TSTP Solution File: MGT035+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : MGT035+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 : n004.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 09:16:20 EDT 2023
% Result : Theorem 137.75s 18.66s
% Output : Proof 139.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT035+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 06:23:52 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.27/1.01 Prover 4: Preprocessing ...
% 2.27/1.01 Prover 1: Preprocessing ...
% 2.80/1.07 Prover 5: Preprocessing ...
% 2.80/1.07 Prover 2: Preprocessing ...
% 2.80/1.07 Prover 0: Preprocessing ...
% 3.01/1.07 Prover 3: Preprocessing ...
% 3.01/1.07 Prover 6: Preprocessing ...
% 4.34/1.34 Prover 3: Constructing countermodel ...
% 4.34/1.34 Prover 6: Proving ...
% 4.34/1.36 Prover 5: Proving ...
% 4.34/1.36 Prover 2: Proving ...
% 4.34/1.37 Prover 1: Constructing countermodel ...
% 5.02/1.44 Prover 4: Constructing countermodel ...
% 5.70/1.47 Prover 0: Proving ...
% 9.32/1.95 Prover 3: gave up
% 9.32/1.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.32/1.98 Prover 7: Preprocessing ...
% 9.78/2.07 Prover 7: Warning: ignoring some quantifiers
% 9.78/2.07 Prover 7: Constructing countermodel ...
% 10.63/2.13 Prover 7: gave up
% 10.73/2.14 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.73/2.19 Prover 8: Preprocessing ...
% 11.25/2.27 Prover 8: Warning: ignoring some quantifiers
% 11.73/2.27 Prover 8: Constructing countermodel ...
% 12.61/2.38 Prover 1: gave up
% 12.61/2.41 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 12.92/2.43 Prover 9: Preprocessing ...
% 13.62/2.56 Prover 9: Constructing countermodel ...
% 14.10/2.59 Prover 8: gave up
% 14.10/2.59 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.10/2.62 Prover 10: Preprocessing ...
% 14.10/2.67 Prover 10: Warning: ignoring some quantifiers
% 14.10/2.67 Prover 10: Constructing countermodel ...
% 14.10/2.71 Prover 10: gave up
% 14.10/2.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.10/2.76 Prover 11: Preprocessing ...
% 16.19/2.92 Prover 11: Constructing countermodel ...
% 61.66/8.88 Prover 2: stopped
% 61.66/8.88 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 61.66/8.88 Prover 12: Preprocessing ...
% 61.66/8.93 Prover 12: Proving ...
% 77.08/10.77 Prover 12: stopped
% 77.08/10.78 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 77.08/10.80 Prover 13: Preprocessing ...
% 77.08/10.83 Prover 13: Warning: ignoring some quantifiers
% 77.08/10.84 Prover 13: Constructing countermodel ...
% 101.19/13.96 Prover 5: stopped
% 101.65/13.98 Prover 14: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=414236379
% 101.65/14.00 Prover 14: Preprocessing ...
% 102.45/14.10 Prover 14: Proving ...
% 112.88/15.49 Prover 13: stopped
% 112.88/15.49 Prover 15: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=723048181
% 112.88/15.51 Prover 15: Preprocessing ...
% 113.61/15.54 Prover 15: Proving ...
% 131.43/17.88 Prover 6: stopped
% 131.83/17.89 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 131.83/17.92 Prover 16: Preprocessing ...
% 132.38/17.96 Prover 16: Warning: ignoring some quantifiers
% 132.38/17.96 Prover 16: Constructing countermodel ...
% 137.75/18.66 Prover 0: proved (17865ms)
% 137.75/18.66
% 137.75/18.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 137.75/18.66
% 137.75/18.66 Prover 9: stopped
% 137.75/18.66 Prover 15: stopped
% 137.75/18.66 Prover 14: stopped
% 137.75/18.66 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 137.75/18.67 Prover 19: Preprocessing ...
% 137.75/18.70 Prover 19: Warning: ignoring some quantifiers
% 137.75/18.70 Prover 19: Constructing countermodel ...
% 138.15/18.75 Prover 16: Found proof (size 934)
% 138.15/18.75 Prover 16: proved (863ms)
% 138.15/18.75 Prover 19: stopped
% 138.49/18.76 Prover 4: stopped
% 138.49/18.76 Prover 11: stopped
% 138.49/18.76
% 138.49/18.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 138.49/18.76
% 138.49/18.78 % SZS output start Proof for theBenchmark
% 138.49/18.78 Assumptions after simplification:
% 138.49/18.78 ---------------------------------
% 138.49/18.78
% 138.49/18.78 (a4)
% 138.49/18.80 ! [v0: $i] : ( ~ $i(v0) | ~ stable(v0) | ~ environment(v0) | ? [v1: $i] :
% 138.49/18.80 ? [v2: $i] : (equilibrium(v0) = v1 & $i(v2) & $i(v1) & greater_or_equal(v2,
% 138.49/18.80 v1) & in_environment(v0, v2)))
% 138.49/18.80
% 138.49/18.80 (d2)
% 138.49/18.81 $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3)
% 138.49/18.81 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ subpopulations(v1, v2, v0, v3) | ~
% 138.49/18.81 environment(v0) | ? [v4: $i] : ? [v5: $i] : (( ~ outcompetes(v2, v1, v3) |
% 138.49/18.81 (growth_rate(v2, v3) = v4 & growth_rate(v1, v3) = v5 & $i(v5) & $i(v4) &
% 138.49/18.81 greater_or_equal(v4, zero) & greater(zero, v5))) & (outcompetes(v2,
% 138.49/18.81 v1, v3) | (growth_rate(v2, v3) = v4 & $i(v4) & ~ greater_or_equal(v4,
% 138.49/18.81 zero)) | (growth_rate(v1, v3) = v5 & $i(v5) & ~ greater(zero,
% 138.49/18.81 v5)))))
% 138.49/18.81
% 138.49/18.81 (l1)
% 138.49/18.81 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ( ~ $i(v0) | ~
% 138.49/18.81 stable(v0) | ~ environment(v0) | ? [v1: $i] : ($i(v1) & in_environment(v0,
% 138.49/18.81 v1) & ! [v2: $i] : ( ~ $i(v2) | ~ subpopulations(first_movers,
% 138.49/18.81 efficient_producers, v0, v2) | ~ greater_or_equal(v2, v1) | ? [v3:
% 138.49/18.81 $i] : ? [v4: $i] : (growth_rate(efficient_producers, v2) = v3 &
% 138.49/18.81 growth_rate(first_movers, v2) = v4 & $i(v4) & $i(v3) & greater(v3,
% 138.49/18.81 v4)))))
% 138.49/18.81
% 138.49/18.81 (l6)
% 138.49/18.81 $i(efficient_producers) & $i(first_movers) & $i(zero) & ! [v0: $i] : ! [v1:
% 138.49/18.81 $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subpopulations(first_movers,
% 138.49/18.81 efficient_producers, v0, v1) | ~ environment(v0) | ? [v2: $i] : ? [v3:
% 138.49/18.81 $i] : ? [v4: $i] : ((v4 = zero & v3 = zero &
% 138.49/18.81 growth_rate(efficient_producers, v1) = zero & growth_rate(first_movers,
% 138.49/18.81 v1) = zero) | (equilibrium(v0) = v2 & $i(v2) & ~ greater_or_equal(v1,
% 138.49/18.81 v2)) | (growth_rate(efficient_producers, v1) = v4 &
% 138.49/18.81 growth_rate(first_movers, v1) = v3 & $i(v4) & $i(v3) & greater(v4, zero)
% 138.49/18.81 & greater(zero, v3)) | (growth_rate(efficient_producers, v1) = v4 &
% 138.49/18.81 growth_rate(first_movers, v1) = v3 & $i(v4) & $i(v3) & greater(v3, zero)
% 138.49/18.81 & greater(zero, v4))))
% 138.49/18.81
% 138.49/18.81 (mp_greater_or_equal)
% 138.49/18.81 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 138.49/18.81 greater_or_equal(v0, v1) | greater(v0, v1)) & ! [v0: $i] : ! [v1: $i] : (
% 138.49/18.81 ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1) | greater_or_equal(v0, v1)) & ?
% 138.49/18.81 [v0: $i] : ( ~ $i(v0) | greater_or_equal(v0, v0))
% 138.49/18.81
% 138.49/18.81 (mp_greater_transitivity)
% 138.49/18.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 138.49/18.81 ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 138.49/18.81
% 138.49/18.81 (mp_times_in_environment)
% 138.49/18.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ $i(v2) | ~ $i(v1) |
% 138.49/18.82 ~ $i(v0) | ~ in_environment(v0, v2) | ~ in_environment(v0, v1) |
% 138.49/18.82 greater(v2, v1) | greater(v1, v2))
% 138.49/18.82
% 138.49/18.82 (prove_t4)
% 138.49/18.82 $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ($i(v0) &
% 138.49/18.82 stable(v0) & environment(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 138.49/18.82 in_environment(v0, v1) | ? [v2: $i] : ($i(v2) &
% 138.49/18.82 subpopulations(first_movers, efficient_producers, v0, v2) &
% 138.49/18.82 greater_or_equal(v2, v1) & ~ outcompetes(efficient_producers,
% 138.49/18.82 first_movers, v2))))
% 138.49/18.82
% 138.49/18.82 (function-axioms)
% 138.49/18.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 138.49/18.82 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) & ! [v0: $i] :
% 138.49/18.82 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (equilibrium(v2) = v1) | ~
% 138.49/18.82 (equilibrium(v2) = v0))
% 138.49/18.82
% 138.49/18.82 Those formulas are unsatisfiable:
% 138.49/18.82 ---------------------------------
% 138.49/18.82
% 138.49/18.82 Begin of proof
% 138.49/18.82 |
% 138.49/18.82 | ALPHA: (mp_greater_or_equal) implies:
% 138.49/18.82 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1)
% 138.49/18.82 | | greater_or_equal(v0, v1))
% 138.49/18.82 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 138.49/18.82 | greater_or_equal(v0, v1) | greater(v0, v1))
% 138.49/18.82 |
% 138.49/18.82 | ALPHA: (d2) implies:
% 138.49/18.82 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 138.49/18.82 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ subpopulations(v1, v2, v0, v3) |
% 138.49/18.82 | ~ environment(v0) | ? [v4: $i] : ? [v5: $i] : (( ~ outcompetes(v2,
% 138.49/18.82 | v1, v3) | (growth_rate(v2, v3) = v4 & growth_rate(v1, v3) = v5
% 138.49/18.82 | & $i(v5) & $i(v4) & greater_or_equal(v4, zero) & greater(zero,
% 138.49/18.82 | v5))) & (outcompetes(v2, v1, v3) | (growth_rate(v2, v3) = v4
% 138.49/18.82 | & $i(v4) & ~ greater_or_equal(v4, zero)) | (growth_rate(v1,
% 138.49/18.82 | v3) = v5 & $i(v5) & ~ greater(zero, v5)))))
% 138.49/18.82 |
% 138.49/18.82 | ALPHA: (l6) implies:
% 138.49/18.82 | (4) $i(zero)
% 138.49/18.83 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 138.49/18.83 | subpopulations(first_movers, efficient_producers, v0, v1) | ~
% 138.49/18.83 | environment(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ((v4 =
% 138.49/18.83 | zero & v3 = zero & growth_rate(efficient_producers, v1) = zero &
% 138.49/18.83 | growth_rate(first_movers, v1) = zero) | (equilibrium(v0) = v2 &
% 138.49/18.83 | $i(v2) & ~ greater_or_equal(v1, v2)) |
% 138.49/18.83 | (growth_rate(efficient_producers, v1) = v4 &
% 138.49/18.83 | growth_rate(first_movers, v1) = v3 & $i(v4) & $i(v3) &
% 138.49/18.83 | greater(v4, zero) & greater(zero, v3)) |
% 138.49/18.83 | (growth_rate(efficient_producers, v1) = v4 &
% 138.49/18.83 | growth_rate(first_movers, v1) = v3 & $i(v4) & $i(v3) &
% 138.49/18.83 | greater(v3, zero) & greater(zero, v4))))
% 138.49/18.83 |
% 138.49/18.83 | ALPHA: (l1) implies:
% 138.49/18.83 | (6) ! [v0: $i] : ( ~ $i(v0) | ~ stable(v0) | ~ environment(v0) | ? [v1:
% 138.49/18.83 | $i] : ($i(v1) & in_environment(v0, v1) & ! [v2: $i] : ( ~ $i(v2) |
% 138.49/18.83 | ~ subpopulations(first_movers, efficient_producers, v0, v2) | ~
% 138.49/18.83 | greater_or_equal(v2, v1) | ? [v3: $i] : ? [v4: $i] :
% 138.49/18.83 | (growth_rate(efficient_producers, v2) = v3 &
% 138.49/18.83 | growth_rate(first_movers, v2) = v4 & $i(v4) & $i(v3) &
% 138.49/18.83 | greater(v3, v4)))))
% 138.49/18.83 |
% 138.49/18.83 | ALPHA: (prove_t4) implies:
% 138.49/18.83 | (7) $i(first_movers)
% 138.49/18.83 | (8) $i(efficient_producers)
% 138.49/18.83 | (9) ? [v0: $i] : ($i(v0) & stable(v0) & environment(v0) & ! [v1: $i] : (
% 138.49/18.83 | ~ $i(v1) | ~ in_environment(v0, v1) | ? [v2: $i] : ($i(v2) &
% 138.49/18.83 | subpopulations(first_movers, efficient_producers, v0, v2) &
% 138.49/18.83 | greater_or_equal(v2, v1) & ~ outcompetes(efficient_producers,
% 138.49/18.83 | first_movers, v2))))
% 138.49/18.83 |
% 138.49/18.83 | ALPHA: (function-axioms) implies:
% 138.49/18.83 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 138.49/18.83 | (equilibrium(v2) = v1) | ~ (equilibrium(v2) = v0))
% 138.49/18.83 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 138.49/18.83 | (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 138.49/18.83 |
% 138.49/18.83 | DELTA: instantiating (9) with fresh symbol all_12_0 gives:
% 138.49/18.83 | (12) $i(all_12_0) & stable(all_12_0) & environment(all_12_0) & ! [v0: $i]
% 138.49/18.83 | : ( ~ $i(v0) | ~ in_environment(all_12_0, v0) | ? [v1: $i] : ($i(v1)
% 138.49/18.83 | & subpopulations(first_movers, efficient_producers, all_12_0, v1)
% 138.49/18.83 | & greater_or_equal(v1, v0) & ~ outcompetes(efficient_producers,
% 138.49/18.83 | first_movers, v1)))
% 138.49/18.83 |
% 138.49/18.83 | ALPHA: (12) implies:
% 138.49/18.83 | (13) environment(all_12_0)
% 138.49/18.83 | (14) stable(all_12_0)
% 138.49/18.83 | (15) $i(all_12_0)
% 138.49/18.83 | (16) ! [v0: $i] : ( ~ $i(v0) | ~ in_environment(all_12_0, v0) | ? [v1:
% 138.49/18.83 | $i] : ($i(v1) & subpopulations(first_movers, efficient_producers,
% 138.49/18.83 | all_12_0, v1) & greater_or_equal(v1, v0) & ~
% 138.49/18.83 | outcompetes(efficient_producers, first_movers, v1)))
% 138.49/18.83 |
% 138.49/18.83 | GROUND_INST: instantiating (a4) with all_12_0, simplifying with (13), (14),
% 138.49/18.83 | (15) gives:
% 138.49/18.83 | (17) ? [v0: $i] : ? [v1: $i] : (equilibrium(all_12_0) = v0 & $i(v1) &
% 138.49/18.83 | $i(v0) & greater_or_equal(v1, v0) & in_environment(all_12_0, v1))
% 138.49/18.83 |
% 138.49/18.83 | GROUND_INST: instantiating (6) with all_12_0, simplifying with (13), (14),
% 138.49/18.83 | (15) gives:
% 138.49/18.84 | (18) ? [v0: $i] : ($i(v0) & in_environment(all_12_0, v0) & ! [v1: $i] : (
% 138.49/18.84 | ~ $i(v1) | ~ subpopulations(first_movers, efficient_producers,
% 138.49/18.84 | all_12_0, v1) | ~ greater_or_equal(v1, v0) | ? [v2: $i] : ?
