%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT022+2 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n020.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 6.29s 1.62s % Output : Proof 8.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT022+2 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.36 % Computer : n020.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Mon Sep 7 12:06:13 UTC 2026 % 0.10/0.36 % CPUTime : % 0.10/0.38 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/sandbox/benchmark/theBenchmark.p ... % 0.71/0.74 Running up to 7 provers in parallel. % 0.71/0.76 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.71/0.76 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.71/0.76 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.71/0.76 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.71/0.76 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.71/0.76 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.71/0.76 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.88/1.10 Prover 1: Preprocessing ... % 1.88/1.12 Prover 4: Preprocessing ... % 2.66/1.16 Prover 0: Preprocessing ... % 2.66/1.16 Prover 2: Preprocessing ... % 2.66/1.16 Prover 3: Preprocessing ... % 2.66/1.17 Prover 5: Preprocessing ... % 2.66/1.17 Prover 6: Preprocessing ... % 3.98/1.39 Prover 0: Proving ... % 4.72/1.41 Prover 6: Constructing countermodel ... % 4.72/1.41 Prover 3: Constructing countermodel ... % 4.72/1.42 Prover 1: Constructing countermodel ... % 4.72/1.44 Prover 4: Constructing countermodel ... % 4.72/1.44 Prover 5: Constructing countermodel ... % 4.72/1.44 Prover 2: Proving ... % 6.29/1.61 Prover 3: proved (859ms) % 6.29/1.62 % 6.29/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.29/1.62 % 6.29/1.62 Prover 6: stopped % 6.29/1.62 Prover 5: stopped % 6.29/1.63 Prover 2: stopped % 6.29/1.63 Prover 0: stopped % 6.29/1.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.29/1.63 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.29/1.63 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.29/1.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.29/1.63 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.29/1.65 Prover 10: Preprocessing ... % 6.29/1.67 Prover 8: Preprocessing ... % 6.29/1.67 Prover 13: Preprocessing ... % 6.29/1.68 Prover 7: Preprocessing ... % 6.29/1.69 Prover 10: Constructing countermodel ... % 6.29/1.70 Prover 11: Preprocessing ... % 7.07/1.76 Prover 8: Warning: ignoring some quantifiers % 7.07/1.78 Prover 8: Constructing countermodel ... % 7.07/1.79 Prover 11: Constructing countermodel ... % 7.07/1.79 Prover 13: Constructing countermodel ... % 7.07/1.79 Prover 7: Constructing countermodel ... % 7.07/1.80 Prover 10: Found proof (size 31) % 7.07/1.80 Prover 10: proved (172ms) % 7.87/1.80 Prover 4: stopped % 7.87/1.80 Prover 13: stopped % 7.87/1.80 Prover 8: stopped % 7.87/1.80 Prover 11: stopped % 7.87/1.80 Prover 7: stopped % 7.87/1.80 Prover 1: Found proof (size 58) % 7.87/1.80 Prover 1: proved (1053ms) % 7.87/1.80 % 7.87/1.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.87/1.81 % 7.87/1.82 % SZS output start Proof for theBenchmark % 7.87/1.82 Assumptions after simplification: % 7.87/1.82 --------------------------------- % 7.87/1.82 % 7.87/1.82 (a2) % 7.87/1.87 $i(first_movers) & $i(efficient_producers) & ? [v0: $i] : ? [v1: $i] : % 7.87/1.87 (resilience(first_movers) = v1 & resilience(efficient_producers) = v0 & $i(v1) % 7.87/1.88 & $i(v0) & greater(v0, v1)) % 7.87/1.88 % 7.87/1.88 (a6) % 7.87/1.