%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT024+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 : n014.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 8.88s 1.99s % Output : Proof 15.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT024+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.36 % Computer : n014.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % 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 12:08:41 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. % 0.72/0.71 ________ _____ % 0.72/0.71 ___ __ \_________(_)________________________________ % 0.72/0.71 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.72/0.71 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.72/0.71 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.72/0.71 % 0.72/0.71 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.72/0.71 (2023-06-19) % 0.72/0.71 % 0.72/0.71 (c) Philipp Rümmer, 2009-2023 % 0.72/0.71 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.72/0.71 Amanda Stjerna. % 0.72/0.71 Free software under BSD-3-Clause. % 0.72/0.71 % 0.72/0.71 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.72/0.71 % 0.72/0.71 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.72/0.73 Running up to 7 provers in parallel. % 0.72/0.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.72/0.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.72/0.75 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.72/0.75 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.72/0.75 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.72/0.75 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.72/0.75 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.39/1.20 Prover 4: Preprocessing ... % 3.39/1.21 Prover 1: Preprocessing ... % 3.39/1.27 Prover 6: Preprocessing ... % 3.39/1.27 Prover 3: Preprocessing ... % 3.39/1.27 Prover 2: Preprocessing ... % 3.39/1.27 Prover 5: Preprocessing ... % 3.39/1.27 Prover 0: Preprocessing ... % 6.49/1.63 Prover 6: Constructing countermodel ... % 6.49/1.63 Prover 3: Constructing countermodel ... % 6.49/1.63 Prover 1: Constructing countermodel ... % 6.49/1.66 Prover 5: Proving ... % 6.49/1.66 Prover 2: Proving ... % 6.49/1.68 Prover 4: Constructing countermodel ... % 8.07/1.81 Prover 0: Proving ... % 8.88/1.98 Prover 3: proved (1240ms) % 8.88/1.99 % 8.88/1.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.88/1.99 % 8.88/1.99 Prover 6: stopped % 8.88/1.99 Prover 0: stopped % 8.88/1.99 Prover 5: stopped % 8.88/2.00 Prover 2: stopped % 8.88/2.00 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.88/2.00 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.88/2.00 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.88/2.00 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.88/2.00 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.87/2.07 Prover 10: Preprocessing ... % 9.87/2.10 Prover 13: Preprocessing ... % 9.87/2.10 Prover 7: Preprocessing ... % 9.87/2.11 Prover 11: Preprocessing ... % 9.87/2.12 Prover 8: Preprocessing ... % 10.67/2.18 Prover 13: Warning: ignoring some quantifiers % 10.67/2.19 Prover 13: Constructing countermodel ... % 11.17/2.21 Prover 10: Constructing countermodel ... % 11.17/2.24 Prover 7: Constructing countermodel ... % 11.17/2.26 Prover 8: Warning: ignoring some quantifiers % 11.17/2.26 Prover 8: Constructing countermodel ... % 11.97/2.35 Prover 10: gave up % 11.97/2.36 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.97/2.36 Prover 7: gave up % 11.97/2.36 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 11.97/2.39 Prover 16: Preprocessing ... % 12.78/2.41 Prover 19: Preprocessing ... % 12.78/2.43 Prover 16: Warning: ignoring some quantifiers % 12.78/2.43 Prover 16: Constructing countermodel ... % 13.56/2.50 Prover 11: Constructing countermodel ... % 13.56/2.56 Prover 1: Found proof (size 219) % 13.56/2.56 Prover 1: proved (1814ms) % 13.56/2.56 Prover 4: stopped % 13.56/2.56 Prover 16: stopped % 13.56/2.56 Prover 8: stopped % 13.56/2.56 Prover 11: stopped % 13.56/2.56 Prover 13: stopped % 13.56/2.58 Prover 19: Warning: ignoring some quantifiers % 13.56/2.59 Prover 19: Constructing countermodel ... % 14.24/2.61 Prover 19: stopped % 14.24/2.61 % 14.24/2.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.24/2.61 % 14.24/2.66 % SZS output start Proof for theBenchmark % 14.24/2.67 Assumptions after simplification: % 14.24/2.67 --------------------------------- % 14.24/2.67 % 14.24/2.67 (a3) % 14.72/2.72 $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 14.72/2.72 (equilibrium(v0) = v2) | ~ (greater(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | % 14.72/2.72 ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? % 14.72/2.72 [v9: any] : ? [v10: any] : (resources(v0, v1) = v8 & decreases(v8) = v9 & % 14.72/2.72 constant(v8) = v10 & number_of_organizations(v0, v1) = v6 & greater(v6, % 14.72/2.72 zero) = v7 & environment(v0) = v4 & in_environment(v0, v1) = v5 & $i(v8) % 14.72/2.72 & $i(v6) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | (( ~ (v3 = 0) | v9 = % 14.72/2.72 0) & (v10 = 0 | v3 = 0))))) % 14.72/2.72 % 14.72/2.72 (a6) % 14.72/2.73 ! [v0: $i] : ! [v1: $i] : ( ~ (in_environment(v0, v1) = 0) | ~ $i(v1) | ~ % 14.72/2.73 $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: % 14.72/2.73 any] : ? [v7: any] : ? [v8: any] : (resources(v0, v1) = v3 & % 14.72/2.73 decreases(v5) = v6 & decreases(v3) = v4 & constant(v5) = v8 & constant(v3) % 14.72/2.73 = v7 & number_of_organizations(v0, v1) = v5 & environment(v0) = v2 & % 14.72/2.73 $i(v5) & $i(v3) & ( ~ (v2 = 0) | (( ~ (v7 = 0) | v8 = 0) & ( ~ (v6 = 0) | % 14.72/2.73 ~ (v4 = 0)))))) % 14.72/2.73 % 14.72/2.73 (l7) % 14.72/2.74 $i(zero) & $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: % 14.72/2.74 $i] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | % 14.72/2.74 ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: % 14.72/2.74 $i] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10: % 14.72/2.74 any] : (growth_rate(efficient_producers, v1) = v6 & % 14.72/2.74 growth_rate(first_movers, v1) = v5 & constant(v3) = v4 & % 14.72/2.74 number_of_organizations(v0, v1) = v3 & greater(v6, zero) = v9 & % 14.72/2.74 greater(v5, zero) = v7 & greater(zero, v6) = v8 & greater(zero, v5) = v10 % 14.72/2.74 & environment(v0) = v2 & $i(v6) & $i(v5) & $i(v3) & ( ~ (v4 = 0) | ~ (v2 % 14.72/2.74 = 0) | (v10 = 0 & v9 = 0) | (v8 = 0 & v7 = 0) | (v6 = zero & v5 = % 14.72/2.74 zero)))) % 14.72/2.75 % 14.72/2.75 (mp_equilibrium) % 14.72/2.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (equilibrium(v0) = v2) | ~ % 14.72/2.75 (greater_or_equal(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? % 14.72/2.75 [v4: any] : (greater(v2, v1) = v4 & environment(v0) = v3 & ( ~ (v4 = 0) | ~ % 14.72/2.75 (v3 = 0)))) % 14.72/2.75 % 14.72/2.75 (mp_positive_number_of_organizations) % 14.72/2.75 $i(zero) & $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: % 14.72/2.75 $i] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | % 14.72/2.75 ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 14.72/2.75 (number_of_organizations(v0, v1) = v3 & greater(v3, zero) = v4 & % 14.72/2.75 environment(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v4 = 0))) % 14.72/2.75 % 14.72/2.75 (mp_time_point_occur) % 14.72/2.76 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : ( ~ % 14.72/2.76 (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ~ $i(v1) % 14.72/2.76 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (environment(v0) = v2 & % 14.72/2.76 in_environment(v0, v1) = v3 & ( ~ (v2 = 0) | v3 = 0))) % 14.72/2.76 % 14.72/2.76 (prove_l6) % 14.72/2.77 $i(zero) & $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ? [v1: % 14.72/2.77 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: any] : ? [v6: any] % 14.72/2.77 : ? [v7: any] : ? [v8: any] : (growth_rate(efficient_producers, v1) = v4 & % 14.72/2.77 growth_rate(first_movers, v1) = v3 & equilibrium(v0) = v2 & % 14.72/2.77 greater_or_equal(v1, v2) = 0 & greater(v4, zero) = v7 & greater(v3, zero) = % 14.72/2.77 v5 & greater(zero, v4) = v6 & greater(zero, v3) = v8 & % 14.72/2.77 subpopulations(first_movers, efficient_producers, v0, v1) = 0 & % 14.72/2.77 environment(v0) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v8 = % 14.72/2.77 0) | ~ (v7 = 0)) & ( ~ (v6 = 0) | ~ (v5 = 0)) & ( ~ (v4 = zero) | ~ % 14.72/2.77 (v3 = zero))) % 14.72/2.77 % 14.72/2.77 (function-axioms) % 14.72/2.78 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 14.72/2.78 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (subpopulations(v5, v4, % 14.72/2.78 v3, v2) = v1) | ~ (subpopulations(v5, v4, v3, v2) = v0)) & ! [v0: $i] % 14.72/2.78 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (growth_rate(v3, v2) % 14.72/2.78 = v1) | ~ (growth_rate(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 14.72/2.78 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (resources(v3, v2) = v1) | ~ % 14.72/2.78 (resources(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.72/2.78 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.72/2.78 (greater_or_equal(v3, v2) = v1) | ~ (greater_or_equal(v3, v2) = v0)) & ! % 14.72/2.78 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.72/2.78 (number_of_organizations(v3, v2) = v1) | ~ (number_of_organizations(v3, v2) % 14.72/2.78 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.72/2.78 $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, % 14.72/2.78 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 14.72/2.78 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~ % 14.72/2.78 (in_environment(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.72/2.78 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (decreases(v2) = v1) | ~ % 14.72/2.78 (decreases(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.72/2.78 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (constant(v2) = v1) | ~ % 14.72/2.78 (constant(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 14.72/2.78 ~ (equilibrium(v2) = v1) | ~ (equilibrium(v2) = v0)) & ! [v0: % 14.72/2.78 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 14.72/2.78 ~ (environment(v2) = v1) | ~ (environment(v2) = v0)) % 14.72/2.78 % 14.72/2.78 Those formulas are unsatisfiable: % 14.72/2.78 --------------------------------- % 14.72/2.78 % 14.72/2.78 Begin of proof % 14.72/2.78 | % 14.72/2.78 | ALPHA: (mp_time_point_occur) implies: % 14.72/2.79 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subpopulations(first_movers, % 14.72/2.79 | efficient_producers, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 14.72/2.79 | [v2: any] : ? [v3: any] : (environment(v0) = v2 & in_environment(v0, % 14.72/2.79 | v1) = v3 & ( ~ (v2 = 0) | v3 = 0))) % 14.72/2.79 | % 14.72/2.79 | ALPHA: (mp_positive_number_of_organizations) implies: % 14.72/2.79 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (subpopulations(first_movers, % 14.72/2.79 | efficient_producers, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 14.72/2.79 | [v2: any] : ? [v3: $i] : ? [v4: any] : (number_of_organizations(v0, % 14.72/2.79 | v1) = v3 & greater(v3, zero) = v4 & environment(v0) = v2 & $i(v3) % 14.72/2.79 | & ( ~ (v2 = 0) | v4 = 0))) % 14.72/2.79 | % 14.72/2.79 | ALPHA: (a3) implies: % 14.72/2.79 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 14.72/2.79 | (equilibrium(v0) = v2) | ~ (greater(v2, v1) = v3) | ~ $i(v1) | ~ % 14.72/2.79 | $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: any] : % 14.72/2.79 | ? [v8: $i] : ? [v9: any] : ? [v10: any] : (resources(v0, v1) = v8 & % 14.72/2.79 | decreases(v8) = v9 & constant(v8) = v10 & % 14.72/2.79 | number_of_organizations(v0, v1) = v6 & greater(v6, zero) = v7 & % 14.72/2.79 | environment(v0) = v4 & in_environment(v0, v1) = v5 & $i(v8) & % 14.72/2.79 | $i(v6) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | (( ~ (v3 = 0) | % 14.72/2.79 | v9 = 0) & (v10 = 0 | v3 = 0))))) % 14.72/2.79 | % 14.72/2.79 | ALPHA: (l7) implies: % 14.72/2.80 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (subpopulations(first_movers, % 14.72/2.80 | efficient_producers, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 14.72/2.80 | [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : % 14.72/2.80 | ? [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10: any] : % 15.23/2.80 | (growth_rate(efficient_producers, v1) = v6 & % 15.23/2.80 | growth_rate(first_movers, v1) = v5 & constant(v3) = v4 & % 15.23/2.80 | number_of_organizations(v0, v1) = v3 & greater(v6, zero) = v9 & % 15.23/2.80 | greater(v5, zero) = v7 & greater(zero, v6) = v8 & greater(zero, v5) % 15.23/2.80 | = v10 & environment(v0) = v2 & $i(v6) & $i(v5) & $i(v3) & ( ~ (v4 = % 15.23/2.80 | 0) | ~ (v2 = 0) | (v10 = 0 & v9 = 0) | (v8 = 0 & v7 = 0) | (v6 % 15.23/2.80 | = zero & v5 = zero)))) % 15.23/2.80 | % 15.23/2.80 | ALPHA: (prove_l6) implies: % 15.23/2.80 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 15.23/2.80 | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 15.23/2.80 | (growth_rate(efficient_producers, v1) = v4 & growth_rate(first_movers, % 15.23/2.80 | v1) = v3 & equilibrium(v0) = v2 & greater_or_equal(v1, v2) = 0 & % 15.23/2.80 | greater(v4, zero) = v7 & greater(v3, zero) = v5 & greater(zero, v4) = % 15.23/2.80 | v6 & greater(zero, v3) = v8 & subpopulations(first_movers, % 15.23/2.80 | efficient_producers, v0, v1) = 0 & environment(v0) = 0 & $i(v4) & % 15.23/2.80 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v8 = 0) | ~ (v7 = 0)) & ( ~ % 15.23/2.80 | (v6 = 0) | ~ (v5 = 0)) & ( ~ (v4 = zero) | ~ (v3 = zero))) % 15.23/2.80 | % 15.23/2.80 | ALPHA: (function-axioms) implies: % 15.23/2.81 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.23/2.81 | (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0)) % 15.23/2.81 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.23/2.81 | (v1 = v0 | ~ (constant(v2) = v1) | ~ (constant(v2) = v0)) % 15.23/2.81 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.23/2.81 | ! [v3: $i] : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~ % 15.23/2.81 | (in_environment(v3, v2) = v0)) % 15.23/2.81 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.23/2.81 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, % 15.23/2.81 | v2) = v0)) % 15.23/2.81 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.23/2.81 | (number_of_organizations(v3, v2) = v1) | ~ % 15.23/2.81 | (number_of_organizations(v3, v2) = v0)) % 15.23/2.81 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.23/2.81 | (resources(v3, v2) = v1) | ~ (resources(v3, v2) = v0)) % 15.23/2.81 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.23/2.81 | (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) % 15.23/2.81 | % 15.23/2.82 | DELTA: instantiating (5) with fresh symbols all_10_0, all_10_1, all_10_2, % 15.23/2.82 | all_10_3, all_10_4, all_10_5, all_10_6, all_10_7, all_10_8 gives: % 15.23/2.82 | (13) growth_rate(efficient_producers, all_10_7) = all_10_4 & % 15.23/2.82 | growth_rate(first_movers, all_10_7) = all_10_5 & equilibrium(all_10_8) % 15.23/2.82 | = all_10_6 & greater_or_equal(all_10_7, all_10_6) = 0 & % 15.23/2.82 | greater(all_10_4, zero) = all_10_1 & greater(all_10_5, zero) = % 15.23/2.82 | all_10_3 & greater(zero, all_10_4) = all_10_2 & greater(zero, % 15.23/2.82 | all_10_5) = all_10_0 & subpopulations(first_movers, % 15.23/2.82 | efficient_producers, all_10_8, all_10_7) = 0 & environment(all_10_8) % 