TSTP Solution File: MGT021+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : MGT021+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 09:16:13 EDT 2023
% Result : Theorem 5.62s 1.51s
% Output : Proof 8.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT021+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 06:20:22 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.61 ________ _____
% 0.18/0.61 ___ __ \_________(_)________________________________
% 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.61
% 0.18/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.61 (2023-06-19)
% 0.18/0.61
% 0.18/0.61 (c) Philipp Rümmer, 2009-2023
% 0.18/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.61 Amanda Stjerna.
% 0.18/0.61 Free software under BSD-3-Clause.
% 0.18/0.61
% 0.18/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.61
% 0.18/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.62 Running up to 7 provers in parallel.
% 0.18/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.18/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.22/0.97 Prover 1: Preprocessing ...
% 2.22/0.97 Prover 4: Preprocessing ...
% 2.22/1.01 Prover 6: Preprocessing ...
% 2.22/1.01 Prover 5: Preprocessing ...
% 2.22/1.01 Prover 3: Preprocessing ...
% 2.22/1.01 Prover 0: Preprocessing ...
% 2.22/1.01 Prover 2: Preprocessing ...
% 4.32/1.27 Prover 5: Constructing countermodel ...
% 4.32/1.27 Prover 6: Constructing countermodel ...
% 4.32/1.28 Prover 3: Constructing countermodel ...
% 4.32/1.29 Prover 2: Proving ...
% 4.32/1.30 Prover 1: Constructing countermodel ...
% 4.32/1.32 Prover 4: Constructing countermodel ...
% 4.32/1.34 Prover 0: Proving ...
% 5.62/1.51 Prover 5: proved (865ms)
% 5.62/1.51
% 5.62/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.62/1.51
% 5.62/1.52 Prover 3: gave up
% 5.62/1.52 Prover 0: proved (888ms)
% 5.62/1.52
% 5.62/1.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.62/1.52
% 5.62/1.52 Prover 2: proved (886ms)
% 5.62/1.52
% 5.96/1.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.96/1.52
% 5.96/1.52 Prover 6: stopped
% 5.96/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.96/1.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.96/1.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.96/1.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.96/1.54 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.22/1.58 Prover 11: Preprocessing ...
% 6.22/1.58 Prover 13: Preprocessing ...
% 6.22/1.58 Prover 8: Preprocessing ...
% 6.22/1.58 Prover 10: Preprocessing ...
% 6.22/1.59 Prover 7: Preprocessing ...
% 6.22/1.62 Prover 1: gave up
% 6.22/1.62 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.74/1.66 Prover 7: Constructing countermodel ...
% 6.74/1.66 Prover 16: Preprocessing ...
% 6.74/1.66 Prover 13: Constructing countermodel ...
% 6.74/1.67 Prover 10: Constructing countermodel ...
% 6.99/1.69 Prover 8: Warning: ignoring some quantifiers
% 6.99/1.69 Prover 8: Constructing countermodel ...
% 6.99/1.69 Prover 10: gave up
% 6.99/1.71 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 6.99/1.72 Prover 16: Constructing countermodel ...
% 6.99/1.72 Prover 11: Constructing countermodel ...
% 6.99/1.72 Prover 7: gave up
% 7.38/1.74 Prover 19: Preprocessing ...
% 7.58/1.81 Prover 4: Found proof (size 113)
% 7.58/1.81 Prover 4: proved (1179ms)
% 7.58/1.81 Prover 11: stopped
% 7.58/1.81 Prover 8: stopped
% 7.58/1.81 Prover 13: stopped
% 7.58/1.81 Prover 19: Warning: ignoring some quantifiers
% 7.58/1.81 Prover 16: stopped
% 7.58/1.82 Prover 19: Constructing countermodel ...
% 8.09/1.83 Prover 19: stopped
% 8.09/1.83
% 8.09/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.09/1.83
% 8.09/1.85 % SZS output start Proof for theBenchmark
% 8.09/1.85 Assumptions after simplification:
% 8.09/1.85 ---------------------------------
% 8.09/1.85
% 8.09/1.85 (a3)
% 8.30/1.89 $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 8.30/1.89 (equilibrium(v0) = v2) | ~ (greater(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) |
% 8.30/1.89 ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ?
% 8.30/1.89 [v9: any] : ? [v10: any] : (resources(v0, v1) = v8 & constant(v8) = v10 &
% 8.30/1.89 decreases(v8) = v9 & number_of_organizations(v0, v1) = v6 & greater(v6,
% 8.30/1.89 zero) = v7 & in_environment(v0, v1) = v5 & environment(v0) = v4 & $i(v8)
% 8.30/1.89 & $i(v6) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | (( ~ (v3 = 0) | v9 =
% 8.30/1.89 0) & (v10 = 0 | v3 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 8.30/1.89 $i] : ( ~ (resources(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 8.30/1.89 ? [v4: any] : ? [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ?
% 8.30/1.89 [v9: any] : ? [v10: any] : (equilibrium(v0) = v7 & constant(v2) = v10 &
% 8.30/1.89 decreases(v2) = v9 & number_of_organizations(v0, v1) = v5 & greater(v7,
% 8.30/1.89 v1) = v8 & greater(v5, zero) = v6 & in_environment(v0, v1) = v4 &
% 8.30/1.89 environment(v0) = v3 & $i(v7) & $i(v5) & ( ~ (v6 = 0) | ~ (v4 = 0) | ~
% 8.30/1.89 (v3 = 0) | (( ~ (v8 = 0) | v9 = 0) & (v10 = 0 | v8 = 0))))) & ! [v0:
% 8.30/1.89 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (number_of_organizations(v0, v1) = v2)
% 8.30/1.89 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ?
% 8.30/1.89 [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : ? [v10: any] :
% 8.30/1.89 (resources(v0, v1) = v8 & equilibrium(v0) = v6 & constant(v8) = v10 &
% 8.30/1.89 decreases(v8) = v9 & greater(v6, v1) = v7 & greater(v2, zero) = v5 &
% 8.30/1.89 in_environment(v0, v1) = v4 & environment(v0) = v3 & $i(v8) & $i(v6) & ( ~
% 8.30/1.89 (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v7 = 0) | v9 = 0) & (v10 =
% 8.30/1.89 0 | v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.30/1.89 (in_environment(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ?
% 8.30/1.89 [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8:
% 8.30/1.89 any] : ? [v9: any] : (resources(v0, v1) = v7 & equilibrium(v0) = v5 &
% 8.30/1.89 constant(v7) = v9 & decreases(v7) = v8 & number_of_organizations(v0, v1) =
% 8.30/1.89 v3 & greater(v5, v1) = v6 & greater(v3, zero) = v4 & environment(v0) = v2
% 8.30/1.89 & $i(v7) & $i(v5) & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0) | (( ~ (v6 = 0) |
% 8.30/1.89 v8 = 0) & (v9 = 0 | v6 = 0)))))
% 8.30/1.89
% 8.30/1.89 (l4)
% 8.30/1.90 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : !
