TSTP Solution File: MGT024+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : MGT024+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 : n005.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 09:16:15 EDT 2023
% Result : Theorem 6.45s 1.61s
% Output : Proof 10.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MGT024+1 : TPTP v8.1.2. Released v2.0.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 06:07:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.09/1.05 Prover 4: Preprocessing ...
% 2.09/1.05 Prover 1: Preprocessing ...
% 2.76/1.09 Prover 5: Preprocessing ...
% 2.76/1.09 Prover 2: Preprocessing ...
% 2.76/1.09 Prover 3: Preprocessing ...
% 2.76/1.09 Prover 0: Preprocessing ...
% 2.76/1.09 Prover 6: Preprocessing ...
% 4.71/1.36 Prover 3: Constructing countermodel ...
% 4.71/1.37 Prover 6: Constructing countermodel ...
% 4.71/1.39 Prover 2: Proving ...
% 4.71/1.40 Prover 5: Proving ...
% 4.71/1.41 Prover 1: Constructing countermodel ...
% 5.27/1.44 Prover 4: Constructing countermodel ...
% 6.45/1.58 Prover 0: Proving ...
% 6.45/1.60 Prover 3: proved (974ms)
% 6.45/1.61
% 6.45/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.45/1.61
% 6.45/1.61 Prover 6: stopped
% 6.45/1.61 Prover 0: stopped
% 6.45/1.61 Prover 2: stopped
% 6.45/1.62 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.45/1.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.45/1.62 Prover 5: stopped
% 6.78/1.63 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.78/1.63 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.78/1.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.92/1.65 Prover 8: Preprocessing ...
% 6.92/1.66 Prover 7: Preprocessing ...
% 6.92/1.67 Prover 11: Preprocessing ...
% 6.92/1.67 Prover 10: Preprocessing ...
% 6.92/1.67 Prover 13: Preprocessing ...
% 7.47/1.73 Prover 13: Warning: ignoring some quantifiers
% 7.47/1.74 Prover 13: Constructing countermodel ...
% 7.47/1.74 Prover 8: Warning: ignoring some quantifiers
% 7.47/1.75 Prover 8: Constructing countermodel ...
% 7.47/1.76 Prover 7: Constructing countermodel ...
% 7.47/1.77 Prover 10: Constructing countermodel ...
% 7.90/1.84 Prover 7: gave up
% 7.90/1.84 Prover 10: gave up
% 8.52/1.86 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.52/1.87 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 8.52/1.90 Prover 19: Preprocessing ...
% 8.52/1.90 Prover 16: Preprocessing ...
% 8.52/1.91 Prover 11: Constructing countermodel ...
% 8.76/1.95 Prover 16: Warning: ignoring some quantifiers
% 8.76/1.96 Prover 16: Constructing countermodel ...
% 9.53/2.00 Prover 19: Warning: ignoring some quantifiers
% 9.53/2.01 Prover 1: Found proof (size 219)
% 9.53/2.01 Prover 1: proved (1385ms)
% 9.53/2.01 Prover 19: Constructing countermodel ...
% 9.53/2.01 Prover 16: stopped
% 9.53/2.01 Prover 11: stopped
% 9.53/2.01 Prover 4: stopped
% 9.53/2.01 Prover 13: stopped
% 9.53/2.01 Prover 8: stopped
% 9.53/2.01 Prover 19: stopped
% 9.53/2.02
% 9.53/2.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.53/2.02
% 9.68/2.04 % SZS output start Proof for theBenchmark
% 9.68/2.05 Assumptions after simplification:
% 9.68/2.05 ---------------------------------
% 9.68/2.05
% 9.68/2.05 (a3)
% 9.68/2.07 $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 9.68/2.07 (equilibrium(v0) = v2) | ~ (greater(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) |
% 9.68/2.07 ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ?
% 9.68/2.07 [v9: any] : ? [v10: any] : (resources(v0, v1) = v8 & decreases(v8) = v9 &
% 9.68/2.07 constant(v8) = v10 & number_of_organizations(v0, v1) = v6 & greater(v6,
% 9.68/2.07 zero) = v7 & environment(v0) = v4 & in_environment(v0, v1) = v5 & $i(v8)
% 9.68/2.07 & $i(v6) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | (( ~ (v3 = 0) | v9 =
% 9.68/2.07 0) & (v10 = 0 | v3 = 0)))))
% 9.68/2.07
% 9.68/2.07 (a6)
% 9.68/2.08 ! [v0: $i] : ! [v1: $i] : ( ~ (in_environment(v0, v1) = 0) | ~ $i(v1) | ~
% 9.68/2.08 $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6:
% 9.68/2.08 any] : ? [v7: any] : ? [v8: any] : (resources(v0, v1) = v3 &
% 9.68/2.08 decreases(v5) = v6 & decreases(v3) = v4 & constant(v5) = v8 & constant(v3)
% 9.68/2.08 = v7 & number_of_organizations(v0, v1) = v5 & environment(v0) = v2 &
% 9.68/2.08 $i(v5) & $i(v3) & ( ~ (v2 = 0) | (( ~ (v7 = 0) | v8 = 0) & ( ~ (v6 = 0) |
% 9.68/2.08 ~ (v4 = 0))))))
% 9.68/2.08
% 9.68/2.08 (l7)
% 9.68/2.08 $i(zero) & $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1:
% 9.68/2.08 $i] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v1) = 0) |
% 9.68/2.08 ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5:
% 9.68/2.08 $i] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10:
% 9.68/2.08 any] : (growth_rate(efficient_producers, v1) = v6 &
% 9.68/2.08 growth_rate(first_movers, v1) = v5 & constant(v3) = v4 &
% 9.68/2.08 number_of_organizations(v0, v1) = v3 & greater(v6, zero) = v9 &
% 9.68/2.08 greater(v5, zero) = v7 & greater(zero, v6) = v8 & greater(zero, v5) = v10
% 9.68/2.08 & environment(v0) = v2 & $i(v6) & $i(v5) & $i(v3) & ( ~ (v4 = 0) | ~ (v2
% 9.68/2.08 = 0) | (v10 = 0 & v9 = 0) | (v8 = 0 & v7 = 0) | (v6 = zero & v5 =
% 9.68/2.08 zero))))
% 9.68/2.08
% 9.68/2.08 (mp_equilibrium)
% 9.68/2.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (equilibrium(v0) = v2) | ~
% 9.68/2.09 (greater_or_equal(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ?
% 9.68/2.09 [v4: any] : (greater(v2, v1) = v4 & environment(v0) = v3 & ( ~ (v4 = 0) | ~
% 9.68/2.09 (v3 = 0))))
% 9.68/2.09
% 9.68/2.09 (mp_positive_number_of_organizations)
% 9.68/2.09 $i(zero) & $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1:
% 9.68/2.09 $i] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v1) = 0) |
% 9.68/2.09 ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 9.68/2.09 (number_of_organizations(v0, v1) = v3 & greater(v3, zero) = v4 &
% 9.68/2.09 environment(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v4 = 0)))
% 9.68/2.09
% 9.68/2.09 (mp_time_point_occur)
% 9.68/2.09 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : ( ~
% 9.68/2.09 (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ~ $i(v1)
% 9.68/2.09 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (environment(v0) = v2 &
% 9.68/2.09 in_environment(v0, v1) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 9.68/2.09
% 9.68/2.09 (prove_l6)
% 9.68/2.09 $i(zero) & $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ? [v1:
% 9.68/2.09 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: any] : ? [v6: any]
% 9.68/2.09 : ? [v7: any] : ? [v8: any] : (growth_rate(efficient_producers, v1) = v4 &
% 9.68/2.09 growth_rate(first_movers, v1) = v3 & equilibrium(v0) = v2 &
% 9.68/2.09 greater_or_equal(v1, v2) = 0 & greater(v4, zero) = v7 & greater(v3, zero) =
% 9.68/2.09 v5 & greater(zero, v4) = v6 & greater(zero, v3) = v8 &
% 9.68/2.09 subpopulations(first_movers, efficient_producers, v0, v1) = 0 &
% 9.68/2.09 environment(v0) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v8 =
% 9.68/2.09 0) | ~ (v7 = 0)) & ( ~ (v6 = 0) | ~ (v5 = 0)) & ( ~ (v4 = zero) | ~
% 9.68/2.09 (v3 = zero)))
% 9.68/2.09
% 9.68/2.09 (function-axioms)
% 10.08/2.10 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.08/2.10 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (subpopulations(v5, v4,
% 10.08/2.10 v3, v2) = v1) | ~ (subpopulations(v5, v4, v3, v2) = v0)) & ! [v0: $i]
% 10.08/2.10 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (growth_rate(v3, v2)
% 10.08/2.10 = v1) | ~ (growth_rate(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 10.08/2.10 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (resources(v3, v2) = v1) | ~
% 10.08/2.10 (resources(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.08/2.10 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.08/2.10 (greater_or_equal(v3, v2) = v1) | ~ (greater_or_equal(v3, v2) = v0)) & !
