%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET719+4 : TPTP v8.1.2. Bugfixed v2.2.1. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n026.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 15:26:08 EDT 2023 % Result : Theorem 23.10s 3.89s % Output : Proof 39.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET719+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n026.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sat Aug 26 16:41:48 EDT 2023 % 0.14/0.35 % CPUTime : % 0.22/0.63 ________ _____ % 0.22/0.63 ___ __ \_________(_)________________________________ % 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.63 % 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.63 (2023-06-19) % 0.22/0.63 % 0.22/0.63 (c) Philipp Rümmer, 2009-2023 % 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.63 Amanda Stjerna. % 0.22/0.63 Free software under BSD-3-Clause. % 0.22/0.63 % 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.63 % 0.22/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.22/0.64 Running up to 7 provers in parallel. % 0.22/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.60/1.30 Prover 1: Preprocessing ... % 3.60/1.31 Prover 4: Preprocessing ... % 4.04/1.35 Prover 5: Preprocessing ... % 4.04/1.35 Prover 3: Preprocessing ... % 4.04/1.35 Prover 6: Preprocessing ... % 4.04/1.36 Prover 0: Preprocessing ... % 4.04/1.36 Prover 2: Preprocessing ... % 8.98/2.09 Prover 5: Proving ... % 8.98/2.10 Prover 2: Proving ... % 8.98/2.19 Prover 6: Proving ... % 8.98/2.19 Prover 1: Constructing countermodel ... % 8.98/2.20 Prover 3: Constructing countermodel ... % 12.32/2.51 Prover 3: gave up % 12.32/2.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.37/2.62 Prover 7: Preprocessing ... % 14.20/2.74 Prover 0: Proving ... % 14.20/2.77 Prover 4: Constructing countermodel ... % 14.20/2.78 Prover 7: Warning: ignoring some quantifiers % 14.20/2.87 Prover 7: Constructing countermodel ... % 16.20/2.99 Prover 1: gave up % 16.20/3.00 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.75/3.04 Prover 8: Preprocessing ... % 19.10/3.35 Prover 8: Warning: ignoring some quantifiers % 19.10/3.38 Prover 8: Constructing countermodel ... % 22.49/3.85 Prover 8: gave up % 22.49/3.86 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 23.10/3.89 Prover 0: proved (3235ms) % 23.10/3.89 % 23.10/3.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 23.10/3.89 % 23.10/3.89 Prover 5: stopped % 23.10/3.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 23.10/3.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 23.10/3.89 Prover 6: stopped % 23.10/3.90 Prover 2: stopped % 23.10/3.90 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 23.10/3.90 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 23.10/3.95 Prover 9: Preprocessing ... % 23.10/3.97 Prover 13: Preprocessing ... % 23.83/3.98 Prover 16: Preprocessing ... % 23.83/3.99 Prover 10: Preprocessing ... % 23.96/4.01 Prover 11: Preprocessing ... % 24.12/4.11 Prover 10: Warning: ignoring some quantifiers % 24.12/4.14 Prover 13: Warning: ignoring some quantifiers % 24.12/4.14 Prover 10: Constructing countermodel ... % 24.12/4.17 Prover 16: Warning: ignoring some quantifiers % 24.12/4.17 Prover 13: Constructing countermodel ... % 24.12/4.22 Prover 16: Constructing countermodel ... % 25.49/4.28 Prover 10: gave up % 25.49/4.29 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 26.32/4.36 Prover 19: Preprocessing ... % 27.06/4.49 Prover 9: Constructing countermodel ... % 27.61/4.50 Prover 9: stopped % 28.44/4.62 Prover 19: Warning: ignoring some quantifiers % 28.61/4.65 Prover 19: Constructing countermodel ... % 28.61/4.67 Prover 11: Constructing countermodel ... % 34.09/5.35 Prover 19: gave up % 38.08/5.88 Prover 4: Found proof (size 455) % 38.08/5.88 Prover 4: proved (5229ms) % 38.08/5.88 Prover 16: stopped % 38.08/5.88 Prover 11: stopped % 38.08/5.88 Prover 7: stopped % 38.08/5.88 Prover 13: stopped % 38.08/5.88 % 38.08/5.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 38.08/5.88 % 38.25/5.91 % SZS output start Proof for theBenchmark % 38.25/5.91 Assumptions after simplification: % 38.25/5.91 --------------------------------- % 38.25/5.91 % 38.25/5.91 (compose_function) % 38.36/5.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 38.36/5.95 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 38.36/5.95 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 38.36/5.95 ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | % 38.36/5.95 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] % 38.36/5.95 : ((apply(v0, v9, v6) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 % 38.36/5.95 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = % 38.36/5.95 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 38.36/5.95 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 38.36/5.95 int] : ! [v9: $i] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = % 38.36/5.95 v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) % 38.36/5.95 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 38.36/5.95 $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v11 & % 38.36/5.95 member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4) % 38.36/5.95 = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! % 38.36/5.95 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 38.36/5.95 : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 38.36/5.95 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 38.36/5.95 ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ % 38.36/5.95 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] : % 38.36/5.95 ((apply(v1, v5, v9) = v10 & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~ % 38.36/5.95 (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 % 38.36/5.95 = 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 38.36/5.95 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 38.36/5.95 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | % 38.36/5.95 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 38.36/5.95 $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ? % 38.36/5.95 [v12: int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 & % 38.36/5.95 apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, v3) = 0) % 38.36/5.95 | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 = % 38.36/5.95 0)))))) % 38.36/5.95 % 38.36/5.95 (equal_maps) % 38.36/5.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 38.36/5.95 $i] : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ % 38.36/5.95 (apply(v1, v4, v6) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ $i(v6) | ~ $i(v5) % 38.36/5.95 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : % 38.36/5.95 ? [v8: any] : ? [v9: any] : (member(v6, v3) = v9 & member(v5, v3) = v8 & % 38.36/5.95 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! % 38.36/5.95 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 38.36/5.95 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1, % 38.36/5.95 v4, v6) = 0) | ~ (member(v5, v3) = 0) | ~ $i(v6) | ~ $i(v5) | ~ % 38.36/5.95 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? % 38.36/5.95 [v8: any] : ? [v9: any] : (apply(v0, v4, v5) = v9 & member(v6, v3) = v8 & % 38.36/5.95 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! % 38.36/5.95 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 38.36/5.95 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v0, % 38.36/5.95 v4, v5) = 0) | ~ (member(v6, v3) = 0) | ~ $i(v6) | ~ $i(v5) | ~ % 38.36/5.95 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? % 38.36/5.95 [v8: any] : ? [v9: any] : (apply(v1, v4, v6) = v9 & member(v5, v3) = v8 & % 38.36/5.95 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! % 38.36/5.95 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 38.36/5.95 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ % 38.36/5.95 (member(v6, v3) = 0) | ~ (member(v5, v3) = 0) | ~ (member(v4, v2) = 0) | % 38.36/5.95 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 38.36/5.95 $i(v0) | ? [v7: any] : ? [v8: any] : (apply(v1, v4, v6) = v8 & apply(v0, % 38.36/5.95 v4, v5) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! [v1: $i] % 38.36/5.95 : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (equal_maps(v0, v1, % 38.36/5.95 v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 38.36/5.95 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v6) & apply(v1, v5, v7) = 0 & % 38.36/5.95 apply(v0, v5, v6) = 0 & member(v7, v3) = 0 & member(v6, v3) = 0 & % 38.36/5.95 member(v5, v2) = 0 & $i(v7) & $i(v6) & $i(v5))) % 38.36/5.95 % 38.36/5.96 (injective) % 38.36/5.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 38.36/5.96 $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) % 38.36/5.96 | ~ (apply(v0, v3, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 38.36/5.96 | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 38.36/5.96 (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 = % 38.36/5.96 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 38.36/5.96 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ % 38.36/5.96 (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v3, % 38.36/5.96 v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 38.36/5.96 ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v5) = % 38.36/5.96 v8 & member(v5, v2) = v7 & member(v4, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = % 38.36/5.96 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 38.36/5.96 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = % 38.36/5.96 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v1) = 0) | ~ $i(v5) | ~ % 38.36/5.96 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 38.36/5.96 [v7: any] : ? [v8: any] : (apply(v0, v4, v5) = v8 & member(v5, v2) = v7 & % 38.36/5.96 member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! % 38.36/5.96 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 38.36/5.96 : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ % 38.36/5.96 (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 38.36/5.96 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 38.36/5.96 (apply(v0, v4, v5) = v7 & apply(v0, v3, v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = % 38.36/5.96 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = % 38.36/5.96 0 | ~ (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 38.36/5.96 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0 % 38.36/5.96 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 & % 38.36/5.96 member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4))) % 38.36/5.96 % 38.36/5.96 (inverse_function) % 38.36/5.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 38.36/5.96 $i] : ! [v6: any] : ( ~ (inverse_function(v0, v1, v2) = v5) | ~ (apply(v5, % 38.36/5.96 v4, v3) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 38.36/5.96 $i(v0) | ? [v7: any] : ? [v8: any] : ? [v9: any] : (apply(v0, v3, v4) = % 38.36/5.96 v9 & member(v4, v2) = v8 & member(v3, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = % 38.36/5.96 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) % 38.36/5.96 % 38.36/5.96 (maps) % 38.36/5.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 38.36/5.97 $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ % 38.36/5.97 (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 38.36/5.97 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 38.36/5.97 (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = % 38.36/5.97 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 38.36/5.97 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, % 38.36/5.97 v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ~ % 38.36/5.97 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 38.36/5.97 any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5, % 38.36/5.97 v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 38.36/5.97 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 38.36/5.97 [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, % 38.36/5.97 v3, v4) = 0) | ~ (member(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 38.36/5.97 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 38.36/5.97 ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v4, v2) = v7 & member(v3, v1) % 38.36/5.97 = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: % 38.36/5.97 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ % 38.36/5.97 (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) | % 38.36/5.97 ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 38.36/5.97 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & % 38.36/5.97 apply(v0, v3, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! % 38.36/5.97 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) | % 38.36/5.97 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 38.36/5.97 : ? [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int] % 38.36/5.97 : ? [v12: $i] : ? [v13: int] : ($i(v12) & $i(v6) & $i(v5) & $i(v4) & ((v13 % 38.36/5.97 = 0 & member(v12, v1) = 0 & ! [v14: $i] : ( ~ (apply(v0, v12, v14) = % 38.36/5.97 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & member(v14, v2) % 38.36/5.97 = v15)) & ! [v14: $i] : ( ~ (member(v14, v2) = 0) | ~ $i(v14) | % 38.36/5.97 ? [v15: int] : ( ~ (v15 = 0) & apply(v0, v12, v14) = v15))) | (v11 = % 38.36/5.97 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4, % 38.36/5.97 v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, % 38.36/5.97 v2) = 0 & member(v4, v1) = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 38.36/5.97 [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) % 38.36/5.97 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, % 38.36/5.97 v3, v4) = 0 & member(v4, v2) = 0 & $i(v4))) % 38.36/5.97 % 38.36/5.97 (one_to_one) % 38.36/5.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 38.36/5.98 (one_to_one(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 38.36/5.98 any] : ? [v5: any] : (surjective(v0, v1, v2) = v5 & injective(v0, v1, v2) % 38.36/5.98 = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 38.36/5.98 $i] : ! [v3: any] : ( ~ (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ % 38.36/5.98 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (one_to_one(v0, v1, v2) = % 38.36/5.98 v4 & injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! % 38.36/5.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (injective(v0, v1, % 38.36/5.98 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 38.36/5.98 any] : (one_to_one(v0, v1, v2) = v4 & surjective(v0, v1, v2) = v5 & ( ~ % 38.36/5.98 (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 38.36/5.98 $i] : ( ~ (one_to_one(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 38.36/5.98 (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0)) & ! [v0: $i] : ! % 38.36/5.98 [v1: $i] : ! [v2: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ $i(v2) | ~ % 38.36/5.98 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) = % 38.36/5.98 v4 & injective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : % 38.36/5.98 ! [v1: $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) = 0) | ~ $i(v2) | ~ % 38.36/5.98 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) = % 38.36/5.98 v4 & surjective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 38.36/5.98 % 38.36/5.98 (surjective) % 38.36/5.