%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT028+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 : n017.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 06:17:22 AM UTC 2026 % Result : Theorem 8.82s 2.07s % Output : Proof 12.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT028+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.08/0.35 % Computer : n017.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Mon Sep 7 12:09:54 UTC 2026 % 0.08/0.35 % 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. % 0.70/0.71 ________ _____ % 0.70/0.71 ___ __ \_________(_)________________________________ % 0.70/0.71 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.70/0.71 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.70/0.71 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.70/0.71 % 0.70/0.71 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.70/0.71 (2023-06-19) % 0.70/0.71 % 0.70/0.71 (c) Philipp Rümmer, 2009-2023 % 0.70/0.71 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.70/0.71 Amanda Stjerna. % 0.70/0.71 Free software under BSD-3-Clause. % 0.70/0.71 % 0.70/0.71 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.70/0.71 % 0.70/0.72 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.70/0.74 Running up to 7 provers in parallel. % 0.70/0.75 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.70/0.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.70/0.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.70/0.75 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.70/0.75 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.70/0.75 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.70/0.75 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.37/1.27 Prover 4: Preprocessing ... % 2.37/1.27 Prover 1: Preprocessing ... % 3.10/1.36 Prover 2: Preprocessing ... % 3.10/1.36 Prover 3: Preprocessing ... % 3.10/1.36 Prover 5: Preprocessing ... % 3.10/1.36 Prover 0: Preprocessing ... % 3.10/1.36 Prover 6: Preprocessing ... % 5.42/1.68 Prover 6: Proving ... % 5.42/1.70 Prover 1: Constructing countermodel ... % 6.23/1.73 Prover 5: Constructing countermodel ... % 6.23/1.73 Prover 3: Constructing countermodel ... % 6.23/1.75 Prover 2: Proving ... % 7.78/1.91 Prover 4: Constructing countermodel ... % 8.82/2.05 Prover 0: Proving ... % 8.82/2.07 Prover 3: proved (1322ms) % 8.82/2.07 % 8.82/2.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.82/2.07 % 8.82/2.07 Prover 5: stopped % 8.82/2.08 Prover 6: stopped % 8.82/2.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.82/2.08 Prover 0: stopped % 8.82/2.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.82/2.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.82/2.08 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.82/2.11 Prover 2: stopped % 8.82/2.11 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.82/2.13 Prover 11: Preprocessing ... % 8.82/2.14 Prover 7: Preprocessing ... % 9.65/2.14 Prover 10: Preprocessing ... % 9.65/2.17 Prover 8: Preprocessing ... % 10.10/2.20 Prover 13: Preprocessing ... % 10.10/2.23 Prover 7: Constructing countermodel ... % 10.10/2.26 Prover 10: Constructing countermodel ... % 10.87/2.33 Prover 13: Constructing countermodel ... % 10.87/2.34 Prover 10: gave up % 