TSTP Solution File: NUM375+1.010 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM375+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 08:43:43 EDT 2022
% Result : Unsatisfiable 5.67s 1.97s
% Output : Proof 14.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM375+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 : Thu Jul 7 19:50:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.56/0.58 ____ _
% 0.56/0.58 ___ / __ \_____(_)___ ________ __________
% 0.56/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.58
% 0.56/0.58 A Theorem Prover for First-Order Logic
% 0.56/0.58 (ePrincess v.1.0)
% 0.56/0.58
% 0.56/0.58 (c) Philipp Rümmer, 2009-2015
% 0.56/0.58 (c) Peter Backeman, 2014-2015
% 0.56/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.58 Bug reports to peter@backeman.se
% 0.56/0.58
% 0.56/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.58
% 0.56/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.78/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.69/0.97 Prover 0: Preprocessing ...
% 2.53/1.22 Prover 0: Constructing countermodel ...
% 5.67/1.97 Prover 0: proved (1340ms)
% 5.67/1.97
% 5.67/1.97 No countermodel exists, formula is valid
% 5.67/1.97 % SZS status Unsatisfiable for theBenchmark
% 5.67/1.97
% 5.67/1.97 Generating proof ... found it (size 2123)
% 11.98/3.39
% 11.98/3.39 % SZS output start Proof for theBenchmark
% 11.98/3.39 Assumed formulas after preprocessing and simplification:
% 11.98/3.39 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v2 = n10) & ~ (v2 = n9) & ~ (v2 = n8) & ~ (v2 = n7) & ~ (v2 = n6) & ~ (v2 = n5) & ~ (v2 = n4) & ~ (v2 = n3) & ~ (v2 = n2) & ~ (v2 = n1) & ~ (v2 = n0) & ~ (n10 = n9) & ~ (n10 = n8) & ~ (n10 = n7) & ~ (n10 = n6) & ~ (n10 = n5) & ~ (n10 = n4) & ~ (n10 = n3) & ~ (n10 = n2) & ~ (n10 = n1) & ~ (n10 = n0) & ~ (n9 = n8) & ~ (n9 = n7) & ~ (n9 = n6) & ~ (n9 = n5) & ~ (n9 = n4) & ~ (n9 = n3) & ~ (n9 = n2) & ~ (n9 = n1) & ~ (n9 = n0) & ~ (n8 = n7) & ~ (n8 = n6) & ~ (n8 = n5) & ~ (n8 = n4) & ~ (n8 = n3) & ~ (n8 = n2) & ~ (n8 = n1) & ~ (n8 = n0) & ~ (n7 = n6) & ~ (n7 = n5) & ~ (n7 = n4) & ~ (n7 = n3) & ~ (n7 = n2) & ~ (n7 = n1) & ~ (n7 = n0) & ~ (n6 = n5) & ~ (n6 = n4) & ~ (n6 = n3) & ~ (n6 = n2) & ~ (n6 = n1) & ~ (n6 = n0) & ~ (n5 = n4) & ~ (n5 = n3) & ~ (n5 = n2) & ~ (n5 = n1) & ~ (n5 = n0) & ~ (n4 = n3) & ~ (n4 = n2) & ~ (n4 = n1) & ~ (n4 = n0) & ~ (n3 = n2) & ~ (n3 = n1) & ~ (n3 = n0) & ~ (n2 = n1) & ~ (n2 = n0) & ~ (n1 = n0) & succ(v1) = v3 & succ(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 & pred(v6) = v7 & pred(v4) = v5 & 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 & sum(v5, v8) = v2 & sum(v1, v7) = v8 & sum(v0, v3) = v4 & sum(v0, v1) = v6 & 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 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sum(v12, v11) = v10) | ~ (sum(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (succ(v11) = v10) | ~ (succ(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (pred(v11) = v10) | ~ (pred(v11) = v9)) & (v1 = 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))
% 12.25/3.45 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 yields:
% 12.25/3.45 | (1) ~ (all_0_6_6 = n10) & ~ (all_0_6_6 = n9) & ~ (all_0_6_6 = n8) & ~ (all_0_6_6 = n7) & ~ (all_0_6_6 = n6) & ~ (all_0_6_6 = n5) & ~ (all_0_6_6 = n4) & ~ (all_0_6_6 = n3) & ~ (all_0_6_6 = n2) & ~ (all_0_6_6 = n1) & ~ (all_0_6_6 = n0) & ~ (n10 = n9) & ~ (n10 = n8) & ~ (n10 = n7) & ~ (n10 = n6) & ~ (n10 = n5) & ~ (n10 = n4) & ~ (n10 = n3) & ~ (n10 = n2) & ~ (n10 = n1) & ~ (n10 = n0) & ~ (n9 = n8) & ~ (n9 = n7) & ~ (n9 = n6) & ~ (n9 = n5) & ~ (n9 = n4) & ~ (n9 = n3) & ~ (n9 = n2) & ~ (n9 = n1) & ~ (n9 = n0) & ~ (n8 = n7) & ~ (n8 = n6) & ~ (n8 = n5) & ~ (n8 = n4) & ~ (n8 = n3) & ~ (n8 = n2) & ~ (n8 = n1) & ~ (n8 = n0) & ~ (n7 = n6) & ~ (n7 = n5) & ~ (n7 = n4) & ~ (n7 = n3) & ~ (n7 = n2) & ~ (n7 = n1) & ~ (n7 = n0) & ~ (n6 = n5) & ~ (n6 = n4) & ~ (n6 = n3) & ~ (n6 = n2) & ~ (n6 = n1) & ~ (n6 = n0) & ~ (n5 = n4) & ~ (n5 = n3) & ~ (n5 = n2) & ~ (n5 = n1) & ~ (n5 = n0) & ~ (n4 = n3) & ~ (n4 = n2) & ~ (n4 = n1) & ~ (n4 = n0) & ~ (n3 = n2) & ~ (n3 = n1) & ~ (n3 = n0) & ~ (n2 = n1) & ~ (n2 = n0) & ~ (n1 = n0) & succ(all_0_7_7) = all_0_5_5 & succ(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 & pred(all_0_2_2) = all_0_1_1 & pred(all_0_4_4) = all_0_3_3 & 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 & sum(all_0_3_3, all_0_0_0) = all_0_6_6 & sum(all_0_7_7, all_0_1_1) = all_0_0_0 & sum(all_0_8_8, all_0_5_5) = all_0_4_4 & sum(all_0_8_8, all_0_7_7) = all_0_2_2 & sum(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 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) & (all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0) & (all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0)
% 12.58/3.46 |
% 12.58/3.46 | Applying alpha-rule on (1) yields:
% 12.58/3.46 | (2) pred(n2) = n1
% 12.58/3.46 | (3) sum(all_0_7_7, all_0_1_1) = all_0_0_0
% 12.58/3.46 | (4) ~ (all_0_6_6 = n5)
% 12.58/3.46 | (5) ~ (n5 = n4)
% 12.58/3.46 | (6) succ(n1) = n2
% 12.58/3.46 | (7) ~ (n6 = n1)
% 12.58/3.46 | (8) sum(n6, n4) = n10
% 12.58/3.46 | (9) sum(n10, n7) = n6
% 12.58/3.47 | (10) succ(all_0_7_7) = all_0_5_5
% 12.58/3.47 | (11) sum(n9, n0) = n9
% 12.58/3.47 | (12) ~ (n9 = n4)
% 12.58/3.47 | (13) sum(n2, n6) = n8
% 12.58/3.47 | (14) sum(n0, n9) = n9
% 12.58/3.47 | (15) pred(n5) = n4
% 12.58/3.47 | (16) pred(n6) = n5
% 12.58/3.47 | (17) sum(n1, n7) = n8
% 12.58/3.47 | (18) sum(n10, n0) = n10
% 12.58/3.47 | (19) sum(n7, n9) = n5
% 12.58/3.47 | (20) sum(n10, n3) = n2
% 12.58/3.47 | (21) ~ (n9 = n0)
% 12.58/3.47 | (22) ~ (n6 = n3)
% 12.58/3.47 | (23) sum(n5, n4) = n9
% 12.58/3.47 | (24) sum(n7, n10) = n6
% 12.58/3.47 | (25) sum(n1, n1) = n2
% 12.58/3.47 | (26) sum(n7, n5) = n1
% 12.58/3.47 | (27) ~ (n7 = n5)
% 12.58/3.47 | (28) ~ (all_0_6_6 = n1)
% 12.58/3.47 | (29) sum(n2, n2) = n4
% 12.58/3.47 | (30) sum(n0, n5) = n5
% 12.58/3.47 | (31) pred(n10) = n9
% 12.58/3.47 | (32) ~ (n10 = n3)
% 12.58/3.47 | (33) sum(n1, n8) = n9
% 12.58/3.47 | (34) ~ (all_0_6_6 = n6)
% 12.58/3.47 | (35) ~ (n4 = n2)
% 12.58/3.47 | (36) ~ (n4 = n0)
% 12.58/3.47 | (37) ~ (n9 = n1)
% 12.58/3.47 | (38) sum(n3, n10) = n2
% 12.58/3.47 | (39) sum(n9, n7) = n5
% 12.58/3.47 | (40) sum(n4, n0) = n4
% 12.58/3.47 | (41) sum(n1, n10) = n0
% 12.58/3.47 | (42) ~ (n6 = n0)
% 12.58/3.47 | (43) sum(n0, n10) = n10
% 12.58/3.47 | (44) ~ (n9 = n3)
% 12.58/3.47 | (45) ~ (n8 = n6)
% 12.58/3.47 | (46) ~ (n10 = n0)
% 12.58/3.47 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0))
% 12.58/3.47 | (48) sum(n7, n1) = n8
% 12.58/3.47 | (49) sum(n5, n5) = n10
% 12.58/3.47 | (50) ~ (n10 = n4)
% 12.58/3.47 | (51) sum(n0, n8) = n8
% 12.58/3.47 | (52) sum(n5, n8) = n2
% 12.58/3.47 | (53) ~ (n5 = n1)
% 12.58/3.47 | (54) all_0_8_8 = n10 | all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 12.58/3.47 | (55) sum(n1, n2) = n3
% 12.58/3.47 | (56) sum(n8, n0) = n8
% 12.58/3.47 | (57) ~ (n5 = n2)
% 12.58/3.47 | (58) ~ (n8 = n0)
% 12.58/3.47 | (59) sum(n9, n10) = n8
% 12.58/3.47 | (60) succ(n6) = n7
% 12.58/3.47 | (61) sum(n6, n3) = n9
% 12.58/3.47 | (62) pred(n3) = n2
% 12.58/3.47 | (63) sum(n5, n0) = n5
% 12.58/3.47 | (64) ~ (n10 = n7)
% 12.58/3.47 | (65) sum(n7, n2) = n9
% 12.58/3.47 | (66) sum(n4, n7) = n0
% 12.58/3.47 | (67) succ(n10) = n0
% 12.58/3.47 | (68) sum(n8, n1) = n9
% 12.58/3.47 | (69) sum(n9, n5) = n3
% 12.58/3.47 | (70) ~ (n7 = n6)
% 12.58/3.47 | (71) ~ (n3 = n0)
% 12.58/3.47 | (72) sum(n9, n6) = n4
% 12.58/3.47 | (73) ~ (n5 = n0)
% 12.58/3.47 | (74) sum(n5, n3) = n8
% 12.58/3.47 | (75) pred(n9) = n8
% 12.58/3.47 | (76) ~ (n10 = n2)
% 12.58/3.47 | (77) sum(all_0_8_8, all_0_5_5) = all_0_4_4
% 12.58/3.48 | (78) ~ (all_0_6_6 = n9)
% 12.58/3.48 | (79) sum(n4, n3) = n7
% 12.58/3.48 | (80) ~ (n8 = n7)
% 12.58/3.48 | (81) sum(n2, n1) = n3
% 12.58/3.48 | (82) succ(n0) = n1
% 12.58/3.48 | (83) sum(n10, n4) = n3
% 12.58/3.48 | (84) sum(n8, n6) = n3
% 12.58/3.48 | (85) pred(n4) = n3
% 12.58/3.48 | (86) ~ (n8 = n1)
% 12.58/3.48 | (87) ~ (n10 = n5)
% 12.58/3.48 | (88) ~ (all_0_6_6 = n7)
% 12.58/3.48 | (89) sum(n6, n1) = n7
% 12.58/3.48 | (90) all_0_7_7 = n10 | all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 12.58/3.48 | (91) sum(n5, n10) = n4
% 12.58/3.48 | (92) sum(n8, n7) = n4
% 12.58/3.48 | (93) sum(n1, n9) = n10
% 12.58/3.48 | (94) sum(n3, n3) = n6
% 12.58/3.48 | (95) ~ (n8 = n2)
% 12.58/3.48 | (96) sum(n4, n5) = n9
% 12.58/3.48 | (97) sum(n1, n4) = n5
% 12.58/3.48 | (98) sum(n3, n0) = n3
% 12.58/3.48 | (99) ~ (n7 = n4)
% 12.58/3.48 | (100) ~ (all_0_6_6 = n3)
% 12.58/3.48 | (101) ~ (n10 = n8)
% 12.58/3.48 | (102) pred(n0) = n10
% 12.58/3.48 | (103) sum(n2, n8) = n10
% 12.58/3.48 | (104) ~ (n8 = n3)
% 12.58/3.48 | (105) ~ (n4 = n1)
% 12.58/3.48 | (106) sum(n9, n4) = n2
% 12.58/3.48 | (107) ~ (n7 = n0)
% 12.58/3.48 | (108) sum(n4, n10) = n3
% 12.58/3.48 | (109) sum(n0, n6) = n6
% 12.58/3.48 | (110) sum(n5, n7) = n1
% 12.58/3.48 | (111) sum(n7, n4) = n0
% 12.58/3.48 | (112) succ(n2) = n3
% 12.58/3.48 | (113) sum(n3, n9) = n1
% 12.58/3.48 | (114) ~ (n10 = n9)
% 12.58/3.48 | (115) ~ (n2 = n1)
% 12.58/3.48 | (116) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 12.58/3.48 | (117) sum(n2, n0) = n2
% 12.58/3.48 | (118) sum(n7, n3) = n10
% 12.58/3.48 | (119) ~ (all_0_6_6 = n0)
% 12.58/3.48 | (120) sum(all_0_8_8, all_0_7_7) = all_0_2_2
% 12.58/3.48 | (121) sum(n10, n1) = n0
% 12.58/3.48 | (122) sum(n10, n6) = n5
% 12.58/3.48 | (123) ~ (n2 = n0)
% 12.58/3.48 | (124) sum(n6, n7) = n2
% 12.58/3.48 | (125) sum(n3, n4) = n7
% 12.58/3.48 | (126) sum(n5, n9) = n3
% 12.58/3.48 | (127) sum(n2, n4) = n6
% 12.58/3.48 | (128) succ(n5) = n6
% 12.58/3.48 | (129) sum(n0, n2) = n2
% 12.58/3.48 | (130) sum(n4, n1) = n5
% 12.58/3.48 | (131) ~ (all_0_6_6 = n2)
% 12.58/3.48 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0))
% 12.58/3.48 | (133) sum(n0, n1) = n1
% 12.58/3.49 | (134) sum(n10, n9) = n8
% 12.58/3.49 | (135) sum(n3, n2) = n5
% 12.58/3.49 | (136) sum(n10, n5) = n4
% 12.58/3.49 | (137) sum(n7, n8) = n4
% 12.58/3.49 | (138) pred(all_0_4_4) = all_0_3_3
% 12.58/3.49 | (139) sum(n3, n5) = n8
% 12.58/3.49 | (140) succ(n8) = n9
% 12.58/3.49 | (141) sum(n3, n6) = n9
% 12.58/3.49 | (142) sum(n9, n9) = n7
% 12.58/3.49 | (143) sum(n0, n7) = n7
% 12.58/3.49 | (144) pred(n1) = n0
% 12.58/3.49 | (145) sum(n3, n1) = n4
% 12.58/3.49 | (146) sum(n7, n7) = n3
% 12.58/3.49 | (147) ~ (all_0_6_6 = n10)
% 12.58/3.49 | (148) sum(n6, n5) = n0
% 12.58/3.49 | (149) ~ (n5 = n3)
% 12.58/3.49 | (150) ~ (n9 = n2)
% 12.58/3.49 | (151) ~ (n9 = n6)
% 12.58/3.49 | (152) sum(n10, n2) = n1
% 12.58/3.49 | (153) succ(n4) = n5
% 12.58/3.49 | (154) ~ (n9 = n8)
% 12.58/3.49 | (155) ~ (n8 = n5)
% 12.58/3.49 | (156) ~ (n7 = n1)
% 12.58/3.49 | (157) sum(n9, n3) = n1
% 12.58/3.49 | (158) sum(n1, n6) = n7
% 12.58/3.49 | (159) sum(n6, n6) = n1
% 12.58/3.49 | (160) sum(n0, n0) = n0
% 12.58/3.49 | (161) ~ (n6 = n5)
% 12.58/3.49 | (162) ~ (n8 = n4)
% 12.58/3.49 | (163) sum(n5, n6) = n0
% 12.58/3.49 | (164) sum(n2, n10) = n1
% 12.58/3.49 | (165) ~ (all_0_6_6 = n8)
% 12.58/3.49 | (166) ~ (n10 = n1)
% 12.58/3.49 | (167) sum(all_0_3_3, all_0_0_0) = all_0_6_6
% 12.58/3.49 | (168) sum(n2, n3) = n5
% 12.58/3.49 | (169) sum(n3, n8) = n0
% 12.58/3.49 | (170) sum(n8, n10) = n7
% 12.58/3.49 | (171) sum(n0, n3) = n3
% 12.58/3.49 | (172) sum(n6, n9) = n4
% 12.58/3.49 | (173) ~ (n6 = n2)
% 12.58/3.49 | (174) sum(n8, n5) = n2
% 12.58/3.49 | (175) ~ (n4 = n3)
% 12.58/3.49 | (176) sum(n9, n8) = n6
% 12.58/3.49 | (177) sum(n9, n1) = n10
% 12.58/3.49 | (178) sum(n4, n9) = n2
% 12.58/3.49 | (179) sum(n8, n9) = n6
% 12.58/3.49 | (180) sum(n7, n6) = n2
% 12.58/3.49 | (181) sum(n4, n8) = n1
% 12.58/3.49 | (182) sum(n2, n5) = n7
% 12.58/3.49 | (183) sum(n8, n4) = n1
% 12.58/3.50 | (184) ~ (n7 = n2)
% 12.58/3.50 | (185) pred(n7) = n6
% 12.58/3.50 | (186) sum(n8, n2) = n10
% 12.58/3.50 | (187) sum(n2, n9) = n0
% 12.58/3.50 | (188) ~ (n9 = n5)
% 12.58/3.50 | (189) sum(n4, n2) = n6
% 12.58/3.50 | (190) sum(n5, n1) = n6
% 12.58/3.50 | (191) sum(n9, n2) = n0
% 12.58/3.50 | (192) ~ (n3 = n2)
% 12.58/3.50 | (193) ~ (n3 = n1)
% 12.58/3.50 | (194) sum(n0, n4) = n4
% 12.58/3.50 | (195) sum(n4, n4) = n8
% 12.58/3.50 | (196) ~ (n9 = n7)
% 12.58/3.50 | (197) ~ (n10 = n6)
% 12.58/3.50 | (198) sum(n6, n2) = n8
% 12.58/3.50 | (199) sum(n6, n0) = n6
% 12.58/3.50 | (200) sum(n7, n0) = n7
% 12.58/3.50 | (201) succ(n3) = n4
% 12.58/3.50 | (202) sum(n5, n2) = n7
% 12.58/3.50 | (203) sum(n1, n0) = n1
% 12.58/3.50 | (204) succ(n9) = n10
% 12.58/3.50 | (205) pred(all_0_2_2) = all_0_1_1
% 12.58/3.50 | (206) sum(n10, n8) = n7
% 12.58/3.50 | (207) succ(n7) = n8
% 12.58/3.50 | (208) sum(n1, n3) = n4
% 12.58/3.50 | (209) ~ (n1 = n0)
% 12.58/3.50 | (210) sum(n2, n7) = n9
% 12.58/3.50 | (211) sum(n10, n10) = n9
% 12.58/3.50 | (212) sum(n1, n5) = n6
% 12.58/3.50 | (213) pred(n8) = n7
% 12.58/3.50 | (214) sum(n8, n3) = n0
% 12.58/3.50 | (215) sum(n8, n8) = n5
% 12.58/3.50 | (216) ~ (all_0_6_6 = n4)
% 12.58/3.50 | (217) ~ (n6 = n4)
% 12.58/3.50 | (218) sum(n6, n8) = n3
% 12.58/3.50 | (219) sum(n6, n10) = n5
% 12.58/3.50 | (220) sum(n3, n7) = n10
% 12.58/3.50 | (221) sum(n4, n6) = n10
% 12.58/3.50 | (222) ~ (n7 = n3)
% 12.58/3.50 |
% 12.58/3.50 +-Applying beta-rule and splitting (90), into two cases.
% 12.58/3.50 |-Branch one:
% 12.58/3.50 | (223) all_0_7_7 = n10
% 12.58/3.50 |
% 12.58/3.50 | From (223) and (10) follows:
% 12.58/3.51 | (224) succ(n10) = all_0_5_5
% 12.58/3.51 |
% 12.58/3.51 | From (223) and (3) follows:
% 12.58/3.51 | (225) sum(n10, all_0_1_1) = all_0_0_0
% 12.58/3.51 |
% 12.58/3.51 | From (223) and (120) follows:
% 12.58/3.51 | (226) sum(all_0_8_8, n10) = all_0_2_2
% 12.58/3.51 |
% 12.58/3.51 | Instantiating formula (47) with n10, all_0_5_5, n0 and discharging atoms succ(n10) = all_0_5_5, succ(n10) = n0, yields:
% 12.58/3.51 | (227) all_0_5_5 = n0
% 12.58/3.51 |
% 12.58/3.51 | From (227) and (77) follows:
% 12.58/3.51 | (228) sum(all_0_8_8, n0) = all_0_4_4
% 12.58/3.51 |
% 12.58/3.51 +-Applying beta-rule and splitting (54), into two cases.
% 12.58/3.51 |-Branch one:
% 12.58/3.51 | (229) all_0_8_8 = n10
% 12.58/3.51 |
% 12.58/3.51 | From (229) and (226) follows:
% 12.58/3.51 | (230) sum(n10, n10) = all_0_2_2
% 12.58/3.51 |
% 12.58/3.51 | From (229) and (228) follows:
% 12.58/3.51 | (231) sum(n10, n0) = all_0_4_4
% 12.58/3.51 |
% 12.58/3.51 | Instantiating formula (132) with n10, n10, all_0_2_2, n9 and discharging atoms sum(n10, n10) = all_0_2_2, sum(n10, n10) = n9, yields:
% 12.58/3.51 | (232) all_0_2_2 = n9
% 12.58/3.51 |
% 12.58/3.51 | Instantiating formula (132) with n10, n0, all_0_4_4, n10 and discharging atoms sum(n10, n0) = all_0_4_4, sum(n10, n0) = n10, yields:
% 12.58/3.51 | (233) all_0_4_4 = n10
% 12.58/3.51 |
% 12.58/3.51 | From (232) and (205) follows:
% 12.58/3.51 | (234) pred(n9) = all_0_1_1
% 12.58/3.51 |
% 12.58/3.51 | From (233) and (138) follows:
% 12.58/3.51 | (235) pred(n10) = all_0_3_3
% 12.58/3.51 |
% 12.58/3.51 | Instantiating formula (116) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 12.58/3.51 | (236) all_0_3_3 = n9
% 12.58/3.51 |
% 12.58/3.51 | Instantiating formula (116) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 12.58/3.51 | (237) all_0_1_1 = n8
% 12.58/3.51 |
% 12.58/3.51 | From (236) and (167) follows:
% 12.58/3.51 | (238) sum(n9, all_0_0_0) = all_0_6_6
% 12.58/3.51 |
% 12.58/3.51 | From (237) and (225) follows:
% 12.58/3.51 | (239) sum(n10, n8) = all_0_0_0
% 12.58/3.51 |
% 12.58/3.51 | Instantiating formula (132) with n10, n8, all_0_0_0, n7 and discharging atoms sum(n10, n8) = all_0_0_0, sum(n10, n8) = n7, yields:
% 12.58/3.51 | (240) all_0_0_0 = n7
% 12.58/3.51 |
% 12.58/3.51 | From (240) and (238) follows:
% 12.58/3.51 | (241) sum(n9, n7) = all_0_6_6
% 12.58/3.51 |
% 12.58/3.51 | Instantiating formula (132) with n9, n7, all_0_6_6, n5 and discharging atoms sum(n9, n7) = all_0_6_6, sum(n9, n7) = n5, yields:
% 12.58/3.51 | (242) all_0_6_6 = n5
% 12.58/3.51 |
% 12.58/3.51 | Equations (242) can reduce 4 to:
% 12.58/3.51 | (243) $false
% 12.58/3.51 |
% 12.58/3.51 |-The branch is then unsatisfiable
% 12.58/3.51 |-Branch two:
% 12.58/3.51 | (244) ~ (all_0_8_8 = n10)
% 12.58/3.52 | (245) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 12.58/3.52 |
% 12.58/3.52 +-Applying beta-rule and splitting (245), into two cases.
% 12.58/3.52 |-Branch one:
% 12.58/3.52 | (246) all_0_8_8 = n9
% 12.58/3.52 |
% 12.58/3.52 | From (246) and (226) follows:
% 12.58/3.52 | (247) sum(n9, n10) = all_0_2_2
% 12.58/3.52 |
% 12.58/3.52 | From (246) and (228) follows:
% 12.58/3.52 | (248) sum(n9, n0) = all_0_4_4
% 12.58/3.52 |
% 12.58/3.52 | Instantiating formula (132) with n9, n10, all_0_2_2, n8 and discharging atoms sum(n9, n10) = all_0_2_2, sum(n9, n10) = n8, yields:
% 12.58/3.52 | (249) all_0_2_2 = n8
% 12.58/3.52 |
% 12.58/3.52 | Instantiating formula (132) with n9, n0, all_0_4_4, n9 and discharging atoms sum(n9, n0) = all_0_4_4, sum(n9, n0) = n9, yields:
% 12.58/3.52 | (250) all_0_4_4 = n9
% 12.58/3.52 |
% 12.58/3.52 | From (249) and (205) follows:
% 12.58/3.52 | (251) pred(n8) = all_0_1_1
% 12.58/3.52 |
% 12.58/3.52 | From (250) and (138) follows:
% 12.58/3.52 | (252) pred(n9) = all_0_3_3
% 12.58/3.52 |
% 12.58/3.52 | Instantiating formula (116) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 12.58/3.52 | (253) all_0_3_3 = n8
% 12.58/3.52 |
% 12.58/3.52 | Instantiating formula (116) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 12.58/3.52 | (254) all_0_1_1 = n7
% 12.58/3.52 |
% 12.58/3.52 | From (253) and (167) follows:
% 12.58/3.52 | (255) sum(n8, all_0_0_0) = all_0_6_6
% 12.58/3.52 |
% 12.58/3.52 | From (254) and (225) follows:
% 12.58/3.52 | (256) sum(n10, n7) = all_0_0_0
% 12.58/3.52 |
% 12.58/3.52 | Instantiating formula (132) with n10, n7, all_0_0_0, n6 and discharging atoms sum(n10, n7) = all_0_0_0, sum(n10, n7) = n6, yields:
% 12.58/3.52 | (257) all_0_0_0 = n6
% 12.58/3.52 |
% 12.58/3.52 | From (257) and (255) follows:
% 12.58/3.52 | (258) sum(n8, n6) = all_0_6_6
% 12.58/3.52 |
% 12.58/3.52 | Instantiating formula (132) with n8, n6, all_0_6_6, n3 and discharging atoms sum(n8, n6) = all_0_6_6, sum(n8, n6) = n3, yields:
% 12.58/3.52 | (259) all_0_6_6 = n3
% 12.58/3.52 |
% 12.58/3.52 | Equations (259) can reduce 100 to:
% 12.58/3.52 | (243) $false
% 12.58/3.52 |
% 12.58/3.52 |-The branch is then unsatisfiable
% 12.58/3.52 |-Branch two:
% 12.58/3.52 | (261) ~ (all_0_8_8 = n9)
% 12.58/3.52 | (262) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 12.58/3.52 |
% 12.58/3.52 +-Applying beta-rule and splitting (262), into two cases.
% 12.58/3.52 |-Branch one:
% 12.58/3.52 | (263) all_0_8_8 = n8
% 12.58/3.52 |
% 12.58/3.52 | From (263) and (226) follows:
% 12.58/3.52 | (264) sum(n8, n10) = all_0_2_2
% 12.58/3.52 |
% 12.58/3.52 | From (263) and (228) follows:
% 12.58/3.52 | (265) sum(n8, n0) = all_0_4_4
% 12.58/3.52 |
% 12.58/3.53 | Instantiating formula (132) with n8, n10, all_0_2_2, n7 and discharging atoms sum(n8, n10) = all_0_2_2, sum(n8, n10) = n7, yields:
% 12.58/3.53 | (266) all_0_2_2 = n7
% 12.58/3.53 |
% 12.58/3.53 | Instantiating formula (132) with n8, n0, all_0_4_4, n8 and discharging atoms sum(n8, n0) = all_0_4_4, sum(n8, n0) = n8, yields:
% 12.58/3.53 | (267) all_0_4_4 = n8
% 12.58/3.53 |
% 12.58/3.53 | From (266) and (205) follows:
% 12.58/3.53 | (268) pred(n7) = all_0_1_1
% 12.58/3.53 |
% 12.58/3.53 | From (267) and (138) follows:
% 12.58/3.53 | (269) pred(n8) = all_0_3_3
% 12.58/3.53 |
% 12.58/3.53 | Instantiating formula (116) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 12.58/3.53 | (270) all_0_3_3 = n7
% 12.58/3.53 |
% 12.58/3.53 | Instantiating formula (116) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 12.58/3.53 | (271) all_0_1_1 = n6
% 12.58/3.53 |
% 12.58/3.53 | From (270) and (167) follows:
% 12.58/3.53 | (272) sum(n7, all_0_0_0) = all_0_6_6
% 12.58/3.53 |
% 12.58/3.53 | From (271) and (225) follows:
% 12.58/3.53 | (273) sum(n10, n6) = all_0_0_0
% 12.58/3.53 |
% 12.58/3.53 | Instantiating formula (132) with n10, n6, all_0_0_0, n5 and discharging atoms sum(n10, n6) = all_0_0_0, sum(n10, n6) = n5, yields:
% 12.58/3.53 | (274) all_0_0_0 = n5
% 12.58/3.53 |
% 12.58/3.53 | From (274) and (272) follows:
% 12.58/3.53 | (275) sum(n7, n5) = all_0_6_6
% 12.58/3.53 |
% 12.58/3.53 | Instantiating formula (132) with n7, n5, all_0_6_6, n1 and discharging atoms sum(n7, n5) = all_0_6_6, sum(n7, n5) = n1, yields:
% 12.58/3.53 | (276) all_0_6_6 = n1
% 12.58/3.53 |
% 12.58/3.53 | Equations (276) can reduce 28 to:
% 12.58/3.53 | (243) $false
% 12.58/3.53 |
% 12.58/3.53 |-The branch is then unsatisfiable
% 12.58/3.53 |-Branch two:
% 12.58/3.53 | (278) ~ (all_0_8_8 = n8)
% 12.58/3.53 | (279) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 12.58/3.53 |
% 12.58/3.53 +-Applying beta-rule and splitting (279), into two cases.
% 12.58/3.53 |-Branch one:
% 12.58/3.53 | (280) all_0_8_8 = n7
% 12.58/3.53 |
% 12.58/3.53 | From (280) and (226) follows:
% 12.58/3.53 | (281) sum(n7, n10) = all_0_2_2
% 12.58/3.53 |
% 12.58/3.53 | From (280) and (228) follows:
% 12.58/3.53 | (282) sum(n7, n0) = all_0_4_4
% 12.58/3.53 |
% 12.58/3.53 | Instantiating formula (132) with n7, n10, all_0_2_2, n6 and discharging atoms sum(n7, n10) = all_0_2_2, sum(n7, n10) = n6, yields:
% 12.58/3.53 | (283) all_0_2_2 = n6
% 12.58/3.53 |
% 12.58/3.53 | Instantiating formula (132) with n7, n0, all_0_4_4, n7 and discharging atoms sum(n7, n0) = all_0_4_4, sum(n7, n0) = n7, yields:
% 12.58/3.53 | (284) all_0_4_4 = n7
% 12.58/3.53 |
% 12.58/3.53 | From (283) and (205) follows:
% 12.58/3.53 | (285) pred(n6) = all_0_1_1
% 12.58/3.53 |
% 12.58/3.53 | From (284) and (138) follows:
% 12.58/3.53 | (286) pred(n7) = all_0_3_3
% 12.58/3.53 |
% 12.58/3.53 | Instantiating formula (116) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 12.58/3.53 | (287) all_0_3_3 = n6
% 12.58/3.53 |
% 12.58/3.53 | Instantiating formula (116) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 12.58/3.53 | (288) all_0_1_1 = n5
% 12.58/3.53 |
% 12.58/3.53 | From (287) and (167) follows:
% 12.58/3.53 | (289) sum(n6, all_0_0_0) = all_0_6_6
% 12.58/3.53 |
% 12.58/3.53 | From (288) and (225) follows:
% 12.58/3.53 | (290) sum(n10, n5) = all_0_0_0
% 12.58/3.53 |
% 12.58/3.53 | Instantiating formula (132) with n10, n5, all_0_0_0, n4 and discharging atoms sum(n10, n5) = all_0_0_0, sum(n10, n5) = n4, yields:
% 12.58/3.53 | (291) all_0_0_0 = n4
% 12.58/3.53 |
% 12.58/3.53 | From (291) and (289) follows:
% 12.58/3.53 | (292) sum(n6, n4) = all_0_6_6
% 12.58/3.53 |
% 12.58/3.53 | Instantiating formula (132) with n6, n4, all_0_6_6, n10 and discharging atoms sum(n6, n4) = all_0_6_6, sum(n6, n4) = n10, yields:
% 12.58/3.53 | (293) all_0_6_6 = n10
% 12.58/3.53 |
% 12.58/3.53 | Equations (293) can reduce 147 to:
% 12.58/3.53 | (243) $false
% 12.58/3.53 |
% 12.58/3.53 |-The branch is then unsatisfiable
% 12.58/3.53 |-Branch two:
% 12.58/3.53 | (295) ~ (all_0_8_8 = n7)
% 12.58/3.53 | (296) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 12.58/3.53 |
% 12.58/3.53 +-Applying beta-rule and splitting (296), into two cases.
% 12.58/3.53 |-Branch one:
% 12.58/3.53 | (297) all_0_8_8 = n6
% 12.58/3.53 |
% 12.58/3.53 | From (297) and (226) follows:
% 12.58/3.53 | (298) sum(n6, n10) = all_0_2_2
% 12.58/3.53 |
% 12.58/3.53 | From (297) and (228) follows:
% 12.58/3.53 | (299) sum(n6, n0) = all_0_4_4
% 12.58/3.53 |
% 12.58/3.53 | Instantiating formula (132) with n6, n10, all_0_2_2, n5 and discharging atoms sum(n6, n10) = all_0_2_2, sum(n6, n10) = n5, yields:
% 12.58/3.53 | (300) all_0_2_2 = n5
% 12.58/3.53 |
% 12.58/3.53 | Instantiating formula (132) with n6, n0, all_0_4_4, n6 and discharging atoms sum(n6, n0) = all_0_4_4, sum(n6, n0) = n6, yields:
% 12.58/3.53 | (301) all_0_4_4 = n6
% 12.58/3.53 |
% 12.58/3.53 | From (300) and (205) follows:
% 12.58/3.53 | (302) pred(n5) = all_0_1_1
% 12.58/3.53 |
% 12.58/3.53 | From (301) and (138) follows:
% 12.58/3.53 | (303) pred(n6) = all_0_3_3
% 12.58/3.53 |
% 12.58/3.53 | Instantiating formula (116) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 12.58/3.53 | (304) all_0_3_3 = n5
% 12.58/3.53 |
% 12.58/3.53 | Instantiating formula (116) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 12.58/3.54 | (305) all_0_1_1 = n4
% 12.58/3.54 |
% 12.58/3.54 | From (304) and (167) follows:
% 12.58/3.54 | (306) sum(n5, all_0_0_0) = all_0_6_6
% 12.58/3.54 |
% 12.58/3.54 | From (305) and (225) follows:
% 12.58/3.54 | (307) sum(n10, n4) = all_0_0_0
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (132) with n10, n4, all_0_0_0, n3 and discharging atoms sum(n10, n4) = all_0_0_0, sum(n10, n4) = n3, yields:
% 12.58/3.54 | (308) all_0_0_0 = n3
% 12.58/3.54 |
% 12.58/3.54 | From (308) and (306) follows:
% 12.58/3.54 | (309) sum(n5, n3) = all_0_6_6
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (132) with n5, n3, all_0_6_6, n8 and discharging atoms sum(n5, n3) = all_0_6_6, sum(n5, n3) = n8, yields:
% 12.58/3.54 | (310) all_0_6_6 = n8
% 12.58/3.54 |
% 12.58/3.54 | Equations (310) can reduce 165 to:
% 12.58/3.54 | (243) $false
% 12.58/3.54 |
% 12.58/3.54 |-The branch is then unsatisfiable
% 12.58/3.54 |-Branch two:
% 12.58/3.54 | (312) ~ (all_0_8_8 = n6)
% 12.58/3.54 | (313) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 12.58/3.54 |
% 12.58/3.54 +-Applying beta-rule and splitting (313), into two cases.
% 12.58/3.54 |-Branch one:
% 12.58/3.54 | (314) all_0_8_8 = n5
% 12.58/3.54 |
% 12.58/3.54 | From (314) and (226) follows:
% 12.58/3.54 | (315) sum(n5, n10) = all_0_2_2
% 12.58/3.54 |
% 12.58/3.54 | From (314) and (228) follows:
% 12.58/3.54 | (316) sum(n5, n0) = all_0_4_4
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (132) with n5, n10, all_0_2_2, n4 and discharging atoms sum(n5, n10) = all_0_2_2, sum(n5, n10) = n4, yields:
% 12.58/3.54 | (317) all_0_2_2 = n4
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (132) with n5, n0, all_0_4_4, n5 and discharging atoms sum(n5, n0) = all_0_4_4, sum(n5, n0) = n5, yields:
% 12.58/3.54 | (318) all_0_4_4 = n5
% 12.58/3.54 |
% 12.58/3.54 | From (317) and (205) follows:
% 12.58/3.54 | (319) pred(n4) = all_0_1_1
% 12.58/3.54 |
% 12.58/3.54 | From (318) and (138) follows:
% 12.58/3.54 | (320) pred(n5) = all_0_3_3
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (116) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 12.58/3.54 | (321) all_0_3_3 = n4
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (116) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 12.58/3.54 | (322) all_0_1_1 = n3
% 12.58/3.54 |
% 12.58/3.54 | From (321) and (167) follows:
% 12.58/3.54 | (323) sum(n4, all_0_0_0) = all_0_6_6
% 12.58/3.54 |
% 12.58/3.54 | From (322) and (225) follows:
% 12.58/3.54 | (324) sum(n10, n3) = all_0_0_0
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (132) with n10, n3, all_0_0_0, n2 and discharging atoms sum(n10, n3) = all_0_0_0, sum(n10, n3) = n2, yields:
% 12.58/3.54 | (325) all_0_0_0 = n2
% 12.58/3.54 |
% 12.58/3.54 | From (325) and (323) follows:
% 12.58/3.54 | (326) sum(n4, n2) = all_0_6_6
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (132) with n4, n2, all_0_6_6, n6 and discharging atoms sum(n4, n2) = all_0_6_6, sum(n4, n2) = n6, yields:
% 12.58/3.54 | (327) all_0_6_6 = n6
% 12.58/3.54 |
% 12.58/3.54 | Equations (327) can reduce 34 to:
% 12.58/3.54 | (243) $false
% 12.58/3.54 |
% 12.58/3.54 |-The branch is then unsatisfiable
% 12.58/3.54 |-Branch two:
% 12.58/3.54 | (329) ~ (all_0_8_8 = n5)
% 12.58/3.54 | (330) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 12.58/3.54 |
% 12.58/3.54 +-Applying beta-rule and splitting (330), into two cases.
% 12.58/3.54 |-Branch one:
% 12.58/3.54 | (331) all_0_8_8 = n4
% 12.58/3.54 |
% 12.58/3.54 | From (331) and (226) follows:
% 12.58/3.54 | (332) sum(n4, n10) = all_0_2_2
% 12.58/3.54 |
% 12.58/3.54 | From (331) and (228) follows:
% 12.58/3.54 | (333) sum(n4, n0) = all_0_4_4
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (132) with n4, n10, all_0_2_2, n3 and discharging atoms sum(n4, n10) = all_0_2_2, sum(n4, n10) = n3, yields:
% 12.58/3.54 | (334) all_0_2_2 = n3
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (132) with n4, n0, all_0_4_4, n4 and discharging atoms sum(n4, n0) = all_0_4_4, sum(n4, n0) = n4, yields:
% 12.58/3.54 | (335) all_0_4_4 = n4
% 12.58/3.54 |
% 12.58/3.54 | From (334) and (205) follows:
% 12.58/3.54 | (336) pred(n3) = all_0_1_1
% 12.58/3.54 |
% 12.58/3.54 | From (335) and (138) follows:
% 12.58/3.54 | (337) pred(n4) = all_0_3_3
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (116) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 12.58/3.54 | (338) all_0_3_3 = n3
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (116) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 12.58/3.54 | (339) all_0_1_1 = n2
% 12.58/3.54 |
% 12.58/3.54 | From (338) and (167) follows:
% 12.58/3.54 | (340) sum(n3, all_0_0_0) = all_0_6_6
% 12.58/3.54 |
% 12.58/3.54 | From (339) and (225) follows:
% 12.58/3.54 | (341) sum(n10, n2) = all_0_0_0
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (132) with n10, n2, all_0_0_0, n1 and discharging atoms sum(n10, n2) = all_0_0_0, sum(n10, n2) = n1, yields:
% 12.58/3.54 | (342) all_0_0_0 = n1
% 12.58/3.54 |
% 12.58/3.54 | From (342) and (340) follows:
% 12.58/3.54 | (343) sum(n3, n1) = all_0_6_6
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (132) with n3, n1, all_0_6_6, n4 and discharging atoms sum(n3, n1) = all_0_6_6, sum(n3, n1) = n4, yields:
% 12.58/3.54 | (344) all_0_6_6 = n4
% 12.58/3.54 |
% 12.58/3.54 | Equations (344) can reduce 216 to:
% 12.58/3.54 | (243) $false
% 12.58/3.54 |
% 12.58/3.54 |-The branch is then unsatisfiable
% 12.58/3.54 |-Branch two:
% 12.58/3.54 | (346) ~ (all_0_8_8 = n4)
% 12.58/3.54 | (347) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 12.58/3.54 |
% 12.58/3.54 +-Applying beta-rule and splitting (347), into two cases.
% 12.58/3.54 |-Branch one:
% 12.58/3.54 | (348) all_0_8_8 = n3
% 12.58/3.54 |
% 12.58/3.54 | From (348) and (226) follows:
% 12.58/3.54 | (349) sum(n3, n10) = all_0_2_2
% 12.58/3.54 |
% 12.58/3.54 | From (348) and (228) follows:
% 12.58/3.54 | (350) sum(n3, n0) = all_0_4_4
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (132) with n3, n10, all_0_2_2, n2 and discharging atoms sum(n3, n10) = all_0_2_2, sum(n3, n10) = n2, yields:
% 12.58/3.54 | (351) all_0_2_2 = n2
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (132) with n3, n0, all_0_4_4, n3 and discharging atoms sum(n3, n0) = all_0_4_4, sum(n3, n0) = n3, yields:
% 12.58/3.54 | (352) all_0_4_4 = n3
% 12.58/3.54 |
% 12.58/3.54 | From (351) and (205) follows:
% 12.58/3.54 | (353) pred(n2) = all_0_1_1
% 12.58/3.54 |
% 12.58/3.54 | From (352) and (138) follows:
% 12.58/3.54 | (354) pred(n3) = all_0_3_3
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (116) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 12.58/3.54 | (355) all_0_3_3 = n2
% 12.58/3.54 |
% 12.58/3.54 | Instantiating formula (116) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 12.58/3.54 | (356) all_0_1_1 = n1
% 12.58/3.54 |
% 12.58/3.54 | From (355) and (167) follows:
% 12.58/3.54 | (357) sum(n2, all_0_0_0) = all_0_6_6
% 12.58/3.54 |
% 12.58/3.54 | From (356) and (225) follows:
% 12.58/3.54 | (358) sum(n10, n1) = all_0_0_0
% 12.58/3.54 |
% 12.58/3.55 | Instantiating formula (132) with n10, n1, all_0_0_0, n0 and discharging atoms sum(n10, n1) = all_0_0_0, sum(n10, n1) = n0, yields:
% 12.58/3.55 | (359) all_0_0_0 = n0
% 12.58/3.55 |
% 12.58/3.55 | From (359) and (357) follows:
% 12.58/3.55 | (360) sum(n2, n0) = all_0_6_6
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (132) with n2, n0, all_0_6_6, n2 and discharging atoms sum(n2, n0) = all_0_6_6, sum(n2, n0) = n2, yields:
% 12.58/3.55 | (361) all_0_6_6 = n2
% 12.58/3.55 |
% 12.58/3.55 | Equations (361) can reduce 131 to:
% 12.58/3.55 | (243) $false
% 12.58/3.55 |
% 12.58/3.55 |-The branch is then unsatisfiable
% 12.58/3.55 |-Branch two:
% 12.58/3.55 | (363) ~ (all_0_8_8 = n3)
% 12.58/3.55 | (364) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 12.58/3.55 |
% 12.58/3.55 +-Applying beta-rule and splitting (364), into two cases.
% 12.58/3.55 |-Branch one:
% 12.58/3.55 | (365) all_0_8_8 = n2
% 12.58/3.55 |
% 12.58/3.55 | From (365) and (226) follows:
% 12.58/3.55 | (366) sum(n2, n10) = all_0_2_2
% 12.58/3.55 |
% 12.58/3.55 | From (365) and (228) follows:
% 12.58/3.55 | (367) sum(n2, n0) = all_0_4_4
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (132) with n2, n10, all_0_2_2, n1 and discharging atoms sum(n2, n10) = all_0_2_2, sum(n2, n10) = n1, yields:
% 12.58/3.55 | (368) all_0_2_2 = n1
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (132) with n2, n0, all_0_4_4, n2 and discharging atoms sum(n2, n0) = all_0_4_4, sum(n2, n0) = n2, yields:
% 12.58/3.55 | (369) all_0_4_4 = n2
% 12.58/3.55 |
% 12.58/3.55 | From (368) and (205) follows:
% 12.58/3.55 | (370) pred(n1) = all_0_1_1
% 12.58/3.55 |
% 12.58/3.55 | From (369) and (138) follows:
% 12.58/3.55 | (371) pred(n2) = all_0_3_3
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (116) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 12.58/3.55 | (372) all_0_3_3 = n1
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (116) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 12.58/3.55 | (373) all_0_1_1 = n0
% 12.58/3.55 |
% 12.58/3.55 | From (372) and (167) follows:
% 12.58/3.55 | (374) sum(n1, all_0_0_0) = all_0_6_6
% 12.58/3.55 |
% 12.58/3.55 | From (373) and (225) follows:
% 12.58/3.55 | (375) sum(n10, n0) = all_0_0_0
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (132) with n10, n0, all_0_0_0, n10 and discharging atoms sum(n10, n0) = all_0_0_0, sum(n10, n0) = n10, yields:
% 12.58/3.55 | (376) all_0_0_0 = n10
% 12.58/3.55 |
% 12.58/3.55 | From (376) and (374) follows:
% 12.58/3.55 | (377) sum(n1, n10) = all_0_6_6
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (132) with n1, n10, all_0_6_6, n0 and discharging atoms sum(n1, n10) = all_0_6_6, sum(n1, n10) = n0, yields:
% 12.58/3.55 | (378) all_0_6_6 = n0
% 12.58/3.55 |
% 12.58/3.55 | Equations (378) can reduce 119 to:
% 12.58/3.55 | (243) $false
% 12.58/3.55 |
% 12.58/3.55 |-The branch is then unsatisfiable
% 12.58/3.55 |-Branch two:
% 12.58/3.55 | (380) ~ (all_0_8_8 = n2)
% 12.58/3.55 | (381) all_0_8_8 = n1 | all_0_8_8 = n0
% 12.58/3.55 |
% 12.58/3.55 +-Applying beta-rule and splitting (381), into two cases.