% 8.30/1.90 [v2: $i] : ( ~ (resources(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any]
% 8.30/1.90 : ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 8.30/1.90 [v9: any] : ? [v10: any] : ? [v11: any] :
% 8.30/1.90 (disbanding_rate(efficient_producers, v1) = v7 &
% 8.30/1.90 disbanding_rate(first_movers, v1) = v6 & difference(v6, v7) = v8 &
% 8.30/1.90 constant(v2) = v10 & decreases(v8) = v11 & decreases(v2) = v5 &
% 8.30/1.90 increases(v8) = v9 & environment(v0) = v3 & subpopulations(first_movers,
% 8.30/1.90 efficient_producers, v0, v1) = v4 & $i(v8) & $i(v7) & $i(v6) & ( ~ (v4 =
% 8.30/1.90 0) | ~ (v3 = 0) | (( ~ (v11 = 0) | ~ (v10 = 0)) & ( ~ (v5 = 0) | v9
% 8.30/1.90 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.30/1.90 (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ~ $i(v1)
% 8.30/1.90 | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ?
% 8.30/1.90 [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : ? [v10: any] :
% 8.30/1.90 (disbanding_rate(efficient_producers, v1) = v6 &
% 8.30/1.90 disbanding_rate(first_movers, v1) = v5 & difference(v5, v6) = v7 &
% 8.30/1.90 resources(v0, v1) = v3 & constant(v3) = v9 & decreases(v7) = v10 &
% 8.30/1.90 decreases(v3) = v4 & increases(v7) = v8 & environment(v0) = v2 & $i(v7) &
% 8.30/1.90 $i(v6) & $i(v5) & $i(v3) & ( ~ (v2 = 0) | (( ~ (v10 = 0) | ~ (v9 = 0)) &
% 8.30/1.90 ( ~ (v4 = 0) | v8 = 0)))))
% 8.30/1.90
% 8.30/1.90 (mp_environment_not_empty)
% 8.30/1.90 $i(zero) & $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1:
% 8.30/1.90 $i] : ! [v2: $i] : ( ~ (number_of_organizations(v0, v1) = v2) | ~ $i(v1) |
% 8.30/1.90 ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : (greater(v2, zero)
% 8.30/1.90 = v5 & environment(v0) = v3 & subpopulations(first_movers,
% 8.30/1.90 efficient_producers, v0, v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 =
% 8.30/1.90 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (subpopulations(first_movers,
% 8.30/1.90 efficient_producers, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any]
% 8.30/1.90 : ? [v3: $i] : ? [v4: any] : (number_of_organizations(v0, v1) = v3 &
% 8.30/1.90 greater(v3, zero) = v4 & environment(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v4
% 8.30/1.90 = 0)))
% 8.30/1.90
% 8.30/1.90 (mp_increase_not_decrease)
% 8.30/1.90 ! [v0: $i] : ( ~ (decreases(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 =
% 8.30/1.90 0) & increases(v0) = v1)) & ! [v0: $i] : ( ~ (increases(v0) = 0) | ~
% 8.30/1.90 $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & decreases(v0) = v1))
% 8.30/1.90
% 8.30/1.90 (mp_time_point_in_environment)
% 8.30/1.90 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : !
% 8.30/1.90 [v2: int] : (v2 = 0 | ~ (in_environment(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 8.30/1.90 | ? [v3: any] : ? [v4: any] : (environment(v0) = v3 &
% 8.30/1.90 subpopulations(first_movers, efficient_producers, v0, v1) = v4 & ( ~ (v4 =
% 8.30/1.90 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.30/1.90 (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ~ $i(v1)
% 8.30/1.90 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in_environment(v0, v1) = v3 &
% 8.30/1.90 environment(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 8.30/1.90
% 8.30/1.90 (prove_l3)
% 8.30/1.90 $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ? [v1: $i] : ?
% 8.30/1.90 [v2: $i] : ? [v3: $i] : ? [v4: $i] : (disbanding_rate(efficient_producers,
% 8.30/1.90 v1) = v3 & disbanding_rate(first_movers, v1) = v2 & difference(v2, v3) =
% 8.30/1.90 v4 & decreases(v4) = 0 & environment(v0) = 0 & subpopulations(first_movers,
% 8.30/1.90 efficient_producers, v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 8.30/1.90 $i(v0))
% 8.30/1.90
% 8.30/1.90 (function-axioms)
% 8.30/1.91 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.30/1.91 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (subpopulations(v5, v4,
% 8.30/1.91 v3, v2) = v1) | ~ (subpopulations(v5, v4, v3, v2) = v0)) & ! [v0: $i]
% 8.30/1.91 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disbanding_rate(v3,
% 8.30/1.91 v2) = v1) | ~ (disbanding_rate(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 8.30/1.91 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (difference(v3, v2) = v1) |
% 8.30/1.91 ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 8.30/1.91 [v3: $i] : (v1 = v0 | ~ (resources(v3, v2) = v1) | ~ (resources(v3, v2) =
% 8.30/1.91 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.30/1.91 $i] : ! [v3: $i] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~
% 8.30/1.91 (greater_or_equal(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 8.30/1.91 ! [v3: $i] : (v1 = v0 | ~ (number_of_organizations(v3, v2) = v1) | ~
% 8.30/1.91 (number_of_organizations(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 8.30/1.91 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.30/1.91 (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0:
% 8.30/1.91 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 8.30/1.91 : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~ (in_environment(v3, v2) =
% 8.30/1.91 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 8.30/1.91 (equilibrium(v2) = v1) | ~ (equilibrium(v2) = v0)) & ! [v0:
% 8.30/1.91 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 8.30/1.91 ~ (constant(v2) = v1) | ~ (constant(v2) = v0)) & ! [v0: MultipleValueBool]
% 8.30/1.91 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (decreases(v2) =
% 8.30/1.91 v1) | ~ (decreases(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.30/1.91 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (increases(v2) = v1) | ~
% 8.30/1.91 (increases(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.30/1.91 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (environment(v2) = v1) | ~
% 8.30/1.91 (environment(v2) = v0))
% 8.30/1.91
% 8.30/1.91 Further assumptions not needed in the proof:
% 8.30/1.91 --------------------------------------------
% 8.30/1.91 mp_greater_or_equal
% 8.30/1.91
% 8.30/1.91 Those formulas are unsatisfiable:
% 8.30/1.91 ---------------------------------
% 8.30/1.91
% 8.30/1.91 Begin of proof
% 8.30/1.91 |
% 8.30/1.91 | ALPHA: (mp_time_point_in_environment) implies:
% 8.30/1.91 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subpopulations(first_movers,
% 8.30/1.91 | efficient_producers, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 8.30/1.91 | [v2: any] : ? [v3: any] : (in_environment(v0, v1) = v3 &
% 8.30/1.91 | environment(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 8.30/1.91 |
% 8.30/1.91 | ALPHA: (mp_environment_not_empty) implies:
% 8.30/1.91 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (subpopulations(first_movers,
% 8.30/1.91 | efficient_producers, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 8.30/1.91 | [v2: any] : ? [v3: $i] : ? [v4: any] : (number_of_organizations(v0,
% 8.30/1.91 | v1) = v3 & greater(v3, zero) = v4 & environment(v0) = v2 & $i(v3)
% 8.30/1.91 | & ( ~ (v2 = 0) | v4 = 0)))
% 8.30/1.91 |
% 8.30/1.91 | ALPHA: (mp_increase_not_decrease) implies:
% 8.30/1.91 | (3) ! [v0: $i] : ( ~ (decreases(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~
% 8.30/1.91 | (v1 = 0) & increases(v0) = v1))
% 8.30/1.91 |
% 8.30/1.91 | ALPHA: (a3) implies:
% 8.30/1.92 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (in_environment(v0, v1) = 0) | ~
% 8.30/1.92 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : ?
