TSTP Solution File: NUM858+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM858+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 08:49:15 EDT 2022
% Result : Theorem 166.23s 126.42s
% Output : Proof 176.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM858+1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jul 6 14:05:58 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.57 ____ _
% 0.19/0.57 ___ / __ \_____(_)___ ________ __________
% 0.19/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.57
% 0.19/0.57 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.69/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.47/0.88 Prover 0: Preprocessing ...
% 1.82/1.04 Prover 0: Warning: ignoring some quantifiers
% 1.82/1.06 Prover 0: Constructing countermodel ...
% 4.03/1.60 Prover 0: gave up
% 4.03/1.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.03/1.62 Prover 1: Preprocessing ...
% 4.67/1.70 Prover 1: Constructing countermodel ...
% 5.10/1.80 Prover 1: gave up
% 5.10/1.80 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.10/1.82 Prover 2: Preprocessing ...
% 5.43/1.90 Prover 2: Warning: ignoring some quantifiers
% 5.43/1.91 Prover 2: Constructing countermodel ...
% 14.41/4.03 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 14.53/4.06 Prover 3: Preprocessing ...
% 14.53/4.09 Prover 3: Warning: ignoring some quantifiers
% 14.53/4.09 Prover 3: Constructing countermodel ...
% 15.47/4.27 Prover 3: gave up
% 15.47/4.27 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 15.47/4.28 Prover 4: Preprocessing ...
% 15.86/4.34 Prover 4: Warning: ignoring some quantifiers
% 15.86/4.34 Prover 4: Constructing countermodel ...
% 19.63/5.29 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 19.63/5.31 Prover 5: Preprocessing ...
% 20.17/5.38 Prover 5: Constructing countermodel ...
% 43.39/20.77 Prover 5: stopped
% 43.68/20.97 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 43.68/20.99 Prover 6: Preprocessing ...
% 44.01/21.04 Prover 6: Warning: ignoring some quantifiers
% 44.01/21.04 Prover 6: Constructing countermodel ...
% 122.58/92.86 Prover 2: stopped
% 122.80/93.06 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 122.80/93.07 Prover 7: Preprocessing ...
% 122.80/93.09 Prover 7: Proving ...
% 166.23/126.41 Prover 6: proved (45647ms)
% 166.23/126.41 Prover 4: stopped
% 166.23/126.42 Prover 7: stopped
% 166.23/126.42
% 166.23/126.42 No countermodel exists, formula is valid
% 166.23/126.42 % SZS status Theorem for theBenchmark
% 166.23/126.42
% 166.23/126.42 Generating proof ... Warning: ignoring some quantifiers
% 174.93/129.47 found it (size 571)
% 174.93/129.47
% 174.93/129.47 % SZS output start Proof for theBenchmark
% 174.93/129.47 Assumed formulas after preprocessing and simplification:
% 174.93/129.47 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (minsol_model_ub(v0, v1, v2) = v3 & minsol_model_max(v0, v1, v2) = v4 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (model_ub(v5, v6, v7) = v8) | ~ (lesseq(v7, v9) = v10) | ? [v11] : (( ~ (v11 = 0) & minsol_model_ub(v5, v6, v7) = v11) | ( ~ (v11 = 0) & model_ub(v5, v6, v9) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (model_max(v5, v6, v7) = v8) | ~ (lesseq(v7, v9) = v10) | ? [v11] : (( ~ (v11 = 0) & minsol_model_max(v5, v6, v7) = v11) | ( ~ (v11 = 0) & model_max(v5, v6, v9) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (sum(v7, v6) = v9) | ~ (sum(v7, v5) = v8) | ~ (lesseq(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & lesseq(v5, v6) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (minsol_model_ub(v5, v6, v7) = 0) | ~ (lesseq(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & model_ub(v5, v6, v8) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (minsol_model_max(v5, v6, v7) = 0) | ~ (lesseq(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & model_max(v5, v6, v8) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (summation(v6) = v8) | ~ (summation(v5) = v7) | ~ (lesseq(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & lesseq(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (minsol_model_ub(v9, v8, v7) = v6) | ~ (minsol_model_ub(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (minsol_model_max(v9, v8, v7) = v6) | ~ (minsol_model_max(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (model_ub(v9, v8, v7) = v6) | ~ (model_ub(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (model_max(v9, v8, v7) = v6) | ~ (model_max(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (ub(v9, v8, v7) = v6) | ~ (ub(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (model_ub(v5, v6, v9) = 0) | ~ (model_ub(v5, v6, v7) = v8) | ? [v10] : ((v10 = 0 & lesseq(v7, v9) = 0) | ( ~ (v10 = 0) & minsol_model_ub(v5, v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (model_max(v5, v6, v9) = 0) | ~ (model_max(v5, v6, v7) = v8) | ? [v10] : ((v10 = 0 & lesseq(v7, v9) = 0) | ( ~ (v10 = 0) & minsol_model_max(v5, v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sum(v7, v6) = v9) | ~ (sum(v7, v5) = v8) | ~ (lesseq(v8, v9) = 0) | lesseq(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (minsol_model_ub(v5, v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & ~ (v11 = 0) & model_ub(v5, v6, v9) = 0 & lesseq(v7, v9) = v11) | ( ~ (v9 = 0) & model_ub(v5, v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (minsol_model_max(v5, v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & ~ (v11 = 0) & model_max(v5, v6, v9) = 0 & lesseq(v7, v9) = v11) | ( ~ (v9 = 0) & model_max(v5, v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (model_ub(v5, v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & minsol_model_ub(v5, v6, v7) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (model_ub(v5, v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & ub(v5, v6, v7) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (model_max(v5, v6, v7) = v8) | ? [v9] : ( ~ (v9 = v7) & max(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (model_max(v5, v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & minsol_model_max(v5, v6, v7) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (ub(v5, v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & model_ub(v5, v6, v7) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (ub(v5, v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & lesseq(v6, v7) = v9) | ( ~ (v9 = 0) & lesseq(v5, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (lesseq(v6, v7) = 0) | ~ (lesseq(v5, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & lesseq(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (lesseq(v5, v7) = v8) | ~ (lesseq(v5, v6) = 0) | ? [v9] : ( ~ (v9 = 0) & lesseq(v6, v7) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (max(v8, v7) = v6) | ~ (max(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sum(v8, v7) = v6) | ~ (sum(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (lesseq(v8, v7) = v6) | ~ (lesseq(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (minsol_model_ub(v5, v6, v7) = 0) | ~ (model_ub(v5, v6, v8) = 0) | lesseq(v7, v8) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (minsol_model_max(v5, v6, v7) = 0) | ~ (model_max(v5, v6, v8) = 0) | lesseq(v7, v8) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (summation(v6) = v8) | ~ (summation(v5) = v7) | ~ (lesseq(v7, v8) = 0) | lesseq(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (max(v5, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & lesseq(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (max(v5, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & lesseq(v6, v5) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (lesseq(v6, v5) = v7) | lesseq(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (lesseq(v5, v6) = v7) | lesseq(v6, v5) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (lesseq(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & summation(v6) = v9 & summation(v5) = v8 & lesseq(v8, v9) = v10)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (summation(v7) = v6) | ~ (summation(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (minsol_model_ub(v5, v6, v7) = 0) | model_ub(v5, v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (minsol_model_max(v5, v6, v7) = 0) | model_max(v5, v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (model_ub(v5, v6, v7) = 0) | ub(v5, v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (model_ub(v5, v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v9 = 0 & ~ (v10 = 0) & model_ub(v5, v6, v8) = 0 & lesseq(v7, v8) = v10) | (v8 = 0 & minsol_model_ub(v5, v6, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (model_max(v5, v6, v7) = 0) | max(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (model_max(v5, v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v9 = 0 & ~ (v10 = 0) & model_max(v5, v6, v8) = 0 & lesseq(v7, v8) = v10) | (v8 = 0 & minsol_model_max(v5, v6, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (ub(v5, v6, v7) = 0) | model_ub(v5, v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (ub(v5, v6, v7) = 0) | (lesseq(v6, v7) = 0 & lesseq(v5, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (lesseq(v6, v7) = 0) | ~ (lesseq(v5, v6) = 0) | lesseq(v5, v7) = 0) & ! [v5] : ! [v6] : (v6 = v5 | ~ (lesseq(v6, v5) = 0) | ? [v7] : ( ~ (v7 = 0) & lesseq(v5, v6) = v7)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (lesseq(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & lesseq(v6, v5) = v7)) & ! [v5] : ! [v6] : (v6 = 0 | ~ (lesseq(v5, v5) = v6)) & ! [v5] : ! [v6] : ( ~ (lesseq(v6, v5) = 0) | max(v5, v6) = v5) & ! [v5] : ! [v6] : ( ~ (lesseq(v5, v6) = 0) | max(v5, v6) = v6) & ! [v5] : ! [v6] : ( ~ (lesseq(v5, v6) = 0) | ? [v7] : ? [v8] : (summation(v6) = v8 & summation(v5) = v7 & lesseq(v7, v8) = 0)) & ? [v5] : ? [v6] : ? [v7] : ? [v8] : minsol_model_ub(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : minsol_model_max(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : model_ub(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : model_max(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : ub(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : max(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : sum(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : lesseq(v6, v5) = v7 & ? [v5] : ? [v6] : summation(v5) = v6 & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0))))
% 174.93/129.50 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 174.93/129.50 | (1) minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1 & minsol_model_max(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (model_ub(v0, v1, v2) = v3) | ~ (lesseq(v2, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & minsol_model_ub(v0, v1, v2) = v6) | ( ~ (v6 = 0) & model_ub(v0, v1, v4) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (model_max(v0, v1, v2) = v3) | ~ (lesseq(v2, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & minsol_model_max(v0, v1, v2) = v6) | ( ~ (v6 = 0) & model_max(v0, v1, v4) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (sum(v2, v1) = v4) | ~ (sum(v2, v0) = v3) | ~ (lesseq(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & lesseq(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (minsol_model_ub(v0, v1, v2) = 0) | ~ (lesseq(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & model_ub(v0, v1, v3) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (minsol_model_max(v0, v1, v2) = 0) | ~ (lesseq(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & model_max(v0, v1, v3) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (summation(v1) = v3) | ~ (summation(v0) = v2) | ~ (lesseq(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & lesseq(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (minsol_model_ub(v4, v3, v2) = v1) | ~ (minsol_model_ub(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (minsol_model_max(v4, v3, v2) = v1) | ~ (minsol_model_max(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (model_ub(v4, v3, v2) = v1) | ~ (model_ub(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (model_max(v4, v3, v2) = v1) | ~ (model_max(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (ub(v4, v3, v2) = v1) | ~ (ub(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (model_ub(v0, v1, v4) = 0) | ~ (model_ub(v0, v1, v2) = v3) | ? [v5] : ((v5 = 0 & lesseq(v2, v4) = 0) | ( ~ (v5 = 0) & minsol_model_ub(v0, v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (model_max(v0, v1, v4) = 0) | ~ (model_max(v0, v1, v2) = v3) | ? [v5] : ((v5 = 0 & lesseq(v2, v4) = 0) | ( ~ (v5 = 0) & minsol_model_max(v0, v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sum(v2, v1) = v4) | ~ (sum(v2, v0) = v3) | ~ (lesseq(v3, v4) = 0) | lesseq(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (minsol_model_ub(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & model_ub(v0, v1, v4) = 0 & lesseq(v2, v4) = v6) | ( ~ (v4 = 0) & model_ub(v0, v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (minsol_model_max(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & model_max(v0, v1, v4) = 0 & lesseq(v2, v4) = v6) | ( ~ (v4 = 0) & model_max(v0, v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (model_ub(v0, v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & minsol_model_ub(v0, v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (model_ub(v0, v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & ub(v0, v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (model_max(v0, v1, v2) = v3) | ? [v4] : ( ~ (v4 = v2) & max(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (model_max(v0, v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & minsol_model_max(v0, v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (ub(v0, v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & model_ub(v0, v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (ub(v0, v1, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & lesseq(v1, v2) = v4) | ( ~ (v4 = 0) & lesseq(v0, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lesseq(v1, v2) = 0) | ~ (lesseq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & lesseq(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lesseq(v0, v2) = v3) | ~ (lesseq(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & lesseq(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (max(v3, v2) = v1) | ~ (max(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lesseq(v3, v2) = v1) | ~ (lesseq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (minsol_model_ub(v0, v1, v2) = 0) | ~ (model_ub(v0, v1, v3) = 0) | lesseq(v2, v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (minsol_model_max(v0, v1, v2) = 0) | ~ (model_max(v0, v1, v3) = 0) | lesseq(v2, v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (summation(v1) = v3) | ~ (summation(v0) = v2) | ~ (lesseq(v2, v3) = 0) | lesseq(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (max(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & lesseq(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (max(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & lesseq(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (lesseq(v1, v0) = v2) | lesseq(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (lesseq(v0, v1) = v2) | lesseq(v1, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (lesseq(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & summation(v1) = v4 & summation(v0) = v3 & lesseq(v3, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (summation(v2) = v1) | ~ (summation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (minsol_model_ub(v0, v1, v2) = 0) | model_ub(v0, v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (minsol_model_max(v0, v1, v2) = 0) | model_max(v0, v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (model_ub(v0, v1, v2) = 0) | ub(v0, v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (model_ub(v0, v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v4 = 0 & ~ (v5 = 0) & model_ub(v0, v1, v3) = 0 & lesseq(v2, v3) = v5) | (v3 = 0 & minsol_model_ub(v0, v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (model_max(v0, v1, v2) = 0) | max(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (model_max(v0, v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v4 = 0 & ~ (v5 = 0) & model_max(v0, v1, v3) = 0 & lesseq(v2, v3) = v5) | (v3 = 0 & minsol_model_max(v0, v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ub(v0, v1, v2) = 0) | model_ub(v0, v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ub(v0, v1, v2) = 0) | (lesseq(v1, v2) = 0 & lesseq(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (lesseq(v1, v2) = 0) | ~ (lesseq(v0, v1) = 0) | lesseq(v0, v2) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (lesseq(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & lesseq(v0, v1) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (lesseq(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & lesseq(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (lesseq(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (lesseq(v1, v0) = 0) | max(v0, v1) = v0) & ! [v0] : ! [v1] : ( ~ (lesseq(v0, v1) = 0) | max(v0, v1) = v1) & ! [v0] : ! [v1] : ( ~ (lesseq(v0, v1) = 0) | ? [v2] : ? [v3] : (summation(v1) = v3 & summation(v0) = v2 & lesseq(v2, v3) = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : minsol_model_ub(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : minsol_model_max(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : model_ub(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : model_max(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ub(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : max(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : sum(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : lesseq(v1, v0) = v2 & ? [v0] : ? [v1] : summation(v0) = v1 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)))
% 175.17/129.52 |
% 175.17/129.52 | Applying alpha-rule on (1) yields:
% 175.17/129.52 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (minsol_model_max(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & model_max(v0, v1, v4) = 0 & lesseq(v2, v4) = v6) | ( ~ (v4 = 0) & model_max(v0, v1, v2) = v4)))
% 175.17/129.52 | (3) minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1
% 175.17/129.52 | (4) ? [v0] : ? [v1] : ? [v2] : ? [v3] : model_ub(v2, v1, v0) = v3
% 175.17/129.52 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (ub(v0, v1, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & lesseq(v1, v2) = v4) | ( ~ (v4 = 0) & lesseq(v0, v2) = v4)))
% 175.17/129.52 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (model_max(v0, v1, v2) = 0) | max(v0, v1) = v2)
% 175.17/129.52 | (7) ? [v0] : ? [v1] : ? [v2] : max(v1, v0) = v2
% 175.17/129.52 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (minsol_model_max(v0, v1, v2) = 0) | ~ (model_max(v0, v1, v3) = 0) | lesseq(v2, v3) = 0)
% 175.17/129.52 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (lesseq(v0, v1) = v2) | lesseq(v1, v0) = 0)
% 175.17/129.52 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (lesseq(v1, v0) = v2) | lesseq(v0, v1) = 0)
% 175.17/129.52 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lesseq(v3, v2) = v1) | ~ (lesseq(v3, v2) = v0))
% 175.17/129.52 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (minsol_model_ub(v4, v3, v2) = v1) | ~ (minsol_model_ub(v4, v3, v2) = v0))
% 175.17/129.52 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (minsol_model_ub(v0, v1, v2) = 0) | ~ (model_ub(v0, v1, v3) = 0) | lesseq(v2, v3) = 0)
% 175.17/129.52 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (minsol_model_ub(v0, v1, v2) = 0) | model_ub(v0, v1, v2) = 0)
% 175.17/129.52 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (max(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & lesseq(v1, v0) = v3))
% 175.17/129.52 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (model_max(v0, v1, v2) = v3) | ~ (lesseq(v2, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & minsol_model_max(v0, v1, v2) = v6) | ( ~ (v6 = 0) & model_max(v0, v1, v4) = v6)))
% 175.17/129.52 | (17) ? [v0] : ? [v1] : ? [v2] : ? [v3] : minsol_model_ub(v2, v1, v0) = v3
% 175.17/129.52 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (model_ub(v0, v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v4 = 0 & ~ (v5 = 0) & model_ub(v0, v1, v3) = 0 & lesseq(v2, v3) = v5) | (v3 = 0 & minsol_model_ub(v0, v1, v2) = 0)))
% 175.17/129.52 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (model_max(v0, v1, v4) = 0) | ~ (model_max(v0, v1, v2) = v3) | ? [v5] : ((v5 = 0 & lesseq(v2, v4) = 0) | ( ~ (v5 = 0) & minsol_model_max(v0, v1, v2) = v5)))
% 175.17/129.52 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (model_ub(v0, v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & minsol_model_ub(v0, v1, v2) = v4))
% 175.17/129.52 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lesseq(v0, v2) = v3) | ~ (lesseq(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & lesseq(v1, v2) = v4))
% 175.17/129.52 | (22) minsol_model_max(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_0_0
% 175.17/129.52 | (23) ! [v0] : ! [v1] : ( ~ (lesseq(v1, v0) = 0) | max(v0, v1) = v0)
% 175.17/129.52 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sum(v2, v1) = v4) | ~ (sum(v2, v0) = v3) | ~ (lesseq(v3, v4) = 0) | lesseq(v0, v1) = 0)
% 175.17/129.52 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (minsol_model_ub(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & model_ub(v0, v1, v4) = 0 & lesseq(v2, v4) = v6) | ( ~ (v4 = 0) & model_ub(v0, v1, v2) = v4)))
% 175.17/129.53 | (26) ? [v0] : ? [v1] : ? [v2] : ? [v3] : model_max(v2, v1, v0) = v3
% 175.17/129.53 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0))
% 175.17/129.53 | (28) ? [v0] : ? [v1] : ? [v2] : ? [v3] : minsol_model_max(v2, v1, v0) = v3
% 175.17/129.53 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lesseq(v1, v2) = 0) | ~ (lesseq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & lesseq(v0, v1) = v4))
% 175.17/129.53 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (summation(v1) = v3) | ~ (summation(v0) = v2) | ~ (lesseq(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & lesseq(v0, v1) = v5))
% 175.17/129.53 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (summation(v2) = v1) | ~ (summation(v2) = v0))
% 175.17/129.53 | (32) ! [v0] : ! [v1] : ( ~ (lesseq(v0, v1) = 0) | max(v0, v1) = v1)
% 175.17/129.53 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (model_ub(v0, v1, v2) = v3) | ~ (lesseq(v2, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & minsol_model_ub(v0, v1, v2) = v6) | ( ~ (v6 = 0) & model_ub(v0, v1, v4) = v6)))
% 175.17/129.53 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (ub(v0, v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & model_ub(v0, v1, v2) = v4))
% 175.17/129.53 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (model_ub(v0, v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & ub(v0, v1, v2) = v4))
% 175.17/129.53 | (36) ! [v0] : ! [v1] : (v1 = v0 | ~ (lesseq(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & lesseq(v1, v0) = v2))
% 175.17/129.53 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (minsol_model_max(v0, v1, v2) = 0) | model_max(v0, v1, v2) = 0)
% 175.17/129.53 | (38) ? [v0] : ? [v1] : ? [v2] : sum(v1, v0) = v2
% 175.17/129.53 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (minsol_model_ub(v0, v1, v2) = 0) | ~ (lesseq(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & model_ub(v0, v1, v3) = v5))
% 175.17/129.53 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (lesseq(v1, v2) = 0) | ~ (lesseq(v0, v1) = 0) | lesseq(v0, v2) = 0)
% 175.17/129.53 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (model_max(v0, v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & minsol_model_max(v0, v1, v2) = v4))
% 175.17/129.53 | (42) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (lesseq(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & summation(v1) = v4 & summation(v0) = v3 & lesseq(v3, v4) = v5))
% 175.17/129.53 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (ub(v0, v1, v2) = 0) | (lesseq(v1, v2) = 0 & lesseq(v0, v2) = 0))
% 175.17/129.53 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (sum(v2, v1) = v4) | ~ (sum(v2, v0) = v3) | ~ (lesseq(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & lesseq(v0, v1) = v6))
% 175.17/129.53 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (model_max(v0, v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v4 = 0 & ~ (v5 = 0) & model_max(v0, v1, v3) = 0 & lesseq(v2, v3) = v5) | (v3 = 0 & minsol_model_max(v0, v1, v2) = 0)))
% 175.17/129.53 | (46) ? [v0] : ? [v1] : ? [v2] : lesseq(v1, v0) = v2
% 175.17/129.53 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (max(v3, v2) = v1) | ~ (max(v3, v2) = v0))
% 175.17/129.53 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (model_max(v0, v1, v2) = v3) | ? [v4] : ( ~ (v4 = v2) & max(v0, v1) = v4))
% 175.17/129.53 | (49) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (max(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & lesseq(v0, v1) = v3))
% 175.17/129.53 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (ub(v0, v1, v2) = 0) | model_ub(v0, v1, v2) = 0)
% 175.17/129.53 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (model_ub(v0, v1, v2) = 0) | ub(v0, v1, v2) = 0)
% 175.17/129.53 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (model_ub(v4, v3, v2) = v1) | ~ (model_ub(v4, v3, v2) = v0))
% 175.17/129.53 | (53) ! [v0] : ! [v1] : ( ~ (lesseq(v0, v1) = 0) | ? [v2] : ? [v3] : (summation(v1) = v3 & summation(v0) = v2 & lesseq(v2, v3) = 0))
% 175.17/129.53 | (54) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ub(v2, v1, v0) = v3
% 175.17/129.53 | (55) ? [v0] : ? [v1] : summation(v0) = v1
% 175.17/129.53 | (56) ! [v0] : ! [v1] : (v1 = 0 | ~ (lesseq(v0, v0) = v1))
% 175.17/129.53 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (summation(v1) = v3) | ~ (summation(v0) = v2) | ~ (lesseq(v2, v3) = 0) | lesseq(v0, v1) = 0)
% 175.17/129.54 | (58) ! [v0] : ! [v1] : (v1 = v0 | ~ (lesseq(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & lesseq(v0, v1) = v2))
% 175.17/129.54 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (model_ub(v0, v1, v4) = 0) | ~ (model_ub(v0, v1, v2) = v3) | ? [v5] : ((v5 = 0 & lesseq(v2, v4) = 0) | ( ~ (v5 = 0) & minsol_model_ub(v0, v1, v2) = v5)))
% 175.17/129.54 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (ub(v4, v3, v2) = v1) | ~ (ub(v4, v3, v2) = v0))
% 175.17/129.54 | (61) (all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0))
% 175.17/129.54 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (minsol_model_max(v0, v1, v2) = 0) | ~ (lesseq(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & model_max(v0, v1, v3) = v5))
% 175.17/129.54 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (model_max(v4, v3, v2) = v1) | ~ (model_max(v4, v3, v2) = v0))
% 175.17/129.54 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (minsol_model_max(v4, v3, v2) = v1) | ~ (minsol_model_max(v4, v3, v2) = v0))
% 175.17/129.54 |
% 175.17/129.54 | Instantiating formula (25) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 175.17/129.54 | (65) all_0_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & model_ub(all_0_4_4, all_0_3_3, v0) = 0 & lesseq(all_0_2_2, v0) = v2) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = v0))
% 175.17/129.54 |
% 175.17/129.54 | Instantiating formula (2) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms minsol_model_max(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_0_0, yields:
% 175.17/129.54 | (66) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & model_max(all_0_4_4, all_0_3_3, v0) = 0 & lesseq(all_0_2_2, v0) = v2) | ( ~ (v0 = 0) & model_max(all_0_4_4, all_0_3_3, all_0_2_2) = v0))
% 175.17/129.54 |
% 175.17/129.54 +-Applying beta-rule and splitting (61), into two cases.