% 12.58/3.55 |-Branch one:
% 12.58/3.55 | (382) all_0_8_8 = n1
% 12.58/3.55 |
% 12.58/3.55 | From (382) and (226) follows:
% 12.58/3.55 | (383) sum(n1, n10) = all_0_2_2
% 12.58/3.55 |
% 12.58/3.55 | From (382) and (228) follows:
% 12.58/3.55 | (384) sum(n1, n0) = all_0_4_4
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (132) with n1, n10, all_0_2_2, n0 and discharging atoms sum(n1, n10) = all_0_2_2, sum(n1, n10) = n0, yields:
% 12.58/3.55 | (385) all_0_2_2 = n0
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (132) with n1, n0, all_0_4_4, n1 and discharging atoms sum(n1, n0) = all_0_4_4, sum(n1, n0) = n1, yields:
% 12.58/3.55 | (386) all_0_4_4 = n1
% 12.58/3.55 |
% 12.58/3.55 | From (385) and (205) follows:
% 12.58/3.55 | (387) pred(n0) = all_0_1_1
% 12.58/3.55 |
% 12.58/3.55 | From (386) and (138) follows:
% 12.58/3.55 | (388) pred(n1) = all_0_3_3
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (116) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 12.58/3.55 | (389) all_0_3_3 = n0
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (116) with n0, all_0_1_1, n10 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n10, yields:
% 12.58/3.55 | (390) all_0_1_1 = n10
% 12.58/3.55 |
% 12.58/3.55 | From (389) and (167) follows:
% 12.58/3.55 | (391) sum(n0, all_0_0_0) = all_0_6_6
% 12.58/3.55 |
% 12.58/3.55 | From (390) and (225) follows:
% 12.58/3.55 | (392) sum(n10, n10) = all_0_0_0
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (132) with n10, n10, all_0_0_0, n9 and discharging atoms sum(n10, n10) = all_0_0_0, sum(n10, n10) = n9, yields:
% 12.58/3.55 | (393) all_0_0_0 = n9
% 12.58/3.55 |
% 12.58/3.55 | From (393) and (391) follows:
% 12.58/3.55 | (394) sum(n0, n9) = all_0_6_6
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (132) with n0, n9, all_0_6_6, n9 and discharging atoms sum(n0, n9) = all_0_6_6, sum(n0, n9) = n9, yields:
% 12.58/3.55 | (395) all_0_6_6 = n9
% 12.58/3.55 |
% 12.58/3.55 | Equations (395) can reduce 78 to:
% 12.58/3.55 | (243) $false
% 12.58/3.55 |
% 12.58/3.55 |-The branch is then unsatisfiable
% 12.58/3.55 |-Branch two:
% 12.58/3.55 | (397) ~ (all_0_8_8 = n1)
% 12.58/3.55 | (398) all_0_8_8 = n0
% 12.58/3.55 |
% 12.58/3.55 | From (398) and (226) follows:
% 12.58/3.55 | (399) sum(n0, n10) = all_0_2_2
% 12.58/3.55 |
% 12.58/3.55 | From (398) and (228) follows:
% 12.58/3.55 | (400) sum(n0, n0) = all_0_4_4
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (132) with n0, n10, all_0_2_2, n10 and discharging atoms sum(n0, n10) = all_0_2_2, sum(n0, n10) = n10, yields:
% 12.58/3.55 | (401) all_0_2_2 = n10
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (132) with n0, n0, all_0_4_4, n0 and discharging atoms sum(n0, n0) = all_0_4_4, sum(n0, n0) = n0, yields:
% 12.58/3.55 | (402) all_0_4_4 = n0
% 12.58/3.55 |
% 12.58/3.55 | From (401) and (205) follows:
% 12.58/3.55 | (403) pred(n10) = all_0_1_1
% 12.58/3.55 |
% 12.58/3.55 | From (402) and (138) follows:
% 12.58/3.55 | (404) pred(n0) = all_0_3_3
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (116) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 12.58/3.55 | (405) all_0_1_1 = n9
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (116) with n0, all_0_3_3, n10 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n10, yields:
% 12.58/3.55 | (406) all_0_3_3 = n10
% 12.58/3.55 |
% 12.58/3.55 | From (406) and (167) follows:
% 12.58/3.55 | (407) sum(n10, all_0_0_0) = all_0_6_6
% 12.58/3.55 |
% 12.58/3.55 | From (405) and (225) follows:
% 12.58/3.55 | (408) sum(n10, n9) = all_0_0_0
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (132) with n10, n9, all_0_0_0, n8 and discharging atoms sum(n10, n9) = all_0_0_0, sum(n10, n9) = n8, yields:
% 12.58/3.55 | (409) all_0_0_0 = n8
% 12.58/3.55 |
% 12.58/3.55 | From (409) and (407) follows:
% 12.58/3.55 | (410) sum(n10, n8) = all_0_6_6
% 12.58/3.55 |
% 12.58/3.55 | Instantiating formula (132) with n10, n8, all_0_6_6, n7 and discharging atoms sum(n10, n8) = all_0_6_6, sum(n10, n8) = n7, yields:
% 12.58/3.55 | (411) all_0_6_6 = n7
% 12.58/3.55 |
% 12.58/3.55 | Equations (411) can reduce 88 to:
% 12.58/3.55 | (243) $false
% 12.58/3.55 |
% 12.58/3.55 |-The branch is then unsatisfiable
% 12.58/3.55 |-Branch two:
% 12.58/3.55 | (413) ~ (all_0_7_7 = n10)
% 12.58/3.55 | (414) all_0_7_7 = n9 | all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 12.58/3.55 |
% 12.58/3.55 +-Applying beta-rule and splitting (54), into two cases.
% 12.58/3.55 |-Branch one:
% 12.58/3.55 | (229) all_0_8_8 = n10
% 12.58/3.55 |
% 12.58/3.55 | From (229) and (77) follows:
% 12.58/3.55 | (416) sum(n10, all_0_5_5) = all_0_4_4
% 12.58/3.56 |
% 12.58/3.56 | From (229) and (120) follows:
% 12.58/3.56 | (417) sum(n10, all_0_7_7) = all_0_2_2
% 12.58/3.56 |
% 12.58/3.56 +-Applying beta-rule and splitting (414), into two cases.
% 12.58/3.56 |-Branch one:
% 12.58/3.56 | (418) all_0_7_7 = n9
% 12.58/3.56 |
% 12.58/3.56 | From (418) and (10) follows:
% 12.58/3.56 | (419) succ(n9) = all_0_5_5
% 12.58/3.56 |
% 12.58/3.56 | From (418) and (3) follows:
% 12.58/3.56 | (420) sum(n9, all_0_1_1) = all_0_0_0
% 12.58/3.56 |
% 12.58/3.56 | From (418) and (417) follows:
% 12.58/3.56 | (421) sum(n10, n9) = all_0_2_2
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (47) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 12.58/3.56 | (422) all_0_5_5 = n10
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (132) with n10, n9, all_0_2_2, n8 and discharging atoms sum(n10, n9) = all_0_2_2, sum(n10, n9) = n8, yields:
% 12.58/3.56 | (249) all_0_2_2 = n8
% 12.58/3.56 |
% 12.58/3.56 | From (249) and (205) follows:
% 12.58/3.56 | (251) pred(n8) = all_0_1_1
% 12.58/3.56 |
% 12.58/3.56 | From (422) and (416) follows:
% 12.58/3.56 | (425) sum(n10, n10) = all_0_4_4
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (116) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 12.58/3.56 | (254) all_0_1_1 = n7
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (132) with n10, n10, all_0_4_4, n9 and discharging atoms sum(n10, n10) = all_0_4_4, sum(n10, n10) = n9, yields:
% 12.58/3.56 | (250) all_0_4_4 = n9
% 12.58/3.56 |
% 12.58/3.56 | From (250) and (138) follows:
% 12.58/3.56 | (252) pred(n9) = all_0_3_3
% 12.58/3.56 |
% 12.58/3.56 | From (254) and (420) follows:
% 12.58/3.56 | (429) sum(n9, n7) = all_0_0_0
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (116) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 12.58/3.56 | (253) all_0_3_3 = n8
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (132) with n9, n7, all_0_0_0, n5 and discharging atoms sum(n9, n7) = all_0_0_0, sum(n9, n7) = n5, yields:
% 12.58/3.56 | (274) all_0_0_0 = n5
% 12.58/3.56 |
% 12.58/3.56 | From (253)(274) and (167) follows:
% 12.58/3.56 | (432) sum(n8, n5) = all_0_6_6
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (132) with n8, n5, all_0_6_6, n2 and discharging atoms sum(n8, n5) = all_0_6_6, sum(n8, n5) = n2, yields:
% 12.58/3.56 | (361) all_0_6_6 = n2
% 12.58/3.56 |
% 12.58/3.56 | Equations (361) can reduce 131 to:
% 12.58/3.56 | (243) $false
% 12.58/3.56 |
% 12.58/3.56 |-The branch is then unsatisfiable
% 12.58/3.56 |-Branch two:
% 12.58/3.56 | (435) ~ (all_0_7_7 = n9)
% 12.58/3.56 | (436) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 12.58/3.56 |
% 12.58/3.56 +-Applying beta-rule and splitting (436), into two cases.
% 12.58/3.56 |-Branch one:
% 12.58/3.56 | (437) all_0_7_7 = n8
% 12.58/3.56 |
% 12.58/3.56 | From (437) and (10) follows:
% 12.58/3.56 | (438) succ(n8) = all_0_5_5
% 12.58/3.56 |
% 12.58/3.56 | From (437) and (3) follows:
% 12.58/3.56 | (439) sum(n8, all_0_1_1) = all_0_0_0
% 12.58/3.56 |
% 12.58/3.56 | From (437) and (417) follows:
% 12.58/3.56 | (440) sum(n10, n8) = all_0_2_2
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (47) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 12.58/3.56 | (441) all_0_5_5 = n9
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (132) with n10, n8, all_0_2_2, n7 and discharging atoms sum(n10, n8) = all_0_2_2, sum(n10, n8) = n7, yields:
% 12.58/3.56 | (266) all_0_2_2 = n7
% 12.58/3.56 |
% 12.58/3.56 | From (266) and (205) follows:
% 12.58/3.56 | (268) pred(n7) = all_0_1_1
% 12.58/3.56 |
% 12.58/3.56 | From (441) and (416) follows:
% 12.58/3.56 | (444) sum(n10, n9) = all_0_4_4
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (116) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 12.58/3.56 | (271) all_0_1_1 = n6
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (132) with n10, n9, all_0_4_4, n8 and discharging atoms sum(n10, n9) = all_0_4_4, sum(n10, n9) = n8, yields:
% 12.58/3.56 | (267) all_0_4_4 = n8
% 12.58/3.56 |
% 12.58/3.56 | From (267) and (138) follows:
% 12.58/3.56 | (269) pred(n8) = all_0_3_3
% 12.58/3.56 |
% 12.58/3.56 | From (271) and (439) follows:
% 12.58/3.56 | (448) sum(n8, n6) = all_0_0_0
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (116) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 12.58/3.56 | (270) all_0_3_3 = n7
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (132) with n8, n6, all_0_0_0, n3 and discharging atoms sum(n8, n6) = all_0_0_0, sum(n8, n6) = n3, yields:
% 12.58/3.56 | (308) all_0_0_0 = n3
% 12.58/3.56 |
% 12.58/3.56 | From (270)(308) and (167) follows:
% 12.58/3.56 | (451) sum(n7, n3) = all_0_6_6
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (132) with n7, n3, all_0_6_6, n10 and discharging atoms sum(n7, n3) = all_0_6_6, sum(n7, n3) = n10, yields:
% 12.58/3.56 | (293) all_0_6_6 = n10
% 12.58/3.56 |
% 12.58/3.56 | Equations (293) can reduce 147 to:
% 12.58/3.56 | (243) $false
% 12.58/3.56 |
% 12.58/3.56 |-The branch is then unsatisfiable
% 12.58/3.56 |-Branch two:
% 12.58/3.56 | (454) ~ (all_0_7_7 = n8)
% 12.58/3.56 | (455) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 12.58/3.56 |
% 12.58/3.56 +-Applying beta-rule and splitting (455), into two cases.
% 12.58/3.56 |-Branch one:
% 12.58/3.56 | (456) all_0_7_7 = n7
% 12.58/3.56 |
% 12.58/3.56 | From (456) and (10) follows:
% 12.58/3.56 | (457) succ(n7) = all_0_5_5
% 12.58/3.56 |
% 12.58/3.56 | From (456) and (3) follows:
% 12.58/3.56 | (458) sum(n7, all_0_1_1) = all_0_0_0
% 12.58/3.56 |
% 12.58/3.56 | From (456) and (417) follows:
% 12.58/3.56 | (459) sum(n10, n7) = all_0_2_2
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (47) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 12.58/3.56 | (460) all_0_5_5 = n8
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (132) with n10, n7, all_0_2_2, n6 and discharging atoms sum(n10, n7) = all_0_2_2, sum(n10, n7) = n6, yields:
% 12.58/3.56 | (283) all_0_2_2 = n6
% 12.58/3.56 |
% 12.58/3.56 | From (283) and (205) follows:
% 12.58/3.56 | (285) pred(n6) = all_0_1_1
% 12.58/3.56 |
% 12.58/3.56 | From (460) and (416) follows:
% 12.58/3.56 | (463) sum(n10, n8) = all_0_4_4
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (116) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 12.58/3.56 | (288) all_0_1_1 = n5
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (132) with n10, n8, all_0_4_4, n7 and discharging atoms sum(n10, n8) = all_0_4_4, sum(n10, n8) = n7, yields:
% 12.58/3.56 | (284) all_0_4_4 = n7
% 12.58/3.56 |
% 12.58/3.56 | From (284) and (138) follows:
% 12.58/3.56 | (286) pred(n7) = all_0_3_3
% 12.58/3.56 |
% 12.58/3.56 | From (288) and (458) follows:
% 12.58/3.56 | (467) sum(n7, n5) = all_0_0_0
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (116) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 12.58/3.56 | (287) all_0_3_3 = n6
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (132) with n7, n5, all_0_0_0, n1 and discharging atoms sum(n7, n5) = all_0_0_0, sum(n7, n5) = n1, yields:
% 12.58/3.56 | (342) all_0_0_0 = n1
% 12.58/3.56 |
% 12.58/3.56 | From (287)(342) and (167) follows:
% 12.58/3.56 | (470) sum(n6, n1) = all_0_6_6
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (132) with n6, n1, all_0_6_6, n7 and discharging atoms sum(n6, n1) = all_0_6_6, sum(n6, n1) = n7, yields:
% 12.58/3.56 | (411) all_0_6_6 = n7
% 12.58/3.56 |
% 12.58/3.56 | Equations (411) can reduce 88 to:
% 12.58/3.56 | (243) $false
% 12.58/3.56 |
% 12.58/3.56 |-The branch is then unsatisfiable
% 12.58/3.56 |-Branch two:
% 12.58/3.56 | (473) ~ (all_0_7_7 = n7)
% 12.58/3.56 | (474) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 12.58/3.56 |
% 12.58/3.56 +-Applying beta-rule and splitting (474), into two cases.
% 12.58/3.56 |-Branch one:
% 12.58/3.56 | (475) all_0_7_7 = n6
% 12.58/3.56 |
% 12.58/3.56 | From (475) and (10) follows:
% 12.58/3.56 | (476) succ(n6) = all_0_5_5
% 12.58/3.56 |
% 12.58/3.56 | From (475) and (3) follows:
% 12.58/3.56 | (477) sum(n6, all_0_1_1) = all_0_0_0
% 12.58/3.56 |
% 12.58/3.56 | From (475) and (417) follows:
% 12.58/3.56 | (478) sum(n10, n6) = all_0_2_2
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (47) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 12.58/3.56 | (479) all_0_5_5 = n7
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (132) with n10, n6, all_0_2_2, n5 and discharging atoms sum(n10, n6) = all_0_2_2, sum(n10, n6) = n5, yields:
% 12.58/3.56 | (300) all_0_2_2 = n5
% 12.58/3.56 |
% 12.58/3.56 | From (300) and (205) follows:
% 12.58/3.56 | (302) pred(n5) = all_0_1_1
% 12.58/3.56 |
% 12.58/3.56 | From (479) and (416) follows:
% 12.58/3.56 | (482) sum(n10, n7) = all_0_4_4
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (116) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 12.58/3.56 | (305) all_0_1_1 = n4
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (132) with n10, n7, all_0_4_4, n6 and discharging atoms sum(n10, n7) = all_0_4_4, sum(n10, n7) = n6, yields:
% 12.58/3.56 | (301) all_0_4_4 = n6
% 12.58/3.56 |
% 12.58/3.56 | From (301) and (138) follows:
% 12.58/3.56 | (303) pred(n6) = all_0_3_3
% 12.58/3.56 |
% 12.58/3.56 | From (305) and (477) follows:
% 12.58/3.56 | (486) sum(n6, n4) = all_0_0_0
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (116) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 12.58/3.56 | (304) all_0_3_3 = n5
% 12.58/3.56 |
% 12.58/3.56 | Instantiating formula (132) with n6, n4, all_0_0_0, n10 and discharging atoms sum(n6, n4) = all_0_0_0, sum(n6, n4) = n10, yields:
% 12.58/3.57 | (376) all_0_0_0 = n10
% 12.58/3.57 |
% 12.58/3.57 | From (304)(376) and (167) follows:
% 12.58/3.57 | (489) sum(n5, n10) = all_0_6_6
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (132) with n5, n10, all_0_6_6, n4 and discharging atoms sum(n5, n10) = all_0_6_6, sum(n5, n10) = n4, yields:
% 12.58/3.57 | (344) all_0_6_6 = n4
% 12.58/3.57 |
% 12.58/3.57 | Equations (344) can reduce 216 to:
% 12.58/3.57 | (243) $false
% 12.58/3.57 |
% 12.58/3.57 |-The branch is then unsatisfiable
% 12.58/3.57 |-Branch two:
% 12.58/3.57 | (492) ~ (all_0_7_7 = n6)
% 12.58/3.57 | (493) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 12.58/3.57 |
% 12.58/3.57 +-Applying beta-rule and splitting (493), into two cases.
% 12.58/3.57 |-Branch one:
% 12.58/3.57 | (494) all_0_7_7 = n5
% 12.58/3.57 |
% 12.58/3.57 | From (494) and (10) follows:
% 12.58/3.57 | (495) succ(n5) = all_0_5_5
% 12.58/3.57 |
% 12.58/3.57 | From (494) and (3) follows:
% 12.58/3.57 | (496) sum(n5, all_0_1_1) = all_0_0_0
% 12.58/3.57 |
% 12.58/3.57 | From (494) and (417) follows:
% 12.58/3.57 | (497) sum(n10, n5) = all_0_2_2
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (47) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 12.58/3.57 | (498) all_0_5_5 = n6
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (132) with n10, n5, all_0_2_2, n4 and discharging atoms sum(n10, n5) = all_0_2_2, sum(n10, n5) = n4, yields:
% 12.58/3.57 | (317) all_0_2_2 = n4
% 12.58/3.57 |
% 12.58/3.57 | From (317) and (205) follows:
% 12.58/3.57 | (319) pred(n4) = all_0_1_1
% 12.58/3.57 |
% 12.58/3.57 | From (498) and (416) follows:
% 12.58/3.57 | (501) sum(n10, n6) = all_0_4_4
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (116) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 12.58/3.57 | (322) all_0_1_1 = n3
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (132) with n10, n6, all_0_4_4, n5 and discharging atoms sum(n10, n6) = all_0_4_4, sum(n10, n6) = n5, yields:
% 12.58/3.57 | (318) all_0_4_4 = n5
% 12.58/3.57 |
% 12.58/3.57 | From (318) and (138) follows:
% 12.58/3.57 | (320) pred(n5) = all_0_3_3
% 12.58/3.57 |
% 12.58/3.57 | From (322) and (496) follows:
% 12.58/3.57 | (505) sum(n5, n3) = all_0_0_0
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (116) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 12.58/3.57 | (321) all_0_3_3 = n4
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (132) with n5, n3, all_0_0_0, n8 and discharging atoms sum(n5, n3) = all_0_0_0, sum(n5, n3) = n8, yields:
% 12.58/3.57 | (409) all_0_0_0 = n8
% 12.58/3.57 |
% 12.58/3.57 | From (321)(409) and (167) follows:
% 12.58/3.57 | (508) sum(n4, n8) = all_0_6_6
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (132) with n4, n8, all_0_6_6, n1 and discharging atoms sum(n4, n8) = all_0_6_6, sum(n4, n8) = n1, yields:
% 12.58/3.57 | (276) all_0_6_6 = n1
% 12.58/3.57 |
% 12.58/3.57 | Equations (276) can reduce 28 to:
% 12.58/3.57 | (243) $false
% 12.58/3.57 |
% 12.58/3.57 |-The branch is then unsatisfiable
% 12.58/3.57 |-Branch two:
% 12.58/3.57 | (511) ~ (all_0_7_7 = n5)
% 12.58/3.57 | (512) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 12.58/3.57 |
% 12.58/3.57 +-Applying beta-rule and splitting (512), into two cases.
% 12.58/3.57 |-Branch one:
% 12.58/3.57 | (513) all_0_7_7 = n4
% 12.58/3.57 |
% 12.58/3.57 | From (513) and (10) follows:
% 12.58/3.57 | (514) succ(n4) = all_0_5_5
% 12.58/3.57 |
% 12.58/3.57 | From (513) and (3) follows:
% 12.58/3.57 | (515) sum(n4, all_0_1_1) = all_0_0_0
% 12.58/3.57 |
% 12.58/3.57 | From (513) and (417) follows:
% 12.58/3.57 | (516) sum(n10, n4) = all_0_2_2
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (47) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 12.58/3.57 | (517) all_0_5_5 = n5
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (132) with n10, n4, all_0_2_2, n3 and discharging atoms sum(n10, n4) = all_0_2_2, sum(n10, n4) = n3, yields:
% 12.58/3.57 | (334) all_0_2_2 = n3
% 12.58/3.57 |
% 12.58/3.57 | From (334) and (205) follows:
% 12.58/3.57 | (336) pred(n3) = all_0_1_1
% 12.58/3.57 |
% 12.58/3.57 | From (517) and (416) follows:
% 12.58/3.57 | (520) sum(n10, n5) = all_0_4_4
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (116) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 12.58/3.57 | (339) all_0_1_1 = n2
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (132) with n10, n5, all_0_4_4, n4 and discharging atoms sum(n10, n5) = all_0_4_4, sum(n10, n5) = n4, yields:
% 12.58/3.57 | (335) all_0_4_4 = n4
% 12.58/3.57 |
% 12.58/3.57 | From (335) and (138) follows:
% 12.58/3.57 | (337) pred(n4) = all_0_3_3
% 12.58/3.57 |
% 12.58/3.57 | From (339) and (515) follows:
% 12.58/3.57 | (524) sum(n4, n2) = all_0_0_0
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (116) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 12.58/3.57 | (338) all_0_3_3 = n3
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (132) with n4, n2, all_0_0_0, n6 and discharging atoms sum(n4, n2) = all_0_0_0, sum(n4, n2) = n6, yields:
% 12.58/3.57 | (257) all_0_0_0 = n6
% 12.58/3.57 |
% 12.58/3.57 | From (338)(257) and (167) follows:
% 12.58/3.57 | (527) sum(n3, n6) = all_0_6_6
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (132) with n3, n6, all_0_6_6, n9 and discharging atoms sum(n3, n6) = all_0_6_6, sum(n3, n6) = n9, yields:
% 12.58/3.57 | (395) all_0_6_6 = n9
% 12.58/3.57 |
% 12.58/3.57 | Equations (395) can reduce 78 to:
% 12.58/3.57 | (243) $false
% 12.58/3.57 |
% 12.58/3.57 |-The branch is then unsatisfiable
% 12.58/3.57 |-Branch two:
% 12.58/3.57 | (530) ~ (all_0_7_7 = n4)
% 12.58/3.57 | (531) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 12.58/3.57 |
% 12.58/3.57 +-Applying beta-rule and splitting (531), into two cases.
% 12.58/3.57 |-Branch one:
% 12.58/3.57 | (532) all_0_7_7 = n3
% 12.58/3.57 |
% 12.58/3.57 | From (532) and (10) follows:
% 12.58/3.57 | (533) succ(n3) = all_0_5_5
% 12.58/3.57 |
% 12.58/3.57 | From (532) and (3) follows:
% 12.58/3.57 | (534) sum(n3, all_0_1_1) = all_0_0_0
% 12.58/3.57 |
% 12.58/3.57 | From (532) and (417) follows:
% 12.58/3.57 | (535) sum(n10, n3) = all_0_2_2
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (47) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 12.58/3.57 | (536) all_0_5_5 = n4
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (132) with n10, n3, all_0_2_2, n2 and discharging atoms sum(n10, n3) = all_0_2_2, sum(n10, n3) = n2, yields:
% 12.58/3.57 | (351) all_0_2_2 = n2
% 12.58/3.57 |
% 12.58/3.57 | From (351) and (205) follows:
% 12.58/3.57 | (353) pred(n2) = all_0_1_1
% 12.58/3.57 |
% 12.58/3.57 | From (536) and (416) follows:
% 12.58/3.57 | (539) sum(n10, n4) = all_0_4_4
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (116) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 12.58/3.57 | (356) all_0_1_1 = n1
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (132) with n10, n4, all_0_4_4, n3 and discharging atoms sum(n10, n4) = all_0_4_4, sum(n10, n4) = n3, yields:
% 12.58/3.57 | (352) all_0_4_4 = n3
% 12.58/3.57 |
% 12.58/3.57 | From (352) and (138) follows:
% 12.58/3.57 | (354) pred(n3) = all_0_3_3
% 12.58/3.57 |
% 12.58/3.57 | From (356) and (534) follows:
% 12.58/3.57 | (543) sum(n3, n1) = all_0_0_0
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (116) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 12.58/3.57 | (355) all_0_3_3 = n2
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (132) with n3, n1, all_0_0_0, n4 and discharging atoms sum(n3, n1) = all_0_0_0, sum(n3, n1) = n4, yields:
% 12.58/3.57 | (291) all_0_0_0 = n4
% 12.58/3.57 |
% 12.58/3.57 | From (355)(291) and (167) follows:
% 12.58/3.57 | (546) sum(n2, n4) = all_0_6_6
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (132) with n2, n4, all_0_6_6, n6 and discharging atoms sum(n2, n4) = all_0_6_6, sum(n2, n4) = n6, yields:
% 12.58/3.57 | (327) all_0_6_6 = n6
% 12.58/3.57 |
% 12.58/3.57 | Equations (327) can reduce 34 to:
% 12.58/3.57 | (243) $false
% 12.58/3.57 |
% 12.58/3.57 |-The branch is then unsatisfiable
% 12.58/3.57 |-Branch two:
% 12.58/3.57 | (549) ~ (all_0_7_7 = n3)
% 12.58/3.57 | (550) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 12.58/3.57 |
% 12.58/3.57 +-Applying beta-rule and splitting (550), into two cases.
% 12.58/3.57 |-Branch one:
% 12.58/3.57 | (551) all_0_7_7 = n2
% 12.58/3.57 |
% 12.58/3.57 | From (551) and (10) follows:
% 12.58/3.57 | (552) succ(n2) = all_0_5_5
% 12.58/3.57 |
% 12.58/3.57 | From (551) and (3) follows:
% 12.58/3.57 | (553) sum(n2, all_0_1_1) = all_0_0_0
% 12.58/3.57 |
% 12.58/3.57 | From (551) and (417) follows:
% 12.58/3.57 | (554) sum(n10, n2) = all_0_2_2
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (47) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 12.58/3.57 | (555) all_0_5_5 = n3
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (132) with n10, n2, all_0_2_2, n1 and discharging atoms sum(n10, n2) = all_0_2_2, sum(n10, n2) = n1, yields:
% 12.58/3.57 | (368) all_0_2_2 = n1
% 12.58/3.57 |
% 12.58/3.57 | From (368) and (205) follows:
% 12.58/3.57 | (370) pred(n1) = all_0_1_1
% 12.58/3.57 |
% 12.58/3.57 | From (555) and (416) follows:
% 12.58/3.57 | (558) sum(n10, n3) = all_0_4_4
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (116) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 12.58/3.57 | (373) all_0_1_1 = n0
% 12.58/3.57 |
% 12.58/3.57 | Instantiating formula (132) with n10, n3, all_0_4_4, n2 and discharging atoms sum(n10, n3) = all_0_4_4, sum(n10, n3) = n2, yields:
% 12.58/3.57 | (369) all_0_4_4 = n2
% 12.58/3.57 |
% 12.58/3.57 | From (369) and (138) follows:
% 12.58/3.57 | (371) pred(n2) = all_0_3_3
% 12.58/3.58 |
% 12.58/3.58 | From (373) and (553) follows:
% 12.58/3.58 | (562) sum(n2, n0) = all_0_0_0
% 12.58/3.58 |
% 12.58/3.58 | Instantiating formula (116) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 12.58/3.58 | (372) all_0_3_3 = n1
% 12.58/3.58 |
% 12.58/3.58 | Instantiating formula (132) with n2, n0, all_0_0_0, n2 and discharging atoms sum(n2, n0) = all_0_0_0, sum(n2, n0) = n2, yields:
% 12.58/3.58 | (325) all_0_0_0 = n2
% 12.58/3.58 |
% 12.58/3.58 | From (372)(325) and (167) follows:
% 12.58/3.58 | (565) sum(n1, n2) = all_0_6_6
% 12.58/3.58 |
% 12.58/3.58 | Instantiating formula (132) with n1, n2, all_0_6_6, n3 and discharging atoms sum(n1, n2) = all_0_6_6, sum(n1, n2) = n3, yields:
% 12.58/3.58 | (259) all_0_6_6 = n3
% 12.58/3.58 |
% 12.58/3.58 | Equations (259) can reduce 100 to:
% 12.58/3.58 | (243) $false
% 12.58/3.58 |
% 12.58/3.58 |-The branch is then unsatisfiable
% 12.58/3.58 |-Branch two:
% 12.58/3.58 | (568) ~ (all_0_7_7 = n2)
% 12.58/3.58 | (569) all_0_7_7 = n1 | all_0_7_7 = n0
% 12.58/3.58 |
% 12.58/3.58 +-Applying beta-rule and splitting (569), into two cases.
% 12.58/3.58 |-Branch one:
% 12.58/3.58 | (570) all_0_7_7 = n1
% 12.58/3.58 |
% 12.58/3.58 | From (570) and (10) follows:
% 12.58/3.58 | (571) succ(n1) = all_0_5_5
% 12.58/3.58 |
% 12.58/3.58 | From (570) and (3) follows:
% 12.58/3.58 | (572) sum(n1, all_0_1_1) = all_0_0_0
% 12.58/3.58 |
% 12.58/3.58 | From (570) and (417) follows:
% 12.58/3.58 | (573) sum(n10, n1) = all_0_2_2
% 12.58/3.58 |
% 12.58/3.58 | Instantiating formula (47) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 12.58/3.58 | (574) all_0_5_5 = n2
% 12.58/3.58 |
% 12.58/3.58 | Instantiating formula (132) with n10, n1, all_0_2_2, n0 and discharging atoms sum(n10, n1) = all_0_2_2, sum(n10, n1) = n0, yields:
% 12.58/3.58 | (385) all_0_2_2 = n0
% 12.58/3.58 |
% 12.58/3.58 | From (385) and (205) follows:
% 12.58/3.58 | (387) pred(n0) = all_0_1_1
% 12.58/3.58 |
% 12.58/3.58 | From (574) and (416) follows:
% 12.58/3.58 | (577) sum(n10, n2) = all_0_4_4
% 12.58/3.58 |
% 12.58/3.58 | Instantiating formula (116) with n0, all_0_1_1, n10 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n10, yields:
% 12.58/3.58 | (390) all_0_1_1 = n10
% 12.58/3.58 |
% 12.58/3.58 | Instantiating formula (132) with n10, n2, all_0_4_4, n1 and discharging atoms sum(n10, n2) = all_0_4_4, sum(n10, n2) = n1, yields:
% 12.58/3.58 | (386) all_0_4_4 = n1
% 12.58/3.58 |
% 12.58/3.58 | From (386) and (138) follows:
% 12.58/3.58 | (388) pred(n1) = all_0_3_3
% 12.58/3.58 |
% 12.58/3.58 | From (390) and (572) follows:
% 12.58/3.58 | (581) sum(n1, n10) = all_0_0_0
% 12.58/3.58 |
% 12.58/3.58 | Instantiating formula (116) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 12.58/3.58 | (389) all_0_3_3 = n0
% 12.58/3.58 |
% 12.58/3.58 | Instantiating formula (132) with n1, n10, all_0_0_0, n0 and discharging atoms sum(n1, n10) = all_0_0_0, sum(n1, n10) = n0, yields:
% 12.58/3.58 | (359) all_0_0_0 = n0
% 12.58/3.58 |
% 12.58/3.58 | From (389)(359) and (167) follows:
% 12.58/3.58 | (584) sum(n0, n0) = all_0_6_6
% 12.58/3.58 |
% 12.58/3.58 | Instantiating formula (132) with n0, n0, all_0_6_6, n0 and discharging atoms sum(n0, n0) = all_0_6_6, sum(n0, n0) = n0, yields:
% 12.58/3.58 | (378) all_0_6_6 = n0
% 12.58/3.58 |
% 12.58/3.58 | Equations (378) can reduce 119 to:
% 12.58/3.58 | (243) $false
% 12.58/3.58 |
% 12.58/3.58 |-The branch is then unsatisfiable
% 12.58/3.58 |-Branch two:
% 12.58/3.58 | (587) ~ (all_0_7_7 = n1)
% 12.58/3.58 | (588) all_0_7_7 = n0
% 12.58/3.58 |
% 12.58/3.58 | From (588) and (10) follows:
% 12.58/3.58 | (589) succ(n0) = all_0_5_5
% 12.58/3.58 |
% 12.58/3.58 | From (588) and (3) follows:
% 12.58/3.58 | (590) sum(n0, all_0_1_1) = all_0_0_0
% 12.58/3.58 |
% 12.58/3.58 | From (588) and (417) follows:
% 12.58/3.58 | (591) sum(n10, n0) = all_0_2_2
% 12.58/3.58 |
% 12.58/3.58 | Instantiating formula (47) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 12.58/3.58 | (592) all_0_5_5 = n1
% 12.58/3.58 |
% 12.58/3.58 | Instantiating formula (132) with n10, n0, all_0_2_2, n10 and discharging atoms sum(n10, n0) = all_0_2_2, sum(n10, n0) = n10, yields:
% 12.58/3.58 | (401) all_0_2_2 = n10
% 12.58/3.58 |
% 12.58/3.58 | From (401) and (205) follows:
% 12.58/3.58 | (403) pred(n10) = all_0_1_1
% 12.58/3.58 |
% 12.58/3.58 | From (592) and (416) follows:
% 12.58/3.58 | (595) sum(n10, n1) = all_0_4_4
% 12.58/3.58 |
% 12.58/3.58 | Instantiating formula (116) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 12.58/3.58 | (405) all_0_1_1 = n9
% 12.58/3.58 |
% 12.58/3.58 | Instantiating formula (132) with n10, n1, all_0_4_4, n0 and discharging atoms sum(n10, n1) = all_0_4_4, sum(n10, n1) = n0, yields:
% 12.58/3.58 | (402) all_0_4_4 = n0
% 12.58/3.58 |
% 12.58/3.58 | From (402) and (138) follows:
% 12.58/3.58 | (404) pred(n0) = all_0_3_3
% 12.58/3.58 |
% 12.58/3.58 | From (405) and (590) follows:
% 12.58/3.58 | (599) sum(n0, n9) = all_0_0_0
% 12.58/3.58 |
% 12.58/3.58 | Instantiating formula (116) with n0, all_0_3_3, n10 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n10, yields:
% 12.58/3.58 | (406) all_0_3_3 = n10
% 12.58/3.58 |
% 12.58/3.58 | Instantiating formula (132) with n0, n9, all_0_0_0, n9 and discharging atoms sum(n0, n9) = all_0_0_0, sum(n0, n9) = n9, yields:
% 12.58/3.58 | (393) all_0_0_0 = n9
% 12.58/3.58 |
% 12.58/3.58 | From (406)(393) and (167) follows:
% 13.15/3.58 | (602) sum(n10, n9) = all_0_6_6
% 13.15/3.58 |
% 13.15/3.58 | Instantiating formula (132) with n10, n9, all_0_6_6, n8 and discharging atoms sum(n10, n9) = all_0_6_6, sum(n10, n9) = n8, yields:
% 13.15/3.58 | (310) all_0_6_6 = n8
% 13.15/3.58 |
% 13.15/3.58 | Equations (310) can reduce 165 to:
% 13.15/3.58 | (243) $false
% 13.15/3.58 |
% 13.15/3.58 |-The branch is then unsatisfiable
% 13.15/3.58 |-Branch two:
% 13.15/3.58 | (244) ~ (all_0_8_8 = n10)
% 13.15/3.58 | (245) all_0_8_8 = n9 | all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.15/3.58 |
% 13.15/3.58 +-Applying beta-rule and splitting (414), into two cases.
% 13.15/3.58 |-Branch one:
% 13.15/3.58 | (418) all_0_7_7 = n9
% 13.15/3.58 |
% 13.15/3.58 | From (418) and (10) follows:
% 13.15/3.58 | (419) succ(n9) = all_0_5_5
% 13.15/3.58 |
% 13.15/3.58 | From (418) and (3) follows:
% 13.15/3.58 | (420) sum(n9, all_0_1_1) = all_0_0_0
% 13.15/3.58 |
% 13.15/3.58 | From (418) and (120) follows:
% 13.15/3.58 | (610) sum(all_0_8_8, n9) = all_0_2_2
% 13.15/3.58 |
% 13.15/3.58 | Instantiating formula (47) with n9, all_0_5_5, n10 and discharging atoms succ(n9) = all_0_5_5, succ(n9) = n10, yields:
% 13.15/3.58 | (422) all_0_5_5 = n10
% 13.15/3.58 |
% 13.15/3.58 | From (422) and (77) follows:
% 13.15/3.58 | (612) sum(all_0_8_8, n10) = all_0_4_4
% 13.15/3.58 |
% 13.15/3.58 +-Applying beta-rule and splitting (245), into two cases.
% 13.15/3.58 |-Branch one:
% 13.15/3.58 | (246) all_0_8_8 = n9
% 13.15/3.58 |
% 13.15/3.58 | From (246) and (612) follows:
% 13.15/3.58 | (614) sum(n9, n10) = all_0_4_4
% 13.15/3.58 |
% 13.15/3.58 | From (246) and (610) follows:
% 13.15/3.58 | (615) sum(n9, n9) = all_0_2_2
% 13.15/3.58 |
% 13.15/3.58 | Instantiating formula (132) with n9, n10, all_0_4_4, n8 and discharging atoms sum(n9, n10) = all_0_4_4, sum(n9, n10) = n8, yields:
% 13.15/3.58 | (267) all_0_4_4 = n8
% 13.15/3.58 |
% 13.15/3.58 | Instantiating formula (132) with n9, n9, all_0_2_2, n7 and discharging atoms sum(n9, n9) = all_0_2_2, sum(n9, n9) = n7, yields:
% 13.15/3.58 | (266) all_0_2_2 = n7
% 13.15/3.58 |
% 13.15/3.58 | From (266) and (205) follows:
% 13.15/3.58 | (268) pred(n7) = all_0_1_1
% 13.15/3.58 |
% 13.15/3.58 | From (267) and (138) follows:
% 13.15/3.58 | (269) pred(n8) = all_0_3_3
% 13.15/3.58 |
% 13.15/3.58 | Instantiating formula (116) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 13.15/3.58 | (270) all_0_3_3 = n7
% 13.15/3.58 |
% 13.15/3.58 | Instantiating formula (116) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 13.15/3.58 | (271) all_0_1_1 = n6
% 13.15/3.58 |
% 13.15/3.58 | From (270) and (167) follows:
% 13.15/3.58 | (272) sum(n7, all_0_0_0) = all_0_6_6
% 13.15/3.58 |
% 13.15/3.58 | From (271) and (420) follows:
% 13.15/3.58 | (623) sum(n9, n6) = all_0_0_0
% 13.15/3.58 |
% 13.15/3.58 | Instantiating formula (132) with n9, n6, all_0_0_0, n4 and discharging atoms sum(n9, n6) = all_0_0_0, sum(n9, n6) = n4, yields:
% 13.15/3.58 | (291) all_0_0_0 = n4
% 13.15/3.58 |
% 13.15/3.58 | From (291) and (272) follows:
% 13.15/3.58 | (625) sum(n7, n4) = all_0_6_6
% 13.15/3.58 |
% 13.15/3.58 | Instantiating formula (132) with n7, n4, all_0_6_6, n0 and discharging atoms sum(n7, n4) = all_0_6_6, sum(n7, n4) = n0, yields:
% 13.15/3.58 | (378) all_0_6_6 = n0
% 13.15/3.58 |
% 13.15/3.58 | Equations (378) can reduce 119 to:
% 13.15/3.58 | (243) $false
% 13.15/3.58 |
% 13.15/3.58 |-The branch is then unsatisfiable
% 13.15/3.58 |-Branch two:
% 13.15/3.58 | (261) ~ (all_0_8_8 = n9)
% 13.15/3.58 | (262) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.15/3.58 |
% 13.15/3.58 +-Applying beta-rule and splitting (262), into two cases.
% 13.15/3.58 |-Branch one:
% 13.15/3.58 | (263) all_0_8_8 = n8
% 13.15/3.58 |
% 13.15/3.58 | From (263) and (612) follows:
% 13.15/3.58 | (631) sum(n8, n10) = all_0_4_4
% 13.15/3.58 |
% 13.15/3.58 | From (263) and (610) follows:
% 13.15/3.58 | (632) sum(n8, n9) = all_0_2_2
% 13.15/3.58 |
% 13.15/3.58 | Instantiating formula (132) with n8, n10, all_0_4_4, n7 and discharging atoms sum(n8, n10) = all_0_4_4, sum(n8, n10) = n7, yields:
% 13.15/3.58 | (284) all_0_4_4 = n7
% 13.15/3.58 |
% 13.15/3.58 | Instantiating formula (132) with n8, n9, all_0_2_2, n6 and discharging atoms sum(n8, n9) = all_0_2_2, sum(n8, n9) = n6, yields:
% 13.15/3.58 | (283) all_0_2_2 = n6
% 13.15/3.58 |
% 13.15/3.58 | From (283) and (205) follows:
% 13.15/3.58 | (285) pred(n6) = all_0_1_1
% 13.15/3.58 |
% 13.15/3.58 | From (284) and (138) follows:
% 13.15/3.58 | (286) pred(n7) = all_0_3_3
% 13.15/3.58 |
% 13.15/3.58 | Instantiating formula (116) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 13.15/3.59 | (287) all_0_3_3 = n6
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (116) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 13.15/3.59 | (288) all_0_1_1 = n5
% 13.15/3.59 |
% 13.15/3.59 | From (287) and (167) follows:
% 13.15/3.59 | (289) sum(n6, all_0_0_0) = all_0_6_6
% 13.15/3.59 |
% 13.15/3.59 | From (288) and (420) follows:
% 13.15/3.59 | (640) sum(n9, n5) = all_0_0_0
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n9, n5, all_0_0_0, n3 and discharging atoms sum(n9, n5) = all_0_0_0, sum(n9, n5) = n3, yields:
% 13.15/3.59 | (308) all_0_0_0 = n3
% 13.15/3.59 |
% 13.15/3.59 | From (308) and (289) follows:
% 13.15/3.59 | (642) sum(n6, n3) = all_0_6_6
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n6, n3, all_0_6_6, n9 and discharging atoms sum(n6, n3) = all_0_6_6, sum(n6, n3) = n9, yields:
% 13.15/3.59 | (395) all_0_6_6 = n9
% 13.15/3.59 |
% 13.15/3.59 | Equations (395) can reduce 78 to:
% 13.15/3.59 | (243) $false
% 13.15/3.59 |
% 13.15/3.59 |-The branch is then unsatisfiable
% 13.15/3.59 |-Branch two:
% 13.15/3.59 | (278) ~ (all_0_8_8 = n8)
% 13.15/3.59 | (279) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.15/3.59 |
% 13.15/3.59 +-Applying beta-rule and splitting (279), into two cases.
% 13.15/3.59 |-Branch one:
% 13.15/3.59 | (280) all_0_8_8 = n7
% 13.15/3.59 |
% 13.15/3.59 | From (280) and (612) follows:
% 13.15/3.59 | (648) sum(n7, n10) = all_0_4_4
% 13.15/3.59 |
% 13.15/3.59 | From (280) and (610) follows:
% 13.15/3.59 | (649) sum(n7, n9) = all_0_2_2
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n7, n10, all_0_4_4, n6 and discharging atoms sum(n7, n10) = all_0_4_4, sum(n7, n10) = n6, yields:
% 13.15/3.59 | (301) all_0_4_4 = n6
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n7, n9, all_0_2_2, n5 and discharging atoms sum(n7, n9) = all_0_2_2, sum(n7, n9) = n5, yields:
% 13.15/3.59 | (300) all_0_2_2 = n5
% 13.15/3.59 |
% 13.15/3.59 | From (300) and (205) follows:
% 13.15/3.59 | (302) pred(n5) = all_0_1_1
% 13.15/3.59 |
% 13.15/3.59 | From (301) and (138) follows:
% 13.15/3.59 | (303) pred(n6) = all_0_3_3
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (116) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 13.15/3.59 | (304) all_0_3_3 = n5
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (116) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 13.15/3.59 | (305) all_0_1_1 = n4
% 13.15/3.59 |
% 13.15/3.59 | From (304) and (167) follows:
% 13.15/3.59 | (306) sum(n5, all_0_0_0) = all_0_6_6
% 13.15/3.59 |
% 13.15/3.59 | From (305) and (420) follows:
% 13.15/3.59 | (657) sum(n9, n4) = all_0_0_0
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n9, n4, all_0_0_0, n2 and discharging atoms sum(n9, n4) = all_0_0_0, sum(n9, n4) = n2, yields:
% 13.15/3.59 | (325) all_0_0_0 = n2
% 13.15/3.59 |
% 13.15/3.59 | From (325) and (306) follows:
% 13.15/3.59 | (659) sum(n5, n2) = all_0_6_6
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n5, n2, all_0_6_6, n7 and discharging atoms sum(n5, n2) = all_0_6_6, sum(n5, n2) = n7, yields:
% 13.15/3.59 | (411) all_0_6_6 = n7
% 13.15/3.59 |
% 13.15/3.59 | Equations (411) can reduce 88 to:
% 13.15/3.59 | (243) $false
% 13.15/3.59 |
% 13.15/3.59 |-The branch is then unsatisfiable
% 13.15/3.59 |-Branch two:
% 13.15/3.59 | (295) ~ (all_0_8_8 = n7)
% 13.15/3.59 | (296) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.15/3.59 |
% 13.15/3.59 +-Applying beta-rule and splitting (296), into two cases.
% 13.15/3.59 |-Branch one:
% 13.15/3.59 | (297) all_0_8_8 = n6
% 13.15/3.59 |
% 13.15/3.59 | From (297) and (612) follows:
% 13.15/3.59 | (665) sum(n6, n10) = all_0_4_4
% 13.15/3.59 |
% 13.15/3.59 | From (297) and (610) follows:
% 13.15/3.59 | (666) sum(n6, n9) = all_0_2_2
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n6, n10, all_0_4_4, n5 and discharging atoms sum(n6, n10) = all_0_4_4, sum(n6, n10) = n5, yields:
% 13.15/3.59 | (318) all_0_4_4 = n5
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n6, n9, all_0_2_2, n4 and discharging atoms sum(n6, n9) = all_0_2_2, sum(n6, n9) = n4, yields:
% 13.15/3.59 | (317) all_0_2_2 = n4
% 13.15/3.59 |
% 13.15/3.59 | From (317) and (205) follows:
% 13.15/3.59 | (319) pred(n4) = all_0_1_1
% 13.15/3.59 |
% 13.15/3.59 | From (318) and (138) follows:
% 13.15/3.59 | (320) pred(n5) = all_0_3_3
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (116) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 13.15/3.59 | (321) all_0_3_3 = n4
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (116) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 13.15/3.59 | (322) all_0_1_1 = n3
% 13.15/3.59 |
% 13.15/3.59 | From (321) and (167) follows:
% 13.15/3.59 | (323) sum(n4, all_0_0_0) = all_0_6_6
% 13.15/3.59 |
% 13.15/3.59 | From (322) and (420) follows:
% 13.15/3.59 | (674) sum(n9, n3) = all_0_0_0
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n9, n3, all_0_0_0, n1 and discharging atoms sum(n9, n3) = all_0_0_0, sum(n9, n3) = n1, yields:
% 13.15/3.59 | (342) all_0_0_0 = n1
% 13.15/3.59 |
% 13.15/3.59 | From (342) and (323) follows:
% 13.15/3.59 | (676) sum(n4, n1) = all_0_6_6
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n4, n1, all_0_6_6, n5 and discharging atoms sum(n4, n1) = all_0_6_6, sum(n4, n1) = n5, yields:
% 13.15/3.59 | (242) all_0_6_6 = n5
% 13.15/3.59 |
% 13.15/3.59 | Equations (242) can reduce 4 to:
% 13.15/3.59 | (243) $false
% 13.15/3.59 |
% 13.15/3.59 |-The branch is then unsatisfiable
% 13.15/3.59 |-Branch two:
% 13.15/3.59 | (312) ~ (all_0_8_8 = n6)
% 13.15/3.59 | (313) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.15/3.59 |
% 13.15/3.59 +-Applying beta-rule and splitting (313), into two cases.
