TSTP Solution File: MGT020+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : MGT020+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 09:16:13 EDT 2023
% Result : Theorem 9.65s 2.07s
% Output : Proof 12.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT020+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 06:36:38 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.41/1.04 Prover 4: Preprocessing ...
% 2.41/1.04 Prover 1: Preprocessing ...
% 2.70/1.08 Prover 2: Preprocessing ...
% 2.70/1.08 Prover 0: Preprocessing ...
% 2.70/1.08 Prover 3: Preprocessing ...
% 2.70/1.08 Prover 5: Preprocessing ...
% 2.70/1.08 Prover 6: Preprocessing ...
% 4.92/1.41 Prover 3: Constructing countermodel ...
% 4.92/1.41 Prover 1: Constructing countermodel ...
% 4.92/1.41 Prover 6: Constructing countermodel ...
% 4.92/1.44 Prover 5: Proving ...
% 4.92/1.45 Prover 2: Proving ...
% 5.84/1.53 Prover 4: Constructing countermodel ...
% 5.84/1.58 Prover 0: Proving ...
% 6.62/1.67 Prover 3: gave up
% 6.62/1.69 Prover 6: gave up
% 6.62/1.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.37/1.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.37/1.72 Prover 7: Preprocessing ...
% 7.37/1.73 Prover 1: gave up
% 7.37/1.75 Prover 8: Preprocessing ...
% 7.37/1.75 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 7.37/1.79 Prover 9: Preprocessing ...
% 8.11/1.80 Prover 7: Constructing countermodel ...
% 8.11/1.80 Prover 8: Warning: ignoring some quantifiers
% 8.11/1.81 Prover 8: Constructing countermodel ...
% 8.83/1.90 Prover 7: gave up
% 8.83/1.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.83/1.92 Prover 10: Preprocessing ...
% 8.83/1.96 Prover 10: Constructing countermodel ...
% 8.83/1.99 Prover 10: gave up
% 8.83/1.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.58/2.00 Prover 8: gave up
% 9.59/2.02 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 9.59/2.04 Prover 12: Preprocessing ...
% 9.59/2.04 Prover 11: Preprocessing ...
% 9.65/2.07 Prover 0: proved (1432ms)
% 9.65/2.07 Prover 9: Constructing countermodel ...
% 9.65/2.07
% 9.65/2.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.65/2.07
% 9.65/2.07 Prover 5: stopped
% 9.65/2.07 Prover 2: stopped
% 9.65/2.07 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.65/2.07 Prover 9: stopped
% 9.65/2.07 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 9.65/2.07 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.65/2.08 Prover 12: stopped
% 9.65/2.09 Prover 16: Preprocessing ...
% 9.65/2.09 Prover 13: Preprocessing ...
% 9.65/2.09 Prover 19: Preprocessing ...
% 9.65/2.12 Prover 16: Warning: ignoring some quantifiers
% 9.65/2.12 Prover 16: Constructing countermodel ...
% 9.65/2.13 Prover 13: Warning: ignoring some quantifiers
% 9.65/2.14 Prover 13: Constructing countermodel ...
% 10.70/2.17 Prover 19: Warning: ignoring some quantifiers
% 10.70/2.18 Prover 11: Constructing countermodel ...
% 10.70/2.18 Prover 19: Constructing countermodel ...
% 11.49/2.27 Prover 16: gave up
% 12.08/2.38 Prover 13: Found proof (size 92)
% 12.08/2.38 Prover 13: proved (310ms)
% 12.08/2.38 Prover 11: stopped
% 12.08/2.38 Prover 19: stopped
% 12.08/2.39 Prover 4: stopped
% 12.08/2.39
% 12.08/2.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.08/2.39
% 12.53/2.41 % SZS output start Proof for theBenchmark
% 12.53/2.41 Assumptions after simplification:
% 12.53/2.41 ---------------------------------
% 12.53/2.41
% 12.53/2.41 (a8)
% 12.53/2.43 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : ( ~
% 12.53/2.43 (initial_FM_EP(v0) = v1) | ~ $i(v0) | ~ environment(v0) | ? [v2: $i] : ?
% 12.53/2.43 [v3: $i] : (disbanding_rate(efficient_producers, v1) = v3 &
% 12.53/2.43 disbanding_rate(first_movers, v1) = v2 & $i(v3) & $i(v2) & greater(v2,
% 12.53/2.43 v3))) & ! [v0: $i] : ( ~ $i(v0) | ~ environment(v0) | ? [v1: $i] : ?
% 12.53/2.43 [v2: $i] : ? [v3: $i] : (initial_FM_EP(v0) = v1 &
% 12.53/2.43 disbanding_rate(efficient_producers, v1) = v3 &
% 12.53/2.43 disbanding_rate(first_movers, v1) = v2 & $i(v3) & $i(v2) & $i(v1) &
% 12.53/2.43 greater(v2, v3)))
% 12.53/2.43
% 12.53/2.43 (l3)
% 12.53/2.44 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : !
% 12.53/2.44 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 12.53/2.44 (disbanding_rate(efficient_producers, v1) = v3) | ~
% 12.53/2.44 (disbanding_rate(first_movers, v1) = v2) | ~ (difference(v2, v3) = v4) | ~
% 12.53/2.44 $i(v1) | ~ $i(v0) | ~ decreases(v4) | ~ subpopulations(first_movers,
% 12.53/2.44 efficient_producers, v0, v1) | ~ environment(v0)) & ! [v0: $i] : ! [v1:
% 12.53/2.44 $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subpopulations(first_movers,
% 12.53/2.44 efficient_producers, v0, v1) | ~ environment(v0) | ? [v2: $i] : ? [v3:
% 12.53/2.44 $i] : ? [v4: $i] : (disbanding_rate(efficient_producers, v1) = v3 &
% 12.53/2.44 disbanding_rate(first_movers, v1) = v2 & difference(v2, v3) = v4 & $i(v4)
% 12.53/2.44 & $i(v3) & $i(v2) & ~ decreases(v4)))
% 12.53/2.44
% 12.53/2.44 (mp_earliest_time_point)
% 12.53/2.44 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : !
% 12.53/2.44 [v2: $i] : ( ~ (initial_FM_EP(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 12.53/2.44 subpopulations(first_movers, efficient_producers, v0, v1) | ~
% 12.53/2.44 environment(v0) | greater_or_equal(v1, v2)) & ! [v0: $i] : ! [v1: $i] : (
% 12.53/2.44 ~ (initial_FM_EP(v0) = v1) | ~ $i(v0) | ~ in_environment(v0, v1) | ~
% 12.53/2.44 environment(v0) | subpopulations(first_movers, efficient_producers, v0, v1))
% 12.53/2.44 & ? [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ environment(v1) | ?
% 12.53/2.44 [v2: $i] : (initial_FM_EP(v1) = v2 & $i(v2) & ( ~ in_environment(v1, v2) |
% 12.53/2.44 subpopulations(first_movers, efficient_producers, v1, v2)) & ( ~
% 12.53/2.44 subpopulations(first_movers, efficient_producers, v1, v0) |
% 12.53/2.44 greater_or_equal(v0, v2))))
% 12.53/2.44
% 12.53/2.44 (mp_greater_or_equal)
% 12.53/2.44 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 12.53/2.44 greater_or_equal(v0, v1) | greater(v0, v1))
% 12.53/2.44
% 12.53/2.44 (mp_initial_time)
% 12.53/2.45 ! [v0: $i] : ! [v1: $i] : ( ~ (start_time(v0) = v1) | ~ $i(v0) | ~
% 12.53/2.45 environment(v0) | ? [v2: $i] : (initial_FM_EP(v0) = v2 & $i(v2) &
% 12.53/2.45 greater_or_equal(v2, v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ environment(v0)
% 12.53/2.45 | ? [v1: $i] : ? [v2: $i] : (start_time(v0) = v2 & initial_FM_EP(v0) = v1
% 12.53/2.45 & $i(v2) & $i(v1) & greater_or_equal(v1, v2)))
% 12.53/2.45
% 12.53/2.45 (mp_positive_function_difference)
% 12.53/2.45 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : !
% 12.53/2.45 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 12.53/2.45 : ! [v8: $i] : ( ~ (disbanding_rate(efficient_producers, v1) = v6) | ~
% 12.53/2.45 (disbanding_rate(first_movers, v3) = v8) | ~ (disbanding_rate(first_movers,
% 12.53/2.45 v2) = v4) | ~ (disbanding_rate(first_movers, v1) = v5) | ~
% 12.53/2.45 (difference(v5, v6) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 12.53/2.45 ~ greater_or_equal(v3, v1) | ~ greater_or_equal(v1, v2) | ~
% 12.53/2.45 subpopulations(first_movers, efficient_producers, v0, v3) | ~
% 12.53/2.45 environment(v0) | decreases(v7) | ? [v9: $i] : ? [v10: $i] :
% 12.53/2.45 (disbanding_rate(efficient_producers, v3) = v10 &
% 12.53/2.45 disbanding_rate(efficient_producers, v2) = v9 & $i(v10) & $i(v9) & ( ~
% 12.53/2.45 greater(v4, v9) | greater(v8, v10)))) & ! [v0: $i] : ! [v1: $i] : !
% 12.53/2.45 [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 12.53/2.45 greater_or_equal(v3, v1) | ~ greater_or_equal(v1, v2) | ~
% 12.53/2.45 subpopulations(first_movers, efficient_producers, v0, v3) | ~
% 12.53/2.45 environment(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 12.53/2.45 [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 12.53/2.45 (disbanding_rate(efficient_producers, v3) = v10 &
% 12.53/2.45 disbanding_rate(efficient_producers, v2) = v5 &
% 12.53/2.45 disbanding_rate(efficient_producers, v1) = v7 &
% 12.53/2.45 disbanding_rate(first_movers, v3) = v9 & disbanding_rate(first_movers, v2)
% 12.53/2.45 = v4 & disbanding_rate(first_movers, v1) = v6 & difference(v6, v7) = v8 &
% 12.53/2.45 $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & ( ~
% 12.53/2.45 greater(v4, v5) | greater(v9, v10) | decreases(v8))))
% 12.53/2.45
% 12.53/2.45 (mp_time_point_occurs)
% 12.53/2.45 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : ( ~
% 12.53/2.45 $i(v1) | ~ $i(v0) | ~ subpopulations(first_movers, efficient_producers,
% 12.53/2.45 v0, v1) | ~ environment(v0) | in_environment(v0, v1))
% 12.53/2.45
% 12.53/2.45 (mp_times_in_order)
% 12.53/2.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (start_time(v0) =
% 12.53/2.45 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ greater(v2, v1) | ~
% 12.53/2.45 greater_or_equal(v1, v3) | ~ in_environment(v0, v2) | ~ environment(v0) |
% 12.53/2.45 in_environment(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 12.53/2.45 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ greater(v2, v1) | ~ in_environment(v0,
% 12.53/2.45 v2) | ~ environment(v0) | in_environment(v0, v1) | ? [v3: $i] :
% 12.53/2.45 (start_time(v0) = v3 & $i(v3) & ~ greater_or_equal(v1, v3)))
% 12.53/2.45
% 12.53/2.45 (prove_l2)
% 12.53/2.46 $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ? [v1: $i] : ?