% 138.49/18.84 | [v3: $i] : (growth_rate(efficient_producers, v1) = v2 &
% 138.49/18.84 | growth_rate(first_movers, v1) = v3 & $i(v3) & $i(v2) &
% 138.49/18.84 | greater(v2, v3))))
% 138.49/18.84 |
% 138.49/18.84 | DELTA: instantiating (17) with fresh symbols all_20_0, all_20_1 gives:
% 138.49/18.84 | (19) equilibrium(all_12_0) = all_20_1 & $i(all_20_0) & $i(all_20_1) &
% 138.49/18.84 | greater_or_equal(all_20_0, all_20_1) & in_environment(all_12_0,
% 138.49/18.84 | all_20_0)
% 138.49/18.84 |
% 138.49/18.84 | ALPHA: (19) implies:
% 138.49/18.84 | (20) in_environment(all_12_0, all_20_0)
% 138.49/18.84 | (21) greater_or_equal(all_20_0, all_20_1)
% 138.49/18.84 | (22) $i(all_20_1)
% 138.49/18.84 | (23) $i(all_20_0)
% 138.49/18.84 | (24) equilibrium(all_12_0) = all_20_1
% 138.49/18.84 |
% 138.49/18.84 | DELTA: instantiating (18) with fresh symbol all_22_0 gives:
% 138.49/18.84 | (25) $i(all_22_0) & in_environment(all_12_0, all_22_0) & ! [v0: $i] : ( ~
% 138.49/18.84 | $i(v0) | ~ subpopulations(first_movers, efficient_producers,
% 138.49/18.84 | all_12_0, v0) | ~ greater_or_equal(v0, all_22_0) | ? [v1: $i] :
% 138.49/18.84 | ? [v2: $i] : (growth_rate(efficient_producers, v0) = v1 &
% 138.49/18.84 | growth_rate(first_movers, v0) = v2 & $i(v2) & $i(v1) & greater(v1,
% 138.49/18.84 | v2)))
% 138.49/18.84 |
% 138.49/18.84 | ALPHA: (25) implies:
% 138.49/18.84 | (26) in_environment(all_12_0, all_22_0)
% 138.49/18.84 | (27) $i(all_22_0)
% 138.49/18.84 | (28) ! [v0: $i] : ( ~ $i(v0) | ~ subpopulations(first_movers,
% 138.49/18.84 | efficient_producers, all_12_0, v0) | ~ greater_or_equal(v0,
% 138.49/18.84 | all_22_0) | ? [v1: $i] : ? [v2: $i] :
% 138.49/18.84 | (growth_rate(efficient_producers, v0) = v1 &
% 138.49/18.84 | growth_rate(first_movers, v0) = v2 & $i(v2) & $i(v1) & greater(v1,
% 138.49/18.84 | v2)))
% 138.49/18.84 |
% 138.49/18.84 | GROUND_INST: instantiating (16) with all_20_0, simplifying with (20), (23)
% 138.49/18.84 | gives:
% 138.49/18.84 | (29) ? [v0: $i] : ($i(v0) & subpopulations(first_movers,
% 138.49/18.84 | efficient_producers, all_12_0, v0) & greater_or_equal(v0,
% 138.49/18.84 | all_20_0) & ~ outcompetes(efficient_producers, first_movers, v0))
% 138.49/18.84 |
% 138.49/18.84 | GROUND_INST: instantiating (mp_times_in_environment) with all_12_0, all_20_0,
% 138.49/18.84 | all_22_0, simplifying with (15), (20), (23), (26), (27) gives:
% 138.49/18.84 | (30) all_22_0 = all_20_0 | greater(all_22_0, all_20_0) | greater(all_20_0,
% 138.49/18.84 | all_22_0)
% 138.49/18.84 |
% 138.49/18.84 | GROUND_INST: instantiating (16) with all_22_0, simplifying with (26), (27)
% 138.49/18.84 | gives:
% 138.49/18.84 | (31) ? [v0: $i] : ($i(v0) & subpopulations(first_movers,
% 138.49/18.84 | efficient_producers, all_12_0, v0) & greater_or_equal(v0,
% 138.49/18.84 | all_22_0) & ~ outcompetes(efficient_producers, first_movers, v0))
% 138.49/18.84 |
% 138.49/18.84 | GROUND_INST: instantiating (2) with all_20_0, all_20_1, simplifying with (21),
% 138.49/18.84 | (22), (23) gives:
% 138.49/18.84 | (32) all_20_0 = all_20_1 | greater(all_20_0, all_20_1)
% 138.49/18.84 |
% 138.49/18.84 | DELTA: instantiating (31) with fresh symbol all_30_0 gives:
% 138.49/18.84 | (33) $i(all_30_0) & subpopulations(first_movers, efficient_producers,
% 138.49/18.84 | all_12_0, all_30_0) & greater_or_equal(all_30_0, all_22_0) & ~
% 138.49/18.84 | outcompetes(efficient_producers, first_movers, all_30_0)
% 138.49/18.84 |
% 138.49/18.84 | ALPHA: (33) implies:
% 138.49/18.84 | (34) ~ outcompetes(efficient_producers, first_movers, all_30_0)
% 138.49/18.84 | (35) greater_or_equal(all_30_0, all_22_0)
% 138.49/18.84 | (36) subpopulations(first_movers, efficient_producers, all_12_0, all_30_0)
% 138.49/18.84 | (37) $i(all_30_0)
% 138.49/18.84 |
% 138.49/18.84 | DELTA: instantiating (29) with fresh symbol all_32_0 gives:
% 138.49/18.84 | (38) $i(all_32_0) & subpopulations(first_movers, efficient_producers,
% 138.49/18.84 | all_12_0, all_32_0) & greater_or_equal(all_32_0, all_20_0) & ~
% 138.49/18.84 | outcompetes(efficient_producers, first_movers, all_32_0)
% 138.49/18.84 |
% 138.49/18.84 | ALPHA: (38) implies:
% 138.49/18.84 | (39) ~ outcompetes(efficient_producers, first_movers, all_32_0)
% 138.49/18.84 | (40) greater_or_equal(all_32_0, all_20_0)
% 138.49/18.84 | (41) subpopulations(first_movers, efficient_producers, all_12_0, all_32_0)
% 138.49/18.84 | (42) $i(all_32_0)
% 138.49/18.84 |
% 138.91/18.84 | GROUND_INST: instantiating (2) with all_30_0, all_22_0, simplifying with (27),
% 138.91/18.84 | (35), (37) gives:
% 138.91/18.85 | (43) all_30_0 = all_22_0 | greater(all_30_0, all_22_0)
% 138.91/18.85 |
% 138.91/18.85 | GROUND_INST: instantiating (2) with all_32_0, all_20_0, simplifying with (23),
% 138.91/18.85 | (40), (42) gives:
% 138.91/18.85 | (44) all_32_0 = all_20_0 | greater(all_32_0, all_20_0)
% 138.91/18.85 |
% 138.91/18.85 | GROUND_INST: instantiating (3) with all_12_0, first_movers,
% 138.91/18.85 | efficient_producers, all_30_0, simplifying with (7), (8), (13),
% 138.91/18.85 | (15), (36), (37) gives:
% 138.91/18.85 | (45) ? [v0: $i] : ? [v1: $i] : (( ~ outcompetes(efficient_producers,
% 138.91/18.85 | first_movers, all_30_0) | (growth_rate(efficient_producers,
% 138.91/18.85 | all_30_0) = v0 & growth_rate(first_movers, all_30_0) = v1 &
% 138.91/18.85 | $i(v1) & $i(v0) & greater_or_equal(v0, zero) & greater(zero,
% 138.91/18.85 | v1))) & (outcompetes(efficient_producers, first_movers,
% 138.91/18.85 | all_30_0) | (growth_rate(efficient_producers, all_30_0) = v0 &
% 138.91/18.85 | $i(v0) & ~ greater_or_equal(v0, zero)) |
% 138.91/18.85 | (growth_rate(first_movers, all_30_0) = v1 & $i(v1) & ~
% 138.91/18.85 | greater(zero, v1))))
% 138.91/18.85 |
% 138.91/18.85 | GROUND_INST: instantiating (5) with all_12_0, all_30_0, simplifying with (13),
% 138.91/18.85 | (15), (36), (37) gives:
% 138.91/18.85 | (46) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ((v2 = zero & v1 = zero &
% 138.91/18.85 | growth_rate(efficient_producers, all_30_0) = zero &
% 138.91/18.85 | growth_rate(first_movers, all_30_0) = zero) |
% 138.91/18.85 | (equilibrium(all_12_0) = v0 & $i(v0) & ~ greater_or_equal(all_30_0,
% 138.91/18.85 | v0)) | (growth_rate(efficient_producers, all_30_0) = v2 &
% 138.91/18.85 | growth_rate(first_movers, all_30_0) = v1 & $i(v2) & $i(v1) &
% 138.91/18.85 | greater(v2, zero) & greater(zero, v1)) |
% 138.91/18.85 | (growth_rate(efficient_producers, all_30_0) = v2 &
% 138.91/18.85 | growth_rate(first_movers, all_30_0) = v1 & $i(v2) & $i(v1) &
% 138.91/18.85 | greater(v1, zero) & greater(zero, v2)))
% 138.91/18.85 |
% 138.91/18.85 | GROUND_INST: instantiating (28) with all_30_0, simplifying with (35), (36),
% 138.91/18.85 | (37) gives:
% 138.91/18.85 | (47) ? [v0: $i] : ? [v1: $i] : (growth_rate(efficient_producers,
% 138.91/18.85 | all_30_0) = v0 & growth_rate(first_movers, all_30_0) = v1 & $i(v1)
% 138.91/18.85 | & $i(v0) & greater(v0, v1))
% 138.91/18.85 |
% 138.91/18.85 | GROUND_INST: instantiating (3) with all_12_0, first_movers,
% 138.91/18.85 | efficient_producers, all_32_0, simplifying with (7), (8), (13),
% 138.91/18.85 | (15), (41), (42) gives:
% 138.91/18.85 | (48) ? [v0: $i] : ? [v1: $i] : (( ~ outcompetes(efficient_producers,
% 138.91/18.85 | first_movers, all_32_0) | (growth_rate(efficient_producers,
% 138.91/18.85 | all_32_0) = v0 & growth_rate(first_movers, all_32_0) = v1 &
% 138.91/18.85 | $i(v1) & $i(v0) & greater_or_equal(v0, zero) & greater(zero,
% 138.91/18.85 | v1))) & (outcompetes(efficient_producers, first_movers,
% 138.91/18.85 | all_32_0) | (growth_rate(efficient_producers, all_32_0) = v0 &
% 138.91/18.85 | $i(v0) & ~ greater_or_equal(v0, zero)) |
% 138.91/18.85 | (growth_rate(first_movers, all_32_0) = v1 & $i(v1) & ~
% 138.91/18.85 | greater(zero, v1))))
% 138.91/18.85 |
% 138.91/18.85 | GROUND_INST: instantiating (5) with all_12_0, all_32_0, simplifying with (13),
% 138.91/18.85 | (15), (41), (42) gives:
% 138.91/18.86 | (49) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ((v2 = zero & v1 = zero &
% 138.91/18.86 | growth_rate(efficient_producers, all_32_0) = zero &
% 138.91/18.86 | growth_rate(first_movers, all_32_0) = zero) |
% 138.91/18.86 | (equilibrium(all_12_0) = v0 & $i(v0) & ~ greater_or_equal(all_32_0,
% 138.91/18.86 | v0)) | (growth_rate(efficient_producers, all_32_0) = v2 &
% 138.91/18.86 | growth_rate(first_movers, all_32_0) = v1 & $i(v2) & $i(v1) &
% 138.91/18.86 | greater(v2, zero) & greater(zero, v1)) |
% 138.91/18.86 | (growth_rate(efficient_producers, all_32_0) = v2 &
% 138.91/18.86 | growth_rate(first_movers, all_32_0) = v1 & $i(v2) & $i(v1) &
% 138.91/18.86 | greater(v1, zero) & greater(zero, v2)))
% 138.91/18.86 |
% 138.91/18.86 | GROUND_INST: instantiating (28) with all_32_0, simplifying with (41), (42)
% 138.91/18.86 | gives:
% 138.91/18.86 | (50) ~ greater_or_equal(all_32_0, all_22_0) | ? [v0: $i] : ? [v1: $i] :
% 138.91/18.86 | (growth_rate(efficient_producers, all_32_0) = v0 &
% 138.91/18.86 | growth_rate(first_movers, all_32_0) = v1 & $i(v1) & $i(v0) &
% 138.91/18.86 | greater(v0, v1))
% 138.91/18.86 |
% 138.91/18.86 | DELTA: instantiating (47) with fresh symbols all_39_0, all_39_1 gives:
% 138.91/18.86 | (51) growth_rate(efficient_producers, all_30_0) = all_39_1 &
% 138.91/18.86 | growth_rate(first_movers, all_30_0) = all_39_0 & $i(all_39_0) &
% 138.91/18.86 | $i(all_39_1) & greater(all_39_1, all_39_0)
% 138.91/18.86 |
% 138.91/18.86 | ALPHA: (51) implies:
% 138.91/18.86 | (52) greater(all_39_1, all_39_0)
% 138.91/18.86 | (53) $i(all_39_1)
% 138.91/18.86 | (54) $i(all_39_0)
% 138.91/18.86 | (55) growth_rate(first_movers, all_30_0) = all_39_0
% 138.91/18.86 | (56) growth_rate(efficient_producers, all_30_0) = all_39_1
% 138.91/18.86 |
% 138.91/18.86 | DELTA: instantiating (48) with fresh symbols all_41_0, all_41_1 gives:
% 138.91/18.86 | (57) ( ~ outcompetes(efficient_producers, first_movers, all_32_0) |
% 138.91/18.86 | (growth_rate(efficient_producers, all_32_0) = all_41_1 &
% 138.91/18.86 | growth_rate(first_movers, all_32_0) = all_41_0 & $i(all_41_0) &
% 138.91/18.86 | $i(all_41_1) & greater_or_equal(all_41_1, zero) & greater(zero,
% 138.91/18.86 | all_41_0))) & (outcompetes(efficient_producers, first_movers,
% 138.91/18.86 | all_32_0) | (growth_rate(efficient_producers, all_32_0) = all_41_1
% 138.91/18.86 | & $i(all_41_1) & ~ greater_or_equal(all_41_1, zero)) |
% 138.91/18.86 | (growth_rate(first_movers, all_32_0) = all_41_0 & $i(all_41_0) & ~
% 138.91/18.86 | greater(zero, all_41_0)))
% 138.91/18.86 |
% 138.91/18.86 | ALPHA: (57) implies:
% 138.91/18.86 | (58) outcompetes(efficient_producers, first_movers, all_32_0) |
% 138.91/18.86 | (growth_rate(efficient_producers, all_32_0) = all_41_1 & $i(all_41_1)
% 138.91/18.86 | & ~ greater_or_equal(all_41_1, zero)) | (growth_rate(first_movers,
% 138.91/18.86 | all_32_0) = all_41_0 & $i(all_41_0) & ~ greater(zero, all_41_0))
% 138.91/18.86 |
% 138.91/18.86 | DELTA: instantiating (45) with fresh symbols all_42_0, all_42_1 gives:
% 138.91/18.86 | (59) ( ~ outcompetes(efficient_producers, first_movers, all_30_0) |
% 138.91/18.86 | (growth_rate(efficient_producers, all_30_0) = all_42_1 &
% 138.91/18.86 | growth_rate(first_movers, all_30_0) = all_42_0 & $i(all_42_0) &
% 138.91/18.86 | $i(all_42_1) & greater_or_equal(all_42_1, zero) & greater(zero,
% 138.91/18.86 | all_42_0))) & (outcompetes(efficient_producers, first_movers,
% 138.91/18.86 | all_30_0) | (growth_rate(efficient_producers, all_30_0) = all_42_1
% 138.91/18.86 | & $i(all_42_1) & ~ greater_or_equal(all_42_1, zero)) |
% 138.91/18.86 | (growth_rate(first_movers, all_30_0) = all_42_0 & $i(all_42_0) & ~
% 138.91/18.86 | greater(zero, all_42_0)))
% 138.91/18.86 |
% 138.91/18.86 | ALPHA: (59) implies:
% 138.91/18.86 | (60) outcompetes(efficient_producers, first_movers, all_30_0) |
% 138.91/18.86 | (growth_rate(efficient_producers, all_30_0) = all_42_1 & $i(all_42_1)
% 138.91/18.86 | & ~ greater_or_equal(all_42_1, zero)) | (growth_rate(first_movers,
% 138.91/18.86 | all_30_0) = all_42_0 & $i(all_42_0) & ~ greater(zero, all_42_0))
% 138.91/18.86 |
% 138.91/18.86 | DELTA: instantiating (46) with fresh symbols all_43_0, all_43_1, all_43_2
% 138.91/18.86 | gives:
% 138.91/18.86 | (61) (all_43_0 = zero & all_43_1 = zero & growth_rate(efficient_producers,
% 138.91/18.86 | all_30_0) = zero & growth_rate(first_movers, all_30_0) = zero) |
% 138.91/18.86 | (equilibrium(all_12_0) = all_43_2 & $i(all_43_2) & ~
% 138.91/18.86 | greater_or_equal(all_30_0, all_43_2)) |
% 138.91/18.86 | (growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 138.91/18.86 | growth_rate(first_movers, all_30_0) = all_43_1 & $i(all_43_0) &
% 138.91/18.86 | $i(all_43_1) & greater(all_43_0, zero) & greater(zero, all_43_1)) |
% 138.91/18.86 | (growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 138.91/18.86 | growth_rate(first_movers, all_30_0) = all_43_1 & $i(all_43_0) &
% 138.91/18.86 | $i(all_43_1) & greater(all_43_1, zero) & greater(zero, all_43_0))
% 138.91/18.86 |
% 138.91/18.86 | DELTA: instantiating (49) with fresh symbols all_44_0, all_44_1, all_44_2
% 138.91/18.86 | gives:
% 138.91/18.86 | (62) (all_44_0 = zero & all_44_1 = zero & growth_rate(efficient_producers,
% 138.91/18.86 | all_32_0) = zero & growth_rate(first_movers, all_32_0) = zero) |
% 138.91/18.86 | (equilibrium(all_12_0) = all_44_2 & $i(all_44_2) & ~
% 138.91/18.86 | greater_or_equal(all_32_0, all_44_2)) |
% 138.91/18.86 | (growth_rate(efficient_producers, all_32_0) = all_44_0 &
% 138.91/18.86 | growth_rate(first_movers, all_32_0) = all_44_1 & $i(all_44_0) &
% 138.91/18.86 | $i(all_44_1) & greater(all_44_0, zero) & greater(zero, all_44_1)) |
% 138.91/18.86 | (growth_rate(efficient_producers, all_32_0) = all_44_0 &
% 138.91/18.86 | growth_rate(first_movers, all_32_0) = all_44_1 & $i(all_44_0) &
% 138.91/18.86 | $i(all_44_1) & greater(all_44_1, zero) & greater(zero, all_44_0))
% 138.91/18.86 |
% 138.91/18.86 | GROUND_INST: instantiating (11) with all_39_0, all_39_1, all_30_0,
% 138.91/18.86 | first_movers, simplifying with (55) gives:
% 138.91/18.87 | (63) all_39_0 = all_39_1 | ~ (growth_rate(first_movers, all_30_0) =
% 138.91/18.87 | all_39_1)
% 138.91/18.87 |
% 138.91/18.87 | GROUND_INST: instantiating (1) with all_39_1, all_39_0, simplifying with (52),
% 138.91/18.87 | (53), (54) gives:
% 138.91/18.87 | (64) greater_or_equal(all_39_1, all_39_0)
% 138.91/18.87 |
% 138.91/18.87 | BETA: splitting (32) gives:
% 138.91/18.87 |
% 138.91/18.87 | Case 1:
% 138.91/18.87 | |
% 138.91/18.87 | | (65) greater(all_20_0, all_20_1)
% 138.91/18.87 | |
% 138.91/18.87 | | BETA: splitting (30) gives:
% 138.91/18.87 | |
% 138.91/18.87 | | Case 1:
% 138.91/18.87 | | |
% 138.91/18.87 | | | (66) greater(all_22_0, all_20_0)
% 138.91/18.87 | | |
% 138.91/18.87 | | | GROUND_INST: instantiating (mp_greater_transitivity) with all_22_0,
% 138.91/18.87 | | | all_20_0, all_20_1, simplifying with (22), (23), (27), (65),
% 138.91/18.87 | | | (66) gives:
% 138.91/18.87 | | | (67) greater(all_22_0, all_20_1)
% 138.91/18.87 | | |
% 138.91/18.87 | | | REF_CLOSE: (1), (4), (10), (11), (22), (24), (27), (34), (37), (43), (52),
% 138.91/18.87 | | | (55), (56), (60), (61), (63), (64), (67),
% 138.91/18.87 | | | (mp_greater_transitivity) are inconsistent by sub-proof #8.
% 138.91/18.87 | | |
% 138.91/18.87 | | Case 2:
% 138.91/18.87 | | |
% 138.91/18.87 | | | (68) ~ greater(all_22_0, all_20_0)
% 138.91/18.87 | | | (69) all_22_0 = all_20_0 | greater(all_20_0, all_22_0)
% 138.91/18.87 | | |
% 138.91/18.87 | | | BETA: splitting (50) gives:
% 138.91/18.87 | | |
% 138.91/18.87 | | | Case 1:
% 138.91/18.87 | | | |
% 138.91/18.87 | | | | (70) ~ greater_or_equal(all_32_0, all_22_0)
% 138.91/18.87 | | | |
% 138.91/18.87 | | | | PRED_UNIFY: (40), (70) imply:
% 138.91/18.87 | | | | (71) ~ (all_22_0 = all_20_0)
% 138.91/18.87 | | | |
% 138.91/18.87 | | | | BETA: splitting (69) gives:
% 138.91/18.87 | | | |
% 138.91/18.87 | | | | Case 1:
% 138.91/18.87 | | | | |
% 138.91/18.87 | | | | | (72) greater(all_20_0, all_22_0)
% 138.91/18.87 | | | | |
% 138.91/18.87 | | | | | GROUND_INST: instantiating (1) with all_20_0, all_22_0, simplifying
% 138.91/18.87 | | | | | with (23), (27), (72) gives:
% 138.91/18.87 | | | | | (73) greater_or_equal(all_20_0, all_22_0)
% 138.91/18.87 | | | | |
% 138.91/18.87 | | | | | PRED_UNIFY: (70), (73) imply:
% 138.91/18.87 | | | | | (74) ~ (all_32_0 = all_20_0)
% 138.91/18.87 | | | | |
% 138.91/18.87 | | | | | BETA: splitting (44) gives:
% 138.91/18.87 | | | | |
% 138.91/18.87 | | | | | Case 1:
% 138.91/18.87 | | | | | |
% 138.91/18.87 | | | | | | (75) greater(all_32_0, all_20_0)
% 138.91/18.87 | | | | | |
% 138.91/18.87 | | | | | | GROUND_INST: instantiating (mp_greater_transitivity) with all_32_0,
% 138.91/18.87 | | | | | | all_20_0, all_22_0, simplifying with (23), (27), (42),
% 138.91/18.87 | | | | | | (72), (75) gives:
% 138.91/18.87 | | | | | | (76) greater(all_32_0, all_22_0)
% 138.91/18.87 | | | | | |
% 138.91/18.87 | | | | | | GROUND_INST: instantiating (1) with all_32_0, all_22_0, simplifying
% 138.91/18.87 | | | | | | with (27), (42), (70), (76) gives:
% 138.91/18.87 | | | | | | (77) $false
% 138.91/18.87 | | | | | |
% 138.91/18.87 | | | | | | CLOSE: (77) is inconsistent.
% 138.91/18.87 | | | | | |
% 138.91/18.87 | | | | | Case 2:
% 138.91/18.87 | | | | | |
% 138.91/18.87 | | | | | | (78) all_32_0 = all_20_0
% 138.91/18.87 | | | | | |
% 138.91/18.87 | | | | | | REDUCE: (74), (78) imply:
% 138.91/18.87 | | | | | | (79) $false
% 138.91/18.87 | | | | | |
% 138.91/18.87 | | | | | | CLOSE: (79) is inconsistent.
% 138.91/18.87 | | | | | |
% 138.91/18.87 | | | | | End of split
% 138.91/18.87 | | | | |
% 138.91/18.88 | | | | Case 2:
% 138.91/18.88 | | | | |
% 138.91/18.88 | | | | | (80) all_22_0 = all_20_0
% 138.91/18.88 | | | | |
% 138.91/18.88 | | | | | REDUCE: (71), (80) imply:
% 138.91/18.88 | | | | | (81) $false
% 138.91/18.88 | | | | |
% 138.91/18.88 | | | | | CLOSE: (81) is inconsistent.
% 138.91/18.88 | | | | |
% 138.91/18.88 | | | | End of split
% 138.91/18.88 | | | |
% 138.91/18.88 | | | Case 2:
% 138.91/18.88 | | | |
% 138.91/18.88 | | | | (82) greater_or_equal(all_32_0, all_22_0)
% 138.91/18.88 | | | | (83) ? [v0: $i] : ? [v1: $i] : (growth_rate(efficient_producers,
% 138.91/18.88 | | | | all_32_0) = v0 & growth_rate(first_movers, all_32_0) = v1 &
% 138.91/18.88 | | | | $i(v1) & $i(v0) & greater(v0, v1))
% 138.91/18.88 | | | |
% 138.91/18.88 | | | | DELTA: instantiating (83) with fresh symbols all_83_0, all_83_1 gives:
% 138.91/18.88 | | | | (84) growth_rate(efficient_producers, all_32_0) = all_83_1 &
% 138.91/18.88 | | | | growth_rate(first_movers, all_32_0) = all_83_0 & $i(all_83_0) &
% 138.91/18.88 | | | | $i(all_83_1) & greater(all_83_1, all_83_0)
% 138.91/18.88 | | | |
% 138.91/18.88 | | | | ALPHA: (84) implies:
% 138.91/18.88 | | | | (85) greater(all_83_1, all_83_0)
% 138.91/18.88 | | | | (86) $i(all_83_1)
% 138.91/18.88 | | | | (87) $i(all_83_0)
% 138.91/18.88 | | | | (88) growth_rate(first_movers, all_32_0) = all_83_0
% 138.91/18.88 | | | | (89) growth_rate(efficient_producers, all_32_0) = all_83_1
% 138.91/18.88 | | | |
% 138.91/18.88 | | | | GROUND_INST: instantiating (1) with all_83_1, all_83_0, simplifying with
% 138.91/18.88 | | | | (85), (86), (87) gives:
% 138.91/18.88 | | | | (90) greater_or_equal(all_83_1, all_83_0)
% 138.91/18.88 | | | |
% 138.91/18.88 | | | | GROUND_INST: instantiating (2) with all_32_0, all_22_0, simplifying with
% 138.91/18.88 | | | | (27), (42), (82) gives:
% 138.91/18.88 | | | | (91) all_32_0 = all_22_0 | greater(all_32_0, all_22_0)
% 138.91/18.88 | | | |
% 138.91/18.88 | | | | BETA: splitting (44) gives:
% 138.91/18.88 | | | |
% 138.91/18.88 | | | | Case 1:
% 138.91/18.88 | | | | |
% 138.91/18.88 | | | | | (92) greater(all_32_0, all_20_0)
% 138.91/18.88 | | | | |
% 138.91/18.88 | | | | | PRED_UNIFY: (68), (92) imply:
% 138.91/18.88 | | | | | (93) ~ (all_32_0 = all_22_0)
% 138.91/18.88 | | | | |
% 138.91/18.88 | | | | | BETA: splitting (91) gives:
% 138.91/18.88 | | | | |
% 138.91/18.88 | | | | | Case 1:
% 138.91/18.88 | | | | | |
% 138.91/18.88 | | | | | |
% 138.91/18.88 | | | | | | GROUND_INST: instantiating (mp_greater_transitivity) with all_32_0,
% 138.91/18.88 | | | | | | all_20_0, all_20_1, simplifying with (22), (23), (42),
% 138.91/18.88 | | | | | | (65), (92) gives:
% 138.91/18.88 | | | | | | (94) greater(all_32_0, all_20_1)
% 138.91/18.88 | | | | | |
% 138.91/18.88 | | | | | | GROUND_INST: instantiating (1) with all_32_0, all_20_1, simplifying
% 138.91/18.88 | | | | | | with (22), (42), (94) gives:
% 138.91/18.88 | | | | | | (95) greater_or_equal(all_32_0, all_20_1)
% 138.91/18.88 | | | | | |
% 138.91/18.88 | | | | | | BETA: splitting (58) gives:
% 138.91/18.88 | | | | | |
% 138.91/18.88 | | | | | | Case 1:
% 138.91/18.88 | | | | | | |
% 138.91/18.88 | | | | | | | (96) outcompetes(efficient_producers, first_movers, all_32_0)
% 138.91/18.88 | | | | | | |
% 138.91/18.88 | | | | | | | PRED_UNIFY: (39), (96) imply:
% 138.91/18.88 | | | | | | | (97) $false
% 138.91/18.88 | | | | | | |
% 138.91/18.88 | | | | | | | CLOSE: (97) is inconsistent.
