TSTP Solution File: MGT028+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : MGT028+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 : n024.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 09:16:17 EDT 2023
% Result : Theorem 5.80s 1.54s
% Output : Proof 8.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT028+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 06:20:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.42/0.62 ________ _____
% 0.42/0.62 ___ __ \_________(_)________________________________
% 0.42/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.42/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.42/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.42/0.62
% 0.42/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.42/0.62 (2023-06-19)
% 0.42/0.62
% 0.42/0.62 (c) Philipp Rümmer, 2009-2023
% 0.42/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.42/0.62 Amanda Stjerna.
% 0.42/0.62 Free software under BSD-3-Clause.
% 0.42/0.62
% 0.42/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.42/0.62
% 0.42/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.42/0.64 Running up to 7 provers in parallel.
% 0.42/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.42/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.42/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.42/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.42/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.42/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.42/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.04/1.06 Prover 1: Preprocessing ...
% 2.04/1.06 Prover 4: Preprocessing ...
% 2.80/1.11 Prover 6: Preprocessing ...
% 2.80/1.11 Prover 0: Preprocessing ...
% 2.80/1.11 Prover 3: Preprocessing ...
% 2.80/1.11 Prover 2: Preprocessing ...
% 2.80/1.11 Prover 5: Preprocessing ...
% 3.67/1.31 Prover 5: Constructing countermodel ...
% 3.67/1.32 Prover 1: Constructing countermodel ...
% 3.67/1.33 Prover 6: Proving ...
% 3.67/1.33 Prover 3: Constructing countermodel ...
% 3.67/1.34 Prover 2: Proving ...
% 5.38/1.47 Prover 4: Constructing countermodel ...
% 5.59/1.52 Prover 0: Proving ...
% 5.80/1.53 Prover 3: proved (885ms)
% 5.80/1.53
% 5.80/1.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.80/1.54
% 5.80/1.54 Prover 5: stopped
% 5.80/1.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.80/1.54 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.80/1.55 Prover 6: stopped
% 5.80/1.55 Prover 2: stopped
% 5.80/1.55 Prover 0: stopped
% 5.80/1.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.80/1.56 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.80/1.56 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.80/1.57 Prover 7: Preprocessing ...
% 5.80/1.58 Prover 8: Preprocessing ...
% 5.80/1.58 Prover 10: Preprocessing ...
% 5.80/1.58 Prover 13: Preprocessing ...
% 5.80/1.59 Prover 11: Preprocessing ...
% 6.30/1.62 Prover 10: Constructing countermodel ...
% 6.30/1.64 Prover 7: Constructing countermodel ...
% 6.30/1.66 Prover 13: Constructing countermodel ...
% 6.83/1.68 Prover 10: gave up
% 6.83/1.68 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.83/1.68 Prover 8: Warning: ignoring some quantifiers
% 6.83/1.69 Prover 8: Constructing countermodel ...
% 6.83/1.69 Prover 16: Preprocessing ...
% 6.83/1.74 Prover 16: Constructing countermodel ...
% 6.83/1.76 Prover 1: Found proof (size 72)
% 6.83/1.76 Prover 1: proved (1114ms)
% 6.83/1.76 Prover 7: stopped
% 6.83/1.76 Prover 13: stopped
% 6.83/1.76 Prover 4: stopped
% 6.83/1.76 Prover 16: stopped
% 6.83/1.76 Prover 8: stopped
% 7.68/1.80 Prover 11: Constructing countermodel ...
% 7.68/1.80 Prover 11: stopped
% 7.68/1.80
% 7.68/1.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.68/1.80
% 7.68/1.81 % SZS output start Proof for theBenchmark
% 7.68/1.82 Assumptions after simplification:
% 7.68/1.82 ---------------------------------
% 7.68/1.82
% 7.68/1.82 (l11)
% 7.83/1.85 $i(zero) & $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ( ~
% 7.83/1.85 (stable(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & environment(v0)
% 7.83/1.85 = v1) | ? [v1: $i] : (in_environment(v0, v1) = 0 & $i(v1) & ! [v2: $i] :
% 7.83/1.85 ( ~ (subpopulations(first_movers, efficient_producers, v0, v2) = 0) | ~
% 7.83/1.85 $i(v2) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ?
