%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT023+2 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n005.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 9.08s 1.82s % Output : Proof 13.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT023+2 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.36 % Computer : n005.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Mon Sep 7 12:07:20 UTC 2026 % 0.14/0.36 % CPUTime : % 0.14/0.38 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. % 0.50/0.58 ________ _____ % 0.50/0.58 ___ __ \_________(_)________________________________ % 0.50/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.50/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.50/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.50/0.58 % 0.50/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.50/0.58 (2023-06-19) % 0.50/0.58 % 0.50/0.58 (c) Philipp Rümmer, 2009-2023 % 0.50/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.50/0.58 Amanda Stjerna. % 0.50/0.58 Free software under BSD-3-Clause. % 0.50/0.58 % 0.50/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.50/0.58 % 0.50/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.50/0.59 Running up to 7 provers in parallel. % 0.50/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.50/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.50/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.50/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.50/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.50/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.50/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.03/0.98 Prover 1: Preprocessing ... % 2.03/1.01 Prover 4: Preprocessing ... % 3.06/1.06 Prover 0: Preprocessing ... % 3.06/1.06 Prover 5: Preprocessing ... % 3.06/1.06 Prover 3: Preprocessing ... % 3.06/1.06 Prover 2: Preprocessing ... % 3.06/1.06 Prover 6: Preprocessing ... % 5.15/1.36 Prover 3: Constructing countermodel ... % 5.15/1.38 Prover 5: Constructing countermodel ... % 5.92/1.40 Prover 1: Constructing countermodel ... % 5.92/1.42 Prover 6: Proving ... % 5.92/1.42 Prover 2: Proving ... % 6.73/1.52 Prover 4: Constructing countermodel ... % 6.73/1.54 Prover 0: Proving ... % 9.08/1.81 Prover 3: proved (1216ms) % 9.08/1.82 % 9.08/1.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.08/1.82 % 9.08/1.82 Prover 5: stopped % 9.08/1.82 Prover 0: stopped % 9.08/1.82 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.08/1.82 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.08/1.82 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.08/1.82 Prover 6: stopped % 9.08/1.83 Prover 2: stopped % 9.08/1.83 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.08/1.83 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.08/1.89 Prover 11: Preprocessing ... % 9.87/1.91 Prover 13: Preprocessing ... % 9.87/1.92 Prover 10: Preprocessing ... % 9.87/1.93 Prover 8: Preprocessing ... % 9.87/1.94 Prover 7: Preprocessing ... % 9.87/1.97 Prover 10: Constructing countermodel ... % 9.87/2.03 Prover 13: Constructing countermodel ... % 10.97/2.05 Prover 8: Warning: ignoring some quantifiers % 10.97/2.05 Prover 8: Constructing countermodel ... % 10.97/2.08 Prover 7: Constructing countermodel ... % 10.97/2.10 Prover 11: Constructing countermodel ... % 11.76/2.17 Prover 1: Found proof (size 80) % 11.76/2.17 Prover 1: proved (1577ms) % 11.76/2.18 Prover 11: stopped % 11.76/2.18 Prover 7: stopped % 11.76/2.18 Prover 13: stopped % 11.76/2.18 Prover 8: stopped % 11.76/2.18 Prover 10: stopped % 11.76/2.18 Prover 4: stopped % 11.76/2.18 % 11.76/2.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.76/2.18 % 12.13/2.20 % SZS output start Proof for theBenchmark % 12.13/2.21 Assumptions after simplification: % 12.13/2.21 --------------------------------- % 12.13/2.21 % 12.13/2.21 (d1) % 12.13/2.26 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : ! % 12.13/2.26 [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: $i] : (v5 = v1 | v4 = 0 | ~ % 12.13/2.26 (critical_point(v0) = v5) | ~ (growth_rate(efficient_producers, v1) = v2) | % 12.13/2.26 ~ (growth_rate(first_movers, v1) = v3) | ~ (greater(v2, v3) = v4) | ~ % 12.13/2.26 $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] % 12.13/2.26 : ( ~ (v9 = 0) & subpopulations(first_movers, efficient_producers, v0, v6) = % 12.13/2.26 0 & growth_rate(efficient_producers, v6) = v7 & growth_rate(first_movers, % 12.13/2.26 v6) = v8 & greater(v7, v8) = v9 & greater(v6, v1) = 0 & $i(v8) & $i(v7) % 12.13/2.26 & $i(v6)) | ? [v6: any] : ? [v7: any] : (environment(v0) = v6 & % 12.13/2.27 in_environment(v0, v1) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 12.13/2.27 % 12.13/2.27 (l1) % 12.13/2.27 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ( ~ (stable(v0) = % 12.13/2.27 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & environment(v0) = v1) | ? % 12.13/2.27 [v1: $i] : (in_environment(v0, v1) = 0 & $i(v1) & ! [v2: $i] : ! [v3: $i] % 12.13/2.27 : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 12.13/2.27 (growth_rate(efficient_producers, v2) = v3) | ~ % 12.13/2.28 (growth_rate(first_movers, v2) = v4) | ~ (greater(v3, v4) = v5) | ~ % 12.13/2.28 $i(v2) | ? [v6: any] : ? [v7: any] : (subpopulations(first_movers, % 12.13/2.28 efficient_producers, v0, v2) = v6 & greater_or_equal(v2, v1) = v7 & % 12.13/2.28 ( ~ (v7 = 0) | ~ (v6 = 0)))))) % 12.13/2.28 % 12.13/2.28 (mp_earliest_time_growth_rate_exceeds) % 12.13/2.29 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ( ~ % 12.13/2.29 (environment(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 12.13/2.29 : ? [v4: int] : ( ~ (v4 = 0) & in_environment(v0, v1) = 0 & % 12.13/2.29 growth_rate(efficient_producers, v1) = v2 & growth_rate(first_movers, v1) % 12.13/2.29 = v3 & greater(v2, v3) = v4 & $i(v3) & $i(v2) & $i(v1) & ! [v5: $i] : ! % 12.13/2.29 [v6: $i] : ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ % 12.13/2.29 (growth_rate(efficient_producers, v5) = v6) | ~ % 12.13/2.29 (growth_rate(first_movers, v5) = v7) | ~ (greater(v6, v7) = v8) | ~ % 12.13/2.29 $i(v5) | ? [v9: any] : ? [v10: any] : (subpopulations(first_movers, % 12.13/2.29 efficient_producers, v0, v5) = v9 & greater(v5, v1) = v10 & ( ~ (v10 % 12.13/2.29 = 0) | ~ (v9 = 0))))) | ! [v1: $i] : ( ~ (in_environment(v0, v1) % 12.13/2.29 = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 12.13/2.29 int] : ( ~ (v5 = 0) & subpopulations(first_movers, efficient_producers, % 12.13/2.29 v0, v2) = 0 & greater_or_equal(v2, v1) = 0 & % 12.13/2.29 growth_rate(efficient_producers, v2) = v3 & growth_rate(first_movers, % 12.13/2.29 v2) = v4 & greater(v3, v4) = v5 & $i(v4) & $i(v3) & $i(v2)))) % 12.13/2.29 % 12.13/2.29 (prove_l5) % 12.13/2.30 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & stable(v0) = 0 & % 12.13/2.30 critical_point(v0) = v1 & environment(v0) = 0 & in_environment(v0, v1) = v2 % 12.13/2.30 & $i(v1) & $i(v0)) % 12.13/2.30 % 12.13/2.30 (function-axioms) % 12.63/2.31 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 12.63/2.31 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (subpopulations(v5, v4, % 12.63/2.31 v3, v2) = v1) | ~ (subpopulations(v5, v4, v3, v2) = v0)) & ! [v0: % 12.63/2.31 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.63/2.31 : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~ (in_environment(v3, v2) = % 12.63/2.31 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 12.63/2.31 $i] : ! [v3: $i] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~ % 12.63/2.31 (greater_or_equal(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 12.63/2.31 ! [v3: $i] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, % 12.63/2.31 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 12.63/2.31 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ % 12.63/2.31 (greater(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.63/2.31 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (stable(v2) = v1) | ~ % 12.63/2.31 (stable(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 12.63/2.31 (critical_point(v2) = v1) | ~ (critical_point(v2) = v0)) & ! [v0: % 12.63/2.31 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 12.63/2.31 ~ (environment(v2) = v1) | ~ (environment(v2) = v0)) % 12.63/2.31 % 12.63/2.31 Those formulas are unsatisfiable: % 12.63/2.31 --------------------------------- % 12.63/2.31 % 12.63/2.31 Begin of proof % 12.63/2.31 | % 12.63/2.31 | ALPHA: (mp_earliest_time_growth_rate_exceeds) implies: % 12.63/2.32 | (1) ! [v0: $i] : ( ~ (environment(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 12.63/2.32 | [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 12.63/2.32 | in_environment(v0, v1) = 0 & growth_rate(efficient_producers, v1) = % 12.63/2.32 | v2 & growth_rate(first_movers, v1) = v3 & greater(v2, v3) = v4 & % 12.63/2.32 | $i(v3) & $i(v2) & $i(v1) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 12.63/2.32 | : ! [v8: int] : (v8 = 0 | ~ (growth_rate(efficient_producers, v5) % 12.63/2.32 | = v6) | ~ (growth_rate(first_movers, v5) = v7) | ~ % 12.63/2.32 | (greater(v6, v7) = v8) | ~ $i(v5) | ? [v9: any] : ? [v10: any] % 12.63/2.32 | : (subpopulations(first_movers, efficient_producers, v0, v5) = v9 % 12.63/2.32 | & greater(v5, v1) = v10 & ( ~ (v10 = 0) | ~ (v9 = 0))))) | ! % 12.63/2.32 | [v1: $i] : ( ~ (in_environment(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] % 12.63/2.32 | : ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 12.63/2.32 | subpopulations(first_movers, efficient_producers, v0, v2) = 0 & % 12.63/2.32 | greater_or_equal(v2, v1) = 0 & growth_rate(efficient_producers, % 12.63/2.32 | v2) = v3 & growth_rate(first_movers, v2) = v4 & greater(v3, v4) % 12.63/2.32 | = v5 & $i(v4) & $i(v3) & $i(v2)))) % 12.63/2.32 | % 12.63/2.32 | ALPHA: (d1) implies: % 12.63/2.33 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 12.63/2.33 | ! [v5: $i] : (v5 = v1 | v4 = 0 | ~ (critical_point(v0) = v5) | ~ % 12.63/2.33 | (growth_rate(efficient_producers, v1) = v2) | ~ % 12.63/2.33 | (growth_rate(first_movers, v1) = v3) | ~ (greater(v2, v3) = v4) | ~ % 12.63/2.33 | $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 12.63/2.33 | [v9: int] : ( ~ (v9 = 0) & subpopulations(first_movers, % 12.63/2.33 | efficient_producers, v0, v6) = 0 & % 12.63/2.33 | growth_rate(efficient_producers, v6) = v7 & % 12.63/2.33 | growth_rate(first_movers, v6) = v8 & greater(v7, v8) = v9 & % 12.63/2.33 | greater(v6, v1) = 0 & $i(v8) & $i(v7) & $i(v6)) | ? [v6: any] : ? % 12.63/2.33 | [v7: any] : (environment(v0) = v6 & in_environment(v0, v1) = v7 & ( ~ % 12.63/2.33 | (v7 = 0) | ~ (v6 = 0)))) % 12.63/2.33 | % 12.63/2.33 | ALPHA: (l1) implies: % 12.63/2.33 | (3) ! [v0: $i] : ( ~ (stable(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 12.63/2.33 | = 0) & environment(v0) = v1) | ? [v1: $i] : (in_environment(v0, % 12.63/2.33 | v1) = 0 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 12.63/2.33 | [v5: int] : (v5 = 0 | ~ (growth_rate(efficient_producers, v2) = % 12.63/2.33 | v3) | ~ (growth_rate(first_movers, v2) = v4) | ~ (greater(v3, % 12.63/2.33 | v4) = v5) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : % 12.63/2.33 | (subpopulations(first_movers, efficient_producers, v0, v2) = v6 & % 12.63/2.33 | greater_or_equal(v2, v1) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0)))))) % 12.63/2.33 | % 12.63/2.33 | ALPHA: (function-axioms) implies: % 12.63/2.34 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.63/2.34 | (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0)) % 12.63/2.34 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.63/2.34 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, % 12.63/2.34 | v2) = v0)) % 12.63/2.34 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.63/2.34 | ! [v3: $i] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~ % 12.63/2.34 | (greater_or_equal(v3, v2) = v0)) % 12.63/2.34 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.63/2.34 | ! [v3: $i] : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~ % 12.63/2.34 | (in_environment(v3, v2) = v0)) % 12.63/2.34 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.63/2.34 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 12.63/2.34 | (subpopulations(v5, v4, v3, v2) = v1) | ~ (subpopulations(v5, v4, % 12.63/2.34 | v3, v2) = v0)) % 12.63/2.34 | % 12.63/2.34 | DELTA: instantiating (prove_l5) with fresh symbols all_7_0, all_7_1, all_7_2 % 12.63/2.34 | gives: % 12.63/2.34 | (9) ~ (all_7_0 = 0) & stable(all_7_2) = 0 & critical_point(all_7_2) = % 12.63/2.34 | all_7_1 & environment(all_7_2) = 0 & in_environment(all_7_2, all_7_1) = % 12.63/2.34 | all_7_0 & $i(all_7_1) & $i(all_7_2) % 12.63/2.34 | % 12.63/2.34 | ALPHA: (9) implies: % 12.63/2.35 | (10) ~ (all_7_0 = 0) % 12.63/2.35 | (11) $i(all_7_2) % 12.63/2.35 | (12) in_environment(all_7_2, all_7_1) = all_7_0 % 12.63/2.35 | (13) environment(all_7_2) = 0 % 12.63/2.35 | (14) critical_point(all_7_2) = all_7_1 % 12.63/2.35 | (15) stable(all_7_2) = 0 % 12.63/2.35 | % 12.63/2.35 | GROUND_INST: instantiating (1) with all_7_2, simplifying with (11), (13) % 12.63/2.35 | gives: % 12.63/2.35 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) % 12.63/2.35 | & in_environment(all_7_2, v0) = 0 & growth_rate(efficient_producers, % 12.63/2.35 | v0) = v1 & growth_rate(first_movers, v0) = v2 & greater(v1, v2) = % 12.63/2.35 | v3 & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: % 12.63/2.35 | $i] : ! [v7: int] : (v7 = 0 | ~ % 12.63/2.35 | (growth_rate(efficient_producers, v4) = v5) | ~ % 12.63/2.35 | (growth_rate(first_movers, v4) = v6) | ~ (greater(v5, v6) = v7) | % 12.63/2.35 | ~ $i(v4) | ? [v8: any] : ? [v9: any] : % 12.63/2.35 | (subpopulations(first_movers, efficient_producers, all_7_2, v4) = % 12.63/2.35 | v8 & greater(v4, v0) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0))))) | ! % 12.63/2.35 | [v0: $i] : ( ~ (in_environment(all_7_2, v0) = 0) | ~ $i(v0) | ? [v1: % 12.63/2.35 | $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 12.63/2.35 | subpopulations(first_movers, efficient_producers, all_7_2, v1) = 0 % 12.63/2.35 | & greater_or_equal(v1, v0) = 0 & growth_rate(efficient_producers, % 12.63/2.35 | v1) = v2 & growth_rate(first_movers, v1) = v3 & greater(v2, v3) % 12.63/2.35 | = v4 & $i(v3) & $i(v2) & $i(v1))) % 12.63/2.35 | % 12.63/2.36 | GROUND_INST: instantiating (3) with all_7_2, simplifying with (11), (15) % 12.63/2.36 | gives: % 12.63/2.36 | (17) ? [v0: int] : ( ~ (v0 = 0) & environment(all_7_2) = v0) | ? [v0: $i] % 12.63/2.36 | : (in_environment(all_7_2, v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: % 12.63/2.36 | $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 12.63/2.36 | (growth_rate(efficient_producers, v1) = v2) | ~ % 12.63/2.36 | (growth_rate(first_movers, v1) = v3) | ~ (greater(v2, v3) = v4) | % 12.63/2.36 | ~ $i(v1) | ? [v5: any] : ? [v6: any] : % 12.63/2.36 | (subpopulations(first_movers, efficient_producers, all_7_2, v1) = % 