15.23/2.82 | = 0 & $i(all_10_4) & $i(all_10_5) & $i(all_10_6) & $i(all_10_7) & % 15.23/2.82 | $i(all_10_8) & ( ~ (all_10_0 = 0) | ~ (all_10_1 = 0)) & ( ~ (all_10_2 % 15.23/2.82 | = 0) | ~ (all_10_3 = 0)) & ( ~ (all_10_4 = zero) | ~ (all_10_5 = % 15.23/2.82 | zero)) % 15.23/2.82 | % 15.23/2.82 | ALPHA: (13) implies: % 15.23/2.82 | (14) $i(all_10_8) % 15.23/2.82 | (15) $i(all_10_7) % 15.23/2.82 | (16) environment(all_10_8) = 0 % 15.23/2.82 | (17) subpopulations(first_movers, efficient_producers, all_10_8, all_10_7) % 15.23/2.82 | = 0 % 15.23/2.82 | (18) greater(zero, all_10_5) = all_10_0 % 15.23/2.82 | (19) greater(zero, all_10_4) = all_10_2 % 15.23/2.82 | (20) greater(all_10_5, zero) = all_10_3 % 15.23/2.82 | (21) greater(all_10_4, zero) = all_10_1 % 15.23/2.82 | (22) greater_or_equal(all_10_7, all_10_6) = 0 % 15.23/2.82 | (23) equilibrium(all_10_8) = all_10_6 % 15.23/2.82 | (24) growth_rate(first_movers, all_10_7) = all_10_5 % 15.23/2.83 | (25) growth_rate(efficient_producers, all_10_7) = all_10_4 % 15.23/2.83 | (26) ~ (all_10_4 = zero) | ~ (all_10_5 = zero) % 15.23/2.83 | (27) ~ (all_10_2 = 0) | ~ (all_10_3 = 0) % 15.23/2.83 | (28) ~ (all_10_0 = 0) | ~ (all_10_1 = 0) % 15.23/2.83 | % 15.23/2.83 | GROUND_INST: instantiating (4) with all_10_8, all_10_7, simplifying with (14), % 15.23/2.83 | (15), (17) gives: % 15.23/2.83 | (29) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 15.23/2.83 | : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 15.23/2.83 | (growth_rate(efficient_producers, all_10_7) = v4 & % 15.23/2.83 | growth_rate(first_movers, all_10_7) = v3 & constant(v1) = v2 & % 15.23/2.83 | number_of_organizations(all_10_8, all_10_7) = v1 & greater(v4, zero) % 15.23/2.83 | = v7 & greater(v3, zero) = v5 & greater(zero, v4) = v6 & % 15.23/2.83 | greater(zero, v3) = v8 & environment(all_10_8) = v0 & $i(v4) & % 15.23/2.83 | $i(v3) & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0) | (v8 = 0 & v7 = 0) | % 15.23/2.83 | (v6 = 0 & v5 = 0) | (v4 = zero & v3 = zero))) % 15.23/2.83 | % 15.23/2.83 | GROUND_INST: instantiating (2) with all_10_8, all_10_7, simplifying with (14), % 15.23/2.83 | (15), (17) gives: % 15.23/2.83 | (30) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 15.23/2.83 | (number_of_organizations(all_10_8, all_10_7) = v1 & greater(v1, zero) % 15.23/2.83 | = v2 & environment(all_10_8) = v0 & $i(v1) & ( ~ (v0 = 0) | v2 = 0)) % 15.23/2.83 | % 15.23/2.84 | GROUND_INST: instantiating (1) with all_10_8, all_10_7, simplifying with (14), % 15.23/2.84 | (15), (17) gives: % 15.23/2.84 | (31) ? [v0: any] : ? [v1: any] : (environment(all_10_8) = v0 & % 15.23/2.84 | in_environment(all_10_8, all_10_7) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 15.23/2.84 | % 15.23/2.84 | GROUND_INST: instantiating (mp_equilibrium) with all_10_8, all_10_7, all_10_6, % 15.23/2.84 | simplifying with (14), (15), (22), (23) gives: % 15.23/2.84 | (32) ? [v0: any] : ? [v1: any] : (greater(all_10_6, all_10_7) = v1 & % 15.23/2.84 | environment(all_10_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 15.23/2.84 | % 15.23/2.84 | DELTA: instantiating (32) with fresh symbols all_17_0, all_17_1 gives: % 15.23/2.84 | (33) greater(all_10_6, all_10_7) = all_17_0 & environment(all_10_8) = % 15.23/2.84 | all_17_1 & ( ~ (all_17_0 = 0) | ~ (all_17_1 = 0)) % 15.23/2.84 | % 15.23/2.84 | ALPHA: (33) implies: % 15.23/2.84 | (34) environment(all_10_8) = all_17_1 % 15.23/2.84 | (35) greater(all_10_6, all_10_7) = all_17_0 % 15.23/2.84 | (36) ~ (all_17_0 = 0) | ~ (all_17_1 = 0) % 15.23/2.84 | % 15.23/2.84 | DELTA: instantiating (31) with fresh symbols all_19_0, all_19_1 gives: % 15.23/2.84 | (37) environment(all_10_8) = all_19_1 & in_environment(all_10_8, all_10_7) % 15.23/2.84 | = all_19_0 & ( ~ (all_19_1 = 0) | all_19_0 = 0) % 15.23/2.84 | % 15.23/2.84 | ALPHA: (37) implies: % 15.23/2.84 | (38) in_environment(all_10_8, all_10_7) = all_19_0 % 15.23/2.84 | (39) environment(all_10_8) = all_19_1 % 15.23/2.84 | (40) ~ (all_19_1 = 0) | all_19_0 = 0 % 15.23/2.84 | % 15.23/2.84 | DELTA: instantiating (30) with fresh symbols all_21_0, all_21_1, all_21_2 % 15.23/2.84 | gives: % 15.23/2.84 | (41) number_of_organizations(all_10_8, all_10_7) = all_21_1 & % 15.23/2.84 | greater(all_21_1, zero) = all_21_0 & environment(all_10_8) = all_21_2 % 15.23/2.84 | & $i(all_21_1) & ( ~ (all_21_2 = 0) | all_21_0 = 0) % 15.23/2.84 | % 15.23/2.84 | ALPHA: (41) implies: % 15.23/2.85 | (42) environment(all_10_8) = all_21_2 % 15.23/2.85 | (43) greater(all_21_1, zero) = all_21_0 % 15.23/2.85 | (44) number_of_organizations(all_10_8, all_10_7) = all_21_1 % 15.23/2.85 | (45) ~ (all_21_2 = 0) | all_21_0 = 0 % 15.23/2.85 | % 15.23/2.85 | DELTA: instantiating (29) with fresh symbols all_23_0, all_23_1, all_23_2, % 15.23/2.85 | all_23_3, all_23_4, all_23_5, all_23_6, all_23_7, all_23_8 gives: % 15.23/2.85 | (46) growth_rate(efficient_producers, all_10_7) = all_23_4 & % 15.23/2.85 | growth_rate(first_movers, all_10_7) = all_23_5 & constant(all_23_7) = % 15.23/2.85 | all_23_6 & number_of_organizations(all_10_8, all_10_7) = all_23_7 & % 15.23/2.85 | greater(all_23_4, zero) = all_23_1 & greater(all_23_5, zero) = % 15.23/2.85 | all_23_3 & greater(zero, all_23_4) = all_23_2 & greater(zero, % 15.23/2.85 | all_23_5) = all_23_0 & environment(all_10_8) = all_23_8 & % 15.23/2.85 | $i(all_23_4) & $i(all_23_5) & $i(all_23_7) & ( ~ (all_23_6 = 0) | ~ % 15.23/2.85 | (all_23_8 = 0) | (all_23_0 = 0 & all_23_1 = 0) | (all_23_2 = 0 & % 15.23/2.85 | all_23_3 = 0) | (all_23_4 = zero & all_23_5 = zero)) % 15.23/2.85 | % 15.23/2.85 | ALPHA: (46) implies: % 15.23/2.85 | (47) environment(all_10_8) = all_23_8 % 15.23/2.85 | (48) greater(zero, all_23_5) = all_23_0 % 15.23/2.85 | (49) greater(zero, all_23_4) = all_23_2 % 15.23/2.85 | (50) greater(all_23_5, zero) = all_23_3 % 15.23/2.85 | (51) greater(all_23_4, zero) = all_23_1 % 15.23/2.85 | (52) number_of_organizations(all_10_8, all_10_7) = all_23_7 % 15.23/2.85 | (53) constant(all_23_7) = all_23_6 % 15.23/2.85 | (54) growth_rate(first_movers, all_10_7) = all_23_5 % 15.23/2.85 | (55) growth_rate(efficient_producers, all_10_7) = all_23_4 % 15.23/2.86 | (56) ~ (all_23_6 = 0) | ~ (all_23_8 = 0) | (all_23_0 = 0 & all_23_1 = 0) % 15.23/2.86 | | (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero & all_23_5 = zero) % 15.23/2.86 | % 15.23/2.86 | GROUND_INST: instantiating (6) with 0, all_23_8, all_10_8, simplifying with % 15.23/2.86 | (16), (47) gives: % 15.23/2.86 | (57) all_23_8 = 0 % 15.23/2.86 | % 15.23/2.86 | GROUND_INST: instantiating (6) with all_21_2, all_23_8, all_10_8, simplifying % 15.23/2.86 | with (42), (47) gives: % 15.23/2.86 | (58) all_23_8 = all_21_2 % 15.23/2.86 | % 15.23/2.86 | GROUND_INST: instantiating (6) with all_19_1, all_23_8, all_10_8, simplifying % 15.23/2.86 | with (39), (47) gives: % 15.23/2.86 | (59) all_23_8 = all_19_1 % 15.23/2.86 | % 15.23/2.86 | GROUND_INST: instantiating (6) with all_17_1, all_23_8, all_10_8, simplifying % 15.23/2.86 | with (34), (47) gives: % 15.23/2.86 | (60) all_23_8 = all_17_1 % 15.23/2.86 | % 15.23/2.86 | GROUND_INST: instantiating (10) with all_21_1, all_23_7, all_10_7, all_10_8, % 15.23/2.86 | simplifying with (44), (52) gives: % 15.23/2.86 | (61) all_23_7 = all_21_1 % 15.23/2.86 | % 15.23/2.86 | GROUND_INST: instantiating (12) with all_10_5, all_23_5, all_10_7, % 15.23/2.86 | first_movers, simplifying with (24), (54) gives: % 15.23/2.86 | (62) all_23_5 = all_10_5 % 15.23/2.86 | % 15.23/2.86 | GROUND_INST: instantiating (12) with all_10_4, all_23_4, all_10_7, % 15.23/2.86 | efficient_producers, simplifying with (25), (55) gives: % 15.23/2.86 | (63) all_23_4 = all_10_4 % 15.23/2.86 | % 15.23/2.86 | COMBINE_EQS: (58), (60) imply: % 15.23/2.86 | (64) all_21_2 = all_17_1 % 15.23/2.86 | % 15.23/2.86 | COMBINE_EQS: (58), (59) imply: % 15.23/2.86 | (65) all_21_2 = all_19_1 % 15.23/2.86 | % 15.23/2.86 | COMBINE_EQS: (57), (58) imply: % 15.23/2.86 | (66) all_21_2 = 0 % 15.23/2.86 | % 15.23/2.86 | COMBINE_EQS: (65), (66) imply: % 15.23/2.87 | (67) all_19_1 = 0 % 15.23/2.87 | % 15.23/2.87 | COMBINE_EQS: (64), (65) imply: % 15.23/2.87 | (68) all_19_1 = all_17_1 % 15.23/2.87 | % 15.23/2.87 | COMBINE_EQS: (67), (68) imply: % 15.23/2.87 | (69) all_17_1 = 0 % 15.23/2.87 | % 15.23/2.87 | REDUCE: (53), (61) imply: % 15.23/2.87 | (70) constant(all_21_1) = all_23_6 % 15.23/2.87 | % 15.23/2.87 | REDUCE: (51), (63) imply: % 15.23/2.87 | (71) greater(all_10_4, zero) = all_23_1 % 15.23/2.87 | % 15.23/2.87 | REDUCE: (50), (62) imply: % 15.23/2.87 | (72) greater(all_10_5, zero) = all_23_3 % 15.23/2.87 | % 15.23/2.87 | REDUCE: (49), (63) imply: % 15.23/2.87 | (73) greater(zero, all_10_4) = all_23_2 % 15.23/2.87 | % 15.23/2.87 | REDUCE: (48), (62) imply: % 15.23/2.87 | (74) greater(zero, all_10_5) = all_23_0 % 15.23/2.87 | % 15.23/2.87 | BETA: splitting (36) gives: % 15.23/2.87 | % 15.23/2.87 | Case 1: % 15.23/2.87 | | % 15.23/2.87 | | (75) ~ (all_17_0 = 0) % 15.23/2.87 | | % 15.23/2.87 | | BETA: splitting (40) gives: % 15.23/2.87 | | % 15.23/2.87 | | Case 1: % 15.23/2.87 | | | % 15.23/2.87 | | | (76) ~ (all_19_1 = 0) % 15.23/2.87 | | | % 15.23/2.87 | | | REDUCE: (67), (76) imply: % 15.23/2.87 | | | (77) $false % 15.23/2.87 | | | % 15.23/2.87 | | | CLOSE: (77) is inconsistent. % 15.23/2.87 | | | % 15.23/2.87 | | Case 2: % 15.23/2.87 | | | % 15.23/2.88 | | | (78) all_19_0 = 0 % 15.23/2.88 | | | % 15.23/2.88 | | | REDUCE: (38), (78) imply: % 15.23/2.88 | | | (79) in_environment(all_10_8, all_10_7) = 0 % 15.23/2.88 | | | % 15.23/2.88 | | | BETA: splitting (45) gives: % 15.23/2.88 | | | % 15.23/2.88 | | | Case 1: % 15.23/2.88 | | | | % 15.23/2.88 | | | | (80) ~ (all_21_2 = 0) % 15.23/2.88 | | | | % 15.23/2.88 | | | | REDUCE: (66), (80) imply: % 15.23/2.88 | | | | (81) $false % 15.23/2.88 | | | | % 15.23/2.88 | | | | CLOSE: (81) is inconsistent. % 15.23/2.88 | | | | % 15.23/2.88 | | | Case 2: % 15.23/2.88 | | | | % 15.23/2.88 | | | | (82) all_21_0 = 0 % 15.23/2.88 | | | | % 15.23/2.88 | | | | REDUCE: (43), (82) imply: % 15.23/2.88 | | | | (83) greater(all_21_1, zero) = 0 % 15.23/2.88 | | | | % 15.23/2.88 | | | | GROUND_INST: instantiating (9) with all_10_0, all_23_0, all_10_5, zero, % 15.23/2.88 | | | | simplifying with (18), (74) gives: % 15.23/2.88 | | | | (84) all_23_0 = all_10_0 % 15.23/2.88 | | | | % 15.23/2.88 | | | | GROUND_INST: instantiating (9) with all_10_2, all_23_2, all_10_4, zero, % 15.23/2.88 | | | | simplifying with (19), (73) gives: % 15.23/2.88 | | | | (85) all_23_2 = all_10_2 % 15.23/2.88 | | | | % 15.23/2.88 | | | | GROUND_INST: instantiating (9) with all_10_3, all_23_3, zero, all_10_5, % 15.23/2.88 | | | | simplifying with (20), (72) gives: % 15.23/2.88 | | | | (86) all_23_3 = all_10_3 % 15.23/2.88 | | | | % 15.23/2.88 | | | | GROUND_INST: instantiating (9) with all_10_1, all_23_1, zero, all_10_4, % 15.23/2.88 | | | | simplifying with (21), (71) gives: % 15.23/2.88 | | | | (87) all_23_1 = all_10_1 % 15.23/2.88 | | | | % 15.23/2.88 | | | | GROUND_INST: instantiating (a6) with all_10_8, all_10_7, simplifying % 15.23/2.88 | | | | with (14), (15), (79) gives: % 15.23/2.89 | | | | (88) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? % 15.23/2.89 | | | | [v4: any] : ? [v5: any] : ? [v6: any] : (resources(all_10_8, % 15.23/2.89 | | | | all_10_7) = v1 & decreases(v3) = v4 & decreases(v1) = v2 & % 15.23/2.89 | | | | constant(v3) = v6 & constant(v1) = v5 & % 15.23/2.89 | | | | number_of_organizations(all_10_8, all_10_7) = v3 & % 15.23/2.89 | | | | environment(all_10_8) = v0 & $i(v3) & $i(v1) & ( ~ (v0 = 0) | % 15.23/2.89 | | | | (( ~ (v5 = 0) | v6 = 0) & ( ~ (v4 = 0) | ~ (v2 = 0))))) % 15.23/2.89 | | | | % 15.23/2.89 | | | | GROUND_INST: instantiating (3) with all_10_8, all_10_7, all_10_6, % 15.23/2.89 | | | | all_17_0, simplifying with (14), (15), (23), (35) gives: % 15.23/2.89 | | | | (89) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? % 15.23/2.89 | | | | [v4: $i] : ? [v5: any] : ? [v6: any] : (resources(all_10_8, % 15.23/2.89 | | | | all_10_7) = v4 & decreases(v4) = v5 & constant(v4) = v6 & % 15.23/2.89 | | | | number_of_organizations(all_10_8, all_10_7) = v2 & greater(v2, % 15.23/2.89 | | | | zero) = v3 & environment(all_10_8) = v0 & % 15.23/2.89 | | | | in_environment(all_10_8, all_10_7) = v1 & $i(v4) & $i(v2) & ( % 15.23/2.89 | | | | ~ (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (all_17_0 = 0) % 15.23/2.89 | | | | | v5 = 0) & (v6 = 0 | all_17_0 = 0)))) % 15.23/2.89 | | | | % 15.23/2.89 | | | | DELTA: instantiating (88) with fresh symbols all_50_0, all_50_1, % 15.23/2.89 | | | | all_50_2, all_50_3, all_50_4, all_50_5, all_50_6 gives: % 15.23/2.89 | | | | (90) resources(all_10_8, all_10_7) = all_50_5 & decreases(all_50_3) = % 15.23/2.89 | | | | all_50_2 & decreases(all_50_5) = all_50_4 & constant(all_50_3) = % 15.23/2.89 | | | | all_50_0 & constant(all_50_5) = all_50_1 & % 15.23/2.89 | | | | number_of_organizations(all_10_8, all_10_7) = all_50_3 & % 15.23/2.89 | | | | environment(all_10_8) = all_50_6 & $i(all_50_3) & $i(all_50_5) & % 15.23/2.89 | | | | ( ~ (all_50_6 = 0) | (( ~ (all_50_1 = 0) | all_50_0 = 0) & ( ~ % 15.23/2.89 | | | | (all_50_2 = 0) | ~ (all_50_4 = 0)))) % 15.23/2.89 | | | | % 15.23/2.89 | | | | ALPHA: (90) implies: % 15.23/2.90 | | | | (91) environment(all_10_8) = all_50_6 % 15.23/2.90 | | | | (92) number_of_organizations(all_10_8, all_10_7) = all_50_3 % 15.23/2.90 | | | | (93) constant(all_50_5) = all_50_1 % 15.71/2.90 | | | | (94) constant(all_50_3) = all_50_0 % 15.71/2.90 | | | | (95) resources(all_10_8, all_10_7) = all_50_5 % 15.71/2.90 | | | | (96) ~ (all_50_6 = 0) | (( ~ (all_50_1 = 0) | all_50_0 = 0) & ( ~ % 15.71/2.90 | | | | (all_50_2 = 0) | ~ (all_50_4 = 0))) % 15.71/2.90 | | | | % 15.71/2.90 | | | | DELTA: instantiating (89) with fresh symbols all_52_0, all_52_1, % 15.71/2.90 | | | | all_52_2, all_52_3, all_52_4, all_52_5, all_52_6 gives: % 15.71/2.90 | | | | (97) resources(all_10_8, all_10_7) = all_52_2 & decreases(all_52_2) = % 15.71/2.90 | | | | all_52_1 & constant(all_52_2) = all_52_0 & % 15.71/2.90 | | | | number_of_organizations(all_10_8, all_10_7) = all_52_4 & % 15.71/2.90 | | | | greater(all_52_4, zero) = all_52_3 & environment(all_10_8) = % 15.71/2.90 | | | | all_52_6 & in_environment(all_10_8, all_10_7) = all_52_5 & % 15.71/2.90 | | | | $i(all_52_2) & $i(all_52_4) & ( ~ (all_52_3 = 0) | ~ (all_52_5 % 15.71/2.90 | | | | = 0) | ~ (all_52_6 = 0) | (( ~ (all_17_0 = 0) | all_52_1 = % 15.71/2.90 | | | | 0) & (all_52_0 = 0 | all_17_0 = 0))) % 15.71/2.90 | | | | % 15.71/2.90 | | | | ALPHA: (97) implies: % 15.71/2.90 | | | | (98) in_environment(all_10_8, all_10_7) = all_52_5 % 15.71/2.90 | | | | (99) environment(all_10_8) = all_52_6 % 15.71/2.90 | | | | (100) greater(all_52_4, zero) = all_52_3 % 15.71/2.90 | | | | (101) number_of_organizations(all_10_8, all_10_7) = all_52_4 % 15.71/2.90 | | | | (102) constant(all_52_2) = all_52_0 % 15.71/2.90 | | | | (103) resources(all_10_8, all_10_7) = all_52_2 % 15.71/2.90 | | | | (104) ~ (all_52_3 = 0) | ~ (all_52_5 = 0) | ~ (all_52_6 = 0) | (( % 15.71/2.90 | | | | ~ (all_17_0 = 0) | all_52_1 = 0) & (all_52_0 = 0 | all_17_0 % 15.71/2.90 | | | | = 0)) % 15.71/2.90 | | | | % 15.71/2.90 | | | | GROUND_INST: instantiating (8) with 0, all_52_5, all_10_7, all_10_8, % 15.71/2.90 | | | | simplifying with (79), (98) gives: % 15.71/2.91 | | | | (105) all_52_5 = 0 % 15.71/2.91 | | | | % 15.71/2.91 | | | | GROUND_INST: instantiating (6) with 0, all_52_6, all_10_8, simplifying % 15.71/2.91 | | | | with (16), (99) gives: % 15.71/2.91 | | | | (106) all_52_6 = 0 % 15.71/2.91 | | | | % 15.71/2.91 | | | | GROUND_INST: instantiating (6) with all_50_6, all_52_6, all_10_8, % 15.71/2.91 | | | | simplifying with (91), (99) gives: % 15.71/2.91 | | | | (107) all_52_6 = all_50_6 % 15.71/2.91 | | | | % 15.71/2.91 | | | | GROUND_INST: instantiating (10) with all_21_1, all_52_4, all_10_7, % 15.71/2.91 | | | | all_10_8, simplifying with (44), (101) gives: % 15.71/2.91 | | | | (108) all_52_4 = all_21_1 % 15.71/2.91 | | | | % 15.71/2.91 | | | | GROUND_INST: instantiating (10) with all_50_3, all_52_4, all_10_7, % 15.71/2.91 | | | | all_10_8, simplifying with (92), (101) gives: % 15.71/2.91 | | | | (109) all_52_4 = all_50_3 % 15.71/2.91 | | | | % 15.71/2.91 | | | | GROUND_INST: instantiating (11) with all_50_5, all_52_2, all_10_7, % 15.71/2.91 | | | | all_10_8, simplifying with (95), (103) gives: % 15.71/2.91 | | | | (110) all_52_2 = all_50_5 % 15.71/2.91 | | | | % 15.71/2.91 | | | | COMBINE_EQS: (108), (109) imply: % 15.71/2.91 | | | | (111) all_50_3 = all_21_1 % 15.71/2.91 | | | | % 15.71/2.91 | | | | SIMP: (111) implies: % 15.71/2.91 | | | | (112) all_50_3 = all_21_1 % 15.71/2.91 | | | | % 15.71/2.91 | | | | COMBINE_EQS: (106), (107) imply: % 15.71/2.91 | | | | (113) all_50_6 = 0 % 15.71/2.91 | | | | % 15.71/2.91 | | | | SIMP: (113) implies: % 15.71/2.91 | | | | (114) all_50_6 = 0 % 15.71/2.91 | | | | % 15.71/2.91 | | | | REDUCE: (102), (110) imply: % 15.71/2.91 | | | | (115) constant(all_50_5) = all_52_0 % 15.71/2.91 | | | | % 15.71/2.91 | | | | REDUCE: (94), (112) imply: % 15.71/2.91 | | | | (116) constant(all_21_1) = all_50_0 % 15.71/2.91 | | | | % 15.71/2.91 | | | | REDUCE: (100), (108) imply: % 15.71/2.91 | | | | (117) greater(all_21_1, zero) = all_52_3 % 15.71/2.91 | | | | % 15.71/2.91 | | | | GROUND_INST: instantiating (9) with 0, all_52_3, zero, all_21_1, % 15.71/2.91 | | | | simplifying with (83), (117) gives: % 15.71/2.91 | | | | (118) all_52_3 = 0 % 15.71/2.91 | | | | % 15.71/2.92 | | | | GROUND_INST: instantiating (7) with all_23_6, all_50_0, all_21_1, % 15.71/2.92 | | | | simplifying with (70), (116) gives: % 15.71/2.92 | | | | (119) all_50_0 = all_23_6 % 15.71/2.92 | | | | % 15.71/2.92 | | | | GROUND_INST: instantiating (7) with all_50_1, all_52_0, all_50_5, % 15.71/2.92 | | | | simplifying with (93), (115) gives: % 15.71/2.92 | | | | (120) all_52_0 = all_50_1 % 15.71/2.92 | | | | % 15.71/2.92 | | | | BETA: splitting (104) gives: % 15.71/2.92 | | | | % 15.71/2.92 | | | | Case 1: % 15.71/2.92 | | | | | % 15.71/2.92 | | | | | (121) ~ (all_52_3 = 0) % 15.71/2.92 | | | | | % 15.71/2.92 | | | | | REDUCE: (118), (121) imply: % 15.71/2.92 | | | | | (122) $false % 15.71/2.92 | | | | | % 15.71/2.92 | | | | | CLOSE: (122) is inconsistent. % 15.71/2.92 | | | | | % 15.71/2.92 | | | | Case 2: % 15.71/2.92 | | | | | % 15.71/2.92 | | | | | (123) ~ (all_52_5 = 0) | ~ (all_52_6 = 0) | (( ~ (all_17_0 = 0) | % 15.71/2.92 | | | | | all_52_1 = 0) & (all_52_0 = 0 | all_17_0 = 0)) % 15.71/2.92 | | | | | % 15.71/2.92 | | | | | BETA: splitting (123) gives: % 15.71/2.92 | | | | | % 15.71/2.92 | | | | | Case 1: % 15.71/2.92 | | | | | | % 15.71/2.92 | | | | | | (124) ~ (all_52_5 = 0) % 15.71/2.92 | | | | | | % 15.71/2.92 | | | | | | REDUCE: (105), (124) imply: % 15.71/2.92 | | | | | | (125) $false % 15.71/2.92 | | | | | | % 15.71/2.92 | | | | | | CLOSE: (125) is inconsistent. % 15.71/2.92 | | | | | | % 15.71/2.92 | | | | | Case 2: % 15.71/2.92 | | | | | | % 15.71/2.92 | | | | | | (126) ~ (all_52_6 = 0) | (( ~ (all_17_0 = 0) | all_52_1 = 0) & % 15.71/2.92 | | | | | | (all_52_0 = 0 | all_17_0 = 0)) % 15.71/2.92 | | | | | | % 15.71/2.92 | | | | | | BETA: splitting (126) gives: % 15.71/2.92 | | | | | | % 15.71/2.92 | | | | | | Case 1: % 15.71/2.92 | | | | | | | % 15.71/2.92 | | | | | | | (127) ~ (all_52_6 = 0) % 15.71/2.92 | | | | | | | % 15.71/2.92 | | | | | | | REDUCE: (106), (127) imply: % 15.71/2.92 | | | | | | | (128) $false % 15.71/2.92 | | | | | | | % 15.71/2.92 | | | | | | | CLOSE: (128) is inconsistent. % 15.71/2.92 | | | | | | | % 15.71/2.92 | | | | | | Case 2: % 15.71/2.92 | | | | | | | % 15.71/2.92 | | | | | | | (129) ( ~ (all_17_0 = 0) | all_52_1 = 0) & (all_52_0 = 0 | % 15.71/2.92 | | | | | | | all_17_0 = 0) % 15.71/2.92 | | | | | | | % 15.71/2.92 | | | | | | | ALPHA: (129) implies: % 15.71/2.92 | | | | | | | (130) all_52_0 = 0 | all_17_0 = 0 % 15.71/2.92 | | | | | | | % 15.71/2.92 | | | | | | | BETA: splitting (130) gives: % 15.71/2.92 | | | | | | | % 15.71/2.92 | | | | | | | Case 1: % 15.71/2.92 | | | | | | | | % 15.71/2.92 | | | | | | | | (131) all_52_0 = 0 % 15.71/2.92 | | | | | | | | % 15.71/2.92 | | | | | | | | COMBINE_EQS: (120), (131) imply: % 15.71/2.92 | | | | | | | | (132) all_50_1 = 0 % 15.71/2.92 | | | | | | | | % 15.71/2.92 | | | | | | | | BETA: splitting (96) gives: % 15.71/2.92 | | | | | | | | % 15.71/2.92 | | | | | | | | Case 1: % 15.71/2.92 | | | | | | | | | % 15.71/2.92 | | | | | | | | | (133) ~ (all_50_6 = 0) % 15.71/2.92 | | | | | | | | | % 15.71/2.92 | | | | | | | | | REDUCE: (114), (133) imply: % 15.71/2.92 | | | | | | | | | (134) $false % 15.71/2.92 | | | | | | | | | % 15.71/2.92 | | | | | | | | | CLOSE: (134) is inconsistent. % 15.71/2.92 | | | | | | | | | % 15.71/2.92 | | | | | | | | Case 2: % 15.71/2.92 | | | | | | | | | % 15.71/2.92 | | | | | | | | | (135) ( ~ (all_50_1 = 0) | all_50_0 = 0) & ( ~ (all_50_2 = % 15.71/2.92 | | | | | | | | | 0) | ~ (all_50_4 = 0)) % 15.71/2.92 | | | | | | | | | % 15.71/2.92 | | | | | | | | | ALPHA: (135) implies: % 15.71/2.92 | | | | | | | | | (136) ~ (all_50_1 = 0) | all_50_0 = 0 % 15.71/2.92 | | | | | | | | | % 15.71/2.92 | | | | | | | | | BETA: splitting (136) gives: % 15.71/2.92 | | | | | | | | | % 15.71/2.92 | | | | | | | | | Case 1: % 15.71/2.92 | | | | | | | | | | % 15.71/2.92 | | | | | | | | | | (137) ~ (all_50_1 = 0) % 15.71/2.92 | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | REDUCE: (132), (137) imply: % 15.71/2.93 | | | | | | | | | | (138) $false % 15.71/2.93 | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | CLOSE: (138) is inconsistent. % 15.71/2.93 | | | | | | | | | | % 15.71/2.93 | | | | | | | | | Case 2: % 15.71/2.93 | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | (139) all_50_0 = 0 % 15.71/2.93 | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | COMBINE_EQS: (119), (139) imply: % 15.71/2.93 | | | | | | | | | | (140) all_23_6 = 0 % 15.71/2.93 | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | BETA: splitting (26) gives: % 15.71/2.93 | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | Case 1: % 15.71/2.93 | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | (141) ~ (all_10_4 = zero) % 15.71/2.93 | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | BETA: splitting (28) gives: % 15.71/2.93 | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | Case 1: % 15.71/2.93 | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | (142) ~ (all_10_0 = 0) % 15.71/2.93 | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | BETA: splitting (56) gives: % 15.71/2.93 | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | Case 1: % 15.71/2.93 | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | (143) ~ (all_23_6 = 0) % 15.71/2.93 | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | REDUCE: (140), (143) imply: % 15.71/2.93 | | | | | | | | | | | | | (144) $false % 15.71/2.93 | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | CLOSE: (144) is inconsistent. % 15.71/2.93 | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | Case 2: % 15.71/2.93 | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | (145) ~ (all_23_8 = 0) | (all_23_0 = 0 & all_23_1 = 0) % 15.71/2.93 | | | | | | | | | | | | | | (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero % 15.71/2.93 | | | | | | | | | | | | | & all_23_5 = zero) % 15.71/2.93 | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | BETA: splitting (145) gives: % 15.71/2.93 | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | Case 1: % 15.71/2.93 | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | (146) ~ (all_23_8 = 0) % 15.71/2.93 | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | REDUCE: (57), (146) imply: % 15.71/2.93 | | | | | | | | | | | | | | (147) $false % 15.71/2.93 | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | CLOSE: (147) is inconsistent. % 15.71/2.93 | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | Case 2: % 15.71/2.93 | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | (148) (all_23_0 = 0 & all_23_1 = 0) | (all_23_2 = 0 & % 15.71/2.93 | | | | | | | | | | | | | | all_23_3 = 0) | (all_23_4 = zero & all_23_5 = % 15.71/2.93 | | | | | | | | | | | | | | zero) % 15.71/2.93 | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | BETA: splitting (148) gives: % 15.71/2.93 | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | Case 1: % 15.71/2.93 | | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | | (149) all_23_0 = 0 & all_23_1 = 0 % 15.71/2.93 | | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | | REF_CLOSE: (84), (142), (149) are inconsistent by sub-proof % 15.71/2.93 | | | | | | | | | | | | | | | #4. % 15.71/2.93 | | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | Case 2: % 15.71/2.93 | | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | | (150) (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero & % 15.71/2.93 | | | | | | | | | | | | | | | all_23_5 = zero) % 15.71/2.93 | | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | | BETA: splitting (150) gives: % 15.71/2.93 | | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | | Case 1: % 15.71/2.93 | | | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | | | (151) all_23_2 = 0 & all_23_3 = 0 % 15.71/2.93 | | | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (85), (86), (151) are inconsistent by % 15.71/2.93 | | | | | | | | | | | | | | | | sub-proof #2. % 15.71/2.93 | | | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | | Case 2: % 15.71/2.93 | | | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | | | (152) all_23_4 = zero & all_23_5 = zero % 15.71/2.93 | | | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | | | ALPHA: (152) implies: % 15.71/2.93 | | | | | | | | | | | | | | | | (153) all_23_4 = zero % 15.71/2.93 | | | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (153) imply: % 15.71/2.93 | | | | | | | | | | | | | | | | (154) all_10_4 = zero % 15.71/2.93 | | | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | | | SIMP: (154) implies: % 15.71/2.93 | | | | | | | | | | | | | | | | (155) all_10_4 = zero % 15.71/2.93 | | | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | | | REDUCE: (141), (155) imply: % 15.71/2.93 | | | | | | | | | | | | | | | | (156) $false % 15.71/2.93 | | | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | | | CLOSE: (156) is inconsistent. % 15.71/2.93 | | | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | | End of split % 15.71/2.93 | | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | | End of split % 15.71/2.93 | | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | | End of split % 15.71/2.93 | | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | End of split % 15.71/2.93 | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | Case 2: % 15.71/2.93 | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | (157) ~ (all_10_1 = 0) % 15.71/2.93 | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | BETA: splitting (56) gives: % 15.71/2.93 | | | | | | | | | | | | % 15.71/2.93 | | | | | | | | | | | | Case 1: % 15.71/2.93 | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | (158) ~ (all_23_6 = 0) % 15.71/2.94 | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | REDUCE: (140), (158) imply: % 15.71/2.94 | | | | | | | | | | | | | (159) $false % 15.71/2.94 | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | CLOSE: (159) is inconsistent. % 15.71/2.94 | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | Case 2: % 15.71/2.94 | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | (160) ~ (all_23_8 = 0) | (all_23_0 = 0 & all_23_1 = 0) % 15.71/2.94 | | | | | | | | | | | | | | (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero % 15.71/2.94 | | | | | | | | | | | | | & all_23_5 = zero) % 15.71/2.94 | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | BETA: splitting (160) gives: % 15.71/2.94 | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | Case 1: % 15.71/2.94 | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | (161) ~ (all_23_8 = 0) % 15.71/2.94 | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | REDUCE: (57), (161) imply: % 15.71/2.94 | | | | | | | | | | | | | | (162) $false % 15.71/2.94 | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | CLOSE: (162) is inconsistent. % 15.71/2.94 | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | Case 2: % 15.71/2.94 | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | (163) (all_23_0 = 0 & all_23_1 = 0) | (all_23_2 = 0 & % 15.71/2.94 | | | | | | | | | | | | | | all_23_3 = 0) | (all_23_4 = zero & all_23_5 = % 15.71/2.94 | | | | | | | | | | | | | | zero) % 15.71/2.94 | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | BETA: splitting (163) gives: % 15.71/2.94 | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | Case 1: % 15.71/2.94 | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | (164) all_23_0 = 0 & all_23_1 = 0 % 15.71/2.94 | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | ALPHA: (164) implies: % 15.71/2.94 | | | | | | | | | | | | | | | (165) all_23_1 = 0 % 15.71/2.94 | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | COMBINE_EQS: (87), (165) imply: % 15.71/2.94 | | | | | | | | | | | | | | | (166) all_10_1 = 0 % 15.71/2.94 | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | SIMP: (166) implies: % 15.71/2.94 | | | | | | | | | | | | | | | (167) all_10_1 = 0 % 15.71/2.94 | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | REDUCE: (157), (167) imply: % 15.71/2.94 | | | | | | | | | | | | | | | (168) $false % 15.71/2.94 | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | CLOSE: (168) is inconsistent. % 15.71/2.94 | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | Case 2: % 15.71/2.94 | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | (169) (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero & % 15.71/2.94 | | | | | | | | | | | | | | | all_23_5 = zero) % 15.71/2.94 | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 15.71/2.94 | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | Case 1: % 15.71/2.94 | | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | | (170) all_23_2 = 0 & all_23_3 = 0 % 15.71/2.94 | | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (85), (86), (170) are inconsistent by % 15.71/2.94 | | | | | | | | | | | | | | | | sub-proof #2. % 15.71/2.94 | | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | Case 2: % 15.71/2.94 | | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | | (171) all_23_4 = zero & all_23_5 = zero % 15.71/2.94 | | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | | ALPHA: (171) implies: % 15.71/2.94 | | | | | | | | | | | | | | | | (172) all_23_4 = zero % 15.71/2.94 | | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (172) imply: % 15.71/2.94 | | | | | | | | | | | | | | | | (173) all_10_4 = zero % 15.71/2.94 | | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | | REDUCE: (141), (173) imply: % 15.71/2.94 | | | | | | | | | | | | | | | | (174) $false % 15.71/2.94 | | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | | CLOSE: (174) is inconsistent. % 15.71/2.94 | | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | | End of split % 15.71/2.94 | | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | | End of split % 15.71/2.94 | | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | | End of split % 15.71/2.94 | | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | | End of split % 15.71/2.94 | | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | End of split % 15.71/2.94 | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | Case 2: % 15.71/2.94 | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | (175) all_10_4 = zero % 15.71/2.94 | | | | | | | | | | | (176) ~ (all_10_5 = zero) % 15.71/2.94 | | | | | | | | | | | % 15.71/2.94 | | | | | | | | | | | REDUCE: (21), (175) imply: % 15.71/2.95 | | | | | | | | | | | (177) greater(zero, zero) = all_10_1 % 15.71/2.95 | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | REDUCE: (19), (175) imply: % 15.71/2.95 | | | | | | | | | | | (178) greater(zero, zero) = all_10_2 % 15.71/2.95 | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | GROUND_INST: instantiating (9) with all_10_2, all_10_1, zero, % 15.71/2.95 | | | | | | | | | | | zero, simplifying with (177), (178) gives: % 15.71/2.95 | | | | | | | | | | | (179) all_10_1 = all_10_2 % 15.71/2.95 | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | COMBINE_EQS: (87), (179) imply: % 15.71/2.95 | | | | | | | | | | | (180) all_23_1 = all_10_2 % 15.71/2.95 | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | BETA: splitting (28) gives: % 15.71/2.95 | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | Case 1: % 15.71/2.95 | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | (181) ~ (all_10_0 = 0) % 15.71/2.95 | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | BETA: splitting (56) gives: % 15.71/2.95 | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | Case 1: % 15.71/2.95 | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | (182) ~ (all_23_6 = 0) % 15.71/2.95 | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | REDUCE: (140), (182) imply: % 15.71/2.95 | | | | | | | | | | | | | (183) $false % 15.71/2.95 | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | CLOSE: (183) is inconsistent. % 15.71/2.95 | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | Case 2: % 15.71/2.95 | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | (184) ~ (all_23_8 = 0) | (all_23_0 = 0 & all_23_1 = 0) % 15.71/2.95 | | | | | | | | | | | | | | (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero % 15.71/2.95 | | | | | | | | | | | | | & all_23_5 = zero) % 15.71/2.95 | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | BETA: splitting (184) gives: % 15.71/2.95 | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | Case 1: % 15.71/2.95 | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | (185) ~ (all_23_8 = 0) % 15.71/2.95 | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | REDUCE: (57), (185) imply: % 15.71/2.95 | | | | | | | | | | | | | | (186) $false % 15.71/2.95 | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | CLOSE: (186) is inconsistent. % 15.71/2.95 | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | Case 2: % 15.71/2.95 | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | (187) (all_23_0 = 0 & all_23_1 = 0) | (all_23_2 = 0 & % 15.71/2.95 | | | | | | | | | | | | | | all_23_3 = 0) | (all_23_4 = zero & all_23_5 = % 15.71/2.95 | | | | | | | | | | | | | | zero) % 15.71/2.95 | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | BETA: splitting (187) gives: % 15.71/2.95 | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | Case 1: % 15.71/2.95 | | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | | (188) all_23_0 = 0 & all_23_1 = 0 % 15.71/2.95 | | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | | REF_CLOSE: (84), (181), (188) are inconsistent by sub-proof % 15.71/2.95 | | | | | | | | | | | | | | | #4. % 15.71/2.95 | | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | Case 2: % 15.71/2.95 | | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | | (189) (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero & % 15.71/2.95 | | | | | | | | | | | | | | | all_23_5 = zero) % 15.71/2.95 | | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 15.71/2.95 | | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | | Case 1: % 15.71/2.95 | | | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | | | (190) all_23_2 = 0 & all_23_3 = 0 % 15.71/2.95 | | | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | | | ALPHA: (190) implies: % 15.71/2.95 | | | | | | | | | | | | | | | | (191) all_23_3 = 0 % 15.71/2.95 | | | | | | | | | | | | | | | | (192) all_23_2 = 0 % 15.71/2.95 | | | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (192) imply: % 15.71/2.95 | | | | | | | | | | | | | | | | (193) all_10_2 = 0 % 15.71/2.95 | | | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | | | SIMP: (193) implies: % 15.71/2.95 | | | | | | | | | | | | | | | | (194) all_10_2 = 0 % 15.71/2.95 | | | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (191) imply: % 15.71/2.95 | | | | | | | | | | | | | | | | (195) all_10_3 = 0 % 15.71/2.95 | | | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (194), (195) are inconsistent by sub-proof % 15.71/2.95 | | | | | | | | | | | | | | | | #3. % 15.71/2.95 | | | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | | Case 2: % 15.71/2.95 | | | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | | | (196) all_23_4 = zero & all_23_5 = zero % 15.71/2.95 | | | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | | | REF_CLOSE: (62), (176), (196) are inconsistent by sub-proof % 15.71/2.95 | | | | | | | | | | | | | | | | #1. % 15.71/2.95 | | | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | | End of split % 15.71/2.95 | | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | | End of split % 15.71/2.95 | | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | | End of split % 15.71/2.95 | | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | | End of split % 15.71/2.95 | | | | | | | | | | | | % 15.71/2.95 | | | | | | | | | | | Case 2: % 15.71/2.96 | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | (197) ~ (all_10_1 = 0) % 15.71/2.96 | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | REDUCE: (179), (197) imply: % 15.71/2.96 | | | | | | | | | | | | (198) ~ (all_10_2 = 0) % 15.71/2.96 | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | BETA: splitting (56) gives: % 15.71/2.96 | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | Case 1: % 15.71/2.96 | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | (199) ~ (all_23_6 = 0) % 15.71/2.96 | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | REDUCE: (140), (199) imply: % 15.71/2.96 | | | | | | | | | | | | | (200) $false % 15.71/2.96 | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | CLOSE: (200) is inconsistent. % 15.71/2.96 | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | Case 2: % 15.71/2.96 | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | (201) ~ (all_23_8 = 0) | (all_23_0 = 0 & all_23_1 = 0) % 15.71/2.96 | | | | | | | | | | | | | | (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero % 15.71/2.96 | | | | | | | | | | | | | & all_23_5 = zero) % 15.71/2.96 | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | BETA: splitting (201) gives: % 15.71/2.96 | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | Case 1: % 15.71/2.96 | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | (202) ~ (all_23_8 = 0) % 