%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT036+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 : n031.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 06:17:23 AM UTC 2026 % Result : Theorem 7.66s 2.01s % Output : Proof 14.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT036+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.37 % Computer : n031.cluster.edu % 0.09/0.37 % Model : x86_64 x86_64 % 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.37 % Memory : 8046.5625MB % 0.09/0.37 % OS : Linux 6.8.0-71-generic % 0.09/0.37 % CPULimit : 300 % 0.09/0.37 % WCLimit : 300 % 0.09/0.37 % DateTime : Mon Sep 7 12:42:26 UTC 2026 % 0.09/0.37 % CPUTime : % 0.09/0.39 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/sandbox/benchmark/theBenchmark.p ... % 0.70/0.73 Running up to 7 provers in parallel. % 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 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 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 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 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 % 2.36/1.28 Prover 4: Preprocessing ... % 2.36/1.29 Prover 1: Preprocessing ... % 3.08/1.34 Prover 3: Preprocessing ... % 3.08/1.34 Prover 5: Preprocessing ... % 3.08/1.34 Prover 2: Preprocessing ... % 3.08/1.35 Prover 6: Preprocessing ... % 3.08/1.35 Prover 0: Preprocessing ... % 5.37/1.69 Prover 5: Proving ... % 6.12/1.72 Prover 2: Proving ... % 6.12/1.76 Prover 1: Constructing countermodel ... % 6.12/1.78 Prover 3: Constructing countermodel ... % 6.12/1.78 Prover 6: Constructing countermodel ... % 6.12/1.79 Prover 4: Constructing countermodel ... % 7.66/1.91 Prover 0: Proving ... % 7.66/2.00 Prover 3: proved (1260ms) % 7.66/2.01 % 7.66/2.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.66/2.01 % 7.66/2.01 Prover 6: stopped % 7.66/2.01 Prover 2: stopped % 7.66/2.01 Prover 5: stopped % 7.66/2.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.66/2.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.66/2.02 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.66/2.02 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.66/2.02 Prover 0: stopped % 7.66/2.03 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.66/2.05 Prover 8: Preprocessing ... % 7.66/2.06 Prover 7: Preprocessing ... % 8.92/2.07 Prover 11: Preprocessing ... % 8.92/2.10 Prover 13: Preprocessing ... % 8.92/2.10 Prover 10: Preprocessing ... % 8.92/2.15 Prover 7: Warning: ignoring some quantifiers % 8.92/2.16 Prover 8: Warning: ignoring some quantifiers % 9.72/2.17 Prover 8: Constructing countermodel ... % 9.72/2.19 Prover 7: Constructing countermodel ... % 9.95/2.24 Prover 13: Warning: ignoring some quantifiers % 9.95/2.26 Prover 13: Constructing countermodel ... % 9.95/2.28 Prover 10: Warning: ignoring some quantifiers % 9.95/2.30 Prover 10: Constructing countermodel ... % 10.73/2.36 Prover 7: gave up % 10.73/2.37 Prover 11: Constructing countermodel ... % 10.73/2.37 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.53/2.40 Prover 10: gave up % 11.53/2.41 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 11.53/2.41 Prover 13: gave up % 11.53/2.43 Prover 16: Preprocessing ... % 11.53/2.44 Prover 19: Preprocessing ... % 12.31/2.51 Prover 1: Found proof (size 114) % 12.31/2.51 Prover 1: proved (1765ms) % 12.31/2.51 Prover 11: stopped % 12.31/2.51 Prover 4: stopped % 12.31/2.52 Prover 8: Found proof (size 114) % 12.31/2.52 Prover 8: proved (509ms) % 12.31/2.53 Prover 16: Warning: ignoring some quantifiers % 12.31/2.54 Prover 16: Constructing countermodel ... % 12.31/2.54 Prover 16: stopped % 12.31/2.59 Prover 19: Warning: ignoring some quantifiers % 12.31/2.60 Prover 19: Constructing countermodel ... % 12.90/2.61 Prover 19: stopped % 12.90/2.61 % 12.90/2.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.90/2.61 % 12.90/2.66 % SZS output start Proof for theBenchmark % 12.90/2.66 Assumptions after simplification: % 12.90/2.66 --------------------------------- % 12.90/2.66 % 12.90/2.66 (a12) % 13.37/2.72 $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 13.37/2.72 : ! [v5: $i] : ( ~ (resilience(v2) = v4) | ~ (resilience(v1) = v5) | ~ % 13.37/2.72 (greater(v4, v5) = 0) | ~ (in_environment(v0, v3) = 0) | ~ $i(v3) | ~ % 13.37/2.72 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : % 13.37/2.72 ? [v9: $i] : ? [v10: any] : (growth_rate(v2, v3) = v9 & growth_rate(v1, % 13.37/2.72 v3) = v7 & greater(zero, v9) = v10 & greater(zero, v7) = v8 & % 13.37/2.72 environment(v0) = v6 & $i(v9) & $i(v7) & ( ~ (v10 = 0) | ~ (v6 = 0) | v8 % 13.37/2.72 = 0))) % 13.37/2.72 % 13.37/2.72 (a2) % 13.37/2.73 $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ? [v1: $i] : % 13.37/2.73 (resilience(efficient_producers) = v0 & resilience(first_movers) = v1 & % 13.37/2.73 greater(v0, v1) = 0 & $i(v1) & $i(v0)) % 13.37/2.73 % 13.37/2.73 (d2) % 13.37/2.74 $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 13.37/2.74 any] : ( ~ (outcompetes(v2, v1, v3) = v4) | ~ (environment(v0) = 0) | ~ % 13.37/2.74 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? % 13.37/2.74 [v7: any] : ? [v8: $i] : ? [v9: any] : (growth_rate(v2, v3) = v6 & % 13.37/2.74 growth_rate(v1, v3) = v8 & greater_or_equal(v6, zero) = v7 & greater(zero, % 13.37/2.74 v8) = v9 & subpopulations(v1, v2, v0, v3) = v5 & $i(v8) & $i(v6) & ( ~ % 13.37/2.74 (v5 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v4 = 0) & ( ~ (v4 = 0) | (v9 = % 13.37/2.74 0 & v7 = 0)))))) % 13.37/2.74 % 13.37/2.74 (mp_growth_rate_relationships) % 13.37/2.75 $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 13.37/2.75 any] : ( ~ (subpopulations(v1, v2, v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | % 13.37/2.75 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: % 13.37/2.75 any] : (growth_rate(v1, v3) = v6 & greater_or_equal(v6, zero) = v7 & % 13.37/2.75 greater(zero, v6) = v8 & environment(v0) = v5 & $i(v6) & ( ~ (v8 = 0) | % 13.37/2.75 (v5 = 0 & v4 = 0 & ~ (v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 13.37/2.75 $i] : ! [v3: $i] : ( ~ (subpopulations(v1, v2, v0, v3) = 0) | ~ $i(v3) | % 13.37/2.75 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] % 13.37/2.75 : ? [v7: any] : (growth_rate(v1, v3) = v4 & greater_or_equal(v4, zero) = v7 % 13.37/2.75 & greater(zero, v4) = v5 & environment(v0) = v6 & $i(v4) & ( ~ (v6 = 0) | % 13.37/2.75 v7 = 0 | v5 = 0))) % 13.37/2.75 % 13.37/2.75 (mp_symmetry_of_FM_and_EP) % 13.37/2.75 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : ( ~ % 13.37/2.75 (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ~ $i(v1) % 13.37/2.75 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (environment(v0) = v2 & % 13.37/2.75 subpopulations(efficient_producers, first_movers, v0, v1) = v3 & ( ~ (v2 = % 13.37/2.75 0) | v3 = 0))) % 13.37/2.75 % 13.37/2.75 (mp_time_point_occur) % 13.37/2.76 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : ( ~ % 13.37/2.76 (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ~ $i(v1) % 13.37/2.76 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in_environment(v0, v1) = v3 & % 13.37/2.76 environment(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 13.37/2.76 % 13.37/2.76 (prove_t5) % 13.37/2.76 $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ? [v1: $i] : % 13.37/2.76 (outcompetes(first_movers, efficient_producers, v1) = 0 & environment(v0) = 0 % 13.37/2.76 & subpopulations(first_movers, efficient_producers, v0, v1) = 0 & $i(v1) & % 13.37/2.76 $i(v0)) % 13.37/2.76 % 13.37/2.76 (function-axioms) % 13.37/2.77 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.37/2.77 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (subpopulations(v5, v4, % 13.37/2.77 v3, v2) = v1) | ~ (subpopulations(v5, v4, v3, v2) = v0)) & ! [v0: % 13.37/2.77 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.37/2.77 : ! [v4: $i] : (v1 = v0 | ~ (outcompetes(v4, v3, v2) = v1) | ~ % 13.37/2.77 (outcompetes(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 13.37/2.77 ! [v3: $i] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, % 13.37/2.77 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 13.37/2.77 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~ % 13.37/2.77 (greater_or_equal(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.37/2.77 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, % 13.37/2.77 v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.37/2.77 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.37/2.77 (in_environment(v3, v2) = v1) | ~ (in_environment(v3, v2) = v0)) & ! [v0: % 13.37/2.77 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (resilience(v2) = v1) | ~ % 13.37/2.77 (resilience(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.37/2.77 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (environment(v2) = v1) | ~ % 13.37/2.77 (environment(v2) = v0)) % 13.37/2.77 % 13.37/2.77 Those formulas are unsatisfiable: % 13.37/2.77 --------------------------------- % 13.37/2.77 % 13.37/2.77 Begin of proof % 13.37/2.77 | % 13.37/2.77 | ALPHA: (mp_symmetry_of_FM_and_EP) implies: % 13.37/2.77 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subpopulations(first_movers, % 13.37/2.77 | efficient_producers, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 