% 8.30/1.92 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] :
% 8.30/1.92 | (resources(v0, v1) = v7 & equilibrium(v0) = v5 & constant(v7) = v9 &
% 8.30/1.92 | decreases(v7) = v8 & number_of_organizations(v0, v1) = v3 &
% 8.30/1.92 | greater(v5, v1) = v6 & greater(v3, zero) = v4 & environment(v0) =
% 8.30/1.92 | v2 & $i(v7) & $i(v5) & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0) | (( ~
% 8.30/1.92 | (v6 = 0) | v8 = 0) & (v9 = 0 | v6 = 0)))))
% 8.30/1.92 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 8.30/1.92 | (number_of_organizations(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 8.30/1.92 | [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: any]
% 8.30/1.92 | : ? [v8: $i] : ? [v9: any] : ? [v10: any] : (resources(v0, v1) =
% 8.30/1.92 | v8 & equilibrium(v0) = v6 & constant(v8) = v10 & decreases(v8) = v9
% 8.30/1.92 | & greater(v6, v1) = v7 & greater(v2, zero) = v5 &
% 8.30/1.92 | in_environment(v0, v1) = v4 & environment(v0) = v3 & $i(v8) &
% 8.30/1.92 | $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v7 = 0) |
% 8.30/1.92 | v9 = 0) & (v10 = 0 | v7 = 0)))))
% 8.30/1.92 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (resources(v0, v1) = v2)
% 8.30/1.92 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 8.30/1.92 | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : ? [v10:
% 8.30/1.92 | any] : (equilibrium(v0) = v7 & constant(v2) = v10 & decreases(v2) =
% 8.30/1.92 | v9 & number_of_organizations(v0, v1) = v5 & greater(v7, v1) = v8 &
% 8.30/1.92 | greater(v5, zero) = v6 & in_environment(v0, v1) = v4 &
% 8.30/1.92 | environment(v0) = v3 & $i(v7) & $i(v5) & ( ~ (v6 = 0) | ~ (v4 = 0)
% 8.30/1.92 | | ~ (v3 = 0) | (( ~ (v8 = 0) | v9 = 0) & (v10 = 0 | v8 = 0)))))
% 8.30/1.92 |
% 8.30/1.92 | ALPHA: (l4) implies:
% 8.30/1.92 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (subpopulations(first_movers,
% 8.30/1.92 | efficient_producers, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 8.30/1.92 | [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] :
% 8.30/1.92 | ? [v7: $i] : ? [v8: any] : ? [v9: any] : ? [v10: any] :
% 8.30/1.92 | (disbanding_rate(efficient_producers, v1) = v6 &
% 8.30/1.92 | disbanding_rate(first_movers, v1) = v5 & difference(v5, v6) = v7 &
% 8.30/1.92 | resources(v0, v1) = v3 & constant(v3) = v9 & decreases(v7) = v10 &
% 8.30/1.92 | decreases(v3) = v4 & increases(v7) = v8 & environment(v0) = v2 &
% 8.30/1.92 | $i(v7) & $i(v6) & $i(v5) & $i(v3) & ( ~ (v2 = 0) | (( ~ (v10 = 0) |
% 8.30/1.92 | ~ (v9 = 0)) & ( ~ (v4 = 0) | v8 = 0)))))
% 8.30/1.92 |
% 8.30/1.92 | ALPHA: (prove_l3) implies:
% 8.30/1.92 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 8.30/1.92 | (disbanding_rate(efficient_producers, v1) = v3 &
% 8.30/1.92 | disbanding_rate(first_movers, v1) = v2 & difference(v2, v3) = v4 &
% 8.30/1.92 | decreases(v4) = 0 & environment(v0) = 0 &
% 8.30/1.92 | subpopulations(first_movers, efficient_producers, v0, v1) = 0 &
% 8.30/1.92 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.30/1.92 |
% 8.30/1.92 | ALPHA: (function-axioms) implies:
% 8.30/1.92 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.30/1.92 | (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0))
% 8.30/1.93 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 8.30/1.93 | : (v1 = v0 | ~ (increases(v2) = v1) | ~ (increases(v2) = v0))
% 8.30/1.93 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 8.30/1.93 | : (v1 = v0 | ~ (decreases(v2) = v1) | ~ (decreases(v2) = v0))
% 8.30/1.93 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 8.30/1.93 | : (v1 = v0 | ~ (constant(v2) = v1) | ~ (constant(v2) = v0))
% 8.30/1.93 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 8.30/1.93 | : ! [v3: $i] : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~
% 8.30/1.93 | (in_environment(v3, v2) = v0))
% 8.30/1.93 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 8.30/1.93 | : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3,
% 8.30/1.93 | v2) = v0))
% 8.30/1.93 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.30/1.93 | (number_of_organizations(v3, v2) = v1) | ~
% 8.30/1.93 | (number_of_organizations(v3, v2) = v0))
% 8.30/1.93 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.30/1.93 | (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 8.30/1.93 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.30/1.93 | (disbanding_rate(v3, v2) = v1) | ~ (disbanding_rate(v3, v2) = v0))
% 8.30/1.93 |
% 8.30/1.93 | DELTA: instantiating (8) with fresh symbols all_10_0, all_10_1, all_10_2,
% 8.30/1.93 | all_10_3, all_10_4 gives:
% 8.30/1.93 | (18) disbanding_rate(efficient_producers, all_10_3) = all_10_1 &
% 8.30/1.93 | disbanding_rate(first_movers, all_10_3) = all_10_2 &
% 8.30/1.93 | difference(all_10_2, all_10_1) = all_10_0 & decreases(all_10_0) = 0 &
% 8.30/1.93 | environment(all_10_4) = 0 & subpopulations(first_movers,