% 175.17/129.54 |-Branch one:
% 175.17/129.54 | (67) all_0_0_0 = 0 & ~ (all_0_1_1 = 0)
% 175.17/129.54 |
% 175.17/129.54 | Applying alpha-rule on (67) yields:
% 175.17/129.54 | (68) all_0_0_0 = 0
% 175.17/129.54 | (69) ~ (all_0_1_1 = 0)
% 175.17/129.54 |
% 175.17/129.54 | From (68) and (22) follows:
% 175.17/129.54 | (70) minsol_model_max(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 175.17/129.54 |
% 175.17/129.54 +-Applying beta-rule and splitting (65), into two cases.
% 175.17/129.54 |-Branch one:
% 175.17/129.54 | (71) all_0_1_1 = 0
% 175.17/129.54 |
% 175.17/129.54 | Equations (71) can reduce 69 to:
% 175.17/129.54 | (72) $false
% 175.17/129.54 |
% 175.17/129.54 |-The branch is then unsatisfiable
% 175.17/129.54 |-Branch two:
% 175.17/129.54 | (69) ~ (all_0_1_1 = 0)
% 175.17/129.54 | (74) ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & model_ub(all_0_4_4, all_0_3_3, v0) = 0 & lesseq(all_0_2_2, v0) = v2) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = v0))
% 175.17/129.54 |
% 175.17/129.54 | Instantiating (74) with all_32_0_36, all_32_1_37, all_32_2_38 yields:
% 175.17/129.54 | (75) (all_32_1_37 = 0 & ~ (all_32_0_36 = 0) & model_ub(all_0_4_4, all_0_3_3, all_32_2_38) = 0 & lesseq(all_0_2_2, all_32_2_38) = all_32_0_36) | ( ~ (all_32_2_38 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_32_2_38)
% 175.17/129.54 |
% 175.17/129.54 | Instantiating formula (37) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms minsol_model_max(all_0_4_4, all_0_3_3, all_0_2_2) = 0, yields:
% 175.17/129.54 | (76) model_max(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 175.17/129.54 |
% 175.17/129.54 | Instantiating formula (6) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms model_max(all_0_4_4, all_0_3_3, all_0_2_2) = 0, yields:
% 175.17/129.54 | (77) max(all_0_4_4, all_0_3_3) = all_0_2_2
% 175.17/129.54 |
% 175.17/129.54 | Instantiating formula (49) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms max(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 175.17/129.54 | (78) all_0_2_2 = all_0_3_3 | ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_3_3) = v0)
% 175.17/129.54 |
% 175.17/129.54 | Instantiating formula (15) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms max(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 175.17/129.54 | (79) all_0_2_2 = all_0_4_4 | ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_4_4) = v0)
% 175.17/129.54 |
% 175.17/129.54 +-Applying beta-rule and splitting (75), into two cases.
% 175.17/129.54 |-Branch one:
% 175.17/129.54 | (80) all_32_1_37 = 0 & ~ (all_32_0_36 = 0) & model_ub(all_0_4_4, all_0_3_3, all_32_2_38) = 0 & lesseq(all_0_2_2, all_32_2_38) = all_32_0_36
% 175.17/129.54 |
% 175.17/129.54 | Applying alpha-rule on (80) yields:
% 175.17/129.54 | (81) all_32_1_37 = 0
% 175.17/129.54 | (82) ~ (all_32_0_36 = 0)
% 175.17/129.54 | (83) model_ub(all_0_4_4, all_0_3_3, all_32_2_38) = 0
% 175.17/129.54 | (84) lesseq(all_0_2_2, all_32_2_38) = all_32_0_36
% 175.17/129.54 |
% 175.17/129.54 | Instantiating formula (51) with all_32_2_38, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_32_2_38) = 0, yields:
% 175.17/129.54 | (85) ub(all_0_4_4, all_0_3_3, all_32_2_38) = 0
% 175.17/129.54 |
% 175.17/129.55 | Instantiating formula (16) with all_32_0_36, all_32_2_38, 0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms model_max(all_0_4_4, all_0_3_3, all_0_2_2) = 0, lesseq(all_0_2_2, all_32_2_38) = all_32_0_36, yields:
% 175.17/129.55 | (86) all_32_0_36 = 0 | ? [v0] : (( ~ (v0 = 0) & minsol_model_max(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_max(all_0_4_4, all_0_3_3, all_32_2_38) = v0))
% 175.17/129.55 |
% 175.17/129.55 | Instantiating formula (62) with all_32_0_36, all_32_2_38, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms minsol_model_max(all_0_4_4, all_0_3_3, all_0_2_2) = 0, lesseq(all_0_2_2, all_32_2_38) = all_32_0_36, yields:
% 175.17/129.55 | (87) all_32_0_36 = 0 | ? [v0] : ( ~ (v0 = 0) & model_max(all_0_4_4, all_0_3_3, all_32_2_38) = v0)
% 175.17/129.55 |
% 175.17/129.55 | Instantiating formula (42) with all_32_0_36, all_32_2_38, all_0_2_2 and discharging atoms lesseq(all_0_2_2, all_32_2_38) = all_32_0_36, yields:
% 175.17/129.55 | (88) all_32_0_36 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_32_2_38) = v1 & summation(all_0_2_2) = v0 & lesseq(v0, v1) = v2)
% 175.17/129.55 |
% 175.17/129.55 +-Applying beta-rule and splitting (88), into two cases.
% 175.17/129.55 |-Branch one:
% 175.17/129.55 | (89) all_32_0_36 = 0
% 175.17/129.55 |
% 175.17/129.55 | Equations (89) can reduce 82 to:
% 175.17/129.55 | (72) $false
% 175.17/129.55 |
% 175.17/129.55 |-The branch is then unsatisfiable
% 175.17/129.55 |-Branch two:
% 175.17/129.55 | (82) ~ (all_32_0_36 = 0)
% 175.17/129.55 | (92) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_32_2_38) = v1 & summation(all_0_2_2) = v0 & lesseq(v0, v1) = v2)
% 175.17/129.55 |
% 175.17/129.55 +-Applying beta-rule and splitting (86), into two cases.
% 175.17/129.55 |-Branch one:
% 175.17/129.55 | (89) all_32_0_36 = 0
% 175.17/129.55 |
% 175.17/129.55 | Equations (89) can reduce 82 to:
% 175.17/129.55 | (72) $false
% 175.17/129.55 |
% 175.17/129.55 |-The branch is then unsatisfiable
% 175.17/129.55 |-Branch two:
% 175.17/129.55 | (82) ~ (all_32_0_36 = 0)
% 175.17/129.55 | (96) ? [v0] : (( ~ (v0 = 0) & minsol_model_max(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_max(all_0_4_4, all_0_3_3, all_32_2_38) = v0))
% 175.17/129.55 |
% 175.17/129.55 +-Applying beta-rule and splitting (87), into two cases.
% 175.17/129.55 |-Branch one:
% 175.17/129.55 | (89) all_32_0_36 = 0
% 175.17/129.55 |
% 175.17/129.55 | Equations (89) can reduce 82 to:
% 175.17/129.55 | (72) $false
% 175.17/129.55 |
% 175.17/129.55 |-The branch is then unsatisfiable
% 175.17/129.55 |-Branch two:
% 175.17/129.55 | (82) ~ (all_32_0_36 = 0)
% 175.17/129.55 | (100) ? [v0] : ( ~ (v0 = 0) & model_max(all_0_4_4, all_0_3_3, all_32_2_38) = v0)
% 175.17/129.55 |
% 175.17/129.55 +-Applying beta-rule and splitting (78), into two cases.
% 175.17/129.55 |-Branch one:
% 175.17/129.55 | (101) all_0_2_2 = all_0_3_3
% 175.17/129.55 |
% 175.17/129.55 | From (101) and (84) follows:
% 175.17/129.55 | (102) lesseq(all_0_3_3, all_32_2_38) = all_32_0_36
% 175.17/129.55 |
% 175.17/129.55 | Instantiating formula (43) with all_32_2_38, all_0_3_3, all_0_4_4 and discharging atoms ub(all_0_4_4, all_0_3_3, all_32_2_38) = 0, yields:
% 175.17/129.55 | (103) lesseq(all_0_3_3, all_32_2_38) = 0 & lesseq(all_0_4_4, all_32_2_38) = 0
% 175.17/129.55 |
% 175.17/129.55 | Applying alpha-rule on (103) yields:
% 175.17/129.55 | (104) lesseq(all_0_3_3, all_32_2_38) = 0
% 175.17/129.55 | (105) lesseq(all_0_4_4, all_32_2_38) = 0
% 175.17/129.55 |
% 175.17/129.55 | Instantiating formula (11) with all_0_3_3, all_32_2_38, 0, all_32_0_36 and discharging atoms lesseq(all_0_3_3, all_32_2_38) = all_32_0_36, lesseq(all_0_3_3, all_32_2_38) = 0, yields:
% 175.17/129.55 | (89) all_32_0_36 = 0
% 175.17/129.55 |
% 175.17/129.55 | Equations (89) can reduce 82 to:
% 175.17/129.55 | (72) $false
% 175.17/129.55 |
% 175.17/129.55 |-The branch is then unsatisfiable
% 175.17/129.55 |-Branch two:
% 175.17/129.55 | (108) ~ (all_0_2_2 = all_0_3_3)
% 175.17/129.55 | (109) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_3_3) = v0)
% 175.17/129.55 |
% 175.17/129.55 | Instantiating (109) with all_201_0_237 yields:
% 175.17/129.55 | (110) ~ (all_201_0_237 = 0) & lesseq(all_0_4_4, all_0_3_3) = all_201_0_237
% 175.17/129.55 |
% 175.17/129.55 | Applying alpha-rule on (110) yields:
% 175.17/129.55 | (111) ~ (all_201_0_237 = 0)
% 175.17/129.55 | (112) lesseq(all_0_4_4, all_0_3_3) = all_201_0_237
% 175.17/129.55 |
% 175.17/129.55 +-Applying beta-rule and splitting (79), into two cases.
% 175.17/129.55 |-Branch one:
% 175.17/129.55 | (113) all_0_2_2 = all_0_4_4
% 175.17/129.55 |
% 175.17/129.55 | From (113) and (84) follows:
% 175.17/129.55 | (114) lesseq(all_0_4_4, all_32_2_38) = all_32_0_36
% 175.17/129.55 |
% 175.17/129.55 | Instantiating formula (43) with all_32_2_38, all_0_3_3, all_0_4_4 and discharging atoms ub(all_0_4_4, all_0_3_3, all_32_2_38) = 0, yields:
% 175.17/129.55 | (103) lesseq(all_0_3_3, all_32_2_38) = 0 & lesseq(all_0_4_4, all_32_2_38) = 0
% 175.17/129.55 |
% 175.17/129.55 | Applying alpha-rule on (103) yields:
% 175.17/129.55 | (104) lesseq(all_0_3_3, all_32_2_38) = 0
% 175.17/129.55 | (105) lesseq(all_0_4_4, all_32_2_38) = 0
% 175.17/129.55 |
% 175.17/129.55 | Instantiating formula (11) with all_0_4_4, all_32_2_38, 0, all_32_0_36 and discharging atoms lesseq(all_0_4_4, all_32_2_38) = all_32_0_36, lesseq(all_0_4_4, all_32_2_38) = 0, yields:
% 175.17/129.55 | (89) all_32_0_36 = 0
% 175.17/129.55 |
% 175.17/129.55 | Equations (89) can reduce 82 to:
% 175.17/129.55 | (72) $false
% 175.17/129.55 |
% 175.17/129.55 |-The branch is then unsatisfiable
% 175.17/129.55 |-Branch two:
% 175.17/129.55 | (120) ~ (all_0_2_2 = all_0_4_4)
% 175.17/129.55 | (121) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_4_4) = v0)
% 175.17/129.55 |
% 175.17/129.55 | Instantiating (121) with all_209_0_259 yields:
% 175.17/129.55 | (122) ~ (all_209_0_259 = 0) & lesseq(all_0_3_3, all_0_4_4) = all_209_0_259
% 175.17/129.55 |
% 175.17/129.55 | Applying alpha-rule on (122) yields:
% 175.17/129.55 | (123) ~ (all_209_0_259 = 0)
% 175.17/129.55 | (124) lesseq(all_0_3_3, all_0_4_4) = all_209_0_259
% 175.17/129.55 |
% 175.17/129.55 | Instantiating formula (10) with all_209_0_259, all_0_3_3, all_0_4_4 and discharging atoms lesseq(all_0_3_3, all_0_4_4) = all_209_0_259, yields:
% 175.17/129.55 | (125) all_209_0_259 = 0 | lesseq(all_0_4_4, all_0_3_3) = 0
% 175.17/129.55 |
% 175.17/129.55 | Instantiating formula (42) with all_201_0_237, all_0_3_3, all_0_4_4 and discharging atoms lesseq(all_0_4_4, all_0_3_3) = all_201_0_237, yields:
% 175.17/129.55 | (126) all_201_0_237 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_0_3_3) = v1 & summation(all_0_4_4) = v0 & lesseq(v0, v1) = v2)
% 175.17/129.55 |
% 175.17/129.55 +-Applying beta-rule and splitting (125), into two cases.
% 175.17/129.55 |-Branch one:
% 175.17/129.55 | (127) lesseq(all_0_4_4, all_0_3_3) = 0
% 175.17/129.55 |
% 175.17/129.55 +-Applying beta-rule and splitting (126), into two cases.
% 175.17/129.55 |-Branch one:
% 175.17/129.55 | (128) all_201_0_237 = 0
% 175.17/129.55 |
% 175.17/129.55 | Equations (128) can reduce 111 to:
% 175.17/129.55 | (72) $false
% 175.17/129.55 |
% 175.17/129.55 |-The branch is then unsatisfiable
% 175.17/129.55 |-Branch two:
% 175.17/129.55 | (111) ~ (all_201_0_237 = 0)
% 175.17/129.55 | (131) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_0_3_3) = v1 & summation(all_0_4_4) = v0 & lesseq(v0, v1) = v2)
% 175.17/129.55 |
% 175.17/129.55 | Instantiating formula (11) with all_0_4_4, all_0_3_3, 0, all_201_0_237 and discharging atoms lesseq(all_0_4_4, all_0_3_3) = all_201_0_237, lesseq(all_0_4_4, all_0_3_3) = 0, yields:
% 175.17/129.55 | (128) all_201_0_237 = 0
% 175.17/129.55 |
% 175.17/129.55 | Equations (128) can reduce 111 to:
% 175.17/129.55 | (72) $false
% 175.17/129.55 |
% 175.17/129.55 |-The branch is then unsatisfiable
% 175.17/129.55 |-Branch two:
% 175.17/129.55 | (134) ~ (lesseq(all_0_4_4, all_0_3_3) = 0)
% 175.17/129.56 | (135) all_209_0_259 = 0
% 175.43/129.56 |
% 175.43/129.56 | Equations (135) can reduce 123 to:
% 175.43/129.56 | (72) $false
% 175.43/129.56 |
% 175.43/129.56 |-The branch is then unsatisfiable
% 175.43/129.56 |-Branch two:
% 175.43/129.56 | (137) ~ (all_32_2_38 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_32_2_38
% 175.43/129.56 |
% 175.43/129.56 | Applying alpha-rule on (137) yields:
% 175.43/129.56 | (138) ~ (all_32_2_38 = 0)
% 175.43/129.56 | (139) model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_32_2_38
% 175.43/129.56 |
% 175.43/129.56 | Instantiating formula (35) with all_32_2_38, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_32_2_38, yields:
% 175.43/129.56 | (140) all_32_2_38 = 0 | ? [v0] : ( ~ (v0 = 0) & ub(all_0_4_4, all_0_3_3, all_0_2_2) = v0)
% 175.43/129.56 |
% 175.43/129.56 +-Applying beta-rule and splitting (140), into two cases.
% 175.43/129.56 |-Branch one:
% 175.43/129.56 | (141) all_32_2_38 = 0
% 175.43/129.56 |
% 175.43/129.56 | Equations (141) can reduce 138 to:
% 175.43/129.56 | (72) $false
% 175.43/129.56 |
% 175.43/129.56 |-The branch is then unsatisfiable
% 175.43/129.56 |-Branch two:
% 175.43/129.56 | (138) ~ (all_32_2_38 = 0)
% 175.43/129.56 | (144) ? [v0] : ( ~ (v0 = 0) & ub(all_0_4_4, all_0_3_3, all_0_2_2) = v0)
% 175.43/129.56 |
% 175.43/129.56 | Instantiating (144) with all_165_0_278 yields:
% 175.43/129.56 | (145) ~ (all_165_0_278 = 0) & ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_165_0_278
% 175.43/129.56 |
% 175.43/129.56 | Applying alpha-rule on (145) yields:
% 175.43/129.56 | (146) ~ (all_165_0_278 = 0)
% 175.43/129.56 | (147) ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_165_0_278
% 175.43/129.56 |
% 175.43/129.56 +-Applying beta-rule and splitting (79), into two cases.
% 175.43/129.56 |-Branch one:
% 175.43/129.56 | (113) all_0_2_2 = all_0_4_4
% 175.43/129.56 |
% 175.43/129.56 | From (113) and (147) follows:
% 175.43/129.56 | (149) ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_165_0_278
% 175.43/129.56 |
% 175.43/129.56 +-Applying beta-rule and splitting (78), into two cases.
% 175.43/129.56 |-Branch one:
% 175.43/129.56 | (101) all_0_2_2 = all_0_3_3
% 175.43/129.56 |
% 175.43/129.56 | Combining equations (101,113) yields a new equation:
% 175.43/129.56 | (151) all_0_3_3 = all_0_4_4
% 175.43/129.56 |
% 175.43/129.56 | Simplifying 151 yields:
% 175.43/129.56 | (152) all_0_3_3 = all_0_4_4
% 175.43/129.56 |
% 175.43/129.56 | From (152) and (149) follows:
% 175.43/129.56 | (153) ub(all_0_4_4, all_0_4_4, all_0_4_4) = all_165_0_278
% 175.43/129.56 |
% 175.43/129.56 | Instantiating formula (5) with all_165_0_278, all_0_4_4, all_0_4_4, all_0_4_4 and discharging atoms ub(all_0_4_4, all_0_4_4, all_0_4_4) = all_165_0_278, yields:
% 175.43/129.56 | (154) all_165_0_278 = 0 | ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_4_4) = v0)
% 175.43/129.56 |
% 175.43/129.56 +-Applying beta-rule and splitting (154), into two cases.
