%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT022+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 : n011.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 06:17:21 AM UTC 2026 % Result : Theorem 6.35s 1.67s % Output : Proof 9.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT022+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.36 % Computer : n011.cluster.edu % 0.11/0.36 % Model : x86_64 x86_64 % 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.36 % Memory : 8046.5625MB % 0.11/0.36 % OS : Linux 6.8.0-71-generic % 0.11/0.36 % CPULimit : 300 % 0.11/0.36 % WCLimit : 300 % 0.11/0.36 % DateTime : Mon Sep 7 12:04:00 UTC 2026 % 0.11/0.36 % CPUTime : % 0.14/0.38 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. % 0.71/0.72 ________ _____ % 0.71/0.72 ___ __ \_________(_)________________________________ % 0.71/0.72 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.71/0.72 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.71/0.72 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.71/0.72 % 0.71/0.72 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.71/0.72 (2023-06-19) % 0.71/0.72 % 0.71/0.72 (c) Philipp Rümmer, 2009-2023 % 0.71/0.72 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.71/0.72 Amanda Stjerna. % 0.71/0.72 Free software under BSD-3-Clause. % 0.71/0.72 % 0.71/0.72 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.71/0.72 % 0.71/0.72 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.71/0.74 Running up to 7 provers in parallel. % 0.71/0.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.71/0.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.71/0.75 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.71/0.75 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.71/0.75 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.71/0.75 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.71/0.75 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.02/1.10 Prover 4: Preprocessing ... % 2.02/1.10 Prover 1: Preprocessing ... % 2.79/1.17 Prover 6: Preprocessing ... % 2.79/1.18 Prover 2: Preprocessing ... % 2.79/1.18 Prover 0: Preprocessing ... % 2.79/1.18 Prover 5: Preprocessing ... % 2.79/1.18 Prover 3: Preprocessing ... % 4.81/1.42 Prover 1: Constructing countermodel ... % 4.81/1.42 Prover 5: Constructing countermodel ... % 4.81/1.42 Prover 6: Constructing countermodel ... % 4.81/1.43 Prover 3: Constructing countermodel ... % 4.81/1.43 Prover 4: Constructing countermodel ... % 4.81/1.44 Prover 2: Proving ... % 4.81/1.47 Prover 0: Proving ... % 6.35/1.67 Prover 3: proved (917ms) % 6.35/1.67 % 6.35/1.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.35/1.67 % 6.35/1.68 Prover 6: stopped % 6.35/1.68 Prover 5: stopped % 6.35/1.68 Prover 2: stopped % 6.35/1.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.35/1.