TSTP Solution File: MGT036+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : MGT036+3 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n012.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 09:16:21 EDT 2023
% Result : Theorem 4.18s 1.35s
% Output : Proof 5.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT036+3 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n012.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 06:04:09 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.64 ________ _____
% 0.20/0.64 ___ __ \_________(_)________________________________
% 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.64
% 0.20/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.64 (2023-06-19)
% 0.20/0.64
% 0.20/0.64 (c) Philipp Rümmer, 2009-2023
% 0.20/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.64 Amanda Stjerna.
% 0.20/0.64 Free software under BSD-3-Clause.
% 0.20/0.64
% 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.64
% 0.20/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.66 Running up to 7 provers in parallel.
% 0.20/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.05/1.01 Prover 4: Preprocessing ...
% 2.05/1.01 Prover 1: Preprocessing ...
% 2.49/1.05 Prover 3: Preprocessing ...
% 2.49/1.05 Prover 0: Preprocessing ...
% 2.49/1.05 Prover 5: Preprocessing ...
% 2.49/1.05 Prover 6: Preprocessing ...
% 2.49/1.05 Prover 2: Preprocessing ...
% 3.52/1.19 Prover 5: Constructing countermodel ...
% 3.52/1.19 Prover 2: Proving ...
% 3.52/1.19 Prover 3: Constructing countermodel ...
% 3.52/1.20 Prover 6: Proving ...
% 3.52/1.20 Prover 1: Constructing countermodel ...
% 3.52/1.22 Prover 4: Constructing countermodel ...
% 3.52/1.22 Prover 0: Proving ...
% 4.18/1.31 Prover 3: gave up
% 4.18/1.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.18/1.33 Prover 1: gave up
% 4.18/1.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.18/1.35 Prover 7: Preprocessing ...
% 4.18/1.35 Prover 8: Preprocessing ...
% 4.18/1.35 Prover 2: proved (682ms)
% 4.18/1.35
% 4.18/1.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.18/1.35
% 4.18/1.35 Prover 0: proved (686ms)
% 4.18/1.35
% 4.18/1.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.18/1.35
% 4.18/1.36 Prover 6: stopped
% 4.18/1.36 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.18/1.36 Prover 5: stopped
% 4.18/1.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.18/1.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.18/1.37 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.18/1.38 Prover 10: Preprocessing ...
% 4.18/1.39 Prover 7: Constructing countermodel ...
% 4.18/1.39 Prover 11: Preprocessing ...
% 4.18/1.40 Prover 13: Preprocessing ...
% 4.18/1.40 Prover 16: Preprocessing ...
% 4.18/1.42 Prover 8: Warning: ignoring some quantifiers
% 4.18/1.43 Prover 10: Constructing countermodel ...
% 4.18/1.44 Prover 16: Constructing countermodel ...
% 4.18/1.44 Prover 8: Constructing countermodel ...
% 5.11/1.45 Prover 11: Constructing countermodel ...
% 5.11/1.46 Prover 7: Found proof (size 9)
% 5.11/1.46 Prover 7: proved (148ms)
% 5.11/1.46 Prover 11: stopped
% 5.11/1.46 Prover 4: stopped
% 5.11/1.46 Prover 10: stopped
% 5.11/1.46 Prover 16: stopped
% 5.11/1.46 Prover 8: stopped
% 5.11/1.46 Prover 13: Constructing countermodel ...
% 5.11/1.47 Prover 13: stopped
% 5.11/1.47
% 5.11/1.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.11/1.47
% 5.11/1.47 % SZS output start Proof for theBenchmark
% 5.59/1.47 Assumptions after simplification:
% 5.59/1.47 ---------------------------------
% 5.59/1.47
% 5.59/1.47 (a13_star)
% 5.59/1.50 $i(efficient_producers) & $i(first_movers) & $i(zero) & ? [v0: $i] : ? [v1:
% 5.59/1.50 $i] : ? [v2: $i] : ? [v3: $i] : (growth_rate(efficient_producers, v1) = v3
% 5.59/1.50 & growth_rate(first_movers, v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 5.59/1.51 greater(zero, v3) & greater_or_equal(v2, zero) &
% 5.59/1.51 subpopulations(first_movers, efficient_producers, v0, v1) & environment(v0))
% 5.59/1.51
% 5.59/1.51 (d2)
% 5.59/1.51 $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 5.59/1.51 : ! [v5: $i] : ( ~ (growth_rate(v2, v3) = v4) | ~ (growth_rate(v1, v3) = v5)
% 5.59/1.51 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ outcompetes(v2, v1, v3)
% 5.59/1.51 | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | greater(zero,
% 5.59/1.51 v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 5.59/1.51 : ! [v5: $i] : ( ~ (growth_rate(v2, v3) = v4) | ~ (growth_rate(v1, v3) = v5)
