TSTP Solution File: MGT023+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : MGT023+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 : n015.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 4.80s 1.44s
% Output : Proof 6.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT023+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 06:37:24 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.30/0.99 Prover 1: Preprocessing ...
% 2.30/0.99 Prover 4: Preprocessing ...
% 2.30/1.03 Prover 3: Preprocessing ...
% 2.30/1.03 Prover 5: Preprocessing ...
% 2.30/1.03 Prover 6: Preprocessing ...
% 2.30/1.03 Prover 2: Preprocessing ...
% 2.30/1.03 Prover 0: Preprocessing ...
% 3.44/1.22 Prover 3: Constructing countermodel ...
% 3.44/1.22 Prover 1: Constructing countermodel ...
% 3.44/1.23 Prover 5: Constructing countermodel ...
% 4.01/1.24 Prover 2: Proving ...
% 4.01/1.24 Prover 6: Proving ...
% 4.01/1.28 Prover 4: Constructing countermodel ...
% 4.36/1.32 Prover 0: Proving ...
% 4.80/1.44 Prover 3: proved (816ms)
% 4.80/1.44
% 4.80/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.80/1.44
% 4.80/1.45 Prover 5: stopped
% 4.80/1.45 Prover 6: stopped
% 4.80/1.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.80/1.46 Prover 2: stopped
% 4.80/1.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.80/1.46 Prover 0: stopped
% 4.80/1.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.80/1.47 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.80/1.47 Prover 8: Preprocessing ...
% 4.80/1.48 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.80/1.48 Prover 10: Preprocessing ...
% 4.80/1.49 Prover 11: Preprocessing ...
% 4.80/1.50 Prover 7: Preprocessing ...
% 4.80/1.51 Prover 13: Preprocessing ...
% 5.32/1.53 Prover 10: Constructing countermodel ...
% 5.32/1.56 Prover 7: Constructing countermodel ...
% 6.24/1.57 Prover 13: Constructing countermodel ...
% 6.24/1.58 Prover 8: Warning: ignoring some quantifiers
% 6.24/1.59 Prover 8: Constructing countermodel ...
% 6.50/1.61 Prover 10: Found proof (size 29)
% 6.50/1.61 Prover 10: proved (150ms)
% 6.50/1.62 Prover 8: stopped
% 6.50/1.62 Prover 1: stopped
% 6.50/1.62 Prover 7: stopped
% 6.50/1.62 Prover 13: stopped
% 6.50/1.62 Prover 4: stopped
% 6.50/1.63 Prover 11: Constructing countermodel ...
% 6.50/1.63 Prover 11: stopped
% 6.50/1.63
% 6.50/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.50/1.63
% 6.69/1.64 % SZS output start Proof for theBenchmark
% 6.69/1.64 Assumptions after simplification:
% 6.69/1.64 ---------------------------------
% 6.69/1.64
% 6.69/1.64 (d1)
% 6.69/1.67 $i(first_movers) & $i(efficient_producers) & ! [v0: $i] : ! [v1: $i] : !
% 6.69/1.67 [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (critical_point(v0) = v3) | ~
% 6.69/1.67 (growth_rate(first_movers, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 6.69/1.67 in_environment(v0, v1) | ~ environment(v0) | ? [v4: $i] : ? [v5: $i] : ?