% 138.91/18.88 | | | | | | |
% 138.91/18.88 | | | | | | Case 2:
% 138.91/18.88 | | | | | | |
% 138.91/18.88 | | | | | | | (98) (growth_rate(efficient_producers, all_32_0) = all_41_1 &
% 138.91/18.88 | | | | | | | $i(all_41_1) & ~ greater_or_equal(all_41_1, zero)) |
% 138.91/18.88 | | | | | | | (growth_rate(first_movers, all_32_0) = all_41_0 &
% 138.91/18.88 | | | | | | | $i(all_41_0) & ~ greater(zero, all_41_0))
% 138.91/18.88 | | | | | | |
% 138.91/18.88 | | | | | | | BETA: splitting (62) gives:
% 138.91/18.88 | | | | | | |
% 138.91/18.88 | | | | | | | Case 1:
% 138.91/18.88 | | | | | | | |
% 138.91/18.88 | | | | | | | | (99) (all_44_0 = zero & all_44_1 = zero &
% 138.91/18.88 | | | | | | | | growth_rate(efficient_producers, all_32_0) = zero &
% 138.91/18.88 | | | | | | | | growth_rate(first_movers, all_32_0) = zero) |
% 138.91/18.88 | | | | | | | | (equilibrium(all_12_0) = all_44_2 & $i(all_44_2) & ~
% 138.91/18.88 | | | | | | | | greater_or_equal(all_32_0, all_44_2))
% 138.91/18.88 | | | | | | | |
% 138.91/18.88 | | | | | | | | BETA: splitting (99) gives:
% 138.91/18.88 | | | | | | | |
% 138.91/18.88 | | | | | | | | Case 1:
% 138.91/18.88 | | | | | | | | |
% 138.91/18.88 | | | | | | | | | (100) all_44_0 = zero & all_44_1 = zero &
% 138.91/18.88 | | | | | | | | | growth_rate(efficient_producers, all_32_0) = zero &
% 138.91/18.88 | | | | | | | | | growth_rate(first_movers, all_32_0) = zero
% 138.91/18.88 | | | | | | | | |
% 138.91/18.88 | | | | | | | | | ALPHA: (100) implies:
% 138.91/18.88 | | | | | | | | | (101) growth_rate(first_movers, all_32_0) = zero
% 138.91/18.88 | | | | | | | | | (102) growth_rate(efficient_producers, all_32_0) = zero
% 138.91/18.88 | | | | | | | | |
% 138.91/18.88 | | | | | | | | | REF_CLOSE: (11), (85), (88), (89), (90), (98), (101), (102)
% 138.91/18.88 | | | | | | | | | are inconsistent by sub-proof #5.
% 138.91/18.88 | | | | | | | | |
% 138.91/18.88 | | | | | | | | Case 2:
% 138.91/18.88 | | | | | | | | |
% 138.91/18.88 | | | | | | | | | (103) equilibrium(all_12_0) = all_44_2 & $i(all_44_2) & ~
% 138.91/18.88 | | | | | | | | | greater_or_equal(all_32_0, all_44_2)
% 138.91/18.88 | | | | | | | | |
% 138.91/18.88 | | | | | | | | | ALPHA: (103) implies:
% 138.91/18.88 | | | | | | | | | (104) ~ greater_or_equal(all_32_0, all_44_2)
% 138.91/18.88 | | | | | | | | | (105) equilibrium(all_12_0) = all_44_2
% 138.91/18.88 | | | | | | | | |
% 138.91/18.88 | | | | | | | | | REF_CLOSE: (10), (24), (95), (104), (105) are inconsistent by
% 138.91/18.88 | | | | | | | | | sub-proof #4.
% 138.91/18.88 | | | | | | | | |
% 138.91/18.88 | | | | | | | | End of split
% 138.91/18.88 | | | | | | | |
% 138.91/18.88 | | | | | | | Case 2:
% 138.91/18.88 | | | | | | | |
% 138.91/18.88 | | | | | | | | (106) (growth_rate(efficient_producers, all_32_0) = all_44_0
% 138.91/18.88 | | | | | | | | & growth_rate(first_movers, all_32_0) = all_44_1 &
% 138.91/18.88 | | | | | | | | $i(all_44_0) & $i(all_44_1) & greater(all_44_0, zero)
% 138.91/18.88 | | | | | | | | & greater(zero, all_44_1)) |
% 138.91/18.88 | | | | | | | | (growth_rate(efficient_producers, all_32_0) = all_44_0
% 138.91/18.88 | | | | | | | | & growth_rate(first_movers, all_32_0) = all_44_1 &
% 138.91/18.88 | | | | | | | | $i(all_44_0) & $i(all_44_1) & greater(all_44_1, zero)
% 138.91/18.88 | | | | | | | | & greater(zero, all_44_0))
% 139.10/18.88 | | | | | | | |
% 139.10/18.88 | | | | | | | | BETA: splitting (106) gives:
% 139.10/18.88 | | | | | | | |
% 139.10/18.88 | | | | | | | | Case 1:
% 139.10/18.88 | | | | | | | | |
% 139.10/18.88 | | | | | | | | | (107) growth_rate(efficient_producers, all_32_0) = all_44_0
% 139.10/18.88 | | | | | | | | | & growth_rate(first_movers, all_32_0) = all_44_1 &
% 139.10/18.88 | | | | | | | | | $i(all_44_0) & $i(all_44_1) & greater(all_44_0, zero)
% 139.10/18.88 | | | | | | | | | & greater(zero, all_44_1)
% 139.10/18.89 | | | | | | | | |
% 139.10/18.89 | | | | | | | | | ALPHA: (107) implies:
% 139.10/18.89 | | | | | | | | | (108) greater(zero, all_44_1)
% 139.10/18.89 | | | | | | | | | (109) greater(all_44_0, zero)
% 139.10/18.89 | | | | | | | | | (110) growth_rate(first_movers, all_32_0) = all_44_1
% 139.10/18.89 | | | | | | | | | (111) growth_rate(efficient_producers, all_32_0) = all_44_0
% 139.10/18.89 | | | | | | | | |
% 139.10/18.89 | | | | | | | | | GROUND_INST: instantiating (11) with all_83_0, all_44_1,
% 139.10/18.89 | | | | | | | | | all_32_0, first_movers, simplifying with (88),
% 139.10/18.89 | | | | | | | | | (110) gives:
% 139.10/18.89 | | | | | | | | | (112) all_83_0 = all_44_1
% 139.10/18.89 | | | | | | | | |
% 139.10/18.89 | | | | | | | | | GROUND_INST: instantiating (11) with all_83_1, all_44_0,
% 139.10/18.89 | | | | | | | | | all_32_0, efficient_producers, simplifying with
% 139.10/18.89 | | | | | | | | | (89), (111) gives:
% 139.10/18.89 | | | | | | | | | (113) all_83_1 = all_44_0
% 139.10/18.89 | | | | | | | | |
% 139.10/18.89 | | | | | | | | | REDUCE: (86), (113) imply:
% 139.10/18.89 | | | | | | | | | (114) $i(all_44_0)
% 139.10/18.89 | | | | | | | | |
% 139.10/18.89 | | | | | | | | | GROUND_INST: instantiating (1) with all_44_0, zero, simplifying
% 139.10/18.89 | | | | | | | | | with (4), (109), (114) gives:
% 139.10/18.89 | | | | | | | | | (115) greater_or_equal(all_44_0, zero)
% 139.10/18.89 | | | | | | | | |
% 139.10/18.89 | | | | | | | | | REF_CLOSE: (11), (98), (108), (110), (111), (115) are
% 139.10/18.89 | | | | | | | | | inconsistent by sub-proof #3.
% 139.10/18.89 | | | | | | | | |
% 139.10/18.89 | | | | | | | | Case 2:
% 139.10/18.89 | | | | | | | | |
% 139.10/18.89 | | | | | | | | | (116) growth_rate(efficient_producers, all_32_0) = all_44_0
% 139.10/18.89 | | | | | | | | | & growth_rate(first_movers, all_32_0) = all_44_1 &
% 139.10/18.89 | | | | | | | | | $i(all_44_0) & $i(all_44_1) & greater(all_44_1, zero)
% 139.10/18.89 | | | | | | | | | & greater(zero, all_44_0)
% 139.10/18.89 | | | | | | | | |
% 139.10/18.89 | | | | | | | | | ALPHA: (116) implies:
% 139.10/18.89 | | | | | | | | | (117) greater(zero, all_44_0)
% 139.10/18.89 | | | | | | | | | (118) greater(all_44_1, zero)
% 139.10/18.89 | | | | | | | | | (119) growth_rate(first_movers, all_32_0) = all_44_1
% 139.10/18.89 | | | | | | | | | (120) growth_rate(efficient_producers, all_32_0) = all_44_0
% 139.10/18.89 | | | | | | | | |
% 139.10/18.89 | | | | | | | | | GROUND_INST: instantiating (11) with all_83_0, all_44_1,
% 139.10/18.89 | | | | | | | | | all_32_0, first_movers, simplifying with (88),
% 139.10/18.89 | | | | | | | | | (119) gives:
% 139.10/18.89 | | | | | | | | | (121) all_83_0 = all_44_1
% 139.10/18.89 | | | | | | | | |
% 139.10/18.89 | | | | | | | | | GROUND_INST: instantiating (11) with all_83_1, all_44_0,
% 139.10/18.89 | | | | | | | | | all_32_0, efficient_producers, simplifying with
% 139.10/18.89 | | | | | | | | | (89), (120) gives:
% 139.10/18.89 | | | | | | | | | (122) all_83_1 = all_44_0
% 139.10/18.89 | | | | | | | | |
% 139.10/18.89 | | | | | | | | | REF_CLOSE: (1), (4), (11), (85), (86), (87), (98), (117),
% 139.10/18.89 | | | | | | | | | (118), (119), (120), (121), (122),
% 139.10/18.89 | | | | | | | | | (mp_greater_transitivity) are inconsistent by
% 139.10/18.89 | | | | | | | | | sub-proof #1.
% 139.10/18.89 | | | | | | | | |
% 139.10/18.89 | | | | | | | | End of split
% 139.10/18.89 | | | | | | | |
% 139.10/18.89 | | | | | | | End of split
% 139.10/18.89 | | | | | | |
% 139.10/18.89 | | | | | | End of split
% 139.10/18.89 | | | | | |
% 139.10/18.89 | | | | | Case 2:
% 139.10/18.89 | | | | | |
% 139.10/18.89 | | | | | | (123) all_32_0 = all_22_0
% 139.10/18.89 | | | | | |
% 139.10/18.89 | | | | | | REDUCE: (93), (123) imply:
% 139.10/18.89 | | | | | | (124) $false
% 139.10/18.89 | | | | | |
% 139.10/18.89 | | | | | | CLOSE: (124) is inconsistent.
% 139.10/18.89 | | | | | |
% 139.10/18.89 | | | | | End of split
% 139.10/18.89 | | | | |
% 139.10/18.89 | | | | Case 2:
% 139.10/18.89 | | | | |
% 139.10/18.89 | | | | | (125) all_32_0 = all_20_0
% 139.10/18.89 | | | | |
% 139.10/18.89 | | | | | REDUCE: (89), (125) imply:
% 139.10/18.89 | | | | | (126) growth_rate(efficient_producers, all_20_0) = all_83_1
% 139.10/18.89 | | | | |
% 139.10/18.89 | | | | | REDUCE: (88), (125) imply:
% 139.10/18.89 | | | | | (127) growth_rate(first_movers, all_20_0) = all_83_0
% 139.10/18.89 | | | | |
% 139.10/18.89 | | | | | BETA: splitting (58) gives:
% 139.10/18.89 | | | | |
% 139.10/18.89 | | | | | Case 1:
% 139.10/18.89 | | | | | |
% 139.10/18.89 | | | | | | (128) outcompetes(efficient_producers, first_movers, all_32_0)
% 139.10/18.89 | | | | | |
% 139.10/18.89 | | | | | | PRED_UNIFY: (39), (128) imply:
% 139.10/18.89 | | | | | | (129) $false
% 139.10/18.89 | | | | | |
% 139.10/18.89 | | | | | | CLOSE: (129) is inconsistent.
% 139.10/18.89 | | | | | |
% 139.10/18.89 | | | | | Case 2:
% 139.10/18.89 | | | | | |
% 139.10/18.89 | | | | | | (130) (growth_rate(efficient_producers, all_32_0) = all_41_1 &
% 139.10/18.89 | | | | | | $i(all_41_1) & ~ greater_or_equal(all_41_1, zero)) |
% 139.10/18.89 | | | | | | (growth_rate(first_movers, all_32_0) = all_41_0 &
% 139.10/18.89 | | | | | | $i(all_41_0) & ~ greater(zero, all_41_0))
% 139.10/18.89 | | | | | |
% 139.10/18.89 | | | | | | BETA: splitting (62) gives:
% 139.10/18.89 | | | | | |
% 139.10/18.89 | | | | | | Case 1:
% 139.10/18.89 | | | | | | |
% 139.10/18.89 | | | | | | | (131) (all_44_0 = zero & all_44_1 = zero &
% 139.10/18.89 | | | | | | | growth_rate(efficient_producers, all_32_0) = zero &
% 139.10/18.89 | | | | | | | growth_rate(first_movers, all_32_0) = zero) |
% 139.10/18.89 | | | | | | | (equilibrium(all_12_0) = all_44_2 & $i(all_44_2) & ~
% 139.10/18.89 | | | | | | | greater_or_equal(all_32_0, all_44_2))
% 139.10/18.89 | | | | | | |
% 139.10/18.89 | | | | | | | BETA: splitting (131) gives:
% 139.10/18.89 | | | | | | |
% 139.10/18.89 | | | | | | | Case 1:
% 139.10/18.89 | | | | | | | |
% 139.10/18.89 | | | | | | | | (132) all_44_0 = zero & all_44_1 = zero &
% 139.10/18.89 | | | | | | | | growth_rate(efficient_producers, all_32_0) = zero &
% 139.10/18.89 | | | | | | | | growth_rate(first_movers, all_32_0) = zero
% 139.10/18.89 | | | | | | | |
% 139.10/18.89 | | | | | | | | ALPHA: (132) implies:
% 139.10/18.89 | | | | | | | | (133) growth_rate(first_movers, all_32_0) = zero
% 139.10/18.89 | | | | | | | | (134) growth_rate(efficient_producers, all_32_0) = zero
% 139.10/18.89 | | | | | | | |
% 139.10/18.89 | | | | | | | | REF_CLOSE: (11), (85), (88), (89), (90), (130), (133), (134) are
% 139.10/18.89 | | | | | | | | inconsistent by sub-proof #5.
% 139.10/18.89 | | | | | | | |
% 139.10/18.89 | | | | | | | Case 2:
% 139.10/18.89 | | | | | | | |
% 139.10/18.89 | | | | | | | | (135) equilibrium(all_12_0) = all_44_2 & $i(all_44_2) & ~
% 139.10/18.89 | | | | | | | | greater_or_equal(all_32_0, all_44_2)
% 139.10/18.89 | | | | | | | |
% 139.10/18.89 | | | | | | | | ALPHA: (135) implies:
% 139.10/18.89 | | | | | | | | (136) ~ greater_or_equal(all_32_0, all_44_2)
% 139.10/18.89 | | | | | | | | (137) equilibrium(all_12_0) = all_44_2
% 139.10/18.89 | | | | | | | |
% 139.10/18.89 | | | | | | | | REDUCE: (125), (136) imply:
% 139.10/18.89 | | | | | | | | (138) ~ greater_or_equal(all_20_0, all_44_2)
% 139.10/18.89 | | | | | | | |
% 139.10/18.89 | | | | | | | | GROUND_INST: instantiating (10) with all_20_1, all_44_2,
% 139.10/18.89 | | | | | | | | all_12_0, simplifying with (24), (137) gives:
% 139.10/18.89 | | | | | | | | (139) all_44_2 = all_20_1
% 139.10/18.89 | | | | | | | |
% 139.10/18.89 | | | | | | | | PRED_UNIFY: (21), (138) imply:
% 139.10/18.89 | | | | | | | | (140) ~ (all_44_2 = all_20_1)
% 139.10/18.89 | | | | | | | |
% 139.10/18.90 | | | | | | | | REDUCE: (139), (140) imply:
% 139.10/18.90 | | | | | | | | (141) $false
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | | CLOSE: (141) is inconsistent.
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | End of split
% 139.10/18.90 | | | | | | |
% 139.10/18.90 | | | | | | Case 2:
% 139.10/18.90 | | | | | | |
% 139.10/18.90 | | | | | | | (142) (growth_rate(efficient_producers, all_32_0) = all_44_0 &
% 139.10/18.90 | | | | | | | growth_rate(first_movers, all_32_0) = all_44_1 &
% 139.10/18.90 | | | | | | | $i(all_44_0) & $i(all_44_1) & greater(all_44_0, zero) &
% 139.10/18.90 | | | | | | | greater(zero, all_44_1)) |
% 139.10/18.90 | | | | | | | (growth_rate(efficient_producers, all_32_0) = all_44_0 &
% 139.10/18.90 | | | | | | | growth_rate(first_movers, all_32_0) = all_44_1 &
% 139.10/18.90 | | | | | | | $i(all_44_0) & $i(all_44_1) & greater(all_44_1, zero) &
% 139.10/18.90 | | | | | | | greater(zero, all_44_0))
% 139.10/18.90 | | | | | | |
% 139.10/18.90 | | | | | | | BETA: splitting (142) gives:
% 139.10/18.90 | | | | | | |
% 139.10/18.90 | | | | | | | Case 1:
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | | (143) growth_rate(efficient_producers, all_32_0) = all_44_0 &
% 139.10/18.90 | | | | | | | | growth_rate(first_movers, all_32_0) = all_44_1 &
% 139.10/18.90 | | | | | | | | $i(all_44_0) & $i(all_44_1) & greater(all_44_0, zero) &
% 139.10/18.90 | | | | | | | | greater(zero, all_44_1)
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | | ALPHA: (143) implies:
% 139.10/18.90 | | | | | | | | (144) greater(zero, all_44_1)
% 139.10/18.90 | | | | | | | | (145) greater(all_44_0, zero)
% 139.10/18.90 | | | | | | | | (146) growth_rate(first_movers, all_32_0) = all_44_1
% 139.10/18.90 | | | | | | | | (147) growth_rate(efficient_producers, all_32_0) = all_44_0
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | | REDUCE: (125), (147) imply:
% 139.10/18.90 | | | | | | | | (148) growth_rate(efficient_producers, all_20_0) = all_44_0
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | | GROUND_INST: instantiating (11) with all_83_1, all_44_0,
% 139.10/18.90 | | | | | | | | all_20_0, efficient_producers, simplifying with
% 139.10/18.90 | | | | | | | | (126), (148) gives:
% 139.10/18.90 | | | | | | | | (149) all_83_1 = all_44_0
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | | REDUCE: (86), (149) imply:
% 139.10/18.90 | | | | | | | | (150) $i(all_44_0)
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | | GROUND_INST: instantiating (1) with all_44_0, zero, simplifying
% 139.10/18.90 | | | | | | | | with (4), (145), (150) gives:
% 139.10/18.90 | | | | | | | | (151) greater_or_equal(all_44_0, zero)
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | | REF_CLOSE: (11), (130), (144), (146), (147), (151) are
% 139.10/18.90 | | | | | | | | inconsistent by sub-proof #3.