% 7.83/1.85 [v7: any] : (greater_or_equal(v2, v1) = v3 &
% 7.83/1.85 growth_rate(efficient_producers, v2) = v4 & growth_rate(first_movers,
% 7.83/1.85 v2) = v6 & greater(v4, zero) = v5 & greater(zero, v6) = v7 & $i(v6)
% 7.83/1.85 & $i(v4) & ( ~ (v3 = 0) | (v7 = 0 & v5 = 0))))))
% 7.83/1.85
% 7.83/1.85 (mp_first_movers_negative_growth)
% 7.83/1.86 $i(zero) & $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1:
% 7.83/1.86 $i] : ( ~ (appear(efficient_producers, v0) = v1) | ~ $i(v0) | ? [v2: any]
% 7.83/1.86 : ? [v3: any] : (environment(v0) = v2 & stable(v0) = v3 & ( ~ (v3 = 0) | ~
% 7.83/1.86 (v2 = 0))) | ? [v2: $i] : (greater(v2, v1) = 0 & $i(v2) & ! [v3: $i] :
% 7.83/1.86 ( ~ (subpopulations(first_movers, efficient_producers, v0, v3) = 0) | ~
% 7.83/1.86 $i(v3) | ? [v4: any] : ? [v5: $i] : ? [v6: any] :
% 7.83/1.86 (greater_or_equal(v3, v2) = v4 & growth_rate(first_movers, v3) = v5 &
% 7.83/1.86 greater(zero, v5) = v6 & $i(v5) & ( ~ (v4 = 0) | v6 = 0)))) | ! [v2:
% 7.83/1.86 $i] : ( ~ (in_environment(v0, v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4:
% 7.83/1.86 $i] : ? [v5: int] : ( ~ (v5 = 0) & subpopulations(first_movers,
% 7.83/1.86 efficient_producers, v0, v3) = 0 & greater_or_equal(v3, v2) = 0 &
% 7.83/1.86 growth_rate(first_movers, v3) = v4 & greater(zero, v4) = v5 & $i(v4) &
% 7.83/1.86 $i(v3))))
% 7.83/1.86
% 7.83/1.86 (prove_l10)
% 7.83/1.86 $i(zero) & $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ? [v1:
% 7.83/1.86 $i] : (appear(efficient_producers, v0) = v1 & environment(v0) = 0 &
% 7.83/1.86 stable(v0) = 0 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ (greater(v2, v1) = 0) |
% 7.83/1.86 ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 7.83/1.86 subpopulations(first_movers, efficient_producers, v0, v3) = 0 &
% 7.83/1.86 greater_or_equal(v3, v2) = 0 & growth_rate(first_movers, v3) = v4 &
% 7.83/1.86 greater(zero, v4) = v5 & $i(v4) & $i(v3))))
% 7.83/1.86
% 7.83/1.86 (function-axioms)
% 7.83/1.87 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.83/1.87 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (subpopulations(v5, v4,
% 7.83/1.87 v3, v2) = v1) | ~ (subpopulations(v5, v4, v3, v2) = v0)) & ! [v0: $i]
% 7.83/1.87 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (appear(v3, v2) =
% 7.83/1.87 v1) | ~ (appear(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.83/1.87 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.83/1.87 (in_environment(v3, v2) = v1) | ~ (in_environment(v3, v2) = v0)) & ! [v0:
% 7.83/1.87 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.83/1.87 : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~ (greater_or_equal(v3, v2)
% 7.83/1.87 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 7.83/1.87 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) & ! [v0:
% 7.83/1.87 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.83/1.87 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0:
% 7.83/1.87 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.83/1.87 ~ (environment(v2) = v1) | ~ (environment(v2) = v0)) & ! [v0:
% 7.83/1.87 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.83/1.87 ~ (stable(v2) = v1) | ~ (stable(v2) = v0))
% 7.83/1.87
% 7.83/1.87 Those formulas are unsatisfiable:
% 7.83/1.87 ---------------------------------
% 7.83/1.87
% 7.83/1.87 Begin of proof
% 7.83/1.87 |
% 7.83/1.87 | ALPHA: (mp_first_movers_negative_growth) implies:
% 7.91/1.88 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (appear(efficient_producers, v0) = v1)
% 7.91/1.88 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (environment(v0) = v2 &
% 7.91/1.88 | stable(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0))) | ? [v2: $i] :
% 7.91/1.88 | (greater(v2, v1) = 0 & $i(v2) & ! [v3: $i] : ( ~
% 7.91/1.88 | (subpopulations(first_movers, efficient_producers, v0, v3) = 0) |
% 7.91/1.88 | ~ $i(v3) | ? [v4: any] : ? [v5: $i] : ? [v6: any] :
% 7.91/1.88 | (greater_or_equal(v3, v2) = v4 & growth_rate(first_movers, v3) =
% 7.91/1.88 | v5 & greater(zero, v5) = v6 & $i(v5) & ( ~ (v4 = 0) | v6 =
% 7.91/1.88 | 0)))) | ! [v2: $i] : ( ~ (in_environment(v0, v2) = 0) | ~
% 7.91/1.88 | $i(v2) | ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 7.91/1.88 | subpopulations(first_movers, efficient_producers, v0, v3) = 0 &
% 7.91/1.88 | greater_or_equal(v3, v2) = 0 & growth_rate(first_movers, v3) = v4
% 7.91/1.88 | & greater(zero, v4) = v5 & $i(v4) & $i(v3))))
% 7.91/1.88 |
% 7.91/1.88 | ALPHA: (l11) implies:
% 7.91/1.88 | (2) ! [v0: $i] : ( ~ (stable(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1
% 7.91/1.88 | = 0) & environment(v0) = v1) | ? [v1: $i] : (in_environment(v0,
% 7.91/1.88 | v1) = 0 & $i(v1) & ! [v2: $i] : ( ~
% 7.91/1.88 | (subpopulations(first_movers, efficient_producers, v0, v2) = 0) |
% 7.91/1.88 | ~ $i(v2) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : ? [v6:
% 7.91/1.88 | $i] : ? [v7: any] : (greater_or_equal(v2, v1) = v3 &
% 7.91/1.88 | growth_rate(efficient_producers, v2) = v4 &
% 7.91/1.88 | growth_rate(first_movers, v2) = v6 & greater(v4, zero) = v5 &
% 7.91/1.88 | greater(zero, v6) = v7 & $i(v6) & $i(v4) & ( ~ (v3 = 0) | (v7 =
% 7.91/1.88 | 0 & v5 = 0))))))
% 7.91/1.88 |
