5 = n10
% 13.26/3.60 |
% 13.26/3.60 | From (257)(258) and (48) follows:
% 13.26/3.60 | (259) sum(n8, n10) = all_0_2_2
% 13.26/3.60 |
% 13.26/3.60 | From (257) and (635) follows:
% 13.26/3.60 | (645) sum(n8, n10) = all_0_7_7
% 13.26/3.60 |
% 13.26/3.60 | From (258) and (633) follows:
% 13.26/3.60 | (646) sum(n8, n10) = all_0_4_4
% 13.26/3.60 |
% 13.26/3.60 | Instantiating formula (31) with n8, n10, all_0_2_2, n7 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n7, yields:
% 13.26/3.60 | (263) all_0_2_2 = n7
% 13.26/3.60 |
% 13.26/3.60 | Instantiating formula (31) 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:
% 13.26/3.60 | (238) all_0_2_2 = all_0_4_4
% 13.26/3.60 |
% 13.26/3.60 | Instantiating formula (31) 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:
% 13.26/3.60 | (239) all_0_2_2 = all_0_7_7
% 13.26/3.60 |
% 13.26/3.60 | Combining equations (239,238) yields a new equation:
% 13.26/3.60 | (240) all_0_4_4 = all_0_7_7
% 13.26/3.60 |
% 13.26/3.60 | Combining equations (263,238) yields a new equation:
% 13.26/3.60 | (280) all_0_4_4 = n7
% 13.26/3.60 |
% 13.26/3.60 | Combining equations (280,240) yields a new equation:
% 13.26/3.60 | (282) all_0_7_7 = n7
% 13.26/3.60 |
% 13.26/3.60 | Combining equations (282,240) yields a new equation:
% 13.26/3.60 | (280) all_0_4_4 = n7
% 13.26/3.60 |
% 13.26/3.60 | Combining equations (280,238) yields a new equation:
% 13.26/3.60 | (263) all_0_2_2 = n7
% 13.26/3.60 |
% 13.26/3.60 | From (263) and (637) follows:
% 13.26/3.60 | (655) sum(n7, n7) = all_0_0_0
% 13.26/3.60 |
% 13.26/3.60 | From (282)(280) and (119) follows:
% 13.26/3.60 | (284) sum(n7, n7) = all_0_3_3
% 13.26/3.60 |
% 13.26/3.60 | Instantiating formula (31) with n7, n7, all_0_0_0, n3 and discharging atoms sum(n7, n7) = all_0_0_0, sum(n7, n7) = n3, yields:
% 13.26/3.60 | (286) all_0_0_0 = n3
% 13.26/3.60 |
% 13.26/3.60 | Instantiating formula (31) with n7, n7, all_0_3_3, all_0_0_0 and discharging atoms sum(n7, n7) = all_0_0_0, sum(n7, n7) = all_0_3_3, yields:
% 13.26/3.60 | (248) all_0_0_0 = all_0_3_3
% 13.26/3.60 |
% 13.26/3.60 | Combining equations (286,248) yields a new equation:
% 13.26/3.60 | (285) all_0_3_3 = n3
% 13.26/3.60 |
% 13.26/3.60 | Combining equations (285,248) yields a new equation:
% 13.26/3.60 | (286) all_0_0_0 = n3
% 13.26/3.60 |
% 13.26/3.60 | Equations (286,285) can reduce 104 to:
% 13.26/3.60 | (251) $false
% 13.26/3.60 |
% 13.26/3.60 |-The branch is then unsatisfiable
% 13.26/3.60 |-Branch two:
% 13.26/3.60 | (270) ~ (all_0_11_11 = n9)
% 13.26/3.60 | (271) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.26/3.60 |
% 13.26/3.60 +-Applying beta-rule and splitting (271), into two cases.
% 13.26/3.60 |-Branch one:
% 13.26/3.60 | (272) all_0_11_11 = n8
% 13.26/3.60 |
% 13.26/3.60 | From (272) and (84) follows:
% 13.26/3.60 | (273) pred(n8) = all_0_9_9
% 13.26/3.60 |
% 13.26/3.60 | From (272) and (210) follows:
% 13.26/3.60 | (274) succ(n8) = all_0_5_5
% 13.26/3.60 |
% 13.26/3.60 | Instantiating formula (158) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 13.26/3.60 | (275) all_0_9_9 = n7
% 13.26/3.60 |
% 13.26/3.60 | Instantiating formula (141) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 13.26/3.60 | (276) all_0_5_5 = n9
% 13.26/3.60 |
% 13.26/3.60 | From (275)(276) and (48) follows:
% 13.26/3.60 | (277) sum(n7, n9) = all_0_2_2
% 13.26/3.60 |
% 13.26/3.60 | From (275) and (635) follows:
% 13.26/3.60 | (670) sum(n7, n10) = all_0_7_7
% 13.26/3.60 |
% 13.26/3.60 | From (276) and (633) follows:
% 13.26/3.60 | (671) sum(n8, n9) = all_0_4_4
% 13.26/3.60 |
% 13.26/3.60 | Instantiating formula (31) with n8, n9, all_0_4_4, n6 and discharging atoms sum(n8, n9) = all_0_4_4, sum(n8, n9) = n6, yields:
% 13.26/3.60 | (298) all_0_4_4 = n6
% 13.26/3.60 |
% 13.26/3.60 | Instantiating formula (31) with n7, n10, all_0_7_7, n6 and discharging atoms sum(n7, n10) = all_0_7_7, sum(n7, n10) = n6, yields:
% 13.26/3.60 | (300) all_0_7_7 = n6
% 13.26/3.60 |
% 13.26/3.60 | Instantiating formula (31) with n7, n9, all_0_2_2, n5 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n5, yields:
% 13.26/3.60 | (281) all_0_2_2 = n5
% 13.26/3.60 |
% 13.26/3.60 | From (281) and (637) follows:
% 13.26/3.60 | (675) sum(n5, n7) = all_0_0_0
% 13.26/3.60 |
% 13.26/3.60 | From (300)(298) and (119) follows:
% 13.26/3.60 | (302) sum(n6, n6) = all_0_3_3
% 13.26/3.60 |
% 13.26/3.60 | Instantiating formula (31) with n6, n6, all_0_3_3, n1 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n1, yields:
% 13.26/3.60 | (303) all_0_3_3 = n1
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n5, n7, all_0_0_0, n1 and discharging atoms sum(n5, n7) = all_0_0_0, sum(n5, n7) = n1, yields:
% 13.26/3.61 | (304) all_0_0_0 = n1
% 13.26/3.61 |
% 13.26/3.61 | Equations (304,303) can reduce 104 to:
% 13.26/3.61 | (251) $false
% 13.26/3.61 |
% 13.26/3.61 |-The branch is then unsatisfiable
% 13.26/3.61 |-Branch two:
% 13.26/3.61 | (288) ~ (all_0_11_11 = n8)
% 13.26/3.61 | (289) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.26/3.61 |
% 13.26/3.61 +-Applying beta-rule and splitting (289), into two cases.
% 13.26/3.61 |-Branch one:
% 13.26/3.61 | (290) all_0_11_11 = n7
% 13.26/3.61 |
% 13.26/3.61 | From (290) and (84) follows:
% 13.26/3.61 | (291) pred(n7) = all_0_9_9
% 13.26/3.61 |
% 13.26/3.61 | From (290) and (210) follows:
% 13.26/3.61 | (292) succ(n7) = all_0_5_5
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (158) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 13.26/3.61 | (293) all_0_9_9 = n6
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (141) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 13.26/3.61 | (294) all_0_5_5 = n8
% 13.26/3.61 |
% 13.26/3.61 | From (293)(294) and (48) follows:
% 13.26/3.61 | (295) sum(n6, n8) = all_0_2_2
% 13.26/3.61 |
% 13.26/3.61 | From (293) and (635) follows:
% 13.26/3.61 | (688) sum(n6, n10) = all_0_7_7
% 13.26/3.61 |
% 13.26/3.61 | From (294) and (633) follows:
% 13.26/3.61 | (689) sum(n8, n8) = all_0_4_4
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n8, n8, all_0_4_4, n5 and discharging atoms sum(n8, n8) = all_0_4_4, sum(n8, n8) = n5, yields:
% 13.26/3.61 | (316) all_0_4_4 = n5
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n6, n10, all_0_7_7, n5 and discharging atoms sum(n6, n10) = all_0_7_7, sum(n6, n10) = n5, yields:
% 13.26/3.61 | (318) all_0_7_7 = n5
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n6, n8, all_0_2_2, n3 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n3, yields:
% 13.26/3.61 | (299) all_0_2_2 = n3
% 13.26/3.61 |
% 13.26/3.61 | From (299) and (637) follows:
% 13.26/3.61 | (693) sum(n3, n7) = all_0_0_0
% 13.26/3.61 |
% 13.26/3.61 | From (318)(316) and (119) follows:
% 13.26/3.61 | (320) sum(n5, n5) = all_0_3_3
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 13.26/3.61 | (321) all_0_3_3 = n10
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n3, n7, all_0_0_0, n10 and discharging atoms sum(n3, n7) = all_0_0_0, sum(n3, n7) = n10, yields:
% 13.26/3.61 | (322) all_0_0_0 = n10
% 13.26/3.61 |
% 13.26/3.61 | Equations (322,321) can reduce 104 to:
% 13.26/3.61 | (251) $false
% 13.26/3.61 |
% 13.26/3.61 |-The branch is then unsatisfiable
% 13.26/3.61 |-Branch two:
% 13.26/3.61 | (306) ~ (all_0_11_11 = n7)
% 13.26/3.61 | (307) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.26/3.61 |
% 13.26/3.61 +-Applying beta-rule and splitting (307), into two cases.
% 13.26/3.61 |-Branch one:
% 13.26/3.61 | (308) all_0_11_11 = n6
% 13.26/3.61 |
% 13.26/3.61 | From (308) and (84) follows:
% 13.26/3.61 | (309) pred(n6) = all_0_9_9
% 13.26/3.61 |
% 13.26/3.61 | From (308) and (210) follows:
% 13.26/3.61 | (310) succ(n6) = all_0_5_5
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (158) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 13.26/3.61 | (311) all_0_9_9 = n5
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (141) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 13.26/3.61 | (312) all_0_5_5 = n7
% 13.26/3.61 |
% 13.26/3.61 | From (311)(312) and (48) follows:
% 13.26/3.61 | (313) sum(n5, n7) = all_0_2_2
% 13.26/3.61 |
% 13.26/3.61 | From (311) and (635) follows:
% 13.26/3.61 | (706) sum(n5, n10) = all_0_7_7
% 13.26/3.61 |
% 13.26/3.61 | From (312) and (633) follows:
% 13.26/3.61 | (707) sum(n8, n7) = all_0_4_4
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n8, n7, all_0_4_4, n4 and discharging atoms sum(n8, n7) = all_0_4_4, sum(n8, n7) = n4, yields:
% 13.26/3.61 | (334) all_0_4_4 = n4
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n5, n10, all_0_7_7, n4 and discharging atoms sum(n5, n10) = all_0_7_7, sum(n5, n10) = n4, yields:
% 13.26/3.61 | (336) all_0_7_7 = n4
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n5, n7, all_0_2_2, n1 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n1, yields:
% 13.26/3.61 | (317) all_0_2_2 = n1
% 13.26/3.61 |
% 13.26/3.61 | From (317) and (637) follows:
% 13.26/3.61 | (711) sum(n1, n7) = all_0_0_0
% 13.26/3.61 |
% 13.26/3.61 | From (336)(334) and (119) follows:
% 13.26/3.61 | (338) sum(n4, n4) = all_0_3_3
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 13.26/3.61 | (340) all_0_3_3 = n8
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n1, n7, all_0_0_0, n8 and discharging atoms sum(n1, n7) = all_0_0_0, sum(n1, n7) = n8, yields:
% 13.26/3.61 | (339) all_0_0_0 = n8
% 13.26/3.61 |
% 13.26/3.61 | Equations (339,340) can reduce 104 to:
% 13.26/3.61 | (251) $false
% 13.26/3.61 |
% 13.26/3.61 |-The branch is then unsatisfiable
% 13.26/3.61 |-Branch two:
% 13.26/3.61 | (324) ~ (all_0_11_11 = n6)
% 13.26/3.61 | (325) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.26/3.61 |
% 13.26/3.61 +-Applying beta-rule and splitting (325), into two cases.
% 13.26/3.61 |-Branch one:
% 13.26/3.61 | (326) all_0_11_11 = n5
% 13.26/3.61 |
% 13.26/3.61 | From (326) and (84) follows:
% 13.26/3.61 | (327) pred(n5) = all_0_9_9
% 13.26/3.61 |
% 13.26/3.61 | From (326) and (210) follows:
% 13.26/3.61 | (328) succ(n5) = all_0_5_5
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (158) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 13.26/3.61 | (329) all_0_9_9 = n4
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (141) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 13.26/3.61 | (330) all_0_5_5 = n6
% 13.26/3.61 |
% 13.26/3.61 | From (329)(330) and (48) follows:
% 13.26/3.61 | (331) sum(n4, n6) = all_0_2_2
% 13.26/3.61 |
% 13.26/3.61 | From (329) and (635) follows:
% 13.26/3.61 | (724) sum(n4, n10) = all_0_7_7
% 13.26/3.61 |
% 13.26/3.61 | From (330) and (633) follows:
% 13.26/3.61 | (725) sum(n8, n6) = all_0_4_4
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n8, n6, all_0_4_4, n3 and discharging atoms sum(n8, n6) = all_0_4_4, sum(n8, n6) = n3, yields:
% 13.26/3.61 | (352) all_0_4_4 = n3
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n4, n10, all_0_7_7, n3 and discharging atoms sum(n4, n10) = all_0_7_7, sum(n4, n10) = n3, yields:
% 13.26/3.61 | (354) all_0_7_7 = n3
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 13.26/3.61 | (335) all_0_2_2 = n10
% 13.26/3.61 |
% 13.26/3.61 | From (335) and (637) follows:
% 13.26/3.61 | (729) sum(n10, n7) = all_0_0_0
% 13.26/3.61 |
% 13.26/3.61 | From (354)(352) and (119) follows:
% 13.26/3.61 | (356) sum(n3, n3) = all_0_3_3
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n10, n7, all_0_0_0, n6 and discharging atoms sum(n10, n7) = all_0_0_0, sum(n10, n7) = n6, yields:
% 13.26/3.61 | (357) all_0_0_0 = n6
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 13.26/3.61 | (358) all_0_3_3 = n6
% 13.26/3.61 |
% 13.26/3.61 | Equations (357,358) can reduce 104 to:
% 13.26/3.61 | (251) $false
% 13.26/3.61 |
% 13.26/3.61 |-The branch is then unsatisfiable
% 13.26/3.61 |-Branch two:
% 13.26/3.61 | (342) ~ (all_0_11_11 = n5)
% 13.26/3.61 | (343) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.26/3.61 |
% 13.26/3.61 +-Applying beta-rule and splitting (343), into two cases.
% 13.26/3.61 |-Branch one:
% 13.26/3.61 | (344) all_0_11_11 = n4
% 13.26/3.61 |
% 13.26/3.61 | From (344) and (84) follows:
% 13.26/3.61 | (345) pred(n4) = all_0_9_9
% 13.26/3.61 |
% 13.26/3.61 | From (344) and (210) follows:
% 13.26/3.61 | (346) succ(n4) = all_0_5_5
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (158) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 13.26/3.61 | (347) all_0_9_9 = n3
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (141) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 13.26/3.61 | (348) all_0_5_5 = n5
% 13.26/3.61 |
% 13.26/3.61 | From (347)(348) and (48) follows:
% 13.26/3.61 | (349) sum(n3, n5) = all_0_2_2
% 13.26/3.61 |
% 13.26/3.61 | From (347) and (635) follows:
% 13.26/3.61 | (742) sum(n3, n10) = all_0_7_7
% 13.26/3.61 |
% 13.26/3.61 | From (348) and (633) follows:
% 13.26/3.61 | (743) sum(n8, n5) = all_0_4_4
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n8, n5, all_0_4_4, n2 and discharging atoms sum(n8, n5) = all_0_4_4, sum(n8, n5) = n2, yields:
% 13.26/3.61 | (370) all_0_4_4 = n2
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n3, n10, all_0_7_7, n2 and discharging atoms sum(n3, n10) = all_0_7_7, sum(n3, n10) = n2, yields:
% 13.26/3.61 | (372) all_0_7_7 = n2
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 13.26/3.61 | (353) all_0_2_2 = n8
% 13.26/3.61 |
% 13.26/3.61 | From (353) and (637) follows:
% 13.26/3.61 | (747) sum(n8, n7) = all_0_0_0
% 13.26/3.61 |
% 13.26/3.61 | From (372)(370) and (119) follows:
% 13.26/3.61 | (374) sum(n2, n2) = all_0_3_3
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n8, n7, all_0_0_0, n4 and discharging atoms sum(n8, n7) = all_0_0_0, sum(n8, n7) = n4, yields:
% 13.26/3.61 | (375) all_0_0_0 = n4
% 13.26/3.61 |
% 13.26/3.61 | Instantiating formula (31) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 13.26/3.61 | (376) all_0_3_3 = n4
% 13.26/3.61 |
% 13.26/3.61 | Equations (375,376) can reduce 104 to:
% 13.26/3.61 | (251) $false
% 13.26/3.61 |
% 13.26/3.61 |-The branch is then unsatisfiable
% 13.26/3.61 |-Branch two:
% 13.26/3.61 | (360) ~ (all_0_11_11 = n4)
% 13.26/3.61 | (361) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.26/3.62 |
% 13.26/3.62 +-Applying beta-rule and splitting (361), into two cases.
% 13.26/3.62 |-Branch one:
% 13.26/3.62 | (362) all_0_11_11 = n3
% 13.26/3.62 |
% 13.26/3.62 | From (362) and (84) follows:
% 13.26/3.62 | (363) pred(n3) = all_0_9_9
% 13.26/3.62 |
% 13.26/3.62 | From (362) and (210) follows:
% 13.26/3.62 | (364) succ(n3) = all_0_5_5
% 13.26/3.62 |
% 13.26/3.62 | Instantiating formula (158) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 13.26/3.62 | (365) all_0_9_9 = n2
% 13.26/3.62 |
% 13.26/3.62 | Instantiating formula (141) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 13.26/3.62 | (366) all_0_5_5 = n4
% 13.26/3.62 |
% 13.26/3.62 | From (365)(366) and (48) follows:
% 13.26/3.62 | (367) sum(n2, n4) = all_0_2_2
% 13.26/3.62 |
% 13.26/3.62 | From (365) and (635) follows:
% 13.26/3.62 | (760) sum(n2, n10) = all_0_7_7
% 13.26/3.62 |
% 13.26/3.62 | From (366) and (633) follows:
% 13.26/3.62 | (761) sum(n8, n4) = all_0_4_4
% 13.26/3.62 |
% 13.26/3.62 | Instantiating formula (31) with n8, n4, all_0_4_4, n1 and discharging atoms sum(n8, n4) = all_0_4_4, sum(n8, n4) = n1, yields:
% 13.26/3.62 | (388) all_0_4_4 = n1
% 13.26/3.62 |
% 13.26/3.62 | Instantiating formula (31) with n2, n10, all_0_7_7, n1 and discharging atoms sum(n2, n10) = all_0_7_7, sum(n2, n10) = n1, yields:
% 13.26/3.62 | (390) all_0_7_7 = n1
% 13.26/3.62 |
% 13.26/3.62 | Instantiating formula (31) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 13.26/3.62 | (371) all_0_2_2 = n6
% 13.26/3.62 |
% 13.26/3.62 | From (371) and (637) follows:
% 13.26/3.62 | (765) sum(n6, n7) = all_0_0_0
% 13.26/3.62 |
% 13.26/3.62 | From (390)(388) and (119) follows:
% 13.26/3.62 | (392) sum(n1, n1) = all_0_3_3
% 13.26/3.62 |
% 13.26/3.62 | Instantiating formula (31) with n6, n7, all_0_0_0, n2 and discharging atoms sum(n6, n7) = all_0_0_0, sum(n6, n7) = n2, yields:
% 13.26/3.62 | (393) all_0_0_0 = n2
% 13.26/3.62 |
% 13.26/3.62 | Instantiating formula (31) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 13.26/3.62 | (394) all_0_3_3 = n2
% 13.26/3.62 |
% 13.26/3.62 | Equations (393,394) can reduce 104 to:
% 13.26/3.62 | (251) $false
% 13.26/3.62 |
% 13.26/3.62 |-The branch is then unsatisfiable
% 13.26/3.62 |-Branch two:
% 13.26/3.62 | (378) ~ (all_0_11_11 = n3)
% 13.26/3.62 | (379) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.26/3.62 |
% 13.26/3.62 +-Applying beta-rule and splitting (379), into two cases.
% 13.26/3.62 |-Branch one:
% 13.26/3.62 | (380) all_0_11_11 = n2
% 13.36/3.62 |
% 13.36/3.62 | From (380) and (84) follows:
% 13.36/3.62 | (381) pred(n2) = all_0_9_9
% 13.36/3.62 |
% 13.36/3.62 | From (380) and (210) follows:
% 13.36/3.62 | (382) succ(n2) = all_0_5_5
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (158) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 13.36/3.62 | (383) all_0_9_9 = n1
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (141) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 13.36/3.62 | (384) all_0_5_5 = n3
% 13.36/3.62 |
% 13.36/3.62 | From (383)(384) and (48) follows:
% 13.36/3.62 | (385) sum(n1, n3) = all_0_2_2
% 13.36/3.62 |
% 13.36/3.62 | From (383) and (635) follows:
% 13.36/3.62 | (778) sum(n1, n10) = all_0_7_7
% 13.36/3.62 |
% 13.36/3.62 | From (384) and (633) follows:
% 13.36/3.62 | (779) sum(n8, n3) = all_0_4_4
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (31) with n8, n3, all_0_4_4, n0 and discharging atoms sum(n8, n3) = all_0_4_4, sum(n8, n3) = n0, yields:
% 13.36/3.62 | (406) all_0_4_4 = n0
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (31) with n1, n10, all_0_7_7, n0 and discharging atoms sum(n1, n10) = all_0_7_7, sum(n1, n10) = n0, yields:
% 13.36/3.62 | (408) all_0_7_7 = n0
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (31) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 13.36/3.62 | (389) all_0_2_2 = n4
% 13.36/3.62 |
% 13.36/3.62 | From (389) and (637) follows:
% 13.36/3.62 | (783) sum(n4, n7) = all_0_0_0
% 13.36/3.62 |
% 13.36/3.62 | From (408)(406) and (119) follows:
% 13.36/3.62 | (410) sum(n0, n0) = all_0_3_3
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (31) with n4, n7, all_0_0_0, n0 and discharging atoms sum(n4, n7) = all_0_0_0, sum(n4, n7) = n0, yields:
% 13.36/3.62 | (412) all_0_0_0 = n0
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (31) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 13.36/3.62 | (413) all_0_3_3 = n0
% 13.36/3.62 |
% 13.36/3.62 | Equations (412,413) can reduce 104 to:
% 13.36/3.62 | (251) $false
% 13.36/3.62 |
% 13.36/3.62 |-The branch is then unsatisfiable
% 13.36/3.62 |-Branch two:
% 13.36/3.62 | (396) ~ (all_0_11_11 = n2)
% 13.36/3.62 | (397) all_0_11_11 = n1 | all_0_11_11 = n0
% 13.36/3.62 |
% 13.36/3.62 +-Applying beta-rule and splitting (397), into two cases.
% 13.36/3.62 |-Branch one:
% 13.36/3.62 | (398) all_0_11_11 = n1
% 13.36/3.62 |
% 13.36/3.62 | From (398) and (84) follows:
% 13.36/3.62 | (399) pred(n1) = all_0_9_9
% 13.36/3.62 |
% 13.36/3.62 | From (398) and (210) follows:
% 13.36/3.62 | (400) succ(n1) = all_0_5_5
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (158) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 13.36/3.62 | (401) all_0_9_9 = n0
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (141) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 13.36/3.62 | (402) all_0_5_5 = n2
% 13.36/3.62 |
% 13.36/3.62 | From (401)(402) and (48) follows:
% 13.36/3.62 | (403) sum(n0, n2) = all_0_2_2
% 13.36/3.62 |
% 13.36/3.62 | From (401) and (635) follows:
% 13.36/3.62 | (796) sum(n0, n10) = all_0_7_7
% 13.36/3.62 |
% 13.36/3.62 | From (402) and (633) follows:
% 13.36/3.62 | (797) sum(n8, n2) = all_0_4_4
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (31) with n8, n2, all_0_4_4, n10 and discharging atoms sum(n8, n2) = all_0_4_4, sum(n8, n2) = n10, yields:
% 13.36/3.62 | (426) all_0_4_4 = n10
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (31) with n0, n10, all_0_7_7, n10 and discharging atoms sum(n0, n10) = all_0_7_7, sum(n0, n10) = n10, yields:
% 13.36/3.62 | (425) all_0_7_7 = n10
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (31) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 13.36/3.62 | (407) all_0_2_2 = n2
% 13.36/3.62 |
% 13.36/3.62 | From (407) and (637) follows:
% 13.36/3.62 | (801) sum(n2, n7) = all_0_0_0
% 13.36/3.62 |
% 13.36/3.62 | From (425)(426) and (119) follows:
% 13.36/3.62 | (428) sum(n10, n10) = all_0_3_3
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (31) with n10, n10, all_0_3_3, n9 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n9, yields:
% 13.36/3.62 | (429) all_0_3_3 = n9
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (31) with n2, n7, all_0_0_0, n9 and discharging atoms sum(n2, n7) = all_0_0_0, sum(n2, n7) = n9, yields:
% 13.36/3.62 | (430) all_0_0_0 = n9
% 13.36/3.62 |
% 13.36/3.62 | Equations (430,429) can reduce 104 to:
% 13.36/3.62 | (251) $false
% 13.36/3.62 |
% 13.36/3.62 |-The branch is then unsatisfiable
% 13.36/3.62 |-Branch two:
% 13.36/3.62 | (415) ~ (all_0_11_11 = n1)
% 13.36/3.62 | (416) all_0_11_11 = n0
% 13.36/3.62 |
% 13.36/3.62 | From (416) and (84) follows:
% 13.36/3.62 | (417) pred(n0) = all_0_9_9
% 13.36/3.62 |
% 13.36/3.62 | From (416) and (210) follows:
% 13.36/3.62 | (418) succ(n0) = all_0_5_5
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (158) with n0, all_0_9_9, n10 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n10, yields:
% 13.36/3.62 | (419) all_0_9_9 = n10
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (141) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 13.36/3.62 | (420) all_0_5_5 = n1
% 13.36/3.62 |
% 13.36/3.62 | From (419)(420) and (48) follows:
% 13.36/3.62 | (421) sum(n10, n1) = all_0_2_2
% 13.36/3.62 |
% 13.36/3.62 | From (419) and (635) follows:
% 13.36/3.62 | (813) sum(n10, n10) = all_0_7_7
% 13.36/3.62 |
% 13.36/3.62 | From (420) and (633) follows:
% 13.36/3.62 | (814) sum(n8, n1) = all_0_4_4
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (31) with n10, n10, all_0_7_7, n9 and discharging atoms sum(n10, n10) = all_0_7_7, sum(n10, n10) = n9, yields:
% 13.36/3.62 | (242) all_0_7_7 = n9
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (31) with n10, n1, all_0_2_2, n0 and discharging atoms sum(n10, n1) = all_0_2_2, sum(n10, n1) = n0, yields:
% 13.36/3.62 | (424) all_0_2_2 = n0
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (31) with n8, n1, all_0_4_4, n9 and discharging atoms sum(n8, n1) = all_0_4_4, sum(n8, n1) = n9, yields:
% 13.36/3.62 | (241) all_0_4_4 = n9
% 13.36/3.62 |
% 13.36/3.62 | From (424) and (637) follows:
% 13.36/3.62 | (818) sum(n0, n7) = all_0_0_0
% 13.36/3.62 |
% 13.36/3.62 | From (242)(241) and (119) follows:
% 13.36/3.62 | (246) sum(n9, n9) = all_0_3_3
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (31) with n9, n9, all_0_3_3, n7 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n7, yields:
% 13.36/3.62 | (249) all_0_3_3 = n7
% 13.36/3.62 |
% 13.36/3.62 | Instantiating formula (31) with n0, n7, all_0_0_0, n7 and discharging atoms sum(n0, n7) = all_0_0_0, sum(n0, n7) = n7, yields:
% 13.36/3.62 | (247) all_0_0_0 = n7
% 13.36/3.62 |
% 13.36/3.62 | Equations (247,249) can reduce 104 to:
% 13.36/3.62 | (251) $false
% 13.36/3.62 |
% 13.36/3.62 |-The branch is then unsatisfiable
% 13.36/3.62 |-Branch two:
% 13.36/3.62 | (461) ~ (all_0_10_10 = n9)
% 13.36/3.63 | (462) all_0_10_10 = n8 | all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.36/3.63 |
% 13.36/3.63 +-Applying beta-rule and splitting (253), into two cases.
% 13.36/3.63 |-Branch one:
% 13.36/3.63 | (254) all_0_11_11 = n9
% 13.36/3.63 |
% 13.36/3.63 | From (254) and (84) follows:
% 13.36/3.63 | (255) pred(n9) = all_0_9_9
% 13.36/3.63 |
% 13.36/3.63 | From (254) and (210) follows:
% 13.36/3.63 | (256) succ(n9) = all_0_5_5
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (158) with n9, all_0_9_9, n8 and discharging atoms pred(n9) = all_0_9_9, pred(n9) = n8, yields:
% 13.36/3.63 | (257) all_0_9_9 = n8
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (141) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 13.36/3.63 | (258) all_0_5_5 = n10
% 13.36/3.63 |
% 13.36/3.63 | From (258) and (33) follows:
% 13.36/3.63 | (830) sum(all_0_6_6, n10) = all_0_4_4
% 13.36/3.63 |
% 13.36/3.63 | From (257)(258) and (48) follows:
% 13.36/3.63 | (259) sum(n8, n10) = all_0_2_2
% 13.36/3.63 |
% 13.36/3.63 | From (257) and (137) follows:
% 13.36/3.63 | (832) sum(n8, all_0_8_8) = all_0_7_7
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (31) with n8, n10, all_0_2_2, n7 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n7, yields:
% 13.36/3.63 | (263) all_0_2_2 = n7
% 13.36/3.63 |
% 13.36/3.63 | From (263) and (4) follows:
% 13.36/3.63 | (834) sum(n7, all_0_1_1) = all_0_0_0
% 13.36/3.63 |
% 13.36/3.63 +-Applying beta-rule and splitting (462), into two cases.
% 13.36/3.63 |-Branch one:
% 13.36/3.63 | (463) all_0_10_10 = n8
% 13.36/3.63 |
% 13.36/3.63 | From (463) and (211) follows:
% 13.36/3.63 | (464) pred(n8) = all_0_6_6
% 13.36/3.63 |
% 13.36/3.63 | From (463) and (41) follows:
% 13.36/3.63 | (465) succ(n8) = all_0_8_8
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (158) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 13.36/3.63 | (466) all_0_6_6 = n7
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (141) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 13.36/3.63 | (467) all_0_8_8 = n9
% 13.36/3.63 |
% 13.36/3.63 | From (466)(467) and (178) follows:
% 13.36/3.63 | (468) sum(n7, n9) = all_0_1_1
% 13.36/3.63 |
% 13.36/3.63 | From (466) and (830) follows:
% 13.36/3.63 | (841) sum(n7, n10) = all_0_4_4
% 13.36/3.63 |
% 13.36/3.63 | From (467) and (832) follows:
% 13.36/3.63 | (842) sum(n8, n9) = all_0_7_7
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (31) with n8, n9, all_0_7_7, n6 and discharging atoms sum(n8, n9) = all_0_7_7, sum(n8, n9) = n6, yields:
% 13.36/3.63 | (300) all_0_7_7 = n6
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (31) with n7, n10, all_0_4_4, n6 and discharging atoms sum(n7, n10) = all_0_4_4, sum(n7, n10) = n6, yields:
% 13.36/3.63 | (298) all_0_4_4 = n6
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (31) with n7, n9, all_0_1_1, n5 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n5, yields:
% 13.36/3.63 | (472) all_0_1_1 = n5
% 13.36/3.63 |
% 13.36/3.63 | From (300)(298) and (119) follows:
% 13.36/3.63 | (302) sum(n6, n6) = all_0_3_3
% 13.36/3.63 |
% 13.36/3.63 | From (472) and (834) follows:
% 13.36/3.63 | (847) sum(n7, n5) = all_0_0_0
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (31) with n7, n5, all_0_0_0, n1 and discharging atoms sum(n7, n5) = all_0_0_0, sum(n7, n5) = n1, yields:
% 13.36/3.63 | (304) all_0_0_0 = n1
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (31) with n6, n6, all_0_3_3, n1 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n1, yields:
% 13.36/3.63 | (303) all_0_3_3 = n1
% 13.36/3.63 |
% 13.36/3.63 | Equations (304,303) can reduce 104 to:
% 13.36/3.63 | (251) $false
% 13.36/3.63 |
% 13.36/3.63 |-The branch is then unsatisfiable
% 13.36/3.63 |-Branch two:
% 13.36/3.63 | (479) ~ (all_0_10_10 = n8)
% 13.36/3.63 | (480) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.36/3.63 |
% 13.36/3.63 +-Applying beta-rule and splitting (480), into two cases.
% 13.36/3.63 |-Branch one:
% 13.36/3.63 | (481) all_0_10_10 = n7
% 13.36/3.63 |
% 13.36/3.63 | From (481) and (211) follows:
% 13.36/3.63 | (482) pred(n7) = all_0_6_6
% 13.36/3.63 |
% 13.36/3.63 | From (481) and (41) follows:
% 13.36/3.63 | (483) succ(n7) = all_0_8_8
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (158) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 13.36/3.63 | (484) all_0_6_6 = n6
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (141) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 13.36/3.63 | (485) all_0_8_8 = n8
% 13.36/3.63 |
% 13.36/3.63 | From (484)(485) and (178) follows:
% 13.36/3.63 | (486) sum(n6, n8) = all_0_1_1
% 13.36/3.63 |
% 13.36/3.63 | From (484) and (830) follows:
% 13.36/3.63 | (859) sum(n6, n10) = all_0_4_4
% 13.36/3.63 |
% 13.36/3.63 | From (485) and (832) follows:
% 13.36/3.63 | (860) sum(n8, n8) = all_0_7_7
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (31) with n8, n8, all_0_7_7, n5 and discharging atoms sum(n8, n8) = all_0_7_7, sum(n8, n8) = n5, yields:
% 13.36/3.63 | (318) all_0_7_7 = n5
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (31) with n6, n10, all_0_4_4, n5 and discharging atoms sum(n6, n10) = all_0_4_4, sum(n6, n10) = n5, yields:
% 13.36/3.63 | (316) all_0_4_4 = n5
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (31) with n6, n8, all_0_1_1, n3 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n3, yields:
% 13.36/3.63 | (490) all_0_1_1 = n3
% 13.36/3.63 |
% 13.36/3.63 | From (318)(316) and (119) follows:
% 13.36/3.63 | (320) sum(n5, n5) = all_0_3_3
% 13.36/3.63 |
% 13.36/3.63 | From (490) and (834) follows:
% 13.36/3.63 | (865) sum(n7, n3) = all_0_0_0
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (31) with n7, n3, all_0_0_0, n10 and discharging atoms sum(n7, n3) = all_0_0_0, sum(n7, n3) = n10, yields:
% 13.36/3.63 | (322) all_0_0_0 = n10
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (31) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 13.36/3.63 | (321) all_0_3_3 = n10
% 13.36/3.63 |
% 13.36/3.63 | Equations (322,321) can reduce 104 to:
% 13.36/3.63 | (251) $false
% 13.36/3.63 |
% 13.36/3.63 |-The branch is then unsatisfiable
% 13.36/3.63 |-Branch two:
% 13.36/3.63 | (497) ~ (all_0_10_10 = n7)
% 13.36/3.63 | (498) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.36/3.63 |
% 13.36/3.63 +-Applying beta-rule and splitting (498), into two cases.
% 13.36/3.63 |-Branch one:
% 13.36/3.63 | (499) all_0_10_10 = n6
% 13.36/3.63 |
% 13.36/3.63 | From (499) and (211) follows:
% 13.36/3.63 | (500) pred(n6) = all_0_6_6
% 13.36/3.63 |
% 13.36/3.63 | From (499) and (41) follows:
% 13.36/3.63 | (501) succ(n6) = all_0_8_8
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (158) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 13.36/3.63 | (502) all_0_6_6 = n5
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (141) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 13.36/3.63 | (503) all_0_8_8 = n7
% 13.36/3.63 |
% 13.36/3.63 | From (502)(503) and (178) follows:
% 13.36/3.63 | (504) sum(n5, n7) = all_0_1_1
% 13.36/3.63 |
% 13.36/3.63 | From (502) and (830) follows:
% 13.36/3.63 | (877) sum(n5, n10) = all_0_4_4
% 13.36/3.63 |
% 13.36/3.63 | From (503) and (832) follows:
% 13.36/3.63 | (878) sum(n8, n7) = all_0_7_7
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (31) with n8, n7, all_0_7_7, n4 and discharging atoms sum(n8, n7) = all_0_7_7, sum(n8, n7) = n4, yields:
% 13.36/3.63 | (336) all_0_7_7 = n4
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (31) with n5, n10, all_0_4_4, n4 and discharging atoms sum(n5, n10) = all_0_4_4, sum(n5, n10) = n4, yields:
% 13.36/3.63 | (334) all_0_4_4 = n4
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (31) with n5, n7, all_0_1_1, n1 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n1, yields:
% 13.36/3.63 | (508) all_0_1_1 = n1
% 13.36/3.63 |
% 13.36/3.63 | From (336)(334) and (119) follows:
% 13.36/3.63 | (338) sum(n4, n4) = all_0_3_3
% 13.36/3.63 |
% 13.36/3.63 | From (508) and (834) follows:
% 13.36/3.63 | (883) sum(n7, n1) = all_0_0_0
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (31) with n7, n1, all_0_0_0, n8 and discharging atoms sum(n7, n1) = all_0_0_0, sum(n7, n1) = n8, yields:
% 13.36/3.63 | (339) all_0_0_0 = n8
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (31) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 13.36/3.63 | (340) all_0_3_3 = n8
% 13.36/3.63 |
% 13.36/3.63 | Equations (339,340) can reduce 104 to:
% 13.36/3.63 | (251) $false
% 13.36/3.63 |
% 13.36/3.63 |-The branch is then unsatisfiable
% 13.36/3.63 |-Branch two:
% 13.36/3.63 | (515) ~ (all_0_10_10 = n6)
% 13.36/3.63 | (516) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.36/3.63 |
% 13.36/3.63 +-Applying beta-rule and splitting (516), into two cases.
