%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT036+2 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n012.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 4.84s 1.20s % Output : Proof 7.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.01 % Problem : MGT036+2 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.02 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.03/0.29 % Computer : n012.cluster.edu % 0.03/0.29 % Model : x86_64 x86_64 % 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.03/0.29 % Memory : 8046.5625MB % 0.03/0.29 % OS : Linux 6.8.0-71-generic % 0.03/0.30 % CPULimit : 300 % 0.03/0.30 % WCLimit : 300 % 0.03/0.30 % DateTime : Mon Sep 7 12:40:56 UTC 2026 % 0.03/0.30 % CPUTime : % 0.03/0.31 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. % 0.24/0.48 ________ _____ % 0.24/0.48 ___ __ \_________(_)________________________________ % 0.24/0.48 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.24/0.48 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.24/0.48 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.24/0.48 % 0.24/0.48 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.24/0.48 (2023-06-19) % 0.24/0.48 % 0.24/0.48 (c) Philipp Rümmer, 2009-2023 % 0.24/0.48 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.24/0.48 Amanda Stjerna. % 0.24/0.48 Free software under BSD-3-Clause. % 0.24/0.48 % 0.24/0.48 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.24/0.48 % 0.24/0.48 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.24/0.49 Running up to 7 provers in parallel. % 0.24/0.50 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.24/0.50 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.24/0.50 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.24/0.50 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.24/0.50 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.24/0.50 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.24/0.50 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.01/0.78 Prover 4: Preprocessing ... % 1.01/0.78 Prover 1: Preprocessing ... % 1.76/0.81 Prover 0: Preprocessing ... % 1.76/0.81 Prover 2: Preprocessing ... % 1.76/0.81 Prover 3: Preprocessing ... % 1.76/0.82 Prover 6: Preprocessing ... % 1.76/0.82 Prover 5: Preprocessing ... % 3.48/1.03 Prover 6: Constructing countermodel ... % 3.48/1.03 Prover 1: Constructing countermodel ... % 3.48/1.04 Prover 5: Proving ... % 3.48/1.04 Prover 3: Constructing countermodel ... % 3.48/1.04 Prover 2: Proving ... % 3.48/1.06 Prover 4: Constructing countermodel ... % 3.48/1.09 Prover 0: Proving ... % 4.84/1.20 Prover 3: proved (705ms) % 4.84/1.20 % 4.84/1.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.84/1.20 % 4.84/1.20 Prover 6: stopped % 4.84/1.20 Prover 0: stopped % 4.84/1.20 Prover 2: stopped % 4.84/1.21 Prover 5: stopped % 4.84/1.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.84/1.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.84/1.21 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.84/1.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.84/1.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.84/1.24 Prover 7: Preprocessing ... % 4.84/1.24 Prover 8: Preprocessing ... % 4.84/1.25 Prover 13: Preprocessing ... % 4.84/1.25 Prover 11: Preprocessing ... % 4.84/1.27 Prover 10: Preprocessing ... % 5.63/1.30 Prover 13: Warning: ignoring some quantifiers % 5.63/1.31 Prover 10: Warning: ignoring some quantifiers % 5.63/1.32 Prover 13: Constructing countermodel ... % 5.63/1.32 Prover 10: Constructing countermodel ... % 5.63/1.32 Prover 7: Warning: ignoring some quantifiers % 5.63/1.35 Prover 8: Warning: ignoring some quantifiers % 5.63/1.35 Prover 7: Constructing countermodel ... % 5.63/1.35 Prover 8: Constructing countermodel ... % 5.63/1.38 Prover 10: gave up % 5.63/1.39 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 5.63/1.39 Prover 11: Constructing countermodel ... % 6.41/1.40 Prover 7: gave up % 6.41/1.40 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 6.41/1.41 Prover 16: Preprocessing ... % 6.41/1.42 Prover 13: gave up % 6.41/1.43 Prover 19: Preprocessing ... % 6.41/1.45 Prover 16: Warning: ignoring some quantifiers % 6.41/1.45 Prover 16: Constructing countermodel ... % 6.41/1.46 Prover 1: Found proof (size 113) % 6.41/1.46 Prover 1: proved (966ms) % 6.41/1.46 Prover 11: stopped % 6.41/1.46 Prover 16: stopped % 6.41/1.46 Prover 4: stopped % 6.41/1.46 Prover 8: stopped % 7.10/1.50 Prover 19: Warning: ignoring some quantifiers % 7.10/1.51 Prover 19: Constructing countermodel ... % 7.10/1.51 Prover 19: stopped % 7.10/1.51 % 