TSTP Solution File: MGT022+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : MGT022+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 : n028.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 09:16:14 EDT 2023
% Result : Theorem 4.52s 1.42s
% Output : Proof 6.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT022+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 06:47:24 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.60 ________ _____
% 0.21/0.60 ___ __ \_________(_)________________________________
% 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.60
% 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.60 (2023-06-19)
% 0.21/0.60
% 0.21/0.60 (c) Philipp Rümmer, 2009-2023
% 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.60 Amanda Stjerna.
% 0.21/0.60 Free software under BSD-3-Clause.
% 0.21/0.60
% 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.60
% 0.21/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.29/1.03 Prover 4: Preprocessing ...
% 2.29/1.03 Prover 1: Preprocessing ...
% 2.57/1.07 Prover 3: Preprocessing ...
% 2.57/1.07 Prover 2: Preprocessing ...
% 2.57/1.07 Prover 0: Preprocessing ...
% 2.57/1.07 Prover 5: Preprocessing ...
% 2.57/1.07 Prover 6: Preprocessing ...
% 4.01/1.25 Prover 3: Constructing countermodel ...
% 4.01/1.25 Prover 6: Constructing countermodel ...
% 4.01/1.26 Prover 5: Constructing countermodel ...
% 4.01/1.26 Prover 4: Constructing countermodel ...
% 4.01/1.27 Prover 1: Constructing countermodel ...
% 4.01/1.27 Prover 0: Proving ...
% 4.01/1.27 Prover 2: Proving ...
% 4.01/1.42 Prover 3: proved (793ms)
% 4.01/1.42
% 4.52/1.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.52/1.42
% 4.52/1.42 Prover 5: stopped
% 4.52/1.42 Prover 6: stopped
% 4.52/1.42 Prover 0: stopped
% 4.52/1.42 Prover 2: stopped
% 4.52/1.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.52/1.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.52/1.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.52/1.43 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.52/1.43 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.52/1.46 Prover 11: Preprocessing ...
% 4.52/1.46 Prover 8: Preprocessing ...
% 4.52/1.46 Prover 7: Preprocessing ...
% 5.42/1.46 Prover 10: Preprocessing ...
% 5.42/1.47 Prover 13: Preprocessing ...
% 5.42/1.51 Prover 10: Constructing countermodel ...
% 5.42/1.52 Prover 8: Warning: ignoring some quantifiers
% 5.42/1.52 Prover 13: Constructing countermodel ...
% 5.42/1.53 Prover 11: Constructing countermodel ...
% 5.42/1.54 Prover 7: Constructing countermodel ...
% 5.42/1.55 Prover 8: Constructing countermodel ...
% 6.10/1.56 Prover 4: Found proof (size 65)
% 6.10/1.56 Prover 4: proved (936ms)
% 6.10/1.56 Prover 1: stopped
% 6.10/1.56 Prover 7: stopped
% 6.10/1.56 Prover 13: stopped
% 6.10/1.56 Prover 10: stopped
% 6.10/1.56 Prover 11: stopped
% 6.10/1.56 Prover 8: stopped
% 6.10/1.57
% 6.10/1.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.10/1.57
% 6.10/1.58 % SZS output start Proof for theBenchmark
% 6.31/1.59 Assumptions after simplification:
% 6.31/1.59 ---------------------------------
% 6.31/1.59
