%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET723+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 : n016.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 15:26:09 EDT 2023 % Result : Theorem 30.33s 4.92s % Output : Proof 31.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET723+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n016.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Aug 26 14:10:42 EDT 2023 % 0.12/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.08/1.29 Prover 1: Preprocessing ... % 4.08/1.29 Prover 4: Preprocessing ... % 4.08/1.33 Prover 2: Preprocessing ... % 4.08/1.33 Prover 6: Preprocessing ... % 4.08/1.33 Prover 0: Preprocessing ... % 4.08/1.33 Prover 5: Preprocessing ... % 4.08/1.33 Prover 3: Preprocessing ... % 8.81/2.16 Prover 5: Proving ... % 9.95/2.17 Prover 2: Proving ... % 10.89/2.26 Prover 6: Proving ... % 11.53/2.33 Prover 3: Constructing countermodel ... % 11.53/2.33 Prover 1: Constructing countermodel ... % 13.74/2.62 Prover 3: gave up % 13.74/2.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.25/2.73 Prover 7: Preprocessing ... % 14.25/2.74 Prover 0: Proving ... % 14.25/2.75 Prover 1: gave up % 14.25/2.75 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.80/2.83 Prover 8: Preprocessing ... % 14.80/2.87 Prover 4: Constructing countermodel ... % 14.80/2.89 Prover 7: Warning: ignoring some quantifiers % 14.80/2.94 Prover 7: Constructing countermodel ... % 16.62/3.08 Prover 8: Warning: ignoring some quantifiers % 17.33/3.13 Prover 8: Constructing countermodel ... % 18.81/3.36 Prover 8: gave up % 18.81/3.36 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 18.81/3.40 Prover 9: Preprocessing ... % 23.62/3.99 Prover 9: Constructing countermodel ... % 30.33/4.91 Prover 4: Found proof (size 1342) % 30.33/4.91 Prover 4: proved (4273ms) % 30.33/4.91 Prover 9: stopped % 30.33/4.91 Prover 5: stopped % 30.33/4.91 Prover 6: stopped % 30.33/4.91 Prover 0: stopped % 30.33/4.91 Prover 2: stopped % 30.33/4.92 Prover 7: stopped % 30.33/4.92 % 30.33/4.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 30.33/4.92 % 30.94/4.98 % SZS output start Proof for theBenchmark % 30.94/4.98 Assumptions after simplification: % 30.94/4.98 --------------------------------- % 30.94/4.98 % 30.94/4.98 (compose_function) % 31.15/5.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 31.15/5.02 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 31.15/5.02 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 31.15/5.02 ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | % 31.15/5.02 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] % 31.15/5.02 : ((apply(v0, v9, v6) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 % 31.15/5.02 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = % 31.15/5.02 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 31.15/5.02 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 31.15/5.02 int] : ! [v9: $i] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = % 31.15/5.02 v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) % 31.15/5.02 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 31.15/5.02 $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v11 & % 31.15/5.02 member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4) % 31.15/5.02 = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! % 31.15/5.02 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 31.15/5.02 : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 31.15/5.02 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 31.15/5.02 ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ % 31.15/5.02 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] : % 31.15/5.02 ((apply(v1, v5, v9) = v10 & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~ % 31.15/5.02 (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 % 31.15/5.02 = 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 31.15/5.02 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 31.15/5.02 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | % 31.15/5.02 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 31.15/5.02 $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ? % 31.15/5.02 [v12: int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 & % 31.15/5.02 apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, v3) = 0) % 31.15/5.02 | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 = % 31.15/5.02 0)))))) % 31.15/5.02 % 31.15/5.02 (equal_maps) % 31.15/5.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 31.15/5.02 $i] : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ % 31.15/5.02 (apply(v1, v4, v6) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ $i(v6) | ~ $i(v5) % 31.15/5.02 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : % 31.15/5.02 ? [v8: any] : ? [v9: any] : (member(v6, v3) = v9 & member(v5, v3) = v8 & % 31.15/5.02 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! % 31.15/5.02 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 31.15/5.02 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1, % 31.15/5.02 v4, v6) = 0) | ~ (member(v5, v3) = 0) | ~ $i(v6) | ~ $i(v5) | ~ % 31.15/5.02 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? % 31.15/5.02 [v8: any] : ? [v9: any] : (apply(v0, v4, v5) = v9 & member(v6, v3) = v8 & % 31.15/5.02 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! % 31.15/5.02 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 31.15/5.02 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v0, % 31.15/5.02 v4, v5) = 0) | ~ (member(v6, v3) = 0) | ~ $i(v6) | ~ $i(v5) | ~ % 31.15/5.02 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? % 31.15/5.02 [v8: any] : ? [v9: any] : (apply(v1, v4, v6) = v9 & member(v5, v3) = v8 & % 31.15/5.02 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! % 31.15/5.02 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 31.15/5.02 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ % 31.15/5.02 (member(v6, v3) = 0) | ~ (member(v5, v3) = 0) | ~ (member(v4, v2) = 0) | % 31.15/5.02 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 31.15/5.02 $i(v0) | ? [v7: any] : ? [v8: any] : (apply(v1, v4, v6) = v8 & apply(v0, % 31.15/5.03 v4, v5) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! [v1: $i] % 31.15/5.03 : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (equal_maps(v0, v1, % 31.15/5.03 v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 31.15/5.03 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v6) & apply(v1, v5, v7) = 0 & % 31.15/5.03 apply(v0, v5, v6) = 0 & member(v7, v3) = 0 & member(v6, v3) = 0 & % 31.15/5.03 member(v5, v2) = 0 & $i(v7) & $i(v6) & $i(v5))) % 31.15/5.03 % 31.15/5.03 (injective) % 31.15/5.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 31.15/5.03 $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) % 31.15/5.03 | ~ (apply(v0, v3, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 31.15/5.03 | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 31.15/5.03 (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 = % 31.15/5.03 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 31.15/5.03 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ % 31.15/5.03 (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v3, % 31.15/5.03 v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 31.15/5.03 ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v5) = % 31.15/5.03 v8 & member(v5, v2) = v7 & member(v4, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = % 31.15/5.03 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 31.15/5.03 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = % 31.15/5.03 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v1) = 0) | ~ $i(v5) | ~ % 31.15/5.03 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 31.15/5.03 [v7: any] : ? [v8: any] : (apply(v0, v4, v5) = v8 & member(v5, v2) = v7 & % 31.15/5.03 member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! % 31.15/5.03 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 31.15/5.03 : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ % 31.15/5.03 (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 31.15/5.03 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 31.15/5.03 (apply(v0, v4, v5) = v7 & apply(v0, v3, v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = % 31.15/5.03 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = % 31.15/5.03 0 | ~ (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 31.15/5.03 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0 % 31.15/5.03 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 & % 31.15/5.03 member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4))) % 31.15/5.03 % 31.15/5.03 (maps) % 31.15/5.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 31.15/5.04 $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ % 31.15/5.04 (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 31.15/5.04 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 31.15/5.04 (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = % 31.15/5.04 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 31.15/5.04 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, % 31.15/5.04 v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ~ % 31.15/5.04 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 31.15/5.04 any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5, % 31.15/5.04 v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 31.15/5.04 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 31.15/5.04 [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, % 31.15/5.04 v3, v4) = 0) | ~ (member(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 31.15/5.04 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 31.15/5.04 ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v4, v2) = v7 & member(v3, v1) % 31.15/5.04 = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: % 31.15/5.04 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ % 31.15/5.04 (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) | % 31.15/5.04 ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 31.15/5.04 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & % 31.15/5.04 apply(v0, v3, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! % 31.15/5.04 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) | % 31.15/5.04 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 31.15/5.04 : ? [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int] % 31.15/5.04 : ? [v12: $i] : ? [v13: int] : ($i(v12) & $i(v6) & $i(v5) & $i(v4) & ((v13 % 31.15/5.04 = 0 & member(v12, v1) = 0 & ! [v14: $i] : ( ~ (apply(v0, v12, v14) = % 31.15/5.04 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & member(v14, v2) % 31.15/5.04 = v15)) & ! [v14: $i] : ( ~ (member(v14, v2) = 0) | ~ $i(v14) | % 31.15/5.04 ? [v15: int] : ( ~ (v15 = 0) & apply(v0, v12, v14) = v15))) | (v11 = % 31.15/5.04 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4, % 31.15/5.04 v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, % 31.15/5.04 v2) = 0 & member(v4, v1) = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 31.15/5.04 [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) % 31.15/5.04 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, % 31.15/5.04 v3, v4) = 0 & member(v4, v2) = 0 & $i(v4))) % 31.15/5.04 % 31.15/5.04 (thII14) % 31.15/5.04 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 31.15/5.04 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & % 31.15/5.04 injective(v0, v4, v5) = 0 & equal_maps(v6, v7, v3, v5) = 0 & equal_maps(v1, % 31.15/5.04 v2, v3, v4) = v8 & compose_function(v0, v2, v3, v4, v5) = v7 & % 31.15/5.04 compose_function(v0, v1, v3, v4, v5) = v6 & maps(v2, v3, v4) = 0 & maps(v1, % 31.15/5.04 v3, v4) = 0 & maps(v0, v4, v5) = 0 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 31.15/5.04 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 31.15/5.04 % 31.15/5.04 (function-axioms) % 31.15/5.04 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 31.15/5.04 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 31.15/5.04 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 31.15/5.04 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 31.15/5.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 31.15/5.04 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 31.15/5.04 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 31.15/5.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 31.15/5.04 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 31.15/5.04 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 31.15/5.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 31.15/5.04 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 31.15/5.04 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 31.15/5.04 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 31.15/5.04 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 31.15/5.04 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 31.15/5.04 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 31.15/5.04 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 31.15/5.04 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 31.15/5.04 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 31.15/5.04 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 31.15/5.05 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 31.15/5.05 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 31.15/5.05 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 31.15/5.05 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 31.15/5.05 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 31.15/5.05 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 31.15/5.05 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 31.15/5.05 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 31.15/5.05 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 31.15/5.05 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 31.15/5.05 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 31.15/5.05 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 31.15/5.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 31.15/5.05 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 31.15/5.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 31.15/5.05 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 31.15/5.05 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 31.15/5.05 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 31.15/5.05 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 31.15/5.05 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 31.15/5.05 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 31.15/5.05 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 31.15/5.05 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 31.15/5.05 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 31.15/5.05 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 31.15/5.05 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 31.15/5.05 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 31.15/5.05 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 31.15/5.05 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 31.15/5.05 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 31.15/5.05 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 31.15/5.05 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 31.15/5.05 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 31.15/5.05 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 31.15/5.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 31.15/5.05 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 31.15/5.05 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 31.15/5.05 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 31.40/5.05 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 31.40/5.05 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 31.40/5.05 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 31.40/5.05 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 31.40/5.05 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 31.40/5.05 (power_set(v2) = v0)) % 31.40/5.05 % 31.40/5.05 Further assumptions not needed in the proof: % 31.40/5.05 -------------------------------------------- % 31.40/5.05 compose_predicate, decreasing_function, difference, empty_set, equal_set, % 31.40/5.05 identity, image2, image3, increasing_function, intersection, inverse_function, % 31.40/5.05 inverse_image2, inverse_image3, inverse_predicate, isomorphism, one_to_one, % 31.40/5.05 power_set, product, singleton, subset, sum, surjective, union, unordered_pair % 31.40/5.05 % 31.40/5.05 Those formulas are unsatisfiable: % 31.40/5.05 --------------------------------- % 31.40/5.05 % 31.40/5.05 Begin of proof % 31.40/5.05 | % 31.40/5.05 | ALPHA: (maps) implies: % 31.40/5.05 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, % 31.40/5.05 | v1, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v2) | % 31.40/5.05 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & % 31.40/5.05 | member(v4, v2) = 0 & $i(v4))) % 31.40/5.05 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 31.40/5.05 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) % 31.40/5.05 | = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ~ % 31.40/5.05 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 31.40/5.05 | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & apply(v0, v3, % 31.40/5.05 | v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 31.40/5.05 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 31.40/5.05 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, % 31.40/5.05 | v5) = 0) | ~ (member(v4, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 31.40/5.05 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 31.40/5.05 | any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5, v2) = v7 % 31.40/5.05 | & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 31.40/5.05 | % 31.40/5.05 | ALPHA: (compose_function) implies: % 31.40/5.05 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 31.40/5.05 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : % 31.40/5.05 | (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ % 31.40/5.05 | (apply(v7, v5, v6) = v8) | ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ % 31.40/5.05 | $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 31.40/5.05 | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v10 % 31.40/5.05 | & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0))) | % 31.40/5.05 | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ % 31.40/5.05 | (v10 = 0))))) % 31.40/5.05 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 31.40/5.05 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : % 31.40/5.05 | (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ % 31.40/5.05 | (apply(v7, v5, v6) = v8) | ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | % 31.40/5.05 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 31.40/5.05 | | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v0, v9, v6) = % 31.40/5.05 | v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | % 31.40/5.05 | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ % 31.40/5.05 | (v10 = 0))))) % 31.40/5.06 | % 31.40/5.06 | ALPHA: (equal_maps) implies: % 31.40/5.06 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 31.40/5.06 | (v4 = 0 | ~ (equal_maps(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) % 31.40/5.06 | | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ( % 31.40/5.06 | ~ (v7 = v6) & apply(v1, v5, v7) = 0 & apply(v0, v5, v6) = 0 & % 31.40/5.06 | member(v7, v3) = 0 & member(v6, v3) = 0 & member(v5, v2) = 0 & % 31.40/5.06 | $i(v7) & $i(v6) & $i(v5))) % 31.40/5.06 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 31.40/5.06 | ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = % 31.40/5.06 | 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v3) = 0) | ~ % 31.40/5.06 | (member(v4, v2) = 0) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 31.40/5.06 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : % 31.40/5.06 | (apply(v1, v4, v6) = v8 & apply(v0, v4, v5) = v7 & ( ~ (v8 = 0) | ~ % 31.40/5.06 | (v7 = 0)))) % 31.40/5.06 | % 31.40/5.06 | ALPHA: (injective) implies: % 31.40/5.06 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 31.40/5.06 | ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, % 31.40/5.06 | v2) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ % 31.40/5.06 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 31.40/5.06 | ? [v6: any] : ? [v7: any] : (apply(v0, v4, v5) = v7 & apply(v0, v3, % 31.40/5.06 | v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 31.40/5.06 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 31.40/5.06 | ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, % 31.40/5.06 | v4, v5) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | % 31.40/5.06 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 31.40/5.06 | any] : ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v5, v2) = v7 % 31.40/5.06 | & member(v4, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 31.40/5.06 | % 31.40/5.06 | ALPHA: (function-axioms) implies: % 31.40/5.06 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 31.40/5.06 