% 8.30/1.93 | efficient_producers, all_10_4, all_10_3) = 0 & $i(all_10_0) &
% 8.30/1.93 | $i(all_10_1) & $i(all_10_2) & $i(all_10_3) & $i(all_10_4)
% 8.30/1.93 |
% 8.30/1.93 | ALPHA: (18) implies:
% 8.30/1.93 | (19) $i(all_10_4)
% 8.30/1.93 | (20) $i(all_10_3)
% 8.30/1.93 | (21) $i(all_10_0)
% 8.30/1.93 | (22) subpopulations(first_movers, efficient_producers, all_10_4, all_10_3)
% 8.30/1.93 | = 0
% 8.30/1.93 | (23) environment(all_10_4) = 0
% 8.30/1.93 | (24) decreases(all_10_0) = 0
% 8.30/1.93 | (25) difference(all_10_2, all_10_1) = all_10_0
% 8.30/1.93 | (26) disbanding_rate(first_movers, all_10_3) = all_10_2
% 8.30/1.93 | (27) disbanding_rate(efficient_producers, all_10_3) = all_10_1
% 8.30/1.93 |
% 8.30/1.93 | GROUND_INST: instantiating (7) with all_10_4, all_10_3, simplifying with (19),
% 8.30/1.93 | (20), (22) gives:
% 8.30/1.93 | (28) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: $i]
% 8.30/1.93 | : ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 8.30/1.93 | (disbanding_rate(efficient_producers, all_10_3) = v4 &
% 8.30/1.93 | disbanding_rate(first_movers, all_10_3) = v3 & difference(v3, v4) =
% 8.30/1.93 | v5 & resources(all_10_4, all_10_3) = v1 & constant(v1) = v7 &
% 8.30/1.93 | decreases(v5) = v8 & decreases(v1) = v2 & increases(v5) = v6 &
% 8.30/1.93 | environment(all_10_4) = v0 & $i(v5) & $i(v4) & $i(v3) & $i(v1) & ( ~
% 8.30/1.93 | (v0 = 0) | (( ~ (v8 = 0) | ~ (v7 = 0)) & ( ~ (v2 = 0) | v6 =
% 8.30/1.93 | 0))))
% 8.30/1.93 |
% 8.30/1.93 | GROUND_INST: instantiating (2) with all_10_4, all_10_3, simplifying with (19),
% 8.30/1.93 | (20), (22) gives:
% 8.30/1.94 | (29) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 8.30/1.94 | (number_of_organizations(all_10_4, all_10_3) = v1 & greater(v1, zero)
% 8.30/1.94 | = v2 & environment(all_10_4) = v0 & $i(v1) & ( ~ (v0 = 0) | v2 = 0))
% 8.30/1.94 |
% 8.30/1.94 | GROUND_INST: instantiating (1) with all_10_4, all_10_3, simplifying with (19),
% 8.30/1.94 | (20), (22) gives:
% 8.30/1.94 | (30) ? [v0: any] : ? [v1: any] : (in_environment(all_10_4, all_10_3) = v1
% 8.30/1.94 | & environment(all_10_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 8.30/1.94 |
% 8.30/1.94 | GROUND_INST: instantiating (3) with all_10_0, simplifying with (21), (24)
% 8.30/1.94 | gives:
% 8.30/1.94 | (31) ? [v0: int] : ( ~ (v0 = 0) & increases(all_10_0) = v0)
% 8.30/1.94 |
% 8.30/1.94 | DELTA: instantiating (31) with fresh symbol all_17_0 gives:
% 8.30/1.94 | (32) ~ (all_17_0 = 0) & increases(all_10_0) = all_17_0
% 8.30/1.94 |
% 8.30/1.94 | ALPHA: (32) implies:
% 8.30/1.94 | (33) ~ (all_17_0 = 0)
% 8.30/1.94 | (34) increases(all_10_0) = all_17_0
% 8.30/1.94 |
% 8.30/1.94 | DELTA: instantiating (30) with fresh symbols all_19_0, all_19_1 gives:
% 8.30/1.94 | (35) in_environment(all_10_4, all_10_3) = all_19_0 & environment(all_10_4)
% 8.30/1.94 | = all_19_1 & ( ~ (all_19_1 = 0) | all_19_0 = 0)
% 8.30/1.94 |
% 8.30/1.94 | ALPHA: (35) implies:
% 8.30/1.94 | (36) environment(all_10_4) = all_19_1
% 8.30/1.94 | (37) in_environment(all_10_4, all_10_3) = all_19_0
% 8.30/1.94 | (38) ~ (all_19_1 = 0) | all_19_0 = 0
% 8.30/1.94 |
% 8.30/1.94 | DELTA: instantiating (29) with fresh symbols all_21_0, all_21_1, all_21_2
% 8.30/1.94 | gives:
% 8.67/1.94 | (39) number_of_organizations(all_10_4, all_10_3) = all_21_1 &
% 8.67/1.94 | greater(all_21_1, zero) = all_21_0 & environment(all_10_4) = all_21_2
% 8.67/1.94 | & $i(all_21_1) & ( ~ (all_21_2 = 0) | all_21_0 = 0)
% 8.67/1.94 |
% 8.67/1.94 | ALPHA: (39) implies:
% 8.67/1.94 | (40) environment(all_10_4) = all_21_2
% 8.67/1.94 | (41) greater(all_21_1, zero) = all_21_0
% 8.67/1.94 | (42) number_of_organizations(all_10_4, all_10_3) = all_21_1
% 8.67/1.94 | (43) ~ (all_21_2 = 0) | all_21_0 = 0
% 8.67/1.94 |
% 8.67/1.94 | DELTA: instantiating (28) with fresh symbols all_23_0, all_23_1, all_23_2,
% 8.67/1.94 | all_23_3, all_23_4, all_23_5, all_23_6, all_23_7, all_23_8 gives:
% 8.67/1.94 | (44) disbanding_rate(efficient_producers, all_10_3) = all_23_4 &
% 8.67/1.94 | disbanding_rate(first_movers, all_10_3) = all_23_5 &
% 8.67/1.94 | difference(all_23_5, all_23_4) = all_23_3 & resources(all_10_4,
% 8.67/1.94 | all_10_3) = all_23_7 & constant(all_23_7) = all_23_1 &
% 8.67/1.94 | decreases(all_23_3) = all_23_0 & decreases(all_23_7) = all_23_6 &
% 8.67/1.94 | increases(all_23_3) = all_23_2 & environment(all_10_4) = all_23_8 &
% 8.67/1.94 | $i(all_23_3) & $i(all_23_4) & $i(all_23_5) & $i(all_23_7) & ( ~
% 8.67/1.94 | (all_23_8 = 0) | (( ~ (all_23_0 = 0) | ~ (all_23_1 = 0)) & ( ~
% 8.67/1.94 | (all_23_6 = 0) | all_23_2 = 0)))
% 8.67/1.94 |
% 8.67/1.94 | ALPHA: (44) implies:
% 8.67/1.94 | (45) environment(all_10_4) = all_23_8
% 8.67/1.94 | (46) increases(all_23_3) = all_23_2
% 8.67/1.94 | (47) decreases(all_23_7) = all_23_6
% 8.67/1.94 | (48) decreases(all_23_3) = all_23_0
% 8.67/1.94 | (49) constant(all_23_7) = all_23_1
% 8.67/1.94 | (50) resources(all_10_4, all_10_3) = all_23_7