% 6.31/1.59 (a2)
% 6.31/1.62 $i(first_movers) & $i(efficient_producers) & ? [v0: $i] : ? [v1: $i] :
% 6.31/1.62 (resilience(first_movers) = v1 & resilience(efficient_producers) = v0 &
% 6.31/1.62 greater(v0, v1) = 0 & $i(v1) & $i(v0))
% 6.31/1.62
% 6.31/1.62 (a5)
% 6.31/1.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 6.31/1.62 (subpopulations(v1, v2, v0, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 6.31/1.62 ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: any] : ? [v8:
% 6.31/1.62 $i] : ? [v9: any] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 6.31/1.62 any] : ? [v14: any] : ? [v15: any] : (environment(v0) = v4 &
% 6.31/1.62 resilience(v2) = v5 & resilience(v1) = v6 & greater(v5, v6) = v7 &
% 6.31/1.62 resources(v0, v3) = v8 & disbanding_rate(v2, v3) = v11 &
% 6.31/1.62 disbanding_rate(v1, v3) = v10 & difference(v10, v11) = v12 &
% 6.31/1.62 increases(v12) = v13 & decreases(v8) = v9 & constant(v12) = v15 &
% 6.31/1.63 constant(v8) = v14 & $i(v12) & $i(v11) & $i(v10) & $i(v8) & $i(v6) &
% 6.31/1.63 $i(v5) & ( ~ (v7 = 0) | ~ (v4 = 0) | (( ~ (v14 = 0) | v15 = 0) & ( ~ (v9
% 6.31/1.63 = 0) | v13 = 0)))))
% 6.31/1.63
% 6.31/1.63 (mp_constant_not_decrease)
% 6.31/1.63 ! [v0: $i] : ( ~ (decreases(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 =
% 6.31/1.63 0) & constant(v0) = v1)) & ! [v0: $i] : ( ~ (constant(v0) = 0) | ~
% 6.31/1.63 $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & decreases(v0) = v1))
% 6.31/1.63
% 6.31/1.63 (prove_l4)
% 6.53/1.63 $i(first_movers) & $i(efficient_producers) & ? [v0: $i] : ? [v1: $i] : ?
% 6.53/1.63 [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7:
% 6.53/1.63 any] : ? [v8: any] : ? [v9: any] : (subpopulations(first_movers,
% 6.53/1.63 efficient_producers, v0, v1) = 0 & environment(v0) = 0 & resources(v0, v1)
% 6.53/1.63 = v2 & disbanding_rate(first_movers, v1) = v4 &
% 6.53/1.63 disbanding_rate(efficient_producers, v1) = v5 & difference(v4, v5) = v6 &
% 6.53/1.63 increases(v6) = v7 & decreases(v6) = v9 & decreases(v2) = v3 & constant(v2)
% 6.53/1.63 = v8 & $i(v6) & $i(v5) & $i(v4) & $i(v2) & $i(v1) & $i(v0) & ((v9 = 0 & v8 =
% 6.53/1.63 0) | (v3 = 0 & ~ (v7 = 0))))
% 6.53/1.63
% 6.53/1.63 (function-axioms)
% 6.53/1.64 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 6.53/1.64 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (subpopulations(v5, v4,
% 6.53/1.64 v3, v2) = v1) | ~ (subpopulations(v5, v4, v3, v2) = v0)) & ! [v0:
% 6.53/1.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 6.53/1.64 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0:
% 6.53/1.64 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (resources(v3,
% 6.53/1.64 v2) = v1) | ~ (resources(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 6.53/1.64 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disbanding_rate(v3, v2) = v1) | ~
% 6.53/1.64 (disbanding_rate(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 6.53/1.64 ! [v3: $i] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2)
% 6.53/1.64 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 6.53/1.64 $i] : (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0)) & !
