%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT025+1 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Tue Sep 8 06:17:21 AM UTC 2026 % Result : Theorem 11.22s 2.26s % Output : Proof 19.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT025+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.35 % Computer : n011.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Mon Sep 7 12:09:45 UTC 2026 % 0.09/0.35 % CPUTime : % 0.13/0.37 OpenJDK 64-Bit Server VM warning: Options -Xverify:none and -noverify were deprecated in JDK 13 and will likely be removed in a future release. % 0.69/0.70 ________ _____ % 0.69/0.70 ___ __ \_________(_)________________________________ % 0.69/0.70 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.69/0.70 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.69/0.70 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.69/0.70 % 0.69/0.70 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.69/0.70 (2023-06-19) % 0.69/0.70 % 0.69/0.70 (c) Philipp Rümmer, 2009-2023 % 0.69/0.70 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.69/0.70 Amanda Stjerna. % 0.69/0.70 Free software under BSD-3-Clause. % 0.69/0.70 % 0.69/0.70 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.69/0.70 % 0.69/0.70 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.69/0.72 Running up to 7 provers in parallel. % 0.69/0.73 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.69/0.73 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.69/0.73 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.69/0.74 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.69/0.74 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.69/0.74 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.69/0.74 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.37/1.22 Prover 4: Preprocessing ... % 3.37/1.25 Prover 1: Preprocessing ... % 3.37/1.30 Prover 2: Preprocessing ... % 3.37/1.30 Prover 3: Preprocessing ... % 3.37/1.30 Prover 6: Preprocessing ... % 4.11/1.30 Prover 5: Preprocessing ... % 4.11/1.30 Prover 0: Preprocessing ... % 7.27/1.75 Prover 3: Constructing countermodel ... % 7.27/1.75 Prover 6: Constructing countermodel ... % 7.27/1.75 Prover 1: Constructing countermodel ... % 7.27/1.79 Prover 5: Proving ... % 8.06/1.86 Prover 2: Proving ... % 8.85/1.91 Prover 4: Constructing countermodel ... % 8.85/1.97 Prover 0: Proving ... % 11.22/2.26 Prover 3: proved (1523ms) % 11.22/2.26 % 11.22/2.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.22/2.26 % 11.22/2.26 Prover 6: stopped % 11.22/2.26 Prover 0: stopped % 11.22/2.26 Prover 2: stopped % 11.22/2.27 Prover 5: stopped % 11.22/2.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.22/2.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.22/2.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.22/2.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.22/2.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.98/2.37 Prover 10: Preprocessing ... % 11.98/2.37 Prover 11: Preprocessing ... % 11.98/2.37 Prover 8: Preprocessing ... % 12.77/2.40 Prover 13: Preprocessing ... % 12.77/2.40 Prover 7: Preprocessing ... % 13.56/2.53 Prover 10: Constructing countermodel ... % 13.56/2.57 Prover 13: Warning: ignoring some quantifiers % 13.56/2.59 Prover 8: Warning: ignoring some quantifiers % 13.56/2.60 Prover 13: Constructing countermodel ... % 14.36/2.62 Prover 8: Constructing countermodel ... % 14.36/2.63 Prover 7: Constructing countermodel ... % 15.16/2.77 Prover 11: Constructing countermodel ... % 16.74/3.02 Prover 1: Found proof (size 318) % 16.74/3.02 Prover 1: proved (2287ms) % 16.74/3.02 Prover 4: stopped % 16.74/3.02 Prover 7: stopped % 16.74/3.02 Prover 11: stopped % 16.74/3.02 Prover 10: stopped % 16.74/3.02 Prover 8: stopped % 16.74/3.03 Prover 13: stopped % 16.74/3.03 % 16.74/3.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.74/3.03 % 17.78/3.12 % SZS output start Proof for theBenchmark % 17.78/3.12 Assumptions after simplification: % 17.78/3.12 --------------------------------- % 17.78/3.12 % 17.78/3.12 (mp_abc_sum_increase) % 18.22/3.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (constant(v0) = 0) | ~ (sum(v1, % 18.22/3.18 v2) = v0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 18.22/3.18 any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 18.22/3.18 (constant(v2) = v4 & constant(v1) = v3 & decreases(v2) = v6 & decreases(v1) % 18.22/3.18 = v7 & increases(v2) = v8 & increases(v1) = v5 & ((v8 = 0 & v7 = 0) | (v6 % 18.22/3.18 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) % 18.22/3.18 % 18.22/3.18 (mp_growth_rate) % 18.22/3.19 $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 18.22/3.19 (growth_rate(v0, v2) = v3) | ~ (in_environment(v1, v2) = 0) | ~ $i(v2) | % 18.22/3.19 ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: % 18.22/3.19 any] : ? [v8: any] : ? [v9: any] : ? [v10: any] : ? [v11: any] : ? % 18.22/3.19 [v12: any] : (constant(v6) = v8 & decreases(v6) = v11 & increases(v6) = v9 & % 18.22/3.19 environment(v1) = v4 & subpopulation(v0, v1, v2) = v5 & greater(v6, zero) % 18.22/3.19 = v7 & greater(v3, zero) = v10 & greater(zero, v3) = v12 & % 18.22/3.19 cardinality_at_time(v0, v2) = v6 & $i(v6) & ( ~ (v7 = 0) | ~ (v5 = 0) | % 18.22/3.19 ~ (v4 = 0) | (( ~ (v11 = 0) | v12 = 0) & ( ~ (v9 = 0) | v10 = 0) & ( ~ % 18.22/3.19 (v8 = 0) | v3 = zero))))) % 18.22/3.19 % 18.22/3.19 (mp_non_zero_producers) % 18.22/3.20 $i(first_movers) & $i(efficient_producers) & $i(zero) & ! [v0: $i] : ! [v1: % 18.22/3.20 $i] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | % 18.54/3.20 ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: % 18.54/3.20 $i] : ? [v6: any] : (environment(v0) = v2 & greater(v5, zero) = v6 & % 18.54/3.20 greater(v3, zero) = v4 & cardinality_at_time(first_movers, v1) = v3 & % 18.54/3.20 cardinality_at_time(efficient_producers, v1) = v5 & $i(v5) & $i(v3) & ( ~ % 18.54/3.20 (v2 = 0) | (v6 = 0 & v4 = 0)))) % 18.54/3.20 % 18.54/3.20 (mp_only_members) % 18.54/3.20 $i(first_movers) & $i(efficient_producers) & $i(zero) & ! [v0: $i] : ! [v1: % 18.54/3.20 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 18.54/3.20 (number_of_organizations(v0, v2) = v4) | ~ (cardinality_at_time(v1, v2) = % 18.54/3.20 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? % 18.54/3.20 [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : (environment(v0) = v5 % 18.54/3.20 & subpopulation(v1, v0, v2) = v6 & greater(v3, zero) = v7 & % 18.54/3.20 cardinality_at_time(first_movers, v2) = v8 & % 18.54/3.20 cardinality_at_time(efficient_producers, v2) = v9 & sum(v8, v9) = v10 & % 18.54/3.20 $i(v10) & $i(v9) & $i(v8) & ( ~ (v6 = 0) | ~ (v5 = 0) | v10 = v4 | (v7 = % 18.54/3.20 0 & ~ (v1 = first_movers) & ~ (v1 = efficient_producers))))) % 18.54/3.20 % 18.54/3.20 (mp_subpopulations) % 18.54/3.21 $i(first_movers) & $i(efficient_producers) & ! [v0: $i] : ! [v1: $i] : ! % 18.54/3.21 [v2: any] : ( ~ (subpopulation(first_movers, v0, v1) = v2) | ~ $i(v1) | ~ % 18.54/3.21 $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : (in_environment(v0, % 18.54/3.21 v1) = v4 & environment(v0) = v3 & subpopulation(efficient_producers, v0, % 18.54/3.21 v1) = v5 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v5 = 0 & v2 = 0)))) % 18.54/3.21 % 18.54/3.21 (mp_time_point_occur) % 18.54/3.21 $i(first_movers) & $i(efficient_producers) & ! [v0: $i] : ! [v1: $i] : ( ~ % 18.54/3.21 (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ~ $i(v1) % 18.54/3.21 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in_environment(v0, v1) = v3 & % 18.54/3.21 environment(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 18.54/3.21 % 18.54/3.21 (prove_l7) % 18.54/3.22 $i(first_movers) & $i(efficient_producers) & $i(zero) & ? [v0: $i] : ? [v1: % 18.54/3.22 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: any] : ? [v6: any] % 18.54/3.22 : ? [v7: any] : ? [v8: any] : (subpopulations(first_movers, % 18.54/3.22 efficient_producers, v0, v1) = 0 & growth_rate(first_movers, v1) = v3 & % 18.54/3.22 growth_rate(efficient_producers, v1) = v4 & constant(v2) = 0 & % 18.54/3.22 number_of_organizations(v0, v1) = v2 & environment(v0) = 0 & greater(v4, % 18.54/3.22 zero) = v7 & greater(v3, zero) = v5 & greater(zero, v4) = v6 & % 18.54/3.22 greater(zero, v3) = v8 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ % 18.54/3.22 (v8 = 0) | ~ (v7 = 0)) & ( ~ (v6 = 0) | ~ (v5 = 0)) & ( ~ (v4 = zero) | % 18.54/3.22 ~ (v3 = zero))) % 18.54/3.22 % 18.54/3.22 (function-axioms) % 18.54/3.23 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 18.54/3.23 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (subpopulations(v5, v4, % 18.54/3.23 v3, v2) = v1) | ~ (subpopulations(v5, v4, v3, v2) = v0)) & ! [v0: % 18.54/3.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.54/3.23 : ! [v4: $i] : (v1 = v0 | ~ (subpopulation(v4, v3, v2) = v1) | ~ % 18.54/3.23 (subpopulation(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 18.54/3.23 : ! [v3: $i] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, % 18.54/3.23 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 18.54/3.23 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~ % 18.54/3.23 (in_environment(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 18.54/3.23 ! [v3: $i] : (v1 = v0 | ~ (number_of_organizations(v3, v2) = v1) | ~ % 18.54/3.23 (number_of_organizations(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 18.54/3.23 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.54/3.23 (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 18.54/3.23 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cardinality_at_time(v3, v2) % 18.54/3.23 = v1) | ~ (cardinality_at_time(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 18.54/3.23 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, % 18.54/3.23 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 18.54/3.23 ! [v2: $i] : (v1 = v0 | ~ (constant(v2) = v1) | ~ (constant(v2) = v0)) & ! % 18.54/3.23 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 18.54/3.23 | ~ (decreases(v2) = v1) | ~ (decreases(v2) = v0)) & ! [v0: % 18.54/3.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 18.54/3.23 ~ (increases(v2) = v1) | ~ (increases(v2) = v0)) & ! [v0: % 18.54/3.