12.63/2.36 | v5 & greater_or_equal(v1, v0) = v6 & ( ~ (v6 = 0) | ~ (v5 = % 12.63/2.36 | 0))))) % 12.63/2.36 | % 12.63/2.36 | BETA: splitting (17) gives: % 12.63/2.36 | % 12.63/2.36 | Case 1: % 12.63/2.36 | | % 12.63/2.36 | | (18) ? [v0: int] : ( ~ (v0 = 0) & environment(all_7_2) = v0) % 12.63/2.36 | | % 12.63/2.36 | | DELTA: instantiating (18) with fresh symbol all_15_0 gives: % 12.63/2.36 | | (19) ~ (all_15_0 = 0) & environment(all_7_2) = all_15_0 % 12.63/2.36 | | % 12.63/2.36 | | ALPHA: (19) implies: % 12.63/2.36 | | (20) ~ (all_15_0 = 0) % 12.63/2.36 | | (21) environment(all_7_2) = all_15_0 % 12.63/2.36 | | % 12.63/2.36 | | GROUND_INST: instantiating (4) with 0, all_15_0, all_7_2, simplifying with % 12.63/2.36 | | (13), (21) gives: % 12.63/2.36 | | (22) all_15_0 = 0 % 12.63/2.36 | | % 12.63/2.36 | | REDUCE: (20), (22) imply: % 12.63/2.36 | | (23) $false % 12.63/2.36 | | % 12.63/2.37 | | CLOSE: (23) is inconsistent. % 12.63/2.37 | | % 12.63/2.37 | Case 2: % 12.63/2.37 | | % 12.63/2.37 | | (24) ? [v0: $i] : (in_environment(all_7_2, v0) = 0 & $i(v0) & ! [v1: % 12.63/2.37 | | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 12.63/2.37 | | (growth_rate(efficient_producers, v1) = v2) | ~ % 12.63/2.37 | | (growth_rate(first_movers, v1) = v3) | ~ (greater(v2, v3) = v4) % 12.63/2.37 | | | ~ $i(v1) | ? [v5: any] : ? [v6: any] : % 12.63/2.37 | | (subpopulations(first_movers, efficient_producers, all_7_2, v1) % 12.63/2.37 | | = v5 & greater_or_equal(v1, v0) = v6 & ( ~ (v6 = 0) | ~ (v5 = % 12.63/2.37 | | 0))))) % 12.63/2.37 | | % 12.63/2.37 | | DELTA: instantiating (24) with fresh symbol all_15_0 gives: % 12.63/2.37 | | (25) in_environment(all_7_2, all_15_0) = 0 & $i(all_15_0) & ! [v0: $i] : % 12.63/2.37 | | ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.63/2.37 | | (growth_rate(efficient_producers, v0) = v1) | ~ % 12.63/2.37 | | (growth_rate(first_movers, v0) = v2) | ~ (greater(v1, v2) = v3) | % 12.63/2.37 | | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 12.63/2.37 | | (subpopulations(first_movers, efficient_producers, all_7_2, v0) = % 12.63/2.37 | | v4 & greater_or_equal(v0, all_15_0) = v5 & ( ~ (v5 = 0) | ~ (v4 % 12.63/2.37 | | = 0)))) % 12.63/2.37 | | % 12.63/2.37 | | ALPHA: (25) implies: % 12.63/2.37 | | (26) $i(all_15_0) % 12.63/2.37 | | (27) in_environment(all_7_2, all_15_0) = 0 % 12.63/2.37 | | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | % 12.63/2.37 | | ~ (growth_rate(efficient_producers, v0) = v1) | ~ % 12.63/2.37 | | (growth_rate(first_movers, v0) = v2) | ~ (greater(v1, v2) = v3) | % 12.63/2.37 | | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 12.63/2.37 | | (subpopulations(first_movers, efficient_producers, all_7_2, v0) = % 12.63/2.37 | | v4 & greater_or_equal(v0, all_15_0) = v5 & ( ~ (v5 = 0) | ~ (v4 % 12.63/2.37 | | = 0)))) % 12.63/2.37 | | % 12.63/2.37 | | BETA: splitting (16) gives: % 12.63/2.37 | | % 12.63/2.37 | | Case 1: % 12.63/2.37 | | | % 12.63/2.38 | | | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 12.63/2.38 | | | 0) & in_environment(all_7_2, v0) = 0 & % 12.63/2.38 | | | growth_rate(efficient_producers, v0) = v1 & % 12.63/2.38 | | | growth_rate(first_movers, v0) = v2 & greater(v1, v2) = v3 & % 12.63/2.38 | | | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: % 12.63/2.38 | | | $i] : ! [v7: int] : (v7 = 0 | ~ % 12.63/2.38 | | | (growth_rate(efficient_producers, v4) = v5) | ~ % 12.63/2.38 | | | (growth_rate(first_movers, v4) = v6) | ~ (greater(v5, v6) = % 12.63/2.38 | | | v7) | ~ $i(v4) | ? [v8: any] : ? [v9: any] : % 12.63/2.38 | | | (subpopulations(first_movers, efficient_producers, all_7_2, % 12.63/2.38 | | | v4) = v8 & greater(v4, v0) = v9 & ( ~ (v9 = 0) | ~ (v8 = % 12.63/2.38 | | | 0))))) % 12.63/2.38 | | | % 12.63/2.38 | | | DELTA: instantiating (29) with fresh symbols all_24_0, all_24_1, all_24_2, % 12.63/2.38 | | | all_24_3 gives: % 12.63/2.38 | | | (30) ~ (all_24_0 = 0) & in_environment(all_7_2, all_24_3) = 0 & % 12.63/2.38 | | | growth_rate(efficient_producers, all_24_3) = all_24_2 & % 12.63/2.38 | | | growth_rate(first_movers, all_24_3) = all_24_1 & greater(all_24_2, % 12.63/2.38 | | | all_24_1) = all_24_0 & $i(all_24_1) & $i(all_24_2) & % 12.63/2.38 | | | $i(all_24_3) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 12.63/2.38 | | | int] : (v3 = 0 | ~ (growth_rate(efficient_producers, v0) = v1) % 12.63/2.38 | | | | ~ (growth_rate(first_movers, v0) = v2) | ~ (greater(v1, v2) % 12.63/2.38 | | | = v3) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 12.63/2.38 | | | (subpopulations(first_movers, efficient_producers, all_7_2, v0) % 12.63/2.38 | | | = v4 & greater(v0, all_24_3) = v5 & ( ~ (v5 = 0) | ~ (v4 = % 12.63/2.38 | | | 0)))) % 12.63/2.38 | | | % 12.63/2.38 | | | ALPHA: (30) implies: % 12.63/2.38 | | | (31) ~ (all_24_0 = 0) % 12.63/2.38 | | | (32) $i(all_24_3) % 12.63/2.38 | | | (33) greater(all_24_2, all_24_1) = all_24_0 % 12.63/2.38 | | | (34) growth_rate(first_movers, all_24_3) = all_24_1 % 12.63/2.39 | | | (35) growth_rate(efficient_producers, all_24_3) = all_24_2 % 12.63/2.39 | | | (36) in_environment(all_7_2, all_24_3) = 0 % 12.63/2.39 | | | (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | % 12.63/2.39 | | | ~ (growth_rate(efficient_producers, v0) = v1) | ~ % 12.63/2.39 | | | (growth_rate(first_movers, v0) = v2) | ~ (greater(v1, v2) = v3) % 12.63/2.39 | | | | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 12.63/2.39 | | | (subpopulations(first_movers, efficient_producers, all_7_2, v0) % 12.63/2.39 | | | = v4 & greater(v0, all_24_3) = v5 & ( ~ (v5 = 0) | ~ (v4 = % 12.63/2.39 | | | 0)))) % 12.63/2.39 | | | % 12.63/2.39 | | | GROUND_INST: instantiating (2) with all_7_2, all_24_3, all_24_2, all_24_1, % 12.63/2.39 | | | all_24_0, all_7_1, simplifying with (11), (14), (32), (33), % 12.63/2.39 | | | (34), (35) gives: % 12.63/2.39 | | | (38) all_24_0 = 0 | all_24_3 = all_7_1 | ? [v0: $i] : ? [v1: $i] : ? % 12.63/2.39 | | | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 12.63/2.39 | | | subpopulations(first_movers, efficient_producers, all_7_2, v0) = % 12.63/2.39 | | | 0 & growth_rate(efficient_producers, v0) = v1 & % 12.63/2.39 | | | growth_rate(first_movers, v0) = v2 & greater(v1, v2) = v3 & % 12.63/2.39 | | | greater(v0, all_24_3) = 0 & $i(v2) & $i(v1) & $i(v0)) | ? [v0: % 12.63/2.39 | | | any] : ? [v1: any] : (environment(all_7_2) = v0 & % 12.63/2.39 | | | in_environment(all_7_2, all_24_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = % 12.63/2.39 | | | 0))) % 12.63/2.39 | | | % 12.63/2.39 | | | BETA: splitting (38) gives: % 12.63/2.39 | | | % 12.63/2.39 | | | Case 1: % 12.63/2.39 | | | | % 12.63/2.39 | | | | (39) all_24_0 = 0 % 12.63/2.39 | | | | % 12.63/2.39 | | | | REDUCE: (31), (39) imply: % 12.63/2.39 | | | | (40) $false % 12.63/2.39 | | | | % 12.63/2.39 | | | | CLOSE: (40) is inconsistent. % 12.63/2.39 | | | | % 12.63/2.39 | | | Case 2: % 12.63/2.39 | | | | % 12.63/2.40 | | | | (41) all_24_3 = all_7_1 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.63/2.40 | | | | ? [v3: int] : ( ~ (v3 = 0) & subpopulations(first_movers, % 12.63/2.40 | | | | efficient_producers, all_7_2, v0) = 0 & % 12.63/2.40 | | | | growth_rate(efficient_producers, v0) = v1 & % 12.63/2.40 | | | | growth_rate(first_movers, v0) = v2 & greater(v1, v2) = v3 & % 13.12/2.40 | | | | greater(v0, all_24_3) = 0 & $i(v2) & $i(v1) & $i(v0)) | ? % 13.12/2.40 | | | | [v0: any] : ? [v1: any] : (environment(all_7_2) = v0 & % 13.12/2.40 | | | | in_environment(all_7_2, all_24_3) = v1 & ( ~ (v1 = 0) | ~ (v0 % 13.12/2.40 | | | | = 0))) % 13.12/2.40 | | | | % 13.12/2.40 | | | | BETA: splitting (41) gives: % 13.12/2.40 | | | | % 13.12/2.40 | | | | Case 1: % 13.12/2.40 | | | | | % 13.12/2.40 | | | | | (42) all_24_3 = all_7_1 % 13.12/2.40 | | | | | % 13.12/2.40 | | | | | REDUCE: (36), (42) imply: % 13.12/2.40 | | | | | (43) in_environment(all_7_2, all_7_1) = 0 % 13.12/2.40 | | | | | % 13.12/2.40 | | | | | GROUND_INST: instantiating (7) with all_7_0, 0, all_7_1, all_7_2, % 13.12/2.40 | | | | | simplifying with (12), (43) gives: % 13.12/2.40 | | | | | (44) all_7_0 = 0 % 13.12/2.40 | | | | | % 13.12/2.40 | | | | | REDUCE: (10), (44) imply: % 13.12/2.40 | | | | | (45) $false % 13.12/2.40 | | | | | % 13.12/2.40 | | | | | CLOSE: (45) is inconsistent. % 13.12/2.40 | | | | | % 13.12/2.40 | | | | Case 2: % 13.12/2.40 | | | | | % 13.12/2.40 | | | | | (46) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ % 13.12/2.40 | | | | | (v3 = 0) & subpopulations(first_movers, efficient_producers, % 13.12/2.40 | | | | | all_7_2, v0) = 0 & growth_rate(efficient_producers, v0) = % 13.12/2.40 | | | | | v1 & growth_rate(first_movers, v0) = v2 & greater(v1, v2) = % 13.12/2.40 | | | | | v3 & greater(v0, all_24_3) = 0 & $i(v2) & $i(v1) & $i(v0)) | % 13.12/2.40 | | | | | ? [v0: any] : ? [v1: any] : (environment(all_7_2) = v0 & % 13.12/2.40 | | | | | in_environment(all_7_2, all_24_3) = v1 & ( ~ (v1 = 0) | ~ % 13.12/2.40 | | | | | (v0 = 0))) % 13.12/2.40 | | | | | % 13.12/2.40 | | | | | BETA: splitting (46) gives: % 13.12/2.40 | | | | | % 13.12/2.40 | | | | | Case 1: % 13.12/2.40 | | | | | | % 13.12/2.41 | | | | | | (47) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ % 13.12/2.41 | | | | | | (v3 = 0) & subpopulations(first_movers, % 13.12/2.41 | | | | | | efficient_producers, all_7_2, v0) = 0 & % 13.12/2.41 | | | | | | growth_rate(efficient_producers, v0) = v1 & % 13.12/2.41 | | | | | | growth_rate(first_movers, v0) = v2 & greater(v1, v2) = v3 % 13.12/2.41 | | | | | | & greater(v0, all_24_3) = 0 & $i(v2) & $i(v1) & $i(v0)) % 13.12/2.41 | | | | | | % 13.12/2.41 | | | | | | DELTA: instantiating (47) with fresh symbols all_70_0, all_70_1, % 13.12/2.41 | | | | | | all_70_2, all_70_3 gives: % 13.12/2.41 | | | | | | (48) ~ (all_70_0 = 0) & subpopulations(first_movers, % 13.12/2.41 | | | | | | efficient_producers, all_7_2, all_70_3) = 0 & % 13.12/2.41 | | | | | | growth_rate(efficient_producers, all_70_3) = all_70_2 & % 13.12/2.41 | | | | | | growth_rate(first_movers, all_70_3) = all_70_1 & % 13.12/2.41 | | | | | | greater(all_70_2, all_70_1) = all_70_0 & greater(all_70_3, % 13.12/2.41 | | | | | | all_24_3) = 0 & $i(all_70_1) & $i(all_70_2) & $i(all_70_3) % 13.12/2.41 | | | | | | % 13.12/2.41 | | | | | | ALPHA: (48) implies: % 13.12/2.41 | | | | | | (49) ~ (all_70_0 = 0) % 13.12/2.41 | | | | | | (50) $i(all_70_3) % 13.12/2.41 | | | | | | (51) greater(all_70_3, all_24_3) = 0 % 13.12/2.41 | | | | | | (52) greater(all_70_2, all_70_1) = all_70_0 % 13.12/2.41 | | | | | | (53) growth_rate(first_movers, all_70_3) = all_70_1 % 13.12/2.41 | | | | | | (54) growth_rate(efficient_producers, all_70_3) = all_70_2 % 13.12/2.41 | | | | | | (55) subpopulations(first_movers, efficient_producers, all_7_2, % 13.12/2.41 | | | | | | all_70_3) = 0 % 13.12/2.41 | | | | | | % 13.12/2.41 | | | | | | GROUND_INST: instantiating (28) with all_70_3, all_70_2, all_70_1, % 13.12/2.41 | | | | | | all_70_0, simplifying with (50), (52), (53), (54) % 13.12/2.41 | | | | | | gives: % 13.12/2.41 | | | | | | (56) all_70_0 = 0 | ? [v0: any] : ? [v1: any] : % 13.12/2.41 | | | | | | (subpopulations(first_movers, efficient_producers, all_7_2, % 13.12/2.41 | | | | | | all_70_3) = v0 & greater_or_equal(all_70_3, all_15_0) = % 13.12/2.41 | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.12/2.41 | | | | | | % 13.12/2.42 | | | | | | GROUND_INST: instantiating (37) with all_70_3, all_70_2, all_70_1, % 13.12/2.42 | | | | | | all_70_0, simplifying with (50), (52), (53), (54) % 13.12/2.42 | | | | | | gives: % 13.12/2.42 | | | | | | (57) all_70_0 = 0 | ? [v0: any] : ? [v1: any] : % 13.12/2.42 | | | | | | (subpopulations(first_movers, efficient_producers, all_7_2, % 13.12/2.42 | | | | | | all_70_3) = v0 & greater(all_70_3, all_24_3) = v1 & ( ~ % 13.12/2.42 | | | | | | (v1 = 0) | ~ (v0 = 0))) % 13.12/2.42 | | | | | | % 13.12/2.42 | | | | | | BETA: splitting (57) gives: % 13.12/2.42 | | | | | | % 13.12/2.42 | | | | | | Case 1: % 13.12/2.42 | | | | | | | % 13.12/2.42 | | | | | | | (58) all_70_0 = 0 % 13.12/2.42 | | | | | | | % 13.12/2.42 | | | | | | | REDUCE: (49), (58) imply: % 13.12/2.42 | | | | | | | (59) $false % 13.12/2.42 | | | | | | | % 13.12/2.42 | | | | | | | CLOSE: (59) is inconsistent. % 13.12/2.42 | | | | | | | % 13.12/2.42 | | | | | | Case 2: % 13.12/2.42 | | | | | | | % 13.12/2.42 | | | | | | | (60) ? [v0: any] : ? [v1: any] : % 13.12/2.42 | | | | | | | (subpopulations(first_movers, efficient_producers, % 13.12/2.42 | | | | | | | all_7_2, all_70_3) = v0 & greater(all_70_3, all_24_3) % 13.12/2.42 | | | | | | | = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.12/2.42 | | | | | | | % 13.12/2.42 | | | | | | | DELTA: instantiating (60) with fresh symbols all_79_0, all_79_1 % 13.12/2.42 | | | | | | | gives: % 13.12/2.42 | | | | | | | (61) subpopulations(first_movers, efficient_producers, all_7_2, % 13.12/2.42 | | | | | | | all_70_3) = all_79_1 & greater(all_70_3, all_24_3) = % 13.12/2.42 | | | | | | | all_79_0 & ( ~ (all_79_0 = 0) | ~ (all_79_1 = 0)) % 13.12/2.42 | | | | | | | % 13.12/2.42 | | | | | | | ALPHA: (61) implies: % 13.12/2.42 | | | | | | | (62) greater(all_70_3, all_24_3) = all_79_0 % 13.12/2.42 | | | | | | | (63) subpopulations(first_movers, efficient_producers, all_7_2, % 13.12/2.42 | | | | | | | all_70_3) = all_79_1 % 13.12/2.42 | | | | | | | (64) ~ (all_79_0 = 0) | ~ (all_79_1 = 0) % 13.12/2.42 | | | | | | | % 13.12/2.42 | | | | | | | BETA: splitting (56) gives: % 13.12/2.42 | | | | | | | % 13.12/2.42 | | | | | | | Case 1: % 13.12/2.42 | | | | | | | | % 13.12/2.42 | | | | | | | | (65) all_70_0 = 0 % 13.12/2.42 | | | | | | | | % 13.12/2.42 | | | | | | | | REDUCE: (49), (65) imply: % 13.12/2.42 | | | | | | | | (66) $false % 13.12/2.42 | | | | | | | | % 13.12/2.42 | | | | | | | | CLOSE: (66) is inconsistent. % 13.12/2.42 | | | | | | | | % 13.12/2.42 | | | | | | | Case 2: % 13.12/2.42 | | | | | | | | % 13.12/2.43 | | | | | | | | (67) ? [v0: any] : ? [v1: any] : % 13.12/2.43 | | | | | | | | (subpopulations(first_movers, efficient_producers, % 13.12/2.43 | | | | | | | | all_7_2, all_70_3) = v0 & greater_or_equal(all_70_3, % 13.12/2.43 | | | | | | | | all_15_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.12/2.43 | | | | | | | | % 13.12/2.43 | | | | | | | | DELTA: instantiating (67) with fresh symbols all_85_0, all_85_1 % 13.12/2.43 | | | | | | | | gives: % 13.12/2.43 | | | | | | | | (68) subpopulations(first_movers, efficient_producers, % 13.12/2.43 | | | | | | | | all_7_2, all_70_3) = all_85_1 & % 13.12/2.43 | | | | | | | | greater_or_equal(all_70_3, all_15_0) = all_85_0 & ( ~ % 13.12/2.43 | | | | | | | | (all_85_0 = 0) | ~ (all_85_1 = 0)) % 13.12/2.43 | | | | | | | | % 13.12/2.43 | | | | | | | | ALPHA: (68) implies: % 13.12/2.43 | | | | | | | | (69) subpopulations(first_movers, efficient_producers, % 13.12/2.43 | | | | | | | | all_7_2, all_70_3) = all_85_1 % 13.12/2.43 | | | | | | | | % 13.12/2.43 | | | | | | | | GROUND_INST: instantiating (5) with 0, all_79_0, all_24_3, % 13.12/2.43 | | | | | | | | all_70_3, simplifying with (51), (62) gives: % 13.12/2.43 | | | | | | | | (70) all_79_0 = 0 % 13.12/2.43 | | | | | | | | % 13.12/2.43 | | | | | | | | GROUND_INST: instantiating (8) with 0, all_85_1, all_70_3, % 13.12/2.43 | | | | | | | | all_7_2, efficient_producers, first_movers, % 13.12/2.43 | | | | | | | | simplifying with (55), (69) gives: % 13.12/2.43 | | | | | | | | (71) all_85_1 = 0 % 13.12/2.43 | | | | | | | | % 13.12/2.43 | | | | | | | | GROUND_INST: instantiating (8) with all_79_1, all_85_1, % 13.12/2.43 | | | | | | | | all_70_3, all_7_2, efficient_producers, % 13.12/2.43 | | | | | | | | first_movers, simplifying with (63), (69) gives: % 13.12/2.43 | | | | | | | | (72) all_85_1 = all_79_1 % 13.12/2.43 | | | | | | | | % 13.12/2.43 | | | | | | | | COMBINE_EQS: (71), (72) imply: % 13.12/2.43 | | | | | | | | (73) all_79_1 = 0 % 13.12/2.43 | | | | | | | | % 13.12/2.43 | | | | | | | | BETA: splitting (64) gives: % 13.12/2.43 | | | | | | | | % 13.12/2.43 | | | | | | | | Case 1: % 13.12/2.43 | | | | | | | | | % 13.12/2.43 | | | | | | | | | (74) ~ (all_79_0 = 0) % 13.12/2.43 | | | | | | | | | % 13.12/2.43 | | | | | | | | | REDUCE: (70), (74) imply: % 13.12/2.43 | | | | | | | | | (75) $false % 13.12/2.43 | | | | | | | | | % 13.12/2.43 | | | | | | | | | CLOSE: (75) is inconsistent. % 13.12/2.43 | | | | | | | | | % 13.12/2.43 | | | | | | | | Case 2: % 13.12/2.43 | | | | | | | | | % 13.12/2.43 | | | | | | | | | (76) ~ (all_79_1 = 0) % 13.12/2.43 | | | | | | | | | % 13.12/2.43 | | | | | | | | | REDUCE: (73), (76) imply: % 13.12/2.43 | | | | | | | | | (77) $false % 13.12/2.43 | | | | | | | | | % 13.12/2.43 | | | | | | | | | CLOSE: (77) is inconsistent. % 13.12/2.43 | | | | | | | | | % 13.12/2.44 | | | | | | | | End of split % 13.12/2.44 | | | | | | | | % 13.12/2.44 | | | | | | | End of split % 13.12/2.44 | | | | | | | % 13.12/2.44 | | | | | | End of split % 13.12/2.44 | | | | | | % 13.12/2.44 | | | | | Case 2: % 13.12/2.44 | | | | | | % 13.12/2.44 | | | | | | (78) ? [v0: any] : ? [v1: any] : (environment(all_7_2) = v0 & % 13.12/2.44 | | | | | | in_environment(all_7_2, all_24_3) = v1 & ( ~ (v1 = 0) | ~ % 13.12/2.44 | | | | | | (v0 = 0))) % 13.12/2.44 | | | | | | % 13.12/2.44 | | | | | | DELTA: instantiating (78) with fresh symbols all_70_0, all_70_1 % 13.12/2.44 | | | | | | gives: % 13.12/2.44 | | | | | | (79) environment(all_7_2) = all_70_1 & in_environment(all_7_2, % 13.12/2.44 | | | | | | all_24_3) = all_70_0 & ( ~ (all_70_0 = 0) | ~ (all_70_1 = % 13.12/2.44 | | | | | | 0)) % 13.12/2.44 | | | | | | % 13.12/2.44 | | | | | | ALPHA: (79) implies: % 13.12/2.44 | | | | | | (80) in_environment(all_7_2, all_24_3) = all_70_0 % 13.12/2.44 | | | | | | (81) environment(all_7_2) = all_70_1 % 13.12/2.44 | | | | | | (82) ~ (all_70_0 = 0) | ~ (all_70_1 = 0) % 13.12/2.44 | | | | | | % 13.12/2.44 | | | | | | GROUND_INST: instantiating (7) with 0, all_70_0, all_24_3, all_7_2, % 13.12/2.44 | | | | | | simplifying with (36), (80) gives: % 13.12/2.44 | | | | | | (83) all_70_0 = 0 % 13.12/2.44 | | | | | | % 13.12/2.44 | | | | | | GROUND_INST: instantiating (4) with 0, all_70_1, all_7_2, % 13.12/2.44 | | | | | | simplifying with (13), (81) gives: % 13.12/2.44 | | | | | | (84) all_70_1 = 0 % 13.12/2.44 | | | | | | % 13.12/2.44 | | | | | | BETA: splitting (82) gives: % 13.12/2.44 | | | | | | % 13.12/2.44 | | | | | | Case 1: % 13.12/2.44 | | | | | | | % 13.12/2.44 | | | | | | | (85) ~ (all_70_0 = 0) % 13.12/2.44 | | | | | | | % 13.12/2.44 | | | | | | | REDUCE: (83), (85) imply: % 13.12/2.44 | | | | | | | (86) $false % 13.12/2.44 | | | | | | | % 13.12/2.44 | | | | | | | CLOSE: (86) is inconsistent. % 13.12/2.44 | | | | | | | % 13.12/2.44 | | | | | | Case 2: % 13.12/2.44 | | | | | | | % 13.12/2.44 | | | | | | | (87) ~ (all_70_1 = 0) % 13.12/2.44 | | | | | | | % 13.12/2.44 | | | | | | | REDUCE: (84), (87) imply: % 13.12/2.44 | | | | | | | (88) $false % 13.12/2.44 | | | | | | | % 13.12/2.44 | | | | | | | CLOSE: (88) is inconsistent. % 13.12/2.44 | | | | | | | % 13.12/2.44 | | | | | | End of split % 13.12/2.44 | | | | | | % 13.12/2.44 | | | | | End of split % 13.12/2.44 | | | | | % 13.12/2.44 | | | | End of split % 13.12/2.44 | | | | % 13.12/2.44 | | | End of split % 13.12/2.44 | | | % 13.12/2.44 | | Case 2: % 13.12/2.44 | | | % 13.12/2.45 | | | (89) ! [v0: $i] : ( ~ (in_environment(all_7_2, v0) = 0) | ~ $i(v0) | % 13.12/2.45 | | | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 13.12/2.45 | | | = 0) & subpopulations(first_movers, efficient_producers, % 13.12/2.45 | | | all_7_2, v1) = 0 & greater_or_equal(v1, v0) = 0 & % 13.12/2.45 | | | growth_rate(efficient_producers, v1) = v2 & % 13.12/2.45 | | | growth_rate(first_movers, v1) = v3 & greater(v2, v3) = v4 & % 13.12/2.45 | | | $i(v3) & $i(v2) & $i(v1))) % 13.12/2.45 | | | % 13.12/2.45 | | | GROUND_INST: instantiating (89) with all_15_0, simplifying with (26), (27) % 13.12/2.45 | | | gives: % 13.12/2.45 | | | (90) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 13.12/2.45 | | | 0) & subpopulations(first_movers, efficient_producers, % 13.12/2.45 | | | all_7_2, v0) = 0 & greater_or_equal(v0, all_15_0) = 0 & % 13.12/2.45 | | | growth_rate(efficient_producers, v0) = v1 & % 13.12/2.45 | | | growth_rate(first_movers, v0) = v2 & greater(v1, v2) = v3 & % 13.12/2.45 | | | $i(v2) & $i(v1) & $i(v0)) % 13.12/2.45 | | | % 13.12/2.45 | | | DELTA: instantiating (90) with fresh symbols all_25_0, all_25_1, all_25_2, % 13.12/2.45 | | | all_25_3 gives: % 13.12/2.45 | | | (91) ~ (all_25_0 = 0) & subpopulations(first_movers, % 13.12/2.45 | | | efficient_producers, all_7_2, all_25_3) = 0 & % 13.12/2.45 | | | greater_or_equal(all_25_3, all_15_0) = 0 & % 13.12/2.45 | | | growth_rate(efficient_producers, all_25_3) = all_25_2 & % 13.12/2.45 | | | growth_rate(first_movers, all_25_3) = all_25_1 & greater(all_25_2, % 13.12/2.45 | | | all_25_1) = all_25_0 & $i(all_25_1) & $i(all_25_2) & % 13.12/2.45 | | | $i(all_25_3) % 13.12/2.45 | | | % 13.12/2.45 | | | ALPHA: (91) implies: % 13.12/2.45 | | | (92) ~ (all_25_0 = 0) % 13.12/2.45 | | | (93) $i(all_25_3) % 13.12/2.45 | | | (94) greater(all_25_2, all_25_1) = all_25_0 % 13.12/2.45 | | | (95) growth_rate(first_movers, all_25_3) = all_25_1 % 13.12/2.45 | | | (96) growth_rate(efficient_producers, all_25_3) = all_25_2 % 13.12/2.45 | | | (97) greater_or_equal(all_25_3, all_15_0) = 0 % 13.12/2.45 | | | (98) subpopulations(first_movers, efficient_producers, all_7_2, % 13.12/2.45 | | | all_25_3) = 0 % 13.12/2.45 | | | % 13.12/2.46 | | | GROUND_INST: instantiating (28) with all_25_3, all_25_2, all_25_1, % 13.12/2.46 | | | all_25_0, simplifying with (93), (94), (95), (96) gives: % 13.12/2.46 | | | (99) all_25_0 = 0 | ? [v0: any] : ? [v1: any] : % 13.12/2.46 | | | (subpopulations(first_movers, efficient_producers, all_7_2, % 13.12/2.46 | | | all_25_3) = v0 & greater_or_equal(all_25_3, all_15_0) = v1 & ( % 13.12/2.46 | | | ~ (v1 = 0) | ~ (v0 = 0))) % 13.12/2.46 | | | % 13.12/2.46 | | | BETA: splitting (99) gives: % 13.12/2.46 | | | % 13.12/2.46 | | | Case 1: % 13.12/2.46 | | | | % 13.12/2.46 | | | | (100) all_25_0 = 0 % 13.12/2.46 | | | | % 13.12/2.46 | | | | REDUCE: (92), (100) imply: % 13.12/2.46 | | | | (101) $false % 13.12/2.46 | | | | % 13.12/2.46 | | | | CLOSE: (101) is inconsistent. % 13.12/2.46 | | | | % 13.12/2.46 | | | Case 2: % 13.12/2.46 | | | | % 13.12/2.46 | | | | (102) ? [v0: any] : ? [v1: any] : (subpopulations(first_movers, % 13.12/2.46 | | | | efficient_producers, all_7_2, all_25_3) = v0 & % 13.12/2.46 | | | | greater_or_equal(all_25_3, all_15_0) = v1 & ( ~ (v1 = 0) | ~ % 13.12/2.46 | | | | (v0 = 0))) % 13.12/2.46 | | | | % 13.12/2.46 | | | | DELTA: instantiating (102) with fresh symbols all_34_0, all_34_1 gives: % 13.12/2.46 | | | | (103) subpopulations(first_movers, efficient_producers, all_7_2, % 13.12/2.46 | | | | all_25_3) = all_34_1 & greater_or_equal(all_25_3, all_15_0) = % 13.12/2.46 | | | | all_34_0 & ( ~ (all_34_0 = 0) | ~ (all_34_1 = 0)) % 13.12/2.46 | | | | % 13.12/2.46 | | | | ALPHA: (103) implies: % 13.12/2.46 | | | | (104) greater_or_equal(all_25_3, all_15_0) = all_34_0 % 13.12/2.46 | | | | (105) subpopulations(first_movers, efficient_producers, all_7_2, % 13.12/2.46 | | | | all_25_3) = all_34_1 % 13.12/2.46 | | | | (106) ~ (all_34_0 = 0) | ~ (all_34_1 = 0) % 13.12/2.46 | | | | % 13.12/2.46 | | | | GROUND_INST: instantiating (6) with 0, all_34_0, all_15_0, all_25_3, % 13.12/2.46 | | | | simplifying with (97), (104) gives: % 13.12/2.46 | | | | (107) all_34_0 = 0 % 13.12/2.46 | | | | % 13.12/2.46 | | | | GROUND_INST: instantiating (8) with 0, all_34_1, all_25_3, all_7_2, % 13.12/2.46 | | | | efficient_producers, first_movers, simplifying with (98), % 13.12/2.46 | | | | (105) gives: % 13.12/2.46 | | | | (108) all_34_1 = 0 % 13.12/2.46 | | | | % 13.12/2.46 | | | | BETA: splitting (106) gives: % 13.12/2.46 | | | | % 13.12/2.46 | | | | Case 1: % 13.12/2.46 | | | | | % 13.12/2.46 | | | | | (109) ~ (all_34_0 = 0) % 13.12/2.46 | | | | | % 13.12/2.46 | | | | | REDUCE: (107), (109) imply: % 13.12/2.46 | | | | | (110) $false % 13.12/2.46 | | | | | % 13.12/2.46 | | | | | CLOSE: (110) is inconsistent. % 13.12/2.46 | | | | | % 13.12/2.46 | | | | Case 2: % 13.12/2.46 | | | | | % 13.12/2.46 | | | | | (111) ~ (all_34_1 = 0) % 13.12/2.46 | | | | | % 13.12/2.46 | | | | | REDUCE: (108), (111) imply: % 13.12/2.46 | | | | | (112) $false % 13.12/2.46 | | | | | % 13.12/2.46 | | | | | CLOSE: (112) is inconsistent. % 13.12/2.47 | | | | | % 13.12/2.47 | | | | End of split % 13.12/2.47 | | | | % 13.12/2.47 | | | End of split % 13.12/2.47 | | | % 13.12/2.47 | | End of split % 13.12/2.47 | | % 13.12/2.47 | End of split % 13.12/2.47 | % 13.12/2.47 End of proof % 13.12/2.47 % SZS output end Proof for theBenchmark % 13.12/2.47 % 13.12/2.47 1886ms %------------------------------------------------------------------------------