10.87/2.34 Prover 8: Warning: ignoring some quantifiers % 10.87/2.34 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 10.87/2.35 Prover 8: Constructing countermodel ... % 10.87/2.37 Prover 16: Preprocessing ... % 11.69/2.41 Prover 16: Constructing countermodel ... % 11.69/2.43 Prover 7: Found proof (size 21) % 11.69/2.43 Prover 7: proved (351ms) % 11.69/2.43 Prover 1: stopped % 11.69/2.43 Prover 8: stopped % 11.69/2.43 Prover 16: stopped % 11.69/2.43 Prover 13: stopped % 11.69/2.43 Prover 4: stopped % 11.69/2.45 Prover 11: Constructing countermodel ... % 11.69/2.46 Prover 11: stopped % 11.69/2.46 % 11.69/2.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.69/2.46 % 11.69/2.47 % SZS output start Proof for theBenchmark % 11.69/2.48 Assumptions after simplification: % 11.69/2.48 --------------------------------- % 11.69/2.48 % 11.69/2.48 (l11) % 12.26/2.55 $i(zero) & $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ( ~ % 12.26/2.55 $i(v0) | ~ stable(v0) | ~ environment(v0) | ? [v1: $i] : ($i(v1) & % 12.26/2.55 in_environment(v0, v1) & ! [v2: $i] : ! [v3: $i] : ( ~ % 12.26/2.55 (growth_rate(efficient_producers, v2) = v3) | ~ $i(v2) | ~ % 12.26/2.55 greater_or_equal(v2, v1) | ~ subpopulations(first_movers, % 12.26/2.55 efficient_producers, v0, v2) | greater(v3, zero)) & ! [v2: $i] : ! % 12.26/2.55 [v3: $i] : ( ~ (growth_rate(efficient_producers, v2) = v3) | ~ $i(v2) | % 12.26/2.55 ~ greater_or_equal(v2, v1) | ~ subpopulations(first_movers, % 12.26/2.55 efficient_producers, v0, v2) | ? [v4: $i] : % 12.26/2.55 (growth_rate(first_movers, v2) = v4 & $i(v4) & greater(zero, v4))) & ! % 12.26/2.55 [v2: $i] : ! [v3: $i] : ( ~ (growth_rate(first_movers, v2) = v3) | ~ % 12.26/2.55 $i(v2) | ~ greater_or_equal(v2, v1) | ~ subpopulations(first_movers, % 12.26/2.55 efficient_producers, v0, v2) | greater(zero, v3)) & ! [v2: $i] : ! % 12.26/2.55 [v3: $i] : ( ~ (growth_rate(first_movers, v2) = v3) | ~ $i(v2) | ~ % 12.26/2.55 greater_or_equal(v2, v1) | ~ subpopulations(first_movers, % 12.26/2.55 efficient_producers, v0, v2) | ? [v4: $i] : % 12.26/2.55 (growth_rate(efficient_producers, v2) = v4 & $i(v4) & greater(v4, % 12.26/2.55 zero))))) % 12.26/2.55 % 12.26/2.55 (mp_first_movers_negative_growth) % 12.26/2.56 $i(zero) & $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: % 12.26/2.56 $i] : ! [v2: $i] : ( ~ (appear(efficient_producers, v0) = v1) | ~ $i(v2) | % 12.26/2.56 ~ $i(v0) | ~ in_environment(v0, v2) | ~ stable(v0) | ~ environment(v0) | % 12.26/2.56 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v3) & % 12.26/2.56 ((growth_rate(first_movers, v4) = v5 & $i(v5) & greater_or_equal(v4, v2) & % 12.26/2.56 subpopulations(first_movers, efficient_producers, v0, v4) & ~ % 12.26/2.56 greater(zero, v5)) | (greater(v3, v1) & ! [v6: $i] : ! [v7: $i] : ( % 12.26/2.56 ~ (growth_rate(first_movers, v6) = v7) | ~ $i(v6) | ~ % 12.26/2.56 greater_or_equal(v6, v3) | ~ subpopulations(first_movers, % 12.26/2.56 efficient_producers, v0, v6) | greater(zero, v7)))))) % 12.26/2.56 % 12.26/2.56 (prove_l10) % 12.26/2.57 $i(zero) & $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ? [v1: % 12.26/2.57 $i] : (appear(efficient_producers, v0) = v1 & $i(v1) & $i(v0) & stable(v0) & % 12.26/2.57 