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 38.36/5.98 (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 38.36/5.98 $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~ (apply(v0, v5, v4) % 38.36/5.98 = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6)) % 38.36/5.98 & ! [v5: $i] : ( ~ (member(v5, v1) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ % 38.36/5.98 (v6 = 0) & apply(v0, v5, v4) = v6)))) & ! [v0: $i] : ! [v1: $i] : ! % 38.36/5.98 [v2: $i] : ! [v3: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) % 38.36/5.98 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 38.36/5.98 (apply(v0, v4, v3) = 0 & member(v4, v1) = 0 & $i(v4))) % 38.36/5.98 % 38.36/5.98 (thII10) % 38.36/5.98 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 38.36/5.98 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] % 38.36/5.98 : ( ~ (v10 = 0) & inverse_function(v5, v2, v4) = v6 & inverse_function(v1, v3, % 38.36/5.98 v4) = v8 & inverse_function(v0, v2, v3) = v7 & one_to_one(v1, v3, v4) = 0 % 38.36/5.98 & one_to_one(v0, v2, v3) = 0 & equal_maps(v6, v9, v4, v2) = v10 & % 38.36/5.98 compose_function(v7, v8, v4, v3, v2) = v9 & compose_function(v1, v0, v2, v3, % 38.36/5.98 v4) = v5 & maps(v1, v3, v4) = 0 & maps(v0, v2, v3) = 0 & $i(v9) & $i(v8) & % 38.36/5.98 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 38.36/5.98 % 38.36/5.98 (function-axioms) % 38.36/5.99 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 38.36/5.99 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 38.36/5.99 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 38.36/5.99 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 38.36/5.99 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 38.36/5.99 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 38.36/5.99 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 38.36/5.99 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 38.36/5.99 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 38.36/5.99 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 38.36/5.99 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 38.36/5.99 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 38.36/5.99 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 38.36/5.99 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 38.36/5.99 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 38.36/5.99 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 38.36/5.99 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 38.36/5.99 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 38.36/5.99 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 38.36/5.99 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 38.36/5.99 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 38.36/5.99 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 38.36/5.99 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 38.36/5.99 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 38.36/5.99 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 38.36/5.99 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 38.36/5.99 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 38.36/5.99 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 38.36/5.99 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 38.36/5.99 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 38.36/5.99 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 38.36/5.99 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 38.36/5.99 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.36/5.99 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 38.36/5.99 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 38.36/5.99 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 38.36/5.99 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 38.36/5.99 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 38.36/5.99 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 38.36/5.99 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 38.36/5.99 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 38.36/5.99 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 38.36/5.99 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 38.36/5.99 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 38.36/5.99 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 38.36/5.99 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.36/5.99 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 38.36/5.99 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.36/5.99 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 38.36/5.99 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 38.36/5.99 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 38.36/5.99 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 38.36/5.99 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 38.36/5.99 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 38.36/5.99 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.36/5.99 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 38.36/5.99 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 38.36/5.99 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.36/5.99 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 38.36/5.99 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 38.36/5.99 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 38.36/5.99 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 38.36/5.99 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 38.36/5.99 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 38.36/5.99 (power_set(v2) = v0)) % 38.36/5.99 % 38.36/5.99 Further assumptions not needed in the proof: % 38.36/5.99 -------------------------------------------- % 38.36/5.99 compose_predicate, decreasing_function, difference, empty_set, equal_set, % 38.36/5.99 identity, image2, image3, increasing_function, intersection, inverse_image2, % 38.36/5.99 inverse_image3, inverse_predicate, isomorphism, power_set, product, singleton, % 38.36/5.99 subset, sum, union, unordered_pair % 38.36/5.99 % 38.36/5.99 Those formulas are unsatisfiable: % 38.36/5.99 --------------------------------- % 38.36/5.99 % 38.36/5.99 Begin of proof % 38.36/5.99 | % 38.36/5.99 | ALPHA: (maps) implies: % 38.36/5.99 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, % 38.36/5.99 | v1, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v2) | % 38.36/5.99 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & % 38.36/5.99 | member(v4, v2) = 0 & $i(v4))) % 38.36/5.99 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 38.36/5.99 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) % 38.36/5.99 | = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ~ % 38.36/5.99 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 38.36/5.99 | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & apply(v0, v3, % 38.36/5.99 | v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 38.36/6.00 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 38.36/6.00 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, % 38.36/6.00 | v5) = 0) | ~ (member(v4, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 38.36/6.00 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 38.36/6.00 | any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5, v2) = v7 % 38.36/6.00 | & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 38.36/6.00 | % 38.36/6.00 | ALPHA: (compose_function) implies: % 38.36/6.00 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 38.36/6.00 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (compose_function(v0, v1, % 38.36/6.00 | v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | ~ $i(v6) | ~ % 38.36/6.00 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 38.36/6.00 | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ? [v12: % 38.36/6.00 | int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 & % 38.36/6.00 | apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, % 38.36/6.00 | v3) = 0) | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ % 38.36/6.00 | (v9 = 0) | ~ (v8 = 0)))))) % 38.36/6.00 | % 38.36/6.00 | ALPHA: (equal_maps) implies: % 38.36/6.00 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 38.36/6.00 | (v4 = 0 | ~ (equal_maps(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) % 38.36/6.00 | | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ( % 38.36/6.00 | ~ (v7 = v6) & apply(v1, v5, v7) = 0 & apply(v0, v5, v6) = 0 & % 38.36/6.00 | member(v7, v3) = 0 & member(v6, v3) = 0 & member(v5, v2) = 0 & % 38.36/6.00 | $i(v7) & $i(v6) & $i(v5))) % 38.36/6.00 | % 38.36/6.00 | ALPHA: (injective) implies: % 38.36/6.00 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 38.36/6.00 | ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, % 38.36/6.00 | v2) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ % 38.36/6.00 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 38.36/6.00 | ? [v6: any] : ? [v7: any] : (apply(v0, v4, v5) = v7 & apply(v0, v3, % 38.36/6.00 | v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 38.36/6.00 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 38.36/6.00 | ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, % 38.36/6.00 | v4, v5) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | % 38.36/6.00 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 38.36/6.00 | any] : ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v5, v2) = v7 % 38.36/6.00 | & member(v4, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 38.36/6.00 | % 38.36/6.00 | ALPHA: (surjective) implies: % 38.36/6.00 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 38.36/6.00 | (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ~ $i(v3) | % 38.36/6.00 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v4, v3) = % 38.36/6.00 | 0 & member(v4, v1) = 0 & $i(v4))) % 38.36/6.00 | % 38.36/6.00 | ALPHA: (one_to_one) implies: % 38.36/6.00 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (one_to_one(v0, v1, v2) = % 38.36/6.00 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (surjective(v0, v1, v2) = % 38.36/6.00 | 0 & injective(v0, v1, v2) = 0)) % 38.36/6.00 | % 38.36/6.00 | ALPHA: (function-axioms) implies: % 38.36/6.00 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 38.36/6.00 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, % 38.36/6.00 | v2) = v0)) % 38.36/6.00 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 38.36/6.00 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 38.36/6.00 | ~ (apply(v4, v3, v2) = v0)) % 38.36/6.00 | % 38.36/6.00 | DELTA: instantiating (thII10) with fresh symbols all_32_0, all_32_1, all_32_2, % 38.36/6.00 | all_32_3, all_32_4, all_32_5, all_32_6, all_32_7, all_32_8, all_32_9, % 38.36/6.00 | all_32_10 gives: % 38.36/6.01 | (12) ~ (all_32_0 = 0) & inverse_function(all_32_5, all_32_8, all_32_6) = % 38.36/6.01 | all_32_4 & inverse_function(all_32_9, all_32_7, all_32_6) = all_32_2 & % 38.36/6.01 | inverse_function(all_32_10, all_32_8, all_32_7) = all_32_3 & % 38.36/6.01 | one_to_one(all_32_9, all_32_7, all_32_6) = 0 & one_to_one(all_32_10, % 38.36/6.01 | all_32_8, all_32_7) = 0 & equal_maps(all_32_4, all_32_1, all_32_6, % 38.36/6.01 | all_32_8) = all_32_0 & compose_function(all_32_3, all_32_2, % 38.36/6.01 | all_32_6, all_32_7, all_32_8) = all_32_1 & % 38.36/6.01 | compose_function(all_32_9, all_32_10, all_32_8, all_32_7, all_32_6) = % 38.36/6.01 | all_32_5 & maps(all_32_9, all_32_7, all_32_6) = 0 & maps(all_32_10, % 38.36/6.01 | all_32_8, all_32_7) = 0 & $i(all_32_1) & $i(all_32_2) & $i(all_32_3) % 38.36/6.01 | & $i(all_32_4) & $i(all_32_5) & $i(all_32_6) & $i(all_32_7) & % 38.36/6.01 | $i(all_32_8) & $i(all_32_9) & $i(all_32_10) % 38.36/6.01 | % 38.36/6.01 | ALPHA: (12) implies: % 38.36/6.01 | (13) ~ (all_32_0 = 0) % 38.36/6.01 | (14) $i(all_32_10) % 38.36/6.01 | (15) $i(all_32_9) % 38.36/6.01 | (16) $i(all_32_8) % 38.36/6.01 | (17) $i(all_32_7) % 38.36/6.01 | (18) $i(all_32_6) % 38.36/6.01 | (19) $i(all_32_5) % 38.36/6.01 | (20) $i(all_32_4) % 38.36/6.01 | (21) $i(all_32_3) % 38.36/6.01 | (22) $i(all_32_2) % 38.36/6.01 | (23) $i(all_32_1) % 38.36/6.01 | (24) maps(all_32_10, all_32_8, all_32_7) = 0 % 38.36/6.01 | (25) maps(all_32_9, all_32_7, all_32_6) = 0 % 38.36/6.01 | (26) compose_function(all_32_9, all_32_10, all_32_8, all_32_7, all_32_6) = % 38.36/6.01 | all_32_5 % 38.36/6.01 | (27) compose_function(all_32_3, all_32_2, all_32_6, all_32_7, all_32_8) = % 38.36/6.01 | all_32_1 % 38.36/6.01 | (28) equal_maps(all_32_4, all_32_1, all_32_6, all_32_8) = all_32_0 % 38.36/6.01 | (29) one_to_one(all_32_10, all_32_8, all_32_7) = 0 % 38.36/6.01 | (30) one_to_one(all_32_9, all_32_7, all_32_6) = 0 % 38.36/6.01 | (31) inverse_function(all_32_10, all_32_8, all_32_7) = all_32_3 % 38.36/6.01 | (32) inverse_function(all_32_9, all_32_7, all_32_6) = all_32_2 % 38.36/6.01 | (33) inverse_function(all_32_5, all_32_8, all_32_6) = all_32_4 % 38.36/6.01 | % 38.36/6.01 | GROUND_INST: instantiating (5) with all_32_4, all_32_1, all_32_6, all_32_8, % 38.36/6.01 | all_32_0, simplifying with (16), (18), (20), (23), (28) gives: % 38.36/6.01 | (34) all_32_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) % 38.36/6.01 | & apply(all_32_1, v0, v2) = 0 & apply(all_32_4, v0, v1) = 0 & % 38.36/6.01 | member(v2, all_32_8) = 0 & member(v1, all_32_8) = 0 & member(v0, % 38.36/6.01 | all_32_6) = 0 & $i(v2) & $i(v1) & $i(v0)) % 38.36/6.01 | % 38.36/6.01 | GROUND_INST: instantiating (9) with all_32_10, all_32_8, all_32_7, simplifying % 38.36/6.01 | with (14), (16), (17), (29) gives: % 38.36/6.01 | (35) surjective(all_32_10, all_32_8, all_32_7) = 0 & injective(all_32_10, % 38.36/6.01 | all_32_8, all_32_7) = 0 % 38.36/6.01 | % 38.36/6.01 | ALPHA: (35) implies: % 38.36/6.01 | (36) injective(all_32_10, all_32_8, all_32_7) = 0 % 38.36/6.01 | % 38.36/6.01 | GROUND_INST: instantiating (9) with all_32_9, all_32_7, all_32_6, simplifying % 38.36/6.01 | with (15), (17), (18), (30) gives: % 38.36/6.01 | (37) surjective(all_32_9, all_32_7, all_32_6) = 0 & injective(all_32_9, % 38.36/6.01 | all_32_7, all_32_6) = 0 % 38.36/6.01 | % 38.36/6.01 | ALPHA: (37) implies: % 38.36/6.01 | (38) injective(all_32_9, all_32_7, all_32_6) = 0 % 38.36/6.01 | (39) surjective(all_32_9, all_32_7, all_32_6) = 0 % 38.36/6.01 | % 38.36/6.01 | BETA: splitting (34) gives: % 38.36/6.01 | % 38.36/6.01 | Case 1: % 38.36/6.01 | | % 38.36/6.01 | | (40) all_32_0 = 0 % 38.36/6.01 | | % 38.36/6.01 | | REDUCE: (13), (40) imply: % 38.36/6.01 | | (41) $false % 38.36/6.01 | | % 38.36/6.01 | | CLOSE: (41) is inconsistent. % 38.36/6.01 | | % 38.36/6.01 | Case 2: % 38.36/6.01 | | % 38.36/6.01 | | (42) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & % 38.36/6.01 | | apply(all_32_1, v0, v2) = 0 & apply(all_32_4, v0, v1) = 0 & % 38.36/6.01 | | member(v2, all_32_8) = 0 & member(v1, all_32_8) = 0 & member(v0, % 38.36/6.01 | | all_32_6) = 0 & $i(v2) & $i(v1) & $i(v0)) % 38.36/6.01 | | % 38.36/6.01 | | DELTA: instantiating (42) with fresh symbols all_44_0, all_44_1, all_44_2 % 38.36/6.01 | | gives: % 38.36/6.01 | | (43) ~ (all_44_0 = all_44_1) & apply(all_32_1, all_44_2, all_44_0) = 0 & % 38.36/6.01 | | apply(all_32_4, all_44_2, all_44_1) = 0 & member(all_44_0, all_32_8) % 38.36/6.01 | | = 0 & member(all_44_1, all_32_8) = 0 & member(all_44_2, all_32_6) = % 38.36/6.01 | | 0 & $i(all_44_0) & $i(all_44_1) & $i(all_44_2) % 38.36/6.01 | | % 38.36/6.01 | | ALPHA: (43) implies: % 38.36/6.01 | | (44) ~ (all_44_0 = all_44_1) % 38.36/6.01 | | (45) $i(all_44_2) % 38.36/6.01 | | (46) $i(all_44_1) % 38.36/6.01 | | (47) $i(all_44_0) % 38.36/6.01 | | (48) member(all_44_2, all_32_6) = 0 % 38.36/6.02 | | (49) member(all_44_1, all_32_8) = 0 % 38.36/6.02 | | (50) member(all_44_0, all_32_8) = 0 % 38.36/6.02 | | (51) apply(all_32_4, all_44_2, all_44_1) = 0 % 38.36/6.02 | | (52) apply(all_32_1, all_44_2, all_44_0) = 0 % 38.36/6.02 | | % 38.36/6.02 | | GROUND_INST: instantiating (1) with all_32_10, all_32_8, all_32_7, all_44_1, % 38.36/6.02 | | simplifying with (14), (16), (17), (24), (46), (49) gives: % 38.36/6.02 | | (53) ? [v0: $i] : (apply(all_32_10, all_44_1, v0) = 0 & member(v0, % 38.36/6.02 | | all_32_7) = 0 & $i(v0)) % 38.36/6.02 | | % 38.36/6.02 | | GROUND_INST: instantiating (1) with all_32_10, all_32_8, all_32_7, all_44_0, % 38.36/6.02 | | simplifying with (14), (16), (17), (24), (47), (50) gives: % 38.36/6.02 | | (54) ? [v0: $i] : (apply(all_32_10, all_44_0, v0) = 0 & member(v0, % 38.36/6.02 | | all_32_7) = 0 & $i(v0)) % 38.36/6.02 | | % 38.36/6.02 | | GROUND_INST: instantiating (inverse_function) with all_32_5, all_32_8, % 38.36/6.02 | | all_32_6, all_44_1, all_44_2, all_32_4, 0, simplifying with % 38.36/6.02 | | (16), (18), (19), (33), (45), (46), (51) gives: % 38.36/6.02 | | (55) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_5, % 38.36/6.02 | | all_44_1, all_44_2) = v2 & member(all_44_1, all_32_8) = v0 & % 38.36/6.02 | | member(all_44_2, all_32_6) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 % 38.36/6.02 | | = 0)) % 38.36/6.02 | | % 38.36/6.02 | | GROUND_INST: instantiating (4) with all_32_3, all_32_2, all_32_6, all_32_7, % 38.36/6.02 | | all_32_8, all_44_2, all_44_0, all_32_1, simplifying with (16), % 38.36/6.02 | | (17), (18), (21), (22), (27), (45), (47), (52) gives: % 38.36/6.02 | | (56) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: int] : ? [v4: % 38.36/6.02 | | int] : ? [v5: int] : ($i(v2) & ((v5 = 0 & v4 = 0 & v3 = 0 & % 38.36/6.02 | | apply(all_32_2, all_44_2, v2) = 0 & apply(all_32_3, v2, % 38.36/6.02 | | all_44_0) = 0 & member(v2, all_32_7) = 0) | % 38.36/6.02 | | (member(all_44_0, all_32_8) = v1 & member(all_44_2, all_32_6) = % 38.36/6.02 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))) % 38.36/6.02 | | % 38.36/6.02 | | GROUND_INST: instantiating (8) with all_32_9, all_32_7, all_32_6, all_44_2, % 38.36/6.02 | | simplifying with (15), (17), (18), (39), (45), (48) gives: % 38.36/6.02 | | (57) ? [v0: $i] : (apply(all_32_9, v0, all_44_2) = 0 & member(v0, % 38.36/6.02 | | all_32_7) = 0 & $i(v0)) % 38.36/6.02 | | % 38.36/6.02 | | DELTA: instantiating (57) with fresh symbol all_51_0 gives: % 38.36/6.02 | | (58) apply(all_32_9, all_51_0, all_44_2) = 0 & member(all_51_0, all_32_7) % 38.36/6.02 | | = 0 & $i(all_51_0) % 38.36/6.02 | | % 38.36/6.02 | | ALPHA: (58) implies: % 38.36/6.02 | | (59) $i(all_51_0) % 38.36/6.02 | | (60) member(all_51_0, all_32_7) = 0 % 38.36/6.02 | | (61) apply(all_32_9, all_51_0, all_44_2) = 0 % 38.36/6.02 | | % 38.36/6.02 | | DELTA: instantiating (54) with fresh symbol all_53_0 gives: % 38.36/6.02 | | (62) apply(all_32_10, all_44_0, all_53_0) = 0 & member(all_53_0, % 38.36/6.02 | | all_32_7) = 0 & $i(all_53_0) % 38.36/6.02 | | % 38.36/6.02 | | ALPHA: (62) implies: % 38.36/6.02 | | (63) $i(all_53_0) % 38.36/6.02 | | (64) member(all_53_0, all_32_7) = 0 % 38.36/6.02 | | (65) apply(all_32_10, all_44_0, all_53_0) = 0 % 38.36/6.02 | | % 38.36/6.02 | | DELTA: instantiating (53) with fresh symbol all_55_0 gives: % 38.36/6.02 | | (66) apply(all_32_10, all_44_1, all_55_0) = 0 & member(all_55_0, % 38.36/6.02 | | all_32_7) = 0 & $i(all_55_0) % 38.36/6.02 | | % 38.36/6.02 | | ALPHA: (66) implies: % 38.36/6.02 | | (67) $i(all_55_0) % 38.36/6.02 | | (68) member(all_55_0, all_32_7) = 0 % 38.36/6.02 | | (69) apply(all_32_10, all_44_1, all_55_0) = 0 % 38.36/6.02 | | % 38.36/6.02 | | DELTA: instantiating (55) with fresh symbols all_57_0, all_57_1, all_57_2 % 38.36/6.02 | | gives: % 38.36/6.02 | | (70) apply(all_32_5, all_44_1, all_44_2) = all_57_0 & member(all_44_1, % 38.36/6.02 | | all_32_8) = all_57_2 & member(all_44_2, all_32_6) = all_57_1 & ( ~ % 38.36/6.02 | | (all_57_1 = 0) | ~ (all_57_2 = 0) | all_57_0 = 0) % 38.36/6.02 | | % 38.36/6.02 | | ALPHA: (70) implies: % 38.83/6.02 | | (71) member(all_44_2, all_32_6) = all_57_1 % 38.83/6.02 | | (72) member(all_44_1, all_32_8) = all_57_2 % 38.83/6.02 | | (73) apply(all_32_5, all_44_1, all_44_2) = all_57_0 % 38.83/6.02 | | (74) ~ (all_57_1 = 0) | ~ (all_57_2 = 0) | all_57_0 = 0 % 38.83/6.02 | | % 38.83/6.02 | | DELTA: instantiating (56) with fresh symbols all_59_0, all_59_1, all_59_2, % 38.83/6.02 | | all_59_3, all_59_4, all_59_5 gives: % 38.83/6.02 | | (75) $i(all_59_3) & ((all_59_0 = 0 & all_59_1 = 0 & all_59_2 = 0 & % 38.83/6.02 | | apply(all_32_2, all_44_2, all_59_3) = 0 & apply(all_32_3, % 38.83/6.02 | | all_59_3, all_44_0) = 0 & member(all_59_3, all_32_7) = 0) | % 38.83/6.02 | | (member(all_44_0, all_32_8) = all_59_4 & member(all_44_2, % 38.83/6.02 | | all_32_6) = all_59_5 & ( ~ (all_59_4 = 0) | ~ (all_59_5 = % 38.83/6.02 | | 0)))) % 38.83/6.02 | | % 38.83/6.02 | | ALPHA: (75) implies: % 38.83/6.02 | | (76) $i(all_59_3) % 38.83/6.02 | | (77) (all_59_0 = 0 & all_59_1 = 0 & all_59_2 = 0 & apply(all_32_2, % 38.83/6.02 | | all_44_2, all_59_3) = 0 & apply(all_32_3, all_59_3, all_44_0) = % 38.83/6.02 | | 0 & member(all_59_3, all_32_7) = 0) | (member(all_44_0, all_32_8) % 38.83/6.02 | | = all_59_4 & member(all_44_2, all_32_6) = all_59_5 & ( ~ (all_59_4 % 38.83/6.02 | | = 0) | ~ (all_59_5 = 0))) % 38.83/6.02 | | % 38.83/6.02 | | GROUND_INST: instantiating (10) with 0, all_57_1, all_32_6, all_44_2, % 38.83/6.02 | | simplifying with (48), (71) gives: % 38.83/6.02 | | (78) all_57_1 = 0 % 38.83/6.02 | | % 38.83/6.02 | | GROUND_INST: instantiating (10) with 0, all_57_2, all_32_8, all_44_1, % 38.83/6.02 | | simplifying with (49), (72) gives: % 38.83/6.02 | | (79) all_57_2 = 0 % 38.83/6.02 | | % 38.83/6.02 | | BETA: splitting (77) gives: % 38.83/6.02 | | % 38.83/6.02 | | Case 1: % 38.83/6.02 | | | % 38.83/6.02 | | | (80) all_59_0 = 0 & all_59_1 = 0 & all_59_2 = 0 & apply(all_32_2, % 38.83/6.03 | | | all_44_2, all_59_3) = 0 & apply(all_32_3, all_59_3, all_44_0) = % 38.83/6.03 | | | 0 & member(all_59_3, all_32_7) = 0 % 38.83/6.03 | | | % 38.83/6.03 | | | ALPHA: (80) implies: % 38.83/6.03 | | | (81) member(all_59_3, all_32_7) = 0 % 38.83/6.03 | | | (82) apply(all_32_3, all_59_3, all_44_0) = 0 % 38.83/6.03 | | | (83) apply(all_32_2, all_44_2, all_59_3) = 0 % 38.83/6.03 | | | % 38.83/6.03 | | | BETA: splitting (74) gives: % 38.83/6.03 | | | % 38.83/6.03 | | | Case 1: % 38.83/6.03 | | | | % 38.83/6.03 | | | | (84) ~ (all_57_1 = 0) % 38.83/6.03 | | | | % 38.83/6.03 | | | | REDUCE: (78), (84) imply: % 38.83/6.03 | | | | (85) $false % 38.83/6.03 | | | | % 38.83/6.03 | | | | CLOSE: (85) is inconsistent. % 38.83/6.03 | | | | % 38.83/6.03 | | | Case 2: % 38.83/6.03 | | | | % 38.83/6.03 | | | | (86) ~ (all_57_2 = 0) | all_57_0 = 0 % 38.83/6.03 | | | | % 38.83/6.03 | | | | BETA: splitting (86) gives: % 38.83/6.03 | | | | % 38.83/6.03 | | | | Case 1: % 38.83/6.03 | | | | | % 38.83/6.03 | | | | | (87) ~ (all_57_2 = 0) % 38.83/6.03 | | | | | % 38.83/6.03 | | | | | REDUCE: (79), (87) imply: % 38.83/6.03 | | | | | (88) $false % 38.83/6.03 | | | | | % 38.83/6.03 | | | | | CLOSE: (88) is inconsistent. % 38.83/6.03 | | | | | % 38.83/6.03 | | | | Case 2: % 38.83/6.03 | | | | | % 38.83/6.03 | | | | | (89) all_57_0 = 0 % 38.83/6.03 | | | | | % 38.83/6.03 | | | | | REDUCE: (73), (89) imply: % 38.83/6.03 | | | | | (90) apply(all_32_5, all_44_1, all_44_2) = 0 % 38.83/6.03 | | | | | % 38.83/6.03 | | | | | GROUND_INST: instantiating (6) with all_32_10, all_32_8, all_32_7, % 38.83/6.03 | | | | | all_44_1, all_44_0, all_51_0, simplifying with (14), % 38.83/6.03 | | | | | (16), (17), (36), (46), (47), (49), (50), (59), (60) % 38.83/6.03 | | | | | gives: % 38.83/6.03 | | | | | (91) all_44_0 = all_44_1 | ? [v0: any] : ? [v1: any] : % 38.83/6.03 | | | | | (apply(all_32_10, all_44_0, all_51_0) = v1 & apply(all_32_10, % 38.83/6.03 | | | | | all_44_1, all_51_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.03 | | | | | % 38.83/6.03 | | | | | GROUND_INST: instantiating (6) with all_32_10, all_32_8, all_32_7, % 38.83/6.03 | | | | | all_44_0, all_44_1, all_51_0, simplifying with (14), % 38.83/6.03 | | | | | (16), (17), (36), (46), (47), (49), (50), (59), (60) % 38.83/6.03 | | | | | gives: % 38.83/6.03 | | | | | (92) all_44_0 = all_44_1 | ? [v0: any] : ? [v1: any] : % 38.83/6.03 | | | | | (apply(all_32_10, all_44_0, all_51_0) = v0 & apply(all_32_10, % 38.83/6.03 | | | | | all_44_1, all_51_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.03 | | | | | % 38.83/6.03 | | | | | GROUND_INST: instantiating (2) with all_32_10, all_32_8, all_32_7, % 38.83/6.03 | | | | | all_44_0, all_51_0, all_53_0, simplifying with (14), % 38.83/6.03 | | | | | (16), (17), (24), (47), (50), (59), (60), (63), (64) % 38.83/6.03 | | | | | gives: % 38.83/6.03 | | | | | (93) all_53_0 = all_51_0 | ? [v0: any] : ? [v1: any] : % 38.83/6.03 | | | | | (apply(all_32_10, all_44_0, all_53_0) = v1 & apply(all_32_10, % 38.83/6.03 | | | | | all_44_0, all_51_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.03 | | | | | % 38.83/6.03 | | | | | GROUND_INST: instantiating (2) with all_32_10, all_32_8, all_32_7, % 38.83/6.03 | | | | | all_44_0, all_53_0, all_51_0, simplifying with (14), % 38.83/6.03 | | | | | (16), (17), (24), (47), (50), (59), (60), (63), (64) % 38.83/6.03 | | | | | gives: % 38.83/6.03 | | | | | (94) all_53_0 = all_51_0 | ? [v0: any] : ? [v1: any] : % 38.83/6.03 | | | | | (apply(all_32_10, all_44_0, all_53_0) = v0 & apply(all_32_10, % 38.83/6.03 | | | | | all_44_0, all_51_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.03 | | | | | % 38.83/6.03 | | | | | GROUND_INST: instantiating (6) with all_32_9, all_32_7, all_32_6, % 38.83/6.03 | | | | | all_51_0, all_53_0, all_44_2, simplifying with (15), % 38.83/6.03 | | | | | (17), (18), (38), (45), (48), (59), (60), (63), (64) % 38.83/6.03 | | | | | gives: % 38.83/6.03 | | | | | (95) all_53_0 = all_51_0 | ? [v0: any] : ? [v1: any] : % 38.83/6.03 | | | | | (apply(all_32_9, all_53_0, all_44_2) = v1 & apply(all_32_9, % 38.83/6.03 | | | | | all_51_0, all_44_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.03 | | | | | % 38.83/6.03 | | | | | GROUND_INST: instantiating (6) with all_32_9, all_32_7, all_32_6, % 38.83/6.03 | | | | | all_53_0, all_51_0, all_44_2, simplifying with (15), % 38.83/6.03 | | | | | (17), (18), (38), (45), (48), (59), (60), (63), (64) % 38.83/6.03 | | | | | gives: % 38.83/6.03 | | | | | (96) all_53_0 = all_51_0 | ? [v0: any] : ? [v1: any] : % 38.83/6.03 | | | | | (apply(all_32_9, all_53_0, all_44_2) = v0 & apply(all_32_9, % 38.83/6.03 | | | | | all_51_0, all_44_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.03 | | | | | % 38.83/6.03 | | | | | GROUND_INST: instantiating (6) with all_32_10, all_32_8, all_32_7, % 38.83/6.03 | | | | | all_44_1, all_44_0, all_53_0, simplifying with (14), % 38.83/6.03 | | | | | (16), (17), (36), (46), (47), (49), (50), (63), (64) % 38.83/6.03 | | | | | gives: % 38.83/6.03 | | | | | (97) all_44_0 = all_44_1 | ? [v0: any] : ? [v1: any] : % 38.83/6.03 | | | | | (apply(all_32_10, all_44_0, all_53_0) = v1 & apply(all_32_10, % 38.83/6.03 | | | | | all_44_1, all_53_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.03 | | | | | % 38.83/6.03 | | | | | GROUND_INST: instantiating (6) with all_32_10, all_32_8, all_32_7, % 38.83/6.03 | | | | | all_44_0, all_44_1, all_53_0, simplifying with (14), % 38.83/6.03 | | | | | (16), (17), (36), (46), (47), (49), (50), (63), (64) % 38.83/6.03 | | | | | gives: % 38.83/6.03 | | | | | (98) all_44_0 = all_44_1 | ? [v0: any] : ? [v1: any] : % 38.83/6.03 | | | | | (apply(all_32_10, all_44_0, all_53_0) = v0 & apply(all_32_10, % 38.83/6.03 | | | | | all_44_1, all_53_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.03 | | | | | % 38.83/6.04 | | | | | GROUND_INST: instantiating (1) with all_32_9, all_32_7, all_32_6, % 38.83/6.04 | | | | | all_55_0, simplifying with (15), (17), (18), (25), (67), % 38.83/6.04 | | | | | (68) gives: % 38.83/6.04 | | | | | (99) ? [v0: $i] : (apply(all_32_9, all_55_0, v0) = 0 & member(v0, % 38.83/6.04 | | | | | all_32_6) = 0 & $i(v0)) % 38.83/6.04 | | | | | % 38.83/6.04 | | | | | GROUND_INST: instantiating (2) with all_32_10, all_32_8, all_32_7, % 38.83/6.04 | | | | | all_44_0, all_53_0, all_59_3, simplifying with (14), % 38.83/6.04 | | | | | (16), (17), (24), (47), (50), (63), (64), (76), (81) % 38.83/6.04 | | | | | gives: % 38.83/6.04 | | | | | (100) all_59_3 = all_53_0 | ? [v0: any] : ? [v1: any] : % 38.83/6.04 | | | | | (apply(all_32_10, all_44_0, all_59_3) = v1 & apply(all_32_10, % 38.83/6.04 | | | | | all_44_0, all_53_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.04 | | | | | % 38.83/6.04 | | | | | GROUND_INST: instantiating (2) with all_32_10, all_32_8, all_32_7, % 38.83/6.04 | | | | | all_44_0, all_59_3, all_53_0, simplifying with (14), % 38.83/6.04 | | | | | (16), (17), (24), (47), (50), (63), (64), (76), (81) % 38.83/6.04 | | | | | gives: % 38.83/6.04 | | | | | (101) all_59_3 = all_53_0 | ? [v0: any] : ? [v1: any] : % 38.83/6.04 | | | | | (apply(all_32_10, all_44_0, all_59_3) = v0 & apply(all_32_10, % 38.83/6.04 | | | | | all_44_0, all_53_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.04 | | | | | % 38.83/6.04 | | | | | GROUND_INST: instantiating (6) with all_32_9, all_32_7, all_32_6, % 38.83/6.04 | | | | | all_51_0, all_59_3, all_44_2, simplifying with (15), % 38.83/6.04 | | | | | (17), (18), (38), (45), (48), (59), (60), (76), (81) % 38.83/6.04 | | | | | gives: % 38.83/6.04 | | | | | (102) all_59_3 = all_51_0 | ? [v0: any] : ? [v1: any] : % 38.83/6.04 | | | | | (apply(all_32_9, all_59_3, all_44_2) = v1 & apply(all_32_9, % 38.83/6.04 | | | | | all_51_0, all_44_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.04 | | | | | % 38.83/6.04 | | | | | GROUND_INST: instantiating (6) with all_32_9, all_32_7, all_32_6, % 38.83/6.04 | | | | | all_59_3, all_51_0, all_44_2, simplifying with (15), % 38.83/6.04 | | | | | (17), (18), (38), (45), (48), (59), (60), (76), (81) % 38.83/6.04 | | | | | gives: % 38.83/6.04 | | | | | (103) all_59_3 = all_51_0 | ? [v0: any] : ? [v1: any] : % 38.83/6.04 | | | | | (apply(all_32_9, all_59_3, all_44_2) = v0 & apply(all_32_9, % 38.83/6.04 | | | | | all_51_0, all_44_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.04 | | | | | % 38.83/6.04 | | | | | GROUND_INST: instantiating (6) with all_32_10, all_32_8, all_32_7, % 38.83/6.04 | | | | | all_44_1, all_44_0, all_59_3, simplifying with (14), % 38.83/6.04 | | | | | (16), (17), (36), (46), (47), (49), (50), (76), (81) % 38.83/6.04 | | | | | gives: % 38.83/6.04 | | | | | (104) all_44_0 = all_44_1 | ? [v0: any] : ? [v1: any] : % 38.83/6.04 | | | | | (apply(all_32_10, all_44_0, all_59_3) = v1 & apply(all_32_10, % 38.83/6.04 | | | | | all_44_1, all_59_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.04 | | | | | % 38.83/6.04 | | | | | GROUND_INST: instantiating (6) with all_32_10, all_32_8, all_32_7, % 38.83/6.04 | | | | | all_44_0, all_44_1, all_59_3, simplifying with (14), % 38.83/6.04 | | | | | (16), (17), (36), (46), (47), (49), (50), (76), (81) % 38.83/6.04 | | | | | gives: % 38.83/6.04 | | | | | (105) all_44_0 = all_44_1 | ? [v0: any] : ? [v1: any] : % 38.83/6.04 | | | | | (apply(all_32_10, all_44_0, all_59_3) = v0 & apply(all_32_10, % 38.83/6.04 | | | | | all_44_1, all_59_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.04 | | | | | % 38.83/6.04 | | | | | GROUND_INST: instantiating (7) with all_32_10, all_32_8, all_32_7, % 38.83/6.04 | | | | | all_44_0, all_44_1, all_55_0, simplifying with (14), % 38.83/6.04 | | | | | (16), (17), (36), (46), (47), (50), (67), (69) gives: % 38.83/6.04 | | | | | (106) all_44_0 = all_44_1 | ? [v0: any] : ? [v1: any] : ? [v2: % 38.83/6.04 | | | | | any] : (apply(all_32_10, all_44_0, all_55_0) = v2 & % 38.83/6.04 | | | | | member(all_55_0, all_32_7) = v1 & member(all_44_1, % 38.83/6.04 | | | | | all_32_8) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 38.83/6.04 | | | | | 0))) % 38.83/6.04 | | | | | % 38.83/6.04 | | | | | GROUND_INST: instantiating (3) with all_32_10, all_32_8, all_32_7, % 38.83/6.04 | | | | | all_44_0, all_59_3, all_53_0, simplifying with (14), % 38.83/6.04 | | | | | (16), (17), (24), (47), (63), (65), (76), (81) gives: % 38.83/6.04 | | | | | (107) all_59_3 = all_53_0 | ? [v0: any] : ? [v1: any] : ? [v2: % 38.83/6.04 | | | | | any] : (apply(all_32_10, all_44_0, all_59_3) = v2 & % 38.83/6.04 | | | | | member(all_53_0, all_32_7) = v1 & member(all_44_0, % 38.83/6.04 | | | | | all_32_8) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 38.83/6.04 | | | | | 0))) % 38.83/6.04 | | | | | % 38.83/6.04 | | | | | GROUND_INST: instantiating (3) with all_32_10, all_32_8, all_32_7, % 38.83/6.04 | | | | | all_44_0, all_51_0, all_53_0, simplifying with (14), % 38.83/6.04 | | | | | (16), (17), (24), (47), (59), (60), (63), (65) gives: % 38.83/6.04 | | | | | (108) all_53_0 = all_51_0 | ? [v0: any] : ? [v1: any] : ? [v2: % 38.83/6.04 | | | | | any] : (apply(all_32_10, all_44_0, all_51_0) = v2 & % 38.83/6.04 | | | | | member(all_53_0, all_32_7) = v1 & member(all_44_0, % 38.83/6.04 | | | | | all_32_8) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 38.83/6.04 | | | | | 0))) % 38.83/6.04 | | | | | % 38.83/6.04 | | | | | GROUND_INST: instantiating (7) with all_32_10, all_32_8, all_32_7, % 38.83/6.04 | | | | | all_44_1, all_44_0, all_53_0, simplifying with (14), % 38.83/6.04 | | | | | (16), (17), (36), (46), (47), (49), (63), (65) gives: % 38.83/6.04 | | | | | (109) all_44_0 = all_44_1 | ? [v0: any] : ? [v1: any] : ? [v2: % 38.83/6.04 | | | | | any] : (apply(all_32_10, all_44_1, all_53_0) = v2 & % 38.83/6.04 | | | | | member(all_53_0, all_32_7) = v1 & member(all_44_0, % 38.83/6.04 | | | | | all_32_8) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 38.83/6.04 | | | | | 0))) % 38.83/6.04 | | | | | % 38.83/6.04 | | | | | GROUND_INST: instantiating (7) with all_32_9, all_32_7, all_32_6, % 38.83/6.04 | | | | | all_59_3, all_51_0, all_44_2, simplifying with (15), % 38.83/6.04 | | | | | (17), (18), (38), (45), (59), (61), (76), (81) gives: % 38.83/6.04 | | | | | (110) all_59_3 = all_51_0 | ? [v0: any] : ? [v1: any] : ? [v2: % 38.83/6.04 | | | | | any] : (apply(all_32_9, all_59_3, all_44_2) = v2 & % 38.83/6.04 | | | | | member(all_51_0, all_32_7) = v0 & member(all_44_2, % 38.83/6.04 | | | | | all_32_6) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 38.83/6.04 | | | | | 0))) % 38.83/6.04 | | | | | % 38.83/6.04 | | | | | GROUND_INST: instantiating (7) with all_32_9, all_32_7, all_32_6, % 38.83/6.04 | | | | | all_53_0, all_51_0, all_44_2, simplifying with (15), % 38.83/6.04 | | | | | (17), (18), (38), (45), (59), (61), (63), (64) gives: % 38.83/6.04 | | | | | (111) all_53_0 = all_51_0 | ? [v0: any] : ? [v1: any] : ? [v2: % 38.83/6.04 | | | | | any] : (apply(all_32_9, all_53_0, all_44_2) = v2 & % 38.83/6.04 | | | | | member(all_51_0, all_32_7) = v0 & member(all_44_2, % 38.83/6.04 | | | | | all_32_6) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 38.83/6.04 | | | | | 0))) % 38.83/6.04 | | | | | % 38.83/6.04 | | | | | GROUND_INST: instantiating (4) with all_32_9, all_32_10, all_32_8, % 38.83/6.04 | | | | | all_32_7, all_32_6, all_44_1, all_44_2, all_32_5, % 38.83/6.04 | | | | | simplifying with (14), (15), (16), (17), (18), (26), % 38.83/6.04 | | | | | (45), (46), (90) gives: % 38.83/6.05 | | | | | (112) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: int] : ? % 38.83/6.05 | | | | | [v4: int] : ? [v5: int] : ($i(v2) & ((v5 = 0 & v4 = 0 & v3 = % 38.83/6.05 | | | | | 0 & apply(all_32_9, v2, all_44_2) = 0 & % 38.83/6.05 | | | | | apply(all_32_10, all_44_1, v2) = 0 & member(v2, % 38.83/6.05 | | | | | all_32_7) = 0) | (member(all_44_1, all_32_8) = v0 & % 38.83/6.05 | | | | | member(all_44_2, all_32_6) = v1 & ( ~ (v1 = 0) | ~ (v0 % 38.83/6.05 | | | | | = 0))))) % 38.83/6.05 | | | | | % 38.83/6.05 | | | | | GROUND_INST: instantiating (inverse_function) with all_32_10, % 38.83/6.05 | | | | | all_32_8, all_32_7, all_44_0, all_59_3, all_32_3, 0, % 38.83/6.05 | | | | | simplifying with (14), (16), (17), (31), (47), (76), (82) % 38.83/6.05 | | | | | gives: % 38.83/6.05 | | | | | (113) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 38.83/6.05 | | | | | (apply(all_32_10, all_44_0, all_59_3) = v2 & member(all_59_3, % 38.83/6.05 | | | | | all_32_7) = v1 & member(all_44_0, all_32_8) = v0 & ( ~ % 38.83/6.05 | | | | | (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 38.83/6.05 | | | | | % 38.83/6.05 | | | | | GROUND_INST: instantiating (inverse_function) with all_32_9, all_32_7, % 38.83/6.05 | | | | | all_32_6, all_59_3, all_44_2, all_32_2, 0, simplifying % 38.83/6.05 | | | | | with (15), (17), (18), (32), (45), (76), (83) gives: % 38.83/6.05 | | | | | (114) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_9, % 38.83/6.05 | | | | | all_59_3, all_44_2) = v2 & member(all_59_3, all_32_7) = % 38.83/6.05 | | | | | v0 & member(all_44_2, all_32_6) = v1 & ( ~ (v1 = 0) | ~ % 38.83/6.05 | | | | | (v0 = 0) | v2 = 0)) % 38.83/6.05 | | | | | % 38.83/6.05 | | | | | DELTA: instantiating (99) with fresh symbol all_86_0 gives: % 38.83/6.05 | | | | | (115) apply(all_32_9, all_55_0, all_86_0) = 0 & member(all_86_0, % 38.83/6.05 | | | | | all_32_6) = 0 & $i(all_86_0) % 38.83/6.05 | | | | | % 38.83/6.05 | | | | | ALPHA: (115) implies: % 38.83/6.05 | | | | | (116) $i(all_86_0) % 38.83/6.05 | | | | | (117) member(all_86_0, all_32_6) = 0 % 38.83/6.05 | | | | | (118) apply(all_32_9, all_55_0, all_86_0) = 0 % 38.83/6.05 | | | | | % 38.83/6.05 | | | | | DELTA: instantiating (114) with fresh symbols all_98_0, all_98_1, % 38.83/6.05 | | | | | all_98_2 gives: % 38.83/6.05 | | | | | (119) apply(all_32_9, all_59_3, all_44_2) = all_98_0 & % 38.83/6.05 | | | | | member(all_59_3, all_32_7) = all_98_2 & member(all_44_2, % 38.83/6.05 | | | | | all_32_6) = all_98_1 & ( ~ (all_98_1 = 0) | ~ (all_98_2 = % 38.83/6.05 | | | | | 0) | all_98_0 = 0) % 38.83/6.05 | | | | | % 38.83/6.05 | | | | | ALPHA: (119) implies: % 38.83/6.05 | | | | | (120) member(all_44_2, all_32_6) = all_98_1 % 38.83/6.05 | | | | | (121) member(all_59_3, all_32_7) = all_98_2 % 38.83/6.05 | | | | | (122) apply(all_32_9, all_59_3, all_44_2) = all_98_0 % 38.83/6.05 | | | | | (123) ~ (all_98_1 = 0) | ~ (all_98_2 = 0) | all_98_0 = 0 % 38.83/6.05 | | | | | % 38.83/6.05 | | | | | DELTA: instantiating (113) with fresh symbols all_100_0, all_100_1, % 38.83/6.05 | | | | | all_100_2 gives: % 38.83/6.05 | | | | | (124) apply(all_32_10, all_44_0, all_59_3) = all_100_0 & % 38.83/6.05 | | | | | member(all_59_3, all_32_7) = all_100_1 & member(all_44_0, % 38.83/6.05 | | | | | all_32_8) = all_100_2 & ( ~ (all_100_1 = 0) | ~ (all_100_2 % 38.83/6.05 | | | | | = 0) | all_100_0 = 0) % 38.83/6.05 | | | | | % 38.83/6.05 | | | | | ALPHA: (124) implies: % 38.83/6.05 | | | | | (125) member(all_44_0, all_32_8) = all_100_2 % 38.83/6.05 | | | | | (126) member(all_59_3, all_32_7) = all_100_1 % 38.83/6.05 | | | | | (127) apply(all_32_10, all_44_0, all_59_3) = all_100_0 % 38.83/6.05 | | | | | (128) ~ (all_100_1 = 0) | ~ (all_100_2 = 0) | all_100_0 = 0 % 38.83/6.05 | | | | | % 38.83/6.05 | | | | | DELTA: instantiating (112) with fresh symbols all_102_0, all_102_1, % 38.83/6.05 | | | | | all_102_2, all_102_3, all_102_4, all_102_5 gives: % 38.83/6.05 | | | | | (129) $i(all_102_3) & ((all_102_0 = 0 & all_102_1 = 0 & all_102_2 = % 38.83/6.05 | | | | | 0 & apply(all_32_9, all_102_3, all_44_2) = 0 & % 38.83/6.05 | | | | | apply(all_32_10, all_44_1, all_102_3) = 0 & % 38.83/6.05 | | | | | member(all_102_3, all_32_7) = 0) | (member(all_44_1, % 38.83/6.05 | | | | | all_32_8) = all_102_5 & member(all_44_2, all_32_6) = % 38.83/6.05 | | | | | all_102_4 & ( ~ (all_102_4 = 0) | ~ (all_102_5 = 0)))) % 38.83/6.05 | | | | | % 38.83/6.05 | | | | | ALPHA: (129) implies: % 38.83/6.05 | | | | | (130) $i(all_102_3) % 38.83/6.05 | | | | | (131) (all_102_0 = 0 & all_102_1 = 0 & all_102_2 = 0 & % 38.83/6.05 | | | | | apply(all_32_9, all_102_3, all_44_2) = 0 & apply(all_32_10, % 38.83/6.05 | | | | | all_44_1, all_102_3) = 0 & member(all_102_3, all_32_7) = % 38.83/6.05 | | | | | 0) | (member(all_44_1, all_32_8) = all_102_5 & % 38.83/6.05 | | | | | member(all_44_2, all_32_6) = all_102_4 & ( ~ (all_102_4 = % 38.83/6.05 | | | | | 0) | ~ (all_102_5 = 0))) % 38.83/6.05 | | | | | % 38.83/6.05 | | | | | BETA: splitting (106) gives: % 38.83/6.05 | | | | | % 38.83/6.05 | | | | | Case 1: % 38.83/6.05 | | | | | | % 38.83/6.05 | | | | | | (132) all_44_0 = all_44_1 % 38.83/6.05 | | | | | | % 38.83/6.05 | | | | | | REDUCE: (44), (132) imply: % 38.83/6.05 | | | | | | (133) $false % 38.83/6.05 | | | | | | % 38.83/6.05 | | | | | | CLOSE: (133) is inconsistent. % 38.83/6.05 | | | | | | % 38.83/6.05 | | | | | Case 2: % 38.83/6.05 | | | | | | % 38.83/6.05 | | | | | | (134) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 38.83/6.05 | | | | | | (apply(all_32_10, all_44_0, all_55_0) = v2 & % 38.83/6.05 | | | | | | member(all_55_0, all_32_7) = v1 & member(all_44_1, % 38.83/6.05 | | | | | | all_32_8) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 38.83/6.05 | | | | | | 0))) % 38.83/6.05 | | | | | | % 38.83/6.05 | | | | | | DELTA: instantiating (134) with fresh symbols all_113_0, all_113_1, % 38.83/6.05 | | | | | | all_113_2 gives: % 38.83/6.05 | | | | | | (135) apply(all_32_10, all_44_0, all_55_0) = all_113_0 & % 38.83/6.05 | | | | | | member(all_55_0, all_32_7) = all_113_1 & member(all_44_1, % 38.83/6.05 | | | | | | all_32_8) = all_113_2 & ( ~ (all_113_0 = 0) | ~ % 38.83/6.05 | | | | | | (all_113_1 = 0) | ~ (all_113_2 = 0)) % 38.83/6.05 | | | | | | % 38.83/6.05 | | | | | | ALPHA: (135) implies: % 38.83/6.05 | | | | | | (136) member(all_44_1, all_32_8) = all_113_2 % 38.83/6.05 | | | | | | (137) member(all_55_0, all_32_7) = all_113_1 % 38.83/6.05 | | | | | | % 38.83/6.05 | | | | | | BETA: splitting (109) gives: % 38.83/6.05 | | | | | | % 38.83/6.05 | | | | | | Case 1: % 38.83/6.05 | | | | | | | % 38.83/6.05 | | | | | | | (138) all_44_0 = all_44_1 % 38.83/6.05 | | | | | | | % 38.83/6.05 | | | | | | | REDUCE: (44), (138) imply: % 38.83/6.05 | | | | | | | (139) $false % 38.83/6.05 | | | | | | | % 38.83/6.05 | | | | | | | CLOSE: (139) is inconsistent. % 38.83/6.05 | | | | | | | % 38.83/6.05 | | | | | | Case 2: % 38.83/6.05 | | | | | | | % 38.83/6.05 | | | | | | | (140) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 38.83/6.05 | | | | | | | (apply(all_32_10, all_44_1, all_53_0) = v2 & % 38.83/6.05 | | | | | | | member(all_53_0, all_32_7) = v1 & member(all_44_0, % 38.83/6.05 | | | | | | | all_32_8) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 % 38.83/6.05 | | | | | | | = 0))) % 38.83/6.05 | | | | | | | % 38.83/6.05 | | | | | | | DELTA: instantiating (140) with fresh symbols all_118_0, % 38.83/6.05 | | | | | | | all_118_1, all_118_2 gives: % 38.83/6.05 | | | | | | | (141) apply(all_32_10, all_44_1, all_53_0) = all_118_0 & % 38.83/6.05 | | | | | | | member(all_53_0, all_32_7) = all_118_1 & member(all_44_0, % 38.83/6.05 | | | | | | | all_32_8) = all_118_2 & ( ~ (all_118_0 = 0) | ~ % 38.83/6.05 | | | | | | | (all_118_1 = 0) | ~ (all_118_2 = 0)) % 38.83/6.05 | | | | | | | % 38.83/6.05 | | | | | | | ALPHA: (141) implies: % 38.83/6.05 | | | | | | | (142) member(all_44_0, all_32_8) = all_118_2 % 38.83/6.05 | | | | | | | (143) apply(all_32_10, all_44_1, all_53_0) = all_118_0 % 38.83/6.05 | | | | | | | % 38.83/6.05 | | | | | | | BETA: splitting (98) gives: % 38.83/6.05 | | | | | | | % 38.83/6.05 | | | | | | | Case 1: % 38.83/6.05 | | | | | | | | % 38.83/6.05 | | | | | | | | (144) all_44_0 = all_44_1 % 38.83/6.05 | | | | | | | | % 38.83/6.05 | | | | | | | | REDUCE: (44), (144) imply: % 38.83/6.05 | | | | | | | | (145) $false % 38.83/6.05 | | | | | | | | % 38.83/6.05 | | | | | | | | CLOSE: (145) is inconsistent. % 38.83/6.05 | | | | | | | | % 38.83/6.05 | | | | | | | Case 2: % 38.83/6.05 | | | | | | | | % 38.83/6.05 | | | | | | | | (146) ? [v0: any] : ? [v1: any] : (apply(all_32_10, % 38.83/6.05 | | | | | | | | all_44_0, all_53_0) = v0 & apply(all_32_10, % 38.83/6.05 | | | | | | | | all_44_1, all_53_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = % 38.83/6.05 | | | | | | | | 0))) % 38.83/6.05 | | | | | | | | % 38.83/6.05 | | | | | | | | DELTA: instantiating (146) with fresh symbols all_123_0, % 38.83/6.05 | | | | | | | | all_123_1 gives: % 38.83/6.05 | | | | | | | | (147) apply(all_32_10, all_44_0, all_53_0) = all_123_1 & % 38.83/6.05 | | | | | | | | apply(all_32_10, all_44_1, all_53_0) = all_123_0 & ( ~ % 38.83/6.05 | | | | | | | | (all_123_0 = 0) | ~ (all_123_1 = 0)) % 38.83/6.05 | | | | | | | | % 38.83/6.05 | | | | | | | | ALPHA: (147) implies: % 38.83/6.05 | | | | | | | | (148) apply(all_32_10, all_44_1, all_53_0) = all_123_0 % 38.83/6.05 | | | | | | | | (149) apply(all_32_10, all_44_0, all_53_0) = all_123_1 % 38.83/6.05 | | | | | | | | % 38.83/6.05 | | | | | | | | BETA: splitting (104) gives: % 38.83/6.05 | | | | | | | | % 38.83/6.05 | | | | | | | | Case 1: % 38.83/6.05 | | | | | | | | | % 38.83/6.05 | | | | | | | | | (150) all_44_0 = all_44_1 % 38.83/6.05 | | | | | | | | | % 38.83/6.05 | | | | | | | | | REDUCE: (44), (150) imply: % 38.83/6.05 | | | | | | | | | (151) $false % 38.83/6.05 | | | | | | | | | % 38.83/6.05 | | | | | | | | | CLOSE: (151) is inconsistent. % 38.83/6.05 | | | | | | | | | % 38.83/6.05 | | | | | | | | Case 2: % 38.83/6.05 | | | | | | | | | % 38.83/6.06 | | | | | | | | | (152) ? [v0: any] : ? [v1: any] : (apply(all_32_10, % 38.83/6.06 | | | | | | | | | all_44_0, all_59_3) = v1 & apply(all_32_10, % 38.83/6.06 | | | | | | | | | all_44_1, all_59_3) = v0 & ( ~ (v1 = 0) | ~ (v0 % 38.83/6.06 | | | | | | | | | = 0))) % 38.83/6.06 | | | | | | | | | % 38.83/6.06 | | | | | | | | | DELTA: instantiating (152) with fresh symbols all_128_0, % 38.83/6.06 | | | | | | | | | all_128_1 gives: % 38.83/6.06 | | | | | | | | | (153) apply(all_32_10, all_44_0, all_59_3) = all_128_0 & % 38.83/6.06 | | | | | | | | | apply(all_32_10, all_44_1, all_59_3) = all_128_1 & ( % 38.83/6.06 | | | | | | | | | ~ (all_128_0 = 0) | ~ (all_128_1 = 0)) % 38.83/6.06 | | | | | | | | | % 38.83/6.06 | | | | | | | | | ALPHA: (153) implies: % 38.83/6.06 | | | | | | | | | (154) apply(all_32_10, all_44_1, all_59_3) = all_128_1 % 38.83/6.06 | | | | | | | | | (155) apply(all_32_10, all_44_0, all_59_3) = all_128_0 % 38.83/6.06 | | | | | | | | | % 38.83/6.06 | | | | | | | | | BETA: splitting (97) gives: % 38.83/6.06 | | | | | | | | | % 38.83/6.06 | | | | | | | | | Case 1: % 38.83/6.06 | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | (156) all_44_0 = all_44_1 % 38.83/6.06 | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | REDUCE: (44), (156) imply: % 38.83/6.06 | | | | | | | | | | (157) $false % 38.83/6.06 | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | CLOSE: (157) is inconsistent. % 38.83/6.06 | | | | | | | | | | % 38.83/6.06 | | | | | | | | | Case 2: % 38.83/6.06 | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | (158) ? [v0: any] : ? [v1: any] : (apply(all_32_10, % 38.83/6.06 | | | | | | | | | | all_44_0, all_53_0) = v1 & apply(all_32_10, % 38.83/6.06 | | | | | | | | | | all_44_1, all_53_0) = v0 & ( ~ (v1 = 0) | ~ % 38.83/6.06 | | | | | | | | | | (v0 = 0))) % 38.83/6.06 | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | DELTA: instantiating (158) with fresh symbols all_138_0, % 38.83/6.06 | | | | | | | | | | all_138_1 gives: % 38.83/6.06 | | | | | | | | | | (159) apply(all_32_10, all_44_0, all_53_0) = all_138_0 & % 38.83/6.06 | | | | | | | | | | apply(all_32_10, all_44_1, all_53_0) = all_138_1 & % 38.83/6.06 | | | | | | | | | | ( ~ (all_138_0 = 0) | ~ (all_138_1 = 0)) % 38.83/6.06 | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | ALPHA: (159) implies: % 38.83/6.06 | | | | | | | | | | (160) apply(all_32_10, all_44_1, all_53_0) = all_138_1 % 38.83/6.06 | | | | | | | | | | (161) apply(all_32_10, all_44_0, all_53_0) = all_138_0 % 38.83/6.06 | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | BETA: splitting (105) gives: % 38.83/6.06 | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | Case 1: % 38.83/6.06 | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | (162) all_44_0 = all_44_1 % 38.83/6.06 | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | REDUCE: (44), (162) imply: % 38.83/6.06 | | | | | | | | | | | (163) $false % 38.83/6.06 | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | CLOSE: (163) is inconsistent. % 38.83/6.06 | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | Case 2: % 38.83/6.06 | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | (164) ? [v0: any] : ? [v1: any] : (apply(all_32_10, % 38.83/6.06 | | | | | | | | | | | all_44_0, all_59_3) = v0 & apply(all_32_10, % 38.83/6.06 | | | | | | | | | | | all_44_1, all_59_3) = v1 & ( ~ (v1 = 0) | ~ % 38.83/6.06 | | | | | | | | | | | (v0 = 0))) % 38.83/6.06 | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | DELTA: instantiating (164) with fresh symbols all_143_0, % 38.83/6.06 | | | | | | | | | | | all_143_1 gives: % 38.83/6.06 | | | | | | | | | | | (165) apply(all_32_10, all_44_0, all_59_3) = all_143_1 & % 38.83/6.06 | | | | | | | | | | | apply(all_32_10, all_44_1, all_59_3) = all_143_0 & % 38.83/6.06 | | | | | | | | | | | ( ~ (all_143_0 = 0) | ~ (all_143_1 = 0)) % 38.83/6.06 | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | ALPHA: (165) implies: % 38.83/6.06 | | | | | | | | | | | (166) apply(all_32_10, all_44_1, all_59_3) = all_143_0 % 38.83/6.06 | | | | | | | | | | | (167) apply(all_32_10, all_44_0, all_59_3) = all_143_1 % 38.83/6.06 | | | | | | | | | | | (168) ~ (all_143_0 = 0) | ~ (all_143_1 = 0) % 38.83/6.06 | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | BETA: splitting (91) gives: % 38.83/6.06 | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | Case 1: % 38.83/6.06 | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | (169) all_44_0 = all_44_1 % 38.83/6.06 | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | REDUCE: (44), (169) imply: % 38.83/6.06 | | | | | | | | | | | | (170) $false % 38.83/6.06 | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | CLOSE: (170) is inconsistent. % 38.83/6.06 | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | Case 2: % 38.83/6.06 | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | (171) ? [v0: any] : ? [v1: any] : (apply(all_32_10, % 38.83/6.06 | | | | | | | | | | | | all_44_0, all_51_0) = v1 & apply(all_32_10, % 38.83/6.06 | | | | | | | | | | | | all_44_1, all_51_0) = v0 & ( ~ (v1 = 0) | ~ % 38.83/6.06 | | | | | | | | | | | | (v0 = 0))) % 38.83/6.06 | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | DELTA: instantiating (171) with fresh symbols all_148_0, % 38.83/6.06 | | | | | | | | | | | | all_148_1 gives: % 38.83/6.06 | | | | | | | | | | | | (172) apply(all_32_10, all_44_0, all_51_0) = all_148_0 & % 38.83/6.06 | | | | | | | | | | | | apply(all_32_10, all_44_1, all_51_0) = all_148_1 & % 38.83/6.06 | | | | | | | | | | | | ( ~ (all_148_0 = 0) | ~ (all_148_1 = 0)) % 38.83/6.06 | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | ALPHA: (172) implies: % 38.83/6.06 | | | | | | | | | | | | (173) apply(all_32_10, all_44_1, all_51_0) = all_148_1 % 38.83/6.06 | | | | | | | | | | | | (174) apply(all_32_10, all_44_0, all_51_0) = all_148_0 % 38.83/6.06 | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | BETA: splitting (92) gives: % 38.83/6.06 | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | Case 1: % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | (175) all_44_0 = all_44_1 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | REDUCE: (44), (175) imply: % 38.83/6.06 | | | | | | | | | | | | | (176) $false % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | CLOSE: (176) is inconsistent. % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | Case 2: % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | (177) ? [v0: any] : ? [v1: any] : (apply(all_32_10, % 38.83/6.06 | | | | | | | | | | | | | all_44_0, all_51_0) = v0 & apply(all_32_10, % 38.83/6.06 | | | | | | | | | | | | | all_44_1, all_51_0) = v1 & ( ~ (v1 = 0) | ~ % 38.83/6.06 | | | | | | | | | | | | | (v0 = 0))) % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | DELTA: instantiating (177) with fresh symbols all_153_0, % 38.83/6.06 | | | | | | | | | | | | | all_153_1 gives: % 38.83/6.06 | | | | | | | | | | | | | (178) apply(all_32_10, all_44_0, all_51_0) = all_153_1 & % 38.83/6.06 | | | | | | | | | | | | | apply(all_32_10, all_44_1, all_51_0) = all_153_0 & % 38.83/6.06 | | | | | | | | | | | | | ( ~ (all_153_0 = 0) | ~ (all_153_1 = 0)) % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | ALPHA: (178) implies: % 38.83/6.06 | | | | | | | | | | | | | (179) apply(all_32_10, all_44_1, all_51_0) = all_153_0 % 38.83/6.06 | | | | | | | | | | | | | (180) apply(all_32_10, all_44_0, all_51_0) = all_153_1 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_98_1, all_32_6, % 38.83/6.06 | | | | | | | | | | | | | all_44_2, simplifying with (48), (120) gives: % 38.83/6.06 | | | | | | | | | | | | | (181) all_98_1 = 0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_113_2, all_32_8, % 38.83/6.06 | | | | | | | | | | | | | all_44_1, simplifying with (49), (136) gives: % 38.83/6.06 | | | | | | | | | | | | | (182) all_113_2 = 0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_118_2, all_32_8, % 38.83/6.06 | | | | | | | | | | | | | all_44_0, simplifying with (50), (142) gives: % 38.83/6.06 | | | | | | | | | | | | | (183) all_118_2 = 0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_100_2, all_118_2, % 38.83/6.06 | | | | | | | | | | | | | all_32_8, all_44_0, simplifying with (125), (142) % 38.83/6.06 | | | | | | | | | | | | | gives: % 38.83/6.06 | | | | | | | | | | | | | (184) all_118_2 = all_100_2 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_113_1, all_32_7, % 38.83/6.06 | | | | | | | | | | | | | all_55_0, simplifying with (68), (137) gives: % 38.83/6.06 | | | | | | | | | | | | | (185) all_113_1 = 0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_100_1, all_32_7, % 38.83/6.06 | | | | | | | | | | | | | all_59_3, simplifying with (81), (126) gives: % 38.83/6.06 | | | | | | | | | | | | | (186) all_100_1 = 0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_98_2, all_100_1, % 38.83/6.06 | | | | | | | | | | | | | all_32_7, all_59_3, simplifying with (121), (126) % 38.83/6.06 | | | | | | | | | | | | | gives: % 38.83/6.06 | | | | | | | | | | | | | (187) all_100_1 = all_98_2 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_148_1, all_153_0, % 38.83/6.06 | | | | | | | | | | | | | all_51_0, all_44_1, all_32_10, simplifying with % 38.83/6.06 | | | | | | | | | | | | | (173), (179) gives: % 38.83/6.06 | | | | | | | | | | | | | (188) all_153_0 = all_148_1 