% 8.67/1.94 | (51) difference(all_23_5, all_23_4) = all_23_3
% 8.67/1.94 | (52) disbanding_rate(first_movers, all_10_3) = all_23_5
% 8.67/1.94 | (53) disbanding_rate(efficient_producers, all_10_3) = all_23_4
% 8.67/1.95 | (54) ~ (all_23_8 = 0) | (( ~ (all_23_0 = 0) | ~ (all_23_1 = 0)) & ( ~
% 8.67/1.95 | (all_23_6 = 0) | all_23_2 = 0))
% 8.67/1.95 |
% 8.67/1.95 | GROUND_INST: instantiating (9) with 0, all_23_8, all_10_4, simplifying with
% 8.67/1.95 | (23), (45) gives:
% 8.67/1.95 | (55) all_23_8 = 0
% 8.67/1.95 |
% 8.67/1.95 | GROUND_INST: instantiating (9) with all_21_2, all_23_8, all_10_4, simplifying
% 8.67/1.95 | with (40), (45) gives:
% 8.67/1.95 | (56) all_23_8 = all_21_2
% 8.67/1.95 |
% 8.67/1.95 | GROUND_INST: instantiating (9) with all_19_1, all_23_8, all_10_4, simplifying
% 8.67/1.95 | with (36), (45) gives:
% 8.67/1.95 | (57) all_23_8 = all_19_1
% 8.67/1.95 |
% 8.67/1.95 | GROUND_INST: instantiating (17) with all_10_2, all_23_5, all_10_3,
% 8.67/1.95 | first_movers, simplifying with (26), (52) gives:
% 8.67/1.95 | (58) all_23_5 = all_10_2
% 8.67/1.95 |
% 8.67/1.95 | GROUND_INST: instantiating (17) with all_10_1, all_23_4, all_10_3,
% 8.67/1.95 | efficient_producers, simplifying with (27), (53) gives:
% 8.67/1.95 | (59) all_23_4 = all_10_1
% 8.67/1.95 |
% 8.67/1.95 | COMBINE_EQS: (56), (57) imply:
% 8.67/1.95 | (60) all_21_2 = all_19_1
% 8.67/1.95 |
% 8.67/1.95 | COMBINE_EQS: (55), (56) imply:
% 8.67/1.95 | (61) all_21_2 = 0
% 8.67/1.95 |
% 8.67/1.95 | COMBINE_EQS: (60), (61) imply:
% 8.67/1.95 | (62) all_19_1 = 0
% 8.67/1.95 |
% 8.67/1.95 | SIMP: (62) implies:
% 8.67/1.95 | (63) all_19_1 = 0
% 8.67/1.95 |
% 8.67/1.95 | REDUCE: (51), (58), (59) imply:
% 8.67/1.95 | (64) difference(all_10_2, all_10_1) = all_23_3
% 8.67/1.95 |
% 8.67/1.95 | BETA: splitting (38) gives:
% 8.67/1.95 |
% 8.67/1.95 | Case 1:
% 8.67/1.95 | |
% 8.67/1.95 | | (65) ~ (all_19_1 = 0)
% 8.67/1.95 | |
% 8.67/1.95 | | REDUCE: (63), (65) imply:
% 8.67/1.95 | | (66) $false
% 8.67/1.95 | |
% 8.67/1.95 | | CLOSE: (66) is inconsistent.
% 8.67/1.95 | |
% 8.67/1.95 | Case 2:
% 8.67/1.95 | |
% 8.67/1.95 | | (67) all_19_0 = 0
% 8.67/1.95 | |
% 8.67/1.95 | | REDUCE: (37), (67) imply:
% 8.67/1.95 | | (68) in_environment(all_10_4, all_10_3) = 0
% 8.67/1.95 | |
% 8.67/1.95 | | BETA: splitting (43) gives:
% 8.67/1.95 | |
% 8.67/1.95 | | Case 1:
% 8.67/1.95 | | |
% 8.67/1.95 | | | (69) ~ (all_21_2 = 0)
% 8.67/1.95 | | |
% 8.67/1.95 | | | REDUCE: (61), (69) imply:
% 8.67/1.95 | | | (70) $false
% 8.67/1.95 | | |
% 8.67/1.95 | | | CLOSE: (70) is inconsistent.
% 8.67/1.95 | | |
% 8.67/1.95 | | Case 2:
% 8.67/1.95 | | |
% 8.67/1.95 | | | (71) all_21_0 = 0
% 8.67/1.95 | | |
% 8.67/1.95 | | | REDUCE: (41), (71) imply:
% 8.67/1.95 | | | (72) greater(all_21_1, zero) = 0
% 8.67/1.95 | | |
% 8.67/1.95 | | | GROUND_INST: instantiating (16) with all_10_0, all_23_3, all_10_1,
% 8.67/1.95 | | | all_10_2, simplifying with (25), (64) gives:
% 8.67/1.95 | | | (73) all_23_3 = all_10_0
% 8.67/1.95 | | |
% 8.67/1.95 | | | REDUCE: (48), (73) imply:
% 8.67/1.95 | | | (74) decreases(all_10_0) = all_23_0
% 8.67/1.95 | | |
% 8.67/1.95 | | | REDUCE: (46), (73) imply:
% 8.67/1.95 | | | (75) increases(all_10_0) = all_23_2
% 8.67/1.95 | | |
% 8.67/1.95 | | | GROUND_INST: instantiating (10) with all_17_0, all_23_2, all_10_0,
% 8.67/1.95 | | | simplifying with (34), (75) gives:
% 8.67/1.95 | | | (76) all_23_2 = all_17_0
% 8.67/1.95 | | |
% 8.67/1.95 | | | GROUND_INST: instantiating (11) with 0, all_23_0, all_10_0, simplifying
% 8.67/1.95 | | | with (24), (74) gives:
% 8.67/1.95 | | | (77) all_23_0 = 0
% 8.67/1.95 | | |
% 8.67/1.95 | | | BETA: splitting (54) gives:
% 8.67/1.95 | | |
% 8.67/1.95 | | | Case 1:
% 8.67/1.95 | | | |
% 8.67/1.95 | | | | (78) ~ (all_23_8 = 0)
% 8.67/1.95 | | | |
% 8.67/1.95 | | | | REDUCE: (55), (78) imply:
% 8.67/1.95 | | | | (79) $false
% 8.67/1.95 | | | |
% 8.67/1.96 | | | | CLOSE: (79) is inconsistent.
% 8.67/1.96 | | | |
% 8.67/1.96 | | | Case 2:
% 8.67/1.96 | | | |
% 8.67/1.96 | | | | (80) ( ~ (all_23_0 = 0) | ~ (all_23_1 = 0)) & ( ~ (all_23_6 = 0) |
% 8.67/1.96 | | | | all_23_2 = 0)
% 8.67/1.96 | | | |
% 8.67/1.96 | | | | ALPHA: (80) implies:
% 8.67/1.96 | | | | (81) ~ (all_23_6 = 0) | all_23_2 = 0
% 8.67/1.96 | | | | (82) ~ (all_23_0 = 0) | ~ (all_23_1 = 0)
% 8.67/1.96 | | | |
% 8.67/1.96 | | | | BETA: splitting (81) gives:
% 8.67/1.96 | | | |
% 8.67/1.96 | | | | Case 1:
% 8.67/1.96 | | | | |
% 8.67/1.96 | | | | | (83) ~ (all_23_6 = 0)
% 8.67/1.96 | | | | |
% 8.67/1.96 | | | | | BETA: splitting (82) gives:
% 8.67/1.96 | | | | |
% 8.67/1.96 | | | | | Case 1:
% 8.67/1.96 | | | | | |
% 8.67/1.96 | | | | | | (84) ~ (all_23_0 = 0)
% 8.67/1.96 | | | | | |
% 8.67/1.96 | | | | | | REDUCE: (77), (84) imply:
% 8.67/1.96 | | | | | | (85) $false
% 8.67/1.96 | | | | | |
% 8.67/1.96 | | | | | | CLOSE: (85) is inconsistent.