% 6.53/1.64 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (resilience(v2) = v1) |
% 6.53/1.64 ~ (resilience(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 6.53/1.64 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (increases(v2) = v1) | ~
% 6.53/1.64 (increases(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 6.53/1.64 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (decreases(v2) = v1) | ~
% 6.53/1.64 (decreases(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 6.53/1.64 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (constant(v2) = v1) | ~
% 6.53/1.64 (constant(v2) = v0))
% 6.53/1.64
% 6.53/1.64 Those formulas are unsatisfiable:
% 6.53/1.64 ---------------------------------
% 6.53/1.64
% 6.53/1.64 Begin of proof
% 6.58/1.64 |
% 6.58/1.64 | ALPHA: (mp_constant_not_decrease) implies:
% 6.58/1.65 | (1) ! [v0: $i] : ( ~ (decreases(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~
% 6.58/1.65 | (v1 = 0) & constant(v0) = v1))
% 6.58/1.65 |
% 6.58/1.65 | ALPHA: (a2) implies:
% 6.58/1.65 | (2) ? [v0: $i] : ? [v1: $i] : (resilience(first_movers) = v1 &
% 6.58/1.65 | resilience(efficient_producers) = v0 & greater(v0, v1) = 0 & $i(v1) &
% 6.58/1.65 | $i(v0))
% 6.58/1.65 |
% 6.58/1.65 | ALPHA: (prove_l4) implies:
% 6.58/1.65 | (3) $i(efficient_producers)
% 6.58/1.65 | (4) $i(first_movers)
% 6.58/1.65 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] :
% 6.58/1.65 | ? [v5: $i] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : ? [v9: any] :
% 6.58/1.65 | (subpopulations(first_movers, efficient_producers, v0, v1) = 0 &
% 6.58/1.65 | environment(v0) = 0 & resources(v0, v1) = v2 &
% 6.58/1.65 | disbanding_rate(first_movers, v1) = v4 &
% 6.58/1.65 | disbanding_rate(efficient_producers, v1) = v5 & difference(v4, v5) =
% 6.58/1.65 | v6 & increases(v6) = v7 & decreases(v6) = v9 & decreases(v2) = v3 &
% 6.58/1.65 | constant(v2) = v8 & $i(v6) & $i(v5) & $i(v4) & $i(v2) & $i(v1) &
% 6.58/1.65 | $i(v0) & ((v9 = 0 & v8 = 0) | (v3 = 0 & ~ (v7 = 0))))
% 6.58/1.65 |
% 6.58/1.65 | ALPHA: (function-axioms) implies:
% 6.58/1.65 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.58/1.65 | (v1 = v0 | ~ (constant(v2) = v1) | ~ (constant(v2) = v0))
% 6.58/1.65 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.58/1.65 | (v1 = v0 | ~ (decreases(v2) = v1) | ~ (decreases(v2) = v0))
% 6.58/1.66 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.58/1.66 | (v1 = v0 | ~ (increases(v2) = v1) | ~ (increases(v2) = v0))
% 6.58/1.66 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (resilience(v2)
% 6.58/1.66 | = v1) | ~ (resilience(v2) = v0))
% 6.58/1.66 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 6.58/1.66 | : (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0))
% 6.58/1.66 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.58/1.66 | (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 6.58/1.66 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.58/1.66 | (disbanding_rate(v3, v2) = v1) | ~ (disbanding_rate(v3, v2) = v0))