% 13.15/3.59 |-Branch one:
% 13.15/3.59 | (314) all_0_8_8 = n5
% 13.15/3.59 |
% 13.15/3.59 | From (314) and (612) follows:
% 13.15/3.59 | (682) sum(n5, n10) = all_0_4_4
% 13.15/3.59 |
% 13.15/3.59 | From (314) and (610) follows:
% 13.15/3.59 | (683) sum(n5, n9) = all_0_2_2
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n5, n10, all_0_4_4, n4 and discharging atoms sum(n5, n10) = all_0_4_4, sum(n5, n10) = n4, yields:
% 13.15/3.59 | (335) all_0_4_4 = n4
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n5, n9, all_0_2_2, n3 and discharging atoms sum(n5, n9) = all_0_2_2, sum(n5, n9) = n3, yields:
% 13.15/3.59 | (334) all_0_2_2 = n3
% 13.15/3.59 |
% 13.15/3.59 | From (334) and (205) follows:
% 13.15/3.59 | (336) pred(n3) = all_0_1_1
% 13.15/3.59 |
% 13.15/3.59 | From (335) and (138) follows:
% 13.15/3.59 | (337) pred(n4) = all_0_3_3
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (116) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 13.15/3.59 | (338) all_0_3_3 = n3
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (116) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 13.15/3.59 | (339) all_0_1_1 = n2
% 13.15/3.59 |
% 13.15/3.59 | From (338) and (167) follows:
% 13.15/3.59 | (340) sum(n3, all_0_0_0) = all_0_6_6
% 13.15/3.59 |
% 13.15/3.59 | From (339) and (420) follows:
% 13.15/3.59 | (691) sum(n9, n2) = all_0_0_0
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n9, n2, all_0_0_0, n0 and discharging atoms sum(n9, n2) = all_0_0_0, sum(n9, n2) = n0, yields:
% 13.15/3.59 | (359) all_0_0_0 = n0
% 13.15/3.59 |
% 13.15/3.59 | From (359) and (340) follows:
% 13.15/3.59 | (693) sum(n3, n0) = all_0_6_6
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n3, n0, all_0_6_6, n3 and discharging atoms sum(n3, n0) = all_0_6_6, sum(n3, n0) = n3, yields:
% 13.15/3.59 | (259) all_0_6_6 = n3
% 13.15/3.59 |
% 13.15/3.59 | Equations (259) can reduce 100 to:
% 13.15/3.59 | (243) $false
% 13.15/3.59 |
% 13.15/3.59 |-The branch is then unsatisfiable
% 13.15/3.59 |-Branch two:
% 13.15/3.59 | (329) ~ (all_0_8_8 = n5)
% 13.15/3.59 | (330) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.15/3.59 |
% 13.15/3.59 +-Applying beta-rule and splitting (330), into two cases.
% 13.15/3.59 |-Branch one:
% 13.15/3.59 | (331) all_0_8_8 = n4
% 13.15/3.59 |
% 13.15/3.59 | From (331) and (612) follows:
% 13.15/3.59 | (699) sum(n4, n10) = all_0_4_4
% 13.15/3.59 |
% 13.15/3.59 | From (331) and (610) follows:
% 13.15/3.59 | (700) sum(n4, n9) = all_0_2_2
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n4, n10, all_0_4_4, n3 and discharging atoms sum(n4, n10) = all_0_4_4, sum(n4, n10) = n3, yields:
% 13.15/3.59 | (352) all_0_4_4 = n3
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n4, n9, all_0_2_2, n2 and discharging atoms sum(n4, n9) = all_0_2_2, sum(n4, n9) = n2, yields:
% 13.15/3.59 | (351) all_0_2_2 = n2
% 13.15/3.59 |
% 13.15/3.59 | From (351) and (205) follows:
% 13.15/3.59 | (353) pred(n2) = all_0_1_1
% 13.15/3.59 |
% 13.15/3.59 | From (352) and (138) follows:
% 13.15/3.59 | (354) pred(n3) = all_0_3_3
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (116) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 13.15/3.59 | (355) all_0_3_3 = n2
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (116) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 13.15/3.59 | (356) all_0_1_1 = n1
% 13.15/3.59 |
% 13.15/3.59 | From (355) and (167) follows:
% 13.15/3.59 | (357) sum(n2, all_0_0_0) = all_0_6_6
% 13.15/3.59 |
% 13.15/3.59 | From (356) and (420) follows:
% 13.15/3.59 | (708) sum(n9, n1) = all_0_0_0
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n9, n1, all_0_0_0, n10 and discharging atoms sum(n9, n1) = all_0_0_0, sum(n9, n1) = n10, yields:
% 13.15/3.59 | (376) all_0_0_0 = n10
% 13.15/3.59 |
% 13.15/3.59 | From (376) and (357) follows:
% 13.15/3.59 | (710) sum(n2, n10) = all_0_6_6
% 13.15/3.59 |
% 13.15/3.59 | Instantiating formula (132) with n2, n10, all_0_6_6, n1 and discharging atoms sum(n2, n10) = all_0_6_6, sum(n2, n10) = n1, yields:
% 13.15/3.59 | (276) all_0_6_6 = n1
% 13.15/3.59 |
% 13.15/3.59 | Equations (276) can reduce 28 to:
% 13.15/3.59 | (243) $false
% 13.15/3.59 |
% 13.15/3.59 |-The branch is then unsatisfiable
% 13.15/3.59 |-Branch two:
% 13.15/3.59 | (346) ~ (all_0_8_8 = n4)
% 13.15/3.59 | (347) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.15/3.59 |
% 13.15/3.59 +-Applying beta-rule and splitting (347), into two cases.
% 13.15/3.59 |-Branch one:
% 13.15/3.59 | (348) all_0_8_8 = n3
% 13.15/3.59 |
% 13.15/3.59 | From (348) and (612) follows:
% 13.15/3.59 | (716) sum(n3, n10) = all_0_4_4
% 13.15/3.59 |
% 13.15/3.59 | From (348) and (610) follows:
% 13.15/3.59 | (717) sum(n3, n9) = all_0_2_2
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n3, n10, all_0_4_4, n2 and discharging atoms sum(n3, n10) = all_0_4_4, sum(n3, n10) = n2, yields:
% 13.15/3.60 | (369) all_0_4_4 = n2
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n3, n9, all_0_2_2, n1 and discharging atoms sum(n3, n9) = all_0_2_2, sum(n3, n9) = n1, yields:
% 13.15/3.60 | (368) all_0_2_2 = n1
% 13.15/3.60 |
% 13.15/3.60 | From (368) and (205) follows:
% 13.15/3.60 | (370) pred(n1) = all_0_1_1
% 13.15/3.60 |
% 13.15/3.60 | From (369) and (138) follows:
% 13.15/3.60 | (371) pred(n2) = all_0_3_3
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (116) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 13.15/3.60 | (372) all_0_3_3 = n1
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (116) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 13.15/3.60 | (373) all_0_1_1 = n0
% 13.15/3.60 |
% 13.15/3.60 | From (372) and (167) follows:
% 13.15/3.60 | (374) sum(n1, all_0_0_0) = all_0_6_6
% 13.15/3.60 |
% 13.15/3.60 | From (373) and (420) follows:
% 13.15/3.60 | (725) sum(n9, n0) = all_0_0_0
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n9, n0, all_0_0_0, n9 and discharging atoms sum(n9, n0) = all_0_0_0, sum(n9, n0) = n9, yields:
% 13.15/3.60 | (393) all_0_0_0 = n9
% 13.15/3.60 |
% 13.15/3.60 | From (393) and (374) follows:
% 13.15/3.60 | (727) sum(n1, n9) = all_0_6_6
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n1, n9, all_0_6_6, n10 and discharging atoms sum(n1, n9) = all_0_6_6, sum(n1, n9) = n10, yields:
% 13.15/3.60 | (293) all_0_6_6 = n10
% 13.15/3.60 |
% 13.15/3.60 | Equations (293) can reduce 147 to:
% 13.15/3.60 | (243) $false
% 13.15/3.60 |
% 13.15/3.60 |-The branch is then unsatisfiable
% 13.15/3.60 |-Branch two:
% 13.15/3.60 | (363) ~ (all_0_8_8 = n3)
% 13.15/3.60 | (364) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.15/3.60 |
% 13.15/3.60 +-Applying beta-rule and splitting (364), into two cases.
% 13.15/3.60 |-Branch one:
% 13.15/3.60 | (365) all_0_8_8 = n2
% 13.15/3.60 |
% 13.15/3.60 | From (365) and (612) follows:
% 13.15/3.60 | (733) sum(n2, n10) = all_0_4_4
% 13.15/3.60 |
% 13.15/3.60 | From (365) and (610) follows:
% 13.15/3.60 | (734) sum(n2, n9) = all_0_2_2
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n2, n10, all_0_4_4, n1 and discharging atoms sum(n2, n10) = all_0_4_4, sum(n2, n10) = n1, yields:
% 13.15/3.60 | (386) all_0_4_4 = n1
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n2, n9, all_0_2_2, n0 and discharging atoms sum(n2, n9) = all_0_2_2, sum(n2, n9) = n0, yields:
% 13.15/3.60 | (385) all_0_2_2 = n0
% 13.15/3.60 |
% 13.15/3.60 | From (385) and (205) follows:
% 13.15/3.60 | (387) pred(n0) = all_0_1_1
% 13.15/3.60 |
% 13.15/3.60 | From (386) and (138) follows:
% 13.15/3.60 | (388) pred(n1) = all_0_3_3
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (116) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 13.15/3.60 | (389) all_0_3_3 = n0
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (116) with n0, all_0_1_1, n10 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n10, yields:
% 13.15/3.60 | (390) all_0_1_1 = n10
% 13.15/3.60 |
% 13.15/3.60 | From (389) and (167) follows:
% 13.15/3.60 | (391) sum(n0, all_0_0_0) = all_0_6_6
% 13.15/3.60 |
% 13.15/3.60 | From (390) and (420) follows:
% 13.15/3.60 | (742) sum(n9, n10) = all_0_0_0
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n9, n10, all_0_0_0, n8 and discharging atoms sum(n9, n10) = all_0_0_0, sum(n9, n10) = n8, yields:
% 13.15/3.60 | (409) all_0_0_0 = n8
% 13.15/3.60 |
% 13.15/3.60 | From (409) and (391) follows:
% 13.15/3.60 | (744) sum(n0, n8) = all_0_6_6
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n0, n8, all_0_6_6, n8 and discharging atoms sum(n0, n8) = all_0_6_6, sum(n0, n8) = n8, yields:
% 13.15/3.60 | (310) all_0_6_6 = n8
% 13.15/3.60 |
% 13.15/3.60 | Equations (310) can reduce 165 to:
% 13.15/3.60 | (243) $false
% 13.15/3.60 |
% 13.15/3.60 |-The branch is then unsatisfiable
% 13.15/3.60 |-Branch two:
% 13.15/3.60 | (380) ~ (all_0_8_8 = n2)
% 13.15/3.60 | (381) all_0_8_8 = n1 | all_0_8_8 = n0
% 13.15/3.60 |
% 13.15/3.60 +-Applying beta-rule and splitting (381), into two cases.
% 13.15/3.60 |-Branch one:
% 13.15/3.60 | (382) all_0_8_8 = n1
% 13.15/3.60 |
% 13.15/3.60 | From (382) and (612) follows:
% 13.15/3.60 | (750) sum(n1, n10) = all_0_4_4
% 13.15/3.60 |
% 13.15/3.60 | From (382) and (610) follows:
% 13.15/3.60 | (751) sum(n1, n9) = all_0_2_2
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n1, n10, all_0_4_4, n0 and discharging atoms sum(n1, n10) = all_0_4_4, sum(n1, n10) = n0, yields:
% 13.15/3.60 | (402) all_0_4_4 = n0
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n1, n9, all_0_2_2, n10 and discharging atoms sum(n1, n9) = all_0_2_2, sum(n1, n9) = n10, yields:
% 13.15/3.60 | (401) all_0_2_2 = n10
% 13.15/3.60 |
% 13.15/3.60 | From (401) and (205) follows:
% 13.15/3.60 | (403) pred(n10) = all_0_1_1
% 13.15/3.60 |
% 13.15/3.60 | From (402) and (138) follows:
% 13.15/3.60 | (404) pred(n0) = all_0_3_3
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (116) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 13.15/3.60 | (405) all_0_1_1 = n9
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (116) with n0, all_0_3_3, n10 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n10, yields:
% 13.15/3.60 | (406) all_0_3_3 = n10
% 13.15/3.60 |
% 13.15/3.60 | From (406) and (167) follows:
% 13.15/3.60 | (407) sum(n10, all_0_0_0) = all_0_6_6
% 13.15/3.60 |
% 13.15/3.60 | From (405) and (420) follows:
% 13.15/3.60 | (759) sum(n9, n9) = all_0_0_0
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n9, n9, all_0_0_0, n7 and discharging atoms sum(n9, n9) = all_0_0_0, sum(n9, n9) = n7, yields:
% 13.15/3.60 | (240) all_0_0_0 = n7
% 13.15/3.60 |
% 13.15/3.60 | From (240) and (407) follows:
% 13.15/3.60 | (761) sum(n10, n7) = all_0_6_6
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n10, n7, all_0_6_6, n6 and discharging atoms sum(n10, n7) = all_0_6_6, sum(n10, n7) = n6, yields:
% 13.15/3.60 | (327) all_0_6_6 = n6
% 13.15/3.60 |
% 13.15/3.60 | Equations (327) can reduce 34 to:
% 13.15/3.60 | (243) $false
% 13.15/3.60 |
% 13.15/3.60 |-The branch is then unsatisfiable
% 13.15/3.60 |-Branch two:
% 13.15/3.60 | (397) ~ (all_0_8_8 = n1)
% 13.15/3.60 | (398) all_0_8_8 = n0
% 13.15/3.60 |
% 13.15/3.60 | From (398) and (612) follows:
% 13.15/3.60 | (766) sum(n0, n10) = all_0_4_4
% 13.15/3.60 |
% 13.15/3.60 | From (398) and (610) follows:
% 13.15/3.60 | (767) sum(n0, n9) = all_0_2_2
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n0, n10, all_0_4_4, n10 and discharging atoms sum(n0, n10) = all_0_4_4, sum(n0, n10) = n10, yields:
% 13.15/3.60 | (233) all_0_4_4 = n10
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n0, n9, all_0_2_2, n9 and discharging atoms sum(n0, n9) = all_0_2_2, sum(n0, n9) = n9, yields:
% 13.15/3.60 | (232) all_0_2_2 = n9
% 13.15/3.60 |
% 13.15/3.60 | From (232) and (205) follows:
% 13.15/3.60 | (234) pred(n9) = all_0_1_1
% 13.15/3.60 |
% 13.15/3.60 | From (233) and (138) follows:
% 13.15/3.60 | (235) pred(n10) = all_0_3_3
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (116) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 13.15/3.60 | (236) all_0_3_3 = n9
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (116) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 13.15/3.60 | (237) all_0_1_1 = n8
% 13.15/3.60 |
% 13.15/3.60 | From (236) and (167) follows:
% 13.15/3.60 | (238) sum(n9, all_0_0_0) = all_0_6_6
% 13.15/3.60 |
% 13.15/3.60 | From (237) and (420) follows:
% 13.15/3.60 | (775) sum(n9, n8) = all_0_0_0
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n9, n8, all_0_0_0, n6 and discharging atoms sum(n9, n8) = all_0_0_0, sum(n9, n8) = n6, yields:
% 13.15/3.60 | (257) all_0_0_0 = n6
% 13.15/3.60 |
% 13.15/3.60 | From (257) and (238) follows:
% 13.15/3.60 | (777) sum(n9, n6) = all_0_6_6
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n9, n6, all_0_6_6, n4 and discharging atoms sum(n9, n6) = all_0_6_6, sum(n9, n6) = n4, yields:
% 13.15/3.60 | (344) all_0_6_6 = n4
% 13.15/3.60 |
% 13.15/3.60 | Equations (344) can reduce 216 to:
% 13.15/3.60 | (243) $false
% 13.15/3.60 |
% 13.15/3.60 |-The branch is then unsatisfiable
% 13.15/3.60 |-Branch two:
% 13.15/3.60 | (435) ~ (all_0_7_7 = n9)
% 13.15/3.60 | (436) all_0_7_7 = n8 | all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.15/3.60 |
% 13.15/3.60 +-Applying beta-rule and splitting (245), into two cases.
% 13.15/3.60 |-Branch one:
% 13.15/3.60 | (246) all_0_8_8 = n9
% 13.15/3.60 |
% 13.15/3.60 | From (246) and (77) follows:
% 13.15/3.60 | (783) sum(n9, all_0_5_5) = all_0_4_4
% 13.15/3.60 |
% 13.15/3.60 | From (246) and (120) follows:
% 13.15/3.60 | (784) sum(n9, all_0_7_7) = all_0_2_2
% 13.15/3.60 |
% 13.15/3.60 +-Applying beta-rule and splitting (436), into two cases.
% 13.15/3.60 |-Branch one:
% 13.15/3.60 | (437) all_0_7_7 = n8
% 13.15/3.60 |
% 13.15/3.60 | From (437) and (10) follows:
% 13.15/3.60 | (438) succ(n8) = all_0_5_5
% 13.15/3.60 |
% 13.15/3.60 | From (437) and (3) follows:
% 13.15/3.60 | (439) sum(n8, all_0_1_1) = all_0_0_0
% 13.15/3.60 |
% 13.15/3.60 | From (437) and (784) follows:
% 13.15/3.60 | (788) sum(n9, n8) = all_0_2_2
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (47) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 13.15/3.60 | (441) all_0_5_5 = n9
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n9, n8, all_0_2_2, n6 and discharging atoms sum(n9, n8) = all_0_2_2, sum(n9, n8) = n6, yields:
% 13.15/3.60 | (283) all_0_2_2 = n6
% 13.15/3.60 |
% 13.15/3.60 | From (283) and (205) follows:
% 13.15/3.60 | (285) pred(n6) = all_0_1_1
% 13.15/3.60 |
% 13.15/3.60 | From (441) and (783) follows:
% 13.15/3.60 | (792) sum(n9, n9) = all_0_4_4
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (116) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 13.15/3.60 | (288) all_0_1_1 = n5
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n9, n9, all_0_4_4, n7 and discharging atoms sum(n9, n9) = all_0_4_4, sum(n9, n9) = n7, yields:
% 13.15/3.60 | (284) all_0_4_4 = n7
% 13.15/3.60 |
% 13.15/3.60 | From (284) and (138) follows:
% 13.15/3.60 | (286) pred(n7) = all_0_3_3
% 13.15/3.60 |
% 13.15/3.60 | From (288) and (439) follows:
% 13.15/3.60 | (796) sum(n8, n5) = all_0_0_0
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (116) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 13.15/3.60 | (287) all_0_3_3 = n6
% 13.15/3.60 |
% 13.15/3.60 | Instantiating formula (132) with n8, n5, all_0_0_0, n2 and discharging atoms sum(n8, n5) = all_0_0_0, sum(n8, n5) = n2, yields:
% 13.15/3.61 | (325) all_0_0_0 = n2
% 13.15/3.61 |
% 13.15/3.61 | From (287)(325) and (167) follows:
% 13.15/3.61 | (799) sum(n6, n2) = all_0_6_6
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (132) with n6, n2, all_0_6_6, n8 and discharging atoms sum(n6, n2) = all_0_6_6, sum(n6, n2) = n8, yields:
% 13.15/3.61 | (310) all_0_6_6 = n8
% 13.15/3.61 |
% 13.15/3.61 | Equations (310) can reduce 165 to:
% 13.15/3.61 | (243) $false
% 13.15/3.61 |
% 13.15/3.61 |-The branch is then unsatisfiable
% 13.15/3.61 |-Branch two:
% 13.15/3.61 | (454) ~ (all_0_7_7 = n8)
% 13.15/3.61 | (455) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.15/3.61 |
% 13.15/3.61 +-Applying beta-rule and splitting (455), into two cases.
% 13.15/3.61 |-Branch one:
% 13.15/3.61 | (456) all_0_7_7 = n7
% 13.15/3.61 |
% 13.15/3.61 | From (456) and (10) follows:
% 13.15/3.61 | (457) succ(n7) = all_0_5_5
% 13.15/3.61 |
% 13.15/3.61 | From (456) and (3) follows:
% 13.15/3.61 | (458) sum(n7, all_0_1_1) = all_0_0_0
% 13.15/3.61 |
% 13.15/3.61 | From (456) and (784) follows:
% 13.15/3.61 | (807) sum(n9, n7) = all_0_2_2
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (47) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 13.15/3.61 | (460) all_0_5_5 = n8
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (132) with n9, n7, all_0_2_2, n5 and discharging atoms sum(n9, n7) = all_0_2_2, sum(n9, n7) = n5, yields:
% 13.15/3.61 | (300) all_0_2_2 = n5
% 13.15/3.61 |
% 13.15/3.61 | From (300) and (205) follows:
% 13.15/3.61 | (302) pred(n5) = all_0_1_1
% 13.15/3.61 |
% 13.15/3.61 | From (460) and (783) follows:
% 13.15/3.61 | (811) sum(n9, n8) = all_0_4_4
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (116) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 13.15/3.61 | (305) all_0_1_1 = n4
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (132) with n9, n8, all_0_4_4, n6 and discharging atoms sum(n9, n8) = all_0_4_4, sum(n9, n8) = n6, yields:
% 13.15/3.61 | (301) all_0_4_4 = n6
% 13.15/3.61 |
% 13.15/3.61 | From (301) and (138) follows:
% 13.15/3.61 | (303) pred(n6) = all_0_3_3
% 13.15/3.61 |
% 13.15/3.61 | From (305) and (458) follows:
% 13.15/3.61 | (815) sum(n7, n4) = all_0_0_0
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (116) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 13.15/3.61 | (304) all_0_3_3 = n5
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (132) with n7, n4, all_0_0_0, n0 and discharging atoms sum(n7, n4) = all_0_0_0, sum(n7, n4) = n0, yields:
% 13.15/3.61 | (359) all_0_0_0 = n0
% 13.15/3.61 |
% 13.15/3.61 | From (304)(359) and (167) follows:
% 13.15/3.61 | (818) sum(n5, n0) = all_0_6_6
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (132) with n5, n0, all_0_6_6, n5 and discharging atoms sum(n5, n0) = all_0_6_6, sum(n5, n0) = n5, yields:
% 13.15/3.61 | (242) all_0_6_6 = n5
% 13.15/3.61 |
% 13.15/3.61 | Equations (242) can reduce 4 to:
% 13.15/3.61 | (243) $false
% 13.15/3.61 |
% 13.15/3.61 |-The branch is then unsatisfiable
% 13.15/3.61 |-Branch two:
% 13.15/3.61 | (473) ~ (all_0_7_7 = n7)
% 13.15/3.61 | (474) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.15/3.61 |
% 13.15/3.61 +-Applying beta-rule and splitting (474), into two cases.
% 13.15/3.61 |-Branch one:
% 13.15/3.61 | (475) all_0_7_7 = n6
% 13.15/3.61 |
% 13.15/3.61 | From (475) and (10) follows:
% 13.15/3.61 | (476) succ(n6) = all_0_5_5
% 13.15/3.61 |
% 13.15/3.61 | From (475) and (3) follows:
% 13.15/3.61 | (477) sum(n6, all_0_1_1) = all_0_0_0
% 13.15/3.61 |
% 13.15/3.61 | From (475) and (784) follows:
% 13.15/3.61 | (826) sum(n9, n6) = all_0_2_2
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (47) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 13.15/3.61 | (479) all_0_5_5 = n7
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (132) with n9, n6, all_0_2_2, n4 and discharging atoms sum(n9, n6) = all_0_2_2, sum(n9, n6) = n4, yields:
% 13.15/3.61 | (317) all_0_2_2 = n4
% 13.15/3.61 |
% 13.15/3.61 | From (317) and (205) follows:
% 13.15/3.61 | (319) pred(n4) = all_0_1_1
% 13.15/3.61 |
% 13.15/3.61 | From (479) and (783) follows:
% 13.15/3.61 | (830) sum(n9, n7) = all_0_4_4
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (116) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 13.15/3.61 | (322) all_0_1_1 = n3
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (132) with n9, n7, all_0_4_4, n5 and discharging atoms sum(n9, n7) = all_0_4_4, sum(n9, n7) = n5, yields:
% 13.15/3.61 | (318) all_0_4_4 = n5
% 13.15/3.61 |
% 13.15/3.61 | From (318) and (138) follows:
% 13.15/3.61 | (320) pred(n5) = all_0_3_3
% 13.15/3.61 |
% 13.15/3.61 | From (322) and (477) follows:
% 13.15/3.61 | (834) sum(n6, n3) = all_0_0_0
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (116) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 13.15/3.61 | (321) all_0_3_3 = n4
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (132) with n6, n3, all_0_0_0, n9 and discharging atoms sum(n6, n3) = all_0_0_0, sum(n6, n3) = n9, yields:
% 13.15/3.61 | (393) all_0_0_0 = n9
% 13.15/3.61 |
% 13.15/3.61 | From (321)(393) and (167) follows:
% 13.15/3.61 | (837) sum(n4, n9) = all_0_6_6
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (132) with n4, n9, all_0_6_6, n2 and discharging atoms sum(n4, n9) = all_0_6_6, sum(n4, n9) = n2, yields:
% 13.15/3.61 | (361) all_0_6_6 = n2
% 13.15/3.61 |
% 13.15/3.61 | Equations (361) can reduce 131 to:
% 13.15/3.61 | (243) $false
% 13.15/3.61 |
% 13.15/3.61 |-The branch is then unsatisfiable
% 13.15/3.61 |-Branch two:
% 13.15/3.61 | (492) ~ (all_0_7_7 = n6)
% 13.15/3.61 | (493) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.15/3.61 |
% 13.15/3.61 +-Applying beta-rule and splitting (493), into two cases.
% 13.15/3.61 |-Branch one:
% 13.15/3.61 | (494) all_0_7_7 = n5
% 13.15/3.61 |
% 13.15/3.61 | From (494) and (10) follows:
% 13.15/3.61 | (495) succ(n5) = all_0_5_5
% 13.15/3.61 |
% 13.15/3.61 | From (494) and (3) follows:
% 13.15/3.61 | (496) sum(n5, all_0_1_1) = all_0_0_0
% 13.15/3.61 |
% 13.15/3.61 | From (494) and (784) follows:
% 13.15/3.61 | (845) sum(n9, n5) = all_0_2_2
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (47) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 13.15/3.61 | (498) all_0_5_5 = n6
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (132) with n9, n5, all_0_2_2, n3 and discharging atoms sum(n9, n5) = all_0_2_2, sum(n9, n5) = n3, yields:
% 13.15/3.61 | (334) all_0_2_2 = n3
% 13.15/3.61 |
% 13.15/3.61 | From (334) and (205) follows:
% 13.15/3.61 | (336) pred(n3) = all_0_1_1
% 13.15/3.61 |
% 13.15/3.61 | From (498) and (783) follows:
% 13.15/3.61 | (849) sum(n9, n6) = all_0_4_4
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (116) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 13.15/3.61 | (339) all_0_1_1 = n2
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (132) with n9, n6, all_0_4_4, n4 and discharging atoms sum(n9, n6) = all_0_4_4, sum(n9, n6) = n4, yields:
% 13.15/3.61 | (335) all_0_4_4 = n4
% 13.15/3.61 |
% 13.15/3.61 | From (335) and (138) follows:
% 13.15/3.61 | (337) pred(n4) = all_0_3_3
% 13.15/3.61 |
% 13.15/3.61 | From (339) and (496) follows:
% 13.15/3.61 | (853) sum(n5, n2) = all_0_0_0
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (116) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 13.15/3.61 | (338) all_0_3_3 = n3
% 13.15/3.61 |
% 13.15/3.61 | Instantiating formula (132) with n5, n2, all_0_0_0, n7 and discharging atoms sum(n5, n2) = all_0_0_0, sum(n5, n2) = n7, yields:
% 13.15/3.61 | (240) all_0_0_0 = n7
% 13.31/3.61 |
% 13.31/3.61 | From (338)(240) and (167) follows:
% 13.31/3.61 | (856) sum(n3, n7) = all_0_6_6
% 13.31/3.61 |
% 13.31/3.61 | Instantiating formula (132) with n3, n7, all_0_6_6, n10 and discharging atoms sum(n3, n7) = all_0_6_6, sum(n3, n7) = n10, yields:
% 13.31/3.61 | (293) all_0_6_6 = n10
% 13.31/3.61 |
% 13.31/3.61 | Equations (293) can reduce 147 to:
% 13.31/3.61 | (243) $false
% 13.31/3.61 |
% 13.31/3.61 |-The branch is then unsatisfiable
% 13.31/3.61 |-Branch two:
% 13.31/3.61 | (511) ~ (all_0_7_7 = n5)
% 13.31/3.61 | (512) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.31/3.61 |
% 13.31/3.61 +-Applying beta-rule and splitting (512), into two cases.
% 13.31/3.61 |-Branch one:
% 13.31/3.61 | (513) all_0_7_7 = n4
% 13.31/3.61 |
% 13.31/3.61 | From (513) and (10) follows:
% 13.31/3.61 | (514) succ(n4) = all_0_5_5
% 13.31/3.61 |
% 13.31/3.61 | From (513) and (3) follows:
% 13.31/3.61 | (515) sum(n4, all_0_1_1) = all_0_0_0
% 13.31/3.61 |
% 13.31/3.61 | From (513) and (784) follows:
% 13.31/3.61 | (864) sum(n9, n4) = all_0_2_2
% 13.31/3.61 |
% 13.31/3.61 | Instantiating formula (47) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 13.31/3.61 | (517) all_0_5_5 = n5
% 13.31/3.61 |
% 13.31/3.61 | Instantiating formula (132) with n9, n4, all_0_2_2, n2 and discharging atoms sum(n9, n4) = all_0_2_2, sum(n9, n4) = n2, yields:
% 13.31/3.61 | (351) all_0_2_2 = n2
% 13.31/3.61 |
% 13.31/3.61 | From (351) and (205) follows:
% 13.31/3.61 | (353) pred(n2) = all_0_1_1
% 13.31/3.61 |
% 13.31/3.61 | From (517) and (783) follows:
% 13.31/3.61 | (868) sum(n9, n5) = all_0_4_4
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (116) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 13.31/3.62 | (356) all_0_1_1 = n1
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n9, n5, all_0_4_4, n3 and discharging atoms sum(n9, n5) = all_0_4_4, sum(n9, n5) = n3, yields:
% 13.31/3.62 | (352) all_0_4_4 = n3
% 13.31/3.62 |
% 13.31/3.62 | From (352) and (138) follows:
% 13.31/3.62 | (354) pred(n3) = all_0_3_3
% 13.31/3.62 |
% 13.31/3.62 | From (356) and (515) follows:
% 13.31/3.62 | (872) sum(n4, n1) = all_0_0_0
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (116) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 13.31/3.62 | (355) all_0_3_3 = n2
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n4, n1, all_0_0_0, n5 and discharging atoms sum(n4, n1) = all_0_0_0, sum(n4, n1) = n5, yields:
% 13.31/3.62 | (274) all_0_0_0 = n5
% 13.31/3.62 |
% 13.31/3.62 | From (355)(274) and (167) follows:
% 13.31/3.62 | (875) sum(n2, n5) = all_0_6_6
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n2, n5, all_0_6_6, n7 and discharging atoms sum(n2, n5) = all_0_6_6, sum(n2, n5) = n7, yields:
% 13.31/3.62 | (411) all_0_6_6 = n7
% 13.31/3.62 |
% 13.31/3.62 | Equations (411) can reduce 88 to:
% 13.31/3.62 | (243) $false
% 13.31/3.62 |
% 13.31/3.62 |-The branch is then unsatisfiable
% 13.31/3.62 |-Branch two:
% 13.31/3.62 | (530) ~ (all_0_7_7 = n4)
% 13.31/3.62 | (531) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.31/3.62 |
% 13.31/3.62 +-Applying beta-rule and splitting (531), into two cases.
% 13.31/3.62 |-Branch one:
% 13.31/3.62 | (532) all_0_7_7 = n3
% 13.31/3.62 |
% 13.31/3.62 | From (532) and (10) follows:
% 13.31/3.62 | (533) succ(n3) = all_0_5_5
% 13.31/3.62 |
% 13.31/3.62 | From (532) and (3) follows:
% 13.31/3.62 | (534) sum(n3, all_0_1_1) = all_0_0_0
% 13.31/3.62 |
% 13.31/3.62 | From (532) and (784) follows:
% 13.31/3.62 | (883) sum(n9, n3) = all_0_2_2
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (47) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 13.31/3.62 | (536) all_0_5_5 = n4
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n9, n3, all_0_2_2, n1 and discharging atoms sum(n9, n3) = all_0_2_2, sum(n9, n3) = n1, yields:
% 13.31/3.62 | (368) all_0_2_2 = n1
% 13.31/3.62 |
% 13.31/3.62 | From (368) and (205) follows:
% 13.31/3.62 | (370) pred(n1) = all_0_1_1
% 13.31/3.62 |
% 13.31/3.62 | From (536) and (783) follows:
% 13.31/3.62 | (887) sum(n9, n4) = all_0_4_4
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (116) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 13.31/3.62 | (373) all_0_1_1 = n0
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n9, n4, all_0_4_4, n2 and discharging atoms sum(n9, n4) = all_0_4_4, sum(n9, n4) = n2, yields:
% 13.31/3.62 | (369) all_0_4_4 = n2
% 13.31/3.62 |
% 13.31/3.62 | From (369) and (138) follows:
% 13.31/3.62 | (371) pred(n2) = all_0_3_3
% 13.31/3.62 |
% 13.31/3.62 | From (373) and (534) follows:
% 13.31/3.62 | (891) sum(n3, n0) = all_0_0_0
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (116) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 13.31/3.62 | (372) all_0_3_3 = n1
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n3, n0, all_0_0_0, n3 and discharging atoms sum(n3, n0) = all_0_0_0, sum(n3, n0) = n3, yields:
% 13.31/3.62 | (308) all_0_0_0 = n3
% 13.31/3.62 |
% 13.31/3.62 | From (372)(308) and (167) follows:
% 13.31/3.62 | (894) sum(n1, n3) = all_0_6_6
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n1, n3, all_0_6_6, n4 and discharging atoms sum(n1, n3) = all_0_6_6, sum(n1, n3) = n4, yields:
% 13.31/3.62 | (344) all_0_6_6 = n4
% 13.31/3.62 |
% 13.31/3.62 | Equations (344) can reduce 216 to:
% 13.31/3.62 | (243) $false
% 13.31/3.62 |
% 13.31/3.62 |-The branch is then unsatisfiable
% 13.31/3.62 |-Branch two:
% 13.31/3.62 | (549) ~ (all_0_7_7 = n3)
% 13.31/3.62 | (550) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.31/3.62 |
% 13.31/3.62 +-Applying beta-rule and splitting (550), into two cases.
% 13.31/3.62 |-Branch one:
% 13.31/3.62 | (551) all_0_7_7 = n2
% 13.31/3.62 |
% 13.31/3.62 | From (551) and (10) follows:
% 13.31/3.62 | (552) succ(n2) = all_0_5_5
% 13.31/3.62 |
% 13.31/3.62 | From (551) and (3) follows:
% 13.31/3.62 | (553) sum(n2, all_0_1_1) = all_0_0_0
% 13.31/3.62 |
% 13.31/3.62 | From (551) and (784) follows:
% 13.31/3.62 | (902) sum(n9, n2) = all_0_2_2
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (47) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 13.31/3.62 | (555) all_0_5_5 = n3
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n9, n2, all_0_2_2, n0 and discharging atoms sum(n9, n2) = all_0_2_2, sum(n9, n2) = n0, yields:
% 13.31/3.62 | (385) all_0_2_2 = n0
% 13.31/3.62 |
% 13.31/3.62 | From (385) and (205) follows:
% 13.31/3.62 | (387) pred(n0) = all_0_1_1
% 13.31/3.62 |
% 13.31/3.62 | From (555) and (783) follows:
% 13.31/3.62 | (906) sum(n9, n3) = all_0_4_4
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (116) with n0, all_0_1_1, n10 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n10, yields:
% 13.31/3.62 | (390) all_0_1_1 = n10
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n9, n3, all_0_4_4, n1 and discharging atoms sum(n9, n3) = all_0_4_4, sum(n9, n3) = n1, yields:
% 13.31/3.62 | (386) all_0_4_4 = n1
% 13.31/3.62 |
% 13.31/3.62 | From (386) and (138) follows:
% 13.31/3.62 | (388) pred(n1) = all_0_3_3
% 13.31/3.62 |
% 13.31/3.62 | From (390) and (553) follows:
% 13.31/3.62 | (910) sum(n2, n10) = all_0_0_0
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (116) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 13.31/3.62 | (389) all_0_3_3 = n0
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n2, n10, all_0_0_0, n1 and discharging atoms sum(n2, n10) = all_0_0_0, sum(n2, n10) = n1, yields:
% 13.31/3.62 | (342) all_0_0_0 = n1
% 13.31/3.62 |
% 13.31/3.62 | From (389)(342) and (167) follows:
% 13.31/3.62 | (913) sum(n0, n1) = all_0_6_6
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n0, n1, all_0_6_6, n1 and discharging atoms sum(n0, n1) = all_0_6_6, sum(n0, n1) = n1, yields:
% 13.31/3.62 | (276) all_0_6_6 = n1
% 13.31/3.62 |
% 13.31/3.62 | Equations (276) can reduce 28 to:
% 13.31/3.62 | (243) $false
% 13.31/3.62 |
% 13.31/3.62 |-The branch is then unsatisfiable
% 13.31/3.62 |-Branch two:
% 13.31/3.62 | (568) ~ (all_0_7_7 = n2)
% 13.31/3.62 | (569) all_0_7_7 = n1 | all_0_7_7 = n0
% 13.31/3.62 |
% 13.31/3.62 +-Applying beta-rule and splitting (569), into two cases.
% 13.31/3.62 |-Branch one:
% 13.31/3.62 | (570) all_0_7_7 = n1
% 13.31/3.62 |
% 13.31/3.62 | From (570) and (10) follows:
% 13.31/3.62 | (571) succ(n1) = all_0_5_5
% 13.31/3.62 |
% 13.31/3.62 | From (570) and (3) follows:
% 13.31/3.62 | (572) sum(n1, all_0_1_1) = all_0_0_0
% 13.31/3.62 |
% 13.31/3.62 | From (570) and (784) follows:
% 13.31/3.62 | (921) sum(n9, n1) = all_0_2_2
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (47) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 13.31/3.62 | (574) all_0_5_5 = n2
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n9, n1, all_0_2_2, n10 and discharging atoms sum(n9, n1) = all_0_2_2, sum(n9, n1) = n10, yields:
% 13.31/3.62 | (401) all_0_2_2 = n10
% 13.31/3.62 |
% 13.31/3.62 | From (401) and (205) follows:
% 13.31/3.62 | (403) pred(n10) = all_0_1_1
% 13.31/3.62 |
% 13.31/3.62 | From (574) and (783) follows:
% 13.31/3.62 | (925) sum(n9, n2) = all_0_4_4
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (116) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 13.31/3.62 | (405) all_0_1_1 = n9
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n9, n2, all_0_4_4, n0 and discharging atoms sum(n9, n2) = all_0_4_4, sum(n9, n2) = n0, yields:
% 13.31/3.62 | (402) all_0_4_4 = n0
% 13.31/3.62 |
% 13.31/3.62 | From (402) and (138) follows:
% 13.31/3.62 | (404) pred(n0) = all_0_3_3
% 13.31/3.62 |
% 13.31/3.62 | From (405) and (572) follows:
% 13.31/3.62 | (929) sum(n1, n9) = all_0_0_0
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (116) with n0, all_0_3_3, n10 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n10, yields:
% 13.31/3.62 | (406) all_0_3_3 = n10
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n1, n9, all_0_0_0, n10 and discharging atoms sum(n1, n9) = all_0_0_0, sum(n1, n9) = n10, yields:
% 13.31/3.62 | (376) all_0_0_0 = n10
% 13.31/3.62 |
% 13.31/3.62 | From (406)(376) and (167) follows:
% 13.31/3.62 | (932) sum(n10, n10) = all_0_6_6
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n10, n10, all_0_6_6, n9 and discharging atoms sum(n10, n10) = all_0_6_6, sum(n10, n10) = n9, yields:
% 13.31/3.62 | (395) all_0_6_6 = n9
% 13.31/3.62 |
% 13.31/3.62 | Equations (395) can reduce 78 to:
% 13.31/3.62 | (243) $false
% 13.31/3.62 |
% 13.31/3.62 |-The branch is then unsatisfiable
% 13.31/3.62 |-Branch two:
% 13.31/3.62 | (587) ~ (all_0_7_7 = n1)
% 13.31/3.62 | (588) all_0_7_7 = n0
% 13.31/3.62 |
% 13.31/3.62 | From (588) and (10) follows:
% 13.31/3.62 | (589) succ(n0) = all_0_5_5
% 13.31/3.62 |
% 13.31/3.62 | From (588) and (3) follows:
% 13.31/3.62 | (590) sum(n0, all_0_1_1) = all_0_0_0
% 13.31/3.62 |
% 13.31/3.62 | From (588) and (784) follows:
% 13.31/3.62 | (939) sum(n9, n0) = all_0_2_2
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (47) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 13.31/3.62 | (592) all_0_5_5 = n1
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n9, n0, all_0_2_2, n9 and discharging atoms sum(n9, n0) = all_0_2_2, sum(n9, n0) = n9, yields:
% 13.31/3.62 | (232) all_0_2_2 = n9
% 13.31/3.62 |
% 13.31/3.62 | From (232) and (205) follows:
% 13.31/3.62 | (234) pred(n9) = all_0_1_1
% 13.31/3.62 |
% 13.31/3.62 | From (592) and (783) follows:
% 13.31/3.62 | (943) sum(n9, n1) = all_0_4_4
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (116) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 13.31/3.62 | (237) all_0_1_1 = n8
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n9, n1, all_0_4_4, n10 and discharging atoms sum(n9, n1) = all_0_4_4, sum(n9, n1) = n10, yields:
% 13.31/3.62 | (233) all_0_4_4 = n10
% 13.31/3.62 |
% 13.31/3.62 | From (233) and (138) follows:
% 13.31/3.62 | (235) pred(n10) = all_0_3_3
% 13.31/3.62 |
% 13.31/3.62 | From (237) and (590) follows:
% 13.31/3.62 | (947) sum(n0, n8) = all_0_0_0
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (116) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 13.31/3.62 | (236) all_0_3_3 = n9
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n0, n8, all_0_0_0, n8 and discharging atoms sum(n0, n8) = all_0_0_0, sum(n0, n8) = n8, yields:
% 13.31/3.62 | (409) all_0_0_0 = n8
% 13.31/3.62 |
% 13.31/3.62 | From (236)(409) and (167) follows:
% 13.31/3.62 | (950) sum(n9, n8) = all_0_6_6
% 13.31/3.62 |
% 13.31/3.62 | Instantiating formula (132) with n9, n8, all_0_6_6, n6 and discharging atoms sum(n9, n8) = all_0_6_6, sum(n9, n8) = n6, yields:
% 13.31/3.62 | (327) all_0_6_6 = n6
% 13.31/3.62 |
% 13.31/3.62 | Equations (327) can reduce 34 to:
% 13.31/3.63 | (243) $false
% 13.31/3.63 |
% 13.31/3.63 |-The branch is then unsatisfiable
% 13.31/3.63 |-Branch two:
% 13.31/3.63 | (261) ~ (all_0_8_8 = n9)
% 13.31/3.63 | (262) all_0_8_8 = n8 | all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.31/3.63 |
% 13.31/3.63 +-Applying beta-rule and splitting (436), into two cases.
% 13.31/3.63 |-Branch one:
% 13.31/3.63 | (437) all_0_7_7 = n8
% 13.31/3.63 |
% 13.31/3.63 | From (437) and (10) follows:
% 13.31/3.63 | (438) succ(n8) = all_0_5_5
% 13.31/3.63 |
% 13.31/3.63 | From (437) and (3) follows:
% 13.31/3.63 | (439) sum(n8, all_0_1_1) = all_0_0_0
% 13.31/3.63 |
% 13.31/3.63 | From (437) and (120) follows:
% 13.31/3.63 | (958) sum(all_0_8_8, n8) = all_0_2_2
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (47) with n8, all_0_5_5, n9 and discharging atoms succ(n8) = all_0_5_5, succ(n8) = n9, yields:
% 13.31/3.63 | (441) all_0_5_5 = n9
% 13.31/3.63 |
% 13.31/3.63 | From (441) and (77) follows:
% 13.31/3.63 | (960) sum(all_0_8_8, n9) = all_0_4_4
% 13.31/3.63 |
% 13.31/3.63 +-Applying beta-rule and splitting (262), into two cases.
% 13.31/3.63 |-Branch one:
% 13.31/3.63 | (263) all_0_8_8 = n8
% 13.31/3.63 |
% 13.31/3.63 | From (263) and (960) follows:
% 13.31/3.63 | (962) sum(n8, n9) = all_0_4_4
% 13.31/3.63 |
% 13.31/3.63 | From (263) and (958) follows:
% 13.31/3.63 | (963) sum(n8, n8) = all_0_2_2
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n8, n9, all_0_4_4, n6 and discharging atoms sum(n8, n9) = all_0_4_4, sum(n8, n9) = n6, yields:
% 13.31/3.63 | (301) all_0_4_4 = n6
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n8, n8, all_0_2_2, n5 and discharging atoms sum(n8, n8) = all_0_2_2, sum(n8, n8) = n5, yields:
% 13.31/3.63 | (300) all_0_2_2 = n5
% 13.31/3.63 |
% 13.31/3.63 | From (300) and (205) follows:
% 13.31/3.63 | (302) pred(n5) = all_0_1_1
% 13.31/3.63 |
% 13.31/3.63 | From (301) and (138) follows:
% 13.31/3.63 | (303) pred(n6) = all_0_3_3
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (116) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 13.31/3.63 | (304) all_0_3_3 = n5
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (116) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 13.31/3.63 | (305) all_0_1_1 = n4
% 13.31/3.63 |
% 13.31/3.63 | From (304) and (167) follows:
% 13.31/3.63 | (306) sum(n5, all_0_0_0) = all_0_6_6
% 13.31/3.63 |
% 13.31/3.63 | From (305) and (439) follows:
% 13.31/3.63 | (971) sum(n8, n4) = all_0_0_0
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n8, n4, all_0_0_0, n1 and discharging atoms sum(n8, n4) = all_0_0_0, sum(n8, n4) = n1, yields:
% 13.31/3.63 | (342) all_0_0_0 = n1
% 13.31/3.63 |
% 13.31/3.63 | From (342) and (306) follows:
% 13.31/3.63 | (973) sum(n5, n1) = all_0_6_6
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n5, n1, all_0_6_6, n6 and discharging atoms sum(n5, n1) = all_0_6_6, sum(n5, n1) = n6, yields:
% 13.31/3.63 | (327) all_0_6_6 = n6
% 13.31/3.63 |
% 13.31/3.63 | Equations (327) can reduce 34 to:
% 13.31/3.63 | (243) $false
% 13.31/3.63 |
% 13.31/3.63 |-The branch is then unsatisfiable
% 13.31/3.63 |-Branch two:
% 13.31/3.63 | (278) ~ (all_0_8_8 = n8)
% 13.31/3.63 | (279) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.31/3.63 |
% 13.31/3.63 +-Applying beta-rule and splitting (279), into two cases.