% 6.69/1.67 [v6: $i] : ? [v7: $i] : ($i(v5) & ((growth_rate(first_movers, v5) = v7 &
% 6.69/1.67 growth_rate(efficient_producers, v5) = v6 & $i(v7) & $i(v6) &
% 6.69/1.67 subpopulations(first_movers, efficient_producers, v0, v5) &
% 6.69/1.67 greater(v5, v1) & ~ greater(v6, v7)) |
% 6.69/1.67 (growth_rate(efficient_producers, v1) = v4 & $i(v4) & greater(v4,
% 6.69/1.67 v2)))))
% 6.69/1.67
% 6.69/1.67 (l12)
% 6.69/1.67 $i(first_movers) & $i(efficient_producers) & ! [v0: $i] : ( ~ $i(v0) | ~
% 6.69/1.67 stable(v0) | ~ environment(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 6.69/1.67 (growth_rate(first_movers, v1) = v3 & growth_rate(efficient_producers, v1) =
% 6.69/1.67 v2 & $i(v3) & $i(v2) & $i(v1) & in_environment(v0, v1) & ~ greater(v2,
% 6.69/1.67 v3) & ! [v4: $i] : ! [v5: $i] : ( ~ (growth_rate(first_movers, v4) =
% 6.69/1.67 v5) | ~ $i(v4) | ~ subpopulations(first_movers, efficient_producers,
% 6.69/1.67 v0, v4) | ~ greater(v4, v1) | ? [v6: $i] :
% 6.69/1.67 (growth_rate(efficient_producers, v4) = v6 & $i(v6) & greater(v6,
% 6.69/1.67 v5)))))
% 6.69/1.67
% 6.69/1.67 (prove_l5)
% 6.69/1.67 ? [v0: $i] : ? [v1: $i] : (critical_point(v0) = v1 & $i(v1) & $i(v0) &
% 6.69/1.67 stable(v0) & environment(v0) & ~ in_environment(v0, v1))
% 6.69/1.67
% 6.69/1.67 (function-axioms)
% 6.69/1.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.69/1.67 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) & ! [v0: $i] :
% 6.69/1.68 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (critical_point(v2) = v1) | ~
% 6.69/1.68 (critical_point(v2) = v0))
% 6.69/1.68
% 6.69/1.68 Those formulas are unsatisfiable:
% 6.69/1.68 ---------------------------------
% 6.69/1.68
% 6.69/1.68 Begin of proof
% 6.69/1.68 |
% 6.69/1.68 | ALPHA: (d1) implies:
% 6.69/1.68 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 6.69/1.68 | (critical_point(v0) = v3) | ~ (growth_rate(first_movers, v1) = v2) |
% 6.69/1.68 | ~ $i(v1) | ~ $i(v0) | ~ in_environment(v0, v1) | ~
% 6.69/1.68 | environment(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7:
% 6.69/1.68 | $i] : ($i(v5) & ((growth_rate(first_movers, v5) = v7 &
% 6.69/1.68 | growth_rate(efficient_producers, v5) = v6 & $i(v7) & $i(v6) &
% 6.69/1.68 | subpopulations(first_movers, efficient_producers, v0, v5) &
% 6.69/1.68 | greater(v5, v1) & ~ greater(v6, v7)) |
% 6.69/1.68 | (growth_rate(efficient_producers, v1) = v4 & $i(v4) & greater(v4,
% 6.69/1.68 | v2)))))
% 6.69/1.68 |
% 6.69/1.68 | ALPHA: (l12) implies:
% 6.69/1.68 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ stable(v0) | ~ environment(v0) | ? [v1:
% 6.69/1.68 | $i] : ? [v2: $i] : ? [v3: $i] : (growth_rate(first_movers, v1) =
% 6.69/1.68 | v3 & growth_rate(efficient_producers, v1) = v2 & $i(v3) & $i(v2) &
% 6.69/1.68 | $i(v1) & in_environment(v0, v1) & ~ greater(v2, v3) & ! [v4: $i]
% 6.69/1.68 | : ! [v5: $i] : ( ~ (growth_rate(first_movers, v4) = v5) | ~
% 6.69/1.68 | $i(v4) | ~ subpopulations(first_movers, efficient_producers, v0,
% 6.69/1.68 | v4) | ~ greater(v4, v1) | ? [v6: $i] :
% 6.69/1.68 | (growth_rate(efficient_producers, v4) = v6 & $i(v6) & greater(v6,
% 6.69/1.68 | v5)))))
% 6.69/1.68 |
% 6.69/1.68 | ALPHA: (function-axioms) implies:
% 6.69/1.69 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.69/1.69 | (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 6.69/1.69 |
% 6.69/1.69 | DELTA: instantiating (prove_l5) with fresh symbols all_6_0, all_6_1 gives:
% 6.69/1.69 | (4) critical_point(all_6_1) = all_6_0 & $i(all_6_0) & $i(all_6_1) &