% 6.58/1.66 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.58/1.66 | (resources(v3, v2) = v1) | ~ (resources(v3, v2) = v0))
% 6.58/1.66 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 6.58/1.66 | : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3,
% 6.58/1.66 | v2) = v0))
% 6.58/1.66 |
% 6.58/1.66 | DELTA: instantiating (2) with fresh symbols all_6_0, all_6_1 gives:
% 6.58/1.66 | (15) resilience(first_movers) = all_6_0 & resilience(efficient_producers) =
% 6.58/1.66 | all_6_1 & greater(all_6_1, all_6_0) = 0 & $i(all_6_0) & $i(all_6_1)
% 6.58/1.66 |
% 6.58/1.66 | ALPHA: (15) implies:
% 6.58/1.66 | (16) greater(all_6_1, all_6_0) = 0
% 6.58/1.66 | (17) resilience(efficient_producers) = all_6_1
% 6.58/1.66 | (18) resilience(first_movers) = all_6_0
% 6.58/1.66 |
% 6.58/1.66 | DELTA: instantiating (5) with fresh symbols all_8_0, all_8_1, all_8_2,
% 6.58/1.66 | all_8_3, all_8_4, all_8_5, all_8_6, all_8_7, all_8_8, all_8_9 gives:
% 6.58/1.66 | (19) subpopulations(first_movers, efficient_producers, all_8_9, all_8_8) =
% 6.58/1.66 | 0 & environment(all_8_9) = 0 & resources(all_8_9, all_8_8) = all_8_7 &
% 6.58/1.66 | disbanding_rate(first_movers, all_8_8) = all_8_5 &
% 6.58/1.66 | disbanding_rate(efficient_producers, all_8_8) = all_8_4 &
% 6.58/1.66 | difference(all_8_5, all_8_4) = all_8_3 & increases(all_8_3) = all_8_2
% 6.58/1.66 | & decreases(all_8_3) = all_8_0 & decreases(all_8_7) = all_8_6 &
% 6.58/1.66 | constant(all_8_7) = all_8_1 & $i(all_8_3) & $i(all_8_4) & $i(all_8_5)
% 6.58/1.66 | & $i(all_8_7) & $i(all_8_8) & $i(all_8_9) & ((all_8_0 = 0 & all_8_1 =
% 6.58/1.66 | 0) | (all_8_6 = 0 & ~ (all_8_2 = 0)))
% 6.58/1.66 |
% 6.58/1.66 | ALPHA: (19) implies:
% 6.58/1.67 | (20) $i(all_8_9)
% 6.58/1.67 | (21) $i(all_8_8)
% 6.58/1.67 | (22) constant(all_8_7) = all_8_1
% 6.58/1.67 | (23) decreases(all_8_7) = all_8_6
% 6.58/1.67 | (24) decreases(all_8_3) = all_8_0
% 6.58/1.67 | (25) increases(all_8_3) = all_8_2
% 6.58/1.67 | (26) difference(all_8_5, all_8_4) = all_8_3
% 6.58/1.67 | (27) disbanding_rate(efficient_producers, all_8_8) = all_8_4
% 6.58/1.67 | (28) disbanding_rate(first_movers, all_8_8) = all_8_5
% 6.58/1.67 | (29) resources(all_8_9, all_8_8) = all_8_7
% 6.58/1.67 | (30) environment(all_8_9) = 0
% 6.58/1.67 | (31) subpopulations(first_movers, efficient_producers, all_8_9, all_8_8) =
% 6.58/1.67 | 0
% 6.58/1.67 | (32) (all_8_0 = 0 & all_8_1 = 0) | (all_8_6 = 0 & ~ (all_8_2 = 0))
% 6.58/1.67 |
% 6.58/1.67 | GROUND_INST: instantiating (a5) with all_8_9, first_movers,
% 6.58/1.67 | efficient_producers, all_8_8, simplifying with (3), (4), (20),
% 6.58/1.67 | (21), (31) gives:
% 6.58/1.67 | (33) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i]
% 6.58/1.67 | : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 6.58/1.67 | any] : ? [v10: any] : ? [v11: any] : (environment(all_8_9) = v0 &
% 6.58/1.67 | resilience(first_movers) = v2 & resilience(efficient_producers) = v1
% 6.58/1.67 | & greater(v1, v2) = v3 & resources(all_8_9, all_8_8) = v4 &
