TSTP Solution File: MGT029+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : MGT029+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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 09:16:17 EDT 2023
% Result : Theorem 32.48s 5.14s
% Output : Proof 40.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT029+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 06:38:43 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.44/1.03 Prover 1: Preprocessing ...
% 2.44/1.03 Prover 4: Preprocessing ...
% 2.70/1.08 Prover 5: Preprocessing ...
% 2.70/1.08 Prover 6: Preprocessing ...
% 2.70/1.08 Prover 2: Preprocessing ...
% 2.70/1.09 Prover 3: Preprocessing ...
% 2.70/1.09 Prover 0: Preprocessing ...
% 4.45/1.36 Prover 6: Proving ...
% 4.45/1.36 Prover 5: Proving ...
% 4.45/1.37 Prover 2: Proving ...
% 4.45/1.37 Prover 3: Constructing countermodel ...
% 4.45/1.39 Prover 1: Constructing countermodel ...
% 5.38/1.52 Prover 4: Constructing countermodel ...
% 5.38/1.54 Prover 0: Proving ...
% 8.97/1.95 Prover 3: gave up
% 8.97/1.97 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.97/1.99 Prover 7: Preprocessing ...
% 9.65/2.04 Prover 7: Warning: ignoring some quantifiers
% 9.65/2.05 Prover 7: Constructing countermodel ...
% 9.65/2.18 Prover 7: gave up
% 10.64/2.24 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.64/2.27 Prover 8: Preprocessing ...
% 11.63/2.34 Prover 8: Warning: ignoring some quantifiers
% 11.63/2.34 Prover 8: Constructing countermodel ...
% 13.76/2.61 Prover 8: gave up
% 13.76/2.61 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 13.84/2.64 Prover 9: Preprocessing ...
% 13.84/2.82 Prover 9: Constructing countermodel ...
% 16.23/2.95 Prover 1: gave up
% 16.23/2.95 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 16.23/2.98 Prover 10: Preprocessing ...
% 16.23/3.01 Prover 10: Warning: ignoring some quantifiers
% 16.23/3.02 Prover 10: Constructing countermodel ...
% 16.91/3.05 Prover 10: gave up
% 16.91/3.05 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 16.91/3.06 Prover 11: Preprocessing ...
% 17.73/3.14 Prover 11: Constructing countermodel ...
% 32.48/5.14 Prover 2: proved (4507ms)
% 32.48/5.14
% 32.48/5.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.48/5.14
% 32.48/5.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 32.48/5.14 Prover 6: stopped
% 32.48/5.15 Prover 0: stopped
% 32.48/5.15 Prover 9: stopped
% 32.48/5.15 Prover 5: stopped
% 32.48/5.15 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 32.48/5.15 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 33.04/5.16 Prover 13: Preprocessing ...
% 33.04/5.16 Prover 19: Preprocessing ...
% 33.04/5.17 Prover 16: Preprocessing ...
% 33.11/5.18 Prover 13: Warning: ignoring some quantifiers
% 33.11/5.18 Prover 13: Constructing countermodel ...
% 33.11/5.20 Prover 16: Warning: ignoring some quantifiers
% 33.11/5.20 Prover 16: Constructing countermodel ...
% 33.11/5.20 Prover 19: Warning: ignoring some quantifiers
% 33.42/5.21 Prover 19: Constructing countermodel ...
% 35.50/5.49 Prover 19: gave up
% 39.55/6.11 Prover 16: Found proof (size 1213)
% 39.55/6.11 Prover 16: proved (957ms)
% 39.55/6.11 Prover 13: stopped
% 39.55/6.11 Prover 11: stopped
% 39.55/6.11 Prover 4: stopped
% 39.55/6.11
% 39.55/6.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.99/6.11
% 39.99/6.13 % SZS output start Proof for theBenchmark
% 39.99/6.13 Assumptions after simplification:
% 39.99/6.13 ---------------------------------
% 39.99/6.13
% 39.99/6.14 (a4)
% 39.99/6.16 ! [v0: $i] : ( ~ $i(v0) | ~ stable(v0) | ~ environment(v0) | ? [v1: $i] :
% 39.99/6.16 ? [v2: $i] : (equilibrium(v0) = v1 & $i(v2) & $i(v1) & greater_or_equal(v2,
% 39.99/6.16 v1) & in_environment(v0, v2)))
% 39.99/6.16
% 39.99/6.16 (l1)
% 40.21/6.16 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ( ~ $i(v0) | ~
% 40.21/6.16 stable(v0) | ~ environment(v0) | ? [v1: $i] : ($i(v1) & in_environment(v0,
% 40.21/6.16 v1) & ! [v2: $i] : ( ~ $i(v2) | ~ subpopulations(first_movers,
% 40.21/6.16 efficient_producers, v0, v2) | ~ greater_or_equal(v2, v1) | ? [v3:
% 40.21/6.16 $i] : ? [v4: $i] : (growth_rate(efficient_producers, v2) = v3 &
% 40.21/6.16 growth_rate(first_movers, v2) = v4 & $i(v4) & $i(v3) & greater(v3,
% 40.21/6.16 v4)))))
% 40.21/6.16
% 40.21/6.16 (l6)
% 40.21/6.17 $i(zero) & $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1:
% 40.21/6.17 $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subpopulations(first_movers,
% 40.21/6.17 efficient_producers, v0, v1) | ~ environment(v0) | ? [v2: $i] : ? [v3:
% 40.21/6.17 $i] : ? [v4: $i] : ((v4 = zero & v3 = zero &
% 40.21/6.17 growth_rate(efficient_producers, v1) = zero & growth_rate(first_movers,
% 40.21/6.17 v1) = zero) | (equilibrium(v0) = v2 & $i(v2) & ~ greater_or_equal(v1,
% 40.21/6.17 v2)) | (growth_rate(efficient_producers, v1) = v4 &
% 40.21/6.17 growth_rate(first_movers, v1) = v3 & $i(v4) & $i(v3) & greater(v4, zero)
% 40.21/6.17 & greater(zero, v3)) | (growth_rate(efficient_producers, v1) = v4 &
% 40.21/6.17 growth_rate(first_movers, v1) = v3 & $i(v4) & $i(v3) & greater(v3, zero)
% 40.21/6.17 & greater(zero, v4))))
% 40.21/6.17
% 40.21/6.17 (mp_greater_or_equal)
% 40.21/6.17 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 40.21/6.17 greater_or_equal(v0, v1) | greater(v0, v1)) & ! [v0: $i] : ! [v1: $i] : (
% 40.21/6.17 ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1) | greater_or_equal(v0, v1)) & ?
% 40.21/6.17 [v0: $i] : ( ~ $i(v0) | greater_or_equal(v0, v0))
% 40.21/6.17
% 40.21/6.17 (mp_greater_transitivity)
% 40.21/6.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 40.21/6.17 ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 40.21/6.17
% 40.21/6.17 (mp_times_in_environment)
% 40.21/6.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ $i(v2) | ~ $i(v1) |
% 40.21/6.17 ~ $i(v0) | ~ in_environment(v0, v2) | ~ in_environment(v0, v1) |
% 40.21/6.17 greater(v2, v1) | greater(v1, v2))
% 40.21/6.17
% 40.21/6.17 (prove_l11)
% 40.21/6.17 $i(zero) & $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ($i(v0)
% 40.21/6.17 & stable(v0) & environment(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 40.21/6.17 in_environment(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ($i(v2)
% 40.21/6.17 & subpopulations(first_movers, efficient_producers, v0, v2) &
% 40.21/6.17 greater_or_equal(v2, v1) & ((growth_rate(efficient_producers, v2) = v3 &
% 40.21/6.17 $i(v3) & ~ greater(v3, zero)) | (growth_rate(first_movers, v2) = v4
% 40.21/6.17 & $i(v4) & ~ greater(zero, v4))))))
% 40.21/6.17
% 40.21/6.17 (function-axioms)
% 40.21/6.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.21/6.17 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) & ! [v0: $i] :
% 40.21/6.17 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (equilibrium(v2) = v1) | ~
% 40.21/6.17 (equilibrium(v2) = v0))
% 40.21/6.17
% 40.21/6.17 Those formulas are unsatisfiable:
% 40.21/6.17 ---------------------------------
% 40.21/6.17
% 40.21/6.17 Begin of proof
% 40.21/6.18 |
% 40.21/6.18 | ALPHA: (mp_greater_or_equal) implies:
% 40.21/6.18 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1)
% 40.21/6.18 | | greater_or_equal(v0, v1))
% 40.21/6.18 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 40.21/6.18 | greater_or_equal(v0, v1) | greater(v0, v1))
% 40.21/6.18 |
% 40.21/6.18 | ALPHA: (l6) implies:
% 40.21/6.18 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 40.21/6.18 | subpopulations(first_movers, efficient_producers, v0, v1) | ~
% 40.21/6.18 | environment(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ((v4 =
% 40.21/6.18 | zero & v3 = zero & growth_rate(efficient_producers, v1) = zero &
% 40.21/6.18 | growth_rate(first_movers, v1) = zero) | (equilibrium(v0) = v2 &
% 40.21/6.18 | $i(v2) & ~ greater_or_equal(v1, v2)) |
% 40.21/6.18 | (growth_rate(efficient_producers, v1) = v4 &
% 40.21/6.18 | growth_rate(first_movers, v1) = v3 & $i(v4) & $i(v3) &
% 40.21/6.18 | greater(v4, zero) & greater(zero, v3)) |
% 40.21/6.18 | (growth_rate(efficient_producers, v1) = v4 &
% 40.21/6.18 | growth_rate(first_movers, v1) = v3 & $i(v4) & $i(v3) &
% 40.21/6.18 | greater(v3, zero) & greater(zero, v4))))
% 40.21/6.18 |
% 40.21/6.18 | ALPHA: (l1) implies:
% 40.21/6.18 | (4) ! [v0: $i] : ( ~ $i(v0) | ~ stable(v0) | ~ environment(v0) | ? [v1:
% 40.21/6.18 | $i] : ($i(v1) & in_environment(v0, v1) & ! [v2: $i] : ( ~ $i(v2) |
% 40.21/6.18 | ~ subpopulations(first_movers, efficient_producers, v0, v2) | ~
% 40.21/6.18 | greater_or_equal(v2, v1) | ? [v3: $i] : ? [v4: $i] :
% 40.21/6.18 | (growth_rate(efficient_producers, v2) = v3 &
% 40.21/6.18 | growth_rate(first_movers, v2) = v4 & $i(v4) & $i(v3) &
% 40.21/6.18 | greater(v3, v4)))))
% 40.21/6.18 |
% 40.21/6.18 | ALPHA: (prove_l11) implies:
% 40.21/6.18 | (5) $i(zero)
% 40.21/6.18 | (6) ? [v0: $i] : ($i(v0) & stable(v0) & environment(v0) & ! [v1: $i] : (
% 40.21/6.18 | ~ $i(v1) | ~ in_environment(v0, v1) | ? [v2: $i] : ? [v3: $i] :
% 40.21/6.18 | ? [v4: $i] : ($i(v2) & subpopulations(first_movers,
% 40.21/6.18 | efficient_producers, v0, v2) & greater_or_equal(v2, v1) &
% 40.21/6.18 | ((growth_rate(efficient_producers, v2) = v3 & $i(v3) & ~
% 40.21/6.18 | greater(v3, zero)) | (growth_rate(first_movers, v2) = v4 &
% 40.21/6.18 | $i(v4) & ~ greater(zero, v4))))))
% 40.21/6.18 |
% 40.21/6.18 | ALPHA: (function-axioms) implies:
% 40.21/6.18 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 40.21/6.18 | (equilibrium(v2) = v1) | ~ (equilibrium(v2) = v0))
% 40.21/6.18 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.21/6.18 | (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 40.21/6.18 |
% 40.21/6.19 | DELTA: instantiating (6) with fresh symbol all_11_0 gives:
% 40.21/6.19 | (9) $i(all_11_0) & stable(all_11_0) & environment(all_11_0) & ! [v0: $i] :
% 40.21/6.19 | ( ~ $i(v0) | ~ in_environment(all_11_0, v0) | ? [v1: $i] : ? [v2:
% 40.21/6.19 | $i] : ? [v3: $i] : ($i(v1) & subpopulations(first_movers,
% 40.21/6.19 | efficient_producers, all_11_0, v1) & greater_or_equal(v1, v0) &
% 40.21/6.19 | ((growth_rate(efficient_producers, v1) = v2 & $i(v2) & ~
% 40.21/6.19 | greater(v2, zero)) | (growth_rate(first_movers, v1) = v3 &
% 40.21/6.19 | $i(v3) & ~ greater(zero, v3)))))
% 40.21/6.19 |
% 40.21/6.19 | ALPHA: (9) implies:
% 40.21/6.19 | (10) environment(all_11_0)
% 40.21/6.19 | (11) stable(all_11_0)
% 40.21/6.19 | (12) $i(all_11_0)
% 40.21/6.19 | (13) ! [v0: $i] : ( ~ $i(v0) | ~ in_environment(all_11_0, v0) | ? [v1:
% 40.21/6.19 | $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) &
% 40.21/6.19 | subpopulations(first_movers, efficient_producers, all_11_0, v1) &
% 40.21/6.19 | greater_or_equal(v1, v0) & ((growth_rate(efficient_producers, v1)
% 40.21/6.19 | = v2 & $i(v2) & ~ greater(v2, zero)) |
% 40.21/6.19 | (growth_rate(first_movers, v1) = v3 & $i(v3) & ~ greater(zero,
% 40.21/6.19 | v3)))))
% 40.21/6.19 |
% 40.21/6.19 | GROUND_INST: instantiating (a4) with all_11_0, simplifying with (10), (11),
% 40.21/6.19 | (12) gives:
% 40.21/6.19 | (14) ? [v0: $i] : ? [v1: $i] : (equilibrium(all_11_0) = v0 & $i(v1) &
% 40.21/6.19 | $i(v0) & greater_or_equal(v1, v0) & in_environment(all_11_0, v1))
% 40.21/6.19 |
% 40.21/6.19 | GROUND_INST: instantiating (4) with all_11_0, simplifying with (10), (11),
% 40.21/6.19 | (12) gives:
% 40.21/6.19 | (15) ? [v0: $i] : ($i(v0) & in_environment(all_11_0, v0) & ! [v1: $i] : (
% 40.21/6.19 | ~ $i(v1) | ~ subpopulations(first_movers, efficient_producers,
% 40.21/6.19 | all_11_0, v1) | ~ greater_or_equal(v1, v0) | ? [v2: $i] : ?
% 40.21/6.19 | [v3: $i] : (growth_rate(efficient_producers, v1) = v2 &
% 40.21/6.19 | growth_rate(first_movers, v1) = v3 & $i(v3) & $i(v2) &
% 40.21/6.19 | greater(v2, v3))))
% 40.21/6.19 |
% 40.21/6.19 | DELTA: instantiating (14) with fresh symbols all_19_0, all_19_1 gives:
% 40.21/6.19 | (16) equilibrium(all_11_0) = all_19_1 & $i(all_19_0) & $i(all_19_1) &
% 40.21/6.19 | greater_or_equal(all_19_0, all_19_1) & in_environment(all_11_0,
% 40.21/6.19 | all_19_0)
% 40.21/6.19 |
% 40.21/6.19 | ALPHA: (16) implies:
% 40.21/6.19 | (17) in_environment(all_11_0, all_19_0)
% 40.21/6.19 | (18) greater_or_equal(all_19_0, all_19_1)
% 40.21/6.19 | (19) $i(all_19_1)
% 40.21/6.19 | (20) $i(all_19_0)
% 40.21/6.19 | (21) equilibrium(all_11_0) = all_19_1
% 40.21/6.19 |
% 40.21/6.19 | DELTA: instantiating (15) with fresh symbol all_21_0 gives:
% 40.21/6.19 | (22) $i(all_21_0) & in_environment(all_11_0, all_21_0) & ! [v0: $i] : ( ~
% 40.21/6.19 | $i(v0) | ~ subpopulations(first_movers, efficient_producers,
% 40.21/6.19 | all_11_0, v0) | ~ greater_or_equal(v0, all_21_0) | ? [v1: $i] :
% 40.21/6.19 | ? [v2: $i] : (growth_rate(efficient_producers, v0) = v1 &
% 40.21/6.19 | growth_rate(first_movers, v0) = v2 & $i(v2) & $i(v1) & greater(v1,
% 40.21/6.19 | v2)))
% 40.21/6.19 |
% 40.21/6.19 | ALPHA: (22) implies:
% 40.21/6.19 | (23) in_environment(all_11_0, all_21_0)
% 40.21/6.19 | (24) $i(all_21_0)
% 40.21/6.19 | (25) ! [v0: $i] : ( ~ $i(v0) | ~ subpopulations(first_movers,
% 40.21/6.19 | efficient_producers, all_11_0, v0) | ~ greater_or_equal(v0,
% 40.21/6.19 | all_21_0) | ? [v1: $i] : ? [v2: $i] :
% 40.21/6.19 | (growth_rate(efficient_producers, v0) = v1 &
% 40.21/6.19 | growth_rate(first_movers, v0) = v2 & $i(v2) & $i(v1) & greater(v1,
% 40.21/6.19 | v2)))
% 40.21/6.19 |
% 40.21/6.20 | GROUND_INST: instantiating (13) with all_19_0, simplifying with (17), (20)
% 40.21/6.20 | gives:
% 40.21/6.20 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v0) &
% 40.21/6.20 | subpopulations(first_movers, efficient_producers, all_11_0, v0) &
% 40.21/6.20 | greater_or_equal(v0, all_19_0) & ((growth_rate(efficient_producers,
% 40.21/6.20 | v0) = v1 & $i(v1) & ~ greater(v1, zero)) |
% 40.21/6.20 | (growth_rate(first_movers, v0) = v2 & $i(v2) & ~ greater(zero,
% 40.21/6.20 | v2))))
% 40.21/6.20 |
% 40.21/6.20 | GROUND_INST: instantiating (mp_times_in_environment) with all_11_0, all_19_0,
% 40.21/6.20 | all_21_0, simplifying with (12), (17), (20), (23), (24) gives:
% 40.21/6.20 | (27) all_21_0 = all_19_0 | greater(all_21_0, all_19_0) | greater(all_19_0,
% 40.21/6.20 | all_21_0)
% 40.21/6.20 |
% 40.21/6.20 | GROUND_INST: instantiating (13) with all_21_0, simplifying with (23), (24)
% 40.21/6.20 | gives:
% 40.21/6.20 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v0) &
% 40.21/6.20 | subpopulations(first_movers, efficient_producers, all_11_0, v0) &
% 40.21/6.20 | greater_or_equal(v0, all_21_0) & ((growth_rate(efficient_producers,
% 40.21/6.20 | v0) = v1 & $i(v1) & ~ greater(v1, zero)) |
% 40.21/6.20 | (growth_rate(first_movers, v0) = v2 & $i(v2) & ~ greater(zero,
% 40.21/6.20 | v2))))
% 40.21/6.20 |
% 40.21/6.20 | GROUND_INST: instantiating (2) with all_19_0, all_19_1, simplifying with (18),
% 40.21/6.20 | (19), (20) gives:
% 40.21/6.20 | (29) all_19_0 = all_19_1 | greater(all_19_0, all_19_1)
% 40.21/6.20 |
% 40.21/6.20 | DELTA: instantiating (28) with fresh symbols all_29_0, all_29_1, all_29_2
% 40.21/6.20 | gives:
% 40.21/6.20 | (30) $i(all_29_2) & subpopulations(first_movers, efficient_producers,
% 40.21/6.20 | all_11_0, all_29_2) & greater_or_equal(all_29_2, all_21_0) &
% 40.21/6.20 | ((growth_rate(efficient_producers, all_29_2) = all_29_1 & $i(all_29_1)
% 40.21/6.20 | & ~ greater(all_29_1, zero)) | (growth_rate(first_movers,
% 40.21/6.20 | all_29_2) = all_29_0 & $i(all_29_0) & ~ greater(zero,
% 40.21/6.20 | all_29_0)))
% 40.21/6.20 |
% 40.21/6.20 | ALPHA: (30) implies:
% 40.21/6.20 | (31) greater_or_equal(all_29_2, all_21_0)
% 40.21/6.20 | (32) subpopulations(first_movers, efficient_producers, all_11_0, all_29_2)
% 40.21/6.20 | (33) $i(all_29_2)
% 40.21/6.20 | (34) (growth_rate(efficient_producers, all_29_2) = all_29_1 & $i(all_29_1)
% 40.21/6.20 | & ~ greater(all_29_1, zero)) | (growth_rate(first_movers, all_29_2)
% 40.21/6.20 | = all_29_0 & $i(all_29_0) & ~ greater(zero, all_29_0))
% 40.21/6.20 |
% 40.21/6.20 | DELTA: instantiating (26) with fresh symbols all_31_0, all_31_1, all_31_2
% 40.21/6.20 | gives:
% 40.21/6.20 | (35) $i(all_31_2) & subpopulations(first_movers, efficient_producers,
% 40.21/6.20 | all_11_0, all_31_2) & greater_or_equal(all_31_2, all_19_0) &
% 40.21/6.20 | ((growth_rate(efficient_producers, all_31_2) = all_31_1 & $i(all_31_1)
% 40.21/6.20 | & ~ greater(all_31_1, zero)) | (growth_rate(first_movers,
% 40.21/6.20 | all_31_2) = all_31_0 & $i(all_31_0) & ~ greater(zero,
% 40.21/6.20 | all_31_0)))
% 40.21/6.20 |
% 40.21/6.20 | ALPHA: (35) implies:
% 40.21/6.20 | (36) greater_or_equal(all_31_2, all_19_0)
% 40.21/6.20 | (37) subpopulations(first_movers, efficient_producers, all_11_0, all_31_2)
% 40.21/6.20 | (38) $i(all_31_2)
% 40.21/6.20 | (39) (growth_rate(efficient_producers, all_31_2) = all_31_1 & $i(all_31_1)
% 40.21/6.20 | & ~ greater(all_31_1, zero)) | (growth_rate(first_movers, all_31_2)
% 40.21/6.20 | = all_31_0 & $i(all_31_0) & ~ greater(zero, all_31_0))
% 40.21/6.20 |
% 40.21/6.20 | GROUND_INST: instantiating (2) with all_29_2, all_21_0, simplifying with (24),
% 40.21/6.20 | (31), (33) gives:
% 40.21/6.21 | (40) all_29_2 = all_21_0 | greater(all_29_2, all_21_0)
% 40.21/6.21 |
% 40.21/6.21 | GROUND_INST: instantiating (2) with all_31_2, all_19_0, simplifying with (20),
% 40.21/6.21 | (36), (38) gives:
% 40.21/6.21 | (41) all_31_2 = all_19_0 | greater(all_31_2, all_19_0)
% 40.21/6.21 |
% 40.21/6.21 | GROUND_INST: instantiating (3) with all_11_0, all_29_2, simplifying with (10),
% 40.21/6.21 | (12), (32), (33) gives:
% 40.21/6.21 | (42) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ((v2 = zero & v1 = zero &
% 40.21/6.21 | growth_rate(efficient_producers, all_29_2) = zero &
% 40.21/6.21 | growth_rate(first_movers, all_29_2) = zero) |
% 40.21/6.21 | (equilibrium(all_11_0) = v0 & $i(v0) & ~ greater_or_equal(all_29_2,
% 40.21/6.21 | v0)) | (growth_rate(efficient_producers, all_29_2) = v2 &
% 40.21/6.21 | growth_rate(first_movers, all_29_2) = v1 & $i(v2) & $i(v1) &
% 40.21/6.21 | greater(v2, zero) & greater(zero, v1)) |
% 40.21/6.21 | (growth_rate(efficient_producers, all_29_2) = v2 &
% 40.21/6.21 | growth_rate(first_movers, all_29_2) = v1 & $i(v2) & $i(v1) &
% 40.21/6.21 | greater(v1, zero) & greater(zero, v2)))
% 40.21/6.21 |
% 40.21/6.21 | GROUND_INST: instantiating (25) with all_29_2, simplifying with (31), (32),
% 40.21/6.21 | (33) gives:
% 40.21/6.21 | (43) ? [v0: $i] : ? [v1: $i] : (growth_rate(efficient_producers,
% 40.21/6.21 | all_29_2) = v0 & growth_rate(first_movers, all_29_2) = v1 & $i(v1)
% 40.21/6.21 | & $i(v0) & greater(v0, v1))
% 40.21/6.21 |
% 40.21/6.21 | GROUND_INST: instantiating (3) with all_11_0, all_31_2, simplifying with (10),
% 40.21/6.21 | (12), (37), (38) gives:
% 40.21/6.21 | (44) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ((v2 = zero & v1 = zero &
% 40.21/6.21 | growth_rate(efficient_producers, all_31_2) = zero &
% 40.21/6.21 | growth_rate(first_movers, all_31_2) = zero) |
% 40.21/6.21 | (equilibrium(all_11_0) = v0 & $i(v0) & ~ greater_or_equal(all_31_2,
% 40.21/6.21 | v0)) | (growth_rate(efficient_producers, all_31_2) = v2 &
% 40.21/6.21 | growth_rate(first_movers, all_31_2) = v1 & $i(v2) & $i(v1) &
% 40.21/6.21 | greater(v2, zero) & greater(zero, v1)) |
% 40.21/6.21 | (growth_rate(efficient_producers, all_31_2) = v2 &
% 40.21/6.21 | growth_rate(first_movers, all_31_2) = v1 & $i(v2) & $i(v1) &
% 40.21/6.21 | greater(v1, zero) & greater(zero, v2)))
% 40.21/6.21 |
% 40.21/6.21 | GROUND_INST: instantiating (25) with all_31_2, simplifying with (37), (38)
% 40.21/6.21 | gives:
% 40.21/6.21 | (45) ~ greater_or_equal(all_31_2, all_21_0) | ? [v0: $i] : ? [v1: $i] :
% 40.21/6.21 | (growth_rate(efficient_producers, all_31_2) = v0 &
% 40.21/6.21 | growth_rate(first_movers, all_31_2) = v1 & $i(v1) & $i(v0) &
% 40.21/6.21 | greater(v0, v1))
% 40.21/6.21 |
% 40.21/6.21 | DELTA: instantiating (43) with fresh symbols all_38_0, all_38_1 gives:
% 40.21/6.21 | (46) growth_rate(efficient_producers, all_29_2) = all_38_1 &
% 40.21/6.21 | growth_rate(first_movers, all_29_2) = all_38_0 & $i(all_38_0) &
% 40.21/6.21 | $i(all_38_1) & greater(all_38_1, all_38_0)
% 40.21/6.21 |
% 40.21/6.21 | ALPHA: (46) implies:
% 40.21/6.21 | (47) greater(all_38_1, all_38_0)
% 40.21/6.21 | (48) growth_rate(first_movers, all_29_2) = all_38_0
% 40.21/6.21 | (49) growth_rate(efficient_producers, all_29_2) = all_38_1
% 40.21/6.21 |
% 40.21/6.21 | DELTA: instantiating (44) with fresh symbols all_40_0, all_40_1, all_40_2
% 40.21/6.21 | gives:
% 40.21/6.21 | (50) (all_40_0 = zero & all_40_1 = zero & growth_rate(efficient_producers,
% 40.21/6.21 | all_31_2) = zero & growth_rate(first_movers, all_31_2) = zero) |
% 40.21/6.21 | (equilibrium(all_11_0) = all_40_2 & $i(all_40_2) & ~
% 40.21/6.21 | greater_or_equal(all_31_2, all_40_2)) |
% 40.21/6.21 | (growth_rate(efficient_producers, all_31_2) = all_40_0 &
% 40.21/6.21 | growth_rate(first_movers, all_31_2) = all_40_1 & $i(all_40_0) &
% 40.21/6.21 | $i(all_40_1) & greater(all_40_0, zero) & greater(zero, all_40_1)) |
% 40.21/6.21 | (growth_rate(efficient_producers, all_31_2) = all_40_0 &
% 40.21/6.22 | growth_rate(first_movers, all_31_2) = all_40_1 & $i(all_40_0) &
% 40.21/6.22 | $i(all_40_1) & greater(all_40_1, zero) & greater(zero, all_40_0))
% 40.21/6.22 |
% 40.21/6.22 | DELTA: instantiating (42) with fresh symbols all_41_0, all_41_1, all_41_2
% 40.21/6.22 | gives:
% 40.21/6.22 | (51) (all_41_0 = zero & all_41_1 = zero & growth_rate(efficient_producers,
% 40.21/6.22 | all_29_2) = zero & growth_rate(first_movers, all_29_2) = zero) |
% 40.21/6.22 | (equilibrium(all_11_0) = all_41_2 & $i(all_41_2) & ~
% 40.21/6.22 | greater_or_equal(all_29_2, all_41_2)) |
% 40.21/6.22 | (growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.21/6.22 | growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0) &
% 40.21/6.22 | $i(all_41_1) & greater(all_41_0, zero) & greater(zero, all_41_1)) |
% 40.21/6.22 | (growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.21/6.22 | growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0) &
% 40.21/6.22 | $i(all_41_1) & greater(all_41_1, zero) & greater(zero, all_41_0))
% 40.21/6.22 |
% 40.21/6.22 | GROUND_INST: instantiating (8) with all_38_0, all_38_1, all_29_2,
% 40.21/6.22 | first_movers, simplifying with (48) gives:
% 40.21/6.22 | (52) all_38_0 = all_38_1 | ~ (growth_rate(first_movers, all_29_2) =
% 40.21/6.22 | all_38_1)
% 40.21/6.22 |
% 40.21/6.22 | BETA: splitting (34) gives:
% 40.21/6.22 |
% 40.21/6.22 | Case 1:
% 40.21/6.22 | |
% 40.21/6.22 | | (53) growth_rate(efficient_producers, all_29_2) = all_29_1 & $i(all_29_1)
% 40.21/6.22 | | & ~ greater(all_29_1, zero)
% 40.21/6.22 | |
% 40.21/6.22 | | ALPHA: (53) implies:
% 40.21/6.22 | | (54) ~ greater(all_29_1, zero)
% 40.21/6.22 | | (55) growth_rate(efficient_producers, all_29_2) = all_29_1
% 40.21/6.22 | |
% 40.21/6.22 | | GROUND_INST: instantiating (8) with all_38_1, all_29_1, all_29_2,
% 40.21/6.22 | | efficient_producers, simplifying with (49), (55) gives:
% 40.21/6.22 | | (56) all_38_1 = all_29_1
% 40.21/6.22 | |
% 40.21/6.22 | | REDUCE: (47), (56) imply:
% 40.21/6.22 | | (57) greater(all_29_1, all_38_0)
% 40.21/6.22 | |
% 40.21/6.22 | | PRED_UNIFY: (54), (57) imply:
% 40.21/6.22 | | (58) ~ (all_38_0 = zero)
% 40.21/6.22 | |
% 40.21/6.22 | | BETA: splitting (29) gives:
% 40.21/6.22 | |
% 40.21/6.22 | | Case 1:
% 40.21/6.22 | | |
% 40.21/6.22 | | | (59) greater(all_19_0, all_19_1)
% 40.21/6.22 | | |
% 40.21/6.22 | | | BETA: splitting (27) gives:
% 40.21/6.22 | | |
% 40.21/6.22 | | | Case 1:
% 40.21/6.22 | | | |
% 40.21/6.22 | | | | (60) greater(all_21_0, all_19_0)
% 40.21/6.22 | | | |
% 40.21/6.22 | | | | GROUND_INST: instantiating (mp_greater_transitivity) with all_21_0,
% 40.21/6.22 | | | | all_19_0, all_19_1, simplifying with (19), (20), (24),
% 40.21/6.22 | | | | (59), (60) gives:
% 40.21/6.22 | | | | (61) greater(all_21_0, all_19_1)
% 40.21/6.22 | | | |
% 40.21/6.22 | | | | REF_CLOSE: (1), (5), (7), (8), (19), (21), (24), (33), (40), (48), (51),
% 40.21/6.22 | | | | (52), (54), (55), (56), (57), (58), (61),
% 40.21/6.22 | | | | (mp_greater_transitivity) are inconsistent by sub-proof #15.