% 10.08/2.10 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.08/2.10 (number_of_organizations(v3, v2) = v1) | ~ (number_of_organizations(v3, v2)
% 10.08/2.10 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.08/2.10 $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3,
% 10.08/2.10 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 10.08/2.10 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~
% 10.08/2.10 (in_environment(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.08/2.10 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (decreases(v2) = v1) | ~
% 10.08/2.10 (decreases(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.08/2.10 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (constant(v2) = v1) | ~
% 10.08/2.10 (constant(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 10.08/2.10 ~ (equilibrium(v2) = v1) | ~ (equilibrium(v2) = v0)) & ! [v0:
% 10.08/2.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 10.08/2.10 ~ (environment(v2) = v1) | ~ (environment(v2) = v0))
% 10.08/2.10
% 10.08/2.10 Those formulas are unsatisfiable:
% 10.08/2.10 ---------------------------------
% 10.08/2.10
% 10.08/2.10 Begin of proof
% 10.08/2.10 |
% 10.08/2.10 | ALPHA: (mp_time_point_occur) implies:
% 10.08/2.10 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subpopulations(first_movers,
% 10.08/2.10 | efficient_producers, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 10.08/2.10 | [v2: any] : ? [v3: any] : (environment(v0) = v2 & in_environment(v0,
% 10.08/2.10 | v1) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 10.08/2.10 |
% 10.08/2.10 | ALPHA: (mp_positive_number_of_organizations) implies:
% 10.08/2.10 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (subpopulations(first_movers,
% 10.08/2.10 | efficient_producers, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 10.08/2.10 | [v2: any] : ? [v3: $i] : ? [v4: any] : (number_of_organizations(v0,
% 10.08/2.10 | v1) = v3 & greater(v3, zero) = v4 & environment(v0) = v2 & $i(v3)
% 10.08/2.10 | & ( ~ (v2 = 0) | v4 = 0)))
% 10.08/2.10 |
% 10.08/2.10 | ALPHA: (a3) implies:
% 10.08/2.11 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 10.08/2.11 | (equilibrium(v0) = v2) | ~ (greater(v2, v1) = v3) | ~ $i(v1) | ~
% 10.08/2.11 | $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: any] :
% 10.08/2.11 | ? [v8: $i] : ? [v9: any] : ? [v10: any] : (resources(v0, v1) = v8 &
% 10.08/2.11 | decreases(v8) = v9 & constant(v8) = v10 &
% 10.08/2.11 | number_of_organizations(v0, v1) = v6 & greater(v6, zero) = v7 &
% 10.08/2.11 | environment(v0) = v4 & in_environment(v0, v1) = v5 & $i(v8) &
% 10.08/2.11 | $i(v6) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | (( ~ (v3 = 0) |
% 10.08/2.11 | v9 = 0) & (v10 = 0 | v3 = 0)))))
% 10.08/2.11 |
% 10.08/2.11 | ALPHA: (l7) implies:
% 10.08/2.11 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (subpopulations(first_movers,
% 10.08/2.11 | efficient_producers, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 10.08/2.11 | [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] :
% 10.08/2.11 | ? [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10: any] :
% 10.08/2.11 | (growth_rate(efficient_producers, v1) = v6 &
% 10.08/2.11 | growth_rate(first_movers, v1) = v5 & constant(v3) = v4 &
% 10.08/2.11 | number_of_organizations(v0, v1) = v3 & greater(v6, zero) = v9 &
% 10.08/2.11 | greater(v5, zero) = v7 & greater(zero, v6) = v8 & greater(zero, v5)
% 10.08/2.11 | = v10 & environment(v0) = v2 & $i(v6) & $i(v5) & $i(v3) & ( ~ (v4 =
% 10.08/2.11 | 0) | ~ (v2 = 0) | (v10 = 0 & v9 = 0) | (v8 = 0 & v7 = 0) | (v6
% 10.08/2.11 | = zero & v5 = zero))))
% 10.08/2.11 |
% 10.08/2.11 | ALPHA: (prove_l6) implies:
% 10.08/2.11 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 10.08/2.11 | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 10.08/2.11 | (growth_rate(efficient_producers, v1) = v4 & growth_rate(first_movers,
% 10.08/2.11 | v1) = v3 & equilibrium(v0) = v2 & greater_or_equal(v1, v2) = 0 &
% 10.08/2.11 | greater(v4, zero) = v7 & greater(v3, zero) = v5 & greater(zero, v4) =
% 10.08/2.11 | v6 & greater(zero, v3) = v8 & subpopulations(first_movers,
% 10.08/2.11 | efficient_producers, v0, v1) = 0 & environment(v0) = 0 & $i(v4) &
% 10.08/2.11 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v8 = 0) | ~ (v7 = 0)) & ( ~
% 10.08/2.11 | (v6 = 0) | ~ (v5 = 0)) & ( ~ (v4 = zero) | ~ (v3 = zero)))
% 10.08/2.11 |
% 10.08/2.11 | ALPHA: (function-axioms) implies:
% 10.08/2.12 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.08/2.12 | (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0))
% 10.08/2.12 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.08/2.12 | (v1 = v0 | ~ (constant(v2) = v1) | ~ (constant(v2) = v0))
% 10.08/2.12 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.08/2.12 | ! [v3: $i] : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~
% 10.08/2.12 | (in_environment(v3, v2) = v0))
% 10.08/2.12 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.08/2.12 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3,
% 10.08/2.12 | v2) = v0))
% 10.08/2.12 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.08/2.12 | (number_of_organizations(v3, v2) = v1) | ~
% 10.08/2.12 | (number_of_organizations(v3, v2) = v0))
% 10.08/2.12 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.08/2.12 | (resources(v3, v2) = v1) | ~ (resources(v3, v2) = v0))
% 10.08/2.12 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.08/2.12 | (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 10.08/2.12 |
% 10.08/2.12 | DELTA: instantiating (5) with fresh symbols all_10_0, all_10_1, all_10_2,
% 10.08/2.12 | all_10_3, all_10_4, all_10_5, all_10_6, all_10_7, all_10_8 gives:
% 10.08/2.12 | (13) growth_rate(efficient_producers, all_10_7) = all_10_4 &
% 10.08/2.12 | growth_rate(first_movers, all_10_7) = all_10_5 & equilibrium(all_10_8)
% 10.08/2.12 | = all_10_6 & greater_or_equal(all_10_7, all_10_6) = 0 &
% 10.08/2.12 | greater(all_10_4, zero) = all_10_1 & greater(all_10_5, zero) =
% 10.08/2.12 | all_10_3 & greater(zero, all_10_4) = all_10_2 & greater(zero,
% 10.08/2.12 | all_10_5) = all_10_0 & subpopulations(first_movers,
% 10.08/2.12 | efficient_producers, all_10_8, all_10_7) = 0 & environment(all_10_8)
% 10.08/2.12 | = 0 & $i(all_10_4) & $i(all_10_5) & $i(all_10_6) & $i(all_10_7) &
% 10.08/2.12 | $i(all_10_8) & ( ~ (all_10_0 = 0) | ~ (all_10_1 = 0)) & ( ~ (all_10_2
% 10.08/2.12 | = 0) | ~ (all_10_3 = 0)) & ( ~ (all_10_4 = zero) | ~ (all_10_5 =
% 10.08/2.12 | zero))
% 10.08/2.12 |
% 10.08/2.12 | ALPHA: (13) implies:
% 10.08/2.12 | (14) $i(all_10_8)
% 10.08/2.12 | (15) $i(all_10_7)
% 10.08/2.12 | (16) environment(all_10_8) = 0
% 10.08/2.12 | (17) subpopulations(first_movers, efficient_producers, all_10_8, all_10_7)
% 10.08/2.12 | = 0
% 10.08/2.12 | (18) greater(zero, all_10_5) = all_10_0
% 10.08/2.13 | (19) greater(zero, all_10_4) = all_10_2
% 10.08/2.13 | (20) greater(all_10_5, zero) = all_10_3
% 10.08/2.13 | (21) greater(all_10_4, zero) = all_10_1
% 10.08/2.13 | (22) greater_or_equal(all_10_7, all_10_6) = 0
% 10.08/2.13 | (23) equilibrium(all_10_8) = all_10_6
% 10.08/2.13 | (24) growth_rate(first_movers, all_10_7) = all_10_5
% 10.08/2.13 | (25) growth_rate(efficient_producers, all_10_7) = all_10_4
% 10.08/2.13 | (26) ~ (all_10_4 = zero) | ~ (all_10_5 = zero)
% 10.08/2.13 | (27) ~ (all_10_2 = 0) | ~ (all_10_3 = 0)
% 10.08/2.13 | (28) ~ (all_10_0 = 0) | ~ (all_10_1 = 0)
% 10.08/2.13 |
% 10.08/2.13 | GROUND_INST: instantiating (4) with all_10_8, all_10_7, simplifying with (14),
% 10.08/2.13 | (15), (17) gives:
% 10.08/2.13 | (29) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: $i]
% 10.08/2.13 | : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 10.08/2.13 | (growth_rate(efficient_producers, all_10_7) = v4 &
