%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET727+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 : n012.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 15:26:10 EDT 2023 % Result : Theorem 38.79s 6.04s % Output : Proof 170.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SET727+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.30 % Computer : n012.cluster.edu % 0.12/0.30 % Model : x86_64 x86_64 % 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.30 % Memory : 8042.1875MB % 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.30 % CPULimit : 300 % 0.12/0.30 % WCLimit : 300 % 0.12/0.30 % DateTime : Sat Aug 26 14:26:40 EDT 2023 % 0.12/0.31 % CPUTime : % 0.15/0.56 ________ _____ % 0.15/0.56 ___ __ \_________(_)________________________________ % 0.15/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.15/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.15/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.15/0.56 % 0.15/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.15/0.56 (2023-06-19) % 0.15/0.56 % 0.15/0.56 (c) Philipp Rümmer, 2009-2023 % 0.15/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.15/0.56 Amanda Stjerna. % 0.15/0.56 Free software under BSD-3-Clause. % 0.15/0.56 % 0.15/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.15/0.56 % 0.15/0.56 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.15/0.58 Running up to 7 provers in parallel. % 0.15/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.15/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.15/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.15/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.15/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.15/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.15/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.20/1.30 Prover 1: Preprocessing ... % 4.20/1.30 Prover 4: Preprocessing ... % 4.20/1.33 Prover 6: Preprocessing ... % 4.20/1.33 Prover 3: Preprocessing ... % 4.20/1.33 Prover 0: Preprocessing ... % 4.20/1.33 Prover 5: Preprocessing ... % 4.20/1.34 Prover 2: Preprocessing ... % 11.65/2.43 Prover 2: Proving ... % 12.37/2.44 Prover 5: Proving ... % 13.23/2.58 Prover 1: Constructing countermodel ... % 13.23/2.58 Prover 6: Proving ... % 13.57/2.62 Prover 3: Constructing countermodel ... % 17.58/3.21 Prover 4: Constructing countermodel ... % 18.42/3.30 Prover 0: Proving ... % 38.79/6.04 Prover 0: proved (5419ms) % 38.79/6.04 % 38.79/6.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 38.79/6.04 % 38.79/6.04 Prover 3: stopped % 38.79/6.04 Prover 2: stopped % 38.79/6.04 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 38.79/6.04 Prover 6: stopped % 38.79/6.04 Prover 5: stopped % 38.79/6.04 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 38.79/6.04 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 38.79/6.05 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 39.47/6.08 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 39.79/6.14 Prover 8: Preprocessing ... % 39.79/6.15 Prover 11: Preprocessing ... % 39.79/6.15 Prover 7: Preprocessing ... % 39.79/6.19 Prover 10: Preprocessing ... % 39.79/6.20 Prover 13: Preprocessing ... % 41.05/6.34 Prover 7: Warning: ignoring some quantifiers % 41.05/6.38 Prover 10: Warning: ignoring some quantifiers % 41.84/6.38 Prover 7: Constructing countermodel ... % 41.98/6.40 Prover 10: Constructing countermodel ... % 41.98/6.40 Prover 8: Warning: ignoring some quantifiers % 42.10/6.42 Prover 8: Constructing countermodel ... % 42.10/6.59 Prover 10: gave up % 42.10/6.60 Prover 13: Warning: ignoring some quantifiers % 42.10/6.61 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 42.10/6.66 Prover 13: Constructing countermodel ... % 42.10/6.66 Prover 16: Preprocessing ... % 44.21/6.78 Prover 16: Warning: ignoring some quantifiers % 44.21/6.79 Prover 16: Constructing countermodel ... % 47.26/7.11 Prover 11: Constructing countermodel ... % 75.90/10.85 Prover 13: stopped % 75.90/10.86 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 76.53/10.95 Prover 19: Preprocessing ... % 79.76/11.40 Prover 19: Warning: ignoring some quantifiers % 80.42/11.44 Prover 19: Constructing countermodel ... % 90.33/12.77 Prover 16: stopped % 105.82/14.79 Prover 19: stopped % 114.87/15.95 Prover 1: stopped % 167.16/25.65 Prover 4: Found proof (size 8227) % 167.16/25.65 Prover 4: proved (25052ms) % 167.16/25.65 Prover 7: stopped % 167.16/25.65 Prover 11: stopped % 167.16/25.65 Prover 8: stopped % 168.33/25.65 % 168.33/25.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 168.33/25.65 % 168.33/25.74 % SZS output start Proof for theBenchmark % 168.58/25.75 Assumptions after simplification: % 168.58/25.75 --------------------------------- % 168.58/25.75 % 168.58/25.75 (compose_function) % 168.58/25.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 168.58/25.79 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 168.58/25.79 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 168.58/25.79 ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | % 168.58/25.79 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] % 168.58/25.80 : ((apply(v0, v9, v6) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 % 168.58/25.80 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = % 168.58/25.80 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 168.58/25.80 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 168.58/25.80 int] : ! [v9: $i] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = % 168.58/25.80 v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) % 168.58/25.80 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 168.58/25.80 $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v11 & % 168.58/25.80 member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4) % 168.58/25.80 = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! % 168.58/25.80 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 168.58/25.80 : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 168.58/25.80 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 168.58/25.80 ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ % 168.58/25.80 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] : % 168.58/25.80 ((apply(v1, v5, v9) = v10 & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~ % 168.58/25.80 (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 % 168.58/25.80 = 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 168.58/25.80 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 168.58/25.80 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | % 168.58/25.80 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 168.58/25.80 $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ? % 168.58/25.80 [v12: int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 & % 168.58/25.80 apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, v3) = 0) % 168.58/25.80 | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 = % 168.58/25.80 0)))))) % 168.58/25.80 % 168.58/25.80 (equal_maps) % 168.58/25.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 168.58/25.81 $i] : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ % 168.58/25.81 (apply(v1, v4, v6) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ $i(v6) | ~ $i(v5) % 168.58/25.81 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : % 168.58/25.81 ? [v8: any] : ? [v9: any] : (member(v6, v3) = v9 & member(v5, v3) = v8 & % 168.58/25.81 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! % 168.58/25.81 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 168.58/25.81 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1, % 168.58/25.81 v4, v6) = 0) | ~ (member(v5, v3) = 0) | ~ $i(v6) | ~ $i(v5) | ~ % 168.58/25.81 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? % 168.58/25.81 [v8: any] : ? [v9: any] : (apply(v0, v4, v5) = v9 & member(v6, v3) = v8 & % 168.58/25.81 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! % 168.58/25.81 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 168.58/25.81 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v0, % 168.58/25.81 v4, v5) = 0) | ~ (member(v6, v3) = 0) | ~ $i(v6) | ~ $i(v5) | ~ % 168.58/25.81 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? % 168.58/25.81 [v8: any] : ? [v9: any] : (apply(v1, v4, v6) = v9 & member(v5, v3) = v8 & % 168.58/25.81 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! % 168.58/25.81 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 168.58/25.81 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ % 168.58/25.81 (member(v6, v3) = 0) | ~ (member(v5, v3) = 0) | ~ (member(v4, v2) = 0) | % 168.58/25.81 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 168.58/25.81 $i(v0) | ? [v7: any] : ? [v8: any] : (apply(v1, v4, v6) = v8 & apply(v0, % 168.58/25.81 v4, v5) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! [v1: $i] % 168.58/25.81 : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (equal_maps(v0, v1, % 168.58/25.81 v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 168.58/25.81 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v6) & apply(v1, v5, v7) = 0 & % 168.58/25.81 apply(v0, v5, v6) = 0 & member(v7, v3) = 0 & member(v6, v3) = 0 & % 168.58/25.81 member(v5, v2) = 0 & $i(v7) & $i(v6) & $i(v5))) % 168.58/25.81 % 168.58/25.81 (identity) % 168.58/25.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 168.58/25.82 (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 168.58/25.82 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0: % 168.58/25.82 $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ~ % 168.58/25.82 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & apply(v0, % 168.58/25.82 v3, v3) = v4 & member(v3, v1) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] % 168.58/25.82 : ! [v2: $i] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ~ % 168.58/25.82 $i(v2) | ~ $i(v1) | ~ $i(v0) | apply(v0, v2, v2) = 0) % 168.58/25.82 % 168.58/25.82 (inverse_function) % 168.58/25.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 168.58/25.82 $i] : ! [v6: any] : ( ~ (inverse_function(v0, v1, v2) = v5) | ~ (apply(v5, % 168.58/25.82 v4, v3) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 168.58/25.82 $i(v0) | ? [v7: any] : ? [v8: any] : ? [v9: any] : (apply(v0, v3, v4) = % 168.58/25.82 v9 & member(v4, v2) = v8 & member(v3, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = % 168.58/25.82 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) % 168.58/25.82 % 168.58/25.82 (maps) % 168.58/25.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 168.58/25.83 $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ % 168.58/25.83 (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 168.58/25.83 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 168.58/25.83 (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = % 168.58/25.83 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 168.58/25.83 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, % 168.58/25.83 v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ~ % 168.58/25.83 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 168.58/25.83 any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5, % 168.58/25.83 v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 168.58/25.83 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 168.58/25.83 [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, % 168.58/25.83 v3, v4) = 0) | ~ (member(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 168.58/25.83 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 168.58/25.83 ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v4, v2) = v7 & member(v3, v1) % 168.58/25.83 = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: % 168.58/25.83 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ % 168.58/25.83 (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) | % 168.58/25.83 ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 168.58/25.83 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & % 168.58/25.83 apply(v0, v3, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! % 168.58/25.83 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) | % 168.58/25.83 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 168.58/25.83 : ? [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int] % 168.58/25.83 : ? [v12: $i] : ? [v13: int] : ($i(v12) & $i(v6) & $i(v5) & $i(v4) & ((v13 % 168.58/25.83 = 0 & member(v12, v1) = 0 & ! [v14: $i] : ( ~ (apply(v0, v12, v14) = % 168.58/25.83 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & member(v14, v2) % 168.58/25.83 = v15)) & ! [v14: $i] : ( ~ (member(v14, v2) = 0) | ~ $i(v14) | % 168.58/25.83 ? [v15: int] : ( ~ (v15 = 0) & apply(v0, v12, v14) = v15))) | (v11 = % 168.58/25.83 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4, % 168.58/25.83 v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, % 168.58/25.83 v2) = 0 & member(v4, v1) = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 168.58/25.83 [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) % 168.58/25.83 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, % 168.58/25.83 v3, v4) = 0 & member(v4, v2) = 0 & $i(v4))) % 168.58/25.83 % 168.58/25.83 (thII18) % 168.58/25.83 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 168.58/25.83 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & % 168.58/25.83 inverse_function(v0, v3, v4) = v7 & identity(v6, v4) = 0 & identity(v5, v3) % 168.58/25.83 = 0 & equal_maps(v7, v2, v4, v3) = v8 & compose_function(v1, v0, v3, v4, v3) % 168.58/25.83 = v5 & compose_function(v0, v2, v4, v3, v4) = v6 & maps(v2, v4, v3) = 0 & % 168.58/25.83 maps(v1, v4, v3) = 0 & maps(v0, v3, v4) = 0 & $i(v7) & $i(v6) & $i(v5) & % 168.58/25.83 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 168.58/25.83 % 168.58/25.83 (function-axioms) % 168.98/25.85 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 168.98/25.85 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 168.98/25.85 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 168.98/25.85 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 168.98/25.85 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 168.98/25.85 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 168.98/25.85 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 168.98/25.85 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 168.98/25.85 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 168.98/25.85 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 168.98/25.85 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 168.98/25.85 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 168.98/25.85 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 168.98/25.85 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 168.98/25.85 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 168.98/25.85 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 168.98/25.85 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 168.98/25.85 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 168.98/25.85 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 168.98/25.85 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 168.98/25.85 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 168.98/25.85 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 168.98/25.85 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 168.98/25.85 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 168.98/25.85 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 168.98/25.85 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 168.98/25.85 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 168.98/25.85 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 168.98/25.85 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 168.98/25.85 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 168.98/25.85 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 168.98/25.85 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 168.98/25.85 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 168.98/25.85 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 168.98/25.85 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 168.98/25.85 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 168.98/25.85 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 168.98/25.85 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 168.98/25.85 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 168.98/25.85 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 168.98/25.85 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 168.98/25.85 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 168.98/25.85 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 168.98/25.85 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 168.98/25.85 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 168.98/25.85 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 168.98/25.85 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 168.98/25.85 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 168.98/25.85 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 168.98/25.85 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 168.98/25.85 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 168.98/25.85 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 168.98/25.85 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 168.98/25.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 168.98/25.85 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 168.98/25.85 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 168.98/25.85 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 168.98/25.85 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 168.98/25.85 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 168.98/25.85 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 168.98/25.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 168.98/25.85 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 168.98/25.85 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 168.98/25.85 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 168.98/25.85 (power_set(v2) = v0)) % 168.98/25.85 % 168.98/25.85 Further assumptions not needed in the proof: % 168.98/25.85 -------------------------------------------- % 168.98/25.85 compose_predicate, decreasing_function, difference, empty_set, equal_set, % 168.98/25.85 image2, image3, increasing_function, injective, intersection, inverse_image2, % 168.98/25.85 inverse_image3, inverse_predicate, isomorphism, one_to_one, power_set, product, % 168.98/25.85 singleton, subset, sum, surjective, union, unordered_pair % 168.98/25.85 % 168.98/25.85 Those formulas are unsatisfiable: % 168.98/25.85 --------------------------------- % 168.98/25.85 % 168.98/25.85 Begin of proof % 168.98/25.85 | % 168.98/25.85 | ALPHA: (maps) implies: % 168.98/25.85 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, % 168.98/25.85 | v1, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v2) | % 168.98/25.85 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & % 168.98/25.85 | member(v4, v2) = 0 & $i(v4))) % 168.98/25.86 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 168.98/25.86 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) % 168.98/25.86 | = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ~ % 168.98/25.86 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 168.98/25.86 | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & apply(v0, v3, % 168.98/25.86 | v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 168.98/25.86 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 168.98/25.86 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, % 168.98/25.86 | v5) = 0) | ~ (member(v4, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 168.98/25.86 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 168.98/25.86 | any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5, v2) = v7 % 168.98/25.86 | & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 168.98/25.86 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 168.98/25.86 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, % 168.98/25.86 | v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | % 168.98/25.86 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 168.98/25.86 | any] : ? [v8: any] : (member(v5, v2) = v8 & member(v4, v2) = v7 & % 168.98/25.86 | member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 168.98/25.86 | % 168.98/25.86 | ALPHA: (compose_function) implies: % 168.98/25.86 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 168.98/25.86 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (compose_function(v0, v1, % 168.98/25.86 | v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | ~ $i(v6) | ~ % 168.98/25.86 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 168.98/25.86 | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ? [v12: % 168.98/25.86 | int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 & % 168.98/25.86 | apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, % 168.98/25.86 | v3) = 0) | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ % 168.98/25.86 | (v9 = 0) | ~ (v8 = 0)))))) % 168.98/25.86 | % 168.98/25.86 | ALPHA: (equal_maps) implies: % 168.98/25.86 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 168.98/25.86 | (v4 = 0 | ~ (equal_maps(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) % 168.98/25.86 | | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ( % 168.98/25.86 | ~ (v7 = v6) & apply(v1, v5, v7) = 0 & apply(v0, v5, v6) = 0 & % 168.98/25.86 | member(v7, v3) = 0 & member(v6, v3) = 0 & member(v5, v2) = 0 & % 168.98/25.86 | $i(v7) & $i(v6) & $i(v5))) % 168.98/25.87 | % 168.98/25.87 | ALPHA: (identity) implies: % 168.98/25.87 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (identity(v0, v1) = 0) | % 168.98/25.87 | ~ (member(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 168.98/25.87 | apply(v0, v2, v2) = 0) % 168.98/25.87 | % 168.98/25.87 | ALPHA: (function-axioms) implies: % 168.98/25.87 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 168.98/25.87 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 168.98/25.87 | = v0)) % 168.98/25.87 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 168.98/25.87 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ % 168.98/25.87 | (apply(v4, v3, v2) = v0)) % 168.98/25.87 | % 168.98/25.87 | DELTA: instantiating (thII18) with fresh symbols all_32_0, all_32_1, all_32_2, % 168.98/25.87 | all_32_3, all_32_4, all_32_5, all_32_6, all_32_7, all_32_8 gives: % 168.98/25.87 | (10) ~ (all_32_0 = 0) & inverse_function(all_32_8, all_32_5, all_32_4) = % 168.98/25.87 | all_32_1 & identity(all_32_2, all_32_4) = 0 & identity(all_32_3, % 168.98/25.87 | all_32_5) = 0 & equal_maps(all_32_1, all_32_6, all_32_4, all_32_5) = % 168.98/25.87 | all_32_0 & compose_function(all_32_7, all_32_8, all_32_5, all_32_4, % 168.98/25.87 | all_32_5) = all_32_3 & compose_function(all_32_8, all_32_6, % 168.98/25.87 | all_32_4, all_32_5, all_32_4) = all_32_2 & maps(all_32_6, all_32_4, % 168.98/25.87 | all_32_5) = 0 & maps(all_32_7, all_32_4, all_32_5) = 0 & % 168.98/25.87 | maps(all_32_8, all_32_5, all_32_4) = 0 & $i(all_32_1) & $i(all_32_2) & % 168.98/25.87 | $i(all_32_3) & $i(all_32_4) & $i(all_32_5) & $i(all_32_6) & % 168.98/25.87 | $i(all_32_7) & $i(all_32_8) % 168.98/25.87 | % 168.98/25.87 | ALPHA: (10) implies: % 168.98/25.87 | (11) ~ (all_32_0 = 0) % 168.98/25.87 | (12) $i(all_32_8) % 168.98/25.87 | (13) $i(all_32_7) % 168.98/25.87 | (14) $i(all_32_6) % 168.98/25.87 | (15) $i(all_32_5) % 168.98/25.87 | (16) $i(all_32_4) % 168.98/25.87 | (17) $i(all_32_3) % 168.98/25.87 | (18) $i(all_32_2) % 168.98/25.87 | (19) $i(all_32_1) % 168.98/25.87 | (20) maps(all_32_8, all_32_5, all_32_4) = 0 % 168.98/25.87 | (21) maps(all_32_7, all_32_4, all_32_5) = 0 % 168.98/25.87 | (22) maps(all_32_6, all_32_4, all_32_5) = 0 % 168.98/25.87 | (23) compose_function(all_32_8, all_32_6, all_32_4, all_32_5, all_32_4) = % 168.98/25.87 | all_32_2 % 168.98/25.87 | (24) compose_function(all_32_7, all_32_8, all_32_5, all_32_4, all_32_5) = % 168.98/25.87 | all_32_3 % 168.98/25.87 | (25) equal_maps(all_32_1, all_32_6, all_32_4, all_32_5) = all_32_0 % 168.98/25.87 | (26) identity(all_32_3, all_32_5) = 0 % 168.98/25.87 | (27) identity(all_32_2, all_32_4) = 0 % 168.98/25.87 | (28) inverse_function(all_32_8, all_32_5, all_32_4) = all_32_1 % 168.98/25.88 | % 168.98/25.88 | GROUND_INST: instantiating (6) with all_32_1, all_32_6, all_32_4, all_32_5, % 168.98/25.88 | all_32_0, simplifying with (14), (15), (16), (19), (25) gives: % 168.98/25.88 | (29) all_32_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) % 168.98/25.88 | & apply(all_32_1, v0, v1) = 0 & apply(all_32_6, v0, v2) = 0 & % 168.98/25.88 | member(v2, all_32_5) = 0 & member(v1, all_32_5) = 0 & member(v0, % 168.98/25.88 | all_32_4) = 0 & $i(v2) & $i(v1) & $i(v0)) % 168.98/25.88 | % 168.98/25.88 | BETA: splitting (29) gives: % 168.98/25.88 | % 168.98/25.88 | Case 1: % 168.98/25.88 | | % 168.98/25.88 | | (30) all_32_0 = 0 % 168.98/25.88 | | % 168.98/25.88 | | REDUCE: (11), (30) imply: % 168.98/25.88 | | (31) $false % 168.98/25.88 | | % 168.98/25.88 | | CLOSE: (31) is inconsistent. % 168.98/25.88 | | % 168.98/25.88 | Case 2: % 168.98/25.88 | | % 168.98/25.88 | | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & % 168.98/25.88 | | apply(all_32_1, v0, v1) = 0 & apply(all_32_6, v0, v2) = 0 & % 168.98/25.88 | | member(v2, all_32_5) = 0 & member(v1, all_32_5) = 0 & member(v0, % 168.98/25.88 | | all_32_4) = 0 & $i(v2) & $i(v1) & $i(v0)) % 168.98/25.88 | | % 168.98/25.88 | | DELTA: instantiating (32) with fresh symbols all_41_0, all_41_1, all_41_2 % 168.98/25.88 | | gives: % 168.98/25.89 | | (33) ~ (all_41_0 = all_41_1) & apply(all_32_1, all_41_2, all_41_1) = 0 & % 168.98/25.89 | | apply(all_32_6, all_41_2, all_41_0) = 0 & member(all_41_0, all_32_5) % 168.98/25.89 | | = 0 & member(all_41_1, all_32_5) = 0 & member(all_41_2, all_32_4) = % 168.98/25.89 | | 0 & $i(all_41_0) & $i(all_41_1) & $i(all_41_2) % 168.98/25.89 | | % 168.98/25.89 | | ALPHA: (33) implies: % 168.98/25.89 | | (34) ~ (all_41_0 = all_41_1) % 168.98/25.89 | | (35) $i(all_41_2) % 168.98/25.89 | | (36) $i(all_41_1) % 168.98/25.89 | | (37) $i(all_41_0) % 168.98/25.89 | | (38) member(all_41_2, all_32_4) = 0 % 168.98/25.89 | | (39) member(all_41_1, all_32_5) = 0 % 168.98/25.89 | | (40) member(all_41_0, all_32_5) = 0 % 168.98/25.89 | | (41) apply(all_32_6, all_41_2, all_41_0) = 0 % 168.98/25.89 | | (42) apply(all_32_1, all_41_2, all_41_1) = 0 % 168.98/25.89 | | % 168.98/25.89 | | GROUND_INST: instantiating (1) with all_32_6, all_32_4, all_32_5, all_41_2, % 168.98/25.89 | | simplifying with (14), (15), (16), (22), (35), (38) gives: % 168.98/25.89 | | (43) ? [v0: $i] : (apply(all_32_6, all_41_2, v0) = 0 & member(v0, % 168.98/25.89 | | all_32_5) = 0 & $i(v0)) % 168.98/25.89 | | % 168.98/25.89 | | GROUND_INST: instantiating (1) with all_32_7, all_32_4, all_32_5, all_41_2, % 168.98/25.89 | | simplifying with (13), (15), (16), (21), (35), (38) gives: % 168.98/25.89 | | (44) ? [v0: $i] : (apply(all_32_7, all_41_2, v0) = 0 & member(v0, % 168.98/25.89 | | all_32_5) = 0 & $i(v0)) % 168.98/25.89 | | % 168.98/25.89 | | GROUND_INST: instantiating (7) with all_32_2, all_32_4, all_41_2, % 168.98/25.89 | | simplifying with (16), (18), (27), (35), (38) gives: % 168.98/25.89 | | (45) apply(all_32_2, all_41_2, all_41_2) = 0 % 168.98/25.89 | | % 168.98/25.89 | | GROUND_INST: instantiating (1) with all_32_8, all_32_5, all_32_4, all_41_1, % 168.98/25.89 | | simplifying with (12), (15), (16), (20), (36), (39) gives: % 168.98/25.89 | | (46) ? [v0: $i] : (apply(all_32_8, all_41_1, v0) = 0 & member(v0, % 168.98/25.89 | | all_32_4) = 0 & $i(v0)) % 168.98/25.89 | | % 169.25/25.89 | | GROUND_INST: instantiating (7) with all_32_3, all_32_5, all_41_1, % 169.25/25.89 | | simplifying with (15), (17), (26), (36), (39) gives: % 169.25/25.89 | | (47) apply(all_32_3, all_41_1, all_41_1) = 0 % 169.25/25.89 | | % 169.25/25.89 | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, all_32_5, all_41_2, % 169.25/25.89 | | all_41_1, all_41_0, simplifying with (14), (15), (16), (22), % 169.25/25.89 | | (35), (36), (37), (38), (39), (40) gives: % 169.25/25.89 | | (48) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.25/25.89 | | all_41_2, all_41_0) = v1 & apply(all_32_6, all_41_2, all_41_1) = % 169.25/25.89 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.25/25.89 | | % 169.25/25.90 | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, all_32_5, all_41_2, % 169.25/25.90 | | all_41_0, all_41_1, simplifying with (14), (15), (16), (22), % 169.25/25.90 | | (35), (36), (37), (38), (39), (40) gives: % 169.25/25.90 | | (49) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.25/25.90 | | all_41_2, all_41_0) = v0 & apply(all_32_6, all_41_2, all_41_1) = % 169.25/25.90 | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.25/25.90 | | % 169.25/25.90 | | GROUND_INST: instantiating (2) with all_32_7, all_32_4, all_32_5, all_41_2, % 169.25/25.90 | | all_41_1, all_41_0, simplifying with (13), (15), (16), (21), % 169.25/25.90 | | (35), (36), (37), (38), (39), (40) gives: % 169.25/25.90 | | (50) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_7, % 169.25/25.90 | | all_41_2, all_41_0) = v1 & apply(all_32_7, all_41_2, all_41_1) = % 169.25/25.90 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.25/25.90 | | % 169.25/25.90 | | GROUND_INST: instantiating (2) with all_32_7, all_32_4, all_32_5, all_41_2, % 169.25/25.90 | | all_41_0, all_41_1, simplifying with (13), (15), (16), (21), % 169.25/25.90 | | (35), (36), (37), (38), (39), (40) gives: % 169.25/25.90 | | (51) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_7, % 169.25/25.90 | | all_41_2, all_41_0) = v0 & apply(all_32_7, all_41_2, all_41_1) = % 169.25/25.90 | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.25/25.90 | | % 169.25/25.90 | | GROUND_INST: instantiating (1) with all_32_8, all_32_5, all_32_4, all_41_0, % 169.25/25.90 | | simplifying with (12), (15), (16), (20), (37), (40) gives: % 169.25/25.90 | | (52) ? [v0: $i] : (apply(all_32_8, all_41_0, v0) = 0 & member(v0, % 169.25/25.90 | | all_32_4) = 0 & $i(v0)) % 169.25/25.90 | | % 169.25/25.90 | | GROUND_INST: instantiating (7) with all_32_3, all_32_5, all_41_0, % 169.25/25.90 | | simplifying with (15), (17), (26), (37), (40) gives: % 169.25/25.90 | | (53) apply(all_32_3, all_41_0, all_41_0) = 0 % 169.25/25.90 | | % 169.25/25.90 | | GROUND_INST: instantiating (3) with all_32_6, all_32_4, all_32_5, all_41_2, % 169.25/25.90 | | all_41_1, all_41_0, simplifying with (14), (15), (16), (22), % 169.25/25.90 | | (35), (36), (37), (39), (41) gives: % 169.25/25.91 | | (54) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 169.25/25.91 | | (apply(all_32_6, all_41_2, all_41_1) = v2 & member(all_41_0, % 169.25/25.91 | | all_32_5) = v1 & member(all_41_2, all_32_4) = v0 & ( ~ (v2 = 0) % 169.25/25.91 | | | ~ (v1 = 0) | ~ (v0 = 0))) % 169.25/25.91 | | % 169.25/25.91 | | GROUND_INST: instantiating (inverse_function) with all_32_8, all_32_5, % 169.25/25.91 | | all_32_4, all_41_1, all_41_2, all_32_1, 0, simplifying with % 169.25/25.91 | | (12), (15), (16), (28), (35), (36), (42) gives: % 169.25/25.91 | | (55) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_8, % 169.25/25.91 | | all_41_1, all_41_2) = v2 & member(all_41_1, all_32_5) = v0 & % 169.25/25.91 | | member(all_41_2, all_32_4) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 % 169.25/25.91 | | = 0)) % 169.25/25.91 | | % 169.25/25.91 | | DELTA: instantiating (46) with fresh symbol all_49_0 gives: % 169.25/25.91 | | (56) apply(all_32_8, all_41_1, all_49_0) = 0 & member(all_49_0, all_32_4) % 169.25/25.91 | | = 0 & $i(all_49_0) % 169.25/25.91 | | % 169.25/25.91 | | ALPHA: (56) implies: % 169.25/25.91 | | (57) $i(all_49_0) % 169.25/25.91 | | (58) member(all_49_0, all_32_4) = 0 % 169.25/25.91 | | (59) apply(all_32_8, all_41_1, all_49_0) = 0 % 169.25/25.91 | | % 169.25/25.91 | | DELTA: instantiating (52) with fresh symbol all_51_0 gives: % 169.25/25.91 | | (60) apply(all_32_8, all_41_0, all_51_0) = 0 & member(all_51_0, all_32_4) % 169.25/25.91 | | = 0 & $i(all_51_0) % 169.25/25.91 | | % 169.25/25.91 | | ALPHA: (60) implies: % 169.25/25.91 | | (61) $i(all_51_0) % 169.25/25.91 | | (62) member(all_51_0, all_32_4) = 0 % 169.25/25.91 | | (63) apply(all_32_8, all_41_0, all_51_0) = 0 % 169.25/25.91 | | % 169.25/25.91 | | DELTA: instantiating (44) with fresh symbol all_53_0 gives: % 169.25/25.91 | | (64) apply(all_32_7, all_41_2, all_53_0) = 0 & member(all_53_0, all_32_5) % 169.25/25.91 | | = 0 & $i(all_53_0) % 169.25/25.91 | | % 169.25/25.91 | | ALPHA: (64) implies: % 169.25/25.91 | | (65) $i(all_53_0) % 169.25/25.91 | | (66) member(all_53_0, all_32_5) = 0 % 169.25/25.91 | | % 169.25/25.91 | | DELTA: instantiating (43) with fresh symbol all_55_0 gives: % 169.25/25.91 | | (67) apply(all_32_6, all_41_2, all_55_0) = 0 & member(all_55_0, all_32_5) % 169.25/25.91 | | = 0 & $i(all_55_0) % 169.25/25.91 | | % 169.25/25.91 | | ALPHA: (67) implies: % 169.25/25.91 | | (68) $i(all_55_0) % 169.25/25.91 | | (69) member(all_55_0, all_32_5) = 0 % 169.25/25.91 | | (70) apply(all_32_6, all_41_2, all_55_0) = 0 % 169.25/25.91 | | % 169.25/25.91 | | DELTA: instantiating (55) with fresh symbols all_57_0, all_57_1, all_57_2 % 169.25/25.91 | | gives: % 169.25/25.91 | | (71) apply(all_32_8, all_41_1, all_41_2) = all_57_0 & member(all_41_1, % 169.25/25.91 | | all_32_5) = all_57_2 & member(all_41_2, all_32_4) = all_57_1 & ( ~ % 169.25/25.91 | | (all_57_1 = 0) | ~ (all_57_2 = 0) | all_57_0 = 0) % 169.25/25.91 | | % 169.25/25.91 | | ALPHA: (71) implies: % 169.25/25.91 | | (72) member(all_41_2, all_32_4) = all_57_1 % 169.25/25.91 | | (73) member(all_41_1, all_32_5) = all_57_2 % 169.25/25.91 | | (74) apply(all_32_8, all_41_1, all_41_2) = all_57_0 % 169.25/25.91 | | (75) ~ (all_57_1 = 0) | ~ (all_57_2 = 0) | all_57_0 = 0 % 169.25/25.91 | | % 169.25/25.91 | | BETA: splitting (49) gives: % 169.25/25.91 | | % 169.25/25.91 | | Case 1: % 169.25/25.91 | | | % 169.25/25.91 | | | (76) all_41_0 = all_41_1 % 169.25/25.91 | | | % 169.25/25.91 | | | REDUCE: (34), (76) imply: % 169.25/25.91 | | | (77) $false % 169.25/25.91 | | | % 169.25/25.91 | | | CLOSE: (77) is inconsistent. % 169.25/25.91 | | | % 169.25/25.91 | | Case 2: % 169.25/25.91 | | | % 169.25/25.91 | | | (78) ? [v0: any] : ? [v1: any] : (apply(all_32_6, all_41_2, all_41_0) % 169.25/25.91 | | | = v0 & apply(all_32_6, all_41_2, all_41_1) = v1 & ( ~ (v1 = 0) | % 169.25/25.91 | | | ~ (v0 = 0))) % 169.25/25.91 | | | % 169.25/25.91 | | | DELTA: instantiating (78) with fresh symbols all_63_0, all_63_1 gives: % 169.25/25.91 | | | (79) apply(all_32_6, all_41_2, all_41_0) = all_63_1 & apply(all_32_6, % 169.25/25.91 | | | all_41_2, all_41_1) = all_63_0 & ( ~ (all_63_0 = 0) | ~ % 169.25/25.91 | | | (all_63_1 = 0)) % 169.25/25.91 | | | % 169.25/25.91 | | | ALPHA: (79) implies: % 169.25/25.91 | | | (80) apply(all_32_6, all_41_2, all_41_0) = all_63_1 % 169.25/25.91 | | | % 169.25/25.91 | | | BETA: splitting (48) gives: % 169.25/25.91 | | | % 169.25/25.91 | | | Case 1: % 169.25/25.91 | | | | % 169.25/25.91 | | | | (81) all_41_0 = all_41_1 % 169.25/25.91 | | | | % 169.25/25.91 | | | | REDUCE: (34), (81) imply: % 169.25/25.91 | | | | (82) $false % 169.25/25.91 | | | | % 169.25/25.91 | | | | CLOSE: (82) is inconsistent. % 169.25/25.91 | | | | % 169.25/25.91 | | | Case 2: % 169.25/25.91 | | | | % 169.25/25.91 | | | | (83) ? [v0: any] : ? [v1: any] : (apply(all_32_6, all_41_2, % 169.25/25.91 | | | | all_41_0) = v1 & apply(all_32_6, all_41_2, all_41_1) = v0 & % 169.25/25.91 | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.25/25.91 | | | | % 169.25/25.91 | | | | DELTA: instantiating (83) with fresh symbols all_68_0, all_68_1 gives: % 169.25/25.91 | | | | (84) apply(all_32_6, all_41_2, all_41_0) = all_68_0 & apply(all_32_6, % 169.25/25.91 | | | | all_41_2, all_41_1) = all_68_1 & ( ~ (all_68_0 = 0) | ~ % 169.25/25.91 | | | | (all_68_1 = 0)) % 169.25/25.91 | | | | % 169.25/25.91 | | | | ALPHA: (84) implies: % 169.25/25.91 | | | | (85) apply(all_32_6, all_41_2, all_41_0) = all_68_0 % 169.25/25.91 | | | | % 169.25/25.91 | | | | BETA: splitting (54) gives: % 169.25/25.91 | | | | % 169.25/25.91 | | | | Case 1: % 169.25/25.91 | | | | | % 169.25/25.91 | | | | | (86) all_41_0 = all_41_1 % 169.25/25.91 | | | | | % 169.25/25.91 | | | | | REDUCE: (34), (86) imply: % 169.25/25.91 | | | | | (87) $false % 169.25/25.91 | | | | | % 169.25/25.92 | | | | | CLOSE: (87) is inconsistent. % 169.25/25.92 | | | | | % 169.25/25.92 | | | | Case 2: % 169.25/25.92 | | | | | % 169.25/25.92 | | | | | (88) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_6, % 169.25/25.92 | | | | | all_41_2, all_41_1) = v2 & member(all_41_0, all_32_5) = v1 % 169.25/25.92 | | | | | & member(all_41_2, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = % 169.25/25.92 | | | | | 0) | ~ (v0 = 0))) % 169.25/25.92 | | | | | % 169.25/25.92 | | | | | DELTA: instantiating (88) with fresh symbols all_73_0, all_73_1, % 169.25/25.92 | | | | | all_73_2 gives: % 169.25/25.92 | | | | | (89) apply(all_32_6, all_41_2, all_41_1) = all_73_0 & % 169.25/25.92 | | | | | member(all_41_0, all_32_5) = all_73_1 & member(all_41_2, % 169.25/25.92 | | | | | all_32_4) = all_73_2 & ( ~ (all_73_0 = 0) | ~ (all_73_1 = % 169.25/25.92 | | | | | 0) | ~ (all_73_2 = 0)) % 169.25/25.92 | | | | | % 169.25/25.92 | | | | | ALPHA: (89) implies: % 169.25/25.92 | | | | | (90) member(all_41_2, all_32_4) = all_73_2 % 169.25/25.92 | | | | | (91) member(all_41_0, all_32_5) = all_73_1 % 169.25/25.92 | | | | | % 169.25/25.92 | | | | | BETA: splitting (51) gives: % 169.25/25.92 | | | | | % 169.25/25.92 | | | | | Case 1: % 169.25/25.92 | | | | | | % 169.25/25.92 | | | | | | (92) all_41_0 = all_41_1 % 169.25/25.92 | | | | | | % 169.25/25.92 | | | | | | REDUCE: (34), (92) imply: % 169.25/25.92 | | | | | | (93) $false % 169.25/25.92 | | | | | | % 169.25/25.92 | | | | | | CLOSE: (93) is inconsistent. % 169.25/25.92 | | | | | | % 169.25/25.92 | | | | | Case 2: % 169.25/25.92 | | | | | | % 169.25/25.92 | | | | | | (94) ? [v0: any] : ? [v1: any] : (apply(all_32_7, all_41_2, % 169.25/25.92 | | | | | | all_41_0) = v0 & apply(all_32_7, all_41_2, all_41_1) = % 169.25/25.92 | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.25/25.92 | | | | | | % 169.25/25.92 | | | | | | DELTA: instantiating (94) with fresh symbols all_78_0, all_78_1 % 169.25/25.92 | | | | | | gives: % 169.25/25.92 | | | | | | (95) apply(all_32_7, all_41_2, all_41_0) = all_78_1 & % 169.25/25.92 | | | | | | apply(all_32_7, all_41_2, all_41_1) = all_78_0 & ( ~ % 169.25/25.92 | | | | | | (all_78_0 = 0) | ~ (all_78_1 = 0)) % 169.25/25.92 | | | | | | % 169.25/25.92 | | | | | | ALPHA: (95) implies: % 169.25/25.92 | | | | | | (96) apply(all_32_7, all_41_2, all_41_1) = all_78_0 % 169.25/25.92 | | | | | | (97) apply(all_32_7, all_41_2, all_41_0) = all_78_1 % 169.25/25.92 | | | | | | (98) ~ (all_78_0 = 0) | ~ (all_78_1 = 0) % 169.25/25.92 | | | | | | % 169.25/25.92 | | | | | | BETA: splitting (50) gives: % 169.25/25.92 | | | | | | % 169.25/25.92 | | | | | | Case 1: % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | (99) all_41_0 = all_41_1 % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | REDUCE: (34), (99) imply: % 169.25/25.92 | | | | | | | (100) $false % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | CLOSE: (100) is inconsistent. % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | Case 2: % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | (101) ? [v0: any] : ? [v1: any] : (apply(all_32_7, all_41_2, % 169.25/25.92 | | | | | | | all_41_0) = v1 & apply(all_32_7, all_41_2, all_41_1) % 169.25/25.92 | | | | | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | DELTA: instantiating (101) with fresh symbols all_83_0, all_83_1 % 169.25/25.92 | | | | | | | gives: % 169.25/25.92 | | | | | | | (102) apply(all_32_7, all_41_2, all_41_0) = all_83_0 & % 169.25/25.92 | | | | | | | apply(all_32_7, all_41_2, all_41_1) = all_83_1 & ( ~ % 169.25/25.92 | | | | | | | (all_83_0 = 0) | ~ (all_83_1 = 0)) % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | ALPHA: (102) implies: % 169.25/25.92 | | | | | | | (103) apply(all_32_7, all_41_2, all_41_1) = all_83_1 % 169.25/25.92 | | | | | | | (104) apply(all_32_7, all_41_2, all_41_0) = all_83_0 % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | GROUND_INST: instantiating (8) with 0, all_73_2, all_32_4, % 169.25/25.92 | | | | | | | all_41_2, simplifying with (38), (90) gives: % 169.25/25.92 | | | | | | | (105) all_73_2 = 0 % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | GROUND_INST: instantiating (8) with all_57_1, all_73_2, all_32_4, % 169.25/25.92 | | | | | | | all_41_2, simplifying with (72), (90) gives: % 169.25/25.92 | | | | | | | (106) all_73_2 = all_57_1 % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | GROUND_INST: instantiating (8) with 0, all_57_2, all_32_5, % 169.25/25.92 | | | | | | | all_41_1, simplifying with (39), (73) gives: % 169.25/25.92 | | | | | | | (107) all_57_2 = 0 % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | GROUND_INST: instantiating (8) with 0, all_73_1, all_32_5, % 169.25/25.92 | | | | | | | all_41_0, simplifying with (40), (91) gives: % 169.25/25.92 | | | | | | | (108) all_73_1 = 0 % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | GROUND_INST: instantiating (9) with all_78_0, all_83_1, all_41_1, % 169.25/25.92 | | | | | | | all_41_2, all_32_7, simplifying with (96), (103) % 169.25/25.92 | | | | | | | gives: % 169.25/25.92 | | | | | | | (109) all_83_1 = all_78_0 % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | GROUND_INST: instantiating (9) with all_78_1, all_83_0, all_41_0, % 169.25/25.92 | | | | | | | all_41_2, all_32_7, simplifying with (97), (104) % 169.25/25.92 | | | | | | | gives: % 169.25/25.92 | | | | | | | (110) all_83_0 = all_78_1 % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | GROUND_INST: instantiating (9) with 0, all_68_0, all_41_0, % 169.25/25.92 | | | | | | | all_41_2, all_32_6, simplifying with (41), (85) % 169.25/25.92 | | | | | | | gives: % 169.25/25.92 | | | | | | | (111) all_68_0 = 0 % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | GROUND_INST: instantiating (9) with all_63_1, all_68_0, all_41_0, % 169.25/25.92 | | | | | | | all_41_2, all_32_6, simplifying with (80), (85) % 169.25/25.92 | | | | | | | gives: % 169.25/25.92 | | | | | | | (112) all_68_0 = all_63_1 % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | COMBINE_EQS: (105), (106) imply: % 169.25/25.92 | | | | | | | (113) all_57_1 = 0 % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | SIMP: (113) implies: % 169.25/25.92 | | | | | | | (114) all_57_1 = 0 % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | COMBINE_EQS: (111), (112) imply: % 169.25/25.92 | | | | | | | (115) all_63_1 = 0 % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | SIMP: (115) implies: % 169.25/25.92 | | | | | | | (116) all_63_1 = 0 % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | BETA: splitting (75) gives: % 169.25/25.92 | | | | | | | % 169.25/25.92 | | | | | | | Case 1: % 169.25/25.92 | | | | | | | | % 169.25/25.92 | | | | | | | | (117) ~ (all_57_1 = 0) % 169.25/25.92 | | | | | | | | % 169.25/25.92 | | | | | | | | REDUCE: (114), (117) imply: % 169.25/25.92 | | | | | | | | (118) $false % 169.25/25.92 | | | | | | | | % 169.25/25.92 | | | | | | | | CLOSE: (118) is inconsistent. % 169.25/25.92 | | | | | | | | % 169.25/25.92 | | | | | | | Case 2: % 169.25/25.92 | | | | | | | | % 169.25/25.92 | | | | | | | | (119) ~ (all_57_2 = 0) | all_57_0 = 0 % 169.25/25.92 | | | | | | | | % 169.25/25.92 | | | | | | | | BETA: splitting (119) gives: % 169.25/25.92 | | | | | | | | % 169.25/25.92 | | | | | | | | Case 1: % 169.25/25.92 | | | | | | | | | % 169.25/25.92 | | | | | | | | | (120) ~ (all_57_2 = 0) % 169.25/25.92 | | | | | | | | | % 169.25/25.92 | | | | | | | | | REDUCE: (107), (120) imply: % 169.25/25.92 | | | | | | | | | (121) $false % 169.25/25.92 | | | | | | | | | % 169.25/25.92 | | | | | | | | | CLOSE: (121) is inconsistent. % 169.25/25.92 | | | | | | | | | % 169.25/25.92 | | | | | | | | Case 2: % 169.25/25.92 | | | | | | | | | % 169.25/25.92 | | | | | | | | | (122) all_57_0 = 0 % 169.25/25.93 | | | | | | | | | % 169.25/25.93 | | | | | | | | | REDUCE: (74), (122) imply: % 169.25/25.93 | | | | | | | | | (123) apply(all_32_8, all_41_1, all_41_2) = 0 % 169.25/25.93 | | | | | | | | | % 169.25/25.93 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.25/25.93 | | | | | | | | | all_32_5, all_49_0, all_41_1, all_41_0, % 169.25/25.93 | | | | | | | | | simplifying with (14), (15), (16), (22), (36), % 169.25/25.93 | | | | | | | | | (37), (39), (40), (57), (58) gives: % 169.25/25.93 | | | | | | | | | (124) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] : % 169.25/25.93 | | | | | | | | | (apply(all_32_6, all_49_0, all_41_0) = v1 & % 169.25/25.93 | | | | | | | | | apply(all_32_6, all_49_0, all_41_1) = v0 & ( ~ (v1 % 169.25/25.93 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.93 | | | | | | | | | % 169.25/25.93 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.25/25.93 | | | | | | | | | all_32_5, all_49_0, all_41_0, all_41_1, % 169.25/25.93 | | | | | | | | | simplifying with (14), (15), (16), (22), (36), % 169.25/25.93 | | | | | | | | | (37), (39), (40), (57), (58) gives: % 169.25/25.93 | | | | | | | | | (125) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] : % 169.25/25.93 | | | | | | | | | (apply(all_32_6, all_49_0, all_41_0) = v0 & % 169.25/25.93 | | | | | | | | | apply(all_32_6, all_49_0, all_41_1) = v1 & ( ~ (v1 % 169.25/25.93 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.93 | | | | | | | | | % 169.25/25.93 | | | | | | | | | GROUND_INST: instantiating (1) with all_32_6, all_32_4, % 169.25/25.93 | | | | | | | | | all_32_5, all_49_0, simplifying with (14), (15), % 169.25/25.93 | | | | | | | | | (16), (22), (57), (58) gives: % 169.25/25.93 | | | | | | | | | (126) ? [v0: $i] : (apply(all_32_6, all_49_0, v0) = 0 & % 169.25/25.93 | | | | | | | | | member(v0, all_32_5) = 0 & $i(v0)) % 169.25/25.93 | | | | | | | | | % 169.25/25.93 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.25/25.93 | | | | | | | | | all_32_4, all_41_1, all_49_0, all_41_2, % 169.25/25.93 | | | | | | | | | simplifying with (12), (15), (16), (20), (35), % 169.25/25.93 | | | | | | | | | (36), (38), (39), (57), (58) gives: % 169.25/25.93 | | | | | | | | | (127) all_49_0 = all_41_2 | ? [v0: any] : ? [v1: any] : % 169.25/25.93 | | | | | | | | | (apply(all_32_8, all_41_1, all_49_0) = v0 & % 169.25/25.93 | | | | | | | | | apply(all_32_8, all_41_1, all_41_2) = v1 & ( ~ (v1 % 169.25/25.93 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.93 | | | | | | | | | % 169.25/25.93 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.25/25.93 | | | | | | | | | all_32_5, all_51_0, all_41_0, all_41_1, % 169.25/25.93 | | | | | | | | | simplifying with (14), (15), (16), (22), (36), % 169.25/25.93 | | | | | | | | | (37), (39), (40), (61), (62) gives: % 169.25/25.93 | | | | | | | | | (128) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] : % 169.25/25.93 | | | | | | | | | (apply(all_32_6, all_51_0, all_41_0) = v0 & % 169.25/25.93 | | | | | | | | | apply(all_32_6, all_51_0, all_41_1) = v1 & ( ~ (v1 % 169.25/25.93 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.93 | | | | | | | | | % 169.25/25.93 | | | | | | | | | GROUND_INST: instantiating (1) with all_32_6, all_32_4, % 169.25/25.93 | | | | | | | | | all_32_5, all_51_0, simplifying with (14), (15), % 169.25/25.93 | | | | | | | | | (16), (22), (61), (62) gives: % 169.25/25.93 | | | | | | | | | (129) ? [v0: $i] : (apply(all_32_6, all_51_0, v0) = 0 & % 169.25/25.93 | | | | | | | | | member(v0, all_32_5) = 0 & $i(v0)) % 169.25/25.93 | | | | | | | | | % 169.25/25.93 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.25/25.93 | | | | | | | | | all_32_4, all_41_0, all_41_2, all_51_0, % 169.25/25.93 | | | | | | | | | simplifying with (12), (15), (16), (20), (35), % 169.25/25.93 | | | | | | | | | (37), (38), (40), (61), (62) gives: % 169.25/25.93 | | | | | | | | | (130) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : % 169.25/25.93 | | | | | | | | | (apply(all_32_8, all_41_0, all_51_0) = v1 & % 169.25/25.93 | | | | | | | | | apply(all_32_8, all_41_0, all_41_2) = v0 & ( ~ (v1 % 169.25/25.93 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.93 | | | | | | | | | % 169.25/25.93 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.25/25.93 | | | | | | | | | all_32_4, all_41_0, all_51_0, all_41_2, % 169.25/25.93 | | | | | | | | | simplifying with (12), (15), (16), (20), (35), % 169.25/25.93 | | | | | | | | | (37), (38), (40), (61), (62) gives: % 169.25/25.93 | | | | | | | | | (131) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : % 169.25/25.93 | | | | | | | | | (apply(all_32_8, all_41_0, all_51_0) = v0 & % 169.25/25.93 | | | | | | | | | apply(all_32_8, all_41_0, all_41_2) = v1 & ( ~ (v1 % 169.25/25.93 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.93 | | | | | | | | | % 169.25/25.93 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.25/25.93 | | | | | | | | | all_32_4, all_41_0, all_49_0, all_51_0, % 169.25/25.93 | | | | | | | | | simplifying with (12), (15), (16), (20), (37), % 169.25/25.93 | | | | | | | | | (40), (57), (58), (61), (62) gives: % 169.25/25.93 | | | | | | | | | (132) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : % 169.25/25.93 | | | | | | | | | (apply(all_32_8, all_41_0, all_51_0) = v1 & % 169.25/25.93 | | | | | | | | | apply(all_32_8, all_41_0, all_49_0) = v0 & ( ~ (v1 % 169.25/25.93 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.93 | | | | | | | | | % 169.25/25.93 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.25/25.93 | | | | | | | | | all_32_4, all_41_0, all_51_0, all_49_0, % 169.25/25.93 | | | | | | | | | simplifying with (12), (15), (16), (20), (37), % 169.25/25.93 | | | | | | | | | (40), (57), (58), (61), (62) gives: % 169.25/25.93 | | | | | | | | | (133) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : % 169.25/25.93 | | | | | | | | | (apply(all_32_8, all_41_0, all_51_0) = v0 & % 169.25/25.94 | | | | | | | | | apply(all_32_8, all_41_0, all_49_0) = v1 & ( ~ (v1 % 169.25/25.94 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.94 | | | | | | | | | % 169.25/25.94 | | | | | | | | | GROUND_INST: instantiating (1) with all_32_8, all_32_5, % 169.25/25.94 | | | | | | | | | all_32_4, all_53_0, simplifying with (12), (15), % 169.25/25.94 | | | | | | | | | (16), (20), (65), (66) gives: % 169.25/25.94 | | | | | | | | | (134) ? [v0: $i] : (apply(all_32_8, all_53_0, v0) = 0 & % 169.25/25.94 | | | | | | | | | member(v0, all_32_4) = 0 & $i(v0)) % 169.25/25.94 | | | | | | | | | % 169.25/25.94 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.25/25.94 | | | | | | | | | all_32_5, all_41_2, all_55_0, all_41_0, % 169.25/25.94 | | | | | | | | | simplifying with (14), (15), (16), (22), (35), % 169.25/25.94 | | | | | | | | | (37), (38), (40), (68), (69) gives: % 169.25/25.94 | | | | | | | | | (135) all_55_0 = all_41_0 | ? [v0: any] : ? [v1: any] : % 169.25/25.94 | | | | | | | | | (apply(all_32_6, all_41_2, all_55_0) = v0 & % 169.25/25.94 | | | | | | | | | apply(all_32_6, all_41_2, all_41_0) = v1 & ( ~ (v1 % 169.25/25.94 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.94 | | | | | | | | | % 169.25/25.94 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.25/25.94 | | | | | | | | | all_32_5, all_49_0, all_41_0, all_55_0, % 169.25/25.94 | | | | | | | | | simplifying with (14), (15), (16), (22), (37), % 169.25/25.94 | | | | | | | | | (40), (57), (58), (68), (69) gives: % 169.25/25.94 | | | | | | | | | (136) all_55_0 = all_41_0 | ? [v0: any] : ? [v1: any] : % 169.25/25.94 | | | | | | | | | (apply(all_32_6, all_49_0, all_55_0) = v1 & % 169.25/25.94 | | | | | | | | | apply(all_32_6, all_49_0, all_41_0) = v0 & ( ~ (v1 % 169.25/25.94 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.94 | | | | | | | | | % 169.25/25.94 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.25/25.94 | | | | | | | | | all_32_5, all_49_0, all_55_0, all_41_0, % 169.25/25.94 | | | | | | | | | simplifying with (14), (15), (16), (22), (37), % 169.25/25.94 | | | | | | | | | (40), (57), (58), (68), (69) gives: % 169.25/25.94 | | | | | | | | | (137) all_55_0 = all_41_0 | ? [v0: any] : ? [v1: any] : % 169.25/25.94 | | | | | | | | | (apply(all_32_6, all_49_0, all_55_0) = v0 & % 169.25/25.94 | | | | | | | | | apply(all_32_6, all_49_0, all_41_0) = v1 & ( ~ (v1 % 169.25/25.94 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.94 | | | | | | | | | % 169.25/25.94 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_7, all_32_4, % 169.25/25.94 | | | | | | | | | all_32_5, all_51_0, all_41_1, all_55_0, % 169.25/25.94 | | | | | | | | | simplifying with (13), (15), (16), (21), (36), % 169.25/25.94 | | | | | | | | | (39), (61), (62), (68), (69) gives: % 169.25/25.94 | | | | | | | | | (138) all_55_0 = all_41_1 | ? [v0: any] : ? [v1: any] : % 169.25/25.94 | | | | | | | | | (apply(all_32_7, all_51_0, all_55_0) = v1 & % 169.25/25.94 | | | | | | | | | apply(all_32_7, all_51_0, all_41_1) = v0 & ( ~ (v1 % 169.25/25.94 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.94 | | | | | | | | | % 169.25/25.94 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_7, all_32_4, % 169.25/25.94 | | | | | | | | | all_32_5, all_51_0, all_55_0, all_41_1, % 169.25/25.94 | | | | | | | | | simplifying with (13), (15), (16), (21), (36), % 169.25/25.94 | | | | | | | | | (39), (61), (62), (68), (69) gives: % 169.25/25.94 | | | | | | | | | (139) all_55_0 = all_41_1 | ? [v0: any] : ? [v1: any] : % 169.25/25.94 | | | | | | | | | (apply(all_32_7, all_51_0, all_55_0) = v0 & % 169.25/25.94 | | | | | | | | | apply(all_32_7, all_51_0, all_41_1) = v1 & ( ~ (v1 % 169.25/25.94 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.94 | | | | | | | | | % 169.25/25.94 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_7, all_32_4, % 169.25/25.94 | | | | | | | | | all_32_5, all_49_0, all_41_1, all_55_0, % 169.25/25.94 | | | | | | | | | simplifying with (13), (15), (16), (21), (36), % 169.25/25.94 | | | | | | | | | (39), (57), (58), (68), (69) gives: % 169.25/25.94 | | | | | | | | | (140) all_55_0 = all_41_1 | ? [v0: any] : ? [v1: any] : % 169.25/25.94 | | | | | | | | | (apply(all_32_7, all_49_0, all_55_0) = v1 & % 169.25/25.94 | | | | | | | | | apply(all_32_7, all_49_0, all_41_1) = v0 & ( ~ (v1 % 169.25/25.94 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.94 | | | | | | | | | % 169.25/25.94 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_7, all_32_4, % 169.25/25.94 | | | | | | | | | all_32_5, all_49_0, all_55_0, all_41_1, % 169.25/25.94 | | | | | | | | | simplifying with (13), (15), (16), (21), (36), % 169.25/25.94 | | | | | | | | | (39), (57), (58), (68), (69) gives: % 169.25/25.94 | | | | | | | | | (141) all_55_0 = all_41_1 | ? [v0: any] : ? [v1: any] : % 169.25/25.94 | | | | | | | | | (apply(all_32_7, all_49_0, all_55_0) = v0 & % 169.25/25.94 | | | | | | | | | apply(all_32_7, all_49_0, all_41_1) = v1 & ( ~ (v1 % 169.25/25.94 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.94 | | | | | | | | | % 169.25/25.94 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.25/25.94 | | | | | | | | | all_32_4, all_55_0, all_51_0, all_41_2, % 169.25/25.94 | | | | | | | | | simplifying with (12), (15), (16), (20), (35), % 169.25/25.94 | | | | | | | | | (38), (61), (62), (68), (69) gives: % 169.25/25.94 | | | | | | | | | (142) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : % 169.25/25.94 | | | | | | | | | (apply(all_32_8, all_55_0, all_51_0) = v0 & % 169.25/25.94 | | | | | | | | | apply(all_32_8, all_55_0, all_41_2) = v1 & ( ~ (v1 % 169.25/25.94 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.94 | | | | | | | | | % 169.25/25.94 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.25/25.94 | | | | | | | | | all_32_4, all_55_0, all_41_2, all_51_0, % 169.25/25.94 | | | | | | | | | simplifying with (12), (15), (16), (20), (35), % 169.25/25.94 | | | | | | | | | (38), (61), (62), (68), (69) gives: % 169.25/25.94 | | | | | | | | | (143) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : % 169.25/25.94 | | | | | | | | | (apply(all_32_8, all_55_0, all_51_0) = v1 & % 169.25/25.94 | | | | | | | | | apply(all_32_8, all_55_0, all_41_2) = v0 & ( ~ (v1 % 169.25/25.94 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.94 | | | | | | | | | % 169.25/25.94 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.25/25.94 | | | | | | | | | all_32_4, all_55_0, all_49_0, all_51_0, % 169.25/25.94 | | | | | | | | | simplifying with (12), (15), (16), (20), (57), % 169.25/25.94 | | | | | | | | | (58), (61), (62), (68), (69) gives: % 169.25/25.94 | | | | | | | | | (144) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : % 169.25/25.94 | | | | | | | | | (apply(all_32_8, all_55_0, all_51_0) = v1 & % 169.25/25.94 | | | | | | | | | apply(all_32_8, all_55_0, all_49_0) = v0 & ( ~ (v1 % 169.25/25.94 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.94 | | | | | | | | | % 169.25/25.94 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.25/25.94 | | | | | | | | | all_32_4, all_55_0, all_51_0, all_49_0, % 169.25/25.94 | | | | | | | | | simplifying with (12), (15), (16), (20), (57), % 169.25/25.94 | | | | | | | | | (58), (61), (62), (68), (69) gives: % 169.25/25.94 | | | | | | | | | (145) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : % 169.25/25.94 | | | | | | | | | (apply(all_32_8, all_55_0, all_51_0) = v0 & % 169.25/25.94 | | | | | | | | | apply(all_32_8, all_55_0, all_49_0) = v1 & ( ~ (v1 % 169.25/25.94 | | | | | | | | | = 0) | ~ (v0 = 0))) % 169.25/25.94 | | | | | | | | | % 169.25/25.95 | | | | | | | | | GROUND_INST: instantiating (1) with all_32_8, all_32_5, % 169.25/25.95 | | | | | | | | | all_32_4, all_55_0, simplifying with (12), (15), % 169.25/25.95 | | | | | | | | | (16), (20), (68), (69) gives: % 169.25/25.95 | | | | | | | | | (146) ? [v0: $i] : (apply(all_32_8, all_55_0, v0) = 0 & % 169.25/25.95 | | | | | | | | | member(v0, all_32_4) = 0 & $i(v0)) % 169.25/25.95 | | | | | | | | | % 169.25/25.95 | | | | | | | | | GROUND_INST: instantiating (4) with all_32_8, all_32_5, % 169.25/25.95 | | | | | | | | | all_32_4, all_41_1, all_49_0, all_41_2, % 169.25/25.95 | | | | | | | | | simplifying with (12), (15), (16), (20), (35), % 169.25/25.95 | | | | | | | | | (36), (57), (59), (123) gives: % 169.25/25.95 | | | | | | | | | (147) all_49_0 = all_41_2 | ? [v0: any] : ? [v1: any] : % 169.25/25.95 | | | | | | | | | ? [v2: any] : (member(all_49_0, all_32_4) = v1 & % 169.25/25.95 | | | | | | | | | member(all_41_1, all_32_5) = v0 & member(all_41_2, % 169.25/25.95 | | | | | | | | | all_32_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 169.25/25.95 | | | | | | | | | (v0 = 0))) % 169.25/25.95 | | | | | | | | | % 169.25/25.95 | | | | | | | | | GROUND_INST: instantiating (3) with all_32_8, all_32_5, % 169.25/25.95 | | | | | | | | | all_32_4, all_41_1, all_41_2, all_49_0, % 169.25/25.95 | | | | | | | | | simplifying with (12), (15), (16), (20), (35), % 169.25/25.95 | | | | | | | | | (36), (38), (57), (59) gives: % 169.25/25.95 | | | | | | | | | (148) all_49_0 = all_41_2 | ? [v0: any] : ? [v1: any] : % 169.25/25.95 | | | | | | | | | ? [v2: any] : (apply(all_32_8, all_41_1, all_41_2) = % 169.25/25.95 | | | | | | | | | v2 & member(all_49_0, all_32_4) = v1 & % 169.25/25.95 | | | | | | | | | member(all_41_1, all_32_5) = v0 & ( ~ (v2 = 0) | ~ % 169.25/25.95 | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.25/25.95 | | | | | | | | | % 169.25/25.95 | | | | | | | | | GROUND_INST: instantiating (3) with all_32_8, all_32_5, % 169.25/25.95 | | | | | | | | | all_32_4, all_41_0, all_41_2, all_51_0, % 169.25/25.95 | | | | | | | | | simplifying with (12), (15), (16), (20), (35), % 169.25/25.95 | | | | | | | | | (37), (38), (61), (63) gives: % 169.25/25.95 | | | | | | | | | (149) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : % 169.25/25.95 | | | | | | | | | ? [v2: any] : (apply(all_32_8, all_41_0, all_41_2) = % 169.25/25.95 | | | | | | | | | v2 & member(all_51_0, all_32_4) = v1 & % 169.25/25.95 | | | | | | | | | member(all_41_0, all_32_5) = v0 & ( ~ (v2 = 0) | ~ % 169.25/25.95 | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.25/25.95 | | | | | | | | | % 169.25/25.95 | | | | | | | | | GROUND_INST: instantiating (3) with all_32_8, all_32_5, % 169.25/25.95 | | | | | | | | | all_32_4, all_41_0, all_49_0, all_51_0, % 169.25/25.95 | | | | | | | | | simplifying with (12), (15), (16), (20), (37), % 169.25/25.95 | | | | | | | | | (57), (58), (61), (63) gives: % 169.25/25.95 | | | | | | | | | (150) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : % 169.25/25.95 | | | | | | | | | ? [v2: any] : (apply(all_32_8, all_41_0, all_49_0) = % 169.25/25.95 | | | | | | | | | v2 & member(all_51_0, all_32_4) = v1 & % 169.25/25.95 | | | | | | | | | member(all_41_0, all_32_5) = v0 & ( ~ (v2 = 0) | ~ % 169.25/25.95 | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.25/25.95 | | | | | | | | | % 169.25/25.95 | | | | | | | | | GROUND_INST: instantiating (3) with all_32_6, all_32_4, % 169.25/25.95 | | | | | | | | | all_32_5, all_41_2, all_41_0, all_55_0, % 169.25/25.95 | | | | | | | | | simplifying with (14), (15), (16), (22), (35), % 169.25/25.95 | | | | | | | | | (37), (40), (68), (70) gives: % 169.25/25.95 | | | | | | | | | (151) all_55_0 = all_41_0 | ? [v0: any] : ? [v1: any] : % 169.25/25.95 | | | | | | | | | ? [v2: any] : (apply(all_32_6, all_41_2, all_41_0) = % 169.25/25.95 | | | | | | | | | v2 & member(all_55_0, all_32_5) = v1 & % 169.25/25.95 | | | | | | | | | member(all_41_2, all_32_4) = v0 & ( ~ (v2 = 0) | ~ % 169.25/25.95 | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.25/25.95 | | | | | | | | | % 169.25/25.95 | | | | | | | | | GROUND_INST: instantiating (5) with all_32_7, all_32_8, % 169.25/25.95 | | | | | | | | | all_32_5, all_32_4, all_32_5, all_41_1, all_41_1, % 169.25/25.95 | | | | | | | | | all_32_3, simplifying with (12), (13), (15), (16), % 169.25/25.95 | | | | | | | | | (24), (36), (47) gives: % 169.53/25.95 | | | | | | | | | (152) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: % 169.53/25.95 | | | | | | | | | int] : ? [v4: int] : ? [v5: int] : ($i(v2) & ((v5 % 169.53/25.95 | | | | | | | | | = 0 & v4 = 0 & v3 = 0 & apply(all_32_7, v2, % 169.53/25.95 | | | | | | | | | all_41_1) = 0 & apply(all_32_8, all_41_1, v2) % 169.53/25.95 | | | | | | | | | = 0 & member(v2, all_32_4) = 0) | % 169.53/25.95 | | | | | | | | | (member(all_41_1, all_32_5) = v1 & % 169.53/25.95 | | | | | | | | | member(all_41_1, all_32_5) = v0 & ( ~ (v1 = 0) % 169.53/25.95 | | | | | | | | | | ~ (v0 = 0))))) % 169.53/25.95 | | | | | | | | | % 169.53/25.95 | | | | | | | | | GROUND_INST: instantiating (5) with all_32_7, all_32_8, % 169.53/25.95 | | | | | | | | | all_32_5, all_32_4, all_32_5, all_41_0, all_41_0, % 169.53/25.95 | | | | | | | | | all_32_3, simplifying with (12), (13), (15), (16), % 169.53/25.95 | | | | | | | | | (24), (37), (53) gives: % 169.53/25.95 | | | | | | | | | (153) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: % 169.53/25.95 | | | | | | | | | int] : ? [v4: int] : ? [v5: int] : ($i(v2) & ((v5 % 169.53/25.95 | | | | | | | | | = 0 & v4 = 0 & v3 = 0 & apply(all_32_7, v2, % 169.53/25.95 | | | | | | | | | all_41_0) = 0 & apply(all_32_8, all_41_0, v2) % 169.53/25.95 | | | | | | | | | = 0 & member(v2, all_32_4) = 0) | % 169.53/25.95 | | | | | | | | | (member(all_41_0, all_32_5) = v1 & % 169.53/25.95 | | | | | | | | | member(all_41_0, all_32_5) = v0 & ( ~ (v1 = 0) % 169.53/25.95 | | | | | | | | | | ~ (v0 = 0))))) % 169.53/25.95 | | | | | | | | | % 169.53/25.95 | | | | | | | | | GROUND_INST: instantiating (5) with all_32_8, all_32_6, % 169.53/25.95 | | | | | | | | | all_32_4, all_32_5, all_32_4, all_41_2, all_41_2, % 169.53/25.95 | | | | | | | | | all_32_2, simplifying with (12), (14), (15), (16), % 169.53/25.95 | | | | | | | | | (23), (35), (45) gives: % 169.53/25.95 | | | | | | | | | (154) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: % 169.53/25.95 | | | | | | | | | int] : ? [v4: int] : ? [v5: int] : ($i(v2) & ((v5 % 169.53/25.95 | | | | | | | | | = 0 & v4 = 0 & v3 = 0 & apply(all_32_6, % 169.53/25.95 | | | | | | | | | all_41_2, v2) = 0 & apply(all_32_8, v2, % 169.53/25.95 | | | | | | | | | all_41_2) = 0 & member(v2, all_32_5) = 0) | % 169.53/25.95 | | | | | | | | | (member(all_41_2, all_32_4) = v1 & % 169.53/25.95 | | | | | | | | | member(all_41_2, all_32_4) = v0 & ( ~ (v1 = 0) % 169.53/25.95 | | | | | | | | | | ~ (v0 = 0))))) % 169.53/25.95 | | | | | | | | | % 169.53/25.95 | | | | | | | | | DELTA: instantiating (129) with fresh symbol all_109_0 gives: % 169.53/25.95 | | | | | | | | | (155) apply(all_32_6, all_51_0, all_109_0) = 0 & % 169.53/25.95 | | | | | | | | | member(all_109_0, all_32_5) = 0 & $i(all_109_0) % 169.53/25.95 | | | | | | | | | % 169.53/25.95 | | | | | | | | | ALPHA: (155) implies: % 169.53/25.95 | | | | | | | | | (156) $i(all_109_0) % 169.53/25.95 | | | | | | | | | (157) member(all_109_0, all_32_5) = 0 % 169.53/25.95 | | | | | | | | | (158) apply(all_32_6, all_51_0, all_109_0) = 0 % 169.53/25.95 | | | | | | | | | % 169.53/25.95 | | | | | | | | | DELTA: instantiating (146) with fresh symbol all_111_0 gives: % 169.53/25.96 | | | | | | | | | (159) apply(all_32_8, all_55_0, all_111_0) = 0 & % 169.53/25.96 | | | | | | | | | member(all_111_0, all_32_4) = 0 & $i(all_111_0) % 169.53/25.96 | | | | | | | | | % 169.53/25.96 | | | | | | | | | ALPHA: (159) implies: % 169.53/25.96 | | | | | | | | | (160) $i(all_111_0) % 169.53/25.96 | | | | | | | | | (161) member(all_111_0, all_32_4) = 0 % 169.55/25.96 | | | | | | | | | (162) apply(all_32_8, all_55_0, all_111_0) = 0 % 169.55/25.96 | | | | | | | | | % 169.55/25.96 | | | | | | | | | DELTA: instantiating (134) with fresh symbol all_113_0 gives: % 169.55/25.96 | | | | | | | | | (163) apply(all_32_8, all_53_0, all_113_0) = 0 & % 169.55/25.96 | | | | | | | | | member(all_113_0, all_32_4) = 0 & $i(all_113_0) % 169.55/25.96 | | | | | | | | | % 169.55/25.96 | | | | | | | | | ALPHA: (163) implies: % 169.55/25.96 | | | | | | | | | (164) $i(all_113_0) % 169.55/25.96 | | | | | | | | | (165) member(all_113_0, all_32_4) = 0 % 169.55/25.96 | | | | | | | | | % 169.55/25.96 | | | | | | | | | DELTA: instantiating (126) with fresh symbol all_117_0 gives: % 169.55/25.96 | | | | | | | | | (166) apply(all_32_6, all_49_0, all_117_0) = 0 & % 169.55/25.96 | | | | | | | | | member(all_117_0, all_32_5) = 0 & $i(all_117_0) % 169.55/25.96 | | | | | | | | | % 169.55/25.96 | | | | | | | | | ALPHA: (166) implies: % 169.55/25.96 | | | | | | | | | (167) $i(all_117_0) % 169.55/25.96 | | | | | | | | | (168) member(all_117_0, all_32_5) = 0 % 169.55/25.96 | | | | | | | | | (169) apply(all_32_6, all_49_0, all_117_0) = 0 % 169.55/25.96 | | | | | | | | | % 169.55/25.96 | | | | | | | | | DELTA: instantiating (154) with fresh symbols all_119_0, % 169.55/25.96 | | | | | | | | | all_119_1, all_119_2, all_119_3, all_119_4, all_119_5 % 169.55/25.96 | | | | | | | | | gives: % 169.55/25.96 | | | | | | | | | (170) $i(all_119_3) & ((all_119_0 = 0 & all_119_1 = 0 & % 169.55/25.96 | | | | | | | | | all_119_2 = 0 & apply(all_32_6, all_41_2, % 169.55/25.96 | | | | | | | | | all_119_3) = 0 & apply(all_32_8, all_119_3, % 169.55/25.96 | | | | | | | | | all_41_2) = 0 & member(all_119_3, all_32_5) = % 169.55/25.96 | | | | | | | | | 0) | (member(all_41_2, all_32_4) = all_119_4 & % 169.55/25.96 | | | | | | | | | member(all_41_2, all_32_4) = all_119_5 & ( ~ % 169.55/25.96 | | | | | | | | | (all_119_4 = 0) | ~ (all_119_5 = 0)))) % 169.55/25.96 | | | | | | | | | % 169.55/25.96 | | | | | | | | | ALPHA: (170) implies: % 169.55/25.96 | | | | | | | | | (171) $i(all_119_3) % 169.55/25.96 | | | | | | | | | (172) (all_119_0 = 0 & all_119_1 = 0 & all_119_2 = 0 & % 169.55/25.96 | | | | | | | | | apply(all_32_6, all_41_2, all_119_3) = 0 & % 169.55/25.96 | | | | | | | | | apply(all_32_8, all_119_3, all_41_2) = 0 & % 169.55/25.96 | | | | | | | | | member(all_119_3, all_32_5) = 0) | % 169.55/25.96 | | | | | | | | | (member(all_41_2, all_32_4) = all_119_4 & % 169.55/25.96 | | | | | | | | | member(all_41_2, all_32_4) = all_119_5 & ( ~ % 169.55/25.96 | | | | | | | | | (all_119_4 = 0) | ~ (all_119_5 = 0))) % 169.55/25.96 | | | | | | | | | % 169.55/25.96 | | | | | | | | | DELTA: instantiating (152) with fresh symbols all_121_0, % 169.55/25.96 | | | | | | | | | all_121_1, all_121_2, all_121_3, all_121_4, all_121_5 % 169.55/25.96 | | | | | | | | | gives: % 169.55/25.96 | | | | | | | | | (173) $i(all_121_3) & ((all_121_0 = 0 & all_121_1 = 0 & % 169.55/25.96 | | | | | | | | | all_121_2 = 0 & apply(all_32_7, all_121_3, % 169.55/25.96 | | | | | | | | | all_41_1) = 0 & apply(all_32_8, all_41_1, % 169.55/25.96 | | | | | | | | | all_121_3) = 0 & member(all_121_3, all_32_4) = % 169.55/25.96 | | | | | | | | | 0) | (member(all_41_1, all_32_5) = all_121_4 & % 169.55/25.96 | | | | | | | | | member(all_41_1, all_32_5) = all_121_5 & ( ~ % 169.55/25.96 | | | | | | | | | (all_121_4 = 0) | ~ (all_121_5 = 0)))) % 169.55/25.96 | | | | | | | | | % 169.55/25.96 | | | | | | | | | ALPHA: (173) implies: % 169.55/25.96 | | | | | | | | | (174) $i(all_121_3) % 169.55/25.96 | | | | | | | | | (175) (all_121_0 = 0 & all_121_1 = 0 & all_121_2 = 0 & % 169.55/25.96 | | | | | | | | | apply(all_32_7, all_121_3, all_41_1) = 0 & % 169.55/25.96 | | | | | | | | | apply(all_32_8, all_41_1, all_121_3) = 0 & % 169.55/25.96 | | | | | | | | | member(all_121_3, all_32_4) = 0) | % 169.55/25.96 | | | | | | | | | (member(all_41_1, all_32_5) = all_121_4 & % 169.55/25.96 | | | | | | | | | member(all_41_1, all_32_5) = all_121_5 & ( ~ % 169.55/25.96 | | | | | | | | | (all_121_4 = 0) | ~ (all_121_5 = 0))) % 169.55/25.96 | | | | | | | | | % 169.55/25.96 | | | | | | | | | DELTA: instantiating (153) with fresh symbols all_123_0, % 169.55/25.96 | | | | | | | | | all_123_1, all_123_2, all_123_3, all_123_4, all_123_5 % 169.55/25.96 | | | | | | | | | gives: % 169.55/25.96 | | | | | | | | | (176) $i(all_123_3) & ((all_123_0 = 0 & all_123_1 = 0 & % 169.55/25.96 | | | | | | | | | all_123_2 = 0 & apply(all_32_7, all_123_3, % 169.55/25.96 | | | | | | | | | all_41_0) = 0 & apply(all_32_8, all_41_0, % 169.55/25.96 | | | | | | | | | all_123_3) = 0 & member(all_123_3, all_32_4) = % 169.55/25.96 | | | | | | | | | 0) | (member(all_41_0, all_32_5) = all_123_4 & % 169.55/25.96 | | | | | | | | | member(all_41_0, all_32_5) = all_123_5 & ( ~ % 169.55/25.96 | | | | | | | | | (all_123_4 = 0) | ~ (all_123_5 = 0)))) % 169.55/25.96 | | | | | | | | | % 169.55/25.96 | | | | | | | | | ALPHA: (176) implies: % 169.55/25.96 | | | | | | | | | (177) $i(all_123_3) % 169.55/25.96 | | | | | | | | | (178) (all_123_0 = 0 & all_123_1 = 0 & all_123_2 = 0 & % 169.55/25.96 | | | | | | | | | apply(all_32_7, all_123_3, all_41_0) = 0 & % 169.55/25.96 | | | | | | | | | apply(all_32_8, all_41_0, all_123_3) = 0 & % 169.55/25.96 | | | | | | | | | member(all_123_3, all_32_4) = 0) | % 169.55/25.96 | | | | | | | | | (member(all_41_0, all_32_5) = all_123_4 & % 169.55/25.96 | | | | | | | | | member(all_41_0, all_32_5) = all_123_5 & ( ~ % 169.55/25.96 | | | | | | | | | (all_123_4 = 0) | ~ (all_123_5 = 0))) % 169.55/25.96 | | | | | | | | | % 169.55/25.96 | | | | | | | | | BETA: splitting (178) gives: % 169.55/25.96 | | | | | | | | | % 169.55/25.96 | | | | | | | | | Case 1: % 169.55/25.96 | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | (179) all_123_0 = 0 & all_123_1 = 0 & all_123_2 = 0 & % 169.55/25.96 | | | | | | | | | | apply(all_32_7, all_123_3, all_41_0) = 0 & % 169.55/25.96 | | | | | | | | | | apply(all_32_8, all_41_0, all_123_3) = 0 & % 169.55/25.96 | | | | | | | | | | member(all_123_3, all_32_4) = 0 % 169.55/25.96 | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | ALPHA: (179) implies: % 169.55/25.96 | | | | | | | | | | (180) member(all_123_3, all_32_4) = 0 % 169.55/25.96 | | | | | | | | | | (181) apply(all_32_8, all_41_0, all_123_3) = 0 % 169.55/25.96 | | | | | | | | | | (182) apply(all_32_7, all_123_3, all_41_0) = 0 % 169.55/25.96 | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | BETA: splitting (125) gives: % 169.55/25.96 | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | Case 1: % 169.55/25.96 | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | | (183) all_41_0 = all_41_1 % 169.55/25.96 | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | | REDUCE: (34), (183) imply: % 169.55/25.96 | | | | | | | | | | | (184) $false % 169.55/25.96 | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | | CLOSE: (184) is inconsistent. % 169.55/25.96 | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | Case 2: % 169.55/25.96 | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | | (185) ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.55/25.96 | | | | | | | | | | | all_49_0, all_41_0) = v0 & apply(all_32_6, % 169.55/25.96 | | | | | | | | | | | all_49_0, all_41_1) = v1 & ( ~ (v1 = 0) | ~ % 169.55/25.96 | | | | | | | | | | | (v0 = 0))) % 169.55/25.96 | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | | DELTA: instantiating (185) with fresh symbols all_132_0, % 169.55/25.96 | | | | | | | | | | | all_132_1 gives: % 169.55/25.96 | | | | | | | | | | | (186) apply(all_32_6, all_49_0, all_41_0) = all_132_1 & % 169.55/25.96 | | | | | | | | | | | apply(all_32_6, all_49_0, all_41_1) = all_132_0 & % 169.55/25.96 | | | | | | | | | | | ( ~ (all_132_0 = 0) | ~ (all_132_1 = 0)) % 169.55/25.96 | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | | ALPHA: (186) implies: % 169.55/25.96 | | | | | | | | | | | (187) apply(all_32_6, all_49_0, all_41_0) = all_132_1 % 169.55/25.96 | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | | BETA: splitting (124) gives: % 169.55/25.96 | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | | Case 1: % 169.55/25.96 | | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | | | (188) all_41_0 = all_41_1 % 169.55/25.96 | | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | | | REDUCE: (34), (188) imply: % 169.55/25.96 | | | | | | | | | | | | (189) $false % 169.55/25.96 | | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | | | CLOSE: (189) is inconsistent. % 169.55/25.96 | | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | | Case 2: % 169.55/25.96 | | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | | | (190) ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.55/25.96 | | | | | | | | | | | | all_49_0, all_41_0) = v1 & apply(all_32_6, % 169.55/25.96 | | | | | | | | | | | | all_49_0, all_41_1) = v0 & ( ~ (v1 = 0) | ~ % 169.55/25.96 | | | | | | | | | | | | (v0 = 0))) % 169.55/25.96 | | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | | | DELTA: instantiating (190) with fresh symbols all_137_0, % 169.55/25.96 | | | | | | | | | | | | all_137_1 gives: % 169.55/25.96 | | | | | | | | | | | | (191) apply(all_32_6, all_49_0, all_41_0) = all_137_0 & % 169.55/25.96 | | | | | | | | | | | | apply(all_32_6, all_49_0, all_41_1) = all_137_1 & % 169.55/25.96 | | | | | | | | | | | | ( ~ (all_137_0 = 0) | ~ (all_137_1 = 0)) % 169.55/25.96 | | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | | | ALPHA: (191) implies: % 169.55/25.96 | | | | | | | | | | | | (192) apply(all_32_6, all_49_0, all_41_0) = all_137_0 % 169.55/25.96 | | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | | | BETA: splitting (172) gives: % 169.55/25.96 | | | | | | | | | | | | % 169.55/25.96 | | | | | | | | | | | | Case 1: % 169.55/25.96 | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | (193) all_119_0 = 0 & all_119_1 = 0 & all_119_2 = 0 & % 169.55/25.97 | | | | | | | | | | | | | apply(all_32_6, all_41_2, all_119_3) = 0 & % 169.55/25.97 | | | | | | | | | | | | | apply(all_32_8, all_119_3, all_41_2) = 0 & % 169.55/25.97 | | | | | | | | | | | | | member(all_119_3, all_32_5) = 0 % 169.55/25.97 | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | ALPHA: (193) implies: % 169.55/25.97 | | | | | | | | | | | | | (194) member(all_119_3, all_32_5) = 0 % 169.55/25.97 | | | | | | | | | | | | | (195) apply(all_32_8, all_119_3, all_41_2) = 0 % 169.55/25.97 | | | | | | | | | | | | | (196) apply(all_32_6, all_41_2, all_119_3) = 0 % 169.55/25.97 | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | BETA: splitting (151) gives: % 169.55/25.97 | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | Case 1: % 169.55/25.97 | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | (197) all_55_0 = all_41_0 % 169.55/25.97 | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | REDUCE: (162), (197) imply: % 169.55/25.97 | | | | | | | | | | | | | | (198) apply(all_32_8, all_41_0, all_111_0) = 0 % 169.55/25.97 | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | BETA: splitting (175) gives: % 169.55/25.97 | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | Case 1: % 169.55/25.97 | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | (199) all_121_0 = 0 & all_121_1 = 0 & all_121_2 = 0 & % 169.55/25.97 | | | | | | | | | | | | | | | apply(all_32_7, all_121_3, all_41_1) = 0 & % 169.55/25.97 | | | | | | | | | | | | | | | apply(all_32_8, all_41_1, all_121_3) = 0 & % 169.55/25.97 | | | | | | | | | | | | | | | member(all_121_3, all_32_4) = 0 % 169.55/25.97 | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | ALPHA: (199) implies: % 169.55/25.97 | | | | | | | | | | | | | | | (200) member(all_121_3, all_32_4) = 0 % 169.55/25.97 | | | | | | | | | | | | | | | (201) apply(all_32_8, all_41_1, all_121_3) = 0 % 169.55/25.97 | | | | | | | | | | | | | | | (202) apply(all_32_7, all_121_3, all_41_1) = 0 % 169.55/25.97 | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | BETA: splitting (128) gives: % 169.55/25.97 | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | Case 1: % 169.55/25.97 | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | (203) all_41_0 = all_41_1 % 169.55/25.97 | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | REDUCE: (34), (203) imply: % 169.55/25.97 | | | | | | | | | | | | | | | | (204) $false % 169.55/25.97 | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | CLOSE: (204) is inconsistent. % 169.55/25.97 | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | Case 2: % 169.55/25.97 | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | (205) ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.55/25.97 | | | | | | | | | | | | | | | | all_51_0, all_41_0) = v0 & apply(all_32_6, % 169.55/25.97 | | | | | | | | | | | | | | | | all_51_0, all_41_1) = v1 & ( ~ (v1 = 0) | ~ % 169.55/25.97 | | | | | | | | | | | | | | | | (v0 = 0))) % 169.55/25.97 | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | DELTA: instantiating (205) with fresh symbols all_154_0, % 169.55/25.97 | | | | | | | | | | | | | | | | all_154_1 gives: % 169.55/25.97 | | | | | | | | | | | | | | | | (206) apply(all_32_6, all_51_0, all_41_0) = all_154_1 & % 169.55/25.97 | | | | | | | | | | | | | | | | apply(all_32_6, all_51_0, all_41_1) = all_154_0 & % 169.55/25.97 | | | | | | | | | | | | | | | | ( ~ (all_154_0 = 0) | ~ (all_154_1 = 0)) % 169.55/25.97 | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | ALPHA: (206) implies: % 169.55/25.97 | | | | | | | | | | | | | | | | (207) apply(all_32_6, all_51_0, all_41_0) = all_154_1 % 169.55/25.97 | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | BETA: splitting (147) gives: % 169.55/25.97 | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | Case 1: % 169.55/25.97 | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | (208) all_49_0 = all_41_2 % 169.55/25.97 | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | REDUCE: (169), (208) imply: % 169.55/25.97 | | | | | | | | | | | | | | | | | (209) apply(all_32_6, all_41_2, all_117_0) = 0 % 169.55/25.97 | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | REDUCE: (192), (208) imply: % 169.55/25.97 | | | | | | | | | | | | | | | | | (210) apply(all_32_6, all_41_2, all_41_0) = all_137_0 % 169.55/25.97 | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | REDUCE: (187), (208) imply: % 169.55/25.97 | | | | | | | | | | | | | | | | | (211) apply(all_32_6, all_41_2, all_41_0) = all_132_1 % 169.55/25.97 | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | BETA: splitting (141) gives: % 169.55/25.97 | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | Case 1: % 169.55/25.97 | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | (212) all_55_0 = all_41_1 % 169.55/25.97 | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (212) imply: % 169.55/25.97 | | | | | | | | | | | | | | | | | | (213) all_41_0 = all_41_1 % 169.55/25.97 | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | SIMP: (213) implies: % 169.55/25.97 | | | | | | | | | | | | | | | | | | (214) all_41_0 = all_41_1 % 169.55/25.97 | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | REDUCE: (34), (214) imply: % 169.55/25.97 | | | | | | | | | | | | | | | | | | (215) $false % 169.55/25.97 | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | CLOSE: (215) is inconsistent. % 169.55/25.97 | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | Case 2: % 169.55/25.97 | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | (216) ~ (all_55_0 = all_41_1) % 169.55/25.97 | | | | | | | | | | | | | | | | | | (217) ? [v0: any] : ? [v1: any] : (apply(all_32_7, % 169.55/25.97 | | | | | | | | | | | | | | | | | | all_49_0, all_55_0) = v0 & apply(all_32_7, % 169.55/25.97 | | | | | | | | | | | | | | | | | | all_49_0, all_41_1) = v1 & ( ~ (v1 = 0) | ~ % 169.55/25.97 | | | | | | | | | | | | | | | | | | (v0 = 0))) % 169.55/25.97 | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | DELTA: instantiating (217) with fresh symbols all_163_0, % 169.55/25.97 | | | | | | | | | | | | | | | | | | all_163_1 gives: % 169.55/25.97 | | | | | | | | | | | | | | | | | | (218) apply(all_32_7, all_49_0, all_55_0) = all_163_1 & % 169.55/25.97 | | | | | | | | | | | | | | | | | | apply(all_32_7, all_49_0, all_41_1) = all_163_0 & % 169.55/25.97 | | | | | | | | | | | | | | | | | | ( ~ (all_163_0 = 0) | ~ (all_163_1 = 0)) % 169.55/25.97 | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | ALPHA: (218) implies: % 169.55/25.97 | | | | | | | | | | | | | | | | | | (219) apply(all_32_7, all_49_0, all_41_1) = all_163_0 % 169.55/25.97 | | | | | | | | | | | | | | | | | | (220) apply(all_32_7, all_49_0, all_55_0) = all_163_1 % 169.55/25.97 | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | REDUCE: (197), (208), (220) imply: % 169.55/25.97 | | | | | | | | | | | | | | | | | | (221) apply(all_32_7, all_41_2, all_41_0) = all_163_1 % 169.55/25.97 | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | REDUCE: (208), (219) imply: % 169.55/25.97 | | | | | | | | | | | | | | | | | | (222) apply(all_32_7, all_41_2, all_41_1) = all_163_0 % 169.55/25.97 | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives: % 169.55/25.97 | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | Case 1: % 169.55/25.97 | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | (223) all_55_0 = all_41_1 % 169.55/25.97 | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (223) imply: % 169.55/25.97 | | | | | | | | | | | | | | | | | | | (224) all_41_0 = all_41_1 % 169.55/25.97 | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | SIMP: (224) implies: % 169.55/25.97 | | | | | | | | | | | | | | | | | | | (225) all_41_0 = all_41_1 % 169.55/25.97 | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | REDUCE: (34), (225) imply: % 169.55/25.97 | | | | | | | | | | | | | | | | | | | (226) $false % 169.55/25.97 | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | CLOSE: (226) is inconsistent. % 169.55/25.97 | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | Case 2: % 169.55/25.97 | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | (227) ? [v0: any] : ? [v1: any] : (apply(all_32_7, % 169.55/25.97 | | | | | | | | | | | | | | | | | | | all_49_0, all_55_0) = v1 & apply(all_32_7, % 169.55/25.97 | | | | | | | | | | | | | | | | | | | all_49_0, all_41_1) = v0 & ( ~ (v1 = 0) | ~ % 169.55/25.97 | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 169.55/25.97 | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (227) with fresh symbols all_168_0, % 169.55/25.97 | | | | | | | | | | | | | | | | | | | all_168_1 gives: % 169.55/25.97 | | | | | | | | | | | | | | | | | | | (228) apply(all_32_7, all_49_0, all_55_0) = all_168_0 & % 169.55/25.97 | | | | | | | | | | | | | | | | | | | apply(all_32_7, all_49_0, all_41_1) = all_168_1 & % 169.55/25.97 | | | | | | | | | | | | | | | | | | | ( ~ (all_168_0 = 0) | ~ (all_168_1 = 0)) % 169.55/25.97 | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | ALPHA: (228) implies: % 169.55/25.97 | | | | | | | | | | | | | | | | | | | (229) apply(all_32_7, all_49_0, all_41_1) = all_168_1 % 169.55/25.97 | | | | | | | | | | | | | | | | | | | (230) apply(all_32_7, all_49_0, all_55_0) = all_168_0 % 169.55/25.97 | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | REDUCE: (197), (208), (230) imply: % 169.55/25.97 | | | | | | | | | | | | | | | | | | | (231) apply(all_32_7, all_41_2, all_41_0) = all_168_0 % 169.55/25.97 | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | REDUCE: (208), (229) imply: % 169.55/25.97 | | | | | | | | | | | | | | | | | | | (232) apply(all_32_7, all_41_2, all_41_1) = all_168_1 % 169.55/25.97 | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | BETA: splitting (139) gives: % 169.55/25.97 | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | Case 1: % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | (233) all_55_0 = all_41_1 % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (233) imply: % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | (234) all_41_0 = all_41_1 % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | SIMP: (234) implies: % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | (235) all_41_0 = all_41_1 % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (235) imply: % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | (236) $false % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | CLOSE: (236) is inconsistent. % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | Case 2: % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | (237) ? [v0: any] : ? [v1: any] : (apply(all_32_7, % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | all_51_0, all_55_0) = v0 & apply(all_32_7, % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | all_51_0, all_41_1) = v1 & ( ~ (v1 = 0) | ~ % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (237) with fresh symbols all_173_0, % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | all_173_1 gives: % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | (238) apply(all_32_7, all_51_0, all_55_0) = all_173_1 & % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | apply(all_32_7, all_51_0, all_41_1) = all_173_0 & % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | ( ~ (all_173_0 = 0) | ~ (all_173_1 = 0)) % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies: % 169.55/25.97 | | | | | | | | | | | | | | | | | | | | (239) apply(all_32_7, all_51_0, all_41_1) = all_173_0 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | (240) apply(all_32_7, all_51_0, all_55_0) = all_173_1 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (240) imply: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | (241) apply(all_32_7, all_51_0, all_41_0) = all_173_1 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | Case 1: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (242) all_55_0 = all_41_1 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (242) imply: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (243) all_41_0 = all_41_1 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | SIMP: (243) implies: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (244) all_41_0 = all_41_1 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (244) imply: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (245) $false % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | CLOSE: (245) is inconsistent. % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | Case 2: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (246) ? [v0: any] : ? [v1: any] : (apply(all_32_7, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_51_0, all_55_0) = v1 & apply(all_32_7, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_51_0, all_41_1) = v0 & ( ~ (v1 = 0) | ~ % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (246) with fresh symbols all_178_0, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_178_1 gives: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (247) apply(all_32_7, all_51_0, all_55_0) = all_178_0 & % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | apply(all_32_7, all_51_0, all_41_1) = all_178_1 & % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | ( ~ (all_178_0 = 0) | ~ (all_178_1 = 0)) % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (248) apply(all_32_7, all_51_0, all_41_1) = all_178_1 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (249) apply(all_32_7, all_51_0, all_55_0) = all_178_0 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (249) imply: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (250) apply(all_32_7, all_51_0, all_41_0) = all_178_0 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_78_0, all_168_1, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_41_1, all_41_2, all_32_7, simplifying with % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (96), (232) gives: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (251) all_168_1 = all_78_0 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_163_0, all_168_1, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_41_1, all_41_2, all_32_7, simplifying with % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (222), (232) gives: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (252) all_168_1 = all_163_0 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_78_1, all_168_0, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_41_0, all_41_2, all_32_7, simplifying with % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (97), (231) gives: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (253) all_168_0 = all_78_1 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_163_1, all_168_0, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_41_0, all_41_2, all_32_7, simplifying with % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (221), (231) gives: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (254) all_168_0 = all_163_1 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_173_0, all_178_1, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_41_1, all_51_0, all_32_7, simplifying with % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (239), (248) gives: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (255) all_178_1 = all_173_0 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_173_1, all_178_0, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_41_0, all_51_0, all_32_7, simplifying with % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (241), (250) gives: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (256) all_178_0 = all_173_1 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_137_0, all_41_0, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_41_2, all_32_6, simplifying with (41), (210) % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | gives: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (257) all_137_0 = 0 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_132_1, all_137_0, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_41_0, all_41_2, all_32_6, simplifying with % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (210), (211) gives: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (258) all_137_0 = all_132_1 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (253), (254) imply: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (259) all_163_1 = all_78_1 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (252) imply: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (260) all_163_0 = all_78_0 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (258) imply: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (261) all_132_1 = 0 % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_32_5, all_41_2, all_109_0, all_41_1, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | simplifying with (14), (15), (16), (22), (35), % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (36), (38), (39), (156), (157) gives: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (262) all_109_0 = all_41_1 | ? [v0: any] : ? [v1: any] % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_6, all_41_2, all_109_0) = v0 & % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | apply(all_32_6, all_41_2, all_41_1) = v1 & ( ~ % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_7, all_32_4, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_32_5, all_111_0, all_41_0, all_41_1, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | simplifying with (13), (15), (16), (21), (36), % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (37), (39), (40), (160), (161) gives: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (263) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_7, all_111_0, all_41_0) = v0 & % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | apply(all_32_7, all_111_0, all_41_1) = v1 & ( ~ % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_32_8, all_32_5, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_41_0, all_111_0, all_51_0, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (37), % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (61), (63), (160), (161) gives: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (264) all_111_0 = all_51_0 | ? [v0: any] : ? [v1: any] % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | : ? [v2: any] : (apply(all_32_8, all_41_0, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_111_0) = v2 & member(all_51_0, all_32_4) = % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | v1 & member(all_41_0, all_32_5) = v0 & ( ~ (v2 = % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_41_0, all_111_0, all_51_0, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (37), % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (40), (61), (62), (160), (161) gives: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (265) all_111_0 = all_51_0 | ? [v0: any] : ? [v1: any] % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_8, all_41_0, all_111_0) = v0 & % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_41_0, all_51_0) = v1 & ( ~ % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_32_5, all_113_0, all_41_1, all_41_0, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | simplifying with (14), (15), (16), (22), (36), % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (37), (39), (40), (164), (165) gives: % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (266) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_6, all_113_0, all_41_0) = v1 & % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | apply(all_32_6, all_113_0, all_41_1) = v0 & ( ~ % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | all_32_5, all_41_2, all_117_0, all_41_0, % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | simplifying with (14), (15), (16), (22), (35), % 169.55/25.98 | | | | | | | | | | | | | | | | | | | | | (37), (38), (40), (167), (168) gives: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (267) all_117_0 = all_41_0 | ? [v0: any] : ? [v1: any] % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_6, all_41_2, all_117_0) = v0 & % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | apply(all_32_6, all_41_2, all_41_0) = v1 & ( ~ % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_117_0, all_41_2, all_111_0, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (35), % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (38), (160), (161), (167), (168) gives: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (268) all_111_0 = all_41_2 | ? [v0: any] : ? [v1: any] % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_8, all_117_0, all_111_0) = v1 & % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_117_0, all_41_2) = v0 & ( ~ % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | all_32_5, all_41_2, all_119_3, all_117_0, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | simplifying with (14), (15), (16), (22), (35), % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (38), (167), (168), (171), (194) gives: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (269) all_119_3 = all_117_0 | ? [v0: any] : ? [v1: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_6, all_41_2, all_119_3) = % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | v0 & apply(all_32_6, all_41_2, all_117_0) = v1 & % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | all_32_5, all_51_0, all_109_0, all_119_3, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | simplifying with (14), (15), (16), (22), (61), % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (62), (156), (157), (171), (194) gives: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (270) all_119_3 = all_109_0 | ? [v0: any] : ? [v1: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_6, all_51_0, all_119_3) = % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | v1 & apply(all_32_6, all_51_0, all_109_0) = v0 & % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | all_32_5, all_51_0, all_119_3, all_109_0, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | simplifying with (14), (15), (16), (22), (61), % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (62), (156), (157), (171), (194) gives: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (271) all_119_3 = all_109_0 | ? [v0: any] : ? [v1: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_6, all_51_0, all_119_3) = % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | v0 & apply(all_32_6, all_51_0, all_109_0) = v1 & % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | all_32_5, all_41_2, all_109_0, all_119_3, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | simplifying with (14), (15), (16), (22), (35), % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (38), (156), (157), (171), (194) gives: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (272) all_119_3 = all_109_0 | ? [v0: any] : ? [v1: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_6, all_41_2, all_119_3) = % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | v1 & apply(all_32_6, all_41_2, all_109_0) = v0 & % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | all_32_5, all_41_2, all_119_3, all_109_0, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | simplifying with (14), (15), (16), (22), (35), % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (38), (156), (157), (171), (194) gives: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (273) all_119_3 = all_109_0 | ? [v0: any] : ? [v1: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_6, all_41_2, all_119_3) = % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | v0 & apply(all_32_6, all_41_2, all_109_0) = v1 & % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | all_32_5, all_111_0, all_109_0, all_119_3, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | simplifying with (14), (15), (16), (22), (156), % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (157), (160), (161), (171), (194) gives: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (274) all_119_3 = all_109_0 | ? [v0: any] : ? [v1: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_6, all_111_0, all_119_3) = % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | v1 & apply(all_32_6, all_111_0, all_109_0) = v0 % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | all_32_5, all_111_0, all_119_3, all_109_0, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | simplifying with (14), (15), (16), (22), (156), % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (157), (160), (161), (171), (194) gives: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (275) all_119_3 = all_109_0 | ? [v0: any] : ? [v1: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_6, all_111_0, all_119_3) = % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | v0 & apply(all_32_6, all_111_0, all_109_0) = v1 % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_7, all_32_4, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | all_32_5, all_41_2, all_117_0, all_119_3, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | simplifying with (13), (15), (16), (21), (35), % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (38), (167), (168), (171), (194) gives: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (276) all_119_3 = all_117_0 | ? [v0: any] : ? [v1: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_7, all_41_2, all_119_3) = % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | v1 & apply(all_32_7, all_41_2, all_117_0) = v0 & % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_119_3, all_121_3, all_41_2, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (35), % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (38), (171), (174), (194), (200) gives: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (277) all_121_3 = all_41_2 | ? [v0: any] : ? [v1: any] % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_8, all_119_3, all_121_3) = v0 & % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_119_3, all_41_2) = v1 & ( ~ % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_117_0, all_41_2, all_121_3, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (35), % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (38), (167), (168), (174), (200) gives: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (278) all_121_3 = all_41_2 | ? [v0: any] : ? [v1: any] % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_8, all_117_0, all_121_3) = v1 & % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_117_0, all_41_2) = v0 & ( ~ % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_117_0, all_121_3, all_41_2, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (35), % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (38), (167), (168), (174), (200) gives: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (279) all_121_3 = all_41_2 | ? [v0: any] : ? [v1: any] % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_8, all_117_0, all_121_3) = v0 & % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_117_0, all_41_2) = v1 & ( ~ % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_41_1, all_121_3, all_111_0, % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (36), % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (39), (160), (161), (174), (200) gives: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | (280) all_121_3 = all_111_0 | ? [v0: any] : ? [v1: % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_8, all_41_1, all_121_3) = % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | v0 & apply(all_32_8, all_41_1, all_111_0) = v1 & % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.55/25.99 | | | | | | | | | | | | | | | | | | | | | % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | all_32_5, all_123_3, all_41_0, all_41_1, % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | simplifying with (14), (15), (16), (22), (36), % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (37), (39), (40), (177), (180) gives: % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (281) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_6, all_123_3, all_41_0) = v0 & % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | apply(all_32_6, all_123_3, all_41_1) = v1 & ( ~ % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | all_32_5, all_123_3, all_41_1, all_119_3, % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | simplifying with (14), (15), (16), (22), (36), % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (39), (171), (177), (180), (194) gives: % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (282) all_119_3 = all_41_1 | ? [v0: any] : ? [v1: any] % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_6, all_123_3, all_119_3) = v1 & % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | apply(all_32_6, all_123_3, all_41_1) = v0 & ( ~ % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_41_0, all_123_3, all_51_0, % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (37), % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (40), (61), (62), (177), (180) gives: % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (283) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_8, all_41_0, all_123_3) = v0 & % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_41_0, all_51_0) = v1 & ( ~ % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_119_3, all_51_0, all_123_3, % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (61), % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (62), (171), (177), (180), (194) gives: % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (284) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_8, all_119_3, all_123_3) = v1 & % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_119_3, all_51_0) = v0 & ( ~ % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_119_3, all_123_3, all_51_0, % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (61), % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (62), (171), (177), (180), (194) gives: % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (285) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_8, all_119_3, all_123_3) = v0 & % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_119_3, all_51_0) = v1 & ( ~ % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_117_0, all_51_0, all_123_3, % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (61), % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (62), (167), (168), (177), (180) gives: % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (286) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_8, all_117_0, all_123_3) = v1 & % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_117_0, all_51_0) = v0 & ( ~ % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_117_0, all_123_3, all_51_0, % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (61), % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (62), (167), (168), (177), (180) gives: % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (287) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_8, all_117_0, all_123_3) = v0 & % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_117_0, all_51_0) = v1 & ( ~ % 169.55/26.00 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_109_0, all_51_0, all_123_3, % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (61), % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | (62), (156), (157), (177), (180) gives: % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | (288) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_8, all_109_0, all_123_3) = v1 & % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_109_0, all_51_0) = v0 & ( ~ % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_109_0, all_123_3, all_51_0, % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (61), % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | (62), (156), (157), (177), (180) gives: % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | (289) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_8, all_109_0, all_123_3) = v0 & % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_109_0, all_51_0) = v1 & ( ~ % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_109_0, all_41_2, all_123_3, % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (35), % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | (38), (156), (157), (177), (180) gives: % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | (290) all_123_3 = all_41_2 | ? [v0: any] : ? [v1: any] % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_8, all_109_0, all_123_3) = v1 & % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_109_0, all_41_2) = v0 & ( ~ % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_109_0, all_123_3, all_41_2, % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (35), % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | (38), (156), (157), (177), (180) gives: % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | (291) all_123_3 = all_41_2 | ? [v0: any] : ? [v1: any] % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_8, all_109_0, all_123_3) = v0 & % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_109_0, all_41_2) = v1 & ( ~ % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_41_0, all_121_3, all_123_3, % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (37), % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | (40), (174), (177), (180), (200) gives: % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | (292) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_8, all_41_0, all_123_3) = % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | v1 & apply(all_32_8, all_41_0, all_121_3) = v0 & % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_41_0, all_123_3, all_121_3, % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (37), % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | (40), (174), (177), (180), (200) gives: % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | (293) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_8, all_41_0, all_123_3) = % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | v0 & apply(all_32_8, all_41_0, all_121_3) = v1 & % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.75/26.00 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_119_3, all_121_3, all_123_3, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (171), % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (174), (177), (180), (194), (200) gives: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (294) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_8, all_119_3, all_123_3) = % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | v1 & apply(all_32_8, all_119_3, all_121_3) = v0 % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_119_3, all_123_3, all_121_3, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (171), % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (174), (177), (180), (194), (200) gives: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (295) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_8, all_119_3, all_123_3) = % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | v0 & apply(all_32_8, all_119_3, all_121_3) = v1 % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_117_0, all_123_3, all_121_3, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (167), % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (168), (174), (177), (180), (200) gives: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (296) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_8, all_117_0, all_123_3) = % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | v0 & apply(all_32_8, all_117_0, all_121_3) = v1 % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_109_0, all_121_3, all_123_3, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (156), % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (157), (174), (177), (180), (200) gives: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (297) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_8, all_109_0, all_123_3) = % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | v1 & apply(all_32_8, all_109_0, all_121_3) = v0 % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_109_0, all_123_3, all_121_3, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (156), % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (157), (174), (177), (180), (200) gives: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (298) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_8, all_109_0, all_123_3) = % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | v0 & apply(all_32_8, all_109_0, all_121_3) = v1 % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_109_0, all_111_0, all_123_3, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (156), % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (157), (160), (161), (177), (180) gives: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (299) all_123_3 = all_111_0 | ? [v0: any] : ? [v1: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_8, all_109_0, all_123_3) = % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | v1 & apply(all_32_8, all_109_0, all_111_0) = v0 % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_109_0, all_123_3, all_111_0, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (156), % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (157), (160), (161), (177), (180) gives: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (300) all_123_3 = all_111_0 | ? [v0: any] : ? [v1: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | any] : (apply(all_32_8, all_109_0, all_123_3) = % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | v0 & apply(all_32_8, all_109_0, all_111_0) = v1 % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_32_8, all_32_5, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_41_0, all_41_2, all_111_0, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (35), % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (37), (38), (160), (198) gives: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (301) all_111_0 = all_41_2 | ? [v0: any] : ? [v1: any] % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | : ? [v2: any] : (apply(all_32_8, all_41_0, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | all_41_2) = v2 & member(all_111_0, all_32_4) = % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | v1 & member(all_41_0, all_32_5) = v0 & ( ~ (v2 = % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_32_8, all_32_5, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | all_32_4, all_119_3, all_123_3, all_41_2, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (15), (16), (20), (35), % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (171), (177), (180), (195) gives: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (302) all_123_3 = all_41_2 | ? [v0: any] : ? [v1: any] % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | : ? [v2: any] : (apply(all_32_8, all_119_3, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | all_123_3) = v2 & member(all_119_3, all_32_5) % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | = v0 & member(all_41_2, all_32_4) = v1 & ( ~ (v2 % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_32_6, all_32_4, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | all_32_5, all_41_2, all_41_0, all_119_3, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | simplifying with (14), (15), (16), (22), (35), % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (37), (41), (171), (196) gives: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (303) all_119_3 = all_41_0 | ? [v0: any] : ? [v1: any] % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | : ? [v2: any] : (member(all_119_3, all_32_5) = v2 % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | & member(all_41_0, all_32_5) = v1 & % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | member(all_41_2, all_32_4) = v0 & ( ~ (v2 = 0) | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_32_6, all_32_4, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | all_32_5, all_41_2, all_117_0, all_119_3, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | simplifying with (14), (15), (16), (22), (35), % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (167), (171), (196), (209) gives: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | (304) all_119_3 = all_117_0 | ? [v0: any] : ? [v1: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | any] : ? [v2: any] : (member(all_119_3, % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | all_32_5) = v2 & member(all_117_0, all_32_5) = % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | v1 & member(all_41_2, all_32_4) = v0 & ( ~ (v2 = % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | Case 1: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | (305) all_119_3 = all_117_0 % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (195), (305) imply: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | (306) apply(all_32_8, all_117_0, all_41_2) = 0 % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | (307) all_119_3 = all_41_0 % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (305), (307) imply: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | (308) all_117_0 = all_41_0 % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (308) implies: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | (309) all_117_0 = all_41_0 % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (306), (309) imply: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | (310) apply(all_32_8, all_41_0, all_41_2) = 0 % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (264) gives: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | | (311) all_111_0 = all_51_0 % 169.75/26.01 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (34), (40), (41), (62), (63), (96), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (97), (98), (123), (130), (131), (132), (133), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (142), (143), (144), (145), (149), (150), (158), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (181), (182), (197), (201), (202), (207), (208), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (239), (241), (262), (263), (268), (270), (271), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (272), (273), (274), (275), (277), (278), (279), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (280), (281), (283), (284), (285), (286), (287), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (288), (289), (290), (291), (292), (293), (294), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (295), (296), (297), (298), (299), (300), (301), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (302), (307), (309), (310), (311) are inconsistent % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #2. % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (312) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (apply(all_32_8, all_41_0, all_111_0) = v2 & % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | member(all_51_0, all_32_4) = v1 & % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | member(all_41_0, all_32_5) = v0 & ( ~ (v2 = 0) | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (312) with fresh symbols all_241_0, % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | all_241_1, all_241_2 gives: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (313) apply(all_32_8, all_41_0, all_111_0) = all_241_0 & % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | member(all_51_0, all_32_4) = all_241_1 & % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | member(all_41_0, all_32_5) = all_241_2 & ( ~ % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (all_241_0 = 0) | ~ (all_241_1 = 0) | ~ % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (all_241_2 = 0)) % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (313) implies: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (314) apply(all_32_8, all_41_0, all_111_0) = all_241_0 % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_111_0 = all_51_0 % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (34), (40), (41), (62), (63), (96), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (97), (98), (123), (130), (131), (132), (133), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (142), (143), (144), (145), (149), (150), (158), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (181), (182), (197), (201), (202), (207), (208), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (239), (241), (262), (263), (268), (270), (271), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (272), (273), (274), (275), (277), (278), (279), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (280), (281), (283), (284), (285), (286), (287), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (288), (289), (290), (291), (292), (293), (294), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (295), (296), (297), (298), (299), (300), (301), % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (302), (307), (309), (310), (315) are inconsistent % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #2. % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (316) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | all_41_0, all_111_0) = v0 & apply(all_32_8, % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | all_41_0, all_51_0) = v1 & ( ~ (v1 = 0) | ~ % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (316) with fresh symbols all_354_0, % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | all_354_1 gives: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (317) apply(all_32_8, all_41_0, all_111_0) = all_354_1 & % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_41_0, all_51_0) = all_354_0 & % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_354_0 = 0) | ~ (all_354_1 = 0)) % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (317) implies: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (318) apply(all_32_8, all_41_0, all_51_0) = all_354_0 % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (319) apply(all_32_8, all_41_0, all_111_0) = all_354_1 % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (320) ~ (all_354_0 = 0) | ~ (all_354_1 = 0) % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_119_3 = all_41_1 % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (321) imply: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_41_0 = all_41_1 % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (322) implies: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_41_0 = all_41_1 % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (323) imply: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (324) $false % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (324) is inconsistent. % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_354_0, all_51_0, % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | all_41_0, all_32_8, simplifying with (63), (318) % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_354_0 = 0 % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_354_1, all_111_0, % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | all_41_0, all_32_8, simplifying with (198), (319) % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_354_1 = 0 % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_241_0, all_354_1, % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | all_111_0, all_41_0, all_32_8, simplifying with % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (314), (319) gives: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_354_1 = all_241_0 % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (326), (327) imply: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_241_0 = 0 % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) ~ (all_354_0 = 0) % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (325), (329) imply: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) $false % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (330) is inconsistent. % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) ~ (all_354_1 = 0) % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (326), (331) imply: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) $false % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (332) is inconsistent. % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | End of split % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | (333) ~ (all_119_3 = all_41_0) % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (305), (333) imply: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | (334) ~ (all_117_0 = all_41_0) % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (335) all_117_0 = all_41_0 % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (305), (335) imply: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (336) all_119_3 = all_41_0 % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (334), (335) imply: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (337) $false % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (337) is inconsistent. % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (338) ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | all_41_2, all_119_3) = v0 & apply(all_32_6, % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | all_41_2, all_117_0) = v1 & ( ~ (v1 = 0) | ~ % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (338) with fresh symbols all_358_0, % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | all_358_1 gives: % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | (339) apply(all_32_6, all_41_2, all_119_3) = all_358_1 & % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | apply(all_32_6, all_41_2, all_117_0) = all_358_0 & % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_358_0 = 0) | ~ (all_358_1 = 0)) % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (339) implies: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | (340) apply(all_32_6, all_41_2, all_117_0) = all_358_0 % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | (341) apply(all_32_6, all_41_2, all_119_3) = all_358_1 % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | (342) ~ (all_358_0 = 0) | ~ (all_358_1 = 0) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (336), (341) imply: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | (343) apply(all_32_6, all_41_2, all_41_0) = all_358_1 % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_358_1, all_41_0, % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | all_41_2, all_32_6, simplifying with (41), (343) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | (344) all_358_1 = 0 % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_358_0, all_117_0, % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | all_41_2, all_32_6, simplifying with (209), (340) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | (345) all_358_0 = 0 % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (342) gives: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (346) ~ (all_358_0 = 0) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (345), (346) imply: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (347) $false % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (347) is inconsistent. % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (348) ~ (all_358_1 = 0) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (348) imply: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (349) $false % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (349) is inconsistent. % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | (350) ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | all_41_2, all_117_0) = v0 & apply(all_32_6, % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | all_41_2, all_41_0) = v1 & ( ~ (v1 = 0) | ~ % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (350) with fresh symbols all_303_0, % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | all_303_1 gives: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | (351) apply(all_32_6, all_41_2, all_117_0) = all_303_1 & % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | apply(all_32_6, all_41_2, all_41_0) = all_303_0 & % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_303_0 = 0) | ~ (all_303_1 = 0)) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (351) implies: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | (352) apply(all_32_6, all_41_2, all_41_0) = all_303_0 % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | (353) apply(all_32_6, all_41_2, all_117_0) = all_303_1 % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | (354) ~ (all_303_0 = 0) | ~ (all_303_1 = 0) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (266) gives: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_41_0 = all_41_1 % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (355) imply: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | (356) $false % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (356) is inconsistent. % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_303_0, all_41_0, % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | all_41_2, all_32_6, simplifying with (41), (352) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | (357) all_303_0 = 0 % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_303_1, all_117_0, % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | all_41_2, all_32_6, simplifying with (209), (353) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_303_1 = 0 % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (354) gives: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (359) ~ (all_303_0 = 0) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (357), (359) imply: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (360) $false % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (360) is inconsistent. % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (361) ~ (all_303_1 = 0) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (361) imply: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (362) $false % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (362) is inconsistent. % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | End of split % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | End of split % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | Case 2: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | (363) ~ (all_119_3 = all_117_0) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | (364) all_119_3 = all_117_0 % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (364) imply: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | (365) $false % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (365) is inconsistent. % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | (366) ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | all_41_2, all_119_3) = v0 & apply(all_32_6, % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | all_41_2, all_117_0) = v1 & ( ~ (v1 = 0) | ~ % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (366) with fresh symbols all_360_0, % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | all_360_1 gives: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | (367) apply(all_32_6, all_41_2, all_119_3) = all_360_1 & % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | apply(all_32_6, all_41_2, all_117_0) = all_360_0 & % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_360_0 = 0) | ~ (all_360_1 = 0)) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (367) implies: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | (368) apply(all_32_6, all_41_2, all_117_0) = all_360_0 % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | (369) apply(all_32_6, all_41_2, all_119_3) = all_360_1 % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | (370) ~ (all_360_0 = 0) | ~ (all_360_1 = 0) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | (371) all_119_3 = all_117_0 % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (371) imply: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | (372) $false % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (372) is inconsistent. % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_360_0, all_117_0, % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | all_41_2, all_32_6, simplifying with (209), (368) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | (373) all_360_0 = 0 % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_360_1, all_119_3, % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | all_41_2, all_32_6, simplifying with (196), (369) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | (374) all_360_1 = 0 % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (370) gives: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | (375) ~ (all_360_0 = 0) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (375) imply: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | (376) $false % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (376) is inconsistent. % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | (377) ~ (all_360_1 = 0) % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (377) imply: % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | (378) $false % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (378) is inconsistent. % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | End of split % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | End of split % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | End of split % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | End of split % 169.75/26.03 | | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | | End of split % 169.75/26.03 | | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | | End of split % 169.75/26.03 | | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | End of split % 169.75/26.03 | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | Case 2: % 169.75/26.03 | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | (379) ~ (all_49_0 = all_41_2) % 169.75/26.03 | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (59), (123), (127), (379) are inconsistent by % 169.75/26.03 | | | | | | | | | | | | | | | | | sub-proof #1. % 169.75/26.03 | | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | | End of split % 169.75/26.03 | | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | End of split % 169.75/26.03 | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | Case 2: % 169.75/26.03 | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | (380) member(all_41_1, all_32_5) = all_121_4 & % 169.75/26.03 | | | | | | | | | | | | | | | member(all_41_1, all_32_5) = all_121_5 & ( ~ % 169.75/26.03 | | | | | | | | | | | | | | | (all_121_4 = 0) | ~ (all_121_5 = 0)) % 169.75/26.03 | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | ALPHA: (380) implies: % 169.75/26.03 | | | | | | | | | | | | | | | (381) member(all_41_1, all_32_5) = all_121_5 % 169.75/26.03 | | | | | | | | | | | | | | | (382) member(all_41_1, all_32_5) = all_121_4 % 169.75/26.03 | | | | | | | | | | | | | | | (383) ~ (all_121_4 = 0) | ~ (all_121_5 = 0) % 169.75/26.03 | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_121_4, all_32_5, % 169.75/26.03 | | | | | | | | | | | | | | | all_41_1, simplifying with (39), (382) gives: % 169.75/26.03 | | | | | | | | | | | | | | | (384) all_121_4 = 0 % 169.75/26.03 | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_121_5, all_121_4, % 169.75/26.03 | | | | | | | | | | | | | | | all_32_5, all_41_1, simplifying with (381), (382) % 169.75/26.03 | | | | | | | | | | | | | | | gives: % 169.75/26.03 | | | | | | | | | | | | | | | (385) all_121_4 = all_121_5 % 169.75/26.03 | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | COMBINE_EQS: (384), (385) imply: % 169.75/26.03 | | | | | | | | | | | | | | | (386) all_121_5 = 0 % 169.75/26.03 | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | BETA: splitting (383) gives: % 169.75/26.03 | | | | | | | | | | | | | | | % 169.75/26.03 | | | | | | | | | | | | | | | Case 1: % 169.75/26.03 | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | (387) ~ (all_121_4 = 0) % 169.75/26.04 | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | REDUCE: (384), (387) imply: % 169.75/26.04 | | | | | | | | | | | | | | | | (388) $false % 169.75/26.04 | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | CLOSE: (388) is inconsistent. % 169.75/26.04 | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | Case 2: % 169.75/26.04 | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | (389) ~ (all_121_5 = 0) % 169.75/26.04 | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | REDUCE: (386), (389) imply: % 169.75/26.04 | | | | | | | | | | | | | | | | (390) $false % 169.75/26.04 | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | CLOSE: (390) is inconsistent. % 169.75/26.04 | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | End of split % 169.75/26.04 | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | End of split % 169.75/26.04 | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | Case 2: % 169.75/26.04 | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | (391) ~ (all_55_0 = all_41_0) % 169.75/26.04 | | | | | | | | | | | | | | (392) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 169.75/26.04 | | | | | | | | | | | | | | (apply(all_32_6, all_41_2, all_41_0) = v2 & % 169.75/26.04 | | | | | | | | | | | | | | member(all_55_0, all_32_5) = v1 & % 169.75/26.04 | | | | | | | | | | | | | | member(all_41_2, all_32_4) = v0 & ( ~ (v2 = 0) | % 169.75/26.04 | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 169.75/26.04 | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | DELTA: instantiating (392) with fresh symbols all_147_0, % 169.75/26.04 | | | | | | | | | | | | | | all_147_1, all_147_2 gives: % 169.75/26.04 | | | | | | | | | | | | | | (393) apply(all_32_6, all_41_2, all_41_0) = all_147_0 & % 169.75/26.04 | | | | | | | | | | | | | | member(all_55_0, all_32_5) = all_147_1 & % 169.75/26.04 | | | | | | | | | | | | | | member(all_41_2, all_32_4) = all_147_2 & ( ~ % 169.75/26.04 | | | | | | | | | | | | | | (all_147_0 = 0) | ~ (all_147_1 = 0) | ~ % 169.75/26.04 | | | | | | | | | | | | | | (all_147_2 = 0)) % 169.75/26.04 | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | ALPHA: (393) implies: % 169.75/26.04 | | | | | | | | | | | | | | (394) apply(all_32_6, all_41_2, all_41_0) = all_147_0 % 169.75/26.04 | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | BETA: splitting (135) gives: % 169.75/26.04 | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | Case 1: % 169.75/26.04 | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | (395) all_55_0 = all_41_0 % 169.75/26.04 | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | REDUCE: (391), (395) imply: % 169.75/26.04 | | | | | | | | | | | | | | | (396) $false % 169.75/26.04 | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | CLOSE: (396) is inconsistent. % 169.75/26.04 | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | Case 2: % 169.75/26.04 | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | (397) ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.75/26.04 | | | | | | | | | | | | | | | all_41_2, all_55_0) = v0 & apply(all_32_6, % 169.75/26.04 | | | | | | | | | | | | | | | all_41_2, all_41_0) = v1 & ( ~ (v1 = 0) | ~ % 169.75/26.04 | | | | | | | | | | | | | | | (v0 = 0))) % 169.75/26.04 | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | DELTA: instantiating (397) with fresh symbols all_153_0, % 169.75/26.04 | | | | | | | | | | | | | | | all_153_1 gives: % 169.75/26.04 | | | | | | | | | | | | | | | (398) apply(all_32_6, all_41_2, all_55_0) = all_153_1 & % 169.75/26.04 | | | | | | | | | | | | | | | apply(all_32_6, all_41_2, all_41_0) = all_153_0 & % 169.75/26.04 | | | | | | | | | | | | | | | ( ~ (all_153_0 = 0) | ~ (all_153_1 = 0)) % 169.75/26.04 | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | ALPHA: (398) implies: % 169.75/26.04 | | | | | | | | | | | | | | | (399) apply(all_32_6, all_41_2, all_41_0) = all_153_0 % 169.75/26.04 | | | | | | | | | | | | | | | (400) apply(all_32_6, all_41_2, all_55_0) = all_153_1 % 169.75/26.04 | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | BETA: splitting (148) gives: % 169.75/26.04 | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | Case 1: % 169.75/26.04 | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | (401) all_49_0 = all_41_2 % 169.75/26.04 | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | REDUCE: (192), (401) imply: % 169.75/26.04 | | | | | | | | | | | | | | | | (402) apply(all_32_6, all_41_2, all_41_0) = all_137_0 % 169.75/26.04 | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | REDUCE: (187), (401) imply: % 169.75/26.04 | | | | | | | | | | | | | | | | (403) apply(all_32_6, all_41_2, all_41_0) = all_132_1 % 169.75/26.04 | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | BETA: splitting (137) gives: % 169.75/26.04 | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | Case 1: % 169.75/26.04 | | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | | (404) all_55_0 = all_41_0 % 169.75/26.04 | | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | | REDUCE: (391), (404) imply: % 169.75/26.04 | | | | | | | | | | | | | | | | | (405) $false % 169.75/26.04 | | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | | CLOSE: (405) is inconsistent. % 169.75/26.04 | | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | Case 2: % 169.75/26.04 | | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | | (406) ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.75/26.04 | | | | | | | | | | | | | | | | | all_49_0, all_55_0) = v0 & apply(all_32_6, % 169.75/26.04 | | | | | | | | | | | | | | | | | all_49_0, all_41_0) = v1 & ( ~ (v1 = 0) | ~ % 169.75/26.04 | | | | | | | | | | | | | | | | | (v0 = 0))) % 169.75/26.04 | | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | | DELTA: instantiating (406) with fresh symbols all_172_0, % 169.75/26.04 | | | | | | | | | | | | | | | | | all_172_1 gives: % 169.75/26.04 | | | | | | | | | | | | | | | | | (407) apply(all_32_6, all_49_0, all_55_0) = all_172_1 & % 169.75/26.04 | | | | | | | | | | | | | | | | | apply(all_32_6, all_49_0, all_41_0) = all_172_0 & % 169.75/26.04 | | | | | | | | | | | | | | | | | ( ~ (all_172_0 = 0) | ~ (all_172_1 = 0)) % 169.75/26.04 | | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | | ALPHA: (407) implies: % 169.75/26.04 | | | | | | | | | | | | | | | | | (408) apply(all_32_6, all_49_0, all_41_0) = all_172_0 % 169.75/26.04 | | | | | | | | | | | | | | | | | (409) apply(all_32_6, all_49_0, all_55_0) = all_172_1 % 169.75/26.04 | | | | | | | | | | | | | | | | | (410) ~ (all_172_0 = 0) | ~ (all_172_1 = 0) % 169.75/26.04 | | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | | REDUCE: (401), (409) imply: % 169.75/26.04 | | | | | | | | | | | | | | | | | (411) apply(all_32_6, all_41_2, all_55_0) = all_172_1 % 169.75/26.04 | | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | | REDUCE: (401), (408) imply: % 169.75/26.04 | | | | | | | | | | | | | | | | | (412) apply(all_32_6, all_41_2, all_41_0) = all_172_0 % 169.75/26.04 | | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | | BETA: splitting (136) gives: % 169.75/26.04 | | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | | Case 1: % 169.75/26.04 | | | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | | | (413) all_55_0 = all_41_0 % 169.75/26.04 | | | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | | | REDUCE: (391), (413) imply: % 169.75/26.04 | | | | | | | | | | | | | | | | | | (414) $false % 169.75/26.04 | | | | | | | | | | | | | | | | | | % 169.75/26.04 | | | | | | | | | | | | | | | | | | CLOSE: (414) is inconsistent. % 169.92/26.04 | | | | | | | | | | | | | | | | | | % 169.92/26.04 | | | | | | | | | | | | | | | | | Case 2: % 169.92/26.04 | | | | | | | | | | | | | | | | | | % 169.92/26.04 | | | | | | | | | | | | | | | | | | (415) ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.92/26.04 | | | | | | | | | | | | | | | | | | all_49_0, all_55_0) = v1 & apply(all_32_6, % 169.92/26.04 | | | | | | | | | | | | | | | | | | all_49_0, all_41_0) = v0 & ( ~ (v1 = 0) | ~ % 169.92/26.04 | | | | | | | | | | | | | | | | | | (v0 = 0))) % 169.92/26.04 | | | | | | | | | | | | | | | | | | % 169.92/26.04 | | | | | | | | | | | | | | | | | | DELTA: instantiating (415) with fresh symbols all_192_0, % 169.92/26.04 | | | | | | | | | | | | | | | | | | all_192_1 gives: % 169.92/26.04 | | | | | | | | | | | | | | | | | | (416) apply(all_32_6, all_49_0, all_55_0) = all_192_0 & % 169.92/26.04 | | | | | | | | | | | | | | | | | | apply(all_32_6, all_49_0, all_41_0) = all_192_1 & % 169.92/26.04 | | | | | | | | | | | | | | | | | | ( ~ (all_192_0 = 0) | ~ (all_192_1 = 0)) % 169.92/26.04 | | | | | | | | | | | | | | | | | | % 169.92/26.04 | | | | | | | | | | | | | | | | | | ALPHA: (416) implies: % 169.92/26.04 | | | | | | | | | | | | | | | | | | (417) apply(all_32_6, all_49_0, all_41_0) = all_192_1 % 169.92/26.04 | | | | | | | | | | | | | | | | | | (418) apply(all_32_6, all_49_0, all_55_0) = all_192_0 % 169.92/26.04 | | | | | | | | | | | | | | | | | | % 169.92/26.04 | | | | | | | | | | | | | | | | | | REDUCE: (401), (418) imply: % 169.92/26.04 | | | | | | | | | | | | | | | | | | (419) apply(all_32_6, all_41_2, all_55_0) = all_192_0 % 169.92/26.04 | | | | | | | | | | | | | | | | | | % 169.92/26.04 | | | | | | | | | | | | | | | | | | REDUCE: (401), (417) imply: % 169.92/26.04 | | | | | | | | | | | | | | | | | | (420) apply(all_32_6, all_41_2, all_41_0) = all_192_1 % 169.92/26.04 | | | | | | | | | | | | | | | | | | % 169.92/26.04 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_153_0, all_41_0, % 169.92/26.04 | | | | | | | | | | | | | | | | | | all_41_2, all_32_6, simplifying with (41), (399) % 169.92/26.04 | | | | | | | | | | | | | | | | | | gives: % 169.92/26.04 | | | | | | | | | | | | | | | | | | (421) all_153_0 = 0 % 169.92/26.04 | | | | | | | | | | | | | | | | | | % 169.92/26.04 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_137_0, all_153_0, % 169.92/26.04 | | | | | | | | | | | | | | | | | | all_41_0, all_41_2, all_32_6, simplifying with % 169.92/26.04 | | | | | | | | | | | | | | | | | | (399), (402) gives: % 169.92/26.04 | | | | | | | | | | | | | | | | | | (422) all_153_0 = all_137_0 % 169.92/26.04 | | | | | | | | | | | | | | | | | | % 169.92/26.04 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_132_1, all_172_0, % 169.92/26.04 | | | | | | | | | | | | | | | | | | all_41_0, all_41_2, all_32_6, simplifying with % 169.92/26.04 | | | | | | | | | | | | | | | | | | (403), (412) gives: % 169.92/26.04 | | | | | | | | | | | | | | | | | | (423) all_172_0 = all_132_1 % 169.92/26.04 | | | | | | | | | | | | | | | | | | % 169.92/26.04 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_172_0, all_192_1, % 169.92/26.04 | | | | | | | | | | | | | | | | | | all_41_0, all_41_2, all_32_6, simplifying with % 169.92/26.04 | | | | | | | | | | | | | | | | | | (412), (420) gives: % 169.92/26.04 | | | | | | | | | | | | | | | | | | (424) all_192_1 = all_172_0 % 169.92/26.04 | | | | | | | | | | | | | | | | | | % 169.92/26.04 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_147_0, all_192_1, % 169.92/26.04 | | | | | | | | | | | | | | | | | | all_41_0, all_41_2, all_32_6, simplifying with % 169.92/26.04 | | | | | | | | | | | | | | | | | | (394), (420) gives: % 169.92/26.04 | | | | | | | | | | | | | | | | | | (425) all_192_1 = all_147_0 % 169.92/26.04 | | | | | | | | | | | | | | | | | | % 169.92/26.04 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_137_0, all_192_1, % 169.92/26.04 | | | | | | | | | | | | | | | | | | all_41_0, all_41_2, all_32_6, simplifying with % 169.92/26.04 | | | | | | | | | | | | | | | | | | (402), (420) gives: % 169.92/26.04 | | | | | | | | | | | | | | | | | | (426) all_192_1 = all_137_0 % 169.92/26.04 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_153_1, all_172_1, % 169.92/26.05 | | | | | | | | | | | | | | | | | | all_55_0, all_41_2, all_32_6, simplifying with % 169.92/26.05 | | | | | | | | | | | | | | | | | | (400), (411) gives: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (427) all_172_1 = all_153_1 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_192_0, all_55_0, % 169.92/26.05 | | | | | | | | | | | | | | | | | | all_41_2, all_32_6, simplifying with (70), (419) % 169.92/26.05 | | | | | | | | | | | | | | | | | | gives: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (428) all_192_0 = 0 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_172_1, all_192_0, % 169.92/26.05 | | | | | | | | | | | | | | | | | | all_55_0, all_41_2, all_32_6, simplifying with % 169.92/26.05 | | | | | | | | | | | | | | | | | | (411), (419) gives: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (429) all_192_0 = all_172_1 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (428), (429) imply: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (430) all_172_1 = 0 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | SIMP: (430) implies: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (431) all_172_1 = 0 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (424), (425) imply: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (432) all_172_0 = all_147_0 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | SIMP: (432) implies: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (433) all_172_0 = all_147_0 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (426) imply: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (434) all_147_0 = all_137_0 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (423), (433) imply: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (435) all_147_0 = all_132_1 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | SIMP: (435) implies: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (436) all_147_0 = all_132_1 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (431) imply: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (437) all_153_1 = 0 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (421), (422) imply: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (438) all_137_0 = 0 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | SIMP: (438) implies: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (439) all_137_0 = 0 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (434), (436) imply: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (440) all_137_0 = all_132_1 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | SIMP: (440) implies: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (441) all_137_0 = all_132_1 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (439), (441) imply: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (442) all_132_1 = 0 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | SIMP: (442) implies: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (443) all_132_1 = 0 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (423), (443) imply: % 169.92/26.05 | | | | | | | | | | | | | | | | | | (444) all_172_0 = 0 % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | BETA: splitting (410) gives: % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | Case 1: % 169.92/26.05 | | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | | (445) ~ (all_172_0 = 0) % 169.92/26.05 | | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | | REDUCE: (444), (445) imply: % 169.92/26.05 | | | | | | | | | | | | | | | | | | | (446) $false % 169.92/26.05 | | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | | CLOSE: (446) is inconsistent. % 169.92/26.05 | | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | Case 2: % 169.92/26.05 | | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | | (447) ~ (all_172_1 = 0) % 169.92/26.05 | | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | | REDUCE: (431), (447) imply: % 169.92/26.05 | | | | | | | | | | | | | | | | | | | (448) $false % 169.92/26.05 | | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | | CLOSE: (448) is inconsistent. % 169.92/26.05 | | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | | End of split % 169.92/26.05 | | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | | End of split % 169.92/26.05 | | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | End of split % 169.92/26.05 | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | Case 2: % 169.92/26.05 | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | (449) ~ (all_49_0 = all_41_2) % 169.92/26.05 | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (59), (123), (127), (449) are inconsistent by % 169.92/26.05 | | | | | | | | | | | | | | | | sub-proof #1. % 169.92/26.05 | | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | | End of split % 169.92/26.05 | | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | End of split % 169.92/26.05 | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | End of split % 169.92/26.05 | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | Case 2: % 169.92/26.05 | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | (450) member(all_41_2, all_32_4) = all_119_4 & % 169.92/26.05 | | | | | | | | | | | | | member(all_41_2, all_32_4) = all_119_5 & ( ~ % 169.92/26.05 | | | | | | | | | | | | | (all_119_4 = 0) | ~ (all_119_5 = 0)) % 169.92/26.05 | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | ALPHA: (450) implies: % 169.92/26.05 | | | | | | | | | | | | | (451) member(all_41_2, all_32_4) = all_119_5 % 169.92/26.05 | | | | | | | | | | | | | (452) member(all_41_2, all_32_4) = all_119_4 % 169.92/26.05 | | | | | | | | | | | | | (453) ~ (all_119_4 = 0) | ~ (all_119_5 = 0) % 169.92/26.05 | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_119_4, all_32_4, % 169.92/26.05 | | | | | | | | | | | | | all_41_2, simplifying with (38), (452) gives: % 169.92/26.05 | | | | | | | | | | | | | (454) all_119_4 = 0 % 169.92/26.05 | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_119_5, all_119_4, % 169.92/26.05 | | | | | | | | | | | | | all_32_4, all_41_2, simplifying with (451), (452) % 169.92/26.05 | | | | | | | | | | | | | gives: % 169.92/26.05 | | | | | | | | | | | | | (455) all_119_4 = all_119_5 % 169.92/26.05 | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | COMBINE_EQS: (454), (455) imply: % 169.92/26.05 | | | | | | | | | | | | | (456) all_119_5 = 0 % 169.92/26.05 | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | BETA: splitting (453) gives: % 169.92/26.05 | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | Case 1: % 169.92/26.05 | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | (457) ~ (all_119_4 = 0) % 169.92/26.05 | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | REDUCE: (454), (457) imply: % 169.92/26.05 | | | | | | | | | | | | | | (458) $false % 169.92/26.05 | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | CLOSE: (458) is inconsistent. % 169.92/26.05 | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | Case 2: % 169.92/26.05 | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | (459) ~ (all_119_5 = 0) % 169.92/26.05 | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | REDUCE: (456), (459) imply: % 169.92/26.05 | | | | | | | | | | | | | | (460) $false % 169.92/26.05 | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | | CLOSE: (460) is inconsistent. % 169.92/26.05 | | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | | End of split % 169.92/26.05 | | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | | End of split % 169.92/26.05 | | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | End of split % 169.92/26.05 | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | End of split % 169.92/26.05 | | | | | | | | | | % 169.92/26.05 | | | | | | | | | Case 2: % 169.92/26.05 | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | (461) member(all_41_0, all_32_5) = all_123_4 & % 169.92/26.05 | | | | | | | | | | member(all_41_0, all_32_5) = all_123_5 & ( ~ % 169.92/26.05 | | | | | | | | | | (all_123_4 = 0) | ~ (all_123_5 = 0)) % 169.92/26.05 | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | ALPHA: (461) implies: % 169.92/26.05 | | | | | | | | | | (462) member(all_41_0, all_32_5) = all_123_5 % 169.92/26.05 | | | | | | | | | | (463) member(all_41_0, all_32_5) = all_123_4 % 169.92/26.05 | | | | | | | | | | (464) ~ (all_123_4 = 0) | ~ (all_123_5 = 0) % 169.92/26.05 | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_123_4, all_32_5, % 169.92/26.05 | | | | | | | | | | all_41_0, simplifying with (40), (463) gives: % 169.92/26.05 | | | | | | | | | | (465) all_123_4 = 0 % 169.92/26.05 | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | GROUND_INST: instantiating (8) with all_123_5, all_123_4, % 169.92/26.05 | | | | | | | | | | all_32_5, all_41_0, simplifying with (462), (463) % 169.92/26.05 | | | | | | | | | | gives: % 169.92/26.05 | | | | | | | | | | (466) all_123_4 = all_123_5 % 169.92/26.05 | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | COMBINE_EQS: (465), (466) imply: % 169.92/26.05 | | | | | | | | | | (467) all_123_5 = 0 % 169.92/26.05 | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | SIMP: (467) implies: % 169.92/26.05 | | | | | | | | | | (468) all_123_5 = 0 % 169.92/26.05 | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | BETA: splitting (464) gives: % 169.92/26.05 | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | Case 1: % 169.92/26.05 | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | (469) ~ (all_123_4 = 0) % 169.92/26.05 | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | REDUCE: (465), (469) imply: % 169.92/26.05 | | | | | | | | | | | (470) $false % 169.92/26.05 | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | CLOSE: (470) is inconsistent. % 169.92/26.05 | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | Case 2: % 169.92/26.05 | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | (471) ~ (all_123_5 = 0) % 169.92/26.05 | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | REDUCE: (468), (471) imply: % 169.92/26.05 | | | | | | | | | | | (472) $false % 169.92/26.05 | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | | CLOSE: (472) is inconsistent. % 169.92/26.05 | | | | | | | | | | | % 169.92/26.05 | | | | | | | | | | End of split % 169.92/26.05 | | | | | | | | | | % 169.92/26.05 | | | | | | | | | End of split % 169.92/26.05 | | | | | | | | | % 169.92/26.05 | | | | | | | | End of split % 169.92/26.05 | | | | | | | | % 169.92/26.05 | | | | | | | End of split % 169.92/26.05 | | | | | | | % 169.92/26.05 | | | | | | End of split % 169.92/26.05 | | | | | | % 169.92/26.06 | | | | | End of split % 169.92/26.06 | | | | | % 169.92/26.06 | | | | End of split % 169.92/26.06 | | | | % 169.92/26.06 | | | End of split % 169.92/26.06 | | | % 169.92/26.06 | | End of split % 169.92/26.06 | | % 169.92/26.06 | End of split % 169.92/26.06 | % 169.92/26.06 End of proof % 169.92/26.06 % 169.92/26.06 Sub-proof #1 shows that the following formulas are inconsistent: % 169.92/26.06 ---------------------------------------------------------------- % 169.92/26.06 (1) apply(all_32_8, all_41_1, all_49_0) = 0 % 169.92/26.06 (2) apply(all_32_8, all_41_1, all_41_2) = 0 % 169.92/26.06 (3) all_49_0 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.06 all_41_1, all_49_0) = v0 & apply(all_32_8, all_41_1, all_41_2) = v1 & % 169.92/26.06 ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.06 (4) ~ (all_49_0 = all_41_2) % 169.92/26.06 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 169.92/26.06 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ % 169.92/26.06 (apply(v4, v3, v2) = v0)) % 169.92/26.06 % 169.92/26.06 Begin of proof % 169.92/26.06 | % 169.92/26.06 | BETA: splitting (3) gives: % 169.92/26.06 | % 169.92/26.06 | Case 1: % 169.92/26.06 | | % 169.92/26.06 | | (6) all_49_0 = all_41_2 % 169.92/26.06 | | % 169.92/26.06 | | REDUCE: (4), (6) imply: % 169.92/26.06 | | (7) $false % 169.92/26.06 | | % 169.92/26.06 | | CLOSE: (7) is inconsistent. % 169.92/26.06 | | % 169.92/26.06 | Case 2: % 169.92/26.06 | | % 169.92/26.06 | | (8) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_41_1, all_49_0) = % 169.92/26.06 | | v0 & apply(all_32_8, all_41_1, all_41_2) = v1 & ( ~ (v1 = 0) | ~ % 169.92/26.06 | | (v0 = 0))) % 169.92/26.06 | | % 169.92/26.06 | | DELTA: instantiating (8) with fresh symbols all_186_0, all_186_1 gives: % 169.92/26.06 | | (9) apply(all_32_8, all_41_1, all_49_0) = all_186_1 & apply(all_32_8, % 169.92/26.06 | | all_41_1, all_41_2) = all_186_0 & ( ~ (all_186_0 = 0) | ~ % 169.92/26.06 | | (all_186_1 = 0)) % 169.92/26.06 | | % 169.92/26.06 | | ALPHA: (9) implies: % 169.92/26.06 | | (10) apply(all_32_8, all_41_1, all_41_2) = all_186_0 % 169.92/26.06 | | (11) apply(all_32_8, all_41_1, all_49_0) = all_186_1 % 169.92/26.06 | | (12) ~ (all_186_0 = 0) | ~ (all_186_1 = 0) % 169.92/26.06 | | % 169.92/26.06 | | GROUND_INST: instantiating (5) with 0, all_186_0, all_41_2, all_41_1, % 169.92/26.06 | | all_32_8, simplifying with (2), (10) gives: % 169.92/26.06 | | (13) all_186_0 = 0 % 169.92/26.06 | | % 169.92/26.06 | | GROUND_INST: instantiating (5) with 0, all_186_1, all_49_0, all_41_1, % 169.92/26.06 | | all_32_8, simplifying with (1), (11) gives: % 169.92/26.06 | | (14) all_186_1 = 0 % 169.92/26.06 | | % 169.92/26.06 | | BETA: splitting (12) gives: % 169.92/26.06 | | % 169.92/26.06 | | Case 1: % 169.92/26.06 | | | % 169.92/26.06 | | | (15) ~ (all_186_0 = 0) % 169.92/26.06 | | | % 169.92/26.06 | | | REDUCE: (13), (15) imply: % 169.92/26.06 | | | (16) $false % 169.92/26.06 | | | % 169.92/26.06 | | | CLOSE: (16) is inconsistent. % 169.92/26.06 | | | % 169.92/26.06 | | Case 2: % 169.92/26.06 | | | % 169.92/26.06 | | | (17) ~ (all_186_1 = 0) % 169.92/26.06 | | | % 169.92/26.06 | | | REDUCE: (14), (17) imply: % 169.92/26.06 | | | (18) $false % 169.92/26.06 | | | % 169.92/26.06 | | | CLOSE: (18) is inconsistent. % 169.92/26.06 | | | % 169.92/26.06 | | End of split % 169.92/26.06 | | % 169.92/26.06 | End of split % 169.92/26.06 | % 169.92/26.06 End of proof % 169.92/26.06 % 169.92/26.06 Sub-proof #2 shows that the following formulas are inconsistent: % 169.92/26.06 ---------------------------------------------------------------- % 169.92/26.06 (1) all_123_3 = all_41_2 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 169.92/26.06 (apply(all_32_8, all_119_3, all_123_3) = v2 & member(all_119_3, all_32_5) % 169.92/26.06 = v0 & member(all_41_2, all_32_4) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | % 169.92/26.06 ~ (v0 = 0))) % 169.92/26.06 (2) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.06 all_55_0, all_51_0) = v0 & apply(all_32_8, all_55_0, all_49_0) = v1 & % 169.92/26.06 ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.06 (3) apply(all_32_7, all_41_2, all_41_0) = all_78_1 % 169.92/26.06 (4) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_7, % 169.92/26.06 all_111_0, all_41_0) = v0 & apply(all_32_7, all_111_0, all_41_1) = v1 % 169.92/26.06 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.06 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 169.92/26.06 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = % 169.92/26.06 v0)) % 169.92/26.06 (6) ~ (all_41_0 = all_41_1) % 169.92/26.06 (7) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.06 all_117_0, all_123_3) = v1 & apply(all_32_8, all_117_0, all_51_0) = % 169.92/26.06 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.06 (8) apply(all_32_8, all_41_1, all_121_3) = 0 % 169.92/26.06 (9) all_109_0 = all_41_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.92/26.06 all_41_2, all_109_0) = v0 & apply(all_32_6, all_41_2, all_41_1) = v1 % 169.92/26.06 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.06 (10) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.06 all_41_0, all_51_0) = v0 & apply(all_32_8, all_41_0, all_49_0) = v1 % 169.92/26.06 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.06 (11) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.06 all_41_0, all_123_3) = v0 & apply(all_32_8, all_41_0, all_121_3) = % 169.92/26.06 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.06 (12) all_119_3 = all_109_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.92/26.06 all_51_0, all_119_3) = v0 & apply(all_32_6, all_51_0, all_109_0) = % 169.92/26.06 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.06 (13) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.06 all_55_0, all_51_0) = v0 & apply(all_32_8, all_55_0, all_41_2) = v1 % 169.92/26.06 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.06 (14) all_121_3 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.06 all_117_0, all_121_3) = v0 & apply(all_32_8, all_117_0, all_41_2) = % 169.92/26.06 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.06 (15) all_117_0 = all_41_0 % 169.92/26.06 (16) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.06 all_41_0, all_51_0) = v0 & apply(all_32_8, all_41_0, all_41_2) = v1 % 169.92/26.06 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.06 (17) apply(all_32_8, all_41_1, all_41_2) = 0 % 169.92/26.07 (18) all_123_3 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.07 all_109_0, all_123_3) = v1 & apply(all_32_8, all_109_0, all_41_2) = % 169.92/26.07 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (19) apply(all_32_6, all_41_2, all_41_0) = 0 % 169.92/26.07 (20) all_119_3 = all_109_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.92/26.07 all_51_0, all_119_3) = v1 & apply(all_32_6, all_51_0, all_109_0) = % 169.92/26.07 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (21) apply(all_32_8, all_41_0, all_41_2) = 0 % 169.92/26.07 (22) all_111_0 = all_41_2 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 169.92/26.07 (apply(all_32_8, all_41_0, all_41_2) = v2 & member(all_111_0, all_32_4) % 169.92/26.07 = v1 & member(all_41_0, all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | % 169.92/26.07 ~ (v0 = 0))) % 169.92/26.07 (23) all_123_3 = all_111_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.07 all_109_0, all_123_3) = v1 & apply(all_32_8, all_109_0, all_111_0) = % 169.92/26.07 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (24) all_119_3 = all_109_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.92/26.07 all_111_0, all_119_3) = v1 & apply(all_32_6, all_111_0, all_109_0) = % 169.92/26.07 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (25) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.07 all_41_0, all_123_3) = v0 & apply(all_32_8, all_41_0, all_51_0) = v1 % 169.92/26.07 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (26) apply(all_32_6, all_51_0, all_41_0) = all_154_1 % 169.92/26.07 (27) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.07 all_117_0, all_123_3) = v0 & apply(all_32_8, all_117_0, all_121_3) = % 169.92/26.07 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (28) ~ (all_78_0 = 0) | ~ (all_78_1 = 0) % 169.92/26.07 (29) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.07 all_109_0, all_123_3) = v1 & apply(all_32_8, all_109_0, all_51_0) = % 169.92/26.07 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (30) apply(all_32_7, all_123_3, all_41_0) = 0 % 169.92/26.07 (31) apply(all_32_7, all_41_2, all_41_1) = all_78_0 % 169.92/26.07 (32) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.07 all_117_0, all_123_3) = v0 & apply(all_32_8, all_117_0, all_51_0) = % 169.92/26.07 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (33) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.07 all_119_3, all_123_3) = v1 & apply(all_32_8, all_119_3, all_121_3) = % 169.92/26.07 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (34) all_111_0 = all_51_0 % 169.92/26.07 (35) all_123_3 = all_111_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.07 all_109_0, all_123_3) = v0 & apply(all_32_8, all_109_0, all_111_0) = % 169.92/26.07 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (36) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.07 all_55_0, all_51_0) = v1 & apply(all_32_8, all_55_0, all_49_0) = v0 % 169.92/26.07 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (37) member(all_41_0, all_32_5) = 0 % 169.92/26.07 (38) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.07 all_55_0, all_51_0) = v1 & apply(all_32_8, all_55_0, all_41_2) = v0 % 169.92/26.07 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (39) all_119_3 = all_109_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.92/26.07 all_111_0, all_119_3) = v0 & apply(all_32_6, all_111_0, all_109_0) = % 169.92/26.07 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (40) member(all_51_0, all_32_4) = 0 % 169.92/26.07 (41) all_121_3 = all_111_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.07 all_41_1, all_121_3) = v0 & apply(all_32_8, all_41_1, all_111_0) = % 169.92/26.07 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (42) apply(all_32_8, all_41_0, all_123_3) = 0 % 169.92/26.07 (43) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.07 all_41_0, all_123_3) = v1 & apply(all_32_8, all_41_0, all_121_3) = % 169.92/26.07 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (44) all_119_3 = all_41_0 % 169.92/26.07 (45) all_121_3 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.07 all_119_3, all_121_3) = v0 & apply(all_32_8, all_119_3, all_41_2) = % 169.92/26.07 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (46) all_55_0 = all_41_0 % 169.92/26.07 (47) all_119_3 = all_109_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.92/26.07 all_41_2, all_119_3) = v0 & apply(all_32_6, all_41_2, all_109_0) = % 169.92/26.07 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (48) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.07 all_119_3, all_123_3) = v0 & apply(all_32_8, all_119_3, all_51_0) = % 169.92/26.07 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (49) apply(all_32_7, all_51_0, all_41_0) = all_173_1 % 169.92/26.07 (50) all_49_0 = all_41_2 % 169.92/26.07 (51) apply(all_32_7, all_51_0, all_41_1) = all_173_0 % 169.92/26.07 (52) apply(all_32_8, all_41_0, all_51_0) = 0 % 169.92/26.07 (53) all_119_3 = all_109_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.92/26.07 all_41_2, all_119_3) = v1 & apply(all_32_6, all_41_2, all_109_0) = % 169.92/26.07 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.07 (54) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.07 all_41_0, all_51_0) = v1 & apply(all_32_8, all_41_0, all_49_0) = v0 % 169.92/26.07 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.08 (55) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 169.92/26.08 (apply(all_32_8, all_41_0, all_49_0) = v2 & member(all_51_0, all_32_4) = % 169.92/26.08 v1 & member(all_41_0, all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 169.92/26.08 (v0 = 0))) % 169.92/26.08 (56) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.08 all_119_3, all_123_3) = v0 & apply(all_32_8, all_119_3, all_121_3) = % 169.92/26.08 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.08 (57) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 169.92/26.08 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ % 169.92/26.08 (apply(v4, v3, v2) = v0)) % 169.92/26.08 (58) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.08 all_109_0, all_123_3) = v0 & apply(all_32_8, all_109_0, all_51_0) = % 169.92/26.08 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.08 (59) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.08 all_109_0, all_123_3) = v0 & apply(all_32_8, all_109_0, all_121_3) = % 169.92/26.08 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.08 (60) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.92/26.08 all_123_3, all_41_0) = v0 & apply(all_32_6, all_123_3, all_41_1) = % 169.92/26.08 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.08 (61) apply(all_32_7, all_121_3, all_41_1) = 0 % 169.92/26.08 (62) all_111_0 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.08 all_117_0, all_111_0) = v1 & apply(all_32_8, all_117_0, all_41_2) = % 169.92/26.08 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.08 (63) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.08 all_109_0, all_123_3) = v1 & apply(all_32_8, all_109_0, all_121_3) = % 169.92/26.08 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.08 (64) all_123_3 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.08 all_109_0, all_123_3) = v0 & apply(all_32_8, all_109_0, all_41_2) = % 169.92/26.08 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.08 (65) apply(all_32_6, all_51_0, all_109_0) = 0 % 169.92/26.08 (66) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.08 all_41_0, all_51_0) = v1 & apply(all_32_8, all_41_0, all_41_2) = v0 % 169.92/26.08 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.08 (67) all_121_3 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.08 all_117_0, all_121_3) = v1 & apply(all_32_8, all_117_0, all_41_2) = % 169.92/26.08 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.08 (68) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 169.92/26.08 (apply(all_32_8, all_41_0, all_41_2) = v2 & member(all_51_0, all_32_4) = % 169.92/26.08 v1 & member(all_41_0, all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 169.92/26.08 (v0 = 0))) % 169.92/26.08 (69) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.08 all_119_3, all_123_3) = v1 & apply(all_32_8, all_119_3, all_51_0) = % 169.92/26.08 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.08 % 169.92/26.08 Begin of proof % 169.92/26.08 | % 169.92/26.08 | BETA: splitting (4) gives: % 169.92/26.08 | % 169.92/26.08 | Case 1: % 169.92/26.08 | | % 169.92/26.08 | | (70) all_41_0 = all_41_1 % 169.92/26.08 | | % 169.92/26.08 | | REDUCE: (6), (70) imply: % 169.92/26.08 | | (71) $false % 169.92/26.08 | | % 169.92/26.08 | | CLOSE: (71) is inconsistent. % 169.92/26.08 | | % 169.92/26.08 | Case 2: % 169.92/26.08 | | % 169.92/26.08 | | (72) ? [v0: any] : ? [v1: any] : (apply(all_32_7, all_111_0, all_41_0) % 169.92/26.08 | | = v0 & apply(all_32_7, all_111_0, all_41_1) = v1 & ( ~ (v1 = 0) | % 169.92/26.08 | | ~ (v0 = 0))) % 169.92/26.08 | | % 169.92/26.08 | | DELTA: instantiating (72) with fresh symbols all_244_0, all_244_1 gives: % 169.92/26.08 | | (73) apply(all_32_7, all_111_0, all_41_0) = all_244_1 & apply(all_32_7, % 169.92/26.08 | | all_111_0, all_41_1) = all_244_0 & ( ~ (all_244_0 = 0) | ~ % 169.92/26.08 | | (all_244_1 = 0)) % 169.92/26.08 | | % 169.92/26.08 | | ALPHA: (73) implies: % 169.92/26.08 | | (74) apply(all_32_7, all_111_0, all_41_1) = all_244_0 % 169.92/26.08 | | (75) apply(all_32_7, all_111_0, all_41_0) = all_244_1 % 169.92/26.08 | | % 169.92/26.08 | | REDUCE: (34), (75) imply: % 169.92/26.08 | | (76) apply(all_32_7, all_51_0, all_41_0) = all_244_1 % 169.92/26.08 | | % 169.92/26.08 | | REDUCE: (34), (74) imply: % 169.92/26.08 | | (77) apply(all_32_7, all_51_0, all_41_1) = all_244_0 % 169.92/26.08 | | % 169.92/26.08 | | BETA: splitting (62) gives: % 169.92/26.08 | | % 169.92/26.08 | | Case 1: % 169.92/26.08 | | | % 169.92/26.08 | | | (78) all_111_0 = all_41_2 % 169.92/26.08 | | | % 169.92/26.08 | | | COMBINE_EQS: (34), (78) imply: % 169.92/26.08 | | | (79) all_51_0 = all_41_2 % 169.92/26.08 | | | % 169.92/26.08 | | | SIMP: (79) implies: % 169.92/26.08 | | | (80) all_51_0 = all_41_2 % 169.92/26.08 | | | % 169.92/26.08 | | | REDUCE: (65), (80) imply: % 169.92/26.08 | | | (81) apply(all_32_6, all_41_2, all_109_0) = 0 % 169.92/26.08 | | | % 169.92/26.08 | | | REDUCE: (26), (80) imply: % 169.92/26.08 | | | (82) apply(all_32_6, all_41_2, all_41_0) = all_154_1 % 169.92/26.08 | | | % 169.92/26.08 | | | REDUCE: (76), (80) imply: % 169.92/26.08 | | | (83) apply(all_32_7, all_41_2, all_41_0) = all_244_1 % 169.92/26.08 | | | % 169.92/26.08 | | | REDUCE: (49), (80) imply: % 169.92/26.08 | | | (84) apply(all_32_7, all_41_2, all_41_0) = all_173_1 % 169.92/26.08 | | | % 169.92/26.08 | | | REDUCE: (77), (80) imply: % 169.92/26.08 | | | (85) apply(all_32_7, all_41_2, all_41_1) = all_244_0 % 169.92/26.08 | | | % 169.92/26.08 | | | REDUCE: (51), (80) imply: % 169.92/26.08 | | | (86) apply(all_32_7, all_41_2, all_41_1) = all_173_0 % 169.92/26.08 | | | % 169.92/26.08 | | | BETA: splitting (41) gives: % 169.92/26.08 | | | % 169.92/26.08 | | | Case 1: % 169.92/26.08 | | | | % 169.92/26.08 | | | | (87) all_121_3 = all_111_0 % 169.92/26.08 | | | | % 169.92/26.08 | | | | COMBINE_EQS: (78), (87) imply: % 169.92/26.08 | | | | (88) all_121_3 = all_41_2 % 169.92/26.08 | | | | % 169.92/26.08 | | | | REDUCE: (61), (88) imply: % 169.92/26.08 | | | | (89) apply(all_32_7, all_41_2, all_41_1) = 0 % 169.92/26.08 | | | | % 169.92/26.08 | | | | BETA: splitting (7) gives: % 169.92/26.08 | | | | % 169.92/26.08 | | | | Case 1: % 169.92/26.08 | | | | | % 169.92/26.08 | | | | | (90) all_123_3 = all_51_0 % 169.92/26.08 | | | | | % 169.92/26.08 | | | | | COMBINE_EQS: (80), (90) imply: % 169.92/26.08 | | | | | (91) all_123_3 = all_41_2 % 169.92/26.08 | | | | | % 169.92/26.08 | | | | | REDUCE: (30), (91) imply: % 169.92/26.08 | | | | | (92) apply(all_32_7, all_41_2, all_41_0) = 0 % 169.92/26.08 | | | | | % 169.92/26.08 | | | | | GROUND_INST: instantiating (57) with all_78_0, all_173_0, all_41_1, % 169.92/26.08 | | | | | all_41_2, all_32_7, simplifying with (31), (86) gives: % 169.92/26.08 | | | | | (93) all_173_0 = all_78_0 % 169.92/26.08 | | | | | % 169.92/26.08 | | | | | GROUND_INST: instantiating (57) with all_173_0, all_244_0, all_41_1, % 169.92/26.08 | | | | | all_41_2, all_32_7, simplifying with (85), (86) gives: % 169.92/26.08 | | | | | (94) all_244_0 = all_173_0 % 169.92/26.08 | | | | | % 169.92/26.08 | | | | | GROUND_INST: instantiating (57) with 0, all_244_0, all_41_1, all_41_2, % 169.92/26.08 | | | | | all_32_7, simplifying with (85), (89) gives: % 169.92/26.08 | | | | | (95) all_244_0 = 0 % 169.92/26.08 | | | | | % 169.92/26.08 | | | | | GROUND_INST: instantiating (57) with 0, all_173_1, all_41_0, all_41_2, % 169.92/26.08 | | | | | all_32_7, simplifying with (84), (92) gives: % 169.92/26.08 | | | | | (96) all_173_1 = 0 % 169.92/26.08 | | | | | % 169.92/26.08 | | | | | GROUND_INST: instantiating (57) with all_78_1, all_244_1, all_41_0, % 169.92/26.08 | | | | | all_41_2, all_32_7, simplifying with (3), (83) gives: % 169.92/26.08 | | | | | (97) all_244_1 = all_78_1 % 169.92/26.08 | | | | | % 169.92/26.08 | | | | | GROUND_INST: instantiating (57) with all_173_1, all_244_1, all_41_0, % 169.92/26.08 | | | | | all_41_2, all_32_7, simplifying with (83), (84) gives: % 169.92/26.08 | | | | | (98) all_244_1 = all_173_1 % 169.92/26.08 | | | | | % 169.92/26.08 | | | | | COMBINE_EQS: (94), (95) imply: % 169.92/26.08 | | | | | (99) all_173_0 = 0 % 169.92/26.08 | | | | | % 169.92/26.08 | | | | | SIMP: (99) implies: % 169.92/26.08 | | | | | (100) all_173_0 = 0 % 169.92/26.08 | | | | | % 169.92/26.08 | | | | | COMBINE_EQS: (97), (98) imply: % 169.92/26.08 | | | | | (101) all_173_1 = all_78_1 % 169.92/26.08 | | | | | % 169.92/26.08 | | | | | SIMP: (101) implies: % 169.92/26.09 | | | | | (102) all_173_1 = all_78_1 % 169.92/26.09 | | | | | % 169.92/26.09 | | | | | COMBINE_EQS: (93), (100) imply: % 169.92/26.09 | | | | | (103) all_78_0 = 0 % 169.92/26.09 | | | | | % 169.92/26.09 | | | | | SIMP: (103) implies: % 169.92/26.09 | | | | | (104) all_78_0 = 0 % 169.92/26.09 | | | | | % 169.92/26.09 | | | | | COMBINE_EQS: (96), (102) imply: % 169.92/26.09 | | | | | (105) all_78_1 = 0 % 169.92/26.09 | | | | | % 169.92/26.09 | | | | | BETA: splitting (28) gives: % 169.92/26.09 | | | | | % 169.92/26.09 | | | | | Case 1: % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | | (106) ~ (all_78_0 = 0) % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | | REDUCE: (104), (106) imply: % 169.92/26.09 | | | | | | (107) $false % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | | CLOSE: (107) is inconsistent. % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | Case 2: % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | | (108) ~ (all_78_1 = 0) % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | | REDUCE: (105), (108) imply: % 169.92/26.09 | | | | | | (109) $false % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | | CLOSE: (109) is inconsistent. % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | End of split % 169.92/26.09 | | | | | % 169.92/26.09 | | | | Case 2: % 169.92/26.09 | | | | | % 169.92/26.09 | | | | | (110) ~ (all_123_3 = all_51_0) % 169.92/26.09 | | | | | % 169.92/26.09 | | | | | REDUCE: (80), (110) imply: % 169.92/26.09 | | | | | (111) ~ (all_123_3 = all_41_2) % 169.92/26.09 | | | | | % 169.92/26.09 | | | | | BETA: splitting (23) gives: % 169.92/26.09 | | | | | % 169.92/26.09 | | | | | Case 1: % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | | (112) all_123_3 = all_111_0 % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | | COMBINE_EQS: (78), (112) imply: % 169.92/26.09 | | | | | | (113) all_123_3 = all_41_2 % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | | REDUCE: (111), (113) imply: % 169.92/26.09 | | | | | | (114) $false % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | | CLOSE: (114) is inconsistent. % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | Case 2: % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | | (115) ~ (all_123_3 = all_111_0) % 169.92/26.09 | | | | | | (116) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_109_0, % 169.92/26.09 | | | | | | all_123_3) = v1 & apply(all_32_8, all_109_0, all_111_0) % 169.92/26.09 | | | | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | | DELTA: instantiating (116) with fresh symbols all_506_0, all_506_1 % 169.92/26.09 | | | | | | gives: % 169.92/26.09 | | | | | | (117) apply(all_32_8, all_109_0, all_123_3) = all_506_0 & % 169.92/26.09 | | | | | | apply(all_32_8, all_109_0, all_111_0) = all_506_1 & ( ~ % 169.92/26.09 | | | | | | (all_506_0 = 0) | ~ (all_506_1 = 0)) % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | | ALPHA: (117) implies: % 169.92/26.09 | | | | | | (118) apply(all_32_8, all_109_0, all_123_3) = all_506_0 % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | | BETA: splitting (35) gives: % 169.92/26.09 | | | | | | % 169.92/26.09 | | | | | | Case 1: % 169.92/26.09 | | | | | | | % 169.92/26.09 | | | | | | | (119) all_123_3 = all_111_0 % 169.92/26.09 | | | | | | | % 169.92/26.09 | | | | | | | COMBINE_EQS: (78), (119) imply: % 169.92/26.09 | | | | | | | (120) all_123_3 = all_41_2 % 169.92/26.09 | | | | | | | % 169.92/26.09 | | | | | | | REDUCE: (111), (120) imply: % 169.92/26.09 | | | | | | | (121) $false % 169.92/26.09 | | | | | | | % 169.92/26.09 | | | | | | | CLOSE: (121) is inconsistent. % 169.92/26.09 | | | | | | | % 169.92/26.09 | | | | | | Case 2: % 169.92/26.09 | | | | | | | % 169.92/26.09 | | | | | | | (122) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_109_0, % 169.92/26.09 | | | | | | | all_123_3) = v0 & apply(all_32_8, all_109_0, % 169.92/26.09 | | | | | | | all_111_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.09 | | | | | | | % 169.92/26.09 | | | | | | | DELTA: instantiating (122) with fresh symbols all_511_0, all_511_1 % 169.92/26.09 | | | | | | | gives: % 169.92/26.09 | | | | | | | (123) apply(all_32_8, all_109_0, all_123_3) = all_511_1 & % 169.92/26.09 | | | | | | | apply(all_32_8, all_109_0, all_111_0) = all_511_0 & ( ~ % 169.92/26.09 | | | | | | | (all_511_0 = 0) | ~ (all_511_1 = 0)) % 169.92/26.09 | | | | | | | % 169.92/26.09 | | | | | | | ALPHA: (123) implies: % 169.92/26.09 | | | | | | | (124) apply(all_32_8, all_109_0, all_111_0) = all_511_0 % 169.92/26.09 | | | | | | | (125) apply(all_32_8, all_109_0, all_123_3) = all_511_1 % 169.92/26.09 | | | | | | | (126) ~ (all_511_0 = 0) | ~ (all_511_1 = 0) % 169.92/26.09 | | | | | | | % 169.92/26.09 | | | | | | | REDUCE: (78), (124) imply: % 169.92/26.09 | | | | | | | (127) apply(all_32_8, all_109_0, all_41_2) = all_511_0 % 169.92/26.09 | | | | | | | % 169.92/26.09 | | | | | | | BETA: splitting (63) gives: % 169.92/26.09 | | | | | | | % 169.92/26.09 | | | | | | | Case 1: % 169.92/26.09 | | | | | | | | % 169.92/26.09 | | | | | | | | (128) all_123_3 = all_121_3 % 169.92/26.09 | | | | | | | | % 169.92/26.09 | | | | | | | | COMBINE_EQS: (88), (128) imply: % 169.92/26.09 | | | | | | | | (129) all_123_3 = all_41_2 % 169.92/26.09 | | | | | | | | % 169.92/26.09 | | | | | | | | REDUCE: (111), (129) imply: % 169.92/26.09 | | | | | | | | (130) $false % 169.92/26.09 | | | | | | | | % 169.92/26.09 | | | | | | | | CLOSE: (130) is inconsistent. % 169.92/26.09 | | | | | | | | % 169.92/26.09 | | | | | | | Case 2: % 169.92/26.09 | | | | | | | | % 169.92/26.09 | | | | | | | | (131) ~ (all_123_3 = all_121_3) % 169.92/26.09 | | | | | | | | (132) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.09 | | | | | | | | all_109_0, all_123_3) = v1 & apply(all_32_8, % 169.92/26.09 | | | | | | | | all_109_0, all_121_3) = v0 & ( ~ (v1 = 0) | ~ (v0 % 169.92/26.09 | | | | | | | | = 0))) % 169.92/26.09 | | | | | | | | % 169.92/26.09 | | | | | | | | DELTA: instantiating (132) with fresh symbols all_576_0, % 169.92/26.09 | | | | | | | | all_576_1 gives: % 169.92/26.09 | | | | | | | | (133) apply(all_32_8, all_109_0, all_123_3) = all_576_0 & % 169.92/26.09 | | | | | | | | apply(all_32_8, all_109_0, all_121_3) = all_576_1 & ( ~ % 169.92/26.09 | | | | | | | | (all_576_0 = 0) | ~ (all_576_1 = 0)) % 169.92/26.09 | | | | | | | | % 169.92/26.09 | | | | | | | | ALPHA: (133) implies: % 169.92/26.09 | | | | | | | | (134) apply(all_32_8, all_109_0, all_123_3) = all_576_0 % 169.92/26.09 | | | | | | | | % 169.92/26.09 | | | | | | | | BETA: splitting (59) gives: % 169.92/26.09 | | | | | | | | % 169.92/26.09 | | | | | | | | Case 1: % 169.92/26.09 | | | | | | | | | % 169.92/26.09 | | | | | | | | | (135) all_123_3 = all_121_3 % 169.92/26.09 | | | | | | | | | % 169.92/26.09 | | | | | | | | | COMBINE_EQS: (88), (135) imply: % 169.92/26.09 | | | | | | | | | (136) all_123_3 = all_41_2 % 169.92/26.09 | | | | | | | | | % 169.92/26.09 | | | | | | | | | REDUCE: (111), (136) imply: % 169.92/26.09 | | | | | | | | | (137) $false % 169.92/26.09 | | | | | | | | | % 169.92/26.09 | | | | | | | | | CLOSE: (137) is inconsistent. % 169.92/26.09 | | | | | | | | | % 169.92/26.09 | | | | | | | | Case 2: % 169.92/26.09 | | | | | | | | | % 169.92/26.09 | | | | | | | | | (138) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.09 | | | | | | | | | all_109_0, all_123_3) = v0 & apply(all_32_8, % 169.92/26.09 | | | | | | | | | all_109_0, all_121_3) = v1 & ( ~ (v1 = 0) | ~ % 169.92/26.09 | | | | | | | | | (v0 = 0))) % 169.92/26.09 | | | | | | | | | % 169.92/26.09 | | | | | | | | | DELTA: instantiating (138) with fresh symbols all_586_0, % 169.92/26.09 | | | | | | | | | all_586_1 gives: % 169.92/26.09 | | | | | | | | | (139) apply(all_32_8, all_109_0, all_123_3) = all_586_1 & % 169.92/26.09 | | | | | | | | | apply(all_32_8, all_109_0, all_121_3) = all_586_0 & ( % 169.92/26.09 | | | | | | | | | ~ (all_586_0 = 0) | ~ (all_586_1 = 0)) % 169.92/26.09 | | | | | | | | | % 169.92/26.09 | | | | | | | | | ALPHA: (139) implies: % 169.92/26.09 | | | | | | | | | (140) apply(all_32_8, all_109_0, all_123_3) = all_586_1 % 169.92/26.09 | | | | | | | | | % 169.92/26.09 | | | | | | | | | BETA: splitting (29) gives: % 169.92/26.09 | | | | | | | | | % 169.92/26.09 | | | | | | | | | Case 1: % 169.92/26.09 | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | (141) all_123_3 = all_51_0 % 169.92/26.09 | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | COMBINE_EQS: (80), (141) imply: % 169.92/26.09 | | | | | | | | | | (142) all_123_3 = all_41_2 % 169.92/26.09 | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | REDUCE: (111), (142) imply: % 169.92/26.09 | | | | | | | | | | (143) $false % 169.92/26.09 | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | CLOSE: (143) is inconsistent. % 169.92/26.09 | | | | | | | | | | % 169.92/26.09 | | | | | | | | | Case 2: % 169.92/26.09 | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | (144) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.09 | | | | | | | | | | all_109_0, all_123_3) = v1 & apply(all_32_8, % 169.92/26.09 | | | | | | | | | | all_109_0, all_51_0) = v0 & ( ~ (v1 = 0) | ~ % 169.92/26.09 | | | | | | | | | | (v0 = 0))) % 169.92/26.09 | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | DELTA: instantiating (144) with fresh symbols all_591_0, % 169.92/26.09 | | | | | | | | | | all_591_1 gives: % 169.92/26.09 | | | | | | | | | | (145) apply(all_32_8, all_109_0, all_123_3) = all_591_0 & % 169.92/26.09 | | | | | | | | | | apply(all_32_8, all_109_0, all_51_0) = all_591_1 & % 169.92/26.09 | | | | | | | | | | ( ~ (all_591_0 = 0) | ~ (all_591_1 = 0)) % 169.92/26.09 | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | ALPHA: (145) implies: % 169.92/26.09 | | | | | | | | | | (146) apply(all_32_8, all_109_0, all_123_3) = all_591_0 % 169.92/26.09 | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | BETA: splitting (18) gives: % 169.92/26.09 | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | Case 1: % 169.92/26.09 | | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | | (147) all_123_3 = all_41_2 % 169.92/26.09 | | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | | REDUCE: (111), (147) imply: % 169.92/26.09 | | | | | | | | | | | (148) $false % 169.92/26.09 | | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | | CLOSE: (148) is inconsistent. % 169.92/26.09 | | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | Case 2: % 169.92/26.09 | | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | | (149) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.09 | | | | | | | | | | | all_109_0, all_123_3) = v1 & apply(all_32_8, % 169.92/26.09 | | | | | | | | | | | all_109_0, all_41_2) = v0 & ( ~ (v1 = 0) | ~ % 169.92/26.09 | | | | | | | | | | | (v0 = 0))) % 169.92/26.09 | | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | | DELTA: instantiating (149) with fresh symbols all_606_0, % 169.92/26.09 | | | | | | | | | | | all_606_1 gives: % 169.92/26.09 | | | | | | | | | | | (150) apply(all_32_8, all_109_0, all_123_3) = all_606_0 % 169.92/26.09 | | | | | | | | | | | & apply(all_32_8, all_109_0, all_41_2) = all_606_1 % 169.92/26.09 | | | | | | | | | | | & ( ~ (all_606_0 = 0) | ~ (all_606_1 = 0)) % 169.92/26.09 | | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | | ALPHA: (150) implies: % 169.92/26.09 | | | | | | | | | | | (151) apply(all_32_8, all_109_0, all_41_2) = all_606_1 % 169.92/26.09 | | | | | | | | | | | (152) apply(all_32_8, all_109_0, all_123_3) = all_606_0 % 169.92/26.09 | | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | | BETA: splitting (58) gives: % 169.92/26.09 | | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | | Case 1: % 169.92/26.09 | | | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | | | (153) all_123_3 = all_51_0 % 169.92/26.09 | | | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | | | COMBINE_EQS: (80), (153) imply: % 169.92/26.09 | | | | | | | | | | | | (154) all_123_3 = all_41_2 % 169.92/26.09 | | | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | | | REDUCE: (111), (154) imply: % 169.92/26.09 | | | | | | | | | | | | (155) $false % 169.92/26.09 | | | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | | | CLOSE: (155) is inconsistent. % 169.92/26.09 | | | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | | Case 2: % 169.92/26.09 | | | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | | | (156) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.09 | | | | | | | | | | | | all_109_0, all_123_3) = v0 & apply(all_32_8, % 169.92/26.09 | | | | | | | | | | | | all_109_0, all_51_0) = v1 & ( ~ (v1 = 0) | ~ % 169.92/26.09 | | | | | | | | | | | | (v0 = 0))) % 169.92/26.09 | | | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | | | DELTA: instantiating (156) with fresh symbols all_616_0, % 169.92/26.09 | | | | | | | | | | | | all_616_1 gives: % 169.92/26.09 | | | | | | | | | | | | (157) apply(all_32_8, all_109_0, all_123_3) = all_616_1 % 169.92/26.09 | | | | | | | | | | | | & apply(all_32_8, all_109_0, all_51_0) = all_616_0 % 169.92/26.09 | | | | | | | | | | | | & ( ~ (all_616_0 = 0) | ~ (all_616_1 = 0)) % 169.92/26.09 | | | | | | | | | | | | % 169.92/26.09 | | | | | | | | | | | | ALPHA: (157) implies: % 169.92/26.09 | | | | | | | | | | | | (158) apply(all_32_8, all_109_0, all_51_0) = all_616_0 % 169.92/26.09 | | | | | | | | | | | | (159) apply(all_32_8, all_109_0, all_123_3) = all_616_1 % 169.92/26.09 | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | REDUCE: (80), (158) imply: % 169.92/26.10 | | | | | | | | | | | | (160) apply(all_32_8, all_109_0, all_41_2) = all_616_0 % 169.92/26.10 | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | BETA: splitting (64) gives: % 169.92/26.10 | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | Case 1: % 169.92/26.10 | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | (161) all_123_3 = all_41_2 % 169.92/26.10 | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | REDUCE: (111), (161) imply: % 169.92/26.10 | | | | | | | | | | | | | (162) $false % 169.92/26.10 | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | CLOSE: (162) is inconsistent. % 169.92/26.10 | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | Case 2: % 169.92/26.10 | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | (163) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.10 | | | | | | | | | | | | | all_109_0, all_123_3) = v0 & apply(all_32_8, % 169.92/26.10 | | | | | | | | | | | | | all_109_0, all_41_2) = v1 & ( ~ (v1 = 0) | ~ % 169.92/26.10 | | | | | | | | | | | | | (v0 = 0))) % 169.92/26.10 | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | DELTA: instantiating (163) with fresh symbols all_621_0, % 169.92/26.10 | | | | | | | | | | | | | all_621_1 gives: % 169.92/26.10 | | | | | | | | | | | | | (164) apply(all_32_8, all_109_0, all_123_3) = all_621_1 % 169.92/26.10 | | | | | | | | | | | | | & apply(all_32_8, all_109_0, all_41_2) = all_621_0 % 169.92/26.10 | | | | | | | | | | | | | & ( ~ (all_621_0 = 0) | ~ (all_621_1 = 0)) % 169.92/26.10 | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | ALPHA: (164) implies: % 169.92/26.10 | | | | | | | | | | | | | (165) apply(all_32_8, all_109_0, all_123_3) = all_621_1 % 169.92/26.10 | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | BETA: splitting (47) gives: % 169.92/26.10 | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | Case 1: % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | (166) all_119_3 = all_109_0 % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | COMBINE_EQS: (44), (166) imply: % 169.92/26.10 | | | | | | | | | | | | | | (167) all_109_0 = all_41_0 % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | REDUCE: (165), (167) imply: % 169.92/26.10 | | | | | | | | | | | | | | (168) apply(all_32_8, all_41_0, all_123_3) = all_621_1 % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | REDUCE: (159), (167) imply: % 169.92/26.10 | | | | | | | | | | | | | | (169) apply(all_32_8, all_41_0, all_123_3) = all_616_1 % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | REDUCE: (152), (167) imply: % 169.92/26.10 | | | | | | | | | | | | | | (170) apply(all_32_8, all_41_0, all_123_3) = all_606_0 % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | REDUCE: (146), (167) imply: % 169.92/26.10 | | | | | | | | | | | | | | (171) apply(all_32_8, all_41_0, all_123_3) = all_591_0 % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | REDUCE: (140), (167) imply: % 169.92/26.10 | | | | | | | | | | | | | | (172) apply(all_32_8, all_41_0, all_123_3) = all_586_1 % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | REDUCE: (134), (167) imply: % 169.92/26.10 | | | | | | | | | | | | | | (173) apply(all_32_8, all_41_0, all_123_3) = all_576_0 % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | REDUCE: (125), (167) imply: % 169.92/26.10 | | | | | | | | | | | | | | (174) apply(all_32_8, all_41_0, all_123_3) = all_511_1 % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | REDUCE: (118), (167) imply: % 169.92/26.10 | | | | | | | | | | | | | | (175) apply(all_32_8, all_41_0, all_123_3) = all_506_0 % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | REDUCE: (160), (167) imply: % 169.92/26.10 | | | | | | | | | | | | | | (176) apply(all_32_8, all_41_0, all_41_2) = all_616_0 % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | REDUCE: (151), (167) imply: % 169.92/26.10 | | | | | | | | | | | | | | (177) apply(all_32_8, all_41_0, all_41_2) = all_606_1 % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | REDUCE: (127), (167) imply: % 169.92/26.10 | | | | | | | | | | | | | | (178) apply(all_32_8, all_41_0, all_41_2) = all_511_0 % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | BETA: splitting (9) gives: % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | Case 1: % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | (179) all_109_0 = all_41_1 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | COMBINE_EQS: (167), (179) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (180) all_41_0 = all_41_1 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | SIMP: (180) implies: % 169.92/26.10 | | | | | | | | | | | | | | | (181) all_41_0 = all_41_1 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | REDUCE: (6), (181) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (182) $false % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | CLOSE: (182) is inconsistent. % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | Case 2: % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_606_1, all_616_0, % 169.92/26.10 | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 169.92/26.10 | | | | | | | | | | | | | | | (176), (177) gives: % 169.92/26.10 | | | | | | | | | | | | | | | (183) all_616_0 = all_606_1 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_511_0, all_616_0, % 169.92/26.10 | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 169.92/26.10 | | | | | | | | | | | | | | | (176), (178) gives: % 169.92/26.10 | | | | | | | | | | | | | | | (184) all_616_0 = all_511_0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with 0, all_616_0, all_41_2, % 169.92/26.10 | | | | | | | | | | | | | | | all_41_0, all_32_8, simplifying with (21), (176) % 169.92/26.10 | | | | | | | | | | | | | | | gives: % 169.92/26.10 | | | | | | | | | | | | | | | (185) all_616_0 = 0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with 0, all_586_1, all_123_3, % 169.92/26.10 | | | | | | | | | | | | | | | all_41_0, all_32_8, simplifying with (42), (172) % 169.92/26.10 | | | | | | | | | | | | | | | gives: % 169.92/26.10 | | | | | | | | | | | | | | | (186) all_586_1 = 0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_586_1, all_591_0, % 169.92/26.10 | | | | | | | | | | | | | | | all_123_3, all_41_0, all_32_8, simplifying with % 169.92/26.10 | | | | | | | | | | | | | | | (171), (172) gives: % 169.92/26.10 | | | | | | | | | | | | | | | (187) all_591_0 = all_586_1 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_506_0, all_591_0, % 169.92/26.10 | | | | | | | | | | | | | | | all_123_3, all_41_0, all_32_8, simplifying with % 169.92/26.10 | | | | | | | | | | | | | | | (171), (175) gives: % 169.92/26.10 | | | | | | | | | | | | | | | (188) all_591_0 = all_506_0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_586_1, all_606_0, % 169.92/26.10 | | | | | | | | | | | | | | | all_123_3, all_41_0, all_32_8, simplifying with % 169.92/26.10 | | | | | | | | | | | | | | | (170), (172) gives: % 169.92/26.10 | | | | | | | | | | | | | | | (189) all_606_0 = all_586_1 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_511_1, all_606_0, % 169.92/26.10 | | | | | | | | | | | | | | | all_123_3, all_41_0, all_32_8, simplifying with % 169.92/26.10 | | | | | | | | | | | | | | | (170), (174) gives: % 169.92/26.10 | | | | | | | | | | | | | | | (190) all_606_0 = all_511_1 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_586_1, all_616_1, % 169.92/26.10 | | | | | | | | | | | | | | | all_123_3, all_41_0, all_32_8, simplifying with % 169.92/26.10 | | | | | | | | | | | | | | | (169), (172) gives: % 169.92/26.10 | | | | | | | | | | | | | | | (191) all_616_1 = all_586_1 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_616_1, all_621_1, % 169.92/26.10 | | | | | | | | | | | | | | | all_123_3, all_41_0, all_32_8, simplifying with % 169.92/26.10 | | | | | | | | | | | | | | | (168), (169) gives: % 169.92/26.10 | | | | | | | | | | | | | | | (192) all_621_1 = all_616_1 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_576_0, all_621_1, % 169.92/26.10 | | | | | | | | | | | | | | | all_123_3, all_41_0, all_32_8, simplifying with % 169.92/26.10 | | | | | | | | | | | | | | | (168), (173) gives: % 169.92/26.10 | | | | | | | | | | | | | | | (193) all_621_1 = all_576_0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | COMBINE_EQS: (192), (193) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (194) all_616_1 = all_576_0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | SIMP: (194) implies: % 169.92/26.10 | | | | | | | | | | | | | | | (195) all_616_1 = all_576_0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | COMBINE_EQS: (183), (185) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (196) all_606_1 = 0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | COMBINE_EQS: (183), (184) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (197) all_606_1 = all_511_0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | COMBINE_EQS: (191), (195) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (198) all_586_1 = all_576_0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | SIMP: (198) implies: % 169.92/26.10 | | | | | | | | | | | | | | | (199) all_586_1 = all_576_0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | COMBINE_EQS: (189), (190) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (200) all_586_1 = all_511_1 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | SIMP: (200) implies: % 169.92/26.10 | | | | | | | | | | | | | | | (201) all_586_1 = all_511_1 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | COMBINE_EQS: (196), (197) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (202) all_511_0 = 0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | SIMP: (202) implies: % 169.92/26.10 | | | | | | | | | | | | | | | (203) all_511_0 = 0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | COMBINE_EQS: (187), (188) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (204) all_586_1 = all_506_0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | SIMP: (204) implies: % 169.92/26.10 | | | | | | | | | | | | | | | (205) all_586_1 = all_506_0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | COMBINE_EQS: (186), (199) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (206) all_576_0 = 0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | COMBINE_EQS: (199), (205) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (207) all_576_0 = all_506_0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | COMBINE_EQS: (199), (201) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (208) all_576_0 = all_511_1 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | COMBINE_EQS: (207), (208) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (209) all_511_1 = all_506_0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | COMBINE_EQS: (206), (208) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (210) all_511_1 = 0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | COMBINE_EQS: (209), (210) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (211) all_506_0 = 0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | BETA: splitting (126) gives: % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | Case 1: % 169.92/26.10 | | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | | (212) ~ (all_511_0 = 0) % 169.92/26.10 | | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | | REDUCE: (203), (212) imply: % 169.92/26.10 | | | | | | | | | | | | | | | | (213) $false % 169.92/26.10 | | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | | CLOSE: (213) is inconsistent. % 169.92/26.10 | | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | Case 2: % 169.92/26.10 | | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | | (214) ~ (all_511_1 = 0) % 169.92/26.10 | | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | | REDUCE: (210), (214) imply: % 169.92/26.10 | | | | | | | | | | | | | | | | (215) $false % 169.92/26.10 | | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | | CLOSE: (215) is inconsistent. % 169.92/26.10 | | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | End of split % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | End of split % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | Case 2: % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | (216) ~ (all_119_3 = all_109_0) % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | REDUCE: (44), (216) imply: % 169.92/26.10 | | | | | | | | | | | | | | (217) ~ (all_109_0 = all_41_0) % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | SIMP: (217) implies: % 169.92/26.10 | | | | | | | | | | | | | | (218) ~ (all_109_0 = all_41_0) % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | BETA: splitting (24) gives: % 169.92/26.10 | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | Case 1: % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | (219) all_119_3 = all_109_0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | COMBINE_EQS: (44), (219) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (220) all_109_0 = all_41_0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | REDUCE: (218), (220) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (221) $false % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | CLOSE: (221) is inconsistent. % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | Case 2: % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | (222) ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.92/26.10 | | | | | | | | | | | | | | | all_111_0, all_119_3) = v1 & apply(all_32_6, % 169.92/26.10 | | | | | | | | | | | | | | | all_111_0, all_109_0) = v0 & ( ~ (v1 = 0) | ~ % 169.92/26.10 | | | | | | | | | | | | | | | (v0 = 0))) % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | DELTA: instantiating (222) with fresh symbols all_298_0, % 169.92/26.10 | | | | | | | | | | | | | | | all_298_1 gives: % 169.92/26.10 | | | | | | | | | | | | | | | (223) apply(all_32_6, all_111_0, all_119_3) = all_298_0 % 169.92/26.10 | | | | | | | | | | | | | | | & apply(all_32_6, all_111_0, all_109_0) = % 169.92/26.10 | | | | | | | | | | | | | | | all_298_1 & ( ~ (all_298_0 = 0) | ~ (all_298_1 = % 169.92/26.10 | | | | | | | | | | | | | | | 0)) % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | ALPHA: (223) implies: % 169.92/26.10 | | | | | | | | | | | | | | | (224) apply(all_32_6, all_111_0, all_119_3) = all_298_0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | REDUCE: (44), (78), (224) imply: % 169.92/26.10 | | | | | | | | | | | | | | | (225) apply(all_32_6, all_41_2, all_41_0) = all_298_0 % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | BETA: splitting (47) gives: % 169.92/26.10 | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | Case 1: % 169.92/26.10 | | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | | (226) all_119_3 = all_109_0 % 169.92/26.10 | | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (226) imply: % 169.92/26.10 | | | | | | | | | | | | | | | | (227) all_109_0 = all_41_0 % 169.92/26.10 | | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | | REDUCE: (218), (227) imply: % 169.92/26.10 | | | | | | | | | | | | | | | | (228) $false % 169.92/26.10 | | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | | CLOSE: (228) is inconsistent. % 169.92/26.10 | | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | Case 2: % 169.92/26.10 | | | | | | | | | | | | | | | | % 169.92/26.10 | | | | | | | | | | | | | | | | (229) ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.92/26.10 | | | | | | | | | | | | | | | | all_41_2, all_119_3) = v0 & apply(all_32_6, % 169.92/26.10 | | | | | | | | | | | | | | | | all_41_2, all_109_0) = v1 & ( ~ (v1 = 0) | ~ % 169.92/26.10 | | | | | | | | | | | | | | | | (v0 = 0))) % 169.92/26.11 | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | DELTA: instantiating (229) with fresh symbols all_304_0, % 169.92/26.11 | | | | | | | | | | | | | | | | all_304_1 gives: % 169.92/26.11 | | | | | | | | | | | | | | | | (230) apply(all_32_6, all_41_2, all_119_3) = all_304_1 & % 169.92/26.11 | | | | | | | | | | | | | | | | apply(all_32_6, all_41_2, all_109_0) = all_304_0 & % 169.92/26.11 | | | | | | | | | | | | | | | | ( ~ (all_304_0 = 0) | ~ (all_304_1 = 0)) % 169.92/26.11 | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | ALPHA: (230) implies: % 169.92/26.11 | | | | | | | | | | | | | | | | (231) apply(all_32_6, all_41_2, all_119_3) = all_304_1 % 169.92/26.11 | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | REDUCE: (44), (231) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | (232) apply(all_32_6, all_41_2, all_41_0) = all_304_1 % 169.92/26.11 | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | BETA: splitting (53) gives: % 169.92/26.11 | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | Case 1: % 169.92/26.11 | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | (233) all_119_3 = all_109_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (233) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | (234) all_109_0 = all_41_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | REDUCE: (218), (234) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | (235) $false % 169.92/26.11 | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | CLOSE: (235) is inconsistent. % 169.92/26.11 | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | Case 2: % 169.92/26.11 | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | (236) ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.92/26.11 | | | | | | | | | | | | | | | | | all_41_2, all_119_3) = v1 & apply(all_32_6, % 169.92/26.11 | | | | | | | | | | | | | | | | | all_41_2, all_109_0) = v0 & ( ~ (v1 = 0) | ~ % 169.92/26.11 | | | | | | | | | | | | | | | | | (v0 = 0))) % 169.92/26.11 | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | DELTA: instantiating (236) with fresh symbols all_386_0, % 169.92/26.11 | | | | | | | | | | | | | | | | | all_386_1 gives: % 169.92/26.11 | | | | | | | | | | | | | | | | | (237) apply(all_32_6, all_41_2, all_119_3) = all_386_0 & % 169.92/26.11 | | | | | | | | | | | | | | | | | apply(all_32_6, all_41_2, all_109_0) = all_386_1 & % 169.92/26.11 | | | | | | | | | | | | | | | | | ( ~ (all_386_0 = 0) | ~ (all_386_1 = 0)) % 169.92/26.11 | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | ALPHA: (237) implies: % 169.92/26.11 | | | | | | | | | | | | | | | | | (238) apply(all_32_6, all_41_2, all_119_3) = all_386_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | REDUCE: (44), (238) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | (239) apply(all_32_6, all_41_2, all_41_0) = all_386_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 169.92/26.11 | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | Case 1: % 169.92/26.11 | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | (240) all_119_3 = all_109_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (240) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | (241) all_109_0 = all_41_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | REDUCE: (218), (241) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | (242) $false % 169.92/26.11 | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | CLOSE: (242) is inconsistent. % 169.92/26.11 | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | Case 2: % 169.92/26.11 | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | (243) ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.92/26.11 | | | | | | | | | | | | | | | | | | all_111_0, all_119_3) = v0 & apply(all_32_6, % 169.92/26.11 | | | | | | | | | | | | | | | | | | all_111_0, all_109_0) = v1 & ( ~ (v1 = 0) | ~ % 169.92/26.11 | | | | | | | | | | | | | | | | | | (v0 = 0))) % 169.92/26.11 | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | DELTA: instantiating (243) with fresh symbols all_427_0, % 169.92/26.11 | | | | | | | | | | | | | | | | | | all_427_1 gives: % 169.92/26.11 | | | | | | | | | | | | | | | | | | (244) apply(all_32_6, all_111_0, all_119_3) = all_427_1 % 169.92/26.11 | | | | | | | | | | | | | | | | | | & apply(all_32_6, all_111_0, all_109_0) = % 169.92/26.11 | | | | | | | | | | | | | | | | | | all_427_0 & ( ~ (all_427_0 = 0) | ~ (all_427_1 = % 169.92/26.11 | | | | | | | | | | | | | | | | | | 0)) % 169.92/26.11 | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | ALPHA: (244) implies: % 169.92/26.11 | | | | | | | | | | | | | | | | | | (245) apply(all_32_6, all_111_0, all_109_0) = all_427_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | (246) apply(all_32_6, all_111_0, all_119_3) = all_427_1 % 169.92/26.11 | | | | | | | | | | | | | | | | | | (247) ~ (all_427_0 = 0) | ~ (all_427_1 = 0) % 169.92/26.11 | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | REDUCE: (44), (78), (246) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | (248) apply(all_32_6, all_41_2, all_41_0) = all_427_1 % 169.92/26.11 | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | REDUCE: (78), (245) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | (249) apply(all_32_6, all_41_2, all_109_0) = all_427_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives: % 169.92/26.11 | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | Case 1: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | (250) all_119_3 = all_109_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (250) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | (251) all_109_0 = all_41_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | REDUCE: (218), (251) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | (252) $false % 169.92/26.11 | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | CLOSE: (252) is inconsistent. % 169.92/26.11 | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | Case 2: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | (253) ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.92/26.11 | | | | | | | | | | | | | | | | | | | all_51_0, all_119_3) = v0 & apply(all_32_6, % 169.92/26.11 | | | | | | | | | | | | | | | | | | | all_51_0, all_109_0) = v1 & ( ~ (v1 = 0) | ~ % 169.92/26.11 | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 169.92/26.11 | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (253) with fresh symbols all_596_0, % 169.92/26.11 | | | | | | | | | | | | | | | | | | | all_596_1 gives: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | (254) apply(all_32_6, all_51_0, all_119_3) = all_596_1 & % 169.92/26.11 | | | | | | | | | | | | | | | | | | | apply(all_32_6, all_51_0, all_109_0) = all_596_0 & % 169.92/26.11 | | | | | | | | | | | | | | | | | | | ( ~ (all_596_0 = 0) | ~ (all_596_1 = 0)) % 169.92/26.11 | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | (255) apply(all_32_6, all_51_0, all_109_0) = all_596_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | (256) apply(all_32_6, all_51_0, all_119_3) = all_596_1 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | REDUCE: (44), (80), (256) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | (257) apply(all_32_6, all_41_2, all_41_0) = all_596_1 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | REDUCE: (80), (255) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | (258) apply(all_32_6, all_41_2, all_109_0) = all_596_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | Case 1: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (259) all_119_3 = all_109_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (259) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (260) all_109_0 = all_41_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | REDUCE: (218), (260) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (261) $false % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | CLOSE: (261) is inconsistent. % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | Case 2: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (262) ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | all_51_0, all_119_3) = v1 & apply(all_32_6, % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | all_51_0, all_109_0) = v0 & ( ~ (v1 = 0) | ~ % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (262) with fresh symbols all_620_0, % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | all_620_1 gives: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (263) apply(all_32_6, all_51_0, all_119_3) = all_620_0 & % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | apply(all_32_6, all_51_0, all_109_0) = all_620_1 & % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | ( ~ (all_620_0 = 0) | ~ (all_620_1 = 0)) % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | ALPHA: (263) implies: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (264) apply(all_32_6, all_51_0, all_119_3) = all_620_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (80), (264) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (265) apply(all_32_6, all_41_2, all_41_0) = all_620_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_298_0, all_386_0, % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | all_41_0, all_41_2, all_32_6, simplifying with % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (225), (239) gives: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (266) all_386_0 = all_298_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_386_0, all_427_1, % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | all_41_0, all_41_2, all_32_6, simplifying with % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (239), (248) gives: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (267) all_427_1 = all_386_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_154_1, all_427_1, % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | all_41_0, all_41_2, all_32_6, simplifying with % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (82), (248) gives: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (268) all_427_1 = all_154_1 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with 0, all_596_1, all_41_0, % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | all_41_2, all_32_6, simplifying with (19), (257) % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | gives: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (269) all_596_1 = 0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_298_0, all_596_1, % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | all_41_0, all_41_2, all_32_6, simplifying with % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (225), (257) gives: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (270) all_596_1 = all_298_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_386_0, all_620_0, % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | all_41_0, all_41_2, all_32_6, simplifying with % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (239), (265) gives: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (271) all_620_0 = all_386_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_304_1, all_620_0, % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | all_41_0, all_41_2, all_32_6, simplifying with % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (232), (265) gives: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (272) all_620_0 = all_304_1 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_427_0, all_596_0, % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | all_109_0, all_41_2, all_32_6, simplifying with % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (249), (258) gives: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (273) all_596_0 = all_427_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with 0, all_596_0, all_109_0, % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | all_41_2, all_32_6, simplifying with (81), (258) % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | gives: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (274) all_596_0 = 0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (272) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (275) all_386_0 = all_304_1 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | SIMP: (275) implies: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (276) all_386_0 = all_304_1 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (274) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (277) all_427_0 = 0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | SIMP: (277) implies: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (278) all_427_0 = 0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (270) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (279) all_298_0 = 0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | SIMP: (279) implies: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (280) all_298_0 = 0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (268) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (281) all_386_0 = all_154_1 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | SIMP: (281) implies: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (282) all_386_0 = all_154_1 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (276) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (283) all_304_1 = all_298_0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (282) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (284) all_304_1 = all_154_1 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (284) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (285) all_298_0 = all_154_1 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | SIMP: (285) implies: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (286) all_298_0 = all_154_1 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (286) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (287) all_154_1 = 0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | SIMP: (287) implies: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (288) all_154_1 = 0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (288) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | (289) all_427_1 = 0 % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | Case 1: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | | (290) ~ (all_427_0 = 0) % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | | REDUCE: (278), (290) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | | (291) $false % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | | CLOSE: (291) is inconsistent. % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | Case 2: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | | (292) ~ (all_427_1 = 0) % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | | REDUCE: (289), (292) imply: % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | | (293) $false % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | | CLOSE: (293) is inconsistent. % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | End of split % 169.92/26.11 | | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | | End of split % 169.92/26.11 | | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | | End of split % 169.92/26.11 | | | | | | | | | | | | | | | | | | % 169.92/26.11 | | | | | | | | | | | | | | | | | End of split % 169.92/26.11 | | | | | | | | | | | | | | | | | % 169.92/26.12 | | | | | | | | | | | | | | | | End of split % 169.92/26.12 | | | | | | | | | | | | | | | | % 169.92/26.12 | | | | | | | | | | | | | | | End of split % 169.92/26.12 | | | | | | | | | | | | | | | % 169.92/26.12 | | | | | | | | | | | | | | End of split % 169.92/26.12 | | | | | | | | | | | | | | % 169.92/26.12 | | | | | | | | | | | | | End of split % 169.92/26.12 | | | | | | | | | | | | | % 169.92/26.12 | | | | | | | | | | | | End of split % 169.92/26.12 | | | | | | | | | | | | % 169.92/26.12 | | | | | | | | | | | End of split % 169.92/26.12 | | | | | | | | | | | % 169.92/26.12 | | | | | | | | | | End of split % 169.92/26.12 | | | | | | | | | | % 169.92/26.12 | | | | | | | | | End of split % 169.92/26.12 | | | | | | | | | % 169.92/26.12 | | | | | | | | End of split % 169.92/26.12 | | | | | | | | % 169.92/26.12 | | | | | | | End of split % 169.92/26.12 | | | | | | | % 169.92/26.12 | | | | | | End of split % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | End of split % 169.92/26.12 | | | | | % 169.92/26.12 | | | | End of split % 169.92/26.12 | | | | % 169.92/26.12 | | | Case 2: % 169.92/26.12 | | | | % 169.92/26.12 | | | | (294) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_41_1, % 169.92/26.12 | | | | all_121_3) = v0 & apply(all_32_8, all_41_1, all_111_0) = v1 % 169.92/26.12 | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.12 | | | | % 169.92/26.12 | | | | DELTA: instantiating (294) with fresh symbols all_268_0, all_268_1 % 169.92/26.12 | | | | gives: % 169.92/26.12 | | | | (295) apply(all_32_8, all_41_1, all_121_3) = all_268_1 & % 169.92/26.12 | | | | apply(all_32_8, all_41_1, all_111_0) = all_268_0 & ( ~ % 169.92/26.12 | | | | (all_268_0 = 0) | ~ (all_268_1 = 0)) % 169.92/26.12 | | | | % 169.92/26.12 | | | | ALPHA: (295) implies: % 169.92/26.12 | | | | (296) apply(all_32_8, all_41_1, all_111_0) = all_268_0 % 169.92/26.12 | | | | (297) apply(all_32_8, all_41_1, all_121_3) = all_268_1 % 169.92/26.12 | | | | (298) ~ (all_268_0 = 0) | ~ (all_268_1 = 0) % 169.92/26.12 | | | | % 169.92/26.12 | | | | REDUCE: (78), (296) imply: % 169.92/26.12 | | | | (299) apply(all_32_8, all_41_1, all_41_2) = all_268_0 % 169.92/26.12 | | | | % 169.92/26.12 | | | | BETA: splitting (60) gives: % 169.92/26.12 | | | | % 169.92/26.12 | | | | Case 1: % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | (300) all_41_0 = all_41_1 % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | REDUCE: (6), (300) imply: % 169.92/26.12 | | | | | (301) $false % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | CLOSE: (301) is inconsistent. % 169.92/26.12 | | | | | % 169.92/26.12 | | | | Case 2: % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | GROUND_INST: instantiating (57) with 0, all_268_0, all_41_2, all_41_1, % 169.92/26.12 | | | | | all_32_8, simplifying with (17), (299) gives: % 169.92/26.12 | | | | | (302) all_268_0 = 0 % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | GROUND_INST: instantiating (57) with 0, all_268_1, all_121_3, % 169.92/26.12 | | | | | all_41_1, all_32_8, simplifying with (8), (297) gives: % 169.92/26.12 | | | | | (303) all_268_1 = 0 % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | BETA: splitting (298) gives: % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | Case 1: % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | | (304) ~ (all_268_0 = 0) % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | | REDUCE: (302), (304) imply: % 169.92/26.12 | | | | | | (305) $false % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | | CLOSE: (305) is inconsistent. % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | Case 2: % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | | (306) ~ (all_268_1 = 0) % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | | REDUCE: (303), (306) imply: % 169.92/26.12 | | | | | | (307) $false % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | | CLOSE: (307) is inconsistent. % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | End of split % 169.92/26.12 | | | | | % 169.92/26.12 | | | | End of split % 169.92/26.12 | | | | % 169.92/26.12 | | | End of split % 169.92/26.12 | | | % 169.92/26.12 | | Case 2: % 169.92/26.12 | | | % 169.92/26.12 | | | (308) ~ (all_111_0 = all_41_2) % 169.92/26.12 | | | (309) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_117_0, % 169.92/26.12 | | | all_111_0) = v1 & apply(all_32_8, all_117_0, all_41_2) = v0 & % 169.92/26.12 | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.12 | | | % 169.92/26.12 | | | DELTA: instantiating (309) with fresh symbols all_256_0, all_256_1 gives: % 169.92/26.12 | | | (310) apply(all_32_8, all_117_0, all_111_0) = all_256_0 & % 169.92/26.12 | | | apply(all_32_8, all_117_0, all_41_2) = all_256_1 & ( ~ (all_256_0 % 169.92/26.12 | | | = 0) | ~ (all_256_1 = 0)) % 169.92/26.12 | | | % 169.92/26.12 | | | ALPHA: (310) implies: % 169.92/26.12 | | | (311) apply(all_32_8, all_117_0, all_41_2) = all_256_1 % 169.92/26.12 | | | % 169.92/26.12 | | | REDUCE: (34), (308) imply: % 169.92/26.12 | | | (312) ~ (all_51_0 = all_41_2) % 169.92/26.12 | | | % 169.92/26.12 | | | REDUCE: (15), (311) imply: % 169.92/26.12 | | | (313) apply(all_32_8, all_41_0, all_41_2) = all_256_1 % 169.92/26.12 | | | % 169.92/26.12 | | | BETA: splitting (10) gives: % 169.92/26.12 | | | % 169.92/26.12 | | | Case 1: % 169.92/26.12 | | | | % 169.92/26.12 | | | | (314) all_51_0 = all_49_0 % 169.92/26.12 | | | | % 169.92/26.12 | | | | COMBINE_EQS: (50), (314) imply: % 169.92/26.12 | | | | (315) all_51_0 = all_41_2 % 169.92/26.12 | | | | % 169.92/26.12 | | | | REDUCE: (312), (315) imply: % 169.92/26.12 | | | | (316) $false % 169.92/26.12 | | | | % 169.92/26.12 | | | | CLOSE: (316) is inconsistent. % 169.92/26.12 | | | | % 169.92/26.12 | | | Case 2: % 169.92/26.12 | | | | % 169.92/26.12 | | | | (317) ~ (all_51_0 = all_49_0) % 169.92/26.12 | | | | (318) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_41_0, % 169.92/26.12 | | | | all_51_0) = v0 & apply(all_32_8, all_41_0, all_49_0) = v1 & % 169.92/26.12 | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.12 | | | | % 169.92/26.12 | | | | DELTA: instantiating (318) with fresh symbols all_393_0, all_393_1 % 169.92/26.12 | | | | gives: % 169.92/26.12 | | | | (319) apply(all_32_8, all_41_0, all_51_0) = all_393_1 & % 169.92/26.12 | | | | apply(all_32_8, all_41_0, all_49_0) = all_393_0 & ( ~ % 169.92/26.12 | | | | (all_393_0 = 0) | ~ (all_393_1 = 0)) % 169.92/26.12 | | | | % 169.92/26.12 | | | | ALPHA: (319) implies: % 169.92/26.12 | | | | (320) apply(all_32_8, all_41_0, all_49_0) = all_393_0 % 169.92/26.12 | | | | (321) apply(all_32_8, all_41_0, all_51_0) = all_393_1 % 169.92/26.12 | | | | % 169.92/26.12 | | | | REDUCE: (50), (320) imply: % 169.92/26.12 | | | | (322) apply(all_32_8, all_41_0, all_41_2) = all_393_0 % 169.92/26.12 | | | | % 169.92/26.12 | | | | BETA: splitting (54) gives: % 169.92/26.12 | | | | % 169.92/26.12 | | | | Case 1: % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | (323) all_51_0 = all_49_0 % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | COMBINE_EQS: (50), (323) imply: % 169.92/26.12 | | | | | (324) all_51_0 = all_41_2 % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | REDUCE: (312), (324) imply: % 169.92/26.12 | | | | | (325) $false % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | CLOSE: (325) is inconsistent. % 169.92/26.12 | | | | | % 169.92/26.12 | | | | Case 2: % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | (326) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_41_0, % 169.92/26.12 | | | | | all_51_0) = v1 & apply(all_32_8, all_41_0, all_49_0) = v0 % 169.92/26.12 | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | DELTA: instantiating (326) with fresh symbols all_399_0, all_399_1 % 169.92/26.12 | | | | | gives: % 169.92/26.12 | | | | | (327) apply(all_32_8, all_41_0, all_51_0) = all_399_0 & % 169.92/26.12 | | | | | apply(all_32_8, all_41_0, all_49_0) = all_399_1 & ( ~ % 169.92/26.12 | | | | | (all_399_0 = 0) | ~ (all_399_1 = 0)) % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | ALPHA: (327) implies: % 169.92/26.12 | | | | | (328) apply(all_32_8, all_41_0, all_49_0) = all_399_1 % 169.92/26.12 | | | | | (329) apply(all_32_8, all_41_0, all_51_0) = all_399_0 % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | REDUCE: (50), (328) imply: % 169.92/26.12 | | | | | (330) apply(all_32_8, all_41_0, all_41_2) = all_399_1 % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | BETA: splitting (14) gives: % 169.92/26.12 | | | | | % 169.92/26.12 | | | | | Case 1: % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | | (331) all_121_3 = all_41_2 % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | | REF_CLOSE: (1), (2), (5), (7), (10), (11), (13), (15), (16), (21), % 169.92/26.12 | | | | | | (22), (25), (27), (32), (33), (34), (36), (37), (38), % 169.92/26.12 | | | | | | (40), (42), (43), (44), (46), (48), (50), (52), (54), % 169.92/26.12 | | | | | | (55), (56), (57), (66), (68), (69), (312), (331) are % 169.92/26.12 | | | | | | inconsistent by sub-proof #3. % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | Case 2: % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | | (332) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_117_0, % 169.92/26.12 | | | | | | all_121_3) = v0 & apply(all_32_8, all_117_0, all_41_2) % 169.92/26.12 | | | | | | = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | | DELTA: instantiating (332) with fresh symbols all_416_0, all_416_1 % 169.92/26.12 | | | | | | gives: % 169.92/26.12 | | | | | | (333) apply(all_32_8, all_117_0, all_121_3) = all_416_1 & % 169.92/26.12 | | | | | | apply(all_32_8, all_117_0, all_41_2) = all_416_0 & ( ~ % 169.92/26.12 | | | | | | (all_416_0 = 0) | ~ (all_416_1 = 0)) % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | | ALPHA: (333) implies: % 169.92/26.12 | | | | | | (334) apply(all_32_8, all_117_0, all_41_2) = all_416_0 % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | | REDUCE: (15), (334) imply: % 169.92/26.12 | | | | | | (335) apply(all_32_8, all_41_0, all_41_2) = all_416_0 % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | | BETA: splitting (67) gives: % 169.92/26.12 | | | | | | % 169.92/26.12 | | | | | | Case 1: % 169.92/26.12 | | | | | | | % 169.92/26.12 | | | | | | | (336) all_121_3 = all_41_2 % 169.92/26.12 | | | | | | | % 169.92/26.12 | | | | | | | REF_CLOSE: (1), (2), (5), (7), (10), (11), (13), (15), (16), (21), % 169.92/26.12 | | | | | | | (22), (25), (27), (32), (33), (34), (36), (37), (38), % 169.92/26.12 | | | | | | | (40), (42), (43), (44), (46), (48), (50), (52), (54), % 169.92/26.12 | | | | | | | (55), (56), (57), (66), (68), (69), (312), (336) are % 169.92/26.12 | | | | | | | inconsistent by sub-proof #3. % 169.92/26.12 | | | | | | | % 169.92/26.12 | | | | | | Case 2: % 169.92/26.12 | | | | | | | % 169.92/26.12 | | | | | | | (337) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_117_0, % 169.92/26.12 | | | | | | | all_121_3) = v1 & apply(all_32_8, all_117_0, % 169.92/26.12 | | | | | | | all_41_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.12 | | | | | | | % 169.92/26.12 | | | | | | | DELTA: instantiating (337) with fresh symbols all_421_0, all_421_1 % 169.92/26.12 | | | | | | | gives: % 169.92/26.12 | | | | | | | (338) apply(all_32_8, all_117_0, all_121_3) = all_421_0 & % 169.92/26.12 | | | | | | | apply(all_32_8, all_117_0, all_41_2) = all_421_1 & ( ~ % 169.92/26.12 | | | | | | | (all_421_0 = 0) | ~ (all_421_1 = 0)) % 169.92/26.12 | | | | | | | % 169.92/26.12 | | | | | | | ALPHA: (338) implies: % 169.92/26.12 | | | | | | | (339) apply(all_32_8, all_117_0, all_41_2) = all_421_1 % 169.92/26.12 | | | | | | | % 169.92/26.12 | | | | | | | REDUCE: (15), (339) imply: % 169.92/26.12 | | | | | | | (340) apply(all_32_8, all_41_0, all_41_2) = all_421_1 % 169.92/26.12 | | | | | | | % 169.92/26.12 | | | | | | | BETA: splitting (45) gives: % 169.92/26.12 | | | | | | | % 169.92/26.12 | | | | | | | Case 1: % 169.92/26.12 | | | | | | | | % 169.92/26.12 | | | | | | | | (341) all_121_3 = all_41_2 % 169.92/26.12 | | | | | | | | % 169.92/26.12 | | | | | | | | REF_CLOSE: (1), (2), (5), (7), (10), (11), (13), (15), (16), % 169.92/26.12 | | | | | | | | (21), (22), (25), (27), (32), (33), (34), (36), (37), % 169.92/26.12 | | | | | | | | (38), (40), (42), (43), (44), (46), (48), (50), (52), % 169.92/26.12 | | | | | | | | (54), (55), (56), (57), (66), (68), (69), (312), % 169.92/26.12 | | | | | | | | (341) are inconsistent by sub-proof #3. % 169.92/26.12 | | | | | | | | % 169.92/26.12 | | | | | | | Case 2: % 169.92/26.12 | | | | | | | | % 169.92/26.12 | | | | | | | | (342) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.12 | | | | | | | | all_119_3, all_121_3) = v0 & apply(all_32_8, % 169.92/26.12 | | | | | | | | all_119_3, all_41_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = % 169.92/26.12 | | | | | | | | 0))) % 169.92/26.12 | | | | | | | | % 169.92/26.12 | | | | | | | | DELTA: instantiating (342) with fresh symbols all_451_0, % 169.92/26.12 | | | | | | | | all_451_1 gives: % 169.92/26.12 | | | | | | | | (343) apply(all_32_8, all_119_3, all_121_3) = all_451_1 & % 169.92/26.12 | | | | | | | | apply(all_32_8, all_119_3, all_41_2) = all_451_0 & ( ~ % 169.92/26.12 | | | | | | | | (all_451_0 = 0) | ~ (all_451_1 = 0)) % 169.92/26.12 | | | | | | | | % 169.92/26.12 | | | | | | | | ALPHA: (343) implies: % 169.92/26.12 | | | | | | | | (344) apply(all_32_8, all_119_3, all_41_2) = all_451_0 % 169.92/26.12 | | | | | | | | % 169.92/26.12 | | | | | | | | REDUCE: (44), (344) imply: % 169.92/26.12 | | | | | | | | (345) apply(all_32_8, all_41_0, all_41_2) = all_451_0 % 169.92/26.12 | | | | | | | | % 169.92/26.12 | | | | | | | | BETA: splitting (36) gives: % 169.92/26.12 | | | | | | | | % 169.92/26.12 | | | | | | | | Case 1: % 169.92/26.12 | | | | | | | | | % 169.92/26.12 | | | | | | | | | (346) all_51_0 = all_49_0 % 169.92/26.12 | | | | | | | | | % 169.92/26.12 | | | | | | | | | COMBINE_EQS: (50), (346) imply: % 169.92/26.12 | | | | | | | | | (347) all_51_0 = all_41_2 % 169.92/26.12 | | | | | | | | | % 169.92/26.13 | | | | | | | | | REDUCE: (312), (347) imply: % 169.92/26.13 | | | | | | | | | (348) $false % 169.92/26.13 | | | | | | | | | % 169.92/26.13 | | | | | | | | | CLOSE: (348) is inconsistent. % 169.92/26.13 | | | | | | | | | % 169.92/26.13 | | | | | | | | Case 2: % 169.92/26.13 | | | | | | | | | % 169.92/26.13 | | | | | | | | | (349) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.13 | | | | | | | | | all_55_0, all_51_0) = v1 & apply(all_32_8, % 169.92/26.13 | | | | | | | | | all_55_0, all_49_0) = v0 & ( ~ (v1 = 0) | ~ (v0 % 169.92/26.13 | | | | | | | | | = 0))) % 169.92/26.13 | | | | | | | | | % 169.92/26.13 | | | | | | | | | DELTA: instantiating (349) with fresh symbols all_512_0, % 169.92/26.13 | | | | | | | | | all_512_1 gives: % 169.92/26.13 | | | | | | | | | (350) apply(all_32_8, all_55_0, all_51_0) = all_512_0 & % 169.92/26.13 | | | | | | | | | apply(all_32_8, all_55_0, all_49_0) = all_512_1 & ( ~ % 169.92/26.13 | | | | | | | | | (all_512_0 = 0) | ~ (all_512_1 = 0)) % 169.92/26.13 | | | | | | | | | % 169.92/26.13 | | | | | | | | | ALPHA: (350) implies: % 169.92/26.13 | | | | | | | | | (351) apply(all_32_8, all_55_0, all_49_0) = all_512_1 % 169.92/26.13 | | | | | | | | | (352) apply(all_32_8, all_55_0, all_51_0) = all_512_0 % 169.92/26.13 | | | | | | | | | (353) ~ (all_512_0 = 0) | ~ (all_512_1 = 0) % 169.92/26.13 | | | | | | | | | % 169.92/26.13 | | | | | | | | | REDUCE: (46), (352) imply: % 169.92/26.13 | | | | | | | | | (354) apply(all_32_8, all_41_0, all_51_0) = all_512_0 % 169.92/26.13 | | | | | | | | | % 169.92/26.13 | | | | | | | | | REDUCE: (46), (50), (351) imply: % 169.92/26.13 | | | | | | | | | (355) apply(all_32_8, all_41_0, all_41_2) = all_512_1 % 169.92/26.13 | | | | | | | | | % 169.92/26.13 | | | | | | | | | BETA: splitting (55) gives: % 169.92/26.13 | | | | | | | | | % 169.92/26.13 | | | | | | | | | Case 1: % 169.92/26.13 | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | (356) all_51_0 = all_49_0 % 169.92/26.13 | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | COMBINE_EQS: (50), (356) imply: % 169.92/26.13 | | | | | | | | | | (357) all_51_0 = all_41_2 % 169.92/26.13 | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | REDUCE: (312), (357) imply: % 169.92/26.13 | | | | | | | | | | (358) $false % 169.92/26.13 | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | CLOSE: (358) is inconsistent. % 169.92/26.13 | | | | | | | | | | % 169.92/26.13 | | | | | | | | | Case 2: % 169.92/26.13 | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | (359) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 169.92/26.13 | | | | | | | | | | (apply(all_32_8, all_41_0, all_49_0) = v2 & % 169.92/26.13 | | | | | | | | | | member(all_51_0, all_32_4) = v1 & % 169.92/26.13 | | | | | | | | | | member(all_41_0, all_32_5) = v0 & ( ~ (v2 = 0) | % 169.92/26.13 | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.13 | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | DELTA: instantiating (359) with fresh symbols all_544_0, % 169.92/26.13 | | | | | | | | | | all_544_1, all_544_2 gives: % 169.92/26.13 | | | | | | | | | | (360) apply(all_32_8, all_41_0, all_49_0) = all_544_0 & % 169.92/26.13 | | | | | | | | | | member(all_51_0, all_32_4) = all_544_1 & % 169.92/26.13 | | | | | | | | | | member(all_41_0, all_32_5) = all_544_2 & ( ~ % 169.92/26.13 | | | | | | | | | | (all_544_0 = 0) | ~ (all_544_1 = 0) | ~ % 169.92/26.13 | | | | | | | | | | (all_544_2 = 0)) % 169.92/26.13 | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | ALPHA: (360) implies: % 169.92/26.13 | | | | | | | | | | (361) apply(all_32_8, all_41_0, all_49_0) = all_544_0 % 169.92/26.13 | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | REDUCE: (50), (361) imply: % 169.92/26.13 | | | | | | | | | | (362) apply(all_32_8, all_41_0, all_41_2) = all_544_0 % 169.92/26.13 | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | BETA: splitting (38) gives: % 169.92/26.13 | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | Case 1: % 169.92/26.13 | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | (363) all_51_0 = all_41_2 % 169.92/26.13 | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | REDUCE: (312), (363) imply: % 169.92/26.13 | | | | | | | | | | | (364) $false % 169.92/26.13 | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | CLOSE: (364) is inconsistent. % 169.92/26.13 | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | Case 2: % 169.92/26.13 | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | (365) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.13 | | | | | | | | | | | all_55_0, all_51_0) = v1 & apply(all_32_8, % 169.92/26.13 | | | | | | | | | | | all_55_0, all_41_2) = v0 & ( ~ (v1 = 0) | ~ % 169.92/26.13 | | | | | | | | | | | (v0 = 0))) % 169.92/26.13 | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | DELTA: instantiating (365) with fresh symbols all_626_0, % 169.92/26.13 | | | | | | | | | | | all_626_1 gives: % 169.92/26.13 | | | | | | | | | | | (366) apply(all_32_8, all_55_0, all_51_0) = all_626_0 & % 169.92/26.13 | | | | | | | | | | | apply(all_32_8, all_55_0, all_41_2) = all_626_1 & % 169.92/26.13 | | | | | | | | | | | ( ~ (all_626_0 = 0) | ~ (all_626_1 = 0)) % 169.92/26.13 | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | ALPHA: (366) implies: % 169.92/26.13 | | | | | | | | | | | (367) apply(all_32_8, all_55_0, all_41_2) = all_626_1 % 169.92/26.13 | | | | | | | | | | | (368) apply(all_32_8, all_55_0, all_51_0) = all_626_0 % 169.92/26.13 | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | REDUCE: (46), (368) imply: % 169.92/26.13 | | | | | | | | | | | (369) apply(all_32_8, all_41_0, all_51_0) = all_626_0 % 169.92/26.13 | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | REDUCE: (46), (367) imply: % 169.92/26.13 | | | | | | | | | | | (370) apply(all_32_8, all_41_0, all_41_2) = all_626_1 % 169.92/26.13 | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | BETA: splitting (66) gives: % 169.92/26.13 | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | Case 1: % 169.92/26.13 | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | (371) all_51_0 = all_41_2 % 169.92/26.13 | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | REDUCE: (312), (371) imply: % 169.92/26.13 | | | | | | | | | | | | (372) $false % 169.92/26.13 | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | CLOSE: (372) is inconsistent. % 169.92/26.13 | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | Case 2: % 169.92/26.13 | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | (373) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.13 | | | | | | | | | | | | all_41_0, all_51_0) = v1 & apply(all_32_8, % 169.92/26.13 | | | | | | | | | | | | all_41_0, all_41_2) = v0 & ( ~ (v1 = 0) | ~ % 169.92/26.13 | | | | | | | | | | | | (v0 = 0))) % 169.92/26.13 | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | DELTA: instantiating (373) with fresh symbols all_632_0, % 169.92/26.13 | | | | | | | | | | | | all_632_1 gives: % 169.92/26.13 | | | | | | | | | | | | (374) apply(all_32_8, all_41_0, all_51_0) = all_632_0 & % 169.92/26.13 | | | | | | | | | | | | apply(all_32_8, all_41_0, all_41_2) = all_632_1 & % 169.92/26.13 | | | | | | | | | | | | ( ~ (all_632_0 = 0) | ~ (all_632_1 = 0)) % 169.92/26.13 | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | ALPHA: (374) implies: % 169.92/26.13 | | | | | | | | | | | | (375) apply(all_32_8, all_41_0, all_41_2) = all_632_1 % 169.92/26.13 | | | | | | | | | | | | (376) apply(all_32_8, all_41_0, all_51_0) = all_632_0 % 169.92/26.13 | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | BETA: splitting (13) gives: % 169.92/26.13 | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | Case 1: % 169.92/26.13 | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | (377) all_51_0 = all_41_2 % 169.92/26.13 | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | REDUCE: (312), (377) imply: % 169.92/26.13 | | | | | | | | | | | | | (378) $false % 169.92/26.13 | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | CLOSE: (378) is inconsistent. % 169.92/26.13 | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | Case 2: % 169.92/26.13 | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | (379) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.13 | | | | | | | | | | | | | all_55_0, all_51_0) = v0 & apply(all_32_8, % 169.92/26.13 | | | | | | | | | | | | | all_55_0, all_41_2) = v1 & ( ~ (v1 = 0) | ~ % 169.92/26.13 | | | | | | | | | | | | | (v0 = 0))) % 169.92/26.13 | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | DELTA: instantiating (379) with fresh symbols all_638_0, % 169.92/26.13 | | | | | | | | | | | | | all_638_1 gives: % 169.92/26.13 | | | | | | | | | | | | | (380) apply(all_32_8, all_55_0, all_51_0) = all_638_1 & % 169.92/26.13 | | | | | | | | | | | | | apply(all_32_8, all_55_0, all_41_2) = all_638_0 & % 169.92/26.13 | | | | | | | | | | | | | ( ~ (all_638_0 = 0) | ~ (all_638_1 = 0)) % 169.92/26.13 | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | ALPHA: (380) implies: % 169.92/26.13 | | | | | | | | | | | | | (381) apply(all_32_8, all_55_0, all_41_2) = all_638_0 % 169.92/26.13 | | | | | | | | | | | | | (382) apply(all_32_8, all_55_0, all_51_0) = all_638_1 % 169.92/26.13 | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | REDUCE: (46), (382) imply: % 169.92/26.13 | | | | | | | | | | | | | (383) apply(all_32_8, all_41_0, all_51_0) = all_638_1 % 169.92/26.13 | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | REDUCE: (46), (381) imply: % 169.92/26.13 | | | | | | | | | | | | | (384) apply(all_32_8, all_41_0, all_41_2) = all_638_0 % 169.92/26.13 | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | BETA: splitting (16) gives: % 169.92/26.13 | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | Case 1: % 169.92/26.13 | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | (385) all_51_0 = all_41_2 % 169.92/26.13 | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | REDUCE: (312), (385) imply: % 169.92/26.13 | | | | | | | | | | | | | | (386) $false % 169.92/26.13 | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | CLOSE: (386) is inconsistent. % 169.92/26.13 | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | Case 2: % 169.92/26.13 | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | (387) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.13 | | | | | | | | | | | | | | all_41_0, all_51_0) = v0 & apply(all_32_8, % 169.92/26.13 | | | | | | | | | | | | | | all_41_0, all_41_2) = v1 & ( ~ (v1 = 0) | ~ % 169.92/26.13 | | | | | | | | | | | | | | (v0 = 0))) % 169.92/26.13 | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | DELTA: instantiating (387) with fresh symbols all_650_0, % 169.92/26.13 | | | | | | | | | | | | | | all_650_1 gives: % 169.92/26.13 | | | | | | | | | | | | | | (388) apply(all_32_8, all_41_0, all_51_0) = all_650_1 & % 169.92/26.13 | | | | | | | | | | | | | | apply(all_32_8, all_41_0, all_41_2) = all_650_0 & % 169.92/26.13 | | | | | | | | | | | | | | ( ~ (all_650_0 = 0) | ~ (all_650_1 = 0)) % 169.92/26.13 | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | ALPHA: (388) implies: % 169.92/26.13 | | | | | | | | | | | | | | (389) apply(all_32_8, all_41_0, all_41_2) = all_650_0 % 169.92/26.13 | | | | | | | | | | | | | | (390) apply(all_32_8, all_41_0, all_51_0) = all_650_1 % 169.92/26.13 | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | BETA: splitting (68) gives: % 169.92/26.13 | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | Case 1: % 169.92/26.13 | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | (391) all_51_0 = all_41_2 % 169.92/26.13 | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | REDUCE: (312), (391) imply: % 169.92/26.13 | | | | | | | | | | | | | | | (392) $false % 169.92/26.13 | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | CLOSE: (392) is inconsistent. % 169.92/26.13 | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | Case 2: % 169.92/26.13 | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | (393) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 169.92/26.13 | | | | | | | | | | | | | | | (apply(all_32_8, all_41_0, all_41_2) = v2 & % 169.92/26.13 | | | | | | | | | | | | | | | member(all_51_0, all_32_4) = v1 & % 169.92/26.13 | | | | | | | | | | | | | | | member(all_41_0, all_32_5) = v0 & ( ~ (v2 = 0) | % 169.92/26.13 | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 169.92/26.13 | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | DELTA: instantiating (393) with fresh symbols all_656_0, % 169.92/26.13 | | | | | | | | | | | | | | | all_656_1, all_656_2 gives: % 169.92/26.13 | | | | | | | | | | | | | | | (394) apply(all_32_8, all_41_0, all_41_2) = all_656_0 & % 169.92/26.13 | | | | | | | | | | | | | | | member(all_51_0, all_32_4) = all_656_1 & % 169.92/26.13 | | | | | | | | | | | | | | | member(all_41_0, all_32_5) = all_656_2 & ( ~ % 169.92/26.13 | | | | | | | | | | | | | | | (all_656_0 = 0) | ~ (all_656_1 = 0) | ~ % 169.92/26.13 | | | | | | | | | | | | | | | (all_656_2 = 0)) % 169.92/26.13 | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | ALPHA: (394) implies: % 169.92/26.13 | | | | | | | | | | | | | | | (395) apply(all_32_8, all_41_0, all_41_2) = all_656_0 % 169.92/26.13 | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | BETA: splitting (2) gives: % 169.92/26.13 | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | Case 1: % 169.92/26.13 | | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | | (396) all_51_0 = all_49_0 % 169.92/26.13 | | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (396) imply: % 169.92/26.13 | | | | | | | | | | | | | | | | (397) all_51_0 = all_41_2 % 169.92/26.13 | | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | | REDUCE: (312), (397) imply: % 169.92/26.13 | | | | | | | | | | | | | | | | (398) $false % 169.92/26.13 | | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | | CLOSE: (398) is inconsistent. % 169.92/26.13 | | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | Case 2: % 169.92/26.13 | | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | | (399) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 169.92/26.13 | | | | | | | | | | | | | | | | all_55_0, all_51_0) = v0 & apply(all_32_8, % 169.92/26.13 | | | | | | | | | | | | | | | | all_55_0, all_49_0) = v1 & ( ~ (v1 = 0) | ~ % 169.92/26.13 | | | | | | | | | | | | | | | | (v0 = 0))) % 169.92/26.13 | | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | | DELTA: instantiating (399) with fresh symbols all_674_0, % 169.92/26.13 | | | | | | | | | | | | | | | | all_674_1 gives: % 169.92/26.13 | | | | | | | | | | | | | | | | (400) apply(all_32_8, all_55_0, all_51_0) = all_674_1 & % 169.92/26.13 | | | | | | | | | | | | | | | | apply(all_32_8, all_55_0, all_49_0) = all_674_0 & % 169.92/26.13 | | | | | | | | | | | | | | | | ( ~ (all_674_0 = 0) | ~ (all_674_1 = 0)) % 169.92/26.13 | | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | | ALPHA: (400) implies: % 169.92/26.13 | | | | | | | | | | | | | | | | (401) apply(all_32_8, all_55_0, all_49_0) = all_674_0 % 169.92/26.13 | | | | | | | | | | | | | | | | (402) apply(all_32_8, all_55_0, all_51_0) = all_674_1 % 169.92/26.13 | | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | | REDUCE: (46), (402) imply: % 169.92/26.13 | | | | | | | | | | | | | | | | (403) apply(all_32_8, all_41_0, all_51_0) = all_674_1 % 169.92/26.13 | | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | | REDUCE: (46), (50), (401) imply: % 169.92/26.13 | | | | | | | | | | | | | | | | (404) apply(all_32_8, all_41_0, all_41_2) = all_674_0 % 169.92/26.13 | | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_451_0, all_512_1, % 169.92/26.13 | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 169.92/26.13 | | | | | | | | | | | | | | | | (345), (355) gives: % 169.92/26.13 | | | | | | | | | | | | | | | | (405) all_512_1 = all_451_0 % 169.92/26.13 | | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_421_1, all_512_1, % 169.92/26.13 | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 169.92/26.13 | | | | | | | | | | | | | | | | (340), (355) gives: % 169.92/26.13 | | | | | | | | | | | | | | | | (406) all_512_1 = all_421_1 % 169.92/26.13 | | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_416_0, all_512_1, % 169.92/26.13 | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 169.92/26.13 | | | | | | | | | | | | | | | | (335), (355) gives: % 169.92/26.13 | | | | | | | | | | | | | | | | (407) all_512_1 = all_416_0 % 169.92/26.13 | | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_512_1, all_544_0, % 169.92/26.13 | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 169.92/26.13 | | | | | | | | | | | | | | | | (355), (362) gives: % 169.92/26.13 | | | | | | | | | | | | | | | | (408) all_544_0 = all_512_1 % 169.92/26.13 | | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_399_1, all_544_0, % 169.92/26.13 | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 169.92/26.13 | | | | | | | | | | | | | | | | (330), (362) gives: % 169.92/26.13 | | | | | | | | | | | | | | | | (409) all_544_0 = all_399_1 % 169.92/26.13 | | | | | | | | | | | | | | | | % 169.92/26.13 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_512_1, all_626_1, % 169.92/26.13 | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 169.92/26.13 | | | | | | | | | | | | | | | | (355), (370) gives: % 169.92/26.13 | | | | | | | | | | | | | | | | (410) all_626_1 = all_512_1 % 169.92/26.13 | | | | | | | | | | | | | | | | % 169.92/26.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_393_0, all_626_1, % 169.92/26.14 | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 169.92/26.14 | | | | | | | | | | | | | | | | (322), (370) gives: % 169.92/26.14 | | | | | | | | | | | | | | | | (411) all_626_1 = all_393_0 % 169.92/26.14 | | | | | | | | | | | | | | | | % 169.92/26.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_638_0, all_650_0, % 169.92/26.14 | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 169.92/26.14 | | | | | | | | | | | | | | | | (384), (389) gives: % 169.92/26.14 | | | | | | | | | | | | | | | | (412) all_650_0 = all_638_0 % 169.92/26.14 | | | | | | | | | | | | | | | | % 169.92/26.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_256_1, all_650_0, % 169.92/26.14 | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 169.92/26.14 | | | | | | | | | | | | | | | | (313), (389) gives: % 169.92/26.14 | | | | | | | | | | | | | | | | (413) all_650_0 = all_256_1 % 169.92/26.14 | | | | | | | | | | | | | | | | % 169.92/26.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_638_0, all_656_0, % 169.92/26.14 | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 169.92/26.14 | | | | | | | | | | | | | | | | (384), (395) gives: % 169.92/26.14 | | | | | | | | | | | | | | | | (414) all_656_0 = all_638_0 % 169.92/26.14 | | | | | | | | | | | | | | | | % 169.92/26.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_632_1, all_656_0, % 169.92/26.14 | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 169.92/26.14 | | | | | | | | | | | | | | | | (375), (395) gives: % 169.92/26.14 | | | | | | | | | | | | | | | | (415) all_656_0 = all_632_1 % 169.92/26.14 | | | | | | | | | | | | | | | | % 169.92/26.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_544_0, all_656_0, % 169.92/26.14 | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 169.92/26.14 | | | | | | | | | | | | | | | | (362), (395) gives: % 169.92/26.14 | | | | | | | | | | | | | | | | (416) all_656_0 = all_544_0 % 169.92/26.14 | | | | | | | | | | | | | | | | % 169.92/26.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_421_1, all_674_0, % 169.92/26.14 | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 169.92/26.14 | | | | | | | | | | | | | | | | (340), (404) gives: % 169.92/26.14 | | | | | | | | | | | | | | | | (417) all_674_0 = all_421_1 % 169.92/26.14 | | | | | | | | | | | | | | | | % 169.92/26.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with 0, all_674_0, all_41_2, % 169.92/26.14 | | | | | | | | | | | | | | | | all_41_0, all_32_8, simplifying with (21), (404) % 169.92/26.14 | | | | | | | | | | | | | | | | gives: % 169.92/26.14 | | | | | | | | | | | | | | | | (418) all_674_0 = 0 % 169.92/26.14 | | | | | | | | | | | | | | | | % 169.92/26.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with 0, all_512_0, all_51_0, % 169.92/26.14 | | | | | | | | | | | | | | | | all_41_0, all_32_8, simplifying with (52), (354) % 169.92/26.14 | | | | | | | | | | | | | | | | gives: % 169.92/26.14 | | | | | | | | | | | | | | | | (419) all_512_0 = 0 % 169.92/26.14 | | | | | | | | | | | | | | | | % 169.92/26.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_393_1, all_632_0, % 169.92/26.14 | | | | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 169.92/26.14 | | | | | | | | | | | | | | | | (321), (376) gives: % 169.92/26.14 | | | | | | | | | | | | | | | | (420) all_632_0 = all_393_1 % 169.92/26.14 | | | | | | | | | | | | | | | | % 169.92/26.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_632_0, all_638_1, % 169.92/26.14 | | | | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 169.92/26.14 | | | | | | | | | | | | | | | | (376), (383) gives: % 169.92/26.14 | | | | | | | | | | | | | | | | (421) all_638_1 = all_632_0 % 169.92/26.14 | | | | | | | | | | | | | | | | % 169.92/26.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_626_0, all_638_1, % 169.92/26.14 | | | | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 169.92/26.14 | | | | | | | | | | | | | | | | (369), (383) gives: % 170.34/26.14 | | | | | | | | | | | | | | | | (422) all_638_1 = all_626_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_512_0, all_638_1, % 170.34/26.14 | | | | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 170.34/26.14 | | | | | | | | | | | | | | | | (354), (383) gives: % 170.34/26.14 | | | | | | | | | | | | | | | | (423) all_638_1 = all_512_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_650_1, all_674_1, % 170.34/26.14 | | | | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 170.34/26.14 | | | | | | | | | | | | | | | | (390), (403) gives: % 170.34/26.14 | | | | | | | | | | | | | | | | (424) all_674_1 = all_650_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_512_0, all_674_1, % 170.34/26.14 | | | | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 170.34/26.14 | | | | | | | | | | | | | | | | (354), (403) gives: % 170.34/26.14 | | | | | | | | | | | | | | | | (425) all_674_1 = all_512_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_399_0, all_674_1, % 170.34/26.14 | | | | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 170.34/26.14 | | | | | | | | | | | | | | | | (329), (403) gives: % 170.34/26.14 | | | | | | | | | | | | | | | | (426) all_674_1 = all_399_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (417), (418) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (427) all_421_1 = 0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | SIMP: (427) implies: % 170.34/26.14 | | | | | | | | | | | | | | | | (428) all_421_1 = 0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (424), (426) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (429) all_650_1 = all_399_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (424), (425) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (430) all_650_1 = all_512_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (414), (415) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (431) all_638_0 = all_632_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | SIMP: (431) implies: % 170.34/26.14 | | | | | | | | | | | | | | | | (432) all_638_0 = all_632_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (416) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (433) all_632_1 = all_544_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (412), (413) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (434) all_638_0 = all_256_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | SIMP: (434) implies: % 170.34/26.14 | | | | | | | | | | | | | | | | (435) all_638_0 = all_256_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (430) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (436) all_512_0 = all_399_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | SIMP: (436) implies: % 170.34/26.14 | | | | | | | | | | | | | | | | (437) all_512_0 = all_399_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (432), (435) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (438) all_632_1 = all_256_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | SIMP: (438) implies: % 170.34/26.14 | | | | | | | | | | | | | | | | (439) all_632_1 = all_256_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (422), (423) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (440) all_626_0 = all_512_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (421), (422) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (441) all_632_0 = all_626_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | SIMP: (441) implies: % 170.34/26.14 | | | | | | | | | | | | | | | | (442) all_632_0 = all_626_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (420), (442) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (443) all_626_0 = all_393_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | SIMP: (443) implies: % 170.34/26.14 | | | | | | | | | | | | | | | | (444) all_626_0 = all_393_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (433), (439) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (445) all_544_0 = all_256_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | SIMP: (445) implies: % 170.34/26.14 | | | | | | | | | | | | | | | | (446) all_544_0 = all_256_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (440), (444) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (447) all_512_0 = all_393_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | SIMP: (447) implies: % 170.34/26.14 | | | | | | | | | | | | | | | | (448) all_512_0 = all_393_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (410), (411) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (449) all_512_1 = all_393_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | SIMP: (449) implies: % 170.34/26.14 | | | | | | | | | | | | | | | | (450) all_512_1 = all_393_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (409) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (451) all_512_1 = all_399_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | SIMP: (451) implies: % 170.34/26.14 | | | | | | | | | | | | | | | | (452) all_512_1 = all_399_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (446) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (453) all_399_1 = all_256_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (437) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (454) all_399_0 = 0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (437), (448) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (455) all_399_0 = all_393_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (407) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (456) all_451_0 = all_416_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (450) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (457) all_451_0 = all_393_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (452) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (458) all_451_0 = all_399_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (406) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (459) all_451_0 = all_421_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (456), (459) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (460) all_421_1 = all_416_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | SIMP: (460) implies: % 170.34/26.14 | | | | | | | | | | | | | | | | (461) all_421_1 = all_416_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (456), (457) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (462) all_416_0 = all_393_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (456), (458) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (463) all_416_0 = all_399_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (428), (461) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (464) all_416_0 = 0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | SIMP: (464) implies: % 170.34/26.14 | | | | | | | | | | | | | | | | (465) all_416_0 = 0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (462), (463) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (466) all_399_1 = all_393_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | SIMP: (466) implies: % 170.34/26.14 | | | | | | | | | | | | | | | | (467) all_399_1 = all_393_0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (462), (465) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (468) all_393_0 = 0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (454), (455) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (469) all_393_1 = 0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (467) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (470) all_393_0 = all_256_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | SIMP: (470) implies: % 170.34/26.14 | | | | | | | | | | | | | | | | (471) all_393_0 = all_256_1 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (468), (471) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (472) all_256_1 = 