% 40.21/6.22 | | | |
% 40.21/6.22 | | | Case 2:
% 40.21/6.22 | | | |
% 40.21/6.22 | | | | (62) ~ greater(all_21_0, all_19_0)
% 40.21/6.22 | | | | (63) all_21_0 = all_19_0 | greater(all_19_0, all_21_0)
% 40.21/6.22 | | | |
% 40.21/6.22 | | | | BETA: splitting (39) gives:
% 40.21/6.22 | | | |
% 40.21/6.22 | | | | Case 1:
% 40.21/6.22 | | | | |
% 40.21/6.22 | | | | | (64) growth_rate(efficient_producers, all_31_2) = all_31_1 &
% 40.21/6.22 | | | | | $i(all_31_1) & ~ greater(all_31_1, zero)
% 40.21/6.22 | | | | |
% 40.21/6.22 | | | | | ALPHA: (64) implies:
% 40.21/6.22 | | | | | (65) ~ greater(all_31_1, zero)
% 40.21/6.22 | | | | | (66) growth_rate(efficient_producers, all_31_2) = all_31_1
% 40.21/6.22 | | | | |
% 40.21/6.22 | | | | | BETA: splitting (45) gives:
% 40.21/6.22 | | | | |
% 40.21/6.22 | | | | | Case 1:
% 40.21/6.22 | | | | | |
% 40.21/6.22 | | | | | | (67) ~ greater_or_equal(all_31_2, all_21_0)
% 40.21/6.22 | | | | | |
% 40.21/6.22 | | | | | | PRED_UNIFY: (36), (67) imply:
% 40.21/6.22 | | | | | | (68) ~ (all_21_0 = all_19_0)
% 40.21/6.22 | | | | | |
% 40.21/6.22 | | | | | | REF_CLOSE: (1), (20), (24), (38), (41), (63), (67), (68),
% 40.21/6.22 | | | | | | (mp_greater_transitivity) are inconsistent by sub-proof
% 40.21/6.22 | | | | | | #14.
% 40.21/6.22 | | | | | |
% 40.21/6.22 | | | | | Case 2:
% 40.21/6.22 | | | | | |
% 40.21/6.22 | | | | | | (69) greater_or_equal(all_31_2, all_21_0)
% 40.21/6.23 | | | | | | (70) ? [v0: $i] : ? [v1: $i] :
% 40.21/6.23 | | | | | | (growth_rate(efficient_producers, all_31_2) = v0 &
% 40.21/6.23 | | | | | | growth_rate(first_movers, all_31_2) = v1 & $i(v1) & $i(v0)
% 40.21/6.23 | | | | | | & greater(v0, v1))
% 40.21/6.23 | | | | | |
% 40.21/6.23 | | | | | | DELTA: instantiating (70) with fresh symbols all_106_0, all_106_1
% 40.21/6.23 | | | | | | gives:
% 40.21/6.23 | | | | | | (71) growth_rate(efficient_producers, all_31_2) = all_106_1 &
% 40.21/6.23 | | | | | | growth_rate(first_movers, all_31_2) = all_106_0 &
% 40.21/6.23 | | | | | | $i(all_106_0) & $i(all_106_1) & greater(all_106_1,
% 40.21/6.23 | | | | | | all_106_0)
% 40.21/6.23 | | | | | |
% 40.21/6.23 | | | | | | ALPHA: (71) implies:
% 40.21/6.23 | | | | | | (72) greater(all_106_1, all_106_0)
% 40.21/6.23 | | | | | | (73) $i(all_106_0)
% 40.21/6.23 | | | | | | (74) growth_rate(first_movers, all_31_2) = all_106_0
% 40.21/6.23 | | | | | | (75) growth_rate(efficient_producers, all_31_2) = all_106_1
% 40.21/6.23 | | | | | |
% 40.21/6.23 | | | | | | GROUND_INST: instantiating (8) with all_31_1, all_106_1, all_31_2,
% 40.21/6.23 | | | | | | efficient_producers, simplifying with (66), (75) gives:
% 40.21/6.23 | | | | | | (76) all_106_1 = all_31_1
% 40.21/6.23 | | | | | |
% 40.21/6.23 | | | | | | REDUCE: (72), (76) imply:
% 40.21/6.23 | | | | | | (77) greater(all_31_1, all_106_0)
% 40.21/6.23 | | | | | |
% 40.21/6.23 | | | | | | PRED_UNIFY: (65), (77) imply:
% 40.21/6.23 | | | | | | (78) ~ (all_106_0 = zero)
% 40.21/6.23 | | | | | |
% 40.21/6.23 | | | | | | GROUND_INST: instantiating (2) with all_31_2, all_21_0, simplifying
% 40.21/6.23 | | | | | | with (24), (38), (69) gives:
% 40.21/6.23 | | | | | | (79) all_31_2 = all_21_0 | greater(all_31_2, all_21_0)
% 40.21/6.23 | | | | | |
% 40.21/6.23 | | | | | | BETA: splitting (41) gives:
% 40.21/6.23 | | | | | |
% 40.21/6.23 | | | | | | Case 1:
% 40.21/6.23 | | | | | | |
% 40.21/6.23 | | | | | | | (80) greater(all_31_2, all_19_0)
% 40.21/6.23 | | | | | | |
% 40.21/6.23 | | | | | | | PRED_UNIFY: (62), (80) imply:
% 40.21/6.23 | | | | | | | (81) ~ (all_31_2 = all_21_0)
% 40.21/6.23 | | | | | | |
% 40.21/6.23 | | | | | | | BETA: splitting (79) gives:
% 40.21/6.23 | | | | | | |
% 40.21/6.23 | | | | | | | Case 1:
% 40.21/6.23 | | | | | | | |
% 40.21/6.23 | | | | | | | |
% 40.21/6.23 | | | | | | | | GROUND_INST: instantiating (mp_greater_transitivity) with
% 40.21/6.23 | | | | | | | | all_31_2, all_19_0, all_19_1, simplifying with
% 40.21/6.23 | | | | | | | | (19), (20), (38), (59), (80) gives:
% 40.21/6.23 | | | | | | | | (82) greater(all_31_2, all_19_1)
% 40.21/6.23 | | | | | | | |
% 40.21/6.23 | | | | | | | | BETA: splitting (52) gives:
% 40.21/6.23 | | | | | | | |
% 40.21/6.23 | | | | | | | | Case 1:
% 40.21/6.23 | | | | | | | | |
% 40.21/6.23 | | | | | | | | |
% 40.21/6.23 | | | | | | | | | GROUND_INST: instantiating (1) with all_31_2, all_19_1,
% 40.21/6.23 | | | | | | | | | simplifying with (19), (38), (82) gives:
% 40.21/6.23 | | | | | | | | | (83) greater_or_equal(all_31_2, all_19_1)
% 40.21/6.23 | | | | | | | | |
% 40.21/6.23 | | | | | | | | | DELTA: instantiating (70) with fresh symbols all_106_0,
% 40.21/6.23 | | | | | | | | | all_106_1 gives:
% 40.21/6.23 | | | | | | | | | (84) growth_rate(efficient_producers, all_31_2) = all_106_1
% 40.21/6.23 | | | | | | | | | & growth_rate(first_movers, all_31_2) = all_106_0 &
% 40.21/6.23 | | | | | | | | | $i(all_106_0) & $i(all_106_1) & greater(all_106_1,
% 40.21/6.23 | | | | | | | | | all_106_0)
% 40.21/6.23 | | | | | | | | |
% 40.21/6.23 | | | | | | | | | REF_CLOSE: (5), (7), (8), (21), (50), (65), (66), (83), (84),
% 40.21/6.23 | | | | | | | | | (mp_greater_transitivity) are inconsistent by
% 40.21/6.23 | | | | | | | | | sub-proof #11.
% 40.21/6.23 | | | | | | | | |
% 40.21/6.23 | | | | | | | | Case 2:
% 40.21/6.23 | | | | | | | | |
% 40.21/6.23 | | | | | | | | | (85) all_38_0 = all_38_1
% 40.21/6.23 | | | | | | | | |
% 40.21/6.23 | | | | | | | | | COMBINE_EQS: (56), (85) imply:
% 40.21/6.23 | | | | | | | | | (86) all_38_0 = all_29_1
% 40.21/6.23 | | | | | | | | |
% 40.21/6.23 | | | | | | | | | REDUCE: (58), (86) imply:
% 40.21/6.23 | | | | | | | | | (87) ~ (all_29_1 = zero)
% 40.21/6.23 | | | | | | | | |
% 40.21/6.23 | | | | | | | | | BETA: splitting (51) gives:
% 40.21/6.23 | | | | | | | | |
% 40.21/6.23 | | | | | | | | | Case 1:
% 40.21/6.23 | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | (88) (all_41_0 = zero & all_41_1 = zero &
% 40.21/6.23 | | | | | | | | | | growth_rate(efficient_producers, all_29_2) = zero
% 40.21/6.23 | | | | | | | | | | & growth_rate(first_movers, all_29_2) = zero) |
% 40.21/6.23 | | | | | | | | | | (equilibrium(all_11_0) = all_41_2 & $i(all_41_2) &
% 40.21/6.23 | | | | | | | | | | ~ greater_or_equal(all_29_2, all_41_2))
% 40.21/6.23 | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | BETA: splitting (88) gives:
% 40.21/6.23 | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | Case 1:
% 40.21/6.23 | | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | | (89) all_41_0 = zero & all_41_1 = zero &
% 40.21/6.23 | | | | | | | | | | | growth_rate(efficient_producers, all_29_2) = zero
% 40.21/6.23 | | | | | | | | | | | & growth_rate(first_movers, all_29_2) = zero
% 40.21/6.23 | | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | | ALPHA: (89) implies:
% 40.21/6.23 | | | | | | | | | | | (90) growth_rate(efficient_producers, all_29_2) = zero
% 40.21/6.23 | | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | | REF_CLOSE: (8), (55), (87), (90) are inconsistent by
% 40.21/6.23 | | | | | | | | | | | sub-proof #10.
% 40.21/6.23 | | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | Case 2:
% 40.21/6.23 | | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | | (91) equilibrium(all_11_0) = all_41_2 & $i(all_41_2) &
% 40.21/6.23 | | | | | | | | | | | ~ greater_or_equal(all_29_2, all_41_2)
% 40.21/6.23 | | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | | ALPHA: (91) implies:
% 40.21/6.23 | | | | | | | | | | | (92) $i(all_41_2)
% 40.21/6.23 | | | | | | | | | | | (93) equilibrium(all_11_0) = all_41_2
% 40.21/6.23 | | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_19_1, all_41_2,
% 40.21/6.23 | | | | | | | | | | | all_11_0, simplifying with (21), (93) gives:
% 40.21/6.23 | | | | | | | | | | | (94) all_41_2 = all_19_1
% 40.21/6.23 | | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_31_2, all_19_1,
% 40.21/6.23 | | | | | | | | | | | simplifying with (19), (38), (82) gives:
% 40.21/6.23 | | | | | | | | | | | (95) greater_or_equal(all_31_2, all_19_1)
% 40.21/6.23 | | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | | DELTA: instantiating (70) with fresh symbols all_106_0,
% 40.21/6.23 | | | | | | | | | | | all_106_1 gives:
% 40.21/6.23 | | | | | | | | | | | (96) growth_rate(efficient_producers, all_31_2) =
% 40.21/6.23 | | | | | | | | | | | all_106_1 & growth_rate(first_movers, all_31_2) =
% 40.21/6.23 | | | | | | | | | | | all_106_0 & $i(all_106_0) & $i(all_106_1) &
% 40.21/6.23 | | | | | | | | | | | greater(all_106_1, all_106_0)
% 40.21/6.23 | | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (21), (50), (65), (66), (95), (96),
% 40.21/6.23 | | | | | | | | | | | (mp_greater_transitivity) are inconsistent by
% 40.21/6.23 | | | | | | | | | | | sub-proof #11.
% 40.21/6.23 | | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | End of split
% 40.21/6.23 | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | Case 2:
% 40.21/6.23 | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | (97) (growth_rate(efficient_producers, all_29_2) =
% 40.21/6.23 | | | | | | | | | | all_41_0 & growth_rate(first_movers, all_29_2) =
% 40.21/6.23 | | | | | | | | | | all_41_1 & $i(all_41_0) & $i(all_41_1) &
% 40.21/6.23 | | | | | | | | | | greater(all_41_0, zero) & greater(zero, all_41_1))
% 40.21/6.23 | | | | | | | | | | | (growth_rate(efficient_producers, all_29_2) =
% 40.21/6.23 | | | | | | | | | | all_41_0 & growth_rate(first_movers, all_29_2) =
% 40.21/6.23 | | | | | | | | | | all_41_1 & $i(all_41_0) & $i(all_41_1) &
% 40.21/6.23 | | | | | | | | | | greater(all_41_1, zero) & greater(zero, all_41_0))
% 40.21/6.23 | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | BETA: splitting (97) gives:
% 40.21/6.23 | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | Case 1:
% 40.21/6.23 | | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | | (98) growth_rate(efficient_producers, all_29_2) =
% 40.21/6.23 | | | | | | | | | | | all_41_0 & growth_rate(first_movers, all_29_2) =
% 40.21/6.23 | | | | | | | | | | | all_41_1 & $i(all_41_0) & $i(all_41_1) &
% 40.21/6.23 | | | | | | | | | | | greater(all_41_0, zero) & greater(zero, all_41_1)
% 40.21/6.23 | | | | | | | | | | |
% 40.21/6.23 | | | | | | | | | | | ALPHA: (98) implies:
% 40.21/6.24 | | | | | | | | | | | (99) greater(all_41_0, zero)
% 40.21/6.24 | | | | | | | | | | | (100) growth_rate(efficient_producers, all_29_2) =
% 40.21/6.24 | | | | | | | | | | | all_41_0
% 40.21/6.24 | | | | | | | | | | |
% 40.21/6.24 | | | | | | | | | | | REF_CLOSE: (8), (54), (55), (99), (100) are inconsistent by
% 40.21/6.24 | | | | | | | | | | | sub-proof #19.
% 40.21/6.24 | | | | | | | | | | |
% 40.21/6.24 | | | | | | | | | | Case 2:
% 40.21/6.24 | | | | | | | | | | |
% 40.21/6.24 | | | | | | | | | | | (101) growth_rate(efficient_producers, all_29_2) =
% 40.21/6.24 | | | | | | | | | | | all_41_0 & growth_rate(first_movers, all_29_2) =
% 40.21/6.24 | | | | | | | | | | | all_41_1 & $i(all_41_0) & $i(all_41_1) &
% 40.21/6.24 | | | | | | | | | | | greater(all_41_1, zero) & greater(zero, all_41_0)
% 40.21/6.24 | | | | | | | | | | |
% 40.21/6.24 | | | | | | | | | | | ALPHA: (101) implies:
% 40.21/6.24 | | | | | | | | | | | (102) greater(all_41_1, zero)
% 40.21/6.24 | | | | | | | | | | | (103) $i(all_41_1)
% 40.21/6.24 | | | | | | | | | | | (104) $i(all_41_0)
% 40.21/6.24 | | | | | | | | | | | (105) growth_rate(first_movers, all_29_2) = all_41_1
% 40.21/6.24 | | | | | | | | | | | (106) growth_rate(efficient_producers, all_29_2) =
% 40.21/6.24 | | | | | | | | | | | all_41_0
% 40.21/6.24 | | | | | | | | | | |
% 40.21/6.24 | | | | | | | | | | | REF_CLOSE: (5), (8), (48), (54), (55), (57), (102), (103),
% 40.21/6.24 | | | | | | | | | | | (104), (105), (106), (mp_greater_transitivity) are
% 40.21/6.24 | | | | | | | | | | | inconsistent by sub-proof #18.
% 40.21/6.24 | | | | | | | | | | |
% 40.21/6.24 | | | | | | | | | | End of split
% 40.21/6.24 | | | | | | | | | |
% 40.21/6.24 | | | | | | | | | End of split
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | End of split
% 40.21/6.24 | | | | | | | |
% 40.21/6.24 | | | | | | | Case 2:
% 40.21/6.24 | | | | | | | |
% 40.21/6.24 | | | | | | | | (107) all_31_2 = all_21_0
% 40.21/6.24 | | | | | | | |
% 40.21/6.24 | | | | | | | | REDUCE: (81), (107) imply:
% 40.21/6.24 | | | | | | | | (108) $false
% 40.21/6.24 | | | | | | | |
% 40.21/6.24 | | | | | | | | CLOSE: (108) is inconsistent.
% 40.21/6.24 | | | | | | | |
% 40.21/6.24 | | | | | | | End of split
% 40.21/6.24 | | | | | | |
% 40.21/6.24 | | | | | | Case 2:
% 40.21/6.24 | | | | | | |
% 40.21/6.24 | | | | | | | (109) all_31_2 = all_19_0
% 40.21/6.24 | | | | | | |
% 40.21/6.24 | | | | | | | REDUCE: (66), (109) imply:
% 40.21/6.24 | | | | | | | (110) growth_rate(efficient_producers, all_19_0) = all_31_1
% 40.21/6.24 | | | | | | |
% 40.21/6.24 | | | | | | | REDUCE: (74), (109) imply:
% 40.21/6.24 | | | | | | | (111) growth_rate(first_movers, all_19_0) = all_106_0
% 40.21/6.24 | | | | | | |
% 40.21/6.24 | | | | | | | BETA: splitting (50) gives:
% 40.21/6.24 | | | | | | |
% 40.21/6.24 | | | | | | | Case 1:
% 40.21/6.24 | | | | | | | |
% 40.21/6.24 | | | | | | | | (112) (all_40_0 = zero & all_40_1 = zero &
% 40.21/6.24 | | | | | | | | growth_rate(efficient_producers, all_31_2) = zero &
% 40.21/6.24 | | | | | | | | growth_rate(first_movers, all_31_2) = zero) |
% 40.21/6.24 | | | | | | | | (equilibrium(all_11_0) = all_40_2 & $i(all_40_2) & ~
% 40.21/6.24 | | | | | | | | greater_or_equal(all_31_2, all_40_2))
% 40.21/6.24 | | | | | | | |
% 40.21/6.24 | | | | | | | | BETA: splitting (112) gives:
% 40.21/6.24 | | | | | | | |
% 40.21/6.24 | | | | | | | | Case 1:
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | (113) all_40_0 = zero & all_40_1 = zero &
% 40.21/6.24 | | | | | | | | | growth_rate(efficient_producers, all_31_2) = zero &
% 40.21/6.24 | | | | | | | | | growth_rate(first_movers, all_31_2) = zero
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | ALPHA: (113) implies:
% 40.21/6.24 | | | | | | | | | (114) growth_rate(first_movers, all_31_2) = zero
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | REDUCE: (109), (114) imply:
% 40.21/6.24 | | | | | | | | | (115) growth_rate(first_movers, all_19_0) = zero
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | GROUND_INST: instantiating (8) with zero, all_106_0, all_19_0,
% 40.21/6.24 | | | | | | | | | first_movers, simplifying with (111), (115) gives:
% 40.21/6.24 | | | | | | | | | (116) all_106_0 = zero
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | REDUCE: (78), (116) imply:
% 40.21/6.24 | | | | | | | | | (117) $false
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | CLOSE: (117) is inconsistent.
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | Case 2:
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | (118) equilibrium(all_11_0) = all_40_2 & $i(all_40_2) & ~
% 40.21/6.24 | | | | | | | | | greater_or_equal(all_31_2, all_40_2)
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | ALPHA: (118) implies:
% 40.21/6.24 | | | | | | | | | (119) ~ greater_or_equal(all_31_2, all_40_2)
% 40.21/6.24 | | | | | | | | | (120) equilibrium(all_11_0) = all_40_2
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | REDUCE: (109), (119) imply:
% 40.21/6.24 | | | | | | | | | (121) ~ greater_or_equal(all_19_0, all_40_2)
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | REF_CLOSE: (7), (18), (21), (120), (121) are inconsistent by
% 40.21/6.24 | | | | | | | | | sub-proof #9.
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | End of split
% 40.21/6.24 | | | | | | | |
% 40.21/6.24 | | | | | | | Case 2:
% 40.21/6.24 | | | | | | | |
% 40.21/6.24 | | | | | | | | (122) (growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.21/6.24 | | | | | | | | & growth_rate(first_movers, all_31_2) = all_40_1 &
% 40.21/6.24 | | | | | | | | $i(all_40_0) & $i(all_40_1) & greater(all_40_0, zero)
% 40.21/6.24 | | | | | | | | & greater(zero, all_40_1)) |
% 40.21/6.24 | | | | | | | | (growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.21/6.24 | | | | | | | | & growth_rate(first_movers, all_31_2) = all_40_1 &
% 40.21/6.24 | | | | | | | | $i(all_40_0) & $i(all_40_1) & greater(all_40_1, zero)
% 40.21/6.24 | | | | | | | | & greater(zero, all_40_0))
% 40.21/6.24 | | | | | | | |
% 40.21/6.24 | | | | | | | | BETA: splitting (122) gives:
% 40.21/6.24 | | | | | | | |
% 40.21/6.24 | | | | | | | | Case 1:
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | (123) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.21/6.24 | | | | | | | | | & growth_rate(first_movers, all_31_2) = all_40_1 &
% 40.21/6.24 | | | | | | | | | $i(all_40_0) & $i(all_40_1) & greater(all_40_0, zero)
% 40.21/6.24 | | | | | | | | | & greater(zero, all_40_1)
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | ALPHA: (123) implies:
% 40.21/6.24 | | | | | | | | | (124) greater(all_40_0, zero)
% 40.21/6.24 | | | | | | | | | (125) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | REF_CLOSE: (8), (65), (66), (124), (125) are inconsistent by
% 40.21/6.24 | | | | | | | | | sub-proof #12.
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | Case 2:
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | (126) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.21/6.24 | | | | | | | | | & growth_rate(first_movers, all_31_2) = all_40_1 &
% 40.21/6.24 | | | | | | | | | $i(all_40_0) & $i(all_40_1) & greater(all_40_1, zero)
% 40.21/6.24 | | | | | | | | | & greater(zero, all_40_0)
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | ALPHA: (126) implies:
% 40.21/6.24 | | | | | | | | | (127) greater(all_40_1, zero)
% 40.21/6.24 | | | | | | | | | (128) $i(all_40_0)
% 40.21/6.24 | | | | | | | | | (129) growth_rate(first_movers, all_31_2) = all_40_1
% 40.21/6.24 | | | | | | | | | (130) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | REDUCE: (109), (130) imply:
% 40.21/6.24 | | | | | | | | | (131) growth_rate(efficient_producers, all_19_0) = all_40_0
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | REDUCE: (109), (129) imply:
% 40.21/6.24 | | | | | | | | | (132) growth_rate(first_movers, all_19_0) = all_40_1
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | GROUND_INST: instantiating (8) with all_40_1, all_106_0,
% 40.21/6.24 | | | | | | | | | all_19_0, first_movers, simplifying with (111),
% 40.21/6.24 | | | | | | | | | (132) gives:
% 40.21/6.24 | | | | | | | | | (133) all_106_0 = all_40_1
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | GROUND_INST: instantiating (8) with all_31_1, all_40_0,
% 40.21/6.24 | | | | | | | | | all_19_0, efficient_producers, simplifying with
% 40.21/6.24 | | | | | | | | | (110), (131) gives:
% 40.21/6.24 | | | | | | | | | (134) all_40_0 = all_31_1
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | REDUCE: (73), (133) imply:
% 40.21/6.24 | | | | | | | | | (135) $i(all_40_1)
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | REDUCE: (128), (134) imply:
% 40.21/6.24 | | | | | | | | | (136) $i(all_31_1)
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | REDUCE: (77), (133) imply:
% 40.21/6.24 | | | | | | | | | (137) greater(all_31_1, all_40_1)
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | GROUND_INST: instantiating (mp_greater_transitivity) with
% 40.21/6.24 | | | | | | | | | all_31_1, all_40_1, zero, simplifying with (5),
% 40.21/6.24 | | | | | | | | | (65), (127), (135), (136), (137) gives:
% 40.21/6.24 | | | | | | | | | (138) $false
% 40.21/6.24 | | | | | | | | |
% 40.21/6.24 | | | | | | | | | CLOSE: (138) is inconsistent.
