TSTP Solution File: MGT032+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : MGT032+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 : n003.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 09:16:18 EDT 2023
% Result : Theorem 4.76s 1.42s
% Output : Proof 6.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : MGT032+2 : TPTP v8.1.2. Released v2.0.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 06:39:10 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 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/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 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 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 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 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
% 2.12/1.05 Prover 4: Preprocessing ...
% 2.12/1.05 Prover 1: Preprocessing ...
% 2.50/1.09 Prover 3: Preprocessing ...
% 2.50/1.09 Prover 5: Preprocessing ...
% 2.50/1.09 Prover 0: Preprocessing ...
% 2.50/1.09 Prover 6: Preprocessing ...
% 2.50/1.09 Prover 2: Preprocessing ...
% 3.60/1.26 Prover 5: Constructing countermodel ...
% 3.60/1.27 Prover 2: Proving ...
% 3.60/1.28 Prover 1: Constructing countermodel ...
% 3.60/1.29 Prover 3: Constructing countermodel ...
% 3.60/1.29 Prover 6: Proving ...
% 4.13/1.34 Prover 4: Constructing countermodel ...
% 4.13/1.36 Prover 0: Proving ...
% 4.76/1.41 Prover 1: gave up
% 4.76/1.41 Prover 3: gave up
% 4.76/1.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.76/1.42 Prover 5: proved (774ms)
% 4.76/1.42
% 4.76/1.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.76/1.42
% 4.76/1.43 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.76/1.43 Prover 6: stopped
% 4.76/1.43 Prover 0: stopped
% 4.76/1.44 Prover 2: proved (786ms)
% 4.76/1.44
% 4.76/1.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.76/1.44
% 4.76/1.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.76/1.46 Prover 7: Preprocessing ...
% 4.76/1.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.76/1.46 Prover 8: Preprocessing ...
% 4.76/1.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.76/1.46 Prover 10: Preprocessing ...
% 4.76/1.46 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 5.20/1.46 Prover 7: Constructing countermodel ...
% 5.20/1.46 Prover 11: Preprocessing ...
% 5.20/1.48 Prover 16: Preprocessing ...
% 5.20/1.48 Prover 13: Preprocessing ...
% 5.20/1.48 Prover 10: Constructing countermodel ...
% 5.20/1.50 Prover 7: gave up
% 5.20/1.50 Prover 8: Warning: ignoring some quantifiers
% 5.20/1.50 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 5.20/1.51 Prover 16: Constructing countermodel ...
% 5.20/1.51 Prover 8: Constructing countermodel ...
% 5.20/1.52 Prover 19: Preprocessing ...
% 5.20/1.53 Prover 10: gave up
% 5.20/1.53 Prover 13: Constructing countermodel ...
% 5.92/1.59 Prover 8: gave up
% 5.92/1.59 Prover 16: Found proof (size 21)
% 5.92/1.59 Prover 16: proved (133ms)
% 5.92/1.59 Prover 13: stopped
% 5.92/1.59 Prover 19: Warning: ignoring some quantifiers
% 5.92/1.59 Prover 11: Constructing countermodel ...
% 5.92/1.59 Prover 4: stopped
% 5.92/1.59 Prover 11: stopped
% 5.92/1.60 Prover 19: Constructing countermodel ...