% 13.36/3.63 |-Branch one:
% 13.36/3.63 | (517) all_0_10_10 = n5
% 13.36/3.63 |
% 13.36/3.63 | From (517) and (211) follows:
% 13.36/3.63 | (518) pred(n5) = all_0_6_6
% 13.36/3.63 |
% 13.36/3.63 | From (517) and (41) follows:
% 13.36/3.63 | (519) succ(n5) = all_0_8_8
% 13.36/3.63 |
% 13.36/3.63 | Instantiating formula (158) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 13.43/3.63 | (520) all_0_6_6 = n4
% 13.43/3.63 |
% 13.43/3.63 | Instantiating formula (141) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 13.43/3.63 | (521) all_0_8_8 = n6
% 13.43/3.63 |
% 13.43/3.63 | From (520)(521) and (178) follows:
% 13.43/3.63 | (522) sum(n4, n6) = all_0_1_1
% 13.43/3.63 |
% 13.43/3.63 | From (520) and (830) follows:
% 13.43/3.63 | (895) sum(n4, n10) = all_0_4_4
% 13.43/3.63 |
% 13.43/3.63 | From (521) and (832) follows:
% 13.43/3.63 | (896) sum(n8, n6) = all_0_7_7
% 13.43/3.63 |
% 13.43/3.63 | Instantiating formula (31) with n8, n6, all_0_7_7, n3 and discharging atoms sum(n8, n6) = all_0_7_7, sum(n8, n6) = n3, yields:
% 13.43/3.63 | (354) all_0_7_7 = n3
% 13.43/3.63 |
% 13.43/3.63 | Instantiating formula (31) with n4, n10, all_0_4_4, n3 and discharging atoms sum(n4, n10) = all_0_4_4, sum(n4, n10) = n3, yields:
% 13.43/3.63 | (352) all_0_4_4 = n3
% 13.43/3.63 |
% 13.43/3.63 | Instantiating formula (31) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 13.43/3.63 | (526) all_0_1_1 = n10
% 13.43/3.63 |
% 13.43/3.63 | From (354)(352) and (119) follows:
% 13.43/3.63 | (356) sum(n3, n3) = all_0_3_3
% 13.43/3.63 |
% 13.43/3.63 | From (526) and (834) follows:
% 13.43/3.63 | (901) sum(n7, n10) = all_0_0_0
% 13.43/3.63 |
% 13.43/3.63 | Instantiating formula (31) with n7, n10, all_0_0_0, n6 and discharging atoms sum(n7, n10) = all_0_0_0, sum(n7, n10) = n6, yields:
% 13.43/3.63 | (357) all_0_0_0 = n6
% 13.43/3.63 |
% 13.43/3.63 | Instantiating formula (31) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 13.43/3.64 | (358) all_0_3_3 = n6
% 13.43/3.64 |
% 13.43/3.64 | Equations (357,358) can reduce 104 to:
% 13.43/3.64 | (251) $false
% 13.43/3.64 |
% 13.43/3.64 |-The branch is then unsatisfiable
% 13.43/3.64 |-Branch two:
% 13.43/3.64 | (533) ~ (all_0_10_10 = n5)
% 13.43/3.64 | (534) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.43/3.64 |
% 13.43/3.64 +-Applying beta-rule and splitting (534), into two cases.
% 13.43/3.64 |-Branch one:
% 13.43/3.64 | (535) all_0_10_10 = n4
% 13.43/3.64 |
% 13.43/3.64 | From (535) and (211) follows:
% 13.43/3.64 | (536) pred(n4) = all_0_6_6
% 13.43/3.64 |
% 13.43/3.64 | From (535) and (41) follows:
% 13.43/3.64 | (537) succ(n4) = all_0_8_8
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (158) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 13.43/3.64 | (538) all_0_6_6 = n3
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (141) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 13.43/3.64 | (539) all_0_8_8 = n5
% 13.43/3.64 |
% 13.43/3.64 | From (538)(539) and (178) follows:
% 13.43/3.64 | (540) sum(n3, n5) = all_0_1_1
% 13.43/3.64 |
% 13.43/3.64 | From (538) and (830) follows:
% 13.43/3.64 | (913) sum(n3, n10) = all_0_4_4
% 13.43/3.64 |
% 13.43/3.64 | From (539) and (832) follows:
% 13.43/3.64 | (914) sum(n8, n5) = all_0_7_7
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n8, n5, all_0_7_7, n2 and discharging atoms sum(n8, n5) = all_0_7_7, sum(n8, n5) = n2, yields:
% 13.43/3.64 | (372) all_0_7_7 = n2
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n3, n10, all_0_4_4, n2 and discharging atoms sum(n3, n10) = all_0_4_4, sum(n3, n10) = n2, yields:
% 13.43/3.64 | (370) all_0_4_4 = n2
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 13.43/3.64 | (544) all_0_1_1 = n8
% 13.43/3.64 |
% 13.43/3.64 | From (372)(370) and (119) follows:
% 13.43/3.64 | (374) sum(n2, n2) = all_0_3_3
% 13.43/3.64 |
% 13.43/3.64 | From (544) and (834) follows:
% 13.43/3.64 | (919) sum(n7, n8) = all_0_0_0
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n7, n8, all_0_0_0, n4 and discharging atoms sum(n7, n8) = all_0_0_0, sum(n7, n8) = n4, yields:
% 13.43/3.64 | (375) all_0_0_0 = n4
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 13.43/3.64 | (376) all_0_3_3 = n4
% 13.43/3.64 |
% 13.43/3.64 | Equations (375,376) can reduce 104 to:
% 13.43/3.64 | (251) $false
% 13.43/3.64 |
% 13.43/3.64 |-The branch is then unsatisfiable
% 13.43/3.64 |-Branch two:
% 13.43/3.64 | (551) ~ (all_0_10_10 = n4)
% 13.43/3.64 | (552) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.43/3.64 |
% 13.43/3.64 +-Applying beta-rule and splitting (552), into two cases.
% 13.43/3.64 |-Branch one:
% 13.43/3.64 | (553) all_0_10_10 = n3
% 13.43/3.64 |
% 13.43/3.64 | From (553) and (211) follows:
% 13.43/3.64 | (554) pred(n3) = all_0_6_6
% 13.43/3.64 |
% 13.43/3.64 | From (553) and (41) follows:
% 13.43/3.64 | (555) succ(n3) = all_0_8_8
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (158) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 13.43/3.64 | (556) all_0_6_6 = n2
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (141) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 13.43/3.64 | (557) all_0_8_8 = n4
% 13.43/3.64 |
% 13.43/3.64 | From (556)(557) and (178) follows:
% 13.43/3.64 | (558) sum(n2, n4) = all_0_1_1
% 13.43/3.64 |
% 13.43/3.64 | From (556) and (830) follows:
% 13.43/3.64 | (931) sum(n2, n10) = all_0_4_4
% 13.43/3.64 |
% 13.43/3.64 | From (557) and (832) follows:
% 13.43/3.64 | (932) sum(n8, n4) = all_0_7_7
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n8, n4, all_0_7_7, n1 and discharging atoms sum(n8, n4) = all_0_7_7, sum(n8, n4) = n1, yields:
% 13.43/3.64 | (390) all_0_7_7 = n1
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n2, n10, all_0_4_4, n1 and discharging atoms sum(n2, n10) = all_0_4_4, sum(n2, n10) = n1, yields:
% 13.43/3.64 | (388) all_0_4_4 = n1
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 13.43/3.64 | (562) all_0_1_1 = n6
% 13.43/3.64 |
% 13.43/3.64 | From (390)(388) and (119) follows:
% 13.43/3.64 | (392) sum(n1, n1) = all_0_3_3
% 13.43/3.64 |
% 13.43/3.64 | From (562) and (834) follows:
% 13.43/3.64 | (937) sum(n7, n6) = all_0_0_0
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n7, n6, all_0_0_0, n2 and discharging atoms sum(n7, n6) = all_0_0_0, sum(n7, n6) = n2, yields:
% 13.43/3.64 | (393) all_0_0_0 = n2
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 13.43/3.64 | (394) all_0_3_3 = n2
% 13.43/3.64 |
% 13.43/3.64 | Equations (393,394) can reduce 104 to:
% 13.43/3.64 | (251) $false
% 13.43/3.64 |
% 13.43/3.64 |-The branch is then unsatisfiable
% 13.43/3.64 |-Branch two:
% 13.43/3.64 | (569) ~ (all_0_10_10 = n3)
% 13.43/3.64 | (570) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.43/3.64 |
% 13.43/3.64 +-Applying beta-rule and splitting (570), into two cases.
% 13.43/3.64 |-Branch one:
% 13.43/3.64 | (571) all_0_10_10 = n2
% 13.43/3.64 |
% 13.43/3.64 | From (571) and (211) follows:
% 13.43/3.64 | (572) pred(n2) = all_0_6_6
% 13.43/3.64 |
% 13.43/3.64 | From (571) and (41) follows:
% 13.43/3.64 | (573) succ(n2) = all_0_8_8
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (158) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 13.43/3.64 | (574) all_0_6_6 = n1
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (141) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 13.43/3.64 | (575) all_0_8_8 = n3
% 13.43/3.64 |
% 13.43/3.64 | From (574)(575) and (178) follows:
% 13.43/3.64 | (576) sum(n1, n3) = all_0_1_1
% 13.43/3.64 |
% 13.43/3.64 | From (574) and (830) follows:
% 13.43/3.64 | (949) sum(n1, n10) = all_0_4_4
% 13.43/3.64 |
% 13.43/3.64 | From (575) and (832) follows:
% 13.43/3.64 | (950) sum(n8, n3) = all_0_7_7
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n8, n3, all_0_7_7, n0 and discharging atoms sum(n8, n3) = all_0_7_7, sum(n8, n3) = n0, yields:
% 13.43/3.64 | (408) all_0_7_7 = n0
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n1, n10, all_0_4_4, n0 and discharging atoms sum(n1, n10) = all_0_4_4, sum(n1, n10) = n0, yields:
% 13.43/3.64 | (406) all_0_4_4 = n0
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 13.43/3.64 | (580) all_0_1_1 = n4
% 13.43/3.64 |
% 13.43/3.64 | From (408)(406) and (119) follows:
% 13.43/3.64 | (410) sum(n0, n0) = all_0_3_3
% 13.43/3.64 |
% 13.43/3.64 | From (580) and (834) follows:
% 13.43/3.64 | (955) sum(n7, n4) = all_0_0_0
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n7, n4, all_0_0_0, n0 and discharging atoms sum(n7, n4) = all_0_0_0, sum(n7, n4) = n0, yields:
% 13.43/3.64 | (412) all_0_0_0 = n0
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 13.43/3.64 | (413) all_0_3_3 = n0
% 13.43/3.64 |
% 13.43/3.64 | Equations (412,413) can reduce 104 to:
% 13.43/3.64 | (251) $false
% 13.43/3.64 |
% 13.43/3.64 |-The branch is then unsatisfiable
% 13.43/3.64 |-Branch two:
% 13.43/3.64 | (587) ~ (all_0_10_10 = n2)
% 13.43/3.64 | (588) all_0_10_10 = n1 | all_0_10_10 = n0
% 13.43/3.64 |
% 13.43/3.64 +-Applying beta-rule and splitting (588), into two cases.
% 13.43/3.64 |-Branch one:
% 13.43/3.64 | (589) all_0_10_10 = n1
% 13.43/3.64 |
% 13.43/3.64 | From (589) and (211) follows:
% 13.43/3.64 | (590) pred(n1) = all_0_6_6
% 13.43/3.64 |
% 13.43/3.64 | From (589) and (41) follows:
% 13.43/3.64 | (591) succ(n1) = all_0_8_8
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (158) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 13.43/3.64 | (592) all_0_6_6 = n0
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (141) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 13.43/3.64 | (593) all_0_8_8 = n2
% 13.43/3.64 |
% 13.43/3.64 | From (592)(593) and (178) follows:
% 13.43/3.64 | (594) sum(n0, n2) = all_0_1_1
% 13.43/3.64 |
% 13.43/3.64 | From (592) and (830) follows:
% 13.43/3.64 | (967) sum(n0, n10) = all_0_4_4
% 13.43/3.64 |
% 13.43/3.64 | From (593) and (832) follows:
% 13.43/3.64 | (968) sum(n8, n2) = all_0_7_7
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n8, n2, all_0_7_7, n10 and discharging atoms sum(n8, n2) = all_0_7_7, sum(n8, n2) = n10, yields:
% 13.43/3.64 | (425) all_0_7_7 = n10
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n0, n10, all_0_4_4, n10 and discharging atoms sum(n0, n10) = all_0_4_4, sum(n0, n10) = n10, yields:
% 13.43/3.64 | (426) all_0_4_4 = n10
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 13.43/3.64 | (598) all_0_1_1 = n2
% 13.43/3.64 |
% 13.43/3.64 | From (425)(426) and (119) follows:
% 13.43/3.64 | (428) sum(n10, n10) = all_0_3_3
% 13.43/3.64 |
% 13.43/3.64 | From (598) and (834) follows:
% 13.43/3.64 | (973) sum(n7, n2) = all_0_0_0
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n10, n10, all_0_3_3, n9 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n9, yields:
% 13.43/3.64 | (429) all_0_3_3 = n9
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n7, n2, all_0_0_0, n9 and discharging atoms sum(n7, n2) = all_0_0_0, sum(n7, n2) = n9, yields:
% 13.43/3.64 | (430) all_0_0_0 = n9
% 13.43/3.64 |
% 13.43/3.64 | Equations (430,429) can reduce 104 to:
% 13.43/3.64 | (251) $false
% 13.43/3.64 |
% 13.43/3.64 |-The branch is then unsatisfiable
% 13.43/3.64 |-Branch two:
% 13.43/3.64 | (607) ~ (all_0_10_10 = n1)
% 13.43/3.64 | (608) all_0_10_10 = n0
% 13.43/3.64 |
% 13.43/3.64 | From (608) and (211) follows:
% 13.43/3.64 | (609) pred(n0) = all_0_6_6
% 13.43/3.64 |
% 13.43/3.64 | From (608) and (41) follows:
% 13.43/3.64 | (610) succ(n0) = all_0_8_8
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (158) with n0, all_0_6_6, n10 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n10, yields:
% 13.43/3.64 | (611) all_0_6_6 = n10
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (141) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 13.43/3.64 | (612) all_0_8_8 = n1
% 13.43/3.64 |
% 13.43/3.64 | From (611)(612) and (178) follows:
% 13.43/3.64 | (613) sum(n10, n1) = all_0_1_1
% 13.43/3.64 |
% 13.43/3.64 | From (611) and (830) follows:
% 13.43/3.64 | (984) sum(n10, n10) = all_0_4_4
% 13.43/3.64 |
% 13.43/3.64 | From (612) and (832) follows:
% 13.43/3.64 | (985) sum(n8, n1) = all_0_7_7
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n10, n10, all_0_4_4, n9 and discharging atoms sum(n10, n10) = all_0_4_4, sum(n10, n10) = n9, yields:
% 13.43/3.64 | (241) all_0_4_4 = n9
% 13.43/3.64 |
% 13.43/3.64 | Instantiating formula (31) with n10, n1, all_0_1_1, n0 and discharging atoms sum(n10, n1) = all_0_1_1, sum(n10, n1) = n0, yields:
% 13.43/3.65 | (616) all_0_1_1 = n0
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) with n8, n1, all_0_7_7, n9 and discharging atoms sum(n8, n1) = all_0_7_7, sum(n8, n1) = n9, yields:
% 13.43/3.65 | (242) all_0_7_7 = n9
% 13.43/3.65 |
% 13.43/3.65 | From (242)(241) and (119) follows:
% 13.43/3.65 | (246) sum(n9, n9) = all_0_3_3
% 13.43/3.65 |
% 13.43/3.65 | From (616) and (834) follows:
% 13.43/3.65 | (990) sum(n7, n0) = all_0_0_0
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) with n9, n9, all_0_3_3, n7 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n7, yields:
% 13.43/3.65 | (249) all_0_3_3 = n7
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) with n7, n0, all_0_0_0, n7 and discharging atoms sum(n7, n0) = all_0_0_0, sum(n7, n0) = n7, yields:
% 13.43/3.65 | (247) all_0_0_0 = n7
% 13.43/3.65 |
% 13.43/3.65 | Equations (247,249) can reduce 104 to:
% 13.43/3.65 | (251) $false
% 13.43/3.65 |
% 13.43/3.65 |-The branch is then unsatisfiable
% 13.43/3.65 |-Branch two:
% 13.43/3.65 | (270) ~ (all_0_11_11 = n9)
% 13.43/3.65 | (271) all_0_11_11 = n8 | all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.43/3.65 |
% 13.43/3.65 +-Applying beta-rule and splitting (462), into two cases.
% 13.43/3.65 |-Branch one:
% 13.43/3.65 | (463) all_0_10_10 = n8
% 13.43/3.65 |
% 13.43/3.65 | From (463) and (211) follows:
% 13.43/3.65 | (464) pred(n8) = all_0_6_6
% 13.43/3.65 |
% 13.43/3.65 | From (463) and (41) follows:
% 13.43/3.65 | (465) succ(n8) = all_0_8_8
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (158) with n8, all_0_6_6, n7 and discharging atoms pred(n8) = all_0_6_6, pred(n8) = n7, yields:
% 13.43/3.65 | (466) all_0_6_6 = n7
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (141) with n8, all_0_8_8, n9 and discharging atoms succ(n8) = all_0_8_8, succ(n8) = n9, yields:
% 13.43/3.65 | (467) all_0_8_8 = n9
% 13.43/3.65 |
% 13.43/3.65 | From (466) and (464) follows:
% 13.43/3.65 | (87) pred(n8) = n7
% 13.43/3.65 |
% 13.43/3.65 | From (467) and (465) follows:
% 13.43/3.65 | (74) succ(n8) = n9
% 13.43/3.65 |
% 13.43/3.65 | From (466) and (33) follows:
% 13.43/3.65 | (1003) sum(n7, all_0_5_5) = all_0_4_4
% 13.43/3.65 |
% 13.43/3.65 | From (466)(467) and (178) follows:
% 13.43/3.65 | (468) sum(n7, n9) = all_0_1_1
% 13.43/3.65 |
% 13.43/3.65 | From (467) and (137) follows:
% 13.43/3.65 | (1005) sum(all_0_9_9, n9) = all_0_7_7
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) with n7, n9, all_0_1_1, n5 and discharging atoms sum(n7, n9) = all_0_1_1, sum(n7, n9) = n5, yields:
% 13.43/3.65 | (472) all_0_1_1 = n5
% 13.43/3.65 |
% 13.43/3.65 | From (472) and (4) follows:
% 13.43/3.65 | (1007) sum(all_0_2_2, n5) = all_0_0_0
% 13.43/3.65 |
% 13.43/3.65 | From (472) and (468) follows:
% 13.43/3.65 | (32) sum(n7, n9) = n5
% 13.43/3.65 |
% 13.43/3.65 +-Applying beta-rule and splitting (271), into two cases.
% 13.43/3.65 |-Branch one:
% 13.43/3.65 | (272) all_0_11_11 = n8
% 13.43/3.65 |
% 13.43/3.65 | From (272) and (84) follows:
% 13.43/3.65 | (273) pred(n8) = all_0_9_9
% 13.43/3.65 |
% 13.43/3.65 | From (272) and (210) follows:
% 13.43/3.65 | (274) succ(n8) = all_0_5_5
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (158) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 13.43/3.65 | (275) all_0_9_9 = n7
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (141) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 13.43/3.65 | (276) all_0_5_5 = n9
% 13.43/3.65 |
% 13.43/3.65 | From (275)(276) and (48) follows:
% 13.43/3.65 | (277) sum(n7, n9) = all_0_2_2
% 13.43/3.65 |
% 13.43/3.65 | From (275) and (1005) follows:
% 13.43/3.65 | (1015) sum(n7, n9) = all_0_7_7
% 13.43/3.65 |
% 13.43/3.65 | From (276) and (1003) follows:
% 13.43/3.65 | (1016) sum(n7, n9) = all_0_4_4
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) with n7, n9, all_0_2_2, n5 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n5, yields:
% 13.43/3.65 | (281) all_0_2_2 = n5
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) 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:
% 13.43/3.65 | (238) all_0_2_2 = all_0_4_4
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) 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:
% 13.43/3.65 | (239) all_0_2_2 = all_0_7_7
% 13.43/3.65 |
% 13.43/3.65 | Combining equations (239,238) yields a new equation:
% 13.43/3.65 | (240) all_0_4_4 = all_0_7_7
% 13.43/3.65 |
% 13.43/3.65 | Combining equations (281,238) yields a new equation:
% 13.43/3.65 | (316) all_0_4_4 = n5
% 13.43/3.65 |
% 13.43/3.65 | Combining equations (316,240) yields a new equation:
% 13.43/3.65 | (318) all_0_7_7 = n5
% 13.43/3.65 |
% 13.43/3.65 | Combining equations (318,240) yields a new equation:
% 13.43/3.65 | (316) all_0_4_4 = n5
% 13.43/3.65 |
% 13.43/3.65 | Combining equations (316,238) yields a new equation:
% 13.43/3.65 | (281) all_0_2_2 = n5
% 13.43/3.65 |
% 13.43/3.65 | From (281) and (1007) follows:
% 13.43/3.65 | (1025) sum(n5, n5) = all_0_0_0
% 13.43/3.65 |
% 13.43/3.65 | From (318)(316) and (119) follows:
% 13.43/3.65 | (320) sum(n5, n5) = all_0_3_3
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) with n5, n5, all_0_0_0, n10 and discharging atoms sum(n5, n5) = all_0_0_0, sum(n5, n5) = n10, yields:
% 13.43/3.65 | (322) all_0_0_0 = n10
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) with n5, n5, all_0_3_3, all_0_0_0 and discharging atoms sum(n5, n5) = all_0_0_0, sum(n5, n5) = all_0_3_3, yields:
% 13.43/3.65 | (248) all_0_0_0 = all_0_3_3
% 13.43/3.65 |
% 13.43/3.65 | Combining equations (322,248) yields a new equation:
% 13.43/3.65 | (321) all_0_3_3 = n10
% 13.43/3.65 |
% 13.43/3.65 | Combining equations (321,248) yields a new equation:
% 13.43/3.65 | (322) all_0_0_0 = n10
% 13.43/3.65 |
% 13.43/3.65 | Equations (322,321) can reduce 104 to:
% 13.43/3.65 | (251) $false
% 13.43/3.65 |
% 13.43/3.65 |-The branch is then unsatisfiable
% 13.43/3.65 |-Branch two:
% 13.43/3.65 | (288) ~ (all_0_11_11 = n8)
% 13.43/3.65 | (289) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.43/3.65 |
% 13.43/3.65 +-Applying beta-rule and splitting (289), into two cases.
% 13.43/3.65 |-Branch one:
% 13.43/3.65 | (290) all_0_11_11 = n7
% 13.43/3.65 |
% 13.43/3.65 | From (290) and (84) follows:
% 13.43/3.65 | (291) pred(n7) = all_0_9_9
% 13.43/3.65 |
% 13.43/3.65 | From (290) and (210) follows:
% 13.43/3.65 | (292) succ(n7) = all_0_5_5
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (158) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 13.43/3.65 | (293) all_0_9_9 = n6
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (141) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 13.43/3.65 | (294) all_0_5_5 = n8
% 13.43/3.65 |
% 13.43/3.65 | From (293)(294) and (48) follows:
% 13.43/3.65 | (295) sum(n6, n8) = all_0_2_2
% 13.43/3.65 |
% 13.43/3.65 | From (293) and (1005) follows:
% 13.43/3.65 | (1040) sum(n6, n9) = all_0_7_7
% 13.43/3.65 |
% 13.43/3.65 | From (294) and (1003) follows:
% 13.43/3.65 | (1041) sum(n7, n8) = all_0_4_4
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) with n7, n8, all_0_4_4, n4 and discharging atoms sum(n7, n8) = all_0_4_4, sum(n7, n8) = n4, yields:
% 13.43/3.65 | (334) all_0_4_4 = n4
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) with n6, n9, all_0_7_7, n4 and discharging atoms sum(n6, n9) = all_0_7_7, sum(n6, n9) = n4, yields:
% 13.43/3.65 | (336) all_0_7_7 = n4
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) with n6, n8, all_0_2_2, n3 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n3, yields:
% 13.43/3.65 | (299) all_0_2_2 = n3
% 13.43/3.65 |
% 13.43/3.65 | From (299) and (1007) follows:
% 13.43/3.65 | (1045) sum(n3, n5) = all_0_0_0
% 13.43/3.65 |
% 13.43/3.65 | From (336)(334) and (119) follows:
% 13.43/3.65 | (338) sum(n4, n4) = all_0_3_3
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 13.43/3.65 | (340) all_0_3_3 = n8
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) with n3, n5, all_0_0_0, n8 and discharging atoms sum(n3, n5) = all_0_0_0, sum(n3, n5) = n8, yields:
% 13.43/3.65 | (339) all_0_0_0 = n8
% 13.43/3.65 |
% 13.43/3.65 | Equations (339,340) can reduce 104 to:
% 13.43/3.65 | (251) $false
% 13.43/3.65 |
% 13.43/3.65 |-The branch is then unsatisfiable
% 13.43/3.65 |-Branch two:
% 13.43/3.65 | (306) ~ (all_0_11_11 = n7)
% 13.43/3.65 | (307) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.43/3.65 |
% 13.43/3.65 +-Applying beta-rule and splitting (307), into two cases.
% 13.43/3.65 |-Branch one:
% 13.43/3.65 | (308) all_0_11_11 = n6
% 13.43/3.65 |
% 13.43/3.65 | From (308) and (84) follows:
% 13.43/3.65 | (309) pred(n6) = all_0_9_9
% 13.43/3.65 |
% 13.43/3.65 | From (308) and (210) follows:
% 13.43/3.65 | (310) succ(n6) = all_0_5_5
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (158) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 13.43/3.65 | (311) all_0_9_9 = n5
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (141) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 13.43/3.65 | (312) all_0_5_5 = n7
% 13.43/3.65 |
% 13.43/3.65 | From (311)(312) and (48) follows:
% 13.43/3.65 | (313) sum(n5, n7) = all_0_2_2
% 13.43/3.65 |
% 13.43/3.65 | From (311) and (1005) follows:
% 13.43/3.65 | (1058) sum(n5, n9) = all_0_7_7
% 13.43/3.65 |
% 13.43/3.65 | From (312) and (1003) follows:
% 13.43/3.65 | (1059) sum(n7, n7) = all_0_4_4
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) with n7, n7, all_0_4_4, n3 and discharging atoms sum(n7, n7) = all_0_4_4, sum(n7, n7) = n3, yields:
% 13.43/3.65 | (352) all_0_4_4 = n3
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) with n5, n9, all_0_7_7, n3 and discharging atoms sum(n5, n9) = all_0_7_7, sum(n5, n9) = n3, yields:
% 13.43/3.65 | (354) all_0_7_7 = n3
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) with n5, n7, all_0_2_2, n1 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n1, yields:
% 13.43/3.65 | (317) all_0_2_2 = n1
% 13.43/3.65 |
% 13.43/3.65 | From (317) and (1007) follows:
% 13.43/3.65 | (1063) sum(n1, n5) = all_0_0_0
% 13.43/3.65 |
% 13.43/3.65 | From (354)(352) and (119) follows:
% 13.43/3.65 | (356) sum(n3, n3) = all_0_3_3
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 13.43/3.65 | (358) all_0_3_3 = n6
% 13.43/3.65 |
% 13.43/3.65 | Instantiating formula (31) with n1, n5, all_0_0_0, n6 and discharging atoms sum(n1, n5) = all_0_0_0, sum(n1, n5) = n6, yields:
% 13.43/3.65 | (357) all_0_0_0 = n6
% 13.43/3.65 |
% 13.43/3.65 | Equations (357,358) can reduce 104 to:
% 13.43/3.65 | (251) $false
% 13.43/3.65 |
% 13.43/3.65 |-The branch is then unsatisfiable
% 13.43/3.65 |-Branch two:
% 13.43/3.65 | (324) ~ (all_0_11_11 = n6)
% 13.43/3.65 | (325) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.43/3.65 |
% 13.43/3.65 +-Applying beta-rule and splitting (325), into two cases.
% 13.43/3.65 |-Branch one:
% 13.43/3.65 | (326) all_0_11_11 = n5
% 13.43/3.65 |
% 13.43/3.65 | From (326) and (84) follows:
% 13.43/3.65 | (327) pred(n5) = all_0_9_9
% 13.43/3.65 |
% 13.43/3.65 | From (326) and (210) follows:
% 13.43/3.65 | (328) succ(n5) = all_0_5_5
% 13.43/3.65 |
% 13.43/3.66 | Instantiating formula (158) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 13.43/3.66 | (329) all_0_9_9 = n4
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (141) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 13.43/3.66 | (330) all_0_5_5 = n6
% 13.43/3.66 |
% 13.43/3.66 | From (329)(330) and (48) follows:
% 13.43/3.66 | (331) sum(n4, n6) = all_0_2_2
% 13.43/3.66 |
% 13.43/3.66 | From (329) and (1005) follows:
% 13.43/3.66 | (1076) sum(n4, n9) = all_0_7_7
% 13.43/3.66 |
% 13.43/3.66 | From (330) and (1003) follows:
% 13.43/3.66 | (1077) sum(n7, n6) = all_0_4_4
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n7, n6, all_0_4_4, n2 and discharging atoms sum(n7, n6) = all_0_4_4, sum(n7, n6) = n2, yields:
% 13.43/3.66 | (370) all_0_4_4 = n2
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n4, n9, all_0_7_7, n2 and discharging atoms sum(n4, n9) = all_0_7_7, sum(n4, n9) = n2, yields:
% 13.43/3.66 | (372) all_0_7_7 = n2
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 13.43/3.66 | (335) all_0_2_2 = n10
% 13.43/3.66 |
% 13.43/3.66 | From (335) and (1007) follows:
% 13.43/3.66 | (1081) sum(n10, n5) = all_0_0_0
% 13.43/3.66 |
% 13.43/3.66 | From (372)(370) and (119) follows:
% 13.43/3.66 | (374) sum(n2, n2) = all_0_3_3
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n10, n5, all_0_0_0, n4 and discharging atoms sum(n10, n5) = all_0_0_0, sum(n10, n5) = n4, yields:
% 13.43/3.66 | (375) all_0_0_0 = n4
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 13.43/3.66 | (376) all_0_3_3 = n4
% 13.43/3.66 |
% 13.43/3.66 | Equations (375,376) can reduce 104 to:
% 13.43/3.66 | (251) $false
% 13.43/3.66 |
% 13.43/3.66 |-The branch is then unsatisfiable
% 13.43/3.66 |-Branch two:
% 13.43/3.66 | (342) ~ (all_0_11_11 = n5)
% 13.43/3.66 | (343) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.43/3.66 |
% 13.43/3.66 +-Applying beta-rule and splitting (343), into two cases.
% 13.43/3.66 |-Branch one:
% 13.43/3.66 | (344) all_0_11_11 = n4
% 13.43/3.66 |
% 13.43/3.66 | From (344) and (84) follows:
% 13.43/3.66 | (345) pred(n4) = all_0_9_9
% 13.43/3.66 |
% 13.43/3.66 | From (344) and (210) follows:
% 13.43/3.66 | (346) succ(n4) = all_0_5_5
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (158) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 13.43/3.66 | (347) all_0_9_9 = n3
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (141) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 13.43/3.66 | (348) all_0_5_5 = n5
% 13.43/3.66 |
% 13.43/3.66 | From (347)(348) and (48) follows:
% 13.43/3.66 | (349) sum(n3, n5) = all_0_2_2
% 13.43/3.66 |
% 13.43/3.66 | From (347) and (1005) follows:
% 13.43/3.66 | (1094) sum(n3, n9) = all_0_7_7
% 13.43/3.66 |
% 13.43/3.66 | From (348) and (1003) follows:
% 13.43/3.66 | (1095) sum(n7, n5) = all_0_4_4
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n7, n5, all_0_4_4, n1 and discharging atoms sum(n7, n5) = all_0_4_4, sum(n7, n5) = n1, yields:
% 13.43/3.66 | (388) all_0_4_4 = n1
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n3, n9, all_0_7_7, n1 and discharging atoms sum(n3, n9) = all_0_7_7, sum(n3, n9) = n1, yields:
% 13.43/3.66 | (390) all_0_7_7 = n1
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 13.43/3.66 | (353) all_0_2_2 = n8
% 13.43/3.66 |
% 13.43/3.66 | From (353) and (1007) follows:
% 13.43/3.66 | (1099) sum(n8, n5) = all_0_0_0
% 13.43/3.66 |
% 13.43/3.66 | From (390)(388) and (119) follows:
% 13.43/3.66 | (392) sum(n1, n1) = all_0_3_3
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n8, n5, all_0_0_0, n2 and discharging atoms sum(n8, n5) = all_0_0_0, sum(n8, n5) = n2, yields:
% 13.43/3.66 | (393) all_0_0_0 = n2
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 13.43/3.66 | (394) all_0_3_3 = n2
% 13.43/3.66 |
% 13.43/3.66 | Equations (393,394) can reduce 104 to:
% 13.43/3.66 | (251) $false
% 13.43/3.66 |
% 13.43/3.66 |-The branch is then unsatisfiable
% 13.43/3.66 |-Branch two:
% 13.43/3.66 | (360) ~ (all_0_11_11 = n4)
% 13.43/3.66 | (361) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.43/3.66 |
% 13.43/3.66 +-Applying beta-rule and splitting (361), into two cases.
% 13.43/3.66 |-Branch one:
% 13.43/3.66 | (362) all_0_11_11 = n3
% 13.43/3.66 |
% 13.43/3.66 | From (362) and (84) follows:
% 13.43/3.66 | (363) pred(n3) = all_0_9_9
% 13.43/3.66 |
% 13.43/3.66 | From (362) and (210) follows:
% 13.43/3.66 | (364) succ(n3) = all_0_5_5
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (158) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 13.43/3.66 | (365) all_0_9_9 = n2
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (141) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 13.43/3.66 | (366) all_0_5_5 = n4
% 13.43/3.66 |
% 13.43/3.66 | From (365)(366) and (48) follows:
% 13.43/3.66 | (367) sum(n2, n4) = all_0_2_2
% 13.43/3.66 |
% 13.43/3.66 | From (365) and (1005) follows:
% 13.43/3.66 | (1112) sum(n2, n9) = all_0_7_7
% 13.43/3.66 |
% 13.43/3.66 | From (366) and (1003) follows:
% 13.43/3.66 | (1113) sum(n7, n4) = all_0_4_4
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n7, n4, all_0_4_4, n0 and discharging atoms sum(n7, n4) = all_0_4_4, sum(n7, n4) = n0, yields:
% 13.43/3.66 | (406) all_0_4_4 = n0
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n2, n9, all_0_7_7, n0 and discharging atoms sum(n2, n9) = all_0_7_7, sum(n2, n9) = n0, yields:
% 13.43/3.66 | (408) all_0_7_7 = n0
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 13.43/3.66 | (371) all_0_2_2 = n6
% 13.43/3.66 |
% 13.43/3.66 | From (371) and (1007) follows:
% 13.43/3.66 | (1117) sum(n6, n5) = all_0_0_0
% 13.43/3.66 |
% 13.43/3.66 | From (408)(406) and (119) follows:
% 13.43/3.66 | (410) sum(n0, n0) = all_0_3_3
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n6, n5, all_0_0_0, n0 and discharging atoms sum(n6, n5) = all_0_0_0, sum(n6, n5) = n0, yields:
% 13.43/3.66 | (412) all_0_0_0 = n0
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 13.43/3.66 | (413) all_0_3_3 = n0
% 13.43/3.66 |
% 13.43/3.66 | Equations (412,413) can reduce 104 to:
% 13.43/3.66 | (251) $false
% 13.43/3.66 |
% 13.43/3.66 |-The branch is then unsatisfiable
% 13.43/3.66 |-Branch two:
% 13.43/3.66 | (378) ~ (all_0_11_11 = n3)
% 13.43/3.66 | (379) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.43/3.66 |
% 13.43/3.66 +-Applying beta-rule and splitting (379), into two cases.
% 13.43/3.66 |-Branch one:
% 13.43/3.66 | (380) all_0_11_11 = n2
% 13.43/3.66 |
% 13.43/3.66 | From (380) and (84) follows:
% 13.43/3.66 | (381) pred(n2) = all_0_9_9
% 13.43/3.66 |
% 13.43/3.66 | From (380) and (210) follows:
% 13.43/3.66 | (382) succ(n2) = all_0_5_5
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (158) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 13.43/3.66 | (383) all_0_9_9 = n1
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (141) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 13.43/3.66 | (384) all_0_5_5 = n3
% 13.43/3.66 |
% 13.43/3.66 | From (383)(384) and (48) follows:
% 13.43/3.66 | (385) sum(n1, n3) = all_0_2_2
% 13.43/3.66 |
% 13.43/3.66 | From (383) and (1005) follows:
% 13.43/3.66 | (1130) sum(n1, n9) = all_0_7_7
% 13.43/3.66 |
% 13.43/3.66 | From (384) and (1003) follows:
% 13.43/3.66 | (1131) sum(n7, n3) = all_0_4_4
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n7, n3, all_0_4_4, n10 and discharging atoms sum(n7, n3) = all_0_4_4, sum(n7, n3) = n10, yields:
% 13.43/3.66 | (426) all_0_4_4 = n10
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n1, n9, all_0_7_7, n10 and discharging atoms sum(n1, n9) = all_0_7_7, sum(n1, n9) = n10, yields:
% 13.43/3.66 | (425) all_0_7_7 = n10
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 13.43/3.66 | (389) all_0_2_2 = n4
% 13.43/3.66 |
% 13.43/3.66 | From (389) and (1007) follows:
% 13.43/3.66 | (1135) sum(n4, n5) = all_0_0_0
% 13.43/3.66 |
% 13.43/3.66 | From (425)(426) and (119) follows:
% 13.43/3.66 | (428) sum(n10, n10) = all_0_3_3
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n10, n10, all_0_3_3, n9 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n9, yields:
% 13.43/3.66 | (429) all_0_3_3 = n9
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n4, n5, all_0_0_0, n9 and discharging atoms sum(n4, n5) = all_0_0_0, sum(n4, n5) = n9, yields:
% 13.43/3.66 | (430) all_0_0_0 = n9
% 13.43/3.66 |
% 13.43/3.66 | Equations (430,429) can reduce 104 to:
% 13.43/3.66 | (251) $false
% 13.43/3.66 |
% 13.43/3.66 |-The branch is then unsatisfiable
% 13.43/3.66 |-Branch two:
% 13.43/3.66 | (396) ~ (all_0_11_11 = n2)
% 13.43/3.66 | (397) all_0_11_11 = n1 | all_0_11_11 = n0
% 13.43/3.66 |
% 13.43/3.66 +-Applying beta-rule and splitting (397), into two cases.