% 6.69/1.69 | stable(all_6_1) & environment(all_6_1) & ~ in_environment(all_6_1,
% 6.69/1.69 | all_6_0)
% 6.69/1.69 |
% 6.69/1.69 | ALPHA: (4) implies:
% 6.69/1.69 | (5) ~ in_environment(all_6_1, all_6_0)
% 6.69/1.69 | (6) environment(all_6_1)
% 6.69/1.69 | (7) stable(all_6_1)
% 6.69/1.69 | (8) $i(all_6_1)
% 6.69/1.69 | (9) critical_point(all_6_1) = all_6_0
% 6.69/1.69 |
% 6.69/1.69 | GROUND_INST: instantiating (2) with all_6_1, simplifying with (6), (7), (8)
% 6.69/1.69 | gives:
% 6.69/1.69 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (growth_rate(first_movers,
% 6.69/1.69 | v0) = v2 & growth_rate(efficient_producers, v0) = v1 & $i(v2) &
% 6.69/1.69 | $i(v1) & $i(v0) & in_environment(all_6_1, v0) & ~ greater(v1, v2) &
% 6.69/1.69 | ! [v3: $i] : ! [v4: $i] : ( ~ (growth_rate(first_movers, v3) = v4)
% 6.69/1.69 | | ~ $i(v3) | ~ subpopulations(first_movers, efficient_producers,
% 6.69/1.69 | all_6_1, v3) | ~ greater(v3, v0) | ? [v5: $i] :
% 6.69/1.69 | (growth_rate(efficient_producers, v3) = v5 & $i(v5) & greater(v5,
% 6.69/1.69 | v4))))
% 6.69/1.69 |
% 6.69/1.69 | DELTA: instantiating (10) with fresh symbols all_13_0, all_13_1, all_13_2
% 6.69/1.69 | gives:
% 6.69/1.69 | (11) growth_rate(first_movers, all_13_2) = all_13_0 &
% 6.69/1.69 | growth_rate(efficient_producers, all_13_2) = all_13_1 & $i(all_13_0) &
% 6.69/1.69 | $i(all_13_1) & $i(all_13_2) & in_environment(all_6_1, all_13_2) & ~
% 6.69/1.69 | greater(all_13_1, all_13_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 6.69/1.69 | (growth_rate(first_movers, v0) = v1) | ~ $i(v0) | ~
% 6.69/1.69 | subpopulations(first_movers, efficient_producers, all_6_1, v0) | ~
% 6.69/1.69 | greater(v0, all_13_2) | ? [v2: $i] :
% 6.69/1.69 | (growth_rate(efficient_producers, v0) = v2 & $i(v2) & greater(v2,
% 6.69/1.69 | v1)))
% 6.69/1.69 |
% 6.69/1.69 | ALPHA: (11) implies:
% 6.69/1.69 | (12) ~ greater(all_13_1, all_13_0)
% 6.69/1.70 | (13) in_environment(all_6_1, all_13_2)
% 6.69/1.70 | (14) $i(all_13_2)
% 6.69/1.70 | (15) growth_rate(efficient_producers, all_13_2) = all_13_1
% 6.69/1.70 | (16) growth_rate(first_movers, all_13_2) = all_13_0
% 6.69/1.70 | (17) ! [v0: $i] : ! [v1: $i] : ( ~ (growth_rate(first_movers, v0) = v1) |
% 6.69/1.70 | ~ $i(v0) | ~ subpopulations(first_movers, efficient_producers,
% 6.69/1.70 | all_6_1, v0) | ~ greater(v0, all_13_2) | ? [v2: $i] :
% 6.69/1.70 | (growth_rate(efficient_producers, v0) = v2 & $i(v2) & greater(v2,
% 6.69/1.70 | v1)))
% 6.69/1.70 |
% 6.69/1.70 | GROUND_INST: instantiating (1) with all_6_1, all_13_2, all_13_0, all_6_0,
% 6.69/1.70 | simplifying with (6), (8), (9), (13), (14), (16) gives:
% 6.69/1.70 | (18) all_13_2 = all_6_0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 6.69/1.70 | $i] : ($i(v1) & ((growth_rate(first_movers, v1) = v3 &
% 6.69/1.70 | growth_rate(efficient_producers, v1) = v2 & $i(v3) & $i(v2) &
% 6.69/1.70 | subpopulations(first_movers, efficient_producers, all_6_1, v1) &
% 6.69/1.70 | greater(v1, all_13_2) & ~ greater(v2, v3)) |
% 6.69/1.70 | (growth_rate(efficient_producers, all_13_2) = v0 & $i(v0) &
% 6.69/1.70 | greater(v0, all_13_0))))
% 6.69/1.70 |
% 6.69/1.70 | BETA: splitting (18) gives:
% 6.69/1.70 |
% 6.69/1.70 | Case 1:
% 6.69/1.70 | |
% 6.69/1.70 | | (19) all_13_2 = all_6_0
% 6.69/1.70 | |
% 6.69/1.70 | | REDUCE: (13), (19) imply:
% 6.69/1.70 | | (20) in_environment(all_6_1, all_6_0)
% 6.69/1.70 | |
% 6.69/1.70 | | PRED_UNIFY: (5), (20) imply:
% 6.69/1.70 | | (21) $false
% 6.69/1.70 | |
% 6.69/1.70 | | CLOSE: (21) is inconsistent.