% 40.21/6.24 | | | | | | | | |
% 40.21/6.25 | | | | | | | | End of split
% 40.21/6.25 | | | | | | | |
% 40.21/6.25 | | | | | | | End of split
% 40.21/6.25 | | | | | | |
% 40.21/6.25 | | | | | | End of split
% 40.21/6.25 | | | | | |
% 40.21/6.25 | | | | | End of split
% 40.21/6.25 | | | | |
% 40.21/6.25 | | | | Case 2:
% 40.21/6.25 | | | | |
% 40.21/6.25 | | | | | (139) growth_rate(first_movers, all_31_2) = all_31_0 & $i(all_31_0)
% 40.21/6.25 | | | | | & ~ greater(zero, all_31_0)
% 40.21/6.25 | | | | |
% 40.21/6.25 | | | | | ALPHA: (139) implies:
% 40.21/6.25 | | | | | (140) ~ greater(zero, all_31_0)
% 40.21/6.25 | | | | | (141) growth_rate(first_movers, all_31_2) = all_31_0
% 40.21/6.25 | | | | |
% 40.21/6.25 | | | | | BETA: splitting (45) gives:
% 40.21/6.25 | | | | |
% 40.21/6.25 | | | | | Case 1:
% 40.21/6.25 | | | | | |
% 40.21/6.25 | | | | | | (142) ~ greater_or_equal(all_31_2, all_21_0)
% 40.21/6.25 | | | | | |
% 40.21/6.25 | | | | | | PRED_UNIFY: (36), (142) imply:
% 40.21/6.25 | | | | | | (143) ~ (all_21_0 = all_19_0)
% 40.21/6.25 | | | | | |
% 40.21/6.25 | | | | | | REF_CLOSE: (1), (20), (24), (38), (41), (63), (142), (143),
% 40.21/6.25 | | | | | | (mp_greater_transitivity) are inconsistent by sub-proof
% 40.21/6.25 | | | | | | #14.
% 40.21/6.25 | | | | | |
% 40.21/6.25 | | | | | Case 2:
% 40.21/6.25 | | | | | |
% 40.21/6.25 | | | | | | (144) ? [v0: $i] : ? [v1: $i] :
% 40.21/6.25 | | | | | | (growth_rate(efficient_producers, all_31_2) = v0 &
% 40.21/6.25 | | | | | | growth_rate(first_movers, all_31_2) = v1 & $i(v1) &
% 40.21/6.25 | | | | | | $i(v0) & greater(v0, v1))
% 40.65/6.25 | | | | | |
% 40.65/6.25 | | | | | | DELTA: instantiating (144) with fresh symbols all_106_0, all_106_1
% 40.65/6.25 | | | | | | gives:
% 40.65/6.25 | | | | | | (145) growth_rate(efficient_producers, all_31_2) = all_106_1 &
% 40.65/6.25 | | | | | | growth_rate(first_movers, all_31_2) = all_106_0 &
% 40.65/6.25 | | | | | | $i(all_106_0) & $i(all_106_1) & greater(all_106_1,
% 40.65/6.25 | | | | | | all_106_0)
% 40.65/6.25 | | | | | |
% 40.65/6.25 | | | | | | ALPHA: (145) implies:
% 40.65/6.25 | | | | | | (146) greater(all_106_1, all_106_0)
% 40.65/6.25 | | | | | | (147) $i(all_106_1)
% 40.65/6.25 | | | | | | (148) growth_rate(first_movers, all_31_2) = all_106_0
% 40.65/6.25 | | | | | | (149) growth_rate(efficient_producers, all_31_2) = all_106_1
% 40.65/6.25 | | | | | |
% 40.65/6.25 | | | | | | GROUND_INST: instantiating (8) with all_31_0, all_106_0, all_31_2,
% 40.65/6.25 | | | | | | first_movers, simplifying with (141), (148) gives:
% 40.65/6.25 | | | | | | (150) all_106_0 = all_31_0
% 40.65/6.25 | | | | | |
% 40.65/6.25 | | | | | | REDUCE: (146), (150) imply:
% 40.65/6.25 | | | | | | (151) greater(all_106_1, all_31_0)
% 40.65/6.25 | | | | | |
% 40.65/6.25 | | | | | | PRED_UNIFY: (140), (151) imply:
% 40.65/6.25 | | | | | | (152) ~ (all_106_1 = zero)
% 40.65/6.25 | | | | | |
% 40.65/6.25 | | | | | | BETA: splitting (41) gives:
% 40.65/6.25 | | | | | |
% 40.65/6.25 | | | | | | Case 1:
% 40.65/6.25 | | | | | | |
% 40.65/6.25 | | | | | | | (153) greater(all_31_2, all_19_0)
% 40.65/6.25 | | | | | | |
% 40.65/6.25 | | | | | | | GROUND_INST: instantiating (mp_greater_transitivity) with
% 40.65/6.25 | | | | | | | all_31_2, all_19_0, all_19_1, simplifying with (19),
% 40.65/6.25 | | | | | | | (20), (38), (59), (153) gives:
% 40.65/6.25 | | | | | | | (154) greater(all_31_2, all_19_1)
% 40.65/6.25 | | | | | | |
% 40.65/6.25 | | | | | | | BETA: splitting (52) gives:
% 40.65/6.25 | | | | | | |
% 40.65/6.25 | | | | | | | Case 1:
% 40.65/6.25 | | | | | | | |
% 40.65/6.25 | | | | | | | |
% 40.65/6.25 | | | | | | | | GROUND_INST: instantiating (1) with all_31_2, all_19_1,
% 40.65/6.25 | | | | | | | | simplifying with (19), (38), (154) gives:
% 40.65/6.25 | | | | | | | | (155) greater_or_equal(all_31_2, all_19_1)
% 40.65/6.25 | | | | | | | |
% 40.65/6.25 | | | | | | | | DELTA: instantiating (144) with fresh symbols all_106_0,
% 40.65/6.25 | | | | | | | | all_106_1 gives:
% 40.65/6.25 | | | | | | | | (156) growth_rate(efficient_producers, all_31_2) = all_106_1
% 40.65/6.25 | | | | | | | | & growth_rate(first_movers, all_31_2) = all_106_0 &
% 40.65/6.25 | | | | | | | | $i(all_106_0) & $i(all_106_1) & greater(all_106_1,
% 40.65/6.25 | | | | | | | | all_106_0)
% 40.65/6.25 | | | | | | | |
% 40.65/6.25 | | | | | | | | REF_CLOSE: (5), (7), (8), (21), (50), (140), (141), (155),
% 40.65/6.25 | | | | | | | | (156), (mp_greater_transitivity) are inconsistent by
% 40.65/6.25 | | | | | | | | sub-proof #7.
% 40.65/6.25 | | | | | | | |
% 40.65/6.25 | | | | | | | Case 2:
% 40.65/6.25 | | | | | | | |
% 40.65/6.25 | | | | | | | | (157) all_38_0 = all_38_1
% 40.65/6.25 | | | | | | | |
% 40.65/6.25 | | | | | | | | COMBINE_EQS: (56), (157) imply:
% 40.65/6.25 | | | | | | | | (158) all_38_0 = all_29_1
% 40.65/6.25 | | | | | | | |
% 40.65/6.25 | | | | | | | | REDUCE: (58), (158) imply:
% 40.65/6.25 | | | | | | | | (159) ~ (all_29_1 = zero)
% 40.65/6.25 | | | | | | | |
% 40.65/6.25 | | | | | | | | BETA: splitting (51) gives:
% 40.65/6.25 | | | | | | | |
% 40.65/6.25 | | | | | | | | Case 1:
% 40.65/6.25 | | | | | | | | |
% 40.65/6.25 | | | | | | | | | (160) (all_41_0 = zero & all_41_1 = zero &
% 40.65/6.25 | | | | | | | | | growth_rate(efficient_producers, all_29_2) = zero &
% 40.65/6.25 | | | | | | | | | growth_rate(first_movers, all_29_2) = zero) |
% 40.65/6.25 | | | | | | | | | (equilibrium(all_11_0) = all_41_2 & $i(all_41_2) & ~
% 40.65/6.25 | | | | | | | | | greater_or_equal(all_29_2, all_41_2))
% 40.65/6.25 | | | | | | | | |
% 40.65/6.25 | | | | | | | | | BETA: splitting (160) gives:
% 40.65/6.25 | | | | | | | | |
% 40.65/6.25 | | | | | | | | | Case 1:
% 40.65/6.25 | | | | | | | | | |
% 40.65/6.25 | | | | | | | | | | (161) all_41_0 = zero & all_41_1 = zero &
% 40.65/6.25 | | | | | | | | | | growth_rate(efficient_producers, all_29_2) = zero &
% 40.65/6.25 | | | | | | | | | | growth_rate(first_movers, all_29_2) = zero
% 40.65/6.25 | | | | | | | | | |
% 40.65/6.25 | | | | | | | | | | ALPHA: (161) implies:
% 40.65/6.25 | | | | | | | | | | (162) growth_rate(efficient_producers, all_29_2) = zero
% 40.65/6.25 | | | | | | | | | |
% 40.65/6.25 | | | | | | | | | | REF_CLOSE: (8), (55), (159), (162) are inconsistent by
% 40.65/6.25 | | | | | | | | | | sub-proof #10.
% 40.65/6.25 | | | | | | | | | |
% 40.65/6.25 | | | | | | | | | Case 2:
% 40.65/6.25 | | | | | | | | | |
% 40.65/6.25 | | | | | | | | | | (163) equilibrium(all_11_0) = all_41_2 & $i(all_41_2) &
% 40.65/6.25 | | | | | | | | | | ~ greater_or_equal(all_29_2, all_41_2)
% 40.65/6.25 | | | | | | | | | |
% 40.65/6.25 | | | | | | | | | | ALPHA: (163) implies:
% 40.65/6.25 | | | | | | | | | | (164) $i(all_41_2)
% 40.65/6.25 | | | | | | | | | | (165) equilibrium(all_11_0) = all_41_2
% 40.65/6.25 | | | | | | | | | |
% 40.65/6.25 | | | | | | | | | | GROUND_INST: instantiating (7) with all_19_1, all_41_2,
% 40.65/6.25 | | | | | | | | | | all_11_0, simplifying with (21), (165) gives:
% 40.65/6.25 | | | | | | | | | | (166) all_41_2 = all_19_1
% 40.65/6.25 | | | | | | | | | |
% 40.65/6.25 | | | | | | | | | | GROUND_INST: instantiating (1) with all_31_2, all_19_1,
% 40.65/6.25 | | | | | | | | | | simplifying with (19), (38), (154) gives:
% 40.65/6.25 | | | | | | | | | | (167) greater_or_equal(all_31_2, all_19_1)
% 40.65/6.25 | | | | | | | | | |
% 40.65/6.25 | | | | | | | | | | DELTA: instantiating (144) with fresh symbols all_106_0,
% 40.65/6.25 | | | | | | | | | | all_106_1 gives:
% 40.65/6.25 | | | | | | | | | | (168) growth_rate(efficient_producers, all_31_2) =
% 40.65/6.25 | | | | | | | | | | all_106_1 & growth_rate(first_movers, all_31_2) =
% 40.65/6.25 | | | | | | | | | | all_106_0 & $i(all_106_0) & $i(all_106_1) &
% 40.65/6.25 | | | | | | | | | | greater(all_106_1, all_106_0)
% 40.65/6.25 | | | | | | | | | |
% 40.65/6.25 | | | | | | | | | | REF_CLOSE: (5), (7), (8), (21), (50), (140), (141), (167),
% 40.65/6.25 | | | | | | | | | | (168), (mp_greater_transitivity) are inconsistent
% 40.65/6.25 | | | | | | | | | | by sub-proof #7.
% 40.65/6.25 | | | | | | | | | |
% 40.65/6.25 | | | | | | | | | End of split
% 40.65/6.25 | | | | | | | | |
% 40.65/6.25 | | | | | | | | Case 2:
% 40.65/6.25 | | | | | | | | |
% 40.65/6.25 | | | | | | | | | (169) (growth_rate(efficient_producers, all_29_2) =
% 40.65/6.25 | | | | | | | | | all_41_0 & growth_rate(first_movers, all_29_2) =
% 40.65/6.25 | | | | | | | | | all_41_1 & $i(all_41_0) & $i(all_41_1) &
% 40.65/6.25 | | | | | | | | | greater(all_41_0, zero) & greater(zero, all_41_1))
% 40.65/6.25 | | | | | | | | | | (growth_rate(efficient_producers, all_29_2) =
% 40.65/6.25 | | | | | | | | | all_41_0 & growth_rate(first_movers, all_29_2) =
% 40.65/6.25 | | | | | | | | | all_41_1 & $i(all_41_0) & $i(all_41_1) &
% 40.65/6.25 | | | | | | | | | greater(all_41_1, zero) & greater(zero, all_41_0))
% 40.65/6.25 | | | | | | | | |
% 40.65/6.25 | | | | | | | | | BETA: splitting (169) gives:
% 40.65/6.25 | | | | | | | | |
% 40.65/6.25 | | | | | | | | | Case 1:
% 40.65/6.25 | | | | | | | | | |
% 40.65/6.25 | | | | | | | | | | (170) growth_rate(efficient_producers, all_29_2) =
% 40.65/6.25 | | | | | | | | | | all_41_0 & growth_rate(first_movers, all_29_2) =
% 40.65/6.25 | | | | | | | | | | all_41_1 & $i(all_41_0) & $i(all_41_1) &
% 40.65/6.25 | | | | | | | | | | greater(all_41_0, zero) & greater(zero, all_41_1)
% 40.65/6.25 | | | | | | | | | |
% 40.65/6.25 | | | | | | | | | | ALPHA: (170) implies:
% 40.65/6.25 | | | | | | | | | | (171) greater(all_41_0, zero)
% 40.65/6.25 | | | | | | | | | | (172) growth_rate(efficient_producers, all_29_2) =
% 40.65/6.25 | | | | | | | | | | all_41_0
% 40.65/6.25 | | | | | | | | | |
% 40.65/6.25 | | | | | | | | | | REF_CLOSE: (8), (54), (55), (171), (172) are inconsistent by
% 40.65/6.25 | | | | | | | | | | sub-proof #19.
% 40.65/6.25 | | | | | | | | | |
% 40.65/6.25 | | | | | | | | | Case 2:
% 40.65/6.25 | | | | | | | | | |
% 40.65/6.25 | | | | | | | | | | (173) growth_rate(efficient_producers, all_29_2) =
% 40.65/6.25 | | | | | | | | | | all_41_0 & growth_rate(first_movers, all_29_2) =
% 40.65/6.25 | | | | | | | | | | all_41_1 & $i(all_41_0) & $i(all_41_1) &
% 40.65/6.25 | | | | | | | | | | greater(all_41_1, zero) & greater(zero, all_41_0)
% 40.65/6.25 | | | | | | | | | |
% 40.65/6.25 | | | | | | | | | | ALPHA: (173) implies:
% 40.65/6.25 | | | | | | | | | | (174) greater(all_41_1, zero)
% 40.65/6.26 | | | | | | | | | | (175) $i(all_41_1)
% 40.65/6.26 | | | | | | | | | | (176) $i(all_41_0)
% 40.65/6.26 | | | | | | | | | | (177) growth_rate(first_movers, all_29_2) = all_41_1
% 40.65/6.26 | | | | | | | | | | (178) growth_rate(efficient_producers, all_29_2) =
% 40.65/6.26 | | | | | | | | | | all_41_0
% 40.65/6.26 | | | | | | | | | |
% 40.65/6.26 | | | | | | | | | | REF_CLOSE: (5), (8), (48), (54), (55), (57), (174), (175),
% 40.65/6.26 | | | | | | | | | | (176), (177), (178), (mp_greater_transitivity) are
% 40.65/6.26 | | | | | | | | | | inconsistent by sub-proof #18.
% 40.65/6.26 | | | | | | | | | |
% 40.65/6.26 | | | | | | | | | End of split
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | End of split
% 40.65/6.26 | | | | | | | |
% 40.65/6.26 | | | | | | | End of split
% 40.65/6.26 | | | | | | |
% 40.65/6.26 | | | | | | Case 2:
% 40.65/6.26 | | | | | | |
% 40.65/6.26 | | | | | | | (179) all_31_2 = all_19_0
% 40.65/6.26 | | | | | | |
% 40.65/6.26 | | | | | | | REDUCE: (149), (179) imply:
% 40.65/6.26 | | | | | | | (180) growth_rate(efficient_producers, all_19_0) = all_106_1
% 40.65/6.26 | | | | | | |
% 40.65/6.26 | | | | | | | REDUCE: (141), (179) imply:
% 40.65/6.26 | | | | | | | (181) growth_rate(first_movers, all_19_0) = all_31_0
% 40.65/6.26 | | | | | | |
% 40.65/6.26 | | | | | | | BETA: splitting (50) gives:
% 40.65/6.26 | | | | | | |
% 40.65/6.26 | | | | | | | Case 1:
% 40.65/6.26 | | | | | | | |
% 40.65/6.26 | | | | | | | | (182) (all_40_0 = zero & all_40_1 = zero &
% 40.65/6.26 | | | | | | | | growth_rate(efficient_producers, all_31_2) = zero &
% 40.65/6.26 | | | | | | | | growth_rate(first_movers, all_31_2) = zero) |
% 40.65/6.26 | | | | | | | | (equilibrium(all_11_0) = all_40_2 & $i(all_40_2) & ~
% 40.65/6.26 | | | | | | | | greater_or_equal(all_31_2, all_40_2))
% 40.65/6.26 | | | | | | | |
% 40.65/6.26 | | | | | | | | BETA: splitting (182) gives:
% 40.65/6.26 | | | | | | | |
% 40.65/6.26 | | | | | | | | Case 1:
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | (183) all_40_0 = zero & all_40_1 = zero &
% 40.65/6.26 | | | | | | | | | growth_rate(efficient_producers, all_31_2) = zero &
% 40.65/6.26 | | | | | | | | | growth_rate(first_movers, all_31_2) = zero
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | ALPHA: (183) implies:
% 40.65/6.26 | | | | | | | | | (184) growth_rate(efficient_producers, all_31_2) = zero
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | REDUCE: (179), (184) imply:
% 40.65/6.26 | | | | | | | | | (185) growth_rate(efficient_producers, all_19_0) = zero
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | GROUND_INST: instantiating (8) with zero, all_106_1, all_19_0,
% 40.65/6.26 | | | | | | | | | efficient_producers, simplifying with (180), (185)
% 40.65/6.26 | | | | | | | | | gives:
% 40.65/6.26 | | | | | | | | | (186) all_106_1 = zero
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | REDUCE: (152), (186) imply:
% 40.65/6.26 | | | | | | | | | (187) $false
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | CLOSE: (187) is inconsistent.
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | Case 2:
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | (188) equilibrium(all_11_0) = all_40_2 & $i(all_40_2) & ~
% 40.65/6.26 | | | | | | | | | greater_or_equal(all_31_2, all_40_2)
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | ALPHA: (188) implies:
% 40.65/6.26 | | | | | | | | | (189) ~ greater_or_equal(all_31_2, all_40_2)
% 40.65/6.26 | | | | | | | | | (190) equilibrium(all_11_0) = all_40_2
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | REDUCE: (179), (189) imply:
% 40.65/6.26 | | | | | | | | | (191) ~ greater_or_equal(all_19_0, all_40_2)
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | REF_CLOSE: (7), (18), (21), (190), (191) are inconsistent by
% 40.65/6.26 | | | | | | | | | sub-proof #9.
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | End of split
% 40.65/6.26 | | | | | | | |
% 40.65/6.26 | | | | | | | Case 2:
% 40.65/6.26 | | | | | | | |
% 40.65/6.26 | | | | | | | | (192) (growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.26 | | | | | | | | & growth_rate(first_movers, all_31_2) = all_40_1 &
% 40.65/6.26 | | | | | | | | $i(all_40_0) & $i(all_40_1) & greater(all_40_0, zero)
% 40.65/6.26 | | | | | | | | & greater(zero, all_40_1)) |
% 40.65/6.26 | | | | | | | | (growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.26 | | | | | | | | & growth_rate(first_movers, all_31_2) = all_40_1 &
% 40.65/6.26 | | | | | | | | $i(all_40_0) & $i(all_40_1) & greater(all_40_1, zero)
% 40.65/6.26 | | | | | | | | & greater(zero, all_40_0))
% 40.65/6.26 | | | | | | | |
% 40.65/6.26 | | | | | | | | BETA: splitting (192) gives:
% 40.65/6.26 | | | | | | | |
% 40.65/6.26 | | | | | | | | Case 1:
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | (193) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.26 | | | | | | | | | & growth_rate(first_movers, all_31_2) = all_40_1 &
% 40.65/6.26 | | | | | | | | | $i(all_40_0) & $i(all_40_1) & greater(all_40_0, zero)
% 40.65/6.26 | | | | | | | | | & greater(zero, all_40_1)
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | ALPHA: (193) implies:
% 40.65/6.26 | | | | | | | | | (194) greater(zero, all_40_1)
% 40.65/6.26 | | | | | | | | | (195) growth_rate(first_movers, all_31_2) = all_40_1
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | REF_CLOSE: (8), (140), (141), (194), (195) are inconsistent by
% 40.65/6.26 | | | | | | | | | sub-proof #8.
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | Case 2:
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | (196) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.26 | | | | | | | | | & growth_rate(first_movers, all_31_2) = all_40_1 &
% 40.65/6.26 | | | | | | | | | $i(all_40_0) & $i(all_40_1) & greater(all_40_1, zero)
% 40.65/6.26 | | | | | | | | | & greater(zero, all_40_0)
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | ALPHA: (196) implies:
% 40.65/6.26 | | | | | | | | | (197) greater(zero, all_40_0)
% 40.65/6.26 | | | | | | | | | (198) $i(all_40_1)
% 40.65/6.26 | | | | | | | | | (199) growth_rate(first_movers, all_31_2) = all_40_1
% 40.65/6.26 | | | | | | | | | (200) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | REDUCE: (179), (200) imply:
% 40.65/6.26 | | | | | | | | | (201) growth_rate(efficient_producers, all_19_0) = all_40_0
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | REDUCE: (179), (199) imply:
% 40.65/6.26 | | | | | | | | | (202) growth_rate(first_movers, all_19_0) = all_40_1
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | GROUND_INST: instantiating (8) with all_31_0, all_40_1,
% 40.65/6.26 | | | | | | | | | all_19_0, first_movers, simplifying with (181),
% 40.65/6.26 | | | | | | | | | (202) gives:
% 40.65/6.26 | | | | | | | | | (203) all_40_1 = all_31_0
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | GROUND_INST: instantiating (8) with all_40_0, all_106_1,
% 40.65/6.26 | | | | | | | | | all_19_0, efficient_producers, simplifying with
% 40.65/6.26 | | | | | | | | | (180), (201) gives:
% 40.65/6.26 | | | | | | | | | (204) all_106_1 = all_40_0
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | REDUCE: (147), (204) imply:
% 40.65/6.26 | | | | | | | | | (205) $i(all_40_0)
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | REDUCE: (198), (203) imply:
% 40.65/6.26 | | | | | | | | | (206) $i(all_31_0)
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | REDUCE: (151), (204) imply:
% 40.65/6.26 | | | | | | | | | (207) greater(all_40_0, all_31_0)
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | GROUND_INST: instantiating (mp_greater_transitivity) with zero,
% 40.65/6.26 | | | | | | | | | all_40_0, all_31_0, simplifying with (5), (140),
% 40.65/6.26 | | | | | | | | | (197), (205), (206), (207) gives:
% 40.65/6.26 | | | | | | | | | (208) $false
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | | CLOSE: (208) is inconsistent.
% 40.65/6.26 | | | | | | | | |
% 40.65/6.26 | | | | | | | | End of split
% 40.65/6.26 | | | | | | | |
% 40.65/6.26 | | | | | | | End of split
% 40.65/6.26 | | | | | | |
% 40.65/6.26 | | | | | | End of split
% 40.65/6.26 | | | | | |
% 40.65/6.26 | | | | | End of split
% 40.65/6.26 | | | | |
% 40.65/6.26 | | | | End of split
% 40.65/6.26 | | | |
% 40.65/6.26 | | | End of split
% 40.65/6.26 | | |
% 40.65/6.26 | | Case 2:
% 40.65/6.26 | | |
% 40.65/6.26 | | | (209) all_19_0 = all_19_1
% 40.65/6.26 | | |
% 40.65/6.26 | | | REDUCE: (36), (209) imply:
% 40.65/6.26 | | | (210) greater_or_equal(all_31_2, all_19_1)
% 40.65/6.26 | | |
% 40.65/6.26 | | | BETA: splitting (27) gives:
% 40.65/6.26 | | |
% 40.65/6.26 | | | Case 1:
% 40.65/6.26 | | | |
% 40.65/6.26 | | | | (211) greater(all_21_0, all_19_0)
% 40.65/6.26 | | | |
% 40.65/6.26 | | | | REDUCE: (209), (211) imply:
% 40.65/6.26 | | | | (212) greater(all_21_0, all_19_1)
% 40.65/6.26 | | | |
% 40.65/6.26 | | | | REF_CLOSE: (1), (5), (7), (8), (19), (21), (24), (33), (40), (48), (51),
% 40.65/6.26 | | | | (52), (54), (55), (56), (57), (58), (212),
% 40.65/6.26 | | | | (mp_greater_transitivity) are inconsistent by sub-proof #15.
% 40.65/6.26 | | | |
% 40.65/6.26 | | | Case 2:
% 40.65/6.26 | | | |
% 40.65/6.26 | | | | (213) all_21_0 = all_19_0 | greater(all_19_0, all_21_0)
% 40.65/6.26 | | | |
% 40.65/6.26 | | | | REF_CLOSE: (1), (5), (7), (8), (19), (21), (24), (38), (39), (41), (45),
% 40.65/6.26 | | | | (50), (209), (210), (213), (mp_greater_transitivity) are
% 40.65/6.26 | | | | inconsistent by sub-proof #5.
% 40.65/6.26 | | | |
% 40.65/6.26 | | | End of split
% 40.65/6.26 | | |
% 40.65/6.26 | | End of split
% 40.65/6.26 | |
% 40.65/6.26 | Case 2:
% 40.65/6.26 | |
% 40.65/6.26 | | (214) growth_rate(first_movers, all_29_2) = all_29_0 & $i(all_29_0) & ~
% 40.65/6.26 | | greater(zero, all_29_0)
% 40.65/6.26 | |
% 40.65/6.26 | | ALPHA: (214) implies:
% 40.65/6.26 | | (215) ~ greater(zero, all_29_0)
% 40.65/6.26 | | (216) growth_rate(first_movers, all_29_2) = all_29_0
% 40.65/6.26 | |
% 40.65/6.26 | | GROUND_INST: instantiating (8) with all_38_0, all_29_0, all_29_2,
% 40.65/6.26 | | first_movers, simplifying with (48), (216) gives:
% 40.65/6.26 | | (217) all_38_0 = all_29_0
% 40.65/6.26 | |
% 40.65/6.26 | | REDUCE: (47), (217) imply:
% 40.65/6.26 | | (218) greater(all_38_1, all_29_0)
% 40.65/6.26 | |
% 40.65/6.26 | | PRED_UNIFY: (215), (218) imply:
% 40.65/6.27 | | (219) ~ (all_38_1 = zero)
% 40.65/6.27 | |
% 40.65/6.27 | | BETA: splitting (29) gives:
% 40.65/6.27 | |
% 40.65/6.27 | | Case 1:
% 40.65/6.27 | | |
% 40.65/6.27 | | | (220) greater(all_19_0, all_19_1)
% 40.65/6.27 | | |
% 40.65/6.27 | | | BETA: splitting (27) gives:
% 40.65/6.27 | | |
% 40.65/6.27 | | | Case 1:
% 40.65/6.27 | | | |
% 40.65/6.27 | | | | (221) greater(all_21_0, all_19_0)
% 40.65/6.27 | | | |
% 40.65/6.27 | | | | GROUND_INST: instantiating (mp_greater_transitivity) with all_21_0,
% 40.65/6.27 | | | | all_19_0, all_19_1, simplifying with (19), (20), (24),
% 40.65/6.27 | | | | (220), (221) gives:
% 40.65/6.27 | | | | (222) greater(all_21_0, all_19_1)
% 40.65/6.27 | | | |
% 40.65/6.27 | | | | REF_CLOSE: (1), (5), (7), (8), (19), (21), (24), (33), (40), (49), (51),
% 40.65/6.27 | | | | (215), (216), (218), (219), (222), (mp_greater_transitivity)
% 40.65/6.27 | | | | are inconsistent by sub-proof #3.