environment(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ greater(v2, v1) | ? [v3: % 12.26/2.57 $i] : ? [v4: $i] : (growth_rate(first_movers, v3) = v4 & $i(v4) & % 12.26/2.57 $i(v3) & greater_or_equal(v3, v2) & subpopulations(first_movers, % 12.26/2.57 efficient_producers, v0, v3) & ~ greater(zero, v4)))) % 12.26/2.57 % 12.26/2.57 Those formulas are unsatisfiable: % 12.26/2.57 --------------------------------- % 12.26/2.57 % 12.26/2.57 Begin of proof % 12.26/2.57 | % 12.26/2.57 | ALPHA: (mp_first_movers_negative_growth) implies: % 12.26/2.58 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 12.26/2.58 | (appear(efficient_producers, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ % 12.26/2.58 | in_environment(v0, v2) | ~ stable(v0) | ~ environment(v0) | ? [v3: % 12.26/2.58 | $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v3) & % 12.26/2.58 | ((growth_rate(first_movers, v4) = v5 & $i(v5) & % 12.26/2.58 | greater_or_equal(v4, v2) & subpopulations(first_movers, % 12.26/2.58 | efficient_producers, v0, v4) & ~ greater(zero, v5)) | % 12.26/2.58 | (greater(v3, v1) & ! [v6: $i] : ! [v7: $i] : ( ~ % 12.26/2.58 | (growth_rate(first_movers, v6) = v7) | ~ $i(v6) | ~ % 12.26/2.58 | greater_or_equal(v6, v3) | ~ subpopulations(first_movers, % 12.26/2.58 | efficient_producers, v0, v6) | greater(zero, v7)))))) % 12.26/2.58 | % 12.26/2.58 | ALPHA: (l11) implies: % 12.26/2.59 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ stable(v0) | ~ environment(v0) | ? [v1: % 12.26/2.59 | $i] : ($i(v1) & in_environment(v0, v1) & ! [v2: $i] : ! [v3: $i] % 12.26/2.59 | : ( ~ (growth_rate(efficient_producers, v2) = v3) | ~ $i(v2) | ~ % 12.26/2.59 | greater_or_equal(v2, v1) | ~ subpopulations(first_movers, % 12.26/2.59 | efficient_producers, v0, v2) | greater(v3, zero)) & ! [v2: $i] % 12.26/2.59 | : ! [v3: $i] : ( ~ (growth_rate(efficient_producers, v2) = v3) | % 12.26/2.59 | ~ $i(v2) | ~ greater_or_equal(v2, v1) | ~ % 12.26/2.59 | subpopulations(first_movers, efficient_producers, v0, v2) | ? % 12.26/2.59 | [v4: $i] : (growth_rate(first_movers, v2) = v4 & $i(v4) & % 12.26/2.59 | greater(zero, v4))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 12.26/2.59 | (growth_rate(first_movers, v2) = v3) | ~ $i(v2) | ~ % 12.26/2.59 | greater_or_equal(v2, v1) | ~ subpopulations(first_movers, % 12.26/2.59 | efficient_producers, v0, v2) | greater(zero, v3)) & ! [v2: $i] % 12.26/2.59 | : ! [v3: $i] : ( ~ (growth_rate(first_movers, v2) = v3) | ~ % 12.26/2.59 | $i(v2) | ~ greater_or_equal(v2, v1) | ~ % 12.26/2.59 | subpopulations(first_movers, efficient_producers, v0, v2) | ? % 12.26/2.59 | [v4: $i] : (growth_rate(efficient_producers, v2) = v4 & $i(v4) & % 12.26/2.59 | greater(v4, zero))))) % 12.26/2.59 | % 12.26/2.59 | ALPHA: (prove_l10) implies: % 12.26/2.59 | (3) ? [v0: $i] : ? [v1: $i] : (appear(efficient_producers, v0) = v1 & % 12.26/2.59 | $i(v1) & $i(v0) & stable(v0) & environment(v0) & ! [v2: $i] : ( ~ % 12.26/2.59 | $i(v2) | ~ greater(v2, v1) | ? [v3: $i] : ? [v4: $i] : % 12.26/2.59 | (growth_rate(first_movers, v3) = v4 & $i(v4) & $i(v3) & % 12.26/2.59 | greater_or_equal(v3, v2) & subpopulations(first_movers, % 12.26/2.59 | efficient_producers, v0, v3) & ~ greater(zero, v4)))) % 12.26/2.59 | % 12.26/2.60 | DELTA: instantiating (3) with