% 10.08/2.13 | growth_rate(first_movers, all_10_7) = v3 & constant(v1) = v2 &
% 10.08/2.13 | number_of_organizations(all_10_8, all_10_7) = v1 & greater(v4, zero)
% 10.08/2.13 | = v7 & greater(v3, zero) = v5 & greater(zero, v4) = v6 &
% 10.08/2.13 | greater(zero, v3) = v8 & environment(all_10_8) = v0 & $i(v4) &
% 10.08/2.13 | $i(v3) & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0) | (v8 = 0 & v7 = 0) |
% 10.08/2.13 | (v6 = 0 & v5 = 0) | (v4 = zero & v3 = zero)))
% 10.08/2.13 |
% 10.08/2.13 | GROUND_INST: instantiating (2) with all_10_8, all_10_7, simplifying with (14),
% 10.08/2.13 | (15), (17) gives:
% 10.08/2.13 | (30) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 10.08/2.13 | (number_of_organizations(all_10_8, all_10_7) = v1 & greater(v1, zero)
% 10.08/2.13 | = v2 & environment(all_10_8) = v0 & $i(v1) & ( ~ (v0 = 0) | v2 = 0))
% 10.08/2.13 |
% 10.08/2.13 | GROUND_INST: instantiating (1) with all_10_8, all_10_7, simplifying with (14),
% 10.08/2.13 | (15), (17) gives:
% 10.08/2.13 | (31) ? [v0: any] : ? [v1: any] : (environment(all_10_8) = v0 &
% 10.08/2.13 | in_environment(all_10_8, all_10_7) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 10.08/2.13 |
% 10.08/2.13 | GROUND_INST: instantiating (mp_equilibrium) with all_10_8, all_10_7, all_10_6,
% 10.08/2.13 | simplifying with (14), (15), (22), (23) gives:
% 10.08/2.13 | (32) ? [v0: any] : ? [v1: any] : (greater(all_10_6, all_10_7) = v1 &
% 10.08/2.13 | environment(all_10_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 10.08/2.13 |
% 10.08/2.13 | DELTA: instantiating (32) with fresh symbols all_17_0, all_17_1 gives:
% 10.08/2.13 | (33) greater(all_10_6, all_10_7) = all_17_0 & environment(all_10_8) =
% 10.08/2.13 | all_17_1 & ( ~ (all_17_0 = 0) | ~ (all_17_1 = 0))
% 10.08/2.13 |
% 10.08/2.13 | ALPHA: (33) implies:
% 10.08/2.13 | (34) environment(all_10_8) = all_17_1
% 10.08/2.13 | (35) greater(all_10_6, all_10_7) = all_17_0
% 10.08/2.13 | (36) ~ (all_17_0 = 0) | ~ (all_17_1 = 0)
% 10.08/2.13 |
% 10.08/2.13 | DELTA: instantiating (31) with fresh symbols all_19_0, all_19_1 gives:
% 10.08/2.13 | (37) environment(all_10_8) = all_19_1 & in_environment(all_10_8, all_10_7)
% 10.08/2.13 | = all_19_0 & ( ~ (all_19_1 = 0) | all_19_0 = 0)
% 10.08/2.13 |
% 10.08/2.13 | ALPHA: (37) implies:
% 10.08/2.13 | (38) in_environment(all_10_8, all_10_7) = all_19_0
% 10.08/2.13 | (39) environment(all_10_8) = all_19_1
% 10.08/2.13 | (40) ~ (all_19_1 = 0) | all_19_0 = 0
% 10.08/2.13 |
% 10.08/2.13 | DELTA: instantiating (30) with fresh symbols all_21_0, all_21_1, all_21_2
% 10.08/2.13 | gives:
% 10.08/2.14 | (41) number_of_organizations(all_10_8, all_10_7) = all_21_1 &
% 10.08/2.14 | greater(all_21_1, zero) = all_21_0 & environment(all_10_8) = all_21_2
% 10.08/2.14 | & $i(all_21_1) & ( ~ (all_21_2 = 0) | all_21_0 = 0)
% 10.08/2.14 |
% 10.08/2.14 | ALPHA: (41) implies:
% 10.08/2.15 | (42) environment(all_10_8) = all_21_2
% 10.08/2.15 | (43) greater(all_21_1, zero) = all_21_0
% 10.08/2.15 | (44) number_of_organizations(all_10_8, all_10_7) = all_21_1
% 10.08/2.15 | (45) ~ (all_21_2 = 0) | all_21_0 = 0
% 10.08/2.15 |
% 10.08/2.15 | DELTA: instantiating (29) with fresh symbols all_23_0, all_23_1, all_23_2,
% 10.08/2.15 | all_23_3, all_23_4, all_23_5, all_23_6, all_23_7, all_23_8 gives:
% 10.08/2.15 | (46) growth_rate(efficient_producers, all_10_7) = all_23_4 &
% 10.08/2.15 | growth_rate(first_movers, all_10_7) = all_23_5 & constant(all_23_7) =
% 10.08/2.15 | all_23_6 & number_of_organizations(all_10_8, all_10_7) = all_23_7 &
% 10.08/2.15 | greater(all_23_4, zero) = all_23_1 & greater(all_23_5, zero) =
% 10.08/2.15 | all_23_3 & greater(zero, all_23_4) = all_23_2 & greater(zero,
% 10.08/2.15 | all_23_5) = all_23_0 & environment(all_10_8) = all_23_8 &
% 10.08/2.15 | $i(all_23_4) & $i(all_23_5) & $i(all_23_7) & ( ~ (all_23_6 = 0) | ~
% 10.08/2.15 | (all_23_8 = 0) | (all_23_0 = 0 & all_23_1 = 0) | (all_23_2 = 0 &
% 10.08/2.15 | all_23_3 = 0) | (all_23_4 = zero & all_23_5 = zero))
% 10.08/2.15 |
% 10.08/2.15 | ALPHA: (46) implies:
% 10.08/2.15 | (47) environment(all_10_8) = all_23_8
% 10.08/2.15 | (48) greater(zero, all_23_5) = all_23_0
% 10.08/2.15 | (49) greater(zero, all_23_4) = all_23_2
% 10.08/2.15 | (50) greater(all_23_5, zero) = all_23_3
% 10.08/2.15 | (51) greater(all_23_4, zero) = all_23_1
% 10.08/2.15 | (52) number_of_organizations(all_10_8, all_10_7) = all_23_7
% 10.08/2.15 | (53) constant(all_23_7) = all_23_6
% 10.08/2.15 | (54) growth_rate(first_movers, all_10_7) = all_23_5
% 10.08/2.15 | (55) growth_rate(efficient_producers, all_10_7) = all_23_4
% 10.08/2.15 | (56) ~ (all_23_6 = 0) | ~ (all_23_8 = 0) | (all_23_0 = 0 & all_23_1 = 0)
% 10.08/2.15 | | (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero & all_23_5 = zero)
% 10.08/2.15 |
% 10.08/2.15 | GROUND_INST: instantiating (6) with 0, all_23_8, all_10_8, simplifying with
% 10.08/2.15 | (16), (47) gives:
% 10.08/2.15 | (57) all_23_8 = 0
% 10.08/2.15 |
% 10.08/2.15 | GROUND_INST: instantiating (6) with all_21_2, all_23_8, all_10_8, simplifying
% 10.08/2.15 | with (42), (47) gives:
% 10.08/2.15 | (58) all_23_8 = all_21_2
% 10.08/2.15 |
% 10.08/2.15 | GROUND_INST: instantiating (6) with all_19_1, all_23_8, all_10_8, simplifying
% 10.08/2.15 | with (39), (47) gives:
% 10.08/2.15 | (59) all_23_8 = all_19_1
% 10.08/2.16 |
% 10.08/2.16 | GROUND_INST: instantiating (6) with all_17_1, all_23_8, all_10_8, simplifying
% 10.08/2.16 | with (34), (47) gives:
% 10.08/2.16 | (60) all_23_8 = all_17_1
% 10.08/2.16 |
% 10.08/2.16 | GROUND_INST: instantiating (10) with all_21_1, all_23_7, all_10_7, all_10_8,
% 10.08/2.16 | simplifying with (44), (52) gives:
% 10.08/2.16 | (61) all_23_7 = all_21_1
% 10.08/2.16 |
% 10.08/2.16 | GROUND_INST: instantiating (12) with all_10_5, all_23_5, all_10_7,
% 10.08/2.16 | first_movers, simplifying with (24), (54) gives:
% 10.08/2.16 | (62) all_23_5 = all_10_5
% 10.08/2.16 |
% 10.08/2.16 | GROUND_INST: instantiating (12) with all_10_4, all_23_4, all_10_7,
% 10.08/2.16 | efficient_producers, simplifying with (25), (55) gives:
% 10.08/2.16 | (63) all_23_4 = all_10_4
% 10.08/2.16 |
% 10.08/2.16 | COMBINE_EQS: (58), (60) imply:
% 10.08/2.16 | (64) all_21_2 = all_17_1
% 10.08/2.16 |
% 10.08/2.16 | COMBINE_EQS: (58), (59) imply:
% 10.08/2.16 | (65) all_21_2 = all_19_1
% 10.08/2.16 |
% 10.08/2.16 | COMBINE_EQS: (57), (58) imply:
% 10.08/2.16 | (66) all_21_2 = 0
% 10.08/2.16 |
% 10.08/2.16 | COMBINE_EQS: (65), (66) imply:
% 10.08/2.16 | (67) all_19_1 = 0
% 10.08/2.16 |
% 10.08/2.16 | COMBINE_EQS: (64), (65) imply:
% 10.08/2.16 | (68) all_19_1 = all_17_1
% 10.08/2.16 |
% 10.08/2.16 | COMBINE_EQS: (67), (68) imply:
% 10.08/2.16 | (69) all_17_1 = 0
% 10.08/2.16 |
% 10.08/2.16 | REDUCE: (53), (61) imply:
% 10.08/2.16 | (70) constant(all_21_1) = all_23_6
% 10.08/2.16 |
% 10.08/2.16 | REDUCE: (51), (63) imply:
% 10.08/2.16 | (71) greater(all_10_4, zero) = all_23_1
% 10.08/2.16 |
% 10.08/2.16 | REDUCE: (50), (62) imply:
% 10.08/2.16 | (72) greater(all_10_5, zero) = all_23_3
% 10.08/2.16 |
% 10.08/2.16 | REDUCE: (49), (63) imply:
% 10.08/2.16 | (73) greater(zero, all_10_4) = all_23_2
% 10.08/2.16 |
% 10.08/2.16 | REDUCE: (48), (62) imply:
% 10.08/2.16 | (74) greater(zero, all_10_5) = all_23_0
% 10.08/2.16 |
% 10.08/2.16 | BETA: splitting (36) gives:
% 10.08/2.16 |
% 10.08/2.16 | Case 1:
% 10.08/2.16 | |
% 10.08/2.16 | | (75) ~ (all_17_0 = 0)
% 10.08/2.16 | |
% 10.08/2.16 | | BETA: splitting (40) gives:
% 10.08/2.16 | |
% 10.08/2.16 | | Case 1:
% 10.08/2.16 | | |
% 10.08/2.16 | | | (76) ~ (all_19_1 = 0)
% 10.08/2.16 | | |
% 10.08/2.16 | | | REDUCE: (67), (76) imply:
% 10.08/2.16 | | | (77) $false
% 10.08/2.16 | | |
% 10.08/2.16 | | | CLOSE: (77) is inconsistent.