% 6.20/1.60 Prover 19: stopped
% 6.20/1.60
% 6.20/1.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.20/1.60
% 6.20/1.61 % SZS output start Proof for theBenchmark
% 6.20/1.61 Assumptions after simplification:
% 6.20/1.61 ---------------------------------
% 6.20/1.61
% 6.20/1.61 (l1)
% 6.39/1.64 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ( ~ $i(v0) | ~
% 6.39/1.64 stable(v0) | ~ environment(v0) | ? [v1: $i] : ($i(v1) & in_environment(v0,
% 6.39/1.64 v1) & ! [v2: $i] : ( ~ $i(v2) | ~ greater_or_equal(v2, v1) | ~
% 6.39/1.64 subpopulations(first_movers, efficient_producers, v0, v2) | ? [v3: $i]
% 6.39/1.64 : ? [v4: $i] : (growth_rate(efficient_producers, v2) = v3 &
% 6.39/1.64 growth_rate(first_movers, v2) = v4 & $i(v4) & $i(v3) & greater(v3,
% 6.39/1.64 v4)))))
% 6.39/1.64
% 6.39/1.64 (mp1_high_growth_rates)
% 6.39/1.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 6.39/1.64 | ~ $i(v1) | ~ $i(v0) | ~ subpopulations(v1, v2, v0, v3) | ~
% 6.39/1.64 environment(v0) | selection_favors(v2, v1, v3) | ? [v4: $i] : ? [v5: $i] :
% 6.39/1.64 (growth_rate(v2, v3) = v4 & growth_rate(v1, v3) = v5 & $i(v5) & $i(v4) & ~
% 6.39/1.64 greater(v4, v5)))
% 6.39/1.64
% 6.39/1.64 (prove_t1)
% 6.39/1.64 $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ($i(v0) &
% 6.39/1.64 stable(v0) & environment(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 6.39/1.64 in_environment(v0, v1) | ? [v2: $i] : ($i(v2) & greater_or_equal(v2, v1)
% 6.39/1.64 & subpopulations(first_movers, efficient_producers, v0, v2) & ~
% 6.39/1.64 selection_favors(efficient_producers, first_movers, v2))))
% 6.39/1.64
% 6.39/1.64 (function-axioms)
% 6.39/1.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.39/1.64 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 6.39/1.64
% 6.39/1.64 Those formulas are unsatisfiable:
% 6.39/1.64 ---------------------------------
% 6.39/1.64
% 6.39/1.64 Begin of proof
% 6.39/1.64 |
% 6.39/1.65 | ALPHA: (l1) implies:
% 6.39/1.65 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ stable(v0) | ~ environment(v0) | ? [v1:
% 6.39/1.65 | $i] : ($i(v1) & in_environment(v0, v1) & ! [v2: $i] : ( ~ $i(v2) |
% 6.39/1.65 | ~ greater_or_equal(v2, v1) | ~ subpopulations(first_movers,
% 6.39/1.65 | efficient_producers, v0, v2) | ? [v3: $i] : ? [v4: $i] :
% 6.39/1.65 | (growth_rate(efficient_producers, v2) = v3 &
% 6.39/1.65 | growth_rate(first_movers, v2) = v4 & $i(v4) & $i(v3) &
% 6.39/1.65 | greater(v3, v4)))))
% 6.39/1.65 |
% 6.39/1.65 | ALPHA: (prove_t1) implies:
% 6.39/1.65 | (2) $i(first_movers)
% 6.39/1.65 | (3) $i(efficient_producers)
% 6.39/1.65 | (4) ? [v0: $i] : ($i(v0) & stable(v0) & environment(v0) & ! [v1: $i] : (
% 6.39/1.65 | ~ $i(v1) | ~ in_environment(v0, v1) | ? [v2: $i] : ($i(v2) &
% 6.39/1.65 | greater_or_equal(v2, v1) & subpopulations(first_movers,
% 6.39/1.65 | efficient_producers, v0, v2) & ~
% 6.39/1.65 | selection_favors(efficient_producers, first_movers, v2))))
% 6.39/1.65 |
% 6.39/1.65 | DELTA: instantiating (4) with fresh symbol all_6_0 gives:
% 6.39/1.65 | (5) $i(all_6_0) & stable(all_6_0) & environment(all_6_0) & ! [v0: $i] : (
% 6.39/1.65 | ~ $i(v0) | ~ in_environment(all_6_0, v0) | ? [v1: $i] : ($i(v1) &
% 6.39/1.65 | greater_or_equal(v1, v0) & subpopulations(first_movers,
% 6.39/1.65 | efficient_producers, all_6_0, v1) & ~
% 6.39/1.65 | selection_favors(efficient_producers, first_movers, v1)))
% 6.39/1.65 |
% 6.39/1.65 | ALPHA: (5) implies:
% 6.39/1.65 | (6) environment(all_6_0)
% 6.39/1.65 | (7) stable(all_6_0)
% 6.39/1.65 | (8) $i(all_6_0)
% 6.39/1.66 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ in_environment(all_6_0, v0) | ? [v1: $i]
% 6.39/1.66 | : ($i(v1) & greater_or_equal(v1, v0) & subpopulations(first_movers,
% 6.39/1.66 | efficient_producers, all_6_0, v1) & ~
% 6.39/1.66 | selection_favors(efficient_producers, first_movers, v1)))
% 6.39/1.66 |
% 6.39/1.66 | GROUND_INST: instantiating (1) with all_6_0, simplifying with (6), (7), (8)
% 6.39/1.66 | gives:
% 6.39/1.66 | (10) ? [v0: $i] : ($i(v0) & in_environment(all_6_0, v0) & ! [v1: $i] : (
% 6.39/1.66 | ~ $i(v1) | ~ greater_or_equal(v1, v0) | ~
% 6.39/1.66 | subpopulations(first_movers, efficient_producers, all_6_0, v1) |
% 6.39/1.66 | ? [v2: $i] : ? [v3: $i] : (growth_rate(efficient_producers, v1) =
% 6.39/1.66 | v2 & growth_rate(first_movers, v1) = v3 & $i(v3) & $i(v2) &
% 6.39/1.66 | greater(v2, v3))))
% 6.39/1.66 |
% 6.39/1.66 | DELTA: instantiating (10) with fresh symbol all_14_0 gives:
% 6.39/1.66 | (11) $i(all_14_0) & in_environment(all_6_0, all_14_0) & ! [v0: $i] : ( ~
% 6.39/1.66 | $i(v0) | ~ greater_or_equal(v0, all_14_0) | ~
% 6.39/1.66 | subpopulations(first_movers, efficient_producers, all_6_0, v0) | ?
% 6.39/1.66 | [v1: $i] : ? [v2: $i] : (growth_rate(efficient_producers, v0) = v1
% 6.39/1.66 | & growth_rate(first_movers, v0) = v2 & $i(v2) & $i(v1) &
% 6.39/1.66 | greater(v1, v2)))
% 6.39/1.66 |
% 6.39/1.66 | ALPHA: (11) implies:
% 6.39/1.66 | (12) in_environment(all_6_0, all_14_0)
% 6.39/1.66 | (13) $i(all_14_0)
% 6.39/1.66 | (14) ! [v0: $i] : ( ~ $i(v0) | ~ greater_or_equal(v0, all_14_0) | ~
% 6.39/1.66 | subpopulations(first_movers, efficient_producers, all_6_0, v0) | ?
% 6.39/1.66 | [v1: $i] : ? [v2: $i] : (growth_rate(efficient_producers, v0) = v1
% 6.39/1.66 | & growth_rate(first_movers, v0) = v2 & $i(v2) & $i(v1) &
% 6.39/1.66 | greater(v1, v2)))
% 6.39/1.66 |
% 6.39/1.66 | GROUND_INST: instantiating (9) with all_14_0, simplifying with (12), (13)
% 6.39/1.66 | gives:
% 6.39/1.66 | (15) ? [v0: $i] : ($i(v0) & greater_or_equal(v0, all_14_0) &
% 6.39/1.66 | subpopulations(first_movers, efficient_producers, all_6_0, v0) & ~
% 6.39/1.66 | selection_favors(efficient_producers, first_movers, v0))
% 6.39/1.66 |
% 6.39/1.66 | DELTA: instantiating (15) with fresh symbol all_22_0 gives:
% 6.39/1.67 | (16) $i(all_22_0) & greater_or_equal(all_22_0, all_14_0) &
% 6.39/1.67 | subpopulations(first_movers, efficient_producers, all_6_0, all_22_0) &
% 6.39/1.67 | ~ selection_favors(efficient_producers, first_movers, all_22_0)
% 6.39/1.67 |