% 40.65/6.27 | | | |
% 40.65/6.27 | | | Case 2:
% 40.65/6.27 | | | |
% 40.65/6.27 | | | | (223) ~ greater(all_21_0, all_19_0)
% 40.65/6.27 | | | | (224) all_21_0 = all_19_0 | greater(all_19_0, all_21_0)
% 40.65/6.27 | | | |
% 40.65/6.27 | | | | BETA: splitting (39) gives:
% 40.65/6.27 | | | |
% 40.65/6.27 | | | | Case 1:
% 40.65/6.27 | | | | |
% 40.65/6.27 | | | | | (225) growth_rate(efficient_producers, all_31_2) = all_31_1 &
% 40.65/6.27 | | | | | $i(all_31_1) & ~ greater(all_31_1, zero)
% 40.65/6.27 | | | | |
% 40.65/6.27 | | | | | ALPHA: (225) implies:
% 40.65/6.27 | | | | | (226) ~ greater(all_31_1, zero)
% 40.65/6.27 | | | | | (227) growth_rate(efficient_producers, all_31_2) = all_31_1
% 40.65/6.27 | | | | |
% 40.65/6.27 | | | | | BETA: splitting (45) gives:
% 40.65/6.27 | | | | |
% 40.65/6.27 | | | | | Case 1:
% 40.65/6.27 | | | | | |
% 40.65/6.27 | | | | | | (228) ~ greater_or_equal(all_31_2, all_21_0)
% 40.65/6.27 | | | | | |
% 40.65/6.27 | | | | | | PRED_UNIFY: (36), (228) imply:
% 40.65/6.27 | | | | | | (229) ~ (all_21_0 = all_19_0)
% 40.65/6.27 | | | | | |
% 40.65/6.27 | | | | | | REF_CLOSE: (1), (20), (24), (38), (41), (224), (228), (229),
% 40.65/6.27 | | | | | | (mp_greater_transitivity) are inconsistent by sub-proof
% 40.65/6.27 | | | | | | #14.
% 40.65/6.27 | | | | | |
% 40.65/6.27 | | | | | Case 2:
% 40.65/6.27 | | | | | |
% 40.65/6.27 | | | | | | (230) greater_or_equal(all_31_2, all_21_0)
% 40.65/6.27 | | | | | | (231) ? [v0: $i] : ? [v1: $i] :
% 40.65/6.27 | | | | | | (growth_rate(efficient_producers, all_31_2) = v0 &
% 40.65/6.27 | | | | | | growth_rate(first_movers, all_31_2) = v1 & $i(v1) &
% 40.65/6.27 | | | | | | $i(v0) & greater(v0, v1))
% 40.65/6.27 | | | | | |
% 40.65/6.27 | | | | | | DELTA: instantiating (231) with fresh symbols all_106_0, all_106_1
% 40.65/6.27 | | | | | | gives:
% 40.65/6.27 | | | | | | (232) growth_rate(efficient_producers, all_31_2) = all_106_1 &
% 40.65/6.27 | | | | | | growth_rate(first_movers, all_31_2) = all_106_0 &
% 40.65/6.27 | | | | | | $i(all_106_0) & $i(all_106_1) & greater(all_106_1,
% 40.65/6.27 | | | | | | all_106_0)
% 40.65/6.27 | | | | | |
% 40.65/6.27 | | | | | | ALPHA: (232) implies:
% 40.65/6.27 | | | | | | (233) greater(all_106_1, all_106_0)
% 40.65/6.27 | | | | | | (234) $i(all_106_0)
% 40.65/6.27 | | | | | | (235) growth_rate(first_movers, all_31_2) = all_106_0
% 40.65/6.27 | | | | | | (236) growth_rate(efficient_producers, all_31_2) = all_106_1
% 40.65/6.27 | | | | | |
% 40.65/6.27 | | | | | | GROUND_INST: instantiating (8) with all_31_1, all_106_1, all_31_2,
% 40.65/6.27 | | | | | | efficient_producers, simplifying with (227), (236)
% 40.65/6.27 | | | | | | gives:
% 40.65/6.27 | | | | | | (237) all_106_1 = all_31_1
% 40.65/6.27 | | | | | |
% 40.65/6.27 | | | | | | REDUCE: (233), (237) imply:
% 40.65/6.27 | | | | | | (238) greater(all_31_1, all_106_0)
% 40.65/6.27 | | | | | |
% 40.65/6.27 | | | | | | PRED_UNIFY: (226), (238) imply:
% 40.65/6.27 | | | | | | (239) ~ (all_106_0 = zero)
% 40.65/6.27 | | | | | |
% 40.65/6.27 | | | | | | GROUND_INST: instantiating (2) with all_31_2, all_21_0, simplifying
% 40.65/6.27 | | | | | | with (24), (38), (230) gives:
% 40.65/6.27 | | | | | | (240) all_31_2 = all_21_0 | greater(all_31_2, all_21_0)
% 40.65/6.27 | | | | | |
% 40.65/6.27 | | | | | | BETA: splitting (41) gives:
% 40.65/6.27 | | | | | |
% 40.65/6.27 | | | | | | Case 1:
% 40.65/6.27 | | | | | | |
% 40.65/6.27 | | | | | | | (241) greater(all_31_2, all_19_0)
% 40.65/6.27 | | | | | | |
% 40.65/6.27 | | | | | | | PRED_UNIFY: (223), (241) imply:
% 40.65/6.27 | | | | | | | (242) ~ (all_31_2 = all_21_0)
% 40.65/6.27 | | | | | | |
% 40.65/6.27 | | | | | | | BETA: splitting (240) gives:
% 40.65/6.27 | | | | | | |
% 40.65/6.27 | | | | | | | Case 1:
% 40.65/6.27 | | | | | | | |
% 40.65/6.27 | | | | | | | |
% 40.65/6.27 | | | | | | | | GROUND_INST: instantiating (mp_greater_transitivity) with
% 40.65/6.27 | | | | | | | | all_31_2, all_19_0, all_19_1, simplifying with
% 40.65/6.27 | | | | | | | | (19), (20), (38), (220), (241) gives:
% 40.65/6.27 | | | | | | | | (243) greater(all_31_2, all_19_1)
% 40.65/6.27 | | | | | | | |
% 40.65/6.27 | | | | | | | | BETA: splitting (52) gives:
% 40.65/6.27 | | | | | | | |
% 40.65/6.27 | | | | | | | | Case 1:
% 40.65/6.27 | | | | | | | | |
% 40.65/6.27 | | | | | | | | |
% 40.65/6.27 | | | | | | | | | GROUND_INST: instantiating (1) with all_31_2, all_19_1,
% 40.65/6.27 | | | | | | | | | simplifying with (19), (38), (243) gives:
% 40.65/6.27 | | | | | | | | | (244) greater_or_equal(all_31_2, all_19_1)
% 40.65/6.27 | | | | | | | | |
% 40.65/6.27 | | | | | | | | | DELTA: instantiating (231) with fresh symbols all_106_0,
% 40.65/6.27 | | | | | | | | | all_106_1 gives:
% 40.65/6.27 | | | | | | | | | (245) growth_rate(efficient_producers, all_31_2) =
% 40.65/6.27 | | | | | | | | | all_106_1 & growth_rate(first_movers, all_31_2) =
% 40.65/6.27 | | | | | | | | | all_106_0 & $i(all_106_0) & $i(all_106_1) &
% 40.65/6.27 | | | | | | | | | greater(all_106_1, all_106_0)
% 40.65/6.27 | | | | | | | | |
% 40.65/6.27 | | | | | | | | | REF_CLOSE: (5), (7), (8), (21), (50), (226), (227), (244),
% 40.65/6.27 | | | | | | | | | (245), (mp_greater_transitivity) are inconsistent
% 40.65/6.27 | | | | | | | | | by sub-proof #11.
% 40.65/6.27 | | | | | | | | |
% 40.65/6.27 | | | | | | | | Case 2:
% 40.65/6.27 | | | | | | | | |
% 40.65/6.27 | | | | | | | | | (246) all_38_0 = all_38_1
% 40.65/6.27 | | | | | | | | | (247) growth_rate(first_movers, all_29_2) = all_38_1
% 40.65/6.27 | | | | | | | | |
% 40.65/6.27 | | | | | | | | | COMBINE_EQS: (217), (246) imply:
% 40.65/6.27 | | | | | | | | | (248) all_38_1 = all_29_0
% 40.65/6.27 | | | | | | | | |
% 40.65/6.27 | | | | | | | | | REDUCE: (219), (248) imply:
% 40.65/6.27 | | | | | | | | | (249) ~ (all_29_0 = zero)
% 40.65/6.27 | | | | | | | | |
% 40.65/6.27 | | | | | | | | | REDUCE: (49), (248) imply:
% 40.65/6.27 | | | | | | | | | (250) growth_rate(efficient_producers, all_29_2) = all_29_0
% 40.65/6.27 | | | | | | | | |
% 40.65/6.27 | | | | | | | | | BETA: splitting (51) gives:
% 40.65/6.27 | | | | | | | | |
% 40.65/6.27 | | | | | | | | | Case 1:
% 40.65/6.27 | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | (251) (all_41_0 = zero & all_41_1 = zero &
% 40.65/6.27 | | | | | | | | | | growth_rate(efficient_producers, all_29_2) = zero
% 40.65/6.27 | | | | | | | | | | & growth_rate(first_movers, all_29_2) = zero) |
% 40.65/6.27 | | | | | | | | | | (equilibrium(all_11_0) = all_41_2 & $i(all_41_2) &
% 40.65/6.27 | | | | | | | | | | ~ greater_or_equal(all_29_2, all_41_2))
% 40.65/6.27 | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | BETA: splitting (251) gives:
% 40.65/6.27 | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | Case 1:
% 40.65/6.27 | | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | | (252) all_41_0 = zero & all_41_1 = zero &
% 40.65/6.27 | | | | | | | | | | | growth_rate(efficient_producers, all_29_2) = zero
% 40.65/6.27 | | | | | | | | | | | & growth_rate(first_movers, all_29_2) = zero
% 40.65/6.27 | | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | | ALPHA: (252) implies:
% 40.65/6.27 | | | | | | | | | | | (253) growth_rate(efficient_producers, all_29_2) = zero
% 40.65/6.27 | | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | | REF_CLOSE: (8), (249), (250), (253) are inconsistent by
% 40.65/6.27 | | | | | | | | | | | sub-proof #2.
% 40.65/6.27 | | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | Case 2:
% 40.65/6.27 | | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | | (254) equilibrium(all_11_0) = all_41_2 & $i(all_41_2) &
% 40.65/6.27 | | | | | | | | | | | ~ greater_or_equal(all_29_2, all_41_2)
% 40.65/6.27 | | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | | ALPHA: (254) implies:
% 40.65/6.27 | | | | | | | | | | | (255) $i(all_41_2)
% 40.65/6.27 | | | | | | | | | | | (256) equilibrium(all_11_0) = all_41_2
% 40.65/6.27 | | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_19_1, all_41_2,
% 40.65/6.27 | | | | | | | | | | | all_11_0, simplifying with (21), (256) gives:
% 40.65/6.27 | | | | | | | | | | | (257) all_41_2 = all_19_1
% 40.65/6.27 | | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_31_2, all_19_1,
% 40.65/6.27 | | | | | | | | | | | simplifying with (19), (38), (243) gives:
% 40.65/6.27 | | | | | | | | | | | (258) greater_or_equal(all_31_2, all_19_1)
% 40.65/6.27 | | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | | DELTA: instantiating (231) with fresh symbols all_106_0,
% 40.65/6.27 | | | | | | | | | | | all_106_1 gives:
% 40.65/6.27 | | | | | | | | | | | (259) growth_rate(efficient_producers, all_31_2) =
% 40.65/6.27 | | | | | | | | | | | all_106_1 & growth_rate(first_movers, all_31_2) =
% 40.65/6.27 | | | | | | | | | | | all_106_0 & $i(all_106_0) & $i(all_106_1) &
% 40.65/6.27 | | | | | | | | | | | greater(all_106_1, all_106_0)
% 40.65/6.27 | | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (21), (50), (226), (227), (258),
% 40.65/6.27 | | | | | | | | | | | (259), (mp_greater_transitivity) are inconsistent
% 40.65/6.27 | | | | | | | | | | | by sub-proof #11.
% 40.65/6.27 | | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | End of split
% 40.65/6.27 | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | Case 2:
% 40.65/6.27 | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | (260) (growth_rate(efficient_producers, all_29_2) =
% 40.65/6.27 | | | | | | | | | | all_41_0 & growth_rate(first_movers, all_29_2) =
% 40.65/6.27 | | | | | | | | | | all_41_1 & $i(all_41_0) & $i(all_41_1) &
% 40.65/6.27 | | | | | | | | | | greater(all_41_0, zero) & greater(zero,
% 40.65/6.27 | | | | | | | | | | all_41_1)) | (growth_rate(efficient_producers,
% 40.65/6.27 | | | | | | | | | | all_29_2) = all_41_0 &
% 40.65/6.27 | | | | | | | | | | growth_rate(first_movers, all_29_2) = all_41_1 &
% 40.65/6.27 | | | | | | | | | | $i(all_41_0) & $i(all_41_1) & greater(all_41_1,
% 40.65/6.27 | | | | | | | | | | zero) & greater(zero, all_41_0))
% 40.65/6.27 | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | BETA: splitting (260) gives:
% 40.65/6.27 | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | Case 1:
% 40.65/6.27 | | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | | (261) growth_rate(efficient_producers, all_29_2) =
% 40.65/6.27 | | | | | | | | | | | all_41_0 & growth_rate(first_movers, all_29_2) =
% 40.65/6.27 | | | | | | | | | | | all_41_1 & $i(all_41_0) & $i(all_41_1) &
% 40.65/6.27 | | | | | | | | | | | greater(all_41_0, zero) & greater(zero, all_41_1)
% 40.65/6.27 | | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | | ALPHA: (261) implies:
% 40.65/6.27 | | | | | | | | | | | (262) greater(zero, all_41_1)
% 40.65/6.27 | | | | | | | | | | | (263) growth_rate(first_movers, all_29_2) = all_41_1
% 40.65/6.27 | | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | | REF_CLOSE: (8), (215), (216), (262), (263) are inconsistent
% 40.65/6.27 | | | | | | | | | | | by sub-proof #4.
% 40.65/6.27 | | | | | | | | | | |
% 40.65/6.27 | | | | | | | | | | Case 2:
% 40.65/6.27 | | | | | | | | | | |
% 40.65/6.28 | | | | | | | | | | | (264) growth_rate(efficient_producers, all_29_2) =
% 40.65/6.28 | | | | | | | | | | | all_41_0 & growth_rate(first_movers, all_29_2) =
% 40.65/6.28 | | | | | | | | | | | all_41_1 & $i(all_41_0) & $i(all_41_1) &
% 40.65/6.28 | | | | | | | | | | | greater(all_41_1, zero) & greater(zero, all_41_0)
% 40.65/6.28 | | | | | | | | | | |
% 40.65/6.28 | | | | | | | | | | | ALPHA: (264) implies:
% 40.65/6.28 | | | | | | | | | | | (265) greater(zero, all_41_0)
% 40.65/6.28 | | | | | | | | | | | (266) growth_rate(efficient_producers, all_29_2) =
% 40.65/6.28 | | | | | | | | | | | all_41_0
% 40.65/6.28 | | | | | | | | | | |
% 40.65/6.28 | | | | | | | | | | | REF_CLOSE: (8), (215), (250), (265), (266) are inconsistent
% 40.65/6.28 | | | | | | | | | | | by sub-proof #1.
% 40.65/6.28 | | | | | | | | | | |
% 40.65/6.28 | | | | | | | | | | End of split
% 40.65/6.28 | | | | | | | | | |
% 40.65/6.28 | | | | | | | | | End of split
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | End of split
% 40.65/6.28 | | | | | | | |
% 40.65/6.28 | | | | | | | Case 2:
% 40.65/6.28 | | | | | | | |
% 40.65/6.28 | | | | | | | | (267) all_31_2 = all_21_0
% 40.65/6.28 | | | | | | | |
% 40.65/6.28 | | | | | | | | REDUCE: (242), (267) imply:
% 40.65/6.28 | | | | | | | | (268) $false
% 40.65/6.28 | | | | | | | |
% 40.65/6.28 | | | | | | | | CLOSE: (268) is inconsistent.
% 40.65/6.28 | | | | | | | |
% 40.65/6.28 | | | | | | | End of split
% 40.65/6.28 | | | | | | |
% 40.65/6.28 | | | | | | Case 2:
% 40.65/6.28 | | | | | | |
% 40.65/6.28 | | | | | | | (269) all_31_2 = all_19_0
% 40.65/6.28 | | | | | | |
% 40.65/6.28 | | | | | | | REDUCE: (227), (269) imply:
% 40.65/6.28 | | | | | | | (270) growth_rate(efficient_producers, all_19_0) = all_31_1
% 40.65/6.28 | | | | | | |
% 40.65/6.28 | | | | | | | REDUCE: (235), (269) imply:
% 40.65/6.28 | | | | | | | (271) growth_rate(first_movers, all_19_0) = all_106_0
% 40.65/6.28 | | | | | | |
% 40.65/6.28 | | | | | | | BETA: splitting (50) gives:
% 40.65/6.28 | | | | | | |
% 40.65/6.28 | | | | | | | Case 1:
% 40.65/6.28 | | | | | | | |
% 40.65/6.28 | | | | | | | | (272) (all_40_0 = zero & all_40_1 = zero &
% 40.65/6.28 | | | | | | | | growth_rate(efficient_producers, all_31_2) = zero &
% 40.65/6.28 | | | | | | | | growth_rate(first_movers, all_31_2) = zero) |
% 40.65/6.28 | | | | | | | | (equilibrium(all_11_0) = all_40_2 & $i(all_40_2) & ~
% 40.65/6.28 | | | | | | | | greater_or_equal(all_31_2, all_40_2))
% 40.65/6.28 | | | | | | | |
% 40.65/6.28 | | | | | | | | BETA: splitting (272) gives:
% 40.65/6.28 | | | | | | | |
% 40.65/6.28 | | | | | | | | Case 1:
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | (273) all_40_0 = zero & all_40_1 = zero &
% 40.65/6.28 | | | | | | | | | growth_rate(efficient_producers, all_31_2) = zero &
% 40.65/6.28 | | | | | | | | | growth_rate(first_movers, all_31_2) = zero
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | ALPHA: (273) implies:
% 40.65/6.28 | | | | | | | | | (274) growth_rate(first_movers, all_31_2) = zero
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | REDUCE: (269), (274) imply:
% 40.65/6.28 | | | | | | | | | (275) growth_rate(first_movers, all_19_0) = zero
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | GROUND_INST: instantiating (8) with zero, all_106_0, all_19_0,
% 40.65/6.28 | | | | | | | | | first_movers, simplifying with (271), (275) gives:
% 40.65/6.28 | | | | | | | | | (276) all_106_0 = zero
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | REDUCE: (239), (276) imply:
% 40.65/6.28 | | | | | | | | | (277) $false
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | CLOSE: (277) is inconsistent.
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | Case 2:
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | (278) equilibrium(all_11_0) = all_40_2 & $i(all_40_2) & ~
% 40.65/6.28 | | | | | | | | | greater_or_equal(all_31_2, all_40_2)
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | ALPHA: (278) implies:
% 40.65/6.28 | | | | | | | | | (279) ~ greater_or_equal(all_31_2, all_40_2)
% 40.65/6.28 | | | | | | | | | (280) equilibrium(all_11_0) = all_40_2
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | REDUCE: (269), (279) imply:
% 40.65/6.28 | | | | | | | | | (281) ~ greater_or_equal(all_19_0, all_40_2)
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | REF_CLOSE: (7), (18), (21), (280), (281) are inconsistent by
% 40.65/6.28 | | | | | | | | | sub-proof #9.
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | End of split
% 40.65/6.28 | | | | | | | |
% 40.65/6.28 | | | | | | | Case 2:
% 40.65/6.28 | | | | | | | |
% 40.65/6.28 | | | | | | | | (282) (growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.28 | | | | | | | | & growth_rate(first_movers, all_31_2) = all_40_1 &
% 40.65/6.28 | | | | | | | | $i(all_40_0) & $i(all_40_1) & greater(all_40_0, zero)
% 40.65/6.28 | | | | | | | | & greater(zero, all_40_1)) |
% 40.65/6.28 | | | | | | | | (growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.28 | | | | | | | | & growth_rate(first_movers, all_31_2) = all_40_1 &
% 40.65/6.28 | | | | | | | | $i(all_40_0) & $i(all_40_1) & greater(all_40_1, zero)
% 40.65/6.28 | | | | | | | | & greater(zero, all_40_0))
% 40.65/6.28 | | | | | | | |
% 40.65/6.28 | | | | | | | | BETA: splitting (282) gives:
% 40.65/6.28 | | | | | | | |
% 40.65/6.28 | | | | | | | | Case 1:
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | (283) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.28 | | | | | | | | | & growth_rate(first_movers, all_31_2) = all_40_1 &
% 40.65/6.28 | | | | | | | | | $i(all_40_0) & $i(all_40_1) & greater(all_40_0, zero)
% 40.65/6.28 | | | | | | | | | & greater(zero, all_40_1)
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | ALPHA: (283) implies:
% 40.65/6.28 | | | | | | | | | (284) greater(all_40_0, zero)
% 40.65/6.28 | | | | | | | | | (285) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | REF_CLOSE: (8), (226), (227), (284), (285) are inconsistent by
% 40.65/6.28 | | | | | | | | | sub-proof #12.
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | Case 2:
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | (286) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.28 | | | | | | | | | & growth_rate(first_movers, all_31_2) = all_40_1 &
% 40.65/6.28 | | | | | | | | | $i(all_40_0) & $i(all_40_1) & greater(all_40_1, zero)
% 40.65/6.28 | | | | | | | | | & greater(zero, all_40_0)
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | ALPHA: (286) implies:
% 40.65/6.28 | | | | | | | | | (287) greater(all_40_1, zero)
% 40.65/6.28 | | | | | | | | | (288) $i(all_40_0)
% 40.65/6.28 | | | | | | | | | (289) growth_rate(first_movers, all_31_2) = all_40_1
% 40.65/6.28 | | | | | | | | | (290) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | REDUCE: (269), (290) imply:
% 40.65/6.28 | | | | | | | | | (291) growth_rate(efficient_producers, all_19_0) = all_40_0
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | REDUCE: (269), (289) imply:
% 40.65/6.28 | | | | | | | | | (292) growth_rate(first_movers, all_19_0) = all_40_1
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | GROUND_INST: instantiating (8) with all_40_1, all_106_0,
% 40.65/6.28 | | | | | | | | | all_19_0, first_movers, simplifying with (271),
% 40.65/6.28 | | | | | | | | | (292) gives:
% 40.65/6.28 | | | | | | | | | (293) all_106_0 = all_40_1
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | GROUND_INST: instantiating (8) with all_31_1, all_40_0,
% 40.65/6.28 | | | | | | | | | all_19_0, efficient_producers, simplifying with
% 40.65/6.28 | | | | | | | | | (270), (291) gives:
% 40.65/6.28 | | | | | | | | | (294) all_40_0 = all_31_1
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | REDUCE: (234), (293) imply:
% 40.65/6.28 | | | | | | | | | (295) $i(all_40_1)
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | REDUCE: (288), (294) imply:
% 40.65/6.28 | | | | | | | | | (296) $i(all_31_1)
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | REDUCE: (238), (293) imply:
% 40.65/6.28 | | | | | | | | | (297) greater(all_31_1, all_40_1)
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | GROUND_INST: instantiating (mp_greater_transitivity) with
% 40.65/6.28 | | | | | | | | | all_31_1, all_40_1, zero, simplifying with (5),
% 40.65/6.28 | | | | | | | | | (226), (287), (295), (296), (297) gives:
% 40.65/6.28 | | | | | | | | | (298) $false
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | | CLOSE: (298) is inconsistent.
% 40.65/6.28 | | | | | | | | |
% 40.65/6.28 | | | | | | | | End of split
% 40.65/6.28 | | | | | | | |
% 40.65/6.28 | | | | | | | End of split
% 40.65/6.28 | | | | | | |
% 40.65/6.28 | | | | | | End of split
% 40.65/6.28 | | | | | |
% 40.65/6.28 | | | | | End of split
% 40.65/6.28 | | | | |
% 40.65/6.28 | | | | Case 2:
% 40.65/6.28 | | | | |
% 40.65/6.28 | | | | | (299) growth_rate(first_movers, all_31_2) = all_31_0 & $i(all_31_0)
% 40.65/6.28 | | | | | & ~ greater(zero, all_31_0)
% 40.65/6.28 | | | | |
% 40.65/6.28 | | | | | ALPHA: (299) implies:
% 40.65/6.28 | | | | | (300) ~ greater(zero, all_31_0)
% 40.65/6.28 | | | | | (301) growth_rate(first_movers, all_31_2) = all_31_0
% 40.65/6.28 | | | | |
% 40.65/6.28 | | | | | BETA: splitting (45) gives:
% 40.65/6.28 | | | | |
% 40.65/6.28 | | | | | Case 1:
% 40.65/6.28 | | | | | |
% 40.65/6.28 | | | | | | (302) ~ greater_or_equal(all_31_2, all_21_0)
% 40.65/6.28 | | | | | |
% 40.65/6.28 | | | | | | PRED_UNIFY: (36), (302) imply:
% 40.65/6.28 | | | | | | (303) ~ (all_21_0 = all_19_0)
% 40.65/6.28 | | | | | |
% 40.65/6.28 | | | | | | REF_CLOSE: (1), (20), (24), (38), (41), (224), (302), (303),
% 40.65/6.28 | | | | | | (mp_greater_transitivity) are inconsistent by sub-proof
% 40.65/6.28 | | | | | | #14.
% 40.65/6.28 | | | | | |
% 40.65/6.28 | | | | | Case 2:
% 40.65/6.28 | | | | | |
% 40.65/6.28 | | | | | | (304) ? [v0: $i] : ? [v1: $i] :
% 40.65/6.28 | | | | | | (growth_rate(efficient_producers, all_31_2) = v0 &
% 40.65/6.28 | | | | | | growth_rate(first_movers, all_31_2) = v1 & $i(v1) &
% 40.65/6.28 | | | | | | $i(v0) & greater(v0, v1))
% 40.65/6.28 | | | | | |
% 40.65/6.28 | | | | | | DELTA: instantiating (304) with fresh symbols all_106_0, all_106_1
% 40.65/6.28 | | | | | | gives:
% 40.65/6.28 | | | | | | (305) growth_rate(efficient_producers, all_31_2) = all_106_1 &
% 40.65/6.28 | | | | | | growth_rate(first_movers, all_31_2) = all_106_0 &
% 40.65/6.28 | | | | | | $i(all_106_0) & $i(all_106_1) & greater(all_106_1,
% 40.65/6.28 | | | | | | all_106_0)
% 40.65/6.28 | | | | | |
% 40.65/6.28 | | | | | | ALPHA: (305) implies:
% 40.65/6.28 | | | | | | (306) greater(all_106_1, all_106_0)
% 40.65/6.28 | | | | | | (307) $i(all_106_1)
% 40.65/6.28 | | | | | | (308) growth_rate(first_movers, all_31_2) = all_106_0
% 40.65/6.28 | | | | | | (309) growth_rate(efficient_producers, all_31_2) = all_106_1
% 40.65/6.28 | | | | | |
% 40.65/6.28 | | | | | | GROUND_INST: instantiating (8) with all_31_0, all_106_0, all_31_2,
% 40.65/6.28 | | | | | | first_movers, simplifying with (301), (308) gives:
% 40.65/6.28 | | | | | | (310) all_106_0 = all_31_0
% 40.65/6.28 | | | | | |
% 40.65/6.28 | | | | | | REDUCE: (306), (310) imply:
% 40.65/6.29 | | | | | | (311) greater(all_106_1, all_31_0)
% 40.65/6.29 | | | | | |
% 40.65/6.29 | | | | | | PRED_UNIFY: (300), (311) imply:
% 40.65/6.29 | | | | | | (312) ~ (all_106_1 = zero)
% 40.65/6.29 | | | | | |
% 40.65/6.29 | | | | | | BETA: splitting (41) gives:
% 40.65/6.29 | | | | | |
% 40.65/6.29 | | | | | | Case 1:
% 40.65/6.29 | | | | | | |
% 40.65/6.29 | | | | | | | (313) greater(all_31_2, all_19_0)
% 40.65/6.29 | | | | | | |
% 40.65/6.29 | | | | | | | GROUND_INST: instantiating (mp_greater_transitivity) with
% 40.65/6.29 | | | | | | | all_31_2, all_19_0, all_19_1, simplifying with (19),
% 40.65/6.29 | | | | | | | (20), (38), (220), (313) gives:
% 40.65/6.29 | | | | | | | (314) greater(all_31_2, all_19_1)
% 40.65/6.29 | | | | | | |
% 40.65/6.29 | | | | | | | BETA: splitting (52) gives:
% 40.65/6.29 | | | | | | |
% 40.65/6.29 | | | | | | | Case 1:
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | | GROUND_INST: instantiating (1) with all_31_2, all_19_1,
% 40.65/6.29 | | | | | | | | simplifying with (19), (38), (314) gives:
% 40.65/6.29 | | | | | | | | (315) greater_or_equal(all_31_2, all_19_1)
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | | DELTA: instantiating (304) with fresh symbols all_106_0,
% 40.65/6.29 | | | | | | | | all_106_1 gives:
% 40.65/6.29 | | | | | | | | (316) growth_rate(efficient_producers, all_31_2) = all_106_1
% 40.65/6.29 | | | | | | | | & growth_rate(first_movers, all_31_2) = all_106_0 &
% 40.65/6.29 | | | | | | | | $i(all_106_0) & $i(all_106_1) & greater(all_106_1,
% 40.65/6.29 | | | | | | | | all_106_0)
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | | REF_CLOSE: (5), (7), (8), (21), (50), (300), (301), (315),
% 40.65/6.29 | | | | | | | | (316), (mp_greater_transitivity) are inconsistent by
% 40.65/6.29 | | | | | | | | sub-proof #7.