% 12.53/2.46 [v2: $i] : ? [v3: $i] : (disbanding_rate(efficient_producers, v1) = v3 &
% 12.53/2.46 disbanding_rate(first_movers, v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 12.53/2.46 subpopulations(first_movers, efficient_producers, v0, v1) & environment(v0)
% 12.53/2.46 & ~ greater(v2, v3))
% 12.53/2.46
% 12.53/2.46 (function-axioms)
% 12.53/2.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.53/2.46 (disbanding_rate(v3, v2) = v1) | ~ (disbanding_rate(v3, v2) = v0)) & !
% 12.53/2.46 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.53/2.46 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 12.53/2.46 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (start_time(v2) = v1) | ~
% 12.53/2.46 (start_time(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 12.53/2.46 | ~ (initial_FM_EP(v2) = v1) | ~ (initial_FM_EP(v2) = v0))
% 12.53/2.46
% 12.53/2.46 Further assumptions not needed in the proof:
% 12.53/2.46 --------------------------------------------
% 12.53/2.46 a10, mp_greater_transitivity
% 12.53/2.46
% 12.53/2.46 Those formulas are unsatisfiable:
% 12.53/2.46 ---------------------------------
% 12.53/2.46
% 12.53/2.46 Begin of proof
% 12.53/2.46 |
% 12.84/2.46 | ALPHA: (l3) implies:
% 12.84/2.46 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 12.84/2.46 | subpopulations(first_movers, efficient_producers, v0, v1) | ~
% 12.84/2.46 | environment(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 12.84/2.46 | (disbanding_rate(efficient_producers, v1) = v3 &
% 12.84/2.46 | disbanding_rate(first_movers, v1) = v2 & difference(v2, v3) = v4 &
% 12.84/2.46 | $i(v4) & $i(v3) & $i(v2) & ~ decreases(v4)))
% 12.84/2.46 |
% 12.84/2.46 | ALPHA: (mp_earliest_time_point) implies:
% 12.84/2.46 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (initial_FM_EP(v0) = v1) | ~ $i(v0) |
% 12.84/2.46 | ~ in_environment(v0, v1) | ~ environment(v0) |
% 12.84/2.46 | subpopulations(first_movers, efficient_producers, v0, v1))
% 12.84/2.46 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (initial_FM_EP(v0) = v2)
% 12.84/2.46 | | ~ $i(v1) | ~ $i(v0) | ~ subpopulations(first_movers,
% 12.84/2.46 | efficient_producers, v0, v1) | ~ environment(v0) |
% 12.84/2.46 | greater_or_equal(v1, v2))
% 12.84/2.46 |
% 12.84/2.46 | ALPHA: (mp_positive_function_difference) implies:
% 12.84/2.46 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 12.84/2.46 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ greater_or_equal(v3, v1) | ~
% 12.84/2.46 | greater_or_equal(v1, v2) | ~ subpopulations(first_movers,
% 12.84/2.46 | efficient_producers, v0, v3) | ~ environment(v0) | ? [v4: $i] :
% 12.84/2.46 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 12.84/2.46 | ? [v10: $i] : (disbanding_rate(efficient_producers, v3) = v10 &
% 12.84/2.46 | disbanding_rate(efficient_producers, v2) = v5 &
% 12.84/2.46 | disbanding_rate(efficient_producers, v1) = v7 &
% 12.84/2.47 | disbanding_rate(first_movers, v3) = v9 &
% 12.84/2.47 | disbanding_rate(first_movers, v2) = v4 &
% 12.84/2.47 | disbanding_rate(first_movers, v1) = v6 & difference(v6, v7) = v8 &
% 12.84/2.47 | $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & ( ~
% 12.84/2.47 | greater(v4, v5) | greater(v9, v10) | decreases(v8))))
% 12.84/2.47 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 12.84/2.47 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 12.84/2.47 | (disbanding_rate(efficient_producers, v1) = v6) | ~
% 12.84/2.47 | (disbanding_rate(first_movers, v3) = v8) | ~
% 12.84/2.47 | (disbanding_rate(first_movers, v2) = v4) | ~
% 12.84/2.47 | (disbanding_rate(first_movers, v1) = v5) | ~ (difference(v5, v6) =
% 12.84/2.47 | v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 12.84/2.47 | greater_or_equal(v3, v1) | ~ greater_or_equal(v1, v2) | ~
% 12.84/2.47 | subpopulations(first_movers, efficient_producers, v0, v3) | ~
% 12.84/2.47 | environment(v0) | decreases(v7) | ? [v9: $i] : ? [v10: $i] :
% 12.84/2.47 | (disbanding_rate(efficient_producers, v3) = v10 &
% 12.84/2.47 | disbanding_rate(efficient_producers, v2) = v9 & $i(v10) & $i(v9) &
% 12.84/2.47 | ( ~ greater(v4, v9) | greater(v8, v10))))
% 12.84/2.47 |
% 12.84/2.47 | ALPHA: (mp_time_point_occurs) implies:
% 12.84/2.47 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 12.84/2.47 | subpopulations(first_movers, efficient_producers, v0, v1) | ~
% 12.84/2.47 | environment(v0) | in_environment(v0, v1))
% 12.84/2.47 |
% 12.84/2.47 | ALPHA: (mp_initial_time) implies:
% 12.84/2.47 | (7) ! [v0: $i] : ( ~ $i(v0) | ~ environment(v0) | ? [v1: $i] : ? [v2:
% 12.84/2.47 | $i] : (start_time(v0) = v2 & initial_FM_EP(v0) = v1 & $i(v2) &
% 12.84/2.47 | $i(v1) & greater_or_equal(v1, v2)))
% 12.84/2.47 |
% 12.84/2.47 | ALPHA: (mp_times_in_order) implies:
% 12.84/2.47 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 12.84/2.47 | (start_time(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 12.84/2.47 | greater(v2, v1) | ~ greater_or_equal(v1, v3) | ~ in_environment(v0,
% 12.84/2.47 | v2) | ~ environment(v0) | in_environment(v0, v1))
% 12.84/2.47 |
% 12.84/2.47 | ALPHA: (a8) implies:
% 12.84/2.47 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ environment(v0) | ? [v1: $i] : ? [v2:
% 12.84/2.47 | $i] : ? [v3: $i] : (initial_FM_EP(v0) = v1 &
% 12.84/2.47 | disbanding_rate(efficient_producers, v1) = v3 &
% 12.84/2.47 | disbanding_rate(first_movers, v1) = v2 & $i(v3) & $i(v2) & $i(v1) &
% 12.84/2.47 | greater(v2, v3)))
% 12.84/2.47 |
% 12.84/2.47 | ALPHA: (prove_l2) implies:
% 12.84/2.47 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 12.84/2.47 | (disbanding_rate(efficient_producers, v1) = v3 &
% 12.84/2.47 | disbanding_rate(first_movers, v1) = v2 & $i(v3) & $i(v2) & $i(v1) &
% 12.84/2.47 | $i(v0) & subpopulations(first_movers, efficient_producers, v0, v1) &
% 12.84/2.47 | environment(v0) & ~ greater(v2, v3))
% 12.84/2.47 |
% 12.84/2.47 | ALPHA: (function-axioms) implies:
% 12.84/2.47 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 12.84/2.47 | (initial_FM_EP(v2) = v1) | ~ (initial_FM_EP(v2) = v0))
% 12.84/2.47 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.84/2.47 | (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 12.84/2.47 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.84/2.47 | (disbanding_rate(v3, v2) = v1) | ~ (disbanding_rate(v3, v2) = v0))
% 12.84/2.47 |
% 12.84/2.47 | DELTA: instantiating (10) with fresh symbols all_16_0, all_16_1, all_16_2,
% 12.84/2.47 | all_16_3 gives:
% 12.84/2.48 | (14) disbanding_rate(efficient_producers, all_16_2) = all_16_0 &
% 12.84/2.48 | disbanding_rate(first_movers, all_16_2) = all_16_1 & $i(all_16_0) &
% 12.84/2.48 | $i(all_16_1) & $i(all_16_2) & $i(all_16_3) &
% 12.84/2.48 | subpopulations(first_movers, efficient_producers, all_16_3, all_16_2)
% 12.84/2.48 | & environment(all_16_3) & ~ greater(all_16_1, all_16_0)
% 12.84/2.48 |
% 12.84/2.48 | ALPHA: (14) implies:
% 12.84/2.48 | (15) ~ greater(all_16_1, all_16_0)
% 12.84/2.48 | (16) environment(all_16_3)
% 12.84/2.48 | (17) subpopulations(first_movers, efficient_producers, all_16_3, all_16_2)
% 12.84/2.48 | (18) $i(all_16_3)
% 12.84/2.48 | (19) $i(all_16_2)
% 12.84/2.48 | (20) disbanding_rate(first_movers, all_16_2) = all_16_1
% 12.84/2.48 | (21) disbanding_rate(efficient_producers, all_16_2) = all_16_0
% 12.84/2.48 |
% 12.84/2.48 | GROUND_INST: instantiating (9) with all_16_3, simplifying with (16), (18)
% 12.84/2.48 | gives:
% 12.84/2.48 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (initial_FM_EP(all_16_3) =
% 12.84/2.48 | v0 & disbanding_rate(efficient_producers, v0) = v2 &
% 12.84/2.48 | disbanding_rate(first_movers, v0) = v1 & $i(v2) & $i(v1) & $i(v0) &
% 12.84/2.48 | greater(v1, v2))
% 12.84/2.48 |
% 12.84/2.48 | GROUND_INST: instantiating (7) with all_16_3, simplifying with (16), (18)
% 12.84/2.48 | gives:
% 12.84/2.48 | (23) ? [v0: $i] : ? [v1: $i] : (start_time(all_16_3) = v1 &
% 12.84/2.48 | initial_FM_EP(all_16_3) = v0 & $i(v1) & $i(v0) &
% 12.84/2.48 | greater_or_equal(v0, v1))
% 12.84/2.48 |
% 12.84/2.48 | GROUND_INST: instantiating (6) with all_16_3, all_16_2, simplifying with (16),
% 12.84/2.48 | (17), (18), (19) gives:
% 12.84/2.48 | (24) in_environment(all_16_3, all_16_2)
% 12.84/2.48 |
% 12.84/2.48 | GROUND_INST: instantiating (1) with all_16_3, all_16_2, simplifying with (16),
% 12.84/2.48 | (17), (18), (19) gives:
% 12.84/2.48 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 12.84/2.48 | (disbanding_rate(efficient_producers, all_16_2) = v1 &