% 13.31/3.63 |-Branch one:
% 13.31/3.63 | (280) all_0_8_8 = n7
% 13.31/3.63 |
% 13.31/3.63 | From (280) and (960) follows:
% 13.31/3.63 | (979) sum(n7, n9) = all_0_4_4
% 13.31/3.63 |
% 13.31/3.63 | From (280) and (958) follows:
% 13.31/3.63 | (980) sum(n7, n8) = all_0_2_2
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n7, n9, all_0_4_4, n5 and discharging atoms sum(n7, n9) = all_0_4_4, sum(n7, n9) = n5, yields:
% 13.31/3.63 | (318) all_0_4_4 = n5
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n7, n8, all_0_2_2, n4 and discharging atoms sum(n7, n8) = all_0_2_2, sum(n7, n8) = n4, yields:
% 13.31/3.63 | (317) all_0_2_2 = n4
% 13.31/3.63 |
% 13.31/3.63 | From (317) and (205) follows:
% 13.31/3.63 | (319) pred(n4) = all_0_1_1
% 13.31/3.63 |
% 13.31/3.63 | From (318) and (138) follows:
% 13.31/3.63 | (320) pred(n5) = all_0_3_3
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (116) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 13.31/3.63 | (321) all_0_3_3 = n4
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (116) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 13.31/3.63 | (322) all_0_1_1 = n3
% 13.31/3.63 |
% 13.31/3.63 | From (321) and (167) follows:
% 13.31/3.63 | (323) sum(n4, all_0_0_0) = all_0_6_6
% 13.31/3.63 |
% 13.31/3.63 | From (322) and (439) follows:
% 13.31/3.63 | (988) sum(n8, n3) = all_0_0_0
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n8, n3, all_0_0_0, n0 and discharging atoms sum(n8, n3) = all_0_0_0, sum(n8, n3) = n0, yields:
% 13.31/3.63 | (359) all_0_0_0 = n0
% 13.31/3.63 |
% 13.31/3.63 | From (359) and (323) follows:
% 13.31/3.63 | (990) sum(n4, n0) = all_0_6_6
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n4, n0, all_0_6_6, n4 and discharging atoms sum(n4, n0) = all_0_6_6, sum(n4, n0) = n4, yields:
% 13.31/3.63 | (344) all_0_6_6 = n4
% 13.31/3.63 |
% 13.31/3.63 | Equations (344) can reduce 216 to:
% 13.31/3.63 | (243) $false
% 13.31/3.63 |
% 13.31/3.63 |-The branch is then unsatisfiable
% 13.31/3.63 |-Branch two:
% 13.31/3.63 | (295) ~ (all_0_8_8 = n7)
% 13.31/3.63 | (296) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.31/3.63 |
% 13.31/3.63 +-Applying beta-rule and splitting (296), into two cases.
% 13.31/3.63 |-Branch one:
% 13.31/3.63 | (297) all_0_8_8 = n6
% 13.31/3.63 |
% 13.31/3.63 | From (297) and (960) follows:
% 13.31/3.63 | (996) sum(n6, n9) = all_0_4_4
% 13.31/3.63 |
% 13.31/3.63 | From (297) and (958) follows:
% 13.31/3.63 | (997) sum(n6, n8) = all_0_2_2
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n6, n9, all_0_4_4, n4 and discharging atoms sum(n6, n9) = all_0_4_4, sum(n6, n9) = n4, yields:
% 13.31/3.63 | (335) all_0_4_4 = n4
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n6, n8, all_0_2_2, n3 and discharging atoms sum(n6, n8) = all_0_2_2, sum(n6, n8) = n3, yields:
% 13.31/3.63 | (334) all_0_2_2 = n3
% 13.31/3.63 |
% 13.31/3.63 | From (334) and (205) follows:
% 13.31/3.63 | (336) pred(n3) = all_0_1_1
% 13.31/3.63 |
% 13.31/3.63 | From (335) and (138) follows:
% 13.31/3.63 | (337) pred(n4) = all_0_3_3
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (116) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 13.31/3.63 | (338) all_0_3_3 = n3
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (116) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 13.31/3.63 | (339) all_0_1_1 = n2
% 13.31/3.63 |
% 13.31/3.63 | From (338) and (167) follows:
% 13.31/3.63 | (340) sum(n3, all_0_0_0) = all_0_6_6
% 13.31/3.63 |
% 13.31/3.63 | From (339) and (439) follows:
% 13.31/3.63 | (1005) sum(n8, n2) = all_0_0_0
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n8, n2, all_0_0_0, n10 and discharging atoms sum(n8, n2) = all_0_0_0, sum(n8, n2) = n10, yields:
% 13.31/3.63 | (376) all_0_0_0 = n10
% 13.31/3.63 |
% 13.31/3.63 | From (376) and (340) follows:
% 13.31/3.63 | (1007) sum(n3, n10) = all_0_6_6
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n3, n10, all_0_6_6, n2 and discharging atoms sum(n3, n10) = all_0_6_6, sum(n3, n10) = n2, yields:
% 13.31/3.63 | (361) all_0_6_6 = n2
% 13.31/3.63 |
% 13.31/3.63 | Equations (361) can reduce 131 to:
% 13.31/3.63 | (243) $false
% 13.31/3.63 |
% 13.31/3.63 |-The branch is then unsatisfiable
% 13.31/3.63 |-Branch two:
% 13.31/3.63 | (312) ~ (all_0_8_8 = n6)
% 13.31/3.63 | (313) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.31/3.63 |
% 13.31/3.63 +-Applying beta-rule and splitting (313), into two cases.
% 13.31/3.63 |-Branch one:
% 13.31/3.63 | (314) all_0_8_8 = n5
% 13.31/3.63 |
% 13.31/3.63 | From (314) and (960) follows:
% 13.31/3.63 | (1013) sum(n5, n9) = all_0_4_4
% 13.31/3.63 |
% 13.31/3.63 | From (314) and (958) follows:
% 13.31/3.63 | (1014) sum(n5, n8) = all_0_2_2
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n5, n9, all_0_4_4, n3 and discharging atoms sum(n5, n9) = all_0_4_4, sum(n5, n9) = n3, yields:
% 13.31/3.63 | (352) all_0_4_4 = n3
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n5, n8, all_0_2_2, n2 and discharging atoms sum(n5, n8) = all_0_2_2, sum(n5, n8) = n2, yields:
% 13.31/3.63 | (351) all_0_2_2 = n2
% 13.31/3.63 |
% 13.31/3.63 | From (351) and (205) follows:
% 13.31/3.63 | (353) pred(n2) = all_0_1_1
% 13.31/3.63 |
% 13.31/3.63 | From (352) and (138) follows:
% 13.31/3.63 | (354) pred(n3) = all_0_3_3
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (116) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 13.31/3.63 | (355) all_0_3_3 = n2
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (116) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 13.31/3.63 | (356) all_0_1_1 = n1
% 13.31/3.63 |
% 13.31/3.63 | From (355) and (167) follows:
% 13.31/3.63 | (357) sum(n2, all_0_0_0) = all_0_6_6
% 13.31/3.63 |
% 13.31/3.63 | From (356) and (439) follows:
% 13.31/3.63 | (1022) sum(n8, n1) = all_0_0_0
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n8, n1, all_0_0_0, n9 and discharging atoms sum(n8, n1) = all_0_0_0, sum(n8, n1) = n9, yields:
% 13.31/3.63 | (393) all_0_0_0 = n9
% 13.31/3.63 |
% 13.31/3.63 | From (393) and (357) follows:
% 13.31/3.63 | (1024) sum(n2, n9) = all_0_6_6
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n2, n9, all_0_6_6, n0 and discharging atoms sum(n2, n9) = all_0_6_6, sum(n2, n9) = n0, yields:
% 13.31/3.63 | (378) all_0_6_6 = n0
% 13.31/3.63 |
% 13.31/3.63 | Equations (378) can reduce 119 to:
% 13.31/3.63 | (243) $false
% 13.31/3.63 |
% 13.31/3.63 |-The branch is then unsatisfiable
% 13.31/3.63 |-Branch two:
% 13.31/3.63 | (329) ~ (all_0_8_8 = n5)
% 13.31/3.63 | (330) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.31/3.63 |
% 13.31/3.63 +-Applying beta-rule and splitting (330), into two cases.
% 13.31/3.63 |-Branch one:
% 13.31/3.63 | (331) all_0_8_8 = n4
% 13.31/3.63 |
% 13.31/3.63 | From (331) and (960) follows:
% 13.31/3.63 | (1030) sum(n4, n9) = all_0_4_4
% 13.31/3.63 |
% 13.31/3.63 | From (331) and (958) follows:
% 13.31/3.63 | (1031) sum(n4, n8) = all_0_2_2
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n4, n9, all_0_4_4, n2 and discharging atoms sum(n4, n9) = all_0_4_4, sum(n4, n9) = n2, yields:
% 13.31/3.63 | (369) all_0_4_4 = n2
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n4, n8, all_0_2_2, n1 and discharging atoms sum(n4, n8) = all_0_2_2, sum(n4, n8) = n1, yields:
% 13.31/3.63 | (368) all_0_2_2 = n1
% 13.31/3.63 |
% 13.31/3.63 | From (368) and (205) follows:
% 13.31/3.63 | (370) pred(n1) = all_0_1_1
% 13.31/3.63 |
% 13.31/3.63 | From (369) and (138) follows:
% 13.31/3.63 | (371) pred(n2) = all_0_3_3
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (116) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 13.31/3.63 | (372) all_0_3_3 = n1
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (116) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 13.31/3.63 | (373) all_0_1_1 = n0
% 13.31/3.63 |
% 13.31/3.63 | From (372) and (167) follows:
% 13.31/3.63 | (374) sum(n1, all_0_0_0) = all_0_6_6
% 13.31/3.63 |
% 13.31/3.63 | From (373) and (439) follows:
% 13.31/3.63 | (1039) sum(n8, n0) = all_0_0_0
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n8, n0, all_0_0_0, n8 and discharging atoms sum(n8, n0) = all_0_0_0, sum(n8, n0) = n8, yields:
% 13.31/3.63 | (409) all_0_0_0 = n8
% 13.31/3.63 |
% 13.31/3.63 | From (409) and (374) follows:
% 13.31/3.63 | (1041) sum(n1, n8) = all_0_6_6
% 13.31/3.63 |
% 13.31/3.63 | Instantiating formula (132) with n1, n8, all_0_6_6, n9 and discharging atoms sum(n1, n8) = all_0_6_6, sum(n1, n8) = n9, yields:
% 13.31/3.64 | (395) all_0_6_6 = n9
% 13.31/3.64 |
% 13.31/3.64 | Equations (395) can reduce 78 to:
% 13.31/3.64 | (243) $false
% 13.31/3.64 |
% 13.31/3.64 |-The branch is then unsatisfiable
% 13.31/3.64 |-Branch two:
% 13.31/3.64 | (346) ~ (all_0_8_8 = n4)
% 13.31/3.64 | (347) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.31/3.64 |
% 13.31/3.64 +-Applying beta-rule and splitting (347), into two cases.
% 13.31/3.64 |-Branch one:
% 13.31/3.64 | (348) all_0_8_8 = n3
% 13.31/3.64 |
% 13.31/3.64 | From (348) and (960) follows:
% 13.31/3.64 | (1047) sum(n3, n9) = all_0_4_4
% 13.31/3.64 |
% 13.31/3.64 | From (348) and (958) follows:
% 13.31/3.64 | (1048) sum(n3, n8) = all_0_2_2
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n3, n9, all_0_4_4, n1 and discharging atoms sum(n3, n9) = all_0_4_4, sum(n3, n9) = n1, yields:
% 13.31/3.64 | (386) all_0_4_4 = n1
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n3, n8, all_0_2_2, n0 and discharging atoms sum(n3, n8) = all_0_2_2, sum(n3, n8) = n0, yields:
% 13.31/3.64 | (385) all_0_2_2 = n0
% 13.31/3.64 |
% 13.31/3.64 | From (385) and (205) follows:
% 13.31/3.64 | (387) pred(n0) = all_0_1_1
% 13.31/3.64 |
% 13.31/3.64 | From (386) and (138) follows:
% 13.31/3.64 | (388) pred(n1) = all_0_3_3
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (116) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 13.31/3.64 | (389) all_0_3_3 = n0
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (116) with n0, all_0_1_1, n10 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n10, yields:
% 13.31/3.64 | (390) all_0_1_1 = n10
% 13.31/3.64 |
% 13.31/3.64 | From (389) and (167) follows:
% 13.31/3.64 | (391) sum(n0, all_0_0_0) = all_0_6_6
% 13.31/3.64 |
% 13.31/3.64 | From (390) and (439) follows:
% 13.31/3.64 | (1056) sum(n8, n10) = all_0_0_0
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n8, n10, all_0_0_0, n7 and discharging atoms sum(n8, n10) = all_0_0_0, sum(n8, n10) = n7, yields:
% 13.31/3.64 | (240) all_0_0_0 = n7
% 13.31/3.64 |
% 13.31/3.64 | From (240) and (391) follows:
% 13.31/3.64 | (1058) sum(n0, n7) = all_0_6_6
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n0, n7, all_0_6_6, n7 and discharging atoms sum(n0, n7) = all_0_6_6, sum(n0, n7) = n7, yields:
% 13.31/3.64 | (411) all_0_6_6 = n7
% 13.31/3.64 |
% 13.31/3.64 | Equations (411) can reduce 88 to:
% 13.31/3.64 | (243) $false
% 13.31/3.64 |
% 13.31/3.64 |-The branch is then unsatisfiable
% 13.31/3.64 |-Branch two:
% 13.31/3.64 | (363) ~ (all_0_8_8 = n3)
% 13.31/3.64 | (364) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.31/3.64 |
% 13.31/3.64 +-Applying beta-rule and splitting (364), into two cases.
% 13.31/3.64 |-Branch one:
% 13.31/3.64 | (365) all_0_8_8 = n2
% 13.31/3.64 |
% 13.31/3.64 | From (365) and (960) follows:
% 13.31/3.64 | (1064) sum(n2, n9) = all_0_4_4
% 13.31/3.64 |
% 13.31/3.64 | From (365) and (958) follows:
% 13.31/3.64 | (1065) sum(n2, n8) = all_0_2_2
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n2, n9, all_0_4_4, n0 and discharging atoms sum(n2, n9) = all_0_4_4, sum(n2, n9) = n0, yields:
% 13.31/3.64 | (402) all_0_4_4 = n0
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n2, n8, all_0_2_2, n10 and discharging atoms sum(n2, n8) = all_0_2_2, sum(n2, n8) = n10, yields:
% 13.31/3.64 | (401) all_0_2_2 = n10
% 13.31/3.64 |
% 13.31/3.64 | From (401) and (205) follows:
% 13.31/3.64 | (403) pred(n10) = all_0_1_1
% 13.31/3.64 |
% 13.31/3.64 | From (402) and (138) follows:
% 13.31/3.64 | (404) pred(n0) = all_0_3_3
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (116) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 13.31/3.64 | (405) all_0_1_1 = n9
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (116) with n0, all_0_3_3, n10 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n10, yields:
% 13.31/3.64 | (406) all_0_3_3 = n10
% 13.31/3.64 |
% 13.31/3.64 | From (406) and (167) follows:
% 13.31/3.64 | (407) sum(n10, all_0_0_0) = all_0_6_6
% 13.31/3.64 |
% 13.31/3.64 | From (405) and (439) follows:
% 13.31/3.64 | (1073) sum(n8, n9) = all_0_0_0
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n8, n9, all_0_0_0, n6 and discharging atoms sum(n8, n9) = all_0_0_0, sum(n8, n9) = n6, yields:
% 13.31/3.64 | (257) all_0_0_0 = n6
% 13.31/3.64 |
% 13.31/3.64 | From (257) and (407) follows:
% 13.31/3.64 | (1075) sum(n10, n6) = all_0_6_6
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n10, n6, all_0_6_6, n5 and discharging atoms sum(n10, n6) = all_0_6_6, sum(n10, n6) = n5, yields:
% 13.31/3.64 | (242) all_0_6_6 = n5
% 13.31/3.64 |
% 13.31/3.64 | Equations (242) can reduce 4 to:
% 13.31/3.64 | (243) $false
% 13.31/3.64 |
% 13.31/3.64 |-The branch is then unsatisfiable
% 13.31/3.64 |-Branch two:
% 13.31/3.64 | (380) ~ (all_0_8_8 = n2)
% 13.31/3.64 | (381) all_0_8_8 = n1 | all_0_8_8 = n0
% 13.31/3.64 |
% 13.31/3.64 +-Applying beta-rule and splitting (381), into two cases.
% 13.31/3.64 |-Branch one:
% 13.31/3.64 | (382) all_0_8_8 = n1
% 13.31/3.64 |
% 13.31/3.64 | From (382) and (960) follows:
% 13.31/3.64 | (1081) sum(n1, n9) = all_0_4_4
% 13.31/3.64 |
% 13.31/3.64 | From (382) and (958) follows:
% 13.31/3.64 | (1082) sum(n1, n8) = all_0_2_2
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n1, n9, all_0_4_4, n10 and discharging atoms sum(n1, n9) = all_0_4_4, sum(n1, n9) = n10, yields:
% 13.31/3.64 | (233) all_0_4_4 = n10
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n1, n8, all_0_2_2, n9 and discharging atoms sum(n1, n8) = all_0_2_2, sum(n1, n8) = n9, yields:
% 13.31/3.64 | (232) all_0_2_2 = n9
% 13.31/3.64 |
% 13.31/3.64 | From (232) and (205) follows:
% 13.31/3.64 | (234) pred(n9) = all_0_1_1
% 13.31/3.64 |
% 13.31/3.64 | From (233) and (138) follows:
% 13.31/3.64 | (235) pred(n10) = all_0_3_3
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (116) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 13.31/3.64 | (236) all_0_3_3 = n9
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (116) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 13.31/3.64 | (237) all_0_1_1 = n8
% 13.31/3.64 |
% 13.31/3.64 | From (236) and (167) follows:
% 13.31/3.64 | (238) sum(n9, all_0_0_0) = all_0_6_6
% 13.31/3.64 |
% 13.31/3.64 | From (237) and (439) follows:
% 13.31/3.64 | (1090) sum(n8, n8) = all_0_0_0
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n8, n8, all_0_0_0, n5 and discharging atoms sum(n8, n8) = all_0_0_0, sum(n8, n8) = n5, yields:
% 13.31/3.64 | (274) all_0_0_0 = n5
% 13.31/3.64 |
% 13.31/3.64 | From (274) and (238) follows:
% 13.31/3.64 | (1092) sum(n9, n5) = all_0_6_6
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n9, n5, all_0_6_6, n3 and discharging atoms sum(n9, n5) = all_0_6_6, sum(n9, n5) = n3, yields:
% 13.31/3.64 | (259) all_0_6_6 = n3
% 13.31/3.64 |
% 13.31/3.64 | Equations (259) can reduce 100 to:
% 13.31/3.64 | (243) $false
% 13.31/3.64 |
% 13.31/3.64 |-The branch is then unsatisfiable
% 13.31/3.64 |-Branch two:
% 13.31/3.64 | (397) ~ (all_0_8_8 = n1)
% 13.31/3.64 | (398) all_0_8_8 = n0
% 13.31/3.64 |
% 13.31/3.64 | From (398) and (960) follows:
% 13.31/3.64 | (1097) sum(n0, n9) = all_0_4_4
% 13.31/3.64 |
% 13.31/3.64 | From (398) and (958) follows:
% 13.31/3.64 | (1098) sum(n0, n8) = all_0_2_2
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n0, n9, all_0_4_4, n9 and discharging atoms sum(n0, n9) = all_0_4_4, sum(n0, n9) = n9, yields:
% 13.31/3.64 | (250) all_0_4_4 = n9
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n0, n8, all_0_2_2, n8 and discharging atoms sum(n0, n8) = all_0_2_2, sum(n0, n8) = n8, yields:
% 13.31/3.64 | (249) all_0_2_2 = n8
% 13.31/3.64 |
% 13.31/3.64 | From (249) and (205) follows:
% 13.31/3.64 | (251) pred(n8) = all_0_1_1
% 13.31/3.64 |
% 13.31/3.64 | From (250) and (138) follows:
% 13.31/3.64 | (252) pred(n9) = all_0_3_3
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (116) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 13.31/3.64 | (253) all_0_3_3 = n8
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (116) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 13.31/3.64 | (254) all_0_1_1 = n7
% 13.31/3.64 |
% 13.31/3.64 | From (253) and (167) follows:
% 13.31/3.64 | (255) sum(n8, all_0_0_0) = all_0_6_6
% 13.31/3.64 |
% 13.31/3.64 | From (254) and (439) follows:
% 13.31/3.64 | (1106) sum(n8, n7) = all_0_0_0
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n8, n7, all_0_0_0, n4 and discharging atoms sum(n8, n7) = all_0_0_0, sum(n8, n7) = n4, yields:
% 13.31/3.64 | (291) all_0_0_0 = n4
% 13.31/3.64 |
% 13.31/3.64 | From (291) and (255) follows:
% 13.31/3.64 | (1108) sum(n8, n4) = all_0_6_6
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n8, n4, all_0_6_6, n1 and discharging atoms sum(n8, n4) = all_0_6_6, sum(n8, n4) = n1, yields:
% 13.31/3.64 | (276) all_0_6_6 = n1
% 13.31/3.64 |
% 13.31/3.64 | Equations (276) can reduce 28 to:
% 13.31/3.64 | (243) $false
% 13.31/3.64 |
% 13.31/3.64 |-The branch is then unsatisfiable
% 13.31/3.64 |-Branch two:
% 13.31/3.64 | (454) ~ (all_0_7_7 = n8)
% 13.31/3.64 | (455) all_0_7_7 = n7 | all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.31/3.64 |
% 13.31/3.64 +-Applying beta-rule and splitting (262), into two cases.
% 13.31/3.64 |-Branch one:
% 13.31/3.64 | (263) all_0_8_8 = n8
% 13.31/3.64 |
% 13.31/3.64 | From (263) and (77) follows:
% 13.31/3.64 | (1114) sum(n8, all_0_5_5) = all_0_4_4
% 13.31/3.64 |
% 13.31/3.64 | From (263) and (120) follows:
% 13.31/3.64 | (1115) sum(n8, all_0_7_7) = all_0_2_2
% 13.31/3.64 |
% 13.31/3.64 +-Applying beta-rule and splitting (455), into two cases.
% 13.31/3.64 |-Branch one:
% 13.31/3.64 | (456) all_0_7_7 = n7
% 13.31/3.64 |
% 13.31/3.64 | From (456) and (10) follows:
% 13.31/3.64 | (457) succ(n7) = all_0_5_5
% 13.31/3.64 |
% 13.31/3.64 | From (456) and (3) follows:
% 13.31/3.64 | (458) sum(n7, all_0_1_1) = all_0_0_0
% 13.31/3.64 |
% 13.31/3.64 | From (456) and (1115) follows:
% 13.31/3.64 | (1119) sum(n8, n7) = all_0_2_2
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (47) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 13.31/3.64 | (460) all_0_5_5 = n8
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n8, n7, all_0_2_2, n4 and discharging atoms sum(n8, n7) = all_0_2_2, sum(n8, n7) = n4, yields:
% 13.31/3.64 | (317) all_0_2_2 = n4
% 13.31/3.64 |
% 13.31/3.64 | From (317) and (205) follows:
% 13.31/3.64 | (319) pred(n4) = all_0_1_1
% 13.31/3.64 |
% 13.31/3.64 | From (460) and (1114) follows:
% 13.31/3.64 | (1123) sum(n8, n8) = all_0_4_4
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (116) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 13.31/3.64 | (322) all_0_1_1 = n3
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n8, n8, all_0_4_4, n5 and discharging atoms sum(n8, n8) = all_0_4_4, sum(n8, n8) = n5, yields:
% 13.31/3.64 | (318) all_0_4_4 = n5
% 13.31/3.64 |
% 13.31/3.64 | From (318) and (138) follows:
% 13.31/3.64 | (320) pred(n5) = all_0_3_3
% 13.31/3.64 |
% 13.31/3.64 | From (322) and (458) follows:
% 13.31/3.64 | (1127) sum(n7, n3) = all_0_0_0
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (116) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 13.31/3.64 | (321) all_0_3_3 = n4
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n7, n3, all_0_0_0, n10 and discharging atoms sum(n7, n3) = all_0_0_0, sum(n7, n3) = n10, yields:
% 13.31/3.64 | (376) all_0_0_0 = n10
% 13.31/3.64 |
% 13.31/3.64 | From (321)(376) and (167) follows:
% 13.31/3.64 | (1130) sum(n4, n10) = all_0_6_6
% 13.31/3.64 |
% 13.31/3.64 | Instantiating formula (132) with n4, n10, all_0_6_6, n3 and discharging atoms sum(n4, n10) = all_0_6_6, sum(n4, n10) = n3, yields:
% 13.31/3.65 | (259) all_0_6_6 = n3
% 13.31/3.65 |
% 13.31/3.65 | Equations (259) can reduce 100 to:
% 13.31/3.65 | (243) $false
% 13.31/3.65 |
% 13.31/3.65 |-The branch is then unsatisfiable
% 13.31/3.65 |-Branch two:
% 13.31/3.65 | (473) ~ (all_0_7_7 = n7)
% 13.31/3.65 | (474) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.31/3.65 |
% 13.31/3.65 +-Applying beta-rule and splitting (474), into two cases.
% 13.31/3.65 |-Branch one:
% 13.31/3.65 | (475) all_0_7_7 = n6
% 13.31/3.65 |
% 13.31/3.65 | From (475) and (10) follows:
% 13.31/3.65 | (476) succ(n6) = all_0_5_5
% 13.31/3.65 |
% 13.31/3.65 | From (475) and (3) follows:
% 13.31/3.65 | (477) sum(n6, all_0_1_1) = all_0_0_0
% 13.31/3.65 |
% 13.31/3.65 | From (475) and (1115) follows:
% 13.31/3.65 | (1138) sum(n8, n6) = all_0_2_2
% 13.31/3.65 |
% 13.31/3.65 | Instantiating formula (47) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 13.31/3.65 | (479) all_0_5_5 = n7
% 13.31/3.65 |
% 13.31/3.65 | Instantiating formula (132) with n8, n6, all_0_2_2, n3 and discharging atoms sum(n8, n6) = all_0_2_2, sum(n8, n6) = n3, yields:
% 13.31/3.65 | (334) all_0_2_2 = n3
% 13.31/3.65 |
% 13.31/3.65 | From (334) and (205) follows:
% 13.31/3.65 | (336) pred(n3) = all_0_1_1
% 13.31/3.65 |
% 13.31/3.65 | From (479) and (1114) follows:
% 13.31/3.65 | (1142) sum(n8, n7) = all_0_4_4
% 13.31/3.65 |
% 13.31/3.65 | Instantiating formula (116) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 13.31/3.65 | (339) all_0_1_1 = n2
% 13.31/3.65 |
% 13.31/3.65 | Instantiating formula (132) with n8, n7, all_0_4_4, n4 and discharging atoms sum(n8, n7) = all_0_4_4, sum(n8, n7) = n4, yields:
% 13.31/3.65 | (335) all_0_4_4 = n4
% 13.31/3.65 |
% 13.31/3.65 | From (335) and (138) follows:
% 13.31/3.65 | (337) pred(n4) = all_0_3_3
% 13.31/3.65 |
% 13.31/3.65 | From (339) and (477) follows:
% 13.31/3.65 | (1146) sum(n6, n2) = all_0_0_0
% 13.31/3.65 |
% 13.31/3.65 | Instantiating formula (116) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 13.31/3.65 | (338) all_0_3_3 = n3
% 13.31/3.65 |
% 13.31/3.65 | Instantiating formula (132) with n6, n2, all_0_0_0, n8 and discharging atoms sum(n6, n2) = all_0_0_0, sum(n6, n2) = n8, yields:
% 13.31/3.65 | (409) all_0_0_0 = n8
% 13.31/3.65 |
% 13.31/3.65 | From (338)(409) and (167) follows:
% 13.31/3.65 | (1149) sum(n3, n8) = all_0_6_6
% 13.31/3.65 |
% 13.31/3.65 | Instantiating formula (132) with n3, n8, all_0_6_6, n0 and discharging atoms sum(n3, n8) = all_0_6_6, sum(n3, n8) = n0, yields:
% 13.31/3.65 | (378) all_0_6_6 = n0
% 13.31/3.65 |
% 13.31/3.65 | Equations (378) can reduce 119 to:
% 13.31/3.65 | (243) $false
% 13.31/3.65 |
% 13.31/3.65 |-The branch is then unsatisfiable
% 13.31/3.65 |-Branch two:
% 13.45/3.65 | (492) ~ (all_0_7_7 = n6)
% 13.45/3.65 | (493) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.45/3.65 |
% 13.45/3.65 +-Applying beta-rule and splitting (493), into two cases.
% 13.45/3.65 |-Branch one:
% 13.45/3.65 | (494) all_0_7_7 = n5
% 13.45/3.65 |
% 13.45/3.65 | From (494) and (10) follows:
% 13.45/3.65 | (495) succ(n5) = all_0_5_5
% 13.45/3.65 |
% 13.45/3.65 | From (494) and (3) follows:
% 13.45/3.65 | (496) sum(n5, all_0_1_1) = all_0_0_0
% 13.45/3.65 |
% 13.45/3.65 | From (494) and (1115) follows:
% 13.45/3.65 | (1157) sum(n8, n5) = all_0_2_2
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (47) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 13.45/3.65 | (498) all_0_5_5 = n6
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (132) with n8, n5, all_0_2_2, n2 and discharging atoms sum(n8, n5) = all_0_2_2, sum(n8, n5) = n2, yields:
% 13.45/3.65 | (351) all_0_2_2 = n2
% 13.45/3.65 |
% 13.45/3.65 | From (351) and (205) follows:
% 13.45/3.65 | (353) pred(n2) = all_0_1_1
% 13.45/3.65 |
% 13.45/3.65 | From (498) and (1114) follows:
% 13.45/3.65 | (1161) sum(n8, n6) = all_0_4_4
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (116) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 13.45/3.65 | (356) all_0_1_1 = n1
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (132) with n8, n6, all_0_4_4, n3 and discharging atoms sum(n8, n6) = all_0_4_4, sum(n8, n6) = n3, yields:
% 13.45/3.65 | (352) all_0_4_4 = n3
% 13.45/3.65 |
% 13.45/3.65 | From (352) and (138) follows:
% 13.45/3.65 | (354) pred(n3) = all_0_3_3
% 13.45/3.65 |
% 13.45/3.65 | From (356) and (496) follows:
% 13.45/3.65 | (1165) sum(n5, n1) = all_0_0_0
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (116) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 13.45/3.65 | (355) all_0_3_3 = n2
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (132) with n5, n1, all_0_0_0, n6 and discharging atoms sum(n5, n1) = all_0_0_0, sum(n5, n1) = n6, yields:
% 13.45/3.65 | (257) all_0_0_0 = n6
% 13.45/3.65 |
% 13.45/3.65 | From (355)(257) and (167) follows:
% 13.45/3.65 | (1168) sum(n2, n6) = all_0_6_6
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (132) with n2, n6, all_0_6_6, n8 and discharging atoms sum(n2, n6) = all_0_6_6, sum(n2, n6) = n8, yields:
% 13.45/3.65 | (310) all_0_6_6 = n8
% 13.45/3.65 |
% 13.45/3.65 | Equations (310) can reduce 165 to:
% 13.45/3.65 | (243) $false
% 13.45/3.65 |
% 13.45/3.65 |-The branch is then unsatisfiable
% 13.45/3.65 |-Branch two:
% 13.45/3.65 | (511) ~ (all_0_7_7 = n5)
% 13.45/3.65 | (512) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.45/3.65 |
% 13.45/3.65 +-Applying beta-rule and splitting (512), into two cases.
% 13.45/3.65 |-Branch one:
% 13.45/3.65 | (513) all_0_7_7 = n4
% 13.45/3.65 |
% 13.45/3.65 | From (513) and (10) follows:
% 13.45/3.65 | (514) succ(n4) = all_0_5_5
% 13.45/3.65 |
% 13.45/3.65 | From (513) and (3) follows:
% 13.45/3.65 | (515) sum(n4, all_0_1_1) = all_0_0_0
% 13.45/3.65 |
% 13.45/3.65 | From (513) and (1115) follows:
% 13.45/3.65 | (1176) sum(n8, n4) = all_0_2_2
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (47) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 13.45/3.65 | (517) all_0_5_5 = n5
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (132) with n8, n4, all_0_2_2, n1 and discharging atoms sum(n8, n4) = all_0_2_2, sum(n8, n4) = n1, yields:
% 13.45/3.65 | (368) all_0_2_2 = n1
% 13.45/3.65 |
% 13.45/3.65 | From (368) and (205) follows:
% 13.45/3.65 | (370) pred(n1) = all_0_1_1
% 13.45/3.65 |
% 13.45/3.65 | From (517) and (1114) follows:
% 13.45/3.65 | (1180) sum(n8, n5) = all_0_4_4
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (116) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 13.45/3.65 | (373) all_0_1_1 = n0
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (132) with n8, n5, all_0_4_4, n2 and discharging atoms sum(n8, n5) = all_0_4_4, sum(n8, n5) = n2, yields:
% 13.45/3.65 | (369) all_0_4_4 = n2
% 13.45/3.65 |
% 13.45/3.65 | From (369) and (138) follows:
% 13.45/3.65 | (371) pred(n2) = all_0_3_3
% 13.45/3.65 |
% 13.45/3.65 | From (373) and (515) follows:
% 13.45/3.65 | (1184) sum(n4, n0) = all_0_0_0
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (116) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 13.45/3.65 | (372) all_0_3_3 = n1
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (132) with n4, n0, all_0_0_0, n4 and discharging atoms sum(n4, n0) = all_0_0_0, sum(n4, n0) = n4, yields:
% 13.45/3.65 | (291) all_0_0_0 = n4
% 13.45/3.65 |
% 13.45/3.65 | From (372)(291) and (167) follows:
% 13.45/3.65 | (1187) sum(n1, n4) = all_0_6_6
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (132) with n1, n4, all_0_6_6, n5 and discharging atoms sum(n1, n4) = all_0_6_6, sum(n1, n4) = n5, yields:
% 13.45/3.65 | (242) all_0_6_6 = n5
% 13.45/3.65 |
% 13.45/3.65 | Equations (242) can reduce 4 to:
% 13.45/3.65 | (243) $false
% 13.45/3.65 |
% 13.45/3.65 |-The branch is then unsatisfiable
% 13.45/3.65 |-Branch two:
% 13.45/3.65 | (530) ~ (all_0_7_7 = n4)
% 13.45/3.65 | (531) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.45/3.65 |
% 13.45/3.65 +-Applying beta-rule and splitting (531), into two cases.
% 13.45/3.65 |-Branch one:
% 13.45/3.65 | (532) all_0_7_7 = n3
% 13.45/3.65 |
% 13.45/3.65 | From (532) and (10) follows:
% 13.45/3.65 | (533) succ(n3) = all_0_5_5
% 13.45/3.65 |
% 13.45/3.65 | From (532) and (3) follows:
% 13.45/3.65 | (534) sum(n3, all_0_1_1) = all_0_0_0
% 13.45/3.65 |
% 13.45/3.65 | From (532) and (1115) follows:
% 13.45/3.65 | (1195) sum(n8, n3) = all_0_2_2
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (47) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 13.45/3.65 | (536) all_0_5_5 = n4
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (132) with n8, n3, all_0_2_2, n0 and discharging atoms sum(n8, n3) = all_0_2_2, sum(n8, n3) = n0, yields:
% 13.45/3.65 | (385) all_0_2_2 = n0
% 13.45/3.65 |
% 13.45/3.65 | From (385) and (205) follows:
% 13.45/3.65 | (387) pred(n0) = all_0_1_1
% 13.45/3.65 |
% 13.45/3.65 | From (536) and (1114) follows:
% 13.45/3.65 | (1199) sum(n8, n4) = all_0_4_4
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (116) with n0, all_0_1_1, n10 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n10, yields:
% 13.45/3.65 | (390) all_0_1_1 = n10
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (132) with n8, n4, all_0_4_4, n1 and discharging atoms sum(n8, n4) = all_0_4_4, sum(n8, n4) = n1, yields:
% 13.45/3.65 | (386) all_0_4_4 = n1
% 13.45/3.65 |
% 13.45/3.65 | From (386) and (138) follows:
% 13.45/3.65 | (388) pred(n1) = all_0_3_3
% 13.45/3.65 |
% 13.45/3.65 | From (390) and (534) follows:
% 13.45/3.65 | (1203) sum(n3, n10) = all_0_0_0
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (116) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 13.45/3.65 | (389) all_0_3_3 = n0
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (132) with n3, n10, all_0_0_0, n2 and discharging atoms sum(n3, n10) = all_0_0_0, sum(n3, n10) = n2, yields:
% 13.45/3.65 | (325) all_0_0_0 = n2
% 13.45/3.65 |
% 13.45/3.65 | From (389)(325) and (167) follows:
% 13.45/3.65 | (1206) sum(n0, n2) = all_0_6_6
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (132) with n0, n2, all_0_6_6, n2 and discharging atoms sum(n0, n2) = all_0_6_6, sum(n0, n2) = n2, yields:
% 13.45/3.65 | (361) all_0_6_6 = n2
% 13.45/3.65 |
% 13.45/3.65 | Equations (361) can reduce 131 to:
% 13.45/3.65 | (243) $false
% 13.45/3.65 |
% 13.45/3.65 |-The branch is then unsatisfiable
% 13.45/3.65 |-Branch two:
% 13.45/3.65 | (549) ~ (all_0_7_7 = n3)
% 13.45/3.65 | (550) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.45/3.65 |
% 13.45/3.65 +-Applying beta-rule and splitting (550), into two cases.
% 13.45/3.65 |-Branch one:
% 13.45/3.65 | (551) all_0_7_7 = n2
% 13.45/3.65 |
% 13.45/3.65 | From (551) and (10) follows:
% 13.45/3.65 | (552) succ(n2) = all_0_5_5
% 13.45/3.65 |
% 13.45/3.65 | From (551) and (3) follows:
% 13.45/3.65 | (553) sum(n2, all_0_1_1) = all_0_0_0
% 13.45/3.65 |
% 13.45/3.65 | From (551) and (1115) follows:
% 13.45/3.65 | (1214) sum(n8, n2) = all_0_2_2
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (47) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 13.45/3.65 | (555) all_0_5_5 = n3
% 13.45/3.65 |
% 13.45/3.65 | Instantiating formula (132) with n8, n2, all_0_2_2, n10 and discharging atoms sum(n8, n2) = all_0_2_2, sum(n8, n2) = n10, yields:
% 13.45/3.65 | (401) all_0_2_2 = n10
% 13.45/3.65 |
% 13.45/3.65 | From (401) and (205) follows:
% 13.45/3.65 | (403) pred(n10) = all_0_1_1
% 13.45/3.65 |
% 13.45/3.65 | From (555) and (1114) follows:
% 13.45/3.66 | (1218) sum(n8, n3) = all_0_4_4
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (116) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 13.45/3.66 | (405) all_0_1_1 = n9
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n8, n3, all_0_4_4, n0 and discharging atoms sum(n8, n3) = all_0_4_4, sum(n8, n3) = n0, yields:
% 13.45/3.66 | (402) all_0_4_4 = n0
% 13.45/3.66 |
% 13.45/3.66 | From (402) and (138) follows:
% 13.45/3.66 | (404) pred(n0) = all_0_3_3
% 13.45/3.66 |
% 13.45/3.66 | From (405) and (553) follows:
% 13.45/3.66 | (1222) sum(n2, n9) = all_0_0_0
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (116) with n0, all_0_3_3, n10 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n10, yields:
% 13.45/3.66 | (406) all_0_3_3 = n10
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n2, n9, all_0_0_0, n0 and discharging atoms sum(n2, n9) = all_0_0_0, sum(n2, n9) = n0, yields:
% 13.45/3.66 | (359) all_0_0_0 = n0
% 13.45/3.66 |
% 13.45/3.66 | From (406)(359) and (167) follows:
% 13.45/3.66 | (1225) sum(n10, n0) = all_0_6_6
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n10, n0, all_0_6_6, n10 and discharging atoms sum(n10, n0) = all_0_6_6, sum(n10, n0) = n10, yields:
% 13.45/3.66 | (293) all_0_6_6 = n10
% 13.45/3.66 |
% 13.45/3.66 | Equations (293) can reduce 147 to:
% 13.45/3.66 | (243) $false
% 13.45/3.66 |
% 13.45/3.66 |-The branch is then unsatisfiable
% 13.45/3.66 |-Branch two:
% 13.45/3.66 | (568) ~ (all_0_7_7 = n2)
% 13.45/3.66 | (569) all_0_7_7 = n1 | all_0_7_7 = n0
% 13.45/3.66 |
% 13.45/3.66 +-Applying beta-rule and splitting (569), into two cases.
% 13.45/3.66 |-Branch one:
% 13.45/3.66 | (570) all_0_7_7 = n1
% 13.45/3.66 |
% 13.45/3.66 | From (570) and (10) follows:
% 13.45/3.66 | (571) succ(n1) = all_0_5_5
% 13.45/3.66 |
% 13.45/3.66 | From (570) and (3) follows:
% 13.45/3.66 | (572) sum(n1, all_0_1_1) = all_0_0_0
% 13.45/3.66 |
% 13.45/3.66 | From (570) and (1115) follows:
% 13.45/3.66 | (1233) sum(n8, n1) = all_0_2_2
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (47) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 13.45/3.66 | (574) all_0_5_5 = n2
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n8, n1, all_0_2_2, n9 and discharging atoms sum(n8, n1) = all_0_2_2, sum(n8, n1) = n9, yields:
% 13.45/3.66 | (232) all_0_2_2 = n9
% 13.45/3.66 |
% 13.45/3.66 | From (232) and (205) follows:
% 13.45/3.66 | (234) pred(n9) = all_0_1_1
% 13.45/3.66 |
% 13.45/3.66 | From (574) and (1114) follows:
% 13.45/3.66 | (1237) sum(n8, n2) = all_0_4_4
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (116) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 13.45/3.66 | (237) all_0_1_1 = n8
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n8, n2, all_0_4_4, n10 and discharging atoms sum(n8, n2) = all_0_4_4, sum(n8, n2) = n10, yields:
% 13.45/3.66 | (233) all_0_4_4 = n10
% 13.45/3.66 |
% 13.45/3.66 | From (233) and (138) follows:
% 13.45/3.66 | (235) pred(n10) = all_0_3_3
% 13.45/3.66 |
% 13.45/3.66 | From (237) and (572) follows:
% 13.45/3.66 | (1241) sum(n1, n8) = all_0_0_0
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (116) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 13.45/3.66 | (236) all_0_3_3 = n9
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n1, n8, all_0_0_0, n9 and discharging atoms sum(n1, n8) = all_0_0_0, sum(n1, n8) = n9, yields:
% 13.45/3.66 | (393) all_0_0_0 = n9
% 13.45/3.66 |
% 13.45/3.66 | From (236)(393) and (167) follows:
% 13.45/3.66 | (1244) sum(n9, n9) = all_0_6_6
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n9, n9, all_0_6_6, n7 and discharging atoms sum(n9, n9) = all_0_6_6, sum(n9, n9) = n7, yields:
% 13.45/3.66 | (411) all_0_6_6 = n7
% 13.45/3.66 |
% 13.45/3.66 | Equations (411) can reduce 88 to:
% 13.45/3.66 | (243) $false
% 13.45/3.66 |
% 13.45/3.66 |-The branch is then unsatisfiable
% 13.45/3.66 |-Branch two:
% 13.45/3.66 | (587) ~ (all_0_7_7 = n1)
% 13.45/3.66 | (588) all_0_7_7 = n0
% 13.45/3.66 |
% 13.45/3.66 | From (588) and (10) follows:
% 13.45/3.66 | (589) succ(n0) = all_0_5_5
% 13.45/3.66 |
% 13.45/3.66 | From (588) and (3) follows:
% 13.45/3.66 | (590) sum(n0, all_0_1_1) = all_0_0_0
% 13.45/3.66 |
% 13.45/3.66 | From (588) and (1115) follows:
% 13.45/3.66 | (1251) sum(n8, n0) = all_0_2_2
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (47) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 13.45/3.66 | (592) all_0_5_5 = n1
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n8, n0, all_0_2_2, n8 and discharging atoms sum(n8, n0) = all_0_2_2, sum(n8, n0) = n8, yields:
% 13.45/3.66 | (249) all_0_2_2 = n8
% 13.45/3.66 |
% 13.45/3.66 | From (249) and (205) follows:
% 13.45/3.66 | (251) pred(n8) = all_0_1_1
% 13.45/3.66 |
% 13.45/3.66 | From (592) and (1114) follows:
% 13.45/3.66 | (1255) sum(n8, n1) = all_0_4_4
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (116) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 13.45/3.66 | (254) all_0_1_1 = n7
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n8, n1, all_0_4_4, n9 and discharging atoms sum(n8, n1) = all_0_4_4, sum(n8, n1) = n9, yields:
% 13.45/3.66 | (250) all_0_4_4 = n9
% 13.45/3.66 |
% 13.45/3.66 | From (250) and (138) follows:
% 13.45/3.66 | (252) pred(n9) = all_0_3_3
% 13.45/3.66 |
% 13.45/3.66 | From (254) and (590) follows:
% 13.45/3.66 | (1259) sum(n0, n7) = all_0_0_0
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (116) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 13.45/3.66 | (253) all_0_3_3 = n8
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n0, n7, all_0_0_0, n7 and discharging atoms sum(n0, n7) = all_0_0_0, sum(n0, n7) = n7, yields:
% 13.45/3.66 | (240) all_0_0_0 = n7
% 13.45/3.66 |
% 13.45/3.66 | From (253)(240) and (167) follows:
% 13.45/3.66 | (1262) sum(n8, n7) = all_0_6_6
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n8, n7, all_0_6_6, n4 and discharging atoms sum(n8, n7) = all_0_6_6, sum(n8, n7) = n4, yields:
% 13.45/3.66 | (344) all_0_6_6 = n4
% 13.45/3.66 |
% 13.45/3.66 | Equations (344) can reduce 216 to:
% 13.45/3.66 | (243) $false
% 13.45/3.66 |
% 13.45/3.66 |-The branch is then unsatisfiable
% 13.45/3.66 |-Branch two:
% 13.45/3.66 | (278) ~ (all_0_8_8 = n8)
% 13.45/3.66 | (279) all_0_8_8 = n7 | all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.66 |
% 13.45/3.66 +-Applying beta-rule and splitting (455), into two cases.
% 13.45/3.66 |-Branch one:
% 13.45/3.66 | (456) all_0_7_7 = n7
% 13.45/3.66 |
% 13.45/3.66 | From (456) and (10) follows:
% 13.45/3.66 | (457) succ(n7) = all_0_5_5
% 13.45/3.66 |
% 13.45/3.66 | From (456) and (3) follows:
% 13.45/3.66 | (458) sum(n7, all_0_1_1) = all_0_0_0
% 13.45/3.66 |
% 13.45/3.66 | From (456) and (120) follows:
% 13.45/3.66 | (1270) sum(all_0_8_8, n7) = all_0_2_2
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (47) with n7, all_0_5_5, n8 and discharging atoms succ(n7) = all_0_5_5, succ(n7) = n8, yields:
% 13.45/3.66 | (460) all_0_5_5 = n8
% 13.45/3.66 |
% 13.45/3.66 | From (460) and (77) follows:
% 13.45/3.66 | (1272) sum(all_0_8_8, n8) = all_0_4_4
% 13.45/3.66 |
% 13.45/3.66 +-Applying beta-rule and splitting (279), into two cases.
% 13.45/3.66 |-Branch one:
% 13.45/3.66 | (280) all_0_8_8 = n7
% 13.45/3.66 |
% 13.45/3.66 | From (280) and (1272) follows:
% 13.45/3.66 | (1274) sum(n7, n8) = all_0_4_4
% 13.45/3.66 |
% 13.45/3.66 | From (280) and (1270) follows:
% 13.45/3.66 | (1275) sum(n7, n7) = all_0_2_2
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n7, n8, all_0_4_4, n4 and discharging atoms sum(n7, n8) = all_0_4_4, sum(n7, n8) = n4, yields:
% 13.45/3.66 | (335) all_0_4_4 = n4
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n7, n7, all_0_2_2, n3 and discharging atoms sum(n7, n7) = all_0_2_2, sum(n7, n7) = n3, yields:
% 13.45/3.66 | (334) all_0_2_2 = n3
% 13.45/3.66 |
% 13.45/3.66 | From (334) and (205) follows:
% 13.45/3.66 | (336) pred(n3) = all_0_1_1
% 13.45/3.66 |
% 13.45/3.66 | From (335) and (138) follows:
% 13.45/3.66 | (337) pred(n4) = all_0_3_3
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (116) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 13.45/3.66 | (338) all_0_3_3 = n3
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (116) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 13.45/3.66 | (339) all_0_1_1 = n2
% 13.45/3.66 |
% 13.45/3.66 | From (338) and (167) follows:
% 13.45/3.66 | (340) sum(n3, all_0_0_0) = all_0_6_6
% 13.45/3.66 |
% 13.45/3.66 | From (339) and (458) follows:
% 13.45/3.66 | (1283) sum(n7, n2) = all_0_0_0
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n7, n2, all_0_0_0, n9 and discharging atoms sum(n7, n2) = all_0_0_0, sum(n7, n2) = n9, yields:
% 13.45/3.66 | (393) all_0_0_0 = n9
% 13.45/3.66 |
% 13.45/3.66 | From (393) and (340) follows:
% 13.45/3.66 | (1285) sum(n3, n9) = all_0_6_6
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n3, n9, all_0_6_6, n1 and discharging atoms sum(n3, n9) = all_0_6_6, sum(n3, n9) = n1, yields:
% 13.45/3.66 | (276) all_0_6_6 = n1
% 13.45/3.66 |
% 13.45/3.66 | Equations (276) can reduce 28 to:
% 13.45/3.66 | (243) $false
% 13.45/3.66 |
% 13.45/3.66 |-The branch is then unsatisfiable
% 13.45/3.66 |-Branch two:
% 13.45/3.66 | (295) ~ (all_0_8_8 = n7)
% 13.45/3.66 | (296) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.66 |
% 13.45/3.66 +-Applying beta-rule and splitting (296), into two cases.
