%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT044+1 : TPTP v9.3.0. Released v2.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n003.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Tue Sep 8 06:17:25 AM UTC 2026 % Result : Theorem 14.12s 2.62s % Output : Proof 21.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT044+1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.37 % Computer : n003.cluster.edu % 0.10/0.37 % Model : x86_64 x86_64 % 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.37 % Memory : 8046.5625MB % 0.10/0.37 % OS : Linux 6.8.0-71-generic % 0.10/0.37 % CPULimit : 300 % 0.10/0.37 % WCLimit : 300 % 0.10/0.37 % DateTime : Mon Sep 7 13:08:24 UTC 2026 % 0.10/0.37 % CPUTime : % 0.10/0.39 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. % 0.66/0.73 ________ _____ % 0.66/0.73 ___ __ \_________(_)________________________________ % 0.66/0.73 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.66/0.73 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.66/0.73 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.66/0.73 % 0.66/0.73 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.66/0.73 (2023-06-19) % 0.66/0.73 % 0.66/0.73 (c) Philipp Rümmer, 2009-2023 % 0.66/0.73 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.66/0.73 Amanda Stjerna. % 0.66/0.73 Free software under BSD-3-Clause. % 0.66/0.73 % 0.66/0.73 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.66/0.73 % 0.66/0.74 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.66/0.76 Running up to 7 provers in parallel. % 0.66/0.77 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.66/0.77 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.66/0.77 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.66/0.77 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.66/0.77 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.66/0.77 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.66/0.77 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.18/1.21 Prover 1: Preprocessing ... % 3.18/1.21 Prover 4: Preprocessing ... % 3.18/1.27 Prover 2: Preprocessing ... % 3.18/1.27 Prover 6: Preprocessing ... % 3.18/1.28 Prover 0: Preprocessing ... % 3.18/1.28 Prover 3: Preprocessing ... % 3.18/1.28 Prover 5: Preprocessing ... % 6.27/1.67 Prover 1: Constructing countermodel ... % 6.27/1.67 Prover 3: Constructing countermodel ... % 6.27/1.67 Prover 6: Constructing countermodel ... % 7.06/1.74 Prover 2: Proving ... % 7.06/1.75 Prover 4: Constructing countermodel ... % 7.82/1.85 Prover 5: Proving ... % 8.64/1.91 Prover 0: Proving ... % 8.64/1.95 Prover 1: gave up % 8.64/1.95 Prover 3: gave up % 8.64/1.95 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.64/1.95 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.64/2.01 Prover 7: Preprocessing ... % 8.64/2.02 Prover 8: Preprocessing ... % 9.65/2.05 Prover 6: gave up % 9.65/2.05 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 9.65/2.09 Prover 9: Preprocessing ... % 9.65/2.10 Prover 8: Warning: ignoring some quantifiers % 9.65/2.11 Prover 8: Constructing countermodel ... % 10.97/2.21 Prover 8: gave up % 10.97/2.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.97/2.29 Prover 10: Preprocessing ... % 12.51/2.40 Prover 9: Constructing countermodel ... % 12.51/2.42 Prover 10: Warning: ignoring some quantifiers % 12.51/2.43 Prover 7: Warning: ignoring some quantifiers % 12.51/2.43 Prover 10: Constructing countermodel ... % 12.51/2.45 Prover 7: Constructing countermodel ... % 14.12/2.62 Prover 0: proved (1852ms) % 14.12/2.62 % 14.12/2.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.12/2.62 % 14.12/2.63 Prover 9: stopped % 14.12/2.63 Prover 2: stopped % 14.12/2.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.12/2.64 Prover 5: stopped % 14.12/2.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.12/2.64 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 14.12/2.64 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 14.12/2.67 Prover 13: Preprocessing ... % 14.92/2.71 Prover 16: Preprocessing ... % 14.92/2.71 Prover 19: Preprocessing ... % 14.92/2.74 Prover 11: Preprocessing ... % 14.92/2.78 Prover 16: Warning: ignoring some quantifiers % 14.92/2.79 Prover 13: Warning: ignoring some quantifiers % 14.92/2.79 Prover 16: Constructing countermodel ... % 15.70/2.81 Prover 13: Constructing countermodel ... % 15.70/2.84 Prover 19: Warning: ignoring some quantifiers % 15.70/2.85 Prover 19: Constructing countermodel ... % 16.50/2.98 Prover 19: gave up % 16.50/3.02 Prover 11: Constructing countermodel ... % 18.33/3.16 Prover 10: gave up % 18.33/3.17 Prover 16: gave up % 19.65/3.38 Prover 11: Found proof (size 76) % 19.65/3.38 Prover 11: proved (748ms) % 19.65/3.38 Prover 13: stopped % 19.65/3.38 Prover 7: stopped % 19.65/3.38 Prover 4: stopped % 19.65/3.38 % 19.65/3.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.65/3.38 % 19.65/3.39 % SZS output start Proof for theBenchmark % 19.65/3.40 Assumptions after simplification: % 19.65/3.40 --------------------------------- % 19.65/3.40 % 19.65/3.40 (assumption_5) % 20.88/3.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 20.88/3.53 any] : ( ~ (internal_friction(v0, v2) = v3) | ~ (internal_friction(v0, v1) % 20.88/3.53 = v4) | ~ (greater(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 20.88/3.53 [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10: int] : ? % 20.88/3.53 [v11: $i] : ? [v12: $i] : ? [v13: int] : ? [v14: int] : ? [v15: int] : % 20.88/3.53 (( ~ (v6 = 0) & organization(v0) = v6) | (( ~ (v5 = 0) | (v15 = 0 & % 20.88/3.53 capability(v0, v2) = v11 & capability(v0, v1) = v12 & smaller(v11, % 20.88/3.53 v12) = 0 & $i(v12) & $i(v11)) | ( ~ (v14 = 0) & % 20.88/3.53 stock_of_knowledge(v0, v2) = v7 & stock_of_knowledge(v0, v1) = v8 & % 20.88/3.53 smaller_or_equal(v7, v8) = v14 & $i(v8) & $i(v7))) & ( ~ (v4 = v3) | % 20.88/3.53 (v12 = v11 & capability(v0, v2) = v11 & capability(v0, v1) = v11 & % 20.88/3.53 $i(v11)) | ( ~ (v8 = v7) & stock_of_knowledge(v0, v2) = v7 & % 20.88/3.53 stock_of_knowledge(v0, v1) = v8 & $i(v8) & $i(v7))) & ((v13 = 0 & % 20.88/3.53 capability(v0, v2) = v11 & capability(v0, v1) = v12 & greater(v11, % 20.88/3.53 v12) = 0 & $i(v12) & $i(v11)) | ( ~ (v10 = 0) & % 20.88/3.53 smaller_or_equal(v3, v4) = v10) | ( ~ (v9 = 0) & % 20.88/3.53 stock_of_knowledge(v0, v2) = v7 & stock_of_knowledge(v0, v1) = v8 & % 20.88/3.53 greater(v7, v8) = v9 & $i(v8) & $i(v7)))))) & ! [v0: $i] : ! [v1: % 20.88/3.53 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ % 20.88/3.53 (internal_friction(v0, v2) = v3) | ~ (internal_friction(v0, v1) = v4) | ~ % 20.88/3.53 (smaller_or_equal(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 20.88/3.53 [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ? % 20.88/3.53 [v11: $i] : ? [v12: int] : ? [v13: int] : ? [v14: int] : ? [v15: int] : % 20.88/3.53 (( ~ (v6 = 0) & organization(v0) = v6) | (( ~ (v5 = 0) | (v12 = 0 & % 20.88/3.53 capability(v0, v2) = v10 & capability(v0, v1) = v11 & greater(v10, % 20.88/3.53 v11) = 0 & $i(v11) & $i(v10)) | ( ~ (v9 = 0) & % 20.88/3.53 stock_of_knowledge(v0, v2) = v7 & stock_of_knowledge(v0, v1) = v8 & % 20.88/3.53 greater(v7, v8) = v9 & $i(v8) & $i(v7))) & ( ~ (v4 = v3) | (v11 = % 20.88/3.53 v10 & capability(v0, v2) = v10 & capability(v0, v1) = v10 & $i(v10)) % 20.88/3.53 | ( ~ (v8 = v7) & stock_of_knowledge(v0, v2) = v7 & % 20.88/3.53 stock_of_knowledge(v0, v1) = v8 & $i(v8) & $i(v7))) & ((v15 = 0 & % 20.88/3.53 capability(v0, v2) = v10 & capability(v0, v1) = v11 & smaller(v10, % 20.88/3.53 v11) = 0 & $i(v11) & $i(v10)) | ( ~ (v14 = 0) & greater(v3, v4) = % 20.88/3.53 v14) | ( ~ (v13 = 0) & stock_of_knowledge(v0, v2) = v7 & % 20.88/3.53 stock_of_knowledge(v0, v1) = v8 & smaller_or_equal(v7, v8) = v13 & % 20.88/3.53 $i(v8) & $i(v7)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 20.88/3.53 [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (stock_of_knowledge(v0, v2) = v3) % 20.88/3.53 | ~ (stock_of_knowledge(v0, v1) = v4) | ~ (greater(v3, v4) = v5) | ~ % 20.88/3.53 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: $i] : ? [v8: $i] : % 20.88/3.53 ? [v9: int] : ? [v10: $i] : ? [v11: $i] : ? [v12: int] : ? [v13: int] : % 20.88/3.53 ? [v14: int] : ? [v15: int] : (( ~ (v6 = 0) & organization(v0) = v6) | (( ~ % 20.88/3.53 (v5 = 0) | (v12 = 0 & capability(v0, v2) = v10 & capability(v0, v1) = % 20.88/3.53 v11 & greater(v10, v11) = 0 & $i(v11) & $i(v10)) | ( ~ (v9 = 0) & % 20.88/3.53 internal_friction(v0, v2) = v7 & internal_friction(v0, v1) = v8 & % 20.88/3.53 smaller_or_equal(v7, v8) = v9 & $i(v8) & $i(v7))) & ( ~ (v4 = v3) | % 20.88/3.53 (v11 = v10 & capability(v0, v2) = v10 & capability(v0, v1) = v10 & % 20.88/3.53 $i(v10)) | ( ~ (v8 = v7) & internal_friction(v0, v2) = v7 & % 20.88/3.53 internal_friction(v0, v1) = v8 & $i(v8) & $i(v7))) & ((v15 = 0 & % 20.88/3.53 capability(v0, v2) = v10 & capability(v0, v1) = v11 & smaller(v10, % 20.88/3.53 v11) = 0 & $i(v11) & $i(v10)) | ( ~ (v14 = 0) & % 20.88/3.53 internal_friction(v0, v2) = v7 & internal_friction(v0, v1) = v8 & % 20.88/3.53 greater(v7, v8) = v14 & $i(v8) & $i(v7)) | ( ~ (v13 = 0) & % 20.88/3.53 smaller_or_equal(v3, v4) = v13))))) & ! [v0: $i] : ! [v1: $i] : ! % 20.88/3.53 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ % 20.88/3.53 (stock_of_knowledge(v0, v2) = v3) | ~ (stock_of_knowledge(v0, v1) = v4) | % 20.88/3.53 ~ (smaller_or_equal(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 20.88/3.53 [v6: int] : ? [v7: int] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] : ? % 20.88/3.53 [v11: $i] : ? [v12: $i] : ? [v13: int] : ? [v14: int] : ? [v15: int] : % 20.88/3.53 (( ~ (v6 = 0) & organization(v0) = v6) | (( ~ (v5 = 0) | (v15 = 0 & % 20.88/3.53 capability(v0, v2) = v11 & capability(v0, v1) = v12 & smaller(v11, % 20.88/3.53 v12) = 0 & $i(v12) & $i(v11)) | ( ~ (v14 = 0) & % 20.88/3.53 internal_friction(v0, v2) = v8 & internal_friction(v0, v1) = v9 & % 20.88/3.53 greater(v8, v9) = v14 & $i(v9) & $i(v8))) & ( ~ (v4 = v3) | (v12 = % 20.88/3.53 v11 & capability(v0, v2) = v11 & capability(v0, v1) = v11 & $i(v11)) % 20.88/3.53 | ( ~ (v9 = v8) & internal_friction(v0, v2) = v8 & % 20.88/3.53 internal_friction(v0, v1) = v9 & $i(v9) & $i(v8))) & ((v13 = 0 & % 20.88/3.54 capability(v0, v2) = v11 & capability(v0, v1) = v12 & greater(v11, % 20.88/3.54 v12) = 0 & $i(v12) & $i(v11)) | ( ~ (v10 = 0) & % 20.88/3.54 internal_friction(v0, v2) = v8 & internal_friction(v0, v1) = v9 & % 20.88/3.54 smaller_or_equal(v8, v9) = v10 & $i(v9) & $i(v8)) | ( ~ (v7 = 0) & % 20.88/3.54 greater(v3, v4) = v7))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 20.88/3.54 : ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (capability(v0, v2) = v3) | % 20.88/3.54 ~ (capability(v0, v1) = v4) | ~ (greater(v3, v4) = v5) | ~ $i(v2) | ~ % 20.88/3.54 $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] % 20.88/3.54 : ? [v10: $i] : ? [v11: $i] : ? [v12: int] : ? [v13: int] : ? [v14: % 20.88/3.54 int] : ? [v15: int] : (( ~ (v6 = 0) & organization(v0) = v6) | ((v5 = 0 | % 20.88/3.54 ( ~ (v12 = 0) & internal_friction(v0, v2) = v10 & % 20.88/3.54 internal_friction(v0, v1) = v11 & smaller_or_equal(v10, v11) = v12 & % 20.88/3.54 $i(v11) & $i(v10)) | ( ~ (v9 = 0) & stock_of_knowledge(v0, v2) = v7 % 20.88/3.54 & stock_of_knowledge(v0, v1) = v8 & greater(v7, v8) = v9 & $i(v8) & % 20.88/3.54 $i(v7))) & (v4 = v3 | ( ~ (v11 = v10) & internal_friction(v0, v2) = % 20.88/3.54 v10 & internal_friction(v0, v1) = v11 & $i(v11) & $i(v10)) | ( ~ (v8 % 20.88/3.54 = v7) & stock_of_knowledge(v0, v2) = v7 & stock_of_knowledge(v0, % 20.88/3.54 v1) = v8 & $i(v8) & $i(v7))) & ((v15 = 0 & smaller(v3, v4) = 0) | % 20.88/3.54 ( ~ (v14 = 0) & internal_friction(v0, v2) = v10 & % 20.88/3.54 internal_friction(v0, v1) = v11 & greater(v10, v11) = v14 & $i(v11) % 20.88/3.54 & $i(v10)) | ( ~ (v13 = 0) & stock_of_knowledge(v0, v2) = v7 & % 20.88/3.54 stock_of_knowledge(v0, v1) = v8 & smaller_or_equal(v7, v8) = v13 & % 20.88/3.54 $i(v8) & $i(v7)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 20.88/3.54 [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (capability(v0, v2) = v3) | ~ % 20.88/3.54 (capability(v0, v1) = v4) | ~ (smaller(v3, v4) = v5) | ~ $i(v2) | ~ % 20.88/3.54 $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] % 20.88/3.54 : ? [v10: $i] : ? [v11: $i] : ? [v12: int] : ? [v13: int] : ? [v14: % 20.88/3.54 int] : ? [v15: int] : (( ~ (v6 = 0) & organization(v0) = v6) | ((v5 = 0 | % 20.88/3.54 ( ~ (v15 = 0) & internal_friction(v0, v2) = v10 & % 20.88/3.54 internal_friction(v0, v1) = v11 & greater(v10, v11) = v15 & $i(v11) % 20.88/3.54 & $i(v10)) | ( ~ (v14 = 0) & stock_of_knowledge(v0, v2) = v7 & % 20.88/3.54 stock_of_knowledge(v0, v1) = v8 & smaller_or_equal(v7, v8) = v14 & % 20.88/3.54 $i(v8) & $i(v7))) & (v4 = v3 | ( ~ (v11 = v10) & % 20.88/3.54 internal_friction(v0, v2) = v10 & internal_friction(v0, v1) = v11 & % 20.88/3.54 $i(v11) & $i(v10)) | ( ~ (v8 = v7) & stock_of_knowledge(v0, v2) = v7 % 20.88/3.54 & stock_of_knowledge(v0, v1) = v8 & $i(v8) & $i(v7))) & ((v13 = 0 & % 20.88/3.54 greater(v3, v4) = 0) | ( ~ (v12 = 0) & internal_friction(v0, v2) = % 20.88/3.54 v10 & internal_friction(v0, v1) = v11 & smaller_or_equal(v10, v11) = % 20.88/3.54 v12 & $i(v11) & $i(v10)) | ( ~ (v9 = 0) & stock_of_knowledge(v0, v2) % 20.88/3.54 = v7 & stock_of_knowledge(v0, v1) = v8 & greater(v7, v8) = v9 & % 20.88/3.54 $i(v8) & $i(v7)))))) % 20.88/3.54 % 20.88/3.54 (assumption_7) % 20.88/3.