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | Case 2:
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | | (152) growth_rate(efficient_producers, all_32_0) = all_44_0 &
% 139.10/18.90 | | | | | | | | growth_rate(first_movers, all_32_0) = all_44_1 &
% 139.10/18.90 | | | | | | | | $i(all_44_0) & $i(all_44_1) & greater(all_44_1, zero) &
% 139.10/18.90 | | | | | | | | greater(zero, all_44_0)
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | | ALPHA: (152) implies:
% 139.10/18.90 | | | | | | | | (153) greater(zero, all_44_0)
% 139.10/18.90 | | | | | | | | (154) greater(all_44_1, zero)
% 139.10/18.90 | | | | | | | | (155) growth_rate(first_movers, all_32_0) = all_44_1
% 139.10/18.90 | | | | | | | | (156) growth_rate(efficient_producers, all_32_0) = all_44_0
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | | REDUCE: (125), (156) imply:
% 139.10/18.90 | | | | | | | | (157) growth_rate(efficient_producers, all_20_0) = all_44_0
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | | REDUCE: (125), (155) imply:
% 139.10/18.90 | | | | | | | | (158) growth_rate(first_movers, all_20_0) = all_44_1
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | | GROUND_INST: instantiating (11) with all_83_0, all_44_1,
% 139.10/18.90 | | | | | | | | all_20_0, first_movers, simplifying with (127),
% 139.10/18.90 | | | | | | | | (158) gives:
% 139.10/18.90 | | | | | | | | (159) all_83_0 = all_44_1
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | | GROUND_INST: instantiating (11) with all_83_1, all_44_0,
% 139.10/18.90 | | | | | | | | all_20_0, efficient_producers, simplifying with
% 139.10/18.90 | | | | | | | | (126), (157) gives:
% 139.10/18.90 | | | | | | | | (160) all_83_1 = all_44_0
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | | REF_CLOSE: (1), (4), (11), (85), (86), (87), (130), (153),
% 139.10/18.90 | | | | | | | | (154), (155), (156), (159), (160),
% 139.10/18.90 | | | | | | | | (mp_greater_transitivity) are inconsistent by
% 139.10/18.90 | | | | | | | | sub-proof #1.
% 139.10/18.90 | | | | | | | |
% 139.10/18.90 | | | | | | | End of split
% 139.10/18.90 | | | | | | |
% 139.10/18.90 | | | | | | End of split
% 139.10/18.90 | | | | | |
% 139.10/18.90 | | | | | End of split
% 139.10/18.90 | | | | |
% 139.10/18.90 | | | | End of split
% 139.10/18.90 | | | |
% 139.10/18.90 | | | End of split
% 139.10/18.90 | | |
% 139.10/18.90 | | End of split
% 139.10/18.90 | |
% 139.10/18.90 | Case 2:
% 139.10/18.90 | |
% 139.10/18.90 | | (161) all_20_0 = all_20_1
% 139.10/18.90 | |
% 139.10/18.90 | | REDUCE: (40), (161) imply:
% 139.10/18.90 | | (162) greater_or_equal(all_32_0, all_20_1)
% 139.10/18.90 | |
% 139.10/18.90 | | BETA: splitting (30) gives:
% 139.10/18.90 | |
% 139.10/18.90 | | Case 1:
% 139.10/18.90 | | |
% 139.10/18.90 | | | (163) greater(all_22_0, all_20_0)
% 139.10/18.90 | | |
% 139.10/18.90 | | | REDUCE: (161), (163) imply:
% 139.10/18.90 | | | (164) greater(all_22_0, all_20_1)
% 139.10/18.90 | | |
% 139.10/18.90 | | | REF_CLOSE: (1), (4), (10), (11), (22), (24), (27), (34), (37), (43), (52),
% 139.10/18.90 | | | (55), (56), (60), (61), (63), (64), (164),
% 139.10/18.90 | | | (mp_greater_transitivity) are inconsistent by sub-proof #8.
% 139.10/18.90 | | |
% 139.10/18.90 | | Case 2:
% 139.10/18.90 | | |
% 139.10/18.90 | | | (165) all_22_0 = all_20_0 | greater(all_20_0, all_22_0)
% 139.10/18.90 | | |
% 139.10/18.90 | | | BETA: splitting (50) gives:
% 139.10/18.90 | | |
% 139.10/18.90 | | | Case 1:
% 139.10/18.90 | | | |
% 139.10/18.90 | | | | (166) ~ greater_or_equal(all_32_0, all_22_0)
% 139.10/18.90 | | | |
% 139.10/18.90 | | | | PRED_UNIFY: (162), (166) imply:
% 139.10/18.90 | | | | (167) ~ (all_22_0 = all_20_1)
% 139.10/18.90 | | | |
% 139.10/18.90 | | | | BETA: splitting (165) gives:
% 139.10/18.90 | | | |
% 139.10/18.90 | | | | Case 1:
% 139.10/18.90 | | | | |
% 139.10/18.90 | | | | | (168) greater(all_20_0, all_22_0)
% 139.10/18.90 | | | | |
% 139.10/18.90 | | | | | REDUCE: (161), (168) imply:
% 139.10/18.90 | | | | | (169) greater(all_20_1, all_22_0)
% 139.10/18.90 | | | | |
% 139.10/18.90 | | | | | GROUND_INST: instantiating (1) with all_20_1, all_22_0, simplifying
% 139.10/18.90 | | | | | with (22), (27), (169) gives:
% 139.10/18.90 | | | | | (170) greater_or_equal(all_20_1, all_22_0)
% 139.10/18.90 | | | | |
% 139.10/18.90 | | | | | PRED_UNIFY: (166), (170) imply:
% 139.10/18.90 | | | | | (171) ~ (all_32_0 = all_20_1)
% 139.10/18.90 | | | | |
% 139.10/18.90 | | | | | BETA: splitting (44) gives:
% 139.10/18.90 | | | | |
% 139.10/18.90 | | | | | Case 1:
% 139.10/18.90 | | | | | |
% 139.10/18.90 | | | | | | (172) greater(all_32_0, all_20_0)
% 139.10/18.90 | | | | | |
% 139.10/18.90 | | | | | | REDUCE: (161), (172) imply:
% 139.10/18.90 | | | | | | (173) greater(all_32_0, all_20_1)
% 139.10/18.90 | | | | | |
% 139.10/18.90 | | | | | | GROUND_INST: instantiating (mp_greater_transitivity) with all_32_0,
% 139.10/18.90 | | | | | | all_20_1, all_22_0, simplifying with (22), (27), (42),
% 139.10/18.90 | | | | | | (169), (173) gives:
% 139.10/18.90 | | | | | | (174) greater(all_32_0, all_22_0)
% 139.10/18.90 | | | | | |
% 139.10/18.90 | | | | | | GROUND_INST: instantiating (1) with all_32_0, all_22_0, simplifying
% 139.10/18.90 | | | | | | with (27), (42), (166), (174) gives:
% 139.10/18.90 | | | | | | (175) $false
% 139.10/18.90 | | | | | |
% 139.10/18.90 | | | | | | CLOSE: (175) is inconsistent.
% 139.10/18.90 | | | | | |
% 139.10/18.90 | | | | | Case 2:
% 139.10/18.90 | | | | | |
% 139.10/18.90 | | | | | | (176) all_32_0 = all_20_0
% 139.10/18.90 | | | | | |
% 139.10/18.90 | | | | | | COMBINE_EQS: (161), (176) imply:
% 139.10/18.90 | | | | | | (177) all_32_0 = all_20_1
% 139.10/18.90 | | | | | |
% 139.10/18.90 | | | | | | REDUCE: (171), (177) imply:
% 139.10/18.90 | | | | | | (178) $false
% 139.10/18.90 | | | | | |
% 139.10/18.90 | | | | | | CLOSE: (178) is inconsistent.
% 139.10/18.90 | | | | | |
% 139.10/18.90 | | | | | End of split
% 139.10/18.90 | | | | |
% 139.10/18.90 | | | | Case 2:
% 139.10/18.90 | | | | |
% 139.10/18.90 | | | | | (179) all_22_0 = all_20_0
% 139.10/18.90 | | | | |
% 139.10/18.90 | | | | | COMBINE_EQS: (161), (179) imply:
% 139.10/18.90 | | | | | (180) all_22_0 = all_20_1
% 139.10/18.90 | | | | |
% 139.10/18.90 | | | | | REDUCE: (167), (180) imply:
% 139.10/18.90 | | | | | (181) $false
% 139.10/18.90 | | | | |
% 139.10/18.90 | | | | | CLOSE: (181) is inconsistent.
% 139.10/18.90 | | | | |
% 139.10/18.90 | | | | End of split
% 139.10/18.90 | | | |
% 139.10/18.90 | | | Case 2:
% 139.10/18.90 | | | |
% 139.10/18.90 | | | | (182) ? [v0: $i] : ? [v1: $i] : (growth_rate(efficient_producers,
% 139.10/18.90 | | | | all_32_0) = v0 & growth_rate(first_movers, all_32_0) = v1 &
% 139.10/18.90 | | | | $i(v1) & $i(v0) & greater(v0, v1))
% 139.10/18.90 | | | |
% 139.10/18.90 | | | | DELTA: instantiating (182) with fresh symbols all_83_0, all_83_1 gives:
% 139.10/18.91 | | | | (183) growth_rate(efficient_producers, all_32_0) = all_83_1 &
% 139.10/18.91 | | | | growth_rate(first_movers, all_32_0) = all_83_0 & $i(all_83_0) &
% 139.10/18.91 | | | | $i(all_83_1) & greater(all_83_1, all_83_0)
% 139.10/18.91 | | | |
% 139.10/18.91 | | | | ALPHA: (183) implies:
% 139.10/18.91 | | | | (184) greater(all_83_1, all_83_0)
% 139.10/18.91 | | | | (185) $i(all_83_1)
% 139.10/18.91 | | | | (186) $i(all_83_0)
% 139.10/18.91 | | | | (187) growth_rate(first_movers, all_32_0) = all_83_0
% 139.10/18.91 | | | | (188) growth_rate(efficient_producers, all_32_0) = all_83_1
% 139.10/18.91 | | | |
% 139.10/18.91 | | | | GROUND_INST: instantiating (1) with all_83_1, all_83_0, simplifying with
% 139.10/18.91 | | | | (184), (185), (186) gives:
% 139.10/18.91 | | | | (189) greater_or_equal(all_83_1, all_83_0)
% 139.10/18.91 | | | |
% 139.10/18.91 | | | | BETA: splitting (58) gives:
% 139.10/18.91 | | | |
% 139.10/18.91 | | | | Case 1:
% 139.10/18.91 | | | | |
% 139.10/18.91 | | | | | (190) outcompetes(efficient_producers, first_movers, all_32_0)
% 139.10/18.91 | | | | |
% 139.10/18.91 | | | | | PRED_UNIFY: (39), (190) imply:
% 139.10/18.91 | | | | | (191) $false
% 139.10/18.91 | | | | |
% 139.10/18.91 | | | | | CLOSE: (191) is inconsistent.
% 139.10/18.91 | | | | |
% 139.10/18.91 | | | | Case 2:
% 139.10/18.91 | | | | |
% 139.10/18.91 | | | | | (192) (growth_rate(efficient_producers, all_32_0) = all_41_1 &
% 139.10/18.91 | | | | | $i(all_41_1) & ~ greater_or_equal(all_41_1, zero)) |
% 139.10/18.91 | | | | | (growth_rate(first_movers, all_32_0) = all_41_0 &
% 139.10/18.91 | | | | | $i(all_41_0) & ~ greater(zero, all_41_0))
% 139.10/18.91 | | | | |
% 139.10/18.91 | | | | | BETA: splitting (62) gives:
% 139.10/18.91 | | | | |
% 139.10/18.91 | | | | | Case 1:
% 139.10/18.91 | | | | | |
% 139.10/18.91 | | | | | | (193) (all_44_0 = zero & all_44_1 = zero &
% 139.10/18.91 | | | | | | growth_rate(efficient_producers, all_32_0) = zero &
% 139.10/18.91 | | | | | | growth_rate(first_movers, all_32_0) = zero) |
% 139.10/18.91 | | | | | | (equilibrium(all_12_0) = all_44_2 & $i(all_44_2) & ~
% 139.10/18.91 | | | | | | greater_or_equal(all_32_0, all_44_2))
% 139.10/18.91 | | | | | |
% 139.10/18.91 | | | | | | BETA: splitting (193) gives:
% 139.10/18.91 | | | | | |
% 139.10/18.91 | | | | | | Case 1:
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | (194) all_44_0 = zero & all_44_1 = zero &
% 139.10/18.91 | | | | | | | growth_rate(efficient_producers, all_32_0) = zero &
% 139.10/18.91 | | | | | | | growth_rate(first_movers, all_32_0) = zero
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | ALPHA: (194) implies:
% 139.10/18.91 | | | | | | | (195) growth_rate(first_movers, all_32_0) = zero
% 139.10/18.91 | | | | | | | (196) growth_rate(efficient_producers, all_32_0) = zero
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | GROUND_INST: instantiating (11) with all_83_0, zero, all_32_0,
% 139.10/18.91 | | | | | | | first_movers, simplifying with (187), (195) gives:
% 139.10/18.91 | | | | | | | (197) all_83_0 = zero
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | GROUND_INST: instantiating (11) with all_83_1, zero, all_32_0,
% 139.10/18.91 | | | | | | | efficient_producers, simplifying with (188), (196)
% 139.10/18.91 | | | | | | | gives:
% 139.10/18.91 | | | | | | | (198) all_83_1 = zero
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | REDUCE: (189), (197), (198) imply:
% 139.10/18.91 | | | | | | | (199) greater_or_equal(zero, zero)
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | REDUCE: (184), (197), (198) imply:
% 139.10/18.91 | | | | | | | (200) greater(zero, zero)
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | BETA: splitting (192) gives:
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | Case 1:
% 139.10/18.91 | | | | | | | |
% 139.10/18.91 | | | | | | | | (201) growth_rate(efficient_producers, all_32_0) = all_41_1 &
% 139.10/18.91 | | | | | | | | $i(all_41_1) & ~ greater_or_equal(all_41_1, zero)
% 139.10/18.91 | | | | | | | |
% 139.10/18.91 | | | | | | | | ALPHA: (201) implies:
% 139.10/18.91 | | | | | | | | (202) ~ greater_or_equal(all_41_1, zero)
% 139.10/18.91 | | | | | | | | (203) growth_rate(efficient_producers, all_32_0) = all_41_1
% 139.10/18.91 | | | | | | | |
% 139.10/18.91 | | | | | | | | REF_CLOSE: (11), (196), (199), (202), (203) are inconsistent by
% 139.10/18.91 | | | | | | | | sub-proof #7.
% 139.10/18.91 | | | | | | | |
% 139.10/18.91 | | | | | | | Case 2:
% 139.10/18.91 | | | | | | | |
% 139.10/18.91 | | | | | | | | (204) growth_rate(first_movers, all_32_0) = all_41_0 &
% 139.10/18.91 | | | | | | | | $i(all_41_0) & ~ greater(zero, all_41_0)
% 139.10/18.91 | | | | | | | |
% 139.10/18.91 | | | | | | | | ALPHA: (204) implies:
% 139.10/18.91 | | | | | | | | (205) ~ greater(zero, all_41_0)
% 139.10/18.91 | | | | | | | | (206) growth_rate(first_movers, all_32_0) = all_41_0
% 139.10/18.91 | | | | | | | |
% 139.10/18.91 | | | | | | | | REF_CLOSE: (11), (195), (200), (205), (206) are inconsistent by
% 139.10/18.91 | | | | | | | | sub-proof #6.
% 139.10/18.91 | | | | | | | |
% 139.10/18.91 | | | | | | | End of split
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | Case 2:
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | (207) equilibrium(all_12_0) = all_44_2 & $i(all_44_2) & ~
% 139.10/18.91 | | | | | | | greater_or_equal(all_32_0, all_44_2)
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | ALPHA: (207) implies:
% 139.10/18.91 | | | | | | | (208) ~ greater_or_equal(all_32_0, all_44_2)
% 139.10/18.91 | | | | | | | (209) equilibrium(all_12_0) = all_44_2
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | REF_CLOSE: (10), (24), (162), (208), (209) are inconsistent by
% 139.10/18.91 | | | | | | | sub-proof #4.
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | End of split
% 139.10/18.91 | | | | | |
% 139.10/18.91 | | | | | Case 2:
% 139.10/18.91 | | | | | |
% 139.10/18.91 | | | | | | (210) (growth_rate(efficient_producers, all_32_0) = all_44_0 &
% 139.10/18.91 | | | | | | growth_rate(first_movers, all_32_0) = all_44_1 &
% 139.10/18.91 | | | | | | $i(all_44_0) & $i(all_44_1) & greater(all_44_0, zero) &
% 139.10/18.91 | | | | | | greater(zero, all_44_1)) |
% 139.10/18.91 | | | | | | (growth_rate(efficient_producers, all_32_0) = all_44_0 &
% 139.10/18.91 | | | | | | growth_rate(first_movers, all_32_0) = all_44_1 &
% 139.10/18.91 | | | | | | $i(all_44_0) & $i(all_44_1) & greater(all_44_1, zero) &
% 139.10/18.91 | | | | | | greater(zero, all_44_0))
% 139.10/18.91 | | | | | |
% 139.10/18.91 | | | | | | BETA: splitting (210) gives:
% 139.10/18.91 | | | | | |
% 139.10/18.91 | | | | | | Case 1:
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | (211) growth_rate(efficient_producers, all_32_0) = all_44_0 &
% 139.10/18.91 | | | | | | | growth_rate(first_movers, all_32_0) = all_44_1 &
% 139.10/18.91 | | | | | | | $i(all_44_0) & $i(all_44_1) & greater(all_44_0, zero) &
% 139.10/18.91 | | | | | | | greater(zero, all_44_1)
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | ALPHA: (211) implies:
% 139.10/18.91 | | | | | | | (212) greater(zero, all_44_1)
% 139.10/18.91 | | | | | | | (213) greater(all_44_0, zero)
% 139.10/18.91 | | | | | | | (214) growth_rate(first_movers, all_32_0) = all_44_1
% 139.10/18.91 | | | | | | | (215) growth_rate(efficient_producers, all_32_0) = all_44_0
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | GROUND_INST: instantiating (11) with all_83_0, all_44_1, all_32_0,
% 139.10/18.91 | | | | | | | first_movers, simplifying with (187), (214) gives:
% 139.10/18.91 | | | | | | | (216) all_83_0 = all_44_1
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | GROUND_INST: instantiating (11) with all_83_1, all_44_0, all_32_0,
% 139.10/18.91 | | | | | | | efficient_producers, simplifying with (188), (215)
% 139.10/18.91 | | | | | | | gives:
% 139.10/18.91 | | | | | | | (217) all_83_1 = all_44_0
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | REDUCE: (185), (217) imply:
% 139.10/18.91 | | | | | | | (218) $i(all_44_0)
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | GROUND_INST: instantiating (1) with all_44_0, zero, simplifying
% 139.10/18.91 | | | | | | | with (4), (213), (218) gives:
% 139.10/18.91 | | | | | | | (219) greater_or_equal(all_44_0, zero)
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | REF_CLOSE: (11), (192), (212), (214), (215), (219) are
% 139.10/18.91 | | | | | | | inconsistent by sub-proof #3.
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | Case 2:
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | (220) growth_rate(efficient_producers, all_32_0) = all_44_0 &
% 139.10/18.91 | | | | | | | growth_rate(first_movers, all_32_0) = all_44_1 &
% 139.10/18.91 | | | | | | | $i(all_44_0) & $i(all_44_1) & greater(all_44_1, zero) &
% 139.10/18.91 | | | | | | | greater(zero, all_44_0)
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | ALPHA: (220) implies:
% 139.10/18.91 | | | | | | | (221) greater(zero, all_44_0)
% 139.10/18.91 | | | | | | | (222) greater(all_44_1, zero)
% 139.10/18.91 | | | | | | | (223) growth_rate(first_movers, all_32_0) = all_44_1
% 139.10/18.91 | | | | | | | (224) growth_rate(efficient_producers, all_32_0) = all_44_0
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | GROUND_INST: instantiating (11) with all_83_0, all_44_1, all_32_0,
% 139.10/18.91 | | | | | | | first_movers, simplifying with (187), (223) gives:
% 139.10/18.91 | | | | | | | (225) all_83_0 = all_44_1
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | GROUND_INST: instantiating (11) with all_83_1, all_44_0, all_32_0,
% 139.10/18.91 | | | | | | | efficient_producers, simplifying with (188), (224)
% 139.10/18.91 | | | | | | | gives:
% 139.10/18.91 | | | | | | | (226) all_83_1 = all_44_0
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | REDUCE: (186), (225) imply:
% 139.10/18.91 | | | | | | | (227) $i(all_44_1)
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | REDUCE: (185), (226) imply:
% 139.10/18.91 | | | | | | | (228) $i(all_44_0)
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | REDUCE: (184), (225), (226) imply:
% 139.10/18.91 | | | | | | | (229) greater(all_44_0, all_44_1)
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | GROUND_INST: instantiating (mp_greater_transitivity) with
% 139.10/18.91 | | | | | | | all_44_1, zero, all_44_1, simplifying with (4),
% 139.10/18.91 | | | | | | | (222), (227) gives:
% 139.10/18.91 | | | | | | | (230) ~ greater(zero, all_44_1) | greater(all_44_1, all_44_1)
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | GROUND_INST: instantiating (mp_greater_transitivity) with
% 139.10/18.91 | | | | | | | all_44_0, all_44_1, zero, simplifying with (4),
% 139.10/18.91 | | | | | | | (222), (227), (228), (229) gives:
% 139.10/18.91 | | | | | | | (231) greater(all_44_0, zero)
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | GROUND_INST: instantiating (mp_greater_transitivity) with zero,
% 139.10/18.91 | | | | | | | all_44_0, all_44_1, simplifying with (4), (221),
% 139.10/18.91 | | | | | | | (227), (228), (229) gives:
% 139.10/18.91 | | | | | | | (232) greater(zero, all_44_1)
% 139.10/18.91 | | | | | | |
% 139.10/18.91 | | | | | | | REF_CLOSE: (1), (4), (11), (192), (223), (224), (228), (230),
% 139.10/18.91 | | | | | | | (231), (232) are inconsistent by sub-proof #2.