% 13.43/3.66 |-Branch one:
% 13.43/3.66 | (398) all_0_11_11 = n1
% 13.43/3.66 |
% 13.43/3.66 | From (398) and (84) follows:
% 13.43/3.66 | (399) pred(n1) = all_0_9_9
% 13.43/3.66 |
% 13.43/3.66 | From (398) and (210) follows:
% 13.43/3.66 | (400) succ(n1) = all_0_5_5
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (158) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 13.43/3.66 | (401) all_0_9_9 = n0
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (141) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 13.43/3.66 | (402) all_0_5_5 = n2
% 13.43/3.66 |
% 13.43/3.66 | From (401)(402) and (48) follows:
% 13.43/3.66 | (403) sum(n0, n2) = all_0_2_2
% 13.43/3.66 |
% 13.43/3.66 | From (401) and (1005) follows:
% 13.43/3.66 | (1148) sum(n0, n9) = all_0_7_7
% 13.43/3.66 |
% 13.43/3.66 | From (402) and (1003) follows:
% 13.43/3.66 | (1149) sum(n7, n2) = all_0_4_4
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n7, n2, all_0_4_4, n9 and discharging atoms sum(n7, n2) = all_0_4_4, sum(n7, n2) = n9, yields:
% 13.43/3.66 | (241) all_0_4_4 = n9
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n0, n9, all_0_7_7, n9 and discharging atoms sum(n0, n9) = all_0_7_7, sum(n0, n9) = n9, yields:
% 13.43/3.66 | (242) all_0_7_7 = n9
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 13.43/3.66 | (407) all_0_2_2 = n2
% 13.43/3.66 |
% 13.43/3.66 | From (407) and (1007) follows:
% 13.43/3.66 | (1153) sum(n2, n5) = all_0_0_0
% 13.43/3.66 |
% 13.43/3.66 | From (242)(241) and (119) follows:
% 13.43/3.66 | (246) sum(n9, n9) = all_0_3_3
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n9, n9, all_0_3_3, n7 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n7, yields:
% 13.43/3.66 | (249) all_0_3_3 = n7
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (31) with n2, n5, all_0_0_0, n7 and discharging atoms sum(n2, n5) = all_0_0_0, sum(n2, n5) = n7, yields:
% 13.43/3.66 | (247) all_0_0_0 = n7
% 13.43/3.66 |
% 13.43/3.66 | Equations (247,249) can reduce 104 to:
% 13.43/3.66 | (251) $false
% 13.43/3.66 |
% 13.43/3.66 |-The branch is then unsatisfiable
% 13.43/3.66 |-Branch two:
% 13.43/3.66 | (415) ~ (all_0_11_11 = n1)
% 13.43/3.66 | (416) all_0_11_11 = n0
% 13.43/3.66 |
% 13.43/3.66 | From (416) and (84) follows:
% 13.43/3.66 | (417) pred(n0) = all_0_9_9
% 13.43/3.66 |
% 13.43/3.66 | From (416) and (210) follows:
% 13.43/3.66 | (418) succ(n0) = all_0_5_5
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (158) with n0, all_0_9_9, n10 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n10, yields:
% 13.43/3.66 | (419) all_0_9_9 = n10
% 13.43/3.66 |
% 13.43/3.66 | Instantiating formula (141) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 13.43/3.66 | (420) all_0_5_5 = n1
% 13.43/3.67 |
% 13.43/3.67 | From (419)(420) and (48) follows:
% 13.43/3.67 | (421) sum(n10, n1) = all_0_2_2
% 13.43/3.67 |
% 13.43/3.67 | From (419) and (1005) follows:
% 13.43/3.67 | (1165) sum(n10, n9) = all_0_7_7
% 13.43/3.67 |
% 13.43/3.67 | From (420) and (1003) follows:
% 13.43/3.67 | (1166) sum(n7, n1) = all_0_4_4
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n10, n9, all_0_7_7, n8 and discharging atoms sum(n10, n9) = all_0_7_7, sum(n10, n9) = n8, yields:
% 13.43/3.67 | (264) all_0_7_7 = n8
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n10, n1, all_0_2_2, n0 and discharging atoms sum(n10, n1) = all_0_2_2, sum(n10, n1) = n0, yields:
% 13.43/3.67 | (424) all_0_2_2 = n0
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n7, n1, all_0_4_4, n8 and discharging atoms sum(n7, n1) = all_0_4_4, sum(n7, n1) = n8, yields:
% 13.43/3.67 | (262) all_0_4_4 = n8
% 13.43/3.67 |
% 13.43/3.67 | From (424) and (1007) follows:
% 13.43/3.67 | (1170) sum(n0, n5) = all_0_0_0
% 13.43/3.67 |
% 13.43/3.67 | From (264)(262) and (119) follows:
% 13.43/3.67 | (266) sum(n8, n8) = all_0_3_3
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n8, n8, all_0_3_3, n5 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n5, yields:
% 13.43/3.67 | (267) all_0_3_3 = n5
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n0, n5, all_0_0_0, n5 and discharging atoms sum(n0, n5) = all_0_0_0, sum(n0, n5) = n5, yields:
% 13.43/3.67 | (268) all_0_0_0 = n5
% 13.43/3.67 |
% 13.43/3.67 | Equations (268,267) can reduce 104 to:
% 13.43/3.67 | (251) $false
% 13.43/3.67 |
% 13.43/3.67 |-The branch is then unsatisfiable
% 13.43/3.67 |-Branch two:
% 13.43/3.67 | (479) ~ (all_0_10_10 = n8)
% 13.43/3.67 | (480) all_0_10_10 = n7 | all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.43/3.67 |
% 13.43/3.67 +-Applying beta-rule and splitting (271), into two cases.
% 13.43/3.67 |-Branch one:
% 13.43/3.67 | (272) all_0_11_11 = n8
% 13.43/3.67 |
% 13.43/3.67 | From (272) and (84) follows:
% 13.43/3.67 | (273) pred(n8) = all_0_9_9
% 13.43/3.67 |
% 13.43/3.67 | From (272) and (210) follows:
% 13.43/3.67 | (274) succ(n8) = all_0_5_5
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (158) with n8, all_0_9_9, n7 and discharging atoms pred(n8) = all_0_9_9, pred(n8) = n7, yields:
% 13.43/3.67 | (275) all_0_9_9 = n7
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (141) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 13.43/3.67 | (276) all_0_5_5 = n9
% 13.43/3.67 |
% 13.43/3.67 | From (276) and (33) follows:
% 13.43/3.67 | (1182) sum(all_0_6_6, n9) = all_0_4_4
% 13.43/3.67 |
% 13.43/3.67 | From (275)(276) and (48) follows:
% 13.43/3.67 | (277) sum(n7, n9) = all_0_2_2
% 13.43/3.67 |
% 13.43/3.67 | From (275) and (137) follows:
% 13.43/3.67 | (1184) sum(n7, all_0_8_8) = all_0_7_7
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n7, n9, all_0_2_2, n5 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n5, yields:
% 13.43/3.67 | (281) all_0_2_2 = n5
% 13.43/3.67 |
% 13.43/3.67 | From (281) and (4) follows:
% 13.43/3.67 | (1186) sum(n5, all_0_1_1) = all_0_0_0
% 13.43/3.67 |
% 13.43/3.67 +-Applying beta-rule and splitting (480), into two cases.
% 13.43/3.67 |-Branch one:
% 13.43/3.67 | (481) all_0_10_10 = n7
% 13.43/3.67 |
% 13.43/3.67 | From (481) and (211) follows:
% 13.43/3.67 | (482) pred(n7) = all_0_6_6
% 13.43/3.67 |
% 13.43/3.67 | From (481) and (41) follows:
% 13.43/3.67 | (483) succ(n7) = all_0_8_8
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (158) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 13.43/3.67 | (484) all_0_6_6 = n6
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (141) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 13.43/3.67 | (485) all_0_8_8 = n8
% 13.43/3.67 |
% 13.43/3.67 | From (484)(485) and (178) follows:
% 13.43/3.67 | (486) sum(n6, n8) = all_0_1_1
% 13.43/3.67 |
% 13.43/3.67 | From (484) and (1182) follows:
% 13.43/3.67 | (1193) sum(n6, n9) = all_0_4_4
% 13.43/3.67 |
% 13.43/3.67 | From (485) and (1184) follows:
% 13.43/3.67 | (1194) sum(n7, n8) = all_0_7_7
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n7, n8, all_0_7_7, n4 and discharging atoms sum(n7, n8) = all_0_7_7, sum(n7, n8) = n4, yields:
% 13.43/3.67 | (336) all_0_7_7 = n4
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n6, n9, all_0_4_4, n4 and discharging atoms sum(n6, n9) = all_0_4_4, sum(n6, n9) = n4, yields:
% 13.43/3.67 | (334) all_0_4_4 = n4
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n6, n8, all_0_1_1, n3 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n3, yields:
% 13.43/3.67 | (490) all_0_1_1 = n3
% 13.43/3.67 |
% 13.43/3.67 | From (336)(334) and (119) follows:
% 13.43/3.67 | (338) sum(n4, n4) = all_0_3_3
% 13.43/3.67 |
% 13.43/3.67 | From (490) and (1186) follows:
% 13.43/3.67 | (1199) sum(n5, n3) = all_0_0_0
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n5, n3, all_0_0_0, n8 and discharging atoms sum(n5, n3) = all_0_0_0, sum(n5, n3) = n8, yields:
% 13.43/3.67 | (339) all_0_0_0 = n8
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 13.43/3.67 | (340) all_0_3_3 = n8
% 13.43/3.67 |
% 13.43/3.67 | Equations (339,340) can reduce 104 to:
% 13.43/3.67 | (251) $false
% 13.43/3.67 |
% 13.43/3.67 |-The branch is then unsatisfiable
% 13.43/3.67 |-Branch two:
% 13.43/3.67 | (497) ~ (all_0_10_10 = n7)
% 13.43/3.67 | (498) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.43/3.67 |
% 13.43/3.67 +-Applying beta-rule and splitting (498), into two cases.
% 13.43/3.67 |-Branch one:
% 13.43/3.67 | (499) all_0_10_10 = n6
% 13.43/3.67 |
% 13.43/3.67 | From (499) and (211) follows:
% 13.43/3.67 | (500) pred(n6) = all_0_6_6
% 13.43/3.67 |
% 13.43/3.67 | From (499) and (41) follows:
% 13.43/3.67 | (501) succ(n6) = all_0_8_8
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (158) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 13.43/3.67 | (502) all_0_6_6 = n5
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (141) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 13.43/3.67 | (503) all_0_8_8 = n7
% 13.43/3.67 |
% 13.43/3.67 | From (502)(503) and (178) follows:
% 13.43/3.67 | (504) sum(n5, n7) = all_0_1_1
% 13.43/3.67 |
% 13.43/3.67 | From (502) and (1182) follows:
% 13.43/3.67 | (1211) sum(n5, n9) = all_0_4_4
% 13.43/3.67 |
% 13.43/3.67 | From (503) and (1184) follows:
% 13.43/3.67 | (1212) sum(n7, n7) = all_0_7_7
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n7, n7, all_0_7_7, n3 and discharging atoms sum(n7, n7) = all_0_7_7, sum(n7, n7) = n3, yields:
% 13.43/3.67 | (354) all_0_7_7 = n3
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n5, n9, all_0_4_4, n3 and discharging atoms sum(n5, n9) = all_0_4_4, sum(n5, n9) = n3, yields:
% 13.43/3.67 | (352) all_0_4_4 = n3
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n5, n7, all_0_1_1, n1 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n1, yields:
% 13.43/3.67 | (508) all_0_1_1 = n1
% 13.43/3.67 |
% 13.43/3.67 | From (354)(352) and (119) follows:
% 13.43/3.67 | (356) sum(n3, n3) = all_0_3_3
% 13.43/3.67 |
% 13.43/3.67 | From (508) and (1186) follows:
% 13.43/3.67 | (1217) sum(n5, n1) = all_0_0_0
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n5, n1, all_0_0_0, n6 and discharging atoms sum(n5, n1) = all_0_0_0, sum(n5, n1) = n6, yields:
% 13.43/3.67 | (357) all_0_0_0 = n6
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 13.43/3.67 | (358) all_0_3_3 = n6
% 13.43/3.67 |
% 13.43/3.67 | Equations (357,358) can reduce 104 to:
% 13.43/3.67 | (251) $false
% 13.43/3.67 |
% 13.43/3.67 |-The branch is then unsatisfiable
% 13.43/3.67 |-Branch two:
% 13.43/3.67 | (515) ~ (all_0_10_10 = n6)
% 13.43/3.67 | (516) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.43/3.67 |
% 13.43/3.67 +-Applying beta-rule and splitting (516), into two cases.
% 13.43/3.67 |-Branch one:
% 13.43/3.67 | (517) all_0_10_10 = n5
% 13.43/3.67 |
% 13.43/3.67 | From (517) and (211) follows:
% 13.43/3.67 | (518) pred(n5) = all_0_6_6
% 13.43/3.67 |
% 13.43/3.67 | From (517) and (41) follows:
% 13.43/3.67 | (519) succ(n5) = all_0_8_8
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (158) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 13.43/3.67 | (520) all_0_6_6 = n4
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (141) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 13.43/3.67 | (521) all_0_8_8 = n6
% 13.43/3.67 |
% 13.43/3.67 | From (520)(521) and (178) follows:
% 13.43/3.67 | (522) sum(n4, n6) = all_0_1_1
% 13.43/3.67 |
% 13.43/3.67 | From (520) and (1182) follows:
% 13.43/3.67 | (1229) sum(n4, n9) = all_0_4_4
% 13.43/3.67 |
% 13.43/3.67 | From (521) and (1184) follows:
% 13.43/3.67 | (1230) sum(n7, n6) = all_0_7_7
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n7, n6, all_0_7_7, n2 and discharging atoms sum(n7, n6) = all_0_7_7, sum(n7, n6) = n2, yields:
% 13.43/3.67 | (372) all_0_7_7 = n2
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n4, n9, all_0_4_4, n2 and discharging atoms sum(n4, n9) = all_0_4_4, sum(n4, n9) = n2, yields:
% 13.43/3.67 | (370) all_0_4_4 = n2
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 13.43/3.67 | (526) all_0_1_1 = n10
% 13.43/3.67 |
% 13.43/3.67 | From (372)(370) and (119) follows:
% 13.43/3.67 | (374) sum(n2, n2) = all_0_3_3
% 13.43/3.67 |
% 13.43/3.67 | From (526) and (1186) follows:
% 13.43/3.67 | (1235) sum(n5, n10) = all_0_0_0
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n5, n10, all_0_0_0, n4 and discharging atoms sum(n5, n10) = all_0_0_0, sum(n5, n10) = n4, yields:
% 13.43/3.67 | (375) all_0_0_0 = n4
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (31) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 13.43/3.67 | (376) all_0_3_3 = n4
% 13.43/3.67 |
% 13.43/3.67 | Equations (375,376) can reduce 104 to:
% 13.43/3.67 | (251) $false
% 13.43/3.67 |
% 13.43/3.67 |-The branch is then unsatisfiable
% 13.43/3.67 |-Branch two:
% 13.43/3.67 | (533) ~ (all_0_10_10 = n5)
% 13.43/3.67 | (534) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.43/3.67 |
% 13.43/3.67 +-Applying beta-rule and splitting (534), into two cases.
% 13.43/3.67 |-Branch one:
% 13.43/3.67 | (535) all_0_10_10 = n4
% 13.43/3.67 |
% 13.43/3.67 | From (535) and (211) follows:
% 13.43/3.67 | (536) pred(n4) = all_0_6_6
% 13.43/3.67 |
% 13.43/3.67 | From (535) and (41) follows:
% 13.43/3.67 | (537) succ(n4) = all_0_8_8
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (158) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 13.43/3.67 | (538) all_0_6_6 = n3
% 13.43/3.67 |
% 13.43/3.67 | Instantiating formula (141) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 13.43/3.67 | (539) all_0_8_8 = n5
% 13.43/3.67 |
% 13.43/3.67 | From (538)(539) and (178) follows:
% 13.43/3.67 | (540) sum(n3, n5) = all_0_1_1
% 13.43/3.67 |
% 13.43/3.67 | From (538) and (1182) follows:
% 13.43/3.67 | (1247) sum(n3, n9) = all_0_4_4
% 13.43/3.68 |
% 13.43/3.68 | From (539) and (1184) follows:
% 13.43/3.68 | (1248) sum(n7, n5) = all_0_7_7
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n7, n5, all_0_7_7, n1 and discharging atoms sum(n7, n5) = all_0_7_7, sum(n7, n5) = n1, yields:
% 13.43/3.68 | (390) all_0_7_7 = n1
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n3, n9, all_0_4_4, n1 and discharging atoms sum(n3, n9) = all_0_4_4, sum(n3, n9) = n1, yields:
% 13.43/3.68 | (388) all_0_4_4 = n1
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 13.43/3.68 | (544) all_0_1_1 = n8
% 13.43/3.68 |
% 13.43/3.68 | From (390)(388) and (119) follows:
% 13.43/3.68 | (392) sum(n1, n1) = all_0_3_3
% 13.43/3.68 |
% 13.43/3.68 | From (544) and (1186) follows:
% 13.43/3.68 | (1253) sum(n5, n8) = all_0_0_0
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n5, n8, all_0_0_0, n2 and discharging atoms sum(n5, n8) = all_0_0_0, sum(n5, n8) = n2, yields:
% 13.43/3.68 | (393) all_0_0_0 = n2
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 13.43/3.68 | (394) all_0_3_3 = n2
% 13.43/3.68 |
% 13.43/3.68 | Equations (393,394) can reduce 104 to:
% 13.43/3.68 | (251) $false
% 13.43/3.68 |
% 13.43/3.68 |-The branch is then unsatisfiable
% 13.43/3.68 |-Branch two:
% 13.43/3.68 | (551) ~ (all_0_10_10 = n4)
% 13.43/3.68 | (552) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.43/3.68 |
% 13.43/3.68 +-Applying beta-rule and splitting (552), into two cases.
% 13.43/3.68 |-Branch one:
% 13.43/3.68 | (553) all_0_10_10 = n3
% 13.43/3.68 |
% 13.43/3.68 | From (553) and (211) follows:
% 13.43/3.68 | (554) pred(n3) = all_0_6_6
% 13.43/3.68 |
% 13.43/3.68 | From (553) and (41) follows:
% 13.43/3.68 | (555) succ(n3) = all_0_8_8
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (158) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 13.43/3.68 | (556) all_0_6_6 = n2
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (141) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 13.43/3.68 | (557) all_0_8_8 = n4
% 13.43/3.68 |
% 13.43/3.68 | From (556)(557) and (178) follows:
% 13.43/3.68 | (558) sum(n2, n4) = all_0_1_1
% 13.43/3.68 |
% 13.43/3.68 | From (556) and (1182) follows:
% 13.43/3.68 | (1265) sum(n2, n9) = all_0_4_4
% 13.43/3.68 |
% 13.43/3.68 | From (557) and (1184) follows:
% 13.43/3.68 | (1266) sum(n7, n4) = all_0_7_7
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n7, n4, all_0_7_7, n0 and discharging atoms sum(n7, n4) = all_0_7_7, sum(n7, n4) = n0, yields:
% 13.43/3.68 | (408) all_0_7_7 = n0
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n2, n9, all_0_4_4, n0 and discharging atoms sum(n2, n9) = all_0_4_4, sum(n2, n9) = n0, yields:
% 13.43/3.68 | (406) all_0_4_4 = n0
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 13.43/3.68 | (562) all_0_1_1 = n6
% 13.43/3.68 |
% 13.43/3.68 | From (408)(406) and (119) follows:
% 13.43/3.68 | (410) sum(n0, n0) = all_0_3_3
% 13.43/3.68 |
% 13.43/3.68 | From (562) and (1186) follows:
% 13.43/3.68 | (1271) sum(n5, n6) = all_0_0_0
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n5, n6, all_0_0_0, n0 and discharging atoms sum(n5, n6) = all_0_0_0, sum(n5, n6) = n0, yields:
% 13.43/3.68 | (412) all_0_0_0 = n0
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 13.43/3.68 | (413) all_0_3_3 = n0
% 13.43/3.68 |
% 13.43/3.68 | Equations (412,413) can reduce 104 to:
% 13.43/3.68 | (251) $false
% 13.43/3.68 |
% 13.43/3.68 |-The branch is then unsatisfiable
% 13.43/3.68 |-Branch two:
% 13.43/3.68 | (569) ~ (all_0_10_10 = n3)
% 13.43/3.68 | (570) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.43/3.68 |
% 13.43/3.68 +-Applying beta-rule and splitting (570), into two cases.
% 13.43/3.68 |-Branch one:
% 13.43/3.68 | (571) all_0_10_10 = n2
% 13.43/3.68 |
% 13.43/3.68 | From (571) and (211) follows:
% 13.43/3.68 | (572) pred(n2) = all_0_6_6
% 13.43/3.68 |
% 13.43/3.68 | From (571) and (41) follows:
% 13.43/3.68 | (573) succ(n2) = all_0_8_8
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (158) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 13.43/3.68 | (574) all_0_6_6 = n1
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (141) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 13.43/3.68 | (575) all_0_8_8 = n3
% 13.43/3.68 |
% 13.43/3.68 | From (574)(575) and (178) follows:
% 13.43/3.68 | (576) sum(n1, n3) = all_0_1_1
% 13.43/3.68 |
% 13.43/3.68 | From (574) and (1182) follows:
% 13.43/3.68 | (1283) sum(n1, n9) = all_0_4_4
% 13.43/3.68 |
% 13.43/3.68 | From (575) and (1184) follows:
% 13.43/3.68 | (1284) sum(n7, n3) = all_0_7_7
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n7, n3, all_0_7_7, n10 and discharging atoms sum(n7, n3) = all_0_7_7, sum(n7, n3) = n10, yields:
% 13.43/3.68 | (425) all_0_7_7 = n10
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n1, n9, all_0_4_4, n10 and discharging atoms sum(n1, n9) = all_0_4_4, sum(n1, n9) = n10, yields:
% 13.43/3.68 | (426) all_0_4_4 = n10
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 13.43/3.68 | (580) all_0_1_1 = n4
% 13.43/3.68 |
% 13.43/3.68 | From (425)(426) and (119) follows:
% 13.43/3.68 | (428) sum(n10, n10) = all_0_3_3
% 13.43/3.68 |
% 13.43/3.68 | From (580) and (1186) follows:
% 13.43/3.68 | (1289) sum(n5, n4) = all_0_0_0
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n10, n10, all_0_3_3, n9 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n9, yields:
% 13.43/3.68 | (429) all_0_3_3 = n9
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n5, n4, all_0_0_0, n9 and discharging atoms sum(n5, n4) = all_0_0_0, sum(n5, n4) = n9, yields:
% 13.43/3.68 | (430) all_0_0_0 = n9
% 13.43/3.68 |
% 13.43/3.68 | Equations (430,429) can reduce 104 to:
% 13.43/3.68 | (251) $false
% 13.43/3.68 |
% 13.43/3.68 |-The branch is then unsatisfiable
% 13.43/3.68 |-Branch two:
% 13.43/3.68 | (587) ~ (all_0_10_10 = n2)
% 13.43/3.68 | (588) all_0_10_10 = n1 | all_0_10_10 = n0
% 13.43/3.68 |
% 13.43/3.68 +-Applying beta-rule and splitting (588), into two cases.
% 13.43/3.68 |-Branch one:
% 13.43/3.68 | (589) all_0_10_10 = n1
% 13.43/3.68 |
% 13.43/3.68 | From (589) and (211) follows:
% 13.43/3.68 | (590) pred(n1) = all_0_6_6
% 13.43/3.68 |
% 13.43/3.68 | From (589) and (41) follows:
% 13.43/3.68 | (591) succ(n1) = all_0_8_8
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (158) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 13.43/3.68 | (592) all_0_6_6 = n0
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (141) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 13.43/3.68 | (593) all_0_8_8 = n2
% 13.43/3.68 |
% 13.43/3.68 | From (592)(593) and (178) follows:
% 13.43/3.68 | (594) sum(n0, n2) = all_0_1_1
% 13.43/3.68 |
% 13.43/3.68 | From (592) and (1182) follows:
% 13.43/3.68 | (1301) sum(n0, n9) = all_0_4_4
% 13.43/3.68 |
% 13.43/3.68 | From (593) and (1184) follows:
% 13.43/3.68 | (1302) sum(n7, n2) = all_0_7_7
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n7, n2, all_0_7_7, n9 and discharging atoms sum(n7, n2) = all_0_7_7, sum(n7, n2) = n9, yields:
% 13.43/3.68 | (242) all_0_7_7 = n9
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n0, n9, all_0_4_4, n9 and discharging atoms sum(n0, n9) = all_0_4_4, sum(n0, n9) = n9, yields:
% 13.43/3.68 | (241) all_0_4_4 = n9
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 13.43/3.68 | (598) all_0_1_1 = n2
% 13.43/3.68 |
% 13.43/3.68 | From (242)(241) and (119) follows:
% 13.43/3.68 | (246) sum(n9, n9) = all_0_3_3
% 13.43/3.68 |
% 13.43/3.68 | From (598) and (1186) follows:
% 13.43/3.68 | (1307) sum(n5, n2) = all_0_0_0
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n9, n9, all_0_3_3, n7 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n7, yields:
% 13.43/3.68 | (249) all_0_3_3 = n7
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n5, n2, all_0_0_0, n7 and discharging atoms sum(n5, n2) = all_0_0_0, sum(n5, n2) = n7, yields:
% 13.43/3.68 | (247) all_0_0_0 = n7
% 13.43/3.68 |
% 13.43/3.68 | Equations (247,249) can reduce 104 to:
% 13.43/3.68 | (251) $false
% 13.43/3.68 |
% 13.43/3.68 |-The branch is then unsatisfiable
% 13.43/3.68 |-Branch two:
% 13.43/3.68 | (607) ~ (all_0_10_10 = n1)
% 13.43/3.68 | (608) all_0_10_10 = n0
% 13.43/3.68 |
% 13.43/3.68 | From (608) and (211) follows:
% 13.43/3.68 | (609) pred(n0) = all_0_6_6
% 13.43/3.68 |
% 13.43/3.68 | From (608) and (41) follows:
% 13.43/3.68 | (610) succ(n0) = all_0_8_8
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (158) with n0, all_0_6_6, n10 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n10, yields:
% 13.43/3.68 | (611) all_0_6_6 = n10
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (141) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 13.43/3.68 | (612) all_0_8_8 = n1
% 13.43/3.68 |
% 13.43/3.68 | From (611)(612) and (178) follows:
% 13.43/3.68 | (613) sum(n10, n1) = all_0_1_1
% 13.43/3.68 |
% 13.43/3.68 | From (611) and (1182) follows:
% 13.43/3.68 | (1318) sum(n10, n9) = all_0_4_4
% 13.43/3.68 |
% 13.43/3.68 | From (612) and (1184) follows:
% 13.43/3.68 | (1319) sum(n7, n1) = all_0_7_7
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n10, n9, all_0_4_4, n8 and discharging atoms sum(n10, n9) = all_0_4_4, sum(n10, n9) = n8, yields:
% 13.43/3.68 | (262) all_0_4_4 = n8
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n10, n1, all_0_1_1, n0 and discharging atoms sum(n10, n1) = all_0_1_1, sum(n10, n1) = n0, yields:
% 13.43/3.68 | (616) all_0_1_1 = n0
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n7, n1, all_0_7_7, n8 and discharging atoms sum(n7, n1) = all_0_7_7, sum(n7, n1) = n8, yields:
% 13.43/3.68 | (264) all_0_7_7 = n8
% 13.43/3.68 |
% 13.43/3.68 | From (264)(262) and (119) follows:
% 13.43/3.68 | (266) sum(n8, n8) = all_0_3_3
% 13.43/3.68 |
% 13.43/3.68 | From (616) and (1186) follows:
% 13.43/3.68 | (1324) sum(n5, n0) = all_0_0_0
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n8, n8, all_0_3_3, n5 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n5, yields:
% 13.43/3.68 | (267) all_0_3_3 = n5
% 13.43/3.68 |
% 13.43/3.68 | Instantiating formula (31) with n5, n0, all_0_0_0, n5 and discharging atoms sum(n5, n0) = all_0_0_0, sum(n5, n0) = n5, yields:
% 13.43/3.68 | (268) all_0_0_0 = n5
% 13.43/3.68 |
% 13.43/3.68 | Equations (268,267) can reduce 104 to:
% 13.43/3.68 | (251) $false
% 13.43/3.68 |
% 13.43/3.68 |-The branch is then unsatisfiable
% 13.43/3.68 |-Branch two:
% 13.43/3.68 | (288) ~ (all_0_11_11 = n8)
% 13.43/3.68 | (289) all_0_11_11 = n7 | all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.43/3.68 |
% 13.43/3.68 +-Applying beta-rule and splitting (480), into two cases.
% 13.43/3.68 |-Branch one:
% 13.43/3.69 | (481) all_0_10_10 = n7
% 13.43/3.69 |
% 13.43/3.69 | From (481) and (211) follows:
% 13.43/3.69 | (482) pred(n7) = all_0_6_6
% 13.43/3.69 |
% 13.43/3.69 | From (481) and (41) follows:
% 13.43/3.69 | (483) succ(n7) = all_0_8_8
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (158) with n7, all_0_6_6, n6 and discharging atoms pred(n7) = all_0_6_6, pred(n7) = n6, yields:
% 13.43/3.69 | (484) all_0_6_6 = n6
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (141) with n7, all_0_8_8, n8 and discharging atoms succ(n7) = all_0_8_8, succ(n7) = n8, yields:
% 13.43/3.69 | (485) all_0_8_8 = n8
% 13.43/3.69 |
% 13.43/3.69 | From (484) and (482) follows:
% 13.43/3.69 | (51) pred(n7) = n6
% 13.43/3.69 |
% 13.43/3.69 | From (485) and (483) follows:
% 13.43/3.69 | (114) succ(n7) = n8
% 13.43/3.69 |
% 13.43/3.69 | From (484) and (33) follows:
% 13.43/3.69 | (1337) sum(n6, all_0_5_5) = all_0_4_4
% 13.43/3.69 |
% 13.43/3.69 | From (484)(485) and (178) follows:
% 13.43/3.69 | (486) sum(n6, n8) = all_0_1_1
% 13.43/3.69 |
% 13.43/3.69 | From (485) and (137) follows:
% 13.43/3.69 | (1339) sum(all_0_9_9, n8) = all_0_7_7
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (31) with n6, n8, all_0_1_1, n3 and discharging atoms sum(n6, n8) = all_0_1_1, sum(n6, n8) = n3, yields:
% 13.43/3.69 | (490) all_0_1_1 = n3
% 13.43/3.69 |
% 13.43/3.69 | From (490) and (4) follows:
% 13.43/3.69 | (1341) sum(all_0_2_2, n3) = all_0_0_0
% 13.43/3.69 |
% 13.43/3.69 | From (490) and (486) follows:
% 13.43/3.69 | (198) sum(n6, n8) = n3
% 13.43/3.69 |
% 13.43/3.69 +-Applying beta-rule and splitting (289), into two cases.
% 13.43/3.69 |-Branch one:
% 13.43/3.69 | (290) all_0_11_11 = n7
% 13.43/3.69 |
% 13.43/3.69 | From (290) and (84) follows:
% 13.43/3.69 | (291) pred(n7) = all_0_9_9
% 13.43/3.69 |
% 13.43/3.69 | From (290) and (210) follows:
% 13.43/3.69 | (292) succ(n7) = all_0_5_5
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (158) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 13.43/3.69 | (293) all_0_9_9 = n6
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (141) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 13.43/3.69 | (294) all_0_5_5 = n8
% 13.43/3.69 |
% 13.43/3.69 | From (293)(294) and (48) follows:
% 13.43/3.69 | (295) sum(n6, n8) = all_0_2_2
% 13.43/3.69 |
% 13.43/3.69 | From (293) and (1339) follows:
% 13.43/3.69 | (1349) sum(n6, n8) = all_0_7_7
% 13.43/3.69 |
% 13.43/3.69 | From (294) and (1337) follows:
% 13.43/3.69 | (1350) sum(n6, n8) = all_0_4_4
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (31) with n6, n8, all_0_2_2, n3 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n3, yields:
% 13.43/3.69 | (299) all_0_2_2 = n3
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (31) 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:
% 13.43/3.69 | (238) all_0_2_2 = all_0_4_4
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (31) 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:
% 13.43/3.69 | (239) all_0_2_2 = all_0_7_7
% 13.43/3.69 |
% 13.43/3.69 | Combining equations (239,238) yields a new equation:
% 13.43/3.69 | (240) all_0_4_4 = all_0_7_7
% 13.43/3.69 |
% 13.43/3.69 | Combining equations (299,238) yields a new equation:
% 13.43/3.69 | (352) all_0_4_4 = n3
% 13.43/3.69 |
% 13.43/3.69 | Combining equations (352,240) yields a new equation:
% 13.43/3.69 | (354) all_0_7_7 = n3
% 13.43/3.69 |
% 13.43/3.69 | Combining equations (354,240) yields a new equation:
% 13.43/3.69 | (352) all_0_4_4 = n3
% 13.43/3.69 |
% 13.43/3.69 | Combining equations (352,238) yields a new equation:
% 13.43/3.69 | (299) all_0_2_2 = n3
% 13.43/3.69 |
% 13.43/3.69 | From (299) and (1341) follows:
% 13.43/3.69 | (1359) sum(n3, n3) = all_0_0_0
% 13.43/3.69 |
% 13.43/3.69 | From (354)(352) and (119) follows:
% 13.43/3.69 | (356) sum(n3, n3) = all_0_3_3
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (31) with n3, n3, all_0_0_0, n6 and discharging atoms sum(n3, n3) = all_0_0_0, sum(n3, n3) = n6, yields:
% 13.43/3.69 | (357) all_0_0_0 = n6
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (31) with n3, n3, all_0_3_3, all_0_0_0 and discharging atoms sum(n3, n3) = all_0_0_0, sum(n3, n3) = all_0_3_3, yields:
% 13.43/3.69 | (248) all_0_0_0 = all_0_3_3
% 13.43/3.69 |
% 13.43/3.69 | Combining equations (357,248) yields a new equation:
% 13.43/3.69 | (358) all_0_3_3 = n6
% 13.43/3.69 |
% 13.43/3.69 | Combining equations (358,248) yields a new equation:
% 13.43/3.69 | (357) all_0_0_0 = n6
% 13.43/3.69 |
% 13.43/3.69 | Equations (357,358) can reduce 104 to:
% 13.43/3.69 | (251) $false
% 13.43/3.69 |
% 13.43/3.69 |-The branch is then unsatisfiable
% 13.43/3.69 |-Branch two:
% 13.43/3.69 | (306) ~ (all_0_11_11 = n7)
% 13.43/3.69 | (307) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.43/3.69 |
% 13.43/3.69 +-Applying beta-rule and splitting (307), into two cases.
% 13.43/3.69 |-Branch one:
% 13.43/3.69 | (308) all_0_11_11 = n6
% 13.43/3.69 |
% 13.43/3.69 | From (308) and (84) follows:
% 13.43/3.69 | (309) pred(n6) = all_0_9_9
% 13.43/3.69 |
% 13.43/3.69 | From (308) and (210) follows:
% 13.43/3.69 | (310) succ(n6) = all_0_5_5
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (158) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 13.43/3.69 | (311) all_0_9_9 = n5
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (141) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 13.43/3.69 | (312) all_0_5_5 = n7
% 13.43/3.69 |
% 13.43/3.69 | From (311)(312) and (48) follows:
% 13.43/3.69 | (313) sum(n5, n7) = all_0_2_2
% 13.43/3.69 |
% 13.43/3.69 | From (311) and (1339) follows:
% 13.43/3.69 | (1374) sum(n5, n8) = all_0_7_7
% 13.43/3.69 |
% 13.43/3.69 | From (312) and (1337) follows:
% 13.43/3.69 | (1375) sum(n6, n7) = all_0_4_4
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (31) with n6, n7, all_0_4_4, n2 and discharging atoms sum(n6, n7) = all_0_4_4, sum(n6, n7) = n2, yields:
% 13.43/3.69 | (370) all_0_4_4 = n2
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (31) with n5, n8, all_0_7_7, n2 and discharging atoms sum(n5, n8) = all_0_7_7, sum(n5, n8) = n2, yields:
% 13.43/3.69 | (372) all_0_7_7 = n2
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (31) with n5, n7, all_0_2_2, n1 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n1, yields:
% 13.43/3.69 | (317) all_0_2_2 = n1
% 13.43/3.69 |
% 13.43/3.69 | From (317) and (1341) follows:
% 13.43/3.69 | (1379) sum(n1, n3) = all_0_0_0
% 13.43/3.69 |
% 13.43/3.69 | From (372)(370) and (119) follows:
% 13.43/3.69 | (374) sum(n2, n2) = all_0_3_3
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (31) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 13.43/3.69 | (376) all_0_3_3 = n4
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (31) with n1, n3, all_0_0_0, n4 and discharging atoms sum(n1, n3) = all_0_0_0, sum(n1, n3) = n4, yields:
% 13.43/3.69 | (375) all_0_0_0 = n4
% 13.43/3.69 |
% 13.43/3.69 | Equations (375,376) can reduce 104 to:
% 13.43/3.69 | (251) $false
% 13.43/3.69 |
% 13.43/3.69 |-The branch is then unsatisfiable
% 13.43/3.69 |-Branch two:
% 13.43/3.69 | (324) ~ (all_0_11_11 = n6)
% 13.43/3.69 | (325) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.43/3.69 |
% 13.43/3.69 +-Applying beta-rule and splitting (325), into two cases.
% 13.43/3.69 |-Branch one:
% 13.43/3.69 | (326) all_0_11_11 = n5
% 13.43/3.69 |
% 13.43/3.69 | From (326) and (84) follows:
% 13.43/3.69 | (327) pred(n5) = all_0_9_9
% 13.43/3.69 |
% 13.43/3.69 | From (326) and (210) follows:
% 13.43/3.69 | (328) succ(n5) = all_0_5_5
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (158) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 13.43/3.69 | (329) all_0_9_9 = n4
% 13.43/3.69 |
% 13.43/3.69 | Instantiating formula (141) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 13.43/3.69 | (330) all_0_5_5 = n6
% 13.43/3.69 |
% 13.43/3.69 | From (329)(330) and (48) follows:
% 13.43/3.69 | (331) sum(n4, n6) = all_0_2_2
% 13.43/3.69 |
% 13.43/3.69 | From (329) and (1339) follows:
% 13.43/3.69 | (1392) sum(n4, n8) = all_0_7_7
% 13.43/3.69 |
% 13.43/3.69 | From (330) and (1337) follows:
% 13.43/3.70 | (1393) sum(n6, n6) = all_0_4_4
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n6, n6, all_0_4_4, n1 and discharging atoms sum(n6, n6) = all_0_4_4, sum(n6, n6) = n1, yields:
% 13.43/3.70 | (388) all_0_4_4 = n1
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n4, n8, all_0_7_7, n1 and discharging atoms sum(n4, n8) = all_0_7_7, sum(n4, n8) = n1, yields:
% 13.43/3.70 | (390) all_0_7_7 = n1
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 13.43/3.70 | (335) all_0_2_2 = n10
% 13.43/3.70 |
% 13.43/3.70 | From (335) and (1341) follows:
% 13.43/3.70 | (1397) sum(n10, n3) = all_0_0_0
% 13.43/3.70 |
% 13.43/3.70 | From (390)(388) and (119) follows:
% 13.43/3.70 | (392) sum(n1, n1) = all_0_3_3
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n10, n3, all_0_0_0, n2 and discharging atoms sum(n10, n3) = all_0_0_0, sum(n10, n3) = n2, yields:
% 13.43/3.70 | (393) all_0_0_0 = n2
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 13.43/3.70 | (394) all_0_3_3 = n2
% 13.43/3.70 |
% 13.43/3.70 | Equations (393,394) can reduce 104 to:
% 13.43/3.70 | (251) $false
% 13.43/3.70 |
% 13.43/3.70 |-The branch is then unsatisfiable
% 13.43/3.70 |-Branch two:
% 13.43/3.70 | (342) ~ (all_0_11_11 = n5)
% 13.43/3.70 | (343) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.43/3.70 |
% 13.43/3.70 +-Applying beta-rule and splitting (343), into two cases.
% 13.43/3.70 |-Branch one:
% 13.43/3.70 | (344) all_0_11_11 = n4
% 13.43/3.70 |
% 13.43/3.70 | From (344) and (84) follows:
% 13.43/3.70 | (345) pred(n4) = all_0_9_9
% 13.43/3.70 |
% 13.43/3.70 | From (344) and (210) follows:
% 13.43/3.70 | (346) succ(n4) = all_0_5_5
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (158) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 13.43/3.70 | (347) all_0_9_9 = n3
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (141) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 13.43/3.70 | (348) all_0_5_5 = n5
% 13.43/3.70 |
% 13.43/3.70 | From (347)(348) and (48) follows:
% 13.43/3.70 | (349) sum(n3, n5) = all_0_2_2
% 13.43/3.70 |
% 13.43/3.70 | From (347) and (1339) follows:
% 13.43/3.70 | (1410) sum(n3, n8) = all_0_7_7
% 13.43/3.70 |
% 13.43/3.70 | From (348) and (1337) follows:
% 13.43/3.70 | (1411) sum(n6, n5) = all_0_4_4
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n6, n5, all_0_4_4, n0 and discharging atoms sum(n6, n5) = all_0_4_4, sum(n6, n5) = n0, yields:
% 13.43/3.70 | (406) all_0_4_4 = n0
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n3, n8, all_0_7_7, n0 and discharging atoms sum(n3, n8) = all_0_7_7, sum(n3, n8) = n0, yields:
% 13.43/3.70 | (408) all_0_7_7 = n0
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 13.43/3.70 | (353) all_0_2_2 = n8
% 13.43/3.70 |
% 13.43/3.70 | From (353) and (1341) follows:
% 13.43/3.70 | (1415) sum(n8, n3) = all_0_0_0
% 13.43/3.70 |
% 13.43/3.70 | From (408)(406) and (119) follows:
% 13.43/3.70 | (410) sum(n0, n0) = all_0_3_3
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n8, n3, all_0_0_0, n0 and discharging atoms sum(n8, n3) = all_0_0_0, sum(n8, n3) = n0, yields:
% 13.43/3.70 | (412) all_0_0_0 = n0
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 13.43/3.70 | (413) all_0_3_3 = n0
% 13.43/3.70 |
% 13.43/3.70 | Equations (412,413) can reduce 104 to:
% 13.43/3.70 | (251) $false
% 13.43/3.70 |
% 13.43/3.70 |-The branch is then unsatisfiable
% 13.43/3.70 |-Branch two:
% 13.43/3.70 | (360) ~ (all_0_11_11 = n4)
% 13.43/3.70 | (361) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.43/3.70 |
% 13.43/3.70 +-Applying beta-rule and splitting (361), into two cases.
