%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT023+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 : n028.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 6.94s 1.70s % Output : Proof 9.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT023+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.36 % Computer : n028.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Mon Sep 7 12:08:32 UTC 2026 % 0.09/0.36 % CPUTime : % 0.09/0.38 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. % 0.67/0.72 ________ _____ % 0.67/0.72 ___ __ \_________(_)________________________________ % 0.67/0.72 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.67/0.72 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.67/0.72 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.67/0.72 % 0.67/0.72 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.67/0.72 (2023-06-19) % 0.67/0.72 % 0.67/0.72 (c) Philipp Rümmer, 2009-2023 % 0.67/0.72 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.67/0.72 Amanda Stjerna. % 0.67/0.72 Free software under BSD-3-Clause. % 0.67/0.72 % 0.67/0.72 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.67/0.72 % 0.67/0.73 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.67/0.75 Running up to 7 provers in parallel. % 0.67/0.76 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.67/0.76 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.67/0.76 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.67/0.76 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.67/0.76 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.67/0.76 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.67/0.76 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.80/1.11 Prover 1: Preprocessing ... % 1.80/1.12 Prover 4: Preprocessing ... % 2.55/1.19 Prover 2: Preprocessing ... % 2.55/1.19 Prover 0: Preprocessing ... % 2.55/1.19 Prover 5: Preprocessing ... % 2.55/1.19 Prover 6: Preprocessing ... % 2.55/1.19 Prover 3: Preprocessing ... % 4.60/1.42 Prover 3: Constructing countermodel ... % 4.60/1.42 Prover 1: Constructing countermodel ... % 4.60/1.44 Prover 5: Constructing countermodel ... % 4.60/1.45 Prover 6: Proving ... % 4.60/1.46 Prover 2: Proving ... % 5.41/1.51 Prover 4: Constructing countermodel ... % 5.41/1.59 Prover 0: Proving ... % 6.15/1.70 Prover 3: proved (937ms) % 6.94/1.70 % 6.94/1.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.94/1.70 % 6.94/1.70 Prover 5: stopped % 6.94/1.71 Prover 6: stopped % 6.94/1.71 Prover 2: stopped % 6.94/1.71 Prover 0: stopped % 6.94/1.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.94/1.72 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.94/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.94/1.