%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT058+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 : n018.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 06:17:27 AM UTC 2026 % Result : Theorem 15.69s 2.88s % Output : Proof 17.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT058+1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.37 % Computer : n018.cluster.edu % 0.11/0.37 % Model : x86_64 x86_64 % 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.37 % Memory : 8046.5625MB % 0.11/0.37 % OS : Linux 6.8.0-71-generic % 0.11/0.37 % CPULimit : 300 % 0.11/0.37 % WCLimit : 300 % 0.11/0.37 % DateTime : Mon Sep 7 13:33:07 UTC 2026 % 0.11/0.37 % CPUTime : % 0.16/0.38 OpenJDK 64-Bit Server VM warning: Options -Xverify:none and -noverify were deprecated in JDK 13 and will likely be removed in a future release. % 0.71/0.72 ________ _____ % 0.71/0.72 ___ __ \_________(_)________________________________ % 0.71/0.72 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.71/0.72 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.71/0.72 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.71/0.72 % 0.71/0.72 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.71/0.72 (2023-06-19) % 0.71/0.72 % 0.71/0.72 (c) Philipp Rümmer, 2009-2023 % 0.71/0.72 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.71/0.72 Amanda Stjerna. % 0.71/0.72 Free software under BSD-3-Clause. % 0.71/0.72 % 0.71/0.72 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.71/0.72 % 0.71/0.72 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.71/0.74 Running up to 7 provers in parallel. % 0.71/0.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.71/0.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.71/0.75 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.71/0.75 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.71/0.75 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.71/0.75 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.71/0.75 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.66/1.20 Prover 1: Preprocessing ... % 3.18/1.20 Prover 4: Preprocessing ... % 3.18/1.23 Prover 2: Preprocessing ... % 3.18/1.23 Prover 5: Preprocessing ... % 3.18/1.23 Prover 0: Preprocessing ... % 3.18/1.23 Prover 6: Preprocessing ... % 3.18/1.23 Prover 3: Preprocessing ... % 5.55/1.50 Prover 5: Proving ... % 6.29/1.64 Prover 6: Proving ... % 6.29/1.64 Prover 2: Proving ... % 6.29/1.65 Prover 3: Constructing countermodel ... % 7.07/1.71 Prover 1: Constructing countermodel ... % 7.85/1.83 Prover 3: gave up % 7.85/1.83 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.85/1.87 Prover 0: Proving ... % 7.85/1.90 Prover 1: gave up % 8.68/1.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.68/1.92 Prover 4: Constructing countermodel ... % 8.68/1.92 Prover 7: Preprocessing ... % 8.68/1.99 Prover 8: Preprocessing ... % 9.92/2.07 Prover 7: Warning: ignoring some quantifiers % 9.92/2.09 Prover 7: Constructing countermodel ... % 10.97/2.26 Prover 8: Warning: ignoring some quantifiers % 10.97/2.27 Prover 8: Constructing countermodel ... % 11.76/2.31 Prover 7: gave up % 11.76/2.32 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 12.51/2.40 Prover 9: Preprocessing ... % 13.31/2.53 Prover 8: gave up % 13.31/2.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.11/2.60 Prover 10: Preprocessing ... % 14.11/2.66 Prover 10: Warning: ignoring some quantifiers % 14.11/2.68 Prover 10: Constructing countermodel ... % 14.91/2.73 Prover 9: Constructing countermodel ... % 15.69/2.86 Prover 4: Found proof (size 109) % 15.69/2.86 Prover 4: proved (2112ms) % 15.69/2.87 Prover 9: stopped % 15.69/2.87 Prover 5: stopped % 15.69/2.87 Prover 6: stopped % 15.69/2.87 Prover 10: stopped % 15.69/2.87 Prover 2: stopped % 15.69/2.87 Prover 0: proved (2125ms) % 15.69/2.87 % 15.69/2.