% 13.43/3.70 |-Branch one:
% 13.43/3.70 | (362) all_0_11_11 = n3
% 13.43/3.70 |
% 13.43/3.70 | From (362) and (84) follows:
% 13.43/3.70 | (363) pred(n3) = all_0_9_9
% 13.43/3.70 |
% 13.43/3.70 | From (362) and (210) follows:
% 13.43/3.70 | (364) succ(n3) = all_0_5_5
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (158) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 13.43/3.70 | (365) all_0_9_9 = n2
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (141) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 13.43/3.70 | (366) all_0_5_5 = n4
% 13.43/3.70 |
% 13.43/3.70 | From (365)(366) and (48) follows:
% 13.43/3.70 | (367) sum(n2, n4) = all_0_2_2
% 13.43/3.70 |
% 13.43/3.70 | From (365) and (1339) follows:
% 13.43/3.70 | (1428) sum(n2, n8) = all_0_7_7
% 13.43/3.70 |
% 13.43/3.70 | From (366) and (1337) follows:
% 13.43/3.70 | (1429) sum(n6, n4) = all_0_4_4
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n6, n4, all_0_4_4, n10 and discharging atoms sum(n6, n4) = all_0_4_4, sum(n6, n4) = n10, yields:
% 13.43/3.70 | (426) all_0_4_4 = n10
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n2, n8, all_0_7_7, n10 and discharging atoms sum(n2, n8) = all_0_7_7, sum(n2, n8) = n10, yields:
% 13.43/3.70 | (425) all_0_7_7 = n10
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 13.43/3.70 | (371) all_0_2_2 = n6
% 13.43/3.70 |
% 13.43/3.70 | From (371) and (1341) follows:
% 13.43/3.70 | (1433) sum(n6, n3) = all_0_0_0
% 13.43/3.70 |
% 13.43/3.70 | From (425)(426) and (119) follows:
% 13.43/3.70 | (428) sum(n10, n10) = all_0_3_3
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n10, n10, all_0_3_3, n9 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n9, yields:
% 13.43/3.70 | (429) all_0_3_3 = n9
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n6, n3, all_0_0_0, n9 and discharging atoms sum(n6, n3) = all_0_0_0, sum(n6, n3) = n9, yields:
% 13.43/3.70 | (430) all_0_0_0 = n9
% 13.43/3.70 |
% 13.43/3.70 | Equations (430,429) can reduce 104 to:
% 13.43/3.70 | (251) $false
% 13.43/3.70 |
% 13.43/3.70 |-The branch is then unsatisfiable
% 13.43/3.70 |-Branch two:
% 13.43/3.70 | (378) ~ (all_0_11_11 = n3)
% 13.43/3.70 | (379) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.43/3.70 |
% 13.43/3.70 +-Applying beta-rule and splitting (379), into two cases.
% 13.43/3.70 |-Branch one:
% 13.43/3.70 | (380) all_0_11_11 = n2
% 13.43/3.70 |
% 13.43/3.70 | From (380) and (84) follows:
% 13.43/3.70 | (381) pred(n2) = all_0_9_9
% 13.43/3.70 |
% 13.43/3.70 | From (380) and (210) follows:
% 13.43/3.70 | (382) succ(n2) = all_0_5_5
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (158) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 13.43/3.70 | (383) all_0_9_9 = n1
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (141) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 13.43/3.70 | (384) all_0_5_5 = n3
% 13.43/3.70 |
% 13.43/3.70 | From (383)(384) and (48) follows:
% 13.43/3.70 | (385) sum(n1, n3) = all_0_2_2
% 13.43/3.70 |
% 13.43/3.70 | From (383) and (1339) follows:
% 13.43/3.70 | (1446) sum(n1, n8) = all_0_7_7
% 13.43/3.70 |
% 13.43/3.70 | From (384) and (1337) follows:
% 13.43/3.70 | (1447) sum(n6, n3) = all_0_4_4
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n6, n3, all_0_4_4, n9 and discharging atoms sum(n6, n3) = all_0_4_4, sum(n6, n3) = n9, yields:
% 13.43/3.70 | (241) all_0_4_4 = n9
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n1, n8, all_0_7_7, n9 and discharging atoms sum(n1, n8) = all_0_7_7, sum(n1, n8) = n9, yields:
% 13.43/3.70 | (242) all_0_7_7 = n9
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 13.43/3.70 | (389) all_0_2_2 = n4
% 13.43/3.70 |
% 13.43/3.70 | From (389) and (1341) follows:
% 13.43/3.70 | (1451) sum(n4, n3) = all_0_0_0
% 13.43/3.70 |
% 13.43/3.70 | From (242)(241) and (119) follows:
% 13.43/3.70 | (246) sum(n9, n9) = all_0_3_3
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n9, n9, all_0_3_3, n7 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n7, yields:
% 13.43/3.70 | (249) all_0_3_3 = n7
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n4, n3, all_0_0_0, n7 and discharging atoms sum(n4, n3) = all_0_0_0, sum(n4, n3) = n7, yields:
% 13.43/3.70 | (247) all_0_0_0 = n7
% 13.43/3.70 |
% 13.43/3.70 | Equations (247,249) can reduce 104 to:
% 13.43/3.70 | (251) $false
% 13.43/3.70 |
% 13.43/3.70 |-The branch is then unsatisfiable
% 13.43/3.70 |-Branch two:
% 13.43/3.70 | (396) ~ (all_0_11_11 = n2)
% 13.43/3.70 | (397) all_0_11_11 = n1 | all_0_11_11 = n0
% 13.43/3.70 |
% 13.43/3.70 +-Applying beta-rule and splitting (397), into two cases.
% 13.43/3.70 |-Branch one:
% 13.43/3.70 | (398) all_0_11_11 = n1
% 13.43/3.70 |
% 13.43/3.70 | From (398) and (84) follows:
% 13.43/3.70 | (399) pred(n1) = all_0_9_9
% 13.43/3.70 |
% 13.43/3.70 | From (398) and (210) follows:
% 13.43/3.70 | (400) succ(n1) = all_0_5_5
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (158) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 13.43/3.70 | (401) all_0_9_9 = n0
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (141) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 13.43/3.70 | (402) all_0_5_5 = n2
% 13.43/3.70 |
% 13.43/3.70 | From (401)(402) and (48) follows:
% 13.43/3.70 | (403) sum(n0, n2) = all_0_2_2
% 13.43/3.70 |
% 13.43/3.70 | From (401) and (1339) follows:
% 13.43/3.70 | (1464) sum(n0, n8) = all_0_7_7
% 13.43/3.70 |
% 13.43/3.70 | From (402) and (1337) follows:
% 13.43/3.70 | (1465) sum(n6, n2) = all_0_4_4
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n6, n2, all_0_4_4, n8 and discharging atoms sum(n6, n2) = all_0_4_4, sum(n6, n2) = n8, yields:
% 13.43/3.70 | (262) all_0_4_4 = n8
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n0, n8, all_0_7_7, n8 and discharging atoms sum(n0, n8) = all_0_7_7, sum(n0, n8) = n8, yields:
% 13.43/3.70 | (264) all_0_7_7 = n8
% 13.43/3.70 |
% 13.43/3.70 | Instantiating formula (31) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 13.43/3.70 | (407) all_0_2_2 = n2
% 13.43/3.70 |
% 13.43/3.70 | From (407) and (1341) follows:
% 13.43/3.70 | (1469) sum(n2, n3) = all_0_0_0
% 13.43/3.70 |
% 13.43/3.70 | From (264)(262) and (119) follows:
% 13.43/3.71 | (266) sum(n8, n8) = all_0_3_3
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (31) with n8, n8, all_0_3_3, n5 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n5, yields:
% 13.43/3.71 | (267) all_0_3_3 = n5
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (31) with n2, n3, all_0_0_0, n5 and discharging atoms sum(n2, n3) = all_0_0_0, sum(n2, n3) = n5, yields:
% 13.43/3.71 | (268) all_0_0_0 = n5
% 13.43/3.71 |
% 13.43/3.71 | Equations (268,267) can reduce 104 to:
% 13.43/3.71 | (251) $false
% 13.43/3.71 |
% 13.43/3.71 |-The branch is then unsatisfiable
% 13.43/3.71 |-Branch two:
% 13.43/3.71 | (415) ~ (all_0_11_11 = n1)
% 13.43/3.71 | (416) all_0_11_11 = n0
% 13.43/3.71 |
% 13.43/3.71 | From (416) and (84) follows:
% 13.43/3.71 | (417) pred(n0) = all_0_9_9
% 13.43/3.71 |
% 13.43/3.71 | From (416) and (210) follows:
% 13.43/3.71 | (418) succ(n0) = all_0_5_5
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (158) with n0, all_0_9_9, n10 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n10, yields:
% 13.43/3.71 | (419) all_0_9_9 = n10
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (141) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 13.43/3.71 | (420) all_0_5_5 = n1
% 13.43/3.71 |
% 13.43/3.71 | From (419)(420) and (48) follows:
% 13.43/3.71 | (421) sum(n10, n1) = all_0_2_2
% 13.43/3.71 |
% 13.43/3.71 | From (419) and (1339) follows:
% 13.43/3.71 | (1481) sum(n10, n8) = all_0_7_7
% 13.43/3.71 |
% 13.43/3.71 | From (420) and (1337) follows:
% 13.43/3.71 | (1482) sum(n6, n1) = all_0_4_4
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (31) with n10, n8, all_0_7_7, n7 and discharging atoms sum(n10, n8) = all_0_7_7, sum(n10, n8) = n7, yields:
% 13.43/3.71 | (282) all_0_7_7 = n7
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (31) with n10, n1, all_0_2_2, n0 and discharging atoms sum(n10, n1) = all_0_2_2, sum(n10, n1) = n0, yields:
% 13.43/3.71 | (424) all_0_2_2 = n0
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (31) with n6, n1, all_0_4_4, n7 and discharging atoms sum(n6, n1) = all_0_4_4, sum(n6, n1) = n7, yields:
% 13.43/3.71 | (280) all_0_4_4 = n7
% 13.43/3.71 |
% 13.43/3.71 | From (424) and (1341) follows:
% 13.43/3.71 | (1486) sum(n0, n3) = all_0_0_0
% 13.43/3.71 |
% 13.43/3.71 | From (282)(280) and (119) follows:
% 13.43/3.71 | (284) sum(n7, n7) = all_0_3_3
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (31) with n7, n7, all_0_3_3, n3 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n3, yields:
% 13.43/3.71 | (285) all_0_3_3 = n3
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (31) with n0, n3, all_0_0_0, n3 and discharging atoms sum(n0, n3) = all_0_0_0, sum(n0, n3) = n3, yields:
% 13.43/3.71 | (286) all_0_0_0 = n3
% 13.43/3.71 |
% 13.43/3.71 | Equations (286,285) can reduce 104 to:
% 13.43/3.71 | (251) $false
% 13.43/3.71 |
% 13.43/3.71 |-The branch is then unsatisfiable
% 13.43/3.71 |-Branch two:
% 13.43/3.71 | (497) ~ (all_0_10_10 = n7)
% 13.43/3.71 | (498) all_0_10_10 = n6 | all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.43/3.71 |
% 13.43/3.71 +-Applying beta-rule and splitting (289), into two cases.
% 13.43/3.71 |-Branch one:
% 13.43/3.71 | (290) all_0_11_11 = n7
% 13.43/3.71 |
% 13.43/3.71 | From (290) and (84) follows:
% 13.43/3.71 | (291) pred(n7) = all_0_9_9
% 13.43/3.71 |
% 13.43/3.71 | From (290) and (210) follows:
% 13.43/3.71 | (292) succ(n7) = all_0_5_5
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (158) with n7, all_0_9_9, n6 and discharging atoms pred(n7) = all_0_9_9, pred(n7) = n6, yields:
% 13.43/3.71 | (293) all_0_9_9 = n6
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (141) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 13.43/3.71 | (294) all_0_5_5 = n8
% 13.43/3.71 |
% 13.43/3.71 | From (294) and (33) follows:
% 13.43/3.71 | (1498) sum(all_0_6_6, n8) = all_0_4_4
% 13.43/3.71 |
% 13.43/3.71 | From (293)(294) and (48) follows:
% 13.43/3.71 | (295) sum(n6, n8) = all_0_2_2
% 13.43/3.71 |
% 13.43/3.71 | From (293) and (137) follows:
% 13.43/3.71 | (1500) sum(n6, all_0_8_8) = all_0_7_7
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (31) with n6, n8, all_0_2_2, n3 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n3, yields:
% 13.43/3.71 | (299) all_0_2_2 = n3
% 13.43/3.71 |
% 13.43/3.71 | From (299) and (4) follows:
% 13.43/3.71 | (1502) sum(n3, all_0_1_1) = all_0_0_0
% 13.43/3.71 |
% 13.43/3.71 +-Applying beta-rule and splitting (498), into two cases.
% 13.43/3.71 |-Branch one:
% 13.43/3.71 | (499) all_0_10_10 = n6
% 13.43/3.71 |
% 13.43/3.71 | From (499) and (211) follows:
% 13.43/3.71 | (500) pred(n6) = all_0_6_6
% 13.43/3.71 |
% 13.43/3.71 | From (499) and (41) follows:
% 13.43/3.71 | (501) succ(n6) = all_0_8_8
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (158) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 13.43/3.71 | (502) all_0_6_6 = n5
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (141) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 13.43/3.71 | (503) all_0_8_8 = n7
% 13.43/3.71 |
% 13.43/3.71 | From (502)(503) and (178) follows:
% 13.43/3.71 | (504) sum(n5, n7) = all_0_1_1
% 13.43/3.71 |
% 13.43/3.71 | From (502) and (1498) follows:
% 13.43/3.71 | (1509) sum(n5, n8) = all_0_4_4
% 13.43/3.71 |
% 13.43/3.71 | From (503) and (1500) follows:
% 13.43/3.71 | (1510) sum(n6, n7) = all_0_7_7
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (31) with n6, n7, all_0_7_7, n2 and discharging atoms sum(n6, n7) = all_0_7_7, sum(n6, n7) = n2, yields:
% 13.43/3.71 | (372) all_0_7_7 = n2
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (31) with n5, n8, all_0_4_4, n2 and discharging atoms sum(n5, n8) = all_0_4_4, sum(n5, n8) = n2, yields:
% 13.43/3.71 | (370) all_0_4_4 = n2
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (31) with n5, n7, all_0_1_1, n1 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n1, yields:
% 13.43/3.71 | (508) all_0_1_1 = n1
% 13.43/3.71 |
% 13.43/3.71 | From (372)(370) and (119) follows:
% 13.43/3.71 | (374) sum(n2, n2) = all_0_3_3
% 13.43/3.71 |
% 13.43/3.71 | From (508) and (1502) follows:
% 13.43/3.71 | (1515) sum(n3, n1) = all_0_0_0
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (31) with n3, n1, all_0_0_0, n4 and discharging atoms sum(n3, n1) = all_0_0_0, sum(n3, n1) = n4, yields:
% 13.43/3.71 | (375) all_0_0_0 = n4
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (31) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 13.43/3.71 | (376) all_0_3_3 = n4
% 13.43/3.71 |
% 13.43/3.71 | Equations (375,376) can reduce 104 to:
% 13.43/3.71 | (251) $false
% 13.43/3.71 |
% 13.43/3.71 |-The branch is then unsatisfiable
% 13.43/3.71 |-Branch two:
% 13.43/3.71 | (515) ~ (all_0_10_10 = n6)
% 13.43/3.71 | (516) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.43/3.71 |
% 13.43/3.71 +-Applying beta-rule and splitting (516), into two cases.
% 13.43/3.71 |-Branch one:
% 13.43/3.71 | (517) all_0_10_10 = n5
% 13.43/3.71 |
% 13.43/3.71 | From (517) and (211) follows:
% 13.43/3.71 | (518) pred(n5) = all_0_6_6
% 13.43/3.71 |
% 13.43/3.71 | From (517) and (41) follows:
% 13.43/3.71 | (519) succ(n5) = all_0_8_8
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (158) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 13.43/3.71 | (520) all_0_6_6 = n4
% 13.43/3.71 |
% 13.43/3.71 | Instantiating formula (141) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 13.43/3.71 | (521) all_0_8_8 = n6
% 13.43/3.71 |
% 13.43/3.71 | From (520)(521) and (178) follows:
% 13.43/3.71 | (522) sum(n4, n6) = all_0_1_1
% 13.43/3.71 |
% 13.43/3.71 | From (520) and (1498) follows:
% 13.82/3.71 | (1527) sum(n4, n8) = all_0_4_4
% 13.82/3.71 |
% 13.82/3.71 | From (521) and (1500) follows:
% 13.82/3.71 | (1528) sum(n6, n6) = all_0_7_7
% 13.82/3.71 |
% 13.82/3.71 | Instantiating formula (31) with n6, n6, all_0_7_7, n1 and discharging atoms sum(n6, n6) = all_0_7_7, sum(n6, n6) = n1, yields:
% 13.82/3.71 | (390) all_0_7_7 = n1
% 13.82/3.71 |
% 13.82/3.71 | Instantiating formula (31) with n4, n8, all_0_4_4, n1 and discharging atoms sum(n4, n8) = all_0_4_4, sum(n4, n8) = n1, yields:
% 13.82/3.71 | (388) all_0_4_4 = n1
% 13.82/3.71 |
% 13.82/3.71 | Instantiating formula (31) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 13.82/3.71 | (526) all_0_1_1 = n10
% 13.82/3.71 |
% 13.82/3.71 | From (390)(388) and (119) follows:
% 13.82/3.71 | (392) sum(n1, n1) = all_0_3_3
% 13.82/3.71 |
% 13.82/3.71 | From (526) and (1502) follows:
% 13.82/3.71 | (1533) sum(n3, n10) = all_0_0_0
% 13.82/3.71 |
% 13.82/3.71 | Instantiating formula (31) with n3, n10, all_0_0_0, n2 and discharging atoms sum(n3, n10) = all_0_0_0, sum(n3, n10) = n2, yields:
% 13.82/3.71 | (393) all_0_0_0 = n2
% 13.82/3.71 |
% 13.82/3.71 | Instantiating formula (31) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 13.82/3.71 | (394) all_0_3_3 = n2
% 13.82/3.71 |
% 13.82/3.71 | Equations (393,394) can reduce 104 to:
% 13.82/3.71 | (251) $false
% 13.82/3.71 |
% 13.82/3.71 |-The branch is then unsatisfiable
% 13.82/3.71 |-Branch two:
% 13.82/3.71 | (533) ~ (all_0_10_10 = n5)
% 13.82/3.71 | (534) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.82/3.71 |
% 13.82/3.71 +-Applying beta-rule and splitting (534), into two cases.
% 13.82/3.71 |-Branch one:
% 13.82/3.71 | (535) all_0_10_10 = n4
% 13.82/3.71 |
% 13.82/3.71 | From (535) and (211) follows:
% 13.82/3.71 | (536) pred(n4) = all_0_6_6
% 13.82/3.71 |
% 13.82/3.71 | From (535) and (41) follows:
% 13.82/3.71 | (537) succ(n4) = all_0_8_8
% 13.82/3.71 |
% 13.82/3.71 | Instantiating formula (158) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 13.82/3.71 | (538) all_0_6_6 = n3
% 13.82/3.71 |
% 13.82/3.71 | Instantiating formula (141) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 13.82/3.71 | (539) all_0_8_8 = n5
% 13.82/3.71 |
% 13.82/3.71 | From (538)(539) and (178) follows:
% 13.82/3.71 | (540) sum(n3, n5) = all_0_1_1
% 13.82/3.71 |
% 13.82/3.71 | From (538) and (1498) follows:
% 13.82/3.71 | (1545) sum(n3, n8) = all_0_4_4
% 13.82/3.71 |
% 13.82/3.71 | From (539) and (1500) follows:
% 13.82/3.72 | (1546) sum(n6, n5) = all_0_7_7
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n6, n5, all_0_7_7, n0 and discharging atoms sum(n6, n5) = all_0_7_7, sum(n6, n5) = n0, yields:
% 13.82/3.72 | (408) all_0_7_7 = n0
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n3, n8, all_0_4_4, n0 and discharging atoms sum(n3, n8) = all_0_4_4, sum(n3, n8) = n0, yields:
% 13.82/3.72 | (406) all_0_4_4 = n0
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 13.82/3.72 | (544) all_0_1_1 = n8
% 13.82/3.72 |
% 13.82/3.72 | From (408)(406) and (119) follows:
% 13.82/3.72 | (410) sum(n0, n0) = all_0_3_3
% 13.82/3.72 |
% 13.82/3.72 | From (544) and (1502) follows:
% 13.82/3.72 | (1551) sum(n3, n8) = all_0_0_0
% 13.82/3.72 |
% 13.82/3.72 | From (406) and (1545) follows:
% 13.82/3.72 | (66) sum(n3, n8) = n0
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n3, n8, all_0_0_0, n0 and discharging atoms sum(n3, n8) = all_0_0_0, sum(n3, n8) = n0, yields:
% 13.82/3.72 | (412) all_0_0_0 = n0
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 13.82/3.72 | (413) all_0_3_3 = n0
% 13.82/3.72 |
% 13.82/3.72 | Equations (412,413) can reduce 104 to:
% 13.82/3.72 | (251) $false
% 13.82/3.72 |
% 13.82/3.72 |-The branch is then unsatisfiable
% 13.82/3.72 |-Branch two:
% 13.82/3.72 | (551) ~ (all_0_10_10 = n4)
% 13.82/3.72 | (552) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.82/3.72 |
% 13.82/3.72 +-Applying beta-rule and splitting (552), into two cases.
% 13.82/3.72 |-Branch one:
% 13.82/3.72 | (553) all_0_10_10 = n3
% 13.82/3.72 |
% 13.82/3.72 | From (553) and (211) follows:
% 13.82/3.72 | (554) pred(n3) = all_0_6_6
% 13.82/3.72 |
% 13.82/3.72 | From (553) and (41) follows:
% 13.82/3.72 | (555) succ(n3) = all_0_8_8
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (158) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 13.82/3.72 | (556) all_0_6_6 = n2
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (141) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 13.82/3.72 | (557) all_0_8_8 = n4
% 13.82/3.72 |
% 13.82/3.72 | From (556)(557) and (178) follows:
% 13.82/3.72 | (558) sum(n2, n4) = all_0_1_1
% 13.82/3.72 |
% 13.82/3.72 | From (556) and (1498) follows:
% 13.82/3.72 | (1564) sum(n2, n8) = all_0_4_4
% 13.82/3.72 |
% 13.82/3.72 | From (557) and (1500) follows:
% 13.82/3.72 | (1565) sum(n6, n4) = all_0_7_7
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n6, n4, all_0_7_7, n10 and discharging atoms sum(n6, n4) = all_0_7_7, sum(n6, n4) = n10, yields:
% 13.82/3.72 | (425) all_0_7_7 = n10
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n2, n8, all_0_4_4, n10 and discharging atoms sum(n2, n8) = all_0_4_4, sum(n2, n8) = n10, yields:
% 13.82/3.72 | (426) all_0_4_4 = n10
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 13.82/3.72 | (562) all_0_1_1 = n6
% 13.82/3.72 |
% 13.82/3.72 | From (425)(426) and (119) follows:
% 13.82/3.72 | (428) sum(n10, n10) = all_0_3_3
% 13.82/3.72 |
% 13.82/3.72 | From (562) and (1502) follows:
% 13.82/3.72 | (1570) sum(n3, n6) = all_0_0_0
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n10, n10, all_0_3_3, n9 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n9, yields:
% 13.82/3.72 | (429) all_0_3_3 = n9
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n3, n6, all_0_0_0, n9 and discharging atoms sum(n3, n6) = all_0_0_0, sum(n3, n6) = n9, yields:
% 13.82/3.72 | (430) all_0_0_0 = n9
% 13.82/3.72 |
% 13.82/3.72 | Equations (430,429) can reduce 104 to:
% 13.82/3.72 | (251) $false
% 13.82/3.72 |
% 13.82/3.72 |-The branch is then unsatisfiable
% 13.82/3.72 |-Branch two:
% 13.82/3.72 | (569) ~ (all_0_10_10 = n3)
% 13.82/3.72 | (570) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.82/3.72 |
% 13.82/3.72 +-Applying beta-rule and splitting (570), into two cases.
% 13.82/3.72 |-Branch one:
% 13.82/3.72 | (571) all_0_10_10 = n2
% 13.82/3.72 |
% 13.82/3.72 | From (571) and (211) follows:
% 13.82/3.72 | (572) pred(n2) = all_0_6_6
% 13.82/3.72 |
% 13.82/3.72 | From (571) and (41) follows:
% 13.82/3.72 | (573) succ(n2) = all_0_8_8
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (158) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 13.82/3.72 | (574) all_0_6_6 = n1
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (141) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 13.82/3.72 | (575) all_0_8_8 = n3
% 13.82/3.72 |
% 13.82/3.72 | From (574)(575) and (178) follows:
% 13.82/3.72 | (576) sum(n1, n3) = all_0_1_1
% 13.82/3.72 |
% 13.82/3.72 | From (574) and (1498) follows:
% 13.82/3.72 | (1582) sum(n1, n8) = all_0_4_4
% 13.82/3.72 |
% 13.82/3.72 | From (575) and (1500) follows:
% 13.82/3.72 | (1583) sum(n6, n3) = all_0_7_7
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n6, n3, all_0_7_7, n9 and discharging atoms sum(n6, n3) = all_0_7_7, sum(n6, n3) = n9, yields:
% 13.82/3.72 | (242) all_0_7_7 = n9
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n1, n8, all_0_4_4, n9 and discharging atoms sum(n1, n8) = all_0_4_4, sum(n1, n8) = n9, yields:
% 13.82/3.72 | (241) all_0_4_4 = n9
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 13.82/3.72 | (580) all_0_1_1 = n4
% 13.82/3.72 |
% 13.82/3.72 | From (242)(241) and (119) follows:
% 13.82/3.72 | (246) sum(n9, n9) = all_0_3_3
% 13.82/3.72 |
% 13.82/3.72 | From (580) and (1502) follows:
% 13.82/3.72 | (1588) sum(n3, n4) = all_0_0_0
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n9, n9, all_0_3_3, n7 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n7, yields:
% 13.82/3.72 | (249) all_0_3_3 = n7
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n3, n4, all_0_0_0, n7 and discharging atoms sum(n3, n4) = all_0_0_0, sum(n3, n4) = n7, yields:
% 13.82/3.72 | (247) all_0_0_0 = n7
% 13.82/3.72 |
% 13.82/3.72 | Equations (247,249) can reduce 104 to:
% 13.82/3.72 | (251) $false
% 13.82/3.72 |
% 13.82/3.72 |-The branch is then unsatisfiable
% 13.82/3.72 |-Branch two:
% 13.82/3.72 | (587) ~ (all_0_10_10 = n2)
% 13.82/3.72 | (588) all_0_10_10 = n1 | all_0_10_10 = n0
% 13.82/3.72 |
% 13.82/3.72 +-Applying beta-rule and splitting (588), into two cases.
% 13.82/3.72 |-Branch one:
% 13.82/3.72 | (589) all_0_10_10 = n1
% 13.82/3.72 |
% 13.82/3.72 | From (589) and (211) follows:
% 13.82/3.72 | (590) pred(n1) = all_0_6_6
% 13.82/3.72 |
% 13.82/3.72 | From (589) and (41) follows:
% 13.82/3.72 | (591) succ(n1) = all_0_8_8
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (158) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 13.82/3.72 | (592) all_0_6_6 = n0
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (141) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 13.82/3.72 | (593) all_0_8_8 = n2
% 13.82/3.72 |
% 13.82/3.72 | From (592)(593) and (178) follows:
% 13.82/3.72 | (594) sum(n0, n2) = all_0_1_1
% 13.82/3.72 |
% 13.82/3.72 | From (592) and (1498) follows:
% 13.82/3.72 | (1600) sum(n0, n8) = all_0_4_4
% 13.82/3.72 |
% 13.82/3.72 | From (593) and (1500) follows:
% 13.82/3.72 | (1601) sum(n6, n2) = all_0_7_7
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n6, n2, all_0_7_7, n8 and discharging atoms sum(n6, n2) = all_0_7_7, sum(n6, n2) = n8, yields:
% 13.82/3.72 | (264) all_0_7_7 = n8
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n0, n8, all_0_4_4, n8 and discharging atoms sum(n0, n8) = all_0_4_4, sum(n0, n8) = n8, yields:
% 13.82/3.72 | (262) all_0_4_4 = n8
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 13.82/3.72 | (598) all_0_1_1 = n2
% 13.82/3.72 |
% 13.82/3.72 | From (264)(262) and (119) follows:
% 13.82/3.72 | (266) sum(n8, n8) = all_0_3_3
% 13.82/3.72 |
% 13.82/3.72 | From (598) and (1502) follows:
% 13.82/3.72 | (1606) sum(n3, n2) = all_0_0_0
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n8, n8, all_0_3_3, n5 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n5, yields:
% 13.82/3.72 | (267) all_0_3_3 = n5
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n3, n2, all_0_0_0, n5 and discharging atoms sum(n3, n2) = all_0_0_0, sum(n3, n2) = n5, yields:
% 13.82/3.72 | (268) all_0_0_0 = n5
% 13.82/3.72 |
% 13.82/3.72 | Equations (268,267) can reduce 104 to:
% 13.82/3.72 | (251) $false
% 13.82/3.72 |
% 13.82/3.72 |-The branch is then unsatisfiable
% 13.82/3.72 |-Branch two:
% 13.82/3.72 | (607) ~ (all_0_10_10 = n1)
% 13.82/3.72 | (608) all_0_10_10 = n0
% 13.82/3.72 |
% 13.82/3.72 | From (608) and (211) follows:
% 13.82/3.72 | (609) pred(n0) = all_0_6_6
% 13.82/3.72 |
% 13.82/3.72 | From (608) and (41) follows:
% 13.82/3.72 | (610) succ(n0) = all_0_8_8
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (158) with n0, all_0_6_6, n10 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n10, yields:
% 13.82/3.72 | (611) all_0_6_6 = n10
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (141) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 13.82/3.72 | (612) all_0_8_8 = n1
% 13.82/3.72 |
% 13.82/3.72 | From (611)(612) and (178) follows:
% 13.82/3.72 | (613) sum(n10, n1) = all_0_1_1
% 13.82/3.72 |
% 13.82/3.72 | From (611) and (1498) follows:
% 13.82/3.72 | (1617) sum(n10, n8) = all_0_4_4
% 13.82/3.72 |
% 13.82/3.72 | From (612) and (1500) follows:
% 13.82/3.72 | (1618) sum(n6, n1) = all_0_7_7
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n10, n8, all_0_4_4, n7 and discharging atoms sum(n10, n8) = all_0_4_4, sum(n10, n8) = n7, yields:
% 13.82/3.72 | (280) all_0_4_4 = n7
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n10, n1, all_0_1_1, n0 and discharging atoms sum(n10, n1) = all_0_1_1, sum(n10, n1) = n0, yields:
% 13.82/3.72 | (616) all_0_1_1 = n0
% 13.82/3.72 |
% 13.82/3.72 | Instantiating formula (31) with n6, n1, all_0_7_7, n7 and discharging atoms sum(n6, n1) = all_0_7_7, sum(n6, n1) = n7, yields:
% 13.82/3.72 | (282) all_0_7_7 = n7
% 13.82/3.72 |
% 13.82/3.72 | From (282)(280) and (119) follows:
% 13.82/3.72 | (284) sum(n7, n7) = all_0_3_3
% 13.82/3.72 |
% 13.82/3.72 | From (616) and (1502) follows:
% 13.82/3.73 | (1623) sum(n3, n0) = all_0_0_0
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) with n7, n7, all_0_3_3, n3 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n3, yields:
% 13.82/3.73 | (285) all_0_3_3 = n3
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) with n3, n0, all_0_0_0, n3 and discharging atoms sum(n3, n0) = all_0_0_0, sum(n3, n0) = n3, yields:
% 13.82/3.73 | (286) all_0_0_0 = n3
% 13.82/3.73 |
% 13.82/3.73 | Equations (286,285) can reduce 104 to:
% 13.82/3.73 | (251) $false
% 13.82/3.73 |
% 13.82/3.73 |-The branch is then unsatisfiable
% 13.82/3.73 |-Branch two:
% 13.82/3.73 | (306) ~ (all_0_11_11 = n7)
% 13.82/3.73 | (307) all_0_11_11 = n6 | all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.82/3.73 |
% 13.82/3.73 +-Applying beta-rule and splitting (498), into two cases.
% 13.82/3.73 |-Branch one:
% 13.82/3.73 | (499) all_0_10_10 = n6
% 13.82/3.73 |
% 13.82/3.73 | From (499) and (211) follows:
% 13.82/3.73 | (500) pred(n6) = all_0_6_6
% 13.82/3.73 |
% 13.82/3.73 | From (499) and (41) follows:
% 13.82/3.73 | (501) succ(n6) = all_0_8_8
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (158) with n6, all_0_6_6, n5 and discharging atoms pred(n6) = all_0_6_6, pred(n6) = n5, yields:
% 13.82/3.73 | (502) all_0_6_6 = n5
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (141) with n6, all_0_8_8, n7 and discharging atoms succ(n6) = all_0_8_8, succ(n6) = n7, yields:
% 13.82/3.73 | (503) all_0_8_8 = n7
% 13.82/3.73 |
% 13.82/3.73 | From (502) and (500) follows:
% 13.82/3.73 | (21) pred(n6) = n5
% 13.82/3.73 |
% 13.82/3.73 | From (503) and (501) follows:
% 13.82/3.73 | (13) succ(n6) = n7
% 13.82/3.73 |
% 13.82/3.73 | From (502) and (33) follows:
% 13.82/3.73 | (1636) sum(n5, all_0_5_5) = all_0_4_4
% 13.82/3.73 |
% 13.82/3.73 | From (502)(503) and (178) follows:
% 13.82/3.73 | (504) sum(n5, n7) = all_0_1_1
% 13.82/3.73 |
% 13.82/3.73 | From (503) and (137) follows:
% 13.82/3.73 | (1638) sum(all_0_9_9, n7) = all_0_7_7
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) with n5, n7, all_0_1_1, n1 and discharging atoms sum(n5, n7) = all_0_1_1, sum(n5, n7) = n1, yields:
% 13.82/3.73 | (508) all_0_1_1 = n1
% 13.82/3.73 |
% 13.82/3.73 | From (508) and (4) follows:
% 13.82/3.73 | (1640) sum(all_0_2_2, n1) = all_0_0_0
% 13.82/3.73 |
% 13.82/3.73 | From (508) and (504) follows:
% 13.82/3.73 | (30) sum(n5, n7) = n1
% 13.82/3.73 |
% 13.82/3.73 +-Applying beta-rule and splitting (307), into two cases.
% 13.82/3.73 |-Branch one:
% 13.82/3.73 | (308) all_0_11_11 = n6
% 13.82/3.73 |
% 13.82/3.73 | From (308) and (84) follows:
% 13.82/3.73 | (309) pred(n6) = all_0_9_9
% 13.82/3.73 |
% 13.82/3.73 | From (308) and (210) follows:
% 13.82/3.73 | (310) succ(n6) = all_0_5_5
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (158) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 13.82/3.73 | (311) all_0_9_9 = n5
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (141) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 13.82/3.73 | (312) all_0_5_5 = n7
% 13.82/3.73 |
% 13.82/3.73 | From (311)(312) and (48) follows:
% 13.82/3.73 | (313) sum(n5, n7) = all_0_2_2
% 13.82/3.73 |
% 13.82/3.73 | From (311) and (1638) follows:
% 13.82/3.73 | (1648) sum(n5, n7) = all_0_7_7
% 13.82/3.73 |
% 13.82/3.73 | From (312) and (1636) follows:
% 13.82/3.73 | (1649) sum(n5, n7) = all_0_4_4
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) with n5, n7, all_0_2_2, n1 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n1, yields:
% 13.82/3.73 | (317) all_0_2_2 = n1
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) 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:
% 13.82/3.73 | (238) all_0_2_2 = all_0_4_4
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) 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:
% 13.82/3.73 | (239) all_0_2_2 = all_0_7_7
% 13.82/3.73 |
% 13.82/3.73 | Combining equations (239,238) yields a new equation:
% 13.82/3.73 | (240) all_0_4_4 = all_0_7_7
% 13.82/3.73 |
% 13.82/3.73 | Combining equations (317,238) yields a new equation:
% 13.82/3.73 | (388) all_0_4_4 = n1
% 13.82/3.73 |
% 13.82/3.73 | Combining equations (388,240) yields a new equation:
% 13.82/3.73 | (390) all_0_7_7 = n1
% 13.82/3.73 |
% 13.82/3.73 | Combining equations (390,240) yields a new equation:
% 13.82/3.73 | (388) all_0_4_4 = n1
% 13.82/3.73 |
% 13.82/3.73 | Combining equations (388,238) yields a new equation:
% 13.82/3.73 | (317) all_0_2_2 = n1
% 13.82/3.73 |
% 13.82/3.73 | From (317) and (1640) follows:
% 13.82/3.73 | (1658) sum(n1, n1) = all_0_0_0
% 13.82/3.73 |
% 13.82/3.73 | From (390)(388) and (119) follows:
% 13.82/3.73 | (392) sum(n1, n1) = all_0_3_3
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) with n1, n1, all_0_0_0, n2 and discharging atoms sum(n1, n1) = all_0_0_0, sum(n1, n1) = n2, yields:
% 13.82/3.73 | (393) all_0_0_0 = n2
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) with n1, n1, all_0_3_3, all_0_0_0 and discharging atoms sum(n1, n1) = all_0_0_0, sum(n1, n1) = all_0_3_3, yields:
% 13.82/3.73 | (248) all_0_0_0 = all_0_3_3
% 13.82/3.73 |
% 13.82/3.73 | Combining equations (393,248) yields a new equation:
% 13.82/3.73 | (394) all_0_3_3 = n2
% 13.82/3.73 |
% 13.82/3.73 | Combining equations (394,248) yields a new equation:
% 13.82/3.73 | (393) all_0_0_0 = n2
% 13.82/3.73 |
% 13.82/3.73 | Equations (393,394) can reduce 104 to:
% 13.82/3.73 | (251) $false
% 13.82/3.73 |
% 13.82/3.73 |-The branch is then unsatisfiable
% 13.82/3.73 |-Branch two:
% 13.82/3.73 | (324) ~ (all_0_11_11 = n6)
% 13.82/3.73 | (325) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.82/3.73 |
% 13.82/3.73 +-Applying beta-rule and splitting (325), into two cases.