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 7.87/1.89 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (resources(v0, v3) = v4) | ~ % 7.87/1.89 (disbanding_rate(v2, v3) = v6) | ~ (disbanding_rate(v1, v3) = v5) | ~ % 7.87/1.89 (difference(v5, v6) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 7.87/1.89 ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | ~ decreases(v4) | % 7.87/1.89 increases(v7) | ? [v8: $i] : ? [v9: $i] : (resilience(v2) = v8 & % 7.87/1.89 resilience(v1) = v9 & $i(v9) & $i(v8) & ~ greater(v8, v9))) & ! [v0: $i] % 7.87/1.89 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 7.87/1.89 [v6: $i] : ! [v7: $i] : ( ~ (resources(v0, v3) = v4) | ~ % 7.87/1.89 (disbanding_rate(v2, v3) = v6) | ~ (disbanding_rate(v1, v3) = v5) | ~ % 7.87/1.89 (difference(v5, v6) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 7.87/1.89 ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | ~ constant(v4) | % 7.87/1.89 constant(v7) | ? [v8: $i] : ? [v9: $i] : (resilience(v2) = v8 & % 7.87/1.89 resilience(v1) = v9 & $i(v9) & $i(v8) & ~ greater(v8, v9))) % 7.87/1.89 % 7.87/1.90 (mp_constant_not_decrease) % 8.38/1.90 ! [v0: $i] : ( ~ $i(v0) | ~ decreases(v0) | ~ constant(v0)) % 8.38/1.90 % 8.38/1.90 (prove_l4) % 8.38/1.90 $i(first_movers) & $i(efficient_producers) & ? [v0: $i] : ? [v1: $i] : ? % 8.38/1.90 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (resources(v0, v1) = v2 & % 8.38/1.90 disbanding_rate(first_movers, v1) = v3 & % 8.38/1.91 disbanding_rate(efficient_producers, v1) = v4 & difference(v3, v4) = v5 & % 8.38/1.91 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 8.38/1.91 subpopulations(first_movers, efficient_producers, v0, v1) & environment(v0) % 8.38/1.91 & ((decreases(v5) & constant(v2)) | (decreases(v2) & ~ increases(v5)))) % 8.38/1.91 % 8.38/1.91 (function-axioms) % 8.38/1.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.38/1.91 (resources(v3, v2) = v1) | ~ (resources(v3, v2) = v0)) & ! [v0: $i] : ! % 8.38/1.91 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disbanding_rate(v3, v2) % 8.38/1.91 = v1) | ~ (disbanding_rate(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 8.38/1.91 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ % 8.38/1.91 (difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 8.38/1.91 v0 | ~ (resilience(v2) = v1) | ~ (resilience(v2) = v0)) % 8.38/1.91 % 8.38/1.91 Those formulas are unsatisfiable: % 8.38/1.91 --------------------------------- % 8.38/1.91 % 8.38/1.91 Begin of proof % 8.38/1.92 | % 8.38/1.92 | ALPHA: (a6) implies: % 8.38/1.93 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 8.38/1.93 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (resources(v0, v3) = v4) | % 8.38/1.93 | ~ (disbanding_rate(v2, v3) = v6) | ~ (disbanding_rate(v1, v3) = v5) % 8.38/1.93 | | ~ (difference(v5, v6) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 8.38/1.93 | ~ $i(v0) | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | % 8.38/1.93 | ~ constant(v4) | constant(v7) | ? [v8: $i] : ? [v9: $i] : % 8.38/1.93 | (resilience(v2) = v8 & resilience(v1) = v9 & $i(v9) & $i(v8) & ~ % 8.38/1.93 | greater(v8, v9))) % 8.38/1.93 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 8.38/1.93 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (resources(v0, v3) = v4) | % 8.38/1.93 | ~ (disbanding_rate(v2, v3) = v6) | ~ (disbanding_rate(v1, v3) = v5) % 8.38/1.93 | | ~ (difference(v5, v6) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 8.38/1.93 | ~ $i(v0) | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | % 8.38/1.93 | ~ decreases(v4) | increases(v7) | ? [v8: $i] : ? [v9: $i] : % 8.38/1.93 | (resilience(v2) = v8 & resilience(v1) = v9 & $i(v9) & $i(v8) & ~ % 8.38/1.93 | greater(v8, v9))) % 8.38/1.93 | % 8.38/1.94 | ALPHA: (a2) implies: % 8.38/1.94 | (3) ? [v0: $i] : ? [v1: $i] : (resilience(first_movers) = v1 & % 8.38/1.94 | resilience(efficient_producers) = v0 & $i(v1) & $i(v0) & greater(v0, % 8.38/1.94 | v1)) % 