TSTP Solution File: MGT023+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : MGT023+2 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n007.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 6.40s 1.63s
% Output : Proof 8.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT023+2 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n007.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 06:12:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.62 ___ __ \_________(_)________________________________
% 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62
% 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62 (2023-06-19)
% 0.19/0.62
% 0.19/0.62 (c) Philipp Rümmer, 2009-2023
% 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62 Amanda Stjerna.
% 0.19/0.62 Free software under BSD-3-Clause.
% 0.19/0.62
% 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62
% 0.19/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.26/1.05 Prover 1: Preprocessing ...
% 2.26/1.05 Prover 4: Preprocessing ...
% 2.61/1.10 Prover 2: Preprocessing ...
% 2.61/1.10 Prover 3: Preprocessing ...
% 2.61/1.10 Prover 5: Preprocessing ...
% 2.61/1.10 Prover 6: Preprocessing ...
% 2.61/1.10 Prover 0: Preprocessing ...
% 4.24/1.35 Prover 5: Constructing countermodel ...
% 4.24/1.36 Prover 3: Constructing countermodel ...
% 4.24/1.37 Prover 6: Proving ...
% 4.24/1.37 Prover 2: Proving ...
% 4.24/1.37 Prover 1: Constructing countermodel ...
% 4.75/1.42 Prover 4: Constructing countermodel ...
% 4.75/1.44 Prover 0: Proving ...
% 6.40/1.62 Prover 3: proved (976ms)
% 6.40/1.62
% 6.40/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.40/1.63
% 6.40/1.63 Prover 0: stopped
% 6.40/1.64 Prover 6: stopped
% 6.40/1.64 Prover 5: stopped
% 6.40/1.65 Prover 2: stopped
% 6.40/1.65 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.40/1.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.40/1.65 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.40/1.65 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.40/1.66 Prover 7: Preprocessing ...
% 6.40/1.66 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.40/1.67 Prover 8: Preprocessing ...
% 6.40/1.67 Prover 10: Preprocessing ...
% 6.88/1.69 Prover 11: Preprocessing ...
% 6.88/1.70 Prover 13: Preprocessing ...
% 6.88/1.72 Prover 10: Constructing countermodel ...
% 6.88/1.72 Prover 7: Constructing countermodel ...
% 6.88/1.75 Prover 8: Warning: ignoring some quantifiers
% 6.88/1.76 Prover 13: Constructing countermodel ...
% 6.88/1.76 Prover 8: Constructing countermodel ...
% 7.59/1.83 Prover 11: Constructing countermodel ...
% 7.94/1.88 Prover 10: Found proof (size 43)
% 7.94/1.88 Prover 10: proved (241ms)
% 7.94/1.88 Prover 1: Found proof (size 80)
% 7.94/1.88 Prover 1: proved (1246ms)
% 7.94/1.88 Prover 8: stopped
% 7.94/1.88 Prover 11: stopped
% 7.94/1.88 Prover 7: stopped
% 7.94/1.88 Prover 4: stopped
% 7.94/1.88 Prover 13: stopped
% 7.94/1.88
% 7.94/1.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.94/1.88
% 8.35/1.89 % SZS output start Proof for theBenchmark
% 8.35/1.89 Assumptions after simplification:
% 8.35/1.89 ---------------------------------
% 8.35/1.89
% 8.35/1.89 (d1)
% 8.35/1.92 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : !
% 8.35/1.92 [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (critical_point(v0) = v3) | ~
% 8.35/1.92 (growth_rate(first_movers, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 8.35/1.92 in_environment(v0, v1) | ~ environment(v0) | ? [v4: $i] : ? [v5: $i] : ?