% 12.84/2.48 | disbanding_rate(first_movers, all_16_2) = v0 & difference(v0, v1) =
% 12.84/2.48 | v2 & $i(v2) & $i(v1) & $i(v0) & ~ decreases(v2))
% 12.84/2.48 |
% 12.84/2.48 | DELTA: instantiating (23) with fresh symbols all_24_0, all_24_1 gives:
% 12.84/2.48 | (26) start_time(all_16_3) = all_24_0 & initial_FM_EP(all_16_3) = all_24_1 &
% 12.84/2.48 | $i(all_24_0) & $i(all_24_1) & greater_or_equal(all_24_1, all_24_0)
% 12.84/2.48 |
% 12.84/2.48 | ALPHA: (26) implies:
% 12.84/2.48 | (27) greater_or_equal(all_24_1, all_24_0)
% 12.84/2.48 | (28) $i(all_24_0)
% 12.84/2.48 | (29) initial_FM_EP(all_16_3) = all_24_1
% 12.84/2.48 | (30) start_time(all_16_3) = all_24_0
% 12.84/2.48 |
% 12.84/2.48 | DELTA: instantiating (25) with fresh symbols all_26_0, all_26_1, all_26_2
% 12.84/2.48 | gives:
% 12.84/2.48 | (31) disbanding_rate(efficient_producers, all_16_2) = all_26_1 &
% 12.84/2.48 | disbanding_rate(first_movers, all_16_2) = all_26_2 &
% 12.84/2.48 | difference(all_26_2, all_26_1) = all_26_0 & $i(all_26_0) &
% 12.84/2.48 | $i(all_26_1) & $i(all_26_2) & ~ decreases(all_26_0)
% 12.84/2.48 |
% 12.84/2.48 | ALPHA: (31) implies:
% 12.84/2.48 | (32) disbanding_rate(first_movers, all_16_2) = all_26_2
% 12.84/2.48 | (33) disbanding_rate(efficient_producers, all_16_2) = all_26_1
% 12.84/2.48 |
% 12.84/2.48 | DELTA: instantiating (22) with fresh symbols all_28_0, all_28_1, all_28_2
% 12.84/2.48 | gives:
% 12.84/2.48 | (34) initial_FM_EP(all_16_3) = all_28_2 &
% 12.84/2.48 | disbanding_rate(efficient_producers, all_28_2) = all_28_0 &
% 12.84/2.48 | disbanding_rate(first_movers, all_28_2) = all_28_1 & $i(all_28_0) &
% 12.84/2.48 | $i(all_28_1) & $i(all_28_2) & greater(all_28_1, all_28_0)
% 12.84/2.48 |
% 12.84/2.48 | ALPHA: (34) implies:
% 12.84/2.48 | (35) greater(all_28_1, all_28_0)
% 12.84/2.48 | (36) $i(all_28_2)
% 12.84/2.48 | (37) disbanding_rate(first_movers, all_28_2) = all_28_1
% 12.84/2.49 | (38) disbanding_rate(efficient_producers, all_28_2) = all_28_0
% 12.84/2.49 | (39) initial_FM_EP(all_16_3) = all_28_2
% 12.84/2.49 |
% 12.84/2.49 | GROUND_INST: instantiating (13) with all_16_1, all_26_2, all_16_2,
% 12.84/2.49 | first_movers, simplifying with (20), (32) gives:
% 12.84/2.49 | (40) all_26_2 = all_16_1
% 12.84/2.49 |
% 12.84/2.49 | GROUND_INST: instantiating (13) with all_16_0, all_26_1, all_16_2,
% 12.84/2.49 | efficient_producers, simplifying with (21), (33) gives:
% 12.84/2.49 | (41) all_26_1 = all_16_0
% 12.84/2.49 |
% 12.84/2.49 | GROUND_INST: instantiating (11) with all_24_1, all_28_2, all_16_3, simplifying
% 12.84/2.49 | with (29), (39) gives:
% 12.84/2.49 | (42) all_28_2 = all_24_1
% 12.84/2.49 |
% 12.84/2.49 | REDUCE: (38), (42) imply:
% 12.84/2.49 | (43) disbanding_rate(efficient_producers, all_24_1) = all_28_0
% 12.84/2.49 |
% 12.84/2.49 | REDUCE: (37), (42) imply:
% 12.84/2.49 | (44) disbanding_rate(first_movers, all_24_1) = all_28_1
% 12.84/2.49 |
% 12.84/2.49 | REDUCE: (36), (42) imply:
% 12.84/2.49 | (45) $i(all_24_1)
% 12.84/2.49 |
% 12.84/2.49 | GROUND_INST: instantiating (3) with all_16_3, all_16_2, all_24_1, simplifying
% 12.84/2.49 | with (16), (17), (18), (19), (29) gives:
% 12.84/2.49 | (46) greater_or_equal(all_16_2, all_24_1)
% 12.84/2.49 |
% 12.84/2.49 | GROUND_INST: instantiating (4) with all_16_3, all_24_1, all_24_0, all_16_2,
% 12.84/2.49 | simplifying with (16), (17), (18), (19), (27), (28), (45), (46)
% 12.84/2.49 | gives:
% 12.84/2.49 | (47) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 12.84/2.49 | ? [v5: $i] : ? [v6: $i] : (disbanding_rate(efficient_producers,
% 12.84/2.49 | all_24_0) = v1 & disbanding_rate(efficient_producers, all_24_1) =
% 12.84/2.49 | v3 & disbanding_rate(efficient_producers, all_16_2) = v6 &
% 12.84/2.49 | disbanding_rate(first_movers, all_24_0) = v0 &
% 12.84/2.49 | disbanding_rate(first_movers, all_24_1) = v2 &
% 12.84/2.49 | disbanding_rate(first_movers, all_16_2) = v5 & difference(v2, v3) =
% 12.84/2.49 | v4 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 12.84/2.49 | ( ~ greater(v0, v1) | greater(v5, v6) | decreases(v4)))
% 12.84/2.49 |
% 12.84/2.49 | GROUND_INST: instantiating (mp_greater_or_equal) with all_16_2, all_24_1,