% 175.43/129.56 |-Branch one:
% 175.43/129.56 | (155) all_165_0_278 = 0
% 175.43/129.56 |
% 175.43/129.56 | Equations (155) can reduce 146 to:
% 175.43/129.56 | (72) $false
% 175.43/129.56 |
% 175.43/129.56 |-The branch is then unsatisfiable
% 175.43/129.56 |-Branch two:
% 175.43/129.56 | (146) ~ (all_165_0_278 = 0)
% 175.43/129.56 | (158) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_4_4) = v0)
% 175.43/129.56 |
% 175.43/129.56 | Instantiating (158) with all_202_0_429 yields:
% 175.43/129.56 | (159) ~ (all_202_0_429 = 0) & lesseq(all_0_4_4, all_0_4_4) = all_202_0_429
% 175.43/129.56 |
% 175.43/129.56 | Applying alpha-rule on (159) yields:
% 175.43/129.56 | (160) ~ (all_202_0_429 = 0)
% 175.43/129.56 | (161) lesseq(all_0_4_4, all_0_4_4) = all_202_0_429
% 175.43/129.56 |
% 175.43/129.56 | Instantiating formula (56) with all_202_0_429, all_0_4_4 and discharging atoms lesseq(all_0_4_4, all_0_4_4) = all_202_0_429, yields:
% 175.43/129.56 | (162) all_202_0_429 = 0
% 175.43/129.56 |
% 175.43/129.56 | Equations (162) can reduce 160 to:
% 175.43/129.56 | (72) $false
% 175.43/129.56 |
% 175.43/129.56 |-The branch is then unsatisfiable
% 175.43/129.56 |-Branch two:
% 175.43/129.56 | (108) ~ (all_0_2_2 = all_0_3_3)
% 175.43/129.56 | (109) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_3_3) = v0)
% 175.43/129.56 |
% 175.43/129.56 | Instantiating (109) with all_189_0_433 yields:
% 175.43/129.56 | (166) ~ (all_189_0_433 = 0) & lesseq(all_0_4_4, all_0_3_3) = all_189_0_433
% 175.43/129.56 |
% 175.43/129.56 | Applying alpha-rule on (166) yields:
% 175.43/129.56 | (167) ~ (all_189_0_433 = 0)
% 175.43/129.56 | (168) lesseq(all_0_4_4, all_0_3_3) = all_189_0_433
% 175.43/129.56 |
% 175.43/129.56 | Instantiating formula (5) with all_165_0_278, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_165_0_278, yields:
% 175.43/129.56 | (169) all_165_0_278 = 0 | ? [v0] : (( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_4_4) = v0))
% 175.43/129.56 |
% 175.43/129.56 | Instantiating formula (10) with all_189_0_433, all_0_4_4, all_0_3_3 and discharging atoms lesseq(all_0_4_4, all_0_3_3) = all_189_0_433, yields:
% 175.43/129.56 | (170) all_189_0_433 = 0 | lesseq(all_0_3_3, all_0_4_4) = 0
% 175.43/129.56 |
% 175.43/129.56 +-Applying beta-rule and splitting (170), into two cases.
% 175.43/129.56 |-Branch one:
% 175.43/129.56 | (171) lesseq(all_0_3_3, all_0_4_4) = 0
% 175.43/129.56 |
% 175.43/129.56 +-Applying beta-rule and splitting (169), into two cases.
% 175.43/129.56 |-Branch one:
% 175.43/129.56 | (155) all_165_0_278 = 0
% 175.43/129.56 |
% 175.43/129.56 | Equations (155) can reduce 146 to:
% 175.43/129.56 | (72) $false
% 175.43/129.56 |
% 175.43/129.56 |-The branch is then unsatisfiable
% 175.43/129.56 |-Branch two:
% 175.43/129.56 | (146) ~ (all_165_0_278 = 0)
% 175.43/129.56 | (175) ? [v0] : (( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_4_4) = v0))
% 175.43/129.56 |
% 175.43/129.56 | Instantiating (175) with all_207_0_439 yields:
% 175.43/129.56 | (176) ( ~ (all_207_0_439 = 0) & lesseq(all_0_3_3, all_0_4_4) = all_207_0_439) | ( ~ (all_207_0_439 = 0) & lesseq(all_0_4_4, all_0_4_4) = all_207_0_439)
% 175.43/129.56 |
% 175.43/129.56 +-Applying beta-rule and splitting (176), into two cases.
% 175.43/129.56 |-Branch one:
% 175.43/129.56 | (177) ~ (all_207_0_439 = 0) & lesseq(all_0_3_3, all_0_4_4) = all_207_0_439
% 175.43/129.56 |
% 175.43/129.56 | Applying alpha-rule on (177) yields:
% 175.43/129.56 | (178) ~ (all_207_0_439 = 0)
% 175.43/129.57 | (179) lesseq(all_0_3_3, all_0_4_4) = all_207_0_439
% 175.43/129.57 |
% 175.43/129.57 | Instantiating formula (11) with all_0_3_3, all_0_4_4, 0, all_207_0_439 and discharging atoms lesseq(all_0_3_3, all_0_4_4) = all_207_0_439, lesseq(all_0_3_3, all_0_4_4) = 0, yields:
% 175.43/129.57 | (180) all_207_0_439 = 0
% 175.43/129.57 |
% 175.43/129.57 | Equations (180) can reduce 178 to:
% 175.43/129.57 | (72) $false
% 175.43/129.57 |
% 175.43/129.57 |-The branch is then unsatisfiable
% 175.43/129.57 |-Branch two:
% 175.43/129.57 | (182) ~ (all_207_0_439 = 0) & lesseq(all_0_4_4, all_0_4_4) = all_207_0_439
% 175.43/129.57 |
% 175.43/129.57 | Applying alpha-rule on (182) yields:
% 175.43/129.57 | (178) ~ (all_207_0_439 = 0)
% 175.43/129.57 | (184) lesseq(all_0_4_4, all_0_4_4) = all_207_0_439
% 175.43/129.57 |
% 175.43/129.57 | Instantiating formula (56) with all_207_0_439, all_0_4_4 and discharging atoms lesseq(all_0_4_4, all_0_4_4) = all_207_0_439, yields:
% 175.43/129.57 | (180) all_207_0_439 = 0
% 175.43/129.57 |
% 175.43/129.57 | Equations (180) can reduce 178 to:
% 175.43/129.57 | (72) $false
% 175.43/129.57 |
% 175.43/129.57 |-The branch is then unsatisfiable
% 175.43/129.57 |-Branch two:
% 175.43/129.57 | (187) ~ (lesseq(all_0_3_3, all_0_4_4) = 0)
% 175.43/129.57 | (188) all_189_0_433 = 0
% 175.43/129.57 |
% 175.43/129.57 | Equations (188) can reduce 167 to:
% 175.43/129.57 | (72) $false
% 175.43/129.57 |
% 175.43/129.57 |-The branch is then unsatisfiable
% 175.43/129.57 |-Branch two:
% 175.43/129.57 | (120) ~ (all_0_2_2 = all_0_4_4)
% 175.43/129.57 | (121) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_4_4) = v0)
% 175.43/129.57 |
% 175.43/129.57 | Instantiating (121) with all_183_0_457 yields:
% 175.43/129.57 | (192) ~ (all_183_0_457 = 0) & lesseq(all_0_3_3, all_0_4_4) = all_183_0_457
% 175.43/129.57 |
% 175.43/129.57 | Applying alpha-rule on (192) yields:
% 175.43/129.57 | (193) ~ (all_183_0_457 = 0)
% 175.43/129.57 | (194) lesseq(all_0_3_3, all_0_4_4) = all_183_0_457
% 175.43/129.57 |
% 175.43/129.57 +-Applying beta-rule and splitting (78), into two cases.
% 175.43/129.57 |-Branch one:
% 175.43/129.57 | (101) all_0_2_2 = all_0_3_3
% 175.43/129.57 |
% 175.43/129.57 | From (101) and (147) follows:
% 175.43/129.57 | (196) ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_165_0_278
% 175.43/129.57 |
% 175.43/129.57 | Instantiating formula (5) with all_165_0_278, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_165_0_278, yields:
% 175.43/129.57 | (197) all_165_0_278 = 0 | ? [v0] : (( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_3_3) = v0))
% 175.43/129.57 |
% 175.43/129.57 | Instantiating formula (10) with all_183_0_457, all_0_3_3, all_0_4_4 and discharging atoms lesseq(all_0_3_3, all_0_4_4) = all_183_0_457, yields:
% 175.43/129.57 | (198) all_183_0_457 = 0 | lesseq(all_0_4_4, all_0_3_3) = 0
% 175.43/129.57 |
% 175.43/129.57 +-Applying beta-rule and splitting (198), into two cases.
% 175.43/129.57 |-Branch one:
% 175.43/129.57 | (127) lesseq(all_0_4_4, all_0_3_3) = 0
% 175.43/129.57 |
% 175.43/129.57 +-Applying beta-rule and splitting (197), into two cases.
% 175.43/129.57 |-Branch one:
% 175.43/129.57 | (155) all_165_0_278 = 0
% 175.43/129.57 |
% 175.43/129.57 | Equations (155) can reduce 146 to:
% 175.43/129.57 | (72) $false
% 175.43/129.57 |
% 175.43/129.57 |-The branch is then unsatisfiable
% 175.43/129.57 |-Branch two:
% 175.43/129.57 | (146) ~ (all_165_0_278 = 0)
% 175.43/129.57 | (203) ? [v0] : (( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_3_3) = v0))
% 175.43/129.57 |
% 175.43/129.57 | Instantiating (203) with all_207_0_463 yields:
% 175.43/129.57 | (204) ( ~ (all_207_0_463 = 0) & lesseq(all_0_3_3, all_0_3_3) = all_207_0_463) | ( ~ (all_207_0_463 = 0) & lesseq(all_0_4_4, all_0_3_3) = all_207_0_463)
% 175.43/129.57 |
% 175.43/129.57 +-Applying beta-rule and splitting (204), into two cases.
% 175.43/129.57 |-Branch one:
% 175.43/129.57 | (205) ~ (all_207_0_463 = 0) & lesseq(all_0_3_3, all_0_3_3) = all_207_0_463
% 175.43/129.57 |
% 175.43/129.57 | Applying alpha-rule on (205) yields:
% 175.43/129.57 | (206) ~ (all_207_0_463 = 0)
% 175.43/129.57 | (207) lesseq(all_0_3_3, all_0_3_3) = all_207_0_463
% 175.43/129.57 |
% 175.43/129.57 | Instantiating formula (56) with all_207_0_463, all_0_3_3 and discharging atoms lesseq(all_0_3_3, all_0_3_3) = all_207_0_463, yields:
% 175.43/129.57 | (208) all_207_0_463 = 0
% 175.43/129.57 |
% 175.43/129.57 | Equations (208) can reduce 206 to:
% 175.43/129.57 | (72) $false
% 175.43/129.57 |
% 175.43/129.57 |-The branch is then unsatisfiable
% 175.43/129.57 |-Branch two:
% 175.43/129.57 | (210) ~ (all_207_0_463 = 0) & lesseq(all_0_4_4, all_0_3_3) = all_207_0_463
% 175.43/129.57 |
% 175.43/129.57 | Applying alpha-rule on (210) yields:
% 175.43/129.57 | (206) ~ (all_207_0_463 = 0)
% 175.43/129.57 | (212) lesseq(all_0_4_4, all_0_3_3) = all_207_0_463
% 175.43/129.57 |
% 175.43/129.57 | Instantiating formula (11) with all_0_4_4, all_0_3_3, 0, all_207_0_463 and discharging atoms lesseq(all_0_4_4, all_0_3_3) = all_207_0_463, lesseq(all_0_4_4, all_0_3_3) = 0, yields:
% 175.43/129.57 | (208) all_207_0_463 = 0
% 175.43/129.57 |
% 175.43/129.57 | Equations (208) can reduce 206 to:
% 175.43/129.57 | (72) $false
% 175.43/129.57 |
% 175.43/129.57 |-The branch is then unsatisfiable
% 175.43/129.57 |-Branch two:
% 175.43/129.57 | (134) ~ (lesseq(all_0_4_4, all_0_3_3) = 0)
% 175.43/129.57 | (216) all_183_0_457 = 0
% 175.43/129.57 |
% 175.43/129.57 | Equations (216) can reduce 193 to:
% 175.43/129.57 | (72) $false
% 175.43/129.57 |
% 175.43/129.57 |-The branch is then unsatisfiable
% 175.43/129.57 |-Branch two:
% 175.43/129.57 | (108) ~ (all_0_2_2 = all_0_3_3)
% 175.43/129.57 | (109) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_3_3) = v0)
% 175.43/129.57 |
% 175.43/129.57 | Instantiating (109) with all_191_0_481 yields:
% 175.43/129.57 | (220) ~ (all_191_0_481 = 0) & lesseq(all_0_4_4, all_0_3_3) = all_191_0_481
% 175.43/129.57 |
% 175.43/129.57 | Applying alpha-rule on (220) yields:
% 175.43/129.57 | (221) ~ (all_191_0_481 = 0)
% 175.43/129.57 | (222) lesseq(all_0_4_4, all_0_3_3) = all_191_0_481
% 175.43/129.57 |
% 175.43/129.57 | Instantiating formula (42) with all_183_0_457, all_0_4_4, all_0_3_3 and discharging atoms lesseq(all_0_3_3, all_0_4_4) = all_183_0_457, yields:
% 175.43/129.57 | (223) all_183_0_457 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_0_3_3) = v0 & summation(all_0_4_4) = v1 & lesseq(v0, v1) = v2)
% 175.43/129.58 |
% 175.43/129.58 | Instantiating formula (10) with all_191_0_481, all_0_4_4, all_0_3_3 and discharging atoms lesseq(all_0_4_4, all_0_3_3) = all_191_0_481, yields:
% 175.43/129.58 | (224) all_191_0_481 = 0 | lesseq(all_0_3_3, all_0_4_4) = 0
% 175.43/129.58 |
% 175.43/129.58 +-Applying beta-rule and splitting (224), into two cases.
% 175.43/129.58 |-Branch one:
% 175.43/129.58 | (171) lesseq(all_0_3_3, all_0_4_4) = 0
% 175.43/129.58 |
% 175.43/129.58 +-Applying beta-rule and splitting (223), into two cases.
% 175.43/129.58 |-Branch one:
% 175.43/129.58 | (216) all_183_0_457 = 0
% 175.43/129.58 |
% 175.43/129.58 | Equations (216) can reduce 193 to:
% 175.43/129.58 | (72) $false
% 175.43/129.58 |
% 175.43/129.58 |-The branch is then unsatisfiable
% 175.43/129.58 |-Branch two:
% 175.43/129.58 | (193) ~ (all_183_0_457 = 0)
% 175.43/129.58 | (229) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_0_3_3) = v0 & summation(all_0_4_4) = v1 & lesseq(v0, v1) = v2)
% 175.43/129.58 |
% 175.43/129.58 | Instantiating formula (11) with all_0_3_3, all_0_4_4, 0, all_183_0_457 and discharging atoms lesseq(all_0_3_3, all_0_4_4) = all_183_0_457, lesseq(all_0_3_3, all_0_4_4) = 0, yields:
% 175.43/129.58 | (216) all_183_0_457 = 0
% 175.43/129.58 |
% 175.43/129.58 | Equations (216) can reduce 193 to:
% 175.43/129.58 | (72) $false
% 175.43/129.58 |
% 175.43/129.58 |-The branch is then unsatisfiable
% 175.43/129.58 |-Branch two:
% 175.43/129.58 | (187) ~ (lesseq(all_0_3_3, all_0_4_4) = 0)
% 175.43/129.58 | (233) all_191_0_481 = 0
% 175.43/129.58 |
% 175.43/129.58 | Equations (233) can reduce 221 to:
% 175.43/129.58 | (72) $false
% 175.43/129.58 |
% 175.43/129.58 |-The branch is then unsatisfiable
% 175.43/129.58 |-Branch two:
% 175.43/129.58 | (235) all_0_1_1 = 0 & ~ (all_0_0_0 = 0)
% 175.43/129.58 |
% 175.43/129.58 | Applying alpha-rule on (235) yields:
% 175.43/129.58 | (71) all_0_1_1 = 0
% 175.43/129.58 | (237) ~ (all_0_0_0 = 0)
% 175.43/129.58 |
% 175.43/129.58 | From (71) and (3) follows:
% 175.43/129.58 | (238) minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 175.43/129.58 |
% 175.43/129.58 +-Applying beta-rule and splitting (66), into two cases.
% 175.43/129.58 |-Branch one:
% 175.43/129.58 | (68) all_0_0_0 = 0
% 175.43/129.58 |
% 175.43/129.58 | Equations (68) can reduce 237 to:
% 175.43/129.58 | (72) $false
% 175.43/129.58 |
% 175.43/129.58 |-The branch is then unsatisfiable
% 175.43/129.58 |-Branch two:
% 175.43/129.58 | (237) ~ (all_0_0_0 = 0)
% 175.43/129.58 | (242) ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & model_max(all_0_4_4, all_0_3_3, v0) = 0 & lesseq(all_0_2_2, v0) = v2) | ( ~ (v0 = 0) & model_max(all_0_4_4, all_0_3_3, all_0_2_2) = v0))
% 175.43/129.58 |
% 175.43/129.58 | Instantiating (242) with all_32_0_491, all_32_1_492, all_32_2_493 yields:
% 175.43/129.58 | (243) (all_32_1_492 = 0 & ~ (all_32_0_491 = 0) & model_max(all_0_4_4, all_0_3_3, all_32_2_493) = 0 & lesseq(all_0_2_2, all_32_2_493) = all_32_0_491) | ( ~ (all_32_2_493 = 0) & model_max(all_0_4_4, all_0_3_3, all_0_2_2) = all_32_2_493)
% 175.43/129.58 |
% 175.43/129.58 | Instantiating formula (14) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, yields:
% 175.43/129.58 | (244) model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 175.43/129.58 |
% 175.43/129.58 | Instantiating formula (51) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, yields:
% 175.43/129.58 | (245) ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 175.43/129.58 |
% 175.43/129.58 | Instantiating formula (18) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, yields:
% 175.43/129.58 | (246) ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & model_ub(all_0_4_4, all_0_3_3, v0) = 0 & lesseq(all_0_2_2, v0) = v2) | (v0 = 0 & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0))
% 175.43/129.58 |
% 175.43/129.58 | Instantiating (246) with all_46_0_495, all_46_1_496, all_46_2_497 yields:
% 175.43/129.58 | (247) (all_46_1_496 = 0 & ~ (all_46_0_495 = 0) & model_ub(all_0_4_4, all_0_3_3, all_46_2_497) = 0 & lesseq(all_0_2_2, all_46_2_497) = all_46_0_495) | (all_46_2_497 = 0 & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0)
% 175.43/129.58 |
% 175.43/129.58 | Instantiating formula (43) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, yields:
% 175.43/129.58 | (248) lesseq(all_0_3_3, all_0_2_2) = 0 & lesseq(all_0_4_4, all_0_2_2) = 0
% 175.43/129.58 |
% 175.43/129.58 | Applying alpha-rule on (248) yields:
% 175.43/129.58 | (249) lesseq(all_0_3_3, all_0_2_2) = 0
% 175.43/129.58 | (250) lesseq(all_0_4_4, all_0_2_2) = 0
% 175.43/129.58 |
% 175.43/129.58 | Instantiating formula (23) with all_0_3_3, all_0_2_2 and discharging atoms lesseq(all_0_3_3, all_0_2_2) = 0, yields:
% 175.43/129.58 | (251) max(all_0_2_2, all_0_3_3) = all_0_2_2
% 175.43/129.58 |
% 175.43/129.58 | Instantiating formula (32) with all_0_2_2, all_0_3_3 and discharging atoms lesseq(all_0_3_3, all_0_2_2) = 0, yields:
% 175.43/129.58 | (252) max(all_0_3_3, all_0_2_2) = all_0_2_2
% 175.43/129.58 |
% 175.43/129.58 | Instantiating formula (32) with all_0_2_2, all_0_4_4 and discharging atoms lesseq(all_0_4_4, all_0_2_2) = 0, yields:
% 175.43/129.58 | (253) max(all_0_4_4, all_0_2_2) = all_0_2_2
% 175.43/129.58 |
% 175.43/129.58 | Instantiating formula (15) with all_0_2_2, all_0_2_2, all_0_3_3 and discharging atoms max(all_0_3_3, all_0_2_2) = all_0_2_2, yields:
% 175.43/129.58 | (254) all_0_2_2 = all_0_3_3 | ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_2_2, all_0_3_3) = v0)
% 175.43/129.58 |
% 175.43/129.58 | Instantiating formula (15) with all_0_2_2, all_0_2_2, all_0_4_4 and discharging atoms max(all_0_4_4, all_0_2_2) = all_0_2_2, yields:
% 175.43/129.58 | (255) all_0_2_2 = all_0_4_4 | ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_2_2, all_0_4_4) = v0)
% 175.43/129.58 |
% 175.43/129.58 +-Applying beta-rule and splitting (243), into two cases.