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_123_0, all_138_1, % 38.83/6.06 | | | | | | | | | | | | | all_53_0, all_44_1, all_32_10, simplifying with % 38.83/6.06 | | | | | | | | | | | | | (148), (160) gives: % 38.83/6.06 | | | | | | | | | | | | | (189) all_138_1 = all_123_0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_118_0, all_138_1, % 38.83/6.06 | | | | | | | | | | | | | all_53_0, all_44_1, all_32_10, simplifying with % 38.83/6.06 | | | | | | | | | | | | | (143), (160) gives: % 38.83/6.06 | | | | | | | | | | | | | (190) all_138_1 = all_118_0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_128_1, all_143_0, % 38.83/6.06 | | | | | | | | | | | | | all_59_3, all_44_1, all_32_10, simplifying with % 38.83/6.06 | | | | | | | | | | | | | (154), (166) gives: % 38.83/6.06 | | | | | | | | | | | | | (191) all_143_0 = all_128_1 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_148_0, all_153_1, % 38.83/6.06 | | | | | | | | | | | | | all_51_0, all_44_0, all_32_10, simplifying with % 38.83/6.06 | | | | | | | | | | | | | (174), (180) gives: % 38.83/6.06 | | | | | | | | | | | | | (192) all_153_1 = all_148_0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_138_0, all_53_0, % 38.83/6.06 | | | | | | | | | | | | | all_44_0, all_32_10, simplifying with (65), (161) % 38.83/6.06 | | | | | | | | | | | | | gives: % 38.83/6.06 | | | | | | | | | | | | | (193) all_138_0 = 0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_123_1, all_138_0, % 38.83/6.06 | | | | | | | | | | | | | all_53_0, all_44_0, all_32_10, simplifying with % 38.83/6.06 | | | | | | | | | | | | | (149), (161) gives: % 38.83/6.06 | | | | | | | | | | | | | (194) all_138_0 = all_123_1 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_128_0, all_143_1, % 38.83/6.06 | | | | | | | | | | | | | all_59_3, all_44_0, all_32_10, simplifying with % 38.83/6.06 | | | | | | | | | | | | | (155), (167) gives: % 38.83/6.06 | | | | | | | | | | | | | (195) all_143_1 = all_128_0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_100_0, all_143_1, % 38.83/6.06 | | | | | | | | | | | | | all_59_3, all_44_0, all_32_10, simplifying with % 38.83/6.06 | | | | | | | | | | | | | (127), (167) gives: % 38.83/6.06 | | | | | | | | | | | | | (196) all_143_1 = all_100_0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | COMBINE_EQS: (195), (196) imply: % 38.83/6.06 | | | | | | | | | | | | | (197) all_128_0 = all_100_0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | SIMP: (197) implies: % 38.83/6.06 | | | | | | | | | | | | | (198) all_128_0 = all_100_0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | COMBINE_EQS: (193), (194) imply: % 38.83/6.06 | | | | | | | | | | | | | (199) all_123_1 = 0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | SIMP: (199) implies: % 38.83/6.06 | | | | | | | | | | | | | (200) all_123_1 = 0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | COMBINE_EQS: (189), (190) imply: % 38.83/6.06 | | | | | | | | | | | | | (201) all_123_0 = all_118_0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | COMBINE_EQS: (183), (184) imply: % 38.83/6.06 | | | | | | | | | | | | | (202) all_100_2 = 0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | SIMP: (202) implies: % 38.83/6.06 | | | | | | | | | | | | | (203) all_100_2 = 0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | COMBINE_EQS: (186), (187) imply: % 38.83/6.06 | | | | | | | | | | | | | (204) all_98_2 = 0 % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.06 | | | | | | | | | | | | | BETA: splitting (123) gives: % 38.83/6.06 | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | Case 1: % 38.83/6.07 | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | (205) ~ (all_98_1 = 0) % 38.83/6.07 | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | REDUCE: (181), (205) imply: % 38.83/6.07 | | | | | | | | | | | | | | (206) $false % 38.83/6.07 | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | CLOSE: (206) is inconsistent. % 38.83/6.07 | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | Case 2: % 38.83/6.07 | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | (207) ~ (all_98_2 = 0) | all_98_0 = 0 % 38.83/6.07 | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | BETA: splitting (131) gives: % 38.83/6.07 | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | Case 1: % 38.83/6.07 | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | (208) all_102_0 = 0 & all_102_1 = 0 & all_102_2 = 0 & % 38.83/6.07 | | | | | | | | | | | | | | | apply(all_32_9, all_102_3, all_44_2) = 0 & % 38.83/6.07 | | | | | | | | | | | | | | | apply(all_32_10, all_44_1, all_102_3) = 0 & % 38.83/6.07 | | | | | | | | | | | | | | | member(all_102_3, all_32_7) = 0 % 38.83/6.07 | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | ALPHA: (208) implies: % 38.83/6.07 | | | | | | | | | | | | | | | (209) member(all_102_3, all_32_7) = 0 % 38.83/6.07 | | | | | | | | | | | | | | | (210) apply(all_32_10, all_44_1, all_102_3) = 0 % 38.83/6.07 | | | | | | | | | | | | | | | (211) apply(all_32_9, all_102_3, all_44_2) = 0 % 38.83/6.07 | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | BETA: splitting (128) gives: % 38.83/6.07 | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | Case 1: % 38.83/6.07 | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | (212) ~ (all_100_1 = 0) % 38.83/6.07 | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | REDUCE: (186), (212) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | (213) $false % 38.83/6.07 | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | CLOSE: (213) is inconsistent. % 38.83/6.07 | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | Case 2: % 38.83/6.07 | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | (214) ~ (all_100_2 = 0) | all_100_0 = 0 % 38.83/6.07 | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 38.83/6.07 | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | Case 1: % 38.83/6.07 | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | (215) ~ (all_100_2 = 0) % 38.83/6.07 | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | REDUCE: (203), (215) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | | (216) $false % 38.83/6.07 | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | CLOSE: (216) is inconsistent. % 38.83/6.07 | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | Case 2: % 38.83/6.07 | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | (217) all_100_0 = 0 % 38.83/6.07 | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (217) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | | (218) all_143_1 = 0 % 38.83/6.07 | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | REDUCE: (127), (217) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | | (219) apply(all_32_10, all_44_0, all_59_3) = 0 % 38.83/6.07 | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | BETA: splitting (101) gives: % 38.83/6.07 | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | Case 1: % 38.83/6.07 | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | (220) all_59_3 = all_53_0 % 38.83/6.07 | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | REDUCE: (122), (220) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | | | (221) apply(all_32_9, all_53_0, all_44_2) = all_98_0 % 38.83/6.07 | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | REDUCE: (154), (220) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | | | (222) apply(all_32_10, all_44_1, all_53_0) = all_128_1 % 38.83/6.07 | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives: % 38.83/6.07 | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | Case 1: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | (223) ~ (all_98_2 = 0) % 38.83/6.07 | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | REDUCE: (204), (223) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | (224) $false % 38.83/6.07 | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | CLOSE: (224) is inconsistent. % 38.83/6.07 | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | Case 2: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | (225) all_98_0 = 0 % 38.83/6.07 | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | REDUCE: (221), (225) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | (226) apply(all_32_9, all_53_0, all_44_2) = 0 % 38.83/6.07 | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | Case 1: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | (227) all_53_0 = all_51_0 % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | REDUCE: (222), (227) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | (228) apply(all_32_10, all_44_1, all_51_0) = all_128_1 % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (227) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | (229) apply(all_32_10, all_44_1, all_51_0) = all_118_0 % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | Case 1: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (230) ~ (all_143_0 = 0) % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (230) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (231) ~ (all_128_1 = 0) % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_148_1, all_118_0, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | all_51_0, all_44_1, all_32_10, simplifying with % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (173), (229) gives: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (232) all_148_1 = all_118_0 % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_148_1, all_128_1, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | all_51_0, all_44_1, all_32_10, simplifying with % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (173), (228) gives: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (233) all_148_1 = all_128_1 % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (232), (233) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (234) all_128_1 = all_118_0 % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | SIMP: (234) implies: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (235) all_128_1 = all_118_0 % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | REDUCE: (231), (235) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (236) ~ (all_118_0 = 0) % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_10, all_32_8, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | all_32_7, all_44_1, all_102_3, all_55_0, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | simplifying with (14), (16), (17), (24), (46), % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (49), (67), (68), (130), (209) gives: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (237) all_102_3 = all_55_0 | ? [v0: any] : ? [v1: any] % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_10, all_44_1, all_102_3) = v0 & % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | apply(all_32_10, all_44_1, all_55_0) = v1 & ( ~ % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_32_9, all_32_7, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | all_32_6, all_51_0, all_102_3, all_44_2, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | simplifying with (15), (17), (18), (38), (45), % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (48), (59), (60), (130), (209) gives: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (238) all_102_3 = all_51_0 | ? [v0: any] : ? [v1: any] % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_9, all_102_3, all_44_2) = v1 & % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | apply(all_32_9, all_51_0, all_44_2) = v0 & ( ~ % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_32_9, all_32_7, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | all_32_6, all_55_0, all_102_3, all_86_0, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | simplifying with (15), (17), (18), (38), (67), % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (68), (116), (117), (130), (209) gives: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (239) all_102_3 = all_55_0 | ? [v0: any] : ? [v1: any] % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_9, all_102_3, all_86_0) = v1 & % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | apply(all_32_9, all_55_0, all_86_0) = v0 & ( ~ % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_32_9, all_32_7, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | all_32_6, all_51_0, all_55_0, all_86_0, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | simplifying with (15), (17), (18), (38), (59), % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (60), (67), (116), (118) gives: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (240) all_55_0 = all_51_0 | ? [v0: any] : ? [v1: any] % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | : ? [v2: any] : (apply(all_32_9, all_51_0, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | all_86_0) = v2 & member(all_86_0, all_32_6) = % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | v1 & member(all_55_0, all_32_7) = v0 & ( ~ (v2 = % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_32_9, all_32_7, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | all_32_6, all_51_0, all_102_3, all_44_2, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | simplifying with (15), (17), (18), (38), (45), % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (59), (60), (130), (211) gives: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | (241) all_102_3 = all_51_0 | ? [v0: any] : ? [v1: any] % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | : ? [v2: any] : (apply(all_32_9, all_51_0, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | all_44_2) = v2 & member(all_102_3, all_32_7) = % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | v0 & member(all_44_2, all_32_6) = v1 & ( ~ (v2 = % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | Case 1: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | (242) all_102_3 = all_51_0 % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (210), (242) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | (243) apply(all_32_10, all_44_1, all_51_0) = 0 % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_118_0, 0, all_51_0, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | all_44_1, all_32_10, simplifying with (229), (243) % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | gives: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | (244) all_118_0 = 0 % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (236), (244) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | (245) $false % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (245) is inconsistent. % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | Case 2: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | (246) ~ (all_102_3 = all_51_0) % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | (247) ? [v0: any] : ? [v1: any] : (apply(all_32_9, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | all_102_3, all_44_2) = v1 & apply(all_32_9, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | all_51_0, all_44_2) = v0 & ( ~ (v1 = 0) | ~ % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (247) with fresh symbols all_242_0, % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | all_242_1 gives: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | (248) apply(all_32_9, all_102_3, all_44_2) = all_242_0 & % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | apply(all_32_9, all_51_0, all_44_2) = all_242_1 & % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_242_0 = 0) | ~ (all_242_1 = 0)) % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | (249) apply(all_32_9, all_51_0, all_44_2) = all_242_1 % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | (250) apply(all_32_9, all_102_3, all_44_2) = all_242_0 % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | (251) ~ (all_242_0 = 0) | ~ (all_242_1 = 0) % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | | (252) all_102_3 = all_55_0 % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (246), (252) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | | (253) ~ (all_55_0 = all_51_0) % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (250), (252) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | | (254) apply(all_32_9, all_55_0, all_44_2) = all_242_0 % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (211), (252) imply: % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | | (255) apply(all_32_9, all_55_0, all_44_2) = 0 % 38.83/6.07 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (256) all_55_0 = all_51_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (253), (256) imply: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (257) $false % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (257) is inconsistent. % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_242_1, all_44_2, % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | all_51_0, all_32_9, simplifying with (61), (249) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (258) all_242_1 = 0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_242_0, all_44_2, % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | all_55_0, all_32_9, simplifying with (254), (255) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (259) all_242_0 = 0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (251), (258), (259) are inconsistent by sub-proof % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | #1. % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | End of split % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | (260) ~ (all_102_3 = all_55_0) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (261) all_102_3 = all_51_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (246), (261) imply: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (262) $false % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (262) is inconsistent. % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (263) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (apply(all_32_9, all_51_0, all_44_2) = v2 & % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | member(all_102_3, all_32_7) = v0 & % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | member(all_44_2, all_32_6) = v1 & ( ~ (v2 = 0) | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (263) with fresh symbols all_362_0, % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | all_362_1, all_362_2 gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (264) apply(all_32_9, all_51_0, all_44_2) = all_362_0 & % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | member(all_102_3, all_32_7) = all_362_2 & % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | member(all_44_2, all_32_6) = all_362_1 & ( ~ % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (all_362_0 = 0) | ~ (all_362_1 = 0) | ~ % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (all_362_2 = 0)) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (264) implies: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (265) apply(all_32_9, all_51_0, all_44_2) = all_362_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_102_3 = all_55_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (260), (266) imply: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | (267) $false % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (267) is inconsistent. % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_362_0, all_44_2, % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | all_51_0, all_32_9, simplifying with (61), (265) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_362_0 = 0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_242_1, all_362_0, % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | all_44_2, all_51_0, all_32_9, simplifying with % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | (249), (265) gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_362_0 = all_242_1 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_242_0, all_44_2, % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | all_102_3, all_32_9, simplifying with (211), (250) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_242_0 = 0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (269) imply: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_242_1 = 0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (271) implies: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_242_1 = 0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (251), (270), (272) are inconsistent by sub-proof % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | #1. % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | End of split % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | End of split % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | End of split % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | Case 2: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | (273) ~ (all_143_1 = 0) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | REDUCE: (218), (273) imply: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | (274) $false % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | CLOSE: (274) is inconsistent. % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | End of split % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | Case 2: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | (275) ~ (all_53_0 = all_51_0) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | Case 1: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | (276) all_59_3 = all_51_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (220), (276) imply: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | (277) all_53_0 = all_51_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | SIMP: (277) implies: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | (278) all_53_0 = all_51_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | REDUCE: (275), (278) imply: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | (279) $false % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | CLOSE: (279) is inconsistent. % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | Case 2: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | (280) ~ (all_59_3 = all_51_0) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | (281) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | (apply(all_32_9, all_59_3, all_44_2) = v2 & % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | member(all_51_0, all_32_7) = v0 & % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | member(all_44_2, all_32_6) = v1 & ( ~ (v2 = 0) | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (281) with fresh symbols all_199_0, % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | all_199_1, all_199_2 gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | (282) apply(all_32_9, all_59_3, all_44_2) = all_199_0 & % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | member(all_51_0, all_32_7) = all_199_2 & % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | member(all_44_2, all_32_6) = all_199_1 & ( ~ % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | (all_199_0 = 0) | ~ (all_199_1 = 0) | ~ % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | (all_199_2 = 0)) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | (283) apply(all_32_9, all_59_3, all_44_2) = all_199_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | REDUCE: (220), (283) imply: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | (284) apply(all_32_9, all_53_0, all_44_2) = all_199_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | Case 1: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | (285) all_53_0 = all_51_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (275), (285) imply: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | (286) $false % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (286) is inconsistent. % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | Case 2: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | (287) ? [v0: any] : ? [v1: any] : (apply(all_32_9, % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | all_53_0, all_44_2) = v0 & apply(all_32_9, % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | all_51_0, all_44_2) = v1 & ( ~ (v1 = 0) | ~ % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (287) with fresh symbols all_205_0, % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | all_205_1 gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | (288) apply(all_32_9, all_53_0, all_44_2) = all_205_1 & % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | apply(all_32_9, all_51_0, all_44_2) = all_205_0 & % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_205_0 = 0) | ~ (all_205_1 = 0)) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (288) implies: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | (289) apply(all_32_9, all_51_0, all_44_2) = all_205_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | (290) apply(all_32_9, all_53_0, all_44_2) = all_205_1 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | (291) ~ (all_205_0 = 0) | ~ (all_205_1 = 0) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | (292) all_53_0 = all_51_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (275), (292) imply: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | (293) $false % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (293) is inconsistent. % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | (294) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | (apply(all_32_9, all_53_0, all_44_2) = v2 & % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | member(all_51_0, all_32_7) = v0 & % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | member(all_44_2, all_32_6) = v1 & ( ~ (v2 = 0) | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (294) with fresh symbols all_217_0, % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | all_217_1, all_217_2 gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | (295) apply(all_32_9, all_53_0, all_44_2) = all_217_0 & % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | member(all_51_0, all_32_7) = all_217_2 & % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | member(all_44_2, all_32_6) = all_217_1 & ( ~ % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | (all_217_0 = 0) | ~ (all_217_1 = 0) | ~ % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | (all_217_2 = 0)) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (295) implies: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | (296) apply(all_32_9, all_53_0, all_44_2) = all_217_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (297) all_59_3 = all_51_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (220), (297) imply: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (298) all_53_0 = all_51_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (298) implies: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (299) all_53_0 = all_51_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (275), (299) imply: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (300) $false % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (300) is inconsistent. % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (301) ? [v0: any] : ? [v1: any] : (apply(all_32_9, % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | all_59_3, all_44_2) = v0 & apply(all_32_9, % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | all_51_0, all_44_2) = v1 & ( ~ (v1 = 0) | ~ % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (301) with fresh symbols all_223_0, % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | all_223_1 gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (302) apply(all_32_9, all_59_3, all_44_2) = all_223_1 & % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | apply(all_32_9, all_51_0, all_44_2) = all_223_0 & % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_223_0 = 0) | ~ (all_223_1 = 0)) % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (302) implies: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (303) apply(all_32_9, all_51_0, all_44_2) = all_223_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (304) apply(all_32_9, all_59_3, all_44_2) = all_223_1 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (220), (304) imply: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | (305) apply(all_32_9, all_53_0, all_44_2) = all_223_1 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (95) gives: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_53_0 = all_51_0 % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (275), (306) imply: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | (307) $false % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (307) is inconsistent. % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | (308) ? [v0: any] : ? [v1: any] : (apply(all_32_9, % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | all_53_0, all_44_2) = v1 & apply(all_32_9, % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | all_51_0, all_44_2) = v0 & ( ~ (v1 = 0) | ~ % 38.83/6.08 | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (308) with fresh symbols all_229_0, % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | all_229_1 gives: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | (309) apply(all_32_9, all_53_0, all_44_2) = all_229_0 & % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | apply(all_32_9, all_51_0, all_44_2) = all_229_1 & % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_229_0 = 0) | ~ (all_229_1 = 0)) % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (309) implies: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | (310) apply(all_32_9, all_51_0, all_44_2) = all_229_1 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | (311) apply(all_32_9, all_53_0, all_44_2) = all_229_0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_59_3 = all_51_0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (220), (312) imply: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_53_0 = all_51_0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (313) implies: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_53_0 = all_51_0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (275), (314) imply: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (315) $false % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (315) is inconsistent. % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (316) ? [v0: any] : ? [v1: any] : (apply(all_32_9, % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | all_59_3, all_44_2) = v1 & apply(all_32_9, % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | all_51_0, all_44_2) = v0 & ( ~ (v1 = 0) | ~ % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (316) with fresh symbols all_241_0, % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | all_241_1 gives: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (317) apply(all_32_9, all_59_3, all_44_2) = all_241_0 & % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | apply(all_32_9, all_51_0, all_44_2) = all_241_1 & % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_241_0 = 0) | ~ (all_241_1 = 0)) % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (317) implies: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (318) apply(all_32_9, all_51_0, all_44_2) = all_241_1 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (319) apply(all_32_9, all_59_3, all_44_2) = all_241_0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (220), (319) imply: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (320) apply(all_32_9, all_53_0, all_44_2) = all_241_0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_205_0, all_223_0, % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | all_44_2, all_51_0, all_32_9, simplifying with % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (303) gives: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_223_0 = all_205_0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_241_1, all_44_2, % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | all_51_0, all_32_9, simplifying with (61), (318) % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_241_1 = 0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_229_1, all_241_1, % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | all_44_2, all_51_0, all_32_9, simplifying with % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (310), (318) gives: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_241_1 = all_229_1 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_223_0, all_241_1, % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | all_44_2, all_51_0, all_32_9, simplifying with % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (303), (318) gives: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_241_1 = all_223_0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_217_0, all_44_2, % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | all_53_0, all_32_9, simplifying with (226), (296) % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_217_0 = 0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_223_1, all_229_0, % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | all_44_2, all_53_0, all_32_9, simplifying with % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (305), (311) gives: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_229_0 = all_223_1 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_217_0, all_229_0, % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | all_44_2, all_53_0, all_32_9, simplifying with % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (296), (311) gives: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_229_0 = all_217_0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_205_1, all_229_0, % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | all_44_2, all_53_0, all_32_9, simplifying with % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (290), (311) gives: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_229_0 = all_205_1 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_223_1, all_241_0, % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | all_44_2, all_53_0, all_32_9, simplifying with % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (305), (320) gives: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_241_0 = all_223_1 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_199_0, all_241_0, % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | all_44_2, all_53_0, all_32_9, simplifying with % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (284), (320) gives: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_241_0 = all_199_0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (329), (330) imply: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (331) all_223_1 = all_199_0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (331) implies: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_223_1 = all_199_0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (323) imply: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_229_1 = 