% 7.91/1.88 | ALPHA: (prove_l10) implies:
% 7.91/1.89 | (3) ? [v0: $i] : ? [v1: $i] : (appear(efficient_producers, v0) = v1 &
% 7.91/1.89 | environment(v0) = 0 & stable(v0) = 0 & $i(v1) & $i(v0) & ! [v2: $i]
% 7.91/1.89 | : ( ~ (greater(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] :
% 7.91/1.89 | ? [v5: int] : ( ~ (v5 = 0) & subpopulations(first_movers,
% 7.91/1.89 | efficient_producers, v0, v3) = 0 & greater_or_equal(v3, v2) = 0
% 7.91/1.89 | & growth_rate(first_movers, v3) = v4 & greater(zero, v4) = v5 &
% 7.91/1.89 | $i(v4) & $i(v3))))
% 7.91/1.89 |
% 7.91/1.89 | ALPHA: (function-axioms) implies:
% 7.91/1.89 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.91/1.89 | (v1 = v0 | ~ (stable(v2) = v1) | ~ (stable(v2) = v0))
% 7.91/1.89 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.91/1.89 | (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0))
% 7.91/1.89 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.91/1.89 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3,
% 7.91/1.89 | v2) = v0))
% 7.91/1.89 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.91/1.89 | (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 7.91/1.89 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.91/1.89 | ! [v3: $i] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~
% 7.91/1.89 | (greater_or_equal(v3, v2) = v0))
% 7.91/1.89 |
% 7.91/1.89 | DELTA: instantiating (3) with fresh symbols all_6_0, all_6_1 gives:
% 7.91/1.89 | (9) appear(efficient_producers, all_6_1) = all_6_0 & environment(all_6_1) =
% 7.91/1.89 | 0 & stable(all_6_1) = 0 & $i(all_6_0) & $i(all_6_1) & ! [v0: $i] : ( ~
% 7.91/1.89 | (greater(v0, all_6_0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 7.91/1.89 | ? [v3: int] : ( ~ (v3 = 0) & subpopulations(first_movers,
% 7.91/1.89 | efficient_producers, all_6_1, v1) = 0 & greater_or_equal(v1, v0)
% 7.91/1.89 | = 0 & growth_rate(first_movers, v1) = v2 & greater(zero, v2) = v3 &
% 7.91/1.89 | $i(v2) & $i(v1)))
% 7.91/1.89 |
% 7.91/1.89 | ALPHA: (9) implies:
% 7.91/1.89 | (10) $i(all_6_1)
% 7.91/1.89 | (11) stable(all_6_1) = 0
% 7.91/1.89 | (12) environment(all_6_1) = 0
% 7.91/1.89 | (13) appear(efficient_producers, all_6_1) = all_6_0
% 7.91/1.90 | (14) ! [v0: $i] : ( ~ (greater(v0, all_6_0) = 0) | ~ $i(v0) | ? [v1: $i]
% 7.91/1.90 | : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 7.91/1.90 | subpopulations(first_movers, efficient_producers, all_6_1, v1) = 0
% 7.91/1.90 | & greater_or_equal(v1, v0) = 0 & growth_rate(first_movers, v1) =
% 7.91/1.90 | v2 & greater(zero, v2) = v3 & $i(v2) & $i(v1)))
% 7.91/1.90 |
% 7.91/1.90 | GROUND_INST: instantiating (2) with all_6_1, simplifying with (10), (11)
% 7.91/1.90 | gives:
% 7.91/1.90 | (15) ? [v0: int] : ( ~ (v0 = 0) & environment(all_6_1) = v0) | ? [v0: $i]
% 7.91/1.90 | : (in_environment(all_6_1, v0) = 0 & $i(v0) & ! [v1: $i] : ( ~
% 7.91/1.90 | (subpopulations(first_movers, efficient_producers, all_6_1, v1) =
% 7.91/1.90 | 0) | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : ?
% 7.91/1.90 | [v5: $i] : ? [v6: any] : (greater_or_equal(v1, v0) = v2 &
% 7.91/1.90 | growth_rate(efficient_producers, v1) = v3 &
% 7.91/1.90 | growth_rate(first_movers, v1) = v5 & greater(v3, zero) = v4 &
% 7.91/1.90 | greater(zero, v5) = v6 & $i(v5) & $i(v3) & ( ~ (v2 = 0) | (v6 =
% 7.91/1.90 | 0 & v4 = 0)))))
% 7.91/1.90 |
% 7.91/1.90 | GROUND_INST: instantiating (1) with all_6_1, all_6_0, simplifying with (10),
% 7.91/1.90 | (13) gives:
% 7.91/1.90 | (16) ? [v0: any] : ? [v1: any] : (environment(all_6_1) = v0 &
% 7.91/1.90 | stable(all_6_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0: $i] :
% 7.91/1.90 | (greater(v0, all_6_0) = 0 & $i(v0) & ! [v1: $i] : ( ~
% 7.91/1.90 | (subpopulations(first_movers, efficient_producers, all_6_1, v1) =
% 7.91/1.90 | 0) | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 7.91/1.90 | (greater_or_equal(v1, v0) = v2 & growth_rate(first_movers, v1) =
% 7.91/1.90 | v3 & greater(zero, v3) = v4 & $i(v3) & ( ~ (v2 = 0) | v4 = 0))))
% 7.91/1.90 | | ! [v0: $i] : ( ~ (in_environment(all_6_1, v0) = 0) | ~ $i(v0) | ?
% 7.91/1.90 | [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 7.91/1.90 | subpopulations(first_movers, efficient_producers, all_6_1, v1) = 0
% 7.91/1.90 | & greater_or_equal(v1, v0) = 0 & growth_rate(first_movers, v1) =
% 7.91/1.90 | v2 & greater(zero, v2) = v3 & $i(v2) & $i(v1)))
% 7.91/1.90 |
% 7.91/1.90 | BETA: splitting (15) gives:
% 7.91/1.90 |
% 7.91/1.90 | Case 1:
% 7.91/1.90 | |
% 7.91/1.90 | | (17) ? [v0: int] : ( ~ (v0 = 0) & environment(all_6_1) = v0)
% 7.91/1.90 | |
% 7.91/1.90 | | DELTA: instantiating (17) with fresh symbol all_15_0 gives:
% 7.91/1.90 | | (18) ~ (all_15_0 = 0) & environment(all_6_1) = all_15_0
% 7.91/1.90 | |
% 7.91/1.90 | | ALPHA: (18) implies:
% 7.91/1.90 | | (19) ~ (all_15_0 = 0)
% 7.91/1.90 | | (20) environment(all_6_1) = all_15_0
% 7.91/1.90 | |
% 7.91/1.91 | | GROUND_INST: instantiating (5) with 0, all_15_0, all_6_1, simplifying with
% 7.91/1.91 | | (12), (20) gives:
% 7.91/1.91 | | (21) all_15_0 = 0
% 7.91/1.91 | |
% 7.91/1.91 | | REDUCE: (19), (21) imply:
% 7.91/1.91 | | (22) $false
% 7.91/1.91 | |
% 7.91/1.91 | | CLOSE: (22) is inconsistent.