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.35/1.68 Prover 0: proved (927ms) % 6.35/1.68 % 6.35/1.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.35/1.68 % 6.35/1.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.35/1.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.35/1.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.14/1.73 Prover 8: Preprocessing ... % 7.14/1.73 Prover 11: Preprocessing ... % 7.14/1.74 Prover 7: Preprocessing ... % 7.14/1.74 Prover 10: Preprocessing ... % 7.14/1.75 Prover 13: Preprocessing ... % 7.91/1.80 Prover 13: Constructing countermodel ... % 7.91/1.82 Prover 8: Warning: ignoring some quantifiers % 7.91/1.83 Prover 10: Constructing countermodel ... % 7.91/1.83 Prover 8: Constructing countermodel ... % 7.91/1.84 Prover 7: Constructing countermodel ... % 7.91/1.87 Prover 1: Found proof (size 58) % 7.91/1.87 Prover 1: proved (1119ms) % 7.91/1.87 Prover 7: stopped % 7.91/1.87 Prover 10: stopped % 7.91/1.87 Prover 8: stopped % 7.91/1.87 Prover 13: stopped % 7.91/1.88 Prover 4: Found proof (size 65) % 7.91/1.88 Prover 4: proved (1125ms) % 7.91/1.88 Prover 11: Constructing countermodel ... % 7.91/1.89 Prover 11: stopped % 7.91/1.89 % 7.91/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.91/1.89 % 8.64/1.92 % SZS output start Proof for theBenchmark % 8.64/1.92 Assumptions after simplification: % 8.64/1.92 --------------------------------- % 8.64/1.92 % 8.64/1.92 (a2) % 8.64/1.97 $i(first_movers) & $i(efficient_producers) & ? [v0: $i] : ? [v1: $i] : % 8.64/1.97 (resilience(first_movers) = v1 & resilience(efficient_producers) = v0 & % 8.64/1.97 greater(v0, v1) = 0 & $i(v1) & $i(v0)) % 8.64/1.97 % 8.64/1.97 (a5) % 8.64/1.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 8.64/1.99 $i] : ! [v6: $i] : ( ~ (resilience(v2) = v4) | ~ (resilience(v1) = v5) | % 8.64/1.99 ~ (greater(v4, v5) = 0) | ~ (resources(v0, v3) = v6) | ~ $i(v3) | ~ % 8.64/1.99 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : ? [v9: any] % 8.64/1.99 : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: any] : ? [v14: any] % 8.64/1.99 : ? [v15: any] : (environment(v0) = v7 & subpopulations(v1, v2, v0, v3) = % 8.64/1.99 v8 & disbanding_rate(v2, v3) = v11 & disbanding_rate(v1, v3) = v10 & % 8.64/1.99 difference(v10, v11) = v12 & increases(v12) = v13 & decreases(v6) = v9 & % 8.64/1.99 constant(v12) = v15 & constant(v6) = v14 & $i(v12) & $i(v11) & $i(v10) & ( % 8.64/1.99 ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v14 = 0) | v15 = 0) & ( ~ (v9 = 0) | % 8.64/1.99 v13 = 0))))) % 8.64/1.99 % 8.64/1.99 (mp_constant_not_decrease) % 8.64/1.99 ! [v0: $i] : ( ~ (decreases(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 8.64/1.99 0) & constant(v0) = v1)) % 8.64/1.99 % 8.64/1.99 (prove_l4) % 8.64/2.00 $i(first_movers) & $i(efficient_producers) & ? [v0: $i] : ? [v1: $i] : ? % 