% 10.08/2.16 | | |
% 10.08/2.16 | | Case 2:
% 10.08/2.16 | | |
% 10.08/2.16 | | | (78) all_19_0 = 0
% 10.08/2.16 | | |
% 10.08/2.16 | | | REDUCE: (38), (78) imply:
% 10.08/2.16 | | | (79) in_environment(all_10_8, all_10_7) = 0
% 10.08/2.16 | | |
% 10.08/2.16 | | | BETA: splitting (45) gives:
% 10.08/2.16 | | |
% 10.08/2.16 | | | Case 1:
% 10.08/2.16 | | | |
% 10.08/2.16 | | | | (80) ~ (all_21_2 = 0)
% 10.08/2.16 | | | |
% 10.08/2.16 | | | | REDUCE: (66), (80) imply:
% 10.08/2.16 | | | | (81) $false
% 10.08/2.16 | | | |
% 10.08/2.16 | | | | CLOSE: (81) is inconsistent.
% 10.08/2.16 | | | |
% 10.08/2.16 | | | Case 2:
% 10.08/2.16 | | | |
% 10.08/2.16 | | | | (82) all_21_0 = 0
% 10.08/2.16 | | | |
% 10.08/2.16 | | | | REDUCE: (43), (82) imply:
% 10.08/2.16 | | | | (83) greater(all_21_1, zero) = 0
% 10.08/2.16 | | | |
% 10.08/2.16 | | | | GROUND_INST: instantiating (9) with all_10_0, all_23_0, all_10_5, zero,
% 10.08/2.16 | | | | simplifying with (18), (74) gives:
% 10.08/2.16 | | | | (84) all_23_0 = all_10_0
% 10.08/2.16 | | | |
% 10.08/2.16 | | | | GROUND_INST: instantiating (9) with all_10_2, all_23_2, all_10_4, zero,
% 10.08/2.16 | | | | simplifying with (19), (73) gives:
% 10.08/2.17 | | | | (85) all_23_2 = all_10_2
% 10.08/2.17 | | | |
% 10.08/2.17 | | | | GROUND_INST: instantiating (9) with all_10_3, all_23_3, zero, all_10_5,
% 10.08/2.17 | | | | simplifying with (20), (72) gives:
% 10.08/2.17 | | | | (86) all_23_3 = all_10_3
% 10.08/2.17 | | | |
% 10.08/2.17 | | | | GROUND_INST: instantiating (9) with all_10_1, all_23_1, zero, all_10_4,
% 10.08/2.17 | | | | simplifying with (21), (71) gives:
% 10.08/2.17 | | | | (87) all_23_1 = all_10_1
% 10.08/2.17 | | | |
% 10.08/2.17 | | | | GROUND_INST: instantiating (a6) with all_10_8, all_10_7, simplifying
% 10.08/2.17 | | | | with (14), (15), (79) gives:
% 10.08/2.17 | | | | (88) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ?
% 10.08/2.17 | | | | [v4: any] : ? [v5: any] : ? [v6: any] : (resources(all_10_8,
% 10.08/2.17 | | | | all_10_7) = v1 & decreases(v3) = v4 & decreases(v1) = v2 &
% 10.08/2.17 | | | | constant(v3) = v6 & constant(v1) = v5 &
% 10.08/2.17 | | | | number_of_organizations(all_10_8, all_10_7) = v3 &
% 10.08/2.17 | | | | environment(all_10_8) = v0 & $i(v3) & $i(v1) & ( ~ (v0 = 0) |
% 10.08/2.17 | | | | (( ~ (v5 = 0) | v6 = 0) & ( ~ (v4 = 0) | ~ (v2 = 0)))))
% 10.08/2.17 | | | |
% 10.08/2.17 | | | | GROUND_INST: instantiating (3) with all_10_8, all_10_7, all_10_6,
% 10.08/2.17 | | | | all_17_0, simplifying with (14), (15), (23), (35) gives:
% 10.08/2.17 | | | | (89) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ?