% 8.67/1.96 | | | | | |
% 8.67/1.96 | | | | | Case 2:
% 8.67/1.96 | | | | | |
% 8.67/1.96 | | | | | | (86) ~ (all_23_1 = 0)
% 8.67/1.96 | | | | | |
% 8.67/1.96 | | | | | | GROUND_INST: instantiating (4) with all_10_4, all_10_3, simplifying
% 8.67/1.96 | | | | | | with (19), (20), (68) gives:
% 8.67/1.96 | | | | | | (87) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ?
% 8.67/1.96 | | | | | | [v4: any] : ? [v5: $i] : ? [v6: any] : ? [v7: any] :
% 8.67/1.96 | | | | | | (resources(all_10_4, all_10_3) = v5 & equilibrium(all_10_4)
% 8.67/1.96 | | | | | | = v3 & constant(v5) = v7 & decreases(v5) = v6 &
% 8.67/1.96 | | | | | | number_of_organizations(all_10_4, all_10_3) = v1 &
% 8.67/1.96 | | | | | | greater(v3, all_10_3) = v4 & greater(v1, zero) = v2 &
% 8.67/1.96 | | | | | | environment(all_10_4) = v0 & $i(v5) & $i(v3) & $i(v1) & (
% 8.67/1.96 | | | | | | ~ (v2 = 0) | ~ (v0 = 0) | (( ~ (v4 = 0) | v6 = 0) & (v7
% 8.67/1.96 | | | | | | = 0 | v4 = 0))))
% 8.67/1.96 | | | | | |
% 8.67/1.96 | | | | | | GROUND_INST: instantiating (5) with all_10_4, all_10_3, all_21_1,
% 8.67/1.96 | | | | | | simplifying with (19), (20), (42) gives:
% 8.67/1.96 | | | | | | (88) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] :
% 8.67/1.96 | | | | | | ? [v4: any] : ? [v5: $i] : ? [v6: any] : ? [v7: any] :
% 8.67/1.96 | | | | | | (resources(all_10_4, all_10_3) = v5 & equilibrium(all_10_4)
% 8.67/1.96 | | | | | | = v3 & constant(v5) = v7 & decreases(v5) = v6 &
% 8.67/1.96 | | | | | | greater(v3, all_10_3) = v4 & greater(all_21_1, zero) = v2
% 8.67/1.96 | | | | | | & in_environment(all_10_4, all_10_3) = v1 &
% 8.67/1.96 | | | | | | environment(all_10_4) = v0 & $i(v5) & $i(v3) & ( ~ (v2 =
% 8.67/1.96 | | | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v4 = 0) | v6 =
% 8.67/1.96 | | | | | | 0) & (v7 = 0 | v4 = 0))))
% 8.67/1.96 | | | | | |
% 8.67/1.96 | | | | | | GROUND_INST: instantiating (6) with all_10_4, all_10_3, all_23_7,
% 8.67/1.96 | | | | | | simplifying with (19), (20), (50) gives:
% 8.67/1.96 | | | | | | (89) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 8.67/1.96 | | | | | | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 8.67/1.96 | | | | | | (equilibrium(all_10_4) = v4 & constant(all_23_7) = v7 &
% 8.67/1.96 | | | | | | decreases(all_23_7) = v6 &
% 8.67/1.96 | | | | | | number_of_organizations(all_10_4, all_10_3) = v2 &
% 8.67/1.96 | | | | | | greater(v4, all_10_3) = v5 & greater(v2, zero) = v3 &
% 8.67/1.96 | | | | | | in_environment(all_10_4, all_10_3) = v1 &
% 8.67/1.96 | | | | | | environment(all_10_4) = v0 & $i(v4) & $i(v2) & ( ~ (v3 =
% 8.67/1.96 | | | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v5 = 0) | v6 =
% 8.67/1.96 | | | | | | 0) & (v7 = 0 | v5 = 0))))
% 8.67/1.96 | | | | | |
% 8.67/1.96 | | | | | | DELTA: instantiating (89) with fresh symbols all_62_0, all_62_1,
% 8.67/1.96 | | | | | | all_62_2, all_62_3, all_62_4, all_62_5, all_62_6, all_62_7
% 8.67/1.96 | | | | | | gives:
% 8.67/1.96 | | | | | | (90) equilibrium(all_10_4) = all_62_3 & constant(all_23_7) =
% 8.67/1.96 | | | | | | all_62_0 & decreases(all_23_7) = all_62_1 &
% 8.67/1.96 | | | | | | number_of_organizations(all_10_4, all_10_3) = all_62_5 &
% 8.67/1.96 | | | | | | greater(all_62_3, all_10_3) = all_62_2 & greater(all_62_5,
% 8.67/1.96 | | | | | | zero) = all_62_4 & in_environment(all_10_4, all_10_3) =
% 8.67/1.96 | | | | | | all_62_6 & environment(all_10_4) = all_62_7 & $i(all_62_3) &
% 8.67/1.96 | | | | | | $i(all_62_5) & ( ~ (all_62_4 = 0) | ~ (all_62_6 = 0) | ~
% 8.67/1.96 | | | | | | (all_62_7 = 0) | (( ~ (all_62_2 = 0) | all_62_1 = 0) &
% 8.67/1.96 | | | | | | (all_62_0 = 0 | all_62_2 = 0)))
% 8.67/1.96 | | | | | |
% 8.67/1.96 | | | | | | ALPHA: (90) implies:
% 8.67/1.96 | | | | | | (91) environment(all_10_4) = all_62_7
% 8.67/1.96 | | | | | | (92) in_environment(all_10_4, all_10_3) = all_62_6
% 8.67/1.96 | | | | | | (93) greater(all_62_5, zero) = all_62_4
% 8.67/1.96 | | | | | | (94) number_of_organizations(all_10_4, all_10_3) = all_62_5
% 8.67/1.96 | | | | | | (95) decreases(all_23_7) = all_62_1
% 8.67/1.96 | | | | | | (96) constant(all_23_7) = all_62_0
% 8.67/1.96 | | | | | | (97) ~ (all_62_4 = 0) | ~ (all_62_6 = 0) | ~ (all_62_7 = 0) |
% 8.67/1.96 | | | | | | (( ~ (all_62_2 = 0) | all_62_1 = 0) & (all_62_0 = 0 |
% 8.67/1.96 | | | | | | all_62_2 = 0))
% 8.67/1.96 | | | | | |
% 8.67/1.96 | | | | | | DELTA: instantiating (88) with fresh symbols all_64_0, all_64_1,
% 8.67/1.96 | | | | | | all_64_2, all_64_3, all_64_4, all_64_5, all_64_6, all_64_7
% 8.67/1.96 | | | | | | gives:
% 8.67/1.97 | | | | | | (98) resources(all_10_4, all_10_3) = all_64_2 &
% 8.67/1.97 | | | | | | equilibrium(all_10_4) = all_64_4 & constant(all_64_2) =
% 8.67/1.97 | | | | | | all_64_0 & decreases(all_64_2) = all_64_1 &
% 8.67/1.97 | | | | | | greater(all_64_4, all_10_3) = all_64_3 & greater(all_21_1,
% 8.67/1.97 | | | | | | zero) = all_64_5 & in_environment(all_10_4, all_10_3) =
% 8.67/1.97 | | | | | | all_64_6 & environment(all_10_4) = all_64_7 & $i(all_64_2) &
% 8.67/1.97 | | | | | | $i(all_64_4) & ( ~ (all_64_5 = 0) | ~ (all_64_6 = 0) | ~
% 8.67/1.97 | | | | | | (all_64_7 = 0) | (( ~ (all_64_3 = 0) | all_64_1 = 0) &
% 8.67/1.97 | | | | | | (all_64_0 = 0 | all_64_3 = 0)))
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | ALPHA: (98) implies:
% 8.67/1.97 | | | | | | (99) environment(all_10_4) = all_64_7
% 8.67/1.97 | | | | | | (100) in_environment(all_10_4, all_10_3) = all_64_6
% 8.67/1.97 | | | | | | (101) greater(all_21_1, zero) = all_64_5
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | DELTA: instantiating (87) with fresh symbols all_66_0, all_66_1,
% 8.67/1.97 | | | | | | all_66_2, all_66_3, all_66_4, all_66_5, all_66_6, all_66_7
% 8.67/1.97 | | | | | | gives:
% 8.67/1.97 | | | | | | (102) resources(all_10_4, all_10_3) = all_66_2 &
% 8.67/1.97 | | | | | | equilibrium(all_10_4) = all_66_4 & constant(all_66_2) =
% 8.67/1.97 | | | | | | all_66_0 & decreases(all_66_2) = all_66_1 &
% 8.67/1.97 | | | | | | number_of_organizations(all_10_4, all_10_3) = all_66_6 &
% 8.67/1.97 | | | | | | greater(all_66_4, all_10_3) = all_66_3 & greater(all_66_6,
% 8.67/1.97 | | | | | | zero) = all_66_5 & environment(all_10_4) = all_66_7 &
% 8.67/1.97 | | | | | | $i(all_66_2) & $i(all_66_4) & $i(all_66_6) & ( ~ (all_66_5
% 8.67/1.97 | | | | | | = 0) | ~ (all_66_7 = 0) | (( ~ (all_66_3 = 0) |
% 8.67/1.97 | | | | | | all_66_1 = 0) & (all_66_0 = 0 | all_66_3 = 0)))
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | ALPHA: (102) implies:
% 8.67/1.97 | | | | | | (103) environment(all_10_4) = all_66_7
% 8.67/1.97 | | | | | | (104) greater(all_66_6, zero) = all_66_5
% 8.67/1.97 | | | | | | (105) number_of_organizations(all_10_4, all_10_3) = all_66_6
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | GROUND_INST: instantiating (9) with all_62_7, all_64_7, all_10_4,
% 8.67/1.97 | | | | | | simplifying with (91), (99) gives:
% 8.67/1.97 | | | | | | (106) all_64_7 = all_62_7
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | GROUND_INST: instantiating (9) with 0, all_66_7, all_10_4,
% 8.67/1.97 | | | | | | simplifying with (23), (103) gives:
% 8.67/1.97 | | | | | | (107) all_66_7 = 0
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | GROUND_INST: instantiating (9) with all_64_7, all_66_7, all_10_4,
% 8.67/1.97 | | | | | | simplifying with (99), (103) gives:
% 8.67/1.97 | | | | | | (108) all_66_7 = all_64_7
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | GROUND_INST: instantiating (13) with 0, all_64_6, all_10_3,
% 8.67/1.97 | | | | | | all_10_4, simplifying with (68), (100) gives:
% 8.67/1.97 | | | | | | (109) all_64_6 = 0
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | GROUND_INST: instantiating (13) with all_62_6, all_64_6, all_10_3,
% 8.67/1.97 | | | | | | all_10_4, simplifying with (92), (100) gives:
% 8.67/1.97 | | | | | | (110) all_64_6 = all_62_6
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | GROUND_INST: instantiating (14) with 0, all_64_5, zero, all_21_1,
% 8.67/1.97 | | | | | | simplifying with (72), (101) gives:
% 8.67/1.97 | | | | | | (111) all_64_5 = 0
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | GROUND_INST: instantiating (15) with all_21_1, all_66_6, all_10_3,
% 8.67/1.97 | | | | | | all_10_4, simplifying with (42), (105) gives:
% 8.67/1.97 | | | | | | (112) all_66_6 = all_21_1
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | GROUND_INST: instantiating (15) with all_62_5, all_66_6, all_10_3,
% 8.67/1.97 | | | | | | all_10_4, simplifying with (94), (105) gives:
% 8.67/1.97 | | | | | | (113) all_66_6 = all_62_5
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | GROUND_INST: instantiating (11) with all_23_6, all_62_1, all_23_7,
% 8.67/1.97 | | | | | | simplifying with (47), (95) gives:
% 8.67/1.97 | | | | | | (114) all_62_1 = all_23_6
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | GROUND_INST: instantiating (12) with all_23_1, all_62_0, all_23_7,
% 8.67/1.97 | | | | | | simplifying with (49), (96) gives:
% 8.67/1.97 | | | | | | (115) all_62_0 = all_23_1
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | COMBINE_EQS: (112), (113) imply:
% 8.67/1.97 | | | | | | (116) all_62_5 = all_21_1
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | SIMP: (116) implies:
% 8.67/1.97 | | | | | | (117) all_62_5 = all_21_1
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | COMBINE_EQS: (107), (108) imply:
% 8.67/1.97 | | | | | | (118) all_64_7 = 0
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | SIMP: (118) implies:
% 8.67/1.97 | | | | | | (119) all_64_7 = 0
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | COMBINE_EQS: (109), (110) imply:
% 8.67/1.97 | | | | | | (120) all_62_6 = 0
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | SIMP: (120) implies:
% 8.67/1.97 | | | | | | (121) all_62_6 = 0
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | COMBINE_EQS: (106), (119) imply:
% 8.67/1.97 | | | | | | (122) all_62_7 = 0
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | SIMP: (122) implies:
% 8.67/1.97 | | | | | | (123) all_62_7 = 0
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | REDUCE: (104), (112) imply:
% 8.67/1.97 | | | | | | (124) greater(all_21_1, zero) = all_66_5
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | REDUCE: (93), (117) imply:
% 8.67/1.97 | | | | | | (125) greater(all_21_1, zero) = all_62_4
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | BETA: splitting (97) gives:
% 8.67/1.97 | | | | | |
% 8.67/1.97 | | | | | | Case 1:
% 8.67/1.97 | | | | | | |
% 8.67/1.97 | | | | | | | (126) ~ (all_62_4 = 0)
% 8.67/1.97 | | | | | | |
% 8.67/1.97 | | | | | | | GROUND_INST: instantiating (14) with 0, all_66_5, zero, all_21_1,
% 8.67/1.97 | | | | | | | simplifying with (72), (124) gives:
% 8.67/1.97 | | | | | | | (127) all_66_5 = 0
% 8.67/1.97 | | | | | | |
% 8.67/1.97 | | | | | | | GROUND_INST: instantiating (14) with all_62_4, all_66_5, zero,
% 8.67/1.97 | | | | | | | all_21_1, simplifying with (124), (125) gives:
% 8.67/1.97 | | | | | | | (128) all_66_5 = all_62_4
% 8.67/1.97 | | | | | | |
% 8.67/1.97 | | | | | | | COMBINE_EQS: (127), (128) imply:
% 8.67/1.97 | | | | | | | (129) all_62_4 = 0
% 8.67/1.97 | | | | | | |
% 8.67/1.97 | | | | | | | SIMP: (129) implies:
% 8.67/1.97 | | | | | | | (130) all_62_4 = 0
% 8.67/1.97 | | | | | | |
% 8.67/1.97 | | | | | | | REDUCE: (126), (130) imply:
% 8.67/1.97 | | | | | | | (131) $false
% 8.67/1.98 | | | | | | |
% 8.67/1.98 | | | | | | | CLOSE: (131) is inconsistent.