% 7.91/1.91 | |
% 7.91/1.91 | Case 2:
% 7.91/1.91 | |
% 7.91/1.91 | | (23) ? [v0: $i] : (in_environment(all_6_1, v0) = 0 & $i(v0) & ! [v1:
% 7.91/1.91 | | $i] : ( ~ (subpopulations(first_movers, efficient_producers,
% 7.91/1.91 | | all_6_1, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: $i] :
% 7.91/1.91 | | ? [v4: any] : ? [v5: $i] : ? [v6: any] :
% 7.91/1.91 | | (greater_or_equal(v1, v0) = v2 &
% 7.91/1.91 | | growth_rate(efficient_producers, v1) = v3 &
% 7.91/1.91 | | growth_rate(first_movers, v1) = v5 & greater(v3, zero) = v4 &
% 7.91/1.91 | | greater(zero, v5) = v6 & $i(v5) & $i(v3) & ( ~ (v2 = 0) | (v6
% 7.91/1.91 | | = 0 & v4 = 0)))))
% 7.91/1.91 | |
% 7.91/1.91 | | DELTA: instantiating (23) with fresh symbol all_15_0 gives:
% 7.91/1.91 | | (24) in_environment(all_6_1, all_15_0) = 0 & $i(all_15_0) & ! [v0: $i] :
% 7.91/1.91 | | ( ~ (subpopulations(first_movers, efficient_producers, all_6_1, v0)
% 7.91/1.91 | | = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 7.91/1.91 | | ? [v4: $i] : ? [v5: any] : (greater_or_equal(v0, all_15_0) = v1 &
% 7.91/1.91 | | growth_rate(efficient_producers, v0) = v2 &
% 7.91/1.91 | | growth_rate(first_movers, v0) = v4 & greater(v2, zero) = v3 &
% 7.91/1.91 | | greater(zero, v4) = v5 & $i(v4) & $i(v2) & ( ~ (v1 = 0) | (v5 =
% 7.91/1.91 | | 0 & v3 = 0))))
% 7.91/1.91 | |
% 7.91/1.91 | | ALPHA: (24) implies:
% 7.91/1.91 | | (25) $i(all_15_0)
% 7.91/1.91 | | (26) in_environment(all_6_1, all_15_0) = 0
% 7.91/1.91 | | (27) ! [v0: $i] : ( ~ (subpopulations(first_movers, efficient_producers,
% 7.91/1.91 | | all_6_1, v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] :
% 7.91/1.91 | | ? [v3: any] : ? [v4: $i] : ? [v5: any] : (greater_or_equal(v0,
% 7.91/1.91 | | all_15_0) = v1 & growth_rate(efficient_producers, v0) = v2 &
% 7.91/1.91 | | growth_rate(first_movers, v0) = v4 & greater(v2, zero) = v3 &
% 7.91/1.91 | | greater(zero, v4) = v5 & $i(v4) & $i(v2) & ( ~ (v1 = 0) | (v5 =
% 7.91/1.91 | | 0 & v3 = 0))))
% 7.91/1.91 | |
% 7.91/1.91 | | BETA: splitting (16) gives:
% 7.91/1.91 | |
% 7.91/1.91 | | Case 1:
% 7.91/1.91 | | |
% 7.91/1.91 | | | (28) ? [v0: any] : ? [v1: any] : (environment(all_6_1) = v0 &
% 7.91/1.91 | | | stable(all_6_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.91/1.91 | | |
% 7.91/1.91 | | | DELTA: instantiating (28) with fresh symbols all_24_0, all_24_1 gives:
% 7.91/1.92 | | | (29) environment(all_6_1) = all_24_1 & stable(all_6_1) = all_24_0 & ( ~
% 7.91/1.92 | | | (all_24_0 = 0) | ~ (all_24_1 = 0))
% 7.91/1.92 | | |
% 7.91/1.92 | | | ALPHA: (29) implies:
% 7.91/1.92 | | | (30) stable(all_6_1) = all_24_0
% 7.91/1.92 | | | (31) environment(all_6_1) = all_24_1
% 7.91/1.92 | | | (32) ~ (all_24_0 = 0) | ~ (all_24_1 = 0)
% 7.91/1.92 | | |
% 7.91/1.92 | | | GROUND_INST: instantiating (4) with 0, all_24_0, all_6_1, simplifying with
% 7.91/1.92 | | | (11), (30) gives:
% 7.91/1.92 | | | (33) all_24_0 = 0
% 7.91/1.92 | | |
% 7.91/1.92 | | | GROUND_INST: instantiating (5) with 0, all_24_1, all_6_1, simplifying with
% 7.91/1.92 | | | (12), (31) gives:
% 7.91/1.92 | | | (34) all_24_1 = 0
% 7.91/1.92 | | |
% 7.91/1.92 | | | BETA: splitting (32) gives:
% 7.91/1.92 | | |
% 7.91/1.92 | | | Case 1:
% 7.91/1.92 | | | |
% 7.91/1.92 | | | | (35) ~ (all_24_0 = 0)
% 7.91/1.92 | | | |
% 7.91/1.92 | | | | REDUCE: (33), (35) imply:
% 7.91/1.92 | | | | (36) $false
% 7.91/1.92 | | | |
% 7.91/1.92 | | | | CLOSE: (36) is inconsistent.
