TSTP Solution File: MGT036+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : MGT036+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 09:16:21 EDT 2023
% Result : Theorem 7.33s 1.90s
% Output : Proof 11.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT036+1 : TPTP v8.1.2. Released v2.0.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Aug 28 06:17:51 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.18/0.63 ________ _____
% 0.18/0.63 ___ __ \_________(_)________________________________
% 0.18/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.63
% 0.18/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.63 (2023-06-19)
% 0.18/0.63
% 0.18/0.63 (c) Philipp Rümmer, 2009-2023
% 0.18/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.63 Amanda Stjerna.
% 0.18/0.63 Free software under BSD-3-Clause.
% 0.18/0.63
% 0.18/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.63
% 0.18/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.65 Running up to 7 provers in parallel.
% 0.18/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.23/1.14 Prover 1: Preprocessing ...
% 2.23/1.14 Prover 4: Preprocessing ...
% 2.72/1.21 Prover 5: Preprocessing ...
% 2.72/1.21 Prover 0: Preprocessing ...
% 2.72/1.21 Prover 3: Preprocessing ...
% 2.72/1.21 Prover 6: Preprocessing ...
% 2.72/1.21 Prover 2: Preprocessing ...
% 4.82/1.56 Prover 6: Constructing countermodel ...
% 4.82/1.56 Prover 3: Constructing countermodel ...
% 5.35/1.58 Prover 2: Proving ...
% 5.35/1.59 Prover 5: Proving ...
% 5.35/1.60 Prover 1: Constructing countermodel ...
% 5.35/1.62 Prover 4: Constructing countermodel ...
% 6.00/1.69 Prover 0: Proving ...
% 7.33/1.90 Prover 6: proved (1224ms)
% 7.33/1.90
% 7.33/1.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.33/1.90
% 7.33/1.90 Prover 5: stopped
% 7.33/1.90 Prover 0: stopped
% 7.33/1.91 Prover 2: stopped
% 7.33/1.91 Prover 3: proved (1227ms)
% 7.33/1.91
% 7.33/1.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.33/1.91
% 7.33/1.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.33/1.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.33/1.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.33/1.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.33/1.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.33/1.95 Prover 10: Preprocessing ...
% 7.33/1.95 Prover 7: Preprocessing ...
% 7.33/1.96 Prover 8: Preprocessing ...
% 7.33/1.97 Prover 13: Preprocessing ...
% 8.03/1.98 Prover 11: Preprocessing ...
% 8.22/2.00 Prover 10: Warning: ignoring some quantifiers
% 8.22/2.01 Prover 7: Warning: ignoring some quantifiers
% 8.22/2.01 Prover 10: Constructing countermodel ...
% 8.22/2.03 Prover 7: Constructing countermodel ...
% 8.22/2.05 Prover 13: Warning: ignoring some quantifiers
% 8.22/2.06 Prover 8: Warning: ignoring some quantifiers
% 8.22/2.07 Prover 13: Constructing countermodel ...
% 8.22/2.07 Prover 8: Constructing countermodel ...
% 8.22/2.10 Prover 10: gave up
% 8.22/2.10 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.22/2.13 Prover 16: Preprocessing ...
% 8.22/2.16 Prover 7: gave up
% 9.35/2.17 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 9.35/2.19 Prover 19: Preprocessing ...
% 9.35/2.20 Prover 11: Constructing countermodel ...
% 9.35/2.20 Prover 16: Warning: ignoring some quantifiers
% 9.35/2.21 Prover 16: Constructing countermodel ...
% 9.35/2.24 Prover 13: gave up
% 10.15/2.28 Prover 1: Found proof (size 114)
% 10.15/2.28 Prover 1: proved (1616ms)
% 10.15/2.28 Prover 19: Warning: ignoring some quantifiers
% 10.15/2.28 Prover 4: stopped
% 10.15/2.28 Prover 16: stopped
% 10.15/2.28 Prover 8: stopped
% 10.15/2.28 Prover 11: stopped
% 10.15/2.29 Prover 19: Constructing countermodel ...
% 10.15/2.30 Prover 19: stopped
% 10.15/2.30
% 10.15/2.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.15/2.30
% 10.42/2.34 % SZS output start Proof for theBenchmark
% 10.42/2.34 Assumptions after simplification:
% 10.42/2.34 ---------------------------------
% 10.42/2.34
% 10.42/2.34 (a12)
% 10.53/2.39 $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 10.53/2.39 : ! [v5: $i] : ( ~ (resilience(v2) = v4) | ~ (resilience(v1) = v5) | ~
% 10.53/2.39 (greater(v4, v5) = 0) | ~ (in_environment(v0, v3) = 0) | ~ $i(v3) | ~
% 10.53/2.39 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] :
% 10.53/2.39 ? [v9: $i] : ? [v10: any] : (growth_rate(v2, v3) = v9 & growth_rate(v1,
% 10.53/2.39 v3) = v7 & greater(zero, v9) = v10 & greater(zero, v7) = v8 &
% 10.53/2.39 environment(v0) = v6 & $i(v9) & $i(v7) & ( ~ (v10 = 0) | ~ (v6 = 0) | v8
% 10.53/2.39 = 0)))
% 10.53/2.39
% 10.53/2.39 (a2)
% 10.53/2.40 $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ? [v1: $i] :
% 10.53/2.40 (resilience(efficient_producers) = v0 & resilience(first_movers) = v1 &
% 10.53/2.40 greater(v0, v1) = 0 & $i(v1) & $i(v0))
% 10.53/2.40
% 10.53/2.40 (d2)
% 10.53/2.41 $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 10.53/2.41 any] : ( ~ (outcompetes(v2, v1, v3) = v4) | ~ (environment(v0) = 0) | ~
% 10.53/2.41 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ?
