%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT021+1 : TPTP v9.3.0. 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 : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Tue Sep 8 06:17:20 AM UTC 2026 % Result : Theorem 7.64s 2.03s % Output : Proof 13.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT021+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.37 % Computer : n003.cluster.edu % 0.09/0.37 % Model : x86_64 x86_64 % 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.37 % Memory : 8046.5625MB % 0.09/0.37 % OS : Linux 6.8.0-71-generic % 0.09/0.37 % CPULimit : 300 % 0.09/0.37 % WCLimit : 300 % 0.09/0.37 % DateTime : Mon Sep 7 12:03:54 UTC 2026 % 0.09/0.37 % CPUTime : % 0.09/0.38 OpenJDK 64-Bit Server VM warning: Options -Xverify:none and -noverify were deprecated in JDK 13 and will likely be removed in a future release. % 0.65/0.73 ________ _____ % 0.65/0.73 ___ __ \_________(_)________________________________ % 0.65/0.73 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.65/0.73 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.65/0.73 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.65/0.73 % 0.65/0.73 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.65/0.73 (2023-06-19) % 0.65/0.73 % 0.65/0.73 (c) Philipp Rümmer, 2009-2023 % 0.65/0.73 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.65/0.73 Amanda Stjerna. % 0.65/0.73 Free software under BSD-3-Clause. % 0.65/0.73 % 0.65/0.73 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.65/0.73 % 0.65/0.73 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.65/0.75 Running up to 7 provers in parallel. % 0.65/0.77 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.65/0.77 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.65/0.77 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.65/0.77 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.65/0.77 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.65/0.77 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.65/0.77 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.93/1.33 Prover 4: Preprocessing ... % 2.93/1.34 Prover 1: Preprocessing ... % 3.66/1.40 Prover 5: Preprocessing ... % 3.66/1.40 Prover 6: Preprocessing ... % 3.66/1.40 Prover 3: Preprocessing ... % 3.66/1.40 Prover 0: Preprocessing ... % 3.66/1.40 Prover 2: Preprocessing ... % 6.05/1.72 Prover 1: Constructing countermodel ... % 6.05/1.73 Prover 5: Constructing countermodel ... % 6.05/1.73 Prover 2: Proving ... % 6.05/1.74 Prover 3: Constructing countermodel ... % 6.05/1.74 Prover 6: Constructing countermodel ... % 6.81/1.81 Prover 4: Constructing countermodel ... % 6.81/1.83 Prover 0: Proving ... % 7.64/2.01 Prover 3: gave up % 7.64/2.02 Prover 6: gave up % 7.64/2.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.64/2.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.64/2.03 Prover 5: proved (1260ms) % 7.64/2.03 % 7.64/2.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.64/2.03 % 7.64/2.03 Prover 0: stopped % 7.64/2.04 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.64/2.04 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.65/2.05 Prover 2: proved (1288ms) % 8.65/2.05 % 8.65/2.