% 7.91/1.92 | | | |
% 7.91/1.92 | | | Case 2:
% 7.91/1.92 | | | |
% 7.91/1.92 | | | | (37) ~ (all_24_1 = 0)
% 7.91/1.92 | | | |
% 7.91/1.92 | | | | REDUCE: (34), (37) imply:
% 7.91/1.92 | | | | (38) $false
% 7.91/1.92 | | | |
% 7.91/1.92 | | | | CLOSE: (38) is inconsistent.
% 7.91/1.92 | | | |
% 7.91/1.92 | | | End of split
% 7.91/1.92 | | |
% 7.91/1.92 | | Case 2:
% 7.91/1.92 | | |
% 7.91/1.92 | | | (39) ? [v0: $i] : (greater(v0, all_6_0) = 0 & $i(v0) & ! [v1: $i] : (
% 7.91/1.92 | | | ~ (subpopulations(first_movers, efficient_producers, all_6_1,
% 7.91/1.92 | | | v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : ?
% 7.91/1.92 | | | [v4: any] : (greater_or_equal(v1, v0) = v2 &
% 7.91/1.92 | | | growth_rate(first_movers, v1) = v3 & greater(zero, v3) = v4
% 7.91/1.92 | | | & $i(v3) & ( ~ (v2 = 0) | v4 = 0)))) | ! [v0: $i] : ( ~
% 7.91/1.92 | | | (in_environment(all_6_1, v0) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 7.91/1.92 | | | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 7.91/1.92 | | | subpopulations(first_movers, efficient_producers, all_6_1, v1)
% 7.91/1.92 | | | = 0 & greater_or_equal(v1, v0) = 0 & growth_rate(first_movers,
% 7.91/1.92 | | | v1) = v2 & greater(zero, v2) = v3 & $i(v2) & $i(v1)))
% 7.91/1.92 | | |
% 7.91/1.92 | | | BETA: splitting (39) gives:
% 7.91/1.92 | | |
% 7.91/1.92 | | | Case 1:
% 7.91/1.92 | | | |
% 7.91/1.92 | | | | (40) ? [v0: $i] : (greater(v0, all_6_0) = 0 & $i(v0) & ! [v1: $i] :
% 7.91/1.92 | | | | ( ~ (subpopulations(first_movers, efficient_producers,
% 7.91/1.92 | | | | all_6_1, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3:
% 7.91/1.92 | | | | $i] : ? [v4: any] : (greater_or_equal(v1, v0) = v2 &
% 7.91/1.92 | | | | growth_rate(first_movers, v1) = v3 & greater(zero, v3) =
% 7.91/1.92 | | | | v4 & $i(v3) & ( ~ (v2 = 0) | v4 = 0))))
% 7.91/1.92 | | | |
% 7.91/1.92 | | | | DELTA: instantiating (40) with fresh symbol all_24_0 gives:
% 7.91/1.92 | | | | (41) greater(all_24_0, all_6_0) = 0 & $i(all_24_0) & ! [v0: $i] : (
% 7.91/1.92 | | | | ~ (subpopulations(first_movers, efficient_producers, all_6_1,
% 7.91/1.92 | | | | v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ?
% 7.91/1.92 | | | | [v3: any] : (greater_or_equal(v0, all_24_0) = v1 &
% 7.91/1.92 | | | | growth_rate(first_movers, v0) = v2 & greater(zero, v2) = v3
% 7.91/1.92 | | | | & $i(v2) & ( ~ (v1 = 0) | v3 = 0)))
% 7.91/1.92 | | | |
% 7.91/1.92 | | | | ALPHA: (41) implies:
% 7.91/1.92 | | | | (42) $i(all_24_0)
% 7.91/1.93 | | | | (43) greater(all_24_0, all_6_0) = 0
% 7.91/1.93 | | | | (44) ! [v0: $i] : ( ~ (subpopulations(first_movers,
% 7.91/1.93 | | | | efficient_producers, all_6_1, v0) = 0) | ~ $i(v0) | ?