% 175.43/129.58 |-Branch one:
% 175.43/129.58 | (256) all_32_1_492 = 0 & ~ (all_32_0_491 = 0) & model_max(all_0_4_4, all_0_3_3, all_32_2_493) = 0 & lesseq(all_0_2_2, all_32_2_493) = all_32_0_491
% 175.43/129.58 |
% 175.43/129.58 | Applying alpha-rule on (256) yields:
% 175.43/129.58 | (257) all_32_1_492 = 0
% 175.43/129.58 | (258) ~ (all_32_0_491 = 0)
% 175.43/129.58 | (259) model_max(all_0_4_4, all_0_3_3, all_32_2_493) = 0
% 175.43/129.59 | (260) lesseq(all_0_2_2, all_32_2_493) = all_32_0_491
% 175.43/129.59 |
% 175.43/129.59 | Instantiating formula (19) with all_32_2_493, 0, all_32_2_493, all_0_3_3, all_0_4_4 and discharging atoms model_max(all_0_4_4, all_0_3_3, all_32_2_493) = 0, yields:
% 175.43/129.59 | (261) ? [v0] : ((v0 = 0 & lesseq(all_32_2_493, all_32_2_493) = 0) | ( ~ (v0 = 0) & minsol_model_max(all_0_4_4, all_0_3_3, all_32_2_493) = v0))
% 175.43/129.59 |
% 175.43/129.59 | Instantiating formula (6) with all_32_2_493, all_0_3_3, all_0_4_4 and discharging atoms model_max(all_0_4_4, all_0_3_3, all_32_2_493) = 0, yields:
% 175.43/129.59 | (262) max(all_0_4_4, all_0_3_3) = all_32_2_493
% 175.43/129.59 |
% 175.43/129.59 | Instantiating formula (45) with all_32_2_493, all_0_3_3, all_0_4_4 and discharging atoms model_max(all_0_4_4, all_0_3_3, all_32_2_493) = 0, yields:
% 175.43/129.59 | (263) ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & model_max(all_0_4_4, all_0_3_3, v0) = 0 & lesseq(all_32_2_493, v0) = v2) | (v0 = 0 & minsol_model_max(all_0_4_4, all_0_3_3, all_32_2_493) = 0))
% 175.43/129.59 |
% 175.43/129.59 | Instantiating formula (33) with all_32_0_491, all_32_2_493, 0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, lesseq(all_0_2_2, all_32_2_493) = all_32_0_491, yields:
% 175.43/129.59 | (264) all_32_0_491 = 0 | ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = v0))
% 175.43/129.59 |
% 175.43/129.59 | Instantiating formula (39) with all_32_0_491, all_32_2_493, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, lesseq(all_0_2_2, all_32_2_493) = all_32_0_491, yields:
% 175.43/129.59 | (265) all_32_0_491 = 0 | ? [v0] : ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = v0)
% 175.43/129.59 |
% 175.43/129.59 | Instantiating formula (10) with all_32_0_491, all_0_2_2, all_32_2_493 and discharging atoms lesseq(all_0_2_2, all_32_2_493) = all_32_0_491, yields:
% 175.43/129.59 | (266) all_32_0_491 = 0 | lesseq(all_32_2_493, all_0_2_2) = 0
% 175.43/129.59 |
% 175.43/129.59 | Instantiating formula (42) with all_32_0_491, all_32_2_493, all_0_2_2 and discharging atoms lesseq(all_0_2_2, all_32_2_493) = all_32_0_491, yields:
% 175.43/129.59 | (267) all_32_0_491 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_32_2_493) = v1 & summation(all_0_2_2) = v0 & lesseq(v0, v1) = v2)
% 175.43/129.59 |
% 175.43/129.59 | Instantiating (263) with all_157_0_532, all_157_1_533, all_157_2_534 yields:
% 175.43/129.59 | (268) (all_157_1_533 = 0 & ~ (all_157_0_532 = 0) & model_max(all_0_4_4, all_0_3_3, all_157_2_534) = 0 & lesseq(all_32_2_493, all_157_2_534) = all_157_0_532) | (all_157_2_534 = 0 & minsol_model_max(all_0_4_4, all_0_3_3, all_32_2_493) = 0)
% 175.43/129.59 |
% 175.43/129.59 | Instantiating (261) with all_162_0_539 yields:
% 175.43/129.59 | (269) (all_162_0_539 = 0 & lesseq(all_32_2_493, all_32_2_493) = 0) | ( ~ (all_162_0_539 = 0) & minsol_model_max(all_0_4_4, all_0_3_3, all_32_2_493) = all_162_0_539)
% 175.43/129.59 |
% 175.43/129.59 +-Applying beta-rule and splitting (266), into two cases.
% 175.43/129.59 |-Branch one:
% 175.43/129.59 | (270) lesseq(all_32_2_493, all_0_2_2) = 0
% 175.43/129.59 |
% 175.43/129.59 +-Applying beta-rule and splitting (267), into two cases.
% 175.43/129.59 |-Branch one:
% 175.43/129.59 | (271) all_32_0_491 = 0
% 175.43/129.59 |
% 175.43/129.59 | Equations (271) can reduce 258 to:
% 175.43/129.59 | (72) $false
% 175.43/129.59 |
% 175.43/129.59 |-The branch is then unsatisfiable
% 175.43/129.59 |-Branch two:
% 175.43/129.59 | (258) ~ (all_32_0_491 = 0)
% 175.43/129.59 | (274) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_32_2_493) = v1 & summation(all_0_2_2) = v0 & lesseq(v0, v1) = v2)
% 175.43/129.59 |
% 175.43/129.59 +-Applying beta-rule and splitting (265), into two cases.
% 175.43/129.59 |-Branch one:
% 175.43/129.59 | (271) all_32_0_491 = 0
% 175.43/129.59 |
% 175.43/129.59 | Equations (271) can reduce 258 to:
% 175.43/129.59 | (72) $false
% 175.43/129.59 |
% 175.43/129.59 |-The branch is then unsatisfiable
% 175.43/129.59 |-Branch two:
% 175.43/129.59 | (258) ~ (all_32_0_491 = 0)
% 175.43/129.59 | (278) ? [v0] : ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = v0)
% 175.43/129.59 |
% 175.43/129.59 | Instantiating (278) with all_176_0_543 yields:
% 175.43/129.59 | (279) ~ (all_176_0_543 = 0) & model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = all_176_0_543
% 175.43/129.59 |
% 175.43/129.59 | Applying alpha-rule on (279) yields:
% 175.43/129.59 | (280) ~ (all_176_0_543 = 0)
% 175.43/129.59 | (281) model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = all_176_0_543
% 175.43/129.59 |
% 175.43/129.59 +-Applying beta-rule and splitting (264), into two cases.
% 175.43/129.59 |-Branch one:
% 175.43/129.59 | (271) all_32_0_491 = 0
% 175.43/129.59 |
% 175.43/129.59 | Equations (271) can reduce 258 to:
% 175.43/129.59 | (72) $false
% 175.43/129.59 |
% 175.43/129.59 |-The branch is then unsatisfiable
% 175.43/129.59 |-Branch two:
% 175.43/129.59 | (258) ~ (all_32_0_491 = 0)
% 175.43/129.59 | (285) ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = v0))
% 175.43/129.59 |
% 175.43/129.59 | Instantiating (285) with all_181_0_544 yields:
% 175.43/129.59 | (286) ( ~ (all_181_0_544 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_181_0_544) | ( ~ (all_181_0_544 = 0) & model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = all_181_0_544)
% 175.43/129.59 |
% 175.43/129.59 +-Applying beta-rule and splitting (286), into two cases.
% 175.43/129.59 |-Branch one:
% 175.43/129.59 | (287) ~ (all_181_0_544 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_181_0_544
% 175.43/129.59 |
% 175.43/129.59 | Applying alpha-rule on (287) yields:
% 175.43/129.59 | (288) ~ (all_181_0_544 = 0)
% 175.43/129.59 | (289) minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_181_0_544
% 175.43/129.59 |
% 175.43/129.59 | Instantiating formula (12) with all_0_4_4, all_0_3_3, all_0_2_2, all_181_0_544, 0 and discharging atoms minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_181_0_544, minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, yields:
% 175.43/129.59 | (290) all_181_0_544 = 0
% 175.43/129.59 |
% 175.43/129.59 | Equations (290) can reduce 288 to:
% 175.43/129.59 | (72) $false
% 175.43/129.59 |
% 175.43/129.59 |-The branch is then unsatisfiable
% 175.43/129.59 |-Branch two:
% 175.43/129.59 | (292) ~ (all_181_0_544 = 0) & model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = all_181_0_544
% 175.43/129.59 |
% 175.43/129.60 | Applying alpha-rule on (292) yields:
% 175.43/129.60 | (288) ~ (all_181_0_544 = 0)
% 175.43/129.60 | (294) model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = all_181_0_544
% 175.43/129.60 |
% 175.43/129.60 | Instantiating formula (52) with all_0_4_4, all_0_3_3, all_32_2_493, all_176_0_543, all_181_0_544 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = all_181_0_544, model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = all_176_0_543, yields:
% 175.43/129.60 | (295) all_181_0_544 = all_176_0_543
% 175.43/129.60 |
% 175.43/129.60 | Equations (295) can reduce 288 to:
% 175.43/129.60 | (280) ~ (all_176_0_543 = 0)
% 175.43/129.60 |
% 175.43/129.60 | From (295) and (294) follows:
% 175.43/129.60 | (281) model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = all_176_0_543
% 175.43/129.60 |
% 175.43/129.60 +-Applying beta-rule and splitting (247), into two cases.
% 175.43/129.60 |-Branch one:
% 175.43/129.60 | (298) all_46_1_496 = 0 & ~ (all_46_0_495 = 0) & model_ub(all_0_4_4, all_0_3_3, all_46_2_497) = 0 & lesseq(all_0_2_2, all_46_2_497) = all_46_0_495
% 175.43/129.60 |
% 175.43/129.60 | Applying alpha-rule on (298) yields:
% 175.43/129.60 | (299) all_46_1_496 = 0
% 175.43/129.60 | (300) ~ (all_46_0_495 = 0)
% 175.43/129.60 | (301) model_ub(all_0_4_4, all_0_3_3, all_46_2_497) = 0
% 175.43/129.60 | (302) lesseq(all_0_2_2, all_46_2_497) = all_46_0_495
% 175.43/129.60 |
% 175.43/129.60 | Instantiating formula (13) with all_46_2_497, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, model_ub(all_0_4_4, all_0_3_3, all_46_2_497) = 0, yields:
% 175.43/129.60 | (303) lesseq(all_0_2_2, all_46_2_497) = 0
% 175.43/129.60 |
% 175.43/129.60 | Instantiating formula (33) with all_46_0_495, all_46_2_497, 0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, lesseq(all_0_2_2, all_46_2_497) = all_46_0_495, yields:
% 175.43/129.60 | (304) all_46_0_495 = 0 | ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_46_2_497) = v0))
% 175.43/129.60 |
% 175.43/129.60 | Instantiating formula (39) with all_46_0_495, all_46_2_497, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, lesseq(all_0_2_2, all_46_2_497) = all_46_0_495, yields:
% 175.43/129.60 | (305) all_46_0_495 = 0 | ? [v0] : ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_46_2_497) = v0)
% 175.43/129.60 |
% 175.43/129.60 | Instantiating formula (42) with all_46_0_495, all_46_2_497, all_0_2_2 and discharging atoms lesseq(all_0_2_2, all_46_2_497) = all_46_0_495, yields:
% 175.43/129.60 | (306) all_46_0_495 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_46_2_497) = v1 & summation(all_0_2_2) = v0 & lesseq(v0, v1) = v2)
% 175.43/129.60 |
% 175.43/129.60 +-Applying beta-rule and splitting (304), into two cases.
% 175.43/129.60 |-Branch one:
% 175.43/129.60 | (307) all_46_0_495 = 0
% 175.43/129.60 |
% 175.43/129.60 | Equations (307) can reduce 300 to:
% 175.43/129.60 | (72) $false
% 175.43/129.60 |
% 175.43/129.60 |-The branch is then unsatisfiable
% 175.43/129.60 |-Branch two:
% 175.43/129.60 | (300) ~ (all_46_0_495 = 0)
% 175.43/129.60 | (310) ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_46_2_497) = v0))
% 175.43/129.60 |
% 175.43/129.60 +-Applying beta-rule and splitting (306), into two cases.
% 175.43/129.60 |-Branch one:
% 175.43/129.60 | (307) all_46_0_495 = 0
% 175.43/129.60 |
% 175.43/129.60 | Equations (307) can reduce 300 to:
% 175.43/129.60 | (72) $false
% 175.43/129.60 |
% 175.43/129.60 |-The branch is then unsatisfiable
% 175.43/129.60 |-Branch two:
% 175.43/129.60 | (300) ~ (all_46_0_495 = 0)
% 175.43/129.60 | (314) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_46_2_497) = v1 & summation(all_0_2_2) = v0 & lesseq(v0, v1) = v2)
% 175.43/129.60 |
% 175.43/129.60 +-Applying beta-rule and splitting (305), into two cases.
% 175.43/129.60 |-Branch one:
% 175.43/129.60 | (307) all_46_0_495 = 0
% 175.43/129.60 |
% 175.43/129.60 | Equations (307) can reduce 300 to:
% 175.43/129.60 | (72) $false
% 175.43/129.60 |
% 175.43/129.60 |-The branch is then unsatisfiable
% 175.43/129.60 |-Branch two:
% 175.43/129.60 | (300) ~ (all_46_0_495 = 0)
% 175.43/129.60 | (318) ? [v0] : ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_46_2_497) = v0)
% 175.43/129.60 |
% 175.43/129.60 | Instantiating formula (11) with all_0_2_2, all_46_2_497, 0, all_46_0_495 and discharging atoms lesseq(all_0_2_2, all_46_2_497) = all_46_0_495, lesseq(all_0_2_2, all_46_2_497) = 0, yields:
% 175.43/129.60 | (307) all_46_0_495 = 0
% 175.43/129.60 |
% 175.43/129.60 | Equations (307) can reduce 300 to:
% 175.43/129.60 | (72) $false
% 175.43/129.60 |
% 175.43/129.60 |-The branch is then unsatisfiable
% 175.43/129.60 |-Branch two:
% 175.43/129.60 | (321) all_46_2_497 = 0 & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 175.43/129.60 |
% 175.43/129.60 | Applying alpha-rule on (321) yields:
% 175.43/129.60 | (322) all_46_2_497 = 0
% 175.43/129.60 | (238) minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 175.43/129.60 |
% 175.43/129.60 | Instantiating formula (20) with all_176_0_543, all_32_2_493, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = all_176_0_543, yields:
% 175.43/129.60 | (324) all_176_0_543 = 0 | ? [v0] : ( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = v0)
% 175.43/129.61 |
% 175.43/129.61 | Instantiating formula (35) with all_176_0_543, all_32_2_493, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = all_176_0_543, yields:
% 175.43/129.61 | (325) all_176_0_543 = 0 | ? [v0] : ( ~ (v0 = 0) & ub(all_0_4_4, all_0_3_3, all_32_2_493) = v0)
% 175.43/129.61 |
% 175.43/129.61 | Instantiating formula (49) with all_32_2_493, all_0_3_3, all_0_4_4 and discharging atoms max(all_0_4_4, all_0_3_3) = all_32_2_493, yields:
% 175.43/129.61 | (326) all_32_2_493 = all_0_3_3 | ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_3_3) = v0)
% 175.43/129.61 |
% 175.43/129.61 | Instantiating formula (15) with all_32_2_493, all_0_3_3, all_0_4_4 and discharging atoms max(all_0_4_4, all_0_3_3) = all_32_2_493, yields:
% 175.43/129.61 | (327) all_32_2_493 = all_0_4_4 | ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_4_4) = v0)
% 175.43/129.61 |
% 175.43/129.61 +-Applying beta-rule and splitting (324), into two cases.
% 175.43/129.61 |-Branch one:
% 175.43/129.61 | (328) all_176_0_543 = 0
% 175.43/129.61 |
% 175.43/129.61 | Equations (328) can reduce 280 to:
% 175.43/129.61 | (72) $false
% 175.43/129.61 |
% 175.43/129.61 |-The branch is then unsatisfiable
% 175.43/129.61 |-Branch two:
% 175.43/129.61 | (280) ~ (all_176_0_543 = 0)
% 175.43/129.61 | (331) ? [v0] : ( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = v0)
% 175.43/129.61 |
% 175.43/129.61 +-Applying beta-rule and splitting (325), into two cases.
% 175.43/129.61 |-Branch one:
% 175.43/129.61 | (328) all_176_0_543 = 0
% 175.43/129.61 |
% 175.43/129.61 | Equations (328) can reduce 280 to:
% 175.43/129.61 | (72) $false
% 175.43/129.61 |
% 175.43/129.61 |-The branch is then unsatisfiable
% 175.43/129.61 |-Branch two:
% 175.43/129.61 | (280) ~ (all_176_0_543 = 0)
% 175.43/129.61 | (335) ? [v0] : ( ~ (v0 = 0) & ub(all_0_4_4, all_0_3_3, all_32_2_493) = v0)
% 175.43/129.61 |
% 175.43/129.61 | Instantiating (335) with all_229_0_584 yields:
% 175.43/129.61 | (336) ~ (all_229_0_584 = 0) & ub(all_0_4_4, all_0_3_3, all_32_2_493) = all_229_0_584
% 175.43/129.61 |
% 175.43/129.61 | Applying alpha-rule on (336) yields:
% 175.43/129.61 | (337) ~ (all_229_0_584 = 0)
% 175.43/129.61 | (338) ub(all_0_4_4, all_0_3_3, all_32_2_493) = all_229_0_584
% 175.43/129.61 |
% 175.43/129.61 +-Applying beta-rule and splitting (254), into two cases.
% 175.43/129.61 |-Branch one:
% 175.43/129.61 | (101) all_0_2_2 = all_0_3_3
% 175.43/129.61 |
% 175.43/129.61 | From (101)(101) and (253) follows:
% 175.43/129.61 | (340) max(all_0_4_4, all_0_3_3) = all_0_3_3
% 175.43/129.61 |
% 175.43/129.61 | From (101) and (270) follows:
% 175.43/129.61 | (341) lesseq(all_32_2_493, all_0_3_3) = 0
% 175.43/129.61 |
% 175.43/129.61 | From (101) and (260) follows:
% 175.43/129.61 | (342) lesseq(all_0_3_3, all_32_2_493) = all_32_0_491
% 175.43/129.61 |
% 175.43/129.61 +-Applying beta-rule and splitting (326), into two cases.
% 175.43/129.61 |-Branch one:
% 175.43/129.61 | (343) all_32_2_493 = all_0_3_3
% 175.43/129.61 |
% 175.43/129.61 | From (343) and (341) follows:
% 175.43/129.61 | (344) lesseq(all_0_3_3, all_0_3_3) = 0
% 175.43/129.61 |
% 175.43/129.61 | From (343) and (342) follows:
% 175.43/129.61 | (345) lesseq(all_0_3_3, all_0_3_3) = all_32_0_491
% 175.43/129.61 |
% 175.43/129.61 | Instantiating formula (11) with all_0_3_3, all_0_3_3, 0, all_32_0_491 and discharging atoms lesseq(all_0_3_3, all_0_3_3) = all_32_0_491, lesseq(all_0_3_3, all_0_3_3) = 0, yields:
% 175.43/129.61 | (271) all_32_0_491 = 0
% 175.43/129.61 |
% 175.43/129.61 | Equations (271) can reduce 258 to:
% 175.43/129.61 | (72) $false
% 175.43/129.61 |
% 175.43/129.61 |-The branch is then unsatisfiable
% 175.43/129.61 |-Branch two:
% 175.43/129.61 | (348) ~ (all_32_2_493 = all_0_3_3)
% 175.43/129.61 | (109) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_3_3) = v0)
% 175.43/129.61 |
% 175.43/129.61 | Instantiating formula (47) with all_0_4_4, all_0_3_3, all_0_3_3, all_32_2_493 and discharging atoms max(all_0_4_4, all_0_3_3) = all_32_2_493, max(all_0_4_4, all_0_3_3) = all_0_3_3, yields:
% 175.43/129.61 | (343) all_32_2_493 = all_0_3_3
% 175.43/129.61 |
% 175.43/129.61 | Equations (343) can reduce 348 to:
% 175.43/129.61 | (72) $false
% 175.43/129.61 |
% 175.43/129.61 |-The branch is then unsatisfiable
% 175.43/129.61 |-Branch two:
% 175.43/129.61 | (108) ~ (all_0_2_2 = all_0_3_3)
% 175.43/129.61 | (353) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_2_2, all_0_3_3) = v0)
% 175.43/129.61 |
% 175.43/129.61 | Instantiating (353) with all_241_0_586 yields:
% 175.43/129.61 | (354) ~ (all_241_0_586 = 0) & lesseq(all_0_2_2, all_0_3_3) = all_241_0_586
% 175.43/129.61 |
% 175.43/129.61 | Applying alpha-rule on (354) yields:
% 175.43/129.61 | (355) ~ (all_241_0_586 = 0)
% 175.43/129.61 | (356) lesseq(all_0_2_2, all_0_3_3) = all_241_0_586
% 175.43/129.61 |
% 175.43/129.61 +-Applying beta-rule and splitting (255), into two cases.
% 175.43/129.61 |-Branch one:
% 175.43/129.61 | (113) all_0_2_2 = all_0_4_4
% 175.43/129.61 |
% 175.43/129.61 | From (113)(113) and (251) follows:
% 175.43/129.61 | (358) max(all_0_4_4, all_0_3_3) = all_0_4_4
% 175.43/129.61 |
% 175.43/129.61 | From (113) and (270) follows:
% 175.43/129.61 | (359) lesseq(all_32_2_493, all_0_4_4) = 0
% 175.43/129.61 |
% 175.43/129.61 | From (113) and (260) follows:
% 175.43/129.61 | (360) lesseq(all_0_4_4, all_32_2_493) = all_32_0_491
% 175.43/129.61 |
% 175.43/129.61 +-Applying beta-rule and splitting (327), into two cases.