% 8.35/1.92 [v6: $i] : ? [v7: $i] : ($i(v5) & ((growth_rate(efficient_producers, v5) =
% 8.35/1.92 v6 & growth_rate(first_movers, v5) = v7 & $i(v7) & $i(v6) &
% 8.35/1.92 greater(v5, v1) & subpopulations(first_movers, efficient_producers,
% 8.35/1.92 v0, v5) & ~ greater(v6, v7)) | (growth_rate(efficient_producers,
% 8.35/1.92 v1) = v4 & $i(v4) & greater(v4, v2)))))
% 8.35/1.92
% 8.35/1.92 (l1)
% 8.35/1.92 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ( ~ $i(v0) | ~
% 8.35/1.92 stable(v0) | ~ environment(v0) | ? [v1: $i] : ($i(v1) & in_environment(v0,
% 8.35/1.92 v1) & ! [v2: $i] : ! [v3: $i] : ( ~ (growth_rate(first_movers, v2) =
% 8.35/1.92 v3) | ~ $i(v2) | ~ greater_or_equal(v2, v1) | ~
% 8.35/1.92 subpopulations(first_movers, efficient_producers, v0, v2) | ? [v4: $i]
% 8.35/1.92 : (growth_rate(efficient_producers, v2) = v4 & $i(v4) & greater(v4,
% 8.35/1.92 v3)))))
% 8.35/1.92
% 8.35/1.92 (mp_earliest_time_growth_rate_exceeds)
% 8.35/1.92 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.35/1.92 $i(v1) | ~ $i(v0) | ~ in_environment(v0, v1) | ~ environment(v0) | ?
% 8.35/1.92 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7:
% 8.35/1.92 $i] : ($i(v5) & $i(v2) & ((growth_rate(efficient_producers, v5) = v6 &
% 8.35/1.92 growth_rate(first_movers, v5) = v7 & $i(v7) & $i(v6) &
% 8.35/1.92 greater_or_equal(v5, v1) & subpopulations(first_movers,
% 8.35/1.92 efficient_producers, v0, v5) & ~ greater(v6, v7)) |
% 8.35/1.92 (growth_rate(efficient_producers, v2) = v3 & growth_rate(first_movers,
% 8.35/1.92 v2) = v4 & $i(v4) & $i(v3) & in_environment(v0, v2) & ~ greater(v3,
% 8.35/1.93 v4) & ! [v8: $i] : ! [v9: $i] : ( ~ (growth_rate(first_movers, v8)
% 8.35/1.93 = v9) | ~ $i(v8) | ~ greater(v8, v2) | ~
% 8.35/1.93 subpopulations(first_movers, efficient_producers, v0, v8) | ? [v10:
% 8.35/1.93 $i] : (growth_rate(efficient_producers, v8) = v10 & $i(v10) &
% 8.35/1.93 greater(v10, v9)))))))
% 8.35/1.93
% 8.35/1.93 (prove_l5)
% 8.35/1.93 ? [v0: $i] : ? [v1: $i] : (critical_point(v0) = v1 & $i(v1) & $i(v0) &
% 8.35/1.93 stable(v0) & environment(v0) & ~ in_environment(v0, v1))
% 8.35/1.93
% 8.35/1.93 (function-axioms)
% 8.35/1.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.35/1.93 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) & ! [v0: $i] :
% 8.35/1.93 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (critical_point(v2) = v1) | ~
% 8.35/1.93 (critical_point(v2) = v0))
% 8.35/1.93
% 8.35/1.93 Those formulas are unsatisfiable:
% 8.35/1.93 ---------------------------------
% 8.35/1.93
% 8.35/1.93 Begin of proof
% 8.35/1.93 |
% 8.35/1.93 | ALPHA: (mp_earliest_time_growth_rate_exceeds) implies:
% 8.35/1.93 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 8.35/1.93 | in_environment(v0, v1) | ~ environment(v0) | ? [v2: $i] : ? [v3:
% 8.35/1.93 | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 8.35/1.93 | ($i(v5) & $i(v2) & ((growth_rate(efficient_producers, v5) = v6 &
% 8.35/1.93 | growth_rate(first_movers, v5) = v7 & $i(v7) & $i(v6) &
% 8.35/1.93 | greater_or_equal(v5, v1) & subpopulations(first_movers,
% 8.35/1.93 | efficient_producers, v0, v5) & ~ greater(v6, v7)) |
% 8.35/1.93 | (growth_rate(efficient_producers, v2) = v3 &
% 8.35/1.93 | growth_rate(first_movers, v2) = v4 & $i(v4) & $i(v3) &
% 8.35/1.93 | in_environment(v0, v2) & ~ greater(v3, v4) & ! [v8: $i] : !