% 10.08/2.17 | | | | [v4: $i] : ? [v5: any] : ? [v6: any] : (resources(all_10_8,
% 10.08/2.17 | | | | all_10_7) = v4 & decreases(v4) = v5 & constant(v4) = v6 &
% 10.08/2.17 | | | | number_of_organizations(all_10_8, all_10_7) = v2 & greater(v2,
% 10.08/2.17 | | | | zero) = v3 & environment(all_10_8) = v0 &
% 10.08/2.17 | | | | in_environment(all_10_8, all_10_7) = v1 & $i(v4) & $i(v2) & (
% 10.08/2.17 | | | | ~ (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (all_17_0 = 0)
% 10.08/2.17 | | | | | v5 = 0) & (v6 = 0 | all_17_0 = 0))))
% 10.08/2.17 | | | |
% 10.08/2.17 | | | | DELTA: instantiating (88) with fresh symbols all_50_0, all_50_1,
% 10.08/2.17 | | | | all_50_2, all_50_3, all_50_4, all_50_5, all_50_6 gives:
% 10.08/2.17 | | | | (90) resources(all_10_8, all_10_7) = all_50_5 & decreases(all_50_3) =
% 10.08/2.17 | | | | all_50_2 & decreases(all_50_5) = all_50_4 & constant(all_50_3) =
% 10.08/2.17 | | | | all_50_0 & constant(all_50_5) = all_50_1 &
% 10.08/2.17 | | | | number_of_organizations(all_10_8, all_10_7) = all_50_3 &
% 10.08/2.17 | | | | environment(all_10_8) = all_50_6 & $i(all_50_3) & $i(all_50_5) &
% 10.08/2.17 | | | | ( ~ (all_50_6 = 0) | (( ~ (all_50_1 = 0) | all_50_0 = 0) & ( ~
% 10.08/2.17 | | | | (all_50_2 = 0) | ~ (all_50_4 = 0))))
% 10.08/2.17 | | | |
% 10.08/2.17 | | | | ALPHA: (90) implies:
% 10.08/2.17 | | | | (91) environment(all_10_8) = all_50_6
% 10.08/2.17 | | | | (92) number_of_organizations(all_10_8, all_10_7) = all_50_3
% 10.08/2.17 | | | | (93) constant(all_50_5) = all_50_1
% 10.08/2.17 | | | | (94) constant(all_50_3) = all_50_0
% 10.08/2.17 | | | | (95) resources(all_10_8, all_10_7) = all_50_5
% 10.08/2.17 | | | | (96) ~ (all_50_6 = 0) | (( ~ (all_50_1 = 0) | all_50_0 = 0) & ( ~
% 10.08/2.17 | | | | (all_50_2 = 0) | ~ (all_50_4 = 0)))
% 10.08/2.17 | | | |
% 10.08/2.17 | | | | DELTA: instantiating (89) with fresh symbols all_52_0, all_52_1,
% 10.08/2.17 | | | | all_52_2, all_52_3, all_52_4, all_52_5, all_52_6 gives:
% 10.08/2.17 | | | | (97) resources(all_10_8, all_10_7) = all_52_2 & decreases(all_52_2) =
% 10.08/2.17 | | | | all_52_1 & constant(all_52_2) = all_52_0 &
% 10.08/2.17 | | | | number_of_organizations(all_10_8, all_10_7) = all_52_4 &
% 10.08/2.17 | | | | greater(all_52_4, zero) = all_52_3 & environment(all_10_8) =
% 10.08/2.17 | | | | all_52_6 & in_environment(all_10_8, all_10_7) = all_52_5 &
% 10.08/2.17 | | | | $i(all_52_2) & $i(all_52_4) & ( ~ (all_52_3 = 0) | ~ (all_52_5
% 10.08/2.17 | | | | = 0) | ~ (all_52_6 = 0) | (( ~ (all_17_0 = 0) | all_52_1 =
% 10.08/2.17 | | | | 0) & (all_52_0 = 0 | all_17_0 = 0)))
% 10.08/2.17 | | | |
% 10.08/2.17 | | | | ALPHA: (97) implies:
% 10.08/2.18 | | | | (98) in_environment(all_10_8, all_10_7) = all_52_5
% 10.08/2.18 | | | | (99) environment(all_10_8) = all_52_6
% 10.08/2.18 | | | | (100) greater(all_52_4, zero) = all_52_3
% 10.08/2.18 | | | | (101) number_of_organizations(all_10_8, all_10_7) = all_52_4
% 10.08/2.18 | | | | (102) constant(all_52_2) = all_52_0
% 10.08/2.18 | | | | (103) resources(all_10_8, all_10_7) = all_52_2
% 10.46/2.18 | | | | (104) ~ (all_52_3 = 0) | ~ (all_52_5 = 0) | ~ (all_52_6 = 0) | ((
% 10.46/2.18 | | | | ~ (all_17_0 = 0) | all_52_1 = 0) & (all_52_0 = 0 | all_17_0
% 10.46/2.18 | | | | = 0))
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | GROUND_INST: instantiating (8) with 0, all_52_5, all_10_7, all_10_8,
% 10.46/2.18 | | | | simplifying with (79), (98) gives:
% 10.46/2.18 | | | | (105) all_52_5 = 0
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | GROUND_INST: instantiating (6) with 0, all_52_6, all_10_8, simplifying
% 10.46/2.18 | | | | with (16), (99) gives:
% 10.46/2.18 | | | | (106) all_52_6 = 0
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | GROUND_INST: instantiating (6) with all_50_6, all_52_6, all_10_8,
% 10.46/2.18 | | | | simplifying with (91), (99) gives:
% 10.46/2.18 | | | | (107) all_52_6 = all_50_6
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | GROUND_INST: instantiating (10) with all_21_1, all_52_4, all_10_7,
% 10.46/2.18 | | | | all_10_8, simplifying with (44), (101) gives:
% 10.46/2.18 | | | | (108) all_52_4 = all_21_1
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | GROUND_INST: instantiating (10) with all_50_3, all_52_4, all_10_7,
% 10.46/2.18 | | | | all_10_8, simplifying with (92), (101) gives:
% 10.46/2.18 | | | | (109) all_52_4 = all_50_3
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | GROUND_INST: instantiating (11) with all_50_5, all_52_2, all_10_7,
% 10.46/2.18 | | | | all_10_8, simplifying with (95), (103) gives:
% 10.46/2.18 | | | | (110) all_52_2 = all_50_5
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | COMBINE_EQS: (108), (109) imply:
% 10.46/2.18 | | | | (111) all_50_3 = all_21_1
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | SIMP: (111) implies:
% 10.46/2.18 | | | | (112) all_50_3 = all_21_1
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | COMBINE_EQS: (106), (107) imply:
% 10.46/2.18 | | | | (113) all_50_6 = 0
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | SIMP: (113) implies:
% 10.46/2.18 | | | | (114) all_50_6 = 0
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | REDUCE: (102), (110) imply:
% 10.46/2.18 | | | | (115) constant(all_50_5) = all_52_0
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | REDUCE: (94), (112) imply:
% 10.46/2.18 | | | | (116) constant(all_21_1) = all_50_0
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | REDUCE: (100), (108) imply:
% 10.46/2.18 | | | | (117) greater(all_21_1, zero) = all_52_3
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | GROUND_INST: instantiating (9) with 0, all_52_3, zero, all_21_1,
% 10.46/2.18 | | | | simplifying with (83), (117) gives:
% 10.46/2.18 | | | | (118) all_52_3 = 0
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | GROUND_INST: instantiating (7) with all_23_6, all_50_0, all_21_1,
% 10.46/2.18 | | | | simplifying with (70), (116) gives:
% 10.46/2.18 | | | | (119) all_50_0 = all_23_6
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | GROUND_INST: instantiating (7) with all_50_1, all_52_0, all_50_5,
% 10.46/2.18 | | | | simplifying with (93), (115) gives:
% 10.46/2.18 | | | | (120) all_52_0 = all_50_1
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | BETA: splitting (104) gives:
% 10.46/2.18 | | | |
% 10.46/2.18 | | | | Case 1:
% 10.46/2.18 | | | | |
% 10.46/2.18 | | | | | (121) ~ (all_52_3 = 0)
% 10.46/2.18 | | | | |
% 10.46/2.18 | | | | | REDUCE: (118), (121) imply:
% 10.46/2.18 | | | | | (122) $false
% 10.46/2.18 | | | | |
% 10.46/2.18 | | | | | CLOSE: (122) is inconsistent.
% 10.46/2.18 | | | | |
% 10.46/2.18 | | | | Case 2:
% 10.46/2.18 | | | | |
% 10.46/2.18 | | | | | (123) ~ (all_52_5 = 0) | ~ (all_52_6 = 0) | (( ~ (all_17_0 = 0) |
% 10.46/2.18 | | | | | all_52_1 = 0) & (all_52_0 = 0 | all_17_0 = 0))
% 10.46/2.18 | | | | |
% 10.46/2.18 | | | | | BETA: splitting (123) gives:
% 10.46/2.18 | | | | |
% 10.46/2.18 | | | | | Case 1:
% 10.46/2.18 | | | | | |
% 10.46/2.18 | | | | | | (124) ~ (all_52_5 = 0)
% 10.46/2.18 | | | | | |
% 10.46/2.18 | | | | | | REDUCE: (105), (124) imply:
% 10.46/2.18 | | | | | | (125) $false
% 10.46/2.18 | | | | | |
% 10.46/2.18 | | | | | | CLOSE: (125) is inconsistent.
% 10.46/2.18 | | | | | |
% 10.46/2.18 | | | | | Case 2:
% 10.46/2.18 | | | | | |
% 10.46/2.18 | | | | | | (126) ~ (all_52_6 = 0) | (( ~ (all_17_0 = 0) | all_52_1 = 0) &
% 10.46/2.18 | | | | | | (all_52_0 = 0 | all_17_0 = 0))
% 10.46/2.18 | | | | | |
% 10.46/2.18 | | | | | | BETA: splitting (126) gives:
% 10.46/2.18 | | | | | |
% 10.46/2.18 | | | | | | Case 1:
% 10.46/2.18 | | | | | | |
% 10.46/2.18 | | | | | | | (127) ~ (all_52_6 = 0)
% 10.46/2.18 | | | | | | |
% 10.46/2.18 | | | | | | | REDUCE: (106), (127) imply:
% 10.46/2.18 | | | | | | | (128) $false
% 10.46/2.18 | | | | | | |
% 10.46/2.18 | | | | | | | CLOSE: (128) is inconsistent.
% 10.46/2.18 | | | | | | |
% 10.46/2.18 | | | | | | Case 2:
% 10.46/2.18 | | | | | | |
% 10.46/2.18 | | | | | | | (129) ( ~ (all_17_0 = 0) | all_52_1 = 0) & (all_52_0 = 0 |
% 10.46/2.18 | | | | | | | all_17_0 = 0)
% 10.46/2.18 | | | | | | |
% 10.46/2.18 | | | | | | | ALPHA: (129) implies:
% 10.46/2.18 | | | | | | | (130) all_52_0 = 0 | all_17_0 = 0
% 10.46/2.18 | | | | | | |
% 10.46/2.18 | | | | | | | BETA: splitting (130) gives:
% 10.46/2.18 | | | | | | |
% 10.46/2.18 | | | | | | | Case 1:
% 10.46/2.18 | | | | | | | |
% 10.46/2.18 | | | | | | | | (131) all_52_0 = 0
% 10.46/2.18 | | | | | | | |
% 10.46/2.18 | | | | | | | | COMBINE_EQS: (120), (131) imply:
% 10.46/2.18 | | | | | | | | (132) all_50_1 = 0
% 10.46/2.18 | | | | | | | |
% 10.46/2.18 | | | | | | | | BETA: splitting (96) gives:
% 10.46/2.18 | | | | | | | |
% 10.46/2.18 | | | | | | | | Case 1:
% 10.46/2.18 | | | | | | | | |
% 10.46/2.19 | | | | | | | | | (133) ~ (all_50_6 = 0)
% 10.46/2.19 | | | | | | | | |
% 10.46/2.19 | | | | | | | | | REDUCE: (114), (133) imply:
% 10.46/2.19 | | | | | | | | | (134) $false
% 10.46/2.19 | | | | | | | | |
% 10.46/2.19 | | | | | | | | | CLOSE: (134) is inconsistent.