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.94/1.72 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.94/1.74 Prover 7: Preprocessing ... % 6.94/1.74 Prover 8: Preprocessing ... % 6.94/1.76 Prover 11: Preprocessing ... % 6.94/1.77 Prover 10: Preprocessing ... % 6.94/1.78 Prover 13: Preprocessing ... % 7.73/1.80 Prover 8: Warning: ignoring some quantifiers % 7.73/1.80 Prover 7: Constructing countermodel ... % 7.73/1.81 Prover 8: Constructing countermodel ... % 7.73/1.85 Prover 10: Constructing countermodel ... % 7.73/1.89 Prover 1: Found proof (size 50) % 7.73/1.89 Prover 1: proved (1131ms) % 7.73/1.89 Prover 10: stopped % 7.73/1.89 Prover 8: stopped % 7.73/1.89 Prover 4: stopped % 7.73/1.89 Prover 7: stopped % 8.51/1.91 Prover 13: Constructing countermodel ... % 8.51/1.91 Prover 13: stopped % 8.51/1.98 Prover 11: Constructing countermodel ... % 8.51/1.99 Prover 11: stopped % 8.51/1.99 % 8.51/1.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.51/1.99 % 8.51/2.00 % SZS output start Proof for theBenchmark % 8.51/2.00 Assumptions after simplification: % 8.51/2.00 --------------------------------- % 8.51/2.00 % 8.51/2.00 (d1) % 9.17/2.03 $i(first_movers) & $i(efficient_producers) & ! [v0: $i] : ! [v1: $i] : ! % 9.17/2.03 [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: $i] : (v5 = v1 | v4 = 0 | ~ % 9.17/2.03 (critical_point(v0) = v5) | ~ (growth_rate(first_movers, v1) = v3) | ~ % 9.17/2.03 (growth_rate(efficient_producers, v1) = v2) | ~ (greater(v2, v3) = v4) | ~ % 9.17/2.03 $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] % 9.17/2.03 : ( ~ (v9 = 0) & subpopulations(first_movers, efficient_producers, v0, v6) = % 9.17/2.03 0 & growth_rate(first_movers, v6) = v8 & growth_rate(efficient_producers, % 9.17/2.03 v6) = v7 & greater(v7, v8) = v9 & greater(v6, v1) = 0 & $i(v8) & $i(v7) % 9.17/2.03 & $i(v6)) | ? [v6: any] : ? [v7: any] : (environment(v0) = v6 & % 9.17/2.03 in_environment(v0, v1) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 9.17/2.03 % 9.17/2.04 (l12) % 9.17/2.04 $i(first_movers) & $i(efficient_producers) & ! [v0: $i] : ( ~ (stable(v0) = % 9.17/2.04 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : % 9.17/2.04 ( ~ (v4 = 0) & in_environment(v0, v1) = 0 & growth_rate(first_movers, v1) = % 9.17/2.04 v3 & growth_rate(efficient_producers, v1) = v2 & greater(v2, v3) = v4 & % 9.17/2.04 $i(v3) & $i(v2) & $i(v1) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 9.17/2.04 [v8: int] : (v8 = 0 | ~ (growth_rate(first_movers, v5) = v7) | ~ % 9.17/2.04 (growth_rate(efficient_producers, v5) = v6) | ~ (greater(v6, v7) = v8) % 9.17/2.04 | ~ $i(v5) | ? [v9: any] : ? [v10: any] : % 9.17/2.04 (subpopulations(first_movers, efficient_producers, v0, v5) = v9 & % 9.17/2.04 greater(v5, v1) = v10 & ( ~ (v10 = 0) | ~ (v9 = 0))))) | ? [v1: int] % 9.17/2.04 : ( ~ (v1 = 0) & environment(v0) = v1)) % 9.17/2.04 % 9.17/2.04 (prove_l5) % 9.17/2.04 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & stable(v0) = 0 & % 9.17/2.04 critical_point(v0) = v1 & environment(v0) = 0 & in_environment(v0, v1) = v2 % 9.17/2.04 & $i(v1) & $i(v0)) % 9.17/2.04 % 9.17/2.05 (function-axioms) % 9.17/2.05 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 9.17/2.05 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (subpopulations(v5, v4, % 9.17/2.05 v3, v2) = v1) | ~ (subpopulations(v5, v4, v3, v2) = v0)) & ! [v0: % 9.17/2.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.17/2.05 : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~ (in_environment(v3, v2) = % 9.17/2.05 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 9.17/2.05 ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) & ! [v0: % 9.17/2.