% 12.84/2.49 | simplifying with (19), (45), (46) gives:
% 12.84/2.49 | (48) all_24_1 = all_16_2 | greater(all_16_2, all_24_1)
% 12.84/2.49 |
% 12.84/2.49 | DELTA: instantiating (47) with fresh symbols all_45_0, all_45_1, all_45_2,
% 12.84/2.49 | all_45_3, all_45_4, all_45_5, all_45_6 gives:
% 12.84/2.49 | (49) disbanding_rate(efficient_producers, all_24_0) = all_45_5 &
% 12.84/2.49 | disbanding_rate(efficient_producers, all_24_1) = all_45_3 &
% 12.84/2.49 | disbanding_rate(efficient_producers, all_16_2) = all_45_0 &
% 12.84/2.49 | disbanding_rate(first_movers, all_24_0) = all_45_6 &
% 12.84/2.49 | disbanding_rate(first_movers, all_24_1) = all_45_4 &
% 12.84/2.49 | disbanding_rate(first_movers, all_16_2) = all_45_1 &
% 12.84/2.49 | difference(all_45_4, all_45_3) = all_45_2 & $i(all_45_0) &
% 12.84/2.49 | $i(all_45_1) & $i(all_45_2) & $i(all_45_3) & $i(all_45_4) &
% 12.84/2.49 | $i(all_45_5) & $i(all_45_6) & ( ~ greater(all_45_6, all_45_5) |
% 12.84/2.49 | greater(all_45_1, all_45_0) | decreases(all_45_2))
% 12.84/2.49 |
% 12.84/2.49 | ALPHA: (49) implies:
% 12.84/2.49 | (50) difference(all_45_4, all_45_3) = all_45_2
% 12.84/2.49 | (51) disbanding_rate(first_movers, all_16_2) = all_45_1
% 12.84/2.49 | (52) disbanding_rate(first_movers, all_24_1) = all_45_4
% 12.84/2.49 | (53) disbanding_rate(efficient_producers, all_16_2) = all_45_0
% 12.84/2.49 | (54) disbanding_rate(efficient_producers, all_24_1) = all_45_3
% 12.84/2.49 |
% 12.84/2.49 | GROUND_INST: instantiating (13) with all_16_1, all_45_1, all_16_2,
% 12.84/2.49 | first_movers, simplifying with (20), (51) gives:
% 12.84/2.49 | (55) all_45_1 = all_16_1
% 12.84/2.49 |
% 12.84/2.49 | GROUND_INST: instantiating (13) with all_28_1, all_45_4, all_24_1,
% 12.84/2.49 | first_movers, simplifying with (44), (52) gives:
% 12.84/2.50 | (56) all_45_4 = all_28_1
% 12.84/2.50 |
% 12.84/2.50 | GROUND_INST: instantiating (13) with all_16_0, all_45_0, all_16_2,
% 12.84/2.50 | efficient_producers, simplifying with (21), (53) gives:
% 12.84/2.50 | (57) all_45_0 = all_16_0
% 12.84/2.50 |
% 12.84/2.50 | GROUND_INST: instantiating (13) with all_28_0, all_45_3, all_24_1,
% 12.84/2.50 | efficient_producers, simplifying with (43), (54) gives:
% 12.84/2.50 | (58) all_45_3 = all_28_0
% 12.84/2.50 |
% 12.84/2.50 | REDUCE: (50), (56), (58) imply:
% 12.84/2.50 | (59) difference(all_28_1, all_28_0) = all_45_2
% 12.84/2.50 |
% 12.84/2.50 | BETA: splitting (48) gives:
% 12.84/2.50 |
% 12.84/2.50 | Case 1:
% 12.84/2.50 | |
% 12.84/2.50 | | (60) greater(all_16_2, all_24_1)
% 12.84/2.50 | |
% 12.84/2.50 | | GROUND_INST: instantiating (8) with all_16_3, all_24_1, all_16_2, all_24_0,
% 12.84/2.50 | | simplifying with (16), (18), (19), (24), (27), (30), (45), (60)
% 12.84/2.50 | | gives:
% 12.84/2.50 | | (61) in_environment(all_16_3, all_24_1)
% 12.84/2.50 | |
% 12.84/2.50 | | GROUND_INST: instantiating (2) with all_16_3, all_24_1, simplifying with
% 12.84/2.50 | | (16), (18), (29), (61) gives:
% 12.84/2.50 | | (62) subpopulations(first_movers, efficient_producers, all_16_3,
% 12.84/2.50 | | all_24_1)
% 12.84/2.50 | |
% 12.84/2.50 | | GROUND_INST: instantiating (3) with all_16_3, all_24_1, all_24_1,
% 12.84/2.50 | | simplifying with (16), (18), (29), (45), (62) gives:
% 12.84/2.50 | | (63) greater_or_equal(all_24_1, all_24_1)
% 12.84/2.50 | |
% 12.84/2.50 | | GROUND_INST: instantiating (1) with all_16_3, all_24_1, simplifying with
% 12.84/2.50 | | (16), (18), (45), (62) gives:
% 12.84/2.50 | | (64) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 12.84/2.50 | | (disbanding_rate(efficient_producers, all_24_1) = v1 &
% 12.84/2.50 | | disbanding_rate(first_movers, all_24_1) = v0 & difference(v0, v1)
% 12.84/2.50 | | = v2 & $i(v2) & $i(v1) & $i(v0) & ~ decreases(v2))
% 12.84/2.50 | |
% 12.84/2.50 | | DELTA: instantiating (64) with fresh symbols all_97_0, all_97_1, all_97_2
% 12.84/2.50 | | gives:
% 12.84/2.50 | | (65) disbanding_rate(efficient_producers, all_24_1) = all_97_1 &
% 12.84/2.50 | | disbanding_rate(first_movers, all_24_1) = all_97_2 &
% 12.84/2.50 | | difference(all_97_2, all_97_1) = all_97_0 & $i(all_97_0) &
% 12.84/2.50 | | $i(all_97_1) & $i(all_97_2) & ~ decreases(all_97_0)
% 12.84/2.50 | |
% 12.84/2.50 | | ALPHA: (65) implies:
% 12.84/2.50 | | (66) ~ decreases(all_97_0)
% 12.84/2.50 | | (67) difference(all_97_2, all_97_1) = all_97_0
% 12.84/2.50 | | (68) disbanding_rate(first_movers, all_24_1) = all_97_2
% 12.84/2.50 | | (69) disbanding_rate(efficient_producers, all_24_1) = all_97_1
% 12.84/2.50 | |
% 12.84/2.50 | | GROUND_INST: instantiating (13) with all_28_1, all_97_2, all_24_1,
% 12.84/2.50 | | first_movers, simplifying with (44), (68) gives:
% 12.84/2.50 | | (70) all_97_2 = all_28_1
% 12.84/2.50 | |
% 12.84/2.50 | | GROUND_INST: instantiating (13) with all_28_0, all_97_1, all_24_1,
% 12.84/2.50 | | efficient_producers, simplifying with (43), (69) gives:
% 12.84/2.50 | | (71) all_97_1 = all_28_0
% 12.84/2.50 | |
% 12.84/2.50 | | REDUCE: (67), (70), (71) imply:
% 12.84/2.50 | | (72) difference(all_28_1, all_28_0) = all_97_0
% 12.84/2.50 | |
% 12.84/2.50 | | GROUND_INST: instantiating (12) with all_45_2, all_97_0, all_28_0, all_28_1,
% 12.84/2.50 | | simplifying with (59), (72) gives:
% 12.84/2.50 | | (73) all_97_0 = all_45_2
% 12.84/2.50 | |
% 12.84/2.50 | | REDUCE: (66), (73) imply:
% 12.84/2.50 | | (74) ~ decreases(all_45_2)
% 12.84/2.50 | |
% 12.84/2.51 | | GROUND_INST: instantiating (5) with all_16_3, all_24_1, all_24_1, all_16_2,
% 12.84/2.51 | | all_28_1, all_28_1, all_28_0, all_45_2, all_16_1, simplifying
% 12.84/2.51 | | with (16), (17), (18), (19), (20), (43), (44), (45), (46),
% 12.84/2.51 | | (59), (63), (74) gives:
% 12.84/2.51 | | (75) ? [v0: $i] : ? [v1: $i] : (disbanding_rate(efficient_producers,
% 12.84/2.51 | | all_24_1) = v0 & disbanding_rate(efficient_producers, all_16_2)
% 12.84/2.51 | | = v1 & $i(v1) & $i(v0) & ( ~ greater(all_28_1, v0) |
% 12.84/2.51 | | greater(all_16_1, v1)))
% 12.84/2.51 | |
% 12.84/2.51 | | GROUND_INST: instantiating (4) with all_16_3, all_24_1, all_24_1, all_16_2,
% 12.84/2.51 | | simplifying with (16), (17), (18), (19), (45), (46), (63)
% 12.84/2.51 | | gives:
% 12.84/2.51 | | (76) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 12.84/2.51 | | : ? [v5: $i] : ? [v6: $i] : (disbanding_rate(efficient_producers,
% 12.84/2.51 | | all_24_1) = v3 & disbanding_rate(efficient_producers, all_24_1)
% 12.84/2.51 | | = v1 & disbanding_rate(efficient_producers, all_16_2) = v6 &
% 12.84/2.51 | | disbanding_rate(first_movers, all_24_1) = v2 &
% 12.84/2.51 | | disbanding_rate(first_movers, all_24_1) = v0 &
% 12.84/2.51 | | disbanding_rate(first_movers, all_16_2) = v5 & difference(v2, v3)
% 12.84/2.51 | | = v4 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 12.84/2.51 | | $i(v0) & ( ~ greater(v0, v1) | greater(v5, v6) | decreases(v4)))
% 12.84/2.51 | |
% 12.84/2.51 | | DELTA: instantiating (75) with fresh symbols all_112_0, all_112_1 gives:
% 12.84/2.51 | | (77) disbanding_rate(efficient_producers, all_24_1) = all_112_1 &
% 12.84/2.51 | | disbanding_rate(efficient_producers, all_16_2) = all_112_0 &
% 12.84/2.51 | | $i(all_112_0) & $i(all_112_1) & ( ~ greater(all_28_1, all_112_1) |
% 12.84/2.51 | | greater(all_16_1, all_112_0))
% 12.84/2.51 | |
% 12.84/2.51 | | ALPHA: (77) implies:
% 12.84/2.51 | | (78) disbanding_rate(efficient_producers, all_16_2) = all_112_0
% 12.84/2.51 | | (79) disbanding_rate(efficient_producers, all_24_1) = all_112_1
% 12.84/2.51 | | (80) ~ greater(all_28_1, all_112_1) | greater(all_16_1, all_112_0)
% 12.84/2.51 | |
% 12.84/2.51 | | DELTA: instantiating (76) with fresh symbols all_114_0, all_114_1,
% 12.84/2.51 | | all_114_2, all_114_3, all_114_4, all_114_5, all_114_6 gives:
% 12.84/2.51 | | (81) disbanding_rate(efficient_producers, all_24_1) = all_114_3 &
% 12.84/2.51 | | disbanding_rate(efficient_producers, all_24_1) = all_114_5 &
% 12.84/2.51 | | disbanding_rate(efficient_producers, all_16_2) = all_114_0 &
% 12.84/2.51 | | disbanding_rate(first_movers, all_24_1) = all_114_4 &
% 12.84/2.51 | | disbanding_rate(first_movers, all_24_1) = all_114_6 &
% 12.84/2.51 | | disbanding_rate(first_movers, all_16_2) = all_114_1 &
% 12.84/2.51 | | difference(all_114_4, all_114_3) = all_114_2 & $i(all_114_0) &
% 12.84/2.51 | | $i(all_114_1) & $i(all_114_2) & $i(all_114_3) & $i(all_114_4) &
% 12.84/2.51 | | $i(all_114_5) & $i(all_114_6) & ( ~ greater(all_114_6, all_114_5) |