8.64/2.00 [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 8.64/2.00 any] : ? [v8: any] : ? [v9: any] : (resources(v0, v1) = v2 & % 8.64/2.00 environment(v0) = 0 & subpopulations(first_movers, efficient_producers, v0, % 8.64/2.00 v1) = 0 & disbanding_rate(first_movers, v1) = v4 & % 8.64/2.00 disbanding_rate(efficient_producers, v1) = v5 & difference(v4, v5) = v6 & % 8.64/2.00 increases(v6) = v7 & decreases(v6) = v9 & decreases(v2) = v3 & constant(v2) % 8.64/2.00 = v8 & $i(v6) & $i(v5) & $i(v4) & $i(v2) & $i(v1) & $i(v0) & ((v9 = 0 & v8 = % 8.64/2.00 0) | (v3 = 0 & ~ (v7 = 0)))) % 8.64/2.00 % 8.64/2.00 (function-axioms) % 8.64/2.02 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.64/2.02 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (subpopulations(v5, v4, % 8.64/2.02 v3, v2) = v1) | ~ (subpopulations(v5, v4, v3, v2) = v0)) & ! [v0: % 8.64/2.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 8.64/2.02 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: % 8.64/2.02 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (resources(v3, % 8.64/2.02 v2) = v1) | ~ (resources(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 8.64/2.02 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disbanding_rate(v3, v2) = v1) | ~ % 8.64/2.02 (disbanding_rate(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 8.64/2.02 ! [v3: $i] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) % 8.64/2.02 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 8.64/2.02 (resilience(v2) = v1) | ~ (resilience(v2) = v0)) & ! [v0: % 8.64/2.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 8.64/2.02 ~ (environment(v2) = v1) | ~ (environment(v2) = v0)) & ! [v0: % 8.64/2.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 8.64/2.02 ~ (increases(v2) = v1) | ~ (increases(v2) = v0)) & ! [v0: % 8.64/2.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 8.64/2.02 ~ (decreases(v2) = v1) | ~ (decreases(v2) = v0)) & ! [v0: % 8.64/2.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 8.64/2.02 ~ (constant(v2) = v1) | ~ (constant(v2) = v0)) % 8.64/2.02 % 8.64/2.02 Those formulas are unsatisfiable: % 8.64/2.02 --------------------------------- % 8.64/2.02 % 8.64/2.02 Begin of proof % 8.64/2.02 | % 8.64/2.03 | ALPHA: (a2) implies: % 9.28/2.03 | (1) ? [v0: $i] : ? [v1: $i] : (resilience(first_movers) = v1 & % 9.28/2.03 | resilience(efficient_producers) = v0 & greater(v0, v1) = 0 & $i(v1) & % 9.28/2.03 | $i(v0)) % 9.28/2.03 | % 9.28/2.03 | ALPHA: (prove_l4) implies: % 9.28/2.03 | (2) $i(efficient_producers) % 9.28/2.03 | (3) $i(first_movers) % 9.28/2.04 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] : % 9.28/2.04 | ? [v5: $i] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : ? [v9: any] : % 9.28/2.04 | (resources(v0, v1) = v2 & environment(v0) = 0 & % 9.28/2.04 | subpopulations(first_movers, efficient_producers, v0, v1) = 0 & % 9.28/2.04 | disbanding_rate(first_movers, v1) = v4 & % 9.28/2.04 | disbanding_rate(efficient_producers, v1) = v5 & difference(v4, v5) = % 9.28/2.04 | v6 & increases(v6) = v7 & decreases(v6) = v9 & decreases(v2) = v3 & % 9.28/2.04 | constant(v2) = v8 & $i(v6) & $i(v5) & $i(v4) & $i(v2) & $i(v1) & % 9.28/2.04 | $i(v0) & ((v9 = 0 & v8 = 0) | (v3 = 0 & ~ (v7 = 0)))) % 9.28/2.04 | % 9.28/2.04 | ALPHA: (function-axioms) implies: % 9.28/2.04 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.28/2.04 | (v1 = v0 | ~ (constant(v2) = v1) | ~ (constant(v2) = v0)) % 9.28/2.04 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.28/2.04 | (v1 = v0 | ~ (decreases(v2) = v1) | ~ (decreases(v2) = v0)) % 9.28/2.04 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.28/2.04 | (v1 = v0 | ~ (increases(v2) = v1) | ~ (increases(v2) = v0)) % 9.28/2.04 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.28/2.04 | (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0)) % 9.28/2.05 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.28/2.05 | (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 9.28/2.05 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.28/2.05 | (disbanding_rate(v3, v2) = v1) | ~ (disbanding_rate(v3, v2) = v0)) % 9.28/2.05 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 9.28/2.05 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 9.28/2.05 | (subpopulations(v5, v4, v3, v2) = v1) | ~ (subpopulations(v5, v4, % 9.28/2.05 | v3, v2) = v0)) % 9.28/2.05 | % 9.28/2.05 | DELTA: instantiating (1) with fresh symbols all_6_0, all_6_1 gives: % 9.28/2.05 | (12) resilience(first_movers) = all_6_0 & resilience(efficient_producers) = % 9.28/2.05 | all_6_1 & greater(all_6_1, all_6_0) = 0 & $i(all_6_0) & $i(all_6_1) % 9.28/2.05 | % 9.28/2.05 | ALPHA: (12) implies: % 9.28/2.05 | (13) greater(all_6_1, all_6_0) = 0 % 9.28/2.05 | (14) resilience(efficient_producers) = all_6_1 % 9.28/2.05 | (15) resilience(first_movers) = all_6_0 % 9.28/2.05 | % 9.28/2.05 | DELTA: instantiating (4) with fresh symbols all_8_0, all_8_1, all_8_2, % 9.28/2.05 | all_8_3, all_8_4, all_8_5, all_8_6, all_8_7, all_8_8, all_8_9 gives: % 9.28/2.06 | (16) resources(all_8_9, all_8_8) = all_8_7 & environment(all_8_9) = 0 & % 9.28/2.06 | subpopulations(first_movers, efficient_producers, all_8_9, all_8_8) = % 9.28/2.06 | 0 & disbanding_rate(first_movers, all_8_8) = all_8_5 & % 9.28/2.06 | disbanding_rate(efficient_producers, all_8_8) = all_8_4 & % 9.28/2.06 | difference(all_8_5, all_8_4) = all_8_3 & increases(all_8_3) = all_8_2 % 9.28/2.06 | & decreases(all_8_3) = all_8_0 & decreases(all_8_7) = all_8_6 & % 9.28/2.06 | constant(all_8_7) = all_8_1 & $i(all_8_3) & $i(all_8_4) & $i(all_8_5) % 9.28/2.06 | & $i(all_8_7) & $i(all_8_8) & $i(all_8_9) & ((all_8_0 = 0 & all_8_1 = % 9.28/2.06 | 0) | (all_8_6 = 0 & ~ (all_8_2 = 0))) % 9.28/2.06 | % 9.28/2.06 | ALPHA: (16) implies: % 9.28/2.06 | (17) $i(all_8_9) % 9.28/2.06 | (18) $i(all_8_8) % 9.28/2.06 | (19) constant(all_8_7) = all_8_1 % 9.28/2.06 | (20) decreases(all_8_7) = all_8_6 % 9.28/2.06 | (21) decreases(all_8_3) = all_8_0 % 9.28/2.06 | (22) increases(all_8_3) = all_8_2 % 9.28/2.06 | (23) difference(all_8_5, all_8_4) = all_8_3 % 9.28/2.06 | (24) disbanding_rate(efficient_producers, all_8_8) = all_8_4 % 9.28/2.06 | (25) disbanding_rate(first_movers, all_8_8) = all_8_5 % 9.28/2.06 | (26) subpopulations(first_movers, efficient_producers, all_8_9, all_8_8) = % 9.28/2.06 | 0 % 9.28/2.06 | (27) environment(all_8_9) = 0 % 9.28/2.06 | (28) resources(all_8_9, all_8_8) = all_8_7 % 9.28/2.06 | (29) (all_8_0 = 0 & all_8_1 = 0) | (all_8_6 = 0 & ~ (all_8_2 = 0)) % 9.28/2.06 | % 9.28/2.07 | GROUND_INST: instantiating (a5) with all_8_9, first_movers, % 9.28/2.07 | efficient_producers, all_8_8, all_6_1, all_6_0, all_8_7, % 9.28/2.07 | simplifying with (2), (3), (13), (14), (15), (17), (18), (28) % 9.28/2.07 | gives: % 9.28/2.07 | (30) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 9.28/2.07 | : ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 9.28/2.07 | (environment(all_8_9) = v0 & subpopulations(first_movers, % 9.28/2.07 | efficient_producers, all_8_9, all_8_8) = v1 & % 9.28/2.07 | disbanding_rate(first_movers, all_8_8) = v3 & % 9.28/2.07 | disbanding_rate(efficient_producers, all_8_8) = v4 & difference(v3, % 9.28/2.07 | v4) = v5 & increases(v5) = v6 & decreases(all_8_7) = v2 & % 9.28/2.07 | constant(v5) = v8 & constant(all_8_7) = v7 & $i(v5) & $i(v4) & % 9.28/2.07 | $i(v3) & ( ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v7 = 0) | v8 = 0) & ( ~ % 9.28/2.07 | (v2 = 0) | v6 = 0)))) % 9.28/2.07 | % 9.28/2.07 | DELTA: instantiating (30) with fresh symbols all_15_0, all_15_1, all_15_2, % 9.28/2.07 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7, all_15_8 gives: % 9.28/2.07 | (31) environment(all_8_9) = all_15_8 & subpopulations(first_movers, % 9.28/2.07 | efficient_producers, all_8_9, all_8_8) = all_15_7 & % 9.28/2.07 | disbanding_rate(first_movers, all_8_8) = all_15_5 & % 9.28/2.07 | disbanding_rate(efficient_producers, all_8_8) = all_15_4 & % 9.28/2.07 | difference(all_15_5, all_15_4) = all_15_3 & increases(all_15_3) = % 9.28/2.07 | all_15_2 & decreases(all_8_7) = all_15_6 & constant(all_15_3) = % 9.28/2.07 | all_15_0 & constant(all_8_7) = all_15_1 & $i(all_15_3) & $i(all_15_4) % 9.28/2.07 | & $i(all_15_5) & ( ~ (all_15_7 = 0) | ~ (all_15_8 = 0) | (( ~ % 9.28/2.07 | (all_15_1 = 0) | all_15_0 = 0) & ( ~ (all_15_6 = 0) | all_15_2 = % 9.28/2.07 | 0))) % 9.28/2.07 | % 9.28/2.07 | ALPHA: (31) implies: % 9.28/2.07 | (32) $i(all_15_3) % 9.28/2.07 | (33) constant(all_8_7) = all_15_1 % 9.28/2.08 | (34) constant(all_15_3) = all_15_0 % 9.28/2.08 | (35) decreases(all_8_7) = all_15_6 % 9.28/2.08 | (36) increases(all_15_3) = all_15_2 % 9.28/2.08 | (37) difference(all_15_5, all_15_4) = all_15_3 % 9.28/2.08 | (38) disbanding_rate(efficient_producers, all_8_8) = all_15_4 % 9.28/2.08 | (39) disbanding_rate(first_movers, all_8_8) = all_15_5 % 9.28/2.08 | (40) subpopulations(first_movers, efficient_producers, all_8_9, all_8_8) = % 9.28/2.08 | all_15_7 % 9.28/2.08 | (41) environment(all_8_9) = all_15_8 % 9.28/2.08 | (42) ~ (all_15_7 = 0) | ~ (all_15_8 = 0) | (( ~ (all_15_1 = 0) | all_15_0 % 9.28/2.08 | = 0) & ( ~ (all_15_6 = 0) | all_15_2 = 0)) % 9.28/2.08 | % 9.28/2.08 | GROUND_INST: instantiating (5) with all_8_1, all_15_1, all_8_7, simplifying % 9.28/2.08 | with (19), (33) gives: % 9.28/2.08 | (43) all_15_1 = all_8_1 % 9.28/2.08 | % 9.28/2.08 | GROUND_INST: instantiating (6) with all_8_6, all_15_6, all_8_7, simplifying % 9.28/2.08 | with (20), (35) gives: % 9.28/2.08 | (44) all_15_6 = all_8_6 % 9.28/2.08 | % 9.28/2.08 | GROUND_INST: instantiating (10) with all_8_4, all_15_4, all_8_8, % 9.28/2.08 | efficient_producers, simplifying with (24), (38) gives: % 9.28/2.08 | (45) all_15_4 = all_8_4 % 9.28/2.08 | % 9.28/2.08 | GROUND_INST: instantiating (10) with all_8_5, all_15_5, all_8_8, first_movers, % 9.28/2.08 | simplifying with (25), (39) gives: % 9.28/2.08 | (46) all_15_5 = all_8_5 % 9.28/2.08 | % 9.28/2.08 | GROUND_INST: instantiating (11) with 0, all_15_7, all_8_8, all_8_9, % 9.28/2.08 | efficient_producers, first_movers, simplifying with (26), (40) % 9.28/2.08 | gives: % 9.28/2.08 | (47) all_15_7 = 0 % 9.28/2.08 | % 9.28/2.08 | GROUND_INST: instantiating (8) with 0, all_15_8, all_8_9, simplifying with % 9.28/2.08 | (27), (41) gives: % 9.28/2.09 | (48) all_15_8 = 0 % 9.28/2.09 | % 9.28/2.09 | REDUCE: (37), (45), (46) imply: % 9.28/2.09 | (49) difference(all_8_5, all_8_4) = all_15_3 % 9.28/2.09 | % 9.28/2.09 | GROUND_INST: instantiating (9) with all_8_3, all_15_3, all_8_4, all_8_5, % 9.28/2.09 | simplifying with (23), (49) gives: % 9.28/2.09 | (50) all_15_3 = all_8_3 % 9.28/2.09 | % 9.28/2.09 | REDUCE: (36), (50) imply: % 9.28/2.09 | (51) increases(all_8_3) = all_15_2 % 9.28/2.09 | % 9.28/2.09 | REDUCE: (34), (50) imply: % 9.28/2.09 | (52) constant(all_8_3) = all_15_0 % 9.28/2.09 | % 9.28/2.09 | REDUCE: (32), (50) imply: % 9.28/2.09 | (53) $i(all_8_3) % 9.28/2.09 | % 9.28/2.09 | GROUND_INST: instantiating (7) with all_8_2, all_15_2, all_8_3, simplifying % 9.28/2.09 | with (22), (51) gives: % 9.28/2.09 | (54) all_15_2 = all_8_2 % 9.28/2.09 | % 9.28/2.09 | BETA: splitting (29) gives: % 9.28/2.09 | % 9.28/2.09 | Case 1: % 9.28/2.09 | | % 9.28/2.09 | | (55) all_8_0 = 0 & all_8_1 = 0 % 9.28/2.09 | | % 9.28/2.09 | | ALPHA: (55) implies: % 9.28/2.09 | | (56) all_8_1 = 0 % 9.28/2.09 | | (57) all_8_0 = 0 % 9.28/2.09 | | % 9.28/2.09 | | COMBINE_EQS: (43), (56) imply: % 9.28/2.09 | | (58) all_15_1 = 0 % 9.28/2.09 | | % 9.28/2.09 | | REDUCE: (21), (57) imply: % 9.28/2.09 | | (59) decreases(all_8_3) = 0 % 9.28/2.09 | | % 9.28/2.09 | | BETA: splitting (42) gives: % 9.28/2.09 | | % 9.28/2.09 | | Case 1: % 9.28/2.09 | | | % 9.28/2.09 | | | (60) ~ (all_15_7 = 0) % 9.28/2.09 | | | % 9.28/2.09 | | | REDUCE: (47), (60) imply: % 9.28/2.09 | | | (61) $false % 9.28/2.10 | | | % 9.28/2.10 | | | CLOSE: (61) is inconsistent. % 9.28/2.10 | | | % 9.28/2.10 | | Case 2: % 9.28/2.10 | | | % 9.28/2.10 | | | (62) ~ (all_15_8 = 0) | (( ~ (all_15_1 = 0) | all_15_0 = 0) & ( ~ % 9.28/2.10 | | | (all_15_6 = 0) | all_15_2 = 0)) % 9.28/2.10 | | | % 9.28/2.10 | | | BETA: splitting (62) gives: % 9.28/2.10 | | | % 9.28/2.10 | | | Case 1: % 9.28/2.10 | | | | % 9.28/2.10 | | | | (63) ~ (all_15_8 = 0) % 9.28/2.10 | | | | % 9.28/2.10 | | | | REDUCE: (48), (63) imply: % 9.28/2.10 | | | | (64) $false % 9.28/2.10 | | | | % 9.28/2.10 | | | | CLOSE: (64) is inconsistent. % 9.28/2.10 | | | | % 9.28/2.10 | | | Case 2: % 9.28/2.10 | | | | % 9.28/2.10 | | | | (65) ( ~ (all_15_1 = 0) | all_15_0 = 0) & ( ~ (all_15_6 = 0) | % 9.28/2.10 | | | | all_15_2 = 0) % 9.28/2.10 | | | | % 9.28/2.10 | | | | ALPHA: (65) implies: % 9.28/2.10 | | | | (66) ~ (all_15_1 = 0) | all_15_0 = 0 % 9.28/2.10 | | | | % 9.28/2.10 | | | | BETA: splitting (66) gives: % 9.28/2.10 | | | | % 9.28/2.10 | | | | Case 1: % 9.28/2.10 | | | | | % 9.28/2.10 | | | | | (67) ~ (all_15_1 = 0) % 9.28/2.10 | | | | | % 9.28/2.10 | | | | | REDUCE: (58), (67) imply: % 9.28/2.10 | | | | | (68) $false % 9.28/2.10 | | | | | % 9.28/2.10 | | | | | CLOSE: (68) is inconsistent. % 9.28/2.10 | | | | | % 9.28/2.10 | | | | Case 2: % 9.28/2.10 | | | | | % 9.28/2.10 | | | | | (69) all_15_0 = 0 % 9.28/2.10 | | | | | % 9.28/2.10 | | | | | REDUCE: (52), (69) imply: % 9.28/2.10 | | | | | (70) constant(all_8_3) = 0 % 9.28/2.10 | | | | | % 9.28/2.10 | | | | | GROUND_INST: instantiating (mp_constant_not_decrease) with all_8_3, % 9.28/2.10 | | | | | simplifying with (53), (59) gives: % 9.28/2.10 | | | | | (71) ? [v0: int] : ( ~ (v0 = 0) & constant(all_8_3) = v0) % 9.28/2.10 | | | | | % 9.28/2.10 | | | | | DELTA: instantiating (71) with fresh symbol all_53_0 gives: % 9.28/2.10 | | | | | (72) ~ (all_53_0 = 0) & constant(all_8_3) = all_53_0 % 9.28/2.10 | | | | | % 9.28/2.10 | | | | | ALPHA: (72) implies: % 9.28/2.10 | | | | | (73) ~ (all_53_0 = 0) % 9.28/2.10 | | | | | (74) constant(all_8_3) = all_53_0 % 9.28/2.10 | | | | | % 9.28/2.10 | | | | | GROUND_INST: instantiating (5) with 0, all_53_0, all_8_3, simplifying % 9.28/2.10 | | | | | with (70), (74) gives: % 9.28/2.11 | | | | | (75) all_53_0 = 0 % 9.28/2.11 | | | | | % 9.28/2.11 | | | | | REDUCE: (73), (75) imply: % 9.28/2.11 | | | | | (76) $false % 9.28/2.11 | | | | | % 