% 175.43/129.61 |-Branch one:
% 175.43/129.61 | (361) all_32_2_493 = all_0_4_4
% 175.43/129.61 |
% 175.43/129.61 | From (361) and (359) follows:
% 175.43/129.62 | (362) lesseq(all_0_4_4, all_0_4_4) = 0
% 175.43/129.62 |
% 175.43/129.62 | From (361) and (360) follows:
% 175.43/129.62 | (363) lesseq(all_0_4_4, all_0_4_4) = all_32_0_491
% 175.43/129.62 |
% 175.43/129.62 | Instantiating formula (11) with all_0_4_4, all_0_4_4, 0, all_32_0_491 and discharging atoms lesseq(all_0_4_4, all_0_4_4) = all_32_0_491, lesseq(all_0_4_4, all_0_4_4) = 0, yields:
% 175.43/129.62 | (271) all_32_0_491 = 0
% 175.43/129.62 |
% 175.43/129.62 | Equations (271) can reduce 258 to:
% 175.43/129.62 | (72) $false
% 175.43/129.62 |
% 175.43/129.62 |-The branch is then unsatisfiable
% 175.43/129.62 |-Branch two:
% 175.43/129.62 | (366) ~ (all_32_2_493 = all_0_4_4)
% 175.43/129.62 | (121) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_4_4) = v0)
% 175.43/129.62 |
% 175.43/129.62 | Instantiating formula (47) with all_0_4_4, all_0_3_3, all_0_4_4, all_32_2_493 and discharging atoms max(all_0_4_4, all_0_3_3) = all_32_2_493, max(all_0_4_4, all_0_3_3) = all_0_4_4, yields:
% 175.43/129.62 | (361) all_32_2_493 = all_0_4_4
% 175.43/129.62 |
% 175.43/129.62 | Equations (361) can reduce 366 to:
% 175.43/129.62 | (72) $false
% 175.43/129.62 |
% 175.43/129.62 |-The branch is then unsatisfiable
% 175.43/129.62 |-Branch two:
% 175.43/129.62 | (120) ~ (all_0_2_2 = all_0_4_4)
% 175.43/129.62 | (371) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_2_2, all_0_4_4) = v0)
% 175.43/129.62 |
% 175.43/129.62 | Instantiating (371) with all_249_0_588 yields:
% 175.43/129.62 | (372) ~ (all_249_0_588 = 0) & lesseq(all_0_2_2, all_0_4_4) = all_249_0_588
% 175.43/129.62 |
% 175.43/129.62 | Applying alpha-rule on (372) yields:
% 175.43/129.62 | (373) ~ (all_249_0_588 = 0)
% 175.43/129.62 | (374) lesseq(all_0_2_2, all_0_4_4) = all_249_0_588
% 175.43/129.62 |
% 175.43/129.62 | Instantiating formula (5) with all_229_0_584, all_32_2_493, all_0_3_3, all_0_4_4 and discharging atoms ub(all_0_4_4, all_0_3_3, all_32_2_493) = all_229_0_584, yields:
% 175.43/129.62 | (375) all_229_0_584 = 0 | ? [v0] : (( ~ (v0 = 0) & lesseq(all_0_3_3, all_32_2_493) = v0) | ( ~ (v0 = 0) & lesseq(all_0_4_4, all_32_2_493) = v0))
% 175.43/129.62 |
% 175.43/129.62 | Instantiating formula (33) with all_241_0_586, all_0_3_3, 0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, lesseq(all_0_2_2, all_0_3_3) = all_241_0_586, yields:
% 175.43/129.62 | (376) all_241_0_586 = 0 | ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0))
% 175.43/129.62 |
% 175.43/129.62 | Instantiating formula (39) with all_241_0_586, all_0_3_3, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, lesseq(all_0_2_2, all_0_3_3) = all_241_0_586, yields:
% 175.43/129.62 | (377) all_241_0_586 = 0 | ? [v0] : ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0)
% 175.43/129.62 |
% 175.43/129.62 | Instantiating formula (39) with all_249_0_588, all_0_4_4, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, lesseq(all_0_2_2, all_0_4_4) = all_249_0_588, yields:
% 175.43/129.62 | (378) all_249_0_588 = 0 | ? [v0] : ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = v0)
% 175.43/129.62 |
% 175.43/129.62 +-Applying beta-rule and splitting (375), into two cases.
% 175.43/129.62 |-Branch one:
% 175.43/129.62 | (379) all_229_0_584 = 0
% 175.43/129.62 |
% 175.43/129.62 | Equations (379) can reduce 337 to:
% 175.43/129.62 | (72) $false
% 175.43/129.62 |
% 175.43/129.62 |-The branch is then unsatisfiable
% 175.43/129.62 |-Branch two:
% 175.43/129.62 | (337) ~ (all_229_0_584 = 0)
% 175.43/129.62 | (382) ? [v0] : (( ~ (v0 = 0) & lesseq(all_0_3_3, all_32_2_493) = v0) | ( ~ (v0 = 0) & lesseq(all_0_4_4, all_32_2_493) = v0))
% 175.43/129.62 |
% 175.43/129.62 | Instantiating (382) with all_308_0_812 yields:
% 175.43/129.62 | (383) ( ~ (all_308_0_812 = 0) & lesseq(all_0_3_3, all_32_2_493) = all_308_0_812) | ( ~ (all_308_0_812 = 0) & lesseq(all_0_4_4, all_32_2_493) = all_308_0_812)
% 175.43/129.62 |
% 175.43/129.62 +-Applying beta-rule and splitting (378), into two cases.
% 175.43/129.62 |-Branch one:
% 175.43/129.62 | (384) all_249_0_588 = 0
% 175.43/129.62 |
% 175.43/129.62 | Equations (384) can reduce 373 to:
% 175.43/129.62 | (72) $false
% 175.43/129.62 |
% 175.43/129.62 |-The branch is then unsatisfiable
% 175.43/129.62 |-Branch two:
% 175.43/129.62 | (373) ~ (all_249_0_588 = 0)
% 175.43/129.62 | (387) ? [v0] : ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = v0)
% 175.43/129.62 |
% 175.43/129.62 | Instantiating (387) with all_322_0_819 yields:
% 175.43/129.62 | (388) ~ (all_322_0_819 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_322_0_819
% 175.43/129.62 |
% 175.43/129.62 | Applying alpha-rule on (388) yields:
% 175.43/129.62 | (389) ~ (all_322_0_819 = 0)
% 175.43/129.62 | (390) model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_322_0_819
% 175.43/129.62 |
% 175.43/129.62 +-Applying beta-rule and splitting (377), into two cases.
% 175.43/129.62 |-Branch one:
% 175.43/129.62 | (391) all_241_0_586 = 0
% 175.43/129.62 |
% 175.43/129.62 | Equations (391) can reduce 355 to:
% 175.43/129.62 | (72) $false
% 175.43/129.62 |
% 175.43/129.62 |-The branch is then unsatisfiable
% 175.43/129.62 |-Branch two:
% 175.43/129.62 | (355) ~ (all_241_0_586 = 0)
% 175.43/129.62 | (394) ? [v0] : ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0)
% 175.43/129.62 |
% 175.43/129.62 | Instantiating (394) with all_333_0_823 yields:
% 175.43/129.62 | (395) ~ (all_333_0_823 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_333_0_823
% 175.43/129.62 |
% 175.43/129.62 | Applying alpha-rule on (395) yields:
% 175.43/129.62 | (396) ~ (all_333_0_823 = 0)
% 175.43/129.62 | (397) model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_333_0_823
% 175.43/129.62 |
% 175.43/129.62 +-Applying beta-rule and splitting (376), into two cases.
% 175.43/129.62 |-Branch one:
% 175.43/129.62 | (391) all_241_0_586 = 0
% 175.43/129.62 |
% 175.43/129.62 | Equations (391) can reduce 355 to:
% 175.43/129.62 | (72) $false
% 175.43/129.62 |
% 175.43/129.62 |-The branch is then unsatisfiable
% 175.43/129.62 |-Branch two:
% 175.43/129.62 | (355) ~ (all_241_0_586 = 0)
% 175.43/129.62 | (401) ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0))
% 175.43/129.62 |
% 175.43/129.62 | Instantiating (401) with all_338_0_824 yields:
% 175.43/129.62 | (402) ( ~ (all_338_0_824 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_338_0_824) | ( ~ (all_338_0_824 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_338_0_824)
% 175.43/129.62 |
% 175.43/129.62 +-Applying beta-rule and splitting (402), into two cases.
% 175.43/129.62 |-Branch one:
% 175.43/129.62 | (403) ~ (all_338_0_824 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_338_0_824
% 175.43/129.62 |
% 175.43/129.62 | Applying alpha-rule on (403) yields:
% 175.43/129.62 | (404) ~ (all_338_0_824 = 0)
% 175.43/129.62 | (405) minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_338_0_824
% 175.43/129.62 |
% 175.43/129.62 | Instantiating formula (12) with all_0_4_4, all_0_3_3, all_0_2_2, all_338_0_824, 0 and discharging atoms minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_338_0_824, minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, yields:
% 175.43/129.62 | (406) all_338_0_824 = 0
% 175.43/129.62 |
% 175.43/129.62 | Equations (406) can reduce 404 to:
% 175.43/129.62 | (72) $false
% 175.43/129.62 |
% 175.43/129.63 |-The branch is then unsatisfiable
% 175.43/129.63 |-Branch two:
% 175.43/129.63 | (408) ~ (all_338_0_824 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_338_0_824
% 175.43/129.63 |
% 175.43/129.63 | Applying alpha-rule on (408) yields:
% 175.43/129.63 | (404) ~ (all_338_0_824 = 0)
% 175.43/129.63 | (410) model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_338_0_824
% 175.43/129.63 |
% 175.43/129.63 | Instantiating formula (52) with all_0_4_4, all_0_3_3, all_0_3_3, all_333_0_823, all_338_0_824 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_338_0_824, model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_333_0_823, yields:
% 175.43/129.63 | (411) all_338_0_824 = all_333_0_823
% 175.43/129.63 |
% 175.43/129.63 | From (411) and (410) follows:
% 175.43/129.63 | (397) model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_333_0_823
% 175.43/129.63 |
% 175.43/129.63 +-Applying beta-rule and splitting (268), into two cases.
% 175.43/129.63 |-Branch one:
% 175.43/129.63 | (413) all_157_1_533 = 0 & ~ (all_157_0_532 = 0) & model_max(all_0_4_4, all_0_3_3, all_157_2_534) = 0 & lesseq(all_32_2_493, all_157_2_534) = all_157_0_532
% 175.43/129.63 |
% 175.43/129.63 | Applying alpha-rule on (413) yields:
% 175.43/129.63 | (414) all_157_1_533 = 0
% 175.43/129.63 | (415) ~ (all_157_0_532 = 0)
% 175.43/129.63 | (416) model_max(all_0_4_4, all_0_3_3, all_157_2_534) = 0
% 175.43/129.63 | (417) lesseq(all_32_2_493, all_157_2_534) = all_157_0_532
% 175.43/129.63 |
% 175.43/129.63 | Instantiating formula (6) with all_157_2_534, all_0_3_3, all_0_4_4 and discharging atoms model_max(all_0_4_4, all_0_3_3, all_157_2_534) = 0, yields:
% 175.43/129.63 | (418) max(all_0_4_4, all_0_3_3) = all_157_2_534
% 175.43/129.63 |
% 175.43/129.63 | Instantiating formula (33) with all_157_0_532, all_157_2_534, all_176_0_543, all_32_2_493, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = all_176_0_543, lesseq(all_32_2_493, all_157_2_534) = all_157_0_532, yields:
% 175.43/129.63 | (419) all_157_0_532 = 0 | ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_157_2_534) = v0))
% 175.43/129.63 |
% 175.43/129.63 | Instantiating formula (16) with all_157_0_532, all_157_2_534, 0, all_32_2_493, all_0_3_3, all_0_4_4 and discharging atoms model_max(all_0_4_4, all_0_3_3, all_32_2_493) = 0, lesseq(all_32_2_493, all_157_2_534) = all_157_0_532, yields:
% 175.43/129.63 | (420) all_157_0_532 = 0 | ? [v0] : (( ~ (v0 = 0) & minsol_model_max(all_0_4_4, all_0_3_3, all_32_2_493) = v0) | ( ~ (v0 = 0) & model_max(all_0_4_4, all_0_3_3, all_157_2_534) = v0))
% 175.43/129.63 |
% 175.43/129.63 | Instantiating formula (21) with all_157_0_532, all_157_2_534, all_0_2_2, all_32_2_493 and discharging atoms lesseq(all_32_2_493, all_157_2_534) = all_157_0_532, lesseq(all_32_2_493, all_0_2_2) = 0, yields:
% 175.43/129.63 | (421) all_157_0_532 = 0 | ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_2_2, all_157_2_534) = v0)
% 175.43/129.63 |
% 175.43/129.63 | Instantiating formula (42) with all_157_0_532, all_157_2_534, all_32_2_493 and discharging atoms lesseq(all_32_2_493, all_157_2_534) = all_157_0_532, yields:
% 175.43/129.63 | (422) all_157_0_532 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_157_2_534) = v1 & summation(all_32_2_493) = v0 & lesseq(v0, v1) = v2)
% 175.43/129.63 |
% 175.43/129.63 +-Applying beta-rule and splitting (422), into two cases.
% 175.43/129.63 |-Branch one:
% 175.43/129.63 | (423) all_157_0_532 = 0
% 175.43/129.63 |
% 175.43/129.63 | Equations (423) can reduce 415 to:
% 175.43/129.63 | (72) $false
% 175.43/129.63 |
% 175.43/129.63 |-The branch is then unsatisfiable
% 175.43/129.63 |-Branch two:
% 175.43/129.63 | (415) ~ (all_157_0_532 = 0)
% 175.43/129.63 | (426) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_157_2_534) = v1 & summation(all_32_2_493) = v0 & lesseq(v0, v1) = v2)
% 175.43/129.63 |
% 175.43/129.63 +-Applying beta-rule and splitting (421), into two cases.
% 175.43/129.63 |-Branch one:
% 175.43/129.63 | (423) all_157_0_532 = 0
% 175.43/129.63 |
% 175.43/129.63 | Equations (423) can reduce 415 to:
% 175.43/129.63 | (72) $false
% 175.43/129.63 |
% 175.43/129.63 |-The branch is then unsatisfiable
% 175.43/129.63 |-Branch two:
% 175.43/129.63 | (415) ~ (all_157_0_532 = 0)
% 175.43/129.63 | (430) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_2_2, all_157_2_534) = v0)
% 175.43/129.63 |
% 175.43/129.63 +-Applying beta-rule and splitting (420), into two cases.
% 175.43/129.63 |-Branch one:
% 175.43/129.63 | (423) all_157_0_532 = 0
% 175.43/129.63 |
% 175.43/129.63 | Equations (423) can reduce 415 to:
% 175.43/129.63 | (72) $false
% 175.43/129.63 |
% 175.43/129.63 |-The branch is then unsatisfiable
% 175.43/129.63 |-Branch two:
% 175.43/129.63 | (415) ~ (all_157_0_532 = 0)
% 175.43/129.63 | (434) ? [v0] : (( ~ (v0 = 0) & minsol_model_max(all_0_4_4, all_0_3_3, all_32_2_493) = v0) | ( ~ (v0 = 0) & model_max(all_0_4_4, all_0_3_3, all_157_2_534) = v0))
% 175.43/129.63 |
% 175.43/129.63 +-Applying beta-rule and splitting (419), into two cases.
% 175.43/129.63 |-Branch one:
% 175.43/129.63 | (423) all_157_0_532 = 0
% 175.43/129.63 |
% 175.43/129.63 | Equations (423) can reduce 415 to:
% 175.43/129.63 | (72) $false
% 175.43/129.63 |
% 175.43/129.63 |-The branch is then unsatisfiable
% 175.43/129.63 |-Branch two:
% 175.43/129.63 | (415) ~ (all_157_0_532 = 0)
% 175.43/129.63 | (438) ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_32_2_493) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_157_2_534) = v0))
% 175.43/129.63 |
% 175.43/129.63 | Instantiating formula (47) with all_0_4_4, all_0_3_3, all_157_2_534, all_32_2_493 and discharging atoms max(all_0_4_4, all_0_3_3) = all_157_2_534, max(all_0_4_4, all_0_3_3) = all_32_2_493, yields:
% 175.43/129.63 | (439) all_157_2_534 = all_32_2_493
% 175.43/129.63 |
% 175.43/129.63 | From (439) and (417) follows:
% 175.43/129.63 | (440) lesseq(all_32_2_493, all_32_2_493) = all_157_0_532
% 175.43/129.63 |
% 175.43/129.63 | Instantiating formula (56) with all_157_0_532, all_32_2_493 and discharging atoms lesseq(all_32_2_493, all_32_2_493) = all_157_0_532, yields:
% 175.43/129.63 | (423) all_157_0_532 = 0
% 175.43/129.63 |
% 175.43/129.63 | Equations (423) can reduce 415 to:
% 175.43/129.63 | (72) $false
% 175.43/129.63 |
% 175.43/129.63 |-The branch is then unsatisfiable
% 175.43/129.63 |-Branch two:
% 175.43/129.63 | (443) all_157_2_534 = 0 & minsol_model_max(all_0_4_4, all_0_3_3, all_32_2_493) = 0
% 175.43/129.63 |
% 175.43/129.63 | Applying alpha-rule on (443) yields:
% 175.43/129.63 | (444) all_157_2_534 = 0
% 175.43/129.63 | (445) minsol_model_max(all_0_4_4, all_0_3_3, all_32_2_493) = 0
% 175.43/129.63 |
% 175.43/129.63 +-Applying beta-rule and splitting (269), into two cases.
% 175.43/129.63 |-Branch one:
% 175.43/129.63 | (446) all_162_0_539 = 0 & lesseq(all_32_2_493, all_32_2_493) = 0
% 175.43/129.63 |
% 175.43/129.63 | Applying alpha-rule on (446) yields:
% 175.43/129.63 | (447) all_162_0_539 = 0
% 175.43/129.63 | (448) lesseq(all_32_2_493, all_32_2_493) = 0
% 175.43/129.63 |
% 175.43/129.63 +-Applying beta-rule and splitting (326), into two cases.
% 175.43/129.63 |-Branch one:
% 175.43/129.63 | (343) all_32_2_493 = all_0_3_3
% 175.43/129.63 |
% 175.43/129.63 | From (343)(343) and (448) follows:
% 175.43/129.63 | (344) lesseq(all_0_3_3, all_0_3_3) = 0
% 175.43/129.63 |
% 175.43/129.63 +-Applying beta-rule and splitting (383), into two cases.
% 175.43/129.63 |-Branch one:
% 175.43/129.63 | (451) ~ (all_308_0_812 = 0) & lesseq(all_0_3_3, all_32_2_493) = all_308_0_812
% 175.43/129.63 |
% 175.43/129.63 | Applying alpha-rule on (451) yields:
% 175.43/129.63 | (452) ~ (all_308_0_812 = 0)
% 175.43/129.63 | (453) lesseq(all_0_3_3, all_32_2_493) = all_308_0_812
% 175.43/129.63 |
% 175.43/129.63 | From (343) and (453) follows:
% 175.43/129.63 | (454) lesseq(all_0_3_3, all_0_3_3) = all_308_0_812
% 175.43/129.63 |
% 175.43/129.63 | Instantiating formula (11) with all_0_3_3, all_0_3_3, 0, all_308_0_812 and discharging atoms lesseq(all_0_3_3, all_0_3_3) = all_308_0_812, lesseq(all_0_3_3, all_0_3_3) = 0, yields:
% 175.43/129.63 | (455) all_308_0_812 = 0
% 175.43/129.63 |
% 175.43/129.63 | Equations (455) can reduce 452 to:
% 175.43/129.63 | (72) $false
% 175.43/129.63 |
% 175.43/129.63 |-The branch is then unsatisfiable
% 175.43/129.63 |-Branch two:
% 175.43/129.63 | (457) ~ (all_308_0_812 = 0) & lesseq(all_0_4_4, all_32_2_493) = all_308_0_812
% 175.43/129.64 |
% 175.43/129.64 | Applying alpha-rule on (457) yields:
% 175.43/129.64 | (452) ~ (all_308_0_812 = 0)
% 175.43/129.64 | (459) lesseq(all_0_4_4, all_32_2_493) = all_308_0_812
% 175.43/129.64 |
% 175.43/129.64 | From (343) and (459) follows:
% 175.43/129.64 | (460) lesseq(all_0_4_4, all_0_3_3) = all_308_0_812
% 175.43/129.64 |
% 175.43/129.64 +-Applying beta-rule and splitting (327), into two cases.