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.17/2.05 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: % 9.17/2.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.17/2.05 ~ (stable(v2) = v1) | ~ (stable(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 9.17/2.05 [v2: $i] : (v1 = v0 | ~ (critical_point(v2) = v1) | ~ (critical_point(v2) = % 9.17/2.05 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.17/2.05 $i] : (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0)) % 9.17/2.05 % 9.17/2.05 Those formulas are unsatisfiable: % 9.17/2.05 --------------------------------- % 9.17/2.05 % 9.17/2.05 Begin of proof % 9.17/2.05 | % 9.17/2.05 | ALPHA: (d1) implies: % 9.17/2.06 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 9.17/2.06 | ! [v5: $i] : (v5 = v1 | v4 = 0 | ~ (critical_point(v0) = v5) | ~ % 9.17/2.06 | (growth_rate(first_movers, v1) = v3) | ~ % 9.17/2.06 | (growth_rate(efficient_producers, v1) = v2) | ~ (greater(v2, v3) = % 9.17/2.06 | v4) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: % 9.17/2.06 | $i] : ? [v9: int] : ( ~ (v9 = 0) & subpopulations(first_movers, % 9.17/2.06 | efficient_producers, v0, v6) = 0 & growth_rate(first_movers, v6) % 9.17/2.06 | = v8 & growth_rate(efficient_producers, v6) = v7 & greater(v7, v8) % 9.17/2.06 | = v9 & greater(v6, v1) = 0 & $i(v8) & $i(v7) & $i(v6)) | ? [v6: % 9.17/2.06 | any] : ? [v7: any] : (environment(v0) = v6 & in_environment(v0, % 9.17/2.06 | v1) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 9.17/2.06 | % 9.17/2.06 | ALPHA: (l12) implies: % 9.17/2.07 | (2) ! [v0: $i] : ( ~ (stable(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 9.17/2.07 | $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 9.17/2.07 | in_environment(v0, v1) = 0 & growth_rate(first_movers, v1) = v3 & % 9.17/2.07 | growth_rate(efficient_producers, v1) = v2 & greater(v2, v3) = v4 & % 9.17/2.07 | $i(v3) & $i(v2) & $i(v1) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 9.17/2.07 | : ! [v8: int] : (v8 = 0 | ~ (growth_rate(first_movers, v5) = v7) % 9.17/2.07 | | ~ (growth_rate(efficient_producers, v5) = v6) | ~ % 9.17/2.07 | (greater(v6, v7) = v8) | ~ $i(v5) | ? [v9: any] : ? [v10: any] % 9.17/2.07 | : (subpopulations(first_movers, efficient_producers, v0, v5) = v9 % 9.17/2.07 | & greater(v5, v1) = v10 & ( ~ (v10 = 0) | ~ (v9 = 0))))) | ? % 9.17/2.07 | [v1: int] : ( ~ (v1 = 0) & environment(v0) = v1)) % 9.17/2.07 | % 9.17/2.07 | ALPHA: (function-axioms) implies: % 9.17/2.07 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.17/2.07 | (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0)) % 9.17/2.07 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.17/2.07 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, % 9.17/2.07 | v2) = v0)) % 9.17/2.07 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.17/2.07 | ! [v3: $i] : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~ % 9.17/2.07 | (in_environment(v3, v2) = v0)) % 9.17/2.07 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.17/2.07 