% 10.53/2.41 [v7: any] : ? [v8: $i] : ? [v9: any] : (growth_rate(v2, v3) = v6 &
% 10.53/2.41 growth_rate(v1, v3) = v8 & greater_or_equal(v6, zero) = v7 & greater(zero,
% 10.53/2.41 v8) = v9 & subpopulations(v1, v2, v0, v3) = v5 & $i(v8) & $i(v6) & ( ~
% 10.53/2.41 (v5 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v4 = 0) & ( ~ (v4 = 0) | (v9 =
% 10.53/2.41 0 & v7 = 0))))))
% 10.53/2.41
% 10.53/2.41 (mp_growth_rate_relationships)
% 10.53/2.42 $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 10.53/2.42 any] : ( ~ (subpopulations(v1, v2, v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 10.53/2.42 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8:
% 10.53/2.42 any] : (growth_rate(v1, v3) = v6 & greater_or_equal(v6, zero) = v7 &
% 10.53/2.42 greater(zero, v6) = v8 & environment(v0) = v5 & $i(v6) & ( ~ (v8 = 0) |
% 10.53/2.42 (v5 = 0 & v4 = 0 & ~ (v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 10.53/2.42 $i] : ! [v3: $i] : ( ~ (subpopulations(v1, v2, v0, v3) = 0) | ~ $i(v3) |
% 10.53/2.42 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any]
% 10.87/2.42 : ? [v7: any] : (growth_rate(v1, v3) = v4 & greater_or_equal(v4, zero) = v7
% 10.87/2.42 & greater(zero, v4) = v5 & environment(v0) = v6 & $i(v4) & ( ~ (v6 = 0) |
% 10.87/2.42 v7 = 0 | v5 = 0)))
% 10.87/2.42
% 10.87/2.42 (mp_symmetry_of_FM_and_EP)
% 10.87/2.42 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : ( ~
% 10.87/2.42 (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ~ $i(v1)
% 10.87/2.42 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (environment(v0) = v2 &
% 10.87/2.42 subpopulations(efficient_producers, first_movers, v0, v1) = v3 & ( ~ (v2 =
% 10.87/2.42 0) | v3 = 0)))
% 10.87/2.42
% 10.87/2.42 (mp_time_point_occur)
% 10.87/2.43 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : ( ~
% 10.87/2.43 (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ~ $i(v1)
% 10.87/2.43 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in_environment(v0, v1) = v3 &
% 10.87/2.43 environment(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 10.87/2.43
% 10.87/2.43 (prove_t5)
% 10.87/2.43 $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ? [v1: $i] :
% 10.87/2.43 (outcompetes(first_movers, efficient_producers, v1) = 0 & environment(v0) = 0
% 10.87/2.43 & subpopulations(first_movers, efficient_producers, v0, v1) = 0 & $i(v1) &
% 10.87/2.43 $i(v0))
% 10.87/2.43
% 10.87/2.43 (function-axioms)
% 10.87/2.44 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.87/2.44 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (subpopulations(v5, v4,
% 10.87/2.44 v3, v2) = v1) | ~ (subpopulations(v5, v4, v3, v2) = v0)) & ! [v0:
% 10.87/2.44 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.87/2.44 : ! [v4: $i] : (v1 = v0 | ~ (outcompetes(v4, v3, v2) = v1) | ~
% 10.87/2.44 (outcompetes(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 10.87/2.44 ! [v3: $i] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3,
% 10.87/2.44 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 10.87/2.44 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~
% 10.87/2.44 (greater_or_equal(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.87/2.44 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3,
% 10.87/2.44 v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 10.87/2.44 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.87/2.44 (in_environment(v3, v2) = v1) | ~ (in_environment(v3, v2) = v0)) & ! [v0:
% 10.87/2.44 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (resilience(v2) = v1) | ~
% 10.87/2.44 (resilience(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.87/2.44 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (environment(v2) = v1) | ~
% 10.87/2.44 (environment(v2) = v0))
% 10.87/2.44
% 10.87/2.44 Those formulas are unsatisfiable:
% 10.87/2.44 ---------------------------------
% 10.87/2.44
% 10.87/2.44 Begin of proof
% 10.87/2.45 |
% 10.87/2.45 | ALPHA: (mp_symmetry_of_FM_and_EP) implies:
% 10.87/2.45 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subpopulations(first_movers,
% 10.87/2.45 | efficient_producers, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 10.87/2.45 | [v2: any] : ? [v3: any] : (environment(v0) = v2 &
% 10.87/2.45 | subpopulations(efficient_producers, first_movers, v0, v1) = v3 & (
% 10.87/2.45 | ~ (v2 = 0) | v3 = 0)))
% 10.87/2.45 |
% 10.87/2.45 | ALPHA: (mp_time_point_occur) implies:
% 10.87/2.45 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (subpopulations(first_movers,
% 10.87/2.45 | efficient_producers, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 10.87/2.45 | [v2: any] : ? [v3: any] : (in_environment(v0, v1) = v3 &
% 10.87/2.45 | environment(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 10.87/2.45 |
% 10.87/2.45 | ALPHA: (mp_growth_rate_relationships) implies:
% 10.87/2.46 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 10.87/2.46 | (subpopulations(v1, v2, v0, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~
% 10.87/2.46 | $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ?
% 10.87/2.46 | [v7: any] : (growth_rate(v1, v3) = v4 & greater_or_equal(v4, zero) =
% 10.87/2.46 | v7 & greater(zero, v4) = v5 & environment(v0) = v6 & $i(v4) & ( ~
% 10.87/2.46 | (v6 = 0) | v7 = 0 | v5 = 0)))
% 10.87/2.46 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] :
% 10.87/2.46 | ( ~ (subpopulations(v1, v2, v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 10.87/2.46 | $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ?
% 10.87/2.46 | [v8: any] : (growth_rate(v1, v3) = v6 & greater_or_equal(v6, zero) =
% 10.87/2.46 | v7 & greater(zero, v6) = v8 & environment(v0) = v5 & $i(v6) & ( ~
% 10.87/2.46 | (v8 = 0) | (v5 = 0 & v4 = 0 & ~ (v7 = 0)))))
% 10.87/2.46 |
% 10.87/2.46 | ALPHA: (d2) implies:
% 11.11/2.47 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] :
% 11.11/2.47 | ( ~ (outcompetes(v2, v1, v3) = v4) | ~ (environment(v0) = 0) | ~
% 11.11/2.47 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 11.11/2.47 | $i] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : (growth_rate(v2,
% 11.11/2.47 | v3) = v6 & growth_rate(v1, v3) = v8 & greater_or_equal(v6, zero)
% 11.11/2.47 | = v7 & greater(zero, v8) = v9 & subpopulations(v1, v2, v0, v3) = v5
% 11.11/2.47 | & $i(v8) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v4
% 11.11/2.47 | = 0) & ( ~ (v4 = 0) | (v9 = 0 & v7 = 0))))))
% 11.11/2.47 |
% 11.11/2.47 | ALPHA: (a12) implies:
% 11.11/2.47 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 11.11/2.47 | ! [v5: $i] : ( ~ (resilience(v2) = v4) | ~ (resilience(v1) = v5) | ~
% 11.11/2.47 | (greater(v4, v5) = 0) | ~ (in_environment(v0, v3) = 0) | ~ $i(v3) |
% 11.11/2.47 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ?