% 175.43/129.64 |-Branch one:
% 175.43/129.64 | (361) all_32_2_493 = all_0_4_4
% 175.43/129.64 |
% 175.43/129.64 | Combining equations (361,343) yields a new equation:
% 175.43/129.64 | (152) all_0_3_3 = all_0_4_4
% 175.43/129.64 |
% 175.43/129.64 | From (152)(152) and (344) follows:
% 175.43/129.64 | (362) lesseq(all_0_4_4, all_0_4_4) = 0
% 175.43/129.64 |
% 175.43/129.64 | From (152) and (460) follows:
% 175.43/129.64 | (464) lesseq(all_0_4_4, all_0_4_4) = all_308_0_812
% 175.43/129.64 |
% 175.43/129.64 | Instantiating formula (11) with all_0_4_4, all_0_4_4, 0, all_308_0_812 and discharging atoms lesseq(all_0_4_4, all_0_4_4) = all_308_0_812, lesseq(all_0_4_4, all_0_4_4) = 0, yields:
% 175.43/129.64 | (455) all_308_0_812 = 0
% 175.43/129.64 |
% 175.43/129.64 | Equations (455) can reduce 452 to:
% 175.43/129.64 | (72) $false
% 175.43/129.64 |
% 175.43/129.64 |-The branch is then unsatisfiable
% 175.43/129.64 |-Branch two:
% 175.43/129.64 | (366) ~ (all_32_2_493 = all_0_4_4)
% 175.43/129.64 | (121) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_4_4) = v0)
% 175.43/129.64 |
% 175.43/129.64 | Instantiating (121) with all_487_0_1209 yields:
% 175.43/129.64 | (469) ~ (all_487_0_1209 = 0) & lesseq(all_0_3_3, all_0_4_4) = all_487_0_1209
% 175.43/129.64 |
% 175.43/129.64 | Applying alpha-rule on (469) yields:
% 175.43/129.64 | (470) ~ (all_487_0_1209 = 0)
% 175.43/129.64 | (471) lesseq(all_0_3_3, all_0_4_4) = all_487_0_1209
% 175.43/129.64 |
% 175.43/129.64 | Instantiating formula (10) with all_487_0_1209, all_0_3_3, all_0_4_4 and discharging atoms lesseq(all_0_3_3, all_0_4_4) = all_487_0_1209, yields:
% 175.43/129.64 | (472) all_487_0_1209 = 0 | lesseq(all_0_4_4, all_0_3_3) = 0
% 175.43/129.64 |
% 175.43/129.64 | Instantiating formula (33) with all_308_0_812, all_0_3_3, all_322_0_819, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_322_0_819, lesseq(all_0_4_4, all_0_3_3) = all_308_0_812, yields:
% 175.43/129.64 | (473) all_308_0_812 = 0 | ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0))
% 175.43/129.64 |
% 175.43/129.64 | Instantiating formula (42) with all_308_0_812, all_0_3_3, all_0_4_4 and discharging atoms lesseq(all_0_4_4, all_0_3_3) = all_308_0_812, yields:
% 175.43/129.64 | (474) all_308_0_812 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_0_3_3) = v1 & summation(all_0_4_4) = v0 & lesseq(v0, v1) = v2)
% 175.43/129.64 |
% 175.43/129.64 +-Applying beta-rule and splitting (472), into two cases.
% 175.43/129.64 |-Branch one:
% 175.43/129.64 | (127) lesseq(all_0_4_4, all_0_3_3) = 0
% 175.43/129.64 |
% 175.43/129.64 +-Applying beta-rule and splitting (473), into two cases.
% 175.43/129.64 |-Branch one:
% 175.43/129.64 | (455) all_308_0_812 = 0
% 175.43/129.64 |
% 175.43/129.64 | Equations (455) can reduce 452 to:
% 175.43/129.64 | (72) $false
% 175.43/129.64 |
% 175.43/129.64 |-The branch is then unsatisfiable
% 175.43/129.64 |-Branch two:
% 175.43/129.64 | (452) ~ (all_308_0_812 = 0)
% 175.43/129.64 | (479) ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0))
% 175.43/129.64 |
% 175.43/129.64 +-Applying beta-rule and splitting (474), into two cases.
% 175.43/129.64 |-Branch one:
% 175.43/129.64 | (455) all_308_0_812 = 0
% 175.43/129.64 |
% 175.43/129.64 | Equations (455) can reduce 452 to:
% 175.43/129.64 | (72) $false
% 175.43/129.64 |
% 175.43/129.64 |-The branch is then unsatisfiable
% 175.43/129.64 |-Branch two:
% 175.43/129.64 | (452) ~ (all_308_0_812 = 0)
% 175.43/129.64 | (131) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_0_3_3) = v1 & summation(all_0_4_4) = v0 & lesseq(v0, v1) = v2)
% 175.43/129.64 |
% 175.43/129.64 | Instantiating formula (11) with all_0_4_4, all_0_3_3, 0, all_308_0_812 and discharging atoms lesseq(all_0_4_4, all_0_3_3) = all_308_0_812, lesseq(all_0_4_4, all_0_3_3) = 0, yields:
% 175.43/129.64 | (455) all_308_0_812 = 0
% 175.43/129.64 |
% 175.43/129.64 | Equations (455) can reduce 452 to:
% 175.43/129.64 | (72) $false
% 175.43/129.64 |
% 175.43/129.64 |-The branch is then unsatisfiable
% 175.43/129.64 |-Branch two:
% 175.43/129.64 | (134) ~ (lesseq(all_0_4_4, all_0_3_3) = 0)
% 175.43/129.64 | (487) all_487_0_1209 = 0
% 175.43/129.64 |
% 175.43/129.64 | Equations (487) can reduce 470 to:
% 175.43/129.64 | (72) $false
% 175.43/129.64 |
% 175.43/129.64 |-The branch is then unsatisfiable
% 175.43/129.64 |-Branch two:
% 175.43/129.64 | (348) ~ (all_32_2_493 = all_0_3_3)
% 175.43/129.64 | (109) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_3_3) = v0)
% 175.43/129.64 |
% 175.43/129.64 | Instantiating (109) with all_457_0_1234 yields:
% 175.43/129.64 | (491) ~ (all_457_0_1234 = 0) & lesseq(all_0_4_4, all_0_3_3) = all_457_0_1234
% 175.43/129.64 |
% 175.43/129.64 | Applying alpha-rule on (491) yields:
% 175.43/129.64 | (492) ~ (all_457_0_1234 = 0)
% 175.43/129.64 | (493) lesseq(all_0_4_4, all_0_3_3) = all_457_0_1234
% 175.43/129.64 |
% 175.43/129.64 +-Applying beta-rule and splitting (327), into two cases.
% 175.43/129.64 |-Branch one:
% 175.43/129.64 | (361) all_32_2_493 = all_0_4_4
% 175.43/129.64 |
% 175.43/129.64 | From (361)(361) and (448) follows:
% 175.43/129.64 | (362) lesseq(all_0_4_4, all_0_4_4) = 0
% 175.43/129.64 |
% 175.43/129.64 +-Applying beta-rule and splitting (383), into two cases.
% 175.43/129.64 |-Branch one:
% 175.43/129.64 | (451) ~ (all_308_0_812 = 0) & lesseq(all_0_3_3, all_32_2_493) = all_308_0_812
% 175.43/129.64 |
% 175.43/129.64 | Applying alpha-rule on (451) yields:
% 175.43/129.64 | (452) ~ (all_308_0_812 = 0)
% 175.43/129.64 | (453) lesseq(all_0_3_3, all_32_2_493) = all_308_0_812
% 175.43/129.64 |
% 175.43/129.64 | From (361) and (453) follows:
% 175.43/129.64 | (499) lesseq(all_0_3_3, all_0_4_4) = all_308_0_812
% 175.43/129.64 |
% 175.43/129.64 | Instantiating formula (33) with all_308_0_812, all_0_4_4, all_333_0_823, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_333_0_823, lesseq(all_0_3_3, all_0_4_4) = all_308_0_812, yields:
% 175.43/129.64 | (500) all_308_0_812 = 0 | ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = v0))
% 175.43/129.64 |
% 175.43/129.64 | Instantiating formula (42) with all_308_0_812, all_0_4_4, all_0_3_3 and discharging atoms lesseq(all_0_3_3, all_0_4_4) = all_308_0_812, yields:
% 175.43/129.64 | (501) all_308_0_812 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_0_3_3) = v0 & summation(all_0_4_4) = v1 & lesseq(v0, v1) = v2)
% 175.43/129.64 |
% 175.43/129.64 | Instantiating formula (10) with all_457_0_1234, all_0_4_4, all_0_3_3 and discharging atoms lesseq(all_0_4_4, all_0_3_3) = all_457_0_1234, yields:
% 175.43/129.64 | (502) all_457_0_1234 = 0 | lesseq(all_0_3_3, all_0_4_4) = 0
% 175.43/129.64 |
% 175.43/129.64 +-Applying beta-rule and splitting (502), into two cases.
% 175.43/129.64 |-Branch one:
% 175.43/129.64 | (171) lesseq(all_0_3_3, all_0_4_4) = 0
% 175.43/129.64 |
% 175.43/129.64 +-Applying beta-rule and splitting (501), into two cases.
% 175.43/129.64 |-Branch one:
% 175.43/129.64 | (455) all_308_0_812 = 0
% 175.43/129.64 |
% 175.43/129.64 | Equations (455) can reduce 452 to:
% 175.43/129.64 | (72) $false
% 175.43/129.64 |
% 175.43/129.64 |-The branch is then unsatisfiable
% 175.43/129.64 |-Branch two:
% 175.43/129.64 | (452) ~ (all_308_0_812 = 0)
% 175.43/129.64 | (229) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_0_3_3) = v0 & summation(all_0_4_4) = v1 & lesseq(v0, v1) = v2)
% 175.43/129.64 |
% 175.43/129.64 +-Applying beta-rule and splitting (500), into two cases.
% 175.43/129.64 |-Branch one:
% 175.43/129.64 | (455) all_308_0_812 = 0
% 175.43/129.64 |
% 175.43/129.64 | Equations (455) can reduce 452 to:
% 175.43/129.64 | (72) $false
% 175.43/129.64 |
% 175.43/129.64 |-The branch is then unsatisfiable
% 175.43/129.64 |-Branch two:
% 175.43/129.64 | (452) ~ (all_308_0_812 = 0)
% 175.43/129.64 | (511) ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = v0))
% 175.43/129.64 |
% 175.43/129.64 | Instantiating formula (11) with all_0_3_3, all_0_4_4, 0, all_308_0_812 and discharging atoms lesseq(all_0_3_3, all_0_4_4) = all_308_0_812, lesseq(all_0_3_3, all_0_4_4) = 0, yields:
% 175.43/129.65 | (455) all_308_0_812 = 0
% 175.43/129.65 |
% 175.43/129.65 | Equations (455) can reduce 452 to:
% 175.43/129.65 | (72) $false
% 175.43/129.65 |
% 175.43/129.65 |-The branch is then unsatisfiable
% 175.43/129.65 |-Branch two:
% 175.43/129.65 | (187) ~ (lesseq(all_0_3_3, all_0_4_4) = 0)
% 175.43/129.65 | (515) all_457_0_1234 = 0
% 175.43/129.65 |
% 175.43/129.65 | Equations (515) can reduce 492 to:
% 175.43/129.65 | (72) $false
% 175.43/129.65 |
% 175.43/129.65 |-The branch is then unsatisfiable
% 175.43/129.65 |-Branch two:
% 175.43/129.65 | (457) ~ (all_308_0_812 = 0) & lesseq(all_0_4_4, all_32_2_493) = all_308_0_812
% 175.43/129.65 |
% 175.43/129.65 | Applying alpha-rule on (457) yields:
% 175.43/129.65 | (452) ~ (all_308_0_812 = 0)
% 175.43/129.65 | (459) lesseq(all_0_4_4, all_32_2_493) = all_308_0_812
% 175.43/129.65 |
% 175.43/129.65 | From (361) and (459) follows:
% 175.43/129.65 | (464) lesseq(all_0_4_4, all_0_4_4) = all_308_0_812
% 175.43/129.65 |
% 175.43/129.65 | Instantiating formula (11) with all_0_4_4, all_0_4_4, 0, all_308_0_812 and discharging atoms lesseq(all_0_4_4, all_0_4_4) = all_308_0_812, lesseq(all_0_4_4, all_0_4_4) = 0, yields:
% 175.43/129.65 | (455) all_308_0_812 = 0
% 175.43/129.65 |
% 175.43/129.65 | Equations (455) can reduce 452 to:
% 175.43/129.65 | (72) $false
% 175.43/129.65 |
% 175.43/129.65 |-The branch is then unsatisfiable
% 175.43/129.65 |-Branch two:
% 175.43/129.65 | (366) ~ (all_32_2_493 = all_0_4_4)
% 175.43/129.65 | (121) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_4_4) = v0)
% 175.43/129.65 |
% 175.43/129.65 | Instantiating (121) with all_465_0_1259 yields:
% 175.43/129.65 | (525) ~ (all_465_0_1259 = 0) & lesseq(all_0_3_3, all_0_4_4) = all_465_0_1259
% 175.43/129.65 |
% 175.43/129.65 | Applying alpha-rule on (525) yields:
% 175.43/129.65 | (526) ~ (all_465_0_1259 = 0)
% 175.43/129.65 | (527) lesseq(all_0_3_3, all_0_4_4) = all_465_0_1259
% 175.43/129.65 |
% 175.43/129.65 | Instantiating formula (10) with all_465_0_1259, all_0_3_3, all_0_4_4 and discharging atoms lesseq(all_0_3_3, all_0_4_4) = all_465_0_1259, yields:
% 175.43/129.65 | (528) all_465_0_1259 = 0 | lesseq(all_0_4_4, all_0_3_3) = 0
% 175.43/129.65 |
% 175.89/129.65 | Instantiating formula (33) with all_457_0_1234, all_0_3_3, all_322_0_819, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_322_0_819, lesseq(all_0_4_4, all_0_3_3) = all_457_0_1234, yields:
% 175.89/129.65 | (529) all_457_0_1234 = 0 | ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0))
% 175.89/129.65 |
% 175.89/129.65 | Instantiating formula (42) with all_457_0_1234, all_0_3_3, all_0_4_4 and discharging atoms lesseq(all_0_4_4, all_0_3_3) = all_457_0_1234, yields:
% 175.89/129.65 | (530) all_457_0_1234 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_0_3_3) = v1 & summation(all_0_4_4) = v0 & lesseq(v0, v1) = v2)
% 175.89/129.65 |
% 175.89/129.65 +-Applying beta-rule and splitting (528), into two cases.
% 175.89/129.65 |-Branch one:
% 175.89/129.65 | (127) lesseq(all_0_4_4, all_0_3_3) = 0
% 175.89/129.65 |
% 175.89/129.65 +-Applying beta-rule and splitting (530), into two cases.
% 175.89/129.65 |-Branch one:
% 175.89/129.65 | (515) all_457_0_1234 = 0
% 175.89/129.65 |
% 175.89/129.65 | Equations (515) can reduce 492 to:
% 175.89/129.65 | (72) $false
% 175.89/129.65 |
% 175.89/129.65 |-The branch is then unsatisfiable
% 175.89/129.65 |-Branch two:
% 175.89/129.65 | (492) ~ (all_457_0_1234 = 0)
% 175.89/129.65 | (131) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_0_3_3) = v1 & summation(all_0_4_4) = v0 & lesseq(v0, v1) = v2)
% 175.89/129.65 |
% 175.89/129.65 +-Applying beta-rule and splitting (529), into two cases.
% 175.89/129.65 |-Branch one:
% 175.89/129.65 | (515) all_457_0_1234 = 0
% 175.89/129.65 |
% 175.89/129.65 | Equations (515) can reduce 492 to:
% 175.89/129.65 | (72) $false
% 175.89/129.65 |
% 175.89/129.65 |-The branch is then unsatisfiable
% 175.89/129.65 |-Branch two:
% 175.89/129.65 | (492) ~ (all_457_0_1234 = 0)
% 175.89/129.65 | (479) ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0))
% 175.89/129.65 |
% 175.89/129.65 | Instantiating formula (11) with all_0_4_4, all_0_3_3, 0, all_457_0_1234 and discharging atoms lesseq(all_0_4_4, all_0_3_3) = all_457_0_1234, lesseq(all_0_4_4, all_0_3_3) = 0, yields:
% 175.89/129.65 | (515) all_457_0_1234 = 0
% 175.89/129.65 |
% 175.89/129.65 | Equations (515) can reduce 492 to:
% 175.89/129.65 | (72) $false
% 175.89/129.65 |
% 175.89/129.65 |-The branch is then unsatisfiable
% 175.89/129.65 |-Branch two:
% 175.89/129.65 | (134) ~ (lesseq(all_0_4_4, all_0_3_3) = 0)
% 175.89/129.65 | (543) all_465_0_1259 = 0
% 175.89/129.65 |
% 175.89/129.65 | Equations (543) can reduce 526 to:
% 175.89/129.65 | (72) $false
% 175.89/129.65 |
% 175.89/129.65 |-The branch is then unsatisfiable
% 175.89/129.65 |-Branch two:
% 175.89/129.65 | (545) ~ (all_162_0_539 = 0) & minsol_model_max(all_0_4_4, all_0_3_3, all_32_2_493) = all_162_0_539
% 175.89/129.65 |
% 175.89/129.65 | Applying alpha-rule on (545) yields:
% 175.89/129.65 | (546) ~ (all_162_0_539 = 0)
% 175.89/129.65 | (547) minsol_model_max(all_0_4_4, all_0_3_3, all_32_2_493) = all_162_0_539
% 175.89/129.65 |
% 175.89/129.65 | Instantiating formula (64) with all_0_4_4, all_0_3_3, all_32_2_493, 0, all_162_0_539 and discharging atoms minsol_model_max(all_0_4_4, all_0_3_3, all_32_2_493) = all_162_0_539, minsol_model_max(all_0_4_4, all_0_3_3, all_32_2_493) = 0, yields:
% 175.89/129.65 | (447) all_162_0_539 = 0
% 175.89/129.65 |
% 175.89/129.65 | Equations (447) can reduce 546 to:
% 175.89/129.65 | (72) $false
% 175.89/129.65 |
% 175.89/129.65 |-The branch is then unsatisfiable
% 175.89/129.65 |-Branch two:
% 175.89/129.65 | (550) ~ (lesseq(all_32_2_493, all_0_2_2) = 0)
% 175.89/129.65 | (271) all_32_0_491 = 0
% 175.89/129.65 |
% 175.89/129.65 | Equations (271) can reduce 258 to:
% 175.89/129.65 | (72) $false
% 175.89/129.65 |
% 175.89/129.65 |-The branch is then unsatisfiable
% 175.89/129.65 |-Branch two:
% 175.89/129.65 | (553) ~ (all_32_2_493 = 0) & model_max(all_0_4_4, all_0_3_3, all_0_2_2) = all_32_2_493
% 175.89/129.65 |
% 175.89/129.65 | Applying alpha-rule on (553) yields:
% 175.89/129.65 | (554) ~ (all_32_2_493 = 0)
% 175.89/129.65 | (555) model_max(all_0_4_4, all_0_3_3, all_0_2_2) = all_32_2_493
% 175.89/129.65 |
% 175.89/129.65 | Instantiating formula (48) with all_32_2_493, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms model_max(all_0_4_4, all_0_3_3, all_0_2_2) = all_32_2_493, yields:
% 175.89/129.65 | (556) all_32_2_493 = 0 | ? [v0] : ( ~ (v0 = all_0_2_2) & max(all_0_4_4, all_0_3_3) = v0)
% 175.89/129.65 |
% 175.89/129.65 +-Applying beta-rule and splitting (556), into two cases.
% 175.89/129.65 |-Branch one:
% 175.89/129.65 | (557) all_32_2_493 = 0
% 175.89/129.65 |
% 175.89/129.65 | Equations (557) can reduce 554 to:
% 175.89/129.65 | (72) $false
% 175.89/129.65 |
% 175.89/129.65 |-The branch is then unsatisfiable
% 175.89/129.65 |-Branch two:
% 175.89/129.65 | (554) ~ (all_32_2_493 = 0)
% 175.89/129.65 | (560) ? [v0] : ( ~ (v0 = all_0_2_2) & max(all_0_4_4, all_0_3_3) = v0)
% 175.89/129.65 |
% 175.89/129.65 | Instantiating (560) with all_165_0_1403 yields:
% 175.89/129.65 | (561) ~ (all_165_0_1403 = all_0_2_2) & max(all_0_4_4, all_0_3_3) = all_165_0_1403
% 175.89/129.66 |
% 175.89/129.66 | Applying alpha-rule on (561) yields:
% 175.89/129.66 | (562) ~ (all_165_0_1403 = all_0_2_2)
% 175.89/129.66 | (563) max(all_0_4_4, all_0_3_3) = all_165_0_1403
% 175.89/129.66 |
% 175.89/129.66 +-Applying beta-rule and splitting (247), into two cases.
% 175.89/129.66 |-Branch one:
% 175.89/129.66 | (298) all_46_1_496 = 0 & ~ (all_46_0_495 = 0) & model_ub(all_0_4_4, all_0_3_3, all_46_2_497) = 0 & lesseq(all_0_2_2, all_46_2_497) = all_46_0_495
% 175.89/129.66 |
% 175.89/129.66 | Applying alpha-rule on (298) yields:
% 175.89/129.66 | (299) all_46_1_496 = 0
% 175.89/129.66 | (300) ~ (all_46_0_495 = 0)
% 175.89/129.66 | (301) model_ub(all_0_4_4, all_0_3_3, all_46_2_497) = 0
% 175.89/129.66 | (302) lesseq(all_0_2_2, all_46_2_497) = all_46_0_495
% 175.89/129.66 |
% 175.89/129.66 | Instantiating formula (13) with all_46_2_497, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, model_ub(all_0_4_4, all_0_3_3, all_46_2_497) = 0, yields:
% 175.89/129.66 | (303) lesseq(all_0_2_2, all_46_2_497) = 0
% 175.89/129.66 |
% 175.89/129.66 | Instantiating formula (33) with all_46_0_495, all_46_2_497, 0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, lesseq(all_0_2_2, all_46_2_497) = all_46_0_495, yields:
% 175.89/129.66 | (304) all_46_0_495 = 0 | ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_46_2_497) = v0))
% 175.89/129.66 |
% 175.89/129.66 | Instantiating formula (16) with all_46_0_495, all_46_2_497, all_32_2_493, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms model_max(all_0_4_4, all_0_3_3, all_0_2_2) = all_32_2_493, lesseq(all_0_2_2, all_46_2_497) = all_46_0_495, yields:
% 175.89/129.66 | (571) all_46_0_495 = 0 | ? [v0] : (( ~ (v0 = 0) & minsol_model_max(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_max(all_0_4_4, all_0_3_3, all_46_2_497) = v0))
% 175.89/129.66 |
% 175.89/129.66 | Instantiating formula (39) with all_46_0_495, all_46_2_497, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, lesseq(all_0_2_2, all_46_2_497) = all_46_0_495, yields:
% 175.89/129.66 | (305) all_46_0_495 = 0 | ? [v0] : ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_46_2_497) = v0)
% 175.89/129.66 |
% 175.89/129.66 | Instantiating formula (42) with all_46_0_495, all_46_2_497, all_0_2_2 and discharging atoms lesseq(all_0_2_2, all_46_2_497) = all_46_0_495, yields:
% 175.89/129.66 | (306) all_46_0_495 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_46_2_497) = v1 & summation(all_0_2_2) = v0 & lesseq(v0, v1) = v2)
% 175.89/129.66 |
% 175.89/129.66 +-Applying beta-rule and splitting (306), into two cases.