% 10.46/2.19 | | | | | | | | |
% 10.46/2.19 | | | | | | | | Case 2:
% 10.46/2.19 | | | | | | | | |
% 10.46/2.19 | | | | | | | | | (135) ( ~ (all_50_1 = 0) | all_50_0 = 0) & ( ~ (all_50_2 =
% 10.46/2.19 | | | | | | | | | 0) | ~ (all_50_4 = 0))
% 10.46/2.19 | | | | | | | | |
% 10.46/2.19 | | | | | | | | | ALPHA: (135) implies:
% 10.46/2.19 | | | | | | | | | (136) ~ (all_50_1 = 0) | all_50_0 = 0
% 10.46/2.19 | | | | | | | | |
% 10.46/2.19 | | | | | | | | | BETA: splitting (136) gives:
% 10.46/2.19 | | | | | | | | |
% 10.46/2.19 | | | | | | | | | Case 1:
% 10.46/2.19 | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | (137) ~ (all_50_1 = 0)
% 10.46/2.19 | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | REDUCE: (132), (137) imply:
% 10.46/2.19 | | | | | | | | | | (138) $false
% 10.46/2.19 | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | CLOSE: (138) is inconsistent.
% 10.46/2.19 | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | Case 2:
% 10.46/2.19 | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | (139) all_50_0 = 0
% 10.46/2.19 | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | COMBINE_EQS: (119), (139) imply:
% 10.46/2.19 | | | | | | | | | | (140) all_23_6 = 0
% 10.46/2.19 | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | BETA: splitting (26) gives:
% 10.46/2.19 | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | Case 1:
% 10.46/2.19 | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | (141) ~ (all_10_4 = zero)
% 10.46/2.19 | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | BETA: splitting (28) gives:
% 10.46/2.19 | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | Case 1:
% 10.46/2.19 | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | (142) ~ (all_10_0 = 0)
% 10.46/2.19 | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | BETA: splitting (56) gives:
% 10.46/2.19 | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | Case 1:
% 10.46/2.19 | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | (143) ~ (all_23_6 = 0)
% 10.46/2.19 | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | REDUCE: (140), (143) imply:
% 10.46/2.19 | | | | | | | | | | | | | (144) $false
% 10.46/2.19 | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | CLOSE: (144) is inconsistent.
% 10.46/2.19 | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | Case 2:
% 10.46/2.19 | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | (145) ~ (all_23_8 = 0) | (all_23_0 = 0 & all_23_1 = 0)
% 10.46/2.19 | | | | | | | | | | | | | | (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero
% 10.46/2.19 | | | | | | | | | | | | | & all_23_5 = zero)
% 10.46/2.19 | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | BETA: splitting (145) gives:
% 10.46/2.19 | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | Case 1:
% 10.46/2.19 | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | (146) ~ (all_23_8 = 0)
% 10.46/2.19 | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | REDUCE: (57), (146) imply:
% 10.46/2.19 | | | | | | | | | | | | | | (147) $false
% 10.46/2.19 | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | CLOSE: (147) is inconsistent.
% 10.46/2.19 | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | Case 2:
% 10.46/2.19 | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | (148) (all_23_0 = 0 & all_23_1 = 0) | (all_23_2 = 0 &
% 10.46/2.19 | | | | | | | | | | | | | | all_23_3 = 0) | (all_23_4 = zero & all_23_5 =
% 10.46/2.19 | | | | | | | | | | | | | | zero)
% 10.46/2.19 | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 10.46/2.19 | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | Case 1:
% 10.46/2.19 | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | (149) all_23_0 = 0 & all_23_1 = 0
% 10.46/2.19 | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | REF_CLOSE: (84), (142), (149) are inconsistent by sub-proof
% 10.46/2.19 | | | | | | | | | | | | | | | #4.
% 10.46/2.19 | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | Case 2:
% 10.46/2.19 | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | (150) (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero &
% 10.46/2.19 | | | | | | | | | | | | | | | all_23_5 = zero)
% 10.46/2.19 | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 10.46/2.19 | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | Case 1:
% 10.46/2.19 | | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | | (151) all_23_2 = 0 & all_23_3 = 0
% 10.46/2.19 | | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (85), (86), (151) are inconsistent by
% 10.46/2.19 | | | | | | | | | | | | | | | | sub-proof #2.
% 10.46/2.19 | | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | Case 2:
% 10.46/2.19 | | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | | (152) all_23_4 = zero & all_23_5 = zero
% 10.46/2.19 | | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 10.46/2.19 | | | | | | | | | | | | | | | | (153) all_23_4 = zero
% 10.46/2.19 | | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (153) imply:
% 10.46/2.19 | | | | | | | | | | | | | | | | (154) all_10_4 = zero
% 10.46/2.19 | | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | | SIMP: (154) implies:
% 10.46/2.19 | | | | | | | | | | | | | | | | (155) all_10_4 = zero
% 10.46/2.19 | | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | | REDUCE: (141), (155) imply:
% 10.46/2.19 | | | | | | | | | | | | | | | | (156) $false
% 10.46/2.19 | | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | | CLOSE: (156) is inconsistent.
% 10.46/2.19 | | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | End of split
% 10.46/2.19 | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | End of split
% 10.46/2.19 | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | End of split
% 10.46/2.19 | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | End of split
% 10.46/2.19 | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | Case 2:
% 10.46/2.19 | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | (157) ~ (all_10_1 = 0)
% 10.46/2.19 | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | BETA: splitting (56) gives:
% 10.46/2.19 | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | Case 1:
% 10.46/2.19 | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | (158) ~ (all_23_6 = 0)
% 10.46/2.19 | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | REDUCE: (140), (158) imply:
% 10.46/2.19 | | | | | | | | | | | | | (159) $false
% 10.46/2.19 | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 10.46/2.19 | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | Case 2:
% 10.46/2.19 | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | (160) ~ (all_23_8 = 0) | (all_23_0 = 0 & all_23_1 = 0)
% 10.46/2.19 | | | | | | | | | | | | | | (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero
% 10.46/2.19 | | | | | | | | | | | | | & all_23_5 = zero)
% 10.46/2.19 | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | BETA: splitting (160) gives:
% 10.46/2.19 | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | Case 1:
% 10.46/2.19 | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | (161) ~ (all_23_8 = 0)
% 10.46/2.19 | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | REDUCE: (57), (161) imply:
% 10.46/2.19 | | | | | | | | | | | | | | (162) $false
% 10.46/2.19 | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | CLOSE: (162) is inconsistent.
% 10.46/2.19 | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | Case 2:
% 10.46/2.19 | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | (163) (all_23_0 = 0 & all_23_1 = 0) | (all_23_2 = 0 &
% 10.46/2.19 | | | | | | | | | | | | | | all_23_3 = 0) | (all_23_4 = zero & all_23_5 =
% 10.46/2.19 | | | | | | | | | | | | | | zero)
% 10.46/2.19 | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 10.46/2.19 | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | Case 1:
% 10.46/2.19 | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | (164) all_23_0 = 0 & all_23_1 = 0
% 10.46/2.19 | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 10.46/2.19 | | | | | | | | | | | | | | | (165) all_23_1 = 0
% 10.46/2.19 | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | COMBINE_EQS: (87), (165) imply:
% 10.46/2.19 | | | | | | | | | | | | | | | (166) all_10_1 = 0
% 10.46/2.19 | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | SIMP: (166) implies:
% 10.46/2.19 | | | | | | | | | | | | | | | (167) all_10_1 = 0
% 10.46/2.19 | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | REDUCE: (157), (167) imply:
% 10.46/2.19 | | | | | | | | | | | | | | | (168) $false
% 10.46/2.19 | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | CLOSE: (168) is inconsistent.
% 10.46/2.19 | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | Case 2:
% 10.46/2.19 | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | (169) (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero &
% 10.46/2.19 | | | | | | | | | | | | | | | all_23_5 = zero)
% 10.46/2.19 | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 10.46/2.19 | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | Case 1:
% 10.46/2.19 | | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | | (170) all_23_2 = 0 & all_23_3 = 0
% 10.46/2.19 | | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (85), (86), (170) are inconsistent by
% 10.46/2.19 | | | | | | | | | | | | | | | | sub-proof #2.