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, % 31.40/5.06 | v2) = v0)) % 31.40/5.06 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 31.40/5.06 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 31.40/5.06 | ~ (apply(v4, v3, v2) = v0)) % 31.40/5.06 | % 31.40/5.06 | DELTA: instantiating (thII14) with fresh symbols all_32_0, all_32_1, all_32_2, % 31.40/5.06 | all_32_3, all_32_4, all_32_5, all_32_6, all_32_7, all_32_8 gives: % 31.40/5.06 | (12) ~ (all_32_0 = 0) & injective(all_32_8, all_32_4, all_32_3) = 0 & % 31.40/5.06 | equal_maps(all_32_2, all_32_1, all_32_5, all_32_3) = 0 & % 31.40/5.06 | equal_maps(all_32_7, all_32_6, all_32_5, all_32_4) = all_32_0 & % 31.40/5.06 | compose_function(all_32_8, all_32_6, all_32_5, all_32_4, all_32_3) = % 31.40/5.06 | all_32_1 & compose_function(all_32_8, all_32_7, all_32_5, all_32_4, % 31.40/5.06 | all_32_3) = all_32_2 & maps(all_32_6, all_32_5, all_32_4) = 0 & % 31.40/5.06 | maps(all_32_7, all_32_5, all_32_4) = 0 & maps(all_32_8, all_32_4, % 31.40/5.06 | all_32_3) = 0 & $i(all_32_1) & $i(all_32_2) & $i(all_32_3) & % 31.40/5.06 | $i(all_32_4) & $i(all_32_5) & $i(all_32_6) & $i(all_32_7) & % 31.40/5.06 | $i(all_32_8) % 31.40/5.06 | % 31.40/5.06 | ALPHA: (12) implies: % 31.40/5.06 | (13) ~ (all_32_0 = 0) % 31.40/5.06 | (14) $i(all_32_8) % 31.40/5.06 | (15) $i(all_32_7) % 31.40/5.06 | (16) $i(all_32_6) % 31.40/5.06 | (17) $i(all_32_5) % 31.40/5.06 | (18) $i(all_32_4) % 31.40/5.06 | (19) $i(all_32_3) % 31.40/5.06 | (20) $i(all_32_2) % 31.40/5.06 | (21) $i(all_32_1) % 31.40/5.07 | (22) maps(all_32_8, all_32_4, all_32_3) = 0 % 31.40/5.07 | (23) maps(all_32_7, all_32_5, all_32_4) = 0 % 31.40/5.07 | (24) maps(all_32_6, all_32_5, all_32_4) = 0 % 31.40/5.07 | (25) compose_function(all_32_8, all_32_7, all_32_5, all_32_4, all_32_3) = % 31.40/5.07 | all_32_2 % 31.40/5.07 | (26) compose_function(all_32_8, all_32_6, all_32_5, all_32_4, all_32_3) = % 31.40/5.07 | all_32_1 % 31.40/5.07 | (27) equal_maps(all_32_7, all_32_6, all_32_5, all_32_4) = all_32_0 % 31.40/5.07 | (28) equal_maps(all_32_2, all_32_1, all_32_5, all_32_3) = 0 % 31.40/5.07 | (29) injective(all_32_8, all_32_4, all_32_3) = 0 % 31.40/5.07 | % 31.40/5.07 | GROUND_INST: instantiating (6) with all_32_7, all_32_6, all_32_5, all_32_4, % 31.40/5.07 | all_32_0, simplifying with (15), (16), (17), (18), (27) gives: % 31.40/5.07 | (30) all_32_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) % 31.40/5.07 | & apply(all_32_6, v0, v2) = 0 & apply(all_32_7, v0, v1) = 0 & % 31.40/5.07 | member(v2, all_32_4) = 0 & member(v1, all_32_4) = 0 & member(v0, % 31.40/5.07 | all_32_5) = 0 & $i(v2) & $i(v1) & $i(v0)) % 31.40/5.07 | % 31.40/5.07 | BETA: splitting (30) gives: % 31.40/5.07 | % 31.40/5.07 | Case 1: % 31.40/5.07 | | % 31.40/5.07 | | (31) all_32_0 = 0 % 31.40/5.07 | | % 31.40/5.07 | | REDUCE: (13), (31) imply: % 31.40/5.07 | | (32) $false % 31.40/5.07 | | % 31.40/5.07 | | CLOSE: (32) is inconsistent. % 31.40/5.07 | | % 31.40/5.07 | Case 2: % 31.40/5.07 | | % 31.40/5.07 | | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & % 31.40/5.07 | | apply(all_32_6, v0, v2) = 0 & apply(all_32_7, v0, v1) = 0 & % 31.40/5.07 | | member(v2, all_32_4) = 0 & member(v1, all_32_4) = 0 & member(v0, % 31.40/5.07 | | all_32_5) = 0 & $i(v2) & $i(v1) & $i(v0)) % 31.40/5.07 | | % 31.40/5.07 | | DELTA: instantiating (33) with fresh symbols all_47_0, all_47_1, all_47_2 % 31.40/5.07 | | gives: % 31.40/5.07 | | (34) ~ (all_47_0 = all_47_1) & apply(all_32_6, all_47_2, all_47_0) = 0 & % 31.40/5.07 | | apply(all_32_7, all_47_2, all_47_1) = 0 & member(all_47_0, all_32_4) % 31.40/5.07 | | = 0 & member(all_47_1, all_32_4) = 0 & member(all_47_2, all_32_5) = % 31.40/5.07 | | 0 & $i(all_47_0) & $i(all_47_1) & $i(all_47_2) % 31.40/5.07 | | % 31.40/5.07 | | ALPHA: (34) implies: % 31.40/5.07 | | (35) ~ (all_47_0 = all_47_1) % 31.40/5.07 | | (36) $i(all_47_2) % 31.40/5.07 | | (37) $i(all_47_1) % 31.40/5.07 | | (38) $i(all_47_0) % 31.40/5.07 | | (39) member(all_47_2, all_32_5) = 0 % 31.40/5.07 | | (40) member(all_47_1, all_32_4) = 0 % 31.40/5.07 | | (41) member(all_47_0, all_32_4) = 0 % 31.40/5.07 | | (42) apply(all_32_7, all_47_2, all_47_1) = 0 % 31.40/5.07 | | (43) apply(all_32_6, all_47_2, all_47_0) = 0 % 31.40/5.07 | | % 31.40/5.07 | | GROUND_INST: instantiating (1) with all_32_6, all_32_5, all_32_4, all_47_2, % 31.40/5.07 | | simplifying with (16), (17), (18), (24), (36), (39) gives: % 31.40/5.07 | | (44) ? [v0: $i] : (apply(all_32_6, all_47_2, v0) = 0 & member(v0, % 31.40/5.07 | | all_32_4) = 0 & $i(v0)) % 31.40/5.07 | | % 31.40/5.07 | | GROUND_INST: instantiating (1) with all_32_7, all_32_5, all_32_4, all_47_2, % 31.40/5.07 | | simplifying with (15), (17), (18), (23), (36), (39) gives: % 31.40/5.07 | | (45) ? [v0: $i] : (apply(all_32_7, all_47_2, v0) = 0 & member(v0, % 31.40/5.07 | | all_32_4) = 0 & $i(v0)) % 31.40/5.07 | | % 31.40/5.08 | | GROUND_INST: instantiating (1) with all_32_8, all_32_4, all_32_3, all_47_1, % 31.40/5.08 | | simplifying with (14), (18), (19), (22), (37), (40) gives: % 31.40/5.08 | | (46) ? [v0: $i] : (apply(all_32_8, all_47_1, v0) = 0 & member(v0, % 31.40/5.08 | | all_32_3) = 0 & $i(v0)) % 31.40/5.08 | | % 31.40/5.08 | | GROUND_INST: instantiating (1) with all_32_8, all_32_4, all_32_3, all_47_0, % 31.40/5.08 | | simplifying with (14), (18), (19), (22), (38), (41) gives: % 31.40/5.08 | | (47) ? [v0: $i] : (apply(all_32_8, all_47_0, v0) = 0 & member(v0, % 31.40/5.08 | | all_32_3) = 0 & $i(v0)) % 31.40/5.08 | | % 31.40/5.08 | | DELTA: instantiating (47) with fresh symbol all_58_0 gives: % 31.40/5.08 | | (48) apply(all_32_8, all_47_0, all_58_0) = 0 & member(all_58_0, all_32_3) % 31.40/5.08 | | = 0 & $i(all_58_0) % 31.40/5.08 | | % 31.40/5.08 | | ALPHA: (48) implies: % 31.40/5.08 | | (49) $i(all_58_0) % 31.40/5.08 | | (50) member(all_58_0, all_32_3) = 0 % 31.40/5.08 | | (51) apply(all_32_8, all_47_0, all_58_0) = 0 % 31.40/5.08 | | % 31.40/5.08 | | DELTA: instantiating (46) with fresh symbol all_60_0 gives: % 31.40/5.08 | | (52) apply(all_32_8, all_47_1, all_60_0) = 0 & member(all_60_0, all_32_3) % 31.40/5.08 | | = 0 & $i(all_60_0) % 31.40/5.08 | | % 31.40/5.08 | | ALPHA: (52) implies: % 31.40/5.08 | | (53) $i(all_60_0) % 31.40/5.08 | | (54) member(all_60_0, all_32_3) = 0 % 31.40/5.08 | | (55) apply(all_32_8, all_47_1, all_60_0) = 0 % 31.40/5.08 | | % 31.40/5.08 | | DELTA: instantiating (45) with fresh symbol all_62_0 gives: % 31.40/5.08 | | (56) apply(all_32_7, all_47_2, all_62_0) = 0 & member(all_62_0, all_32_4) % 31.40/5.08 | | = 0 & $i(all_62_0) % 31.40/5.08 | | % 31.40/5.08 | | ALPHA: (56) implies: % 31.40/5.08 | | (57) $i(all_62_0) % 31.40/5.08 | | (58) member(all_62_0, all_32_4) = 0 % 31.40/5.08 | | (59) apply(all_32_7, all_47_2, all_62_0) = 0 % 31.40/5.08 | | % 31.40/5.08 | | DELTA: instantiating (44) with fresh symbol all_64_0 gives: % 31.40/5.08 | | (60) apply(all_32_6, all_47_2, all_64_0) = 0 & member(all_64_0, all_32_4) % 31.40/5.08 | | = 0 & $i(all_64_0) % 31.40/5.08 | | % 31.40/5.08 | | ALPHA: (60) implies: % 31.40/5.08 | | (61) $i(all_64_0) % 31.40/5.08 | | (62) member(all_64_0, all_32_4) = 0 % 31.40/5.08 | | (63) apply(all_32_6, all_47_2, all_64_0) = 0 % 31.40/5.08 | | % 31.40/5.08 | | GROUND_INST: instantiating (8) with all_32_8, all_32_4, all_32_3, all_47_1, % 31.40/5.08 | | all_47_0, all_58_0, simplifying with (14), (18), (19), (29), % 31.40/5.08 | | (37), (38), (40), (41), (49), (50) gives: % 31.40/5.08 | | (64) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.08 | | all_47_0, all_58_0) = v1 & apply(all_32_8, all_47_1, all_58_0) = % 31.40/5.08 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.08 | | % 31.40/5.08 | | GROUND_INST: instantiating (8) with all_32_8, all_32_4, all_32_3, all_47_0, % 31.40/5.08 | | all_47_1, all_58_0, simplifying with (14), (18), (19), (29), % 31.40/5.08 | | (37), (38), (40), (41), (49), (50) gives: % 31.40/5.08 | | (65) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.08 | | all_47_0, all_58_0) = v0 & apply(all_32_8, all_47_1, all_58_0) = % 31.40/5.08 | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.08 | | % 31.40/5.08 | | GROUND_INST: instantiating (7) with all_32_2, all_32_1, all_32_5, all_32_3, % 31.40/5.08 | | all_47_2, all_60_0, all_58_0, simplifying with (17), (19), % 31.40/5.08 | | (20), (21), (28), (36), (39), (49), (50), (53), (54) gives: % 31.40/5.08 | | (66) all_60_0 = all_58_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_1, % 31.40/5.08 | | all_47_2, all_58_0) = v1 & apply(all_32_2, all_47_2, all_60_0) = % 31.40/5.08 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.08 | | % 31.40/5.08 | | GROUND_INST: instantiating (8) with all_32_8, all_32_4, all_32_3, all_47_1, % 31.40/5.08 | | all_47_0, all_60_0, simplifying with (14), (18), (19), (29), % 31.40/5.08 | | (37), (38), (40), (41), (53), (54) gives: % 31.40/5.08 | | (67) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.08 | | all_47_0, all_60_0) = v1 & apply(all_32_8, all_47_1, all_60_0) = % 31.40/5.08 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.08 | | % 31.40/5.08 | | GROUND_INST: instantiating (8) with all_32_8, all_32_4, all_32_3, all_47_0, % 31.40/5.08 | | all_47_1, all_60_0, simplifying with (14), (18), (19), (29), % 31.40/5.08 | | (37), (38), (40), (41), (53), (54) gives: % 31.40/5.08 | | (68) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.08 | | all_47_0, all_60_0) = v0 & apply(all_32_8, all_47_1, all_60_0) = % 31.40/5.08 | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.08 | | % 31.40/5.08 | | GROUND_INST: instantiating (2) with all_32_6, all_32_5, all_32_4, all_47_2, % 31.40/5.08 | | all_47_1, all_62_0, simplifying with (16), (17), (18), (24), % 31.40/5.08 | | (36), (37), (39), (40), (57), (58) gives: % 31.40/5.08 | | (69) all_62_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 31.40/5.08 | | all_47_2, all_62_0) = v1 & apply(all_32_6, all_47_2, all_47_1) = % 31.40/5.08 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.08 | | % 31.40/5.09 | | GROUND_INST: instantiating (3) with all_32_7, all_32_5, all_32_4, all_47_2, % 31.40/5.09 | | all_62_0, all_47_1, simplifying with (15), (17), (18), (23), % 31.40/5.09 | | (36), (37), (42), (57), (58) gives: % 31.40/5.09 | | (70) all_62_0 = all_47_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.40/5.09 | | (apply(all_32_7, all_47_2, all_62_0) = v2 & member(all_47_1, % 31.40/5.09 | | all_32_4) = v1 & member(all_47_2, all_32_5) = v0 & ( ~ (v2 = 0) % 31.40/5.09 | | | ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.09 | | % 31.40/5.09 | | GROUND_INST: instantiating (2) with all_32_7, all_32_5, all_32_4, all_47_2, % 31.40/5.09 | | all_62_0, all_47_1, simplifying with (15), (17), (18), (23), % 31.40/5.09 | | (36), (37), (39), (40), (57), (58) gives: % 31.40/5.09 | | (71) all_62_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_7, % 31.40/5.09 | | all_47_2, all_62_0) = v0 & apply(all_32_7, all_47_2, all_47_1) = % 31.40/5.09 | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.09 | | % 31.40/5.09 | | GROUND_INST: instantiating (8) with all_32_8, all_32_4, all_32_3, all_47_0, % 31.40/5.09 | | all_62_0, all_60_0, simplifying with (14), (18), (19), (29), % 31.40/5.09 | | (38), (41), (53), (54), (57), (58) gives: % 31.40/5.09 | | (72) all_62_0 = all_47_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.09 | | all_62_0, all_60_0) = v1 & apply(all_32_8, all_47_0, all_60_0) = % 31.40/5.09 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.09 | | % 31.40/5.09 | | GROUND_INST: instantiating (8) with all_32_8, all_32_4, all_32_3, all_62_0, % 31.40/5.09 | | all_47_0, all_60_0, simplifying with (14), (18), (19), (29), % 31.40/5.09 | | (38), (41), (53), (54), (57), (58) gives: % 31.40/5.09 | | (73) all_62_0 = all_47_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.09 | | all_62_0, all_60_0) = v0 & apply(all_32_8, all_47_0, all_60_0) = % 31.40/5.09 | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.09 | | % 31.40/5.09 | | GROUND_INST: instantiating (8) with all_32_8, all_32_4, all_32_3, all_47_1, % 31.40/5.09 | | all_62_0, all_60_0, simplifying with (14), (18), (19), (29), % 31.40/5.09 | | (37), (40), (53), (54), (57), (58) gives: % 31.40/5.09 | | (74) all_62_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.09 | | all_62_0, all_60_0) = v1 & apply(all_32_8, all_47_1, all_60_0) = % 31.40/5.09 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.09 | | % 31.40/5.09 | | GROUND_INST: instantiating (8) with all_32_8, all_32_4, all_32_3, all_47_0, % 31.40/5.09 | | all_62_0, all_58_0, simplifying with (14), (18), (19), (29), % 31.40/5.09 | | (38), (41), (49), (50), (57), (58) gives: % 31.40/5.09 | | (75) all_62_0 = all_47_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.09 | | all_62_0, all_58_0) = v1 & apply(all_32_8, all_47_0, all_58_0) = % 31.40/5.09 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.09 | | % 31.40/5.09 | | GROUND_INST: instantiating (8) with all_32_8, all_32_4, all_32_3, all_62_0, % 31.40/5.09 | | all_47_0, all_58_0, simplifying with (14), (18), (19), (29), % 31.40/5.09 | | (38), (41), (49), (50), (57), (58) gives: % 31.40/5.09 | | (76) all_62_0 = all_47_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.09 | | all_62_0, all_58_0) = v0 & apply(all_32_8, all_47_0, all_58_0) = % 31.40/5.09 | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.09 | | % 31.40/5.09 | | GROUND_INST: instantiating (2) with all_32_6, all_32_5, all_32_4, all_47_2, % 31.40/5.09 | | all_64_0, all_47_0, simplifying with (16), (17), (18), (24), % 31.40/5.09 | | (36), (38), (39), (41), (61), (62) gives: % 31.40/5.09 | | (77) all_64_0 = all_47_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 31.40/5.09 | | all_47_2, all_64_0) = v0 & apply(all_32_6, all_47_2, all_47_0) = % 31.40/5.09 | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.09 | | % 31.40/5.09 | | GROUND_INST: instantiating (1) with all_32_8, all_32_4, all_32_3, all_64_0, % 31.40/5.09 | | simplifying with (14), (18), (19), (22), (61), (62) gives: % 31.40/5.09 | | (78) ? [v0: $i] : (apply(all_32_8, all_64_0, v0) = 0 & member(v0, % 31.40/5.09 | | all_32_3) = 0 & $i(v0)) % 31.40/5.09 | | % 31.40/5.09 | | GROUND_INST: instantiating (8) with all_32_8, all_32_4, all_32_3, all_47_1, % 31.40/5.09 | | all_64_0, all_60_0, simplifying with (14), (18), (19), (29), % 31.40/5.09 | | (37), (40), (53), (54), (61), (62) gives: % 31.40/5.09 | | (79) all_64_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.09 | | all_64_0, all_60_0) = v1 & apply(all_32_8, all_47_1, all_60_0) = % 31.40/5.09 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.09 | | % 31.40/5.09 | | GROUND_INST: instantiating (8) with all_32_8, all_32_4, all_32_3, all_64_0, % 31.40/5.09 | | all_47_1, all_60_0, simplifying with (14), (18), (19), (29), % 31.40/5.09 | | (37), (40), (53), (54), (61), (62) gives: % 31.40/5.09 | | (80) all_64_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.09 | | all_64_0, all_60_0) = v0 & apply(all_32_8, all_47_1, all_60_0) = % 31.40/5.09 | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.09 | | % 31.40/5.09 | | GROUND_INST: instantiating (8) with all_32_8, all_32_4, all_32_3, all_62_0, % 31.40/5.09 | | all_64_0, all_60_0, simplifying with (14), (18), (19), (29), % 31.40/5.09 | | (53), (54), (57), (58), (61), (62) gives: % 31.40/5.09 | | (81) all_64_0 = all_62_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.09 | | all_64_0, all_60_0) = v1 & apply(all_32_8, all_62_0, all_60_0) = % 31.40/5.09 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.09 | | % 31.40/5.09 | | GROUND_INST: instantiating (8) with all_32_8, all_32_4, all_32_3, all_64_0, % 31.40/5.09 | | all_62_0, all_60_0, simplifying with (14), (18), (19), (29), % 31.40/5.09 | | (53), (54), (57), (58), (61), (62) gives: % 31.40/5.09 | | (82) all_64_0 = all_62_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.09 | | all_64_0, all_60_0) = v0 & apply(all_32_8, all_62_0, all_60_0) = % 31.40/5.09 | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.09 | | % 31.40/5.09 | | GROUND_INST: instantiating (8) with all_32_8, all_32_4, all_32_3, all_47_1, % 31.40/5.09 | | all_64_0, all_58_0, simplifying with (14), (18), (19), (29), % 31.40/5.09 | | (37), (40), (49), (50), (61), (62) gives: % 31.40/5.09 | | (83) all_64_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.09 | | all_64_0, all_58_0) = v1 & apply(all_32_8, all_47_1, all_58_0) = % 31.40/5.09 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.09 | | % 31.40/5.10 | | GROUND_INST: instantiating (8) with all_32_8, all_32_4, all_32_3, all_64_0, % 31.40/5.10 | | all_47_1, all_58_0, simplifying with (14), (18), (19), (29), % 31.40/5.10 | | (37), (40), (49), (50), (61), (62) gives: % 31.40/5.10 | | (84) all_64_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.10 | | all_64_0, all_58_0) = v0 & apply(all_32_8, all_47_1, all_58_0) = % 31.40/5.10 | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.10 | | % 31.40/5.10 | | GROUND_INST: instantiating (8) with all_32_8, all_32_4, all_32_3, all_62_0, % 31.40/5.10 | | all_64_0, all_58_0, simplifying with (14), (18), (19), (29), % 31.40/5.10 | | (49), (50), (57), (58), (61), (62) gives: % 31.40/5.10 | | (85) all_64_0 = all_62_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.10 | | all_64_0, all_58_0) = v1 & apply(all_32_8, all_62_0, all_58_0) = % 31.40/5.10 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.10 | | % 31.40/5.10 | | GROUND_INST: instantiating (8) with all_32_8, all_32_4, all_32_3, all_64_0, % 31.40/5.10 | | all_62_0, all_58_0, simplifying with (14), (18), (19), (29), % 31.40/5.10 | | (49), (50), (57), (58), (61), (62) gives: % 31.40/5.10 | | (86) all_64_0 = all_62_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.10 | | all_64_0, all_58_0) = v0 & apply(all_32_8, all_62_0, all_58_0) = % 31.40/5.10 | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.10 | | % 31.40/5.10 | | GROUND_INST: instantiating (9) with all_32_8, all_32_4, all_32_3, all_47_0, % 31.40/5.10 | | all_47_1, all_60_0, simplifying with (14), (18), (19), (29), % 31.40/5.10 | | (37), (38), (41), (53), (55) gives: % 31.40/5.10 | | (87) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.40/5.10 | | (apply(all_32_8, all_47_0, all_60_0) = v2 & member(all_60_0, % 31.40/5.10 | | all_32_3) = v1 & member(all_47_1, all_32_4) = v0 & ( ~ (v2 = 0) % 31.40/5.10 | | | ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.10 | | % 31.40/5.10 | | GROUND_INST: instantiating (9) with all_32_8, all_32_4, all_32_3, all_64_0, % 31.40/5.10 | | all_47_1, all_60_0, simplifying with (14), (18), (19), (29), % 31.40/5.10 | | (37), (53), (55), (61), (62) gives: % 31.40/5.10 | | (88) all_64_0 = all_47_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.40/5.10 | | (apply(all_32_8, all_64_0, all_60_0) = v2 & member(all_60_0, % 31.40/5.10 | | all_32_3) = v1 & member(all_47_1, all_32_4) = v0 & ( ~ (v2 = 0) % 31.40/5.10 | | | ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.10 | | % 31.40/5.10 | | GROUND_INST: instantiating (9) with all_32_8, all_32_4, all_32_3, all_47_1, % 31.40/5.10 | | all_47_0, all_58_0, simplifying with (14), (18), (19), (29), % 31.40/5.10 | | (37), (38), (40), (49), (51) gives: % 31.40/5.10 | | (89) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.40/5.10 | | (apply(all_32_8, all_47_1, all_58_0) = v2 & member(all_58_0, % 31.40/5.10 | | all_32_3) = v1 & member(all_47_0, all_32_4) = v0 & ( ~ (v2 = 0) % 31.40/5.10 | | | ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.10 | | % 31.40/5.10 | | GROUND_INST: instantiating (9) with all_32_8, all_32_4, all_32_3, all_62_0, % 31.40/5.10 | | all_47_0, all_58_0, simplifying with (14), (18), (19), (29), % 31.40/5.10 | | (38), (49), (51), (57), (58) gives: % 31.40/5.10 | | (90) all_62_0 = all_47_0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.40/5.10 | | (apply(all_32_8, all_62_0, all_58_0) = v2 & member(all_58_0, % 31.40/5.10 | | all_32_3) = v1 & member(all_47_0, all_32_4) = v0 & ( ~ (v2 = 0) % 31.40/5.10 | | | ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.10 | | % 31.40/5.10 | | GROUND_INST: instantiating (3) with all_32_7, all_32_5, all_32_4, all_47_2, % 31.40/5.10 | | all_47_1, all_62_0, simplifying with (15), (17), (18), (23), % 31.40/5.10 | | (36), (37), (40), (57), (59) gives: % 31.40/5.10 | | (91) all_62_0 = all_47_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.40/5.10 | | (apply(all_32_7, all_47_2, all_47_1) = v2 & member(all_62_0, % 31.40/5.10 | | all_32_4) = v1 & member(all_47_2, all_32_5) = v0 & ( ~ (v2 = 0) % 31.40/5.10 | | | ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.10 | | % 31.40/5.10 | | GROUND_INST: instantiating (3) with all_32_6, all_32_5, all_32_4, all_47_2, % 31.40/5.10 | | all_47_0, all_64_0, simplifying with (16), (17), (18), (24), % 31.40/5.10 | | (36), (38), (41), (61), (63) gives: % 31.40/5.10 | | (92) all_64_0 = all_47_0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.40/5.10 | | (apply(all_32_6, all_47_2, all_47_0) = v2 & member(all_64_0, % 31.40/5.10 | | all_32_4) = v1 & member(all_47_2, all_32_5) = v0 & ( ~ (v2 = 0) % 31.40/5.10 | | | ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.10 | | % 31.40/5.10 | | DELTA: instantiating (78) with fresh symbol all_116_0 gives: % 31.40/5.10 | | (93) apply(all_32_8, all_64_0, all_116_0) = 0 & member(all_116_0, % 31.40/5.10 | | all_32_3) = 0 & $i(all_116_0) % 31.40/5.10 | | % 31.40/5.10 | | ALPHA: (93) implies: % 31.40/5.10 | | (94) $i(all_116_0) % 31.40/5.10 | | (95) member(all_116_0, all_32_3) = 0 % 31.40/5.10 | | (96) apply(all_32_8, all_64_0, all_116_0) = 0 % 31.40/5.10 | | % 31.40/5.10 | | BETA: splitting (92) gives: % 31.40/5.10 | | % 31.40/5.10 | | Case 1: % 31.40/5.10 | | | % 31.40/5.10 | | | (97) all_64_0 = all_47_0 % 31.40/5.10 | | | % 31.40/5.10 | | | REDUCE: (96), (97) imply: % 31.40/5.10 | | | (98) apply(all_32_8, all_47_0, all_116_0) = 0 % 31.40/5.10 | | | % 31.40/5.10 | | | BETA: splitting (70) gives: % 31.40/5.10 | | | % 31.40/5.10 | | | Case 1: % 31.40/5.10 | | | | % 31.40/5.10 | | | | (99) all_62_0 = all_47_1 % 31.40/5.10 | | | | % 31.40/5.10 | | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (14), (15), (16), % 31.40/5.10 | | | | (17), (18), (19), (20), (21), (22), (25), (26), (28), (29), % 31.40/5.10 | | | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (49), % 31.40/5.10 | | | | (50), (51), (53), (54), (55), (64), (65), (66), (67), (68), % 31.40/5.10 | | | | (72), (73), (75), (76), (79), (80), (81), (82), (83), (84), % 31.40/5.10 | | | | (85), (86), (87), (88), (89), (90), (94), (95), (97), (98), % 31.40/5.10 | | | | (99) are inconsistent by sub-proof #2. % 31.40/5.10 | | | | % 31.40/5.10 | | | Case 2: % 31.40/5.10 | | | | % 31.40/5.10 | | | | (100) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_7, % 31.40/5.10 | | | | all_47_2, all_62_0) = v2 & member(all_47_1, all_32_4) = v1 % 31.40/5.10 | | | | & member(all_47_2, all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = % 31.40/5.10 | | | | 0) | ~ (v0 = 0))) % 31.40/5.10 | | | | % 31.40/5.10 | | | | DELTA: instantiating (100) with fresh symbols all_128_0, all_128_1, % 31.40/5.10 | | | | all_128_2 gives: % 31.40/5.10 | | | | (101) apply(all_32_7, all_47_2, all_62_0) = all_128_0 & % 31.40/5.10 | | | | member(all_47_1, all_32_4) = all_128_1 & member(all_47_2, % 31.40/5.10 | | | | all_32_5) = all_128_2 & ( ~ (all_128_0 = 0) | ~ (all_128_1 = % 31.40/5.10 | | | | 0) | ~ (all_128_2 = 0)) % 31.40/5.10 | | | | % 31.40/5.10 | | | | ALPHA: (101) implies: % 31.40/5.10 | | | | (102) member(all_47_2, all_32_5) = all_128_2 % 31.40/5.10 | | | | (103) member(all_47_1, all_32_4) = all_128_1 % 31.40/5.10 | | | | (104) apply(all_32_7, all_47_2, all_62_0) = all_128_0 % 31.40/5.10 | | | | (105) ~ (all_128_0 = 0) | ~ (all_128_1 = 0) | ~ (all_128_2 = 0) % 31.40/5.10 | | | | % 31.40/5.10 | | | | BETA: splitting (71) gives: % 31.40/5.10 | | | | % 31.40/5.10 | | | | Case 1: % 31.40/5.10 | | | | | % 31.40/5.10 | | | | | (106) all_62_0 = all_47_1 % 31.40/5.10 | | | | | % 31.40/5.11 | | | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (14), (15), (16), % 31.40/5.11 | | | | | (17), (18), (19), (20), (21), (22), (25), (26), (28), (29), % 31.40/5.11 | | | | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (49), % 31.40/5.11 | | | | | (50), (51), (53), (54), (55), (64), (65), (66), (67), (68), % 31.40/5.11 | | | | | (72), (73), (75), (76), (79), (80), (81), (82), (83), (84), % 31.40/5.11 | | | | | (85), (86), (87), (88), (89), (90), (94), (95), (97), (98), % 31.40/5.11 | | | | | (106) are inconsistent by sub-proof #2. % 31.40/5.11 | | | | | % 31.40/5.11 | | | | Case 2: % 31.40/5.11 | | | | | % 31.40/5.11 | | | | | (107) ? [v0: any] : ? [v1: any] : (apply(all_32_7, all_47_2, % 31.40/5.11 | | | | | all_62_0) = v0 & apply(all_32_7, all_47_2, all_47_1) = v1 % 31.40/5.11 | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.11 | | | | | % 31.40/5.11 | | | | | DELTA: instantiating (107) with fresh symbols all_134_0, all_134_1 % 31.40/5.11 | | | | | gives: % 31.40/5.11 | | | | | (108) apply(all_32_7, all_47_2, all_62_0) = all_134_1 & % 31.40/5.11 | | | | | apply(all_32_7, all_47_2, all_47_1) = all_134_0 & ( ~ % 31.40/5.11 | | | | | (all_134_0 = 0) | ~ (all_134_1 = 0)) % 31.40/5.11 | | | | | % 31.40/5.11 | | | | | ALPHA: (108) implies: % 31.40/5.11 | | | | | (109) apply(all_32_7, all_47_2, all_62_0) = all_134_1 % 31.40/5.11 | | | | | % 31.40/5.11 | | | | | BETA: splitting (80) gives: % 31.40/5.11 | | | | | % 31.40/5.11 | | | | | Case 1: % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | (110) all_64_0 = all_47_1 % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | COMBINE_EQS: (97), (110) imply: % 31.40/5.11 | | | | | | (111) all_47_0 = all_47_1 % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | SIMP: (111) implies: % 31.40/5.11 | | | | | | (112) all_47_0 = all_47_1 % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | REDUCE: (35), (112) imply: % 31.40/5.11 | | | | | | (113) $false % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | CLOSE: (113) is inconsistent. % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | Case 2: % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | (114) ~ (all_64_0 = all_47_1) % 31.40/5.11 | | | | | | (115) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_64_0, % 31.40/5.11 | | | | | | all_60_0) = v0 & apply(all_32_8, all_47_1, all_60_0) = % 31.40/5.11 | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | BETA: splitting (69) gives: % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | Case 1: % 31.40/5.11 | | | | | | | % 31.40/5.11 | | | | | | | (116) all_62_0 = all_47_1 % 31.40/5.11 | | | | | | | % 31.40/5.11 | | | | | | | DELTA: instantiating (115) with fresh symbols all_132_0, all_132_1 % 31.40/5.11 | | | | | | | gives: % 31.40/5.11 | | | | | | | (117) apply(all_32_8, all_64_0, all_60_0) = all_132_1 & % 31.40/5.11 | | | | | | | apply(all_32_8, all_47_1, all_60_0) = all_132_0 & ( ~ % 31.40/5.11 | | | | | | | (all_132_0 = 0) | ~ (all_132_1 = 0)) % 31.40/5.11 | | | | | | | % 31.40/5.11 | | | | | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (14), (15), % 31.40/5.11 | | | | | | | (16), (17), (18), (19), (20), (21), (22), (25), (26), % 31.40/5.11 | | | | | | | (28), (29), (36), (37), (38), (39), (40), (41), (42), % 31.40/5.11 | | | | | | | (43), (49), (50), (51), (53), (54), (55), (64), (65), % 31.40/5.11 | | | | | | | (66), (67), (68), (72), (73), (75), (76), (79), (81), % 31.40/5.11 | | | | | | | (82), (83), (84), (85), (86), (87), (88), (89), (90), % 31.40/5.11 | | | | | | | (94), (95), (97), (98), (114), (116), (117) are % 31.40/5.11 | | | | | | | inconsistent by sub-proof #3. % 31.40/5.11 | | | | | | | % 31.40/5.11 | | | | | | Case 2: % 31.40/5.11 | | | | | | | % 31.40/5.11 | | | | | | | % 31.40/5.11 | | | | | | | GROUND_INST: instantiating (10) with 0, all_128_2, all_32_5, % 31.40/5.11 | | | | | | | all_47_2, simplifying with (39), (102) gives: % 31.40/5.11 | | | | | | | (118) all_128_2 = 0 % 31.40/5.11 | | | | | | | % 31.40/5.11 | | | | | | | GROUND_INST: instantiating (10) with 0, all_128_1, all_32_4, % 31.40/5.11 | | | | | | | all_47_1, simplifying with (40), (103) gives: % 31.40/5.11 | | | | | | | (119) all_128_1 = 0 % 31.40/5.11 | | | | | | | % 31.40/5.11 | | | | | | | GROUND_INST: instantiating (11) with 0, all_134_1, all_62_0, % 31.40/5.11 | | | | | | | all_47_2, all_32_7, simplifying with (59), (109) % 31.40/5.11 | | | | | | | gives: % 31.40/5.11 | | | | | | | (120) all_134_1 = 0 % 31.40/5.11 | | | | | | | % 31.40/5.11 | | | | | | | GROUND_INST: instantiating (11) with all_128_0, all_134_1, % 31.40/5.11 | | | | | | | all_62_0, all_47_2, all_32_7, simplifying with (104), % 31.40/5.11 | | | | | | | (109) gives: % 31.40/5.11 | | | | | | | (121) all_134_1 = all_128_0 % 31.40/5.11 | | | | | | | % 31.40/5.11 | | | | | | | COMBINE_EQS: (120), (121) imply: % 31.40/5.11 | | | | | | | (122) all_128_0 = 0 % 31.40/5.11 | | | | | | | % 31.40/5.11 | | | | | | | SIMP: (122) implies: % 31.40/5.11 | | | | | | | (123) all_128_0 = 0 % 31.40/5.11 | | | | | | | % 31.40/5.11 | | | | | | | BETA: splitting (105) gives: % 31.40/5.11 | | | | | | | % 31.40/5.11 | | | | | | | Case 1: % 31.40/5.11 | | | | | | | | % 31.40/5.11 | | | | | | | | (124) ~ (all_128_0 = 0) % 31.40/5.11 | | | | | | | | % 31.40/5.11 | | | | | | | | REDUCE: (123), (124) imply: % 31.40/5.11 | | | | | | | | (125) $false % 31.40/5.11 | | | | | | | | % 31.40/5.11 | | | | | | | | CLOSE: (125) is inconsistent. % 31.40/5.11 | | | | | | | | % 31.40/5.11 | | | | | | | Case 2: % 31.40/5.11 | | | | | | | | % 31.40/5.11 | | | | | | | | (126) ~ (all_128_1 = 0) | ~ (all_128_2 = 0) % 31.40/5.11 | | | | | | | | % 31.40/5.11 | | | | | | | | BETA: splitting (126) gives: % 31.40/5.11 | | | | | | | | % 31.40/5.11 | | | | | | | | Case 1: % 31.40/5.11 | | | | | | | | | % 31.40/5.11 | | | | | | | | | (127) ~ (all_128_1 = 0) % 31.40/5.11 | | | | | | | | | % 31.40/5.11 | | | | | | | | | REDUCE: (119), (127) imply: % 31.40/5.11 | | | | | | | | | (128) $false % 31.40/5.11 | | | | | | | | | % 31.40/5.11 | | | | | | | | | CLOSE: (128) is inconsistent. % 31.40/5.11 | | | | | | | | | % 31.40/5.11 | | | | | | | | Case 2: % 31.40/5.11 | | | | | | | | | % 31.40/5.11 | | | | | | | | | (129) ~ (all_128_2 = 0) % 31.40/5.11 | | | | | | | | | % 31.40/5.11 | | | | | | | | | REDUCE: (118), (129) imply: % 31.40/5.11 | | | | | | | | | (130) $false % 31.40/5.11 | | | | | | | | | % 31.40/5.11 | | | | | | | | | CLOSE: (130) is inconsistent. % 31.40/5.11 | | | | | | | | | % 31.40/5.11 | | | | | | | | End of split % 31.40/5.11 | | | | | | | | % 31.40/5.11 | | | | | | | End of split % 31.40/5.11 | | | | | | | % 31.40/5.11 | | | | | | End of split % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | End of split % 31.40/5.11 | | | | | % 31.40/5.11 | | | | End of split % 31.40/5.11 | | | | % 31.40/5.11 | | | End of split % 31.40/5.11 | | | % 31.40/5.11 | | Case 2: % 31.40/5.11 | | | % 31.40/5.11 | | | (131) ~ (all_64_0 = all_47_0) % 31.40/5.11 | | | (132) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_6, % 31.40/5.11 | | | all_47_2, all_47_0) = v2 & member(all_64_0, all_32_4) = v1 & % 31.40/5.11 | | | member(all_47_2, all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | % 31.40/5.11 | | | ~ (v0 = 0))) % 31.40/5.11 | | | % 31.40/5.11 | | | DELTA: instantiating (132) with fresh symbols all_124_0, all_124_1, % 31.40/5.11 | | | all_124_2 gives: % 31.40/5.11 | | | (133) apply(all_32_6, all_47_2, all_47_0) = all_124_0 & % 31.40/5.11 | | | member(all_64_0, all_32_4) = all_124_1 & member(all_47_2, % 31.40/5.11 | | | all_32_5) = all_124_2 & ( ~ (all_124_0 = 0) | ~ (all_124_1 = % 31.40/5.11 | | | 0) | ~ (all_124_2 = 0)) % 31.40/5.11 | | | % 31.40/5.11 | | | ALPHA: (133) implies: % 31.40/5.11 | | | (134) member(all_47_2, all_32_5) = all_124_2 % 31.40/5.11 | | | (135) member(all_64_0, all_32_4) = all_124_1 % 31.40/5.11 | | | (136) apply(all_32_6, all_47_2, all_47_0) = all_124_0 % 31.40/5.11 | | | (137) ~ (all_124_0 = 0) | ~ (all_124_1 = 0) | ~ (all_124_2 = 0) % 31.40/5.11 | | | % 31.40/5.11 | | | BETA: splitting (77) gives: % 31.40/5.11 | | | % 31.40/5.11 | | | Case 1: % 31.40/5.11 | | | | % 31.40/5.11 | | | | (138) all_64_0 = all_47_0 % 31.40/5.11 | | | | % 31.40/5.11 | | | | REDUCE: (131), (138) imply: % 31.40/5.11 | | | | (139) $false % 31.40/5.11 | | | | % 31.40/5.11 | | | | CLOSE: (139) is inconsistent. % 31.40/5.11 | | | | % 31.40/5.11 | | | Case 2: % 31.40/5.11 | | | | % 31.40/5.11 | | | | (140) ? [v0: any] : ? [v1: any] : (apply(all_32_6, all_47_2, % 31.40/5.11 | | | | all_64_0) = v0 & apply(all_32_6, all_47_2, all_47_0) = v1 & % 31.40/5.11 | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.11 | | | | % 31.40/5.11 | | | | DELTA: instantiating (140) with fresh symbols all_130_0, all_130_1 % 31.40/5.11 | | | | gives: % 31.40/5.11 | | | | (141) apply(all_32_6, all_47_2, all_64_0) = all_130_1 & % 31.40/5.11 | | | | apply(all_32_6, all_47_2, all_47_0) = all_130_0 & ( ~ % 31.40/5.11 | | | | (all_130_0 = 0) | ~ (all_130_1 = 0)) % 31.40/5.11 | | | | % 31.40/5.11 | | | | ALPHA: (141) implies: % 31.40/5.11 | | | | (142) apply(all_32_6, all_47_2, all_47_0) = all_130_0 % 31.40/5.11 | | | | % 31.40/5.11 | | | | BETA: splitting (71) gives: % 31.40/5.11 | | | | % 31.40/5.11 | | | | Case 1: % 31.40/5.11 | | | | | % 31.40/5.11 | | | | | (143) all_62_0 = all_47_1 % 31.40/5.11 | | | | | % 31.40/5.11 | | | | | BETA: splitting (90) gives: % 31.40/5.11 | | | | | % 31.40/5.11 | | | | | Case 1: % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | (144) all_62_0 = all_47_0 % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | COMBINE_EQS: (143), (144) imply: % 31.40/5.11 | | | | | | (145) all_47_0 = all_47_1 % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | REDUCE: (35), (145) imply: % 31.40/5.11 | | | | | | (146) $false % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | CLOSE: (146) is inconsistent. % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | Case 2: % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | GROUND_INST: instantiating (10) with 0, all_124_2, all_32_5, % 31.40/5.11 | | | | | | all_47_2, simplifying with (39), (134) gives: % 31.40/5.11 | | | | | | (147) all_124_2 = 0 % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | GROUND_INST: instantiating (10) with 0, all_124_1, all_32_4, % 31.40/5.11 | | | | | | all_64_0, simplifying with (62), (135) gives: % 31.40/5.11 | | | | | | (148) all_124_1 = 0 % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | GROUND_INST: instantiating (11) with 0, all_124_0, all_47_0, % 31.40/5.11 | | | | | | all_47_2, all_32_6, simplifying with (43), (136) gives: % 31.40/5.11 | | | | | | (149) all_124_0 = 0 % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | REF_CLOSE: (137), (147), (148), (149) are inconsistent by sub-proof % 31.40/5.11 | | | | | | #1. % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | End of split % 31.40/5.11 | | | | | % 31.40/5.11 | | | | Case 2: % 31.40/5.11 | | | | | % 31.40/5.11 | | | | | (150) ~ (all_62_0 = all_47_1) % 31.40/5.11 | | | | | % 31.40/5.11 | | | | | BETA: splitting (70) gives: % 31.40/5.11 | | | | | % 31.40/5.11 | | | | | Case 1: % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | (151) all_62_0 = all_47_1 % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | REDUCE: (150), (151) imply: % 31.40/5.11 | | | | | | (152) $false % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | CLOSE: (152) is inconsistent. % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | Case 2: % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | (153) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.40/5.11 | | | | | | (apply(all_32_7, all_47_2, all_62_0) = v2 & % 31.40/5.11 | | | | | | member(all_47_1, all_32_4) = v1 & member(all_47_2, % 31.40/5.11 | | | | | | all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 31.40/5.11 | | | | | | 0))) % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | DELTA: instantiating (153) with fresh symbols all_169_0, all_169_1, % 31.40/5.11 | | | | | | all_169_2 gives: % 31.40/5.11 | | | | | | (154) apply(all_32_7, all_47_2, all_62_0) = all_169_0 & % 31.40/5.11 | | | | | | member(all_47_1, all_32_4) = all_169_1 & member(all_47_2, % 31.40/5.11 | | | | | | all_32_5) = all_169_2 & ( ~ (all_169_0 = 0) | ~ % 31.40/5.11 | | | | | | (all_169_1 = 0) | ~ (all_169_2 = 0)) % 31.40/5.11 | | | | | | % 31.40/5.11 | | | | | | ALPHA: (154) implies: % 31.40/5.12 | | | | | | (155) member(all_47_2, all_32_5) = all_169_2 % 31.40/5.12 | | | | | | % 31.40/5.12 | | | | | | BETA: splitting (91) gives: % 31.40/5.12 | | | | | | % 31.40/5.12 | | | | | | Case 1: % 31.40/5.12 | | | | | | | % 31.40/5.12 | | | | | | | (156) all_62_0 = all_47_1 % 31.40/5.12 | | | | | | | % 31.40/5.12 | | | | | | | REDUCE: (150), (156) imply: % 31.40/5.12 | | | | | | | (157) $false % 31.40/5.12 | | | | | | | % 31.40/5.12 | | | | | | | CLOSE: (157) is inconsistent. % 31.40/5.12 | | | | | | | % 31.40/5.12 | | | | | | Case 2: % 31.40/5.12 | | | | | | | % 31.40/5.12 | | | | | | | (158) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.40/5.12 | | | | | | | (apply(all_32_7, all_47_2, all_47_1) = v2 & % 31.40/5.12 | | | | | | | member(all_62_0, all_32_4) = v1 & member(all_47_2, % 31.40/5.12 | | | | | | | all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 % 31.40/5.12 | | | | | | | = 0))) % 31.40/5.12 | | | | | | | % 31.40/5.12 | | | | | | | DELTA: instantiating (158) with fresh symbols all_190_0, % 31.40/5.12 | | | | | | | all_190_1, all_190_2 gives: % 31.40/5.12 | | | | | | | (159) apply(all_32_7, all_47_2, all_47_1) = all_190_0 & % 31.40/5.12 | | | | | | | member(all_62_0, all_32_4) = all_190_1 & member(all_47_2, % 31.40/5.12 | | | | | | | all_32_5) = all_190_2 & ( ~ (all_190_0 = 0) | ~ % 31.40/5.12 | | | | | | | (all_190_1 = 0) | ~ (all_190_2 = 0)) % 31.40/5.12 | | | | | | | % 31.40/5.12 | | | | | | | ALPHA: (159) implies: % 31.40/5.12 | | | | | | | (160) member(all_47_2, all_32_5) = all_190_2 % 31.40/5.12 | | | | | | | % 31.40/5.12 | | | | | | | BETA: splitting (74) gives: % 31.40/5.12 | | | | | | | % 31.40/5.12 | | | | | | | Case 1: % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | | (161) all_62_0 = all_47_1 % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | | REDUCE: (150), (161) imply: % 31.40/5.12 | | | | | | | | (162) $false % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | | CLOSE: (162) is inconsistent. % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | Case 2: % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | | GROUND_INST: instantiating (10) with all_124_2, all_169_2, % 31.40/5.12 | | | | | | | | all_32_5, all_47_2, simplifying with (134), (155) % 31.40/5.12 | | | | | | | | gives: % 31.40/5.12 | | | | | | | | (163) all_169_2 = all_124_2 % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | | GROUND_INST: instantiating (10) with 0, all_190_2, all_32_5, % 31.40/5.12 | | | | | | | | all_47_2, simplifying with (39), (160) gives: % 31.40/5.12 | | | | | | | | (164) all_190_2 = 0 % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | | GROUND_INST: instantiating (10) with all_169_2, all_190_2, % 31.40/5.12 | | | | | | | | all_32_5, all_47_2, simplifying with (155), (160) % 31.40/5.12 | | | | | | | | gives: % 31.40/5.12 | | | | | | | | (165) all_190_2 = all_169_2 % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | | GROUND_INST: instantiating (10) with 0, all_124_1, all_32_4, % 31.40/5.12 | | | | | | | | all_64_0, simplifying with (62), (135) gives: % 31.40/5.12 | | | | | | | | (166) all_124_1 = 0 % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | | GROUND_INST: instantiating (11) with 0, all_130_0, all_47_0, % 31.40/5.12 | | | | | | | | all_47_2, all_32_6, simplifying with (43), (142) % 31.40/5.12 | | | | | | | | gives: % 31.40/5.12 | | | | | | | | (167) all_130_0 = 0 % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | | GROUND_INST: instantiating (11) with all_124_0, all_130_0, % 31.40/5.12 | | | | | | | | all_47_0, all_47_2, all_32_6, simplifying with % 31.40/5.12 | | | | | | | | (136), (142) gives: % 31.40/5.12 | | | | | | | | (168) all_130_0 = all_124_0 % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | | COMBINE_EQS: (164), (165) imply: % 31.40/5.12 | | | | | | | | (169) all_169_2 = 0 % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | | SIMP: (169) implies: % 31.40/5.12 | | | | | | | | (170) all_169_2 = 0 % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | | COMBINE_EQS: (163), (170) imply: % 31.40/5.12 | | | | | | | | (171) all_124_2 = 0 % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | | SIMP: (171) implies: % 31.40/5.12 | | | | | | | | (172) all_124_2 = 0 % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | | COMBINE_EQS: (167), (168) imply: % 31.40/5.12 | | | | | | | | (173) all_124_0 = 0 % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | | SIMP: (173) implies: % 31.40/5.12 | | | | | | | | (174) all_124_0 = 0 % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | | REF_CLOSE: (137), (166), (172), (174) are inconsistent by % 31.40/5.12 | | | | | | | | sub-proof #1. % 31.40/5.12 | | | | | | | | % 31.40/5.12 | | | | | | | End of split % 31.40/5.12 | | | | | | | % 31.40/5.12 | | | | | | End of split % 31.40/5.12 | | | | | | % 31.40/5.12 | | | | | End of split % 31.40/5.12 | | | | | % 31.40/5.12 | | | | End of split % 31.40/5.12 | | | | % 31.40/5.12 | | | End of split % 31.40/5.12 | | | % 31.40/5.12 | | End of split % 31.40/5.12 | | % 31.40/5.12 | End of split % 31.40/5.12 | % 31.40/5.12 End of proof % 31.40/5.12 % 31.40/5.12 Sub-proof #1 shows that the following formulas are inconsistent: % 31.40/5.12 ---------------------------------------------------------------- % 31.40/5.12 (1) ~ (all_124_0 = 0) | ~ (all_124_1 = 0) | ~ (all_124_2 = 0) % 31.40/5.12 (2) all_124_0 = 0 % 31.40/5.12 (3) all_124_1 = 0 % 31.40/5.12 (4) all_124_2 = 0 % 31.40/5.12 % 31.40/5.12 Begin of proof % 31.40/5.12 | % 31.40/5.12 | BETA: splitting (1) gives: % 31.40/5.12 | % 31.40/5.12 | Case 1: % 31.40/5.12 | | % 31.40/5.12 | | (5) ~ (all_124_0 = 0) % 31.40/5.12 | | % 31.40/5.12 | | REDUCE: (2), (5) imply: % 31.40/5.12 | | (6) $false % 31.40/5.12 | | % 31.40/5.12 | | CLOSE: (6) is inconsistent. % 31.40/5.12 | | % 31.40/5.12 | Case 2: % 31.40/5.12 | | % 31.40/5.12 | | (7) ~ (all_124_1 = 0) | ~ (all_124_2 = 0) % 31.40/5.12 | | % 31.40/5.12 | | BETA: splitting (7) gives: % 31.40/5.12 | | % 31.40/5.12 | | Case 1: % 31.40/5.12 | | | % 31.40/5.12 | | | (8) ~ (all_124_1 = 0) % 31.40/5.12 | | | % 31.40/5.12 | | | REDUCE: (3), (8) imply: % 31.40/5.12 | | | (9) $false % 31.40/5.12 | | | % 31.40/5.12 | | | CLOSE: (9) is inconsistent. % 31.40/5.12 | | | % 31.40/5.12 | | Case 2: % 31.40/5.12 | | | % 31.40/5.12 | | | (10) ~ (all_124_2 = 0) % 31.40/5.12 | | | % 31.40/5.12 | | | REDUCE: (4), (10) imply: % 31.40/5.12 | | | (11) $false % 31.40/5.12 | | | % 31.40/5.12 | | | CLOSE: (11) is inconsistent. % 31.40/5.12 | | | % 31.40/5.12 | | End of split % 31.40/5.12 | | % 31.40/5.12 | End of split % 31.40/5.12 | % 31.40/5.12 End of proof % 31.40/5.12 % 31.40/5.12 Sub-proof #2 shows that the following formulas are inconsistent: % 31.40/5.12 ---------------------------------------------------------------- % 31.40/5.12 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 31.40/5.12 [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, % 31.40/5.12 v5) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 31.40/5.12 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 31.40/5.12 any] : ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v5, v2) = v7 & % 31.40/5.12 member(v4, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 31.40/5.12 (2) all_62_0 = all_47_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.12 all_62_0, all_60_0) = v1 & apply(all_32_8, all_47_0, all_60_0) = v0 & % 31.40/5.12 ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.12 (3) member(all_116_0, all_32_3) = 0 % 31.40/5.12 (4) apply(all_32_8, all_47_1, all_60_0) = 0 % 31.40/5.12 (5) apply(all_32_7, all_47_2, all_47_1) = 0 % 31.40/5.12 (6) $i(all_32_5) % 31.40/5.12 (7) $i(all_58_0) % 31.40/5.12 (8) all_64_0 = all_62_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.12 all_64_0, all_60_0) = v0 & apply(all_32_8, all_62_0, all_60_0) = v1 & % 31.40/5.12 ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.12 (9) all_64_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.12 all_64_0, all_58_0) = v1 & apply(all_32_8, all_47_1, all_58_0) = v0 & % 31.40/5.12 ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.12 (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 31.40/5.12 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ % 31.40/5.12 (apply(v4, v3, v2) = v0)) % 31.40/5.12 (11) compose_function(all_32_8, all_32_7, all_32_5, all_32_4, all_32_3) = % 31.40/5.12 all_32_2 % 31.40/5.12 (12) $i(all_32_4) % 31.40/5.12 (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 31.40/5.12 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = % 31.40/5.12 v0)) % 31.40/5.12 (14) all_64_0 = all_62_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.12 all_64_0, all_58_0) = v1 & apply(all_32_8, all_62_0, all_58_0) = v0 % 31.40/5.12 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.12 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 31.40/5.12 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 % 31.40/5.12 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, % 31.40/5.12 v5, v6) = v8) | ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ $i(v6) | % 31.40/5.12 ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 31.40/5.12 ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v10 & apply(v0, % 31.40/5.12 v9, v6) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4) % 31.40/5.12 = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) % 31.40/5.12 (16) $i(all_116_0) % 31.40/5.12 (17) all_62_0 = all_47_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.12 all_62_0, all_60_0) = v0 & apply(all_32_8, all_47_0, all_60_0) = v1 % 31.40/5.12 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.12 (18) $i(all_32_2) % 31.40/5.12 (19) $i(all_32_6) % 31.40/5.12 (20) $i(all_47_0) % 31.40/5.12 (21) $i(all_32_3) % 31.40/5.12 (22) $i(all_32_1) % 31.40/5.13 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 31.40/5.13 [v5: $i] : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) % 31.40/5.13 | ~ (member(v6, v3) = 0) | ~ (member(v5, v3) = 0) | ~ (member(v4, % 31.40/5.13 v2) = 0) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 31.40/5.13 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : % 31.40/5.13 (apply(v1, v4, v6) = v8 & apply(v0, v4, v5) = v7 & ( ~ (v8 = 0) | ~ % 31.40/5.13 (v7 = 0)))) % 31.40/5.13 (24) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.13 all_47_0, all_58_0) = v0 & apply(all_32_8, all_47_1, all_58_0) = v1 % 31.40/5.13 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.13 (25) apply(all_32_8, all_47_0, all_58_0) = 0 % 31.40/5.13 (26) maps(all_32_8, all_32_4, all_32_3) = 0 % 31.40/5.13 (27) apply(all_32_6, all_47_2, all_47_0) = 0 % 31.40/5.13 (28) all_62_0 = all_47_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.13 all_62_0, all_58_0) = v1 & apply(all_32_8, all_47_0, all_58_0) = v0 % 31.40/5.13 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.13 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 31.40/5.13 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 % 31.40/5.13 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, % 31.40/5.13 v5, v6) = v8) | ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | ~ $i(v6) % 31.40/5.13 | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 31.40/5.13 $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v0, v9, v6) = v11 & % 31.40/5.13 member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | % 31.40/5.13 (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ % 31.40/5.13 (v10 = 0))))) % 31.40/5.13 (30) all_64_0 = all_47_0 % 31.40/5.13 (31) ~ (all_47_0 = all_47_1) % 31.40/5.13 (32) compose_function(all_32_8, all_32_6, all_32_5, all_32_4, all_32_3) = % 31.40/5.13 all_32_1 % 31.40/5.13 (33) all_62_0 = all_47_1 % 31.40/5.13 (34) all_64_0 = all_62_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.13 all_64_0, all_58_0) = v0 & apply(all_32_8, all_62_0, all_58_0) = v1 % 31.40/5.13 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.13 (35) member(all_47_0, all_32_4) = 0 % 31.40/5.13 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 31.40/5.13 [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = % 31.40/5.13 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | % 31.40/5.13 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 31.40/5.13 any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & apply(v0, v3, v4) = % 31.40/5.13 v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 31.40/5.13 (37) $i(all_32_7) % 31.40/5.13 (38) apply(all_32_8, all_47_0, all_116_0) = 0 % 31.40/5.13 (39) $i(all_60_0) % 31.40/5.13 (40) member(all_60_0, all_32_3) = 0 % 31.40/5.13 (41) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.40/5.13 (apply(all_32_8, all_47_1, all_58_0) = v2 & member(all_58_0, all_32_3) = % 31.40/5.13 v1 & member(all_47_0, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 31.40/5.13 (v0 = 0))) % 31.40/5.13 (42) all_64_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.13 all_64_0, all_60_0) = v0 & apply(all_32_8, all_47_1, all_60_0) = v1 % 31.40/5.13 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.13 (43) injective(all_32_8, all_32_4, all_32_3) = 0 % 31.40/5.13 (44) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.13 all_47_0, all_60_0) = v0 & apply(all_32_8, all_47_1, all_60_0) = v1 % 31.40/5.13 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.13 (45) member(all_58_0, all_32_3) = 0 % 31.40/5.13 (46) all_62_0 = all_47_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.13 all_62_0, all_58_0) = v0 & apply(all_32_8, all_47_0, all_58_0) = v1 % 31.40/5.13 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.13 (47) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 31.40/5.13 [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, % 31.40/5.13 v2) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ % 31.40/5.13 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 31.40/5.13 ? [v6: any] : ? [v7: any] : (apply(v0, v4, v5) = v7 & apply(v0, v3, % 31.40/5.13 v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 31.40/5.13 (48) all_60_0 = all_58_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_1, % 31.40/5.13 all_47_2, all_58_0) = v1 & apply(all_32_2, all_47_2, all_60_0) = v0 % 31.40/5.13 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.13 (49) member(all_47_1, all_32_4) = 0 % 31.40/5.13 (50) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.40/5.13 (apply(all_32_8, all_47_0, all_60_0) = v2 & member(all_60_0, all_32_3) = % 31.40/5.13 v1 & member(all_47_1, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 31.40/5.13 (v0 = 0))) % 31.40/5.13 (51) member(all_47_2, all_32_5) = 0 % 31.40/5.13 (52) $i(all_47_2) % 31.40/5.13 (53) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.13 all_47_0, all_58_0) = v1 & apply(all_32_8, all_47_1, all_58_0) = v0 % 31.40/5.13 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.13 (54) equal_maps(all_32_2, all_32_1, all_32_5, all_32_3) = 0 % 31.40/5.13 (55) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.13 all_47_0, all_60_0) = v1 & apply(all_32_8, all_47_1, all_60_0) = v0 % 31.40/5.13 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.13 (56) all_64_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.13 all_64_0, all_60_0) = v1 & apply(all_32_8, all_47_1, all_60_0) = v0 % 31.40/5.13 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.13 (57) all_64_0 = all_62_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.13 all_64_0, all_60_0) = v1 & apply(all_32_8, all_62_0, all_60_0) = v0 % 31.40/5.13 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.13 (58) $i(all_32_8) % 31.40/5.13 (59) all_62_0 = all_47_0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.40/5.13 (apply(all_32_8, all_62_0, all_58_0) = v2 & member(all_58_0, all_32_3) = % 31.40/5.13 v1 & member(all_47_0, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 31.40/5.13 (v0 = 0))) % 31.40/5.13 (60) all_64_0 = all_47_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.40/5.13 (apply(all_32_8, all_64_0, all_60_0) = v2 & member(all_60_0, all_32_3) = % 31.40/5.13 v1 & member(all_47_1, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 31.40/5.13 (v0 = 0))) % 31.40/5.13 (61) all_64_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.13 all_64_0, all_58_0) = v0 & apply(all_32_8, all_47_1, all_58_0) = v1 % 31.40/5.13 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.13 (62) $i(all_47_1) % 31.40/5.13 % 31.40/5.13 Begin of proof % 31.40/5.13 | % 31.40/5.13 | BETA: splitting (42) gives: % 31.40/5.13 | % 31.40/5.13 | Case 1: % 31.40/5.13 | | % 31.40/5.13 | | (63) all_64_0 = all_47_1 % 31.40/5.13 | | % 31.40/5.13 | | COMBINE_EQS: (30), (63) imply: % 31.40/5.13 | | (64) all_47_0 = all_47_1 % 31.40/5.13 | | % 31.40/5.13 | | SIMP: (64) implies: % 31.40/5.13 | | (65) all_47_0 = all_47_1 % 31.40/5.13 | | % 31.40/5.13 | | REDUCE: (31), (65) imply: % 31.40/5.13 | | (66) $false % 31.40/5.13 | | % 31.40/5.13 | | CLOSE: (66) is inconsistent. % 31.40/5.13 | | % 31.40/5.13 | Case 2: % 31.40/5.13 | | % 31.40/5.13 | | (67) ~ (all_64_0 = all_47_1) % 31.40/5.13 | | (68) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_64_0, all_60_0) = % 31.40/5.13 | | v0 & apply(all_32_8, all_47_1, all_60_0) = v1 & ( ~ (v1 = 0) | ~ % 31.40/5.13 | | (v0 = 0))) % 31.40/5.13 | | % 31.40/5.13 | | DELTA: instantiating (68) with fresh symbols all_132_0, all_132_1 gives: % 31.40/5.13 | | (69) apply(all_32_8, all_64_0, all_60_0) = all_132_1 & apply(all_32_8, % 31.40/5.13 | | all_47_1, all_60_0) = all_132_0 & ( ~ (all_132_0 = 0) | ~ % 31.40/5.13 | | (all_132_1 = 0)) % 31.40/5.13 | | % 31.40/5.13 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 31.40/5.13 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 31.40/5.13 | | (24), (25), (26), (27), (28), (29), (30), (32), (33), (34), (35), % 31.40/5.13 | | (36), (37), (38), (39), (40), (41), (43), (44), (45), (46), (47), % 31.40/5.13 | | (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), % 31.40/5.13 | | (59), (60), (61), (62), (67), (69) are inconsistent by sub-proof % 31.40/5.13 | | #3. % 31.40/5.13 | | % 31.40/5.13 | End of split % 31.40/5.13 | % 31.40/5.13 End of proof % 31.40/5.13 % 31.40/5.13 Sub-proof #3 shows that the following formulas are inconsistent: % 31.40/5.13 ---------------------------------------------------------------- % 31.40/5.14 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 31.40/5.14 [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, % 31.40/5.14 v5) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 31.40/5.14 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 31.40/5.14 any] : ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v5, v2) = v7 & % 31.40/5.14 member(v4, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 31.40/5.14 (2) all_62_0 = all_47_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.14 all_62_0, all_60_0) = v1 & apply(all_32_8, all_47_0, all_60_0) = v0 & % 31.40/5.14 ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.14 (3) member(all_116_0, all_32_3) = 0 % 31.40/5.14 (4) apply(all_32_8, all_47_1, all_60_0) = 0 % 31.40/5.14 (5) apply(all_32_7, all_47_2, all_47_1) = 0 % 31.40/5.14 (6) $i(all_32_5) % 31.40/5.14 (7) $i(all_58_0) % 31.40/5.14 (8) all_64_0 = all_62_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.14 all_64_0, all_60_0) = v0 & apply(all_32_8, all_62_0, all_60_0) = v1 & % 31.40/5.14 ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.14 (9) all_64_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.14 all_64_0, all_58_0) = v1 & apply(all_32_8, all_47_1, all_58_0) = v0 & % 31.40/5.14 ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.14 (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 31.40/5.14 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ % 31.40/5.14 (apply(v4, v3, v2) = v0)) % 31.40/5.14 (11) compose_function(all_32_8, all_32_7, all_32_5, all_32_4, all_32_3) = % 31.40/5.14 all_32_2 % 31.40/5.14 (12) $i(all_32_4) % 31.40/5.14 (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 31.40/5.14 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = % 31.40/5.14 v0)) % 31.40/5.14 (14) all_64_0 = all_62_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.14 all_64_0, all_58_0) = v1 & apply(all_32_8, all_62_0, all_58_0) = v0 % 31.40/5.14 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.14 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 31.40/5.14 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 % 31.40/5.14 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, % 31.40/5.14 v5, v6) = v8) | ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ $i(v6) | % 31.40/5.14 ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 31.40/5.14 ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v10 & apply(v0, % 31.40/5.14 v9, v6) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4) % 31.40/5.14 = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) % 31.40/5.14 (16) $i(all_116_0) % 31.40/5.14 (17) all_62_0 = all_47_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.14 all_62_0, all_60_0) = v0 & apply(all_32_8, all_47_0, all_60_0) = v1 % 31.40/5.14 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.14 (18) $i(all_32_2) % 31.40/5.14 (19) $i(all_32_6) % 31.40/5.14 (20) $i(all_47_0) % 31.40/5.14 (21) $i(all_32_3) % 31.40/5.14 (22) $i(all_32_1) % 31.40/5.14 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 31.40/5.14 [v5: $i] : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) % 31.40/5.14 | ~ (member(v6, v3) = 0) | ~ (member(v5, v3) = 0) | ~ (member(v4, % 31.40/5.14 v2) = 0) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 31.40/5.14 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : % 31.40/5.14 (apply(v1, v4, v6) = v8 & apply(v0, v4, v5) = v7 & ( ~ (v8 = 0) | ~ % 31.40/5.14 (v7 = 0)))) % 31.40/5.14 (24) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.14 all_47_0, all_58_0) = v0 & apply(all_32_8, all_47_1, all_58_0) = v1 % 31.40/5.14 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.14 (25) apply(all_32_8, all_47_0, all_58_0) = 0 % 31.40/5.14 (26) maps(all_32_8, all_32_4, all_32_3) = 0 % 31.40/5.14 (27) apply(all_32_6, all_47_2, all_47_0) = 0 % 31.40/5.14 (28) all_62_0 = all_47_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.14 all_62_0, all_58_0) = v1 & apply(all_32_8, all_47_0, all_58_0) = v0 % 31.40/5.14 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.14 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 31.40/5.14 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 % 31.40/5.14 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, % 31.40/5.14 v5, v6) = v8) | ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | ~ $i(v6) % 31.40/5.14 | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 31.40/5.14 $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v0, v9, v6) = v11 & % 31.40/5.14 member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | % 31.40/5.14 (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ % 31.40/5.14 (v10 = 0))))) % 31.40/5.14 (30) all_64_0 = all_47_0 % 31.40/5.14 (31) compose_function(all_32_8, all_32_6, all_32_5, all_32_4, all_32_3) = % 31.40/5.14 all_32_1 % 31.40/5.14 (32) all_62_0 = all_47_1 % 31.40/5.14 (33) all_64_0 = all_62_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.14 all_64_0, all_58_0) = v0 & apply(all_32_8, all_62_0, all_58_0) = v1 % 31.40/5.14 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.14 (34) member(all_47_0, all_32_4) = 0 % 31.40/5.14 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 31.40/5.14 [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = % 31.40/5.14 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | % 31.40/5.14 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 31.40/5.14 any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & apply(v0, v3, v4) = % 31.40/5.14 v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 31.40/5.14 (36) $i(all_32_7) % 31.40/5.14 (37) apply(all_32_8, all_47_0, all_116_0) = 0 % 31.40/5.14 (38) $i(all_60_0) % 31.40/5.14 (39) member(all_60_0, all_32_3) = 0 % 31.40/5.14 (40) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.40/5.14 (apply(all_32_8, all_47_1, all_58_0) = v2 & member(all_58_0, all_32_3) = % 31.40/5.14 v1 & member(all_47_0, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 31.40/5.14 (v0 = 0))) % 31.40/5.14 (41) injective(all_32_8, all_32_4, all_32_3) = 0 % 31.40/5.14 (42) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.14 all_47_0, all_60_0) = v0 & apply(all_32_8, all_47_1, all_60_0) = v1 % 31.40/5.14 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.14 (43) member(all_58_0, all_32_3) = 0 % 31.40/5.14 (44) all_62_0 = all_47_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.14 all_62_0, all_58_0) = v0 & apply(all_32_8, all_47_0, all_58_0) = v1 % 31.40/5.14 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.14 (45) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 31.40/5.14 [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, % 31.40/5.14 v2) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ % 31.40/5.14 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 31.40/5.14 ? [v6: any] : ? [v7: any] : (apply(v0, v4, v5) = v7 & apply(v0, v3, % 31.40/5.14 v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 31.40/5.14 (46) all_60_0 = all_58_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_1, % 31.40/5.14 all_47_2, all_58_0) = v1 & apply(all_32_2, all_47_2, all_60_0) = v0 % 31.40/5.14 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.14 (47) member(all_47_1, all_32_4) = 0 % 31.40/5.14 (48) ~ (all_64_0 = all_47_1) % 31.40/5.14 (49) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.40/5.14 (apply(all_32_8, all_47_0, all_60_0) = v2 & member(all_60_0, all_32_3) = % 31.40/5.14 v1 & member(all_47_1, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 31.40/5.14 (v0 = 0))) % 31.40/5.14 (50) member(all_47_2, all_32_5) = 0 % 31.40/5.14 (51) $i(all_47_2) % 31.40/5.14 (52) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.14 all_47_0, all_58_0) = v1 & apply(all_32_8, all_47_1, all_58_0) = v0 % 31.40/5.14 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.14 (53) equal_maps(all_32_2, all_32_1, all_32_5, all_32_3) = 0 % 31.40/5.14 (54) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.14 all_47_0, all_60_0) = v1 & apply(all_32_8, all_47_1, all_60_0) = v0 % 31.40/5.14 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.14 (55) all_64_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.14 all_64_0, all_60_0) = v1 & apply(all_32_8, all_47_1, all_60_0) = v0 % 31.40/5.14 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.14 (56) all_64_0 = all_62_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.14 all_64_0, all_60_0) = v1 & apply(all_32_8, all_62_0, all_60_0) = v0 % 31.40/5.14 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.14 (57) $i(all_32_8) % 31.40/5.15 (58) all_62_0 = all_47_0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.40/5.15 (apply(all_32_8, all_62_0, all_58_0) = v2 & member(all_58_0, all_32_3) = % 31.40/5.15 v1 & member(all_47_0, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 31.40/5.15 (v0 = 0))) % 31.40/5.15 (59) all_64_0 = all_47_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.40/5.15 (apply(all_32_8, all_64_0, all_60_0) = v2 & member(all_60_0, all_32_3) = % 31.40/5.15 v1 & member(all_47_1, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 31.40/5.15 (v0 = 0))) % 31.40/5.15 (60) all_64_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.40/5.15 