% 175.89/129.66 |-Branch one:
% 175.89/129.66 | (307) all_46_0_495 = 0
% 175.89/129.66 |
% 175.89/129.66 | Equations (307) can reduce 300 to:
% 175.89/129.66 | (72) $false
% 175.89/129.66 |
% 175.89/129.66 |-The branch is then unsatisfiable
% 175.89/129.66 |-Branch two:
% 175.89/129.66 | (300) ~ (all_46_0_495 = 0)
% 175.89/129.66 | (314) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_46_2_497) = v1 & summation(all_0_2_2) = v0 & lesseq(v0, v1) = v2)
% 175.89/129.66 |
% 175.89/129.66 +-Applying beta-rule and splitting (305), into two cases.
% 175.89/129.66 |-Branch one:
% 175.89/129.66 | (307) all_46_0_495 = 0
% 175.89/129.66 |
% 175.89/129.66 | Equations (307) can reduce 300 to:
% 175.89/129.66 | (72) $false
% 175.89/129.66 |
% 175.89/129.66 |-The branch is then unsatisfiable
% 175.89/129.66 |-Branch two:
% 175.89/129.66 | (300) ~ (all_46_0_495 = 0)
% 175.89/129.66 | (318) ? [v0] : ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_46_2_497) = v0)
% 175.89/129.66 |
% 175.89/129.66 +-Applying beta-rule and splitting (304), into two cases.
% 175.89/129.66 |-Branch one:
% 175.89/129.66 | (307) all_46_0_495 = 0
% 175.89/129.66 |
% 175.89/129.66 | Equations (307) can reduce 300 to:
% 175.89/129.66 | (72) $false
% 175.89/129.66 |
% 175.89/129.66 |-The branch is then unsatisfiable
% 175.89/129.66 |-Branch two:
% 175.89/129.66 | (300) ~ (all_46_0_495 = 0)
% 175.89/129.66 | (310) ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_46_2_497) = v0))
% 175.89/129.66 |
% 175.89/129.66 +-Applying beta-rule and splitting (571), into two cases.
% 175.89/129.66 |-Branch one:
% 175.89/129.66 | (307) all_46_0_495 = 0
% 175.89/129.66 |
% 175.89/129.66 | Equations (307) can reduce 300 to:
% 175.89/129.66 | (72) $false
% 175.89/129.66 |
% 175.89/129.66 |-The branch is then unsatisfiable
% 175.89/129.66 |-Branch two:
% 175.89/129.66 | (300) ~ (all_46_0_495 = 0)
% 175.89/129.66 | (589) ? [v0] : (( ~ (v0 = 0) & minsol_model_max(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_max(all_0_4_4, all_0_3_3, all_46_2_497) = v0))
% 175.89/129.66 |
% 175.89/129.66 | Instantiating formula (11) with all_0_2_2, all_46_2_497, 0, all_46_0_495 and discharging atoms lesseq(all_0_2_2, all_46_2_497) = all_46_0_495, lesseq(all_0_2_2, all_46_2_497) = 0, yields:
% 175.89/129.66 | (307) all_46_0_495 = 0
% 175.89/129.66 |
% 175.89/129.66 | Equations (307) can reduce 300 to:
% 175.89/129.66 | (72) $false
% 175.89/129.66 |
% 175.89/129.66 |-The branch is then unsatisfiable
% 175.89/129.66 |-Branch two:
% 175.89/129.66 | (321) all_46_2_497 = 0 & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 175.89/129.66 |
% 175.89/129.66 | Applying alpha-rule on (321) yields:
% 175.89/129.66 | (322) all_46_2_497 = 0
% 175.89/129.66 | (238) minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 175.89/129.66 |
% 175.89/129.66 | Instantiating formula (49) with all_165_0_1403, all_0_3_3, all_0_4_4 and discharging atoms max(all_0_4_4, all_0_3_3) = all_165_0_1403, yields:
% 175.89/129.66 | (595) all_165_0_1403 = all_0_3_3 | ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_3_3) = v0)
% 175.89/129.66 |
% 175.89/129.66 | Instantiating formula (15) with all_165_0_1403, all_0_3_3, all_0_4_4 and discharging atoms max(all_0_4_4, all_0_3_3) = all_165_0_1403, yields:
% 175.89/129.66 | (596) all_165_0_1403 = all_0_4_4 | ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_4_4) = v0)
% 175.89/129.66 |
% 175.89/129.66 +-Applying beta-rule and splitting (254), into two cases.
% 175.89/129.66 |-Branch one:
% 175.89/129.66 | (101) all_0_2_2 = all_0_3_3
% 175.89/129.66 |
% 175.89/129.66 | Equations (101) can reduce 562 to:
% 175.89/129.66 | (598) ~ (all_165_0_1403 = all_0_3_3)
% 175.89/129.66 |
% 175.89/129.66 | From (101)(101) and (253) follows:
% 175.89/129.66 | (340) max(all_0_4_4, all_0_3_3) = all_0_3_3
% 175.89/129.66 |
% 175.89/129.66 +-Applying beta-rule and splitting (595), into two cases.
% 175.89/129.66 |-Branch one:
% 175.89/129.66 | (600) all_165_0_1403 = all_0_3_3
% 175.89/129.66 |
% 175.89/129.66 | Equations (600) can reduce 598 to:
% 175.89/129.66 | (72) $false
% 175.89/129.66 |
% 175.89/129.66 |-The branch is then unsatisfiable
% 175.89/129.66 |-Branch two:
% 175.89/129.66 | (598) ~ (all_165_0_1403 = all_0_3_3)
% 175.89/129.66 | (109) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_3_3) = v0)
% 175.89/129.66 |
% 175.89/129.66 | Instantiating formula (47) with all_0_4_4, all_0_3_3, all_0_3_3, all_165_0_1403 and discharging atoms max(all_0_4_4, all_0_3_3) = all_165_0_1403, max(all_0_4_4, all_0_3_3) = all_0_3_3, yields:
% 175.89/129.66 | (600) all_165_0_1403 = all_0_3_3
% 175.89/129.66 |
% 175.89/129.66 | Equations (600) can reduce 598 to:
% 175.89/129.66 | (72) $false
% 175.89/129.66 |
% 175.89/129.66 |-The branch is then unsatisfiable
% 175.89/129.66 |-Branch two:
% 175.89/129.66 | (108) ~ (all_0_2_2 = all_0_3_3)
% 175.89/129.66 | (353) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_2_2, all_0_3_3) = v0)
% 175.89/129.66 |
% 175.89/129.66 | Instantiating (353) with all_199_0_1434 yields:
% 175.89/129.66 | (608) ~ (all_199_0_1434 = 0) & lesseq(all_0_2_2, all_0_3_3) = all_199_0_1434
% 175.89/129.66 |
% 175.89/129.66 | Applying alpha-rule on (608) yields:
% 175.89/129.66 | (609) ~ (all_199_0_1434 = 0)
% 175.89/129.66 | (610) lesseq(all_0_2_2, all_0_3_3) = all_199_0_1434
% 175.89/129.66 |
% 175.89/129.66 +-Applying beta-rule and splitting (255), into two cases.
% 175.89/129.66 |-Branch one:
% 175.89/129.66 | (113) all_0_2_2 = all_0_4_4
% 175.89/129.66 |
% 175.89/129.66 | Equations (113) can reduce 562 to:
% 175.89/129.66 | (612) ~ (all_165_0_1403 = all_0_4_4)
% 175.89/129.66 |
% 175.89/129.66 | From (113)(113) and (251) follows:
% 175.89/129.66 | (358) max(all_0_4_4, all_0_3_3) = all_0_4_4
% 175.89/129.66 |
% 175.89/129.66 +-Applying beta-rule and splitting (596), into two cases.
% 175.89/129.66 |-Branch one:
% 175.89/129.66 | (614) all_165_0_1403 = all_0_4_4
% 175.89/129.66 |
% 175.89/129.66 | Equations (614) can reduce 612 to:
% 175.89/129.66 | (72) $false
% 175.89/129.66 |
% 175.89/129.66 |-The branch is then unsatisfiable
% 175.89/129.66 |-Branch two:
% 175.89/129.66 | (612) ~ (all_165_0_1403 = all_0_4_4)
% 175.89/129.66 | (121) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_4_4) = v0)
% 175.89/129.66 |
% 175.89/129.66 | Instantiating formula (47) with all_0_4_4, all_0_3_3, all_0_4_4, all_165_0_1403 and discharging atoms max(all_0_4_4, all_0_3_3) = all_165_0_1403, max(all_0_4_4, all_0_3_3) = all_0_4_4, yields:
% 175.89/129.66 | (614) all_165_0_1403 = all_0_4_4
% 175.89/129.66 |
% 175.89/129.66 | Equations (614) can reduce 612 to:
% 175.89/129.66 | (72) $false
% 175.89/129.67 |
% 175.89/129.67 |-The branch is then unsatisfiable
% 175.89/129.67 |-Branch two:
% 175.89/129.67 | (120) ~ (all_0_2_2 = all_0_4_4)
% 175.89/129.67 | (371) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_2_2, all_0_4_4) = v0)
% 175.89/129.67 |
% 175.89/129.67 | Instantiating (371) with all_207_0_1436 yields:
% 175.89/129.67 | (622) ~ (all_207_0_1436 = 0) & lesseq(all_0_2_2, all_0_4_4) = all_207_0_1436
% 175.89/129.67 |
% 175.89/129.67 | Applying alpha-rule on (622) yields:
% 175.89/129.67 | (623) ~ (all_207_0_1436 = 0)
% 175.89/129.67 | (624) lesseq(all_0_2_2, all_0_4_4) = all_207_0_1436
% 175.89/129.67 |
% 175.89/129.67 | Instantiating formula (33) with all_199_0_1434, all_0_3_3, 0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, lesseq(all_0_2_2, all_0_3_3) = all_199_0_1434, yields:
% 175.89/129.67 | (625) all_199_0_1434 = 0 | ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0))
% 175.89/129.67 |
% 175.89/129.67 | Instantiating formula (39) with all_199_0_1434, all_0_3_3, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, lesseq(all_0_2_2, all_0_3_3) = all_199_0_1434, yields:
% 175.89/129.67 | (626) all_199_0_1434 = 0 | ? [v0] : ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0)
% 175.89/129.67 |
% 175.89/129.67 | Instantiating formula (42) with all_199_0_1434, all_0_3_3, all_0_2_2 and discharging atoms lesseq(all_0_2_2, all_0_3_3) = all_199_0_1434, yields:
% 175.89/129.67 | (627) all_199_0_1434 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_0_2_2) = v0 & summation(all_0_3_3) = v1 & lesseq(v0, v1) = v2)
% 175.89/129.67 |
% 175.89/129.67 | Instantiating formula (33) with all_207_0_1436, all_0_4_4, 0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, lesseq(all_0_2_2, all_0_4_4) = all_207_0_1436, yields:
% 175.89/129.67 | (628) all_207_0_1436 = 0 | ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = v0))
% 175.89/129.67 |
% 175.89/129.67 | Instantiating formula (16) with all_207_0_1436, all_0_4_4, all_32_2_493, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms model_max(all_0_4_4, all_0_3_3, all_0_2_2) = all_32_2_493, lesseq(all_0_2_2, all_0_4_4) = all_207_0_1436, yields:
% 175.89/129.67 | (629) all_207_0_1436 = 0 | ? [v0] : (( ~ (v0 = 0) & minsol_model_max(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_max(all_0_4_4, all_0_3_3, all_0_4_4) = v0))
% 175.89/129.67 |
% 175.89/129.67 | Instantiating formula (39) with all_207_0_1436, all_0_4_4, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, lesseq(all_0_2_2, all_0_4_4) = all_207_0_1436, yields:
% 175.89/129.67 | (630) all_207_0_1436 = 0 | ? [v0] : ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = v0)
% 175.89/129.67 |
% 175.89/129.67 | Instantiating formula (42) with all_207_0_1436, all_0_4_4, all_0_2_2 and discharging atoms lesseq(all_0_2_2, all_0_4_4) = all_207_0_1436, yields:
% 175.89/129.67 | (631) all_207_0_1436 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_0_2_2) = v0 & summation(all_0_4_4) = v1 & lesseq(v0, v1) = v2)
% 175.89/129.67 |
% 175.89/129.67 +-Applying beta-rule and splitting (631), into two cases.
% 175.89/129.67 |-Branch one:
% 175.89/129.67 | (632) all_207_0_1436 = 0
% 175.89/129.67 |
% 175.89/129.67 | Equations (632) can reduce 623 to:
% 175.89/129.67 | (72) $false
% 175.89/129.67 |
% 175.89/129.67 |-The branch is then unsatisfiable
% 175.89/129.67 |-Branch two:
% 175.89/129.67 | (623) ~ (all_207_0_1436 = 0)
% 175.89/129.67 | (635) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_0_2_2) = v0 & summation(all_0_4_4) = v1 & lesseq(v0, v1) = v2)
% 175.89/129.67 |
% 175.89/129.67 +-Applying beta-rule and splitting (627), into two cases.
% 175.89/129.67 |-Branch one:
% 175.89/129.67 | (636) all_199_0_1434 = 0
% 175.89/129.67 |
% 175.89/129.67 | Equations (636) can reduce 609 to:
% 175.89/129.67 | (72) $false
% 175.89/129.67 |
% 175.89/129.67 |-The branch is then unsatisfiable
% 175.89/129.67 |-Branch two:
% 175.89/129.67 | (609) ~ (all_199_0_1434 = 0)
% 175.89/129.67 | (639) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & summation(all_0_2_2) = v0 & summation(all_0_3_3) = v1 & lesseq(v0, v1) = v2)
% 175.89/129.67 |
% 175.89/129.67 +-Applying beta-rule and splitting (626), into two cases.
% 175.89/129.67 |-Branch one:
% 175.89/129.67 | (636) all_199_0_1434 = 0
% 175.89/129.67 |
% 175.89/129.67 | Equations (636) can reduce 609 to:
% 175.89/129.67 | (72) $false
% 175.89/129.67 |
% 175.89/129.67 |-The branch is then unsatisfiable
% 175.89/129.67 |-Branch two:
% 175.89/129.67 | (609) ~ (all_199_0_1434 = 0)
% 175.89/129.67 | (394) ? [v0] : ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0)
% 175.89/129.67 |
% 175.89/129.67 | Instantiating (394) with all_235_0_1449 yields:
% 175.89/129.67 | (644) ~ (all_235_0_1449 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_235_0_1449
% 175.89/129.67 |
% 175.89/129.67 | Applying alpha-rule on (644) yields:
% 175.89/129.67 | (645) ~ (all_235_0_1449 = 0)
% 175.89/129.67 | (646) model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_235_0_1449
% 175.89/129.67 |
% 175.89/129.67 +-Applying beta-rule and splitting (625), into two cases.
% 175.89/129.67 |-Branch one:
% 175.89/129.67 | (636) all_199_0_1434 = 0
% 175.89/129.67 |
% 175.89/129.67 | Equations (636) can reduce 609 to:
% 175.89/129.67 | (72) $false
% 175.89/129.67 |
% 175.89/129.67 |-The branch is then unsatisfiable
% 175.89/129.67 |-Branch two:
% 175.89/129.67 | (609) ~ (all_199_0_1434 = 0)
% 175.89/129.67 | (401) ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0))
% 175.89/129.67 |
% 175.89/129.67 | Instantiating (401) with all_240_0_1450 yields:
% 175.89/129.67 | (651) ( ~ (all_240_0_1450 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_240_0_1450) | ( ~ (all_240_0_1450 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_240_0_1450)
% 175.89/129.67 |
% 175.89/129.67 +-Applying beta-rule and splitting (628), into two cases.
% 175.89/129.67 |-Branch one:
% 175.89/129.67 | (632) all_207_0_1436 = 0
% 175.89/129.67 |
% 175.89/129.67 | Equations (632) can reduce 623 to:
% 175.89/129.67 | (72) $false
% 175.89/129.67 |
% 175.89/129.67 |-The branch is then unsatisfiable
% 175.89/129.67 |-Branch two:
% 175.89/129.67 | (623) ~ (all_207_0_1436 = 0)
% 175.89/129.67 | (655) ? [v0] : (( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = v0))
% 175.89/129.67 |
% 175.89/129.67 | Instantiating (655) with all_244_0_1451 yields:
% 175.89/129.67 | (656) ( ~ (all_244_0_1451 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_244_0_1451) | ( ~ (all_244_0_1451 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_244_0_1451)
% 175.89/129.67 |
% 175.89/129.67 +-Applying beta-rule and splitting (629), into two cases.
% 175.89/129.67 |-Branch one:
% 175.89/129.67 | (632) all_207_0_1436 = 0
% 175.89/129.67 |
% 175.89/129.67 | Equations (632) can reduce 623 to:
% 175.89/129.67 | (72) $false
% 175.89/129.67 |
% 175.89/129.67 |-The branch is then unsatisfiable
% 175.89/129.67 |-Branch two:
% 175.89/129.67 | (623) ~ (all_207_0_1436 = 0)
% 175.89/129.67 | (660) ? [v0] : (( ~ (v0 = 0) & minsol_model_max(all_0_4_4, all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & model_max(all_0_4_4, all_0_3_3, all_0_4_4) = v0))
% 175.89/129.67 |
% 175.89/129.67 +-Applying beta-rule and splitting (630), into two cases.
% 175.89/129.67 |-Branch one:
% 175.89/129.67 | (632) all_207_0_1436 = 0
% 175.89/129.67 |
% 175.89/129.67 | Equations (632) can reduce 623 to:
% 175.89/129.67 | (72) $false
% 175.89/129.67 |
% 175.89/129.67 |-The branch is then unsatisfiable
% 175.89/129.67 |-Branch two:
% 175.89/129.67 | (623) ~ (all_207_0_1436 = 0)
% 175.89/129.67 | (387) ? [v0] : ( ~ (v0 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = v0)
% 175.89/129.67 |
% 175.89/129.67 | Instantiating (387) with all_256_0_1454 yields:
% 175.89/129.67 | (665) ~ (all_256_0_1454 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_256_0_1454
% 175.89/129.67 |
% 175.89/129.67 | Applying alpha-rule on (665) yields:
% 175.89/129.67 | (666) ~ (all_256_0_1454 = 0)
% 175.89/129.67 | (667) model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_256_0_1454
% 175.89/129.67 |
% 175.89/129.67 +-Applying beta-rule and splitting (656), into two cases.
% 175.89/129.67 |-Branch one:
% 175.89/129.67 | (668) ~ (all_244_0_1451 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_244_0_1451
% 175.89/129.67 |
% 175.89/129.67 | Applying alpha-rule on (668) yields:
% 175.89/129.67 | (669) ~ (all_244_0_1451 = 0)
% 175.89/129.67 | (670) minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_244_0_1451
% 175.89/129.67 |
% 175.89/129.67 | Instantiating formula (12) with all_0_4_4, all_0_3_3, all_0_2_2, all_244_0_1451, 0 and discharging atoms minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_244_0_1451, minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, yields:
% 175.89/129.67 | (671) all_244_0_1451 = 0
% 175.89/129.67 |
% 175.89/129.67 | Equations (671) can reduce 669 to:
% 175.89/129.67 | (72) $false
% 175.89/129.67 |
% 175.89/129.67 |-The branch is then unsatisfiable
% 175.89/129.67 |-Branch two:
% 175.89/129.67 | (673) ~ (all_244_0_1451 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_244_0_1451
% 175.89/129.67 |
% 175.89/129.67 | Applying alpha-rule on (673) yields:
% 175.89/129.67 | (669) ~ (all_244_0_1451 = 0)
% 175.89/129.68 | (675) model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_244_0_1451
% 175.89/129.68 |
% 175.89/129.68 +-Applying beta-rule and splitting (651), into two cases.