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.65/2.05 % 8.65/2.06 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.65/2.09 Prover 8: Preprocessing ... % 8.65/2.09 Prover 7: Preprocessing ... % 8.65/2.11 Prover 11: Preprocessing ... % 8.65/2.11 Prover 1: gave up % 8.65/2.12 Prover 10: Preprocessing ... % 8.65/2.12 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.65/2.13 Prover 13: Preprocessing ... % 9.51/2.17 Prover 16: Preprocessing ... % 9.92/2.22 Prover 7: Constructing countermodel ... % 9.92/2.24 Prover 10: Constructing countermodel ... % 9.92/2.29 Prover 13: Constructing countermodel ... % 9.92/2.29 Prover 8: Warning: ignoring some quantifiers % 9.92/2.29 Prover 11: Constructing countermodel ... % 9.92/2.29 Prover 10: gave up % 9.92/2.29 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 9.92/2.29 Prover 16: Constructing countermodel ... % 10.72/2.30 Prover 8: Constructing countermodel ... % 10.72/2.30 Prover 7: gave up % 10.72/2.32 Prover 19: Preprocessing ... % 11.53/2.48 Prover 19: Warning: ignoring some quantifiers % 12.30/2.51 Prover 19: Constructing countermodel ... % 12.30/2.52 Prover 13: Found proof (size 59) % 12.30/2.52 Prover 13: proved (458ms) % 12.30/2.52 Prover 8: stopped % 12.30/2.52 Prover 11: stopped % 12.30/2.52 Prover 16: stopped % 12.30/2.52 Prover 19: stopped % 12.30/2.52 Prover 4: Found proof (size 113) % 12.30/2.52 Prover 4: proved (1757ms) % 12.30/2.52 % 12.30/2.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.30/2.52 % 12.30/2.55 % SZS output start Proof for theBenchmark % 12.30/2.55 Assumptions after simplification: % 12.30/2.55 --------------------------------- % 12.30/2.55 % 12.30/2.55 (a3) % 12.87/2.61 $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 12.87/2.61 (number_of_organizations(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 12.87/2.61 greater(v2, zero) | ~ in_environment(v0, v1) | ~ environment(v0) | ? [v3: % 12.87/2.61 $i] : ? [v4: $i] : (equilibrium(v0) = v3 & resources(v0, v1) = v4 & % 12.87/2.61 $i(v4) & $i(v3) & ( ~ greater(v3, v1) | decreases(v4)) & (constant(v4) | % 12.87/2.61 greater(v3, v1)))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) % 12.87/2.61 | ~ in_environment(v0, v1) | ~ environment(v0) | ? [v2: $i] : ? [v3: $i] % 12.87/2.61 : ? [v4: $i] : (equilibrium(v0) = v3 & resources(v0, v1) = v4 & % 12.87/2.61 number_of_organizations(v0, v1) = v2 & $i(v4) & $i(v3) & $i(v2) & ( ~ % 12.87/2.61 greater(v2, zero) | (( ~ greater(v3, v1) | decreases(v4)) & % 12.87/2.61 (constant(v4) | greater(v3, v1)))))) % 12.87/2.61 % 12.87/2.61 (l4) % 12.87/2.62 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : ! % 12.87/2.62 [v2: $i] : ( ~ (resources(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 12.87/2.62 subpopulations(first_movers, efficient_producers, v0, v1) | ~ % 12.87/2.62 environment(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 12.87/2.62 (disbanding_rate(efficient_producers, v1) = v4 & % 12.87/2.62 disbanding_rate(first_movers, v1) = v3 & difference(v3, v4) = v5 & $i(v5) % 12.87/2.62 & $i(v4) & $i(v3) & ( ~ constant(v2) | ~ decreases(v5)) & ( ~ % 12.87/2.62 decreases(v2) | increases(v5)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 