% 6.58/1.67 | disbanding_rate(first_movers, all_8_8) = v6 &
% 6.58/1.67 | disbanding_rate(efficient_producers, all_8_8) = v7 & difference(v6,
% 6.58/1.67 | v7) = v8 & increases(v8) = v9 & decreases(v4) = v5 & constant(v8)
% 6.58/1.67 | = v11 & constant(v4) = v10 & $i(v8) & $i(v7) & $i(v6) & $i(v4) &
% 6.58/1.67 | $i(v2) & $i(v1) & ( ~ (v3 = 0) | ~ (v0 = 0) | (( ~ (v10 = 0) | v11
% 6.58/1.67 | = 0) & ( ~ (v5 = 0) | v9 = 0))))
% 6.58/1.67 |
% 6.58/1.67 | DELTA: instantiating (33) with fresh symbols all_15_0, all_15_1, all_15_2,
% 6.58/1.67 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7, all_15_8, all_15_9,
% 6.58/1.67 | all_15_10, all_15_11 gives:
% 6.58/1.67 | (34) environment(all_8_9) = all_15_11 & resilience(first_movers) = all_15_9
% 6.58/1.67 | & resilience(efficient_producers) = all_15_10 & greater(all_15_10,
% 6.58/1.67 | all_15_9) = all_15_8 & resources(all_8_9, all_8_8) = all_15_7 &
% 6.58/1.67 | disbanding_rate(first_movers, all_8_8) = all_15_5 &
% 6.58/1.67 | disbanding_rate(efficient_producers, all_8_8) = all_15_4 &
% 6.58/1.67 | difference(all_15_5, all_15_4) = all_15_3 & increases(all_15_3) =
% 6.58/1.67 | all_15_2 & decreases(all_15_7) = all_15_6 & constant(all_15_3) =
% 6.58/1.67 | all_15_0 & constant(all_15_7) = all_15_1 & $i(all_15_3) & $i(all_15_4)
% 6.58/1.67 | & $i(all_15_5) & $i(all_15_7) & $i(all_15_9) & $i(all_15_10) & ( ~
% 6.58/1.67 | (all_15_8 = 0) | ~ (all_15_11 = 0) | (( ~ (all_15_1 = 0) | all_15_0
% 6.58/1.67 | = 0) & ( ~ (all_15_6 = 0) | all_15_2 = 0)))
% 6.58/1.67 |
% 6.58/1.67 | ALPHA: (34) implies:
% 6.58/1.68 | (35) $i(all_15_3)
% 6.58/1.68 | (36) constant(all_15_7) = all_15_1
% 6.58/1.68 | (37) constant(all_15_3) = all_15_0
% 6.58/1.68 | (38) decreases(all_15_7) = all_15_6
% 6.58/1.68 | (39) increases(all_15_3) = all_15_2
% 6.58/1.68 | (40) difference(all_15_5, all_15_4) = all_15_3
% 6.58/1.68 | (41) disbanding_rate(efficient_producers, all_8_8) = all_15_4
% 6.58/1.68 | (42) disbanding_rate(first_movers, all_8_8) = all_15_5
% 6.58/1.68 | (43) resources(all_8_9, all_8_8) = all_15_7
% 6.58/1.68 | (44) greater(all_15_10, all_15_9) = all_15_8
% 6.58/1.68 | (45) resilience(efficient_producers) = all_15_10
% 6.58/1.68 | (46) resilience(first_movers) = all_15_9
% 6.58/1.68 | (47) environment(all_8_9) = all_15_11
% 6.58/1.68 | (48) ~ (all_15_8 = 0) | ~ (all_15_11 = 0) | (( ~ (all_15_1 = 0) |
% 6.58/1.68 | all_15_0 = 0) & ( ~ (all_15_6 = 0) | all_15_2 = 0))
% 6.58/1.68 |
% 6.58/1.68 | GROUND_INST: instantiating (12) with all_8_4, all_15_4, all_8_8,
% 6.58/1.68 | efficient_producers, simplifying with (27), (41) gives:
% 6.58/1.68 | (49) all_15_4 = all_8_4
% 6.58/1.68 |
% 6.58/1.68 | GROUND_INST: instantiating (12) with all_8_5, all_15_5, all_8_8, first_movers,
% 6.58/1.68 | simplifying with (28), (42) gives:
% 6.58/1.68 | (50) all_15_5 = all_8_5
% 6.58/1.68 |
% 6.58/1.68 | GROUND_INST: instantiating (13) with all_8_7, all_15_7, all_8_8, all_8_9,
% 6.58/1.68 | simplifying with (29), (43) gives:
% 6.58/1.68 | (51) all_15_7 = all_8_7
% 6.58/1.68 |
% 6.58/1.68 | GROUND_INST: instantiating (9) with all_6_1, all_15_10, efficient_producers,
% 6.58/1.68 | simplifying with (17), (45) gives:
% 6.58/1.68 | (52) all_15_10 = all_6_1
% 6.58/1.68 |
% 6.58/1.68 | GROUND_INST: instantiating (9) with all_6_0, all_15_9, first_movers,
% 6.58/1.68 | simplifying with (18), (46) gives:
% 6.58/1.68 | (53) all_15_9 = all_6_0
% 6.58/1.68 |
% 6.58/1.68 | GROUND_INST: instantiating (10) with 0, all_15_11, all_8_9, simplifying with
% 6.58/1.68 | (30), (47) gives:
% 6.58/1.68 | (54) all_15_11 = 0
% 6.58/1.68 |
% 6.58/1.68 | REDUCE: (44), (52), (53) imply:
% 6.58/1.68 | (55) greater(all_6_1, all_6_0) = all_15_8
% 6.58/1.68 |
% 6.58/1.68 | REDUCE: (40), (49), (50) imply:
% 6.58/1.68 | (56) difference(all_8_5, all_8_4) = all_15_3
% 6.58/1.68 |
% 6.58/1.68 | REDUCE: (38), (51) imply:
% 6.58/1.68 | (57) decreases(all_8_7) = all_15_6
% 6.58/1.68 |
% 6.58/1.68 | REDUCE: (36), (51) imply:
% 6.58/1.68 | (58) constant(all_8_7) = all_15_1
% 6.58/1.68 |
% 6.58/1.68 | GROUND_INST: instantiating (6) with all_8_1, all_15_1, all_8_7, simplifying
% 6.58/1.68 | with (22), (58) gives:
% 6.58/1.68 | (59) all_15_1 = all_8_1
% 6.58/1.68 |
% 6.58/1.68 | GROUND_INST: instantiating (7) with all_8_6, all_15_6, all_8_7, simplifying
% 6.58/1.68 | with (23), (57) gives:
% 6.58/1.68 | (60) all_15_6 = all_8_6
% 6.58/1.68 |
% 6.58/1.69 | GROUND_INST: instantiating (11) with all_8_3, all_15_3, all_8_4, all_8_5,
% 6.58/1.69 | simplifying with (26), (56) gives:
% 6.58/1.69 | (61) all_15_3 = all_8_3
% 6.58/1.69 |
% 6.58/1.69 | GROUND_INST: instantiating (14) with 0, all_15_8, all_6_0, all_6_1,
% 6.58/1.69 | simplifying with (16), (55) gives:
% 6.58/1.69 | (62) all_15_8 = 0
% 6.58/1.69 |
% 6.58/1.69 | REDUCE: (39), (61) imply:
% 6.58/1.69 | (63) increases(all_8_3) = all_15_2
% 6.58/1.69 |
% 6.58/1.69 | REDUCE: (37), (61) imply:
% 6.58/1.69 | (64) constant(all_8_3) = all_15_0
% 6.58/1.69 |
% 6.58/1.69 | REDUCE: (35), (61) imply:
% 6.58/1.69 | (65) $i(all_8_3)
% 6.58/1.69 |
% 6.58/1.69 | GROUND_INST: instantiating (8) with all_8_2, all_15_2, all_8_3, simplifying
% 6.58/1.69 | with (25), (63) gives:
% 6.58/1.69 | (66) all_15_2 = all_8_2
% 6.58/1.69 |
% 6.58/1.69 | BETA: splitting (32) gives:
% 6.58/1.69 |
% 6.58/1.69 | Case 1:
% 6.58/1.69 | |
% 6.58/1.69 | | (67) all_8_0 = 0 & all_8_1 = 0
% 6.58/1.69 | |
% 6.58/1.69 | | ALPHA: (67) implies:
% 6.58/1.69 | | (68) all_8_1 = 0
% 6.58/1.69 | | (69) all_8_0 = 0
% 6.58/1.69 | |
% 6.58/1.69 | | COMBINE_EQS: (59), (68) imply:
% 6.58/1.69 | | (70) all_15_1 = 0
% 6.58/1.69 | |
% 6.58/1.69 | | REDUCE: (24), (69) imply:
% 6.58/1.69 | | (71) decreases(all_8_3) = 0
% 6.58/1.69 | |
% 6.58/1.69 | | BETA: splitting (48) gives:
% 6.58/1.69 | |
% 6.58/1.69 | | Case 1:
% 6.58/1.69 | | |
% 6.58/1.69 | | | (72) ~ (all_15_8 = 0)
% 6.58/1.69 | | |
% 6.58/1.69 | | | REDUCE: (62), (72) imply:
% 6.58/1.69 | | | (73) $false
% 6.58/1.69 | | |
% 6.58/1.69 | | | CLOSE: (73) is inconsistent.