0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (323), (324) imply: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_229_1 = all_223_0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (326), (328) imply: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_223_1 = all_205_1 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (335) implies: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (336) all_223_1 = all_205_1 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (327), (328) imply: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_217_0 = all_205_1 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (337) implies: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_217_0 = all_205_1 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (333), (334) imply: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (339) all_223_0 = 0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (339) implies: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (340) all_223_0 = 0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (321), (340) imply: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_205_0 = 0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (341) implies: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_205_0 = 0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (332), (336) imply: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (343) all_205_1 = all_199_0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (343) implies: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (344) all_205_1 = all_199_0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (325), (338) imply: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (345) all_205_1 = 0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (345) implies: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (346) all_205_1 = 0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (344), (346) imply: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (347) all_199_0 = 0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) ~ (all_205_0 = 0) % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (342), (348) imply: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) $false % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (349) is inconsistent. % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) ~ (all_205_1 = 0) % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (350) imply: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) $false % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (351) is inconsistent. % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | End of split % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | End of split % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | End of split % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | End of split % 38.83/6.09 | | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | End of split % 38.83/6.09 | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | End of split % 38.83/6.09 | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | Case 2: % 38.83/6.09 | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | (352) ~ (all_59_3 = all_53_0) % 38.83/6.09 | | | | | | | | | | | | | | | | | | (353) ? [v0: any] : ? [v1: any] : (apply(all_32_10, % 38.83/6.09 | | | | | | | | | | | | | | | | | | all_44_0, all_59_3) = v0 & apply(all_32_10, % 38.83/6.09 | | | | | | | | | | | | | | | | | | all_44_0, all_53_0) = v1 & ( ~ (v1 = 0) | ~ % 38.83/6.09 | | | | | | | | | | | | | | | | | | (v0 = 0))) % 38.83/6.09 | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | DELTA: instantiating (353) with fresh symbols all_187_0, % 38.83/6.09 | | | | | | | | | | | | | | | | | | all_187_1 gives: % 38.83/6.09 | | | | | | | | | | | | | | | | | | (354) apply(all_32_10, all_44_0, all_59_3) = all_187_1 & % 38.83/6.09 | | | | | | | | | | | | | | | | | | apply(all_32_10, all_44_0, all_53_0) = all_187_0 & % 38.83/6.09 | | | | | | | | | | | | | | | | | | ( ~ (all_187_0 = 0) | ~ (all_187_1 = 0)) % 38.83/6.09 | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | ALPHA: (354) implies: % 38.83/6.09 | | | | | | | | | | | | | | | | | | (355) apply(all_32_10, all_44_0, all_53_0) = all_187_0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | (356) apply(all_32_10, all_44_0, all_59_3) = all_187_1 % 38.83/6.09 | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives: % 38.83/6.09 | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | Case 1: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | (357) all_59_3 = all_53_0 % 38.83/6.09 | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | REDUCE: (352), (357) imply: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | (358) $false % 38.83/6.09 | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | | CLOSE: (358) is inconsistent. % 38.83/6.09 | | | | | | | | | | | | | | | | | | | % 38.83/6.09 | | | | | | | | | | | | | | | | | | Case 2: % 38.83/6.09 | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | (359) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 39.15/6.09 | | | | | | | | | | | | | | | | | | | (apply(all_32_10, all_44_0, all_59_3) = v2 & % 39.15/6.09 | | | | | | | | | | | | | | | | | | | member(all_53_0, all_32_7) = v1 & % 39.15/6.09 | | | | | | | | | | | | | | | | | | | member(all_44_0, all_32_8) = v0 & ( ~ (v2 = 0) | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 39.15/6.09 | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (359) with fresh symbols all_193_0, % 39.15/6.09 | | | | | | | | | | | | | | | | | | | all_193_1, all_193_2 gives: % 39.15/6.09 | | | | | | | | | | | | | | | | | | | (360) apply(all_32_10, all_44_0, all_59_3) = all_193_0 & % 39.15/6.09 | | | | | | | | | | | | | | | | | | | member(all_53_0, all_32_7) = all_193_1 & % 39.15/6.09 | | | | | | | | | | | | | | | | | | | member(all_44_0, all_32_8) = all_193_2 & ( ~ % 39.15/6.09 | | | | | | | | | | | | | | | | | | | (all_193_0 = 0) | ~ (all_193_1 = 0) | ~ % 39.15/6.09 | | | | | | | | | | | | | | | | | | | (all_193_2 = 0)) % 39.15/6.09 | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | ALPHA: (360) implies: % 39.15/6.09 | | | | | | | | | | | | | | | | | | | (361) apply(all_32_10, all_44_0, all_59_3) = all_193_0 % 39.15/6.09 | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives: % 39.15/6.09 | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | Case 1: % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | (362) ~ (all_98_2 = 0) % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | REDUCE: (204), (362) imply: % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | (363) $false % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | CLOSE: (363) is inconsistent. % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | Case 2: % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | (364) all_98_0 = 0 % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (364) imply: % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | (365) apply(all_32_9, all_59_3, all_44_2) = 0 % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives: % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | Case 1: % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | | (366) all_59_3 = all_51_0 % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | | REDUCE: (352), (366) imply: % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | | (367) ~ (all_53_0 = all_51_0) % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | | SIMP: (367) implies: % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | | (368) ~ (all_53_0 = all_51_0) % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (366) imply: % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | | (369) apply(all_32_10, all_44_0, all_51_0) = all_193_0 % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (366) imply: % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | | (370) apply(all_32_10, all_44_0, all_51_0) = all_187_1 % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | | % 39.15/6.09 | | | | | | | | | | | | | | | | | | | | | REDUCE: (219), (366) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | (371) apply(all_32_10, all_44_0, all_51_0) = 0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | Case 1: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | (372) all_53_0 = all_51_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (372) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | (373) $false % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (373) is inconsistent. % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | Case 2: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | (374) ? [v0: any] : ? [v1: any] : (apply(all_32_10, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | all_44_0, all_53_0) = v1 & apply(all_32_10, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | all_44_0, all_51_0) = v0 & ( ~ (v1 = 0) | ~ % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (374) with fresh symbols all_221_0, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | all_221_1 gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | (375) apply(all_32_10, all_44_0, all_53_0) = all_221_0 & % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | apply(all_32_10, all_44_0, all_51_0) = all_221_1 & % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_221_0 = 0) | ~ (all_221_1 = 0)) % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (375) implies: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | (376) apply(all_32_10, all_44_0, all_51_0) = all_221_1 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | (377) apply(all_32_10, all_44_0, all_53_0) = all_221_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | (378) ~ (all_221_0 = 0) | ~ (all_221_1 = 0) % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | (379) all_59_3 = all_53_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (379) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | (380) all_53_0 = all_51_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (380) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | (381) $false % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (381) is inconsistent. % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | (382) ? [v0: any] : ? [v1: any] : (apply(all_32_10, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | all_44_0, all_59_3) = v1 & apply(all_32_10, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | all_44_0, all_53_0) = v0 & ( ~ (v1 = 0) | ~ % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (382) with fresh symbols all_239_0, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | all_239_1 gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | (383) apply(all_32_10, all_44_0, all_59_3) = all_239_0 & % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | apply(all_32_10, all_44_0, all_53_0) = all_239_1 & % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_239_0 = 0) | ~ (all_239_1 = 0)) % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (383) implies: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | (384) apply(all_32_10, all_44_0, all_53_0) = all_239_1 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | (385) apply(all_32_10, all_44_0, all_59_3) = all_239_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (385) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | (386) apply(all_32_10, all_44_0, all_51_0) = all_239_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | (387) all_53_0 = all_51_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (387) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | (388) $false % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (388) is inconsistent. % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | (389) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | (apply(all_32_10, all_44_0, all_51_0) = v2 & % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | member(all_53_0, all_32_7) = v1 & % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | member(all_44_0, all_32_8) = v0 & ( ~ (v2 = 0) | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (389) with fresh symbols all_245_0, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | all_245_1, all_245_2 gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | (390) apply(all_32_10, all_44_0, all_51_0) = all_245_0 & % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | member(all_53_0, all_32_7) = all_245_1 & % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | member(all_44_0, all_32_8) = all_245_2 & ( ~ % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | (all_245_0 = 0) | ~ (all_245_1 = 0) | ~ % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | (all_245_2 = 0)) % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (390) implies: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | (391) apply(all_32_10, all_44_0, all_51_0) = all_245_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | (392) all_53_0 = all_51_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (392) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | (393) $false % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (393) is inconsistent. % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | (394) ? [v0: any] : ? [v1: any] : (apply(all_32_10, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | all_44_0, all_53_0) = v0 & apply(all_32_10, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | all_44_0, all_51_0) = v1 & ( ~ (v1 = 0) | ~ % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (394) with fresh symbols all_251_0, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | all_251_1 gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | (395) apply(all_32_10, all_44_0, all_53_0) = all_251_1 & % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | apply(all_32_10, all_44_0, all_51_0) = all_251_0 & % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_251_0 = 0) | ~ (all_251_1 = 0)) % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (395) implies: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | (396) apply(all_32_10, all_44_0, all_51_0) = all_251_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | (397) apply(all_32_10, all_44_0, all_53_0) = all_251_1 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (398) all_53_0 = all_51_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (398) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (399) $false % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (399) is inconsistent. % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_187_1, all_193_0, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | all_51_0, all_44_0, all_32_10, simplifying with % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (369), (370) gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (400) all_193_0 = all_187_1 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_193_0, all_221_1, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | all_51_0, all_44_0, all_32_10, simplifying with % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (369), (376) gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (401) all_221_1 = all_193_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_187_1, all_239_0, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | all_51_0, all_44_0, all_32_10, simplifying with % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (370), (386) gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (402) all_239_0 = all_187_1 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_239_0, all_51_0, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | all_44_0, all_32_10, simplifying with (371), (386) % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (403) all_239_0 = 0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_148_0, all_251_0, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | all_51_0, all_44_0, all_32_10, simplifying with % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (396) gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (404) all_251_0 = all_148_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_245_0, all_251_0, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | all_51_0, all_44_0, all_32_10, simplifying with % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (391), (396) gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (405) all_251_0 = all_245_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_221_1, all_251_0, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | all_51_0, all_44_0, all_32_10, simplifying with % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (376), (396) gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (406) all_251_0 = all_221_1 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_187_0, all_239_1, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | all_53_0, all_44_0, all_32_10, simplifying with % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (355), (384) gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_239_1 = all_187_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_251_1, all_53_0, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | all_44_0, all_32_10, simplifying with (65), (397) % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (408) all_251_1 = 0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_239_1, all_251_1, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | all_53_0, all_44_0, all_32_10, simplifying with % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (384), (397) gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (409) all_251_1 = all_239_1 