% 11.11/2.47 | [v8: any] : ? [v9: $i] : ? [v10: any] : (growth_rate(v2, v3) = v9 &
% 11.11/2.47 | growth_rate(v1, v3) = v7 & greater(zero, v9) = v10 & greater(zero,
% 11.11/2.47 | v7) = v8 & environment(v0) = v6 & $i(v9) & $i(v7) & ( ~ (v10 = 0)
% 11.11/2.47 | | ~ (v6 = 0) | v8 = 0)))
% 11.11/2.47 |
% 11.11/2.47 | ALPHA: (a2) implies:
% 11.11/2.48 | (7) ? [v0: $i] : ? [v1: $i] : (resilience(efficient_producers) = v0 &
% 11.11/2.48 | resilience(first_movers) = v1 & greater(v0, v1) = 0 & $i(v1) &
% 11.11/2.48 | $i(v0))
% 11.11/2.48 |
% 11.11/2.48 | ALPHA: (prove_t5) implies:
% 11.11/2.48 | (8) $i(first_movers)
% 11.11/2.48 | (9) $i(efficient_producers)
% 11.11/2.48 | (10) ? [v0: $i] : ? [v1: $i] : (outcompetes(first_movers,
% 11.11/2.48 | efficient_producers, v1) = 0 & environment(v0) = 0 &
% 11.11/2.48 | subpopulations(first_movers, efficient_producers, v0, v1) = 0 &
% 11.11/2.48 | $i(v1) & $i(v0))
% 11.11/2.48 |
% 11.11/2.48 | ALPHA: (function-axioms) implies:
% 11.11/2.48 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 11.11/2.48 | : (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0))
% 11.11/2.48 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 11.11/2.48 | : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3,
% 11.11/2.48 | v2) = v0))
% 11.11/2.48 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 11.11/2.48 | : ! [v3: $i] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~
% 11.11/2.48 | (greater_or_equal(v3, v2) = v0))
% 11.11/2.48 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.11/2.48 | (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 11.11/2.49 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 11.11/2.49 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~
% 11.11/2.49 | (subpopulations(v5, v4, v3, v2) = v1) | ~ (subpopulations(v5, v4,
% 11.11/2.49 | v3, v2) = v0))
% 11.11/2.49 |
% 11.11/2.49 | DELTA: instantiating (7) with fresh symbols all_9_0, all_9_1 gives:
% 11.11/2.49 | (16) resilience(efficient_producers) = all_9_1 & resilience(first_movers) =
% 11.11/2.49 | all_9_0 & greater(all_9_1, all_9_0) = 0 & $i(all_9_0) & $i(all_9_1)
% 11.11/2.49 |
% 11.11/2.49 | ALPHA: (16) implies:
% 11.11/2.49 | (17) greater(all_9_1, all_9_0) = 0
% 11.11/2.49 | (18) resilience(first_movers) = all_9_0
% 11.11/2.49 | (19) resilience(efficient_producers) = all_9_1
% 11.11/2.49 |
% 11.11/2.49 | DELTA: instantiating (10) with fresh symbols all_11_0, all_11_1 gives:
% 11.11/2.49 | (20) outcompetes(first_movers, efficient_producers, all_11_0) = 0 &
% 11.11/2.49 | environment(all_11_1) = 0 & subpopulations(first_movers,
% 11.11/2.49 | efficient_producers, all_11_1, all_11_0) = 0 & $i(all_11_0) &
% 11.11/2.49 | $i(all_11_1)
% 11.11/2.49 |
% 11.11/2.49 | ALPHA: (20) implies:
% 11.11/2.49 | (21) $i(all_11_1)
% 11.11/2.49 | (22) $i(all_11_0)
% 11.11/2.49 | (23) subpopulations(first_movers, efficient_producers, all_11_1, all_11_0)
% 11.11/2.49 | = 0
% 11.11/2.49 | (24) environment(all_11_1) = 0
% 11.11/2.49 | (25) outcompetes(first_movers, efficient_producers, all_11_0) = 0
% 11.11/2.49 |
% 11.11/2.49 | GROUND_INST: instantiating (2) with all_11_1, all_11_0, simplifying with (21),
% 11.11/2.49 | (22), (23) gives:
% 11.11/2.50 | (26) ? [v0: any] : ? [v1: any] : (in_environment(all_11_1, all_11_0) = v1
% 11.11/2.50 | & environment(all_11_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 11.11/2.50 |
% 11.11/2.50 | GROUND_INST: instantiating (1) with all_11_1, all_11_0, simplifying with (21),
% 11.11/2.50 | (22), (23) gives:
% 11.11/2.50 | (27) ? [v0: any] : ? [v1: any] : (environment(all_11_1) = v0 &
% 11.11/2.50 | subpopulations(efficient_producers, first_movers, all_11_1,
% 11.11/2.50 | all_11_0) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 11.11/2.50 |
% 11.11/2.50 | GROUND_INST: instantiating (3) with all_11_1, first_movers,
% 11.11/2.50 | efficient_producers, all_11_0, simplifying with (8), (9), (21),
% 11.11/2.50 | (22), (23) gives:
% 11.11/2.50 | (28) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 11.11/2.50 | (growth_rate(first_movers, all_11_0) = v0 & greater_or_equal(v0, zero)
% 11.11/2.50 | = v3 & greater(zero, v0) = v1 & environment(all_11_1) = v2 & $i(v0)