8.38/1.94 | % 8.38/1.94 | ALPHA: (prove_l4) implies: % 8.38/1.94 | (4) $i(efficient_producers) % 8.38/1.94 | (5) $i(first_movers) % 8.38/1.94 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 8.38/1.94 | ? [v5: $i] : (resources(v0, v1) = v2 & disbanding_rate(first_movers, % 8.38/1.94 | v1) = v3 & disbanding_rate(efficient_producers, v1) = v4 & % 8.38/1.94 | difference(v3, v4) = v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 8.38/1.94 | & $i(v0) & subpopulations(first_movers, efficient_producers, v0, v1) % 8.38/1.94 | & environment(v0) & ((decreases(v5) & constant(v2)) | (decreases(v2) % 8.38/1.94 | & ~ increases(v5)))) % 8.38/1.94 | % 8.38/1.94 | ALPHA: (function-axioms) implies: % 8.38/1.95 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (resilience(v2) % 8.38/1.95 | = v1) | ~ (resilience(v2) = v0)) % 8.38/1.95 | % 8.38/1.95 | DELTA: instantiating (3) with fresh symbols all_6_0, all_6_1 gives: % 8.38/1.95 | (8) resilience(first_movers) = all_6_0 & resilience(efficient_producers) = % 8.38/1.95 | all_6_1 & $i(all_6_0) & $i(all_6_1) & greater(all_6_1, all_6_0) % 8.38/1.95 | % 8.38/1.95 | ALPHA: (8) implies: % 8.38/1.95 | (9) greater(all_6_1, all_6_0) % 8.38/1.95 | (10) resilience(efficient_producers) = all_6_1 % 8.38/1.95 | (11) resilience(first_movers) = all_6_0 % 8.38/1.95 | % 8.38/1.95 | DELTA: instantiating (6) with fresh symbols all_8_0, all_8_1, all_8_2, % 8.38/1.95 | all_8_3, all_8_4, all_8_5 gives: % 8.38/1.95 | (12) resources(all_8_5, all_8_4) = all_8_3 & disbanding_rate(first_movers, % 8.38/1.95 | all_8_4) = all_8_2 & disbanding_rate(efficient_producers, all_8_4) = % 8.38/1.95 | all_8_1 & difference(all_8_2, all_8_1) = all_8_0 & $i(all_8_0) & % 8.38/1.95 | $i(all_8_1) & $i(all_8_2) & $i(all_8_3) & $i(all_8_4) & $i(all_8_5) & % 8.38/1.95 | subpopulations(first_movers, efficient_producers, all_8_5, all_8_4) & % 8.38/1.95 | environment(all_8_5) & ((decreases(all_8_0) & constant(all_8_3)) | % 8.38/1.95 | (decreases(all_8_3) & ~ increases(all_8_0))) % 8.38/1.95 | % 8.38/1.95 | ALPHA: (12) implies: % 8.38/1.96 | (13) environment(all_8_5) % 8.38/1.96 | (14) subpopulations(first_movers, efficient_producers, all_8_5, all_8_4) % 8.38/1.96 | (15) $i(all_8_5) % 8.38/1.96 | (16) $i(all_8_4) % 8.38/1.96 | (17) $i(all_8_0) % 8.38/1.96 | (18) difference(all_8_2, all_8_1) = all_8_0 % 8.38/1.96 | (19) disbanding_rate(efficient_producers, all_8_4) = all_8_1 % 8.38/1.96 | (20) disbanding_rate(first_movers, all_8_4) = all_8_2 % 8.38/1.96 | (21) resources(all_8_5, all_8_4) = all_8_3 % 8.38/1.96 | (22) (decreases(all_8_0) & constant(all_8_3)) | (decreases(all_8_3) & ~ % 8.38/1.96 | increases(all_8_0)) % 8.38/1.96 | % 8.38/1.96 | BETA: splitting (22) gives: % 8.38/1.96 | % 8.38/1.96 | Case 1: % 8.38/1.96 | | % 8.38/1.96 | | (23) decreases(all_8_0) & constant(all_8_3) % 8.38/1.96 | | % 8.38/1.96 | | ALPHA: (23) implies: % 8.38/1.96 | | (24) constant(all_8_3) % 8.38/1.96 | | (25) decreases(all_8_0) % 8.38/1.96 | | % 8.38/1.96 | | GROUND_INST: instantiating (1) with all_8_5, first_movers, % 8.38/1.97 | | efficient_producers, all_8_4, all_8_3, all_8_2, all_8_1, % 8.38/1.97 | | all_8_0, simplifying with (4), (5), (13), (14), (15), (16), % 8.38/1.97 | | (18), (19), (20), (21), (24) gives: % 8.38/1.97 | | (26) constant(all_8_0) | ? [v0: $i] : ? [v1: $i] : % 8.38/1.97 | | (resilience(first_movers) = v1 & resilience(efficient_producers) = % 8.38/1.97 | | v0 & $i(v1) & $i(v0) & ~ greater(v0, v1)) % 8.38/1.97 | | % 8.38/1.97 | | BETA: splitting (26) gives: % 8.38/1.97 | | % 8.38/1.97 | | Case 1: % 8.38/1.97 | | | % 8.38/1.97 | | | (27) constant(all_8_0) % 8.38/1.97 | | | % 8.38/1.97 | | | GROUND_INST: instantiating (mp_constant_not_decrease) with all_8_0, % 8.38/1.97 | | | simplifying