fresh symbols all_6_0, all_6_1 gives: % 12.76/2.60 | (4) appear(efficient_producers, all_6_1) = all_6_0 & $i(all_6_0) & % 12.76/2.60 | $i(all_6_1) & stable(all_6_1) & environment(all_6_1) & ! [v0: $i] : ( % 12.76/2.60 | ~ $i(v0) | ~ greater(v0, all_6_0) | ? [v1: $i] : ? [v2: $i] : % 12.76/2.60 | (growth_rate(first_movers, v1) = v2 & $i(v2) & $i(v1) & % 12.76/2.60 | greater_or_equal(v1, v0) & subpopulations(first_movers, % 12.76/2.60 | efficient_producers, all_6_1, v1) & ~ greater(zero, v2))) % 12.76/2.60 | % 12.76/2.60 | ALPHA: (4) implies: % 12.76/2.60 | (5) environment(all_6_1) % 12.76/2.60 | (6) stable(all_6_1) % 12.76/2.60 | (7) $i(all_6_1) % 12.76/2.60 | (8) appear(efficient_producers, all_6_1) = all_6_0 % 12.76/2.60 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ greater(v0, all_6_0) | ? [v1: $i] : ? % 12.76/2.60 | [v2: $i] : (growth_rate(first_movers, v1) = v2 & $i(v2) & $i(v1) & % 12.76/2.60 | greater_or_equal(v1, v0) & subpopulations(first_movers, % 12.76/2.60 | efficient_producers, all_6_1, v1) & ~ greater(zero, v2))) % 12.76/2.60 | % 12.76/2.61 | GROUND_INST: instantiating (2) with all_6_1, simplifying with (5), (6), (7) % 12.76/2.61 | gives: % 12.76/2.61 | (10) ? [v0: $i] : ($i(v0) & in_environment(all_6_1, v0) & ! [v1: $i] : ! % 12.76/2.61 | [v2: $i] : ( ~ (growth_rate(efficient_producers, v1) = v2) | ~ % 12.76/2.61 | $i(v1) | ~ greater_or_equal(v1, v0) | ~ % 12.76/2.61 | subpopulations(first_movers, efficient_producers, all_6_1, v1) | % 12.76/2.61 | greater(v2, zero)) & ! [v1: $i] : ! [v2: $i] : ( ~ % 12.76/2.61 | (growth_rate(efficient_producers, v1) = v2) | ~ $i(v1) | ~ % 12.76/2.61 | greater_or_equal(v1, v0) | ~ subpopulations(first_movers, % 12.76/2.61 | efficient_producers, all_6_1, v1) | ? [v3: $i] : % 12.76/2.61 | (growth_rate(first_movers, v1) = v3 & $i(v3) & greater(zero, v3))) % 12.76/2.61 | & ! [v1: $i] : ! [v2: $i] : ( ~ (growth_rate(first_movers, v1) = % 12.76/2.61 | v2) | ~ $i(v1) | ~ greater_or_equal(v1, v0) | ~ % 12.76/2.61 | subpopulations(first_movers, efficient_producers, all_6_1, v1) | % 12.76/2.61 | greater(zero, v2)) & ! [v1: $i] : ! [v2: $i] : ( ~ % 12.76/2.61 | (growth_rate(first_movers, v1) = v2) | ~ $i(v1) | ~ % 12.76/2.61 | greater_or_equal(v1, v0) | ~ subpopulations(first_movers, % 12.76/2.61 | efficient_producers, all_6_1, v1) | ? [v3: $i] : % 12.76/2.61 | (growth_rate(efficient_producers, v1) = v3 & $i(v3) & greater(v3, % 12.76/2.61 | zero)))) % 12.76/2.61 | % 12.76/2.61 | DELTA: instantiating (10) with fresh symbol all_14_0 gives: % 12.76/2.62 | (11) $i(all_14_0) & in_environment(all_6_1, all_14_0) & ! [v0: $i] : ! % 12.76/2.62 | [v1: $i] : ( ~ (growth_rate(efficient_producers, v0) = v1) | ~ $i(v0) % 12.76/2.62 | | ~ greater_or_equal(v0, all_14_0) | ~ % 12.76/2.62 | subpopulations(first_movers, efficient_producers, all_6_1, v0) | % 12.76/2.62 | greater(v1, zero)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 12.76/2.62 | (growth_rate(efficient_producers, v0) = v1) | ~ $i(v0) | ~ % 12.76/2.62 | greater_or_equal(v0, all_14_0) | ~ subpopulations(first_movers, % 12.76/2.62 | efficient_producers, all_6_1, v0) | ? [v2: $i] : % 12.76/2.62 | (growth_rate(first_movers, v0) = v2 & $i(v2) & greater(zero, v2))) & % 12.76/2.62 | ! [v0: $i] : ! [v1: $i] : ( ~ (growth_rate(first_movers, v0) = v1) | % 12.76/2.62 | ~ $i(v0) | ~ greater_or_equal(v0, all_14_0) | ~ % 12.76/2.62 | subpopulations(first_movers, efficient_producers, all_6_1, v0) | % 12.76/2.62 | greater(zero, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 12.76/2.62 | (growth_rate(first_movers, v0) = v1) | ~ $i(v0) | ~ % 12.76/2.62 | greater_or_equal(v0, all_14_0) | ~ subpopulations(first_movers, % 12.76/2.62 | efficient_producers, all_6_1, v0) | ? [v2: $i] : % 12.76/2.62 | (growth_rate(efficient_producers, v0) = v2 & $i(v2) & greater(v2, % 12.76/2.62 | zero))) % 12.76/2.62 | % 12.76/2.62 | ALPHA: (11) implies: % 12.76/2.62 | (12) in_environment(all_6_1, all_14_0) % 12.76/2.62 | (13) $i(all_14_0) % 12.76/2.62 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (growth_rate(first_movers, v0) = v1) | % 12.76/2.62 | ~ $i(v0) | ~ greater_or_equal(v0, all_14_0) | ~ % 12.76/2.62 | subpopulations(first_movers, efficient_producers, all_6_1, v0) | % 12.76/2.62 | greater(zero, v1)) % 12.76/2.62 | % 12.76/2.62 | GROUND_INST: instantiating (1) with all_6_1, all_6_0, all_14_0, simplifying % 12.76/2.62 | with (5), (6), (7), (8), (12), (13) gives: % 12.76/2.62 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v1) & $i(v0) & % 12.76/2.62 | ((growth_rate(first_movers, v1) = v2 & $i(v2) & greater_or_equal(v1, % 12.76/2.62 | all_14_0) & subpopulations(first_movers, efficient_producers, % 12.76/2.62 | all_6_1, v1) & ~ greater(zero, v2)) | (greater(v0, all_6_0) & % 12.76/2.62 | ! [v3: $i] : ! [v4: $i] : ( ~ (growth_rate(first_movers, v3) = % 12.76/2.62 | v4) | ~ $i(v3) | ~ greater_or_equal(v3, v0) | ~ % 12.76/2.62 | subpopulations(first_movers, efficient_producers, all_6_1, v3) % 12.76/2.62 | | greater(zero, v4))))) % 12.76/2.62 | % 12.76/2.62 | DELTA: instantiating (15) with fresh symbols all_22_0, all_22_1, all_22_2 % 12.76/2.62 | gives: % 12.76/2.63 | (16) $i(all_22_1) & $i(all_22_2) & ((growth_rate(first_movers, all_22_1) = % 12.76/2.63 | all_22_0 & $i(all_22_0) & greater_or_equal(all_22_1, all_14_0) & % 12.76/2.63 | subpopulations(first_movers, efficient_producers, all_6_1, % 12.76/2.63 | all_22_1) & ~ greater(zero, all_22_0)) | (greater(all_22_2, % 12.76/2.63 | all_6_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 12.76/2.63 | (growth_rate(first_movers, v0) = v1) | ~ $i(v0) | ~ % 12.76/2.63 | greater_or_equal(v0, all_22_2) | ~ subpopulations(first_movers, % 12.76/2.63 | efficient_producers, all_6_1, v0) | greater(zero, v1)))) % 12.76/2.63 | % 12.76/2.63 | ALPHA: (16) implies: % 12.76/2.63 | (17) $i(all_22_2) % 12.76/2.63 | (18) $i(all_22_1) % 12.76/2.63 | (19) (growth_rate(first_movers, all_22_1) = all_22_0 & $i(all_22_0) & % 12.76/2.63 | greater_or_equal(all_22_1, all_14_0) & subpopulations(first_movers, % 12.76/2.63 | efficient_producers, all_6_1, all_22_1) & ~ greater(zero, % 12.76/2.63 | all_22_0)) | (greater(all_22_2, all_6_0) & ! [v0: $i] : ! [v1: % 12.76/2.63 | $i] : ( ~ (growth_rate(first_movers, v0) = v1) | ~ $i(v0) | ~ % 12.76/2.63 | greater_or_equal(v0, all_22_2) | ~ subpopulations(first_movers, % 12.76/2.63 | efficient_producers, all_6_1, v0) | greater(zero, v1))) % 12.76/2.63 | % 12.76/2.63 | BETA: splitting (19) gives: % 12.76/2.63 | % 12.76/2.63 | Case 1: % 12.76/2.63 | | % 