% 11.11/2.50 | & ( ~ (v2 = 0) | v3 = 0 | v1 = 0))
% 11.11/2.50 |
% 11.11/2.50 | GROUND_INST: instantiating (4) with all_11_1, first_movers,
% 11.11/2.50 | efficient_producers, all_11_0, 0, simplifying with (8), (9),
% 11.11/2.50 | (21), (22), (23) gives:
% 11.11/2.50 | (29) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] :
% 11.11/2.50 | (growth_rate(first_movers, all_11_0) = v1 & greater_or_equal(v1, zero)
% 11.11/2.50 | = v2 & greater(zero, v1) = v3 & environment(all_11_1) = v0 & $i(v1)
% 11.11/2.50 | & ( ~ (v3 = 0) | (v0 = 0 & ~ (v2 = 0))))
% 11.11/2.50 |
% 11.11/2.51 | GROUND_INST: instantiating (5) with all_11_1, efficient_producers,
% 11.11/2.51 | first_movers, all_11_0, 0, simplifying with (8), (9), (21), (22),
% 11.11/2.51 | (24), (25) gives:
% 11.11/2.51 | (30) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any]
% 11.11/2.51 | : (growth_rate(efficient_producers, all_11_0) = v3 &
% 11.11/2.51 | growth_rate(first_movers, all_11_0) = v1 & greater_or_equal(v1,
% 11.11/2.51 | zero) = v2 & greater(zero, v3) = v4 &
% 11.11/2.51 | subpopulations(efficient_producers, first_movers, all_11_1,
% 11.11/2.51 | all_11_0) = v0 & $i(v3) & $i(v1) & ( ~ (v0 = 0) | (v4 = 0 & v2 =
% 11.11/2.51 | 0)))
% 11.11/2.51 |
% 11.11/2.51 | DELTA: instantiating (27) with fresh symbols all_18_0, all_18_1 gives:
% 11.11/2.51 | (31) environment(all_11_1) = all_18_1 & subpopulations(efficient_producers,
% 11.11/2.51 | first_movers, all_11_1, all_11_0) = all_18_0 & ( ~ (all_18_1 = 0) |
% 11.11/2.51 | all_18_0 = 0)
% 11.11/2.51 |
% 11.11/2.51 | ALPHA: (31) implies:
% 11.11/2.51 | (32) subpopulations(efficient_producers, first_movers, all_11_1, all_11_0)
% 11.11/2.51 | = all_18_0
% 11.11/2.51 | (33) environment(all_11_1) = all_18_1
% 11.11/2.51 | (34) ~ (all_18_1 = 0) | all_18_0 = 0
% 11.11/2.51 |
% 11.11/2.51 | DELTA: instantiating (26) with fresh symbols all_20_0, all_20_1 gives:
% 11.11/2.51 | (35) in_environment(all_11_1, all_11_0) = all_20_0 & environment(all_11_1)
% 11.11/2.51 | = all_20_1 & ( ~ (all_20_1 = 0) | all_20_0 = 0)
% 11.11/2.51 |
% 11.11/2.51 | ALPHA: (35) implies:
% 11.11/2.51 | (36) environment(all_11_1) = all_20_1
% 11.11/2.51 | (37) in_environment(all_11_1, all_11_0) = all_20_0
% 11.11/2.51 | (38) ~ (all_20_1 = 0) | all_20_0 = 0
% 11.11/2.51 |
% 11.11/2.51 | DELTA: instantiating (29) with fresh symbols all_22_0, all_22_1, all_22_2,
% 11.11/2.51 | all_22_3 gives:
% 11.11/2.51 | (39) growth_rate(first_movers, all_11_0) = all_22_2 &
% 11.11/2.51 | greater_or_equal(all_22_2, zero) = all_22_1 & greater(zero, all_22_2)
% 11.11/2.51 | = all_22_0 & environment(all_11_1) = all_22_3 & $i(all_22_2) & ( ~
% 11.11/2.51 | (all_22_0 = 0) | (all_22_3 = 0 & ~ (all_22_1 = 0)))
% 11.11/2.51 |
% 11.11/2.51 | ALPHA: (39) implies:
% 11.11/2.52 | (40) environment(all_11_1) = all_22_3
% 11.11/2.52 | (41) greater(zero, all_22_2) = all_22_0
% 11.11/2.52 | (42) greater_or_equal(all_22_2, zero) = all_22_1
% 11.11/2.52 | (43) growth_rate(first_movers, all_11_0) = all_22_2
% 11.11/2.52 | (44) ~ (all_22_0 = 0) | (all_22_3 = 0 & ~ (all_22_1 = 0))
% 11.11/2.52 |
% 11.11/2.52 | DELTA: instantiating (28) with fresh symbols all_24_0, all_24_1, all_24_2,
% 11.11/2.52 | all_24_3 gives:
% 11.11/2.52 | (45) growth_rate(first_movers, all_11_0) = all_24_3 &
% 11.11/2.52 | greater_or_equal(all_24_3, zero) = all_24_0 & greater(zero, all_24_3)
% 11.11/2.52 | = all_24_2 & environment(all_11_1) = all_24_1 & $i(all_24_3) & ( ~
% 11.11/2.52 | (all_24_1 = 0) | all_24_0 = 0 | all_24_2 = 0)
% 11.11/2.52 |
% 11.11/2.52 | ALPHA: (45) implies:
% 11.11/2.52 | (46) environment(all_11_1) = all_24_1
% 11.11/2.52 | (47) greater(zero, all_24_3) = all_24_2
% 11.11/2.52 | (48) greater_or_equal(all_24_3, zero) = all_24_0
% 11.11/2.52 | (49) growth_rate(first_movers, all_11_0) = all_24_3
% 11.11/2.52 |
% 11.11/2.52 | DELTA: instantiating (30) with fresh symbols all_26_0, all_26_1, all_26_2,
% 11.11/2.52 | all_26_3, all_26_4 gives:
% 11.11/2.52 | (50) growth_rate(efficient_producers, all_11_0) = all_26_1 &
% 11.11/2.52 | growth_rate(first_movers, all_11_0) = all_26_3 &
% 11.11/2.52 | greater_or_equal(all_26_3, zero) = all_26_2 & greater(zero, all_26_1)