% 8.35/1.93 | [v9: $i] : ( ~ (growth_rate(first_movers, v8) = v9) | ~ $i(v8)
% 8.35/1.93 | | ~ greater(v8, v2) | ~ subpopulations(first_movers,
% 8.35/1.93 | efficient_producers, v0, v8) | ? [v10: $i] :
% 8.35/1.93 | (growth_rate(efficient_producers, v8) = v10 & $i(v10) &
% 8.35/1.93 | greater(v10, v9)))))))
% 8.35/1.93 |
% 8.35/1.93 | ALPHA: (d1) implies:
% 8.35/1.94 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 8.35/1.94 | (critical_point(v0) = v3) | ~ (growth_rate(first_movers, v1) = v2) |
% 8.35/1.94 | ~ $i(v1) | ~ $i(v0) | ~ in_environment(v0, v1) | ~
% 8.35/1.94 | environment(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7:
% 8.35/1.94 | $i] : ($i(v5) & ((growth_rate(efficient_producers, v5) = v6 &
% 8.35/1.94 | growth_rate(first_movers, v5) = v7 & $i(v7) & $i(v6) &
% 8.35/1.94 | greater(v5, v1) & subpopulations(first_movers,
% 8.35/1.94 | efficient_producers, v0, v5) & ~ greater(v6, v7)) |
% 8.35/1.94 | (growth_rate(efficient_producers, v1) = v4 & $i(v4) & greater(v4,
% 8.35/1.94 | v2)))))
% 8.35/1.94 |
% 8.35/1.94 | ALPHA: (l1) implies:
% 8.35/1.94 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ stable(v0) | ~ environment(v0) | ? [v1:
% 8.35/1.94 | $i] : ($i(v1) & in_environment(v0, v1) & ! [v2: $i] : ! [v3: $i]
% 8.35/1.94 | : ( ~ (growth_rate(first_movers, v2) = v3) | ~ $i(v2) | ~
% 8.35/1.94 | greater_or_equal(v2, v1) | ~ subpopulations(first_movers,
% 8.35/1.94 | efficient_producers, v0, v2) | ? [v4: $i] :
% 8.35/1.94 | (growth_rate(efficient_producers, v2) = v4 & $i(v4) & greater(v4,
% 8.35/1.94 | v3)))))
% 8.35/1.94 |
% 8.35/1.94 | ALPHA: (function-axioms) implies:
% 8.35/1.94 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.35/1.94 | (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 8.35/1.94 |
% 8.35/1.94 | DELTA: instantiating (prove_l5) with fresh symbols all_7_0, all_7_1 gives:
% 8.35/1.94 | (5) critical_point(all_7_1) = all_7_0 & $i(all_7_0) & $i(all_7_1) &
% 8.35/1.94 | stable(all_7_1) & environment(all_7_1) & ~ in_environment(all_7_1,
% 8.35/1.94 | all_7_0)
% 8.35/1.94 |
% 8.35/1.94 | ALPHA: (5) implies:
% 8.35/1.94 | (6) ~ in_environment(all_7_1, all_7_0)
% 8.35/1.94 | (7) environment(all_7_1)
% 8.35/1.94 | (8) stable(all_7_1)
% 8.35/1.94 | (9) $i(all_7_1)
% 8.35/1.94 | (10) critical_point(all_7_1) = all_7_0
% 8.35/1.94 |
% 8.35/1.94 | GROUND_INST: instantiating (3) with all_7_1, simplifying with (7), (8), (9)
% 8.35/1.94 | gives:
% 8.35/1.95 | (11) ? [v0: $i] : ($i(v0) & in_environment(all_7_1, v0) & ! [v1: $i] : !
% 8.35/1.95 | [v2: $i] : ( ~ (growth_rate(first_movers, v1) = v2) | ~ $i(v1) | ~
% 8.35/1.95 | greater_or_equal(v1, v0) | ~ subpopulations(first_movers,
% 8.35/1.95 | efficient_producers, all_7_1, v1) | ? [v3: $i] :
% 8.35/1.95 | (growth_rate(efficient_producers, v1) = v3 & $i(v3) & greater(v3,
% 8.35/1.95 | v2))))
% 8.35/1.95 |
% 8.35/1.95 | DELTA: instantiating (11) with fresh symbol all_14_0 gives:
% 8.35/1.95 | (12) $i(all_14_0) & in_environment(all_7_1, all_14_0) & ! [v0: $i] : !