% 139.10/18.91 | | | | | | |
% 139.10/18.92 | | | | | | End of split
% 139.10/18.92 | | | | | |
% 139.10/18.92 | | | | | End of split
% 139.10/18.92 | | | | |
% 139.10/18.92 | | | | End of split
% 139.10/18.92 | | | |
% 139.10/18.92 | | | End of split
% 139.10/18.92 | | |
% 139.10/18.92 | | End of split
% 139.10/18.92 | |
% 139.10/18.92 | End of split
% 139.10/18.92 |
% 139.10/18.92 End of proof
% 139.10/18.92
% 139.10/18.92 Sub-proof #1 shows that the following formulas are inconsistent:
% 139.10/18.92 ----------------------------------------------------------------
% 139.10/18.92 (1) all_83_1 = all_44_0
% 139.10/18.92 (2) $i(all_83_1)
% 139.10/18.92 (3) growth_rate(efficient_producers, all_32_0) = all_44_0
% 139.10/18.92 (4) $i(all_83_0)
% 139.10/18.92 (5) greater(zero, all_44_0)
% 139.10/18.92 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 139.10/18.92 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 139.10/18.92 (7) greater(all_44_1, zero)
% 139.10/18.92 (8) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1) |
% 139.10/18.92 greater_or_equal(v0, v1))
% 139.10/18.92 (9) all_83_0 = all_44_1
% 139.10/18.92 (10) greater(all_83_1, all_83_0)
% 139.10/18.92 (11) growth_rate(first_movers, all_32_0) = all_44_1
% 139.10/18.92 (12) $i(zero)
% 139.10/18.92 (13) (growth_rate(efficient_producers, all_32_0) = all_41_1 & $i(all_41_1) &
% 139.10/18.92 ~ greater_or_equal(all_41_1, zero)) | (growth_rate(first_movers,
% 139.10/18.92 all_32_0) = all_41_0 & $i(all_41_0) & ~ greater(zero, all_41_0))
% 139.10/18.92 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 139.10/18.92 $i(v0) | ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 139.10/18.92
% 139.10/18.92 Begin of proof
% 139.10/18.92 |
% 139.10/18.92 | REDUCE: (4), (9) imply:
% 139.10/18.92 | (15) $i(all_44_1)
% 139.10/18.92 |
% 139.10/18.92 | REDUCE: (1), (2) imply:
% 139.10/18.92 | (16) $i(all_44_0)
% 139.10/18.92 |
% 139.10/18.92 | REDUCE: (1), (9), (10) imply:
% 139.10/18.92 | (17) greater(all_44_0, all_44_1)
% 139.10/18.92 |
% 139.10/18.92 | GROUND_INST: instantiating (14) with all_44_1, zero, all_44_1, simplifying
% 139.10/18.92 | with (7), (12), (15) gives:
% 139.10/18.92 | (18) ~ greater(zero, all_44_1) | greater(all_44_1, all_44_1)
% 139.10/18.92 |
% 139.10/18.92 | GROUND_INST: instantiating (14) with all_44_0, all_44_1, zero, simplifying
% 139.10/18.92 | with (7), (12), (15), (16), (17) gives:
% 139.10/18.92 | (19) greater(all_44_0, zero)
% 139.10/18.92 |
% 139.10/18.92 | GROUND_INST: instantiating (14) with zero, all_44_0, all_44_1, simplifying
% 139.10/18.92 | with (5), (12), (15), (16), (17) gives:
% 139.10/18.92 | (20) greater(zero, all_44_1)
% 139.10/18.92 |
% 139.10/18.92 | REF_CLOSE: (3), (6), (8), (11), (12), (13), (16), (18), (19), (20) are
% 139.10/18.92 | inconsistent by sub-proof #2.
% 139.10/18.92 |
% 139.10/18.92 End of proof
% 139.10/18.92
% 139.10/18.92 Sub-proof #2 shows that the following formulas are inconsistent:
% 139.10/18.92 ----------------------------------------------------------------
% 139.10/18.92 (1) growth_rate(efficient_producers, all_32_0) = all_44_0
% 139.10/18.92 (2) greater(all_44_0, zero)
% 139.10/18.92 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 139.10/18.92 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 139.10/18.92 (4) ~ greater(zero, all_44_1) | greater(all_44_1, all_44_1)
% 139.10/18.92 (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1) |
% 139.10/18.92 greater_or_equal(v0, v1))
% 139.10/18.92 (6) growth_rate(first_movers, all_32_0) = all_44_1
% 139.10/18.92 (7) $i(all_44_0)
% 139.10/18.92 (8) $i(zero)
% 139.10/18.92 (9) (growth_rate(efficient_producers, all_32_0) = all_41_1 & $i(all_41_1) &
% 139.10/18.92 ~ greater_or_equal(all_41_1, zero)) | (growth_rate(first_movers,
% 139.10/18.92 all_32_0) = all_41_0 & $i(all_41_0) & ~ greater(zero, all_41_0))
% 139.10/18.92 (10) greater(zero, all_44_1)
% 139.10/18.92
% 139.10/18.92 Begin of proof
% 139.10/18.92 |
% 139.10/18.92 | BETA: splitting (4) gives:
% 139.10/18.92 |
% 139.10/18.92 | Case 1:
% 139.10/18.92 | |
% 139.10/18.92 | | (11) ~ greater(zero, all_44_1)
% 139.10/18.92 | |
% 139.10/18.92 | | PRED_UNIFY: (10), (11) imply:
% 139.10/18.92 | | (12) $false
% 139.10/18.92 | |
% 139.10/18.92 | | CLOSE: (12) is inconsistent.
% 139.10/18.92 | |
% 139.10/18.92 | Case 2:
% 139.10/18.92 | |
% 139.10/18.92 | |
% 139.10/18.92 | | GROUND_INST: instantiating (5) with all_44_0, zero, simplifying with (2),
% 139.10/18.92 | | (7), (8) gives:
% 139.10/18.92 | | (13) greater_or_equal(all_44_0, zero)
% 139.10/18.92 | |
% 139.10/18.92 | | REF_CLOSE: (1), (3), (6), (9), (10), (13) are inconsistent by sub-proof #3.
% 139.10/18.92 | |
% 139.10/18.92 | End of split
% 139.10/18.92 |
% 139.10/18.92 End of proof
% 139.10/18.92
% 139.10/18.92 Sub-proof #3 shows that the following formulas are inconsistent:
% 139.10/18.92 ----------------------------------------------------------------
% 139.10/18.92 (1) growth_rate(efficient_producers, all_32_0) = all_44_0
% 139.10/18.92 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 139.10/18.92 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 139.10/18.92 (3) greater_or_equal(all_44_0, zero)
% 139.10/18.92 (4) growth_rate(first_movers, all_32_0) = all_44_1
% 139.10/18.92 (5) (growth_rate(efficient_producers, all_32_0) = all_41_1 & $i(all_41_1) &
% 139.10/18.92 ~ greater_or_equal(all_41_1, zero)) | (growth_rate(first_movers,
% 139.10/18.92 all_32_0) = all_41_0 & $i(all_41_0) & ~ greater(zero, all_41_0))
% 139.10/18.92 (6) greater(zero, all_44_1)
% 139.10/18.92
% 139.10/18.92 Begin of proof
% 139.10/18.92 |
% 139.10/18.92 | BETA: splitting (5) gives:
% 139.10/18.92 |
% 139.10/18.92 | Case 1:
% 139.10/18.92 | |
% 139.10/18.92 | | (7) growth_rate(efficient_producers, all_32_0) = all_41_1 & $i(all_41_1)
% 139.10/18.92 | | & ~ greater_or_equal(all_41_1, zero)
% 139.10/18.92 | |
% 139.10/18.92 | | ALPHA: (7) implies:
% 139.10/18.92 | | (8) ~ greater_or_equal(all_41_1, zero)
% 139.10/18.92 | | (9) growth_rate(efficient_producers, all_32_0) = all_41_1
% 139.10/18.92 | |
% 139.10/18.92 | | GROUND_INST: instantiating (2) with all_44_0, all_41_1, all_32_0,
% 139.10/18.92 | | efficient_producers, simplifying with (1), (9) gives:
% 139.10/18.92 | | (10) all_44_0 = all_41_1
% 139.10/18.92 | |
% 139.10/18.92 | | PRED_UNIFY: (3), (8) imply:
% 139.10/18.92 | | (11) ~ (all_44_0 = all_41_1)
% 139.10/18.92 | |
% 139.10/18.92 | | REDUCE: (10), (11) imply:
% 139.10/18.92 | | (12) $false
% 139.10/18.92 | |
% 139.10/18.92 | | CLOSE: (12) is inconsistent.
% 139.10/18.92 | |
% 139.10/18.92 | Case 2:
% 139.10/18.92 | |
% 139.10/18.92 | | (13) growth_rate(first_movers, all_32_0) = all_41_0 & $i(all_41_0) & ~
% 139.10/18.92 | | greater(zero, all_41_0)
% 139.10/18.92 | |
% 139.10/18.92 | | ALPHA: (13) implies:
% 139.10/18.92 | | (14) ~ greater(zero, all_41_0)
% 139.10/18.92 | | (15) growth_rate(first_movers, all_32_0) = all_41_0
% 139.10/18.92 | |
% 139.10/18.92 | | GROUND_INST: instantiating (2) with all_44_1, all_41_0, all_32_0,
% 139.10/18.92 | | first_movers, simplifying with (4), (15) gives:
% 139.10/18.92 | | (16) all_44_1 = all_41_0
% 139.10/18.92 | |
% 139.10/18.92 | | PRED_UNIFY: (6), (14) imply:
% 139.10/18.92 | | (17) ~ (all_44_1 = all_41_0)
% 139.10/18.92 | |
% 139.10/18.92 | | REDUCE: (16), (17) imply:
% 139.10/18.92 | | (18) $false
% 139.10/18.92 | |
% 139.10/18.92 | | CLOSE: (18) is inconsistent.
% 139.10/18.92 | |
% 139.10/18.92 | End of split
% 139.10/18.92 |
% 139.10/18.92 End of proof
% 139.10/18.92
% 139.10/18.92 Sub-proof #4 shows that the following formulas are inconsistent:
% 139.10/18.92 ----------------------------------------------------------------
% 139.10/18.92 (1) equilibrium(all_12_0) = all_20_1
% 139.10/18.92 (2) ~ greater_or_equal(all_32_0, all_44_2)
% 139.10/18.92 (3) greater_or_equal(all_32_0, all_20_1)
% 139.10/18.92 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (equilibrium(v2)
% 139.10/18.92 = v1) | ~ (equilibrium(v2) = v0))
% 139.10/18.92 (5) equilibrium(all_12_0) = all_44_2
% 139.10/18.92
% 139.10/18.92 Begin of proof
% 139.10/18.92 |
% 139.10/18.92 | GROUND_INST: instantiating (4) with all_20_1, all_44_2, all_12_0, simplifying
% 139.10/18.92 | with (1), (5) gives:
% 139.10/18.92 | (6) all_44_2 = all_20_1
% 139.10/18.92 |
% 139.10/18.92 | PRED_UNIFY: (2), (3) imply:
% 139.10/18.92 | (7) ~ (all_44_2 = all_20_1)
% 139.10/18.92 |
% 139.10/18.92 | REDUCE: (6), (7) imply:
% 139.10/18.92 | (8) $false
% 139.10/18.92 |
% 139.10/18.92 | CLOSE: (8) is inconsistent.
% 139.10/18.92 |
% 139.10/18.92 End of proof
% 139.10/18.92
% 139.10/18.92 Sub-proof #5 shows that the following formulas are inconsistent:
% 139.10/18.92 ----------------------------------------------------------------
% 139.10/18.92 (1) growth_rate(first_movers, all_32_0) = all_83_0
% 139.10/18.92 (2) growth_rate(efficient_producers, all_32_0) = zero
% 139.10/18.93 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 139.10/18.93 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 139.10/18.93 (4) growth_rate(efficient_producers, all_32_0) = all_83_1
% 139.10/18.93 (5) greater(all_83_1, all_83_0)
% 139.10/18.93 (6) greater_or_equal(all_83_1, all_83_0)
% 139.10/18.93 (7) growth_rate(first_movers, all_32_0) = zero
% 139.10/18.93 (8) (growth_rate(efficient_producers, all_32_0) = all_41_1 & $i(all_41_1) &
% 139.10/18.93 ~ greater_or_equal(all_41_1, zero)) | (growth_rate(first_movers,
% 139.10/18.93 all_32_0) = all_41_0 & $i(all_41_0) & ~ greater(zero, all_41_0))
% 139.10/18.93
% 139.10/18.93 Begin of proof
% 139.10/18.93 |
% 139.10/18.93 | GROUND_INST: instantiating (3) with all_83_0, zero, all_32_0, first_movers,
% 139.10/18.93 | simplifying with (1), (7) gives:
% 139.10/18.93 | (9) all_83_0 = zero
% 139.10/18.93 |
% 139.10/18.93 | GROUND_INST: instantiating (3) with all_83_1, zero, all_32_0,
% 139.10/18.93 | efficient_producers, simplifying with (2), (4) gives:
% 139.10/18.93 | (10) all_83_1 = zero
% 139.10/18.93 |
% 139.10/18.93 | REDUCE: (6), (9), (10) imply:
% 139.10/18.93 | (11) greater_or_equal(zero, zero)
% 139.10/18.93 |
% 139.10/18.93 | REDUCE: (5), (9), (10) imply:
% 139.10/18.93 | (12) greater(zero, zero)
% 139.10/18.93 |
% 139.10/18.93 | BETA: splitting (8) gives:
% 139.10/18.93 |
% 139.10/18.93 | Case 1:
% 139.10/18.93 | |
% 139.10/18.93 | | (13) growth_rate(efficient_producers, all_32_0) = all_41_1 & $i(all_41_1)
% 139.10/18.93 | | & ~ greater_or_equal(all_41_1, zero)
% 139.10/18.93 | |
% 139.10/18.93 | | ALPHA: (13) implies:
% 139.10/18.93 | | (14) ~ greater_or_equal(all_41_1, zero)
% 139.10/18.93 | | (15) growth_rate(efficient_producers, all_32_0) = all_41_1
% 139.10/18.93 | |
% 139.10/18.93 | | REF_CLOSE: (2), (3), (11), (14), (15) are inconsistent by sub-proof #7.
% 139.10/18.93 | |
% 139.10/18.93 | Case 2:
% 139.10/18.93 | |
% 139.10/18.93 | | (16) growth_rate(first_movers, all_32_0) = all_41_0 & $i(all_41_0) & ~
% 139.10/18.93 | | greater(zero, all_41_0)
% 139.10/18.93 | |
% 139.10/18.93 | | ALPHA: (16) implies:
% 139.10/18.93 | | (17) ~ greater(zero, all_41_0)
% 139.10/18.93 | | (18) growth_rate(first_movers, all_32_0) = all_41_0
% 139.10/18.93 | |
% 139.10/18.93 | | REF_CLOSE: (3), (7), (12), (17), (18) are inconsistent by sub-proof #6.
% 139.10/18.93 | |
% 139.10/18.93 | End of split
% 139.10/18.93 |
% 139.10/18.93 End of proof
% 139.10/18.93
% 139.10/18.93 Sub-proof #6 shows that the following formulas are inconsistent:
% 139.10/18.93 ----------------------------------------------------------------
% 139.10/18.93 (1) growth_rate(first_movers, all_32_0) = all_41_0
% 139.10/18.93 (2) ~ greater(zero, all_41_0)
% 139.10/18.93 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 139.10/18.93 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 139.10/18.93 (4) growth_rate(first_movers, all_32_0) = zero
% 139.10/18.93 (5) greater(zero, zero)
% 139.10/18.93
% 139.10/18.93 Begin of proof
% 139.10/18.93 |
% 139.10/18.93 | GROUND_INST: instantiating (3) with zero, all_41_0, all_32_0, first_movers,
% 139.10/18.93 | simplifying with (1), (4) gives:
% 139.10/18.93 | (6) all_41_0 = zero
% 139.10/18.93 |
% 139.10/18.93 | PRED_UNIFY: (2), (5) imply:
% 139.10/18.93 | (7) ~ (all_41_0 = zero)
% 139.10/18.93 |
% 139.10/18.93 | REDUCE: (6), (7) imply:
% 139.10/18.93 | (8) $false
% 139.10/18.93 |
% 139.10/18.93 | CLOSE: (8) is inconsistent.
% 139.10/18.93 |
% 139.10/18.93 End of proof
% 139.10/18.93
% 139.10/18.93 Sub-proof #7 shows that the following formulas are inconsistent:
% 139.10/18.93 ----------------------------------------------------------------
% 139.10/18.93 (1) growth_rate(efficient_producers, all_32_0) = zero
% 139.10/18.93 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 139.10/18.93 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 139.10/18.93 (3) growth_rate(efficient_producers, all_32_0) = all_41_1
% 139.10/18.93 (4) ~ greater_or_equal(all_41_1, zero)
% 139.10/18.93 (5) greater_or_equal(zero, zero)
% 139.10/18.93
% 139.10/18.93 Begin of proof
% 139.10/18.93 |
% 139.10/18.93 | GROUND_INST: instantiating (2) with zero, all_41_1, all_32_0,
% 139.10/18.93 | efficient_producers, simplifying with (1), (3) gives:
% 139.10/18.93 | (6) all_41_1 = zero
% 139.10/18.93 |
% 139.10/18.93 | PRED_UNIFY: (4), (5) imply:
% 139.10/18.93 | (7) ~ (all_41_1 = zero)
% 139.10/18.93 |
% 139.10/18.93 | REDUCE: (6), (7) imply:
% 139.10/18.93 | (8) $false
% 139.10/18.93 |
% 139.10/18.93 | CLOSE: (8) is inconsistent.
% 139.10/18.93 |
% 139.10/18.93 End of proof
% 139.10/18.93
% 139.10/18.93 Sub-proof #8 shows that the following formulas are inconsistent:
% 139.10/18.93 ----------------------------------------------------------------
% 139.10/18.93 (1) $i(all_20_1)
% 139.10/18.93 (2) equilibrium(all_12_0) = all_20_1
% 139.10/18.93 (3) ~ outcompetes(efficient_producers, first_movers, all_30_0)
% 139.10/18.93 (4) outcompetes(efficient_producers, first_movers, all_30_0) |
% 139.10/18.93 (growth_rate(efficient_producers, all_30_0) = all_42_1 & $i(all_42_1) &
% 139.10/18.93 ~ greater_or_equal(all_42_1, zero)) | (growth_rate(first_movers,
% 139.10/18.93 all_30_0) = all_42_0 & $i(all_42_0) & ~ greater(zero, all_42_0))
% 139.10/18.93 (5) all_39_0 = all_39_1 | ~ (growth_rate(first_movers, all_30_0) = all_39_1)
% 139.10/18.93 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 139.10/18.93 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 139.10/18.93 (7) greater(all_39_1, all_39_0)
% 139.10/18.93 (8) $i(all_22_0)
% 139.10/18.93 (9) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1) |
% 139.10/18.93 greater_or_equal(v0, v1))
% 139.10/18.93 (10) (all_43_0 = zero & all_43_1 = zero & growth_rate(efficient_producers,
% 139.10/18.93 all_30_0) = zero & growth_rate(first_movers, all_30_0) = zero) |
% 139.10/18.93 (equilibrium(all_12_0) = all_43_2 & $i(all_43_2) & ~
% 139.10/18.93 greater_or_equal(all_30_0, all_43_2)) |
% 139.10/18.93 (growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 139.10/18.93 growth_rate(first_movers, all_30_0) = all_43_1 & $i(all_43_0) &
% 139.10/18.93 $i(all_43_1) & greater(all_43_0, zero) & greater(zero, all_43_1)) |
% 139.10/18.93 (growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 139.10/18.93 growth_rate(first_movers, all_30_0) = all_43_1 & $i(all_43_0) &
% 139.10/18.93 $i(all_43_1) & greater(all_43_1, zero) & greater(zero, all_43_0))
% 139.10/18.93 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (equilibrium(v2)
% 139.10/18.93 = v1) | ~ (equilibrium(v2) = v0))
% 139.10/18.93 (12) growth_rate(efficient_producers, all_30_0) = all_39_1
% 139.10/18.93 (13) $i(all_30_0)
% 139.10/18.93 (14) greater(all_22_0, all_20_1)
% 139.10/18.93 (15) $i(zero)
% 139.10/18.93 (16) all_30_0 = all_22_0 | greater(all_30_0, all_22_0)
% 139.10/18.93 (17) greater_or_equal(all_39_1, all_39_0)
% 139.10/18.93 (18) growth_rate(first_movers, all_30_0) = all_39_0
% 139.10/18.93 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 139.10/18.93 $i(v0) | ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 139.10/18.93
% 139.10/18.93 Begin of proof
% 139.10/18.93 |
% 139.10/18.93 | GROUND_INST: instantiating (9) with all_22_0, all_20_1, simplifying with (1),
% 139.10/18.93 | (8), (14) gives:
% 139.10/18.93 | (20) greater_or_equal(all_22_0, all_20_1)
% 139.10/18.93 |
% 139.10/18.93 | BETA: splitting (16) gives:
% 139.10/18.93 |
% 139.10/18.93 | Case 1:
% 139.10/18.93 | |
% 139.10/18.93 | | (21) greater(all_30_0, all_22_0)
% 139.10/18.93 | |
% 139.10/18.93 | | GROUND_INST: instantiating (19) with all_30_0, all_22_0, all_20_1,
% 139.10/18.93 | | simplifying with (1), (8), (13), (14), (21) gives:
% 139.10/18.93 | | (22) greater(all_30_0, all_20_1)
% 139.10/18.93 | |
% 139.10/18.93 | | GROUND_INST: instantiating (9) with all_30_0, all_20_1, simplifying with
% 139.10/18.93 | | (1), (13), (22) gives:
% 139.10/18.93 | | (23) greater_or_equal(all_30_0, all_20_1)
% 139.10/18.93 | |
% 139.10/18.93 | | BETA: splitting (4) gives:
% 139.10/18.93 | |
% 139.10/18.93 | | Case 1:
% 139.10/18.93 | | |
% 139.10/18.93 | | | (24) outcompetes(efficient_producers, first_movers, all_30_0)
% 139.10/18.93 | | |
% 139.10/18.93 | | | PRED_UNIFY: (3), (24) imply:
% 139.10/18.93 | | | (25) $false
% 139.10/18.93 | | |
% 139.10/18.93 | | | CLOSE: (25) is inconsistent.