% 11.11/2.52 | = all_26_0 & subpopulations(efficient_producers, first_movers,
% 11.11/2.52 | all_11_1, all_11_0) = all_26_4 & $i(all_26_1) & $i(all_26_3) & ( ~
% 11.11/2.52 | (all_26_4 = 0) | (all_26_0 = 0 & all_26_2 = 0))
% 11.11/2.52 |
% 11.11/2.52 | ALPHA: (50) implies:
% 11.11/2.52 | (51) subpopulations(efficient_producers, first_movers, all_11_1, all_11_0)
% 11.11/2.52 | = all_26_4
% 11.11/2.52 | (52) greater(zero, all_26_1) = all_26_0
% 11.11/2.52 | (53) greater_or_equal(all_26_3, zero) = all_26_2
% 11.11/2.52 | (54) growth_rate(first_movers, all_11_0) = all_26_3
% 11.11/2.52 | (55) growth_rate(efficient_producers, all_11_0) = all_26_1
% 11.11/2.52 | (56) ~ (all_26_4 = 0) | (all_26_0 = 0 & all_26_2 = 0)
% 11.11/2.52 |
% 11.11/2.53 | GROUND_INST: instantiating (15) with all_18_0, all_26_4, all_11_0, all_11_1,
% 11.11/2.53 | first_movers, efficient_producers, simplifying with (32), (51)
% 11.11/2.53 | gives:
% 11.11/2.53 | (57) all_26_4 = all_18_0
% 11.11/2.53 |
% 11.11/2.53 | GROUND_INST: instantiating (11) with 0, all_22_3, all_11_1, simplifying with
% 11.11/2.53 | (24), (40) gives:
% 11.11/2.53 | (58) all_22_3 = 0
% 11.11/2.53 |
% 11.11/2.53 | GROUND_INST: instantiating (11) with all_18_1, all_22_3, all_11_1, simplifying
% 11.11/2.53 | with (33), (40) gives:
% 11.11/2.53 | (59) all_22_3 = all_18_1
% 11.11/2.53 |
% 11.11/2.53 | GROUND_INST: instantiating (11) with all_22_3, all_24_1, all_11_1, simplifying
% 11.11/2.53 | with (40), (46) gives:
% 11.11/2.53 | (60) all_24_1 = all_22_3
% 11.11/2.53 |
% 11.11/2.53 | GROUND_INST: instantiating (11) with all_20_1, all_24_1, all_11_1, simplifying
% 11.11/2.53 | with (36), (46) gives:
% 11.11/2.53 | (61) all_24_1 = all_20_1
% 11.11/2.53 |
% 11.11/2.53 | GROUND_INST: instantiating (14) with all_24_3, all_26_3, all_11_0,
% 11.11/2.53 | first_movers, simplifying with (49), (54) gives:
% 11.11/2.53 | (62) all_26_3 = all_24_3
% 11.11/2.53 |
% 11.11/2.53 | GROUND_INST: instantiating (14) with all_22_2, all_26_3, all_11_0,
% 11.11/2.53 | first_movers, simplifying with (43), (54) gives:
% 11.11/2.53 | (63) all_26_3 = all_22_2
% 11.11/2.53 |
% 11.11/2.53 | COMBINE_EQS: (62), (63) imply:
% 11.11/2.53 | (64) all_24_3 = all_22_2
% 11.11/2.53 |
% 11.11/2.53 | SIMP: (64) implies:
% 11.11/2.53 | (65) all_24_3 = all_22_2
% 11.11/2.53 |
% 11.11/2.53 | COMBINE_EQS: (60), (61) imply:
% 11.11/2.53 | (66) all_22_3 = all_20_1
% 11.11/2.53 |
% 11.11/2.53 | SIMP: (66) implies:
% 11.11/2.53 | (67) all_22_3 = all_20_1
% 11.11/2.53 |
% 11.11/2.53 | COMBINE_EQS: (58), (67) imply:
% 11.11/2.53 | (68) all_20_1 = 0
% 11.11/2.53 |
% 11.11/2.53 | COMBINE_EQS: (59), (67) imply:
% 11.11/2.53 | (69) all_20_1 = all_18_1
% 11.11/2.53 |
% 11.11/2.53 | COMBINE_EQS: (68), (69) imply:
% 11.11/2.53 | (70) all_18_1 = 0
% 11.11/2.53 |
% 11.11/2.53 | REDUCE: (53), (63) imply:
% 11.11/2.54 | (71) greater_or_equal(all_22_2, zero) = all_26_2
% 11.11/2.54 |
% 11.11/2.54 | REDUCE: (48), (65) imply:
% 11.11/2.54 | (72) greater_or_equal(all_22_2, zero) = all_24_0
% 11.11/2.54 |
% 11.11/2.54 | REDUCE: (47), (65) imply:
% 11.11/2.54 | (73) greater(zero, all_22_2) = all_24_2
% 11.11/2.54 |
% 11.11/2.54 | BETA: splitting (34) gives:
% 11.11/2.54 |
% 11.11/2.54 | Case 1:
% 11.11/2.54 | |
% 11.11/2.54 | | (74) ~ (all_18_1 = 0)
% 11.11/2.54 | |
% 11.11/2.54 | | REDUCE: (70), (74) imply:
% 11.11/2.54 | | (75) $false
% 11.11/2.54 | |
% 11.11/2.54 | | CLOSE: (75) is inconsistent.
% 11.11/2.54 | |
% 11.11/2.54 | Case 2:
% 11.11/2.54 | |
% 11.11/2.54 | | (76) all_18_0 = 0
% 11.11/2.54 | |
% 11.11/2.54 | | COMBINE_EQS: (57), (76) imply:
% 11.11/2.54 | | (77) all_26_4 = 0
% 11.11/2.54 | |
% 11.11/2.54 | | REDUCE: (32), (76) imply:
% 11.11/2.54 | | (78) subpopulations(efficient_producers, first_movers, all_11_1,
% 11.11/2.54 | | all_11_0) = 0
% 11.11/2.54 | |
% 11.11/2.54 | | BETA: splitting (38) gives:
% 11.11/2.54 | |
% 11.11/2.54 | | Case 1:
% 11.11/2.54 | | |
% 11.11/2.54 | | | (79) ~ (all_20_1 = 0)
% 11.11/2.54 | | |
% 11.11/2.54 | | | REDUCE: (68), (79) imply:
% 11.11/2.54 | | | (80) $false
% 11.11/2.54 | | |
% 11.11/2.54 | | | CLOSE: (80) is inconsistent.