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_221_0, all_251_1, % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | all_53_0, all_44_0, all_32_10, simplifying with % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (377), (397) gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (410) all_251_1 = all_221_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (406) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (411) all_245_0 = all_221_1 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (404), (405) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_245_0 = all_148_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (410) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (413) all_239_1 = all_221_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (413) implies: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (414) all_239_1 = all_221_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (410) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (415) all_221_0 = 0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (411), (412) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (416) all_221_1 = all_148_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (416) implies: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (417) all_221_1 = all_148_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (402), (403) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_187_1 = 0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (418) implies: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (419) all_187_1 = 0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (414) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (420) all_221_0 = all_187_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (420) implies: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (421) all_221_0 = all_187_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (421) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (422) all_187_0 = 0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (417) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (423) all_193_0 = all_148_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (423) implies: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (424) all_193_0 = all_148_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (400), (424) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (425) all_187_1 = all_148_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (425) implies: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (426) all_187_1 = all_148_0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (426) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (427) all_148_0 = 0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (417), (427) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (428) all_221_1 = 0 % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (378) gives: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) ~ (all_221_0 = 0) % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (415), (429) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) $false % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (430) is inconsistent. % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) ~ (all_221_1 = 0) % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (428), (431) imply: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) $false % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (432) is inconsistent. % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | End of split % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | End of split % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | End of split % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | Case 2: % 39.15/6.10 | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | (433) ~ (all_59_3 = all_51_0) % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | (434) ? [v0: any] : ? [v1: any] : (apply(all_32_9, % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | all_59_3, all_44_2) = v1 & apply(all_32_9, % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | all_51_0, all_44_2) = v0 & ( ~ (v1 = 0) | ~ % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (434) with fresh symbols all_217_0, % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | all_217_1 gives: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | (435) apply(all_32_9, all_59_3, all_44_2) = all_217_0 & % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | apply(all_32_9, all_51_0, all_44_2) = all_217_1 & % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | ( ~ (all_217_0 = 0) | ~ (all_217_1 = 0)) % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | ALPHA: (435) implies: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | (436) apply(all_32_9, all_51_0, all_44_2) = all_217_1 % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | (437) apply(all_32_9, all_59_3, all_44_2) = all_217_0 % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | Case 1: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | (438) all_59_3 = all_51_0 % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (433), (438) imply: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | (439) $false % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (439) is inconsistent. % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | Case 2: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | (440) ? [v0: any] : ? [v1: any] : (apply(all_32_9, % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | all_59_3, all_44_2) = v0 & apply(all_32_9, % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | all_51_0, all_44_2) = v1 & ( ~ (v1 = 0) | ~ % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (440) with fresh symbols all_235_0, % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | all_235_1 gives: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | (441) apply(all_32_9, all_59_3, all_44_2) = all_235_1 & % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | apply(all_32_9, all_51_0, all_44_2) = all_235_0 & % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_235_0 = 0) | ~ (all_235_1 = 0)) % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (441) implies: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | (442) apply(all_32_9, all_51_0, all_44_2) = all_235_0 % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | (443) apply(all_32_9, all_59_3, all_44_2) = all_235_1 % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | (444) ~ (all_235_0 = 0) | ~ (all_235_1 = 0) % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (445) all_59_3 = all_51_0 % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (433), (445) imply: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (446) $false % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (446) is inconsistent. % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (447) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (apply(all_32_9, all_59_3, all_44_2) = v2 & % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | member(all_51_0, all_32_7) = v0 & % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | member(all_44_2, all_32_6) = v1 & ( ~ (v2 = 0) | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (447) with fresh symbols all_241_0, % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | all_241_1, all_241_2 gives: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (448) apply(all_32_9, all_59_3, all_44_2) = all_241_0 & % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | member(all_51_0, all_32_7) = all_241_2 & % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | member(all_44_2, all_32_6) = all_241_1 & ( ~ % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (all_241_0 = 0) | ~ (all_241_1 = 0) | ~ % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (all_241_2 = 0)) % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (448) implies: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (449) apply(all_32_9, all_59_3, all_44_2) = all_241_0 % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_235_0, all_44_2, % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | all_51_0, all_32_9, simplifying with (61), (442) % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | gives: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (450) all_235_0 = 0 % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_217_1, all_235_0, % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | all_44_2, all_51_0, all_32_9, simplifying with % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (436), (442) gives: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (451) all_235_0 = all_217_1 % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_235_1, all_44_2, % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | all_59_3, all_32_9, simplifying with (365), (443) % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | gives: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (452) all_235_1 = 0 % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_235_1, all_241_0, % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | all_44_2, all_59_3, all_32_9, simplifying with % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (443), (449) gives: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (453) all_241_0 = all_235_1 % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_217_0, all_241_0, % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | all_44_2, all_59_3, all_32_9, simplifying with % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (437), (449) gives: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (454) all_241_0 = all_217_0 % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (454) imply: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (455) all_235_1 = all_217_0 % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (455) implies: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (456) all_235_1 = all_217_0 % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (450), (451) imply: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (457) all_217_1 = 0 % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (452), (456) imply: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | (458) all_217_0 = 0 % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (444) gives: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | | (459) ~ (all_235_0 = 0) % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (450), (459) imply: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | | (460) $false % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (460) is inconsistent. % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | | (461) ~ (all_235_1 = 0) % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (452), (461) imply: % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | | (462) $false % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (462) is inconsistent. % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | End of split % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | End of split % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | End of split % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | End of split % 39.15/6.11 | | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | | End of split % 39.15/6.11 | | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | | End of split % 39.15/6.11 | | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | | End of split % 39.15/6.11 | | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | End of split % 39.15/6.11 | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | End of split % 39.15/6.11 | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | Case 2: % 39.15/6.11 | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | (463) member(all_44_1, all_32_8) = all_102_5 & % 39.15/6.11 | | | | | | | | | | | | | | | member(all_44_2, all_32_6) = all_102_4 & ( ~ % 39.15/6.11 | | | | | | | | | | | | | | | (all_102_4 = 0) | ~ (all_102_5 = 0)) % 39.15/6.11 | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | ALPHA: (463) implies: % 39.15/6.11 | | | | | | | | | | | | | | | (464) member(all_44_2, all_32_6) = all_102_4 % 39.15/6.11 | | | | | | | | | | | | | | | (465) member(all_44_1, all_32_8) = all_102_5 % 39.15/6.11 | | | | | | | | | | | | | | | (466) ~ (all_102_4 = 0) | ~ (all_102_5 = 0) % 39.15/6.11 | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_102_4, all_32_6, % 39.15/6.11 | | | | | | | | | | | | | | | all_44_2, simplifying with (48), (464) gives: % 39.15/6.11 | | | | | | | | | | | | | | | (467) all_102_4 = 0 % 39.15/6.11 | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_102_5, all_32_8, % 39.15/6.11 | | | | | | | | | | | | | | | all_44_1, simplifying with (49), (465) gives: % 39.15/6.11 | | | | | | | | | | | | | | | (468) all_102_5 = 0 % 39.15/6.11 | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | BETA: splitting (466) gives: % 39.15/6.11 | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | Case 1: % 39.15/6.11 | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | (469) ~ (all_102_4 = 0) % 39.15/6.11 | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | REDUCE: (467), (469) imply: % 39.15/6.11 | | | | | | | | | | | | | | | | (470) $false % 39.15/6.11 | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | CLOSE: (470) is inconsistent. % 39.15/6.11 | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | Case 2: % 39.15/6.11 | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | (471) ~ (all_102_5 = 0) % 39.15/6.11 | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | REDUCE: (468), (471) imply: % 39.15/6.11 | | | | | | | | | | | | | | | | (472) $false % 39.15/6.11 | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | | CLOSE: (472) is inconsistent. % 39.15/6.11 | | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | | End of split % 39.15/6.11 | | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | | End of split % 39.15/6.11 | | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | | End of split % 39.15/6.11 | | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | | End of split % 39.15/6.11 | | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | | End of split % 39.15/6.11 | | | | | | | | | | | % 39.15/6.11 | | | | | | | | | | End of split % 39.15/6.11 | | | | | | | | | | % 39.15/6.11 | | | | | | | | | End of split % 39.15/6.11 | | | | | | | | | % 39.15/6.11 | | | | | | | | End of split % 39.15/6.11 | | | | | | | | % 39.15/6.11 | | | | | | | End of split % 39.15/6.11 | | | | | | | % 39.15/6.11 | | | | | | End of split % 39.15/6.11 | | | | | | % 39.15/6.11 | | | | | End of split % 39.15/6.11 | | | | | % 39.15/6.11 | | | | End of split % 39.15/6.11 | | | | % 39.15/6.11 | | | End of split % 39.15/6.11 | | | % 39.15/6.11 | | Case 2: % 39.15/6.11 | | | % 39.15/6.11 | | | (473) member(all_44_0, all_32_8) = all_59_4 & member(all_44_2, % 39.15/6.11 | | | all_32_6) = all_59_5 & ( ~ (all_59_4 = 0) | ~ (all_59_5 = 0)) % 39.15/6.11 | | | % 39.15/6.11 | | | ALPHA: (473) implies: % 39.15/6.11 | | | (474) member(all_44_2, all_32_6) = all_59_5 % 39.15/6.11 | | | (475) member(all_44_0, all_32_8) = all_59_4 % 39.15/6.11 | | | (476) ~ (all_59_4 = 0) | ~ (all_59_5 = 0) % 39.15/6.11 | | | % 39.15/6.11 | | | GROUND_INST: instantiating (10) with 0, all_59_5, all_32_6, all_44_2, % 39.15/6.11 | | | simplifying with (48), (474) gives: % 39.15/6.11 | | | (477) all_59_5 = 0 % 39.15/6.11 | | | % 39.15/6.11 | | | GROUND_INST: instantiating (10) with 0, all_59_4, all_32_8, all_44_0, % 39.15/6.11 | | | simplifying with (50), (475) gives: % 39.15/6.11 | | | (478) all_59_4 = 0 % 39.15/6.11 | | | % 39.15/6.11 | | | BETA: splitting (476) gives: % 39.15/6.11 | | | % 39.15/6.11 | | | Case 1: % 39.15/6.11 | | | | % 39.15/6.11 | | | | (479) ~ (all_59_4 = 0) % 39.15/6.11 | | | | % 39.15/6.11 | | | | REDUCE: (478), (479) imply: % 39.15/6.11 | | | | (480) $false % 39.15/6.11 | | | | % 39.15/6.11 | | | | CLOSE: (480) is inconsistent. % 39.15/6.11 | | | | % 39.15/6.11 | | | Case 2: % 39.15/6.11 | | | | % 39.15/6.11 | | | | (481) ~ (all_59_5 = 0) % 39.15/6.11 | | | | % 39.15/6.11 | | | | REDUCE: (477), (481) imply: % 39.15/6.11 | | | | (482) $false % 39.15/6.11 | | | | % 39.15/6.11 | | | | CLOSE: (482) is inconsistent. % 39.15/6.11 | | | | % 39.15/6.11 | | | End of split % 39.15/6.11 | | | % 39.15/6.11 | | End of split % 39.15/6.11 | | % 39.15/6.11 | End of split % 39.15/6.11 | % 39.15/6.11 End of proof % 39.15/6.11 % 39.15/6.11 Sub-proof #1 shows that the following formulas are inconsistent: % 39.15/6.11 ---------------------------------------------------------------- % 39.15/6.12 (1) ~ (all_242_0 = 0) | ~ (all_242_1 = 0) % 39.15/6.12 (2) all_242_0 = 0 % 39.15/6.12 (3) all_242_1 = 0 % 39.15/6.12 % 39.15/6.12 Begin of proof % 39.15/6.12 | % 39.15/6.12 | BETA: splitting (1) gives: % 39.15/6.12 | % 39.15/6.12 | Case 1: % 39.15/6.12 | | % 39.15/6.12 | | (4) ~ (all_242_0 = 0) % 39.15/6.12 | | % 39.15/6.12 | | REDUCE: (2), (4) imply: % 39.15/6.12 | | (5) $false % 39.15/6.12 | | % 39.15/6.12 | | CLOSE: (5) is inconsistent. % 39.15/6.12 | | % 39.15/6.12 | Case 2: % 39.15/6.12 | | % 39.15/6.12 | | (6) ~ (all_242_1 = 0) % 39.15/6.12 | | % 39.15/6.12 | | REDUCE: (3), (6) imply: % 39.15/6.12 | | (7) $false % 39.15/6.12 | | % 39.15/6.12 | | CLOSE: (7) is inconsistent. % 39.15/6.12 | | % 39.15/6.12 | End of split % 39.15/6.12 | % 39.15/6.12 End of proof % 39.15/6.12 % SZS output end Proof for theBenchmark % 39.15/6.12 % 39.15/6.12 5483ms %------------------------------------------------------------------------------