% 8.35/1.95 | [v1: $i] : ( ~ (growth_rate(first_movers, v0) = v1) | ~ $i(v0) | ~
% 8.35/1.95 | greater_or_equal(v0, all_14_0) | ~ subpopulations(first_movers,
% 8.35/1.95 | efficient_producers, all_7_1, v0) | ? [v2: $i] :
% 8.35/1.95 | (growth_rate(efficient_producers, v0) = v2 & $i(v2) & greater(v2,
% 8.35/1.95 | v1)))
% 8.35/1.95 |
% 8.35/1.95 | ALPHA: (12) implies:
% 8.35/1.95 | (13) in_environment(all_7_1, all_14_0)
% 8.35/1.95 | (14) $i(all_14_0)
% 8.35/1.95 | (15) ! [v0: $i] : ! [v1: $i] : ( ~ (growth_rate(first_movers, v0) = v1) |
% 8.35/1.95 | ~ $i(v0) | ~ greater_or_equal(v0, all_14_0) | ~
% 8.35/1.95 | subpopulations(first_movers, efficient_producers, all_7_1, v0) | ?
% 8.35/1.95 | [v2: $i] : (growth_rate(efficient_producers, v0) = v2 & $i(v2) &
% 8.35/1.95 | greater(v2, v1)))
% 8.35/1.95 |
% 8.35/1.95 | GROUND_INST: instantiating (1) with all_7_1, all_14_0, simplifying with (7),
% 8.35/1.95 | (9), (13), (14) gives:
% 8.35/1.95 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 8.35/1.95 | ? [v5: $i] : ($i(v3) & $i(v0) & ((growth_rate(efficient_producers, v3)
% 8.35/1.95 | = v4 & growth_rate(first_movers, v3) = v5 & $i(v5) & $i(v4) &
% 8.35/1.95 | greater_or_equal(v3, all_14_0) & subpopulations(first_movers,
% 8.35/1.95 | efficient_producers, all_7_1, v3) & ~ greater(v4, v5)) |
% 8.35/1.95 | (growth_rate(efficient_producers, v0) = v1 &
% 8.35/1.95 | growth_rate(first_movers, v0) = v2 & $i(v2) & $i(v1) &
% 8.35/1.95 | in_environment(all_7_1, v0) & ~ greater(v1, v2) & ! [v6: $i] :
% 8.35/1.95 | ! [v7: $i] : ( ~ (growth_rate(first_movers, v6) = v7) | ~
% 8.35/1.95 | $i(v6) | ~ greater(v6, v0) | ~ subpopulations(first_movers,
% 8.35/1.95 | efficient_producers, all_7_1, v6) | ? [v8: $i] :
% 8.35/1.95 | (growth_rate(efficient_producers, v6) = v8 & $i(v8) &
% 8.35/1.95 | greater(v8, v7))))))
% 8.35/1.95 |
% 8.35/1.95 | DELTA: instantiating (16) with fresh symbols all_22_0, all_22_1, all_22_2,
% 8.35/1.95 | all_22_3, all_22_4, all_22_5 gives:
% 8.35/1.95 | (17) $i(all_22_2) & $i(all_22_5) & ((growth_rate(efficient_producers,
% 8.35/1.95 | all_22_2) = all_22_1 & growth_rate(first_movers, all_22_2) =
% 8.35/1.95 | all_22_0 & $i(all_22_0) & $i(all_22_1) &
% 8.35/1.95 | greater_or_equal(all_22_2, all_14_0) &
% 8.35/1.95 | subpopulations(first_movers, efficient_producers, all_7_1,
% 8.35/1.95 | all_22_2) & ~ greater(all_22_1, all_22_0)) |
% 8.35/1.95 | (growth_rate(efficient_producers, all_22_5) = all_22_4 &
% 8.35/1.95 | growth_rate(first_movers, all_22_5) = all_22_3 & $i(all_22_3) &
% 8.35/1.95 | $i(all_22_4) & in_environment(all_7_1, all_22_5) & ~
% 8.35/1.95 | greater(all_22_4, all_22_3) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.35/1.95 | (growth_rate(first_movers, v0) = v1) | ~ $i(v0) | ~
% 8.35/1.95 | greater(v0, all_22_5) | ~ subpopulations(first_movers,
% 8.35/1.95 | efficient_producers, all_7_1, v0) | ? [v2: $i] :
% 8.35/1.95 | (growth_rate(efficient_producers, v0) = v2 & $i(v2) &
% 8.35/1.95 | greater(v2, v1)))))
% 8.35/1.95 |
% 8.35/1.95 | ALPHA: (17) implies:
% 8.35/1.95 | (18) $i(all_22_5)
% 8.35/1.95 | (19) $i(all_22_2)
% 8.35/1.96 | (20) (growth_rate(efficient_producers, all_22_2) = all_22_1 &
% 8.35/1.96 | growth_rate(first_movers, all_22_2) = all_22_0 & $i(all_22_0) &
% 8.35/1.96 | $i(all_22_1) & greater_or_equal(all_22_2, all_14_0) &
% 8.35/1.96 | subpopulations(first_movers, efficient_producers, all_7_1, all_22_2)
% 8.35/1.96 | & ~ greater(all_22_1, all_22_0)) |
% 8.35/1.96 | (growth_rate(efficient_producers, all_22_5) = all_22_4 &
% 8.35/1.96 | growth_rate(first_movers, all_22_5) = all_22_3 & $i(all_22_3) &
% 8.35/1.96 | $i(all_22_4) & in_environment(all_7_1, all_22_5) & ~
% 8.35/1.96 | greater(all_22_4, all_22_3) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.35/1.96 | (growth_rate(first_movers, v0) = v1) | ~ $i(v0) | ~ greater(v0,
% 8.35/1.96 | all_22_5) | ~ subpopulations(first_movers, efficient_producers,
% 8.35/1.96 | all_7_1, v0) | ? [v2: $i] : (growth_rate(efficient_producers,
% 8.35/1.96 | v0) = v2 & $i(v2) & greater(v2, v1))))
% 8.35/1.96 |
% 8.35/1.96 | BETA: splitting (20) gives:
% 8.35/1.96 |
% 8.35/1.96 | Case 1:
% 8.35/1.96 | |
% 8.35/1.96 | | (21) growth_rate(efficient_producers, all_22_2) = all_22_1 &
% 8.35/1.96 | | growth_rate(first_movers, all_22_2) = all_22_0 & $i(all_22_0) &
% 8.35/1.96 | | $i(all_22_1) & greater_or_equal(all_22_2, all_14_0) &
% 8.35/1.96 | | subpopulations(first_movers, efficient_producers, all_7_1, all_22_2)
% 8.35/1.96 | | & ~ greater(all_22_1, all_22_0)
% 8.35/1.96 | |
% 8.35/1.96 | | ALPHA: (21) implies:
% 8.35/1.96 | | (22) ~ greater(all_22_1, all_22_0)
% 8.35/1.96 | | (23) subpopulations(first_movers, efficient_producers, all_7_1, all_22_2)
% 8.35/1.96 | | (24) greater_or_equal(all_22_2, all_14_0)
% 8.35/1.96 | | (25) growth_rate(first_movers, all_22_2) = all_22_0
% 8.35/1.96 | | (26) growth_rate(efficient_producers, all_22_2) = all_22_1
% 8.35/1.96 | |
% 8.35/1.96 | | GROUND_INST: instantiating (15) with all_22_2, all_22_0, simplifying with
% 8.35/1.96 | | (19), (23), (24), (25) gives:
% 8.35/1.96 | | (27) ? [v0: $i] : (growth_rate(efficient_producers, all_22_2) = v0 &
% 8.35/1.96 | | $i(v0) & greater(v0, all_22_0))
% 8.35/1.96 | |
% 8.35/1.96 | | DELTA: instantiating (27) with fresh symbol all_36_0 gives:
% 8.35/1.96 | | (28) growth_rate(efficient_producers, all_22_2) = all_36_0 & $i(all_36_0)
% 8.35/1.96 | | & greater(all_36_0, all_22_0)
% 8.35/1.96 | |
% 8.35/1.96 | | ALPHA: (28) implies:
% 8.35/1.96 | | (29) greater(all_36_0, all_22_0)
% 8.35/1.96 | | (30) growth_rate(efficient_producers, all_22_2) = all_36_0
% 8.35/1.96 | |
% 8.35/1.96 | | GROUND_INST: instantiating (4) with all_22_1, all_36_0, all_22_2,
% 8.35/1.96 | | efficient_producers, simplifying with (26), (30) gives:
% 8.35/1.96 | | (31) all_36_0 = all_22_1
% 8.35/1.96 | |
% 8.35/1.96 | | REDUCE: (29), (31) imply:
% 8.35/1.96 | | (32) greater(all_22_1, all_22_0)
% 8.35/1.96 | |
% 8.35/1.96 | | PRED_UNIFY: (22), (32) imply:
% 8.35/1.96 | | (33) $false
% 8.35/1.96 | |
% 8.35/1.96 | | CLOSE: (33) is inconsistent.