with (17), (25), (27) gives: % 8.38/1.97 | | | (28) $false % 8.38/1.97 | | | % 8.38/1.97 | | | CLOSE: (28) is inconsistent. % 8.38/1.97 | | | % 8.38/1.97 | | Case 2: % 8.38/1.97 | | | % 8.38/1.97 | | | (29) ? [v0: $i] : ? [v1: $i] : (resilience(first_movers) = v1 & % 8.38/1.97 | | | resilience(efficient_producers) = v0 & $i(v1) & $i(v0) & ~ % 8.38/1.97 | | | greater(v0, v1)) % 8.38/1.97 | | | % 8.38/1.97 | | | DELTA: instantiating (29) with fresh symbols all_24_0, all_24_1 gives: % 8.38/1.97 | | | (30) resilience(first_movers) = all_24_0 & % 8.38/1.97 | | | resilience(efficient_producers) = all_24_1 & $i(all_24_0) & % 8.38/1.97 | | | $i(all_24_1) & ~ greater(all_24_1, all_24_0) % 8.38/1.97 | | | % 8.38/1.97 | | | REF_CLOSE: (7), (9), (10), (11), (30) are inconsistent by sub-proof #1. % 8.38/1.97 | | | % 8.38/1.97 | | End of split % 8.38/1.97 | | % 8.38/1.97 | Case 2: % 8.38/1.97 | | % 8.38/1.98 | | (31) decreases(all_8_3) & ~ increases(all_8_0) % 8.38/1.98 | | % 8.38/1.98 | | ALPHA: (31) implies: % 8.38/1.98 | | (32) ~ increases(all_8_0) % 8.38/1.98 | | (33) decreases(all_8_3) % 8.38/1.98 | | % 8.38/1.98 | | GROUND_INST: instantiating (2) with all_8_5, first_movers, % 8.38/1.98 | | efficient_producers, all_8_4, all_8_3, all_8_2, all_8_1, % 8.38/1.98 | | all_8_0, simplifying with (4), (5), (13), (14), (15), (16), % 8.38/1.98 | | (18), (19), (20), (21), (32), (33) gives: % 8.38/1.98 | | (34) ? [v0: $i] : ? [v1: $i] : (resilience(first_movers) = v1 & % 8.38/1.98 | | resilience(efficient_producers) = v0 & $i(v1) & $i(v0) & ~ % 8.38/1.98 | | greater(v0, v1)) % 8.38/1.98 | | % 8.38/1.98 | | DELTA: instantiating (34) with fresh symbols all_24_0, all_24_1 gives: % 8.38/1.98 | | (35) resilience(first_movers) = all_24_0 & % 8.38/1.98 | | resilience(efficient_producers) = all_24_1 & $i(all_24_0) & % 8.38/1.98 | | $i(all_24_1) & ~ greater(all_24_1, all_24_0) % 8.38/1.98 | | % 8.38/1.98 | | REF_CLOSE: (7), (9), (10), (11), (35) are inconsistent by sub-proof #1. % 8.38/1.98 | | % 8.38/1.98 | End of split % 8.38/1.98 | % 8.38/1.98 End of proof % 8.38/1.98 % 8.38/1.98 Sub-proof #1 shows that the following formulas are inconsistent: % 8.38/1.98 ---------------------------------------------------------------- % 8.38/1.98 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (resilience(v2) = % 8.38/1.98 v1) | ~ (resilience(v2) = v0)) % 8.38/1.99 (2) resilience(efficient_producers) = all_6_1 % 8.38/1.99 (3) resilience(first_movers) = all_24_0 & resilience(efficient_producers) = % 8.38/1.99 all_24_1 & $i(all_24_0) & $i(all_24_1) & ~ greater(all_24_1, all_24_0) % 8.38/1.99 (4) resilience(first_movers) = all_6_0 % 8.38/1.99 (5) greater(all_6_1, all_6_0) % 8.38/1.99 % 8.38/1.99 Begin of proof % 8.38/1.99 | % 8.38/1.99 | ALPHA: (3) implies: % 8.38/1.99 | (6) ~ greater(all_24_1, all_24_0) % 8.38/1.99 | (7) resilience(efficient_producers) = all_24_1 % 8.38/1.99 | (8) resilience(first_movers) = all_24_0 % 8.38/1.99 | % 8.38/1.99 | GROUND_INST: instantiating (1) with all_6_1, all_24_1, efficient_producers, % 8.38/1.99 | simplifying with (2), (7) gives: % 8.38/1.99 | (9) all_24_1 = all_6_1 % 8.38/1.99 | % 8.38/1.99 | GROUND_INST: instantiating (1) with all_6_0, all_24_0, first_movers, % 8.38/1.99 | simplifying with (4), (8) gives: % 8.38/1.99 | (10) all_24_0 = all_6_0 % 8.38/1.99 | % 8.38/1.99 | REDUCE: (6), (9), (10) imply: % 8.38/1.99 | (11) ~ greater(all_6_1, all_6_0) % 8.38/1.99 | % 8.38/1.99 | PRED_UNIFY: (5), (11) imply: % 8.38/1.99 | (12) $false % 8.38/1.99 | % 8.38/1.99 | CLOSE: (12) is inconsistent. % 8.38/1.99 | % 8.38/1.99 End of proof % 8.38/1.99 % SZS output end Proof for theBenchmark % 8.38/1.99 % 8.38/1.99 1270ms %------------------------------------------------------------------------------