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | Case 2:
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | | (317) all_38_0 = all_38_1
% 40.65/6.29 | | | | | | | | (318) growth_rate(first_movers, all_29_2) = all_38_1
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | | COMBINE_EQS: (217), (317) imply:
% 40.65/6.29 | | | | | | | | (319) all_38_1 = all_29_0
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | | REDUCE: (219), (319) imply:
% 40.65/6.29 | | | | | | | | (320) ~ (all_29_0 = zero)
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | | REDUCE: (49), (319) imply:
% 40.65/6.29 | | | | | | | | (321) growth_rate(efficient_producers, all_29_2) = all_29_0
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | | BETA: splitting (51) gives:
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | | Case 1:
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | | (322) (all_41_0 = zero & all_41_1 = zero &
% 40.65/6.29 | | | | | | | | | growth_rate(efficient_producers, all_29_2) = zero &
% 40.65/6.29 | | | | | | | | | growth_rate(first_movers, all_29_2) = zero) |
% 40.65/6.29 | | | | | | | | | (equilibrium(all_11_0) = all_41_2 & $i(all_41_2) & ~
% 40.65/6.29 | | | | | | | | | greater_or_equal(all_29_2, all_41_2))
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | | BETA: splitting (322) gives:
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | | Case 1:
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | | (323) all_41_0 = zero & all_41_1 = zero &
% 40.65/6.29 | | | | | | | | | | growth_rate(efficient_producers, all_29_2) = zero &
% 40.65/6.29 | | | | | | | | | | growth_rate(first_movers, all_29_2) = zero
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | | ALPHA: (323) implies:
% 40.65/6.29 | | | | | | | | | | (324) growth_rate(efficient_producers, all_29_2) = zero
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | | REF_CLOSE: (8), (320), (321), (324) are inconsistent by
% 40.65/6.29 | | | | | | | | | | sub-proof #2.
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | Case 2:
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | | (325) equilibrium(all_11_0) = all_41_2 & $i(all_41_2) &
% 40.65/6.29 | | | | | | | | | | ~ greater_or_equal(all_29_2, all_41_2)
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | | ALPHA: (325) implies:
% 40.65/6.29 | | | | | | | | | | (326) $i(all_41_2)
% 40.65/6.29 | | | | | | | | | | (327) equilibrium(all_11_0) = all_41_2
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | | GROUND_INST: instantiating (7) with all_19_1, all_41_2,
% 40.65/6.29 | | | | | | | | | | all_11_0, simplifying with (21), (327) gives:
% 40.65/6.29 | | | | | | | | | | (328) all_41_2 = all_19_1
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | | GROUND_INST: instantiating (1) with all_31_2, all_19_1,
% 40.65/6.29 | | | | | | | | | | simplifying with (19), (38), (314) gives:
% 40.65/6.29 | | | | | | | | | | (329) greater_or_equal(all_31_2, all_19_1)
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | | DELTA: instantiating (304) with fresh symbols all_106_0,
% 40.65/6.29 | | | | | | | | | | all_106_1 gives:
% 40.65/6.29 | | | | | | | | | | (330) growth_rate(efficient_producers, all_31_2) =
% 40.65/6.29 | | | | | | | | | | all_106_1 & growth_rate(first_movers, all_31_2) =
% 40.65/6.29 | | | | | | | | | | all_106_0 & $i(all_106_0) & $i(all_106_1) &
% 40.65/6.29 | | | | | | | | | | greater(all_106_1, all_106_0)
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | | REF_CLOSE: (5), (7), (8), (21), (50), (300), (301), (329),
% 40.65/6.29 | | | | | | | | | | (330), (mp_greater_transitivity) are inconsistent
% 40.65/6.29 | | | | | | | | | | by sub-proof #7.
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | End of split
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | Case 2:
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | | (331) (growth_rate(efficient_producers, all_29_2) =
% 40.65/6.29 | | | | | | | | | all_41_0 & growth_rate(first_movers, all_29_2) =
% 40.65/6.29 | | | | | | | | | all_41_1 & $i(all_41_0) & $i(all_41_1) &
% 40.65/6.29 | | | | | | | | | greater(all_41_0, zero) & greater(zero, all_41_1))
% 40.65/6.29 | | | | | | | | | | (growth_rate(efficient_producers, all_29_2) =
% 40.65/6.29 | | | | | | | | | all_41_0 & growth_rate(first_movers, all_29_2) =
% 40.65/6.29 | | | | | | | | | all_41_1 & $i(all_41_0) & $i(all_41_1) &
% 40.65/6.29 | | | | | | | | | greater(all_41_1, zero) & greater(zero, all_41_0))
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | | BETA: splitting (331) gives:
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | | Case 1:
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | | (332) growth_rate(efficient_producers, all_29_2) =
% 40.65/6.29 | | | | | | | | | | all_41_0 & growth_rate(first_movers, all_29_2) =
% 40.65/6.29 | | | | | | | | | | all_41_1 & $i(all_41_0) & $i(all_41_1) &
% 40.65/6.29 | | | | | | | | | | greater(all_41_0, zero) & greater(zero, all_41_1)
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | | ALPHA: (332) implies:
% 40.65/6.29 | | | | | | | | | | (333) greater(zero, all_41_1)
% 40.65/6.29 | | | | | | | | | | (334) growth_rate(first_movers, all_29_2) = all_41_1
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | | REF_CLOSE: (8), (215), (216), (333), (334) are inconsistent
% 40.65/6.29 | | | | | | | | | | by sub-proof #4.
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | Case 2:
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | | (335) growth_rate(efficient_producers, all_29_2) =
% 40.65/6.29 | | | | | | | | | | all_41_0 & growth_rate(first_movers, all_29_2) =
% 40.65/6.29 | | | | | | | | | | all_41_1 & $i(all_41_0) & $i(all_41_1) &
% 40.65/6.29 | | | | | | | | | | greater(all_41_1, zero) & greater(zero, all_41_0)
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | | ALPHA: (335) implies:
% 40.65/6.29 | | | | | | | | | | (336) greater(zero, all_41_0)
% 40.65/6.29 | | | | | | | | | | (337) growth_rate(efficient_producers, all_29_2) =
% 40.65/6.29 | | | | | | | | | | all_41_0
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | | REF_CLOSE: (8), (215), (321), (336), (337) are inconsistent
% 40.65/6.29 | | | | | | | | | | by sub-proof #1.
% 40.65/6.29 | | | | | | | | | |
% 40.65/6.29 | | | | | | | | | End of split
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | End of split
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | End of split
% 40.65/6.29 | | | | | | |
% 40.65/6.29 | | | | | | Case 2:
% 40.65/6.29 | | | | | | |
% 40.65/6.29 | | | | | | | (338) all_31_2 = all_19_0
% 40.65/6.29 | | | | | | |
% 40.65/6.29 | | | | | | | REDUCE: (309), (338) imply:
% 40.65/6.29 | | | | | | | (339) growth_rate(efficient_producers, all_19_0) = all_106_1
% 40.65/6.29 | | | | | | |
% 40.65/6.29 | | | | | | | REDUCE: (301), (338) imply:
% 40.65/6.29 | | | | | | | (340) growth_rate(first_movers, all_19_0) = all_31_0
% 40.65/6.29 | | | | | | |
% 40.65/6.29 | | | | | | | BETA: splitting (50) gives:
% 40.65/6.29 | | | | | | |
% 40.65/6.29 | | | | | | | Case 1:
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | | (341) (all_40_0 = zero & all_40_1 = zero &
% 40.65/6.29 | | | | | | | | growth_rate(efficient_producers, all_31_2) = zero &
% 40.65/6.29 | | | | | | | | growth_rate(first_movers, all_31_2) = zero) |
% 40.65/6.29 | | | | | | | | (equilibrium(all_11_0) = all_40_2 & $i(all_40_2) & ~
% 40.65/6.29 | | | | | | | | greater_or_equal(all_31_2, all_40_2))
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | | BETA: splitting (341) gives:
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | | Case 1:
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | | (342) all_40_0 = zero & all_40_1 = zero &
% 40.65/6.29 | | | | | | | | | growth_rate(efficient_producers, all_31_2) = zero &
% 40.65/6.29 | | | | | | | | | growth_rate(first_movers, all_31_2) = zero
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | | ALPHA: (342) implies:
% 40.65/6.29 | | | | | | | | | (343) growth_rate(efficient_producers, all_31_2) = zero
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | | REDUCE: (338), (343) imply:
% 40.65/6.29 | | | | | | | | | (344) growth_rate(efficient_producers, all_19_0) = zero
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | | GROUND_INST: instantiating (8) with zero, all_106_1, all_19_0,
% 40.65/6.29 | | | | | | | | | efficient_producers, simplifying with (339), (344)
% 40.65/6.29 | | | | | | | | | gives:
% 40.65/6.29 | | | | | | | | | (345) all_106_1 = zero
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | | REDUCE: (312), (345) imply:
% 40.65/6.29 | | | | | | | | | (346) $false
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | | CLOSE: (346) is inconsistent.
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | Case 2:
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | | (347) equilibrium(all_11_0) = all_40_2 & $i(all_40_2) & ~
% 40.65/6.29 | | | | | | | | | greater_or_equal(all_31_2, all_40_2)
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | | ALPHA: (347) implies:
% 40.65/6.29 | | | | | | | | | (348) ~ greater_or_equal(all_31_2, all_40_2)
% 40.65/6.29 | | | | | | | | | (349) equilibrium(all_11_0) = all_40_2
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | | REDUCE: (338), (348) imply:
% 40.65/6.29 | | | | | | | | | (350) ~ greater_or_equal(all_19_0, all_40_2)
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | | REF_CLOSE: (7), (18), (21), (349), (350) are inconsistent by
% 40.65/6.29 | | | | | | | | | sub-proof #9.
% 40.65/6.29 | | | | | | | | |
% 40.65/6.29 | | | | | | | | End of split
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | Case 2:
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | | (351) (growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.29 | | | | | | | | & growth_rate(first_movers, all_31_2) = all_40_1 &
% 40.65/6.29 | | | | | | | | $i(all_40_0) & $i(all_40_1) & greater(all_40_0, zero)
% 40.65/6.29 | | | | | | | | & greater(zero, all_40_1)) |
% 40.65/6.29 | | | | | | | | (growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.29 | | | | | | | | & growth_rate(first_movers, all_31_2) = all_40_1 &
% 40.65/6.29 | | | | | | | | $i(all_40_0) & $i(all_40_1) & greater(all_40_1, zero)
% 40.65/6.29 | | | | | | | | & greater(zero, all_40_0))
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | | BETA: splitting (351) gives:
% 40.65/6.29 | | | | | | | |
% 40.65/6.29 | | | | | | | | Case 1:
% 40.65/6.29 | | | | | | | | |
% 40.65/6.30 | | | | | | | | | (352) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.30 | | | | | | | | | & growth_rate(first_movers, all_31_2) = all_40_1 &
% 40.65/6.30 | | | | | | | | | $i(all_40_0) & $i(all_40_1) & greater(all_40_0, zero)
% 40.65/6.30 | | | | | | | | | & greater(zero, all_40_1)
% 40.65/6.30 | | | | | | | | |
% 40.65/6.30 | | | | | | | | | ALPHA: (352) implies:
% 40.65/6.30 | | | | | | | | | (353) greater(zero, all_40_1)
% 40.65/6.30 | | | | | | | | | (354) growth_rate(first_movers, all_31_2) = all_40_1
% 40.65/6.30 | | | | | | | | |
% 40.65/6.30 | | | | | | | | | REF_CLOSE: (8), (300), (301), (353), (354) are inconsistent by
% 40.65/6.30 | | | | | | | | | sub-proof #8.
% 40.65/6.30 | | | | | | | | |
% 40.65/6.30 | | | | | | | | Case 2:
% 40.65/6.30 | | | | | | | | |
% 40.65/6.30 | | | | | | | | | (355) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.30 | | | | | | | | | & growth_rate(first_movers, all_31_2) = all_40_1 &
% 40.65/6.30 | | | | | | | | | $i(all_40_0) & $i(all_40_1) & greater(all_40_1, zero)
% 40.65/6.30 | | | | | | | | | & greater(zero, all_40_0)
% 40.65/6.30 | | | | | | | | |
% 40.65/6.30 | | | | | | | | | ALPHA: (355) implies:
% 40.65/6.30 | | | | | | | | | (356) greater(zero, all_40_0)
% 40.65/6.30 | | | | | | | | | (357) $i(all_40_1)
% 40.65/6.30 | | | | | | | | | (358) growth_rate(first_movers, all_31_2) = all_40_1
% 40.65/6.30 | | | | | | | | | (359) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.30 | | | | | | | | |
% 40.65/6.30 | | | | | | | | | REDUCE: (338), (359) imply:
% 40.65/6.30 | | | | | | | | | (360) growth_rate(efficient_producers, all_19_0) = all_40_0
% 40.65/6.30 | | | | | | | | |
% 40.65/6.30 | | | | | | | | | REDUCE: (338), (358) imply:
% 40.65/6.30 | | | | | | | | | (361) growth_rate(first_movers, all_19_0) = all_40_1
% 40.65/6.30 | | | | | | | | |
% 40.65/6.30 | | | | | | | | | GROUND_INST: instantiating (8) with all_31_0, all_40_1,
% 40.65/6.30 | | | | | | | | | all_19_0, first_movers, simplifying with (340),
% 40.65/6.30 | | | | | | | | | (361) gives:
% 40.65/6.30 | | | | | | | | | (362) all_40_1 = all_31_0
% 40.65/6.30 | | | | | | | | |
% 40.65/6.30 | | | | | | | | | GROUND_INST: instantiating (8) with all_40_0, all_106_1,
% 40.65/6.30 | | | | | | | | | all_19_0, efficient_producers, simplifying with
% 40.65/6.30 | | | | | | | | | (339), (360) gives:
% 40.65/6.30 | | | | | | | | | (363) all_106_1 = all_40_0
% 40.65/6.30 | | | | | | | | |
% 40.65/6.30 | | | | | | | | | REDUCE: (307), (363) imply:
% 40.65/6.30 | | | | | | | | | (364) $i(all_40_0)
% 40.65/6.30 | | | | | | | | |
% 40.65/6.30 | | | | | | | | | REDUCE: (357), (362) imply:
% 40.65/6.30 | | | | | | | | | (365) $i(all_31_0)
% 40.65/6.30 | | | | | | | | |
% 40.65/6.30 | | | | | | | | | REDUCE: (311), (363) imply:
% 40.65/6.30 | | | | | | | | | (366) greater(all_40_0, all_31_0)
% 40.65/6.30 | | | | | | | | |
% 40.65/6.30 | | | | | | | | | GROUND_INST: instantiating (mp_greater_transitivity) with zero,
% 40.65/6.30 | | | | | | | | | all_40_0, all_31_0, simplifying with (5), (300),
% 40.65/6.30 | | | | | | | | | (356), (364), (365), (366) gives:
% 40.65/6.30 | | | | | | | | | (367) $false
% 40.65/6.30 | | | | | | | | |
% 40.65/6.30 | | | | | | | | | CLOSE: (367) is inconsistent.
% 40.65/6.30 | | | | | | | | |
% 40.65/6.30 | | | | | | | | End of split
% 40.65/6.30 | | | | | | | |
% 40.65/6.30 | | | | | | | End of split
% 40.65/6.30 | | | | | | |
% 40.65/6.30 | | | | | | End of split
% 40.65/6.30 | | | | | |
% 40.65/6.30 | | | | | End of split
% 40.65/6.30 | | | | |
% 40.65/6.30 | | | | End of split
% 40.65/6.30 | | | |
% 40.65/6.30 | | | End of split
% 40.65/6.30 | | |
% 40.65/6.30 | | Case 2:
% 40.65/6.30 | | |
% 40.65/6.30 | | | (368) all_19_0 = all_19_1
% 40.65/6.30 | | |
% 40.65/6.30 | | | REDUCE: (36), (368) imply:
% 40.65/6.30 | | | (369) greater_or_equal(all_31_2, all_19_1)
% 40.65/6.30 | | |
% 40.65/6.30 | | | BETA: splitting (27) gives:
% 40.65/6.30 | | |
% 40.65/6.30 | | | Case 1:
% 40.65/6.30 | | | |
% 40.65/6.30 | | | | (370) greater(all_21_0, all_19_0)
% 40.65/6.30 | | | |
% 40.65/6.30 | | | | REDUCE: (368), (370) imply:
% 40.65/6.30 | | | | (371) greater(all_21_0, all_19_1)
% 40.65/6.30 | | | |
% 40.65/6.30 | | | | REF_CLOSE: (1), (5), (7), (8), (19), (21), (24), (33), (40), (49), (51),
% 40.65/6.30 | | | | (215), (216), (218), (219), (371), (mp_greater_transitivity)
% 40.65/6.30 | | | | are inconsistent by sub-proof #3.
% 40.65/6.30 | | | |
% 40.65/6.30 | | | Case 2:
% 40.65/6.30 | | | |
% 40.65/6.30 | | | | (372) all_21_0 = all_19_0 | greater(all_19_0, all_21_0)
% 40.65/6.30 | | | |
% 40.65/6.30 | | | | REF_CLOSE: (1), (5), (7), (8), (19), (21), (24), (38), (39), (41), (45),
% 40.65/6.30 | | | | (50), (368), (369), (372), (mp_greater_transitivity) are
% 40.65/6.30 | | | | inconsistent by sub-proof #5.
% 40.65/6.30 | | | |
% 40.65/6.30 | | | End of split
% 40.65/6.30 | | |
% 40.65/6.30 | | End of split
% 40.65/6.30 | |
% 40.65/6.30 | End of split
% 40.65/6.30 |
% 40.65/6.30 End of proof
% 40.65/6.30
% 40.65/6.30 Sub-proof #1 shows that the following formulas are inconsistent:
% 40.65/6.30 ----------------------------------------------------------------
% 40.65/6.30 (1) growth_rate(efficient_producers, all_29_2) = all_41_0
% 40.65/6.30 (2) greater(zero, all_41_0)
% 40.65/6.30 (3) growth_rate(efficient_producers, all_29_2) = all_29_0
% 40.65/6.30 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.30 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 40.65/6.30 (5) ~ greater(zero, all_29_0)
% 40.65/6.30
% 40.65/6.30 Begin of proof
% 40.65/6.30 |
% 40.65/6.30 | PRED_UNIFY: (2), (5) imply:
% 40.65/6.30 | (6) ~ (all_41_0 = all_29_0)
% 40.65/6.30 |
% 40.65/6.30 | GROUND_INST: instantiating (4) with all_29_0, all_41_0, all_29_2,
% 40.65/6.30 | efficient_producers, simplifying with (1), (3) gives:
% 40.65/6.30 | (7) all_41_0 = all_29_0
% 40.65/6.30 |
% 40.65/6.30 | REDUCE: (6), (7) imply:
% 40.65/6.30 | (8) $false
% 40.65/6.30 |
% 40.65/6.30 | CLOSE: (8) is inconsistent.
% 40.65/6.30 |
% 40.65/6.30 End of proof
% 40.65/6.30
% 40.65/6.30 Sub-proof #2 shows that the following formulas are inconsistent:
% 40.65/6.30 ----------------------------------------------------------------
% 40.65/6.30 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.30 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 40.65/6.30 (2) growth_rate(efficient_producers, all_29_2) = all_29_0
% 40.65/6.30 (3) growth_rate(efficient_producers, all_29_2) = zero
% 40.65/6.30 (4) ~ (all_29_0 = zero)
% 40.65/6.30
% 40.65/6.30 Begin of proof
% 40.65/6.30 |
% 40.65/6.30 | GROUND_INST: instantiating (1) with zero, all_29_0, all_29_2,
% 40.65/6.30 | efficient_producers, simplifying with (2), (3) gives:
% 40.65/6.30 | (5) all_29_0 = zero
% 40.65/6.30 |
% 40.65/6.30 | REDUCE: (4), (5) imply:
% 40.65/6.30 | (6) $false
% 40.65/6.30 |
% 40.65/6.30 | CLOSE: (6) is inconsistent.
% 40.65/6.30 |
% 40.65/6.30 End of proof
% 40.65/6.30
% 40.65/6.30 Sub-proof #3 shows that the following formulas are inconsistent:
% 40.65/6.30 ----------------------------------------------------------------
% 40.65/6.30 (1) growth_rate(first_movers, all_29_2) = all_29_0
% 40.65/6.30 (2) ~ (all_38_1 = zero)
% 40.65/6.30 (3) $i(all_21_0)
% 40.65/6.30 (4) greater(all_21_0, all_19_1)
% 40.65/6.30 (5) (all_41_0 = zero & all_41_1 = zero & growth_rate(efficient_producers,
% 40.65/6.30 all_29_2) = zero & growth_rate(first_movers, all_29_2) = zero) |
% 40.65/6.30 (equilibrium(all_11_0) = all_41_2 & $i(all_41_2) & ~
% 40.65/6.30 greater_or_equal(all_29_2, all_41_2)) |
% 40.65/6.30 (growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.30 growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0) &
% 40.65/6.30 $i(all_41_1) & greater(all_41_0, zero) & greater(zero, all_41_1)) |
% 40.65/6.30 (growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.30 growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0) &
% 40.65/6.30 $i(all_41_1) & greater(all_41_1, zero) & greater(zero, all_41_0))
% 40.65/6.30 (6) $i(all_19_1)
% 40.65/6.30 (7) all_29_2 = all_21_0 | greater(all_29_2, all_21_0)
% 40.65/6.30 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 40.65/6.30 $i(v0) | ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 40.65/6.30 (9) greater(all_38_1, all_29_0)
% 40.65/6.30 (10) $i(zero)
% 40.65/6.30 (11) $i(all_29_2)
% 40.65/6.30 (12) growth_rate(efficient_producers, all_29_2) = all_38_1
% 40.65/6.30 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (equilibrium(v2)
% 40.65/6.30 = v1) | ~ (equilibrium(v2) = v0))
% 40.65/6.30 (14) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1)
% 40.65/6.30 | greater_or_equal(v0, v1))
% 40.65/6.30 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.30 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 40.65/6.30 (16) ~ greater(zero, all_29_0)
% 40.65/6.30 (17) equilibrium(all_11_0) = all_19_1
% 40.65/6.30
% 40.65/6.30 Begin of proof
% 40.65/6.30 |
% 40.65/6.30 | GROUND_INST: instantiating (14) with all_21_0, all_19_1, simplifying with (3),
% 40.65/6.30 | (4), (6) gives:
% 40.65/6.30 | (18) greater_or_equal(all_21_0, all_19_1)
% 40.65/6.30 |
% 40.65/6.30 | BETA: splitting (7) gives:
% 40.65/6.30 |
% 40.65/6.30 | Case 1:
% 40.65/6.30 | |
% 40.65/6.30 | | (19) greater(all_29_2, all_21_0)
% 40.65/6.30 | |
% 40.65/6.30 | | GROUND_INST: instantiating (8) with all_29_2, all_21_0, all_19_1,
% 40.65/6.30 | | simplifying with (3), (4), (6), (11), (19) gives:
% 40.65/6.31 | | (20) greater(all_29_2, all_19_1)
% 40.65/6.31 | |
% 40.65/6.31 | | BETA: splitting (5) gives:
% 40.65/6.31 | |
% 40.65/6.31 | | Case 1:
% 40.65/6.31 | | |
% 40.65/6.31 | | | (21) (all_41_0 = zero & all_41_1 = zero &
% 40.65/6.31 | | | growth_rate(efficient_producers, all_29_2) = zero &
% 40.65/6.31 | | | growth_rate(first_movers, all_29_2) = zero) |
% 40.65/6.31 | | | (equilibrium(all_11_0) = all_41_2 & $i(all_41_2) & ~
% 40.65/6.31 | | | greater_or_equal(all_29_2, all_41_2))
% 40.65/6.31 | | |
% 40.65/6.31 | | | BETA: splitting (21) gives:
% 40.65/6.31 | | |
% 40.65/6.31 | | | Case 1:
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | (22) all_41_0 = zero & all_41_1 = zero &
% 40.65/6.31 | | | | growth_rate(efficient_producers, all_29_2) = zero &
% 40.65/6.31 | | | | growth_rate(first_movers, all_29_2) = zero
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | ALPHA: (22) implies:
% 40.65/6.31 | | | | (23) growth_rate(efficient_producers, all_29_2) = zero
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | GROUND_INST: instantiating (15) with all_38_1, zero, all_29_2,
% 40.65/6.31 | | | | efficient_producers, simplifying with (12), (23) gives:
% 40.65/6.31 | | | | (24) all_38_1 = zero
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | REDUCE: (2), (24) imply:
% 40.65/6.31 | | | | (25) $false
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | CLOSE: (25) is inconsistent.
% 40.65/6.31 | | | |
% 40.65/6.31 | | | Case 2:
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | (26) equilibrium(all_11_0) = all_41_2 & $i(all_41_2) & ~
% 40.65/6.31 | | | | greater_or_equal(all_29_2, all_41_2)
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | ALPHA: (26) implies:
% 40.65/6.31 | | | | (27) ~ greater_or_equal(all_29_2, all_41_2)
% 40.65/6.31 | | | | (28) $i(all_41_2)
% 40.65/6.31 | | | | (29) equilibrium(all_11_0) = all_41_2
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | REF_CLOSE: (11), (13), (14), (17), (20), (27), (28), (29) are
% 40.65/6.31 | | | | inconsistent by sub-proof #20.
% 40.65/6.31 | | | |
% 40.65/6.31 | | | End of split
% 40.65/6.31 | | |
% 40.65/6.31 | | Case 2:
% 40.65/6.31 | | |
% 40.65/6.31 | | | (30) (growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.31 | | | growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0) &
% 40.65/6.31 | | | $i(all_41_1) & greater(all_41_0, zero) & greater(zero,
% 40.65/6.31 | | | all_41_1)) | (growth_rate(efficient_producers, all_29_2) =
% 40.65/6.31 | | | all_41_0 & growth_rate(first_movers, all_29_2) = all_41_1 &
% 40.65/6.31 | | | $i(all_41_0) & $i(all_41_1) & greater(all_41_1, zero) &
% 40.65/6.31 | | | greater(zero, all_41_0))
% 40.65/6.31 | | |
% 40.65/6.31 | | | BETA: splitting (30) gives:
% 40.65/6.31 | | |
% 40.65/6.31 | | | Case 1:
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | (31) growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.31 | | | | growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0) &
% 40.65/6.31 | | | | $i(all_41_1) & greater(all_41_0, zero) & greater(zero, all_41_1)
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | ALPHA: (31) implies:
% 40.65/6.31 | | | | (32) greater(zero, all_41_1)
% 40.65/6.31 | | | | (33) growth_rate(first_movers, all_29_2) = all_41_1
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | REF_CLOSE: (1), (15), (16), (32), (33) are inconsistent by sub-proof #4.