% 139.10/18.93 | | |
% 139.10/18.93 | | Case 2:
% 139.10/18.93 | | |
% 139.10/18.93 | | | (26) (growth_rate(efficient_producers, all_30_0) = all_42_1 &
% 139.10/18.93 | | | $i(all_42_1) & ~ greater_or_equal(all_42_1, zero)) |
% 139.10/18.93 | | | (growth_rate(first_movers, all_30_0) = all_42_0 & $i(all_42_0) &
% 139.10/18.93 | | | ~ greater(zero, all_42_0))
% 139.10/18.93 | | |
% 139.10/18.93 | | | BETA: splitting (5) gives:
% 139.10/18.93 | | |
% 139.10/18.93 | | | Case 1:
% 139.10/18.93 | | | |
% 139.10/18.93 | | | | (27) ~ (growth_rate(first_movers, all_30_0) = all_39_1)
% 139.10/18.93 | | | |
% 139.10/18.93 | | | | BETA: splitting (10) gives:
% 139.10/18.93 | | | |
% 139.10/18.93 | | | | Case 1:
% 139.10/18.93 | | | | |
% 139.10/18.93 | | | | | (28) (all_43_0 = zero & all_43_1 = zero &
% 139.10/18.93 | | | | | growth_rate(efficient_producers, all_30_0) = zero &
% 139.10/18.93 | | | | | growth_rate(first_movers, all_30_0) = zero) |
% 139.10/18.93 | | | | | (equilibrium(all_12_0) = all_43_2 & $i(all_43_2) & ~
% 139.10/18.93 | | | | | greater_or_equal(all_30_0, all_43_2))
% 139.10/18.93 | | | | |
% 139.10/18.93 | | | | | BETA: splitting (28) gives:
% 139.10/18.93 | | | | |
% 139.10/18.93 | | | | | Case 1:
% 139.10/18.93 | | | | | |
% 139.10/18.93 | | | | | | (29) all_43_0 = zero & all_43_1 = zero &
% 139.10/18.93 | | | | | | growth_rate(efficient_producers, all_30_0) = zero &
% 139.10/18.93 | | | | | | growth_rate(first_movers, all_30_0) = zero
% 139.10/18.93 | | | | | |
% 139.10/18.93 | | | | | | ALPHA: (29) implies:
% 139.10/18.93 | | | | | | (30) growth_rate(first_movers, all_30_0) = zero
% 139.10/18.94 | | | | | | (31) growth_rate(efficient_producers, all_30_0) = zero
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | PRED_UNIFY: (27), (30) imply:
% 139.10/18.94 | | | | | | (32) ~ (all_39_1 = zero)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | GROUND_INST: instantiating (6) with all_39_1, zero, all_30_0,
% 139.10/18.94 | | | | | | efficient_producers, simplifying with (12), (31) gives:
% 139.10/18.94 | | | | | | (33) all_39_1 = zero
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | REDUCE: (32), (33) imply:
% 139.10/18.94 | | | | | | (34) $false
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | CLOSE: (34) is inconsistent.
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | Case 2:
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | (35) equilibrium(all_12_0) = all_43_2 & $i(all_43_2) & ~
% 139.10/18.94 | | | | | | greater_or_equal(all_30_0, all_43_2)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | ALPHA: (35) implies:
% 139.10/18.94 | | | | | | (36) ~ greater_or_equal(all_30_0, all_43_2)
% 139.10/18.94 | | | | | | (37) equilibrium(all_12_0) = all_43_2
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | REF_CLOSE: (2), (11), (23), (36), (37) are inconsistent by sub-proof
% 139.10/18.94 | | | | | | #18.
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | End of split
% 139.10/18.94 | | | | |
% 139.10/18.94 | | | | Case 2:
% 139.10/18.94 | | | | |
% 139.10/18.94 | | | | | (38) (growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 139.10/18.94 | | | | | growth_rate(first_movers, all_30_0) = all_43_1 &
% 139.10/18.94 | | | | | $i(all_43_0) & $i(all_43_1) & greater(all_43_0, zero) &
% 139.10/18.94 | | | | | greater(zero, all_43_1)) | (growth_rate(efficient_producers,
% 139.10/18.94 | | | | | all_30_0) = all_43_0 & growth_rate(first_movers, all_30_0)
% 139.10/18.94 | | | | | = all_43_1 & $i(all_43_0) & $i(all_43_1) & greater(all_43_1,
% 139.10/18.94 | | | | | zero) & greater(zero, all_43_0))
% 139.10/18.94 | | | | |
% 139.10/18.94 | | | | | BETA: splitting (38) gives:
% 139.10/18.94 | | | | |
% 139.10/18.94 | | | | | Case 1:
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | (39) growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 139.10/18.94 | | | | | | growth_rate(first_movers, all_30_0) = all_43_1 &
% 139.10/18.94 | | | | | | $i(all_43_0) & $i(all_43_1) & greater(all_43_0, zero) &
% 139.10/18.94 | | | | | | greater(zero, all_43_1)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | ALPHA: (39) implies:
% 139.10/18.94 | | | | | | (40) greater(zero, all_43_1)
% 139.10/18.94 | | | | | | (41) greater(all_43_0, zero)
% 139.10/18.94 | | | | | | (42) growth_rate(first_movers, all_30_0) = all_43_1
% 139.10/18.94 | | | | | | (43) growth_rate(efficient_producers, all_30_0) = all_43_0
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | GROUND_INST: instantiating (6) with all_39_0, all_43_1, all_30_0,
% 139.10/18.94 | | | | | | first_movers, simplifying with (18), (42) gives:
% 139.10/18.94 | | | | | | (44) all_43_1 = all_39_0
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | GROUND_INST: instantiating (6) with all_39_1, all_43_0, all_30_0,
% 139.10/18.94 | | | | | | efficient_producers, simplifying with (12), (43) gives:
% 139.10/18.94 | | | | | | (45) all_43_0 = all_39_1
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | REDUCE: (41), (45) imply:
% 139.10/18.94 | | | | | | (46) greater(all_39_1, zero)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | REDUCE: (40), (44) imply:
% 139.10/18.94 | | | | | | (47) greater(zero, all_39_0)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | REF_CLOSE: (6), (9), (12), (15), (18), (26), (46), (47) are
% 139.10/18.94 | | | | | | inconsistent by sub-proof #16.
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | Case 2:
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | (48) growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 139.10/18.94 | | | | | | growth_rate(first_movers, all_30_0) = all_43_1 &
% 139.10/18.94 | | | | | | $i(all_43_0) & $i(all_43_1) & greater(all_43_1, zero) &
% 139.10/18.94 | | | | | | greater(zero, all_43_0)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | ALPHA: (48) implies:
% 139.10/18.94 | | | | | | (49) greater(zero, all_43_0)
% 139.10/18.94 | | | | | | (50) greater(all_43_1, zero)
% 139.10/18.94 | | | | | | (51) $i(all_43_1)
% 139.10/18.94 | | | | | | (52) $i(all_43_0)
% 139.10/18.94 | | | | | | (53) growth_rate(first_movers, all_30_0) = all_43_1
% 139.10/18.94 | | | | | | (54) growth_rate(efficient_producers, all_30_0) = all_43_0
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | GROUND_INST: instantiating (6) with all_39_0, all_43_1, all_30_0,
% 139.10/18.94 | | | | | | first_movers, simplifying with (18), (53) gives:
% 139.10/18.94 | | | | | | (55) all_43_1 = all_39_0
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | GROUND_INST: instantiating (6) with all_39_1, all_43_0, all_30_0,
% 139.10/18.94 | | | | | | efficient_producers, simplifying with (12), (54) gives:
% 139.10/18.94 | | | | | | (56) all_43_0 = all_39_1
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | REDUCE: (52), (56) imply:
% 139.10/18.94 | | | | | | (57) $i(all_39_1)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | REDUCE: (51), (55) imply:
% 139.10/18.94 | | | | | | (58) $i(all_39_0)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | REDUCE: (50), (55) imply:
% 139.10/18.94 | | | | | | (59) greater(all_39_0, zero)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | REDUCE: (49), (56) imply:
% 139.10/18.94 | | | | | | (60) greater(zero, all_39_1)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | GROUND_INST: instantiating (19) with zero, all_39_1, all_39_0,
% 139.10/18.94 | | | | | | simplifying with (7), (15), (57), (58), (60) gives:
% 139.10/18.94 | | | | | | (61) greater(zero, all_39_0)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | GROUND_INST: instantiating (19) with all_39_1, all_39_0, zero,
% 139.10/18.94 | | | | | | simplifying with (7), (15), (57), (58), (59) gives:
% 139.10/18.94 | | | | | | (62) greater(all_39_1, zero)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | REF_CLOSE: (6), (9), (12), (15), (18), (26), (61), (62) are
% 139.10/18.94 | | | | | | inconsistent by sub-proof #16.
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | End of split
% 139.10/18.94 | | | | |
% 139.10/18.94 | | | | End of split
% 139.10/18.94 | | | |
% 139.10/18.94 | | | Case 2:
% 139.10/18.94 | | | |
% 139.10/18.94 | | | | (63) all_39_0 = all_39_1
% 139.10/18.94 | | | |
% 139.10/18.94 | | | | REDUCE: (18), (63) imply:
% 139.10/18.94 | | | | (64) growth_rate(first_movers, all_30_0) = all_39_1
% 139.10/18.94 | | | |
% 139.10/18.94 | | | | REDUCE: (17), (63) imply:
% 139.10/18.94 | | | | (65) greater_or_equal(all_39_1, all_39_1)
% 139.10/18.94 | | | |
% 139.10/18.94 | | | | REDUCE: (7), (63) imply:
% 139.10/18.94 | | | | (66) greater(all_39_1, all_39_1)
% 139.10/18.94 | | | |
% 139.10/18.94 | | | | BETA: splitting (10) gives:
% 139.10/18.94 | | | |
% 139.10/18.94 | | | | Case 1:
% 139.10/18.94 | | | | |
% 139.10/18.94 | | | | | (67) (all_43_0 = zero & all_43_1 = zero &
% 139.10/18.94 | | | | | growth_rate(efficient_producers, all_30_0) = zero &
% 139.10/18.94 | | | | | growth_rate(first_movers, all_30_0) = zero) |
% 139.10/18.94 | | | | | (equilibrium(all_12_0) = all_43_2 & $i(all_43_2) & ~
% 139.10/18.94 | | | | | greater_or_equal(all_30_0, all_43_2))
% 139.10/18.94 | | | | |
% 139.10/18.94 | | | | | BETA: splitting (67) gives:
% 139.10/18.94 | | | | |
% 139.10/18.94 | | | | | Case 1:
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | (68) all_43_0 = zero & all_43_1 = zero &
% 139.10/18.94 | | | | | | growth_rate(efficient_producers, all_30_0) = zero &
% 139.10/18.94 | | | | | | growth_rate(first_movers, all_30_0) = zero
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | REF_CLOSE: (6), (12), (26), (64), (65), (66), (68) are inconsistent
% 139.10/18.94 | | | | | | by sub-proof #15.
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | Case 2:
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | (69) equilibrium(all_12_0) = all_43_2 & $i(all_43_2) & ~
% 139.10/18.94 | | | | | | greater_or_equal(all_30_0, all_43_2)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | ALPHA: (69) implies:
% 139.10/18.94 | | | | | | (70) ~ greater_or_equal(all_30_0, all_43_2)
% 139.10/18.94 | | | | | | (71) equilibrium(all_12_0) = all_43_2
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | REF_CLOSE: (2), (11), (23), (70), (71) are inconsistent by sub-proof
% 139.10/18.94 | | | | | | #18.
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | End of split
% 139.10/18.94 | | | | |
% 139.10/18.94 | | | | Case 2:
% 139.10/18.94 | | | | |
% 139.10/18.94 | | | | | (72) (growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 139.10/18.94 | | | | | growth_rate(first_movers, all_30_0) = all_43_1 &
% 139.10/18.94 | | | | | $i(all_43_0) & $i(all_43_1) & greater(all_43_0, zero) &
% 139.10/18.94 | | | | | greater(zero, all_43_1)) | (growth_rate(efficient_producers,
% 139.10/18.94 | | | | | all_30_0) = all_43_0 & growth_rate(first_movers, all_30_0)
% 139.10/18.94 | | | | | = all_43_1 & $i(all_43_0) & $i(all_43_1) & greater(all_43_1,
% 139.10/18.94 | | | | | zero) & greater(zero, all_43_0))
% 139.10/18.94 | | | | |
% 139.10/18.94 | | | | | BETA: splitting (72) gives:
% 139.10/18.94 | | | | |
% 139.10/18.94 | | | | | Case 1:
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | (73) growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 139.10/18.94 | | | | | | growth_rate(first_movers, all_30_0) = all_43_1 &
% 139.10/18.94 | | | | | | $i(all_43_0) & $i(all_43_1) & greater(all_43_0, zero) &
% 139.10/18.94 | | | | | | greater(zero, all_43_1)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | ALPHA: (73) implies:
% 139.10/18.94 | | | | | | (74) greater(zero, all_43_1)
% 139.10/18.94 | | | | | | (75) greater(all_43_0, zero)
% 139.10/18.94 | | | | | | (76) growth_rate(first_movers, all_30_0) = all_43_1
% 139.10/18.94 | | | | | | (77) growth_rate(efficient_producers, all_30_0) = all_43_0
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | GROUND_INST: instantiating (6) with all_39_1, all_43_1, all_30_0,
% 139.10/18.94 | | | | | | first_movers, simplifying with (64), (76) gives:
% 139.10/18.94 | | | | | | (78) all_43_1 = all_39_1
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | GROUND_INST: instantiating (6) with all_39_1, all_43_0, all_30_0,
% 139.10/18.94 | | | | | | efficient_producers, simplifying with (12), (77) gives:
% 139.10/18.94 | | | | | | (79) all_43_0 = all_39_1
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | REDUCE: (75), (79) imply:
% 139.10/18.94 | | | | | | (80) greater(all_39_1, zero)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | REDUCE: (74), (78) imply:
% 139.10/18.94 | | | | | | (81) greater(zero, all_39_1)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | BETA: splitting (26) gives:
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | Case 1:
% 139.10/18.94 | | | | | | |
% 139.10/18.94 | | | | | | | (82) growth_rate(efficient_producers, all_30_0) = all_42_1 &
% 139.10/18.94 | | | | | | | $i(all_42_1) & ~ greater_or_equal(all_42_1, zero)
% 139.10/18.94 | | | | | | |
% 139.10/18.94 | | | | | | | REF_CLOSE: (6), (9), (12), (15), (80), (82) are inconsistent by
% 139.10/18.94 | | | | | | | sub-proof #17.
% 139.10/18.94 | | | | | | |
% 139.10/18.94 | | | | | | Case 2:
% 139.10/18.94 | | | | | | |
% 139.10/18.94 | | | | | | | (83) growth_rate(first_movers, all_30_0) = all_42_0 &
% 139.10/18.94 | | | | | | | $i(all_42_0) & ~ greater(zero, all_42_0)
% 139.10/18.94 | | | | | | |
% 139.10/18.94 | | | | | | | REF_CLOSE: (6), (64), (81), (83) are inconsistent by sub-proof
% 139.10/18.94 | | | | | | | #14.
% 139.10/18.94 | | | | | | |
% 139.10/18.94 | | | | | | End of split
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | Case 2:
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | (84) growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 139.10/18.94 | | | | | | growth_rate(first_movers, all_30_0) = all_43_1 &
% 139.10/18.94 | | | | | | $i(all_43_0) & $i(all_43_1) & greater(all_43_1, zero) &
% 139.10/18.94 | | | | | | greater(zero, all_43_0)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | ALPHA: (84) implies:
% 139.10/18.94 | | | | | | (85) greater(zero, all_43_0)
% 139.10/18.94 | | | | | | (86) greater(all_43_1, zero)
% 139.10/18.94 | | | | | | (87) growth_rate(first_movers, all_30_0) = all_43_1
% 139.10/18.94 | | | | | | (88) growth_rate(efficient_producers, all_30_0) = all_43_0
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | GROUND_INST: instantiating (6) with all_39_1, all_43_1, all_30_0,
% 139.10/18.94 | | | | | | first_movers, simplifying with (64), (87) gives:
% 139.10/18.94 | | | | | | (89) all_43_1 = all_39_1
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | GROUND_INST: instantiating (6) with all_39_1, all_43_0, all_30_0,
% 139.10/18.94 | | | | | | efficient_producers, simplifying with (12), (88) gives:
% 139.10/18.94 | | | | | | (90) all_43_0 = all_39_1
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | REDUCE: (86), (89) imply:
% 139.10/18.94 | | | | | | (91) greater(all_39_1, zero)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | REDUCE: (85), (90) imply:
% 139.10/18.94 | | | | | | (92) greater(zero, all_39_1)
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | BETA: splitting (26) gives:
% 139.10/18.94 | | | | | |
% 139.10/18.94 | | | | | | Case 1:
% 139.10/18.94 | | | | | | |
% 139.10/18.95 | | | | | | | (93) growth_rate(efficient_producers, all_30_0) = all_42_1 &
% 139.10/18.95 | | | | | | | $i(all_42_1) & ~ greater_or_equal(all_42_1, zero)
% 139.10/18.95 | | | | | | |
% 139.10/18.95 | | | | | | | REF_CLOSE: (6), (9), (12), (15), (91), (93) are inconsistent by
% 139.10/18.95 | | | | | | | sub-proof #17.
% 139.10/18.95 | | | | | | |
% 139.10/18.95 | | | | | | Case 2:
% 139.10/18.95 | | | | | | |
% 139.10/18.95 | | | | | | | (94) growth_rate(first_movers, all_30_0) = all_42_0 &
% 139.10/18.95 | | | | | | | $i(all_42_0) & ~ greater(zero, all_42_0)
% 139.10/18.95 | | | | | | |
% 139.10/18.95 | | | | | | | REF_CLOSE: (6), (64), (92), (94) are inconsistent by sub-proof
% 139.10/18.95 | | | | | | | #14.
% 139.10/18.95 | | | | | | |
% 139.10/18.95 | | | | | | End of split
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | End of split
% 139.10/18.95 | | | | |
% 139.10/18.95 | | | | End of split
% 139.10/18.95 | | | |
% 139.10/18.95 | | | End of split
% 139.10/18.95 | | |
% 139.10/18.95 | | End of split
% 139.10/18.95 | |
% 139.10/18.95 | Case 2:
% 139.10/18.95 | |
% 139.10/18.95 | | (95) all_30_0 = all_22_0
% 139.10/18.95 | |
% 139.10/18.95 | | REDUCE: (12), (95) imply:
% 139.10/18.95 | | (96) growth_rate(efficient_producers, all_22_0) = all_39_1
% 139.10/18.95 | |
% 139.10/18.95 | | REDUCE: (18), (95) imply:
% 139.10/18.95 | | (97) growth_rate(first_movers, all_22_0) = all_39_0
% 139.10/18.95 | |
% 139.10/18.95 | | BETA: splitting (4) gives:
% 139.10/18.95 | |
% 139.10/18.95 | | Case 1:
% 139.10/18.95 | | |
% 139.10/18.95 | | | (98) outcompetes(efficient_producers, first_movers, all_30_0)
% 139.10/18.95 | | |
% 139.10/18.95 | | | PRED_UNIFY: (3), (98) imply:
% 139.10/18.95 | | | (99) $false
% 139.10/18.95 | | |
% 139.10/18.95 | | | CLOSE: (99) is inconsistent.