% 8.35/1.96 | |
% 8.35/1.96 | Case 2:
% 8.35/1.96 | |
% 8.35/1.96 | | (34) growth_rate(efficient_producers, all_22_5) = all_22_4 &
% 8.35/1.96 | | growth_rate(first_movers, all_22_5) = all_22_3 & $i(all_22_3) &
% 8.35/1.96 | | $i(all_22_4) & in_environment(all_7_1, all_22_5) & ~
% 8.35/1.96 | | greater(all_22_4, all_22_3) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.35/1.96 | | (growth_rate(first_movers, v0) = v1) | ~ $i(v0) | ~ greater(v0,
% 8.35/1.96 | | all_22_5) | ~ subpopulations(first_movers, efficient_producers,
% 8.35/1.96 | | all_7_1, v0) | ? [v2: $i] : (growth_rate(efficient_producers,
% 8.35/1.96 | | v0) = v2 & $i(v2) & greater(v2, v1)))
% 8.35/1.96 | |
% 8.35/1.96 | | ALPHA: (34) implies:
% 8.35/1.96 | | (35) ~ greater(all_22_4, all_22_3)
% 8.35/1.96 | | (36) in_environment(all_7_1, all_22_5)
% 8.35/1.96 | | (37) growth_rate(first_movers, all_22_5) = all_22_3
% 8.35/1.96 | | (38) growth_rate(efficient_producers, all_22_5) = all_22_4
% 8.35/1.97 | | (39) ! [v0: $i] : ! [v1: $i] : ( ~ (growth_rate(first_movers, v0) = v1)
% 8.35/1.97 | | | ~ $i(v0) | ~ greater(v0, all_22_5) | ~
% 8.35/1.97 | | subpopulations(first_movers, efficient_producers, all_7_1, v0) |
% 8.35/1.97 | | ? [v2: $i] : (growth_rate(efficient_producers, v0) = v2 & $i(v2) &
% 8.35/1.97 | | greater(v2, v1)))
% 8.35/1.97 | |
% 8.35/1.97 | | GROUND_INST: instantiating (2) with all_7_1, all_22_5, all_22_3, all_7_0,
% 8.35/1.97 | | simplifying with (7), (9), (10), (18), (36), (37) gives:
% 8.35/1.97 | | (40) all_22_5 = all_7_0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 8.35/1.97 | | [v3: $i] : ($i(v1) & ((growth_rate(efficient_producers, v1) = v2 &
% 8.35/1.97 | | growth_rate(first_movers, v1) = v3 & $i(v3) & $i(v2) &
% 8.35/1.97 | | greater(v1, all_22_5) & subpopulations(first_movers,
% 8.35/1.97 | | efficient_producers, all_7_1, v1) & ~ greater(v2, v3)) |
% 8.35/1.97 | | (growth_rate(efficient_producers, all_22_5) = v0 & $i(v0) &
% 8.35/1.97 | | greater(v0, all_22_3))))
% 8.35/1.97 | |
% 8.35/1.97 | | BETA: splitting (40) gives:
% 8.35/1.97 | |
% 8.35/1.97 | | Case 1:
% 8.35/1.97 | | |
% 8.35/1.97 | | | (41) all_22_5 = all_7_0
% 8.35/1.97 | | |
% 8.35/1.97 | | | REDUCE: (36), (41) imply:
% 8.35/1.97 | | | (42) in_environment(all_7_1, all_7_0)
% 8.35/1.97 | | |
% 8.35/1.97 | | | PRED_UNIFY: (6), (42) imply:
% 8.35/1.97 | | | (43) $false
% 8.35/1.97 | | |
% 8.35/1.97 | | | CLOSE: (43) is inconsistent.