% 6.69/1.70 | |
% 6.69/1.70 | Case 2:
% 6.69/1.70 | |
% 6.69/1.70 | | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) &
% 6.69/1.70 | | ((growth_rate(first_movers, v1) = v3 &
% 6.69/1.70 | | growth_rate(efficient_producers, v1) = v2 & $i(v3) & $i(v2) &
% 6.69/1.70 | | subpopulations(first_movers, efficient_producers, all_6_1, v1)
% 6.69/1.70 | | & greater(v1, all_13_2) & ~ greater(v2, v3)) |
% 6.69/1.70 | | (growth_rate(efficient_producers, all_13_2) = v0 & $i(v0) &
% 6.69/1.70 | | greater(v0, all_13_0))))
% 6.69/1.70 | |
% 6.69/1.70 | | DELTA: instantiating (22) with fresh symbols all_23_0, all_23_1, all_23_2,
% 6.69/1.70 | | all_23_3 gives:
% 6.69/1.70 | | (23) $i(all_23_2) & ((growth_rate(first_movers, all_23_2) = all_23_0 &
% 6.69/1.70 | | growth_rate(efficient_producers, all_23_2) = all_23_1 &
% 6.69/1.70 | | $i(all_23_0) & $i(all_23_1) & subpopulations(first_movers,
% 6.69/1.70 | | efficient_producers, all_6_1, all_23_2) & greater(all_23_2,
% 6.69/1.70 | | all_13_2) & ~ greater(all_23_1, all_23_0)) |
% 6.69/1.70 | | (growth_rate(efficient_producers, all_13_2) = all_23_3 &
% 6.69/1.70 | | $i(all_23_3) & greater(all_23_3, all_13_0)))
% 6.69/1.70 | |
% 6.69/1.70 | | ALPHA: (23) implies:
% 6.69/1.70 | | (24) $i(all_23_2)
% 6.69/1.71 | | (25) (growth_rate(first_movers, all_23_2) = all_23_0 &
% 6.69/1.71 | | growth_rate(efficient_producers, all_23_2) = all_23_1 &
% 6.69/1.71 | | $i(all_23_0) & $i(all_23_1) & subpopulations(first_movers,
% 6.69/1.71 | | efficient_producers, all_6_1, all_23_2) & greater(all_23_2,
% 6.69/1.71 | | all_13_2) & ~ greater(all_23_1, all_23_0)) |
% 6.69/1.71 | | (growth_rate(efficient_producers, all_13_2) = all_23_3 &
% 6.69/1.71 | | $i(all_23_3) & greater(all_23_3, all_13_0))
% 6.69/1.71 | |
% 6.69/1.71 | | BETA: splitting (25) gives:
% 6.69/1.71 | |
% 6.69/1.71 | | Case 1:
% 6.69/1.71 | | |
% 6.69/1.71 | | | (26) growth_rate(first_movers, all_23_2) = all_23_0 &
% 6.69/1.71 | | | growth_rate(efficient_producers, all_23_2) = all_23_1 &
% 6.69/1.71 | | | $i(all_23_0) & $i(all_23_1) & subpopulations(first_movers,
% 6.69/1.71 | | | efficient_producers, all_6_1, all_23_2) & greater(all_23_2,
% 6.69/1.71 | | | all_13_2) & ~ greater(all_23_1, all_23_0)
% 6.69/1.71 | | |
% 6.69/1.71 | | | ALPHA: (26) implies:
% 6.69/1.71 | | | (27) ~ greater(all_23_1, all_23_0)
% 6.69/1.71 | | | (28) greater(all_23_2, all_13_2)
% 6.69/1.71 | | | (29) subpopulations(first_movers, efficient_producers, all_6_1,
% 6.69/1.71 | | | all_23_2)