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 20.88/3.55 int] : (v5 = 0 | ~ (stock_of_knowledge(v0, v2) = v3) | ~ % 20.88/3.55 (stock_of_knowledge(v0, v1) = v4) | ~ (greater(v3, v4) = v5) | ~ $i(v2) | % 20.88/3.55 ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 20.88/3.55 int] : (( ~ (v9 = 0) & age(v0, v2) = v7 & age(v0, v1) = v8 & greater(v7, % 20.88/3.55 v8) = v9 & $i(v8) & $i(v7)) | ( ~ (v6 = 0) & organization(v0) = v6))) % 20.88/3.55 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 20.88/3.55 (age(v0, v2) = v3) | ~ (age(v0, v1) = v4) | ~ (greater(v3, v4) = 0) | ~ % 20.88/3.55 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: $i] : ? [v7: $i] : % 20.88/3.55 ? [v8: int] : ((v8 = 0 & stock_of_knowledge(v0, v2) = v6 & % 20.88/3.55 stock_of_knowledge(v0, v1) = v7 & greater(v6, v7) = 0 & $i(v7) & $i(v6)) % 20.88/3.55 | ( ~ (v5 = 0) & organization(v0) = v5))) % 20.88/3.55 % 20.88/3.55 (assumption_9) % 20.88/3.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 % 20.88/3.55 | ~ (internal_friction(v0, v2) = v3) | ~ (internal_friction(v0, v1) = v4) % 20.88/3.55 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 20.88/3.55 organization(v0) = v5)) % 20.88/3.55 % 20.88/3.55 (definition_smaller_or_equal) % 20.88/3.55 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (smaller(v0, % 20.88/3.55 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 20.88/3.55 smaller_or_equal(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] % 20.88/3.55 : (v2 = 0 | ~ (smaller_or_equal(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 20.88/3.55 [v3: int] : ( ~ (v3 = 0) & smaller(v0, v1) = v3)) & ! [v0: $i] : ! [v1: % 20.88/3.55 $i] : (v1 = v0 | ~ (smaller_or_equal(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 20.88/3.56 smaller(v0, v1) = 0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 20.88/3.56 (smaller_or_equal(v0, v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ( % 20.88/3.56 ~ (smaller(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | smaller_or_equal(v0, v1) = % 20.88/3.56 0) & ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (smaller(v0, v0) = v1) | % 20.88/3.56 ~ $i(v0) | smaller_or_equal(v0, v0) = 0) % 20.88/3.56 % 20.88/3.56 (lemma_3) % 20.88/3.56 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 20.88/3.56 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & age(v0, v2) = v3 & age(v0, % 20.88/3.56 v1) = v4 & organization(v0) = 0 & capability(v0, v2) = v5 & capability(v0, % 20.88/3.56 v1) = v6 & greater(v5, v6) = v7 & greater(v3, v4) = 0 & $i(v6) & $i(v5) & % 20.88/3.56 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 20.88/3.56 % 20.88/3.56 (function-axioms) % 20.88/3.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (age(v3, % 20.88/3.57 v2) = v1) | ~ (age(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 20.88/3.57 $i] : ! [v3: $i] : (v1 = v0 | ~ (internal_friction(v3, v2) = v1) | ~ % 20.88/3.57 (internal_friction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 20.88/3.57 : ! [v3: $i] : (v1 = v0 | ~ (stock_of_knowledge(v3, v2) = v1) | ~ % 20.88/3.57 (stock_of_knowledge(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 20.88/3.57 : ! [v3: $i] : (v1 = v0 | ~ (capability(v3, v2) = v1) | ~ (capability(v3, % 20.88/3.57 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 20.88/3.57 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ % 20.88/3.57 (greater(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.88/3.57 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.88/3.57 (greater_or_equal(v3, v2) = v1) | ~ (greater_or_equal(v3, v2) = v0)) & ! % 20.88/3.57 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 20.88/3.57 $i] : (v1 = v0 | ~ (smaller(v3, v2) = v1) | ~ (smaller(v3, v2) = v0)) & ! % 20.88/3.57 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 20.88/3.57 $i] : (v1 = v0 | ~ (smaller_or_equal(v3, v2) = v1) | ~ % 20.88/3.57 (smaller_or_equal(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.88/3.57 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (organization(v2) = v1) | % 20.88/3.57 ~ (organization(v2) = v0)) % 20.88/3.57 % 20.88/3.57 Further assumptions not needed in the proof: % 20.88/3.57 -------------------------------------------- % 20.88/3.57 definition_greater_or_equal, definition_smaller, % 20.88/3.57 meaning_postulate_greater_comparable, meaning_postulate_greater_strict, % 20.88/3.57 meaning_postulate_greater_transitive % 20.88/3.57 % 20.88/3.57 Those formulas are unsatisfiable: % 20.88/3.57 --------------------------------- % 20.88/3.57 % 20.88/3.57 Begin of proof % 20.88/3.57 | % 20.88/3.57 | ALPHA: (definition_smaller_or_equal) implies: % 20.88/3.57 | (1) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (smaller_or_equal(v0, v0) = % 20.88/3.57 | v1) | ~ $i(v0)) % 20.88/3.57 | % 20.88/3.57 | ALPHA: (assumption_5) implies: % 20.88/3.58 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 20.88/3.58 | ! [v5: any] : ( ~ (capability(v0, v2) = v3) | ~ (capability(v0, v1) = % 20.88/3.58 | v4) | ~ (greater(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 20.88/3.58 | | ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10: % 20.88/3.58 | $i] : ? [v11: $i] : ? [v12: int] : ? [v13: int] : ? [v14: int] % 20.88/3.58 | : ? [v15: int] : (( ~ (v6 = 0) & organization(v0) = v6) | ((v5 = 0 | % 20.88/3.58 | ( ~ (v12 = 0) & internal_friction(v0, v2) = v10 & % 20.88/3.58 | internal_friction(v0, v1) = v11 & smaller_or_equal(v10, v11) % 20.88/3.58 | = v12 & $i(v11) & $i(v10)) | ( ~ (v9 = 0) & % 20.88/3.58 | stock_of_knowledge(v0, v2) = v7 & stock_of_knowledge(v0, v1) % 20.88/3.58 | = v8 & greater(v7, v8) = v9 & $i(v8) & $i(v7))) & (v4 = v3 | % 20.88/3.58 | ( ~ (v11 = v10) & internal_friction(v0, v2) = v10 & % 20.88/3.58 | internal_friction(v0, v1) = v11 & $i(v11) & $i(v10)) | ( ~ % 20.88/3.58 | (v8 = v7) & stock_of_knowledge(v0, v2) = v7 & % 20.88/3.58 | stock_of_knowledge(v0, v1) = v8 & $i(v8) & $i(v7))) & ((v15 = % 20.88/3.58 | 0 & smaller(v3, v4) = 0) | ( ~ (v14 = 0) & % 20.88/3.58 | internal_friction(v0, v2) = v10 & internal_friction(v0, v1) = % 20.88/3.58 | v11 & greater(v10, v11) = v14 & $i(v11) & $i(v10)) | ( ~ (v13 % 20.88/3.58 | = 0) & stock_of_knowledge(v0, v2) = v7 & % 20.88/3.58 | stock_of_knowledge(v0, v1) = v8 & smaller_or_equal(v7, v8) = % 20.88/3.58 | v13 & $i(v8) & $i(v7)))))) % 20.88/3.59 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 20.88/3.59 | ! [v5: any] : ( ~ (stock_of_knowledge(v0, v2) = v3) | ~ % 20.88/3.59 | (stock_of_knowledge(v0, v1) = v4) | ~ (greater(v3, v4) = v5) | ~ % 20.88/3.59 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: $i] : ? [v8: % 20.88/3.59 | $i] : ? [v9: int] : ? [v10: $i] : ? [v11: $i] : ? [v12: int] : % 20.88/3.59 | ? [v13: int] : ? [v14: int] : ? [v15: int] : (( ~ (v6 = 0) & % 20.88/3.59 | organization(v0) = v6) | (( ~ (v5 = 0) | (v12 = 0 & % 20.88/3.59 | capability(v0, v2) = v10 & capability(v0, v1) = v11 & % 20.88/3.59 | greater(v10, v11) = 0 & $i(v11) & $i(v10)) | ( ~ (v9 = 0) & % 20.88/3.59 | internal_friction(v0, v2) = v7 & internal_friction(v0, v1) = % 20.88/3.59 | v8 & smaller_or_equal(v7, v8) = v9 & $i(v8) & $i(v7))) & ( ~ % 20.88/3.59 | (v4 = v3) | (v11 = v10 & capability(v0, v2) = v10 & % 20.88/3.59 | capability(v0, v1) = v10 & $i(v10)) | ( ~ (v8 = v7) & % 20.88/3.59 | internal_friction(v0, v2) = v7 & internal_friction(v0, v1) = % 20.88/3.59 | v8 & $i(v8) & $i(v7))) & ((v15 = 0 & capability(v0, v2) = v10 % 20.88/3.59 | & capability(v0, v1) = v11 & smaller(v10, v11) = 0 & $i(v11) % 20.88/3.59 | & $i(v10)) | ( ~ (v14 = 0) & internal_friction(v0, v2) = v7 & % 20.88/3.59 | internal_friction(v0, v1) = v8 & greater(v7, v8) = v14 & % 20.88/3.59 | $i(v8) & $i(v7)) | ( ~ (v13 = 0) & smaller_or_equal(v3, v4) = % 20.88/3.59 | v13))))) % 20.88/3.59 | % 20.88/3.59 | ALPHA: (assumption_7) implies: % 20.88/3.59 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 20.88/3.59 | ~ (age(v0, v2) = v3) | ~ (age(v0, v1) = v4) | ~ (greater(v3, v4) = % 20.88/3.59 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: $i] % 20.88/3.59 | : ? [v7: $i] : ? [v8: int] : ((v8 = 0 & stock_of_knowledge(v0, v2) % 20.88/3.59 | = v6 & stock_of_knowledge(v0, v1) = v7 & greater(v6, v7) = 0 & % 20.88/3.59 | $i(v7) & $i(v6)) | ( ~ (v5 = 0) & organization(v0) = v5))) % 20.88/3.59 | % 20.88/3.59 | ALPHA: (function-axioms) implies: % 21.37/3.60 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 21.37/3.60 | (v1 = v0 | ~ (organization(v2) = v1) | ~ (organization(v2) = v0)) % 21.37/3.60 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 21.37/3.60 | ! [v3: $i] : (v1 = v0 | ~ (smaller_or_equal(v3, v2) = v1) | ~ % 21.37/3.60 | (smaller_or_equal(v3, v2) = v0)) % 21.37/3.60 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 21.37/3.60 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, % 21.37/3.60 | v2) = v0)) % 21.37/3.60 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.37/3.60 | (capability(v3, v2) = v1) | ~ (capability(v3, v2) = v0)) % 21.37/3.60 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.37/3.60 | (stock_of_knowledge(v3, v2) = v1) | ~ (stock_of_knowledge(v3, v2) = % 21.37/3.60 | v0)) % 21.37/3.60 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.37/3.60 | (internal_friction(v3, v2) = v1) | ~ (internal_friction(v3, v2) = % 21.37/3.60 | v0)) % 21.37/3.60 | % 21.37/3.60 | DELTA: instantiating (lemma_3) with fresh symbols all_12_0, all_12_1, % 21.37/3.60 | all_12_2, all_12_3, all_12_4, all_12_5, all_12_6, all_12_7 gives: % 21.37/3.61 | (11) ~ (all_12_0 = 0) & age(all_12_7, all_12_5) = all_12_4 & age(all_12_7, % 21.37/3.61 | all_12_6) = all_12_3 & organization(all_12_7) = 0 & % 21.37/3.61 | capability(all_12_7, all_12_5) = all_12_2 & capability(all_12_7, % 21.37/3.61 | all_12_6) = all_12_1 & greater(all_12_2, all_12_1) = all_12_0 & % 21.37/3.61 | greater(all_12_4, all_12_3) = 0 & $i(all_12_1) & $i(all_12_2) & % 21.37/3.61 | $i(all_12_3) & $i(all_12_4) & $i(all_12_5) & $i(all_12_6) & % 21.37/3.61 | $i(all_12_7) % 21.37/3.61 | % 21.37/3.61 | ALPHA: (11) implies: % 21.37/3.61 | (12) ~ (all_12_0 = 0) % 21.37/3.61 | (13) $i(all_12_7) % 21.37/3.61 | (14) $i(all_12_6) % 21.37/3.61 | (15) $i(all_12_5) % 21.37/3.61 | (16) greater(all_12_4, all_12_3) = 0 % 21.37/3.61 | (17) greater(all_12_2, all_12_1) = all_12_0 % 21.37/3.61 | (18) capability(all_12_7, all_12_6) = all_12_1 % 21.37/3.61 | (19) capability(all_12_7, all_12_5) = all_12_2 % 21.37/3.61 | (20) organization(all_12_7) = 0 % 21.37/3.61 | (21) age(all_12_7, all_12_6) = all_12_3 % 21.37/3.61 | (22) age(all_12_7, all_12_5) = all_12_4 % 21.37/3.61 | % 21.37/3.62 | GROUND_INST: instantiating (2) with all_12_7, all_12_6, all_12_5, all_12_2, % 21.37/3.62 | all_12_1, all_12_0, simplifying with (13), (14), (15), (17), % 21.37/3.62 | (18), (19) gives: % 21.37/3.62 | (23) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: $i] % 21.37/3.62 | : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: % 21.37/3.62 | int] : (( ~ (v0 = 0) & organization(all_12_7) = v0) | ((all_12_0 = 0 % 21.37/3.62 | | ( ~ (v6 = 0) & internal_friction(all_12_7, all_12_5) = v4 & % 21.37/3.62 | internal_friction(all_12_7, all_12_6) = v5 & % 21.37/3.62 | smaller_or_equal(v4, v5) = v6 & $i(v5) & $i(v4)) | ( ~ (v3 = % 21.37/3.62 | 0) & stock_of_knowledge(all_12_7, all_12_5) = v1 & % 21.37/3.62 | stock_of_knowledge(all_12_7, all_12_6) = v2 & greater(v1, v2) % 21.37/3.62 | = v3 & $i(v2) & $i(v1))) & (all_12_1 = all_12_2 | ( ~ (v5 = % 21.37/3.62 | v4) & internal_friction(all_12_7, all_12_5) = v4 & % 21.37/3.62 | internal_friction(all_12_7, all_12_6) = v5 & $i(v5) & $i(v4)) % 21.37/3.62 | | ( ~ (v2 = v1) & stock_of_knowledge(all_12_7, all_12_5) = v1 & % 21.37/3.62 | stock_of_knowledge(all_12_7, all_12_6) = v2 & $i(v2) & % 21.37/3.62 | $i(v1))) & ((v9 = 0 & smaller(all_12_2, all_12_1) = 0) | ( ~ % 21.37/3.62 | (v8 = 0) & internal_friction(all_12_7, all_12_5) = v4 & % 21.37/3.62 | internal_friction(all_12_7, all_12_6) = v5 & greater(v4, v5) = % 21.37/3.62 | v8 & $i(v5) & $i(v4)) | ( ~ (v7 = 0) & % 21.37/3.62 | stock_of_knowledge(all_12_7, all_12_5) = v1 & % 21.37/3.62 | stock_of_knowledge(all_12_7, all_12_6) = v2 & % 21.37/3.62 | smaller_or_equal(v1, v2) = v7 & $i(v2) & $i(v1))))) % 21.37/3.63 | % 21.37/3.63 | GROUND_INST: instantiating (4) with all_12_7, all_12_6, all_12_5, all_12_4, % 21.37/3.63 | all_12_3, simplifying with (13), (14), (15), (16), (21), (22) % 21.37/3.63 | gives: % 21.37/3.63 | (24) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ((v3 = 0 & % 21.37/3.63 | stock_of_knowledge(all_12_7, all_12_5) = v1 & % 21.37/3.63 | stock_of_knowledge(all_12_7, all_12_6) = v2 & greater(v1, v2) = 0 % 21.37/3.63 | & $i(v2) & $i(v1)) | ( ~ (v0 = 0) & organization(all_12_7) = v0)) % 21.37/3.63 | % 21.37/3.63 | DELTA: instantiating (24) with fresh symbols all_22_0, all_22_1, all_22_2, % 21.37/3.63 | all_22_3 gives: % 21.37/3.63 | (25) (all_22_0 = 0 & stock_of_knowledge(all_12_7, all_12_5) = all_22_2 & % 21.37/3.63 | stock_of_knowledge(all_12_7, all_12_6) = all_22_1 & % 21.37/3.63 | greater(all_22_2, all_22_1) = 0 & $i(all_22_1) & $i(all_22_2)) | ( ~ % 21.37/3.63 | (all_22_3 = 0) & organization(all_12_7) = all_22_3) % 21.37/3.63 | % 21.37/3.63 | DELTA: instantiating (23) with fresh symbols all_23_0, all_23_1, all_23_2, % 21.37/3.63 | all_23_3, all_23_4, all_23_5, all_23_6, all_23_7, all_23_8, all_23_9 % 21.37/3.63 | gives: % 21.37/3.64 | (26) ( ~ (all_23_9 = 0) & organization(all_12_7) = all_23_9) | ((all_12_0 = % 21.37/3.64 | 0 | ( ~ (all_23_3 = 0) & internal_friction(all_12_7, all_12_5) = % 21.37/3.64 | all_23_5 & internal_friction(all_12_7, all_12_6) = all_23_4 & % 21.37/3.64 | smaller_or_equal(all_23_5, all_23_4) = all_23_3 & $i(all_23_4) & % 21.37/3.64 | $i(all_23_5)) | ( ~ (all_23_6 = 0) & % 21.37/3.64 | stock_of_knowledge(all_12_7, all_12_5) = all_23_8 & % 21.37/3.64 | stock_of_knowledge(all_12_7, all_12_6) = all_23_7 & % 21.37/3.64 | greater(all_23_8, all_23_7) = all_23_6 & $i(all_23_7) & % 21.37/3.64 | $i(all_23_8))) & (all_12_1 = all_12_2 | ( ~ (all_23_4 = % 21.37/3.64 | all_23_5) & internal_friction(all_12_7, all_12_5) = all_23_5 & % 21.37/3.64 | internal_friction(all_12_7, all_12_6) = all_23_4 & $i(all_23_4) % 21.37/3.64 | & $i(all_23_5)) | ( ~ (all_23_7 = all_23_8) & % 21.37/3.64 | stock_of_knowledge(all_12_7, all_12_5) = all_23_8 & % 21.37/3.64 | stock_of_knowledge(all_12_7, all_12_6) = all_23_7 & $i(all_23_7) % 21.37/3.64 | & $i(all_23_8))) & ((all_23_0 = 0 & smaller(all_12_2, all_12_1) % 21.37/3.64 | = 0) | ( ~ (all_23_1 = 0) & internal_friction(all_12_7, % 21.37/3.64 | all_12_5) = all_23_5 & internal_friction(all_12_7, all_12_6) = % 21.37/3.64 | all_23_4 & greater(all_23_5, all_23_4) = all_23_1 & $i(all_23_4) % 21.37/3.64 | & $i(all_23_5)) | ( ~ (all_23_2 = 0) & % 21.37/3.64 | stock_of_knowledge(all_12_7, all_12_5) = all_23_8 & % 21.37/3.64 | stock_of_knowledge(all_12_7, all_12_6) = all_23_7 & % 21.37/3.64 | smaller_or_equal(all_23_8, all_23_7) = all_23_2 & $i(all_23_7) & % 21.37/3.64 | $i(all_23_8)))) % 21.37/3.64 | % 21.37/3.64 | BETA: splitting (25) gives: % 21.37/3.64 | % 21.37/3.64 | Case 1: % 21.37/3.64 | | % 21.37/3.64 | | (27) all_22_0 = 0 & stock_of_knowledge(all_12_7, all_12_5) = all_22_2 & % 21.37/3.64 | | stock_of_knowledge(all_12_7, all_12_6) = all_22_1 & % 21.37/3.64 | | greater(all_22_2, all_22_1) = 0 & $i(all_22_1) & $i(all_22_2) % 21.37/3.64 | | % 21.37/3.64 | | ALPHA: (27) implies: % 21.37/3.64 | | (28) greater(all_22_2, all_22_1) = 0 % 21.37/3.64 | | (29) stock_of_knowledge(all_12_7, all_12_6) = all_22_1 % 21.37/3.64 | | (30) stock_of_knowledge(all_12_7, all_12_5) = all_22_2 % 21.37/3.64 | | % 21.37/3.64 | | BETA: splitting (26) gives: % 21.37/3.64 | | % 21.37/3.64 | | Case 1: % 21.37/3.64 | | | % 21.37/3.64 | | | (31) ~ (all_23_9 = 0) & organization(all_12_7) = all_23_9 % 21.37/3.64 | | | % 21.37/3.64 | | | ALPHA: (31) implies: % 21.37/3.64 | | | (32) ~ (all_23_9 = 0) % 21.37/3.64 | | | (33) organization(all_12_7) = all_23_9 % 21.37/3.64 | | | % 21.37/3.64 | | | GROUND_INST: instantiating (5) with 0, all_23_9, all_12_7, simplifying % 21.37/3.64 | | | with (20), (33) gives: % 21.37/3.64 | | | (34) all_23_9 = 0 % 21.37/3.64 | | | % 21.37/3.64 | | | REDUCE: (32), (34) imply: % 21.37/3.64 | | | (35) $false % 21.37/3.65 | | | % 21.37/3.65 | | | CLOSE: (35) is inconsistent. % 21.37/3.65 | | | % 21.37/3.65 | | Case 2: % 21.37/3.65 | | | % 21.37/3.65 | | | (36) (all_12_0 = 0 | ( ~ (all_23_3 = 0) & internal_friction(all_12_7, % 21.37/3.65 | | | all_12_5) = all_23_5 & internal_friction(all_12_7, all_12_6) % 21.37/3.65 | | | = all_23_4 & smaller_or_equal(all_23_5, all_23_4) = all_23_3 & % 21.37/3.65 | | | $i(all_23_4) & $i(all_23_5)) | ( ~ (all_23_6 = 0) & % 21.37/3.65 | | | stock_of_knowledge(all_12_7, all_12_5) = all_23_8 & % 21.37/3.65 | | | stock_of_knowledge(all_12_7, all_12_6) = all_23_7 & % 21.37/3.65 | | | greater(all_23_8, all_23_7) = all_23_6 & $i(all_23_7) & % 21.37/3.65 | | | $i(all_23_8))) & (all_12_1 = all_12_2 | ( ~ (all_23_4 = % 21.37/3.65 | | | all_23_5) & internal_friction(all_12_7, all_12_5) = all_23_5 % 21.37/3.65 | | | & internal_friction(all_12_7, all_12_6) = all_23_4 & % 21.37/3.65 | | | $i(all_23_4) & $i(all_23_5)) | ( ~ (all_23_7 = all_23_8) & % 21.37/3.65 | | | stock_of_knowledge(all_12_7, all_12_5) = all_23_8 & % 21.37/3.65 | | | stock_of_knowledge(all_12_7, all_12_6) = all_23_7 & % 21.37/3.65 | | | $i(all_23_7) & $i(all_23_8))) & ((all_23_0 = 0 & % 21.37/3.65 | | | smaller(all_12_2, all_12_1) = 0) | ( ~ (all_23_1 = 0) & % 21.37/3.65 | | | internal_friction(all_12_7, all_12_5) = all_23_5 & % 21.37/3.65 | | | internal_friction(all_12_7, all_12_6) = all_23_4 & % 21.37/3.65 | | | greater(all_23_5, all_23_4) = all_23_1 & $i(all_23_4) & % 21.37/3.65 | | | $i(all_23_5)) | ( ~ (all_23_2 = 0) & % 21.37/3.65 | | | stock_of_knowledge(all_12_7, all_12_5) = all_23_8 & % 21.37/3.65 | | | stock_of_knowledge(all_12_7, all_12_6) = all_23_7 & % 21.37/3.65 | | | smaller_or_equal(all_23_8, all_23_7) = all_23_2 & $i(all_23_7) % 21.37/3.65 | | | & $i(all_23_8))) % 21.37/3.65 | | | % 21.37/3.65 | | | ALPHA: (36) implies: % 21.37/3.65 | | | (37) all_12_0 = 0 | ( ~ (all_23_3 = 0) & internal_friction(all_12_7, % 21.37/3.65 | | | all_12_5) = all_23_5 & internal_friction(all_12_7, all_12_6) = % 21.37/3.65 | | | all_23_4 & smaller_or_equal(all_23_5, all_23_4) = all_23_3 & % 21.37/3.65 | | | $i(all_23_4) & $i(all_23_5)) | ( ~ (all_23_6 = 0) & % 21.37/3.65 | | | stock_of_knowledge(all_12_7, all_12_5) = all_23_8 & % 21.37/3.65 | | | stock_of_knowledge(all_12_7, all_12_6) = all_23_7 & % 21.37/3.65 | | | greater(all_23_8, all_23_7) = all_23_6 & $i(all_23_7) & % 21.37/3.65 | | | $i(all_23_8)) % 21.37/3.65 | | | % 21.37/3.65 | | | BETA: splitting (37) gives: % 21.37/3.65 | | | % 21.37/3.65 | | | Case 1: % 21.37/3.65 | | | | % 21.37/3.65 | | | | (38) all_12_0 = 0 % 21.37/3.65 | | | | % 21.37/3.65 | | | | REDUCE: (12), (38) imply: % 21.37/3.65 | | | | (39) $false % 21.37/3.65 | | | | % 21.37/3.65 | | | | CLOSE: (39) is inconsistent. % 21.37/3.65 | | | | % 21.37/3.65 | | | Case 2: % 21.37/3.65 | | | | % 21.37/3.66 | | | | (40) ( ~ (all_23_3 = 0) & internal_friction(all_12_7, all_12_5) = % 21.37/3.66 | | | | all_23_5 & internal_friction(all_12_7, all_12_6) = all_23_4 & % 21.37/3.66 | | | | smaller_or_equal(all_23_5, all_23_4) = all_23_3 & $i(all_23_4) % 21.37/3.66 | | | | & $i(all_23_5)) | ( ~ (all_23_6 = 0) & % 21.37/3.66 | | | | stock_of_knowledge(all_12_7, all_12_5) = all_23_8 & % 21.37/3.66 | | | | stock_of_knowledge(all_12_7, all_12_6) = all_23_7 & % 21.37/3.66 | | | | greater(all_23_8, all_23_7) = all_23_6 & $i(all_23_7) & % 21.37/3.66 | | | | $i(all_23_8)) % 21.37/3.66 | | | | % 21.37/3.66 | | | | BETA: splitting (40) gives: % 21.37/3.66 | | | | % 21.37/3.66 | | | | Case 1: % 21.37/3.66 | | | | | % 21.37/3.66 | | | | | (41) ~ (all_23_3 = 0) & internal_friction(all_12_7, all_12_5) = % 21.37/3.66 | | | | | all_23_5 & internal_friction(all_12_7, all_12_6) = all_23_4 & % 21.37/3.66 | | | | | smaller_or_equal(all_23_5, all_23_4) = all_23_3 & $i(all_23_4) % 21.37/3.66 | | | | | & $i(all_23_5) % 21.37/3.66 | | | | | % 21.37/3.66 | | | | | ALPHA: (41) implies: % 21.37/3.66 | | | | | (42) smaller_or_equal(all_23_5, all_23_4) = all_23_3 % 21.37/3.66 | | | | | (43) internal_friction(all_12_7, all_12_6) = all_23_4 % 21.37/3.66 | | | | | (44) internal_friction(all_12_7, all_12_5) = all_23_5 % 21.37/3.66 | | | | | % 21.37/3.66 | | | | | GROUND_INST: instantiating (3) with all_12_7, all_12_6, all_12_5, % 21.37/3.66 | | | | | all_22_2, all_22_1, 0, simplifying with (13), (14), (15), % 21.37/3.66 | | | | | (28), (29), (30) gives: % 21.37/3.67 | | | | | (45) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? % 21.37/3.67 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8: % 21.37/3.67 | | | | | int] : ? [v9: int] : (( ~ (v0 = 0) & organization(all_12_7) % 21.37/3.67 | | | | | = v0) | (( ~ (all_22_1 = all_22_2) | (v5 = v4 & % 21.37/3.67 | | | | | capability(all_12_7, all_12_5) = v4 & % 21.37/3.67 | | | | | capability(all_12_7, all_12_6) = v4 & $i(v4)) | ( ~ % 21.37/3.67 | | | | | (v2 = v1) & internal_friction(all_12_7, all_12_5) = v1 % 21.37/3.67 | | | | | & internal_friction(all_12_7, all_12_6) = v2 & $i(v2) % 21.37/3.67 | | | | | & $i(v1))) & ((v9 = 0 & capability(all_12_7, all_12_5) % 21.37/3.67 | | | | | = v4 & capability(all_12_7, all_12_6) = v5 & % 21.37/3.67 | | | | | smaller(v4, v5) = 0 & $i(v5) & $i(v4)) | ( ~ (v8 = 0) % 21.37/3.67 | | | | | & internal_friction(all_12_7, all_12_5) = v1 & % 21.37/3.67 | | | | | internal_friction(all_12_7, all_12_6) = v2 & % 21.37/3.67 | | | | | greater(v1, v2) = v8 & $i(v2) & $i(v1)) | ( ~ (v7 = 0) % 21.37/3.67 | | | | | & smaller_or_equal(all_22_2, all_22_1) = v7)) & ((v6 = % 21.37/3.67 | | | | | 0 & capability(all_12_7, all_12_5) = v4 & % 21.37/3.67 | | | | | capability(all_12_7, all_12_6) = v5 & greater(v4, v5) % 21.37/3.67 | | | | | = 0 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) & % 21.37/3.67 | | | | | internal_friction(all_12_7, all_12_5) = v1 & % 21.37/3.67 | | | | | internal_friction(all_12_7, all_12_6) = v2 & % 21.37/3.67 | | | | | smaller_or_equal(v1, v2) = v3 & $i(v2) & $i(v1))))) % 21.37/3.67 | | | | | % 21.37/3.67 | | | | | GROUND_INST: instantiating (assumption_9) with all_12_7, all_12_6, % 21.37/3.67 | | | | | all_12_5, all_23_5, all_23_4, simplifying with (13), % 21.37/3.67 | | | | | (14), (15), (43), (44) gives: % 21.37/3.67 | | | | | (46) all_23_4 = all_23_5 | ? [v0: int] : ( ~ (v0 = 0) & % 21.37/3.67 | | | | | organization(all_12_7) = v0) % 21.37/3.67 | | | | | % 21.37/3.67 | | | | | DELTA: instantiating (45) with fresh symbols all_51_0, all_51_1, % 21.37/3.67 | | | | | all_51_2, all_51_3, all_51_4, all_51_5, all_51_6, all_51_7, % 21.37/3.67 | | | | | all_51_8, all_51_9 gives: % 21.37/3.67 | | | | | (47) ( ~ (all_51_9 = 0) & organization(all_12_7) = all_51_9) | (( ~ % 21.37/3.67 | | | | | (all_22_1 = all_22_2) | (all_51_4 = all_51_5 & % 21.37/3.67 | | | | | capability(all_12_7, all_12_5) = all_51_5 & % 21.37/3.67 | | | | | capability(all_12_7, all_12_6) = all_51_5 & % 21.37/3.67 | | | | | $i(all_51_5)) | ( ~ (all_51_7 = all_51_8) & % 21.37/3.67 | | | | | internal_friction(all_12_7, all_12_5) = all_51_8 & % 21.37/3.67 | | | | | internal_friction(all_12_7, all_12_6) = all_51_7 & % 21.37/3.67 | | | | | $i(all_51_7) & $i(all_51_8))) & ((all_51_0 = 0 & % 21.37/3.67 | | | | | capability(all_12_7, all_12_5) = all_51_5 & % 21.37/3.67 | | | | | capability(all_12_7, all_12_6) = all_51_4 & % 21.37/3.67 | | | | | smaller(all_51_5, all_51_4) = 0 & $i(all_51_4) & % 21.37/3.67 | | | | | $i(all_51_5)) | ( ~ (all_51_1 = 0) & % 21.37/3.67 | | | | | internal_friction(all_12_7, all_12_5) = all_51_8 & % 21.37/3.68 | | | | | internal_friction(all_12_7, all_12_6) = all_51_7 & % 21.37/3.68 | | | | | greater(all_51_8, all_51_7) = all_51_1 & $i(all_51_7) & % 21.37/3.68 | | | | | $i(all_51_8)) | ( ~ (all_51_2 = 0) & % 21.37/3.68 | | | | | smaller_or_equal(all_22_2, all_22_1) = all_51_2)) & % 21.37/3.68 | | | | | ((all_51_3 = 0 & capability(all_12_7, all_12_5) = all_51_5 & % 21.37/3.68 | | | | | capability(all_12_7, all_12_6) = all_51_4 & % 21.37/3.68 | | | | | greater(all_51_5, all_51_4) = 0 & $i(all_51_4) & % 