% 7.91/1.93 | | | | [v1: any] : ? [v2: $i] : ? [v3: any] : (greater_or_equal(v0,
% 7.91/1.93 | | | | all_24_0) = v1 & growth_rate(first_movers, v0) = v2 &
% 7.91/1.93 | | | | greater(zero, v2) = v3 & $i(v2) & ( ~ (v1 = 0) | v3 = 0)))
% 7.91/1.93 | | | |
% 7.91/1.93 | | | | GROUND_INST: instantiating (14) with all_24_0, simplifying with (42),
% 7.91/1.93 | | | | (43) gives:
% 7.91/1.93 | | | | (45) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 7.91/1.93 | | | | subpopulations(first_movers, efficient_producers, all_6_1, v0)
% 7.91/1.93 | | | | = 0 & greater_or_equal(v0, all_24_0) = 0 &
% 7.91/1.93 | | | | growth_rate(first_movers, v0) = v1 & greater(zero, v1) = v2 &
% 7.91/1.93 | | | | $i(v1) & $i(v0))
% 7.91/1.93 | | | |
% 7.91/1.93 | | | | DELTA: instantiating (45) with fresh symbols all_32_0, all_32_1,
% 7.91/1.93 | | | | all_32_2 gives:
% 7.91/1.93 | | | | (46) ~ (all_32_0 = 0) & subpopulations(first_movers,
% 7.91/1.93 | | | | efficient_producers, all_6_1, all_32_2) = 0 &
% 7.91/1.93 | | | | greater_or_equal(all_32_2, all_24_0) = 0 &
% 7.91/1.93 | | | | growth_rate(first_movers, all_32_2) = all_32_1 & greater(zero,
% 7.91/1.93 | | | | all_32_1) = all_32_0 & $i(all_32_1) & $i(all_32_2)
% 7.91/1.93 | | | |
% 7.91/1.93 | | | | ALPHA: (46) implies:
% 7.91/1.93 | | | | (47) ~ (all_32_0 = 0)
% 7.91/1.93 | | | | (48) $i(all_32_2)
% 7.91/1.93 | | | | (49) greater(zero, all_32_1) = all_32_0
% 7.91/1.93 | | | | (50) growth_rate(first_movers, all_32_2) = all_32_1
% 7.91/1.93 | | | | (51) greater_or_equal(all_32_2, all_24_0) = 0
% 7.91/1.93 | | | | (52) subpopulations(first_movers, efficient_producers, all_6_1,
% 7.91/1.93 | | | | all_32_2) = 0
% 7.91/1.93 | | | |
% 7.91/1.93 | | | | GROUND_INST: instantiating (27) with all_32_2, simplifying with (48),
% 7.91/1.93 | | | | (52) gives:
% 7.91/1.93 | | | | (53) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ?
% 7.91/1.93 | | | | [v4: any] : (greater_or_equal(all_32_2, all_15_0) = v0 &
% 7.91/1.93 | | | | growth_rate(efficient_producers, all_32_2) = v1 &
% 7.91/1.93 | | | | growth_rate(first_movers, all_32_2) = v3 & greater(v1, zero) =
% 7.91/1.93 | | | | v2 & greater(zero, v3) = v4 & $i(v3) & $i(v1) & ( ~ (v0 = 0) |
% 7.91/1.93 | | | | (v4 = 0 & v2 = 0)))
% 7.91/1.93 | | | |
% 7.91/1.93 | | | | GROUND_INST: instantiating (44) with all_32_2, simplifying with (48),
% 7.91/1.93 | | | | (52) gives:
% 7.91/1.93 | | | | (54) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 7.91/1.93 | | | | (greater_or_equal(all_32_2, all_24_0) = v0 &
% 7.91/1.93 | | | | growth_rate(first_movers, all_32_2) = v1 & greater(zero, v1) =
% 7.91/1.93 | | | | v2 & $i(v1) & ( ~ (v0 = 0) | v2 = 0))
% 7.91/1.93 | | | |
% 7.91/1.93 | | | | DELTA: instantiating (54) with fresh symbols all_39_0, all_39_1,
% 7.91/1.93 | | | | all_39_2 gives:
% 7.91/1.93 | | | | (55) greater_or_equal(all_32_2, all_24_0) = all_39_2 &
% 7.91/1.93 | | | | growth_rate(first_movers, all_32_2) = all_39_1 & greater(zero,
% 7.91/1.93 | | | | all_39_1) = all_39_0 & $i(all_39_1) & ( ~ (all_39_2 = 0) |
% 7.91/1.93 | | | | all_39_0 = 0)
% 7.91/1.93 | | | |
% 7.91/1.93 | | | | ALPHA: (55) implies:
% 7.91/1.93 | | | | (56) greater(zero, all_39_1) = all_39_0
% 7.91/1.93 | | | | (57) growth_rate(first_movers, all_32_2) = all_39_1
% 7.91/1.94 | | | | (58) greater_or_equal(all_32_2, all_24_0) = all_39_2
% 7.91/1.94 | | | | (59) ~ (all_39_2 = 0) | all_39_0 = 0
% 7.91/1.94 | | | |
% 7.91/1.94 | | | | DELTA: instantiating (53) with fresh symbols all_41_0, all_41_1,
% 7.91/1.94 | | | | all_41_2, all_41_3, all_41_4 gives:
% 7.91/1.94 | | | | (60) greater_or_equal(all_32_2, all_15_0) = all_41_4 &
% 7.91/1.94 | | | | growth_rate(efficient_producers, all_32_2) = all_41_3 &
% 7.91/1.94 | | | | growth_rate(first_movers, all_32_2) = all_41_1 &
% 7.91/1.94 | | | | greater(all_41_3, zero) = all_41_2 & greater(zero, all_41_1) =
% 7.91/1.94 | | | | all_41_0 & $i(all_41_1) & $i(all_41_3) & ( ~ (all_41_4 = 0) |
% 7.91/1.94 | | | | (all_41_0 = 0 & all_41_2 = 0))
% 7.91/1.94 | | | |
% 7.91/1.94 | | | | ALPHA: (60) implies:
% 7.91/1.94 | | | | (61) greater(zero, all_41_1) = all_41_0
% 7.91/1.94 | | | | (62) growth_rate(first_movers, all_32_2) = all_41_1
% 7.91/1.94 | | | |
% 7.91/1.94 | | | | GROUND_INST: instantiating (7) with all_32_1, all_41_1, all_32_2,
% 7.91/1.94 | | | | first_movers, simplifying with (50), (62) gives:
% 7.91/1.94 | | | | (63) all_41_1 = all_32_1
% 7.91/1.94 | | | |
% 7.91/1.94 | | | | GROUND_INST: instantiating (7) with all_39_1, all_41_1, all_32_2,
% 7.91/1.94 | | | | first_movers, simplifying with (57), (62) gives:
% 7.91/1.94 | | | | (64) all_41_1 = all_39_1
% 7.91/1.94 | | | |
% 7.91/1.94 | | | | GROUND_INST: instantiating (8) with 0, all_39_2, all_24_0, all_32_2,
% 7.91/1.94 | | | | simplifying with (51), (58) gives:
% 7.91/1.94 | | | | (65) all_39_2 = 0
% 7.91/1.94 | | | |
% 7.91/1.94 | | | | COMBINE_EQS: (63), (64) imply:
% 7.91/1.94 | | | | (66) all_39_1 = all_32_1
% 7.91/1.94 | | | |
% 7.91/1.94 | | | | REDUCE: (61), (63) imply:
% 7.91/1.94 | | | | (67) greater(zero, all_32_1) = all_41_0
% 7.91/1.94 | | | |
% 7.91/1.94 | | | | REDUCE: (56), (66) imply:
% 7.91/1.94 | | | | (68) greater(zero, all_32_1) = all_39_0
% 7.91/1.94 | | | |
% 7.91/1.94 | | | | BETA: splitting (59) gives:
% 7.91/1.94 | | | |
% 7.91/1.94 | | | | Case 1:
% 7.91/1.94 | | | | |
% 7.91/1.94 | | | | | (69) ~ (all_39_2 = 0)
% 7.91/1.94 | | | | |
% 7.91/1.94 | | | | | REDUCE: (65), (69) imply:
% 7.91/1.94 | | | | | (70) $false
% 7.91/1.94 | | | | |
% 7.91/1.94 | | | | | CLOSE: (70) is inconsistent.