15.71/2.96 | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | REDUCE: (57), (202) imply: % 15.71/2.96 | | | | | | | | | | | | | | (203) $false % 15.71/2.96 | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | CLOSE: (203) is inconsistent. % 15.71/2.96 | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | Case 2: % 15.71/2.96 | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | (204) (all_23_0 = 0 & all_23_1 = 0) | (all_23_2 = 0 & % 15.71/2.96 | | | | | | | | | | | | | | all_23_3 = 0) | (all_23_4 = zero & all_23_5 = % 15.71/2.96 | | | | | | | | | | | | | | zero) % 15.71/2.96 | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | BETA: splitting (204) gives: % 15.71/2.96 | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | Case 1: % 15.71/2.96 | | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | | (205) all_23_0 = 0 & all_23_1 = 0 % 15.71/2.96 | | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | | ALPHA: (205) implies: % 15.71/2.96 | | | | | | | | | | | | | | | (206) all_23_1 = 0 % 15.71/2.96 | | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | | COMBINE_EQS: (180), (206) imply: % 15.71/2.96 | | | | | | | | | | | | | | | (207) all_10_2 = 0 % 15.71/2.96 | | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | | REDUCE: (198), (207) imply: % 15.71/2.96 | | | | | | | | | | | | | | | (208) $false % 15.71/2.96 | | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | | CLOSE: (208) is inconsistent. % 15.71/2.96 | | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | Case 2: % 15.71/2.96 | | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | | (209) (all_23_2 = 0 & all_23_3 = 0) | (all_23_4 = zero & % 15.71/2.96 | | | | | | | | | | | | | | | all_23_5 = zero) % 15.71/2.96 | | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 15.71/2.96 | | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | | Case 1: % 15.71/2.96 | | | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | | | (210) all_23_2 = 0 & all_23_3 = 0 % 15.71/2.96 | | | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (85), (86), (210) are inconsistent by % 15.71/2.96 | | | | | | | | | | | | | | | | sub-proof #2. % 15.71/2.96 | | | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | | Case 2: % 15.71/2.96 | | | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | | | (211) all_23_4 = zero & all_23_5 = zero % 15.71/2.96 | | | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | | | REF_CLOSE: (62), (176), (211) are inconsistent by sub-proof % 15.71/2.96 | | | | | | | | | | | | | | | | #1. % 15.71/2.96 | | | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | | End of split % 15.71/2.96 | | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | | End of split % 15.71/2.96 | | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | | End of split % 15.71/2.96 | | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | | End of split % 15.71/2.96 | | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | | End of split % 15.71/2.96 | | | | | | | | | | | % 15.71/2.96 | | | | | | | | | | End of split % 15.71/2.96 | | | | | | | | | | % 15.71/2.96 | | | | | | | | | End of split % 15.71/2.96 | | | | | | | | | % 15.71/2.96 | | | | | | | | End of split % 15.71/2.96 | | | | | | | | % 15.71/2.96 | | | | | | | Case 2: % 15.71/2.96 | | | | | | | | % 15.71/2.96 | | | | | | | | (212) all_17_0 = 0 % 15.71/2.96 | | | | | | | | % 15.71/2.96 | | | | | | | | REDUCE: (75), (212) imply: % 15.71/2.96 | | | | | | | | (213) $false % 15.71/2.96 | | | | | | | | % 15.71/2.96 | | | | | | | | CLOSE: (213) is inconsistent. % 15.71/2.96 | | | | | | | | % 15.71/2.96 | | | | | | | End of split % 15.71/2.96 | | | | | | | % 15.71/2.96 | | | | | | End of split % 15.71/2.96 | | | | | | % 15.71/2.96 | | | | | End of split % 15.71/2.96 | | | | | % 15.71/2.96 | | | | End of split % 15.71/2.96 | | | | % 15.71/2.96 | | | End of split % 15.71/2.96 | | | % 15.71/2.96 | | End of split % 15.71/2.96 | | % 15.71/2.96 | Case 2: % 15.71/2.96 | | % 15.71/2.96 | | (214) ~ (all_17_1 = 0) % 15.71/2.96 | | % 15.71/2.97 | | REDUCE: (69), (214) imply: % 15.71/2.97 | | (215) $false % 15.71/2.97 | | % 15.71/2.97 | | CLOSE: (215) is inconsistent. % 15.71/2.97 | | % 15.71/2.97 | End of split % 15.71/2.97 | % 15.71/2.97 End of proof % 15.71/2.97 % 15.71/2.97 Sub-proof #1 shows that the following formulas are inconsistent: % 15.71/2.97 ---------------------------------------------------------------- % 15.71/2.97 (1) all_23_4 = zero & all_23_5 = zero % 15.71/2.97 (2) all_23_5 = all_10_5 % 15.71/2.97 (3) ~ (all_10_5 = zero) % 15.71/2.97 % 15.71/2.97 Begin of proof % 15.71/2.97 | % 15.71/2.97 | ALPHA: (1) implies: % 15.71/2.97 | (4) all_23_5 = zero % 15.71/2.97 | % 15.71/2.97 | COMBINE_EQS: (2), (4) imply: % 15.71/2.97 | (5) all_10_5 = zero % 15.71/2.97 | % 15.71/2.97 | SIMP: (5) implies: % 15.71/2.97 | (6) all_10_5 = zero % 15.71/2.97 | % 15.71/2.97 | REDUCE: (3), (6) imply: % 15.71/2.97 | (7) $false % 15.71/2.97 | % 15.71/2.97 | CLOSE: (7) is inconsistent. % 15.71/2.97 | % 15.71/2.97 End of proof % 15.71/2.97 % 15.71/2.97 Sub-proof #2 shows that the following formulas are inconsistent: % 15.71/2.97 ---------------------------------------------------------------- % 15.71/2.97 (1) all_23_2 = 0 & all_23_3 = 0 % 15.71/2.97 (2) all_23_2 = all_10_2 % 15.71/2.97 (3) all_23_3 = all_10_3 % 15.71/2.97 (4) ~ (all_10_2 = 0) | ~ (all_10_3 = 0) % 15.71/2.97 % 15.71/2.97 Begin of proof % 15.71/2.97 | % 15.71/2.97 | ALPHA: (1) implies: % 15.71/2.97 | (5) all_23_3 = 0 % 15.71/2.97 | (6) all_23_2 = 0 % 15.71/2.97 | % 15.71/2.97 | COMBINE_EQS: (2), (6) imply: % 15.71/2.97 | (7) all_10_2 = 0 % 15.71/2.97 | % 15.71/2.97 | SIMP: (7) implies: % 15.71/2.97 | (8) all_10_2 = 0 % 15.71/2.97 | % 15.71/2.97 | COMBINE_EQS: (3), (5) imply: % 15.71/2.97 | (9) all_10_3 = 0 % 15.71/2.97 | % 15.71/2.97 | REF_CLOSE: (4), (8), (9) are inconsistent by sub-proof #3. % 15.71/2.97 | % 15.71/2.97 End of proof % 15.71/2.97 % 15.71/2.97 Sub-proof #3 shows that the following formulas are inconsistent: % 15.71/2.97 ---------------------------------------------------------------- % 15.71/2.97 (1) ~ (all_10_2 = 0) | ~ (all_10_3 = 0) % 15.71/2.97 (2) all_10_2 = 0 % 15.71/2.97 (3) all_10_3 = 0 % 15.71/2.97 % 15.71/2.97 Begin of proof % 15.71/2.97 | % 15.71/2.97 | BETA: splitting (1) gives: % 15.71/2.97 | % 15.71/2.97 | Case 1: % 15.71/2.97 | | % 15.71/2.97 | | (4) ~ (all_10_2 = 0) % 15.71/2.97 | | % 15.71/2.97 | | REDUCE: (2), (4) imply: % 15.71/2.97 | | (5) $false % 15.71/2.97 | | % 15.71/2.97 | | CLOSE: (5) is inconsistent. % 15.71/2.97 | | % 15.71/2.97 | Case 2: % 15.71/2.97 | | % 15.71/2.97 | | (6) ~ (all_10_3 = 0) % 15.71/2.97 | | % 15.71/2.97 | | REDUCE: (3), (6) imply: % 15.71/2.97 | | (7) $false % 15.71/2.97 | | % 15.71/2.97 | | CLOSE: (7) is inconsistent. % 15.71/2.97 | | % 15.71/2.97 | End of split % 15.71/2.97 | % 15.71/2.97 End of proof % 15.71/2.97 % 15.71/2.97 Sub-proof #4 shows that the following formulas are inconsistent: % 15.71/2.97 ---------------------------------------------------------------- % 15.71/2.97 (1) all_23_0 = 0 & all_23_1 = 0 % 15.71/2.97 (2) all_23_0 = all_10_0 % 15.71/2.97 (3) ~ (all_10_0 = 0) % 15.71/2.97 % 15.71/2.97 Begin of proof % 15.71/2.97 | % 15.71/2.97 | ALPHA: (1) implies: % 15.71/2.97 | (4) all_23_0 = 0 % 15.71/2.97 | % 15.71/2.97 | COMBINE_EQS: (2), (4) imply: % 15.71/2.98 | (5) all_10_0 = 0 % 15.71/2.98 | % 15.71/2.98 | REDUCE: (3), (5) imply: % 15.71/2.98 | (6) $false % 15.71/2.98 | % 15.71/2.98 | CLOSE: (6) is inconsistent. % 15.71/2.98 | % 15.71/2.98 End of proof % 15.71/2.98 % SZS output end Proof for theBenchmark % 15.71/2.98 % 15.71/2.98 2261ms %------------------------------------------------------------------------------