% 40.65/6.31 | | | |
% 40.65/6.31 | | | Case 2:
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | (34) growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.31 | | | | growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0) &
% 40.65/6.31 | | | | $i(all_41_1) & greater(all_41_1, zero) & greater(zero, all_41_0)
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | ALPHA: (34) implies:
% 40.65/6.31 | | | | (35) greater(zero, all_41_0)
% 40.65/6.31 | | | | (36) $i(all_41_1)
% 40.65/6.31 | | | | (37) $i(all_41_0)
% 40.65/6.31 | | | | (38) growth_rate(first_movers, all_29_2) = all_41_1
% 40.65/6.31 | | | | (39) growth_rate(efficient_producers, all_29_2) = all_41_0
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | GROUND_INST: instantiating (15) with all_29_0, all_41_1, all_29_2,
% 40.65/6.31 | | | | first_movers, simplifying with (1), (38) gives:
% 40.65/6.31 | | | | (40) all_41_1 = all_29_0
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | GROUND_INST: instantiating (15) with all_38_1, all_41_0, all_29_2,
% 40.65/6.31 | | | | efficient_producers, simplifying with (12), (39) gives:
% 40.65/6.31 | | | | (41) all_41_0 = all_38_1
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | REDUCE: (37), (41) imply:
% 40.65/6.31 | | | | (42) $i(all_38_1)
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | REDUCE: (36), (40) imply:
% 40.65/6.31 | | | | (43) $i(all_29_0)
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | REDUCE: (35), (41) imply:
% 40.65/6.31 | | | | (44) greater(zero, all_38_1)
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | GROUND_INST: instantiating (8) with zero, all_38_1, all_29_0,
% 40.65/6.31 | | | | simplifying with (9), (10), (16), (42), (43), (44) gives:
% 40.65/6.31 | | | | (45) $false
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | CLOSE: (45) is inconsistent.
% 40.65/6.31 | | | |
% 40.65/6.31 | | | End of split
% 40.65/6.31 | | |
% 40.65/6.31 | | End of split
% 40.65/6.31 | |
% 40.65/6.31 | Case 2:
% 40.65/6.31 | |
% 40.65/6.31 | | (46) all_29_2 = all_21_0
% 40.65/6.31 | |
% 40.65/6.31 | | REDUCE: (12), (46) imply:
% 40.65/6.31 | | (47) growth_rate(efficient_producers, all_21_0) = all_38_1
% 40.65/6.31 | |
% 40.65/6.31 | | REDUCE: (1), (46) imply:
% 40.65/6.31 | | (48) growth_rate(first_movers, all_21_0) = all_29_0
% 40.65/6.31 | |
% 40.65/6.31 | | BETA: splitting (5) gives:
% 40.65/6.31 | |
% 40.65/6.31 | | Case 1:
% 40.65/6.31 | | |
% 40.65/6.31 | | | (49) (all_41_0 = zero & all_41_1 = zero &
% 40.65/6.31 | | | growth_rate(efficient_producers, all_29_2) = zero &
% 40.65/6.31 | | | growth_rate(first_movers, all_29_2) = zero) |
% 40.65/6.31 | | | (equilibrium(all_11_0) = all_41_2 & $i(all_41_2) & ~
% 40.65/6.31 | | | greater_or_equal(all_29_2, all_41_2))
% 40.65/6.31 | | |
% 40.65/6.31 | | | BETA: splitting (49) gives:
% 40.65/6.31 | | |
% 40.65/6.31 | | | Case 1:
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | (50) all_41_0 = zero & all_41_1 = zero &
% 40.65/6.31 | | | | growth_rate(efficient_producers, all_29_2) = zero &
% 40.65/6.31 | | | | growth_rate(first_movers, all_29_2) = zero
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | ALPHA: (50) implies:
% 40.65/6.31 | | | | (51) growth_rate(efficient_producers, all_29_2) = zero
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | REDUCE: (46), (51) imply:
% 40.65/6.31 | | | | (52) growth_rate(efficient_producers, all_21_0) = zero
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | GROUND_INST: instantiating (15) with zero, all_38_1, all_21_0,
% 40.65/6.31 | | | | efficient_producers, simplifying with (47), (52) gives:
% 40.65/6.31 | | | | (53) all_38_1 = zero
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | REDUCE: (2), (53) imply:
% 40.65/6.31 | | | | (54) $false
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | CLOSE: (54) is inconsistent.
% 40.65/6.31 | | | |
% 40.65/6.31 | | | Case 2:
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | (55) equilibrium(all_11_0) = all_41_2 & $i(all_41_2) & ~
% 40.65/6.31 | | | | greater_or_equal(all_29_2, all_41_2)
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | ALPHA: (55) implies:
% 40.65/6.31 | | | | (56) ~ greater_or_equal(all_29_2, all_41_2)
% 40.65/6.31 | | | | (57) equilibrium(all_11_0) = all_41_2
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | REDUCE: (46), (56) imply:
% 40.65/6.31 | | | | (58) ~ greater_or_equal(all_21_0, all_41_2)
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | REF_CLOSE: (13), (17), (18), (57), (58) are inconsistent by sub-proof
% 40.65/6.31 | | | | #16.
% 40.65/6.31 | | | |
% 40.65/6.31 | | | End of split
% 40.65/6.31 | | |
% 40.65/6.31 | | Case 2:
% 40.65/6.31 | | |
% 40.65/6.31 | | | (59) (growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.31 | | | growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0) &
% 40.65/6.31 | | | $i(all_41_1) & greater(all_41_0, zero) & greater(zero,
% 40.65/6.31 | | | all_41_1)) | (growth_rate(efficient_producers, all_29_2) =
% 40.65/6.31 | | | all_41_0 & growth_rate(first_movers, all_29_2) = all_41_1 &
% 40.65/6.31 | | | $i(all_41_0) & $i(all_41_1) & greater(all_41_1, zero) &
% 40.65/6.31 | | | greater(zero, all_41_0))
% 40.65/6.31 | | |
% 40.65/6.31 | | | BETA: splitting (59) gives:
% 40.65/6.31 | | |
% 40.65/6.31 | | | Case 1:
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | (60) growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.31 | | | | growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0) &
% 40.65/6.31 | | | | $i(all_41_1) & greater(all_41_0, zero) & greater(zero, all_41_1)
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | ALPHA: (60) implies:
% 40.65/6.31 | | | | (61) greater(zero, all_41_1)
% 40.65/6.31 | | | | (62) growth_rate(first_movers, all_29_2) = all_41_1
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | REDUCE: (46), (62) imply:
% 40.65/6.31 | | | | (63) growth_rate(first_movers, all_21_0) = all_41_1
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | PRED_UNIFY: (16), (61) imply:
% 40.65/6.31 | | | | (64) ~ (all_41_1 = all_29_0)
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | GROUND_INST: instantiating (15) with all_29_0, all_41_1, all_21_0,
% 40.65/6.31 | | | | first_movers, simplifying with (48), (63) gives:
% 40.65/6.31 | | | | (65) all_41_1 = all_29_0
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | REDUCE: (64), (65) imply:
% 40.65/6.31 | | | | (66) $false
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | CLOSE: (66) is inconsistent.
% 40.65/6.31 | | | |
% 40.65/6.31 | | | Case 2:
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | (67) growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.31 | | | | growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0) &
% 40.65/6.31 | | | | $i(all_41_1) & greater(all_41_1, zero) & greater(zero, all_41_0)
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | ALPHA: (67) implies:
% 40.65/6.31 | | | | (68) greater(zero, all_41_0)
% 40.65/6.31 | | | | (69) $i(all_41_1)
% 40.65/6.31 | | | | (70) $i(all_41_0)
% 40.65/6.31 | | | | (71) growth_rate(first_movers, all_29_2) = all_41_1
% 40.65/6.31 | | | | (72) growth_rate(efficient_producers, all_29_2) = all_41_0
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | REDUCE: (46), (72) imply:
% 40.65/6.31 | | | | (73) growth_rate(efficient_producers, all_21_0) = all_41_0
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | REDUCE: (46), (71) imply:
% 40.65/6.31 | | | | (74) growth_rate(first_movers, all_21_0) = all_41_1
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | GROUND_INST: instantiating (15) with all_29_0, all_41_1, all_21_0,
% 40.65/6.31 | | | | first_movers, simplifying with (48), (74) gives:
% 40.65/6.31 | | | | (75) all_41_1 = all_29_0
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | GROUND_INST: instantiating (15) with all_38_1, all_41_0, all_21_0,
% 40.65/6.31 | | | | efficient_producers, simplifying with (47), (73) gives:
% 40.65/6.31 | | | | (76) all_41_0 = all_38_1
% 40.65/6.31 | | | |
% 40.65/6.31 | | | | REDUCE: (70), (76) imply:
% 40.65/6.32 | | | | (77) $i(all_38_1)
% 40.65/6.32 | | | |
% 40.65/6.32 | | | | REDUCE: (69), (75) imply:
% 40.65/6.32 | | | | (78) $i(all_29_0)
% 40.65/6.32 | | | |
% 40.65/6.32 | | | | REDUCE: (68), (76) imply:
% 40.65/6.32 | | | | (79) greater(zero, all_38_1)
% 40.65/6.32 | | | |
% 40.65/6.32 | | | | GROUND_INST: instantiating (8) with zero, all_38_1, all_29_0,
% 40.65/6.32 | | | | simplifying with (9), (10), (16), (77), (78), (79) gives:
% 40.65/6.32 | | | | (80) $false
% 40.65/6.32 | | | |
% 40.65/6.32 | | | | CLOSE: (80) is inconsistent.
% 40.65/6.32 | | | |
% 40.65/6.32 | | | End of split
% 40.65/6.32 | | |
% 40.65/6.32 | | End of split
% 40.65/6.32 | |
% 40.65/6.32 | End of split
% 40.65/6.32 |
% 40.65/6.32 End of proof
% 40.65/6.32
% 40.65/6.32 Sub-proof #4 shows that the following formulas are inconsistent:
% 40.65/6.32 ----------------------------------------------------------------
% 40.65/6.32 (1) growth_rate(first_movers, all_29_2) = all_29_0
% 40.65/6.32 (2) growth_rate(first_movers, all_29_2) = all_41_1
% 40.65/6.32 (3) greater(zero, all_41_1)
% 40.65/6.32 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.32 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 40.65/6.32 (5) ~ greater(zero, all_29_0)
% 40.65/6.32
% 40.65/6.32 Begin of proof
% 40.65/6.32 |
% 40.65/6.32 | PRED_UNIFY: (3), (5) imply:
% 40.65/6.32 | (6) ~ (all_41_1 = all_29_0)
% 40.65/6.32 |
% 40.65/6.32 | GROUND_INST: instantiating (4) with all_29_0, all_41_1, all_29_2,
% 40.65/6.32 | first_movers, simplifying with (1), (2) gives:
% 40.65/6.32 | (7) all_41_1 = all_29_0
% 40.65/6.32 |
% 40.65/6.32 | REDUCE: (6), (7) imply:
% 40.65/6.32 | (8) $false
% 40.65/6.32 |
% 40.65/6.32 | CLOSE: (8) is inconsistent.
% 40.65/6.32 |
% 40.65/6.32 End of proof
% 40.65/6.32
% 40.65/6.32 Sub-proof #5 shows that the following formulas are inconsistent:
% 40.65/6.32 ----------------------------------------------------------------
% 40.65/6.32 (1) ~ greater_or_equal(all_31_2, all_21_0) | ? [v0: $i] : ? [v1: $i] :
% 40.65/6.32 (growth_rate(efficient_producers, all_31_2) = v0 &
% 40.65/6.32 growth_rate(first_movers, all_31_2) = v1 & $i(v1) & $i(v0) &
% 40.65/6.32 greater(v0, v1))
% 40.65/6.32 (2) $i(all_21_0)
% 40.65/6.32 (3) $i(all_31_2)
% 40.65/6.32 (4) (growth_rate(efficient_producers, all_31_2) = all_31_1 & $i(all_31_1) &
% 40.65/6.32 ~ greater(all_31_1, zero)) | (growth_rate(first_movers, all_31_2) =
% 40.65/6.32 all_31_0 & $i(all_31_0) & ~ greater(zero, all_31_0))
% 40.65/6.32 (5) $i(all_19_1)
% 40.65/6.32 (6) (all_40_0 = zero & all_40_1 = zero & growth_rate(efficient_producers,
% 40.65/6.32 all_31_2) = zero & growth_rate(first_movers, all_31_2) = zero) |
% 40.65/6.32 (equilibrium(all_11_0) = all_40_2 & $i(all_40_2) & ~
% 40.65/6.32 greater_or_equal(all_31_2, all_40_2)) |
% 40.65/6.32 (growth_rate(efficient_producers, all_31_2) = all_40_0 &
% 40.65/6.32 growth_rate(first_movers, all_31_2) = all_40_1 & $i(all_40_0) &
% 40.65/6.32 $i(all_40_1) & greater(all_40_0, zero) & greater(zero, all_40_1)) |
% 40.65/6.32 (growth_rate(efficient_producers, all_31_2) = all_40_0 &
% 40.65/6.32 growth_rate(first_movers, all_31_2) = all_40_1 & $i(all_40_0) &
% 40.65/6.32 $i(all_40_1) & greater(all_40_1, zero) & greater(zero, all_40_0))
% 40.65/6.32 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 40.65/6.32 $i(v0) | ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 40.65/6.32 (8) $i(zero)
% 40.65/6.32 (9) greater_or_equal(all_31_2, all_19_1)
% 40.65/6.32 (10) all_19_0 = all_19_1
% 40.65/6.32 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (equilibrium(v2)
% 40.65/6.32 = v1) | ~ (equilibrium(v2) = v0))
% 40.65/6.32 (12) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1)
% 40.65/6.32 | greater_or_equal(v0, v1))
% 40.65/6.32 (13) all_21_0 = all_19_0 | greater(all_19_0, all_21_0)
% 40.65/6.32 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.32 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 40.65/6.32 (15) equilibrium(all_11_0) = all_19_1
% 40.65/6.32 (16) all_31_2 = all_19_0 | greater(all_31_2, all_19_0)
% 40.65/6.32
% 40.65/6.32 Begin of proof
% 40.65/6.32 |
% 40.65/6.32 | BETA: splitting (4) gives:
% 40.65/6.32 |
% 40.65/6.32 | Case 1:
% 40.65/6.32 | |
% 40.65/6.32 | | (17) growth_rate(efficient_producers, all_31_2) = all_31_1 & $i(all_31_1)
% 40.65/6.32 | | & ~ greater(all_31_1, zero)
% 40.65/6.32 | |
% 40.65/6.32 | | ALPHA: (17) implies:
% 40.65/6.32 | | (18) ~ greater(all_31_1, zero)
% 40.65/6.32 | | (19) growth_rate(efficient_producers, all_31_2) = all_31_1
% 40.65/6.32 | |
% 40.65/6.32 | | BETA: splitting (1) gives:
% 40.65/6.32 | |
% 40.65/6.32 | | Case 1:
% 40.65/6.32 | | |
% 40.65/6.32 | | | (20) ~ greater_or_equal(all_31_2, all_21_0)
% 40.65/6.32 | | |
% 40.65/6.32 | | | PRED_UNIFY: (9), (20) imply:
% 40.65/6.32 | | | (21) ~ (all_21_0 = all_19_1)
% 40.65/6.32 | | |
% 40.65/6.32 | | | REF_CLOSE: (2), (3), (5), (7), (10), (12), (13), (16), (20), (21) are
% 40.65/6.32 | | | inconsistent by sub-proof #6.
% 40.65/6.32 | | |
% 40.65/6.32 | | Case 2:
% 40.65/6.32 | | |
% 40.65/6.32 | | | (22) ? [v0: $i] : ? [v1: $i] : (growth_rate(efficient_producers,
% 40.65/6.32 | | | all_31_2) = v0 & growth_rate(first_movers, all_31_2) = v1 &
% 40.65/6.32 | | | $i(v1) & $i(v0) & greater(v0, v1))
% 40.65/6.32 | | |
% 40.65/6.32 | | | DELTA: instantiating (22) with fresh symbols all_106_0, all_106_1 gives:
% 40.65/6.32 | | | (23) growth_rate(efficient_producers, all_31_2) = all_106_1 &
% 40.65/6.32 | | | growth_rate(first_movers, all_31_2) = all_106_0 & $i(all_106_0) &
% 40.65/6.32 | | | $i(all_106_1) & greater(all_106_1, all_106_0)
% 40.65/6.32 | | |
% 40.65/6.32 | | | REF_CLOSE: (6), (7), (8), (9), (11), (14), (15), (18), (19), (23) are
% 40.65/6.32 | | | inconsistent by sub-proof #11.
% 40.65/6.32 | | |
% 40.65/6.32 | | End of split
% 40.65/6.32 | |
% 40.65/6.32 | Case 2:
% 40.65/6.32 | |
% 40.65/6.32 | | (24) growth_rate(first_movers, all_31_2) = all_31_0 & $i(all_31_0) & ~
% 40.65/6.32 | | greater(zero, all_31_0)
% 40.65/6.32 | |
% 40.65/6.32 | | ALPHA: (24) implies:
% 40.65/6.32 | | (25) ~ greater(zero, all_31_0)
% 40.65/6.32 | | (26) growth_rate(first_movers, all_31_2) = all_31_0
% 40.65/6.32 | |
% 40.65/6.32 | | BETA: splitting (1) gives:
% 40.65/6.32 | |
% 40.65/6.32 | | Case 1:
% 40.65/6.32 | | |
% 40.65/6.32 | | | (27) ~ greater_or_equal(all_31_2, all_21_0)
% 40.65/6.32 | | |
% 40.65/6.32 | | | PRED_UNIFY: (9), (27) imply:
% 40.65/6.32 | | | (28) ~ (all_21_0 = all_19_1)
% 40.65/6.32 | | |
% 40.65/6.32 | | | REF_CLOSE: (2), (3), (5), (7), (10), (12), (13), (16), (27), (28) are
% 40.65/6.32 | | | inconsistent by sub-proof #6.
% 40.65/6.32 | | |
% 40.65/6.32 | | Case 2:
% 40.65/6.32 | | |
% 40.65/6.32 | | | (29) ? [v0: $i] : ? [v1: $i] : (growth_rate(efficient_producers,
% 40.65/6.32 | | | all_31_2) = v0 & growth_rate(first_movers, all_31_2) = v1 &
% 40.65/6.32 | | | $i(v1) & $i(v0) & greater(v0, v1))
% 40.65/6.32 | | |
% 40.65/6.32 | | | DELTA: instantiating (29) with fresh symbols all_106_0, all_106_1 gives:
% 40.65/6.32 | | | (30) growth_rate(efficient_producers, all_31_2) = all_106_1 &
% 40.65/6.32 | | | growth_rate(first_movers, all_31_2) = all_106_0 & $i(all_106_0) &
% 40.65/6.32 | | | $i(all_106_1) & greater(all_106_1, all_106_0)
% 40.65/6.32 | | |
% 40.65/6.32 | | | REF_CLOSE: (6), (7), (8), (9), (11), (14), (15), (25), (26), (30) are
% 40.65/6.32 | | | inconsistent by sub-proof #7.
% 40.65/6.32 | | |
% 40.65/6.32 | | End of split
% 40.65/6.32 | |
% 40.65/6.32 | End of split
% 40.65/6.32 |
% 40.65/6.32 End of proof
% 40.65/6.32
% 40.65/6.32 Sub-proof #6 shows that the following formulas are inconsistent:
% 40.65/6.32 ----------------------------------------------------------------
% 40.65/6.32 (1) $i(all_21_0)
% 40.65/6.32 (2) $i(all_31_2)
% 40.65/6.32 (3) $i(all_19_1)
% 40.65/6.32 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 40.65/6.32 $i(v0) | ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 40.65/6.32 (5) all_19_0 = all_19_1
% 40.65/6.32 (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1) |
% 40.65/6.32 greater_or_equal(v0, v1))
% 40.65/6.33 (7) all_21_0 = all_19_0 | greater(all_19_0, all_21_0)
% 40.65/6.33 (8) ~ (all_21_0 = all_19_1)
% 40.65/6.33 (9) ~ greater_or_equal(all_31_2, all_21_0)
% 40.65/6.33 (10) all_31_2 = all_19_0 | greater(all_31_2, all_19_0)
% 40.65/6.33
% 40.65/6.33 Begin of proof
% 40.65/6.33 |
% 40.65/6.33 | BETA: splitting (7) gives:
% 40.65/6.33 |
% 40.65/6.33 | Case 1:
% 40.65/6.33 | |
% 40.65/6.33 | | (11) greater(all_19_0, all_21_0)
% 40.65/6.33 | |
% 40.65/6.33 | | REDUCE: (5), (11) imply:
% 40.65/6.33 | | (12) greater(all_19_1, all_21_0)
% 40.65/6.33 | |
% 40.65/6.33 | | GROUND_INST: instantiating (6) with all_19_1, all_21_0, simplifying with
% 40.65/6.33 | | (1), (3), (12) gives:
% 40.65/6.33 | | (13) greater_or_equal(all_19_1, all_21_0)
% 40.65/6.33 | |
% 40.65/6.33 | | PRED_UNIFY: (9), (13) imply:
% 40.65/6.33 | | (14) ~ (all_31_2 = all_19_1)
% 40.65/6.33 | |
% 40.65/6.33 | | BETA: splitting (10) gives:
% 40.65/6.33 | |
% 40.65/6.33 | | Case 1:
% 40.65/6.33 | | |
% 40.65/6.33 | | | (15) greater(all_31_2, all_19_0)
% 40.65/6.33 | | |
% 40.65/6.33 | | | REDUCE: (5), (15) imply:
% 40.65/6.33 | | | (16) greater(all_31_2, all_19_1)
% 40.65/6.33 | | |
% 40.65/6.33 | | | GROUND_INST: instantiating (4) with all_31_2, all_19_1, all_21_0,
% 40.65/6.33 | | | simplifying with (1), (2), (3), (12), (16) gives:
% 40.65/6.33 | | | (17) greater(all_31_2, all_21_0)
% 40.65/6.33 | | |
% 40.65/6.33 | | | GROUND_INST: instantiating (6) with all_31_2, all_21_0, simplifying with
% 40.65/6.33 | | | (1), (2), (9), (17) gives:
% 40.65/6.33 | | | (18) $false
% 40.65/6.33 | | |
% 40.65/6.33 | | | CLOSE: (18) is inconsistent.
% 40.65/6.33 | | |
% 40.65/6.33 | | Case 2:
% 40.65/6.33 | | |
% 40.65/6.33 | | | (19) all_31_2 = all_19_0
% 40.65/6.33 | | |
% 40.65/6.33 | | | COMBINE_EQS: (5), (19) imply:
% 40.65/6.33 | | | (20) all_31_2 = all_19_1
% 40.65/6.33 | | |
% 40.65/6.33 | | | REDUCE: (14), (20) imply:
% 40.65/6.33 | | | (21) $false
% 40.65/6.33 | | |
% 40.65/6.33 | | | CLOSE: (21) is inconsistent.
% 40.65/6.33 | | |
% 40.65/6.33 | | End of split
% 40.65/6.33 | |
% 40.65/6.33 | Case 2:
% 40.65/6.33 | |
% 40.65/6.33 | | (22) all_21_0 = all_19_0
% 40.65/6.33 | |
% 40.65/6.33 | | COMBINE_EQS: (5), (22) imply:
% 40.65/6.33 | | (23) all_21_0 = all_19_1
% 40.65/6.33 | |
% 40.65/6.33 | | REDUCE: (8), (23) imply:
% 40.65/6.33 | | (24) $false
% 40.65/6.33 | |
% 40.65/6.33 | | CLOSE: (24) is inconsistent.
% 40.65/6.33 | |
% 40.65/6.33 | End of split
% 40.65/6.33 |
% 40.65/6.33 End of proof
% 40.65/6.33
% 40.65/6.33 Sub-proof #7 shows that the following formulas are inconsistent:
% 40.65/6.33 ----------------------------------------------------------------
% 40.65/6.33 (1) ~ greater(zero, all_31_0)
% 40.65/6.33 (2) growth_rate(efficient_producers, all_31_2) = all_106_1 &
% 40.65/6.33 growth_rate(first_movers, all_31_2) = all_106_0 & $i(all_106_0) &
% 40.65/6.33 $i(all_106_1) & greater(all_106_1, all_106_0)
% 40.65/6.33 (3) (all_40_0 = zero & all_40_1 = zero & growth_rate(efficient_producers,
% 40.65/6.33 all_31_2) = zero & growth_rate(first_movers, all_31_2) = zero) |
% 40.65/6.33 (equilibrium(all_11_0) = all_40_2 & $i(all_40_2) & ~
% 40.65/6.33 greater_or_equal(all_31_2, all_40_2)) |
% 40.65/6.33 (growth_rate(efficient_producers, all_31_2) = all_40_0 &
% 40.65/6.33 growth_rate(first_movers, all_31_2) = all_40_1 & $i(all_40_0) &
% 40.65/6.33 $i(all_40_1) & greater(all_40_0, zero) & greater(zero, all_40_1)) |
% 40.65/6.33 (growth_rate(efficient_producers, all_31_2) = all_40_0 &
% 40.65/6.33 growth_rate(first_movers, all_31_2) = all_40_1 & $i(all_40_0) &
% 40.65/6.33 $i(all_40_1) & greater(all_40_1, zero) & greater(zero, all_40_0))
% 40.65/6.33 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 40.65/6.33 $i(v0) | ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 40.65/6.33 (5) $i(zero)
% 40.65/6.33 (6) greater_or_equal(all_31_2, all_19_1)
% 40.65/6.33 (7) growth_rate(first_movers, all_31_2) = all_31_0
% 40.65/6.33 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (equilibrium(v2)
% 40.65/6.33 = v1) | ~ (equilibrium(v2) = v0))
% 40.65/6.33 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.33 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 40.65/6.33 (10) equilibrium(all_11_0) = all_19_1
% 40.65/6.33
% 40.65/6.33 Begin of proof
% 40.65/6.33 |
% 40.65/6.33 | ALPHA: (2) implies:
% 40.65/6.33 | (11) greater(all_106_1, all_106_0)
% 40.65/6.33 | (12) $i(all_106_1)
% 40.65/6.33 | (13) growth_rate(first_movers, all_31_2) = all_106_0
% 40.65/6.33 | (14) growth_rate(efficient_producers, all_31_2) = all_106_1
% 40.65/6.33 |
% 40.65/6.33 | GROUND_INST: instantiating (9) with all_31_0, all_106_0, all_31_2,
% 40.65/6.33 | first_movers, simplifying with (7), (13) gives:
% 40.65/6.33 | (15) all_106_0 = all_31_0
% 40.65/6.33 |
% 40.65/6.33 | REDUCE: (11), (15) imply:
% 40.65/6.33 | (16) greater(all_106_1, all_31_0)
% 40.65/6.33 |
% 40.65/6.33 | PRED_UNIFY: (1), (16) imply:
% 40.65/6.33 | (17) ~ (all_106_1 = zero)
% 40.65/6.33 |
% 40.65/6.33 | BETA: splitting (3) gives:
% 40.65/6.33 |
% 40.65/6.33 | Case 1:
% 40.65/6.33 | |
% 40.65/6.33 | | (18) (all_40_0 = zero & all_40_1 = zero &
% 40.65/6.33 | | growth_rate(efficient_producers, all_31_2) = zero &
% 40.65/6.33 | | growth_rate(first_movers, all_31_2) = zero) |
% 40.65/6.33 | | (equilibrium(all_11_0) = all_40_2 & $i(all_40_2) & ~
% 40.65/6.33 | | greater_or_equal(all_31_2, all_40_2))
% 40.65/6.33 | |
% 40.65/6.33 | | BETA: splitting (18) gives:
% 40.65/6.33 | |
% 40.65/6.33 | | Case 1:
% 40.65/6.33 | | |
% 40.65/6.33 | | | (19) all_40_0 = zero & all_40_1 = zero &
% 40.65/6.33 | | | growth_rate(efficient_producers, all_31_2) = zero &
% 40.65/6.33 | | | growth_rate(first_movers, all_31_2) = zero
% 40.65/6.33 | | |
% 40.65/6.33 | | | ALPHA: (19) implies:
% 40.65/6.33 | | | (20) growth_rate(efficient_producers, all_31_2) = zero
% 40.65/6.33 | | |
% 40.65/6.33 | | | GROUND_INST: instantiating (9) with all_106_1, zero, all_31_2,
% 40.65/6.33 | | | efficient_producers, simplifying with (14), (20) gives:
% 40.65/6.33 | | | (21) all_106_1 = zero
% 40.65/6.33 | | |
% 40.65/6.33 | | | REDUCE: (17), (21) imply:
% 40.65/6.33 | | | (22) $false
% 40.65/6.33 | | |
% 40.65/6.33 | | | CLOSE: (22) is inconsistent.