% 8.67/1.98 | | | | | | |
% 8.67/1.98 | | | | | | Case 2:
% 8.67/1.98 | | | | | | |
% 8.67/1.98 | | | | | | | (132) ~ (all_62_6 = 0) | ~ (all_62_7 = 0) | (( ~ (all_62_2 =
% 8.67/1.98 | | | | | | | 0) | all_62_1 = 0) & (all_62_0 = 0 | all_62_2 = 0))
% 8.67/1.98 | | | | | | |
% 8.67/1.98 | | | | | | | BETA: splitting (132) gives:
% 8.67/1.98 | | | | | | |
% 8.67/1.98 | | | | | | | Case 1:
% 8.67/1.98 | | | | | | | |
% 8.67/1.98 | | | | | | | | (133) ~ (all_62_6 = 0)
% 8.67/1.98 | | | | | | | |
% 8.67/1.98 | | | | | | | | REDUCE: (121), (133) imply:
% 8.67/1.98 | | | | | | | | (134) $false
% 8.67/1.98 | | | | | | | |
% 8.67/1.98 | | | | | | | | CLOSE: (134) is inconsistent.
% 8.67/1.98 | | | | | | | |
% 8.67/1.98 | | | | | | | Case 2:
% 8.67/1.98 | | | | | | | |
% 8.67/1.98 | | | | | | | | (135) ~ (all_62_7 = 0) | (( ~ (all_62_2 = 0) | all_62_1 = 0)
% 8.67/1.98 | | | | | | | | & (all_62_0 = 0 | all_62_2 = 0))
% 8.67/1.98 | | | | | | | |
% 8.67/1.98 | | | | | | | | BETA: splitting (135) gives:
% 8.67/1.98 | | | | | | | |
% 8.67/1.98 | | | | | | | | Case 1:
% 8.67/1.98 | | | | | | | | |
% 8.67/1.98 | | | | | | | | | (136) ~ (all_62_7 = 0)
% 8.67/1.98 | | | | | | | | |
% 8.67/1.98 | | | | | | | | | REDUCE: (123), (136) imply:
% 8.67/1.98 | | | | | | | | | (137) $false
% 8.67/1.98 | | | | | | | | |
% 8.67/1.98 | | | | | | | | | CLOSE: (137) is inconsistent.
% 8.67/1.98 | | | | | | | | |
% 8.67/1.98 | | | | | | | | Case 2:
% 8.67/1.98 | | | | | | | | |
% 8.67/1.98 | | | | | | | | | (138) ( ~ (all_62_2 = 0) | all_62_1 = 0) & (all_62_0 = 0 |
% 8.67/1.98 | | | | | | | | | all_62_2 = 0)
% 8.67/1.98 | | | | | | | | |
% 8.67/1.98 | | | | | | | | | ALPHA: (138) implies:
% 8.67/1.98 | | | | | | | | | (139) all_62_0 = 0 | all_62_2 = 0
% 8.67/1.98 | | | | | | | | | (140) ~ (all_62_2 = 0) | all_62_1 = 0
% 8.67/1.98 | | | | | | | | |
% 8.67/1.98 | | | | | | | | | BETA: splitting (139) gives:
% 8.67/1.98 | | | | | | | | |
% 8.67/1.98 | | | | | | | | | Case 1:
% 8.67/1.98 | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | (141) all_62_0 = 0
% 8.67/1.98 | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | COMBINE_EQS: (115), (141) imply:
% 8.67/1.98 | | | | | | | | | | (142) all_23_1 = 0
% 8.67/1.98 | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | SIMP: (142) implies:
% 8.67/1.98 | | | | | | | | | | (143) all_23_1 = 0
% 8.67/1.98 | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | REDUCE: (86), (143) imply:
% 8.67/1.98 | | | | | | | | | | (144) $false
% 8.67/1.98 | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | CLOSE: (144) is inconsistent.
% 8.67/1.98 | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | Case 2:
% 8.67/1.98 | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | (145) all_62_2 = 0
% 8.67/1.98 | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | BETA: splitting (140) gives:
% 8.67/1.98 | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | Case 1:
% 8.67/1.98 | | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | | (146) ~ (all_62_2 = 0)
% 8.67/1.98 | | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | | REDUCE: (145), (146) imply:
% 8.67/1.98 | | | | | | | | | | | (147) $false
% 8.67/1.98 | | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | | CLOSE: (147) is inconsistent.
% 8.67/1.98 | | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | Case 2:
% 8.67/1.98 | | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | | (148) all_62_1 = 0
% 8.67/1.98 | | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | | COMBINE_EQS: (114), (148) imply:
% 8.67/1.98 | | | | | | | | | | | (149) all_23_6 = 0
% 8.67/1.98 | | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | | SIMP: (149) implies:
% 8.67/1.98 | | | | | | | | | | | (150) all_23_6 = 0
% 8.67/1.98 | | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | | REDUCE: (83), (150) imply:
% 8.67/1.98 | | | | | | | | | | | (151) $false
% 8.67/1.98 | | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | | CLOSE: (151) is inconsistent.
% 8.67/1.98 | | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | | End of split
% 8.67/1.98 | | | | | | | | | |
% 8.67/1.98 | | | | | | | | | End of split
% 8.67/1.98 | | | | | | | | |
% 8.67/1.98 | | | | | | | | End of split
% 8.67/1.98 | | | | | | | |
% 8.67/1.98 | | | | | | | End of split
% 8.67/1.98 | | | | | | |
% 8.67/1.98 | | | | | | End of split
% 8.67/1.98 | | | | | |
% 8.67/1.98 | | | | | End of split
% 8.67/1.98 | | | | |
% 8.67/1.98 | | | | Case 2:
% 8.67/1.98 | | | | |
% 8.67/1.98 | | | | | (152) all_23_2 = 0
% 8.67/1.98 | | | | |
% 8.67/1.98 | | | | | COMBINE_EQS: (76), (152) imply:
% 8.67/1.98 | | | | | (153) all_17_0 = 0
% 8.67/1.98 | | | | |
% 8.67/1.98 | | | | | REDUCE: (33), (153) imply:
% 8.67/1.98 | | | | | (154) $false
% 8.67/1.98 | | | | |
% 8.67/1.98 | | | | | CLOSE: (154) is inconsistent.
% 8.67/1.98 | | | | |
% 8.67/1.98 | | | | End of split
% 8.67/1.98 | | | |
% 8.67/1.98 | | | End of split
% 8.67/1.98 | | |
% 8.67/1.98 | | End of split
% 8.67/1.98 | |
% 8.67/1.98 | End of split
% 8.67/1.98 |
% 8.67/1.98 End of proof
% 8.67/1.98 % SZS output end Proof for theBenchmark
% 8.67/1.98
% 8.67/1.98 1374ms
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