% 13.45/3.66 |-Branch one:
% 13.45/3.66 | (297) all_0_8_8 = n6
% 13.45/3.66 |
% 13.45/3.66 | From (297) and (1272) follows:
% 13.45/3.66 | (1291) sum(n6, n8) = all_0_4_4
% 13.45/3.66 |
% 13.45/3.66 | From (297) and (1270) follows:
% 13.45/3.66 | (1292) sum(n6, n7) = all_0_2_2
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n6, n8, all_0_4_4, n3 and discharging atoms sum(n6, n8) = all_0_4_4, sum(n6, n8) = n3, yields:
% 13.45/3.66 | (352) all_0_4_4 = n3
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n6, n7, all_0_2_2, n2 and discharging atoms sum(n6, n7) = all_0_2_2, sum(n6, n7) = n2, yields:
% 13.45/3.66 | (351) all_0_2_2 = n2
% 13.45/3.66 |
% 13.45/3.66 | From (351) and (205) follows:
% 13.45/3.66 | (353) pred(n2) = all_0_1_1
% 13.45/3.66 |
% 13.45/3.66 | From (352) and (138) follows:
% 13.45/3.66 | (354) pred(n3) = all_0_3_3
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (116) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 13.45/3.66 | (355) all_0_3_3 = n2
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (116) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 13.45/3.66 | (356) all_0_1_1 = n1
% 13.45/3.66 |
% 13.45/3.66 | From (355) and (167) follows:
% 13.45/3.66 | (357) sum(n2, all_0_0_0) = all_0_6_6
% 13.45/3.66 |
% 13.45/3.66 | From (356) and (458) follows:
% 13.45/3.66 | (1300) sum(n7, n1) = all_0_0_0
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n7, n1, all_0_0_0, n8 and discharging atoms sum(n7, n1) = all_0_0_0, sum(n7, n1) = n8, yields:
% 13.45/3.66 | (409) all_0_0_0 = n8
% 13.45/3.66 |
% 13.45/3.66 | From (409) and (357) follows:
% 13.45/3.66 | (1302) sum(n2, n8) = all_0_6_6
% 13.45/3.66 |
% 13.45/3.66 | Instantiating formula (132) with n2, n8, all_0_6_6, n10 and discharging atoms sum(n2, n8) = all_0_6_6, sum(n2, n8) = n10, yields:
% 13.45/3.67 | (293) all_0_6_6 = n10
% 13.45/3.67 |
% 13.45/3.67 | Equations (293) can reduce 147 to:
% 13.45/3.67 | (243) $false
% 13.45/3.67 |
% 13.45/3.67 |-The branch is then unsatisfiable
% 13.45/3.67 |-Branch two:
% 13.45/3.67 | (312) ~ (all_0_8_8 = n6)
% 13.45/3.67 | (313) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.67 |
% 13.45/3.67 +-Applying beta-rule and splitting (313), into two cases.
% 13.45/3.67 |-Branch one:
% 13.45/3.67 | (314) all_0_8_8 = n5
% 13.45/3.67 |
% 13.45/3.67 | From (314) and (1272) follows:
% 13.45/3.67 | (1308) sum(n5, n8) = all_0_4_4
% 13.45/3.67 |
% 13.45/3.67 | From (314) and (1270) follows:
% 13.45/3.67 | (1309) sum(n5, n7) = all_0_2_2
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n5, n8, all_0_4_4, n2 and discharging atoms sum(n5, n8) = all_0_4_4, sum(n5, n8) = n2, yields:
% 13.45/3.67 | (369) all_0_4_4 = n2
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n5, n7, all_0_2_2, n1 and discharging atoms sum(n5, n7) = all_0_2_2, sum(n5, n7) = n1, yields:
% 13.45/3.67 | (368) all_0_2_2 = n1
% 13.45/3.67 |
% 13.45/3.67 | From (368) and (205) follows:
% 13.45/3.67 | (370) pred(n1) = all_0_1_1
% 13.45/3.67 |
% 13.45/3.67 | From (369) and (138) follows:
% 13.45/3.67 | (371) pred(n2) = all_0_3_3
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (116) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 13.45/3.67 | (372) all_0_3_3 = n1
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (116) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 13.45/3.67 | (373) all_0_1_1 = n0
% 13.45/3.67 |
% 13.45/3.67 | From (372) and (167) follows:
% 13.45/3.67 | (374) sum(n1, all_0_0_0) = all_0_6_6
% 13.45/3.67 |
% 13.45/3.67 | From (373) and (458) follows:
% 13.45/3.67 | (1317) sum(n7, n0) = all_0_0_0
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n7, n0, all_0_0_0, n7 and discharging atoms sum(n7, n0) = all_0_0_0, sum(n7, n0) = n7, yields:
% 13.45/3.67 | (240) all_0_0_0 = n7
% 13.45/3.67 |
% 13.45/3.67 | From (240) and (374) follows:
% 13.45/3.67 | (1319) sum(n1, n7) = all_0_6_6
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n1, n7, all_0_6_6, n8 and discharging atoms sum(n1, n7) = all_0_6_6, sum(n1, n7) = n8, yields:
% 13.45/3.67 | (310) all_0_6_6 = n8
% 13.45/3.67 |
% 13.45/3.67 | Equations (310) can reduce 165 to:
% 13.45/3.67 | (243) $false
% 13.45/3.67 |
% 13.45/3.67 |-The branch is then unsatisfiable
% 13.45/3.67 |-Branch two:
% 13.45/3.67 | (329) ~ (all_0_8_8 = n5)
% 13.45/3.67 | (330) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.67 |
% 13.45/3.67 +-Applying beta-rule and splitting (330), into two cases.
% 13.45/3.67 |-Branch one:
% 13.45/3.67 | (331) all_0_8_8 = n4
% 13.45/3.67 |
% 13.45/3.67 | From (331) and (1272) follows:
% 13.45/3.67 | (1325) sum(n4, n8) = all_0_4_4
% 13.45/3.67 |
% 13.45/3.67 | From (331) and (1270) follows:
% 13.45/3.67 | (1326) sum(n4, n7) = all_0_2_2
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n4, n8, all_0_4_4, n1 and discharging atoms sum(n4, n8) = all_0_4_4, sum(n4, n8) = n1, yields:
% 13.45/3.67 | (386) all_0_4_4 = n1
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n4, n7, all_0_2_2, n0 and discharging atoms sum(n4, n7) = all_0_2_2, sum(n4, n7) = n0, yields:
% 13.45/3.67 | (385) all_0_2_2 = n0
% 13.45/3.67 |
% 13.45/3.67 | From (385) and (205) follows:
% 13.45/3.67 | (387) pred(n0) = all_0_1_1
% 13.45/3.67 |
% 13.45/3.67 | From (386) and (138) follows:
% 13.45/3.67 | (388) pred(n1) = all_0_3_3
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (116) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 13.45/3.67 | (389) all_0_3_3 = n0
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (116) with n0, all_0_1_1, n10 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n10, yields:
% 13.45/3.67 | (390) all_0_1_1 = n10
% 13.45/3.67 |
% 13.45/3.67 | From (389) and (167) follows:
% 13.45/3.67 | (391) sum(n0, all_0_0_0) = all_0_6_6
% 13.45/3.67 |
% 13.45/3.67 | From (390) and (458) follows:
% 13.45/3.67 | (1334) sum(n7, n10) = all_0_0_0
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n7, n10, all_0_0_0, n6 and discharging atoms sum(n7, n10) = all_0_0_0, sum(n7, n10) = n6, yields:
% 13.45/3.67 | (257) all_0_0_0 = n6
% 13.45/3.67 |
% 13.45/3.67 | From (257) and (391) follows:
% 13.45/3.67 | (1336) sum(n0, n6) = all_0_6_6
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n0, n6, all_0_6_6, n6 and discharging atoms sum(n0, n6) = all_0_6_6, sum(n0, n6) = n6, yields:
% 13.45/3.67 | (327) all_0_6_6 = n6
% 13.45/3.67 |
% 13.45/3.67 | Equations (327) can reduce 34 to:
% 13.45/3.67 | (243) $false
% 13.45/3.67 |
% 13.45/3.67 |-The branch is then unsatisfiable
% 13.45/3.67 |-Branch two:
% 13.45/3.67 | (346) ~ (all_0_8_8 = n4)
% 13.45/3.67 | (347) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.67 |
% 13.45/3.67 +-Applying beta-rule and splitting (347), into two cases.
% 13.45/3.67 |-Branch one:
% 13.45/3.67 | (348) all_0_8_8 = n3
% 13.45/3.67 |
% 13.45/3.67 | From (348) and (1272) follows:
% 13.45/3.67 | (1342) sum(n3, n8) = all_0_4_4
% 13.45/3.67 |
% 13.45/3.67 | From (348) and (1270) follows:
% 13.45/3.67 | (1343) sum(n3, n7) = all_0_2_2
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n3, n8, all_0_4_4, n0 and discharging atoms sum(n3, n8) = all_0_4_4, sum(n3, n8) = n0, yields:
% 13.45/3.67 | (402) all_0_4_4 = n0
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n3, n7, all_0_2_2, n10 and discharging atoms sum(n3, n7) = all_0_2_2, sum(n3, n7) = n10, yields:
% 13.45/3.67 | (401) all_0_2_2 = n10
% 13.45/3.67 |
% 13.45/3.67 | From (401) and (205) follows:
% 13.45/3.67 | (403) pred(n10) = all_0_1_1
% 13.45/3.67 |
% 13.45/3.67 | From (402) and (138) follows:
% 13.45/3.67 | (404) pred(n0) = all_0_3_3
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (116) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 13.45/3.67 | (405) all_0_1_1 = n9
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (116) with n0, all_0_3_3, n10 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n10, yields:
% 13.45/3.67 | (406) all_0_3_3 = n10
% 13.45/3.67 |
% 13.45/3.67 | From (406) and (167) follows:
% 13.45/3.67 | (407) sum(n10, all_0_0_0) = all_0_6_6
% 13.45/3.67 |
% 13.45/3.67 | From (405) and (458) follows:
% 13.45/3.67 | (1351) sum(n7, n9) = all_0_0_0
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n7, n9, all_0_0_0, n5 and discharging atoms sum(n7, n9) = all_0_0_0, sum(n7, n9) = n5, yields:
% 13.45/3.67 | (274) all_0_0_0 = n5
% 13.45/3.67 |
% 13.45/3.67 | From (274) and (407) follows:
% 13.45/3.67 | (1353) sum(n10, n5) = all_0_6_6
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n10, n5, all_0_6_6, n4 and discharging atoms sum(n10, n5) = all_0_6_6, sum(n10, n5) = n4, yields:
% 13.45/3.67 | (344) all_0_6_6 = n4
% 13.45/3.67 |
% 13.45/3.67 | Equations (344) can reduce 216 to:
% 13.45/3.67 | (243) $false
% 13.45/3.67 |
% 13.45/3.67 |-The branch is then unsatisfiable
% 13.45/3.67 |-Branch two:
% 13.45/3.67 | (363) ~ (all_0_8_8 = n3)
% 13.45/3.67 | (364) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.67 |
% 13.45/3.67 +-Applying beta-rule and splitting (364), into two cases.
% 13.45/3.67 |-Branch one:
% 13.45/3.67 | (365) all_0_8_8 = n2
% 13.45/3.67 |
% 13.45/3.67 | From (365) and (1272) follows:
% 13.45/3.67 | (1359) sum(n2, n8) = all_0_4_4
% 13.45/3.67 |
% 13.45/3.67 | From (365) and (1270) follows:
% 13.45/3.67 | (1360) sum(n2, n7) = all_0_2_2
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n2, n8, all_0_4_4, n10 and discharging atoms sum(n2, n8) = all_0_4_4, sum(n2, n8) = n10, yields:
% 13.45/3.67 | (233) all_0_4_4 = n10
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n2, n7, all_0_2_2, n9 and discharging atoms sum(n2, n7) = all_0_2_2, sum(n2, n7) = n9, yields:
% 13.45/3.67 | (232) all_0_2_2 = n9
% 13.45/3.67 |
% 13.45/3.67 | From (232) and (205) follows:
% 13.45/3.67 | (234) pred(n9) = all_0_1_1
% 13.45/3.67 |
% 13.45/3.67 | From (233) and (138) follows:
% 13.45/3.67 | (235) pred(n10) = all_0_3_3
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (116) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 13.45/3.67 | (236) all_0_3_3 = n9
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (116) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 13.45/3.67 | (237) all_0_1_1 = n8
% 13.45/3.67 |
% 13.45/3.67 | From (236) and (167) follows:
% 13.45/3.67 | (238) sum(n9, all_0_0_0) = all_0_6_6
% 13.45/3.67 |
% 13.45/3.67 | From (237) and (458) follows:
% 13.45/3.67 | (1368) sum(n7, n8) = all_0_0_0
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n7, n8, all_0_0_0, n4 and discharging atoms sum(n7, n8) = all_0_0_0, sum(n7, n8) = n4, yields:
% 13.45/3.67 | (291) all_0_0_0 = n4
% 13.45/3.67 |
% 13.45/3.67 | From (291) and (238) follows:
% 13.45/3.67 | (1370) sum(n9, n4) = all_0_6_6
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n9, n4, all_0_6_6, n2 and discharging atoms sum(n9, n4) = all_0_6_6, sum(n9, n4) = n2, yields:
% 13.45/3.67 | (361) all_0_6_6 = n2
% 13.45/3.67 |
% 13.45/3.67 | Equations (361) can reduce 131 to:
% 13.45/3.67 | (243) $false
% 13.45/3.67 |
% 13.45/3.67 |-The branch is then unsatisfiable
% 13.45/3.67 |-Branch two:
% 13.45/3.67 | (380) ~ (all_0_8_8 = n2)
% 13.45/3.67 | (381) all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.67 |
% 13.45/3.67 +-Applying beta-rule and splitting (381), into two cases.
% 13.45/3.67 |-Branch one:
% 13.45/3.67 | (382) all_0_8_8 = n1
% 13.45/3.67 |
% 13.45/3.67 | From (382) and (1272) follows:
% 13.45/3.67 | (1376) sum(n1, n8) = all_0_4_4
% 13.45/3.67 |
% 13.45/3.67 | From (382) and (1270) follows:
% 13.45/3.67 | (1377) sum(n1, n7) = all_0_2_2
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n1, n8, all_0_4_4, n9 and discharging atoms sum(n1, n8) = all_0_4_4, sum(n1, n8) = n9, yields:
% 13.45/3.67 | (250) all_0_4_4 = n9
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n1, n7, all_0_2_2, n8 and discharging atoms sum(n1, n7) = all_0_2_2, sum(n1, n7) = n8, yields:
% 13.45/3.67 | (249) all_0_2_2 = n8
% 13.45/3.67 |
% 13.45/3.67 | From (249) and (205) follows:
% 13.45/3.67 | (251) pred(n8) = all_0_1_1
% 13.45/3.67 |
% 13.45/3.67 | From (250) and (138) follows:
% 13.45/3.67 | (252) pred(n9) = all_0_3_3
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (116) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 13.45/3.67 | (253) all_0_3_3 = n8
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (116) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 13.45/3.67 | (254) all_0_1_1 = n7
% 13.45/3.67 |
% 13.45/3.67 | From (253) and (167) follows:
% 13.45/3.67 | (255) sum(n8, all_0_0_0) = all_0_6_6
% 13.45/3.67 |
% 13.45/3.67 | From (254) and (458) follows:
% 13.45/3.67 | (1385) sum(n7, n7) = all_0_0_0
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n7, n7, all_0_0_0, n3 and discharging atoms sum(n7, n7) = all_0_0_0, sum(n7, n7) = n3, yields:
% 13.45/3.67 | (308) all_0_0_0 = n3
% 13.45/3.67 |
% 13.45/3.67 | From (308) and (255) follows:
% 13.45/3.67 | (1387) sum(n8, n3) = all_0_6_6
% 13.45/3.67 |
% 13.45/3.67 | Instantiating formula (132) with n8, n3, all_0_6_6, n0 and discharging atoms sum(n8, n3) = all_0_6_6, sum(n8, n3) = n0, yields:
% 13.45/3.67 | (378) all_0_6_6 = n0
% 13.45/3.67 |
% 13.45/3.67 | Equations (378) can reduce 119 to:
% 13.45/3.67 | (243) $false
% 13.45/3.67 |
% 13.45/3.67 |-The branch is then unsatisfiable
% 13.45/3.67 |-Branch two:
% 13.45/3.67 | (397) ~ (all_0_8_8 = n1)
% 13.45/3.67 | (398) all_0_8_8 = n0
% 13.45/3.67 |
% 13.45/3.67 | From (398) and (1272) follows:
% 13.45/3.68 | (1392) sum(n0, n8) = all_0_4_4
% 13.45/3.68 |
% 13.45/3.68 | From (398) and (1270) follows:
% 13.45/3.68 | (1393) sum(n0, n7) = all_0_2_2
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (132) with n0, n8, all_0_4_4, n8 and discharging atoms sum(n0, n8) = all_0_4_4, sum(n0, n8) = n8, yields:
% 13.45/3.68 | (267) all_0_4_4 = n8
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (132) with n0, n7, all_0_2_2, n7 and discharging atoms sum(n0, n7) = all_0_2_2, sum(n0, n7) = n7, yields:
% 13.45/3.68 | (266) all_0_2_2 = n7
% 13.45/3.68 |
% 13.45/3.68 | From (266) and (205) follows:
% 13.45/3.68 | (268) pred(n7) = all_0_1_1
% 13.45/3.68 |
% 13.45/3.68 | From (267) and (138) follows:
% 13.45/3.68 | (269) pred(n8) = all_0_3_3
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (116) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 13.45/3.68 | (270) all_0_3_3 = n7
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (116) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 13.45/3.68 | (271) all_0_1_1 = n6
% 13.45/3.68 |
% 13.45/3.68 | From (270) and (167) follows:
% 13.45/3.68 | (272) sum(n7, all_0_0_0) = all_0_6_6
% 13.45/3.68 |
% 13.45/3.68 | From (271) and (458) follows:
% 13.45/3.68 | (1401) sum(n7, n6) = all_0_0_0
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (132) with n7, n6, all_0_0_0, n2 and discharging atoms sum(n7, n6) = all_0_0_0, sum(n7, n6) = n2, yields:
% 13.45/3.68 | (325) all_0_0_0 = n2
% 13.45/3.68 |
% 13.45/3.68 | From (325) and (272) follows:
% 13.45/3.68 | (1403) sum(n7, n2) = all_0_6_6
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (132) with n7, n2, all_0_6_6, n9 and discharging atoms sum(n7, n2) = all_0_6_6, sum(n7, n2) = n9, yields:
% 13.45/3.68 | (395) all_0_6_6 = n9
% 13.45/3.68 |
% 13.45/3.68 | Equations (395) can reduce 78 to:
% 13.45/3.68 | (243) $false
% 13.45/3.68 |
% 13.45/3.68 |-The branch is then unsatisfiable
% 13.45/3.68 |-Branch two:
% 13.45/3.68 | (473) ~ (all_0_7_7 = n7)
% 13.45/3.68 | (474) all_0_7_7 = n6 | all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.45/3.68 |
% 13.45/3.68 +-Applying beta-rule and splitting (279), into two cases.
% 13.45/3.68 |-Branch one:
% 13.45/3.68 | (280) all_0_8_8 = n7
% 13.45/3.68 |
% 13.45/3.68 | From (280) and (77) follows:
% 13.45/3.68 | (1409) sum(n7, all_0_5_5) = all_0_4_4
% 13.45/3.68 |
% 13.45/3.68 | From (280) and (120) follows:
% 13.45/3.68 | (1410) sum(n7, all_0_7_7) = all_0_2_2
% 13.45/3.68 |
% 13.45/3.68 +-Applying beta-rule and splitting (474), into two cases.
% 13.45/3.68 |-Branch one:
% 13.45/3.68 | (475) all_0_7_7 = n6
% 13.45/3.68 |
% 13.45/3.68 | From (475) and (10) follows:
% 13.45/3.68 | (476) succ(n6) = all_0_5_5
% 13.45/3.68 |
% 13.45/3.68 | From (475) and (3) follows:
% 13.45/3.68 | (477) sum(n6, all_0_1_1) = all_0_0_0
% 13.45/3.68 |
% 13.45/3.68 | From (475) and (1410) follows:
% 13.45/3.68 | (1414) sum(n7, n6) = all_0_2_2
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (47) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 13.45/3.68 | (479) all_0_5_5 = n7
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (132) with n7, n6, all_0_2_2, n2 and discharging atoms sum(n7, n6) = all_0_2_2, sum(n7, n6) = n2, yields:
% 13.45/3.68 | (351) all_0_2_2 = n2
% 13.45/3.68 |
% 13.45/3.68 | From (351) and (205) follows:
% 13.45/3.68 | (353) pred(n2) = all_0_1_1
% 13.45/3.68 |
% 13.45/3.68 | From (479) and (1409) follows:
% 13.45/3.68 | (1418) sum(n7, n7) = all_0_4_4
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (116) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 13.45/3.68 | (356) all_0_1_1 = n1
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (132) with n7, n7, all_0_4_4, n3 and discharging atoms sum(n7, n7) = all_0_4_4, sum(n7, n7) = n3, yields:
% 13.45/3.68 | (352) all_0_4_4 = n3
% 13.45/3.68 |
% 13.45/3.68 | From (352) and (138) follows:
% 13.45/3.68 | (354) pred(n3) = all_0_3_3
% 13.45/3.68 |
% 13.45/3.68 | From (356) and (477) follows:
% 13.45/3.68 | (1422) sum(n6, n1) = all_0_0_0
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (116) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 13.45/3.68 | (355) all_0_3_3 = n2
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (132) with n6, n1, all_0_0_0, n7 and discharging atoms sum(n6, n1) = all_0_0_0, sum(n6, n1) = n7, yields:
% 13.45/3.68 | (240) all_0_0_0 = n7
% 13.45/3.68 |
% 13.45/3.68 | From (355)(240) and (167) follows:
% 13.45/3.68 | (1425) sum(n2, n7) = all_0_6_6
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (132) with n2, n7, all_0_6_6, n9 and discharging atoms sum(n2, n7) = all_0_6_6, sum(n2, n7) = n9, yields:
% 13.45/3.68 | (395) all_0_6_6 = n9
% 13.45/3.68 |
% 13.45/3.68 | Equations (395) can reduce 78 to:
% 13.45/3.68 | (243) $false
% 13.45/3.68 |
% 13.45/3.68 |-The branch is then unsatisfiable
% 13.45/3.68 |-Branch two:
% 13.45/3.68 | (492) ~ (all_0_7_7 = n6)
% 13.45/3.68 | (493) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.45/3.68 |
% 13.45/3.68 +-Applying beta-rule and splitting (493), into two cases.
% 13.45/3.68 |-Branch one:
% 13.45/3.68 | (494) all_0_7_7 = n5
% 13.45/3.68 |
% 13.45/3.68 | From (494) and (10) follows:
% 13.45/3.68 | (495) succ(n5) = all_0_5_5
% 13.45/3.68 |
% 13.45/3.68 | From (494) and (3) follows:
% 13.45/3.68 | (496) sum(n5, all_0_1_1) = all_0_0_0
% 13.45/3.68 |
% 13.45/3.68 | From (494) and (1410) follows:
% 13.45/3.68 | (1433) sum(n7, n5) = all_0_2_2
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (47) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 13.45/3.68 | (498) all_0_5_5 = n6
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (132) with n7, n5, all_0_2_2, n1 and discharging atoms sum(n7, n5) = all_0_2_2, sum(n7, n5) = n1, yields:
% 13.45/3.68 | (368) all_0_2_2 = n1
% 13.45/3.68 |
% 13.45/3.68 | From (368) and (205) follows:
% 13.45/3.68 | (370) pred(n1) = all_0_1_1
% 13.45/3.68 |
% 13.45/3.68 | From (498) and (1409) follows:
% 13.45/3.68 | (1437) sum(n7, n6) = all_0_4_4
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (116) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 13.45/3.68 | (373) all_0_1_1 = n0
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (132) with n7, n6, all_0_4_4, n2 and discharging atoms sum(n7, n6) = all_0_4_4, sum(n7, n6) = n2, yields:
% 13.45/3.68 | (369) all_0_4_4 = n2
% 13.45/3.68 |
% 13.45/3.68 | From (369) and (138) follows:
% 13.45/3.68 | (371) pred(n2) = all_0_3_3
% 13.45/3.68 |
% 13.45/3.68 | From (373) and (496) follows:
% 13.45/3.68 | (1441) sum(n5, n0) = all_0_0_0
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (116) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 13.45/3.68 | (372) all_0_3_3 = n1
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (132) with n5, n0, all_0_0_0, n5 and discharging atoms sum(n5, n0) = all_0_0_0, sum(n5, n0) = n5, yields:
% 13.45/3.68 | (274) all_0_0_0 = n5
% 13.45/3.68 |
% 13.45/3.68 | From (372)(274) and (167) follows:
% 13.45/3.68 | (1444) sum(n1, n5) = all_0_6_6
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (132) with n1, n5, all_0_6_6, n6 and discharging atoms sum(n1, n5) = all_0_6_6, sum(n1, n5) = n6, yields:
% 13.45/3.68 | (327) all_0_6_6 = n6
% 13.45/3.68 |
% 13.45/3.68 | Equations (327) can reduce 34 to:
% 13.45/3.68 | (243) $false
% 13.45/3.68 |
% 13.45/3.68 |-The branch is then unsatisfiable
% 13.45/3.68 |-Branch two:
% 13.45/3.68 | (511) ~ (all_0_7_7 = n5)
% 13.45/3.68 | (512) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.45/3.68 |
% 13.45/3.68 +-Applying beta-rule and splitting (512), into two cases.
% 13.45/3.68 |-Branch one:
% 13.45/3.68 | (513) all_0_7_7 = n4
% 13.45/3.68 |
% 13.45/3.68 | From (513) and (10) follows:
% 13.45/3.68 | (514) succ(n4) = all_0_5_5
% 13.45/3.68 |
% 13.45/3.68 | From (513) and (3) follows:
% 13.45/3.68 | (515) sum(n4, all_0_1_1) = all_0_0_0
% 13.45/3.68 |
% 13.45/3.68 | From (513) and (1410) follows:
% 13.45/3.68 | (1452) sum(n7, n4) = all_0_2_2
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (47) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 13.45/3.68 | (517) all_0_5_5 = n5
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (132) with n7, n4, all_0_2_2, n0 and discharging atoms sum(n7, n4) = all_0_2_2, sum(n7, n4) = n0, yields:
% 13.45/3.68 | (385) all_0_2_2 = n0
% 13.45/3.68 |
% 13.45/3.68 | From (385) and (205) follows:
% 13.45/3.68 | (387) pred(n0) = all_0_1_1
% 13.45/3.68 |
% 13.45/3.68 | From (517) and (1409) follows:
% 13.45/3.68 | (1456) sum(n7, n5) = all_0_4_4
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (116) with n0, all_0_1_1, n10 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n10, yields:
% 13.45/3.68 | (390) all_0_1_1 = n10
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (132) with n7, n5, all_0_4_4, n1 and discharging atoms sum(n7, n5) = all_0_4_4, sum(n7, n5) = n1, yields:
% 13.45/3.68 | (386) all_0_4_4 = n1
% 13.45/3.68 |
% 13.45/3.68 | From (386) and (138) follows:
% 13.45/3.68 | (388) pred(n1) = all_0_3_3
% 13.45/3.68 |
% 13.45/3.68 | From (390) and (515) follows:
% 13.45/3.68 | (1460) sum(n4, n10) = all_0_0_0
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (116) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 13.45/3.68 | (389) all_0_3_3 = n0
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (132) with n4, n10, all_0_0_0, n3 and discharging atoms sum(n4, n10) = all_0_0_0, sum(n4, n10) = n3, yields:
% 13.45/3.68 | (308) all_0_0_0 = n3
% 13.45/3.68 |
% 13.45/3.68 | From (389)(308) and (167) follows:
% 13.45/3.68 | (1463) sum(n0, n3) = all_0_6_6
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (132) with n0, n3, all_0_6_6, n3 and discharging atoms sum(n0, n3) = all_0_6_6, sum(n0, n3) = n3, yields:
% 13.45/3.68 | (259) all_0_6_6 = n3
% 13.45/3.68 |
% 13.45/3.68 | Equations (259) can reduce 100 to:
% 13.45/3.68 | (243) $false
% 13.45/3.68 |
% 13.45/3.68 |-The branch is then unsatisfiable
% 13.45/3.68 |-Branch two:
% 13.45/3.68 | (530) ~ (all_0_7_7 = n4)
% 13.45/3.68 | (531) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.45/3.68 |
% 13.45/3.68 +-Applying beta-rule and splitting (531), into two cases.
% 13.45/3.68 |-Branch one:
% 13.45/3.68 | (532) all_0_7_7 = n3
% 13.45/3.68 |
% 13.45/3.68 | From (532) and (10) follows:
% 13.45/3.68 | (533) succ(n3) = all_0_5_5
% 13.45/3.68 |
% 13.45/3.68 | From (532) and (3) follows:
% 13.45/3.68 | (534) sum(n3, all_0_1_1) = all_0_0_0
% 13.45/3.68 |
% 13.45/3.68 | From (532) and (1410) follows:
% 13.45/3.68 | (1471) sum(n7, n3) = all_0_2_2
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (47) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 13.45/3.68 | (536) all_0_5_5 = n4
% 13.45/3.68 |
% 13.45/3.68 | Instantiating formula (132) with n7, n3, all_0_2_2, n10 and discharging atoms sum(n7, n3) = all_0_2_2, sum(n7, n3) = n10, yields:
% 13.45/3.68 | (401) all_0_2_2 = n10
% 13.45/3.68 |
% 13.45/3.68 | From (401) and (205) follows:
% 13.45/3.68 | (403) pred(n10) = all_0_1_1
% 13.45/3.68 |
% 13.45/3.68 | From (536) and (1409) follows:
% 13.45/3.69 | (1475) sum(n7, n4) = all_0_4_4
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (116) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 13.45/3.69 | (405) all_0_1_1 = n9
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n7, n4, all_0_4_4, n0 and discharging atoms sum(n7, n4) = all_0_4_4, sum(n7, n4) = n0, yields:
% 13.45/3.69 | (402) all_0_4_4 = n0
% 13.45/3.69 |
% 13.45/3.69 | From (402) and (138) follows:
% 13.45/3.69 | (404) pred(n0) = all_0_3_3
% 13.45/3.69 |
% 13.45/3.69 | From (405) and (534) follows:
% 13.45/3.69 | (1479) sum(n3, n9) = all_0_0_0
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (116) with n0, all_0_3_3, n10 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n10, yields:
% 13.45/3.69 | (406) all_0_3_3 = n10
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n3, n9, all_0_0_0, n1 and discharging atoms sum(n3, n9) = all_0_0_0, sum(n3, n9) = n1, yields:
% 13.45/3.69 | (342) all_0_0_0 = n1
% 13.45/3.69 |
% 13.45/3.69 | From (406)(342) and (167) follows:
% 13.45/3.69 | (1482) sum(n10, n1) = all_0_6_6
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n10, n1, all_0_6_6, n0 and discharging atoms sum(n10, n1) = all_0_6_6, sum(n10, n1) = n0, yields:
% 13.45/3.69 | (378) all_0_6_6 = n0
% 13.45/3.69 |
% 13.45/3.69 | Equations (378) can reduce 119 to:
% 13.45/3.69 | (243) $false
% 13.45/3.69 |
% 13.45/3.69 |-The branch is then unsatisfiable
% 13.45/3.69 |-Branch two:
% 13.45/3.69 | (549) ~ (all_0_7_7 = n3)
% 13.45/3.69 | (550) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.45/3.69 |
% 13.45/3.69 +-Applying beta-rule and splitting (550), into two cases.
% 13.45/3.69 |-Branch one:
% 13.45/3.69 | (551) all_0_7_7 = n2
% 13.45/3.69 |
% 13.45/3.69 | From (551) and (10) follows:
% 13.45/3.69 | (552) succ(n2) = all_0_5_5
% 13.45/3.69 |
% 13.45/3.69 | From (551) and (3) follows:
% 13.45/3.69 | (553) sum(n2, all_0_1_1) = all_0_0_0
% 13.45/3.69 |
% 13.45/3.69 | From (551) and (1410) follows:
% 13.45/3.69 | (1490) sum(n7, n2) = all_0_2_2
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (47) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 13.45/3.69 | (555) all_0_5_5 = n3
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n7, n2, all_0_2_2, n9 and discharging atoms sum(n7, n2) = all_0_2_2, sum(n7, n2) = n9, yields:
% 13.45/3.69 | (232) all_0_2_2 = n9
% 13.45/3.69 |
% 13.45/3.69 | From (232) and (205) follows:
% 13.45/3.69 | (234) pred(n9) = all_0_1_1
% 13.45/3.69 |
% 13.45/3.69 | From (555) and (1409) follows:
% 13.45/3.69 | (1494) sum(n7, n3) = all_0_4_4
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (116) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 13.45/3.69 | (237) all_0_1_1 = n8
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n7, n3, all_0_4_4, n10 and discharging atoms sum(n7, n3) = all_0_4_4, sum(n7, n3) = n10, yields:
% 13.45/3.69 | (233) all_0_4_4 = n10
% 13.45/3.69 |
% 13.45/3.69 | From (233) and (138) follows:
% 13.45/3.69 | (235) pred(n10) = all_0_3_3
% 13.45/3.69 |
% 13.45/3.69 | From (237) and (553) follows:
% 13.45/3.69 | (1498) sum(n2, n8) = all_0_0_0
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (116) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 13.45/3.69 | (236) all_0_3_3 = n9
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n2, n8, all_0_0_0, n10 and discharging atoms sum(n2, n8) = all_0_0_0, sum(n2, n8) = n10, yields:
% 13.45/3.69 | (376) all_0_0_0 = n10
% 13.45/3.69 |
% 13.45/3.69 | From (236)(376) and (167) follows:
% 13.45/3.69 | (1501) sum(n9, n10) = all_0_6_6
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n9, n10, all_0_6_6, n8 and discharging atoms sum(n9, n10) = all_0_6_6, sum(n9, n10) = n8, yields:
% 13.45/3.69 | (310) all_0_6_6 = n8
% 13.45/3.69 |
% 13.45/3.69 | Equations (310) can reduce 165 to:
% 13.45/3.69 | (243) $false
% 13.45/3.69 |
% 13.45/3.69 |-The branch is then unsatisfiable
% 13.45/3.69 |-Branch two:
% 13.45/3.69 | (568) ~ (all_0_7_7 = n2)
% 13.45/3.69 | (569) all_0_7_7 = n1 | all_0_7_7 = n0
% 13.45/3.69 |
% 13.45/3.69 +-Applying beta-rule and splitting (569), into two cases.
% 13.45/3.69 |-Branch one:
% 13.45/3.69 | (570) all_0_7_7 = n1
% 13.45/3.69 |
% 13.45/3.69 | From (570) and (10) follows:
% 13.45/3.69 | (571) succ(n1) = all_0_5_5
% 13.45/3.69 |
% 13.45/3.69 | From (570) and (3) follows:
% 13.45/3.69 | (572) sum(n1, all_0_1_1) = all_0_0_0
% 13.45/3.69 |
% 13.45/3.69 | From (570) and (1410) follows:
% 13.45/3.69 | (1509) sum(n7, n1) = all_0_2_2
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (47) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 13.45/3.69 | (574) all_0_5_5 = n2
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n7, n1, all_0_2_2, n8 and discharging atoms sum(n7, n1) = all_0_2_2, sum(n7, n1) = n8, yields:
% 13.45/3.69 | (249) all_0_2_2 = n8
% 13.45/3.69 |
% 13.45/3.69 | From (249) and (205) follows:
% 13.45/3.69 | (251) pred(n8) = all_0_1_1
% 13.45/3.69 |
% 13.45/3.69 | From (574) and (1409) follows:
% 13.45/3.69 | (1513) sum(n7, n2) = all_0_4_4
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (116) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 13.45/3.69 | (254) all_0_1_1 = n7
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n7, n2, all_0_4_4, n9 and discharging atoms sum(n7, n2) = all_0_4_4, sum(n7, n2) = n9, yields:
% 13.45/3.69 | (250) all_0_4_4 = n9
% 13.45/3.69 |
% 13.45/3.69 | From (250) and (138) follows:
% 13.45/3.69 | (252) pred(n9) = all_0_3_3
% 13.45/3.69 |
% 13.45/3.69 | From (254) and (572) follows:
% 13.45/3.69 | (1517) sum(n1, n7) = all_0_0_0
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (116) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 13.45/3.69 | (253) all_0_3_3 = n8
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n1, n7, all_0_0_0, n8 and discharging atoms sum(n1, n7) = all_0_0_0, sum(n1, n7) = n8, yields:
% 13.45/3.69 | (409) all_0_0_0 = n8
% 13.45/3.69 |
% 13.45/3.69 | From (253)(409) and (167) follows:
% 13.45/3.69 | (1520) sum(n8, n8) = all_0_6_6
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n8, n8, all_0_6_6, n5 and discharging atoms sum(n8, n8) = all_0_6_6, sum(n8, n8) = n5, yields:
% 13.45/3.69 | (242) all_0_6_6 = n5
% 13.45/3.69 |
% 13.45/3.69 | Equations (242) can reduce 4 to:
% 13.45/3.69 | (243) $false
% 13.45/3.69 |
% 13.45/3.69 |-The branch is then unsatisfiable
% 13.45/3.69 |-Branch two:
% 13.45/3.69 | (587) ~ (all_0_7_7 = n1)
% 13.45/3.69 | (588) all_0_7_7 = n0
% 13.45/3.69 |
% 13.45/3.69 | From (588) and (10) follows:
% 13.45/3.69 | (589) succ(n0) = all_0_5_5
% 13.45/3.69 |
% 13.45/3.69 | From (588) and (3) follows:
% 13.45/3.69 | (590) sum(n0, all_0_1_1) = all_0_0_0
% 13.45/3.69 |
% 13.45/3.69 | From (588) and (1410) follows:
% 13.45/3.69 | (1527) sum(n7, n0) = all_0_2_2
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (47) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 13.45/3.69 | (592) all_0_5_5 = n1
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n7, n0, all_0_2_2, n7 and discharging atoms sum(n7, n0) = all_0_2_2, sum(n7, n0) = n7, yields:
% 13.45/3.69 | (266) all_0_2_2 = n7
% 13.45/3.69 |
% 13.45/3.69 | From (266) and (205) follows:
% 13.45/3.69 | (268) pred(n7) = all_0_1_1
% 13.45/3.69 |
% 13.45/3.69 | From (592) and (1409) follows:
% 13.45/3.69 | (1531) sum(n7, n1) = all_0_4_4
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (116) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 13.45/3.69 | (271) all_0_1_1 = n6
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n7, n1, all_0_4_4, n8 and discharging atoms sum(n7, n1) = all_0_4_4, sum(n7, n1) = n8, yields:
% 13.45/3.69 | (267) all_0_4_4 = n8
% 13.45/3.69 |
% 13.45/3.69 | From (267) and (138) follows:
% 13.45/3.69 | (269) pred(n8) = all_0_3_3
% 13.45/3.69 |
% 13.45/3.69 | From (271) and (590) follows:
% 13.45/3.69 | (1535) sum(n0, n6) = all_0_0_0
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (116) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 13.45/3.69 | (270) all_0_3_3 = n7
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n0, n6, all_0_0_0, n6 and discharging atoms sum(n0, n6) = all_0_0_0, sum(n0, n6) = n6, yields:
% 13.45/3.69 | (257) all_0_0_0 = n6
% 13.45/3.69 |
% 13.45/3.69 | From (270)(257) and (167) follows:
% 13.45/3.69 | (1538) sum(n7, n6) = all_0_6_6
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n7, n6, all_0_6_6, n2 and discharging atoms sum(n7, n6) = all_0_6_6, sum(n7, n6) = n2, yields:
% 13.45/3.69 | (361) all_0_6_6 = n2
% 13.45/3.69 |
% 13.45/3.69 | Equations (361) can reduce 131 to:
% 13.45/3.69 | (243) $false
% 13.45/3.69 |
% 13.45/3.69 |-The branch is then unsatisfiable
% 13.45/3.69 |-Branch two:
% 13.45/3.69 | (295) ~ (all_0_8_8 = n7)
% 13.45/3.69 | (296) all_0_8_8 = n6 | all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.69 |
% 13.45/3.69 +-Applying beta-rule and splitting (474), into two cases.
% 13.45/3.69 |-Branch one:
% 13.45/3.69 | (475) all_0_7_7 = n6
% 13.45/3.69 |
% 13.45/3.69 | From (475) and (10) follows:
% 13.45/3.69 | (476) succ(n6) = all_0_5_5
% 13.45/3.69 |
% 13.45/3.69 | From (475) and (3) follows:
% 13.45/3.69 | (477) sum(n6, all_0_1_1) = all_0_0_0
% 13.45/3.69 |
% 13.45/3.69 | From (475) and (120) follows:
% 13.45/3.69 | (1546) sum(all_0_8_8, n6) = all_0_2_2
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (47) with n6, all_0_5_5, n7 and discharging atoms succ(n6) = all_0_5_5, succ(n6) = n7, yields:
% 13.45/3.69 | (479) all_0_5_5 = n7
% 13.45/3.69 |
% 13.45/3.69 | From (479) and (77) follows:
% 13.45/3.69 | (1548) sum(all_0_8_8, n7) = all_0_4_4
% 13.45/3.69 |
% 13.45/3.69 +-Applying beta-rule and splitting (296), into two cases.
% 13.45/3.69 |-Branch one:
% 13.45/3.69 | (297) all_0_8_8 = n6
% 13.45/3.69 |
% 13.45/3.69 | From (297) and (1548) follows:
% 13.45/3.69 | (1550) sum(n6, n7) = all_0_4_4
% 13.45/3.69 |
% 13.45/3.69 | From (297) and (1546) follows:
% 13.45/3.69 | (1551) sum(n6, n6) = all_0_2_2
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n6, n7, all_0_4_4, n2 and discharging atoms sum(n6, n7) = all_0_4_4, sum(n6, n7) = n2, yields:
% 13.45/3.69 | (369) all_0_4_4 = n2
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n6, n6, all_0_2_2, n1 and discharging atoms sum(n6, n6) = all_0_2_2, sum(n6, n6) = n1, yields:
% 13.45/3.69 | (368) all_0_2_2 = n1
% 13.45/3.69 |
% 13.45/3.69 | From (368) and (205) follows:
% 13.45/3.69 | (370) pred(n1) = all_0_1_1
% 13.45/3.69 |
% 13.45/3.69 | From (369) and (138) follows:
% 13.45/3.69 | (371) pred(n2) = all_0_3_3
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (116) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 13.45/3.69 | (372) all_0_3_3 = n1
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (116) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 13.45/3.69 | (373) all_0_1_1 = n0
% 13.45/3.69 |
% 13.45/3.69 | From (372) and (167) follows:
% 13.45/3.69 | (374) sum(n1, all_0_0_0) = all_0_6_6
% 13.45/3.69 |
% 13.45/3.69 | From (373) and (477) follows:
% 13.45/3.69 | (1559) sum(n6, n0) = all_0_0_0
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n6, n0, all_0_0_0, n6 and discharging atoms sum(n6, n0) = all_0_0_0, sum(n6, n0) = n6, yields:
% 13.45/3.69 | (257) all_0_0_0 = n6
% 13.45/3.69 |
% 13.45/3.69 | From (257) and (374) follows:
% 13.45/3.69 | (1561) sum(n1, n6) = all_0_6_6
% 13.45/3.69 |
% 13.45/3.69 | Instantiating formula (132) with n1, n6, all_0_6_6, n7 and discharging atoms sum(n1, n6) = all_0_6_6, sum(n1, n6) = n7, yields:
% 13.45/3.70 | (411) all_0_6_6 = n7
% 13.45/3.70 |
% 13.45/3.70 | Equations (411) can reduce 88 to:
% 13.45/3.70 | (243) $false
% 13.45/3.70 |
% 13.45/3.70 |-The branch is then unsatisfiable
% 13.45/3.70 |-Branch two:
% 13.45/3.70 | (312) ~ (all_0_8_8 = n6)
% 13.45/3.70 | (313) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.70 |
% 13.45/3.70 +-Applying beta-rule and splitting (313), into two cases.
% 13.45/3.70 |-Branch one:
% 13.45/3.70 | (314) all_0_8_8 = n5
% 13.45/3.70 |
% 13.45/3.70 | From (314) and (1548) follows:
% 13.45/3.70 | (1567) sum(n5, n7) = all_0_4_4
% 13.45/3.70 |
% 13.45/3.70 | From (314) and (1546) follows:
% 13.45/3.70 | (1568) sum(n5, n6) = all_0_2_2
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n5, n7, all_0_4_4, n1 and discharging atoms sum(n5, n7) = all_0_4_4, sum(n5, n7) = n1, yields:
% 13.45/3.70 | (386) all_0_4_4 = n1
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n5, n6, all_0_2_2, n0 and discharging atoms sum(n5, n6) = all_0_2_2, sum(n5, n6) = n0, yields:
% 13.45/3.70 | (385) all_0_2_2 = n0
% 13.45/3.70 |
% 13.45/3.70 | From (385) and (205) follows:
% 13.45/3.70 | (387) pred(n0) = all_0_1_1
% 13.45/3.70 |
% 13.45/3.70 | From (386) and (138) follows:
% 13.45/3.70 | (388) pred(n1) = all_0_3_3
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (116) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 13.45/3.70 | (389) all_0_3_3 = n0
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (116) with n0, all_0_1_1, n10 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n10, yields:
% 13.45/3.70 | (390) all_0_1_1 = n10
% 13.45/3.70 |
% 13.45/3.70 | From (389) and (167) follows:
% 13.45/3.70 | (391) sum(n0, all_0_0_0) = all_0_6_6
% 13.45/3.70 |
% 13.45/3.70 | From (390) and (477) follows:
% 13.45/3.70 | (1576) sum(n6, n10) = all_0_0_0
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n6, n10, all_0_0_0, n5 and discharging atoms sum(n6, n10) = all_0_0_0, sum(n6, n10) = n5, yields:
% 13.45/3.70 | (274) all_0_0_0 = n5
% 13.45/3.70 |
% 13.45/3.70 | From (274) and (391) follows:
% 13.45/3.70 | (1578) sum(n0, n5) = all_0_6_6
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n0, n5, all_0_6_6, n5 and discharging atoms sum(n0, n5) = all_0_6_6, sum(n0, n5) = n5, yields:
% 13.45/3.70 | (242) all_0_6_6 = n5
% 13.45/3.70 |
% 13.45/3.70 | Equations (242) can reduce 4 to:
% 13.45/3.70 | (243) $false
% 13.45/3.70 |
% 13.45/3.70 |-The branch is then unsatisfiable
% 13.45/3.70 |-Branch two:
% 13.45/3.70 | (329) ~ (all_0_8_8 = n5)
% 13.45/3.70 | (330) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.70 |
% 13.45/3.70 +-Applying beta-rule and splitting (330), into two cases.
% 13.45/3.70 |-Branch one:
% 13.45/3.70 | (331) all_0_8_8 = n4
% 13.45/3.70 |
% 13.45/3.70 | From (331) and (1548) follows:
% 13.45/3.70 | (1584) sum(n4, n7) = all_0_4_4
% 13.45/3.70 |
% 13.45/3.70 | From (331) and (1546) follows:
% 13.45/3.70 | (1585) sum(n4, n6) = all_0_2_2
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n4, n7, all_0_4_4, n0 and discharging atoms sum(n4, n7) = all_0_4_4, sum(n4, n7) = n0, yields:
% 13.45/3.70 | (402) all_0_4_4 = n0
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n4, n6, all_0_2_2, n10 and discharging atoms sum(n4, n6) = all_0_2_2, sum(n4, n6) = n10, yields:
% 13.45/3.70 | (401) all_0_2_2 = n10
% 13.45/3.70 |
% 13.45/3.70 | From (401) and (205) follows:
% 13.45/3.70 | (403) pred(n10) = all_0_1_1
% 13.45/3.70 |
% 13.45/3.70 | From (402) and (138) follows:
% 13.45/3.70 | (404) pred(n0) = all_0_3_3
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (116) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 13.45/3.70 | (405) all_0_1_1 = n9
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (116) with n0, all_0_3_3, n10 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n10, yields:
% 13.45/3.70 | (406) all_0_3_3 = n10
% 13.45/3.70 |
% 13.45/3.70 | From (406) and (167) follows:
% 13.45/3.70 | (407) sum(n10, all_0_0_0) = all_0_6_6
% 13.45/3.70 |
% 13.45/3.70 | From (405) and (477) follows:
% 13.45/3.70 | (1593) sum(n6, n9) = all_0_0_0
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n6, n9, all_0_0_0, n4 and discharging atoms sum(n6, n9) = all_0_0_0, sum(n6, n9) = n4, yields:
% 13.45/3.70 | (291) all_0_0_0 = n4
% 13.45/3.70 |
% 13.45/3.70 | From (291) and (407) follows:
% 13.45/3.70 | (1595) sum(n10, n4) = all_0_6_6
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n10, n4, all_0_6_6, n3 and discharging atoms sum(n10, n4) = all_0_6_6, sum(n10, n4) = n3, yields:
% 13.45/3.70 | (259) all_0_6_6 = n3
% 13.45/3.70 |
% 13.45/3.70 | Equations (259) can reduce 100 to:
% 13.45/3.70 | (243) $false
% 13.45/3.70 |
% 13.45/3.70 |-The branch is then unsatisfiable
% 13.45/3.70 |-Branch two:
% 13.45/3.70 | (346) ~ (all_0_8_8 = n4)
% 13.45/3.70 | (347) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.70 |
% 13.45/3.70 +-Applying beta-rule and splitting (347), into two cases.