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.69/2.88 % 16.39/2.92 % SZS output start Proof for theBenchmark % 16.39/2.92 Assumptions after simplification: % 16.39/2.92 --------------------------------- % 16.39/2.93 % 16.39/2.93 (definition_3) % 16.39/3.00 $i(sigma) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 16.39/3.00 (fragile_position(v0) = 0) | ~ (positional_advantage(v0, v1) = v2) | ~ % 16.39/3.00 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & age(v0, v1) % 16.39/3.00 = v3 & smaller_or_equal(v3, sigma) = v4 & $i(v3))) & ! [v0: $i] : ! [v1: % 16.39/3.00 $i] : ! [v2: $i] : ( ~ (fragile_position(v0) = 0) | ~ (age(v0, v1) = v2) | % 16.39/3.00 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 16.39/3.00 (positional_advantage(v0, v1) = v4 & greater(v2, sigma) = v3 & ( ~ (v4 = 0) % 16.39/3.00 | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 16.39/3.00 (fragile_position(v0) = 0) | ~ (age(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 16.39/3.00 ? [v3: any] : ? [v4: any] : (positional_advantage(v0, v1) = v4 & % 16.39/3.00 smaller_or_equal(v2, sigma) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] % 16.39/3.00 : ! [v1: int] : (v1 = 0 | ~ (fragile_position(v0) = v1) | ~ $i(v0) | ? % 16.39/3.00 [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: any] : ? [v6: any] : % 16.39/3.00 (positional_advantage(v0, v2) = v5 & age(v0, v2) = v3 & greater(v3, sigma) = % 16.39/3.00 v6 & smaller_or_equal(v3, sigma) = v4 & $i(v3) & $i(v2) & ((v6 = 0 & v5 = % 16.39/3.00 0) | (v4 = 0 & ~ (v5 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 16.39/3.00 (fragile_position(v0) = 0) | ~ (positional_advantage(v0, v1) = 0) | ~ % 16.39/3.00 $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & age(v0, v1) % 16.39/3.00 = v2 & greater(v2, sigma) = v3 & $i(v2))) % 16.39/3.00 % 16.39/3.00 (definition_4) % 16.39/3.02 $i(tau) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 16.39/3.02 (robust_position(v0) = 0) | ~ (positional_advantage(v0, v1) = v2) | ~ % 16.39/3.02 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & age(v0, v1) % 16.39/3.02 = v3 & greater(v3, tau) = v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 16.39/3.02 [v2: $i] : ( ~ (robust_position(v0) = 0) | ~ (age(v0, v1) = v2) | ~ $i(v1) | % 16.39/3.02 ~ $i(v0) | ? [v3: any] : ? [v4: any] : (positional_advantage(v0, v1) = v4 % 16.39/3.02 & greater(v2, tau) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: % 16.39/3.02 $i] : ! [v2: $i] : ( ~ (robust_position(v0) = 0) | ~ (age(v0, v1) = v2) | % 16.39/3.02 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 16.39/3.02 (positional_advantage(v0, v1) = v4 & smaller_or_equal(v2, tau) = v3 & ( ~ % 16.39/3.02 (v4 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 16.39/3.02 (robust_position(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: % 16.39/3.02 any] : ? [v5: any] : ? [v6: any] : (positional_advantage(v0, v2) = v5 & % 16.39/3.02 age(v0, v2) = v3 & greater(v3, tau) = v6 & smaller_or_equal(v3, tau) = v4 % 16.39/3.02 & $i(v3) & $i(v2) & ((v6 = 0 & ~ (v5 = 0)) | (v5 = 0 & v4 = 0)))) & ! % 16.39/3.02 [v0: $i] : ! [v1: $i] : ( ~ (robust_position(v0) = 0) | ~ % 16.39/3.02 (positional_advantage(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : % 16.39/3.02 ? [v3: int] : ( ~ (v3 = 0) & age(v0, v1) = v2 & smaller_or_equal(v2, tau) = % 16.39/3.02 v3 & $i(v2))) % 16.39/3.02 % 16.39/3.02 (definition_greater_or_equal) % 16.39/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (greater(v0, % 16.39/3.03 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 16.39/3.03 greater_or_equal(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] % 16.39/3.03 : (v2 = 0 | ~ (greater_or_equal(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 16.39/3.03 [v3: int] : ( ~ (v3 = 0) & greater(v0, v1) = v3)) & ! [v0: $i] : ! [v1: % 16.39/3.03 $i] : (v1 = v0 | ~ (greater_or_equal(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 16.39/3.03 greater(v0, v1) = 0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 16.39/3.03 (greater_or_equal(v0, v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ( % 16.39/3.03 ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | greater_or_equal(v0, v1) = % 16.39/3.03 0) & ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (greater(v0, v0) = v1) | % 16.39/3.03 ~ $i(v0) | greater_or_equal(v0, v0) = 0) % 16.39/3.03 % 16.39/3.03 (definition_smaller) % 17.06/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (greater(v1, v0) = v2) % 17.06/3.04 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & smaller(v0, v1) = % 17.06/3.04 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 17.06/3.04 (smaller(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) % 17.06/3.04 & greater(v1, v0) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, % 17.06/3.04 v0) = 0) | ~ $i(v1) | ~ $i(v0) | smaller(v0, v1) = 