7.10/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.10/1.51 % 7.10/1.53 % SZS output start Proof for theBenchmark % 7.10/1.54 Assumptions after simplification: % 7.10/1.54 --------------------------------- % 7.10/1.54 % 7.10/1.54 (a13) % 7.10/1.57 $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 7.10/1.57 : ! [v5: $i] : ( ~ (resilience(v2) = v4) | ~ (resilience(v1) = v5) | ~ % 7.10/1.57 (greater(v4, v5) = 0) | ~ (in_environment(v0, v3) = 0) | ~ $i(v3) | ~ % 7.10/1.57 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : % 7.10/1.57 ? [v9: $i] : ? [v10: any] : (growth_rate(v2, v3) = v9 & growth_rate(v1, % 7.10/1.57 v3) = v7 & greater(zero, v9) = v10 & greater(zero, v7) = v8 & % 7.10/1.57 environment(v0) = v6 & $i(v9) & $i(v7) & ( ~ (v10 = 0) | ~ (v6 = 0) | v8 % 7.10/1.57 = 0))) % 7.10/1.57 % 7.10/1.57 (a2) % 7.10/1.57 $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ? [v1: $i] : % 7.10/1.57 (resilience(efficient_producers) = v0 & resilience(first_movers) = v1 & % 7.10/1.57 greater(v0, v1) = 0 & $i(v1) & $i(v0)) % 7.10/1.57 % 7.10/1.57 (d2) % 7.10/1.58 $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 7.10/1.58 any] : ( ~ (outcompetes(v2, v1, v3) = v4) | ~ (environment(v0) = 0) | ~ % 7.10/1.58 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? % 7.10/1.58 [v7: any] : ? [v8: $i] : ? [v9: any] : (growth_rate(v2, v3) = v6 & % 7.10/1.58 growth_rate(v1, v3) = v8 & greater_or_equal(v6, zero) = v7 & greater(zero, % 7.10/1.58 v8) = v9 & subpopulations(v1, v2, v0, v3) = v5 & $i(v8) & $i(v6) & ( ~ % 7.10/1.58 (v5 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v4 = 0) & ( ~ (v4 = 0) | (v9 = % 7.10/1.58 0 & v7 = 0)))))) % 7.10/1.58 % 7.10/1.58 (mp_growth_rate_relationships) % 7.10/1.58 $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 7.10/1.58 any] : ( ~ (subpopulations(v1, v2, v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | % 7.10/1.58 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: % 7.10/1.58 any] : (growth_rate(v1, v3) = v6 & greater_or_equal(v6, zero) = v7 & % 7.10/1.58 greater(zero, v6) = v8 & environment(v0) = v5 & $i(v6) & ( ~ (v8 = 0) | % 7.10/1.58 (v5 = 0 & v4 = 0 & ~ (v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 7.10/1.58 $i] : ! [v3: $i] : ( ~ (subpopulations(v1, v2, v0, v3) = 0) | ~ $i(v3) | % 7.10/1.58 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] % 7.10/1.58 : ? [v7: any] : (growth_rate(v1, v3) = v4 & greater_or_equal(v4, zero) = v7 % 7.10/1.58 & greater(zero, v4) = v5 & environment(v0) = v6 & $i(v4) & ( ~ (v6 = 0) | % 7.10/1.58 v7 = 0 | v5 = 0))) % 7.10/1.58 % 7.10/1.58 (mp_symmetry_of_subpopulations) % 7.10/1.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 7.10/1.58 (subpopulations(v1, v2, v0, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 7.10/1.58 ~ $i(v0) | ? [v4: any] : ? [v5: any] : (environment(v0) = v4 & % 7.10/1.58 subpopulations(v2, v1, v0, v3) = v5 & ( ~ (v4 = 0) | v5 = 0))) % 7.10/1.58 % 7.10/1.58 (mp_time_point_occur) % 7.10/1.58 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : ( ~ % 7.10/1.58 (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ~ $i(v1) % 7.10/1.58 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in_environment(v0, v1) = v3 & % 7.10/1.58 environment(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 7.10/1.58 % 7.10/1.58 (prove_t5) % 7.10/1.59 $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ? [v1: $i] : % 7.10/1.59 (outcompetes(first_movers, efficient_producers, v1) = 0 & environment(v0) = 0 % 7.10/1.59 & subpopulations(first_movers, efficient_producers, v0, v1) = 0 & $i(v1) & % 7.10/1.59 $i(v0)) % 7.10/1.59 % 7.10/1.59 (function-axioms) % 7.10/1.59 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 7.10/1.59 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (subpopulations(v5, v4, % 7.10/1.59 v3, v2) = v1) | ~ (subpopulations(v5, v4, v3, v2) = v0)) & ! [v0: % 7.10/1.59 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 7.10/1.59 : ! [v4: $i] : (v1 = v0 | ~ (outcompetes(v4, v3, v2) = v1) | ~ % 7.10/1.59 (outcompetes(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 7.10/1.59 ! [v3: $i] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, % 7.10/1.59 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 7.10/1.59 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~ % 7.10/1.59 (greater_or_equal(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 7.10/1.59 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, % 7.10/1.59 v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 7.10/1.59 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.10/1.59 (in_environment(v3, v2) = v1) | ~ (in_environment(v3, v2) = v0)) & ! [v0: % 7.10/1.59 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (resilience(v2) = v1) | ~ % 7.10/1.59 (resilience(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 7.10/1.59 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (environment(v2) = v1) | ~ % 7.10/1.59 (environment(v2) = v0)) % 7.10/1.59 % 7.10/1.59 Those formulas are unsatisfiable: % 7.10/1.59 --------------------------------- % 7.10/1.59 % 7.10/1.59 Begin of proof % 7.10/1.59 | % 7.10/1.59 | ALPHA: (mp_time_point_occur) implies: % 7.10/1.59 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subpopulations(first_movers, % 7.10/1.59 | efficient_producers, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 7.10/1.59 | [v2: any] : ? [v3: any] : (in_environment(v0, v1) = v3 & % 7.10/1.59 | environment(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 7.10/1.59 | % 7.10/1.59 | ALPHA: (mp_growth_rate_relationships) implies: % 7.10/1.59 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 7.10/1.59 | (subpopulations(v1, v2, v0, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 7.10/1.59 | $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? % 7.10/1.59 | [v7: any] : (growth_rate(v1, v3) = v4 & greater_or_equal(v4, zero) = % 7.10/1.60 | v7 & greater(zero, v4) = v5 & environment(v0) = v6 & $i(v4) & ( ~ % 7.10/1.60 | (v6 = 0) | v7 = 0 | v5 = 0))) % 7.10/1.60 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 7.10/1.60 | ( ~ (subpopulations(v1, v2, v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 7.10/1.60 | $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? % 7.10/1.60 | [v8: any] : (growth_rate(v1, v3) = v6 & greater_or_equal(v6, zero) = % 7.10/1.60 | v7 & greater(zero, v6) = v8 & environment(v0) = v5 & $i(v6) & ( ~ % 7.10/1.60 | (v8 = 0) | (v5 = 0 & v4 = 0 & ~ (v7 = 0))))) % 7.10/1.60 | % 7.10/1.60 | ALPHA: (d2) implies: % 7.60/1.60 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 7.60/1.60 | ( ~ (outcompetes(v2, v1, v3) = v4) | ~ (environment(v0) = 0) | ~ % 7.60/1.60 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 7.60/1.60 | $i] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : (growth_rate(v2, % 7.60/1.60 | v3) = v6 & growth_rate(v1, v3) = v8 & greater_or_equal(v6, zero) % 7.60/1.60 | = v7 & greater(zero, v8) = v9 & subpopulations(v1, v2, v0, v3) = v5 % 7.60/1.60 | & $i(v8) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v4 % 7.60/1.60 | = 0) & ( ~ (v4 = 0) | (v9 = 0 & v7 = 0)))))) % 7.60/1.60 | % 7.60/1.60 | ALPHA: (a2) implies: % 7.60/1.60 | (5) ? [v0: $i] : ? [v1: $i] : (resilience(efficient_producers) = v0 & % 7.60/1.60 | resilience(first_movers) = v1 & greater(v0, v1) = 0 & $i(v1) & % 7.60/1.60 | $i(v0)) % 7.60/1.60 | % 7.60/1.60 | ALPHA: (a13) implies: % 7.60/1.60 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 7.60/1.60 | ! [v5: $i] : ( ~ (resilience(v2) = v4) | ~ (resilience(v1) = v5) | ~ % 7.60/1.60 | (greater(v4, v5) = 0) | ~ (in_environment(v0, v3) = 0) | ~ $i(v3) | % 7.60/1.60 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? % 7.60/1.60 | [v8: any] : ? [v9: $i] : ? [v10: any] : (growth_rate(v2, v3) = v9 & % 7.60/1.60 | growth_rate(v1, v3) = v7 & greater(zero, v9) = v10 & greater(zero, % 7.60/1.60 | v7) = v8 & environment(v0) = v6 & $i(v9) & $i(v7) & ( ~ (v10 = 0) % 7.60/1.60 | | ~ (v6 = 0) | v8 = 0))) % 7.60/1.60 | % 7.60/1.60 | ALPHA: (prove_t5) implies: % 7.60/1.60 | (7) $i(first_movers) % 7.60/1.60 | (8) $i(efficient_producers) % 7.60/1.60 | (9) ? [v0: $i] : ? [v1: $i] : (outcompetes(first_movers, % 7.60/1.60 | efficient_producers, v1) = 0 & environment(v0) = 0 & % 7.60/1.60 | subpopulations(first_movers, efficient_producers, v0, v1) = 0 & % 7.60/1.60 | $i(v1) & $i(v0)) % 7.60/1.60 | % 7.60/1.60 | ALPHA: (function-axioms) implies: % 7.60/1.60 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 7.60/1.60 | : (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0)) % 7.60/1.60 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 7.60/1.60 | : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, % 7.60/1.60 | v2) = v0)) % 7.60/1.60 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 7.60/1.60 | : ! [v3: $i] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~ % 7.60/1.60 | (greater_or_equal(v3, v2) = v0)) % 7.60/1.61 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.60/1.61 | (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) % 7.60/1.61 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 7.60/1.61 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 7.60/1.61 | (subpopulations(v5, v4, v3, v2) = v1) | ~ (subpopulations(v5, v4, % 7.60/1.61 | v3, v2) = v0)) % 