% 7.91/1.94 | | | | |
% 7.91/1.94 | | | | Case 2:
% 7.91/1.94 | | | | |
% 7.91/1.94 | | | | | (71) all_39_0 = 0
% 7.91/1.94 | | | | |
% 7.91/1.94 | | | | | REDUCE: (68), (71) imply:
% 7.91/1.94 | | | | | (72) greater(zero, all_32_1) = 0
% 7.91/1.94 | | | | |
% 7.91/1.94 | | | | | GROUND_INST: instantiating (6) with all_32_0, all_41_0, all_32_1,
% 7.91/1.94 | | | | | zero, simplifying with (49), (67) gives:
% 7.91/1.94 | | | | | (73) all_41_0 = all_32_0
% 7.91/1.94 | | | | |
% 7.91/1.94 | | | | | GROUND_INST: instantiating (6) with 0, all_41_0, all_32_1, zero,
% 7.91/1.94 | | | | | simplifying with (67), (72) gives:
% 7.91/1.94 | | | | | (74) all_41_0 = 0
% 7.91/1.94 | | | | |
% 7.91/1.94 | | | | | COMBINE_EQS: (73), (74) imply:
% 7.91/1.94 | | | | | (75) all_32_0 = 0
% 7.91/1.94 | | | | |
% 7.91/1.94 | | | | | SIMP: (75) implies:
% 7.91/1.94 | | | | | (76) all_32_0 = 0
% 7.91/1.94 | | | | |
% 7.91/1.94 | | | | | REDUCE: (47), (76) imply:
% 7.91/1.94 | | | | | (77) $false
% 7.91/1.94 | | | | |
% 7.91/1.94 | | | | | CLOSE: (77) is inconsistent.
% 7.91/1.94 | | | | |
% 7.91/1.94 | | | | End of split
% 7.91/1.94 | | | |
% 7.91/1.94 | | | Case 2:
% 7.91/1.94 | | | |
% 7.91/1.94 | | | | (78) ! [v0: $i] : ( ~ (in_environment(all_6_1, v0) = 0) | ~ $i(v0)
% 7.91/1.94 | | | | | ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 7.91/1.94 | | | | subpopulations(first_movers, efficient_producers, all_6_1,
% 7.91/1.94 | | | | v1) = 0 & greater_or_equal(v1, v0) = 0 &
% 7.91/1.94 | | | | growth_rate(first_movers, v1) = v2 & greater(zero, v2) = v3
% 7.91/1.94 | | | | & $i(v2) & $i(v1)))
% 7.91/1.94 | | | |
% 7.91/1.94 | | | | GROUND_INST: instantiating (78) with all_15_0, simplifying with (25),
% 7.91/1.94 | | | | (26) gives:
% 7.91/1.95 | | | | (79) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 7.91/1.95 | | | | subpopulations(first_movers, efficient_producers, all_6_1, v0)
% 7.91/1.95 | | | | = 0 & greater_or_equal(v0, all_15_0) = 0 &
% 7.91/1.95 | | | | growth_rate(first_movers, v0) = v1 & greater(zero, v1) = v2 &
% 7.91/1.95 | | | | $i(v1) & $i(v0))
% 7.91/1.95 | | | |
% 7.91/1.95 | | | | DELTA: instantiating (79) with fresh symbols all_25_0, all_25_1,
% 7.91/1.95 | | | | all_25_2 gives:
% 7.91/1.95 | | | | (80) ~ (all_25_0 = 0) & subpopulations(first_movers,
% 7.91/1.95 | | | | efficient_producers, all_6_1, all_25_2) = 0 &
% 7.91/1.95 | | | | greater_or_equal(all_25_2, all_15_0) = 0 &
% 7.91/1.95 | | | | growth_rate(first_movers, all_25_2) = all_25_1 & greater(zero,
% 7.91/1.95 | | | | all_25_1) = all_25_0 & $i(all_25_1) & $i(all_25_2)
% 7.91/1.95 | | | |
% 7.91/1.95 | | | | ALPHA: (80) implies:
% 7.91/1.95 | | | | (81) ~ (all_25_0 = 0)
% 7.91/1.95 | | | | (82) $i(all_25_2)
% 7.91/1.95 | | | | (83) greater(zero, all_25_1) = all_25_0
% 7.91/1.95 | | | | (84) growth_rate(first_movers, all_25_2) = all_25_1
% 7.91/1.95 | | | | (85) greater_or_equal(all_25_2, all_15_0) = 0
% 7.91/1.95 | | | | (86) subpopulations(first_movers, efficient_producers, all_6_1,
% 7.91/1.95 | | | | all_25_2) = 0
% 7.91/1.95 | | | |
% 7.91/1.95 | | | | GROUND_INST: instantiating (27) with all_25_2, simplifying with (82),
% 7.91/1.95 | | | | (86) gives:
% 7.91/1.95 | | | | (87) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ?