% 6.69/1.71 | | | (30) growth_rate(efficient_producers, all_23_2) = all_23_1
% 6.69/1.71 | | | (31) growth_rate(first_movers, all_23_2) = all_23_0
% 6.69/1.71 | | |
% 6.69/1.71 | | | GROUND_INST: instantiating (17) with all_23_2, all_23_0, simplifying with
% 6.69/1.71 | | | (24), (28), (29), (31) gives:
% 6.69/1.71 | | | (32) ? [v0: $i] : (growth_rate(efficient_producers, all_23_2) = v0 &
% 6.69/1.71 | | | $i(v0) & greater(v0, all_23_0))
% 6.69/1.71 | | |
% 6.69/1.71 | | | DELTA: instantiating (32) with fresh symbol all_34_0 gives:
% 6.69/1.71 | | | (33) growth_rate(efficient_producers, all_23_2) = all_34_0 &
% 6.69/1.71 | | | $i(all_34_0) & greater(all_34_0, all_23_0)
% 6.69/1.71 | | |
% 6.69/1.71 | | | ALPHA: (33) implies:
% 6.69/1.71 | | | (34) greater(all_34_0, all_23_0)
% 6.69/1.71 | | | (35) growth_rate(efficient_producers, all_23_2) = all_34_0
% 6.69/1.71 | | |
% 6.69/1.71 | | | GROUND_INST: instantiating (3) with all_23_1, all_34_0, all_23_2,
% 6.69/1.71 | | | efficient_producers, simplifying with (30), (35) gives:
% 6.69/1.71 | | | (36) all_34_0 = all_23_1
% 6.69/1.71 | | |
% 6.69/1.71 | | | REDUCE: (34), (36) imply:
% 6.69/1.71 | | | (37) greater(all_23_1, all_23_0)
% 6.69/1.71 | | |
% 6.69/1.71 | | | PRED_UNIFY: (27), (37) imply:
% 6.69/1.71 | | | (38) $false
% 6.69/1.71 | | |
% 6.69/1.71 | | | CLOSE: (38) is inconsistent.
% 6.69/1.71 | | |
% 6.69/1.71 | | Case 2:
% 6.69/1.71 | | |
% 6.69/1.71 | | | (39) growth_rate(efficient_producers, all_13_2) = all_23_3 &
% 6.69/1.71 | | | $i(all_23_3) & greater(all_23_3, all_13_0)
% 6.69/1.71 | | |
% 6.69/1.71 | | | ALPHA: (39) implies:
% 6.69/1.71 | | | (40) greater(all_23_3, all_13_0)
% 6.69/1.71 | | | (41) growth_rate(efficient_producers, all_13_2) = all_23_3
% 6.69/1.71 | | |
% 6.69/1.71 | | | GROUND_INST: instantiating (3) with all_13_1, all_23_3, all_13_2,
% 6.69/1.71 | | | efficient_producers, simplifying with (15), (41) gives:
% 6.69/1.71 | | | (42) all_23_3 = all_13_1
% 6.69/1.71 | | |
% 6.69/1.71 | | | REDUCE: (40), (42) imply:
% 6.69/1.71 | | | (43) greater(all_13_1, all_13_0)
% 6.69/1.71 | | |
% 6.69/1.71 | | | PRED_UNIFY: (12), (43) imply:
% 6.69/1.71 | | | (44) $false
% 6.69/1.71 | | |
% 6.69/1.71 | | | CLOSE: (44) is inconsistent.
% 6.69/1.71 | | |
% 6.69/1.71 | | End of split
% 6.69/1.71 | |
% 6.69/1.71 | End of split
% 6.69/1.71 |
% 6.69/1.71 End of proof
% 6.69/1.72 % SZS output end Proof for theBenchmark
% 6.69/1.72
% 6.69/1.72 1111ms
%------------------------------------------------------------------------------