13.37/2.77 | [v2: any] : ? [v3: any] : (environment(v0) = v2 & % 13.37/2.78 | subpopulations(efficient_producers, first_movers, v0, v1) = v3 & ( % 13.37/2.78 | ~ (v2 = 0) | v3 = 0))) % 13.37/2.78 | % 13.37/2.78 | ALPHA: (mp_time_point_occur) implies: % 13.37/2.78 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (subpopulations(first_movers, % 13.37/2.78 | efficient_producers, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 13.37/2.78 | [v2: any] : ? [v3: any] : (in_environment(v0, v1) = v3 & % 13.37/2.78 | environment(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 13.37/2.78 | % 13.37/2.78 | ALPHA: (mp_growth_rate_relationships) implies: % 13.37/2.78 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 13.37/2.78 | (subpopulations(v1, v2, v0, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 13.37/2.78 | $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? % 13.37/2.78 | [v7: any] : (growth_rate(v1, v3) = v4 & greater_or_equal(v4, zero) = % 13.37/2.78 | v7 & greater(zero, v4) = v5 & environment(v0) = v6 & $i(v4) & ( ~ % 13.37/2.78 | (v6 = 0) | v7 = 0 | v5 = 0))) % 13.37/2.78 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 13.37/2.78 | ( ~ (subpopulations(v1, v2, v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 13.37/2.78 | $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? % 13.37/2.78 | [v8: any] : (growth_rate(v1, v3) = v6 & greater_or_equal(v6, zero) = % 13.37/2.78 | v7 & greater(zero, v6) = v8 & environment(v0) = v5 & $i(v6) & ( ~ % 13.37/2.78 | (v8 = 0) | (v5 = 0 & v4 = 0 & ~ (v7 = 0))))) % 13.37/2.79 | % 13.37/2.79 | ALPHA: (d2) implies: % 13.37/2.79 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 13.37/2.79 | ( ~ (outcompetes(v2, v1, v3) = v4) | ~ (environment(v0) = 0) | ~ % 13.37/2.79 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 13.37/2.79 | $i] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : (growth_rate(v2, % 13.37/2.79 | v3) = v6 & growth_rate(v1, v3) = v8 & greater_or_equal(v6, zero) % 13.37/2.79 | = v7 & greater(zero, v8) = v9 & subpopulations(v1, v2, v0, v3) = v5 % 13.37/2.79 | & $i(v8) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v4 % 13.37/2.79 | = 0) & ( ~ (v4 = 0) | (v9 = 0 & v7 = 0)))))) % 13.37/2.79 | % 13.37/2.79 | ALPHA: (a12) implies: % 13.37/2.79 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 13.37/2.79 | ! [v5: $i] : ( ~ (resilience(v2) = v4) | ~ (resilience(v1) = v5) | ~ % 13.37/2.79 | (greater(v4, v5) = 0) | ~ (in_environment(v0, v3) = 0) | ~ $i(v3) | % 13.37/2.79 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? % 13.37/2.79 | [v8: any] : ? [v9: $i] : ? [v10: any] : (growth_rate(v2, v3) = v9 & % 13.37/2.79 | growth_rate(v1, v3) = v7 & greater(zero, v9) = v10 & greater(zero, % 13.37/2.79 | v7) = v8 & environment(v0) = v6 & $i(v9) & $i(v7) & ( ~ (v10 = 0) % 13.37/2.79 | | ~ (v6 = 0) | v8 = 0))) % 13.37/2.79 | % 13.37/2.79 | ALPHA: (a2) implies: % 13.37/2.79 | (7) ? [v0: $i] : ? [v1: $i] : (resilience(efficient_producers) = v0 & % 13.37/2.80 | resilience(first_movers) = v1 & greater(v0, v1) = 0 & $i(v1) & % 13.37/2.80 | $i(v0)) % 13.37/2.80 | % 13.37/2.80 | ALPHA: (prove_t5) implies: % 13.87/2.80 | (8) $i(first_movers) % 13.87/2.80 | (9) $i(efficient_producers) % 13.87/2.80 | (10) ? [v0: $i] : ? [v1: $i] : (outcompetes(first_movers, % 13.87/2.80 | efficient_producers, v1) = 0 & environment(v0) = 0 & % 13.87/2.80 | subpopulations(first_movers, efficient_producers, v0, v1) = 0 & % 13.87/2.80 | $i(v1) & $i(v0)) % 13.87/2.80 | % 13.87/2.80 | ALPHA: (function-axioms) implies: % 13.87/2.80 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 13.87/2.80 | : (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0)) % 13.87/2.80 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 13.87/2.80 | : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, % 13.87/2.80 | v2) = v0)) % 13.87/2.80 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 13.87/2.80 | : ! [v3: $i] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~ % 13.87/2.80 | (greater_or_equal(v3, v2) = v0)) % 13.87/2.80 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.87/2.80 | (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) % 13.87/2.80 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 13.87/2.81 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 13.87/2.81 | (subpopulations(v5, v4, v3, v2) = v1) | ~ (subpopulations(v5, v4, % 13.87/2.81 | v3, v2) = v0)) % 13.87/2.81 | % 13.87/2.81 | DELTA: instantiating (7) with fresh symbols all_9_0, all_9_1 gives: % 13.87/2.81 | (16) resilience(efficient_producers) = all_9_1 & resilience(first_movers) = % 13.87/2.81 | all_9_0 & greater(all_9_1, all_9_0) = 0 & $i(all_9_0) & $i(all_9_1) % 13.87/2.81 | % 13.87/2.81 | ALPHA: (16) implies: % 13.87/2.81 | (17) greater(all_9_1, all_9_0) = 0 % 13.87/2.81 | (18) resilience(first_movers) = all_9_0 % 13.87/2.81 | (19) resilience(efficient_producers) = all_9_1 % 13.87/2.81 | % 13.87/2.81 | DELTA: instantiating (10) with fresh symbols all_11_0, all_11_1 gives: % 13.87/2.81 | (20) outcompetes(first_movers, efficient_producers, all_11_0) = 0 & % 13.87/2.81 | environment(all_11_1) = 0 & subpopulations(first_movers, % 13.87/2.81 | efficient_producers, all_11_1, all_11_0) = 0 & $i(all_11_0) & % 13.87/2.81 | $i(all_11_1) % 13.87/2.81 | % 13.87/2.81 | ALPHA: (20) implies: % 13.87/2.81 | (21) $i(all_11_1) % 13.87/2.81 | (22) $i(all_11_0) % 13.87/2.81 | (23) subpopulations(first_movers, efficient_producers, all_11_1, all_11_0) % 13.87/2.81 | = 0 % 13.87/2.81 | (24) environment(all_11_1) = 0 % 13.87/2.81 | (25) outcompetes(first_movers, efficient_producers, all_11_0) = 0 % 13.87/2.81 | % 13.87/2.81 | GROUND_INST: instantiating (2) with all_11_1, all_11_0, simplifying with (21), % 13.87/2.81 | (22), (23) gives: % 13.87/2.81 | (26) ? [v0: any] : ? [v1: any] : (in_environment(all_11_1, all_11_0) = v1 % 13.87/2.82 | & environment(all_11_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 13.87/2.82 | % 13.87/2.82 | GROUND_INST: instantiating (1) with all_11_1, all_11_0, simplifying with (21), % 13.87/2.82 | (22), (23) gives: % 13.87/2.82 | (27) ? [v0: any] : ? [v1: any] : (environment(all_11_1) = v0 & % 13.87/2.82 | subpopulations(efficient_producers, first_movers, all_11_1, % 13.87/2.82 | all_11_0) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 13.87/2.82 | % 13.87/2.82 | GROUND_INST: instantiating (3) with all_11_1, first_movers, % 13.87/2.82 | efficient_producers, all_11_0, simplifying with (8), (9), (21), % 13.87/2.82 | (22), (23) gives: % 13.87/2.82 | (28) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 13.87/2.82 | (growth_rate(first_movers, all_11_0) = v0 & greater_or_equal(v0, zero) % 13.87/2.82 | = v3 & greater(zero, v0) = v1 & environment(all_11_1) = v2 & $i(v0) % 13.87/2.82 | & ( ~ (v2 = 0) | v3 = 0 | v1 = 0)) % 13.87/2.82 | % 13.87/2.82 | GROUND_INST: instantiating (4) with all_11_1, first_movers, % 13.87/2.82 | efficient_producers, all_11_0, 0, simplifying with (8), (9), % 13.87/2.82 | (21), (22), (23) gives: % 13.87/2.82 | (29) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : % 13.87/2.82 | (growth_rate(first_movers, all_11_0) = v1 & greater_or_equal(v1, zero) % 13.87/2.82 | = v2 & greater(zero, v1) = v3 & environment(all_11_1) = v0 & $i(v1) % 13.87/2.82 | & ( ~ (v3 = 0) | (v0 = 0 & ~ (v2 = 0)))) % 13.87/2.82 | % 13.87/2.82 | GROUND_INST: instantiating (5) with all_11_1, efficient_producers, % 13.87/2.82 | first_movers, all_11_0, 0, simplifying with (8), (9), (21), (22), % 13.87/2.82 | (24), (25) gives: % 13.87/2.83 | (30) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] % 13.87/2.83 | : (growth_rate(efficient_producers, all_11_0) = v3 & % 13.87/2.83 | growth_rate(first_movers, all_11_0) = v1 & greater_or_equal(v1, % 13.87/2.83 | zero) = v2 & greater(zero, v3) = v4 & % 13.87/2.83 | subpopulations(efficient_producers, first_movers, all_11_1, % 13.87/2.83 | all_11_0) = v0 & $i(v3) & $i(v1) & ( ~ (v0 = 0) | (v4 = 0 & v2 = % 13.87/2.83 | 0))) % 13.87/2.83 | % 13.87/2.83 | DELTA: instantiating (27) with fresh symbols all_18_0, all_18_1 gives: % 13.87/2.83 | (31) environment(all_11_1) = all_18_1 & subpopulations(efficient_producers, % 13.87/2.83 | first_movers, all_11_1, all_11_0) = all_18_0 & ( ~ (all_18_1 = 0) | % 13.87/2.83 | all_18_0 = 0) % 13.87/2.83 | % 13.87/2.83 | ALPHA: (31) implies: % 13.87/2.83 | (32) subpopulations(efficient_producers, first_movers, all_11_1, all_11_0) % 13.87/2.83 | = all_18_0 % 13.87/2.83 | (33) environment(all_11_1) = all_18_1 % 13.87/2.83 | (34) ~ (all_18_1 = 0) | all_18_0 = 0 % 13.87/2.83 | % 13.87/2.83 | DELTA: instantiating (26) with fresh symbols all_20_0, all_20_1 gives: % 13.87/2.83 | (35) in_environment(all_11_1, all_11_0) = all_20_0 & environment(all_11_1) % 13.87/2.83 | = all_20_1 & ( ~ (all_20_1 = 0) | all_20_0 = 0) % 13.87/2.83 | % 13.87/2.83 | ALPHA: (35) implies: % 13.87/2.83 | (36) environment(all_11_1) = all_20_1 % 13.87/2.83 | (37) in_environment(all_11_1, all_11_0) = all_20_0 % 13.87/2.83 | (38) ~ (all_20_1 = 0) | all_20_0 = 0 % 13.87/2.83 | % 13.87/2.83 | DELTA: instantiating (29) with fresh symbols all_22_0, all_22_1, all_22_2, % 13.87/2.83 | all_22_3 gives: % 13.87/2.83 | (39) growth_rate(first_movers, all_11_0) = all_22_2 & % 13.87/2.83 | greater_or_equal(all_22_2, zero) = all_22_1 & greater(zero, all_22_2) % 13.87/2.83 | = all_22_0 & environment(all_11_1) = all_22_3 & $i(all_22_2) & ( ~ % 13.87/2.83 | (all_22_0 = 0) | (all_22_3 = 0 & ~ (all_22_1 = 0))) % 13.87/2.83 | % 13.87/2.83 | ALPHA: (39) implies: % 13.87/2.83 | (40) environment(all_11_1) = all_22_3 % 13.87/2.83 | (41) greater(zero, all_22_2) = all_22_0 % 13.87/2.83 | (42) greater_or_equal(all_22_2, zero) = all_22_1 % 13.87/2.84 | (43) growth_rate(first_movers, all_11_0) = all_22_2 % 13.87/2.84 | (44) ~ (all_22_0 = 0) | (all_22_3 = 0 & ~ (all_22_1 = 0)) % 13.87/2.84 | % 13.87/2.84 | DELTA: instantiating (28) with fresh symbols all_24_0, all_24_1, all_24_2, % 13.87/2.84 | all_24_3 gives: % 13.87/2.84 | (45) growth_rate(first_movers, all_11_0) = all_24_3 & % 13.87/2.84 | greater_or_equal(all_24_3, zero) = all_24_0 & greater(zero, all_24_3) % 13.87/2.84 | = all_24_2 & environment(all_11_1) = all_24_1 & $i(all_24_3) & ( ~ % 13.87/2.84 | (all_24_1 = 0) | all_24_0 = 0 | all_24_2 = 0) % 13.87/2.84 | % 13.87/2.84 | ALPHA: (45) implies: % 13.87/2.84 | (46) environment(all_11_1) = all_24_1 % 13.87/2.84 | (47) greater(zero, all_24_3) = all_24_2 % 13.87/2.84 | (48) greater_or_equal(all_24_3, zero) = all_24_0 % 13.87/2.84 | (49) growth_rate(first_movers, all_11_0) = all_24_3 % 13.87/2.84 | % 13.87/2.84 | DELTA: instantiating (30) with fresh symbols all_26_0, all_26_1, all_26_2, % 13.87/2.84 | all_26_3, all_26_4 gives: % 13.87/2.84 | (50) growth_rate(efficient_producers, all_11_0) = all_26_1 & % 13.87/2.84 | growth_rate(first_movers, all_11_0) = all_26_3 & % 13.87/2.84 | greater_or_equal(all_26_3, zero) = all_26_2 & greater(zero, all_26_1) % 13.87/2.84 | = all_26_0 & subpopulations(efficient_producers, first_movers, % 13.87/2.84 | all_11_1, all_11_0) = all_26_4 & $i(all_26_1) & $i(all_26_3) & ( ~ % 13.87/2.84 | (all_26_4 = 0) | (all_26_0 = 0 & all_26_2 = 0)) % 13.87/2.84 | % 13.87/2.84 | ALPHA: (50) implies: % 13.87/2.84 | (51) subpopulations(efficient_producers, first_movers, all_11_1, all_11_0) % 13.87/2.84 | = all_26_4 % 13.87/2.84 | (52) greater(zero, all_26_1) = all_26_0 % 13.87/2.84 | (53) greater_or_equal(all_26_3, zero) = all_26_2 % 13.87/2.84 | (54) growth_rate(first_movers, all_11_0) = all_26_3 % 13.87/2.85 | (55) growth_rate(efficient_producers, all_11_0) = all_26_1 % 13.87/2.85 | (56) ~ (all_26_4 = 0) | (all_26_0 = 0 & all_26_2 = 0) % 13.87/2.85 | % 13.87/2.85 | GROUND_INST: instantiating (15) with all_18_0, all_26_4, all_11_0, all_11_1, % 13.87/2.85 | first_movers, efficient_producers, simplifying with (32), (51) % 13.87/2.85 | gives: % 13.87/2.85 | (57) all_26_4 = all_18_0 % 13.87/2.85 | % 13.87/2.85 | GROUND_INST: instantiating (11) with 0, all_22_3, all_11_1, simplifying with % 13.87/2.85 | (24), (40) gives: % 13.87/2.85 | (58) all_22_3 = 0 % 13.87/2.85 | % 13.87/2.85 | GROUND_INST: instantiating (11) with all_18_1, all_22_3, all_11_1, simplifying % 13.87/2.85 | with (33), (40) gives: % 13.87/2.85 | (59) all_22_3 = all_18_1 % 13.87/2.85 | % 13.87/2.85 | GROUND_INST: instantiating (11) with all_22_3, all_24_1, all_11_1, simplifying % 13.87/2.85 | with (40), (46) gives: % 13.87/2.85 | (60) all_24_1 = all_22_3 % 13.87/2.85 | % 13.87/2.85 | GROUND_INST: instantiating (11) with all_20_1, all_24_1, all_11_1, simplifying % 13.87/2.85 | with (36), (46) gives: % 13.87/2.85 | (61) all_24_1 = all_20_1 % 13.87/2.85 | % 13.87/2.85 | GROUND_INST: instantiating (14) with all_24_3, all_26_3, all_11_0, % 13.87/2.85 | first_movers, simplifying with (49), (54) gives: % 13.87/2.85 | (62) all_26_3 = all_24_3 % 13.87/2.85 | % 13.87/2.85 | GROUND_INST: instantiating (14) with all_22_2, all_26_3, all_11_0, % 13.87/2.85 | first_movers, simplifying with (43), (54) gives: % 13.87/2.85 | (63) all_26_3 = all_22_2 % 13.87/2.85 | % 13.87/2.85 | COMBINE_EQS: (62), (63) imply: % 13.87/2.85 | (64) all_24_3 = all_22_2 % 13.87/2.85 | % 13.87/2.85 | SIMP: (64) implies: % 13.87/2.85 | (65) all_24_3 = all_22_2 % 13.87/2.85 | % 13.87/2.85 | COMBINE_EQS: (60), (61) imply: % 13.87/2.85 | (66) all_22_3 = all_20_1 % 13.87/2.86 | % 13.87/2.86 | SIMP: (66) implies: % 13.87/2.86 | (67) all_22_3 = all_20_1 % 13.87/2.86 | % 13.87/2.86 | COMBINE_EQS: (58), (67) imply: % 13.87/2.86 | (68) all_20_1 = 0 % 13.87/2.86 | % 13.87/2.86 | COMBINE_EQS: (59), (67) imply: % 13.87/2.86 | (69) all_20_1 = all_18_1 % 13.87/2.86 | % 13.87/2.86 | COMBINE_EQS: (68), (69) imply: % 13.87/2.86 | (70) all_18_1 = 0 % 13.87/2.86 | % 13.87/2.86 | REDUCE: (53), (63) imply: % 13.87/2.86 | (71) greater_or_equal(all_22_2, zero) = all_26_2 % 