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 9.17/2.07 | (subpopulations(v5, v4, v3, v2) = v1) | ~ (subpopulations(v5, v4, % 9.17/2.07 | v3, v2) = v0)) % 9.17/2.07 | % 9.17/2.07 | DELTA: instantiating (prove_l5) with fresh symbols all_6_0, all_6_1, all_6_2 % 9.17/2.07 | gives: % 9.17/2.08 | (7) ~ (all_6_0 = 0) & stable(all_6_2) = 0 & critical_point(all_6_2) = % 9.17/2.08 | all_6_1 & environment(all_6_2) = 0 & in_environment(all_6_2, all_6_1) = % 9.17/2.08 | all_6_0 & $i(all_6_1) & $i(all_6_2) % 9.17/2.08 | % 9.17/2.08 | ALPHA: (7) implies: % 9.17/2.08 | (8) ~ (all_6_0 = 0) % 9.17/2.08 | (9) $i(all_6_2) % 9.17/2.08 | (10) in_environment(all_6_2, all_6_1) = all_6_0 % 9.17/2.08 | (11) environment(all_6_2) = 0 % 9.17/2.08 | (12) critical_point(all_6_2) = all_6_1 % 9.17/2.08 | (13) stable(all_6_2) = 0 % 9.17/2.08 | % 9.17/2.08 | GROUND_INST: instantiating (2) with all_6_2, simplifying with (9), (13) gives: % 9.17/2.08 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) % 9.17/2.08 | & in_environment(all_6_2, v0) = 0 & growth_rate(first_movers, v0) = % 9.17/2.08 | v2 & growth_rate(efficient_producers, v0) = v1 & greater(v1, v2) = % 9.17/2.08 | v3 & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: % 9.17/2.08 | $i] : ! [v7: int] : (v7 = 0 | ~ (growth_rate(first_movers, v4) = % 9.17/2.08 | v6) | ~ (growth_rate(efficient_producers, v4) = v5) | ~ % 9.17/2.08 | (greater(v5, v6) = v7) | ~ $i(v4) | ? [v8: any] : ? [v9: any] : % 9.17/2.08 | (subpopulations(first_movers, efficient_producers, all_6_2, v4) = % 9.17/2.08 | v8 & greater(v4, v0) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0))))) | ? % 9.17/2.08 | [v0: int] : ( ~ (v0 = 0) & environment(all_6_2) = v0) % 9.17/2.08 | % 9.17/2.08 | BETA: splitting (14) gives: % 9.17/2.08 | % 9.17/2.08 | Case 1: % 9.17/2.08 | | % 9.17/2.09 | | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 9.17/2.09 | | 0) & in_environment(all_6_2, v0) = 0 & growth_rate(first_movers, % 9.17/2.09 | | v0) = v2 & growth_rate(efficient_producers, v0) = v1 & % 9.17/2.09 | | greater(v1, v2) = v3 & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! % 9.17/2.09 | | [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ % 9.17/2.09 | | (growth_rate(first_movers, v4) = v6) | ~ % 9.17/2.09 | | (growth_rate(efficient_producers, v4) = v5) | ~ (greater(v5, % 9.17/2.09 | | v6) = v7) | ~ $i(v4) | ? [v8: any] : ? [v9: any] : % 9.17/2.09 | | (subpopulations(first_movers, efficient_producers, all_6_2, v4) % 9.17/2.09 | | = v8 & greater(v4, v0) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0))))) % 9.17/2.09 | | % 9.17/2.09 | | DELTA: instantiating (15) with fresh symbols all_14_0, all_14_1, all_14_2, % 9.17/2.09 | | all_14_3 gives: % 9.17/2.09 | | (16) ~ (all_14_0 = 0) & in_environment(all_6_2, all_14_3) = 0 & % 9.17/2.09 | | growth_rate(first_movers, all_14_3) = all_14_1 & % 9.17/2.09 | | growth_rate(efficient_producers, all_14_3) = all_14_2 & % 9.17/2.09 | | greater(all_14_2, all_14_1) = all_14_0 & $i(all_14_1) & $i(all_14_2) % 9.17/2.09 | | & $i(all_14_3) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 9.17/2.09 | | int] : (v3 = 0 | ~ (growth_rate(first_movers, v0) = v2) | ~ % 9.17/2.09 | | (growth_rate(efficient_producers, v0) = v1) | ~ (greater(v1, v2) % 9.17/2.09 | | = v3) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 9.17/2.09 | | (subpopulations(first_movers, efficient_producers, all_6_2, v0) = % 9.17/2.09 | | v4 & greater(v0, all_14_3) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0)))) % 9.17/2.09 | | % 9.17/2.09 | | ALPHA: (16) implies: % 9.17/2.09 | | (17) ~ (all_14_0 = 0) % 9.17/2.09 | | (18) $i(all_14_3) % 9.17/2.09 | | (19) greater(all_14_2, all_14_1) = all_14_0 % 9.17/2.09 | | (20) growth_rate(efficient_producers, all_14_3) = all_14_2 % 9.17/2.09 | | (21) growth_rate(first_movers, all_14_3) = all_14_1 % 9.17/2.09 | | (22) in_environment(all_6_2, all_14_3) = 0 % 9.17/2.09 | | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | % 9.17/2.09 | | ~ (growth_rate(first_movers, v0) = v2) | ~ % 9.17/2.09 | | (growth_rate(efficient_producers, v0) = v1) | ~ (greater(v1, v2) % 9.17/2.09 | | = v3) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 9.17/2.09 | | (subpopulations(first_movers, efficient_producers, all_6_2, v0) = % 9.17/2.09 | | v4 & greater(v0, all_14_3) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0)))) % 9.17/2.09 | | % 9.17/2.10 | | GROUND_INST: instantiating (1) with all_6_2, all_14_3, all_14_2, all_14_1, % 9.17/2.10 | | all_14_0, all_6_1, simplifying with (9), (12), (18), (19), % 9.17/2.10 | | (20), (21) gives: % 9.17/2.10 | | (24) all_14_0 = 0 | all_14_3 = all_6_1 | ? [v0: $i] : ? [v1: $i] : ? % 9.17/2.10 | | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 9.17/2.10 | | subpopulations(first_movers, efficient_producers, all_6_2, v0) = 0 % 9.17/2.10 | | & growth_rate(first_movers, v0) = v2 & % 9.17/2.10 | | growth_rate(efficient_producers, v0) = v1 & greater(v1, v2) = v3 & % 9.17/2.10 | | greater(v0, all_14_3) = 0 & $i(v2) & $i(v1) & $i(v0)) | ? [v0: % 9.17/2.10 | | any] : ? [v1: any] : (environment(all_6_2) = v0 & % 9.17/2.10 | | in_environment(all_6_2, all_14_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = % 9.17/2.10 | | 0))) % 9.17/2.10 | | % 9.17/2.10 | | BETA: splitting (24) gives: % 9.17/2.10 | | % 9.17/2.10 | | Case 1: % 9.17/2.10 | | | % 9.17/2.10 | | | (25) all_14_0 = 0 % 9.17/2.10 | | | % 9.17/2.10 | | | REDUCE: (17), (25) imply: % 9.17/2.10 | | | (26) $false % 9.17/2.10 | | | % 9.17/2.10 | | | CLOSE: (26) is inconsistent. % 9.17/2.10 | | | % 9.17/2.10 | | Case 2: % 9.17/2.10 | | | % 9.17/2.10 | | | (27) all_14_3 = all_6_1 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 9.17/2.10 | | | [v3: int] : ( ~ (v3 = 0) & subpopulations(first_movers, % 9.17/2.10 | | | efficient_producers, all_6_2, v0) = 0 & % 9.17/2.10 | | | growth_rate(first_movers, v0) = v2 & % 9.17/2.10 | | | growth_rate(efficient_producers, v0) = v1 & greater(v1, v2) = v3 % 9.17/2.10 | | | & greater(v0, all_14_3) = 0 & $i(v2) & $i(v1) & $i(v0)) | ? % 9.17/2.10 | | | [v0: any] : ? [v1: any] : (environment(all_6_2) = v0 & % 9.17/2.10 | | | in_environment(all_6_2, all_14_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = % 9.17/2.10 | | | 0))) % 9.17/2.10 | | | % 9.17/2.10 | | | BETA: splitting (27) gives: % 9.17/2.10 | | | % 9.17/2.10 | | | Case 1: % 9.17/2.10 | | | | % 9.17/2.10 | | | | (28) all_14_3 = all_6_1 % 9.17/2.10 | | | | % 9.17/2.10 | | | | REDUCE: (22), (28) imply: % 9.17/2.10 | | | | (29) in_environment(all_6_2, all_6_1) = 0 % 9.17/2.10 | | | | % 9.17/2.10 | | | | GROUND_INST: instantiating (5) with all_6_0, 0, all_6_1, all_6_2, % 9.17/2.10 | | | | simplifying with (10), (29) gives: % 9.17/2.10 | | | | (30) all_6_0 = 0 % 9.17/2.10 | | | | % 9.17/2.10 | | | | REDUCE: (8), (30) imply: % 9.17/2.10 | | | | (31) $false % 9.17/2.10 | | | | % 9.17/2.10 | | | | CLOSE: (31) is inconsistent. % 9.17/2.10 | | | | % 9.17/2.10 | | | Case 2: % 9.17/2.10 | | | | % 9.17/2.11 | | | | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 % 9.17/2.11 | | | | = 0) & subpopulations(first_movers, efficient_producers, % 9.17/2.11 | | | | all_6_2, v0) = 0 & growth_rate(first_movers, v0) = v2 & % 9.17/2.11 | | | | growth_rate(efficient_producers, v0) = v1 & greater(v1, v2) = % 9.17/2.11 | | | | v3 & greater(v0, all_14_3) = 0 & $i(v2) & $i(v1) & $i(v0)) | % 9.17/2.11 | | | | ? [v0: any] : ? [v1: any] : (environment(all_6_2) = v0 & % 9.17/2.11 | | | | in_environment(all_6_2, all_14_3) = v1 & ( ~ (v1 = 0) | ~ (v0 % 9.17/2.11 | | | | = 0))) % 9.17/2.11 | | | | % 9.17/2.11 | | | | BETA: splitting (32) gives: % 9.17/2.11 | | | | % 9.17/2.11 | | | | Case 1: % 9.17/2.11 | | | | | % 9.17/2.11 | | | | | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ % 9.17/2.11 | | | | | (v3 = 0) & subpopulations(first_movers, efficient_producers, % 9.17/2.11 | | | | | all_6_2, v0) = 0 & growth_rate(first_movers, v0) = v2 & % 9.17/2.11 | | | | | growth_rate(efficient_producers, v0) = v1 & greater(v1, v2) % 9.17/2.11 | | | | | = v3 & greater(v0, all_14_3) = 0 & $i(v2) & $i(v1) & $i(v0)) % 9.17/2.11 | | | | | % 9.17/2.11 | | | | | DELTA: instantiating (33) with fresh symbols all_50_0, all_50_1, % 9.17/2.11 | | | | | all_50_2, all_50_3 gives: % 9.17/2.11 | | | | | (34) ~ (all_50_0 = 0) & subpopulations(first_movers, % 9.17/2.11 | | | | | efficient_producers, all_6_2, all_50_3) = 0 & % 9.17/2.11 | | | | | growth_rate(first_movers, all_50_3) = all_50_1 & % 9.17/2.11 | | | | | growth_rate(efficient_producers, all_50_3) = all_50_2 & % 9.17/2.11 | | | | | greater(all_50_2, all_50_1) = all_50_0 & greater(all_50_3, % 9.17/2.11 | | | | | all_14_3) = 0 & $i(all_50_1) & $i(all_50_2) & $i(all_50_3) % 9.17/2.11 | | | | | % 9.17/2.11 | | | | | ALPHA: (34) implies: % 9.17/2.11 | | | | | (35) ~ (all_50_0 = 0) % 9.17/2.11 | | | | | (36) $i(all_50_3) % 9.17/2.11 | | | | | (37) greater(all_50_3, all_14_3) = 0 % 9.17/2.11 | | | | | (38) greater(all_50_2, all_50_1) = all_50_0 % 9.17/2.11 | | | | | (39) growth_rate(efficient_producers, all_50_3) = all_50_2 % 9.17/2.11 | | | | | (40) growth_rate(first_movers, all_50_3) = all_50_1 % 9.17/2.11 | | | | | (41) subpopulations(first_movers, efficient_producers, all_6_2, % 9.17/2.11 | | | | | all_50_3) = 0 % 9.17/2.11 | | | | | % 9.17/2.11 | | | | | GROUND_INST: instantiating (23) with all_50_3, all_50_2, all_50_1, % 9.17/2.11 | | | | | all_50_0, simplifying