% 7.91/1.95 | | | | [v4: any] : (greater_or_equal(all_25_2, all_15_0) = v0 &
% 7.91/1.95 | | | | growth_rate(efficient_producers, all_25_2) = v1 &
% 7.91/1.95 | | | | growth_rate(first_movers, all_25_2) = v3 & greater(v1, zero) =
% 7.91/1.95 | | | | v2 & greater(zero, v3) = v4 & $i(v3) & $i(v1) & ( ~ (v0 = 0) |
% 7.91/1.95 | | | | (v4 = 0 & v2 = 0)))
% 7.91/1.95 | | | |
% 7.91/1.95 | | | | DELTA: instantiating (87) with fresh symbols all_32_0, all_32_1,
% 7.91/1.95 | | | | all_32_2, all_32_3, all_32_4 gives:
% 7.91/1.95 | | | | (88) greater_or_equal(all_25_2, all_15_0) = all_32_4 &
% 7.91/1.95 | | | | growth_rate(efficient_producers, all_25_2) = all_32_3 &
% 7.91/1.95 | | | | growth_rate(first_movers, all_25_2) = all_32_1 &
% 7.91/1.95 | | | | greater(all_32_3, zero) = all_32_2 & greater(zero, all_32_1) =
% 7.91/1.95 | | | | all_32_0 & $i(all_32_1) & $i(all_32_3) & ( ~ (all_32_4 = 0) |
% 7.91/1.95 | | | | (all_32_0 = 0 & all_32_2 = 0))
% 7.91/1.95 | | | |
% 8.46/1.95 | | | | ALPHA: (88) implies:
% 8.46/1.95 | | | | (89) greater(zero, all_32_1) = all_32_0
% 8.46/1.95 | | | | (90) growth_rate(first_movers, all_25_2) = all_32_1
% 8.46/1.95 | | | | (91) greater_or_equal(all_25_2, all_15_0) = all_32_4
% 8.46/1.95 | | | | (92) ~ (all_32_4 = 0) | (all_32_0 = 0 & all_32_2 = 0)
% 8.46/1.95 | | | |
% 8.46/1.95 | | | | GROUND_INST: instantiating (7) with all_25_1, all_32_1, all_25_2,
% 8.46/1.95 | | | | first_movers, simplifying with (84), (90) gives:
% 8.46/1.95 | | | | (93) all_32_1 = all_25_1
% 8.46/1.95 | | | |
% 8.46/1.95 | | | | GROUND_INST: instantiating (8) with 0, all_32_4, all_15_0, all_25_2,
% 8.46/1.95 | | | | simplifying with (85), (91) gives:
% 8.46/1.95 | | | | (94) all_32_4 = 0
% 8.46/1.95 | | | |
% 8.46/1.95 | | | | REDUCE: (89), (93) imply:
% 8.46/1.96 | | | | (95) greater(zero, all_25_1) = all_32_0
% 8.46/1.96 | | | |
% 8.46/1.96 | | | | BETA: splitting (92) gives:
% 8.46/1.96 | | | |
% 8.46/1.96 | | | | Case 1:
% 8.46/1.96 | | | | |
% 8.46/1.96 | | | | | (96) ~ (all_32_4 = 0)
% 8.46/1.96 | | | | |
% 8.46/1.96 | | | | | REDUCE: (94), (96) imply:
% 8.46/1.96 | | | | | (97) $false
% 8.46/1.96 | | | | |
% 8.46/1.96 | | | | | CLOSE: (97) is inconsistent.
% 8.46/1.96 | | | | |
% 8.46/1.96 | | | | Case 2:
% 8.46/1.96 | | | | |
% 8.46/1.96 | | | | | (98) all_32_0 = 0 & all_32_2 = 0
% 8.46/1.96 | | | | |
% 8.46/1.96 | | | | | ALPHA: (98) implies:
% 8.46/1.96 | | | | | (99) all_32_0 = 0
% 8.46/1.96 | | | | |
% 8.46/1.96 | | | | | REDUCE: (95), (99) imply:
% 8.46/1.96 | | | | | (100) greater(zero, all_25_1) = 0
% 8.46/1.96 | | | | |
% 8.46/1.96 | | | | | GROUND_INST: instantiating (6) with all_25_0, 0, all_25_1, zero,
% 8.46/1.96 | | | | | simplifying with (83), (100) gives:
% 8.46/1.96 | | | | | (101) all_25_0 = 0
% 8.46/1.96 | | | | |
% 8.46/1.96 | | | | | REDUCE: (81), (101) imply:
% 8.46/1.96 | | | | | (102) $false
% 8.46/1.96 | | | | |
% 8.46/1.96 | | | | | CLOSE: (102) is inconsistent.
% 8.46/1.96 | | | | |
% 8.46/1.96 | | | | End of split
% 8.46/1.96 | | | |
% 8.46/1.96 | | | End of split
% 8.46/1.96 | | |
% 8.46/1.96 | | End of split
% 8.46/1.96 | |
% 8.46/1.96 | End of split
% 8.46/1.96 |
% 8.46/1.96 End of proof
% 8.46/1.96 % SZS output end Proof for theBenchmark
% 8.46/1.96
% 8.46/1.96 1333ms
%------------------------------------------------------------------------------