% 13.45/3.70 |-Branch one:
% 13.45/3.70 | (348) all_0_8_8 = n3
% 13.45/3.70 |
% 13.45/3.70 | From (348) and (1548) follows:
% 13.45/3.70 | (1601) sum(n3, n7) = all_0_4_4
% 13.45/3.70 |
% 13.45/3.70 | From (348) and (1546) follows:
% 13.45/3.70 | (1602) sum(n3, n6) = all_0_2_2
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n3, n7, all_0_4_4, n10 and discharging atoms sum(n3, n7) = all_0_4_4, sum(n3, n7) = n10, yields:
% 13.45/3.70 | (233) all_0_4_4 = n10
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n3, n6, all_0_2_2, n9 and discharging atoms sum(n3, n6) = all_0_2_2, sum(n3, n6) = n9, yields:
% 13.45/3.70 | (232) all_0_2_2 = n9
% 13.45/3.70 |
% 13.45/3.70 | From (232) and (205) follows:
% 13.45/3.70 | (234) pred(n9) = all_0_1_1
% 13.45/3.70 |
% 13.45/3.70 | From (233) and (138) follows:
% 13.45/3.70 | (235) pred(n10) = all_0_3_3
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (116) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 13.45/3.70 | (236) all_0_3_3 = n9
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (116) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 13.45/3.70 | (237) all_0_1_1 = n8
% 13.45/3.70 |
% 13.45/3.70 | From (236) and (167) follows:
% 13.45/3.70 | (238) sum(n9, all_0_0_0) = all_0_6_6
% 13.45/3.70 |
% 13.45/3.70 | From (237) and (477) follows:
% 13.45/3.70 | (1610) sum(n6, n8) = all_0_0_0
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n6, n8, all_0_0_0, n3 and discharging atoms sum(n6, n8) = all_0_0_0, sum(n6, n8) = n3, yields:
% 13.45/3.70 | (308) all_0_0_0 = n3
% 13.45/3.70 |
% 13.45/3.70 | From (308) and (238) follows:
% 13.45/3.70 | (1612) sum(n9, n3) = all_0_6_6
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n9, n3, all_0_6_6, n1 and discharging atoms sum(n9, n3) = all_0_6_6, sum(n9, n3) = n1, yields:
% 13.45/3.70 | (276) all_0_6_6 = n1
% 13.45/3.70 |
% 13.45/3.70 | Equations (276) can reduce 28 to:
% 13.45/3.70 | (243) $false
% 13.45/3.70 |
% 13.45/3.70 |-The branch is then unsatisfiable
% 13.45/3.70 |-Branch two:
% 13.45/3.70 | (363) ~ (all_0_8_8 = n3)
% 13.45/3.70 | (364) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.70 |
% 13.45/3.70 +-Applying beta-rule and splitting (364), into two cases.
% 13.45/3.70 |-Branch one:
% 13.45/3.70 | (365) all_0_8_8 = n2
% 13.45/3.70 |
% 13.45/3.70 | From (365) and (1548) follows:
% 13.45/3.70 | (1618) sum(n2, n7) = all_0_4_4
% 13.45/3.70 |
% 13.45/3.70 | From (365) and (1546) follows:
% 13.45/3.70 | (1619) sum(n2, n6) = all_0_2_2
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n2, n7, all_0_4_4, n9 and discharging atoms sum(n2, n7) = all_0_4_4, sum(n2, n7) = n9, yields:
% 13.45/3.70 | (250) all_0_4_4 = n9
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n2, n6, all_0_2_2, n8 and discharging atoms sum(n2, n6) = all_0_2_2, sum(n2, n6) = n8, yields:
% 13.45/3.70 | (249) all_0_2_2 = n8
% 13.45/3.70 |
% 13.45/3.70 | From (249) and (205) follows:
% 13.45/3.70 | (251) pred(n8) = all_0_1_1
% 13.45/3.70 |
% 13.45/3.70 | From (250) and (138) follows:
% 13.45/3.70 | (252) pred(n9) = all_0_3_3
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (116) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 13.45/3.70 | (253) all_0_3_3 = n8
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (116) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 13.45/3.70 | (254) all_0_1_1 = n7
% 13.45/3.70 |
% 13.45/3.70 | From (253) and (167) follows:
% 13.45/3.70 | (255) sum(n8, all_0_0_0) = all_0_6_6
% 13.45/3.70 |
% 13.45/3.70 | From (254) and (477) follows:
% 13.45/3.70 | (1627) sum(n6, n7) = all_0_0_0
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n6, n7, all_0_0_0, n2 and discharging atoms sum(n6, n7) = all_0_0_0, sum(n6, n7) = n2, yields:
% 13.45/3.70 | (325) all_0_0_0 = n2
% 13.45/3.70 |
% 13.45/3.70 | From (325) and (255) follows:
% 13.45/3.70 | (1629) sum(n8, n2) = all_0_6_6
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n8, n2, all_0_6_6, n10 and discharging atoms sum(n8, n2) = all_0_6_6, sum(n8, n2) = n10, yields:
% 13.45/3.70 | (293) all_0_6_6 = n10
% 13.45/3.70 |
% 13.45/3.70 | Equations (293) can reduce 147 to:
% 13.45/3.70 | (243) $false
% 13.45/3.70 |
% 13.45/3.70 |-The branch is then unsatisfiable
% 13.45/3.70 |-Branch two:
% 13.45/3.70 | (380) ~ (all_0_8_8 = n2)
% 13.45/3.70 | (381) all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.70 |
% 13.45/3.70 +-Applying beta-rule and splitting (381), into two cases.
% 13.45/3.70 |-Branch one:
% 13.45/3.70 | (382) all_0_8_8 = n1
% 13.45/3.70 |
% 13.45/3.70 | From (382) and (1548) follows:
% 13.45/3.70 | (1635) sum(n1, n7) = all_0_4_4
% 13.45/3.70 |
% 13.45/3.70 | From (382) and (1546) follows:
% 13.45/3.70 | (1636) sum(n1, n6) = all_0_2_2
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n1, n7, all_0_4_4, n8 and discharging atoms sum(n1, n7) = all_0_4_4, sum(n1, n7) = n8, yields:
% 13.45/3.70 | (267) all_0_4_4 = n8
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n1, n6, all_0_2_2, n7 and discharging atoms sum(n1, n6) = all_0_2_2, sum(n1, n6) = n7, yields:
% 13.45/3.70 | (266) all_0_2_2 = n7
% 13.45/3.70 |
% 13.45/3.70 | From (266) and (205) follows:
% 13.45/3.70 | (268) pred(n7) = all_0_1_1
% 13.45/3.70 |
% 13.45/3.70 | From (267) and (138) follows:
% 13.45/3.70 | (269) pred(n8) = all_0_3_3
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (116) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 13.45/3.70 | (270) all_0_3_3 = n7
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (116) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 13.45/3.70 | (271) all_0_1_1 = n6
% 13.45/3.70 |
% 13.45/3.70 | From (270) and (167) follows:
% 13.45/3.70 | (272) sum(n7, all_0_0_0) = all_0_6_6
% 13.45/3.70 |
% 13.45/3.70 | From (271) and (477) follows:
% 13.45/3.70 | (1644) sum(n6, n6) = all_0_0_0
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n6, n6, all_0_0_0, n1 and discharging atoms sum(n6, n6) = all_0_0_0, sum(n6, n6) = n1, yields:
% 13.45/3.70 | (342) all_0_0_0 = n1
% 13.45/3.70 |
% 13.45/3.70 | From (342) and (272) follows:
% 13.45/3.70 | (1646) sum(n7, n1) = all_0_6_6
% 13.45/3.70 |
% 13.45/3.70 | Instantiating formula (132) with n7, n1, all_0_6_6, n8 and discharging atoms sum(n7, n1) = all_0_6_6, sum(n7, n1) = n8, yields:
% 13.45/3.70 | (310) all_0_6_6 = n8
% 13.45/3.70 |
% 13.45/3.70 | Equations (310) can reduce 165 to:
% 13.45/3.70 | (243) $false
% 13.45/3.70 |
% 13.45/3.70 |-The branch is then unsatisfiable
% 13.45/3.70 |-Branch two:
% 13.45/3.70 | (397) ~ (all_0_8_8 = n1)
% 13.45/3.70 | (398) all_0_8_8 = n0
% 13.45/3.70 |
% 13.45/3.70 | From (398) and (1548) follows:
% 13.45/3.70 | (1651) sum(n0, n7) = all_0_4_4
% 13.45/3.71 |
% 13.45/3.71 | From (398) and (1546) follows:
% 13.45/3.71 | (1652) sum(n0, n6) = all_0_2_2
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n0, n7, all_0_4_4, n7 and discharging atoms sum(n0, n7) = all_0_4_4, sum(n0, n7) = n7, yields:
% 13.45/3.71 | (284) all_0_4_4 = n7
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n0, n6, all_0_2_2, n6 and discharging atoms sum(n0, n6) = all_0_2_2, sum(n0, n6) = n6, yields:
% 13.45/3.71 | (283) all_0_2_2 = n6
% 13.45/3.71 |
% 13.45/3.71 | From (283) and (205) follows:
% 13.45/3.71 | (285) pred(n6) = all_0_1_1
% 13.45/3.71 |
% 13.45/3.71 | From (284) and (138) follows:
% 13.45/3.71 | (286) pred(n7) = all_0_3_3
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (116) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 13.45/3.71 | (287) all_0_3_3 = n6
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (116) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 13.45/3.71 | (288) all_0_1_1 = n5
% 13.45/3.71 |
% 13.45/3.71 | From (287) and (167) follows:
% 13.45/3.71 | (289) sum(n6, all_0_0_0) = all_0_6_6
% 13.45/3.71 |
% 13.45/3.71 | From (288) and (477) follows:
% 13.45/3.71 | (1660) sum(n6, n5) = all_0_0_0
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n6, n5, all_0_0_0, n0 and discharging atoms sum(n6, n5) = all_0_0_0, sum(n6, n5) = n0, yields:
% 13.45/3.71 | (359) all_0_0_0 = n0
% 13.45/3.71 |
% 13.45/3.71 | From (359) and (289) follows:
% 13.45/3.71 | (1662) sum(n6, n0) = all_0_6_6
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n6, n0, all_0_6_6, n6 and discharging atoms sum(n6, n0) = all_0_6_6, sum(n6, n0) = n6, yields:
% 13.45/3.71 | (327) all_0_6_6 = n6
% 13.45/3.71 |
% 13.45/3.71 | Equations (327) can reduce 34 to:
% 13.45/3.71 | (243) $false
% 13.45/3.71 |
% 13.45/3.71 |-The branch is then unsatisfiable
% 13.45/3.71 |-Branch two:
% 13.45/3.71 | (492) ~ (all_0_7_7 = n6)
% 13.45/3.71 | (493) all_0_7_7 = n5 | all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.45/3.71 |
% 13.45/3.71 +-Applying beta-rule and splitting (296), into two cases.
% 13.45/3.71 |-Branch one:
% 13.45/3.71 | (297) all_0_8_8 = n6
% 13.45/3.71 |
% 13.45/3.71 | From (297) and (77) follows:
% 13.45/3.71 | (1668) sum(n6, all_0_5_5) = all_0_4_4
% 13.45/3.71 |
% 13.45/3.71 | From (297) and (120) follows:
% 13.45/3.71 | (1669) sum(n6, all_0_7_7) = all_0_2_2
% 13.45/3.71 |
% 13.45/3.71 +-Applying beta-rule and splitting (493), into two cases.
% 13.45/3.71 |-Branch one:
% 13.45/3.71 | (494) all_0_7_7 = n5
% 13.45/3.71 |
% 13.45/3.71 | From (494) and (10) follows:
% 13.45/3.71 | (495) succ(n5) = all_0_5_5
% 13.45/3.71 |
% 13.45/3.71 | From (494) and (3) follows:
% 13.45/3.71 | (496) sum(n5, all_0_1_1) = all_0_0_0
% 13.45/3.71 |
% 13.45/3.71 | From (494) and (1669) follows:
% 13.45/3.71 | (1673) sum(n6, n5) = all_0_2_2
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (47) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 13.45/3.71 | (498) all_0_5_5 = n6
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n6, n5, all_0_2_2, n0 and discharging atoms sum(n6, n5) = all_0_2_2, sum(n6, n5) = n0, yields:
% 13.45/3.71 | (385) all_0_2_2 = n0
% 13.45/3.71 |
% 13.45/3.71 | From (385) and (205) follows:
% 13.45/3.71 | (387) pred(n0) = all_0_1_1
% 13.45/3.71 |
% 13.45/3.71 | From (498) and (1668) follows:
% 13.45/3.71 | (1677) sum(n6, n6) = all_0_4_4
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (116) with n0, all_0_1_1, n10 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n10, yields:
% 13.45/3.71 | (390) all_0_1_1 = n10
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n6, n6, all_0_4_4, n1 and discharging atoms sum(n6, n6) = all_0_4_4, sum(n6, n6) = n1, yields:
% 13.45/3.71 | (386) all_0_4_4 = n1
% 13.45/3.71 |
% 13.45/3.71 | From (386) and (138) follows:
% 13.45/3.71 | (388) pred(n1) = all_0_3_3
% 13.45/3.71 |
% 13.45/3.71 | From (390) and (496) follows:
% 13.45/3.71 | (1681) sum(n5, n10) = all_0_0_0
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (116) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 13.45/3.71 | (389) all_0_3_3 = n0
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n5, n10, all_0_0_0, n4 and discharging atoms sum(n5, n10) = all_0_0_0, sum(n5, n10) = n4, yields:
% 13.45/3.71 | (291) all_0_0_0 = n4
% 13.45/3.71 |
% 13.45/3.71 | From (389)(291) and (167) follows:
% 13.45/3.71 | (1684) sum(n0, n4) = all_0_6_6
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n0, n4, all_0_6_6, n4 and discharging atoms sum(n0, n4) = all_0_6_6, sum(n0, n4) = n4, yields:
% 13.45/3.71 | (344) all_0_6_6 = n4
% 13.45/3.71 |
% 13.45/3.71 | Equations (344) can reduce 216 to:
% 13.45/3.71 | (243) $false
% 13.45/3.71 |
% 13.45/3.71 |-The branch is then unsatisfiable
% 13.45/3.71 |-Branch two:
% 13.45/3.71 | (511) ~ (all_0_7_7 = n5)
% 13.45/3.71 | (512) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.45/3.71 |
% 13.45/3.71 +-Applying beta-rule and splitting (512), into two cases.
% 13.45/3.71 |-Branch one:
% 13.45/3.71 | (513) all_0_7_7 = n4
% 13.45/3.71 |
% 13.45/3.71 | From (513) and (10) follows:
% 13.45/3.71 | (514) succ(n4) = all_0_5_5
% 13.45/3.71 |
% 13.45/3.71 | From (513) and (3) follows:
% 13.45/3.71 | (515) sum(n4, all_0_1_1) = all_0_0_0
% 13.45/3.71 |
% 13.45/3.71 | From (513) and (1669) follows:
% 13.45/3.71 | (1692) sum(n6, n4) = all_0_2_2
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (47) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 13.45/3.71 | (517) all_0_5_5 = n5
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n6, n4, all_0_2_2, n10 and discharging atoms sum(n6, n4) = all_0_2_2, sum(n6, n4) = n10, yields:
% 13.45/3.71 | (401) all_0_2_2 = n10
% 13.45/3.71 |
% 13.45/3.71 | From (401) and (205) follows:
% 13.45/3.71 | (403) pred(n10) = all_0_1_1
% 13.45/3.71 |
% 13.45/3.71 | From (517) and (1668) follows:
% 13.45/3.71 | (1696) sum(n6, n5) = all_0_4_4
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (116) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 13.45/3.71 | (405) all_0_1_1 = n9
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n6, n5, all_0_4_4, n0 and discharging atoms sum(n6, n5) = all_0_4_4, sum(n6, n5) = n0, yields:
% 13.45/3.71 | (402) all_0_4_4 = n0
% 13.45/3.71 |
% 13.45/3.71 | From (402) and (138) follows:
% 13.45/3.71 | (404) pred(n0) = all_0_3_3
% 13.45/3.71 |
% 13.45/3.71 | From (405) and (515) follows:
% 13.45/3.71 | (1700) sum(n4, n9) = all_0_0_0
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (116) with n0, all_0_3_3, n10 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n10, yields:
% 13.45/3.71 | (406) all_0_3_3 = n10
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n4, n9, all_0_0_0, n2 and discharging atoms sum(n4, n9) = all_0_0_0, sum(n4, n9) = n2, yields:
% 13.45/3.71 | (325) all_0_0_0 = n2
% 13.45/3.71 |
% 13.45/3.71 | From (406)(325) and (167) follows:
% 13.45/3.71 | (1703) sum(n10, n2) = all_0_6_6
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n10, n2, all_0_6_6, n1 and discharging atoms sum(n10, n2) = all_0_6_6, sum(n10, n2) = n1, yields:
% 13.45/3.71 | (276) all_0_6_6 = n1
% 13.45/3.71 |
% 13.45/3.71 | Equations (276) can reduce 28 to:
% 13.45/3.71 | (243) $false
% 13.45/3.71 |
% 13.45/3.71 |-The branch is then unsatisfiable
% 13.45/3.71 |-Branch two:
% 13.45/3.71 | (530) ~ (all_0_7_7 = n4)
% 13.45/3.71 | (531) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.45/3.71 |
% 13.45/3.71 +-Applying beta-rule and splitting (531), into two cases.
% 13.45/3.71 |-Branch one:
% 13.45/3.71 | (532) all_0_7_7 = n3
% 13.45/3.71 |
% 13.45/3.71 | From (532) and (10) follows:
% 13.45/3.71 | (533) succ(n3) = all_0_5_5
% 13.45/3.71 |
% 13.45/3.71 | From (532) and (3) follows:
% 13.45/3.71 | (534) sum(n3, all_0_1_1) = all_0_0_0
% 13.45/3.71 |
% 13.45/3.71 | From (532) and (1669) follows:
% 13.45/3.71 | (1711) sum(n6, n3) = all_0_2_2
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (47) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 13.45/3.71 | (536) all_0_5_5 = n4
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n6, n3, all_0_2_2, n9 and discharging atoms sum(n6, n3) = all_0_2_2, sum(n6, n3) = n9, yields:
% 13.45/3.71 | (232) all_0_2_2 = n9
% 13.45/3.71 |
% 13.45/3.71 | From (232) and (205) follows:
% 13.45/3.71 | (234) pred(n9) = all_0_1_1
% 13.45/3.71 |
% 13.45/3.71 | From (536) and (1668) follows:
% 13.45/3.71 | (1715) sum(n6, n4) = all_0_4_4
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (116) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 13.45/3.71 | (237) all_0_1_1 = n8
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n6, n4, all_0_4_4, n10 and discharging atoms sum(n6, n4) = all_0_4_4, sum(n6, n4) = n10, yields:
% 13.45/3.71 | (233) all_0_4_4 = n10
% 13.45/3.71 |
% 13.45/3.71 | From (233) and (138) follows:
% 13.45/3.71 | (235) pred(n10) = all_0_3_3
% 13.45/3.71 |
% 13.45/3.71 | From (237) and (534) follows:
% 13.45/3.71 | (1719) sum(n3, n8) = all_0_0_0
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (116) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 13.45/3.71 | (236) all_0_3_3 = n9
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n3, n8, all_0_0_0, n0 and discharging atoms sum(n3, n8) = all_0_0_0, sum(n3, n8) = n0, yields:
% 13.45/3.71 | (359) all_0_0_0 = n0
% 13.45/3.71 |
% 13.45/3.71 | From (236)(359) and (167) follows:
% 13.45/3.71 | (1722) sum(n9, n0) = all_0_6_6
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n9, n0, all_0_6_6, n9 and discharging atoms sum(n9, n0) = all_0_6_6, sum(n9, n0) = n9, yields:
% 13.45/3.71 | (395) all_0_6_6 = n9
% 13.45/3.71 |
% 13.45/3.71 | Equations (395) can reduce 78 to:
% 13.45/3.71 | (243) $false
% 13.45/3.71 |
% 13.45/3.71 |-The branch is then unsatisfiable
% 13.45/3.71 |-Branch two:
% 13.45/3.71 | (549) ~ (all_0_7_7 = n3)
% 13.45/3.71 | (550) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.45/3.71 |
% 13.45/3.71 +-Applying beta-rule and splitting (550), into two cases.
% 13.45/3.71 |-Branch one:
% 13.45/3.71 | (551) all_0_7_7 = n2
% 13.45/3.71 |
% 13.45/3.71 | From (551) and (10) follows:
% 13.45/3.71 | (552) succ(n2) = all_0_5_5
% 13.45/3.71 |
% 13.45/3.71 | From (551) and (3) follows:
% 13.45/3.71 | (553) sum(n2, all_0_1_1) = all_0_0_0
% 13.45/3.71 |
% 13.45/3.71 | From (551) and (1669) follows:
% 13.45/3.71 | (1730) sum(n6, n2) = all_0_2_2
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (47) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 13.45/3.71 | (555) all_0_5_5 = n3
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n6, n2, all_0_2_2, n8 and discharging atoms sum(n6, n2) = all_0_2_2, sum(n6, n2) = n8, yields:
% 13.45/3.71 | (249) all_0_2_2 = n8
% 13.45/3.71 |
% 13.45/3.71 | From (249) and (205) follows:
% 13.45/3.71 | (251) pred(n8) = all_0_1_1
% 13.45/3.71 |
% 13.45/3.71 | From (555) and (1668) follows:
% 13.45/3.71 | (1734) sum(n6, n3) = all_0_4_4
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (116) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 13.45/3.71 | (254) all_0_1_1 = n7
% 13.45/3.71 |
% 13.45/3.71 | Instantiating formula (132) with n6, n3, all_0_4_4, n9 and discharging atoms sum(n6, n3) = all_0_4_4, sum(n6, n3) = n9, yields:
% 13.45/3.71 | (250) all_0_4_4 = n9
% 13.45/3.71 |
% 13.45/3.71 | From (250) and (138) follows:
% 13.45/3.71 | (252) pred(n9) = all_0_3_3
% 13.45/3.71 |
% 13.45/3.71 | From (254) and (553) follows:
% 13.45/3.72 | (1738) sum(n2, n7) = all_0_0_0
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (116) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 13.45/3.72 | (253) all_0_3_3 = n8
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (132) with n2, n7, all_0_0_0, n9 and discharging atoms sum(n2, n7) = all_0_0_0, sum(n2, n7) = n9, yields:
% 13.45/3.72 | (393) all_0_0_0 = n9
% 13.45/3.72 |
% 13.45/3.72 | From (253)(393) and (167) follows:
% 13.45/3.72 | (1741) sum(n8, n9) = all_0_6_6
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (132) with n8, n9, all_0_6_6, n6 and discharging atoms sum(n8, n9) = all_0_6_6, sum(n8, n9) = n6, yields:
% 13.45/3.72 | (327) all_0_6_6 = n6
% 13.45/3.72 |
% 13.45/3.72 | Equations (327) can reduce 34 to:
% 13.45/3.72 | (243) $false
% 13.45/3.72 |
% 13.45/3.72 |-The branch is then unsatisfiable
% 13.45/3.72 |-Branch two:
% 13.45/3.72 | (568) ~ (all_0_7_7 = n2)
% 13.45/3.72 | (569) all_0_7_7 = n1 | all_0_7_7 = n0
% 13.45/3.72 |
% 13.45/3.72 +-Applying beta-rule and splitting (569), into two cases.
% 13.45/3.72 |-Branch one:
% 13.45/3.72 | (570) all_0_7_7 = n1
% 13.45/3.72 |
% 13.45/3.72 | From (570) and (10) follows:
% 13.45/3.72 | (571) succ(n1) = all_0_5_5
% 13.45/3.72 |
% 13.45/3.72 | From (570) and (3) follows:
% 13.45/3.72 | (572) sum(n1, all_0_1_1) = all_0_0_0
% 13.45/3.72 |
% 13.45/3.72 | From (570) and (1669) follows:
% 13.45/3.72 | (1749) sum(n6, n1) = all_0_2_2
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (47) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 13.45/3.72 | (574) all_0_5_5 = n2
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (132) with n6, n1, all_0_2_2, n7 and discharging atoms sum(n6, n1) = all_0_2_2, sum(n6, n1) = n7, yields:
% 13.45/3.72 | (266) all_0_2_2 = n7
% 13.45/3.72 |
% 13.45/3.72 | From (266) and (205) follows:
% 13.45/3.72 | (268) pred(n7) = all_0_1_1
% 13.45/3.72 |
% 13.45/3.72 | From (574) and (1668) follows:
% 13.45/3.72 | (1753) sum(n6, n2) = all_0_4_4
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (116) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 13.45/3.72 | (271) all_0_1_1 = n6
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (132) with n6, n2, all_0_4_4, n8 and discharging atoms sum(n6, n2) = all_0_4_4, sum(n6, n2) = n8, yields:
% 13.45/3.72 | (267) all_0_4_4 = n8
% 13.45/3.72 |
% 13.45/3.72 | From (267) and (138) follows:
% 13.45/3.72 | (269) pred(n8) = all_0_3_3
% 13.45/3.72 |
% 13.45/3.72 | From (271) and (572) follows:
% 13.45/3.72 | (1757) sum(n1, n6) = all_0_0_0
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (116) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 13.45/3.72 | (270) all_0_3_3 = n7
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (132) with n1, n6, all_0_0_0, n7 and discharging atoms sum(n1, n6) = all_0_0_0, sum(n1, n6) = n7, yields:
% 13.45/3.72 | (240) all_0_0_0 = n7
% 13.45/3.72 |
% 13.45/3.72 | From (270)(240) and (167) follows:
% 13.45/3.72 | (1760) sum(n7, n7) = all_0_6_6
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (132) with n7, n7, all_0_6_6, n3 and discharging atoms sum(n7, n7) = all_0_6_6, sum(n7, n7) = n3, yields:
% 13.45/3.72 | (259) all_0_6_6 = n3
% 13.45/3.72 |
% 13.45/3.72 | Equations (259) can reduce 100 to:
% 13.45/3.72 | (243) $false
% 13.45/3.72 |
% 13.45/3.72 |-The branch is then unsatisfiable
% 13.45/3.72 |-Branch two:
% 13.45/3.72 | (587) ~ (all_0_7_7 = n1)
% 13.45/3.72 | (588) all_0_7_7 = n0
% 13.45/3.72 |
% 13.45/3.72 | From (588) and (10) follows:
% 13.45/3.72 | (589) succ(n0) = all_0_5_5
% 13.45/3.72 |
% 13.45/3.72 | From (588) and (3) follows:
% 13.45/3.72 | (590) sum(n0, all_0_1_1) = all_0_0_0
% 13.45/3.72 |
% 13.45/3.72 | From (588) and (1669) follows:
% 13.45/3.72 | (1767) sum(n6, n0) = all_0_2_2
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (47) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 13.45/3.72 | (592) all_0_5_5 = n1
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (132) with n6, n0, all_0_2_2, n6 and discharging atoms sum(n6, n0) = all_0_2_2, sum(n6, n0) = n6, yields:
% 13.45/3.72 | (283) all_0_2_2 = n6
% 13.45/3.72 |
% 13.45/3.72 | From (283) and (205) follows:
% 13.45/3.72 | (285) pred(n6) = all_0_1_1
% 13.45/3.72 |
% 13.45/3.72 | From (592) and (1668) follows:
% 13.45/3.72 | (1771) sum(n6, n1) = all_0_4_4
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (116) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 13.45/3.72 | (288) all_0_1_1 = n5
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (132) with n6, n1, all_0_4_4, n7 and discharging atoms sum(n6, n1) = all_0_4_4, sum(n6, n1) = n7, yields:
% 13.45/3.72 | (284) all_0_4_4 = n7
% 13.45/3.72 |
% 13.45/3.72 | From (284) and (138) follows:
% 13.45/3.72 | (286) pred(n7) = all_0_3_3
% 13.45/3.72 |
% 13.45/3.72 | From (288) and (590) follows:
% 13.45/3.72 | (1775) sum(n0, n5) = all_0_0_0
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (116) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 13.45/3.72 | (287) all_0_3_3 = n6
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (132) with n0, n5, all_0_0_0, n5 and discharging atoms sum(n0, n5) = all_0_0_0, sum(n0, n5) = n5, yields:
% 13.45/3.72 | (274) all_0_0_0 = n5
% 13.45/3.72 |
% 13.45/3.72 | From (287)(274) and (167) follows:
% 13.45/3.72 | (1778) sum(n6, n5) = all_0_6_6
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (132) with n6, n5, all_0_6_6, n0 and discharging atoms sum(n6, n5) = all_0_6_6, sum(n6, n5) = n0, yields:
% 13.45/3.72 | (378) all_0_6_6 = n0
% 13.45/3.72 |
% 13.45/3.72 | Equations (378) can reduce 119 to:
% 13.45/3.72 | (243) $false
% 13.45/3.72 |
% 13.45/3.72 |-The branch is then unsatisfiable
% 13.45/3.72 |-Branch two:
% 13.45/3.72 | (312) ~ (all_0_8_8 = n6)
% 13.45/3.72 | (313) all_0_8_8 = n5 | all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.72 |
% 13.45/3.72 +-Applying beta-rule and splitting (493), into two cases.
% 13.45/3.72 |-Branch one:
% 13.45/3.72 | (494) all_0_7_7 = n5
% 13.45/3.72 |
% 13.45/3.72 | From (494) and (10) follows:
% 13.45/3.72 | (495) succ(n5) = all_0_5_5
% 13.45/3.72 |
% 13.45/3.72 | From (494) and (3) follows:
% 13.45/3.72 | (496) sum(n5, all_0_1_1) = all_0_0_0
% 13.45/3.72 |
% 13.45/3.72 | From (494) and (120) follows:
% 13.45/3.72 | (1786) sum(all_0_8_8, n5) = all_0_2_2
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (47) with n5, all_0_5_5, n6 and discharging atoms succ(n5) = all_0_5_5, succ(n5) = n6, yields:
% 13.45/3.72 | (498) all_0_5_5 = n6
% 13.45/3.72 |
% 13.45/3.72 | From (498) and (77) follows:
% 13.45/3.72 | (1788) sum(all_0_8_8, n6) = all_0_4_4
% 13.45/3.72 |
% 13.45/3.72 +-Applying beta-rule and splitting (313), into two cases.
% 13.45/3.72 |-Branch one:
% 13.45/3.72 | (314) all_0_8_8 = n5
% 13.45/3.72 |
% 13.45/3.72 | From (314) and (1788) follows:
% 13.45/3.72 | (1790) sum(n5, n6) = all_0_4_4
% 13.45/3.72 |
% 13.45/3.72 | From (314) and (1786) follows:
% 13.45/3.72 | (1791) sum(n5, n5) = all_0_2_2
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (132) with n5, n6, all_0_4_4, n0 and discharging atoms sum(n5, n6) = all_0_4_4, sum(n5, n6) = n0, yields:
% 13.45/3.72 | (402) all_0_4_4 = n0
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (132) with n5, n5, all_0_2_2, n10 and discharging atoms sum(n5, n5) = all_0_2_2, sum(n5, n5) = n10, yields:
% 13.45/3.72 | (401) all_0_2_2 = n10
% 13.45/3.72 |
% 13.45/3.72 | From (401) and (205) follows:
% 13.45/3.72 | (403) pred(n10) = all_0_1_1
% 13.45/3.72 |
% 13.45/3.72 | From (402) and (138) follows:
% 13.45/3.72 | (404) pred(n0) = all_0_3_3
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (116) with n10, all_0_1_1, n9 and discharging atoms pred(n10) = all_0_1_1, pred(n10) = n9, yields:
% 13.45/3.72 | (405) all_0_1_1 = n9
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (116) with n0, all_0_3_3, n10 and discharging atoms pred(n0) = all_0_3_3, pred(n0) = n10, yields:
% 13.45/3.72 | (406) all_0_3_3 = n10
% 13.45/3.72 |
% 13.45/3.72 | From (406) and (167) follows:
% 13.45/3.72 | (407) sum(n10, all_0_0_0) = all_0_6_6
% 13.45/3.72 |
% 13.45/3.72 | From (405) and (496) follows:
% 13.45/3.72 | (1799) sum(n5, n9) = all_0_0_0
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (132) with n5, n9, all_0_0_0, n3 and discharging atoms sum(n5, n9) = all_0_0_0, sum(n5, n9) = n3, yields:
% 13.45/3.72 | (308) all_0_0_0 = n3
% 13.45/3.72 |
% 13.45/3.72 | From (308) and (407) follows:
% 13.45/3.72 | (1801) sum(n10, n3) = all_0_6_6
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (132) with n10, n3, all_0_6_6, n2 and discharging atoms sum(n10, n3) = all_0_6_6, sum(n10, n3) = n2, yields:
% 13.45/3.72 | (361) all_0_6_6 = n2
% 13.45/3.72 |
% 13.45/3.72 | Equations (361) can reduce 131 to:
% 13.45/3.72 | (243) $false
% 13.45/3.72 |
% 13.45/3.72 |-The branch is then unsatisfiable
% 13.45/3.72 |-Branch two:
% 13.45/3.72 | (329) ~ (all_0_8_8 = n5)
% 13.45/3.72 | (330) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.72 |
% 13.45/3.72 +-Applying beta-rule and splitting (330), into two cases.
% 13.45/3.72 |-Branch one:
% 13.45/3.72 | (331) all_0_8_8 = n4
% 13.45/3.72 |
% 13.45/3.72 | From (331) and (1788) follows:
% 13.45/3.72 | (1807) sum(n4, n6) = all_0_4_4
% 13.45/3.72 |
% 13.45/3.72 | From (331) and (1786) follows:
% 13.45/3.72 | (1808) sum(n4, n5) = all_0_2_2
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (132) with n4, n6, all_0_4_4, n10 and discharging atoms sum(n4, n6) = all_0_4_4, sum(n4, n6) = n10, yields:
% 13.45/3.72 | (233) all_0_4_4 = n10
% 13.45/3.72 |
% 13.45/3.72 | Instantiating formula (132) with n4, n5, all_0_2_2, n9 and discharging atoms sum(n4, n5) = all_0_2_2, sum(n4, n5) = n9, yields:
% 13.45/3.72 | (232) all_0_2_2 = n9
% 13.45/3.72 |
% 13.45/3.72 | From (232) and (205) follows:
% 13.45/3.72 | (234) pred(n9) = all_0_1_1
% 13.45/3.73 |
% 13.45/3.73 | From (233) and (138) follows:
% 13.45/3.73 | (235) pred(n10) = all_0_3_3
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (116) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 13.45/3.73 | (236) all_0_3_3 = n9
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (116) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 13.45/3.73 | (237) all_0_1_1 = n8
% 13.45/3.73 |
% 13.45/3.73 | From (236) and (167) follows:
% 13.45/3.73 | (238) sum(n9, all_0_0_0) = all_0_6_6
% 13.45/3.73 |
% 13.45/3.73 | From (237) and (496) follows:
% 13.45/3.73 | (1816) sum(n5, n8) = all_0_0_0
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (132) with n5, n8, all_0_0_0, n2 and discharging atoms sum(n5, n8) = all_0_0_0, sum(n5, n8) = n2, yields:
% 13.45/3.73 | (325) all_0_0_0 = n2
% 13.45/3.73 |
% 13.45/3.73 | From (325) and (238) follows:
% 13.45/3.73 | (1818) sum(n9, n2) = all_0_6_6
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (132) with n9, n2, all_0_6_6, n0 and discharging atoms sum(n9, n2) = all_0_6_6, sum(n9, n2) = n0, yields:
% 13.45/3.73 | (378) all_0_6_6 = n0
% 13.45/3.73 |
% 13.45/3.73 | Equations (378) can reduce 119 to:
% 13.45/3.73 | (243) $false
% 13.45/3.73 |
% 13.45/3.73 |-The branch is then unsatisfiable
% 13.45/3.73 |-Branch two:
% 13.45/3.73 | (346) ~ (all_0_8_8 = n4)
% 13.45/3.73 | (347) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.73 |
% 13.45/3.73 +-Applying beta-rule and splitting (347), into two cases.
% 13.45/3.73 |-Branch one:
% 13.45/3.73 | (348) all_0_8_8 = n3
% 13.45/3.73 |
% 13.45/3.73 | From (348) and (1788) follows:
% 13.45/3.73 | (1824) sum(n3, n6) = all_0_4_4
% 13.45/3.73 |
% 13.45/3.73 | From (348) and (1786) follows:
% 13.45/3.73 | (1825) sum(n3, n5) = all_0_2_2
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (132) with n3, n6, all_0_4_4, n9 and discharging atoms sum(n3, n6) = all_0_4_4, sum(n3, n6) = n9, yields:
% 13.45/3.73 | (250) all_0_4_4 = n9
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (132) with n3, n5, all_0_2_2, n8 and discharging atoms sum(n3, n5) = all_0_2_2, sum(n3, n5) = n8, yields:
% 13.45/3.73 | (249) all_0_2_2 = n8
% 13.45/3.73 |
% 13.45/3.73 | From (249) and (205) follows:
% 13.45/3.73 | (251) pred(n8) = all_0_1_1
% 13.45/3.73 |
% 13.45/3.73 | From (250) and (138) follows:
% 13.45/3.73 | (252) pred(n9) = all_0_3_3
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (116) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 13.45/3.73 | (253) all_0_3_3 = n8
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (116) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 13.45/3.73 | (254) all_0_1_1 = n7
% 13.45/3.73 |
% 13.45/3.73 | From (253) and (167) follows:
% 13.45/3.73 | (255) sum(n8, all_0_0_0) = all_0_6_6
% 13.45/3.73 |
% 13.45/3.73 | From (254) and (496) follows:
% 13.45/3.73 | (1833) sum(n5, n7) = all_0_0_0
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (132) with n5, n7, all_0_0_0, n1 and discharging atoms sum(n5, n7) = all_0_0_0, sum(n5, n7) = n1, yields:
% 13.45/3.73 | (342) all_0_0_0 = n1
% 13.45/3.73 |
% 13.45/3.73 | From (342) and (255) follows:
% 13.45/3.73 | (1835) sum(n8, n1) = all_0_6_6
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (132) with n8, n1, all_0_6_6, n9 and discharging atoms sum(n8, n1) = all_0_6_6, sum(n8, n1) = n9, yields:
% 13.45/3.73 | (395) all_0_6_6 = n9
% 13.45/3.73 |
% 13.45/3.73 | Equations (395) can reduce 78 to:
% 13.45/3.73 | (243) $false
% 13.45/3.73 |
% 13.45/3.73 |-The branch is then unsatisfiable
% 13.45/3.73 |-Branch two:
% 13.45/3.73 | (363) ~ (all_0_8_8 = n3)
% 13.45/3.73 | (364) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.73 |
% 13.45/3.73 +-Applying beta-rule and splitting (364), into two cases.
% 13.45/3.73 |-Branch one:
% 13.45/3.73 | (365) all_0_8_8 = n2
% 13.45/3.73 |
% 13.45/3.73 | From (365) and (1788) follows:
% 13.45/3.73 | (1841) sum(n2, n6) = all_0_4_4
% 13.45/3.73 |
% 13.45/3.73 | From (365) and (1786) follows:
% 13.45/3.73 | (1842) sum(n2, n5) = all_0_2_2
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (132) with n2, n6, all_0_4_4, n8 and discharging atoms sum(n2, n6) = all_0_4_4, sum(n2, n6) = n8, yields:
% 13.45/3.73 | (267) all_0_4_4 = n8
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (132) with n2, n5, all_0_2_2, n7 and discharging atoms sum(n2, n5) = all_0_2_2, sum(n2, n5) = n7, yields:
% 13.45/3.73 | (266) all_0_2_2 = n7
% 13.45/3.73 |
% 13.45/3.73 | From (266) and (205) follows:
% 13.45/3.73 | (268) pred(n7) = all_0_1_1
% 13.45/3.73 |
% 13.45/3.73 | From (267) and (138) follows:
% 13.45/3.73 | (269) pred(n8) = all_0_3_3
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (116) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 13.45/3.73 | (270) all_0_3_3 = n7
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (116) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 13.45/3.73 | (271) all_0_1_1 = n6
% 13.45/3.73 |
% 13.45/3.73 | From (270) and (167) follows:
% 13.45/3.73 | (272) sum(n7, all_0_0_0) = all_0_6_6
% 13.45/3.73 |
% 13.45/3.73 | From (271) and (496) follows:
% 13.45/3.73 | (1850) sum(n5, n6) = all_0_0_0
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (132) with n5, n6, all_0_0_0, n0 and discharging atoms sum(n5, n6) = all_0_0_0, sum(n5, n6) = n0, yields:
% 13.45/3.73 | (359) all_0_0_0 = n0
% 13.45/3.73 |
% 13.45/3.73 | From (359) and (272) follows:
% 13.45/3.73 | (1852) sum(n7, n0) = all_0_6_6
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (132) with n7, n0, all_0_6_6, n7 and discharging atoms sum(n7, n0) = all_0_6_6, sum(n7, n0) = n7, yields:
% 13.45/3.73 | (411) all_0_6_6 = n7
% 13.45/3.73 |
% 13.45/3.73 | Equations (411) can reduce 88 to:
% 13.45/3.73 | (243) $false
% 13.45/3.73 |
% 13.45/3.73 |-The branch is then unsatisfiable
% 13.45/3.73 |-Branch two:
% 13.45/3.73 | (380) ~ (all_0_8_8 = n2)
% 13.45/3.73 | (381) all_0_8_8 = n1 | all_0_8_8 = n0
% 13.45/3.73 |
% 13.45/3.73 +-Applying beta-rule and splitting (381), into two cases.
% 13.45/3.73 |-Branch one:
% 13.45/3.73 | (382) all_0_8_8 = n1
% 13.45/3.73 |
% 13.45/3.73 | From (382) and (1788) follows:
% 13.45/3.73 | (1858) sum(n1, n6) = all_0_4_4
% 13.45/3.73 |
% 13.45/3.73 | From (382) and (1786) follows:
% 13.45/3.73 | (1859) sum(n1, n5) = all_0_2_2
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (132) with n1, n6, all_0_4_4, n7 and discharging atoms sum(n1, n6) = all_0_4_4, sum(n1, n6) = n7, yields:
% 13.45/3.73 | (284) all_0_4_4 = n7
% 13.45/3.73 |
% 13.45/3.73 | Instantiating formula (132) with n1, n5, all_0_2_2, n6 and discharging atoms sum(n1, n5) = all_0_2_2, sum(n1, n5) = n6, yields:
% 13.45/3.73 | (283) all_0_2_2 = n6
% 13.45/3.73 |
% 13.45/3.73 | From (283) and (205) follows:
% 13.45/3.73 | (285) pred(n6) = all_0_1_1
% 13.45/3.73 |
% 13.81/3.73 | From (284) and (138) follows:
% 13.81/3.73 | (286) pred(n7) = all_0_3_3
% 13.81/3.73 |
% 13.81/3.73 | Instantiating formula (116) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 13.81/3.73 | (287) all_0_3_3 = n6
% 13.81/3.73 |
% 13.81/3.73 | Instantiating formula (116) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 13.81/3.73 | (288) all_0_1_1 = n5
% 13.81/3.73 |
% 13.81/3.73 | From (287) and (167) follows:
% 13.81/3.73 | (289) sum(n6, all_0_0_0) = all_0_6_6
% 13.81/3.73 |
% 13.81/3.73 | From (288) and (496) follows:
% 13.81/3.73 | (1867) sum(n5, n5) = all_0_0_0
% 13.81/3.73 |
% 13.81/3.73 | Instantiating formula (132) with n5, n5, all_0_0_0, n10 and discharging atoms sum(n5, n5) = all_0_0_0, sum(n5, n5) = n10, yields:
% 13.81/3.73 | (376) all_0_0_0 = n10
% 13.81/3.73 |
% 13.81/3.73 | From (376) and (289) follows:
% 13.81/3.73 | (1869) sum(n6, n10) = all_0_6_6
% 13.81/3.73 |
% 13.81/3.73 | Instantiating formula (132) with n6, n10, all_0_6_6, n5 and discharging atoms sum(n6, n10) = all_0_6_6, sum(n6, n10) = n5, yields:
% 13.81/3.73 | (242) all_0_6_6 = n5
% 13.81/3.73 |
% 13.81/3.73 | Equations (242) can reduce 4 to:
% 13.81/3.73 | (243) $false
% 13.81/3.73 |
% 13.81/3.73 |-The branch is then unsatisfiable
% 13.81/3.73 |-Branch two:
% 13.81/3.73 | (397) ~ (all_0_8_8 = n1)
% 13.81/3.73 | (398) all_0_8_8 = n0
% 13.81/3.73 |
% 13.81/3.73 | From (398) and (1788) follows:
% 13.81/3.73 | (1874) sum(n0, n6) = all_0_4_4
% 13.81/3.73 |
% 13.81/3.73 | From (398) and (1786) follows:
% 13.81/3.73 | (1875) sum(n0, n5) = all_0_2_2
% 13.81/3.73 |
% 13.81/3.73 | Instantiating formula (132) with n0, n6, all_0_4_4, n6 and discharging atoms sum(n0, n6) = all_0_4_4, sum(n0, n6) = n6, yields:
% 13.81/3.73 | (301) all_0_4_4 = n6
% 13.81/3.73 |
% 13.81/3.73 | Instantiating formula (132) with n0, n5, all_0_2_2, n5 and discharging atoms sum(n0, n5) = all_0_2_2, sum(n0, n5) = n5, yields:
% 13.81/3.73 | (300) all_0_2_2 = n5
% 13.81/3.73 |
% 13.81/3.73 | From (300) and (205) follows:
% 13.81/3.73 | (302) pred(n5) = all_0_1_1
% 13.81/3.73 |
% 13.81/3.73 | From (301) and (138) follows:
% 13.81/3.73 | (303) pred(n6) = all_0_3_3
% 13.81/3.73 |
% 13.81/3.73 | Instantiating formula (116) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 13.81/3.73 | (304) all_0_3_3 = n5
% 13.81/3.73 |
% 13.81/3.73 | Instantiating formula (116) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 13.81/3.73 | (305) all_0_1_1 = n4
% 13.81/3.73 |
% 13.81/3.73 | From (304) and (167) follows:
% 13.81/3.73 | (306) sum(n5, all_0_0_0) = all_0_6_6
% 13.81/3.73 |
% 13.81/3.73 | From (305) and (496) follows:
% 13.81/3.73 | (1883) sum(n5, n4) = all_0_0_0
% 13.81/3.73 |
% 13.81/3.73 | Instantiating formula (132) with n5, n4, all_0_0_0, n9 and discharging atoms sum(n5, n4) = all_0_0_0, sum(n5, n4) = n9, yields:
% 13.81/3.73 | (393) all_0_0_0 = n9
% 13.81/3.73 |
% 13.81/3.73 | From (393) and (306) follows:
% 13.81/3.73 | (1885) sum(n5, n9) = all_0_6_6
% 13.81/3.73 |
% 13.81/3.73 | Instantiating formula (132) with n5, n9, all_0_6_6, n3 and discharging atoms sum(n5, n9) = all_0_6_6, sum(n5, n9) = n3, yields:
% 13.81/3.73 | (259) all_0_6_6 = n3
% 13.81/3.73 |
% 13.81/3.73 | Equations (259) can reduce 100 to:
% 13.81/3.73 | (243) $false
% 13.81/3.73 |
% 13.81/3.73 |-The branch is then unsatisfiable
% 13.81/3.73 |-Branch two:
% 13.81/3.73 | (511) ~ (all_0_7_7 = n5)
% 13.81/3.73 | (512) all_0_7_7 = n4 | all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.81/3.73 |
% 13.81/3.73 +-Applying beta-rule and splitting (313), into two cases.