% 11.11/2.54 | | |
% 11.11/2.54 | | Case 2:
% 11.11/2.54 | | |
% 11.11/2.54 | | | (81) all_20_0 = 0
% 11.11/2.54 | | |
% 11.11/2.54 | | | REDUCE: (37), (81) imply:
% 11.11/2.54 | | | (82) in_environment(all_11_1, all_11_0) = 0
% 11.11/2.54 | | |
% 11.11/2.54 | | | BETA: splitting (56) gives:
% 11.11/2.54 | | |
% 11.11/2.54 | | | Case 1:
% 11.11/2.54 | | | |
% 11.48/2.55 | | | | (83) ~ (all_26_4 = 0)
% 11.48/2.55 | | | |
% 11.48/2.55 | | | | REDUCE: (77), (83) imply:
% 11.48/2.55 | | | | (84) $false
% 11.48/2.55 | | | |
% 11.48/2.55 | | | | CLOSE: (84) is inconsistent.
% 11.48/2.55 | | | |
% 11.48/2.55 | | | Case 2:
% 11.48/2.55 | | | |
% 11.48/2.55 | | | | (85) all_26_0 = 0 & all_26_2 = 0
% 11.48/2.55 | | | |
% 11.48/2.55 | | | | ALPHA: (85) implies:
% 11.48/2.55 | | | | (86) all_26_2 = 0
% 11.48/2.55 | | | | (87) all_26_0 = 0
% 11.48/2.55 | | | |
% 11.48/2.55 | | | | REDUCE: (71), (86) imply:
% 11.48/2.55 | | | | (88) greater_or_equal(all_22_2, zero) = 0
% 11.48/2.55 | | | |
% 11.48/2.55 | | | | REDUCE: (52), (87) imply:
% 11.48/2.55 | | | | (89) greater(zero, all_26_1) = 0
% 11.48/2.55 | | | |
% 11.48/2.55 | | | | GROUND_INST: instantiating (12) with all_22_0, all_24_2, all_22_2, zero,
% 11.48/2.55 | | | | simplifying with (41), (73) gives:
% 11.48/2.55 | | | | (90) all_24_2 = all_22_0
% 11.48/2.55 | | | |
% 11.48/2.55 | | | | GROUND_INST: instantiating (13) with all_22_1, all_24_0, zero, all_22_2,
% 11.48/2.55 | | | | simplifying with (42), (72) gives:
% 11.48/2.55 | | | | (91) all_24_0 = all_22_1
% 11.48/2.55 | | | |
% 11.48/2.55 | | | | GROUND_INST: instantiating (13) with 0, all_24_0, zero, all_22_2,
% 11.48/2.55 | | | | simplifying with (72), (88) gives:
% 11.48/2.55 | | | | (92) all_24_0 = 0
% 11.48/2.55 | | | |
% 11.48/2.55 | | | | COMBINE_EQS: (91), (92) imply:
% 11.48/2.55 | | | | (93) all_22_1 = 0
% 11.48/2.55 | | | |
% 11.48/2.55 | | | | SIMP: (93) implies:
% 11.48/2.55 | | | | (94) all_22_1 = 0
% 11.48/2.55 | | | |
% 11.48/2.55 | | | | BETA: splitting (44) gives:
% 11.48/2.55 | | | |
% 11.48/2.55 | | | | Case 1:
% 11.48/2.55 | | | | |
% 11.48/2.55 | | | | | (95) ~ (all_22_0 = 0)
% 11.48/2.55 | | | | |
% 11.48/2.55 | | | | | GROUND_INST: instantiating (3) with all_11_1, efficient_producers,
% 11.48/2.55 | | | | | first_movers, all_11_0, simplifying with (8), (9), (21),
% 11.48/2.55 | | | | | (22), (78) gives:
% 11.48/2.56 | | | | | (96) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 11.48/2.56 | | | | | (growth_rate(efficient_producers, all_11_0) = v0 &
% 11.48/2.56 | | | | | greater_or_equal(v0, zero) = v3 & greater(zero, v0) = v1 &
% 11.48/2.56 | | | | | environment(all_11_1) = v2 & $i(v0) & ( ~ (v2 = 0) | v3 = 0
% 11.48/2.56 | | | | | | v1 = 0))
% 11.48/2.56 | | | | |
% 11.48/2.56 | | | | | GROUND_INST: instantiating (4) with all_11_1, efficient_producers,
% 11.48/2.56 | | | | | first_movers, all_11_0, 0, simplifying with (8), (9),
% 11.48/2.56 | | | | | (21), (22), (78) gives:
% 11.48/2.56 | | | | | (97) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] :
% 11.48/2.56 | | | | | (growth_rate(efficient_producers, all_11_0) = v1 &
% 11.48/2.56 | | | | | greater_or_equal(v1, zero) = v2 & greater(zero, v1) = v3 &
% 11.48/2.56 | | | | | environment(all_11_1) = v0 & $i(v1) & ( ~ (v3 = 0) | (v0 = 0
% 11.48/2.56 | | | | | & ~ (v2 = 0))))
% 11.48/2.56 | | | | |
% 11.48/2.56 | | | | | GROUND_INST: instantiating (6) with all_11_1, first_movers,
% 11.48/2.56 | | | | | efficient_producers, all_11_0, all_9_1, all_9_0,
% 11.48/2.56 | | | | | simplifying with (8), (9), (17), (18), (19), (21), (22),
% 11.48/2.56 | | | | | (82) gives:
% 11.48/2.56 | | | | | (98) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ?