12.87/2.62 $i(v1) | ~ $i(v0) | ~ subpopulations(first_movers, efficient_producers, % 12.87/2.62 v0, v1) | ~ environment(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 12.87/2.62 ? [v5: $i] : (disbanding_rate(efficient_producers, v1) = v4 & % 12.87/2.62 disbanding_rate(first_movers, v1) = v3 & difference(v3, v4) = v5 & % 12.87/2.62 resources(v0, v1) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ % 12.87/2.62 constant(v2) | ~ decreases(v5)) & ( ~ decreases(v2) | increases(v5)))) % 12.87/2.62 % 12.87/2.63 (mp_environment_not_empty) % 12.87/2.63 $i(zero) & $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: % 12.87/2.63 $i] : ! [v2: $i] : ( ~ (number_of_organizations(v0, v1) = v2) | ~ $i(v1) | % 12.87/2.63 ~ $i(v0) | ~ subpopulations(first_movers, efficient_producers, v0, v1) | % 12.87/2.63 ~ environment(v0) | greater(v2, zero)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 12.87/2.63 $i(v1) | ~ $i(v0) | ~ subpopulations(first_movers, efficient_producers, % 12.87/2.63 v0, v1) | ~ environment(v0) | ? [v2: $i] : (number_of_organizations(v0, % 12.87/2.63 v1) = v2 & $i(v2) & greater(v2, zero))) % 12.87/2.63 % 12.87/2.63 (mp_increase_not_decrease) % 12.87/2.63 ! [v0: $i] : ( ~ $i(v0) | ~ decreases(v0) | ~ increases(v0)) % 12.87/2.63 % 12.87/2.63 (mp_time_point_in_environment) % 12.87/2.63 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : ( ~ % 12.87/2.64 $i(v1) | ~ $i(v0) | ~ subpopulations(first_movers, efficient_producers, % 12.87/2.64 v0, v1) | ~ environment(v0) | in_environment(v0, v1)) % 12.87/2.64 % 12.87/2.64 (prove_l3) % 12.87/2.64 $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ? [v1: $i] : ? % 12.87/2.64 [v2: $i] : ? [v3: $i] : ? [v4: $i] : (disbanding_rate(efficient_producers, % 12.87/2.64 v1) = v3 & disbanding_rate(first_movers, v1) = v2 & difference(v2, v3) = % 12.87/2.64 v4 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & decreases(v4) & % 12.87/2.64 subpopulations(first_movers, efficient_producers, v0, v1) & environment(v0)) % 12.87/2.64 % 12.87/2.64 (function-axioms) % 12.87/2.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.87/2.65 (disbanding_rate(v3, v2) = v1) | ~ (disbanding_rate(v3, v2) = v0)) & ! % 12.87/2.65 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.87/2.65 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 12.87/2.65 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (resources(v3, v2) = v1) % 12.87/2.65 | ~ (resources(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 12.87/2.65 ! [v3: $i] : (v1 = v0 | ~ (number_of_organizations(v3, v2) = v1) | ~ % 12.87/2.65 (number_of_organizations(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 12.87/2.65 [v2: $i] : (v1 = v0 | ~ (equilibrium(v2) = v1) | ~ (equilibrium(v2) = v0)) % 12.87/2.65 % 12.87/2.65 Further assumptions not needed in the proof: % 12.87/2.65 -------------------------------------------- % 12.87/2.65 mp_greater_or_equal % 12.87/2.65 % 12.87/2.65 Those formulas are unsatisfiable: % 12.87/2.65 --------------------------------- % 12.87/2.65 % 12.87/2.65 Begin of proof % 12.87/2.65 | % 12.87/2.65 | ALPHA: (mp_time_point_in_environment) implies: % 12.87/2.65 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 