12.76/2.63 | | (20) growth_rate(first_movers, all_22_1) = all_22_0 & $i(all_22_0) & % 12.76/2.63 | | greater_or_equal(all_22_1, all_14_0) & subpopulations(first_movers, % 12.76/2.63 | | efficient_producers, all_6_1, all_22_1) & ~ greater(zero, % 12.76/2.63 | | all_22_0) % 12.76/2.63 | | % 12.76/2.63 | | ALPHA: (20) implies: % 12.76/2.63 | | (21) ~ greater(zero, all_22_0) % 12.76/2.63 | | (22) subpopulations(first_movers, efficient_producers, all_6_1, all_22_1) % 12.76/2.63 | | (23) greater_or_equal(all_22_1, all_14_0) % 12.76/2.63 | | (24) growth_rate(first_movers, all_22_1) = all_22_0 % 12.76/2.63 | | % 12.76/2.64 | | GROUND_INST: instantiating (14) with all_22_1, all_22_0, simplifying with % 12.76/2.64 | | (18), (21), (22), (23), (24) gives: % 12.76/2.64 | | (25) $false % 12.76/2.64 | | % 12.76/2.64 | | CLOSE: (25) is inconsistent. % 12.76/2.64 | | % 12.76/2.64 | Case 2: % 12.76/2.64 | | % 12.76/2.64 | | (26) greater(all_22_2, all_6_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 12.76/2.64 | | (growth_rate(first_movers, v0) = v1) | ~ $i(v0) | ~ % 12.76/2.64 | | greater_or_equal(v0, all_22_2) | ~ subpopulations(first_movers, % 12.76/2.64 | | efficient_producers, all_6_1, v0) | greater(zero, v1)) % 12.76/2.64 | | % 12.76/2.64 | | ALPHA: (26) implies: % 12.76/2.64 | | (27) greater(all_22_2, all_6_0) % 12.76/2.64 | | (28) ! [v0: $i] : ! [v1: $i] : ( ~ (growth_rate(first_movers, v0) = v1) % 12.76/2.64 | | | ~ $i(v0) | ~ greater_or_equal(v0, all_22_2) | ~ % 12.76/2.64 | | subpopulations(first_movers, efficient_producers, all_6_1, v0) | % 12.76/2.64 | | greater(zero, v1)) % 12.76/2.64 | | % 12.76/2.64 | | GROUND_INST: instantiating (9) with all_22_2, simplifying with (17), (27) % 12.76/2.64 | | gives: % 12.76/2.64 | | (29) ? [v0: $i] : ? [v1: $i] : (growth_rate(first_movers, v0) = v1 & % 12.76/2.64 | | $i(v1) & $i(v0) & greater_or_equal(v0, all_22_2) & % 12.76/2.64 | | subpopulations(first_movers, efficient_producers, all_6_1, v0) & % 12.76/2.64 | | ~ greater(zero, v1)) % 12.76/2.64 | | % 12.76/2.64 | | DELTA: instantiating (29) with fresh symbols all_37_0, all_37_1 gives: % 12.76/2.64 | | (30) growth_rate(first_movers, all_37_1) = all_37_0 & $i(all_37_0) & % 12.76/2.64 | | $i(all_37_1) & greater_or_equal(all_37_1, all_22_2) & % 12.76/2.64 | | subpopulations(first_movers, efficient_producers, all_6_1, all_37_1) % 12.76/2.65 | | & ~ greater(zero, all_37_0) % 12.76/2.65 | | % 12.76/2.65 | | ALPHA: (30) implies: % 12.76/2.65 | | (31) ~ greater(zero, all_37_0) % 12.76/2.65 | | (32) subpopulations(first_movers, efficient_producers, all_6_1, all_37_1) % 12.76/2.65 | | (33) greater_or_equal(all_37_1, all_22_2) % 12.76/2.65 | | (34) $i(all_37_1) % 12.76/2.65 | | (35) growth_rate(first_movers, all_37_1) = all_37_0 % 12.76/2.65 | | % 12.76/2.65 | | GROUND_INST: instantiating (28) with all_37_1, all_37_0, simplifying with % 12.76/2.65 | | (31), (32), (33), (34), (35) gives: % 12.76/2.65 | | (36) $false % 12.76/2.65 | | % 12.76/2.65 | | CLOSE: (36) is inconsistent. % 12.76/2.65 | | % 12.76/2.65 | End of split % 12.76/2.65 | % 12.76/2.65 End of proof % 12.76/2.65 % SZS output end Proof for theBenchmark % 12.76/2.65 % 12.76/2.65 1932ms %------------------------------------------------------------------------------