9.28/2.11 | | | | | CLOSE: (76) is inconsistent. % 9.28/2.11 | | | | | % 9.28/2.11 | | | | End of split % 9.28/2.11 | | | | % 9.28/2.11 | | | End of split % 9.28/2.11 | | | % 9.28/2.11 | | End of split % 9.28/2.11 | | % 9.28/2.11 | Case 2: % 9.28/2.11 | | % 9.28/2.11 | | (77) all_8_6 = 0 & ~ (all_8_2 = 0) % 9.28/2.11 | | % 9.28/2.11 | | ALPHA: (77) implies: % 9.28/2.11 | | (78) all_8_6 = 0 % 9.28/2.11 | | (79) ~ (all_8_2 = 0) % 9.28/2.11 | | % 9.28/2.11 | | COMBINE_EQS: (44), (78) imply: % 9.28/2.11 | | (80) all_15_6 = 0 % 9.28/2.11 | | % 9.28/2.11 | | BETA: splitting (42) gives: % 9.28/2.11 | | % 9.28/2.11 | | Case 1: % 9.28/2.11 | | | % 9.28/2.11 | | | (81) ~ (all_15_7 = 0) % 9.28/2.11 | | | % 9.28/2.11 | | | REDUCE: (47), (81) imply: % 9.28/2.11 | | | (82) $false % 9.28/2.11 | | | % 9.28/2.11 | | | CLOSE: (82) is inconsistent. % 9.28/2.11 | | | % 9.28/2.11 | | Case 2: % 9.28/2.11 | | | % 9.28/2.11 | | | (83) ~ (all_15_8 = 0) | (( ~ (all_15_1 = 0) | all_15_0 = 0) & ( ~ % 9.28/2.11 | | | (all_15_6 = 0) | all_15_2 = 0)) % 9.28/2.11 | | | % 9.28/2.11 | | | BETA: splitting (83) gives: % 9.28/2.11 | | | % 9.28/2.11 | | | Case 1: % 9.28/2.11 | | | | % 9.28/2.11 | | | | (84) ~ (all_15_8 = 0) % 9.28/2.11 | | | | % 9.28/2.11 | | | | REDUCE: (48), (84) imply: % 9.28/2.11 | | | | (85) $false % 9.28/2.11 | | | | % 9.28/2.11 | | | | CLOSE: (85) is inconsistent. % 9.28/2.11 | | | | % 9.28/2.11 | | | Case 2: % 9.28/2.11 | | | | % 9.28/2.11 | | | | (86) ( ~ (all_15_1 = 0) | all_15_0 = 0) & ( ~ (all_15_6 = 0) | % 9.28/2.11 | | | | all_15_2 = 0) % 9.28/2.11 | | | | % 9.28/2.11 | | | | ALPHA: (86) implies: % 9.28/2.11 | | | | (87) ~ (all_15_6 = 0) | all_15_2 = 0 % 9.28/2.11 | | | | % 9.28/2.11 | | | | BETA: splitting (87) gives: % 9.28/2.11 | | | | % 9.28/2.11 | | | | Case 1: % 9.28/2.11 | | | | | % 9.28/2.11 | | | | | (88) ~ (all_15_6 = 0) % 9.28/2.11 | | | | | % 9.28/2.11 | | | | | REDUCE: (80), (88) imply: % 9.28/2.11 | | | | | (89) $false % 9.28/2.11 | | | | | % 9.28/2.11 | | | | | CLOSE: (89) is inconsistent. % 9.28/2.11 | | | | | % 9.28/2.11 | | | | Case 2: % 9.28/2.11 | | | | | % 9.28/2.11 | | | | | (90) all_15_2 = 0 % 9.28/2.11 | | | | | % 9.28/2.11 | | | | | COMBINE_EQS: (54), (90) imply: % 9.28/2.11 | | | | | (91) all_8_2 = 0 % 9.28/2.11 | | | | | % 9.28/2.11 | | | | | REDUCE: (79), (91) imply: % 9.28/2.11 | | | | | (92) $false % 9.28/2.11 | | | | | % 9.28/2.11 | | | | | CLOSE: (92) is inconsistent. % 9.28/2.11 | | | | | % 9.28/2.11 | | | | End of split % 9.28/2.11 | | | | % 9.28/2.12 | | | End of split % 9.28/2.12 | | | % 9.28/2.12 | | End of split % 9.28/2.12 | | % 9.28/2.12 | End of split % 9.28/2.12 | % 9.28/2.12 End of proof % 9.28/2.12 % SZS output end Proof for theBenchmark % 9.28/2.12 % 9.28/2.12 1395ms %------------------------------------------------------------------------------