% 6.39/1.67 | ALPHA: (16) implies:
% 6.39/1.67 | (17) ~ selection_favors(efficient_producers, first_movers, all_22_0)
% 6.39/1.67 | (18) subpopulations(first_movers, efficient_producers, all_6_0, all_22_0)
% 6.39/1.67 | (19) greater_or_equal(all_22_0, all_14_0)
% 6.39/1.67 | (20) $i(all_22_0)
% 6.39/1.67 |
% 6.39/1.67 | GROUND_INST: instantiating (mp1_high_growth_rates) with all_6_0, first_movers,
% 6.39/1.67 | efficient_producers, all_22_0, simplifying with (2), (3), (6),
% 6.39/1.67 | (8), (17), (18), (20) gives:
% 6.39/1.67 | (21) ? [v0: $i] : ? [v1: $i] : (growth_rate(efficient_producers,
% 6.39/1.67 | all_22_0) = v0 & growth_rate(first_movers, all_22_0) = v1 & $i(v1)
% 6.39/1.67 | & $i(v0) & ~ greater(v0, v1))
% 6.39/1.67 |
% 6.39/1.67 | GROUND_INST: instantiating (14) with all_22_0, simplifying with (18), (19),
% 6.39/1.67 | (20) gives:
% 6.39/1.67 | (22) ? [v0: $i] : ? [v1: $i] : (growth_rate(efficient_producers,
% 6.39/1.67 | all_22_0) = v0 & growth_rate(first_movers, all_22_0) = v1 & $i(v1)
% 6.39/1.67 | & $i(v0) & greater(v0, v1))
% 6.39/1.67 |
% 6.39/1.67 | DELTA: instantiating (22) with fresh symbols all_29_0, all_29_1 gives:
% 6.39/1.67 | (23) growth_rate(efficient_producers, all_22_0) = all_29_1 &
% 6.39/1.67 | growth_rate(first_movers, all_22_0) = all_29_0 & $i(all_29_0) &
% 6.39/1.67 | $i(all_29_1) & greater(all_29_1, all_29_0)
% 6.39/1.67 |
% 6.39/1.67 | ALPHA: (23) implies:
% 6.39/1.67 | (24) greater(all_29_1, all_29_0)
% 6.39/1.67 | (25) growth_rate(first_movers, all_22_0) = all_29_0
% 6.39/1.67 | (26) growth_rate(efficient_producers, all_22_0) = all_29_1
% 6.39/1.67 |
% 6.39/1.67 | DELTA: instantiating (21) with fresh symbols all_31_0, all_31_1 gives:
% 6.39/1.67 | (27) growth_rate(efficient_producers, all_22_0) = all_31_1 &
% 6.39/1.67 | growth_rate(first_movers, all_22_0) = all_31_0 & $i(all_31_0) &
% 6.39/1.67 | $i(all_31_1) & ~ greater(all_31_1, all_31_0)
% 6.39/1.67 |
% 6.39/1.67 | ALPHA: (27) implies:
% 6.39/1.67 | (28) ~ greater(all_31_1, all_31_0)
% 6.39/1.67 | (29) growth_rate(first_movers, all_22_0) = all_31_0
% 6.39/1.67 | (30) growth_rate(efficient_producers, all_22_0) = all_31_1
% 6.39/1.67 |
% 6.39/1.67 | GROUND_INST: instantiating (function-axioms) with all_29_0, all_31_0,
% 6.39/1.67 | all_22_0, first_movers, simplifying with (25), (29) gives:
% 6.39/1.67 | (31) all_31_0 = all_29_0
% 6.39/1.67 |
% 6.39/1.67 | GROUND_INST: instantiating (function-axioms) with all_29_1, all_31_1,
% 6.39/1.67 | all_22_0, efficient_producers, simplifying with (26), (30) gives:
% 6.39/1.67 | (32) all_31_1 = all_29_1
% 6.39/1.67 |
% 6.39/1.67 | REDUCE: (28), (31), (32) imply:
% 6.39/1.67 | (33) ~ greater(all_29_1, all_29_0)
% 6.39/1.67 |
% 6.39/1.67 | PRED_UNIFY: (24), (33) imply:
% 6.39/1.67 | (34) $false
% 6.39/1.68 |
% 6.39/1.68 | CLOSE: (34) is inconsistent.
% 6.39/1.68 |
% 6.39/1.68 End of proof
% 6.39/1.68 % SZS output end Proof for theBenchmark
% 6.39/1.68
% 6.39/1.68 1060ms
%------------------------------------------------------------------------------