0) & ! [v0: $i] : % 17.06/3.04 ! [v1: $i] : ( ~ (smaller(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | greater(v1, % 17.06/3.04 v0) = 0) % 17.06/3.04 % 17.06/3.04 (definition_smaller_or_equal) % 17.06/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (smaller(v0, % 17.06/3.04 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 17.06/3.04 smaller_or_equal(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] % 17.06/3.04 : (v2 = 0 | ~ (smaller_or_equal(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 17.06/3.04 [v3: int] : ( ~ (v3 = 0) & smaller(v0, v1) = v3)) & ! [v0: $i] : ! [v1: % 17.06/3.04 $i] : (v1 = v0 | ~ (smaller_or_equal(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 17.06/3.04 smaller(v0, v1) = 0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 17.06/3.04 (smaller_or_equal(v0, v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ( % 17.06/3.04 ~ (smaller(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | smaller_or_equal(v0, v1) = % 17.06/3.04 0) & ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (smaller(v0, v0) = v1) | % 17.06/3.04 ~ $i(v0) | smaller_or_equal(v0, v0) = 0) % 17.06/3.04 % 17.06/3.04 (lemma_10) % 17.06/3.05 $i(zero) & $i(tau) & $i(sigma) & ? [v0: $i] : ? [v1: $i] : (organization(v0) % 17.06/3.05 = 0 & robust_position(v0) = 0 & fragile_position(v0) = 0 & age(v0, v1) = % 17.06/3.05 zero & greater_or_equal(tau, zero) = 0 & greater_or_equal(sigma, zero) = 0 & % 17.06/3.05 $i(v1) & $i(v0)) % 17.06/3.05 % 17.06/3.05 (function-axioms) % 17.06/3.05 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 17.06/3.05 [v3: $i] : (v1 = v0 | ~ (positional_advantage(v3, v2) = v1) | ~ % 17.06/3.05 (positional_advantage(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.06/3.05 $i] : ! [v3: $i] : (v1 = v0 | ~ (age(v3, v2) = v1) | ~ (age(v3, v2) = % 17.06/3.05 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 17.06/3.05 $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, % 17.06/3.05 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 17.06/3.05 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~ % 17.06/3.05 (greater_or_equal(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.06/3.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (smaller(v3, % 17.06/3.05 v2) = v1) | ~ (smaller(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 17.06/3.05 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.06/3.05 (smaller_or_equal(v3, v2) = v1) | ~ (smaller_or_equal(v3, v2) = v0)) & ! % 17.06/3.05 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 17.06/3.05 | ~ (organization(v2) = v1) | ~ (organization(v2) = v0)) & ! [v0: % 17.06/3.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 17.06/3.05 ~ (robust_position(v2) = v1) | ~ (robust_position(v2) = v0)) & ! [v0: % 17.06/3.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 17.06/3.05 ~ (fragile_position(v2) = v1) | ~ (fragile_position(v2) = v0)) % 17.06/3.05 % 17.06/3.05 Further assumptions not needed in the proof: % 17.06/3.05 -------------------------------------------- % 17.06/3.06 meaning_postulate_greater_comparable, meaning_postulate_greater_strict, % 17.06/3.06 meaning_postulate_greater_transitive % 17.06/3.06 % 17.06/3.06 Those formulas are unsatisfiable: % 17.06/3.06 --------------------------------- % 17.06/3.06 % 17.06/3.06 Begin of proof % 17.06/3.06 | % 17.06/3.06 | ALPHA: (definition_smaller_or_equal) implies: % 17.06/3.06 | (1) ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (smaller(v0, v0) = v1) | % 17.06/3.06 | ~ $i(v0) | smaller_or_equal(v0, v0) = 0) % 17.06/3.06 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (smaller_or_equal(v0, v0) = % 17.06/3.06 | v1) | ~ $i(v0)) % 17.06/3.06 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 17.06/3.06 | (smaller_or_equal(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 17.06/3.06 | int] : ( ~ (v3 = 0) & smaller(v0, v1) = v3)) % 17.06/3.06 | % 17.06/3.06 | ALPHA: (definition_greater_or_equal) implies: % 17.06/3.07 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (greater_or_equal(v0, v1) = % 17.06/3.07 | 0) | ~ $i(v1) | ~ $i(v0) | greater(v0, v1) = 0) % 17.06/3.07 | % 17.06/3.07 | ALPHA: (definition_smaller) implies: % 17.06/3.07 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~ $i(v1) | ~ % 17.06/3.07 | $i(v0) | smaller(v0, v1) = 0) % 17.06/3.07 