% 6.58/1.69 | | |
% 6.58/1.69 | | Case 2:
% 6.58/1.69 | | |
% 6.58/1.69 | | | (74) ~ (all_15_11 = 0) | (( ~ (all_15_1 = 0) | all_15_0 = 0) & ( ~
% 6.58/1.69 | | | (all_15_6 = 0) | all_15_2 = 0))
% 6.58/1.69 | | |
% 6.58/1.69 | | | BETA: splitting (74) gives:
% 6.58/1.69 | | |
% 6.58/1.69 | | | Case 1:
% 6.58/1.69 | | | |
% 6.58/1.69 | | | | (75) ~ (all_15_11 = 0)
% 6.58/1.69 | | | |
% 6.58/1.69 | | | | REDUCE: (54), (75) imply:
% 6.58/1.69 | | | | (76) $false
% 6.58/1.69 | | | |
% 6.58/1.69 | | | | CLOSE: (76) is inconsistent.
% 6.58/1.69 | | | |
% 6.58/1.69 | | | Case 2:
% 6.58/1.69 | | | |
% 6.58/1.69 | | | | (77) ( ~ (all_15_1 = 0) | all_15_0 = 0) & ( ~ (all_15_6 = 0) |
% 6.58/1.69 | | | | all_15_2 = 0)
% 6.58/1.69 | | | |
% 6.58/1.69 | | | | ALPHA: (77) implies:
% 6.58/1.69 | | | | (78) ~ (all_15_1 = 0) | all_15_0 = 0
% 6.58/1.69 | | | |
% 6.58/1.69 | | | | BETA: splitting (78) gives:
% 6.58/1.69 | | | |
% 6.58/1.69 | | | | Case 1:
% 6.58/1.69 | | | | |
% 6.58/1.69 | | | | | (79) ~ (all_15_1 = 0)
% 6.58/1.69 | | | | |
% 6.58/1.69 | | | | | REDUCE: (70), (79) imply:
% 6.58/1.69 | | | | | (80) $false
% 6.58/1.69 | | | | |
% 6.58/1.69 | | | | | CLOSE: (80) is inconsistent.
% 6.58/1.69 | | | | |
% 6.58/1.69 | | | | Case 2:
% 6.58/1.69 | | | | |
% 6.58/1.69 | | | | | (81) all_15_0 = 0
% 6.58/1.69 | | | | |
% 6.58/1.69 | | | | | REDUCE: (64), (81) imply:
% 6.58/1.69 | | | | | (82) constant(all_8_3) = 0
% 6.58/1.69 | | | | |
% 6.58/1.69 | | | | | GROUND_INST: instantiating (1) with all_8_3, simplifying with (65),
% 6.58/1.69 | | | | | (71) gives:
% 6.58/1.69 | | | | | (83) ? [v0: int] : ( ~ (v0 = 0) & constant(all_8_3) = v0)
% 6.58/1.69 | | | | |
% 6.58/1.69 | | | | | DELTA: instantiating (83) with fresh symbol all_53_0 gives:
% 6.58/1.69 | | | | | (84) ~ (all_53_0 = 0) & constant(all_8_3) = all_53_0
% 6.58/1.69 | | | | |
% 6.58/1.69 | | | | | ALPHA: (84) implies:
% 6.58/1.69 | | | | | (85) ~ (all_53_0 = 0)
% 6.58/1.70 | | | | | (86) constant(all_8_3) = all_53_0
% 6.58/1.70 | | | | |
% 6.58/1.70 | | | | | GROUND_INST: instantiating (6) with 0, all_53_0, all_8_3, simplifying
% 6.58/1.70 | | | | | with (82), (86) gives:
% 6.58/1.70 | | | | | (87) all_53_0 = 0
% 6.58/1.70 | | | | |
% 6.58/1.70 | | | | | REDUCE: (85), (87) imply:
% 6.58/1.70 | | | | | (88) $false
% 6.58/1.70 | | | | |
% 6.58/1.70 | | | | | CLOSE: (88) is inconsistent.