% 10.46/2.19 | | | | | | | | | | | | | | | |
% 10.46/2.19 | | | | | | | | | | | | | | | Case 2:
% 10.46/2.19 | | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | | (171) all_23_4 = zero & all_23_5 = zero
% 10.46/2.20 | | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 10.46/2.20 | | | | | | | | | | | | | | | | (172) all_23_4 = zero
% 10.46/2.20 | | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (172) imply:
% 10.46/2.20 | | | | | | | | | | | | | | | | (173) all_10_4 = zero
% 10.46/2.20 | | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | | REDUCE: (141), (173) imply:
% 10.46/2.20 | | | | | | | | | | | | | | | | (174) $false
% 10.46/2.20 | | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | | CLOSE: (174) is inconsistent.
% 10.46/2.20 | | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | End of split
% 10.46/2.20 | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | End of split
% 10.46/2.20 | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | End of split
% 10.46/2.20 | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | End of split
% 10.46/2.20 | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | End of split
% 10.46/2.20 | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | Case 2:
% 10.46/2.20 | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | (175) all_10_4 = zero
% 10.46/2.20 | | | | | | | | | | | (176) ~ (all_10_5 = zero)
% 10.46/2.20 | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | REDUCE: (21), (175) imply:
% 10.46/2.20 | | | | | | | | | | | (177) greater(zero, zero) = all_10_1
% 10.46/2.20 | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | REDUCE: (19), (175) imply:
% 10.46/2.20 | | | | | | | | | | | (178) greater(zero, zero) = all_10_2
% 10.46/2.20 | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | GROUND_INST: instantiating (9) with all_10_2, all_10_1, zero,
% 10.46/2.20 | | | | | | | | | | | zero, simplifying with (177), (178) gives:
% 10.46/2.20 | | | | | | | | | | | (179) all_10_1 = all_10_2
% 10.46/2.20 | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | COMBINE_EQS: (87), (179) imply:
% 10.46/2.20 | | | | | | | | | | | (180) all_23_1 = all_10_2
% 10.46/2.20 | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | BETA: splitting (28) gives:
% 10.46/2.20 | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | Case 1:
% 10.46/2.20 | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | (181) ~ (all_10_0 = 0)
% 10.46/2.20 | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | BETA: splitting (56) gives:
% 10.46/2.20 | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | Case 1:
% 10.46/2.20 | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | (182) ~ (all_23_6 = 0)
% 10.46/2.20 | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | REDUCE: (140), (182) imply:
% 10.46/2.20 | | | | | | | | | | | | | (183) $false
% 10.46/2.20 | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | CLOSE: (183) is inconsistent.
% 10.46/2.20 | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | Case 2:
% 10.46/2.20 | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | (184) ~ (all_23_8 = 0) | (all_23_0 = 0 & all_23_1 = 0)
% 10.46/2.20 | | | | | | | | | | | | | | (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero
% 10.46/2.20 | | | | | | | | | | | | | & all_23_5 = zero)
% 10.46/2.20 | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | BETA: splitting (184) gives:
% 10.46/2.20 | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | Case 1:
% 10.46/2.20 | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | (185) ~ (all_23_8 = 0)
% 10.46/2.20 | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | REDUCE: (57), (185) imply:
% 10.46/2.20 | | | | | | | | | | | | | | (186) $false
% 10.46/2.20 | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | CLOSE: (186) is inconsistent.
% 10.46/2.20 | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | Case 2:
% 10.46/2.20 | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | (187) (all_23_0 = 0 & all_23_1 = 0) | (all_23_2 = 0 &
% 10.46/2.20 | | | | | | | | | | | | | | all_23_3 = 0) | (all_23_4 = zero & all_23_5 =
% 10.46/2.20 | | | | | | | | | | | | | | zero)
% 10.46/2.20 | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 10.46/2.20 | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | Case 1:
% 10.46/2.20 | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | (188) all_23_0 = 0 & all_23_1 = 0
% 10.46/2.20 | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | REF_CLOSE: (84), (181), (188) are inconsistent by sub-proof
% 10.46/2.20 | | | | | | | | | | | | | | | #4.
% 10.46/2.20 | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | Case 2:
% 10.46/2.20 | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | (189) (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero &
% 10.46/2.20 | | | | | | | | | | | | | | | all_23_5 = zero)
% 10.46/2.20 | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 10.46/2.20 | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | Case 1:
% 10.46/2.20 | | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | | (190) all_23_2 = 0 & all_23_3 = 0
% 10.46/2.20 | | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 10.46/2.20 | | | | | | | | | | | | | | | | (191) all_23_3 = 0
% 10.46/2.20 | | | | | | | | | | | | | | | | (192) all_23_2 = 0
% 10.46/2.20 | | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (192) imply:
% 10.46/2.20 | | | | | | | | | | | | | | | | (193) all_10_2 = 0
% 10.46/2.20 | | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | | SIMP: (193) implies:
% 10.46/2.20 | | | | | | | | | | | | | | | | (194) all_10_2 = 0
% 10.46/2.20 | | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (191) imply:
% 10.46/2.20 | | | | | | | | | | | | | | | | (195) all_10_3 = 0
% 10.46/2.20 | | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (194), (195) are inconsistent by sub-proof
% 10.46/2.20 | | | | | | | | | | | | | | | | #3.
% 10.46/2.20 | | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | Case 2:
% 10.46/2.20 | | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | | (196) all_23_4 = zero & all_23_5 = zero
% 10.46/2.20 | | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | | REF_CLOSE: (62), (176), (196) are inconsistent by sub-proof
% 10.46/2.20 | | | | | | | | | | | | | | | | #1.
% 10.46/2.20 | | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | End of split
% 10.46/2.20 | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | End of split
% 10.46/2.20 | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | End of split
% 10.46/2.20 | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | End of split
% 10.46/2.20 | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | Case 2:
% 10.46/2.20 | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | (197) ~ (all_10_1 = 0)
% 10.46/2.20 | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | REDUCE: (179), (197) imply:
% 10.46/2.20 | | | | | | | | | | | | (198) ~ (all_10_2 = 0)
% 10.46/2.20 | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | BETA: splitting (56) gives:
% 10.46/2.20 | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | Case 1:
% 10.46/2.20 | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | (199) ~ (all_23_6 = 0)
% 10.46/2.20 | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | REDUCE: (140), (199) imply:
% 10.46/2.20 | | | | | | | | | | | | | (200) $false
% 10.46/2.20 | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | CLOSE: (200) is inconsistent.
% 10.46/2.20 | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | Case 2:
% 10.46/2.20 | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | (201) ~ (all_23_8 = 0) | (all_23_0 = 0 & all_23_1 = 0)
% 10.46/2.20 | | | | | | | | | | | | | | (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero
% 10.46/2.20 | | | | | | | | | | | | | & all_23_5 = zero)
% 10.46/2.20 | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | BETA: splitting (201) gives:
% 10.46/2.20 | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | Case 1:
% 10.46/2.20 | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | (202) ~ (all_23_8 = 0)
% 10.46/2.20 | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | REDUCE: (57), (202) imply:
% 10.46/2.20 | | | | | | | | | | | | | | (203) $false
% 10.46/2.20 | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | CLOSE: (203) is inconsistent.
% 10.46/2.20 | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | Case 2:
% 10.46/2.20 | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | (204) (all_23_0 = 0 & all_23_1 = 0) | (all_23_2 = 0 &
% 10.46/2.20 | | | | | | | | | | | | | | all_23_3 = 0) | (all_23_4 = zero & all_23_5 =
% 10.46/2.20 | | | | | | | | | | | | | | zero)
% 10.46/2.20 | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 10.46/2.20 | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | Case 1:
% 10.46/2.20 | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | (205) all_23_0 = 0 & all_23_1 = 0
% 10.46/2.20 | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 10.46/2.20 | | | | | | | | | | | | | | | (206) all_23_1 = 0
% 10.46/2.20 | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | COMBINE_EQS: (180), (206) imply:
% 10.46/2.20 | | | | | | | | | | | | | | | (207) all_10_2 = 0
% 10.46/2.20 | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | REDUCE: (198), (207) imply:
% 10.46/2.20 | | | | | | | | | | | | | | | (208) $false
% 10.46/2.20 | | | | | | | | | | | | | | |
% 10.46/2.20 | | | | | | | | | | | | | | | CLOSE: (208) is inconsistent.
% 10.46/2.20 | | | | | | | | | | | | | | |
% 10.46/2.21 | | | | | | | | | | | | | | Case 2:
% 10.46/2.21 | | | | | | | | | | | | | | |
% 10.46/2.21 | | | | | | | | | | | | | | | (209) (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero &
% 10.46/2.21 | | | | | | | | | | | | | | | all_23_5 = zero)
% 10.46/2.21 | | | | | | | | | | | | | | |
% 10.46/2.21 | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 10.46/2.21 | | | | | | | | | | | | | | |
% 10.46/2.21 | | | | | | | | | | | | | | | Case 1:
% 10.46/2.21 | | | | | | | | | | | | | | | |
% 10.46/2.21 | | | | | | | | | | | | | | | | (210) all_23_2 = 0 & all_23_3 = 0
% 10.46/2.21 | | | | | | | | | | | | | | | |
% 10.46/2.21 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (85), (86), (210) are inconsistent by
% 10.46/2.21 | | | | | | | | | | | | | | | | sub-proof #2.