% 13.82/3.73 |-Branch one:
% 13.82/3.73 | (326) all_0_11_11 = n5
% 13.82/3.73 |
% 13.82/3.73 | From (326) and (84) follows:
% 13.82/3.73 | (327) pred(n5) = all_0_9_9
% 13.82/3.73 |
% 13.82/3.73 | From (326) and (210) follows:
% 13.82/3.73 | (328) succ(n5) = all_0_5_5
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (158) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 13.82/3.73 | (329) all_0_9_9 = n4
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (141) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 13.82/3.73 | (330) all_0_5_5 = n6
% 13.82/3.73 |
% 13.82/3.73 | From (329)(330) and (48) follows:
% 13.82/3.73 | (331) sum(n4, n6) = all_0_2_2
% 13.82/3.73 |
% 13.82/3.73 | From (329) and (1638) follows:
% 13.82/3.73 | (1673) sum(n4, n7) = all_0_7_7
% 13.82/3.73 |
% 13.82/3.73 | From (330) and (1636) follows:
% 13.82/3.73 | (1674) sum(n5, n6) = all_0_4_4
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) with n5, n6, all_0_4_4, n0 and discharging atoms sum(n5, n6) = all_0_4_4, sum(n5, n6) = n0, yields:
% 13.82/3.73 | (406) all_0_4_4 = n0
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) with n4, n7, all_0_7_7, n0 and discharging atoms sum(n4, n7) = all_0_7_7, sum(n4, n7) = n0, yields:
% 13.82/3.73 | (408) all_0_7_7 = n0
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 13.82/3.73 | (335) all_0_2_2 = n10
% 13.82/3.73 |
% 13.82/3.73 | From (335) and (1640) follows:
% 13.82/3.73 | (1678) sum(n10, n1) = all_0_0_0
% 13.82/3.73 |
% 13.82/3.73 | From (408)(406) and (119) follows:
% 13.82/3.73 | (410) sum(n0, n0) = all_0_3_3
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) with n10, n1, all_0_0_0, n0 and discharging atoms sum(n10, n1) = all_0_0_0, sum(n10, n1) = n0, yields:
% 13.82/3.73 | (412) all_0_0_0 = n0
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 13.82/3.73 | (413) all_0_3_3 = n0
% 13.82/3.73 |
% 13.82/3.73 | Equations (412,413) can reduce 104 to:
% 13.82/3.73 | (251) $false
% 13.82/3.73 |
% 13.82/3.73 |-The branch is then unsatisfiable
% 13.82/3.73 |-Branch two:
% 13.82/3.73 | (342) ~ (all_0_11_11 = n5)
% 13.82/3.73 | (343) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.82/3.73 |
% 13.82/3.73 +-Applying beta-rule and splitting (343), into two cases.
% 13.82/3.73 |-Branch one:
% 13.82/3.73 | (344) all_0_11_11 = n4
% 13.82/3.73 |
% 13.82/3.73 | From (344) and (84) follows:
% 13.82/3.73 | (345) pred(n4) = all_0_9_9
% 13.82/3.73 |
% 13.82/3.73 | From (344) and (210) follows:
% 13.82/3.73 | (346) succ(n4) = all_0_5_5
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (158) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 13.82/3.73 | (347) all_0_9_9 = n3
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (141) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 13.82/3.73 | (348) all_0_5_5 = n5
% 13.82/3.73 |
% 13.82/3.73 | From (347)(348) and (48) follows:
% 13.82/3.73 | (349) sum(n3, n5) = all_0_2_2
% 13.82/3.73 |
% 13.82/3.73 | From (347) and (1638) follows:
% 13.82/3.73 | (1691) sum(n3, n7) = all_0_7_7
% 13.82/3.73 |
% 13.82/3.73 | From (348) and (1636) follows:
% 13.82/3.73 | (1692) sum(n5, n5) = all_0_4_4
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) with n5, n5, all_0_4_4, n10 and discharging atoms sum(n5, n5) = all_0_4_4, sum(n5, n5) = n10, yields:
% 13.82/3.73 | (426) all_0_4_4 = n10
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) with n3, n7, all_0_7_7, n10 and discharging atoms sum(n3, n7) = all_0_7_7, sum(n3, n7) = n10, yields:
% 13.82/3.73 | (425) all_0_7_7 = n10
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 13.82/3.73 | (353) all_0_2_2 = n8
% 13.82/3.73 |
% 13.82/3.73 | From (353) and (1640) follows:
% 13.82/3.73 | (1696) sum(n8, n1) = all_0_0_0
% 13.82/3.73 |
% 13.82/3.73 | From (425)(426) and (119) follows:
% 13.82/3.73 | (428) sum(n10, n10) = all_0_3_3
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) with n10, n10, all_0_3_3, n9 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n9, yields:
% 13.82/3.73 | (429) all_0_3_3 = n9
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) with n8, n1, all_0_0_0, n9 and discharging atoms sum(n8, n1) = all_0_0_0, sum(n8, n1) = n9, yields:
% 13.82/3.73 | (430) all_0_0_0 = n9
% 13.82/3.73 |
% 13.82/3.73 | Equations (430,429) can reduce 104 to:
% 13.82/3.73 | (251) $false
% 13.82/3.73 |
% 13.82/3.73 |-The branch is then unsatisfiable
% 13.82/3.73 |-Branch two:
% 13.82/3.73 | (360) ~ (all_0_11_11 = n4)
% 13.82/3.73 | (361) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.82/3.73 |
% 13.82/3.73 +-Applying beta-rule and splitting (361), into two cases.
% 13.82/3.73 |-Branch one:
% 13.82/3.73 | (362) all_0_11_11 = n3
% 13.82/3.73 |
% 13.82/3.73 | From (362) and (84) follows:
% 13.82/3.73 | (363) pred(n3) = all_0_9_9
% 13.82/3.73 |
% 13.82/3.73 | From (362) and (210) follows:
% 13.82/3.73 | (364) succ(n3) = all_0_5_5
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (158) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 13.82/3.73 | (365) all_0_9_9 = n2
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (141) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 13.82/3.73 | (366) all_0_5_5 = n4
% 13.82/3.73 |
% 13.82/3.73 | From (365)(366) and (48) follows:
% 13.82/3.73 | (367) sum(n2, n4) = all_0_2_2
% 13.82/3.73 |
% 13.82/3.73 | From (365) and (1638) follows:
% 13.82/3.73 | (1709) sum(n2, n7) = all_0_7_7
% 13.82/3.73 |
% 13.82/3.73 | From (366) and (1636) follows:
% 13.82/3.73 | (1710) sum(n5, n4) = all_0_4_4
% 13.82/3.73 |
% 13.82/3.73 | Instantiating formula (31) with n5, n4, all_0_4_4, n9 and discharging atoms sum(n5, n4) = all_0_4_4, sum(n5, n4) = n9, yields:
% 13.82/3.74 | (241) all_0_4_4 = n9
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n2, n7, all_0_7_7, n9 and discharging atoms sum(n2, n7) = all_0_7_7, sum(n2, n7) = n9, yields:
% 13.82/3.74 | (242) all_0_7_7 = n9
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 13.82/3.74 | (371) all_0_2_2 = n6
% 13.82/3.74 |
% 13.82/3.74 | From (371) and (1640) follows:
% 13.82/3.74 | (1714) sum(n6, n1) = all_0_0_0
% 13.82/3.74 |
% 13.82/3.74 | From (242)(241) and (119) follows:
% 13.82/3.74 | (246) sum(n9, n9) = all_0_3_3
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n9, n9, all_0_3_3, n7 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n7, yields:
% 13.82/3.74 | (249) all_0_3_3 = n7
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n6, n1, all_0_0_0, n7 and discharging atoms sum(n6, n1) = all_0_0_0, sum(n6, n1) = n7, yields:
% 13.82/3.74 | (247) all_0_0_0 = n7
% 13.82/3.74 |
% 13.82/3.74 | Equations (247,249) can reduce 104 to:
% 13.82/3.74 | (251) $false
% 13.82/3.74 |
% 13.82/3.74 |-The branch is then unsatisfiable
% 13.82/3.74 |-Branch two:
% 13.82/3.74 | (378) ~ (all_0_11_11 = n3)
% 13.82/3.74 | (379) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.82/3.74 |
% 13.82/3.74 +-Applying beta-rule and splitting (379), into two cases.
% 13.82/3.74 |-Branch one:
% 13.82/3.74 | (380) all_0_11_11 = n2
% 13.82/3.74 |
% 13.82/3.74 | From (380) and (84) follows:
% 13.82/3.74 | (381) pred(n2) = all_0_9_9
% 13.82/3.74 |
% 13.82/3.74 | From (380) and (210) follows:
% 13.82/3.74 | (382) succ(n2) = all_0_5_5
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (158) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 13.82/3.74 | (383) all_0_9_9 = n1
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (141) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 13.82/3.74 | (384) all_0_5_5 = n3
% 13.82/3.74 |
% 13.82/3.74 | From (383)(384) and (48) follows:
% 13.82/3.74 | (385) sum(n1, n3) = all_0_2_2
% 13.82/3.74 |
% 13.82/3.74 | From (383) and (1638) follows:
% 13.82/3.74 | (1727) sum(n1, n7) = all_0_7_7
% 13.82/3.74 |
% 13.82/3.74 | From (384) and (1636) follows:
% 13.82/3.74 | (1728) sum(n5, n3) = all_0_4_4
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n5, n3, all_0_4_4, n8 and discharging atoms sum(n5, n3) = all_0_4_4, sum(n5, n3) = n8, yields:
% 13.82/3.74 | (262) all_0_4_4 = n8
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n1, n7, all_0_7_7, n8 and discharging atoms sum(n1, n7) = all_0_7_7, sum(n1, n7) = n8, yields:
% 13.82/3.74 | (264) all_0_7_7 = n8
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 13.82/3.74 | (389) all_0_2_2 = n4
% 13.82/3.74 |
% 13.82/3.74 | From (389) and (1640) follows:
% 13.82/3.74 | (1732) sum(n4, n1) = all_0_0_0
% 13.82/3.74 |
% 13.82/3.74 | From (264)(262) and (119) follows:
% 13.82/3.74 | (266) sum(n8, n8) = all_0_3_3
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n8, n8, all_0_3_3, n5 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n5, yields:
% 13.82/3.74 | (267) all_0_3_3 = n5
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n4, n1, all_0_0_0, n5 and discharging atoms sum(n4, n1) = all_0_0_0, sum(n4, n1) = n5, yields:
% 13.82/3.74 | (268) all_0_0_0 = n5
% 13.82/3.74 |
% 13.82/3.74 | Equations (268,267) can reduce 104 to:
% 13.82/3.74 | (251) $false
% 13.82/3.74 |
% 13.82/3.74 |-The branch is then unsatisfiable
% 13.82/3.74 |-Branch two:
% 13.82/3.74 | (396) ~ (all_0_11_11 = n2)
% 13.82/3.74 | (397) all_0_11_11 = n1 | all_0_11_11 = n0
% 13.82/3.74 |
% 13.82/3.74 +-Applying beta-rule and splitting (397), into two cases.
% 13.82/3.74 |-Branch one:
% 13.82/3.74 | (398) all_0_11_11 = n1
% 13.82/3.74 |
% 13.82/3.74 | From (398) and (84) follows:
% 13.82/3.74 | (399) pred(n1) = all_0_9_9
% 13.82/3.74 |
% 13.82/3.74 | From (398) and (210) follows:
% 13.82/3.74 | (400) succ(n1) = all_0_5_5
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (158) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 13.82/3.74 | (401) all_0_9_9 = n0
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (141) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 13.82/3.74 | (402) all_0_5_5 = n2
% 13.82/3.74 |
% 13.82/3.74 | From (401)(402) and (48) follows:
% 13.82/3.74 | (403) sum(n0, n2) = all_0_2_2
% 13.82/3.74 |
% 13.82/3.74 | From (401) and (1638) follows:
% 13.82/3.74 | (1745) sum(n0, n7) = all_0_7_7
% 13.82/3.74 |
% 13.82/3.74 | From (402) and (1636) follows:
% 13.82/3.74 | (1746) sum(n5, n2) = all_0_4_4
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n5, n2, all_0_4_4, n7 and discharging atoms sum(n5, n2) = all_0_4_4, sum(n5, n2) = n7, yields:
% 13.82/3.74 | (280) all_0_4_4 = n7
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n0, n7, all_0_7_7, n7 and discharging atoms sum(n0, n7) = all_0_7_7, sum(n0, n7) = n7, yields:
% 13.82/3.74 | (282) all_0_7_7 = n7
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 13.82/3.74 | (407) all_0_2_2 = n2
% 13.82/3.74 |
% 13.82/3.74 | From (407) and (1640) follows:
% 13.82/3.74 | (1750) sum(n2, n1) = all_0_0_0
% 13.82/3.74 |
% 13.82/3.74 | From (282)(280) and (119) follows:
% 13.82/3.74 | (284) sum(n7, n7) = all_0_3_3
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n7, n7, all_0_3_3, n3 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n3, yields:
% 13.82/3.74 | (285) all_0_3_3 = n3
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n2, n1, all_0_0_0, n3 and discharging atoms sum(n2, n1) = all_0_0_0, sum(n2, n1) = n3, yields:
% 13.82/3.74 | (286) all_0_0_0 = n3
% 13.82/3.74 |
% 13.82/3.74 | Equations (286,285) can reduce 104 to:
% 13.82/3.74 | (251) $false
% 13.82/3.74 |
% 13.82/3.74 |-The branch is then unsatisfiable
% 13.82/3.74 |-Branch two:
% 13.82/3.74 | (415) ~ (all_0_11_11 = n1)
% 13.82/3.74 | (416) all_0_11_11 = n0
% 13.82/3.74 |
% 13.82/3.74 | From (416) and (84) follows:
% 13.82/3.74 | (417) pred(n0) = all_0_9_9
% 13.82/3.74 |
% 13.82/3.74 | From (416) and (210) follows:
% 13.82/3.74 | (418) succ(n0) = all_0_5_5
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (158) with n0, all_0_9_9, n10 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n10, yields:
% 13.82/3.74 | (419) all_0_9_9 = n10
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (141) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 13.82/3.74 | (420) all_0_5_5 = n1
% 13.82/3.74 |
% 13.82/3.74 | From (419)(420) and (48) follows:
% 13.82/3.74 | (421) sum(n10, n1) = all_0_2_2
% 13.82/3.74 |
% 13.82/3.74 | From (419) and (1638) follows:
% 13.82/3.74 | (1762) sum(n10, n7) = all_0_7_7
% 13.82/3.74 |
% 13.82/3.74 | From (420) and (1636) follows:
% 13.82/3.74 | (1763) sum(n5, n1) = all_0_4_4
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n10, n7, all_0_7_7, n6 and discharging atoms sum(n10, n7) = all_0_7_7, sum(n10, n7) = n6, yields:
% 13.82/3.74 | (300) all_0_7_7 = n6
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n10, n1, all_0_2_2, n0 and discharging atoms sum(n10, n1) = all_0_2_2, sum(n10, n1) = n0, yields:
% 13.82/3.74 | (424) all_0_2_2 = n0
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n5, n1, all_0_4_4, n6 and discharging atoms sum(n5, n1) = all_0_4_4, sum(n5, n1) = n6, yields:
% 13.82/3.74 | (298) all_0_4_4 = n6
% 13.82/3.74 |
% 13.82/3.74 | From (424) and (1640) follows:
% 13.82/3.74 | (1767) sum(n0, n1) = all_0_0_0
% 13.82/3.74 |
% 13.82/3.74 | From (300)(298) and (119) follows:
% 13.82/3.74 | (302) sum(n6, n6) = all_0_3_3
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n6, n6, all_0_3_3, n1 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n1, yields:
% 13.82/3.74 | (303) all_0_3_3 = n1
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n0, n1, all_0_0_0, n1 and discharging atoms sum(n0, n1) = all_0_0_0, sum(n0, n1) = n1, yields:
% 13.82/3.74 | (304) all_0_0_0 = n1
% 13.82/3.74 |
% 13.82/3.74 | Equations (304,303) can reduce 104 to:
% 13.82/3.74 | (251) $false
% 13.82/3.74 |
% 13.82/3.74 |-The branch is then unsatisfiable
% 13.82/3.74 |-Branch two:
% 13.82/3.74 | (515) ~ (all_0_10_10 = n6)
% 13.82/3.74 | (516) all_0_10_10 = n5 | all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.82/3.74 |
% 13.82/3.74 +-Applying beta-rule and splitting (307), into two cases.
% 13.82/3.74 |-Branch one:
% 13.82/3.74 | (308) all_0_11_11 = n6
% 13.82/3.74 |
% 13.82/3.74 | From (308) and (84) follows:
% 13.82/3.74 | (309) pred(n6) = all_0_9_9
% 13.82/3.74 |
% 13.82/3.74 | From (308) and (210) follows:
% 13.82/3.74 | (310) succ(n6) = all_0_5_5
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (158) with n6, all_0_9_9, n5 and discharging atoms pred(n6) = all_0_9_9, pred(n6) = n5, yields:
% 13.82/3.74 | (311) all_0_9_9 = n5
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (141) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 13.82/3.74 | (312) all_0_5_5 = n7
% 13.82/3.74 |
% 13.82/3.74 | From (312) and (33) follows:
% 13.82/3.74 | (1779) sum(all_0_6_6, n7) = all_0_4_4
% 13.82/3.74 |
% 13.82/3.74 | From (311)(312) and (48) follows:
% 13.82/3.74 | (313) sum(n5, n7) = all_0_2_2
% 13.82/3.74 |
% 13.82/3.74 | From (311) and (137) follows:
% 13.82/3.74 | (1781) sum(n5, all_0_8_8) = all_0_7_7
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n5, n7, all_0_2_2, n1 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n1, yields:
% 13.82/3.74 | (317) all_0_2_2 = n1
% 13.82/3.74 |
% 13.82/3.74 | From (317) and (4) follows:
% 13.82/3.74 | (1783) sum(n1, all_0_1_1) = all_0_0_0
% 13.82/3.74 |
% 13.82/3.74 +-Applying beta-rule and splitting (516), into two cases.
% 13.82/3.74 |-Branch one:
% 13.82/3.74 | (517) all_0_10_10 = n5
% 13.82/3.74 |
% 13.82/3.74 | From (517) and (211) follows:
% 13.82/3.74 | (518) pred(n5) = all_0_6_6
% 13.82/3.74 |
% 13.82/3.74 | From (517) and (41) follows:
% 13.82/3.74 | (519) succ(n5) = all_0_8_8
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (158) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 13.82/3.74 | (520) all_0_6_6 = n4
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (141) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 13.82/3.74 | (521) all_0_8_8 = n6
% 13.82/3.74 |
% 13.82/3.74 | From (520)(521) and (178) follows:
% 13.82/3.74 | (522) sum(n4, n6) = all_0_1_1
% 13.82/3.74 |
% 13.82/3.74 | From (520) and (1779) follows:
% 13.82/3.74 | (1790) sum(n4, n7) = all_0_4_4
% 13.82/3.74 |
% 13.82/3.74 | From (521) and (1781) follows:
% 13.82/3.74 | (1791) sum(n5, n6) = all_0_7_7
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n5, n6, all_0_7_7, n0 and discharging atoms sum(n5, n6) = all_0_7_7, sum(n5, n6) = n0, yields:
% 13.82/3.74 | (408) all_0_7_7 = n0
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n4, n7, all_0_4_4, n0 and discharging atoms sum(n4, n7) = all_0_4_4, sum(n4, n7) = n0, yields:
% 13.82/3.74 | (406) all_0_4_4 = n0
% 13.82/3.74 |
% 13.82/3.74 | Instantiating formula (31) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 13.82/3.74 | (526) all_0_1_1 = n10
% 13.82/3.74 |
% 13.82/3.74 | From (408)(406) and (119) follows:
% 13.82/3.74 | (410) sum(n0, n0) = all_0_3_3
% 13.82/3.75 |
% 13.82/3.75 | From (526) and (1783) follows:
% 13.82/3.75 | (1796) sum(n1, n10) = all_0_0_0
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n1, n10, all_0_0_0, n0 and discharging atoms sum(n1, n10) = all_0_0_0, sum(n1, n10) = n0, yields:
% 13.82/3.75 | (412) all_0_0_0 = n0
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n0, n0, all_0_3_3, n0 and discharging atoms sum(n0, n0) = all_0_3_3, sum(n0, n0) = n0, yields:
% 13.82/3.75 | (413) all_0_3_3 = n0
% 13.82/3.75 |
% 13.82/3.75 | Equations (412,413) can reduce 104 to:
% 13.82/3.75 | (251) $false
% 13.82/3.75 |
% 13.82/3.75 |-The branch is then unsatisfiable
% 13.82/3.75 |-Branch two:
% 13.82/3.75 | (533) ~ (all_0_10_10 = n5)
% 13.82/3.75 | (534) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.82/3.75 |
% 13.82/3.75 +-Applying beta-rule and splitting (534), into two cases.
% 13.82/3.75 |-Branch one:
% 13.82/3.75 | (535) all_0_10_10 = n4
% 13.82/3.75 |
% 13.82/3.75 | From (535) and (211) follows:
% 13.82/3.75 | (536) pred(n4) = all_0_6_6
% 13.82/3.75 |
% 13.82/3.75 | From (535) and (41) follows:
% 13.82/3.75 | (537) succ(n4) = all_0_8_8
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (158) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 13.82/3.75 | (538) all_0_6_6 = n3
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (141) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 13.82/3.75 | (539) all_0_8_8 = n5
% 13.82/3.75 |
% 13.82/3.75 | From (538)(539) and (178) follows:
% 13.82/3.75 | (540) sum(n3, n5) = all_0_1_1
% 13.82/3.75 |
% 13.82/3.75 | From (538) and (1779) follows:
% 13.82/3.75 | (1808) sum(n3, n7) = all_0_4_4
% 13.82/3.75 |
% 13.82/3.75 | From (539) and (1781) follows:
% 13.82/3.75 | (1809) sum(n5, n5) = all_0_7_7
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n5, n5, all_0_7_7, n10 and discharging atoms sum(n5, n5) = all_0_7_7, sum(n5, n5) = n10, yields:
% 13.82/3.75 | (425) all_0_7_7 = n10
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n3, n7, all_0_4_4, n10 and discharging atoms sum(n3, n7) = all_0_4_4, sum(n3, n7) = n10, yields:
% 13.82/3.75 | (426) all_0_4_4 = n10
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 13.82/3.75 | (544) all_0_1_1 = n8
% 13.82/3.75 |
% 13.82/3.75 | From (425)(426) and (119) follows:
% 13.82/3.75 | (428) sum(n10, n10) = all_0_3_3
% 13.82/3.75 |
% 13.82/3.75 | From (544) and (1783) follows:
% 13.82/3.75 | (1814) sum(n1, n8) = all_0_0_0
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n10, n10, all_0_3_3, n9 and discharging atoms sum(n10, n10) = all_0_3_3, sum(n10, n10) = n9, yields:
% 13.82/3.75 | (429) all_0_3_3 = n9
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n1, n8, all_0_0_0, n9 and discharging atoms sum(n1, n8) = all_0_0_0, sum(n1, n8) = n9, yields:
% 13.82/3.75 | (430) all_0_0_0 = n9
% 13.82/3.75 |
% 13.82/3.75 | Equations (430,429) can reduce 104 to:
% 13.82/3.75 | (251) $false
% 13.82/3.75 |
% 13.82/3.75 |-The branch is then unsatisfiable
% 13.82/3.75 |-Branch two:
% 13.82/3.75 | (551) ~ (all_0_10_10 = n4)
% 13.82/3.75 | (552) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.82/3.75 |
% 13.82/3.75 +-Applying beta-rule and splitting (552), into two cases.
% 13.82/3.75 |-Branch one:
% 13.82/3.75 | (553) all_0_10_10 = n3
% 13.82/3.75 |
% 13.82/3.75 | From (553) and (211) follows:
% 13.82/3.75 | (554) pred(n3) = all_0_6_6
% 13.82/3.75 |
% 13.82/3.75 | From (553) and (41) follows:
% 13.82/3.75 | (555) succ(n3) = all_0_8_8
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (158) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 13.82/3.75 | (556) all_0_6_6 = n2
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (141) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 13.82/3.75 | (557) all_0_8_8 = n4
% 13.82/3.75 |
% 13.82/3.75 | From (556)(557) and (178) follows:
% 13.82/3.75 | (558) sum(n2, n4) = all_0_1_1
% 13.82/3.75 |
% 13.82/3.75 | From (556) and (1779) follows:
% 13.82/3.75 | (1826) sum(n2, n7) = all_0_4_4
% 13.82/3.75 |
% 13.82/3.75 | From (557) and (1781) follows:
% 13.82/3.75 | (1827) sum(n5, n4) = all_0_7_7
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n5, n4, all_0_7_7, n9 and discharging atoms sum(n5, n4) = all_0_7_7, sum(n5, n4) = n9, yields:
% 13.82/3.75 | (242) all_0_7_7 = n9
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n2, n7, all_0_4_4, n9 and discharging atoms sum(n2, n7) = all_0_4_4, sum(n2, n7) = n9, yields:
% 13.82/3.75 | (241) all_0_4_4 = n9
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 13.82/3.75 | (562) all_0_1_1 = n6
% 13.82/3.75 |
% 13.82/3.75 | From (242)(241) and (119) follows:
% 13.82/3.75 | (246) sum(n9, n9) = all_0_3_3
% 13.82/3.75 |
% 13.82/3.75 | From (562) and (1783) follows:
% 13.82/3.75 | (1832) sum(n1, n6) = all_0_0_0
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n9, n9, all_0_3_3, n7 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n7, yields:
% 13.82/3.75 | (249) all_0_3_3 = n7
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n1, n6, all_0_0_0, n7 and discharging atoms sum(n1, n6) = all_0_0_0, sum(n1, n6) = n7, yields:
% 13.82/3.75 | (247) all_0_0_0 = n7
% 13.82/3.75 |
% 13.82/3.75 | Equations (247,249) can reduce 104 to:
% 13.82/3.75 | (251) $false
% 13.82/3.75 |
% 13.82/3.75 |-The branch is then unsatisfiable
% 13.82/3.75 |-Branch two:
% 13.82/3.75 | (569) ~ (all_0_10_10 = n3)
% 13.82/3.75 | (570) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.82/3.75 |
% 13.82/3.75 +-Applying beta-rule and splitting (570), into two cases.
% 13.82/3.75 |-Branch one:
% 13.82/3.75 | (571) all_0_10_10 = n2
% 13.82/3.75 |
% 13.82/3.75 | From (571) and (211) follows:
% 13.82/3.75 | (572) pred(n2) = all_0_6_6
% 13.82/3.75 |
% 13.82/3.75 | From (571) and (41) follows:
% 13.82/3.75 | (573) succ(n2) = all_0_8_8
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (158) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 13.82/3.75 | (574) all_0_6_6 = n1
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (141) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 13.82/3.75 | (575) all_0_8_8 = n3
% 13.82/3.75 |
% 13.82/3.75 | From (574)(575) and (178) follows:
% 13.82/3.75 | (576) sum(n1, n3) = all_0_1_1
% 13.82/3.75 |
% 13.82/3.75 | From (574) and (1779) follows:
% 13.82/3.75 | (1844) sum(n1, n7) = all_0_4_4
% 13.82/3.75 |
% 13.82/3.75 | From (575) and (1781) follows:
% 13.82/3.75 | (1845) sum(n5, n3) = all_0_7_7
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n5, n3, all_0_7_7, n8 and discharging atoms sum(n5, n3) = all_0_7_7, sum(n5, n3) = n8, yields:
% 13.82/3.75 | (264) all_0_7_7 = n8
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n1, n7, all_0_4_4, n8 and discharging atoms sum(n1, n7) = all_0_4_4, sum(n1, n7) = n8, yields:
% 13.82/3.75 | (262) all_0_4_4 = n8
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 13.82/3.75 | (580) all_0_1_1 = n4
% 13.82/3.75 |
% 13.82/3.75 | From (264)(262) and (119) follows:
% 13.82/3.75 | (266) sum(n8, n8) = all_0_3_3
% 13.82/3.75 |
% 13.82/3.75 | From (580) and (1783) follows:
% 13.82/3.75 | (1850) sum(n1, n4) = all_0_0_0
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n8, n8, all_0_3_3, n5 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n5, yields:
% 13.82/3.75 | (267) all_0_3_3 = n5
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n1, n4, all_0_0_0, n5 and discharging atoms sum(n1, n4) = all_0_0_0, sum(n1, n4) = n5, yields:
% 13.82/3.75 | (268) all_0_0_0 = n5
% 13.82/3.75 |
% 13.82/3.75 | Equations (268,267) can reduce 104 to:
% 13.82/3.75 | (251) $false
% 13.82/3.75 |
% 13.82/3.75 |-The branch is then unsatisfiable
% 13.82/3.75 |-Branch two:
% 13.82/3.75 | (587) ~ (all_0_10_10 = n2)
% 13.82/3.75 | (588) all_0_10_10 = n1 | all_0_10_10 = n0
% 13.82/3.75 |
% 13.82/3.75 +-Applying beta-rule and splitting (588), into two cases.
% 13.82/3.75 |-Branch one:
% 13.82/3.75 | (589) all_0_10_10 = n1
% 13.82/3.75 |
% 13.82/3.75 | From (589) and (211) follows:
% 13.82/3.75 | (590) pred(n1) = all_0_6_6
% 13.82/3.75 |
% 13.82/3.75 | From (589) and (41) follows:
% 13.82/3.75 | (591) succ(n1) = all_0_8_8
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (158) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 13.82/3.75 | (592) all_0_6_6 = n0
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (141) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 13.82/3.75 | (593) all_0_8_8 = n2
% 13.82/3.75 |
% 13.82/3.75 | From (592)(593) and (178) follows:
% 13.82/3.75 | (594) sum(n0, n2) = all_0_1_1
% 13.82/3.75 |
% 13.82/3.75 | From (592) and (1779) follows:
% 13.82/3.75 | (1862) sum(n0, n7) = all_0_4_4
% 13.82/3.75 |
% 13.82/3.75 | From (593) and (1781) follows:
% 13.82/3.75 | (1863) sum(n5, n2) = all_0_7_7
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n5, n2, all_0_7_7, n7 and discharging atoms sum(n5, n2) = all_0_7_7, sum(n5, n2) = n7, yields:
% 13.82/3.75 | (282) all_0_7_7 = n7
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n0, n7, all_0_4_4, n7 and discharging atoms sum(n0, n7) = all_0_4_4, sum(n0, n7) = n7, yields:
% 13.82/3.75 | (280) all_0_4_4 = n7
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 13.82/3.75 | (598) all_0_1_1 = n2
% 13.82/3.75 |
% 13.82/3.75 | From (282)(280) and (119) follows:
% 13.82/3.75 | (284) sum(n7, n7) = all_0_3_3
% 13.82/3.75 |
% 13.82/3.75 | From (598) and (1783) follows:
% 13.82/3.75 | (1868) sum(n1, n2) = all_0_0_0
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n7, n7, all_0_3_3, n3 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n3, yields:
% 13.82/3.75 | (285) all_0_3_3 = n3
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (31) with n1, n2, all_0_0_0, n3 and discharging atoms sum(n1, n2) = all_0_0_0, sum(n1, n2) = n3, yields:
% 13.82/3.75 | (286) all_0_0_0 = n3
% 13.82/3.75 |
% 13.82/3.75 | Equations (286,285) can reduce 104 to:
% 13.82/3.75 | (251) $false
% 13.82/3.75 |
% 13.82/3.75 |-The branch is then unsatisfiable
% 13.82/3.75 |-Branch two:
% 13.82/3.75 | (607) ~ (all_0_10_10 = n1)
% 13.82/3.75 | (608) all_0_10_10 = n0
% 13.82/3.75 |
% 13.82/3.75 | From (608) and (211) follows:
% 13.82/3.75 | (609) pred(n0) = all_0_6_6
% 13.82/3.75 |
% 13.82/3.75 | From (608) and (41) follows:
% 13.82/3.75 | (610) succ(n0) = all_0_8_8
% 13.82/3.75 |
% 13.82/3.75 | Instantiating formula (158) with n0, all_0_6_6, n10 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n10, yields:
% 13.82/3.75 | (611) all_0_6_6 = n10
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (141) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 13.82/3.76 | (612) all_0_8_8 = n1
% 13.82/3.76 |
% 13.82/3.76 | From (611)(612) and (178) follows:
% 13.82/3.76 | (613) sum(n10, n1) = all_0_1_1
% 13.82/3.76 |
% 13.82/3.76 | From (611) and (1779) follows:
% 13.82/3.76 | (1879) sum(n10, n7) = all_0_4_4
% 13.82/3.76 |
% 13.82/3.76 | From (612) and (1781) follows:
% 13.82/3.76 | (1880) sum(n5, n1) = all_0_7_7
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n10, n7, all_0_4_4, n6 and discharging atoms sum(n10, n7) = all_0_4_4, sum(n10, n7) = n6, yields:
% 13.82/3.76 | (298) all_0_4_4 = n6
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n10, n1, all_0_1_1, n0 and discharging atoms sum(n10, n1) = all_0_1_1, sum(n10, n1) = n0, yields:
% 13.82/3.76 | (616) all_0_1_1 = n0
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n5, n1, all_0_7_7, n6 and discharging atoms sum(n5, n1) = all_0_7_7, sum(n5, n1) = n6, yields:
% 13.82/3.76 | (300) all_0_7_7 = n6
% 13.82/3.76 |
% 13.82/3.76 | From (300)(298) and (119) follows:
% 13.82/3.76 | (302) sum(n6, n6) = all_0_3_3
% 13.82/3.76 |
% 13.82/3.76 | From (616) and (1783) follows:
% 13.82/3.76 | (1885) sum(n1, n0) = all_0_0_0
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n6, n6, all_0_3_3, n1 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n1, yields:
% 13.82/3.76 | (303) all_0_3_3 = n1
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n1, n0, all_0_0_0, n1 and discharging atoms sum(n1, n0) = all_0_0_0, sum(n1, n0) = n1, yields:
% 13.82/3.76 | (304) all_0_0_0 = n1
% 13.82/3.76 |
% 13.82/3.76 | Equations (304,303) can reduce 104 to:
% 13.82/3.76 | (251) $false
% 13.82/3.76 |
% 13.82/3.76 |-The branch is then unsatisfiable
% 13.82/3.76 |-Branch two:
% 13.82/3.76 | (324) ~ (all_0_11_11 = n6)
% 13.82/3.76 | (325) all_0_11_11 = n5 | all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.82/3.76 |
% 13.82/3.76 +-Applying beta-rule and splitting (516), into two cases.
% 13.82/3.76 |-Branch one:
% 13.82/3.76 | (517) all_0_10_10 = n5
% 13.82/3.76 |
% 13.82/3.76 | From (517) and (211) follows:
% 13.82/3.76 | (518) pred(n5) = all_0_6_6
% 13.82/3.76 |
% 13.82/3.76 | From (517) and (41) follows:
% 13.82/3.76 | (519) succ(n5) = all_0_8_8
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (158) with n5, all_0_6_6, n4 and discharging atoms pred(n5) = all_0_6_6, pred(n5) = n4, yields:
% 13.82/3.76 | (520) all_0_6_6 = n4
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (141) with n5, all_0_8_8, n6 and discharging atoms succ(n5) = all_0_8_8, succ(n5) = n6, yields:
% 13.82/3.76 | (521) all_0_8_8 = n6
% 13.82/3.76 |
% 13.82/3.76 | From (520) and (518) follows:
% 13.82/3.76 | (36) pred(n5) = n4
% 13.82/3.76 |
% 13.82/3.76 | From (521) and (519) follows:
% 13.82/3.76 | (177) succ(n5) = n6
% 13.82/3.76 |
% 13.82/3.76 | From (520) and (33) follows:
% 13.82/3.76 | (1898) sum(n4, all_0_5_5) = all_0_4_4
% 13.82/3.76 |
% 13.82/3.76 | From (520)(521) and (178) follows:
% 13.82/3.76 | (522) sum(n4, n6) = all_0_1_1
% 13.82/3.76 |
% 13.82/3.76 | From (521) and (137) follows:
% 13.82/3.76 | (1900) sum(all_0_9_9, n6) = all_0_7_7
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n4, n6, all_0_1_1, n10 and discharging atoms sum(n4, n6) = all_0_1_1, sum(n4, n6) = n10, yields:
% 13.82/3.76 | (526) all_0_1_1 = n10
% 13.82/3.76 |
% 13.82/3.76 | From (526) and (4) follows:
% 13.82/3.76 | (1902) sum(all_0_2_2, n10) = all_0_0_0
% 13.82/3.76 |
% 13.82/3.76 | From (526) and (522) follows:
% 13.82/3.76 | (107) sum(n4, n6) = n10
% 13.82/3.76 |
% 13.82/3.76 +-Applying beta-rule and splitting (325), into two cases.
% 13.82/3.76 |-Branch one:
% 13.82/3.76 | (326) all_0_11_11 = n5
% 13.82/3.76 |
% 13.82/3.76 | From (326) and (84) follows:
% 13.82/3.76 | (327) pred(n5) = all_0_9_9
% 13.82/3.76 |
% 13.82/3.76 | From (326) and (210) follows:
% 13.82/3.76 | (328) succ(n5) = all_0_5_5
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (158) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 13.82/3.76 | (329) all_0_9_9 = n4
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (141) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 13.82/3.76 | (330) all_0_5_5 = n6
% 13.82/3.76 |
% 13.82/3.76 | From (329)(330) and (48) follows:
% 13.82/3.76 | (331) sum(n4, n6) = all_0_2_2
% 13.82/3.76 |
% 13.82/3.76 | From (329) and (1900) follows:
% 13.82/3.76 | (1910) sum(n4, n6) = all_0_7_7
% 13.82/3.76 |
% 13.82/3.76 | From (330) and (1898) follows:
% 13.82/3.76 | (1911) sum(n4, n6) = all_0_4_4
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 13.82/3.76 | (335) all_0_2_2 = n10
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) 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:
% 13.82/3.76 | (238) all_0_2_2 = all_0_4_4
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) 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:
% 13.82/3.76 | (239) all_0_2_2 = all_0_7_7
% 13.82/3.76 |
% 13.82/3.76 | Combining equations (239,238) yields a new equation:
% 13.82/3.76 | (240) all_0_4_4 = all_0_7_7
% 13.82/3.76 |
% 13.82/3.76 | Combining equations (335,238) yields a new equation:
% 13.82/3.76 | (426) all_0_4_4 = n10
% 13.82/3.76 |
% 13.82/3.76 | Combining equations (426,240) yields a new equation:
% 13.82/3.76 | (425) all_0_7_7 = n10
% 13.82/3.76 |
% 13.82/3.76 | Combining equations (425,240) yields a new equation:
% 13.82/3.76 | (426) all_0_4_4 = n10
% 13.82/3.76 |
% 13.82/3.76 | Combining equations (426,238) yields a new equation:
% 13.82/3.76 | (335) all_0_2_2 = n10
% 13.82/3.76 |
% 13.82/3.76 | From (335) and (1902) follows:
% 13.82/3.76 | (1920) sum(n10, n10) = all_0_0_0
% 13.82/3.76 |
% 13.82/3.76 | From (425)(426) and (119) follows:
% 13.82/3.76 | (428) sum(n10, n10) = all_0_3_3
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n10, n10, all_0_0_0, n9 and discharging atoms sum(n10, n10) = all_0_0_0, sum(n10, n10) = n9, yields:
% 13.82/3.76 | (430) all_0_0_0 = n9
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) 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:
% 13.82/3.76 | (248) all_0_0_0 = all_0_3_3
% 13.82/3.76 |
% 13.82/3.76 | Combining equations (430,248) yields a new equation:
% 13.82/3.76 | (429) all_0_3_3 = n9
% 13.82/3.76 |
% 13.82/3.76 | Combining equations (429,248) yields a new equation:
% 13.82/3.76 | (430) all_0_0_0 = n9
% 13.82/3.76 |
% 13.82/3.76 | Equations (430,429) can reduce 104 to:
% 13.82/3.76 | (251) $false
% 13.82/3.76 |
% 13.82/3.76 |-The branch is then unsatisfiable
% 13.82/3.76 |-Branch two:
% 13.82/3.76 | (342) ~ (all_0_11_11 = n5)
% 13.82/3.76 | (343) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.82/3.76 |
% 13.82/3.76 +-Applying beta-rule and splitting (343), into two cases.