% 12.84/2.51 | | greater(all_114_1, all_114_0) | decreases(all_114_2))
% 12.84/2.51 | |
% 12.84/2.51 | | ALPHA: (81) implies:
% 12.84/2.51 | | (82) disbanding_rate(efficient_producers, all_16_2) = all_114_0
% 12.84/2.51 | | (83) disbanding_rate(efficient_producers, all_24_1) = all_114_5
% 12.84/2.51 | | (84) disbanding_rate(efficient_producers, all_24_1) = all_114_3
% 12.84/2.51 | |
% 12.84/2.51 | | GROUND_INST: instantiating (13) with all_16_0, all_114_0, all_16_2,
% 12.84/2.51 | | efficient_producers, simplifying with (21), (82) gives:
% 12.84/2.51 | | (85) all_114_0 = all_16_0
% 12.84/2.51 | |
% 12.84/2.51 | | GROUND_INST: instantiating (13) with all_112_0, all_114_0, all_16_2,
% 12.84/2.51 | | efficient_producers, simplifying with (78), (82) gives:
% 12.84/2.51 | | (86) all_114_0 = all_112_0
% 12.84/2.51 | |
% 12.84/2.51 | | GROUND_INST: instantiating (13) with all_112_1, all_114_5, all_24_1,
% 12.84/2.51 | | efficient_producers, simplifying with (79), (83) gives:
% 12.84/2.51 | | (87) all_114_5 = all_112_1
% 12.84/2.51 | |
% 12.84/2.51 | | GROUND_INST: instantiating (13) with all_28_0, all_114_3, all_24_1,
% 12.84/2.51 | | efficient_producers, simplifying with (43), (84) gives:
% 12.84/2.51 | | (88) all_114_3 = all_28_0
% 12.84/2.51 | |
% 12.84/2.51 | | GROUND_INST: instantiating (13) with all_114_5, all_114_3, all_24_1,
% 12.84/2.51 | | efficient_producers, simplifying with (83), (84) gives:
% 12.84/2.51 | | (89) all_114_3 = all_114_5
% 12.84/2.51 | |
% 12.84/2.51 | | COMBINE_EQS: (85), (86) imply:
% 12.84/2.51 | | (90) all_112_0 = all_16_0
% 12.84/2.51 | |
% 12.84/2.51 | | COMBINE_EQS: (88), (89) imply:
% 12.84/2.51 | | (91) all_114_5 = all_28_0
% 12.84/2.51 | |
% 12.84/2.51 | | SIMP: (91) implies:
% 12.84/2.51 | | (92) all_114_5 = all_28_0
% 12.84/2.51 | |
% 12.84/2.51 | | COMBINE_EQS: (87), (92) imply:
% 12.84/2.51 | | (93) all_112_1 = all_28_0
% 12.84/2.51 | |
% 12.84/2.51 | | SIMP: (93) implies:
% 12.84/2.51 | | (94) all_112_1 = all_28_0
% 12.84/2.51 | |
% 12.84/2.51 | | BETA: splitting (80) gives:
% 12.84/2.51 | |
% 12.84/2.51 | | Case 1:
% 12.84/2.51 | | |
% 12.84/2.51 | | | (95) ~ greater(all_28_1, all_112_1)
% 12.84/2.51 | | |
% 12.84/2.51 | | | REDUCE: (94), (95) imply:
% 12.84/2.51 | | | (96) ~ greater(all_28_1, all_28_0)
% 12.84/2.51 | | |
% 12.84/2.52 | | | PRED_UNIFY: (35), (96) imply:
% 12.84/2.52 | | | (97) $false
% 12.84/2.52 | | |
% 12.84/2.52 | | | CLOSE: (97) is inconsistent.
% 12.84/2.52 | | |
% 12.84/2.52 | | Case 2:
% 12.84/2.52 | | |
% 12.84/2.52 | | | (98) greater(all_16_1, all_112_0)
% 12.84/2.52 | | |
% 12.84/2.52 | | | REDUCE: (90), (98) imply:
% 12.84/2.52 | | | (99) greater(all_16_1, all_16_0)
% 12.84/2.52 | | |
% 12.84/2.52 | | | PRED_UNIFY: (15), (99) imply:
% 12.84/2.52 | | | (100) $false
% 12.84/2.52 | | |
% 12.84/2.52 | | | CLOSE: (100) is inconsistent.
% 12.84/2.52 | | |
% 12.84/2.52 | | End of split
% 12.84/2.52 | |
% 12.84/2.52 | Case 2:
% 12.84/2.52 | |
% 12.84/2.52 | | (101) all_24_1 = all_16_2
% 12.84/2.52 | |
% 12.84/2.52 | | REDUCE: (43), (101) imply:
% 12.84/2.52 | | (102) disbanding_rate(efficient_producers, all_16_2) = all_28_0
% 12.84/2.52 | |
% 12.84/2.52 | | REDUCE: (44), (101) imply:
% 12.84/2.52 | | (103) disbanding_rate(first_movers, all_16_2) = all_28_1
% 12.84/2.52 | |
% 12.84/2.52 | | GROUND_INST: instantiating (13) with all_16_1, all_28_1, all_16_2,
% 12.84/2.52 | | first_movers, simplifying with (20), (103) gives:
% 12.84/2.52 | | (104) all_28_1 = all_16_1
% 12.84/2.52 | |
% 12.84/2.52 | | GROUND_INST: instantiating (13) with all_16_0, all_28_0, all_16_2,
% 12.84/2.52 | | efficient_producers, simplifying with (21), (102) gives:
% 12.84/2.52 | | (105) all_28_0 = all_16_0
% 12.84/2.52 | |
% 12.84/2.52 | | REDUCE: (35), (104), (105) imply:
% 12.84/2.52 | | (106) greater(all_16_1, all_16_0)
% 12.84/2.52 | |
% 12.84/2.52 | | PRED_UNIFY: (15), (106) imply:
% 12.84/2.52 | | (107) $false
% 12.84/2.52 | |
% 12.84/2.52 | | CLOSE: (107) is inconsistent.
% 12.84/2.52 | |
% 12.84/2.52 | End of split
% 12.84/2.52 |
% 12.84/2.52 End of proof
% 12.84/2.52 % SZS output end Proof for theBenchmark
% 12.84/2.52
% 12.84/2.52 1915ms
%------------------------------------------------------------------------------