with (36), (38), (39), (40) gives: % 9.17/2.11 | | | | | (42) all_50_0 = 0 | ? [v0: any] : ? [v1: any] : % 9.17/2.11 | | | | | (subpopulations(first_movers, efficient_producers, all_6_2, % 9.17/2.11 | | | | | all_50_3) = v0 & greater(all_50_3, all_14_3) = v1 & ( ~ % 9.17/2.11 | | | | | (v1 = 0) | ~ (v0 = 0))) % 9.17/2.11 | | | | | % 9.17/2.11 | | | | | BETA: splitting (42) gives: % 9.17/2.11 | | | | | % 9.17/2.11 | | | | | Case 1: % 9.17/2.11 | | | | | | % 9.17/2.11 | | | | | | (43) all_50_0 = 0 % 9.17/2.11 | | | | | | % 9.17/2.11 | | | | | | REDUCE: (35), (43) imply: % 9.17/2.11 | | | | | | (44) $false % 9.17/2.11 | | | | | | % 9.17/2.11 | | | | | | CLOSE: (44) is inconsistent. % 9.17/2.11 | | | | | | % 9.17/2.11 | | | | | Case 2: % 9.17/2.11 | | | | | | % 9.17/2.11 | | | | | | (45) ? [v0: any] : ? [v1: any] : (subpopulations(first_movers, % 9.17/2.11 | | | | | | efficient_producers, all_6_2, all_50_3) = v0 & % 9.17/2.11 | | | | | | greater(all_50_3, all_14_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = % 9.17/2.11 | | | | | | 0))) % 9.17/2.12 | | | | | | % 9.17/2.12 | | | | | | DELTA: instantiating (45) with fresh symbols all_59_0, all_59_1 % 9.17/2.12 | | | | | | gives: % 9.17/2.12 | | | | | | (46) subpopulations(first_movers, efficient_producers, all_6_2, % 9.17/2.12 | | | | | | all_50_3) = all_59_1 & greater(all_50_3, all_14_3) = % 9.17/2.12 | | | | | | all_59_0 & ( ~ (all_59_0 = 0) | ~ (all_59_1 = 0)) % 9.17/2.12 | | | | | | % 9.17/2.12 | | | | | | ALPHA: (46) implies: % 9.17/2.12 | | | | | | (47) greater(all_50_3, all_14_3) = all_59_0 % 9.17/2.12 | | | | | | (48) subpopulations(first_movers, efficient_producers, all_6_2, % 9.17/2.12 | | | | | | all_50_3) = all_59_1 % 9.17/2.12 | | | | | | (49) ~ (all_59_0 = 0) | ~ (all_59_1 = 0) % 9.17/2.12 | | | | | | % 9.17/2.12 | | | | | | GROUND_INST: instantiating (4) with 0, all_59_0, all_14_3, all_50_3, % 9.17/2.12 | | | | | | simplifying with (37), (47) gives: % 9.17/2.12 | | | | | | (50) all_59_0 = 0 % 9.17/2.12 | | | | | | % 9.17/2.12 | | | | | | GROUND_INST: instantiating (6) with 0, all_59_1, all_50_3, all_6_2, % 9.17/2.12 | | | | | | efficient_producers, first_movers, simplifying with % 9.17/2.12 | | | | | | (41), (48) gives: % 9.17/2.12 | | | | | | (51) all_59_1 = 0 % 9.17/2.12 | | | | | | % 9.17/2.12 | | | | | | BETA: splitting (49) gives: % 9.17/2.12 | | | | | | % 9.17/2.12 | | | | | | Case 1: % 9.17/2.12 | | | | | | | % 9.17/2.12 | | | | | | | (52) ~ (all_59_0 = 0) % 9.17/2.12 | | | | | | | % 9.17/2.12 | | | | | | | REDUCE: (50), (52) imply: % 9.17/2.12 | | | | | | | (53) $false % 9.17/2.12 | | | | | | | % 9.17/2.12 | | | | | | | CLOSE: (53) is inconsistent. % 9.17/2.12 | | | | | | | % 9.17/2.12 | | | | | | Case 2: % 9.17/2.12 | | | | | | | % 9.17/2.12 | | | | | | | (54) ~ (all_59_1 = 0) % 9.17/2.12 | | | | | | | % 9.17/2.12 | | | | | | | REDUCE: (51), (54) imply: % 9.17/2.12 | | | | | | | (55) $false % 9.17/2.12 | | | | | | | % 9.17/2.12 | | | | | | | CLOSE: (55) is inconsistent. % 9.17/2.12 | | | | | | | % 9.17/2.12 | | | | | | End of split % 9.17/2.12 | | | | | | % 9.17/2.12 | | | | | End of split % 9.17/2.12 | | | | | % 9.17/2.12 | | | | Case 2: % 9.17/2.12 | | | | | % 9.17/2.12 | | | | | (56) ? [v0: any] : ? [v1: any] : (environment(all_6_2) = v0 & % 9.17/2.12 | | | | | in_environment(all_6_2, all_14_3) = v1 & ( ~ (v1 = 0) | ~ % 9.17/2.12 | | | | | (v0 = 0))) % 9.17/2.12 | | | | | % 9.17/2.12 | | | | | DELTA: instantiating (56) with fresh symbols all_50_0, all_50_1 gives: % 9.17/2.12 | | | | | (57) environment(all_6_2) = all_50_1 & in_environment(all_6_2, % 9.17/2.12 | | | | | all_14_3) = all_50_0 & ( ~ (all_50_0 = 0) | ~ (all_50_1 = % 9.17/2.12 | | | | | 0)) % 9.17/2.12 | | | | | % 9.17/2.12 | | | | | ALPHA: (57) implies: % 9.17/2.12 | | | | | (58) in_environment(all_6_2, all_14_3) = all_50_0 % 9.17/2.12 | | | | | (59) environment(all_6_2) = all_50_1 % 9.17/2.12 | | | | | (60) ~ (all_50_0 = 0) | ~ (all_50_1 = 0) % 9.17/2.12 | | | | | % 9.17/2.12 | | | | | GROUND_INST: instantiating (5) with 0, all_50_0, all_14_3, all_6_2, % 9.17/2.12 | | | | | simplifying with (22), (58) gives: % 9.17/2.12 | | | | | (61) all_50_0 = 0 % 9.17/2.12 | | | | | % 9.17/2.12 | | | | | GROUND_INST: instantiating (3) with 0, all_50_1, all_6_2, simplifying % 9.17/2.12 | | | | | with (11), (59) gives: % 9.17/2.12 | | | | | (62) all_50_1 = 0 % 9.17/2.12 | | | | | % 9.17/2.12 | | | | | BETA: splitting (60) gives: % 9.17/2.12 | | | | | % 9.17/2.12 | | | | | Case 1: % 9.17/2.12 | | | | | | % 9.17/2.12 | | | | | | (63) ~ (all_50_0 = 0) % 9.17/2.12 | | | | | | % 9.17/2.12 | | | | | | REDUCE: (61), (63) imply: % 9.17/2.12 | | | | | | (64) $false % 9.17/2.12 | | | | | | % 9.17/2.12 | | | | | | CLOSE: (64) is inconsistent. % 9.17/2.12 | | | | | | % 9.17/2.12 | | | | | Case 2: % 9.17/2.12 | | | | | | % 9.17/2.12 | | | | | | (65) ~ (all_50_1 = 0) % 9.17/2.12 | | | | | | % 9.17/2.12 | | | | | | REDUCE: (62), (65) imply: % 9.17/2.12 | | | | | | (66) $false % 9.17/2.12 | | | | | | % 9.17/2.12 | | | | | | CLOSE: (66) is inconsistent. % 9.17/2.12 | | | | | | % 9.17/2.12 | | | | | End of split % 9.17/2.12 | | | | | % 9.17/2.12 | | | | End of split % 9.17/2.12 | | | | % 9.17/2.12 | | | End of split % 9.17/2.12 | | | % 9.17/2.12 | | End of split % 9.17/2.12 | | % 9.17/2.12 | Case 2: % 9.17/2.12 | | % 9.17/2.13 | | (67) ? [v0: int] : ( ~ (v0 = 0) & environment(all_6_2) = v0) % 9.17/2.13 | | % 9.17/2.13 | | DELTA: instantiating (67) with fresh symbol all_14_0 gives: % 9.17/2.13 | | (68) ~ (all_14_0 = 0) & environment(all_6_2) = all_14_0 % 9.17/2.13 | | % 9.17/2.13 | | ALPHA: (68) implies: % 9.17/2.13 | | (69) ~ (all_14_0 = 0) % 9.17/2.13 | | (70) environment(all_6_2) = all_14_0 % 9.17/2.13 | | % 9.17/2.13 | | GROUND_INST: instantiating (3) with 0, all_14_0, all_6_2, simplifying with % 9.17/2.13 | | (11), (70) gives: % 9.17/2.13 | | (71) all_14_0 = 0 % 9.17/2.13 | | % 9.17/2.13 | | REDUCE: (69), (71) imply: % 9.17/2.13 | | (72) $false % 9.17/2.13 | | % 9.17/2.13 | | CLOSE: (72) is inconsistent. % 9.17/2.13 | | % 9.17/2.13 | End of split % 9.17/2.13 | % 9.67/2.13 End of proof % 9.67/2.13 % SZS output end Proof for theBenchmark % 9.67/2.13 % 9.67/2.13 1400ms %------------------------------------------------------------------------------