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (smaller(v0, % 17.06/3.07 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 17.06/3.07 | greater(v1, v0) = v3)) % 17.06/3.07 | % 17.06/3.07 | ALPHA: (definition_3) implies: % 17.06/3.07 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (fragile_position(v0) = % 17.06/3.07 | 0) | ~ (age(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 17.06/3.07 | ? [v4: any] : (positional_advantage(v0, v1) = v4 & % 17.06/3.07 | smaller_or_equal(v2, sigma) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 17.06/3.07 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (fragile_position(v0) = % 17.06/3.07 | 0) | ~ (age(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 17.06/3.07 | ? [v4: any] : (positional_advantage(v0, v1) = v4 & greater(v2, % 17.06/3.07 | sigma) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 17.06/3.07 | % 17.06/3.07 | ALPHA: (definition_4) implies: % 17.06/3.08 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (robust_position(v0) = 0) % 17.06/3.08 | | ~ (age(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? % 17.06/3.08 | [v4: any] : (positional_advantage(v0, v1) = v4 & smaller_or_equal(v2, % 17.06/3.08 | tau) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 17.06/3.08 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (robust_position(v0) = % 17.06/3.08 | 0) | ~ (age(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] % 17.06/3.08 | : ? [v4: any] : (positional_advantage(v0, v1) = v4 & greater(v2, % 17.06/3.08 | tau) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 17.06/3.08 | % 17.06/3.08 | ALPHA: (lemma_10) implies: % 17.06/3.08 | (11) $i(sigma) % 17.06/3.08 | (12) $i(tau) % 17.06/3.08 | (13) $i(zero) % 17.06/3.08 | (14) ? [v0: $i] : ? [v1: $i] : (organization(v0) = 0 & % 17.06/3.08 | robust_position(v0) = 0 & fragile_position(v0) = 0 & age(v0, v1) = % 17.06/3.08 | zero & greater_or_equal(tau, zero) = 0 & greater_or_equal(sigma, % 17.06/3.08 | zero) = 0 & $i(v1) & $i(v0)) % 17.06/3.08 | % 17.06/3.08 | ALPHA: (function-axioms) implies: % 17.06/3.09 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 17.06/3.09 | : ! [v3: $i] : (v1 = v0 | ~ (smaller_or_equal(v3, v2) = v1) | ~ % 17.06/3.09 | (smaller_or_equal(v3, v2) = v0)) % 17.06/3.09 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 17.06/3.09 | : ! [v3: $i] : (v1 = v0 | ~ (smaller(v3, v2) = v1) | ~ (smaller(v3, % 17.06/3.09 | v2) = v0)) % 17.06/3.09 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 17.06/3.09 | : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, % 17.06/3.09 | v2) = v0)) % 17.06/3.09 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 17.06/3.09 | : ! [v3: $i] : (v1 = v0 | ~ (positional_advantage(v3, v2) = v1) | ~ % 17.06/3.09 | (positional_advantage(v3, v2) = v0)) % 17.06/3.09 | % 17.06/3.09 | DELTA: instantiating (14) with fresh symbols all_12_0, all_12_1 gives: % 17.06/3.09 | (19) organization(all_12_1) = 0 & robust_position(all_12_1) = 0 & % 17.06/3.09 | fragile_position(all_12_1) = 0 & age(all_12_1, all_12_0) = zero & % 17.06/3.09 | greater_or_equal(tau, zero) = 0 & greater_or_equal(sigma, zero) = 0 & % 17.06/3.09 | $i(all_12_0) & $i(all_12_1) % 17.06/3.09 | % 17.06/3.09 | ALPHA: (19) implies: % 17.06/3.10 | (20) $i(all_12_1) % 17.06/3.10 | (21) $i(all_12_0) % 17.06/3.10 | (22) greater_or_equal(sigma, zero) = 0 % 17.06/3.10 | (23) greater_or_equal(tau, zero) = 0 % 17.06/3.10 | (24) age(all_12_1, all_12_0) = zero % 17.06/3.10 | (25) fragile_position(all_12_1) = 0 % 17.06/3.10 | (26) robust_position(all_12_1) = 0 % 17.06/3.10 | % 17.06/3.10 | GROUND_INST: instantiating (4) with sigma, zero, simplifying with (11), (13), % 17.06/3.10 | (22) gives: % 17.06/3.10 | (27) zero = sigma | greater(sigma, zero) = 0 % 17.06/3.10 | % 17.06/3.10 | GROUND_INST: instantiating (4) with tau, zero, simplifying with (12), (13), % 17.06/3.10 | (23) gives: % 17.06/3.10 | (28) zero = tau | greater(tau, zero) = 0 % 17.06/3.10 | % 17.06/3.10 | GROUND_INST: instantiating (8) with all_12_1, all_12_0, zero, simplifying with % 17.06/3.10 | (20), (21), (24), (25) gives: % 17.06/3.10 | (29) ? [v0: any] : ? [v1: any] : (positional_advantage(all_12_1, % 17.06/3.10 | all_12_0) = v1 & greater(zero, sigma) = v0 & ( ~ (v1 = 0) | ~ (v0 % 17.06/3.10 | = 0))) % 17.06/3.10 | % 17.06/3.10 | GROUND_INST: instantiating (7) with all_12_1, all_12_0, zero, simplifying with % 17.06/3.10 | (20), (21), (24), (25) gives: % 17.06/3.11 | (30) ? [v0: any] : ? [v1: any] : (positional_advantage(all_12_1, % 17.06/3.11 | all_12_0) = v1 & smaller_or_equal(zero, sigma) = v0 & ( ~ (v0 = 0) % 17.06/3.11 | | v1 = 0)) % 17.06/3.11 | % 17.06/3.11 | GROUND_INST: instantiating (10) with all_12_1, all_12_0, zero, simplifying % 17.06/3.11 | with (20), (21), (24), (26) gives: % 17.06/3.11 | (31) ? [v0: any] : ? [v1: any] : (positional_advantage(all_12_1, % 17.06/3.11 | all_12_0) = v1 & greater(zero, tau) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 17.06/3.11 | % 17.06/3.11 | GROUND_INST: instantiating (9) with all_12_1, all_12_0, zero, simplifying with % 17.06/3.11 | (20), (21), (24), (26) gives: % 17.06/3.11 | (32) ? [v0: any] : ? [v1: any] : (positional_advantage(all_12_1, % 17.06/3.11 | all_12_0) = v1 & smaller_or_equal(zero, tau) = v0 & ( ~ (v1 = 0) | % 17.06/3.11 | ~ (v0 = 0))) % 17.06/3.11 | % 17.06/3.11 | DELTA: instantiating (32) with fresh symbols all_19_0, all_19_1 gives: % 17.06/3.11 | (33) positional_advantage(all_12_1, all_12_0) = all_19_0 & % 17.06/3.11 | smaller_or_equal(zero, tau) = all_19_1 & ( ~ (all_19_0 = 0) | ~ % 17.06/3.11 | (all_19_1 = 0)) % 17.06/3.11 | % 17.06/3.11 | ALPHA: (33) implies: % 17.06/3.11 | (34) smaller_or_equal(zero, tau) = all_19_1 % 17.06/3.11 | (35) positional_advantage(all_12_1, all_12_0) = all_19_0 % 17.06/3.12 | (36) ~ (all_19_0 = 0) | ~ (all_19_1 = 0) % 17.06/3.12 | % 17.06/3.12 | DELTA: instantiating (30) with fresh symbols all_21_0, all_21_1 gives: % 17.06/3.12 | (37) positional_advantage(all_12_1, all_12_0) = all_21_0 & % 17.06/3.12 | smaller_or_equal(zero, sigma) = all_21_1 & ( ~ (all_21_1 = 0) | % 17.06/3.12 | all_21_0 = 0) % 17.06/3.12 | % 17.06/3.12 | ALPHA: (37) implies: % 17.06/3.12 | (38) smaller_or_equal(zero, sigma) = all_21_1 % 17.06/3.12 | (39) positional_advantage(all_12_1, all_12_0) = all_21_0 % 17.06/3.12 | (40) ~ (all_21_1 = 0) | all_21_0 = 0 % 17.06/3.12 | % 17.06/3.12 | DELTA: instantiating (29) with fresh symbols all_23_0, all_23_1 gives: % 17.06/3.12 | (41) positional_advantage(all_12_1, all_12_0) = all_23_0 & greater(zero, % 17.06/3.12 | sigma) = all_23_1 & ( ~ (all_23_0 = 0) | ~ (all_23_1 = 0)) % 17.06/3.12 | % 17.06/3.12 | ALPHA: (41) implies: % 17.06/3.12 | (42) positional_advantage(all_12_1, all_12_0) = all_23_0 % 17.06/3.12 | % 17.06/3.12 | DELTA: instantiating (31) with fresh symbols all_25_0, all_25_1 gives: % 17.06/3.12 | (43) positional_advantage(all_12_1, all_12_0) = all_25_0 & greater(zero, % 17.06/3.12 | tau) = all_25_1 & ( ~ (all_25_1 = 0) | all_25_0 = 0) % 17.06/3.12 | % 17.06/3.12 | ALPHA: (43) implies: % 17.06/3.12 | (44) positional_advantage(all_12_1, all_12_0) = all_25_0 % 17.06/3.12 | % 17.06/3.12 | GROUND_INST: instantiating (18) with all_21_0, all_23_0, all_12_0, all_12_1, % 17.06/3.12 | simplifying with (39), (42) gives: % 17.06/3.12 | (45) all_23_0 = all_21_0 % 17.06/3.12 | % 17.06/3.12 | GROUND_INST: instantiating (18) with all_23_0, all_25_0, all_12_0, all_12_1, % 17.06/3.12 | simplifying with (42), (44) gives: % 17.06/3.12 | (46) all_25_0 = all_23_0 % 17.06/3.12 | % 17.06/3.13 | GROUND_INST: instantiating (18) with all_19_0, all_25_0, all_12_0, all_12_1, % 17.06/3.13 | simplifying with (35), (44) gives: % 17.06/3.13 | (47) all_25_0 = all_19_0 % 17.06/3.13 | % 17.06/3.13 | COMBINE_EQS: (46), (47) imply: % 17.06/3.13 | (48) all_23_0 = all_19_0 % 17.06/3.13 | % 17.06/3.13 | SIMP: (48) implies: % 17.06/3.13 | (49) all_23_0 = all_19_0 % 17.06/3.13 | % 17.06/3.13 | COMBINE_EQS: (45), (49) imply: % 17.06/3.13 | (50) all_21_0 = all_19_0 % 17.06/3.13 | % 17.06/3.13 | GROUND_INST: instantiating (3) with zero, sigma, all_21_1, simplifying with % 17.06/3.13 | (11), (13), (38) gives: % 17.06/3.13 | (51) all_21_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & smaller(zero, sigma) = % 17.06/3.13 | v0) % 17.55/3.13 | % 17.55/3.13 | GROUND_INST: instantiating (3) with zero, tau, all_19_1, simplifying with % 17.55/3.13 | (12), (13), (34) gives: % 17.55/3.13 | (52) all_19_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & smaller(zero, tau) = v0) % 17.55/3.13 | % 17.55/3.13 | BETA: splitting (28) gives: % 17.55/3.13 | % 17.55/3.13 | Case 1: % 17.55/3.13 | | % 17.55/3.13 | | (53) greater(tau, zero) = 0 % 