% 6.58/1.70 | | | | |
% 6.58/1.70 | | | | End of split
% 6.58/1.70 | | | |
% 6.58/1.70 | | | End of split
% 6.58/1.70 | | |
% 6.58/1.70 | | End of split
% 6.58/1.70 | |
% 6.58/1.70 | Case 2:
% 6.58/1.70 | |
% 6.58/1.70 | | (89) all_8_6 = 0 & ~ (all_8_2 = 0)
% 6.58/1.70 | |
% 6.58/1.70 | | ALPHA: (89) implies:
% 6.58/1.70 | | (90) all_8_6 = 0
% 6.58/1.70 | | (91) ~ (all_8_2 = 0)
% 6.58/1.70 | |
% 6.58/1.70 | | COMBINE_EQS: (60), (90) imply:
% 6.58/1.70 | | (92) all_15_6 = 0
% 6.58/1.70 | |
% 6.58/1.70 | | BETA: splitting (48) gives:
% 6.58/1.70 | |
% 6.58/1.70 | | Case 1:
% 6.58/1.70 | | |
% 6.58/1.70 | | | (93) ~ (all_15_8 = 0)
% 6.58/1.70 | | |
% 6.58/1.70 | | | REDUCE: (62), (93) imply:
% 6.58/1.70 | | | (94) $false
% 6.58/1.70 | | |
% 6.58/1.70 | | | CLOSE: (94) is inconsistent.
% 6.58/1.70 | | |
% 6.58/1.70 | | Case 2:
% 6.58/1.70 | | |
% 6.58/1.70 | | | (95) ~ (all_15_11 = 0) | (( ~ (all_15_1 = 0) | all_15_0 = 0) & ( ~
% 6.58/1.70 | | | (all_15_6 = 0) | all_15_2 = 0))
% 6.58/1.70 | | |
% 6.58/1.70 | | | BETA: splitting (95) gives:
% 6.58/1.70 | | |
% 6.58/1.70 | | | Case 1:
% 6.58/1.70 | | | |
% 6.58/1.70 | | | | (96) ~ (all_15_11 = 0)
% 6.58/1.70 | | | |
% 6.58/1.70 | | | | REDUCE: (54), (96) imply:
% 6.58/1.70 | | | | (97) $false
% 6.58/1.70 | | | |
% 6.58/1.70 | | | | CLOSE: (97) is inconsistent.
% 6.58/1.70 | | | |
% 6.58/1.70 | | | Case 2:
% 6.58/1.70 | | | |
% 6.58/1.70 | | | | (98) ( ~ (all_15_1 = 0) | all_15_0 = 0) & ( ~ (all_15_6 = 0) |
% 6.58/1.70 | | | | all_15_2 = 0)
% 6.58/1.70 | | | |
% 6.58/1.70 | | | | ALPHA: (98) implies:
% 6.58/1.70 | | | | (99) ~ (all_15_6 = 0) | all_15_2 = 0
% 6.58/1.70 | | | |
% 6.58/1.70 | | | | BETA: splitting (99) gives:
% 6.58/1.70 | | | |
% 6.58/1.70 | | | | Case 1:
% 6.58/1.70 | | | | |
% 6.58/1.70 | | | | | (100) ~ (all_15_6 = 0)
% 6.58/1.70 | | | | |
% 6.58/1.70 | | | | | REDUCE: (92), (100) imply:
% 6.58/1.70 | | | | | (101) $false
% 6.58/1.70 | | | | |
% 6.58/1.70 | | | | | CLOSE: (101) is inconsistent.
% 6.58/1.70 | | | | |
% 6.58/1.70 | | | | Case 2:
% 6.58/1.70 | | | | |
% 6.58/1.70 | | | | | (102) all_15_2 = 0
% 6.58/1.70 | | | | |
% 6.58/1.70 | | | | | COMBINE_EQS: (66), (102) imply:
% 6.58/1.70 | | | | | (103) all_8_2 = 0
% 6.58/1.70 | | | | |
% 6.58/1.70 | | | | | REDUCE: (91), (103) imply:
% 6.58/1.70 | | | | | (104) $false
% 6.58/1.70 | | | | |
% 6.58/1.70 | | | | | CLOSE: (104) is inconsistent.
% 6.58/1.70 | | | | |
% 6.58/1.70 | | | | End of split
% 6.58/1.70 | | | |
% 6.58/1.70 | | | End of split
% 6.58/1.70 | | |
% 6.58/1.70 | | End of split
% 6.58/1.70 | |
% 6.58/1.70 | End of split
% 6.58/1.70 |
% 6.58/1.70 End of proof
% 6.58/1.70 % SZS output end Proof for theBenchmark
% 6.58/1.70
% 6.58/1.70 1097ms
%------------------------------------------------------------------------------