% 5.59/1.51 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ outcompetes(v2, v1, v3)
% 5.59/1.51 | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) |
% 5.59/1.51 greater_or_equal(v4, zero)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 5.59/1.51 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (growth_rate(v2, v3) = v4) | ~
% 5.59/1.51 (growth_rate(v1, v3) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 5.59/1.51 ~ greater(zero, v5) | ~ greater_or_equal(v4, zero) | ~ subpopulations(v1,
% 5.59/1.51 v2, v0, v3) | ~ environment(v0) | outcompetes(v2, v1, v3))
% 5.59/1.52
% 5.59/1.52 (mp_symmetry_of_subpopulations)
% 5.59/1.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 5.59/1.52 | ~ $i(v1) | ~ $i(v0) | ~ subpopulations(v1, v2, v0, v3) | ~
% 5.59/1.52 environment(v0) | subpopulations(v2, v1, v0, v3))
% 5.59/1.52
% 5.59/1.52 (prove_t5_star)
% 5.59/1.52 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : ( ~
% 5.59/1.52 $i(v1) | ~ $i(v0) | ~ outcompetes(first_movers, efficient_producers, v1) |
% 5.59/1.52 ~ subpopulations(first_movers, efficient_producers, v0, v1) | ~
% 5.59/1.52 environment(v0))
% 5.59/1.52
% 5.59/1.52 Those formulas are unsatisfiable:
% 5.59/1.52 ---------------------------------
% 5.59/1.52
% 5.59/1.52 Begin of proof
% 5.59/1.52 |
% 5.59/1.52 | ALPHA: (d2) implies:
% 5.59/1.52 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 5.59/1.52 | ! [v5: $i] : ( ~ (growth_rate(v2, v3) = v4) | ~ (growth_rate(v1, v3) =
% 5.59/1.52 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 5.59/1.52 | greater(zero, v5) | ~ greater_or_equal(v4, zero) | ~
% 5.59/1.52 | subpopulations(v1, v2, v0, v3) | ~ environment(v0) | outcompetes(v2,
% 5.59/1.52 | v1, v3))
% 5.59/1.52 |
% 5.59/1.52 | ALPHA: (a13_star) implies:
% 5.59/1.53 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 5.59/1.53 | (growth_rate(efficient_producers, v1) = v3 & growth_rate(first_movers,
% 5.59/1.53 | v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & greater(zero, v3) &
% 5.59/1.53 | greater_or_equal(v2, zero) & subpopulations(first_movers,
% 5.59/1.53 | efficient_producers, v0, v1) & environment(v0))
% 5.59/1.53 |
% 5.59/1.53 | ALPHA: (prove_t5_star) implies:
% 5.59/1.53 | (3) $i(first_movers)
% 5.59/1.53 | (4) $i(efficient_producers)
% 5.59/1.53 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 5.59/1.53 | outcompetes(first_movers, efficient_producers, v1) | ~
% 5.59/1.53 | subpopulations(first_movers, efficient_producers, v0, v1) | ~
% 5.59/1.53 | environment(v0))
% 5.59/1.53 |
% 5.59/1.53 | DELTA: instantiating (2) with fresh symbols all_7_0, all_7_1, all_7_2, all_7_3
% 5.59/1.53 | gives:
% 5.59/1.53 | (6) growth_rate(efficient_producers, all_7_2) = all_7_0 &
% 5.59/1.53 | growth_rate(first_movers, all_7_2) = all_7_1 & $i(all_7_0) &
% 5.59/1.53 | $i(all_7_1) & $i(all_7_2) & $i(all_7_3) & greater(zero, all_7_0) &
% 5.59/1.53 | greater_or_equal(all_7_1, zero) & subpopulations(first_movers,
% 5.59/1.53 | efficient_producers, all_7_3, all_7_2) & environment(all_7_3)
% 5.59/1.53 |
% 5.59/1.53 | ALPHA: (6) implies:
% 5.59/1.53 | (7) environment(all_7_3)
% 5.59/1.53 | (8) subpopulations(first_movers, efficient_producers, all_7_3, all_7_2)
% 5.59/1.53 | (9) greater_or_equal(all_7_1, zero)
% 5.59/1.53 | (10) greater(zero, all_7_0)
% 5.59/1.53 | (11) $i(all_7_3)
% 5.59/1.53 | (12) $i(all_7_2)
% 5.59/1.53 | (13) growth_rate(first_movers, all_7_2) = all_7_1
% 5.59/1.53 | (14) growth_rate(efficient_producers, all_7_2) = all_7_0
% 5.59/1.53 |
% 5.59/1.54 | GROUND_INST: instantiating (mp_symmetry_of_subpopulations) with all_7_3,
% 5.59/1.54 | first_movers, efficient_producers, all_7_2, simplifying with (3),
% 5.59/1.54 | (4), (7), (8), (11), (12) gives:
% 5.59/1.54 | (15) subpopulations(efficient_producers, first_movers, all_7_3, all_7_2)
% 5.59/1.54 |
% 5.59/1.54 | GROUND_INST: instantiating (1) with all_7_3, efficient_producers,
% 5.59/1.54 | first_movers, all_7_2, all_7_1, all_7_0, simplifying with (3),
% 5.59/1.54 | (4), (7), (9), (10), (11), (12), (13), (14), (15) gives:
% 5.59/1.54 | (16) outcompetes(first_movers, efficient_producers, all_7_2)
% 5.59/1.54 |
% 5.59/1.54 | GROUND_INST: instantiating (5) with all_7_3, all_7_2, simplifying with (7),
% 5.59/1.54 | (8), (11), (12), (16) gives:
% 5.59/1.54 | (17) $false
% 5.59/1.54 |
% 5.59/1.54 | CLOSE: (17) is inconsistent.
% 5.59/1.54 |
% 5.59/1.54 End of proof
% 5.59/1.54 % SZS output end Proof for theBenchmark
% 5.59/1.54
% 5.59/1.54 900ms
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