% 175.89/129.68 |-Branch one:
% 175.89/129.68 | (676) ~ (all_240_0_1450 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_240_0_1450
% 175.89/129.68 |
% 175.89/129.68 | Applying alpha-rule on (676) yields:
% 175.89/129.68 | (677) ~ (all_240_0_1450 = 0)
% 175.89/129.68 | (678) minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_240_0_1450
% 175.89/129.68 |
% 175.89/129.68 | Instantiating formula (12) with all_0_4_4, all_0_3_3, all_0_2_2, all_240_0_1450, 0 and discharging atoms minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = all_240_0_1450, minsol_model_ub(all_0_4_4, all_0_3_3, all_0_2_2) = 0, yields:
% 175.89/129.68 | (679) all_240_0_1450 = 0
% 175.89/129.68 |
% 175.89/129.68 | Equations (679) can reduce 677 to:
% 175.89/129.68 | (72) $false
% 175.89/129.68 |
% 175.89/129.68 |-The branch is then unsatisfiable
% 175.89/129.68 |-Branch two:
% 175.89/129.68 | (681) ~ (all_240_0_1450 = 0) & model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_240_0_1450
% 175.89/129.68 |
% 175.89/129.68 | Applying alpha-rule on (681) yields:
% 175.89/129.68 | (677) ~ (all_240_0_1450 = 0)
% 175.89/129.68 | (683) model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_240_0_1450
% 175.89/129.68 |
% 175.89/129.68 | Instantiating formula (52) with all_0_4_4, all_0_3_3, all_0_3_3, all_235_0_1449, all_240_0_1450 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_240_0_1450, model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_235_0_1449, yields:
% 175.89/129.68 | (684) all_240_0_1450 = all_235_0_1449
% 175.89/129.68 |
% 175.89/129.68 | Instantiating formula (52) with all_0_4_4, all_0_3_3, all_0_4_4, all_244_0_1451, all_256_0_1454 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_256_0_1454, model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_244_0_1451, yields:
% 175.89/129.68 | (685) all_256_0_1454 = all_244_0_1451
% 175.89/129.68 |
% 175.89/129.68 | Equations (685) can reduce 666 to:
% 175.89/129.68 | (669) ~ (all_244_0_1451 = 0)
% 175.89/129.68 |
% 175.89/129.68 | Equations (684) can reduce 677 to:
% 175.89/129.68 | (645) ~ (all_235_0_1449 = 0)
% 175.89/129.68 |
% 175.89/129.68 | From (684) and (683) follows:
% 175.89/129.68 | (646) model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_235_0_1449
% 175.89/129.68 |
% 175.89/129.68 | From (685) and (667) follows:
% 175.89/129.68 | (675) model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_244_0_1451
% 175.89/129.68 |
% 175.89/129.68 | Instantiating formula (20) with all_235_0_1449, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_235_0_1449, yields:
% 175.89/129.68 | (690) all_235_0_1449 = 0 | ? [v0] : ( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0)
% 175.89/129.68 |
% 175.89/129.68 | Instantiating formula (35) with all_235_0_1449, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_235_0_1449, yields:
% 175.89/129.68 | (691) all_235_0_1449 = 0 | ? [v0] : ( ~ (v0 = 0) & ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0)
% 175.89/129.68 |
% 175.89/129.68 | Instantiating formula (20) with all_244_0_1451, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_244_0_1451, yields:
% 175.89/129.68 | (692) all_244_0_1451 = 0 | ? [v0] : ( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = v0)
% 175.89/129.68 |
% 175.89/129.68 | Instantiating formula (35) with all_244_0_1451, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_244_0_1451, yields:
% 175.89/129.68 | (693) all_244_0_1451 = 0 | ? [v0] : ( ~ (v0 = 0) & ub(all_0_4_4, all_0_3_3, all_0_4_4) = v0)
% 175.89/129.68 |
% 175.89/129.68 +-Applying beta-rule and splitting (690), into two cases.
% 175.89/129.68 |-Branch one:
% 175.89/129.68 | (694) all_235_0_1449 = 0
% 175.89/129.68 |
% 175.89/129.68 | Equations (694) can reduce 645 to:
% 175.89/129.68 | (72) $false
% 175.89/129.68 |
% 175.89/129.68 |-The branch is then unsatisfiable
% 175.89/129.68 |-Branch two:
% 175.89/129.68 | (645) ~ (all_235_0_1449 = 0)
% 175.89/129.68 | (697) ? [v0] : ( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0)
% 175.89/129.68 |
% 175.89/129.68 +-Applying beta-rule and splitting (691), into two cases.
% 175.89/129.68 |-Branch one:
% 175.89/129.68 | (694) all_235_0_1449 = 0
% 175.89/129.68 |
% 175.89/129.68 | Equations (694) can reduce 645 to:
% 175.89/129.68 | (72) $false
% 175.89/129.68 |
% 175.89/129.68 |-The branch is then unsatisfiable
% 175.89/129.68 |-Branch two:
% 175.89/129.68 | (645) ~ (all_235_0_1449 = 0)
% 175.89/129.68 | (701) ? [v0] : ( ~ (v0 = 0) & ub(all_0_4_4, all_0_3_3, all_0_3_3) = v0)
% 175.89/129.68 |
% 175.89/129.68 | Instantiating (701) with all_319_0_1521 yields:
% 175.89/129.68 | (702) ~ (all_319_0_1521 = 0) & ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_319_0_1521
% 175.89/129.68 |
% 175.89/129.68 | Applying alpha-rule on (702) yields:
% 175.89/129.68 | (703) ~ (all_319_0_1521 = 0)
% 175.89/129.68 | (704) ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_319_0_1521
% 175.89/129.68 |
% 175.89/129.68 +-Applying beta-rule and splitting (692), into two cases.
% 175.89/129.68 |-Branch one:
% 175.89/129.68 | (671) all_244_0_1451 = 0
% 175.89/129.68 |
% 175.89/129.68 | Equations (671) can reduce 669 to:
% 175.89/129.68 | (72) $false
% 175.89/129.68 |
% 175.89/129.68 |-The branch is then unsatisfiable
% 175.89/129.68 |-Branch two:
% 175.89/129.68 | (669) ~ (all_244_0_1451 = 0)
% 175.89/129.68 | (708) ? [v0] : ( ~ (v0 = 0) & minsol_model_ub(all_0_4_4, all_0_3_3, all_0_4_4) = v0)
% 175.89/129.68 |
% 175.89/129.68 +-Applying beta-rule and splitting (693), into two cases.
% 175.89/129.68 |-Branch one:
% 175.89/129.68 | (671) all_244_0_1451 = 0
% 175.89/129.68 |
% 175.89/129.68 | Equations (671) can reduce 669 to:
% 175.89/129.68 | (72) $false
% 175.89/129.68 |
% 175.89/129.68 |-The branch is then unsatisfiable
% 175.89/129.68 |-Branch two:
% 175.89/129.68 | (669) ~ (all_244_0_1451 = 0)
% 175.89/129.68 | (712) ? [v0] : ( ~ (v0 = 0) & ub(all_0_4_4, all_0_3_3, all_0_4_4) = v0)
% 175.89/129.68 |
% 175.89/129.68 | Instantiating (712) with all_329_0_1523 yields:
% 175.89/129.68 | (713) ~ (all_329_0_1523 = 0) & ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_329_0_1523
% 175.89/129.68 |
% 175.89/129.68 | Applying alpha-rule on (713) yields:
% 175.89/129.68 | (714) ~ (all_329_0_1523 = 0)
% 175.89/129.68 | (715) ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_329_0_1523
% 175.89/129.68 |
% 175.89/129.68 +-Applying beta-rule and splitting (595), into two cases.
% 175.89/129.68 |-Branch one:
% 175.89/129.68 | (600) all_165_0_1403 = all_0_3_3
% 175.89/129.68 |
% 175.89/129.68 +-Applying beta-rule and splitting (596), into two cases.
% 175.89/129.68 |-Branch one:
% 175.89/129.68 | (614) all_165_0_1403 = all_0_4_4
% 175.89/129.68 |
% 175.89/129.68 | Combining equations (614,600) yields a new equation:
% 175.89/129.68 | (152) all_0_3_3 = all_0_4_4
% 175.89/129.68 |
% 175.89/129.68 | From (152)(152) and (704) follows:
% 175.89/129.68 | (719) ub(all_0_4_4, all_0_4_4, all_0_4_4) = all_319_0_1521
% 175.89/129.68 |
% 175.89/129.68 | From (152) and (715) follows:
% 175.89/129.68 | (720) ub(all_0_4_4, all_0_4_4, all_0_4_4) = all_329_0_1523
% 175.89/129.68 |
% 175.89/129.68 | Instantiating formula (60) with all_0_4_4, all_0_4_4, all_0_4_4, all_319_0_1521, all_329_0_1523 and discharging atoms ub(all_0_4_4, all_0_4_4, all_0_4_4) = all_329_0_1523, ub(all_0_4_4, all_0_4_4, all_0_4_4) = all_319_0_1521, yields:
% 175.89/129.68 | (721) all_329_0_1523 = all_319_0_1521
% 175.89/129.68 |
% 175.89/129.68 | Equations (721) can reduce 714 to:
% 175.89/129.68 | (703) ~ (all_319_0_1521 = 0)
% 175.89/129.68 |
% 175.89/129.68 | From (721) and (720) follows:
% 175.89/129.68 | (719) ub(all_0_4_4, all_0_4_4, all_0_4_4) = all_319_0_1521
% 175.89/129.68 |
% 175.89/129.68 | Instantiating formula (5) with all_319_0_1521, all_0_4_4, all_0_4_4, all_0_4_4 and discharging atoms ub(all_0_4_4, all_0_4_4, all_0_4_4) = all_319_0_1521, yields:
% 175.89/129.68 | (724) all_319_0_1521 = 0 | ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_4_4) = v0)
% 175.89/129.68 |
% 175.89/129.68 +-Applying beta-rule and splitting (724), into two cases.
% 175.89/129.68 |-Branch one:
% 175.89/129.68 | (725) all_319_0_1521 = 0
% 175.89/129.68 |
% 175.89/129.68 | Equations (725) can reduce 703 to:
% 175.89/129.68 | (72) $false
% 175.89/129.68 |
% 175.89/129.68 |-The branch is then unsatisfiable
% 175.89/129.68 |-Branch two:
% 175.89/129.68 | (703) ~ (all_319_0_1521 = 0)
% 175.89/129.68 | (158) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_4_4) = v0)
% 175.89/129.68 |
% 175.89/129.68 | Instantiating (158) with all_454_0_1769 yields:
% 175.89/129.68 | (729) ~ (all_454_0_1769 = 0) & lesseq(all_0_4_4, all_0_4_4) = all_454_0_1769
% 175.89/129.68 |
% 175.89/129.68 | Applying alpha-rule on (729) yields:
% 175.89/129.68 | (730) ~ (all_454_0_1769 = 0)
% 175.89/129.68 | (731) lesseq(all_0_4_4, all_0_4_4) = all_454_0_1769
% 175.89/129.68 |
% 175.89/129.68 | Instantiating formula (56) with all_454_0_1769, all_0_4_4 and discharging atoms lesseq(all_0_4_4, all_0_4_4) = all_454_0_1769, yields:
% 175.89/129.69 | (732) all_454_0_1769 = 0
% 175.89/129.69 |
% 175.89/129.69 | Equations (732) can reduce 730 to:
% 175.89/129.69 | (72) $false
% 175.89/129.69 |
% 175.89/129.69 |-The branch is then unsatisfiable
% 175.89/129.69 |-Branch two:
% 175.89/129.69 | (612) ~ (all_165_0_1403 = all_0_4_4)
% 175.89/129.69 | (121) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_4_4) = v0)
% 175.89/129.69 |
% 175.89/129.69 | Instantiating (121) with all_395_0_1770 yields:
% 175.89/129.69 | (736) ~ (all_395_0_1770 = 0) & lesseq(all_0_3_3, all_0_4_4) = all_395_0_1770
% 175.89/129.69 |
% 175.89/129.69 | Applying alpha-rule on (736) yields:
% 175.89/129.69 | (737) ~ (all_395_0_1770 = 0)
% 175.89/129.69 | (738) lesseq(all_0_3_3, all_0_4_4) = all_395_0_1770
% 175.89/129.69 |
% 175.89/129.69 | Instantiating formula (5) with all_319_0_1521, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms ub(all_0_4_4, all_0_3_3, all_0_3_3) = all_319_0_1521, yields:
% 175.89/129.69 | (739) all_319_0_1521 = 0 | ? [v0] : (( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_3_3) = v0))
% 175.89/129.69 |
% 175.89/129.69 | Instantiating formula (10) with all_395_0_1770, all_0_3_3, all_0_4_4 and discharging atoms lesseq(all_0_3_3, all_0_4_4) = all_395_0_1770, yields:
% 175.89/129.69 | (740) all_395_0_1770 = 0 | lesseq(all_0_4_4, all_0_3_3) = 0
% 175.89/129.69 |
% 175.89/129.69 +-Applying beta-rule and splitting (740), into two cases.
% 175.89/129.69 |-Branch one:
% 175.89/129.69 | (127) lesseq(all_0_4_4, all_0_3_3) = 0
% 175.89/129.69 |
% 175.89/129.69 +-Applying beta-rule and splitting (739), into two cases.
% 175.89/129.69 |-Branch one:
% 175.89/129.69 | (725) all_319_0_1521 = 0
% 175.89/129.69 |
% 175.89/129.69 | Equations (725) can reduce 703 to:
% 175.89/129.69 | (72) $false
% 175.89/129.69 |
% 175.89/129.69 |-The branch is then unsatisfiable
% 175.89/129.69 |-Branch two:
% 175.89/129.69 | (703) ~ (all_319_0_1521 = 0)
% 175.89/129.69 | (203) ? [v0] : (( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_3_3) = v0))
% 175.89/129.69 |
% 175.89/129.69 | Instantiating (203) with all_425_0_1783 yields:
% 175.89/129.69 | (746) ( ~ (all_425_0_1783 = 0) & lesseq(all_0_3_3, all_0_3_3) = all_425_0_1783) | ( ~ (all_425_0_1783 = 0) & lesseq(all_0_4_4, all_0_3_3) = all_425_0_1783)
% 175.89/129.69 |
% 175.89/129.69 +-Applying beta-rule and splitting (746), into two cases.
% 175.89/129.69 |-Branch one:
% 175.89/129.69 | (747) ~ (all_425_0_1783 = 0) & lesseq(all_0_3_3, all_0_3_3) = all_425_0_1783
% 175.89/129.69 |
% 175.89/129.69 | Applying alpha-rule on (747) yields:
% 175.89/129.69 | (748) ~ (all_425_0_1783 = 0)
% 175.89/129.69 | (749) lesseq(all_0_3_3, all_0_3_3) = all_425_0_1783
% 175.89/129.69 |
% 175.89/129.69 | Instantiating formula (56) with all_425_0_1783, all_0_3_3 and discharging atoms lesseq(all_0_3_3, all_0_3_3) = all_425_0_1783, yields:
% 175.89/129.69 | (750) all_425_0_1783 = 0
% 175.89/129.69 |
% 175.89/129.69 | Equations (750) can reduce 748 to:
% 175.89/129.69 | (72) $false
% 175.89/129.69 |
% 175.89/129.69 |-The branch is then unsatisfiable
% 175.89/129.69 |-Branch two:
% 175.89/129.69 | (752) ~ (all_425_0_1783 = 0) & lesseq(all_0_4_4, all_0_3_3) = all_425_0_1783
% 175.89/129.69 |
% 175.89/129.69 | Applying alpha-rule on (752) yields:
% 175.89/129.69 | (748) ~ (all_425_0_1783 = 0)
% 175.89/129.69 | (754) lesseq(all_0_4_4, all_0_3_3) = all_425_0_1783
% 175.89/129.69 |
% 175.89/129.69 | Instantiating formula (11) with all_0_4_4, all_0_3_3, 0, all_425_0_1783 and discharging atoms lesseq(all_0_4_4, all_0_3_3) = all_425_0_1783, lesseq(all_0_4_4, all_0_3_3) = 0, yields:
% 175.89/129.69 | (750) all_425_0_1783 = 0
% 175.89/129.69 |
% 175.89/129.69 | Equations (750) can reduce 748 to:
% 175.89/129.69 | (72) $false
% 175.89/129.69 |
% 175.89/129.69 |-The branch is then unsatisfiable
% 175.89/129.69 |-Branch two:
% 175.89/129.69 | (134) ~ (lesseq(all_0_4_4, all_0_3_3) = 0)
% 175.89/129.69 | (758) all_395_0_1770 = 0
% 175.89/129.69 |
% 175.89/129.69 | Equations (758) can reduce 737 to:
% 175.89/129.69 | (72) $false
% 175.89/129.69 |
% 175.89/129.69 |-The branch is then unsatisfiable
% 176.07/129.69 |-Branch two:
% 176.07/129.69 | (598) ~ (all_165_0_1403 = all_0_3_3)
% 176.07/129.69 | (109) ? [v0] : ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_3_3) = v0)
% 176.07/129.69 |
% 176.07/129.69 | Instantiating (109) with all_381_0_1795 yields:
% 176.07/129.69 | (762) ~ (all_381_0_1795 = 0) & lesseq(all_0_4_4, all_0_3_3) = all_381_0_1795
% 176.07/129.69 |
% 176.07/129.69 | Applying alpha-rule on (762) yields:
% 176.07/129.69 | (763) ~ (all_381_0_1795 = 0)
% 176.07/129.69 | (764) lesseq(all_0_4_4, all_0_3_3) = all_381_0_1795
% 176.07/129.69 |
% 176.07/129.69 | Instantiating formula (5) with all_329_0_1523, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms ub(all_0_4_4, all_0_3_3, all_0_4_4) = all_329_0_1523, yields:
% 176.07/129.69 | (765) all_329_0_1523 = 0 | ? [v0] : (( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_4_4) = v0))
% 176.07/129.69 |
% 176.07/129.69 | Instantiating formula (10) with all_381_0_1795, all_0_4_4, all_0_3_3 and discharging atoms lesseq(all_0_4_4, all_0_3_3) = all_381_0_1795, yields:
% 176.07/129.69 | (766) all_381_0_1795 = 0 | lesseq(all_0_3_3, all_0_4_4) = 0
% 176.07/129.69 |
% 176.07/129.69 +-Applying beta-rule and splitting (766), into two cases.
% 176.07/129.69 |-Branch one:
% 176.07/129.69 | (171) lesseq(all_0_3_3, all_0_4_4) = 0
% 176.07/129.69 |
% 176.07/129.69 +-Applying beta-rule and splitting (765), into two cases.
% 176.07/129.69 |-Branch one:
% 176.07/129.69 | (768) all_329_0_1523 = 0
% 176.07/129.69 |
% 176.07/129.69 | Equations (768) can reduce 714 to:
% 176.07/129.69 | (72) $false
% 176.07/129.69 |
% 176.07/129.69 |-The branch is then unsatisfiable
% 176.07/129.69 |-Branch two:
% 176.07/129.69 | (714) ~ (all_329_0_1523 = 0)
% 176.07/129.69 | (175) ? [v0] : (( ~ (v0 = 0) & lesseq(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & lesseq(all_0_4_4, all_0_4_4) = v0))
% 176.07/129.69 |
% 176.07/129.69 | Instantiating (175) with all_429_0_1833 yields:
% 176.07/129.69 | (772) ( ~ (all_429_0_1833 = 0) & lesseq(all_0_3_3, all_0_4_4) = all_429_0_1833) | ( ~ (all_429_0_1833 = 0) & lesseq(all_0_4_4, all_0_4_4) = all_429_0_1833)
% 176.07/129.69 |
% 176.07/129.69 +-Applying beta-rule and splitting (772), into two cases.
% 176.07/129.69 |-Branch one:
% 176.07/129.69 | (773) ~ (all_429_0_1833 = 0) & lesseq(all_0_3_3, all_0_4_4) = all_429_0_1833
% 176.07/129.69 |
% 176.07/129.69 | Applying alpha-rule on (773) yields:
% 176.07/129.69 | (774) ~ (all_429_0_1833 = 0)
% 176.07/129.69 | (775) lesseq(all_0_3_3, all_0_4_4) = all_429_0_1833
% 176.07/129.69 |
% 176.07/129.69 | Instantiating formula (11) with all_0_3_3, all_0_4_4, 0, all_429_0_1833 and discharging atoms lesseq(all_0_3_3, all_0_4_4) = all_429_0_1833, lesseq(all_0_3_3, all_0_4_4) = 0, yields:
% 176.07/129.69 | (776) all_429_0_1833 = 0
% 176.07/129.69 |
% 176.07/129.69 | Equations (776) can reduce 774 to:
% 176.07/129.69 | (72) $false
% 176.07/129.69 |
% 176.07/129.69 |-The branch is then unsatisfiable
% 176.07/129.69 |-Branch two:
% 176.07/129.69 | (778) ~ (all_429_0_1833 = 0) & lesseq(all_0_4_4, all_0_4_4) = all_429_0_1833
% 176.07/129.69 |
% 176.07/129.69 | Applying alpha-rule on (778) yields:
% 176.07/129.69 | (774) ~ (all_429_0_1833 = 0)
% 176.07/129.69 | (780) lesseq(all_0_4_4, all_0_4_4) = all_429_0_1833
% 176.07/129.69 |
% 176.07/129.69 | Instantiating formula (56) with all_429_0_1833, all_0_4_4 and discharging atoms lesseq(all_0_4_4, all_0_4_4) = all_429_0_1833, yields:
% 176.07/129.69 | (776) all_429_0_1833 = 0
% 176.07/129.69 |
% 176.07/129.69 | Equations (776) can reduce 774 to:
% 176.07/129.69 | (72) $false
% 176.07/129.69 |
% 176.07/129.69 |-The branch is then unsatisfiable
% 176.07/129.69 |-Branch two:
% 176.07/129.69 | (187) ~ (lesseq(all_0_3_3, all_0_4_4) = 0)
% 176.07/129.69 | (784) all_381_0_1795 = 0
% 176.07/129.69 |
% 176.07/129.69 | Equations (784) can reduce 763 to:
% 176.07/129.69 | (72) $false
% 176.07/129.69 |
% 176.07/129.69 |-The branch is then unsatisfiable
% 176.07/129.70 % SZS output end Proof for theBenchmark
% 176.07/129.70
% 176.07/129.70 129111ms
%------------------------------------------------------------------------------