% 11.48/2.56 | | | | | [v4: any] : (growth_rate(efficient_producers, all_11_0) = v3 &
% 11.48/2.56 | | | | | growth_rate(first_movers, all_11_0) = v1 & greater(zero, v3)
% 11.48/2.56 | | | | | = v4 & greater(zero, v1) = v2 & environment(all_11_1) = v0 &
% 11.48/2.56 | | | | | $i(v3) & $i(v1) & ( ~ (v4 = 0) | ~ (v0 = 0) | v2 = 0))
% 11.48/2.56 | | | | |
% 11.48/2.56 | | | | | DELTA: instantiating (97) with fresh symbols all_57_0, all_57_1,
% 11.48/2.56 | | | | | all_57_2, all_57_3 gives:
% 11.48/2.57 | | | | | (99) growth_rate(efficient_producers, all_11_0) = all_57_2 &
% 11.48/2.57 | | | | | greater_or_equal(all_57_2, zero) = all_57_1 & greater(zero,
% 11.48/2.57 | | | | | all_57_2) = all_57_0 & environment(all_11_1) = all_57_3 &
% 11.48/2.57 | | | | | $i(all_57_2) & ( ~ (all_57_0 = 0) | (all_57_3 = 0 & ~
% 11.48/2.57 | | | | | (all_57_1 = 0)))
% 11.48/2.57 | | | | |
% 11.48/2.57 | | | | | ALPHA: (99) implies:
% 11.48/2.57 | | | | | (100) greater(zero, all_57_2) = all_57_0
% 11.48/2.57 | | | | | (101) growth_rate(efficient_producers, all_11_0) = all_57_2
% 11.48/2.57 | | | | |
% 11.48/2.57 | | | | | DELTA: instantiating (96) with fresh symbols all_59_0, all_59_1,
% 11.48/2.57 | | | | | all_59_2, all_59_3 gives:
% 11.48/2.57 | | | | | (102) growth_rate(efficient_producers, all_11_0) = all_59_3 &
% 11.48/2.57 | | | | | greater_or_equal(all_59_3, zero) = all_59_0 & greater(zero,
% 11.48/2.57 | | | | | all_59_3) = all_59_2 & environment(all_11_1) = all_59_1 &
% 11.48/2.57 | | | | | $i(all_59_3) & ( ~ (all_59_1 = 0) | all_59_0 = 0 | all_59_2 =
% 11.48/2.57 | | | | | 0)
% 11.48/2.57 | | | | |
% 11.48/2.57 | | | | | ALPHA: (102) implies:
% 11.48/2.57 | | | | | (103) greater(zero, all_59_3) = all_59_2
% 11.48/2.57 | | | | | (104) growth_rate(efficient_producers, all_11_0) = all_59_3
% 11.48/2.57 | | | | |
% 11.48/2.57 | | | | | DELTA: instantiating (98) with fresh symbols all_61_0, all_61_1,
% 11.48/2.57 | | | | | all_61_2, all_61_3, all_61_4 gives:
% 11.48/2.57 | | | | | (105) growth_rate(efficient_producers, all_11_0) = all_61_1 &
% 11.48/2.57 | | | | | growth_rate(first_movers, all_11_0) = all_61_3 &
% 11.48/2.57 | | | | | greater(zero, all_61_1) = all_61_0 & greater(zero, all_61_3)
% 11.48/2.57 | | | | | = all_61_2 & environment(all_11_1) = all_61_4 & $i(all_61_1)
% 11.48/2.57 | | | | | & $i(all_61_3) & ( ~ (all_61_0 = 0) | ~ (all_61_4 = 0) |
% 11.48/2.57 | | | | | all_61_2 = 0)
% 11.48/2.57 | | | | |
% 11.48/2.57 | | | | | ALPHA: (105) implies:
% 11.48/2.57 | | | | | (106) environment(all_11_1) = all_61_4
% 11.63/2.57 | | | | | (107) greater(zero, all_61_3) = all_61_2
% 11.63/2.58 | | | | | (108) greater(zero, all_61_1) = all_61_0
% 11.63/2.58 | | | | | (109) growth_rate(first_movers, all_11_0) = all_61_3
% 11.63/2.58 | | | | | (110) growth_rate(efficient_producers, all_11_0) = all_61_1
% 11.63/2.58 | | | | | (111) ~ (all_61_0 = 0) | ~ (all_61_4 = 0) | all_61_2 = 0
% 11.63/2.58 | | | | |
% 11.63/2.58 | | | | | GROUND_INST: instantiating (11) with 0, all_61_4, all_11_1,
% 11.63/2.58 | | | | | simplifying with (24), (106) gives:
% 11.63/2.58 | | | | | (112) all_61_4 = 0
% 11.63/2.58 | | | | |
% 11.63/2.58 | | | | | GROUND_INST: instantiating (14) with all_22_2, all_61_3, all_11_0,
% 11.63/2.58 | | | | | first_movers, simplifying with (43), (109) gives:
% 11.63/2.58 | | | | | (113) all_61_3 = all_22_2
% 11.63/2.58 | | | | |
% 11.63/2.58 | | | | | GROUND_INST: instantiating (14) with all_26_1, all_59_3, all_11_0,
% 11.63/2.58 | | | | | efficient_producers, simplifying with (55), (104) gives:
% 11.63/2.58 | | | | | (114) all_59_3 = all_26_1
% 11.63/2.58 | | | | |
% 11.63/2.58 | | | | | GROUND_INST: instantiating (14) with all_59_3, all_61_1, all_11_0,
% 11.63/2.58 | | | | | efficient_producers, simplifying with (104), (110) gives:
% 11.63/2.58 | | | | | (115) all_61_1 = all_59_3
% 11.63/2.58 | | | | |
% 11.63/2.58 | | | | | GROUND_INST: instantiating (14) with all_57_2, all_61_1, all_11_0,
% 11.63/2.58 | | | | | efficient_producers, simplifying with (101), (110) gives:
% 11.63/2.58 | | | | | (116) all_61_1 = all_57_2
% 11.63/2.58 | | | | |
% 11.63/2.58 | | | | | COMBINE_EQS: (115), (116) imply:
% 11.63/2.58 | | | | | (117) all_59_3 = all_57_2
% 11.63/2.58 | | | | |
% 11.63/2.58 | | | | | SIMP: (117) implies:
% 11.63/2.58 | | | | | (118) all_59_3 = all_57_2
% 11.63/2.58 | | | | |
% 11.63/2.58 | | | | | COMBINE_EQS: (114), (118) imply:
% 11.63/2.58 | | | | | (119) all_57_2 = all_26_1