% 13.82/3.76 |-Branch one:
% 13.82/3.76 | (344) all_0_11_11 = n4
% 13.82/3.76 |
% 13.82/3.76 | From (344) and (84) follows:
% 13.82/3.76 | (345) pred(n4) = all_0_9_9
% 13.82/3.76 |
% 13.82/3.76 | From (344) and (210) follows:
% 13.82/3.76 | (346) succ(n4) = all_0_5_5
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (158) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 13.82/3.76 | (347) all_0_9_9 = n3
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (141) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 13.82/3.76 | (348) all_0_5_5 = n5
% 13.82/3.76 |
% 13.82/3.76 | From (347)(348) and (48) follows:
% 13.82/3.76 | (349) sum(n3, n5) = all_0_2_2
% 13.82/3.76 |
% 13.82/3.76 | From (347) and (1900) follows:
% 13.82/3.76 | (1935) sum(n3, n6) = all_0_7_7
% 13.82/3.76 |
% 13.82/3.76 | From (348) and (1898) follows:
% 13.82/3.76 | (1936) sum(n4, n5) = all_0_4_4
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n4, n5, all_0_4_4, n9 and discharging atoms sum(n4, n5) = all_0_4_4, sum(n4, n5) = n9, yields:
% 13.82/3.76 | (241) all_0_4_4 = n9
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n3, n6, all_0_7_7, n9 and discharging atoms sum(n3, n6) = all_0_7_7, sum(n3, n6) = n9, yields:
% 13.82/3.76 | (242) all_0_7_7 = n9
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 13.82/3.76 | (353) all_0_2_2 = n8
% 13.82/3.76 |
% 13.82/3.76 | From (353) and (1902) follows:
% 13.82/3.76 | (1940) sum(n8, n10) = all_0_0_0
% 13.82/3.76 |
% 13.82/3.76 | From (242)(241) and (119) follows:
% 13.82/3.76 | (246) sum(n9, n9) = all_0_3_3
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n9, n9, all_0_3_3, n7 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n7, yields:
% 13.82/3.76 | (249) all_0_3_3 = n7
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n8, n10, all_0_0_0, n7 and discharging atoms sum(n8, n10) = all_0_0_0, sum(n8, n10) = n7, yields:
% 13.82/3.76 | (247) all_0_0_0 = n7
% 13.82/3.76 |
% 13.82/3.76 | Equations (247,249) can reduce 104 to:
% 13.82/3.76 | (251) $false
% 13.82/3.76 |
% 13.82/3.76 |-The branch is then unsatisfiable
% 13.82/3.76 |-Branch two:
% 13.82/3.76 | (360) ~ (all_0_11_11 = n4)
% 13.82/3.76 | (361) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.82/3.76 |
% 13.82/3.76 +-Applying beta-rule and splitting (361), into two cases.
% 13.82/3.76 |-Branch one:
% 13.82/3.76 | (362) all_0_11_11 = n3
% 13.82/3.76 |
% 13.82/3.76 | From (362) and (84) follows:
% 13.82/3.76 | (363) pred(n3) = all_0_9_9
% 13.82/3.76 |
% 13.82/3.76 | From (362) and (210) follows:
% 13.82/3.76 | (364) succ(n3) = all_0_5_5
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (158) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 13.82/3.76 | (365) all_0_9_9 = n2
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (141) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 13.82/3.76 | (366) all_0_5_5 = n4
% 13.82/3.76 |
% 13.82/3.76 | From (365)(366) and (48) follows:
% 13.82/3.76 | (367) sum(n2, n4) = all_0_2_2
% 13.82/3.76 |
% 13.82/3.76 | From (365) and (1900) follows:
% 13.82/3.76 | (1953) sum(n2, n6) = all_0_7_7
% 13.82/3.76 |
% 13.82/3.76 | From (366) and (1898) follows:
% 13.82/3.76 | (1954) sum(n4, n4) = all_0_4_4
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n4, n4, all_0_4_4, n8 and discharging atoms sum(n4, n4) = all_0_4_4, sum(n4, n4) = n8, yields:
% 13.82/3.76 | (262) all_0_4_4 = n8
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n2, n6, all_0_7_7, n8 and discharging atoms sum(n2, n6) = all_0_7_7, sum(n2, n6) = n8, yields:
% 13.82/3.76 | (264) all_0_7_7 = n8
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 13.82/3.76 | (371) all_0_2_2 = n6
% 13.82/3.76 |
% 13.82/3.76 | From (371) and (1902) follows:
% 13.82/3.76 | (1958) sum(n6, n10) = all_0_0_0
% 13.82/3.76 |
% 13.82/3.76 | From (264)(262) and (119) follows:
% 13.82/3.76 | (266) sum(n8, n8) = all_0_3_3
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n8, n8, all_0_3_3, n5 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n5, yields:
% 13.82/3.76 | (267) all_0_3_3 = n5
% 13.82/3.76 |
% 13.82/3.76 | Instantiating formula (31) with n6, n10, all_0_0_0, n5 and discharging atoms sum(n6, n10) = all_0_0_0, sum(n6, n10) = n5, yields:
% 13.82/3.76 | (268) all_0_0_0 = n5
% 13.82/3.76 |
% 13.82/3.76 | Equations (268,267) can reduce 104 to:
% 13.82/3.76 | (251) $false
% 13.82/3.76 |
% 13.82/3.76 |-The branch is then unsatisfiable
% 13.82/3.76 |-Branch two:
% 13.82/3.76 | (378) ~ (all_0_11_11 = n3)
% 13.82/3.77 | (379) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 13.82/3.77 |
% 13.82/3.77 +-Applying beta-rule and splitting (379), into two cases.
% 13.82/3.77 |-Branch one:
% 13.82/3.77 | (380) all_0_11_11 = n2
% 13.82/3.77 |
% 13.82/3.77 | From (380) and (84) follows:
% 13.82/3.77 | (381) pred(n2) = all_0_9_9
% 13.82/3.77 |
% 13.82/3.77 | From (380) and (210) follows:
% 13.82/3.77 | (382) succ(n2) = all_0_5_5
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (158) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 13.82/3.77 | (383) all_0_9_9 = n1
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (141) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 13.82/3.77 | (384) all_0_5_5 = n3
% 13.82/3.77 |
% 13.82/3.77 | From (383)(384) and (48) follows:
% 13.82/3.77 | (385) sum(n1, n3) = all_0_2_2
% 13.82/3.77 |
% 13.82/3.77 | From (383) and (1900) follows:
% 13.82/3.77 | (1971) sum(n1, n6) = all_0_7_7
% 13.82/3.77 |
% 13.82/3.77 | From (384) and (1898) follows:
% 13.82/3.77 | (1972) sum(n4, n3) = all_0_4_4
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n4, n3, all_0_4_4, n7 and discharging atoms sum(n4, n3) = all_0_4_4, sum(n4, n3) = n7, yields:
% 13.82/3.77 | (280) all_0_4_4 = n7
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n1, n6, all_0_7_7, n7 and discharging atoms sum(n1, n6) = all_0_7_7, sum(n1, n6) = n7, yields:
% 13.82/3.77 | (282) all_0_7_7 = n7
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 13.82/3.77 | (389) all_0_2_2 = n4
% 13.82/3.77 |
% 13.82/3.77 | From (389) and (1902) follows:
% 13.82/3.77 | (1976) sum(n4, n10) = all_0_0_0
% 13.82/3.77 |
% 13.82/3.77 | From (282)(280) and (119) follows:
% 13.82/3.77 | (284) sum(n7, n7) = all_0_3_3
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n7, n7, all_0_3_3, n3 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n3, yields:
% 13.82/3.77 | (285) all_0_3_3 = n3
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n4, n10, all_0_0_0, n3 and discharging atoms sum(n4, n10) = all_0_0_0, sum(n4, n10) = n3, yields:
% 13.82/3.77 | (286) all_0_0_0 = n3
% 13.82/3.77 |
% 13.82/3.77 | Equations (286,285) can reduce 104 to:
% 13.82/3.77 | (251) $false
% 13.82/3.77 |
% 13.82/3.77 |-The branch is then unsatisfiable
% 13.82/3.77 |-Branch two:
% 13.82/3.77 | (396) ~ (all_0_11_11 = n2)
% 13.82/3.77 | (397) all_0_11_11 = n1 | all_0_11_11 = n0
% 13.82/3.77 |
% 13.82/3.77 +-Applying beta-rule and splitting (397), into two cases.
% 13.82/3.77 |-Branch one:
% 13.82/3.77 | (398) all_0_11_11 = n1
% 13.82/3.77 |
% 13.82/3.77 | From (398) and (84) follows:
% 13.82/3.77 | (399) pred(n1) = all_0_9_9
% 13.82/3.77 |
% 13.82/3.77 | From (398) and (210) follows:
% 13.82/3.77 | (400) succ(n1) = all_0_5_5
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (158) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 13.82/3.77 | (401) all_0_9_9 = n0
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (141) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 13.82/3.77 | (402) all_0_5_5 = n2
% 13.82/3.77 |
% 13.82/3.77 | From (401)(402) and (48) follows:
% 13.82/3.77 | (403) sum(n0, n2) = all_0_2_2
% 13.82/3.77 |
% 13.82/3.77 | From (401) and (1900) follows:
% 13.82/3.77 | (1989) sum(n0, n6) = all_0_7_7
% 13.82/3.77 |
% 13.82/3.77 | From (402) and (1898) follows:
% 13.82/3.77 | (1990) sum(n4, n2) = all_0_4_4
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n4, n2, all_0_4_4, n6 and discharging atoms sum(n4, n2) = all_0_4_4, sum(n4, n2) = n6, yields:
% 13.82/3.77 | (298) all_0_4_4 = n6
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n0, n6, all_0_7_7, n6 and discharging atoms sum(n0, n6) = all_0_7_7, sum(n0, n6) = n6, yields:
% 13.82/3.77 | (300) all_0_7_7 = n6
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 13.82/3.77 | (407) all_0_2_2 = n2
% 13.82/3.77 |
% 13.82/3.77 | From (407) and (1902) follows:
% 13.82/3.77 | (1994) sum(n2, n10) = all_0_0_0
% 13.82/3.77 |
% 13.82/3.77 | From (300)(298) and (119) follows:
% 13.82/3.77 | (302) sum(n6, n6) = all_0_3_3
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n6, n6, all_0_3_3, n1 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n1, yields:
% 13.82/3.77 | (303) all_0_3_3 = n1
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n2, n10, all_0_0_0, n1 and discharging atoms sum(n2, n10) = all_0_0_0, sum(n2, n10) = n1, yields:
% 13.82/3.77 | (304) all_0_0_0 = n1
% 13.82/3.77 |
% 13.82/3.77 | Equations (304,303) can reduce 104 to:
% 13.82/3.77 | (251) $false
% 13.82/3.77 |
% 13.82/3.77 |-The branch is then unsatisfiable
% 13.82/3.77 |-Branch two:
% 13.82/3.77 | (415) ~ (all_0_11_11 = n1)
% 13.82/3.77 | (416) all_0_11_11 = n0
% 13.82/3.77 |
% 13.82/3.77 | From (416) and (84) follows:
% 13.82/3.77 | (417) pred(n0) = all_0_9_9
% 13.82/3.77 |
% 13.82/3.77 | From (416) and (210) follows:
% 13.82/3.77 | (418) succ(n0) = all_0_5_5
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (158) with n0, all_0_9_9, n10 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n10, yields:
% 13.82/3.77 | (419) all_0_9_9 = n10
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (141) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 13.82/3.77 | (420) all_0_5_5 = n1
% 13.82/3.77 |
% 13.82/3.77 | From (419)(420) and (48) follows:
% 13.82/3.77 | (421) sum(n10, n1) = all_0_2_2
% 13.82/3.77 |
% 13.82/3.77 | From (419) and (1900) follows:
% 13.82/3.77 | (2006) sum(n10, n6) = all_0_7_7
% 13.82/3.77 |
% 13.82/3.77 | From (420) and (1898) follows:
% 13.82/3.77 | (2007) sum(n4, n1) = all_0_4_4
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n10, n6, all_0_7_7, n5 and discharging atoms sum(n10, n6) = all_0_7_7, sum(n10, n6) = n5, yields:
% 13.82/3.77 | (318) all_0_7_7 = n5
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n10, n1, all_0_2_2, n0 and discharging atoms sum(n10, n1) = all_0_2_2, sum(n10, n1) = n0, yields:
% 13.82/3.77 | (424) all_0_2_2 = n0
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n4, n1, all_0_4_4, n5 and discharging atoms sum(n4, n1) = all_0_4_4, sum(n4, n1) = n5, yields:
% 13.82/3.77 | (316) all_0_4_4 = n5
% 13.82/3.77 |
% 13.82/3.77 | From (424) and (1902) follows:
% 13.82/3.77 | (2011) sum(n0, n10) = all_0_0_0
% 13.82/3.77 |
% 13.82/3.77 | From (318)(316) and (119) follows:
% 13.82/3.77 | (320) sum(n5, n5) = all_0_3_3
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 13.82/3.77 | (321) all_0_3_3 = n10
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n0, n10, all_0_0_0, n10 and discharging atoms sum(n0, n10) = all_0_0_0, sum(n0, n10) = n10, yields:
% 13.82/3.77 | (322) all_0_0_0 = n10
% 13.82/3.77 |
% 13.82/3.77 | Equations (322,321) can reduce 104 to:
% 13.82/3.77 | (251) $false
% 13.82/3.77 |
% 13.82/3.77 |-The branch is then unsatisfiable
% 13.82/3.77 |-Branch two:
% 13.82/3.77 | (533) ~ (all_0_10_10 = n5)
% 13.82/3.77 | (534) all_0_10_10 = n4 | all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.82/3.77 |
% 13.82/3.77 +-Applying beta-rule and splitting (325), into two cases.
% 13.82/3.77 |-Branch one:
% 13.82/3.77 | (326) all_0_11_11 = n5
% 13.82/3.77 |
% 13.82/3.77 | From (326) and (84) follows:
% 13.82/3.77 | (327) pred(n5) = all_0_9_9
% 13.82/3.77 |
% 13.82/3.77 | From (326) and (210) follows:
% 13.82/3.77 | (328) succ(n5) = all_0_5_5
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (158) with n5, all_0_9_9, n4 and discharging atoms pred(n5) = all_0_9_9, pred(n5) = n4, yields:
% 13.82/3.77 | (329) all_0_9_9 = n4
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (141) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 13.82/3.77 | (330) all_0_5_5 = n6
% 13.82/3.77 |
% 13.82/3.77 | From (330) and (33) follows:
% 13.82/3.77 | (2023) sum(all_0_6_6, n6) = all_0_4_4
% 13.82/3.77 |
% 13.82/3.77 | From (329)(330) and (48) follows:
% 13.82/3.77 | (331) sum(n4, n6) = all_0_2_2
% 13.82/3.77 |
% 13.82/3.77 | From (329) and (137) follows:
% 13.82/3.77 | (2025) sum(n4, all_0_8_8) = all_0_7_7
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 13.82/3.77 | (335) all_0_2_2 = n10
% 13.82/3.77 |
% 13.82/3.77 | From (335) and (4) follows:
% 13.82/3.77 | (2027) sum(n10, all_0_1_1) = all_0_0_0
% 13.82/3.77 |
% 13.82/3.77 +-Applying beta-rule and splitting (534), into two cases.
% 13.82/3.77 |-Branch one:
% 13.82/3.77 | (535) all_0_10_10 = n4
% 13.82/3.77 |
% 13.82/3.77 | From (535) and (211) follows:
% 13.82/3.77 | (536) pred(n4) = all_0_6_6
% 13.82/3.77 |
% 13.82/3.77 | From (535) and (41) follows:
% 13.82/3.77 | (537) succ(n4) = all_0_8_8
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (158) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 13.82/3.77 | (538) all_0_6_6 = n3
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (141) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 13.82/3.77 | (539) all_0_8_8 = n5
% 13.82/3.77 |
% 13.82/3.77 | From (538)(539) and (178) follows:
% 13.82/3.77 | (540) sum(n3, n5) = all_0_1_1
% 13.82/3.77 |
% 13.82/3.77 | From (538) and (2023) follows:
% 13.82/3.77 | (2034) sum(n3, n6) = all_0_4_4
% 13.82/3.77 |
% 13.82/3.77 | From (539) and (2025) follows:
% 13.82/3.77 | (2035) sum(n4, n5) = all_0_7_7
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n4, n5, all_0_7_7, n9 and discharging atoms sum(n4, n5) = all_0_7_7, sum(n4, n5) = n9, yields:
% 13.82/3.77 | (242) all_0_7_7 = n9
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n3, n6, all_0_4_4, n9 and discharging atoms sum(n3, n6) = all_0_4_4, sum(n3, n6) = n9, yields:
% 13.82/3.77 | (241) all_0_4_4 = n9
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 13.82/3.77 | (544) all_0_1_1 = n8
% 13.82/3.77 |
% 13.82/3.77 | From (242)(241) and (119) follows:
% 13.82/3.77 | (246) sum(n9, n9) = all_0_3_3
% 13.82/3.77 |
% 13.82/3.77 | From (544) and (2027) follows:
% 13.82/3.77 | (2040) sum(n10, n8) = all_0_0_0
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n10, n8, all_0_0_0, n7 and discharging atoms sum(n10, n8) = all_0_0_0, sum(n10, n8) = n7, yields:
% 13.82/3.77 | (247) all_0_0_0 = n7
% 13.82/3.77 |
% 13.82/3.77 | Instantiating formula (31) with n9, n9, all_0_3_3, n7 and discharging atoms sum(n9, n9) = all_0_3_3, sum(n9, n9) = n7, yields:
% 13.82/3.77 | (249) all_0_3_3 = n7
% 13.82/3.77 |
% 13.82/3.77 | Equations (247,249) can reduce 104 to:
% 13.82/3.77 | (251) $false
% 13.82/3.77 |
% 13.82/3.77 |-The branch is then unsatisfiable
% 13.82/3.77 |-Branch two:
% 13.82/3.77 | (551) ~ (all_0_10_10 = n4)
% 13.82/3.77 | (552) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 13.82/3.78 |
% 13.82/3.78 +-Applying beta-rule and splitting (552), into two cases.
% 13.82/3.78 |-Branch one:
% 13.82/3.78 | (553) all_0_10_10 = n3
% 13.82/3.78 |
% 13.82/3.78 | From (553) and (211) follows:
% 13.82/3.78 | (554) pred(n3) = all_0_6_6
% 13.82/3.78 |
% 13.82/3.78 | From (553) and (41) follows:
% 13.82/3.78 | (555) succ(n3) = all_0_8_8
% 13.82/3.78 |
% 13.82/3.78 | Instantiating formula (158) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 13.82/3.78 | (556) all_0_6_6 = n2
% 13.82/3.78 |
% 13.82/3.78 | Instantiating formula (141) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 13.82/3.78 | (557) all_0_8_8 = n4
% 13.82/3.78 |
% 13.82/3.78 | From (556)(557) and (178) follows:
% 13.82/3.78 | (558) sum(n2, n4) = all_0_1_1
% 13.82/3.78 |
% 13.82/3.78 | From (556) and (2023) follows:
% 13.82/3.78 | (2052) sum(n2, n6) = all_0_4_4
% 14.08/3.78 |
% 14.08/3.78 | From (557) and (2025) follows:
% 14.08/3.78 | (2053) sum(n4, n4) = all_0_7_7
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n4, n4, all_0_7_7, n8 and discharging atoms sum(n4, n4) = all_0_7_7, sum(n4, n4) = n8, yields:
% 14.08/3.78 | (264) all_0_7_7 = n8
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n2, n6, all_0_4_4, n8 and discharging atoms sum(n2, n6) = all_0_4_4, sum(n2, n6) = n8, yields:
% 14.08/3.78 | (262) all_0_4_4 = n8
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 14.08/3.78 | (562) all_0_1_1 = n6
% 14.08/3.78 |
% 14.08/3.78 | From (264)(262) and (119) follows:
% 14.08/3.78 | (266) sum(n8, n8) = all_0_3_3
% 14.08/3.78 |
% 14.08/3.78 | From (562) and (2027) follows:
% 14.08/3.78 | (2058) sum(n10, n6) = all_0_0_0
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n10, n6, all_0_0_0, n5 and discharging atoms sum(n10, n6) = all_0_0_0, sum(n10, n6) = n5, yields:
% 14.08/3.78 | (268) all_0_0_0 = n5
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n8, n8, all_0_3_3, n5 and discharging atoms sum(n8, n8) = all_0_3_3, sum(n8, n8) = n5, yields:
% 14.08/3.78 | (267) all_0_3_3 = n5
% 14.08/3.78 |
% 14.08/3.78 | Equations (268,267) can reduce 104 to:
% 14.08/3.78 | (251) $false
% 14.08/3.78 |
% 14.08/3.78 |-The branch is then unsatisfiable
% 14.08/3.78 |-Branch two:
% 14.08/3.78 | (569) ~ (all_0_10_10 = n3)
% 14.08/3.78 | (570) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 14.08/3.78 |
% 14.08/3.78 +-Applying beta-rule and splitting (570), into two cases.
% 14.08/3.78 |-Branch one:
% 14.08/3.78 | (571) all_0_10_10 = n2
% 14.08/3.78 |
% 14.08/3.78 | From (571) and (211) follows:
% 14.08/3.78 | (572) pred(n2) = all_0_6_6
% 14.08/3.78 |
% 14.08/3.78 | From (571) and (41) follows:
% 14.08/3.78 | (573) succ(n2) = all_0_8_8
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (158) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 14.08/3.78 | (574) all_0_6_6 = n1
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (141) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 14.08/3.78 | (575) all_0_8_8 = n3
% 14.08/3.78 |
% 14.08/3.78 | From (574)(575) and (178) follows:
% 14.08/3.78 | (576) sum(n1, n3) = all_0_1_1
% 14.08/3.78 |
% 14.08/3.78 | From (574) and (2023) follows:
% 14.08/3.78 | (2070) sum(n1, n6) = all_0_4_4
% 14.08/3.78 |
% 14.08/3.78 | From (575) and (2025) follows:
% 14.08/3.78 | (2071) sum(n4, n3) = all_0_7_7
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n4, n3, all_0_7_7, n7 and discharging atoms sum(n4, n3) = all_0_7_7, sum(n4, n3) = n7, yields:
% 14.08/3.78 | (282) all_0_7_7 = n7
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n1, n6, all_0_4_4, n7 and discharging atoms sum(n1, n6) = all_0_4_4, sum(n1, n6) = n7, yields:
% 14.08/3.78 | (280) all_0_4_4 = n7
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 14.08/3.78 | (580) all_0_1_1 = n4
% 14.08/3.78 |
% 14.08/3.78 | From (282)(280) and (119) follows:
% 14.08/3.78 | (284) sum(n7, n7) = all_0_3_3
% 14.08/3.78 |
% 14.08/3.78 | From (580) and (2027) follows:
% 14.08/3.78 | (2076) sum(n10, n4) = all_0_0_0
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n10, n4, all_0_0_0, n3 and discharging atoms sum(n10, n4) = all_0_0_0, sum(n10, n4) = n3, yields:
% 14.08/3.78 | (286) all_0_0_0 = n3
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n7, n7, all_0_3_3, n3 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n3, yields:
% 14.08/3.78 | (285) all_0_3_3 = n3
% 14.08/3.78 |
% 14.08/3.78 | Equations (286,285) can reduce 104 to:
% 14.08/3.78 | (251) $false
% 14.08/3.78 |
% 14.08/3.78 |-The branch is then unsatisfiable
% 14.08/3.78 |-Branch two:
% 14.08/3.78 | (587) ~ (all_0_10_10 = n2)
% 14.08/3.78 | (588) all_0_10_10 = n1 | all_0_10_10 = n0
% 14.08/3.78 |
% 14.08/3.78 +-Applying beta-rule and splitting (588), into two cases.
% 14.08/3.78 |-Branch one:
% 14.08/3.78 | (589) all_0_10_10 = n1
% 14.08/3.78 |
% 14.08/3.78 | From (589) and (211) follows:
% 14.08/3.78 | (590) pred(n1) = all_0_6_6
% 14.08/3.78 |
% 14.08/3.78 | From (589) and (41) follows:
% 14.08/3.78 | (591) succ(n1) = all_0_8_8
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (158) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 14.08/3.78 | (592) all_0_6_6 = n0
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (141) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 14.08/3.78 | (593) all_0_8_8 = n2
% 14.08/3.78 |
% 14.08/3.78 | From (592)(593) and (178) follows:
% 14.08/3.78 | (594) sum(n0, n2) = all_0_1_1
% 14.08/3.78 |
% 14.08/3.78 | From (592) and (2023) follows:
% 14.08/3.78 | (2088) sum(n0, n6) = all_0_4_4
% 14.08/3.78 |
% 14.08/3.78 | From (593) and (2025) follows:
% 14.08/3.78 | (2089) sum(n4, n2) = all_0_7_7
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n4, n2, all_0_7_7, n6 and discharging atoms sum(n4, n2) = all_0_7_7, sum(n4, n2) = n6, yields:
% 14.08/3.78 | (300) all_0_7_7 = n6
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n0, n6, all_0_4_4, n6 and discharging atoms sum(n0, n6) = all_0_4_4, sum(n0, n6) = n6, yields:
% 14.08/3.78 | (298) all_0_4_4 = n6
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 14.08/3.78 | (598) all_0_1_1 = n2
% 14.08/3.78 |
% 14.08/3.78 | From (300)(298) and (119) follows:
% 14.08/3.78 | (302) sum(n6, n6) = all_0_3_3
% 14.08/3.78 |
% 14.08/3.78 | From (598) and (2027) follows:
% 14.08/3.78 | (2094) sum(n10, n2) = all_0_0_0
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n10, n2, all_0_0_0, n1 and discharging atoms sum(n10, n2) = all_0_0_0, sum(n10, n2) = n1, yields:
% 14.08/3.78 | (304) all_0_0_0 = n1
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n6, n6, all_0_3_3, n1 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n1, yields:
% 14.08/3.78 | (303) all_0_3_3 = n1
% 14.08/3.78 |
% 14.08/3.78 | Equations (304,303) can reduce 104 to:
% 14.08/3.78 | (251) $false
% 14.08/3.78 |
% 14.08/3.78 |-The branch is then unsatisfiable
% 14.08/3.78 |-Branch two:
% 14.08/3.78 | (607) ~ (all_0_10_10 = n1)
% 14.08/3.78 | (608) all_0_10_10 = n0
% 14.08/3.78 |
% 14.08/3.78 | From (608) and (211) follows:
% 14.08/3.78 | (609) pred(n0) = all_0_6_6
% 14.08/3.78 |
% 14.08/3.78 | From (608) and (41) follows:
% 14.08/3.78 | (610) succ(n0) = all_0_8_8
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (158) with n0, all_0_6_6, n10 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n10, yields:
% 14.08/3.78 | (611) all_0_6_6 = n10
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (141) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 14.08/3.78 | (612) all_0_8_8 = n1
% 14.08/3.78 |
% 14.08/3.78 | From (611)(612) and (178) follows:
% 14.08/3.78 | (613) sum(n10, n1) = all_0_1_1
% 14.08/3.78 |
% 14.08/3.78 | From (611) and (2023) follows:
% 14.08/3.78 | (2105) sum(n10, n6) = all_0_4_4
% 14.08/3.78 |
% 14.08/3.78 | From (612) and (2025) follows:
% 14.08/3.78 | (2106) sum(n4, n1) = all_0_7_7
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n10, n6, all_0_4_4, n5 and discharging atoms sum(n10, n6) = all_0_4_4, sum(n10, n6) = n5, yields:
% 14.08/3.78 | (316) all_0_4_4 = n5
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n10, n1, all_0_1_1, n0 and discharging atoms sum(n10, n1) = all_0_1_1, sum(n10, n1) = n0, yields:
% 14.08/3.78 | (616) all_0_1_1 = n0
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n4, n1, all_0_7_7, n5 and discharging atoms sum(n4, n1) = all_0_7_7, sum(n4, n1) = n5, yields:
% 14.08/3.78 | (318) all_0_7_7 = n5
% 14.08/3.78 |
% 14.08/3.78 | From (318)(316) and (119) follows:
% 14.08/3.78 | (320) sum(n5, n5) = all_0_3_3
% 14.08/3.78 |
% 14.08/3.78 | From (616) and (2027) follows:
% 14.08/3.78 | (2111) sum(n10, n0) = all_0_0_0
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n10, n0, all_0_0_0, n10 and discharging atoms sum(n10, n0) = all_0_0_0, sum(n10, n0) = n10, yields:
% 14.08/3.78 | (322) all_0_0_0 = n10
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (31) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 14.08/3.78 | (321) all_0_3_3 = n10
% 14.08/3.78 |
% 14.08/3.78 | Equations (322,321) can reduce 104 to:
% 14.08/3.78 | (251) $false
% 14.08/3.78 |
% 14.08/3.78 |-The branch is then unsatisfiable
% 14.08/3.78 |-Branch two:
% 14.08/3.78 | (342) ~ (all_0_11_11 = n5)
% 14.08/3.78 | (343) all_0_11_11 = n4 | all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 14.08/3.78 |
% 14.08/3.78 +-Applying beta-rule and splitting (534), into two cases.
% 14.08/3.78 |-Branch one:
% 14.08/3.78 | (535) all_0_10_10 = n4
% 14.08/3.78 |
% 14.08/3.78 | From (535) and (211) follows:
% 14.08/3.78 | (536) pred(n4) = all_0_6_6
% 14.08/3.78 |
% 14.08/3.78 | From (535) and (41) follows:
% 14.08/3.78 | (537) succ(n4) = all_0_8_8
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (158) with n4, all_0_6_6, n3 and discharging atoms pred(n4) = all_0_6_6, pred(n4) = n3, yields:
% 14.08/3.78 | (538) all_0_6_6 = n3
% 14.08/3.78 |
% 14.08/3.78 | Instantiating formula (141) with n4, all_0_8_8, n5 and discharging atoms succ(n4) = all_0_8_8, succ(n4) = n5, yields:
% 14.08/3.78 | (539) all_0_8_8 = n5
% 14.08/3.79 |
% 14.08/3.79 | From (538) and (536) follows:
% 14.08/3.79 | (157) pred(n4) = n3
% 14.08/3.79 |
% 14.08/3.79 | From (539) and (537) follows:
% 14.08/3.79 | (37) succ(n4) = n5
% 14.08/3.79 |
% 14.08/3.79 | From (538) and (33) follows:
% 14.08/3.79 | (2124) sum(n3, all_0_5_5) = all_0_4_4
% 14.08/3.79 |
% 14.08/3.79 | From (538)(539) and (178) follows:
% 14.08/3.79 | (540) sum(n3, n5) = all_0_1_1
% 14.08/3.79 |
% 14.08/3.79 | From (539) and (137) follows:
% 14.08/3.79 | (2126) sum(all_0_9_9, n5) = all_0_7_7
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) with n3, n5, all_0_1_1, n8 and discharging atoms sum(n3, n5) = all_0_1_1, sum(n3, n5) = n8, yields:
% 14.08/3.79 | (544) all_0_1_1 = n8
% 14.08/3.79 |
% 14.08/3.79 | From (544) and (4) follows:
% 14.08/3.79 | (2128) sum(all_0_2_2, n8) = all_0_0_0
% 14.08/3.79 |
% 14.08/3.79 | From (544) and (540) follows:
% 14.08/3.79 | (117) sum(n3, n5) = n8
% 14.08/3.79 |
% 14.08/3.79 +-Applying beta-rule and splitting (343), into two cases.
% 14.08/3.79 |-Branch one:
% 14.08/3.79 | (344) all_0_11_11 = n4
% 14.08/3.79 |
% 14.08/3.79 | From (344) and (84) follows:
% 14.08/3.79 | (345) pred(n4) = all_0_9_9
% 14.08/3.79 |
% 14.08/3.79 | From (344) and (210) follows:
% 14.08/3.79 | (346) succ(n4) = all_0_5_5
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (158) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 14.08/3.79 | (347) all_0_9_9 = n3
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (141) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 14.08/3.79 | (348) all_0_5_5 = n5
% 14.08/3.79 |
% 14.08/3.79 | From (347)(348) and (48) follows:
% 14.08/3.79 | (349) sum(n3, n5) = all_0_2_2
% 14.08/3.79 |
% 14.08/3.79 | From (347) and (2126) follows:
% 14.08/3.79 | (2136) sum(n3, n5) = all_0_7_7
% 14.08/3.79 |
% 14.08/3.79 | From (348) and (2124) follows:
% 14.08/3.79 | (2137) sum(n3, n5) = all_0_4_4
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 14.08/3.79 | (353) all_0_2_2 = n8
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) 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:
% 14.08/3.79 | (238) all_0_2_2 = all_0_4_4
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) 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:
% 14.08/3.79 | (239) all_0_2_2 = all_0_7_7
% 14.08/3.79 |
% 14.08/3.79 | Combining equations (239,238) yields a new equation:
% 14.08/3.79 | (240) all_0_4_4 = all_0_7_7
% 14.08/3.79 |
% 14.08/3.79 | Combining equations (353,238) yields a new equation:
% 14.08/3.79 | (262) all_0_4_4 = n8
% 14.08/3.79 |
% 14.08/3.79 | Combining equations (262,240) yields a new equation:
% 14.08/3.79 | (264) all_0_7_7 = n8
% 14.08/3.79 |
% 14.08/3.79 | Combining equations (264,240) yields a new equation:
% 14.08/3.79 | (262) all_0_4_4 = n8
% 14.08/3.79 |
% 14.08/3.79 | Combining equations (262,238) yields a new equation:
% 14.08/3.79 | (353) all_0_2_2 = n8
% 14.08/3.79 |
% 14.08/3.79 | From (353) and (2128) follows:
% 14.08/3.79 | (2146) sum(n8, n8) = all_0_0_0
% 14.08/3.79 |
% 14.08/3.79 | From (264)(262) and (119) follows:
% 14.08/3.79 | (266) sum(n8, n8) = all_0_3_3
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) with n8, n8, all_0_0_0, n5 and discharging atoms sum(n8, n8) = all_0_0_0, sum(n8, n8) = n5, yields:
% 14.08/3.79 | (268) all_0_0_0 = n5
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) 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:
% 14.08/3.79 | (248) all_0_0_0 = all_0_3_3
% 14.08/3.79 |
% 14.08/3.79 | Combining equations (268,248) yields a new equation:
% 14.08/3.79 | (267) all_0_3_3 = n5
% 14.08/3.79 |
% 14.08/3.79 | Combining equations (267,248) yields a new equation:
% 14.08/3.79 | (268) all_0_0_0 = n5
% 14.08/3.79 |
% 14.08/3.79 | Equations (268,267) can reduce 104 to:
% 14.08/3.79 | (251) $false
% 14.08/3.79 |
% 14.08/3.79 |-The branch is then unsatisfiable
% 14.08/3.79 |-Branch two:
% 14.08/3.79 | (360) ~ (all_0_11_11 = n4)
% 14.08/3.79 | (361) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 14.08/3.79 |
% 14.08/3.79 +-Applying beta-rule and splitting (361), into two cases.
% 14.08/3.79 |-Branch one:
% 14.08/3.79 | (362) all_0_11_11 = n3
% 14.08/3.79 |
% 14.08/3.79 | From (362) and (84) follows:
% 14.08/3.79 | (363) pred(n3) = all_0_9_9
% 14.08/3.79 |
% 14.08/3.79 | From (362) and (210) follows:
% 14.08/3.79 | (364) succ(n3) = all_0_5_5
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (158) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 14.08/3.79 | (365) all_0_9_9 = n2
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (141) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 14.08/3.79 | (366) all_0_5_5 = n4
% 14.08/3.79 |
% 14.08/3.79 | From (365)(366) and (48) follows:
% 14.08/3.79 | (367) sum(n2, n4) = all_0_2_2
% 14.08/3.79 |
% 14.08/3.79 | From (365) and (2126) follows:
% 14.08/3.79 | (2161) sum(n2, n5) = all_0_7_7
% 14.08/3.79 |
% 14.08/3.79 | From (366) and (2124) follows:
% 14.08/3.79 | (2162) sum(n3, n4) = all_0_4_4
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) with n3, n4, all_0_4_4, n7 and discharging atoms sum(n3, n4) = all_0_4_4, sum(n3, n4) = n7, yields:
% 14.08/3.79 | (280) all_0_4_4 = n7
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) with n2, n5, all_0_7_7, n7 and discharging atoms sum(n2, n5) = all_0_7_7, sum(n2, n5) = n7, yields:
% 14.08/3.79 | (282) all_0_7_7 = n7
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 14.08/3.79 | (371) all_0_2_2 = n6
% 14.08/3.79 |
% 14.08/3.79 | From (371) and (2128) follows:
% 14.08/3.79 | (2166) sum(n6, n8) = all_0_0_0
% 14.08/3.79 |
% 14.08/3.79 | From (282)(280) and (119) follows:
% 14.08/3.79 | (284) sum(n7, n7) = all_0_3_3
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) with n7, n7, all_0_3_3, n3 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n3, yields:
% 14.08/3.79 | (285) all_0_3_3 = n3
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) with n6, n8, all_0_0_0, n3 and discharging atoms sum(n6, n8) = all_0_0_0, sum(n6, n8) = n3, yields:
% 14.08/3.79 | (286) all_0_0_0 = n3
% 14.08/3.79 |
% 14.08/3.79 | Equations (286,285) can reduce 104 to:
% 14.08/3.79 | (251) $false
% 14.08/3.79 |
% 14.08/3.79 |-The branch is then unsatisfiable
% 14.08/3.79 |-Branch two:
% 14.08/3.79 | (378) ~ (all_0_11_11 = n3)
% 14.08/3.79 | (379) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 14.08/3.79 |
% 14.08/3.79 +-Applying beta-rule and splitting (379), into two cases.
% 14.08/3.79 |-Branch one:
% 14.08/3.79 | (380) all_0_11_11 = n2
% 14.08/3.79 |
% 14.08/3.79 | From (380) and (84) follows:
% 14.08/3.79 | (381) pred(n2) = all_0_9_9
% 14.08/3.79 |
% 14.08/3.79 | From (380) and (210) follows:
% 14.08/3.79 | (382) succ(n2) = all_0_5_5
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (158) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 14.08/3.79 | (383) all_0_9_9 = n1
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (141) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 14.08/3.79 | (384) all_0_5_5 = n3
% 14.08/3.79 |
% 14.08/3.79 | From (383)(384) and (48) follows:
% 14.08/3.79 | (385) sum(n1, n3) = all_0_2_2
% 14.08/3.79 |
% 14.08/3.79 | From (383) and (2126) follows:
% 14.08/3.79 | (2179) sum(n1, n5) = all_0_7_7
% 14.08/3.79 |
% 14.08/3.79 | From (384) and (2124) follows:
% 14.08/3.79 | (2180) sum(n3, n3) = all_0_4_4
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) with n3, n3, all_0_4_4, n6 and discharging atoms sum(n3, n3) = all_0_4_4, sum(n3, n3) = n6, yields:
% 14.08/3.79 | (298) all_0_4_4 = n6
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) with n1, n5, all_0_7_7, n6 and discharging atoms sum(n1, n5) = all_0_7_7, sum(n1, n5) = n6, yields:
% 14.08/3.79 | (300) all_0_7_7 = n6
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 14.08/3.79 | (389) all_0_2_2 = n4
% 14.08/3.79 |
% 14.08/3.79 | From (389) and (2128) follows:
% 14.08/3.79 | (2184) sum(n4, n8) = all_0_0_0
% 14.08/3.79 |
% 14.08/3.79 | From (300)(298) and (119) follows:
% 14.08/3.79 | (302) sum(n6, n6) = all_0_3_3
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) with n6, n6, all_0_3_3, n1 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n1, yields:
% 14.08/3.79 | (303) all_0_3_3 = n1
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) with n4, n8, all_0_0_0, n1 and discharging atoms sum(n4, n8) = all_0_0_0, sum(n4, n8) = n1, yields:
% 14.08/3.79 | (304) all_0_0_0 = n1
% 14.08/3.79 |
% 14.08/3.79 | Equations (304,303) can reduce 104 to:
% 14.08/3.79 | (251) $false
% 14.08/3.79 |
% 14.08/3.79 |-The branch is then unsatisfiable
% 14.08/3.79 |-Branch two:
% 14.08/3.79 | (396) ~ (all_0_11_11 = n2)
% 14.08/3.79 | (397) all_0_11_11 = n1 | all_0_11_11 = n0
% 14.08/3.79 |
% 14.08/3.79 +-Applying beta-rule and splitting (397), into two cases.