% 139.10/18.95 | | |
% 139.10/18.95 | | Case 2:
% 139.10/18.95 | | |
% 139.10/18.95 | | | (100) (growth_rate(efficient_producers, all_30_0) = all_42_1 &
% 139.10/18.95 | | | $i(all_42_1) & ~ greater_or_equal(all_42_1, zero)) |
% 139.10/18.95 | | | (growth_rate(first_movers, all_30_0) = all_42_0 & $i(all_42_0) &
% 139.10/18.95 | | | ~ greater(zero, all_42_0))
% 139.10/18.95 | | |
% 139.10/18.95 | | | BETA: splitting (5) gives:
% 139.10/18.95 | | |
% 139.10/18.95 | | | Case 1:
% 139.10/18.95 | | | |
% 139.10/18.95 | | | | (101) ~ (growth_rate(first_movers, all_30_0) = all_39_1)
% 139.10/18.95 | | | |
% 139.10/18.95 | | | | REDUCE: (95), (101) imply:
% 139.10/18.95 | | | | (102) ~ (growth_rate(first_movers, all_22_0) = all_39_1)
% 139.10/18.95 | | | |
% 139.10/18.95 | | | | BETA: splitting (10) gives:
% 139.10/18.95 | | | |
% 139.10/18.95 | | | | Case 1:
% 139.10/18.95 | | | | |
% 139.10/18.95 | | | | | (103) (all_43_0 = zero & all_43_1 = zero &
% 139.10/18.95 | | | | | growth_rate(efficient_producers, all_30_0) = zero &
% 139.10/18.95 | | | | | growth_rate(first_movers, all_30_0) = zero) |
% 139.10/18.95 | | | | | (equilibrium(all_12_0) = all_43_2 & $i(all_43_2) & ~
% 139.10/18.95 | | | | | greater_or_equal(all_30_0, all_43_2))
% 139.10/18.95 | | | | |
% 139.10/18.95 | | | | | BETA: splitting (103) gives:
% 139.10/18.95 | | | | |
% 139.10/18.95 | | | | | Case 1:
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | (104) all_43_0 = zero & all_43_1 = zero &
% 139.10/18.95 | | | | | | growth_rate(efficient_producers, all_30_0) = zero &
% 139.10/18.95 | | | | | | growth_rate(first_movers, all_30_0) = zero
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | ALPHA: (104) implies:
% 139.10/18.95 | | | | | | (105) growth_rate(first_movers, all_30_0) = zero
% 139.10/18.95 | | | | | | (106) growth_rate(efficient_producers, all_30_0) = zero
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | REDUCE: (95), (106) imply:
% 139.10/18.95 | | | | | | (107) growth_rate(efficient_producers, all_22_0) = zero
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | REDUCE: (95), (105) imply:
% 139.10/18.95 | | | | | | (108) growth_rate(first_movers, all_22_0) = zero
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | PRED_UNIFY: (102), (108) imply:
% 139.10/18.95 | | | | | | (109) ~ (all_39_1 = zero)
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | GROUND_INST: instantiating (6) with all_39_1, zero, all_22_0,
% 139.10/18.95 | | | | | | efficient_producers, simplifying with (96), (107)
% 139.10/18.95 | | | | | | gives:
% 139.10/18.95 | | | | | | (110) all_39_1 = zero
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | REDUCE: (109), (110) imply:
% 139.10/18.95 | | | | | | (111) $false
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | CLOSE: (111) is inconsistent.
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | Case 2:
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | (112) equilibrium(all_12_0) = all_43_2 & $i(all_43_2) & ~
% 139.10/18.95 | | | | | | greater_or_equal(all_30_0, all_43_2)
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | ALPHA: (112) implies:
% 139.10/18.95 | | | | | | (113) ~ greater_or_equal(all_30_0, all_43_2)
% 139.10/18.95 | | | | | | (114) equilibrium(all_12_0) = all_43_2
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | REDUCE: (95), (113) imply:
% 139.10/18.95 | | | | | | (115) ~ greater_or_equal(all_22_0, all_43_2)
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | REF_CLOSE: (2), (11), (20), (114), (115) are inconsistent by
% 139.10/18.95 | | | | | | sub-proof #13.
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | End of split
% 139.10/18.95 | | | | |
% 139.10/18.95 | | | | Case 2:
% 139.10/18.95 | | | | |
% 139.10/18.95 | | | | | (116) (growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 139.10/18.95 | | | | | growth_rate(first_movers, all_30_0) = all_43_1 &
% 139.10/18.95 | | | | | $i(all_43_0) & $i(all_43_1) & greater(all_43_0, zero) &
% 139.10/18.95 | | | | | greater(zero, all_43_1)) |
% 139.10/18.95 | | | | | (growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 139.10/18.95 | | | | | growth_rate(first_movers, all_30_0) = all_43_1 &
% 139.10/18.95 | | | | | $i(all_43_0) & $i(all_43_1) & greater(all_43_1, zero) &
% 139.10/18.95 | | | | | greater(zero, all_43_0))
% 139.10/18.95 | | | | |
% 139.10/18.95 | | | | | BETA: splitting (116) gives:
% 139.10/18.95 | | | | |
% 139.10/18.95 | | | | | Case 1:
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | (117) growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 139.10/18.95 | | | | | | growth_rate(first_movers, all_30_0) = all_43_1 &
% 139.10/18.95 | | | | | | $i(all_43_0) & $i(all_43_1) & greater(all_43_0, zero) &
% 139.10/18.95 | | | | | | greater(zero, all_43_1)
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | ALPHA: (117) implies:
% 139.10/18.95 | | | | | | (118) greater(zero, all_43_1)
% 139.10/18.95 | | | | | | (119) greater(all_43_0, zero)
% 139.10/18.95 | | | | | | (120) growth_rate(first_movers, all_30_0) = all_43_1
% 139.10/18.95 | | | | | | (121) growth_rate(efficient_producers, all_30_0) = all_43_0
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | REDUCE: (95), (121) imply:
% 139.10/18.95 | | | | | | (122) growth_rate(efficient_producers, all_22_0) = all_43_0
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | REDUCE: (95), (120) imply:
% 139.10/18.95 | | | | | | (123) growth_rate(first_movers, all_22_0) = all_43_1
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | REF_CLOSE: (6), (9), (15), (95), (96), (97), (100), (118), (119),
% 139.10/18.95 | | | | | | (122), (123) are inconsistent by sub-proof #10.
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | Case 2:
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | (124) growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 139.10/18.95 | | | | | | growth_rate(first_movers, all_30_0) = all_43_1 &
% 139.10/18.95 | | | | | | $i(all_43_0) & $i(all_43_1) & greater(all_43_1, zero) &
% 139.10/18.95 | | | | | | greater(zero, all_43_0)
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | ALPHA: (124) implies:
% 139.10/18.95 | | | | | | (125) greater(zero, all_43_0)
% 139.10/18.95 | | | | | | (126) greater(all_43_1, zero)
% 139.10/18.95 | | | | | | (127) $i(all_43_1)
% 139.10/18.95 | | | | | | (128) $i(all_43_0)
% 139.10/18.95 | | | | | | (129) growth_rate(first_movers, all_30_0) = all_43_1
% 139.10/18.95 | | | | | | (130) growth_rate(efficient_producers, all_30_0) = all_43_0
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | REDUCE: (95), (130) imply:
% 139.10/18.95 | | | | | | (131) growth_rate(efficient_producers, all_22_0) = all_43_0
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | REDUCE: (95), (129) imply:
% 139.10/18.95 | | | | | | (132) growth_rate(first_movers, all_22_0) = all_43_1
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | GROUND_INST: instantiating (6) with all_39_0, all_43_1, all_22_0,
% 139.10/18.95 | | | | | | first_movers, simplifying with (97), (132) gives:
% 139.10/18.95 | | | | | | (133) all_43_1 = all_39_0
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | GROUND_INST: instantiating (6) with all_39_1, all_43_0, all_22_0,
% 139.10/18.95 | | | | | | efficient_producers, simplifying with (96), (131)
% 139.10/18.95 | | | | | | gives:
% 139.10/18.95 | | | | | | (134) all_43_0 = all_39_1
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | REDUCE: (128), (134) imply:
% 139.10/18.95 | | | | | | (135) $i(all_39_1)
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | REDUCE: (127), (133) imply:
% 139.10/18.95 | | | | | | (136) $i(all_39_0)
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | REDUCE: (126), (133) imply:
% 139.10/18.95 | | | | | | (137) greater(all_39_0, zero)
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | REDUCE: (125), (134) imply:
% 139.10/18.95 | | | | | | (138) greater(zero, all_39_1)
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | GROUND_INST: instantiating (19) with zero, all_39_1, all_39_0,
% 139.10/18.95 | | | | | | simplifying with (7), (15), (135), (136), (138) gives:
% 139.10/18.95 | | | | | | (139) greater(zero, all_39_0)
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | GROUND_INST: instantiating (19) with all_39_1, all_39_0, zero,
% 139.10/18.95 | | | | | | simplifying with (7), (15), (135), (136), (137) gives:
% 139.10/18.95 | | | | | | (140) greater(all_39_1, zero)
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | BETA: splitting (100) gives:
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | Case 1:
% 139.10/18.95 | | | | | | |
% 139.10/18.95 | | | | | | | (141) growth_rate(efficient_producers, all_30_0) = all_42_1 &
% 139.10/18.95 | | | | | | | $i(all_42_1) & ~ greater_or_equal(all_42_1, zero)
% 139.10/18.95 | | | | | | |
% 139.10/18.95 | | | | | | | REF_CLOSE: (6), (9), (15), (95), (96), (140), (141) are
% 139.10/18.95 | | | | | | | inconsistent by sub-proof #9.
% 139.10/18.95 | | | | | | |
% 139.10/18.95 | | | | | | Case 2:
% 139.10/18.95 | | | | | | |
% 139.10/18.95 | | | | | | | (142) growth_rate(first_movers, all_30_0) = all_42_0 &
% 139.10/18.95 | | | | | | | $i(all_42_0) & ~ greater(zero, all_42_0)
% 139.10/18.95 | | | | | | |
% 139.10/18.95 | | | | | | | ALPHA: (142) implies:
% 139.10/18.95 | | | | | | | (143) ~ greater(zero, all_42_0)
% 139.10/18.95 | | | | | | | (144) growth_rate(first_movers, all_30_0) = all_42_0
% 139.10/18.95 | | | | | | |
% 139.10/18.95 | | | | | | | REDUCE: (95), (144) imply:
% 139.10/18.95 | | | | | | | (145) growth_rate(first_movers, all_22_0) = all_42_0
% 139.10/18.95 | | | | | | |
% 139.10/18.95 | | | | | | | REF_CLOSE: (6), (97), (139), (143), (145) are inconsistent by
% 139.10/18.95 | | | | | | | sub-proof #11.
% 139.10/18.95 | | | | | | |
% 139.10/18.95 | | | | | | End of split
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | End of split
% 139.10/18.95 | | | | |
% 139.10/18.95 | | | | End of split
% 139.10/18.95 | | | |
% 139.10/18.95 | | | Case 2:
% 139.10/18.95 | | | |
% 139.10/18.95 | | | | (146) all_39_0 = all_39_1
% 139.10/18.95 | | | | (147) growth_rate(first_movers, all_30_0) = all_39_1
% 139.10/18.95 | | | |
% 139.10/18.95 | | | | REDUCE: (97), (146) imply:
% 139.10/18.95 | | | | (148) growth_rate(first_movers, all_22_0) = all_39_1
% 139.10/18.95 | | | |
% 139.10/18.95 | | | | REDUCE: (17), (146) imply:
% 139.10/18.95 | | | | (149) greater_or_equal(all_39_1, all_39_1)
% 139.10/18.95 | | | |
% 139.10/18.95 | | | | REDUCE: (7), (146) imply:
% 139.10/18.95 | | | | (150) greater(all_39_1, all_39_1)
% 139.10/18.95 | | | |
% 139.10/18.95 | | | | BETA: splitting (10) gives:
% 139.10/18.95 | | | |
% 139.10/18.95 | | | | Case 1:
% 139.10/18.95 | | | | |
% 139.10/18.95 | | | | | (151) (all_43_0 = zero & all_43_1 = zero &
% 139.10/18.95 | | | | | growth_rate(efficient_producers, all_30_0) = zero &
% 139.10/18.95 | | | | | growth_rate(first_movers, all_30_0) = zero) |
% 139.10/18.95 | | | | | (equilibrium(all_12_0) = all_43_2 & $i(all_43_2) & ~
% 139.10/18.95 | | | | | greater_or_equal(all_30_0, all_43_2))
% 139.10/18.95 | | | | |
% 139.10/18.95 | | | | | BETA: splitting (151) gives:
% 139.10/18.95 | | | | |
% 139.10/18.95 | | | | | Case 1:
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | (152) all_43_0 = zero & all_43_1 = zero &
% 139.10/18.95 | | | | | | growth_rate(efficient_producers, all_30_0) = zero &
% 139.10/18.95 | | | | | | growth_rate(first_movers, all_30_0) = zero
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | REF_CLOSE: (6), (12), (100), (147), (149), (150), (152) are
% 139.10/18.95 | | | | | | inconsistent by sub-proof #15.
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | Case 2:
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | (153) equilibrium(all_12_0) = all_43_2 & $i(all_43_2) & ~
% 139.10/18.95 | | | | | | greater_or_equal(all_30_0, all_43_2)
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | ALPHA: (153) implies:
% 139.10/18.95 | | | | | | (154) ~ greater_or_equal(all_30_0, all_43_2)
% 139.10/18.95 | | | | | | (155) equilibrium(all_12_0) = all_43_2
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | REDUCE: (95), (154) imply:
% 139.10/18.95 | | | | | | (156) ~ greater_or_equal(all_22_0, all_43_2)
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | | REF_CLOSE: (2), (11), (20), (155), (156) are inconsistent by
% 139.10/18.95 | | | | | | sub-proof #13.
% 139.10/18.95 | | | | | |
% 139.10/18.95 | | | | | End of split
% 139.10/18.95 | | | | |
% 139.10/18.95 | | | | Case 2:
% 139.10/18.95 | | | | |
% 139.10/18.96 | | | | | (157) (growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 139.10/18.96 | | | | | growth_rate(first_movers, all_30_0) = all_43_1 &
% 139.10/18.96 | | | | | $i(all_43_0) & $i(all_43_1) & greater(all_43_0, zero) &
% 139.10/18.96 | | | | | greater(zero, all_43_1)) |
% 139.10/18.96 | | | | | (growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 139.10/18.96 | | | | | growth_rate(first_movers, all_30_0) = all_43_1 &
% 139.10/18.96 | | | | | $i(all_43_0) & $i(all_43_1) & greater(all_43_1, zero) &
% 139.10/18.96 | | | | | greater(zero, all_43_0))
% 139.10/18.96 | | | | |
% 139.10/18.96 | | | | | BETA: splitting (157) gives:
% 139.10/18.96 | | | | |
% 139.10/18.96 | | | | | Case 1:
% 139.10/18.96 | | | | | |
% 139.10/18.96 | | | | | | (158) growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 139.10/18.96 | | | | | | growth_rate(first_movers, all_30_0) = all_43_1 &
% 139.10/18.96 | | | | | | $i(all_43_0) & $i(all_43_1) & greater(all_43_0, zero) &
% 139.10/18.96 | | | | | | greater(zero, all_43_1)
% 139.10/18.96 | | | | | |
% 139.10/18.96 | | | | | | ALPHA: (158) implies:
% 139.10/18.96 | | | | | | (159) greater(zero, all_43_1)
% 139.10/18.96 | | | | | | (160) greater(all_43_0, zero)
% 139.10/18.96 | | | | | | (161) growth_rate(first_movers, all_30_0) = all_43_1
% 139.10/18.96 | | | | | | (162) growth_rate(efficient_producers, all_30_0) = all_43_0
% 139.10/18.96 | | | | | |
% 139.10/18.96 | | | | | | REDUCE: (95), (162) imply:
% 139.10/18.96 | | | | | | (163) growth_rate(efficient_producers, all_22_0) = all_43_0
% 139.10/18.96 | | | | | |
% 139.10/18.96 | | | | | | REDUCE: (95), (161) imply:
% 139.10/18.96 | | | | | | (164) growth_rate(first_movers, all_22_0) = all_43_1
% 139.10/18.96 | | | | | |
% 139.10/18.96 | | | | | | REF_CLOSE: (6), (9), (15), (95), (96), (97), (100), (159), (160),
% 139.10/18.96 | | | | | | (163), (164) are inconsistent by sub-proof #10.
% 139.10/18.96 | | | | | |
% 139.10/18.96 | | | | | Case 2:
% 139.10/18.96 | | | | | |
% 139.10/18.96 | | | | | | (165) growth_rate(efficient_producers, all_30_0) = all_43_0 &
% 139.10/18.96 | | | | | | growth_rate(first_movers, all_30_0) = all_43_1 &
% 139.10/18.96 | | | | | | $i(all_43_0) & $i(all_43_1) & greater(all_43_1, zero) &
% 139.10/18.96 | | | | | | greater(zero, all_43_0)
% 139.10/18.96 | | | | | |
% 139.10/18.96 | | | | | | ALPHA: (165) implies:
% 139.10/18.96 | | | | | | (166) greater(zero, all_43_0)
% 139.10/18.96 | | | | | | (167) greater(all_43_1, zero)
% 139.10/18.96 | | | | | | (168) growth_rate(first_movers, all_30_0) = all_43_1
% 139.10/18.96 | | | | | | (169) growth_rate(efficient_producers, all_30_0) = all_43_0
% 139.10/18.96 | | | | | |
% 139.10/18.96 | | | | | | REDUCE: (95), (169) imply:
% 139.10/18.96 | | | | | | (170) growth_rate(efficient_producers, all_22_0) = all_43_0
% 139.10/18.96 | | | | | |
% 139.10/18.96 | | | | | | REDUCE: (95), (168) imply:
% 139.10/18.96 | | | | | | (171) growth_rate(first_movers, all_22_0) = all_43_1
% 139.10/18.96 | | | | | |
% 139.10/18.96 | | | | | | GROUND_INST: instantiating (6) with all_39_1, all_43_1, all_22_0,
% 139.10/18.96 | | | | | | first_movers, simplifying with (148), (171) gives:
% 139.10/18.96 | | | | | | (172) all_43_1 = all_39_1
% 139.10/18.96 | | | | | |
% 139.10/18.96 | | | | | | GROUND_INST: instantiating (6) with all_39_1, all_43_0, all_22_0,
% 139.10/18.96 | | | | | | efficient_producers, simplifying with (96), (170)
% 139.10/18.96 | | | | | | gives:
% 139.10/18.96 | | | | | | (173) all_43_0 = all_39_1
% 139.10/18.96 | | | | | |
% 139.10/18.96 | | | | | | REDUCE: (167), (172) imply:
% 139.10/18.96 | | | | | | (174) greater(all_39_1, zero)
% 139.10/18.96 | | | | | |
% 139.10/18.96 | | | | | | REDUCE: (166), (173) imply:
% 139.10/18.96 | | | | | | (175) greater(zero, all_39_1)
% 139.10/18.96 | | | | | |
% 139.10/18.96 | | | | | | BETA: splitting (100) gives:
% 139.10/18.96 | | | | | |
% 139.10/18.96 | | | | | | Case 1:
% 139.10/18.96 | | | | | | |
% 139.10/18.96 | | | | | | | (176) growth_rate(efficient_producers, all_30_0) = all_42_1 &
% 139.10/18.96 | | | | | | | $i(all_42_1) & ~ greater_or_equal(all_42_1, zero)
% 139.10/18.96 | | | | | | |
% 139.10/18.96 | | | | | | | REF_CLOSE: (6), (9), (15), (95), (96), (174), (176) are
% 139.10/18.96 | | | | | | | inconsistent by sub-proof #9.
% 139.10/18.96 | | | | | | |
% 139.10/18.96 | | | | | | Case 2:
% 139.10/18.96 | | | | | | |
% 139.10/18.96 | | | | | | | (177) growth_rate(first_movers, all_30_0) = all_42_0 &
% 139.10/18.96 | | | | | | | $i(all_42_0) & ~ greater(zero, all_42_0)
% 139.10/18.96 | | | | | | |
% 139.10/18.96 | | | | | | | REF_CLOSE: (6), (147), (175), (177) are inconsistent by sub-proof
% 139.10/18.96 | | | | | | | #14.
% 139.10/18.96 | | | | | | |
% 139.10/18.96 | | | | | | End of split
% 139.10/18.96 | | | | | |
% 139.10/18.96 | | | | | End of split
% 139.10/18.96 | | | | |
% 139.10/18.96 | | | | End of split
% 139.10/18.96 | | | |
% 139.10/18.96 | | | End of split
% 139.10/18.96 | | |
% 139.10/18.96 | | End of split
% 139.10/18.96 | |
% 139.10/18.96 | End of split
% 139.10/18.96 |
% 139.10/18.96 End of proof
% 139.10/18.96
% 139.10/18.96 Sub-proof #9 shows that the following formulas are inconsistent:
% 139.10/18.96 ----------------------------------------------------------------
% 139.10/18.96 (1) greater(all_39_1, zero)
% 139.10/18.96 (2) growth_rate(efficient_producers, all_22_0) = all_39_1
% 139.10/18.96 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 139.10/18.96 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 139.10/18.96 (4) growth_rate(efficient_producers, all_30_0) = all_42_1 & $i(all_42_1) & ~
% 139.10/18.96 greater_or_equal(all_42_1, zero)
% 139.10/18.96 (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1) |
% 139.10/18.96 greater_or_equal(v0, v1))
% 139.10/18.96 (6) $i(zero)
% 139.10/18.96 (7) all_30_0 = all_22_0
% 139.10/18.96
% 139.10/18.96 Begin of proof
% 139.10/18.96 |
% 139.10/18.96 | ALPHA: (4) implies:
% 139.10/18.96 | (8) ~ greater_or_equal(all_42_1, zero)
% 139.10/18.96 | (9) $i(all_42_1)
% 139.10/18.96 | (10) growth_rate(efficient_producers, all_30_0) = all_42_1
% 139.10/18.96 |
% 139.10/18.96 | REDUCE: (7), (10) imply:
% 139.10/18.96 | (11) growth_rate(efficient_producers, all_22_0) = all_42_1
% 139.10/18.96 |
% 139.10/18.96 | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (11) are inconsistent by
% 139.10/18.96 | sub-proof #12.