% 40.65/6.33 | | |
% 40.65/6.33 | | Case 2:
% 40.65/6.33 | | |
% 40.65/6.33 | | | (23) equilibrium(all_11_0) = all_40_2 & $i(all_40_2) & ~
% 40.65/6.33 | | | greater_or_equal(all_31_2, all_40_2)
% 40.65/6.33 | | |
% 40.65/6.33 | | | ALPHA: (23) implies:
% 40.65/6.33 | | | (24) ~ greater_or_equal(all_31_2, all_40_2)
% 40.65/6.33 | | | (25) equilibrium(all_11_0) = all_40_2
% 40.65/6.33 | | |
% 40.65/6.33 | | | REF_CLOSE: (6), (8), (10), (24), (25) are inconsistent by sub-proof #13.
% 40.65/6.33 | | |
% 40.65/6.33 | | End of split
% 40.65/6.33 | |
% 40.65/6.33 | Case 2:
% 40.65/6.33 | |
% 40.65/6.33 | | (26) (growth_rate(efficient_producers, all_31_2) = all_40_0 &
% 40.65/6.33 | | growth_rate(first_movers, all_31_2) = all_40_1 & $i(all_40_0) &
% 40.65/6.33 | | $i(all_40_1) & greater(all_40_0, zero) & greater(zero, all_40_1))
% 40.65/6.33 | | | (growth_rate(efficient_producers, all_31_2) = all_40_0 &
% 40.65/6.33 | | growth_rate(first_movers, all_31_2) = all_40_1 & $i(all_40_0) &
% 40.65/6.33 | | $i(all_40_1) & greater(all_40_1, zero) & greater(zero, all_40_0))
% 40.65/6.33 | |
% 40.65/6.33 | | BETA: splitting (26) gives:
% 40.65/6.33 | |
% 40.65/6.33 | | Case 1:
% 40.65/6.33 | | |
% 40.65/6.33 | | | (27) growth_rate(efficient_producers, all_31_2) = all_40_0 &
% 40.65/6.33 | | | growth_rate(first_movers, all_31_2) = all_40_1 & $i(all_40_0) &
% 40.65/6.33 | | | $i(all_40_1) & greater(all_40_0, zero) & greater(zero, all_40_1)
% 40.65/6.33 | | |
% 40.65/6.33 | | | ALPHA: (27) implies:
% 40.65/6.33 | | | (28) greater(zero, all_40_1)
% 40.65/6.33 | | | (29) growth_rate(first_movers, all_31_2) = all_40_1
% 40.65/6.33 | | |
% 40.65/6.33 | | | REF_CLOSE: (1), (7), (9), (28), (29) are inconsistent by sub-proof #8.
% 40.65/6.33 | | |
% 40.65/6.33 | | Case 2:
% 40.65/6.33 | | |
% 40.65/6.33 | | | (30) growth_rate(efficient_producers, all_31_2) = all_40_0 &
% 40.65/6.33 | | | growth_rate(first_movers, all_31_2) = all_40_1 & $i(all_40_0) &
% 40.65/6.33 | | | $i(all_40_1) & greater(all_40_1, zero) & greater(zero, all_40_0)
% 40.65/6.33 | | |
% 40.65/6.33 | | | ALPHA: (30) implies:
% 40.65/6.33 | | | (31) greater(zero, all_40_0)
% 40.65/6.33 | | | (32) $i(all_40_1)
% 40.65/6.33 | | | (33) growth_rate(first_movers, all_31_2) = all_40_1
% 40.65/6.33 | | | (34) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.33 | | |
% 40.65/6.33 | | | GROUND_INST: instantiating (9) with all_31_0, all_40_1, all_31_2,
% 40.65/6.33 | | | first_movers, simplifying with (7), (33) gives:
% 40.65/6.33 | | | (35) all_40_1 = all_31_0
% 40.65/6.33 | | |
% 40.65/6.33 | | | GROUND_INST: instantiating (9) with all_106_1, all_40_0, all_31_2,
% 40.65/6.33 | | | efficient_producers, simplifying with (14), (34) gives:
% 40.65/6.33 | | | (36) all_106_1 = all_40_0
% 40.65/6.33 | | |
% 40.65/6.33 | | | REDUCE: (12), (36) imply:
% 40.65/6.33 | | | (37) $i(all_40_0)
% 40.65/6.33 | | |
% 40.65/6.33 | | | REDUCE: (32), (35) imply:
% 40.65/6.33 | | | (38) $i(all_31_0)
% 40.65/6.33 | | |
% 40.65/6.33 | | | REDUCE: (16), (36) imply:
% 40.65/6.33 | | | (39) greater(all_40_0, all_31_0)
% 40.65/6.33 | | |
% 40.65/6.33 | | | GROUND_INST: instantiating (4) with zero, all_40_0, all_31_0, simplifying
% 40.65/6.33 | | | with (1), (5), (31), (37), (38), (39) gives:
% 40.65/6.33 | | | (40) $false
% 40.65/6.33 | | |
% 40.65/6.33 | | | CLOSE: (40) is inconsistent.
% 40.65/6.33 | | |
% 40.65/6.33 | | End of split
% 40.65/6.33 | |
% 40.65/6.33 | End of split
% 40.65/6.33 |
% 40.65/6.33 End of proof
% 40.65/6.33
% 40.65/6.33 Sub-proof #8 shows that the following formulas are inconsistent:
% 40.65/6.33 ----------------------------------------------------------------
% 40.65/6.33 (1) ~ greater(zero, all_31_0)
% 40.65/6.33 (2) growth_rate(first_movers, all_31_2) = all_31_0
% 40.65/6.33 (3) growth_rate(first_movers, all_31_2) = all_40_1
% 40.65/6.33 (4) greater(zero, all_40_1)
% 40.65/6.33 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.33 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 40.65/6.33
% 40.65/6.33 Begin of proof
% 40.65/6.33 |
% 40.65/6.33 | PRED_UNIFY: (1), (4) imply:
% 40.65/6.34 | (6) ~ (all_40_1 = all_31_0)
% 40.65/6.34 |
% 40.65/6.34 | GROUND_INST: instantiating (5) with all_31_0, all_40_1, all_31_2,
% 40.65/6.34 | first_movers, simplifying with (2), (3) gives:
% 40.65/6.34 | (7) all_40_1 = all_31_0
% 40.65/6.34 |
% 40.65/6.34 | REDUCE: (6), (7) imply:
% 40.65/6.34 | (8) $false
% 40.65/6.34 |
% 40.65/6.34 | CLOSE: (8) is inconsistent.
% 40.65/6.34 |
% 40.65/6.34 End of proof
% 40.65/6.34
% 40.65/6.34 Sub-proof #9 shows that the following formulas are inconsistent:
% 40.65/6.34 ----------------------------------------------------------------
% 40.65/6.34 (1) equilibrium(all_11_0) = all_40_2
% 40.65/6.34 (2) ~ greater_or_equal(all_19_0, all_40_2)
% 40.65/6.34 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (equilibrium(v2)
% 40.65/6.34 = v1) | ~ (equilibrium(v2) = v0))
% 40.65/6.34 (4) greater_or_equal(all_19_0, all_19_1)
% 40.65/6.34 (5) equilibrium(all_11_0) = all_19_1
% 40.65/6.34
% 40.65/6.34 Begin of proof
% 40.65/6.34 |
% 40.65/6.34 | GROUND_INST: instantiating (3) with all_19_1, all_40_2, all_11_0, simplifying
% 40.65/6.34 | with (1), (5) gives:
% 40.65/6.34 | (6) all_40_2 = all_19_1
% 40.65/6.34 |
% 40.65/6.34 | PRED_UNIFY: (2), (4) imply:
% 40.65/6.34 | (7) ~ (all_40_2 = all_19_1)
% 40.65/6.34 |
% 40.65/6.34 | REDUCE: (6), (7) imply:
% 40.65/6.34 | (8) $false
% 40.65/6.34 |
% 40.65/6.34 | CLOSE: (8) is inconsistent.
% 40.65/6.34 |
% 40.65/6.34 End of proof
% 40.65/6.34
% 40.65/6.34 Sub-proof #10 shows that the following formulas are inconsistent:
% 40.65/6.34 ----------------------------------------------------------------
% 40.65/6.34 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.34 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 40.65/6.34 (2) growth_rate(efficient_producers, all_29_2) = all_29_1
% 40.65/6.34 (3) growth_rate(efficient_producers, all_29_2) = zero
% 40.65/6.34 (4) ~ (all_29_1 = zero)
% 40.65/6.34
% 40.65/6.34 Begin of proof
% 40.65/6.34 |
% 40.65/6.34 | GROUND_INST: instantiating (1) with all_29_1, zero, all_29_2,
% 40.65/6.34 | efficient_producers, simplifying with (2), (3) gives:
% 40.65/6.34 | (5) all_29_1 = zero
% 40.65/6.34 |
% 40.65/6.34 | REDUCE: (4), (5) imply:
% 40.65/6.34 | (6) $false
% 40.65/6.34 |
% 40.65/6.34 | CLOSE: (6) is inconsistent.
% 40.65/6.34 |
% 40.65/6.34 End of proof
% 40.65/6.34
% 40.65/6.34 Sub-proof #11 shows that the following formulas are inconsistent:
% 40.65/6.34 ----------------------------------------------------------------
% 40.65/6.34 (1) ~ greater(all_31_1, zero)
% 40.65/6.34 (2) (all_40_0 = zero & all_40_1 = zero & growth_rate(efficient_producers,
% 40.65/6.34 all_31_2) = zero & growth_rate(first_movers, all_31_2) = zero) |
% 40.65/6.34 (equilibrium(all_11_0) = all_40_2 & $i(all_40_2) & ~
% 40.65/6.34 greater_or_equal(all_31_2, all_40_2)) |
% 40.65/6.34 (growth_rate(efficient_producers, all_31_2) = all_40_0 &
% 40.65/6.34 growth_rate(first_movers, all_31_2) = all_40_1 & $i(all_40_0) &
% 40.65/6.34 $i(all_40_1) & greater(all_40_0, zero) & greater(zero, all_40_1)) |
% 40.65/6.34 (growth_rate(efficient_producers, all_31_2) = all_40_0 &
% 40.65/6.34 growth_rate(first_movers, all_31_2) = all_40_1 & $i(all_40_0) &
% 40.65/6.34 $i(all_40_1) & greater(all_40_1, zero) & greater(zero, all_40_0))
% 40.65/6.34 (3) growth_rate(efficient_producers, all_31_2) = all_31_1
% 40.65/6.34 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 40.65/6.34 $i(v0) | ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 40.65/6.34 (5) $i(zero)
% 40.65/6.34 (6) growth_rate(efficient_producers, all_31_2) = all_106_1 &
% 40.65/6.34 growth_rate(first_movers, all_31_2) = all_106_0 & $i(all_106_0) &
% 40.65/6.34 $i(all_106_1) & greater(all_106_1, all_106_0)
% 40.65/6.34 (7) greater_or_equal(all_31_2, all_19_1)
% 40.65/6.34 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (equilibrium(v2)
% 40.65/6.34 = v1) | ~ (equilibrium(v2) = v0))
% 40.65/6.34 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.34 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 40.65/6.34 (10) equilibrium(all_11_0) = all_19_1
% 40.65/6.34
% 40.65/6.34 Begin of proof
% 40.65/6.34 |
% 40.65/6.34 | ALPHA: (6) implies:
% 40.65/6.34 | (11) greater(all_106_1, all_106_0)
% 40.65/6.34 | (12) $i(all_106_0)
% 40.65/6.34 | (13) growth_rate(first_movers, all_31_2) = all_106_0
% 40.65/6.34 | (14) growth_rate(efficient_producers, all_31_2) = all_106_1
% 40.65/6.34 |
% 40.65/6.34 | GROUND_INST: instantiating (9) with all_31_1, all_106_1, all_31_2,
% 40.65/6.34 | efficient_producers, simplifying with (3), (14) gives:
% 40.65/6.34 | (15) all_106_1 = all_31_1
% 40.65/6.34 |
% 40.65/6.34 | REDUCE: (11), (15) imply:
% 40.65/6.34 | (16) greater(all_31_1, all_106_0)
% 40.65/6.34 |
% 40.65/6.34 | PRED_UNIFY: (1), (16) imply:
% 40.65/6.34 | (17) ~ (all_106_0 = zero)
% 40.65/6.34 |
% 40.65/6.34 | BETA: splitting (2) gives:
% 40.65/6.34 |
% 40.65/6.34 | Case 1:
% 40.65/6.34 | |
% 40.65/6.34 | | (18) (all_40_0 = zero & all_40_1 = zero &
% 40.65/6.34 | | growth_rate(efficient_producers, all_31_2) = zero &
% 40.65/6.34 | | growth_rate(first_movers, all_31_2) = zero) |
% 40.65/6.34 | | (equilibrium(all_11_0) = all_40_2 & $i(all_40_2) & ~
% 40.65/6.34 | | greater_or_equal(all_31_2, all_40_2))
% 40.65/6.34 | |
% 40.65/6.34 | | BETA: splitting (18) gives:
% 40.65/6.34 | |
% 40.65/6.34 | | Case 1:
% 40.65/6.34 | | |
% 40.65/6.34 | | | (19) all_40_0 = zero & all_40_1 = zero &
% 40.65/6.34 | | | growth_rate(efficient_producers, all_31_2) = zero &
% 40.65/6.34 | | | growth_rate(first_movers, all_31_2) = zero
% 40.65/6.34 | | |
% 40.65/6.34 | | | ALPHA: (19) implies:
% 40.65/6.34 | | | (20) growth_rate(first_movers, all_31_2) = zero
% 40.65/6.34 | | |
% 40.65/6.34 | | | GROUND_INST: instantiating (9) with all_106_0, zero, all_31_2,
% 40.65/6.34 | | | first_movers, simplifying with (13), (20) gives:
% 40.65/6.34 | | | (21) all_106_0 = zero
% 40.65/6.34 | | |
% 40.65/6.34 | | | REDUCE: (17), (21) imply:
% 40.65/6.34 | | | (22) $false
% 40.65/6.34 | | |
% 40.65/6.34 | | | CLOSE: (22) is inconsistent.
% 40.65/6.34 | | |
% 40.65/6.34 | | Case 2:
% 40.65/6.34 | | |
% 40.65/6.34 | | | (23) equilibrium(all_11_0) = all_40_2 & $i(all_40_2) & ~
% 40.65/6.34 | | | greater_or_equal(all_31_2, all_40_2)
% 40.65/6.34 | | |
% 40.65/6.34 | | | ALPHA: (23) implies:
% 40.65/6.34 | | | (24) ~ greater_or_equal(all_31_2, all_40_2)
% 40.65/6.34 | | | (25) equilibrium(all_11_0) = all_40_2
% 40.65/6.34 | | |
% 40.65/6.34 | | | REF_CLOSE: (7), (8), (10), (24), (25) are inconsistent by sub-proof #13.
% 40.65/6.34 | | |
% 40.65/6.34 | | End of split
% 40.65/6.34 | |
% 40.65/6.34 | Case 2:
% 40.65/6.34 | |
% 40.65/6.34 | | (26) (growth_rate(efficient_producers, all_31_2) = all_40_0 &
% 40.65/6.34 | | growth_rate(first_movers, all_31_2) = all_40_1 & $i(all_40_0) &
% 40.65/6.34 | | $i(all_40_1) & greater(all_40_0, zero) & greater(zero, all_40_1))
% 40.65/6.34 | | | (growth_rate(efficient_producers, all_31_2) = all_40_0 &
% 40.65/6.34 | | growth_rate(first_movers, all_31_2) = all_40_1 & $i(all_40_0) &
% 40.65/6.34 | | $i(all_40_1) & greater(all_40_1, zero) & greater(zero, all_40_0))
% 40.65/6.34 | |
% 40.65/6.34 | | BETA: splitting (26) gives:
% 40.65/6.34 | |
% 40.65/6.34 | | Case 1:
% 40.65/6.34 | | |
% 40.65/6.34 | | | (27) growth_rate(efficient_producers, all_31_2) = all_40_0 &
% 40.65/6.34 | | | growth_rate(first_movers, all_31_2) = all_40_1 & $i(all_40_0) &
% 40.65/6.34 | | | $i(all_40_1) & greater(all_40_0, zero) & greater(zero, all_40_1)
% 40.65/6.34 | | |
% 40.65/6.34 | | | ALPHA: (27) implies:
% 40.65/6.34 | | | (28) greater(all_40_0, zero)
% 40.65/6.34 | | | (29) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.34 | | |
% 40.65/6.34 | | | REF_CLOSE: (1), (3), (9), (28), (29) are inconsistent by sub-proof #12.
% 40.65/6.34 | | |
% 40.65/6.34 | | Case 2:
% 40.65/6.34 | | |
% 40.65/6.34 | | | (30) growth_rate(efficient_producers, all_31_2) = all_40_0 &
% 40.65/6.34 | | | growth_rate(first_movers, all_31_2) = all_40_1 & $i(all_40_0) &
% 40.65/6.34 | | | $i(all_40_1) & greater(all_40_1, zero) & greater(zero, all_40_0)
% 40.65/6.34 | | |
% 40.65/6.34 | | | ALPHA: (30) implies:
% 40.65/6.34 | | | (31) greater(all_40_1, zero)
% 40.65/6.34 | | | (32) $i(all_40_0)
% 40.65/6.34 | | | (33) growth_rate(first_movers, all_31_2) = all_40_1
% 40.65/6.34 | | | (34) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.34 | | |
% 40.65/6.34 | | | GROUND_INST: instantiating (9) with all_106_0, all_40_1, all_31_2,
% 40.65/6.34 | | | first_movers, simplifying with (13), (33) gives:
% 40.65/6.34 | | | (35) all_106_0 = all_40_1
% 40.65/6.34 | | |
% 40.65/6.34 | | | GROUND_INST: instantiating (9) with all_31_1, all_40_0, all_31_2,
% 40.65/6.34 | | | efficient_producers, simplifying with (3), (34) gives:
% 40.65/6.34 | | | (36) all_40_0 = all_31_1
% 40.65/6.34 | | |
% 40.65/6.34 | | | REDUCE: (12), (35) imply:
% 40.65/6.34 | | | (37) $i(all_40_1)
% 40.65/6.34 | | |
% 40.65/6.34 | | | REDUCE: (32), (36) imply:
% 40.65/6.34 | | | (38) $i(all_31_1)
% 40.65/6.34 | | |
% 40.65/6.34 | | | REDUCE: (16), (35) imply:
% 40.65/6.34 | | | (39) greater(all_31_1, all_40_1)
% 40.65/6.34 | | |
% 40.65/6.34 | | | GROUND_INST: instantiating (4) with all_31_1, all_40_1, zero, simplifying
% 40.65/6.34 | | | with (1), (5), (31), (37), (38), (39) gives:
% 40.65/6.34 | | | (40) $false
% 40.65/6.34 | | |
% 40.65/6.34 | | | CLOSE: (40) is inconsistent.
% 40.65/6.34 | | |
% 40.65/6.34 | | End of split
% 40.65/6.34 | |
% 40.65/6.34 | End of split
% 40.65/6.34 |
% 40.65/6.34 End of proof
% 40.65/6.34
% 40.65/6.34 Sub-proof #12 shows that the following formulas are inconsistent:
% 40.65/6.34 ----------------------------------------------------------------
% 40.65/6.34 (1) growth_rate(efficient_producers, all_31_2) = all_40_0
% 40.65/6.34 (2) ~ greater(all_31_1, zero)
% 40.65/6.34 (3) growth_rate(efficient_producers, all_31_2) = all_31_1
% 40.65/6.34 (4) greater(all_40_0, zero)
% 40.65/6.34 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.34 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 40.65/6.34
% 40.65/6.34 Begin of proof
% 40.65/6.34 |
% 40.65/6.34 | PRED_UNIFY: (2), (4) imply:
% 40.65/6.34 | (6) ~ (all_40_0 = all_31_1)
% 40.65/6.34 |
% 40.65/6.34 | GROUND_INST: instantiating (5) with all_31_1, all_40_0, all_31_2,
% 40.65/6.34 | efficient_producers, simplifying with (1), (3) gives:
% 40.65/6.34 | (7) all_40_0 = all_31_1
% 40.65/6.34 |
% 40.65/6.34 | REDUCE: (6), (7) imply:
% 40.65/6.34 | (8) $false
% 40.65/6.34 |
% 40.65/6.34 | CLOSE: (8) is inconsistent.
% 40.65/6.34 |
% 40.65/6.34 End of proof
% 40.65/6.35
% 40.65/6.35 Sub-proof #13 shows that the following formulas are inconsistent:
% 40.65/6.35 ----------------------------------------------------------------
% 40.65/6.35 (1) equilibrium(all_11_0) = all_40_2
% 40.65/6.35 (2) greater_or_equal(all_31_2, all_19_1)
% 40.65/6.35 (3) ~ greater_or_equal(all_31_2, all_40_2)
% 40.65/6.35 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (equilibrium(v2)
% 40.65/6.35 = v1) | ~ (equilibrium(v2) = v0))
% 40.65/6.35 (5) equilibrium(all_11_0) = all_19_1
% 40.65/6.35
% 40.65/6.35 Begin of proof
% 40.65/6.35 |
% 40.65/6.35 | GROUND_INST: instantiating (4) with all_19_1, all_40_2, all_11_0, simplifying
% 40.65/6.35 | with (1), (5) gives:
% 40.65/6.35 | (6) all_40_2 = all_19_1
% 40.65/6.35 |
% 40.65/6.35 | PRED_UNIFY: (2), (3) imply:
% 40.65/6.35 | (7) ~ (all_40_2 = all_19_1)
% 40.65/6.35 |
% 40.65/6.35 | REDUCE: (6), (7) imply:
% 40.65/6.35 | (8) $false
% 40.65/6.35 |
% 40.65/6.35 | CLOSE: (8) is inconsistent.
% 40.65/6.35 |
% 40.65/6.35 End of proof
% 40.65/6.35
% 40.65/6.35 Sub-proof #14 shows that the following formulas are inconsistent:
% 40.65/6.35 ----------------------------------------------------------------
% 40.65/6.35 (1) $i(all_21_0)
% 40.65/6.35 (2) $i(all_31_2)
% 40.65/6.35 (3) $i(all_19_0)
% 40.65/6.35 (4) ~ (all_21_0 = all_19_0)
% 40.65/6.35 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 40.65/6.35 $i(v0) | ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 40.65/6.35 (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1) |
% 40.65/6.35 greater_or_equal(v0, v1))
% 40.65/6.35 (7) all_21_0 = all_19_0 | greater(all_19_0, all_21_0)
% 40.65/6.35 (8) ~ greater_or_equal(all_31_2, all_21_0)
% 40.65/6.35 (9) all_31_2 = all_19_0 | greater(all_31_2, all_19_0)
% 40.65/6.35
% 40.65/6.35 Begin of proof
% 40.65/6.35 |
% 40.65/6.35 | BETA: splitting (7) gives:
% 40.65/6.35 |
% 40.65/6.35 | Case 1:
% 40.65/6.35 | |
% 40.65/6.35 | | (10) greater(all_19_0, all_21_0)
% 40.65/6.35 | |
% 40.65/6.35 | | GROUND_INST: instantiating (6) with all_19_0, all_21_0, simplifying with
% 40.65/6.35 | | (1), (3), (10) gives:
% 40.65/6.35 | | (11) greater_or_equal(all_19_0, all_21_0)
% 40.65/6.35 | |
% 40.65/6.35 | | PRED_UNIFY: (8), (11) imply:
% 40.65/6.35 | | (12) ~ (all_31_2 = all_19_0)
% 40.65/6.35 | |
% 40.65/6.35 | | BETA: splitting (9) gives:
% 40.65/6.35 | |
% 40.65/6.35 | | Case 1:
% 40.65/6.35 | | |
% 40.65/6.35 | | | (13) greater(all_31_2, all_19_0)
% 40.65/6.35 | | |
% 40.65/6.35 | | | GROUND_INST: instantiating (5) with all_31_2, all_19_0, all_21_0,
% 40.65/6.35 | | | simplifying with (1), (2), (3), (10), (13) gives:
% 40.65/6.35 | | | (14) greater(all_31_2, all_21_0)
% 40.65/6.35 | | |
% 40.65/6.35 | | | GROUND_INST: instantiating (6) with all_31_2, all_21_0, simplifying with
% 40.65/6.35 | | | (1), (2), (8), (14) gives:
% 40.65/6.35 | | | (15) $false
% 40.65/6.35 | | |
% 40.65/6.35 | | | CLOSE: (15) is inconsistent.
% 40.65/6.35 | | |
% 40.65/6.35 | | Case 2:
% 40.65/6.35 | | |
% 40.65/6.35 | | | (16) all_31_2 = all_19_0
% 40.65/6.35 | | |
% 40.65/6.35 | | | REDUCE: (12), (16) imply:
% 40.65/6.35 | | | (17) $false
% 40.65/6.35 | | |
% 40.65/6.35 | | | CLOSE: (17) is inconsistent.
% 40.65/6.35 | | |
% 40.65/6.35 | | End of split
% 40.65/6.35 | |
% 40.65/6.35 | Case 2:
% 40.65/6.35 | |
% 40.65/6.35 | | (18) all_21_0 = all_19_0
% 40.65/6.35 | |
% 40.65/6.35 | | REDUCE: (4), (18) imply:
% 40.65/6.35 | | (19) $false
% 40.65/6.35 | |
% 40.65/6.35 | | CLOSE: (19) is inconsistent.