% 11.63/2.58 | | | | |
% 11.63/2.58 | | | | | COMBINE_EQS: (116), (119) imply:
% 11.63/2.58 | | | | | (120) all_61_1 = all_26_1
% 11.63/2.58 | | | | |
% 11.63/2.58 | | | | | REDUCE: (108), (120) imply:
% 11.63/2.58 | | | | | (121) greater(zero, all_26_1) = all_61_0
% 11.63/2.58 | | | | |
% 11.63/2.58 | | | | | REDUCE: (107), (113) imply:
% 11.63/2.58 | | | | | (122) greater(zero, all_22_2) = all_61_2
% 11.63/2.58 | | | | |
% 11.63/2.58 | | | | | REDUCE: (103), (114) imply:
% 11.63/2.58 | | | | | (123) greater(zero, all_26_1) = all_59_2
% 11.63/2.59 | | | | |
% 11.63/2.59 | | | | | REDUCE: (100), (119) imply:
% 11.63/2.59 | | | | | (124) greater(zero, all_26_1) = all_57_0
% 11.63/2.59 | | | | |
% 11.63/2.59 | | | | | GROUND_INST: instantiating (12) with all_22_0, all_61_2, all_22_2,
% 11.63/2.59 | | | | | zero, simplifying with (41), (122) gives:
% 11.63/2.59 | | | | | (125) all_61_2 = all_22_0
% 11.63/2.59 | | | | |
% 11.63/2.59 | | | | | GROUND_INST: instantiating (12) with 0, all_59_2, all_26_1, zero,
% 11.63/2.59 | | | | | simplifying with (89), (123) gives:
% 11.63/2.59 | | | | | (126) all_59_2 = 0
% 11.63/2.59 | | | | |
% 11.63/2.59 | | | | | GROUND_INST: instantiating (12) with all_59_2, all_61_0, all_26_1,
% 11.63/2.59 | | | | | zero, simplifying with (121), (123) gives:
% 11.63/2.59 | | | | | (127) all_61_0 = all_59_2
% 11.63/2.59 | | | | |
% 11.63/2.59 | | | | | GROUND_INST: instantiating (12) with all_57_0, all_61_0, all_26_1,
% 11.63/2.59 | | | | | zero, simplifying with (121), (124) gives:
% 11.63/2.59 | | | | | (128) all_61_0 = all_57_0
% 11.63/2.59 | | | | |
% 11.63/2.59 | | | | | COMBINE_EQS: (127), (128) imply:
% 11.63/2.59 | | | | | (129) all_59_2 = all_57_0
% 11.63/2.59 | | | | |
% 11.63/2.59 | | | | | SIMP: (129) implies:
% 11.63/2.59 | | | | | (130) all_59_2 = all_57_0
% 11.63/2.59 | | | | |
% 11.63/2.59 | | | | | COMBINE_EQS: (126), (130) imply:
% 11.63/2.59 | | | | | (131) all_57_0 = 0
% 11.63/2.59 | | | | |
% 11.63/2.59 | | | | | COMBINE_EQS: (128), (131) imply:
% 11.63/2.59 | | | | | (132) all_61_0 = 0
% 11.63/2.59 | | | | |
% 11.63/2.59 | | | | | BETA: splitting (111) gives:
% 11.63/2.59 | | | | |
% 11.63/2.59 | | | | | Case 1:
% 11.63/2.59 | | | | | |
% 11.63/2.59 | | | | | | (133) ~ (all_61_0 = 0)
% 11.63/2.59 | | | | | |
% 11.63/2.59 | | | | | | REDUCE: (132), (133) imply:
% 11.63/2.59 | | | | | | (134) $false
% 11.63/2.59 | | | | | |
% 11.63/2.59 | | | | | | CLOSE: (134) is inconsistent.
% 11.63/2.59 | | | | | |
% 11.63/2.59 | | | | | Case 2:
% 11.63/2.59 | | | | | |
% 11.63/2.59 | | | | | | (135) ~ (all_61_4 = 0) | all_61_2 = 0
% 11.63/2.59 | | | | | |
% 11.63/2.59 | | | | | | BETA: splitting (135) gives:
% 11.63/2.59 | | | | | |
% 11.63/2.59 | | | | | | Case 1:
% 11.63/2.59 | | | | | | |
% 11.63/2.59 | | | | | | | (136) ~ (all_61_4 = 0)
% 11.63/2.59 | | | | | | |
% 11.63/2.59 | | | | | | | REDUCE: (112), (136) imply:
% 11.63/2.59 | | | | | | | (137) $false
% 11.63/2.59 | | | | | | |
% 11.63/2.59 | | | | | | | CLOSE: (137) is inconsistent.
% 11.63/2.59 | | | | | | |
% 11.63/2.59 | | | | | | Case 2:
% 11.63/2.59 | | | | | | |
% 11.63/2.59 | | | | | | | (138) all_61_2 = 0
% 11.63/2.59 | | | | | | |
% 11.63/2.59 | | | | | | | COMBINE_EQS: (125), (138) imply:
% 11.63/2.59 | | | | | | | (139) all_22_0 = 0
% 11.63/2.59 | | | | | | |
% 11.63/2.59 | | | | | | | REDUCE: (95), (139) imply:
% 11.63/2.59 | | | | | | | (140) $false
% 11.63/2.59 | | | | | | |
% 11.63/2.59 | | | | | | | CLOSE: (140) is inconsistent.
% 11.63/2.59 | | | | | | |
% 11.63/2.59 | | | | | | End of split
% 11.63/2.59 | | | | | |
% 11.63/2.59 | | | | | End of split
% 11.63/2.59 | | | | |
% 11.63/2.59 | | | | Case 2:
% 11.63/2.59 | | | | |
% 11.63/2.59 | | | | | (141) all_22_3 = 0 & ~ (all_22_1 = 0)
% 11.63/2.59 | | | | |
% 11.63/2.59 | | | | | ALPHA: (141) implies:
% 11.63/2.60 | | | | | (142) ~ (all_22_1 = 0)
% 11.63/2.60 | | | | |
% 11.63/2.60 | | | | | REDUCE: (94), (142) imply:
% 11.63/2.60 | | | | | (143) $false
% 11.63/2.60 | | | | |
% 11.63/2.60 | | | | | CLOSE: (143) is inconsistent.
% 11.63/2.60 | | | | |
% 11.63/2.60 | | | | End of split
% 11.63/2.60 | | | |
% 11.63/2.60 | | | End of split
% 11.63/2.60 | | |
% 11.63/2.60 | | End of split
% 11.63/2.60 | |
% 11.63/2.60 | End of split
% 11.63/2.60 |
% 11.63/2.60 End of proof
% 11.63/2.60 % SZS output end Proof for theBenchmark
% 11.63/2.60
% 11.63/2.60 1965ms
%------------------------------------------------------------------------------