21.37/3.68 | | | | | $i(all_51_5)) | ( ~ (all_51_6 = 0) & % 21.37/3.68 | | | | | internal_friction(all_12_7, all_12_5) = all_51_8 & % 21.37/3.68 | | | | | internal_friction(all_12_7, all_12_6) = all_51_7 & % 21.37/3.68 | | | | | smaller_or_equal(all_51_8, all_51_7) = all_51_6 & % 21.37/3.68 | | | | | $i(all_51_7) & $i(all_51_8)))) % 21.37/3.68 | | | | | % 21.37/3.68 | | | | | BETA: splitting (47) gives: % 21.37/3.68 | | | | | % 21.37/3.68 | | | | | Case 1: % 21.37/3.68 | | | | | | % 21.37/3.68 | | | | | | (48) ~ (all_51_9 = 0) & organization(all_12_7) = all_51_9 % 21.37/3.68 | | | | | | % 21.37/3.68 | | | | | | ALPHA: (48) implies: % 21.37/3.68 | | | | | | (49) ~ (all_51_9 = 0) % 21.37/3.68 | | | | | | (50) organization(all_12_7) = all_51_9 % 21.37/3.68 | | | | | | % 21.37/3.68 | | | | | | GROUND_INST: instantiating (5) with 0, all_51_9, all_12_7, % 21.37/3.68 | | | | | | simplifying with (20), (50) gives: % 21.37/3.68 | | | | | | (51) all_51_9 = 0 % 21.37/3.68 | | | | | | % 21.37/3.68 | | | | | | REDUCE: (49), (51) imply: % 21.37/3.68 | | | | | | (52) $false % 21.37/3.68 | | | | | | % 21.37/3.68 | | | | | | CLOSE: (52) is inconsistent. % 21.37/3.68 | | | | | | % 21.37/3.68 | | | | | Case 2: % 21.37/3.68 | | | | | | % 21.37/3.68 | | | | | | (53) ( ~ (all_22_1 = all_22_2) | (all_51_4 = all_51_5 & % 21.37/3.68 | | | | | | capability(all_12_7, all_12_5) = all_51_5 & % 21.37/3.68 | | | | | | capability(all_12_7, all_12_6) = all_51_5 & % 21.37/3.68 | | | | | | $i(all_51_5)) | ( ~ (all_51_7 = all_51_8) & % 21.37/3.68 | | | | | | internal_friction(all_12_7, all_12_5) = all_51_8 & % 21.37/3.68 | | | | | | internal_friction(all_12_7, all_12_6) = all_51_7 & % 21.37/3.68 | | | | | | $i(all_51_7) & $i(all_51_8))) & ((all_51_0 = 0 & % 21.37/3.68 | | | | | | capability(all_12_7, all_12_5) = all_51_5 & % 21.37/3.68 | | | | | | capability(all_12_7, all_12_6) = all_51_4 & % 21.37/3.68 | | | | | | smaller(all_51_5, all_51_4) = 0 & $i(all_51_4) & % 21.37/3.68 | | | | | | $i(all_51_5)) | ( ~ (all_51_1 = 0) & % 21.37/3.68 | | | | | | internal_friction(all_12_7, all_12_5) = all_51_8 & % 21.37/3.68 | | | | | | internal_friction(all_12_7, all_12_6) = all_51_7 & % 21.37/3.68 | | | | | | greater(all_51_8, all_51_7) = all_51_1 & $i(all_51_7) & % 21.37/3.68 | | | | | | $i(all_51_8)) | ( ~ (all_51_2 = 0) & % 21.37/3.68 | | | | | | smaller_or_equal(all_22_2, all_22_1) = all_51_2)) & % 21.37/3.68 | | | | | | ((all_51_3 = 0 & capability(all_12_7, all_12_5) = all_51_5 & % 21.37/3.68 | | | | | | capability(all_12_7, all_12_6) = all_51_4 & % 21.37/3.68 | | | | | | greater(all_51_5, all_51_4) = 0 & $i(all_51_4) & % 21.37/3.68 | | | | | | $i(all_51_5)) | ( ~ (all_51_6 = 0) & % 21.37/3.68 | | | | | | internal_friction(all_12_7, all_12_5) = all_51_8 & % 21.37/3.68 | | | | | | internal_friction(all_12_7, all_12_6) = all_51_7 & % 21.37/3.68 | | | | | | smaller_or_equal(all_51_8, all_51_7) = all_51_6 & % 21.37/3.68 | | | | | | $i(all_51_7) & $i(all_51_8))) % 21.37/3.69 | | | | | | % 21.37/3.69 | | | | | | ALPHA: (53) implies: % 21.37/3.69 | | | | | | (54) (all_51_3 = 0 & capability(all_12_7, all_12_5) = all_51_5 & % 21.37/3.69 | | | | | | capability(all_12_7, all_12_6) = all_51_4 & % 21.37/3.69 | | | | | | greater(all_51_5, all_51_4) = 0 & $i(all_51_4) & % 21.37/3.69 | | | | | | $i(all_51_5)) | ( ~ (all_51_6 = 0) & % 21.37/3.69 | | | | | | internal_friction(all_12_7, all_12_5) = all_51_8 & % 21.37/3.69 | | | | | | internal_friction(all_12_7, all_12_6) = all_51_7 & % 21.37/3.69 | | | | | | smaller_or_equal(all_51_8, all_51_7) = all_51_6 & % 21.37/3.69 | | | | | | $i(all_51_7) & $i(all_51_8)) % 21.37/3.69 | | | | | | % 21.37/3.69 | | | | | | BETA: splitting (46) gives: % 21.37/3.69 | | | | | | % 21.37/3.69 | | | | | | Case 1: % 21.37/3.69 | | | | | | | % 21.37/3.69 | | | | | | | (55) all_23_4 = all_23_5 % 21.37/3.69 | | | | | | | % 21.37/3.69 | | | | | | | REDUCE: (43), (55) imply: % 21.37/3.69 | | | | | | | (56) internal_friction(all_12_7, all_12_6) = all_23_5 % 21.37/3.69 | | | | | | | % 21.37/3.69 | | | | | | | REDUCE: (42), (55) imply: % 21.37/3.69 | | | | | | | (57) smaller_or_equal(all_23_5, all_23_5) = all_23_3 % 21.37/3.69 | | | | | | | % 21.37/3.69 | | | | | | | BETA: splitting (54) gives: % 21.37/3.69 | | | | | | | % 21.37/3.69 | | | | | | | Case 1: % 21.37/3.69 | | | | | | | | % 21.37/3.69 | | | | | | | | (58) all_51_3 = 0 & capability(all_12_7, all_12_5) = all_51_5 % 21.37/3.69 | | | | | | | | & capability(all_12_7, all_12_6) = all_51_4 & % 21.37/3.69 | | | | | | | | greater(all_51_5, all_51_4) = 0 & $i(all_51_4) & % 21.37/3.69 | | | | | | | | $i(all_51_5) % 21.37/3.69 | | | | | | | | % 21.37/3.69 | | | | | | | | ALPHA: (58) implies: % 21.37/3.69 | | | | | | | | (59) greater(all_51_5, all_51_4) = 0 % 21.37/3.69 | | | | | | | | (60) capability(all_12_7, all_12_6) = all_51_4 % 21.37/3.69 | | | | | | | | (61) capability(all_12_7, all_12_5) = all_51_5 % 21.37/3.69 | | | | | | | | % 21.37/3.69 | | | | | | | | GROUND_INST: instantiating (8) with all_12_1, all_51_4, % 21.37/3.69 | | | | | | | | all_12_6, all_12_7, simplifying with (18), (60) % 21.37/3.69 | | | | | | | | gives: % 21.37/3.69 | | | | | | | | (62) all_51_4 = all_12_1 % 21.37/3.69 | | | | | | | | % 21.37/3.69 | | | | | | | | GROUND_INST: instantiating (8) with all_12_2, all_51_5, % 21.37/3.69 | | | | | | | | all_12_5, all_12_7, simplifying with (19), (61) % 21.37/3.69 | | | | | | | | gives: % 21.37/3.69 | | | | | | | | (63) all_51_5 = all_12_2 % 21.37/3.69 | | | | | | | | % 21.37/3.70 | | | | | | | | REDUCE: (59), (62), (63) imply: % 21.37/3.70 | | | | | | | | (64) greater(all_12_2, all_12_1) = 0 % 21.37/3.70 | | | | | | | | % 21.37/3.70 | | | | | | | | GROUND_INST: instantiating (7) with all_12_0, 0, all_12_1, % 21.37/3.70 | | | | | | | | all_12_2, simplifying with (17), (64) gives: % 21.37/3.70 | | | | | | | | (65) all_12_0 = 0 % 21.87/3.70 | | | | | | | | % 21.87/3.70 | | | | | | | | REDUCE: (12), (65) imply: % 21.87/3.70 | | | | | | | | (66) $false % 21.87/3.70 | | | | | | | | % 21.87/3.70 | | | | | | | | CLOSE: (66) is inconsistent. % 21.87/3.70 | | | | | | | | % 21.87/3.70 | | | | | | | Case 2: % 21.87/3.70 | | | | | | | | % 21.87/3.70 | | | | | | | | (67) ~ (all_51_6 = 0) & internal_friction(all_12_7, % 21.87/3.70 | | | | | | | | all_12_5) = all_51_8 & internal_friction(all_12_7, % 21.87/3.70 | | | | | | | | all_12_6) = all_51_7 & smaller_or_equal(all_51_8, % 21.87/3.70 | | | | | | | | all_51_7) = all_51_6 & $i(all_51_7) & $i(all_51_8) % 21.87/3.70 | | | | | | | | % 21.87/3.70 | | | | | | | | ALPHA: (67) implies: % 21.87/3.70 | | | | | | | | (68) ~ (all_51_6 = 0) % 21.87/3.70 | | | | | | | | (69) $i(all_51_8) % 21.87/3.70 | | | | | | | | (70) smaller_or_equal(all_51_8, all_51_7) = all_51_6 % 21.87/3.70 | | | | | | | | (71) internal_friction(all_12_7, all_12_6) = all_51_7 % 21.87/3.70 | | | | | | | | (72) internal_friction(all_12_7, all_12_5) = all_51_8 % 21.87/3.70 | | | | | | | | % 21.87/3.70 | | | | | | | | GROUND_INST: instantiating (10) with all_23_5, all_51_7, % 21.87/3.70 | | | | | | | | all_12_6, all_12_7, simplifying with (56), (71) % 21.87/3.70 | | | | | | | | gives: % 21.87/3.70 | | | | | | | | (73) all_51_7 = all_23_5 % 21.87/3.70 | | | | | | | | % 21.87/3.70 | | | | | | | | GROUND_INST: instantiating (10) with all_23_5, all_51_8, % 21.87/3.70 | | | | | | | | all_12_5, all_12_7, simplifying with (44), (72) % 21.87/3.70 | | | | | | | | gives: % 21.87/3.70 | | | | | | | | (74) all_51_8 = all_23_5 % 21.87/3.70 | | | | | | | | % 21.87/3.70 | | | | | | | | REDUCE: (70), (73), (74) imply: % 21.87/3.70 | | | | | | | | (75) smaller_or_equal(all_23_5, all_23_5) = all_51_6 % 21.87/3.70 | | | | | | | | % 21.87/3.70 | | | | | | | | REDUCE: (69), (74) imply: % 21.87/3.70 | | | | | | | | (76) $i(all_23_5) % 21.87/3.70 | | | | | | | | % 21.87/3.70 | | | | | | | | GROUND_INST: instantiating (6) with all_23_3, all_51_6, % 21.87/3.70 | | | | | | | | all_23_5, all_23_5, simplifying with (57), (75) % 21.87/3.71 | | | | | | | | gives: % 21.87/3.71 | | | | | | | | (77) all_51_6 = all_23_3 % 21.87/3.71 | | | | | | | | % 21.87/3.71 | | | | | | | | REDUCE: (68), (77) imply: % 21.87/3.71 | | | | | | | | (78) ~ (all_23_3 = 0) % 21.87/3.71 | | | | | | | | % 21.87/3.71 | | | | | | | | GROUND_INST: instantiating (1) with all_23_5, all_23_3, % 21.87/3.71 | | | | | | | | simplifying with (57), (76) gives: % 21.87/3.71 | | | | | | | | (79) all_23_3 = 0 % 21.87/3.71 | | | | | | | | % 21.87/3.71 | | | | | | | | REDUCE: (78), (79) imply: % 21.87/3.71 | | | | | | | | (80) $false % 21.87/3.71 | | | | | | | | % 21.87/3.71 | | | | | | | | CLOSE: (80) is inconsistent. % 21.87/3.71 | | | | | | | | % 21.87/3.71 | | | | | | | End of split % 21.87/3.71 | | | | | | | % 21.87/3.71 | | | | | | Case 2: % 21.87/3.71 | | | | | | | % 21.87/3.71 | | | | | | | (81) ? [v0: int] : ( ~ (v0 = 0) & organization(all_12_7) = v0) % 21.87/3.71 | | | | | | | % 21.87/3.71 | | | | | | | DELTA: instantiating (81) with fresh symbol all_65_0 gives: % 21.87/3.71 | | | | | | | (82) ~ (all_65_0 = 0) & organization(all_12_7) = all_65_0 % 21.87/3.71 | | | | | | | % 21.87/3.71 | | | | | | | ALPHA: (82) implies: % 21.87/3.71 | | | | | | | (83) ~ (all_65_0 = 0) % 21.87/3.71 | | | | | | | (84) organization(all_12_7) = all_65_0 % 21.87/3.71 | | | | | | | % 21.87/3.71 | | | | | | | GROUND_INST: instantiating (5) with 0, all_65_0, all_12_7, % 21.87/3.71 | | | | | | | simplifying with (20), (84) gives: % 21.87/3.71 | | | | | | | (85) all_65_0 = 0 % 21.87/3.71 | | | | | | | % 21.87/3.71 | | | | | | | REDUCE: (83), (85) imply: % 21.87/3.71 | | | | | | | (86) $false % 21.87/3.71 | | | | | | | % 21.87/3.71 | | | | | | | CLOSE: (86) is inconsistent. % 21.87/3.71 | | | | | | | % 21.87/3.71 | | | | | | End of split % 21.87/3.71 | | | | | | % 21.87/3.71 | | | | | End of split % 21.87/3.71 | | | | | % 21.87/3.71 | | | | Case 2: % 21.87/3.71 | | | | | % 21.87/3.71 | | | | | (87) ~ (all_23_6 = 0) & stock_of_knowledge(all_12_7, all_12_5) = % 21.87/3.71 | | | | | all_23_8 & stock_of_knowledge(all_12_7, all_12_6) = all_23_7 & % 21.87/3.71 | | | | | greater(all_23_8, all_23_7) = all_23_6 & $i(all_23_7) & % 21.87/3.71 | | | | | $i(all_23_8) % 21.87/3.71 | | | | | % 21.87/3.71 | | | | | ALPHA: (87) implies: % 21.87/3.71 | | | | | (88) ~ (all_23_6 = 0) % 21.87/3.71 | | | | | (89) greater(all_23_8, all_23_7) = all_23_6 % 21.87/3.71 | | | | | (90) stock_of_knowledge(all_12_7, all_12_6) = all_23_7 % 21.87/3.71 | | | | | (91) stock_of_knowledge(all_12_7, all_12_5) = all_23_8 % 21.87/3.71 | | | | | % 21.87/3.72 | | | | | GROUND_INST: instantiating (9) with all_22_1, all_23_7, all_12_6, % 21.87/3.72 | | | | | all_12_7, simplifying with (29), (90) gives: % 21.87/3.72 | | | | | (92) all_23_7 = all_22_1 % 21.87/3.72 | | | | | % 21.87/3.72 | | | | | GROUND_INST: instantiating (9) with all_22_2, all_23_8, all_12_5, % 21.87/3.72 | | | | | all_12_7, simplifying with (30), (91) gives: % 21.87/3.72 | | | | | (93) all_23_8 = all_22_2 % 21.87/3.72 | | | | | % 21.87/3.72 | | | | | REDUCE: (89), (92), (93) imply: % 21.87/3.72 | | | | | (94) greater(all_22_2, all_22_1) = all_23_6 % 21.87/3.72 | | | | | % 21.87/3.72 | | | | | GROUND_INST: instantiating (7) with 0, all_23_6, all_22_1, all_22_2, % 21.87/3.72 | | | | | simplifying with (28), (94) gives: % 21.87/3.72 | | | | | (95) all_23_6 = 0 % 21.87/3.72 | | | | | % 21.87/3.72 | | | | | REDUCE: (88), (95) imply: % 21.87/3.72 | | | | | (96) $false % 21.87/3.72 | | | | | % 21.87/3.72 | | | | | CLOSE: (96) is inconsistent. % 21.87/3.72 | | | | | % 21.87/3.72 | | | | End of split % 21.87/3.72 | | | | % 21.87/3.72 | | | End of split % 21.87/3.72 | | | % 21.87/3.72 | | End of split % 21.87/3.72 | | % 21.87/3.72 | Case 2: % 21.87/3.72 | | % 21.87/3.72 | | (97) ~ (all_22_3 = 0) & organization(all_12_7) = all_22_3 % 21.87/3.72 | | % 21.87/3.72 | | ALPHA: (97) implies: % 21.87/3.72 | | (98) ~ (all_22_3 = 0) % 21.87/3.72 | | (99) organization(all_12_7) = all_22_3 % 21.87/3.72 | | % 21.87/3.72 | | GROUND_INST: instantiating (5) with 0, all_22_3, all_12_7, simplifying with % 21.87/3.72 | | (20), (99) gives: % 21.87/3.72 | | (100) all_22_3 = 0 % 21.87/3.72 | | % 21.87/3.72 | | REDUCE: (98), (100) imply: % 21.87/3.72 | | (101) $false % 21.87/3.72 | | % 21.87/3.72 | | CLOSE: (101) is inconsistent. % 21.87/3.72 | | % 21.87/3.72 | End of split % 21.87/3.72 | % 21.87/3.72 End of proof % 21.87/3.72 % SZS output end Proof for theBenchmark % 21.87/3.72 % 21.87/3.72 2988ms %------------------------------------------------------------------------------