% 14.08/3.79 |-Branch one:
% 14.08/3.79 | (398) all_0_11_11 = n1
% 14.08/3.79 |
% 14.08/3.79 | From (398) and (84) follows:
% 14.08/3.79 | (399) pred(n1) = all_0_9_9
% 14.08/3.79 |
% 14.08/3.79 | From (398) and (210) follows:
% 14.08/3.79 | (400) succ(n1) = all_0_5_5
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (158) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 14.08/3.79 | (401) all_0_9_9 = n0
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (141) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 14.08/3.79 | (402) all_0_5_5 = n2
% 14.08/3.79 |
% 14.08/3.79 | From (401)(402) and (48) follows:
% 14.08/3.79 | (403) sum(n0, n2) = all_0_2_2
% 14.08/3.79 |
% 14.08/3.79 | From (401) and (2126) follows:
% 14.08/3.79 | (2197) sum(n0, n5) = all_0_7_7
% 14.08/3.79 |
% 14.08/3.79 | From (402) and (2124) follows:
% 14.08/3.79 | (2198) sum(n3, n2) = all_0_4_4
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) with n3, n2, all_0_4_4, n5 and discharging atoms sum(n3, n2) = all_0_4_4, sum(n3, n2) = n5, yields:
% 14.08/3.79 | (316) all_0_4_4 = n5
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) with n0, n5, all_0_7_7, n5 and discharging atoms sum(n0, n5) = all_0_7_7, sum(n0, n5) = n5, yields:
% 14.08/3.79 | (318) all_0_7_7 = n5
% 14.08/3.79 |
% 14.08/3.79 | Instantiating formula (31) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 14.08/3.79 | (407) all_0_2_2 = n2
% 14.08/3.79 |
% 14.08/3.79 | From (407) and (2128) follows:
% 14.08/3.80 | (2202) sum(n2, n8) = all_0_0_0
% 14.08/3.80 |
% 14.08/3.80 | From (318)(316) and (119) follows:
% 14.08/3.80 | (320) sum(n5, n5) = all_0_3_3
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 14.08/3.80 | (321) all_0_3_3 = n10
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n2, n8, all_0_0_0, n10 and discharging atoms sum(n2, n8) = all_0_0_0, sum(n2, n8) = n10, yields:
% 14.08/3.80 | (322) all_0_0_0 = n10
% 14.08/3.80 |
% 14.08/3.80 | Equations (322,321) can reduce 104 to:
% 14.08/3.80 | (251) $false
% 14.08/3.80 |
% 14.08/3.80 |-The branch is then unsatisfiable
% 14.08/3.80 |-Branch two:
% 14.08/3.80 | (415) ~ (all_0_11_11 = n1)
% 14.08/3.80 | (416) all_0_11_11 = n0
% 14.08/3.80 |
% 14.08/3.80 | From (416) and (84) follows:
% 14.08/3.80 | (417) pred(n0) = all_0_9_9
% 14.08/3.80 |
% 14.08/3.80 | From (416) and (210) follows:
% 14.08/3.80 | (418) succ(n0) = all_0_5_5
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (158) with n0, all_0_9_9, n10 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n10, yields:
% 14.08/3.80 | (419) all_0_9_9 = n10
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (141) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 14.08/3.80 | (420) all_0_5_5 = n1
% 14.08/3.80 |
% 14.08/3.80 | From (419)(420) and (48) follows:
% 14.08/3.80 | (421) sum(n10, n1) = all_0_2_2
% 14.08/3.80 |
% 14.08/3.80 | From (419) and (2126) follows:
% 14.08/3.80 | (2214) sum(n10, n5) = all_0_7_7
% 14.08/3.80 |
% 14.08/3.80 | From (420) and (2124) follows:
% 14.08/3.80 | (2215) sum(n3, n1) = all_0_4_4
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n10, n5, all_0_7_7, n4 and discharging atoms sum(n10, n5) = all_0_7_7, sum(n10, n5) = n4, yields:
% 14.08/3.80 | (336) all_0_7_7 = n4
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n10, n1, all_0_2_2, n0 and discharging atoms sum(n10, n1) = all_0_2_2, sum(n10, n1) = n0, yields:
% 14.08/3.80 | (424) all_0_2_2 = n0
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n3, n1, all_0_4_4, n4 and discharging atoms sum(n3, n1) = all_0_4_4, sum(n3, n1) = n4, yields:
% 14.08/3.80 | (334) all_0_4_4 = n4
% 14.08/3.80 |
% 14.08/3.80 | From (424) and (2128) follows:
% 14.08/3.80 | (2219) sum(n0, n8) = all_0_0_0
% 14.08/3.80 |
% 14.08/3.80 | From (336)(334) and (119) follows:
% 14.08/3.80 | (338) sum(n4, n4) = all_0_3_3
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 14.08/3.80 | (340) all_0_3_3 = n8
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n0, n8, all_0_0_0, n8 and discharging atoms sum(n0, n8) = all_0_0_0, sum(n0, n8) = n8, yields:
% 14.08/3.80 | (339) all_0_0_0 = n8
% 14.08/3.80 |
% 14.08/3.80 | Equations (339,340) can reduce 104 to:
% 14.08/3.80 | (251) $false
% 14.08/3.80 |
% 14.08/3.80 |-The branch is then unsatisfiable
% 14.08/3.80 |-Branch two:
% 14.08/3.80 | (551) ~ (all_0_10_10 = n4)
% 14.08/3.80 | (552) all_0_10_10 = n3 | all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 14.08/3.80 |
% 14.08/3.80 +-Applying beta-rule and splitting (343), into two cases.
% 14.08/3.80 |-Branch one:
% 14.08/3.80 | (344) all_0_11_11 = n4
% 14.08/3.80 |
% 14.08/3.80 | From (344) and (84) follows:
% 14.08/3.80 | (345) pred(n4) = all_0_9_9
% 14.08/3.80 |
% 14.08/3.80 | From (344) and (210) follows:
% 14.08/3.80 | (346) succ(n4) = all_0_5_5
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (158) with n4, all_0_9_9, n3 and discharging atoms pred(n4) = all_0_9_9, pred(n4) = n3, yields:
% 14.08/3.80 | (347) all_0_9_9 = n3
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (141) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 14.08/3.80 | (348) all_0_5_5 = n5
% 14.08/3.80 |
% 14.08/3.80 | From (348) and (33) follows:
% 14.08/3.80 | (2231) sum(all_0_6_6, n5) = all_0_4_4
% 14.08/3.80 |
% 14.08/3.80 | From (347)(348) and (48) follows:
% 14.08/3.80 | (349) sum(n3, n5) = all_0_2_2
% 14.08/3.80 |
% 14.08/3.80 | From (347) and (137) follows:
% 14.08/3.80 | (2233) sum(n3, all_0_8_8) = all_0_7_7
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 14.08/3.80 | (353) all_0_2_2 = n8
% 14.08/3.80 |
% 14.08/3.80 | From (353) and (4) follows:
% 14.08/3.80 | (2235) sum(n8, all_0_1_1) = all_0_0_0
% 14.08/3.80 |
% 14.08/3.80 +-Applying beta-rule and splitting (552), into two cases.
% 14.08/3.80 |-Branch one:
% 14.08/3.80 | (553) all_0_10_10 = n3
% 14.08/3.80 |
% 14.08/3.80 | From (553) and (211) follows:
% 14.08/3.80 | (554) pred(n3) = all_0_6_6
% 14.08/3.80 |
% 14.08/3.80 | From (553) and (41) follows:
% 14.08/3.80 | (555) succ(n3) = all_0_8_8
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (158) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 14.08/3.80 | (556) all_0_6_6 = n2
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (141) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 14.08/3.80 | (557) all_0_8_8 = n4
% 14.08/3.80 |
% 14.08/3.80 | From (556)(557) and (178) follows:
% 14.08/3.80 | (558) sum(n2, n4) = all_0_1_1
% 14.08/3.80 |
% 14.08/3.80 | From (556) and (2231) follows:
% 14.08/3.80 | (2242) sum(n2, n5) = all_0_4_4
% 14.08/3.80 |
% 14.08/3.80 | From (557) and (2233) follows:
% 14.08/3.80 | (2243) sum(n3, n4) = all_0_7_7
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n3, n4, all_0_7_7, n7 and discharging atoms sum(n3, n4) = all_0_7_7, sum(n3, n4) = n7, yields:
% 14.08/3.80 | (282) all_0_7_7 = n7
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n2, n5, all_0_4_4, n7 and discharging atoms sum(n2, n5) = all_0_4_4, sum(n2, n5) = n7, yields:
% 14.08/3.80 | (280) all_0_4_4 = n7
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 14.08/3.80 | (562) all_0_1_1 = n6
% 14.08/3.80 |
% 14.08/3.80 | From (282)(280) and (119) follows:
% 14.08/3.80 | (284) sum(n7, n7) = all_0_3_3
% 14.08/3.80 |
% 14.08/3.80 | From (562) and (2235) follows:
% 14.08/3.80 | (2248) sum(n8, n6) = all_0_0_0
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n8, n6, all_0_0_0, n3 and discharging atoms sum(n8, n6) = all_0_0_0, sum(n8, n6) = n3, yields:
% 14.08/3.80 | (286) all_0_0_0 = n3
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n7, n7, all_0_3_3, n3 and discharging atoms sum(n7, n7) = all_0_3_3, sum(n7, n7) = n3, yields:
% 14.08/3.80 | (285) all_0_3_3 = n3
% 14.08/3.80 |
% 14.08/3.80 | Equations (286,285) can reduce 104 to:
% 14.08/3.80 | (251) $false
% 14.08/3.80 |
% 14.08/3.80 |-The branch is then unsatisfiable
% 14.08/3.80 |-Branch two:
% 14.08/3.80 | (569) ~ (all_0_10_10 = n3)
% 14.08/3.80 | (570) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 14.08/3.80 |
% 14.08/3.80 +-Applying beta-rule and splitting (570), into two cases.
% 14.08/3.80 |-Branch one:
% 14.08/3.80 | (571) all_0_10_10 = n2
% 14.08/3.80 |
% 14.08/3.80 | From (571) and (211) follows:
% 14.08/3.80 | (572) pred(n2) = all_0_6_6
% 14.08/3.80 |
% 14.08/3.80 | From (571) and (41) follows:
% 14.08/3.80 | (573) succ(n2) = all_0_8_8
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (158) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 14.08/3.80 | (574) all_0_6_6 = n1
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (141) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 14.08/3.80 | (575) all_0_8_8 = n3
% 14.08/3.80 |
% 14.08/3.80 | From (574)(575) and (178) follows:
% 14.08/3.80 | (576) sum(n1, n3) = all_0_1_1
% 14.08/3.80 |
% 14.08/3.80 | From (574) and (2231) follows:
% 14.08/3.80 | (2260) sum(n1, n5) = all_0_4_4
% 14.08/3.80 |
% 14.08/3.80 | From (575) and (2233) follows:
% 14.08/3.80 | (2261) sum(n3, n3) = all_0_7_7
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n3, n3, all_0_7_7, n6 and discharging atoms sum(n3, n3) = all_0_7_7, sum(n3, n3) = n6, yields:
% 14.08/3.80 | (300) all_0_7_7 = n6
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n1, n5, all_0_4_4, n6 and discharging atoms sum(n1, n5) = all_0_4_4, sum(n1, n5) = n6, yields:
% 14.08/3.80 | (298) all_0_4_4 = n6
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 14.08/3.80 | (580) all_0_1_1 = n4
% 14.08/3.80 |
% 14.08/3.80 | From (300)(298) and (119) follows:
% 14.08/3.80 | (302) sum(n6, n6) = all_0_3_3
% 14.08/3.80 |
% 14.08/3.80 | From (580) and (2235) follows:
% 14.08/3.80 | (2266) sum(n8, n4) = all_0_0_0
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n8, n4, all_0_0_0, n1 and discharging atoms sum(n8, n4) = all_0_0_0, sum(n8, n4) = n1, yields:
% 14.08/3.80 | (304) all_0_0_0 = n1
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n6, n6, all_0_3_3, n1 and discharging atoms sum(n6, n6) = all_0_3_3, sum(n6, n6) = n1, yields:
% 14.08/3.80 | (303) all_0_3_3 = n1
% 14.08/3.80 |
% 14.08/3.80 | Equations (304,303) can reduce 104 to:
% 14.08/3.80 | (251) $false
% 14.08/3.80 |
% 14.08/3.80 |-The branch is then unsatisfiable
% 14.08/3.80 |-Branch two:
% 14.08/3.80 | (587) ~ (all_0_10_10 = n2)
% 14.08/3.80 | (588) all_0_10_10 = n1 | all_0_10_10 = n0
% 14.08/3.80 |
% 14.08/3.80 +-Applying beta-rule and splitting (588), into two cases.
% 14.08/3.80 |-Branch one:
% 14.08/3.80 | (589) all_0_10_10 = n1
% 14.08/3.80 |
% 14.08/3.80 | From (589) and (211) follows:
% 14.08/3.80 | (590) pred(n1) = all_0_6_6
% 14.08/3.80 |
% 14.08/3.80 | From (589) and (41) follows:
% 14.08/3.80 | (591) succ(n1) = all_0_8_8
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (158) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 14.08/3.80 | (592) all_0_6_6 = n0
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (141) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 14.08/3.80 | (593) all_0_8_8 = n2
% 14.08/3.80 |
% 14.08/3.80 | From (592)(593) and (178) follows:
% 14.08/3.80 | (594) sum(n0, n2) = all_0_1_1
% 14.08/3.80 |
% 14.08/3.80 | From (592) and (2231) follows:
% 14.08/3.80 | (2278) sum(n0, n5) = all_0_4_4
% 14.08/3.80 |
% 14.08/3.80 | From (593) and (2233) follows:
% 14.08/3.80 | (2279) sum(n3, n2) = all_0_7_7
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n3, n2, all_0_7_7, n5 and discharging atoms sum(n3, n2) = all_0_7_7, sum(n3, n2) = n5, yields:
% 14.08/3.80 | (318) all_0_7_7 = n5
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n0, n5, all_0_4_4, n5 and discharging atoms sum(n0, n5) = all_0_4_4, sum(n0, n5) = n5, yields:
% 14.08/3.80 | (316) all_0_4_4 = n5
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 14.08/3.80 | (598) all_0_1_1 = n2
% 14.08/3.80 |
% 14.08/3.80 | From (318)(316) and (119) follows:
% 14.08/3.80 | (320) sum(n5, n5) = all_0_3_3
% 14.08/3.80 |
% 14.08/3.80 | From (598) and (2235) follows:
% 14.08/3.80 | (2284) sum(n8, n2) = all_0_0_0
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n8, n2, all_0_0_0, n10 and discharging atoms sum(n8, n2) = all_0_0_0, sum(n8, n2) = n10, yields:
% 14.08/3.80 | (322) all_0_0_0 = n10
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (31) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 14.08/3.80 | (321) all_0_3_3 = n10
% 14.08/3.80 |
% 14.08/3.80 | Equations (322,321) can reduce 104 to:
% 14.08/3.80 | (251) $false
% 14.08/3.80 |
% 14.08/3.80 |-The branch is then unsatisfiable
% 14.08/3.80 |-Branch two:
% 14.08/3.80 | (607) ~ (all_0_10_10 = n1)
% 14.08/3.80 | (608) all_0_10_10 = n0
% 14.08/3.80 |
% 14.08/3.80 | From (608) and (211) follows:
% 14.08/3.80 | (609) pred(n0) = all_0_6_6
% 14.08/3.80 |
% 14.08/3.80 | From (608) and (41) follows:
% 14.08/3.80 | (610) succ(n0) = all_0_8_8
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (158) with n0, all_0_6_6, n10 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n10, yields:
% 14.08/3.80 | (611) all_0_6_6 = n10
% 14.08/3.80 |
% 14.08/3.80 | Instantiating formula (141) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 14.08/3.81 | (612) all_0_8_8 = n1
% 14.08/3.81 |
% 14.08/3.81 | From (611)(612) and (178) follows:
% 14.08/3.81 | (613) sum(n10, n1) = all_0_1_1
% 14.08/3.81 |
% 14.08/3.81 | From (611) and (2231) follows:
% 14.08/3.81 | (2295) sum(n10, n5) = all_0_4_4
% 14.08/3.81 |
% 14.08/3.81 | From (612) and (2233) follows:
% 14.08/3.81 | (2296) sum(n3, n1) = all_0_7_7
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n10, n5, all_0_4_4, n4 and discharging atoms sum(n10, n5) = all_0_4_4, sum(n10, n5) = n4, yields:
% 14.08/3.81 | (334) all_0_4_4 = n4
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n10, n1, all_0_1_1, n0 and discharging atoms sum(n10, n1) = all_0_1_1, sum(n10, n1) = n0, yields:
% 14.08/3.81 | (616) all_0_1_1 = n0
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n3, n1, all_0_7_7, n4 and discharging atoms sum(n3, n1) = all_0_7_7, sum(n3, n1) = n4, yields:
% 14.08/3.81 | (336) all_0_7_7 = n4
% 14.08/3.81 |
% 14.08/3.81 | From (336)(334) and (119) follows:
% 14.08/3.81 | (338) sum(n4, n4) = all_0_3_3
% 14.08/3.81 |
% 14.08/3.81 | From (616) and (2235) follows:
% 14.08/3.81 | (2301) sum(n8, n0) = all_0_0_0
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n8, n0, all_0_0_0, n8 and discharging atoms sum(n8, n0) = all_0_0_0, sum(n8, n0) = n8, yields:
% 14.08/3.81 | (339) all_0_0_0 = n8
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 14.08/3.81 | (340) all_0_3_3 = n8
% 14.08/3.81 |
% 14.08/3.81 | Equations (339,340) can reduce 104 to:
% 14.08/3.81 | (251) $false
% 14.08/3.81 |
% 14.08/3.81 |-The branch is then unsatisfiable
% 14.08/3.81 |-Branch two:
% 14.08/3.81 | (360) ~ (all_0_11_11 = n4)
% 14.08/3.81 | (361) all_0_11_11 = n3 | all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 14.08/3.81 |
% 14.08/3.81 +-Applying beta-rule and splitting (552), into two cases.
% 14.08/3.81 |-Branch one:
% 14.08/3.81 | (553) all_0_10_10 = n3
% 14.08/3.81 |
% 14.08/3.81 | From (553) and (211) follows:
% 14.08/3.81 | (554) pred(n3) = all_0_6_6
% 14.08/3.81 |
% 14.08/3.81 | From (553) and (41) follows:
% 14.08/3.81 | (555) succ(n3) = all_0_8_8
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (158) with n3, all_0_6_6, n2 and discharging atoms pred(n3) = all_0_6_6, pred(n3) = n2, yields:
% 14.08/3.81 | (556) all_0_6_6 = n2
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (141) with n3, all_0_8_8, n4 and discharging atoms succ(n3) = all_0_8_8, succ(n3) = n4, yields:
% 14.08/3.81 | (557) all_0_8_8 = n4
% 14.08/3.81 |
% 14.08/3.81 | From (556) and (554) follows:
% 14.08/3.81 | (131) pred(n3) = n2
% 14.08/3.81 |
% 14.08/3.81 | From (557) and (555) follows:
% 14.08/3.81 | (196) succ(n3) = n4
% 14.08/3.81 |
% 14.08/3.81 | From (556) and (33) follows:
% 14.08/3.81 | (2314) sum(n2, all_0_5_5) = all_0_4_4
% 14.08/3.81 |
% 14.08/3.81 | From (556)(557) and (178) follows:
% 14.08/3.81 | (558) sum(n2, n4) = all_0_1_1
% 14.08/3.81 |
% 14.08/3.81 | From (557) and (137) follows:
% 14.08/3.81 | (2316) sum(all_0_9_9, n4) = all_0_7_7
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n2, n4, all_0_1_1, n6 and discharging atoms sum(n2, n4) = all_0_1_1, sum(n2, n4) = n6, yields:
% 14.08/3.81 | (562) all_0_1_1 = n6
% 14.08/3.81 |
% 14.08/3.81 | From (562) and (4) follows:
% 14.08/3.81 | (2318) sum(all_0_2_2, n6) = all_0_0_0
% 14.08/3.81 |
% 14.08/3.81 | From (562) and (558) follows:
% 14.08/3.81 | (206) sum(n2, n4) = n6
% 14.08/3.81 |
% 14.08/3.81 +-Applying beta-rule and splitting (361), into two cases.
% 14.08/3.81 |-Branch one:
% 14.08/3.81 | (362) all_0_11_11 = n3
% 14.08/3.81 |
% 14.08/3.81 | From (362) and (84) follows:
% 14.08/3.81 | (363) pred(n3) = all_0_9_9
% 14.08/3.81 |
% 14.08/3.81 | From (362) and (210) follows:
% 14.08/3.81 | (364) succ(n3) = all_0_5_5
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (158) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 14.08/3.81 | (365) all_0_9_9 = n2
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (141) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 14.08/3.81 | (366) all_0_5_5 = n4
% 14.08/3.81 |
% 14.08/3.81 | From (365)(366) and (48) follows:
% 14.08/3.81 | (367) sum(n2, n4) = all_0_2_2
% 14.08/3.81 |
% 14.08/3.81 | From (365) and (2316) follows:
% 14.08/3.81 | (2326) sum(n2, n4) = all_0_7_7
% 14.08/3.81 |
% 14.08/3.81 | From (366) and (2314) follows:
% 14.08/3.81 | (2327) sum(n2, n4) = all_0_4_4
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 14.08/3.81 | (371) all_0_2_2 = n6
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) 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:
% 14.08/3.81 | (238) all_0_2_2 = all_0_4_4
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) 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:
% 14.08/3.81 | (239) all_0_2_2 = all_0_7_7
% 14.08/3.81 |
% 14.08/3.81 | Combining equations (239,238) yields a new equation:
% 14.08/3.81 | (240) all_0_4_4 = all_0_7_7
% 14.08/3.81 |
% 14.08/3.81 | Combining equations (371,238) yields a new equation:
% 14.08/3.81 | (298) all_0_4_4 = n6
% 14.08/3.81 |
% 14.08/3.81 | Combining equations (298,240) yields a new equation:
% 14.08/3.81 | (300) all_0_7_7 = n6
% 14.08/3.81 |
% 14.08/3.81 | Combining equations (300,240) yields a new equation:
% 14.08/3.81 | (298) all_0_4_4 = n6
% 14.08/3.81 |
% 14.08/3.81 | Combining equations (298,238) yields a new equation:
% 14.08/3.81 | (371) all_0_2_2 = n6
% 14.08/3.81 |
% 14.08/3.81 | From (371) and (2318) follows:
% 14.08/3.81 | (2336) sum(n6, n6) = all_0_0_0
% 14.08/3.81 |
% 14.08/3.81 | From (300)(298) and (119) follows:
% 14.08/3.81 | (302) sum(n6, n6) = all_0_3_3
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n6, n6, all_0_0_0, n1 and discharging atoms sum(n6, n6) = all_0_0_0, sum(n6, n6) = n1, yields:
% 14.08/3.81 | (304) all_0_0_0 = n1
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) 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:
% 14.08/3.81 | (248) all_0_0_0 = all_0_3_3
% 14.08/3.81 |
% 14.08/3.81 | Combining equations (304,248) yields a new equation:
% 14.08/3.81 | (303) all_0_3_3 = n1
% 14.08/3.81 |
% 14.08/3.81 | Combining equations (303,248) yields a new equation:
% 14.08/3.81 | (304) all_0_0_0 = n1
% 14.08/3.81 |
% 14.08/3.81 | Equations (304,303) can reduce 104 to:
% 14.08/3.81 | (251) $false
% 14.08/3.81 |
% 14.08/3.81 |-The branch is then unsatisfiable
% 14.08/3.81 |-Branch two:
% 14.08/3.81 | (378) ~ (all_0_11_11 = n3)
% 14.08/3.81 | (379) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 14.08/3.81 |
% 14.08/3.81 +-Applying beta-rule and splitting (379), into two cases.
% 14.08/3.81 |-Branch one:
% 14.08/3.81 | (380) all_0_11_11 = n2
% 14.08/3.81 |
% 14.08/3.81 | From (380) and (84) follows:
% 14.08/3.81 | (381) pred(n2) = all_0_9_9
% 14.08/3.81 |
% 14.08/3.81 | From (380) and (210) follows:
% 14.08/3.81 | (382) succ(n2) = all_0_5_5
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (158) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 14.08/3.81 | (383) all_0_9_9 = n1
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (141) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 14.08/3.81 | (384) all_0_5_5 = n3
% 14.08/3.81 |
% 14.08/3.81 | From (383)(384) and (48) follows:
% 14.08/3.81 | (385) sum(n1, n3) = all_0_2_2
% 14.08/3.81 |
% 14.08/3.81 | From (383) and (2316) follows:
% 14.08/3.81 | (2351) sum(n1, n4) = all_0_7_7
% 14.08/3.81 |
% 14.08/3.81 | From (384) and (2314) follows:
% 14.08/3.81 | (2352) sum(n2, n3) = all_0_4_4
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n2, n3, all_0_4_4, n5 and discharging atoms sum(n2, n3) = all_0_4_4, sum(n2, n3) = n5, yields:
% 14.08/3.81 | (316) all_0_4_4 = n5
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n1, n4, all_0_7_7, n5 and discharging atoms sum(n1, n4) = all_0_7_7, sum(n1, n4) = n5, yields:
% 14.08/3.81 | (318) all_0_7_7 = n5
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 14.08/3.81 | (389) all_0_2_2 = n4
% 14.08/3.81 |
% 14.08/3.81 | From (389) and (2318) follows:
% 14.08/3.81 | (2356) sum(n4, n6) = all_0_0_0
% 14.08/3.81 |
% 14.08/3.81 | From (318)(316) and (119) follows:
% 14.08/3.81 | (320) sum(n5, n5) = all_0_3_3
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 14.08/3.81 | (321) all_0_3_3 = n10
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n4, n6, all_0_0_0, n10 and discharging atoms sum(n4, n6) = all_0_0_0, sum(n4, n6) = n10, yields:
% 14.08/3.81 | (322) all_0_0_0 = n10
% 14.08/3.81 |
% 14.08/3.81 | Equations (322,321) can reduce 104 to:
% 14.08/3.81 | (251) $false
% 14.08/3.81 |
% 14.08/3.81 |-The branch is then unsatisfiable
% 14.08/3.81 |-Branch two:
% 14.08/3.81 | (396) ~ (all_0_11_11 = n2)
% 14.08/3.81 | (397) all_0_11_11 = n1 | all_0_11_11 = n0
% 14.08/3.81 |
% 14.08/3.81 +-Applying beta-rule and splitting (397), into two cases.
% 14.08/3.81 |-Branch one:
% 14.08/3.81 | (398) all_0_11_11 = n1
% 14.08/3.81 |
% 14.08/3.81 | From (398) and (84) follows:
% 14.08/3.81 | (399) pred(n1) = all_0_9_9
% 14.08/3.81 |
% 14.08/3.81 | From (398) and (210) follows:
% 14.08/3.81 | (400) succ(n1) = all_0_5_5
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (158) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 14.08/3.81 | (401) all_0_9_9 = n0
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (141) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 14.08/3.81 | (402) all_0_5_5 = n2
% 14.08/3.81 |
% 14.08/3.81 | From (401)(402) and (48) follows:
% 14.08/3.81 | (403) sum(n0, n2) = all_0_2_2
% 14.08/3.81 |
% 14.08/3.81 | From (401) and (2316) follows:
% 14.08/3.81 | (2369) sum(n0, n4) = all_0_7_7
% 14.08/3.81 |
% 14.08/3.81 | From (402) and (2314) follows:
% 14.08/3.81 | (2370) sum(n2, n2) = all_0_4_4
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n2, n2, all_0_4_4, n4 and discharging atoms sum(n2, n2) = all_0_4_4, sum(n2, n2) = n4, yields:
% 14.08/3.81 | (334) all_0_4_4 = n4
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n0, n4, all_0_7_7, n4 and discharging atoms sum(n0, n4) = all_0_7_7, sum(n0, n4) = n4, yields:
% 14.08/3.81 | (336) all_0_7_7 = n4
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 14.08/3.81 | (407) all_0_2_2 = n2
% 14.08/3.81 |
% 14.08/3.81 | From (407) and (2318) follows:
% 14.08/3.81 | (2374) sum(n2, n6) = all_0_0_0
% 14.08/3.81 |
% 14.08/3.81 | From (336)(334) and (119) follows:
% 14.08/3.81 | (338) sum(n4, n4) = all_0_3_3
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 14.08/3.81 | (340) all_0_3_3 = n8
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (31) with n2, n6, all_0_0_0, n8 and discharging atoms sum(n2, n6) = all_0_0_0, sum(n2, n6) = n8, yields:
% 14.08/3.81 | (339) all_0_0_0 = n8
% 14.08/3.81 |
% 14.08/3.81 | Equations (339,340) can reduce 104 to:
% 14.08/3.81 | (251) $false
% 14.08/3.81 |
% 14.08/3.81 |-The branch is then unsatisfiable
% 14.08/3.81 |-Branch two:
% 14.08/3.81 | (415) ~ (all_0_11_11 = n1)
% 14.08/3.81 | (416) all_0_11_11 = n0
% 14.08/3.81 |
% 14.08/3.81 | From (416) and (84) follows:
% 14.08/3.81 | (417) pred(n0) = all_0_9_9
% 14.08/3.81 |
% 14.08/3.81 | From (416) and (210) follows:
% 14.08/3.81 | (418) succ(n0) = all_0_5_5
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (158) with n0, all_0_9_9, n10 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n10, yields:
% 14.08/3.81 | (419) all_0_9_9 = n10
% 14.08/3.81 |
% 14.08/3.81 | Instantiating formula (141) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 14.08/3.81 | (420) all_0_5_5 = n1
% 14.08/3.81 |
% 14.08/3.81 | From (419)(420) and (48) follows:
% 14.08/3.81 | (421) sum(n10, n1) = all_0_2_2
% 14.08/3.81 |
% 14.08/3.81 | From (419) and (2316) follows:
% 14.08/3.81 | (2386) sum(n10, n4) = all_0_7_7
% 14.08/3.81 |
% 14.08/3.81 | From (420) and (2314) follows:
% 14.08/3.82 | (2387) sum(n2, n1) = all_0_4_4
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n10, n4, all_0_7_7, n3 and discharging atoms sum(n10, n4) = all_0_7_7, sum(n10, n4) = n3, yields:
% 14.08/3.82 | (354) all_0_7_7 = n3
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n10, n1, all_0_2_2, n0 and discharging atoms sum(n10, n1) = all_0_2_2, sum(n10, n1) = n0, yields:
% 14.08/3.82 | (424) all_0_2_2 = n0
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n2, n1, all_0_4_4, n3 and discharging atoms sum(n2, n1) = all_0_4_4, sum(n2, n1) = n3, yields:
% 14.08/3.82 | (352) all_0_4_4 = n3
% 14.08/3.82 |
% 14.08/3.82 | From (424) and (2318) follows:
% 14.08/3.82 | (2391) sum(n0, n6) = all_0_0_0
% 14.08/3.82 |
% 14.08/3.82 | From (354)(352) and (119) follows:
% 14.08/3.82 | (356) sum(n3, n3) = all_0_3_3
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 14.08/3.82 | (358) all_0_3_3 = n6
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n0, n6, all_0_0_0, n6 and discharging atoms sum(n0, n6) = all_0_0_0, sum(n0, n6) = n6, yields:
% 14.08/3.82 | (357) all_0_0_0 = n6
% 14.08/3.82 |
% 14.08/3.82 | Equations (357,358) can reduce 104 to:
% 14.08/3.82 | (251) $false
% 14.08/3.82 |
% 14.08/3.82 |-The branch is then unsatisfiable
% 14.08/3.82 |-Branch two:
% 14.08/3.82 | (569) ~ (all_0_10_10 = n3)
% 14.08/3.82 | (570) all_0_10_10 = n2 | all_0_10_10 = n1 | all_0_10_10 = n0
% 14.08/3.82 |
% 14.08/3.82 +-Applying beta-rule and splitting (361), into two cases.
% 14.08/3.82 |-Branch one:
% 14.08/3.82 | (362) all_0_11_11 = n3
% 14.08/3.82 |
% 14.08/3.82 | From (362) and (84) follows:
% 14.08/3.82 | (363) pred(n3) = all_0_9_9
% 14.08/3.82 |
% 14.08/3.82 | From (362) and (210) follows:
% 14.08/3.82 | (364) succ(n3) = all_0_5_5
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (158) with n3, all_0_9_9, n2 and discharging atoms pred(n3) = all_0_9_9, pred(n3) = n2, yields:
% 14.08/3.82 | (365) all_0_9_9 = n2
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (141) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 14.08/3.82 | (366) all_0_5_5 = n4
% 14.08/3.82 |
% 14.08/3.82 | From (366) and (33) follows:
% 14.08/3.82 | (2403) sum(all_0_6_6, n4) = all_0_4_4
% 14.08/3.82 |
% 14.08/3.82 | From (365)(366) and (48) follows:
% 14.08/3.82 | (367) sum(n2, n4) = all_0_2_2
% 14.08/3.82 |
% 14.08/3.82 | From (365) and (137) follows:
% 14.08/3.82 | (2405) sum(n2, all_0_8_8) = all_0_7_7
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 14.08/3.82 | (371) all_0_2_2 = n6
% 14.08/3.82 |
% 14.08/3.82 | From (371) and (4) follows:
% 14.08/3.82 | (2407) sum(n6, all_0_1_1) = all_0_0_0
% 14.08/3.82 |
% 14.08/3.82 +-Applying beta-rule and splitting (570), into two cases.
% 14.08/3.82 |-Branch one:
% 14.08/3.82 | (571) all_0_10_10 = n2
% 14.08/3.82 |
% 14.08/3.82 | From (571) and (211) follows:
% 14.08/3.82 | (572) pred(n2) = all_0_6_6
% 14.08/3.82 |
% 14.08/3.82 | From (571) and (41) follows:
% 14.08/3.82 | (573) succ(n2) = all_0_8_8
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (158) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 14.08/3.82 | (574) all_0_6_6 = n1
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (141) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 14.08/3.82 | (575) all_0_8_8 = n3
% 14.08/3.82 |
% 14.08/3.82 | From (574)(575) and (178) follows:
% 14.08/3.82 | (576) sum(n1, n3) = all_0_1_1
% 14.08/3.82 |
% 14.08/3.82 | From (574) and (2403) follows:
% 14.08/3.82 | (2414) sum(n1, n4) = all_0_4_4
% 14.08/3.82 |
% 14.08/3.82 | From (575) and (2405) follows:
% 14.08/3.82 | (2415) sum(n2, n3) = all_0_7_7
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n2, n3, all_0_7_7, n5 and discharging atoms sum(n2, n3) = all_0_7_7, sum(n2, n3) = n5, yields:
% 14.08/3.82 | (318) all_0_7_7 = n5
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n1, n4, all_0_4_4, n5 and discharging atoms sum(n1, n4) = all_0_4_4, sum(n1, n4) = n5, yields:
% 14.08/3.82 | (316) all_0_4_4 = n5
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 14.08/3.82 | (580) all_0_1_1 = n4
% 14.08/3.82 |
% 14.08/3.82 | From (318)(316) and (119) follows:
% 14.08/3.82 | (320) sum(n5, n5) = all_0_3_3
% 14.08/3.82 |
% 14.08/3.82 | From (580) and (2407) follows:
% 14.08/3.82 | (2420) sum(n6, n4) = all_0_0_0
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n6, n4, all_0_0_0, n10 and discharging atoms sum(n6, n4) = all_0_0_0, sum(n6, n4) = n10, yields:
% 14.08/3.82 | (322) all_0_0_0 = n10
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n5, n5, all_0_3_3, n10 and discharging atoms sum(n5, n5) = all_0_3_3, sum(n5, n5) = n10, yields:
% 14.08/3.82 | (321) all_0_3_3 = n10
% 14.08/3.82 |
% 14.08/3.82 | Equations (322,321) can reduce 104 to:
% 14.08/3.82 | (251) $false
% 14.08/3.82 |
% 14.08/3.82 |-The branch is then unsatisfiable
% 14.08/3.82 |-Branch two:
% 14.08/3.82 | (587) ~ (all_0_10_10 = n2)
% 14.08/3.82 | (588) all_0_10_10 = n1 | all_0_10_10 = n0
% 14.08/3.82 |
% 14.08/3.82 +-Applying beta-rule and splitting (588), into two cases.