% 8.35/1.97 | | |
% 8.35/1.97 | | Case 2:
% 8.35/1.97 | | |
% 8.35/1.97 | | | (44) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) &
% 8.35/1.97 | | | ((growth_rate(efficient_producers, v1) = v2 &
% 8.35/1.97 | | | growth_rate(first_movers, v1) = v3 & $i(v3) & $i(v2) &
% 8.35/1.97 | | | greater(v1, all_22_5) & subpopulations(first_movers,
% 8.35/1.97 | | | efficient_producers, all_7_1, v1) & ~ greater(v2, v3)) |
% 8.35/1.97 | | | (growth_rate(efficient_producers, all_22_5) = v0 & $i(v0) &
% 8.35/1.97 | | | greater(v0, all_22_3))))
% 8.35/1.97 | | |
% 8.35/1.97 | | | DELTA: instantiating (44) with fresh symbols all_46_0, all_46_1, all_46_2,
% 8.35/1.97 | | | all_46_3 gives:
% 8.35/1.97 | | | (45) $i(all_46_2) & ((growth_rate(efficient_producers, all_46_2) =
% 8.35/1.97 | | | all_46_1 & growth_rate(first_movers, all_46_2) = all_46_0 &
% 8.35/1.97 | | | $i(all_46_0) & $i(all_46_1) & greater(all_46_2, all_22_5) &
% 8.35/1.97 | | | subpopulations(first_movers, efficient_producers, all_7_1,
% 8.35/1.97 | | | all_46_2) & ~ greater(all_46_1, all_46_0)) |
% 8.35/1.97 | | | (growth_rate(efficient_producers, all_22_5) = all_46_3 &
% 8.35/1.97 | | | $i(all_46_3) & greater(all_46_3, all_22_3)))
% 8.35/1.97 | | |
% 8.35/1.97 | | | ALPHA: (45) implies:
% 8.35/1.97 | | | (46) $i(all_46_2)
% 8.35/1.97 | | | (47) (growth_rate(efficient_producers, all_46_2) = all_46_1 &
% 8.35/1.97 | | | growth_rate(first_movers, all_46_2) = all_46_0 & $i(all_46_0) &
% 8.35/1.97 | | | $i(all_46_1) & greater(all_46_2, all_22_5) &
% 8.35/1.97 | | | subpopulations(first_movers, efficient_producers, all_7_1,
% 8.35/1.97 | | | all_46_2) & ~ greater(all_46_1, all_46_0)) |
% 8.35/1.97 | | | (growth_rate(efficient_producers, all_22_5) = all_46_3 &
% 8.35/1.97 | | | $i(all_46_3) & greater(all_46_3, all_22_3))
% 8.35/1.97 | | |
% 8.35/1.97 | | | BETA: splitting (47) gives:
% 8.35/1.97 | | |
% 8.35/1.97 | | | Case 1:
% 8.35/1.97 | | | |
% 8.35/1.97 | | | | (48) growth_rate(efficient_producers, all_46_2) = all_46_1 &
% 8.35/1.97 | | | | growth_rate(first_movers, all_46_2) = all_46_0 & $i(all_46_0) &
% 8.35/1.97 | | | | $i(all_46_1) & greater(all_46_2, all_22_5) &
% 8.35/1.97 | | | | subpopulations(first_movers, efficient_producers, all_7_1,
% 8.35/1.97 | | | | all_46_2) & ~ greater(all_46_1, all_46_0)
% 8.35/1.97 | | | |
% 8.35/1.97 | | | | ALPHA: (48) implies:
% 8.35/1.97 | | | | (49) ~ greater(all_46_1, all_46_0)
% 8.35/1.97 | | | | (50) subpopulations(first_movers, efficient_producers, all_7_1,
% 8.35/1.97 | | | | all_46_2)
% 8.35/1.97 | | | | (51) greater(all_46_2, all_22_5)
% 8.35/1.97 | | | | (52) growth_rate(first_movers, all_46_2) = all_46_0