13.87/2.86 | % 13.87/2.86 | REDUCE: (48), (65) imply: % 13.87/2.86 | (72) greater_or_equal(all_22_2, zero) = all_24_0 % 13.87/2.86 | % 13.87/2.86 | REDUCE: (47), (65) imply: % 13.87/2.86 | (73) greater(zero, all_22_2) = all_24_2 % 13.87/2.86 | % 13.87/2.86 | BETA: splitting (34) gives: % 13.87/2.86 | % 13.87/2.86 | Case 1: % 13.87/2.86 | | % 13.87/2.86 | | (74) ~ (all_18_1 = 0) % 13.87/2.86 | | % 13.87/2.86 | | REDUCE: (70), (74) imply: % 13.87/2.86 | | (75) $false % 13.87/2.86 | | % 13.87/2.86 | | CLOSE: (75) is inconsistent. % 13.87/2.86 | | % 13.87/2.86 | Case 2: % 13.87/2.86 | | % 13.87/2.86 | | (76) all_18_0 = 0 % 13.87/2.86 | | % 13.87/2.86 | | COMBINE_EQS: (57), (76) imply: % 13.87/2.86 | | (77) all_26_4 = 0 % 13.87/2.86 | | % 13.87/2.86 | | REDUCE: (32), (76) imply: % 13.87/2.86 | | (78) subpopulations(efficient_producers, first_movers, all_11_1, % 13.87/2.86 | | all_11_0) = 0 % 13.87/2.86 | | % 13.87/2.86 | | BETA: splitting (38) gives: % 13.87/2.86 | | % 13.87/2.86 | | Case 1: % 13.87/2.86 | | | % 13.87/2.87 | | | (79) ~ (all_20_1 = 0) % 13.87/2.87 | | | % 13.87/2.87 | | | REDUCE: (68), (79) imply: % 13.87/2.87 | | | (80) $false % 13.87/2.87 | | | % 13.87/2.87 | | | CLOSE: (80) is inconsistent. % 13.87/2.87 | | | % 13.87/2.87 | | Case 2: % 13.87/2.87 | | | % 13.87/2.87 | | | (81) all_20_0 = 0 % 13.87/2.87 | | | % 13.87/2.87 | | | REDUCE: (37), (81) imply: % 13.87/2.87 | | | (82) in_environment(all_11_1, all_11_0) = 0 % 13.87/2.87 | | | % 13.87/2.87 | | | BETA: splitting (56) gives: % 13.87/2.87 | | | % 13.87/2.87 | | | Case 1: % 13.87/2.87 | | | | % 13.87/2.87 | | | | (83) ~ (all_26_4 = 0) % 13.87/2.87 | | | | % 13.87/2.87 | | | | REDUCE: (77), (83) imply: % 13.87/2.87 | | | | (84) $false % 13.87/2.87 | | | | % 13.87/2.87 | | | | CLOSE: (84) is inconsistent. % 13.87/2.87 | | | | % 13.87/2.87 | | | Case 2: % 13.87/2.87 | | | | % 13.87/2.87 | | | | (85) all_26_0 = 0 & all_26_2 = 0 % 13.87/2.87 | | | | % 13.87/2.87 | | | | ALPHA: (85) implies: % 13.87/2.87 | | | | (86) all_26_2 = 0 % 13.87/2.87 | | | | (87) all_26_0 = 0 % 13.87/2.87 | | | | % 13.87/2.87 | | | | REDUCE: (71), (86) imply: % 13.87/2.87 | | | | (88) greater_or_equal(all_22_2, zero) = 0 % 13.87/2.87 | | | | % 13.87/2.87 | | | | REDUCE: (52), (87) imply: % 13.87/2.87 | | | | (89) greater(zero, all_26_1) = 0 % 13.87/2.87 | | | | % 13.87/2.87 | | | | GROUND_INST: instantiating (12) with all_22_0, all_24_2, all_22_2, zero, % 13.87/2.87 | | | | simplifying with (41), (73) gives: % 13.87/2.87 | | | | (90) all_24_2 = all_22_0 % 13.87/2.87 | | | | % 13.87/2.87 | | | | GROUND_INST: instantiating (13) with all_22_1, all_24_0, zero, all_22_2, % 13.87/2.87 | | | | simplifying with (42), (72) gives: % 13.87/2.87 | | | | (91) all_24_0 = all_22_1 % 13.87/2.87 | | | | % 13.87/2.87 | | | | GROUND_INST: instantiating (13) with 0, all_24_0, zero, all_22_2, % 13.87/2.87 | | | | simplifying with (72), (88) gives: % 13.87/2.87 | | | | (92) all_24_0 = 0 % 13.87/2.87 | | | | % 13.87/2.87 | | | | COMBINE_EQS: (91), (92) imply: % 13.87/2.87 | | | | (93) all_22_1 = 0 % 13.87/2.87 | | | | % 13.87/2.87 | | | | SIMP: (93) implies: % 13.87/2.87 | | | | (94) all_22_1 = 0 % 13.87/2.87 | | | | % 13.87/2.87 | | | | BETA: splitting (44) gives: % 13.87/2.87 | | | | % 13.87/2.87 | | | | Case 1: % 13.87/2.87 | | | | | % 13.87/2.88 | | | | | (95) ~ (all_22_0 = 0) % 13.87/2.88 | | | | | % 13.87/2.88 | | | | | GROUND_INST: instantiating (3) with all_11_1, efficient_producers, % 13.87/2.88 | | | | | first_movers, all_11_0, simplifying with (8), (9), (21), % 13.87/2.88 | | | | | (22), (78) gives: % 13.87/2.88 | | | | | (96) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 13.87/2.88 | | | | | (growth_rate(efficient_producers, all_11_0) = v0 & % 13.87/2.88 | | | | | greater_or_equal(v0, zero) = v3 & greater(zero, v0) = v1 & % 13.87/2.88 | | | | | environment(all_11_1) = v2 & $i(v0) & ( ~ (v2 = 0) | v3 = 0 % 13.87/2.88 | | | | | | v1 = 0)) % 13.87/2.88 | | | | | % 13.87/2.88 | | | | | GROUND_INST: instantiating (4) with all_11_1, efficient_producers, % 13.87/2.88 | | | | | first_movers, all_11_0, 0, simplifying with (8), (9), % 13.87/2.88 | | | | | (21), (22), (78) gives: % 13.87/2.88 | | | | | (97) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : % 13.87/2.88 | | | | | (growth_rate(efficient_producers, all_11_0) = v1 & % 13.87/2.88 | | | | | greater_or_equal(v1, zero) = v2 & greater(zero, v1) = v3 & % 13.87/2.88 | | | | | environment(all_11_1) = v0 & $i(v1) & ( ~ (v3 = 0) | (v0 = 0 % 13.87/2.88 | | | | | & ~ (v2 = 0)))) % 13.87/2.88 | | | | | % 13.87/2.88 | | | | | GROUND_INST: instantiating (6) with all_11_1, first_movers, % 13.87/2.88 | | | | | efficient_producers, all_11_0, all_9_1, all_9_0, % 13.87/2.88 | | | | | simplifying with (8), (9), (17), (18), (19), (21), (22), % 13.87/2.88 | | | | | (82) gives: % 13.87/2.89 | | | | | (98) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? % 13.87/2.89 | | | | | [v4: any] : (growth_rate(efficient_producers, all_11_0) = v3 & % 13.87/2.89 | | | | | growth_rate(first_movers, all_11_0) = v1 & greater(zero, v3) % 13.87/2.89 | | | | | = v4 & greater(zero, v1) = v2 & environment(all_11_1) = v0 & % 13.87/2.89 | | | | | $i(v3) & $i(v1) & ( ~ (v4 = 0) | ~ (v0 = 0) | v2 = 0)) % 13.87/2.89 | | | | | % 13.87/2.89 | | | | | DELTA: instantiating (97) with fresh symbols all_57_0, all_57_1, % 13.87/2.89 | | | | | all_57_2, all_57_3 gives: % 13.87/2.89 | | | | | (99) growth_rate(efficient_producers, all_11_0) = all_57_2 & % 13.87/2.89 | | | | | greater_or_equal(all_57_2, zero) = all_57_1 & greater(zero, % 13.87/2.89 | | | | | all_57_2) = all_57_0 & environment(all_11_1) = all_57_3 & % 13.87/2.89 | | | | | $i(all_57_2) & ( ~ (all_57_0 = 0) | (all_57_3 = 0 & ~ % 13.87/2.89 | | | | | (all_57_1 = 0))) % 13.87/2.89 | | | | | % 13.87/2.89 | | | | | ALPHA: (99) implies: % 13.87/2.89 | | | | | (100) greater(zero, all_57_2) = all_57_0 % 13.87/2.89 | | | | | (101) growth_rate(efficient_producers, all_11_0) = all_57_2 % 13.87/2.89 | | | | | % 13.87/2.89 | | | | | DELTA: instantiating (96) with fresh symbols all_59_0, all_59_1, % 13.87/2.89 | | | | | all_59_2, all_59_3 gives: % 13.87/2.89 | | | | | (102) growth_rate(efficient_producers, all_11_0) = all_59_3 & % 13.87/2.89 | | | | | greater_or_equal(all_59_3, zero) = all_59_0 & greater(zero, % 13.87/2.89 | | | | | all_59_3) = all_59_2 & environment(all_11_1) = all_59_1 & % 13.87/2.89 | | | | | $i(all_59_3) & ( ~ (all_59_1 = 0) | all_59_0 = 0 | all_59_2 = % 13.87/2.89 | | | | | 0) % 13.87/2.89 | | | | | % 13.87/2.89 | | | | | ALPHA: (102) implies: % 13.87/2.89 | | | | | (103) greater(zero, all_59_3) = all_59_2 % 13.87/2.89 | | | | | (104) growth_rate(efficient_producers, all_11_0) = all_59_3 % 13.87/2.89 | | | | | % 13.87/2.89 | | | | | DELTA: instantiating (98) with fresh symbols all_61_0, all_61_1, % 13.87/2.89 | | | | | all_61_2, all_61_3, all_61_4 gives: % 13.87/2.89 | | | | | (105) growth_rate(efficient_producers, all_11_0) = all_61_1 & % 13.87/2.89 | | | | | growth_rate(first_movers, all_11_0) = all_61_3 & % 13.87/2.89 | | | | | greater(zero, all_61_1) = all_61_0 & greater(zero, all_61_3) % 13.87/2.89 | | | | | = all_61_2 & environment(all_11_1) = all_61_4 & $i(all_61_1) % 13.87/2.89 | | | | | & $i(all_61_3) & ( ~ (all_61_0 = 0) | ~ (all_61_4 = 0) | % 13.87/2.89 | | | | | all_61_2 = 0) % 13.87/2.89 | | | | | % 13.87/2.89 | | | | | ALPHA: (105) implies: % 13.87/2.89 | | | | | (106) environment(all_11_1) = all_61_4 % 13.87/2.90 | | | | | (107) greater(zero, all_61_3) = all_61_2 % 13.87/2.90 | | | | | (108) greater(zero, all_61_1) = all_61_0 % 13.87/2.90 | | | | | (109) growth_rate(first_movers, all_11_0) = all_61_3 % 13.87/2.90 | | | | | (110) growth_rate(efficient_producers, all_11_0) = all_61_1 % 14.37/2.90 | | | | | (111) ~ (all_61_0 = 0) | ~ (all_61_4 = 0) | all_61_2 = 0 % 14.37/2.90 | | | | | % 14.37/2.90 | | | | | GROUND_INST: instantiating (11) with 0, all_61_4, all_11_1, % 14.37/2.90 | | | | | simplifying with (24), (106) gives: % 14.37/2.90 | | | | | (112) all_61_4 = 0 % 14.37/2.90 | | | | | % 14.37/2.90 | | | | | GROUND_INST: instantiating (14) with all_22_2, all_61_3, all_11_0, % 14.37/2.90 | | | | | first_movers, simplifying with (43), (109) gives: % 14.37/2.90 | | | | | (113) all_61_3 = all_22_2 % 14.37/2.90 | | | | | % 14.37/2.90 | | | | | GROUND_INST: instantiating (14) with all_26_1, all_59_3, all_11_0, % 14.37/2.90 | | | | | efficient_producers, simplifying with (55), (104) gives: % 14.37/2.90 | | | | | (114) all_59_3 = all_26_1 % 14.37/2.90 | | | | | % 14.37/2.90 | | | | | GROUND_INST: instantiating (14) with all_59_3, all_61_1, all_11_0, % 14.37/2.90 | | | | | efficient_producers, simplifying with (104), (110) gives: % 14.37/2.90 | | | | | (115) all_61_1 = all_59_3 % 14.37/2.90 | | | | | % 14.37/2.90 | | | | | GROUND_INST: instantiating (14) with all_57_2, all_61_1, all_11_0, % 14.37/2.90 | | | | | efficient_producers, simplifying with (101), (110) gives: % 14.37/2.90 | | | | | (116) all_61_1 = all_57_2 % 14.37/2.90 | | | | | % 14.37/2.90 | | | | | COMBINE_EQS: (115), (116) imply: % 14.37/2.90 | | | | | (117) all_59_3 = all_57_2 % 14.37/2.90 | | | | | % 14.37/2.90 | | | | | SIMP: (117) implies: % 14.37/2.90 | | | | | (118) all_59_3 = all_57_2 % 14.37/2.90 | | | | | % 14.37/2.90 | | | | | COMBINE_EQS: (114), (118) imply: % 14.37/2.90 | | | | | (119) all_57_2 = all_26_1 % 14.37/2.90 | | | | | % 14.37/2.90 | | | | | COMBINE_EQS: (116), (119) imply: % 14.37/2.90 | | | | | (120) all_61_1 = all_26_1 % 14.37/2.90 | | | | | % 14.37/2.90 | | | | | REDUCE: (108), (120) imply: % 14.37/2.90 | | | | | (121) greater(zero, all_26_1) = all_61_0 % 14.37/2.90 | | | | | % 14.37/2.90 | | | | | REDUCE: (107), (113) imply: % 14.37/2.90 | | | | | (122) greater(zero, all_22_2) = all_61_2 % 14.37/2.90 | | | | | % 14.37/2.90 | | | | | REDUCE: (103), (114) imply: % 14.37/2.90 | | | | | (123) greater(zero, all_26_1) = all_59_2 % 14.37/2.90 | | | | | % 14.37/2.90 | | | | | REDUCE: (100), (119) imply: % 14.37/2.91 | | | | | (124) greater(zero, all_26_1) = all_57_0 % 14.37/2.91 | | | | | % 14.37/2.91 | | | | | GROUND_INST: instantiating (12) with all_22_0, all_61_2, all_22_2, % 14.37/2.91 | | | | | zero, simplifying with (41), (122) gives: % 14.37/2.91 | | | | | (125) all_61_2 = all_22_0 % 14.37/2.91 | | | | | % 14.37/2.91 | | | | | GROUND_INST: instantiating (12) with 0, all_59_2, all_26_1, zero, % 14.37/2.91 | | | | | simplifying with (89), (123) gives: % 14.37/2.91 | | | | | (126) all_59_2 = 0 % 14.37/2.91 | | | | | % 14.37/2.91 | | | | | GROUND_INST: instantiating (12) with all_59_2, all_61_0, all_26_1, % 14.37/2.91 | | | | | zero, simplifying with (121), (123) gives: % 14.37/2.91 | | | | | (127) all_61_0 = all_59_2 % 14.37/2.91 | | | | | % 14.37/2.91 | | | | | GROUND_INST: instantiating (12) with all_57_0, all_61_0, all_26_1, % 14.37/2.91 | | | | | zero, simplifying with (121), (124) gives: % 14.37/2.91 | | | | | (128) all_61_0 = all_57_0 % 14.37/2.91 | | | | | % 14.37/2.91 | | | | | COMBINE_EQS: (127), (128) imply: % 14.37/2.91 | | | | | (129) all_59_2 = all_57_0 % 14.37/2.91 | | | | | % 14.37/2.91 | | | | | SIMP: (129) implies: % 14.37/2.91 | | | | | (130) all_59_2 = all_57_0 % 14.37/2.91 | | | | | % 14.37/2.91 | | | | | COMBINE_EQS: (126), (130) imply: % 14.37/2.91 | | | | | (131) all_57_0 = 0 % 14.37/2.91 | | | | | % 14.37/2.91 | | | | | COMBINE_EQS: (128), (131) imply: % 14.37/2.91 | | | | | (132) all_61_0 = 0 % 14.37/2.91 | | | | | % 14.37/2.91 | | | | | BETA: splitting (111) gives: % 14.37/2.91 | | | | | % 14.37/2.91 | | | | | Case 1: % 14.37/2.91 | | | | | | % 14.37/2.91 | | | | | | (133) ~ (all_61_0 = 0) % 14.37/2.91 | | | | | | % 14.37/2.91 | | | | | | REDUCE: (132), (133) imply: % 14.37/2.91 | | | | | | (134) $false % 14.37/2.91 | | | | | | % 14.37/2.91 | | | | | | CLOSE: (134) is inconsistent. % 14.37/2.91 | | | | | | % 14.37/2.91 | | | | | Case 2: % 14.37/2.91 | | | | | | % 14.37/2.91 | | | | | | (135) ~ (all_61_4 = 0) | all_61_2 = 0 % 14.37/2.91 | | | | | | % 14.37/2.91 | | | | | | BETA: splitting (135) gives: % 14.37/2.91 | | | | | | % 14.37/2.91 | | | | | | Case 1: % 14.37/2.91 | | | | | | | % 14.37/2.91 | | | | | | | (136) ~ (all_61_4 = 0) % 14.37/2.91 | | | | | | | % 14.37/2.91 | | | | | | | REDUCE: (112), (136) imply: % 14.37/2.91 | | | | | | | (137) $false % 14.37/2.91 | | | | | | | % 14.37/2.91 | | | | | | | CLOSE: (137) is inconsistent. % 14.37/2.91 | | | | | | | % 14.37/2.91 | | | | | | Case 2: % 14.37/2.91 | | | | | | | % 14.37/2.91 | | | | | | | (138) all_61_2 = 0 % 14.37/2.91 | | | | | | | % 14.37/2.91 | | | | | | | COMBINE_EQS: (125), (138) imply: % 14.37/2.91 | | | | | | | (139) all_22_0 = 0 % 14.37/2.91 | | | | | | | % 14.37/2.91 | | | | | | | REDUCE: (95), (139) imply: % 14.37/2.91 | | | | | | | (140) $false % 14.37/2.91 | | | | | | | % 14.37/2.91 | | | | | | | CLOSE: (140) is inconsistent. % 14.37/2.91 | | | | | | | % 14.37/2.91 | | | | | | End of split % 14.37/2.91 | | | | | | % 14.37/2.91 | | | | | End of split % 14.37/2.91 | | | | | % 14.37/2.92 | | | | Case 2: % 14.37/2.92 | | | | | % 14.37/2.92 | | | | | (141) all_22_3 = 0 & ~ (all_22_1 = 0) % 14.37/2.92 | | | | | % 14.37/2.92 | | | | | ALPHA: (141) implies: % 14.37/2.92 | | | | | (142) ~ (all_22_1 = 0) % 14.37/2.92 | | | | | % 14.37/2.92 | | | | | REDUCE: (94), (142) imply: % 14.37/2.92 | | | | | (143) $false % 14.37/2.92 | | | | | % 14.37/2.92 | | | | | CLOSE: (143) is inconsistent. % 14.37/2.92 | | | | | % 14.37/2.92 | | | | End of split % 14.37/2.92 | | | | % 14.37/2.92 | | | End of split % 14.37/2.92 | | | % 14.37/2.92 | | End of split % 14.37/2.92 | | % 14.37/2.92 | End of split % 14.37/2.92 | % 14.37/2.92 End of proof % 14.37/2.92 % SZS output end Proof for theBenchmark % 14.37/2.92 % 14.37/2.92 2202ms %------------------------------------------------------------------------------