% 13.81/3.73 |-Branch one:
% 13.81/3.73 | (314) all_0_8_8 = n5
% 13.81/3.73 |
% 13.81/3.73 | From (314) and (77) follows:
% 13.81/3.73 | (1891) sum(n5, all_0_5_5) = all_0_4_4
% 13.81/3.73 |
% 13.81/3.73 | From (314) and (120) follows:
% 13.81/3.73 | (1892) sum(n5, all_0_7_7) = all_0_2_2
% 13.81/3.73 |
% 13.81/3.73 +-Applying beta-rule and splitting (512), into two cases.
% 13.81/3.73 |-Branch one:
% 13.81/3.73 | (513) all_0_7_7 = n4
% 13.81/3.73 |
% 13.81/3.73 | From (513) and (10) follows:
% 13.81/3.73 | (514) succ(n4) = all_0_5_5
% 13.81/3.73 |
% 13.81/3.73 | From (513) and (3) follows:
% 13.81/3.73 | (515) sum(n4, all_0_1_1) = all_0_0_0
% 13.81/3.73 |
% 13.81/3.73 | From (513) and (1892) follows:
% 13.81/3.73 | (1896) sum(n5, n4) = all_0_2_2
% 13.81/3.73 |
% 13.81/3.73 | Instantiating formula (47) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 13.81/3.73 | (517) all_0_5_5 = n5
% 13.81/3.73 |
% 13.81/3.73 | Instantiating formula (132) with n5, n4, all_0_2_2, n9 and discharging atoms sum(n5, n4) = all_0_2_2, sum(n5, n4) = n9, yields:
% 13.81/3.73 | (232) all_0_2_2 = n9
% 13.81/3.73 |
% 13.81/3.73 | From (232) and (205) follows:
% 13.81/3.74 | (234) pred(n9) = all_0_1_1
% 13.81/3.74 |
% 13.81/3.74 | From (517) and (1891) follows:
% 13.81/3.74 | (1900) sum(n5, n5) = all_0_4_4
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (116) with n9, all_0_1_1, n8 and discharging atoms pred(n9) = all_0_1_1, pred(n9) = n8, yields:
% 13.81/3.74 | (237) all_0_1_1 = n8
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n5, n5, all_0_4_4, n10 and discharging atoms sum(n5, n5) = all_0_4_4, sum(n5, n5) = n10, yields:
% 13.81/3.74 | (233) all_0_4_4 = n10
% 13.81/3.74 |
% 13.81/3.74 | From (233) and (138) follows:
% 13.81/3.74 | (235) pred(n10) = all_0_3_3
% 13.81/3.74 |
% 13.81/3.74 | From (237) and (515) follows:
% 13.81/3.74 | (1904) sum(n4, n8) = all_0_0_0
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (116) with n10, all_0_3_3, n9 and discharging atoms pred(n10) = all_0_3_3, pred(n10) = n9, yields:
% 13.81/3.74 | (236) all_0_3_3 = n9
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n4, n8, all_0_0_0, n1 and discharging atoms sum(n4, n8) = all_0_0_0, sum(n4, n8) = n1, yields:
% 13.81/3.74 | (342) all_0_0_0 = n1
% 13.81/3.74 |
% 13.81/3.74 | From (236)(342) and (167) follows:
% 13.81/3.74 | (1907) sum(n9, n1) = all_0_6_6
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n9, n1, all_0_6_6, n10 and discharging atoms sum(n9, n1) = all_0_6_6, sum(n9, n1) = n10, yields:
% 13.81/3.74 | (293) all_0_6_6 = n10
% 13.81/3.74 |
% 13.81/3.74 | Equations (293) can reduce 147 to:
% 13.81/3.74 | (243) $false
% 13.81/3.74 |
% 13.81/3.74 |-The branch is then unsatisfiable
% 13.81/3.74 |-Branch two:
% 13.81/3.74 | (530) ~ (all_0_7_7 = n4)
% 13.81/3.74 | (531) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.81/3.74 |
% 13.81/3.74 +-Applying beta-rule and splitting (531), into two cases.
% 13.81/3.74 |-Branch one:
% 13.81/3.74 | (532) all_0_7_7 = n3
% 13.81/3.74 |
% 13.81/3.74 | From (532) and (10) follows:
% 13.81/3.74 | (533) succ(n3) = all_0_5_5
% 13.81/3.74 |
% 13.81/3.74 | From (532) and (3) follows:
% 13.81/3.74 | (534) sum(n3, all_0_1_1) = all_0_0_0
% 13.81/3.74 |
% 13.81/3.74 | From (532) and (1892) follows:
% 13.81/3.74 | (1915) sum(n5, n3) = all_0_2_2
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (47) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 13.81/3.74 | (536) all_0_5_5 = n4
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n5, n3, all_0_2_2, n8 and discharging atoms sum(n5, n3) = all_0_2_2, sum(n5, n3) = n8, yields:
% 13.81/3.74 | (249) all_0_2_2 = n8
% 13.81/3.74 |
% 13.81/3.74 | From (249) and (205) follows:
% 13.81/3.74 | (251) pred(n8) = all_0_1_1
% 13.81/3.74 |
% 13.81/3.74 | From (536) and (1891) follows:
% 13.81/3.74 | (1919) sum(n5, n4) = all_0_4_4
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (116) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 13.81/3.74 | (254) all_0_1_1 = n7
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n5, n4, all_0_4_4, n9 and discharging atoms sum(n5, n4) = all_0_4_4, sum(n5, n4) = n9, yields:
% 13.81/3.74 | (250) all_0_4_4 = n9
% 13.81/3.74 |
% 13.81/3.74 | From (250) and (138) follows:
% 13.81/3.74 | (252) pred(n9) = all_0_3_3
% 13.81/3.74 |
% 13.81/3.74 | From (254) and (534) follows:
% 13.81/3.74 | (1923) sum(n3, n7) = all_0_0_0
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (116) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 13.81/3.74 | (253) all_0_3_3 = n8
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n3, n7, all_0_0_0, n10 and discharging atoms sum(n3, n7) = all_0_0_0, sum(n3, n7) = n10, yields:
% 13.81/3.74 | (376) all_0_0_0 = n10
% 13.81/3.74 |
% 13.81/3.74 | From (253)(376) and (167) follows:
% 13.81/3.74 | (1926) sum(n8, n10) = all_0_6_6
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n8, n10, all_0_6_6, n7 and discharging atoms sum(n8, n10) = all_0_6_6, sum(n8, n10) = n7, yields:
% 13.81/3.74 | (411) all_0_6_6 = n7
% 13.81/3.74 |
% 13.81/3.74 | Equations (411) can reduce 88 to:
% 13.81/3.74 | (243) $false
% 13.81/3.74 |
% 13.81/3.74 |-The branch is then unsatisfiable
% 13.81/3.74 |-Branch two:
% 13.81/3.74 | (549) ~ (all_0_7_7 = n3)
% 13.81/3.74 | (550) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.81/3.74 |
% 13.81/3.74 +-Applying beta-rule and splitting (550), into two cases.
% 13.81/3.74 |-Branch one:
% 13.81/3.74 | (551) all_0_7_7 = n2
% 13.81/3.74 |
% 13.81/3.74 | From (551) and (10) follows:
% 13.81/3.74 | (552) succ(n2) = all_0_5_5
% 13.81/3.74 |
% 13.81/3.74 | From (551) and (3) follows:
% 13.81/3.74 | (553) sum(n2, all_0_1_1) = all_0_0_0
% 13.81/3.74 |
% 13.81/3.74 | From (551) and (1892) follows:
% 13.81/3.74 | (1934) sum(n5, n2) = all_0_2_2
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (47) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 13.81/3.74 | (555) all_0_5_5 = n3
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n5, n2, all_0_2_2, n7 and discharging atoms sum(n5, n2) = all_0_2_2, sum(n5, n2) = n7, yields:
% 13.81/3.74 | (266) all_0_2_2 = n7
% 13.81/3.74 |
% 13.81/3.74 | From (266) and (205) follows:
% 13.81/3.74 | (268) pred(n7) = all_0_1_1
% 13.81/3.74 |
% 13.81/3.74 | From (555) and (1891) follows:
% 13.81/3.74 | (1938) sum(n5, n3) = all_0_4_4
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (116) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 13.81/3.74 | (271) all_0_1_1 = n6
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n5, n3, all_0_4_4, n8 and discharging atoms sum(n5, n3) = all_0_4_4, sum(n5, n3) = n8, yields:
% 13.81/3.74 | (267) all_0_4_4 = n8
% 13.81/3.74 |
% 13.81/3.74 | From (267) and (138) follows:
% 13.81/3.74 | (269) pred(n8) = all_0_3_3
% 13.81/3.74 |
% 13.81/3.74 | From (271) and (553) follows:
% 13.81/3.74 | (1942) sum(n2, n6) = all_0_0_0
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (116) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 13.81/3.74 | (270) all_0_3_3 = n7
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n2, n6, all_0_0_0, n8 and discharging atoms sum(n2, n6) = all_0_0_0, sum(n2, n6) = n8, yields:
% 13.81/3.74 | (409) all_0_0_0 = n8
% 13.81/3.74 |
% 13.81/3.74 | From (270)(409) and (167) follows:
% 13.81/3.74 | (1945) sum(n7, n8) = all_0_6_6
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n7, n8, all_0_6_6, n4 and discharging atoms sum(n7, n8) = all_0_6_6, sum(n7, n8) = n4, yields:
% 13.81/3.74 | (344) all_0_6_6 = n4
% 13.81/3.74 |
% 13.81/3.74 | Equations (344) can reduce 216 to:
% 13.81/3.74 | (243) $false
% 13.81/3.74 |
% 13.81/3.74 |-The branch is then unsatisfiable
% 13.81/3.74 |-Branch two:
% 13.81/3.74 | (568) ~ (all_0_7_7 = n2)
% 13.81/3.74 | (569) all_0_7_7 = n1 | all_0_7_7 = n0
% 13.81/3.74 |
% 13.81/3.74 +-Applying beta-rule and splitting (569), into two cases.
% 13.81/3.74 |-Branch one:
% 13.81/3.74 | (570) all_0_7_7 = n1
% 13.81/3.74 |
% 13.81/3.74 | From (570) and (10) follows:
% 13.81/3.74 | (571) succ(n1) = all_0_5_5
% 13.81/3.74 |
% 13.81/3.74 | From (570) and (3) follows:
% 13.81/3.74 | (572) sum(n1, all_0_1_1) = all_0_0_0
% 13.81/3.74 |
% 13.81/3.74 | From (570) and (1892) follows:
% 13.81/3.74 | (1953) sum(n5, n1) = all_0_2_2
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (47) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 13.81/3.74 | (574) all_0_5_5 = n2
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n5, n1, all_0_2_2, n6 and discharging atoms sum(n5, n1) = all_0_2_2, sum(n5, n1) = n6, yields:
% 13.81/3.74 | (283) all_0_2_2 = n6
% 13.81/3.74 |
% 13.81/3.74 | From (283) and (205) follows:
% 13.81/3.74 | (285) pred(n6) = all_0_1_1
% 13.81/3.74 |
% 13.81/3.74 | From (574) and (1891) follows:
% 13.81/3.74 | (1957) sum(n5, n2) = all_0_4_4
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (116) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 13.81/3.74 | (288) all_0_1_1 = n5
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n5, n2, all_0_4_4, n7 and discharging atoms sum(n5, n2) = all_0_4_4, sum(n5, n2) = n7, yields:
% 13.81/3.74 | (284) all_0_4_4 = n7
% 13.81/3.74 |
% 13.81/3.74 | From (284) and (138) follows:
% 13.81/3.74 | (286) pred(n7) = all_0_3_3
% 13.81/3.74 |
% 13.81/3.74 | From (288) and (572) follows:
% 13.81/3.74 | (1961) sum(n1, n5) = all_0_0_0
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (116) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 13.81/3.74 | (287) all_0_3_3 = n6
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n1, n5, all_0_0_0, n6 and discharging atoms sum(n1, n5) = all_0_0_0, sum(n1, n5) = n6, yields:
% 13.81/3.74 | (257) all_0_0_0 = n6
% 13.81/3.74 |
% 13.81/3.74 | From (287)(257) and (167) follows:
% 13.81/3.74 | (1964) sum(n6, n6) = all_0_6_6
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n6, n6, all_0_6_6, n1 and discharging atoms sum(n6, n6) = all_0_6_6, sum(n6, n6) = n1, yields:
% 13.81/3.74 | (276) all_0_6_6 = n1
% 13.81/3.74 |
% 13.81/3.74 | Equations (276) can reduce 28 to:
% 13.81/3.74 | (243) $false
% 13.81/3.74 |
% 13.81/3.74 |-The branch is then unsatisfiable
% 13.81/3.74 |-Branch two:
% 13.81/3.74 | (587) ~ (all_0_7_7 = n1)
% 13.81/3.74 | (588) all_0_7_7 = n0
% 13.81/3.74 |
% 13.81/3.74 | From (588) and (10) follows:
% 13.81/3.74 | (589) succ(n0) = all_0_5_5
% 13.81/3.74 |
% 13.81/3.74 | From (588) and (3) follows:
% 13.81/3.74 | (590) sum(n0, all_0_1_1) = all_0_0_0
% 13.81/3.74 |
% 13.81/3.74 | From (588) and (1892) follows:
% 13.81/3.74 | (1971) sum(n5, n0) = all_0_2_2
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (47) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 13.81/3.74 | (592) all_0_5_5 = n1
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n5, n0, all_0_2_2, n5 and discharging atoms sum(n5, n0) = all_0_2_2, sum(n5, n0) = n5, yields:
% 13.81/3.74 | (300) all_0_2_2 = n5
% 13.81/3.74 |
% 13.81/3.74 | From (300) and (205) follows:
% 13.81/3.74 | (302) pred(n5) = all_0_1_1
% 13.81/3.74 |
% 13.81/3.74 | From (592) and (1891) follows:
% 13.81/3.74 | (1975) sum(n5, n1) = all_0_4_4
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (116) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 13.81/3.74 | (305) all_0_1_1 = n4
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n5, n1, all_0_4_4, n6 and discharging atoms sum(n5, n1) = all_0_4_4, sum(n5, n1) = n6, yields:
% 13.81/3.74 | (301) all_0_4_4 = n6
% 13.81/3.74 |
% 13.81/3.74 | From (301) and (138) follows:
% 13.81/3.74 | (303) pred(n6) = all_0_3_3
% 13.81/3.74 |
% 13.81/3.74 | From (305) and (590) follows:
% 13.81/3.74 | (1979) sum(n0, n4) = all_0_0_0
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (116) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 13.81/3.74 | (304) all_0_3_3 = n5
% 13.81/3.74 |
% 13.81/3.74 | Instantiating formula (132) with n0, n4, all_0_0_0, n4 and discharging atoms sum(n0, n4) = all_0_0_0, sum(n0, n4) = n4, yields:
% 13.81/3.74 | (291) all_0_0_0 = n4
% 13.81/3.74 |
% 13.81/3.74 | From (304)(291) and (167) follows:
% 13.81/3.75 | (1982) sum(n5, n4) = all_0_6_6
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n5, n4, all_0_6_6, n9 and discharging atoms sum(n5, n4) = all_0_6_6, sum(n5, n4) = n9, yields:
% 13.81/3.75 | (395) all_0_6_6 = n9
% 13.81/3.75 |
% 13.81/3.75 | Equations (395) can reduce 78 to:
% 13.81/3.75 | (243) $false
% 13.81/3.75 |
% 13.81/3.75 |-The branch is then unsatisfiable
% 13.81/3.75 |-Branch two:
% 13.81/3.75 | (329) ~ (all_0_8_8 = n5)
% 13.81/3.75 | (330) all_0_8_8 = n4 | all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.81/3.75 |
% 13.81/3.75 +-Applying beta-rule and splitting (512), into two cases.
% 13.81/3.75 |-Branch one:
% 13.81/3.75 | (513) all_0_7_7 = n4
% 13.81/3.75 |
% 13.81/3.75 | From (513) and (10) follows:
% 13.81/3.75 | (514) succ(n4) = all_0_5_5
% 13.81/3.75 |
% 13.81/3.75 | From (513) and (3) follows:
% 13.81/3.75 | (515) sum(n4, all_0_1_1) = all_0_0_0
% 13.81/3.75 |
% 13.81/3.75 | From (513) and (120) follows:
% 13.81/3.75 | (1990) sum(all_0_8_8, n4) = all_0_2_2
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (47) with n4, all_0_5_5, n5 and discharging atoms succ(n4) = all_0_5_5, succ(n4) = n5, yields:
% 13.81/3.75 | (517) all_0_5_5 = n5
% 13.81/3.75 |
% 13.81/3.75 | From (517) and (77) follows:
% 13.81/3.75 | (1992) sum(all_0_8_8, n5) = all_0_4_4
% 13.81/3.75 |
% 13.81/3.75 +-Applying beta-rule and splitting (330), into two cases.
% 13.81/3.75 |-Branch one:
% 13.81/3.75 | (331) all_0_8_8 = n4
% 13.81/3.75 |
% 13.81/3.75 | From (331) and (1992) follows:
% 13.81/3.75 | (1994) sum(n4, n5) = all_0_4_4
% 13.81/3.75 |
% 13.81/3.75 | From (331) and (1990) follows:
% 13.81/3.75 | (1995) sum(n4, n4) = all_0_2_2
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n4, n5, all_0_4_4, n9 and discharging atoms sum(n4, n5) = all_0_4_4, sum(n4, n5) = n9, yields:
% 13.81/3.75 | (250) all_0_4_4 = n9
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n4, n4, all_0_2_2, n8 and discharging atoms sum(n4, n4) = all_0_2_2, sum(n4, n4) = n8, yields:
% 13.81/3.75 | (249) all_0_2_2 = n8
% 13.81/3.75 |
% 13.81/3.75 | From (249) and (205) follows:
% 13.81/3.75 | (251) pred(n8) = all_0_1_1
% 13.81/3.75 |
% 13.81/3.75 | From (250) and (138) follows:
% 13.81/3.75 | (252) pred(n9) = all_0_3_3
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (116) with n9, all_0_3_3, n8 and discharging atoms pred(n9) = all_0_3_3, pred(n9) = n8, yields:
% 13.81/3.75 | (253) all_0_3_3 = n8
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (116) with n8, all_0_1_1, n7 and discharging atoms pred(n8) = all_0_1_1, pred(n8) = n7, yields:
% 13.81/3.75 | (254) all_0_1_1 = n7
% 13.81/3.75 |
% 13.81/3.75 | From (253) and (167) follows:
% 13.81/3.75 | (255) sum(n8, all_0_0_0) = all_0_6_6
% 13.81/3.75 |
% 13.81/3.75 | From (254) and (515) follows:
% 13.81/3.75 | (2003) sum(n4, n7) = all_0_0_0
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n4, n7, all_0_0_0, n0 and discharging atoms sum(n4, n7) = all_0_0_0, sum(n4, n7) = n0, yields:
% 13.81/3.75 | (359) all_0_0_0 = n0
% 13.81/3.75 |
% 13.81/3.75 | From (359) and (255) follows:
% 13.81/3.75 | (2005) sum(n8, n0) = all_0_6_6
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n8, n0, all_0_6_6, n8 and discharging atoms sum(n8, n0) = all_0_6_6, sum(n8, n0) = n8, yields:
% 13.81/3.75 | (310) all_0_6_6 = n8
% 13.81/3.75 |
% 13.81/3.75 | Equations (310) can reduce 165 to:
% 13.81/3.75 | (243) $false
% 13.81/3.75 |
% 13.81/3.75 |-The branch is then unsatisfiable
% 13.81/3.75 |-Branch two:
% 13.81/3.75 | (346) ~ (all_0_8_8 = n4)
% 13.81/3.75 | (347) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.81/3.75 |
% 13.81/3.75 +-Applying beta-rule and splitting (347), into two cases.
% 13.81/3.75 |-Branch one:
% 13.81/3.75 | (348) all_0_8_8 = n3
% 13.81/3.75 |
% 13.81/3.75 | From (348) and (1992) follows:
% 13.81/3.75 | (2011) sum(n3, n5) = all_0_4_4
% 13.81/3.75 |
% 13.81/3.75 | From (348) and (1990) follows:
% 13.81/3.75 | (2012) sum(n3, n4) = all_0_2_2
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n3, n5, all_0_4_4, n8 and discharging atoms sum(n3, n5) = all_0_4_4, sum(n3, n5) = n8, yields:
% 13.81/3.75 | (267) all_0_4_4 = n8
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n3, n4, all_0_2_2, n7 and discharging atoms sum(n3, n4) = all_0_2_2, sum(n3, n4) = n7, yields:
% 13.81/3.75 | (266) all_0_2_2 = n7
% 13.81/3.75 |
% 13.81/3.75 | From (266) and (205) follows:
% 13.81/3.75 | (268) pred(n7) = all_0_1_1
% 13.81/3.75 |
% 13.81/3.75 | From (267) and (138) follows:
% 13.81/3.75 | (269) pred(n8) = all_0_3_3
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (116) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 13.81/3.75 | (270) all_0_3_3 = n7
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (116) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 13.81/3.75 | (271) all_0_1_1 = n6
% 13.81/3.75 |
% 13.81/3.75 | From (270) and (167) follows:
% 13.81/3.75 | (272) sum(n7, all_0_0_0) = all_0_6_6
% 13.81/3.75 |
% 13.81/3.75 | From (271) and (515) follows:
% 13.81/3.75 | (2020) sum(n4, n6) = all_0_0_0
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n4, n6, all_0_0_0, n10 and discharging atoms sum(n4, n6) = all_0_0_0, sum(n4, n6) = n10, yields:
% 13.81/3.75 | (376) all_0_0_0 = n10
% 13.81/3.75 |
% 13.81/3.75 | From (376) and (272) follows:
% 13.81/3.75 | (2022) sum(n7, n10) = all_0_6_6
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n7, n10, all_0_6_6, n6 and discharging atoms sum(n7, n10) = all_0_6_6, sum(n7, n10) = n6, yields:
% 13.81/3.75 | (327) all_0_6_6 = n6
% 13.81/3.75 |
% 13.81/3.75 | Equations (327) can reduce 34 to:
% 13.81/3.75 | (243) $false
% 13.81/3.75 |
% 13.81/3.75 |-The branch is then unsatisfiable
% 13.81/3.75 |-Branch two:
% 13.81/3.75 | (363) ~ (all_0_8_8 = n3)
% 13.81/3.75 | (364) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.81/3.75 |
% 13.81/3.75 +-Applying beta-rule and splitting (364), into two cases.
% 13.81/3.75 |-Branch one:
% 13.81/3.75 | (365) all_0_8_8 = n2
% 13.81/3.75 |
% 13.81/3.75 | From (365) and (1992) follows:
% 13.81/3.75 | (2028) sum(n2, n5) = all_0_4_4
% 13.81/3.75 |
% 13.81/3.75 | From (365) and (1990) follows:
% 13.81/3.75 | (2029) sum(n2, n4) = all_0_2_2
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n2, n5, all_0_4_4, n7 and discharging atoms sum(n2, n5) = all_0_4_4, sum(n2, n5) = n7, yields:
% 13.81/3.75 | (284) all_0_4_4 = n7
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n2, n4, all_0_2_2, n6 and discharging atoms sum(n2, n4) = all_0_2_2, sum(n2, n4) = n6, yields:
% 13.81/3.75 | (283) all_0_2_2 = n6
% 13.81/3.75 |
% 13.81/3.75 | From (283) and (205) follows:
% 13.81/3.75 | (285) pred(n6) = all_0_1_1
% 13.81/3.75 |
% 13.81/3.75 | From (284) and (138) follows:
% 13.81/3.75 | (286) pred(n7) = all_0_3_3
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (116) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 13.81/3.75 | (287) all_0_3_3 = n6
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (116) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 13.81/3.75 | (288) all_0_1_1 = n5
% 13.81/3.75 |
% 13.81/3.75 | From (287) and (167) follows:
% 13.81/3.75 | (289) sum(n6, all_0_0_0) = all_0_6_6
% 13.81/3.75 |
% 13.81/3.75 | From (288) and (515) follows:
% 13.81/3.75 | (2037) sum(n4, n5) = all_0_0_0
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n4, n5, all_0_0_0, n9 and discharging atoms sum(n4, n5) = all_0_0_0, sum(n4, n5) = n9, yields:
% 13.81/3.75 | (393) all_0_0_0 = n9
% 13.81/3.75 |
% 13.81/3.75 | From (393) and (289) follows:
% 13.81/3.75 | (2039) sum(n6, n9) = all_0_6_6
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n6, n9, all_0_6_6, n4 and discharging atoms sum(n6, n9) = all_0_6_6, sum(n6, n9) = n4, yields:
% 13.81/3.75 | (344) all_0_6_6 = n4
% 13.81/3.75 |
% 13.81/3.75 | Equations (344) can reduce 216 to:
% 13.81/3.75 | (243) $false
% 13.81/3.75 |
% 13.81/3.75 |-The branch is then unsatisfiable
% 13.81/3.75 |-Branch two:
% 13.81/3.75 | (380) ~ (all_0_8_8 = n2)
% 13.81/3.75 | (381) all_0_8_8 = n1 | all_0_8_8 = n0
% 13.81/3.75 |
% 13.81/3.75 +-Applying beta-rule and splitting (381), into two cases.
% 13.81/3.75 |-Branch one:
% 13.81/3.75 | (382) all_0_8_8 = n1
% 13.81/3.75 |
% 13.81/3.75 | From (382) and (1992) follows:
% 13.81/3.75 | (2045) sum(n1, n5) = all_0_4_4
% 13.81/3.75 |
% 13.81/3.75 | From (382) and (1990) follows:
% 13.81/3.75 | (2046) sum(n1, n4) = all_0_2_2
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n1, n5, all_0_4_4, n6 and discharging atoms sum(n1, n5) = all_0_4_4, sum(n1, n5) = n6, yields:
% 13.81/3.75 | (301) all_0_4_4 = n6
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n1, n4, all_0_2_2, n5 and discharging atoms sum(n1, n4) = all_0_2_2, sum(n1, n4) = n5, yields:
% 13.81/3.75 | (300) all_0_2_2 = n5
% 13.81/3.75 |
% 13.81/3.75 | From (300) and (205) follows:
% 13.81/3.75 | (302) pred(n5) = all_0_1_1
% 13.81/3.75 |
% 13.81/3.75 | From (301) and (138) follows:
% 13.81/3.75 | (303) pred(n6) = all_0_3_3
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (116) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 13.81/3.75 | (304) all_0_3_3 = n5
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (116) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 13.81/3.75 | (305) all_0_1_1 = n4
% 13.81/3.75 |
% 13.81/3.75 | From (304) and (167) follows:
% 13.81/3.75 | (306) sum(n5, all_0_0_0) = all_0_6_6
% 13.81/3.75 |
% 13.81/3.75 | From (305) and (515) follows:
% 13.81/3.75 | (2054) sum(n4, n4) = all_0_0_0
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n4, n4, all_0_0_0, n8 and discharging atoms sum(n4, n4) = all_0_0_0, sum(n4, n4) = n8, yields:
% 13.81/3.75 | (409) all_0_0_0 = n8
% 13.81/3.75 |
% 13.81/3.75 | From (409) and (306) follows:
% 13.81/3.75 | (2056) sum(n5, n8) = all_0_6_6
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n5, n8, all_0_6_6, n2 and discharging atoms sum(n5, n8) = all_0_6_6, sum(n5, n8) = n2, yields:
% 13.81/3.75 | (361) all_0_6_6 = n2
% 13.81/3.75 |
% 13.81/3.75 | Equations (361) can reduce 131 to:
% 13.81/3.75 | (243) $false
% 13.81/3.75 |
% 13.81/3.75 |-The branch is then unsatisfiable
% 13.81/3.75 |-Branch two:
% 13.81/3.75 | (397) ~ (all_0_8_8 = n1)
% 13.81/3.75 | (398) all_0_8_8 = n0
% 13.81/3.75 |
% 13.81/3.75 | From (398) and (1992) follows:
% 13.81/3.75 | (2061) sum(n0, n5) = all_0_4_4
% 13.81/3.75 |
% 13.81/3.75 | From (398) and (1990) follows:
% 13.81/3.75 | (2062) sum(n0, n4) = all_0_2_2
% 13.81/3.75 |
% 13.81/3.75 | Instantiating formula (132) with n0, n5, all_0_4_4, n5 and discharging atoms sum(n0, n5) = all_0_4_4, sum(n0, n5) = n5, yields:
% 13.81/3.76 | (318) all_0_4_4 = n5
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (132) with n0, n4, all_0_2_2, n4 and discharging atoms sum(n0, n4) = all_0_2_2, sum(n0, n4) = n4, yields:
% 13.81/3.76 | (317) all_0_2_2 = n4
% 13.81/3.76 |
% 13.81/3.76 | From (317) and (205) follows:
% 13.81/3.76 | (319) pred(n4) = all_0_1_1
% 13.81/3.76 |
% 13.81/3.76 | From (318) and (138) follows:
% 13.81/3.76 | (320) pred(n5) = all_0_3_3
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (116) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 13.81/3.76 | (321) all_0_3_3 = n4
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (116) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 13.81/3.76 | (322) all_0_1_1 = n3
% 13.81/3.76 |
% 13.81/3.76 | From (321) and (167) follows:
% 13.81/3.76 | (323) sum(n4, all_0_0_0) = all_0_6_6
% 13.81/3.76 |
% 13.81/3.76 | From (322) and (515) follows:
% 13.81/3.76 | (2070) sum(n4, n3) = all_0_0_0
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (132) with n4, n3, all_0_0_0, n7 and discharging atoms sum(n4, n3) = all_0_0_0, sum(n4, n3) = n7, yields:
% 13.81/3.76 | (240) all_0_0_0 = n7
% 13.81/3.76 |
% 13.81/3.76 | From (240) and (323) follows:
% 13.81/3.76 | (2072) sum(n4, n7) = all_0_6_6
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (132) with n4, n7, all_0_6_6, n0 and discharging atoms sum(n4, n7) = all_0_6_6, sum(n4, n7) = n0, yields:
% 13.81/3.76 | (378) all_0_6_6 = n0
% 13.81/3.76 |
% 13.81/3.76 | Equations (378) can reduce 119 to:
% 13.81/3.76 | (243) $false
% 13.81/3.76 |
% 13.81/3.76 |-The branch is then unsatisfiable
% 13.81/3.76 |-Branch two:
% 13.81/3.76 | (530) ~ (all_0_7_7 = n4)
% 13.81/3.76 | (531) all_0_7_7 = n3 | all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.81/3.76 |
% 13.81/3.76 +-Applying beta-rule and splitting (330), into two cases.
% 13.81/3.76 |-Branch one:
% 13.81/3.76 | (331) all_0_8_8 = n4
% 13.81/3.76 |
% 13.81/3.76 | From (331) and (77) follows:
% 13.81/3.76 | (2078) sum(n4, all_0_5_5) = all_0_4_4
% 13.81/3.76 |
% 13.81/3.76 | From (331) and (120) follows:
% 13.81/3.76 | (2079) sum(n4, all_0_7_7) = all_0_2_2
% 13.81/3.76 |
% 13.81/3.76 +-Applying beta-rule and splitting (531), into two cases.
% 13.81/3.76 |-Branch one:
% 13.81/3.76 | (532) all_0_7_7 = n3
% 13.81/3.76 |
% 13.81/3.76 | From (532) and (10) follows:
% 13.81/3.76 | (533) succ(n3) = all_0_5_5
% 13.81/3.76 |
% 13.81/3.76 | From (532) and (3) follows:
% 13.81/3.76 | (534) sum(n3, all_0_1_1) = all_0_0_0
% 13.81/3.76 |
% 13.81/3.76 | From (532) and (2079) follows:
% 13.81/3.76 | (2083) sum(n4, n3) = all_0_2_2
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (47) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 13.81/3.76 | (536) all_0_5_5 = n4
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (132) with n4, n3, all_0_2_2, n7 and discharging atoms sum(n4, n3) = all_0_2_2, sum(n4, n3) = n7, yields:
% 13.81/3.76 | (266) all_0_2_2 = n7
% 13.81/3.76 |
% 13.81/3.76 | From (266) and (205) follows:
% 13.81/3.76 | (268) pred(n7) = all_0_1_1
% 13.81/3.76 |
% 13.81/3.76 | From (536) and (2078) follows:
% 13.81/3.76 | (2087) sum(n4, n4) = all_0_4_4
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (116) with n7, all_0_1_1, n6 and discharging atoms pred(n7) = all_0_1_1, pred(n7) = n6, yields:
% 13.81/3.76 | (271) all_0_1_1 = n6
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (132) with n4, n4, all_0_4_4, n8 and discharging atoms sum(n4, n4) = all_0_4_4, sum(n4, n4) = n8, yields:
% 13.81/3.76 | (267) all_0_4_4 = n8
% 13.81/3.76 |
% 13.81/3.76 | From (267) and (138) follows:
% 13.81/3.76 | (269) pred(n8) = all_0_3_3
% 13.81/3.76 |
% 13.81/3.76 | From (271) and (534) follows:
% 13.81/3.76 | (2091) sum(n3, n6) = all_0_0_0
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (116) with n8, all_0_3_3, n7 and discharging atoms pred(n8) = all_0_3_3, pred(n8) = n7, yields:
% 13.81/3.76 | (270) all_0_3_3 = n7
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (132) with n3, n6, all_0_0_0, n9 and discharging atoms sum(n3, n6) = all_0_0_0, sum(n3, n6) = n9, yields:
% 13.81/3.76 | (393) all_0_0_0 = n9
% 13.81/3.76 |
% 13.81/3.76 | From (270)(393) and (167) follows:
% 13.81/3.76 | (2094) sum(n7, n9) = all_0_6_6
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (132) with n7, n9, all_0_6_6, n5 and discharging atoms sum(n7, n9) = all_0_6_6, sum(n7, n9) = n5, yields:
% 13.81/3.76 | (242) all_0_6_6 = n5
% 13.81/3.76 |
% 13.81/3.76 | Equations (242) can reduce 4 to:
% 13.81/3.76 | (243) $false
% 13.81/3.76 |
% 13.81/3.76 |-The branch is then unsatisfiable
% 13.81/3.76 |-Branch two:
% 13.81/3.76 | (549) ~ (all_0_7_7 = n3)
% 13.81/3.76 | (550) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.81/3.76 |
% 13.81/3.76 +-Applying beta-rule and splitting (550), into two cases.
% 13.81/3.76 |-Branch one:
% 13.81/3.76 | (551) all_0_7_7 = n2
% 13.81/3.76 |
% 13.81/3.76 | From (551) and (10) follows:
% 13.81/3.76 | (552) succ(n2) = all_0_5_5
% 13.81/3.76 |
% 13.81/3.76 | From (551) and (3) follows:
% 13.81/3.76 | (553) sum(n2, all_0_1_1) = all_0_0_0
% 13.81/3.76 |
% 13.81/3.76 | From (551) and (2079) follows:
% 13.81/3.76 | (2102) sum(n4, n2) = all_0_2_2
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (47) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 13.81/3.76 | (555) all_0_5_5 = n3
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (132) with n4, n2, all_0_2_2, n6 and discharging atoms sum(n4, n2) = all_0_2_2, sum(n4, n2) = n6, yields:
% 13.81/3.76 | (283) all_0_2_2 = n6
% 13.81/3.76 |
% 13.81/3.76 | From (283) and (205) follows:
% 13.81/3.76 | (285) pred(n6) = all_0_1_1
% 13.81/3.76 |
% 13.81/3.76 | From (555) and (2078) follows:
% 13.81/3.76 | (2106) sum(n4, n3) = all_0_4_4
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (116) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 13.81/3.76 | (288) all_0_1_1 = n5
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (132) with n4, n3, all_0_4_4, n7 and discharging atoms sum(n4, n3) = all_0_4_4, sum(n4, n3) = n7, yields:
% 13.81/3.76 | (284) all_0_4_4 = n7
% 13.81/3.76 |
% 13.81/3.76 | From (284) and (138) follows:
% 13.81/3.76 | (286) pred(n7) = all_0_3_3
% 13.81/3.76 |
% 13.81/3.76 | From (288) and (553) follows:
% 13.81/3.76 | (2110) sum(n2, n5) = all_0_0_0
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (116) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 13.81/3.76 | (287) all_0_3_3 = n6
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (132) with n2, n5, all_0_0_0, n7 and discharging atoms sum(n2, n5) = all_0_0_0, sum(n2, n5) = n7, yields:
% 13.81/3.76 | (240) all_0_0_0 = n7
% 13.81/3.76 |
% 13.81/3.76 | From (287)(240) and (167) follows:
% 13.81/3.76 | (2113) sum(n6, n7) = all_0_6_6
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (132) with n6, n7, all_0_6_6, n2 and discharging atoms sum(n6, n7) = all_0_6_6, sum(n6, n7) = n2, yields:
% 13.81/3.76 | (361) all_0_6_6 = n2
% 13.81/3.76 |
% 13.81/3.76 | Equations (361) can reduce 131 to:
% 13.81/3.76 | (243) $false
% 13.81/3.76 |
% 13.81/3.76 |-The branch is then unsatisfiable
% 13.81/3.76 |-Branch two:
% 13.81/3.76 | (568) ~ (all_0_7_7 = n2)
% 13.81/3.76 | (569) all_0_7_7 = n1 | all_0_7_7 = n0
% 13.81/3.76 |
% 13.81/3.76 +-Applying beta-rule and splitting (569), into two cases.
% 13.81/3.76 |-Branch one:
% 13.81/3.76 | (570) all_0_7_7 = n1
% 13.81/3.76 |
% 13.81/3.76 | From (570) and (10) follows:
% 13.81/3.76 | (571) succ(n1) = all_0_5_5
% 13.81/3.76 |
% 13.81/3.76 | From (570) and (3) follows:
% 13.81/3.76 | (572) sum(n1, all_0_1_1) = all_0_0_0
% 13.81/3.76 |
% 13.81/3.76 | From (570) and (2079) follows:
% 13.81/3.76 | (2121) sum(n4, n1) = all_0_2_2
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (47) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 13.81/3.76 | (574) all_0_5_5 = n2
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (132) with n4, n1, all_0_2_2, n5 and discharging atoms sum(n4, n1) = all_0_2_2, sum(n4, n1) = n5, yields:
% 13.81/3.76 | (300) all_0_2_2 = n5
% 13.81/3.76 |
% 13.81/3.76 | From (300) and (205) follows:
% 13.81/3.76 | (302) pred(n5) = all_0_1_1
% 13.81/3.76 |
% 13.81/3.76 | From (574) and (2078) follows:
% 13.81/3.76 | (2125) sum(n4, n2) = all_0_4_4
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (116) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 13.81/3.76 | (305) all_0_1_1 = n4
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (132) with n4, n2, all_0_4_4, n6 and discharging atoms sum(n4, n2) = all_0_4_4, sum(n4, n2) = n6, yields:
% 13.81/3.76 | (301) all_0_4_4 = n6
% 13.81/3.76 |
% 13.81/3.76 | From (301) and (138) follows:
% 13.81/3.76 | (303) pred(n6) = all_0_3_3
% 13.81/3.76 |
% 13.81/3.76 | From (305) and (572) follows:
% 13.81/3.76 | (2129) sum(n1, n4) = all_0_0_0
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (116) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 13.81/3.76 | (304) all_0_3_3 = n5
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (132) with n1, n4, all_0_0_0, n5 and discharging atoms sum(n1, n4) = all_0_0_0, sum(n1, n4) = n5, yields:
% 13.81/3.76 | (274) all_0_0_0 = n5
% 13.81/3.76 |
% 13.81/3.76 | From (304)(274) and (167) follows:
% 13.81/3.76 | (2132) sum(n5, n5) = all_0_6_6
% 13.81/3.76 |
% 13.81/3.76 | Instantiating formula (132) with n5, n5, all_0_6_6, n10 and discharging atoms sum(n5, n5) = all_0_6_6, sum(n5, n5) = n10, yields:
% 13.81/3.76 | (293) all_0_6_6 = n10
% 13.81/3.76 |
% 13.81/3.77 | Equations (293) can reduce 147 to:
% 13.81/3.77 | (243) $false
% 13.81/3.77 |
% 13.81/3.77 |-The branch is then unsatisfiable
% 13.81/3.77 |-Branch two:
% 13.81/3.77 | (587) ~ (all_0_7_7 = n1)
% 13.81/3.77 | (588) all_0_7_7 = n0
% 13.81/3.77 |
% 13.81/3.77 | From (588) and (10) follows:
% 13.81/3.77 | (589) succ(n0) = all_0_5_5
% 13.81/3.77 |
% 13.81/3.77 | From (588) and (3) follows:
% 13.81/3.77 | (590) sum(n0, all_0_1_1) = all_0_0_0
% 13.81/3.77 |
% 13.81/3.77 | From (588) and (2079) follows:
% 13.81/3.77 | (2139) sum(n4, n0) = all_0_2_2
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (47) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 13.81/3.77 | (592) all_0_5_5 = n1
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (132) with n4, n0, all_0_2_2, n4 and discharging atoms sum(n4, n0) = all_0_2_2, sum(n4, n0) = n4, yields:
% 13.81/3.77 | (317) all_0_2_2 = n4
% 13.81/3.77 |
% 13.81/3.77 | From (317) and (205) follows:
% 13.81/3.77 | (319) pred(n4) = all_0_1_1
% 13.81/3.77 |
% 13.81/3.77 | From (592) and (2078) follows:
% 13.81/3.77 | (2143) sum(n4, n1) = all_0_4_4
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (116) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 13.81/3.77 | (322) all_0_1_1 = n3
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (132) with n4, n1, all_0_4_4, n5 and discharging atoms sum(n4, n1) = all_0_4_4, sum(n4, n1) = n5, yields:
% 13.81/3.77 | (318) all_0_4_4 = n5
% 13.81/3.77 |
% 13.81/3.77 | From (318) and (138) follows:
% 13.81/3.77 | (320) pred(n5) = all_0_3_3
% 13.81/3.77 |
% 13.81/3.77 | From (322) and (590) follows:
% 13.81/3.77 | (2147) sum(n0, n3) = all_0_0_0
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (116) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 13.81/3.77 | (321) all_0_3_3 = n4
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (132) with n0, n3, all_0_0_0, n3 and discharging atoms sum(n0, n3) = all_0_0_0, sum(n0, n3) = n3, yields:
% 13.81/3.77 | (308) all_0_0_0 = n3
% 13.81/3.77 |
% 13.81/3.77 | From (321)(308) and (167) follows:
% 13.81/3.77 | (2150) sum(n4, n3) = all_0_6_6
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (132) with n4, n3, all_0_6_6, n7 and discharging atoms sum(n4, n3) = all_0_6_6, sum(n4, n3) = n7, yields:
% 13.81/3.77 | (411) all_0_6_6 = n7
% 13.81/3.77 |
% 13.81/3.77 | Equations (411) can reduce 88 to:
% 13.81/3.77 | (243) $false
% 13.81/3.77 |
% 13.81/3.77 |-The branch is then unsatisfiable
% 13.81/3.77 |-Branch two:
% 13.81/3.77 | (346) ~ (all_0_8_8 = n4)
% 13.81/3.77 | (347) all_0_8_8 = n3 | all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.81/3.77 |
% 13.81/3.77 +-Applying beta-rule and splitting (531), into two cases.
% 13.81/3.77 |-Branch one:
% 13.81/3.77 | (532) all_0_7_7 = n3
% 13.81/3.77 |
% 13.81/3.77 | From (532) and (10) follows:
% 13.81/3.77 | (533) succ(n3) = all_0_5_5
% 13.81/3.77 |
% 13.81/3.77 | From (532) and (3) follows:
% 13.81/3.77 | (534) sum(n3, all_0_1_1) = all_0_0_0
% 13.81/3.77 |
% 13.81/3.77 | From (532) and (120) follows:
% 13.81/3.77 | (2158) sum(all_0_8_8, n3) = all_0_2_2
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (47) with n3, all_0_5_5, n4 and discharging atoms succ(n3) = all_0_5_5, succ(n3) = n4, yields:
% 13.81/3.77 | (536) all_0_5_5 = n4
% 13.81/3.77 |
% 13.81/3.77 | From (536) and (77) follows:
% 13.81/3.77 | (2160) sum(all_0_8_8, n4) = all_0_4_4
% 13.81/3.77 |
% 13.81/3.77 +-Applying beta-rule and splitting (347), into two cases.
% 13.81/3.77 |-Branch one:
% 13.81/3.77 | (348) all_0_8_8 = n3
% 13.81/3.77 |
% 13.81/3.77 | From (348) and (2160) follows:
% 13.81/3.77 | (2162) sum(n3, n4) = all_0_4_4
% 13.81/3.77 |
% 13.81/3.77 | From (348) and (2158) follows:
% 13.81/3.77 | (2163) sum(n3, n3) = all_0_2_2
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (132) with n3, n4, all_0_4_4, n7 and discharging atoms sum(n3, n4) = all_0_4_4, sum(n3, n4) = n7, yields:
% 13.81/3.77 | (284) all_0_4_4 = n7
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (132) with n3, n3, all_0_2_2, n6 and discharging atoms sum(n3, n3) = all_0_2_2, sum(n3, n3) = n6, yields:
% 13.81/3.77 | (283) all_0_2_2 = n6
% 13.81/3.77 |
% 13.81/3.77 | From (283) and (205) follows:
% 13.81/3.77 | (285) pred(n6) = all_0_1_1
% 13.81/3.77 |
% 13.81/3.77 | From (284) and (138) follows:
% 13.81/3.77 | (286) pred(n7) = all_0_3_3
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (116) with n7, all_0_3_3, n6 and discharging atoms pred(n7) = all_0_3_3, pred(n7) = n6, yields:
% 13.81/3.77 | (287) all_0_3_3 = n6
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (116) with n6, all_0_1_1, n5 and discharging atoms pred(n6) = all_0_1_1, pred(n6) = n5, yields:
% 13.81/3.77 | (288) all_0_1_1 = n5
% 13.81/3.77 |
% 13.81/3.77 | From (287) and (167) follows:
% 13.81/3.77 | (289) sum(n6, all_0_0_0) = all_0_6_6
% 13.81/3.77 |
% 13.81/3.77 | From (288) and (534) follows:
% 13.81/3.77 | (2171) sum(n3, n5) = all_0_0_0
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (132) with n3, n5, all_0_0_0, n8 and discharging atoms sum(n3, n5) = all_0_0_0, sum(n3, n5) = n8, yields:
% 13.81/3.77 | (409) all_0_0_0 = n8
% 13.81/3.77 |
% 13.81/3.77 | From (409) and (289) follows:
% 13.81/3.77 | (2173) sum(n6, n8) = all_0_6_6
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (132) with n6, n8, all_0_6_6, n3 and discharging atoms sum(n6, n8) = all_0_6_6, sum(n6, n8) = n3, yields:
% 13.81/3.77 | (259) all_0_6_6 = n3
% 13.81/3.77 |
% 13.81/3.77 | Equations (259) can reduce 100 to:
% 13.81/3.77 | (243) $false
% 13.81/3.77 |
% 13.81/3.77 |-The branch is then unsatisfiable
% 13.81/3.77 |-Branch two:
% 13.81/3.77 | (363) ~ (all_0_8_8 = n3)
% 13.81/3.77 | (364) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 13.81/3.77 |
% 13.81/3.77 +-Applying beta-rule and splitting (364), into two cases.
% 13.81/3.77 |-Branch one:
% 13.81/3.77 | (365) all_0_8_8 = n2
% 13.81/3.77 |
% 13.81/3.77 | From (365) and (2160) follows:
% 13.81/3.77 | (2179) sum(n2, n4) = all_0_4_4
% 13.81/3.77 |
% 13.81/3.77 | From (365) and (2158) follows:
% 13.81/3.77 | (2180) sum(n2, n3) = all_0_2_2
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (132) with n2, n4, all_0_4_4, n6 and discharging atoms sum(n2, n4) = all_0_4_4, sum(n2, n4) = n6, yields:
% 13.81/3.77 | (301) all_0_4_4 = n6
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (132) with n2, n3, all_0_2_2, n5 and discharging atoms sum(n2, n3) = all_0_2_2, sum(n2, n3) = n5, yields:
% 13.81/3.77 | (300) all_0_2_2 = n5
% 13.81/3.77 |
% 13.81/3.77 | From (300) and (205) follows:
% 13.81/3.77 | (302) pred(n5) = all_0_1_1
% 13.81/3.77 |
% 13.81/3.77 | From (301) and (138) follows:
% 13.81/3.77 | (303) pred(n6) = all_0_3_3
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (116) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 13.81/3.77 | (304) all_0_3_3 = n5
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (116) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 13.81/3.77 | (305) all_0_1_1 = n4
% 13.81/3.77 |
% 13.81/3.77 | From (304) and (167) follows:
% 13.81/3.77 | (306) sum(n5, all_0_0_0) = all_0_6_6
% 13.81/3.77 |
% 13.81/3.77 | From (305) and (534) follows:
% 13.81/3.77 | (2188) sum(n3, n4) = all_0_0_0
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (132) with n3, n4, all_0_0_0, n7 and discharging atoms sum(n3, n4) = all_0_0_0, sum(n3, n4) = n7, yields:
% 13.81/3.77 | (240) all_0_0_0 = n7
% 13.81/3.77 |
% 13.81/3.77 | From (240) and (306) follows:
% 13.81/3.77 | (2190) sum(n5, n7) = all_0_6_6
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (132) with n5, n7, all_0_6_6, n1 and discharging atoms sum(n5, n7) = all_0_6_6, sum(n5, n7) = n1, yields:
% 13.81/3.77 | (276) all_0_6_6 = n1
% 13.81/3.77 |
% 13.81/3.77 | Equations (276) can reduce 28 to:
% 13.81/3.77 | (243) $false
% 13.81/3.77 |
% 13.81/3.77 |-The branch is then unsatisfiable
% 13.81/3.77 |-Branch two:
% 13.81/3.77 | (380) ~ (all_0_8_8 = n2)
% 13.81/3.77 | (381) all_0_8_8 = n1 | all_0_8_8 = n0
% 13.81/3.77 |
% 13.81/3.77 +-Applying beta-rule and splitting (381), into two cases.