% 8.35/1.97 | | | | (53) growth_rate(efficient_producers, all_46_2) = all_46_1
% 8.35/1.97 | | | |
% 8.35/1.97 | | | | GROUND_INST: instantiating (39) with all_46_2, all_46_0, simplifying
% 8.35/1.97 | | | | with (46), (50), (51), (52) gives:
% 8.35/1.97 | | | | (54) ? [v0: $i] : (growth_rate(efficient_producers, all_46_2) = v0 &
% 8.35/1.97 | | | | $i(v0) & greater(v0, all_46_0))
% 8.35/1.97 | | | |
% 8.35/1.97 | | | | DELTA: instantiating (54) with fresh symbol all_57_0 gives:
% 8.35/1.98 | | | | (55) growth_rate(efficient_producers, all_46_2) = all_57_0 &
% 8.35/1.98 | | | | $i(all_57_0) & greater(all_57_0, all_46_0)
% 8.35/1.98 | | | |
% 8.35/1.98 | | | | ALPHA: (55) implies:
% 8.35/1.98 | | | | (56) greater(all_57_0, all_46_0)
% 8.35/1.98 | | | | (57) growth_rate(efficient_producers, all_46_2) = all_57_0
% 8.35/1.98 | | | |
% 8.35/1.98 | | | | GROUND_INST: instantiating (4) with all_46_1, all_57_0, all_46_2,
% 8.35/1.98 | | | | efficient_producers, simplifying with (53), (57) gives:
% 8.35/1.98 | | | | (58) all_57_0 = all_46_1
% 8.35/1.98 | | | |
% 8.35/1.98 | | | | REDUCE: (56), (58) imply:
% 8.35/1.98 | | | | (59) greater(all_46_1, all_46_0)
% 8.35/1.98 | | | |
% 8.35/1.98 | | | | PRED_UNIFY: (49), (59) imply:
% 8.35/1.98 | | | | (60) $false
% 8.35/1.98 | | | |
% 8.80/1.98 | | | | CLOSE: (60) is inconsistent.
% 8.80/1.98 | | | |
% 8.80/1.98 | | | Case 2:
% 8.80/1.98 | | | |
% 8.80/1.98 | | | | (61) growth_rate(efficient_producers, all_22_5) = all_46_3 &
% 8.80/1.98 | | | | $i(all_46_3) & greater(all_46_3, all_22_3)
% 8.80/1.98 | | | |
% 8.80/1.98 | | | | ALPHA: (61) implies:
% 8.80/1.98 | | | | (62) greater(all_46_3, all_22_3)
% 8.80/1.98 | | | | (63) growth_rate(efficient_producers, all_22_5) = all_46_3
% 8.80/1.98 | | | |
% 8.80/1.98 | | | | GROUND_INST: instantiating (4) with all_22_4, all_46_3, all_22_5,
% 8.80/1.98 | | | | efficient_producers, simplifying with (38), (63) gives:
% 8.80/1.98 | | | | (64) all_46_3 = all_22_4
% 8.80/1.98 | | | |
% 8.80/1.98 | | | | REDUCE: (62), (64) imply:
% 8.80/1.98 | | | | (65) greater(all_22_4, all_22_3)
% 8.80/1.98 | | | |
% 8.80/1.98 | | | | PRED_UNIFY: (35), (65) imply:
% 8.80/1.98 | | | | (66) $false
% 8.80/1.98 | | | |
% 8.80/1.98 | | | | CLOSE: (66) is inconsistent.
% 8.80/1.98 | | | |
% 8.80/1.98 | | | End of split
% 8.80/1.98 | | |
% 8.80/1.98 | | End of split
% 8.80/1.98 | |
% 8.80/1.98 | End of split
% 8.80/1.98 |
% 8.80/1.98 End of proof
% 8.80/1.98 % SZS output end Proof for theBenchmark
% 8.80/1.98
% 8.80/1.98 1363ms
%------------------------------------------------------------------------------