% 14.08/3.82 |-Branch one:
% 14.08/3.82 | (589) all_0_10_10 = n1
% 14.08/3.82 |
% 14.08/3.82 | From (589) and (211) follows:
% 14.08/3.82 | (590) pred(n1) = all_0_6_6
% 14.08/3.82 |
% 14.08/3.82 | From (589) and (41) follows:
% 14.08/3.82 | (591) succ(n1) = all_0_8_8
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (158) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 14.08/3.82 | (592) all_0_6_6 = n0
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (141) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 14.08/3.82 | (593) all_0_8_8 = n2
% 14.08/3.82 |
% 14.08/3.82 | From (592)(593) and (178) follows:
% 14.08/3.82 | (594) sum(n0, n2) = all_0_1_1
% 14.08/3.82 |
% 14.08/3.82 | From (592) and (2403) follows:
% 14.08/3.82 | (2432) sum(n0, n4) = all_0_4_4
% 14.08/3.82 |
% 14.08/3.82 | From (593) and (2405) follows:
% 14.08/3.82 | (2433) sum(n2, n2) = all_0_7_7
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n2, n2, all_0_7_7, n4 and discharging atoms sum(n2, n2) = all_0_7_7, sum(n2, n2) = n4, yields:
% 14.08/3.82 | (336) all_0_7_7 = n4
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n0, n4, all_0_4_4, n4 and discharging atoms sum(n0, n4) = all_0_4_4, sum(n0, n4) = n4, yields:
% 14.08/3.82 | (334) all_0_4_4 = n4
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 14.08/3.82 | (598) all_0_1_1 = n2
% 14.08/3.82 |
% 14.08/3.82 | From (336)(334) and (119) follows:
% 14.08/3.82 | (338) sum(n4, n4) = all_0_3_3
% 14.08/3.82 |
% 14.08/3.82 | From (598) and (2407) follows:
% 14.08/3.82 | (2438) sum(n6, n2) = all_0_0_0
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n6, n2, all_0_0_0, n8 and discharging atoms sum(n6, n2) = all_0_0_0, sum(n6, n2) = n8, yields:
% 14.08/3.82 | (339) all_0_0_0 = n8
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n4, n4, all_0_3_3, n8 and discharging atoms sum(n4, n4) = all_0_3_3, sum(n4, n4) = n8, yields:
% 14.08/3.82 | (340) all_0_3_3 = n8
% 14.08/3.82 |
% 14.08/3.82 | Equations (339,340) can reduce 104 to:
% 14.08/3.82 | (251) $false
% 14.08/3.82 |
% 14.08/3.82 |-The branch is then unsatisfiable
% 14.08/3.82 |-Branch two:
% 14.08/3.82 | (607) ~ (all_0_10_10 = n1)
% 14.08/3.82 | (608) all_0_10_10 = n0
% 14.08/3.82 |
% 14.08/3.82 | From (608) and (211) follows:
% 14.08/3.82 | (609) pred(n0) = all_0_6_6
% 14.08/3.82 |
% 14.08/3.82 | From (608) and (41) follows:
% 14.08/3.82 | (610) succ(n0) = all_0_8_8
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (158) with n0, all_0_6_6, n10 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n10, yields:
% 14.08/3.82 | (611) all_0_6_6 = n10
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (141) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 14.08/3.82 | (612) all_0_8_8 = n1
% 14.08/3.82 |
% 14.08/3.82 | From (611)(612) and (178) follows:
% 14.08/3.82 | (613) sum(n10, n1) = all_0_1_1
% 14.08/3.82 |
% 14.08/3.82 | From (611) and (2403) follows:
% 14.08/3.82 | (2449) sum(n10, n4) = all_0_4_4
% 14.08/3.82 |
% 14.08/3.82 | From (612) and (2405) follows:
% 14.08/3.82 | (2450) sum(n2, n1) = all_0_7_7
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n10, n4, all_0_4_4, n3 and discharging atoms sum(n10, n4) = all_0_4_4, sum(n10, n4) = n3, yields:
% 14.08/3.82 | (352) all_0_4_4 = n3
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n10, n1, all_0_1_1, n0 and discharging atoms sum(n10, n1) = all_0_1_1, sum(n10, n1) = n0, yields:
% 14.08/3.82 | (616) all_0_1_1 = n0
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n2, n1, all_0_7_7, n3 and discharging atoms sum(n2, n1) = all_0_7_7, sum(n2, n1) = n3, yields:
% 14.08/3.82 | (354) all_0_7_7 = n3
% 14.08/3.82 |
% 14.08/3.82 | From (354)(352) and (119) follows:
% 14.08/3.82 | (356) sum(n3, n3) = all_0_3_3
% 14.08/3.82 |
% 14.08/3.82 | From (616) and (2407) follows:
% 14.08/3.82 | (2455) sum(n6, n0) = all_0_0_0
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n6, n0, all_0_0_0, n6 and discharging atoms sum(n6, n0) = all_0_0_0, sum(n6, n0) = n6, yields:
% 14.08/3.82 | (357) all_0_0_0 = n6
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 14.08/3.82 | (358) all_0_3_3 = n6
% 14.08/3.82 |
% 14.08/3.82 | Equations (357,358) can reduce 104 to:
% 14.08/3.82 | (251) $false
% 14.08/3.82 |
% 14.08/3.82 |-The branch is then unsatisfiable
% 14.08/3.82 |-Branch two:
% 14.08/3.82 | (378) ~ (all_0_11_11 = n3)
% 14.08/3.82 | (379) all_0_11_11 = n2 | all_0_11_11 = n1 | all_0_11_11 = n0
% 14.08/3.82 |
% 14.08/3.82 +-Applying beta-rule and splitting (570), into two cases.
% 14.08/3.82 |-Branch one:
% 14.08/3.82 | (571) all_0_10_10 = n2
% 14.08/3.82 |
% 14.08/3.82 | From (571) and (211) follows:
% 14.08/3.82 | (572) pred(n2) = all_0_6_6
% 14.08/3.82 |
% 14.08/3.82 | From (571) and (41) follows:
% 14.08/3.82 | (573) succ(n2) = all_0_8_8
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (158) with n2, all_0_6_6, n1 and discharging atoms pred(n2) = all_0_6_6, pred(n2) = n1, yields:
% 14.08/3.82 | (574) all_0_6_6 = n1
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (141) with n2, all_0_8_8, n3 and discharging atoms succ(n2) = all_0_8_8, succ(n2) = n3, yields:
% 14.08/3.82 | (575) all_0_8_8 = n3
% 14.08/3.82 |
% 14.08/3.82 | From (574) and (572) follows:
% 14.08/3.82 | (27) pred(n2) = n1
% 14.08/3.82 |
% 14.08/3.82 | From (575) and (573) follows:
% 14.08/3.82 | (79) succ(n2) = n3
% 14.08/3.82 |
% 14.08/3.82 | From (574) and (33) follows:
% 14.08/3.82 | (2468) sum(n1, all_0_5_5) = all_0_4_4
% 14.08/3.82 |
% 14.08/3.82 | From (574)(575) and (178) follows:
% 14.08/3.82 | (576) sum(n1, n3) = all_0_1_1
% 14.08/3.82 |
% 14.08/3.82 | From (575) and (137) follows:
% 14.08/3.82 | (2470) sum(all_0_9_9, n3) = all_0_7_7
% 14.08/3.82 |
% 14.08/3.82 | Instantiating formula (31) with n1, n3, all_0_1_1, n4 and discharging atoms sum(n1, n3) = all_0_1_1, sum(n1, n3) = n4, yields:
% 14.08/3.82 | (580) all_0_1_1 = n4
% 14.08/3.82 |
% 14.08/3.82 | From (580) and (4) follows:
% 14.08/3.82 | (2472) sum(all_0_2_2, n4) = all_0_0_0
% 14.08/3.82 |
% 14.08/3.82 | From (580) and (576) follows:
% 14.08/3.82 | (121) sum(n1, n3) = n4
% 14.08/3.82 |
% 14.08/3.82 +-Applying beta-rule and splitting (379), into two cases.
% 14.08/3.82 |-Branch one:
% 14.08/3.82 | (380) all_0_11_11 = n2
% 14.08/3.82 |
% 14.08/3.82 | From (380) and (84) follows:
% 14.08/3.82 | (381) pred(n2) = all_0_9_9
% 14.08/3.82 |
% 14.08/3.82 | From (380) and (210) follows:
% 14.08/3.82 | (382) succ(n2) = all_0_5_5
% 14.08/3.82 |
% 14.08/3.83 | Instantiating formula (158) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 14.08/3.83 | (383) all_0_9_9 = n1
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (141) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 14.08/3.83 | (384) all_0_5_5 = n3
% 14.08/3.83 |
% 14.08/3.83 | From (383)(384) and (48) follows:
% 14.08/3.83 | (385) sum(n1, n3) = all_0_2_2
% 14.08/3.83 |
% 14.08/3.83 | From (383) and (2470) follows:
% 14.08/3.83 | (2480) sum(n1, n3) = all_0_7_7
% 14.08/3.83 |
% 14.08/3.83 | From (384) and (2468) follows:
% 14.08/3.83 | (2481) sum(n1, n3) = all_0_4_4
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 14.08/3.83 | (389) all_0_2_2 = n4
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) 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:
% 14.08/3.83 | (238) all_0_2_2 = all_0_4_4
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) 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:
% 14.08/3.83 | (239) all_0_2_2 = all_0_7_7
% 14.08/3.83 |
% 14.08/3.83 | Combining equations (239,238) yields a new equation:
% 14.08/3.83 | (240) all_0_4_4 = all_0_7_7
% 14.08/3.83 |
% 14.08/3.83 | Combining equations (389,238) yields a new equation:
% 14.08/3.83 | (334) all_0_4_4 = n4
% 14.08/3.83 |
% 14.08/3.83 | Combining equations (334,240) yields a new equation:
% 14.08/3.83 | (336) all_0_7_7 = n4
% 14.08/3.83 |
% 14.08/3.83 | Combining equations (336,240) yields a new equation:
% 14.08/3.83 | (334) all_0_4_4 = n4
% 14.08/3.83 |
% 14.08/3.83 | Combining equations (334,238) yields a new equation:
% 14.08/3.83 | (389) all_0_2_2 = n4
% 14.08/3.83 |
% 14.08/3.83 | From (389) and (2472) follows:
% 14.08/3.83 | (2490) sum(n4, n4) = all_0_0_0
% 14.08/3.83 |
% 14.08/3.83 | From (336)(334) and (119) follows:
% 14.08/3.83 | (338) sum(n4, n4) = all_0_3_3
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n4, n4, all_0_0_0, n8 and discharging atoms sum(n4, n4) = all_0_0_0, sum(n4, n4) = n8, yields:
% 14.08/3.83 | (339) all_0_0_0 = n8
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) 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:
% 14.08/3.83 | (248) all_0_0_0 = all_0_3_3
% 14.08/3.83 |
% 14.08/3.83 | Combining equations (339,248) yields a new equation:
% 14.08/3.83 | (340) all_0_3_3 = n8
% 14.08/3.83 |
% 14.08/3.83 | Combining equations (340,248) yields a new equation:
% 14.08/3.83 | (339) all_0_0_0 = n8
% 14.08/3.83 |
% 14.08/3.83 | Equations (339,340) can reduce 104 to:
% 14.08/3.83 | (251) $false
% 14.08/3.83 |
% 14.08/3.83 |-The branch is then unsatisfiable
% 14.08/3.83 |-Branch two:
% 14.08/3.83 | (396) ~ (all_0_11_11 = n2)
% 14.08/3.83 | (397) all_0_11_11 = n1 | all_0_11_11 = n0
% 14.08/3.83 |
% 14.08/3.83 +-Applying beta-rule and splitting (397), into two cases.
% 14.08/3.83 |-Branch one:
% 14.08/3.83 | (398) all_0_11_11 = n1
% 14.08/3.83 |
% 14.08/3.83 | From (398) and (84) follows:
% 14.08/3.83 | (399) pred(n1) = all_0_9_9
% 14.08/3.83 |
% 14.08/3.83 | From (398) and (210) follows:
% 14.08/3.83 | (400) succ(n1) = all_0_5_5
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (158) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 14.08/3.83 | (401) all_0_9_9 = n0
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (141) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 14.08/3.83 | (402) all_0_5_5 = n2
% 14.08/3.83 |
% 14.08/3.83 | From (401)(402) and (48) follows:
% 14.08/3.83 | (403) sum(n0, n2) = all_0_2_2
% 14.08/3.83 |
% 14.08/3.83 | From (401) and (2470) follows:
% 14.08/3.83 | (2505) sum(n0, n3) = all_0_7_7
% 14.08/3.83 |
% 14.08/3.83 | From (402) and (2468) follows:
% 14.08/3.83 | (2506) sum(n1, n2) = all_0_4_4
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n1, n2, all_0_4_4, n3 and discharging atoms sum(n1, n2) = all_0_4_4, sum(n1, n2) = n3, yields:
% 14.08/3.83 | (352) all_0_4_4 = n3
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n0, n3, all_0_7_7, n3 and discharging atoms sum(n0, n3) = all_0_7_7, sum(n0, n3) = n3, yields:
% 14.08/3.83 | (354) all_0_7_7 = n3
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 14.08/3.83 | (407) all_0_2_2 = n2
% 14.08/3.83 |
% 14.08/3.83 | From (407) and (2472) follows:
% 14.08/3.83 | (2510) sum(n2, n4) = all_0_0_0
% 14.08/3.83 |
% 14.08/3.83 | From (354)(352) and (119) follows:
% 14.08/3.83 | (356) sum(n3, n3) = all_0_3_3
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 14.08/3.83 | (358) all_0_3_3 = n6
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n2, n4, all_0_0_0, n6 and discharging atoms sum(n2, n4) = all_0_0_0, sum(n2, n4) = n6, yields:
% 14.08/3.83 | (357) all_0_0_0 = n6
% 14.08/3.83 |
% 14.08/3.83 | Equations (357,358) can reduce 104 to:
% 14.08/3.83 | (251) $false
% 14.08/3.83 |
% 14.08/3.83 |-The branch is then unsatisfiable
% 14.08/3.83 |-Branch two:
% 14.08/3.83 | (415) ~ (all_0_11_11 = n1)
% 14.08/3.83 | (416) all_0_11_11 = n0
% 14.08/3.83 |
% 14.08/3.83 | From (416) and (84) follows:
% 14.08/3.83 | (417) pred(n0) = all_0_9_9
% 14.08/3.83 |
% 14.08/3.83 | From (416) and (210) follows:
% 14.08/3.83 | (418) succ(n0) = all_0_5_5
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (158) with n0, all_0_9_9, n10 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n10, yields:
% 14.08/3.83 | (419) all_0_9_9 = n10
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (141) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 14.08/3.83 | (420) all_0_5_5 = n1
% 14.08/3.83 |
% 14.08/3.83 | From (419)(420) and (48) follows:
% 14.08/3.83 | (421) sum(n10, n1) = all_0_2_2
% 14.08/3.83 |
% 14.08/3.83 | From (419) and (2470) follows:
% 14.08/3.83 | (2522) sum(n10, n3) = all_0_7_7
% 14.08/3.83 |
% 14.08/3.83 | From (420) and (2468) follows:
% 14.08/3.83 | (2523) sum(n1, n1) = all_0_4_4
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n10, n3, all_0_7_7, n2 and discharging atoms sum(n10, n3) = all_0_7_7, sum(n10, n3) = n2, yields:
% 14.08/3.83 | (372) all_0_7_7 = n2
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n10, n1, all_0_2_2, n0 and discharging atoms sum(n10, n1) = all_0_2_2, sum(n10, n1) = n0, yields:
% 14.08/3.83 | (424) all_0_2_2 = n0
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n1, n1, all_0_4_4, n2 and discharging atoms sum(n1, n1) = all_0_4_4, sum(n1, n1) = n2, yields:
% 14.08/3.83 | (370) all_0_4_4 = n2
% 14.08/3.83 |
% 14.08/3.83 | From (424) and (2472) follows:
% 14.08/3.83 | (2527) sum(n0, n4) = all_0_0_0
% 14.08/3.83 |
% 14.08/3.83 | From (372)(370) and (119) follows:
% 14.08/3.83 | (374) sum(n2, n2) = all_0_3_3
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 14.08/3.83 | (376) all_0_3_3 = n4
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n0, n4, all_0_0_0, n4 and discharging atoms sum(n0, n4) = all_0_0_0, sum(n0, n4) = n4, yields:
% 14.08/3.83 | (375) all_0_0_0 = n4
% 14.08/3.83 |
% 14.08/3.83 | Equations (375,376) can reduce 104 to:
% 14.08/3.83 | (251) $false
% 14.08/3.83 |
% 14.08/3.83 |-The branch is then unsatisfiable
% 14.08/3.83 |-Branch two:
% 14.08/3.83 | (587) ~ (all_0_10_10 = n2)
% 14.08/3.83 | (588) all_0_10_10 = n1 | all_0_10_10 = n0
% 14.08/3.83 |
% 14.08/3.83 +-Applying beta-rule and splitting (379), into two cases.
% 14.08/3.83 |-Branch one:
% 14.08/3.83 | (380) all_0_11_11 = n2
% 14.08/3.83 |
% 14.08/3.83 | From (380) and (84) follows:
% 14.08/3.83 | (381) pred(n2) = all_0_9_9
% 14.08/3.83 |
% 14.08/3.83 | From (380) and (210) follows:
% 14.08/3.83 | (382) succ(n2) = all_0_5_5
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (158) with n2, all_0_9_9, n1 and discharging atoms pred(n2) = all_0_9_9, pred(n2) = n1, yields:
% 14.08/3.83 | (383) all_0_9_9 = n1
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (141) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 14.08/3.83 | (384) all_0_5_5 = n3
% 14.08/3.83 |
% 14.08/3.83 | From (384) and (33) follows:
% 14.08/3.83 | (2539) sum(all_0_6_6, n3) = all_0_4_4
% 14.08/3.83 |
% 14.08/3.83 | From (383)(384) and (48) follows:
% 14.08/3.83 | (385) sum(n1, n3) = all_0_2_2
% 14.08/3.83 |
% 14.08/3.83 | From (383) and (137) follows:
% 14.08/3.83 | (2541) sum(n1, all_0_8_8) = all_0_7_7
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 14.08/3.83 | (389) all_0_2_2 = n4
% 14.08/3.83 |
% 14.08/3.83 | From (389) and (4) follows:
% 14.08/3.83 | (2543) sum(n4, all_0_1_1) = all_0_0_0
% 14.08/3.83 |
% 14.08/3.83 +-Applying beta-rule and splitting (588), into two cases.
% 14.08/3.83 |-Branch one:
% 14.08/3.83 | (589) all_0_10_10 = n1
% 14.08/3.83 |
% 14.08/3.83 | From (589) and (211) follows:
% 14.08/3.83 | (590) pred(n1) = all_0_6_6
% 14.08/3.83 |
% 14.08/3.83 | From (589) and (41) follows:
% 14.08/3.83 | (591) succ(n1) = all_0_8_8
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (158) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 14.08/3.83 | (592) all_0_6_6 = n0
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (141) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 14.08/3.83 | (593) all_0_8_8 = n2
% 14.08/3.83 |
% 14.08/3.83 | From (592)(593) and (178) follows:
% 14.08/3.83 | (594) sum(n0, n2) = all_0_1_1
% 14.08/3.83 |
% 14.08/3.83 | From (592) and (2539) follows:
% 14.08/3.83 | (2550) sum(n0, n3) = all_0_4_4
% 14.08/3.83 |
% 14.08/3.83 | From (593) and (2541) follows:
% 14.08/3.83 | (2551) sum(n1, n2) = all_0_7_7
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n1, n2, all_0_7_7, n3 and discharging atoms sum(n1, n2) = all_0_7_7, sum(n1, n2) = n3, yields:
% 14.08/3.83 | (354) all_0_7_7 = n3
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n0, n3, all_0_4_4, n3 and discharging atoms sum(n0, n3) = all_0_4_4, sum(n0, n3) = n3, yields:
% 14.08/3.83 | (352) all_0_4_4 = n3
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 14.08/3.83 | (598) all_0_1_1 = n2
% 14.08/3.83 |
% 14.08/3.83 | From (354)(352) and (119) follows:
% 14.08/3.83 | (356) sum(n3, n3) = all_0_3_3
% 14.08/3.83 |
% 14.08/3.83 | From (598) and (2543) follows:
% 14.08/3.83 | (2556) sum(n4, n2) = all_0_0_0
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n4, n2, all_0_0_0, n6 and discharging atoms sum(n4, n2) = all_0_0_0, sum(n4, n2) = n6, yields:
% 14.08/3.83 | (357) all_0_0_0 = n6
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (31) with n3, n3, all_0_3_3, n6 and discharging atoms sum(n3, n3) = all_0_3_3, sum(n3, n3) = n6, yields:
% 14.08/3.83 | (358) all_0_3_3 = n6
% 14.08/3.83 |
% 14.08/3.83 | Equations (357,358) can reduce 104 to:
% 14.08/3.83 | (251) $false
% 14.08/3.83 |
% 14.08/3.83 |-The branch is then unsatisfiable
% 14.08/3.83 |-Branch two:
% 14.08/3.83 | (607) ~ (all_0_10_10 = n1)
% 14.08/3.83 | (608) all_0_10_10 = n0
% 14.08/3.83 |
% 14.08/3.83 | From (608) and (211) follows:
% 14.08/3.83 | (609) pred(n0) = all_0_6_6
% 14.08/3.83 |
% 14.08/3.83 | From (608) and (41) follows:
% 14.08/3.83 | (610) succ(n0) = all_0_8_8
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (158) with n0, all_0_6_6, n10 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n10, yields:
% 14.08/3.83 | (611) all_0_6_6 = n10
% 14.08/3.83 |
% 14.08/3.83 | Instantiating formula (141) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 14.08/3.83 | (612) all_0_8_8 = n1
% 14.08/3.83 |
% 14.08/3.83 | From (611)(612) and (178) follows:
% 14.08/3.83 | (613) sum(n10, n1) = all_0_1_1
% 14.08/3.83 |
% 14.08/3.83 | From (611) and (2539) follows:
% 14.08/3.84 | (2567) sum(n10, n3) = all_0_4_4
% 14.08/3.84 |
% 14.08/3.84 | From (612) and (2541) follows:
% 14.08/3.84 | (2568) sum(n1, n1) = all_0_7_7
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) with n10, n3, all_0_4_4, n2 and discharging atoms sum(n10, n3) = all_0_4_4, sum(n10, n3) = n2, yields:
% 14.08/3.84 | (370) all_0_4_4 = n2
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) with n10, n1, all_0_1_1, n0 and discharging atoms sum(n10, n1) = all_0_1_1, sum(n10, n1) = n0, yields:
% 14.08/3.84 | (616) all_0_1_1 = n0
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) with n1, n1, all_0_7_7, n2 and discharging atoms sum(n1, n1) = all_0_7_7, sum(n1, n1) = n2, yields:
% 14.08/3.84 | (372) all_0_7_7 = n2
% 14.08/3.84 |
% 14.08/3.84 | From (372)(370) and (119) follows:
% 14.08/3.84 | (374) sum(n2, n2) = all_0_3_3
% 14.08/3.84 |
% 14.08/3.84 | From (616) and (2543) follows:
% 14.08/3.84 | (2573) sum(n4, n0) = all_0_0_0
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) with n4, n0, all_0_0_0, n4 and discharging atoms sum(n4, n0) = all_0_0_0, sum(n4, n0) = n4, yields:
% 14.08/3.84 | (375) all_0_0_0 = n4
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) with n2, n2, all_0_3_3, n4 and discharging atoms sum(n2, n2) = all_0_3_3, sum(n2, n2) = n4, yields:
% 14.08/3.84 | (376) all_0_3_3 = n4
% 14.08/3.84 |
% 14.08/3.84 | Equations (375,376) can reduce 104 to:
% 14.08/3.84 | (251) $false
% 14.08/3.84 |
% 14.08/3.84 |-The branch is then unsatisfiable
% 14.08/3.84 |-Branch two:
% 14.08/3.84 | (396) ~ (all_0_11_11 = n2)
% 14.08/3.84 | (397) all_0_11_11 = n1 | all_0_11_11 = n0
% 14.08/3.84 |
% 14.08/3.84 +-Applying beta-rule and splitting (588), into two cases.
% 14.08/3.84 |-Branch one:
% 14.08/3.84 | (589) all_0_10_10 = n1
% 14.08/3.84 |
% 14.08/3.84 | From (589) and (211) follows:
% 14.08/3.84 | (590) pred(n1) = all_0_6_6
% 14.08/3.84 |
% 14.08/3.84 | From (589) and (41) follows:
% 14.08/3.84 | (591) succ(n1) = all_0_8_8
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (158) with n1, all_0_6_6, n0 and discharging atoms pred(n1) = all_0_6_6, pred(n1) = n0, yields:
% 14.08/3.84 | (592) all_0_6_6 = n0
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (141) with n1, all_0_8_8, n2 and discharging atoms succ(n1) = all_0_8_8, succ(n1) = n2, yields:
% 14.08/3.84 | (593) all_0_8_8 = n2
% 14.08/3.84 |
% 14.08/3.84 | From (592) and (590) follows:
% 14.08/3.84 | (212) pred(n1) = n0
% 14.08/3.84 |
% 14.08/3.84 | From (593) and (591) follows:
% 14.08/3.84 | (99) succ(n1) = n2
% 14.08/3.84 |
% 14.08/3.84 | From (592) and (33) follows:
% 14.08/3.84 | (2586) sum(n0, all_0_5_5) = all_0_4_4
% 14.08/3.84 |
% 14.08/3.84 | From (592)(593) and (178) follows:
% 14.08/3.84 | (594) sum(n0, n2) = all_0_1_1
% 14.08/3.84 |
% 14.08/3.84 | From (593) and (137) follows:
% 14.08/3.84 | (2588) sum(all_0_9_9, n2) = all_0_7_7
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) with n0, n2, all_0_1_1, n2 and discharging atoms sum(n0, n2) = all_0_1_1, sum(n0, n2) = n2, yields:
% 14.08/3.84 | (598) all_0_1_1 = n2
% 14.08/3.84 |
% 14.08/3.84 | From (598) and (4) follows:
% 14.08/3.84 | (2590) sum(all_0_2_2, n2) = all_0_0_0
% 14.08/3.84 |
% 14.08/3.84 | From (598) and (594) follows:
% 14.08/3.84 | (156) sum(n0, n2) = n2
% 14.08/3.84 |
% 14.08/3.84 +-Applying beta-rule and splitting (397), into two cases.
% 14.08/3.84 |-Branch one:
% 14.08/3.84 | (398) all_0_11_11 = n1
% 14.08/3.84 |
% 14.08/3.84 | From (398) and (84) follows:
% 14.08/3.84 | (399) pred(n1) = all_0_9_9
% 14.08/3.84 |
% 14.08/3.84 | From (398) and (210) follows:
% 14.08/3.84 | (400) succ(n1) = all_0_5_5
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (158) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 14.08/3.84 | (401) all_0_9_9 = n0
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (141) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 14.08/3.84 | (402) all_0_5_5 = n2
% 14.08/3.84 |
% 14.08/3.84 | From (401)(402) and (48) follows:
% 14.08/3.84 | (403) sum(n0, n2) = all_0_2_2
% 14.08/3.84 |
% 14.08/3.84 | From (401) and (2588) follows:
% 14.08/3.84 | (2598) sum(n0, n2) = all_0_7_7
% 14.08/3.84 |
% 14.08/3.84 | From (402) and (2586) follows:
% 14.08/3.84 | (2599) sum(n0, n2) = all_0_4_4
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 14.08/3.84 | (407) all_0_2_2 = n2
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) 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:
% 14.08/3.84 | (238) all_0_2_2 = all_0_4_4
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) 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:
% 14.08/3.84 | (239) all_0_2_2 = all_0_7_7
% 14.08/3.84 |
% 14.08/3.84 | Combining equations (239,238) yields a new equation:
% 14.08/3.84 | (240) all_0_4_4 = all_0_7_7
% 14.08/3.84 |
% 14.08/3.84 | Combining equations (407,238) yields a new equation:
% 14.08/3.84 | (370) all_0_4_4 = n2
% 14.08/3.84 |
% 14.08/3.84 | Combining equations (370,240) yields a new equation:
% 14.08/3.84 | (372) all_0_7_7 = n2
% 14.08/3.84 |
% 14.08/3.84 | Combining equations (372,240) yields a new equation:
% 14.08/3.84 | (370) all_0_4_4 = n2
% 14.08/3.84 |
% 14.08/3.84 | Combining equations (370,238) yields a new equation:
% 14.08/3.84 | (407) all_0_2_2 = n2
% 14.08/3.84 |
% 14.08/3.84 | From (407) and (2590) follows:
% 14.08/3.84 | (2608) sum(n2, n2) = all_0_0_0
% 14.08/3.84 |
% 14.08/3.84 | From (372)(370) and (119) follows:
% 14.08/3.84 | (374) sum(n2, n2) = all_0_3_3
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) with n2, n2, all_0_0_0, n4 and discharging atoms sum(n2, n2) = all_0_0_0, sum(n2, n2) = n4, yields:
% 14.08/3.84 | (375) all_0_0_0 = n4
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) 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:
% 14.08/3.84 | (248) all_0_0_0 = all_0_3_3
% 14.08/3.84 |
% 14.08/3.84 | Combining equations (375,248) yields a new equation:
% 14.08/3.84 | (376) all_0_3_3 = n4
% 14.08/3.84 |
% 14.08/3.84 | Combining equations (376,248) yields a new equation:
% 14.08/3.84 | (375) all_0_0_0 = n4
% 14.08/3.84 |
% 14.08/3.84 | Equations (375,376) can reduce 104 to:
% 14.08/3.84 | (251) $false
% 14.08/3.84 |
% 14.08/3.84 |-The branch is then unsatisfiable
% 14.08/3.84 |-Branch two:
% 14.08/3.84 | (415) ~ (all_0_11_11 = n1)
% 14.08/3.84 | (416) all_0_11_11 = n0
% 14.08/3.84 |
% 14.08/3.84 | From (416) and (84) follows:
% 14.08/3.84 | (417) pred(n0) = all_0_9_9
% 14.08/3.84 |
% 14.08/3.84 | From (416) and (210) follows:
% 14.08/3.84 | (418) succ(n0) = all_0_5_5
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (158) with n0, all_0_9_9, n10 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n10, yields:
% 14.08/3.84 | (419) all_0_9_9 = n10
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (141) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 14.08/3.84 | (420) all_0_5_5 = n1
% 14.08/3.84 |
% 14.08/3.84 | From (419)(420) and (48) follows:
% 14.08/3.84 | (421) sum(n10, n1) = all_0_2_2
% 14.08/3.84 |
% 14.08/3.84 | From (419) and (2588) follows:
% 14.08/3.84 | (2622) sum(n10, n2) = all_0_7_7
% 14.08/3.84 |
% 14.08/3.84 | From (420) and (2586) follows:
% 14.08/3.84 | (2623) sum(n0, n1) = all_0_4_4
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) with n10, n2, all_0_7_7, n1 and discharging atoms sum(n10, n2) = all_0_7_7, sum(n10, n2) = n1, yields:
% 14.08/3.84 | (390) all_0_7_7 = n1
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) with n10, n1, all_0_2_2, n0 and discharging atoms sum(n10, n1) = all_0_2_2, sum(n10, n1) = n0, yields:
% 14.08/3.84 | (424) all_0_2_2 = n0
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) with n0, n1, all_0_4_4, n1 and discharging atoms sum(n0, n1) = all_0_4_4, sum(n0, n1) = n1, yields:
% 14.08/3.84 | (388) all_0_4_4 = n1
% 14.08/3.84 |
% 14.08/3.84 | From (424) and (2590) follows:
% 14.08/3.84 | (2627) sum(n0, n2) = all_0_0_0
% 14.08/3.84 |
% 14.08/3.84 | From (390)(388) and (119) follows:
% 14.08/3.84 | (392) sum(n1, n1) = all_0_3_3
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 14.08/3.84 | (394) all_0_3_3 = n2
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) with n0, n2, all_0_0_0, n2 and discharging atoms sum(n0, n2) = all_0_0_0, sum(n0, n2) = n2, yields:
% 14.08/3.84 | (393) all_0_0_0 = n2
% 14.08/3.84 |
% 14.08/3.84 | Equations (393,394) can reduce 104 to:
% 14.08/3.84 | (251) $false
% 14.08/3.84 |
% 14.08/3.84 |-The branch is then unsatisfiable
% 14.08/3.84 |-Branch two:
% 14.08/3.84 | (607) ~ (all_0_10_10 = n1)
% 14.08/3.84 | (608) all_0_10_10 = n0
% 14.08/3.84 |
% 14.08/3.84 | From (608) and (211) follows:
% 14.08/3.84 | (609) pred(n0) = all_0_6_6
% 14.08/3.84 |
% 14.08/3.84 | From (608) and (41) follows:
% 14.08/3.84 | (610) succ(n0) = all_0_8_8
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (158) with n0, all_0_6_6, n10 and discharging atoms pred(n0) = all_0_6_6, pred(n0) = n10, yields:
% 14.08/3.84 | (611) all_0_6_6 = n10
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (141) with n0, all_0_8_8, n1 and discharging atoms succ(n0) = all_0_8_8, succ(n0) = n1, yields:
% 14.08/3.84 | (612) all_0_8_8 = n1
% 14.08/3.84 |
% 14.08/3.84 | From (611) and (609) follows:
% 14.08/3.84 | (54) pred(n0) = n10
% 14.08/3.84 |
% 14.08/3.84 | From (612) and (610) follows:
% 14.08/3.84 | (83) succ(n0) = n1
% 14.08/3.84 |
% 14.08/3.84 | From (611) and (33) follows:
% 14.08/3.84 | (2640) sum(n10, all_0_5_5) = all_0_4_4
% 14.08/3.84 |
% 14.08/3.84 | From (611)(612) and (178) follows:
% 14.08/3.84 | (613) sum(n10, n1) = all_0_1_1
% 14.08/3.84 |
% 14.08/3.84 | From (612) and (137) follows:
% 14.08/3.84 | (2642) sum(all_0_9_9, n1) = all_0_7_7
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) with n10, n1, all_0_1_1, n0 and discharging atoms sum(n10, n1) = all_0_1_1, sum(n10, n1) = n0, yields:
% 14.08/3.84 | (616) all_0_1_1 = n0
% 14.08/3.84 |
% 14.08/3.84 | From (616) and (4) follows:
% 14.08/3.84 | (2644) sum(all_0_2_2, n0) = all_0_0_0
% 14.08/3.84 |
% 14.08/3.84 | From (616) and (613) follows:
% 14.08/3.84 | (140) sum(n10, n1) = n0
% 14.08/3.84 |
% 14.08/3.84 +-Applying beta-rule and splitting (397), into two cases.
% 14.08/3.84 |-Branch one:
% 14.08/3.84 | (398) all_0_11_11 = n1
% 14.08/3.84 |
% 14.08/3.84 | From (398) and (84) follows:
% 14.08/3.84 | (399) pred(n1) = all_0_9_9
% 14.08/3.84 |
% 14.08/3.84 | From (398) and (210) follows:
% 14.08/3.84 | (400) succ(n1) = all_0_5_5
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (158) with n1, all_0_9_9, n0 and discharging atoms pred(n1) = all_0_9_9, pred(n1) = n0, yields:
% 14.08/3.84 | (401) all_0_9_9 = n0
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (141) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 14.08/3.84 | (402) all_0_5_5 = n2
% 14.08/3.84 |
% 14.08/3.84 | From (401)(402) and (48) follows:
% 14.08/3.84 | (403) sum(n0, n2) = all_0_2_2
% 14.08/3.84 |
% 14.08/3.84 | From (401) and (2642) follows:
% 14.08/3.84 | (2652) sum(n0, n1) = all_0_7_7
% 14.08/3.84 |
% 14.08/3.84 | From (402) and (2640) follows:
% 14.08/3.84 | (2653) sum(n10, n2) = all_0_4_4
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) with n10, n2, all_0_4_4, n1 and discharging atoms sum(n10, n2) = all_0_4_4, sum(n10, n2) = n1, yields:
% 14.08/3.84 | (388) all_0_4_4 = n1
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 14.08/3.84 | (407) all_0_2_2 = n2
% 14.08/3.84 |
% 14.08/3.84 | Instantiating formula (31) with n0, n1, all_0_7_7, n1 and discharging atoms sum(n0, n1) = all_0_7_7, sum(n0, n1) = n1, yields:
% 14.08/3.84 | (390) all_0_7_7 = n1
% 14.08/3.84 |
% 14.08/3.84 | From (407) and (2644) follows:
% 14.08/3.85 | (2657) sum(n2, n0) = all_0_0_0
% 14.08/3.85 |
% 14.08/3.85 | From (390)(388) and (119) follows:
% 14.08/3.85 | (392) sum(n1, n1) = all_0_3_3
% 14.08/3.85 |
% 14.08/3.85 | Instantiating formula (31) with n2, n0, all_0_0_0, n2 and discharging atoms sum(n2, n0) = all_0_0_0, sum(n2, n0) = n2, yields:
% 14.08/3.85 | (393) all_0_0_0 = n2
% 14.08/3.85 |
% 14.08/3.85 | Instantiating formula (31) with n1, n1, all_0_3_3, n2 and discharging atoms sum(n1, n1) = all_0_3_3, sum(n1, n1) = n2, yields:
% 14.08/3.85 | (394) all_0_3_3 = n2
% 14.08/3.85 |
% 14.08/3.85 | Equations (393,394) can reduce 104 to:
% 14.08/3.85 | (251) $false
% 14.08/3.85 |
% 14.08/3.85 |-The branch is then unsatisfiable
% 14.08/3.85 |-Branch two:
% 14.08/3.85 | (415) ~ (all_0_11_11 = n1)
% 14.08/3.85 | (416) all_0_11_11 = n0
% 14.08/3.85 |
% 14.08/3.85 | From (416) and (84) follows:
% 14.08/3.85 | (417) pred(n0) = all_0_9_9
% 14.08/3.85 |
% 14.08/3.85 | From (416) and (210) follows:
% 14.08/3.85 | (418) succ(n0) = all_0_5_5
% 14.08/3.85 |
% 14.08/3.85 | Instantiating formula (158) with n0, all_0_9_9, n10 and discharging atoms pred(n0) = all_0_9_9, pred(n0) = n10, yields:
% 14.08/3.85 | (419) all_0_9_9 = n10
% 14.08/3.85 |
% 14.08/3.85 | Instantiating formula (141) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 14.08/3.85 | (420) all_0_5_5 = n1
% 14.08/3.85 |
% 14.08/3.85 | From (419)(420) and (48) follows:
% 14.08/3.85 | (421) sum(n10, n1) = all_0_2_2
% 14.08/3.85 |
% 14.08/3.85 | From (419) and (2642) follows:
% 14.08/3.85 | (2669) sum(n10, n1) = all_0_7_7
% 14.08/3.85 |
% 14.08/3.85 | From (420) and (2640) follows:
% 14.08/3.85 | (2670) sum(n10, n1) = all_0_4_4
% 14.08/3.85 |
% 14.08/3.85 | Instantiating formula (31) with n10, n1, all_0_2_2, n0 and discharging atoms sum(n10, n1) = all_0_2_2, sum(n10, n1) = n0, yields:
% 14.08/3.85 | (424) all_0_2_2 = n0
% 14.08/3.85 |
% 14.08/3.85 | Instantiating formula (31) with n10, n1, all_0_4_4, all_0_2_2 and discharging atoms sum(n10, n1) = all_0_2_2, sum(n10, n1) = all_0_4_4, yields:
% 14.08/3.85 | (238) all_0_2_2 = all_0_4_4
% 14.08/3.85 |
% 14.08/3.85 | Instantiating formula (31) with n10, n1, all_0_7_7, all_0_2_2 and discharging atoms sum(n10, n1) = all_0_2_2, sum(n10, n1) = all_0_7_7, yields:
% 14.08/3.85 | (239) all_0_2_2 = all_0_7_7
% 14.08/3.85 |
% 14.08/3.85 | Combining equations (239,238) yields a new equation:
% 14.08/3.85 | (240) all_0_4_4 = all_0_7_7
% 14.08/3.85 |
% 14.08/3.85 | Combining equations (424,238) yields a new equation:
% 14.08/3.85 | (406) all_0_4_4 = n0
% 14.08/3.85 |
% 14.08/3.85 | Combining equations (406,240) yields a new equation:
% 14.08/3.85 | (408) all_0_7_7 = n0
% 14.08/3.85 |
% 14.08/3.85 | Combining equations (408,240) yields a new equation:
% 14.08/3.85 | (406) all_0_4_4 = n0
% 14.08/3.85 |
% 14.08/3.85 | Combining equations (406,238) yields a new equation:
% 14.08/3.85 | (424) all_0_2_2 = n0
% 14.08/3.85 |
% 14.08/3.85 | From (424) and (2644) follows:
% 14.08/3.85 | (2679) sum(n0, n0) = all_0_0_0
% 14.08/3.85 |
% 14.08/3.85 | From (408)(406) and (119) follows:
% 14.08/3.85 | (410) sum(n0, n0) = all_0_3_3
% 14.08/3.85 |
% 14.08/3.85 | Instantiating formula (31) with n0, n0, all_0_0_0, n0 and discharging atoms sum(n0, n0) = all_0_0_0, sum(n0, n0) = n0, yields:
% 14.08/3.85 | (412) all_0_0_0 = n0
% 14.08/3.85 |
% 14.08/3.85 | Instantiating formula (31) 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:
% 14.08/3.85 | (248) all_0_0_0 = all_0_3_3
% 14.08/3.85 |
% 14.08/3.85 | Combining equations (412,248) yields a new equation:
% 14.08/3.85 | (413) all_0_3_3 = n0
% 14.08/3.85 |
% 14.08/3.85 | Combining equations (413,248) yields a new equation:
% 14.08/3.85 | (412) all_0_0_0 = n0
% 14.08/3.85 |
% 14.08/3.85 | Equations (412,413) can reduce 104 to:
% 14.08/3.85 | (251) $false
% 14.08/3.85 |
% 14.08/3.85 |-The branch is then unsatisfiable
% 14.08/3.85 % SZS output end Proof for theBenchmark
% 14.08/3.85
% 14.08/3.85 3270ms
%------------------------------------------------------------------------------