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 18.54/3.23 ~ (environment(v2) = v1) | ~ (environment(v2) = v0)) % 18.54/3.23 % 18.54/3.23 Further assumptions not needed in the proof: % 18.54/3.23 -------------------------------------------- % 18.54/3.23 a9 % 18.54/3.23 % 18.54/3.23 Those formulas are unsatisfiable: % 18.54/3.23 --------------------------------- % 18.54/3.23 % 18.54/3.23 Begin of proof % 18.54/3.23 | % 18.54/3.23 | ALPHA: (mp_only_members) implies: % 18.54/3.24 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 18.54/3.24 | ~ (number_of_organizations(v0, v2) = v4) | ~ % 18.54/3.24 | (cardinality_at_time(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 18.54/3.24 | $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : % 18.54/3.24 | ? [v9: $i] : ? [v10: $i] : (environment(v0) = v5 & subpopulation(v1, % 18.54/3.24 | v0, v2) = v6 & greater(v3, zero) = v7 & % 18.54/3.24 | cardinality_at_time(first_movers, v2) = v8 & % 18.54/3.24 | cardinality_at_time(efficient_producers, v2) = v9 & sum(v8, v9) = % 18.54/3.24 | v10 & $i(v10) & $i(v9) & $i(v8) & ( ~ (v6 = 0) | ~ (v5 = 0) | v10 % 18.54/3.24 | = v4 | (v7 = 0 & ~ (v1 = first_movers) & ~ (v1 = % 18.54/3.24 | efficient_producers))))) % 18.54/3.24 | % 18.54/3.24 | ALPHA: (mp_subpopulations) implies: % 18.54/3.24 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 18.54/3.24 | (subpopulation(first_movers, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 18.54/3.24 | ? [v3: any] : ? [v4: any] : ? [v5: any] : (in_environment(v0, v1) = % 18.54/3.24 | v4 & environment(v0) = v3 & subpopulation(efficient_producers, v0, % 18.54/3.24 | v1) = v5 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v5 = 0 & v2 = 0)))) % 18.54/3.24 | % 18.54/3.24 | ALPHA: (mp_growth_rate) implies: % 18.54/3.25 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 18.54/3.25 | (growth_rate(v0, v2) = v3) | ~ (in_environment(v1, v2) = 0) | ~ % 18.54/3.25 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? % 18.54/3.25 | [v6: $i] : ? [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10: any] % 18.54/3.25 | : ? [v11: any] : ? [v12: any] : (constant(v6) = v8 & decreases(v6) % 18.54/3.25 | = v11 & increases(v6) = v9 & environment(v1) = v4 & % 18.54/3.25 | subpopulation(v0, v1, v2) = v5 & greater(v6, zero) = v7 & % 18.54/3.25 | greater(v3, zero) = v10 & greater(zero, v3) = v12 & % 18.54/3.25 | cardinality_at_time(v0, v2) = v6 & $i(v6) & ( ~ (v7 = 0) | ~ (v5 = % 18.54/3.25 | 0) | ~ (v4 = 0) | (( ~ (v11 = 0) | v12 = 0) & ( ~ (v9 = 0) | % 18.54/3.25 | v10 = 0) & ( ~ (v8 = 0) | v3 = zero))))) % 18.54/3.25 | % 18.54/3.25 | ALPHA: (mp_non_zero_producers) implies: % 18.54/3.25 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (subpopulations(first_movers, % 18.54/3.25 | efficient_producers, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 18.54/3.25 | [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: any] : % 18.54/3.25 | (environment(v0) = v2 & greater(v5, zero) = v6 & greater(v3, zero) = % 18.54/3.25 | v4 & cardinality_at_time(first_movers, v1) = v3 & % 18.54/3.25 | cardinality_at_time(efficient_producers, v1) = v5 & $i(v5) & $i(v3) % 18.54/3.25 | & ( ~ (v2 = 0) | (v6 = 0 & v4 = 0)))) % 18.54/3.25 | % 18.54/3.25 | ALPHA: (mp_time_point_occur) implies: % 18.54/3.25 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (subpopulations(first_movers, % 18.54/3.25 | efficient_producers, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 18.54/3.25 | [v2: any] : ? [v3: any] : (in_environment(v0, v1) = v3 & % 18.54/3.25 | environment(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 18.54/3.25 | % 18.54/3.25 | ALPHA: (prove_l7) implies: % 18.54/3.26 | (6) $i(efficient_producers) % 18.54/3.26 | (7) $i(first_movers) % 18.54/3.26 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 18.54/3.26 | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 18.54/3.26 | (subpopulations(first_movers, efficient_producers, v0, v1) = 0 & % 18.54/3.26 | growth_rate(first_movers, v1) = v3 & growth_rate(efficient_producers, % 18.54/3.26 | v1) = v4 & constant(v2) = 0 & number_of_organizations(v0, v1) = v2 % 18.54/3.26 | & environment(v0) = 0 & greater(v4, zero) = v7 & greater(v3, zero) = % 18.54/3.26 | v5 & greater(zero, v4) = v6 & greater(zero, v3) = v8 & $i(v4) & % 18.54/3.26 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v8 = 0) | ~ (v7 = 0)) & ( ~ % 18.54/3.26 | (v6 = 0) | ~ (v5 = 0)) & ( ~ (v4 = zero) | ~ (v3 = zero))) % 18.54/3.26 | % 18.54/3.26 | ALPHA: (function-axioms) implies: % 18.54/3.26 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 18.54/3.26 | (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0)) % 18.54/3.26 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 18.54/3.26 | : (v1 = v0 | ~ (increases(v2) = v1) | ~ (increases(v2) = v0)) % 18.54/3.27 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 18.54/3.27 | : (v1 = v0 | ~ (decreases(v2) = v1) | ~ (decreases(v2) = v0)) % 18.54/3.27 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 18.54/3.27 | : (v1 = v0 | ~ (constant(v2) = v1) | ~ (constant(v2) = v0)) % 18.54/3.27 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.54/3.27 | (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0)) % 18.54/3.27 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.54/3.27 | (cardinality_at_time(v3, v2) = v1) | ~ (cardinality_at_time(v3, v2) % 18.54/3.27 | = v0)) % 18.54/3.27 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 18.54/3.27 | : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, % 18.54/3.27 | v2) = v0)) % 18.54/3.27 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 18.54/3.27 | : ! [v3: $i] : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~ % 18.54/3.27 | (in_environment(v3, v2) = v0)) % 18.54/3.27 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 18.54/3.27 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (subpopulation(v4, v3, v2) % 18.54/3.27 | = v1) | ~ (subpopulation(v4, v3, v2) = v0)) % 18.54/3.27 | % 18.54/3.27 | DELTA: instantiating (8) with fresh symbols all_11_0, all_11_1, all_11_2, % 18.54/3.27 | all_11_3, all_11_4, all_11_5, all_11_6, all_11_7, all_11_8 gives: % 18.54/3.28 | (18) subpopulations(first_movers, efficient_producers, all_11_8, all_11_7) % 18.54/3.28 | = 0 & growth_rate(first_movers, all_11_7) = all_11_5 & % 18.54/3.28 | growth_rate(efficient_producers, all_11_7) = all_11_4 & % 18.54/3.28 | constant(all_11_6) = 0 & number_of_organizations(all_11_8, all_11_7) = % 18.54/3.28 | all_11_6 & environment(all_11_8) = 0 & greater(all_11_4, zero) = % 18.54/3.28 | all_11_1 & greater(all_11_5, zero) = all_11_3 & greater(zero, % 18.54/3.28 | all_11_4) = all_11_2 & greater(zero, all_11_5) = all_11_0 & % 18.54/3.28 | $i(all_11_4) & $i(all_11_5) & $i(all_11_6) & $i(all_11_7) & % 18.54/3.28 | $i(all_11_8) & ( ~ (all_11_0 = 0) | ~ (all_11_1 = 0)) & ( ~ (all_11_2 % 18.54/3.28 | = 0) | ~ (all_11_3 = 0)) & ( ~ (all_11_4 = zero) | ~ (all_11_5 = % 18.54/3.28 | zero)) % 18.54/3.28 | % 18.54/3.28 | ALPHA: (18) implies: % 18.54/3.28 | (19) $i(all_11_8) % 18.54/3.28 | (20) $i(all_11_7) % 18.54/3.28 | (21) greater(zero, all_11_5) = all_11_0 % 18.54/3.28 | (22) greater(zero, all_11_4) = all_11_2 % 18.54/3.28 | (23) greater(all_11_5, zero) = all_11_3 % 18.54/3.28 | (24) greater(all_11_4, zero) = all_11_1 % 18.54/3.28 | (25) environment(all_11_8) = 0 % 18.54/3.28 | (26) number_of_organizations(all_11_8, all_11_7) = all_11_6 % 18.54/3.28 | (27) constant(all_11_6) = 0 % 18.54/3.28 | (28) growth_rate(efficient_producers, all_11_7) = all_11_4 % 18.54/3.28 | (29) growth_rate(first_movers, all_11_7) = all_11_5 % 18.54/3.28 | (30) subpopulations(first_movers, efficient_producers, all_11_8, all_11_7) % 18.54/3.28 | = 0 % 18.54/3.28 | (31) ~ (all_11_4 = zero) | ~ (all_11_5 = zero) % 18.54/3.28 | (32) ~ (all_11_2 = 0) | ~ (all_11_3 = 0) % 18.54/3.28 | (33) ~ (all_11_0 = 0) | ~ (all_11_1 = 0) % 18.54/3.28 | % 18.54/3.28 | GROUND_INST: instantiating (4) with all_11_8, all_11_7, simplifying with (19), % 18.54/3.28 | (20), (30) gives: % 18.54/3.29 | (34) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] % 18.54/3.29 | : (environment(all_11_8) = v0 & greater(v3, zero) = v4 & greater(v1, % 18.54/3.29 | zero) = v2 & cardinality_at_time(first_movers, all_11_7) = v1 & % 18.54/3.29 | cardinality_at_time(efficient_producers, all_11_7) = v3 & $i(v3) & % 18.54/3.29 | $i(v1) & ( ~ (v0 = 0) | (v4 = 0 & v2 = 0))) % 18.54/3.29 | % 18.54/3.29 | GROUND_INST: instantiating (5) with all_11_8, all_11_7, simplifying with (19), % 18.54/3.29 | (20), (30) gives: % 18.54/3.29 | (35) ? [v0: any] : ? [v1: any] : (in_environment(all_11_8, all_11_7) = v1 % 18.54/3.29 | & environment(all_11_8) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 18.54/3.29 | % 18.54/3.29 | DELTA: instantiating (35) with fresh symbols all_18_0, all_18_1 gives: % 18.54/3.29 | (36) in_environment(all_11_8, all_11_7) = all_18_0 & environment(all_11_8) % 18.54/3.29 | = all_18_1 & ( ~ (all_18_1 = 0) | all_18_0 = 0) % 18.54/3.29 | % 18.54/3.29 | ALPHA: (36) implies: % 18.54/3.29 | (37) environment(all_11_8) = all_18_1 % 18.54/3.29 | (38) in_environment(all_11_8, all_11_7) = all_18_0 % 18.54/3.29 | (39) ~ (all_18_1 = 0) | all_18_0 = 0 % 18.54/3.29 | % 18.54/3.29 | DELTA: instantiating (34) with fresh symbols all_20_0, all_20_1, all_20_2, % 18.54/3.29 | all_20_3, all_20_4 gives: % 18.54/3.29 | (40) environment(all_11_8) = all_20_4 & greater(all_20_1, zero) = all_20_0 % 18.54/3.29 | & greater(all_20_3, zero) = all_20_2 & % 18.54/3.29 | cardinality_at_time(first_movers, all_11_7) = all_20_3 & % 18.54/3.29 | cardinality_at_time(efficient_producers, all_11_7) = all_20_1 & % 18.54/3.29 | $i(all_20_1) & $i(all_20_3) & ( ~ (all_20_4 = 0) | (all_20_0 = 0 & % 18.54/3.29 | all_20_2 = 0)) % 18.54/3.29 | % 18.54/3.29 | ALPHA: (40) implies: % 18.54/3.29 | (41) cardinality_at_time(efficient_producers, all_11_7) = all_20_1 % 18.54/3.29 | (42) cardinality_at_time(first_movers, all_11_7) = all_20_3 % 18.54/3.29 | (43) greater(all_20_3, zero) = all_20_2 % 18.54/3.30 | (44) greater(all_20_1, zero) = all_20_0 % 18.54/3.30 | (45) environment(all_11_8) = all_20_4 % 18.54/3.30 | (46) ~ (all_20_4 = 0) | (all_20_0 = 0 & all_20_2 = 0) % 18.54/3.30 | % 19.04/3.30 | GROUND_INST: instantiating (9) with 0, all_20_4, all_11_8, simplifying with % 19.04/3.30 | (25), (45) gives: % 19.04/3.30 | (47) all_20_4 = 0 % 19.04/3.30 | % 19.04/3.30 | GROUND_INST: instantiating (9) with all_18_1, all_20_4, all_11_8, simplifying % 19.04/3.30 | with (37), (45) gives: % 19.04/3.30 | (48) all_20_4 = all_18_1 % 19.04/3.30 | % 19.04/3.30 | COMBINE_EQS: (47), (48) imply: % 19.04/3.30 | (49) all_18_1 = 0 % 19.04/3.30 | % 19.04/3.30 | BETA: splitting (39) gives: % 19.04/3.30 | % 19.04/3.30 | Case 1: % 19.04/3.30 | | % 19.04/3.30 | | (50) ~ (all_18_1 = 0) % 19.04/3.30 | | % 19.04/3.30 | | REDUCE: (49), (50) imply: % 19.04/3.30 | | (51) $false % 19.04/3.30 | | % 19.04/3.30 | | CLOSE: (51) is inconsistent. % 19.04/3.30 | | % 19.04/3.30 | Case 2: % 19.04/3.30 | | % 19.04/3.30 | | (52) all_18_0 = 0 % 19.04/3.30 | | % 19.04/3.30 | | REDUCE: (38), (52) imply: % 19.04/3.30 | | (53) in_environment(all_11_8, all_11_7) = 0 % 19.04/3.30 | | % 19.04/3.30 | | BETA: splitting (46) gives: % 19.04/3.30 | | % 19.04/3.30 | | Case 1: % 19.04/3.30 | | | % 19.04/3.30 | | | (54) ~ (all_20_4 = 0) % 19.04/3.30 | | | % 19.04/3.30 | | | REDUCE: (47), (54) imply: % 19.04/3.30 | | | (55) $false % 19.04/3.30 | | | % 19.04/3.30 | | | CLOSE: (55) is inconsistent. % 19.04/3.30 | | | % 19.04/3.30 | | Case 2: % 19.04/3.30 | | | % 19.04/3.30 | | | (56) all_20_0 = 0 & all_20_2 = 0 % 19.04/3.31 | | | % 19.04/3.31 | | | ALPHA: (56) implies: % 19.04/3.31 | | | (57) all_20_2 = 0 % 19.04/3.31 | | | (58) all_20_0 = 0 % 19.04/3.31 | | | % 19.04/3.31 | | | REDUCE: (44), (58) imply: % 19.04/3.31 | | | (59) greater(all_20_1, zero) = 0 % 19.04/3.31 | | | % 19.04/3.31 | | | REDUCE: (43), (57) imply: % 19.04/3.31 | | | (60) greater(all_20_3, zero) = 0 % 19.04/3.31 | | | % 19.04/3.31 | | | GROUND_INST: instantiating (1) with all_11_8, efficient_producers, % 19.04/3.31 | | | all_11_7, all_20_1, all_11_6, simplifying with (6), (19), % 19.04/3.31 | | | (20), (26), (41) gives: % 19.04/3.31 | | | (61) ? [v0: any] : ? [v1: any] : ? [v2: MultipleValueBool] : ? [v3: % 19.04/3.31 | | | $i] : ? [v4: $i] : ? [v5: $i] : (environment(all_11_8) = v0 & % 19.04/3.31 | | | subpopulation(efficient_producers, all_11_8, all_11_7) = v1 & % 19.04/3.31 | | | greater(all_20_1, zero) = v2 & cardinality_at_time(first_movers, % 19.04/3.31 | | | all_11_7) = v3 & cardinality_at_time(efficient_producers, % 19.04/3.31 | | | all_11_7) = v4 & sum(v3, v4) = v5 & $i(v5) & $i(v4) & $i(v3) & % 19.04/3.31 | | | ( ~ (v1 = 0) | ~ (v0 = 0) | v5 = all_11_6)) % 19.04/3.31 | | | % 19.04/3.32 | | | GROUND_INST: instantiating (1) with all_11_8, first_movers, all_11_7, % 19.04/3.32 | | | all_20_3, all_11_6, simplifying with (7), (19), (20), (26), % 19.04/3.32 | | | (42) gives: % 19.04/3.32 | | | (62) ? [v0: any] : ? [v1: any] : ? [v2: MultipleValueBool] : ? [v3: % 19.04/3.32 | | | $i] : ? [v4: $i] : ? [v5: $i] : (environment(all_11_8) = v0 & % 19.04/3.32 | | | subpopulation(first_movers, all_11_8, all_11_7) = v1 & % 19.04/3.32 | | | greater(all_20_3, zero) = v2 & cardinality_at_time(first_movers, % 19.04/3.32 | | | all_11_7) = v3 & cardinality_at_time(efficient_producers, % 19.04/3.32 | | | all_11_7) = v4 & sum(v3, v4) = v5 & $i(v5) & $i(v4) & $i(v3) & % 19.04/3.32 | | | ( ~ (v1 = 0) | ~ (v0 = 0) | v5 = all_11_6)) % 19.04/3.32 | | | % 19.04/3.32 | | | GROUND_INST: instantiating (3) with first_movers, all_11_8, all_11_7, % 19.04/3.32 | | | all_11_5, simplifying with (7), (19), (20), (29), (53) gives: % 19.04/3.32 | | | (63) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? [v4: % 19.04/3.32 | | | any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] % 19.04/3.32 | | | : (constant(v2) = v4 & decreases(v2) = v7 & increases(v2) = v5 & % 19.04/3.32 | | | environment(all_11_8) = v0 & subpopulation(first_movers, % 19.04/3.32 | | | all_11_8, all_11_7) = v1 & greater(v2, zero) = v3 & % 19.04/3.32 | | | greater(all_11_5, zero) = v6 & greater(zero, all_11_5) = v8 & % 19.04/3.32 | | | cardinality_at_time(first_movers, all_11_7) = v2 & $i(v2) & ( ~ % 19.04/3.32 | | | (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v7 = 0) | v8 = 0) % 19.04/3.32 | | | & ( ~ (v5 = 0) | v6 = 0) & ( ~ (v4 = 0) | all_11_5 = % 19.04/3.32 | | | zero)))) % 19.04/3.32 | | | % 19.04/3.32 | | | GROUND_INST: instantiating (3) with efficient_producers, all_11_8, % 19.04/3.32 | | | all_11_7, all_11_4, simplifying with (6), (19), (20), (28), % 19.04/3.32 | | | (53) gives: % 19.04/3.33 | | | (64) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? [v4: % 19.04/3.33 | | | any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] % 19.04/3.33 | | | : (constant(v2) = v4 & decreases(v2) = v7 & increases(v2) = v5 & % 19.04/3.33 | | | environment(all_11_8) = v0 & subpopulation(efficient_producers, % 19.04/3.33 | | | all_11_8, all_11_7) = v1 & greater(v2, zero) = v3 & % 19.04/3.33 | | | greater(all_11_4, zero) = v6 & greater(zero, all_11_4) = v8 & % 19.04/3.33 | | | cardinality_at_time(efficient_producers, all_11_7) = v2 & $i(v2) % 19.04/3.33 | | | & ( ~ (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v7 = 0) | v8 % 19.04/3.33 | | | = 0) & ( ~ (v5 = 0) | v6 = 0) & ( ~ (v4 = 0) | all_11_4 = % 19.04/3.33 | | | zero)))) % 19.04/3.33 | | | % 19.04/3.33 | | | DELTA: instantiating (62) with fresh symbols all_39_0, all_39_1, all_39_2, % 19.04/3.33 | | | all_39_3, all_39_4, all_39_5 gives: % 19.04/3.33 | | | (65) environment(all_11_8) = all_39_5 & subpopulation(first_movers, % 19.04/3.33 | | | all_11_8, all_11_7) = all_39_4 & greater(all_20_3, zero) = % 19.04/3.33 | | | all_39_3 & cardinality_at_time(first_movers, all_11_7) = all_39_2 % 19.04/3.33 | | | & cardinality_at_time(efficient_producers, all_11_7) = all_39_1 & % 19.04/3.33 | | | sum(all_39_2, all_39_1) = all_39_0 & $i(all_39_0) & $i(all_39_1) & % 19.04/3.33 | | | $i(all_39_2) & ( ~ (all_39_4 = 0) | ~ (all_39_5 = 0) | all_39_0 = % 19.04/3.33 | | | all_11_6) % 19.04/3.33 | | | % 19.04/3.33 | | | ALPHA: (65) implies: % 19.04/3.33 | | | (66) $i(all_39_2) % 19.04/3.33 | | | (67) $i(all_39_1) % 19.04/3.33 | | | (68) sum(all_39_2, all_39_1) = all_39_0 % 19.04/3.33 | | | (69) cardinality_at_time(efficient_producers, all_11_7) = all_39_1 % 19.04/3.33 | | | (70) cardinality_at_time(first_movers, all_11_7) = all_39_2 % 19.04/3.33 | | | (71) greater(all_20_3, zero) = all_39_3 % 19.04/3.33 | | | (72) subpopulation(first_movers, all_11_8, all_11_7) = all_39_4 % 19.04/3.33 | | | (73) environment(all_11_8) = all_39_5 % 19.04/3.33 | | | (74) ~ (all_39_4 = 0) | ~ (all_39_5 = 0) | all_39_0 = all_11_6 % 19.04/3.33 | | | % 19.04/3.33 | | | DELTA: instantiating (61) with fresh symbols all_41_0, all_41_1, all_41_2, % 19.04/3.33 | | | all_41_3, all_41_4, all_41_5 gives: % 19.04/3.34 | | | (75) environment(all_11_8) = all_41_5 & % 19.04/3.34 | | | subpopulation(efficient_producers, all_11_8, all_11_7) = all_41_4 % 19.04/3.34 | | | & greater(all_20_1, zero) = all_41_3 & % 19.04/3.34 | | | cardinality_at_time(first_movers, all_11_7) = all_41_2 & % 19.04/3.34 | | | cardinality_at_time(efficient_producers, all_11_7) = all_41_1 & % 19.04/3.34 | | | sum(all_41_2, all_41_1) = all_41_0 & $i(all_41_0) & $i(all_41_1) & % 19.04/3.34 | | | $i(all_41_2) & ( ~ (all_41_4 = 0) | ~ (all_41_5 = 0) | all_41_0 = % 19.04/3.34 | | | all_11_6) % 19.04/3.34 | | | % 19.04/3.34 | | | ALPHA: (75) implies: % 19.04/3.34 | | | (76) $i(all_41_0) % 19.04/3.34 | | | (77) sum(all_41_2, all_41_1) = all_41_0 % 19.04/3.34 | | | (78) cardinality_at_time(efficient_producers, all_11_7) = all_41_1 % 19.04/3.34 | | | (79) cardinality_at_time(first_movers, all_11_7) = all_41_2 % 19.04/3.34 | | | (80) greater(all_20_1, zero) = all_41_3 % 19.04/3.34 | | | (81) subpopulation(efficient_producers, all_11_8, all_11_7) = all_41_4 % 19.04/3.34 | | | (82) environment(all_11_8) = all_41_5 % 19.04/3.34 | | | % 19.04/3.34 | | | DELTA: instantiating (64) with fresh symbols all_43_0, all_43_1, all_43_2, % 19.04/3.34 | | | all_43_3, all_43_4, all_43_5, all_43_6, all_43_7, all_43_8 gives: % 19.04/3.34 | | | (83) constant(all_43_6) = all_43_4 & decreases(all_43_6) = all_43_1 & % 19.04/3.34 | | | increases(all_43_6) = all_43_3 & environment(all_11_8) = all_43_8 % 19.04/3.34 | | | & subpopulation(efficient_producers, all_11_8, all_11_7) = % 19.04/3.34 | | | all_43_7 & greater(all_43_6, zero) = all_43_5 & greater(all_11_4, % 19.04/3.34 | | | zero) = all_43_2 & greater(zero, all_11_4) = all_43_0 & % 19.04/3.34 | | | cardinality_at_time(efficient_producers, all_11_7) = all_43_6 & % 19.04/3.34 | | | $i(all_43_6) & ( ~ (all_43_5 = 0) | ~ (all_43_7 = 0) | ~ % 19.04/3.34 | | | (all_43_8 = 0) | (( ~ (all_43_1 = 0) | all_43_0 = 0) & ( ~ % 19.04/3.34 | | | (all_43_3 = 0) | all_43_2 = 0) & ( ~ (all_43_4 = 0) | % 19.04/3.34 | | | all_11_4 = zero))) % 19.04/3.34 | | | % 19.04/3.34 | | | ALPHA: (83) implies: % 19.04/3.34 | | | (84) cardinality_at_time(efficient_producers, all_11_7) = all_43_6 % 19.04/3.34 | | | (85) greater(zero, all_11_4) = all_43_0 % 19.04/3.34 | | | (86) greater(all_11_4, zero) = all_43_2 % 19.04/3.34 | | | (87) greater(all_43_6, zero) = all_43_5 % 19.04/3.34 | | | (88) subpopulation(efficient_producers, all_11_8, all_11_7) = all_43_7 % 19.04/3.34 | | | (89) environment(all_11_8) = all_43_8 % 19.04/3.34 | | | (90) increases(all_43_6) = all_43_3 % 19.04/3.35 | | | (91) decreases(all_43_6) = all_43_1 % 19.04/3.35 | | | (92) constant(all_43_6) = all_43_4 % 19.04/3.35 | | | (93) ~ (all_43_5 = 0) | ~ (all_43_7 = 0) | ~ (all_43_8 = 0) | (( ~ % 19.04/3.35 | | | (all_43_1 = 0) | all_43_0 = 0) & ( ~ (all_43_3 = 0) | all_43_2 % 19.04/3.35 | | | = 0) & ( ~ (all_43_4 = 0) | all_11_4 = zero)) % 19.04/3.35 | | | % 19.04/3.35 | | | DELTA: instantiating (63) with fresh symbols all_45_0, all_45_1, all_45_2, % 19.04/3.35 | | | all_45_3, all_45_4, all_45_5, all_45_6, all_45_7, all_45_8 gives: % 19.04/3.35 | | | (94) constant(all_45_6) = all_45_4 & decreases(all_45_6) = all_45_1 & % 19.04/3.35 | | | increases(all_45_6) = all_45_3 & environment(all_11_8) = all_45_8 % 19.04/3.35 | | | & subpopulation(first_movers, all_11_8, all_11_7) = all_45_7 & % 19.04/3.35 | | | greater(all_45_6, zero) = all_45_5 & greater(all_11_5, zero) = % 19.04/3.35 | | | all_45_2 & greater(zero, all_11_5) = all_45_0 & % 19.04/3.35 | | | cardinality_at_time(first_movers, all_11_7) = all_45_6 & % 19.04/3.35 | | | $i(all_45_6) & ( ~ (all_45_5 = 0) | ~ (all_45_7 = 0) | ~ % 19.04/3.35 | | | (all_45_8 = 0) | (( ~ (all_45_1 = 0) | all_45_0 = 0) & ( ~ % 19.04/3.35 | | | (all_45_3 = 0) | all_45_2 = 0) & ( ~ (all_45_4 = 0) | % 19.04/3.35 | | | all_11_5 = zero))) % 19.04/3.35 | | | % 19.04/3.35 | | | ALPHA: (94) implies: % 19.04/3.35 | | | (95) cardinality_at_time(first_movers, all_11_7) = all_45_6 % 19.04/3.35 | | | (96) greater(zero, all_11_5) = all_45_0 % 19.04/3.35 | | | (97) greater(all_11_5, zero) = all_45_2 % 19.04/3.35 | | | (98) greater(all_45_6, zero) = all_45_5 % 19.04/3.35 | | | (99) subpopulation(first_movers, all_11_8, all_11_7) = all_45_7 % 19.04/3.35 | | | (100) environment(all_11_8) = all_45_8 % 19.04/3.35 | | | (101) increases(all_45_6) = all_45_3 % 19.04/3.35 | | | (102) decreases(all_45_6) = all_45_1 % 19.04/3.35 | | | (103) constant(all_45_6) = all_45_4 % 19.04/3.35 | | | (104) ~ (all_45_5 = 0) | ~ (all_45_7 = 0) | ~ (all_45_8 = 0) | (( ~ % 19.04/3.35 | | | (all_45_1 = 0) | all_45_0 = 0) & ( ~ (all_45_3 = 0) | % 19.04/3.35 | | | all_45_2 = 0) & ( ~ (all_45_4 = 0) | all_11_5 = zero)) % 19.04/3.35 | | | % 19.04/3.36 | | | GROUND_INST: instantiating (14) with all_20_1, all_41_1, all_11_7, % 19.04/3.36 | | | efficient_producers, simplifying with (41), (78) gives: % 19.04/3.36 | | | (105) all_41_1 = all_20_1 % 19.04/3.36 | | | % 19.04/3.36 | | | GROUND_INST: instantiating (14) with all_41_1, all_43_6, all_11_7, % 19.04/3.36 | | | efficient_producers, simplifying with (78), (84) gives: % 19.04/3.36 | | | (106) all_43_6 = all_41_1 % 19.04/3.36 | | | % 19.04/3.36 | | | GROUND_INST: instantiating (14) with all_39_1, all_43_6, all_11_7, % 19.04/3.36 | | | efficient_producers, simplifying with (69), (84) gives: % 19.04/3.36 | | | (107) all_43_6 = all_39_1 % 19.04/3.36 | | | % 19.04/3.36 | | | GROUND_INST: instantiating (14) with all_20_3, all_41_2, all_11_7, % 19.04/3.36 | | | first_movers, simplifying with (42), (79) gives: % 19.04/3.36 | | | (108) all_41_2 = all_20_3 % 19.04/3.36 | | | % 19.04/3.36 | | | GROUND_INST: instantiating (14) with all_41_2, all_45_6, all_11_7, % 19.04/3.36 | | | first_movers, simplifying with (79), (95) gives: % 19.04/3.36 | | | (109) all_45_6 = all_41_2 % 19.04/3.36 | | | % 19.04/3.36 | | | GROUND_INST: instantiating (14) with all_39_2, all_45_6, all_11_7, % 19.04/3.36 | | | first_movers, simplifying with (70), (95) gives: % 19.04/3.36 | | | (110) all_45_6 = all_39_2 % 19.04/3.36 | | | % 19.04/3.36 | | | GROUND_INST: instantiating (15) with all_11_0, all_45_0, all_11_5, zero, % 19.04/3.36 | | | simplifying with (21), (96) gives: % 19.04/3.36 | | | (111) all_45_0 = all_11_0 % 19.04/3.36 | | | % 19.04/3.36 | | | GROUND_INST: instantiating (15) with all_11_2, all_43_0, all_11_4, zero, % 19.04/3.36 | | | simplifying with (22), (85) gives: % 19.04/3.36 | | | (112) all_43_0 = all_11_2 % 19.04/3.36 | | | % 19.04/3.36 | | | GROUND_INST: instantiating (15) with all_11_3, all_45_2, zero, all_11_5, % 19.04/3.36 | | | simplifying with (23), (97) gives: % 19.04/3.36 | | | (113) all_45_2 = all_11_3 % 19.04/3.36 | | | % 19.04/3.36 | | | GROUND_INST: instantiating (15) with all_11_1, all_43_2, zero, all_11_4, % 19.04/3.36 | | | simplifying with (24), (86) gives: % 19.04/3.36 | | | (114) all_43_2 = all_11_1 % 19.04/3.36 | | | % 19.04/3.36 | | | GROUND_INST: instantiating (15) with 0, all_39_3, zero, all_20_3, % 19.04/3.36 | | | simplifying with (60), (71) gives: % 19.04/3.36 | | | (115) all_39_3 = 0 % 19.04/3.36 | | | % 19.04/3.37 | | | GROUND_INST: instantiating (15) with 0, all_41_3, zero, all_20_1, % 19.04/3.37 | | | simplifying with (59), (80) gives: % 19.04/3.37 | | | (116) all_41_3 = 0 % 19.04/3.37 | | | % 19.04/3.37 | | | GROUND_INST: instantiating (17) with all_41_4, all_43_7, all_11_7, % 19.04/3.37 | | | all_11_8, efficient_producers, simplifying with (81), (88) % 19.04/3.37 | | | gives: % 19.04/3.37 | | | (117) all_43_7 = all_41_4 % 19.04/3.37 | | | % 19.04/3.37 | | | GROUND_INST: instantiating (17) with all_39_4, all_45_7, all_11_7, % 19.04/3.37 | | | all_11_8, first_movers, simplifying with (72), (99) gives: % 19.04/3.37 | | | (118) all_45_7 = all_39_4 % 19.04/3.37 | | | % 19.04/3.37 | | | GROUND_INST: instantiating (9) with 0, all_43_8, all_11_8, simplifying % 19.04/3.37 | | | with (25), (89) gives: % 19.04/3.37 | | | (119) all_43_8 = 0 % 19.04/3.37 | | | % 19.04/3.37 | | | GROUND_INST: instantiating (9) with all_41_5, all_43_8, all_11_8, % 19.04/3.37 | | | simplifying with (82), (89) gives: % 19.04/3.37 | | | (120) all_43_8 = all_41_5 % 19.04/3.37 | | | % 19.04/3.37 | | | GROUND_INST: instantiating (9) with all_41_5, all_45_8, all_11_8, % 19.04/3.37 | | | simplifying with (82), (100) gives: % 19.04/3.37 | | | (121) all_45_8 = all_41_5 % 19.04/3.37 | | | % 19.04/3.37 | | | GROUND_INST: instantiating (9) with all_39_5, all_45_8, all_11_8, % 19.04/3.37 | | | simplifying with (73), (100) gives: % 19.04/3.37 | | | (122) all_45_8 = all_39_5 % 19.04/3.37 | | | % 19.04/3.37 | | | COMBINE_EQS: (109), (110) imply: % 19.04/3.37 | | | (123) all_41_2 = all_39_2 % 19.04/3.37 | | | % 19.04/3.37 | | | SIMP: (123) implies: % 19.04/3.37 | | | (124) all_41_2 = all_39_2 % 19.04/3.37 | | | % 19.04/3.37 | | | COMBINE_EQS: (121), (122) imply: % 19.04/3.37 | | | (125) all_41_5 = all_39_5 % 19.04/3.37 | | | % 19.04/3.37 | | | SIMP: (125) implies: % 19.04/3.37 | | | (126) all_41_5 = all_39_5 % 19.04/3.37 | | | % 19.04/3.37 | | | COMBINE_EQS: (106), (107) imply: % 19.04/3.37 | | | (127) all_41_1 = all_39_1 % 19.04/3.37 | | | % 19.04/3.37 | | | SIMP: (127) implies: % 19.04/3.37 | | | (128) all_41_1 = all_39_1 % 19.04/3.37 | | | % 19.04/3.37 | | | COMBINE_EQS: (119), (120) imply: % 19.04/3.37 | | | (129) all_41_5 = 0 % 19.04/3.37 | | | % 19.04/3.37 | | | SIMP: (129) implies: % 19.04/3.37 | | | (130) all_41_5 = 0 % 19.04/3.37 | | | % 19.04/3.37 | | | COMBINE_EQS: (105), (128) imply: % 19.04/3.37 | | | (131) all_39_1 = all_20_1 % 19.04/3.37 | | | % 19.04/3.37 | | | COMBINE_EQS: (108), (124) imply: % 19.04/3.37 | | | (132) all_39_2 = all_20_3 % 19.04/3.37 | | | % 19.04/3.37 | | | COMBINE_EQS: (126), (130) imply: % 19.04/3.37 | | | (133) all_39_5 = 0 % 19.04/3.37 | | | % 19.04/3.37 | | | SIMP: (133) implies: % 19.04/3.37 | | | (134) all_39_5 = 0 % 19.04/3.38 | | | % 19.04/3.38 | | | COMBINE_EQS: (107), (131) imply: % 19.04/3.38 | | | (135) all_43_6 = all_20_1 % 19.04/3.38 | | | % 19.04/3.38 | | | COMBINE_EQS: (122), (134) imply: % 19.04/3.38 | | | (136) all_45_8 = 0 % 19.04/3.38 | | | % 19.04/3.38 | | | COMBINE_EQS: (110), (132) imply: % 19.04/3.38 | | | (137) all_45_6 = all_20_3 % 19.04/3.38 | | | % 19.04/3.38 | | | REDUCE: (103), (137) imply: % 19.04/3.38 | | | (138) constant(all_20_3) = all_45_4 % 19.04/3.38 | | | % 19.04/3.38 | | | REDUCE: (92), (135) imply: % 19.04/3.38 | | | (139) constant(all_20_1) = all_43_4 % 19.04/3.38 | | | % 19.04/3.38 | | | REDUCE: (102), (137) imply: % 19.04/3.38 | | | (140) decreases(all_20_3) = all_45_1 % 19.04/3.38 | | | % 19.04/3.38 | | | REDUCE: (91), (135) imply: % 19.04/3.38 | | | (141) decreases(all_20_1) = all_43_1 % 19.04/3.38 | | | % 19.04/3.38 | | | REDUCE: (101), (137) imply: % 19.04/3.38 | | | (142) increases(all_20_3) = all_45_3 % 19.04/3.38 | | | % 19.04/3.38 | | | REDUCE: (90), (135) imply: % 19.04/3.38 | | | (143) increases(all_20_1) = all_43_3 % 19.04/3.38 | | | % 19.04/3.38 | | | REDUCE: (98), (137) imply: % 19.04/3.38 | | | (144) greater(all_20_3, zero) = all_45_5 % 19.04/3.38 | | | % 19.04/3.38 | | | REDUCE: (87), (135) imply: % 19.04/3.38 | | | (145) greater(all_20_1, zero) = all_43_5 % 19.04/3.38 | | | % 19.04/3.38 | | | REDUCE: (77), (105), (108) imply: % 19.04/3.38 | | | (146) sum(all_20_3, all_20_1) = all_41_0 % 19.04/3.38 | | | % 19.04/3.38 | | | REDUCE: (68), (131), (132) imply: % 19.04/3.38 | | | (147) sum(all_20_3, all_20_1) = all_39_0 % 19.04/3.38 | | | % 19.04/3.38 | | | REDUCE: (67), (131) imply: % 19.04/3.38 | | | (148) $i(all_20_1) % 19.04/3.38 | | | % 19.04/3.38 | | | REDUCE: (66), (132) imply: % 19.04/3.38 | | | (149) $i(all_20_3) % 19.04/3.38 | | | % 19.04/3.38 | | | GROUND_INST: instantiating (13) with all_39_0, all_41_0, all_20_1, % 19.04/3.38 | | | all_20_3, simplifying with (146), (147) gives: % 19.04/3.38 | | | (150) all_41_0 = all_39_0 % 19.04/3.38 | | | % 19.04/3.38 | | | GROUND_INST: instantiating (15) with 0, all_45_5, zero, all_20_3, % 19.04/3.38 | | | simplifying with (60), (144) gives: % 19.04/3.38 | | | (151) all_45_5 = 0 % 19.04/3.38 | | | % 19.04/3.38 | | | GROUND_INST: instantiating (15) with 0, all_43_5, zero, all_20_1, % 19.04/3.38 | | | simplifying with (59), (145) gives: % 19.04/3.38 | | | (152) all_43_5 = 0 % 19.04/3.38 | | | % 19.04/3.38 | | | REDUCE: (76), (150) imply: % 19.04/3.38 | | | (153) $i(all_39_0) % 19.04/3.38 | | | % 19.04/3.39 | | | GROUND_INST: instantiating (2) with all_11_8, all_11_7, all_39_4, % 19.04/3.39 | | | simplifying with (19), (20), (72) gives: % 19.04/3.39 | | | (154) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 19.04/3.39 | | | (in_environment(all_11_8, all_11_7) = v1 & environment(all_11_8) % 19.04/3.39 | | | = v0 & subpopulation(efficient_producers, all_11_8, all_11_7) = % 19.04/3.39 | | | v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_39_4 = 0))) % 19.04/3.39 | | | % 19.04/3.39 | | | DELTA: instantiating (154) with fresh symbols all_60_0, all_60_1, all_60_2 % 19.04/3.39 | | | gives: % 19.04/3.39 | | | (155) in_environment(all_11_8, all_11_7) = all_60_1 & % 19.04/3.39 | | | environment(all_11_8) = all_60_2 & % 19.04/3.39 | | | subpopulation(efficient_producers, all_11_8, all_11_7) = all_60_0 % 19.04/3.39 | | | & ( ~ (all_60_1 = 0) | ~ (all_60_2 = 0) | (all_60_0 = 0 & % 19.04/3.39 | | | all_39_4 = 0)) % 19.04/3.39 | | | % 19.04/3.39 | | | ALPHA: (155) implies: % 19.04/3.39 | | | (156) subpopulation(efficient_producers, all_11_8, all_11_7) = all_60_0 % 19.04/3.39 | | | (157) environment(all_11_8) = all_60_2 % 19.04/3.39 | | | (158) in_environment(all_11_8, all_11_7) = all_60_1 % 19.04/3.39 | | | (159) ~ (all_60_1 = 0) | ~ (all_60_2 = 0) | (all_60_0 = 0 & all_39_4 % 19.04/3.39 | | | = 0) % 19.04/3.39 | | | % 19.04/3.39 | | | GROUND_INST: instantiating (17) with all_41_4, all_60_0, all_11_7, % 19.04/3.39 | | | all_11_8, efficient_producers, simplifying with (81), (156) % 19.04/3.39 | | | gives: % 19.04/3.39 | | | (160) all_60_0 = all_41_4 % 19.04/3.39 | | | % 19.04/3.39 | | | GROUND_INST: instantiating (9) with 0, all_60_2, all_11_8, simplifying % 19.04/3.39 | | | with (25), (157) gives: % 19.04/3.39 | | | (161) all_60_2 = 0 % 19.04/3.39 | | | % 19.04/3.39 | | | GROUND_INST: instantiating (16) with 0, all_60_1, all_11_7, all_11_8, % 19.04/3.39 | | | simplifying with (53), (158) gives: % 19.04/3.39 | | | (162) all_60_1 = 0 % 19.04/3.39 | | | % 19.04/3.39 | | | BETA: splitting (159) gives: % 19.04/3.39 | | | % 19.04/3.39 | | | Case 1: % 19.04/3.39 | | | | % 19.04/3.39 | | | | (163) ~ (all_60_1 = 0) % 19.04/3.39 | | | | % 19.04/3.39 | | | | REDUCE: (162), (163) imply: % 19.04/3.39 | | | | (164) $false % 19.04/3.39 | | | | % 19.04/3.39 | | | | CLOSE: (164) is inconsistent. % 19.04/3.39 | | | | % 19.04/3.39 | | | Case 2: % 19.04/3.39 | | | | % 19.04/3.39 | | | | (165) ~ (all_60_2 = 0) | (all_60_0 = 0 & all_39_4 = 0) % 19.04/3.39 | | | | % 19.04/3.39 | | | | BETA: splitting (165) gives: % 19.04/3.39 | | | | % 19.04/3.39 | | | | Case 1: % 19.04/3.39 | | | | | % 19.04/3.39 | | | | | (166) ~ (all_60_2 = 0) % 19.04/3.39 | | | | | % 19.04/3.39 | | | | | REDUCE: (161), (166) imply: % 19.04/3.39 | | | | | (167) $false % 19.04/3.39 | | | | | % 19.04/3.39 | | | | | CLOSE: (167) is inconsistent. % 19.04/3.39 | | | | | % 19.04/3.39 | | | | Case 2: % 19.04/3.39 | | | | | % 19.04/3.39 | | | | | (168) all_60_0 = 0 & all_39_4 = 0 % 19.04/3.39 | | | | | % 19.04/3.39 | | | | | ALPHA: (168) implies: % 19.04/3.39 | | | | | (169) all_39_4 = 0 % 19.04/3.39 | | | | | (170) all_60_0 = 0 % 19.04/3.39 | | | | | % 19.04/3.40 | | | | | COMBINE_EQS: (160), (170) imply: % 19.04/3.40 | | | | | (171) all_41_4 = 0 % 19.04/3.40 | | | | | % 19.04/3.40 | | | | | COMBINE_EQS: (117), (171) imply: % 19.04/3.40 | | | | | (172) all_43_7 = 0 % 19.04/3.40 | | | | | % 19.04/3.40 | | | | | COMBINE_EQS: (118), (169) imply: % 19.04/3.40 | | | | | (173) all_45_7 = 0 % 19.04/3.40 | | | | | % 19.04/3.40 | | | | | BETA: splitting (74) gives: % 19.04/3.40 | | | | | % 19.04/3.40 | | | | | Case 1: % 19.04/3.40 | | | | | | % 19.04/3.40 | | | | | | (174) ~ (all_39_4 = 0) % 19.04/3.40 | | | | | | % 19.04/3.40 | | | | | | REDUCE: (169), (174) imply: % 19.53/3.40 | | | | | | (175) $false % 19.53/3.40 | | | | | | % 19.53/3.40 | | | | | | CLOSE: (175) is inconsistent. % 19.53/3.40 | | | | | | % 19.53/3.40 | | | | | Case 2: % 19.53/3.40 | | | | | | % 19.53/3.40 | | | | | | (176) ~ (all_39_5 = 0) | all_39_0 = all_11_6 % 19.53/3.40 | | | | | | % 19.53/3.40 | | | | | | BETA: splitting (176) gives: % 19.53/3.40 | | | | | | % 19.53/3.40 | | | | | | Case 1: % 19.53/3.40 | | | | | | | % 19.53/3.40 | | | | | | | (177) ~ (all_39_5 = 0) % 19.53/3.40 | | | | | | | % 19.53/3.40 | | | | | | | REDUCE: (134), (177) imply: % 19.53/3.40 | | | | | | | (178) $false % 19.53/3.40 | | | | | | | % 19.53/3.40 | | | | | | | CLOSE: (178) is inconsistent. % 19.53/3.40 | | | | | | | % 19.53/3.40 | | | | | | Case 2: % 19.53/3.40 | | | | | | | % 19.53/3.40 | | | | | | | (179) all_39_0 = all_11_6 % 19.53/3.40 | | | | | | | % 19.53/3.40 | | | | | | | REDUCE: (147), (179) imply: % 19.53/3.40 | | | | | | | (180) sum(all_20_3, all_20_1) = all_11_6 % 19.53/3.40 | | | | | | | % 19.53/3.40 | | | | | | | REDUCE: (153), (179) imply: % 19.53/3.40 | | | | | | | (181) $i(all_11_6) % 19.53/3.40 | | | | | | | % 19.53/3.40 | | | | | | | GROUND_INST: instantiating (mp_abc_sum_increase) with all_11_6, % 19.53/3.40 | | | | | | | all_20_3, all_20_1, simplifying with (27), (148), % 19.53/3.40 | | | | | | | (149), (180), (181) gives: % 19.53/3.40 | | | | | | | (182) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] % 19.53/3.40 | | | | | | | : ? [v4: any] : ? [v5: any] : (constant(all_20_1) = v1 % 19.53/3.40 | | | | | | | & constant(all_20_3) = v0 & decreases(all_20_1) = v3 & % 19.53/3.40 | | | | | | | decreases(all_20_3) = v4 & increases(all_20_1) = v5 & % 19.53/3.40 | | | | | | | increases(all_20_3) = v2 & ((v5 = 0 & v4 = 0) | (v3 = 0 % 19.53/3.40 | | | | | | | & v2 = 0) | (v1 = 0 & v0 = 0))) % 19.53/3.40 | | | | | | | % 19.53/3.40 | | | | | | | DELTA: instantiating (182) with fresh symbols all_87_0, all_87_1, % 19.53/3.40 | | | | | | | all_87_2, all_87_3, all_87_4, all_87_5 gives: % 19.53/3.40 | | | | | | | (183) constant(all_20_1) = all_87_4 & constant(all_20_3) = % 19.53/3.40 | | | | | | | all_87_5 & decreases(all_20_1) = all_87_2 & % 19.53/3.40 | | | | | | | decreases(all_20_3) = all_87_1 & increases(all_20_1) = % 19.53/3.40 | | | | | | | all_87_0 & increases(all_20_3) = all_87_3 & ((all_87_0 = % 19.53/3.40 | | | | | | | 0 & all_87_1 = 0) | (all_87_2 = 0 & all_87_3 = 0) | % 19.53/3.40 | | | | | | | (all_87_4 = 0 & all_87_5 = 0)) % 19.53/3.40 | | | | | | | % 19.53/3.40 | | | | | | | ALPHA: (183) implies: % 19.53/3.40 | | | | | | | (184) increases(all_20_3) = all_87_3 % 19.53/3.40 | | | | | | | (185) increases(all_20_1) = all_87_0 % 19.53/3.40 | | | | | | | (186) decreases(all_20_3) = all_87_1 % 19.53/3.40 | | | | | | | (187) decreases(all_20_1) = all_87_2 % 19.53/3.40 | | | | | | | (188) constant(all_20_3) = all_87_5 % 19.53/3.40 | | | | | | | (189) constant(all_20_1) = all_87_4 % 19.53/3.41 | | | | | | | (190) (all_87_0 = 0 & all_87_1 = 0) | (all_87_2 = 0 & all_87_3 % 19.53/3.41 | | | | | | | = 0) | (all_87_4 = 0 & all_87_5 = 0) % 19.53/3.41 | | | | | | | % 19.53/3.41 | | | | | | | GROUND_INST: instantiating (10) with all_45_3, all_87_3, all_20_3, % 19.53/3.41 | | | | | | | simplifying with (142), (184) gives: % 19.53/3.41 | | | | | | | (191) all_87_3 = all_45_3 % 19.53/3.41 | | | | | | | % 19.53/3.41 | | | | | | | GROUND_INST: instantiating (10) with all_43_3, all_87_0, all_20_1, % 19.53/3.41 | | | | | | | simplifying with (143), (185) gives: % 19.53/3.41 | | | | | | | (192) all_87_0 = all_43_3 % 19.53/3.41 | | | | | | | % 19.53/3.41 | | | | | | | GROUND_INST: instantiating (11) with all_45_1, all_87_1, all_20_3, % 19.53/3.41 | | | | | | | simplifying with (140), (186) gives: % 19.53/3.41 | | | | | | | (193) all_87_1 = all_45_1 % 19.53/3.41 | | | | | | | % 19.53/3.41 | | | | | | | GROUND_INST: instantiating (11) with all_43_1, all_87_2, all_20_1, % 19.53/3.41 | | | | | | | simplifying with (141), (187) gives: % 19.53/3.41 | | | | | | | (194) all_87_2 = all_43_1 % 19.53/3.41 | | | | | | | % 19.53/3.41 | | | | | | | GROUND_INST: instantiating (12) with all_45_4, all_87_5, all_20_3, % 19.53/3.41 | | | | | | | simplifying with (138), (188) gives: % 19.53/3.41 | | | | | | | (195) all_87_5 = all_45_4 % 19.53/3.41 | | | | | | | % 19.53/3.41 | | | | | | | GROUND_INST: instantiating (12) with all_43_4, all_87_4, all_20_1, % 19.53/3.41 | | | | | | | simplifying with (139), (189) gives: % 19.53/3.41 | | | | | | | (196) all_87_4 = all_43_4 % 19.53/3.41 | | | | | | | % 19.53/3.41 | | | | | | | BETA: splitting (31) gives: % 19.53/3.41 | | | | | | | % 19.53/3.41 | | | | | | | Case 1: % 19.53/3.41 | | | | | | | | % 19.53/3.41 | | | | | | | | (197) ~ (all_11_4 = zero) % 19.53/3.41 | | | | | | | | % 19.53/3.41 | | | | | | | | BETA: splitting (93) gives: % 19.53/3.41 | | | | | | | | % 19.53/3.41 | | | | | | | | Case 1: % 19.53/3.41 | | | | | | | | | % 19.53/3.41 | | | | | | | | | (198) ~ (all_43_5 = 0) % 19.53/3.41 | | | | | | | | | % 19.53/3.41 | | | | | | | | | REDUCE: (152), (198) imply: % 19.53/3.41 | | | | | | | | | (199) $false % 19.53/3.41 | | | | | | | | | % 19.53/3.41 | | | | | | | | | CLOSE: (199) is inconsistent. % 19.53/3.41 | | | | | | | | | % 19.53/3.41 | | | | | | | | Case 2: % 19.53/3.41 | | | | | | | | | % 19.53/3.41 | | | | | | | | | (200) ~ (all_43_7 = 0) | ~ (all_43_8 = 0) | (( ~ % 19.53/3.41 | | | | | | | | | (all_43_1 = 0) | all_43_0 = 0) & ( ~ (all_43_3 = % 19.53/3.41 | | | | | | | | | 0) | all_43_2 = 0) & ( ~ (all_43_4 = 0) | % 19.53/3.41 | | | | | | | | | all_11_4 = zero)) % 19.53/3.41 | | | | | | | | | % 19.53/3.41 | | | | | | | | | BETA: splitting (200) gives: % 19.53/3.41 | | | | | | | | | % 19.53/3.41 | | | | | | | | | Case 1: % 19.53/3.41 | | | | | | | | | | % 19.53/3.41 | | | | | | | | | | (201) ~ (all_43_7 = 0) % 19.53/3.41 | | | | | | | | | | % 19.53/3.41 | | | | | | | | | | REDUCE: (172), (201) imply: % 19.53/3.41 | | | | | | | | | | (202) $false % 19.53/3.41 | | | | | | | | | | % 19.53/3.41 | | | | | | | | | | CLOSE: (202) is inconsistent. % 19.53/3.41 | | | | | | | | | | % 19.53/3.41 | | | | | | | | | Case 2: % 19.53/3.41 | | | | | | | | | | % 19.53/3.41 | | | | | | | | | | (203) ~ (all_43_8 = 0) | (( ~ (all_43_1 = 0) | all_43_0 % 19.53/3.41 | | | | | | | | | | = 0) & ( ~ (all_43_3 = 0) | all_43_2 = 0) & ( ~ % 19.53/3.41 | | | | | | | | | | (all_43_4 = 0) | all_11_4 = zero)) % 19.53/3.41 | | | | | | | | | | % 19.53/3.41 | | | | | | | | | | BETA: splitting (203) gives: % 19.53/3.41 | | | | | | | | | | % 19.53/3.41 | | | | | | | | | | Case 1: % 19.53/3.41 | | | | | | | | | | | % 19.53/3.41 | | | | | | | | | | | (204) ~ (all_43_8 = 0) % 19.53/3.41 | | | | | | | | | | | % 19.53/3.41 | | | | | | | | | | | REDUCE: (119), (204) imply: % 19.53/3.41 | | | | | | | | | | | (205) $false % 19.53/3.41 | | | | | | | | | | | % 19.53/3.41 | | | | | | | | | | | CLOSE: (205) is inconsistent. % 19.53/3.41 | | | | | | | | | | | % 19.53/3.41 | | | | | | | | | | Case 2: % 19.53/3.41 | | | | | | | | | | | % 19.53/3.41 | | | | | | | | | | | (206) ( ~ (all_43_1 = 0) | all_43_0 = 0) & ( ~ (all_43_3 % 19.53/3.41 | | | | | | | | | | | = 0) | all_43_2 = 0) & ( ~ (all_43_4 = 0) | % 19.53/3.41 | | | | | | | | | | | all_11_4 = zero) % 19.53/3.41 | | | | | | | | | | | % 19.53/3.41 | | | | | | | | | | | ALPHA: (206) implies: % 19.53/3.42 | | | | | | | | | | | (207) ~ (all_43_4 = 0) | all_11_4 = zero % 19.53/3.42 | | | | | | | | | | | (208) ~ (all_43_3 = 0) | all_43_2 = 0 % 19.53/3.42 | | | | | | | | | | | (209) ~ (all_43_1 = 0) | all_43_0 = 0 % 19.53/3.42 | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | BETA: splitting (207) gives: % 19.53/3.42 | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | Case 1: % 19.53/3.42 | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | (210) ~ (all_43_4 = 0) % 19.53/3.42 | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | BETA: splitting (32) gives: % 19.53/3.42 | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | Case 1: % 19.53/3.42 | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | (211) ~ (all_11_2 = 0) % 19.53/3.42 | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | BETA: splitting (209) gives: % 19.53/3.42 | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | Case 1: % 19.53/3.42 | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | (212) ~ (all_43_1 = 0) % 19.53/3.42 | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | BETA: splitting (190) gives: % 19.53/3.42 | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | Case 1: % 19.53/3.42 | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | (213) all_87_0 = 0 & all_87_1 = 0 % 19.53/3.42 | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | ALPHA: (213) implies: % 19.53/3.42 | | | | | | | | | | | | | | | (214) all_87_1 = 0 % 19.53/3.42 | | | | | | | | | | | | | | | (215) all_87_0 = 0 % 19.53/3.42 | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | COMBINE_EQS: (192), (215) imply: % 19.53/3.42 | | | | | | | | | | | | | | | (216) all_43_3 = 0 % 19.53/3.42 | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | COMBINE_EQS: (193), (214) imply: % 19.53/3.42 | | | | | | | | | | | | | | | (217) all_45_1 = 0 % 19.53/3.42 | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | BETA: splitting (104) gives: % 19.53/3.42 | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | Case 1: % 19.53/3.42 | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | (218) ~ (all_45_5 = 0) % 19.53/3.42 | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | REDUCE: (151), (218) imply: % 19.53/3.42 | | | | | | | | | | | | | | | | (219) $false % 19.53/3.42 | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | CLOSE: (219) is inconsistent. % 19.53/3.42 | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | Case 2: % 19.53/3.42 | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | (220) ~ (all_45_7 = 0) | ~ (all_45_8 = 0) | (( ~ % 19.53/3.42 | | | | | | | | | | | | | | | | (all_45_1 = 0) | all_45_0 = 0) & ( ~ (all_45_3 % 19.53/3.42 | | | | | | | | | | | | | | | | = 0) | all_45_2 = 0) & ( ~ (all_45_4 = 0) | % 19.53/3.42 | | | | | | | | | | | | | | | | all_11_5 = zero)) % 19.53/3.42 | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 19.53/3.42 | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | Case 1: % 19.53/3.42 | | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | | (221) ~ (all_45_7 = 0) % 19.53/3.42 | | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | | REDUCE: (173), (221) imply: % 19.53/3.42 | | | | | | | | | | | | | | | | | (222) $false % 19.53/3.42 | | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | | CLOSE: (222) is inconsistent. % 19.53/3.42 | | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | Case 2: % 19.53/3.42 | | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | | (223) ~ (all_45_8 = 0) | (( ~ (all_45_1 = 0) | all_45_0 % 19.53/3.42 | | | | | | | | | | | | | | | | | = 0) & ( ~ (all_45_3 = 0) | all_45_2 = 0) & ( % 19.53/3.42 | | | | | | | | | | | | | | | | | ~ (all_45_4 = 0) | all_11_5 = zero)) % 19.53/3.42 | | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (111), (114), (136), (208), (216), (217), % 19.53/3.42 | | | | | | | | | | | | | | | | | (223) are inconsistent by sub-proof #3. % 19.53/3.42 | | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | End of split % 19.53/3.42 | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | End of split % 19.53/3.42 | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | Case 2: % 19.53/3.42 | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | (224) (all_87_2 = 0 & all_87_3 = 0) | (all_87_4 = 0 & % 19.53/3.42 | | | | | | | | | | | | | | | all_87_5 = 0) % 19.53/3.42 | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 19.53/3.42 | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | Case 1: % 19.53/3.42 | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | (225) all_87_2 = 0 & all_87_3 = 0 % 19.53/3.42 | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | ALPHA: (225) implies: % 19.53/3.42 | | | | | | | | | | | | | | | | (226) all_87_2 = 0 % 19.53/3.42 | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | COMBINE_EQS: (194), (226) imply: % 19.53/3.42 | | | | | | | | | | | | | | | | (227) all_43_1 = 0 % 19.53/3.42 | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | REDUCE: (212), (227) imply: % 19.53/3.42 | | | | | | | | | | | | | | | | (228) $false % 19.53/3.42 | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | CLOSE: (228) is inconsistent. % 19.53/3.42 | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | Case 2: % 19.53/3.42 | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | (229) all_87_4 = 0 & all_87_5 = 0 % 19.53/3.42 | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | | REF_CLOSE: (196), (210), (229) are inconsistent by sub-proof % 19.53/3.42 | | | | | | | | | | | | | | | | #2. % 19.53/3.42 | | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | | End of split % 19.53/3.42 | | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | End of split % 19.53/3.42 | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | Case 2: % 19.53/3.42 | | | | | | | | | | | | | | % 19.53/3.42 | | | | | | | | | | | | | | (230) all_43_0 = 0 % 19.53/3.42 | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | REF_CLOSE: (112), (211), (230) are inconsistent by sub-proof % 19.53/3.43 | | | | | | | | | | | | | | #1. % 19.53/3.43 | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | End of split % 19.53/3.43 | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | Case 2: % 19.53/3.43 | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | (231) ~ (all_11_3 = 0) % 19.53/3.43 | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | BETA: splitting (104) gives: % 19.53/3.43 | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | Case 1: % 19.53/3.43 | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | (232) ~ (all_45_5 = 0) % 19.53/3.43 | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | REDUCE: (151), (232) imply: % 19.53/3.43 | | | | | | | | | | | | | | (233) $false % 19.53/3.43 | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | CLOSE: (233) is inconsistent. % 19.53/3.43 | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | Case 2: % 19.53/3.43 | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | (234) ~ (all_45_7 = 0) | ~ (all_45_8 = 0) | (( ~ % 19.53/3.43 | | | | | | | | | | | | | | (all_45_1 = 0) | all_45_0 = 0) & ( ~ (all_45_3 % 19.53/3.43 | | | | | | | | | | | | | | = 0) | all_45_2 = 0) & ( ~ (all_45_4 = 0) | % 19.53/3.43 | | | | | | | | | | | | | | all_11_5 = zero)) % 19.53/3.43 | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | BETA: splitting (234) gives: % 19.53/3.43 | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | Case 1: % 19.53/3.43 | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | (235) ~ (all_45_7 = 0) % 19.53/3.43 | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | REDUCE: (173), (235) imply: % 19.53/3.43 | | | | | | | | | | | | | | | (236) $false % 19.53/3.43 | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | CLOSE: (236) is inconsistent. % 19.53/3.43 | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | Case 2: % 19.53/3.43 | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | (237) ~ (all_45_8 = 0) | (( ~ (all_45_1 = 0) | all_45_0 % 19.53/3.43 | | | | | | | | | | | | | | | = 0) & ( ~ (all_45_3 = 0) | all_45_2 = 0) & ( % 19.53/3.43 | | | | | | | | | | | | | | | ~ (all_45_4 = 0) | all_11_5 = zero)) % 19.53/3.43 | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 19.53/3.43 | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | Case 1: % 19.53/3.43 | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | (238) ~ (all_45_8 = 0) % 19.53/3.43 | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | REDUCE: (136), (238) imply: % 19.53/3.43 | | | | | | | | | | | | | | | | (239) $false % 19.53/3.43 | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | CLOSE: (239) is inconsistent. % 19.53/3.43 | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | Case 2: % 19.53/3.43 | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | (240) ( ~ (all_45_1 = 0) | all_45_0 = 0) & ( ~ (all_45_3 % 19.53/3.43 | | | | | | | | | | | | | | | | = 0) | all_45_2 = 0) & ( ~ (all_45_4 = 0) | % 19.53/3.43 | | | | | | | | | | | | | | | | all_11_5 = zero) % 19.53/3.43 | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | ALPHA: (240) implies: % 19.53/3.43 | | | | | | | | | | | | | | | | (241) ~ (all_45_3 = 0) | all_45_2 = 0 % 19.53/3.43 | | | | | | | | | | | | | | | | (242) ~ (all_45_1 = 0) | all_45_0 = 0 % 19.53/3.43 | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 19.53/3.43 | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | Case 1: % 19.53/3.43 | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | (243) ~ (all_45_3 = 0) % 19.53/3.43 | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 19.53/3.43 | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | Case 1: % 19.53/3.43 | | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | | (244) all_87_0 = 0 & all_87_1 = 0 % 19.53/3.43 | | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | | ALPHA: (244) implies: % 19.53/3.43 | | | | | | | | | | | | | | | | | | (245) all_87_1 = 0 % 19.53/3.43 | | | | | | | | | | | | | | | | | | (246) all_87_0 = 0 % 19.53/3.43 | | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (192), (246) imply: % 19.53/3.43 | | | | | | | | | | | | | | | | | | (247) all_43_3 = 0 % 19.53/3.43 | | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (193), (245) imply: % 19.53/3.43 | | | | | | | | | | | | | | | | | | (248) all_45_1 = 0 % 19.53/3.43 | | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (111), (114), (208), (242), (247), (248) are % 19.53/3.43 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #4. % 19.53/3.43 | | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | Case 2: % 19.53/3.43 | | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | | (249) (all_87_2 = 0 & all_87_3 = 0) | (all_87_4 = 0 & % 19.53/3.43 | | | | | | | | | | | | | | | | | | all_87_5 = 0) % 19.53/3.43 | | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 19.53/3.43 | | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | | Case 1: % 19.53/3.43 | | | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | | | (250) all_87_2 = 0 & all_87_3 = 0 % 19.53/3.43 | | | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies: % 19.53/3.43 | | | | | | | | | | | | | | | | | | | (251) all_87_3 = 0 % 19.53/3.43 | | | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (191), (251) imply: % 19.53/3.43 | | | | | | | | | | | | | | | | | | | (252) all_45_3 = 0 % 19.53/3.43 | | | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | | | REDUCE: (243), (252) imply: % 19.53/3.43 | | | | | | | | | | | | | | | | | | | (253) $false % 19.53/3.43 | | | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | | | CLOSE: (253) is inconsistent. % 19.53/3.43 | | | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | | Case 2: % 19.53/3.43 | | | | | | | | | | | | | | | | | | | % 19.53/3.43 | | | | | | | | | | | | | | | | | | | (254) all_87_4 = 0 & all_87_5 = 0 % 19.53/3.43 | | | | | | | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (196), (210), (254) are inconsistent by sub-proof % 19.53/3.44 | | | | | | | | | | | | | | | | | | | #2. % 19.53/3.44 | | | | | | | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | | | | | | | End of split % 19.53/3.44 | | | | | | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | | | | | | End of split % 19.53/3.44 | | | | | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | | | | | Case 2: % 19.53/3.44 | | | | | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | | | | | | (255) all_45_2 = 0 % 19.53/3.44 | | | | | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (255) imply: % 19.53/3.44 | | | | | | | | | | | | | | | | | (256) all_11_3 = 0 % 19.53/3.44 | | | | | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | | | | | | SIMP: (256) implies: % 19.53/3.44 | | | | | | | | | | | | | | | | | (257) all_11_3 = 0 % 19.53/3.44 | | | | | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | | | | | | REDUCE: (231), (257) imply: % 19.53/3.44 | | | | | | | | | | | | | | | | | (258) $false % 19.53/3.44 | | | | | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | | | | | | CLOSE: (258) is inconsistent. % 19.53/3.44 | | | | | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | | | | | End of split % 19.53/3.44 | | | | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | | | | End of split % 19.53/3.44 | | | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | | | End of split % 19.53/3.44 | | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | | End of split % 19.53/3.44 | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | End of split % 19.53/3.44 | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | Case 2: % 19.53/3.44 | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | (259) all_11_4 = zero % 19.53/3.44 | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | REDUCE: (197), (259) imply: % 19.53/3.44 | | | | | | | | | | | | (260) $false % 19.53/3.44 | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | CLOSE: (260) is inconsistent. % 19.53/3.44 | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | End of split % 19.53/3.44 | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | End of split % 19.53/3.44 | | | | | | | | | | % 19.53/3.44 | | | | | | | | | End of split % 19.53/3.44 | | | | | | | | | % 19.53/3.44 | | | | | | | | End of split % 19.53/3.44 | | | | | | | | % 19.53/3.44 | | | | | | | Case 2: % 19.53/3.44 | | | | | | | | % 19.53/3.44 | | | | | | | | (261) ~ (all_11_5 = zero) % 19.53/3.44 | | | | | | | | % 19.53/3.44 | | | | | | | | BETA: splitting (104) gives: % 19.53/3.44 | | | | | | | | % 19.53/3.44 | | | | | | | | Case 1: % 19.53/3.44 | | | | | | | | | % 19.53/3.44 | | | | | | | | | (262) ~ (all_45_5 = 0) % 19.53/3.44 | | | | | | | | | % 19.53/3.44 | | | | | | | | | REDUCE: (151), (262) imply: % 19.53/3.44 | | | | | | | | | (263) $false % 19.53/3.44 | | | | | | | | | % 19.53/3.44 | | | | | | | | | CLOSE: (263) is inconsistent. % 19.53/3.44 | | | | | | | | | % 19.53/3.44 | | | | | | | | Case 2: % 19.53/3.44 | | | | | | | | | % 19.53/3.44 | | | | | | | | | (264) ~ (all_45_7 = 0) | ~ (all_45_8 = 0) | (( ~ % 19.53/3.44 | | | | | | | | | (all_45_1 = 0) | all_45_0 = 0) & ( ~ (all_45_3 = % 19.53/3.44 | | | | | | | | | 0) | all_45_2 = 0) & ( ~ (all_45_4 = 0) | % 19.53/3.44 | | | | | | | | | all_11_5 = zero)) % 19.53/3.44 | | | | | | | | | % 19.53/3.44 | | | | | | | | | BETA: splitting (264) gives: % 19.53/3.44 | | | | | | | | | % 19.53/3.44 | | | | | | | | | Case 1: % 19.53/3.44 | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | (265) ~ (all_45_7 = 0) % 19.53/3.44 | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | REDUCE: (173), (265) imply: % 19.53/3.44 | | | | | | | | | | (266) $false % 19.53/3.44 | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | CLOSE: (266) is inconsistent. % 19.53/3.44 | | | | | | | | | | % 19.53/3.44 | | | | | | | | | Case 2: % 19.53/3.44 | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | (267) ~ (all_45_8 = 0) | (( ~ (all_45_1 = 0) | all_45_0 % 19.53/3.44 | | | | | | | | | | = 0) & ( ~ (all_45_3 = 0) | all_45_2 = 0) & ( ~ % 19.53/3.44 | | | | | | | | | | (all_45_4 = 0) | all_11_5 = zero)) % 19.53/3.44 | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | BETA: splitting (267) gives: % 19.53/3.44 | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | Case 1: % 19.53/3.44 | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | (268) ~ (all_45_8 = 0) % 19.53/3.44 | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | REDUCE: (136), (268) imply: % 19.53/3.44 | | | | | | | | | | | (269) $false % 19.53/3.44 | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | CLOSE: (269) is inconsistent. % 19.53/3.44 | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | Case 2: % 19.53/3.44 | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | (270) ( ~ (all_45_1 = 0) | all_45_0 = 0) & ( ~ (all_45_3 % 19.53/3.44 | | | | | | | | | | | = 0) | all_45_2 = 0) & ( ~ (all_45_4 = 0) | % 19.53/3.44 | | | | | | | | | | | all_11_5 = zero) % 19.53/3.44 | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | ALPHA: (270) implies: % 19.53/3.44 | | | | | | | | | | | (271) ~ (all_45_4 = 0) | all_11_5 = zero % 19.53/3.44 | | | | | | | | | | | (272) ~ (all_45_3 = 0) | all_45_2 = 0 % 19.53/3.44 | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | BETA: splitting (271) gives: % 19.53/3.44 | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | Case 1: % 19.53/3.44 | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | (273) ~ (all_45_4 = 0) % 19.53/3.44 | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | BETA: splitting (93) gives: % 19.53/3.44 | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | Case 1: % 19.53/3.44 | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | | (274) ~ (all_43_5 = 0) % 19.53/3.44 | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | | REDUCE: (152), (274) imply: % 19.53/3.44 | | | | | | | | | | | | | (275) $false % 19.53/3.44 | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | | CLOSE: (275) is inconsistent. % 19.53/3.44 | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | Case 2: % 19.53/3.44 | | | | | | | | | | | | | % 19.53/3.44 | | | | | | | | | | | | | (276) ~ (all_43_7 = 0) | ~ (all_43_8 = 0) | (( ~ % 19.53/3.44 | | | | | | | | | | | | | (all_43_1 = 0) | all_43_0 = 0) & ( ~ (all_43_3 % 19.53/3.44 | | | | | | | | | | | | | = 0) | all_43_2 = 0) & ( ~ (all_43_4 = 0) | % 19.53/3.44 | | | | | | | | | | | | | all_11_4 = zero)) % 19.53/3.45 | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | BETA: splitting (276) gives: % 19.53/3.45 | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | Case 1: % 19.53/3.45 | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | (277) ~ (all_43_7 = 0) % 19.53/3.45 | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | REDUCE: (172), (277) imply: % 19.53/3.45 | | | | | | | | | | | | | | (278) $false % 19.53/3.45 | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | CLOSE: (278) is inconsistent. % 19.53/3.45 | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | Case 2: % 19.53/3.45 | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | (279) ~ (all_43_8 = 0) | (( ~ (all_43_1 = 0) | all_43_0 % 19.53/3.45 | | | | | | | | | | | | | | = 0) & ( ~ (all_43_3 = 0) | all_43_2 = 0) & ( % 19.53/3.45 | | | | | | | | | | | | | | ~ (all_43_4 = 0) | all_11_4 = zero)) % 19.53/3.45 | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | BETA: splitting (279) gives: % 19.53/3.45 | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | Case 1: % 19.53/3.45 | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | (280) ~ (all_43_8 = 0) % 19.53/3.45 | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | REDUCE: (119), (280) imply: % 19.53/3.45 | | | | | | | | | | | | | | | (281) $false % 19.53/3.45 | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | CLOSE: (281) is inconsistent. % 19.53/3.45 | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | Case 2: % 19.53/3.45 | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | (282) ( ~ (all_43_1 = 0) | all_43_0 = 0) & ( ~ (all_43_3 % 19.53/3.45 | | | | | | | | | | | | | | | = 0) | all_43_2 = 0) & ( ~ (all_43_4 = 0) | % 19.53/3.45 | | | | | | | | | | | | | | | all_11_4 = zero) % 19.53/3.45 | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | ALPHA: (282) implies: % 19.53/3.45 | | | | | | | | | | | | | | | (283) ~ (all_43_3 = 0) | all_43_2 = 0 % 19.53/3.45 | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 19.53/3.45 | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | Case 1: % 19.53/3.45 | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | (284) all_87_0 = 0 & all_87_1 = 0 % 19.53/3.45 | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | ALPHA: (284) implies: % 19.53/3.45 | | | | | | | | | | | | | | | | (285) all_87_1 = 0 % 19.53/3.45 | | | | | | | | | | | | | | | | (286) all_87_0 = 0 % 19.53/3.45 | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | COMBINE_EQS: (192), (286) imply: % 19.53/3.45 | | | | | | | | | | | | | | | | (287) all_43_3 = 0 % 19.53/3.45 | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | COMBINE_EQS: (193), (285) imply: % 19.53/3.45 | | | | | | | | | | | | | | | | (288) all_45_1 = 0 % 19.53/3.45 | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | REF_CLOSE: (33), (111), (114), (136), (267), (283), (287), % 19.53/3.45 | | | | | | | | | | | | | | | | (288) are inconsistent by sub-proof #3. % 19.53/3.45 | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | Case 2: % 19.53/3.45 | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | (289) (all_87_2 = 0 & all_87_3 = 0) | (all_87_4 = 0 & % 19.53/3.45 | | | | | | | | | | | | | | | | all_87_5 = 0) % 19.53/3.45 | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 19.53/3.45 | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | Case 1: % 19.53/3.45 | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | (290) all_87_2 = 0 & all_87_3 = 0 % 19.53/3.45 | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | ALPHA: (290) implies: % 19.53/3.45 | | | | | | | | | | | | | | | | | (291) all_87_3 = 0 % 19.53/3.45 | | | | | | | | | | | | | | | | | (292) all_87_2 = 0 % 19.53/3.45 | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | COMBINE_EQS: (194), (292) imply: % 19.53/3.45 | | | | | | | | | | | | | | | | | (293) all_43_1 = 0 % 19.53/3.45 | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | SIMP: (293) implies: % 19.53/3.45 | | | | | | | | | | | | | | | | | (294) all_43_1 = 0 % 19.53/3.45 | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | COMBINE_EQS: (191), (291) imply: % 19.53/3.45 | | | | | | | | | | | | | | | | | (295) all_45_3 = 0 % 19.53/3.45 | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: % 19.53/3.45 | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | Case 1: % 19.53/3.45 | | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | | (296) ~ (all_45_3 = 0) % 19.53/3.45 | | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | | REDUCE: (295), (296) imply: % 19.53/3.45 | | | | | | | | | | | | | | | | | | (297) $false % 19.53/3.45 | | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | | CLOSE: (297) is inconsistent. % 19.53/3.45 | | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | Case 2: % 19.53/3.45 | | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | | (298) all_45_2 = 0 % 19.53/3.45 | | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (298) imply: % 19.53/3.45 | | | | | | | | | | | | | | | | | | (299) all_11_3 = 0 % 19.53/3.45 | | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | | BETA: splitting (32) gives: % 19.53/3.45 | | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | | Case 1: % 19.53/3.45 | | | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | | | (300) ~ (all_11_2 = 0) % 19.53/3.45 | | | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives: % 19.53/3.45 | | | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | | | Case 1: % 19.53/3.45 | | | | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | | | | (301) ~ (all_43_7 = 0) % 19.53/3.45 | | | | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | | | | REDUCE: (172), (301) imply: % 19.53/3.45 | | | | | | | | | | | | | | | | | | | | (302) $false % 19.53/3.45 | | | | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | | | | CLOSE: (302) is inconsistent. % 19.53/3.45 | | | | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | | | Case 2: % 19.53/3.45 | | | | | | | | | | | | | | | | | | | | % 19.53/3.45 | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives: % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | Case 1: % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | (303) ~ (all_43_8 = 0) % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (303) imply: % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | (304) $false % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | CLOSE: (304) is inconsistent. % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | Case 2: % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies: % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | (305) ~ (all_43_1 = 0) | all_43_0 = 0 % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives: % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | Case 1: % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | | (306) ~ (all_43_1 = 0) % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (294), (306) imply: % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | | (307) $false % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (307) is inconsistent. % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | Case 2: % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | | (308) all_43_0 = 0 % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (300), (308) are inconsistent by sub-proof % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | | #1. % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | End of split % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | End of split % 19.53/3.46 | | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | End of split % 19.53/3.46 | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | Case 2: % 19.53/3.46 | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | (309) ~ (all_11_3 = 0) % 19.53/3.46 | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | REDUCE: (299), (309) imply: % 19.53/3.46 | | | | | | | | | | | | | | | | | | | (310) $false % 19.53/3.46 | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | | CLOSE: (310) is inconsistent. % 19.53/3.46 | | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | | End of split % 19.53/3.46 | | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | End of split % 19.53/3.46 | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | Case 2: % 19.53/3.46 | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | (311) all_87_4 = 0 & all_87_5 = 0 % 19.53/3.46 | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | ALPHA: (311) implies: % 19.53/3.46 | | | | | | | | | | | | | | | | | (312) all_87_5 = 0 % 19.53/3.46 | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (312) imply: % 19.53/3.46 | | | | | | | | | | | | | | | | | (313) all_45_4 = 0 % 19.53/3.46 | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | SIMP: (313) implies: % 19.53/3.46 | | | | | | | | | | | | | | | | | (314) all_45_4 = 0 % 19.53/3.46 | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | REDUCE: (273), (314) imply: % 19.53/3.46 | | | | | | | | | | | | | | | | | (315) $false % 19.53/3.46 | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | | CLOSE: (315) is inconsistent. % 19.53/3.46 | | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | | End of split % 19.53/3.46 | | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | | End of split % 19.53/3.46 | | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | | End of split % 19.53/3.46 | | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | | End of split % 19.53/3.46 | | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | End of split % 19.53/3.46 | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | Case 2: % 19.53/3.46 | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | (316) all_11_5 = zero % 19.53/3.46 | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | REDUCE: (261), (316) imply: % 19.53/3.46 | | | | | | | | | | | | (317) $false % 19.53/3.46 | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | | CLOSE: (317) is inconsistent. % 19.53/3.46 | | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | | End of split % 19.53/3.46 | | | | | | | | | | | % 19.53/3.46 | | | | | | | | | | End of split % 19.53/3.46 | | | | | | | | | | % 19.53/3.46 | | | | | | | | | End of split % 19.53/3.46 | | | | | | | | | % 19.53/3.46 | | | | | | | | End of split % 19.53/3.46 | | | | | | | | % 19.53/3.46 | | | | | | | End of split % 19.53/3.46 | | | | | | | % 19.53/3.46 | | | | | | End of split % 19.53/3.46 | | | | | | % 19.53/3.46 | | | | | End of split % 19.53/3.46 | | | | | % 19.53/3.46 | | | | End of split % 19.53/3.46 | | | | % 19.53/3.46 | | | End of split % 19.53/3.46 | | | % 19.53/3.46 | | End of split % 19.53/3.46 | | % 19.53/3.46 | End of split % 19.53/3.46 | % 19.53/3.46 End of proof % 19.53/3.46 % 19.53/3.46 Sub-proof #1 shows that the following formulas are inconsistent: % 19.53/3.46 ---------------------------------------------------------------- % 19.53/3.47 (1) all_43_0 = all_11_2 % 19.53/3.47 (2) all_43_0 = 0 % 19.53/3.47 (3) ~ (all_11_2 = 0) % 19.53/3.47 % 19.53/3.47 Begin of proof % 19.53/3.47 | % 19.53/3.47 | COMBINE_EQS: (1), (2) imply: % 19.53/3.47 | (4) all_11_2 = 0 % 19.53/3.47 | % 19.53/3.47 | SIMP: (4) implies: % 19.53/3.47 | (5) all_11_2 = 0 % 19.53/3.47 | % 19.53/3.47 | REDUCE: (3), (5) imply: % 19.53/3.47 | (6) $false % 19.53/3.47 | % 19.53/3.47 | CLOSE: (6) is inconsistent. % 19.53/3.47 | % 19.53/3.47 End of proof % 19.53/3.47 % 19.53/3.47 Sub-proof #2 shows that the following formulas are inconsistent: % 19.53/3.47 ---------------------------------------------------------------- % 19.53/3.47 (1) all_87_4 = 0 & all_87_5 = 0 % 19.53/3.47 (2) all_87_4 = all_43_4 % 19.53/3.47 (3) ~ (all_43_4 = 0) % 19.53/3.47 % 19.53/3.47 Begin of proof % 19.53/3.47 | % 19.53/3.47 | ALPHA: (1) implies: % 19.53/3.47 | (4) all_87_4 = 0 % 19.53/3.47 | % 19.53/3.47 | COMBINE_EQS: (2), (4) imply: % 19.53/3.47 | (5) all_43_4 = 0 % 19.53/3.47 | % 19.53/3.47 | REDUCE: (3), (5) imply: % 19.53/3.47 | (6) $false % 19.53/3.47 | % 19.53/3.47 | CLOSE: (6) is inconsistent. % 19.53/3.47 | % 19.53/3.47 End of proof % 19.53/3.47 % 19.53/3.47 Sub-proof #3 shows that the following formulas are inconsistent: % 19.53/3.47 ---------------------------------------------------------------- % 19.53/3.47 (1) all_45_0 = all_11_0 % 19.53/3.47 (2) all_43_2 = all_11_1 % 19.53/3.47 (3) all_45_8 = 0 % 19.53/3.47 (4) ~ (all_45_8 = 0) | (( ~ (all_45_1 = 0) | all_45_0 = 0) & ( ~ (all_45_3 = % 19.53/3.47 0) | all_45_2 = 0) & ( ~ (all_45_4 = 0) | all_11_5 = zero)) % 19.53/3.47 (5) all_43_3 = 0 % 19.53/3.47 (6) ~ (all_43_3 = 0) | all_43_2 = 0 % 19.53/3.47 (7) ~ (all_11_0 = 0) | ~ (all_11_1 = 0) % 19.53/3.47 (8) all_45_1 = 0 % 19.53/3.47 % 19.53/3.47 Begin of proof % 19.53/3.47 | % 19.53/3.47 | BETA: splitting (4) gives: % 19.53/3.47 | % 19.53/3.47 | Case 1: % 19.53/3.47 | | % 19.53/3.47 | | (9) ~ (all_45_8 = 0) % 19.53/3.47 | | % 19.53/3.47 | | REDUCE: (3), (9) imply: % 19.53/3.47 | | (10) $false % 19.53/3.47 | | % 19.53/3.47 | | CLOSE: (10) is inconsistent. % 19.53/3.47 | | % 19.53/3.47 | Case 2: % 19.53/3.47 | | % 19.53/3.47 | | (11) ( ~ (all_45_1 = 0) | all_45_0 = 0) & ( ~ (all_45_3 = 0) | all_45_2 = % 19.53/3.47 | | 0) & ( ~ (all_45_4 = 0) | all_11_5 = zero) % 19.53/3.47 | | % 19.53/3.47 | | ALPHA: (11) implies: % 19.53/3.47 | | (12) ~ (all_45_1 = 0) | all_45_0 = 0 % 19.53/3.47 | | % 19.53/3.47 | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (12) are inconsistent by sub-proof % 19.53/3.47 | | #4. % 19.53/3.47 | | % 19.53/3.47 | End of split % 19.53/3.47 | % 19.53/3.47 End of proof % 19.53/3.47 % 19.53/3.47 Sub-proof #4 shows that the following formulas are inconsistent: % 19.53/3.47 ---------------------------------------------------------------- % 19.53/3.47 (1) all_45_0 = all_11_0 % 19.53/3.47 (2) all_43_2 = all_11_1 % 19.53/3.47 (3) ~ (all_45_1 = 0) | all_45_0 = 0 % 19.53/3.47 (4) all_43_3 = 0 % 19.53/3.47 (5) ~ (all_43_3 = 0) | all_43_2 = 0 % 19.53/3.47 (6) ~ (all_11_0 = 0) | ~ (all_11_1 = 0) % 19.53/3.47 (7) all_45_1 = 0 % 19.53/3.47 % 19.53/3.47 Begin of proof % 19.53/3.47 | % 19.53/3.47 | BETA: splitting (3) gives: % 19.53/3.47 | % 19.53/3.47 | Case 1: % 19.53/3.47 | | % 19.53/3.47 | | (8) ~ (all_45_1 = 0) % 19.53/3.47 | | % 19.53/3.47 | | REDUCE: (7), (8) imply: % 19.53/3.47 | | (9) $false % 19.53/3.47 | | % 19.53/3.47 | | CLOSE: (9) is inconsistent. % 19.53/3.47 | | % 19.53/3.47 | Case 2: % 19.53/3.47 | | % 19.53/3.48 | | (10) all_45_0 = 0 % 19.53/3.48 | | % 19.53/3.48 | | COMBINE_EQS: (1), (10) imply: % 19.53/3.48 | | (11) all_11_0 = 0 % 19.53/3.48 | | % 19.53/3.48 | | SIMP: (11) implies: % 19.53/3.48 | | (12) all_11_0 = 0 % 19.53/3.48 | | % 19.53/3.48 | | BETA: splitting (6) gives: % 19.53/3.48 | | % 19.53/3.48 | | Case 1: % 19.53/3.48 | | | % 19.53/3.48 | | | (13) ~ (all_11_0 = 0) % 19.53/3.48 | | | % 19.53/3.48 | | | REDUCE: (12), (13) imply: % 19.53/3.48 | | | (14) $false % 19.53/3.48 | | | % 19.53/3.48 | | | CLOSE: (14) is inconsistent. % 19.53/3.48 | | | % 19.53/3.48 | | Case 2: % 19.53/3.48 | | | % 19.53/3.48 | | | (15) ~ (all_11_1 = 0) % 19.53/3.48 | | | % 19.53/3.48 | | | BETA: splitting (5) gives: % 19.53/3.48 | | | % 19.53/3.48 | | | Case 1: % 19.53/3.48 | | | | % 19.53/3.48 | | | | (16) ~ (all_43_3 = 0) % 19.53/3.48 | | | | % 19.53/3.48 | | | | REDUCE: (4), (16) imply: % 19.53/3.48 | | | | (17) $false % 19.53/3.48 | | | | % 19.53/3.48 | | | | CLOSE: (17) is inconsistent. % 19.53/3.48 | | | | % 19.53/3.48 | | | Case 2: % 19.53/3.48 | | | | % 19.53/3.48 | | | | (18) all_43_2 = 0 % 19.53/3.48 | | | | % 19.53/3.48 | | | | COMBINE_EQS: (2), (18) imply: % 19.53/3.48 | | | | (19) all_11_1 = 0 % 19.53/3.48 | | | | % 19.53/3.48 | | | | SIMP: (19) implies: % 19.53/3.48 | | | | (20) all_11_1 = 0 % 19.53/3.48 | | | | % 19.53/3.48 | | | | REDUCE: (15), (20) imply: % 19.53/3.48 | | | | (21) $false % 19.53/3.48 | | | | % 19.53/3.48 | | | | CLOSE: (21) is inconsistent. % 19.53/3.48 | | | | % 19.53/3.48 | | | End of split % 19.53/3.48 | | | % 19.53/3.48 | | End of split % 19.53/3.48 | | % 19.53/3.48 | End of split % 19.53/3.48 | % 19.53/3.48 End of proof % 19.53/3.48 % SZS output end Proof for theBenchmark % 19.53/3.48 % 19.53/3.48 2777ms %------------------------------------------------------------------------------