0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (456), (465) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (473) all_451_0 = 0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (473) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | (474) all_512_1 = 0 % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | BETA: splitting (353) gives: % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | Case 1: % 170.34/26.14 | | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | | (475) ~ (all_512_0 = 0) % 170.34/26.14 | | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | | REDUCE: (419), (475) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | | (476) $false % 170.34/26.14 | | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | | CLOSE: (476) is inconsistent. % 170.34/26.14 | | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | Case 2: % 170.34/26.14 | | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | | (477) ~ (all_512_1 = 0) % 170.34/26.14 | | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | | REDUCE: (474), (477) imply: % 170.34/26.14 | | | | | | | | | | | | | | | | | (478) $false % 170.34/26.14 | | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | | CLOSE: (478) is inconsistent. % 170.34/26.14 | | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | | End of split % 170.34/26.14 | | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | | End of split % 170.34/26.14 | | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | | End of split % 170.34/26.14 | | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | | End of split % 170.34/26.14 | | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | | End of split % 170.34/26.14 | | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | | End of split % 170.34/26.14 | | | | | | | | | | | % 170.34/26.14 | | | | | | | | | | End of split % 170.34/26.14 | | | | | | | | | | % 170.34/26.14 | | | | | | | | | End of split % 170.34/26.14 | | | | | | | | | % 170.34/26.14 | | | | | | | | End of split % 170.34/26.14 | | | | | | | | % 170.34/26.14 | | | | | | | End of split % 170.34/26.14 | | | | | | | % 170.34/26.14 | | | | | | End of split % 170.34/26.14 | | | | | | % 170.34/26.14 | | | | | End of split % 170.34/26.14 | | | | | % 170.34/26.14 | | | | End of split % 170.34/26.14 | | | | % 170.34/26.14 | | | End of split % 170.34/26.14 | | | % 170.34/26.14 | | End of split % 170.34/26.14 | | % 170.34/26.14 | End of split % 170.34/26.14 | % 170.34/26.14 End of proof % 170.34/26.14 % 170.34/26.14 Sub-proof #3 shows that the following formulas are inconsistent: % 170.34/26.14 ---------------------------------------------------------------- % 170.34/26.14 (1) all_123_3 = all_41_2 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 170.34/26.14 (apply(all_32_8, all_119_3, all_123_3) = v2 & member(all_119_3, all_32_5) % 170.34/26.14 = v0 & member(all_41_2, all_32_4) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | % 170.34/26.14 ~ (v0 = 0))) % 170.34/26.14 (2) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.14 all_55_0, all_51_0) = v0 & apply(all_32_8, all_55_0, all_49_0) = v1 & % 170.34/26.14 ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.14 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 170.34/26.14 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = % 170.34/26.14 v0)) % 170.34/26.14 (4) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.14 all_117_0, all_123_3) = v1 & apply(all_32_8, all_117_0, all_51_0) = % 170.34/26.14 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.14 (5) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.14 all_41_0, all_51_0) = v0 & apply(all_32_8, all_41_0, all_49_0) = v1 & % 170.34/26.14 ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.14 (6) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.14 all_41_0, all_123_3) = v0 & apply(all_32_8, all_41_0, all_121_3) = v1 % 170.34/26.14 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.14 (7) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.14 all_55_0, all_51_0) = v0 & apply(all_32_8, all_55_0, all_41_2) = v1 & % 170.34/26.14 ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.14 (8) all_117_0 = all_41_0 % 170.34/26.14 (9) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.14 all_41_0, all_51_0) = v0 & apply(all_32_8, all_41_0, all_41_2) = v1 & % 170.34/26.14 ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.14 (10) apply(all_32_8, all_41_0, all_41_2) = 0 % 170.34/26.15 (11) all_111_0 = all_41_2 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 170.34/26.15 (apply(all_32_8, all_41_0, all_41_2) = v2 & member(all_111_0, all_32_4) % 170.34/26.15 = v1 & member(all_41_0, all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | % 170.34/26.15 ~ (v0 = 0))) % 170.34/26.15 (12) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.15 all_41_0, all_123_3) = v0 & apply(all_32_8, all_41_0, all_51_0) = v1 % 170.34/26.15 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.15 (13) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.15 all_117_0, all_123_3) = v0 & apply(all_32_8, all_117_0, all_121_3) = % 170.34/26.15 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.15 (14) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.15 all_117_0, all_123_3) = v0 & apply(all_32_8, all_117_0, all_51_0) = % 170.34/26.15 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.15 (15) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.15 all_119_3, all_123_3) = v1 & apply(all_32_8, all_119_3, all_121_3) = % 170.34/26.15 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.15 (16) all_111_0 = all_51_0 % 170.34/26.15 (17) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.15 all_55_0, all_51_0) = v1 & apply(all_32_8, all_55_0, all_49_0) = v0 % 170.34/26.15 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.15 (18) member(all_41_0, all_32_5) = 0 % 170.34/26.15 (19) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.15 all_55_0, all_51_0) = v1 & apply(all_32_8, all_55_0, all_41_2) = v0 % 170.34/26.15 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.15 (20) member(all_51_0, all_32_4) = 0 % 170.34/26.15 (21) apply(all_32_8, all_41_0, all_123_3) = 0 % 170.34/26.15 (22) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.15 all_41_0, all_123_3) = v1 & apply(all_32_8, all_41_0, all_121_3) = % 170.34/26.15 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.15 (23) all_121_3 = all_41_2 % 170.34/26.15 (24) all_119_3 = all_41_0 % 170.34/26.15 (25) all_55_0 = all_41_0 % 170.34/26.15 (26) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.15 all_119_3, all_123_3) = v0 & apply(all_32_8, all_119_3, all_51_0) = % 170.34/26.15 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.15 (27) all_49_0 = all_41_2 % 170.34/26.15 (28) apply(all_32_8, all_41_0, all_51_0) = 0 % 170.34/26.15 (29) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.15 all_41_0, all_51_0) = v1 & apply(all_32_8, all_41_0, all_49_0) = v0 % 170.34/26.15 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.15 (30) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 170.34/26.15 (apply(all_32_8, all_41_0, all_49_0) = v2 & member(all_51_0, all_32_4) = % 170.34/26.15 v1 & member(all_41_0, all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 170.34/26.15 (v0 = 0))) % 170.34/26.15 (31) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.15 all_119_3, all_123_3) = v0 & apply(all_32_8, all_119_3, all_121_3) = % 170.34/26.15 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.15 (32) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 170.34/26.15 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ % 170.34/26.15 (apply(v4, v3, v2) = v0)) % 170.34/26.15 (33) ~ (all_51_0 = all_41_2) % 170.34/26.15 (34) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.15 all_41_0, all_51_0) = v1 & apply(all_32_8, all_41_0, all_41_2) = v0 % 170.34/26.15 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.15 (35) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 170.34/26.15 (apply(all_32_8, all_41_0, all_41_2) = v2 & member(all_51_0, all_32_4) = % 170.34/26.15 v1 & member(all_41_0, all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 170.34/26.15 (v0 = 0))) % 170.34/26.15 (36) all_123_3 = all_51_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.15 all_119_3, all_123_3) = v1 & apply(all_32_8, all_119_3, all_51_0) = % 170.34/26.15 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.15 % 170.34/26.15 Begin of proof % 170.34/26.15 | % 170.34/26.15 | BETA: splitting (4) gives: % 170.34/26.15 | % 170.34/26.15 | Case 1: % 170.34/26.15 | | % 170.34/26.15 | | (37) all_123_3 = all_51_0 % 170.34/26.15 | | % 170.34/26.15 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (13), (15), (16), % 170.34/26.15 | | (17), (18), (19), (20), (22), (23), (24), (25), (27), (29), (30), % 170.34/26.15 | | (31), (32), (33), (34), (35), (37) are inconsistent by sub-proof % 170.34/26.15 | | #4. % 170.34/26.15 | | % 170.34/26.15 | Case 2: % 170.34/26.15 | | % 170.34/26.15 | | (38) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_117_0, all_123_3) % 170.34/26.15 | | = v1 & apply(all_32_8, all_117_0, all_51_0) = v0 & ( ~ (v1 = 0) | % 170.34/26.15 | | ~ (v0 = 0))) % 170.34/26.15 | | % 170.34/26.15 | | DELTA: instantiating (38) with fresh symbols all_443_0, all_443_1 gives: % 170.34/26.15 | | (39) apply(all_32_8, all_117_0, all_123_3) = all_443_0 & apply(all_32_8, % 170.34/26.15 | | all_117_0, all_51_0) = all_443_1 & ( ~ (all_443_0 = 0) | ~ % 170.34/26.15 | | (all_443_1 = 0)) % 170.34/26.15 | | % 170.34/26.15 | | ALPHA: (39) implies: % 170.34/26.15 | | (40) apply(all_32_8, all_117_0, all_51_0) = all_443_1 % 170.34/26.15 | | (41) apply(all_32_8, all_117_0, all_123_3) = all_443_0 % 170.34/26.15 | | % 170.34/26.15 | | REDUCE: (8), (41) imply: % 170.34/26.15 | | (42) apply(all_32_8, all_41_0, all_123_3) = all_443_0 % 170.34/26.15 | | % 170.34/26.15 | | REDUCE: (8), (40) imply: % 170.34/26.15 | | (43) apply(all_32_8, all_41_0, all_51_0) = all_443_1 % 170.34/26.15 | | % 170.34/26.15 | | BETA: splitting (14) gives: % 170.34/26.15 | | % 170.34/26.15 | | Case 1: % 170.34/26.15 | | | % 170.34/26.15 | | | (44) all_123_3 = all_51_0 % 170.34/26.15 | | | % 170.34/26.15 | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (13), (15), % 170.34/26.15 | | | (16), (17), (18), (19), (20), (22), (23), (24), (25), (27), % 170.34/26.15 | | | (29), (30), (31), (32), (33), (34), (35), (44) are inconsistent % 170.34/26.15 | | | by sub-proof #4. % 170.34/26.15 | | | % 170.34/26.15 | | Case 2: % 170.34/26.15 | | | % 170.34/26.15 | | | (45) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_117_0, % 170.34/26.15 | | | all_123_3) = v0 & apply(all_32_8, all_117_0, all_51_0) = v1 & % 170.34/26.15 | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.15 | | | % 170.34/26.15 | | | DELTA: instantiating (45) with fresh symbols all_490_0, all_490_1 gives: % 170.34/26.15 | | | (46) apply(all_32_8, all_117_0, all_123_3) = all_490_1 & % 170.34/26.15 | | | apply(all_32_8, all_117_0, all_51_0) = all_490_0 & ( ~ (all_490_0 % 170.34/26.15 | | | = 0) | ~ (all_490_1 = 0)) % 170.34/26.15 | | | % 170.34/26.15 | | | ALPHA: (46) implies: % 170.34/26.15 | | | (47) apply(all_32_8, all_117_0, all_51_0) = all_490_0 % 170.34/26.15 | | | (48) apply(all_32_8, all_117_0, all_123_3) = all_490_1 % 170.34/26.15 | | | % 170.34/26.15 | | | REDUCE: (8), (48) imply: % 170.34/26.15 | | | (49) apply(all_32_8, all_41_0, all_123_3) = all_490_1 % 170.34/26.15 | | | % 170.34/26.15 | | | REDUCE: (8), (47) imply: % 170.34/26.15 | | | (50) apply(all_32_8, all_41_0, all_51_0) = all_490_0 % 170.34/26.15 | | | % 170.34/26.15 | | | BETA: splitting (36) gives: % 170.34/26.15 | | | % 170.34/26.15 | | | Case 1: % 170.34/26.15 | | | | % 170.34/26.15 | | | | (51) all_123_3 = all_51_0 % 170.34/26.15 | | | | % 170.34/26.15 | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (13), (15), % 170.34/26.15 | | | | (16), (17), (18), (19), (20), (22), (23), (24), (25), (27), % 170.34/26.15 | | | | (29), (30), (31), (32), (33), (34), (35), (51) are % 170.34/26.15 | | | | inconsistent by sub-proof #4. % 170.34/26.15 | | | | % 170.34/26.15 | | | Case 2: % 170.34/26.15 | | | | % 170.34/26.15 | | | | (52) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_119_3, % 170.34/26.15 | | | | all_123_3) = v1 & apply(all_32_8, all_119_3, all_51_0) = v0 % 170.34/26.15 | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.15 | | | | % 170.34/26.15 | | | | DELTA: instantiating (52) with fresh symbols all_496_0, all_496_1 gives: % 170.34/26.15 | | | | (53) apply(all_32_8, all_119_3, all_123_3) = all_496_0 & % 170.34/26.15 | | | | apply(all_32_8, all_119_3, all_51_0) = all_496_1 & ( ~ % 170.34/26.15 | | | | (all_496_0 = 0) | ~ (all_496_1 = 0)) % 170.34/26.15 | | | | % 170.34/26.15 | | | | ALPHA: (53) implies: % 170.34/26.15 | | | | (54) apply(all_32_8, all_119_3, all_51_0) = all_496_1 % 170.34/26.15 | | | | (55) apply(all_32_8, all_119_3, all_123_3) = all_496_0 % 170.34/26.15 | | | | (56) ~ (all_496_0 = 0) | ~ (all_496_1 = 0) % 170.34/26.15 | | | | % 170.34/26.15 | | | | REDUCE: (24), (55) imply: % 170.34/26.15 | | | | (57) apply(all_32_8, all_41_0, all_123_3) = all_496_0 % 170.34/26.15 | | | | % 170.34/26.15 | | | | REDUCE: (24), (54) imply: % 170.34/26.15 | | | | (58) apply(all_32_8, all_41_0, all_51_0) = all_496_1 % 170.34/26.15 | | | | % 170.34/26.15 | | | | BETA: splitting (12) gives: % 170.34/26.15 | | | | % 170.34/26.15 | | | | Case 1: % 170.34/26.15 | | | | | % 170.34/26.16 | | | | | (59) all_123_3 = all_51_0 % 170.34/26.16 | | | | | % 170.34/26.16 | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (13), (15), % 170.34/26.16 | | | | | (16), (17), (18), (19), (20), (22), (23), (24), (25), (27), % 170.34/26.16 | | | | | (29), (30), (31), (32), (33), (34), (35), (59) are % 170.34/26.16 | | | | | inconsistent by sub-proof #4. % 170.34/26.16 | | | | | % 170.34/26.16 | | | | Case 2: % 170.34/26.16 | | | | | % 170.34/26.16 | | | | | (60) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_41_0, % 170.34/26.16 | | | | | all_123_3) = v0 & apply(all_32_8, all_41_0, all_51_0) = v1 % 170.34/26.16 | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.16 | | | | | % 170.34/26.16 | | | | | DELTA: instantiating (60) with fresh symbols all_518_0, all_518_1 % 170.34/26.16 | | | | | gives: % 170.34/26.16 | | | | | (61) apply(all_32_8, all_41_0, all_123_3) = all_518_1 & % 170.34/26.16 | | | | | apply(all_32_8, all_41_0, all_51_0) = all_518_0 & ( ~ % 170.34/26.16 | | | | | (all_518_0 = 0) | ~ (all_518_1 = 0)) % 170.34/26.16 | | | | | % 170.34/26.16 | | | | | ALPHA: (61) implies: % 170.34/26.16 | | | | | (62) apply(all_32_8, all_41_0, all_51_0) = all_518_0 % 170.34/26.16 | | | | | (63) apply(all_32_8, all_41_0, all_123_3) = all_518_1 % 170.34/26.16 | | | | | % 170.34/26.16 | | | | | BETA: splitting (5) gives: % 170.34/26.16 | | | | | % 170.34/26.16 | | | | | Case 1: % 170.34/26.16 | | | | | | % 170.34/26.16 | | | | | | (64) all_51_0 = all_49_0 % 170.34/26.16 | | | | | | % 170.34/26.16 | | | | | | COMBINE_EQS: (27), (64) imply: % 170.34/26.16 | | | | | | (65) all_51_0 = all_41_2 % 170.34/26.16 | | | | | | % 170.34/26.16 | | | | | | REDUCE: (33), (65) imply: % 170.34/26.16 | | | | | | (66) $false % 170.34/26.16 | | | | | | % 170.34/26.16 | | | | | | CLOSE: (66) is inconsistent. % 170.34/26.16 | | | | | | % 170.34/26.16 | | | | | Case 2: % 170.34/26.16 | | | | | | % 170.34/26.16 | | | | | | (67) ~ (all_51_0 = all_49_0) % 170.34/26.16 | | | | | | (68) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_41_0, % 170.34/26.16 | | | | | | all_51_0) = v0 & apply(all_32_8, all_41_0, all_49_0) = % 170.34/26.16 | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.16 | | | | | | % 170.34/26.16 | | | | | | DELTA: instantiating (68) with fresh symbols all_524_0, all_524_1 % 170.34/26.16 | | | | | | gives: % 170.34/26.16 | | | | | | (69) apply(all_32_8, all_41_0, all_51_0) = all_524_1 & % 170.34/26.16 | | | | | | apply(all_32_8, all_41_0, all_49_0) = all_524_0 & ( ~ % 170.34/26.16 | | | | | | (all_524_0 = 0) | ~ (all_524_1 = 0)) % 170.34/26.16 | | | | | | % 170.34/26.16 | | | | | | ALPHA: (69) implies: % 170.34/26.16 | | | | | | (70) apply(all_32_8, all_41_0, all_51_0) = all_524_1 % 170.34/26.16 | | | | | | % 170.34/26.16 | | | | | | BETA: splitting (29) gives: % 170.34/26.16 | | | | | | % 170.34/26.16 | | | | | | Case 1: % 170.34/26.16 | | | | | | | % 170.34/26.16 | | | | | | | (71) all_51_0 = all_49_0 % 170.34/26.16 | | | | | | | % 170.34/26.16 | | | | | | | COMBINE_EQS: (27), (71) imply: % 170.34/26.16 | | | | | | | (72) all_51_0 = all_41_2 % 170.34/26.16 | | | | | | | % 170.34/26.16 | | | | | | | REDUCE: (33), (72) imply: % 170.34/26.16 | | | | | | | (73) $false % 170.34/26.16 | | | | | | | % 170.34/26.16 | | | | | | | CLOSE: (73) is inconsistent. % 170.34/26.16 | | | | | | | % 170.34/26.16 | | | | | | Case 2: % 170.34/26.16 | | | | | | | % 170.34/26.16 | | | | | | | (74) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_41_0, % 170.34/26.16 | | | | | | | all_51_0) = v1 & apply(all_32_8, all_41_0, all_49_0) = % 170.34/26.16 | | | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.16 | | | | | | | % 170.34/26.16 | | | | | | | DELTA: instantiating (74) with fresh symbols all_530_0, all_530_1 % 170.34/26.16 | | | | | | | gives: % 170.34/26.16 | | | | | | | (75) apply(all_32_8, all_41_0, all_51_0) = all_530_0 & % 170.34/26.16 | | | | | | | apply(all_32_8, all_41_0, all_49_0) = all_530_1 & ( ~ % 170.34/26.16 | | | | | | | (all_530_0 = 0) | ~ (all_530_1 = 0)) % 170.34/26.16 | | | | | | | % 170.34/26.16 | | | | | | | ALPHA: (75) implies: % 170.34/26.16 | | | | | | | (76) apply(all_32_8, all_41_0, all_51_0) = all_530_0 % 170.34/26.16 | | | | | | | % 170.34/26.16 | | | | | | | BETA: splitting (19) gives: % 170.34/26.16 | | | | | | | % 170.34/26.16 | | | | | | | Case 1: % 170.34/26.16 | | | | | | | | % 170.34/26.16 | | | | | | | | (77) all_51_0 = all_41_2 % 170.34/26.16 | | | | | | | | % 170.34/26.16 | | | | | | | | REDUCE: (33), (77) imply: % 170.34/26.16 | | | | | | | | (78) $false % 170.34/26.16 | | | | | | | | % 170.34/26.16 | | | | | | | | CLOSE: (78) is inconsistent. % 170.34/26.16 | | | | | | | | % 170.34/26.16 | | | | | | | Case 2: % 170.34/26.16 | | | | | | | | % 170.34/26.16 | | | | | | | | (79) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_55_0, % 170.34/26.16 | | | | | | | | all_51_0) = v1 & apply(all_32_8, all_55_0, all_41_2) % 170.34/26.16 | | | | | | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.16 | | | | | | | | % 170.34/26.16 | | | | | | | | DELTA: instantiating (79) with fresh symbols all_542_0, % 170.34/26.16 | | | | | | | | all_542_1 gives: % 170.34/26.16 | | | | | | | | (80) apply(all_32_8, all_55_0, all_51_0) = all_542_0 & % 170.34/26.16 | | | | | | | | apply(all_32_8, all_55_0, all_41_2) = all_542_1 & ( ~ % 170.34/26.16 | | | | | | | | (all_542_0 = 0) | ~ (all_542_1 = 0)) % 170.34/26.16 | | | | | | | | % 170.34/26.16 | | | | | | | | ALPHA: (80) implies: % 170.34/26.16 | | | | | | | | (81) apply(all_32_8, all_55_0, all_51_0) = all_542_0 % 170.34/26.16 | | | | | | | | % 170.34/26.16 | | | | | | | | REDUCE: (25), (81) imply: % 170.34/26.16 | | | | | | | | (82) apply(all_32_8, all_41_0, all_51_0) = all_542_0 % 170.34/26.16 | | | | | | | | % 170.34/26.16 | | | | | | | | BETA: splitting (7) gives: % 170.34/26.16 | | | | | | | | % 170.34/26.16 | | | | | | | | Case 1: % 170.34/26.16 | | | | | | | | | % 170.34/26.16 | | | | | | | | | (83) all_51_0 = all_41_2 % 170.34/26.16 | | | | | | | | | % 170.34/26.16 | | | | | | | | | REDUCE: (33), (83) imply: % 170.34/26.16 | | | | | | | | | (84) $false % 170.34/26.16 | | | | | | | | | % 170.34/26.16 | | | | | | | | | CLOSE: (84) is inconsistent. % 170.34/26.16 | | | | | | | | | % 170.34/26.16 | | | | | | | | Case 2: % 170.34/26.16 | | | | | | | | | % 170.34/26.16 | | | | | | | | | (85) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.16 | | | | | | | | | all_55_0, all_51_0) = v0 & apply(all_32_8, % 170.34/26.16 | | | | | | | | | all_55_0, all_41_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = % 170.34/26.16 | | | | | | | | | 0))) % 170.34/26.16 | | | | | | | | | % 170.34/26.16 | | | | | | | | | DELTA: instantiating (85) with fresh symbols all_548_0, % 170.34/26.16 | | | | | | | | | all_548_1 gives: % 170.34/26.16 | | | | | | | | | (86) apply(all_32_8, all_55_0, all_51_0) = all_548_1 & % 170.34/26.16 | | | | | | | | | apply(all_32_8, all_55_0, all_41_2) = all_548_0 & ( ~ % 170.34/26.16 | | | | | | | | | (all_548_0 = 0) | ~ (all_548_1 = 0)) % 170.34/26.16 | | | | | | | | | % 170.34/26.16 | | | | | | | | | ALPHA: (86) implies: % 170.34/26.16 | | | | | | | | | (87) apply(all_32_8, all_55_0, all_51_0) = all_548_1 % 170.34/26.16 | | | | | | | | | % 170.34/26.16 | | | | | | | | | REDUCE: (25), (87) imply: % 170.34/26.16 | | | | | | | | | (88) apply(all_32_8, all_41_0, all_51_0) = all_548_1 % 170.34/26.16 | | | | | | | | | % 170.34/26.16 | | | | | | | | | BETA: splitting (26) gives: % 170.34/26.16 | | | | | | | | | % 170.34/26.16 | | | | | | | | | Case 1: % 170.34/26.16 | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | (89) all_123_3 = all_51_0 % 170.34/26.16 | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), % 170.34/26.16 | | | | | | | | | | (13), (15), (16), (17), (18), (19), (20), (22), % 170.34/26.16 | | | | | | | | | | (23), (24), (25), (27), (29), (30), (31), (32), % 170.34/26.16 | | | | | | | | | | (33), (34), (35), (89) are inconsistent by % 170.34/26.16 | | | | | | | | | | sub-proof #4. % 170.34/26.16 | | | | | | | | | | % 170.34/26.16 | | | | | | | | | Case 2: % 170.34/26.16 | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | (90) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.16 | | | | | | | | | | all_119_3, all_123_3) = v0 & apply(all_32_8, % 170.34/26.16 | | | | | | | | | | all_119_3, all_51_0) = v1 & ( ~ (v1 = 0) | ~ % 170.34/26.16 | | | | | | | | | | (v0 = 0))) % 170.34/26.16 | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | DELTA: instantiating (90) with fresh symbols all_554_0, % 170.34/26.16 | | | | | | | | | | all_554_1 gives: % 170.34/26.16 | | | | | | | | | | (91) apply(all_32_8, all_119_3, all_123_3) = all_554_1 & % 170.34/26.16 | | | | | | | | | | apply(all_32_8, all_119_3, all_51_0) = all_554_0 & ( % 170.34/26.16 | | | | | | | | | | ~ (all_554_0 = 0) | ~ (all_554_1 = 0)) % 170.34/26.16 | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | ALPHA: (91) implies: % 170.34/26.16 | | | | | | | | | | (92) apply(all_32_8, all_119_3, all_51_0) = all_554_0 % 170.34/26.16 | | | | | | | | | | (93) apply(all_32_8, all_119_3, all_123_3) = all_554_1 % 170.34/26.16 | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | REDUCE: (24), (93) imply: % 170.34/26.16 | | | | | | | | | | (94) apply(all_32_8, all_41_0, all_123_3) = all_554_1 % 170.34/26.16 | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | REDUCE: (24), (92) imply: % 170.34/26.16 | | | | | | | | | | (95) apply(all_32_8, all_41_0, all_51_0) = all_554_0 % 170.34/26.16 | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | BETA: splitting (9) gives: % 170.34/26.16 | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | Case 1: % 170.34/26.16 | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | (96) all_51_0 = all_41_2 % 170.34/26.16 | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | REDUCE: (33), (96) imply: % 170.34/26.16 | | | | | | | | | | | (97) $false % 170.34/26.16 | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | CLOSE: (97) is inconsistent. % 170.34/26.16 | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | Case 2: % 170.34/26.16 | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | (98) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.16 | | | | | | | | | | | all_41_0, all_51_0) = v0 & apply(all_32_8, % 170.34/26.16 | | | | | | | | | | | all_41_0, all_41_2) = v1 & ( ~ (v1 = 0) | ~ % 170.34/26.16 | | | | | | | | | | | (v0 = 0))) % 170.34/26.16 | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | DELTA: instantiating (98) with fresh symbols all_578_0, % 170.34/26.16 | | | | | | | | | | | all_578_1 gives: % 170.34/26.16 | | | | | | | | | | | (99) apply(all_32_8, all_41_0, all_51_0) = all_578_1 & % 170.34/26.16 | | | | | | | | | | | apply(all_32_8, all_41_0, all_41_2) = all_578_0 & % 170.34/26.16 | | | | | | | | | | | ( ~ (all_578_0 = 0) | ~ (all_578_1 = 0)) % 170.34/26.16 | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | ALPHA: (99) implies: % 170.34/26.16 | | | | | | | | | | | (100) apply(all_32_8, all_41_0, all_51_0) = all_578_1 % 170.34/26.16 | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | BETA: splitting (34) gives: % 170.34/26.16 | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | Case 1: % 170.34/26.16 | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | (101) all_51_0 = all_41_2 % 170.34/26.16 | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | REDUCE: (33), (101) imply: % 170.34/26.16 | | | | | | | | | | | | (102) $false % 170.34/26.16 | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | CLOSE: (102) is inconsistent. % 170.34/26.16 | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | Case 2: % 170.34/26.16 | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | (103) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.16 | | | | | | | | | | | | all_41_0, all_51_0) = v1 & apply(all_32_8, % 170.34/26.16 | | | | | | | | | | | | all_41_0, all_41_2) = v0 & ( ~ (v1 = 0) | ~ % 170.34/26.16 | | | | | | | | | | | | (v0 = 0))) % 170.34/26.16 | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | DELTA: instantiating (103) with fresh symbols all_584_0, % 170.34/26.16 | | | | | | | | | | | | all_584_1 gives: % 170.34/26.16 | | | | | | | | | | | | (104) apply(all_32_8, all_41_0, all_51_0) = all_584_0 & % 170.34/26.16 | | | | | | | | | | | | apply(all_32_8, all_41_0, all_41_2) = all_584_1 & % 170.34/26.16 | | | | | | | | | | | | ( ~ (all_584_0 = 0) | ~ (all_584_1 = 0)) % 170.34/26.16 | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | ALPHA: (104) implies: % 170.34/26.16 | | | | | | | | | | | | (105) apply(all_32_8, all_41_0, all_51_0) = all_584_0 % 170.34/26.16 | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | BETA: splitting (2) gives: % 170.34/26.16 | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | Case 1: % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | | (106) all_51_0 = all_49_0 % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | | COMBINE_EQS: (27), (106) imply: % 170.34/26.16 | | | | | | | | | | | | | (107) all_51_0 = all_41_2 % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | | REDUCE: (33), (107) imply: % 170.34/26.16 | | | | | | | | | | | | | (108) $false % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | | CLOSE: (108) is inconsistent. % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | Case 2: % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | | (109) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.16 | | | | | | | | | | | | | all_55_0, all_51_0) = v0 & apply(all_32_8, % 170.34/26.16 | | | | | | | | | | | | | all_55_0, all_49_0) = v1 & ( ~ (v1 = 0) | ~ % 170.34/26.16 | | | | | | | | | | | | | (v0 = 0))) % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | | DELTA: instantiating (109) with fresh symbols all_602_0, % 170.34/26.16 | | | | | | | | | | | | | all_602_1 gives: % 170.34/26.16 | | | | | | | | | | | | | (110) apply(all_32_8, all_55_0, all_51_0) = all_602_1 & % 170.34/26.16 | | | | | | | | | | | | | apply(all_32_8, all_55_0, all_49_0) = all_602_0 & % 170.34/26.16 | | | | | | | | | | | | | ( ~ (all_602_0 = 0) | ~ (all_602_1 = 0)) % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | | ALPHA: (110) implies: % 170.34/26.16 | | | | | | | | | | | | | (111) apply(all_32_8, all_55_0, all_51_0) = all_602_1 % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | | REDUCE: (25), (111) imply: % 170.34/26.16 | | | | | | | | | | | | | (112) apply(all_32_8, all_41_0, all_51_0) = all_602_1 % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_490_0, all_51_0, % 170.34/26.16 | | | | | | | | | | | | | all_41_0, all_32_8, simplifying with (28), (50) % 170.34/26.16 | | | | | | | | | | | | | gives: % 170.34/26.16 | | | | | | | | | | | | | (113) all_490_0 = 0 % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_490_0, all_496_1, % 170.34/26.16 | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 170.34/26.16 | | | | | | | | | | | | | (50), (58) gives: % 170.34/26.16 | | | | | | | | | | | | | (114) all_496_1 = all_490_0 % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_496_1, all_518_0, % 170.34/26.16 | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 170.34/26.16 | | | | | | | | | | | | | (58), (62) gives: % 170.34/26.16 | | | | | | | | | | | | | (115) all_518_0 = all_496_1 % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_530_0, all_542_0, % 170.34/26.16 | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 170.34/26.16 | | | | | | | | | | | | | (76), (82) gives: % 170.34/26.16 | | | | | | | | | | | | | (116) all_542_0 = all_530_0 % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_542_0, all_548_1, % 170.34/26.16 | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 170.34/26.16 | | | | | | | | | | | | | (82), (88) gives: % 170.34/26.16 | | | | | | | | | | | | | (117) all_548_1 = all_542_0 % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_548_1, all_554_0, % 170.34/26.16 | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 170.34/26.16 | | | | | | | | | | | | | (88), (95) gives: % 170.34/26.16 | | | | | | | | | | | | | (118) all_554_0 = all_548_1 % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_554_0, all_578_1, % 170.34/26.16 | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 170.34/26.16 | | | | | | | | | | | | | (95), (100) gives: % 170.34/26.16 | | | | | | | | | | | | | (119) all_578_1 = all_554_0 % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.16 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_578_1, all_584_0, % 170.34/26.16 | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 170.34/26.16 | | | | | | | | | | | | | (100), (105) gives: % 170.34/26.16 | | | | | | | | | | | | | (120) all_584_0 = all_578_1 % 170.34/26.16 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_443_1, all_584_0, % 170.34/26.17 | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 170.34/26.17 | | | | | | | | | | | | | (43), (105) gives: % 170.34/26.17 | | | | | | | | | | | | | (121) all_584_0 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_542_0, all_602_1, % 170.34/26.17 | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 170.34/26.17 | | | | | | | | | | | | | (82), (112) gives: % 170.34/26.17 | | | | | | | | | | | | | (122) all_602_1 = all_542_0 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_524_1, all_602_1, % 170.34/26.17 | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 170.34/26.17 | | | | | | | | | | | | | (70), (112) gives: % 170.34/26.17 | | | | | | | | | | | | | (123) all_602_1 = all_524_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_518_0, all_602_1, % 170.34/26.17 | | | | | | | | | | | | | all_51_0, all_41_0, all_32_8, simplifying with % 170.34/26.17 | | | | | | | | | | | | | (62), (112) gives: % 170.34/26.17 | | | | | | | | | | | | | (124) all_602_1 = all_518_0 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_490_1, all_123_3, % 170.34/26.17 | | | | | | | | | | | | | all_41_0, all_32_8, simplifying with (21), (49) % 170.34/26.17 | | | | | | | | | | | | | gives: % 170.34/26.17 | | | | | | | | | | | | | (125) all_490_1 = 0 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_490_1, all_496_0, % 170.34/26.17 | | | | | | | | | | | | | all_123_3, all_41_0, all_32_8, simplifying with % 170.34/26.17 | | | | | | | | | | | | | (49), (57) gives: % 170.34/26.17 | | | | | | | | | | | | | (126) all_496_0 = all_490_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_496_0, all_518_1, % 170.34/26.17 | | | | | | | | | | | | | all_123_3, all_41_0, all_32_8, simplifying with % 170.34/26.17 | | | | | | | | | | | | | (57), (63) gives: % 170.34/26.17 | | | | | | | | | | | | | (127) all_518_1 = all_496_0 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_518_1, all_554_1, % 170.34/26.17 | | | | | | | | | | | | | all_123_3, all_41_0, all_32_8, simplifying with % 170.34/26.17 | | | | | | | | | | | | | (63), (94) gives: % 170.34/26.17 | | | | | | | | | | | | | (128) all_554_1 = all_518_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_443_0, all_554_1, % 170.34/26.17 | | | | | | | | | | | | | all_123_3, all_41_0, all_32_8, simplifying with % 170.34/26.17 | | | | | | | | | | | | | (42), (94) gives: % 170.34/26.17 | | | | | | | | | | | | | (129) all_554_1 = all_443_0 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (122), (123) imply: % 170.34/26.17 | | | | | | | | | | | | | (130) all_542_0 = all_524_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | SIMP: (130) implies: % 170.34/26.17 | | | | | | | | | | | | | (131) all_542_0 = all_524_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (123), (124) imply: % 170.34/26.17 | | | | | | | | | | | | | (132) all_524_1 = all_518_0 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (120), (121) imply: % 170.34/26.17 | | | | | | | | | | | | | (133) all_578_1 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | SIMP: (133) implies: % 170.34/26.17 | | | | | | | | | | | | | (134) all_578_1 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (119), (134) imply: % 170.34/26.17 | | | | | | | | | | | | | (135) all_554_0 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | SIMP: (135) implies: % 170.34/26.17 | | | | | | | | | | | | | (136) all_554_0 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (118), (136) imply: % 170.34/26.17 | | | | | | | | | | | | | (137) all_548_1 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | SIMP: (137) implies: % 170.34/26.17 | | | | | | | | | | | | | (138) all_548_1 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (128), (129) imply: % 170.34/26.17 | | | | | | | | | | | | | (139) all_518_1 = all_443_0 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | SIMP: (139) implies: % 170.34/26.17 | | | | | | | | | | | | | (140) all_518_1 = all_443_0 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (117), (138) imply: % 170.34/26.17 | | | | | | | | | | | | | (141) all_542_0 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | SIMP: (141) implies: % 170.34/26.17 | | | | | | | | | | | | | (142) all_542_0 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (116), (131) imply: % 170.34/26.17 | | | | | | | | | | | | | (143) all_530_0 = all_524_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (116), (142) imply: % 170.34/26.17 | | | | | | | | | | | | | (144) all_530_0 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (143), (144) imply: % 170.34/26.17 | | | | | | | | | | | | | (145) all_524_1 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | SIMP: (145) implies: % 170.34/26.17 | | | | | | | | | | | | | (146) all_524_1 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (132), (146) imply: % 170.34/26.17 | | | | | | | | | | | | | (147) all_518_0 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | SIMP: (147) implies: % 170.34/26.17 | | | | | | | | | | | | | (148) all_518_0 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (115), (148) imply: % 170.34/26.17 | | | | | | | | | | | | | (149) all_496_1 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | SIMP: (149) implies: % 170.34/26.17 | | | | | | | | | | | | | (150) all_496_1 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (127), (140) imply: % 170.34/26.17 | | | | | | | | | | | | | (151) all_496_0 = all_443_0 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | SIMP: (151) implies: % 170.34/26.17 | | | | | | | | | | | | | (152) all_496_0 = all_443_0 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (126), (152) imply: % 170.34/26.17 | | | | | | | | | | | | | (153) all_490_1 = all_443_0 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | SIMP: (153) implies: % 170.34/26.17 | | | | | | | | | | | | | (154) all_490_1 = all_443_0 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (114), (150) imply: % 170.34/26.17 | | | | | | | | | | | | | (155) all_490_0 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | SIMP: (155) implies: % 170.34/26.17 | | | | | | | | | | | | | (156) all_490_0 = all_443_1 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (113), (156) imply: % 170.34/26.17 | | | | | | | | | | | | | (157) all_443_1 = 0 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (125), (154) imply: % 170.34/26.17 | | | | | | | | | | | | | (158) all_443_0 = 0 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (150), (157) imply: % 170.34/26.17 | | | | | | | | | | | | | (159) all_496_1 = 0 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | COMBINE_EQS: (152), (158) imply: % 170.34/26.17 | | | | | | | | | | | | | (160) all_496_0 = 0 % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | BETA: splitting (56) gives: % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | Case 1: % 170.34/26.17 | | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | | (161) ~ (all_496_0 = 0) % 170.34/26.17 | | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | | REDUCE: (160), (161) imply: % 170.34/26.17 | | | | | | | | | | | | | | (162) $false % 170.34/26.17 | | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | | CLOSE: (162) is inconsistent. % 170.34/26.17 | | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | Case 2: % 170.34/26.17 | | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | | (163) ~ (all_496_1 = 0) % 170.34/26.17 | | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | | REDUCE: (159), (163) imply: % 170.34/26.17 | | | | | | | | | | | | | | (164) $false % 170.34/26.17 | | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | | CLOSE: (164) is inconsistent. % 170.34/26.17 | | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | | End of split % 170.34/26.17 | | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | | End of split % 170.34/26.17 | | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | | End of split % 170.34/26.17 | | | | | | | | | | | % 170.34/26.17 | | | | | | | | | | End of split % 170.34/26.17 | | | | | | | | | | % 170.34/26.17 | | | | | | | | | End of split % 170.34/26.17 | | | | | | | | | % 170.34/26.17 | | | | | | | | End of split % 170.34/26.17 | | | | | | | | % 170.34/26.17 | | | | | | | End of split % 170.34/26.17 | | | | | | | % 170.34/26.17 | | | | | | End of split % 170.34/26.17 | | | | | | % 170.34/26.17 | | | | | End of split % 170.34/26.17 | | | | | % 170.34/26.17 | | | | End of split % 170.34/26.17 | | | | % 170.34/26.17 | | | End of split % 170.34/26.17 | | | % 170.34/26.17 | | End of split % 170.34/26.17 | | % 170.34/26.17 | End of split % 170.34/26.17 | % 170.34/26.17 End of proof % 170.34/26.17 % 170.34/26.17 Sub-proof #4 shows that the following formulas are inconsistent: % 170.34/26.17 ---------------------------------------------------------------- % 170.34/26.17 (1) all_123_3 = all_41_2 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 170.34/26.17 (apply(all_32_8, all_119_3, all_123_3) = v2 & member(all_119_3, all_32_5) % 170.34/26.17 = v0 & member(all_41_2, all_32_4) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | % 170.34/26.17 ~ (v0 = 0))) % 170.34/26.17 (2) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.17 all_55_0, all_51_0) = v0 & apply(all_32_8, all_55_0, all_49_0) = v1 & % 170.34/26.17 ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.17 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 170.34/26.17 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = % 170.34/26.17 v0)) % 170.34/26.17 (4) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.17 all_41_0, all_51_0) = v0 & apply(all_32_8, all_41_0, all_49_0) = v1 & % 170.34/26.17 ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.17 (5) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.17 all_41_0, all_123_3) = v0 & apply(all_32_8, all_41_0, all_121_3) = v1 % 170.34/26.17 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.17 (6) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.17 all_55_0, all_51_0) = v0 & apply(all_32_8, all_55_0, all_41_2) = v1 & % 170.34/26.17 ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.17 (7) all_117_0 = all_41_0 % 170.34/26.17 (8) apply(all_32_8, all_41_0, all_41_2) = 0 % 170.34/26.17 (9) all_111_0 = all_41_2 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 170.34/26.17 (apply(all_32_8, all_41_0, all_41_2) = v2 & member(all_111_0, all_32_4) = % 170.34/26.17 v1 & member(all_41_0, all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 170.34/26.17 (v0 = 0))) % 170.34/26.17 (10) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.17 all_117_0, all_123_3) = v0 & apply(all_32_8, all_117_0, all_121_3) = % 170.34/26.17 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.17 (11) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.17 all_119_3, all_123_3) = v1 & apply(all_32_8, all_119_3, all_121_3) = % 170.34/26.17 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.17 (12) all_111_0 = all_51_0 % 170.34/26.17 (13) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.17 all_55_0, all_51_0) = v1 & apply(all_32_8, all_55_0, all_49_0) = v0 % 170.34/26.17 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.17 (14) member(all_41_0, all_32_5) = 0 % 170.34/26.17 (15) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.17 all_55_0, all_51_0) = v1 & apply(all_32_8, all_55_0, all_41_2) = v0 % 170.34/26.17 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.17 (16) member(all_51_0, all_32_4) = 0 % 170.34/26.17 (17) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.17 all_41_0, all_123_3) = v1 & apply(all_32_8, all_41_0, all_121_3) = % 170.34/26.17 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.17 (18) all_121_3 = all_41_2 % 170.34/26.17 (19) all_119_3 = all_41_0 % 170.34/26.17 (20) all_55_0 = all_41_0 % 170.34/26.17 (21) all_49_0 = all_41_2 % 170.34/26.17 (22) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.17 all_41_0, all_51_0) = v1 & apply(all_32_8, all_41_0, all_49_0) = v0 % 170.34/26.17 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.17 (23) all_51_0 = all_49_0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 170.34/26.17 (apply(all_32_8, all_41_0, all_49_0) = v2 & member(all_51_0, all_32_4) = % 170.34/26.17 v1 & member(all_41_0, all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 170.34/26.17 (v0 = 0))) % 170.34/26.17 (24) all_123_3 = all_121_3 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.17 all_119_3, all_123_3) = v0 & apply(all_32_8, all_119_3, all_121_3) = % 170.34/26.17 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.17 (25) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 170.34/26.17 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ % 170.34/26.17 (apply(v4, v3, v2) = v0)) % 170.34/26.17 (26) ~ (all_51_0 = all_41_2) % 170.34/26.18 (27) all_123_3 = all_51_0 % 170.34/26.18 (28) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.18 all_41_0, all_51_0) = v1 & apply(all_32_8, all_41_0, all_41_2) = v0 % 170.34/26.18 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.18 (29) all_51_0 = all_41_2 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 170.34/26.18 (apply(all_32_8, all_41_0, all_41_2) = v2 & member(all_51_0, all_32_4) = % 170.34/26.18 v1 & member(all_41_0, all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 170.34/26.18 (v0 = 0))) % 170.34/26.18 % 170.34/26.18 Begin of proof % 170.34/26.18 | % 170.34/26.18 | BETA: splitting (9) gives: % 170.34/26.18 | % 170.34/26.18 | Case 1: % 170.34/26.18 | | % 170.34/26.18 | | (30) all_111_0 = all_41_2 % 170.34/26.18 | | % 170.34/26.18 | | COMBINE_EQS: (12), (30) imply: % 170.34/26.18 | | (31) all_51_0 = all_41_2 % 170.34/26.18 | | % 170.34/26.18 | | SIMP: (31) implies: % 170.34/26.18 | | (32) all_51_0 = all_41_2 % 170.34/26.18 | | % 170.34/26.18 | | REDUCE: (26), (32) imply: % 170.34/26.18 | | (33) $false % 170.34/26.18 | | % 170.34/26.18 | | CLOSE: (33) is inconsistent. % 170.34/26.18 | | % 170.34/26.18 | Case 2: % 170.34/26.18 | | % 170.34/26.18 | | (34) ~ (all_111_0 = all_41_2) % 170.34/26.18 | | (35) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_8, % 170.34/26.18 | | all_41_0, all_41_2) = v2 & member(all_111_0, all_32_4) = v1 & % 170.34/26.18 | | member(all_41_0, all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 170.34/26.18 | | (v0 = 0))) % 170.34/26.18 | | % 170.34/26.18 | | DELTA: instantiating (35) with fresh symbols all_441_0, all_441_1, all_441_2 % 170.34/26.18 | | gives: % 170.34/26.18 | | (36) apply(all_32_8, all_41_0, all_41_2) = all_441_0 & member(all_111_0, % 170.34/26.18 | | all_32_4) = all_441_1 & member(all_41_0, all_32_5) = all_441_2 & ( % 170.34/26.18 | | ~ (all_441_0 = 0) | ~ (all_441_1 = 0) | ~ (all_441_2 = 0)) % 170.34/26.18 | | % 170.34/26.18 | | ALPHA: (36) implies: % 170.34/26.18 | | (37) member(all_41_0, all_32_5) = all_441_2 % 170.34/26.18 | | % 170.34/26.18 | | BETA: splitting (1) gives: % 170.34/26.18 | | % 170.34/26.18 | | Case 1: % 170.34/26.18 | | | % 170.34/26.18 | | | (38) all_123_3 = all_41_2 % 170.34/26.18 | | | % 170.34/26.18 | | | COMBINE_EQS: (27), (38) imply: % 170.34/26.18 | | | (39) all_51_0 = all_41_2 % 170.34/26.18 | | | % 170.34/26.18 | | | SIMP: (39) implies: % 170.34/26.18 | | | (40) all_51_0 = all_41_2 % 170.34/26.18 | | | % 170.34/26.18 | | | REDUCE: (26), (40) imply: % 170.34/26.18 | | | (41) $false % 170.34/26.18 | | | % 170.34/26.18 | | | CLOSE: (41) is inconsistent. % 170.34/26.18 | | | % 170.34/26.18 | | Case 2: % 170.34/26.18 | | | % 170.34/26.18 | | | (42) ~ (all_123_3 = all_41_2) % 170.34/26.18 | | | (43) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_8, % 170.34/26.18 | | | all_119_3, all_123_3) = v2 & member(all_119_3, all_32_5) = v0 % 170.34/26.18 | | | & member(all_41_2, all_32_4) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | % 170.34/26.18 | | | ~ (v0 = 0))) % 170.34/26.18 | | | % 170.34/26.18 | | | DELTA: instantiating (43) with fresh symbols all_457_0, all_457_1, % 170.34/26.18 | | | all_457_2 gives: % 170.34/26.18 | | | (44) apply(all_32_8, all_119_3, all_123_3) = all_457_0 & % 170.34/26.18 | | | member(all_119_3, all_32_5) = all_457_2 & member(all_41_2, % 170.34/26.18 | | | all_32_4) = all_457_1 & ( ~ (all_457_0 = 0) | ~ (all_457_1 = 0) % 170.34/26.18 | | | | ~ (all_457_2 = 0)) % 170.34/26.18 | | | % 170.34/26.18 | | | ALPHA: (44) implies: % 170.34/26.18 | | | (45) member(all_119_3, all_32_5) = all_457_2 % 170.34/26.18 | | | % 170.34/26.18 | | | REDUCE: (19), (45) imply: % 170.34/26.18 | | | (46) member(all_41_0, all_32_5) = all_457_2 % 170.34/26.18 | | | % 170.34/26.18 | | | BETA: splitting (17) gives: % 170.34/26.18 | | | % 170.34/26.18 | | | Case 1: % 170.34/26.18 | | | | % 170.34/26.18 | | | | (47) all_123_3 = all_121_3 % 170.34/26.18 | | | | % 170.34/26.18 | | | | COMBINE_EQS: (27), (47) imply: % 170.34/26.18 | | | | (48) all_121_3 = all_51_0 % 170.34/26.18 | | | | % 170.34/26.18 | | | | COMBINE_EQS: (18), (48) imply: % 170.34/26.18 | | | | (49) all_51_0 = all_41_2 % 170.34/26.18 | | | | % 170.34/26.18 | | | | SIMP: (49) implies: % 170.34/26.18 | | | | (50) all_51_0 = all_41_2 % 170.34/26.18 | | | | % 170.34/26.18 | | | | REDUCE: (26), (50) imply: % 170.34/26.18 | | | | (51) $false % 170.34/26.18 | | | | % 170.34/26.18 | | | | CLOSE: (51) is inconsistent. % 170.34/26.18 | | | | % 170.34/26.18 | | | Case 2: % 170.34/26.18 | | | | % 170.34/26.18 | | | | (52) ~ (all_123_3 = all_121_3) % 170.34/26.18 | | | | (53) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_41_0, % 170.34/26.18 | | | | all_123_3) = v1 & apply(all_32_8, all_41_0, all_121_3) = v0 % 170.34/26.18 | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.18 | | | | % 170.34/26.18 | | | | DELTA: instantiating (53) with fresh symbols all_481_0, all_481_1 gives: % 170.34/26.18 | | | | (54) apply(all_32_8, all_41_0, all_123_3) = all_481_0 & % 170.34/26.18 | | | | apply(all_32_8, all_41_0, all_121_3) = all_481_1 & ( ~ % 170.34/26.18 | | | | (all_481_0 = 0) | ~ (all_481_1 = 0)) % 170.34/26.18 | | | | % 170.34/26.18 | | | | ALPHA: (54) implies: % 170.34/26.18 | | | | (55) apply(all_32_8, all_41_0, all_121_3) = all_481_1 % 170.34/26.18 | | | | % 170.34/26.18 | | | | REDUCE: (18), (55) imply: % 170.34/26.18 | | | | (56) apply(all_32_8, all_41_0, all_41_2) = all_481_1 % 170.34/26.18 | | | | % 170.34/26.18 | | | | BETA: splitting (4) gives: % 170.34/26.18 | | | | % 170.34/26.18 | | | | Case 1: % 170.34/26.18 | | | | | % 170.34/26.18 | | | | | (57) all_51_0 = all_49_0 % 170.34/26.18 | | | | | % 170.34/26.18 | | | | | COMBINE_EQS: (21), (57) imply: % 170.34/26.18 | | | | | (58) all_51_0 = all_41_2 % 170.34/26.18 | | | | | % 170.34/26.18 | | | | | REDUCE: (26), (58) imply: % 170.34/26.18 | | | | | (59) $false % 170.34/26.18 | | | | | % 170.34/26.18 | | | | | CLOSE: (59) is inconsistent. % 170.34/26.18 | | | | | % 170.34/26.18 | | | | Case 2: % 170.34/26.18 | | | | | % 170.34/26.18 | | | | | (60) ~ (all_51_0 = all_49_0) % 170.34/26.18 | | | | | (61) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_41_0, % 170.34/26.18 | | | | | all_51_0) = v0 & apply(all_32_8, all_41_0, all_49_0) = v1 % 170.34/26.18 | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.18 | | | | | % 170.34/26.18 | | | | | DELTA: instantiating (61) with fresh symbols all_505_0, all_505_1 % 170.34/26.18 | | | | | gives: % 170.34/26.18 | | | | | (62) apply(all_32_8, all_41_0, all_51_0) = all_505_1 & % 170.34/26.18 | | | | | apply(all_32_8, all_41_0, all_49_0) = all_505_0 & ( ~ % 170.34/26.18 | | | | | (all_505_0 = 0) | ~ (all_505_1 = 0)) % 170.34/26.18 | | | | | % 170.34/26.18 | | | | | ALPHA: (62) implies: % 170.34/26.18 | | | | | (63) apply(all_32_8, all_41_0, all_49_0) = all_505_0 % 170.34/26.18 | | | | | % 170.34/26.18 | | | | | REDUCE: (21), (63) imply: % 170.34/26.18 | | | | | (64) apply(all_32_8, all_41_0, all_41_2) = all_505_0 % 170.34/26.18 | | | | | % 170.34/26.18 | | | | | BETA: splitting (22) gives: % 170.34/26.18 | | | | | % 170.34/26.18 | | | | | Case 1: % 170.34/26.18 | | | | | | % 170.34/26.18 | | | | | | (65) all_51_0 = all_49_0 % 170.34/26.18 | | | | | | % 170.34/26.18 | | | | | | COMBINE_EQS: (21), (65) imply: % 170.34/26.18 | | | | | | (66) all_51_0 = all_41_2 % 170.34/26.18 | | | | | | % 170.34/26.18 | | | | | | REDUCE: (26), (66) imply: % 170.34/26.18 | | | | | | (67) $false % 170.34/26.18 | | | | | | % 170.34/26.18 | | | | | | CLOSE: (67) is inconsistent. % 170.34/26.18 | | | | | | % 170.34/26.18 | | | | | Case 2: % 170.34/26.18 | | | | | | % 170.34/26.18 | | | | | | (68) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_41_0, % 170.34/26.18 | | | | | | all_51_0) = v1 & apply(all_32_8, all_41_0, all_49_0) = % 170.34/26.18 | | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.18 | | | | | | % 170.34/26.18 | | | | | | DELTA: instantiating (68) with fresh symbols all_511_0, all_511_1 % 170.34/26.18 | | | | | | gives: % 170.34/26.18 | | | | | | (69) apply(all_32_8, all_41_0, all_51_0) = all_511_0 & % 170.34/26.18 | | | | | | apply(all_32_8, all_41_0, all_49_0) = all_511_1 & ( ~ % 170.34/26.18 | | | | | | (all_511_0 = 0) | ~ (all_511_1 = 0)) % 170.34/26.18 | | | | | | % 170.34/26.18 | | | | | | ALPHA: (69) implies: % 170.34/26.18 | | | | | | (70) apply(all_32_8, all_41_0, all_49_0) = all_511_1 % 170.34/26.18 | | | | | | % 170.34/26.18 | | | | | | REDUCE: (21), (70) imply: % 170.34/26.18 | | | | | | (71) apply(all_32_8, all_41_0, all_41_2) = all_511_1 % 170.34/26.18 | | | | | | % 170.34/26.18 | | | | | | BETA: splitting (24) gives: % 170.34/26.18 | | | | | | % 170.34/26.18 | | | | | | Case 1: % 170.34/26.18 | | | | | | | % 170.34/26.18 | | | | | | | (72) all_123_3 = all_121_3 % 170.34/26.18 | | | | | | | % 170.34/26.18 | | | | | | | COMBINE_EQS: (27), (72) imply: % 170.34/26.18 | | | | | | | (73) all_121_3 = all_51_0 % 170.34/26.18 | | | | | | | % 170.34/26.18 | | | | | | | COMBINE_EQS: (18), (73) imply: % 170.34/26.18 | | | | | | | (74) all_51_0 = all_41_2 % 170.34/26.18 | | | | | | | % 170.34/26.18 | | | | | | | SIMP: (74) implies: % 170.34/26.18 | | | | | | | (75) all_51_0 = all_41_2 % 170.34/26.18 | | | | | | | % 170.34/26.18 | | | | | | | REDUCE: (26), (75) imply: % 170.34/26.18 | | | | | | | (76) $false % 170.34/26.18 | | | | | | | % 170.34/26.18 | | | | | | | CLOSE: (76) is inconsistent. % 170.34/26.18 | | | | | | | % 170.34/26.18 | | | | | | Case 2: % 170.34/26.18 | | | | | | | % 170.34/26.18 | | | | | | | (77) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_119_3, % 170.34/26.18 | | | | | | | all_123_3) = v0 & apply(all_32_8, all_119_3, % 170.34/26.18 | | | | | | | all_121_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.18 | | | | | | | % 170.34/26.18 | | | | | | | DELTA: instantiating (77) with fresh symbols all_517_0, all_517_1 % 170.34/26.18 | | | | | | | gives: % 170.34/26.18 | | | | | | | (78) apply(all_32_8, all_119_3, all_123_3) = all_517_1 & % 170.34/26.18 | | | | | | | apply(all_32_8, all_119_3, all_121_3) = all_517_0 & ( ~ % 170.34/26.18 | | | | | | | (all_517_0 = 0) | ~ (all_517_1 = 0)) % 170.34/26.18 | | | | | | | % 170.34/26.18 | | | | | | | ALPHA: (78) implies: % 170.34/26.18 | | | | | | | (79) apply(all_32_8, all_119_3, all_121_3) = all_517_0 % 170.34/26.18 | | | | | | | % 170.34/26.18 | | | | | | | REDUCE: (18), (19), (79) imply: % 170.34/26.18 | | | | | | | (80) apply(all_32_8, all_41_0, all_41_2) = all_517_0 % 170.34/26.18 | | | | | | | % 170.34/26.18 | | | | | | | BETA: splitting (10) gives: % 170.34/26.18 | | | | | | | % 170.34/26.18 | | | | | | | Case 1: % 170.34/26.18 | | | | | | | | % 170.34/26.18 | | | | | | | | (81) all_123_3 = all_121_3 % 170.34/26.18 | | | | | | | | % 170.34/26.18 | | | | | | | | COMBINE_EQS: (27), (81) imply: % 170.34/26.18 | | | | | | | | (82) all_121_3 = all_51_0 % 170.34/26.18 | | | | | | | | % 170.34/26.18 | | | | | | | | COMBINE_EQS: (18), (82) imply: % 170.34/26.18 | | | | | | | | (83) all_51_0 = all_41_2 % 170.34/26.18 | | | | | | | | % 170.34/26.18 | | | | | | | | SIMP: (83) implies: % 170.34/26.18 | | | | | | | | (84) all_51_0 = all_41_2 % 170.34/26.18 | | | | | | | | % 170.34/26.18 | | | | | | | | REDUCE: (26), (84) imply: % 170.34/26.18 | | | | | | | | (85) $false % 170.34/26.18 | | | | | | | | % 170.34/26.18 | | | | | | | | CLOSE: (85) is inconsistent. % 170.34/26.18 | | | | | | | | % 170.34/26.18 | | | | | | | Case 2: % 170.34/26.18 | | | | | | | | % 170.34/26.18 | | | | | | | | (86) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.18 | | | | | | | | all_117_0, all_123_3) = v0 & apply(all_32_8, % 170.34/26.18 | | | | | | | | all_117_0, all_121_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = % 170.34/26.18 | | | | | | | | 0))) % 170.34/26.18 | | | | | | | | % 170.34/26.18 | | | | | | | | DELTA: instantiating (86) with fresh symbols all_523_0, % 170.34/26.18 | | | | | | | | all_523_1 gives: % 170.34/26.18 | | | | | | | | (87) apply(all_32_8, all_117_0, all_123_3) = all_523_1 & % 170.34/26.18 | | | | | | | | apply(all_32_8, all_117_0, all_121_3) = all_523_0 & ( ~ % 170.34/26.18 | | | | | | | | (all_523_0 = 0) | ~ (all_523_1 = 0)) % 170.34/26.18 | | | | | | | | % 170.34/26.18 | | | | | | | | ALPHA: (87) implies: % 170.34/26.18 | | | | | | | | (88) apply(all_32_8, all_117_0, all_121_3) = all_523_0 % 170.34/26.18 | | | | | | | | % 170.34/26.18 | | | | | | | | REDUCE: (7), (18), (88) imply: % 170.34/26.18 | | | | | | | | (89) apply(all_32_8, all_41_0, all_41_2) = all_523_0 % 170.34/26.18 | | | | | | | | % 170.34/26.18 | | | | | | | | BETA: splitting (11) gives: % 170.34/26.18 | | | | | | | | % 170.34/26.18 | | | | | | | | Case 1: % 170.34/26.18 | | | | | | | | | % 170.34/26.18 | | | | | | | | | (90) all_123_3 = all_121_3 % 170.34/26.18 | | | | | | | | | % 170.34/26.18 | | | | | | | | | COMBINE_EQS: (27), (90) imply: % 170.34/26.18 | | | | | | | | | (91) all_121_3 = all_51_0 % 170.34/26.18 | | | | | | | | | % 170.34/26.18 | | | | | | | | | COMBINE_EQS: (18), (91) imply: % 170.34/26.18 | | | | | | | | | (92) all_51_0 = all_41_2 % 170.34/26.18 | | | | | | | | | % 170.34/26.18 | | | | | | | | | SIMP: (92) implies: % 170.34/26.18 | | | | | | | | | (93) all_51_0 = all_41_2 % 170.34/26.18 | | | | | | | | | % 170.34/26.18 | | | | | | | | | REDUCE: (26), (93) imply: % 170.34/26.18 | | | | | | | | | (94) $false % 170.34/26.18 | | | | | | | | | % 170.34/26.18 | | | | | | | | | CLOSE: (94) is inconsistent. % 170.34/26.18 | | | | | | | | | % 170.34/26.18 | | | | | | | | Case 2: % 170.34/26.18 | | | | | | | | | % 170.34/26.18 | | | | | | | | | (95) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.18 | | | | | | | | | all_119_3, all_123_3) = v1 & apply(all_32_8, % 170.34/26.18 | | | | | | | | | all_119_3, all_121_3) = v0 & ( ~ (v1 = 0) | ~ (v0 % 170.34/26.18 | | | | | | | | | = 0))) % 170.34/26.18 | | | | | | | | | % 170.34/26.18 | | | | | | | | | DELTA: instantiating (95) with fresh symbols all_529_0, % 170.34/26.18 | | | | | | | | | all_529_1 gives: % 170.34/26.19 | | | | | | | | | (96) apply(all_32_8, all_119_3, all_123_3) = all_529_0 & % 170.34/26.19 | | | | | | | | | apply(all_32_8, all_119_3, all_121_3) = all_529_1 & ( % 170.34/26.19 | | | | | | | | | ~ (all_529_0 = 0) | ~ (all_529_1 = 0)) % 170.34/26.19 | | | | | | | | | % 170.34/26.19 | | | | | | | | | ALPHA: (96) implies: % 170.34/26.19 | | | | | | | | | (97) apply(all_32_8, all_119_3, all_121_3) = all_529_1 % 170.34/26.19 | | | | | | | | | % 170.34/26.19 | | | | | | | | | REDUCE: (18), (19), (97) imply: % 170.34/26.19 | | | | | | | | | (98) apply(all_32_8, all_41_0, all_41_2) = all_529_1 % 170.34/26.19 | | | | | | | | | % 170.34/26.19 | | | | | | | | | BETA: splitting (5) gives: % 170.34/26.19 | | | | | | | | | % 170.34/26.19 | | | | | | | | | Case 1: % 170.34/26.19 | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | (99) all_123_3 = all_121_3 % 170.34/26.19 | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | COMBINE_EQS: (27), (99) imply: % 170.34/26.19 | | | | | | | | | | (100) all_121_3 = all_51_0 % 170.34/26.19 | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | COMBINE_EQS: (18), (100) imply: % 170.34/26.19 | | | | | | | | | | (101) all_51_0 = all_41_2 % 170.34/26.19 | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | SIMP: (101) implies: % 170.34/26.19 | | | | | | | | | | (102) all_51_0 = all_41_2 % 170.34/26.19 | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | REDUCE: (26), (102) imply: % 170.34/26.19 | | | | | | | | | | (103) $false % 170.34/26.19 | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | CLOSE: (103) is inconsistent. % 170.34/26.19 | | | | | | | | | | % 170.34/26.19 | | | | | | | | | Case 2: % 170.34/26.19 | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | (104) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.19 | | | | | | | | | | all_41_0, all_123_3) = v0 & apply(all_32_8, % 170.34/26.19 | | | | | | | | | | all_41_0, all_121_3) = v1 & ( ~ (v1 = 0) | ~ % 170.34/26.19 | | | | | | | | | | (v0 = 0))) % 170.34/26.19 | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | DELTA: instantiating (104) with fresh symbols all_535_0, % 170.34/26.19 | | | | | | | | | | all_535_1 gives: % 170.34/26.19 | | | | | | | | | | (105) apply(all_32_8, all_41_0, all_123_3) = all_535_1 & % 170.34/26.19 | | | | | | | | | | apply(all_32_8, all_41_0, all_121_3) = all_535_0 & % 170.34/26.19 | | | | | | | | | | ( ~ (all_535_0 = 0) | ~ (all_535_1 = 0)) % 170.34/26.19 | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | ALPHA: (105) implies: % 170.34/26.19 | | | | | | | | | | (106) apply(all_32_8, all_41_0, all_121_3) = all_535_0 % 170.34/26.19 | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | REDUCE: (18), (106) imply: % 170.34/26.19 | | | | | | | | | | (107) apply(all_32_8, all_41_0, all_41_2) = all_535_0 % 170.34/26.19 | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | BETA: splitting (13) gives: % 170.34/26.19 | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | Case 1: % 170.34/26.19 | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | (108) all_51_0 = all_49_0 % 170.34/26.19 | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | COMBINE_EQS: (21), (108) imply: % 170.34/26.19 | | | | | | | | | | | (109) all_51_0 = all_41_2 % 170.34/26.19 | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | REDUCE: (26), (109) imply: % 170.34/26.19 | | | | | | | | | | | (110) $false % 170.34/26.19 | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | CLOSE: (110) is inconsistent. % 170.34/26.19 | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | Case 2: % 170.34/26.19 | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | (111) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.19 | | | | | | | | | | | all_55_0, all_51_0) = v1 & apply(all_32_8, % 170.34/26.19 | | | | | | | | | | | all_55_0, all_49_0) = v0 & ( ~ (v1 = 0) | ~ % 170.34/26.19 | | | | | | | | | | | (v0 = 0))) % 170.34/26.19 | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | DELTA: instantiating (111) with fresh symbols all_541_0, % 170.34/26.19 | | | | | | | | | | | all_541_1 gives: % 170.34/26.19 | | | | | | | | | | | (112) apply(all_32_8, all_55_0, all_51_0) = all_541_0 & % 170.34/26.19 | | | | | | | | | | | apply(all_32_8, all_55_0, all_49_0) = all_541_1 & % 170.34/26.19 | | | | | | | | | | | ( ~ (all_541_0 = 0) | ~ (all_541_1 = 0)) % 170.34/26.19 | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | ALPHA: (112) implies: % 170.34/26.19 | | | | | | | | | | | (113) apply(all_32_8, all_55_0, all_49_0) = all_541_1 % 170.34/26.19 | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | REDUCE: (20), (21), (113) imply: % 170.34/26.19 | | | | | | | | | | | (114) apply(all_32_8, all_41_0, all_41_2) = all_541_1 % 170.34/26.19 | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | BETA: splitting (15) gives: % 170.34/26.19 | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | Case 1: % 170.34/26.19 | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | (115) all_51_0 = all_41_2 % 170.34/26.19 | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | REDUCE: (26), (115) imply: % 170.34/26.19 | | | | | | | | | | | | (116) $false % 170.34/26.19 | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | CLOSE: (116) is inconsistent. % 170.34/26.19 | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | Case 2: % 170.34/26.19 | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | (117) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.19 | | | | | | | | | | | | all_55_0, all_51_0) = v1 & apply(all_32_8, % 170.34/26.19 | | | | | | | | | | | | all_55_0, all_41_2) = v0 & ( ~ (v1 = 0) | ~ % 170.34/26.19 | | | | | | | | | | | | (v0 = 0))) % 170.34/26.19 | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | DELTA: instantiating (117) with fresh symbols all_547_0, % 170.34/26.19 | | | | | | | | | | | | all_547_1 gives: % 170.34/26.19 | | | | | | | | | | | | (118) apply(all_32_8, all_55_0, all_51_0) = all_547_0 & % 170.34/26.19 | | | | | | | | | | | | apply(all_32_8, all_55_0, all_41_2) = all_547_1 & % 170.34/26.19 | | | | | | | | | | | | ( ~ (all_547_0 = 0) | ~ (all_547_1 = 0)) % 170.34/26.19 | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | ALPHA: (118) implies: % 170.34/26.19 | | | | | | | | | | | | (119) apply(all_32_8, all_55_0, all_41_2) = all_547_1 % 170.34/26.19 | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | REDUCE: (20), (119) imply: % 170.34/26.19 | | | | | | | | | | | | (120) apply(all_32_8, all_41_0, all_41_2) = all_547_1 % 170.34/26.19 | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | BETA: splitting (6) gives: % 170.34/26.19 | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | Case 1: % 170.34/26.19 | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | (121) all_51_0 = all_41_2 % 170.34/26.19 | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | REDUCE: (26), (121) imply: % 170.34/26.19 | | | | | | | | | | | | | (122) $false % 170.34/26.19 | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | CLOSE: (122) is inconsistent. % 170.34/26.19 | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | Case 2: % 170.34/26.19 | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | (123) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.19 | | | | | | | | | | | | | all_55_0, all_51_0) = v0 & apply(all_32_8, % 170.34/26.19 | | | | | | | | | | | | | all_55_0, all_41_2) = v1 & ( ~ (v1 = 0) | ~ % 170.34/26.19 | | | | | | | | | | | | | (v0 = 0))) % 170.34/26.19 | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | DELTA: instantiating (123) with fresh symbols all_553_0, % 170.34/26.19 | | | | | | | | | | | | | all_553_1 gives: % 170.34/26.19 | | | | | | | | | | | | | (124) apply(all_32_8, all_55_0, all_51_0) = all_553_1 & % 170.34/26.19 | | | | | | | | | | | | | apply(all_32_8, all_55_0, all_41_2) = all_553_0 & % 170.34/26.19 | | | | | | | | | | | | | ( ~ (all_553_0 = 0) | ~ (all_553_1 = 0)) % 170.34/26.19 | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | ALPHA: (124) implies: % 170.34/26.19 | | | | | | | | | | | | | (125) apply(all_32_8, all_55_0, all_41_2) = all_553_0 % 170.34/26.19 | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | REDUCE: (20), (125) imply: % 170.34/26.19 | | | | | | | | | | | | | (126) apply(all_32_8, all_41_0, all_41_2) = all_553_0 % 170.34/26.19 | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | BETA: splitting (23) gives: % 170.34/26.19 | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | Case 1: % 170.34/26.19 | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | (127) all_51_0 = all_49_0 % 170.34/26.19 | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | COMBINE_EQS: (21), (127) imply: % 170.34/26.19 | | | | | | | | | | | | | | (128) all_51_0 = all_41_2 % 170.34/26.19 | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | REDUCE: (26), (128) imply: % 170.34/26.19 | | | | | | | | | | | | | | (129) $false % 170.34/26.19 | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | CLOSE: (129) is inconsistent. % 170.34/26.19 | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | Case 2: % 170.34/26.19 | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | (130) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 170.34/26.19 | | | | | | | | | | | | | | (apply(all_32_8, all_41_0, all_49_0) = v2 & % 170.34/26.19 | | | | | | | | | | | | | | member(all_51_0, all_32_4) = v1 & % 170.34/26.19 | | | | | | | | | | | | | | member(all_41_0, all_32_5) = v0 & ( ~ (v2 = 0) | % 170.34/26.19 | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 170.34/26.19 | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | DELTA: instantiating (130) with fresh symbols all_559_0, % 170.34/26.19 | | | | | | | | | | | | | | all_559_1, all_559_2 gives: % 170.34/26.19 | | | | | | | | | | | | | | (131) apply(all_32_8, all_41_0, all_49_0) = all_559_0 & % 170.34/26.19 | | | | | | | | | | | | | | member(all_51_0, all_32_4) = all_559_1 & % 170.34/26.19 | | | | | | | | | | | | | | member(all_41_0, all_32_5) = all_559_2 & ( ~ % 170.34/26.19 | | | | | | | | | | | | | | (all_559_0 = 0) | ~ (all_559_1 = 0) | ~ % 170.34/26.19 | | | | | | | | | | | | | | (all_559_2 = 0)) % 170.34/26.19 | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | ALPHA: (131) implies: % 170.34/26.19 | | | | | | | | | | | | | | (132) member(all_41_0, all_32_5) = all_559_2 % 170.34/26.19 | | | | | | | | | | | | | | (133) member(all_51_0, all_32_4) = all_559_1 % 170.34/26.19 | | | | | | | | | | | | | | (134) apply(all_32_8, all_41_0, all_49_0) = all_559_0 % 170.34/26.19 | | | | | | | | | | | | | | (135) ~ (all_559_0 = 0) | ~ (all_559_1 = 0) | ~ % 170.34/26.19 | | | | | | | | | | | | | | (all_559_2 = 0) % 170.34/26.19 | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | REDUCE: (21), (134) imply: % 170.34/26.19 | | | | | | | | | | | | | | (136) apply(all_32_8, all_41_0, all_41_2) = all_559_0 % 170.34/26.19 | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | BETA: splitting (28) gives: % 170.34/26.19 | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | Case 1: % 170.34/26.19 | | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | | (137) all_51_0 = all_41_2 % 170.34/26.19 | | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | | REDUCE: (26), (137) imply: % 170.34/26.19 | | | | | | | | | | | | | | | (138) $false % 170.34/26.19 | | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | | CLOSE: (138) is inconsistent. % 170.34/26.19 | | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | Case 2: % 170.34/26.19 | | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | | (139) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.34/26.19 | | | | | | | | | | | | | | | all_41_0, all_51_0) = v1 & apply(all_32_8, % 170.34/26.19 | | | | | | | | | | | | | | | all_41_0, all_41_2) = v0 & ( ~ (v1 = 0) | ~ % 170.34/26.19 | | | | | | | | | | | | | | | (v0 = 0))) % 170.34/26.19 | | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | | DELTA: instantiating (139) with fresh symbols all_583_0, % 170.34/26.19 | | | | | | | | | | | | | | | all_583_1 gives: % 170.34/26.19 | | | | | | | | | | | | | | | (140) apply(all_32_8, all_41_0, all_51_0) = all_583_0 & % 170.34/26.19 | | | | | | | | | | | | | | | apply(all_32_8, all_41_0, all_41_2) = all_583_1 & % 170.34/26.19 | | | | | | | | | | | | | | | ( ~ (all_583_0 = 0) | ~ (all_583_1 = 0)) % 170.34/26.19 | | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | | ALPHA: (140) implies: % 170.34/26.19 | | | | | | | | | | | | | | | (141) apply(all_32_8, all_41_0, all_41_2) = all_583_1 % 170.34/26.19 | | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | | BETA: splitting (29) gives: % 170.34/26.19 | | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | | Case 1: % 170.34/26.19 | | | | | | | | | | | | | | | | % 170.34/26.19 | | | | | | | | | | | | | | | | (142) all_51_0 = all_41_2 % 170.34/26.19 | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | REDUCE: (26), (142) imply: % 170.56/26.19 | | | | | | | | | | | | | | | | (143) $false % 170.56/26.19 | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | CLOSE: (143) is inconsistent. % 170.56/26.19 | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | Case 2: % 170.56/26.19 | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | (144) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 170.56/26.19 | | | | | | | | | | | | | | | | (apply(all_32_8, all_41_0, all_41_2) = v2 & % 170.56/26.19 | | | | | | | | | | | | | | | | member(all_51_0, all_32_4) = v1 & % 170.56/26.19 | | | | | | | | | | | | | | | | member(all_41_0, all_32_5) = v0 & ( ~ (v2 = 0) | % 170.56/26.19 | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 170.56/26.19 | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | DELTA: instantiating (144) with fresh symbols all_589_0, % 170.56/26.19 | | | | | | | | | | | | | | | | all_589_1, all_589_2 gives: % 170.56/26.19 | | | | | | | | | | | | | | | | (145) apply(all_32_8, all_41_0, all_41_2) = all_589_0 & % 170.56/26.19 | | | | | | | | | | | | | | | | member(all_51_0, all_32_4) = all_589_1 & % 170.56/26.19 | | | | | | | | | | | | | | | | member(all_41_0, all_32_5) = all_589_2 & ( ~ % 170.56/26.19 | | | | | | | | | | | | | | | | (all_589_0 = 0) | ~ (all_589_1 = 0) | ~ % 170.56/26.19 | | | | | | | | | | | | | | | | (all_589_2 = 0)) % 170.56/26.19 | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | ALPHA: (145) implies: % 170.56/26.19 | | | | | | | | | | | | | | | | (146) member(all_41_0, all_32_5) = all_589_2 % 170.56/26.19 | | | | | | | | | | | | | | | | (147) member(all_51_0, all_32_4) = all_589_1 % 170.56/26.19 | | | | | | | | | | | | | | | | (148) apply(all_32_8, all_41_0, all_41_2) = all_589_0 % 170.56/26.19 | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | BETA: splitting (2) gives: % 170.56/26.19 | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | Case 1: % 170.56/26.19 | | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | | (149) all_51_0 = all_49_0 % 170.56/26.19 | | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (149) imply: % 170.56/26.19 | | | | | | | | | | | | | | | | | (150) all_51_0 = all_41_2 % 170.56/26.19 | | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | | REDUCE: (26), (150) imply: % 170.56/26.19 | | | | | | | | | | | | | | | | | (151) $false % 170.56/26.19 | | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | | CLOSE: (151) is inconsistent. % 170.56/26.19 | | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | Case 2: % 170.56/26.19 | | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | | (152) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 170.56/26.19 | | | | | | | | | | | | | | | | | all_55_0, all_51_0) = v0 & apply(all_32_8, % 170.56/26.19 | | | | | | | | | | | | | | | | | all_55_0, all_49_0) = v1 & ( ~ (v1 = 0) | ~ % 170.56/26.19 | | | | | | | | | | | | | | | | | (v0 = 0))) % 170.56/26.19 | | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | | DELTA: instantiating (152) with fresh symbols all_607_0, % 170.56/26.19 | | | | | | | | | | | | | | | | | all_607_1 gives: % 170.56/26.19 | | | | | | | | | | | | | | | | | (153) apply(all_32_8, all_55_0, all_51_0) = all_607_1 & % 170.56/26.19 | | | | | | | | | | | | | | | | | apply(all_32_8, all_55_0, all_49_0) = all_607_0 & % 170.56/26.19 | | | | | | | | | | | | | | | | | ( ~ (all_607_0 = 0) | ~ (all_607_1 = 0)) % 170.56/26.19 | | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | | ALPHA: (153) implies: % 170.56/26.19 | | | | | | | | | | | | | | | | | (154) apply(all_32_8, all_55_0, all_49_0) = all_607_0 % 170.56/26.19 | | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | | REDUCE: (20), (21), (154) imply: % 170.56/26.19 | | | | | | | | | | | | | | | | | (155) apply(all_32_8, all_41_0, all_41_2) = all_607_0 % 170.56/26.19 | | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_457_2, all_32_5, % 170.56/26.19 | | | | | | | | | | | | | | | | | all_41_0, simplifying with (14), (46) gives: % 170.56/26.19 | | | | | | | | | | | | | | | | | (156) all_457_2 = 0 % 170.56/26.19 | | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_457_2, all_559_2, % 170.56/26.19 | | | | | | | | | | | | | | | | | all_32_5, all_41_0, simplifying with (46), (132) % 170.56/26.19 | | | | | | | | | | | | | | | | | gives: % 170.56/26.19 | | | | | | | | | | | | | | | | | (157) all_559_2 = all_457_2 % 170.56/26.19 | | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_559_2, all_589_2, % 170.56/26.19 | | | | | | | | | | | | | | | | | all_32_5, all_41_0, simplifying with (132), (146) % 170.56/26.19 | | | | | | | | | | | | | | | | | gives: % 170.56/26.19 | | | | | | | | | | | | | | | | | (158) all_589_2 = all_559_2 % 170.56/26.19 | | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_441_2, all_589_2, % 170.56/26.19 | | | | | | | | | | | | | | | | | all_32_5, all_41_0, simplifying with (37), (146) % 170.56/26.19 | | | | | | | | | | | | | | | | | gives: % 170.56/26.19 | | | | | | | | | | | | | | | | | (159) all_589_2 = all_441_2 % 170.56/26.19 | | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_589_1, all_32_4, % 170.56/26.19 | | | | | | | | | | | | | | | | | all_51_0, simplifying with (16), (147) gives: % 170.56/26.19 | | | | | | | | | | | | | | | | | (160) all_589_1 = 0 % 170.56/26.19 | | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_559_1, all_589_1, % 170.56/26.19 | | | | | | | | | | | | | | | | | all_32_4, all_51_0, simplifying with (133), (147) % 170.56/26.19 | | | | | | | | | | | | | | | | | gives: % 170.56/26.19 | | | | | | | | | | | | | | | | | (161) all_589_1 = all_559_1 % 170.56/26.19 | | | | | | | | | | | | | | | | | % 170.56/26.19 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_523_0, all_535_0, % 170.56/26.19 | | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 170.56/26.19 | | | | | | | | | | | | | | | | | (89), (107) gives: % 170.56/26.20 | | | | | | | | | | | | | | | | | (162) all_535_0 = all_523_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_547_1, all_553_0, % 170.56/26.20 | | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 170.56/26.20 | | | | | | | | | | | | | | | | | (120), (126) gives: % 170.56/26.20 | | | | | | | | | | | | | | | | | (163) all_553_0 = all_547_1 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_535_0, all_553_0, % 170.56/26.20 | | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 170.56/26.20 | | | | | | | | | | | | | | | | | (107), (126) gives: % 170.56/26.20 | | | | | | | | | | | | | | | | | (164) all_553_0 = all_535_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with 0, all_553_0, all_41_2, % 170.56/26.20 | | | | | | | | | | | | | | | | | all_41_0, all_32_8, simplifying with (8), (126) % 170.56/26.20 | | | | | | | | | | | | | | | | | gives: % 170.56/26.20 | | | | | | | | | | | | | | | | | (165) all_553_0 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_541_1, all_583_1, % 170.56/26.20 | | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 170.56/26.20 | | | | | | | | | | | | | | | | | (114), (141) gives: % 170.56/26.20 | | | | | | | | | | | | | | | | | (166) all_583_1 = all_541_1 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_529_1, all_583_1, % 170.56/26.20 | | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 170.56/26.20 | | | | | | | | | | | | | | | | | (98), (141) gives: % 170.56/26.20 | | | | | | | | | | | | | | | | | (167) all_583_1 = all_529_1 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_523_0, all_583_1, % 170.56/26.20 | | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 170.56/26.20 | | | | | | | | | | | | | | | | | (89), (141) gives: % 170.56/26.20 | | | | | | | | | | | | | | | | | (168) all_583_1 = all_523_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_517_0, all_583_1, % 170.56/26.20 | | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 170.56/26.20 | | | | | | | | | | | | | | | | | (80), (141) gives: % 170.56/26.20 | | | | | | | | | | | | | | | | | (169) all_583_1 = all_517_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_511_1, all_583_1, % 170.56/26.20 | | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 170.56/26.20 | | | | | | | | | | | | | | | | | (71), (141) gives: % 170.56/26.20 | | | | | | | | | | | | | | | | | (170) all_583_1 = all_511_1 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_511_1, all_589_0, % 170.56/26.20 | | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 170.56/26.20 | | | | | | | | | | | | | | | | | (71), (148) gives: % 170.56/26.20 | | | | | | | | | | | | | | | | | (171) all_589_0 = all_511_1 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_505_0, all_589_0, % 170.56/26.20 | | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 170.56/26.20 | | | | | | | | | | | | | | | | | (64), (148) gives: % 170.56/26.20 | | | | | | | | | | | | | | | | | (172) all_589_0 = all_505_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_589_0, all_607_0, % 170.56/26.20 | | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 170.56/26.20 | | | | | | | | | | | | | | | | | (148), (155) gives: % 170.56/26.20 | | | | | | | | | | | | | | | | | (173) all_607_0 = all_589_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_559_0, all_607_0, % 170.56/26.20 | | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 170.56/26.20 | | | | | | | | | | | | | | | | | (136), (155) gives: % 170.56/26.20 | | | | | | | | | | | | | | | | | (174) all_607_0 = all_559_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_481_1, all_607_0, % 170.56/26.20 | | | | | | | | | | | | | | | | | all_41_2, all_41_0, all_32_8, simplifying with % 170.56/26.20 | | | | | | | | | | | | | | | | | (56), (155) gives: % 170.56/26.20 | | | | | | | | | | | | | | | | | (175) all_607_0 = all_481_1 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (173), (174) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (176) all_589_0 = all_559_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | SIMP: (176) implies: % 170.56/26.20 | | | | | | | | | | | | | | | | | (177) all_589_0 = all_559_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (175) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (178) all_559_0 = all_481_1 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (177) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (179) all_559_0 = all_505_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | SIMP: (179) implies: % 170.56/26.20 | | | | | | | | | | | | | | | | | (180) all_559_0 = all_505_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (171), (172) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (181) all_511_1 = all_505_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | SIMP: (181) implies: % 170.56/26.20 | | | | | | | | | | | | | | | | | (182) all_511_1 = all_505_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (161) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (183) all_559_1 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (158), (159) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (184) all_559_2 = all_441_2 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | SIMP: (184) implies: % 170.56/26.20 | | | | | | | | | | | | | | | | | (185) all_559_2 = all_441_2 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (167) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (186) all_541_1 = all_529_1 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (169) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (187) all_541_1 = all_517_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (170) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (188) all_541_1 = all_511_1 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (168) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (189) all_541_1 = all_523_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (178), (180) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (190) all_505_0 = all_481_1 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | SIMP: (190) implies: % 170.56/26.20 | | | | | | | | | | | | | | | | | (191) all_505_0 = all_481_1 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (185) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (192) all_457_2 = all_441_2 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | SIMP: (192) implies: % 170.56/26.20 | | | | | | | | | | | | | | | | | (193) all_457_2 = all_441_2 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (163), (165) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (194) all_547_1 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (163), (164) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (195) all_547_1 = all_535_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (194), (195) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (196) all_535_0 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | SIMP: (196) implies: % 170.56/26.20 | | | | | | | | | | | | | | | | | (197) all_535_0 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (186), (189) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (198) all_529_1 = all_523_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (186), (188) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (199) all_529_1 = all_511_1 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (186), (187) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (200) all_529_1 = all_517_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (162), (197) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (201) all_523_0 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | SIMP: (201) implies: % 170.56/26.20 | | | | | | | | | | | | | | | | | (202) all_523_0 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (198), (200) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (203) all_523_0 = all_517_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | SIMP: (203) implies: % 170.56/26.20 | | | | | | | | | | | | | | | | | (204) all_523_0 = all_517_0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (199), (200) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (205) all_517_0 = all_511_1 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (204) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (206) all_517_0 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | SIMP: (206) implies: % 170.56/26.20 | | | | | | | | | | | | | | | | | (207) all_517_0 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (207) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (208) all_511_1 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | SIMP: (208) implies: % 170.56/26.20 | | | | | | | | | | | | | | | | | (209) all_511_1 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (209) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (210) all_505_0 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | SIMP: (210) implies: % 170.56/26.20 | | | | | | | | | | | | | | | | | (211) all_505_0 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (191), (211) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (212) all_481_1 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | SIMP: (212) implies: % 170.56/26.20 | | | | | | | | | | | | | | | | | (213) all_481_1 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (156), (193) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (214) all_441_2 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (185), (214) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (215) all_559_2 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (178), (213) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | (216) all_559_0 = 0 % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | BETA: splitting (135) gives: % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | Case 1: % 170.56/26.20 | | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | | (217) ~ (all_559_0 = 0) % 170.56/26.20 | | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | | REDUCE: (216), (217) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | | (218) $false % 170.56/26.20 | | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | | CLOSE: (218) is inconsistent. % 170.56/26.20 | | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | Case 2: % 170.56/26.20 | | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | | (219) ~ (all_559_1 = 0) | ~ (all_559_2 = 0) % 170.56/26.20 | | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 170.56/26.20 | | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | | Case 1: % 170.56/26.20 | | | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | | | (220) ~ (all_559_1 = 0) % 170.56/26.20 | | | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | | | REDUCE: (183), (220) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | | | (221) $false % 170.56/26.20 | | | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | | | CLOSE: (221) is inconsistent. % 170.56/26.20 | | | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | | Case 2: % 170.56/26.20 | | | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | | | (222) ~ (all_559_2 = 0) % 170.56/26.20 | | | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | | | REDUCE: (215), (222) imply: % 170.56/26.20 | | | | | | | | | | | | | | | | | | | (223) $false % 170.56/26.20 | | | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | | | CLOSE: (223) is inconsistent. % 170.56/26.20 | | | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | | End of split % 170.56/26.20 | | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | | End of split % 170.56/26.20 | | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | | End of split % 170.56/26.20 | | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | | End of split % 170.56/26.20 | | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | | End of split % 170.56/26.20 | | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | | End of split % 170.56/26.20 | | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | | End of split % 170.56/26.20 | | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | | End of split % 170.56/26.20 | | | | | | | | | | | % 170.56/26.20 | | | | | | | | | | End of split % 170.56/26.20 | | | | | | | | | | % 170.56/26.20 | | | | | | | | | End of split % 170.56/26.20 | | | | | | | | | % 170.56/26.20 | | | | | | | | End of split % 170.56/26.20 | | | | | | | | % 170.56/26.20 | | | | | | | End of split % 170.56/26.20 | | | | | | | % 170.56/26.20 | | | | | | End of split % 170.56/26.20 | | | | | | % 170.56/26.20 | | | | | End of split % 170.56/26.20 | | | | | % 170.56/26.20 | | | | End of split % 170.56/26.20 | | | | % 170.56/26.20 | | | End of split % 170.56/26.20 | | | % 170.56/26.20 | | End of split % 170.56/26.20 | | % 170.56/26.20 | End of split % 170.56/26.20 | % 170.56/26.20 End of proof % 170.56/26.20 % SZS output end Proof for theBenchmark % 170.56/26.20 % 170.56/26.20 25638ms %------------------------------------------------------------------------------