12.87/2.65 | subpopulations(first_movers, efficient_producers, v0, v1) | ~ % 12.87/2.65 | environment(v0) | in_environment(v0, v1)) % 12.87/2.65 | % 12.87/2.65 | ALPHA: (mp_environment_not_empty) implies: % 12.87/2.65 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 12.87/2.66 | subpopulations(first_movers, efficient_producers, v0, v1) | ~ % 12.87/2.66 | environment(v0) | ? [v2: $i] : (number_of_organizations(v0, v1) = v2 % 12.87/2.66 | & $i(v2) & greater(v2, zero))) % 12.87/2.66 | % 12.87/2.66 | ALPHA: (a3) implies: % 12.87/2.66 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 12.87/2.66 | in_environment(v0, v1) | ~ environment(v0) | ? [v2: $i] : ? [v3: % 12.87/2.66 | $i] : ? [v4: $i] : (equilibrium(v0) = v3 & resources(v0, v1) = v4 % 12.87/2.66 | & number_of_organizations(v0, v1) = v2 & $i(v4) & $i(v3) & $i(v2) & % 12.87/2.66 | ( ~ greater(v2, zero) | (( ~ greater(v3, v1) | decreases(v4)) & % 12.87/2.66 | (constant(v4) | greater(v3, v1)))))) % 12.87/2.66 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 12.87/2.66 | (number_of_organizations(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 12.87/2.66 | greater(v2, zero) | ~ in_environment(v0, v1) | ~ environment(v0) | % 12.87/2.66 | ? [v3: $i] : ? [v4: $i] : (equilibrium(v0) = v3 & resources(v0, v1) % 12.87/2.66 | = v4 & $i(v4) & $i(v3) & ( ~ greater(v3, v1) | decreases(v4)) & % 12.87/2.66 | (constant(v4) | greater(v3, v1)))) % 12.87/2.66 | % 12.87/2.66 | ALPHA: (l4) implies: % 12.87/2.67 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 12.87/2.67 | subpopulations(first_movers, efficient_producers, v0, v1) | ~ % 12.87/2.67 | environment(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 12.87/2.67 | $i] : (disbanding_rate(efficient_producers, v1) = v4 & % 12.87/2.67 | disbanding_rate(first_movers, v1) = v3 & difference(v3, v4) = v5 & % 12.87/2.67 | resources(v0, v1) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ % 12.87/2.67 | constant(v2) | ~ decreases(v5)) & ( ~ decreases(v2) | % 12.87/2.67 | increases(v5)))) % 12.87/2.67 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (resources(v0, v1) = v2) % 12.87/2.67 | | ~ $i(v1) | ~ $i(v0) | ~ subpopulations(first_movers, % 12.87/2.67 | efficient_producers, v0, v1) | ~ environment(v0) | ? [v3: $i] : % 12.87/2.67 | ? [v4: $i] : ? [v5: $i] : (disbanding_rate(efficient_producers, v1) % 12.87/2.67 | = v4 & disbanding_rate(first_movers, v1) = v3 & difference(v3, v4) % 12.87/2.67 | = v5 & $i(v5) & $i(v4) & $i(v3) & ( ~ constant(v2) | ~ % 12.87/2.67 | decreases(v5)) & ( ~ decreases(v2) | increases(v5)))) % 12.87/2.67 | % 12.87/2.67 | ALPHA: (prove_l3) implies: % 12.87/2.67 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 12.87/2.67 | (disbanding_rate(efficient_producers, v1) = v3 & % 12.87/2.67 | disbanding_rate(first_movers, v1) = v2 & difference(v2, v3) = v4 & % 12.87/2.67 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & decreases(v4) & % 12.87/2.67 | subpopulations(first_movers, efficient_producers, v0, v1) & % 12.87/2.67 | environment(v0)) % 12.87/2.67 | % 12.87/2.67 | ALPHA: (function-axioms) implies: % 12.87/2.68 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.87/2.68 | (resources(v3, v2) = v1) | ~ (resources(v3, v2) = v0)) % 12.87/2.68 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.87/2.68 | (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 12.87/2.68 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.87/2.68 | (disbanding_rate(v3, v2) = v1) | ~ (disbanding_rate(v3, v2) = v0)) % 12.87/2.68 | % 12.87/2.68 | DELTA: instantiating (7) with fresh symbols all_10_0, all_10_1, all_10_2, % 12.87/2.68 | all_10_3, all_10_4 gives: % 12.87/2.68 | (11) disbanding_rate(efficient_producers, all_10_3) = all_10_1 & % 12.87/2.68 | disbanding_rate(first_movers, all_10_3) = all_10_2 & % 12.87/2.68 | difference(all_10_2, all_10_1) = all_10_0 & $i(all_10_0) & % 12.87/2.68 | $i(all_10_1) & $i(all_10_2) & $i(all_10_3) & $i(all_10_4) & % 12.87/2.68 | decreases(all_10_0) & subpopulations(first_movers, % 12.87/2.68 | efficient_producers, all_10_4, all_10_3) & environment(all_10_4) % 12.87/2.68 | % 12.87/2.68 | ALPHA: (11) implies: % 12.87/2.68 | (12) environment(all_10_4) % 12.87/2.68 | (13) subpopulations(first_movers, efficient_producers, all_10_4, all_10_3) % 12.87/2.68 | (14) decreases(all_10_0) % 12.87/2.69 | (15) $i(all_10_4) % 12.87/2.69 | (16) $i(all_10_3) % 12.87/2.69 | (17) difference(all_10_2, all_10_1) = all_10_0 % 12.87/2.69 | (18) disbanding_rate(first_movers, all_10_3) = all_10_2 % 12.87/2.69 | (19) disbanding_rate(efficient_producers, all_10_3) = all_10_1 % 12.87/2.69 | % 12.87/2.69 | GROUND_INST: instantiating (1) with all_10_4, all_10_3, simplifying with (12), % 12.87/2.69 | (13), (15), (16) gives: % 12.87/2.69 | (20) in_environment(all_10_4, all_10_3) % 12.87/2.69 | % 12.87/2.69 | GROUND_INST: instantiating (5) with all_10_4, all_10_3, simplifying with (12), % 12.87/2.69 | (13), (15), (16) gives: % 12.87/2.69 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 12.87/2.69 | (disbanding_rate(efficient_producers, all_10_3) = v2 & % 12.87/2.69 | disbanding_rate(first_movers, all_10_3) = v1 & difference(v1, v2) = % 12.87/2.69 | v3 & resources(all_10_4, all_10_3) = v0 & $i(v3) & $i(v2) & $i(v1) & % 12.87/2.69 | $i(v0) & ( ~ constant(v0) | ~ decreases(v3)) & ( ~ decreases(v0) | % 12.87/2.69 | increases(v3))) % 12.87/2.69 | % 12.87/2.69 | GROUND_INST: instantiating (2) with all_10_4, all_10_3, simplifying with (12), % 12.87/2.69 | (13), (15), (16) gives: % 12.87/2.69 | (22) ? [v0: $i] : (number_of_organizations(all_10_4, all_10_3) = v0 & % 12.87/2.69 | $i(v0) & greater(v0, zero)) % 12.87/2.69 | % 12.87/2.69 | DELTA: instantiating (22) with fresh symbol all_18_0 gives: % 12.87/2.70 | (23) number_of_organizations(all_10_4, all_10_3) = all_18_0 & $i(all_18_0) % 12.87/2.70 | & greater(all_18_0, zero) % 12.87/2.70 | % 12.87/2.70 | ALPHA: (23) implies: % 12.87/2.70 | (24) greater(all_18_0, zero) % 13.36/2.70 | (25) number_of_organizations(all_10_4, all_10_3) = all_18_0 % 13.36/2.70 | % 13.36/2.70 | DELTA: instantiating (21) with fresh symbols all_20_0, all_20_1, all_20_2, % 13.36/2.70 | all_20_3 gives: % 13.36/2.70 | (26) disbanding_rate(efficient_producers, all_10_3) = all_20_1 & % 13.36/2.70 | disbanding_rate(first_movers, all_10_3) = all_20_2 & % 13.36/2.70 | difference(all_20_2, all_20_1) = all_20_0 & resources(all_10_4, % 13.36/2.70 | all_10_3) = all_20_3 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) & % 13.36/2.70 | $i(all_20_3) & ( ~ constant(all_20_3) | ~ decreases(all_20_0)) & ( ~ % 13.36/2.70 | decreases(all_20_3) | increases(all_20_0)) % 13.36/2.70 | % 13.36/2.70 | ALPHA: (26) implies: % 13.36/2.70 | (27) resources(all_10_4, all_10_3) = all_20_3 % 13.36/2.70 | (28) difference(all_20_2, all_20_1) = all_20_0 % 13.36/2.70 | (29) disbanding_rate(first_movers, all_10_3) = all_20_2 % 13.36/2.70 | (30) disbanding_rate(efficient_producers, all_10_3) = all_20_1 % 13.36/2.70 | (31) ~ constant(all_20_3) | ~ decreases(all_20_0) % 13.36/2.70 | % 13.36/2.70 | GROUND_INST: instantiating (10) with all_10_2, all_20_2, all_10_3, % 13.36/2.70 | first_movers, simplifying with (18), (29) gives: % 13.36/2.70 | (32) all_20_2 = all_10_2 % 13.36/2.70 | % 13.36/2.70 | GROUND_INST: instantiating (10) with all_10_1, all_20_1, all_10_3, % 13.36/2.70 | efficient_producers, simplifying with (19), (30) gives: % 13.36/2.70 | (33) all_20_1 = all_10_1 % 13.36/2.70 | % 13.36/2.70 | REDUCE: (28), (32), (33) imply: % 13.36/2.70 | (34) difference(all_10_2, all_10_1) = all_20_0 % 13.36/2.70 | % 13.36/2.71 | GROUND_INST: instantiating (9) with all_10_0, all_20_0, all_10_1, all_10_2, % 13.36/2.71 | simplifying with (17), (34) gives: % 13.36/2.71 | (35) all_20_0 = all_10_0 % 13.36/2.71 | % 13.36/2.71 | BETA: splitting (31) gives: % 13.36/2.71 | % 13.36/2.71 | Case 1: % 13.36/2.71 | | % 13.36/2.71 | | (36) ~ constant(all_20_3) % 13.36/2.71 | | % 13.36/2.71 | | GROUND_INST: instantiating (3) with all_10_4, all_10_3, simplifying with % 13.36/2.71 | | (12), (15), (16), (20) gives: % 13.36/2.71 | | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (equilibrium(all_10_4) = % 13.36/2.71 | | v1 & resources(all_10_4, all_10_3) = v2 & % 13.36/2.71 | | number_of_organizations(all_10_4, all_10_3) = v0 & $i(v2) & $i(v1) % 13.36/2.71 | | & $i(v0) & ( ~ greater(v0, zero) | (( ~ greater(v1, all_10_3) | % 13.36/2.71 | | decreases(v2)) & (constant(v2) | greater(v1, all_10_3))))) % 13.36/2.71 | | % 13.36/2.71 | | GROUND_INST: instantiating (4) with all_10_4, all_10_3, all_18_0, % 13.36/2.71 | | simplifying with (12), (15), (16), (20), (24), (25) gives: % 13.36/2.71 | | (38) ? [v0: $i] : ? [v1: $i] : (equilibrium(all_10_4) = v0 & % 13.36/2.71 | | resources(all_10_4, all_10_3) = v1 & $i(v1) & $i(v0) & ( ~ % 13.36/2.71 | | greater(v0, all_10_3) | decreases(v1)) & (constant(v1) | % 13.36/2.71 | | greater(v0, all_10_3))) % 13.36/2.71 | | % 13.36/2.71 | | GROUND_INST: instantiating (6) with all_10_4, all_10_3, all_20_3, % 13.36/2.71 | | simplifying with (12), (13), (15), (16), (27) gives: % 13.36/2.72 | | (39) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 13.36/2.72 | | (disbanding_rate(efficient_producers, all_10_3) = v1 & % 13.36/2.72 | | disbanding_rate(first_movers, all_10_3) = v0 & difference(v0, v1) % 13.36/2.72 | | = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ constant(all_20_3) | ~ % 13.36/2.72 | | decreases(v2)) & ( ~ decreases(all_20_3) | increases(v2))) % 13.36/2.72 | | % 13.36/2.72 | | DELTA: instantiating (38) with fresh symbols all_39_0, all_39_1 