% 139.10/18.96 |
% 139.10/18.96 End of proof
% 139.10/18.96
% 139.10/18.96 Sub-proof #10 shows that the following formulas are inconsistent:
% 139.10/18.96 ----------------------------------------------------------------
% 139.10/18.96 (1) (growth_rate(efficient_producers, all_30_0) = all_42_1 & $i(all_42_1) &
% 139.10/18.96 ~ greater_or_equal(all_42_1, zero)) | (growth_rate(first_movers,
% 139.10/18.96 all_30_0) = all_42_0 & $i(all_42_0) & ~ greater(zero, all_42_0))
% 139.10/18.96 (2) greater(all_43_0, zero)
% 139.10/18.96 (3) growth_rate(efficient_producers, all_22_0) = all_39_1
% 139.10/18.96 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 139.10/18.96 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 139.10/18.96 (5) growth_rate(first_movers, all_22_0) = all_39_0
% 139.10/18.96 (6) growth_rate(efficient_producers, all_22_0) = all_43_0
% 139.10/18.96 (7) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1) |
% 139.10/18.96 greater_or_equal(v0, v1))
% 139.10/18.96 (8) growth_rate(first_movers, all_22_0) = all_43_1
% 139.10/18.96 (9) greater(zero, all_43_1)
% 139.10/18.96 (10) $i(zero)
% 139.10/18.96 (11) all_30_0 = all_22_0
% 139.10/18.96
% 139.10/18.96 Begin of proof
% 139.10/18.96 |
% 139.10/18.96 | GROUND_INST: instantiating (4) with all_39_0, all_43_1, all_22_0,
% 139.10/18.96 | first_movers, simplifying with (5), (8) gives:
% 139.10/18.96 | (12) all_43_1 = all_39_0
% 139.10/18.96 |
% 139.10/18.96 | GROUND_INST: instantiating (4) with all_39_1, all_43_0, all_22_0,
% 139.10/18.96 | efficient_producers, simplifying with (3), (6) gives:
% 139.10/18.96 | (13) all_43_0 = all_39_1
% 139.10/18.96 |
% 139.10/18.96 | REDUCE: (2), (13) imply:
% 139.10/18.96 | (14) greater(all_39_1, zero)
% 139.10/18.96 |
% 139.10/18.96 | REDUCE: (9), (12) imply:
% 139.10/18.96 | (15) greater(zero, all_39_0)
% 139.10/18.96 |
% 139.10/18.96 | BETA: splitting (1) gives:
% 139.10/18.96 |
% 139.10/18.96 | Case 1:
% 139.10/18.96 | |
% 139.10/18.96 | | (16) growth_rate(efficient_producers, all_30_0) = all_42_1 & $i(all_42_1)
% 139.10/18.96 | | & ~ greater_or_equal(all_42_1, zero)
% 139.10/18.96 | |
% 139.10/18.96 | | ALPHA: (16) implies:
% 139.10/18.96 | | (17) ~ greater_or_equal(all_42_1, zero)
% 139.10/18.96 | | (18) $i(all_42_1)
% 139.10/18.96 | | (19) growth_rate(efficient_producers, all_30_0) = all_42_1
% 139.10/18.96 | |
% 139.10/18.96 | | REDUCE: (11), (19) imply:
% 139.10/18.96 | | (20) growth_rate(efficient_producers, all_22_0) = all_42_1
% 139.10/18.96 | |
% 139.10/18.96 | | REF_CLOSE: (3), (4), (7), (10), (14), (17), (18), (20) are inconsistent by
% 139.10/18.96 | | sub-proof #12.
% 139.10/18.96 | |
% 139.10/18.96 | Case 2:
% 139.10/18.96 | |
% 139.10/18.96 | | (21) growth_rate(first_movers, all_30_0) = all_42_0 & $i(all_42_0) & ~
% 139.10/18.96 | | greater(zero, all_42_0)
% 139.10/18.96 | |
% 139.10/18.96 | | ALPHA: (21) implies:
% 139.10/18.96 | | (22) ~ greater(zero, all_42_0)
% 139.10/18.96 | | (23) growth_rate(first_movers, all_30_0) = all_42_0
% 139.10/18.96 | |
% 139.10/18.96 | | REDUCE: (11), (23) imply:
% 139.10/18.96 | | (24) growth_rate(first_movers, all_22_0) = all_42_0
% 139.10/18.96 | |
% 139.10/18.96 | | REF_CLOSE: (4), (5), (15), (22), (24) are inconsistent by sub-proof #11.
% 139.10/18.96 | |
% 139.10/18.96 | End of split
% 139.10/18.96 |
% 139.10/18.96 End of proof
% 139.10/18.96
% 139.10/18.96 Sub-proof #11 shows that the following formulas are inconsistent:
% 139.10/18.96 ----------------------------------------------------------------
% 139.10/18.96 (1) greater(zero, all_39_0)
% 139.10/18.96 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 139.10/18.96 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 139.10/18.96 (3) growth_rate(first_movers, all_22_0) = all_39_0
% 139.10/18.96 (4) growth_rate(first_movers, all_22_0) = all_42_0
% 139.10/18.96 (5) ~ greater(zero, all_42_0)
% 139.10/18.96
% 139.10/18.96 Begin of proof
% 139.10/18.96 |
% 139.10/18.96 | GROUND_INST: instantiating (2) with all_39_0, all_42_0, all_22_0,
% 139.10/18.96 | first_movers, simplifying with (3), (4) gives:
% 139.10/18.96 | (6) all_42_0 = all_39_0
% 139.10/18.96 |
% 139.10/18.96 | PRED_UNIFY: (1), (5) imply:
% 139.10/18.96 | (7) ~ (all_42_0 = all_39_0)
% 139.10/18.96 |
% 139.10/18.96 | REDUCE: (6), (7) imply:
% 139.10/18.96 | (8) $false
% 139.10/18.96 |
% 139.10/18.96 | CLOSE: (8) is inconsistent.
% 139.10/18.96 |
% 139.10/18.96 End of proof
% 139.10/18.96
% 139.10/18.96 Sub-proof #12 shows that the following formulas are inconsistent:
% 139.10/18.96 ----------------------------------------------------------------
% 139.10/18.96 (1) greater(all_39_1, zero)
% 139.10/18.96 (2) growth_rate(efficient_producers, all_22_0) = all_42_1
% 139.10/18.96 (3) growth_rate(efficient_producers, all_22_0) = all_39_1
% 139.10/18.96 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 139.10/18.96 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 139.10/18.96 (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1) |
% 139.10/18.96 greater_or_equal(v0, v1))
% 139.10/18.96 (6) ~ greater_or_equal(all_42_1, zero)
% 139.10/18.96 (7) $i(zero)
% 139.10/18.96 (8) $i(all_42_1)
% 139.10/18.96
% 139.10/18.96 Begin of proof
% 139.10/18.96 |
% 139.10/18.97 | GROUND_INST: instantiating (4) with all_39_1, all_42_1, all_22_0,
% 139.10/18.97 | efficient_producers, simplifying with (2), (3) gives:
% 139.10/18.97 | (9) all_42_1 = all_39_1
% 139.10/18.97 |
% 139.10/18.97 | REDUCE: (8), (9) imply:
% 139.10/18.97 | (10) $i(all_39_1)
% 139.10/18.97 |
% 139.10/18.97 | REDUCE: (6), (9) imply:
% 139.10/18.97 | (11) ~ greater_or_equal(all_39_1, zero)
% 139.10/18.97 |
% 139.10/18.97 | GROUND_INST: instantiating (5) with all_39_1, zero, simplifying with (1), (7),
% 139.10/18.97 | (10), (11) gives:
% 139.10/18.97 | (12) $false
% 139.10/18.97 |
% 139.10/18.97 | CLOSE: (12) is inconsistent.
% 139.10/18.97 |
% 139.10/18.97 End of proof
% 139.10/18.97
% 139.10/18.97 Sub-proof #13 shows that the following formulas are inconsistent:
% 139.10/18.97 ----------------------------------------------------------------
% 139.10/18.97 (1) equilibrium(all_12_0) = all_20_1
% 139.10/18.97 (2) equilibrium(all_12_0) = all_43_2
% 139.10/18.97 (3) ~ greater_or_equal(all_22_0, all_43_2)
% 139.10/18.97 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (equilibrium(v2)
% 139.10/18.97 = v1) | ~ (equilibrium(v2) = v0))
% 139.10/18.97 (5) greater_or_equal(all_22_0, all_20_1)
% 139.10/18.97
% 139.10/18.97 Begin of proof
% 139.10/18.97 |
% 139.10/18.97 | GROUND_INST: instantiating (4) with all_20_1, all_43_2, all_12_0, simplifying
% 139.10/18.97 | with (1), (2) gives:
% 139.10/18.97 | (6) all_43_2 = all_20_1
% 139.10/18.97 |
% 139.10/18.97 | PRED_UNIFY: (3), (5) imply:
% 139.10/18.97 | (7) ~ (all_43_2 = all_20_1)
% 139.10/18.97 |
% 139.10/18.97 | REDUCE: (6), (7) imply:
% 139.10/18.97 | (8) $false
% 139.10/18.97 |
% 139.10/18.97 | CLOSE: (8) is inconsistent.
% 139.10/18.97 |
% 139.10/18.97 End of proof
% 139.10/18.97
% 139.10/18.97 Sub-proof #14 shows that the following formulas are inconsistent:
% 139.10/18.97 ----------------------------------------------------------------
% 139.10/18.97 (1) growth_rate(first_movers, all_30_0) = all_42_0 & $i(all_42_0) & ~
% 139.10/18.97 greater(zero, all_42_0)
% 139.10/18.97 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 139.10/18.97 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 139.10/18.97 (3) growth_rate(first_movers, all_30_0) = all_39_1
% 139.10/18.97 (4) greater(zero, all_39_1)
% 139.10/18.97
% 139.10/18.97 Begin of proof
% 139.10/18.97 |
% 139.10/18.97 | ALPHA: (1) implies:
% 139.10/18.97 | (5) ~ greater(zero, all_42_0)
% 139.10/18.97 | (6) growth_rate(first_movers, all_30_0) = all_42_0
% 139.10/18.97 |
% 139.10/18.97 | GROUND_INST: instantiating (2) with all_39_1, all_42_0, all_30_0,
% 139.10/18.97 | first_movers, simplifying with (3), (6) gives:
% 139.10/18.97 | (7) all_42_0 = all_39_1
% 139.10/18.97 |
% 139.10/18.97 | PRED_UNIFY: (4), (5) imply:
% 139.10/18.97 | (8) ~ (all_42_0 = all_39_1)
% 139.10/18.97 |
% 139.10/18.97 | REDUCE: (7), (8) imply:
% 139.10/18.97 | (9) $false
% 139.10/18.97 |
% 139.10/18.97 | CLOSE: (9) is inconsistent.
% 139.10/18.97 |
% 139.10/18.97 End of proof
% 139.10/18.97
% 139.10/18.97 Sub-proof #15 shows that the following formulas are inconsistent:
% 139.10/18.97 ----------------------------------------------------------------
% 139.10/18.97 (1) (growth_rate(efficient_producers, all_30_0) = all_42_1 & $i(all_42_1) &
% 139.10/18.97 ~ greater_or_equal(all_42_1, zero)) | (growth_rate(first_movers,
% 139.10/18.97 all_30_0) = all_42_0 & $i(all_42_0) & ~ greater(zero, all_42_0))
% 139.10/18.97 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 139.10/18.97 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 139.10/18.97 (3) greater(all_39_1, all_39_1)
% 139.10/18.97 (4) growth_rate(first_movers, all_30_0) = all_39_1
% 139.10/18.97 (5) greater_or_equal(all_39_1, all_39_1)
% 139.10/18.97 (6) growth_rate(efficient_producers, all_30_0) = all_39_1
% 139.10/18.97 (7) all_43_0 = zero & all_43_1 = zero & growth_rate(efficient_producers,
% 139.10/18.97 all_30_0) = zero & growth_rate(first_movers, all_30_0) = zero
% 139.10/18.97
% 139.10/18.97 Begin of proof
% 139.10/18.97 |
% 139.10/18.97 | ALPHA: (7) implies:
% 139.10/18.97 | (8) growth_rate(efficient_producers, all_30_0) = zero
% 139.10/18.97 |
% 139.10/18.97 | GROUND_INST: instantiating (2) with all_39_1, zero, all_30_0,
% 139.10/18.97 | efficient_producers, simplifying with (6), (8) gives:
% 139.10/18.97 | (9) all_39_1 = zero
% 139.10/18.97 |
% 139.10/18.97 | REDUCE: (4), (9) imply:
% 139.10/18.97 | (10) growth_rate(first_movers, all_30_0) = zero
% 139.10/18.97 |
% 139.10/18.97 | REDUCE: (5), (9) imply:
% 139.10/18.97 | (11) greater_or_equal(zero, zero)
% 139.10/18.97 |
% 139.10/18.97 | REDUCE: (3), (9) imply:
% 139.10/18.97 | (12) greater(zero, zero)
% 139.10/18.97 |
% 139.10/18.97 | BETA: splitting (1) gives:
% 139.10/18.97 |
% 139.10/18.97 | Case 1:
% 139.10/18.97 | |
% 139.10/18.97 | | (13) growth_rate(efficient_producers, all_30_0) = all_42_1 & $i(all_42_1)
% 139.10/18.97 | | & ~ greater_or_equal(all_42_1, zero)
% 139.10/18.97 | |
% 139.10/18.97 | | ALPHA: (13) implies:
% 139.10/18.97 | | (14) ~ greater_or_equal(all_42_1, zero)
% 139.10/18.97 | | (15) growth_rate(efficient_producers, all_30_0) = all_42_1
% 139.10/18.97 | |
% 139.10/18.97 | | GROUND_INST: instantiating (2) with zero, all_42_1, all_30_0,
% 139.10/18.97 | | efficient_producers, simplifying with (8), (15) gives:
% 139.10/18.97 | | (16) all_42_1 = zero
% 139.10/18.97 | |
% 139.10/18.97 | | PRED_UNIFY: (11), (14) imply:
% 139.10/18.97 | | (17) ~ (all_42_1 = zero)
% 139.10/18.97 | |
% 139.10/18.97 | | REDUCE: (16), (17) imply:
% 139.10/18.97 | | (18) $false
% 139.10/18.97 | |
% 139.10/18.97 | | CLOSE: (18) is inconsistent.
% 139.10/18.97 | |
% 139.10/18.97 | Case 2:
% 139.10/18.97 | |
% 139.10/18.97 | | (19) growth_rate(first_movers, all_30_0) = all_42_0 & $i(all_42_0) & ~
% 139.10/18.97 | | greater(zero, all_42_0)
% 139.10/18.97 | |
% 139.10/18.97 | | ALPHA: (19) implies:
% 139.10/18.97 | | (20) ~ greater(zero, all_42_0)
% 139.10/18.97 | | (21) growth_rate(first_movers, all_30_0) = all_42_0
% 139.10/18.97 | |
% 139.10/18.97 | | GROUND_INST: instantiating (2) with zero, all_42_0, all_30_0, first_movers,
% 139.10/18.97 | | simplifying with (10), (21) gives:
% 139.10/18.97 | | (22) all_42_0 = zero
% 139.10/18.97 | |
% 139.10/18.97 | | PRED_UNIFY: (12), (20) imply:
% 139.10/18.97 | | (23) ~ (all_42_0 = zero)
% 139.10/18.97 | |
% 139.10/18.97 | | REDUCE: (22), (23) imply:
% 139.10/18.97 | | (24) $false
% 139.10/18.97 | |
% 139.10/18.97 | | CLOSE: (24) is inconsistent.
% 139.10/18.97 | |
% 139.10/18.97 | End of split
% 139.10/18.97 |
% 139.10/18.97 End of proof
% 139.10/18.97
% 139.10/18.97 Sub-proof #16 shows that the following formulas are inconsistent:
% 139.10/18.97 ----------------------------------------------------------------
% 139.10/18.97 (1) greater(zero, all_39_0)
% 139.10/18.97 (2) greater(all_39_1, zero)
% 139.10/18.97 (3) (growth_rate(efficient_producers, all_30_0) = all_42_1 & $i(all_42_1) &
% 139.10/18.97 ~ greater_or_equal(all_42_1, zero)) | (growth_rate(first_movers,
% 139.10/18.97 all_30_0) = all_42_0 & $i(all_42_0) & ~ greater(zero, all_42_0))
% 139.10/18.97 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 139.10/18.97 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 139.10/18.97 (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1) |
% 139.10/18.97 greater_or_equal(v0, v1))
% 139.10/18.97 (6) growth_rate(efficient_producers, all_30_0) = all_39_1
% 139.10/18.97 (7) $i(zero)
% 139.10/18.97 (8) growth_rate(first_movers, all_30_0) = all_39_0
% 139.10/18.97
% 139.10/18.97 Begin of proof
% 139.10/18.97 |
% 139.10/18.97 | BETA: splitting (3) gives:
% 139.10/18.97 |
% 139.10/18.97 | Case 1:
% 139.10/18.97 | |
% 139.10/18.97 | | (9) growth_rate(efficient_producers, all_30_0) = all_42_1 & $i(all_42_1)
% 139.10/18.97 | | & ~ greater_or_equal(all_42_1, zero)
% 139.10/18.97 | |
% 139.10/18.97 | | REF_CLOSE: (2), (4), (5), (6), (7), (9) are inconsistent by sub-proof #17.
% 139.10/18.97 | |
% 139.10/18.97 | Case 2:
% 139.10/18.97 | |
% 139.10/18.97 | | (10) growth_rate(first_movers, all_30_0) = all_42_0 & $i(all_42_0) & ~
% 139.10/18.97 | | greater(zero, all_42_0)
% 139.10/18.97 | |
% 139.10/18.97 | | ALPHA: (10) implies:
% 139.10/18.97 | | (11) ~ greater(zero, all_42_0)
% 139.10/18.97 | | (12) growth_rate(first_movers, all_30_0) = all_42_0
% 139.10/18.97 | |
% 139.10/18.97 | | GROUND_INST: instantiating (4) with all_39_0, all_42_0, all_30_0,
% 139.10/18.97 | | first_movers, simplifying with (8), (12) gives:
% 139.10/18.97 | | (13) all_42_0 = all_39_0
% 139.10/18.97 | |
% 139.10/18.97 | | PRED_UNIFY: (1), (11) imply:
% 139.10/18.97 | | (14) ~ (all_42_0 = all_39_0)
% 139.10/18.97 | |
% 139.10/18.97 | | REDUCE: (13), (14) imply:
% 139.10/18.97 | | (15) $false
% 139.10/18.97 | |
% 139.10/18.97 | | CLOSE: (15) is inconsistent.
% 139.10/18.97 | |
% 139.10/18.97 | End of split
% 139.10/18.97 |
% 139.10/18.97 End of proof
% 139.10/18.97
% 139.10/18.97 Sub-proof #17 shows that the following formulas are inconsistent:
% 139.10/18.97 ----------------------------------------------------------------
% 139.10/18.97 (1) greater(all_39_1, zero)
% 139.10/18.97 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 139.10/18.97 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 139.10/18.97 (3) growth_rate(efficient_producers, all_30_0) = all_42_1 & $i(all_42_1) & ~
% 139.10/18.97 greater_or_equal(all_42_1, zero)
% 139.10/18.97 (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1) |
% 139.10/18.97 greater_or_equal(v0, v1))
% 139.10/18.97 (5) growth_rate(efficient_producers, all_30_0) = all_39_1
% 139.10/18.97 (6) $i(zero)
% 139.10/18.97
% 139.10/18.97 Begin of proof
% 139.10/18.97 |
% 139.10/18.97 | ALPHA: (3) implies:
% 139.10/18.97 | (7) ~ greater_or_equal(all_42_1, zero)
% 139.10/18.97 | (8) $i(all_42_1)
% 139.10/18.97 | (9) growth_rate(efficient_producers, all_30_0) = all_42_1
% 139.10/18.97 |
% 139.10/18.97 | GROUND_INST: instantiating (2) with all_39_1, all_42_1, all_30_0,
% 139.10/18.97 | efficient_producers, simplifying with (5), (9) gives:
% 139.10/18.97 | (10) all_42_1 = all_39_1
% 139.10/18.97 |
% 139.10/18.97 | REDUCE: (8), (10) imply:
% 139.10/18.97 | (11) $i(all_39_1)
% 139.10/18.97 |
% 139.10/18.97 | REDUCE: (7), (10) imply:
% 139.10/18.97 | (12) ~ greater_or_equal(all_39_1, zero)
% 139.10/18.97 |
% 139.10/18.97 | GROUND_INST: instantiating (4) with all_39_1, zero, simplifying with (1), (6),
% 139.10/18.97 | (11), (12) gives:
% 139.10/18.97 | (13) $false
% 139.10/18.97 |
% 139.10/18.97 | CLOSE: (13) is inconsistent.
% 139.10/18.97 |
% 139.10/18.97 End of proof
% 139.10/18.97
% 139.10/18.97 Sub-proof #18 shows that the following formulas are inconsistent:
% 139.10/18.97 ----------------------------------------------------------------
% 139.10/18.97 (1) equilibrium(all_12_0) = all_20_1
% 139.10/18.97 (2) equilibrium(all_12_0) = all_43_2
% 139.10/18.97 (3) ~ greater_or_equal(all_30_0, all_43_2)
% 139.10/18.97 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (equilibrium(v2)
% 139.10/18.97 = v1) | ~ (equilibrium(v2) = v0))
% 139.10/18.97 (5) greater_or_equal(all_30_0, all_20_1)
% 139.10/18.97
% 139.10/18.97 Begin of proof
% 139.10/18.97 |
% 139.10/18.98 | GROUND_INST: instantiating (4) with all_20_1, all_43_2, all_12_0, simplifying
% 139.10/18.98 | with (1), (2) gives:
% 139.10/18.98 | (6) all_43_2 = all_20_1
% 139.10/18.98 |
% 139.10/18.98 | PRED_UNIFY: (3), (5) imply:
% 139.10/18.98 | (7) ~ (all_43_2 = all_20_1)
% 139.10/18.98 |
% 139.10/18.98 | REDUCE: (6), (7) imply:
% 139.10/18.98 | (8) $false
% 139.10/18.98 |
% 139.10/18.98 | CLOSE: (8) is inconsistent.
% 139.10/18.98 |
% 139.10/18.98 End of proof
% 139.10/18.98 % SZS output end Proof for theBenchmark
% 139.10/18.98
% 139.10/18.98 18364ms
%------------------------------------------------------------------------------