% 10.46/2.21 | | | | | | | | | | | | | | | |
% 10.46/2.21 | | | | | | | | | | | | | | | Case 2:
% 10.46/2.21 | | | | | | | | | | | | | | | |
% 10.46/2.21 | | | | | | | | | | | | | | | | (211) all_23_4 = zero & all_23_5 = zero
% 10.46/2.21 | | | | | | | | | | | | | | | |
% 10.46/2.21 | | | | | | | | | | | | | | | | REF_CLOSE: (62), (176), (211) are inconsistent by sub-proof
% 10.46/2.21 | | | | | | | | | | | | | | | | #1.
% 10.46/2.21 | | | | | | | | | | | | | | | |
% 10.46/2.21 | | | | | | | | | | | | | | | End of split
% 10.46/2.21 | | | | | | | | | | | | | | |
% 10.46/2.21 | | | | | | | | | | | | | | End of split
% 10.46/2.21 | | | | | | | | | | | | | |
% 10.46/2.21 | | | | | | | | | | | | | End of split
% 10.46/2.21 | | | | | | | | | | | | |
% 10.46/2.21 | | | | | | | | | | | | End of split
% 10.46/2.21 | | | | | | | | | | | |
% 10.46/2.21 | | | | | | | | | | | End of split
% 10.46/2.21 | | | | | | | | | | |
% 10.46/2.21 | | | | | | | | | | End of split
% 10.46/2.21 | | | | | | | | | |
% 10.46/2.21 | | | | | | | | | End of split
% 10.46/2.21 | | | | | | | | |
% 10.46/2.21 | | | | | | | | End of split
% 10.46/2.21 | | | | | | | |
% 10.46/2.21 | | | | | | | Case 2:
% 10.46/2.21 | | | | | | | |
% 10.46/2.21 | | | | | | | | (212) all_17_0 = 0
% 10.46/2.21 | | | | | | | |
% 10.46/2.21 | | | | | | | | REDUCE: (75), (212) imply:
% 10.46/2.21 | | | | | | | | (213) $false
% 10.46/2.21 | | | | | | | |
% 10.46/2.21 | | | | | | | | CLOSE: (213) is inconsistent.
% 10.46/2.21 | | | | | | | |
% 10.46/2.21 | | | | | | | End of split
% 10.46/2.21 | | | | | | |
% 10.46/2.21 | | | | | | End of split
% 10.46/2.21 | | | | | |
% 10.46/2.21 | | | | | End of split
% 10.46/2.21 | | | | |
% 10.46/2.21 | | | | End of split
% 10.46/2.21 | | | |
% 10.46/2.21 | | | End of split
% 10.46/2.21 | | |
% 10.46/2.21 | | End of split
% 10.46/2.21 | |
% 10.46/2.21 | Case 2:
% 10.46/2.21 | |
% 10.46/2.21 | | (214) ~ (all_17_1 = 0)
% 10.46/2.21 | |
% 10.46/2.21 | | REDUCE: (69), (214) imply:
% 10.46/2.21 | | (215) $false
% 10.46/2.21 | |
% 10.46/2.21 | | CLOSE: (215) is inconsistent.
% 10.46/2.21 | |
% 10.46/2.21 | End of split
% 10.46/2.21 |
% 10.46/2.21 End of proof
% 10.46/2.21
% 10.46/2.21 Sub-proof #1 shows that the following formulas are inconsistent:
% 10.46/2.21 ----------------------------------------------------------------
% 10.46/2.21 (1) all_23_4 = zero & all_23_5 = zero
% 10.46/2.21 (2) all_23_5 = all_10_5
% 10.46/2.21 (3) ~ (all_10_5 = zero)
% 10.46/2.21
% 10.46/2.21 Begin of proof
% 10.46/2.21 |
% 10.46/2.21 | ALPHA: (1) implies:
% 10.46/2.21 | (4) all_23_5 = zero
% 10.46/2.21 |
% 10.46/2.21 | COMBINE_EQS: (2), (4) imply:
% 10.46/2.21 | (5) all_10_5 = zero
% 10.46/2.21 |
% 10.46/2.21 | SIMP: (5) implies:
% 10.46/2.21 | (6) all_10_5 = zero
% 10.46/2.21 |
% 10.46/2.21 | REDUCE: (3), (6) imply:
% 10.46/2.21 | (7) $false
% 10.46/2.21 |
% 10.46/2.21 | CLOSE: (7) is inconsistent.
% 10.46/2.21 |
% 10.46/2.21 End of proof
% 10.46/2.21
% 10.46/2.21 Sub-proof #2 shows that the following formulas are inconsistent:
% 10.46/2.21 ----------------------------------------------------------------
% 10.46/2.21 (1) all_23_2 = 0 & all_23_3 = 0
% 10.46/2.21 (2) all_23_2 = all_10_2
% 10.46/2.21 (3) all_23_3 = all_10_3
% 10.46/2.21 (4) ~ (all_10_2 = 0) | ~ (all_10_3 = 0)
% 10.46/2.21
% 10.46/2.21 Begin of proof
% 10.46/2.21 |
% 10.46/2.21 | ALPHA: (1) implies:
% 10.46/2.21 | (5) all_23_3 = 0
% 10.46/2.21 | (6) all_23_2 = 0
% 10.46/2.21 |
% 10.46/2.21 | COMBINE_EQS: (2), (6) imply:
% 10.46/2.21 | (7) all_10_2 = 0
% 10.46/2.21 |
% 10.46/2.21 | SIMP: (7) implies:
% 10.46/2.21 | (8) all_10_2 = 0
% 10.46/2.21 |
% 10.46/2.21 | COMBINE_EQS: (3), (5) imply:
% 10.46/2.21 | (9) all_10_3 = 0
% 10.46/2.21 |
% 10.46/2.21 | REF_CLOSE: (4), (8), (9) are inconsistent by sub-proof #3.
% 10.46/2.21 |
% 10.46/2.21 End of proof
% 10.46/2.21
% 10.46/2.21 Sub-proof #3 shows that the following formulas are inconsistent:
% 10.46/2.21 ----------------------------------------------------------------
% 10.46/2.21 (1) ~ (all_10_2 = 0) | ~ (all_10_3 = 0)
% 10.46/2.21 (2) all_10_2 = 0
% 10.46/2.21 (3) all_10_3 = 0
% 10.46/2.21
% 10.46/2.21 Begin of proof
% 10.46/2.21 |
% 10.46/2.21 | BETA: splitting (1) gives:
% 10.46/2.21 |
% 10.46/2.21 | Case 1:
% 10.46/2.21 | |
% 10.46/2.21 | | (4) ~ (all_10_2 = 0)
% 10.46/2.21 | |
% 10.46/2.21 | | REDUCE: (2), (4) imply:
% 10.46/2.21 | | (5) $false
% 10.46/2.21 | |
% 10.46/2.21 | | CLOSE: (5) is inconsistent.
% 10.46/2.21 | |
% 10.46/2.21 | Case 2:
% 10.46/2.21 | |
% 10.46/2.21 | | (6) ~ (all_10_3 = 0)
% 10.46/2.21 | |
% 10.46/2.21 | | REDUCE: (3), (6) imply:
% 10.46/2.21 | | (7) $false
% 10.46/2.21 | |
% 10.46/2.21 | | CLOSE: (7) is inconsistent.
% 10.46/2.21 | |
% 10.46/2.21 | End of split
% 10.46/2.21 |
% 10.46/2.21 End of proof
% 10.46/2.21
% 10.46/2.21 Sub-proof #4 shows that the following formulas are inconsistent:
% 10.46/2.21 ----------------------------------------------------------------
% 10.46/2.21 (1) all_23_0 = 0 & all_23_1 = 0
% 10.46/2.21 (2) all_23_0 = all_10_0
% 10.46/2.21 (3) ~ (all_10_0 = 0)
% 10.46/2.21
% 10.46/2.21 Begin of proof
% 10.46/2.21 |
% 10.46/2.21 | ALPHA: (1) implies:
% 10.46/2.21 | (4) all_23_0 = 0
% 10.46/2.21 |
% 10.46/2.21 | COMBINE_EQS: (2), (4) imply:
% 10.46/2.21 | (5) all_10_0 = 0
% 10.46/2.21 |
% 10.46/2.21 | REDUCE: (3), (5) imply:
% 10.46/2.21 | (6) $false
% 10.46/2.21 |
% 10.46/2.21 | CLOSE: (6) is inconsistent.
% 10.46/2.21 |
% 10.46/2.21 End of proof
% 10.46/2.21 % SZS output end Proof for theBenchmark
% 10.46/2.21
% 10.46/2.21 1608ms
%------------------------------------------------------------------------------