7.60/1.61 | % 7.60/1.61 | DELTA: instantiating (5) with fresh symbols all_9_0, all_9_1 gives: % 7.60/1.61 | (15) resilience(efficient_producers) = all_9_1 & resilience(first_movers) = % 7.60/1.61 | all_9_0 & greater(all_9_1, all_9_0) = 0 & $i(all_9_0) & $i(all_9_1) % 7.60/1.61 | % 7.60/1.61 | ALPHA: (15) implies: % 7.60/1.61 | (16) greater(all_9_1, all_9_0) = 0 % 7.60/1.61 | (17) resilience(first_movers) = all_9_0 % 7.60/1.61 | (18) resilience(efficient_producers) = all_9_1 % 7.60/1.61 | % 7.60/1.61 | DELTA: instantiating (9) with fresh symbols all_11_0, all_11_1 gives: % 7.60/1.61 | (19) outcompetes(first_movers, efficient_producers, all_11_0) = 0 & % 7.60/1.61 | environment(all_11_1) = 0 & subpopulations(first_movers, % 7.60/1.61 | efficient_producers, all_11_1, all_11_0) = 0 & $i(all_11_0) & % 7.60/1.61 | $i(all_11_1) % 7.60/1.61 | % 7.60/1.61 | ALPHA: (19) implies: % 7.60/1.61 | (20) $i(all_11_1) % 7.60/1.61 | (21) $i(all_11_0) % 7.60/1.61 | (22) subpopulations(first_movers, efficient_producers, all_11_1, all_11_0) % 7.60/1.61 | = 0 % 7.60/1.61 | (23) environment(all_11_1) = 0 % 7.60/1.61 | (24) outcompetes(first_movers, efficient_producers, all_11_0) = 0 % 7.60/1.61 | % 7.60/1.61 | GROUND_INST: instantiating (1) with all_11_1, all_11_0, simplifying with (20), % 7.60/1.61 | (21), (22) gives: % 7.60/1.61 | (25) ? [v0: any] : ? [v1: any] : (in_environment(all_11_1, all_11_0) = v1 % 7.60/1.61 | & environment(all_11_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 7.60/1.61 | % 7.60/1.61 | GROUND_INST: instantiating (2) with all_11_1, first_movers, % 7.60/1.61 | efficient_producers, all_11_0, simplifying with (7), (8), (20), % 7.60/1.61 | (21), (22) gives: % 7.60/1.61 | (26) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 7.60/1.61 | (growth_rate(first_movers, all_11_0) = v0 & greater_or_equal(v0, zero) % 7.60/1.61 | = v3 & greater(zero, v0) = v1 & environment(all_11_1) = v2 & $i(v0) % 7.60/1.61 | & ( ~ (v2 = 0) | v3 = 0 | v1 = 0)) % 7.60/1.61 | % 7.60/1.61 | GROUND_INST: instantiating (mp_symmetry_of_subpopulations) with all_11_1, % 7.60/1.61 | first_movers, efficient_producers, all_11_0, simplifying with % 7.60/1.61 | (7), (8), (20), (21), (22) gives: % 7.60/1.61 | (27) ? [v0: any] : ? [v1: any] : (environment(all_11_1) = v0 & % 7.60/1.61 | subpopulations(efficient_producers, first_movers, all_11_1, % 7.60/1.61 | all_11_0) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 7.60/1.61 | % 7.60/1.61 | GROUND_INST: instantiating (3) with all_11_1, first_movers, % 7.60/1.61 | efficient_producers, all_11_0, 0, simplifying with (7), (8), % 7.60/1.61 | (20), (21), (22) gives: % 7.60/1.61 | (28) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : % 7.60/1.61 | (growth_rate(first_movers, all_11_0) = v1 & greater_or_equal(v1, zero) % 7.60/1.61 | = v2 & greater(zero, v1) = v3 & environment(all_11_1) = v0 & $i(v1) % 7.60/1.61 | & ( ~ (v3 = 0) | (v0 = 0 & ~ (v2 = 0)))) % 7.60/1.61 | % 7.60/1.62 | GROUND_INST: instantiating (4) with all_11_1, efficient_producers, % 7.60/1.62 | first_movers, all_11_0, 0, simplifying with (7), (8), (20), (21), % 7.60/1.62 | (23), (24) gives: % 7.60/1.62 | (29) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] % 7.60/1.62 | : (growth_rate(efficient_producers, all_11_0) = v3 & % 7.60/1.62 | growth_rate(first_movers, all_11_0) = v1 & greater_or_equal(v1, % 7.60/1.62 | zero) = v2 & greater(zero, v3) = v4 & % 7.60/1.62 | subpopulations(efficient_producers, first_movers, all_11_1, % 7.60/1.62 | all_11_0) = v0 & $i(v3) & $i(v1) & ( ~ (v0 = 0) | (v4 = 0 & v2 = % 7.60/1.62 | 0))) % 7.60/1.62 | % 7.60/1.62 | DELTA: instantiating (27) with fresh symbols all_18_0, all_18_1 gives: % 7.60/1.62 | (30) environment(all_11_1) = all_18_1 & subpopulations(efficient_producers, % 7.60/1.62 | first_movers, all_11_1, all_11_0) = all_18_0 & ( ~ (all_18_1 = 0) | % 7.60/1.62 | all_18_0 = 0) % 7.60/1.62 | % 7.60/1.62 | ALPHA: (30) implies: % 7.60/1.62 | (31) subpopulations(efficient_producers, first_movers, all_11_1, all_11_0) % 7.60/1.62 | = all_18_0 % 7.60/1.62 | (32) environment(all_11_1) = all_18_1 % 7.60/1.62 | (33) ~ (all_18_1 = 0) | all_18_0 = 0 % 7.60/1.62 | % 7.60/1.62 | DELTA: instantiating (25) with fresh symbols all_20_0, all_20_1 gives: % 7.60/1.62 | (34) in_environment(all_11_1, all_11_0) = all_20_0 & environment(all_11_1) % 7.60/1.62 | = all_20_1 & ( ~ (all_20_1 = 0) | all_20_0 = 0) % 7.60/1.62 | % 7.60/1.62 | ALPHA: (34) implies: % 7.60/1.62 | (35) environment(all_11_1) = all_20_1 % 7.60/1.62 | (36) in_environment(all_11_1, all_11_0) = all_20_0 % 7.60/1.62 | (37) ~ (all_20_1 = 0) | all_20_0 = 0 % 7.60/1.62 | % 7.60/1.62 | DELTA: instantiating (28) with fresh symbols all_22_0, all_22_1, all_22_2, % 7.60/1.62 | all_22_3 gives: % 7.60/1.62 | (38) growth_rate(first_movers, all_11_0) = all_22_2 & % 7.60/1.62 | greater_or_equal(all_22_2, zero) = all_22_1 & greater(zero, all_22_2) % 7.60/1.62 | = all_22_0 & environment(all_11_1) = all_22_3 & $i(all_22_2) & ( ~ % 7.60/1.62 | (all_22_0 = 0) | (all_22_3 = 0 & ~ (all_22_1 = 0))) % 7.60/1.62 | % 7.60/1.62 | ALPHA: (38) implies: % 7.60/1.62 | (39) environment(all_11_1) = all_22_3 % 7.60/1.62 | (40) greater(zero, all_22_2) = all_22_0 % 7.60/1.62 | (41) greater_or_equal(all_22_2, zero) = all_22_1 % 7.60/1.62 | (42) growth_rate(first_movers, all_11_0) = all_22_2 % 7.60/1.62 | (43) ~ (all_22_0 = 0) | (all_22_3 = 0 & ~ (all_22_1 = 0)) % 7.60/1.62 | % 7.60/1.62 | DELTA: instantiating (26) with fresh symbols all_24_0, all_24_1, all_24_2, % 7.60/1.62 | all_24_3 gives: % 7.60/1.62 | (44) growth_rate(first_movers, all_11_0) = all_24_3 & % 7.60/1.62 | greater_or_equal(all_24_3, zero) = all_24_0 & greater(zero, all_24_3) % 7.60/1.62 | = all_24_2 & environment(all_11_1) = all_24_1 & $i(all_24_3) & ( ~ % 7.60/1.62 | (all_24_1 = 0) | all_24_0 = 0 | all_24_2 = 0) % 7.60/1.62 | % 7.60/1.62 | ALPHA: (44) implies: % 7.60/1.62 | (45) environment(all_11_1) = all_24_1 % 7.60/1.62 | (46) greater(zero, all_24_3) = all_24_2 % 7.60/1.62 | (47) greater_or_equal(all_24_3, zero) = all_24_0 % 7.60/1.62 | (48) growth_rate(first_movers, all_11_0) = all_24_3 % 7.60/1.62 | % 7.60/1.62 | DELTA: instantiating (29) with fresh symbols all_26_0, all_26_1, all_26_2, % 7.60/1.62 | all_26_3, all_26_4 gives: % 7.60/1.62 | (49) growth_rate(efficient_producers, all_11_0) = all_26_1 & % 7.60/1.62 | growth_rate(first_movers, all_11_0) = all_26_3 & % 7.60/1.62 | greater_or_equal(all_26_3, zero) = all_26_2 & greater(zero, all_26_1) % 7.60/1.62 | = all_26_0 & subpopulations(efficient_producers, first_movers, % 7.60/1.62 | all_11_1, all_11_0) = all_26_4 & $i(all_26_1) & $i(all_26_3) & ( ~ % 7.60/1.62 | (all_26_4 = 0) | (all_26_0 = 0 & all_26_2 = 0)) % 7.60/1.62 | % 7.60/1.62 | ALPHA: (49) implies: % 7.60/1.63 | (50) subpopulations(efficient_producers, first_movers, all_11_1, all_11_0) % 7.60/1.63 | = all_26_4 % 7.60/1.63 | (51) greater(zero, all_26_1) = all_26_0 % 7.60/1.63 | (52) greater_or_equal(all_26_3, zero) = all_26_2 % 7.60/1.63 | (53) growth_rate(first_movers, all_11_0) = all_26_3 % 7.60/1.63 | (54) growth_rate(efficient_producers, all_11_0) = all_26_1 % 7.60/1.63 | (55) ~ (all_26_4 = 0) | (all_26_0 = 0 & all_26_2 = 0) % 7.60/1.63 | % 7.60/1.63 | GROUND_INST: instantiating (14) with all_18_0, all_26_4, all_11_0, all_11_1, % 7.60/1.63 | first_movers, efficient_producers, simplifying with (31), (50) % 7.60/1.63 | gives: % 7.60/1.63 | (56) all_26_4 = all_18_0 % 7.60/1.63 | % 7.60/1.63 | GROUND_INST: instantiating (10) with 0, all_22_3, all_11_1, simplifying with % 7.60/1.63 | (23), (39) gives: % 7.60/1.63 | (57) all_22_3 = 0 % 7.60/1.63 | % 7.60/1.63 | GROUND_INST: instantiating (10) with all_18_1, all_22_3, all_11_1, simplifying % 7.60/1.63 | with (32), (39) gives: % 7.60/1.63 | (58) all_22_3 = all_18_1 % 7.60/1.63 | % 7.60/1.63 | GROUND_INST: instantiating (10) with all_22_3, all_24_1, all_11_1, simplifying % 7.60/1.63 | with (39), (45) gives: % 7.60/1.63 | (59) all_24_1 = all_22_3 % 7.60/1.63 | % 7.60/1.63 | GROUND_INST: instantiating (10) with all_20_1, all_24_1, all_11_1, simplifying % 7.60/1.63 | with (35), (45) gives: % 7.60/1.63 | (60) all_24_1 = all_20_1 % 7.60/1.63 | % 7.60/1.63 | GROUND_INST: instantiating (13) with all_24_3, all_26_3, all_11_0, % 7.60/1.63 | first_movers, simplifying with (48), (53) gives: % 7.60/1.63 | (61) all_26_3 = all_24_3 % 7.60/1.63 | % 7.60/1.63 | GROUND_INST: instantiating (13) with all_22_2, all_26_3, all_11_0, % 7.60/1.63 | first_movers, simplifying with (42), (53) gives: % 7.60/1.63 | (62) all_26_3 = all_22_2 % 7.60/1.63 | % 7.60/1.63 | COMBINE_EQS: (61), (62) imply: % 7.60/1.63 | (63) all_24_3 = all_22_2 % 7.60/1.63 | % 7.60/1.63 | SIMP: (63) implies: % 7.60/1.63 | (64) all_24_3 = all_22_2 % 7.60/1.63 | % 7.60/1.63 | COMBINE_EQS: (59), (60) imply: % 7.60/1.63 | (65) all_22_3 = all_20_1 % 7.60/1.63 | % 7.60/1.63 | SIMP: (65) implies: % 7.60/1.63 | (66) all_22_3 = all_20_1 % 7.60/1.63 | % 7.60/1.63 | COMBINE_EQS: (57), (66) imply: % 7.60/1.63 | (67) all_20_1 = 0 % 7.60/1.63 | % 7.60/1.63 | COMBINE_EQS: (58), (66) imply: % 7.60/1.63 | (68) all_20_1 = all_18_1 % 7.60/1.63 | % 7.60/1.63 | COMBINE_EQS: (67), (68) imply: % 7.60/1.63 | (69) all_18_1 = 0 % 7.60/1.63 | % 7.60/1.63 | REDUCE: (52), (62) imply: % 7.60/1.63 | (70) greater_or_equal(all_22_2, zero) = all_26_2 % 7.60/1.63 | % 7.60/1.63 | REDUCE: (47), (64) imply: % 7.60/1.63 | (71) greater_or_equal(all_22_2, zero) = all_24_0 % 7.60/1.63 | % 7.60/1.63 | REDUCE: (46), (64) imply: % 7.60/1.63 | (72) greater(zero, all_22_2) = all_24_2 % 7.60/1.63 | % 7.60/1.63 | BETA: splitting (33) gives: % 7.60/1.63 | % 7.60/1.63 | Case 1: % 7.60/1.63 | | % 7.60/1.63 | | (73) ~ (all_18_1 = 0) % 7.60/1.63 | | % 7.60/1.63 | | REDUCE: (69), (73) imply: % 7.60/1.63 | | (74) $false % 7.60/1.63 | | % 7.60/1.63 | | CLOSE: (74) is inconsistent. % 7.60/1.63 | | % 7.60/1.63 | Case 2: % 7.60/1.63 | | % 7.60/1.63 | | (75) all_18_0 = 0 % 7.60/1.63 | | % 7.60/1.63 | | COMBINE_EQS: (56), (75) imply: % 7.60/1.63 | | (76) all_26_4 = 0 % 7.60/1.63 | | % 7.60/1.63 | | REDUCE: (31), (75) imply: % 7.60/1.63 | | (77) subpopulations(efficient_producers, first_movers, all_11_1, % 7.60/1.64 | | all_11_0) = 0 % 7.60/1.64 | | % 7.60/1.64 | | BETA: splitting (37) gives: % 7.60/1.64 | | % 7.60/1.64 | | Case 1: % 7.60/1.64 | | | % 7.60/1.64 | | | (78) ~ (all_20_1 = 0) % 7.60/1.64 | | | % 7.60/1.64 | | | REDUCE: (67), (78) imply: % 7.60/1.64 | | | (79) $false % 7.60/1.64 | | | % 7.60/1.64 | | | CLOSE: (79) is inconsistent. % 7.60/1.64 | | | % 7.60/1.64 | | Case 2: % 7.60/1.64 | | | % 7.60/1.64 | | | (80) all_20_0 = 0 % 7.60/1.64 | | | % 7.60/1.64 | | | REDUCE: (36), (80) imply: % 7.60/1.64 | | | (81) in_environment(all_11_1, all_11_0) = 0 % 7.60/1.64 | | | % 7.60/1.64 | | | BETA: splitting (55) gives: % 7.60/1.64 | | | % 7.60/1.64 | | | Case 1: % 7.60/1.64 | | | | % 7.60/1.64 | | | | (82) ~ (all_26_4 = 0) % 7.60/1.64 | | | | % 7.60/1.64 | | | | REDUCE: (76), (82) imply: % 7.60/1.64 | | | | (83) $false % 7.60/1.64 | | | | % 7.60/1.64 | | | | CLOSE: (83) is inconsistent. % 7.60/1.64 | | | | % 7.60/1.64 | | | Case 2: % 7.60/1.64 | | | | % 7.60/1.64 | | | | (84) all_26_0 = 0 & all_26_2 = 0 % 7.60/1.64 | | | | % 7.60/1.64 | | | | ALPHA: (84) implies: % 7.60/1.64 | | | | (85) all_26_2 = 0 % 7.60/1.64 | | | | (86) all_26_0 = 0 % 7.60/1.64 | | | | % 7.60/1.64 | | | | REDUCE: (70), (85) imply: % 7.60/1.64 | | | | (87) greater_or_equal(all_22_2, zero) = 0 % 7.60/1.64 | | | | % 7.60/1.64 | | | | REDUCE: (51), (86) imply: % 7.60/1.64 | | | | (88) greater(zero, all_26_1) = 0 % 7.60/1.64 | | | | % 7.60/1.64 | | | | GROUND_INST: instantiating (11) with all_22_0, all_24_2, all_22_2, zero, % 7.60/1.64 | | | | simplifying with (40), (72) gives: % 7.60/1.64 | | | | (89) all_24_2 = all_22_0 % 7.60/1.64 | | | | % 7.60/1.64 | | | | GROUND_INST: instantiating (12) with all_22_1, all_24_0, zero, all_22_2, % 7.60/1.64 | | | | simplifying with (41), (71) gives: % 7.60/1.64 | | | | (90) all_24_0 = all_22_1 % 7.60/1.64 | | | | % 7.60/1.64 | | | | GROUND_INST: instantiating (12) with 0, all_24_0, zero, all_22_2, % 7.60/1.64 | | | | simplifying with (71), (87) gives: % 7.60/1.64 | | | | (91) all_24_0 = 0 % 7.60/1.64 | | | | % 7.60/1.64 | | | | COMBINE_EQS: (90), (91) imply: % 7.60/1.64 | | | | (92) all_22_1 = 0 % 7.60/1.64 | | | | % 7.60/1.64 | | | | SIMP: (92) implies: % 7.60/1.64 | | | | (93) all_22_1 = 0 % 7.60/1.64 | | | | % 7.60/1.64 | | | | BETA: splitting (43) gives: % 7.60/1.64 | | | | % 7.60/1.64 | | | | Case 1: % 7.60/1.64 | | | | | % 7.60/1.64 | | | | | (94) ~ (all_22_0 = 0) % 7.60/1.64 | | | | | % 7.60/1.64 | | | | | GROUND_INST: instantiating (2) with all_11_1, efficient_producers, % 7.60/1.64 | | | | | first_movers, all_11_0, simplifying with (7), (8), (20), % 7.60/1.64 | | | | | (21), (77) gives: % 7.60/1.64 | | | | | (95) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 7.60/1.64 | | | | | (growth_rate(efficient_producers, all_11_0) = v0 & % 7.60/1.64 | | | | | greater_or_equal(v0, zero) = v3 & greater(zero, v0) = v1 & % 7.60/1.64 | | | | | environment(all_11_1) = v2 & $i(v0) & ( ~ (v2 = 0) | v3 = 0 % 7.60/1.64 | | | | | | v1 = 0)) % 7.60/1.64 | | | | | % 7.60/1.64 | | | | | GROUND_INST: instantiating (3) with all_11_1, efficient_producers, % 7.60/1.64 | | | | | first_movers, all_11_0, 0, simplifying with (7), (8), % 7.60/1.64 | | | | | (20), (21), (77) gives: % 7.60/1.64 | | | | | (96) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : % 7.60/1.64 | | | | | (growth_rate(efficient_producers, all_11_0) = v1 & % 7.60/1.64 | | | | | greater_or_equal(v1, zero) = v2 & greater(zero, v1) = v3 & % 7.60/1.64 | | | | | environment(all_11_1) = v0 & $i(v1) & ( ~ (v3 = 0) | (v0 = 0 % 7.60/1.64 | | | | | & ~ (v2 = 0)))) % 7.60/1.64 | | | | | % 7.60/1.64 | | | | | GROUND_INST: instantiating (6) with all_11_1, first_movers, % 7.60/1.64 | | | | | efficient_producers, all_11_0, all_9_1, all_9_0, % 7.60/1.64 | | | | | simplifying with (7), (8), (16), (17), (18), (20), (21), % 7.60/1.64 | | | | | (81) gives: % 7.60/1.65 | | | | | (97) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? % 7.60/1.65 | | | | | [v4: any] : (growth_rate(efficient_producers, all_11_0) = v3 & % 7.60/1.65 | | | | | growth_rate(first_movers, all_11_0) = v1 & greater(zero, v3) % 7.60/1.65 | | | | | = v4 & greater(zero, v1) = v2 & environment(all_11_1) = v0 & % 7.60/1.65 | | | | | $i(v3) & $i(v1) & ( ~ (v4 = 0) | ~ (v0 = 0) | v2 = 0)) % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | DELTA: instantiating (96) with fresh symbols all_57_0, all_57_1, % 7.60/1.65 | | | | | all_57_2, all_57_3 gives: % 7.60/1.65 | | | | | (98) growth_rate(efficient_producers, all_11_0) = all_57_2 & % 7.60/1.65 | | | | | greater_or_equal(all_57_2, zero) = all_57_1 & greater(zero, % 7.60/1.65 | | | | | all_57_2) = all_57_0 & environment(all_11_1) = all_57_3 & % 7.60/1.65 | | | | | $i(all_57_2) & ( ~ (all_57_0 = 0) | (all_57_3 = 0 & ~ % 7.60/1.65 | | | | | (all_57_1 = 0))) % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | ALPHA: (98) implies: % 7.60/1.65 | | | | | (99) greater(zero, all_57_2) = all_57_0 % 7.60/1.65 | | | | | (100) growth_rate(efficient_producers, all_11_0) = all_57_2 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | DELTA: instantiating (95) with fresh symbols all_59_0, all_59_1, % 7.60/1.65 | | | | | all_59_2, all_59_3 gives: % 7.60/1.65 | | | | | (101) growth_rate(efficient_producers, all_11_0) = all_59_3 & % 7.60/1.65 | | | | | greater_or_equal(all_59_3, zero) = all_59_0 & greater(zero, % 7.60/1.65 | | | | | all_59_3) = all_59_2 & environment(all_11_1) = all_59_1 & % 7.60/1.65 | | | | | $i(all_59_3) & ( ~ (all_59_1 = 0) | all_59_0 = 0 | all_59_2 = % 7.60/1.65 | | | | | 0) % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | ALPHA: (101) implies: % 7.60/1.65 | | | | | (102) greater(zero, all_59_3) = all_59_2 % 7.60/1.65 | | | | | (103) growth_rate(efficient_producers, all_11_0) = all_59_3 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | DELTA: instantiating (97) with fresh symbols all_61_0, all_61_1, % 7.60/1.65 | | | | | all_61_2, all_61_3, all_61_4 gives: % 7.60/1.65 | | | | | (104) growth_rate(efficient_producers, all_11_0) = all_61_1 & % 7.60/1.65 | | | | | growth_rate(first_movers, all_11_0) = all_61_3 & % 7.60/1.65 | | | | | greater(zero, all_61_1) = all_61_0 & greater(zero, all_61_3) % 7.60/1.65 | | | | | = all_61_2 & environment(all_11_1) = all_61_4 & $i(all_61_1) % 7.60/1.65 | | | | | & $i(all_61_3) & ( ~ (all_61_0 = 0) | ~ (all_61_4 = 0) | % 7.60/1.65 | | | | | all_61_2 = 0) % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | ALPHA: (104) implies: % 7.60/1.65 | | | | | (105) environment(all_11_1) = all_61_4 % 7.60/1.65 | | | | | (106) greater(zero, all_61_3) = all_61_2 % 7.60/1.65 | | | | | (107) greater(zero, all_61_1) = all_61_0 % 7.60/1.65 | | | | | (108) growth_rate(first_movers, all_11_0) = all_61_3 % 7.60/1.65 | | | | | (109) growth_rate(efficient_producers, all_11_0) = all_61_1 % 7.60/1.65 | | | | | (110) ~ (all_61_0 = 0) | ~ (all_61_4 = 0) | all_61_2 = 0 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | GROUND_INST: instantiating (10) with 0, all_61_4, all_11_1, % 7.60/1.65 | | | | | simplifying with (23), (105) gives: % 7.60/1.65 | | | | | (111) all_61_4 = 0 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | GROUND_INST: instantiating (13) with all_22_2, all_61_3, all_11_0, % 7.60/1.65 | | | | | first_movers, simplifying with (42), (108) gives: % 7.60/1.65 | | | | | (112) all_61_3 = all_22_2 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | GROUND_INST: instantiating (13) with all_26_1, all_59_3, all_11_0, % 7.60/1.65 | | | | | efficient_producers, simplifying with (54), (103) gives: % 7.60/1.65 | | | | | (113) all_59_3 = all_26_1 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | GROUND_INST: instantiating (13) with all_59_3, all_61_1, all_11_0, % 7.60/1.65 | | | | | efficient_producers, simplifying with (103), (109) gives: % 7.60/1.65 | | | | | (114) all_61_1 = all_59_3 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | GROUND_INST: instantiating (13) with all_57_2, all_61_1, all_11_0, % 7.60/1.65 | | | | | efficient_producers, simplifying with (100), (109) gives: % 7.60/1.65 | | | | | (115) all_61_1 = all_57_2 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | COMBINE_EQS: (114), (115) imply: % 7.60/1.65 | | | | | (116) all_59_3 = all_57_2 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | SIMP: (116) implies: % 7.60/1.65 | | | | | (117) all_59_3 = all_57_2 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | COMBINE_EQS: (113), (117) imply: % 7.60/1.65 | | | | | (118) all_57_2 = all_26_1 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | COMBINE_EQS: (115), (118) imply: % 7.60/1.65 | | | | | (119) all_61_1 = all_26_1 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | REDUCE: (107), (119) imply: % 7.60/1.65 | | | | | (120) greater(zero, all_26_1) = all_61_0 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | REDUCE: (106), (112) imply: % 7.60/1.65 | | | | | (121) greater(zero, all_22_2) = all_61_2 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | REDUCE: (102), (113) imply: % 7.60/1.65 | | | | | (122) greater(zero, all_26_1) = all_59_2 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | REDUCE: (99), (118) imply: % 7.60/1.65 | | | | | (123) greater(zero, all_26_1) = all_57_0 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | GROUND_INST: instantiating (11) with all_22_0, all_61_2, all_22_2, % 7.60/1.65 | | | | | zero, simplifying with (40), (121) gives: % 7.60/1.65 | | | | | (124) all_61_2 = all_22_0 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | GROUND_INST: instantiating (11) with 0, all_59_2, all_26_1, zero, % 7.60/1.65 | | | | | simplifying with (88), (122) gives: % 7.60/1.65 | | | | | (125) all_59_2 = 0 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | GROUND_INST: instantiating (11) with all_59_2, all_61_0, all_26_1, % 7.60/1.65 | | | | | zero, simplifying with (120), (122) gives: % 7.60/1.65 | | | | | (126) all_61_0 = all_59_2 % 7.60/1.65 | | | | | % 7.60/1.65 | | | | | GROUND_INST: instantiating (11) with all_57_0, all_61_0, all_26_1, % 7.60/1.65 | | | | | zero, simplifying with (120), (123) gives: % 7.60/1.65 | | | | | (127) all_61_0 = all_57_0 % 7.60/1.65 | | | | | % 7.60/1.66 | | | | | COMBINE_EQS: (126), (127) imply: % 7.60/1.66 | | | | | (128) all_59_2 = all_57_0 % 7.60/1.66 | | | | | % 7.60/1.66 | | | | | SIMP: (128) implies: % 7.60/1.66 | | | | | (129) all_59_2 = all_57_0 % 7.60/1.66 | | | | | % 7.60/1.66 | | | | | COMBINE_EQS: (125), (129) imply: % 7.60/1.66 | | | | | (130) all_57_0 = 0 % 7.60/1.66 | | | | | % 7.60/1.66 | | | | | COMBINE_EQS: (127), (130) imply: % 7.60/1.66 | | | | | (131) all_61_0 = 0 % 7.60/1.66 | | | | | % 7.60/1.66 | | | | | BETA: splitting (110) gives: % 7.60/1.66 | | | | | % 7.60/1.66 | | | | | Case 1: % 7.60/1.66 | | | | | | % 7.60/1.66 | | | | | | (132) ~ (all_61_0 = 0) % 7.60/1.66 | | | | | | % 7.60/1.66 | | | | | | REDUCE: (131), (132) imply: % 7.60/1.66 | | | | | | (133) $false % 7.60/1.66 | | | | | | % 7.60/1.66 | | | | | | CLOSE: (133) is inconsistent. % 7.60/1.66 | | | | | | % 7.60/1.66 | | | | | Case 2: % 7.60/1.66 | | | | | | % 7.60/1.66 | | | | | | (134) ~ (all_61_4 = 0) | all_61_2 = 0 % 7.60/1.66 | | | | | | % 7.60/1.66 | | | | | | BETA: splitting (134) gives: % 7.60/1.66 | | | | | | % 7.60/1.66 | | | | | | Case 1: % 7.60/1.66 | | | | | | | % 7.60/1.66 | | | | | | | (135) ~ (all_61_4 = 0) % 7.60/1.66 | | | | | | | % 7.60/1.66 | | | | | | | REDUCE: (111), (135) imply: % 7.60/1.66 | | | | | | | (136) $false % 7.60/1.66 | | | | | | | % 7.60/1.66 | | | | | | | CLOSE: (136) is inconsistent. % 7.60/1.66 | | | | | | | % 7.60/1.66 | | | | | | Case 2: % 7.60/1.66 | | | | | | | % 7.60/1.66 | | | | | | | (137) all_61_2 = 0 % 7.60/1.66 | | | | | | | % 7.60/1.66 | | | | | | | COMBINE_EQS: (124), (137) imply: % 7.60/1.66 | | | | | | | (138) all_22_0 = 0 % 7.60/1.66 | | | | | | | % 7.60/1.66 | | | | | | | REDUCE: (94), (138) imply: % 7.60/1.66 | | | | | | | (139) $false % 7.60/1.66 | | | | | | | % 7.60/1.66 | | | | | | | CLOSE: (139) is inconsistent. % 7.60/1.66 | | | | | | | % 7.60/1.66 | | | | | | End of split % 7.60/1.66 | | | | | | % 7.60/1.66 | | | | | End of split % 7.60/1.66 | | | | | % 7.60/1.66 | | | | Case 2: % 7.60/1.66 | | | | | % 7.60/1.66 | | | | | (140) all_22_3 = 0 & ~ (all_22_1 = 0) % 7.60/1.66 | | | | | % 7.60/1.66 | | | | | ALPHA: (140) implies: % 7.60/1.66 | | | | | (141) ~ (all_22_1 = 0) % 7.60/1.66 | | | | | % 7.60/1.66 | | | | | REDUCE: (93), (141) imply: % 7.60/1.66 | | | | | (142) $false % 7.60/1.66 | | | | | % 7.60/1.66 | | | | | CLOSE: (142) is inconsistent. % 7.60/1.66 | | | | | % 7.60/1.66 | | | | End of split % 7.60/1.66 | | | | % 7.60/1.66 | | | End of split % 7.60/1.66 | | | % 7.60/1.66 | | End of split % 7.60/1.66 | | % 7.60/1.66 | End of split % 7.60/1.66 | % 7.60/1.66 End of proof % 7.60/1.66 % SZS output end Proof for theBenchmark % 7.60/1.66 % 7.60/1.66 1179ms %------------------------------------------------------------------------------