all_64_0, all_58_0) = v0 & apply(all_32_8, all_47_1, all_58_0) = v1 % 31.40/5.15 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.40/5.15 (61) $i(all_47_1) % 31.40/5.15 (62) apply(all_32_8, all_64_0, all_60_0) = all_132_1 & apply(all_32_8, % 31.40/5.15 all_47_1, all_60_0) = all_132_0 & ( ~ (all_132_0 = 0) | ~ (all_132_1 % 31.40/5.15 = 0)) % 31.40/5.15 % 31.40/5.15 Begin of proof % 31.40/5.15 | % 31.40/5.15 | ALPHA: (62) implies: % 31.87/5.15 | (63) apply(all_32_8, all_47_1, all_60_0) = all_132_0 % 31.87/5.15 | (64) apply(all_32_8, all_64_0, all_60_0) = all_132_1 % 31.87/5.15 | % 31.87/5.15 | REDUCE: (30), (48) imply: % 31.87/5.15 | (65) ~ (all_47_0 = all_47_1) % 31.87/5.15 | % 31.87/5.15 | REDUCE: (30), (64) imply: % 31.87/5.15 | (66) apply(all_32_8, all_47_0, all_60_0) = all_132_1 % 31.87/5.15 | % 31.87/5.15 | BETA: splitting (28) gives: % 31.87/5.15 | % 31.87/5.15 | Case 1: % 31.87/5.15 | | % 31.87/5.15 | | (67) all_62_0 = all_47_0 % 31.87/5.15 | | % 31.87/5.15 | | COMBINE_EQS: (32), (67) imply: % 31.87/5.15 | | (68) all_47_0 = all_47_1 % 31.87/5.15 | | % 31.87/5.15 | | REDUCE: (65), (68) imply: % 31.87/5.15 | | (69) $false % 31.87/5.15 | | % 31.87/5.15 | | CLOSE: (69) is inconsistent. % 31.87/5.15 | | % 31.87/5.15 | Case 2: % 31.87/5.15 | | % 31.87/5.15 | | (70) ~ (all_62_0 = all_47_0) % 31.87/5.15 | | (71) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_62_0, all_58_0) = % 31.87/5.15 | | v1 & apply(all_32_8, all_47_0, all_58_0) = v0 & ( ~ (v1 = 0) | ~ % 31.87/5.15 | | (v0 = 0))) % 31.87/5.15 | | % 31.87/5.15 | | DELTA: instantiating (71) with fresh symbols all_137_0, all_137_1 gives: % 31.87/5.15 | | (72) apply(all_32_8, all_62_0, all_58_0) = all_137_0 & apply(all_32_8, % 31.87/5.15 | | all_47_0, all_58_0) = all_137_1 & ( ~ (all_137_0 = 0) | ~ % 31.87/5.15 | | (all_137_1 = 0)) % 31.87/5.15 | | % 31.87/5.15 | | ALPHA: (72) implies: % 31.87/5.15 | | (73) apply(all_32_8, all_47_0, all_58_0) = all_137_1 % 31.87/5.15 | | (74) apply(all_32_8, all_62_0, all_58_0) = all_137_0 % 31.87/5.15 | | % 31.87/5.15 | | REDUCE: (32), (70) imply: % 31.87/5.15 | | (75) ~ (all_47_0 = all_47_1) % 31.87/5.15 | | % 31.87/5.15 | | REDUCE: (32), (74) imply: % 31.87/5.15 | | (76) apply(all_32_8, all_47_1, all_58_0) = all_137_0 % 31.87/5.15 | | % 31.87/5.15 | | BETA: splitting (55) gives: % 31.87/5.15 | | % 31.87/5.15 | | Case 1: % 31.87/5.15 | | | % 31.87/5.15 | | | (77) all_64_0 = all_47_1 % 31.87/5.15 | | | % 31.87/5.15 | | | COMBINE_EQS: (30), (77) imply: % 31.87/5.15 | | | (78) all_47_0 = all_47_1 % 31.87/5.15 | | | % 31.87/5.15 | | | SIMP: (78) implies: % 31.87/5.15 | | | (79) all_47_0 = all_47_1 % 31.87/5.15 | | | % 31.87/5.15 | | | REDUCE: (65), (79) imply: % 31.87/5.15 | | | (80) $false % 31.87/5.15 | | | % 31.87/5.15 | | | CLOSE: (80) is inconsistent. % 31.87/5.15 | | | % 31.87/5.15 | | Case 2: % 31.87/5.15 | | | % 31.87/5.15 | | | (81) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_64_0, all_60_0) % 31.87/5.15 | | | = v1 & apply(all_32_8, all_47_1, all_60_0) = v0 & ( ~ (v1 = 0) | % 31.87/5.15 | | | ~ (v0 = 0))) % 31.87/5.15 | | | % 31.87/5.15 | | | DELTA: instantiating (81) with fresh symbols all_142_0, all_142_1 gives: % 31.87/5.15 | | | (82) apply(all_32_8, all_64_0, all_60_0) = all_142_0 & apply(all_32_8, % 31.87/5.15 | | | all_47_1, all_60_0) = all_142_1 & ( ~ (all_142_0 = 0) | ~ % 31.87/5.15 | | | (all_142_1 = 0)) % 31.87/5.15 | | | % 31.87/5.15 | | | ALPHA: (82) implies: % 31.87/5.15 | | | (83) apply(all_32_8, all_47_1, all_60_0) = all_142_1 % 31.87/5.15 | | | (84) apply(all_32_8, all_64_0, all_60_0) = all_142_0 % 31.87/5.15 | | | (85) ~ (all_142_0 = 0) | ~ (all_142_1 = 0) % 31.87/5.15 | | | % 31.87/5.15 | | | REDUCE: (30), (84) imply: % 31.87/5.15 | | | (86) apply(all_32_8, all_47_0, all_60_0) = all_142_0 % 31.87/5.15 | | | % 31.87/5.15 | | | BETA: splitting (44) gives: % 31.87/5.15 | | | % 31.87/5.15 | | | Case 1: % 31.87/5.15 | | | | % 31.87/5.15 | | | | (87) all_62_0 = all_47_0 % 31.87/5.15 | | | | % 31.87/5.15 | | | | COMBINE_EQS: (32), (87) imply: % 31.87/5.15 | | | | (88) all_47_0 = all_47_1 % 31.87/5.15 | | | | % 31.87/5.15 | | | | REDUCE: (65), (88) imply: % 31.87/5.15 | | | | (89) $false % 31.87/5.15 | | | | % 31.87/5.15 | | | | CLOSE: (89) is inconsistent. % 31.87/5.15 | | | | % 31.87/5.15 | | | Case 2: % 31.87/5.15 | | | | % 31.87/5.15 | | | | (90) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_62_0, % 31.87/5.15 | | | | all_58_0) = v0 & apply(all_32_8, all_47_0, all_58_0) = v1 & % 31.87/5.15 | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.87/5.15 | | | | % 31.87/5.15 | | | | DELTA: instantiating (90) with fresh symbols all_147_0, all_147_1 gives: % 31.87/5.15 | | | | (91) apply(all_32_8, all_62_0, all_58_0) = all_147_1 & % 31.87/5.15 | | | | apply(all_32_8, all_47_0, all_58_0) = all_147_0 & ( ~ (all_147_0 % 31.87/5.15 | | | | = 0) | ~ (all_147_1 = 0)) % 31.87/5.15 | | | | % 31.87/5.15 | | | | ALPHA: (91) implies: % 31.87/5.15 | | | | (92) apply(all_32_8, all_47_0, all_58_0) = all_147_0 % 31.87/5.15 | | | | (93) apply(all_32_8, all_62_0, all_58_0) = all_147_1 % 31.87/5.15 | | | | % 31.87/5.15 | | | | REDUCE: (32), (93) imply: % 31.87/5.15 | | | | (94) apply(all_32_8, all_47_1, all_58_0) = all_147_1 % 31.87/5.15 | | | | % 31.87/5.15 | | | | BETA: splitting (2) gives: % 31.87/5.15 | | | | % 31.87/5.15 | | | | Case 1: % 31.87/5.15 | | | | | % 31.87/5.15 | | | | | (95) all_62_0 = all_47_0 % 31.87/5.15 | | | | | % 31.87/5.15 | | | | | COMBINE_EQS: (32), (95) imply: % 31.87/5.15 | | | | | (96) all_47_0 = all_47_1 % 31.87/5.15 | | | | | % 31.87/5.15 | | | | | REDUCE: (65), (96) imply: % 31.87/5.15 | | | | | (97) $false % 31.87/5.15 | | | | | % 31.87/5.15 | | | | | CLOSE: (97) is inconsistent. % 31.87/5.15 | | | | | % 31.87/5.15 | | | | Case 2: % 31.87/5.15 | | | | | % 31.87/5.15 | | | | | (98) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_62_0, % 31.87/5.15 | | | | | all_60_0) = v1 & apply(all_32_8, all_47_0, all_60_0) = v0 % 31.87/5.15 | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.87/5.15 | | | | | % 31.87/5.15 | | | | | DELTA: instantiating (98) with fresh symbols all_152_0, all_152_1 % 31.87/5.15 | | | | | gives: % 31.87/5.15 | | | | | (99) apply(all_32_8, all_62_0, all_60_0) = all_152_0 & % 31.87/5.15 | | | | | apply(all_32_8, all_47_0, all_60_0) = all_152_1 & ( ~ % 31.87/5.15 | | | | | (all_152_0 = 0) | ~ (all_152_1 = 0)) % 31.87/5.15 | | | | | % 31.87/5.15 | | | | | ALPHA: (99) implies: % 31.87/5.15 | | | | | (100) apply(all_32_8, all_47_0, all_60_0) = all_152_1 % 31.87/5.15 | | | | | (101) apply(all_32_8, all_62_0, all_60_0) = all_152_0 % 31.87/5.15 | | | | | % 31.87/5.15 | | | | | REDUCE: (32), (101) imply: % 31.87/5.15 | | | | | (102) apply(all_32_8, all_47_1, all_60_0) = all_152_0 % 31.87/5.15 | | | | | % 31.87/5.15 | | | | | BETA: splitting (33) gives: % 31.87/5.15 | | | | | % 31.87/5.15 | | | | | Case 1: % 31.87/5.15 | | | | | | % 31.87/5.15 | | | | | | (103) all_64_0 = all_62_0 % 31.87/5.15 | | | | | | % 31.87/5.15 | | | | | | COMBINE_EQS: (30), (103) imply: % 31.87/5.15 | | | | | | (104) all_62_0 = all_47_0 % 31.87/5.15 | | | | | | % 31.87/5.15 | | | | | | COMBINE_EQS: (32), (104) imply: % 31.87/5.15 | | | | | | (105) all_47_0 = all_47_1 % 31.87/5.15 | | | | | | % 31.87/5.15 | | | | | | SIMP: (105) implies: % 31.87/5.15 | | | | | | (106) all_47_0 = all_47_1 % 31.87/5.15 | | | | | | % 31.87/5.15 | | | | | | REDUCE: (65), (106) imply: % 31.87/5.15 | | | | | | (107) $false % 31.87/5.15 | | | | | | % 31.87/5.15 | | | | | | CLOSE: (107) is inconsistent. % 31.87/5.15 | | | | | | % 31.87/5.15 | | | | | Case 2: % 31.87/5.15 | | | | | | % 31.87/5.15 | | | | | | (108) ~ (all_64_0 = all_62_0) % 31.87/5.15 | | | | | | (109) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_64_0, % 31.87/5.15 | | | | | | all_58_0) = v0 & apply(all_32_8, all_62_0, all_58_0) = % 31.87/5.15 | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.87/5.15 | | | | | | % 31.87/5.15 | | | | | | DELTA: instantiating (109) with fresh symbols all_157_0, all_157_1 % 31.87/5.15 | | | | | | gives: % 31.87/5.15 | | | | | | (110) apply(all_32_8, all_64_0, all_58_0) = all_157_1 & % 31.87/5.15 | | | | | | apply(all_32_8, all_62_0, all_58_0) = all_157_0 & ( ~ % 31.87/5.15 | | | | | | (all_157_0 = 0) | ~ (all_157_1 = 0)) % 31.87/5.15 | | | | | | % 31.87/5.15 | | | | | | ALPHA: (110) implies: % 31.87/5.15 | | | | | | (111) apply(all_32_8, all_62_0, all_58_0) = all_157_0 % 31.87/5.15 | | | | | | (112) apply(all_32_8, all_64_0, all_58_0) = all_157_1 % 31.87/5.15 | | | | | | (113) ~ (all_157_0 = 0) | ~ (all_157_1 = 0) % 31.87/5.15 | | | | | | % 31.87/5.15 | | | | | | REDUCE: (30), (112) imply: % 31.87/5.15 | | | | | | (114) apply(all_32_8, all_47_0, all_58_0) = all_157_1 % 31.87/5.15 | | | | | | % 31.87/5.15 | | | | | | REDUCE: (32), (111) imply: % 31.87/5.15 | | | | | | (115) apply(all_32_8, all_47_1, all_58_0) = all_157_0 % 31.87/5.15 | | | | | | % 31.87/5.15 | | | | | | BETA: splitting (58) gives: % 31.87/5.15 | | | | | | % 31.87/5.15 | | | | | | Case 1: % 31.87/5.15 | | | | | | | % 31.87/5.15 | | | | | | | (116) all_62_0 = all_47_0 % 31.87/5.15 | | | | | | | % 31.87/5.15 | | | | | | | COMBINE_EQS: (32), (116) imply: % 31.87/5.15 | | | | | | | (117) all_47_0 = all_47_1 % 31.87/5.15 | | | | | | | % 31.87/5.15 | | | | | | | REDUCE: (65), (117) imply: % 31.87/5.15 | | | | | | | (118) $false % 31.87/5.15 | | | | | | | % 31.87/5.15 | | | | | | | CLOSE: (118) is inconsistent. % 31.87/5.15 | | | | | | | % 31.87/5.15 | | | | | | Case 2: % 31.87/5.15 | | | | | | | % 31.87/5.15 | | | | | | | (119) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.87/5.15 | | | | | | | (apply(all_32_8, all_62_0, all_58_0) = v2 & % 31.87/5.15 | | | | | | | member(all_58_0, all_32_3) = v1 & member(all_47_0, % 31.87/5.15 | | | | | | | all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 % 31.87/5.15 | | | | | | | = 0))) % 31.87/5.15 | | | | | | | % 31.87/5.15 | | | | | | | DELTA: instantiating (119) with fresh symbols all_162_0, % 31.87/5.15 | | | | | | | all_162_1, all_162_2 gives: % 31.87/5.15 | | | | | | | (120) apply(all_32_8, all_62_0, all_58_0) = all_162_0 & % 31.87/5.15 | | | | | | | member(all_58_0, all_32_3) = all_162_1 & member(all_47_0, % 31.87/5.15 | | | | | | | all_32_4) = all_162_2 & ( ~ (all_162_0 = 0) | ~ % 31.87/5.15 | | | | | | | (all_162_1 = 0) | ~ (all_162_2 = 0)) % 31.87/5.15 | | | | | | | % 31.87/5.15 | | | | | | | ALPHA: (120) implies: % 31.87/5.15 | | | | | | | (121) member(all_47_0, all_32_4) = all_162_2 % 31.87/5.15 | | | | | | | (122) member(all_58_0, all_32_3) = all_162_1 % 31.87/5.15 | | | | | | | (123) apply(all_32_8, all_62_0, all_58_0) = all_162_0 % 31.87/5.15 | | | | | | | % 31.87/5.15 | | | | | | | REDUCE: (32), (123) imply: % 31.87/5.15 | | | | | | | (124) apply(all_32_8, all_47_1, all_58_0) = all_162_0 % 31.87/5.15 | | | | | | | % 31.87/5.15 | | | | | | | BETA: splitting (49) gives: % 31.87/5.15 | | | | | | | % 31.87/5.15 | | | | | | | Case 1: % 31.87/5.15 | | | | | | | | % 31.87/5.15 | | | | | | | | (125) all_47_0 = all_47_1 % 31.87/5.15 | | | | | | | | % 31.87/5.15 | | | | | | | | REDUCE: (65), (125) imply: % 31.87/5.15 | | | | | | | | (126) $false % 31.87/5.15 | | | | | | | | % 31.87/5.15 | | | | | | | | CLOSE: (126) is inconsistent. % 31.87/5.15 | | | | | | | | % 31.87/5.15 | | | | | | | Case 2: % 31.87/5.15 | | | | | | | | % 31.87/5.15 | | | | | | | | (127) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.87/5.15 | | | | | | | | (apply(all_32_8, all_47_0, all_60_0) = v2 & % 31.87/5.15 | | | | | | | | member(all_60_0, all_32_3) = v1 & member(all_47_1, % 31.87/5.15 | | | | | | | | all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 31.87/5.15 | | | | | | | | (v0 = 0))) % 31.87/5.15 | | | | | | | | % 31.87/5.15 | | | | | | | | DELTA: instantiating (127) with fresh symbols all_167_0, % 31.87/5.15 | | | | | | | | all_167_1, all_167_2 gives: % 31.87/5.15 | | | | | | | | (128) apply(all_32_8, all_47_0, all_60_0) = all_167_0 & % 31.87/5.15 | | | | | | | | member(all_60_0, all_32_3) = all_167_1 & % 31.87/5.15 | | | | | | | | member(all_47_1, all_32_4) = all_167_2 & ( ~ (all_167_0 % 31.87/5.15 | | | | | | | | = 0) | ~ (all_167_1 = 0) | ~ (all_167_2 = 0)) % 31.87/5.16 | | | | | | | | % 31.87/5.16 | | | | | | | | ALPHA: (128) implies: % 31.87/5.16 | | | | | | | | (129) member(all_47_1, all_32_4) = all_167_2 % 31.87/5.16 | | | | | | | | (130) member(all_60_0, all_32_3) = all_167_1 % 31.87/5.16 | | | | | | | | (131) apply(all_32_8, all_47_0, all_60_0) = all_167_0 % 31.87/5.16 | | | | | | | | % 31.87/5.16 | | | | | | | | BETA: splitting (40) gives: % 31.87/5.16 | | | | | | | | % 31.87/5.16 | | | | | | | | Case 1: % 31.87/5.16 | | | | | | | | | % 31.87/5.16 | | | | | | | | | (132) all_47_0 = all_47_1 % 31.87/5.16 | | | | | | | | | % 31.87/5.16 | | | | | | | | | REDUCE: (65), (132) imply: % 31.87/5.16 | | | | | | | | | (133) $false % 31.87/5.16 | | | | | | | | | % 31.87/5.16 | | | | | | | | | CLOSE: (133) is inconsistent. % 31.87/5.16 | | | | | | | | | % 31.87/5.16 | | | | | | | | Case 2: % 31.87/5.16 | | | | | | | | | % 31.87/5.16 | | | | | | | | | (134) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.87/5.16 | | | | | | | | | (apply(all_32_8, all_47_1, all_58_0) = v2 & % 31.87/5.16 | | | | | | | | | member(all_58_0, all_32_3) = v1 & member(all_47_0, % 31.87/5.16 | | | | | | | | | all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 31.87/5.16 | | | | | | | | | (v0 = 0))) % 31.87/5.16 | | | | | | | | | % 31.87/5.16 | | | | | | | | | DELTA: instantiating (134) with fresh symbols all_172_0, % 31.87/5.16 | | | | | | | | | all_172_1, all_172_2 gives: % 31.87/5.16 | | | | | | | | | (135) apply(all_32_8, all_47_1, all_58_0) = all_172_0 & % 31.87/5.16 | | | | | | | | | member(all_58_0, all_32_3) = all_172_1 & % 31.87/5.16 | | | | | | | | | member(all_47_0, all_32_4) = all_172_2 & ( ~ % 31.87/5.16 | | | | | | | | | (all_172_0 = 0) | ~ (all_172_1 = 0) | ~ % 31.87/5.16 | | | | | | | | | (all_172_2 = 0)) % 31.87/5.16 | | | | | | | | | % 31.87/5.16 | | | | | | | | | ALPHA: (135) implies: % 31.87/5.16 | | | | | | | | | (136) member(all_47_0, all_32_4) = all_172_2 % 31.87/5.16 | | | | | | | | | (137) member(all_58_0, all_32_3) = all_172_1 % 31.87/5.16 | | | | | | | | | (138) apply(all_32_8, all_47_1, all_58_0) = all_172_0 % 31.87/5.16 | | | | | | | | | (139) ~ (all_172_0 = 0) | ~ (all_172_1 = 0) | ~ % 31.87/5.16 | | | | | | | | | (all_172_2 = 0) % 31.87/5.16 | | | | | | | | | % 31.87/5.16 | | | | | | | | | BETA: splitting (59) gives: % 31.87/5.16 | | | | | | | | | % 31.87/5.16 | | | | | | | | | Case 1: % 31.87/5.16 | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | (140) all_64_0 = all_47_1 % 31.87/5.16 | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | COMBINE_EQS: (30), (140) imply: % 31.87/5.16 | | | | | | | | | | (141) all_47_0 = all_47_1 % 31.87/5.16 | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | SIMP: (141) implies: % 31.87/5.16 | | | | | | | | | | (142) all_47_0 = all_47_1 % 31.87/5.16 | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | REDUCE: (65), (142) imply: % 31.87/5.16 | | | | | | | | | | (143) $false % 31.87/5.16 | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | CLOSE: (143) is inconsistent. % 31.87/5.16 | | | | | | | | | | % 31.87/5.16 | | | | | | | | | Case 2: % 31.87/5.16 | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | (144) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.87/5.16 | | | | | | | | | | (apply(all_32_8, all_64_0, all_60_0) = v2 & % 31.87/5.16 | | | | | | | | | | member(all_60_0, all_32_3) = v1 & % 31.87/5.16 | | | | | | | | | | member(all_47_1, all_32_4) = v0 & ( ~ (v2 = 0) | % 31.87/5.16 | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 31.87/5.16 | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | DELTA: instantiating (144) with fresh symbols all_177_0, % 31.87/5.16 | | | | | | | | | | all_177_1, all_177_2 gives: % 31.87/5.16 | | | | | | | | | | (145) apply(all_32_8, all_64_0, all_60_0) = all_177_0 & % 31.87/5.16 | | | | | | | | | | member(all_60_0, all_32_3) = all_177_1 & % 31.87/5.16 | | | | | | | | | | member(all_47_1, all_32_4) = all_177_2 & ( ~ % 31.87/5.16 | | | | | | | | | | (all_177_0 = 0) | ~ (all_177_1 = 0) | ~ % 31.87/5.16 | | | | | | | | | | (all_177_2 = 0)) % 31.87/5.16 | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | ALPHA: (145) implies: % 31.87/5.16 | | | | | | | | | | (146) member(all_47_1, all_32_4) = all_177_2 % 31.87/5.16 | | | | | | | | | | (147) member(all_60_0, all_32_3) = all_177_1 % 31.87/5.16 | | | | | | | | | | (148) apply(all_32_8, all_64_0, all_60_0) = all_177_0 % 31.87/5.16 | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | REDUCE: (30), (148) imply: % 31.87/5.16 | | | | | | | | | | (149) apply(all_32_8, all_47_0, all_60_0) = all_177_0 % 31.87/5.16 | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | BETA: splitting (24) gives: % 31.87/5.16 | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | Case 1: % 31.87/5.16 | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | (150) all_47_0 = all_47_1 % 31.87/5.16 | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | REDUCE: (65), (150) imply: % 31.87/5.16 | | | | | | | | | | | (151) $false % 31.87/5.16 | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | CLOSE: (151) is inconsistent. % 31.87/5.16 | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | Case 2: % 31.87/5.16 | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | (152) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.87/5.16 | | | | | | | | | | | all_47_0, all_58_0) = v0 & apply(all_32_8, % 31.87/5.16 | | | | | | | | | | | all_47_1, all_58_0) = v1 & ( ~ (v1 = 0) | ~ % 31.87/5.16 | | | | | | | | | | | (v0 = 0))) % 31.87/5.16 | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | DELTA: instantiating (152) with fresh symbols all_182_0, % 31.87/5.16 | | | | | | | | | | | all_182_1 gives: % 31.87/5.16 | | | | | | | | | | | (153) apply(all_32_8, all_47_0, all_58_0) = all_182_1 & % 31.87/5.16 | | | | | | | | | | | apply(all_32_8, all_47_1, all_58_0) = all_182_0 & % 31.87/5.16 | | | | | | | | | | | ( ~ (all_182_0 = 0) | ~ (all_182_1 = 0)) % 31.87/5.16 | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | ALPHA: (153) implies: % 31.87/5.16 | | | | | | | | | | | (154) apply(all_32_8, all_47_1, all_58_0) = all_182_0 % 31.87/5.16 | | | | | | | | | | | (155) apply(all_32_8, all_47_0, all_58_0) = all_182_1 % 31.87/5.16 | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | BETA: splitting (14) gives: % 31.87/5.16 | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | Case 1: % 31.87/5.16 | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | (156) all_64_0 = all_62_0 % 31.87/5.16 | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | COMBINE_EQS: (30), (156) imply: % 31.87/5.16 | | | | | | | | | | | | (157) all_62_0 = all_47_0 % 31.87/5.16 | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | COMBINE_EQS: (32), (157) imply: % 31.87/5.16 | | | | | | | | | | | | (158) all_47_0 = all_47_1 % 31.87/5.16 | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | SIMP: (158) implies: % 31.87/5.16 | | | | | | | | | | | | (159) all_47_0 = all_47_1 % 31.87/5.16 | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | REDUCE: (65), (159) imply: % 31.87/5.16 | | | | | | | | | | | | (160) $false % 31.87/5.16 | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | CLOSE: (160) is inconsistent. % 31.87/5.16 | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | Case 2: % 31.87/5.16 | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | (161) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.87/5.16 | | | | | | | | | | | | all_64_0, all_58_0) = v1 & apply(all_32_8, % 31.87/5.16 | | | | | | | | | | | | all_62_0, all_58_0) = v0 & ( ~ (v1 = 0) | ~ % 31.87/5.16 | | | | | | | | | | | | (v0 = 0))) % 31.87/5.16 | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | DELTA: instantiating (161) with fresh symbols all_187_0, % 31.87/5.16 | | | | | | | | | | | | all_187_1 gives: % 31.87/5.16 | | | | | | | | | | | | (162) apply(all_32_8, all_64_0, all_58_0) = all_187_0 & % 31.87/5.16 | | | | | | | | | | | | apply(all_32_8, all_62_0, all_58_0) = all_187_1 & % 31.87/5.16 | | | | | | | | | | | | ( ~ (all_187_0 = 0) | ~ (all_187_1 = 0)) % 31.87/5.16 | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | ALPHA: (162) implies: % 31.87/5.16 | | | | | | | | | | | | (163) apply(all_32_8, all_62_0, all_58_0) = all_187_1 % 31.87/5.16 | | | | | | | | | | | | (164) apply(all_32_8, all_64_0, all_58_0) = all_187_0 % 31.87/5.16 | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | REDUCE: (30), (164) imply: % 31.87/5.16 | | | | | | | | | | | | (165) apply(all_32_8, all_47_0, all_58_0) = all_187_0 % 31.87/5.16 | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | REDUCE: (32), (163) imply: % 31.87/5.16 | | | | | | | | | | | | (166) apply(all_32_8, all_47_1, all_58_0) = all_187_1 % 31.87/5.16 | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | BETA: splitting (60) gives: % 31.87/5.16 | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | Case 1: % 31.87/5.16 | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | (167) all_64_0 = all_47_1 % 31.87/5.16 | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | COMBINE_EQS: (30), (167) imply: % 31.87/5.16 | | | | | | | | | | | | | (168) all_47_0 = all_47_1 % 31.87/5.16 | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | SIMP: (168) implies: % 31.87/5.16 | | | | | | | | | | | | | (169) all_47_0 = all_47_1 % 31.87/5.16 | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | REDUCE: (65), (169) imply: % 31.87/5.16 | | | | | | | | | | | | | (170) $false % 31.87/5.16 | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | CLOSE: (170) is inconsistent. % 31.87/5.16 | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | Case 2: % 31.87/5.16 | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | (171) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.87/5.16 | | | | | | | | | | | | | all_64_0, all_58_0) = v0 & apply(all_32_8, % 31.87/5.16 | | | | | | | | | | | | | all_47_1, all_58_0) = v1 & ( ~ (v1 = 0) | ~ % 31.87/5.16 | | | | | | | | | | | | | (v0 = 0))) % 31.87/5.16 | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | DELTA: instantiating (171) with fresh symbols all_192_0, % 31.87/5.16 | | | | | | | | | | | | | all_192_1 gives: % 31.87/5.16 | | | | | | | | | | | | | (172) apply(all_32_8, all_64_0, all_58_0) = all_192_1 & % 31.87/5.16 | | | | | | | | | | | | | apply(all_32_8, all_47_1, all_58_0) = all_192_0 & % 31.87/5.16 | | | | | | | | | | | | | ( ~ (all_192_0 = 0) | ~ (all_192_1 = 0)) % 31.87/5.16 | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | ALPHA: (172) implies: % 31.87/5.16 | | | | | | | | | | | | | (173) apply(all_32_8, all_47_1, all_58_0) = all_192_0 % 31.87/5.16 | | | | | | | | | | | | | (174) apply(all_32_8, all_64_0, all_58_0) = all_192_1 % 31.87/5.16 | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | REDUCE: (30), (174) imply: % 31.87/5.16 | | | | | | | | | | | | | (175) apply(all_32_8, all_47_0, all_58_0) = all_192_1 % 31.87/5.16 | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | BETA: splitting (9) gives: % 31.87/5.16 | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | Case 1: % 31.87/5.16 | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | (176) all_64_0 = all_47_1 % 31.87/5.16 | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | COMBINE_EQS: (30), (176) imply: % 31.87/5.16 | | | | | | | | | | | | | | (177) all_47_0 = all_47_1 % 31.87/5.16 | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | SIMP: (177) implies: % 31.87/5.16 | | | | | | | | | | | | | | (178) all_47_0 = all_47_1 % 31.87/5.16 | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | REDUCE: (65), (178) imply: % 31.87/5.16 | | | | | | | | | | | | | | (179) $false % 31.87/5.16 | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | CLOSE: (179) is inconsistent. % 31.87/5.16 | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | Case 2: % 31.87/5.16 | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | (180) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.87/5.16 | | | | | | | | | | | | | | all_64_0, all_58_0) = v1 & apply(all_32_8, % 31.87/5.16 | | | | | | | | | | | | | | all_47_1, all_58_0) = v0 & ( ~ (v1 = 0) | ~ % 31.87/5.16 | | | | | | | | | | | | | | (v0 = 0))) % 31.87/5.16 | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | DELTA: instantiating (180) with fresh symbols all_197_0, % 31.87/5.16 | | | | | | | | | | | | | | all_197_1 gives: % 31.87/5.16 | | | | | | | | | | | | | | (181) apply(all_32_8, all_64_0, all_58_0) = all_197_0 & % 31.87/5.16 | | | | | | | | | | | | | | apply(all_32_8, all_47_1, all_58_0) = all_197_1 & % 31.87/5.16 | | | | | | | | | | | | | | ( ~ (all_197_0 = 0) | ~ (all_197_1 = 0)) % 31.87/5.16 | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | ALPHA: (181) implies: % 31.87/5.16 | | | | | | | | | | | | | | (182) apply(all_32_8, all_47_1, all_58_0) = all_197_1 % 31.87/5.16 | | | | | | | | | | | | | | (183) apply(all_32_8, all_64_0, all_58_0) = all_197_0 % 31.87/5.16 | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | REDUCE: (30), (183) imply: % 31.87/5.16 | | | | | | | | | | | | | | (184) apply(all_32_8, all_47_0, all_58_0) = all_197_0 % 31.87/5.16 | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | BETA: splitting (17) gives: % 31.87/5.16 | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | Case 1: % 31.87/5.16 | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | (185) all_62_0 = all_47_0 % 31.87/5.16 | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | COMBINE_EQS: (32), (185) imply: % 31.87/5.16 | | | | | | | | | | | | | | | (186) all_47_0 = all_47_1 % 31.87/5.16 | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | REDUCE: (65), (186) imply: % 31.87/5.16 | | | | | | | | | | | | | | | (187) $false % 31.87/5.16 | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | CLOSE: (187) is inconsistent. % 31.87/5.16 | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | Case 2: % 31.87/5.16 | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | (188) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.87/5.16 | | | | | | | | | | | | | | | all_62_0, all_60_0) = v0 & apply(all_32_8, % 31.87/5.16 | | | | | | | | | | | | | | | all_47_0, all_60_0) = v1 & ( ~ (v1 = 0) | ~ % 31.87/5.16 | | | | | | | | | | | | | | | (v0 = 0))) % 31.87/5.16 | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | DELTA: instantiating (188) with fresh symbols all_202_0, % 31.87/5.16 | | | | | | | | | | | | | | | all_202_1 gives: % 31.87/5.16 | | | | | | | | | | | | | | | (189) apply(all_32_8, all_62_0, all_60_0) = all_202_1 & % 31.87/5.16 | | | | | | | | | | | | | | | apply(all_32_8, all_47_0, all_60_0) = all_202_0 & % 31.87/5.16 | | | | | | | | | | | | | | | ( ~ (all_202_0 = 0) | ~ (all_202_1 = 0)) % 31.87/5.16 | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | ALPHA: (189) implies: % 31.87/5.16 | | | | | | | | | | | | | | | (190) apply(all_32_8, all_47_0, all_60_0) = all_202_0 % 31.87/5.16 | | | | | | | | | | | | | | | (191) apply(all_32_8, all_62_0, all_60_0) = all_202_1 % 31.87/5.16 | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | REDUCE: (32), (191) imply: % 31.87/5.16 | | | | | | | | | | | | | | | (192) apply(all_32_8, all_47_1, all_60_0) = all_202_1 % 31.87/5.16 | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | BETA: splitting (52) gives: % 31.87/5.16 | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | Case 1: % 31.87/5.16 | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | | (193) all_47_0 = all_47_1 % 31.87/5.16 | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | | REDUCE: (65), (193) imply: % 31.87/5.16 | | | | | | | | | | | | | | | | (194) $false % 31.87/5.16 | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | | CLOSE: (194) is inconsistent. % 31.87/5.16 | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | Case 2: % 31.87/5.16 | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | | (195) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.87/5.16 | | | | | | | | | | | | | | | | all_47_0, all_58_0) = v1 & apply(all_32_8, % 31.87/5.16 | | | | | | | | | | | | | | | | all_47_1, all_58_0) = v0 & ( ~ (v1 = 0) | ~ % 31.87/5.16 | | | | | | | | | | | | | | | | (v0 = 0))) % 31.87/5.16 | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | | DELTA: instantiating (195) with fresh symbols all_207_0, % 31.87/5.16 | | | | | | | | | | | | | | | | all_207_1 gives: % 31.87/5.16 | | | | | | | | | | | | | | | | (196) apply(all_32_8, all_47_0, all_58_0) = all_207_0 & % 31.87/5.16 | | | | | | | | | | | | | | | | apply(all_32_8, all_47_1, all_58_0) = all_207_1 & % 31.87/5.16 | | | | | | | | | | | | | | | | ( ~ (all_207_0 = 0) | ~ (all_207_1 = 0)) % 31.87/5.16 | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | | ALPHA: (196) implies: % 31.87/5.16 | | | | | | | | | | | | | | | | (197) apply(all_32_8, all_47_1, all_58_0) = all_207_1 % 31.87/5.16 | | | | | | | | | | | | | | | | (198) apply(all_32_8, all_47_0, all_58_0) = all_207_0 % 31.87/5.16 | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | | BETA: splitting (8) gives: % 31.87/5.16 | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | | Case 1: % 31.87/5.16 | | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | | | (199) all_64_0 = all_62_0 % 31.87/5.16 | | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (199) imply: % 31.87/5.16 | | | | | | | | | | | | | | | | | (200) all_62_0 = all_47_0 % 31.87/5.16 | | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (200) imply: % 31.87/5.16 | | | | | | | | | | | | | | | | | (201) all_47_0 = all_47_1 % 31.87/5.16 | | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | | | SIMP: (201) implies: % 31.87/5.16 | | | | | | | | | | | | | | | | | (202) all_47_0 = all_47_1 % 31.87/5.16 | | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | | | REDUCE: (65), (202) imply: % 31.87/5.16 | | | | | | | | | | | | | | | | | (203) $false % 31.87/5.16 | | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | | | CLOSE: (203) is inconsistent. % 31.87/5.16 | | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | | Case 2: % 31.87/5.16 | | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | | | (204) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.87/5.16 | | | | | | | | | | | | | | | | | all_64_0, all_60_0) = v0 & apply(all_32_8, % 31.87/5.16 | | | | | | | | | | | | | | | | | all_62_0, all_60_0) = v1 & ( ~ (v1 = 0) | ~ % 31.87/5.16 | | | | | | | | | | | | | | | | | (v0 = 0))) % 31.87/5.16 | | | | | | | | | | | | | | | | | % 31.87/5.16 | | | | | | | | | | | | | | | | | DELTA: instantiating (204) with fresh symbols all_212_0, % 31.87/5.16 | | | | | | | | | | | | | | | | | all_212_1 gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | (205) apply(all_32_8, all_64_0, all_60_0) = all_212_1 & % 31.87/5.17 | | | | | | | | | | | | | | | | | apply(all_32_8, all_62_0, all_60_0) = all_212_0 & % 31.87/5.17 | | | | | | | | | | | | | | | | | ( ~ (all_212_0 = 0) | ~ (all_212_1 = 0)) % 31.87/5.17 | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | ALPHA: (205) implies: % 31.87/5.17 | | | | | | | | | | | | | | | | | (206) apply(all_32_8, all_62_0, all_60_0) = all_212_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | (207) apply(all_32_8, all_64_0, all_60_0) = all_212_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | REDUCE: (30), (207) imply: % 31.87/5.17 | | | | | | | | | | | | | | | | | (208) apply(all_32_8, all_47_0, all_60_0) = all_212_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | REDUCE: (32), (206) imply: % 31.87/5.17 | | | | | | | | | | | | | | | | | (209) apply(all_32_8, all_47_1, all_60_0) = all_212_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | BETA: splitting (56) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.17 | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | (210) all_64_0 = all_62_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (210) imply: % 31.87/5.17 | | | | | | | | | | | | | | | | | | (211) all_62_0 = all_47_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (211) imply: % 31.87/5.17 | | | | | | | | | | | | | | | | | | (212) all_47_0 = all_47_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | SIMP: (212) implies: % 31.87/5.17 | | | | | | | | | | | | | | | | | | (213) all_47_0 = all_47_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | REDUCE: (65), (213) imply: % 31.87/5.17 | | | | | | | | | | | | | | | | | | (214) $false % 31.87/5.17 | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | CLOSE: (214) is inconsistent. % 31.87/5.17 | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.17 | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | (215) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.87/5.17 | | | | | | | | | | | | | | | | | | all_64_0, all_60_0) = v1 & apply(all_32_8, % 31.87/5.17 | | | | | | | | | | | | | | | | | | all_62_0, all_60_0) = v0 & ( ~ (v1 = 0) | ~ % 31.87/5.17 | | | | | | | | | | | | | | | | | | (v0 = 0))) % 31.87/5.17 | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | DELTA: instantiating (215) with fresh symbols all_217_0, % 31.87/5.17 | | | | | | | | | | | | | | | | | | all_217_1 gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | (216) apply(all_32_8, all_64_0, all_60_0) = all_217_0 & % 31.87/5.17 | | | | | | | | | | | | | | | | | | apply(all_32_8, all_62_0, all_60_0) = all_217_1 & % 31.87/5.17 | | | | | | | | | | | | | | | | | | ( ~ (all_217_0 = 0) | ~ (all_217_1 = 0)) % 31.87/5.17 | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | ALPHA: (216) implies: % 31.87/5.17 | | | | | | | | | | | | | | | | | | (217) apply(all_32_8, all_62_0, all_60_0) = all_217_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | (218) apply(all_32_8, all_64_0, all_60_0) = all_217_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | REDUCE: (30), (218) imply: % 31.87/5.17 | | | | | | | | | | | | | | | | | | (219) apply(all_32_8, all_47_0, all_60_0) = all_217_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | REDUCE: (32), (217) imply: % 31.87/5.17 | | | | | | | | | | | | | | | | | | (220) apply(all_32_8, all_47_1, all_60_0) = all_217_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | (221) all_47_0 = all_47_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | REDUCE: (65), (221) imply: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | (222) $false % 31.87/5.17 | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | CLOSE: (222) is inconsistent. % 31.87/5.17 | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | (223) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | all_47_0, all_60_0) = v0 & apply(all_32_8, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | all_47_1, all_60_0) = v1 & ( ~ (v1 = 0) | ~ % 31.87/5.17 | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 31.87/5.17 | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (223) with fresh symbols all_222_0, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | all_222_1 gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | (224) apply(all_32_8, all_47_0, all_60_0) = all_222_1 & % 31.87/5.17 | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_47_1, all_60_0) = all_222_0 & % 31.87/5.17 | | | | | | | | | | | | | | | | | | | ( ~ (all_222_0 = 0) | ~ (all_222_1 = 0)) % 31.87/5.17 | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | ALPHA: (224) implies: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | (225) apply(all_32_8, all_47_1, all_60_0) = all_222_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | (226) apply(all_32_8, all_47_0, all_60_0) = all_222_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | BETA: splitting (54) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (227) all_47_0 = all_47_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | REDUCE: (65), (227) imply: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (228) $false % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | CLOSE: (228) is inconsistent. % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (229) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_47_0, all_60_0) = v1 & apply(all_32_8, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_47_1, all_60_0) = v0 & ( ~ (v1 = 0) | ~ % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (229) with fresh symbols all_227_0, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_227_1 gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (230) apply(all_32_8, all_47_0, all_60_0) = all_227_0 & % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_47_1, all_60_0) = all_227_1 & % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | ( ~ (all_227_0 = 0) | ~ (all_227_1 = 0)) % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (231) apply(all_32_8, all_47_1, all_60_0) = all_227_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (232) apply(all_32_8, all_47_0, all_60_0) = all_227_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_177_2, all_32_4, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_47_1, simplifying with (47), (146) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (233) all_177_2 = 0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_167_2, all_177_2, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_32_4, all_47_1, simplifying with (129), (146) % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (234) all_177_2 = all_167_2 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_172_2, all_32_4, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_47_0, simplifying with (34), (136) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (235) all_172_2 = 0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_162_2, all_172_2, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_32_4, all_47_0, simplifying with (121), (136) % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (236) all_172_2 = all_162_2 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_172_1, all_32_3, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_58_0, simplifying with (43), (137) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (237) all_172_1 = 0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_162_1, all_172_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_32_3, all_58_0, simplifying with (122), (137) % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (238) all_172_1 = all_162_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_177_1, all_32_3, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_60_0, simplifying with (39), (147) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (239) all_177_1 = 0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_167_1, all_177_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_32_3, all_60_0, simplifying with (130), (147) % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (240) all_177_1 = all_167_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_162_0, all_172_0, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_58_0, all_47_1, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (124), (138) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (241) all_172_0 = all_162_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_137_0, all_172_0, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_58_0, all_47_1, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (76), (138) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (242) all_172_0 = all_137_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_172_0, all_182_0, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_58_0, all_47_1, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (138), (154) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (243) all_182_0 = all_172_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_172_0, all_192_0, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_58_0, all_47_1, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (138), (173) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (244) all_192_0 = all_172_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_157_0, all_192_0, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_58_0, all_47_1, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (115), (173) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (245) all_192_0 = all_157_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_182_0, all_197_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_58_0, all_47_1, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (154), (182) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (246) all_197_1 = all_182_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_147_1, all_197_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_58_0, all_47_1, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (94), (182) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (247) all_197_1 = all_147_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_197_1, all_207_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_58_0, all_47_1, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (182), (197) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (248) all_207_1 = all_197_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_187_1, all_207_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_58_0, all_47_1, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (166), (197) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (249) all_207_1 = all_187_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_152_0, all_202_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_60_0, all_47_1, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (102), (192) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (250) all_202_1 = all_152_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_202_1, all_212_0, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_60_0, all_47_1, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (192), (209) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (251) all_212_0 = all_202_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_212_0, all_217_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_60_0, all_47_1, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (209), (220) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (252) all_217_1 = all_212_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_132_0, all_217_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_60_0, all_47_1, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (63), (220) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (253) all_217_1 = all_132_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_222_0, all_60_0, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_47_1, all_32_8, simplifying with (4), (225) % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (254) all_222_0 = 0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_152_0, all_222_0, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_60_0, all_47_1, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (102), (225) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (255) all_222_0 = all_152_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_222_0, all_227_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_60_0, all_47_1, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (225), (231) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (256) all_227_1 = all_222_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_142_1, all_227_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_60_0, all_47_1, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (83), (231) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (257) all_227_1 = all_142_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_147_0, all_58_0, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_47_0, all_32_8, simplifying with (25), (92) % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (258) all_147_0 = 0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_147_0, all_182_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_58_0, all_47_0, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (92), (155) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (259) all_182_1 = all_147_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_182_1, all_187_0, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_58_0, all_47_0, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (155), (165) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (260) all_187_0 = all_182_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_182_1, all_192_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_58_0, all_47_0, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (155), (175) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (261) all_192_1 = all_182_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_157_1, all_192_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_58_0, all_47_0, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (114), (175) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (262) all_192_1 = all_157_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_197_0, all_207_0, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_58_0, all_47_0, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (184), (198) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (263) all_207_0 = all_197_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_187_0, all_207_0, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_58_0, all_47_0, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (165), (198) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (264) all_207_0 = all_187_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_137_1, all_207_0, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_58_0, all_47_0, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (73), (198) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (265) all_207_0 = all_137_1 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_142_0, all_177_0, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_60_0, all_47_0, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (86), (149) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (266) all_177_0 = all_142_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_202_0, all_212_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_60_0, all_47_0, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (190), (208) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (267) all_212_1 = all_202_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_177_0, all_212_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_60_0, all_47_0, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (149), (208) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (268) all_212_1 = all_177_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_167_0, all_212_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_60_0, all_47_0, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (131), (208) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (269) all_212_1 = all_167_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_217_0, all_222_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_60_0, all_47_0, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (219), (226) gives: % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (270) all_222_1 = all_217_0 % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_177_0, all_222_1, % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | all_60_0, all_47_0, all_32_8, simplifying with % 31.87/5.17 | | | | | | | | | | | | | | | | | | | | (149), (226) gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (271) all_222_1 = all_177_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_152_1, all_222_1, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | all_60_0, all_47_0, all_32_8, simplifying with % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (100), (226) gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (272) all_222_1 = all_152_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_202_0, all_227_0, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | all_60_0, all_47_0, all_32_8, simplifying with % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (190), (232) gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (273) all_227_0 = all_202_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_132_1, all_227_0, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | all_60_0, all_47_0, all_32_8, simplifying with % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (66), (232) gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (274) all_227_0 = all_132_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (274) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (275) all_202_0 = all_132_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (275) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (276) all_202_0 = all_132_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (257) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (277) all_222_0 = all_142_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (277) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (278) all_222_0 = all_142_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (278) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (279) all_152_0 = all_142_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (279) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (280) all_152_0 = all_142_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (278) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (281) all_142_1 = 0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (271) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (282) all_217_0 = all_177_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (272) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (283) all_217_0 = all_152_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (283) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (284) all_177_0 = all_152_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (284) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (285) all_177_0 = all_152_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (253) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (286) all_212_0 = all_132_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (286) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (287) all_212_0 = all_132_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (287) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (288) all_202_1 = all_132_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (288) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (289) all_202_1 = all_132_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (269) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (290) all_177_0 = all_167_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (290) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (291) all_177_0 = all_167_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (269) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (292) all_202_0 = all_167_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (292) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (293) all_202_0 = all_167_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (264) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (294) all_197_0 = all_187_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (265) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (295) all_197_0 = all_137_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (249) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (296) all_197_1 = all_187_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (296) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (297) all_197_1 = all_187_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (293) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (298) all_167_0 = all_132_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (298) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (299) all_167_0 = all_132_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (289) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (300) all_152_0 = all_132_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (300) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (301) all_152_0 = all_132_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (294), (295) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (302) all_187_0 = all_137_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (302) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (303) all_187_0 = all_137_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (297) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (304) all_187_1 = all_182_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (297) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (305) all_187_1 = all_147_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (245) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (306) all_172_0 = all_157_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (306) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (307) all_172_0 = all_157_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (262) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (308) all_182_1 = all_157_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (308) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (309) all_182_1 = all_157_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (303) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (310) all_182_1 = all_137_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (310) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (311) all_182_1 = all_137_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (305) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (312) all_182_0 = all_147_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (312) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (313) all_182_0 = all_147_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (243), (313) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (314) all_172_0 = all_147_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (314) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (315) all_172_0 = all_147_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (309) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (316) all_157_1 = all_147_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (311) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (317) all_157_1 = all_137_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (285) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (318) all_152_1 = all_142_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (285), (291) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (319) all_167_0 = all_152_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (319) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (320) all_167_0 = all_152_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (240) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (321) all_167_1 = 0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (233), (234) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (322) all_167_2 = 0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (322) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (323) all_167_2 = 0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (241), (315) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (324) all_162_0 = all_147_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (241), (242) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (325) all_162_0 = all_137_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (241), (307) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (326) all_162_0 = all_157_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (237), (238) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (327) all_162_1 = 0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (235), (236) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (328) all_162_2 = 0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (320) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (329) all_152_1 = all_132_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (329) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (330) all_152_1 = all_132_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (324), (326) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (331) all_157_0 = all_147_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (325), (326) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (332) all_157_0 = all_137_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (332) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (333) all_147_1 = all_137_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (317) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (334) all_147_0 = all_137_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (334) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (335) all_147_0 = all_137_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (301) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (336) all_142_1 = all_132_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | SIMP: (336) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (337) all_142_1 = all_132_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (318), (330) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (338) all_142_0 = all_132_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (335) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (339) all_137_1 = 0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (337) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (340) all_132_0 = 0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (317), (339) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | (341) all_157_1 = 0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | (342) ~ (all_142_0 = 0) % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | REDUCE: (338), (342) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | (343) ~ (all_132_1 = 0) % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (139) gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with all_32_2, all_32_1, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | all_32_5, all_32_3, all_47_2, all_116_0, all_60_0, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | simplifying with (3), (6), (16), (18), (21), (22), % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | (38), (39), (50), (51), (53) gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | (344) all_116_0 = all_60_0 | ? [v0: any] : ? [v1: any] % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_1, all_47_2, all_60_0) = v1 & % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | apply(all_32_2, all_47_2, all_116_0) = v0 & ( ~ % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_32_8, all_32_4, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | all_32_3, all_47_0, all_116_0, all_58_0, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | simplifying with (3), (7), (12), (16), (20), (21), % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | (26), (34), (43), (57) gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | (345) all_116_0 = all_58_0 | ? [v0: any] : ? [v1: any] % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_8, all_47_0, all_116_0) = v0 & % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_47_0, all_58_0) = v1 & ( ~ % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (45) with all_32_8, all_32_4, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | all_32_3, all_47_0, all_47_1, all_116_0, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | simplifying with (3), (12), (16), (20), (21), % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | (34), (41), (47), (57), (61) gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | (346) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | : (apply(all_32_8, all_47_0, all_116_0) = v0 & % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_47_1, all_116_0) = v1 & ( ~ % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_32_8, all_32_4, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | all_32_3, all_47_1, all_47_0, all_116_0, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | simplifying with (12), (16), (20), (21), (37), % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | (41), (47), (57), (61) gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | (347) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | : ? [v2: any] : (apply(all_32_8, all_47_1, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | all_116_0) = v2 & member(all_116_0, all_32_3) % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | = v1 & member(all_47_0, all_32_4) = v0 & ( ~ (v2 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | (348) all_116_0 = all_58_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (347) gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (349) all_47_0 = all_47_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (65), (349) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (350) $false % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (350) is inconsistent. % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (351) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (apply(all_32_8, all_47_1, all_116_0) = v2 & % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | member(all_116_0, all_32_3) = v1 & % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | member(all_47_0, all_32_4) = v0 & ( ~ (v2 = 0) | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (351) with fresh symbols all_255_0, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | all_255_1, all_255_2 gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (352) apply(all_32_8, all_47_1, all_116_0) = all_255_0 & % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | member(all_116_0, all_32_3) = all_255_1 & % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | member(all_47_0, all_32_4) = all_255_2 & ( ~ % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_255_0 = 0) | ~ (all_255_1 = 0) | ~ % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_255_2 = 0)) % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (352) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (353) member(all_47_0, all_32_4) = all_255_2 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (354) member(all_116_0, all_32_3) = all_255_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (354) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (355) member(all_58_0, all_32_3) = all_255_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (346) gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | (356) all_47_0 = all_47_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (65), (356) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | (357) $false % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (357) is inconsistent. % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | (358) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | all_47_0, all_116_0) = v0 & apply(all_32_8, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | all_47_1, all_116_0) = v1 & ( ~ (v1 = 0) | ~ % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (358) with fresh symbols all_265_0, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | all_265_1 gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | (359) apply(all_32_8, all_47_0, all_116_0) = all_265_1 & % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_47_1, all_116_0) = all_265_0 & % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_265_0 = 0) | ~ (all_265_1 = 