% 40.65/6.35 | |
% 40.65/6.35 | End of split
% 40.65/6.35 |
% 40.65/6.35 End of proof
% 40.65/6.35
% 40.65/6.35 Sub-proof #15 shows that the following formulas are inconsistent:
% 40.65/6.35 ----------------------------------------------------------------
% 40.65/6.35 (1) $i(all_21_0)
% 40.65/6.35 (2) all_38_0 = all_38_1 | ~ (growth_rate(first_movers, all_29_2) = all_38_1)
% 40.65/6.35 (3) growth_rate(efficient_producers, all_29_2) = all_29_1
% 40.65/6.35 (4) greater(all_21_0, all_19_1)
% 40.65/6.35 (5) all_38_1 = all_29_1
% 40.65/6.35 (6) (all_41_0 = zero & all_41_1 = zero & growth_rate(efficient_producers,
% 40.65/6.35 all_29_2) = zero & growth_rate(first_movers, all_29_2) = zero) |
% 40.65/6.35 (equilibrium(all_11_0) = all_41_2 & $i(all_41_2) & ~
% 40.65/6.35 greater_or_equal(all_29_2, all_41_2)) |
% 40.65/6.35 (growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.35 growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0) &
% 40.65/6.35 $i(all_41_1) & greater(all_41_0, zero) & greater(zero, all_41_1)) |
% 40.65/6.35 (growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.35 growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0) &
% 40.65/6.35 $i(all_41_1) & greater(all_41_1, zero) & greater(zero, all_41_0))
% 40.65/6.35 (7) $i(all_19_1)
% 40.65/6.35 (8) all_29_2 = all_21_0 | greater(all_29_2, all_21_0)
% 40.65/6.35 (9) ~ (all_38_0 = zero)
% 40.65/6.35 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 40.65/6.35 $i(v0) | ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 40.65/6.35 (11) $i(zero)
% 40.65/6.35 (12) $i(all_29_2)
% 40.65/6.35 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (equilibrium(v2)
% 40.65/6.35 = v1) | ~ (equilibrium(v2) = v0))
% 40.65/6.35 (14) ~ greater(all_29_1, zero)
% 40.65/6.35 (15) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1)
% 40.65/6.35 | greater_or_equal(v0, v1))
% 40.65/6.35 (16) growth_rate(first_movers, all_29_2) = all_38_0
% 40.65/6.35 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.35 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 40.65/6.35 (18) equilibrium(all_11_0) = all_19_1
% 40.65/6.35 (19) greater(all_29_1, all_38_0)
% 40.65/6.35
% 40.65/6.35 Begin of proof
% 40.65/6.35 |
% 40.65/6.35 | GROUND_INST: instantiating (15) with all_21_0, all_19_1, simplifying with (1),
% 40.65/6.35 | (4), (7) gives:
% 40.65/6.35 | (20) greater_or_equal(all_21_0, all_19_1)
% 40.65/6.35 |
% 40.65/6.35 | BETA: splitting (8) gives:
% 40.65/6.35 |
% 40.65/6.35 | Case 1:
% 40.65/6.35 | |
% 40.65/6.35 | | (21) greater(all_29_2, all_21_0)
% 40.65/6.35 | |
% 40.65/6.35 | | GROUND_INST: instantiating (10) with all_29_2, all_21_0, all_19_1,
% 40.65/6.35 | | simplifying with (1), (4), (7), (12), (21) gives:
% 40.65/6.35 | | (22) greater(all_29_2, all_19_1)
% 40.65/6.35 | |
% 40.65/6.35 | | BETA: splitting (2) gives:
% 40.65/6.35 | |
% 40.65/6.35 | | Case 1:
% 40.65/6.35 | | |
% 40.65/6.35 | | | (23) ~ (growth_rate(first_movers, all_29_2) = all_38_1)
% 40.65/6.35 | | |
% 40.65/6.35 | | | REDUCE: (5), (23) imply:
% 40.65/6.35 | | | (24) ~ (growth_rate(first_movers, all_29_2) = all_29_1)
% 40.65/6.35 | | |
% 40.65/6.35 | | | BETA: splitting (6) gives:
% 40.65/6.35 | | |
% 40.65/6.35 | | | Case 1:
% 40.65/6.35 | | | |
% 40.65/6.35 | | | | (25) (all_41_0 = zero & all_41_1 = zero &
% 40.65/6.35 | | | | growth_rate(efficient_producers, all_29_2) = zero &
% 40.65/6.35 | | | | growth_rate(first_movers, all_29_2) = zero) |
% 40.65/6.35 | | | | (equilibrium(all_11_0) = all_41_2 & $i(all_41_2) & ~
% 40.65/6.35 | | | | greater_or_equal(all_29_2, all_41_2))
% 40.65/6.35 | | | |
% 40.65/6.35 | | | | BETA: splitting (25) gives:
% 40.65/6.35 | | | |
% 40.65/6.35 | | | | Case 1:
% 40.65/6.35 | | | | |
% 40.65/6.35 | | | | | (26) all_41_0 = zero & all_41_1 = zero &
% 40.65/6.35 | | | | | growth_rate(efficient_producers, all_29_2) = zero &
% 40.65/6.35 | | | | | growth_rate(first_movers, all_29_2) = zero
% 40.65/6.35 | | | | |
% 40.65/6.35 | | | | | ALPHA: (26) implies:
% 40.65/6.35 | | | | | (27) growth_rate(first_movers, all_29_2) = zero
% 40.65/6.35 | | | | | (28) growth_rate(efficient_producers, all_29_2) = zero
% 40.65/6.35 | | | | |
% 40.65/6.35 | | | | | PRED_UNIFY: (24), (27) imply:
% 40.65/6.35 | | | | | (29) ~ (all_29_1 = zero)
% 40.65/6.35 | | | | |
% 40.65/6.35 | | | | | GROUND_INST: instantiating (17) with all_29_1, zero, all_29_2,
% 40.65/6.35 | | | | | efficient_producers, simplifying with (3), (28) gives:
% 40.65/6.35 | | | | | (30) all_29_1 = zero
% 40.65/6.35 | | | | |
% 40.65/6.35 | | | | | REDUCE: (29), (30) imply:
% 40.65/6.35 | | | | | (31) $false
% 40.65/6.35 | | | | |
% 40.65/6.35 | | | | | CLOSE: (31) is inconsistent.
% 40.65/6.35 | | | | |
% 40.65/6.35 | | | | Case 2:
% 40.65/6.35 | | | | |
% 40.65/6.35 | | | | | (32) equilibrium(all_11_0) = all_41_2 & $i(all_41_2) & ~
% 40.65/6.35 | | | | | greater_or_equal(all_29_2, all_41_2)
% 40.65/6.35 | | | | |
% 40.65/6.35 | | | | | ALPHA: (32) implies:
% 40.65/6.35 | | | | | (33) ~ greater_or_equal(all_29_2, all_41_2)
% 40.65/6.35 | | | | | (34) $i(all_41_2)
% 40.65/6.35 | | | | | (35) equilibrium(all_11_0) = all_41_2
% 40.65/6.35 | | | | |
% 40.65/6.35 | | | | | REF_CLOSE: (12), (13), (15), (18), (22), (33), (34), (35) are
% 40.65/6.35 | | | | | inconsistent by sub-proof #20.
% 40.65/6.35 | | | | |
% 40.65/6.35 | | | | End of split
% 40.65/6.35 | | | |
% 40.65/6.35 | | | Case 2:
% 40.65/6.35 | | | |
% 40.65/6.35 | | | | (36) (growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.35 | | | | growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0)
% 40.65/6.35 | | | | & $i(all_41_1) & greater(all_41_0, zero) & greater(zero,
% 40.65/6.35 | | | | all_41_1)) | (growth_rate(efficient_producers, all_29_2) =
% 40.65/6.35 | | | | all_41_0 & growth_rate(first_movers, all_29_2) = all_41_1 &
% 40.65/6.35 | | | | $i(all_41_0) & $i(all_41_1) & greater(all_41_1, zero) &
% 40.65/6.35 | | | | greater(zero, all_41_0))
% 40.65/6.35 | | | |
% 40.65/6.35 | | | | BETA: splitting (36) gives:
% 40.65/6.35 | | | |
% 40.65/6.35 | | | | Case 1:
% 40.65/6.35 | | | | |
% 40.65/6.35 | | | | | (37) growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.35 | | | | | growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0)
% 40.65/6.35 | | | | | & $i(all_41_1) & greater(all_41_0, zero) & greater(zero,
% 40.65/6.35 | | | | | all_41_1)
% 40.65/6.35 | | | | |
% 40.65/6.35 | | | | | ALPHA: (37) implies:
% 40.65/6.35 | | | | | (38) greater(all_41_0, zero)
% 40.65/6.35 | | | | | (39) growth_rate(efficient_producers, all_29_2) = all_41_0
% 40.65/6.35 | | | | |
% 40.65/6.35 | | | | | REF_CLOSE: (3), (14), (17), (38), (39) are inconsistent by sub-proof
% 40.65/6.35 | | | | | #19.
% 40.65/6.35 | | | | |
% 40.65/6.35 | | | | Case 2:
% 40.65/6.35 | | | | |
% 40.65/6.35 | | | | | (40) growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.36 | | | | | growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0)
% 40.65/6.36 | | | | | & $i(all_41_1) & greater(all_41_1, zero) & greater(zero,
% 40.65/6.36 | | | | | all_41_0)
% 40.65/6.36 | | | | |
% 40.65/6.36 | | | | | ALPHA: (40) implies:
% 40.65/6.36 | | | | | (41) greater(all_41_1, zero)
% 40.65/6.36 | | | | | (42) $i(all_41_1)
% 40.65/6.36 | | | | | (43) $i(all_41_0)
% 40.65/6.36 | | | | | (44) growth_rate(first_movers, all_29_2) = all_41_1
% 40.65/6.36 | | | | | (45) growth_rate(efficient_producers, all_29_2) = all_41_0
% 40.65/6.36 | | | | |
% 40.65/6.36 | | | | | REF_CLOSE: (3), (10), (11), (14), (16), (17), (19), (41), (42), (43),
% 40.65/6.36 | | | | | (44), (45) are inconsistent by sub-proof #18.
% 40.65/6.36 | | | | |
% 40.65/6.36 | | | | End of split
% 40.65/6.36 | | | |
% 40.65/6.36 | | | End of split
% 40.65/6.36 | | |
% 40.65/6.36 | | Case 2:
% 40.65/6.36 | | |
% 40.65/6.36 | | | (46) all_38_0 = all_38_1
% 40.65/6.36 | | |
% 40.65/6.36 | | | COMBINE_EQS: (5), (46) imply:
% 40.65/6.36 | | | (47) all_38_0 = all_29_1
% 40.65/6.36 | | |
% 40.65/6.36 | | | REDUCE: (9), (47) imply:
% 40.65/6.36 | | | (48) ~ (all_29_1 = zero)
% 40.65/6.36 | | |
% 40.65/6.36 | | | BETA: splitting (6) gives:
% 40.65/6.36 | | |
% 40.65/6.36 | | | Case 1:
% 40.65/6.36 | | | |
% 40.65/6.36 | | | | (49) (all_41_0 = zero & all_41_1 = zero &
% 40.65/6.36 | | | | growth_rate(efficient_producers, all_29_2) = zero &
% 40.65/6.36 | | | | growth_rate(first_movers, all_29_2) = zero) |
% 40.65/6.36 | | | | (equilibrium(all_11_0) = all_41_2 & $i(all_41_2) & ~
% 40.65/6.36 | | | | greater_or_equal(all_29_2, all_41_2))
% 40.65/6.36 | | | |
% 40.65/6.36 | | | | BETA: splitting (49) gives:
% 40.65/6.36 | | | |
% 40.65/6.36 | | | | Case 1:
% 40.65/6.36 | | | | |
% 40.65/6.36 | | | | | (50) all_41_0 = zero & all_41_1 = zero &
% 40.65/6.36 | | | | | growth_rate(efficient_producers, all_29_2) = zero &
% 40.65/6.36 | | | | | growth_rate(first_movers, all_29_2) = zero
% 40.65/6.36 | | | | |
% 40.65/6.36 | | | | | ALPHA: (50) implies:
% 40.65/6.36 | | | | | (51) growth_rate(efficient_producers, all_29_2) = zero
% 40.65/6.36 | | | | |
% 40.65/6.36 | | | | | GROUND_INST: instantiating (17) with all_29_1, zero, all_29_2,
% 40.65/6.36 | | | | | efficient_producers, simplifying with (3), (51) gives:
% 40.65/6.36 | | | | | (52) all_29_1 = zero
% 40.65/6.36 | | | | |
% 40.65/6.36 | | | | | REDUCE: (48), (52) imply:
% 40.65/6.36 | | | | | (53) $false
% 40.65/6.36 | | | | |
% 40.65/6.36 | | | | | CLOSE: (53) is inconsistent.
% 40.65/6.36 | | | | |
% 40.65/6.36 | | | | Case 2:
% 40.65/6.36 | | | | |
% 40.65/6.36 | | | | | (54) equilibrium(all_11_0) = all_41_2 & $i(all_41_2) & ~
% 40.65/6.36 | | | | | greater_or_equal(all_29_2, all_41_2)
% 40.65/6.36 | | | | |
% 40.65/6.36 | | | | | ALPHA: (54) implies:
% 40.65/6.36 | | | | | (55) ~ greater_or_equal(all_29_2, all_41_2)
% 40.65/6.36 | | | | | (56) $i(all_41_2)
% 40.65/6.36 | | | | | (57) equilibrium(all_11_0) = all_41_2
% 40.65/6.36 | | | | |
% 40.65/6.36 | | | | | REF_CLOSE: (12), (13), (15), (18), (22), (55), (56), (57) are
% 40.65/6.36 | | | | | inconsistent by sub-proof #20.
% 40.65/6.36 | | | | |
% 40.65/6.36 | | | | End of split
% 40.65/6.36 | | | |
% 40.65/6.36 | | | Case 2:
% 40.65/6.36 | | | |
% 40.65/6.36 | | | | (58) (growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.36 | | | | growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0)
% 40.65/6.36 | | | | & $i(all_41_1) & greater(all_41_0, zero) & greater(zero,
% 40.65/6.36 | | | | all_41_1)) | (growth_rate(efficient_producers, all_29_2) =
% 40.65/6.36 | | | | all_41_0 & growth_rate(first_movers, all_29_2) = all_41_1 &
% 40.65/6.36 | | | | $i(all_41_0) & $i(all_41_1) & greater(all_41_1, zero) &
% 40.65/6.36 | | | | greater(zero, all_41_0))
% 40.65/6.36 | | | |
% 40.65/6.36 | | | | REF_CLOSE: (3), (10), (11), (14), (16), (17), (19), (58) are
% 40.65/6.36 | | | | inconsistent by sub-proof #17.
% 40.65/6.36 | | | |
% 40.65/6.36 | | | End of split
% 40.65/6.36 | | |
% 40.65/6.36 | | End of split
% 40.65/6.36 | |
% 40.65/6.36 | Case 2:
% 40.65/6.36 | |
% 40.65/6.36 | | (59) all_29_2 = all_21_0
% 40.65/6.36 | |
% 40.65/6.36 | | REDUCE: (16), (59) imply:
% 40.65/6.36 | | (60) growth_rate(first_movers, all_21_0) = all_38_0
% 40.65/6.36 | |
% 40.65/6.36 | | BETA: splitting (6) gives:
% 40.65/6.36 | |
% 40.65/6.36 | | Case 1:
% 40.65/6.36 | | |
% 40.65/6.36 | | | (61) (all_41_0 = zero & all_41_1 = zero &
% 40.65/6.36 | | | growth_rate(efficient_producers, all_29_2) = zero &
% 40.65/6.36 | | | growth_rate(first_movers, all_29_2) = zero) |
% 40.65/6.36 | | | (equilibrium(all_11_0) = all_41_2 & $i(all_41_2) & ~
% 40.65/6.36 | | | greater_or_equal(all_29_2, all_41_2))
% 40.65/6.36 | | |
% 40.65/6.36 | | | BETA: splitting (61) gives:
% 40.65/6.36 | | |
% 40.65/6.36 | | | Case 1:
% 40.65/6.36 | | | |
% 40.65/6.36 | | | | (62) all_41_0 = zero & all_41_1 = zero &
% 40.65/6.36 | | | | growth_rate(efficient_producers, all_29_2) = zero &
% 40.65/6.36 | | | | growth_rate(first_movers, all_29_2) = zero
% 40.65/6.36 | | | |
% 40.65/6.36 | | | | ALPHA: (62) implies:
% 40.65/6.36 | | | | (63) growth_rate(first_movers, all_29_2) = zero
% 40.65/6.36 | | | |
% 40.65/6.36 | | | | REDUCE: (59), (63) imply:
% 40.65/6.36 | | | | (64) growth_rate(first_movers, all_21_0) = zero
% 40.65/6.36 | | | |
% 40.65/6.36 | | | | GROUND_INST: instantiating (17) with zero, all_38_0, all_21_0,
% 40.65/6.36 | | | | first_movers, simplifying with (60), (64) gives:
% 40.65/6.36 | | | | (65) all_38_0 = zero
% 40.65/6.36 | | | |
% 40.65/6.36 | | | | REDUCE: (9), (65) imply:
% 40.65/6.36 | | | | (66) $false
% 40.65/6.36 | | | |
% 40.65/6.36 | | | | CLOSE: (66) is inconsistent.
% 40.65/6.36 | | | |
% 40.65/6.36 | | | Case 2:
% 40.65/6.36 | | | |
% 40.65/6.36 | | | | (67) equilibrium(all_11_0) = all_41_2 & $i(all_41_2) & ~
% 40.65/6.36 | | | | greater_or_equal(all_29_2, all_41_2)
% 40.65/6.36 | | | |
% 40.65/6.36 | | | | ALPHA: (67) implies:
% 40.65/6.36 | | | | (68) ~ greater_or_equal(all_29_2, all_41_2)
% 40.65/6.36 | | | | (69) equilibrium(all_11_0) = all_41_2
% 40.65/6.36 | | | |
% 40.65/6.36 | | | | REDUCE: (59), (68) imply:
% 40.65/6.36 | | | | (70) ~ greater_or_equal(all_21_0, all_41_2)
% 40.65/6.36 | | | |
% 40.65/6.36 | | | | REF_CLOSE: (13), (18), (20), (69), (70) are inconsistent by sub-proof
% 40.65/6.36 | | | | #16.
% 40.65/6.36 | | | |
% 40.65/6.36 | | | End of split
% 40.65/6.36 | | |
% 40.65/6.36 | | Case 2:
% 40.65/6.36 | | |
% 40.65/6.36 | | | (71) (growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.36 | | | growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0) &
% 40.65/6.36 | | | $i(all_41_1) & greater(all_41_0, zero) & greater(zero,
% 40.65/6.36 | | | all_41_1)) | (growth_rate(efficient_producers, all_29_2) =
% 40.65/6.36 | | | all_41_0 & growth_rate(first_movers, all_29_2) = all_41_1 &
% 40.65/6.36 | | | $i(all_41_0) & $i(all_41_1) & greater(all_41_1, zero) &
% 40.65/6.36 | | | greater(zero, all_41_0))
% 40.65/6.36 | | |
% 40.65/6.36 | | | REF_CLOSE: (3), (10), (11), (14), (16), (17), (19), (71) are inconsistent
% 40.65/6.36 | | | by sub-proof #17.
% 40.65/6.36 | | |
% 40.65/6.36 | | End of split
% 40.65/6.36 | |
% 40.65/6.36 | End of split
% 40.65/6.36 |
% 40.65/6.36 End of proof
% 40.65/6.36
% 40.65/6.36 Sub-proof #16 shows that the following formulas are inconsistent:
% 40.65/6.36 ----------------------------------------------------------------
% 40.65/6.36 (1) ~ greater_or_equal(all_21_0, all_41_2)
% 40.65/6.36 (2) greater_or_equal(all_21_0, all_19_1)
% 40.65/6.36 (3) equilibrium(all_11_0) = all_41_2
% 40.65/6.36 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (equilibrium(v2)
% 40.65/6.36 = v1) | ~ (equilibrium(v2) = v0))
% 40.65/6.36 (5) equilibrium(all_11_0) = all_19_1
% 40.65/6.36
% 40.65/6.36 Begin of proof
% 40.65/6.36 |
% 40.65/6.36 | GROUND_INST: instantiating (4) with all_19_1, all_41_2, all_11_0, simplifying
% 40.65/6.36 | with (3), (5) gives:
% 40.65/6.36 | (6) all_41_2 = all_19_1
% 40.65/6.36 |
% 40.65/6.36 | PRED_UNIFY: (1), (2) imply:
% 40.65/6.36 | (7) ~ (all_41_2 = all_19_1)
% 40.65/6.36 |
% 40.65/6.36 | REDUCE: (6), (7) imply:
% 40.65/6.36 | (8) $false
% 40.65/6.36 |
% 40.65/6.36 | CLOSE: (8) is inconsistent.
% 40.65/6.36 |
% 40.65/6.36 End of proof
% 40.65/6.36
% 40.65/6.36 Sub-proof #17 shows that the following formulas are inconsistent:
% 40.65/6.36 ----------------------------------------------------------------
% 40.65/6.36 (1) (growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.36 growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0) &
% 40.65/6.36 $i(all_41_1) & greater(all_41_0, zero) & greater(zero, all_41_1)) |
% 40.65/6.36 (growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.36 growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0) &
% 40.65/6.36 $i(all_41_1) & greater(all_41_1, zero) & greater(zero, all_41_0))
% 40.65/6.36 (2) growth_rate(efficient_producers, all_29_2) = all_29_1
% 40.65/6.36 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 40.65/6.36 $i(v0) | ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 40.65/6.36 (4) $i(zero)
% 40.65/6.36 (5) ~ greater(all_29_1, zero)
% 40.65/6.36 (6) growth_rate(first_movers, all_29_2) = all_38_0
% 40.65/6.36 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.36 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 40.65/6.36 (8) greater(all_29_1, all_38_0)
% 40.65/6.36
% 40.65/6.36 Begin of proof
% 40.65/6.36 |
% 40.65/6.36 | BETA: splitting (1) gives:
% 40.65/6.36 |
% 40.65/6.36 | Case 1:
% 40.65/6.36 | |
% 40.65/6.36 | | (9) growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.36 | | growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0) &
% 40.65/6.36 | | $i(all_41_1) & greater(all_41_0, zero) & greater(zero, all_41_1)
% 40.65/6.36 | |
% 40.65/6.36 | | ALPHA: (9) implies:
% 40.65/6.36 | | (10) greater(all_41_0, zero)
% 40.65/6.36 | | (11) growth_rate(efficient_producers, all_29_2) = all_41_0
% 40.65/6.36 | |
% 40.65/6.36 | | REF_CLOSE: (2), (5), (7), (10), (11) are inconsistent by sub-proof #19.
% 40.65/6.36 | |
% 40.65/6.36 | Case 2:
% 40.65/6.36 | |
% 40.65/6.36 | | (12) growth_rate(efficient_producers, all_29_2) = all_41_0 &
% 40.65/6.36 | | growth_rate(first_movers, all_29_2) = all_41_1 & $i(all_41_0) &
% 40.65/6.36 | | $i(all_41_1) & greater(all_41_1, zero) & greater(zero, all_41_0)
% 40.65/6.36 | |
% 40.65/6.36 | | ALPHA: (12) implies:
% 40.65/6.36 | | (13) greater(all_41_1, zero)
% 40.65/6.36 | | (14) $i(all_41_1)
% 40.65/6.36 | | (15) $i(all_41_0)
% 40.65/6.36 | | (16) growth_rate(first_movers, all_29_2) = all_41_1
% 40.65/6.36 | | (17) growth_rate(efficient_producers, all_29_2) = all_41_0
% 40.65/6.36 | |
% 40.65/6.36 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (13), (14), (15), (16), (17)
% 40.65/6.36 | | are inconsistent by sub-proof #18.
% 40.65/6.36 | |
% 40.65/6.36 | End of split
% 40.65/6.36 |
% 40.65/6.36 End of proof
% 40.65/6.36
% 40.65/6.36 Sub-proof #18 shows that the following formulas are inconsistent:
% 40.65/6.36 ----------------------------------------------------------------
% 40.65/6.37 (1) growth_rate(efficient_producers, all_29_2) = all_29_1
% 40.65/6.37 (2) growth_rate(first_movers, all_29_2) = all_41_1
% 40.65/6.37 (3) growth_rate(efficient_producers, all_29_2) = all_41_0
% 40.65/6.37 (4) $i(all_41_0)
% 40.65/6.37 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 40.65/6.37 $i(v0) | ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 40.65/6.37 (6) $i(zero)
% 40.65/6.37 (7) $i(all_41_1)
% 40.65/6.37 (8) ~ greater(all_29_1, zero)
% 40.65/6.37 (9) growth_rate(first_movers, all_29_2) = all_38_0
% 40.65/6.37 (10) greater(all_41_1, zero)
% 40.65/6.37 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.37 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 40.65/6.37 (12) greater(all_29_1, all_38_0)
% 40.65/6.37
% 40.65/6.37 Begin of proof
% 40.65/6.37 |
% 40.65/6.37 | GROUND_INST: instantiating (11) with all_38_0, all_41_1, all_29_2,
% 40.65/6.37 | first_movers, simplifying with (2), (9) gives:
% 40.65/6.37 | (13) all_41_1 = all_38_0
% 40.65/6.37 |
% 40.65/6.37 | GROUND_INST: instantiating (11) with all_29_1, all_41_0, all_29_2,
% 40.65/6.37 | efficient_producers, simplifying with (1), (3) gives:
% 40.65/6.37 | (14) all_41_0 = all_29_1
% 40.65/6.37 |
% 40.65/6.37 | REDUCE: (4), (14) imply:
% 40.65/6.37 | (15) $i(all_29_1)
% 40.65/6.37 |
% 40.65/6.37 | REDUCE: (7), (13) imply:
% 40.65/6.37 | (16) $i(all_38_0)
% 40.65/6.37 |
% 40.65/6.37 | REDUCE: (10), (13) imply:
% 40.65/6.37 | (17) greater(all_38_0, zero)
% 40.65/6.37 |
% 40.65/6.37 | GROUND_INST: instantiating (5) with all_29_1, all_38_0, zero, simplifying with
% 40.65/6.37 | (6), (8), (12), (15), (16), (17) gives:
% 40.65/6.37 | (18) $false
% 40.65/6.37 |
% 40.65/6.37 | CLOSE: (18) is inconsistent.
% 40.65/6.37 |
% 40.65/6.37 End of proof
% 40.65/6.37
% 40.65/6.37 Sub-proof #19 shows that the following formulas are inconsistent:
% 40.65/6.37 ----------------------------------------------------------------
% 40.65/6.37 (1) growth_rate(efficient_producers, all_29_2) = all_29_1
% 40.65/6.37 (2) growth_rate(efficient_producers, all_29_2) = all_41_0
% 40.65/6.37 (3) greater(all_41_0, zero)
% 40.65/6.37 (4) ~ greater(all_29_1, zero)
% 40.65/6.37 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.37 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 40.65/6.37
% 40.65/6.37 Begin of proof
% 40.65/6.37 |
% 40.65/6.37 | PRED_UNIFY: (3), (4) imply:
% 40.65/6.37 | (6) ~ (all_41_0 = all_29_1)
% 40.65/6.37 |
% 40.65/6.37 | GROUND_INST: instantiating (5) with all_29_1, all_41_0, all_29_2,
% 40.65/6.37 | efficient_producers, simplifying with (1), (2) gives:
% 40.65/6.37 | (7) all_41_0 = all_29_1
% 40.65/6.37 |
% 40.65/6.37 | REDUCE: (6), (7) imply:
% 40.65/6.37 | (8) $false
% 40.65/6.37 |
% 40.65/6.37 | CLOSE: (8) is inconsistent.
% 40.65/6.37 |
% 40.65/6.37 End of proof
% 40.65/6.37
% 40.65/6.37 Sub-proof #20 shows that the following formulas are inconsistent:
% 40.65/6.37 ----------------------------------------------------------------
% 40.65/6.37 (1) greater(all_29_2, all_19_1)
% 40.65/6.37 (2) equilibrium(all_11_0) = all_41_2
% 40.65/6.37 (3) ~ greater_or_equal(all_29_2, all_41_2)
% 40.65/6.37 (4) $i(all_29_2)
% 40.65/6.37 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (equilibrium(v2)
% 40.65/6.37 = v1) | ~ (equilibrium(v2) = v0))
% 40.65/6.37 (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1) |
% 40.65/6.37 greater_or_equal(v0, v1))
% 40.65/6.37 (7) $i(all_41_2)
% 40.65/6.37 (8) equilibrium(all_11_0) = all_19_1
% 40.65/6.37
% 40.65/6.37 Begin of proof
% 40.65/6.37 |
% 40.65/6.37 | GROUND_INST: instantiating (5) with all_19_1, all_41_2, all_11_0, simplifying
% 40.65/6.37 | with (2), (8) gives:
% 40.65/6.37 | (9) all_41_2 = all_19_1
% 40.65/6.37 |
% 40.65/6.37 | REDUCE: (7), (9) imply:
% 40.65/6.37 | (10) $i(all_19_1)
% 40.65/6.37 |
% 40.65/6.37 | REDUCE: (3), (9) imply:
% 40.65/6.37 | (11) ~ greater_or_equal(all_29_2, all_19_1)
% 40.65/6.37 |
% 40.65/6.37 | GROUND_INST: instantiating (6) with all_29_2, all_19_1, simplifying with (1),
% 40.65/6.37 | (4), (10), (11) gives:
% 40.65/6.37 | (12) $false
% 40.65/6.37 |
% 40.65/6.37 | CLOSE: (12) is inconsistent.
% 40.65/6.37 |
% 40.65/6.37 End of proof
% 40.65/6.37 % SZS output end Proof for theBenchmark
% 40.65/6.37
% 40.65/6.37 5758ms
%------------------------------------------------------------------------------