gives: % 13.36/2.72 | | (40) equilibrium(all_10_4) = all_39_1 & resources(all_10_4, all_10_3) = % 13.36/2.72 | | all_39_0 & $i(all_39_0) & $i(all_39_1) & ( ~ greater(all_39_1, % 13.36/2.72 | | all_10_3) | decreases(all_39_0)) & (constant(all_39_0) | % 13.36/2.72 | | greater(all_39_1, all_10_3)) % 13.36/2.72 | | % 13.36/2.72 | | ALPHA: (40) implies: % 13.36/2.72 | | (41) resources(all_10_4, all_10_3) = all_39_0 % 13.36/2.72 | | (42) constant(all_39_0) | greater(all_39_1, all_10_3) % 13.36/2.72 | | (43) ~ greater(all_39_1, all_10_3) | decreases(all_39_0) % 13.36/2.72 | | % 13.36/2.72 | | DELTA: instantiating (39) with fresh symbols all_41_0, all_41_1, all_41_2 % 13.36/2.72 | | gives: % 13.36/2.72 | | (44) disbanding_rate(efficient_producers, all_10_3) = all_41_1 & % 13.36/2.72 | | disbanding_rate(first_movers, all_10_3) = all_41_2 & % 13.36/2.72 | | difference(all_41_2, all_41_1) = all_41_0 & $i(all_41_0) & % 13.36/2.72 | | $i(all_41_1) & $i(all_41_2) & ( ~ constant(all_20_3) | ~ % 13.36/2.72 | | decreases(all_41_0)) & ( ~ decreases(all_20_3) | % 13.36/2.72 | | increases(all_41_0)) % 13.36/2.72 | | % 13.36/2.72 | | ALPHA: (44) implies: % 13.36/2.72 | | (45) $i(all_41_0) % 13.36/2.72 | | (46) difference(all_41_2, all_41_1) = all_41_0 % 13.36/2.72 | | (47) disbanding_rate(first_movers, all_10_3) = all_41_2 % 13.36/2.72 | | (48) disbanding_rate(efficient_producers, all_10_3) = all_41_1 % 13.36/2.73 | | (49) ~ decreases(all_20_3) | increases(all_41_0) % 13.36/2.73 | | % 13.36/2.73 | | DELTA: instantiating (37) with fresh symbols all_43_0, all_43_1, all_43_2 % 13.36/2.73 | | gives: % 13.36/2.73 | | (50) equilibrium(all_10_4) = all_43_1 & resources(all_10_4, all_10_3) = % 13.36/2.73 | | all_43_0 & number_of_organizations(all_10_4, all_10_3) = all_43_2 & % 13.36/2.73 | | $i(all_43_0) & $i(all_43_1) & $i(all_43_2) & ( ~ greater(all_43_2, % 13.36/2.73 | | zero) | (( ~ greater(all_43_1, all_10_3) | decreases(all_43_0)) % 13.36/2.73 | | & (constant(all_43_0) | greater(all_43_1, all_10_3)))) % 13.36/2.73 | | % 13.36/2.73 | | ALPHA: (50) implies: % 13.36/2.73 | | (51) resources(all_10_4, all_10_3) = all_43_0 % 13.36/2.73 | | % 13.36/2.73 | | GROUND_INST: instantiating (8) with all_20_3, all_43_0, all_10_3, all_10_4, % 13.36/2.73 | | simplifying with (27), (51) gives: % 13.36/2.73 | | (52) all_43_0 = all_20_3 % 13.36/2.73 | | % 13.36/2.73 | | GROUND_INST: instantiating (8) with all_39_0, all_43_0, all_10_3, all_10_4, % 13.36/2.73 | | simplifying with (41), (51) gives: % 13.36/2.73 | | (53) all_43_0 = all_39_0 % 13.36/2.73 | | % 13.36/2.73 | | GROUND_INST: instantiating (10) with all_10_2, all_41_2, all_10_3, % 13.36/2.73 | | first_movers, simplifying with (18), (47) gives: % 13.36/2.73 | | (54) all_41_2 = all_10_2 % 13.36/2.73 | | % 13.36/2.73 | | GROUND_INST: instantiating (10) with all_10_1, all_41_1, all_10_3, % 13.36/2.73 | | efficient_producers, simplifying with (19), (48) gives: % 13.36/2.73 | | (55) all_41_1 = all_10_1 % 13.36/2.73 | | % 13.36/2.73 | | COMBINE_EQS: (52), (53) imply: % 13.36/2.73 | | (56) all_39_0 = all_20_3 % 13.36/2.73 | | % 13.36/2.73 | | REDUCE: (46), (54), (55) imply: % 13.36/2.73 | | (57) difference(all_10_2, all_10_1) = all_41_0 % 13.36/2.73 | | % 13.36/2.73 | | BETA: splitting (42) gives: % 13.36/2.73 | | % 13.36/2.73 | | Case 1: % 13.36/2.73 | | | % 13.36/2.73 | | | (58) constant(all_39_0) % 13.36/2.73 | | | % 13.36/2.73 | | | REDUCE: (56), (58) imply: % 13.36/2.73 | | | (59) constant(all_20_3) % 13.36/2.73 | | | % 13.36/2.73 | | | PRED_UNIFY: (36), (59) imply: % 13.36/2.74 | | | (60) $false % 13.36/2.74 | | | % 13.36/2.74 | | | CLOSE: (60) is inconsistent. % 13.36/2.74 | | | % 13.36/2.74 | | Case 2: % 13.36/2.74 | | | % 13.36/2.74 | | | (61) greater(all_39_1, all_10_3) % 13.36/2.74 | | | % 13.36/2.74 | | | BETA: splitting (43) gives: % 13.36/2.74 | | | % 13.36/2.74 | | | Case 1: % 13.36/2.74 | | | | % 13.36/2.74 | | | | (62) ~ greater(all_39_1, all_10_3) % 13.36/2.74 | | | | % 13.36/2.74 | | | | PRED_UNIFY: (61), (62) imply: % 13.36/2.74 | | | | (63) $false % 13.36/2.74 | | | | % 13.36/2.74 | | | | CLOSE: (63) is inconsistent. % 13.36/2.74 | | | | % 13.36/2.74 | | | Case 2: % 13.36/2.74 | | | | % 13.36/2.74 | | | | (64) decreases(all_39_0) % 13.36/2.74 | | | | % 13.36/2.74 | | | | REDUCE: (56), (64) imply: % 13.36/2.74 | | | | (65) decreases(all_20_3) % 13.36/2.74 | | | | % 13.36/2.74 | | | | BETA: splitting (49) gives: % 13.36/2.74 | | | | % 13.36/2.74 | | | | Case 1: % 13.36/2.74 | | | | | % 13.36/2.74 | | | | | (66) ~ decreases(all_20_3) % 13.36/2.74 | | | | | % 13.36/2.74 | | | | | PRED_UNIFY: (65), (66) imply: % 13.36/2.74 | | | | | (67) $false % 13.36/2.74 | | | | | % 13.36/2.74 | | | | | CLOSE: (67) is inconsistent. % 13.36/2.74 | | | | | % 13.36/2.74 | | | | Case 2: % 13.36/2.74 | | | | | % 13.36/2.74 | | | | | (68) increases(all_41_0) % 13.36/2.74 | | | | | % 13.36/2.74 | | | | | GROUND_INST: instantiating (9) with all_10_0, all_41_0, all_10_1, % 13.36/2.74 | | | | | all_10_2, simplifying with (17), (57) gives: % 13.36/2.74 | | | | | (69) all_41_0 = all_10_0 % 13.36/2.74 | | | | | % 13.36/2.74 | | | | | REDUCE: (45), (69) imply: % 13.36/2.74 | | | | | (70) $i(all_10_0) % 13.36/2.74 | | | | | % 13.36/2.74 | | | | | REDUCE: (68), (69) imply: % 13.36/2.74 | | | | | (71) increases(all_10_0) % 13.36/2.74 | | | | | % 13.36/2.74 | | | | | GROUND_INST: instantiating (mp_increase_not_decrease) with all_10_0, % 13.36/2.74 | | | | | simplifying with (14), (70), (71) gives: % 13.36/2.74 | | | | | (72) $false % 13.36/2.74 | | | | | % 13.36/2.74 | | | | | CLOSE: (72) is inconsistent. % 13.36/2.74 | | | | | % 13.36/2.74 | | | | End of split % 13.36/2.74 | | | | % 13.36/2.75 | | | End of split % 13.36/2.75 | | | % 13.36/2.75 | | End of split % 13.36/2.75 | | % 13.36/2.75 | Case 2: % 13.36/2.75 | | % 13.36/2.75 | | (73) ~ decreases(all_20_0) % 13.36/2.75 | | % 13.36/2.75 | | REDUCE: (35), (73) imply: % 13.36/2.75 | | (74) ~ decreases(all_10_0) % 13.36/2.75 | | % 13.36/2.75 | | PRED_UNIFY: (14), (74) imply: % 13.36/2.75 | | (75) $false % 13.36/2.75 | | % 13.36/2.75 | | CLOSE: (75) is inconsistent. % 13.36/2.75 | | % 13.36/2.75 | End of split % 13.36/2.75 | % 13.36/2.75 End of proof % 13.36/2.75 % SZS output end Proof for theBenchmark % 13.36/2.75 % 13.36/2.75 2014ms %------------------------------------------------------------------------------