% 13.81/3.77 |-Branch one:
% 13.81/3.77 | (382) all_0_8_8 = n1
% 13.81/3.77 |
% 13.81/3.77 | From (382) and (2160) follows:
% 13.81/3.77 | (2196) sum(n1, n4) = all_0_4_4
% 13.81/3.77 |
% 13.81/3.77 | From (382) and (2158) follows:
% 13.81/3.77 | (2197) sum(n1, n3) = all_0_2_2
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (132) with n1, n4, all_0_4_4, n5 and discharging atoms sum(n1, n4) = all_0_4_4, sum(n1, n4) = n5, yields:
% 13.81/3.77 | (318) all_0_4_4 = n5
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (132) with n1, n3, all_0_2_2, n4 and discharging atoms sum(n1, n3) = all_0_2_2, sum(n1, n3) = n4, yields:
% 13.81/3.77 | (317) all_0_2_2 = n4
% 13.81/3.77 |
% 13.81/3.77 | From (317) and (205) follows:
% 13.81/3.77 | (319) pred(n4) = all_0_1_1
% 13.81/3.77 |
% 13.81/3.77 | From (318) and (138) follows:
% 13.81/3.77 | (320) pred(n5) = all_0_3_3
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (116) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 13.81/3.77 | (321) all_0_3_3 = n4
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (116) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 13.81/3.77 | (322) all_0_1_1 = n3
% 13.81/3.77 |
% 13.81/3.77 | From (321) and (167) follows:
% 13.81/3.77 | (323) sum(n4, all_0_0_0) = all_0_6_6
% 13.81/3.77 |
% 13.81/3.77 | From (322) and (534) follows:
% 13.81/3.77 | (2205) sum(n3, n3) = all_0_0_0
% 13.81/3.77 |
% 13.81/3.77 | Instantiating formula (132) with n3, n3, all_0_0_0, n6 and discharging atoms sum(n3, n3) = all_0_0_0, sum(n3, n3) = n6, yields:
% 13.81/3.77 | (257) all_0_0_0 = n6
% 13.81/3.77 |
% 13.81/3.77 | From (257) and (323) follows:
% 13.81/3.77 | (2207) sum(n4, n6) = all_0_6_6
% 13.81/3.77 |
% 13.81/3.78 | Instantiating formula (132) with n4, n6, all_0_6_6, n10 and discharging atoms sum(n4, n6) = all_0_6_6, sum(n4, n6) = n10, yields:
% 13.81/3.78 | (293) all_0_6_6 = n10
% 13.81/3.78 |
% 13.81/3.78 | Equations (293) can reduce 147 to:
% 13.81/3.78 | (243) $false
% 13.81/3.78 |
% 13.81/3.78 |-The branch is then unsatisfiable
% 13.81/3.78 |-Branch two:
% 13.81/3.78 | (397) ~ (all_0_8_8 = n1)
% 13.81/3.78 | (398) all_0_8_8 = n0
% 13.81/3.78 |
% 13.81/3.78 | From (398) and (2160) follows:
% 13.81/3.78 | (2212) sum(n0, n4) = all_0_4_4
% 13.81/3.78 |
% 13.81/3.78 | From (398) and (2158) follows:
% 13.81/3.78 | (2213) sum(n0, n3) = all_0_2_2
% 13.81/3.78 |
% 13.81/3.78 | Instantiating formula (132) with n0, n4, all_0_4_4, n4 and discharging atoms sum(n0, n4) = all_0_4_4, sum(n0, n4) = n4, yields:
% 13.81/3.78 | (335) all_0_4_4 = n4
% 13.81/3.78 |
% 13.81/3.78 | Instantiating formula (132) with n0, n3, all_0_2_2, n3 and discharging atoms sum(n0, n3) = all_0_2_2, sum(n0, n3) = n3, yields:
% 13.81/3.78 | (334) all_0_2_2 = n3
% 13.81/3.78 |
% 13.81/3.78 | From (334) and (205) follows:
% 13.81/3.78 | (336) pred(n3) = all_0_1_1
% 13.81/3.78 |
% 13.81/3.78 | From (335) and (138) follows:
% 13.81/3.78 | (337) pred(n4) = all_0_3_3
% 13.81/3.78 |
% 13.81/3.78 | Instantiating formula (116) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 13.81/3.78 | (338) all_0_3_3 = n3
% 13.81/3.78 |
% 13.81/3.78 | Instantiating formula (116) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 13.81/3.78 | (339) all_0_1_1 = n2
% 13.81/3.78 |
% 13.81/3.78 | From (338) and (167) follows:
% 13.81/3.78 | (340) sum(n3, all_0_0_0) = all_0_6_6
% 13.81/3.78 |
% 13.81/3.78 | From (339) and (534) follows:
% 13.81/3.78 | (2221) sum(n3, n2) = all_0_0_0
% 13.81/3.78 |
% 13.81/3.78 | Instantiating formula (132) with n3, n2, all_0_0_0, n5 and discharging atoms sum(n3, n2) = all_0_0_0, sum(n3, n2) = n5, yields:
% 13.81/3.78 | (274) all_0_0_0 = n5
% 13.81/3.78 |
% 13.81/3.78 | From (274) and (340) follows:
% 13.81/3.78 | (2223) sum(n3, n5) = all_0_6_6
% 13.81/3.78 |
% 13.81/3.78 | Instantiating formula (132) with n3, n5, all_0_6_6, n8 and discharging atoms sum(n3, n5) = all_0_6_6, sum(n3, n5) = n8, yields:
% 13.81/3.78 | (310) all_0_6_6 = n8
% 13.81/3.78 |
% 13.81/3.78 | Equations (310) can reduce 165 to:
% 13.81/3.78 | (243) $false
% 13.81/3.78 |
% 13.81/3.78 |-The branch is then unsatisfiable
% 13.81/3.78 |-Branch two:
% 13.81/3.78 | (549) ~ (all_0_7_7 = n3)
% 13.81/3.78 | (550) all_0_7_7 = n2 | all_0_7_7 = n1 | all_0_7_7 = n0
% 13.81/3.78 |
% 13.81/3.78 +-Applying beta-rule and splitting (347), into two cases.
% 13.81/3.78 |-Branch one:
% 13.81/3.78 | (348) all_0_8_8 = n3
% 13.81/3.78 |
% 13.81/3.78 | From (348) and (77) follows:
% 13.81/3.78 | (2229) sum(n3, all_0_5_5) = all_0_4_4
% 13.81/3.78 |
% 13.81/3.78 | From (348) and (120) follows:
% 13.81/3.78 | (2230) sum(n3, all_0_7_7) = all_0_2_2
% 13.81/3.78 |
% 13.81/3.78 +-Applying beta-rule and splitting (550), into two cases.
% 13.81/3.78 |-Branch one:
% 13.81/3.78 | (551) all_0_7_7 = n2
% 13.81/3.78 |
% 13.81/3.78 | From (551) and (10) follows:
% 13.81/3.78 | (552) succ(n2) = all_0_5_5
% 13.81/3.78 |
% 13.81/3.78 | From (551) and (3) follows:
% 13.81/3.78 | (553) sum(n2, all_0_1_1) = all_0_0_0
% 13.81/3.78 |
% 13.81/3.78 | From (551) and (2230) follows:
% 13.81/3.78 | (2234) sum(n3, n2) = all_0_2_2
% 13.81/3.78 |
% 13.81/3.78 | Instantiating formula (47) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 13.81/3.78 | (555) all_0_5_5 = n3
% 13.81/3.78 |
% 13.81/3.78 | Instantiating formula (132) with n3, n2, all_0_2_2, n5 and discharging atoms sum(n3, n2) = all_0_2_2, sum(n3, n2) = n5, yields:
% 13.81/3.78 | (300) all_0_2_2 = n5
% 13.81/3.78 |
% 13.81/3.78 | From (300) and (205) follows:
% 13.81/3.78 | (302) pred(n5) = all_0_1_1
% 13.81/3.78 |
% 13.81/3.78 | From (555) and (2229) follows:
% 13.81/3.78 | (2238) sum(n3, n3) = all_0_4_4
% 13.81/3.78 |
% 13.81/3.78 | Instantiating formula (116) with n5, all_0_1_1, n4 and discharging atoms pred(n5) = all_0_1_1, pred(n5) = n4, yields:
% 13.81/3.78 | (305) all_0_1_1 = n4
% 13.81/3.78 |
% 13.81/3.78 | Instantiating formula (132) with n3, n3, all_0_4_4, n6 and discharging atoms sum(n3, n3) = all_0_4_4, sum(n3, n3) = n6, yields:
% 13.81/3.78 | (301) all_0_4_4 = n6
% 13.81/3.78 |
% 13.81/3.78 | From (301) and (138) follows:
% 13.81/3.78 | (303) pred(n6) = all_0_3_3
% 13.81/3.78 |
% 13.81/3.78 | From (305) and (553) follows:
% 13.81/3.78 | (2242) sum(n2, n4) = all_0_0_0
% 13.81/3.78 |
% 13.81/3.78 | Instantiating formula (116) with n6, all_0_3_3, n5 and discharging atoms pred(n6) = all_0_3_3, pred(n6) = n5, yields:
% 13.81/3.78 | (304) all_0_3_3 = n5
% 13.81/3.78 |
% 13.81/3.78 | Instantiating formula (132) with n2, n4, all_0_0_0, n6 and discharging atoms sum(n2, n4) = all_0_0_0, sum(n2, n4) = n6, yields:
% 13.81/3.78 | (257) all_0_0_0 = n6
% 13.81/3.78 |
% 13.81/3.78 | From (304)(257) and (167) follows:
% 13.81/3.78 | (2245) sum(n5, n6) = all_0_6_6
% 13.81/3.78 |
% 13.81/3.78 | Instantiating formula (132) with n5, n6, all_0_6_6, n0 and discharging atoms sum(n5, n6) = all_0_6_6, sum(n5, n6) = n0, yields:
% 13.81/3.78 | (378) all_0_6_6 = n0
% 13.81/3.78 |
% 13.81/3.78 | Equations (378) can reduce 119 to:
% 13.81/3.78 | (243) $false
% 13.81/3.78 |
% 13.81/3.78 |-The branch is then unsatisfiable
% 13.81/3.78 |-Branch two:
% 13.81/3.78 | (568) ~ (all_0_7_7 = n2)
% 13.81/3.78 | (569) all_0_7_7 = n1 | all_0_7_7 = n0
% 13.81/3.78 |
% 13.81/3.78 +-Applying beta-rule and splitting (569), into two cases.
% 13.81/3.78 |-Branch one:
% 13.81/3.78 | (570) all_0_7_7 = n1
% 13.81/3.78 |
% 13.81/3.78 | From (570) and (10) follows:
% 14.06/3.78 | (571) succ(n1) = all_0_5_5
% 14.06/3.78 |
% 14.06/3.78 | From (570) and (3) follows:
% 14.06/3.78 | (572) sum(n1, all_0_1_1) = all_0_0_0
% 14.06/3.78 |
% 14.06/3.78 | From (570) and (2230) follows:
% 14.06/3.78 | (2253) sum(n3, n1) = all_0_2_2
% 14.06/3.78 |
% 14.06/3.78 | Instantiating formula (47) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 14.06/3.78 | (574) all_0_5_5 = n2
% 14.06/3.78 |
% 14.06/3.78 | Instantiating formula (132) with n3, n1, all_0_2_2, n4 and discharging atoms sum(n3, n1) = all_0_2_2, sum(n3, n1) = n4, yields:
% 14.06/3.78 | (317) all_0_2_2 = n4
% 14.06/3.78 |
% 14.06/3.78 | From (317) and (205) follows:
% 14.06/3.78 | (319) pred(n4) = all_0_1_1
% 14.06/3.78 |
% 14.06/3.78 | From (574) and (2229) follows:
% 14.06/3.78 | (2257) sum(n3, n2) = all_0_4_4
% 14.06/3.78 |
% 14.06/3.78 | Instantiating formula (116) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 14.06/3.78 | (322) all_0_1_1 = n3
% 14.06/3.78 |
% 14.06/3.78 | Instantiating formula (132) with n3, n2, all_0_4_4, n5 and discharging atoms sum(n3, n2) = all_0_4_4, sum(n3, n2) = n5, yields:
% 14.06/3.78 | (318) all_0_4_4 = n5
% 14.06/3.78 |
% 14.06/3.78 | From (318) and (138) follows:
% 14.06/3.78 | (320) pred(n5) = all_0_3_3
% 14.06/3.78 |
% 14.06/3.78 | From (322) and (572) follows:
% 14.06/3.78 | (2261) sum(n1, n3) = all_0_0_0
% 14.06/3.78 |
% 14.06/3.78 | Instantiating formula (116) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 14.06/3.78 | (321) all_0_3_3 = n4
% 14.06/3.78 |
% 14.06/3.78 | Instantiating formula (132) with n1, n3, all_0_0_0, n4 and discharging atoms sum(n1, n3) = all_0_0_0, sum(n1, n3) = n4, yields:
% 14.06/3.78 | (291) all_0_0_0 = n4
% 14.06/3.78 |
% 14.06/3.78 | From (321)(291) and (167) follows:
% 14.06/3.78 | (2264) sum(n4, n4) = all_0_6_6
% 14.06/3.78 |
% 14.06/3.78 | Instantiating formula (132) with n4, n4, all_0_6_6, n8 and discharging atoms sum(n4, n4) = all_0_6_6, sum(n4, n4) = n8, yields:
% 14.06/3.78 | (310) all_0_6_6 = n8
% 14.06/3.78 |
% 14.06/3.78 | Equations (310) can reduce 165 to:
% 14.06/3.78 | (243) $false
% 14.06/3.78 |
% 14.06/3.78 |-The branch is then unsatisfiable
% 14.06/3.78 |-Branch two:
% 14.06/3.78 | (587) ~ (all_0_7_7 = n1)
% 14.06/3.78 | (588) all_0_7_7 = n0
% 14.06/3.78 |
% 14.06/3.78 | From (588) and (10) follows:
% 14.06/3.78 | (589) succ(n0) = all_0_5_5
% 14.06/3.78 |
% 14.06/3.78 | From (588) and (3) follows:
% 14.06/3.78 | (590) sum(n0, all_0_1_1) = all_0_0_0
% 14.06/3.78 |
% 14.06/3.78 | From (588) and (2230) follows:
% 14.06/3.78 | (2271) sum(n3, n0) = all_0_2_2
% 14.06/3.78 |
% 14.06/3.78 | Instantiating formula (47) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 14.06/3.78 | (592) all_0_5_5 = n1
% 14.06/3.78 |
% 14.06/3.78 | Instantiating formula (132) with n3, n0, all_0_2_2, n3 and discharging atoms sum(n3, n0) = all_0_2_2, sum(n3, n0) = n3, yields:
% 14.06/3.78 | (334) all_0_2_2 = n3
% 14.06/3.78 |
% 14.06/3.78 | From (334) and (205) follows:
% 14.06/3.78 | (336) pred(n3) = all_0_1_1
% 14.06/3.78 |
% 14.06/3.78 | From (592) and (2229) follows:
% 14.06/3.78 | (2275) sum(n3, n1) = all_0_4_4
% 14.06/3.78 |
% 14.06/3.78 | Instantiating formula (116) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 14.06/3.78 | (339) all_0_1_1 = n2
% 14.06/3.78 |
% 14.06/3.78 | Instantiating formula (132) with n3, n1, all_0_4_4, n4 and discharging atoms sum(n3, n1) = all_0_4_4, sum(n3, n1) = n4, yields:
% 14.06/3.78 | (335) all_0_4_4 = n4
% 14.06/3.78 |
% 14.06/3.78 | From (335) and (138) follows:
% 14.06/3.78 | (337) pred(n4) = all_0_3_3
% 14.06/3.78 |
% 14.06/3.78 | From (339) and (590) follows:
% 14.06/3.78 | (2279) sum(n0, n2) = all_0_0_0
% 14.06/3.78 |
% 14.06/3.78 | Instantiating formula (116) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 14.06/3.78 | (338) all_0_3_3 = n3
% 14.06/3.78 |
% 14.06/3.78 | Instantiating formula (132) with n0, n2, all_0_0_0, n2 and discharging atoms sum(n0, n2) = all_0_0_0, sum(n0, n2) = n2, yields:
% 14.06/3.78 | (325) all_0_0_0 = n2
% 14.06/3.78 |
% 14.06/3.78 | From (338)(325) and (167) follows:
% 14.06/3.78 | (2282) sum(n3, n2) = all_0_6_6
% 14.06/3.78 |
% 14.06/3.78 | Instantiating formula (132) with n3, n2, all_0_6_6, n5 and discharging atoms sum(n3, n2) = all_0_6_6, sum(n3, n2) = n5, yields:
% 14.06/3.78 | (242) all_0_6_6 = n5
% 14.06/3.78 |
% 14.06/3.78 | Equations (242) can reduce 4 to:
% 14.06/3.78 | (243) $false
% 14.06/3.78 |
% 14.06/3.78 |-The branch is then unsatisfiable
% 14.06/3.78 |-Branch two:
% 14.06/3.78 | (363) ~ (all_0_8_8 = n3)
% 14.06/3.78 | (364) all_0_8_8 = n2 | all_0_8_8 = n1 | all_0_8_8 = n0
% 14.06/3.79 |
% 14.06/3.79 +-Applying beta-rule and splitting (550), into two cases.
% 14.06/3.79 |-Branch one:
% 14.06/3.79 | (551) all_0_7_7 = n2
% 14.06/3.79 |
% 14.06/3.79 | From (551) and (10) follows:
% 14.06/3.79 | (552) succ(n2) = all_0_5_5
% 14.06/3.79 |
% 14.06/3.79 | From (551) and (3) follows:
% 14.06/3.79 | (553) sum(n2, all_0_1_1) = all_0_0_0
% 14.06/3.79 |
% 14.06/3.79 | From (551) and (120) follows:
% 14.06/3.79 | (2290) sum(all_0_8_8, n2) = all_0_2_2
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (47) with n2, all_0_5_5, n3 and discharging atoms succ(n2) = all_0_5_5, succ(n2) = n3, yields:
% 14.06/3.79 | (555) all_0_5_5 = n3
% 14.06/3.79 |
% 14.06/3.79 | From (555) and (77) follows:
% 14.06/3.79 | (2292) sum(all_0_8_8, n3) = all_0_4_4
% 14.06/3.79 |
% 14.06/3.79 +-Applying beta-rule and splitting (364), into two cases.
% 14.06/3.79 |-Branch one:
% 14.06/3.79 | (365) all_0_8_8 = n2
% 14.06/3.79 |
% 14.06/3.79 | From (365) and (2292) follows:
% 14.06/3.79 | (2294) sum(n2, n3) = all_0_4_4
% 14.06/3.79 |
% 14.06/3.79 | From (365) and (2290) follows:
% 14.06/3.79 | (2295) sum(n2, n2) = all_0_2_2
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (132) with n2, n3, all_0_4_4, n5 and discharging atoms sum(n2, n3) = all_0_4_4, sum(n2, n3) = n5, yields:
% 14.06/3.79 | (318) all_0_4_4 = n5
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (132) with n2, n2, all_0_2_2, n4 and discharging atoms sum(n2, n2) = all_0_2_2, sum(n2, n2) = n4, yields:
% 14.06/3.79 | (317) all_0_2_2 = n4
% 14.06/3.79 |
% 14.06/3.79 | From (317) and (205) follows:
% 14.06/3.79 | (319) pred(n4) = all_0_1_1
% 14.06/3.79 |
% 14.06/3.79 | From (318) and (138) follows:
% 14.06/3.79 | (320) pred(n5) = all_0_3_3
% 14.06/3.79 |
% 14.06/3.79 | From (318) and (2294) follows:
% 14.06/3.79 | (168) sum(n2, n3) = n5
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (116) with n5, all_0_3_3, n4 and discharging atoms pred(n5) = all_0_3_3, pred(n5) = n4, yields:
% 14.06/3.79 | (321) all_0_3_3 = n4
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (116) with n4, all_0_1_1, n3 and discharging atoms pred(n4) = all_0_1_1, pred(n4) = n3, yields:
% 14.06/3.79 | (322) all_0_1_1 = n3
% 14.06/3.79 |
% 14.06/3.79 | From (321) and (167) follows:
% 14.06/3.79 | (323) sum(n4, all_0_0_0) = all_0_6_6
% 14.06/3.79 |
% 14.06/3.79 | From (322) and (553) follows:
% 14.06/3.79 | (2304) sum(n2, n3) = all_0_0_0
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (132) with n2, n3, all_0_0_0, n5 and discharging atoms sum(n2, n3) = all_0_0_0, sum(n2, n3) = n5, yields:
% 14.06/3.79 | (274) all_0_0_0 = n5
% 14.06/3.79 |
% 14.06/3.79 | From (274) and (323) follows:
% 14.06/3.79 | (2306) sum(n4, n5) = all_0_6_6
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (132) with n4, n5, all_0_6_6, n9 and discharging atoms sum(n4, n5) = all_0_6_6, sum(n4, n5) = n9, yields:
% 14.06/3.79 | (395) all_0_6_6 = n9
% 14.06/3.79 |
% 14.06/3.79 | Equations (395) can reduce 78 to:
% 14.06/3.79 | (243) $false
% 14.06/3.79 |
% 14.06/3.79 |-The branch is then unsatisfiable
% 14.06/3.79 |-Branch two:
% 14.06/3.79 | (380) ~ (all_0_8_8 = n2)
% 14.06/3.79 | (381) all_0_8_8 = n1 | all_0_8_8 = n0
% 14.06/3.79 |
% 14.06/3.79 +-Applying beta-rule and splitting (381), into two cases.
% 14.06/3.79 |-Branch one:
% 14.06/3.79 | (382) all_0_8_8 = n1
% 14.06/3.79 |
% 14.06/3.79 | From (382) and (2292) follows:
% 14.06/3.79 | (2312) sum(n1, n3) = all_0_4_4
% 14.06/3.79 |
% 14.06/3.79 | From (382) and (2290) follows:
% 14.06/3.79 | (2313) sum(n1, n2) = all_0_2_2
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (132) with n1, n3, all_0_4_4, n4 and discharging atoms sum(n1, n3) = all_0_4_4, sum(n1, n3) = n4, yields:
% 14.06/3.79 | (335) all_0_4_4 = n4
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (132) with n1, n2, all_0_2_2, n3 and discharging atoms sum(n1, n2) = all_0_2_2, sum(n1, n2) = n3, yields:
% 14.06/3.79 | (334) all_0_2_2 = n3
% 14.06/3.79 |
% 14.06/3.79 | From (334) and (205) follows:
% 14.06/3.79 | (336) pred(n3) = all_0_1_1
% 14.06/3.79 |
% 14.06/3.79 | From (335) and (138) follows:
% 14.06/3.79 | (337) pred(n4) = all_0_3_3
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (116) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 14.06/3.79 | (338) all_0_3_3 = n3
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (116) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 14.06/3.79 | (339) all_0_1_1 = n2
% 14.06/3.79 |
% 14.06/3.79 | From (338) and (167) follows:
% 14.06/3.79 | (340) sum(n3, all_0_0_0) = all_0_6_6
% 14.06/3.79 |
% 14.06/3.79 | From (339) and (553) follows:
% 14.06/3.79 | (2321) sum(n2, n2) = all_0_0_0
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (132) with n2, n2, all_0_0_0, n4 and discharging atoms sum(n2, n2) = all_0_0_0, sum(n2, n2) = n4, yields:
% 14.06/3.79 | (291) all_0_0_0 = n4
% 14.06/3.79 |
% 14.06/3.79 | From (291) and (340) follows:
% 14.06/3.79 | (2323) sum(n3, n4) = all_0_6_6
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (132) with n3, n4, all_0_6_6, n7 and discharging atoms sum(n3, n4) = all_0_6_6, sum(n3, n4) = n7, yields:
% 14.06/3.79 | (411) all_0_6_6 = n7
% 14.06/3.79 |
% 14.06/3.79 | Equations (411) can reduce 88 to:
% 14.06/3.79 | (243) $false
% 14.06/3.79 |
% 14.06/3.79 |-The branch is then unsatisfiable
% 14.06/3.79 |-Branch two:
% 14.06/3.79 | (397) ~ (all_0_8_8 = n1)
% 14.06/3.79 | (398) all_0_8_8 = n0
% 14.06/3.79 |
% 14.06/3.79 | From (398) and (2292) follows:
% 14.06/3.79 | (2328) sum(n0, n3) = all_0_4_4
% 14.06/3.79 |
% 14.06/3.79 | From (398) and (2290) follows:
% 14.06/3.79 | (2329) sum(n0, n2) = all_0_2_2
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (132) with n0, n3, all_0_4_4, n3 and discharging atoms sum(n0, n3) = all_0_4_4, sum(n0, n3) = n3, yields:
% 14.06/3.79 | (352) all_0_4_4 = n3
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (132) with n0, n2, all_0_2_2, n2 and discharging atoms sum(n0, n2) = all_0_2_2, sum(n0, n2) = n2, yields:
% 14.06/3.79 | (351) all_0_2_2 = n2
% 14.06/3.79 |
% 14.06/3.79 | From (351) and (205) follows:
% 14.06/3.79 | (353) pred(n2) = all_0_1_1
% 14.06/3.79 |
% 14.06/3.79 | From (352) and (138) follows:
% 14.06/3.79 | (354) pred(n3) = all_0_3_3
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (116) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 14.06/3.79 | (355) all_0_3_3 = n2
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (116) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 14.06/3.79 | (356) all_0_1_1 = n1
% 14.06/3.79 |
% 14.06/3.79 | From (355) and (167) follows:
% 14.06/3.79 | (357) sum(n2, all_0_0_0) = all_0_6_6
% 14.06/3.79 |
% 14.06/3.79 | From (356) and (553) follows:
% 14.06/3.79 | (2337) sum(n2, n1) = all_0_0_0
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (132) with n2, n1, all_0_0_0, n3 and discharging atoms sum(n2, n1) = all_0_0_0, sum(n2, n1) = n3, yields:
% 14.06/3.79 | (308) all_0_0_0 = n3
% 14.06/3.79 |
% 14.06/3.79 | From (308) and (357) follows:
% 14.06/3.79 | (2339) sum(n2, n3) = all_0_6_6
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (132) with n2, n3, all_0_6_6, n5 and discharging atoms sum(n2, n3) = all_0_6_6, sum(n2, n3) = n5, yields:
% 14.06/3.79 | (242) all_0_6_6 = n5
% 14.06/3.79 |
% 14.06/3.79 | Equations (242) can reduce 4 to:
% 14.06/3.79 | (243) $false
% 14.06/3.79 |
% 14.06/3.79 |-The branch is then unsatisfiable
% 14.06/3.79 |-Branch two:
% 14.06/3.79 | (568) ~ (all_0_7_7 = n2)
% 14.06/3.79 | (569) all_0_7_7 = n1 | all_0_7_7 = n0
% 14.06/3.79 |
% 14.06/3.79 +-Applying beta-rule and splitting (364), into two cases.
% 14.06/3.79 |-Branch one:
% 14.06/3.79 | (365) all_0_8_8 = n2
% 14.06/3.79 |
% 14.06/3.79 | From (365) and (77) follows:
% 14.06/3.79 | (2345) sum(n2, all_0_5_5) = all_0_4_4
% 14.06/3.79 |
% 14.06/3.79 | From (365) and (120) follows:
% 14.06/3.79 | (2346) sum(n2, all_0_7_7) = all_0_2_2
% 14.06/3.79 |
% 14.06/3.79 +-Applying beta-rule and splitting (569), into two cases.
% 14.06/3.79 |-Branch one:
% 14.06/3.79 | (570) all_0_7_7 = n1
% 14.06/3.79 |
% 14.06/3.79 | From (570) and (10) follows:
% 14.06/3.79 | (571) succ(n1) = all_0_5_5
% 14.06/3.79 |
% 14.06/3.79 | From (570) and (3) follows:
% 14.06/3.79 | (572) sum(n1, all_0_1_1) = all_0_0_0
% 14.06/3.79 |
% 14.06/3.79 | From (570) and (2346) follows:
% 14.06/3.79 | (2350) sum(n2, n1) = all_0_2_2
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (47) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 14.06/3.79 | (574) all_0_5_5 = n2
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (132) with n2, n1, all_0_2_2, n3 and discharging atoms sum(n2, n1) = all_0_2_2, sum(n2, n1) = n3, yields:
% 14.06/3.79 | (334) all_0_2_2 = n3
% 14.06/3.79 |
% 14.06/3.79 | From (334) and (205) follows:
% 14.06/3.79 | (336) pred(n3) = all_0_1_1
% 14.06/3.79 |
% 14.06/3.79 | From (574) and (2345) follows:
% 14.06/3.79 | (2354) sum(n2, n2) = all_0_4_4
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (116) with n3, all_0_1_1, n2 and discharging atoms pred(n3) = all_0_1_1, pred(n3) = n2, yields:
% 14.06/3.79 | (339) all_0_1_1 = n2
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (132) with n2, n2, all_0_4_4, n4 and discharging atoms sum(n2, n2) = all_0_4_4, sum(n2, n2) = n4, yields:
% 14.06/3.79 | (335) all_0_4_4 = n4
% 14.06/3.79 |
% 14.06/3.79 | From (335) and (138) follows:
% 14.06/3.79 | (337) pred(n4) = all_0_3_3
% 14.06/3.79 |
% 14.06/3.79 | From (339) and (572) follows:
% 14.06/3.79 | (2358) sum(n1, n2) = all_0_0_0
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (116) with n4, all_0_3_3, n3 and discharging atoms pred(n4) = all_0_3_3, pred(n4) = n3, yields:
% 14.06/3.79 | (338) all_0_3_3 = n3
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (132) with n1, n2, all_0_0_0, n3 and discharging atoms sum(n1, n2) = all_0_0_0, sum(n1, n2) = n3, yields:
% 14.06/3.79 | (308) all_0_0_0 = n3
% 14.06/3.79 |
% 14.06/3.79 | From (338)(308) and (167) follows:
% 14.06/3.79 | (2361) sum(n3, n3) = all_0_6_6
% 14.06/3.79 |
% 14.06/3.79 | Instantiating formula (132) with n3, n3, all_0_6_6, n6 and discharging atoms sum(n3, n3) = all_0_6_6, sum(n3, n3) = n6, yields:
% 14.06/3.79 | (327) all_0_6_6 = n6
% 14.06/3.79 |
% 14.06/3.79 | Equations (327) can reduce 34 to:
% 14.06/3.79 | (243) $false
% 14.06/3.79 |
% 14.06/3.79 |-The branch is then unsatisfiable
% 14.06/3.79 |-Branch two:
% 14.06/3.79 | (587) ~ (all_0_7_7 = n1)
% 14.06/3.79 | (588) all_0_7_7 = n0
% 14.06/3.79 |
% 14.06/3.79 | From (588) and (10) follows:
% 14.06/3.79 | (589) succ(n0) = all_0_5_5
% 14.06/3.79 |
% 14.06/3.79 | From (588) and (3) follows:
% 14.06/3.79 | (590) sum(n0, all_0_1_1) = all_0_0_0
% 14.06/3.79 |
% 14.06/3.79 | From (588) and (2346) follows:
% 14.06/3.80 | (2368) sum(n2, n0) = all_0_2_2
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (47) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 14.06/3.80 | (592) all_0_5_5 = n1
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (132) with n2, n0, all_0_2_2, n2 and discharging atoms sum(n2, n0) = all_0_2_2, sum(n2, n0) = n2, yields:
% 14.06/3.80 | (351) all_0_2_2 = n2
% 14.06/3.80 |
% 14.06/3.80 | From (351) and (205) follows:
% 14.06/3.80 | (353) pred(n2) = all_0_1_1
% 14.06/3.80 |
% 14.06/3.80 | From (592) and (2345) follows:
% 14.06/3.80 | (2372) sum(n2, n1) = all_0_4_4
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (116) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 14.06/3.80 | (356) all_0_1_1 = n1
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (132) with n2, n1, all_0_4_4, n3 and discharging atoms sum(n2, n1) = all_0_4_4, sum(n2, n1) = n3, yields:
% 14.06/3.80 | (352) all_0_4_4 = n3
% 14.06/3.80 |
% 14.06/3.80 | From (352) and (138) follows:
% 14.06/3.80 | (354) pred(n3) = all_0_3_3
% 14.06/3.80 |
% 14.06/3.80 | From (352) and (2372) follows:
% 14.06/3.80 | (81) sum(n2, n1) = n3
% 14.06/3.80 |
% 14.06/3.80 | From (356) and (590) follows:
% 14.06/3.80 | (2377) sum(n0, n1) = all_0_0_0
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (116) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 14.06/3.80 | (355) all_0_3_3 = n2
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (132) with n0, n1, all_0_0_0, n1 and discharging atoms sum(n0, n1) = all_0_0_0, sum(n0, n1) = n1, yields:
% 14.06/3.80 | (342) all_0_0_0 = n1
% 14.06/3.80 |
% 14.06/3.80 | From (355)(342) and (167) follows:
% 14.06/3.80 | (2380) sum(n2, n1) = all_0_6_6
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (132) with n2, n1, all_0_6_6, n3 and discharging atoms sum(n2, n1) = all_0_6_6, sum(n2, n1) = n3, yields:
% 14.06/3.80 | (259) all_0_6_6 = n3
% 14.06/3.80 |
% 14.06/3.80 | Equations (259) can reduce 100 to:
% 14.06/3.80 | (243) $false
% 14.06/3.80 |
% 14.06/3.80 |-The branch is then unsatisfiable
% 14.06/3.80 |-Branch two:
% 14.06/3.80 | (380) ~ (all_0_8_8 = n2)
% 14.06/3.80 | (381) all_0_8_8 = n1 | all_0_8_8 = n0
% 14.06/3.80 |
% 14.06/3.80 +-Applying beta-rule and splitting (569), into two cases.
% 14.06/3.80 |-Branch one:
% 14.06/3.80 | (570) all_0_7_7 = n1
% 14.06/3.80 |
% 14.06/3.80 | From (570) and (10) follows:
% 14.06/3.80 | (571) succ(n1) = all_0_5_5
% 14.06/3.80 |
% 14.06/3.80 | From (570) and (3) follows:
% 14.06/3.80 | (572) sum(n1, all_0_1_1) = all_0_0_0
% 14.06/3.80 |
% 14.06/3.80 | From (570) and (120) follows:
% 14.06/3.80 | (2388) sum(all_0_8_8, n1) = all_0_2_2
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (47) with n1, all_0_5_5, n2 and discharging atoms succ(n1) = all_0_5_5, succ(n1) = n2, yields:
% 14.06/3.80 | (574) all_0_5_5 = n2
% 14.06/3.80 |
% 14.06/3.80 | From (574) and (77) follows:
% 14.06/3.80 | (2390) sum(all_0_8_8, n2) = all_0_4_4
% 14.06/3.80 |
% 14.06/3.80 +-Applying beta-rule and splitting (381), into two cases.
% 14.06/3.80 |-Branch one:
% 14.06/3.80 | (382) all_0_8_8 = n1
% 14.06/3.80 |
% 14.06/3.80 | From (382) and (2390) follows:
% 14.06/3.80 | (2392) sum(n1, n2) = all_0_4_4
% 14.06/3.80 |
% 14.06/3.80 | From (382) and (2388) follows:
% 14.06/3.80 | (2393) sum(n1, n1) = all_0_2_2
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (132) with n1, n2, all_0_4_4, n3 and discharging atoms sum(n1, n2) = all_0_4_4, sum(n1, n2) = n3, yields:
% 14.06/3.80 | (352) all_0_4_4 = n3
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (132) with n1, n1, all_0_2_2, n2 and discharging atoms sum(n1, n1) = all_0_2_2, sum(n1, n1) = n2, yields:
% 14.06/3.80 | (351) all_0_2_2 = n2
% 14.06/3.80 |
% 14.06/3.80 | From (351) and (205) follows:
% 14.06/3.80 | (353) pred(n2) = all_0_1_1
% 14.06/3.80 |
% 14.06/3.80 | From (352) and (138) follows:
% 14.06/3.80 | (354) pred(n3) = all_0_3_3
% 14.06/3.80 |
% 14.06/3.80 | From (351) and (2393) follows:
% 14.06/3.80 | (25) sum(n1, n1) = n2
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (116) with n3, all_0_3_3, n2 and discharging atoms pred(n3) = all_0_3_3, pred(n3) = n2, yields:
% 14.06/3.80 | (355) all_0_3_3 = n2
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (116) with n2, all_0_1_1, n1 and discharging atoms pred(n2) = all_0_1_1, pred(n2) = n1, yields:
% 14.06/3.80 | (356) all_0_1_1 = n1
% 14.06/3.80 |
% 14.06/3.80 | From (355) and (167) follows:
% 14.06/3.80 | (357) sum(n2, all_0_0_0) = all_0_6_6
% 14.06/3.80 |
% 14.06/3.80 | From (356) and (572) follows:
% 14.06/3.80 | (2402) sum(n1, n1) = all_0_0_0
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (132) with n1, n1, all_0_0_0, n2 and discharging atoms sum(n1, n1) = all_0_0_0, sum(n1, n1) = n2, yields:
% 14.06/3.80 | (325) all_0_0_0 = n2
% 14.06/3.80 |
% 14.06/3.80 | From (325) and (357) follows:
% 14.06/3.80 | (2404) sum(n2, n2) = all_0_6_6
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (132) with n2, n2, all_0_6_6, n4 and discharging atoms sum(n2, n2) = all_0_6_6, sum(n2, n2) = n4, yields:
% 14.06/3.80 | (344) all_0_6_6 = n4
% 14.06/3.80 |
% 14.06/3.80 | Equations (344) can reduce 216 to:
% 14.06/3.80 | (243) $false
% 14.06/3.80 |
% 14.06/3.80 |-The branch is then unsatisfiable
% 14.06/3.80 |-Branch two:
% 14.06/3.80 | (397) ~ (all_0_8_8 = n1)
% 14.06/3.80 | (398) all_0_8_8 = n0
% 14.06/3.80 |
% 14.06/3.80 | From (398) and (2390) follows:
% 14.06/3.80 | (2409) sum(n0, n2) = all_0_4_4
% 14.06/3.80 |
% 14.06/3.80 | From (398) and (2388) follows:
% 14.06/3.80 | (2410) sum(n0, n1) = all_0_2_2
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (132) with n0, n2, all_0_4_4, n2 and discharging atoms sum(n0, n2) = all_0_4_4, sum(n0, n2) = n2, yields:
% 14.06/3.80 | (369) all_0_4_4 = n2
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (132) with n0, n1, all_0_2_2, n1 and discharging atoms sum(n0, n1) = all_0_2_2, sum(n0, n1) = n1, yields:
% 14.06/3.80 | (368) all_0_2_2 = n1
% 14.06/3.80 |
% 14.06/3.80 | From (368) and (205) follows:
% 14.06/3.80 | (370) pred(n1) = all_0_1_1
% 14.06/3.80 |
% 14.06/3.80 | From (369) and (138) follows:
% 14.06/3.80 | (371) pred(n2) = all_0_3_3
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (116) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 14.06/3.80 | (372) all_0_3_3 = n1
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (116) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 14.06/3.80 | (373) all_0_1_1 = n0
% 14.06/3.80 |
% 14.06/3.80 | From (372) and (167) follows:
% 14.06/3.80 | (374) sum(n1, all_0_0_0) = all_0_6_6
% 14.06/3.80 |
% 14.06/3.80 | From (373) and (572) follows:
% 14.06/3.80 | (2418) sum(n1, n0) = all_0_0_0
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (132) with n1, n0, all_0_0_0, n1 and discharging atoms sum(n1, n0) = all_0_0_0, sum(n1, n0) = n1, yields:
% 14.06/3.80 | (342) all_0_0_0 = n1
% 14.06/3.80 |
% 14.06/3.80 | From (342) and (374) follows:
% 14.06/3.80 | (2420) sum(n1, n1) = all_0_6_6
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (132) with n1, n1, all_0_6_6, n2 and discharging atoms sum(n1, n1) = all_0_6_6, sum(n1, n1) = n2, yields:
% 14.06/3.80 | (361) all_0_6_6 = n2
% 14.06/3.80 |
% 14.06/3.80 | Equations (361) can reduce 131 to:
% 14.06/3.80 | (243) $false
% 14.06/3.80 |
% 14.06/3.80 |-The branch is then unsatisfiable
% 14.06/3.80 |-Branch two:
% 14.06/3.80 | (587) ~ (all_0_7_7 = n1)
% 14.06/3.80 | (588) all_0_7_7 = n0
% 14.06/3.80 |
% 14.06/3.80 | From (588) and (10) follows:
% 14.06/3.80 | (589) succ(n0) = all_0_5_5
% 14.06/3.80 |
% 14.06/3.80 | From (588) and (3) follows:
% 14.06/3.80 | (590) sum(n0, all_0_1_1) = all_0_0_0
% 14.06/3.80 |
% 14.06/3.80 | From (588) and (120) follows:
% 14.06/3.80 | (2427) sum(all_0_8_8, n0) = all_0_2_2
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (47) with n0, all_0_5_5, n1 and discharging atoms succ(n0) = all_0_5_5, succ(n0) = n1, yields:
% 14.06/3.80 | (592) all_0_5_5 = n1
% 14.06/3.80 |
% 14.06/3.80 | From (592) and (77) follows:
% 14.06/3.80 | (2429) sum(all_0_8_8, n1) = all_0_4_4
% 14.06/3.80 |
% 14.06/3.80 +-Applying beta-rule and splitting (381), into two cases.
% 14.06/3.80 |-Branch one:
% 14.06/3.80 | (382) all_0_8_8 = n1
% 14.06/3.80 |
% 14.06/3.80 | From (382) and (2429) follows:
% 14.06/3.80 | (2431) sum(n1, n1) = all_0_4_4
% 14.06/3.80 |
% 14.06/3.80 | From (382) and (2427) follows:
% 14.06/3.80 | (2432) sum(n1, n0) = all_0_2_2
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (132) with n1, n1, all_0_4_4, n2 and discharging atoms sum(n1, n1) = all_0_4_4, sum(n1, n1) = n2, yields:
% 14.06/3.80 | (369) all_0_4_4 = n2
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (132) with n1, n0, all_0_2_2, n1 and discharging atoms sum(n1, n0) = all_0_2_2, sum(n1, n0) = n1, yields:
% 14.06/3.80 | (368) all_0_2_2 = n1
% 14.06/3.80 |
% 14.06/3.80 | From (368) and (205) follows:
% 14.06/3.80 | (370) pred(n1) = all_0_1_1
% 14.06/3.80 |
% 14.06/3.80 | From (369) and (138) follows:
% 14.06/3.80 | (371) pred(n2) = all_0_3_3
% 14.06/3.80 |
% 14.06/3.80 | From (368) and (2432) follows:
% 14.06/3.80 | (203) sum(n1, n0) = n1
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (116) with n2, all_0_3_3, n1 and discharging atoms pred(n2) = all_0_3_3, pred(n2) = n1, yields:
% 14.06/3.80 | (372) all_0_3_3 = n1
% 14.06/3.80 |
% 14.06/3.80 | Instantiating formula (116) with n1, all_0_1_1, n0 and discharging atoms pred(n1) = all_0_1_1, pred(n1) = n0, yields:
% 14.06/3.80 | (373) all_0_1_1 = n0
% 14.06/3.80 |
% 14.06/3.80 | From (372) and (167) follows:
% 14.06/3.80 | (374) sum(n1, all_0_0_0) = all_0_6_6
% 14.06/3.80 |
% 14.06/3.80 | From (373) and (590) follows:
% 14.06/3.81 | (2441) sum(n0, n0) = all_0_0_0
% 14.06/3.81 |
% 14.06/3.81 | Instantiating formula (132) with n0, n0, all_0_0_0, n0 and discharging atoms sum(n0, n0) = all_0_0_0, sum(n0, n0) = n0, yields:
% 14.06/3.81 | (359) all_0_0_0 = n0
% 14.06/3.81 |
% 14.06/3.81 | From (359) and (374) follows:
% 14.06/3.81 | (2443) sum(n1, n0) = all_0_6_6
% 14.06/3.81 |
% 14.06/3.81 | Instantiating formula (132) with n1, n0, all_0_6_6, n1 and discharging atoms sum(n1, n0) = all_0_6_6, sum(n1, n0) = n1, yields:
% 14.06/3.81 | (276) all_0_6_6 = n1
% 14.06/3.81 |
% 14.06/3.81 | Equations (276) can reduce 28 to:
% 14.06/3.81 | (243) $false
% 14.06/3.81 |
% 14.06/3.81 |-The branch is then unsatisfiable
% 14.06/3.81 |-Branch two:
% 14.06/3.81 | (397) ~ (all_0_8_8 = n1)
% 14.06/3.81 | (398) all_0_8_8 = n0
% 14.06/3.81 |
% 14.06/3.81 | From (398) and (2429) follows:
% 14.06/3.81 | (2448) sum(n0, n1) = all_0_4_4
% 14.06/3.81 |
% 14.06/3.81 | From (398) and (2427) follows:
% 14.06/3.81 | (2449) sum(n0, n0) = all_0_2_2
% 14.06/3.81 |
% 14.06/3.81 | Instantiating formula (132) with n0, n1, all_0_4_4, n1 and discharging atoms sum(n0, n1) = all_0_4_4, sum(n0, n1) = n1, yields:
% 14.06/3.81 | (386) all_0_4_4 = n1
% 14.06/3.81 |
% 14.06/3.81 | Instantiating formula (132) with n0, n0, all_0_2_2, n0 and discharging atoms sum(n0, n0) = all_0_2_2, sum(n0, n0) = n0, yields:
% 14.06/3.81 | (385) all_0_2_2 = n0
% 14.06/3.81 |
% 14.06/3.81 | From (385) and (205) follows:
% 14.06/3.81 | (387) pred(n0) = all_0_1_1
% 14.06/3.81 |
% 14.06/3.81 | From (386) and (138) follows:
% 14.06/3.81 | (388) pred(n1) = all_0_3_3
% 14.06/3.81 |
% 14.06/3.81 | Instantiating formula (116) with n1, all_0_3_3, n0 and discharging atoms pred(n1) = all_0_3_3, pred(n1) = n0, yields:
% 14.06/3.81 | (389) all_0_3_3 = n0
% 14.06/3.81 |
% 14.06/3.81 | Instantiating formula (116) with n0, all_0_1_1, n10 and discharging atoms pred(n0) = all_0_1_1, pred(n0) = n10, yields:
% 14.06/3.81 | (390) all_0_1_1 = n10
% 14.06/3.81 |
% 14.06/3.81 | From (389) and (167) follows:
% 14.06/3.81 | (391) sum(n0, all_0_0_0) = all_0_6_6
% 14.06/3.81 |
% 14.06/3.81 | From (390) and (590) follows:
% 14.06/3.81 | (2457) sum(n0, n10) = all_0_0_0
% 14.06/3.81 |
% 14.06/3.81 | Instantiating formula (132) with n0, n10, all_0_0_0, n10 and discharging atoms sum(n0, n10) = all_0_0_0, sum(n0, n10) = n10, yields:
% 14.06/3.81 | (376) all_0_0_0 = n10
% 14.06/3.81 |
% 14.06/3.81 | From (376) and (391) follows:
% 14.06/3.81 | (2459) sum(n0, n10) = all_0_6_6
% 14.06/3.81 |
% 14.06/3.81 | From (376) and (2457) follows:
% 14.06/3.81 | (43) sum(n0, n10) = n10
% 14.06/3.81 |
% 14.06/3.81 | Instantiating formula (132) with n0, n10, all_0_6_6, n10 and discharging atoms sum(n0, n10) = all_0_6_6, sum(n0, n10) = n10, yields:
% 14.06/3.81 | (293) all_0_6_6 = n10
% 14.06/3.81 |
% 14.06/3.81 | Equations (293) can reduce 147 to:
% 14.06/3.81 | (243) $false
% 14.06/3.81 |
% 14.06/3.81 |-The branch is then unsatisfiable
% 14.06/3.81 % SZS output end Proof for theBenchmark
% 14.06/3.81
% 14.06/3.81 3217ms
%------------------------------------------------------------------------------