17.55/3.13 | | % 17.55/3.13 | | GROUND_INST: instantiating (5) with zero, tau, simplifying with (12), (13), % 17.55/3.13 | | (53) gives: % 17.55/3.14 | | (54) smaller(zero, tau) = 0 % 17.55/3.14 | | % 17.55/3.14 | | BETA: splitting (52) gives: % 17.55/3.14 | | % 17.55/3.14 | | Case 1: % 17.55/3.14 | | | % 17.55/3.14 | | | (55) all_19_1 = 0 % 17.55/3.14 | | | % 17.55/3.14 | | | BETA: splitting (36) gives: % 17.55/3.14 | | | % 17.55/3.14 | | | Case 1: % 17.55/3.14 | | | | % 17.55/3.14 | | | | (56) ~ (all_19_0 = 0) % 17.55/3.14 | | | | % 17.55/3.14 | | | | BETA: splitting (40) gives: % 17.55/3.14 | | | | % 17.55/3.14 | | | | Case 1: % 17.55/3.14 | | | | | % 17.55/3.14 | | | | | (57) ~ (all_21_1 = 0) % 17.55/3.14 | | | | | % 17.55/3.14 | | | | | BETA: splitting (51) gives: % 17.55/3.14 | | | | | % 17.55/3.14 | | | | | Case 1: % 17.55/3.14 | | | | | | % 17.55/3.14 | | | | | | (58) all_21_1 = 0 % 17.55/3.14 | | | | | | % 17.55/3.14 | | | | | | REDUCE: (57), (58) imply: % 17.55/3.14 | | | | | | (59) $false % 17.55/3.14 | | | | | | % 17.55/3.14 | | | | | | CLOSE: (59) is inconsistent. % 17.55/3.14 | | | | | | % 17.55/3.14 | | | | | Case 2: % 17.55/3.14 | | | | | | % 17.55/3.14 | | | | | | (60) ? [v0: int] : ( ~ (v0 = 0) & smaller(zero, sigma) = v0) % 17.55/3.14 | | | | | | % 17.55/3.14 | | | | | | DELTA: instantiating (60) with fresh symbol all_71_0 gives: % 17.55/3.14 | | | | | | (61) ~ (all_71_0 = 0) & smaller(zero, sigma) = all_71_0 % 17.55/3.14 | | | | | | % 17.55/3.14 | | | | | | ALPHA: (61) implies: % 17.55/3.14 | | | | | | (62) ~ (all_71_0 = 0) % 17.55/3.14 | | | | | | (63) smaller(zero, sigma) = all_71_0 % 17.55/3.14 | | | | | | % 17.55/3.15 | | | | | | GROUND_INST: instantiating (6) with zero, sigma, all_71_0, % 17.55/3.15 | | | | | | simplifying with (11), (13), (63) gives: % 17.55/3.15 | | | | | | (64) all_71_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & greater(sigma, % 17.55/3.15 | | | | | | zero) = v0) % 17.55/3.15 | | | | | | % 17.55/3.15 | | | | | | BETA: splitting (27) gives: % 17.55/3.15 | | | | | | % 17.55/3.15 | | | | | | Case 1: % 17.55/3.15 | | | | | | | % 17.55/3.15 | | | | | | | (65) greater(sigma, zero) = 0 % 17.55/3.15 | | | | | | | % 17.55/3.15 | | | | | | | BETA: splitting (64) gives: % 17.55/3.15 | | | | | | | % 17.55/3.15 | | | | | | | Case 1: % 17.55/3.15 | | | | | | | | % 17.55/3.15 | | | | | | | | (66) all_71_0 = 0 % 17.55/3.15 | | | | | | | | % 17.55/3.15 | | | | | | | | REDUCE: (62), (66) imply: % 17.55/3.15 | | | | | | | | (67) $false % 17.55/3.15 | | | | | | | | % 17.55/3.15 | | | | | | | | CLOSE: (67) is inconsistent. % 17.55/3.15 | | | | | | | | % 17.55/3.15 | | | | | | | Case 2: % 17.55/3.15 | | | | | | | | % 17.55/3.15 | | | | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & greater(sigma, zero) = v0) % 17.55/3.15 | | | | | | | | % 17.55/3.15 | | | | | | | | DELTA: instantiating (68) with fresh symbol all_88_0 gives: % 17.55/3.15 | | | | | | | | (69) ~ (all_88_0 = 0) & greater(sigma, zero) = all_88_0 % 17.55/3.15 | | | | | | | | % 17.55/3.15 | | | | | | | | ALPHA: (69) implies: % 17.55/3.15 | | | | | | | | (70) ~ (all_88_0 = 0) % 17.55/3.15 | | | | | | | | (71) greater(sigma, zero) = all_88_0 % 17.55/3.15 | | | | | | | | % 17.55/3.15 | | | | | | | | GROUND_INST: instantiating (17) with 0, all_88_0, zero, sigma, % 17.55/3.15 | | | | | | | | simplifying with (65), (71) gives: % 17.55/3.15 | | | | | | | | (72) all_88_0 = 0 % 17.55/3.15 | | | | | | | | % 17.55/3.15 | | | | | | | | REDUCE: (70), (72) imply: % 17.55/3.15 | | | | | | | | (73) $false % 17.55/3.15 | | | | | | | | % 17.55/3.15 | | | | | | | | CLOSE: (73) is inconsistent. % 17.55/3.15 | | | | | | | | % 17.55/3.15 | | | | | | | End of split % 17.55/3.15 | | | | | | | % 17.55/3.15 | | | | | | Case 2: % 17.55/3.15 | | | | | | | % 17.55/3.15 | | | | | | | (74) zero = sigma % 17.55/3.15 | | | | | | | % 17.55/3.15 | | | | | | | REDUCE: (63), (74) imply: % 17.55/3.15 | | | | | | | (75) smaller(sigma, sigma) = all_71_0 % 17.55/3.15 | | | | | | | % 17.55/3.15 | | | | | | | REDUCE: (38), (74) imply: % 17.55/3.15 | | | | | | | (76) smaller_or_equal(sigma, sigma) = all_21_1 % 17.55/3.15 | | | | | | | % 17.55/3.15 | | | | | | | GROUND_INST: instantiating (1) with sigma, all_71_0, simplifying % 17.55/3.16 | | | | | | | with (11), (75) gives: % 17.55/3.16 | | | | | | | (77) smaller_or_equal(sigma, sigma) = 0 % 17.55/3.16 | | | | | | | % 17.55/3.16 | | | | | | | GROUND_INST: instantiating (15) with 0, all_21_1, sigma, sigma, % 17.55/3.16 | | | | | | | simplifying with (76), (77) gives: % 17.55/3.16 | | | | | | | (78) all_21_1 = 0 % 17.55/3.16 | | | | | | | % 17.55/3.16 | | | | | | | REDUCE: (57), (78) imply: % 17.55/3.16 | | | | | | | (79) $false % 17.55/3.16 | | | | | | | % 17.55/3.16 | | | | | | | CLOSE: (79) is inconsistent. % 17.55/3.16 | | | | | | | % 17.55/3.16 | | | | | | End of split % 17.55/3.16 | | | | | | % 17.55/3.16 | | | | | End of split % 17.55/3.16 | | | | | % 17.55/3.16 | | | | Case 2: % 17.55/3.16 | | | | | % 17.55/3.16 | | | | | (80) all_21_0 = 0 % 17.55/3.16 | | | | | % 17.55/3.16 | | | | | COMBINE_EQS: (50), (80) imply: % 17.55/3.16 | | | | | (81) all_19_0 = 0 % 17.55/3.16 | | | | | % 17.55/3.16 | | | | | SIMP: (81) implies: % 17.55/3.16 | | | | | (82) all_19_0 = 0 % 17.55/3.16 | | | | | % 17.55/3.16 | | | | | REDUCE: (56), (82) imply: % 17.55/3.16 | | | | | (83) $false % 17.55/3.16 | | | | | % 17.55/3.16 | | | | | CLOSE: (83) is inconsistent. % 17.55/3.16 | | | | | % 17.55/3.16 | | | | End of split % 17.55/3.16 | | | | % 17.55/3.16 | | | Case 2: % 17.55/3.16 | | | | % 17.55/3.16 | | | | (84) ~ (all_19_1 = 0) % 17.55/3.16 | | | | % 17.55/3.16 | | | | REDUCE: (55), (84) imply: % 17.55/3.16 | | | | (85) $false % 17.55/3.16 | | | | % 17.55/3.16 | | | | CLOSE: (85) is inconsistent. % 17.55/3.16 | | | | % 17.55/3.16 | | | End of split % 17.55/3.16 | | | % 17.55/3.16 | | Case 2: % 17.55/3.16 | | | % 17.55/3.16 | | | (86) ? [v0: int] : ( ~ (v0 = 0) & smaller(zero, tau) = v0) % 17.55/3.16 | | | % 17.55/3.16 | | | DELTA: instantiating (86) with fresh symbol all_50_0 gives: % 17.55/3.16 | | | (87) ~ (all_50_0 = 0) & smaller(zero, tau) = all_50_0 % 17.55/3.16 | | | % 17.55/3.16 | | | ALPHA: (87) implies: % 17.55/3.16 | | | (88) ~ (all_50_0 = 0) % 17.55/3.16 | | | (89) smaller(zero, tau) = all_50_0 % 17.55/3.16 | | | % 17.55/3.16 | | | GROUND_INST: instantiating (16) with 0, all_50_0, tau, zero, simplifying % 17.55/3.16 | | | with (54), (89) gives: % 17.55/3.16 | | | (90) all_50_0 = 0 % 17.55/3.16 | | | % 17.55/3.16 | | | REDUCE: (88), (90) imply: % 17.55/3.16 | | | (91) $false % 17.55/3.16 | | | % 17.55/3.16 | | | CLOSE: (91) is inconsistent. % 17.55/3.16 | | | % 17.55/3.17 | | End of split % 17.55/3.17 | | % 17.55/3.17 | Case 2: % 17.55/3.17 | | % 17.55/3.17 | | (92) zero = tau % 17.55/3.17 | | % 17.55/3.17 | | REDUCE: (34), (92) imply: % 17.55/3.17 | | (93) smaller_or_equal(tau, tau) = all_19_1 % 17.55/3.17 | | % 17.55/3.17 | | REDUCE: (38), (92) imply: % 17.55/3.17 | | (94) smaller_or_equal(tau, sigma) = all_21_1 % 17.55/3.17 | | % 17.55/3.17 | | GROUND_INST: instantiating (2) with tau, all_19_1, simplifying with (12), % 17.55/3.17 | | (93) gives: % 17.55/3.17 | | (95) all_19_1 = 0 % 17.55/3.17 | | % 17.55/3.17 | | REDUCE: (93), (95) imply: % 17.55/3.17 | | (96) smaller_or_equal(tau, tau) = 0 % 17.55/3.17 | | % 17.55/3.17 | | BETA: splitting (36) gives: % 17.55/3.17 | | % 17.55/3.17 | | Case 1: % 17.55/3.17 | | | % 17.55/3.17 | | | (97) ~ (all_19_0 = 0) % 17.55/3.17 | | | % 17.55/3.17 | | | BETA: splitting (40) gives: % 17.55/3.17 | | | % 17.55/3.17 | | | Case 1: % 17.55/3.17 | | | | % 17.55/3.17 | | | | (98) ~ (all_21_1 = 0) % 17.55/3.17 | | | | % 17.55/3.17 | | | | BETA: splitting (51) gives: % 17.55/3.17 | | | | % 17.55/3.17 | | | | Case 1: % 17.55/3.17 | | | | | % 17.55/3.17 | | | | | (99) all_21_1 = 0 % 17.55/3.17 | | | | | % 17.55/3.17 | | | | | REDUCE: (98), (99) imply: % 17.55/3.17 | | | | | (100) $false % 17.55/3.17 | | | | | % 17.55/3.17 | | | | | CLOSE: (100) is inconsistent. % 17.55/3.17 | | | | | % 17.55/3.17 | | | | Case 2: % 17.55/3.17 | | | | | % 17.55/3.17 | | | | | (101) ? [v0: int] : ( ~ (v0 = 0) & smaller(zero, sigma) = v0) % 17.55/3.17 | | | | | % 17.55/3.17 | | | | | DELTA: instantiating (101) with fresh symbol all_65_0 gives: % 17.55/3.17 | | | | | (102) ~ (all_65_0 = 0) & smaller(zero, sigma) = all_65_0 % 17.55/3.17 | | | | | % 17.55/3.17 | | | | | ALPHA: (102) implies: % 17.55/3.17 | | | | | (103) ~ (all_65_0 = 0) % 17.55/3.17 | | | | | (104) smaller(zero, sigma) = all_65_0 % 17.55/3.17 | | | | | % 17.55/3.17 | | | | | REDUCE: (92), (104) imply: % 17.55/3.17 | | | | | (105) smaller(tau, sigma) = all_65_0 % 17.55/3.17 | | | | | % 17.55/3.17 | | | | | GROUND_INST: instantiating (6) with tau, sigma, all_65_0, simplifying % 17.55/3.17 | | | | | with (11), (12), (105) gives: % 17.55/3.18 | | | | | (106) all_65_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & greater(sigma, % 17.55/3.18 | | | | | tau) = v0) % 17.55/3.18 | | | | | % 17.55/3.18 | | | | | BETA: splitting (27) gives: % 17.55/3.18 | | | | | % 17.55/3.18 | | | | | Case 1: % 17.55/3.18 | | | | | | % 17.55/3.18 | | | | | | (107) greater(sigma, zero) = 0 % 17.55/3.18 | | | | | | % 17.55/3.18 | | | | | | REDUCE: (92), (107) imply: % 17.55/3.18 | | | | | | (108) greater(sigma, tau) = 0 % 17.55/3.18 | | | | | | % 17.55/3.18 | | | | | | BETA: splitting (106) gives: % 17.55/3.18 | | | | | | % 17.55/3.18 | | | | | | Case 1: % 17.55/3.18 | | | | | | | % 17.55/3.18 | | | | | | | (109) all_65_0 = 0 % 17.55/3.18 | | | | | | | % 17.55/3.18 | | | | | | | REDUCE: (103), (109) imply: % 17.55/3.18 | | | | | | | (110) $false % 17.55/3.18 | | | | | | | % 17.55/3.18 | | | | | | | CLOSE: (110) is inconsistent. % 17.55/3.18 | | | | | | | % 17.55/3.18 | | | | | | Case 2: % 17.55/3.18 | | | | | | | % 17.55/3.18 | | | | | | | (111) ? [v0: int] : ( ~ (v0 = 0) & greater(sigma, tau) = v0) % 17.55/3.18 | | | | | | | % 17.55/3.18 | | | | | | | DELTA: instantiating (111) with fresh symbol all_78_0 gives: % 17.55/3.18 | | | | | | | (112) ~ (all_78_0 = 0) & greater(sigma, tau) = all_78_0 % 17.55/3.18 | | | | | | | % 17.55/3.18 | | | | | | | ALPHA: (112) implies: % 17.55/3.18 | | | | | | | (113) ~ (all_78_0 = 0) % 17.55/3.18 | | | | | | | (114) greater(sigma, tau) = all_78_0 % 17.55/3.18 | | | | | | | % 17.55/3.18 | | | | | | | GROUND_INST: instantiating (17) with 0, all_78_0, tau, sigma, % 17.55/3.18 | | | | | | | simplifying with (108), (114) gives: % 17.55/3.18 | | | | | | | (115) all_78_0 = 0 % 17.55/3.18 | | | | | | | % 17.55/3.18 | | | | | | | REDUCE: (113), (115) imply: % 17.55/3.18 | | | | | | | (116) $false % 17.55/3.18 | | | | | | | % 17.55/3.18 | | | | | | | CLOSE: (116) is inconsistent. % 17.55/3.18 | | | | | | | % 17.55/3.18 | | | | | | End of split % 17.55/3.18 | | | | | | % 17.55/3.18 | | | | | Case 2: % 17.55/3.18 | | | | | | % 17.55/3.18 | | | | | | (117) zero = sigma % 17.55/3.18 | | | | | | % 17.55/3.18 | | | | | | COMBINE_EQS: (92), (117) imply: % 17.55/3.18 | | | | | | (118) tau = sigma % 17.55/3.18 | | | | | | % 17.55/3.18 | | | | | | REDUCE: (96), (118) imply: % 17.55/3.18 | | | | | | (119) smaller_or_equal(sigma, sigma) = 0 % 17.55/3.18 | | | | | | % 17.55/3.18 | | | | | | REDUCE: (94), (118) imply: % 17.55/3.18 | | | | | | (120) smaller_or_equal(sigma, sigma) = all_21_1 % 17.55/3.18 | | | | | | % 17.55/3.19 | | | | | | GROUND_INST: instantiating (15) with 0, all_21_1, sigma, sigma, % 17.55/3.19 | | | | | | simplifying with (119), (120) gives: % 17.55/3.19 | | | | | | (121) all_21_1 = 0 % 17.55/3.19 | | | | | | % 17.55/3.19 | | | | | | REDUCE: (98), (121) imply: % 17.55/3.19 | | | | | | (122) $false % 17.55/3.19 | | | | | | % 17.55/3.19 | | | | | | CLOSE: (122) is inconsistent. % 17.55/3.19 | | | | | | % 17.55/3.19 | | | | | End of split % 17.55/3.19 | | | | | % 17.55/3.19 | | | | End of split % 17.55/3.19 | | | | % 17.55/3.19 | | | Case 2: % 17.55/3.19 | | | | % 17.55/3.19 | | | | (123) all_21_0 = 0 % 17.55/3.19 | | | | % 17.55/3.19 | | | | COMBINE_EQS: (50), (123) imply: % 17.55/3.19 | | | | (124) all_19_0 = 0 % 17.55/3.19 | | | | % 17.55/3.19 | | | | SIMP: (124) implies: % 17.55/3.19 | | | | (125) all_19_0 = 0 % 17.55/3.19 | | | | % 17.55/3.19 | | | | REDUCE: (97), (125) imply: % 17.55/3.19 | | | | (126) $false % 17.55/3.19 | | | | % 17.55/3.19 | | | | CLOSE: (126) is inconsistent. % 17.55/3.19 | | | | % 17.55/3.19 | | | End of split % 17.55/3.19 | | | % 17.55/3.19 | | Case 2: % 17.55/3.19 | | | % 17.55/3.19 | | | (127) ~ (all_19_1 = 0) % 17.55/3.19 | | | % 17.55/3.19 | | | REDUCE: (95), (127) imply: % 17.55/3.19 | | | (128) $false % 17.55/3.19 | | | % 17.55/3.19 | | | CLOSE: (128) is inconsistent. % 17.55/3.19 | | | % 17.55/3.19 | | End of split % 17.55/3.19 | | % 17.55/3.19 | End of split % 17.55/3.19 | % 17.55/3.19 End of proof % 17.55/3.19 % SZS output end Proof for theBenchmark % 17.55/3.19 % 17.55/3.19 2470ms %------------------------------------------------------------------------------