0)) % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (359) implies: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | (360) apply(all_32_8, all_47_0, all_116_0) = all_265_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (360) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | (361) apply(all_32_8, all_47_0, all_58_0) = all_265_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_255_2, all_32_4, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | all_47_0, simplifying with (34), (353) gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | (362) all_255_2 = 0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_255_1, all_32_3, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_0, simplifying with (43), (355) gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | (363) all_255_1 = 0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_265_1, all_58_0, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | all_47_0, all_32_8, simplifying with (25), (361) % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | (364) all_265_1 = 0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (365) all_60_0 = all_58_0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (365) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (366) apply(all_32_8, all_47_0, all_58_0) = all_132_1 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_132_1, all_58_0, % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | all_47_0, all_32_8, simplifying with (25), (366) % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_132_1 = 0 % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (343), (367) imply: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (368) $false % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (368) is inconsistent. % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (369) ~ (all_60_0 = all_58_0) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (370) ? [v0: any] : ? [v1: any] : (apply(all_32_1, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | all_47_2, all_58_0) = v1 & apply(all_32_2, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | all_47_2, all_60_0) = v0 & ( ~ (v1 = 0) | ~ % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (370) with fresh symbols all_277_0, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | all_277_1 gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (371) apply(all_32_1, all_47_2, all_58_0) = all_277_0 & % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | apply(all_32_2, all_47_2, all_60_0) = all_277_1 & % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_277_0 = 0) | ~ (all_277_1 = 0)) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (371) implies: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (372) apply(all_32_2, all_47_2, all_60_0) = all_277_1 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (373) apply(all_32_1, all_47_2, all_58_0) = all_277_0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (374) ~ (all_277_0 = 0) | ~ (all_277_1 = 0) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (344) gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_116_0 = all_60_0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (375) imply: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) all_60_0 = all_58_0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (376) imply: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) $false % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (377) is inconsistent. % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_32_8, all_32_7, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_32_5, all_32_4, all_32_3, all_47_2, all_60_0, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_32_2, all_277_1, all_47_1, simplifying with % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6), (11), (12), (21), (36), (38), (47), (51), % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (57), (61), (372) gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) all_277_1 = 0 | ? [v0: any] : ? [v1: any] : % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((apply(all_32_7, all_47_2, all_47_1) = v0 & % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_47_1, all_60_0) = v1 & ( ~ % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) | (member(all_60_0, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_32_3) = v1 & member(all_47_2, all_32_5) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_32_8, all_32_6, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_32_5, all_32_4, all_32_3, all_47_2, all_58_0, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_32_1, all_277_0, all_47_0, simplifying with % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6), (7), (12), (19), (20), (21), (27), (31), % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (51), (57), (373) gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) all_277_0 = 0 | ? [v0: any] : ? [v1: any] : % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((apply(all_32_8, all_47_0, all_58_0) = v1 & % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | member(all_47_0, all_32_4) = v0 & ( ~ (v1 = 0) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v0 = 0))) | (member(all_58_0, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_32_3) = v1 & member(all_47_2, all_32_5) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (379) gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) all_277_0 = 0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (378) gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) all_277_1 = 0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (374) gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) ~ (all_277_0 = 0) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (382) imply: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) $false % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (383) is inconsistent. % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) ~ (all_277_1 = 0) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (384) imply: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) $false % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (385) is inconsistent. % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) ? [v0: any] : ? [v1: any] : ((apply(all_32_7, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_47_2, all_47_1) = v0 & apply(all_32_8, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_47_1, all_60_0) = v1 & ( ~ (v1 = 0) | ~ % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) | (member(all_60_0, all_32_3) = % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1 & member(all_47_2, all_32_5) = v0 & ( ~ (v1 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) | ~ (v0 = 0)))) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (386) with fresh symbols all_339_0, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_339_1 gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) (apply(all_32_7, all_47_2, all_47_1) = all_339_1 & % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_47_1, all_60_0) = all_339_0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ( ~ (all_339_0 = 0) | ~ (all_339_1 = 0))) | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (member(all_60_0, all_32_3) = all_339_0 & % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | member(all_47_2, all_32_5) = all_339_1 & ( ~ % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_339_0 = 0) | ~ (all_339_1 = 0))) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (387) gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) apply(all_32_7, all_47_2, all_47_1) = all_339_1 & % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_47_1, all_60_0) = all_339_0 & % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_339_0 = 0) | ~ (all_339_1 = 0)) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (388) implies: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) apply(all_32_8, all_47_1, all_60_0) = all_339_0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) apply(all_32_7, all_47_2, all_47_1) = all_339_1 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) ~ (all_339_0 = 0) | ~ (all_339_1 = 0) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_339_0, all_60_0, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_47_1, all_32_8, simplifying with (4), (389) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) all_339_0 = 0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_339_1, all_47_1, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_47_2, all_32_7, simplifying with (5), (390) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) all_339_1 = 0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (391) gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) ~ (all_339_0 = 0) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (392), (394) imply: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) $false % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (395) is inconsistent. % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) ~ (all_339_1 = 0) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (393), (396) imply: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) $false % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (397) is inconsistent. % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) member(all_60_0, all_32_3) = all_339_0 & % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | member(all_47_2, all_32_5) = all_339_1 & ( ~ % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_339_0 = 0) | ~ (all_339_1 = 0)) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (398) implies: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) member(all_47_2, all_32_5) = all_339_1 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) member(all_60_0, all_32_3) = all_339_0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) ~ (all_339_0 = 0) | ~ (all_339_1 = 0) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_339_1, all_32_5, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_47_2, simplifying with (50), (399) gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) all_339_1 = 0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_339_0, all_32_3, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_60_0, simplifying with (39), (400) gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) all_339_0 = 0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (401) gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) ~ (all_339_0 = 0) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (403), (404) imply: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) $false % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (405) is inconsistent. % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) ~ (all_339_1 = 0) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (402), (406) imply: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) $false % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (407) is inconsistent. % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) ? [v0: any] : ? [v1: any] : ((apply(all_32_8, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_47_0, all_58_0) = v1 & member(all_47_0, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0))) | (member(all_58_0, all_32_3) = v1 & % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | member(all_47_2, all_32_5) = v0 & ( ~ (v1 = 0) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v0 = 0)))) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (408) with fresh symbols all_322_0, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_322_1 gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) (apply(all_32_8, all_47_0, all_58_0) = all_322_0 & % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | member(all_47_0, all_32_4) = all_322_1 & ( ~ % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_322_0 = 0) | ~ (all_322_1 = 0))) | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (member(all_58_0, all_32_3) = all_322_0 & % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | member(all_47_2, all_32_5) = all_322_1 & ( ~ % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_322_0 = 0) | ~ (all_322_1 = 0))) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (409) gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) apply(all_32_8, all_47_0, all_58_0) = all_322_0 & % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | member(all_47_0, all_32_4) = all_322_1 & ( ~ % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_322_0 = 0) | ~ (all_322_1 = 0)) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (410) implies: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) member(all_47_0, all_32_4) = all_322_1 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) apply(all_32_8, all_47_0, all_58_0) = all_322_0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) ~ (all_322_0 = 0) | ~ (all_322_1 = 0) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_322_1, all_32_4, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_47_0, simplifying with (34), (411) gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) all_322_1 = 0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_322_0, all_58_0, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_47_0, all_32_8, simplifying with (25), (412) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) all_322_0 = 0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (413), (414), (415) are inconsistent by sub-proof % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #4. % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) member(all_58_0, all_32_3) = all_322_0 & % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | member(all_47_2, all_32_5) = all_322_1 & ( ~ % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_322_0 = 0) | ~ (all_322_1 = 0)) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (416) implies: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) member(all_47_2, all_32_5) = all_322_1 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) member(all_58_0, all_32_3) = all_322_0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) ~ (all_322_0 = 0) | ~ (all_322_1 = 0) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_322_1, all_32_5, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_47_2, simplifying with (50), (417) gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) all_322_1 = 0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_322_0, all_32_3, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_0, simplifying with (43), (418) gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) all_322_0 = 0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (419), (420), (421) are inconsistent by sub-proof % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #4. % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | (422) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | all_47_0, all_116_0) = v0 & apply(all_32_8, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | all_47_0, all_58_0) = v1 & ( ~ (v1 = 0) | ~ % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0))) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (422) with fresh symbols all_267_0, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | all_267_1 gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | (423) apply(all_32_8, all_47_0, all_116_0) = all_267_1 & % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | apply(all_32_8, all_47_0, all_58_0) = all_267_0 & % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_267_0 = 0) | ~ (all_267_1 = 0)) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (423) implies: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | (424) apply(all_32_8, all_47_0, all_58_0) = all_267_0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | (425) apply(all_32_8, all_47_0, all_116_0) = all_267_1 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | (426) ~ (all_267_0 = 0) | ~ (all_267_1 = 0) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_267_0, all_58_0, % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | all_47_0, all_32_8, simplifying with (25), (424) % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | (427) all_267_0 = 0 % 31.87/5.19 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_267_1, all_116_0, % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | all_47_0, all_32_8, simplifying with (37), (425) % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | (428) all_267_1 = 0 % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (426) gives: % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | | (429) ~ (all_267_0 = 0) % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (427), (429) imply: % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | | (430) $false % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (430) is inconsistent. % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | | (431) ~ (all_267_1 = 0) % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (428), (431) imply: % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | | (432) $false % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (432) is inconsistent. % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | End of split % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | (433) all_172_0 = 0 % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (242), (433) imply: % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | (434) all_137_0 = 0 % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | SIMP: (434) implies: % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | (435) all_137_0 = 0 % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (332), (435) imply: % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | (436) all_157_0 = 0 % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives: % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | (437) ~ (all_157_0 = 0) % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (436), (437) imply: % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | (438) $false % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (438) is inconsistent. % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | (439) ~ (all_157_1 = 0) % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (341), (439) imply: % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | (440) $false % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (440) is inconsistent. % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | End of split % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | End of split % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | Case 2: % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | (441) ~ (all_142_1 = 0) % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (281), (441) imply: % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | (442) $false % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | CLOSE: (442) is inconsistent. % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | End of split % 31.87/5.20 | | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | | End of split % 31.87/5.20 | | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | | End of split % 31.87/5.20 | | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | | End of split % 31.87/5.20 | | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | | End of split % 31.87/5.20 | | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | | End of split % 31.87/5.20 | | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | | End of split % 31.87/5.20 | | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | | End of split % 31.87/5.20 | | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | | End of split % 31.87/5.20 | | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | | End of split % 31.87/5.20 | | | | | | | | | | | % 31.87/5.20 | | | | | | | | | | End of split % 31.87/5.20 | | | | | | | | | | % 31.87/5.20 | | | | | | | | | End of split % 31.87/5.20 | | | | | | | | | % 31.87/5.20 | | | | | | | | End of split % 31.87/5.20 | | | | | | | | % 31.87/5.20 | | | | | | | End of split % 31.87/5.20 | | | | | | | % 31.87/5.20 | | | | | | End of split % 31.87/5.20 | | | | | | % 31.87/5.20 | | | | | End of split % 31.87/5.20 | | | | | % 31.87/5.20 | | | | End of split % 31.87/5.20 | | | | % 31.87/5.20 | | | End of split % 31.87/5.20 | | | % 31.87/5.20 | | End of split % 31.87/5.20 | | % 31.87/5.20 | End of split % 31.87/5.20 | % 31.87/5.20 End of proof % 31.87/5.20 % 31.87/5.20 Sub-proof #4 shows that the following formulas are inconsistent: % 31.87/5.20 ---------------------------------------------------------------- % 31.87/5.20 (1) ~ (all_322_0 = 0) | ~ (all_322_1 = 0) % 31.87/5.20 (2) all_322_0 = 0 % 31.87/5.20 (3) all_322_1 = 0 % 31.87/5.20 % 31.87/5.20 Begin of proof % 31.87/5.20 | % 31.87/5.20 | BETA: splitting (1) gives: % 31.87/5.20 | % 31.87/5.20 | Case 1: % 31.87/5.20 | | % 31.87/5.20 | | (4) ~ (all_322_0 = 0) % 31.87/5.20 | | % 31.87/5.20 | | REDUCE: (2), (4) imply: % 31.87/5.20 | | (5) $false % 31.87/5.20 | | % 31.87/5.20 | | CLOSE: (5) is inconsistent. % 31.87/5.20 | | % 31.87/5.20 | Case 2: % 31.87/5.20 | | % 31.87/5.20 | | (6) ~ (all_322_1 = 0) % 31.87/5.20 | | % 31.87/5.20 | | REDUCE: (3), (6) imply: % 31.87/5.20 | | (7) $false % 31.87/5.20 | | % 31.87/5.20 | | CLOSE: (7) is inconsistent. % 31.87/5.20 | | % 31.87/5.20 | End of split % 31.87/5.20 | % 31.87/5.20 End of proof % 31.87/5.20 % SZS output end Proof for theBenchmark % 31.87/5.20 % 31.87/5.20 4592ms %------------------------------------------------------------------------------